1,1,119,131,0.565527,"\text{Not used}","int(x^3*(b*x + c*x^2)^(1/2),x)","\frac{x^2\,{\left(c\,x^2+b\,x\right)}^{3/2}}{5\,c}-\frac{7\,b\,\left(\frac{x\,{\left(c\,x^2+b\,x\right)}^{3/2}}{4\,c}-\frac{5\,b\,\left(\frac{b^3\,\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x}\right)}{16\,c^{5/2}}+\frac{\sqrt{c\,x^2+b\,x}\,\left(-3\,b^2+2\,b\,c\,x+8\,c^2\,x^2\right)}{24\,c^2}\right)}{8\,c}\right)}{10\,c}","Not used",1,"(x^2*(b*x + c*x^2)^(3/2))/(5*c) - (7*b*((x*(b*x + c*x^2)^(3/2))/(4*c) - (5*b*((b^3*log((b + 2*c*x)/c^(1/2) + 2*(b*x + c*x^2)^(1/2)))/(16*c^(5/2)) + ((b*x + c*x^2)^(1/2)*(8*c^2*x^2 - 3*b^2 + 2*b*c*x))/(24*c^2)))/(8*c)))/(10*c)","B"
2,1,93,105,0.310096,"\text{Not used}","int(x^2*(b*x + c*x^2)^(1/2),x)","\frac{x\,{\left(c\,x^2+b\,x\right)}^{3/2}}{4\,c}-\frac{5\,b\,\left(\frac{b^3\,\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x}\right)}{16\,c^{5/2}}+\frac{\sqrt{c\,x^2+b\,x}\,\left(-3\,b^2+2\,b\,c\,x+8\,c^2\,x^2\right)}{24\,c^2}\right)}{8\,c}","Not used",1,"(x*(b*x + c*x^2)^(3/2))/(4*c) - (5*b*((b^3*log((b + 2*c*x)/c^(1/2) + 2*(b*x + c*x^2)^(1/2)))/(16*c^(5/2)) + ((b*x + c*x^2)^(1/2)*(8*c^2*x^2 - 3*b^2 + 2*b*c*x))/(24*c^2)))/(8*c)","B"
3,1,69,81,0.087992,"\text{Not used}","int(x*(b*x + c*x^2)^(1/2),x)","\frac{b^3\,\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x}\right)}{16\,c^{5/2}}+\frac{\sqrt{c\,x^2+b\,x}\,\left(-3\,b^2+2\,b\,c\,x+8\,c^2\,x^2\right)}{24\,c^2}","Not used",1,"(b^3*log((b + 2*c*x)/c^(1/2) + 2*(b*x + c*x^2)^(1/2)))/(16*c^(5/2)) + ((b*x + c*x^2)^(1/2)*(8*c^2*x^2 - 3*b^2 + 2*b*c*x))/(24*c^2)","B"
4,1,55,60,0.096187,"\text{Not used}","int((b*x + c*x^2)^(1/2),x)","\sqrt{c\,x^2+b\,x}\,\left(\frac{x}{2}+\frac{b}{4\,c}\right)-\frac{b^2\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{8\,c^{3/2}}","Not used",1,"(b*x + c*x^2)^(1/2)*(x/2 + b/(4*c)) - (b^2*log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2)))/(8*c^(3/2))","B"
5,1,42,42,0.073182,"\text{Not used}","int((b*x + c*x^2)^(1/2)/x,x)","\sqrt{c\,x^2+b\,x}+\frac{b\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{2\,\sqrt{c}}","Not used",1,"(b*x + c*x^2)^(1/2) + (b*log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2)))/(2*c^(1/2))","B"
6,0,-1,47,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/x^2,x)","\int \frac{\sqrt{c\,x^2+b\,x}}{x^2} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/x^2, x)","F"
7,1,24,23,0.259263,"\text{Not used}","int((b*x + c*x^2)^(1/2)/x^3,x)","-\frac{2\,\sqrt{c\,x^2+b\,x}\,\left(b+c\,x\right)}{3\,b\,x^2}","Not used",1,"-(2*(b*x + c*x^2)^(1/2)*(b + c*x))/(3*b*x^2)","B"
8,1,37,48,0.340346,"\text{Not used}","int((b*x + c*x^2)^(1/2)/x^4,x)","-\frac{2\,\sqrt{c\,x^2+b\,x}\,\left(3\,b^2+b\,c\,x-2\,c^2\,x^2\right)}{15\,b^2\,x^3}","Not used",1,"-(2*(b*x + c*x^2)^(1/2)*(3*b^2 - 2*c^2*x^2 + b*c*x))/(15*b^2*x^3)","B"
9,1,81,74,0.420467,"\text{Not used}","int((b*x + c*x^2)^(1/2)/x^5,x)","\frac{8\,c^2\,\sqrt{c\,x^2+b\,x}}{105\,b^2\,x^2}-\frac{2\,\sqrt{c\,x^2+b\,x}}{7\,x^4}-\frac{16\,c^3\,\sqrt{c\,x^2+b\,x}}{105\,b^3\,x}-\frac{2\,c\,\sqrt{c\,x^2+b\,x}}{35\,b\,x^3}","Not used",1,"(8*c^2*(b*x + c*x^2)^(1/2))/(105*b^2*x^2) - (2*(b*x + c*x^2)^(1/2))/(7*x^4) - (16*c^3*(b*x + c*x^2)^(1/2))/(105*b^3*x) - (2*c*(b*x + c*x^2)^(1/2))/(35*b*x^3)","B"
10,1,103,100,0.490087,"\text{Not used}","int((b*x + c*x^2)^(1/2)/x^6,x)","\frac{4\,c^2\,\sqrt{c\,x^2+b\,x}}{105\,b^2\,x^3}-\frac{2\,\sqrt{c\,x^2+b\,x}}{9\,x^5}-\frac{16\,c^3\,\sqrt{c\,x^2+b\,x}}{315\,b^3\,x^2}+\frac{32\,c^4\,\sqrt{c\,x^2+b\,x}}{315\,b^4\,x}-\frac{2\,c\,\sqrt{c\,x^2+b\,x}}{63\,b\,x^4}","Not used",1,"(4*c^2*(b*x + c*x^2)^(1/2))/(105*b^2*x^3) - (2*(b*x + c*x^2)^(1/2))/(9*x^5) - (16*c^3*(b*x + c*x^2)^(1/2))/(315*b^3*x^2) + (32*c^4*(b*x + c*x^2)^(1/2))/(315*b^4*x) - (2*c*(b*x + c*x^2)^(1/2))/(63*b*x^4)","B"
11,1,125,126,0.619259,"\text{Not used}","int((b*x + c*x^2)^(1/2)/x^7,x)","\frac{16\,c^2\,\sqrt{c\,x^2+b\,x}}{693\,b^2\,x^4}-\frac{2\,\sqrt{c\,x^2+b\,x}}{11\,x^6}-\frac{32\,c^3\,\sqrt{c\,x^2+b\,x}}{1155\,b^3\,x^3}+\frac{128\,c^4\,\sqrt{c\,x^2+b\,x}}{3465\,b^4\,x^2}-\frac{256\,c^5\,\sqrt{c\,x^2+b\,x}}{3465\,b^5\,x}-\frac{2\,c\,\sqrt{c\,x^2+b\,x}}{99\,b\,x^5}","Not used",1,"(16*c^2*(b*x + c*x^2)^(1/2))/(693*b^2*x^4) - (2*(b*x + c*x^2)^(1/2))/(11*x^6) - (32*c^3*(b*x + c*x^2)^(1/2))/(1155*b^3*x^3) + (128*c^4*(b*x + c*x^2)^(1/2))/(3465*b^4*x^2) - (256*c^5*(b*x + c*x^2)^(1/2))/(3465*b^5*x) - (2*c*(b*x + c*x^2)^(1/2))/(99*b*x^5)","B"
12,0,-1,134,0.000000,"\text{Not used}","int(x^2*(b*x + c*x^2)^(3/2),x)","\int x^2\,{\left(c\,x^2+b\,x\right)}^{3/2} \,d x","Not used",1,"int(x^2*(b*x + c*x^2)^(3/2), x)","F"
13,1,118,110,0.107012,"\text{Not used}","int(x*(b*x + c*x^2)^(3/2),x)","\frac{{\left(c\,x^2+b\,x\right)}^{5/2}}{5\,c}-\frac{b\,\left(\frac{x\,{\left(c\,x^2+b\,x\right)}^{3/2}}{4}+\frac{b\,{\left(c\,x^2+b\,x\right)}^{3/2}}{8\,c}-\frac{3\,b^2\,\left(\frac{\sqrt{c\,x^2+b\,x}\,\left(b+2\,c\,x\right)}{4\,c}-\frac{b^2\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{8\,c^{3/2}}\right)}{16\,c}\right)}{2\,c}","Not used",1,"(b*x + c*x^2)^(5/2)/(5*c) - (b*((x*(b*x + c*x^2)^(3/2))/4 + (b*(b*x + c*x^2)^(3/2))/(8*c) - (3*b^2*(((b*x + c*x^2)^(1/2)*(b + 2*c*x))/(4*c) - (b^2*log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2)))/(8*c^(3/2))))/(16*c)))/(2*c)","B"
14,1,87,89,0.290484,"\text{Not used}","int((b*x + c*x^2)^(3/2),x)","\frac{{\left(c\,x^2+b\,x\right)}^{3/2}\,\left(\frac{b}{2}+c\,x\right)}{4\,c}-\frac{3\,b^2\,\left(\sqrt{c\,x^2+b\,x}\,\left(\frac{x}{2}+\frac{b}{4\,c}\right)-\frac{b^2\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{8\,c^{3/2}}\right)}{16\,c}","Not used",1,"((b*x + c*x^2)^(3/2)*(b/2 + c*x))/(4*c) - (3*b^2*((b*x + c*x^2)^(1/2)*(x/2 + b/(4*c)) - (b^2*log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2)))/(8*c^(3/2))))/(16*c)","B"
15,0,-1,78,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x,x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{x} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/x, x)","F"
16,0,-1,72,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x^2,x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{x^2} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/x^2, x)","F"
17,0,-1,64,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x^3,x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{x^3} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/x^3, x)","F"
18,0,-1,68,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x^4,x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{x^4} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/x^4, x)","F"
19,1,26,23,0.479357,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x^5,x)","-\frac{2\,\sqrt{c\,x^2+b\,x}\,{\left(b+c\,x\right)}^2}{5\,b\,x^3}","Not used",1,"-(2*(b*x + c*x^2)^(1/2)*(b + c*x)^2)/(5*b*x^3)","B"
20,1,79,48,0.636358,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x^6,x)","\frac{4\,c^3\,\sqrt{c\,x^2+b\,x}}{35\,b^2\,x}-\frac{16\,c\,\sqrt{c\,x^2+b\,x}}{35\,x^3}-\frac{2\,c^2\,\sqrt{c\,x^2+b\,x}}{35\,b\,x^2}-\frac{2\,b\,\sqrt{c\,x^2+b\,x}}{7\,x^4}","Not used",1,"(4*c^3*(b*x + c*x^2)^(1/2))/(35*b^2*x) - (16*c*(b*x + c*x^2)^(1/2))/(35*x^3) - (2*c^2*(b*x + c*x^2)^(1/2))/(35*b*x^2) - (2*b*(b*x + c*x^2)^(1/2))/(7*x^4)","B"
21,1,101,74,0.802298,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x^7,x)","\frac{8\,c^3\,\sqrt{c\,x^2+b\,x}}{315\,b^2\,x^2}-\frac{20\,c\,\sqrt{c\,x^2+b\,x}}{63\,x^4}-\frac{2\,c^2\,\sqrt{c\,x^2+b\,x}}{105\,b\,x^3}-\frac{2\,b\,\sqrt{c\,x^2+b\,x}}{9\,x^5}-\frac{16\,c^4\,\sqrt{c\,x^2+b\,x}}{315\,b^3\,x}","Not used",1,"(8*c^3*(b*x + c*x^2)^(1/2))/(315*b^2*x^2) - (20*c*(b*x + c*x^2)^(1/2))/(63*x^4) - (2*c^2*(b*x + c*x^2)^(1/2))/(105*b*x^3) - (2*b*(b*x + c*x^2)^(1/2))/(9*x^5) - (16*c^4*(b*x + c*x^2)^(1/2))/(315*b^3*x)","B"
22,1,123,100,1.006060,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x^8,x)","\frac{4\,c^3\,\sqrt{c\,x^2+b\,x}}{385\,b^2\,x^3}-\frac{8\,c\,\sqrt{c\,x^2+b\,x}}{33\,x^5}-\frac{2\,c^2\,\sqrt{c\,x^2+b\,x}}{231\,b\,x^4}-\frac{2\,b\,\sqrt{c\,x^2+b\,x}}{11\,x^6}-\frac{16\,c^4\,\sqrt{c\,x^2+b\,x}}{1155\,b^3\,x^2}+\frac{32\,c^5\,\sqrt{c\,x^2+b\,x}}{1155\,b^4\,x}","Not used",1,"(4*c^3*(b*x + c*x^2)^(1/2))/(385*b^2*x^3) - (8*c*(b*x + c*x^2)^(1/2))/(33*x^5) - (2*c^2*(b*x + c*x^2)^(1/2))/(231*b*x^4) - (2*b*(b*x + c*x^2)^(1/2))/(11*x^6) - (16*c^4*(b*x + c*x^2)^(1/2))/(1155*b^3*x^2) + (32*c^5*(b*x + c*x^2)^(1/2))/(1155*b^4*x)","B"
23,1,145,126,1.207536,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x^9,x)","\frac{16\,c^3\,\sqrt{c\,x^2+b\,x}}{3003\,b^2\,x^4}-\frac{28\,c\,\sqrt{c\,x^2+b\,x}}{143\,x^6}-\frac{2\,c^2\,\sqrt{c\,x^2+b\,x}}{429\,b\,x^5}-\frac{2\,b\,\sqrt{c\,x^2+b\,x}}{13\,x^7}-\frac{32\,c^4\,\sqrt{c\,x^2+b\,x}}{5005\,b^3\,x^3}+\frac{128\,c^5\,\sqrt{c\,x^2+b\,x}}{15015\,b^4\,x^2}-\frac{256\,c^6\,\sqrt{c\,x^2+b\,x}}{15015\,b^5\,x}","Not used",1,"(16*c^3*(b*x + c*x^2)^(1/2))/(3003*b^2*x^4) - (28*c*(b*x + c*x^2)^(1/2))/(143*x^6) - (2*c^2*(b*x + c*x^2)^(1/2))/(429*b*x^5) - (2*b*(b*x + c*x^2)^(1/2))/(13*x^7) - (32*c^4*(b*x + c*x^2)^(1/2))/(5005*b^3*x^3) + (128*c^5*(b*x + c*x^2)^(1/2))/(15015*b^4*x^2) - (256*c^6*(b*x + c*x^2)^(1/2))/(15015*b^5*x)","B"
24,0,-1,163,0.000000,"\text{Not used}","int(x^2*(a*x + b*x^2)^(5/2),x)","\int x^2\,{\left(b\,x^2+a\,x\right)}^{5/2} \,d x","Not used",1,"int(x^2*(a*x + b*x^2)^(5/2), x)","F"
25,0,-1,139,0.000000,"\text{Not used}","int(x*(a*x + b*x^2)^(5/2),x)","\int x\,{\left(b\,x^2+a\,x\right)}^{5/2} \,d x","Not used",1,"int(x*(a*x + b*x^2)^(5/2), x)","F"
26,1,119,118,0.559603,"\text{Not used}","int((a*x + b*x^2)^(5/2),x)","\frac{{\left(b\,x^2+a\,x\right)}^{5/2}\,\left(\frac{a}{2}+b\,x\right)}{6\,b}-\frac{5\,a^2\,\left(\frac{{\left(b\,x^2+a\,x\right)}^{3/2}\,\left(\frac{a}{2}+b\,x\right)}{4\,b}-\frac{3\,a^2\,\left(\sqrt{b\,x^2+a\,x}\,\left(\frac{x}{2}+\frac{a}{4\,b}\right)-\frac{a^2\,\ln\left(\frac{\frac{a}{2}+b\,x}{\sqrt{b}}+\sqrt{b\,x^2+a\,x}\right)}{8\,b^{3/2}}\right)}{16\,b}\right)}{24\,b}","Not used",1,"((a*x + b*x^2)^(5/2)*(a/2 + b*x))/(6*b) - (5*a^2*(((a*x + b*x^2)^(3/2)*(a/2 + b*x))/(4*b) - (3*a^2*((a*x + b*x^2)^(1/2)*(x/2 + a/(4*b)) - (a^2*log((a/2 + b*x)/b^(1/2) + (a*x + b*x^2)^(1/2)))/(8*b^(3/2))))/(16*b)))/(24*b)","B"
27,0,-1,107,0.000000,"\text{Not used}","int((a*x + b*x^2)^(5/2)/x,x)","\int \frac{{\left(b\,x^2+a\,x\right)}^{5/2}}{x} \,d x","Not used",1,"int((a*x + b*x^2)^(5/2)/x, x)","F"
28,0,-1,101,0.000000,"\text{Not used}","int((a*x + b*x^2)^(5/2)/x^2,x)","\int \frac{{\left(b\,x^2+a\,x\right)}^{5/2}}{x^2} \,d x","Not used",1,"int((a*x + b*x^2)^(5/2)/x^2, x)","F"
29,0,-1,94,0.000000,"\text{Not used}","int((a*x + b*x^2)^(5/2)/x^3,x)","\int \frac{{\left(b\,x^2+a\,x\right)}^{5/2}}{x^3} \,d x","Not used",1,"int((a*x + b*x^2)^(5/2)/x^3, x)","F"
30,0,-1,92,0.000000,"\text{Not used}","int((a*x + b*x^2)^(5/2)/x^4,x)","\int \frac{{\left(b\,x^2+a\,x\right)}^{5/2}}{x^4} \,d x","Not used",1,"int((a*x + b*x^2)^(5/2)/x^4, x)","F"
31,0,-1,89,0.000000,"\text{Not used}","int((a*x + b*x^2)^(5/2)/x^5,x)","\int \frac{{\left(b\,x^2+a\,x\right)}^{5/2}}{x^5} \,d x","Not used",1,"int((a*x + b*x^2)^(5/2)/x^5, x)","F"
32,0,-1,91,0.000000,"\text{Not used}","int((a*x + b*x^2)^(5/2)/x^6,x)","\int \frac{{\left(b\,x^2+a\,x\right)}^{5/2}}{x^6} \,d x","Not used",1,"int((a*x + b*x^2)^(5/2)/x^6, x)","F"
33,1,79,23,0.776096,"\text{Not used}","int((a*x + b*x^2)^(5/2)/x^7,x)","-\frac{2\,a^2\,\sqrt{b\,x^2+a\,x}}{7\,x^4}-\frac{6\,b^2\,\sqrt{b\,x^2+a\,x}}{7\,x^2}-\frac{2\,b^3\,\sqrt{b\,x^2+a\,x}}{7\,a\,x}-\frac{6\,a\,b\,\sqrt{b\,x^2+a\,x}}{7\,x^3}","Not used",1,"- (2*a^2*(a*x + b*x^2)^(1/2))/(7*x^4) - (6*b^2*(a*x + b*x^2)^(1/2))/(7*x^2) - (2*b^3*(a*x + b*x^2)^(1/2))/(7*a*x) - (6*a*b*(a*x + b*x^2)^(1/2))/(7*x^3)","B"
34,1,101,48,1.006027,"\text{Not used}","int((a*x + b*x^2)^(5/2)/x^8,x)","\frac{4\,b^4\,\sqrt{b\,x^2+a\,x}}{63\,a^2\,x}-\frac{10\,b^2\,\sqrt{b\,x^2+a\,x}}{21\,x^3}-\frac{2\,b^3\,\sqrt{b\,x^2+a\,x}}{63\,a\,x^2}-\frac{2\,a^2\,\sqrt{b\,x^2+a\,x}}{9\,x^5}-\frac{38\,a\,b\,\sqrt{b\,x^2+a\,x}}{63\,x^4}","Not used",1,"(4*b^4*(a*x + b*x^2)^(1/2))/(63*a^2*x) - (10*b^2*(a*x + b*x^2)^(1/2))/(21*x^3) - (2*b^3*(a*x + b*x^2)^(1/2))/(63*a*x^2) - (2*a^2*(a*x + b*x^2)^(1/2))/(9*x^5) - (38*a*b*(a*x + b*x^2)^(1/2))/(63*x^4)","B"
35,1,123,74,1.301917,"\text{Not used}","int((a*x + b*x^2)^(5/2)/x^9,x)","\frac{8\,b^4\,\sqrt{b\,x^2+a\,x}}{693\,a^2\,x^2}-\frac{226\,b^2\,\sqrt{b\,x^2+a\,x}}{693\,x^4}-\frac{2\,b^3\,\sqrt{b\,x^2+a\,x}}{231\,a\,x^3}-\frac{2\,a^2\,\sqrt{b\,x^2+a\,x}}{11\,x^6}-\frac{16\,b^5\,\sqrt{b\,x^2+a\,x}}{693\,a^3\,x}-\frac{46\,a\,b\,\sqrt{b\,x^2+a\,x}}{99\,x^5}","Not used",1,"(8*b^4*(a*x + b*x^2)^(1/2))/(693*a^2*x^2) - (226*b^2*(a*x + b*x^2)^(1/2))/(693*x^4) - (2*b^3*(a*x + b*x^2)^(1/2))/(231*a*x^3) - (2*a^2*(a*x + b*x^2)^(1/2))/(11*x^6) - (16*b^5*(a*x + b*x^2)^(1/2))/(693*a^3*x) - (46*a*b*(a*x + b*x^2)^(1/2))/(99*x^5)","B"
36,1,145,100,1.586993,"\text{Not used}","int((a*x + b*x^2)^(5/2)/x^10,x)","\frac{4\,b^4\,\sqrt{b\,x^2+a\,x}}{1001\,a^2\,x^3}-\frac{106\,b^2\,\sqrt{b\,x^2+a\,x}}{429\,x^5}-\frac{10\,b^3\,\sqrt{b\,x^2+a\,x}}{3003\,a\,x^4}-\frac{2\,a^2\,\sqrt{b\,x^2+a\,x}}{13\,x^7}-\frac{16\,b^5\,\sqrt{b\,x^2+a\,x}}{3003\,a^3\,x^2}+\frac{32\,b^6\,\sqrt{b\,x^2+a\,x}}{3003\,a^4\,x}-\frac{54\,a\,b\,\sqrt{b\,x^2+a\,x}}{143\,x^6}","Not used",1,"(4*b^4*(a*x + b*x^2)^(1/2))/(1001*a^2*x^3) - (106*b^2*(a*x + b*x^2)^(1/2))/(429*x^5) - (10*b^3*(a*x + b*x^2)^(1/2))/(3003*a*x^4) - (2*a^2*(a*x + b*x^2)^(1/2))/(13*x^7) - (16*b^5*(a*x + b*x^2)^(1/2))/(3003*a^3*x^2) + (32*b^6*(a*x + b*x^2)^(1/2))/(3003*a^4*x) - (54*a*b*(a*x + b*x^2)^(1/2))/(143*x^6)","B"
37,1,167,126,1.863854,"\text{Not used}","int((a*x + b*x^2)^(5/2)/x^11,x)","\frac{16\,b^4\,\sqrt{b\,x^2+a\,x}}{9009\,a^2\,x^4}-\frac{142\,b^2\,\sqrt{b\,x^2+a\,x}}{715\,x^6}-\frac{2\,b^3\,\sqrt{b\,x^2+a\,x}}{1287\,a\,x^5}-\frac{2\,a^2\,\sqrt{b\,x^2+a\,x}}{15\,x^8}-\frac{32\,b^5\,\sqrt{b\,x^2+a\,x}}{15015\,a^3\,x^3}+\frac{128\,b^6\,\sqrt{b\,x^2+a\,x}}{45045\,a^4\,x^2}-\frac{256\,b^7\,\sqrt{b\,x^2+a\,x}}{45045\,a^5\,x}-\frac{62\,a\,b\,\sqrt{b\,x^2+a\,x}}{195\,x^7}","Not used",1,"(16*b^4*(a*x + b*x^2)^(1/2))/(9009*a^2*x^4) - (142*b^2*(a*x + b*x^2)^(1/2))/(715*x^6) - (2*b^3*(a*x + b*x^2)^(1/2))/(1287*a*x^5) - (2*a^2*(a*x + b*x^2)^(1/2))/(15*x^8) - (32*b^5*(a*x + b*x^2)^(1/2))/(15015*a^3*x^3) + (128*b^6*(a*x + b*x^2)^(1/2))/(45045*a^4*x^2) - (256*b^7*(a*x + b*x^2)^(1/2))/(45045*a^5*x) - (62*a*b*(a*x + b*x^2)^(1/2))/(195*x^7)","B"
38,1,189,152,2.185112,"\text{Not used}","int((a*x + b*x^2)^(5/2)/x^12,x)","\frac{20\,b^4\,\sqrt{b\,x^2+a\,x}}{21879\,a^2\,x^5}-\frac{110\,b^2\,\sqrt{b\,x^2+a\,x}}{663\,x^7}-\frac{2\,b^3\,\sqrt{b\,x^2+a\,x}}{2431\,a\,x^6}-\frac{2\,a^2\,\sqrt{b\,x^2+a\,x}}{17\,x^9}-\frac{160\,b^5\,\sqrt{b\,x^2+a\,x}}{153153\,a^3\,x^4}+\frac{64\,b^6\,\sqrt{b\,x^2+a\,x}}{51051\,a^4\,x^3}-\frac{256\,b^7\,\sqrt{b\,x^2+a\,x}}{153153\,a^5\,x^2}+\frac{512\,b^8\,\sqrt{b\,x^2+a\,x}}{153153\,a^6\,x}-\frac{14\,a\,b\,\sqrt{b\,x^2+a\,x}}{51\,x^8}","Not used",1,"(20*b^4*(a*x + b*x^2)^(1/2))/(21879*a^2*x^5) - (110*b^2*(a*x + b*x^2)^(1/2))/(663*x^7) - (2*b^3*(a*x + b*x^2)^(1/2))/(2431*a*x^6) - (2*a^2*(a*x + b*x^2)^(1/2))/(17*x^9) - (160*b^5*(a*x + b*x^2)^(1/2))/(153153*a^3*x^4) + (64*b^6*(a*x + b*x^2)^(1/2))/(51051*a^4*x^3) - (256*b^7*(a*x + b*x^2)^(1/2))/(153153*a^5*x^2) + (512*b^8*(a*x + b*x^2)^(1/2))/(153153*a^6*x) - (14*a*b*(a*x + b*x^2)^(1/2))/(51*x^8)","B"
39,1,42,50,0.084147,"\text{Not used}","int(x*(2*x - x^2)^(1/2),x)","-\frac{\sqrt{2\,x-x^2}\,\left(-8\,x^2+4\,x+12\right)}{24}-\frac{\ln\left(x-1-\sqrt{-x\,\left(x-2\right)}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}","Not used",1,"- (log(x - (-x*(x - 2))^(1/2)*1i - 1)*1i)/2 - ((2*x - x^2)^(1/2)*(4*x - 8*x^2 + 12))/24","B"
40,1,44,52,0.198015,"\text{Not used}","int(x*(3*x - 4*x^2)^(1/2),x)","-\frac{\sqrt{3\,x-4\,x^2}\,\left(-128\,x^2+24\,x+27\right)}{384}-\frac{\ln\left(x-\frac{3}{8}-\frac{\sqrt{-x\,\left(4\,x-3\right)}\,1{}\mathrm{i}}{2}\right)\,27{}\mathrm{i}}{512}","Not used",1,"- (log(x - ((-x*(4*x - 3))^(1/2)*1i)/2 - 3/8)*27i)/512 - ((3*x - 4*x^2)^(1/2)*(24*x - 128*x^2 + 27))/384","B"
41,1,33,48,0.079197,"\text{Not used}","int(x*(x + x^2)^(1/2),x)","\frac{\ln\left(x+\sqrt{x\,\left(x+1\right)}+\frac{1}{2}\right)}{16}+\frac{\sqrt{x^2+x}\,\left(8\,x^2+2\,x-3\right)}{24}","Not used",1,"log(x + (x*(x + 1))^(1/2) + 1/2)/16 + ((x + x^2)^(1/2)*(2*x + 8*x^2 - 3))/24","B"
42,0,-1,128,0.000000,"\text{Not used}","int(x^4/(b*x + c*x^2)^(1/2),x)","\int \frac{x^4}{\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int(x^4/(b*x + c*x^2)^(1/2), x)","F"
43,0,-1,102,0.000000,"\text{Not used}","int(x^3/(b*x + c*x^2)^(1/2),x)","\int \frac{x^3}{\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int(x^3/(b*x + c*x^2)^(1/2), x)","F"
44,0,-1,76,0.000000,"\text{Not used}","int(x^2/(b*x + c*x^2)^(1/2),x)","\int \frac{x^2}{\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int(x^2/(b*x + c*x^2)^(1/2), x)","F"
45,1,46,47,0.201532,"\text{Not used}","int(x/(b*x + c*x^2)^(1/2),x)","\frac{\sqrt{c\,x^2+b\,x}}{c}-\frac{b\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{2\,c^{3/2}}","Not used",1,"(b*x + c*x^2)^(1/2)/c - (b*log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2)))/(2*c^(3/2))","B"
46,1,28,28,0.205982,"\text{Not used}","int(1/(b*x + c*x^2)^(1/2),x)","\frac{\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{\sqrt{c}}","Not used",1,"log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2))/c^(1/2)","B"
47,1,19,21,0.173320,"\text{Not used}","int(1/(x*(b*x + c*x^2)^(1/2)),x)","-\frac{2\,\sqrt{c\,x^2+b\,x}}{b\,x}","Not used",1,"-(2*(b*x + c*x^2)^(1/2))/(b*x)","B"
48,1,25,48,0.171195,"\text{Not used}","int(1/(x^2*(b*x + c*x^2)^(1/2)),x)","-\frac{2\,\sqrt{c\,x^2+b\,x}\,\left(b-2\,c\,x\right)}{3\,b^2\,x^2}","Not used",1,"-(2*(b*x + c*x^2)^(1/2)*(b - 2*c*x))/(3*b^2*x^2)","B"
49,1,38,74,0.193934,"\text{Not used}","int(1/(x^3*(b*x + c*x^2)^(1/2)),x)","-\frac{2\,\sqrt{c\,x^2+b\,x}\,\left(3\,b^2-4\,b\,c\,x+8\,c^2\,x^2\right)}{15\,b^3\,x^3}","Not used",1,"-(2*(b*x + c*x^2)^(1/2)*(3*b^2 + 8*c^2*x^2 - 4*b*c*x))/(15*b^3*x^3)","B"
50,1,84,100,0.197287,"\text{Not used}","int(1/(x^4*(b*x + c*x^2)^(1/2)),x)","\frac{32\,c^3\,\sqrt{c\,x^2+b\,x}}{35\,b^4\,x}-\frac{16\,c^2\,\sqrt{c\,x^2+b\,x}}{35\,b^3\,x^2}-\frac{2\,\sqrt{c\,x^2+b\,x}}{7\,b\,x^4}+\frac{12\,c\,\sqrt{c\,x^2+b\,x}}{35\,b^2\,x^3}","Not used",1,"(32*c^3*(b*x + c*x^2)^(1/2))/(35*b^4*x) - (16*c^2*(b*x + c*x^2)^(1/2))/(35*b^3*x^2) - (2*(b*x + c*x^2)^(1/2))/(7*b*x^4) + (12*c*(b*x + c*x^2)^(1/2))/(35*b^2*x^3)","B"
51,1,106,126,0.184736,"\text{Not used}","int(1/(x^5*(b*x + c*x^2)^(1/2)),x)","\frac{128\,c^3\,\sqrt{c\,x^2+b\,x}}{315\,b^4\,x^2}-\frac{32\,c^2\,\sqrt{c\,x^2+b\,x}}{105\,b^3\,x^3}-\frac{2\,\sqrt{c\,x^2+b\,x}}{9\,b\,x^5}-\frac{256\,c^4\,\sqrt{c\,x^2+b\,x}}{315\,b^5\,x}+\frac{16\,c\,\sqrt{c\,x^2+b\,x}}{63\,b^2\,x^4}","Not used",1,"(128*c^3*(b*x + c*x^2)^(1/2))/(315*b^4*x^2) - (32*c^2*(b*x + c*x^2)^(1/2))/(105*b^3*x^3) - (2*(b*x + c*x^2)^(1/2))/(9*b*x^5) - (256*c^4*(b*x + c*x^2)^(1/2))/(315*b^5*x) + (16*c*(b*x + c*x^2)^(1/2))/(63*b^2*x^4)","B"
52,0,-1,97,0.000000,"\text{Not used}","int(x^4/(b*x + c*x^2)^(3/2),x)","\int \frac{x^4}{{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int(x^4/(b*x + c*x^2)^(3/2), x)","F"
53,0,-1,69,0.000000,"\text{Not used}","int(x^3/(b*x + c*x^2)^(3/2),x)","\int \frac{x^3}{{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int(x^3/(b*x + c*x^2)^(3/2), x)","F"
54,1,46,48,0.199780,"\text{Not used}","int(x^2/(b*x + c*x^2)^(3/2),x)","\frac{\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{c^{3/2}}-\frac{2\,x}{c\,\sqrt{c\,x^2+b\,x}}","Not used",1,"log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2))/c^(3/2) - (2*x)/(c*(b*x + c*x^2)^(1/2))","B"
55,1,15,19,0.032237,"\text{Not used}","int(x/(b*x + c*x^2)^(3/2),x)","\frac{2\,x}{b\,\sqrt{x\,\left(b+c\,x\right)}}","Not used",1,"(2*x)/(b*(x*(b + c*x))^(1/2))","B"
56,1,24,24,0.044664,"\text{Not used}","int(1/(b*x + c*x^2)^(3/2),x)","-\frac{2\,b+4\,c\,x}{b^2\,\sqrt{c\,x^2+b\,x}}","Not used",1,"-(2*b + 4*c*x)/(b^2*(b*x + c*x^2)^(1/2))","B"
57,1,45,51,0.237874,"\text{Not used}","int(1/(x*(b*x + c*x^2)^(3/2)),x)","\frac{2\,\sqrt{c\,x^2+b\,x}\,\left(-b^2+4\,b\,c\,x+8\,c^2\,x^2\right)}{3\,b^3\,x^2\,\left(b+c\,x\right)}","Not used",1,"(2*(b*x + c*x^2)^(1/2)*(8*c^2*x^2 - b^2 + 4*b*c*x))/(3*b^3*x^2*(b + c*x))","B"
58,1,54,77,0.282626,"\text{Not used}","int(1/(x^2*(b*x + c*x^2)^(3/2)),x)","-\frac{2\,\sqrt{c\,x^2+b\,x}\,\left(b^3-2\,b^2\,c\,x+8\,b\,c^2\,x^2+16\,c^3\,x^3\right)}{5\,b^4\,x^3\,\left(b+c\,x\right)}","Not used",1,"-(2*(b*x + c*x^2)^(1/2)*(b^3 + 16*c^3*x^3 + 8*b*c^2*x^2 - 2*b^2*c*x))/(5*b^4*x^3*(b + c*x))","B"
59,1,102,103,0.320799,"\text{Not used}","int(1/(x^3*(b*x + c*x^2)^(3/2)),x)","\frac{\sqrt{c\,x^2+b\,x}\,\left(\frac{186\,c^3}{35\,b^4}+\frac{256\,c^4\,x}{35\,b^5}\right)}{x\,\left(b+c\,x\right)}-\frac{58\,c^2\,\sqrt{c\,x^2+b\,x}}{35\,b^4\,x^2}-\frac{2\,\sqrt{c\,x^2+b\,x}}{7\,b^2\,x^4}+\frac{26\,c\,\sqrt{c\,x^2+b\,x}}{35\,b^3\,x^3}","Not used",1,"((b*x + c*x^2)^(1/2)*((186*c^3)/(35*b^4) + (256*c^4*x)/(35*b^5)))/(x*(b + c*x)) - (58*c^2*(b*x + c*x^2)^(1/2))/(35*b^4*x^2) - (2*(b*x + c*x^2)^(1/2))/(7*b^2*x^4) + (26*c*(b*x + c*x^2)^(1/2))/(35*b^3*x^3)","B"
60,0,-1,122,0.000000,"\text{Not used}","int(x^6/(a*x + b*x^2)^(5/2),x)","\int \frac{x^6}{{\left(b\,x^2+a\,x\right)}^{5/2}} \,d x","Not used",1,"int(x^6/(a*x + b*x^2)^(5/2), x)","F"
61,0,-1,94,0.000000,"\text{Not used}","int(x^5/(a*x + b*x^2)^(5/2),x)","\int \frac{x^5}{{\left(b\,x^2+a\,x\right)}^{5/2}} \,d x","Not used",1,"int(x^5/(a*x + b*x^2)^(5/2), x)","F"
62,0,-1,71,0.000000,"\text{Not used}","int(x^4/(a*x + b*x^2)^(5/2),x)","\int \frac{x^4}{{\left(b\,x^2+a\,x\right)}^{5/2}} \,d x","Not used",1,"int(x^4/(a*x + b*x^2)^(5/2), x)","F"
63,1,24,23,0.296907,"\text{Not used}","int(x^3/(a*x + b*x^2)^(5/2),x)","\frac{2\,x\,\sqrt{b\,x^2+a\,x}}{3\,a\,{\left(a+b\,x\right)}^2}","Not used",1,"(2*x*(a*x + b*x^2)^(1/2))/(3*a*(a + b*x)^2)","B"
64,1,31,51,0.205279,"\text{Not used}","int(x^2/(a*x + b*x^2)^(5/2),x)","\frac{2\,\sqrt{b\,x^2+a\,x}\,\left(3\,a+2\,b\,x\right)}{3\,a^2\,{\left(a+b\,x\right)}^2}","Not used",1,"(2*(a*x + b*x^2)^(1/2)*(3*a + 2*b*x))/(3*a^2*(a + b*x)^2)","B"
65,1,45,48,0.237417,"\text{Not used}","int(x/(a*x + b*x^2)^(5/2),x)","-\frac{2\,\sqrt{b\,x^2+a\,x}\,\left(3\,a^2+12\,a\,b\,x+8\,b^2\,x^2\right)}{3\,a^3\,x\,{\left(a+b\,x\right)}^2}","Not used",1,"-(2*(a*x + b*x^2)^(1/2)*(3*a^2 + 8*b^2*x^2 + 12*a*b*x))/(3*a^3*x*(a + b*x)^2)","B"
66,1,43,54,0.043093,"\text{Not used}","int(1/(a*x + b*x^2)^(5/2),x)","\frac{\left(2\,a+4\,b\,x\right)\,\left(-a^2+8\,a\,b\,x+8\,b^2\,x^2\right)}{3\,a^4\,{\left(b\,x^2+a\,x\right)}^{3/2}}","Not used",1,"((2*a + 4*b*x)*(8*b^2*x^2 - a^2 + 8*a*b*x))/(3*a^4*(a*x + b*x^2)^(3/2))","B"
67,1,67,80,0.295747,"\text{Not used}","int(1/(x*(a*x + b*x^2)^(5/2)),x)","-\frac{2\,\sqrt{b\,x^2+a\,x}\,\left(3\,a^4-8\,a^3\,b\,x+48\,a^2\,b^2\,x^2+192\,a\,b^3\,x^3+128\,b^4\,x^4\right)}{15\,a^5\,x^3\,{\left(a+b\,x\right)}^2}","Not used",1,"-(2*(a*x + b*x^2)^(1/2)*(3*a^4 + 128*b^4*x^4 + 192*a*b^3*x^3 + 48*a^2*b^2*x^2 - 8*a^3*b*x))/(15*a^5*x^3*(a + b*x)^2)","B"
68,1,121,106,0.346429,"\text{Not used}","int(1/(x^2*(a*x + b*x^2)^(5/2)),x)","\frac{\sqrt{b\,x^2+a\,x}\,\left(\frac{256\,b^3}{21\,a^5}+\frac{512\,b^4\,x}{21\,a^6}\right)}{x\,\left(a+b\,x\right)}-\frac{\sqrt{b\,x^2+a\,x}\,\left(\frac{74\,b^2}{21\,a^3}+\frac{88\,b^3\,x}{21\,a^4}\right)}{x^2\,{\left(a+b\,x\right)}^2}-\frac{2\,\sqrt{b\,x^2+a\,x}}{7\,a^3\,x^4}+\frac{8\,b\,\sqrt{b\,x^2+a\,x}}{7\,a^4\,x^3}","Not used",1,"((a*x + b*x^2)^(1/2)*((256*b^3)/(21*a^5) + (512*b^4*x)/(21*a^6)))/(x*(a + b*x)) - ((a*x + b*x^2)^(1/2)*((74*b^2)/(21*a^3) + (88*b^3*x)/(21*a^4)))/(x^2*(a + b*x)^2) - (2*(a*x + b*x^2)^(1/2))/(7*a^3*x^4) + (8*b*(a*x + b*x^2)^(1/2))/(7*a^4*x^3)","B"
69,1,22,26,0.156553,"\text{Not used}","int(x/(4*x - x^2)^(1/2),x)","2\,\mathrm{asin}\left(\frac{x}{2}-1\right)-\sqrt{4\,x-x^2}","Not used",1,"2*asin(x/2 - 1) - (4*x - x^2)^(1/2)","B"
70,1,23,28,0.247904,"\text{Not used}","int(x/(x^2 - 4*x)^(1/2),x)","2\,\ln\left(x+\sqrt{x\,\left(x-4\right)}-2\right)+\sqrt{x^2-4\,x}","Not used",1,"2*log(x + (x*(x - 4))^(1/2) - 2) + (x^2 - 4*x)^(1/2)","B"
71,0,-1,46,0.000000,"\text{Not used}","int(x^2/(2*x - x^2)^(1/2),x)","\int \frac{x^2}{\sqrt{2\,x-x^2}} \,d x","Not used",1,"int(x^2/(2*x - x^2)^(1/2), x)","F"
72,0,-1,136,0.000000,"\text{Not used}","int(x^(7/2)*(b*x + c*x^2)^(1/2),x)","\int x^{7/2}\,\sqrt{c\,x^2+b\,x} \,d x","Not used",1,"int(x^(7/2)*(b*x + c*x^2)^(1/2), x)","F"
73,0,-1,108,0.000000,"\text{Not used}","int(x^(5/2)*(b*x + c*x^2)^(1/2),x)","\int x^{5/2}\,\sqrt{c\,x^2+b\,x} \,d x","Not used",1,"int(x^(5/2)*(b*x + c*x^2)^(1/2), x)","F"
74,0,-1,80,0.000000,"\text{Not used}","int(x^(3/2)*(b*x + c*x^2)^(1/2),x)","\int x^{3/2}\,\sqrt{c\,x^2+b\,x} \,d x","Not used",1,"int(x^(3/2)*(b*x + c*x^2)^(1/2), x)","F"
75,0,-1,52,0.000000,"\text{Not used}","int(x^(1/2)*(b*x + c*x^2)^(1/2),x)","\int \sqrt{x}\,\sqrt{c\,x^2+b\,x} \,d x","Not used",1,"int(x^(1/2)*(b*x + c*x^2)^(1/2), x)","F"
76,0,-1,25,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/x^(1/2),x)","\int \frac{\sqrt{c\,x^2+b\,x}}{\sqrt{x}} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/x^(1/2), x)","F"
77,0,-1,53,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/x^(3/2),x)","\int \frac{\sqrt{c\,x^2+b\,x}}{x^{3/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/x^(3/2), x)","F"
78,0,-1,54,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/x^(5/2),x)","\int \frac{\sqrt{c\,x^2+b\,x}}{x^{5/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/x^(5/2), x)","F"
79,0,-1,86,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/x^(7/2),x)","\int \frac{\sqrt{c\,x^2+b\,x}}{x^{7/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/x^(7/2), x)","F"
80,0,-1,114,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/x^(9/2),x)","\int \frac{\sqrt{c\,x^2+b\,x}}{x^{9/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/x^(9/2), x)","F"
81,0,-1,142,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/x^(11/2),x)","\int \frac{\sqrt{c\,x^2+b\,x}}{x^{11/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/x^(11/2), x)","F"
82,0,-1,164,0.000000,"\text{Not used}","int(x^(7/2)*(b*x + c*x^2)^(3/2),x)","\int x^{7/2}\,{\left(c\,x^2+b\,x\right)}^{3/2} \,d x","Not used",1,"int(x^(7/2)*(b*x + c*x^2)^(3/2), x)","F"
83,0,-1,136,0.000000,"\text{Not used}","int(x^(5/2)*(b*x + c*x^2)^(3/2),x)","\int x^{5/2}\,{\left(c\,x^2+b\,x\right)}^{3/2} \,d x","Not used",1,"int(x^(5/2)*(b*x + c*x^2)^(3/2), x)","F"
84,0,-1,108,0.000000,"\text{Not used}","int(x^(3/2)*(b*x + c*x^2)^(3/2),x)","\int x^{3/2}\,{\left(c\,x^2+b\,x\right)}^{3/2} \,d x","Not used",1,"int(x^(3/2)*(b*x + c*x^2)^(3/2), x)","F"
85,0,-1,80,0.000000,"\text{Not used}","int(x^(1/2)*(b*x + c*x^2)^(3/2),x)","\int \sqrt{x}\,{\left(c\,x^2+b\,x\right)}^{3/2} \,d x","Not used",1,"int(x^(1/2)*(b*x + c*x^2)^(3/2), x)","F"
86,0,-1,52,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x^(1/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{\sqrt{x}} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/x^(1/2), x)","F"
87,0,-1,25,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x^(3/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{x^{3/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/x^(3/2), x)","F"
88,0,-1,76,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x^(5/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{x^{5/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/x^(5/2), x)","F"
89,0,-1,75,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x^(7/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{x^{7/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/x^(7/2), x)","F"
90,0,-1,83,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x^(9/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{x^{9/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/x^(9/2), x)","F"
91,0,-1,111,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x^(11/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{x^{11/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/x^(11/2), x)","F"
92,0,-1,139,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x^(13/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{x^{13/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/x^(13/2), x)","F"
93,0,-1,167,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/x^(15/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{x^{15/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/x^(15/2), x)","F"
94,0,-1,108,0.000000,"\text{Not used}","int(x^(7/2)/(b*x + c*x^2)^(1/2),x)","\int \frac{x^{7/2}}{\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int(x^(7/2)/(b*x + c*x^2)^(1/2), x)","F"
95,0,-1,80,0.000000,"\text{Not used}","int(x^(5/2)/(b*x + c*x^2)^(1/2),x)","\int \frac{x^{5/2}}{\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int(x^(5/2)/(b*x + c*x^2)^(1/2), x)","F"
96,0,-1,52,0.000000,"\text{Not used}","int(x^(3/2)/(b*x + c*x^2)^(1/2),x)","\int \frac{x^{3/2}}{\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int(x^(3/2)/(b*x + c*x^2)^(1/2), x)","F"
97,0,-1,23,0.000000,"\text{Not used}","int(x^(1/2)/(b*x + c*x^2)^(1/2),x)","\int \frac{\sqrt{x}}{\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int(x^(1/2)/(b*x + c*x^2)^(1/2), x)","F"
98,0,-1,32,0.000000,"\text{Not used}","int(1/(x^(1/2)*(b*x + c*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{x}\,\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int(1/(x^(1/2)*(b*x + c*x^2)^(1/2)), x)","F"
99,0,-1,56,0.000000,"\text{Not used}","int(1/(x^(3/2)*(b*x + c*x^2)^(1/2)),x)","\int \frac{1}{x^{3/2}\,\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int(1/(x^(3/2)*(b*x + c*x^2)^(1/2)), x)","F"
100,0,-1,89,0.000000,"\text{Not used}","int(1/(x^(5/2)*(b*x + c*x^2)^(1/2)),x)","\int \frac{1}{x^{5/2}\,\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int(1/(x^(5/2)*(b*x + c*x^2)^(1/2)), x)","F"
101,0,-1,117,0.000000,"\text{Not used}","int(1/(x^(7/2)*(b*x + c*x^2)^(1/2)),x)","\int \frac{1}{x^{7/2}\,\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int(1/(x^(7/2)*(b*x + c*x^2)^(1/2)), x)","F"
102,0,-1,164,0.000000,"\text{Not used}","int(x^(13/2)/(b*x + c*x^2)^(3/2),x)","\int \frac{x^{13/2}}{{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int(x^(13/2)/(b*x + c*x^2)^(3/2), x)","F"
103,0,-1,136,0.000000,"\text{Not used}","int(x^(11/2)/(b*x + c*x^2)^(3/2),x)","\int \frac{x^{11/2}}{{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int(x^(11/2)/(b*x + c*x^2)^(3/2), x)","F"
104,0,-1,108,0.000000,"\text{Not used}","int(x^(9/2)/(b*x + c*x^2)^(3/2),x)","\int \frac{x^{9/2}}{{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int(x^(9/2)/(b*x + c*x^2)^(3/2), x)","F"
105,0,-1,80,0.000000,"\text{Not used}","int(x^(7/2)/(b*x + c*x^2)^(3/2),x)","\int \frac{x^{7/2}}{{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int(x^(7/2)/(b*x + c*x^2)^(3/2), x)","F"
106,0,-1,48,0.000000,"\text{Not used}","int(x^(5/2)/(b*x + c*x^2)^(3/2),x)","\int \frac{x^{5/2}}{{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int(x^(5/2)/(b*x + c*x^2)^(3/2), x)","F"
107,0,-1,23,0.000000,"\text{Not used}","int(x^(3/2)/(b*x + c*x^2)^(3/2),x)","\int \frac{x^{3/2}}{{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int(x^(3/2)/(b*x + c*x^2)^(3/2), x)","F"
108,0,-1,56,0.000000,"\text{Not used}","int(x^(1/2)/(b*x + c*x^2)^(3/2),x)","\int \frac{\sqrt{x}}{{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int(x^(1/2)/(b*x + c*x^2)^(3/2), x)","F"
109,0,-1,81,0.000000,"\text{Not used}","int(1/(x^(1/2)*(b*x + c*x^2)^(3/2)),x)","\int \frac{1}{\sqrt{x}\,{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^(1/2)*(b*x + c*x^2)^(3/2)), x)","F"
110,0,-1,117,0.000000,"\text{Not used}","int(1/(x^(3/2)*(b*x + c*x^2)^(3/2)),x)","\int \frac{1}{x^{3/2}\,{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^(3/2)*(b*x + c*x^2)^(3/2)), x)","F"
111,0,-1,145,0.000000,"\text{Not used}","int(1/(x^(5/2)*(b*x + c*x^2)^(3/2)),x)","\int \frac{1}{x^{5/2}\,{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^(5/2)*(b*x + c*x^2)^(3/2)), x)","F"
112,1,171,81,0.277277,"\text{Not used}","int((b*x + c*x^2)^3*(d*x)^m,x)","{\left(d\,x\right)}^m\,\left(\frac{b^3\,x^4\,\left(m^3+18\,m^2+107\,m+210\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}+\frac{c^3\,x^7\,\left(m^3+15\,m^2+74\,m+120\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}+\frac{3\,b\,c^2\,x^6\,\left(m^3+16\,m^2+83\,m+140\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}+\frac{3\,b^2\,c\,x^5\,\left(m^3+17\,m^2+94\,m+168\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}\right)","Not used",1,"(d*x)^m*((b^3*x^4*(107*m + 18*m^2 + m^3 + 210))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840) + (c^3*x^7*(74*m + 15*m^2 + m^3 + 120))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840) + (3*b*c^2*x^6*(83*m + 16*m^2 + m^3 + 140))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840) + (3*b^2*c*x^5*(94*m + 17*m^2 + m^3 + 168))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840))","B"
113,1,97,58,0.228583,"\text{Not used}","int((b*x + c*x^2)^2*(d*x)^m,x)","{\left(d\,x\right)}^m\,\left(\frac{b^2\,x^3\,\left(m^2+9\,m+20\right)}{m^3+12\,m^2+47\,m+60}+\frac{c^2\,x^5\,\left(m^2+7\,m+12\right)}{m^3+12\,m^2+47\,m+60}+\frac{2\,b\,c\,x^4\,\left(m^2+8\,m+15\right)}{m^3+12\,m^2+47\,m+60}\right)","Not used",1,"(d*x)^m*((b^2*x^3*(9*m + m^2 + 20))/(47*m + 12*m^2 + m^3 + 60) + (c^2*x^5*(7*m + m^2 + 12))/(47*m + 12*m^2 + m^3 + 60) + (2*b*c*x^4*(8*m + m^2 + 15))/(47*m + 12*m^2 + m^3 + 60))","B"
114,1,34,35,0.185293,"\text{Not used}","int((b*x + c*x^2)*(d*x)^m,x)","\frac{x^2\,{\left(d\,x\right)}^m\,\left(3\,b+b\,m+2\,c\,x+c\,m\,x\right)}{m^2+5\,m+6}","Not used",1,"(x^2*(d*x)^m*(3*b + b*m + 2*c*x + c*m*x))/(5*m + m^2 + 6)","B"
115,0,-1,25,0.000000,"\text{Not used}","int((d*x)^m/(b*x + c*x^2),x)","\int \frac{{\left(d\,x\right)}^m}{c\,x^2+b\,x} \,d x","Not used",1,"int((d*x)^m/(b*x + c*x^2), x)","F"
116,0,-1,33,0.000000,"\text{Not used}","int((d*x)^m/(b*x + c*x^2)^2,x)","\int \frac{{\left(d\,x\right)}^m}{{\left(c\,x^2+b\,x\right)}^2} \,d x","Not used",1,"int((d*x)^m/(b*x + c*x^2)^2, x)","F"
117,0,-1,37,0.000000,"\text{Not used}","int((d*x)^m/(b*x + c*x^2)^3,x)","\int \frac{{\left(d\,x\right)}^m}{{\left(c\,x^2+b\,x\right)}^3} \,d x","Not used",1,"int((d*x)^m/(b*x + c*x^2)^3, x)","F"
118,0,-1,73,0.000000,"\text{Not used}","int((b*x + c*x^2)^(5/2)*(d*x)^m,x)","\int {\left(c\,x^2+b\,x\right)}^{5/2}\,{\left(d\,x\right)}^m \,d x","Not used",1,"int((b*x + c*x^2)^(5/2)*(d*x)^m, x)","F"
119,0,-1,71,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)*(d*x)^m,x)","\int {\left(c\,x^2+b\,x\right)}^{3/2}\,{\left(d\,x\right)}^m \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)*(d*x)^m, x)","F"
120,0,-1,67,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)*(d*x)^m,x)","\int \sqrt{c\,x^2+b\,x}\,{\left(d\,x\right)}^m \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)*(d*x)^m, x)","F"
121,0,-1,65,0.000000,"\text{Not used}","int((d*x)^m/(b*x + c*x^2)^(1/2),x)","\int \frac{{\left(d\,x\right)}^m}{\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int((d*x)^m/(b*x + c*x^2)^(1/2), x)","F"
122,0,-1,66,0.000000,"\text{Not used}","int((d*x)^m/(b*x + c*x^2)^(3/2),x)","\int \frac{{\left(d\,x\right)}^m}{{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int((d*x)^m/(b*x + c*x^2)^(3/2), x)","F"
123,0,-1,71,0.000000,"\text{Not used}","int((d*x)^m/(b*x + c*x^2)^(5/2),x)","\int \frac{{\left(d\,x\right)}^m}{{\left(c\,x^2+b\,x\right)}^{5/2}} \,d x","Not used",1,"int((d*x)^m/(b*x + c*x^2)^(5/2), x)","F"
124,0,-1,55,0.000000,"\text{Not used}","int((b*x + c*x^2)^p*(d*x)^m,x)","\int {\left(c\,x^2+b\,x\right)}^p\,{\left(d\,x\right)}^m \,d x","Not used",1,"int((b*x + c*x^2)^p*(d*x)^m, x)","F"
125,0,-1,49,0.000000,"\text{Not used}","int(x^3*(b*x + c*x^2)^p,x)","\int x^3\,{\left(c\,x^2+b\,x\right)}^p \,d x","Not used",1,"int(x^3*(b*x + c*x^2)^p, x)","F"
126,0,-1,49,0.000000,"\text{Not used}","int(x^2*(b*x + c*x^2)^p,x)","\int x^2\,{\left(c\,x^2+b\,x\right)}^p \,d x","Not used",1,"int(x^2*(b*x + c*x^2)^p, x)","F"
127,0,-1,49,0.000000,"\text{Not used}","int(x*(b*x + c*x^2)^p,x)","\int x\,{\left(c\,x^2+b\,x\right)}^p \,d x","Not used",1,"int(x*(b*x + c*x^2)^p, x)","F"
128,0,-1,42,0.000000,"\text{Not used}","int((b*x + c*x^2)^p/x,x)","\int \frac{{\left(c\,x^2+b\,x\right)}^p}{x} \,d x","Not used",1,"int((b*x + c*x^2)^p/x, x)","F"
129,0,-1,50,0.000000,"\text{Not used}","int((b*x + c*x^2)^p/x^2,x)","\int \frac{{\left(c\,x^2+b\,x\right)}^p}{x^2} \,d x","Not used",1,"int((b*x + c*x^2)^p/x^2, x)","F"
130,0,-1,52,0.000000,"\text{Not used}","int((b*x + c*x^2)^p/x^3,x)","\int \frac{{\left(c\,x^2+b\,x\right)}^p}{x^3} \,d x","Not used",1,"int((b*x + c*x^2)^p/x^3, x)","F"
131,0,-1,61,0.000000,"\text{Not used}","int((b*x + c*x^2)^p*(d*x)^(5/2),x)","\int {\left(c\,x^2+b\,x\right)}^p\,{\left(d\,x\right)}^{5/2} \,d x","Not used",1,"int((b*x + c*x^2)^p*(d*x)^(5/2), x)","F"
132,0,-1,61,0.000000,"\text{Not used}","int((b*x + c*x^2)^p*(d*x)^(3/2),x)","\int {\left(c\,x^2+b\,x\right)}^p\,{\left(d\,x\right)}^{3/2} \,d x","Not used",1,"int((b*x + c*x^2)^p*(d*x)^(3/2), x)","F"
133,0,-1,61,0.000000,"\text{Not used}","int((b*x + c*x^2)^p*(d*x)^(1/2),x)","\int {\left(c\,x^2+b\,x\right)}^p\,\sqrt{d\,x} \,d x","Not used",1,"int((b*x + c*x^2)^p*(d*x)^(1/2), x)","F"
134,0,-1,61,0.000000,"\text{Not used}","int((b*x + c*x^2)^p/(d*x)^(1/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^p}{\sqrt{d\,x}} \,d x","Not used",1,"int((b*x + c*x^2)^p/(d*x)^(1/2), x)","F"
135,0,-1,61,0.000000,"\text{Not used}","int((b*x + c*x^2)^p/(d*x)^(3/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^p}{{\left(d\,x\right)}^{3/2}} \,d x","Not used",1,"int((b*x + c*x^2)^p/(d*x)^(3/2), x)","F"
136,0,-1,61,0.000000,"\text{Not used}","int((b*x + c*x^2)^p/(d*x)^(5/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^p}{{\left(d\,x\right)}^{5/2}} \,d x","Not used",1,"int((b*x + c*x^2)^p/(d*x)^(5/2), x)","F"
137,1,117,71,0.590907,"\text{Not used}","int(x^4*((a + b*x)^2)^(1/2),x)","\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(a^5+5\,b^3\,x^3\,\left(a^2+2\,a\,b\,x+b^2\,x^2\right)-14\,a^3\,b^2\,x^2-13\,a^4\,b\,x-9\,a\,b^2\,x^2\,\left(a^2+2\,a\,b\,x+b^2\,x^2\right)+12\,a^2\,b\,x\,\left(a^2+2\,a\,b\,x+b^2\,x^2\right)\right)}{30\,b^5}","Not used",1,"((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*(a^5 + 5*b^3*x^3*(a^2 + b^2*x^2 + 2*a*b*x) - 14*a^3*b^2*x^2 - 13*a^4*b*x - 9*a*b^2*x^2*(a^2 + b^2*x^2 + 2*a*b*x) + 12*a^2*b*x*(a^2 + b^2*x^2 + 2*a*b*x)))/(30*b^5)","B"
138,1,92,71,0.252605,"\text{Not used}","int(x^3*((a + b*x)^2)^(1/2),x)","\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(4\,b^2\,x^2\,\left(a^2+2\,a\,b\,x+b^2\,x^2\right)-a^4+9\,a^2\,b^2\,x^2+8\,a^3\,b\,x-7\,a\,b\,x\,\left(a^2+2\,a\,b\,x+b^2\,x^2\right)\right)}{20\,b^4}","Not used",1,"((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*(4*b^2*x^2*(a^2 + b^2*x^2 + 2*a*b*x) - a^4 + 9*a^2*b^2*x^2 + 8*a^3*b*x - 7*a*b*x*(a^2 + b^2*x^2 + 2*a*b*x)))/(20*b^4)","B"
139,1,63,71,0.239346,"\text{Not used}","int(x^2*((a + b*x)^2)^(1/2),x)","\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(a^3-5\,a\,b^2\,x^2+3\,b\,x\,\left(a^2+2\,a\,b\,x+b^2\,x^2\right)-4\,a^2\,b\,x\right)}{12\,b^3}","Not used",1,"((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*(a^3 - 5*a*b^2*x^2 + 3*b*x*(a^2 + b^2*x^2 + 2*a*b*x) - 4*a^2*b*x))/(12*b^3)","B"
140,1,55,61,0.183848,"\text{Not used}","int(x*((a + b*x)^2)^(1/2),x)","\frac{\left(8\,b^2\,\left(a^2+b^2\,x^2\right)-12\,a^2\,b^2+4\,a\,b^3\,x\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{24\,b^4}","Not used",1,"((8*b^2*(a^2 + b^2*x^2) - 12*a^2*b^2 + 4*a*b^3*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(24*b^4)","B"
141,1,19,32,0.197281,"\text{Not used}","int(((a + b*x)^2)^(1/2),x)","\frac{\sqrt{{\left(a+b\,x\right)}^2}\,\left(a+b\,x\right)}{2\,b}","Not used",1,"(((a + b*x)^2)^(1/2)*(a + b*x))/(2*b)","B"
142,1,98,62,0.280881,"\text{Not used}","int(((a + b*x)^2)^(1/2)/x,x)","\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}-\ln\left(a\,b+\frac{a^2}{x}+\frac{\sqrt{a^2}\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{x}\right)\,\sqrt{a^2}+\frac{a\,b\,\ln\left(a\,b+\sqrt{{\left(a+b\,x\right)}^2}\,\sqrt{b^2}+b^2\,x\right)}{\sqrt{b^2}}","Not used",1,"(a^2 + b^2*x^2 + 2*a*b*x)^(1/2) - log(a*b + a^2/x + ((a^2)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/x)*(a^2)^(1/2) + (a*b*log(a*b + ((a + b*x)^2)^(1/2)*(b^2)^(1/2) + b^2*x))/(b^2)^(1/2)","B"
143,1,103,65,0.261260,"\text{Not used}","int(((a + b*x)^2)^(1/2)/x^2,x)","\ln\left(a\,b+\sqrt{{\left(a+b\,x\right)}^2}\,\sqrt{b^2}+b^2\,x\right)\,\sqrt{b^2}-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{x}-\frac{a\,b\,\ln\left(a\,b+\frac{a^2}{x}+\frac{\sqrt{a^2}\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{x}\right)}{\sqrt{a^2}}","Not used",1,"log(a*b + ((a + b*x)^2)^(1/2)*(b^2)^(1/2) + b^2*x)*(b^2)^(1/2) - (a^2 + b^2*x^2 + 2*a*b*x)^(1/2)/x - (a*b*log(a*b + a^2/x + ((a^2)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/x))/(a^2)^(1/2)","B"
144,1,27,35,0.157023,"\text{Not used}","int(((a + b*x)^2)^(1/2)/x^3,x)","-\frac{\sqrt{{\left(a+b\,x\right)}^2}\,\left(a+2\,b\,x\right)}{2\,x^2\,\left(a+b\,x\right)}","Not used",1,"-(((a + b*x)^2)^(1/2)*(a + 2*b*x))/(2*x^2*(a + b*x))","B"
145,1,29,71,0.161393,"\text{Not used}","int(((a + b*x)^2)^(1/2)/x^4,x)","-\frac{\left(2\,a+3\,b\,x\right)\,\sqrt{{\left(a+b\,x\right)}^2}}{6\,x^3\,\left(a+b\,x\right)}","Not used",1,"-((2*a + 3*b*x)*((a + b*x)^2)^(1/2))/(6*x^3*(a + b*x))","B"
146,1,29,71,0.159458,"\text{Not used}","int(((a + b*x)^2)^(1/2)/x^5,x)","-\frac{\left(3\,a+4\,b\,x\right)\,\sqrt{{\left(a+b\,x\right)}^2}}{12\,x^4\,\left(a+b\,x\right)}","Not used",1,"-((3*a + 4*b*x)*((a + b*x)^2)^(1/2))/(12*x^4*(a + b*x))","B"
147,1,29,71,0.160752,"\text{Not used}","int(((a + b*x)^2)^(1/2)/x^6,x)","-\frac{\left(4\,a+5\,b\,x\right)\,\sqrt{{\left(a+b\,x\right)}^2}}{20\,x^5\,\left(a+b\,x\right)}","Not used",1,"-((4*a + 5*b*x)*((a + b*x)^2)^(1/2))/(20*x^5*(a + b*x))","B"
148,0,-1,151,0.000000,"\text{Not used}","int(x^5*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int x^5\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2} \,d x","Not used",1,"int(x^5*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
149,0,-1,151,0.000000,"\text{Not used}","int(x^4*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int x^4\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2} \,d x","Not used",1,"int(x^4*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
150,0,-1,151,0.000000,"\text{Not used}","int(x^3*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int x^3\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2} \,d x","Not used",1,"int(x^3*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
151,0,-1,96,0.000000,"\text{Not used}","int(x^2*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int x^2\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2} \,d x","Not used",1,"int(x^2*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
152,1,42,61,0.163958,"\text{Not used}","int(x*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\frac{\left(-a^2+3\,a\,b\,x+4\,b^2\,x^2\right)\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{20\,b^2}","Not used",1,"((4*b^2*x^2 - a^2 + 3*a*b*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2))/(20*b^2)","B"
153,1,32,32,0.156309,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\frac{\left(x\,b^2+a\,b\right)\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{4\,b^2}","Not used",1,"((a*b + b^2*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2))/(4*b^2)","B"
154,0,-1,143,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/x,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{x} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/x, x)","F"
155,0,-1,142,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/x^2,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{x^2} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/x^2, x)","F"
156,0,-1,141,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/x^3,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{x^3} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/x^3, x)","F"
157,0,-1,145,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/x^4,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{x^4} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/x^4, x)","F"
158,1,135,37,0.194301,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/x^5,x)","-\frac{a^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{4\,x^4\,\left(a+b\,x\right)}-\frac{b^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{x\,\left(a+b\,x\right)}-\frac{3\,a\,b^2\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,x^2\,\left(a+b\,x\right)}-\frac{a^2\,b\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{x^3\,\left(a+b\,x\right)}","Not used",1,"- (a^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(4*x^4*(a + b*x)) - (b^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(x*(a + b*x)) - (3*a*b^2*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(2*x^2*(a + b*x)) - (a^2*b*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(x^3*(a + b*x))","B"
159,1,135,76,0.192086,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/x^6,x)","-\frac{a^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{5\,x^5\,\left(a+b\,x\right)}-\frac{b^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,x^2\,\left(a+b\,x\right)}-\frac{a\,b^2\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{x^3\,\left(a+b\,x\right)}-\frac{3\,a^2\,b\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{4\,x^4\,\left(a+b\,x\right)}","Not used",1,"- (a^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(5*x^5*(a + b*x)) - (b^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(2*x^2*(a + b*x)) - (a*b^2*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(x^3*(a + b*x)) - (3*a^2*b*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(4*x^4*(a + b*x))","B"
160,1,135,151,0.196878,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/x^7,x)","-\frac{a^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{6\,x^6\,\left(a+b\,x\right)}-\frac{b^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{3\,x^3\,\left(a+b\,x\right)}-\frac{3\,a\,b^2\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{4\,x^4\,\left(a+b\,x\right)}-\frac{3\,a^2\,b\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{5\,x^5\,\left(a+b\,x\right)}","Not used",1,"- (a^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(6*x^6*(a + b*x)) - (b^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(3*x^3*(a + b*x)) - (3*a*b^2*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(4*x^4*(a + b*x)) - (3*a^2*b*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(5*x^5*(a + b*x))","B"
161,1,135,151,0.196462,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/x^8,x)","-\frac{a^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{7\,x^7\,\left(a+b\,x\right)}-\frac{b^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{4\,x^4\,\left(a+b\,x\right)}-\frac{3\,a\,b^2\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{5\,x^5\,\left(a+b\,x\right)}-\frac{a^2\,b\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,x^6\,\left(a+b\,x\right)}","Not used",1,"- (a^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(7*x^7*(a + b*x)) - (b^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(4*x^4*(a + b*x)) - (3*a*b^2*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(5*x^5*(a + b*x)) - (a^2*b*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(2*x^6*(a + b*x))","B"
162,1,135,151,0.197988,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/x^9,x)","-\frac{a^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{8\,x^8\,\left(a+b\,x\right)}-\frac{b^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{5\,x^5\,\left(a+b\,x\right)}-\frac{a\,b^2\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,x^6\,\left(a+b\,x\right)}-\frac{3\,a^2\,b\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{7\,x^7\,\left(a+b\,x\right)}","Not used",1,"- (a^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(8*x^8*(a + b*x)) - (b^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(5*x^5*(a + b*x)) - (a*b^2*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(2*x^6*(a + b*x)) - (3*a^2*b*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(7*x^7*(a + b*x))","B"
163,0,-1,231,0.000000,"\text{Not used}","int(x^5*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int x^5\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2} \,d x","Not used",1,"int(x^5*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
164,0,-1,181,0.000000,"\text{Not used}","int(x^4*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int x^4\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2} \,d x","Not used",1,"int(x^4*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
165,0,-1,144,0.000000,"\text{Not used}","int(x^3*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int x^3\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2} \,d x","Not used",1,"int(x^3*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
166,0,-1,107,0.000000,"\text{Not used}","int(x^2*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int x^2\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2} \,d x","Not used",1,"int(x^2*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
167,0,-1,61,0.000000,"\text{Not used}","int(x*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int x\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2} \,d x","Not used",1,"int(x*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
168,1,32,32,0.154502,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\frac{\left(x\,b^2+a\,b\right)\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}}{6\,b^2}","Not used",1,"((a*b + b^2*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2))/(6*b^2)","B"
169,0,-1,221,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}}{x} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x, x)","F"
170,0,-1,220,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x^2,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}}{x^2} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x^2, x)","F"
171,0,-1,222,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x^3,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}}{x^3} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x^3, x)","F"
172,0,-1,222,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x^4,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}}{x^4} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x^4, x)","F"
173,0,-1,219,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x^5,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}}{x^5} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x^5, x)","F"
174,0,-1,223,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x^6,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}}{x^6} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x^6, x)","F"
175,1,207,37,0.185527,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x^7,x)","-\frac{a^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{6\,x^6\,\left(a+b\,x\right)}-\frac{b^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{x\,\left(a+b\,x\right)}-\frac{10\,a^2\,b^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{3\,x^3\,\left(a+b\,x\right)}-\frac{5\,a^3\,b^2\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,x^4\,\left(a+b\,x\right)}-\frac{5\,a\,b^4\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,x^2\,\left(a+b\,x\right)}-\frac{a^4\,b\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{x^5\,\left(a+b\,x\right)}","Not used",1,"- (a^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(6*x^6*(a + b*x)) - (b^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(x*(a + b*x)) - (10*a^2*b^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(3*x^3*(a + b*x)) - (5*a^3*b^2*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(2*x^4*(a + b*x)) - (5*a*b^4*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(2*x^2*(a + b*x)) - (a^4*b*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(x^5*(a + b*x))","B"
176,1,207,76,0.190303,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x^8,x)","-\frac{a^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{7\,x^7\,\left(a+b\,x\right)}-\frac{b^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,x^2\,\left(a+b\,x\right)}-\frac{5\,a^2\,b^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,x^4\,\left(a+b\,x\right)}-\frac{2\,a^3\,b^2\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{x^5\,\left(a+b\,x\right)}-\frac{5\,a\,b^4\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{3\,x^3\,\left(a+b\,x\right)}-\frac{5\,a^4\,b\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{6\,x^6\,\left(a+b\,x\right)}","Not used",1,"- (a^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(7*x^7*(a + b*x)) - (b^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(2*x^2*(a + b*x)) - (5*a^2*b^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(2*x^4*(a + b*x)) - (2*a^3*b^2*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(x^5*(a + b*x)) - (5*a*b^4*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(3*x^3*(a + b*x)) - (5*a^4*b*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(6*x^6*(a + b*x))","B"
177,1,207,116,0.189589,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x^9,x)","-\frac{a^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{8\,x^8\,\left(a+b\,x\right)}-\frac{b^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{3\,x^3\,\left(a+b\,x\right)}-\frac{2\,a^2\,b^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{x^5\,\left(a+b\,x\right)}-\frac{5\,a^3\,b^2\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{3\,x^6\,\left(a+b\,x\right)}-\frac{5\,a\,b^4\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{4\,x^4\,\left(a+b\,x\right)}-\frac{5\,a^4\,b\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{7\,x^7\,\left(a+b\,x\right)}","Not used",1,"- (a^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(8*x^8*(a + b*x)) - (b^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(3*x^3*(a + b*x)) - (2*a^2*b^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(x^5*(a + b*x)) - (5*a^3*b^2*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(3*x^6*(a + b*x)) - (5*a*b^4*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(4*x^4*(a + b*x)) - (5*a^4*b*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(7*x^7*(a + b*x))","B"
178,1,207,229,0.194500,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x^10,x)","-\frac{a^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{9\,x^9\,\left(a+b\,x\right)}-\frac{b^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{4\,x^4\,\left(a+b\,x\right)}-\frac{5\,a^2\,b^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{3\,x^6\,\left(a+b\,x\right)}-\frac{10\,a^3\,b^2\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{7\,x^7\,\left(a+b\,x\right)}-\frac{a\,b^4\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{x^5\,\left(a+b\,x\right)}-\frac{5\,a^4\,b\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{8\,x^8\,\left(a+b\,x\right)}","Not used",1,"- (a^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(9*x^9*(a + b*x)) - (b^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(4*x^4*(a + b*x)) - (5*a^2*b^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(3*x^6*(a + b*x)) - (10*a^3*b^2*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(7*x^7*(a + b*x)) - (a*b^4*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(x^5*(a + b*x)) - (5*a^4*b*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(8*x^8*(a + b*x))","B"
179,1,207,231,0.200340,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x^11,x)","-\frac{a^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{10\,x^{10}\,\left(a+b\,x\right)}-\frac{b^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{5\,x^5\,\left(a+b\,x\right)}-\frac{10\,a^2\,b^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{7\,x^7\,\left(a+b\,x\right)}-\frac{5\,a^3\,b^2\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{4\,x^8\,\left(a+b\,x\right)}-\frac{5\,a\,b^4\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{6\,x^6\,\left(a+b\,x\right)}-\frac{5\,a^4\,b\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{9\,x^9\,\left(a+b\,x\right)}","Not used",1,"- (a^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(10*x^10*(a + b*x)) - (b^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(5*x^5*(a + b*x)) - (10*a^2*b^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(7*x^7*(a + b*x)) - (5*a^3*b^2*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(4*x^8*(a + b*x)) - (5*a*b^4*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(6*x^6*(a + b*x)) - (5*a^4*b*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(9*x^9*(a + b*x))","B"
180,1,207,231,0.198410,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/x^12,x)","-\frac{a^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{11\,x^{11}\,\left(a+b\,x\right)}-\frac{b^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{6\,x^6\,\left(a+b\,x\right)}-\frac{5\,a^2\,b^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{4\,x^8\,\left(a+b\,x\right)}-\frac{10\,a^3\,b^2\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{9\,x^9\,\left(a+b\,x\right)}-\frac{5\,a\,b^4\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{7\,x^7\,\left(a+b\,x\right)}-\frac{a^4\,b\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,x^{10}\,\left(a+b\,x\right)}","Not used",1,"- (a^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(11*x^11*(a + b*x)) - (b^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(6*x^6*(a + b*x)) - (5*a^2*b^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(4*x^8*(a + b*x)) - (10*a^3*b^2*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(9*x^9*(a + b*x)) - (5*a*b^4*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(7*x^7*(a + b*x)) - (a^4*b*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(2*x^10*(a + b*x))","B"
181,0,-1,182,0.000000,"\text{Not used}","int(x^4/((a + b*x)^2)^(1/2),x)","\int \frac{x^4}{\sqrt{{\left(a+b\,x\right)}^2}} \,d x","Not used",1,"int(x^4/((a + b*x)^2)^(1/2), x)","F"
182,0,-1,144,0.000000,"\text{Not used}","int(x^3/((a + b*x)^2)^(1/2),x)","\int \frac{x^3}{\sqrt{{\left(a+b\,x\right)}^2}} \,d x","Not used",1,"int(x^3/((a + b*x)^2)^(1/2), x)","F"
183,0,-1,106,0.000000,"\text{Not used}","int(x^2/((a + b*x)^2)^(1/2),x)","\int \frac{x^2}{\sqrt{{\left(a+b\,x\right)}^2}} \,d x","Not used",1,"int(x^2/((a + b*x)^2)^(1/2), x)","F"
184,1,57,62,0.284274,"\text{Not used}","int(x/((a + b*x)^2)^(1/2),x)","\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{b^2}-\frac{a\,b\,\ln\left(a\,b+\sqrt{{\left(a+b\,x\right)}^2}\,\sqrt{b^2}+b^2\,x\right)}{{\left(b^2\right)}^{3/2}}","Not used",1,"(a^2 + b^2*x^2 + 2*a*b*x)^(1/2)/b^2 - (a*b*log(a*b + ((a + b*x)^2)^(1/2)*(b^2)^(1/2) + b^2*x))/(b^2)^(3/2)","B"
185,1,19,35,0.207751,"\text{Not used}","int(1/((a + b*x)^2)^(1/2),x)","\frac{\ln\left(a+b\,x+\sqrt{{\left(a+b\,x\right)}^2}\right)}{b}","Not used",1,"log(a + b*x + ((a + b*x)^2)^(1/2))/b","B"
186,1,46,68,0.255983,"\text{Not used}","int(1/(x*((a + b*x)^2)^(1/2)),x)","-\frac{\ln\left(a\,b+\frac{a^2}{x}+\frac{\sqrt{a^2}\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{x}\right)}{\sqrt{a^2}}","Not used",1,"-log(a*b + a^2/x + ((a^2)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/x)/(a^2)^(1/2)","B"
187,1,68,103,0.249893,"\text{Not used}","int(1/(x^2*((a + b*x)^2)^(1/2)),x)","\frac{a\,b\,\mathrm{atanh}\left(\frac{a^2+b\,x\,a}{\sqrt{a^2}\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}\right)}{{\left(a^2\right)}^{3/2}}-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{a^2\,x}","Not used",1,"(a*b*atanh((a^2 + a*b*x)/((a^2)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))))/(a^2)^(3/2) - (a^2 + b^2*x^2 + 2*a*b*x)^(1/2)/(a^2*x)","B"
188,0,-1,145,0.000000,"\text{Not used}","int(1/(x^3*((a + b*x)^2)^(1/2)),x)","\int \frac{1}{x^3\,\sqrt{{\left(a+b\,x\right)}^2}} \,d x","Not used",1,"int(1/(x^3*((a + b*x)^2)^(1/2)), x)","F"
189,0,-1,184,0.000000,"\text{Not used}","int(1/(x^4*((a + b*x)^2)^(1/2)),x)","\int \frac{1}{x^4\,\sqrt{{\left(a+b\,x\right)}^2}} \,d x","Not used",1,"int(1/(x^4*((a + b*x)^2)^(1/2)), x)","F"
190,0,-1,172,0.000000,"\text{Not used}","int(x^4/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int \frac{x^4}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(x^4/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
191,0,-1,133,0.000000,"\text{Not used}","int(x^3/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int \frac{x^3}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(x^3/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
192,0,-1,99,0.000000,"\text{Not used}","int(x^2/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int \frac{x^2}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(x^2/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
193,1,36,61,0.203290,"\text{Not used}","int(x/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","-\frac{\left(a+2\,b\,x\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,b^2\,{\left(a+b\,x\right)}^3}","Not used",1,"-((a + 2*b*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(2*b^2*(a + b*x)^3)","B"
194,1,30,34,0.197110,"\text{Not used}","int(1/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,b\,{\left(a+b\,x\right)}^3}","Not used",1,"-(a^2 + b^2*x^2 + 2*a*b*x)^(1/2)/(2*b*(a + b*x)^3)","B"
195,0,-1,126,0.000000,"\text{Not used}","int(1/(x*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)),x)","\int \frac{1}{x\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(1/(x*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)), x)","F"
196,0,-1,165,0.000000,"\text{Not used}","int(1/(x^2*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)),x)","\int \frac{1}{x^2\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^2*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)), x)","F"
197,0,-1,209,0.000000,"\text{Not used}","int(1/(x^3*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)),x)","\int \frac{1}{x^3\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^3*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)), x)","F"
198,0,-1,244,0.000000,"\text{Not used}","int(x^6/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int \frac{x^6}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int(x^6/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
199,0,-1,205,0.000000,"\text{Not used}","int(x^5/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int \frac{x^5}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int(x^5/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
200,0,-1,171,0.000000,"\text{Not used}","int(x^4/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int \frac{x^4}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int(x^4/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
201,1,128,37,0.239039,"\text{Not used}","int(x^3/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\frac{a^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{4\,b^4\,{\left(a+b\,x\right)}^5}-\frac{a^2\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{b^4\,{\left(a+b\,x\right)}^4}-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{b^4\,{\left(a+b\,x\right)}^2}+\frac{3\,a\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,b^4\,{\left(a+b\,x\right)}^3}","Not used",1,"(a^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(4*b^4*(a + b*x)^5) - (a^2*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(b^4*(a + b*x)^4) - (a^2 + b^2*x^2 + 2*a*b*x)^(1/2)/(b^4*(a + b*x)^2) + (3*a*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(2*b^4*(a + b*x)^3)","B"
202,1,47,107,0.237852,"\text{Not used}","int(x^2/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(a^2+4\,a\,b\,x+6\,b^2\,x^2\right)}{12\,b^3\,{\left(a+b\,x\right)}^5}","Not used",1,"-((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*(a^2 + 6*b^2*x^2 + 4*a*b*x))/(12*b^3*(a + b*x)^5)","B"
203,1,36,63,0.217791,"\text{Not used}","int(x/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","-\frac{\left(a+4\,b\,x\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{12\,b^2\,{\left(a+b\,x\right)}^5}","Not used",1,"-((a + 4*b*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(12*b^2*(a + b*x)^5)","B"
204,1,30,34,0.242633,"\text{Not used}","int(1/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{4\,b\,{\left(a+b\,x\right)}^5}","Not used",1,"-(a^2 + b^2*x^2 + 2*a*b*x)^(1/2)/(4*b*(a + b*x)^5)","B"
205,0,-1,194,0.000000,"\text{Not used}","int(1/(x*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)),x)","\int \frac{1}{x\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int(1/(x*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)), x)","F"
206,0,-1,235,0.000000,"\text{Not used}","int(1/(x^2*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)),x)","\int \frac{1}{x^2\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int(1/(x^2*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)), x)","F"
207,0,-1,278,0.000000,"\text{Not used}","int(1/(x^3*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)),x)","\int \frac{1}{x^3\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int(1/(x^3*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)), x)","F"
208,0,-1,42,0.000000,"\text{Not used}","int(x*(12*x + 4*x^2 + 9)^(5/2),x)","\int x\,{\left(4\,x^2+12\,x+9\right)}^{5/2} \,d x","Not used",1,"int(x*(12*x + 4*x^2 + 9)^(5/2), x)","F"
209,1,24,42,0.052832,"\text{Not used}","int(x*(12*x + 4*x^2 + 9)^(3/2),x)","\frac{{\left(4\,x^2+12\,x+9\right)}^{3/2}\,\left(16\,x^2+18\,x-9\right)}{80}","Not used",1,"((12*x + 4*x^2 + 9)^(3/2)*(18*x + 16*x^2 - 9))/80","B"
210,1,23,42,0.029116,"\text{Not used}","int(x*(12*x + 4*x^2 + 9)^(1/2),x)","\left(\frac{x^2}{3}+\frac{x}{4}-\frac{3}{8}\right)\,\sqrt{4\,x^2+12\,x+9}","Not used",1,"(x/4 + x^2/3 - 3/8)*(12*x + 4*x^2 + 9)^(1/2)","B"
211,1,32,48,0.073536,"\text{Not used}","int(x/(12*x + 4*x^2 + 9)^(1/2),x)","\frac{\sqrt{4\,x^2+12\,x+9}}{4}-\frac{3\,\ln\left(x+\frac{\sqrt{{\left(2\,x+3\right)}^2}}{2}+\frac{3}{2}\right)}{4}","Not used",1,"(12*x + 4*x^2 + 9)^(1/2)/4 - (3*log(x + ((2*x + 3)^2)^(1/2)/2 + 3/2))/4","B"
212,1,26,44,0.176824,"\text{Not used}","int(x/(12*x + 4*x^2 + 9)^(3/2),x)","-\frac{\left(4\,x+3\right)\,\sqrt{4\,x^2+12\,x+9}}{8\,{\left(2\,x+3\right)}^3}","Not used",1,"-((4*x + 3)*(12*x + 4*x^2 + 9)^(1/2))/(8*(2*x + 3)^3)","B"
213,1,26,44,0.184778,"\text{Not used}","int(x/(12*x + 4*x^2 + 9)^(5/2),x)","-\frac{\left(8\,x+3\right)\,\sqrt{4\,x^2+12\,x+9}}{48\,{\left(2\,x+3\right)}^5}","Not used",1,"-((8*x + 3)*(12*x + 4*x^2 + 9)^(1/2))/(48*(2*x + 3)^5)","B"
214,1,26,44,0.188311,"\text{Not used}","int(x/(12*x + 4*x^2 + 9)^(7/2),x)","-\frac{\left(4\,x+1\right)\,\sqrt{4\,x^2+12\,x+9}}{40\,{\left(2\,x+3\right)}^7}","Not used",1,"-((4*x + 1)*(12*x + 4*x^2 + 9)^(1/2))/(40*(2*x + 3)^7)","B"
215,1,32,48,0.272076,"\text{Not used}","int(x/((3*x + 2)^2)^(1/2),x)","\frac{\sqrt{9\,x^2+12\,x+4}}{9}-\frac{2\,\ln\left(x+\frac{\sqrt{{\left(3\,x+2\right)}^2}}{3}+\frac{2}{3}\right)}{9}","Not used",1,"(12*x + 9*x^2 + 4)^(1/2)/9 - (2*log(x + ((3*x + 2)^2)^(1/2)/3 + 2/3))/9","B"
216,1,32,48,0.262437,"\text{Not used}","int(x/((3*x - 2)^2)^(1/2),x)","\frac{2\,\ln\left(x+\frac{\sqrt{{\left(3\,x-2\right)}^2}}{3}-\frac{2}{3}\right)}{9}+\frac{\sqrt{9\,x^2-12\,x+4}}{9}","Not used",1,"(2*log(x + ((3*x - 2)^2)^(1/2)/3 - 2/3))/9 + (9*x^2 - 12*x + 4)^(1/2)/9","B"
217,1,36,48,0.269922,"\text{Not used}","int(x/(-(3*x - 2)^2)^(1/2),x)","-\frac{\sqrt{-9\,x^2+12\,x-4}}{9}-\frac{\ln\left(x-\frac{2}{3}-\frac{\sqrt{-{\left(3\,x-2\right)}^2}\,1{}\mathrm{i}}{3}\right)\,2{}\mathrm{i}}{9}","Not used",1,"- (log(x - ((-(3*x - 2)^2)^(1/2)*1i)/3 - 2/3)*2i)/9 - (12*x - 9*x^2 - 4)^(1/2)/9","B"
218,1,36,48,0.268904,"\text{Not used}","int(x/(-(3*x + 2)^2)^(1/2),x)","-\frac{\sqrt{-9\,x^2-12\,x-4}}{9}+\frac{\ln\left(x+\frac{2}{3}-\frac{\sqrt{-{\left(3\,x+2\right)}^2}\,1{}\mathrm{i}}{3}\right)\,2{}\mathrm{i}}{9}","Not used",1,"(log(x - ((-(3*x + 2)^2)^(1/2)*1i)/3 + 2/3)*2i)/9 - (- 12*x - 9*x^2 - 4)^(1/2)/9","B"
219,1,8,12,0.175526,"\text{Not used}","int((x + 1)/(2*x + x^2),x)","\frac{\ln\left(x\,\left(x+2\right)\right)}{2}","Not used",1,"log(x*(x + 2))/2","B"
220,1,8,10,0.058797,"\text{Not used}","int((a + 2*b*x)/(a*x + b*x^2),x)","\ln\left(x\,\left(a+b\,x\right)\right)","Not used",1,"log(x*(a + b*x))","B"
221,1,91,62,0.169507,"\text{Not used}","int((b*x + c*x^2)*(d + e*x)^4,x)","x^3\,\left(\frac{c\,d^4}{3}+\frac{4\,b\,e\,d^3}{3}\right)+x^6\,\left(\frac{b\,e^4}{6}+\frac{2\,c\,d\,e^3}{3}\right)+\frac{b\,d^4\,x^2}{2}+\frac{c\,e^4\,x^7}{7}+\frac{d^2\,e\,x^4\,\left(3\,b\,e+2\,c\,d\right)}{2}+\frac{2\,d\,e^2\,x^5\,\left(2\,b\,e+3\,c\,d\right)}{5}","Not used",1,"x^3*((c*d^4)/3 + (4*b*d^3*e)/3) + x^6*((b*e^4)/6 + (2*c*d*e^3)/3) + (b*d^4*x^2)/2 + (c*e^4*x^7)/7 + (d^2*e*x^4*(3*b*e + 2*c*d))/2 + (2*d*e^2*x^5*(2*b*e + 3*c*d))/5","B"
222,1,68,62,0.148962,"\text{Not used}","int((b*x + c*x^2)*(d + e*x)^3,x)","x^3\,\left(\frac{c\,d^3}{3}+b\,e\,d^2\right)+x^5\,\left(\frac{b\,e^3}{5}+\frac{3\,c\,d\,e^2}{5}\right)+\frac{b\,d^3\,x^2}{2}+\frac{c\,e^3\,x^6}{6}+\frac{3\,d\,e\,x^4\,\left(b\,e+c\,d\right)}{4}","Not used",1,"x^3*((c*d^3)/3 + b*d^2*e) + x^5*((b*e^3)/5 + (3*c*d*e^2)/5) + (b*d^3*x^2)/2 + (c*e^3*x^6)/6 + (3*d*e*x^4*(b*e + c*d))/4","B"
223,1,51,55,0.050018,"\text{Not used}","int((b*x + c*x^2)*(d + e*x)^2,x)","x^3\,\left(\frac{c\,d^2}{3}+\frac{2\,b\,e\,d}{3}\right)+x^4\,\left(\frac{b\,e^2}{4}+\frac{c\,d\,e}{2}\right)+\frac{b\,d^2\,x^2}{2}+\frac{c\,e^2\,x^5}{5}","Not used",1,"x^3*((c*d^2)/3 + (2*b*d*e)/3) + x^4*((b*e^2)/4 + (c*d*e)/2) + (b*d^2*x^2)/2 + (c*e^2*x^5)/5","B"
224,1,28,33,0.038068,"\text{Not used}","int((b*x + c*x^2)*(d + e*x),x)","\frac{c\,e\,x^4}{4}+\left(\frac{b\,e}{3}+\frac{c\,d}{3}\right)\,x^3+\frac{b\,d\,x^2}{2}","Not used",1,"x^3*((b*e)/3 + (c*d)/3) + (b*d*x^2)/2 + (c*e*x^4)/4","B"
225,1,13,17,0.020968,"\text{Not used}","int(b*x + c*x^2,x)","\frac{x^2\,\left(3\,b+2\,c\,x\right)}{6}","Not used",1,"(x^2*(3*b + 2*c*x))/6","B"
226,1,46,45,0.067128,"\text{Not used}","int((b*x + c*x^2)/(d + e*x),x)","x\,\left(\frac{b}{e}-\frac{c\,d}{e^2}\right)+\frac{c\,x^2}{2\,e}+\frac{\ln\left(d+e\,x\right)\,\left(c\,d^2-b\,d\,e\right)}{e^3}","Not used",1,"x*(b/e - (c*d)/e^2) + (c*x^2)/(2*e) + (log(d + e*x)*(c*d^2 - b*d*e))/e^3","B"
227,1,54,48,0.184887,"\text{Not used}","int((b*x + c*x^2)/(d + e*x)^2,x)","\frac{\ln\left(d+e\,x\right)\,\left(b\,e-2\,c\,d\right)}{e^3}-\frac{c\,d^2-b\,d\,e}{e\,\left(x\,e^3+d\,e^2\right)}+\frac{c\,x}{e^2}","Not used",1,"(log(d + e*x)*(b*e - 2*c*d))/e^3 - (c*d^2 - b*d*e)/(e*(d*e^2 + e^3*x)) + (c*x)/e^2","B"
228,1,63,55,0.189412,"\text{Not used}","int((b*x + c*x^2)/(d + e*x)^3,x)","\frac{\frac{3\,c\,d^2-b\,d\,e}{2\,e^3}-\frac{x\,\left(b\,e-2\,c\,d\right)}{e^2}}{d^2+2\,d\,e\,x+e^2\,x^2}+\frac{c\,\ln\left(d+e\,x\right)}{e^3}","Not used",1,"((3*c*d^2 - b*d*e)/(2*e^3) - (x*(b*e - 2*c*d))/e^2)/(d^2 + e^2*x^2 + 2*d*e*x) + (c*log(d + e*x))/e^3","B"
229,1,68,60,0.048215,"\text{Not used}","int((b*x + c*x^2)/(d + e*x)^4,x)","-\frac{\frac{d\,\left(b\,e+2\,c\,d\right)}{6\,e^3}+\frac{x\,\left(b\,e+2\,c\,d\right)}{2\,e^2}+\frac{c\,x^2}{e}}{d^3+3\,d^2\,e\,x+3\,d\,e^2\,x^2+e^3\,x^3}","Not used",1,"-((d*(b*e + 2*c*d))/(6*e^3) + (x*(b*e + 2*c*d))/(2*e^2) + (c*x^2)/e)/(d^3 + e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x)","B"
230,1,78,62,0.172351,"\text{Not used}","int((b*x + c*x^2)/(d + e*x)^5,x)","-\frac{\frac{d\,\left(b\,e+c\,d\right)}{12\,e^3}+\frac{x\,\left(b\,e+c\,d\right)}{3\,e^2}+\frac{c\,x^2}{2\,e}}{d^4+4\,d^3\,e\,x+6\,d^2\,e^2\,x^2+4\,d\,e^3\,x^3+e^4\,x^4}","Not used",1,"-((d*(b*e + c*d))/(12*e^3) + (x*(b*e + c*d))/(3*e^2) + (c*x^2)/(2*e))/(d^4 + e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x)","B"
231,1,149,137,0.074604,"\text{Not used}","int((b*x + c*x^2)^2*(d + e*x)^4,x)","x^5\,\left(\frac{6\,b^2\,d^2\,e^2}{5}+\frac{8\,b\,c\,d^3\,e}{5}+\frac{c^2\,d^4}{5}\right)+x^7\,\left(\frac{b^2\,e^4}{7}+\frac{8\,b\,c\,d\,e^3}{7}+\frac{6\,c^2\,d^2\,e^2}{7}\right)+\frac{b^2\,d^4\,x^3}{3}+\frac{c^2\,e^4\,x^9}{9}+\frac{b\,d^3\,x^4\,\left(2\,b\,e+c\,d\right)}{2}+\frac{c\,e^3\,x^8\,\left(b\,e+2\,c\,d\right)}{4}+\frac{2\,d\,e\,x^6\,\left(b^2\,e^2+3\,b\,c\,d\,e+c^2\,d^2\right)}{3}","Not used",1,"x^5*((c^2*d^4)/5 + (6*b^2*d^2*e^2)/5 + (8*b*c*d^3*e)/5) + x^7*((b^2*e^4)/7 + (6*c^2*d^2*e^2)/7 + (8*b*c*d*e^3)/7) + (b^2*d^4*x^3)/3 + (c^2*e^4*x^9)/9 + (b*d^3*x^4*(2*b*e + c*d))/2 + (c*e^3*x^8*(b*e + 2*c*d))/4 + (2*d*e*x^6*(b^2*e^2 + c^2*d^2 + 3*b*c*d*e))/3","B"
232,1,118,127,0.168692,"\text{Not used}","int((b*x + c*x^2)^2*(d + e*x)^3,x)","x^5\,\left(\frac{3\,b^2\,d\,e^2}{5}+\frac{6\,b\,c\,d^2\,e}{5}+\frac{c^2\,d^3}{5}\right)+x^6\,\left(\frac{b^2\,e^3}{6}+b\,c\,d\,e^2+\frac{c^2\,d^2\,e}{2}\right)+\frac{b^2\,d^3\,x^3}{3}+\frac{c^2\,e^3\,x^8}{8}+\frac{b\,d^2\,x^4\,\left(3\,b\,e+2\,c\,d\right)}{4}+\frac{c\,e^2\,x^7\,\left(2\,b\,e+3\,c\,d\right)}{7}","Not used",1,"x^5*((c^2*d^3)/5 + (3*b^2*d*e^2)/5 + (6*b*c*d^2*e)/5) + x^6*((b^2*e^3)/6 + (c^2*d^2*e)/2 + b*c*d*e^2) + (b^2*d^3*x^3)/3 + (c^2*e^3*x^8)/8 + (b*d^2*x^4*(3*b*e + 2*c*d))/4 + (c*e^2*x^7*(2*b*e + 3*c*d))/7","B"
233,1,78,87,0.035816,"\text{Not used}","int((b*x + c*x^2)^2*(d + e*x)^2,x)","x^5\,\left(\frac{b^2\,e^2}{5}+\frac{4\,b\,c\,d\,e}{5}+\frac{c^2\,d^2}{5}\right)+\frac{b^2\,d^2\,x^3}{3}+\frac{c^2\,e^2\,x^7}{7}+\frac{b\,d\,x^4\,\left(b\,e+c\,d\right)}{2}+\frac{c\,e\,x^6\,\left(b\,e+c\,d\right)}{3}","Not used",1,"x^5*((b^2*e^2)/5 + (c^2*d^2)/5 + (4*b*c*d*e)/5) + (b^2*d^2*x^3)/3 + (c^2*e^2*x^7)/7 + (b*d*x^4*(b*e + c*d))/2 + (c*e*x^6*(b*e + c*d))/3","B"
234,1,51,55,0.051383,"\text{Not used}","int((b*x + c*x^2)^2*(d + e*x),x)","x^4\,\left(\frac{e\,b^2}{4}+\frac{c\,d\,b}{2}\right)+x^5\,\left(\frac{d\,c^2}{5}+\frac{2\,b\,e\,c}{5}\right)+\frac{b^2\,d\,x^3}{3}+\frac{c^2\,e\,x^6}{6}","Not used",1,"x^4*((b^2*e)/4 + (b*c*d)/2) + x^5*((c^2*d)/5 + (2*b*c*e)/5) + (b^2*d*x^3)/3 + (c^2*e*x^6)/6","B"
235,1,24,30,0.032638,"\text{Not used}","int((b*x + c*x^2)^2,x)","\frac{b^2\,x^3}{3}+\frac{b\,c\,x^4}{2}+\frac{c^2\,x^5}{5}","Not used",1,"(b^2*x^3)/3 + (c^2*x^5)/5 + (b*c*x^4)/2","B"
236,1,141,93,0.052462,"\text{Not used}","int((b*x + c*x^2)^2/(d + e*x),x)","x^2\,\left(\frac{b^2}{2\,e}+\frac{d\,\left(\frac{c^2\,d}{e^2}-\frac{2\,b\,c}{e}\right)}{2\,e}\right)-x^3\,\left(\frac{c^2\,d}{3\,e^2}-\frac{2\,b\,c}{3\,e}\right)+\frac{c^2\,x^4}{4\,e}+\frac{\ln\left(d+e\,x\right)\,\left(b^2\,d^2\,e^2-2\,b\,c\,d^3\,e+c^2\,d^4\right)}{e^5}-\frac{d\,x\,\left(\frac{b^2}{e}+\frac{d\,\left(\frac{c^2\,d}{e^2}-\frac{2\,b\,c}{e}\right)}{e}\right)}{e}","Not used",1,"x^2*(b^2/(2*e) + (d*((c^2*d)/e^2 - (2*b*c)/e))/(2*e)) - x^3*((c^2*d)/(3*e^2) - (2*b*c)/(3*e)) + (c^2*x^4)/(4*e) + (log(d + e*x)*(c^2*d^4 + b^2*d^2*e^2 - 2*b*c*d^3*e))/e^5 - (d*x*(b^2/e + (d*((c^2*d)/e^2 - (2*b*c)/e))/e))/e","B"
237,1,158,107,0.182616,"\text{Not used}","int((b*x + c*x^2)^2/(d + e*x)^2,x)","x\,\left(\frac{b^2}{e^2}+\frac{2\,d\,\left(\frac{2\,c^2\,d}{e^3}-\frac{2\,b\,c}{e^2}\right)}{e}-\frac{c^2\,d^2}{e^4}\right)-x^2\,\left(\frac{c^2\,d}{e^3}-\frac{b\,c}{e^2}\right)-\frac{b^2\,d^2\,e^2-2\,b\,c\,d^3\,e+c^2\,d^4}{e\,\left(x\,e^5+d\,e^4\right)}-\frac{\ln\left(d+e\,x\right)\,\left(2\,b^2\,d\,e^2-6\,b\,c\,d^2\,e+4\,c^2\,d^3\right)}{e^5}+\frac{c^2\,x^3}{3\,e^2}","Not used",1,"x*(b^2/e^2 + (2*d*((2*c^2*d)/e^3 - (2*b*c)/e^2))/e - (c^2*d^2)/e^4) - x^2*((c^2*d)/e^3 - (b*c)/e^2) - (c^2*d^4 + b^2*d^2*e^2 - 2*b*c*d^3*e)/(e*(d*e^4 + e^5*x)) - (log(d + e*x)*(4*c^2*d^3 + 2*b^2*d*e^2 - 6*b*c*d^2*e))/e^5 + (c^2*x^3)/(3*e^2)","B"
238,1,151,119,0.083968,"\text{Not used}","int((b*x + c*x^2)^2/(d + e*x)^3,x)","\frac{\frac{3\,b^2\,d^2\,e^2-10\,b\,c\,d^3\,e+7\,c^2\,d^4}{2\,e}+x\,\left(2\,b^2\,d\,e^2-6\,b\,c\,d^2\,e+4\,c^2\,d^3\right)}{d^2\,e^4+2\,d\,e^5\,x+e^6\,x^2}-x\,\left(\frac{3\,c^2\,d}{e^4}-\frac{2\,b\,c}{e^3}\right)+\frac{\ln\left(d+e\,x\right)\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2\right)}{e^5}+\frac{c^2\,x^2}{2\,e^3}","Not used",1,"((7*c^2*d^4 + 3*b^2*d^2*e^2 - 10*b*c*d^3*e)/(2*e) + x*(4*c^2*d^3 + 2*b^2*d*e^2 - 6*b*c*d^2*e))/(d^2*e^4 + e^6*x^2 + 2*d*e^5*x) - x*((3*c^2*d)/e^4 - (2*b*c)/e^3) + (log(d + e*x)*(b^2*e^2 + 6*c^2*d^2 - 6*b*c*d*e))/e^5 + (c^2*x^2)/(2*e^3)","B"
239,1,158,120,0.228153,"\text{Not used}","int((b*x + c*x^2)^2/(d + e*x)^4,x)","\frac{c^2\,x}{e^4}-\frac{x^2\,\left(b^2\,e^3-6\,b\,c\,d\,e^2+6\,c^2\,d^2\,e\right)+\frac{b^2\,d^2\,e^2-11\,b\,c\,d^3\,e+13\,c^2\,d^4}{3\,e}+x\,\left(b^2\,d\,e^2-9\,b\,c\,d^2\,e+10\,c^2\,d^3\right)}{d^3\,e^4+3\,d^2\,e^5\,x+3\,d\,e^6\,x^2+e^7\,x^3}-\frac{\ln\left(d+e\,x\right)\,\left(4\,c^2\,d-2\,b\,c\,e\right)}{e^5}","Not used",1,"(c^2*x)/e^4 - (x^2*(b^2*e^3 + 6*c^2*d^2*e - 6*b*c*d*e^2) + (13*c^2*d^4 + b^2*d^2*e^2 - 11*b*c*d^3*e)/(3*e) + x*(10*c^2*d^3 + b^2*d*e^2 - 9*b*c*d^2*e))/(d^3*e^4 + e^7*x^3 + 3*d^2*e^5*x + 3*d*e^6*x^2) - (log(d + e*x)*(4*c^2*d - 2*b*c*e))/e^5","B"
240,1,167,131,0.229848,"\text{Not used}","int((b*x + c*x^2)^2/(d + e*x)^5,x)","\frac{c^2\,\ln\left(d+e\,x\right)}{e^5}-\frac{\frac{b^2\,d^2\,e^2+6\,b\,c\,d^3\,e-25\,c^2\,d^4}{12\,e^5}+\frac{x^2\,\left(b^2\,e^2+6\,b\,c\,d\,e-18\,c^2\,d^2\right)}{2\,e^3}+\frac{x\,\left(b^2\,d\,e^2+6\,b\,c\,d^2\,e-22\,c^2\,d^3\right)}{3\,e^4}+\frac{2\,c\,x^3\,\left(b\,e-2\,c\,d\right)}{e^2}}{d^4+4\,d^3\,e\,x+6\,d^2\,e^2\,x^2+4\,d\,e^3\,x^3+e^4\,x^4}","Not used",1,"(c^2*log(d + e*x))/e^5 - ((b^2*d^2*e^2 - 25*c^2*d^4 + 6*b*c*d^3*e)/(12*e^5) + (x^2*(b^2*e^2 - 18*c^2*d^2 + 6*b*c*d*e))/(2*e^3) + (x*(b^2*d*e^2 - 22*c^2*d^3 + 6*b*c*d^2*e))/(3*e^4) + (2*c*x^3*(b*e - 2*c*d))/e^2)/(d^4 + e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x)","B"
241,1,169,132,0.197514,"\text{Not used}","int((b*x + c*x^2)^2/(d + e*x)^6,x)","-\frac{\frac{x^2\,\left(b^2\,e^2+3\,b\,c\,d\,e+6\,c^2\,d^2\right)}{3\,e^3}+\frac{c^2\,x^4}{e}+\frac{d^2\,\left(b^2\,e^2+3\,b\,c\,d\,e+6\,c^2\,d^2\right)}{30\,e^5}+\frac{c\,x^3\,\left(b\,e+2\,c\,d\right)}{e^2}+\frac{d\,x\,\left(b^2\,e^2+3\,b\,c\,d\,e+6\,c^2\,d^2\right)}{6\,e^4}}{d^5+5\,d^4\,e\,x+10\,d^3\,e^2\,x^2+10\,d^2\,e^3\,x^3+5\,d\,e^4\,x^4+e^5\,x^5}","Not used",1,"-((x^2*(b^2*e^2 + 6*c^2*d^2 + 3*b*c*d*e))/(3*e^3) + (c^2*x^4)/e + (d^2*(b^2*e^2 + 6*c^2*d^2 + 3*b*c*d*e))/(30*e^5) + (c*x^3*(b*e + 2*c*d))/e^2 + (d*x*(b^2*e^2 + 6*c^2*d^2 + 3*b*c*d*e))/(6*e^4))/(d^5 + e^5*x^5 + 5*d*e^4*x^4 + 10*d^3*e^2*x^2 + 10*d^2*e^3*x^3 + 5*d^4*e*x)","B"
242,1,181,137,0.090842,"\text{Not used}","int((b*x + c*x^2)^2/(d + e*x)^7,x)","-\frac{\frac{x^2\,\left(b^2\,e^2+2\,b\,c\,d\,e+2\,c^2\,d^2\right)}{4\,e^3}+\frac{c^2\,x^4}{2\,e}+\frac{d^2\,\left(b^2\,e^2+2\,b\,c\,d\,e+2\,c^2\,d^2\right)}{60\,e^5}+\frac{2\,c\,x^3\,\left(b\,e+c\,d\right)}{3\,e^2}+\frac{d\,x\,\left(b^2\,e^2+2\,b\,c\,d\,e+2\,c^2\,d^2\right)}{10\,e^4}}{d^6+6\,d^5\,e\,x+15\,d^4\,e^2\,x^2+20\,d^3\,e^3\,x^3+15\,d^2\,e^4\,x^4+6\,d\,e^5\,x^5+e^6\,x^6}","Not used",1,"-((x^2*(b^2*e^2 + 2*c^2*d^2 + 2*b*c*d*e))/(4*e^3) + (c^2*x^4)/(2*e) + (d^2*(b^2*e^2 + 2*c^2*d^2 + 2*b*c*d*e))/(60*e^5) + (2*c*x^3*(b*e + c*d))/(3*e^2) + (d*x*(b^2*e^2 + 2*c^2*d^2 + 2*b*c*d*e))/(10*e^4))/(d^6 + e^6*x^6 + 6*d*e^5*x^5 + 15*d^4*e^2*x^2 + 20*d^3*e^3*x^3 + 15*d^2*e^4*x^4 + 6*d^5*e*x)","B"
243,1,197,137,0.195148,"\text{Not used}","int((b*x + c*x^2)^2/(d + e*x)^8,x)","-\frac{\frac{x^2\,\left(2\,b^2\,e^2+3\,b\,c\,d\,e+2\,c^2\,d^2\right)}{10\,e^3}+\frac{c^2\,x^4}{3\,e}+\frac{d^2\,\left(2\,b^2\,e^2+3\,b\,c\,d\,e+2\,c^2\,d^2\right)}{210\,e^5}+\frac{c\,x^3\,\left(3\,b\,e+2\,c\,d\right)}{6\,e^2}+\frac{d\,x\,\left(2\,b^2\,e^2+3\,b\,c\,d\,e+2\,c^2\,d^2\right)}{30\,e^4}}{d^7+7\,d^6\,e\,x+21\,d^5\,e^2\,x^2+35\,d^4\,e^3\,x^3+35\,d^3\,e^4\,x^4+21\,d^2\,e^5\,x^5+7\,d\,e^6\,x^6+e^7\,x^7}","Not used",1,"-((x^2*(2*b^2*e^2 + 2*c^2*d^2 + 3*b*c*d*e))/(10*e^3) + (c^2*x^4)/(3*e) + (d^2*(2*b^2*e^2 + 2*c^2*d^2 + 3*b*c*d*e))/(210*e^5) + (c*x^3*(3*b*e + 2*c*d))/(6*e^2) + (d*x*(2*b^2*e^2 + 2*c^2*d^2 + 3*b*c*d*e))/(30*e^4))/(d^7 + e^7*x^7 + 7*d*e^6*x^6 + 21*d^5*e^2*x^2 + 35*d^4*e^3*x^3 + 35*d^3*e^4*x^4 + 21*d^2*e^5*x^5 + 7*d^6*e*x)","B"
244,1,213,225,0.086233,"\text{Not used}","int((b*x + c*x^2)^3*(d + e*x)^4,x)","x^7\,\left(\frac{4\,b^3\,d\,e^3}{7}+\frac{18\,b^2\,c\,d^2\,e^2}{7}+\frac{12\,b\,c^2\,d^3\,e}{7}+\frac{c^3\,d^4}{7}\right)+x^8\,\left(\frac{b^3\,e^4}{8}+\frac{3\,b^2\,c\,d\,e^3}{2}+\frac{9\,b\,c^2\,d^2\,e^2}{4}+\frac{c^3\,d^3\,e}{2}\right)+\frac{b^3\,d^4\,x^4}{4}+\frac{c^3\,e^4\,x^{11}}{11}+\frac{b^2\,d^3\,x^5\,\left(4\,b\,e+3\,c\,d\right)}{5}+\frac{c^2\,e^3\,x^{10}\,\left(3\,b\,e+4\,c\,d\right)}{10}+\frac{b\,d^2\,x^6\,\left(2\,b^2\,e^2+4\,b\,c\,d\,e+c^2\,d^2\right)}{2}+\frac{c\,e^2\,x^9\,\left(b^2\,e^2+4\,b\,c\,d\,e+2\,c^2\,d^2\right)}{3}","Not used",1,"x^7*((c^3*d^4)/7 + (4*b^3*d*e^3)/7 + (18*b^2*c*d^2*e^2)/7 + (12*b*c^2*d^3*e)/7) + x^8*((b^3*e^4)/8 + (c^3*d^3*e)/2 + (9*b*c^2*d^2*e^2)/4 + (3*b^2*c*d*e^3)/2) + (b^3*d^4*x^4)/4 + (c^3*e^4*x^11)/11 + (b^2*d^3*x^5*(4*b*e + 3*c*d))/5 + (c^2*e^3*x^10*(3*b*e + 4*c*d))/10 + (b*d^2*x^6*(2*b^2*e^2 + c^2*d^2 + 4*b*c*d*e))/2 + (c*e^2*x^9*(b^2*e^2 + 2*c^2*d^2 + 4*b*c*d*e))/3","B"
245,1,156,162,0.178052,"\text{Not used}","int((b*x + c*x^2)^3*(d + e*x)^3,x)","x^7\,\left(\frac{b^3\,e^3}{7}+\frac{9\,b^2\,c\,d\,e^2}{7}+\frac{9\,b\,c^2\,d^2\,e}{7}+\frac{c^3\,d^3}{7}\right)+\frac{b^3\,d^3\,x^4}{4}+\frac{c^3\,e^3\,x^{10}}{10}+\frac{b\,d\,x^6\,\left(b^2\,e^2+3\,b\,c\,d\,e+c^2\,d^2\right)}{2}+\frac{3\,c\,e\,x^8\,\left(b^2\,e^2+3\,b\,c\,d\,e+c^2\,d^2\right)}{8}+\frac{3\,b^2\,d^2\,x^5\,\left(b\,e+c\,d\right)}{5}+\frac{c^2\,e^2\,x^9\,\left(b\,e+c\,d\right)}{3}","Not used",1,"x^7*((b^3*e^3)/7 + (c^3*d^3)/7 + (9*b*c^2*d^2*e)/7 + (9*b^2*c*d*e^2)/7) + (b^3*d^3*x^4)/4 + (c^3*e^3*x^10)/10 + (b*d*x^6*(b^2*e^2 + c^2*d^2 + 3*b*c*d*e))/2 + (3*c*e*x^8*(b^2*e^2 + c^2*d^2 + 3*b*c*d*e))/8 + (3*b^2*d^2*x^5*(b*e + c*d))/5 + (c^2*e^2*x^9*(b*e + c*d))/3","B"
246,1,118,127,0.053236,"\text{Not used}","int((b*x + c*x^2)^3*(d + e*x)^2,x)","x^6\,\left(\frac{b^3\,e^2}{6}+b^2\,c\,d\,e+\frac{b\,c^2\,d^2}{2}\right)+x^7\,\left(\frac{3\,b^2\,c\,e^2}{7}+\frac{6\,b\,c^2\,d\,e}{7}+\frac{c^3\,d^2}{7}\right)+\frac{b^3\,d^2\,x^4}{4}+\frac{c^3\,e^2\,x^9}{9}+\frac{b^2\,d\,x^5\,\left(2\,b\,e+3\,c\,d\right)}{5}+\frac{c^2\,e\,x^8\,\left(3\,b\,e+2\,c\,d\right)}{8}","Not used",1,"x^6*((b^3*e^2)/6 + (b*c^2*d^2)/2 + b^2*c*d*e) + x^7*((c^3*d^2)/7 + (3*b^2*c*e^2)/7 + (6*b*c^2*d*e)/7) + (b^3*d^2*x^4)/4 + (c^3*e^2*x^9)/9 + (b^2*d*x^5*(2*b*e + 3*c*d))/5 + (c^2*e*x^8*(3*b*e + 2*c*d))/8","B"
247,1,69,75,0.036361,"\text{Not used}","int((b*x + c*x^2)^3*(d + e*x),x)","x^5\,\left(\frac{e\,b^3}{5}+\frac{3\,c\,d\,b^2}{5}\right)+x^7\,\left(\frac{d\,c^3}{7}+\frac{3\,b\,e\,c^2}{7}\right)+\frac{b^3\,d\,x^4}{4}+\frac{c^3\,e\,x^8}{8}+\frac{b\,c\,x^6\,\left(b\,e+c\,d\right)}{2}","Not used",1,"x^5*((b^3*e)/5 + (3*b^2*c*d)/5) + x^7*((c^3*d)/7 + (3*b*c^2*e)/7) + (b^3*d*x^4)/4 + (c^3*e*x^8)/8 + (b*c*x^6*(b*e + c*d))/2","B"
248,1,35,43,0.043426,"\text{Not used}","int((b*x + c*x^2)^3,x)","\frac{b^3\,x^4}{4}+\frac{3\,b^2\,c\,x^5}{5}+\frac{b\,c^2\,x^6}{2}+\frac{c^3\,x^7}{7}","Not used",1,"(b^3*x^4)/4 + (c^3*x^7)/7 + (3*b^2*c*x^5)/5 + (b*c^2*x^6)/2","B"
249,1,294,151,0.177647,"\text{Not used}","int((b*x + c*x^2)^3/(d + e*x),x)","x^3\,\left(\frac{b^3}{3\,e}-\frac{d\,\left(\frac{3\,b^2\,c}{e}-\frac{d\,\left(\frac{3\,b\,c^2}{e}-\frac{c^3\,d}{e^2}\right)}{e}\right)}{3\,e}\right)+x^5\,\left(\frac{3\,b\,c^2}{5\,e}-\frac{c^3\,d}{5\,e^2}\right)+x^4\,\left(\frac{3\,b^2\,c}{4\,e}-\frac{d\,\left(\frac{3\,b\,c^2}{e}-\frac{c^3\,d}{e^2}\right)}{4\,e}\right)+\frac{\ln\left(d+e\,x\right)\,\left(-b^3\,d^3\,e^3+3\,b^2\,c\,d^4\,e^2-3\,b\,c^2\,d^5\,e+c^3\,d^6\right)}{e^7}+\frac{c^3\,x^6}{6\,e}-\frac{d\,x^2\,\left(\frac{b^3}{e}-\frac{d\,\left(\frac{3\,b^2\,c}{e}-\frac{d\,\left(\frac{3\,b\,c^2}{e}-\frac{c^3\,d}{e^2}\right)}{e}\right)}{e}\right)}{2\,e}+\frac{d^2\,x\,\left(\frac{b^3}{e}-\frac{d\,\left(\frac{3\,b^2\,c}{e}-\frac{d\,\left(\frac{3\,b\,c^2}{e}-\frac{c^3\,d}{e^2}\right)}{e}\right)}{e}\right)}{e^2}","Not used",1,"x^3*(b^3/(3*e) - (d*((3*b^2*c)/e - (d*((3*b*c^2)/e - (c^3*d)/e^2))/e))/(3*e)) + x^5*((3*b*c^2)/(5*e) - (c^3*d)/(5*e^2)) + x^4*((3*b^2*c)/(4*e) - (d*((3*b*c^2)/e - (c^3*d)/e^2))/(4*e)) + (log(d + e*x)*(c^3*d^6 - b^3*d^3*e^3 + 3*b^2*c*d^4*e^2 - 3*b*c^2*d^5*e))/e^7 + (c^3*x^6)/(6*e) - (d*x^2*(b^3/e - (d*((3*b^2*c)/e - (d*((3*b*c^2)/e - (c^3*d)/e^2))/e))/e))/(2*e) + (d^2*x*(b^3/e - (d*((3*b^2*c)/e - (d*((3*b*c^2)/e - (c^3*d)/e^2))/e))/e))/e^2","B"
250,1,435,166,0.207982,"\text{Not used}","int((b*x + c*x^2)^3/(d + e*x)^2,x)","x^4\,\left(\frac{3\,b\,c^2}{4\,e^2}-\frac{c^3\,d}{2\,e^3}\right)-x^3\,\left(\frac{2\,d\,\left(\frac{3\,b\,c^2}{e^2}-\frac{2\,c^3\,d}{e^3}\right)}{3\,e}-\frac{b^2\,c}{e^2}+\frac{c^3\,d^2}{3\,e^4}\right)+x^2\,\left(\frac{b^3}{2\,e^2}+\frac{d\,\left(\frac{2\,d\,\left(\frac{3\,b\,c^2}{e^2}-\frac{2\,c^3\,d}{e^3}\right)}{e}-\frac{3\,b^2\,c}{e^2}+\frac{c^3\,d^2}{e^4}\right)}{e}-\frac{d^2\,\left(\frac{3\,b\,c^2}{e^2}-\frac{2\,c^3\,d}{e^3}\right)}{2\,e^2}\right)+x\,\left(\frac{d^2\,\left(\frac{2\,d\,\left(\frac{3\,b\,c^2}{e^2}-\frac{2\,c^3\,d}{e^3}\right)}{e}-\frac{3\,b^2\,c}{e^2}+\frac{c^3\,d^2}{e^4}\right)}{e^2}-\frac{2\,d\,\left(\frac{b^3}{e^2}+\frac{2\,d\,\left(\frac{2\,d\,\left(\frac{3\,b\,c^2}{e^2}-\frac{2\,c^3\,d}{e^3}\right)}{e}-\frac{3\,b^2\,c}{e^2}+\frac{c^3\,d^2}{e^4}\right)}{e}-\frac{d^2\,\left(\frac{3\,b\,c^2}{e^2}-\frac{2\,c^3\,d}{e^3}\right)}{e^2}\right)}{e}\right)-\frac{\ln\left(d+e\,x\right)\,\left(-3\,b^3\,d^2\,e^3+12\,b^2\,c\,d^3\,e^2-15\,b\,c^2\,d^4\,e+6\,c^3\,d^5\right)}{e^7}-\frac{-b^3\,d^3\,e^3+3\,b^2\,c\,d^4\,e^2-3\,b\,c^2\,d^5\,e+c^3\,d^6}{e\,\left(x\,e^7+d\,e^6\right)}+\frac{c^3\,x^5}{5\,e^2}","Not used",1,"x^4*((3*b*c^2)/(4*e^2) - (c^3*d)/(2*e^3)) - x^3*((2*d*((3*b*c^2)/e^2 - (2*c^3*d)/e^3))/(3*e) - (b^2*c)/e^2 + (c^3*d^2)/(3*e^4)) + x^2*(b^3/(2*e^2) + (d*((2*d*((3*b*c^2)/e^2 - (2*c^3*d)/e^3))/e - (3*b^2*c)/e^2 + (c^3*d^2)/e^4))/e - (d^2*((3*b*c^2)/e^2 - (2*c^3*d)/e^3))/(2*e^2)) + x*((d^2*((2*d*((3*b*c^2)/e^2 - (2*c^3*d)/e^3))/e - (3*b^2*c)/e^2 + (c^3*d^2)/e^4))/e^2 - (2*d*(b^3/e^2 + (2*d*((2*d*((3*b*c^2)/e^2 - (2*c^3*d)/e^3))/e - (3*b^2*c)/e^2 + (c^3*d^2)/e^4))/e - (d^2*((3*b*c^2)/e^2 - (2*c^3*d)/e^3))/e^2))/e) - (log(d + e*x)*(6*c^3*d^5 - 3*b^3*d^2*e^3 + 12*b^2*c*d^3*e^2 - 15*b*c^2*d^4*e))/e^7 - (c^3*d^6 - b^3*d^3*e^3 + 3*b^2*c*d^4*e^2 - 3*b*c^2*d^5*e)/(e*(d*e^6 + e^7*x)) + (c^3*x^5)/(5*e^2)","B"
251,1,352,200,0.224708,"\text{Not used}","int((b*x + c*x^2)^3/(d + e*x)^3,x)","x^3\,\left(\frac{b\,c^2}{e^3}-\frac{c^3\,d}{e^4}\right)-x^2\,\left(\frac{3\,d\,\left(\frac{3\,b\,c^2}{e^3}-\frac{3\,c^3\,d}{e^4}\right)}{2\,e}-\frac{3\,b^2\,c}{2\,e^3}+\frac{3\,c^3\,d^2}{2\,e^5}\right)+\frac{x\,\left(-3\,b^3\,d^2\,e^3+12\,b^2\,c\,d^3\,e^2-15\,b\,c^2\,d^4\,e+6\,c^3\,d^5\right)+\frac{-5\,b^3\,d^3\,e^3+21\,b^2\,c\,d^4\,e^2-27\,b\,c^2\,d^5\,e+11\,c^3\,d^6}{2\,e}}{d^2\,e^6+2\,d\,e^7\,x+e^8\,x^2}+x\,\left(\frac{b^3}{e^3}+\frac{3\,d\,\left(\frac{3\,d\,\left(\frac{3\,b\,c^2}{e^3}-\frac{3\,c^3\,d}{e^4}\right)}{e}-\frac{3\,b^2\,c}{e^3}+\frac{3\,c^3\,d^2}{e^5}\right)}{e}-\frac{c^3\,d^3}{e^6}-\frac{3\,d^2\,\left(\frac{3\,b\,c^2}{e^3}-\frac{3\,c^3\,d}{e^4}\right)}{e^2}\right)+\frac{c^3\,x^4}{4\,e^3}+\frac{\ln\left(d+e\,x\right)\,\left(-3\,b^3\,d\,e^3+18\,b^2\,c\,d^2\,e^2-30\,b\,c^2\,d^3\,e+15\,c^3\,d^4\right)}{e^7}","Not used",1,"x^3*((b*c^2)/e^3 - (c^3*d)/e^4) - x^2*((3*d*((3*b*c^2)/e^3 - (3*c^3*d)/e^4))/(2*e) - (3*b^2*c)/(2*e^3) + (3*c^3*d^2)/(2*e^5)) + (x*(6*c^3*d^5 - 3*b^3*d^2*e^3 + 12*b^2*c*d^3*e^2 - 15*b*c^2*d^4*e) + (11*c^3*d^6 - 5*b^3*d^3*e^3 + 21*b^2*c*d^4*e^2 - 27*b*c^2*d^5*e)/(2*e))/(d^2*e^6 + e^8*x^2 + 2*d*e^7*x) + x*(b^3/e^3 + (3*d*((3*d*((3*b*c^2)/e^3 - (3*c^3*d)/e^4))/e - (3*b^2*c)/e^3 + (3*c^3*d^2)/e^5))/e - (c^3*d^3)/e^6 - (3*d^2*((3*b*c^2)/e^3 - (3*c^3*d)/e^4))/e^2) + (c^3*x^4)/(4*e^3) + (log(d + e*x)*(15*c^3*d^4 - 3*b^3*d*e^3 + 18*b^2*c*d^2*e^2 - 30*b*c^2*d^3*e))/e^7","B"
252,1,307,213,0.116247,"\text{Not used}","int((b*x + c*x^2)^3/(d + e*x)^4,x)","x^2\,\left(\frac{3\,b\,c^2}{2\,e^4}-\frac{2\,c^3\,d}{e^5}\right)-x\,\left(\frac{4\,d\,\left(\frac{3\,b\,c^2}{e^4}-\frac{4\,c^3\,d}{e^5}\right)}{e}-\frac{3\,b^2\,c}{e^4}+\frac{6\,c^3\,d^2}{e^6}\right)-\frac{x\,\left(-\frac{9\,b^3\,d^2\,e^3}{2}+30\,b^2\,c\,d^3\,e^2-\frac{105\,b\,c^2\,d^4\,e}{2}+27\,c^3\,d^5\right)-x^2\,\left(3\,b^3\,d\,e^4-18\,b^2\,c\,d^2\,e^3+30\,b\,c^2\,d^3\,e^2-15\,c^3\,d^4\,e\right)+\frac{-11\,b^3\,d^3\,e^3+78\,b^2\,c\,d^4\,e^2-141\,b\,c^2\,d^5\,e+74\,c^3\,d^6}{6\,e}}{d^3\,e^6+3\,d^2\,e^7\,x+3\,d\,e^8\,x^2+e^9\,x^3}+\frac{\ln\left(d+e\,x\right)\,\left(b^3\,e^3-12\,b^2\,c\,d\,e^2+30\,b\,c^2\,d^2\,e-20\,c^3\,d^3\right)}{e^7}+\frac{c^3\,x^3}{3\,e^4}","Not used",1,"x^2*((3*b*c^2)/(2*e^4) - (2*c^3*d)/e^5) - x*((4*d*((3*b*c^2)/e^4 - (4*c^3*d)/e^5))/e - (3*b^2*c)/e^4 + (6*c^3*d^2)/e^6) - (x*(27*c^3*d^5 - (9*b^3*d^2*e^3)/2 + 30*b^2*c*d^3*e^2 - (105*b*c^2*d^4*e)/2) - x^2*(3*b^3*d*e^4 - 15*c^3*d^4*e + 30*b*c^2*d^3*e^2 - 18*b^2*c*d^2*e^3) + (74*c^3*d^6 - 11*b^3*d^3*e^3 + 78*b^2*c*d^4*e^2 - 141*b*c^2*d^5*e)/(6*e))/(d^3*e^6 + e^9*x^3 + 3*d^2*e^7*x + 3*d*e^8*x^2) + (log(d + e*x)*(b^3*e^3 - 20*c^3*d^3 + 30*b*c^2*d^2*e - 12*b^2*c*d*e^2))/e^7 + (c^3*x^3)/(3*e^4)","B"
253,1,302,213,0.117961,"\text{Not used}","int((b*x + c*x^2)^3/(d + e*x)^5,x)","x\,\left(\frac{3\,b\,c^2}{e^5}-\frac{5\,c^3\,d}{e^6}\right)-\frac{x^2\,\left(\frac{3\,b^3\,d\,e^4}{2}-27\,b^2\,c\,d^2\,e^3+75\,b\,c^2\,d^3\,e^2-\frac{105\,c^3\,d^4\,e}{2}\right)-x\,\left(-b^3\,d^2\,e^3+22\,b^2\,c\,d^3\,e^2-65\,b\,c^2\,d^4\,e+47\,c^3\,d^5\right)-\frac{-b^3\,d^3\,e^3+25\,b^2\,c\,d^4\,e^2-77\,b\,c^2\,d^5\,e+57\,c^3\,d^6}{4\,e}+x^3\,\left(b^3\,e^5-12\,b^2\,c\,d\,e^4+30\,b\,c^2\,d^2\,e^3-20\,c^3\,d^3\,e^2\right)}{d^4\,e^6+4\,d^3\,e^7\,x+6\,d^2\,e^8\,x^2+4\,d\,e^9\,x^3+e^{10}\,x^4}+\frac{\ln\left(d+e\,x\right)\,\left(3\,b^2\,c\,e^2-15\,b\,c^2\,d\,e+15\,c^3\,d^2\right)}{e^7}+\frac{c^3\,x^2}{2\,e^5}","Not used",1,"x*((3*b*c^2)/e^5 - (5*c^3*d)/e^6) - (x^2*((3*b^3*d*e^4)/2 - (105*c^3*d^4*e)/2 + 75*b*c^2*d^3*e^2 - 27*b^2*c*d^2*e^3) - x*(47*c^3*d^5 - b^3*d^2*e^3 + 22*b^2*c*d^3*e^2 - 65*b*c^2*d^4*e) - (57*c^3*d^6 - b^3*d^3*e^3 + 25*b^2*c*d^4*e^2 - 77*b*c^2*d^5*e)/(4*e) + x^3*(b^3*e^5 - 20*c^3*d^3*e^2 + 30*b*c^2*d^2*e^3 - 12*b^2*c*d*e^4))/(d^4*e^6 + e^10*x^4 + 4*d^3*e^7*x + 4*d*e^9*x^3 + 6*d^2*e^8*x^2) + (log(d + e*x)*(15*c^3*d^2 + 3*b^2*c*e^2 - 15*b*c^2*d*e))/e^7 + (c^3*x^2)/(2*e^5)","B"
254,1,312,218,0.285857,"\text{Not used}","int((b*x + c*x^2)^3/(d + e*x)^6,x)","\frac{c^3\,x}{e^6}-\frac{x^4\,\left(3\,b^2\,c\,e^5-15\,b\,c^2\,d\,e^4+15\,c^3\,d^2\,e^3\right)+x^2\,\left(\frac{b^3\,d\,e^4}{2}+6\,b^2\,c\,d^2\,e^3-55\,b\,c^2\,d^3\,e^2+65\,c^3\,d^4\,e\right)+x\,\left(\frac{b^3\,d^2\,e^3}{4}+3\,b^2\,c\,d^3\,e^2-\frac{125\,b\,c^2\,d^4\,e}{4}+\frac{77\,c^3\,d^5}{2}\right)+\frac{b^3\,d^3\,e^3+12\,b^2\,c\,d^4\,e^2-137\,b\,c^2\,d^5\,e+174\,c^3\,d^6}{20\,e}+x^3\,\left(\frac{b^3\,e^5}{2}+6\,b^2\,c\,d\,e^4-45\,b\,c^2\,d^2\,e^3+50\,c^3\,d^3\,e^2\right)}{d^5\,e^6+5\,d^4\,e^7\,x+10\,d^3\,e^8\,x^2+10\,d^2\,e^9\,x^3+5\,d\,e^{10}\,x^4+e^{11}\,x^5}-\frac{\ln\left(d+e\,x\right)\,\left(6\,c^3\,d-3\,b\,c^2\,e\right)}{e^7}","Not used",1,"(c^3*x)/e^6 - (x^4*(3*b^2*c*e^5 + 15*c^3*d^2*e^3 - 15*b*c^2*d*e^4) + x^2*((b^3*d*e^4)/2 + 65*c^3*d^4*e - 55*b*c^2*d^3*e^2 + 6*b^2*c*d^2*e^3) + x*((77*c^3*d^5)/2 + (b^3*d^2*e^3)/4 + 3*b^2*c*d^3*e^2 - (125*b*c^2*d^4*e)/4) + (174*c^3*d^6 + b^3*d^3*e^3 + 12*b^2*c*d^4*e^2 - 137*b*c^2*d^5*e)/(20*e) + x^3*((b^3*e^5)/2 + 50*c^3*d^3*e^2 - 45*b*c^2*d^2*e^3 + 6*b^2*c*d*e^4))/(d^5*e^6 + e^11*x^5 + 5*d^4*e^7*x + 5*d*e^10*x^4 + 10*d^3*e^8*x^2 + 10*d^2*e^9*x^3) - (log(d + e*x)*(6*c^3*d - 3*b*c^2*e))/e^7","B"
255,1,268,228,0.164985,"\text{Not used}","int((b*x + c*x^2)^3/(d + e*x)^7,x)","\frac{c^3\,\ln\left(d+e\,x\right)}{e^7}-\frac{x^5\,\left(3\,b\,c^2\,e^6-6\,c^3\,d\,e^5\right)+x^4\,\left(\frac{3\,b^2\,c\,e^6}{2}+\frac{15\,b\,c^2\,d\,e^5}{2}-\frac{45\,c^3\,d^2\,e^4}{2}\right)+x\,\left(\frac{b^3\,d^2\,e^4}{10}+\frac{3\,b^2\,c\,d^3\,e^3}{5}+3\,b\,c^2\,d^4\,e^2-\frac{137\,c^3\,d^5\,e}{10}\right)+x^2\,\left(\frac{b^3\,d\,e^5}{4}+\frac{3\,b^2\,c\,d^2\,e^4}{2}+\frac{15\,b\,c^2\,d^3\,e^3}{2}-\frac{125\,c^3\,d^4\,e^2}{4}\right)+x^3\,\left(\frac{b^3\,e^6}{3}+2\,b^2\,c\,d\,e^5+10\,b\,c^2\,d^2\,e^4-\frac{110\,c^3\,d^3\,e^3}{3}\right)-\frac{49\,c^3\,d^6}{20}+\frac{b^3\,d^3\,e^3}{60}+\frac{b^2\,c\,d^4\,e^2}{10}+\frac{b\,c^2\,d^5\,e}{2}}{e^7\,{\left(d+e\,x\right)}^6}","Not used",1,"(c^3*log(d + e*x))/e^7 - (x^5*(3*b*c^2*e^6 - 6*c^3*d*e^5) + x^4*((3*b^2*c*e^6)/2 - (45*c^3*d^2*e^4)/2 + (15*b*c^2*d*e^5)/2) + x*((b^3*d^2*e^4)/10 - (137*c^3*d^5*e)/10 + 3*b*c^2*d^4*e^2 + (3*b^2*c*d^3*e^3)/5) + x^2*((b^3*d*e^5)/4 - (125*c^3*d^4*e^2)/4 + (15*b*c^2*d^3*e^3)/2 + (3*b^2*c*d^2*e^4)/2) + x^3*((b^3*e^6)/3 - (110*c^3*d^3*e^3)/3 + 10*b*c^2*d^2*e^4 + 2*b^2*c*d*e^5) - (49*c^3*d^6)/20 + (b^3*d^3*e^3)/60 + (b^2*c*d^4*e^2)/10 + (b*c^2*d^5*e)/2)/(e^7*(d + e*x)^6)","B"
256,1,315,230,0.215051,"\text{Not used}","int((b*x + c*x^2)^3/(d + e*x)^8,x)","-\frac{\frac{d^3\,\left(b^3\,e^3+4\,b^2\,c\,d\,e^2+10\,b\,c^2\,d^2\,e+20\,c^3\,d^3\right)}{140\,e^7}+\frac{x^3\,\left(b^3\,e^3+4\,b^2\,c\,d\,e^2+10\,b\,c^2\,d^2\,e+20\,c^3\,d^3\right)}{4\,e^4}+\frac{c^3\,x^6}{e}+\frac{3\,c^2\,x^5\,\left(b\,e+2\,c\,d\right)}{2\,e^2}+\frac{c\,x^4\,\left(2\,b^2\,e^2+5\,b\,c\,d\,e+10\,c^2\,d^2\right)}{2\,e^3}+\frac{3\,d\,x^2\,\left(b^3\,e^3+4\,b^2\,c\,d\,e^2+10\,b\,c^2\,d^2\,e+20\,c^3\,d^3\right)}{20\,e^5}+\frac{d^2\,x\,\left(b^3\,e^3+4\,b^2\,c\,d\,e^2+10\,b\,c^2\,d^2\,e+20\,c^3\,d^3\right)}{20\,e^6}}{d^7+7\,d^6\,e\,x+21\,d^5\,e^2\,x^2+35\,d^4\,e^3\,x^3+35\,d^3\,e^4\,x^4+21\,d^2\,e^5\,x^5+7\,d\,e^6\,x^6+e^7\,x^7}","Not used",1,"-((d^3*(b^3*e^3 + 20*c^3*d^3 + 10*b*c^2*d^2*e + 4*b^2*c*d*e^2))/(140*e^7) + (x^3*(b^3*e^3 + 20*c^3*d^3 + 10*b*c^2*d^2*e + 4*b^2*c*d*e^2))/(4*e^4) + (c^3*x^6)/e + (3*c^2*x^5*(b*e + 2*c*d))/(2*e^2) + (c*x^4*(2*b^2*e^2 + 10*c^2*d^2 + 5*b*c*d*e))/(2*e^3) + (3*d*x^2*(b^3*e^3 + 20*c^3*d^3 + 10*b*c^2*d^2*e + 4*b^2*c*d*e^2))/(20*e^5) + (d^2*x*(b^3*e^3 + 20*c^3*d^3 + 10*b*c^2*d^2*e + 4*b^2*c*d*e^2))/(20*e^6))/(d^7 + e^7*x^7 + 7*d*e^6*x^6 + 21*d^5*e^2*x^2 + 35*d^4*e^3*x^3 + 35*d^3*e^4*x^4 + 21*d^2*e^5*x^5 + 7*d^6*e*x)","B"
257,1,325,231,0.238344,"\text{Not used}","int((b*x + c*x^2)^3/(d + e*x)^9,x)","-\frac{\frac{d^3\,\left(b^3\,e^3+3\,b^2\,c\,d\,e^2+5\,b\,c^2\,d^2\,e+5\,c^3\,d^3\right)}{280\,e^7}+\frac{x^3\,\left(b^3\,e^3+3\,b^2\,c\,d\,e^2+5\,b\,c^2\,d^2\,e+5\,c^3\,d^3\right)}{5\,e^4}+\frac{c^3\,x^6}{2\,e}+\frac{c^2\,x^5\,\left(b\,e+c\,d\right)}{e^2}+\frac{c\,x^4\,\left(3\,b^2\,e^2+5\,b\,c\,d\,e+5\,c^2\,d^2\right)}{4\,e^3}+\frac{d\,x^2\,\left(b^3\,e^3+3\,b^2\,c\,d\,e^2+5\,b\,c^2\,d^2\,e+5\,c^3\,d^3\right)}{10\,e^5}+\frac{d^2\,x\,\left(b^3\,e^3+3\,b^2\,c\,d\,e^2+5\,b\,c^2\,d^2\,e+5\,c^3\,d^3\right)}{35\,e^6}}{d^8+8\,d^7\,e\,x+28\,d^6\,e^2\,x^2+56\,d^5\,e^3\,x^3+70\,d^4\,e^4\,x^4+56\,d^3\,e^5\,x^5+28\,d^2\,e^6\,x^6+8\,d\,e^7\,x^7+e^8\,x^8}","Not used",1,"-((d^3*(b^3*e^3 + 5*c^3*d^3 + 5*b*c^2*d^2*e + 3*b^2*c*d*e^2))/(280*e^7) + (x^3*(b^3*e^3 + 5*c^3*d^3 + 5*b*c^2*d^2*e + 3*b^2*c*d*e^2))/(5*e^4) + (c^3*x^6)/(2*e) + (c^2*x^5*(b*e + c*d))/e^2 + (c*x^4*(3*b^2*e^2 + 5*c^2*d^2 + 5*b*c*d*e))/(4*e^3) + (d*x^2*(b^3*e^3 + 5*c^3*d^3 + 5*b*c^2*d^2*e + 3*b^2*c*d*e^2))/(10*e^5) + (d^2*x*(b^3*e^3 + 5*c^3*d^3 + 5*b*c^2*d^2*e + 3*b^2*c*d*e^2))/(35*e^6))/(d^8 + e^8*x^8 + 8*d*e^7*x^7 + 28*d^6*e^2*x^2 + 56*d^5*e^3*x^3 + 70*d^4*e^4*x^4 + 56*d^3*e^5*x^5 + 28*d^2*e^6*x^6 + 8*d^7*e*x)","B"
258,1,343,234,0.314915,"\text{Not used}","int((b*x + c*x^2)^3/(d + e*x)^10,x)","-\frac{\frac{d^3\,\left(5\,b^3\,e^3+12\,b^2\,c\,d\,e^2+15\,b\,c^2\,d^2\,e+10\,c^3\,d^3\right)}{2520\,e^7}+\frac{x^3\,\left(5\,b^3\,e^3+12\,b^2\,c\,d\,e^2+15\,b\,c^2\,d^2\,e+10\,c^3\,d^3\right)}{30\,e^4}+\frac{c^3\,x^6}{3\,e}+\frac{c^2\,x^5\,\left(3\,b\,e+2\,c\,d\right)}{4\,e^2}+\frac{c\,x^4\,\left(12\,b^2\,e^2+15\,b\,c\,d\,e+10\,c^2\,d^2\right)}{20\,e^3}+\frac{d\,x^2\,\left(5\,b^3\,e^3+12\,b^2\,c\,d\,e^2+15\,b\,c^2\,d^2\,e+10\,c^3\,d^3\right)}{70\,e^5}+\frac{d^2\,x\,\left(5\,b^3\,e^3+12\,b^2\,c\,d\,e^2+15\,b\,c^2\,d^2\,e+10\,c^3\,d^3\right)}{280\,e^6}}{d^9+9\,d^8\,e\,x+36\,d^7\,e^2\,x^2+84\,d^6\,e^3\,x^3+126\,d^5\,e^4\,x^4+126\,d^4\,e^5\,x^5+84\,d^3\,e^6\,x^6+36\,d^2\,e^7\,x^7+9\,d\,e^8\,x^8+e^9\,x^9}","Not used",1,"-((d^3*(5*b^3*e^3 + 10*c^3*d^3 + 15*b*c^2*d^2*e + 12*b^2*c*d*e^2))/(2520*e^7) + (x^3*(5*b^3*e^3 + 10*c^3*d^3 + 15*b*c^2*d^2*e + 12*b^2*c*d*e^2))/(30*e^4) + (c^3*x^6)/(3*e) + (c^2*x^5*(3*b*e + 2*c*d))/(4*e^2) + (c*x^4*(12*b^2*e^2 + 10*c^2*d^2 + 15*b*c*d*e))/(20*e^3) + (d*x^2*(5*b^3*e^3 + 10*c^3*d^3 + 15*b*c^2*d^2*e + 12*b^2*c*d*e^2))/(70*e^5) + (d^2*x*(5*b^3*e^3 + 10*c^3*d^3 + 15*b*c^2*d^2*e + 12*b^2*c*d*e^2))/(280*e^6))/(d^9 + e^9*x^9 + 9*d*e^8*x^8 + 36*d^7*e^2*x^2 + 84*d^6*e^3*x^3 + 126*d^5*e^4*x^4 + 126*d^4*e^5*x^5 + 84*d^3*e^6*x^6 + 36*d^2*e^7*x^7 + 9*d^8*e*x)","B"
259,1,106,99,0.262110,"\text{Not used}","int((d + e*x)^4/(b*x + c*x^2),x)","x\,\left(\frac{b\,\left(\frac{b\,e^4}{c^2}-\frac{4\,d\,e^3}{c}\right)}{c}+\frac{6\,d^2\,e^2}{c}\right)-x^2\,\left(\frac{b\,e^4}{2\,c^2}-\frac{2\,d\,e^3}{c}\right)+\frac{e^4\,x^3}{3\,c}+\frac{d^4\,\ln\left(x\right)}{b}-\frac{\ln\left(b+c\,x\right)\,{\left(b\,e-c\,d\right)}^4}{b\,c^4}","Not used",1,"x*((b*((b*e^4)/c^2 - (4*d*e^3)/c))/c + (6*d^2*e^2)/c) - x^2*((b*e^4)/(2*c^2) - (2*d*e^3)/c) + (e^4*x^3)/(3*c) + (d^4*log(x))/b - (log(b + c*x)*(b*e - c*d)^4)/(b*c^4)","B"
260,1,65,64,0.135103,"\text{Not used}","int((d + e*x)^3/(b*x + c*x^2),x)","\frac{e^3\,x^2}{2\,c}-x\,\left(\frac{b\,e^3}{c^2}-\frac{3\,d\,e^2}{c}\right)+\frac{d^3\,\ln\left(x\right)}{b}+\frac{\ln\left(b+c\,x\right)\,{\left(b\,e-c\,d\right)}^3}{b\,c^3}","Not used",1,"(e^3*x^2)/(2*c) - x*((b*e^3)/c^2 - (3*d*e^2)/c) + (d^3*log(x))/b + (log(b + c*x)*(b*e - c*d)^3)/(b*c^3)","B"
261,1,49,42,0.145449,"\text{Not used}","int((d + e*x)^2/(b*x + c*x^2),x)","\frac{e^2\,x}{c}-\ln\left(b+c\,x\right)\,\left(\frac{d^2}{b}+\frac{b\,e^2}{c^2}-\frac{2\,d\,e}{c}\right)+\frac{d^2\,\ln\left(x\right)}{b}","Not used",1,"(e^2*x)/c - log(b + c*x)*(d^2/b + (b*e^2)/c^2 - (2*d*e)/c) + (d^2*log(x))/b","B"
262,1,28,30,0.096012,"\text{Not used}","int((d + e*x)/(b*x + c*x^2),x)","\frac{d\,\ln\left(x\right)}{b}-\ln\left(b+c\,x\right)\,\left(\frac{d}{b}-\frac{e}{c}\right)","Not used",1,"(d*log(x))/b - log(b + c*x)*(d/b - e/c)","B"
263,1,15,18,0.160714,"\text{Not used}","int(1/(b*x + c*x^2),x)","-\frac{2\,\mathrm{atanh}\left(\frac{2\,c\,x}{b}+1\right)}{b}","Not used",1,"-(2*atanh((2*c*x)/b + 1))/b","B"
264,1,93,53,0.334177,"\text{Not used}","int(1/((b*x + c*x^2)*(d + e*x)),x)","\frac{e\,\ln\left(\frac{{\left(d+e\,x\right)}^2}{x\,\left(b+c\,x\right)}\right)}{2\,c\,d^2-2\,b\,d\,e}-\frac{\ln\left(\frac{b-\sqrt{b^2}+2\,c\,x}{b+\sqrt{b^2}+2\,c\,x}\right)\,\left(b\,e-2\,c\,d\right)}{\left(2\,c\,d^2-2\,b\,d\,e\right)\,\sqrt{b^2}}","Not used",1,"(e*log((d + e*x)^2/(x*(b + c*x))))/(2*c*d^2 - 2*b*d*e) - (log((b - (b^2)^(1/2) + 2*c*x)/(b + (b^2)^(1/2) + 2*c*x))*(b*e - 2*c*d))/((2*c*d^2 - 2*b*d*e)*(b^2)^(1/2))","B"
265,1,116,87,0.472996,"\text{Not used}","int(1/((b*x + c*x^2)*(d + e*x)^2),x)","\frac{\ln\left(x\right)}{b\,d^2}-\frac{c^2\,\ln\left(b+c\,x\right)}{b^3\,e^2-2\,b^2\,c\,d\,e+b\,c^2\,d^2}-\frac{\ln\left(d+e\,x\right)\,\left(b\,e^2-2\,c\,d\,e\right)}{b^2\,d^2\,e^2-2\,b\,c\,d^3\,e+c^2\,d^4}+\frac{e}{d\,\left(b\,e-c\,d\right)\,\left(d+e\,x\right)}","Not used",1,"log(x)/(b*d^2) - (c^2*log(b + c*x))/(b^3*e^2 + b*c^2*d^2 - 2*b^2*c*d*e) - (log(d + e*x)*(b*e^2 - 2*c*d*e))/(c^2*d^4 + b^2*d^2*e^2 - 2*b*c*d^3*e) + e/(d*(b*e - c*d)*(d + e*x))","B"
266,1,235,134,0.657494,"\text{Not used}","int(1/((b*x + c*x^2)*(d + e*x)^3),x)","\frac{\frac{3\,b\,e^2-5\,c\,d\,e}{2\,d\,\left(b^2\,e^2-2\,b\,c\,d\,e+c^2\,d^2\right)}+\frac{e^2\,x\,\left(b\,e-2\,c\,d\right)}{d^2\,\left(b^2\,e^2-2\,b\,c\,d\,e+c^2\,d^2\right)}}{d^2+2\,d\,e\,x+e^2\,x^2}+\frac{c^3\,\ln\left(b+c\,x\right)}{b^4\,e^3-3\,b^3\,c\,d\,e^2+3\,b^2\,c^2\,d^2\,e-b\,c^3\,d^3}+\frac{\ln\left(d+e\,x\right)\,\left(b^2\,e^3-3\,b\,c\,d\,e^2+3\,c^2\,d^2\,e\right)}{-b^3\,d^3\,e^3+3\,b^2\,c\,d^4\,e^2-3\,b\,c^2\,d^5\,e+c^3\,d^6}+\frac{\ln\left(x\right)}{b\,d^3}","Not used",1,"((3*b*e^2 - 5*c*d*e)/(2*d*(b^2*e^2 + c^2*d^2 - 2*b*c*d*e)) + (e^2*x*(b*e - 2*c*d))/(d^2*(b^2*e^2 + c^2*d^2 - 2*b*c*d*e)))/(d^2 + e^2*x^2 + 2*d*e*x) + (c^3*log(b + c*x))/(b^4*e^3 - b*c^3*d^3 + 3*b^2*c^2*d^2*e - 3*b^3*c*d*e^2) + (log(d + e*x)*(b^2*e^3 + 3*c^2*d^2*e - 3*b*c*d*e^2))/(c^3*d^6 - b^3*d^3*e^3 + 3*b^2*c*d^4*e^2 - 3*b*c^2*d^5*e) + log(x)/(b*d^3)","B"
267,1,218,118,0.355434,"\text{Not used}","int((d + e*x)^5/(b*x + c*x^2)^2,x)","\frac{e^5\,x^2}{2\,c^2}-\frac{\frac{c^3\,d^5}{b}-\frac{x\,\left(b^5\,e^5-5\,b^4\,c\,d\,e^4+10\,b^3\,c^2\,d^2\,e^3-10\,b^2\,c^3\,d^3\,e^2+5\,b\,c^4\,d^4\,e-2\,c^5\,d^5\right)}{b^2\,c}}{c^4\,x^2+b\,c^3\,x}-x\,\left(\frac{2\,b\,e^5}{c^3}-\frac{5\,d\,e^4}{c^2}\right)+\frac{\ln\left(b+c\,x\right)\,\left(3\,b^5\,e^5-10\,b^4\,c\,d\,e^4+10\,b^3\,c^2\,d^2\,e^3-5\,b\,c^4\,d^4\,e+2\,c^5\,d^5\right)}{b^3\,c^4}+\frac{d^4\,\ln\left(x\right)\,\left(5\,b\,e-2\,c\,d\right)}{b^3}","Not used",1,"(e^5*x^2)/(2*c^2) - ((c^3*d^5)/b - (x*(b^5*e^5 - 2*c^5*d^5 - 10*b^2*c^3*d^3*e^2 + 10*b^3*c^2*d^2*e^3 + 5*b*c^4*d^4*e - 5*b^4*c*d*e^4))/(b^2*c))/(c^4*x^2 + b*c^3*x) - x*((2*b*e^5)/c^3 - (5*d*e^4)/c^2) + (log(b + c*x)*(3*b^5*e^5 + 2*c^5*d^5 + 10*b^3*c^2*d^2*e^3 - 5*b*c^4*d^4*e - 10*b^4*c*d*e^4))/(b^3*c^4) + (d^4*log(x)*(5*b*e - 2*c*d))/b^3","B"
268,1,166,94,0.286768,"\text{Not used}","int((d + e*x)^4/(b*x + c*x^2)^2,x)","\frac{e^4\,x}{c^2}-\frac{\frac{c^2\,d^4}{b}+\frac{x\,\left(b^4\,e^4-4\,b^3\,c\,d\,e^3+6\,b^2\,c^2\,d^2\,e^2-4\,b\,c^3\,d^3\,e+2\,c^4\,d^4\right)}{b^2\,c}}{c^3\,x^2+b\,c^2\,x}+\frac{2\,d^3\,\ln\left(x\right)\,\left(2\,b\,e-c\,d\right)}{b^3}-\frac{\ln\left(b+c\,x\right)\,\left(2\,b^4\,e^4-4\,b^3\,c\,d\,e^3+4\,b\,c^3\,d^3\,e-2\,c^4\,d^4\right)}{b^3\,c^3}","Not used",1,"(e^4*x)/c^2 - ((c^2*d^4)/b + (x*(b^4*e^4 + 2*c^4*d^4 + 6*b^2*c^2*d^2*e^2 - 4*b*c^3*d^3*e - 4*b^3*c*d*e^3))/(b^2*c))/(c^3*x^2 + b*c^2*x) + (2*d^3*log(x)*(2*b*e - c*d))/b^3 - (log(b + c*x)*(2*b^4*e^4 - 2*c^4*d^4 + 4*b*c^3*d^3*e - 4*b^3*c*d*e^3))/(b^3*c^3)","B"
269,1,118,87,0.302748,"\text{Not used}","int((d + e*x)^3/(b*x + c*x^2)^2,x)","\ln\left(b+c\,x\right)\,\left(\frac{e^3}{c^2}+\frac{2\,c\,d^3}{b^3}-\frac{3\,d^2\,e}{b^2}\right)-\frac{\frac{d^3}{b}-\frac{x\,\left(b^3\,e^3-3\,b^2\,c\,d\,e^2+3\,b\,c^2\,d^2\,e-2\,c^3\,d^3\right)}{b^2\,c^2}}{c\,x^2+b\,x}+\frac{d^2\,\ln\left(x\right)\,\left(3\,b\,e-2\,c\,d\right)}{b^3}","Not used",1,"log(b + c*x)*(e^3/c^2 + (2*c*d^3)/b^3 - (3*d^2*e)/b^2) - (d^3/b - (x*(b^3*e^3 - 2*c^3*d^3 + 3*b*c^2*d^2*e - 3*b^2*c*d*e^2))/(b^2*c^2))/(b*x + c*x^2) + (d^2*log(x)*(3*b*e - 2*c*d))/b^3","B"
270,1,101,73,0.099312,"\text{Not used}","int((d + e*x)^2/(b*x + c*x^2)^2,x)","\frac{4\,d\,\mathrm{atanh}\left(\frac{2\,d\,\left(b\,e-c\,d\right)\,\left(b+2\,c\,x\right)}{b\,\left(2\,c\,d^2-2\,b\,d\,e\right)}\right)\,\left(b\,e-c\,d\right)}{b^3}-\frac{\frac{d^2}{b}+\frac{x\,\left(b^2\,e^2-2\,b\,c\,d\,e+2\,c^2\,d^2\right)}{b^2\,c}}{c\,x^2+b\,x}","Not used",1,"(4*d*atanh((2*d*(b*e - c*d)*(b + 2*c*x))/(b*(2*c*d^2 - 2*b*d*e)))*(b*e - c*d))/b^3 - (d^2/b + (x*(b^2*e^2 + 2*c^2*d^2 - 2*b*c*d*e))/(b^2*c))/(b*x + c*x^2)","B"
271,1,57,65,0.219253,"\text{Not used}","int((d + e*x)/(b*x + c*x^2)^2,x)","-\frac{\frac{d}{b}-\frac{x\,\left(b\,e-2\,c\,d\right)}{b^2}}{c\,x^2+b\,x}-\frac{2\,\mathrm{atanh}\left(\frac{2\,c\,x}{b}+1\right)\,\left(b\,e-2\,c\,d\right)}{b^3}","Not used",1,"- (d/b - (x*(b*e - 2*c*d))/b^2)/(b*x + c*x^2) - (2*atanh((2*c*x)/b + 1)*(b*e - 2*c*d))/b^3","B"
272,1,41,43,0.104940,"\text{Not used}","int(1/(b*x + c*x^2)^2,x)","\frac{4\,c\,\mathrm{atanh}\left(\frac{2\,c\,x}{b}+1\right)}{b^3}-\frac{\frac{1}{b}+\frac{2\,c\,x}{b^2}}{c\,x^2+b\,x}","Not used",1,"(4*c*atanh((2*c*x)/b + 1))/b^3 - (1/b + (2*c*x)/b^2)/(b*x + c*x^2)","B"
273,1,143,110,0.518379,"\text{Not used}","int(1/((b*x + c*x^2)^2*(d + e*x)),x)","\frac{\ln\left(b+c\,x\right)\,\left(2\,c^3\,d-3\,b\,c^2\,e\right)}{b^5\,e^2-2\,b^4\,c\,d\,e+b^3\,c^2\,d^2}-\frac{\frac{1}{b\,d}-\frac{x\,\left(2\,c^2\,d-b\,c\,e\right)}{b^2\,d\,\left(b\,e-c\,d\right)}}{c\,x^2+b\,x}+\frac{e^3\,\ln\left(d+e\,x\right)}{d^2\,{\left(b\,e-c\,d\right)}^2}-\frac{\ln\left(x\right)\,\left(b\,e+2\,c\,d\right)}{b^3\,d^2}","Not used",1,"(log(b + c*x)*(2*c^3*d - 3*b*c^2*e))/(b^5*e^2 + b^3*c^2*d^2 - 2*b^4*c*d*e) - (1/(b*d) - (x*(2*c^2*d - b*c*e))/(b^2*d*(b*e - c*d)))/(b*x + c*x^2) + (e^3*log(d + e*x))/(d^2*(b*e - c*d)^2) - (log(x)*(b*e + 2*c*d))/(b^3*d^2)","B"
274,1,304,144,0.694548,"\text{Not used}","int(1/((b*x + c*x^2)^2*(d + e*x)^2),x)","-\frac{\frac{1}{b\,d}+\frac{2\,x^2\,\left(b^2\,c\,e^3-b\,c^2\,d\,e^2+c^3\,d^2\,e\right)}{b^2\,d^2\,\left(b^2\,e^2-2\,b\,c\,d\,e+c^2\,d^2\right)}+\frac{x\,\left(b\,e+c\,d\right)\,\left(2\,b^2\,e^2-3\,b\,c\,d\,e+2\,c^2\,d^2\right)}{b^2\,d^2\,\left(b^2\,e^2-2\,b\,c\,d\,e+c^2\,d^2\right)}}{c\,e\,x^3+\left(b\,e+c\,d\right)\,x^2+b\,d\,x}-\frac{\ln\left(b+c\,x\right)\,\left(2\,c^4\,d-4\,b\,c^3\,e\right)}{b^6\,e^3-3\,b^5\,c\,d\,e^2+3\,b^4\,c^2\,d^2\,e-b^3\,c^3\,d^3}-\frac{\ln\left(d+e\,x\right)\,\left(2\,b\,e^4-4\,c\,d\,e^3\right)}{-b^3\,d^3\,e^3+3\,b^2\,c\,d^4\,e^2-3\,b\,c^2\,d^5\,e+c^3\,d^6}-\frac{2\,\ln\left(x\right)\,\left(b\,e+c\,d\right)}{b^3\,d^3}","Not used",1,"- (1/(b*d) + (2*x^2*(b^2*c*e^3 + c^3*d^2*e - b*c^2*d*e^2))/(b^2*d^2*(b^2*e^2 + c^2*d^2 - 2*b*c*d*e)) + (x*(b*e + c*d)*(2*b^2*e^2 + 2*c^2*d^2 - 3*b*c*d*e))/(b^2*d^2*(b^2*e^2 + c^2*d^2 - 2*b*c*d*e)))/(x^2*(b*e + c*d) + b*d*x + c*e*x^3) - (log(b + c*x)*(2*c^4*d - 4*b*c^3*e))/(b^6*e^3 - b^3*c^3*d^3 + 3*b^4*c^2*d^2*e - 3*b^5*c*d*e^2) - (log(d + e*x)*(2*b*e^4 - 4*c*d*e^3))/(c^3*d^6 - b^3*d^3*e^3 + 3*b^2*c*d^4*e^2 - 3*b*c^2*d^5*e) - (2*log(x)*(b*e + c*d))/(b^3*d^3)","B"
275,1,399,203,0.494630,"\text{Not used}","int((d + e*x)^7/(b*x + c*x^2)^3,x)","\frac{e^7\,x^2}{2\,c^3}-x\,\left(\frac{3\,b\,e^7}{c^4}-\frac{7\,d\,e^6}{c^3}\right)-\frac{\frac{c^4\,d^7}{2\,b}-\frac{x^3\,\left(4\,b^7\,e^7-21\,b^6\,c\,d\,e^6+42\,b^5\,c^2\,d^2\,e^5-35\,b^4\,c^3\,d^3\,e^4+21\,b^2\,c^5\,d^5\,e^2-21\,b\,c^6\,d^6\,e+6\,c^7\,d^7\right)}{b^4}-\frac{x^2\,\left(7\,b^7\,e^7-35\,b^6\,c\,d\,e^6+63\,b^5\,c^2\,d^2\,e^5-35\,b^4\,c^3\,d^3\,e^4-35\,b^3\,c^4\,d^4\,e^3+63\,b^2\,c^5\,d^5\,e^2-63\,b\,c^6\,d^6\,e+18\,c^7\,d^7\right)}{2\,b^3\,c}+\frac{c^4\,d^6\,x\,\left(7\,b\,e-2\,c\,d\right)}{b^2}}{b^2\,c^4\,x^2+2\,b\,c^5\,x^3+c^6\,x^4}+\frac{\ln\left(b+c\,x\right)\,\left(6\,b^7\,e^7-21\,b^6\,c\,d\,e^6+21\,b^5\,c^2\,d^2\,e^5-21\,b^2\,c^5\,d^5\,e^2+21\,b\,c^6\,d^6\,e-6\,c^7\,d^7\right)}{b^5\,c^5}+\frac{3\,d^5\,\ln\left(x\right)\,\left(7\,b^2\,e^2-7\,b\,c\,d\,e+2\,c^2\,d^2\right)}{b^5}","Not used",1,"(e^7*x^2)/(2*c^3) - x*((3*b*e^7)/c^4 - (7*d*e^6)/c^3) - ((c^4*d^7)/(2*b) - (x^3*(4*b^7*e^7 + 6*c^7*d^7 + 21*b^2*c^5*d^5*e^2 - 35*b^4*c^3*d^3*e^4 + 42*b^5*c^2*d^2*e^5 - 21*b*c^6*d^6*e - 21*b^6*c*d*e^6))/b^4 - (x^2*(7*b^7*e^7 + 18*c^7*d^7 + 63*b^2*c^5*d^5*e^2 - 35*b^3*c^4*d^4*e^3 - 35*b^4*c^3*d^3*e^4 + 63*b^5*c^2*d^2*e^5 - 63*b*c^6*d^6*e - 35*b^6*c*d*e^6))/(2*b^3*c) + (c^4*d^6*x*(7*b*e - 2*c*d))/b^2)/(c^6*x^4 + 2*b*c^5*x^3 + b^2*c^4*x^2) + (log(b + c*x)*(6*b^7*e^7 - 6*c^7*d^7 - 21*b^2*c^5*d^5*e^2 + 21*b^5*c^2*d^2*e^5 + 21*b*c^6*d^6*e - 21*b^6*c*d*e^6))/(b^5*c^5) + (3*d^5*log(x)*(7*b^2*e^2 + 2*c^2*d^2 - 7*b*c*d*e))/b^5","B"
276,1,333,179,0.393287,"\text{Not used}","int((d + e*x)^6/(b*x + c*x^2)^3,x)","\frac{e^6\,x}{c^3}-\frac{\frac{3\,x^3\,\left(b^6\,e^6-4\,b^5\,c\,d\,e^5+5\,b^4\,c^2\,d^2\,e^4-5\,b^2\,c^4\,d^4\,e^2+6\,b\,c^5\,d^5\,e-2\,c^6\,d^6\right)}{b^4}+\frac{c^3\,d^6}{2\,b}+\frac{x^2\,\left(5\,b^6\,e^6-18\,b^5\,c\,d\,e^5+15\,b^4\,c^2\,d^2\,e^4+20\,b^3\,c^3\,d^3\,e^3-45\,b^2\,c^4\,d^4\,e^2+54\,b\,c^5\,d^5\,e-18\,c^6\,d^6\right)}{2\,b^3\,c}+\frac{2\,c^3\,d^5\,x\,\left(3\,b\,e-c\,d\right)}{b^2}}{b^2\,c^3\,x^2+2\,b\,c^4\,x^3+c^5\,x^4}-\frac{\ln\left(b+c\,x\right)\,\left(3\,b^6\,e^6-6\,b^5\,c\,d\,e^5+15\,b^2\,c^4\,d^4\,e^2-18\,b\,c^5\,d^5\,e+6\,c^6\,d^6\right)}{b^5\,c^4}+\frac{3\,d^4\,\ln\left(x\right)\,\left(5\,b^2\,e^2-6\,b\,c\,d\,e+2\,c^2\,d^2\right)}{b^5}","Not used",1,"(e^6*x)/c^3 - ((3*x^3*(b^6*e^6 - 2*c^6*d^6 - 5*b^2*c^4*d^4*e^2 + 5*b^4*c^2*d^2*e^4 + 6*b*c^5*d^5*e - 4*b^5*c*d*e^5))/b^4 + (c^3*d^6)/(2*b) + (x^2*(5*b^6*e^6 - 18*c^6*d^6 - 45*b^2*c^4*d^4*e^2 + 20*b^3*c^3*d^3*e^3 + 15*b^4*c^2*d^2*e^4 + 54*b*c^5*d^5*e - 18*b^5*c*d*e^5))/(2*b^3*c) + (2*c^3*d^5*x*(3*b*e - c*d))/b^2)/(c^5*x^4 + 2*b*c^4*x^3 + b^2*c^3*x^2) - (log(b + c*x)*(3*b^6*e^6 + 6*c^6*d^6 + 15*b^2*c^4*d^4*e^2 - 18*b*c^5*d^5*e - 6*b^5*c*d*e^5))/(b^5*c^4) + (3*d^4*log(x)*(5*b^2*e^2 + 2*c^2*d^2 - 6*b*c*d*e))/b^5","B"
277,1,268,171,0.426715,"\text{Not used}","int((d + e*x)^5/(b*x + c*x^2)^3,x)","\frac{d^3\,\ln\left(x\right)\,\left(10\,b^2\,e^2-15\,b\,c\,d\,e+6\,c^2\,d^2\right)}{b^5}-\frac{\frac{d^5}{2\,b}+\frac{d^4\,x\,\left(5\,b\,e-2\,c\,d\right)}{b^2}-\frac{x^2\,\left(3\,b^5\,e^5-5\,b^4\,c\,d\,e^4-10\,b^3\,c^2\,d^2\,e^3+30\,b^2\,c^3\,d^3\,e^2-45\,b\,c^4\,d^4\,e+18\,c^5\,d^5\right)}{2\,b^3\,c^3}-\frac{x^3\,\left(2\,b^5\,e^5-5\,b^4\,c\,d\,e^4+10\,b^2\,c^3\,d^3\,e^2-15\,b\,c^4\,d^4\,e+6\,c^5\,d^5\right)}{b^4\,c^2}}{b^2\,x^2+2\,b\,c\,x^3+c^2\,x^4}+\frac{\ln\left(b+c\,x\right)\,{\left(b\,e-c\,d\right)}^3\,\left(b^2\,e^2+3\,b\,c\,d\,e+6\,c^2\,d^2\right)}{b^5\,c^3}","Not used",1,"(d^3*log(x)*(10*b^2*e^2 + 6*c^2*d^2 - 15*b*c*d*e))/b^5 - (d^5/(2*b) + (d^4*x*(5*b*e - 2*c*d))/b^2 - (x^2*(3*b^5*e^5 + 18*c^5*d^5 + 30*b^2*c^3*d^3*e^2 - 10*b^3*c^2*d^2*e^3 - 45*b*c^4*d^4*e - 5*b^4*c*d*e^4))/(2*b^3*c^3) - (x^3*(2*b^5*e^5 + 6*c^5*d^5 + 10*b^2*c^3*d^3*e^2 - 15*b*c^4*d^4*e - 5*b^4*c*d*e^4))/(b^4*c^2))/(b^2*x^2 + c^2*x^4 + 2*b*c*x^3) + (log(b + c*x)*(b*e - c*d)^3*(b^2*e^2 + 6*c^2*d^2 + 3*b*c*d*e))/(b^5*c^3)","B"
278,1,238,136,0.148843,"\text{Not used}","int((d + e*x)^4/(b*x + c*x^2)^3,x)","-\frac{\frac{d^4}{2\,b}+\frac{2\,d^3\,x\,\left(2\,b\,e-c\,d\right)}{b^2}+\frac{x^2\,\left(b^4\,e^4+4\,b^3\,c\,d\,e^3-18\,b^2\,c^2\,d^2\,e^2+36\,b\,c^3\,d^3\,e-18\,c^4\,d^4\right)}{2\,b^3\,c^2}+\frac{x^3\,\left(b^4\,e^4-6\,b^2\,c^2\,d^2\,e^2+12\,b\,c^3\,d^3\,e-6\,c^4\,d^4\right)}{b^4\,c}}{b^2\,x^2+2\,b\,c\,x^3+c^2\,x^4}-\frac{12\,d^2\,\mathrm{atanh}\left(\frac{6\,d^2\,{\left(b\,e-c\,d\right)}^2\,\left(b+2\,c\,x\right)}{b\,\left(6\,b^2\,d^2\,e^2-12\,b\,c\,d^3\,e+6\,c^2\,d^4\right)}\right)\,{\left(b\,e-c\,d\right)}^2}{b^5}","Not used",1,"- (d^4/(2*b) + (2*d^3*x*(2*b*e - c*d))/b^2 + (x^2*(b^4*e^4 - 18*c^4*d^4 - 18*b^2*c^2*d^2*e^2 + 36*b*c^3*d^3*e + 4*b^3*c*d*e^3))/(2*b^3*c^2) + (x^3*(b^4*e^4 - 6*c^4*d^4 - 6*b^2*c^2*d^2*e^2 + 12*b*c^3*d^3*e))/(b^4*c))/(b^2*x^2 + c^2*x^4 + 2*b*c*x^3) - (12*d^2*atanh((6*d^2*(b*e - c*d)^2*(b + 2*c*x))/(b*(6*c^2*d^4 + 6*b^2*d^2*e^2 - 12*b*c*d^3*e)))*(b*e - c*d)^2)/b^5","B"
279,1,211,137,0.278254,"\text{Not used}","int((d + e*x)^3/(b*x + c*x^2)^3,x)","-\frac{\frac{d^3}{2\,b}+\frac{d^2\,x\,\left(3\,b\,e-2\,c\,d\right)}{b^2}+\frac{x^2\,\left(b^3\,e^3-9\,b^2\,c\,d\,e^2+27\,b\,c^2\,d^2\,e-18\,c^3\,d^3\right)}{2\,b^3\,c}-\frac{3\,c\,d\,x^3\,\left(b^2\,e^2-3\,b\,c\,d\,e+2\,c^2\,d^2\right)}{b^4}}{b^2\,x^2+2\,b\,c\,x^3+c^2\,x^4}-\frac{6\,d\,\mathrm{atanh}\left(\frac{3\,d\,\left(b\,e-c\,d\right)\,\left(b\,e-2\,c\,d\right)\,\left(b+2\,c\,x\right)}{b\,\left(3\,b^2\,d\,e^2-9\,b\,c\,d^2\,e+6\,c^2\,d^3\right)}\right)\,\left(b\,e-c\,d\right)\,\left(b\,e-2\,c\,d\right)}{b^5}","Not used",1,"- (d^3/(2*b) + (d^2*x*(3*b*e - 2*c*d))/b^2 + (x^2*(b^3*e^3 - 18*c^3*d^3 + 27*b*c^2*d^2*e - 9*b^2*c*d*e^2))/(2*b^3*c) - (3*c*d*x^3*(b^2*e^2 + 2*c^2*d^2 - 3*b*c*d*e))/b^4)/(b^2*x^2 + c^2*x^4 + 2*b*c*x^3) - (6*d*atanh((3*d*(b*e - c*d)*(b*e - 2*c*d)*(b + 2*c*x))/(b*(6*c^2*d^3 + 3*b^2*d*e^2 - 9*b*c*d^2*e)))*(b*e - c*d)*(b*e - 2*c*d))/b^5","B"
280,1,149,144,0.263027,"\text{Not used}","int((d + e*x)^2/(b*x + c*x^2)^3,x)","-\frac{\frac{d^2}{2\,b}-\frac{3\,x^2\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2\right)}{2\,b^3}-\frac{c\,x^3\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2\right)}{b^4}+\frac{2\,d\,x\,\left(b\,e-c\,d\right)}{b^2}}{b^2\,x^2+2\,b\,c\,x^3+c^2\,x^4}-\frac{2\,\mathrm{atanh}\left(\frac{2\,c\,x}{b}+1\right)\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2\right)}{b^5}","Not used",1,"- (d^2/(2*b) - (3*x^2*(b^2*e^2 + 6*c^2*d^2 - 6*b*c*d*e))/(2*b^3) - (c*x^3*(b^2*e^2 + 6*c^2*d^2 - 6*b*c*d*e))/b^4 + (2*d*x*(b*e - c*d))/b^2)/(b^2*x^2 + c^2*x^4 + 2*b*c*x^3) - (2*atanh((2*c*x)/b + 1)*(b^2*e^2 + 6*c^2*d^2 - 6*b*c*d*e))/b^5","B"
281,1,132,110,0.245693,"\text{Not used}","int((d + e*x)/(b*x + c*x^2)^3,x)","-\frac{\frac{d}{2\,b}+\frac{x\,\left(b\,e-2\,c\,d\right)}{b^2}+\frac{9\,c\,x^2\,\left(b\,e-2\,c\,d\right)}{2\,b^3}+\frac{3\,c^2\,x^3\,\left(b\,e-2\,c\,d\right)}{b^4}}{b^2\,x^2+2\,b\,c\,x^3+c^2\,x^4}-\frac{6\,c\,\mathrm{atanh}\left(\frac{3\,c\,\left(b\,e-2\,c\,d\right)\,\left(b+2\,c\,x\right)}{b\,\left(6\,c^2\,d-3\,b\,c\,e\right)}\right)\,\left(b\,e-2\,c\,d\right)}{b^5}","Not used",1,"- (d/(2*b) + (x*(b*e - 2*c*d))/b^2 + (9*c*x^2*(b*e - 2*c*d))/(2*b^3) + (3*c^2*x^3*(b*e - 2*c*d))/b^4)/(b^2*x^2 + c^2*x^4 + 2*b*c*x^3) - (6*c*atanh((3*c*(b*e - 2*c*d)*(b + 2*c*x))/(b*(6*c^2*d - 3*b*c*e)))*(b*e - 2*c*d))/b^5","B"
282,1,79,72,0.104408,"\text{Not used}","int(1/(b*x + c*x^2)^3,x)","\frac{\frac{9\,c^2\,x^2}{b^3}-\frac{1}{2\,b}+\frac{6\,c^3\,x^3}{b^4}+\frac{2\,c\,x}{b^2}}{b^2\,x^2+2\,b\,c\,x^3+c^2\,x^4}-\frac{12\,c^2\,\mathrm{atanh}\left(\frac{2\,c\,x}{b}+1\right)}{b^5}","Not used",1,"((9*c^2*x^2)/b^3 - 1/(2*b) + (6*c^3*x^3)/b^4 + (2*c*x)/b^2)/(b^2*x^2 + c^2*x^4 + 2*b*c*x^3) - (12*c^2*atanh((2*c*x)/b + 1))/b^5","B"
283,1,331,193,0.829118,"\text{Not used}","int(1/((b*x + c*x^2)^3*(d + e*x)),x)","\frac{\frac{x\,\left(b\,e+2\,c\,d\right)}{b^2\,d^2}-\frac{1}{2\,b\,d}+\frac{x^2\,\left(4\,b^3\,c\,e^3+3\,b^2\,c^2\,d\,e^2-27\,b\,c^3\,d^2\,e+18\,c^4\,d^3\right)}{2\,b^3\,d^2\,\left(b^2\,e^2-2\,b\,c\,d\,e+c^2\,d^2\right)}+\frac{x^3\,\left(b^3\,c^2\,e^3+b^2\,c^3\,d\,e^2-9\,b\,c^4\,d^2\,e+6\,c^5\,d^3\right)}{b^4\,d^2\,\left(b^2\,e^2-2\,b\,c\,d\,e+c^2\,d^2\right)}}{b^2\,x^2+2\,b\,c\,x^3+c^2\,x^4}+\frac{\ln\left(b+c\,x\right)\,\left(10\,b^2\,c^3\,e^2-15\,b\,c^4\,d\,e+6\,c^5\,d^2\right)}{b^8\,e^3-3\,b^7\,c\,d\,e^2+3\,b^6\,c^2\,d^2\,e-b^5\,c^3\,d^3}-\frac{e^5\,\ln\left(d+e\,x\right)}{d^3\,{\left(b\,e-c\,d\right)}^3}+\frac{\ln\left(x\right)\,\left(b^2\,e^2+3\,b\,c\,d\,e+6\,c^2\,d^2\right)}{b^5\,d^3}","Not used",1,"((x*(b*e + 2*c*d))/(b^2*d^2) - 1/(2*b*d) + (x^2*(18*c^4*d^3 + 4*b^3*c*e^3 + 3*b^2*c^2*d*e^2 - 27*b*c^3*d^2*e))/(2*b^3*d^2*(b^2*e^2 + c^2*d^2 - 2*b*c*d*e)) + (x^3*(6*c^5*d^3 + b^3*c^2*e^3 + b^2*c^3*d*e^2 - 9*b*c^4*d^2*e))/(b^4*d^2*(b^2*e^2 + c^2*d^2 - 2*b*c*d*e)))/(b^2*x^2 + c^2*x^4 + 2*b*c*x^3) + (log(b + c*x)*(6*c^5*d^2 + 10*b^2*c^3*e^2 - 15*b*c^4*d*e))/(b^8*e^3 - b^5*c^3*d^3 + 3*b^6*c^2*d^2*e - 3*b^7*c*d*e^2) - (e^5*log(d + e*x))/(d^3*(b*e - c*d)^3) + (log(x)*(b^2*e^2 + 6*c^2*d^2 + 3*b*c*d*e))/(b^5*d^3)","B"
284,1,603,230,1.074692,"\text{Not used}","int(1/((b*x + c*x^2)^3*(d + e*x)^2),x)","\frac{\ln\left(x\right)\,\left(3\,b^2\,e^2+6\,b\,c\,d\,e+6\,c^2\,d^2\right)}{b^5\,d^4}-\frac{\ln\left(d+e\,x\right)\,\left(3\,b\,e^6-6\,c\,d\,e^5\right)}{b^4\,d^4\,e^4-4\,b^3\,c\,d^5\,e^3+6\,b^2\,c^2\,d^6\,e^2-4\,b\,c^3\,d^7\,e+c^4\,d^8}-\frac{\ln\left(b+c\,x\right)\,\left(15\,b^2\,c^4\,e^2-18\,b\,c^5\,d\,e+6\,c^6\,d^2\right)}{b^9\,e^4-4\,b^8\,c\,d\,e^3+6\,b^7\,c^2\,d^2\,e^2-4\,b^6\,c^3\,d^3\,e+b^5\,c^4\,d^4}-\frac{\frac{1}{2\,b\,d}-\frac{x\,\left(3\,b\,e+4\,c\,d\right)}{2\,b^2\,d^2}+\frac{x^2\,\left(-6\,b^5\,e^5+13\,b^3\,c^2\,d^2\,e^3+b^2\,c^3\,d^3\,e^2-32\,b\,c^4\,d^4\,e+18\,c^5\,d^5\right)}{2\,b^3\,d^3\,\left(b^3\,e^3-3\,b^2\,c\,d\,e^2+3\,b\,c^2\,d^2\,e-c^3\,d^3\right)}+\frac{3\,x^3\,\left(-4\,b^5\,c\,e^5+3\,b^4\,c^2\,d\,e^4+5\,b^3\,c^3\,d^2\,e^3-10\,b^2\,c^4\,d^3\,e^2-2\,b\,c^5\,d^4\,e+4\,c^6\,d^5\right)}{2\,b^4\,d^3\,\left(b^3\,e^3-3\,b^2\,c\,d\,e^2+3\,b\,c^2\,d^2\,e-c^3\,d^3\right)}+\frac{3\,c^2\,e\,x^4\,\left(-b^4\,e^4+b^3\,c\,d\,e^3+b^2\,c^2\,d^2\,e^2-4\,b\,c^3\,d^3\,e+2\,c^4\,d^4\right)}{b^4\,d^3\,\left(b^3\,e^3-3\,b^2\,c\,d\,e^2+3\,b\,c^2\,d^2\,e-c^3\,d^3\right)}}{x^3\,\left(e\,b^2+2\,c\,d\,b\right)+x^4\,\left(d\,c^2+2\,b\,e\,c\right)+b^2\,d\,x^2+c^2\,e\,x^5}","Not used",1,"(log(x)*(3*b^2*e^2 + 6*c^2*d^2 + 6*b*c*d*e))/(b^5*d^4) - (log(d + e*x)*(3*b*e^6 - 6*c*d*e^5))/(c^4*d^8 + b^4*d^4*e^4 - 4*b^3*c*d^5*e^3 + 6*b^2*c^2*d^6*e^2 - 4*b*c^3*d^7*e) - (log(b + c*x)*(6*c^6*d^2 + 15*b^2*c^4*e^2 - 18*b*c^5*d*e))/(b^9*e^4 + b^5*c^4*d^4 - 4*b^6*c^3*d^3*e + 6*b^7*c^2*d^2*e^2 - 4*b^8*c*d*e^3) - (1/(2*b*d) - (x*(3*b*e + 4*c*d))/(2*b^2*d^2) + (x^2*(18*c^5*d^5 - 6*b^5*e^5 + b^2*c^3*d^3*e^2 + 13*b^3*c^2*d^2*e^3 - 32*b*c^4*d^4*e))/(2*b^3*d^3*(b^3*e^3 - c^3*d^3 + 3*b*c^2*d^2*e - 3*b^2*c*d*e^2)) + (3*x^3*(4*c^6*d^5 - 4*b^5*c*e^5 + 3*b^4*c^2*d*e^4 - 10*b^2*c^4*d^3*e^2 + 5*b^3*c^3*d^2*e^3 - 2*b*c^5*d^4*e))/(2*b^4*d^3*(b^3*e^3 - c^3*d^3 + 3*b*c^2*d^2*e - 3*b^2*c*d*e^2)) + (3*c^2*e*x^4*(2*c^4*d^4 - b^4*e^4 + b^2*c^2*d^2*e^2 - 4*b*c^3*d^3*e + b^3*c*d*e^3))/(b^4*d^3*(b^3*e^3 - c^3*d^3 + 3*b*c^2*d^2*e - 3*b^2*c*d*e^2)))/(x^3*(b^2*e + 2*b*c*d) + x^4*(c^2*d + 2*b*c*e) + b^2*d*x^2 + c^2*e*x^5)","B"
285,1,361,210,0.917839,"\text{Not used}","int((b*x + c*x^2)^(1/2)*(d + e*x)^3,x)","d^3\,\sqrt{c\,x^2+b\,x}\,\left(\frac{x}{2}+\frac{b}{4\,c}\right)-\frac{7\,b\,e^3\,\left(\frac{x\,{\left(c\,x^2+b\,x\right)}^{3/2}}{4\,c}-\frac{5\,b\,\left(\frac{b^3\,\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x}\right)}{16\,c^{5/2}}+\frac{\sqrt{c\,x^2+b\,x}\,\left(-3\,b^2+2\,b\,c\,x+8\,c^2\,x^2\right)}{24\,c^2}\right)}{8\,c}\right)}{10\,c}+\frac{e^3\,x^2\,{\left(c\,x^2+b\,x\right)}^{3/2}}{5\,c}-\frac{b^2\,d^3\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{8\,c^{3/2}}+\frac{3\,d\,e^2\,x\,{\left(c\,x^2+b\,x\right)}^{3/2}}{4\,c}-\frac{15\,b\,d\,e^2\,\left(\frac{b^3\,\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x}\right)}{16\,c^{5/2}}+\frac{\sqrt{c\,x^2+b\,x}\,\left(-3\,b^2+2\,b\,c\,x+8\,c^2\,x^2\right)}{24\,c^2}\right)}{8\,c}+\frac{3\,b^3\,d^2\,e\,\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x}\right)}{16\,c^{5/2}}+\frac{d^2\,e\,\sqrt{c\,x^2+b\,x}\,\left(-3\,b^2+2\,b\,c\,x+8\,c^2\,x^2\right)}{8\,c^2}","Not used",1,"d^3*(b*x + c*x^2)^(1/2)*(x/2 + b/(4*c)) - (7*b*e^3*((x*(b*x + c*x^2)^(3/2))/(4*c) - (5*b*((b^3*log((b + 2*c*x)/c^(1/2) + 2*(b*x + c*x^2)^(1/2)))/(16*c^(5/2)) + ((b*x + c*x^2)^(1/2)*(8*c^2*x^2 - 3*b^2 + 2*b*c*x))/(24*c^2)))/(8*c)))/(10*c) + (e^3*x^2*(b*x + c*x^2)^(3/2))/(5*c) - (b^2*d^3*log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2)))/(8*c^(3/2)) + (3*d*e^2*x*(b*x + c*x^2)^(3/2))/(4*c) - (15*b*d*e^2*((b^3*log((b + 2*c*x)/c^(1/2) + 2*(b*x + c*x^2)^(1/2)))/(16*c^(5/2)) + ((b*x + c*x^2)^(1/2)*(8*c^2*x^2 - 3*b^2 + 2*b*c*x))/(24*c^2)))/(8*c) + (3*b^3*d^2*e*log((b + 2*c*x)/c^(1/2) + 2*(b*x + c*x^2)^(1/2)))/(16*c^(5/2)) + (d^2*e*(b*x + c*x^2)^(1/2)*(8*c^2*x^2 - 3*b^2 + 2*b*c*x))/(8*c^2)","B"
286,1,231,162,0.688590,"\text{Not used}","int((b*x + c*x^2)^(1/2)*(d + e*x)^2,x)","d^2\,\sqrt{c\,x^2+b\,x}\,\left(\frac{x}{2}+\frac{b}{4\,c}\right)-\frac{5\,b\,e^2\,\left(\frac{b^3\,\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x}\right)}{16\,c^{5/2}}+\frac{\sqrt{c\,x^2+b\,x}\,\left(-3\,b^2+2\,b\,c\,x+8\,c^2\,x^2\right)}{24\,c^2}\right)}{8\,c}-\frac{b^2\,d^2\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{8\,c^{3/2}}+\frac{e^2\,x\,{\left(c\,x^2+b\,x\right)}^{3/2}}{4\,c}+\frac{b^3\,d\,e\,\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x}\right)}{8\,c^{5/2}}+\frac{d\,e\,\sqrt{c\,x^2+b\,x}\,\left(-3\,b^2+2\,b\,c\,x+8\,c^2\,x^2\right)}{12\,c^2}","Not used",1,"d^2*(b*x + c*x^2)^(1/2)*(x/2 + b/(4*c)) - (5*b*e^2*((b^3*log((b + 2*c*x)/c^(1/2) + 2*(b*x + c*x^2)^(1/2)))/(16*c^(5/2)) + ((b*x + c*x^2)^(1/2)*(8*c^2*x^2 - 3*b^2 + 2*b*c*x))/(24*c^2)))/(8*c) - (b^2*d^2*log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2)))/(8*c^(3/2)) + (e^2*x*(b*x + c*x^2)^(3/2))/(4*c) + (b^3*d*e*log((b + 2*c*x)/c^(1/2) + 2*(b*x + c*x^2)^(1/2)))/(8*c^(5/2)) + (d*e*(b*x + c*x^2)^(1/2)*(8*c^2*x^2 - 3*b^2 + 2*b*c*x))/(12*c^2)","B"
287,1,127,99,0.505417,"\text{Not used}","int((b*x + c*x^2)^(1/2)*(d + e*x),x)","d\,\sqrt{c\,x^2+b\,x}\,\left(\frac{x}{2}+\frac{b}{4\,c}\right)-\frac{b^2\,d\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{8\,c^{3/2}}+\frac{b^3\,e\,\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x}\right)}{16\,c^{5/2}}+\frac{e\,\sqrt{c\,x^2+b\,x}\,\left(-3\,b^2+2\,b\,c\,x+8\,c^2\,x^2\right)}{24\,c^2}","Not used",1,"d*(b*x + c*x^2)^(1/2)*(x/2 + b/(4*c)) - (b^2*d*log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2)))/(8*c^(3/2)) + (b^3*e*log((b + 2*c*x)/c^(1/2) + 2*(b*x + c*x^2)^(1/2)))/(16*c^(5/2)) + (e*(b*x + c*x^2)^(1/2)*(8*c^2*x^2 - 3*b^2 + 2*b*c*x))/(24*c^2)","B"
288,1,55,60,0.224737,"\text{Not used}","int((b*x + c*x^2)^(1/2),x)","\sqrt{c\,x^2+b\,x}\,\left(\frac{x}{2}+\frac{b}{4\,c}\right)-\frac{b^2\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{8\,c^{3/2}}","Not used",1,"(b*x + c*x^2)^(1/2)*(x/2 + b/(4*c)) - (b^2*log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2)))/(8*c^(3/2))","B"
289,0,-1,129,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/(d + e*x),x)","\int \frac{\sqrt{c\,x^2+b\,x}}{d+e\,x} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/(d + e*x), x)","F"
290,0,-1,140,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/(d + e*x)^2,x)","\int \frac{\sqrt{c\,x^2+b\,x}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/(d + e*x)^2, x)","F"
291,0,-1,127,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/(d + e*x)^3,x)","\int \frac{\sqrt{c\,x^2+b\,x}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/(d + e*x)^3, x)","F"
292,0,-1,183,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/(d + e*x)^4,x)","\int \frac{\sqrt{c\,x^2+b\,x}}{{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/(d + e*x)^4, x)","F"
293,0,-1,258,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/(d + e*x)^5,x)","\int \frac{\sqrt{c\,x^2+b\,x}}{{\left(d+e\,x\right)}^5} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/(d + e*x)^5, x)","F"
294,0,-1,337,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/(d + e*x)^6,x)","\int \frac{\sqrt{c\,x^2+b\,x}}{{\left(d+e\,x\right)}^6} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/(d + e*x)^6, x)","F"
295,0,-1,271,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)*(d + e*x)^3,x)","\int {\left(c\,x^2+b\,x\right)}^{3/2}\,{\left(d+e\,x\right)}^3 \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)*(d + e*x)^3, x)","F"
296,0,-1,214,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)*(d + e*x)^2,x)","\int {\left(c\,x^2+b\,x\right)}^{3/2}\,{\left(d+e\,x\right)}^2 \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)*(d + e*x)^2, x)","F"
297,1,208,137,0.673797,"\text{Not used}","int((b*x + c*x^2)^(3/2)*(d + e*x),x)","\frac{e\,{\left(c\,x^2+b\,x\right)}^{5/2}}{5\,c}-\frac{3\,b^2\,d\,\left(\sqrt{c\,x^2+b\,x}\,\left(\frac{x}{2}+\frac{b}{4\,c}\right)-\frac{b^2\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{8\,c^{3/2}}\right)}{16\,c}+\frac{d\,{\left(c\,x^2+b\,x\right)}^{3/2}\,\left(\frac{b}{2}+c\,x\right)}{4\,c}-\frac{b\,e\,\left(\frac{x\,{\left(c\,x^2+b\,x\right)}^{3/2}}{4}+\frac{b\,{\left(c\,x^2+b\,x\right)}^{3/2}}{8\,c}-\frac{3\,b^2\,\left(\frac{\sqrt{c\,x^2+b\,x}\,\left(b+2\,c\,x\right)}{4\,c}-\frac{b^2\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{8\,c^{3/2}}\right)}{16\,c}\right)}{2\,c}","Not used",1,"(e*(b*x + c*x^2)^(5/2))/(5*c) - (3*b^2*d*((b*x + c*x^2)^(1/2)*(x/2 + b/(4*c)) - (b^2*log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2)))/(8*c^(3/2))))/(16*c) + (d*(b*x + c*x^2)^(3/2)*(b/2 + c*x))/(4*c) - (b*e*((x*(b*x + c*x^2)^(3/2))/4 + (b*(b*x + c*x^2)^(3/2))/(8*c) - (3*b^2*(((b*x + c*x^2)^(1/2)*(b + 2*c*x))/(4*c) - (b^2*log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2)))/(8*c^(3/2))))/(16*c)))/(2*c)","B"
298,1,87,89,0.196720,"\text{Not used}","int((b*x + c*x^2)^(3/2),x)","\frac{{\left(c\,x^2+b\,x\right)}^{3/2}\,\left(\frac{b}{2}+c\,x\right)}{4\,c}-\frac{3\,b^2\,\left(\sqrt{c\,x^2+b\,x}\,\left(\frac{x}{2}+\frac{b}{4\,c}\right)-\frac{b^2\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{8\,c^{3/2}}\right)}{16\,c}","Not used",1,"((b*x + c*x^2)^(3/2)*(b/2 + c*x))/(4*c) - (3*b^2*((b*x + c*x^2)^(1/2)*(x/2 + b/(4*c)) - (b^2*log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2)))/(8*c^(3/2))))/(16*c)","B"
299,0,-1,216,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/(d + e*x),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{d+e\,x} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/(d + e*x), x)","F"
300,0,-1,198,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/(d + e*x)^2,x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/(d + e*x)^2, x)","F"
301,0,-1,205,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/(d + e*x)^3,x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/(d + e*x)^3, x)","F"
302,0,-1,332,0.000000,"\text{Not used}","int((b*x + c*x^2)^(5/2)*(d + e*x)^3,x)","\int {\left(c\,x^2+b\,x\right)}^{5/2}\,{\left(d+e\,x\right)}^3 \,d x","Not used",1,"int((b*x + c*x^2)^(5/2)*(d + e*x)^3, x)","F"
303,0,-1,266,0.000000,"\text{Not used}","int((b*x + c*x^2)^(5/2)*(d + e*x)^2,x)","\int {\left(c\,x^2+b\,x\right)}^{5/2}\,{\left(d+e\,x\right)}^2 \,d x","Not used",1,"int((b*x + c*x^2)^(5/2)*(d + e*x)^2, x)","F"
304,0,-1,175,0.000000,"\text{Not used}","int((b*x + c*x^2)^(5/2)*(d + e*x),x)","\int {\left(c\,x^2+b\,x\right)}^{5/2}\,\left(d+e\,x\right) \,d x","Not used",1,"int((b*x + c*x^2)^(5/2)*(d + e*x), x)","F"
305,1,119,118,0.384503,"\text{Not used}","int((b*x + c*x^2)^(5/2),x)","\frac{{\left(c\,x^2+b\,x\right)}^{5/2}\,\left(\frac{b}{2}+c\,x\right)}{6\,c}-\frac{5\,b^2\,\left(\frac{{\left(c\,x^2+b\,x\right)}^{3/2}\,\left(\frac{b}{2}+c\,x\right)}{4\,c}-\frac{3\,b^2\,\left(\sqrt{c\,x^2+b\,x}\,\left(\frac{x}{2}+\frac{b}{4\,c}\right)-\frac{b^2\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{8\,c^{3/2}}\right)}{16\,c}\right)}{24\,c}","Not used",1,"((b*x + c*x^2)^(5/2)*(b/2 + c*x))/(6*c) - (5*b^2*(((b*x + c*x^2)^(3/2)*(b/2 + c*x))/(4*c) - (3*b^2*((b*x + c*x^2)^(1/2)*(x/2 + b/(4*c)) - (b^2*log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2)))/(8*c^(3/2))))/(16*c)))/(24*c)","B"
306,0,-1,356,0.000000,"\text{Not used}","int((b*x + c*x^2)^(5/2)/(d + e*x),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{5/2}}{d+e\,x} \,d x","Not used",1,"int((b*x + c*x^2)^(5/2)/(d + e*x), x)","F"
307,0,-1,314,0.000000,"\text{Not used}","int((b*x + c*x^2)^(5/2)/(d + e*x)^2,x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{5/2}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((b*x + c*x^2)^(5/2)/(d + e*x)^2, x)","F"
308,0,-1,282,0.000000,"\text{Not used}","int((b*x + c*x^2)^(5/2)/(d + e*x)^3,x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{5/2}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((b*x + c*x^2)^(5/2)/(d + e*x)^3, x)","F"
309,0,-1,26,0.000000,"\text{Not used}","int((2*x + x^2)^(1/2)/(x + 1),x)","\int \frac{\sqrt{x^2+2\,x}}{x+1} \,d x","Not used",1,"int((2*x + x^2)^(1/2)/(x + 1), x)","F"
310,0,-1,53,0.000000,"\text{Not used}","int(-(2*x - x^2)^(3/2)/(2*x - 2),x)","-\int \frac{{\left(2\,x-x^2\right)}^{3/2}}{2\,x-2} \,d x","Not used",1,"-int((2*x - x^2)^(3/2)/(2*x - 2), x)","F"
311,0,-1,36,0.000000,"\text{Not used}","int(-(2*x - x^2)^(1/2)/(2*x - 2),x)","-\int \frac{\sqrt{2\,x-x^2}}{2\,x-2} \,d x","Not used",1,"-int((2*x - x^2)^(1/2)/(2*x - 2), x)","F"
312,0,-1,18,0.000000,"\text{Not used}","int(-1/((2*x - 2)*(2*x - x^2)^(1/2)),x)","-\int \frac{1}{\left(2\,x-2\right)\,\sqrt{2\,x-x^2}} \,d x","Not used",1,"-int(1/((2*x - 2)*(2*x - x^2)^(1/2)), x)","F"
313,0,-1,36,0.000000,"\text{Not used}","int(-1/((2*x - 2)*(2*x - x^2)^(3/2)),x)","-\int \frac{1}{\left(2\,x-2\right)\,{\left(2\,x-x^2\right)}^{3/2}} \,d x","Not used",1,"-int(1/((2*x - 2)*(2*x - x^2)^(3/2)), x)","F"
314,0,-1,53,0.000000,"\text{Not used}","int(-1/((2*x - 2)*(2*x - x^2)^(5/2)),x)","-\int \frac{1}{\left(2\,x-2\right)\,{\left(2\,x-x^2\right)}^{5/2}} \,d x","Not used",1,"-int(1/((2*x - 2)*(2*x - x^2)^(5/2)), x)","F"
315,0,-1,149,0.000000,"\text{Not used}","int((d + e*x)^3/(b*x + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^3}{\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int((d + e*x)^3/(b*x + c*x^2)^(1/2), x)","F"
316,0,-1,110,0.000000,"\text{Not used}","int((d + e*x)^2/(b*x + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^2}{\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int((d + e*x)^2/(b*x + c*x^2)^(1/2), x)","F"
317,1,77,55,0.513837,"\text{Not used}","int((d + e*x)/(b*x + c*x^2)^(1/2),x)","\frac{e\,\sqrt{c\,x^2+b\,x}}{c}+\frac{d\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{\sqrt{c}}-\frac{b\,e\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{2\,c^{3/2}}","Not used",1,"(e*(b*x + c*x^2)^(1/2))/c + (d*log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2)))/c^(1/2) - (b*e*log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2)))/(2*c^(3/2))","B"
318,1,28,28,0.229449,"\text{Not used}","int(1/(b*x + c*x^2)^(1/2),x)","\frac{\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{\sqrt{c}}","Not used",1,"log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2))/c^(1/2)","B"
319,0,-1,68,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(1/2)*(d + e*x)),x)","\int \frac{1}{\sqrt{c\,x^2+b\,x}\,\left(d+e\,x\right)} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(1/2)*(d + e*x)), x)","F"
320,0,-1,117,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(1/2)*(d + e*x)^2),x)","\int \frac{1}{\sqrt{c\,x^2+b\,x}\,{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(1/2)*(d + e*x)^2), x)","F"
321,0,-1,180,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(1/2)*(d + e*x)^3),x)","\int \frac{1}{\sqrt{c\,x^2+b\,x}\,{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(1/2)*(d + e*x)^3), x)","F"
322,0,-1,139,0.000000,"\text{Not used}","int((d + e*x)^3/(b*x + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^3}{{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^3/(b*x + c*x^2)^(3/2), x)","F"
323,1,96,101,0.589410,"\text{Not used}","int((d + e*x)^2/(b*x + c*x^2)^(3/2),x)","\frac{e^2\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x}\right)}{c^{3/2}}-\frac{d^2\,\left(2\,b+4\,c\,x\right)}{b^2\,\sqrt{c\,x^2+b\,x}}-\frac{2\,e^2\,x}{c\,\sqrt{c\,x^2+b\,x}}+\frac{4\,d\,e\,x}{b\,\sqrt{x\,\left(b+c\,x\right)}}","Not used",1,"(e^2*log((b/2 + c*x)/c^(1/2) + (b*x + c*x^2)^(1/2)))/c^(3/2) - (d^2*(2*b + 4*c*x))/(b^2*(b*x + c*x^2)^(1/2)) - (2*e^2*x)/(c*(b*x + c*x^2)^(1/2)) + (4*d*e*x)/(b*(x*(b + c*x))^(1/2))","B"
324,1,31,33,0.270527,"\text{Not used}","int((d + e*x)/(b*x + c*x^2)^(3/2),x)","-\frac{2\,b\,d-2\,b\,e\,x+4\,c\,d\,x}{b^2\,\sqrt{c\,x^2+b\,x}}","Not used",1,"-(2*b*d - 2*b*e*x + 4*c*d*x)/(b^2*(b*x + c*x^2)^(1/2))","B"
325,1,24,24,0.172931,"\text{Not used}","int(1/(b*x + c*x^2)^(3/2),x)","-\frac{2\,b+4\,c\,x}{b^2\,\sqrt{c\,x^2+b\,x}}","Not used",1,"-(2*b + 4*c*x)/(b^2*(b*x + c*x^2)^(1/2))","B"
326,0,-1,126,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(3/2)*(d + e*x)),x)","\int \frac{1}{{\left(c\,x^2+b\,x\right)}^{3/2}\,\left(d+e\,x\right)} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(3/2)*(d + e*x)), x)","F"
327,0,-1,207,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(3/2)*(d + e*x)^2),x)","\int \frac{1}{{\left(c\,x^2+b\,x\right)}^{3/2}\,{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(3/2)*(d + e*x)^2), x)","F"
328,0,-1,296,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(3/2)*(d + e*x)^3),x)","\int \frac{1}{{\left(c\,x^2+b\,x\right)}^{3/2}\,{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(3/2)*(d + e*x)^3), x)","F"
329,0,-1,208,0.000000,"\text{Not used}","int((d + e*x)^4/(b*x + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{{\left(c\,x^2+b\,x\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^4/(b*x + c*x^2)^(5/2), x)","F"
330,1,129,87,0.477149,"\text{Not used}","int((d + e*x)^3/(b*x + c*x^2)^(5/2),x)","\frac{2\,\left(-b^3\,d^3-9\,b^3\,d^2\,e\,x+9\,b^3\,d\,e^2\,x^2+b^3\,e^3\,x^3+6\,b^2\,c\,d^3\,x-36\,b^2\,c\,d^2\,e\,x^2+6\,b^2\,c\,d\,e^2\,x^3+24\,b\,c^2\,d^3\,x^2-24\,b\,c^2\,d^2\,e\,x^3+16\,c^3\,d^3\,x^3\right)}{3\,b^4\,{\left(c\,x^2+b\,x\right)}^{3/2}}","Not used",1,"(2*(b^3*e^3*x^3 - b^3*d^3 + 16*c^3*d^3*x^3 + 24*b*c^2*d^3*x^2 + 9*b^3*d*e^2*x^2 + 6*b^2*c*d^3*x - 9*b^3*d^2*e*x - 36*b^2*c*d^2*e*x^2 - 24*b*c^2*d^2*e*x^3 + 6*b^2*c*d*e^2*x^3))/(3*b^4*(b*x + c*x^2)^(3/2))","B"
331,1,111,78,0.358174,"\text{Not used}","int((d + e*x)^2/(b*x + c*x^2)^(5/2),x)","\frac{2\,\left(-b^3\,d^2-6\,b^3\,d\,e\,x+3\,b^3\,e^2\,x^2+6\,b^2\,c\,d^2\,x-24\,b^2\,c\,d\,e\,x^2+2\,b^2\,c\,e^2\,x^3+24\,b\,c^2\,d^2\,x^2-16\,b\,c^2\,d\,e\,x^3+16\,c^3\,d^2\,x^3\right)}{3\,b^4\,{\left(c\,x^2+b\,x\right)}^{3/2}}","Not used",1,"(2*(3*b^3*e^2*x^2 - b^3*d^2 + 16*c^3*d^2*x^3 + 24*b*c^2*d^2*x^2 + 2*b^2*c*e^2*x^3 - 6*b^3*d*e*x + 6*b^2*c*d^2*x - 24*b^2*c*d*e*x^2 - 16*b*c^2*d*e*x^3))/(3*b^4*(b*x + c*x^2)^(3/2))","B"
332,1,76,71,0.299887,"\text{Not used}","int((d + e*x)/(b*x + c*x^2)^(5/2),x)","-\frac{2\,\left(3\,e\,b^3\,x+d\,b^3+12\,e\,b^2\,c\,x^2-6\,d\,b^2\,c\,x+8\,e\,b\,c^2\,x^3-24\,d\,b\,c^2\,x^2-16\,d\,c^3\,x^3\right)}{3\,b^4\,{\left(c\,x^2+b\,x\right)}^{3/2}}","Not used",1,"-(2*(b^3*d - 16*c^3*d*x^3 + 3*b^3*e*x - 6*b^2*c*d*x - 24*b*c^2*d*x^2 + 12*b^2*c*e*x^2 + 8*b*c^2*e*x^3))/(3*b^4*(b*x + c*x^2)^(3/2))","B"
333,1,43,54,0.034036,"\text{Not used}","int(1/(b*x + c*x^2)^(5/2),x)","\frac{\left(2\,b+4\,c\,x\right)\,\left(-b^2+8\,b\,c\,x+8\,c^2\,x^2\right)}{3\,b^4\,{\left(c\,x^2+b\,x\right)}^{3/2}}","Not used",1,"((2*b + 4*c*x)*(8*c^2*x^2 - b^2 + 8*b*c*x))/(3*b^4*(b*x + c*x^2)^(3/2))","B"
334,0,-1,230,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(5/2)*(d + e*x)),x)","\int \frac{1}{{\left(c\,x^2+b\,x\right)}^{5/2}\,\left(d+e\,x\right)} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(5/2)*(d + e*x)), x)","F"
335,0,-1,348,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(5/2)*(d + e*x)^2),x)","\int \frac{1}{{\left(c\,x^2+b\,x\right)}^{5/2}\,{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(5/2)*(d + e*x)^2), x)","F"
336,1,15,17,0.221880,"\text{Not used}","int(1/((2*x + x^2)^(1/2)*(x + 2)),x)","\frac{\sqrt{x^2+2\,x}}{x+2}","Not used",1,"(2*x + x^2)^(1/2)/(x + 2)","B"
337,1,52,68,0.071495,"\text{Not used}","int((b*x + c*x^2)*(d + e*x)^(7/2),x)","\frac{2\,{\left(d+e\,x\right)}^{9/2}\,\left(99\,c\,{\left(d+e\,x\right)}^2+143\,c\,d^2+117\,b\,e\,\left(d+e\,x\right)-234\,c\,d\,\left(d+e\,x\right)-143\,b\,d\,e\right)}{1287\,e^3}","Not used",1,"(2*(d + e*x)^(9/2)*(99*c*(d + e*x)^2 + 143*c*d^2 + 117*b*e*(d + e*x) - 234*c*d*(d + e*x) - 143*b*d*e))/(1287*e^3)","B"
338,1,52,68,0.203077,"\text{Not used}","int((b*x + c*x^2)*(d + e*x)^(5/2),x)","\frac{2\,{\left(d+e\,x\right)}^{7/2}\,\left(63\,c\,{\left(d+e\,x\right)}^2+99\,c\,d^2+77\,b\,e\,\left(d+e\,x\right)-154\,c\,d\,\left(d+e\,x\right)-99\,b\,d\,e\right)}{693\,e^3}","Not used",1,"(2*(d + e*x)^(7/2)*(63*c*(d + e*x)^2 + 99*c*d^2 + 77*b*e*(d + e*x) - 154*c*d*(d + e*x) - 99*b*d*e))/(693*e^3)","B"
339,1,52,68,0.057578,"\text{Not used}","int((b*x + c*x^2)*(d + e*x)^(3/2),x)","\frac{2\,{\left(d+e\,x\right)}^{5/2}\,\left(35\,c\,{\left(d+e\,x\right)}^2+63\,c\,d^2+45\,b\,e\,\left(d+e\,x\right)-90\,c\,d\,\left(d+e\,x\right)-63\,b\,d\,e\right)}{315\,e^3}","Not used",1,"(2*(d + e*x)^(5/2)*(35*c*(d + e*x)^2 + 63*c*d^2 + 45*b*e*(d + e*x) - 90*c*d*(d + e*x) - 63*b*d*e))/(315*e^3)","B"
340,1,52,68,0.207313,"\text{Not used}","int((b*x + c*x^2)*(d + e*x)^(1/2),x)","\frac{2\,{\left(d+e\,x\right)}^{3/2}\,\left(15\,c\,{\left(d+e\,x\right)}^2+35\,c\,d^2+21\,b\,e\,\left(d+e\,x\right)-42\,c\,d\,\left(d+e\,x\right)-35\,b\,d\,e\right)}{105\,e^3}","Not used",1,"(2*(d + e*x)^(3/2)*(15*c*(d + e*x)^2 + 35*c*d^2 + 21*b*e*(d + e*x) - 42*c*d*(d + e*x) - 35*b*d*e))/(105*e^3)","B"
341,1,52,66,0.060409,"\text{Not used}","int((b*x + c*x^2)/(d + e*x)^(1/2),x)","\frac{2\,\sqrt{d+e\,x}\,\left(3\,c\,{\left(d+e\,x\right)}^2+15\,c\,d^2+5\,b\,e\,\left(d+e\,x\right)-10\,c\,d\,\left(d+e\,x\right)-15\,b\,d\,e\right)}{15\,e^3}","Not used",1,"(2*(d + e*x)^(1/2)*(3*c*(d + e*x)^2 + 15*c*d^2 + 5*b*e*(d + e*x) - 10*c*d*(d + e*x) - 15*b*d*e))/(15*e^3)","B"
342,1,52,64,0.059661,"\text{Not used}","int((b*x + c*x^2)/(d + e*x)^(3/2),x)","\frac{2\,c\,{\left(d+e\,x\right)}^2-6\,c\,d^2+6\,b\,e\,\left(d+e\,x\right)-12\,c\,d\,\left(d+e\,x\right)+6\,b\,d\,e}{3\,e^3\,\sqrt{d+e\,x}}","Not used",1,"(2*c*(d + e*x)^2 - 6*c*d^2 + 6*b*e*(d + e*x) - 12*c*d*(d + e*x) + 6*b*d*e)/(3*e^3*(d + e*x)^(1/2))","B"
343,1,52,64,0.054230,"\text{Not used}","int((b*x + c*x^2)/(d + e*x)^(5/2),x)","\frac{6\,c\,{\left(d+e\,x\right)}^2-2\,c\,d^2-6\,b\,e\,\left(d+e\,x\right)+12\,c\,d\,\left(d+e\,x\right)+2\,b\,d\,e}{3\,e^3\,{\left(d+e\,x\right)}^{3/2}}","Not used",1,"(6*c*(d + e*x)^2 - 2*c*d^2 - 6*b*e*(d + e*x) + 12*c*d*(d + e*x) + 2*b*d*e)/(3*e^3*(d + e*x)^(3/2))","B"
344,1,49,66,0.066408,"\text{Not used}","int((b*x + c*x^2)/(d + e*x)^(7/2),x)","-\frac{\left(\frac{2\,b\,e}{3}-\frac{4\,c\,d}{3}\right)\,\left(d+e\,x\right)+2\,c\,{\left(d+e\,x\right)}^2+\frac{2\,c\,d^2}{5}-\frac{2\,b\,d\,e}{5}}{e^3\,{\left(d+e\,x\right)}^{5/2}}","Not used",1,"-(((2*b*e)/3 - (4*c*d)/3)*(d + e*x) + 2*c*(d + e*x)^2 + (2*c*d^2)/5 - (2*b*d*e)/5)/(e^3*(d + e*x)^(5/2))","B"
345,1,138,147,0.216034,"\text{Not used}","int((b*x + c*x^2)^2*(d + e*x)^(7/2),x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{17/2}}{17\,e^5}-\frac{{\left(d+e\,x\right)}^{11/2}\,\left(4\,b^2\,d\,e^2-12\,b\,c\,d^2\,e+8\,c^2\,d^3\right)}{11\,e^5}+\frac{{\left(d+e\,x\right)}^{13/2}\,\left(2\,b^2\,e^2-12\,b\,c\,d\,e+12\,c^2\,d^2\right)}{13\,e^5}-\frac{\left(8\,c^2\,d-4\,b\,c\,e\right)\,{\left(d+e\,x\right)}^{15/2}}{15\,e^5}+\frac{2\,d^2\,{\left(b\,e-c\,d\right)}^2\,{\left(d+e\,x\right)}^{9/2}}{9\,e^5}","Not used",1,"(2*c^2*(d + e*x)^(17/2))/(17*e^5) - ((d + e*x)^(11/2)*(8*c^2*d^3 + 4*b^2*d*e^2 - 12*b*c*d^2*e))/(11*e^5) + ((d + e*x)^(13/2)*(2*b^2*e^2 + 12*c^2*d^2 - 12*b*c*d*e))/(13*e^5) - ((8*c^2*d - 4*b*c*e)*(d + e*x)^(15/2))/(15*e^5) + (2*d^2*(b*e - c*d)^2*(d + e*x)^(9/2))/(9*e^5)","B"
346,1,138,147,0.043015,"\text{Not used}","int((b*x + c*x^2)^2*(d + e*x)^(5/2),x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{15/2}}{15\,e^5}-\frac{{\left(d+e\,x\right)}^{9/2}\,\left(4\,b^2\,d\,e^2-12\,b\,c\,d^2\,e+8\,c^2\,d^3\right)}{9\,e^5}+\frac{{\left(d+e\,x\right)}^{11/2}\,\left(2\,b^2\,e^2-12\,b\,c\,d\,e+12\,c^2\,d^2\right)}{11\,e^5}-\frac{\left(8\,c^2\,d-4\,b\,c\,e\right)\,{\left(d+e\,x\right)}^{13/2}}{13\,e^5}+\frac{2\,d^2\,{\left(b\,e-c\,d\right)}^2\,{\left(d+e\,x\right)}^{7/2}}{7\,e^5}","Not used",1,"(2*c^2*(d + e*x)^(15/2))/(15*e^5) - ((d + e*x)^(9/2)*(8*c^2*d^3 + 4*b^2*d*e^2 - 12*b*c*d^2*e))/(9*e^5) + ((d + e*x)^(11/2)*(2*b^2*e^2 + 12*c^2*d^2 - 12*b*c*d*e))/(11*e^5) - ((8*c^2*d - 4*b*c*e)*(d + e*x)^(13/2))/(13*e^5) + (2*d^2*(b*e - c*d)^2*(d + e*x)^(7/2))/(7*e^5)","B"
347,1,138,147,0.042564,"\text{Not used}","int((b*x + c*x^2)^2*(d + e*x)^(3/2),x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{13/2}}{13\,e^5}-\frac{{\left(d+e\,x\right)}^{7/2}\,\left(4\,b^2\,d\,e^2-12\,b\,c\,d^2\,e+8\,c^2\,d^3\right)}{7\,e^5}+\frac{{\left(d+e\,x\right)}^{9/2}\,\left(2\,b^2\,e^2-12\,b\,c\,d\,e+12\,c^2\,d^2\right)}{9\,e^5}-\frac{\left(8\,c^2\,d-4\,b\,c\,e\right)\,{\left(d+e\,x\right)}^{11/2}}{11\,e^5}+\frac{2\,d^2\,{\left(b\,e-c\,d\right)}^2\,{\left(d+e\,x\right)}^{5/2}}{5\,e^5}","Not used",1,"(2*c^2*(d + e*x)^(13/2))/(13*e^5) - ((d + e*x)^(7/2)*(8*c^2*d^3 + 4*b^2*d*e^2 - 12*b*c*d^2*e))/(7*e^5) + ((d + e*x)^(9/2)*(2*b^2*e^2 + 12*c^2*d^2 - 12*b*c*d*e))/(9*e^5) - ((8*c^2*d - 4*b*c*e)*(d + e*x)^(11/2))/(11*e^5) + (2*d^2*(b*e - c*d)^2*(d + e*x)^(5/2))/(5*e^5)","B"
348,1,138,147,0.044388,"\text{Not used}","int((b*x + c*x^2)^2*(d + e*x)^(1/2),x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{11/2}}{11\,e^5}-\frac{{\left(d+e\,x\right)}^{5/2}\,\left(4\,b^2\,d\,e^2-12\,b\,c\,d^2\,e+8\,c^2\,d^3\right)}{5\,e^5}+\frac{{\left(d+e\,x\right)}^{7/2}\,\left(2\,b^2\,e^2-12\,b\,c\,d\,e+12\,c^2\,d^2\right)}{7\,e^5}-\frac{\left(8\,c^2\,d-4\,b\,c\,e\right)\,{\left(d+e\,x\right)}^{9/2}}{9\,e^5}+\frac{2\,d^2\,{\left(b\,e-c\,d\right)}^2\,{\left(d+e\,x\right)}^{3/2}}{3\,e^5}","Not used",1,"(2*c^2*(d + e*x)^(11/2))/(11*e^5) - ((d + e*x)^(5/2)*(8*c^2*d^3 + 4*b^2*d*e^2 - 12*b*c*d^2*e))/(5*e^5) + ((d + e*x)^(7/2)*(2*b^2*e^2 + 12*c^2*d^2 - 12*b*c*d*e))/(7*e^5) - ((8*c^2*d - 4*b*c*e)*(d + e*x)^(9/2))/(9*e^5) + (2*d^2*(b*e - c*d)^2*(d + e*x)^(3/2))/(3*e^5)","B"
349,1,138,145,0.039970,"\text{Not used}","int((b*x + c*x^2)^2/(d + e*x)^(1/2),x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{9/2}}{9\,e^5}-\frac{{\left(d+e\,x\right)}^{3/2}\,\left(4\,b^2\,d\,e^2-12\,b\,c\,d^2\,e+8\,c^2\,d^3\right)}{3\,e^5}+\frac{{\left(d+e\,x\right)}^{5/2}\,\left(2\,b^2\,e^2-12\,b\,c\,d\,e+12\,c^2\,d^2\right)}{5\,e^5}-\frac{\left(8\,c^2\,d-4\,b\,c\,e\right)\,{\left(d+e\,x\right)}^{7/2}}{7\,e^5}+\frac{2\,d^2\,{\left(b\,e-c\,d\right)}^2\,\sqrt{d+e\,x}}{e^5}","Not used",1,"(2*c^2*(d + e*x)^(9/2))/(9*e^5) - ((d + e*x)^(3/2)*(8*c^2*d^3 + 4*b^2*d*e^2 - 12*b*c*d^2*e))/(3*e^5) + ((d + e*x)^(5/2)*(2*b^2*e^2 + 12*c^2*d^2 - 12*b*c*d*e))/(5*e^5) - ((8*c^2*d - 4*b*c*e)*(d + e*x)^(7/2))/(7*e^5) + (2*d^2*(b*e - c*d)^2*(d + e*x)^(1/2))/e^5","B"
350,1,153,143,0.190774,"\text{Not used}","int((b*x + c*x^2)^2/(d + e*x)^(3/2),x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{7/2}}{7\,e^5}-\frac{\sqrt{d+e\,x}\,\left(4\,b^2\,d\,e^2-12\,b\,c\,d^2\,e+8\,c^2\,d^3\right)}{e^5}+\frac{{\left(d+e\,x\right)}^{3/2}\,\left(2\,b^2\,e^2-12\,b\,c\,d\,e+12\,c^2\,d^2\right)}{3\,e^5}-\frac{2\,b^2\,d^2\,e^2-4\,b\,c\,d^3\,e+2\,c^2\,d^4}{e^5\,\sqrt{d+e\,x}}-\frac{\left(8\,c^2\,d-4\,b\,c\,e\right)\,{\left(d+e\,x\right)}^{5/2}}{5\,e^5}","Not used",1,"(2*c^2*(d + e*x)^(7/2))/(7*e^5) - ((d + e*x)^(1/2)*(8*c^2*d^3 + 4*b^2*d*e^2 - 12*b*c*d^2*e))/e^5 + ((d + e*x)^(3/2)*(2*b^2*e^2 + 12*c^2*d^2 - 12*b*c*d*e))/(3*e^5) - (2*c^2*d^4 + 2*b^2*d^2*e^2 - 4*b*c*d^3*e)/(e^5*(d + e*x)^(1/2)) - ((8*c^2*d - 4*b*c*e)*(d + e*x)^(5/2))/(5*e^5)","B"
351,1,145,143,0.075827,"\text{Not used}","int((b*x + c*x^2)^2/(d + e*x)^(5/2),x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{5/2}}{5\,e^5}+\frac{\sqrt{d+e\,x}\,\left(2\,b^2\,e^2-12\,b\,c\,d\,e+12\,c^2\,d^2\right)}{e^5}-\frac{\left(8\,c^2\,d-4\,b\,c\,e\right)\,{\left(d+e\,x\right)}^{3/2}}{3\,e^5}+\frac{\left(d+e\,x\right)\,\left(4\,b^2\,d\,e^2-12\,b\,c\,d^2\,e+8\,c^2\,d^3\right)-\frac{2\,c^2\,d^4}{3}-\frac{2\,b^2\,d^2\,e^2}{3}+\frac{4\,b\,c\,d^3\,e}{3}}{e^5\,{\left(d+e\,x\right)}^{3/2}}","Not used",1,"(2*c^2*(d + e*x)^(5/2))/(5*e^5) + ((d + e*x)^(1/2)*(2*b^2*e^2 + 12*c^2*d^2 - 12*b*c*d*e))/e^5 - ((8*c^2*d - 4*b*c*e)*(d + e*x)^(3/2))/(3*e^5) + ((d + e*x)*(8*c^2*d^3 + 4*b^2*d*e^2 - 12*b*c*d^2*e) - (2*c^2*d^4)/3 - (2*b^2*d^2*e^2)/3 + (4*b*c*d^3*e)/3)/(e^5*(d + e*x)^(3/2))","B"
352,1,140,143,0.238317,"\text{Not used}","int((b*x + c*x^2)^2/(d + e*x)^(7/2),x)","-\frac{2\,\left(8\,b^2\,d^2\,e^2+20\,b^2\,d\,e^3\,x+15\,b^2\,e^4\,x^2-96\,b\,c\,d^3\,e-240\,b\,c\,d^2\,e^2\,x-180\,b\,c\,d\,e^3\,x^2-30\,b\,c\,e^4\,x^3+128\,c^2\,d^4+320\,c^2\,d^3\,e\,x+240\,c^2\,d^2\,e^2\,x^2+40\,c^2\,d\,e^3\,x^3-5\,c^2\,e^4\,x^4\right)}{15\,e^5\,{\left(d+e\,x\right)}^{5/2}}","Not used",1,"-(2*(128*c^2*d^4 + 8*b^2*d^2*e^2 + 15*b^2*e^4*x^2 - 5*c^2*e^4*x^4 + 40*c^2*d*e^3*x^3 - 96*b*c*d^3*e + 240*c^2*d^2*e^2*x^2 - 30*b*c*e^4*x^3 + 20*b^2*d*e^3*x + 320*c^2*d^3*e*x - 240*b*c*d^2*e^2*x - 180*b*c*d*e^3*x^2))/(15*e^5*(d + e*x)^(5/2))","B"
353,1,239,248,0.232011,"\text{Not used}","int((b*x + c*x^2)^3*(d + e*x)^(7/2),x)","\frac{{\left(d+e\,x\right)}^{15/2}\,\left(2\,b^3\,e^3-24\,b^2\,c\,d\,e^2+60\,b\,c^2\,d^2\,e-40\,c^3\,d^3\right)}{15\,e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{21/2}}{21\,e^7}-\frac{\left(12\,c^3\,d-6\,b\,c^2\,e\right)\,{\left(d+e\,x\right)}^{19/2}}{19\,e^7}+\frac{{\left(d+e\,x\right)}^{17/2}\,\left(6\,b^2\,c\,e^2-30\,b\,c^2\,d\,e+30\,c^3\,d^2\right)}{17\,e^7}+\frac{{\left(d+e\,x\right)}^{13/2}\,\left(-6\,b^3\,d\,e^3+36\,b^2\,c\,d^2\,e^2-60\,b\,c^2\,d^3\,e+30\,c^3\,d^4\right)}{13\,e^7}-\frac{2\,d^3\,{\left(b\,e-c\,d\right)}^3\,{\left(d+e\,x\right)}^{9/2}}{9\,e^7}+\frac{6\,d^2\,{\left(b\,e-c\,d\right)}^2\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{11/2}}{11\,e^7}","Not used",1,"((d + e*x)^(15/2)*(2*b^3*e^3 - 40*c^3*d^3 + 60*b*c^2*d^2*e - 24*b^2*c*d*e^2))/(15*e^7) + (2*c^3*(d + e*x)^(21/2))/(21*e^7) - ((12*c^3*d - 6*b*c^2*e)*(d + e*x)^(19/2))/(19*e^7) + ((d + e*x)^(17/2)*(30*c^3*d^2 + 6*b^2*c*e^2 - 30*b*c^2*d*e))/(17*e^7) + ((d + e*x)^(13/2)*(30*c^3*d^4 - 6*b^3*d*e^3 + 36*b^2*c*d^2*e^2 - 60*b*c^2*d^3*e))/(13*e^7) - (2*d^3*(b*e - c*d)^3*(d + e*x)^(9/2))/(9*e^7) + (6*d^2*(b*e - c*d)^2*(b*e - 2*c*d)*(d + e*x)^(11/2))/(11*e^7)","B"
354,1,239,248,0.204881,"\text{Not used}","int((b*x + c*x^2)^3*(d + e*x)^(5/2),x)","\frac{{\left(d+e\,x\right)}^{13/2}\,\left(2\,b^3\,e^3-24\,b^2\,c\,d\,e^2+60\,b\,c^2\,d^2\,e-40\,c^3\,d^3\right)}{13\,e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{19/2}}{19\,e^7}-\frac{\left(12\,c^3\,d-6\,b\,c^2\,e\right)\,{\left(d+e\,x\right)}^{17/2}}{17\,e^7}+\frac{{\left(d+e\,x\right)}^{15/2}\,\left(6\,b^2\,c\,e^2-30\,b\,c^2\,d\,e+30\,c^3\,d^2\right)}{15\,e^7}+\frac{{\left(d+e\,x\right)}^{11/2}\,\left(-6\,b^3\,d\,e^3+36\,b^2\,c\,d^2\,e^2-60\,b\,c^2\,d^3\,e+30\,c^3\,d^4\right)}{11\,e^7}-\frac{2\,d^3\,{\left(b\,e-c\,d\right)}^3\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}+\frac{2\,d^2\,{\left(b\,e-c\,d\right)}^2\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{9/2}}{3\,e^7}","Not used",1,"((d + e*x)^(13/2)*(2*b^3*e^3 - 40*c^3*d^3 + 60*b*c^2*d^2*e - 24*b^2*c*d*e^2))/(13*e^7) + (2*c^3*(d + e*x)^(19/2))/(19*e^7) - ((12*c^3*d - 6*b*c^2*e)*(d + e*x)^(17/2))/(17*e^7) + ((d + e*x)^(15/2)*(30*c^3*d^2 + 6*b^2*c*e^2 - 30*b*c^2*d*e))/(15*e^7) + ((d + e*x)^(11/2)*(30*c^3*d^4 - 6*b^3*d*e^3 + 36*b^2*c*d^2*e^2 - 60*b*c^2*d^3*e))/(11*e^7) - (2*d^3*(b*e - c*d)^3*(d + e*x)^(7/2))/(7*e^7) + (2*d^2*(b*e - c*d)^2*(b*e - 2*c*d)*(d + e*x)^(9/2))/(3*e^7)","B"
355,1,239,248,0.205497,"\text{Not used}","int((b*x + c*x^2)^3*(d + e*x)^(3/2),x)","\frac{{\left(d+e\,x\right)}^{11/2}\,\left(2\,b^3\,e^3-24\,b^2\,c\,d\,e^2+60\,b\,c^2\,d^2\,e-40\,c^3\,d^3\right)}{11\,e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{17/2}}{17\,e^7}-\frac{\left(12\,c^3\,d-6\,b\,c^2\,e\right)\,{\left(d+e\,x\right)}^{15/2}}{15\,e^7}+\frac{{\left(d+e\,x\right)}^{13/2}\,\left(6\,b^2\,c\,e^2-30\,b\,c^2\,d\,e+30\,c^3\,d^2\right)}{13\,e^7}+\frac{{\left(d+e\,x\right)}^{9/2}\,\left(-6\,b^3\,d\,e^3+36\,b^2\,c\,d^2\,e^2-60\,b\,c^2\,d^3\,e+30\,c^3\,d^4\right)}{9\,e^7}-\frac{2\,d^3\,{\left(b\,e-c\,d\right)}^3\,{\left(d+e\,x\right)}^{5/2}}{5\,e^7}+\frac{6\,d^2\,{\left(b\,e-c\,d\right)}^2\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}","Not used",1,"((d + e*x)^(11/2)*(2*b^3*e^3 - 40*c^3*d^3 + 60*b*c^2*d^2*e - 24*b^2*c*d*e^2))/(11*e^7) + (2*c^3*(d + e*x)^(17/2))/(17*e^7) - ((12*c^3*d - 6*b*c^2*e)*(d + e*x)^(15/2))/(15*e^7) + ((d + e*x)^(13/2)*(30*c^3*d^2 + 6*b^2*c*e^2 - 30*b*c^2*d*e))/(13*e^7) + ((d + e*x)^(9/2)*(30*c^3*d^4 - 6*b^3*d*e^3 + 36*b^2*c*d^2*e^2 - 60*b*c^2*d^3*e))/(9*e^7) - (2*d^3*(b*e - c*d)^3*(d + e*x)^(5/2))/(5*e^7) + (6*d^2*(b*e - c*d)^2*(b*e - 2*c*d)*(d + e*x)^(7/2))/(7*e^7)","B"
356,1,239,248,0.207864,"\text{Not used}","int((b*x + c*x^2)^3*(d + e*x)^(1/2),x)","\frac{{\left(d+e\,x\right)}^{9/2}\,\left(2\,b^3\,e^3-24\,b^2\,c\,d\,e^2+60\,b\,c^2\,d^2\,e-40\,c^3\,d^3\right)}{9\,e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{15/2}}{15\,e^7}-\frac{\left(12\,c^3\,d-6\,b\,c^2\,e\right)\,{\left(d+e\,x\right)}^{13/2}}{13\,e^7}+\frac{{\left(d+e\,x\right)}^{11/2}\,\left(6\,b^2\,c\,e^2-30\,b\,c^2\,d\,e+30\,c^3\,d^2\right)}{11\,e^7}+\frac{{\left(d+e\,x\right)}^{7/2}\,\left(-6\,b^3\,d\,e^3+36\,b^2\,c\,d^2\,e^2-60\,b\,c^2\,d^3\,e+30\,c^3\,d^4\right)}{7\,e^7}-\frac{2\,d^3\,{\left(b\,e-c\,d\right)}^3\,{\left(d+e\,x\right)}^{3/2}}{3\,e^7}+\frac{6\,d^2\,{\left(b\,e-c\,d\right)}^2\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{5/2}}{5\,e^7}","Not used",1,"((d + e*x)^(9/2)*(2*b^3*e^3 - 40*c^3*d^3 + 60*b*c^2*d^2*e - 24*b^2*c*d*e^2))/(9*e^7) + (2*c^3*(d + e*x)^(15/2))/(15*e^7) - ((12*c^3*d - 6*b*c^2*e)*(d + e*x)^(13/2))/(13*e^7) + ((d + e*x)^(11/2)*(30*c^3*d^2 + 6*b^2*c*e^2 - 30*b*c^2*d*e))/(11*e^7) + ((d + e*x)^(7/2)*(30*c^3*d^4 - 6*b^3*d*e^3 + 36*b^2*c*d^2*e^2 - 60*b*c^2*d^3*e))/(7*e^7) - (2*d^3*(b*e - c*d)^3*(d + e*x)^(3/2))/(3*e^7) + (6*d^2*(b*e - c*d)^2*(b*e - 2*c*d)*(d + e*x)^(5/2))/(5*e^7)","B"
357,1,239,244,0.058886,"\text{Not used}","int((b*x + c*x^2)^3/(d + e*x)^(1/2),x)","\frac{{\left(d+e\,x\right)}^{7/2}\,\left(2\,b^3\,e^3-24\,b^2\,c\,d\,e^2+60\,b\,c^2\,d^2\,e-40\,c^3\,d^3\right)}{7\,e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{13/2}}{13\,e^7}-\frac{\left(12\,c^3\,d-6\,b\,c^2\,e\right)\,{\left(d+e\,x\right)}^{11/2}}{11\,e^7}+\frac{{\left(d+e\,x\right)}^{9/2}\,\left(6\,b^2\,c\,e^2-30\,b\,c^2\,d\,e+30\,c^3\,d^2\right)}{9\,e^7}+\frac{{\left(d+e\,x\right)}^{5/2}\,\left(-6\,b^3\,d\,e^3+36\,b^2\,c\,d^2\,e^2-60\,b\,c^2\,d^3\,e+30\,c^3\,d^4\right)}{5\,e^7}-\frac{2\,d^3\,{\left(b\,e-c\,d\right)}^3\,\sqrt{d+e\,x}}{e^7}+\frac{2\,d^2\,{\left(b\,e-c\,d\right)}^2\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{3/2}}{e^7}","Not used",1,"((d + e*x)^(7/2)*(2*b^3*e^3 - 40*c^3*d^3 + 60*b*c^2*d^2*e - 24*b^2*c*d*e^2))/(7*e^7) + (2*c^3*(d + e*x)^(13/2))/(13*e^7) - ((12*c^3*d - 6*b*c^2*e)*(d + e*x)^(11/2))/(11*e^7) + ((d + e*x)^(9/2)*(30*c^3*d^2 + 6*b^2*c*e^2 - 30*b*c^2*d*e))/(9*e^7) + ((d + e*x)^(5/2)*(30*c^3*d^4 - 6*b^3*d*e^3 + 36*b^2*c*d^2*e^2 - 60*b*c^2*d^3*e))/(5*e^7) - (2*d^3*(b*e - c*d)^3*(d + e*x)^(1/2))/e^7 + (2*d^2*(b*e - c*d)^2*(b*e - 2*c*d)*(d + e*x)^(3/2))/e^7","B"
358,1,268,242,0.209486,"\text{Not used}","int((b*x + c*x^2)^3/(d + e*x)^(3/2),x)","\frac{{\left(d+e\,x\right)}^{5/2}\,\left(2\,b^3\,e^3-24\,b^2\,c\,d\,e^2+60\,b\,c^2\,d^2\,e-40\,c^3\,d^3\right)}{5\,e^7}-\frac{-2\,b^3\,d^3\,e^3+6\,b^2\,c\,d^4\,e^2-6\,b\,c^2\,d^5\,e+2\,c^3\,d^6}{e^7\,\sqrt{d+e\,x}}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{11/2}}{11\,e^7}-\frac{\left(12\,c^3\,d-6\,b\,c^2\,e\right)\,{\left(d+e\,x\right)}^{9/2}}{9\,e^7}+\frac{{\left(d+e\,x\right)}^{7/2}\,\left(6\,b^2\,c\,e^2-30\,b\,c^2\,d\,e+30\,c^3\,d^2\right)}{7\,e^7}+\frac{{\left(d+e\,x\right)}^{3/2}\,\left(-6\,b^3\,d\,e^3+36\,b^2\,c\,d^2\,e^2-60\,b\,c^2\,d^3\,e+30\,c^3\,d^4\right)}{3\,e^7}+\frac{6\,d^2\,{\left(b\,e-c\,d\right)}^2\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}}{e^7}","Not used",1,"((d + e*x)^(5/2)*(2*b^3*e^3 - 40*c^3*d^3 + 60*b*c^2*d^2*e - 24*b^2*c*d*e^2))/(5*e^7) - (2*c^3*d^6 - 2*b^3*d^3*e^3 + 6*b^2*c*d^4*e^2 - 6*b*c^2*d^5*e)/(e^7*(d + e*x)^(1/2)) + (2*c^3*(d + e*x)^(11/2))/(11*e^7) - ((12*c^3*d - 6*b*c^2*e)*(d + e*x)^(9/2))/(9*e^7) + ((d + e*x)^(7/2)*(30*c^3*d^2 + 6*b^2*c*e^2 - 30*b*c^2*d*e))/(7*e^7) + ((d + e*x)^(3/2)*(30*c^3*d^4 - 6*b^3*d*e^3 + 36*b^2*c*d^2*e^2 - 60*b*c^2*d^3*e))/(3*e^7) + (6*d^2*(b*e - c*d)^2*(b*e - 2*c*d)*(d + e*x)^(1/2))/e^7","B"
359,1,281,244,0.069056,"\text{Not used}","int((b*x + c*x^2)^3/(d + e*x)^(5/2),x)","\frac{{\left(d+e\,x\right)}^{3/2}\,\left(2\,b^3\,e^3-24\,b^2\,c\,d\,e^2+60\,b\,c^2\,d^2\,e-40\,c^3\,d^3\right)}{3\,e^7}+\frac{\left(d+e\,x\right)\,\left(-6\,b^3\,d^2\,e^3+24\,b^2\,c\,d^3\,e^2-30\,b\,c^2\,d^4\,e+12\,c^3\,d^5\right)-\frac{2\,c^3\,d^6}{3}+\frac{2\,b^3\,d^3\,e^3}{3}-2\,b^2\,c\,d^4\,e^2+2\,b\,c^2\,d^5\,e}{e^7\,{\left(d+e\,x\right)}^{3/2}}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{9/2}}{9\,e^7}-\frac{\left(12\,c^3\,d-6\,b\,c^2\,e\right)\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}+\frac{{\left(d+e\,x\right)}^{5/2}\,\left(6\,b^2\,c\,e^2-30\,b\,c^2\,d\,e+30\,c^3\,d^2\right)}{5\,e^7}+\frac{\sqrt{d+e\,x}\,\left(-6\,b^3\,d\,e^3+36\,b^2\,c\,d^2\,e^2-60\,b\,c^2\,d^3\,e+30\,c^3\,d^4\right)}{e^7}","Not used",1,"((d + e*x)^(3/2)*(2*b^3*e^3 - 40*c^3*d^3 + 60*b*c^2*d^2*e - 24*b^2*c*d*e^2))/(3*e^7) + ((d + e*x)*(12*c^3*d^5 - 6*b^3*d^2*e^3 + 24*b^2*c*d^3*e^2 - 30*b*c^2*d^4*e) - (2*c^3*d^6)/3 + (2*b^3*d^3*e^3)/3 - 2*b^2*c*d^4*e^2 + 2*b*c^2*d^5*e)/(e^7*(d + e*x)^(3/2)) + (2*c^3*(d + e*x)^(9/2))/(9*e^7) - ((12*c^3*d - 6*b*c^2*e)*(d + e*x)^(7/2))/(7*e^7) + ((d + e*x)^(5/2)*(30*c^3*d^2 + 6*b^2*c*e^2 - 30*b*c^2*d*e))/(5*e^7) + ((d + e*x)^(1/2)*(30*c^3*d^4 - 6*b^3*d*e^3 + 36*b^2*c*d^2*e^2 - 60*b*c^2*d^3*e))/e^7","B"
360,1,278,240,0.075307,"\text{Not used}","int((b*x + c*x^2)^3/(d + e*x)^(7/2),x)","\frac{\sqrt{d+e\,x}\,\left(2\,b^3\,e^3-24\,b^2\,c\,d\,e^2+60\,b\,c^2\,d^2\,e-40\,c^3\,d^3\right)}{e^7}+\frac{\left(d+e\,x\right)\,\left(-2\,b^3\,d^2\,e^3+8\,b^2\,c\,d^3\,e^2-10\,b\,c^2\,d^4\,e+4\,c^3\,d^5\right)-{\left(d+e\,x\right)}^2\,\left(-6\,b^3\,d\,e^3+36\,b^2\,c\,d^2\,e^2-60\,b\,c^2\,d^3\,e+30\,c^3\,d^4\right)-\frac{2\,c^3\,d^6}{5}+\frac{2\,b^3\,d^3\,e^3}{5}-\frac{6\,b^2\,c\,d^4\,e^2}{5}+\frac{6\,b\,c^2\,d^5\,e}{5}}{e^7\,{\left(d+e\,x\right)}^{5/2}}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}-\frac{\left(12\,c^3\,d-6\,b\,c^2\,e\right)\,{\left(d+e\,x\right)}^{5/2}}{5\,e^7}+\frac{{\left(d+e\,x\right)}^{3/2}\,\left(6\,b^2\,c\,e^2-30\,b\,c^2\,d\,e+30\,c^3\,d^2\right)}{3\,e^7}","Not used",1,"((d + e*x)^(1/2)*(2*b^3*e^3 - 40*c^3*d^3 + 60*b*c^2*d^2*e - 24*b^2*c*d*e^2))/e^7 + ((d + e*x)*(4*c^3*d^5 - 2*b^3*d^2*e^3 + 8*b^2*c*d^3*e^2 - 10*b*c^2*d^4*e) - (d + e*x)^2*(30*c^3*d^4 - 6*b^3*d*e^3 + 36*b^2*c*d^2*e^2 - 60*b*c^2*d^3*e) - (2*c^3*d^6)/5 + (2*b^3*d^3*e^3)/5 - (6*b^2*c*d^4*e^2)/5 + (6*b*c^2*d^5*e)/5)/(e^7*(d + e*x)^(5/2)) + (2*c^3*(d + e*x)^(7/2))/(7*e^7) - ((12*c^3*d - 6*b*c^2*e)*(d + e*x)^(5/2))/(5*e^7) + ((d + e*x)^(3/2)*(30*c^3*d^2 + 6*b^2*c*e^2 - 30*b*c^2*d*e))/(3*e^7)","B"
361,1,2482,157,0.587645,"\text{Not used}","int((d + e*x)^(7/2)/(b*x + c*x^2),x)","\left(\frac{2\,e\,{\left(b\,e-2\,c\,d\right)}^2}{c^3}-\frac{2\,e\,\left(c\,d^2-b\,d\,e\right)}{c^2}\right)\,\sqrt{d+e\,x}+\frac{2\,e\,{\left(d+e\,x\right)}^{5/2}}{5\,c}-\frac{2\,e\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{3/2}}{3\,c^2}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\sqrt{d+e\,x}\,\left(b^8\,e^{10}-8\,b^7\,c\,d\,e^9+28\,b^6\,c^2\,d^2\,e^8-56\,b^5\,c^3\,d^3\,e^7+70\,b^4\,c^4\,d^4\,e^6-56\,b^3\,c^5\,d^5\,e^5+28\,b^2\,c^6\,d^6\,e^4-8\,b\,c^7\,d^7\,e^3+2\,c^8\,d^8\,e^2\right)}{c^5}+\frac{\left(\frac{8\,\left(b^5\,c^4\,d\,e^6-4\,b^4\,c^5\,d^2\,e^5+6\,b^3\,c^6\,d^3\,e^4-3\,b^2\,c^7\,d^4\,e^3\right)}{c^5}+\frac{8\,\left(b^3\,c^7\,e^3-2\,b^2\,c^8\,d\,e^2\right)\,\sqrt{d^7}\,\sqrt{d+e\,x}}{b\,c^5}\right)\,\sqrt{d^7}}{b}\right)\,\sqrt{d^7}\,1{}\mathrm{i}}{b}+\frac{\left(\frac{8\,\sqrt{d+e\,x}\,\left(b^8\,e^{10}-8\,b^7\,c\,d\,e^9+28\,b^6\,c^2\,d^2\,e^8-56\,b^5\,c^3\,d^3\,e^7+70\,b^4\,c^4\,d^4\,e^6-56\,b^3\,c^5\,d^5\,e^5+28\,b^2\,c^6\,d^6\,e^4-8\,b\,c^7\,d^7\,e^3+2\,c^8\,d^8\,e^2\right)}{c^5}-\frac{\left(\frac{8\,\left(b^5\,c^4\,d\,e^6-4\,b^4\,c^5\,d^2\,e^5+6\,b^3\,c^6\,d^3\,e^4-3\,b^2\,c^7\,d^4\,e^3\right)}{c^5}-\frac{8\,\left(b^3\,c^7\,e^3-2\,b^2\,c^8\,d\,e^2\right)\,\sqrt{d^7}\,\sqrt{d+e\,x}}{b\,c^5}\right)\,\sqrt{d^7}}{b}\right)\,\sqrt{d^7}\,1{}\mathrm{i}}{b}}{\frac{16\,\left(b^7\,d^4\,e^{10}-8\,b^6\,c\,d^5\,e^9+28\,b^5\,c^2\,d^6\,e^8-56\,b^4\,c^3\,d^7\,e^7+69\,b^3\,c^4\,d^8\,e^6-52\,b^2\,c^5\,d^9\,e^5+22\,b\,c^6\,d^{10}\,e^4-4\,c^7\,d^{11}\,e^3\right)}{c^5}+\frac{\left(\frac{8\,\sqrt{d+e\,x}\,\left(b^8\,e^{10}-8\,b^7\,c\,d\,e^9+28\,b^6\,c^2\,d^2\,e^8-56\,b^5\,c^3\,d^3\,e^7+70\,b^4\,c^4\,d^4\,e^6-56\,b^3\,c^5\,d^5\,e^5+28\,b^2\,c^6\,d^6\,e^4-8\,b\,c^7\,d^7\,e^3+2\,c^8\,d^8\,e^2\right)}{c^5}+\frac{\left(\frac{8\,\left(b^5\,c^4\,d\,e^6-4\,b^4\,c^5\,d^2\,e^5+6\,b^3\,c^6\,d^3\,e^4-3\,b^2\,c^7\,d^4\,e^3\right)}{c^5}+\frac{8\,\left(b^3\,c^7\,e^3-2\,b^2\,c^8\,d\,e^2\right)\,\sqrt{d^7}\,\sqrt{d+e\,x}}{b\,c^5}\right)\,\sqrt{d^7}}{b}\right)\,\sqrt{d^7}}{b}-\frac{\left(\frac{8\,\sqrt{d+e\,x}\,\left(b^8\,e^{10}-8\,b^7\,c\,d\,e^9+28\,b^6\,c^2\,d^2\,e^8-56\,b^5\,c^3\,d^3\,e^7+70\,b^4\,c^4\,d^4\,e^6-56\,b^3\,c^5\,d^5\,e^5+28\,b^2\,c^6\,d^6\,e^4-8\,b\,c^7\,d^7\,e^3+2\,c^8\,d^8\,e^2\right)}{c^5}-\frac{\left(\frac{8\,\left(b^5\,c^4\,d\,e^6-4\,b^4\,c^5\,d^2\,e^5+6\,b^3\,c^6\,d^3\,e^4-3\,b^2\,c^7\,d^4\,e^3\right)}{c^5}-\frac{8\,\left(b^3\,c^7\,e^3-2\,b^2\,c^8\,d\,e^2\right)\,\sqrt{d^7}\,\sqrt{d+e\,x}}{b\,c^5}\right)\,\sqrt{d^7}}{b}\right)\,\sqrt{d^7}}{b}}\right)\,\sqrt{d^7}\,2{}\mathrm{i}}{b}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\sqrt{d+e\,x}\,\left(b^8\,e^{10}-8\,b^7\,c\,d\,e^9+28\,b^6\,c^2\,d^2\,e^8-56\,b^5\,c^3\,d^3\,e^7+70\,b^4\,c^4\,d^4\,e^6-56\,b^3\,c^5\,d^5\,e^5+28\,b^2\,c^6\,d^6\,e^4-8\,b\,c^7\,d^7\,e^3+2\,c^8\,d^8\,e^2\right)}{c^5}+\frac{\left(\frac{8\,\left(b^5\,c^4\,d\,e^6-4\,b^4\,c^5\,d^2\,e^5+6\,b^3\,c^6\,d^3\,e^4-3\,b^2\,c^7\,d^4\,e^3\right)}{c^5}+\frac{8\,\left(b^3\,c^7\,e^3-2\,b^2\,c^8\,d\,e^2\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\sqrt{d+e\,x}}{b\,c^{12}}\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}}{b\,c^7}\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,1{}\mathrm{i}}{b\,c^7}+\frac{\left(\frac{8\,\sqrt{d+e\,x}\,\left(b^8\,e^{10}-8\,b^7\,c\,d\,e^9+28\,b^6\,c^2\,d^2\,e^8-56\,b^5\,c^3\,d^3\,e^7+70\,b^4\,c^4\,d^4\,e^6-56\,b^3\,c^5\,d^5\,e^5+28\,b^2\,c^6\,d^6\,e^4-8\,b\,c^7\,d^7\,e^3+2\,c^8\,d^8\,e^2\right)}{c^5}-\frac{\left(\frac{8\,\left(b^5\,c^4\,d\,e^6-4\,b^4\,c^5\,d^2\,e^5+6\,b^3\,c^6\,d^3\,e^4-3\,b^2\,c^7\,d^4\,e^3\right)}{c^5}-\frac{8\,\left(b^3\,c^7\,e^3-2\,b^2\,c^8\,d\,e^2\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\sqrt{d+e\,x}}{b\,c^{12}}\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}}{b\,c^7}\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,1{}\mathrm{i}}{b\,c^7}}{\frac{16\,\left(b^7\,d^4\,e^{10}-8\,b^6\,c\,d^5\,e^9+28\,b^5\,c^2\,d^6\,e^8-56\,b^4\,c^3\,d^7\,e^7+69\,b^3\,c^4\,d^8\,e^6-52\,b^2\,c^5\,d^9\,e^5+22\,b\,c^6\,d^{10}\,e^4-4\,c^7\,d^{11}\,e^3\right)}{c^5}+\frac{\left(\frac{8\,\sqrt{d+e\,x}\,\left(b^8\,e^{10}-8\,b^7\,c\,d\,e^9+28\,b^6\,c^2\,d^2\,e^8-56\,b^5\,c^3\,d^3\,e^7+70\,b^4\,c^4\,d^4\,e^6-56\,b^3\,c^5\,d^5\,e^5+28\,b^2\,c^6\,d^6\,e^4-8\,b\,c^7\,d^7\,e^3+2\,c^8\,d^8\,e^2\right)}{c^5}+\frac{\left(\frac{8\,\left(b^5\,c^4\,d\,e^6-4\,b^4\,c^5\,d^2\,e^5+6\,b^3\,c^6\,d^3\,e^4-3\,b^2\,c^7\,d^4\,e^3\right)}{c^5}+\frac{8\,\left(b^3\,c^7\,e^3-2\,b^2\,c^8\,d\,e^2\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\sqrt{d+e\,x}}{b\,c^{12}}\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}}{b\,c^7}\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}}{b\,c^7}-\frac{\left(\frac{8\,\sqrt{d+e\,x}\,\left(b^8\,e^{10}-8\,b^7\,c\,d\,e^9+28\,b^6\,c^2\,d^2\,e^8-56\,b^5\,c^3\,d^3\,e^7+70\,b^4\,c^4\,d^4\,e^6-56\,b^3\,c^5\,d^5\,e^5+28\,b^2\,c^6\,d^6\,e^4-8\,b\,c^7\,d^7\,e^3+2\,c^8\,d^8\,e^2\right)}{c^5}-\frac{\left(\frac{8\,\left(b^5\,c^4\,d\,e^6-4\,b^4\,c^5\,d^2\,e^5+6\,b^3\,c^6\,d^3\,e^4-3\,b^2\,c^7\,d^4\,e^3\right)}{c^5}-\frac{8\,\left(b^3\,c^7\,e^3-2\,b^2\,c^8\,d\,e^2\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\sqrt{d+e\,x}}{b\,c^{12}}\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}}{b\,c^7}\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}}{b\,c^7}}\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,2{}\mathrm{i}}{b\,c^7}","Not used",1,"((2*e*(b*e - 2*c*d)^2)/c^3 - (2*e*(c*d^2 - b*d*e))/c^2)*(d + e*x)^(1/2) + (2*e*(d + e*x)^(5/2))/(5*c) + (atan(((((8*(d + e*x)^(1/2)*(b^8*e^10 + 2*c^8*d^8*e^2 - 8*b*c^7*d^7*e^3 + 28*b^2*c^6*d^6*e^4 - 56*b^3*c^5*d^5*e^5 + 70*b^4*c^4*d^4*e^6 - 56*b^5*c^3*d^3*e^7 + 28*b^6*c^2*d^2*e^8 - 8*b^7*c*d*e^9))/c^5 + (((8*(b^5*c^4*d*e^6 - 3*b^2*c^7*d^4*e^3 + 6*b^3*c^6*d^3*e^4 - 4*b^4*c^5*d^2*e^5))/c^5 + (8*(b^3*c^7*e^3 - 2*b^2*c^8*d*e^2)*(d^7)^(1/2)*(d + e*x)^(1/2))/(b*c^5))*(d^7)^(1/2))/b)*(d^7)^(1/2)*1i)/b + (((8*(d + e*x)^(1/2)*(b^8*e^10 + 2*c^8*d^8*e^2 - 8*b*c^7*d^7*e^3 + 28*b^2*c^6*d^6*e^4 - 56*b^3*c^5*d^5*e^5 + 70*b^4*c^4*d^4*e^6 - 56*b^5*c^3*d^3*e^7 + 28*b^6*c^2*d^2*e^8 - 8*b^7*c*d*e^9))/c^5 - (((8*(b^5*c^4*d*e^6 - 3*b^2*c^7*d^4*e^3 + 6*b^3*c^6*d^3*e^4 - 4*b^4*c^5*d^2*e^5))/c^5 - (8*(b^3*c^7*e^3 - 2*b^2*c^8*d*e^2)*(d^7)^(1/2)*(d + e*x)^(1/2))/(b*c^5))*(d^7)^(1/2))/b)*(d^7)^(1/2)*1i)/b)/((16*(b^7*d^4*e^10 - 4*c^7*d^11*e^3 + 22*b*c^6*d^10*e^4 - 8*b^6*c*d^5*e^9 - 52*b^2*c^5*d^9*e^5 + 69*b^3*c^4*d^8*e^6 - 56*b^4*c^3*d^7*e^7 + 28*b^5*c^2*d^6*e^8))/c^5 + (((8*(d + e*x)^(1/2)*(b^8*e^10 + 2*c^8*d^8*e^2 - 8*b*c^7*d^7*e^3 + 28*b^2*c^6*d^6*e^4 - 56*b^3*c^5*d^5*e^5 + 70*b^4*c^4*d^4*e^6 - 56*b^5*c^3*d^3*e^7 + 28*b^6*c^2*d^2*e^8 - 8*b^7*c*d*e^9))/c^5 + (((8*(b^5*c^4*d*e^6 - 3*b^2*c^7*d^4*e^3 + 6*b^3*c^6*d^3*e^4 - 4*b^4*c^5*d^2*e^5))/c^5 + (8*(b^3*c^7*e^3 - 2*b^2*c^8*d*e^2)*(d^7)^(1/2)*(d + e*x)^(1/2))/(b*c^5))*(d^7)^(1/2))/b)*(d^7)^(1/2))/b - (((8*(d + e*x)^(1/2)*(b^8*e^10 + 2*c^8*d^8*e^2 - 8*b*c^7*d^7*e^3 + 28*b^2*c^6*d^6*e^4 - 56*b^3*c^5*d^5*e^5 + 70*b^4*c^4*d^4*e^6 - 56*b^5*c^3*d^3*e^7 + 28*b^6*c^2*d^2*e^8 - 8*b^7*c*d*e^9))/c^5 - (((8*(b^5*c^4*d*e^6 - 3*b^2*c^7*d^4*e^3 + 6*b^3*c^6*d^3*e^4 - 4*b^4*c^5*d^2*e^5))/c^5 - (8*(b^3*c^7*e^3 - 2*b^2*c^8*d*e^2)*(d^7)^(1/2)*(d + e*x)^(1/2))/(b*c^5))*(d^7)^(1/2))/b)*(d^7)^(1/2))/b))*(d^7)^(1/2)*2i)/b + (atan(((((8*(d + e*x)^(1/2)*(b^8*e^10 + 2*c^8*d^8*e^2 - 8*b*c^7*d^7*e^3 + 28*b^2*c^6*d^6*e^4 - 56*b^3*c^5*d^5*e^5 + 70*b^4*c^4*d^4*e^6 - 56*b^5*c^3*d^3*e^7 + 28*b^6*c^2*d^2*e^8 - 8*b^7*c*d*e^9))/c^5 + (((8*(b^5*c^4*d*e^6 - 3*b^2*c^7*d^4*e^3 + 6*b^3*c^6*d^3*e^4 - 4*b^4*c^5*d^2*e^5))/c^5 + (8*(b^3*c^7*e^3 - 2*b^2*c^8*d*e^2)*(-c^7*(b*e - c*d)^7)^(1/2)*(d + e*x)^(1/2))/(b*c^12))*(-c^7*(b*e - c*d)^7)^(1/2))/(b*c^7))*(-c^7*(b*e - c*d)^7)^(1/2)*1i)/(b*c^7) + (((8*(d + e*x)^(1/2)*(b^8*e^10 + 2*c^8*d^8*e^2 - 8*b*c^7*d^7*e^3 + 28*b^2*c^6*d^6*e^4 - 56*b^3*c^5*d^5*e^5 + 70*b^4*c^4*d^4*e^6 - 56*b^5*c^3*d^3*e^7 + 28*b^6*c^2*d^2*e^8 - 8*b^7*c*d*e^9))/c^5 - (((8*(b^5*c^4*d*e^6 - 3*b^2*c^7*d^4*e^3 + 6*b^3*c^6*d^3*e^4 - 4*b^4*c^5*d^2*e^5))/c^5 - (8*(b^3*c^7*e^3 - 2*b^2*c^8*d*e^2)*(-c^7*(b*e - c*d)^7)^(1/2)*(d + e*x)^(1/2))/(b*c^12))*(-c^7*(b*e - c*d)^7)^(1/2))/(b*c^7))*(-c^7*(b*e - c*d)^7)^(1/2)*1i)/(b*c^7))/((16*(b^7*d^4*e^10 - 4*c^7*d^11*e^3 + 22*b*c^6*d^10*e^4 - 8*b^6*c*d^5*e^9 - 52*b^2*c^5*d^9*e^5 + 69*b^3*c^4*d^8*e^6 - 56*b^4*c^3*d^7*e^7 + 28*b^5*c^2*d^6*e^8))/c^5 + (((8*(d + e*x)^(1/2)*(b^8*e^10 + 2*c^8*d^8*e^2 - 8*b*c^7*d^7*e^3 + 28*b^2*c^6*d^6*e^4 - 56*b^3*c^5*d^5*e^5 + 70*b^4*c^4*d^4*e^6 - 56*b^5*c^3*d^3*e^7 + 28*b^6*c^2*d^2*e^8 - 8*b^7*c*d*e^9))/c^5 + (((8*(b^5*c^4*d*e^6 - 3*b^2*c^7*d^4*e^3 + 6*b^3*c^6*d^3*e^4 - 4*b^4*c^5*d^2*e^5))/c^5 + (8*(b^3*c^7*e^3 - 2*b^2*c^8*d*e^2)*(-c^7*(b*e - c*d)^7)^(1/2)*(d + e*x)^(1/2))/(b*c^12))*(-c^7*(b*e - c*d)^7)^(1/2))/(b*c^7))*(-c^7*(b*e - c*d)^7)^(1/2))/(b*c^7) - (((8*(d + e*x)^(1/2)*(b^8*e^10 + 2*c^8*d^8*e^2 - 8*b*c^7*d^7*e^3 + 28*b^2*c^6*d^6*e^4 - 56*b^3*c^5*d^5*e^5 + 70*b^4*c^4*d^4*e^6 - 56*b^5*c^3*d^3*e^7 + 28*b^6*c^2*d^2*e^8 - 8*b^7*c*d*e^9))/c^5 - (((8*(b^5*c^4*d*e^6 - 3*b^2*c^7*d^4*e^3 + 6*b^3*c^6*d^3*e^4 - 4*b^4*c^5*d^2*e^5))/c^5 - (8*(b^3*c^7*e^3 - 2*b^2*c^8*d*e^2)*(-c^7*(b*e - c*d)^7)^(1/2)*(d + e*x)^(1/2))/(b*c^12))*(-c^7*(b*e - c*d)^7)^(1/2))/(b*c^7))*(-c^7*(b*e - c*d)^7)^(1/2))/(b*c^7)))*(-c^7*(b*e - c*d)^7)^(1/2)*2i)/(b*c^7) - (2*e*(b*e - 2*c*d)*(d + e*x)^(3/2))/(3*c^2)","B"
362,1,2048,118,0.385351,"\text{Not used}","int((d + e*x)^(5/2)/(b*x + c*x^2),x)","\frac{2\,e\,{\left(d+e\,x\right)}^{3/2}}{3\,c}-\frac{2\,e\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}}{c^2}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\sqrt{d+e\,x}\,\left(b^6\,e^8-6\,b^5\,c\,d\,e^7+15\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+15\,b^2\,c^4\,d^4\,e^4-6\,b\,c^5\,d^5\,e^3+2\,c^6\,d^6\,e^2\right)}{c^3}+\frac{\left(\frac{8\,\left(b^4\,c^3\,d\,e^5-3\,b^3\,c^4\,d^2\,e^4+2\,b^2\,c^5\,d^3\,e^3\right)}{c^3}+\frac{8\,\left(b^3\,c^5\,e^3-2\,b^2\,c^6\,d\,e^2\right)\,\sqrt{d^5}\,\sqrt{d+e\,x}}{b\,c^3}\right)\,\sqrt{d^5}}{b}\right)\,\sqrt{d^5}\,1{}\mathrm{i}}{b}+\frac{\left(\frac{8\,\sqrt{d+e\,x}\,\left(b^6\,e^8-6\,b^5\,c\,d\,e^7+15\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+15\,b^2\,c^4\,d^4\,e^4-6\,b\,c^5\,d^5\,e^3+2\,c^6\,d^6\,e^2\right)}{c^3}-\frac{\left(\frac{8\,\left(b^4\,c^3\,d\,e^5-3\,b^3\,c^4\,d^2\,e^4+2\,b^2\,c^5\,d^3\,e^3\right)}{c^3}-\frac{8\,\left(b^3\,c^5\,e^3-2\,b^2\,c^6\,d\,e^2\right)\,\sqrt{d^5}\,\sqrt{d+e\,x}}{b\,c^3}\right)\,\sqrt{d^5}}{b}\right)\,\sqrt{d^5}\,1{}\mathrm{i}}{b}}{\frac{16\,\left(b^5\,d^3\,e^8-6\,b^4\,c\,d^4\,e^7+15\,b^3\,c^2\,d^5\,e^6-19\,b^2\,c^3\,d^6\,e^5+12\,b\,c^4\,d^7\,e^4-3\,c^5\,d^8\,e^3\right)}{c^3}-\frac{\left(\frac{8\,\sqrt{d+e\,x}\,\left(b^6\,e^8-6\,b^5\,c\,d\,e^7+15\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+15\,b^2\,c^4\,d^4\,e^4-6\,b\,c^5\,d^5\,e^3+2\,c^6\,d^6\,e^2\right)}{c^3}+\frac{\left(\frac{8\,\left(b^4\,c^3\,d\,e^5-3\,b^3\,c^4\,d^2\,e^4+2\,b^2\,c^5\,d^3\,e^3\right)}{c^3}+\frac{8\,\left(b^3\,c^5\,e^3-2\,b^2\,c^6\,d\,e^2\right)\,\sqrt{d^5}\,\sqrt{d+e\,x}}{b\,c^3}\right)\,\sqrt{d^5}}{b}\right)\,\sqrt{d^5}}{b}+\frac{\left(\frac{8\,\sqrt{d+e\,x}\,\left(b^6\,e^8-6\,b^5\,c\,d\,e^7+15\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+15\,b^2\,c^4\,d^4\,e^4-6\,b\,c^5\,d^5\,e^3+2\,c^6\,d^6\,e^2\right)}{c^3}-\frac{\left(\frac{8\,\left(b^4\,c^3\,d\,e^5-3\,b^3\,c^4\,d^2\,e^4+2\,b^2\,c^5\,d^3\,e^3\right)}{c^3}-\frac{8\,\left(b^3\,c^5\,e^3-2\,b^2\,c^6\,d\,e^2\right)\,\sqrt{d^5}\,\sqrt{d+e\,x}}{b\,c^3}\right)\,\sqrt{d^5}}{b}\right)\,\sqrt{d^5}}{b}}\right)\,\sqrt{d^5}\,2{}\mathrm{i}}{b}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{8\,\sqrt{d+e\,x}\,\left(b^6\,e^8-6\,b^5\,c\,d\,e^7+15\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+15\,b^2\,c^4\,d^4\,e^4-6\,b\,c^5\,d^5\,e^3+2\,c^6\,d^6\,e^2\right)}{c^3}+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{8\,\left(b^4\,c^3\,d\,e^5-3\,b^3\,c^4\,d^2\,e^4+2\,b^2\,c^5\,d^3\,e^3\right)}{c^3}+\frac{8\,\left(b^3\,c^5\,e^3-2\,b^2\,c^6\,d\,e^2\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\sqrt{d+e\,x}}{b\,c^8}\right)}{b\,c^5}\right)\,1{}\mathrm{i}}{b\,c^5}+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{8\,\sqrt{d+e\,x}\,\left(b^6\,e^8-6\,b^5\,c\,d\,e^7+15\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+15\,b^2\,c^4\,d^4\,e^4-6\,b\,c^5\,d^5\,e^3+2\,c^6\,d^6\,e^2\right)}{c^3}-\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{8\,\left(b^4\,c^3\,d\,e^5-3\,b^3\,c^4\,d^2\,e^4+2\,b^2\,c^5\,d^3\,e^3\right)}{c^3}-\frac{8\,\left(b^3\,c^5\,e^3-2\,b^2\,c^6\,d\,e^2\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\sqrt{d+e\,x}}{b\,c^8}\right)}{b\,c^5}\right)\,1{}\mathrm{i}}{b\,c^5}}{\frac{16\,\left(b^5\,d^3\,e^8-6\,b^4\,c\,d^4\,e^7+15\,b^3\,c^2\,d^5\,e^6-19\,b^2\,c^3\,d^6\,e^5+12\,b\,c^4\,d^7\,e^4-3\,c^5\,d^8\,e^3\right)}{c^3}-\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{8\,\sqrt{d+e\,x}\,\left(b^6\,e^8-6\,b^5\,c\,d\,e^7+15\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+15\,b^2\,c^4\,d^4\,e^4-6\,b\,c^5\,d^5\,e^3+2\,c^6\,d^6\,e^2\right)}{c^3}+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{8\,\left(b^4\,c^3\,d\,e^5-3\,b^3\,c^4\,d^2\,e^4+2\,b^2\,c^5\,d^3\,e^3\right)}{c^3}+\frac{8\,\left(b^3\,c^5\,e^3-2\,b^2\,c^6\,d\,e^2\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\sqrt{d+e\,x}}{b\,c^8}\right)}{b\,c^5}\right)}{b\,c^5}+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{8\,\sqrt{d+e\,x}\,\left(b^6\,e^8-6\,b^5\,c\,d\,e^7+15\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+15\,b^2\,c^4\,d^4\,e^4-6\,b\,c^5\,d^5\,e^3+2\,c^6\,d^6\,e^2\right)}{c^3}-\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{8\,\left(b^4\,c^3\,d\,e^5-3\,b^3\,c^4\,d^2\,e^4+2\,b^2\,c^5\,d^3\,e^3\right)}{c^3}-\frac{8\,\left(b^3\,c^5\,e^3-2\,b^2\,c^6\,d\,e^2\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\sqrt{d+e\,x}}{b\,c^8}\right)}{b\,c^5}\right)}{b\,c^5}}\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,2{}\mathrm{i}}{b\,c^5}","Not used",1,"(atan(((((8*(d + e*x)^(1/2)*(b^6*e^8 + 2*c^6*d^6*e^2 - 6*b*c^5*d^5*e^3 + 15*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 + 15*b^4*c^2*d^2*e^6 - 6*b^5*c*d*e^7))/c^3 + (((8*(b^4*c^3*d*e^5 + 2*b^2*c^5*d^3*e^3 - 3*b^3*c^4*d^2*e^4))/c^3 + (8*(b^3*c^5*e^3 - 2*b^2*c^6*d*e^2)*(d^5)^(1/2)*(d + e*x)^(1/2))/(b*c^3))*(d^5)^(1/2))/b)*(d^5)^(1/2)*1i)/b + (((8*(d + e*x)^(1/2)*(b^6*e^8 + 2*c^6*d^6*e^2 - 6*b*c^5*d^5*e^3 + 15*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 + 15*b^4*c^2*d^2*e^6 - 6*b^5*c*d*e^7))/c^3 - (((8*(b^4*c^3*d*e^5 + 2*b^2*c^5*d^3*e^3 - 3*b^3*c^4*d^2*e^4))/c^3 - (8*(b^3*c^5*e^3 - 2*b^2*c^6*d*e^2)*(d^5)^(1/2)*(d + e*x)^(1/2))/(b*c^3))*(d^5)^(1/2))/b)*(d^5)^(1/2)*1i)/b)/((16*(b^5*d^3*e^8 - 3*c^5*d^8*e^3 + 12*b*c^4*d^7*e^4 - 6*b^4*c*d^4*e^7 - 19*b^2*c^3*d^6*e^5 + 15*b^3*c^2*d^5*e^6))/c^3 - (((8*(d + e*x)^(1/2)*(b^6*e^8 + 2*c^6*d^6*e^2 - 6*b*c^5*d^5*e^3 + 15*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 + 15*b^4*c^2*d^2*e^6 - 6*b^5*c*d*e^7))/c^3 + (((8*(b^4*c^3*d*e^5 + 2*b^2*c^5*d^3*e^3 - 3*b^3*c^4*d^2*e^4))/c^3 + (8*(b^3*c^5*e^3 - 2*b^2*c^6*d*e^2)*(d^5)^(1/2)*(d + e*x)^(1/2))/(b*c^3))*(d^5)^(1/2))/b)*(d^5)^(1/2))/b + (((8*(d + e*x)^(1/2)*(b^6*e^8 + 2*c^6*d^6*e^2 - 6*b*c^5*d^5*e^3 + 15*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 + 15*b^4*c^2*d^2*e^6 - 6*b^5*c*d*e^7))/c^3 - (((8*(b^4*c^3*d*e^5 + 2*b^2*c^5*d^3*e^3 - 3*b^3*c^4*d^2*e^4))/c^3 - (8*(b^3*c^5*e^3 - 2*b^2*c^6*d*e^2)*(d^5)^(1/2)*(d + e*x)^(1/2))/(b*c^3))*(d^5)^(1/2))/b)*(d^5)^(1/2))/b))*(d^5)^(1/2)*2i)/b + (2*e*(d + e*x)^(3/2))/(3*c) + (atan((((-c^5*(b*e - c*d)^5)^(1/2)*((8*(d + e*x)^(1/2)*(b^6*e^8 + 2*c^6*d^6*e^2 - 6*b*c^5*d^5*e^3 + 15*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 + 15*b^4*c^2*d^2*e^6 - 6*b^5*c*d*e^7))/c^3 + ((-c^5*(b*e - c*d)^5)^(1/2)*((8*(b^4*c^3*d*e^5 + 2*b^2*c^5*d^3*e^3 - 3*b^3*c^4*d^2*e^4))/c^3 + (8*(b^3*c^5*e^3 - 2*b^2*c^6*d*e^2)*(-c^5*(b*e - c*d)^5)^(1/2)*(d + e*x)^(1/2))/(b*c^8)))/(b*c^5))*1i)/(b*c^5) + ((-c^5*(b*e - c*d)^5)^(1/2)*((8*(d + e*x)^(1/2)*(b^6*e^8 + 2*c^6*d^6*e^2 - 6*b*c^5*d^5*e^3 + 15*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 + 15*b^4*c^2*d^2*e^6 - 6*b^5*c*d*e^7))/c^3 - ((-c^5*(b*e - c*d)^5)^(1/2)*((8*(b^4*c^3*d*e^5 + 2*b^2*c^5*d^3*e^3 - 3*b^3*c^4*d^2*e^4))/c^3 - (8*(b^3*c^5*e^3 - 2*b^2*c^6*d*e^2)*(-c^5*(b*e - c*d)^5)^(1/2)*(d + e*x)^(1/2))/(b*c^8)))/(b*c^5))*1i)/(b*c^5))/((16*(b^5*d^3*e^8 - 3*c^5*d^8*e^3 + 12*b*c^4*d^7*e^4 - 6*b^4*c*d^4*e^7 - 19*b^2*c^3*d^6*e^5 + 15*b^3*c^2*d^5*e^6))/c^3 - ((-c^5*(b*e - c*d)^5)^(1/2)*((8*(d + e*x)^(1/2)*(b^6*e^8 + 2*c^6*d^6*e^2 - 6*b*c^5*d^5*e^3 + 15*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 + 15*b^4*c^2*d^2*e^6 - 6*b^5*c*d*e^7))/c^3 + ((-c^5*(b*e - c*d)^5)^(1/2)*((8*(b^4*c^3*d*e^5 + 2*b^2*c^5*d^3*e^3 - 3*b^3*c^4*d^2*e^4))/c^3 + (8*(b^3*c^5*e^3 - 2*b^2*c^6*d*e^2)*(-c^5*(b*e - c*d)^5)^(1/2)*(d + e*x)^(1/2))/(b*c^8)))/(b*c^5)))/(b*c^5) + ((-c^5*(b*e - c*d)^5)^(1/2)*((8*(d + e*x)^(1/2)*(b^6*e^8 + 2*c^6*d^6*e^2 - 6*b*c^5*d^5*e^3 + 15*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 + 15*b^4*c^2*d^2*e^6 - 6*b^5*c*d*e^7))/c^3 - ((-c^5*(b*e - c*d)^5)^(1/2)*((8*(b^4*c^3*d*e^5 + 2*b^2*c^5*d^3*e^3 - 3*b^3*c^4*d^2*e^4))/c^3 - (8*(b^3*c^5*e^3 - 2*b^2*c^6*d*e^2)*(-c^5*(b*e - c*d)^5)^(1/2)*(d + e*x)^(1/2))/(b*c^8)))/(b*c^5)))/(b*c^5)))*(-c^5*(b*e - c*d)^5)^(1/2)*2i)/(b*c^5) - (2*e*(b*e - 2*c*d)*(d + e*x)^(1/2))/c^2","B"
363,1,697,92,0.373863,"\text{Not used}","int((d + e*x)^(3/2)/(b*x + c*x^2),x)","\frac{2\,e\,\sqrt{d+e\,x}}{c}-\frac{2\,\mathrm{atanh}\left(\frac{16\,b^3\,e^6\,\sqrt{d^3}\,\sqrt{d+e\,x}}{16\,b^3\,d^2\,e^6-64\,b^2\,c\,d^3\,e^5+96\,b\,c^2\,d^4\,e^4-48\,c^3\,d^5\,e^3}+\frac{48\,c^2\,d^3\,e^3\,\sqrt{d^3}\,\sqrt{d+e\,x}}{64\,b^2\,d^3\,e^5+48\,c^2\,d^5\,e^3-\frac{16\,b^3\,d^2\,e^6}{c}-96\,b\,c\,d^4\,e^4}+\frac{64\,b^2\,d\,e^5\,\sqrt{d^3}\,\sqrt{d+e\,x}}{64\,b^2\,d^3\,e^5+48\,c^2\,d^5\,e^3-\frac{16\,b^3\,d^2\,e^6}{c}-96\,b\,c\,d^4\,e^4}-\frac{96\,b\,c\,d^2\,e^4\,\sqrt{d^3}\,\sqrt{d+e\,x}}{64\,b^2\,d^3\,e^5+48\,c^2\,d^5\,e^3-\frac{16\,b^3\,d^2\,e^6}{c}-96\,b\,c\,d^4\,e^4}\right)\,\sqrt{d^3}}{b}+\frac{2\,\mathrm{atanh}\left(\frac{48\,d^3\,e^3\,\sqrt{d+e\,x}\,\sqrt{-b^3\,c^3\,e^3+3\,b^2\,c^4\,d\,e^2-3\,b\,c^5\,d^2\,e+c^6\,d^3}}{48\,c^3\,d^5\,e^3-80\,b^3\,d^2\,e^6-144\,b\,c^2\,d^4\,e^4+160\,b^2\,c\,d^3\,e^5+\frac{16\,b^4\,d\,e^7}{c}}+\frac{16\,b^2\,d\,e^5\,\sqrt{d+e\,x}\,\sqrt{-b^3\,c^3\,e^3+3\,b^2\,c^4\,d\,e^2-3\,b\,c^5\,d^2\,e+c^6\,d^3}}{16\,b^4\,c\,d\,e^7-80\,b^3\,c^2\,d^2\,e^6+160\,b^2\,c^3\,d^3\,e^5-144\,b\,c^4\,d^4\,e^4+48\,c^5\,d^5\,e^3}-\frac{48\,b\,d^2\,e^4\,\sqrt{d+e\,x}\,\sqrt{-b^3\,c^3\,e^3+3\,b^2\,c^4\,d\,e^2-3\,b\,c^5\,d^2\,e+c^6\,d^3}}{16\,b^4\,d\,e^7-80\,b^3\,c\,d^2\,e^6+160\,b^2\,c^2\,d^3\,e^5-144\,b\,c^3\,d^4\,e^4+48\,c^4\,d^5\,e^3}\right)\,\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}}{b\,c^3}","Not used",1,"(2*e*(d + e*x)^(1/2))/c - (2*atanh((16*b^3*e^6*(d^3)^(1/2)*(d + e*x)^(1/2))/(16*b^3*d^2*e^6 - 48*c^3*d^5*e^3 + 96*b*c^2*d^4*e^4 - 64*b^2*c*d^3*e^5) + (48*c^2*d^3*e^3*(d^3)^(1/2)*(d + e*x)^(1/2))/(64*b^2*d^3*e^5 + 48*c^2*d^5*e^3 - (16*b^3*d^2*e^6)/c - 96*b*c*d^4*e^4) + (64*b^2*d*e^5*(d^3)^(1/2)*(d + e*x)^(1/2))/(64*b^2*d^3*e^5 + 48*c^2*d^5*e^3 - (16*b^3*d^2*e^6)/c - 96*b*c*d^4*e^4) - (96*b*c*d^2*e^4*(d^3)^(1/2)*(d + e*x)^(1/2))/(64*b^2*d^3*e^5 + 48*c^2*d^5*e^3 - (16*b^3*d^2*e^6)/c - 96*b*c*d^4*e^4))*(d^3)^(1/2))/b + (2*atanh((48*d^3*e^3*(d + e*x)^(1/2)*(c^6*d^3 - b^3*c^3*e^3 + 3*b^2*c^4*d*e^2 - 3*b*c^5*d^2*e)^(1/2))/(48*c^3*d^5*e^3 - 80*b^3*d^2*e^6 - 144*b*c^2*d^4*e^4 + 160*b^2*c*d^3*e^5 + (16*b^4*d*e^7)/c) + (16*b^2*d*e^5*(d + e*x)^(1/2)*(c^6*d^3 - b^3*c^3*e^3 + 3*b^2*c^4*d*e^2 - 3*b*c^5*d^2*e)^(1/2))/(48*c^5*d^5*e^3 - 144*b*c^4*d^4*e^4 + 160*b^2*c^3*d^3*e^5 - 80*b^3*c^2*d^2*e^6 + 16*b^4*c*d*e^7) - (48*b*d^2*e^4*(d + e*x)^(1/2)*(c^6*d^3 - b^3*c^3*e^3 + 3*b^2*c^4*d*e^2 - 3*b*c^5*d^2*e)^(1/2))/(16*b^4*d*e^7 + 48*c^4*d^5*e^3 - 144*b*c^3*d^4*e^4 - 80*b^3*c*d^2*e^6 + 160*b^2*c^2*d^3*e^5))*(-c^3*(b*e - c*d)^3)^(1/2))/(b*c^3)","B"
364,1,100,77,0.160181,"\text{Not used}","int((d + e*x)^(1/2)/(b*x + c*x^2),x)","\frac{2\,\mathrm{atanh}\left(\frac{16\,b\,c^2\,d\,e^3\,\sqrt{c^2\,d-b\,c\,e}\,\sqrt{d+e\,x}}{16\,b\,c^3\,d^2\,e^3-16\,b^2\,c^2\,d\,e^4}\right)\,\sqrt{c^2\,d-b\,c\,e}}{b\,c}-\frac{2\,\sqrt{d}\,\mathrm{atanh}\left(\frac{\sqrt{d+e\,x}}{\sqrt{d}}\right)}{b}","Not used",1,"(2*atanh((16*b*c^2*d*e^3*(c^2*d - b*c*e)^(1/2)*(d + e*x)^(1/2))/(16*b*c^3*d^2*e^3 - 16*b^2*c^2*d*e^4))*(c^2*d - b*c*e)^(1/2))/(b*c) - (2*d^(1/2)*atanh((d + e*x)^(1/2)/d^(1/2)))/b","B"
365,1,625,77,0.344109,"\text{Not used}","int(1/((b*x + c*x^2)*(d + e*x)^(1/2)),x)","-\frac{2\,\mathrm{atanh}\left(\frac{\sqrt{d+e\,x}}{\sqrt{d}}\right)}{b\,\sqrt{d}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(16\,c^3\,e^2\,\sqrt{d+e\,x}+\frac{\sqrt{c^2\,d-b\,c\,e}\,\left(8\,b^2\,c^2\,e^3+\frac{\left(8\,b^3\,c^2\,e^3-16\,b^2\,c^3\,d\,e^2\right)\,\sqrt{c^2\,d-b\,c\,e}\,\sqrt{d+e\,x}}{b^2\,e-b\,c\,d}\right)}{b^2\,e-b\,c\,d}\right)\,\sqrt{c^2\,d-b\,c\,e}\,1{}\mathrm{i}}{b^2\,e-b\,c\,d}+\frac{\left(16\,c^3\,e^2\,\sqrt{d+e\,x}-\frac{\sqrt{c^2\,d-b\,c\,e}\,\left(8\,b^2\,c^2\,e^3-\frac{\left(8\,b^3\,c^2\,e^3-16\,b^2\,c^3\,d\,e^2\right)\,\sqrt{c^2\,d-b\,c\,e}\,\sqrt{d+e\,x}}{b^2\,e-b\,c\,d}\right)}{b^2\,e-b\,c\,d}\right)\,\sqrt{c^2\,d-b\,c\,e}\,1{}\mathrm{i}}{b^2\,e-b\,c\,d}}{\frac{\left(16\,c^3\,e^2\,\sqrt{d+e\,x}+\frac{\sqrt{c^2\,d-b\,c\,e}\,\left(8\,b^2\,c^2\,e^3+\frac{\left(8\,b^3\,c^2\,e^3-16\,b^2\,c^3\,d\,e^2\right)\,\sqrt{c^2\,d-b\,c\,e}\,\sqrt{d+e\,x}}{b^2\,e-b\,c\,d}\right)}{b^2\,e-b\,c\,d}\right)\,\sqrt{c^2\,d-b\,c\,e}}{b^2\,e-b\,c\,d}-\frac{\left(16\,c^3\,e^2\,\sqrt{d+e\,x}-\frac{\sqrt{c^2\,d-b\,c\,e}\,\left(8\,b^2\,c^2\,e^3-\frac{\left(8\,b^3\,c^2\,e^3-16\,b^2\,c^3\,d\,e^2\right)\,\sqrt{c^2\,d-b\,c\,e}\,\sqrt{d+e\,x}}{b^2\,e-b\,c\,d}\right)}{b^2\,e-b\,c\,d}\right)\,\sqrt{c^2\,d-b\,c\,e}}{b^2\,e-b\,c\,d}}\right)\,\sqrt{c^2\,d-b\,c\,e}\,2{}\mathrm{i}}{b^2\,e-b\,c\,d}","Not used",1,"(atan((((16*c^3*e^2*(d + e*x)^(1/2) + ((c^2*d - b*c*e)^(1/2)*(8*b^2*c^2*e^3 + ((8*b^3*c^2*e^3 - 16*b^2*c^3*d*e^2)*(c^2*d - b*c*e)^(1/2)*(d + e*x)^(1/2))/(b^2*e - b*c*d)))/(b^2*e - b*c*d))*(c^2*d - b*c*e)^(1/2)*1i)/(b^2*e - b*c*d) + ((16*c^3*e^2*(d + e*x)^(1/2) - ((c^2*d - b*c*e)^(1/2)*(8*b^2*c^2*e^3 - ((8*b^3*c^2*e^3 - 16*b^2*c^3*d*e^2)*(c^2*d - b*c*e)^(1/2)*(d + e*x)^(1/2))/(b^2*e - b*c*d)))/(b^2*e - b*c*d))*(c^2*d - b*c*e)^(1/2)*1i)/(b^2*e - b*c*d))/(((16*c^3*e^2*(d + e*x)^(1/2) + ((c^2*d - b*c*e)^(1/2)*(8*b^2*c^2*e^3 + ((8*b^3*c^2*e^3 - 16*b^2*c^3*d*e^2)*(c^2*d - b*c*e)^(1/2)*(d + e*x)^(1/2))/(b^2*e - b*c*d)))/(b^2*e - b*c*d))*(c^2*d - b*c*e)^(1/2))/(b^2*e - b*c*d) - ((16*c^3*e^2*(d + e*x)^(1/2) - ((c^2*d - b*c*e)^(1/2)*(8*b^2*c^2*e^3 - ((8*b^3*c^2*e^3 - 16*b^2*c^3*d*e^2)*(c^2*d - b*c*e)^(1/2)*(d + e*x)^(1/2))/(b^2*e - b*c*d)))/(b^2*e - b*c*d))*(c^2*d - b*c*e)^(1/2))/(b^2*e - b*c*d)))*(c^2*d - b*c*e)^(1/2)*2i)/(b^2*e - b*c*d) - (2*atanh((d + e*x)^(1/2)/d^(1/2)))/(b*d^(1/2))","B"
366,1,2258,102,0.631030,"\text{Not used}","int(1/((b*x + c*x^2)*(d + e*x)^(3/2)),x)","-\frac{2\,e}{\left(c\,d^2-b\,d\,e\right)\,\sqrt{d+e\,x}}-\frac{2\,\mathrm{atanh}\left(\frac{48\,c^7\,d^7\,e^3\,\sqrt{d+e\,x}}{\sqrt{d^3}\,\left(-16\,b^5\,c^2\,d\,e^8+96\,b^4\,c^3\,d^2\,e^7-240\,b^3\,c^4\,d^3\,e^6+304\,b^2\,c^5\,d^4\,e^5-192\,b\,c^6\,d^5\,e^4+48\,c^7\,d^6\,e^3\right)}-\frac{192\,b\,c^6\,d^6\,e^4\,\sqrt{d+e\,x}}{\sqrt{d^3}\,\left(-16\,b^5\,c^2\,d\,e^8+96\,b^4\,c^3\,d^2\,e^7-240\,b^3\,c^4\,d^3\,e^6+304\,b^2\,c^5\,d^4\,e^5-192\,b\,c^6\,d^5\,e^4+48\,c^7\,d^6\,e^3\right)}+\frac{304\,b^2\,c^5\,d^5\,e^5\,\sqrt{d+e\,x}}{\sqrt{d^3}\,\left(-16\,b^5\,c^2\,d\,e^8+96\,b^4\,c^3\,d^2\,e^7-240\,b^3\,c^4\,d^3\,e^6+304\,b^2\,c^5\,d^4\,e^5-192\,b\,c^6\,d^5\,e^4+48\,c^7\,d^6\,e^3\right)}-\frac{240\,b^3\,c^4\,d^4\,e^6\,\sqrt{d+e\,x}}{\sqrt{d^3}\,\left(-16\,b^5\,c^2\,d\,e^8+96\,b^4\,c^3\,d^2\,e^7-240\,b^3\,c^4\,d^3\,e^6+304\,b^2\,c^5\,d^4\,e^5-192\,b\,c^6\,d^5\,e^4+48\,c^7\,d^6\,e^3\right)}+\frac{96\,b^4\,c^3\,d^3\,e^7\,\sqrt{d+e\,x}}{\sqrt{d^3}\,\left(-16\,b^5\,c^2\,d\,e^8+96\,b^4\,c^3\,d^2\,e^7-240\,b^3\,c^4\,d^3\,e^6+304\,b^2\,c^5\,d^4\,e^5-192\,b\,c^6\,d^5\,e^4+48\,c^7\,d^6\,e^3\right)}-\frac{16\,b^5\,c^2\,d^2\,e^8\,\sqrt{d+e\,x}}{\sqrt{d^3}\,\left(-16\,b^5\,c^2\,d\,e^8+96\,b^4\,c^3\,d^2\,e^7-240\,b^3\,c^4\,d^3\,e^6+304\,b^2\,c^5\,d^4\,e^5-192\,b\,c^6\,d^5\,e^4+48\,c^7\,d^6\,e^3\right)}\right)}{b\,\sqrt{d^3}}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(\sqrt{d+e\,x}\,\left(-8\,b^5\,c^3\,d^3\,e^7+40\,b^4\,c^4\,d^4\,e^6-88\,b^3\,c^5\,d^5\,e^5+104\,b^2\,c^6\,d^6\,e^4-64\,b\,c^7\,d^7\,e^3+16\,c^8\,d^8\,e^2\right)-\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(72\,b^3\,c^6\,d^8\,e^4-16\,b^2\,c^7\,d^9\,e^3-128\,b^4\,c^5\,d^7\,e^5+112\,b^5\,c^4\,d^6\,e^6-48\,b^6\,c^3\,d^5\,e^7+8\,b^7\,c^2\,d^4\,e^8+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\sqrt{d+e\,x}\,\left(8\,b^8\,c^2\,d^5\,e^8-56\,b^7\,c^3\,d^6\,e^7+160\,b^6\,c^4\,d^7\,e^6-240\,b^5\,c^5\,d^8\,e^5+200\,b^4\,c^6\,d^9\,e^4-88\,b^3\,c^7\,d^{10}\,e^3+16\,b^2\,c^8\,d^{11}\,e^2\right)}{b\,{\left(b\,e-c\,d\right)}^3}\right)}{b\,{\left(b\,e-c\,d\right)}^3}\right)\,1{}\mathrm{i}}{b\,{\left(b\,e-c\,d\right)}^3}+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(\sqrt{d+e\,x}\,\left(-8\,b^5\,c^3\,d^3\,e^7+40\,b^4\,c^4\,d^4\,e^6-88\,b^3\,c^5\,d^5\,e^5+104\,b^2\,c^6\,d^6\,e^4-64\,b\,c^7\,d^7\,e^3+16\,c^8\,d^8\,e^2\right)-\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(16\,b^2\,c^7\,d^9\,e^3-72\,b^3\,c^6\,d^8\,e^4+128\,b^4\,c^5\,d^7\,e^5-112\,b^5\,c^4\,d^6\,e^6+48\,b^6\,c^3\,d^5\,e^7-8\,b^7\,c^2\,d^4\,e^8+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\sqrt{d+e\,x}\,\left(8\,b^8\,c^2\,d^5\,e^8-56\,b^7\,c^3\,d^6\,e^7+160\,b^6\,c^4\,d^7\,e^6-240\,b^5\,c^5\,d^8\,e^5+200\,b^4\,c^6\,d^9\,e^4-88\,b^3\,c^7\,d^{10}\,e^3+16\,b^2\,c^8\,d^{11}\,e^2\right)}{b\,{\left(b\,e-c\,d\right)}^3}\right)}{b\,{\left(b\,e-c\,d\right)}^3}\right)\,1{}\mathrm{i}}{b\,{\left(b\,e-c\,d\right)}^3}}{16\,c^7\,d^6\,e^3-48\,b\,c^6\,d^5\,e^4+48\,b^2\,c^5\,d^4\,e^5-16\,b^3\,c^4\,d^3\,e^6+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(\sqrt{d+e\,x}\,\left(-8\,b^5\,c^3\,d^3\,e^7+40\,b^4\,c^4\,d^4\,e^6-88\,b^3\,c^5\,d^5\,e^5+104\,b^2\,c^6\,d^6\,e^4-64\,b\,c^7\,d^7\,e^3+16\,c^8\,d^8\,e^2\right)-\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(72\,b^3\,c^6\,d^8\,e^4-16\,b^2\,c^7\,d^9\,e^3-128\,b^4\,c^5\,d^7\,e^5+112\,b^5\,c^4\,d^6\,e^6-48\,b^6\,c^3\,d^5\,e^7+8\,b^7\,c^2\,d^4\,e^8+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\sqrt{d+e\,x}\,\left(8\,b^8\,c^2\,d^5\,e^8-56\,b^7\,c^3\,d^6\,e^7+160\,b^6\,c^4\,d^7\,e^6-240\,b^5\,c^5\,d^8\,e^5+200\,b^4\,c^6\,d^9\,e^4-88\,b^3\,c^7\,d^{10}\,e^3+16\,b^2\,c^8\,d^{11}\,e^2\right)}{b\,{\left(b\,e-c\,d\right)}^3}\right)}{b\,{\left(b\,e-c\,d\right)}^3}\right)}{b\,{\left(b\,e-c\,d\right)}^3}-\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(\sqrt{d+e\,x}\,\left(-8\,b^5\,c^3\,d^3\,e^7+40\,b^4\,c^4\,d^4\,e^6-88\,b^3\,c^5\,d^5\,e^5+104\,b^2\,c^6\,d^6\,e^4-64\,b\,c^7\,d^7\,e^3+16\,c^8\,d^8\,e^2\right)-\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(16\,b^2\,c^7\,d^9\,e^3-72\,b^3\,c^6\,d^8\,e^4+128\,b^4\,c^5\,d^7\,e^5-112\,b^5\,c^4\,d^6\,e^6+48\,b^6\,c^3\,d^5\,e^7-8\,b^7\,c^2\,d^4\,e^8+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\sqrt{d+e\,x}\,\left(8\,b^8\,c^2\,d^5\,e^8-56\,b^7\,c^3\,d^6\,e^7+160\,b^6\,c^4\,d^7\,e^6-240\,b^5\,c^5\,d^8\,e^5+200\,b^4\,c^6\,d^9\,e^4-88\,b^3\,c^7\,d^{10}\,e^3+16\,b^2\,c^8\,d^{11}\,e^2\right)}{b\,{\left(b\,e-c\,d\right)}^3}\right)}{b\,{\left(b\,e-c\,d\right)}^3}\right)}{b\,{\left(b\,e-c\,d\right)}^3}}\right)\,\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,2{}\mathrm{i}}{b\,{\left(b\,e-c\,d\right)}^3}","Not used",1,"(atan((((-c^3*(b*e - c*d)^3)^(1/2)*((d + e*x)^(1/2)*(16*c^8*d^8*e^2 - 64*b*c^7*d^7*e^3 + 104*b^2*c^6*d^6*e^4 - 88*b^3*c^5*d^5*e^5 + 40*b^4*c^4*d^4*e^6 - 8*b^5*c^3*d^3*e^7) - ((-c^3*(b*e - c*d)^3)^(1/2)*(72*b^3*c^6*d^8*e^4 - 16*b^2*c^7*d^9*e^3 - 128*b^4*c^5*d^7*e^5 + 112*b^5*c^4*d^6*e^6 - 48*b^6*c^3*d^5*e^7 + 8*b^7*c^2*d^4*e^8 + ((-c^3*(b*e - c*d)^3)^(1/2)*(d + e*x)^(1/2)*(16*b^2*c^8*d^11*e^2 - 88*b^3*c^7*d^10*e^3 + 200*b^4*c^6*d^9*e^4 - 240*b^5*c^5*d^8*e^5 + 160*b^6*c^4*d^7*e^6 - 56*b^7*c^3*d^6*e^7 + 8*b^8*c^2*d^5*e^8))/(b*(b*e - c*d)^3)))/(b*(b*e - c*d)^3))*1i)/(b*(b*e - c*d)^3) + ((-c^3*(b*e - c*d)^3)^(1/2)*((d + e*x)^(1/2)*(16*c^8*d^8*e^2 - 64*b*c^7*d^7*e^3 + 104*b^2*c^6*d^6*e^4 - 88*b^3*c^5*d^5*e^5 + 40*b^4*c^4*d^4*e^6 - 8*b^5*c^3*d^3*e^7) - ((-c^3*(b*e - c*d)^3)^(1/2)*(16*b^2*c^7*d^9*e^3 - 72*b^3*c^6*d^8*e^4 + 128*b^4*c^5*d^7*e^5 - 112*b^5*c^4*d^6*e^6 + 48*b^6*c^3*d^5*e^7 - 8*b^7*c^2*d^4*e^8 + ((-c^3*(b*e - c*d)^3)^(1/2)*(d + e*x)^(1/2)*(16*b^2*c^8*d^11*e^2 - 88*b^3*c^7*d^10*e^3 + 200*b^4*c^6*d^9*e^4 - 240*b^5*c^5*d^8*e^5 + 160*b^6*c^4*d^7*e^6 - 56*b^7*c^3*d^6*e^7 + 8*b^8*c^2*d^5*e^8))/(b*(b*e - c*d)^3)))/(b*(b*e - c*d)^3))*1i)/(b*(b*e - c*d)^3))/(16*c^7*d^6*e^3 - 48*b*c^6*d^5*e^4 + 48*b^2*c^5*d^4*e^5 - 16*b^3*c^4*d^3*e^6 + ((-c^3*(b*e - c*d)^3)^(1/2)*((d + e*x)^(1/2)*(16*c^8*d^8*e^2 - 64*b*c^7*d^7*e^3 + 104*b^2*c^6*d^6*e^4 - 88*b^3*c^5*d^5*e^5 + 40*b^4*c^4*d^4*e^6 - 8*b^5*c^3*d^3*e^7) - ((-c^3*(b*e - c*d)^3)^(1/2)*(72*b^3*c^6*d^8*e^4 - 16*b^2*c^7*d^9*e^3 - 128*b^4*c^5*d^7*e^5 + 112*b^5*c^4*d^6*e^6 - 48*b^6*c^3*d^5*e^7 + 8*b^7*c^2*d^4*e^8 + ((-c^3*(b*e - c*d)^3)^(1/2)*(d + e*x)^(1/2)*(16*b^2*c^8*d^11*e^2 - 88*b^3*c^7*d^10*e^3 + 200*b^4*c^6*d^9*e^4 - 240*b^5*c^5*d^8*e^5 + 160*b^6*c^4*d^7*e^6 - 56*b^7*c^3*d^6*e^7 + 8*b^8*c^2*d^5*e^8))/(b*(b*e - c*d)^3)))/(b*(b*e - c*d)^3)))/(b*(b*e - c*d)^3) - ((-c^3*(b*e - c*d)^3)^(1/2)*((d + e*x)^(1/2)*(16*c^8*d^8*e^2 - 64*b*c^7*d^7*e^3 + 104*b^2*c^6*d^6*e^4 - 88*b^3*c^5*d^5*e^5 + 40*b^4*c^4*d^4*e^6 - 8*b^5*c^3*d^3*e^7) - ((-c^3*(b*e - c*d)^3)^(1/2)*(16*b^2*c^7*d^9*e^3 - 72*b^3*c^6*d^8*e^4 + 128*b^4*c^5*d^7*e^5 - 112*b^5*c^4*d^6*e^6 + 48*b^6*c^3*d^5*e^7 - 8*b^7*c^2*d^4*e^8 + ((-c^3*(b*e - c*d)^3)^(1/2)*(d + e*x)^(1/2)*(16*b^2*c^8*d^11*e^2 - 88*b^3*c^7*d^10*e^3 + 200*b^4*c^6*d^9*e^4 - 240*b^5*c^5*d^8*e^5 + 160*b^6*c^4*d^7*e^6 - 56*b^7*c^3*d^6*e^7 + 8*b^8*c^2*d^5*e^8))/(b*(b*e - c*d)^3)))/(b*(b*e - c*d)^3)))/(b*(b*e - c*d)^3)))*(-c^3*(b*e - c*d)^3)^(1/2)*2i)/(b*(b*e - c*d)^3) - (2*atanh((48*c^7*d^7*e^3*(d + e*x)^(1/2))/((d^3)^(1/2)*(48*c^7*d^6*e^3 - 192*b*c^6*d^5*e^4 - 16*b^5*c^2*d*e^8 + 304*b^2*c^5*d^4*e^5 - 240*b^3*c^4*d^3*e^6 + 96*b^4*c^3*d^2*e^7)) - (192*b*c^6*d^6*e^4*(d + e*x)^(1/2))/((d^3)^(1/2)*(48*c^7*d^6*e^3 - 192*b*c^6*d^5*e^4 - 16*b^5*c^2*d*e^8 + 304*b^2*c^5*d^4*e^5 - 240*b^3*c^4*d^3*e^6 + 96*b^4*c^3*d^2*e^7)) + (304*b^2*c^5*d^5*e^5*(d + e*x)^(1/2))/((d^3)^(1/2)*(48*c^7*d^6*e^3 - 192*b*c^6*d^5*e^4 - 16*b^5*c^2*d*e^8 + 304*b^2*c^5*d^4*e^5 - 240*b^3*c^4*d^3*e^6 + 96*b^4*c^3*d^2*e^7)) - (240*b^3*c^4*d^4*e^6*(d + e*x)^(1/2))/((d^3)^(1/2)*(48*c^7*d^6*e^3 - 192*b*c^6*d^5*e^4 - 16*b^5*c^2*d*e^8 + 304*b^2*c^5*d^4*e^5 - 240*b^3*c^4*d^3*e^6 + 96*b^4*c^3*d^2*e^7)) + (96*b^4*c^3*d^3*e^7*(d + e*x)^(1/2))/((d^3)^(1/2)*(48*c^7*d^6*e^3 - 192*b*c^6*d^5*e^4 - 16*b^5*c^2*d*e^8 + 304*b^2*c^5*d^4*e^5 - 240*b^3*c^4*d^3*e^6 + 96*b^4*c^3*d^2*e^7)) - (16*b^5*c^2*d^2*e^8*(d + e*x)^(1/2))/((d^3)^(1/2)*(48*c^7*d^6*e^3 - 192*b*c^6*d^5*e^4 - 16*b^5*c^2*d*e^8 + 304*b^2*c^5*d^4*e^5 - 240*b^3*c^4*d^3*e^6 + 96*b^4*c^3*d^2*e^7))))/(b*(d^3)^(1/2)) - (2*e)/((c*d^2 - b*d*e)*(d + e*x)^(1/2))","B"
367,1,4509,138,1.172709,"\text{Not used}","int(1/((b*x + c*x^2)*(d + e*x)^(5/2)),x)","-\frac{\frac{2\,e}{3\,\left(c\,d^2-b\,d\,e\right)}-\frac{2\,e\,\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)}{{\left(c\,d^2-b\,d\,e\right)}^2}}{{\left(d+e\,x\right)}^{3/2}}-\frac{2\,\mathrm{atanh}\left(\frac{80\,c^{12}\,d^{15}\,e^3\,\sqrt{d+e\,x}}{\sqrt{d^5}\,\left(16\,b^{10}\,c^2\,d^3\,e^{13}-176\,b^9\,c^3\,d^4\,e^{12}+880\,b^8\,c^4\,d^5\,e^{11}-2640\,b^7\,c^5\,d^6\,e^{10}+5280\,b^6\,c^6\,d^7\,e^9-7376\,b^5\,c^7\,d^8\,e^8+7296\,b^4\,c^8\,d^9\,e^7-5040\,b^3\,c^9\,d^{10}\,e^6+2320\,b^2\,c^{10}\,d^{11}\,e^5-640\,b\,c^{11}\,d^{12}\,e^4+80\,c^{12}\,d^{13}\,e^3\right)}+\frac{2320\,b^2\,c^{10}\,d^{13}\,e^5\,\sqrt{d+e\,x}}{\sqrt{d^5}\,\left(16\,b^{10}\,c^2\,d^3\,e^{13}-176\,b^9\,c^3\,d^4\,e^{12}+880\,b^8\,c^4\,d^5\,e^{11}-2640\,b^7\,c^5\,d^6\,e^{10}+5280\,b^6\,c^6\,d^7\,e^9-7376\,b^5\,c^7\,d^8\,e^8+7296\,b^4\,c^8\,d^9\,e^7-5040\,b^3\,c^9\,d^{10}\,e^6+2320\,b^2\,c^{10}\,d^{11}\,e^5-640\,b\,c^{11}\,d^{12}\,e^4+80\,c^{12}\,d^{13}\,e^3\right)}-\frac{5040\,b^3\,c^9\,d^{12}\,e^6\,\sqrt{d+e\,x}}{\sqrt{d^5}\,\left(16\,b^{10}\,c^2\,d^3\,e^{13}-176\,b^9\,c^3\,d^4\,e^{12}+880\,b^8\,c^4\,d^5\,e^{11}-2640\,b^7\,c^5\,d^6\,e^{10}+5280\,b^6\,c^6\,d^7\,e^9-7376\,b^5\,c^7\,d^8\,e^8+7296\,b^4\,c^8\,d^9\,e^7-5040\,b^3\,c^9\,d^{10}\,e^6+2320\,b^2\,c^{10}\,d^{11}\,e^5-640\,b\,c^{11}\,d^{12}\,e^4+80\,c^{12}\,d^{13}\,e^3\right)}+\frac{7296\,b^4\,c^8\,d^{11}\,e^7\,\sqrt{d+e\,x}}{\sqrt{d^5}\,\left(16\,b^{10}\,c^2\,d^3\,e^{13}-176\,b^9\,c^3\,d^4\,e^{12}+880\,b^8\,c^4\,d^5\,e^{11}-2640\,b^7\,c^5\,d^6\,e^{10}+5280\,b^6\,c^6\,d^7\,e^9-7376\,b^5\,c^7\,d^8\,e^8+7296\,b^4\,c^8\,d^9\,e^7-5040\,b^3\,c^9\,d^{10}\,e^6+2320\,b^2\,c^{10}\,d^{11}\,e^5-640\,b\,c^{11}\,d^{12}\,e^4+80\,c^{12}\,d^{13}\,e^3\right)}-\frac{7376\,b^5\,c^7\,d^{10}\,e^8\,\sqrt{d+e\,x}}{\sqrt{d^5}\,\left(16\,b^{10}\,c^2\,d^3\,e^{13}-176\,b^9\,c^3\,d^4\,e^{12}+880\,b^8\,c^4\,d^5\,e^{11}-2640\,b^7\,c^5\,d^6\,e^{10}+5280\,b^6\,c^6\,d^7\,e^9-7376\,b^5\,c^7\,d^8\,e^8+7296\,b^4\,c^8\,d^9\,e^7-5040\,b^3\,c^9\,d^{10}\,e^6+2320\,b^2\,c^{10}\,d^{11}\,e^5-640\,b\,c^{11}\,d^{12}\,e^4+80\,c^{12}\,d^{13}\,e^3\right)}+\frac{5280\,b^6\,c^6\,d^9\,e^9\,\sqrt{d+e\,x}}{\sqrt{d^5}\,\left(16\,b^{10}\,c^2\,d^3\,e^{13}-176\,b^9\,c^3\,d^4\,e^{12}+880\,b^8\,c^4\,d^5\,e^{11}-2640\,b^7\,c^5\,d^6\,e^{10}+5280\,b^6\,c^6\,d^7\,e^9-7376\,b^5\,c^7\,d^8\,e^8+7296\,b^4\,c^8\,d^9\,e^7-5040\,b^3\,c^9\,d^{10}\,e^6+2320\,b^2\,c^{10}\,d^{11}\,e^5-640\,b\,c^{11}\,d^{12}\,e^4+80\,c^{12}\,d^{13}\,e^3\right)}-\frac{2640\,b^7\,c^5\,d^8\,e^{10}\,\sqrt{d+e\,x}}{\sqrt{d^5}\,\left(16\,b^{10}\,c^2\,d^3\,e^{13}-176\,b^9\,c^3\,d^4\,e^{12}+880\,b^8\,c^4\,d^5\,e^{11}-2640\,b^7\,c^5\,d^6\,e^{10}+5280\,b^6\,c^6\,d^7\,e^9-7376\,b^5\,c^7\,d^8\,e^8+7296\,b^4\,c^8\,d^9\,e^7-5040\,b^3\,c^9\,d^{10}\,e^6+2320\,b^2\,c^{10}\,d^{11}\,e^5-640\,b\,c^{11}\,d^{12}\,e^4+80\,c^{12}\,d^{13}\,e^3\right)}+\frac{880\,b^8\,c^4\,d^7\,e^{11}\,\sqrt{d+e\,x}}{\sqrt{d^5}\,\left(16\,b^{10}\,c^2\,d^3\,e^{13}-176\,b^9\,c^3\,d^4\,e^{12}+880\,b^8\,c^4\,d^5\,e^{11}-2640\,b^7\,c^5\,d^6\,e^{10}+5280\,b^6\,c^6\,d^7\,e^9-7376\,b^5\,c^7\,d^8\,e^8+7296\,b^4\,c^8\,d^9\,e^7-5040\,b^3\,c^9\,d^{10}\,e^6+2320\,b^2\,c^{10}\,d^{11}\,e^5-640\,b\,c^{11}\,d^{12}\,e^4+80\,c^{12}\,d^{13}\,e^3\right)}-\frac{176\,b^9\,c^3\,d^6\,e^{12}\,\sqrt{d+e\,x}}{\sqrt{d^5}\,\left(16\,b^{10}\,c^2\,d^3\,e^{13}-176\,b^9\,c^3\,d^4\,e^{12}+880\,b^8\,c^4\,d^5\,e^{11}-2640\,b^7\,c^5\,d^6\,e^{10}+5280\,b^6\,c^6\,d^7\,e^9-7376\,b^5\,c^7\,d^8\,e^8+7296\,b^4\,c^8\,d^9\,e^7-5040\,b^3\,c^9\,d^{10}\,e^6+2320\,b^2\,c^{10}\,d^{11}\,e^5-640\,b\,c^{11}\,d^{12}\,e^4+80\,c^{12}\,d^{13}\,e^3\right)}+\frac{16\,b^{10}\,c^2\,d^5\,e^{13}\,\sqrt{d+e\,x}}{\sqrt{d^5}\,\left(16\,b^{10}\,c^2\,d^3\,e^{13}-176\,b^9\,c^3\,d^4\,e^{12}+880\,b^8\,c^4\,d^5\,e^{11}-2640\,b^7\,c^5\,d^6\,e^{10}+5280\,b^6\,c^6\,d^7\,e^9-7376\,b^5\,c^7\,d^8\,e^8+7296\,b^4\,c^8\,d^9\,e^7-5040\,b^3\,c^9\,d^{10}\,e^6+2320\,b^2\,c^{10}\,d^{11}\,e^5-640\,b\,c^{11}\,d^{12}\,e^4+80\,c^{12}\,d^{13}\,e^3\right)}-\frac{640\,b\,c^{11}\,d^{14}\,e^4\,\sqrt{d+e\,x}}{\sqrt{d^5}\,\left(16\,b^{10}\,c^2\,d^3\,e^{13}-176\,b^9\,c^3\,d^4\,e^{12}+880\,b^8\,c^4\,d^5\,e^{11}-2640\,b^7\,c^5\,d^6\,e^{10}+5280\,b^6\,c^6\,d^7\,e^9-7376\,b^5\,c^7\,d^8\,e^8+7296\,b^4\,c^8\,d^9\,e^7-5040\,b^3\,c^9\,d^{10}\,e^6+2320\,b^2\,c^{10}\,d^{11}\,e^5-640\,b\,c^{11}\,d^{12}\,e^4+80\,c^{12}\,d^{13}\,e^3\right)}\right)}{b\,\sqrt{d^5}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{d+e\,x}\,\left(8\,b^{10}\,c^3\,d^6\,e^{12}-80\,b^9\,c^4\,d^7\,e^{11}+360\,b^8\,c^5\,d^8\,e^{10}-960\,b^7\,c^6\,d^9\,e^9+1688\,b^6\,c^7\,d^{10}\,e^8-2064\,b^5\,c^8\,d^{11}\,e^7+1800\,b^4\,c^9\,d^{12}\,e^6-1120\,b^3\,c^{10}\,d^{13}\,e^5+480\,b^2\,c^{11}\,d^{14}\,e^4-128\,b\,c^{12}\,d^{15}\,e^3+16\,c^{13}\,d^{16}\,e^2\right)+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(24\,b^2\,c^{12}\,d^{18}\,e^3-216\,b^3\,c^{11}\,d^{17}\,e^4+872\,b^4\,c^{10}\,d^{16}\,e^5-2080\,b^5\,c^9\,d^{15}\,e^6+3248\,b^6\,c^8\,d^{14}\,e^7-3472\,b^7\,c^7\,d^{13}\,e^8+2576\,b^8\,c^6\,d^{12}\,e^9-1312\,b^9\,c^5\,d^{11}\,e^{10}+440\,b^{10}\,c^4\,d^{10}\,e^{11}-88\,b^{11}\,c^3\,d^9\,e^{12}+8\,b^{12}\,c^2\,d^8\,e^{13}-\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\sqrt{d+e\,x}\,\left(-8\,b^{13}\,c^2\,d^{10}\,e^{13}+96\,b^{12}\,c^3\,d^{11}\,e^{12}-520\,b^{11}\,c^4\,d^{12}\,e^{11}+1680\,b^{10}\,c^5\,d^{13}\,e^{10}-3600\,b^9\,c^6\,d^{14}\,e^9+5376\,b^8\,c^7\,d^{15}\,e^8-5712\,b^7\,c^8\,d^{16}\,e^7+4320\,b^6\,c^9\,d^{17}\,e^6-2280\,b^5\,c^{10}\,d^{18}\,e^5+800\,b^4\,c^{11}\,d^{19}\,e^4-168\,b^3\,c^{12}\,d^{20}\,e^3+16\,b^2\,c^{13}\,d^{21}\,e^2\right)}{b\,{\left(b\,e-c\,d\right)}^5}\right)}{b\,{\left(b\,e-c\,d\right)}^5}\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,1{}\mathrm{i}}{b\,{\left(b\,e-c\,d\right)}^5}+\frac{\left(\sqrt{d+e\,x}\,\left(8\,b^{10}\,c^3\,d^6\,e^{12}-80\,b^9\,c^4\,d^7\,e^{11}+360\,b^8\,c^5\,d^8\,e^{10}-960\,b^7\,c^6\,d^9\,e^9+1688\,b^6\,c^7\,d^{10}\,e^8-2064\,b^5\,c^8\,d^{11}\,e^7+1800\,b^4\,c^9\,d^{12}\,e^6-1120\,b^3\,c^{10}\,d^{13}\,e^5+480\,b^2\,c^{11}\,d^{14}\,e^4-128\,b\,c^{12}\,d^{15}\,e^3+16\,c^{13}\,d^{16}\,e^2\right)-\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(24\,b^2\,c^{12}\,d^{18}\,e^3-216\,b^3\,c^{11}\,d^{17}\,e^4+872\,b^4\,c^{10}\,d^{16}\,e^5-2080\,b^5\,c^9\,d^{15}\,e^6+3248\,b^6\,c^8\,d^{14}\,e^7-3472\,b^7\,c^7\,d^{13}\,e^8+2576\,b^8\,c^6\,d^{12}\,e^9-1312\,b^9\,c^5\,d^{11}\,e^{10}+440\,b^{10}\,c^4\,d^{10}\,e^{11}-88\,b^{11}\,c^3\,d^9\,e^{12}+8\,b^{12}\,c^2\,d^8\,e^{13}+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\sqrt{d+e\,x}\,\left(-8\,b^{13}\,c^2\,d^{10}\,e^{13}+96\,b^{12}\,c^3\,d^{11}\,e^{12}-520\,b^{11}\,c^4\,d^{12}\,e^{11}+1680\,b^{10}\,c^5\,d^{13}\,e^{10}-3600\,b^9\,c^6\,d^{14}\,e^9+5376\,b^8\,c^7\,d^{15}\,e^8-5712\,b^7\,c^8\,d^{16}\,e^7+4320\,b^6\,c^9\,d^{17}\,e^6-2280\,b^5\,c^{10}\,d^{18}\,e^5+800\,b^4\,c^{11}\,d^{19}\,e^4-168\,b^3\,c^{12}\,d^{20}\,e^3+16\,b^2\,c^{13}\,d^{21}\,e^2\right)}{b\,{\left(b\,e-c\,d\right)}^5}\right)}{b\,{\left(b\,e-c\,d\right)}^5}\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,1{}\mathrm{i}}{b\,{\left(b\,e-c\,d\right)}^5}}{32\,c^{12}\,d^{13}\,e^3-208\,b\,c^{11}\,d^{12}\,e^4+576\,b^2\,c^{10}\,d^{11}\,e^5-880\,b^3\,c^9\,d^{10}\,e^6+800\,b^4\,c^8\,d^9\,e^7-432\,b^5\,c^7\,d^8\,e^8+128\,b^6\,c^6\,d^7\,e^9-16\,b^7\,c^5\,d^6\,e^{10}+\frac{\left(\sqrt{d+e\,x}\,\left(8\,b^{10}\,c^3\,d^6\,e^{12}-80\,b^9\,c^4\,d^7\,e^{11}+360\,b^8\,c^5\,d^8\,e^{10}-960\,b^7\,c^6\,d^9\,e^9+1688\,b^6\,c^7\,d^{10}\,e^8-2064\,b^5\,c^8\,d^{11}\,e^7+1800\,b^4\,c^9\,d^{12}\,e^6-1120\,b^3\,c^{10}\,d^{13}\,e^5+480\,b^2\,c^{11}\,d^{14}\,e^4-128\,b\,c^{12}\,d^{15}\,e^3+16\,c^{13}\,d^{16}\,e^2\right)+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(24\,b^2\,c^{12}\,d^{18}\,e^3-216\,b^3\,c^{11}\,d^{17}\,e^4+872\,b^4\,c^{10}\,d^{16}\,e^5-2080\,b^5\,c^9\,d^{15}\,e^6+3248\,b^6\,c^8\,d^{14}\,e^7-3472\,b^7\,c^7\,d^{13}\,e^8+2576\,b^8\,c^6\,d^{12}\,e^9-1312\,b^9\,c^5\,d^{11}\,e^{10}+440\,b^{10}\,c^4\,d^{10}\,e^{11}-88\,b^{11}\,c^3\,d^9\,e^{12}+8\,b^{12}\,c^2\,d^8\,e^{13}-\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\sqrt{d+e\,x}\,\left(-8\,b^{13}\,c^2\,d^{10}\,e^{13}+96\,b^{12}\,c^3\,d^{11}\,e^{12}-520\,b^{11}\,c^4\,d^{12}\,e^{11}+1680\,b^{10}\,c^5\,d^{13}\,e^{10}-3600\,b^9\,c^6\,d^{14}\,e^9+5376\,b^8\,c^7\,d^{15}\,e^8-5712\,b^7\,c^8\,d^{16}\,e^7+4320\,b^6\,c^9\,d^{17}\,e^6-2280\,b^5\,c^{10}\,d^{18}\,e^5+800\,b^4\,c^{11}\,d^{19}\,e^4-168\,b^3\,c^{12}\,d^{20}\,e^3+16\,b^2\,c^{13}\,d^{21}\,e^2\right)}{b\,{\left(b\,e-c\,d\right)}^5}\right)}{b\,{\left(b\,e-c\,d\right)}^5}\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}}{b\,{\left(b\,e-c\,d\right)}^5}-\frac{\left(\sqrt{d+e\,x}\,\left(8\,b^{10}\,c^3\,d^6\,e^{12}-80\,b^9\,c^4\,d^7\,e^{11}+360\,b^8\,c^5\,d^8\,e^{10}-960\,b^7\,c^6\,d^9\,e^9+1688\,b^6\,c^7\,d^{10}\,e^8-2064\,b^5\,c^8\,d^{11}\,e^7+1800\,b^4\,c^9\,d^{12}\,e^6-1120\,b^3\,c^{10}\,d^{13}\,e^5+480\,b^2\,c^{11}\,d^{14}\,e^4-128\,b\,c^{12}\,d^{15}\,e^3+16\,c^{13}\,d^{16}\,e^2\right)-\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(24\,b^2\,c^{12}\,d^{18}\,e^3-216\,b^3\,c^{11}\,d^{17}\,e^4+872\,b^4\,c^{10}\,d^{16}\,e^5-2080\,b^5\,c^9\,d^{15}\,e^6+3248\,b^6\,c^8\,d^{14}\,e^7-3472\,b^7\,c^7\,d^{13}\,e^8+2576\,b^8\,c^6\,d^{12}\,e^9-1312\,b^9\,c^5\,d^{11}\,e^{10}+440\,b^{10}\,c^4\,d^{10}\,e^{11}-88\,b^{11}\,c^3\,d^9\,e^{12}+8\,b^{12}\,c^2\,d^8\,e^{13}+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\sqrt{d+e\,x}\,\left(-8\,b^{13}\,c^2\,d^{10}\,e^{13}+96\,b^{12}\,c^3\,d^{11}\,e^{12}-520\,b^{11}\,c^4\,d^{12}\,e^{11}+1680\,b^{10}\,c^5\,d^{13}\,e^{10}-3600\,b^9\,c^6\,d^{14}\,e^9+5376\,b^8\,c^7\,d^{15}\,e^8-5712\,b^7\,c^8\,d^{16}\,e^7+4320\,b^6\,c^9\,d^{17}\,e^6-2280\,b^5\,c^{10}\,d^{18}\,e^5+800\,b^4\,c^{11}\,d^{19}\,e^4-168\,b^3\,c^{12}\,d^{20}\,e^3+16\,b^2\,c^{13}\,d^{21}\,e^2\right)}{b\,{\left(b\,e-c\,d\right)}^5}\right)}{b\,{\left(b\,e-c\,d\right)}^5}\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}}{b\,{\left(b\,e-c\,d\right)}^5}}\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,2{}\mathrm{i}}{b\,{\left(b\,e-c\,d\right)}^5}","Not used",1,"(atan(((((d + e*x)^(1/2)*(16*c^13*d^16*e^2 - 128*b*c^12*d^15*e^3 + 480*b^2*c^11*d^14*e^4 - 1120*b^3*c^10*d^13*e^5 + 1800*b^4*c^9*d^12*e^6 - 2064*b^5*c^8*d^11*e^7 + 1688*b^6*c^7*d^10*e^8 - 960*b^7*c^6*d^9*e^9 + 360*b^8*c^5*d^8*e^10 - 80*b^9*c^4*d^7*e^11 + 8*b^10*c^3*d^6*e^12) + ((-c^5*(b*e - c*d)^5)^(1/2)*(24*b^2*c^12*d^18*e^3 - 216*b^3*c^11*d^17*e^4 + 872*b^4*c^10*d^16*e^5 - 2080*b^5*c^9*d^15*e^6 + 3248*b^6*c^8*d^14*e^7 - 3472*b^7*c^7*d^13*e^8 + 2576*b^8*c^6*d^12*e^9 - 1312*b^9*c^5*d^11*e^10 + 440*b^10*c^4*d^10*e^11 - 88*b^11*c^3*d^9*e^12 + 8*b^12*c^2*d^8*e^13 - ((-c^5*(b*e - c*d)^5)^(1/2)*(d + e*x)^(1/2)*(16*b^2*c^13*d^21*e^2 - 168*b^3*c^12*d^20*e^3 + 800*b^4*c^11*d^19*e^4 - 2280*b^5*c^10*d^18*e^5 + 4320*b^6*c^9*d^17*e^6 - 5712*b^7*c^8*d^16*e^7 + 5376*b^8*c^7*d^15*e^8 - 3600*b^9*c^6*d^14*e^9 + 1680*b^10*c^5*d^13*e^10 - 520*b^11*c^4*d^12*e^11 + 96*b^12*c^3*d^11*e^12 - 8*b^13*c^2*d^10*e^13))/(b*(b*e - c*d)^5)))/(b*(b*e - c*d)^5))*(-c^5*(b*e - c*d)^5)^(1/2)*1i)/(b*(b*e - c*d)^5) + (((d + e*x)^(1/2)*(16*c^13*d^16*e^2 - 128*b*c^12*d^15*e^3 + 480*b^2*c^11*d^14*e^4 - 1120*b^3*c^10*d^13*e^5 + 1800*b^4*c^9*d^12*e^6 - 2064*b^5*c^8*d^11*e^7 + 1688*b^6*c^7*d^10*e^8 - 960*b^7*c^6*d^9*e^9 + 360*b^8*c^5*d^8*e^10 - 80*b^9*c^4*d^7*e^11 + 8*b^10*c^3*d^6*e^12) - ((-c^5*(b*e - c*d)^5)^(1/2)*(24*b^2*c^12*d^18*e^3 - 216*b^3*c^11*d^17*e^4 + 872*b^4*c^10*d^16*e^5 - 2080*b^5*c^9*d^15*e^6 + 3248*b^6*c^8*d^14*e^7 - 3472*b^7*c^7*d^13*e^8 + 2576*b^8*c^6*d^12*e^9 - 1312*b^9*c^5*d^11*e^10 + 440*b^10*c^4*d^10*e^11 - 88*b^11*c^3*d^9*e^12 + 8*b^12*c^2*d^8*e^13 + ((-c^5*(b*e - c*d)^5)^(1/2)*(d + e*x)^(1/2)*(16*b^2*c^13*d^21*e^2 - 168*b^3*c^12*d^20*e^3 + 800*b^4*c^11*d^19*e^4 - 2280*b^5*c^10*d^18*e^5 + 4320*b^6*c^9*d^17*e^6 - 5712*b^7*c^8*d^16*e^7 + 5376*b^8*c^7*d^15*e^8 - 3600*b^9*c^6*d^14*e^9 + 1680*b^10*c^5*d^13*e^10 - 520*b^11*c^4*d^12*e^11 + 96*b^12*c^3*d^11*e^12 - 8*b^13*c^2*d^10*e^13))/(b*(b*e - c*d)^5)))/(b*(b*e - c*d)^5))*(-c^5*(b*e - c*d)^5)^(1/2)*1i)/(b*(b*e - c*d)^5))/(32*c^12*d^13*e^3 - 208*b*c^11*d^12*e^4 + 576*b^2*c^10*d^11*e^5 - 880*b^3*c^9*d^10*e^6 + 800*b^4*c^8*d^9*e^7 - 432*b^5*c^7*d^8*e^8 + 128*b^6*c^6*d^7*e^9 - 16*b^7*c^5*d^6*e^10 + (((d + e*x)^(1/2)*(16*c^13*d^16*e^2 - 128*b*c^12*d^15*e^3 + 480*b^2*c^11*d^14*e^4 - 1120*b^3*c^10*d^13*e^5 + 1800*b^4*c^9*d^12*e^6 - 2064*b^5*c^8*d^11*e^7 + 1688*b^6*c^7*d^10*e^8 - 960*b^7*c^6*d^9*e^9 + 360*b^8*c^5*d^8*e^10 - 80*b^9*c^4*d^7*e^11 + 8*b^10*c^3*d^6*e^12) + ((-c^5*(b*e - c*d)^5)^(1/2)*(24*b^2*c^12*d^18*e^3 - 216*b^3*c^11*d^17*e^4 + 872*b^4*c^10*d^16*e^5 - 2080*b^5*c^9*d^15*e^6 + 3248*b^6*c^8*d^14*e^7 - 3472*b^7*c^7*d^13*e^8 + 2576*b^8*c^6*d^12*e^9 - 1312*b^9*c^5*d^11*e^10 + 440*b^10*c^4*d^10*e^11 - 88*b^11*c^3*d^9*e^12 + 8*b^12*c^2*d^8*e^13 - ((-c^5*(b*e - c*d)^5)^(1/2)*(d + e*x)^(1/2)*(16*b^2*c^13*d^21*e^2 - 168*b^3*c^12*d^20*e^3 + 800*b^4*c^11*d^19*e^4 - 2280*b^5*c^10*d^18*e^5 + 4320*b^6*c^9*d^17*e^6 - 5712*b^7*c^8*d^16*e^7 + 5376*b^8*c^7*d^15*e^8 - 3600*b^9*c^6*d^14*e^9 + 1680*b^10*c^5*d^13*e^10 - 520*b^11*c^4*d^12*e^11 + 96*b^12*c^3*d^11*e^12 - 8*b^13*c^2*d^10*e^13))/(b*(b*e - c*d)^5)))/(b*(b*e - c*d)^5))*(-c^5*(b*e - c*d)^5)^(1/2))/(b*(b*e - c*d)^5) - (((d + e*x)^(1/2)*(16*c^13*d^16*e^2 - 128*b*c^12*d^15*e^3 + 480*b^2*c^11*d^14*e^4 - 1120*b^3*c^10*d^13*e^5 + 1800*b^4*c^9*d^12*e^6 - 2064*b^5*c^8*d^11*e^7 + 1688*b^6*c^7*d^10*e^8 - 960*b^7*c^6*d^9*e^9 + 360*b^8*c^5*d^8*e^10 - 80*b^9*c^4*d^7*e^11 + 8*b^10*c^3*d^6*e^12) - ((-c^5*(b*e - c*d)^5)^(1/2)*(24*b^2*c^12*d^18*e^3 - 216*b^3*c^11*d^17*e^4 + 872*b^4*c^10*d^16*e^5 - 2080*b^5*c^9*d^15*e^6 + 3248*b^6*c^8*d^14*e^7 - 3472*b^7*c^7*d^13*e^8 + 2576*b^8*c^6*d^12*e^9 - 1312*b^9*c^5*d^11*e^10 + 440*b^10*c^4*d^10*e^11 - 88*b^11*c^3*d^9*e^12 + 8*b^12*c^2*d^8*e^13 + ((-c^5*(b*e - c*d)^5)^(1/2)*(d + e*x)^(1/2)*(16*b^2*c^13*d^21*e^2 - 168*b^3*c^12*d^20*e^3 + 800*b^4*c^11*d^19*e^4 - 2280*b^5*c^10*d^18*e^5 + 4320*b^6*c^9*d^17*e^6 - 5712*b^7*c^8*d^16*e^7 + 5376*b^8*c^7*d^15*e^8 - 3600*b^9*c^6*d^14*e^9 + 1680*b^10*c^5*d^13*e^10 - 520*b^11*c^4*d^12*e^11 + 96*b^12*c^3*d^11*e^12 - 8*b^13*c^2*d^10*e^13))/(b*(b*e - c*d)^5)))/(b*(b*e - c*d)^5))*(-c^5*(b*e - c*d)^5)^(1/2))/(b*(b*e - c*d)^5)))*(-c^5*(b*e - c*d)^5)^(1/2)*2i)/(b*(b*e - c*d)^5) - (2*atanh((80*c^12*d^15*e^3*(d + e*x)^(1/2))/((d^5)^(1/2)*(80*c^12*d^13*e^3 - 640*b*c^11*d^12*e^4 + 2320*b^2*c^10*d^11*e^5 - 5040*b^3*c^9*d^10*e^6 + 7296*b^4*c^8*d^9*e^7 - 7376*b^5*c^7*d^8*e^8 + 5280*b^6*c^6*d^7*e^9 - 2640*b^7*c^5*d^6*e^10 + 880*b^8*c^4*d^5*e^11 - 176*b^9*c^3*d^4*e^12 + 16*b^10*c^2*d^3*e^13)) + (2320*b^2*c^10*d^13*e^5*(d + e*x)^(1/2))/((d^5)^(1/2)*(80*c^12*d^13*e^3 - 640*b*c^11*d^12*e^4 + 2320*b^2*c^10*d^11*e^5 - 5040*b^3*c^9*d^10*e^6 + 7296*b^4*c^8*d^9*e^7 - 7376*b^5*c^7*d^8*e^8 + 5280*b^6*c^6*d^7*e^9 - 2640*b^7*c^5*d^6*e^10 + 880*b^8*c^4*d^5*e^11 - 176*b^9*c^3*d^4*e^12 + 16*b^10*c^2*d^3*e^13)) - (5040*b^3*c^9*d^12*e^6*(d + e*x)^(1/2))/((d^5)^(1/2)*(80*c^12*d^13*e^3 - 640*b*c^11*d^12*e^4 + 2320*b^2*c^10*d^11*e^5 - 5040*b^3*c^9*d^10*e^6 + 7296*b^4*c^8*d^9*e^7 - 7376*b^5*c^7*d^8*e^8 + 5280*b^6*c^6*d^7*e^9 - 2640*b^7*c^5*d^6*e^10 + 880*b^8*c^4*d^5*e^11 - 176*b^9*c^3*d^4*e^12 + 16*b^10*c^2*d^3*e^13)) + (7296*b^4*c^8*d^11*e^7*(d + e*x)^(1/2))/((d^5)^(1/2)*(80*c^12*d^13*e^3 - 640*b*c^11*d^12*e^4 + 2320*b^2*c^10*d^11*e^5 - 5040*b^3*c^9*d^10*e^6 + 7296*b^4*c^8*d^9*e^7 - 7376*b^5*c^7*d^8*e^8 + 5280*b^6*c^6*d^7*e^9 - 2640*b^7*c^5*d^6*e^10 + 880*b^8*c^4*d^5*e^11 - 176*b^9*c^3*d^4*e^12 + 16*b^10*c^2*d^3*e^13)) - (7376*b^5*c^7*d^10*e^8*(d + e*x)^(1/2))/((d^5)^(1/2)*(80*c^12*d^13*e^3 - 640*b*c^11*d^12*e^4 + 2320*b^2*c^10*d^11*e^5 - 5040*b^3*c^9*d^10*e^6 + 7296*b^4*c^8*d^9*e^7 - 7376*b^5*c^7*d^8*e^8 + 5280*b^6*c^6*d^7*e^9 - 2640*b^7*c^5*d^6*e^10 + 880*b^8*c^4*d^5*e^11 - 176*b^9*c^3*d^4*e^12 + 16*b^10*c^2*d^3*e^13)) + (5280*b^6*c^6*d^9*e^9*(d + e*x)^(1/2))/((d^5)^(1/2)*(80*c^12*d^13*e^3 - 640*b*c^11*d^12*e^4 + 2320*b^2*c^10*d^11*e^5 - 5040*b^3*c^9*d^10*e^6 + 7296*b^4*c^8*d^9*e^7 - 7376*b^5*c^7*d^8*e^8 + 5280*b^6*c^6*d^7*e^9 - 2640*b^7*c^5*d^6*e^10 + 880*b^8*c^4*d^5*e^11 - 176*b^9*c^3*d^4*e^12 + 16*b^10*c^2*d^3*e^13)) - (2640*b^7*c^5*d^8*e^10*(d + e*x)^(1/2))/((d^5)^(1/2)*(80*c^12*d^13*e^3 - 640*b*c^11*d^12*e^4 + 2320*b^2*c^10*d^11*e^5 - 5040*b^3*c^9*d^10*e^6 + 7296*b^4*c^8*d^9*e^7 - 7376*b^5*c^7*d^8*e^8 + 5280*b^6*c^6*d^7*e^9 - 2640*b^7*c^5*d^6*e^10 + 880*b^8*c^4*d^5*e^11 - 176*b^9*c^3*d^4*e^12 + 16*b^10*c^2*d^3*e^13)) + (880*b^8*c^4*d^7*e^11*(d + e*x)^(1/2))/((d^5)^(1/2)*(80*c^12*d^13*e^3 - 640*b*c^11*d^12*e^4 + 2320*b^2*c^10*d^11*e^5 - 5040*b^3*c^9*d^10*e^6 + 7296*b^4*c^8*d^9*e^7 - 7376*b^5*c^7*d^8*e^8 + 5280*b^6*c^6*d^7*e^9 - 2640*b^7*c^5*d^6*e^10 + 880*b^8*c^4*d^5*e^11 - 176*b^9*c^3*d^4*e^12 + 16*b^10*c^2*d^3*e^13)) - (176*b^9*c^3*d^6*e^12*(d + e*x)^(1/2))/((d^5)^(1/2)*(80*c^12*d^13*e^3 - 640*b*c^11*d^12*e^4 + 2320*b^2*c^10*d^11*e^5 - 5040*b^3*c^9*d^10*e^6 + 7296*b^4*c^8*d^9*e^7 - 7376*b^5*c^7*d^8*e^8 + 5280*b^6*c^6*d^7*e^9 - 2640*b^7*c^5*d^6*e^10 + 880*b^8*c^4*d^5*e^11 - 176*b^9*c^3*d^4*e^12 + 16*b^10*c^2*d^3*e^13)) + (16*b^10*c^2*d^5*e^13*(d + e*x)^(1/2))/((d^5)^(1/2)*(80*c^12*d^13*e^3 - 640*b*c^11*d^12*e^4 + 2320*b^2*c^10*d^11*e^5 - 5040*b^3*c^9*d^10*e^6 + 7296*b^4*c^8*d^9*e^7 - 7376*b^5*c^7*d^8*e^8 + 5280*b^6*c^6*d^7*e^9 - 2640*b^7*c^5*d^6*e^10 + 880*b^8*c^4*d^5*e^11 - 176*b^9*c^3*d^4*e^12 + 16*b^10*c^2*d^3*e^13)) - (640*b*c^11*d^14*e^4*(d + e*x)^(1/2))/((d^5)^(1/2)*(80*c^12*d^13*e^3 - 640*b*c^11*d^12*e^4 + 2320*b^2*c^10*d^11*e^5 - 5040*b^3*c^9*d^10*e^6 + 7296*b^4*c^8*d^9*e^7 - 7376*b^5*c^7*d^8*e^8 + 5280*b^6*c^6*d^7*e^9 - 2640*b^7*c^5*d^6*e^10 + 880*b^8*c^4*d^5*e^11 - 176*b^9*c^3*d^4*e^12 + 16*b^10*c^2*d^3*e^13))))/(b*(d^5)^(1/2)) - ((2*e)/(3*(c*d^2 - b*d*e)) - (2*e*(b*e - 2*c*d)*(d + e*x))/(c*d^2 - b*d*e)^2)/(d + e*x)^(3/2)","B"
368,1,4068,187,2.252524,"\text{Not used}","int(1/((b*x + c*x^2)*(d + e*x)^(7/2)),x)","-\frac{\frac{2\,e}{5\,\left(c\,d^2-b\,d\,e\right)}+\frac{2\,e\,{\left(d+e\,x\right)}^2\,\left(b^2\,e^2-3\,b\,c\,d\,e+3\,c^2\,d^2\right)}{{\left(c\,d^2-b\,d\,e\right)}^3}-\frac{2\,e\,\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)}{3\,{\left(c\,d^2-b\,d\,e\right)}^2}}{{\left(d+e\,x\right)}^{5/2}}-\frac{\mathrm{atan}\left(\frac{b^{16}\,d^{15}\,e^{16}\,\sqrt{d+e\,x}\,1{}\mathrm{i}-b\,c^{15}\,d^{30}\,e\,\sqrt{d+e\,x}\,7{}\mathrm{i}-b^{15}\,c\,d^{16}\,e^{15}\,\sqrt{d+e\,x}\,16{}\mathrm{i}+b^2\,c^{14}\,d^{29}\,e^2\,\sqrt{d+e\,x}\,84{}\mathrm{i}-b^3\,c^{13}\,d^{28}\,e^3\,\sqrt{d+e\,x}\,476{}\mathrm{i}+b^4\,c^{12}\,d^{27}\,e^4\,\sqrt{d+e\,x}\,1694{}\mathrm{i}-b^5\,c^{11}\,d^{26}\,e^5\,\sqrt{d+e\,x}\,4242{}\mathrm{i}+b^6\,c^{10}\,d^{25}\,e^6\,\sqrt{d+e\,x}\,7924{}\mathrm{i}-b^7\,c^9\,d^{24}\,e^7\,\sqrt{d+e\,x}\,11404{}\mathrm{i}+b^8\,c^8\,d^{23}\,e^8\,\sqrt{d+e\,x}\,12861{}\mathrm{i}-b^9\,c^7\,d^{22}\,e^9\,\sqrt{d+e\,x}\,11439{}\mathrm{i}+b^{10}\,c^6\,d^{21}\,e^{10}\,\sqrt{d+e\,x}\,8008{}\mathrm{i}-b^{11}\,c^5\,d^{20}\,e^{11}\,\sqrt{d+e\,x}\,4368{}\mathrm{i}+b^{12}\,c^4\,d^{19}\,e^{12}\,\sqrt{d+e\,x}\,1820{}\mathrm{i}-b^{13}\,c^3\,d^{18}\,e^{13}\,\sqrt{d+e\,x}\,560{}\mathrm{i}+b^{14}\,c^2\,d^{17}\,e^{14}\,\sqrt{d+e\,x}\,120{}\mathrm{i}}{d^7\,\sqrt{d^7}\,\left(d^7\,\left(d^7\,\left(11404\,b^7\,c^9\,e^7-7924\,b^6\,c^{10}\,d\,e^6+4242\,b^5\,c^{11}\,d^2\,e^5-1694\,b^4\,c^{12}\,d^3\,e^4+476\,b^3\,c^{13}\,d^4\,e^3-84\,b^2\,c^{14}\,d^5\,e^2+7\,b\,c^{15}\,d^6\,e\right)-120\,b^{14}\,c^2\,e^{14}+560\,b^{13}\,c^3\,d\,e^{13}-12861\,b^8\,c^8\,d^6\,e^8+11439\,b^9\,c^7\,d^5\,e^9-8008\,b^{10}\,c^6\,d^4\,e^{10}+4368\,b^{11}\,c^5\,d^3\,e^{11}-1820\,b^{12}\,c^4\,d^2\,e^{12}\right)-b^{16}\,d^5\,e^{16}+16\,b^{15}\,c\,d^6\,e^{15}\right)}\right)\,2{}\mathrm{i}}{b\,\sqrt{d^7}}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(\sqrt{d+e\,x}\,\left(-8\,b^{15}\,c^3\,d^9\,e^{17}+120\,b^{14}\,c^4\,d^{10}\,e^{16}-840\,b^{13}\,c^5\,d^{11}\,e^{15}+3640\,b^{12}\,c^6\,d^{12}\,e^{14}-10920\,b^{11}\,c^7\,d^{13}\,e^{13}+24024\,b^{10}\,c^8\,d^{14}\,e^{12}-40048\,b^9\,c^9\,d^{15}\,e^{11}+51552\,b^8\,c^{10}\,d^{16}\,e^{10}-51768\,b^7\,c^{11}\,d^{17}\,e^9+40712\,b^6\,c^{12}\,d^{18}\,e^8-25032\,b^5\,c^{13}\,d^{19}\,e^7+11928\,b^4\,c^{14}\,d^{20}\,e^6-4312\,b^3\,c^{15}\,d^{21}\,e^5+1128\,b^2\,c^{16}\,d^{22}\,e^4-192\,b\,c^{17}\,d^{23}\,e^3+16\,c^{18}\,d^{24}\,e^2\right)-\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(432\,b^3\,c^{16}\,d^{26}\,e^4-32\,b^2\,c^{17}\,d^{27}\,e^3-2720\,b^4\,c^{15}\,d^{25}\,e^5+10600\,b^5\,c^{14}\,d^{24}\,e^6-28608\,b^6\,c^{13}\,d^{23}\,e^7+56672\,b^7\,c^{12}\,d^{22}\,e^8-85184\,b^8\,c^{11}\,d^{21}\,e^9+99000\,b^9\,c^{10}\,d^{20}\,e^{10}-89760\,b^{10}\,c^9\,d^{19}\,e^{11}+63536\,b^{11}\,c^8\,d^{18}\,e^{12}-34848\,b^{12}\,c^7\,d^{17}\,e^{13}+14552\,b^{13}\,c^6\,d^{16}\,e^{14}-4480\,b^{14}\,c^5\,d^{15}\,e^{15}+960\,b^{15}\,c^4\,d^{14}\,e^{16}-128\,b^{16}\,c^3\,d^{13}\,e^{17}+8\,b^{17}\,c^2\,d^{12}\,e^{18}+\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\sqrt{d+e\,x}\,\left(8\,b^{18}\,c^2\,d^{15}\,e^{18}-136\,b^{17}\,c^3\,d^{16}\,e^{17}+1080\,b^{16}\,c^4\,d^{17}\,e^{16}-5320\,b^{15}\,c^5\,d^{18}\,e^{15}+18200\,b^{14}\,c^6\,d^{19}\,e^{14}-45864\,b^{13}\,c^7\,d^{20}\,e^{13}+88088\,b^{12}\,c^8\,d^{21}\,e^{12}-131560\,b^{11}\,c^9\,d^{22}\,e^{11}+154440\,b^{10}\,c^{10}\,d^{23}\,e^{10}-143000\,b^9\,c^{11}\,d^{24}\,e^9+104104\,b^8\,c^{12}\,d^{25}\,e^8-58968\,b^7\,c^{13}\,d^{26}\,e^7+25480\,b^6\,c^{14}\,d^{27}\,e^6-8120\,b^5\,c^{15}\,d^{28}\,e^5+1800\,b^4\,c^{16}\,d^{29}\,e^4-248\,b^3\,c^{17}\,d^{30}\,e^3+16\,b^2\,c^{18}\,d^{31}\,e^2\right)}{b\,{\left(b\,e-c\,d\right)}^7}\right)}{b\,{\left(b\,e-c\,d\right)}^7}\right)\,1{}\mathrm{i}}{b\,{\left(b\,e-c\,d\right)}^7}+\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(\sqrt{d+e\,x}\,\left(-8\,b^{15}\,c^3\,d^9\,e^{17}+120\,b^{14}\,c^4\,d^{10}\,e^{16}-840\,b^{13}\,c^5\,d^{11}\,e^{15}+3640\,b^{12}\,c^6\,d^{12}\,e^{14}-10920\,b^{11}\,c^7\,d^{13}\,e^{13}+24024\,b^{10}\,c^8\,d^{14}\,e^{12}-40048\,b^9\,c^9\,d^{15}\,e^{11}+51552\,b^8\,c^{10}\,d^{16}\,e^{10}-51768\,b^7\,c^{11}\,d^{17}\,e^9+40712\,b^6\,c^{12}\,d^{18}\,e^8-25032\,b^5\,c^{13}\,d^{19}\,e^7+11928\,b^4\,c^{14}\,d^{20}\,e^6-4312\,b^3\,c^{15}\,d^{21}\,e^5+1128\,b^2\,c^{16}\,d^{22}\,e^4-192\,b\,c^{17}\,d^{23}\,e^3+16\,c^{18}\,d^{24}\,e^2\right)-\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(32\,b^2\,c^{17}\,d^{27}\,e^3-432\,b^3\,c^{16}\,d^{26}\,e^4+2720\,b^4\,c^{15}\,d^{25}\,e^5-10600\,b^5\,c^{14}\,d^{24}\,e^6+28608\,b^6\,c^{13}\,d^{23}\,e^7-56672\,b^7\,c^{12}\,d^{22}\,e^8+85184\,b^8\,c^{11}\,d^{21}\,e^9-99000\,b^9\,c^{10}\,d^{20}\,e^{10}+89760\,b^{10}\,c^9\,d^{19}\,e^{11}-63536\,b^{11}\,c^8\,d^{18}\,e^{12}+34848\,b^{12}\,c^7\,d^{17}\,e^{13}-14552\,b^{13}\,c^6\,d^{16}\,e^{14}+4480\,b^{14}\,c^5\,d^{15}\,e^{15}-960\,b^{15}\,c^4\,d^{14}\,e^{16}+128\,b^{16}\,c^3\,d^{13}\,e^{17}-8\,b^{17}\,c^2\,d^{12}\,e^{18}+\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\sqrt{d+e\,x}\,\left(8\,b^{18}\,c^2\,d^{15}\,e^{18}-136\,b^{17}\,c^3\,d^{16}\,e^{17}+1080\,b^{16}\,c^4\,d^{17}\,e^{16}-5320\,b^{15}\,c^5\,d^{18}\,e^{15}+18200\,b^{14}\,c^6\,d^{19}\,e^{14}-45864\,b^{13}\,c^7\,d^{20}\,e^{13}+88088\,b^{12}\,c^8\,d^{21}\,e^{12}-131560\,b^{11}\,c^9\,d^{22}\,e^{11}+154440\,b^{10}\,c^{10}\,d^{23}\,e^{10}-143000\,b^9\,c^{11}\,d^{24}\,e^9+104104\,b^8\,c^{12}\,d^{25}\,e^8-58968\,b^7\,c^{13}\,d^{26}\,e^7+25480\,b^6\,c^{14}\,d^{27}\,e^6-8120\,b^5\,c^{15}\,d^{28}\,e^5+1800\,b^4\,c^{16}\,d^{29}\,e^4-248\,b^3\,c^{17}\,d^{30}\,e^3+16\,b^2\,c^{18}\,d^{31}\,e^2\right)}{b\,{\left(b\,e-c\,d\right)}^7}\right)}{b\,{\left(b\,e-c\,d\right)}^7}\right)\,1{}\mathrm{i}}{b\,{\left(b\,e-c\,d\right)}^7}}{48\,c^{17}\,d^{20}\,e^3-480\,b\,c^{16}\,d^{19}\,e^4+\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(\sqrt{d+e\,x}\,\left(-8\,b^{15}\,c^3\,d^9\,e^{17}+120\,b^{14}\,c^4\,d^{10}\,e^{16}-840\,b^{13}\,c^5\,d^{11}\,e^{15}+3640\,b^{12}\,c^6\,d^{12}\,e^{14}-10920\,b^{11}\,c^7\,d^{13}\,e^{13}+24024\,b^{10}\,c^8\,d^{14}\,e^{12}-40048\,b^9\,c^9\,d^{15}\,e^{11}+51552\,b^8\,c^{10}\,d^{16}\,e^{10}-51768\,b^7\,c^{11}\,d^{17}\,e^9+40712\,b^6\,c^{12}\,d^{18}\,e^8-25032\,b^5\,c^{13}\,d^{19}\,e^7+11928\,b^4\,c^{14}\,d^{20}\,e^6-4312\,b^3\,c^{15}\,d^{21}\,e^5+1128\,b^2\,c^{16}\,d^{22}\,e^4-192\,b\,c^{17}\,d^{23}\,e^3+16\,c^{18}\,d^{24}\,e^2\right)-\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(432\,b^3\,c^{16}\,d^{26}\,e^4-32\,b^2\,c^{17}\,d^{27}\,e^3-2720\,b^4\,c^{15}\,d^{25}\,e^5+10600\,b^5\,c^{14}\,d^{24}\,e^6-28608\,b^6\,c^{13}\,d^{23}\,e^7+56672\,b^7\,c^{12}\,d^{22}\,e^8-85184\,b^8\,c^{11}\,d^{21}\,e^9+99000\,b^9\,c^{10}\,d^{20}\,e^{10}-89760\,b^{10}\,c^9\,d^{19}\,e^{11}+63536\,b^{11}\,c^8\,d^{18}\,e^{12}-34848\,b^{12}\,c^7\,d^{17}\,e^{13}+14552\,b^{13}\,c^6\,d^{16}\,e^{14}-4480\,b^{14}\,c^5\,d^{15}\,e^{15}+960\,b^{15}\,c^4\,d^{14}\,e^{16}-128\,b^{16}\,c^3\,d^{13}\,e^{17}+8\,b^{17}\,c^2\,d^{12}\,e^{18}+\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\sqrt{d+e\,x}\,\left(8\,b^{18}\,c^2\,d^{15}\,e^{18}-136\,b^{17}\,c^3\,d^{16}\,e^{17}+1080\,b^{16}\,c^4\,d^{17}\,e^{16}-5320\,b^{15}\,c^5\,d^{18}\,e^{15}+18200\,b^{14}\,c^6\,d^{19}\,e^{14}-45864\,b^{13}\,c^7\,d^{20}\,e^{13}+88088\,b^{12}\,c^8\,d^{21}\,e^{12}-131560\,b^{11}\,c^9\,d^{22}\,e^{11}+154440\,b^{10}\,c^{10}\,d^{23}\,e^{10}-143000\,b^9\,c^{11}\,d^{24}\,e^9+104104\,b^8\,c^{12}\,d^{25}\,e^8-58968\,b^7\,c^{13}\,d^{26}\,e^7+25480\,b^6\,c^{14}\,d^{27}\,e^6-8120\,b^5\,c^{15}\,d^{28}\,e^5+1800\,b^4\,c^{16}\,d^{29}\,e^4-248\,b^3\,c^{17}\,d^{30}\,e^3+16\,b^2\,c^{18}\,d^{31}\,e^2\right)}{b\,{\left(b\,e-c\,d\right)}^7}\right)}{b\,{\left(b\,e-c\,d\right)}^7}\right)}{b\,{\left(b\,e-c\,d\right)}^7}-\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(\sqrt{d+e\,x}\,\left(-8\,b^{15}\,c^3\,d^9\,e^{17}+120\,b^{14}\,c^4\,d^{10}\,e^{16}-840\,b^{13}\,c^5\,d^{11}\,e^{15}+3640\,b^{12}\,c^6\,d^{12}\,e^{14}-10920\,b^{11}\,c^7\,d^{13}\,e^{13}+24024\,b^{10}\,c^8\,d^{14}\,e^{12}-40048\,b^9\,c^9\,d^{15}\,e^{11}+51552\,b^8\,c^{10}\,d^{16}\,e^{10}-51768\,b^7\,c^{11}\,d^{17}\,e^9+40712\,b^6\,c^{12}\,d^{18}\,e^8-25032\,b^5\,c^{13}\,d^{19}\,e^7+11928\,b^4\,c^{14}\,d^{20}\,e^6-4312\,b^3\,c^{15}\,d^{21}\,e^5+1128\,b^2\,c^{16}\,d^{22}\,e^4-192\,b\,c^{17}\,d^{23}\,e^3+16\,c^{18}\,d^{24}\,e^2\right)-\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(32\,b^2\,c^{17}\,d^{27}\,e^3-432\,b^3\,c^{16}\,d^{26}\,e^4+2720\,b^4\,c^{15}\,d^{25}\,e^5-10600\,b^5\,c^{14}\,d^{24}\,e^6+28608\,b^6\,c^{13}\,d^{23}\,e^7-56672\,b^7\,c^{12}\,d^{22}\,e^8+85184\,b^8\,c^{11}\,d^{21}\,e^9-99000\,b^9\,c^{10}\,d^{20}\,e^{10}+89760\,b^{10}\,c^9\,d^{19}\,e^{11}-63536\,b^{11}\,c^8\,d^{18}\,e^{12}+34848\,b^{12}\,c^7\,d^{17}\,e^{13}-14552\,b^{13}\,c^6\,d^{16}\,e^{14}+4480\,b^{14}\,c^5\,d^{15}\,e^{15}-960\,b^{15}\,c^4\,d^{14}\,e^{16}+128\,b^{16}\,c^3\,d^{13}\,e^{17}-8\,b^{17}\,c^2\,d^{12}\,e^{18}+\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\sqrt{d+e\,x}\,\left(8\,b^{18}\,c^2\,d^{15}\,e^{18}-136\,b^{17}\,c^3\,d^{16}\,e^{17}+1080\,b^{16}\,c^4\,d^{17}\,e^{16}-5320\,b^{15}\,c^5\,d^{18}\,e^{15}+18200\,b^{14}\,c^6\,d^{19}\,e^{14}-45864\,b^{13}\,c^7\,d^{20}\,e^{13}+88088\,b^{12}\,c^8\,d^{21}\,e^{12}-131560\,b^{11}\,c^9\,d^{22}\,e^{11}+154440\,b^{10}\,c^{10}\,d^{23}\,e^{10}-143000\,b^9\,c^{11}\,d^{24}\,e^9+104104\,b^8\,c^{12}\,d^{25}\,e^8-58968\,b^7\,c^{13}\,d^{26}\,e^7+25480\,b^6\,c^{14}\,d^{27}\,e^6-8120\,b^5\,c^{15}\,d^{28}\,e^5+1800\,b^4\,c^{16}\,d^{29}\,e^4-248\,b^3\,c^{17}\,d^{30}\,e^3+16\,b^2\,c^{18}\,d^{31}\,e^2\right)}{b\,{\left(b\,e-c\,d\right)}^7}\right)}{b\,{\left(b\,e-c\,d\right)}^7}\right)}{b\,{\left(b\,e-c\,d\right)}^7}+2176\,b^2\,c^{15}\,d^{18}\,e^5-5904\,b^3\,c^{14}\,d^{17}\,e^6+10656\,b^4\,c^{13}\,d^{16}\,e^7-13440\,b^5\,c^{12}\,d^{15}\,e^8+12096\,b^6\,c^{11}\,d^{14}\,e^9-7776\,b^7\,c^{10}\,d^{13}\,e^{10}+3504\,b^8\,c^9\,d^{12}\,e^{11}-1056\,b^9\,c^8\,d^{11}\,e^{12}+192\,b^{10}\,c^7\,d^{10}\,e^{13}-16\,b^{11}\,c^6\,d^9\,e^{14}}\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,2{}\mathrm{i}}{b\,{\left(b\,e-c\,d\right)}^7}","Not used",1,"(atan((((-c^7*(b*e - c*d)^7)^(1/2)*((d + e*x)^(1/2)*(16*c^18*d^24*e^2 - 192*b*c^17*d^23*e^3 + 1128*b^2*c^16*d^22*e^4 - 4312*b^3*c^15*d^21*e^5 + 11928*b^4*c^14*d^20*e^6 - 25032*b^5*c^13*d^19*e^7 + 40712*b^6*c^12*d^18*e^8 - 51768*b^7*c^11*d^17*e^9 + 51552*b^8*c^10*d^16*e^10 - 40048*b^9*c^9*d^15*e^11 + 24024*b^10*c^8*d^14*e^12 - 10920*b^11*c^7*d^13*e^13 + 3640*b^12*c^6*d^12*e^14 - 840*b^13*c^5*d^11*e^15 + 120*b^14*c^4*d^10*e^16 - 8*b^15*c^3*d^9*e^17) - ((-c^7*(b*e - c*d)^7)^(1/2)*(432*b^3*c^16*d^26*e^4 - 32*b^2*c^17*d^27*e^3 - 2720*b^4*c^15*d^25*e^5 + 10600*b^5*c^14*d^24*e^6 - 28608*b^6*c^13*d^23*e^7 + 56672*b^7*c^12*d^22*e^8 - 85184*b^8*c^11*d^21*e^9 + 99000*b^9*c^10*d^20*e^10 - 89760*b^10*c^9*d^19*e^11 + 63536*b^11*c^8*d^18*e^12 - 34848*b^12*c^7*d^17*e^13 + 14552*b^13*c^6*d^16*e^14 - 4480*b^14*c^5*d^15*e^15 + 960*b^15*c^4*d^14*e^16 - 128*b^16*c^3*d^13*e^17 + 8*b^17*c^2*d^12*e^18 + ((-c^7*(b*e - c*d)^7)^(1/2)*(d + e*x)^(1/2)*(16*b^2*c^18*d^31*e^2 - 248*b^3*c^17*d^30*e^3 + 1800*b^4*c^16*d^29*e^4 - 8120*b^5*c^15*d^28*e^5 + 25480*b^6*c^14*d^27*e^6 - 58968*b^7*c^13*d^26*e^7 + 104104*b^8*c^12*d^25*e^8 - 143000*b^9*c^11*d^24*e^9 + 154440*b^10*c^10*d^23*e^10 - 131560*b^11*c^9*d^22*e^11 + 88088*b^12*c^8*d^21*e^12 - 45864*b^13*c^7*d^20*e^13 + 18200*b^14*c^6*d^19*e^14 - 5320*b^15*c^5*d^18*e^15 + 1080*b^16*c^4*d^17*e^16 - 136*b^17*c^3*d^16*e^17 + 8*b^18*c^2*d^15*e^18))/(b*(b*e - c*d)^7)))/(b*(b*e - c*d)^7))*1i)/(b*(b*e - c*d)^7) + ((-c^7*(b*e - c*d)^7)^(1/2)*((d + e*x)^(1/2)*(16*c^18*d^24*e^2 - 192*b*c^17*d^23*e^3 + 1128*b^2*c^16*d^22*e^4 - 4312*b^3*c^15*d^21*e^5 + 11928*b^4*c^14*d^20*e^6 - 25032*b^5*c^13*d^19*e^7 + 40712*b^6*c^12*d^18*e^8 - 51768*b^7*c^11*d^17*e^9 + 51552*b^8*c^10*d^16*e^10 - 40048*b^9*c^9*d^15*e^11 + 24024*b^10*c^8*d^14*e^12 - 10920*b^11*c^7*d^13*e^13 + 3640*b^12*c^6*d^12*e^14 - 840*b^13*c^5*d^11*e^15 + 120*b^14*c^4*d^10*e^16 - 8*b^15*c^3*d^9*e^17) - ((-c^7*(b*e - c*d)^7)^(1/2)*(32*b^2*c^17*d^27*e^3 - 432*b^3*c^16*d^26*e^4 + 2720*b^4*c^15*d^25*e^5 - 10600*b^5*c^14*d^24*e^6 + 28608*b^6*c^13*d^23*e^7 - 56672*b^7*c^12*d^22*e^8 + 85184*b^8*c^11*d^21*e^9 - 99000*b^9*c^10*d^20*e^10 + 89760*b^10*c^9*d^19*e^11 - 63536*b^11*c^8*d^18*e^12 + 34848*b^12*c^7*d^17*e^13 - 14552*b^13*c^6*d^16*e^14 + 4480*b^14*c^5*d^15*e^15 - 960*b^15*c^4*d^14*e^16 + 128*b^16*c^3*d^13*e^17 - 8*b^17*c^2*d^12*e^18 + ((-c^7*(b*e - c*d)^7)^(1/2)*(d + e*x)^(1/2)*(16*b^2*c^18*d^31*e^2 - 248*b^3*c^17*d^30*e^3 + 1800*b^4*c^16*d^29*e^4 - 8120*b^5*c^15*d^28*e^5 + 25480*b^6*c^14*d^27*e^6 - 58968*b^7*c^13*d^26*e^7 + 104104*b^8*c^12*d^25*e^8 - 143000*b^9*c^11*d^24*e^9 + 154440*b^10*c^10*d^23*e^10 - 131560*b^11*c^9*d^22*e^11 + 88088*b^12*c^8*d^21*e^12 - 45864*b^13*c^7*d^20*e^13 + 18200*b^14*c^6*d^19*e^14 - 5320*b^15*c^5*d^18*e^15 + 1080*b^16*c^4*d^17*e^16 - 136*b^17*c^3*d^16*e^17 + 8*b^18*c^2*d^15*e^18))/(b*(b*e - c*d)^7)))/(b*(b*e - c*d)^7))*1i)/(b*(b*e - c*d)^7))/(48*c^17*d^20*e^3 - 480*b*c^16*d^19*e^4 + ((-c^7*(b*e - c*d)^7)^(1/2)*((d + e*x)^(1/2)*(16*c^18*d^24*e^2 - 192*b*c^17*d^23*e^3 + 1128*b^2*c^16*d^22*e^4 - 4312*b^3*c^15*d^21*e^5 + 11928*b^4*c^14*d^20*e^6 - 25032*b^5*c^13*d^19*e^7 + 40712*b^6*c^12*d^18*e^8 - 51768*b^7*c^11*d^17*e^9 + 51552*b^8*c^10*d^16*e^10 - 40048*b^9*c^9*d^15*e^11 + 24024*b^10*c^8*d^14*e^12 - 10920*b^11*c^7*d^13*e^13 + 3640*b^12*c^6*d^12*e^14 - 840*b^13*c^5*d^11*e^15 + 120*b^14*c^4*d^10*e^16 - 8*b^15*c^3*d^9*e^17) - ((-c^7*(b*e - c*d)^7)^(1/2)*(432*b^3*c^16*d^26*e^4 - 32*b^2*c^17*d^27*e^3 - 2720*b^4*c^15*d^25*e^5 + 10600*b^5*c^14*d^24*e^6 - 28608*b^6*c^13*d^23*e^7 + 56672*b^7*c^12*d^22*e^8 - 85184*b^8*c^11*d^21*e^9 + 99000*b^9*c^10*d^20*e^10 - 89760*b^10*c^9*d^19*e^11 + 63536*b^11*c^8*d^18*e^12 - 34848*b^12*c^7*d^17*e^13 + 14552*b^13*c^6*d^16*e^14 - 4480*b^14*c^5*d^15*e^15 + 960*b^15*c^4*d^14*e^16 - 128*b^16*c^3*d^13*e^17 + 8*b^17*c^2*d^12*e^18 + ((-c^7*(b*e - c*d)^7)^(1/2)*(d + e*x)^(1/2)*(16*b^2*c^18*d^31*e^2 - 248*b^3*c^17*d^30*e^3 + 1800*b^4*c^16*d^29*e^4 - 8120*b^5*c^15*d^28*e^5 + 25480*b^6*c^14*d^27*e^6 - 58968*b^7*c^13*d^26*e^7 + 104104*b^8*c^12*d^25*e^8 - 143000*b^9*c^11*d^24*e^9 + 154440*b^10*c^10*d^23*e^10 - 131560*b^11*c^9*d^22*e^11 + 88088*b^12*c^8*d^21*e^12 - 45864*b^13*c^7*d^20*e^13 + 18200*b^14*c^6*d^19*e^14 - 5320*b^15*c^5*d^18*e^15 + 1080*b^16*c^4*d^17*e^16 - 136*b^17*c^3*d^16*e^17 + 8*b^18*c^2*d^15*e^18))/(b*(b*e - c*d)^7)))/(b*(b*e - c*d)^7)))/(b*(b*e - c*d)^7) - ((-c^7*(b*e - c*d)^7)^(1/2)*((d + e*x)^(1/2)*(16*c^18*d^24*e^2 - 192*b*c^17*d^23*e^3 + 1128*b^2*c^16*d^22*e^4 - 4312*b^3*c^15*d^21*e^5 + 11928*b^4*c^14*d^20*e^6 - 25032*b^5*c^13*d^19*e^7 + 40712*b^6*c^12*d^18*e^8 - 51768*b^7*c^11*d^17*e^9 + 51552*b^8*c^10*d^16*e^10 - 40048*b^9*c^9*d^15*e^11 + 24024*b^10*c^8*d^14*e^12 - 10920*b^11*c^7*d^13*e^13 + 3640*b^12*c^6*d^12*e^14 - 840*b^13*c^5*d^11*e^15 + 120*b^14*c^4*d^10*e^16 - 8*b^15*c^3*d^9*e^17) - ((-c^7*(b*e - c*d)^7)^(1/2)*(32*b^2*c^17*d^27*e^3 - 432*b^3*c^16*d^26*e^4 + 2720*b^4*c^15*d^25*e^5 - 10600*b^5*c^14*d^24*e^6 + 28608*b^6*c^13*d^23*e^7 - 56672*b^7*c^12*d^22*e^8 + 85184*b^8*c^11*d^21*e^9 - 99000*b^9*c^10*d^20*e^10 + 89760*b^10*c^9*d^19*e^11 - 63536*b^11*c^8*d^18*e^12 + 34848*b^12*c^7*d^17*e^13 - 14552*b^13*c^6*d^16*e^14 + 4480*b^14*c^5*d^15*e^15 - 960*b^15*c^4*d^14*e^16 + 128*b^16*c^3*d^13*e^17 - 8*b^17*c^2*d^12*e^18 + ((-c^7*(b*e - c*d)^7)^(1/2)*(d + e*x)^(1/2)*(16*b^2*c^18*d^31*e^2 - 248*b^3*c^17*d^30*e^3 + 1800*b^4*c^16*d^29*e^4 - 8120*b^5*c^15*d^28*e^5 + 25480*b^6*c^14*d^27*e^6 - 58968*b^7*c^13*d^26*e^7 + 104104*b^8*c^12*d^25*e^8 - 143000*b^9*c^11*d^24*e^9 + 154440*b^10*c^10*d^23*e^10 - 131560*b^11*c^9*d^22*e^11 + 88088*b^12*c^8*d^21*e^12 - 45864*b^13*c^7*d^20*e^13 + 18200*b^14*c^6*d^19*e^14 - 5320*b^15*c^5*d^18*e^15 + 1080*b^16*c^4*d^17*e^16 - 136*b^17*c^3*d^16*e^17 + 8*b^18*c^2*d^15*e^18))/(b*(b*e - c*d)^7)))/(b*(b*e - c*d)^7)))/(b*(b*e - c*d)^7) + 2176*b^2*c^15*d^18*e^5 - 5904*b^3*c^14*d^17*e^6 + 10656*b^4*c^13*d^16*e^7 - 13440*b^5*c^12*d^15*e^8 + 12096*b^6*c^11*d^14*e^9 - 7776*b^7*c^10*d^13*e^10 + 3504*b^8*c^9*d^12*e^11 - 1056*b^9*c^8*d^11*e^12 + 192*b^10*c^7*d^10*e^13 - 16*b^11*c^6*d^9*e^14))*(-c^7*(b*e - c*d)^7)^(1/2)*2i)/(b*(b*e - c*d)^7) - (atan((b^16*d^15*e^16*(d + e*x)^(1/2)*1i - b*c^15*d^30*e*(d + e*x)^(1/2)*7i - b^15*c*d^16*e^15*(d + e*x)^(1/2)*16i + b^2*c^14*d^29*e^2*(d + e*x)^(1/2)*84i - b^3*c^13*d^28*e^3*(d + e*x)^(1/2)*476i + b^4*c^12*d^27*e^4*(d + e*x)^(1/2)*1694i - b^5*c^11*d^26*e^5*(d + e*x)^(1/2)*4242i + b^6*c^10*d^25*e^6*(d + e*x)^(1/2)*7924i - b^7*c^9*d^24*e^7*(d + e*x)^(1/2)*11404i + b^8*c^8*d^23*e^8*(d + e*x)^(1/2)*12861i - b^9*c^7*d^22*e^9*(d + e*x)^(1/2)*11439i + b^10*c^6*d^21*e^10*(d + e*x)^(1/2)*8008i - b^11*c^5*d^20*e^11*(d + e*x)^(1/2)*4368i + b^12*c^4*d^19*e^12*(d + e*x)^(1/2)*1820i - b^13*c^3*d^18*e^13*(d + e*x)^(1/2)*560i + b^14*c^2*d^17*e^14*(d + e*x)^(1/2)*120i)/(d^7*(d^7)^(1/2)*(d^7*(d^7*(11404*b^7*c^9*e^7 - 7924*b^6*c^10*d*e^6 - 84*b^2*c^14*d^5*e^2 + 476*b^3*c^13*d^4*e^3 - 1694*b^4*c^12*d^3*e^4 + 4242*b^5*c^11*d^2*e^5 + 7*b*c^15*d^6*e) - 120*b^14*c^2*e^14 + 560*b^13*c^3*d*e^13 - 12861*b^8*c^8*d^6*e^8 + 11439*b^9*c^7*d^5*e^9 - 8008*b^10*c^6*d^4*e^10 + 4368*b^11*c^5*d^3*e^11 - 1820*b^12*c^4*d^2*e^12) - b^16*d^5*e^16 + 16*b^15*c*d^6*e^15)))*2i)/(b*(d^7)^(1/2)) - ((2*e)/(5*(c*d^2 - b*d*e)) + (2*e*(d + e*x)^2*(b^2*e^2 + 3*c^2*d^2 - 3*b*c*d*e))/(c*d^2 - b*d*e)^3 - (2*e*(b*e - 2*c*d)*(d + e*x))/(3*(c*d^2 - b*d*e)^2))/(d + e*x)^(5/2)","B"
369,1,3360,251,1.015418,"\text{Not used}","int((d + e*x)^(9/2)/(b*x + c*x^2)^2,x)","\frac{\frac{{\left(d+e\,x\right)}^{3/2}\,\left(b^4\,e^5-4\,b^3\,c\,d\,e^4+6\,b^2\,c^2\,d^2\,e^3-4\,b\,c^3\,d^3\,e^2+2\,c^4\,d^4\,e\right)}{b^2}-\frac{\sqrt{d+e\,x}\,\left(b^4\,d\,e^5-4\,b^3\,c\,d^2\,e^4+6\,b^2\,c^2\,d^3\,e^3-5\,b\,c^3\,d^4\,e^2+2\,c^4\,d^5\,e\right)}{b^2}}{\left(2\,c^4\,d-b\,c^3\,e\right)\,\left(d+e\,x\right)-c^4\,{\left(d+e\,x\right)}^2-c^4\,d^2+b\,c^3\,d\,e}+\frac{2\,e^3\,{\left(d+e\,x\right)}^{3/2}}{3\,c^2}+\frac{2\,e^3\,\left(4\,c^2\,d-2\,b\,c\,e\right)\,\sqrt{d+e\,x}}{c^4}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{20\,b^{10}\,c^4\,d\,e^7-64\,b^9\,c^5\,d^2\,e^6+56\,b^8\,c^6\,d^3\,e^5-20\,b^7\,c^7\,d^4\,e^4+8\,b^6\,c^8\,d^5\,e^3}{b^6\,c^5}+\frac{\left(4\,b^7\,c^7\,e^3-8\,b^6\,c^8\,d\,e^2\right)\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d^7}\,\sqrt{d+e\,x}}{b^7\,c^5}\right)\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d^7}}{2\,b^3}+\frac{2\,\sqrt{d+e\,x}\,\left(25\,b^{10}\,e^{12}-160\,b^9\,c\,d\,e^{11}+396\,b^8\,c^2\,d^2\,e^{10}-408\,b^7\,c^3\,d^3\,e^9-42\,b^6\,c^4\,d^4\,e^8+504\,b^5\,c^5\,d^5\,e^7-420\,b^4\,c^6\,d^6\,e^6+24\,b^3\,c^7\,d^7\,e^5+234\,b^2\,c^8\,d^8\,e^4-160\,b\,c^9\,d^9\,e^3+32\,c^{10}\,d^{10}\,e^2\right)}{b^4\,c^5}\right)\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d^7}\,1{}\mathrm{i}}{2\,b^3}-\frac{\left(\frac{\left(\frac{20\,b^{10}\,c^4\,d\,e^7-64\,b^9\,c^5\,d^2\,e^6+56\,b^8\,c^6\,d^3\,e^5-20\,b^7\,c^7\,d^4\,e^4+8\,b^6\,c^8\,d^5\,e^3}{b^6\,c^5}-\frac{\left(4\,b^7\,c^7\,e^3-8\,b^6\,c^8\,d\,e^2\right)\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d^7}\,\sqrt{d+e\,x}}{b^7\,c^5}\right)\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d^7}}{2\,b^3}-\frac{2\,\sqrt{d+e\,x}\,\left(25\,b^{10}\,e^{12}-160\,b^9\,c\,d\,e^{11}+396\,b^8\,c^2\,d^2\,e^{10}-408\,b^7\,c^3\,d^3\,e^9-42\,b^6\,c^4\,d^4\,e^8+504\,b^5\,c^5\,d^5\,e^7-420\,b^4\,c^6\,d^6\,e^6+24\,b^3\,c^7\,d^7\,e^5+234\,b^2\,c^8\,d^8\,e^4-160\,b\,c^9\,d^9\,e^3+32\,c^{10}\,d^{10}\,e^2\right)}{b^4\,c^5}\right)\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d^7}\,1{}\mathrm{i}}{2\,b^3}}{\frac{\left(\frac{\left(\frac{20\,b^{10}\,c^4\,d\,e^7-64\,b^9\,c^5\,d^2\,e^6+56\,b^8\,c^6\,d^3\,e^5-20\,b^7\,c^7\,d^4\,e^4+8\,b^6\,c^8\,d^5\,e^3}{b^6\,c^5}+\frac{\left(4\,b^7\,c^7\,e^3-8\,b^6\,c^8\,d\,e^2\right)\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d^7}\,\sqrt{d+e\,x}}{b^7\,c^5}\right)\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d^7}}{2\,b^3}+\frac{2\,\sqrt{d+e\,x}\,\left(25\,b^{10}\,e^{12}-160\,b^9\,c\,d\,e^{11}+396\,b^8\,c^2\,d^2\,e^{10}-408\,b^7\,c^3\,d^3\,e^9-42\,b^6\,c^4\,d^4\,e^8+504\,b^5\,c^5\,d^5\,e^7-420\,b^4\,c^6\,d^6\,e^6+24\,b^3\,c^7\,d^7\,e^5+234\,b^2\,c^8\,d^8\,e^4-160\,b\,c^9\,d^9\,e^3+32\,c^{10}\,d^{10}\,e^2\right)}{b^4\,c^5}\right)\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d^7}}{2\,b^3}-\frac{2\,\left(225\,b^{10}\,d^4\,e^{13}-1540\,b^9\,c\,d^5\,e^{12}+4204\,b^8\,c^2\,d^6\,e^{11}-5256\,b^7\,c^3\,d^7\,e^{10}+1659\,b^6\,c^4\,d^8\,e^9+3048\,b^5\,c^5\,d^9\,e^8-3430\,b^4\,c^6\,d^{10}\,e^7+956\,b^3\,c^7\,d^{11}\,e^6+326\,b^2\,c^8\,d^{12}\,e^5-224\,b\,c^9\,d^{13}\,e^4+32\,c^{10}\,d^{14}\,e^3\right)}{b^6\,c^5}+\frac{\left(\frac{\left(\frac{20\,b^{10}\,c^4\,d\,e^7-64\,b^9\,c^5\,d^2\,e^6+56\,b^8\,c^6\,d^3\,e^5-20\,b^7\,c^7\,d^4\,e^4+8\,b^6\,c^8\,d^5\,e^3}{b^6\,c^5}-\frac{\left(4\,b^7\,c^7\,e^3-8\,b^6\,c^8\,d\,e^2\right)\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d^7}\,\sqrt{d+e\,x}}{b^7\,c^5}\right)\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d^7}}{2\,b^3}-\frac{2\,\sqrt{d+e\,x}\,\left(25\,b^{10}\,e^{12}-160\,b^9\,c\,d\,e^{11}+396\,b^8\,c^2\,d^2\,e^{10}-408\,b^7\,c^3\,d^3\,e^9-42\,b^6\,c^4\,d^4\,e^8+504\,b^5\,c^5\,d^5\,e^7-420\,b^4\,c^6\,d^6\,e^6+24\,b^3\,c^7\,d^7\,e^5+234\,b^2\,c^8\,d^8\,e^4-160\,b\,c^9\,d^9\,e^3+32\,c^{10}\,d^{10}\,e^2\right)}{b^4\,c^5}\right)\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d^7}}{2\,b^3}}\right)\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d^7}\,1{}\mathrm{i}}{b^3}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(\frac{2\,\sqrt{d+e\,x}\,\left(25\,b^{10}\,e^{12}-160\,b^9\,c\,d\,e^{11}+396\,b^8\,c^2\,d^2\,e^{10}-408\,b^7\,c^3\,d^3\,e^9-42\,b^6\,c^4\,d^4\,e^8+504\,b^5\,c^5\,d^5\,e^7-420\,b^4\,c^6\,d^6\,e^6+24\,b^3\,c^7\,d^7\,e^5+234\,b^2\,c^8\,d^8\,e^4-160\,b\,c^9\,d^9\,e^3+32\,c^{10}\,d^{10}\,e^2\right)}{b^4\,c^5}+\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(5\,b\,e+4\,c\,d\right)\,\left(\frac{20\,b^{10}\,c^4\,d\,e^7-64\,b^9\,c^5\,d^2\,e^6+56\,b^8\,c^6\,d^3\,e^5-20\,b^7\,c^7\,d^4\,e^4+8\,b^6\,c^8\,d^5\,e^3}{b^6\,c^5}+\frac{\left(4\,b^7\,c^7\,e^3-8\,b^6\,c^8\,d\,e^2\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(5\,b\,e+4\,c\,d\right)\,\sqrt{d+e\,x}}{b^7\,c^{12}}\right)}{2\,b^3\,c^7}\right)\,\left(5\,b\,e+4\,c\,d\right)\,1{}\mathrm{i}}{2\,b^3\,c^7}+\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(\frac{2\,\sqrt{d+e\,x}\,\left(25\,b^{10}\,e^{12}-160\,b^9\,c\,d\,e^{11}+396\,b^8\,c^2\,d^2\,e^{10}-408\,b^7\,c^3\,d^3\,e^9-42\,b^6\,c^4\,d^4\,e^8+504\,b^5\,c^5\,d^5\,e^7-420\,b^4\,c^6\,d^6\,e^6+24\,b^3\,c^7\,d^7\,e^5+234\,b^2\,c^8\,d^8\,e^4-160\,b\,c^9\,d^9\,e^3+32\,c^{10}\,d^{10}\,e^2\right)}{b^4\,c^5}-\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(5\,b\,e+4\,c\,d\right)\,\left(\frac{20\,b^{10}\,c^4\,d\,e^7-64\,b^9\,c^5\,d^2\,e^6+56\,b^8\,c^6\,d^3\,e^5-20\,b^7\,c^7\,d^4\,e^4+8\,b^6\,c^8\,d^5\,e^3}{b^6\,c^5}-\frac{\left(4\,b^7\,c^7\,e^3-8\,b^6\,c^8\,d\,e^2\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(5\,b\,e+4\,c\,d\right)\,\sqrt{d+e\,x}}{b^7\,c^{12}}\right)}{2\,b^3\,c^7}\right)\,\left(5\,b\,e+4\,c\,d\right)\,1{}\mathrm{i}}{2\,b^3\,c^7}}{\frac{2\,\left(225\,b^{10}\,d^4\,e^{13}-1540\,b^9\,c\,d^5\,e^{12}+4204\,b^8\,c^2\,d^6\,e^{11}-5256\,b^7\,c^3\,d^7\,e^{10}+1659\,b^6\,c^4\,d^8\,e^9+3048\,b^5\,c^5\,d^9\,e^8-3430\,b^4\,c^6\,d^{10}\,e^7+956\,b^3\,c^7\,d^{11}\,e^6+326\,b^2\,c^8\,d^{12}\,e^5-224\,b\,c^9\,d^{13}\,e^4+32\,c^{10}\,d^{14}\,e^3\right)}{b^6\,c^5}-\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(\frac{2\,\sqrt{d+e\,x}\,\left(25\,b^{10}\,e^{12}-160\,b^9\,c\,d\,e^{11}+396\,b^8\,c^2\,d^2\,e^{10}-408\,b^7\,c^3\,d^3\,e^9-42\,b^6\,c^4\,d^4\,e^8+504\,b^5\,c^5\,d^5\,e^7-420\,b^4\,c^6\,d^6\,e^6+24\,b^3\,c^7\,d^7\,e^5+234\,b^2\,c^8\,d^8\,e^4-160\,b\,c^9\,d^9\,e^3+32\,c^{10}\,d^{10}\,e^2\right)}{b^4\,c^5}+\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(5\,b\,e+4\,c\,d\right)\,\left(\frac{20\,b^{10}\,c^4\,d\,e^7-64\,b^9\,c^5\,d^2\,e^6+56\,b^8\,c^6\,d^3\,e^5-20\,b^7\,c^7\,d^4\,e^4+8\,b^6\,c^8\,d^5\,e^3}{b^6\,c^5}+\frac{\left(4\,b^7\,c^7\,e^3-8\,b^6\,c^8\,d\,e^2\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(5\,b\,e+4\,c\,d\right)\,\sqrt{d+e\,x}}{b^7\,c^{12}}\right)}{2\,b^3\,c^7}\right)\,\left(5\,b\,e+4\,c\,d\right)}{2\,b^3\,c^7}+\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(\frac{2\,\sqrt{d+e\,x}\,\left(25\,b^{10}\,e^{12}-160\,b^9\,c\,d\,e^{11}+396\,b^8\,c^2\,d^2\,e^{10}-408\,b^7\,c^3\,d^3\,e^9-42\,b^6\,c^4\,d^4\,e^8+504\,b^5\,c^5\,d^5\,e^7-420\,b^4\,c^6\,d^6\,e^6+24\,b^3\,c^7\,d^7\,e^5+234\,b^2\,c^8\,d^8\,e^4-160\,b\,c^9\,d^9\,e^3+32\,c^{10}\,d^{10}\,e^2\right)}{b^4\,c^5}-\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(5\,b\,e+4\,c\,d\right)\,\left(\frac{20\,b^{10}\,c^4\,d\,e^7-64\,b^9\,c^5\,d^2\,e^6+56\,b^8\,c^6\,d^3\,e^5-20\,b^7\,c^7\,d^4\,e^4+8\,b^6\,c^8\,d^5\,e^3}{b^6\,c^5}-\frac{\left(4\,b^7\,c^7\,e^3-8\,b^6\,c^8\,d\,e^2\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(5\,b\,e+4\,c\,d\right)\,\sqrt{d+e\,x}}{b^7\,c^{12}}\right)}{2\,b^3\,c^7}\right)\,\left(5\,b\,e+4\,c\,d\right)}{2\,b^3\,c^7}}\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(5\,b\,e+4\,c\,d\right)\,1{}\mathrm{i}}{b^3\,c^7}","Not used",1,"(((d + e*x)^(3/2)*(b^4*e^5 + 2*c^4*d^4*e - 4*b*c^3*d^3*e^2 + 6*b^2*c^2*d^2*e^3 - 4*b^3*c*d*e^4))/b^2 - ((d + e*x)^(1/2)*(b^4*d*e^5 + 2*c^4*d^5*e - 5*b*c^3*d^4*e^2 - 4*b^3*c*d^2*e^4 + 6*b^2*c^2*d^3*e^3))/b^2)/((2*c^4*d - b*c^3*e)*(d + e*x) - c^4*(d + e*x)^2 - c^4*d^2 + b*c^3*d*e) + (2*e^3*(d + e*x)^(3/2))/(3*c^2) + (2*e^3*(4*c^2*d - 2*b*c*e)*(d + e*x)^(1/2))/c^4 - (atan(((((((20*b^10*c^4*d*e^7 + 8*b^6*c^8*d^5*e^3 - 20*b^7*c^7*d^4*e^4 + 56*b^8*c^6*d^3*e^5 - 64*b^9*c^5*d^2*e^6)/(b^6*c^5) + ((4*b^7*c^7*e^3 - 8*b^6*c^8*d*e^2)*(9*b*e - 4*c*d)*(d^7)^(1/2)*(d + e*x)^(1/2))/(b^7*c^5))*(9*b*e - 4*c*d)*(d^7)^(1/2))/(2*b^3) + (2*(d + e*x)^(1/2)*(25*b^10*e^12 + 32*c^10*d^10*e^2 - 160*b*c^9*d^9*e^3 + 234*b^2*c^8*d^8*e^4 + 24*b^3*c^7*d^7*e^5 - 420*b^4*c^6*d^6*e^6 + 504*b^5*c^5*d^5*e^7 - 42*b^6*c^4*d^4*e^8 - 408*b^7*c^3*d^3*e^9 + 396*b^8*c^2*d^2*e^10 - 160*b^9*c*d*e^11))/(b^4*c^5))*(9*b*e - 4*c*d)*(d^7)^(1/2)*1i)/(2*b^3) - (((((20*b^10*c^4*d*e^7 + 8*b^6*c^8*d^5*e^3 - 20*b^7*c^7*d^4*e^4 + 56*b^8*c^6*d^3*e^5 - 64*b^9*c^5*d^2*e^6)/(b^6*c^5) - ((4*b^7*c^7*e^3 - 8*b^6*c^8*d*e^2)*(9*b*e - 4*c*d)*(d^7)^(1/2)*(d + e*x)^(1/2))/(b^7*c^5))*(9*b*e - 4*c*d)*(d^7)^(1/2))/(2*b^3) - (2*(d + e*x)^(1/2)*(25*b^10*e^12 + 32*c^10*d^10*e^2 - 160*b*c^9*d^9*e^3 + 234*b^2*c^8*d^8*e^4 + 24*b^3*c^7*d^7*e^5 - 420*b^4*c^6*d^6*e^6 + 504*b^5*c^5*d^5*e^7 - 42*b^6*c^4*d^4*e^8 - 408*b^7*c^3*d^3*e^9 + 396*b^8*c^2*d^2*e^10 - 160*b^9*c*d*e^11))/(b^4*c^5))*(9*b*e - 4*c*d)*(d^7)^(1/2)*1i)/(2*b^3))/((((((20*b^10*c^4*d*e^7 + 8*b^6*c^8*d^5*e^3 - 20*b^7*c^7*d^4*e^4 + 56*b^8*c^6*d^3*e^5 - 64*b^9*c^5*d^2*e^6)/(b^6*c^5) + ((4*b^7*c^7*e^3 - 8*b^6*c^8*d*e^2)*(9*b*e - 4*c*d)*(d^7)^(1/2)*(d + e*x)^(1/2))/(b^7*c^5))*(9*b*e - 4*c*d)*(d^7)^(1/2))/(2*b^3) + (2*(d + e*x)^(1/2)*(25*b^10*e^12 + 32*c^10*d^10*e^2 - 160*b*c^9*d^9*e^3 + 234*b^2*c^8*d^8*e^4 + 24*b^3*c^7*d^7*e^5 - 420*b^4*c^6*d^6*e^6 + 504*b^5*c^5*d^5*e^7 - 42*b^6*c^4*d^4*e^8 - 408*b^7*c^3*d^3*e^9 + 396*b^8*c^2*d^2*e^10 - 160*b^9*c*d*e^11))/(b^4*c^5))*(9*b*e - 4*c*d)*(d^7)^(1/2))/(2*b^3) - (2*(225*b^10*d^4*e^13 + 32*c^10*d^14*e^3 - 224*b*c^9*d^13*e^4 - 1540*b^9*c*d^5*e^12 + 326*b^2*c^8*d^12*e^5 + 956*b^3*c^7*d^11*e^6 - 3430*b^4*c^6*d^10*e^7 + 3048*b^5*c^5*d^9*e^8 + 1659*b^6*c^4*d^8*e^9 - 5256*b^7*c^3*d^7*e^10 + 4204*b^8*c^2*d^6*e^11))/(b^6*c^5) + (((((20*b^10*c^4*d*e^7 + 8*b^6*c^8*d^5*e^3 - 20*b^7*c^7*d^4*e^4 + 56*b^8*c^6*d^3*e^5 - 64*b^9*c^5*d^2*e^6)/(b^6*c^5) - ((4*b^7*c^7*e^3 - 8*b^6*c^8*d*e^2)*(9*b*e - 4*c*d)*(d^7)^(1/2)*(d + e*x)^(1/2))/(b^7*c^5))*(9*b*e - 4*c*d)*(d^7)^(1/2))/(2*b^3) - (2*(d + e*x)^(1/2)*(25*b^10*e^12 + 32*c^10*d^10*e^2 - 160*b*c^9*d^9*e^3 + 234*b^2*c^8*d^8*e^4 + 24*b^3*c^7*d^7*e^5 - 420*b^4*c^6*d^6*e^6 + 504*b^5*c^5*d^5*e^7 - 42*b^6*c^4*d^4*e^8 - 408*b^7*c^3*d^3*e^9 + 396*b^8*c^2*d^2*e^10 - 160*b^9*c*d*e^11))/(b^4*c^5))*(9*b*e - 4*c*d)*(d^7)^(1/2))/(2*b^3)))*(9*b*e - 4*c*d)*(d^7)^(1/2)*1i)/b^3 + (atan((((-c^7*(b*e - c*d)^7)^(1/2)*((2*(d + e*x)^(1/2)*(25*b^10*e^12 + 32*c^10*d^10*e^2 - 160*b*c^9*d^9*e^3 + 234*b^2*c^8*d^8*e^4 + 24*b^3*c^7*d^7*e^5 - 420*b^4*c^6*d^6*e^6 + 504*b^5*c^5*d^5*e^7 - 42*b^6*c^4*d^4*e^8 - 408*b^7*c^3*d^3*e^9 + 396*b^8*c^2*d^2*e^10 - 160*b^9*c*d*e^11))/(b^4*c^5) + ((-c^7*(b*e - c*d)^7)^(1/2)*(5*b*e + 4*c*d)*((20*b^10*c^4*d*e^7 + 8*b^6*c^8*d^5*e^3 - 20*b^7*c^7*d^4*e^4 + 56*b^8*c^6*d^3*e^5 - 64*b^9*c^5*d^2*e^6)/(b^6*c^5) + ((4*b^7*c^7*e^3 - 8*b^6*c^8*d*e^2)*(-c^7*(b*e - c*d)^7)^(1/2)*(5*b*e + 4*c*d)*(d + e*x)^(1/2))/(b^7*c^12)))/(2*b^3*c^7))*(5*b*e + 4*c*d)*1i)/(2*b^3*c^7) + ((-c^7*(b*e - c*d)^7)^(1/2)*((2*(d + e*x)^(1/2)*(25*b^10*e^12 + 32*c^10*d^10*e^2 - 160*b*c^9*d^9*e^3 + 234*b^2*c^8*d^8*e^4 + 24*b^3*c^7*d^7*e^5 - 420*b^4*c^6*d^6*e^6 + 504*b^5*c^5*d^5*e^7 - 42*b^6*c^4*d^4*e^8 - 408*b^7*c^3*d^3*e^9 + 396*b^8*c^2*d^2*e^10 - 160*b^9*c*d*e^11))/(b^4*c^5) - ((-c^7*(b*e - c*d)^7)^(1/2)*(5*b*e + 4*c*d)*((20*b^10*c^4*d*e^7 + 8*b^6*c^8*d^5*e^3 - 20*b^7*c^7*d^4*e^4 + 56*b^8*c^6*d^3*e^5 - 64*b^9*c^5*d^2*e^6)/(b^6*c^5) - ((4*b^7*c^7*e^3 - 8*b^6*c^8*d*e^2)*(-c^7*(b*e - c*d)^7)^(1/2)*(5*b*e + 4*c*d)*(d + e*x)^(1/2))/(b^7*c^12)))/(2*b^3*c^7))*(5*b*e + 4*c*d)*1i)/(2*b^3*c^7))/((2*(225*b^10*d^4*e^13 + 32*c^10*d^14*e^3 - 224*b*c^9*d^13*e^4 - 1540*b^9*c*d^5*e^12 + 326*b^2*c^8*d^12*e^5 + 956*b^3*c^7*d^11*e^6 - 3430*b^4*c^6*d^10*e^7 + 3048*b^5*c^5*d^9*e^8 + 1659*b^6*c^4*d^8*e^9 - 5256*b^7*c^3*d^7*e^10 + 4204*b^8*c^2*d^6*e^11))/(b^6*c^5) - ((-c^7*(b*e - c*d)^7)^(1/2)*((2*(d + e*x)^(1/2)*(25*b^10*e^12 + 32*c^10*d^10*e^2 - 160*b*c^9*d^9*e^3 + 234*b^2*c^8*d^8*e^4 + 24*b^3*c^7*d^7*e^5 - 420*b^4*c^6*d^6*e^6 + 504*b^5*c^5*d^5*e^7 - 42*b^6*c^4*d^4*e^8 - 408*b^7*c^3*d^3*e^9 + 396*b^8*c^2*d^2*e^10 - 160*b^9*c*d*e^11))/(b^4*c^5) + ((-c^7*(b*e - c*d)^7)^(1/2)*(5*b*e + 4*c*d)*((20*b^10*c^4*d*e^7 + 8*b^6*c^8*d^5*e^3 - 20*b^7*c^7*d^4*e^4 + 56*b^8*c^6*d^3*e^5 - 64*b^9*c^5*d^2*e^6)/(b^6*c^5) + ((4*b^7*c^7*e^3 - 8*b^6*c^8*d*e^2)*(-c^7*(b*e - c*d)^7)^(1/2)*(5*b*e + 4*c*d)*(d + e*x)^(1/2))/(b^7*c^12)))/(2*b^3*c^7))*(5*b*e + 4*c*d))/(2*b^3*c^7) + ((-c^7*(b*e - c*d)^7)^(1/2)*((2*(d + e*x)^(1/2)*(25*b^10*e^12 + 32*c^10*d^10*e^2 - 160*b*c^9*d^9*e^3 + 234*b^2*c^8*d^8*e^4 + 24*b^3*c^7*d^7*e^5 - 420*b^4*c^6*d^6*e^6 + 504*b^5*c^5*d^5*e^7 - 42*b^6*c^4*d^4*e^8 - 408*b^7*c^3*d^3*e^9 + 396*b^8*c^2*d^2*e^10 - 160*b^9*c*d*e^11))/(b^4*c^5) - ((-c^7*(b*e - c*d)^7)^(1/2)*(5*b*e + 4*c*d)*((20*b^10*c^4*d*e^7 + 8*b^6*c^8*d^5*e^3 - 20*b^7*c^7*d^4*e^4 + 56*b^8*c^6*d^3*e^5 - 64*b^9*c^5*d^2*e^6)/(b^6*c^5) - ((4*b^7*c^7*e^3 - 8*b^6*c^8*d*e^2)*(-c^7*(b*e - c*d)^7)^(1/2)*(5*b*e + 4*c*d)*(d + e*x)^(1/2))/(b^7*c^12)))/(2*b^3*c^7))*(5*b*e + 4*c*d))/(2*b^3*c^7)))*(-c^7*(b*e - c*d)^7)^(1/2)*(5*b*e + 4*c*d)*1i)/(b^3*c^7)","B"
370,1,2913,200,0.782836,"\text{Not used}","int((d + e*x)^(7/2)/(b*x + c*x^2)^2,x)","\frac{\frac{\sqrt{d+e\,x}\,\left(b^3\,d\,e^4-3\,b^2\,c\,d^2\,e^3+4\,b\,c^2\,d^3\,e^2-2\,c^3\,d^4\,e\right)}{b^2}-\frac{{\left(d+e\,x\right)}^{3/2}\,\left(b^3\,e^4-3\,b^2\,c\,d\,e^3+3\,b\,c^2\,d^2\,e^2-2\,c^3\,d^3\,e\right)}{b^2}}{\left(2\,c^3\,d-b\,c^2\,e\right)\,\left(d+e\,x\right)-c^3\,{\left(d+e\,x\right)}^2-c^3\,d^2+b\,c^2\,d\,e}+\frac{2\,e^3\,\sqrt{d+e\,x}}{c^2}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{2\,\sqrt{d+e\,x}\,\left(9\,b^8\,e^{10}-30\,b^7\,c\,d\,e^9+7\,b^6\,c^2\,d^2\,e^8+84\,b^5\,c^3\,d^3\,e^7-105\,b^4\,c^4\,d^4\,e^6-14\,b^3\,c^5\,d^5\,e^5+154\,b^2\,c^6\,d^6\,e^4-128\,b\,c^7\,d^7\,e^3+32\,c^8\,d^8\,e^2\right)}{b^4\,c^3}+\frac{\left(\frac{12\,b^9\,c^3\,d\,e^6-20\,b^8\,c^4\,d^2\,e^5+16\,b^7\,c^5\,d^3\,e^4-8\,b^6\,c^6\,d^4\,e^3}{b^6\,c^3}+\frac{\left(4\,b^7\,c^5\,e^3-8\,b^6\,c^6\,d\,e^2\right)\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d^5}\,\sqrt{d+e\,x}}{b^7\,c^3}\right)\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d^5}}{2\,b^3}\right)\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d^5}\,1{}\mathrm{i}}{2\,b^3}+\frac{\left(\frac{2\,\sqrt{d+e\,x}\,\left(9\,b^8\,e^{10}-30\,b^7\,c\,d\,e^9+7\,b^6\,c^2\,d^2\,e^8+84\,b^5\,c^3\,d^3\,e^7-105\,b^4\,c^4\,d^4\,e^6-14\,b^3\,c^5\,d^5\,e^5+154\,b^2\,c^6\,d^6\,e^4-128\,b\,c^7\,d^7\,e^3+32\,c^8\,d^8\,e^2\right)}{b^4\,c^3}-\frac{\left(\frac{12\,b^9\,c^3\,d\,e^6-20\,b^8\,c^4\,d^2\,e^5+16\,b^7\,c^5\,d^3\,e^4-8\,b^6\,c^6\,d^4\,e^3}{b^6\,c^3}-\frac{\left(4\,b^7\,c^5\,e^3-8\,b^6\,c^6\,d\,e^2\right)\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d^5}\,\sqrt{d+e\,x}}{b^7\,c^3}\right)\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d^5}}{2\,b^3}\right)\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d^5}\,1{}\mathrm{i}}{2\,b^3}}{\frac{2\,\left(63\,b^8\,d^3\,e^{11}-246\,b^7\,c\,d^4\,e^{10}+169\,b^6\,c^2\,d^5\,e^9+413\,b^5\,c^3\,d^6\,e^8-658\,b^4\,c^4\,d^7\,e^7+141\,b^3\,c^5\,d^8\,e^6+262\,b^2\,c^6\,d^9\,e^5-176\,b\,c^7\,d^{10}\,e^4+32\,c^8\,d^{11}\,e^3\right)}{b^6\,c^3}+\frac{\left(\frac{2\,\sqrt{d+e\,x}\,\left(9\,b^8\,e^{10}-30\,b^7\,c\,d\,e^9+7\,b^6\,c^2\,d^2\,e^8+84\,b^5\,c^3\,d^3\,e^7-105\,b^4\,c^4\,d^4\,e^6-14\,b^3\,c^5\,d^5\,e^5+154\,b^2\,c^6\,d^6\,e^4-128\,b\,c^7\,d^7\,e^3+32\,c^8\,d^8\,e^2\right)}{b^4\,c^3}+\frac{\left(\frac{12\,b^9\,c^3\,d\,e^6-20\,b^8\,c^4\,d^2\,e^5+16\,b^7\,c^5\,d^3\,e^4-8\,b^6\,c^6\,d^4\,e^3}{b^6\,c^3}+\frac{\left(4\,b^7\,c^5\,e^3-8\,b^6\,c^6\,d\,e^2\right)\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d^5}\,\sqrt{d+e\,x}}{b^7\,c^3}\right)\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d^5}}{2\,b^3}\right)\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d^5}}{2\,b^3}-\frac{\left(\frac{2\,\sqrt{d+e\,x}\,\left(9\,b^8\,e^{10}-30\,b^7\,c\,d\,e^9+7\,b^6\,c^2\,d^2\,e^8+84\,b^5\,c^3\,d^3\,e^7-105\,b^4\,c^4\,d^4\,e^6-14\,b^3\,c^5\,d^5\,e^5+154\,b^2\,c^6\,d^6\,e^4-128\,b\,c^7\,d^7\,e^3+32\,c^8\,d^8\,e^2\right)}{b^4\,c^3}-\frac{\left(\frac{12\,b^9\,c^3\,d\,e^6-20\,b^8\,c^4\,d^2\,e^5+16\,b^7\,c^5\,d^3\,e^4-8\,b^6\,c^6\,d^4\,e^3}{b^6\,c^3}-\frac{\left(4\,b^7\,c^5\,e^3-8\,b^6\,c^6\,d\,e^2\right)\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d^5}\,\sqrt{d+e\,x}}{b^7\,c^3}\right)\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d^5}}{2\,b^3}\right)\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d^5}}{2\,b^3}}\right)\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d^5}\,1{}\mathrm{i}}{b^3}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(3\,b\,e+4\,c\,d\right)\,\left(\frac{2\,\sqrt{d+e\,x}\,\left(9\,b^8\,e^{10}-30\,b^7\,c\,d\,e^9+7\,b^6\,c^2\,d^2\,e^8+84\,b^5\,c^3\,d^3\,e^7-105\,b^4\,c^4\,d^4\,e^6-14\,b^3\,c^5\,d^5\,e^5+154\,b^2\,c^6\,d^6\,e^4-128\,b\,c^7\,d^7\,e^3+32\,c^8\,d^8\,e^2\right)}{b^4\,c^3}+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{12\,b^9\,c^3\,d\,e^6-20\,b^8\,c^4\,d^2\,e^5+16\,b^7\,c^5\,d^3\,e^4-8\,b^6\,c^6\,d^4\,e^3}{b^6\,c^3}+\frac{\left(4\,b^7\,c^5\,e^3-8\,b^6\,c^6\,d\,e^2\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(3\,b\,e+4\,c\,d\right)\,\sqrt{d+e\,x}}{b^7\,c^8}\right)\,\left(3\,b\,e+4\,c\,d\right)}{2\,b^3\,c^5}\right)\,1{}\mathrm{i}}{2\,b^3\,c^5}+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(3\,b\,e+4\,c\,d\right)\,\left(\frac{2\,\sqrt{d+e\,x}\,\left(9\,b^8\,e^{10}-30\,b^7\,c\,d\,e^9+7\,b^6\,c^2\,d^2\,e^8+84\,b^5\,c^3\,d^3\,e^7-105\,b^4\,c^4\,d^4\,e^6-14\,b^3\,c^5\,d^5\,e^5+154\,b^2\,c^6\,d^6\,e^4-128\,b\,c^7\,d^7\,e^3+32\,c^8\,d^8\,e^2\right)}{b^4\,c^3}-\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{12\,b^9\,c^3\,d\,e^6-20\,b^8\,c^4\,d^2\,e^5+16\,b^7\,c^5\,d^3\,e^4-8\,b^6\,c^6\,d^4\,e^3}{b^6\,c^3}-\frac{\left(4\,b^7\,c^5\,e^3-8\,b^6\,c^6\,d\,e^2\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(3\,b\,e+4\,c\,d\right)\,\sqrt{d+e\,x}}{b^7\,c^8}\right)\,\left(3\,b\,e+4\,c\,d\right)}{2\,b^3\,c^5}\right)\,1{}\mathrm{i}}{2\,b^3\,c^5}}{\frac{2\,\left(63\,b^8\,d^3\,e^{11}-246\,b^7\,c\,d^4\,e^{10}+169\,b^6\,c^2\,d^5\,e^9+413\,b^5\,c^3\,d^6\,e^8-658\,b^4\,c^4\,d^7\,e^7+141\,b^3\,c^5\,d^8\,e^6+262\,b^2\,c^6\,d^9\,e^5-176\,b\,c^7\,d^{10}\,e^4+32\,c^8\,d^{11}\,e^3\right)}{b^6\,c^3}+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(3\,b\,e+4\,c\,d\right)\,\left(\frac{2\,\sqrt{d+e\,x}\,\left(9\,b^8\,e^{10}-30\,b^7\,c\,d\,e^9+7\,b^6\,c^2\,d^2\,e^8+84\,b^5\,c^3\,d^3\,e^7-105\,b^4\,c^4\,d^4\,e^6-14\,b^3\,c^5\,d^5\,e^5+154\,b^2\,c^6\,d^6\,e^4-128\,b\,c^7\,d^7\,e^3+32\,c^8\,d^8\,e^2\right)}{b^4\,c^3}+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{12\,b^9\,c^3\,d\,e^6-20\,b^8\,c^4\,d^2\,e^5+16\,b^7\,c^5\,d^3\,e^4-8\,b^6\,c^6\,d^4\,e^3}{b^6\,c^3}+\frac{\left(4\,b^7\,c^5\,e^3-8\,b^6\,c^6\,d\,e^2\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(3\,b\,e+4\,c\,d\right)\,\sqrt{d+e\,x}}{b^7\,c^8}\right)\,\left(3\,b\,e+4\,c\,d\right)}{2\,b^3\,c^5}\right)}{2\,b^3\,c^5}-\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(3\,b\,e+4\,c\,d\right)\,\left(\frac{2\,\sqrt{d+e\,x}\,\left(9\,b^8\,e^{10}-30\,b^7\,c\,d\,e^9+7\,b^6\,c^2\,d^2\,e^8+84\,b^5\,c^3\,d^3\,e^7-105\,b^4\,c^4\,d^4\,e^6-14\,b^3\,c^5\,d^5\,e^5+154\,b^2\,c^6\,d^6\,e^4-128\,b\,c^7\,d^7\,e^3+32\,c^8\,d^8\,e^2\right)}{b^4\,c^3}-\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{12\,b^9\,c^3\,d\,e^6-20\,b^8\,c^4\,d^2\,e^5+16\,b^7\,c^5\,d^3\,e^4-8\,b^6\,c^6\,d^4\,e^3}{b^6\,c^3}-\frac{\left(4\,b^7\,c^5\,e^3-8\,b^6\,c^6\,d\,e^2\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(3\,b\,e+4\,c\,d\right)\,\sqrt{d+e\,x}}{b^7\,c^8}\right)\,\left(3\,b\,e+4\,c\,d\right)}{2\,b^3\,c^5}\right)}{2\,b^3\,c^5}}\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(3\,b\,e+4\,c\,d\right)\,1{}\mathrm{i}}{b^3\,c^5}","Not used",1,"(((d + e*x)^(1/2)*(b^3*d*e^4 - 2*c^3*d^4*e + 4*b*c^2*d^3*e^2 - 3*b^2*c*d^2*e^3))/b^2 - ((d + e*x)^(3/2)*(b^3*e^4 - 2*c^3*d^3*e + 3*b*c^2*d^2*e^2 - 3*b^2*c*d*e^3))/b^2)/((2*c^3*d - b*c^2*e)*(d + e*x) - c^3*(d + e*x)^2 - c^3*d^2 + b*c^2*d*e) + (2*e^3*(d + e*x)^(1/2))/c^2 + (atan(((((2*(d + e*x)^(1/2)*(9*b^8*e^10 + 32*c^8*d^8*e^2 - 128*b*c^7*d^7*e^3 + 154*b^2*c^6*d^6*e^4 - 14*b^3*c^5*d^5*e^5 - 105*b^4*c^4*d^4*e^6 + 84*b^5*c^3*d^3*e^7 + 7*b^6*c^2*d^2*e^8 - 30*b^7*c*d*e^9))/(b^4*c^3) + (((12*b^9*c^3*d*e^6 - 8*b^6*c^6*d^4*e^3 + 16*b^7*c^5*d^3*e^4 - 20*b^8*c^4*d^2*e^5)/(b^6*c^3) + ((4*b^7*c^5*e^3 - 8*b^6*c^6*d*e^2)*(7*b*e - 4*c*d)*(d^5)^(1/2)*(d + e*x)^(1/2))/(b^7*c^3))*(7*b*e - 4*c*d)*(d^5)^(1/2))/(2*b^3))*(7*b*e - 4*c*d)*(d^5)^(1/2)*1i)/(2*b^3) + (((2*(d + e*x)^(1/2)*(9*b^8*e^10 + 32*c^8*d^8*e^2 - 128*b*c^7*d^7*e^3 + 154*b^2*c^6*d^6*e^4 - 14*b^3*c^5*d^5*e^5 - 105*b^4*c^4*d^4*e^6 + 84*b^5*c^3*d^3*e^7 + 7*b^6*c^2*d^2*e^8 - 30*b^7*c*d*e^9))/(b^4*c^3) - (((12*b^9*c^3*d*e^6 - 8*b^6*c^6*d^4*e^3 + 16*b^7*c^5*d^3*e^4 - 20*b^8*c^4*d^2*e^5)/(b^6*c^3) - ((4*b^7*c^5*e^3 - 8*b^6*c^6*d*e^2)*(7*b*e - 4*c*d)*(d^5)^(1/2)*(d + e*x)^(1/2))/(b^7*c^3))*(7*b*e - 4*c*d)*(d^5)^(1/2))/(2*b^3))*(7*b*e - 4*c*d)*(d^5)^(1/2)*1i)/(2*b^3))/((2*(63*b^8*d^3*e^11 + 32*c^8*d^11*e^3 - 176*b*c^7*d^10*e^4 - 246*b^7*c*d^4*e^10 + 262*b^2*c^6*d^9*e^5 + 141*b^3*c^5*d^8*e^6 - 658*b^4*c^4*d^7*e^7 + 413*b^5*c^3*d^6*e^8 + 169*b^6*c^2*d^5*e^9))/(b^6*c^3) + (((2*(d + e*x)^(1/2)*(9*b^8*e^10 + 32*c^8*d^8*e^2 - 128*b*c^7*d^7*e^3 + 154*b^2*c^6*d^6*e^4 - 14*b^3*c^5*d^5*e^5 - 105*b^4*c^4*d^4*e^6 + 84*b^5*c^3*d^3*e^7 + 7*b^6*c^2*d^2*e^8 - 30*b^7*c*d*e^9))/(b^4*c^3) + (((12*b^9*c^3*d*e^6 - 8*b^6*c^6*d^4*e^3 + 16*b^7*c^5*d^3*e^4 - 20*b^8*c^4*d^2*e^5)/(b^6*c^3) + ((4*b^7*c^5*e^3 - 8*b^6*c^6*d*e^2)*(7*b*e - 4*c*d)*(d^5)^(1/2)*(d + e*x)^(1/2))/(b^7*c^3))*(7*b*e - 4*c*d)*(d^5)^(1/2))/(2*b^3))*(7*b*e - 4*c*d)*(d^5)^(1/2))/(2*b^3) - (((2*(d + e*x)^(1/2)*(9*b^8*e^10 + 32*c^8*d^8*e^2 - 128*b*c^7*d^7*e^3 + 154*b^2*c^6*d^6*e^4 - 14*b^3*c^5*d^5*e^5 - 105*b^4*c^4*d^4*e^6 + 84*b^5*c^3*d^3*e^7 + 7*b^6*c^2*d^2*e^8 - 30*b^7*c*d*e^9))/(b^4*c^3) - (((12*b^9*c^3*d*e^6 - 8*b^6*c^6*d^4*e^3 + 16*b^7*c^5*d^3*e^4 - 20*b^8*c^4*d^2*e^5)/(b^6*c^3) - ((4*b^7*c^5*e^3 - 8*b^6*c^6*d*e^2)*(7*b*e - 4*c*d)*(d^5)^(1/2)*(d + e*x)^(1/2))/(b^7*c^3))*(7*b*e - 4*c*d)*(d^5)^(1/2))/(2*b^3))*(7*b*e - 4*c*d)*(d^5)^(1/2))/(2*b^3)))*(7*b*e - 4*c*d)*(d^5)^(1/2)*1i)/b^3 + (atan((((-c^5*(b*e - c*d)^5)^(1/2)*(3*b*e + 4*c*d)*((2*(d + e*x)^(1/2)*(9*b^8*e^10 + 32*c^8*d^8*e^2 - 128*b*c^7*d^7*e^3 + 154*b^2*c^6*d^6*e^4 - 14*b^3*c^5*d^5*e^5 - 105*b^4*c^4*d^4*e^6 + 84*b^5*c^3*d^3*e^7 + 7*b^6*c^2*d^2*e^8 - 30*b^7*c*d*e^9))/(b^4*c^3) + ((-c^5*(b*e - c*d)^5)^(1/2)*((12*b^9*c^3*d*e^6 - 8*b^6*c^6*d^4*e^3 + 16*b^7*c^5*d^3*e^4 - 20*b^8*c^4*d^2*e^5)/(b^6*c^3) + ((4*b^7*c^5*e^3 - 8*b^6*c^6*d*e^2)*(-c^5*(b*e - c*d)^5)^(1/2)*(3*b*e + 4*c*d)*(d + e*x)^(1/2))/(b^7*c^8))*(3*b*e + 4*c*d))/(2*b^3*c^5))*1i)/(2*b^3*c^5) + ((-c^5*(b*e - c*d)^5)^(1/2)*(3*b*e + 4*c*d)*((2*(d + e*x)^(1/2)*(9*b^8*e^10 + 32*c^8*d^8*e^2 - 128*b*c^7*d^7*e^3 + 154*b^2*c^6*d^6*e^4 - 14*b^3*c^5*d^5*e^5 - 105*b^4*c^4*d^4*e^6 + 84*b^5*c^3*d^3*e^7 + 7*b^6*c^2*d^2*e^8 - 30*b^7*c*d*e^9))/(b^4*c^3) - ((-c^5*(b*e - c*d)^5)^(1/2)*((12*b^9*c^3*d*e^6 - 8*b^6*c^6*d^4*e^3 + 16*b^7*c^5*d^3*e^4 - 20*b^8*c^4*d^2*e^5)/(b^6*c^3) - ((4*b^7*c^5*e^3 - 8*b^6*c^6*d*e^2)*(-c^5*(b*e - c*d)^5)^(1/2)*(3*b*e + 4*c*d)*(d + e*x)^(1/2))/(b^7*c^8))*(3*b*e + 4*c*d))/(2*b^3*c^5))*1i)/(2*b^3*c^5))/((2*(63*b^8*d^3*e^11 + 32*c^8*d^11*e^3 - 176*b*c^7*d^10*e^4 - 246*b^7*c*d^4*e^10 + 262*b^2*c^6*d^9*e^5 + 141*b^3*c^5*d^8*e^6 - 658*b^4*c^4*d^7*e^7 + 413*b^5*c^3*d^6*e^8 + 169*b^6*c^2*d^5*e^9))/(b^6*c^3) + ((-c^5*(b*e - c*d)^5)^(1/2)*(3*b*e + 4*c*d)*((2*(d + e*x)^(1/2)*(9*b^8*e^10 + 32*c^8*d^8*e^2 - 128*b*c^7*d^7*e^3 + 154*b^2*c^6*d^6*e^4 - 14*b^3*c^5*d^5*e^5 - 105*b^4*c^4*d^4*e^6 + 84*b^5*c^3*d^3*e^7 + 7*b^6*c^2*d^2*e^8 - 30*b^7*c*d*e^9))/(b^4*c^3) + ((-c^5*(b*e - c*d)^5)^(1/2)*((12*b^9*c^3*d*e^6 - 8*b^6*c^6*d^4*e^3 + 16*b^7*c^5*d^3*e^4 - 20*b^8*c^4*d^2*e^5)/(b^6*c^3) + ((4*b^7*c^5*e^3 - 8*b^6*c^6*d*e^2)*(-c^5*(b*e - c*d)^5)^(1/2)*(3*b*e + 4*c*d)*(d + e*x)^(1/2))/(b^7*c^8))*(3*b*e + 4*c*d))/(2*b^3*c^5)))/(2*b^3*c^5) - ((-c^5*(b*e - c*d)^5)^(1/2)*(3*b*e + 4*c*d)*((2*(d + e*x)^(1/2)*(9*b^8*e^10 + 32*c^8*d^8*e^2 - 128*b*c^7*d^7*e^3 + 154*b^2*c^6*d^6*e^4 - 14*b^3*c^5*d^5*e^5 - 105*b^4*c^4*d^4*e^6 + 84*b^5*c^3*d^3*e^7 + 7*b^6*c^2*d^2*e^8 - 30*b^7*c*d*e^9))/(b^4*c^3) - ((-c^5*(b*e - c*d)^5)^(1/2)*((12*b^9*c^3*d*e^6 - 8*b^6*c^6*d^4*e^3 + 16*b^7*c^5*d^3*e^4 - 20*b^8*c^4*d^2*e^5)/(b^6*c^3) - ((4*b^7*c^5*e^3 - 8*b^6*c^6*d*e^2)*(-c^5*(b*e - c*d)^5)^(1/2)*(3*b*e + 4*c*d)*(d + e*x)^(1/2))/(b^7*c^8))*(3*b*e + 4*c*d))/(2*b^3*c^5)))/(2*b^3*c^5)))*(-c^5*(b*e - c*d)^5)^(1/2)*(3*b*e + 4*c*d)*1i)/(b^3*c^5)","B"
371,1,1127,159,0.498945,"\text{Not used}","int((d + e*x)^(5/2)/(b*x + c*x^2)^2,x)","\frac{\frac{\sqrt{d+e\,x}\,\left(b^2\,d\,e^3-3\,b\,c\,d^2\,e^2+2\,c^2\,d^3\,e\right)}{b^2\,c}-\frac{e\,{\left(d+e\,x\right)}^{3/2}\,\left(b^2\,e^2-2\,b\,c\,d\,e+2\,c^2\,d^2\right)}{b^2\,c}}{\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)+c\,{\left(d+e\,x\right)}^2+c\,d^2-b\,d\,e}-\frac{\mathrm{atanh}\left(\frac{10\,e^9\,\sqrt{d^3}\,\sqrt{d+e\,x}}{10\,d^2\,e^9+\frac{32\,c\,d^3\,e^8}{b}-\frac{132\,c^2\,d^4\,e^7}{b^2}+\frac{130\,c^3\,d^5\,e^6}{b^3}-\frac{40\,c^4\,d^6\,e^5}{b^4}}+\frac{32\,d\,e^8\,\sqrt{d^3}\,\sqrt{d+e\,x}}{32\,d^3\,e^8+\frac{10\,b\,d^2\,e^9}{c}-\frac{132\,c\,d^4\,e^7}{b}+\frac{130\,c^2\,d^5\,e^6}{b^2}-\frac{40\,c^3\,d^6\,e^5}{b^3}}-\frac{132\,c\,d^2\,e^7\,\sqrt{d^3}\,\sqrt{d+e\,x}}{32\,b\,d^3\,e^8-132\,c\,d^4\,e^7+\frac{130\,c^2\,d^5\,e^6}{b}+\frac{10\,b^2\,d^2\,e^9}{c}-\frac{40\,c^3\,d^6\,e^5}{b^2}}+\frac{130\,c^2\,d^3\,e^6\,\sqrt{d^3}\,\sqrt{d+e\,x}}{32\,b^2\,d^3\,e^8+130\,c^2\,d^5\,e^6-\frac{40\,c^3\,d^6\,e^5}{b}+\frac{10\,b^3\,d^2\,e^9}{c}-132\,b\,c\,d^4\,e^7}-\frac{40\,c^3\,d^4\,e^5\,\sqrt{d^3}\,\sqrt{d+e\,x}}{32\,b^3\,d^3\,e^8-40\,c^3\,d^6\,e^5+130\,b\,c^2\,d^5\,e^6-132\,b^2\,c\,d^4\,e^7+\frac{10\,b^4\,d^2\,e^9}{c}}\right)\,\left(5\,b\,e-4\,c\,d\right)\,\sqrt{d^3}}{b^3}-\frac{\mathrm{atanh}\left(\frac{30\,d^3\,e^6\,\sqrt{d+e\,x}\,\sqrt{-b^3\,c^3\,e^3+3\,b^2\,c^4\,d\,e^2-3\,b\,c^5\,d^2\,e+c^6\,d^3}}{14\,b^3\,d^2\,e^9+110\,c^3\,d^5\,e^6-82\,b\,c^2\,d^4\,e^7-4\,b^2\,c\,d^3\,e^8+\frac{2\,b^4\,d\,e^{10}}{c}-\frac{40\,c^4\,d^6\,e^5}{b}}-\frac{2\,d\,e^8\,\sqrt{d+e\,x}\,\sqrt{-b^3\,c^3\,e^3+3\,b^2\,c^4\,d\,e^2-3\,b\,c^5\,d^2\,e+c^6\,d^3}}{4\,c^3\,d^3\,e^8-14\,b\,c^2\,d^2\,e^9+\frac{82\,c^4\,d^4\,e^7}{b}-\frac{110\,c^5\,d^5\,e^6}{b^2}+\frac{40\,c^6\,d^6\,e^5}{b^3}-2\,b^2\,c\,d\,e^{10}}+\frac{18\,d^2\,e^7\,\sqrt{d+e\,x}\,\sqrt{-b^3\,c^3\,e^3+3\,b^2\,c^4\,d\,e^2-3\,b\,c^5\,d^2\,e+c^6\,d^3}}{2\,b^3\,d\,e^{10}-82\,c^3\,d^4\,e^7-4\,b\,c^2\,d^3\,e^8+14\,b^2\,c\,d^2\,e^9+\frac{110\,c^4\,d^5\,e^6}{b}-\frac{40\,c^5\,d^6\,e^5}{b^2}}+\frac{40\,d^4\,e^5\,\sqrt{d+e\,x}\,\sqrt{-b^3\,c^3\,e^3+3\,b^2\,c^4\,d\,e^2-3\,b\,c^5\,d^2\,e+c^6\,d^3}}{4\,b^3\,d^3\,e^8+40\,c^3\,d^6\,e^5-110\,b\,c^2\,d^5\,e^6+82\,b^2\,c\,d^4\,e^7-\frac{2\,b^5\,d\,e^{10}}{c^2}-\frac{14\,b^4\,d^2\,e^9}{c}}\right)\,\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(b\,e+4\,c\,d\right)}{b^3\,c^3}","Not used",1,"(((d + e*x)^(1/2)*(b^2*d*e^3 + 2*c^2*d^3*e - 3*b*c*d^2*e^2))/(b^2*c) - (e*(d + e*x)^(3/2)*(b^2*e^2 + 2*c^2*d^2 - 2*b*c*d*e))/(b^2*c))/((b*e - 2*c*d)*(d + e*x) + c*(d + e*x)^2 + c*d^2 - b*d*e) - (atanh((10*e^9*(d^3)^(1/2)*(d + e*x)^(1/2))/(10*d^2*e^9 + (32*c*d^3*e^8)/b - (132*c^2*d^4*e^7)/b^2 + (130*c^3*d^5*e^6)/b^3 - (40*c^4*d^6*e^5)/b^4) + (32*d*e^8*(d^3)^(1/2)*(d + e*x)^(1/2))/(32*d^3*e^8 + (10*b*d^2*e^9)/c - (132*c*d^4*e^7)/b + (130*c^2*d^5*e^6)/b^2 - (40*c^3*d^6*e^5)/b^3) - (132*c*d^2*e^7*(d^3)^(1/2)*(d + e*x)^(1/2))/(32*b*d^3*e^8 - 132*c*d^4*e^7 + (130*c^2*d^5*e^6)/b + (10*b^2*d^2*e^9)/c - (40*c^3*d^6*e^5)/b^2) + (130*c^2*d^3*e^6*(d^3)^(1/2)*(d + e*x)^(1/2))/(32*b^2*d^3*e^8 + 130*c^2*d^5*e^6 - (40*c^3*d^6*e^5)/b + (10*b^3*d^2*e^9)/c - 132*b*c*d^4*e^7) - (40*c^3*d^4*e^5*(d^3)^(1/2)*(d + e*x)^(1/2))/(32*b^3*d^3*e^8 - 40*c^3*d^6*e^5 + 130*b*c^2*d^5*e^6 - 132*b^2*c*d^4*e^7 + (10*b^4*d^2*e^9)/c))*(5*b*e - 4*c*d)*(d^3)^(1/2))/b^3 - (atanh((30*d^3*e^6*(d + e*x)^(1/2)*(c^6*d^3 - b^3*c^3*e^3 + 3*b^2*c^4*d*e^2 - 3*b*c^5*d^2*e)^(1/2))/(14*b^3*d^2*e^9 + 110*c^3*d^5*e^6 - 82*b*c^2*d^4*e^7 - 4*b^2*c*d^3*e^8 + (2*b^4*d*e^10)/c - (40*c^4*d^6*e^5)/b) - (2*d*e^8*(d + e*x)^(1/2)*(c^6*d^3 - b^3*c^3*e^3 + 3*b^2*c^4*d*e^2 - 3*b*c^5*d^2*e)^(1/2))/(4*c^3*d^3*e^8 - 14*b*c^2*d^2*e^9 + (82*c^4*d^4*e^7)/b - (110*c^5*d^5*e^6)/b^2 + (40*c^6*d^6*e^5)/b^3 - 2*b^2*c*d*e^10) + (18*d^2*e^7*(d + e*x)^(1/2)*(c^6*d^3 - b^3*c^3*e^3 + 3*b^2*c^4*d*e^2 - 3*b*c^5*d^2*e)^(1/2))/(2*b^3*d*e^10 - 82*c^3*d^4*e^7 - 4*b*c^2*d^3*e^8 + 14*b^2*c*d^2*e^9 + (110*c^4*d^5*e^6)/b - (40*c^5*d^6*e^5)/b^2) + (40*d^4*e^5*(d + e*x)^(1/2)*(c^6*d^3 - b^3*c^3*e^3 + 3*b^2*c^4*d*e^2 - 3*b*c^5*d^2*e)^(1/2))/(4*b^3*d^3*e^8 + 40*c^3*d^6*e^5 - 110*b*c^2*d^5*e^6 + 82*b^2*c*d^4*e^7 - (2*b^5*d*e^10)/c^2 - (14*b^4*d^2*e^9)/c))*(-c^3*(b*e - c*d)^3)^(1/2)*(b*e + 4*c*d))/(b^3*c^3)","B"
372,1,429,134,0.421999,"\text{Not used}","int((d + e*x)^(3/2)/(b*x + c*x^2)^2,x)","-\frac{\frac{2\,\left(b\,d\,e^2-c\,d^2\,e\right)\,\sqrt{d+e\,x}}{b^2}-\frac{e\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{3/2}}{b^2}}{\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)+c\,{\left(d+e\,x\right)}^2+c\,d^2-b\,d\,e}-\frac{\sqrt{d}\,\mathrm{atanh}\left(\frac{6\,c\,\sqrt{d}\,e^7\,\sqrt{d+e\,x}}{6\,c\,d\,e^7-\frac{14\,c^2\,d^2\,e^6}{b}+\frac{8\,c^3\,d^3\,e^5}{b^2}}-\frac{14\,c^2\,d^{3/2}\,e^6\,\sqrt{d+e\,x}}{6\,b\,c\,d\,e^7-14\,c^2\,d^2\,e^6+\frac{8\,c^3\,d^3\,e^5}{b}}+\frac{8\,c^3\,d^{5/2}\,e^5\,\sqrt{d+e\,x}}{6\,b^2\,c\,d\,e^7-14\,b\,c^2\,d^2\,e^6+8\,c^3\,d^3\,e^5}\right)\,\left(3\,b\,e-4\,c\,d\right)}{b^3}-\frac{\mathrm{atanh}\left(\frac{2\,c\,d\,e^6\,\sqrt{c^2\,d-b\,c\,e}\,\sqrt{d+e\,x}}{2\,b\,c\,d\,e^7-10\,c^2\,d^2\,e^6+\frac{8\,c^3\,d^3\,e^5}{b}}-\frac{8\,c^2\,d^2\,e^5\,\sqrt{c^2\,d-b\,c\,e}\,\sqrt{d+e\,x}}{2\,b^2\,c\,d\,e^7-10\,b\,c^2\,d^2\,e^6+8\,c^3\,d^3\,e^5}\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(b\,e-4\,c\,d\right)}{b^3\,c}","Not used",1,"- ((2*(b*d*e^2 - c*d^2*e)*(d + e*x)^(1/2))/b^2 - (e*(b*e - 2*c*d)*(d + e*x)^(3/2))/b^2)/((b*e - 2*c*d)*(d + e*x) + c*(d + e*x)^2 + c*d^2 - b*d*e) - (d^(1/2)*atanh((6*c*d^(1/2)*e^7*(d + e*x)^(1/2))/(6*c*d*e^7 - (14*c^2*d^2*e^6)/b + (8*c^3*d^3*e^5)/b^2) - (14*c^2*d^(3/2)*e^6*(d + e*x)^(1/2))/(6*b*c*d*e^7 - 14*c^2*d^2*e^6 + (8*c^3*d^3*e^5)/b) + (8*c^3*d^(5/2)*e^5*(d + e*x)^(1/2))/(8*c^3*d^3*e^5 - 14*b*c^2*d^2*e^6 + 6*b^2*c*d*e^7))*(3*b*e - 4*c*d))/b^3 - (atanh((2*c*d*e^6*(c^2*d - b*c*e)^(1/2)*(d + e*x)^(1/2))/(2*b*c*d*e^7 - 10*c^2*d^2*e^6 + (8*c^3*d^3*e^5)/b) - (8*c^2*d^2*e^5*(c^2*d - b*c*e)^(1/2)*(d + e*x)^(1/2))/(8*c^3*d^3*e^5 - 10*b*c^2*d^2*e^6 + 2*b^2*c*d*e^7))*(-c*(b*e - c*d))^(1/2)*(b*e - 4*c*d))/(b^3*c)","B"
373,1,1174,125,0.532637,"\text{Not used}","int((d + e*x)^(1/2)/(b*x + c*x^2)^2,x)","\frac{\mathrm{atanh}\left(\frac{2\,c^2\,e^6\,\sqrt{d+e\,x}}{d^{3/2}\,\left(\frac{8\,c^3\,e^5}{b}-\frac{2\,c^2\,e^6}{d}\right)}-\frac{8\,c^3\,e^5\,\sqrt{d+e\,x}}{\sqrt{d}\,\left(8\,c^3\,e^5-\frac{2\,b\,c^2\,e^6}{d}\right)}\right)\,\left(b\,e-4\,c\,d\right)}{b^3\,\sqrt{d}}-\frac{\frac{2\,c\,e\,{\left(d+e\,x\right)}^{3/2}}{b^2}+\frac{e\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}}{b^2}}{\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)+c\,{\left(d+e\,x\right)}^2+c\,d^2-b\,d\,e}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{4\,\sqrt{d+e\,x}\,\left(5\,b^2\,c^3\,e^4-16\,b\,c^4\,d\,e^3+16\,c^5\,d^2\,e^2\right)}{b^4}-\frac{\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(3\,b\,e-4\,c\,d\right)\,\left(\frac{2\,\left(2\,b^7\,c^2\,e^4-4\,b^6\,c^3\,d\,e^3\right)}{b^6}-\frac{2\,\left(2\,b^7\,c^2\,e^3-4\,b^6\,c^3\,d\,e^2\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(3\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}}{b^4\,\left(b^4\,e-b^3\,c\,d\right)}\right)}{2\,\left(b^4\,e-b^3\,c\,d\right)}\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(3\,b\,e-4\,c\,d\right)\,1{}\mathrm{i}}{2\,\left(b^4\,e-b^3\,c\,d\right)}+\frac{\left(\frac{4\,\sqrt{d+e\,x}\,\left(5\,b^2\,c^3\,e^4-16\,b\,c^4\,d\,e^3+16\,c^5\,d^2\,e^2\right)}{b^4}+\frac{\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(3\,b\,e-4\,c\,d\right)\,\left(\frac{2\,\left(2\,b^7\,c^2\,e^4-4\,b^6\,c^3\,d\,e^3\right)}{b^6}+\frac{2\,\left(2\,b^7\,c^2\,e^3-4\,b^6\,c^3\,d\,e^2\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(3\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}}{b^4\,\left(b^4\,e-b^3\,c\,d\right)}\right)}{2\,\left(b^4\,e-b^3\,c\,d\right)}\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(3\,b\,e-4\,c\,d\right)\,1{}\mathrm{i}}{2\,\left(b^4\,e-b^3\,c\,d\right)}}{\frac{4\,\left(3\,b^2\,c^3\,e^5-16\,b\,c^4\,d\,e^4+16\,c^5\,d^2\,e^3\right)}{b^6}-\frac{\left(\frac{4\,\sqrt{d+e\,x}\,\left(5\,b^2\,c^3\,e^4-16\,b\,c^4\,d\,e^3+16\,c^5\,d^2\,e^2\right)}{b^4}-\frac{\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(3\,b\,e-4\,c\,d\right)\,\left(\frac{2\,\left(2\,b^7\,c^2\,e^4-4\,b^6\,c^3\,d\,e^3\right)}{b^6}-\frac{2\,\left(2\,b^7\,c^2\,e^3-4\,b^6\,c^3\,d\,e^2\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(3\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}}{b^4\,\left(b^4\,e-b^3\,c\,d\right)}\right)}{2\,\left(b^4\,e-b^3\,c\,d\right)}\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(3\,b\,e-4\,c\,d\right)}{2\,\left(b^4\,e-b^3\,c\,d\right)}+\frac{\left(\frac{4\,\sqrt{d+e\,x}\,\left(5\,b^2\,c^3\,e^4-16\,b\,c^4\,d\,e^3+16\,c^5\,d^2\,e^2\right)}{b^4}+\frac{\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(3\,b\,e-4\,c\,d\right)\,\left(\frac{2\,\left(2\,b^7\,c^2\,e^4-4\,b^6\,c^3\,d\,e^3\right)}{b^6}+\frac{2\,\left(2\,b^7\,c^2\,e^3-4\,b^6\,c^3\,d\,e^2\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(3\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}}{b^4\,\left(b^4\,e-b^3\,c\,d\right)}\right)}{2\,\left(b^4\,e-b^3\,c\,d\right)}\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(3\,b\,e-4\,c\,d\right)}{2\,\left(b^4\,e-b^3\,c\,d\right)}}\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(3\,b\,e-4\,c\,d\right)\,1{}\mathrm{i}}{b^4\,e-b^3\,c\,d}","Not used",1,"(atanh((2*c^2*e^6*(d + e*x)^(1/2))/(d^(3/2)*((8*c^3*e^5)/b - (2*c^2*e^6)/d)) - (8*c^3*e^5*(d + e*x)^(1/2))/(d^(1/2)*(8*c^3*e^5 - (2*b*c^2*e^6)/d)))*(b*e - 4*c*d))/(b^3*d^(1/2)) - ((2*c*e*(d + e*x)^(3/2))/b^2 + (e*(b*e - 2*c*d)*(d + e*x)^(1/2))/b^2)/((b*e - 2*c*d)*(d + e*x) + c*(d + e*x)^2 + c*d^2 - b*d*e) + (atan(((((4*(d + e*x)^(1/2)*(5*b^2*c^3*e^4 + 16*c^5*d^2*e^2 - 16*b*c^4*d*e^3))/b^4 - ((-c*(b*e - c*d))^(1/2)*(3*b*e - 4*c*d)*((2*(2*b^7*c^2*e^4 - 4*b^6*c^3*d*e^3))/b^6 - (2*(2*b^7*c^2*e^3 - 4*b^6*c^3*d*e^2)*(-c*(b*e - c*d))^(1/2)*(3*b*e - 4*c*d)*(d + e*x)^(1/2))/(b^4*(b^4*e - b^3*c*d))))/(2*(b^4*e - b^3*c*d)))*(-c*(b*e - c*d))^(1/2)*(3*b*e - 4*c*d)*1i)/(2*(b^4*e - b^3*c*d)) + (((4*(d + e*x)^(1/2)*(5*b^2*c^3*e^4 + 16*c^5*d^2*e^2 - 16*b*c^4*d*e^3))/b^4 + ((-c*(b*e - c*d))^(1/2)*(3*b*e - 4*c*d)*((2*(2*b^7*c^2*e^4 - 4*b^6*c^3*d*e^3))/b^6 + (2*(2*b^7*c^2*e^3 - 4*b^6*c^3*d*e^2)*(-c*(b*e - c*d))^(1/2)*(3*b*e - 4*c*d)*(d + e*x)^(1/2))/(b^4*(b^4*e - b^3*c*d))))/(2*(b^4*e - b^3*c*d)))*(-c*(b*e - c*d))^(1/2)*(3*b*e - 4*c*d)*1i)/(2*(b^4*e - b^3*c*d)))/((4*(3*b^2*c^3*e^5 + 16*c^5*d^2*e^3 - 16*b*c^4*d*e^4))/b^6 - (((4*(d + e*x)^(1/2)*(5*b^2*c^3*e^4 + 16*c^5*d^2*e^2 - 16*b*c^4*d*e^3))/b^4 - ((-c*(b*e - c*d))^(1/2)*(3*b*e - 4*c*d)*((2*(2*b^7*c^2*e^4 - 4*b^6*c^3*d*e^3))/b^6 - (2*(2*b^7*c^2*e^3 - 4*b^6*c^3*d*e^2)*(-c*(b*e - c*d))^(1/2)*(3*b*e - 4*c*d)*(d + e*x)^(1/2))/(b^4*(b^4*e - b^3*c*d))))/(2*(b^4*e - b^3*c*d)))*(-c*(b*e - c*d))^(1/2)*(3*b*e - 4*c*d))/(2*(b^4*e - b^3*c*d)) + (((4*(d + e*x)^(1/2)*(5*b^2*c^3*e^4 + 16*c^5*d^2*e^2 - 16*b*c^4*d*e^3))/b^4 + ((-c*(b*e - c*d))^(1/2)*(3*b*e - 4*c*d)*((2*(2*b^7*c^2*e^4 - 4*b^6*c^3*d*e^3))/b^6 + (2*(2*b^7*c^2*e^3 - 4*b^6*c^3*d*e^2)*(-c*(b*e - c*d))^(1/2)*(3*b*e - 4*c*d)*(d + e*x)^(1/2))/(b^4*(b^4*e - b^3*c*d))))/(2*(b^4*e - b^3*c*d)))*(-c*(b*e - c*d))^(1/2)*(3*b*e - 4*c*d))/(2*(b^4*e - b^3*c*d))))*(-c*(b*e - c*d))^(1/2)*(3*b*e - 4*c*d)*1i)/(b^4*e - b^3*c*d)","B"
374,1,3784,154,1.224414,"\text{Not used}","int(1/((b*x + c*x^2)^2*(d + e*x)^(1/2)),x)","\frac{\frac{\sqrt{d+e\,x}\,\left(b^2\,e^3-2\,b\,c\,d\,e^2+2\,c^2\,d^2\,e\right)}{b^2\,\left(c\,d^2-b\,d\,e\right)}+\frac{c\,\left(b\,e^2-2\,c\,d\,e\right)\,{\left(d+e\,x\right)}^{3/2}}{b^2\,\left(c\,d^2-b\,d\,e\right)}}{\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)+c\,{\left(d+e\,x\right)}^2+c\,d^2-b\,d\,e}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(\frac{2\,\sqrt{d+e\,x}\,\left(b^4\,c^3\,e^6+6\,b^3\,c^4\,d\,e^5+26\,b^2\,c^5\,d^2\,e^4-64\,b\,c^6\,d^3\,e^3+32\,c^7\,d^4\,e^2\right)}{b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4}-\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(5\,b\,e-4\,c\,d\right)\,\left(\frac{4\,b^9\,c^2\,d\,e^6+4\,b^8\,c^3\,d^2\,e^5-16\,b^7\,c^4\,d^3\,e^4+8\,b^6\,c^5\,d^4\,e^3}{b^8\,d^2\,e^2-2\,b^7\,c\,d^3\,e+b^6\,c^2\,d^4}+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(5\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(-4\,b^9\,c^2\,d^2\,e^5+16\,b^8\,c^3\,d^3\,e^4-20\,b^7\,c^4\,d^4\,e^3+8\,b^6\,c^5\,d^5\,e^2\right)}{\left(b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4\right)\,\left(b^6\,e^3-3\,b^5\,c\,d\,e^2+3\,b^4\,c^2\,d^2\,e-b^3\,c^3\,d^3\right)}\right)}{2\,\left(b^6\,e^3-3\,b^5\,c\,d\,e^2+3\,b^4\,c^2\,d^2\,e-b^3\,c^3\,d^3\right)}\right)\,\left(5\,b\,e-4\,c\,d\right)\,1{}\mathrm{i}}{2\,\left(b^6\,e^3-3\,b^5\,c\,d\,e^2+3\,b^4\,c^2\,d^2\,e-b^3\,c^3\,d^3\right)}+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(\frac{2\,\sqrt{d+e\,x}\,\left(b^4\,c^3\,e^6+6\,b^3\,c^4\,d\,e^5+26\,b^2\,c^5\,d^2\,e^4-64\,b\,c^6\,d^3\,e^3+32\,c^7\,d^4\,e^2\right)}{b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4}+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(5\,b\,e-4\,c\,d\right)\,\left(\frac{4\,b^9\,c^2\,d\,e^6+4\,b^8\,c^3\,d^2\,e^5-16\,b^7\,c^4\,d^3\,e^4+8\,b^6\,c^5\,d^4\,e^3}{b^8\,d^2\,e^2-2\,b^7\,c\,d^3\,e+b^6\,c^2\,d^4}-\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(5\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(-4\,b^9\,c^2\,d^2\,e^5+16\,b^8\,c^3\,d^3\,e^4-20\,b^7\,c^4\,d^4\,e^3+8\,b^6\,c^5\,d^5\,e^2\right)}{\left(b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4\right)\,\left(b^6\,e^3-3\,b^5\,c\,d\,e^2+3\,b^4\,c^2\,d^2\,e-b^3\,c^3\,d^3\right)}\right)}{2\,\left(b^6\,e^3-3\,b^5\,c\,d\,e^2+3\,b^4\,c^2\,d^2\,e-b^3\,c^3\,d^3\right)}\right)\,\left(5\,b\,e-4\,c\,d\right)\,1{}\mathrm{i}}{2\,\left(b^6\,e^3-3\,b^5\,c\,d\,e^2+3\,b^4\,c^2\,d^2\,e-b^3\,c^3\,d^3\right)}}{\frac{2\,\left(5\,b^3\,c^4\,e^6+6\,b^2\,c^5\,d\,e^5-48\,b\,c^6\,d^2\,e^4+32\,c^7\,d^3\,e^3\right)}{b^8\,d^2\,e^2-2\,b^7\,c\,d^3\,e+b^6\,c^2\,d^4}+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(\frac{2\,\sqrt{d+e\,x}\,\left(b^4\,c^3\,e^6+6\,b^3\,c^4\,d\,e^5+26\,b^2\,c^5\,d^2\,e^4-64\,b\,c^6\,d^3\,e^3+32\,c^7\,d^4\,e^2\right)}{b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4}-\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(5\,b\,e-4\,c\,d\right)\,\left(\frac{4\,b^9\,c^2\,d\,e^6+4\,b^8\,c^3\,d^2\,e^5-16\,b^7\,c^4\,d^3\,e^4+8\,b^6\,c^5\,d^4\,e^3}{b^8\,d^2\,e^2-2\,b^7\,c\,d^3\,e+b^6\,c^2\,d^4}+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(5\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(-4\,b^9\,c^2\,d^2\,e^5+16\,b^8\,c^3\,d^3\,e^4-20\,b^7\,c^4\,d^4\,e^3+8\,b^6\,c^5\,d^5\,e^2\right)}{\left(b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4\right)\,\left(b^6\,e^3-3\,b^5\,c\,d\,e^2+3\,b^4\,c^2\,d^2\,e-b^3\,c^3\,d^3\right)}\right)}{2\,\left(b^6\,e^3-3\,b^5\,c\,d\,e^2+3\,b^4\,c^2\,d^2\,e-b^3\,c^3\,d^3\right)}\right)\,\left(5\,b\,e-4\,c\,d\right)}{2\,\left(b^6\,e^3-3\,b^5\,c\,d\,e^2+3\,b^4\,c^2\,d^2\,e-b^3\,c^3\,d^3\right)}-\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(\frac{2\,\sqrt{d+e\,x}\,\left(b^4\,c^3\,e^6+6\,b^3\,c^4\,d\,e^5+26\,b^2\,c^5\,d^2\,e^4-64\,b\,c^6\,d^3\,e^3+32\,c^7\,d^4\,e^2\right)}{b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4}+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(5\,b\,e-4\,c\,d\right)\,\left(\frac{4\,b^9\,c^2\,d\,e^6+4\,b^8\,c^3\,d^2\,e^5-16\,b^7\,c^4\,d^3\,e^4+8\,b^6\,c^5\,d^4\,e^3}{b^8\,d^2\,e^2-2\,b^7\,c\,d^3\,e+b^6\,c^2\,d^4}-\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(5\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(-4\,b^9\,c^2\,d^2\,e^5+16\,b^8\,c^3\,d^3\,e^4-20\,b^7\,c^4\,d^4\,e^3+8\,b^6\,c^5\,d^5\,e^2\right)}{\left(b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4\right)\,\left(b^6\,e^3-3\,b^5\,c\,d\,e^2+3\,b^4\,c^2\,d^2\,e-b^3\,c^3\,d^3\right)}\right)}{2\,\left(b^6\,e^3-3\,b^5\,c\,d\,e^2+3\,b^4\,c^2\,d^2\,e-b^3\,c^3\,d^3\right)}\right)\,\left(5\,b\,e-4\,c\,d\right)}{2\,\left(b^6\,e^3-3\,b^5\,c\,d\,e^2+3\,b^4\,c^2\,d^2\,e-b^3\,c^3\,d^3\right)}}\right)\,\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(5\,b\,e-4\,c\,d\right)\,1{}\mathrm{i}}{b^6\,e^3-3\,b^5\,c\,d\,e^2+3\,b^4\,c^2\,d^2\,e-b^3\,c^3\,d^3}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{2\,\sqrt{d+e\,x}\,\left(b^4\,c^3\,e^6+6\,b^3\,c^4\,d\,e^5+26\,b^2\,c^5\,d^2\,e^4-64\,b\,c^6\,d^3\,e^3+32\,c^7\,d^4\,e^2\right)}{b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4}-\frac{\left(\frac{4\,b^9\,c^2\,d\,e^6+4\,b^8\,c^3\,d^2\,e^5-16\,b^7\,c^4\,d^3\,e^4+8\,b^6\,c^5\,d^4\,e^3}{b^8\,d^2\,e^2-2\,b^7\,c\,d^3\,e+b^6\,c^2\,d^4}+\frac{\left(b\,e+4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(-4\,b^9\,c^2\,d^2\,e^5+16\,b^8\,c^3\,d^3\,e^4-20\,b^7\,c^4\,d^4\,e^3+8\,b^6\,c^5\,d^5\,e^2\right)}{b^3\,\sqrt{d^3}\,\left(b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4\right)}\right)\,\left(b\,e+4\,c\,d\right)}{2\,b^3\,\sqrt{d^3}}\right)\,\left(b\,e+4\,c\,d\right)\,1{}\mathrm{i}}{2\,b^3\,\sqrt{d^3}}+\frac{\left(\frac{2\,\sqrt{d+e\,x}\,\left(b^4\,c^3\,e^6+6\,b^3\,c^4\,d\,e^5+26\,b^2\,c^5\,d^2\,e^4-64\,b\,c^6\,d^3\,e^3+32\,c^7\,d^4\,e^2\right)}{b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4}+\frac{\left(\frac{4\,b^9\,c^2\,d\,e^6+4\,b^8\,c^3\,d^2\,e^5-16\,b^7\,c^4\,d^3\,e^4+8\,b^6\,c^5\,d^4\,e^3}{b^8\,d^2\,e^2-2\,b^7\,c\,d^3\,e+b^6\,c^2\,d^4}-\frac{\left(b\,e+4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(-4\,b^9\,c^2\,d^2\,e^5+16\,b^8\,c^3\,d^3\,e^4-20\,b^7\,c^4\,d^4\,e^3+8\,b^6\,c^5\,d^5\,e^2\right)}{b^3\,\sqrt{d^3}\,\left(b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4\right)}\right)\,\left(b\,e+4\,c\,d\right)}{2\,b^3\,\sqrt{d^3}}\right)\,\left(b\,e+4\,c\,d\right)\,1{}\mathrm{i}}{2\,b^3\,\sqrt{d^3}}}{\frac{2\,\left(5\,b^3\,c^4\,e^6+6\,b^2\,c^5\,d\,e^5-48\,b\,c^6\,d^2\,e^4+32\,c^7\,d^3\,e^3\right)}{b^8\,d^2\,e^2-2\,b^7\,c\,d^3\,e+b^6\,c^2\,d^4}+\frac{\left(\frac{2\,\sqrt{d+e\,x}\,\left(b^4\,c^3\,e^6+6\,b^3\,c^4\,d\,e^5+26\,b^2\,c^5\,d^2\,e^4-64\,b\,c^6\,d^3\,e^3+32\,c^7\,d^4\,e^2\right)}{b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4}-\frac{\left(\frac{4\,b^9\,c^2\,d\,e^6+4\,b^8\,c^3\,d^2\,e^5-16\,b^7\,c^4\,d^3\,e^4+8\,b^6\,c^5\,d^4\,e^3}{b^8\,d^2\,e^2-2\,b^7\,c\,d^3\,e+b^6\,c^2\,d^4}+\frac{\left(b\,e+4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(-4\,b^9\,c^2\,d^2\,e^5+16\,b^8\,c^3\,d^3\,e^4-20\,b^7\,c^4\,d^4\,e^3+8\,b^6\,c^5\,d^5\,e^2\right)}{b^3\,\sqrt{d^3}\,\left(b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4\right)}\right)\,\left(b\,e+4\,c\,d\right)}{2\,b^3\,\sqrt{d^3}}\right)\,\left(b\,e+4\,c\,d\right)}{2\,b^3\,\sqrt{d^3}}-\frac{\left(\frac{2\,\sqrt{d+e\,x}\,\left(b^4\,c^3\,e^6+6\,b^3\,c^4\,d\,e^5+26\,b^2\,c^5\,d^2\,e^4-64\,b\,c^6\,d^3\,e^3+32\,c^7\,d^4\,e^2\right)}{b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4}+\frac{\left(\frac{4\,b^9\,c^2\,d\,e^6+4\,b^8\,c^3\,d^2\,e^5-16\,b^7\,c^4\,d^3\,e^4+8\,b^6\,c^5\,d^4\,e^3}{b^8\,d^2\,e^2-2\,b^7\,c\,d^3\,e+b^6\,c^2\,d^4}-\frac{\left(b\,e+4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(-4\,b^9\,c^2\,d^2\,e^5+16\,b^8\,c^3\,d^3\,e^4-20\,b^7\,c^4\,d^4\,e^3+8\,b^6\,c^5\,d^5\,e^2\right)}{b^3\,\sqrt{d^3}\,\left(b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4\right)}\right)\,\left(b\,e+4\,c\,d\right)}{2\,b^3\,\sqrt{d^3}}\right)\,\left(b\,e+4\,c\,d\right)}{2\,b^3\,\sqrt{d^3}}}\right)\,\left(b\,e+4\,c\,d\right)\,1{}\mathrm{i}}{b^3\,\sqrt{d^3}}","Not used",1,"(((d + e*x)^(1/2)*(b^2*e^3 + 2*c^2*d^2*e - 2*b*c*d*e^2))/(b^2*(c*d^2 - b*d*e)) + (c*(b*e^2 - 2*c*d*e)*(d + e*x)^(3/2))/(b^2*(c*d^2 - b*d*e)))/((b*e - 2*c*d)*(d + e*x) + c*(d + e*x)^2 + c*d^2 - b*d*e) + (atan((((-c^3*(b*e - c*d)^3)^(1/2)*((2*(d + e*x)^(1/2)*(b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4))/(b^4*c^2*d^4 + b^6*d^2*e^2 - 2*b^5*c*d^3*e) - ((-c^3*(b*e - c*d)^3)^(1/2)*(5*b*e - 4*c*d)*((4*b^9*c^2*d*e^6 + 8*b^6*c^5*d^4*e^3 - 16*b^7*c^4*d^3*e^4 + 4*b^8*c^3*d^2*e^5)/(b^6*c^2*d^4 + b^8*d^2*e^2 - 2*b^7*c*d^3*e) + ((-c^3*(b*e - c*d)^3)^(1/2)*(5*b*e - 4*c*d)*(d + e*x)^(1/2)*(8*b^6*c^5*d^5*e^2 - 20*b^7*c^4*d^4*e^3 + 16*b^8*c^3*d^3*e^4 - 4*b^9*c^2*d^2*e^5))/((b^4*c^2*d^4 + b^6*d^2*e^2 - 2*b^5*c*d^3*e)*(b^6*e^3 - b^3*c^3*d^3 + 3*b^4*c^2*d^2*e - 3*b^5*c*d*e^2))))/(2*(b^6*e^3 - b^3*c^3*d^3 + 3*b^4*c^2*d^2*e - 3*b^5*c*d*e^2)))*(5*b*e - 4*c*d)*1i)/(2*(b^6*e^3 - b^3*c^3*d^3 + 3*b^4*c^2*d^2*e - 3*b^5*c*d*e^2)) + ((-c^3*(b*e - c*d)^3)^(1/2)*((2*(d + e*x)^(1/2)*(b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4))/(b^4*c^2*d^4 + b^6*d^2*e^2 - 2*b^5*c*d^3*e) + ((-c^3*(b*e - c*d)^3)^(1/2)*(5*b*e - 4*c*d)*((4*b^9*c^2*d*e^6 + 8*b^6*c^5*d^4*e^3 - 16*b^7*c^4*d^3*e^4 + 4*b^8*c^3*d^2*e^5)/(b^6*c^2*d^4 + b^8*d^2*e^2 - 2*b^7*c*d^3*e) - ((-c^3*(b*e - c*d)^3)^(1/2)*(5*b*e - 4*c*d)*(d + e*x)^(1/2)*(8*b^6*c^5*d^5*e^2 - 20*b^7*c^4*d^4*e^3 + 16*b^8*c^3*d^3*e^4 - 4*b^9*c^2*d^2*e^5))/((b^4*c^2*d^4 + b^6*d^2*e^2 - 2*b^5*c*d^3*e)*(b^6*e^3 - b^3*c^3*d^3 + 3*b^4*c^2*d^2*e - 3*b^5*c*d*e^2))))/(2*(b^6*e^3 - b^3*c^3*d^3 + 3*b^4*c^2*d^2*e - 3*b^5*c*d*e^2)))*(5*b*e - 4*c*d)*1i)/(2*(b^6*e^3 - b^3*c^3*d^3 + 3*b^4*c^2*d^2*e - 3*b^5*c*d*e^2)))/((2*(5*b^3*c^4*e^6 + 32*c^7*d^3*e^3 - 48*b*c^6*d^2*e^4 + 6*b^2*c^5*d*e^5))/(b^6*c^2*d^4 + b^8*d^2*e^2 - 2*b^7*c*d^3*e) + ((-c^3*(b*e - c*d)^3)^(1/2)*((2*(d + e*x)^(1/2)*(b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4))/(b^4*c^2*d^4 + b^6*d^2*e^2 - 2*b^5*c*d^3*e) - ((-c^3*(b*e - c*d)^3)^(1/2)*(5*b*e - 4*c*d)*((4*b^9*c^2*d*e^6 + 8*b^6*c^5*d^4*e^3 - 16*b^7*c^4*d^3*e^4 + 4*b^8*c^3*d^2*e^5)/(b^6*c^2*d^4 + b^8*d^2*e^2 - 2*b^7*c*d^3*e) + ((-c^3*(b*e - c*d)^3)^(1/2)*(5*b*e - 4*c*d)*(d + e*x)^(1/2)*(8*b^6*c^5*d^5*e^2 - 20*b^7*c^4*d^4*e^3 + 16*b^8*c^3*d^3*e^4 - 4*b^9*c^2*d^2*e^5))/((b^4*c^2*d^4 + b^6*d^2*e^2 - 2*b^5*c*d^3*e)*(b^6*e^3 - b^3*c^3*d^3 + 3*b^4*c^2*d^2*e - 3*b^5*c*d*e^2))))/(2*(b^6*e^3 - b^3*c^3*d^3 + 3*b^4*c^2*d^2*e - 3*b^5*c*d*e^2)))*(5*b*e - 4*c*d))/(2*(b^6*e^3 - b^3*c^3*d^3 + 3*b^4*c^2*d^2*e - 3*b^5*c*d*e^2)) - ((-c^3*(b*e - c*d)^3)^(1/2)*((2*(d + e*x)^(1/2)*(b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4))/(b^4*c^2*d^4 + b^6*d^2*e^2 - 2*b^5*c*d^3*e) + ((-c^3*(b*e - c*d)^3)^(1/2)*(5*b*e - 4*c*d)*((4*b^9*c^2*d*e^6 + 8*b^6*c^5*d^4*e^3 - 16*b^7*c^4*d^3*e^4 + 4*b^8*c^3*d^2*e^5)/(b^6*c^2*d^4 + b^8*d^2*e^2 - 2*b^7*c*d^3*e) - ((-c^3*(b*e - c*d)^3)^(1/2)*(5*b*e - 4*c*d)*(d + e*x)^(1/2)*(8*b^6*c^5*d^5*e^2 - 20*b^7*c^4*d^4*e^3 + 16*b^8*c^3*d^3*e^4 - 4*b^9*c^2*d^2*e^5))/((b^4*c^2*d^4 + b^6*d^2*e^2 - 2*b^5*c*d^3*e)*(b^6*e^3 - b^3*c^3*d^3 + 3*b^4*c^2*d^2*e - 3*b^5*c*d*e^2))))/(2*(b^6*e^3 - b^3*c^3*d^3 + 3*b^4*c^2*d^2*e - 3*b^5*c*d*e^2)))*(5*b*e - 4*c*d))/(2*(b^6*e^3 - b^3*c^3*d^3 + 3*b^4*c^2*d^2*e - 3*b^5*c*d*e^2))))*(-c^3*(b*e - c*d)^3)^(1/2)*(5*b*e - 4*c*d)*1i)/(b^6*e^3 - b^3*c^3*d^3 + 3*b^4*c^2*d^2*e - 3*b^5*c*d*e^2) + (atan(((((2*(d + e*x)^(1/2)*(b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4))/(b^4*c^2*d^4 + b^6*d^2*e^2 - 2*b^5*c*d^3*e) - (((4*b^9*c^2*d*e^6 + 8*b^6*c^5*d^4*e^3 - 16*b^7*c^4*d^3*e^4 + 4*b^8*c^3*d^2*e^5)/(b^6*c^2*d^4 + b^8*d^2*e^2 - 2*b^7*c*d^3*e) + ((b*e + 4*c*d)*(d + e*x)^(1/2)*(8*b^6*c^5*d^5*e^2 - 20*b^7*c^4*d^4*e^3 + 16*b^8*c^3*d^3*e^4 - 4*b^9*c^2*d^2*e^5))/(b^3*(d^3)^(1/2)*(b^4*c^2*d^4 + b^6*d^2*e^2 - 2*b^5*c*d^3*e)))*(b*e + 4*c*d))/(2*b^3*(d^3)^(1/2)))*(b*e + 4*c*d)*1i)/(2*b^3*(d^3)^(1/2)) + (((2*(d + e*x)^(1/2)*(b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4))/(b^4*c^2*d^4 + b^6*d^2*e^2 - 2*b^5*c*d^3*e) + (((4*b^9*c^2*d*e^6 + 8*b^6*c^5*d^4*e^3 - 16*b^7*c^4*d^3*e^4 + 4*b^8*c^3*d^2*e^5)/(b^6*c^2*d^4 + b^8*d^2*e^2 - 2*b^7*c*d^3*e) - ((b*e + 4*c*d)*(d + e*x)^(1/2)*(8*b^6*c^5*d^5*e^2 - 20*b^7*c^4*d^4*e^3 + 16*b^8*c^3*d^3*e^4 - 4*b^9*c^2*d^2*e^5))/(b^3*(d^3)^(1/2)*(b^4*c^2*d^4 + b^6*d^2*e^2 - 2*b^5*c*d^3*e)))*(b*e + 4*c*d))/(2*b^3*(d^3)^(1/2)))*(b*e + 4*c*d)*1i)/(2*b^3*(d^3)^(1/2)))/((2*(5*b^3*c^4*e^6 + 32*c^7*d^3*e^3 - 48*b*c^6*d^2*e^4 + 6*b^2*c^5*d*e^5))/(b^6*c^2*d^4 + b^8*d^2*e^2 - 2*b^7*c*d^3*e) + (((2*(d + e*x)^(1/2)*(b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4))/(b^4*c^2*d^4 + b^6*d^2*e^2 - 2*b^5*c*d^3*e) - (((4*b^9*c^2*d*e^6 + 8*b^6*c^5*d^4*e^3 - 16*b^7*c^4*d^3*e^4 + 4*b^8*c^3*d^2*e^5)/(b^6*c^2*d^4 + b^8*d^2*e^2 - 2*b^7*c*d^3*e) + ((b*e + 4*c*d)*(d + e*x)^(1/2)*(8*b^6*c^5*d^5*e^2 - 20*b^7*c^4*d^4*e^3 + 16*b^8*c^3*d^3*e^4 - 4*b^9*c^2*d^2*e^5))/(b^3*(d^3)^(1/2)*(b^4*c^2*d^4 + b^6*d^2*e^2 - 2*b^5*c*d^3*e)))*(b*e + 4*c*d))/(2*b^3*(d^3)^(1/2)))*(b*e + 4*c*d))/(2*b^3*(d^3)^(1/2)) - (((2*(d + e*x)^(1/2)*(b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4))/(b^4*c^2*d^4 + b^6*d^2*e^2 - 2*b^5*c*d^3*e) + (((4*b^9*c^2*d*e^6 + 8*b^6*c^5*d^4*e^3 - 16*b^7*c^4*d^3*e^4 + 4*b^8*c^3*d^2*e^5)/(b^6*c^2*d^4 + b^8*d^2*e^2 - 2*b^7*c*d^3*e) - ((b*e + 4*c*d)*(d + e*x)^(1/2)*(8*b^6*c^5*d^5*e^2 - 20*b^7*c^4*d^4*e^3 + 16*b^8*c^3*d^3*e^4 - 4*b^9*c^2*d^2*e^5))/(b^3*(d^3)^(1/2)*(b^4*c^2*d^4 + b^6*d^2*e^2 - 2*b^5*c*d^3*e)))*(b*e + 4*c*d))/(2*b^3*(d^3)^(1/2)))*(b*e + 4*c*d))/(2*b^3*(d^3)^(1/2))))*(b*e + 4*c*d)*1i)/(b^3*(d^3)^(1/2))","B"
375,1,4234,206,2.425871,"\text{Not used}","int(1/((b*x + c*x^2)^2*(d + e*x)^(3/2)),x)","-\frac{\frac{2\,e^3}{c\,d^2-b\,d\,e}+\frac{e\,{\left(d+e\,x\right)}^2\,\left(3\,b^2\,c\,e^2-2\,b\,c^2\,d\,e+2\,c^3\,d^2\right)}{b^2\,{\left(c\,d^2-b\,d\,e\right)}^2}+\frac{e\,\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)\,\left(3\,b^2\,e^2-b\,c\,d\,e+c^2\,d^2\right)}{b^2\,{\left(c\,d^2-b\,d\,e\right)}^2}}{c\,{\left(d+e\,x\right)}^{5/2}+\left(c\,d^2-b\,d\,e\right)\,\sqrt{d+e\,x}+\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{3/2}}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(7\,b\,e-4\,c\,d\right)\,\left(\sqrt{d+e\,x}\,\left(18\,b^{18}\,c^3\,d^6\,e^{14}-132\,b^{17}\,c^4\,d^7\,e^{13}+362\,b^{16}\,c^5\,d^8\,e^{12}-320\,b^{15}\,c^6\,d^9\,e^{11}-442\,b^{14}\,c^7\,d^{10}\,e^{10}+1004\,b^{13}\,c^8\,d^{11}\,e^9+578\,b^{12}\,c^9\,d^{12}\,e^8-3976\,b^{11}\,c^{10}\,d^{13}\,e^7+5960\,b^{10}\,c^{11}\,d^{14}\,e^6-4768\,b^9\,c^{12}\,d^{15}\,e^5+2228\,b^8\,c^{13}\,d^{16}\,e^4-576\,b^7\,c^{14}\,d^{17}\,e^3+64\,b^6\,c^{15}\,d^{18}\,e^2\right)+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(7\,b\,e-4\,c\,d\right)\,\left(8\,b^{10}\,c^{13}\,d^{19}\,e^3-76\,b^{11}\,c^{12}\,d^{18}\,e^4+300\,b^{12}\,c^{11}\,d^{17}\,e^5-612\,b^{13}\,c^{10}\,d^{16}\,e^6+576\,b^{14}\,c^9\,d^{15}\,e^7+168\,b^{15}\,c^8\,d^{14}\,e^8-1176\,b^{16}\,c^7\,d^{13}\,e^9+1560\,b^{17}\,c^6\,d^{12}\,e^{10}-1128\,b^{18}\,c^5\,d^{11}\,e^{11}+484\,b^{19}\,c^4\,d^{10}\,e^{12}-116\,b^{20}\,c^3\,d^9\,e^{13}+12\,b^{21}\,c^2\,d^8\,e^{14}-\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(-8\,b^{23}\,c^2\,d^{10}\,e^{13}+96\,b^{22}\,c^3\,d^{11}\,e^{12}-520\,b^{21}\,c^4\,d^{12}\,e^{11}+1680\,b^{20}\,c^5\,d^{13}\,e^{10}-3600\,b^{19}\,c^6\,d^{14}\,e^9+5376\,b^{18}\,c^7\,d^{15}\,e^8-5712\,b^{17}\,c^8\,d^{16}\,e^7+4320\,b^{16}\,c^9\,d^{17}\,e^6-2280\,b^{15}\,c^{10}\,d^{18}\,e^5+800\,b^{14}\,c^{11}\,d^{19}\,e^4-168\,b^{13}\,c^{12}\,d^{20}\,e^3+16\,b^{12}\,c^{13}\,d^{21}\,e^2\right)}{2\,\left(b^8\,e^5-5\,b^7\,c\,d\,e^4+10\,b^6\,c^2\,d^2\,e^3-10\,b^5\,c^3\,d^3\,e^2+5\,b^4\,c^4\,d^4\,e-b^3\,c^5\,d^5\right)}\right)}{2\,\left(b^8\,e^5-5\,b^7\,c\,d\,e^4+10\,b^6\,c^2\,d^2\,e^3-10\,b^5\,c^3\,d^3\,e^2+5\,b^4\,c^4\,d^4\,e-b^3\,c^5\,d^5\right)}\right)\,1{}\mathrm{i}}{2\,\left(b^8\,e^5-5\,b^7\,c\,d\,e^4+10\,b^6\,c^2\,d^2\,e^3-10\,b^5\,c^3\,d^3\,e^2+5\,b^4\,c^4\,d^4\,e-b^3\,c^5\,d^5\right)}+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(7\,b\,e-4\,c\,d\right)\,\left(\sqrt{d+e\,x}\,\left(18\,b^{18}\,c^3\,d^6\,e^{14}-132\,b^{17}\,c^4\,d^7\,e^{13}+362\,b^{16}\,c^5\,d^8\,e^{12}-320\,b^{15}\,c^6\,d^9\,e^{11}-442\,b^{14}\,c^7\,d^{10}\,e^{10}+1004\,b^{13}\,c^8\,d^{11}\,e^9+578\,b^{12}\,c^9\,d^{12}\,e^8-3976\,b^{11}\,c^{10}\,d^{13}\,e^7+5960\,b^{10}\,c^{11}\,d^{14}\,e^6-4768\,b^9\,c^{12}\,d^{15}\,e^5+2228\,b^8\,c^{13}\,d^{16}\,e^4-576\,b^7\,c^{14}\,d^{17}\,e^3+64\,b^6\,c^{15}\,d^{18}\,e^2\right)-\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(7\,b\,e-4\,c\,d\right)\,\left(8\,b^{10}\,c^{13}\,d^{19}\,e^3-76\,b^{11}\,c^{12}\,d^{18}\,e^4+300\,b^{12}\,c^{11}\,d^{17}\,e^5-612\,b^{13}\,c^{10}\,d^{16}\,e^6+576\,b^{14}\,c^9\,d^{15}\,e^7+168\,b^{15}\,c^8\,d^{14}\,e^8-1176\,b^{16}\,c^7\,d^{13}\,e^9+1560\,b^{17}\,c^6\,d^{12}\,e^{10}-1128\,b^{18}\,c^5\,d^{11}\,e^{11}+484\,b^{19}\,c^4\,d^{10}\,e^{12}-116\,b^{20}\,c^3\,d^9\,e^{13}+12\,b^{21}\,c^2\,d^8\,e^{14}+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(-8\,b^{23}\,c^2\,d^{10}\,e^{13}+96\,b^{22}\,c^3\,d^{11}\,e^{12}-520\,b^{21}\,c^4\,d^{12}\,e^{11}+1680\,b^{20}\,c^5\,d^{13}\,e^{10}-3600\,b^{19}\,c^6\,d^{14}\,e^9+5376\,b^{18}\,c^7\,d^{15}\,e^8-5712\,b^{17}\,c^8\,d^{16}\,e^7+4320\,b^{16}\,c^9\,d^{17}\,e^6-2280\,b^{15}\,c^{10}\,d^{18}\,e^5+800\,b^{14}\,c^{11}\,d^{19}\,e^4-168\,b^{13}\,c^{12}\,d^{20}\,e^3+16\,b^{12}\,c^{13}\,d^{21}\,e^2\right)}{2\,\left(b^8\,e^5-5\,b^7\,c\,d\,e^4+10\,b^6\,c^2\,d^2\,e^3-10\,b^5\,c^3\,d^3\,e^2+5\,b^4\,c^4\,d^4\,e-b^3\,c^5\,d^5\right)}\right)}{2\,\left(b^8\,e^5-5\,b^7\,c\,d\,e^4+10\,b^6\,c^2\,d^2\,e^3-10\,b^5\,c^3\,d^3\,e^2+5\,b^4\,c^4\,d^4\,e-b^3\,c^5\,d^5\right)}\right)\,1{}\mathrm{i}}{2\,\left(b^8\,e^5-5\,b^7\,c\,d\,e^4+10\,b^6\,c^2\,d^2\,e^3-10\,b^5\,c^3\,d^3\,e^2+5\,b^4\,c^4\,d^4\,e-b^3\,c^5\,d^5\right)}}{64\,b^4\,c^{15}\,d^{16}\,e^3-512\,b^5\,c^{14}\,d^{15}\,e^4+1804\,b^6\,c^{13}\,d^{14}\,e^5-3668\,b^7\,c^{12}\,d^{13}\,e^6+4606\,b^8\,c^{11}\,d^{12}\,e^7-3248\,b^9\,c^{10}\,d^{11}\,e^8+322\,b^{10}\,c^9\,d^{10}\,e^9+1756\,b^{11}\,c^8\,d^9\,e^{10}-1742\,b^{12}\,c^7\,d^8\,e^{11}+744\,b^{13}\,c^6\,d^7\,e^{12}-126\,b^{14}\,c^5\,d^6\,e^{13}-\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(7\,b\,e-4\,c\,d\right)\,\left(\sqrt{d+e\,x}\,\left(18\,b^{18}\,c^3\,d^6\,e^{14}-132\,b^{17}\,c^4\,d^7\,e^{13}+362\,b^{16}\,c^5\,d^8\,e^{12}-320\,b^{15}\,c^6\,d^9\,e^{11}-442\,b^{14}\,c^7\,d^{10}\,e^{10}+1004\,b^{13}\,c^8\,d^{11}\,e^9+578\,b^{12}\,c^9\,d^{12}\,e^8-3976\,b^{11}\,c^{10}\,d^{13}\,e^7+5960\,b^{10}\,c^{11}\,d^{14}\,e^6-4768\,b^9\,c^{12}\,d^{15}\,e^5+2228\,b^8\,c^{13}\,d^{16}\,e^4-576\,b^7\,c^{14}\,d^{17}\,e^3+64\,b^6\,c^{15}\,d^{18}\,e^2\right)+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(7\,b\,e-4\,c\,d\right)\,\left(8\,b^{10}\,c^{13}\,d^{19}\,e^3-76\,b^{11}\,c^{12}\,d^{18}\,e^4+300\,b^{12}\,c^{11}\,d^{17}\,e^5-612\,b^{13}\,c^{10}\,d^{16}\,e^6+576\,b^{14}\,c^9\,d^{15}\,e^7+168\,b^{15}\,c^8\,d^{14}\,e^8-1176\,b^{16}\,c^7\,d^{13}\,e^9+1560\,b^{17}\,c^6\,d^{12}\,e^{10}-1128\,b^{18}\,c^5\,d^{11}\,e^{11}+484\,b^{19}\,c^4\,d^{10}\,e^{12}-116\,b^{20}\,c^3\,d^9\,e^{13}+12\,b^{21}\,c^2\,d^8\,e^{14}-\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(-8\,b^{23}\,c^2\,d^{10}\,e^{13}+96\,b^{22}\,c^3\,d^{11}\,e^{12}-520\,b^{21}\,c^4\,d^{12}\,e^{11}+1680\,b^{20}\,c^5\,d^{13}\,e^{10}-3600\,b^{19}\,c^6\,d^{14}\,e^9+5376\,b^{18}\,c^7\,d^{15}\,e^8-5712\,b^{17}\,c^8\,d^{16}\,e^7+4320\,b^{16}\,c^9\,d^{17}\,e^6-2280\,b^{15}\,c^{10}\,d^{18}\,e^5+800\,b^{14}\,c^{11}\,d^{19}\,e^4-168\,b^{13}\,c^{12}\,d^{20}\,e^3+16\,b^{12}\,c^{13}\,d^{21}\,e^2\right)}{2\,\left(b^8\,e^5-5\,b^7\,c\,d\,e^4+10\,b^6\,c^2\,d^2\,e^3-10\,b^5\,c^3\,d^3\,e^2+5\,b^4\,c^4\,d^4\,e-b^3\,c^5\,d^5\right)}\right)}{2\,\left(b^8\,e^5-5\,b^7\,c\,d\,e^4+10\,b^6\,c^2\,d^2\,e^3-10\,b^5\,c^3\,d^3\,e^2+5\,b^4\,c^4\,d^4\,e-b^3\,c^5\,d^5\right)}\right)}{2\,\left(b^8\,e^5-5\,b^7\,c\,d\,e^4+10\,b^6\,c^2\,d^2\,e^3-10\,b^5\,c^3\,d^3\,e^2+5\,b^4\,c^4\,d^4\,e-b^3\,c^5\,d^5\right)}+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(7\,b\,e-4\,c\,d\right)\,\left(\sqrt{d+e\,x}\,\left(18\,b^{18}\,c^3\,d^6\,e^{14}-132\,b^{17}\,c^4\,d^7\,e^{13}+362\,b^{16}\,c^5\,d^8\,e^{12}-320\,b^{15}\,c^6\,d^9\,e^{11}-442\,b^{14}\,c^7\,d^{10}\,e^{10}+1004\,b^{13}\,c^8\,d^{11}\,e^9+578\,b^{12}\,c^9\,d^{12}\,e^8-3976\,b^{11}\,c^{10}\,d^{13}\,e^7+5960\,b^{10}\,c^{11}\,d^{14}\,e^6-4768\,b^9\,c^{12}\,d^{15}\,e^5+2228\,b^8\,c^{13}\,d^{16}\,e^4-576\,b^7\,c^{14}\,d^{17}\,e^3+64\,b^6\,c^{15}\,d^{18}\,e^2\right)-\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(7\,b\,e-4\,c\,d\right)\,\left(8\,b^{10}\,c^{13}\,d^{19}\,e^3-76\,b^{11}\,c^{12}\,d^{18}\,e^4+300\,b^{12}\,c^{11}\,d^{17}\,e^5-612\,b^{13}\,c^{10}\,d^{16}\,e^6+576\,b^{14}\,c^9\,d^{15}\,e^7+168\,b^{15}\,c^8\,d^{14}\,e^8-1176\,b^{16}\,c^7\,d^{13}\,e^9+1560\,b^{17}\,c^6\,d^{12}\,e^{10}-1128\,b^{18}\,c^5\,d^{11}\,e^{11}+484\,b^{19}\,c^4\,d^{10}\,e^{12}-116\,b^{20}\,c^3\,d^9\,e^{13}+12\,b^{21}\,c^2\,d^8\,e^{14}+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(7\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(-8\,b^{23}\,c^2\,d^{10}\,e^{13}+96\,b^{22}\,c^3\,d^{11}\,e^{12}-520\,b^{21}\,c^4\,d^{12}\,e^{11}+1680\,b^{20}\,c^5\,d^{13}\,e^{10}-3600\,b^{19}\,c^6\,d^{14}\,e^9+5376\,b^{18}\,c^7\,d^{15}\,e^8-5712\,b^{17}\,c^8\,d^{16}\,e^7+4320\,b^{16}\,c^9\,d^{17}\,e^6-2280\,b^{15}\,c^{10}\,d^{18}\,e^5+800\,b^{14}\,c^{11}\,d^{19}\,e^4-168\,b^{13}\,c^{12}\,d^{20}\,e^3+16\,b^{12}\,c^{13}\,d^{21}\,e^2\right)}{2\,\left(b^8\,e^5-5\,b^7\,c\,d\,e^4+10\,b^6\,c^2\,d^2\,e^3-10\,b^5\,c^3\,d^3\,e^2+5\,b^4\,c^4\,d^4\,e-b^3\,c^5\,d^5\right)}\right)}{2\,\left(b^8\,e^5-5\,b^7\,c\,d\,e^4+10\,b^6\,c^2\,d^2\,e^3-10\,b^5\,c^3\,d^3\,e^2+5\,b^4\,c^4\,d^4\,e-b^3\,c^5\,d^5\right)}\right)}{2\,\left(b^8\,e^5-5\,b^7\,c\,d\,e^4+10\,b^6\,c^2\,d^2\,e^3-10\,b^5\,c^3\,d^3\,e^2+5\,b^4\,c^4\,d^4\,e-b^3\,c^5\,d^5\right)}}\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(7\,b\,e-4\,c\,d\right)\,1{}\mathrm{i}}{b^8\,e^5-5\,b^7\,c\,d\,e^4+10\,b^6\,c^2\,d^2\,e^3-10\,b^5\,c^3\,d^3\,e^2+5\,b^4\,c^4\,d^4\,e-b^3\,c^5\,d^5}-\frac{\mathrm{atan}\left(\frac{-b^{14}\,d^{10}\,e^{14}\,\sqrt{d+e\,x}\,27{}\mathrm{i}+b^{13}\,c\,d^{11}\,e^{13}\,\sqrt{d+e\,x}\,189{}\mathrm{i}+b^3\,c^{11}\,d^{21}\,e^3\,\sqrt{d+e\,x}\,140{}\mathrm{i}-b^4\,c^{10}\,d^{20}\,e^4\,\sqrt{d+e\,x}\,1015{}\mathrm{i}+b^5\,c^9\,d^{19}\,e^5\,\sqrt{d+e\,x}\,2996{}\mathrm{i}-b^6\,c^8\,d^{18}\,e^6\,\sqrt{d+e\,x}\,4375{}\mathrm{i}+b^7\,c^7\,d^{17}\,e^7\,\sqrt{d+e\,x}\,2561{}\mathrm{i}+b^8\,c^6\,d^{16}\,e^8\,\sqrt{d+e\,x}\,1316{}\mathrm{i}-b^9\,c^5\,d^{15}\,e^9\,\sqrt{d+e\,x}\,3073{}\mathrm{i}+b^{10}\,c^4\,d^{14}\,e^{10}\,\sqrt{d+e\,x}\,1694{}\mathrm{i}+b^{11}\,c^3\,d^{13}\,e^{11}\,\sqrt{d+e\,x}\,35{}\mathrm{i}-b^{12}\,c^2\,d^{12}\,e^{12}\,\sqrt{d+e\,x}\,441{}\mathrm{i}}{d^5\,\sqrt{d^5}\,\left(d^5\,\left(d^5\,\left(2561\,b^7\,c^7\,e^7-4375\,b^6\,c^8\,d\,e^6+2996\,b^5\,c^9\,d^2\,e^5-1015\,b^4\,c^{10}\,d^3\,e^4+140\,b^3\,c^{11}\,d^4\,e^3\right)-441\,b^{12}\,c^2\,e^{12}+35\,b^{11}\,c^3\,d\,e^{11}+1316\,b^8\,c^6\,d^4\,e^8-3073\,b^9\,c^5\,d^3\,e^9+1694\,b^{10}\,c^4\,d^2\,e^{10}\right)-27\,b^{14}\,d^3\,e^{14}+189\,b^{13}\,c\,d^4\,e^{13}\right)}\right)\,\left(3\,b\,e+4\,c\,d\right)\,1{}\mathrm{i}}{b^3\,\sqrt{d^5}}","Not used",1,"(atan((((-c^5*(b*e - c*d)^5)^(1/2)*(7*b*e - 4*c*d)*((d + e*x)^(1/2)*(64*b^6*c^15*d^18*e^2 - 576*b^7*c^14*d^17*e^3 + 2228*b^8*c^13*d^16*e^4 - 4768*b^9*c^12*d^15*e^5 + 5960*b^10*c^11*d^14*e^6 - 3976*b^11*c^10*d^13*e^7 + 578*b^12*c^9*d^12*e^8 + 1004*b^13*c^8*d^11*e^9 - 442*b^14*c^7*d^10*e^10 - 320*b^15*c^6*d^9*e^11 + 362*b^16*c^5*d^8*e^12 - 132*b^17*c^4*d^7*e^13 + 18*b^18*c^3*d^6*e^14) + ((-c^5*(b*e - c*d)^5)^(1/2)*(7*b*e - 4*c*d)*(8*b^10*c^13*d^19*e^3 - 76*b^11*c^12*d^18*e^4 + 300*b^12*c^11*d^17*e^5 - 612*b^13*c^10*d^16*e^6 + 576*b^14*c^9*d^15*e^7 + 168*b^15*c^8*d^14*e^8 - 1176*b^16*c^7*d^13*e^9 + 1560*b^17*c^6*d^12*e^10 - 1128*b^18*c^5*d^11*e^11 + 484*b^19*c^4*d^10*e^12 - 116*b^20*c^3*d^9*e^13 + 12*b^21*c^2*d^8*e^14 - ((-c^5*(b*e - c*d)^5)^(1/2)*(7*b*e - 4*c*d)*(d + e*x)^(1/2)*(16*b^12*c^13*d^21*e^2 - 168*b^13*c^12*d^20*e^3 + 800*b^14*c^11*d^19*e^4 - 2280*b^15*c^10*d^18*e^5 + 4320*b^16*c^9*d^17*e^6 - 5712*b^17*c^8*d^16*e^7 + 5376*b^18*c^7*d^15*e^8 - 3600*b^19*c^6*d^14*e^9 + 1680*b^20*c^5*d^13*e^10 - 520*b^21*c^4*d^12*e^11 + 96*b^22*c^3*d^11*e^12 - 8*b^23*c^2*d^10*e^13))/(2*(b^8*e^5 - b^3*c^5*d^5 + 5*b^4*c^4*d^4*e - 10*b^5*c^3*d^3*e^2 + 10*b^6*c^2*d^2*e^3 - 5*b^7*c*d*e^4))))/(2*(b^8*e^5 - b^3*c^5*d^5 + 5*b^4*c^4*d^4*e - 10*b^5*c^3*d^3*e^2 + 10*b^6*c^2*d^2*e^3 - 5*b^7*c*d*e^4)))*1i)/(2*(b^8*e^5 - b^3*c^5*d^5 + 5*b^4*c^4*d^4*e - 10*b^5*c^3*d^3*e^2 + 10*b^6*c^2*d^2*e^3 - 5*b^7*c*d*e^4)) + ((-c^5*(b*e - c*d)^5)^(1/2)*(7*b*e - 4*c*d)*((d + e*x)^(1/2)*(64*b^6*c^15*d^18*e^2 - 576*b^7*c^14*d^17*e^3 + 2228*b^8*c^13*d^16*e^4 - 4768*b^9*c^12*d^15*e^5 + 5960*b^10*c^11*d^14*e^6 - 3976*b^11*c^10*d^13*e^7 + 578*b^12*c^9*d^12*e^8 + 1004*b^13*c^8*d^11*e^9 - 442*b^14*c^7*d^10*e^10 - 320*b^15*c^6*d^9*e^11 + 362*b^16*c^5*d^8*e^12 - 132*b^17*c^4*d^7*e^13 + 18*b^18*c^3*d^6*e^14) - ((-c^5*(b*e - c*d)^5)^(1/2)*(7*b*e - 4*c*d)*(8*b^10*c^13*d^19*e^3 - 76*b^11*c^12*d^18*e^4 + 300*b^12*c^11*d^17*e^5 - 612*b^13*c^10*d^16*e^6 + 576*b^14*c^9*d^15*e^7 + 168*b^15*c^8*d^14*e^8 - 1176*b^16*c^7*d^13*e^9 + 1560*b^17*c^6*d^12*e^10 - 1128*b^18*c^5*d^11*e^11 + 484*b^19*c^4*d^10*e^12 - 116*b^20*c^3*d^9*e^13 + 12*b^21*c^2*d^8*e^14 + ((-c^5*(b*e - c*d)^5)^(1/2)*(7*b*e - 4*c*d)*(d + e*x)^(1/2)*(16*b^12*c^13*d^21*e^2 - 168*b^13*c^12*d^20*e^3 + 800*b^14*c^11*d^19*e^4 - 2280*b^15*c^10*d^18*e^5 + 4320*b^16*c^9*d^17*e^6 - 5712*b^17*c^8*d^16*e^7 + 5376*b^18*c^7*d^15*e^8 - 3600*b^19*c^6*d^14*e^9 + 1680*b^20*c^5*d^13*e^10 - 520*b^21*c^4*d^12*e^11 + 96*b^22*c^3*d^11*e^12 - 8*b^23*c^2*d^10*e^13))/(2*(b^8*e^5 - b^3*c^5*d^5 + 5*b^4*c^4*d^4*e - 10*b^5*c^3*d^3*e^2 + 10*b^6*c^2*d^2*e^3 - 5*b^7*c*d*e^4))))/(2*(b^8*e^5 - b^3*c^5*d^5 + 5*b^4*c^4*d^4*e - 10*b^5*c^3*d^3*e^2 + 10*b^6*c^2*d^2*e^3 - 5*b^7*c*d*e^4)))*1i)/(2*(b^8*e^5 - b^3*c^5*d^5 + 5*b^4*c^4*d^4*e - 10*b^5*c^3*d^3*e^2 + 10*b^6*c^2*d^2*e^3 - 5*b^7*c*d*e^4)))/(64*b^4*c^15*d^16*e^3 - 512*b^5*c^14*d^15*e^4 + 1804*b^6*c^13*d^14*e^5 - 3668*b^7*c^12*d^13*e^6 + 4606*b^8*c^11*d^12*e^7 - 3248*b^9*c^10*d^11*e^8 + 322*b^10*c^9*d^10*e^9 + 1756*b^11*c^8*d^9*e^10 - 1742*b^12*c^7*d^8*e^11 + 744*b^13*c^6*d^7*e^12 - 126*b^14*c^5*d^6*e^13 - ((-c^5*(b*e - c*d)^5)^(1/2)*(7*b*e - 4*c*d)*((d + e*x)^(1/2)*(64*b^6*c^15*d^18*e^2 - 576*b^7*c^14*d^17*e^3 + 2228*b^8*c^13*d^16*e^4 - 4768*b^9*c^12*d^15*e^5 + 5960*b^10*c^11*d^14*e^6 - 3976*b^11*c^10*d^13*e^7 + 578*b^12*c^9*d^12*e^8 + 1004*b^13*c^8*d^11*e^9 - 442*b^14*c^7*d^10*e^10 - 320*b^15*c^6*d^9*e^11 + 362*b^16*c^5*d^8*e^12 - 132*b^17*c^4*d^7*e^13 + 18*b^18*c^3*d^6*e^14) + ((-c^5*(b*e - c*d)^5)^(1/2)*(7*b*e - 4*c*d)*(8*b^10*c^13*d^19*e^3 - 76*b^11*c^12*d^18*e^4 + 300*b^12*c^11*d^17*e^5 - 612*b^13*c^10*d^16*e^6 + 576*b^14*c^9*d^15*e^7 + 168*b^15*c^8*d^14*e^8 - 1176*b^16*c^7*d^13*e^9 + 1560*b^17*c^6*d^12*e^10 - 1128*b^18*c^5*d^11*e^11 + 484*b^19*c^4*d^10*e^12 - 116*b^20*c^3*d^9*e^13 + 12*b^21*c^2*d^8*e^14 - ((-c^5*(b*e - c*d)^5)^(1/2)*(7*b*e - 4*c*d)*(d + e*x)^(1/2)*(16*b^12*c^13*d^21*e^2 - 168*b^13*c^12*d^20*e^3 + 800*b^14*c^11*d^19*e^4 - 2280*b^15*c^10*d^18*e^5 + 4320*b^16*c^9*d^17*e^6 - 5712*b^17*c^8*d^16*e^7 + 5376*b^18*c^7*d^15*e^8 - 3600*b^19*c^6*d^14*e^9 + 1680*b^20*c^5*d^13*e^10 - 520*b^21*c^4*d^12*e^11 + 96*b^22*c^3*d^11*e^12 - 8*b^23*c^2*d^10*e^13))/(2*(b^8*e^5 - b^3*c^5*d^5 + 5*b^4*c^4*d^4*e - 10*b^5*c^3*d^3*e^2 + 10*b^6*c^2*d^2*e^3 - 5*b^7*c*d*e^4))))/(2*(b^8*e^5 - b^3*c^5*d^5 + 5*b^4*c^4*d^4*e - 10*b^5*c^3*d^3*e^2 + 10*b^6*c^2*d^2*e^3 - 5*b^7*c*d*e^4))))/(2*(b^8*e^5 - b^3*c^5*d^5 + 5*b^4*c^4*d^4*e - 10*b^5*c^3*d^3*e^2 + 10*b^6*c^2*d^2*e^3 - 5*b^7*c*d*e^4)) + ((-c^5*(b*e - c*d)^5)^(1/2)*(7*b*e - 4*c*d)*((d + e*x)^(1/2)*(64*b^6*c^15*d^18*e^2 - 576*b^7*c^14*d^17*e^3 + 2228*b^8*c^13*d^16*e^4 - 4768*b^9*c^12*d^15*e^5 + 5960*b^10*c^11*d^14*e^6 - 3976*b^11*c^10*d^13*e^7 + 578*b^12*c^9*d^12*e^8 + 1004*b^13*c^8*d^11*e^9 - 442*b^14*c^7*d^10*e^10 - 320*b^15*c^6*d^9*e^11 + 362*b^16*c^5*d^8*e^12 - 132*b^17*c^4*d^7*e^13 + 18*b^18*c^3*d^6*e^14) - ((-c^5*(b*e - c*d)^5)^(1/2)*(7*b*e - 4*c*d)*(8*b^10*c^13*d^19*e^3 - 76*b^11*c^12*d^18*e^4 + 300*b^12*c^11*d^17*e^5 - 612*b^13*c^10*d^16*e^6 + 576*b^14*c^9*d^15*e^7 + 168*b^15*c^8*d^14*e^8 - 1176*b^16*c^7*d^13*e^9 + 1560*b^17*c^6*d^12*e^10 - 1128*b^18*c^5*d^11*e^11 + 484*b^19*c^4*d^10*e^12 - 116*b^20*c^3*d^9*e^13 + 12*b^21*c^2*d^8*e^14 + ((-c^5*(b*e - c*d)^5)^(1/2)*(7*b*e - 4*c*d)*(d + e*x)^(1/2)*(16*b^12*c^13*d^21*e^2 - 168*b^13*c^12*d^20*e^3 + 800*b^14*c^11*d^19*e^4 - 2280*b^15*c^10*d^18*e^5 + 4320*b^16*c^9*d^17*e^6 - 5712*b^17*c^8*d^16*e^7 + 5376*b^18*c^7*d^15*e^8 - 3600*b^19*c^6*d^14*e^9 + 1680*b^20*c^5*d^13*e^10 - 520*b^21*c^4*d^12*e^11 + 96*b^22*c^3*d^11*e^12 - 8*b^23*c^2*d^10*e^13))/(2*(b^8*e^5 - b^3*c^5*d^5 + 5*b^4*c^4*d^4*e - 10*b^5*c^3*d^3*e^2 + 10*b^6*c^2*d^2*e^3 - 5*b^7*c*d*e^4))))/(2*(b^8*e^5 - b^3*c^5*d^5 + 5*b^4*c^4*d^4*e - 10*b^5*c^3*d^3*e^2 + 10*b^6*c^2*d^2*e^3 - 5*b^7*c*d*e^4))))/(2*(b^8*e^5 - b^3*c^5*d^5 + 5*b^4*c^4*d^4*e - 10*b^5*c^3*d^3*e^2 + 10*b^6*c^2*d^2*e^3 - 5*b^7*c*d*e^4))))*(-c^5*(b*e - c*d)^5)^(1/2)*(7*b*e - 4*c*d)*1i)/(b^8*e^5 - b^3*c^5*d^5 + 5*b^4*c^4*d^4*e - 10*b^5*c^3*d^3*e^2 + 10*b^6*c^2*d^2*e^3 - 5*b^7*c*d*e^4) - ((2*e^3)/(c*d^2 - b*d*e) + (e*(d + e*x)^2*(2*c^3*d^2 + 3*b^2*c*e^2 - 2*b*c^2*d*e))/(b^2*(c*d^2 - b*d*e)^2) + (e*(b*e - 2*c*d)*(d + e*x)*(3*b^2*e^2 + c^2*d^2 - b*c*d*e))/(b^2*(c*d^2 - b*d*e)^2))/(c*(d + e*x)^(5/2) + (c*d^2 - b*d*e)*(d + e*x)^(1/2) + (b*e - 2*c*d)*(d + e*x)^(3/2)) - (atan((b^13*c*d^11*e^13*(d + e*x)^(1/2)*189i - b^14*d^10*e^14*(d + e*x)^(1/2)*27i + b^3*c^11*d^21*e^3*(d + e*x)^(1/2)*140i - b^4*c^10*d^20*e^4*(d + e*x)^(1/2)*1015i + b^5*c^9*d^19*e^5*(d + e*x)^(1/2)*2996i - b^6*c^8*d^18*e^6*(d + e*x)^(1/2)*4375i + b^7*c^7*d^17*e^7*(d + e*x)^(1/2)*2561i + b^8*c^6*d^16*e^8*(d + e*x)^(1/2)*1316i - b^9*c^5*d^15*e^9*(d + e*x)^(1/2)*3073i + b^10*c^4*d^14*e^10*(d + e*x)^(1/2)*1694i + b^11*c^3*d^13*e^11*(d + e*x)^(1/2)*35i - b^12*c^2*d^12*e^12*(d + e*x)^(1/2)*441i)/(d^5*(d^5)^(1/2)*(d^5*(d^5*(2561*b^7*c^7*e^7 - 4375*b^6*c^8*d*e^6 + 140*b^3*c^11*d^4*e^3 - 1015*b^4*c^10*d^3*e^4 + 2996*b^5*c^9*d^2*e^5) - 441*b^12*c^2*e^12 + 35*b^11*c^3*d*e^11 + 1316*b^8*c^6*d^4*e^8 - 3073*b^9*c^5*d^3*e^9 + 1694*b^10*c^4*d^2*e^10) - 27*b^14*d^3*e^14 + 189*b^13*c*d^4*e^13)))*(3*b*e + 4*c*d)*1i)/(b^3*(d^5)^(1/2))","B"
376,1,5736,267,3.150210,"\text{Not used}","int(1/((b*x + c*x^2)^2*(d + e*x)^(5/2)),x)","\frac{\frac{10\,e^3\,\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)}{3\,{\left(c\,d^2-b\,d\,e\right)}^2}-\frac{2\,e^3}{3\,\left(c\,d^2-b\,d\,e\right)}+\frac{e\,{\left(d+e\,x\right)}^2\,\left(15\,b^4\,e^4-58\,b^3\,c\,d\,e^3+64\,b^2\,c^2\,d^2\,e^2-12\,b\,c^3\,d^3\,e+6\,c^4\,d^4\right)}{3\,b^2\,{\left(c\,d^2-b\,d\,e\right)}^3}+\frac{e\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^3\,\left(5\,b^2\,c\,e^2-b\,c^2\,d\,e+c^3\,d^2\right)}{b^2\,{\left(c\,d^2-b\,d\,e\right)}^3}}{c\,{\left(d+e\,x\right)}^{7/2}+\left(c\,d^2-b\,d\,e\right)\,{\left(d+e\,x\right)}^{3/2}+\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{5/2}}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(9\,b\,e-4\,c\,d\right)\,\left(\sqrt{d+e\,x}\,\left(-50\,b^{23}\,c^3\,d^9\,e^{19}+670\,b^{22}\,c^4\,d^{10}\,e^{18}-4082\,b^{21}\,c^5\,d^{11}\,e^{17}+14830\,b^{20}\,c^6\,d^{12}\,e^{16}-35210\,b^{19}\,c^7\,d^{13}\,e^{15}+55510\,b^{18}\,c^8\,d^{14}\,e^{14}-53852\,b^{17}\,c^9\,d^{15}\,e^{13}+19048\,b^{16}\,c^{10}\,d^{16}\,e^{12}+25730\,b^{15}\,c^{11}\,d^{17}\,e^{11}-39550\,b^{14}\,c^{12}\,d^{18}\,e^{10}+10670\,b^{13}\,c^{13}\,d^{19}\,e^9+29414\,b^{12}\,c^{14}\,d^{20}\,e^8-45430\,b^{11}\,c^{15}\,d^{21}\,e^7+34490\,b^{10}\,c^{16}\,d^{22}\,e^6-16240\,b^9\,c^{17}\,d^{23}\,e^5+4820\,b^8\,c^{18}\,d^{24}\,e^4-832\,b^7\,c^{19}\,d^{25}\,e^3+64\,b^6\,c^{20}\,d^{26}\,e^2\right)+\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(9\,b\,e-4\,c\,d\right)\,\left(8\,b^{10}\,c^{18}\,d^{28}\,e^3-112\,b^{11}\,c^{17}\,d^{27}\,e^4+664\,b^{12}\,c^{16}\,d^{26}\,e^5-2080\,b^{13}\,c^{15}\,d^{25}\,e^6+2996\,b^{14}\,c^{14}\,d^{24}\,e^7+2528\,b^{15}\,c^{13}\,d^{23}\,e^8-23056\,b^{16}\,c^{12}\,d^{22}\,e^9+59312\,b^{17}\,c^{11}\,d^{21}\,e^{10}-95700\,b^{18}\,c^{10}\,d^{20}\,e^{11}+109648\,b^{19}\,c^9\,d^{19}\,e^{12}-92840\,b^{20}\,c^8\,d^{18}\,e^{13}+58688\,b^{21}\,c^7\,d^{17}\,e^{14}-27476\,b^{22}\,c^6\,d^{16}\,e^{15}+9280\,b^{23}\,c^5\,d^{15}\,e^{16}-2144\,b^{24}\,c^4\,d^{14}\,e^{17}+304\,b^{25}\,c^3\,d^{13}\,e^{18}-20\,b^{26}\,c^2\,d^{12}\,e^{19}-\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(8\,b^{28}\,c^2\,d^{15}\,e^{18}-136\,b^{27}\,c^3\,d^{16}\,e^{17}+1080\,b^{26}\,c^4\,d^{17}\,e^{16}-5320\,b^{25}\,c^5\,d^{18}\,e^{15}+18200\,b^{24}\,c^6\,d^{19}\,e^{14}-45864\,b^{23}\,c^7\,d^{20}\,e^{13}+88088\,b^{22}\,c^8\,d^{21}\,e^{12}-131560\,b^{21}\,c^9\,d^{22}\,e^{11}+154440\,b^{20}\,c^{10}\,d^{23}\,e^{10}-143000\,b^{19}\,c^{11}\,d^{24}\,e^9+104104\,b^{18}\,c^{12}\,d^{25}\,e^8-58968\,b^{17}\,c^{13}\,d^{26}\,e^7+25480\,b^{16}\,c^{14}\,d^{27}\,e^6-8120\,b^{15}\,c^{15}\,d^{28}\,e^5+1800\,b^{14}\,c^{16}\,d^{29}\,e^4-248\,b^{13}\,c^{17}\,d^{30}\,e^3+16\,b^{12}\,c^{18}\,d^{31}\,e^2\right)}{2\,\left(b^{10}\,e^7-7\,b^9\,c\,d\,e^6+21\,b^8\,c^2\,d^2\,e^5-35\,b^7\,c^3\,d^3\,e^4+35\,b^6\,c^4\,d^4\,e^3-21\,b^5\,c^5\,d^5\,e^2+7\,b^4\,c^6\,d^6\,e-b^3\,c^7\,d^7\right)}\right)}{2\,\left(b^{10}\,e^7-7\,b^9\,c\,d\,e^6+21\,b^8\,c^2\,d^2\,e^5-35\,b^7\,c^3\,d^3\,e^4+35\,b^6\,c^4\,d^4\,e^3-21\,b^5\,c^5\,d^5\,e^2+7\,b^4\,c^6\,d^6\,e-b^3\,c^7\,d^7\right)}\right)\,1{}\mathrm{i}}{2\,\left(b^{10}\,e^7-7\,b^9\,c\,d\,e^6+21\,b^8\,c^2\,d^2\,e^5-35\,b^7\,c^3\,d^3\,e^4+35\,b^6\,c^4\,d^4\,e^3-21\,b^5\,c^5\,d^5\,e^2+7\,b^4\,c^6\,d^6\,e-b^3\,c^7\,d^7\right)}+\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(9\,b\,e-4\,c\,d\right)\,\left(\sqrt{d+e\,x}\,\left(-50\,b^{23}\,c^3\,d^9\,e^{19}+670\,b^{22}\,c^4\,d^{10}\,e^{18}-4082\,b^{21}\,c^5\,d^{11}\,e^{17}+14830\,b^{20}\,c^6\,d^{12}\,e^{16}-35210\,b^{19}\,c^7\,d^{13}\,e^{15}+55510\,b^{18}\,c^8\,d^{14}\,e^{14}-53852\,b^{17}\,c^9\,d^{15}\,e^{13}+19048\,b^{16}\,c^{10}\,d^{16}\,e^{12}+25730\,b^{15}\,c^{11}\,d^{17}\,e^{11}-39550\,b^{14}\,c^{12}\,d^{18}\,e^{10}+10670\,b^{13}\,c^{13}\,d^{19}\,e^9+29414\,b^{12}\,c^{14}\,d^{20}\,e^8-45430\,b^{11}\,c^{15}\,d^{21}\,e^7+34490\,b^{10}\,c^{16}\,d^{22}\,e^6-16240\,b^9\,c^{17}\,d^{23}\,e^5+4820\,b^8\,c^{18}\,d^{24}\,e^4-832\,b^7\,c^{19}\,d^{25}\,e^3+64\,b^6\,c^{20}\,d^{26}\,e^2\right)-\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(9\,b\,e-4\,c\,d\right)\,\left(8\,b^{10}\,c^{18}\,d^{28}\,e^3-112\,b^{11}\,c^{17}\,d^{27}\,e^4+664\,b^{12}\,c^{16}\,d^{26}\,e^5-2080\,b^{13}\,c^{15}\,d^{25}\,e^6+2996\,b^{14}\,c^{14}\,d^{24}\,e^7+2528\,b^{15}\,c^{13}\,d^{23}\,e^8-23056\,b^{16}\,c^{12}\,d^{22}\,e^9+59312\,b^{17}\,c^{11}\,d^{21}\,e^{10}-95700\,b^{18}\,c^{10}\,d^{20}\,e^{11}+109648\,b^{19}\,c^9\,d^{19}\,e^{12}-92840\,b^{20}\,c^8\,d^{18}\,e^{13}+58688\,b^{21}\,c^7\,d^{17}\,e^{14}-27476\,b^{22}\,c^6\,d^{16}\,e^{15}+9280\,b^{23}\,c^5\,d^{15}\,e^{16}-2144\,b^{24}\,c^4\,d^{14}\,e^{17}+304\,b^{25}\,c^3\,d^{13}\,e^{18}-20\,b^{26}\,c^2\,d^{12}\,e^{19}+\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(8\,b^{28}\,c^2\,d^{15}\,e^{18}-136\,b^{27}\,c^3\,d^{16}\,e^{17}+1080\,b^{26}\,c^4\,d^{17}\,e^{16}-5320\,b^{25}\,c^5\,d^{18}\,e^{15}+18200\,b^{24}\,c^6\,d^{19}\,e^{14}-45864\,b^{23}\,c^7\,d^{20}\,e^{13}+88088\,b^{22}\,c^8\,d^{21}\,e^{12}-131560\,b^{21}\,c^9\,d^{22}\,e^{11}+154440\,b^{20}\,c^{10}\,d^{23}\,e^{10}-143000\,b^{19}\,c^{11}\,d^{24}\,e^9+104104\,b^{18}\,c^{12}\,d^{25}\,e^8-58968\,b^{17}\,c^{13}\,d^{26}\,e^7+25480\,b^{16}\,c^{14}\,d^{27}\,e^6-8120\,b^{15}\,c^{15}\,d^{28}\,e^5+1800\,b^{14}\,c^{16}\,d^{29}\,e^4-248\,b^{13}\,c^{17}\,d^{30}\,e^3+16\,b^{12}\,c^{18}\,d^{31}\,e^2\right)}{2\,\left(b^{10}\,e^7-7\,b^9\,c\,d\,e^6+21\,b^8\,c^2\,d^2\,e^5-35\,b^7\,c^3\,d^3\,e^4+35\,b^6\,c^4\,d^4\,e^3-21\,b^5\,c^5\,d^5\,e^2+7\,b^4\,c^6\,d^6\,e-b^3\,c^7\,d^7\right)}\right)}{2\,\left(b^{10}\,e^7-7\,b^9\,c\,d\,e^6+21\,b^8\,c^2\,d^2\,e^5-35\,b^7\,c^3\,d^3\,e^4+35\,b^6\,c^4\,d^4\,e^3-21\,b^5\,c^5\,d^5\,e^2+7\,b^4\,c^6\,d^6\,e-b^3\,c^7\,d^7\right)}\right)\,1{}\mathrm{i}}{2\,\left(b^{10}\,e^7-7\,b^9\,c\,d\,e^6+21\,b^8\,c^2\,d^2\,e^5-35\,b^7\,c^3\,d^3\,e^4+35\,b^6\,c^4\,d^4\,e^3-21\,b^5\,c^5\,d^5\,e^2+7\,b^4\,c^6\,d^6\,e-b^3\,c^7\,d^7\right)}}{\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(9\,b\,e-4\,c\,d\right)\,\left(\sqrt{d+e\,x}\,\left(-50\,b^{23}\,c^3\,d^9\,e^{19}+670\,b^{22}\,c^4\,d^{10}\,e^{18}-4082\,b^{21}\,c^5\,d^{11}\,e^{17}+14830\,b^{20}\,c^6\,d^{12}\,e^{16}-35210\,b^{19}\,c^7\,d^{13}\,e^{15}+55510\,b^{18}\,c^8\,d^{14}\,e^{14}-53852\,b^{17}\,c^9\,d^{15}\,e^{13}+19048\,b^{16}\,c^{10}\,d^{16}\,e^{12}+25730\,b^{15}\,c^{11}\,d^{17}\,e^{11}-39550\,b^{14}\,c^{12}\,d^{18}\,e^{10}+10670\,b^{13}\,c^{13}\,d^{19}\,e^9+29414\,b^{12}\,c^{14}\,d^{20}\,e^8-45430\,b^{11}\,c^{15}\,d^{21}\,e^7+34490\,b^{10}\,c^{16}\,d^{22}\,e^6-16240\,b^9\,c^{17}\,d^{23}\,e^5+4820\,b^8\,c^{18}\,d^{24}\,e^4-832\,b^7\,c^{19}\,d^{25}\,e^3+64\,b^6\,c^{20}\,d^{26}\,e^2\right)-\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(9\,b\,e-4\,c\,d\right)\,\left(8\,b^{10}\,c^{18}\,d^{28}\,e^3-112\,b^{11}\,c^{17}\,d^{27}\,e^4+664\,b^{12}\,c^{16}\,d^{26}\,e^5-2080\,b^{13}\,c^{15}\,d^{25}\,e^6+2996\,b^{14}\,c^{14}\,d^{24}\,e^7+2528\,b^{15}\,c^{13}\,d^{23}\,e^8-23056\,b^{16}\,c^{12}\,d^{22}\,e^9+59312\,b^{17}\,c^{11}\,d^{21}\,e^{10}-95700\,b^{18}\,c^{10}\,d^{20}\,e^{11}+109648\,b^{19}\,c^9\,d^{19}\,e^{12}-92840\,b^{20}\,c^8\,d^{18}\,e^{13}+58688\,b^{21}\,c^7\,d^{17}\,e^{14}-27476\,b^{22}\,c^6\,d^{16}\,e^{15}+9280\,b^{23}\,c^5\,d^{15}\,e^{16}-2144\,b^{24}\,c^4\,d^{14}\,e^{17}+304\,b^{25}\,c^3\,d^{13}\,e^{18}-20\,b^{26}\,c^2\,d^{12}\,e^{19}+\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(8\,b^{28}\,c^2\,d^{15}\,e^{18}-136\,b^{27}\,c^3\,d^{16}\,e^{17}+1080\,b^{26}\,c^4\,d^{17}\,e^{16}-5320\,b^{25}\,c^5\,d^{18}\,e^{15}+18200\,b^{24}\,c^6\,d^{19}\,e^{14}-45864\,b^{23}\,c^7\,d^{20}\,e^{13}+88088\,b^{22}\,c^8\,d^{21}\,e^{12}-131560\,b^{21}\,c^9\,d^{22}\,e^{11}+154440\,b^{20}\,c^{10}\,d^{23}\,e^{10}-143000\,b^{19}\,c^{11}\,d^{24}\,e^9+104104\,b^{18}\,c^{12}\,d^{25}\,e^8-58968\,b^{17}\,c^{13}\,d^{26}\,e^7+25480\,b^{16}\,c^{14}\,d^{27}\,e^6-8120\,b^{15}\,c^{15}\,d^{28}\,e^5+1800\,b^{14}\,c^{16}\,d^{29}\,e^4-248\,b^{13}\,c^{17}\,d^{30}\,e^3+16\,b^{12}\,c^{18}\,d^{31}\,e^2\right)}{2\,\left(b^{10}\,e^7-7\,b^9\,c\,d\,e^6+21\,b^8\,c^2\,d^2\,e^5-35\,b^7\,c^3\,d^3\,e^4+35\,b^6\,c^4\,d^4\,e^3-21\,b^5\,c^5\,d^5\,e^2+7\,b^4\,c^6\,d^6\,e-b^3\,c^7\,d^7\right)}\right)}{2\,\left(b^{10}\,e^7-7\,b^9\,c\,d\,e^6+21\,b^8\,c^2\,d^2\,e^5-35\,b^7\,c^3\,d^3\,e^4+35\,b^6\,c^4\,d^4\,e^3-21\,b^5\,c^5\,d^5\,e^2+7\,b^4\,c^6\,d^6\,e-b^3\,c^7\,d^7\right)}\right)}{2\,\left(b^{10}\,e^7-7\,b^9\,c\,d\,e^6+21\,b^8\,c^2\,d^2\,e^5-35\,b^7\,c^3\,d^3\,e^4+35\,b^6\,c^4\,d^4\,e^3-21\,b^5\,c^5\,d^5\,e^2+7\,b^4\,c^6\,d^6\,e-b^3\,c^7\,d^7\right)}-\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(9\,b\,e-4\,c\,d\right)\,\left(\sqrt{d+e\,x}\,\left(-50\,b^{23}\,c^3\,d^9\,e^{19}+670\,b^{22}\,c^4\,d^{10}\,e^{18}-4082\,b^{21}\,c^5\,d^{11}\,e^{17}+14830\,b^{20}\,c^6\,d^{12}\,e^{16}-35210\,b^{19}\,c^7\,d^{13}\,e^{15}+55510\,b^{18}\,c^8\,d^{14}\,e^{14}-53852\,b^{17}\,c^9\,d^{15}\,e^{13}+19048\,b^{16}\,c^{10}\,d^{16}\,e^{12}+25730\,b^{15}\,c^{11}\,d^{17}\,e^{11}-39550\,b^{14}\,c^{12}\,d^{18}\,e^{10}+10670\,b^{13}\,c^{13}\,d^{19}\,e^9+29414\,b^{12}\,c^{14}\,d^{20}\,e^8-45430\,b^{11}\,c^{15}\,d^{21}\,e^7+34490\,b^{10}\,c^{16}\,d^{22}\,e^6-16240\,b^9\,c^{17}\,d^{23}\,e^5+4820\,b^8\,c^{18}\,d^{24}\,e^4-832\,b^7\,c^{19}\,d^{25}\,e^3+64\,b^6\,c^{20}\,d^{26}\,e^2\right)+\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(9\,b\,e-4\,c\,d\right)\,\left(8\,b^{10}\,c^{18}\,d^{28}\,e^3-112\,b^{11}\,c^{17}\,d^{27}\,e^4+664\,b^{12}\,c^{16}\,d^{26}\,e^5-2080\,b^{13}\,c^{15}\,d^{25}\,e^6+2996\,b^{14}\,c^{14}\,d^{24}\,e^7+2528\,b^{15}\,c^{13}\,d^{23}\,e^8-23056\,b^{16}\,c^{12}\,d^{22}\,e^9+59312\,b^{17}\,c^{11}\,d^{21}\,e^{10}-95700\,b^{18}\,c^{10}\,d^{20}\,e^{11}+109648\,b^{19}\,c^9\,d^{19}\,e^{12}-92840\,b^{20}\,c^8\,d^{18}\,e^{13}+58688\,b^{21}\,c^7\,d^{17}\,e^{14}-27476\,b^{22}\,c^6\,d^{16}\,e^{15}+9280\,b^{23}\,c^5\,d^{15}\,e^{16}-2144\,b^{24}\,c^4\,d^{14}\,e^{17}+304\,b^{25}\,c^3\,d^{13}\,e^{18}-20\,b^{26}\,c^2\,d^{12}\,e^{19}-\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(9\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(8\,b^{28}\,c^2\,d^{15}\,e^{18}-136\,b^{27}\,c^3\,d^{16}\,e^{17}+1080\,b^{26}\,c^4\,d^{17}\,e^{16}-5320\,b^{25}\,c^5\,d^{18}\,e^{15}+18200\,b^{24}\,c^6\,d^{19}\,e^{14}-45864\,b^{23}\,c^7\,d^{20}\,e^{13}+88088\,b^{22}\,c^8\,d^{21}\,e^{12}-131560\,b^{21}\,c^9\,d^{22}\,e^{11}+154440\,b^{20}\,c^{10}\,d^{23}\,e^{10}-143000\,b^{19}\,c^{11}\,d^{24}\,e^9+104104\,b^{18}\,c^{12}\,d^{25}\,e^8-58968\,b^{17}\,c^{13}\,d^{26}\,e^7+25480\,b^{16}\,c^{14}\,d^{27}\,e^6-8120\,b^{15}\,c^{15}\,d^{28}\,e^5+1800\,b^{14}\,c^{16}\,d^{29}\,e^4-248\,b^{13}\,c^{17}\,d^{30}\,e^3+16\,b^{12}\,c^{18}\,d^{31}\,e^2\right)}{2\,\left(b^{10}\,e^7-7\,b^9\,c\,d\,e^6+21\,b^8\,c^2\,d^2\,e^5-35\,b^7\,c^3\,d^3\,e^4+35\,b^6\,c^4\,d^4\,e^3-21\,b^5\,c^5\,d^5\,e^2+7\,b^4\,c^6\,d^6\,e-b^3\,c^7\,d^7\right)}\right)}{2\,\left(b^{10}\,e^7-7\,b^9\,c\,d\,e^6+21\,b^8\,c^2\,d^2\,e^5-35\,b^7\,c^3\,d^3\,e^4+35\,b^6\,c^4\,d^4\,e^3-21\,b^5\,c^5\,d^5\,e^2+7\,b^4\,c^6\,d^6\,e-b^3\,c^7\,d^7\right)}\right)}{2\,\left(b^{10}\,e^7-7\,b^9\,c\,d\,e^6+21\,b^8\,c^2\,d^2\,e^5-35\,b^7\,c^3\,d^3\,e^4+35\,b^6\,c^4\,d^4\,e^3-21\,b^5\,c^5\,d^5\,e^2+7\,b^4\,c^6\,d^6\,e-b^3\,c^7\,d^7\right)}+64\,b^4\,c^{20}\,d^{23}\,e^3-736\,b^5\,c^{19}\,d^{22}\,e^4+4012\,b^6\,c^{18}\,d^{21}\,e^5-13790\,b^7\,c^{17}\,d^{20}\,e^6+32500\,b^8\,c^{16}\,d^{19}\,e^7-51528\,b^9\,c^{15}\,d^{18}\,e^8+45702\,b^{10}\,c^{14}\,d^{17}\,e^9+5916\,b^{11}\,c^{13}\,d^{16}\,e^{10}-83040\,b^{12}\,c^{12}\,d^{15}\,e^{11}+129800\,b^{13}\,c^{11}\,d^{14}\,e^{12}-115136\,b^{14}\,c^{10}\,d^{13}\,e^{13}+65234\,b^{15}\,c^9\,d^{12}\,e^{14}-23428\,b^{16}\,c^8\,d^{11}\,e^{15}+4880\,b^{17}\,c^7\,d^{10}\,e^{16}-450\,b^{18}\,c^6\,d^9\,e^{17}}\right)\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(9\,b\,e-4\,c\,d\right)\,1{}\mathrm{i}}{b^{10}\,e^7-7\,b^9\,c\,d\,e^6+21\,b^8\,c^2\,d^2\,e^5-35\,b^7\,c^3\,d^3\,e^4+35\,b^6\,c^4\,d^4\,e^3-21\,b^5\,c^5\,d^5\,e^2+7\,b^4\,c^6\,d^6\,e-b^3\,c^7\,d^7}-\frac{\mathrm{atan}\left(\frac{b^{19}\,d^{15}\,e^{19}\,\sqrt{d+e\,x}\,125{}\mathrm{i}-b^{18}\,c\,d^{16}\,e^{18}\,\sqrt{d+e\,x}\,1700{}\mathrm{i}+b^3\,c^{16}\,d^{31}\,e^3\,\sqrt{d+e\,x}\,420{}\mathrm{i}-b^4\,c^{15}\,d^{30}\,e^4\,\sqrt{d+e\,x}\,4515{}\mathrm{i}+b^5\,c^{14}\,d^{29}\,e^5\,\sqrt{d+e\,x}\,20916{}\mathrm{i}-b^6\,c^{13}\,d^{28}\,e^6\,\sqrt{d+e\,x}\,52836{}\mathrm{i}+b^7\,c^{12}\,d^{27}\,e^7\,\sqrt{d+e\,x}\,71070{}\mathrm{i}-b^8\,c^{11}\,d^{26}\,e^8\,\sqrt{d+e\,x}\,19530{}\mathrm{i}-b^9\,c^{10}\,d^{25}\,e^9\,\sqrt{d+e\,x}\,107740{}\mathrm{i}+b^{10}\,c^9\,d^{24}\,e^{10}\,\sqrt{d+e\,x}\,212608{}\mathrm{i}-b^{11}\,c^8\,d^{23}\,e^{11}\,\sqrt{d+e\,x}\,184563{}\mathrm{i}+b^{12}\,c^7\,d^{22}\,e^{12}\,\sqrt{d+e\,x}\,40965{}\mathrm{i}+b^{13}\,c^6\,d^{21}\,e^{13}\,\sqrt{d+e\,x}\,91560{}\mathrm{i}-b^{14}\,c^5\,d^{20}\,e^{14}\,\sqrt{d+e\,x}\,126720{}\mathrm{i}+b^{15}\,c^4\,d^{19}\,e^{15}\,\sqrt{d+e\,x}\,87276{}\mathrm{i}-b^{16}\,c^3\,d^{18}\,e^{16}\,\sqrt{d+e\,x}\,37776{}\mathrm{i}+b^{17}\,c^2\,d^{17}\,e^{17}\,\sqrt{d+e\,x}\,10440{}\mathrm{i}}{d^7\,\sqrt{d^7}\,\left(d^7\,\left(d^7\,\left(212608\,b^{10}\,c^9\,e^{10}-107740\,b^9\,c^{10}\,d\,e^9-19530\,b^8\,c^{11}\,d^2\,e^8+71070\,b^7\,c^{12}\,d^3\,e^7-52836\,b^6\,c^{13}\,d^4\,e^6+20916\,b^5\,c^{14}\,d^5\,e^5-4515\,b^4\,c^{15}\,d^6\,e^4+420\,b^3\,c^{16}\,d^7\,e^3\right)+10440\,b^{17}\,c^2\,e^{17}-37776\,b^{16}\,c^3\,d\,e^{16}-184563\,b^{11}\,c^8\,d^6\,e^{11}+40965\,b^{12}\,c^7\,d^5\,e^{12}+91560\,b^{13}\,c^6\,d^4\,e^{13}-126720\,b^{14}\,c^5\,d^3\,e^{14}+87276\,b^{15}\,c^4\,d^2\,e^{15}\right)+125\,b^{19}\,d^5\,e^{19}-1700\,b^{18}\,c\,d^6\,e^{18}\right)}\right)\,\left(5\,b\,e+4\,c\,d\right)\,1{}\mathrm{i}}{b^3\,\sqrt{d^7}}","Not used",1,"((10*e^3*(b*e - 2*c*d)*(d + e*x))/(3*(c*d^2 - b*d*e)^2) - (2*e^3)/(3*(c*d^2 - b*d*e)) + (e*(d + e*x)^2*(15*b^4*e^4 + 6*c^4*d^4 + 64*b^2*c^2*d^2*e^2 - 12*b*c^3*d^3*e - 58*b^3*c*d*e^3))/(3*b^2*(c*d^2 - b*d*e)^3) + (e*(b*e - 2*c*d)*(d + e*x)^3*(c^3*d^2 + 5*b^2*c*e^2 - b*c^2*d*e))/(b^2*(c*d^2 - b*d*e)^3))/(c*(d + e*x)^(7/2) + (c*d^2 - b*d*e)*(d + e*x)^(3/2) + (b*e - 2*c*d)*(d + e*x)^(5/2)) + (atan((((-c^7*(b*e - c*d)^7)^(1/2)*(9*b*e - 4*c*d)*((d + e*x)^(1/2)*(64*b^6*c^20*d^26*e^2 - 832*b^7*c^19*d^25*e^3 + 4820*b^8*c^18*d^24*e^4 - 16240*b^9*c^17*d^23*e^5 + 34490*b^10*c^16*d^22*e^6 - 45430*b^11*c^15*d^21*e^7 + 29414*b^12*c^14*d^20*e^8 + 10670*b^13*c^13*d^19*e^9 - 39550*b^14*c^12*d^18*e^10 + 25730*b^15*c^11*d^17*e^11 + 19048*b^16*c^10*d^16*e^12 - 53852*b^17*c^9*d^15*e^13 + 55510*b^18*c^8*d^14*e^14 - 35210*b^19*c^7*d^13*e^15 + 14830*b^20*c^6*d^12*e^16 - 4082*b^21*c^5*d^11*e^17 + 670*b^22*c^4*d^10*e^18 - 50*b^23*c^3*d^9*e^19) + ((-c^7*(b*e - c*d)^7)^(1/2)*(9*b*e - 4*c*d)*(8*b^10*c^18*d^28*e^3 - 112*b^11*c^17*d^27*e^4 + 664*b^12*c^16*d^26*e^5 - 2080*b^13*c^15*d^25*e^6 + 2996*b^14*c^14*d^24*e^7 + 2528*b^15*c^13*d^23*e^8 - 23056*b^16*c^12*d^22*e^9 + 59312*b^17*c^11*d^21*e^10 - 95700*b^18*c^10*d^20*e^11 + 109648*b^19*c^9*d^19*e^12 - 92840*b^20*c^8*d^18*e^13 + 58688*b^21*c^7*d^17*e^14 - 27476*b^22*c^6*d^16*e^15 + 9280*b^23*c^5*d^15*e^16 - 2144*b^24*c^4*d^14*e^17 + 304*b^25*c^3*d^13*e^18 - 20*b^26*c^2*d^12*e^19 - ((-c^7*(b*e - c*d)^7)^(1/2)*(9*b*e - 4*c*d)*(d + e*x)^(1/2)*(16*b^12*c^18*d^31*e^2 - 248*b^13*c^17*d^30*e^3 + 1800*b^14*c^16*d^29*e^4 - 8120*b^15*c^15*d^28*e^5 + 25480*b^16*c^14*d^27*e^6 - 58968*b^17*c^13*d^26*e^7 + 104104*b^18*c^12*d^25*e^8 - 143000*b^19*c^11*d^24*e^9 + 154440*b^20*c^10*d^23*e^10 - 131560*b^21*c^9*d^22*e^11 + 88088*b^22*c^8*d^21*e^12 - 45864*b^23*c^7*d^20*e^13 + 18200*b^24*c^6*d^19*e^14 - 5320*b^25*c^5*d^18*e^15 + 1080*b^26*c^4*d^17*e^16 - 136*b^27*c^3*d^16*e^17 + 8*b^28*c^2*d^15*e^18))/(2*(b^10*e^7 - b^3*c^7*d^7 + 7*b^4*c^6*d^6*e - 21*b^5*c^5*d^5*e^2 + 35*b^6*c^4*d^4*e^3 - 35*b^7*c^3*d^3*e^4 + 21*b^8*c^2*d^2*e^5 - 7*b^9*c*d*e^6))))/(2*(b^10*e^7 - b^3*c^7*d^7 + 7*b^4*c^6*d^6*e - 21*b^5*c^5*d^5*e^2 + 35*b^6*c^4*d^4*e^3 - 35*b^7*c^3*d^3*e^4 + 21*b^8*c^2*d^2*e^5 - 7*b^9*c*d*e^6)))*1i)/(2*(b^10*e^7 - b^3*c^7*d^7 + 7*b^4*c^6*d^6*e - 21*b^5*c^5*d^5*e^2 + 35*b^6*c^4*d^4*e^3 - 35*b^7*c^3*d^3*e^4 + 21*b^8*c^2*d^2*e^5 - 7*b^9*c*d*e^6)) + ((-c^7*(b*e - c*d)^7)^(1/2)*(9*b*e - 4*c*d)*((d + e*x)^(1/2)*(64*b^6*c^20*d^26*e^2 - 832*b^7*c^19*d^25*e^3 + 4820*b^8*c^18*d^24*e^4 - 16240*b^9*c^17*d^23*e^5 + 34490*b^10*c^16*d^22*e^6 - 45430*b^11*c^15*d^21*e^7 + 29414*b^12*c^14*d^20*e^8 + 10670*b^13*c^13*d^19*e^9 - 39550*b^14*c^12*d^18*e^10 + 25730*b^15*c^11*d^17*e^11 + 19048*b^16*c^10*d^16*e^12 - 53852*b^17*c^9*d^15*e^13 + 55510*b^18*c^8*d^14*e^14 - 35210*b^19*c^7*d^13*e^15 + 14830*b^20*c^6*d^12*e^16 - 4082*b^21*c^5*d^11*e^17 + 670*b^22*c^4*d^10*e^18 - 50*b^23*c^3*d^9*e^19) - ((-c^7*(b*e - c*d)^7)^(1/2)*(9*b*e - 4*c*d)*(8*b^10*c^18*d^28*e^3 - 112*b^11*c^17*d^27*e^4 + 664*b^12*c^16*d^26*e^5 - 2080*b^13*c^15*d^25*e^6 + 2996*b^14*c^14*d^24*e^7 + 2528*b^15*c^13*d^23*e^8 - 23056*b^16*c^12*d^22*e^9 + 59312*b^17*c^11*d^21*e^10 - 95700*b^18*c^10*d^20*e^11 + 109648*b^19*c^9*d^19*e^12 - 92840*b^20*c^8*d^18*e^13 + 58688*b^21*c^7*d^17*e^14 - 27476*b^22*c^6*d^16*e^15 + 9280*b^23*c^5*d^15*e^16 - 2144*b^24*c^4*d^14*e^17 + 304*b^25*c^3*d^13*e^18 - 20*b^26*c^2*d^12*e^19 + ((-c^7*(b*e - c*d)^7)^(1/2)*(9*b*e - 4*c*d)*(d + e*x)^(1/2)*(16*b^12*c^18*d^31*e^2 - 248*b^13*c^17*d^30*e^3 + 1800*b^14*c^16*d^29*e^4 - 8120*b^15*c^15*d^28*e^5 + 25480*b^16*c^14*d^27*e^6 - 58968*b^17*c^13*d^26*e^7 + 104104*b^18*c^12*d^25*e^8 - 143000*b^19*c^11*d^24*e^9 + 154440*b^20*c^10*d^23*e^10 - 131560*b^21*c^9*d^22*e^11 + 88088*b^22*c^8*d^21*e^12 - 45864*b^23*c^7*d^20*e^13 + 18200*b^24*c^6*d^19*e^14 - 5320*b^25*c^5*d^18*e^15 + 1080*b^26*c^4*d^17*e^16 - 136*b^27*c^3*d^16*e^17 + 8*b^28*c^2*d^15*e^18))/(2*(b^10*e^7 - b^3*c^7*d^7 + 7*b^4*c^6*d^6*e - 21*b^5*c^5*d^5*e^2 + 35*b^6*c^4*d^4*e^3 - 35*b^7*c^3*d^3*e^4 + 21*b^8*c^2*d^2*e^5 - 7*b^9*c*d*e^6))))/(2*(b^10*e^7 - b^3*c^7*d^7 + 7*b^4*c^6*d^6*e - 21*b^5*c^5*d^5*e^2 + 35*b^6*c^4*d^4*e^3 - 35*b^7*c^3*d^3*e^4 + 21*b^8*c^2*d^2*e^5 - 7*b^9*c*d*e^6)))*1i)/(2*(b^10*e^7 - b^3*c^7*d^7 + 7*b^4*c^6*d^6*e - 21*b^5*c^5*d^5*e^2 + 35*b^6*c^4*d^4*e^3 - 35*b^7*c^3*d^3*e^4 + 21*b^8*c^2*d^2*e^5 - 7*b^9*c*d*e^6)))/(((-c^7*(b*e - c*d)^7)^(1/2)*(9*b*e - 4*c*d)*((d + e*x)^(1/2)*(64*b^6*c^20*d^26*e^2 - 832*b^7*c^19*d^25*e^3 + 4820*b^8*c^18*d^24*e^4 - 16240*b^9*c^17*d^23*e^5 + 34490*b^10*c^16*d^22*e^6 - 45430*b^11*c^15*d^21*e^7 + 29414*b^12*c^14*d^20*e^8 + 10670*b^13*c^13*d^19*e^9 - 39550*b^14*c^12*d^18*e^10 + 25730*b^15*c^11*d^17*e^11 + 19048*b^16*c^10*d^16*e^12 - 53852*b^17*c^9*d^15*e^13 + 55510*b^18*c^8*d^14*e^14 - 35210*b^19*c^7*d^13*e^15 + 14830*b^20*c^6*d^12*e^16 - 4082*b^21*c^5*d^11*e^17 + 670*b^22*c^4*d^10*e^18 - 50*b^23*c^3*d^9*e^19) - ((-c^7*(b*e - c*d)^7)^(1/2)*(9*b*e - 4*c*d)*(8*b^10*c^18*d^28*e^3 - 112*b^11*c^17*d^27*e^4 + 664*b^12*c^16*d^26*e^5 - 2080*b^13*c^15*d^25*e^6 + 2996*b^14*c^14*d^24*e^7 + 2528*b^15*c^13*d^23*e^8 - 23056*b^16*c^12*d^22*e^9 + 59312*b^17*c^11*d^21*e^10 - 95700*b^18*c^10*d^20*e^11 + 109648*b^19*c^9*d^19*e^12 - 92840*b^20*c^8*d^18*e^13 + 58688*b^21*c^7*d^17*e^14 - 27476*b^22*c^6*d^16*e^15 + 9280*b^23*c^5*d^15*e^16 - 2144*b^24*c^4*d^14*e^17 + 304*b^25*c^3*d^13*e^18 - 20*b^26*c^2*d^12*e^19 + ((-c^7*(b*e - c*d)^7)^(1/2)*(9*b*e - 4*c*d)*(d + e*x)^(1/2)*(16*b^12*c^18*d^31*e^2 - 248*b^13*c^17*d^30*e^3 + 1800*b^14*c^16*d^29*e^4 - 8120*b^15*c^15*d^28*e^5 + 25480*b^16*c^14*d^27*e^6 - 58968*b^17*c^13*d^26*e^7 + 104104*b^18*c^12*d^25*e^8 - 143000*b^19*c^11*d^24*e^9 + 154440*b^20*c^10*d^23*e^10 - 131560*b^21*c^9*d^22*e^11 + 88088*b^22*c^8*d^21*e^12 - 45864*b^23*c^7*d^20*e^13 + 18200*b^24*c^6*d^19*e^14 - 5320*b^25*c^5*d^18*e^15 + 1080*b^26*c^4*d^17*e^16 - 136*b^27*c^3*d^16*e^17 + 8*b^28*c^2*d^15*e^18))/(2*(b^10*e^7 - b^3*c^7*d^7 + 7*b^4*c^6*d^6*e - 21*b^5*c^5*d^5*e^2 + 35*b^6*c^4*d^4*e^3 - 35*b^7*c^3*d^3*e^4 + 21*b^8*c^2*d^2*e^5 - 7*b^9*c*d*e^6))))/(2*(b^10*e^7 - b^3*c^7*d^7 + 7*b^4*c^6*d^6*e - 21*b^5*c^5*d^5*e^2 + 35*b^6*c^4*d^4*e^3 - 35*b^7*c^3*d^3*e^4 + 21*b^8*c^2*d^2*e^5 - 7*b^9*c*d*e^6))))/(2*(b^10*e^7 - b^3*c^7*d^7 + 7*b^4*c^6*d^6*e - 21*b^5*c^5*d^5*e^2 + 35*b^6*c^4*d^4*e^3 - 35*b^7*c^3*d^3*e^4 + 21*b^8*c^2*d^2*e^5 - 7*b^9*c*d*e^6)) - ((-c^7*(b*e - c*d)^7)^(1/2)*(9*b*e - 4*c*d)*((d + e*x)^(1/2)*(64*b^6*c^20*d^26*e^2 - 832*b^7*c^19*d^25*e^3 + 4820*b^8*c^18*d^24*e^4 - 16240*b^9*c^17*d^23*e^5 + 34490*b^10*c^16*d^22*e^6 - 45430*b^11*c^15*d^21*e^7 + 29414*b^12*c^14*d^20*e^8 + 10670*b^13*c^13*d^19*e^9 - 39550*b^14*c^12*d^18*e^10 + 25730*b^15*c^11*d^17*e^11 + 19048*b^16*c^10*d^16*e^12 - 53852*b^17*c^9*d^15*e^13 + 55510*b^18*c^8*d^14*e^14 - 35210*b^19*c^7*d^13*e^15 + 14830*b^20*c^6*d^12*e^16 - 4082*b^21*c^5*d^11*e^17 + 670*b^22*c^4*d^10*e^18 - 50*b^23*c^3*d^9*e^19) + ((-c^7*(b*e - c*d)^7)^(1/2)*(9*b*e - 4*c*d)*(8*b^10*c^18*d^28*e^3 - 112*b^11*c^17*d^27*e^4 + 664*b^12*c^16*d^26*e^5 - 2080*b^13*c^15*d^25*e^6 + 2996*b^14*c^14*d^24*e^7 + 2528*b^15*c^13*d^23*e^8 - 23056*b^16*c^12*d^22*e^9 + 59312*b^17*c^11*d^21*e^10 - 95700*b^18*c^10*d^20*e^11 + 109648*b^19*c^9*d^19*e^12 - 92840*b^20*c^8*d^18*e^13 + 58688*b^21*c^7*d^17*e^14 - 27476*b^22*c^6*d^16*e^15 + 9280*b^23*c^5*d^15*e^16 - 2144*b^24*c^4*d^14*e^17 + 304*b^25*c^3*d^13*e^18 - 20*b^26*c^2*d^12*e^19 - ((-c^7*(b*e - c*d)^7)^(1/2)*(9*b*e - 4*c*d)*(d + e*x)^(1/2)*(16*b^12*c^18*d^31*e^2 - 248*b^13*c^17*d^30*e^3 + 1800*b^14*c^16*d^29*e^4 - 8120*b^15*c^15*d^28*e^5 + 25480*b^16*c^14*d^27*e^6 - 58968*b^17*c^13*d^26*e^7 + 104104*b^18*c^12*d^25*e^8 - 143000*b^19*c^11*d^24*e^9 + 154440*b^20*c^10*d^23*e^10 - 131560*b^21*c^9*d^22*e^11 + 88088*b^22*c^8*d^21*e^12 - 45864*b^23*c^7*d^20*e^13 + 18200*b^24*c^6*d^19*e^14 - 5320*b^25*c^5*d^18*e^15 + 1080*b^26*c^4*d^17*e^16 - 136*b^27*c^3*d^16*e^17 + 8*b^28*c^2*d^15*e^18))/(2*(b^10*e^7 - b^3*c^7*d^7 + 7*b^4*c^6*d^6*e - 21*b^5*c^5*d^5*e^2 + 35*b^6*c^4*d^4*e^3 - 35*b^7*c^3*d^3*e^4 + 21*b^8*c^2*d^2*e^5 - 7*b^9*c*d*e^6))))/(2*(b^10*e^7 - b^3*c^7*d^7 + 7*b^4*c^6*d^6*e - 21*b^5*c^5*d^5*e^2 + 35*b^6*c^4*d^4*e^3 - 35*b^7*c^3*d^3*e^4 + 21*b^8*c^2*d^2*e^5 - 7*b^9*c*d*e^6))))/(2*(b^10*e^7 - b^3*c^7*d^7 + 7*b^4*c^6*d^6*e - 21*b^5*c^5*d^5*e^2 + 35*b^6*c^4*d^4*e^3 - 35*b^7*c^3*d^3*e^4 + 21*b^8*c^2*d^2*e^5 - 7*b^9*c*d*e^6)) + 64*b^4*c^20*d^23*e^3 - 736*b^5*c^19*d^22*e^4 + 4012*b^6*c^18*d^21*e^5 - 13790*b^7*c^17*d^20*e^6 + 32500*b^8*c^16*d^19*e^7 - 51528*b^9*c^15*d^18*e^8 + 45702*b^10*c^14*d^17*e^9 + 5916*b^11*c^13*d^16*e^10 - 83040*b^12*c^12*d^15*e^11 + 129800*b^13*c^11*d^14*e^12 - 115136*b^14*c^10*d^13*e^13 + 65234*b^15*c^9*d^12*e^14 - 23428*b^16*c^8*d^11*e^15 + 4880*b^17*c^7*d^10*e^16 - 450*b^18*c^6*d^9*e^17))*(-c^7*(b*e - c*d)^7)^(1/2)*(9*b*e - 4*c*d)*1i)/(b^10*e^7 - b^3*c^7*d^7 + 7*b^4*c^6*d^6*e - 21*b^5*c^5*d^5*e^2 + 35*b^6*c^4*d^4*e^3 - 35*b^7*c^3*d^3*e^4 + 21*b^8*c^2*d^2*e^5 - 7*b^9*c*d*e^6) - (atan((b^19*d^15*e^19*(d + e*x)^(1/2)*125i - b^18*c*d^16*e^18*(d + e*x)^(1/2)*1700i + b^3*c^16*d^31*e^3*(d + e*x)^(1/2)*420i - b^4*c^15*d^30*e^4*(d + e*x)^(1/2)*4515i + b^5*c^14*d^29*e^5*(d + e*x)^(1/2)*20916i - b^6*c^13*d^28*e^6*(d + e*x)^(1/2)*52836i + b^7*c^12*d^27*e^7*(d + e*x)^(1/2)*71070i - b^8*c^11*d^26*e^8*(d + e*x)^(1/2)*19530i - b^9*c^10*d^25*e^9*(d + e*x)^(1/2)*107740i + b^10*c^9*d^24*e^10*(d + e*x)^(1/2)*212608i - b^11*c^8*d^23*e^11*(d + e*x)^(1/2)*184563i + b^12*c^7*d^22*e^12*(d + e*x)^(1/2)*40965i + b^13*c^6*d^21*e^13*(d + e*x)^(1/2)*91560i - b^14*c^5*d^20*e^14*(d + e*x)^(1/2)*126720i + b^15*c^4*d^19*e^15*(d + e*x)^(1/2)*87276i - b^16*c^3*d^18*e^16*(d + e*x)^(1/2)*37776i + b^17*c^2*d^17*e^17*(d + e*x)^(1/2)*10440i)/(d^7*(d^7)^(1/2)*(d^7*(d^7*(212608*b^10*c^9*e^10 - 107740*b^9*c^10*d*e^9 + 420*b^3*c^16*d^7*e^3 - 4515*b^4*c^15*d^6*e^4 + 20916*b^5*c^14*d^5*e^5 - 52836*b^6*c^13*d^4*e^6 + 71070*b^7*c^12*d^3*e^7 - 19530*b^8*c^11*d^2*e^8) + 10440*b^17*c^2*e^17 - 37776*b^16*c^3*d*e^16 - 184563*b^11*c^8*d^6*e^11 + 40965*b^12*c^7*d^5*e^12 + 91560*b^13*c^6*d^4*e^13 - 126720*b^14*c^5*d^3*e^14 + 87276*b^15*c^4*d^2*e^15) + 125*b^19*d^5*e^19 - 1700*b^18*c*d^6*e^18)))*(5*b*e + 4*c*d)*1i)/(b^3*(d^7)^(1/2))","B"
377,1,7254,349,3.821868,"\text{Not used}","int(1/((b*x + c*x^2)^2*(d + e*x)^(7/2)),x)","-\frac{\frac{2\,e^3}{5\,\left(c\,d^2-b\,d\,e\right)}+\frac{2\,e^3\,{\left(d+e\,x\right)}^2\,\left(35\,b^2\,e^2-113\,b\,c\,d\,e+113\,c^2\,d^2\right)}{15\,{\left(c\,d^2-b\,d\,e\right)}^3}-\frac{14\,e^3\,\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)}{15\,{\left(c\,d^2-b\,d\,e\right)}^2}+\frac{e\,{\left(d+e\,x\right)}^4\,\left(7\,b^4\,c\,e^4-24\,b^3\,c^2\,d\,e^3+26\,b^2\,c^3\,d^2\,e^2-4\,b\,c^4\,d^3\,e+2\,c^5\,d^4\right)}{b^2\,{\left(c\,d^2-b\,d\,e\right)}^4}+\frac{e\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^3\,\left(21\,b^4\,e^4-65\,b^3\,c\,d\,e^3+68\,b^2\,c^2\,d^2\,e^2-6\,b\,c^3\,d^3\,e+3\,c^4\,d^4\right)}{3\,b^2\,{\left(c\,d^2-b\,d\,e\right)}^4}}{c\,{\left(d+e\,x\right)}^{9/2}+\left(c\,d^2-b\,d\,e\right)\,{\left(d+e\,x\right)}^{5/2}+\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{7/2}}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\left(11\,b\,e-4\,c\,d\right)\,\left(\sqrt{d+e\,x}\,\left(-98\,b^{28}\,c^3\,d^{12}\,e^{24}+1848\,b^{27}\,c^4\,d^{13}\,e^{23}-16412\,b^{26}\,c^5\,d^{14}\,e^{22}+91080\,b^{25}\,c^6\,d^{15}\,e^{21}-353210\,b^{24}\,c^7\,d^{16}\,e^{20}+1013232\,b^{23}\,c^8\,d^{17}\,e^{19}-2217072\,b^{22}\,c^9\,d^{18}\,e^{18}+3751968\,b^{21}\,c^{10}\,d^{19}\,e^{17}-4903382\,b^{20}\,c^{11}\,d^{20}\,e^{16}+4835160\,b^{19}\,c^{12}\,d^{21}\,e^{15}-3343724\,b^{18}\,c^{13}\,d^{22}\,e^{14}+1207368\,b^{17}\,c^{14}\,d^{23}\,e^{13}+393646\,b^{16}\,c^{15}\,d^{24}\,e^{12}-851136\,b^{15}\,c^{16}\,d^{25}\,e^{11}+473880\,b^{14}\,c^{17}\,d^{26}\,e^{10}+38544\,b^{13}\,c^{18}\,d^{27}\,e^9-267432\,b^{12}\,c^{19}\,d^{28}\,e^8+230912\,b^{11}\,c^{20}\,d^{29}\,e^7-116512\,b^{10}\,c^{21}\,d^{30}\,e^6+38720\,b^9\,c^{22}\,d^{31}\,e^5-8404\,b^8\,c^{23}\,d^{32}\,e^4+1088\,b^7\,c^{24}\,d^{33}\,e^3-64\,b^6\,c^{25}\,d^{34}\,e^2\right)-\frac{\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\left(11\,b\,e-4\,c\,d\right)\,\left(8\,b^{10}\,c^{23}\,d^{37}\,e^3-148\,b^{11}\,c^{22}\,d^{36}\,e^4+1160\,b^{12}\,c^{21}\,d^{35}\,e^5-4760\,b^{13}\,c^{20}\,d^{34}\,e^6+8036\,b^{14}\,c^{19}\,d^{33}\,e^7+21868\,b^{15}\,c^{18}\,d^{32}\,e^8-194304\,b^{16}\,c^{17}\,d^{31}\,e^9+709280\,b^{17}\,c^{16}\,d^{30}\,e^{10}-1744160\,b^{18}\,c^{15}\,d^{29}\,e^{11}+3218072\,b^{19}\,c^{14}\,d^{28}\,e^{12}-4654832\,b^{20}\,c^{13}\,d^{27}\,e^{13}+5394480\,b^{21}\,c^{12}\,d^{26}\,e^{14}-5063240\,b^{22}\,c^{11}\,d^{25}\,e^{15}+3863800\,b^{23}\,c^{10}\,d^{24}\,e^{16}-2393152\,b^{24}\,c^9\,d^{23}\,e^{17}+1194528\,b^{25}\,c^8\,d^{22}\,e^{18}-474056\,b^{26}\,c^7\,d^{21}\,e^{19}+146300\,b^{27}\,c^6\,d^{20}\,e^{20}-33880\,b^{28}\,c^5\,d^{19}\,e^{21}+5544\,b^{29}\,c^4\,d^{18}\,e^{22}-572\,b^{30}\,c^3\,d^{17}\,e^{23}+28\,b^{31}\,c^2\,d^{16}\,e^{24}-\frac{\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\left(11\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(-8\,b^{33}\,c^2\,d^{20}\,e^{23}+176\,b^{32}\,c^3\,d^{21}\,e^{22}-1840\,b^{31}\,c^4\,d^{22}\,e^{21}+12160\,b^{30}\,c^5\,d^{23}\,e^{20}-57000\,b^{29}\,c^6\,d^{24}\,e^{19}+201552\,b^{28}\,c^7\,d^{25}\,e^{18}-558144\,b^{27}\,c^8\,d^{26}\,e^{17}+1240320\,b^{26}\,c^9\,d^{27}\,e^{16}-2248080\,b^{25}\,c^{10}\,d^{28}\,e^{15}+3359200\,b^{24}\,c^{11}\,d^{29}\,e^{14}-4165408\,b^{23}\,c^{12}\,d^{30}\,e^{13}+4299776\,b^{22}\,c^{13}\,d^{31}\,e^{12}-3695120\,b^{21}\,c^{14}\,d^{32}\,e^{11}+2635680\,b^{20}\,c^{15}\,d^{33}\,e^{10}-1550400\,b^{19}\,c^{16}\,d^{34}\,e^9+744192\,b^{18}\,c^{17}\,d^{35}\,e^8-286824\,b^{17}\,c^{18}\,d^{36}\,e^7+86640\,b^{16}\,c^{19}\,d^{37}\,e^6-19760\,b^{15}\,c^{20}\,d^{38}\,e^5+3200\,b^{14}\,c^{21}\,d^{39}\,e^4-328\,b^{13}\,c^{22}\,d^{40}\,e^3+16\,b^{12}\,c^{23}\,d^{41}\,e^2\right)}{2\,\left(b^{12}\,e^9-9\,b^{11}\,c\,d\,e^8+36\,b^{10}\,c^2\,d^2\,e^7-84\,b^9\,c^3\,d^3\,e^6+126\,b^8\,c^4\,d^4\,e^5-126\,b^7\,c^5\,d^5\,e^4+84\,b^6\,c^6\,d^6\,e^3-36\,b^5\,c^7\,d^7\,e^2+9\,b^4\,c^8\,d^8\,e-b^3\,c^9\,d^9\right)}\right)}{2\,\left(b^{12}\,e^9-9\,b^{11}\,c\,d\,e^8+36\,b^{10}\,c^2\,d^2\,e^7-84\,b^9\,c^3\,d^3\,e^6+126\,b^8\,c^4\,d^4\,e^5-126\,b^7\,c^5\,d^5\,e^4+84\,b^6\,c^6\,d^6\,e^3-36\,b^5\,c^7\,d^7\,e^2+9\,b^4\,c^8\,d^8\,e-b^3\,c^9\,d^9\right)}\right)\,1{}\mathrm{i}}{2\,\left(b^{12}\,e^9-9\,b^{11}\,c\,d\,e^8+36\,b^{10}\,c^2\,d^2\,e^7-84\,b^9\,c^3\,d^3\,e^6+126\,b^8\,c^4\,d^4\,e^5-126\,b^7\,c^5\,d^5\,e^4+84\,b^6\,c^6\,d^6\,e^3-36\,b^5\,c^7\,d^7\,e^2+9\,b^4\,c^8\,d^8\,e-b^3\,c^9\,d^9\right)}+\frac{\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\left(11\,b\,e-4\,c\,d\right)\,\left(\sqrt{d+e\,x}\,\left(-98\,b^{28}\,c^3\,d^{12}\,e^{24}+1848\,b^{27}\,c^4\,d^{13}\,e^{23}-16412\,b^{26}\,c^5\,d^{14}\,e^{22}+91080\,b^{25}\,c^6\,d^{15}\,e^{21}-353210\,b^{24}\,c^7\,d^{16}\,e^{20}+1013232\,b^{23}\,c^8\,d^{17}\,e^{19}-2217072\,b^{22}\,c^9\,d^{18}\,e^{18}+3751968\,b^{21}\,c^{10}\,d^{19}\,e^{17}-4903382\,b^{20}\,c^{11}\,d^{20}\,e^{16}+4835160\,b^{19}\,c^{12}\,d^{21}\,e^{15}-3343724\,b^{18}\,c^{13}\,d^{22}\,e^{14}+1207368\,b^{17}\,c^{14}\,d^{23}\,e^{13}+393646\,b^{16}\,c^{15}\,d^{24}\,e^{12}-851136\,b^{15}\,c^{16}\,d^{25}\,e^{11}+473880\,b^{14}\,c^{17}\,d^{26}\,e^{10}+38544\,b^{13}\,c^{18}\,d^{27}\,e^9-267432\,b^{12}\,c^{19}\,d^{28}\,e^8+230912\,b^{11}\,c^{20}\,d^{29}\,e^7-116512\,b^{10}\,c^{21}\,d^{30}\,e^6+38720\,b^9\,c^{22}\,d^{31}\,e^5-8404\,b^8\,c^{23}\,d^{32}\,e^4+1088\,b^7\,c^{24}\,d^{33}\,e^3-64\,b^6\,c^{25}\,d^{34}\,e^2\right)+\frac{\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\left(11\,b\,e-4\,c\,d\right)\,\left(8\,b^{10}\,c^{23}\,d^{37}\,e^3-148\,b^{11}\,c^{22}\,d^{36}\,e^4+1160\,b^{12}\,c^{21}\,d^{35}\,e^5-4760\,b^{13}\,c^{20}\,d^{34}\,e^6+8036\,b^{14}\,c^{19}\,d^{33}\,e^7+21868\,b^{15}\,c^{18}\,d^{32}\,e^8-194304\,b^{16}\,c^{17}\,d^{31}\,e^9+709280\,b^{17}\,c^{16}\,d^{30}\,e^{10}-1744160\,b^{18}\,c^{15}\,d^{29}\,e^{11}+3218072\,b^{19}\,c^{14}\,d^{28}\,e^{12}-4654832\,b^{20}\,c^{13}\,d^{27}\,e^{13}+5394480\,b^{21}\,c^{12}\,d^{26}\,e^{14}-5063240\,b^{22}\,c^{11}\,d^{25}\,e^{15}+3863800\,b^{23}\,c^{10}\,d^{24}\,e^{16}-2393152\,b^{24}\,c^9\,d^{23}\,e^{17}+1194528\,b^{25}\,c^8\,d^{22}\,e^{18}-474056\,b^{26}\,c^7\,d^{21}\,e^{19}+146300\,b^{27}\,c^6\,d^{20}\,e^{20}-33880\,b^{28}\,c^5\,d^{19}\,e^{21}+5544\,b^{29}\,c^4\,d^{18}\,e^{22}-572\,b^{30}\,c^3\,d^{17}\,e^{23}+28\,b^{31}\,c^2\,d^{16}\,e^{24}+\frac{\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\left(11\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(-8\,b^{33}\,c^2\,d^{20}\,e^{23}+176\,b^{32}\,c^3\,d^{21}\,e^{22}-1840\,b^{31}\,c^4\,d^{22}\,e^{21}+12160\,b^{30}\,c^5\,d^{23}\,e^{20}-57000\,b^{29}\,c^6\,d^{24}\,e^{19}+201552\,b^{28}\,c^7\,d^{25}\,e^{18}-558144\,b^{27}\,c^8\,d^{26}\,e^{17}+1240320\,b^{26}\,c^9\,d^{27}\,e^{16}-2248080\,b^{25}\,c^{10}\,d^{28}\,e^{15}+3359200\,b^{24}\,c^{11}\,d^{29}\,e^{14}-4165408\,b^{23}\,c^{12}\,d^{30}\,e^{13}+4299776\,b^{22}\,c^{13}\,d^{31}\,e^{12}-3695120\,b^{21}\,c^{14}\,d^{32}\,e^{11}+2635680\,b^{20}\,c^{15}\,d^{33}\,e^{10}-1550400\,b^{19}\,c^{16}\,d^{34}\,e^9+744192\,b^{18}\,c^{17}\,d^{35}\,e^8-286824\,b^{17}\,c^{18}\,d^{36}\,e^7+86640\,b^{16}\,c^{19}\,d^{37}\,e^6-19760\,b^{15}\,c^{20}\,d^{38}\,e^5+3200\,b^{14}\,c^{21}\,d^{39}\,e^4-328\,b^{13}\,c^{22}\,d^{40}\,e^3+16\,b^{12}\,c^{23}\,d^{41}\,e^2\right)}{2\,\left(b^{12}\,e^9-9\,b^{11}\,c\,d\,e^8+36\,b^{10}\,c^2\,d^2\,e^7-84\,b^9\,c^3\,d^3\,e^6+126\,b^8\,c^4\,d^4\,e^5-126\,b^7\,c^5\,d^5\,e^4+84\,b^6\,c^6\,d^6\,e^3-36\,b^5\,c^7\,d^7\,e^2+9\,b^4\,c^8\,d^8\,e-b^3\,c^9\,d^9\right)}\right)}{2\,\left(b^{12}\,e^9-9\,b^{11}\,c\,d\,e^8+36\,b^{10}\,c^2\,d^2\,e^7-84\,b^9\,c^3\,d^3\,e^6+126\,b^8\,c^4\,d^4\,e^5-126\,b^7\,c^5\,d^5\,e^4+84\,b^6\,c^6\,d^6\,e^3-36\,b^5\,c^7\,d^7\,e^2+9\,b^4\,c^8\,d^8\,e-b^3\,c^9\,d^9\right)}\right)\,1{}\mathrm{i}}{2\,\left(b^{12}\,e^9-9\,b^{11}\,c\,d\,e^8+36\,b^{10}\,c^2\,d^2\,e^7-84\,b^9\,c^3\,d^3\,e^6+126\,b^8\,c^4\,d^4\,e^5-126\,b^7\,c^5\,d^5\,e^4+84\,b^6\,c^6\,d^6\,e^3-36\,b^5\,c^7\,d^7\,e^2+9\,b^4\,c^8\,d^8\,e-b^3\,c^9\,d^9\right)}}{\frac{\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\left(11\,b\,e-4\,c\,d\right)\,\left(\sqrt{d+e\,x}\,\left(-98\,b^{28}\,c^3\,d^{12}\,e^{24}+1848\,b^{27}\,c^4\,d^{13}\,e^{23}-16412\,b^{26}\,c^5\,d^{14}\,e^{22}+91080\,b^{25}\,c^6\,d^{15}\,e^{21}-353210\,b^{24}\,c^7\,d^{16}\,e^{20}+1013232\,b^{23}\,c^8\,d^{17}\,e^{19}-2217072\,b^{22}\,c^9\,d^{18}\,e^{18}+3751968\,b^{21}\,c^{10}\,d^{19}\,e^{17}-4903382\,b^{20}\,c^{11}\,d^{20}\,e^{16}+4835160\,b^{19}\,c^{12}\,d^{21}\,e^{15}-3343724\,b^{18}\,c^{13}\,d^{22}\,e^{14}+1207368\,b^{17}\,c^{14}\,d^{23}\,e^{13}+393646\,b^{16}\,c^{15}\,d^{24}\,e^{12}-851136\,b^{15}\,c^{16}\,d^{25}\,e^{11}+473880\,b^{14}\,c^{17}\,d^{26}\,e^{10}+38544\,b^{13}\,c^{18}\,d^{27}\,e^9-267432\,b^{12}\,c^{19}\,d^{28}\,e^8+230912\,b^{11}\,c^{20}\,d^{29}\,e^7-116512\,b^{10}\,c^{21}\,d^{30}\,e^6+38720\,b^9\,c^{22}\,d^{31}\,e^5-8404\,b^8\,c^{23}\,d^{32}\,e^4+1088\,b^7\,c^{24}\,d^{33}\,e^3-64\,b^6\,c^{25}\,d^{34}\,e^2\right)+\frac{\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\left(11\,b\,e-4\,c\,d\right)\,\left(8\,b^{10}\,c^{23}\,d^{37}\,e^3-148\,b^{11}\,c^{22}\,d^{36}\,e^4+1160\,b^{12}\,c^{21}\,d^{35}\,e^5-4760\,b^{13}\,c^{20}\,d^{34}\,e^6+8036\,b^{14}\,c^{19}\,d^{33}\,e^7+21868\,b^{15}\,c^{18}\,d^{32}\,e^8-194304\,b^{16}\,c^{17}\,d^{31}\,e^9+709280\,b^{17}\,c^{16}\,d^{30}\,e^{10}-1744160\,b^{18}\,c^{15}\,d^{29}\,e^{11}+3218072\,b^{19}\,c^{14}\,d^{28}\,e^{12}-4654832\,b^{20}\,c^{13}\,d^{27}\,e^{13}+5394480\,b^{21}\,c^{12}\,d^{26}\,e^{14}-5063240\,b^{22}\,c^{11}\,d^{25}\,e^{15}+3863800\,b^{23}\,c^{10}\,d^{24}\,e^{16}-2393152\,b^{24}\,c^9\,d^{23}\,e^{17}+1194528\,b^{25}\,c^8\,d^{22}\,e^{18}-474056\,b^{26}\,c^7\,d^{21}\,e^{19}+146300\,b^{27}\,c^6\,d^{20}\,e^{20}-33880\,b^{28}\,c^5\,d^{19}\,e^{21}+5544\,b^{29}\,c^4\,d^{18}\,e^{22}-572\,b^{30}\,c^3\,d^{17}\,e^{23}+28\,b^{31}\,c^2\,d^{16}\,e^{24}+\frac{\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\left(11\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(-8\,b^{33}\,c^2\,d^{20}\,e^{23}+176\,b^{32}\,c^3\,d^{21}\,e^{22}-1840\,b^{31}\,c^4\,d^{22}\,e^{21}+12160\,b^{30}\,c^5\,d^{23}\,e^{20}-57000\,b^{29}\,c^6\,d^{24}\,e^{19}+201552\,b^{28}\,c^7\,d^{25}\,e^{18}-558144\,b^{27}\,c^8\,d^{26}\,e^{17}+1240320\,b^{26}\,c^9\,d^{27}\,e^{16}-2248080\,b^{25}\,c^{10}\,d^{28}\,e^{15}+3359200\,b^{24}\,c^{11}\,d^{29}\,e^{14}-4165408\,b^{23}\,c^{12}\,d^{30}\,e^{13}+4299776\,b^{22}\,c^{13}\,d^{31}\,e^{12}-3695120\,b^{21}\,c^{14}\,d^{32}\,e^{11}+2635680\,b^{20}\,c^{15}\,d^{33}\,e^{10}-1550400\,b^{19}\,c^{16}\,d^{34}\,e^9+744192\,b^{18}\,c^{17}\,d^{35}\,e^8-286824\,b^{17}\,c^{18}\,d^{36}\,e^7+86640\,b^{16}\,c^{19}\,d^{37}\,e^6-19760\,b^{15}\,c^{20}\,d^{38}\,e^5+3200\,b^{14}\,c^{21}\,d^{39}\,e^4-328\,b^{13}\,c^{22}\,d^{40}\,e^3+16\,b^{12}\,c^{23}\,d^{41}\,e^2\right)}{2\,\left(b^{12}\,e^9-9\,b^{11}\,c\,d\,e^8+36\,b^{10}\,c^2\,d^2\,e^7-84\,b^9\,c^3\,d^3\,e^6+126\,b^8\,c^4\,d^4\,e^5-126\,b^7\,c^5\,d^5\,e^4+84\,b^6\,c^6\,d^6\,e^3-36\,b^5\,c^7\,d^7\,e^2+9\,b^4\,c^8\,d^8\,e-b^3\,c^9\,d^9\right)}\right)}{2\,\left(b^{12}\,e^9-9\,b^{11}\,c\,d\,e^8+36\,b^{10}\,c^2\,d^2\,e^7-84\,b^9\,c^3\,d^3\,e^6+126\,b^8\,c^4\,d^4\,e^5-126\,b^7\,c^5\,d^5\,e^4+84\,b^6\,c^6\,d^6\,e^3-36\,b^5\,c^7\,d^7\,e^2+9\,b^4\,c^8\,d^8\,e-b^3\,c^9\,d^9\right)}\right)}{2\,\left(b^{12}\,e^9-9\,b^{11}\,c\,d\,e^8+36\,b^{10}\,c^2\,d^2\,e^7-84\,b^9\,c^3\,d^3\,e^6+126\,b^8\,c^4\,d^4\,e^5-126\,b^7\,c^5\,d^5\,e^4+84\,b^6\,c^6\,d^6\,e^3-36\,b^5\,c^7\,d^7\,e^2+9\,b^4\,c^8\,d^8\,e-b^3\,c^9\,d^9\right)}-\frac{\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\left(11\,b\,e-4\,c\,d\right)\,\left(\sqrt{d+e\,x}\,\left(-98\,b^{28}\,c^3\,d^{12}\,e^{24}+1848\,b^{27}\,c^4\,d^{13}\,e^{23}-16412\,b^{26}\,c^5\,d^{14}\,e^{22}+91080\,b^{25}\,c^6\,d^{15}\,e^{21}-353210\,b^{24}\,c^7\,d^{16}\,e^{20}+1013232\,b^{23}\,c^8\,d^{17}\,e^{19}-2217072\,b^{22}\,c^9\,d^{18}\,e^{18}+3751968\,b^{21}\,c^{10}\,d^{19}\,e^{17}-4903382\,b^{20}\,c^{11}\,d^{20}\,e^{16}+4835160\,b^{19}\,c^{12}\,d^{21}\,e^{15}-3343724\,b^{18}\,c^{13}\,d^{22}\,e^{14}+1207368\,b^{17}\,c^{14}\,d^{23}\,e^{13}+393646\,b^{16}\,c^{15}\,d^{24}\,e^{12}-851136\,b^{15}\,c^{16}\,d^{25}\,e^{11}+473880\,b^{14}\,c^{17}\,d^{26}\,e^{10}+38544\,b^{13}\,c^{18}\,d^{27}\,e^9-267432\,b^{12}\,c^{19}\,d^{28}\,e^8+230912\,b^{11}\,c^{20}\,d^{29}\,e^7-116512\,b^{10}\,c^{21}\,d^{30}\,e^6+38720\,b^9\,c^{22}\,d^{31}\,e^5-8404\,b^8\,c^{23}\,d^{32}\,e^4+1088\,b^7\,c^{24}\,d^{33}\,e^3-64\,b^6\,c^{25}\,d^{34}\,e^2\right)-\frac{\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\left(11\,b\,e-4\,c\,d\right)\,\left(8\,b^{10}\,c^{23}\,d^{37}\,e^3-148\,b^{11}\,c^{22}\,d^{36}\,e^4+1160\,b^{12}\,c^{21}\,d^{35}\,e^5-4760\,b^{13}\,c^{20}\,d^{34}\,e^6+8036\,b^{14}\,c^{19}\,d^{33}\,e^7+21868\,b^{15}\,c^{18}\,d^{32}\,e^8-194304\,b^{16}\,c^{17}\,d^{31}\,e^9+709280\,b^{17}\,c^{16}\,d^{30}\,e^{10}-1744160\,b^{18}\,c^{15}\,d^{29}\,e^{11}+3218072\,b^{19}\,c^{14}\,d^{28}\,e^{12}-4654832\,b^{20}\,c^{13}\,d^{27}\,e^{13}+5394480\,b^{21}\,c^{12}\,d^{26}\,e^{14}-5063240\,b^{22}\,c^{11}\,d^{25}\,e^{15}+3863800\,b^{23}\,c^{10}\,d^{24}\,e^{16}-2393152\,b^{24}\,c^9\,d^{23}\,e^{17}+1194528\,b^{25}\,c^8\,d^{22}\,e^{18}-474056\,b^{26}\,c^7\,d^{21}\,e^{19}+146300\,b^{27}\,c^6\,d^{20}\,e^{20}-33880\,b^{28}\,c^5\,d^{19}\,e^{21}+5544\,b^{29}\,c^4\,d^{18}\,e^{22}-572\,b^{30}\,c^3\,d^{17}\,e^{23}+28\,b^{31}\,c^2\,d^{16}\,e^{24}-\frac{\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\left(11\,b\,e-4\,c\,d\right)\,\sqrt{d+e\,x}\,\left(-8\,b^{33}\,c^2\,d^{20}\,e^{23}+176\,b^{32}\,c^3\,d^{21}\,e^{22}-1840\,b^{31}\,c^4\,d^{22}\,e^{21}+12160\,b^{30}\,c^5\,d^{23}\,e^{20}-57000\,b^{29}\,c^6\,d^{24}\,e^{19}+201552\,b^{28}\,c^7\,d^{25}\,e^{18}-558144\,b^{27}\,c^8\,d^{26}\,e^{17}+1240320\,b^{26}\,c^9\,d^{27}\,e^{16}-2248080\,b^{25}\,c^{10}\,d^{28}\,e^{15}+3359200\,b^{24}\,c^{11}\,d^{29}\,e^{14}-4165408\,b^{23}\,c^{12}\,d^{30}\,e^{13}+4299776\,b^{22}\,c^{13}\,d^{31}\,e^{12}-3695120\,b^{21}\,c^{14}\,d^{32}\,e^{11}+2635680\,b^{20}\,c^{15}\,d^{33}\,e^{10}-1550400\,b^{19}\,c^{16}\,d^{34}\,e^9+744192\,b^{18}\,c^{17}\,d^{35}\,e^8-286824\,b^{17}\,c^{18}\,d^{36}\,e^7+86640\,b^{16}\,c^{19}\,d^{37}\,e^6-19760\,b^{15}\,c^{20}\,d^{38}\,e^5+3200\,b^{14}\,c^{21}\,d^{39}\,e^4-328\,b^{13}\,c^{22}\,d^{40}\,e^3+16\,b^{12}\,c^{23}\,d^{41}\,e^2\right)}{2\,\left(b^{12}\,e^9-9\,b^{11}\,c\,d\,e^8+36\,b^{10}\,c^2\,d^2\,e^7-84\,b^9\,c^3\,d^3\,e^6+126\,b^8\,c^4\,d^4\,e^5-126\,b^7\,c^5\,d^5\,e^4+84\,b^6\,c^6\,d^6\,e^3-36\,b^5\,c^7\,d^7\,e^2+9\,b^4\,c^8\,d^8\,e-b^3\,c^9\,d^9\right)}\right)}{2\,\left(b^{12}\,e^9-9\,b^{11}\,c\,d\,e^8+36\,b^{10}\,c^2\,d^2\,e^7-84\,b^9\,c^3\,d^3\,e^6+126\,b^8\,c^4\,d^4\,e^5-126\,b^7\,c^5\,d^5\,e^4+84\,b^6\,c^6\,d^6\,e^3-36\,b^5\,c^7\,d^7\,e^2+9\,b^4\,c^8\,d^8\,e-b^3\,c^9\,d^9\right)}\right)}{2\,\left(b^{12}\,e^9-9\,b^{11}\,c\,d\,e^8+36\,b^{10}\,c^2\,d^2\,e^7-84\,b^9\,c^3\,d^3\,e^6+126\,b^8\,c^4\,d^4\,e^5-126\,b^7\,c^5\,d^5\,e^4+84\,b^6\,c^6\,d^6\,e^3-36\,b^5\,c^7\,d^7\,e^2+9\,b^4\,c^8\,d^8\,e-b^3\,c^9\,d^9\right)}-64\,b^4\,c^{25}\,d^{30}\,e^3+960\,b^5\,c^{24}\,d^{29}\,e^4-7180\,b^6\,c^{23}\,d^{28}\,e^5+35560\,b^7\,c^{22}\,d^{27}\,e^6-125748\,b^8\,c^{21}\,d^{26}\,e^7+314496\,b^9\,c^{20}\,d^{25}\,e^8-508886\,b^{10}\,c^{19}\,d^{24}\,e^9+326832\,b^{11}\,c^{18}\,d^{23}\,e^{10}+760408\,b^{12}\,c^{17}\,d^{22}\,e^{11}-2806584\,b^{13}\,c^{16}\,d^{21}\,e^{12}+4917990\,b^{14}\,c^{15}\,d^{20}\,e^{13}-5803448\,b^{15}\,c^{14}\,d^{19}\,e^{14}+4974956\,b^{16}\,c^{13}\,d^{18}\,e^{15}-3162096\,b^{17}\,c^{12}\,d^{17}\,e^{16}+1483782\,b^{18}\,c^{11}\,d^{16}\,e^{17}-501472\,b^{19}\,c^{10}\,d^{15}\,e^{18}+115824\,b^{20}\,c^9\,d^{14}\,e^{19}-16408\,b^{21}\,c^8\,d^{13}\,e^{20}+1078\,b^{22}\,c^7\,d^{12}\,e^{21}}\right)\,\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\left(11\,b\,e-4\,c\,d\right)\,1{}\mathrm{i}}{b^{12}\,e^9-9\,b^{11}\,c\,d\,e^8+36\,b^{10}\,c^2\,d^2\,e^7-84\,b^9\,c^3\,d^3\,e^6+126\,b^8\,c^4\,d^4\,e^5-126\,b^7\,c^5\,d^5\,e^4+84\,b^6\,c^6\,d^6\,e^3-36\,b^5\,c^7\,d^7\,e^2+9\,b^4\,c^8\,d^8\,e-b^3\,c^9\,d^9}-\frac{\mathrm{atan}\left(\frac{b^{24}\,d^{20}\,e^{24}\,\sqrt{d+e\,x}\,343{}\mathrm{i}-b^{23}\,c\,d^{21}\,e^{23}\,\sqrt{d+e\,x}\,6615{}\mathrm{i}-b^3\,c^{21}\,d^{41}\,e^3\,\sqrt{d+e\,x}\,924{}\mathrm{i}+b^4\,c^{20}\,d^{40}\,e^4\,\sqrt{d+e\,x}\,13167{}\mathrm{i}-b^5\,c^{19}\,d^{39}\,e^5\,\sqrt{d+e\,x}\,83160{}\mathrm{i}+b^6\,c^{18}\,d^{38}\,e^6\,\sqrt{d+e\,x}\,298914{}\mathrm{i}-b^7\,c^{17}\,d^{37}\,e^7\,\sqrt{d+e\,x}\,627066{}\mathrm{i}+b^8\,c^{16}\,d^{36}\,e^8\,\sqrt{d+e\,x}\,548163{}\mathrm{i}+b^9\,c^{15}\,d^{35}\,e^9\,\sqrt{d+e\,x}\,953260{}\mathrm{i}-b^{10}\,c^{14}\,d^{34}\,e^{10}\,\sqrt{d+e\,x}\,4260564{}\mathrm{i}+b^{11}\,c^{13}\,d^{33}\,e^{11}\,\sqrt{d+e\,x}\,7526715{}\mathrm{i}-b^{12}\,c^{12}\,d^{32}\,e^{12}\,\sqrt{d+e\,x}\,7070070{}\mathrm{i}+b^{13}\,c^{11}\,d^{31}\,e^{13}\,\sqrt{d+e\,x}\,735546{}\mathrm{i}+b^{14}\,c^{10}\,d^{30}\,e^{14}\,\sqrt{d+e\,x}\,9071172{}\mathrm{i}-b^{15}\,c^9\,d^{29}\,e^{15}\,\sqrt{d+e\,x}\,16762207{}\mathrm{i}+b^{16}\,c^8\,d^{28}\,e^{16}\,\sqrt{d+e\,x}\,18354798{}\mathrm{i}-b^{17}\,c^7\,d^{27}\,e^{17}\,\sqrt{d+e\,x}\,14431032{}\mathrm{i}+b^{18}\,c^6\,d^{26}\,e^{18}\,\sqrt{d+e\,x}\,8573180{}\mathrm{i}-b^{19}\,c^5\,d^{25}\,e^{19}\,\sqrt{d+e\,x}\,3893967{}\mathrm{i}+b^{20}\,c^4\,d^{24}\,e^{20}\,\sqrt{d+e\,x}\,1340031{}\mathrm{i}-b^{21}\,c^3\,d^{23}\,e^{21}\,\sqrt{d+e\,x}\,339702{}\mathrm{i}+b^{22}\,c^2\,d^{22}\,e^{22}\,\sqrt{d+e\,x}\,60018{}\mathrm{i}}{d^9\,\sqrt{d^9}\,\left(d^9\,\left(d^9\,\left(d^9\,\left(13167\,b^4\,c^{20}\,e^4-924\,b^3\,c^{21}\,d\,e^3\right)+735546\,b^{13}\,c^{11}\,e^{13}-7070070\,b^{12}\,c^{12}\,d\,e^{12}-83160\,b^5\,c^{19}\,d^8\,e^5+298914\,b^6\,c^{18}\,d^7\,e^6-627066\,b^7\,c^{17}\,d^6\,e^7+548163\,b^8\,c^{16}\,d^5\,e^8+953260\,b^9\,c^{15}\,d^4\,e^9-4260564\,b^{10}\,c^{14}\,d^3\,e^{10}+7526715\,b^{11}\,c^{13}\,d^2\,e^{11}\right)+60018\,b^{22}\,c^2\,e^{22}-339702\,b^{21}\,c^3\,d\,e^{21}+9071172\,b^{14}\,c^{10}\,d^8\,e^{14}-16762207\,b^{15}\,c^9\,d^7\,e^{15}+18354798\,b^{16}\,c^8\,d^6\,e^{16}-14431032\,b^{17}\,c^7\,d^5\,e^{17}+8573180\,b^{18}\,c^6\,d^4\,e^{18}-3893967\,b^{19}\,c^5\,d^3\,e^{19}+1340031\,b^{20}\,c^4\,d^2\,e^{20}\right)+343\,b^{24}\,d^7\,e^{24}-6615\,b^{23}\,c\,d^8\,e^{23}\right)}\right)\,\left(7\,b\,e+4\,c\,d\right)\,1{}\mathrm{i}}{b^3\,\sqrt{d^9}}","Not used",1,"(atan((((-c^9*(b*e - c*d)^9)^(1/2)*(11*b*e - 4*c*d)*((d + e*x)^(1/2)*(1088*b^7*c^24*d^33*e^3 - 64*b^6*c^25*d^34*e^2 - 8404*b^8*c^23*d^32*e^4 + 38720*b^9*c^22*d^31*e^5 - 116512*b^10*c^21*d^30*e^6 + 230912*b^11*c^20*d^29*e^7 - 267432*b^12*c^19*d^28*e^8 + 38544*b^13*c^18*d^27*e^9 + 473880*b^14*c^17*d^26*e^10 - 851136*b^15*c^16*d^25*e^11 + 393646*b^16*c^15*d^24*e^12 + 1207368*b^17*c^14*d^23*e^13 - 3343724*b^18*c^13*d^22*e^14 + 4835160*b^19*c^12*d^21*e^15 - 4903382*b^20*c^11*d^20*e^16 + 3751968*b^21*c^10*d^19*e^17 - 2217072*b^22*c^9*d^18*e^18 + 1013232*b^23*c^8*d^17*e^19 - 353210*b^24*c^7*d^16*e^20 + 91080*b^25*c^6*d^15*e^21 - 16412*b^26*c^5*d^14*e^22 + 1848*b^27*c^4*d^13*e^23 - 98*b^28*c^3*d^12*e^24) - ((-c^9*(b*e - c*d)^9)^(1/2)*(11*b*e - 4*c*d)*(8*b^10*c^23*d^37*e^3 - 148*b^11*c^22*d^36*e^4 + 1160*b^12*c^21*d^35*e^5 - 4760*b^13*c^20*d^34*e^6 + 8036*b^14*c^19*d^33*e^7 + 21868*b^15*c^18*d^32*e^8 - 194304*b^16*c^17*d^31*e^9 + 709280*b^17*c^16*d^30*e^10 - 1744160*b^18*c^15*d^29*e^11 + 3218072*b^19*c^14*d^28*e^12 - 4654832*b^20*c^13*d^27*e^13 + 5394480*b^21*c^12*d^26*e^14 - 5063240*b^22*c^11*d^25*e^15 + 3863800*b^23*c^10*d^24*e^16 - 2393152*b^24*c^9*d^23*e^17 + 1194528*b^25*c^8*d^22*e^18 - 474056*b^26*c^7*d^21*e^19 + 146300*b^27*c^6*d^20*e^20 - 33880*b^28*c^5*d^19*e^21 + 5544*b^29*c^4*d^18*e^22 - 572*b^30*c^3*d^17*e^23 + 28*b^31*c^2*d^16*e^24 - ((-c^9*(b*e - c*d)^9)^(1/2)*(11*b*e - 4*c*d)*(d + e*x)^(1/2)*(16*b^12*c^23*d^41*e^2 - 328*b^13*c^22*d^40*e^3 + 3200*b^14*c^21*d^39*e^4 - 19760*b^15*c^20*d^38*e^5 + 86640*b^16*c^19*d^37*e^6 - 286824*b^17*c^18*d^36*e^7 + 744192*b^18*c^17*d^35*e^8 - 1550400*b^19*c^16*d^34*e^9 + 2635680*b^20*c^15*d^33*e^10 - 3695120*b^21*c^14*d^32*e^11 + 4299776*b^22*c^13*d^31*e^12 - 4165408*b^23*c^12*d^30*e^13 + 3359200*b^24*c^11*d^29*e^14 - 2248080*b^25*c^10*d^28*e^15 + 1240320*b^26*c^9*d^27*e^16 - 558144*b^27*c^8*d^26*e^17 + 201552*b^28*c^7*d^25*e^18 - 57000*b^29*c^6*d^24*e^19 + 12160*b^30*c^5*d^23*e^20 - 1840*b^31*c^4*d^22*e^21 + 176*b^32*c^3*d^21*e^22 - 8*b^33*c^2*d^20*e^23))/(2*(b^12*e^9 - b^3*c^9*d^9 + 9*b^4*c^8*d^8*e - 36*b^5*c^7*d^7*e^2 + 84*b^6*c^6*d^6*e^3 - 126*b^7*c^5*d^5*e^4 + 126*b^8*c^4*d^4*e^5 - 84*b^9*c^3*d^3*e^6 + 36*b^10*c^2*d^2*e^7 - 9*b^11*c*d*e^8))))/(2*(b^12*e^9 - b^3*c^9*d^9 + 9*b^4*c^8*d^8*e - 36*b^5*c^7*d^7*e^2 + 84*b^6*c^6*d^6*e^3 - 126*b^7*c^5*d^5*e^4 + 126*b^8*c^4*d^4*e^5 - 84*b^9*c^3*d^3*e^6 + 36*b^10*c^2*d^2*e^7 - 9*b^11*c*d*e^8)))*1i)/(2*(b^12*e^9 - b^3*c^9*d^9 + 9*b^4*c^8*d^8*e - 36*b^5*c^7*d^7*e^2 + 84*b^6*c^6*d^6*e^3 - 126*b^7*c^5*d^5*e^4 + 126*b^8*c^4*d^4*e^5 - 84*b^9*c^3*d^3*e^6 + 36*b^10*c^2*d^2*e^7 - 9*b^11*c*d*e^8)) + ((-c^9*(b*e - c*d)^9)^(1/2)*(11*b*e - 4*c*d)*((d + e*x)^(1/2)*(1088*b^7*c^24*d^33*e^3 - 64*b^6*c^25*d^34*e^2 - 8404*b^8*c^23*d^32*e^4 + 38720*b^9*c^22*d^31*e^5 - 116512*b^10*c^21*d^30*e^6 + 230912*b^11*c^20*d^29*e^7 - 267432*b^12*c^19*d^28*e^8 + 38544*b^13*c^18*d^27*e^9 + 473880*b^14*c^17*d^26*e^10 - 851136*b^15*c^16*d^25*e^11 + 393646*b^16*c^15*d^24*e^12 + 1207368*b^17*c^14*d^23*e^13 - 3343724*b^18*c^13*d^22*e^14 + 4835160*b^19*c^12*d^21*e^15 - 4903382*b^20*c^11*d^20*e^16 + 3751968*b^21*c^10*d^19*e^17 - 2217072*b^22*c^9*d^18*e^18 + 1013232*b^23*c^8*d^17*e^19 - 353210*b^24*c^7*d^16*e^20 + 91080*b^25*c^6*d^15*e^21 - 16412*b^26*c^5*d^14*e^22 + 1848*b^27*c^4*d^13*e^23 - 98*b^28*c^3*d^12*e^24) + ((-c^9*(b*e - c*d)^9)^(1/2)*(11*b*e - 4*c*d)*(8*b^10*c^23*d^37*e^3 - 148*b^11*c^22*d^36*e^4 + 1160*b^12*c^21*d^35*e^5 - 4760*b^13*c^20*d^34*e^6 + 8036*b^14*c^19*d^33*e^7 + 21868*b^15*c^18*d^32*e^8 - 194304*b^16*c^17*d^31*e^9 + 709280*b^17*c^16*d^30*e^10 - 1744160*b^18*c^15*d^29*e^11 + 3218072*b^19*c^14*d^28*e^12 - 4654832*b^20*c^13*d^27*e^13 + 5394480*b^21*c^12*d^26*e^14 - 5063240*b^22*c^11*d^25*e^15 + 3863800*b^23*c^10*d^24*e^16 - 2393152*b^24*c^9*d^23*e^17 + 1194528*b^25*c^8*d^22*e^18 - 474056*b^26*c^7*d^21*e^19 + 146300*b^27*c^6*d^20*e^20 - 33880*b^28*c^5*d^19*e^21 + 5544*b^29*c^4*d^18*e^22 - 572*b^30*c^3*d^17*e^23 + 28*b^31*c^2*d^16*e^24 + ((-c^9*(b*e - c*d)^9)^(1/2)*(11*b*e - 4*c*d)*(d + e*x)^(1/2)*(16*b^12*c^23*d^41*e^2 - 328*b^13*c^22*d^40*e^3 + 3200*b^14*c^21*d^39*e^4 - 19760*b^15*c^20*d^38*e^5 + 86640*b^16*c^19*d^37*e^6 - 286824*b^17*c^18*d^36*e^7 + 744192*b^18*c^17*d^35*e^8 - 1550400*b^19*c^16*d^34*e^9 + 2635680*b^20*c^15*d^33*e^10 - 3695120*b^21*c^14*d^32*e^11 + 4299776*b^22*c^13*d^31*e^12 - 4165408*b^23*c^12*d^30*e^13 + 3359200*b^24*c^11*d^29*e^14 - 2248080*b^25*c^10*d^28*e^15 + 1240320*b^26*c^9*d^27*e^16 - 558144*b^27*c^8*d^26*e^17 + 201552*b^28*c^7*d^25*e^18 - 57000*b^29*c^6*d^24*e^19 + 12160*b^30*c^5*d^23*e^20 - 1840*b^31*c^4*d^22*e^21 + 176*b^32*c^3*d^21*e^22 - 8*b^33*c^2*d^20*e^23))/(2*(b^12*e^9 - b^3*c^9*d^9 + 9*b^4*c^8*d^8*e - 36*b^5*c^7*d^7*e^2 + 84*b^6*c^6*d^6*e^3 - 126*b^7*c^5*d^5*e^4 + 126*b^8*c^4*d^4*e^5 - 84*b^9*c^3*d^3*e^6 + 36*b^10*c^2*d^2*e^7 - 9*b^11*c*d*e^8))))/(2*(b^12*e^9 - b^3*c^9*d^9 + 9*b^4*c^8*d^8*e - 36*b^5*c^7*d^7*e^2 + 84*b^6*c^6*d^6*e^3 - 126*b^7*c^5*d^5*e^4 + 126*b^8*c^4*d^4*e^5 - 84*b^9*c^3*d^3*e^6 + 36*b^10*c^2*d^2*e^7 - 9*b^11*c*d*e^8)))*1i)/(2*(b^12*e^9 - b^3*c^9*d^9 + 9*b^4*c^8*d^8*e - 36*b^5*c^7*d^7*e^2 + 84*b^6*c^6*d^6*e^3 - 126*b^7*c^5*d^5*e^4 + 126*b^8*c^4*d^4*e^5 - 84*b^9*c^3*d^3*e^6 + 36*b^10*c^2*d^2*e^7 - 9*b^11*c*d*e^8)))/(((-c^9*(b*e - c*d)^9)^(1/2)*(11*b*e - 4*c*d)*((d + e*x)^(1/2)*(1088*b^7*c^24*d^33*e^3 - 64*b^6*c^25*d^34*e^2 - 8404*b^8*c^23*d^32*e^4 + 38720*b^9*c^22*d^31*e^5 - 116512*b^10*c^21*d^30*e^6 + 230912*b^11*c^20*d^29*e^7 - 267432*b^12*c^19*d^28*e^8 + 38544*b^13*c^18*d^27*e^9 + 473880*b^14*c^17*d^26*e^10 - 851136*b^15*c^16*d^25*e^11 + 393646*b^16*c^15*d^24*e^12 + 1207368*b^17*c^14*d^23*e^13 - 3343724*b^18*c^13*d^22*e^14 + 4835160*b^19*c^12*d^21*e^15 - 4903382*b^20*c^11*d^20*e^16 + 3751968*b^21*c^10*d^19*e^17 - 2217072*b^22*c^9*d^18*e^18 + 1013232*b^23*c^8*d^17*e^19 - 353210*b^24*c^7*d^16*e^20 + 91080*b^25*c^6*d^15*e^21 - 16412*b^26*c^5*d^14*e^22 + 1848*b^27*c^4*d^13*e^23 - 98*b^28*c^3*d^12*e^24) + ((-c^9*(b*e - c*d)^9)^(1/2)*(11*b*e - 4*c*d)*(8*b^10*c^23*d^37*e^3 - 148*b^11*c^22*d^36*e^4 + 1160*b^12*c^21*d^35*e^5 - 4760*b^13*c^20*d^34*e^6 + 8036*b^14*c^19*d^33*e^7 + 21868*b^15*c^18*d^32*e^8 - 194304*b^16*c^17*d^31*e^9 + 709280*b^17*c^16*d^30*e^10 - 1744160*b^18*c^15*d^29*e^11 + 3218072*b^19*c^14*d^28*e^12 - 4654832*b^20*c^13*d^27*e^13 + 5394480*b^21*c^12*d^26*e^14 - 5063240*b^22*c^11*d^25*e^15 + 3863800*b^23*c^10*d^24*e^16 - 2393152*b^24*c^9*d^23*e^17 + 1194528*b^25*c^8*d^22*e^18 - 474056*b^26*c^7*d^21*e^19 + 146300*b^27*c^6*d^20*e^20 - 33880*b^28*c^5*d^19*e^21 + 5544*b^29*c^4*d^18*e^22 - 572*b^30*c^3*d^17*e^23 + 28*b^31*c^2*d^16*e^24 + ((-c^9*(b*e - c*d)^9)^(1/2)*(11*b*e - 4*c*d)*(d + e*x)^(1/2)*(16*b^12*c^23*d^41*e^2 - 328*b^13*c^22*d^40*e^3 + 3200*b^14*c^21*d^39*e^4 - 19760*b^15*c^20*d^38*e^5 + 86640*b^16*c^19*d^37*e^6 - 286824*b^17*c^18*d^36*e^7 + 744192*b^18*c^17*d^35*e^8 - 1550400*b^19*c^16*d^34*e^9 + 2635680*b^20*c^15*d^33*e^10 - 3695120*b^21*c^14*d^32*e^11 + 4299776*b^22*c^13*d^31*e^12 - 4165408*b^23*c^12*d^30*e^13 + 3359200*b^24*c^11*d^29*e^14 - 2248080*b^25*c^10*d^28*e^15 + 1240320*b^26*c^9*d^27*e^16 - 558144*b^27*c^8*d^26*e^17 + 201552*b^28*c^7*d^25*e^18 - 57000*b^29*c^6*d^24*e^19 + 12160*b^30*c^5*d^23*e^20 - 1840*b^31*c^4*d^22*e^21 + 176*b^32*c^3*d^21*e^22 - 8*b^33*c^2*d^20*e^23))/(2*(b^12*e^9 - b^3*c^9*d^9 + 9*b^4*c^8*d^8*e - 36*b^5*c^7*d^7*e^2 + 84*b^6*c^6*d^6*e^3 - 126*b^7*c^5*d^5*e^4 + 126*b^8*c^4*d^4*e^5 - 84*b^9*c^3*d^3*e^6 + 36*b^10*c^2*d^2*e^7 - 9*b^11*c*d*e^8))))/(2*(b^12*e^9 - b^3*c^9*d^9 + 9*b^4*c^8*d^8*e - 36*b^5*c^7*d^7*e^2 + 84*b^6*c^6*d^6*e^3 - 126*b^7*c^5*d^5*e^4 + 126*b^8*c^4*d^4*e^5 - 84*b^9*c^3*d^3*e^6 + 36*b^10*c^2*d^2*e^7 - 9*b^11*c*d*e^8))))/(2*(b^12*e^9 - b^3*c^9*d^9 + 9*b^4*c^8*d^8*e - 36*b^5*c^7*d^7*e^2 + 84*b^6*c^6*d^6*e^3 - 126*b^7*c^5*d^5*e^4 + 126*b^8*c^4*d^4*e^5 - 84*b^9*c^3*d^3*e^6 + 36*b^10*c^2*d^2*e^7 - 9*b^11*c*d*e^8)) - ((-c^9*(b*e - c*d)^9)^(1/2)*(11*b*e - 4*c*d)*((d + e*x)^(1/2)*(1088*b^7*c^24*d^33*e^3 - 64*b^6*c^25*d^34*e^2 - 8404*b^8*c^23*d^32*e^4 + 38720*b^9*c^22*d^31*e^5 - 116512*b^10*c^21*d^30*e^6 + 230912*b^11*c^20*d^29*e^7 - 267432*b^12*c^19*d^28*e^8 + 38544*b^13*c^18*d^27*e^9 + 473880*b^14*c^17*d^26*e^10 - 851136*b^15*c^16*d^25*e^11 + 393646*b^16*c^15*d^24*e^12 + 1207368*b^17*c^14*d^23*e^13 - 3343724*b^18*c^13*d^22*e^14 + 4835160*b^19*c^12*d^21*e^15 - 4903382*b^20*c^11*d^20*e^16 + 3751968*b^21*c^10*d^19*e^17 - 2217072*b^22*c^9*d^18*e^18 + 1013232*b^23*c^8*d^17*e^19 - 353210*b^24*c^7*d^16*e^20 + 91080*b^25*c^6*d^15*e^21 - 16412*b^26*c^5*d^14*e^22 + 1848*b^27*c^4*d^13*e^23 - 98*b^28*c^3*d^12*e^24) - ((-c^9*(b*e - c*d)^9)^(1/2)*(11*b*e - 4*c*d)*(8*b^10*c^23*d^37*e^3 - 148*b^11*c^22*d^36*e^4 + 1160*b^12*c^21*d^35*e^5 - 4760*b^13*c^20*d^34*e^6 + 8036*b^14*c^19*d^33*e^7 + 21868*b^15*c^18*d^32*e^8 - 194304*b^16*c^17*d^31*e^9 + 709280*b^17*c^16*d^30*e^10 - 1744160*b^18*c^15*d^29*e^11 + 3218072*b^19*c^14*d^28*e^12 - 4654832*b^20*c^13*d^27*e^13 + 5394480*b^21*c^12*d^26*e^14 - 5063240*b^22*c^11*d^25*e^15 + 3863800*b^23*c^10*d^24*e^16 - 2393152*b^24*c^9*d^23*e^17 + 1194528*b^25*c^8*d^22*e^18 - 474056*b^26*c^7*d^21*e^19 + 146300*b^27*c^6*d^20*e^20 - 33880*b^28*c^5*d^19*e^21 + 5544*b^29*c^4*d^18*e^22 - 572*b^30*c^3*d^17*e^23 + 28*b^31*c^2*d^16*e^24 - ((-c^9*(b*e - c*d)^9)^(1/2)*(11*b*e - 4*c*d)*(d + e*x)^(1/2)*(16*b^12*c^23*d^41*e^2 - 328*b^13*c^22*d^40*e^3 + 3200*b^14*c^21*d^39*e^4 - 19760*b^15*c^20*d^38*e^5 + 86640*b^16*c^19*d^37*e^6 - 286824*b^17*c^18*d^36*e^7 + 744192*b^18*c^17*d^35*e^8 - 1550400*b^19*c^16*d^34*e^9 + 2635680*b^20*c^15*d^33*e^10 - 3695120*b^21*c^14*d^32*e^11 + 4299776*b^22*c^13*d^31*e^12 - 4165408*b^23*c^12*d^30*e^13 + 3359200*b^24*c^11*d^29*e^14 - 2248080*b^25*c^10*d^28*e^15 + 1240320*b^26*c^9*d^27*e^16 - 558144*b^27*c^8*d^26*e^17 + 201552*b^28*c^7*d^25*e^18 - 57000*b^29*c^6*d^24*e^19 + 12160*b^30*c^5*d^23*e^20 - 1840*b^31*c^4*d^22*e^21 + 176*b^32*c^3*d^21*e^22 - 8*b^33*c^2*d^20*e^23))/(2*(b^12*e^9 - b^3*c^9*d^9 + 9*b^4*c^8*d^8*e - 36*b^5*c^7*d^7*e^2 + 84*b^6*c^6*d^6*e^3 - 126*b^7*c^5*d^5*e^4 + 126*b^8*c^4*d^4*e^5 - 84*b^9*c^3*d^3*e^6 + 36*b^10*c^2*d^2*e^7 - 9*b^11*c*d*e^8))))/(2*(b^12*e^9 - b^3*c^9*d^9 + 9*b^4*c^8*d^8*e - 36*b^5*c^7*d^7*e^2 + 84*b^6*c^6*d^6*e^3 - 126*b^7*c^5*d^5*e^4 + 126*b^8*c^4*d^4*e^5 - 84*b^9*c^3*d^3*e^6 + 36*b^10*c^2*d^2*e^7 - 9*b^11*c*d*e^8))))/(2*(b^12*e^9 - b^3*c^9*d^9 + 9*b^4*c^8*d^8*e - 36*b^5*c^7*d^7*e^2 + 84*b^6*c^6*d^6*e^3 - 126*b^7*c^5*d^5*e^4 + 126*b^8*c^4*d^4*e^5 - 84*b^9*c^3*d^3*e^6 + 36*b^10*c^2*d^2*e^7 - 9*b^11*c*d*e^8)) - 64*b^4*c^25*d^30*e^3 + 960*b^5*c^24*d^29*e^4 - 7180*b^6*c^23*d^28*e^5 + 35560*b^7*c^22*d^27*e^6 - 125748*b^8*c^21*d^26*e^7 + 314496*b^9*c^20*d^25*e^8 - 508886*b^10*c^19*d^24*e^9 + 326832*b^11*c^18*d^23*e^10 + 760408*b^12*c^17*d^22*e^11 - 2806584*b^13*c^16*d^21*e^12 + 4917990*b^14*c^15*d^20*e^13 - 5803448*b^15*c^14*d^19*e^14 + 4974956*b^16*c^13*d^18*e^15 - 3162096*b^17*c^12*d^17*e^16 + 1483782*b^18*c^11*d^16*e^17 - 501472*b^19*c^10*d^15*e^18 + 115824*b^20*c^9*d^14*e^19 - 16408*b^21*c^8*d^13*e^20 + 1078*b^22*c^7*d^12*e^21))*(-c^9*(b*e - c*d)^9)^(1/2)*(11*b*e - 4*c*d)*1i)/(b^12*e^9 - b^3*c^9*d^9 + 9*b^4*c^8*d^8*e - 36*b^5*c^7*d^7*e^2 + 84*b^6*c^6*d^6*e^3 - 126*b^7*c^5*d^5*e^4 + 126*b^8*c^4*d^4*e^5 - 84*b^9*c^3*d^3*e^6 + 36*b^10*c^2*d^2*e^7 - 9*b^11*c*d*e^8) - ((2*e^3)/(5*(c*d^2 - b*d*e)) + (2*e^3*(d + e*x)^2*(35*b^2*e^2 + 113*c^2*d^2 - 113*b*c*d*e))/(15*(c*d^2 - b*d*e)^3) - (14*e^3*(b*e - 2*c*d)*(d + e*x))/(15*(c*d^2 - b*d*e)^2) + (e*(d + e*x)^4*(2*c^5*d^4 + 7*b^4*c*e^4 - 24*b^3*c^2*d*e^3 + 26*b^2*c^3*d^2*e^2 - 4*b*c^4*d^3*e))/(b^2*(c*d^2 - b*d*e)^4) + (e*(b*e - 2*c*d)*(d + e*x)^3*(21*b^4*e^4 + 3*c^4*d^4 + 68*b^2*c^2*d^2*e^2 - 6*b*c^3*d^3*e - 65*b^3*c*d*e^3))/(3*b^2*(c*d^2 - b*d*e)^4))/(c*(d + e*x)^(9/2) + (c*d^2 - b*d*e)*(d + e*x)^(5/2) + (b*e - 2*c*d)*(d + e*x)^(7/2)) - (atan((b^24*d^20*e^24*(d + e*x)^(1/2)*343i - b^23*c*d^21*e^23*(d + e*x)^(1/2)*6615i - b^3*c^21*d^41*e^3*(d + e*x)^(1/2)*924i + b^4*c^20*d^40*e^4*(d + e*x)^(1/2)*13167i - b^5*c^19*d^39*e^5*(d + e*x)^(1/2)*83160i + b^6*c^18*d^38*e^6*(d + e*x)^(1/2)*298914i - b^7*c^17*d^37*e^7*(d + e*x)^(1/2)*627066i + b^8*c^16*d^36*e^8*(d + e*x)^(1/2)*548163i + b^9*c^15*d^35*e^9*(d + e*x)^(1/2)*953260i - b^10*c^14*d^34*e^10*(d + e*x)^(1/2)*4260564i + b^11*c^13*d^33*e^11*(d + e*x)^(1/2)*7526715i - b^12*c^12*d^32*e^12*(d + e*x)^(1/2)*7070070i + b^13*c^11*d^31*e^13*(d + e*x)^(1/2)*735546i + b^14*c^10*d^30*e^14*(d + e*x)^(1/2)*9071172i - b^15*c^9*d^29*e^15*(d + e*x)^(1/2)*16762207i + b^16*c^8*d^28*e^16*(d + e*x)^(1/2)*18354798i - b^17*c^7*d^27*e^17*(d + e*x)^(1/2)*14431032i + b^18*c^6*d^26*e^18*(d + e*x)^(1/2)*8573180i - b^19*c^5*d^25*e^19*(d + e*x)^(1/2)*3893967i + b^20*c^4*d^24*e^20*(d + e*x)^(1/2)*1340031i - b^21*c^3*d^23*e^21*(d + e*x)^(1/2)*339702i + b^22*c^2*d^22*e^22*(d + e*x)^(1/2)*60018i)/(d^9*(d^9)^(1/2)*(d^9*(d^9*(d^9*(13167*b^4*c^20*e^4 - 924*b^3*c^21*d*e^3) + 735546*b^13*c^11*e^13 - 7070070*b^12*c^12*d*e^12 - 83160*b^5*c^19*d^8*e^5 + 298914*b^6*c^18*d^7*e^6 - 627066*b^7*c^17*d^6*e^7 + 548163*b^8*c^16*d^5*e^8 + 953260*b^9*c^15*d^4*e^9 - 4260564*b^10*c^14*d^3*e^10 + 7526715*b^11*c^13*d^2*e^11) + 60018*b^22*c^2*e^22 - 339702*b^21*c^3*d*e^21 + 9071172*b^14*c^10*d^8*e^14 - 16762207*b^15*c^9*d^7*e^15 + 18354798*b^16*c^8*d^6*e^16 - 14431032*b^17*c^7*d^5*e^17 + 8573180*b^18*c^6*d^4*e^18 - 3893967*b^19*c^5*d^3*e^19 + 1340031*b^20*c^4*d^2*e^20) + 343*b^24*d^7*e^24 - 6615*b^23*c*d^8*e^23)))*(7*b*e + 4*c*d)*1i)/(b^3*(d^9)^(1/2))","B"
378,1,3946,300,1.473941,"\text{Not used}","int((d + e*x)^(9/2)/(b*x + c*x^2)^3,x)","\frac{\frac{{\left(d+e\,x\right)}^{3/2}\,\left(6\,b^5\,d\,e^6-5\,b^4\,c\,d^2\,e^5-74\,b^3\,c^2\,d^3\,e^4+217\,b^2\,c^3\,d^4\,e^3-216\,b\,c^4\,d^5\,e^2+72\,c^5\,d^6\,e\right)}{4\,b^4\,c^2}-\frac{3\,\sqrt{d+e\,x}\,\left(b^5\,d^2\,e^6-15\,b^3\,c^2\,d^4\,e^4+34\,b^2\,c^3\,d^5\,e^3-28\,b\,c^4\,d^6\,e^2+8\,c^5\,d^7\,e\right)}{4\,b^4\,c^2}+\frac{e\,{\left(d+e\,x\right)}^{7/2}\,\left(-5\,b^4\,e^4+3\,b^3\,c\,d\,e^3+21\,b^2\,c^2\,d^2\,e^2-48\,b\,c^3\,d^3\,e+24\,c^4\,d^4\right)}{4\,b^4\,c}+\frac{\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{5/2}\,\left(-3\,b^4\,e^5+4\,b^3\,c\,d\,e^4+32\,b^2\,c^2\,d^2\,e^3-72\,b\,c^3\,d^3\,e^2+36\,c^4\,d^4\,e\right)}{4\,b^4\,c^2}}{c^2\,{\left(d+e\,x\right)}^4-\left(d+e\,x\right)\,\left(2\,b^2\,d\,e^2-6\,b\,c\,d^2\,e+4\,c^2\,d^3\right)-\left(4\,c^2\,d-2\,b\,c\,e\right)\,{\left(d+e\,x\right)}^3+{\left(d+e\,x\right)}^2\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2\right)+c^2\,d^4+b^2\,d^2\,e^2-2\,b\,c\,d^3\,e}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{3\,\sqrt{d^5}\,\left(\frac{3\,b^{14}\,c^3\,d\,e^7+3\,b^{13}\,c^4\,d^2\,e^6-42\,b^{12}\,c^5\,d^3\,e^5+60\,b^{11}\,c^6\,d^4\,e^4-24\,b^{10}\,c^7\,d^5\,e^3}{b^{12}\,c^3}-\frac{3\,\left(64\,b^{11}\,c^5\,e^3-128\,b^{10}\,c^6\,d\,e^2\right)\,\sqrt{d^5}\,\sqrt{d+e\,x}\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)}{64\,b^{13}\,c^3}\right)\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5}-\frac{\sqrt{d+e\,x}\,\left(9\,b^{10}\,e^{12}+18\,b^9\,c\,d\,e^{11}+135\,b^8\,c^2\,d^2\,e^{10}-540\,b^7\,c^3\,d^3\,e^9+567\,b^6\,c^4\,d^4\,e^8-4158\,b^5\,c^5\,d^5\,e^7+21546\,b^4\,c^6\,d^6\,e^6-44928\,b^3\,c^7\,d^7\,e^5+45792\,b^2\,c^8\,d^8\,e^4-23040\,b\,c^9\,d^9\,e^3+4608\,c^{10}\,d^{10}\,e^2\right)}{8\,b^8\,c^3}\right)\,\sqrt{d^5}\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{8\,b^5}-\frac{\left(\frac{3\,\sqrt{d^5}\,\left(\frac{3\,b^{14}\,c^3\,d\,e^7+3\,b^{13}\,c^4\,d^2\,e^6-42\,b^{12}\,c^5\,d^3\,e^5+60\,b^{11}\,c^6\,d^4\,e^4-24\,b^{10}\,c^7\,d^5\,e^3}{b^{12}\,c^3}+\frac{3\,\left(64\,b^{11}\,c^5\,e^3-128\,b^{10}\,c^6\,d\,e^2\right)\,\sqrt{d^5}\,\sqrt{d+e\,x}\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)}{64\,b^{13}\,c^3}\right)\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5}+\frac{\sqrt{d+e\,x}\,\left(9\,b^{10}\,e^{12}+18\,b^9\,c\,d\,e^{11}+135\,b^8\,c^2\,d^2\,e^{10}-540\,b^7\,c^3\,d^3\,e^9+567\,b^6\,c^4\,d^4\,e^8-4158\,b^5\,c^5\,d^5\,e^7+21546\,b^4\,c^6\,d^6\,e^6-44928\,b^3\,c^7\,d^7\,e^5+45792\,b^2\,c^8\,d^8\,e^4-23040\,b\,c^9\,d^9\,e^3+4608\,c^{10}\,d^{10}\,e^2\right)}{8\,b^8\,c^3}\right)\,\sqrt{d^5}\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{8\,b^5}}{\frac{3\,\left(\frac{3\,\sqrt{d^5}\,\left(\frac{3\,b^{14}\,c^3\,d\,e^7+3\,b^{13}\,c^4\,d^2\,e^6-42\,b^{12}\,c^5\,d^3\,e^5+60\,b^{11}\,c^6\,d^4\,e^4-24\,b^{10}\,c^7\,d^5\,e^3}{b^{12}\,c^3}-\frac{3\,\left(64\,b^{11}\,c^5\,e^3-128\,b^{10}\,c^6\,d\,e^2\right)\,\sqrt{d^5}\,\sqrt{d+e\,x}\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)}{64\,b^{13}\,c^3}\right)\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5}-\frac{\sqrt{d+e\,x}\,\left(9\,b^{10}\,e^{12}+18\,b^9\,c\,d\,e^{11}+135\,b^8\,c^2\,d^2\,e^{10}-540\,b^7\,c^3\,d^3\,e^9+567\,b^6\,c^4\,d^4\,e^8-4158\,b^5\,c^5\,d^5\,e^7+21546\,b^4\,c^6\,d^6\,e^6-44928\,b^3\,c^7\,d^7\,e^5+45792\,b^2\,c^8\,d^8\,e^4-23040\,b\,c^9\,d^9\,e^3+4608\,c^{10}\,d^{10}\,e^2\right)}{8\,b^8\,c^3}\right)\,\sqrt{d^5}\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5}-\frac{\frac{567\,b^{11}\,d^3\,e^{14}}{32}+\frac{81\,b^{10}\,c\,d^4\,e^{13}}{16}+\frac{6993\,b^9\,c^2\,d^5\,e^{12}}{32}-\frac{35829\,b^8\,c^3\,d^6\,e^{11}}{32}+\frac{17901\,b^7\,c^4\,d^7\,e^{10}}{8}-\frac{253449\,b^6\,c^5\,d^8\,e^9}{32}+\frac{109917\,b^5\,c^6\,d^9\,e^8}{4}-\frac{211113\,b^4\,c^7\,d^{10}\,e^7}{4}+57240\,b^3\,c^8\,d^{11}\,e^6-35748\,b^2\,c^9\,d^{12}\,e^5+12096\,b\,c^{10}\,d^{13}\,e^4-1728\,c^{11}\,d^{14}\,e^3}{b^{12}\,c^3}+\frac{3\,\left(\frac{3\,\sqrt{d^5}\,\left(\frac{3\,b^{14}\,c^3\,d\,e^7+3\,b^{13}\,c^4\,d^2\,e^6-42\,b^{12}\,c^5\,d^3\,e^5+60\,b^{11}\,c^6\,d^4\,e^4-24\,b^{10}\,c^7\,d^5\,e^3}{b^{12}\,c^3}+\frac{3\,\left(64\,b^{11}\,c^5\,e^3-128\,b^{10}\,c^6\,d\,e^2\right)\,\sqrt{d^5}\,\sqrt{d+e\,x}\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)}{64\,b^{13}\,c^3}\right)\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5}+\frac{\sqrt{d+e\,x}\,\left(9\,b^{10}\,e^{12}+18\,b^9\,c\,d\,e^{11}+135\,b^8\,c^2\,d^2\,e^{10}-540\,b^7\,c^3\,d^3\,e^9+567\,b^6\,c^4\,d^4\,e^8-4158\,b^5\,c^5\,d^5\,e^7+21546\,b^4\,c^6\,d^6\,e^6-44928\,b^3\,c^7\,d^7\,e^5+45792\,b^2\,c^8\,d^8\,e^4-23040\,b\,c^9\,d^9\,e^3+4608\,c^{10}\,d^{10}\,e^2\right)}{8\,b^8\,c^3}\right)\,\sqrt{d^5}\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5}}\right)\,\sqrt{d^5}\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{4\,b^5}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{d+e\,x}\,\left(9\,b^{10}\,e^{12}+18\,b^9\,c\,d\,e^{11}+135\,b^8\,c^2\,d^2\,e^{10}-540\,b^7\,c^3\,d^3\,e^9+567\,b^6\,c^4\,d^4\,e^8-4158\,b^5\,c^5\,d^5\,e^7+21546\,b^4\,c^6\,d^6\,e^6-44928\,b^3\,c^7\,d^7\,e^5+45792\,b^2\,c^8\,d^8\,e^4-23040\,b\,c^9\,d^9\,e^3+4608\,c^{10}\,d^{10}\,e^2\right)}{8\,b^8\,c^3}-\frac{3\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{3\,b^{14}\,c^3\,d\,e^7+3\,b^{13}\,c^4\,d^2\,e^6-42\,b^{12}\,c^5\,d^3\,e^5+60\,b^{11}\,c^6\,d^4\,e^4-24\,b^{10}\,c^7\,d^5\,e^3}{b^{12}\,c^3}-\frac{3\,\left(64\,b^{11}\,c^5\,e^3-128\,b^{10}\,c^6\,d\,e^2\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\sqrt{d+e\,x}\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)}{64\,b^{13}\,c^8}\right)\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5\,c^5}\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{8\,b^5\,c^5}+\frac{\left(\frac{\sqrt{d+e\,x}\,\left(9\,b^{10}\,e^{12}+18\,b^9\,c\,d\,e^{11}+135\,b^8\,c^2\,d^2\,e^{10}-540\,b^7\,c^3\,d^3\,e^9+567\,b^6\,c^4\,d^4\,e^8-4158\,b^5\,c^5\,d^5\,e^7+21546\,b^4\,c^6\,d^6\,e^6-44928\,b^3\,c^7\,d^7\,e^5+45792\,b^2\,c^8\,d^8\,e^4-23040\,b\,c^9\,d^9\,e^3+4608\,c^{10}\,d^{10}\,e^2\right)}{8\,b^8\,c^3}+\frac{3\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{3\,b^{14}\,c^3\,d\,e^7+3\,b^{13}\,c^4\,d^2\,e^6-42\,b^{12}\,c^5\,d^3\,e^5+60\,b^{11}\,c^6\,d^4\,e^4-24\,b^{10}\,c^7\,d^5\,e^3}{b^{12}\,c^3}+\frac{3\,\left(64\,b^{11}\,c^5\,e^3-128\,b^{10}\,c^6\,d\,e^2\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\sqrt{d+e\,x}\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)}{64\,b^{13}\,c^8}\right)\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5\,c^5}\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{8\,b^5\,c^5}}{\frac{\frac{567\,b^{11}\,d^3\,e^{14}}{32}+\frac{81\,b^{10}\,c\,d^4\,e^{13}}{16}+\frac{6993\,b^9\,c^2\,d^5\,e^{12}}{32}-\frac{35829\,b^8\,c^3\,d^6\,e^{11}}{32}+\frac{17901\,b^7\,c^4\,d^7\,e^{10}}{8}-\frac{253449\,b^6\,c^5\,d^8\,e^9}{32}+\frac{109917\,b^5\,c^6\,d^9\,e^8}{4}-\frac{211113\,b^4\,c^7\,d^{10}\,e^7}{4}+57240\,b^3\,c^8\,d^{11}\,e^6-35748\,b^2\,c^9\,d^{12}\,e^5+12096\,b\,c^{10}\,d^{13}\,e^4-1728\,c^{11}\,d^{14}\,e^3}{b^{12}\,c^3}+\frac{3\,\left(\frac{\sqrt{d+e\,x}\,\left(9\,b^{10}\,e^{12}+18\,b^9\,c\,d\,e^{11}+135\,b^8\,c^2\,d^2\,e^{10}-540\,b^7\,c^3\,d^3\,e^9+567\,b^6\,c^4\,d^4\,e^8-4158\,b^5\,c^5\,d^5\,e^7+21546\,b^4\,c^6\,d^6\,e^6-44928\,b^3\,c^7\,d^7\,e^5+45792\,b^2\,c^8\,d^8\,e^4-23040\,b\,c^9\,d^9\,e^3+4608\,c^{10}\,d^{10}\,e^2\right)}{8\,b^8\,c^3}-\frac{3\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{3\,b^{14}\,c^3\,d\,e^7+3\,b^{13}\,c^4\,d^2\,e^6-42\,b^{12}\,c^5\,d^3\,e^5+60\,b^{11}\,c^6\,d^4\,e^4-24\,b^{10}\,c^7\,d^5\,e^3}{b^{12}\,c^3}-\frac{3\,\left(64\,b^{11}\,c^5\,e^3-128\,b^{10}\,c^6\,d\,e^2\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\sqrt{d+e\,x}\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)}{64\,b^{13}\,c^8}\right)\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5\,c^5}\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5\,c^5}-\frac{3\,\left(\frac{\sqrt{d+e\,x}\,\left(9\,b^{10}\,e^{12}+18\,b^9\,c\,d\,e^{11}+135\,b^8\,c^2\,d^2\,e^{10}-540\,b^7\,c^3\,d^3\,e^9+567\,b^6\,c^4\,d^4\,e^8-4158\,b^5\,c^5\,d^5\,e^7+21546\,b^4\,c^6\,d^6\,e^6-44928\,b^3\,c^7\,d^7\,e^5+45792\,b^2\,c^8\,d^8\,e^4-23040\,b\,c^9\,d^9\,e^3+4608\,c^{10}\,d^{10}\,e^2\right)}{8\,b^8\,c^3}+\frac{3\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{3\,b^{14}\,c^3\,d\,e^7+3\,b^{13}\,c^4\,d^2\,e^6-42\,b^{12}\,c^5\,d^3\,e^5+60\,b^{11}\,c^6\,d^4\,e^4-24\,b^{10}\,c^7\,d^5\,e^3}{b^{12}\,c^3}+\frac{3\,\left(64\,b^{11}\,c^5\,e^3-128\,b^{10}\,c^6\,d\,e^2\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\sqrt{d+e\,x}\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)}{64\,b^{13}\,c^8}\right)\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5\,c^5}\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5\,c^5}}\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{4\,b^5\,c^5}","Not used",1,"(((d + e*x)^(3/2)*(6*b^5*d*e^6 + 72*c^5*d^6*e - 216*b*c^4*d^5*e^2 - 5*b^4*c*d^2*e^5 + 217*b^2*c^3*d^4*e^3 - 74*b^3*c^2*d^3*e^4))/(4*b^4*c^2) - (3*(d + e*x)^(1/2)*(8*c^5*d^7*e + b^5*d^2*e^6 - 28*b*c^4*d^6*e^2 + 34*b^2*c^3*d^5*e^3 - 15*b^3*c^2*d^4*e^4))/(4*b^4*c^2) + (e*(d + e*x)^(7/2)*(24*c^4*d^4 - 5*b^4*e^4 + 21*b^2*c^2*d^2*e^2 - 48*b*c^3*d^3*e + 3*b^3*c*d*e^3))/(4*b^4*c) + ((b*e - 2*c*d)*(d + e*x)^(5/2)*(36*c^4*d^4*e - 3*b^4*e^5 - 72*b*c^3*d^3*e^2 + 32*b^2*c^2*d^2*e^3 + 4*b^3*c*d*e^4))/(4*b^4*c^2))/(c^2*(d + e*x)^4 - (d + e*x)*(4*c^2*d^3 + 2*b^2*d*e^2 - 6*b*c*d^2*e) - (4*c^2*d - 2*b*c*e)*(d + e*x)^3 + (d + e*x)^2*(b^2*e^2 + 6*c^2*d^2 - 6*b*c*d*e) + c^2*d^4 + b^2*d^2*e^2 - 2*b*c*d^3*e) + (atan(((((3*(d^5)^(1/2)*((3*b^14*c^3*d*e^7 - 24*b^10*c^7*d^5*e^3 + 60*b^11*c^6*d^4*e^4 - 42*b^12*c^5*d^3*e^5 + 3*b^13*c^4*d^2*e^6)/(b^12*c^3) - (3*(64*b^11*c^5*e^3 - 128*b^10*c^6*d*e^2)*(d^5)^(1/2)*(d + e*x)^(1/2)*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e))/(64*b^13*c^3))*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e))/(8*b^5) - ((d + e*x)^(1/2)*(9*b^10*e^12 + 4608*c^10*d^10*e^2 - 23040*b*c^9*d^9*e^3 + 45792*b^2*c^8*d^8*e^4 - 44928*b^3*c^7*d^7*e^5 + 21546*b^4*c^6*d^6*e^6 - 4158*b^5*c^5*d^5*e^7 + 567*b^6*c^4*d^4*e^8 - 540*b^7*c^3*d^3*e^9 + 135*b^8*c^2*d^2*e^10 + 18*b^9*c*d*e^11))/(8*b^8*c^3))*(d^5)^(1/2)*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e)*3i)/(8*b^5) - (((3*(d^5)^(1/2)*((3*b^14*c^3*d*e^7 - 24*b^10*c^7*d^5*e^3 + 60*b^11*c^6*d^4*e^4 - 42*b^12*c^5*d^3*e^5 + 3*b^13*c^4*d^2*e^6)/(b^12*c^3) + (3*(64*b^11*c^5*e^3 - 128*b^10*c^6*d*e^2)*(d^5)^(1/2)*(d + e*x)^(1/2)*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e))/(64*b^13*c^3))*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e))/(8*b^5) + ((d + e*x)^(1/2)*(9*b^10*e^12 + 4608*c^10*d^10*e^2 - 23040*b*c^9*d^9*e^3 + 45792*b^2*c^8*d^8*e^4 - 44928*b^3*c^7*d^7*e^5 + 21546*b^4*c^6*d^6*e^6 - 4158*b^5*c^5*d^5*e^7 + 567*b^6*c^4*d^4*e^8 - 540*b^7*c^3*d^3*e^9 + 135*b^8*c^2*d^2*e^10 + 18*b^9*c*d*e^11))/(8*b^8*c^3))*(d^5)^(1/2)*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e)*3i)/(8*b^5))/((3*((3*(d^5)^(1/2)*((3*b^14*c^3*d*e^7 - 24*b^10*c^7*d^5*e^3 + 60*b^11*c^6*d^4*e^4 - 42*b^12*c^5*d^3*e^5 + 3*b^13*c^4*d^2*e^6)/(b^12*c^3) - (3*(64*b^11*c^5*e^3 - 128*b^10*c^6*d*e^2)*(d^5)^(1/2)*(d + e*x)^(1/2)*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e))/(64*b^13*c^3))*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e))/(8*b^5) - ((d + e*x)^(1/2)*(9*b^10*e^12 + 4608*c^10*d^10*e^2 - 23040*b*c^9*d^9*e^3 + 45792*b^2*c^8*d^8*e^4 - 44928*b^3*c^7*d^7*e^5 + 21546*b^4*c^6*d^6*e^6 - 4158*b^5*c^5*d^5*e^7 + 567*b^6*c^4*d^4*e^8 - 540*b^7*c^3*d^3*e^9 + 135*b^8*c^2*d^2*e^10 + 18*b^9*c*d*e^11))/(8*b^8*c^3))*(d^5)^(1/2)*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e))/(8*b^5) - ((567*b^11*d^3*e^14)/32 - 1728*c^11*d^14*e^3 + 12096*b*c^10*d^13*e^4 + (81*b^10*c*d^4*e^13)/16 - 35748*b^2*c^9*d^12*e^5 + 57240*b^3*c^8*d^11*e^6 - (211113*b^4*c^7*d^10*e^7)/4 + (109917*b^5*c^6*d^9*e^8)/4 - (253449*b^6*c^5*d^8*e^9)/32 + (17901*b^7*c^4*d^7*e^10)/8 - (35829*b^8*c^3*d^6*e^11)/32 + (6993*b^9*c^2*d^5*e^12)/32)/(b^12*c^3) + (3*((3*(d^5)^(1/2)*((3*b^14*c^3*d*e^7 - 24*b^10*c^7*d^5*e^3 + 60*b^11*c^6*d^4*e^4 - 42*b^12*c^5*d^3*e^5 + 3*b^13*c^4*d^2*e^6)/(b^12*c^3) + (3*(64*b^11*c^5*e^3 - 128*b^10*c^6*d*e^2)*(d^5)^(1/2)*(d + e*x)^(1/2)*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e))/(64*b^13*c^3))*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e))/(8*b^5) + ((d + e*x)^(1/2)*(9*b^10*e^12 + 4608*c^10*d^10*e^2 - 23040*b*c^9*d^9*e^3 + 45792*b^2*c^8*d^8*e^4 - 44928*b^3*c^7*d^7*e^5 + 21546*b^4*c^6*d^6*e^6 - 4158*b^5*c^5*d^5*e^7 + 567*b^6*c^4*d^4*e^8 - 540*b^7*c^3*d^3*e^9 + 135*b^8*c^2*d^2*e^10 + 18*b^9*c*d*e^11))/(8*b^8*c^3))*(d^5)^(1/2)*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e))/(8*b^5)))*(d^5)^(1/2)*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e)*3i)/(4*b^5) + (atan((((((d + e*x)^(1/2)*(9*b^10*e^12 + 4608*c^10*d^10*e^2 - 23040*b*c^9*d^9*e^3 + 45792*b^2*c^8*d^8*e^4 - 44928*b^3*c^7*d^7*e^5 + 21546*b^4*c^6*d^6*e^6 - 4158*b^5*c^5*d^5*e^7 + 567*b^6*c^4*d^4*e^8 - 540*b^7*c^3*d^3*e^9 + 135*b^8*c^2*d^2*e^10 + 18*b^9*c*d*e^11))/(8*b^8*c^3) - (3*(-c^5*(b*e - c*d)^5)^(1/2)*((3*b^14*c^3*d*e^7 - 24*b^10*c^7*d^5*e^3 + 60*b^11*c^6*d^4*e^4 - 42*b^12*c^5*d^3*e^5 + 3*b^13*c^4*d^2*e^6)/(b^12*c^3) - (3*(64*b^11*c^5*e^3 - 128*b^10*c^6*d*e^2)*(-c^5*(b*e - c*d)^5)^(1/2)*(d + e*x)^(1/2)*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e))/(64*b^13*c^8))*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e))/(8*b^5*c^5))*(-c^5*(b*e - c*d)^5)^(1/2)*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e)*3i)/(8*b^5*c^5) + ((((d + e*x)^(1/2)*(9*b^10*e^12 + 4608*c^10*d^10*e^2 - 23040*b*c^9*d^9*e^3 + 45792*b^2*c^8*d^8*e^4 - 44928*b^3*c^7*d^7*e^5 + 21546*b^4*c^6*d^6*e^6 - 4158*b^5*c^5*d^5*e^7 + 567*b^6*c^4*d^4*e^8 - 540*b^7*c^3*d^3*e^9 + 135*b^8*c^2*d^2*e^10 + 18*b^9*c*d*e^11))/(8*b^8*c^3) + (3*(-c^5*(b*e - c*d)^5)^(1/2)*((3*b^14*c^3*d*e^7 - 24*b^10*c^7*d^5*e^3 + 60*b^11*c^6*d^4*e^4 - 42*b^12*c^5*d^3*e^5 + 3*b^13*c^4*d^2*e^6)/(b^12*c^3) + (3*(64*b^11*c^5*e^3 - 128*b^10*c^6*d*e^2)*(-c^5*(b*e - c*d)^5)^(1/2)*(d + e*x)^(1/2)*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e))/(64*b^13*c^8))*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e))/(8*b^5*c^5))*(-c^5*(b*e - c*d)^5)^(1/2)*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e)*3i)/(8*b^5*c^5))/(((567*b^11*d^3*e^14)/32 - 1728*c^11*d^14*e^3 + 12096*b*c^10*d^13*e^4 + (81*b^10*c*d^4*e^13)/16 - 35748*b^2*c^9*d^12*e^5 + 57240*b^3*c^8*d^11*e^6 - (211113*b^4*c^7*d^10*e^7)/4 + (109917*b^5*c^6*d^9*e^8)/4 - (253449*b^6*c^5*d^8*e^9)/32 + (17901*b^7*c^4*d^7*e^10)/8 - (35829*b^8*c^3*d^6*e^11)/32 + (6993*b^9*c^2*d^5*e^12)/32)/(b^12*c^3) + (3*(((d + e*x)^(1/2)*(9*b^10*e^12 + 4608*c^10*d^10*e^2 - 23040*b*c^9*d^9*e^3 + 45792*b^2*c^8*d^8*e^4 - 44928*b^3*c^7*d^7*e^5 + 21546*b^4*c^6*d^6*e^6 - 4158*b^5*c^5*d^5*e^7 + 567*b^6*c^4*d^4*e^8 - 540*b^7*c^3*d^3*e^9 + 135*b^8*c^2*d^2*e^10 + 18*b^9*c*d*e^11))/(8*b^8*c^3) - (3*(-c^5*(b*e - c*d)^5)^(1/2)*((3*b^14*c^3*d*e^7 - 24*b^10*c^7*d^5*e^3 + 60*b^11*c^6*d^4*e^4 - 42*b^12*c^5*d^3*e^5 + 3*b^13*c^4*d^2*e^6)/(b^12*c^3) - (3*(64*b^11*c^5*e^3 - 128*b^10*c^6*d*e^2)*(-c^5*(b*e - c*d)^5)^(1/2)*(d + e*x)^(1/2)*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e))/(64*b^13*c^8))*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e))/(8*b^5*c^5))*(-c^5*(b*e - c*d)^5)^(1/2)*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e))/(8*b^5*c^5) - (3*(((d + e*x)^(1/2)*(9*b^10*e^12 + 4608*c^10*d^10*e^2 - 23040*b*c^9*d^9*e^3 + 45792*b^2*c^8*d^8*e^4 - 44928*b^3*c^7*d^7*e^5 + 21546*b^4*c^6*d^6*e^6 - 4158*b^5*c^5*d^5*e^7 + 567*b^6*c^4*d^4*e^8 - 540*b^7*c^3*d^3*e^9 + 135*b^8*c^2*d^2*e^10 + 18*b^9*c*d*e^11))/(8*b^8*c^3) + (3*(-c^5*(b*e - c*d)^5)^(1/2)*((3*b^14*c^3*d*e^7 - 24*b^10*c^7*d^5*e^3 + 60*b^11*c^6*d^4*e^4 - 42*b^12*c^5*d^3*e^5 + 3*b^13*c^4*d^2*e^6)/(b^12*c^3) + (3*(64*b^11*c^5*e^3 - 128*b^10*c^6*d*e^2)*(-c^5*(b*e - c*d)^5)^(1/2)*(d + e*x)^(1/2)*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e))/(64*b^13*c^8))*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e))/(8*b^5*c^5))*(-c^5*(b*e - c*d)^5)^(1/2)*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e))/(8*b^5*c^5)))*(-c^5*(b*e - c*d)^5)^(1/2)*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e)*3i)/(4*b^5*c^5)","B"
379,1,1792,248,0.734205,"\text{Not used}","int((d + e*x)^(7/2)/(b*x + c*x^2)^3,x)","-\frac{\frac{\sqrt{d+e\,x}\,\left(b^4\,d^2\,e^5-26\,b^3\,c\,d^3\,e^4+73\,b^2\,c^2\,d^4\,e^3-72\,b\,c^3\,d^5\,e^2+24\,c^4\,d^6\,e\right)}{4\,b^4\,c}-\frac{e\,{\left(d+e\,x\right)}^{7/2}\,\left(b^3\,e^3+10\,b^2\,c\,d\,e^2-36\,b\,c^2\,d^2\,e+24\,c^3\,d^3\right)}{4\,b^4}-\frac{{\left(d+e\,x\right)}^{3/2}\,\left(b^4\,d\,e^5-21\,b^3\,c\,d^2\,e^4+74\,b^2\,c^2\,d^3\,e^3-90\,b\,c^3\,d^4\,e^2+36\,c^4\,d^5\,e\right)}{2\,b^4\,c}+\frac{e\,{\left(d+e\,x\right)}^{5/2}\,\left(b^4\,e^4-13\,b^3\,c\,d\,e^3+85\,b^2\,c^2\,d^2\,e^2-144\,b\,c^3\,d^3\,e+72\,c^4\,d^4\right)}{4\,b^4\,c}}{c^2\,{\left(d+e\,x\right)}^4-\left(d+e\,x\right)\,\left(2\,b^2\,d\,e^2-6\,b\,c\,d^2\,e+4\,c^2\,d^3\right)-\left(4\,c^2\,d-2\,b\,c\,e\right)\,{\left(d+e\,x\right)}^3+{\left(d+e\,x\right)}^2\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2\right)+c^2\,d^4+b^2\,d^2\,e^2-2\,b\,c\,d^3\,e}-\frac{\mathrm{atanh}\left(\frac{35\,e^{12}\,\sqrt{d^3}\,\sqrt{d+e\,x}}{32\,\left(\frac{35\,d^2\,e^{12}}{32}+\frac{77\,c\,d^3\,e^{11}}{4\,b}-\frac{1551\,c^2\,d^4\,e^{10}}{16\,b^2}+\frac{5223\,c^3\,d^5\,e^9}{32\,b^3}-\frac{945\,c^4\,d^6\,e^8}{8\,b^4}+\frac{63\,c^5\,d^7\,e^7}{2\,b^5}\right)}+\frac{77\,d\,e^{11}\,\sqrt{d^3}\,\sqrt{d+e\,x}}{4\,\left(\frac{77\,d^3\,e^{11}}{4}+\frac{35\,b\,d^2\,e^{12}}{32\,c}-\frac{1551\,c\,d^4\,e^{10}}{16\,b}+\frac{5223\,c^2\,d^5\,e^9}{32\,b^2}-\frac{945\,c^3\,d^6\,e^8}{8\,b^3}+\frac{63\,c^4\,d^7\,e^7}{2\,b^4}\right)}+\frac{5223\,c^2\,d^3\,e^9\,\sqrt{d^3}\,\sqrt{d+e\,x}}{32\,\left(\frac{77\,b^2\,d^3\,e^{11}}{4}+\frac{5223\,c^2\,d^5\,e^9}{32}-\frac{945\,c^3\,d^6\,e^8}{8\,b}+\frac{35\,b^3\,d^2\,e^{12}}{32\,c}+\frac{63\,c^4\,d^7\,e^7}{2\,b^2}-\frac{1551\,b\,c\,d^4\,e^{10}}{16}\right)}-\frac{945\,c^3\,d^4\,e^8\,\sqrt{d^3}\,\sqrt{d+e\,x}}{8\,\left(\frac{77\,b^3\,d^3\,e^{11}}{4}-\frac{945\,c^3\,d^6\,e^8}{8}+\frac{5223\,b\,c^2\,d^5\,e^9}{32}-\frac{1551\,b^2\,c\,d^4\,e^{10}}{16}+\frac{63\,c^4\,d^7\,e^7}{2\,b}+\frac{35\,b^4\,d^2\,e^{12}}{32\,c}\right)}+\frac{63\,c^4\,d^5\,e^7\,\sqrt{d^3}\,\sqrt{d+e\,x}}{2\,\left(\frac{77\,b^4\,d^3\,e^{11}}{4}+\frac{63\,c^4\,d^7\,e^7}{2}-\frac{945\,b\,c^3\,d^6\,e^8}{8}-\frac{1551\,b^3\,c\,d^4\,e^{10}}{16}+\frac{5223\,b^2\,c^2\,d^5\,e^9}{32}+\frac{35\,b^5\,d^2\,e^{12}}{32\,c}\right)}-\frac{1551\,c\,d^2\,e^{10}\,\sqrt{d^3}\,\sqrt{d+e\,x}}{16\,\left(\frac{77\,b\,d^3\,e^{11}}{4}-\frac{1551\,c\,d^4\,e^{10}}{16}+\frac{5223\,c^2\,d^5\,e^9}{32\,b}+\frac{35\,b^2\,d^2\,e^{12}}{32\,c}-\frac{945\,c^3\,d^6\,e^8}{8\,b^2}+\frac{63\,c^4\,d^7\,e^7}{2\,b^3}\right)}\right)\,\sqrt{d^3}\,\left(35\,b^2\,e^2-84\,b\,c\,d\,e+48\,c^2\,d^2\right)}{4\,b^5}-\frac{\mathrm{atanh}\left(\frac{183\,d^3\,e^9\,\sqrt{d+e\,x}\,\sqrt{-b^3\,c^3\,e^3+3\,b^2\,c^4\,d\,e^2-3\,b\,c^5\,d^2\,e+c^6\,d^3}}{32\,\left(\frac{31\,b^3\,d^2\,e^{12}}{32}+\frac{3711\,c^3\,d^5\,e^9}{32}-\frac{1593\,b\,c^2\,d^4\,e^{10}}{32}+\frac{59\,b^2\,c\,d^3\,e^{11}}{16}+\frac{b^4\,d\,e^{13}}{32\,c}-\frac{819\,c^4\,d^6\,e^8}{8\,b}+\frac{63\,c^5\,d^7\,e^7}{2\,b^2}\right)}-\frac{315\,d^4\,e^8\,\sqrt{d+e\,x}\,\sqrt{-b^3\,c^3\,e^3+3\,b^2\,c^4\,d\,e^2-3\,b\,c^5\,d^2\,e+c^6\,d^3}}{8\,\left(\frac{59\,b^3\,d^3\,e^{11}}{16}-\frac{819\,c^3\,d^6\,e^8}{8}+\frac{3711\,b\,c^2\,d^5\,e^9}{32}-\frac{1593\,b^2\,c\,d^4\,e^{10}}{32}+\frac{b^5\,d\,e^{13}}{32\,c^2}+\frac{63\,c^4\,d^7\,e^7}{2\,b}+\frac{31\,b^4\,d^2\,e^{12}}{32\,c}\right)}+\frac{33\,d^2\,e^{10}\,\sqrt{d+e\,x}\,\sqrt{-b^3\,c^3\,e^3+3\,b^2\,c^4\,d\,e^2-3\,b\,c^5\,d^2\,e+c^6\,d^3}}{32\,\left(\frac{b^3\,d\,e^{13}}{32}-\frac{1593\,c^3\,d^4\,e^{10}}{32}+\frac{59\,b\,c^2\,d^3\,e^{11}}{16}+\frac{31\,b^2\,c\,d^2\,e^{12}}{32}+\frac{3711\,c^4\,d^5\,e^9}{32\,b}-\frac{819\,c^5\,d^6\,e^8}{8\,b^2}+\frac{63\,c^6\,d^7\,e^7}{2\,b^3}\right)}+\frac{d\,e^{11}\,\sqrt{d+e\,x}\,\sqrt{-b^3\,c^3\,e^3+3\,b^2\,c^4\,d\,e^2-3\,b\,c^5\,d^2\,e+c^6\,d^3}}{32\,\left(\frac{59\,c^3\,d^3\,e^{11}}{16}+\frac{31\,b\,c^2\,d^2\,e^{12}}{32}-\frac{1593\,c^4\,d^4\,e^{10}}{32\,b}+\frac{3711\,c^5\,d^5\,e^9}{32\,b^2}-\frac{819\,c^6\,d^6\,e^8}{8\,b^3}+\frac{63\,c^7\,d^7\,e^7}{2\,b^4}+\frac{b^2\,c\,d\,e^{13}}{32}\right)}+\frac{63\,c\,d^5\,e^7\,\sqrt{d+e\,x}\,\sqrt{-b^3\,c^3\,e^3+3\,b^2\,c^4\,d\,e^2-3\,b\,c^5\,d^2\,e+c^6\,d^3}}{2\,\left(\frac{59\,b^4\,d^3\,e^{11}}{16}+\frac{63\,c^4\,d^7\,e^7}{2}-\frac{819\,b\,c^3\,d^6\,e^8}{8}-\frac{1593\,b^3\,c\,d^4\,e^{10}}{32}+\frac{b^6\,d\,e^{13}}{32\,c^2}+\frac{3711\,b^2\,c^2\,d^5\,e^9}{32}+\frac{31\,b^5\,d^2\,e^{12}}{32\,c}\right)}\right)\,\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(b^2\,e^2+12\,b\,c\,d\,e-48\,c^2\,d^2\right)}{4\,b^5\,c^3}","Not used",1,"- (((d + e*x)^(1/2)*(24*c^4*d^6*e + b^4*d^2*e^5 - 72*b*c^3*d^5*e^2 - 26*b^3*c*d^3*e^4 + 73*b^2*c^2*d^4*e^3))/(4*b^4*c) - (e*(d + e*x)^(7/2)*(b^3*e^3 + 24*c^3*d^3 - 36*b*c^2*d^2*e + 10*b^2*c*d*e^2))/(4*b^4) - ((d + e*x)^(3/2)*(b^4*d*e^5 + 36*c^4*d^5*e - 90*b*c^3*d^4*e^2 - 21*b^3*c*d^2*e^4 + 74*b^2*c^2*d^3*e^3))/(2*b^4*c) + (e*(d + e*x)^(5/2)*(b^4*e^4 + 72*c^4*d^4 + 85*b^2*c^2*d^2*e^2 - 144*b*c^3*d^3*e - 13*b^3*c*d*e^3))/(4*b^4*c))/(c^2*(d + e*x)^4 - (d + e*x)*(4*c^2*d^3 + 2*b^2*d*e^2 - 6*b*c*d^2*e) - (4*c^2*d - 2*b*c*e)*(d + e*x)^3 + (d + e*x)^2*(b^2*e^2 + 6*c^2*d^2 - 6*b*c*d*e) + c^2*d^4 + b^2*d^2*e^2 - 2*b*c*d^3*e) - (atanh((35*e^12*(d^3)^(1/2)*(d + e*x)^(1/2))/(32*((35*d^2*e^12)/32 + (77*c*d^3*e^11)/(4*b) - (1551*c^2*d^4*e^10)/(16*b^2) + (5223*c^3*d^5*e^9)/(32*b^3) - (945*c^4*d^6*e^8)/(8*b^4) + (63*c^5*d^7*e^7)/(2*b^5))) + (77*d*e^11*(d^3)^(1/2)*(d + e*x)^(1/2))/(4*((77*d^3*e^11)/4 + (35*b*d^2*e^12)/(32*c) - (1551*c*d^4*e^10)/(16*b) + (5223*c^2*d^5*e^9)/(32*b^2) - (945*c^3*d^6*e^8)/(8*b^3) + (63*c^4*d^7*e^7)/(2*b^4))) + (5223*c^2*d^3*e^9*(d^3)^(1/2)*(d + e*x)^(1/2))/(32*((77*b^2*d^3*e^11)/4 + (5223*c^2*d^5*e^9)/32 - (945*c^3*d^6*e^8)/(8*b) + (35*b^3*d^2*e^12)/(32*c) + (63*c^4*d^7*e^7)/(2*b^2) - (1551*b*c*d^4*e^10)/16)) - (945*c^3*d^4*e^8*(d^3)^(1/2)*(d + e*x)^(1/2))/(8*((77*b^3*d^3*e^11)/4 - (945*c^3*d^6*e^8)/8 + (5223*b*c^2*d^5*e^9)/32 - (1551*b^2*c*d^4*e^10)/16 + (63*c^4*d^7*e^7)/(2*b) + (35*b^4*d^2*e^12)/(32*c))) + (63*c^4*d^5*e^7*(d^3)^(1/2)*(d + e*x)^(1/2))/(2*((77*b^4*d^3*e^11)/4 + (63*c^4*d^7*e^7)/2 - (945*b*c^3*d^6*e^8)/8 - (1551*b^3*c*d^4*e^10)/16 + (5223*b^2*c^2*d^5*e^9)/32 + (35*b^5*d^2*e^12)/(32*c))) - (1551*c*d^2*e^10*(d^3)^(1/2)*(d + e*x)^(1/2))/(16*((77*b*d^3*e^11)/4 - (1551*c*d^4*e^10)/16 + (5223*c^2*d^5*e^9)/(32*b) + (35*b^2*d^2*e^12)/(32*c) - (945*c^3*d^6*e^8)/(8*b^2) + (63*c^4*d^7*e^7)/(2*b^3))))*(d^3)^(1/2)*(35*b^2*e^2 + 48*c^2*d^2 - 84*b*c*d*e))/(4*b^5) - (atanh((183*d^3*e^9*(d + e*x)^(1/2)*(c^6*d^3 - b^3*c^3*e^3 + 3*b^2*c^4*d*e^2 - 3*b*c^5*d^2*e)^(1/2))/(32*((31*b^3*d^2*e^12)/32 + (3711*c^3*d^5*e^9)/32 - (1593*b*c^2*d^4*e^10)/32 + (59*b^2*c*d^3*e^11)/16 + (b^4*d*e^13)/(32*c) - (819*c^4*d^6*e^8)/(8*b) + (63*c^5*d^7*e^7)/(2*b^2))) - (315*d^4*e^8*(d + e*x)^(1/2)*(c^6*d^3 - b^3*c^3*e^3 + 3*b^2*c^4*d*e^2 - 3*b*c^5*d^2*e)^(1/2))/(8*((59*b^3*d^3*e^11)/16 - (819*c^3*d^6*e^8)/8 + (3711*b*c^2*d^5*e^9)/32 - (1593*b^2*c*d^4*e^10)/32 + (b^5*d*e^13)/(32*c^2) + (63*c^4*d^7*e^7)/(2*b) + (31*b^4*d^2*e^12)/(32*c))) + (33*d^2*e^10*(d + e*x)^(1/2)*(c^6*d^3 - b^3*c^3*e^3 + 3*b^2*c^4*d*e^2 - 3*b*c^5*d^2*e)^(1/2))/(32*((b^3*d*e^13)/32 - (1593*c^3*d^4*e^10)/32 + (59*b*c^2*d^3*e^11)/16 + (31*b^2*c*d^2*e^12)/32 + (3711*c^4*d^5*e^9)/(32*b) - (819*c^5*d^6*e^8)/(8*b^2) + (63*c^6*d^7*e^7)/(2*b^3))) + (d*e^11*(d + e*x)^(1/2)*(c^6*d^3 - b^3*c^3*e^3 + 3*b^2*c^4*d*e^2 - 3*b*c^5*d^2*e)^(1/2))/(32*((59*c^3*d^3*e^11)/16 + (31*b*c^2*d^2*e^12)/32 - (1593*c^4*d^4*e^10)/(32*b) + (3711*c^5*d^5*e^9)/(32*b^2) - (819*c^6*d^6*e^8)/(8*b^3) + (63*c^7*d^7*e^7)/(2*b^4) + (b^2*c*d*e^13)/32)) + (63*c*d^5*e^7*(d + e*x)^(1/2)*(c^6*d^3 - b^3*c^3*e^3 + 3*b^2*c^4*d*e^2 - 3*b*c^5*d^2*e)^(1/2))/(2*((59*b^4*d^3*e^11)/16 + (63*c^4*d^7*e^7)/2 - (819*b*c^3*d^6*e^8)/8 - (1593*b^3*c*d^4*e^10)/32 + (b^6*d*e^13)/(32*c^2) + (3711*b^2*c^2*d^5*e^9)/32 + (31*b^5*d^2*e^12)/(32*c))))*(-c^3*(b*e - c*d)^3)^(1/2)*(b^2*e^2 - 48*c^2*d^2 + 12*b*c*d*e))/(4*b^5*c^3)","B"
380,1,910,232,0.577121,"\text{Not used}","int((d + e*x)^(5/2)/(b*x + c*x^2)^3,x)","\frac{3\,\mathrm{atanh}\left(\frac{81\,c^2\,d^2\,e^8\,\sqrt{c^2\,d-b\,c\,e}\,\sqrt{d+e\,x}}{8\,\left(\frac{189\,c^3\,d^3\,e^8}{8}-\frac{351\,b\,c^2\,d^2\,e^9}{32}-\frac{27\,c^4\,d^4\,e^7}{2\,b}+\frac{27\,b^2\,c\,d\,e^{10}}{32}\right)}+\frac{27\,c^3\,d^3\,e^7\,\sqrt{c^2\,d-b\,c\,e}\,\sqrt{d+e\,x}}{2\,\left(-\frac{27\,b^3\,c\,d\,e^{10}}{32}+\frac{351\,b^2\,c^2\,d^2\,e^9}{32}-\frac{189\,b\,c^3\,d^3\,e^8}{8}+\frac{27\,c^4\,d^4\,e^7}{2}\right)}+\frac{27\,c\,d\,e^9\,\sqrt{c^2\,d-b\,c\,e}\,\sqrt{d+e\,x}}{32\,\left(\frac{351\,c^2\,d^2\,e^9}{32}-\frac{27\,b\,c\,d\,e^{10}}{32}-\frac{189\,c^3\,d^3\,e^8}{8\,b}+\frac{27\,c^4\,d^4\,e^7}{2\,b^2}\right)}\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(b^2\,e^2-12\,b\,c\,d\,e+16\,c^2\,d^2\right)}{4\,b^5\,c}-\frac{3\,\sqrt{d}\,\mathrm{atanh}\left(\frac{135\,c\,\sqrt{d}\,e^{10}\,\sqrt{d+e\,x}}{32\,\left(\frac{135\,c\,d\,e^{10}}{32}-\frac{675\,c^2\,d^2\,e^9}{32\,b}+\frac{243\,c^3\,d^3\,e^8}{8\,b^2}-\frac{27\,c^4\,d^4\,e^7}{2\,b^3}\right)}+\frac{675\,c^2\,d^{3/2}\,e^9\,\sqrt{d+e\,x}}{32\,\left(\frac{675\,c^2\,d^2\,e^9}{32}-\frac{135\,b\,c\,d\,e^{10}}{32}-\frac{243\,c^3\,d^3\,e^8}{8\,b}+\frac{27\,c^4\,d^4\,e^7}{2\,b^2}\right)}+\frac{243\,c^3\,d^{5/2}\,e^8\,\sqrt{d+e\,x}}{8\,\left(\frac{243\,c^3\,d^3\,e^8}{8}-\frac{675\,b\,c^2\,d^2\,e^9}{32}-\frac{27\,c^4\,d^4\,e^7}{2\,b}+\frac{135\,b^2\,c\,d\,e^{10}}{32}\right)}+\frac{27\,c^4\,d^{7/2}\,e^7\,\sqrt{d+e\,x}}{2\,\left(-\frac{135\,b^3\,c\,d\,e^{10}}{32}+\frac{675\,b^2\,c^2\,d^2\,e^9}{32}-\frac{243\,b\,c^3\,d^3\,e^8}{8}+\frac{27\,c^4\,d^4\,e^7}{2}\right)}\right)\,\left(5\,b^2\,e^2-20\,b\,c\,d\,e+16\,c^2\,d^2\right)}{4\,b^5}-\frac{\frac{{\left(d+e\,x\right)}^{3/2}\,\left(19\,b^3\,d\,e^4-91\,b^2\,c\,d^2\,e^3+144\,b\,c^2\,d^3\,e^2-72\,c^3\,d^4\,e\right)}{4\,b^4}+\frac{3\,\sqrt{d+e\,x}\,\left(-b^3\,d^2\,e^4+4\,b^2\,c\,d^3\,e^3-5\,b\,c^2\,d^4\,e^2+2\,c^3\,d^5\,e\right)}{b^4}-\frac{\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{5/2}\,\left(5\,b^2\,e^3-36\,b\,c\,d\,e^2+36\,c^2\,d^2\,e\right)}{4\,b^4}-\frac{3\,c\,e\,{\left(d+e\,x\right)}^{7/2}\,\left(b^2\,e^2-8\,b\,c\,d\,e+8\,c^2\,d^2\right)}{4\,b^4}}{c^2\,{\left(d+e\,x\right)}^4-\left(d+e\,x\right)\,\left(2\,b^2\,d\,e^2-6\,b\,c\,d^2\,e+4\,c^2\,d^3\right)-\left(4\,c^2\,d-2\,b\,c\,e\right)\,{\left(d+e\,x\right)}^3+{\left(d+e\,x\right)}^2\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2\right)+c^2\,d^4+b^2\,d^2\,e^2-2\,b\,c\,d^3\,e}","Not used",1,"(3*atanh((81*c^2*d^2*e^8*(c^2*d - b*c*e)^(1/2)*(d + e*x)^(1/2))/(8*((189*c^3*d^3*e^8)/8 - (351*b*c^2*d^2*e^9)/32 - (27*c^4*d^4*e^7)/(2*b) + (27*b^2*c*d*e^10)/32)) + (27*c^3*d^3*e^7*(c^2*d - b*c*e)^(1/2)*(d + e*x)^(1/2))/(2*((27*c^4*d^4*e^7)/2 - (189*b*c^3*d^3*e^8)/8 + (351*b^2*c^2*d^2*e^9)/32 - (27*b^3*c*d*e^10)/32)) + (27*c*d*e^9*(c^2*d - b*c*e)^(1/2)*(d + e*x)^(1/2))/(32*((351*c^2*d^2*e^9)/32 - (27*b*c*d*e^10)/32 - (189*c^3*d^3*e^8)/(8*b) + (27*c^4*d^4*e^7)/(2*b^2))))*(-c*(b*e - c*d))^(1/2)*(b^2*e^2 + 16*c^2*d^2 - 12*b*c*d*e))/(4*b^5*c) - (3*d^(1/2)*atanh((135*c*d^(1/2)*e^10*(d + e*x)^(1/2))/(32*((135*c*d*e^10)/32 - (675*c^2*d^2*e^9)/(32*b) + (243*c^3*d^3*e^8)/(8*b^2) - (27*c^4*d^4*e^7)/(2*b^3))) + (675*c^2*d^(3/2)*e^9*(d + e*x)^(1/2))/(32*((675*c^2*d^2*e^9)/32 - (135*b*c*d*e^10)/32 - (243*c^3*d^3*e^8)/(8*b) + (27*c^4*d^4*e^7)/(2*b^2))) + (243*c^3*d^(5/2)*e^8*(d + e*x)^(1/2))/(8*((243*c^3*d^3*e^8)/8 - (675*b*c^2*d^2*e^9)/32 - (27*c^4*d^4*e^7)/(2*b) + (135*b^2*c*d*e^10)/32)) + (27*c^4*d^(7/2)*e^7*(d + e*x)^(1/2))/(2*((27*c^4*d^4*e^7)/2 - (243*b*c^3*d^3*e^8)/8 + (675*b^2*c^2*d^2*e^9)/32 - (135*b^3*c*d*e^10)/32)))*(5*b^2*e^2 + 16*c^2*d^2 - 20*b*c*d*e))/(4*b^5) - (((d + e*x)^(3/2)*(19*b^3*d*e^4 - 72*c^3*d^4*e + 144*b*c^2*d^3*e^2 - 91*b^2*c*d^2*e^3))/(4*b^4) + (3*(d + e*x)^(1/2)*(2*c^3*d^5*e - b^3*d^2*e^4 - 5*b*c^2*d^4*e^2 + 4*b^2*c*d^3*e^3))/b^4 - ((b*e - 2*c*d)*(d + e*x)^(5/2)*(5*b^2*e^3 + 36*c^2*d^2*e - 36*b*c*d*e^2))/(4*b^4) - (3*c*e*(d + e*x)^(7/2)*(b^2*e^2 + 8*c^2*d^2 - 8*b*c*d*e))/(4*b^4))/(c^2*(d + e*x)^4 - (d + e*x)*(4*c^2*d^3 + 2*b^2*d*e^2 - 6*b*c*d^2*e) - (4*c^2*d - 2*b*c*e)*(d + e*x)^3 + (d + e*x)^2*(b^2*e^2 + 6*c^2*d^2 - 6*b*c*d*e) + c^2*d^4 + b^2*d^2*e^2 - 2*b*c*d^3*e)","B"
381,1,1880,246,0.792065,"\text{Not used}","int((d + e*x)^(3/2)/(b*x + c*x^2)^3,x)","\frac{\frac{3\,\sqrt{d+e\,x}\,\left(b^3\,d\,e^4-9\,b^2\,c\,d^2\,e^3+16\,b\,c^2\,d^3\,e^2-8\,c^3\,d^4\,e\right)}{4\,b^4}-\frac{{\left(d+e\,x\right)}^{3/2}\,\left(5\,b^3\,e^4-46\,b^2\,c\,d\,e^3+108\,b\,c^2\,d^2\,e^2-72\,c^3\,d^3\,e\right)}{4\,b^4}-\frac{e\,{\left(d+e\,x\right)}^{5/2}\,\left(19\,b^2\,c\,e^2-72\,b\,c^2\,d\,e+72\,c^3\,d^2\right)}{4\,b^4}+\frac{3\,c\,e\,\left(2\,c^2\,d-b\,c\,e\right)\,{\left(d+e\,x\right)}^{7/2}}{b^4}}{c^2\,{\left(d+e\,x\right)}^4-\left(d+e\,x\right)\,\left(2\,b^2\,d\,e^2-6\,b\,c\,d^2\,e+4\,c^2\,d^3\right)-\left(4\,c^2\,d-2\,b\,c\,e\right)\,{\left(d+e\,x\right)}^3+{\left(d+e\,x\right)}^2\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2\right)+c^2\,d^4+b^2\,d^2\,e^2-2\,b\,c\,d^3\,e}-\frac{3\,\mathrm{atanh}\left(\frac{27\,c^2\,e^9\,\sqrt{d+e\,x}}{32\,d^{3/2}\,\left(\frac{27\,c^2\,e^9}{32\,d}-\frac{81\,c^3\,e^8}{8\,b}+\frac{27\,c^4\,d\,e^7}{2\,b^2}\right)}-\frac{81\,c^3\,e^8\,\sqrt{d+e\,x}}{8\,\sqrt{d}\,\left(\frac{27\,b\,c^2\,e^9}{32\,d}-\frac{81\,c^3\,e^8}{8}+\frac{27\,c^4\,d\,e^7}{2\,b}\right)}+\frac{27\,c^4\,\sqrt{d}\,e^7\,\sqrt{d+e\,x}}{2\,\left(\frac{27\,c^4\,d\,e^7}{2}-\frac{81\,b\,c^3\,e^8}{8}+\frac{27\,b^2\,c^2\,e^9}{32\,d}\right)}\right)\,\left(b^2\,e^2-12\,b\,c\,d\,e+16\,c^2\,d^2\right)}{4\,b^5\,\sqrt{d}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{d+e\,x}\,\left(117\,b^4\,c^3\,e^6-1008\,b^3\,c^4\,d\,e^5+3312\,b^2\,c^5\,d^2\,e^4-4608\,b\,c^6\,d^3\,e^3+2304\,c^7\,d^4\,e^2\right)}{4\,b^8}-\frac{3\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(\frac{3\,b^{12}\,c^2\,e^5-24\,b^{11}\,c^3\,d\,e^4+24\,b^{10}\,c^4\,d^2\,e^3}{b^{12}}-\frac{3\,\left(32\,b^{11}\,c^2\,e^3-64\,b^{10}\,c^3\,d\,e^2\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\sqrt{d+e\,x}\,\left(5\,b^2\,e^2-20\,b\,c\,d\,e+16\,c^2\,d^2\right)}{32\,b^8\,\left(b^6\,e-b^5\,c\,d\right)}\right)\,\left(5\,b^2\,e^2-20\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,\left(b^6\,e-b^5\,c\,d\right)}\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(5\,b^2\,e^2-20\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{8\,\left(b^6\,e-b^5\,c\,d\right)}+\frac{\left(\frac{\sqrt{d+e\,x}\,\left(117\,b^4\,c^3\,e^6-1008\,b^3\,c^4\,d\,e^5+3312\,b^2\,c^5\,d^2\,e^4-4608\,b\,c^6\,d^3\,e^3+2304\,c^7\,d^4\,e^2\right)}{4\,b^8}+\frac{3\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(\frac{3\,b^{12}\,c^2\,e^5-24\,b^{11}\,c^3\,d\,e^4+24\,b^{10}\,c^4\,d^2\,e^3}{b^{12}}+\frac{3\,\left(32\,b^{11}\,c^2\,e^3-64\,b^{10}\,c^3\,d\,e^2\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\sqrt{d+e\,x}\,\left(5\,b^2\,e^2-20\,b\,c\,d\,e+16\,c^2\,d^2\right)}{32\,b^8\,\left(b^6\,e-b^5\,c\,d\right)}\right)\,\left(5\,b^2\,e^2-20\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,\left(b^6\,e-b^5\,c\,d\right)}\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(5\,b^2\,e^2-20\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{8\,\left(b^6\,e-b^5\,c\,d\right)}}{\frac{\frac{135\,b^5\,c^3\,e^8}{8}-\frac{1215\,b^4\,c^4\,d\,e^7}{4}+1674\,b^3\,c^5\,d^2\,e^6-3996\,b^2\,c^6\,d^3\,e^5+4320\,b\,c^7\,d^4\,e^4-1728\,c^8\,d^5\,e^3}{b^{12}}-\frac{3\,\left(\frac{\sqrt{d+e\,x}\,\left(117\,b^4\,c^3\,e^6-1008\,b^3\,c^4\,d\,e^5+3312\,b^2\,c^5\,d^2\,e^4-4608\,b\,c^6\,d^3\,e^3+2304\,c^7\,d^4\,e^2\right)}{4\,b^8}-\frac{3\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(\frac{3\,b^{12}\,c^2\,e^5-24\,b^{11}\,c^3\,d\,e^4+24\,b^{10}\,c^4\,d^2\,e^3}{b^{12}}-\frac{3\,\left(32\,b^{11}\,c^2\,e^3-64\,b^{10}\,c^3\,d\,e^2\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\sqrt{d+e\,x}\,\left(5\,b^2\,e^2-20\,b\,c\,d\,e+16\,c^2\,d^2\right)}{32\,b^8\,\left(b^6\,e-b^5\,c\,d\right)}\right)\,\left(5\,b^2\,e^2-20\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,\left(b^6\,e-b^5\,c\,d\right)}\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(5\,b^2\,e^2-20\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,\left(b^6\,e-b^5\,c\,d\right)}+\frac{3\,\left(\frac{\sqrt{d+e\,x}\,\left(117\,b^4\,c^3\,e^6-1008\,b^3\,c^4\,d\,e^5+3312\,b^2\,c^5\,d^2\,e^4-4608\,b\,c^6\,d^3\,e^3+2304\,c^7\,d^4\,e^2\right)}{4\,b^8}+\frac{3\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(\frac{3\,b^{12}\,c^2\,e^5-24\,b^{11}\,c^3\,d\,e^4+24\,b^{10}\,c^4\,d^2\,e^3}{b^{12}}+\frac{3\,\left(32\,b^{11}\,c^2\,e^3-64\,b^{10}\,c^3\,d\,e^2\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\sqrt{d+e\,x}\,\left(5\,b^2\,e^2-20\,b\,c\,d\,e+16\,c^2\,d^2\right)}{32\,b^8\,\left(b^6\,e-b^5\,c\,d\right)}\right)\,\left(5\,b^2\,e^2-20\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,\left(b^6\,e-b^5\,c\,d\right)}\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(5\,b^2\,e^2-20\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,\left(b^6\,e-b^5\,c\,d\right)}}\right)\,\sqrt{-c\,\left(b\,e-c\,d\right)}\,\left(5\,b^2\,e^2-20\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{4\,\left(b^6\,e-b^5\,c\,d\right)}","Not used",1,"((3*(d + e*x)^(1/2)*(b^3*d*e^4 - 8*c^3*d^4*e + 16*b*c^2*d^3*e^2 - 9*b^2*c*d^2*e^3))/(4*b^4) - ((d + e*x)^(3/2)*(5*b^3*e^4 - 72*c^3*d^3*e + 108*b*c^2*d^2*e^2 - 46*b^2*c*d*e^3))/(4*b^4) - (e*(d + e*x)^(5/2)*(72*c^3*d^2 + 19*b^2*c*e^2 - 72*b*c^2*d*e))/(4*b^4) + (3*c*e*(2*c^2*d - b*c*e)*(d + e*x)^(7/2))/b^4)/(c^2*(d + e*x)^4 - (d + e*x)*(4*c^2*d^3 + 2*b^2*d*e^2 - 6*b*c*d^2*e) - (4*c^2*d - 2*b*c*e)*(d + e*x)^3 + (d + e*x)^2*(b^2*e^2 + 6*c^2*d^2 - 6*b*c*d*e) + c^2*d^4 + b^2*d^2*e^2 - 2*b*c*d^3*e) - (3*atanh((27*c^2*e^9*(d + e*x)^(1/2))/(32*d^(3/2)*((27*c^2*e^9)/(32*d) - (81*c^3*e^8)/(8*b) + (27*c^4*d*e^7)/(2*b^2))) - (81*c^3*e^8*(d + e*x)^(1/2))/(8*d^(1/2)*((27*b*c^2*e^9)/(32*d) - (81*c^3*e^8)/8 + (27*c^4*d*e^7)/(2*b))) + (27*c^4*d^(1/2)*e^7*(d + e*x)^(1/2))/(2*((27*c^4*d*e^7)/2 - (81*b*c^3*e^8)/8 + (27*b^2*c^2*e^9)/(32*d))))*(b^2*e^2 + 16*c^2*d^2 - 12*b*c*d*e))/(4*b^5*d^(1/2)) + (atan((((((d + e*x)^(1/2)*(117*b^4*c^3*e^6 + 2304*c^7*d^4*e^2 - 4608*b*c^6*d^3*e^3 - 1008*b^3*c^4*d*e^5 + 3312*b^2*c^5*d^2*e^4))/(4*b^8) - (3*(-c*(b*e - c*d))^(1/2)*((3*b^12*c^2*e^5 - 24*b^11*c^3*d*e^4 + 24*b^10*c^4*d^2*e^3)/b^12 - (3*(32*b^11*c^2*e^3 - 64*b^10*c^3*d*e^2)*(-c*(b*e - c*d))^(1/2)*(d + e*x)^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 - 20*b*c*d*e))/(32*b^8*(b^6*e - b^5*c*d)))*(5*b^2*e^2 + 16*c^2*d^2 - 20*b*c*d*e))/(8*(b^6*e - b^5*c*d)))*(-c*(b*e - c*d))^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 - 20*b*c*d*e)*3i)/(8*(b^6*e - b^5*c*d)) + ((((d + e*x)^(1/2)*(117*b^4*c^3*e^6 + 2304*c^7*d^4*e^2 - 4608*b*c^6*d^3*e^3 - 1008*b^3*c^4*d*e^5 + 3312*b^2*c^5*d^2*e^4))/(4*b^8) + (3*(-c*(b*e - c*d))^(1/2)*((3*b^12*c^2*e^5 - 24*b^11*c^3*d*e^4 + 24*b^10*c^4*d^2*e^3)/b^12 + (3*(32*b^11*c^2*e^3 - 64*b^10*c^3*d*e^2)*(-c*(b*e - c*d))^(1/2)*(d + e*x)^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 - 20*b*c*d*e))/(32*b^8*(b^6*e - b^5*c*d)))*(5*b^2*e^2 + 16*c^2*d^2 - 20*b*c*d*e))/(8*(b^6*e - b^5*c*d)))*(-c*(b*e - c*d))^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 - 20*b*c*d*e)*3i)/(8*(b^6*e - b^5*c*d)))/(((135*b^5*c^3*e^8)/8 - 1728*c^8*d^5*e^3 + 4320*b*c^7*d^4*e^4 - (1215*b^4*c^4*d*e^7)/4 - 3996*b^2*c^6*d^3*e^5 + 1674*b^3*c^5*d^2*e^6)/b^12 - (3*(((d + e*x)^(1/2)*(117*b^4*c^3*e^6 + 2304*c^7*d^4*e^2 - 4608*b*c^6*d^3*e^3 - 1008*b^3*c^4*d*e^5 + 3312*b^2*c^5*d^2*e^4))/(4*b^8) - (3*(-c*(b*e - c*d))^(1/2)*((3*b^12*c^2*e^5 - 24*b^11*c^3*d*e^4 + 24*b^10*c^4*d^2*e^3)/b^12 - (3*(32*b^11*c^2*e^3 - 64*b^10*c^3*d*e^2)*(-c*(b*e - c*d))^(1/2)*(d + e*x)^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 - 20*b*c*d*e))/(32*b^8*(b^6*e - b^5*c*d)))*(5*b^2*e^2 + 16*c^2*d^2 - 20*b*c*d*e))/(8*(b^6*e - b^5*c*d)))*(-c*(b*e - c*d))^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 - 20*b*c*d*e))/(8*(b^6*e - b^5*c*d)) + (3*(((d + e*x)^(1/2)*(117*b^4*c^3*e^6 + 2304*c^7*d^4*e^2 - 4608*b*c^6*d^3*e^3 - 1008*b^3*c^4*d*e^5 + 3312*b^2*c^5*d^2*e^4))/(4*b^8) + (3*(-c*(b*e - c*d))^(1/2)*((3*b^12*c^2*e^5 - 24*b^11*c^3*d*e^4 + 24*b^10*c^4*d^2*e^3)/b^12 + (3*(32*b^11*c^2*e^3 - 64*b^10*c^3*d*e^2)*(-c*(b*e - c*d))^(1/2)*(d + e*x)^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 - 20*b*c*d*e))/(32*b^8*(b^6*e - b^5*c*d)))*(5*b^2*e^2 + 16*c^2*d^2 - 20*b*c*d*e))/(8*(b^6*e - b^5*c*d)))*(-c*(b*e - c*d))^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 - 20*b*c*d*e))/(8*(b^6*e - b^5*c*d))))*(-c*(b*e - c*d))^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 - 20*b*c*d*e)*3i)/(4*(b^6*e - b^5*c*d))","B"
382,1,4815,245,2.010840,"\text{Not used}","int((d + e*x)^(1/2)/(b*x + c*x^2)^3,x)","\frac{\frac{{\left(d+e\,x\right)}^{3/2}\,\left(b^4\,e^5-13\,b^3\,c\,d\,e^4+85\,b^2\,c^2\,d^2\,e^3-144\,b\,c^3\,d^3\,e^2+72\,c^4\,d^4\,e\right)}{4\,b^4\,\left(c\,d^2-b\,d\,e\right)}-\frac{\sqrt{d+e\,x}\,\left(b^3\,e^4+10\,b^2\,c\,d\,e^3-36\,b\,c^2\,d^2\,e^2+24\,c^3\,d^3\,e\right)}{4\,b^4}+\frac{\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{5/2}\,\left(b^2\,c\,e^3-18\,b\,c^2\,d\,e^2+18\,c^3\,d^2\,e\right)}{2\,b^4\,\left(c\,d^2-b\,d\,e\right)}+\frac{c\,e\,{\left(d+e\,x\right)}^{7/2}\,\left(b^2\,c\,e^2-24\,b\,c^2\,d\,e+24\,c^3\,d^2\right)}{4\,b^4\,\left(c\,d^2-b\,d\,e\right)}}{c^2\,{\left(d+e\,x\right)}^4-\left(d+e\,x\right)\,\left(2\,b^2\,d\,e^2-6\,b\,c\,d^2\,e+4\,c^2\,d^3\right)-\left(4\,c^2\,d-2\,b\,c\,e\right)\,{\left(d+e\,x\right)}^3+{\left(d+e\,x\right)}^2\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2\right)+c^2\,d^4+b^2\,d^2\,e^2-2\,b\,c\,d^3\,e}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{d+e\,x}\,\left(b^6\,c^3\,e^8+22\,b^5\,c^4\,d\,e^7+1226\,b^4\,c^5\,d^2\,e^6-7104\,b^3\,c^6\,d^3\,e^5+15072\,b^2\,c^7\,d^4\,e^4-13824\,b\,c^8\,d^5\,e^3+4608\,c^9\,d^6\,e^2\right)}{8\,\left(b^{10}\,d^2\,e^2-2\,b^9\,c\,d^3\,e+b^8\,c^2\,d^4\right)}+\frac{\left(\frac{b^{14}\,c^2\,d\,e^7+9\,b^{13}\,c^3\,d^2\,e^6-46\,b^{12}\,c^4\,d^3\,e^5+60\,b^{11}\,c^5\,d^4\,e^4-24\,b^{10}\,c^6\,d^5\,e^3}{b^{14}\,d^2\,e^2-2\,b^{13}\,c\,d^3\,e+b^{12}\,c^2\,d^4}-\frac{\sqrt{d+e\,x}\,\left(b^2\,e^2+12\,b\,c\,d\,e-48\,c^2\,d^2\right)\,\left(-64\,b^{13}\,c^2\,d^2\,e^5+256\,b^{12}\,c^3\,d^3\,e^4-320\,b^{11}\,c^4\,d^4\,e^3+128\,b^{10}\,c^5\,d^5\,e^2\right)}{64\,b^5\,\sqrt{d^3}\,\left(b^{10}\,d^2\,e^2-2\,b^9\,c\,d^3\,e+b^8\,c^2\,d^4\right)}\right)\,\left(b^2\,e^2+12\,b\,c\,d\,e-48\,c^2\,d^2\right)}{8\,b^5\,\sqrt{d^3}}\right)\,\left(b^2\,e^2+12\,b\,c\,d\,e-48\,c^2\,d^2\right)\,1{}\mathrm{i}}{8\,b^5\,\sqrt{d^3}}+\frac{\left(\frac{\sqrt{d+e\,x}\,\left(b^6\,c^3\,e^8+22\,b^5\,c^4\,d\,e^7+1226\,b^4\,c^5\,d^2\,e^6-7104\,b^3\,c^6\,d^3\,e^5+15072\,b^2\,c^7\,d^4\,e^4-13824\,b\,c^8\,d^5\,e^3+4608\,c^9\,d^6\,e^2\right)}{8\,\left(b^{10}\,d^2\,e^2-2\,b^9\,c\,d^3\,e+b^8\,c^2\,d^4\right)}-\frac{\left(\frac{b^{14}\,c^2\,d\,e^7+9\,b^{13}\,c^3\,d^2\,e^6-46\,b^{12}\,c^4\,d^3\,e^5+60\,b^{11}\,c^5\,d^4\,e^4-24\,b^{10}\,c^6\,d^5\,e^3}{b^{14}\,d^2\,e^2-2\,b^{13}\,c\,d^3\,e+b^{12}\,c^2\,d^4}+\frac{\sqrt{d+e\,x}\,\left(b^2\,e^2+12\,b\,c\,d\,e-48\,c^2\,d^2\right)\,\left(-64\,b^{13}\,c^2\,d^2\,e^5+256\,b^{12}\,c^3\,d^3\,e^4-320\,b^{11}\,c^4\,d^4\,e^3+128\,b^{10}\,c^5\,d^5\,e^2\right)}{64\,b^5\,\sqrt{d^3}\,\left(b^{10}\,d^2\,e^2-2\,b^9\,c\,d^3\,e+b^8\,c^2\,d^4\right)}\right)\,\left(b^2\,e^2+12\,b\,c\,d\,e-48\,c^2\,d^2\right)}{8\,b^5\,\sqrt{d^3}}\right)\,\left(b^2\,e^2+12\,b\,c\,d\,e-48\,c^2\,d^2\right)\,1{}\mathrm{i}}{8\,b^5\,\sqrt{d^3}}}{\frac{-\frac{35\,b^6\,c^4\,e^9}{32}+\frac{63\,b^5\,c^5\,d\,e^8}{4}+\frac{1233\,b^4\,c^6\,d^2\,e^7}{4}-2376\,b^3\,c^7\,d^3\,e^6+5508\,b^2\,c^8\,d^4\,e^5-5184\,b\,c^9\,d^5\,e^4+1728\,c^{10}\,d^6\,e^3}{b^{14}\,d^2\,e^2-2\,b^{13}\,c\,d^3\,e+b^{12}\,c^2\,d^4}+\frac{\left(\frac{\sqrt{d+e\,x}\,\left(b^6\,c^3\,e^8+22\,b^5\,c^4\,d\,e^7+1226\,b^4\,c^5\,d^2\,e^6-7104\,b^3\,c^6\,d^3\,e^5+15072\,b^2\,c^7\,d^4\,e^4-13824\,b\,c^8\,d^5\,e^3+4608\,c^9\,d^6\,e^2\right)}{8\,\left(b^{10}\,d^2\,e^2-2\,b^9\,c\,d^3\,e+b^8\,c^2\,d^4\right)}+\frac{\left(\frac{b^{14}\,c^2\,d\,e^7+9\,b^{13}\,c^3\,d^2\,e^6-46\,b^{12}\,c^4\,d^3\,e^5+60\,b^{11}\,c^5\,d^4\,e^4-24\,b^{10}\,c^6\,d^5\,e^3}{b^{14}\,d^2\,e^2-2\,b^{13}\,c\,d^3\,e+b^{12}\,c^2\,d^4}-\frac{\sqrt{d+e\,x}\,\left(b^2\,e^2+12\,b\,c\,d\,e-48\,c^2\,d^2\right)\,\left(-64\,b^{13}\,c^2\,d^2\,e^5+256\,b^{12}\,c^3\,d^3\,e^4-320\,b^{11}\,c^4\,d^4\,e^3+128\,b^{10}\,c^5\,d^5\,e^2\right)}{64\,b^5\,\sqrt{d^3}\,\left(b^{10}\,d^2\,e^2-2\,b^9\,c\,d^3\,e+b^8\,c^2\,d^4\right)}\right)\,\left(b^2\,e^2+12\,b\,c\,d\,e-48\,c^2\,d^2\right)}{8\,b^5\,\sqrt{d^3}}\right)\,\left(b^2\,e^2+12\,b\,c\,d\,e-48\,c^2\,d^2\right)}{8\,b^5\,\sqrt{d^3}}-\frac{\left(\frac{\sqrt{d+e\,x}\,\left(b^6\,c^3\,e^8+22\,b^5\,c^4\,d\,e^7+1226\,b^4\,c^5\,d^2\,e^6-7104\,b^3\,c^6\,d^3\,e^5+15072\,b^2\,c^7\,d^4\,e^4-13824\,b\,c^8\,d^5\,e^3+4608\,c^9\,d^6\,e^2\right)}{8\,\left(b^{10}\,d^2\,e^2-2\,b^9\,c\,d^3\,e+b^8\,c^2\,d^4\right)}-\frac{\left(\frac{b^{14}\,c^2\,d\,e^7+9\,b^{13}\,c^3\,d^2\,e^6-46\,b^{12}\,c^4\,d^3\,e^5+60\,b^{11}\,c^5\,d^4\,e^4-24\,b^{10}\,c^6\,d^5\,e^3}{b^{14}\,d^2\,e^2-2\,b^{13}\,c\,d^3\,e+b^{12}\,c^2\,d^4}+\frac{\sqrt{d+e\,x}\,\left(b^2\,e^2+12\,b\,c\,d\,e-48\,c^2\,d^2\right)\,\left(-64\,b^{13}\,c^2\,d^2\,e^5+256\,b^{12}\,c^3\,d^3\,e^4-320\,b^{11}\,c^4\,d^4\,e^3+128\,b^{10}\,c^5\,d^5\,e^2\right)}{64\,b^5\,\sqrt{d^3}\,\left(b^{10}\,d^2\,e^2-2\,b^9\,c\,d^3\,e+b^8\,c^2\,d^4\right)}\right)\,\left(b^2\,e^2+12\,b\,c\,d\,e-48\,c^2\,d^2\right)}{8\,b^5\,\sqrt{d^3}}\right)\,\left(b^2\,e^2+12\,b\,c\,d\,e-48\,c^2\,d^2\right)}{8\,b^5\,\sqrt{d^3}}}\right)\,\left(b^2\,e^2+12\,b\,c\,d\,e-48\,c^2\,d^2\right)\,1{}\mathrm{i}}{4\,b^5\,\sqrt{d^3}}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(\frac{\sqrt{d+e\,x}\,\left(b^6\,c^3\,e^8+22\,b^5\,c^4\,d\,e^7+1226\,b^4\,c^5\,d^2\,e^6-7104\,b^3\,c^6\,d^3\,e^5+15072\,b^2\,c^7\,d^4\,e^4-13824\,b\,c^8\,d^5\,e^3+4608\,c^9\,d^6\,e^2\right)}{8\,\left(b^{10}\,d^2\,e^2-2\,b^9\,c\,d^3\,e+b^8\,c^2\,d^4\right)}+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(\frac{b^{14}\,c^2\,d\,e^7+9\,b^{13}\,c^3\,d^2\,e^6-46\,b^{12}\,c^4\,d^3\,e^5+60\,b^{11}\,c^5\,d^4\,e^4-24\,b^{10}\,c^6\,d^5\,e^3}{b^{14}\,d^2\,e^2-2\,b^{13}\,c\,d^3\,e+b^{12}\,c^2\,d^4}-\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\sqrt{d+e\,x}\,\left(35\,b^2\,e^2-84\,b\,c\,d\,e+48\,c^2\,d^2\right)\,\left(-64\,b^{13}\,c^2\,d^2\,e^5+256\,b^{12}\,c^3\,d^3\,e^4-320\,b^{11}\,c^4\,d^4\,e^3+128\,b^{10}\,c^5\,d^5\,e^2\right)}{64\,\left(b^{10}\,d^2\,e^2-2\,b^9\,c\,d^3\,e+b^8\,c^2\,d^4\right)\,\left(b^8\,e^3-3\,b^7\,c\,d\,e^2+3\,b^6\,c^2\,d^2\,e-b^5\,c^3\,d^3\right)}\right)\,\left(35\,b^2\,e^2-84\,b\,c\,d\,e+48\,c^2\,d^2\right)}{8\,\left(b^8\,e^3-3\,b^7\,c\,d\,e^2+3\,b^6\,c^2\,d^2\,e-b^5\,c^3\,d^3\right)}\right)\,\left(35\,b^2\,e^2-84\,b\,c\,d\,e+48\,c^2\,d^2\right)\,1{}\mathrm{i}}{8\,\left(b^8\,e^3-3\,b^7\,c\,d\,e^2+3\,b^6\,c^2\,d^2\,e-b^5\,c^3\,d^3\right)}+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(\frac{\sqrt{d+e\,x}\,\left(b^6\,c^3\,e^8+22\,b^5\,c^4\,d\,e^7+1226\,b^4\,c^5\,d^2\,e^6-7104\,b^3\,c^6\,d^3\,e^5+15072\,b^2\,c^7\,d^4\,e^4-13824\,b\,c^8\,d^5\,e^3+4608\,c^9\,d^6\,e^2\right)}{8\,\left(b^{10}\,d^2\,e^2-2\,b^9\,c\,d^3\,e+b^8\,c^2\,d^4\right)}-\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(\frac{b^{14}\,c^2\,d\,e^7+9\,b^{13}\,c^3\,d^2\,e^6-46\,b^{12}\,c^4\,d^3\,e^5+60\,b^{11}\,c^5\,d^4\,e^4-24\,b^{10}\,c^6\,d^5\,e^3}{b^{14}\,d^2\,e^2-2\,b^{13}\,c\,d^3\,e+b^{12}\,c^2\,d^4}+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\sqrt{d+e\,x}\,\left(35\,b^2\,e^2-84\,b\,c\,d\,e+48\,c^2\,d^2\right)\,\left(-64\,b^{13}\,c^2\,d^2\,e^5+256\,b^{12}\,c^3\,d^3\,e^4-320\,b^{11}\,c^4\,d^4\,e^3+128\,b^{10}\,c^5\,d^5\,e^2\right)}{64\,\left(b^{10}\,d^2\,e^2-2\,b^9\,c\,d^3\,e+b^8\,c^2\,d^4\right)\,\left(b^8\,e^3-3\,b^7\,c\,d\,e^2+3\,b^6\,c^2\,d^2\,e-b^5\,c^3\,d^3\right)}\right)\,\left(35\,b^2\,e^2-84\,b\,c\,d\,e+48\,c^2\,d^2\right)}{8\,\left(b^8\,e^3-3\,b^7\,c\,d\,e^2+3\,b^6\,c^2\,d^2\,e-b^5\,c^3\,d^3\right)}\right)\,\left(35\,b^2\,e^2-84\,b\,c\,d\,e+48\,c^2\,d^2\right)\,1{}\mathrm{i}}{8\,\left(b^8\,e^3-3\,b^7\,c\,d\,e^2+3\,b^6\,c^2\,d^2\,e-b^5\,c^3\,d^3\right)}}{\frac{-\frac{35\,b^6\,c^4\,e^9}{32}+\frac{63\,b^5\,c^5\,d\,e^8}{4}+\frac{1233\,b^4\,c^6\,d^2\,e^7}{4}-2376\,b^3\,c^7\,d^3\,e^6+5508\,b^2\,c^8\,d^4\,e^5-5184\,b\,c^9\,d^5\,e^4+1728\,c^{10}\,d^6\,e^3}{b^{14}\,d^2\,e^2-2\,b^{13}\,c\,d^3\,e+b^{12}\,c^2\,d^4}+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(\frac{\sqrt{d+e\,x}\,\left(b^6\,c^3\,e^8+22\,b^5\,c^4\,d\,e^7+1226\,b^4\,c^5\,d^2\,e^6-7104\,b^3\,c^6\,d^3\,e^5+15072\,b^2\,c^7\,d^4\,e^4-13824\,b\,c^8\,d^5\,e^3+4608\,c^9\,d^6\,e^2\right)}{8\,\left(b^{10}\,d^2\,e^2-2\,b^9\,c\,d^3\,e+b^8\,c^2\,d^4\right)}+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(\frac{b^{14}\,c^2\,d\,e^7+9\,b^{13}\,c^3\,d^2\,e^6-46\,b^{12}\,c^4\,d^3\,e^5+60\,b^{11}\,c^5\,d^4\,e^4-24\,b^{10}\,c^6\,d^5\,e^3}{b^{14}\,d^2\,e^2-2\,b^{13}\,c\,d^3\,e+b^{12}\,c^2\,d^4}-\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\sqrt{d+e\,x}\,\left(35\,b^2\,e^2-84\,b\,c\,d\,e+48\,c^2\,d^2\right)\,\left(-64\,b^{13}\,c^2\,d^2\,e^5+256\,b^{12}\,c^3\,d^3\,e^4-320\,b^{11}\,c^4\,d^4\,e^3+128\,b^{10}\,c^5\,d^5\,e^2\right)}{64\,\left(b^{10}\,d^2\,e^2-2\,b^9\,c\,d^3\,e+b^8\,c^2\,d^4\right)\,\left(b^8\,e^3-3\,b^7\,c\,d\,e^2+3\,b^6\,c^2\,d^2\,e-b^5\,c^3\,d^3\right)}\right)\,\left(35\,b^2\,e^2-84\,b\,c\,d\,e+48\,c^2\,d^2\right)}{8\,\left(b^8\,e^3-3\,b^7\,c\,d\,e^2+3\,b^6\,c^2\,d^2\,e-b^5\,c^3\,d^3\right)}\right)\,\left(35\,b^2\,e^2-84\,b\,c\,d\,e+48\,c^2\,d^2\right)}{8\,\left(b^8\,e^3-3\,b^7\,c\,d\,e^2+3\,b^6\,c^2\,d^2\,e-b^5\,c^3\,d^3\right)}-\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(\frac{\sqrt{d+e\,x}\,\left(b^6\,c^3\,e^8+22\,b^5\,c^4\,d\,e^7+1226\,b^4\,c^5\,d^2\,e^6-7104\,b^3\,c^6\,d^3\,e^5+15072\,b^2\,c^7\,d^4\,e^4-13824\,b\,c^8\,d^5\,e^3+4608\,c^9\,d^6\,e^2\right)}{8\,\left(b^{10}\,d^2\,e^2-2\,b^9\,c\,d^3\,e+b^8\,c^2\,d^4\right)}-\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(\frac{b^{14}\,c^2\,d\,e^7+9\,b^{13}\,c^3\,d^2\,e^6-46\,b^{12}\,c^4\,d^3\,e^5+60\,b^{11}\,c^5\,d^4\,e^4-24\,b^{10}\,c^6\,d^5\,e^3}{b^{14}\,d^2\,e^2-2\,b^{13}\,c\,d^3\,e+b^{12}\,c^2\,d^4}+\frac{\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\sqrt{d+e\,x}\,\left(35\,b^2\,e^2-84\,b\,c\,d\,e+48\,c^2\,d^2\right)\,\left(-64\,b^{13}\,c^2\,d^2\,e^5+256\,b^{12}\,c^3\,d^3\,e^4-320\,b^{11}\,c^4\,d^4\,e^3+128\,b^{10}\,c^5\,d^5\,e^2\right)}{64\,\left(b^{10}\,d^2\,e^2-2\,b^9\,c\,d^3\,e+b^8\,c^2\,d^4\right)\,\left(b^8\,e^3-3\,b^7\,c\,d\,e^2+3\,b^6\,c^2\,d^2\,e-b^5\,c^3\,d^3\right)}\right)\,\left(35\,b^2\,e^2-84\,b\,c\,d\,e+48\,c^2\,d^2\right)}{8\,\left(b^8\,e^3-3\,b^7\,c\,d\,e^2+3\,b^6\,c^2\,d^2\,e-b^5\,c^3\,d^3\right)}\right)\,\left(35\,b^2\,e^2-84\,b\,c\,d\,e+48\,c^2\,d^2\right)}{8\,\left(b^8\,e^3-3\,b^7\,c\,d\,e^2+3\,b^6\,c^2\,d^2\,e-b^5\,c^3\,d^3\right)}}\right)\,\sqrt{-c^3\,{\left(b\,e-c\,d\right)}^3}\,\left(35\,b^2\,e^2-84\,b\,c\,d\,e+48\,c^2\,d^2\right)\,1{}\mathrm{i}}{4\,\left(b^8\,e^3-3\,b^7\,c\,d\,e^2+3\,b^6\,c^2\,d^2\,e-b^5\,c^3\,d^3\right)}","Not used",1,"(((d + e*x)^(3/2)*(b^4*e^5 + 72*c^4*d^4*e - 144*b*c^3*d^3*e^2 + 85*b^2*c^2*d^2*e^3 - 13*b^3*c*d*e^4))/(4*b^4*(c*d^2 - b*d*e)) - ((d + e*x)^(1/2)*(b^3*e^4 + 24*c^3*d^3*e - 36*b*c^2*d^2*e^2 + 10*b^2*c*d*e^3))/(4*b^4) + ((b*e - 2*c*d)*(d + e*x)^(5/2)*(b^2*c*e^3 + 18*c^3*d^2*e - 18*b*c^2*d*e^2))/(2*b^4*(c*d^2 - b*d*e)) + (c*e*(d + e*x)^(7/2)*(24*c^3*d^2 + b^2*c*e^2 - 24*b*c^2*d*e))/(4*b^4*(c*d^2 - b*d*e)))/(c^2*(d + e*x)^4 - (d + e*x)*(4*c^2*d^3 + 2*b^2*d*e^2 - 6*b*c*d^2*e) - (4*c^2*d - 2*b*c*e)*(d + e*x)^3 + (d + e*x)^2*(b^2*e^2 + 6*c^2*d^2 - 6*b*c*d*e) + c^2*d^4 + b^2*d^2*e^2 - 2*b*c*d^3*e) - (atan((((((d + e*x)^(1/2)*(b^6*c^3*e^8 + 4608*c^9*d^6*e^2 - 13824*b*c^8*d^5*e^3 + 22*b^5*c^4*d*e^7 + 15072*b^2*c^7*d^4*e^4 - 7104*b^3*c^6*d^3*e^5 + 1226*b^4*c^5*d^2*e^6))/(8*(b^8*c^2*d^4 + b^10*d^2*e^2 - 2*b^9*c*d^3*e)) + (((b^14*c^2*d*e^7 - 24*b^10*c^6*d^5*e^3 + 60*b^11*c^5*d^4*e^4 - 46*b^12*c^4*d^3*e^5 + 9*b^13*c^3*d^2*e^6)/(b^12*c^2*d^4 + b^14*d^2*e^2 - 2*b^13*c*d^3*e) - ((d + e*x)^(1/2)*(b^2*e^2 - 48*c^2*d^2 + 12*b*c*d*e)*(128*b^10*c^5*d^5*e^2 - 320*b^11*c^4*d^4*e^3 + 256*b^12*c^3*d^3*e^4 - 64*b^13*c^2*d^2*e^5))/(64*b^5*(d^3)^(1/2)*(b^8*c^2*d^4 + b^10*d^2*e^2 - 2*b^9*c*d^3*e)))*(b^2*e^2 - 48*c^2*d^2 + 12*b*c*d*e))/(8*b^5*(d^3)^(1/2)))*(b^2*e^2 - 48*c^2*d^2 + 12*b*c*d*e)*1i)/(8*b^5*(d^3)^(1/2)) + ((((d + e*x)^(1/2)*(b^6*c^3*e^8 + 4608*c^9*d^6*e^2 - 13824*b*c^8*d^5*e^3 + 22*b^5*c^4*d*e^7 + 15072*b^2*c^7*d^4*e^4 - 7104*b^3*c^6*d^3*e^5 + 1226*b^4*c^5*d^2*e^6))/(8*(b^8*c^2*d^4 + b^10*d^2*e^2 - 2*b^9*c*d^3*e)) - (((b^14*c^2*d*e^7 - 24*b^10*c^6*d^5*e^3 + 60*b^11*c^5*d^4*e^4 - 46*b^12*c^4*d^3*e^5 + 9*b^13*c^3*d^2*e^6)/(b^12*c^2*d^4 + b^14*d^2*e^2 - 2*b^13*c*d^3*e) + ((d + e*x)^(1/2)*(b^2*e^2 - 48*c^2*d^2 + 12*b*c*d*e)*(128*b^10*c^5*d^5*e^2 - 320*b^11*c^4*d^4*e^3 + 256*b^12*c^3*d^3*e^4 - 64*b^13*c^2*d^2*e^5))/(64*b^5*(d^3)^(1/2)*(b^8*c^2*d^4 + b^10*d^2*e^2 - 2*b^9*c*d^3*e)))*(b^2*e^2 - 48*c^2*d^2 + 12*b*c*d*e))/(8*b^5*(d^3)^(1/2)))*(b^2*e^2 - 48*c^2*d^2 + 12*b*c*d*e)*1i)/(8*b^5*(d^3)^(1/2)))/((1728*c^10*d^6*e^3 - (35*b^6*c^4*e^9)/32 - 5184*b*c^9*d^5*e^4 + (63*b^5*c^5*d*e^8)/4 + 5508*b^2*c^8*d^4*e^5 - 2376*b^3*c^7*d^3*e^6 + (1233*b^4*c^6*d^2*e^7)/4)/(b^12*c^2*d^4 + b^14*d^2*e^2 - 2*b^13*c*d^3*e) + ((((d + e*x)^(1/2)*(b^6*c^3*e^8 + 4608*c^9*d^6*e^2 - 13824*b*c^8*d^5*e^3 + 22*b^5*c^4*d*e^7 + 15072*b^2*c^7*d^4*e^4 - 7104*b^3*c^6*d^3*e^5 + 1226*b^4*c^5*d^2*e^6))/(8*(b^8*c^2*d^4 + b^10*d^2*e^2 - 2*b^9*c*d^3*e)) + (((b^14*c^2*d*e^7 - 24*b^10*c^6*d^5*e^3 + 60*b^11*c^5*d^4*e^4 - 46*b^12*c^4*d^3*e^5 + 9*b^13*c^3*d^2*e^6)/(b^12*c^2*d^4 + b^14*d^2*e^2 - 2*b^13*c*d^3*e) - ((d + e*x)^(1/2)*(b^2*e^2 - 48*c^2*d^2 + 12*b*c*d*e)*(128*b^10*c^5*d^5*e^2 - 320*b^11*c^4*d^4*e^3 + 256*b^12*c^3*d^3*e^4 - 64*b^13*c^2*d^2*e^5))/(64*b^5*(d^3)^(1/2)*(b^8*c^2*d^4 + b^10*d^2*e^2 - 2*b^9*c*d^3*e)))*(b^2*e^2 - 48*c^2*d^2 + 12*b*c*d*e))/(8*b^5*(d^3)^(1/2)))*(b^2*e^2 - 48*c^2*d^2 + 12*b*c*d*e))/(8*b^5*(d^3)^(1/2)) - ((((d + e*x)^(1/2)*(b^6*c^3*e^8 + 4608*c^9*d^6*e^2 - 13824*b*c^8*d^5*e^3 + 22*b^5*c^4*d*e^7 + 15072*b^2*c^7*d^4*e^4 - 7104*b^3*c^6*d^3*e^5 + 1226*b^4*c^5*d^2*e^6))/(8*(b^8*c^2*d^4 + b^10*d^2*e^2 - 2*b^9*c*d^3*e)) - (((b^14*c^2*d*e^7 - 24*b^10*c^6*d^5*e^3 + 60*b^11*c^5*d^4*e^4 - 46*b^12*c^4*d^3*e^5 + 9*b^13*c^3*d^2*e^6)/(b^12*c^2*d^4 + b^14*d^2*e^2 - 2*b^13*c*d^3*e) + ((d + e*x)^(1/2)*(b^2*e^2 - 48*c^2*d^2 + 12*b*c*d*e)*(128*b^10*c^5*d^5*e^2 - 320*b^11*c^4*d^4*e^3 + 256*b^12*c^3*d^3*e^4 - 64*b^13*c^2*d^2*e^5))/(64*b^5*(d^3)^(1/2)*(b^8*c^2*d^4 + b^10*d^2*e^2 - 2*b^9*c*d^3*e)))*(b^2*e^2 - 48*c^2*d^2 + 12*b*c*d*e))/(8*b^5*(d^3)^(1/2)))*(b^2*e^2 - 48*c^2*d^2 + 12*b*c*d*e))/(8*b^5*(d^3)^(1/2))))*(b^2*e^2 - 48*c^2*d^2 + 12*b*c*d*e)*1i)/(4*b^5*(d^3)^(1/2)) - (atan((((-c^3*(b*e - c*d)^3)^(1/2)*(((d + e*x)^(1/2)*(b^6*c^3*e^8 + 4608*c^9*d^6*e^2 - 13824*b*c^8*d^5*e^3 + 22*b^5*c^4*d*e^7 + 15072*b^2*c^7*d^4*e^4 - 7104*b^3*c^6*d^3*e^5 + 1226*b^4*c^5*d^2*e^6))/(8*(b^8*c^2*d^4 + b^10*d^2*e^2 - 2*b^9*c*d^3*e)) + ((-c^3*(b*e - c*d)^3)^(1/2)*((b^14*c^2*d*e^7 - 24*b^10*c^6*d^5*e^3 + 60*b^11*c^5*d^4*e^4 - 46*b^12*c^4*d^3*e^5 + 9*b^13*c^3*d^2*e^6)/(b^12*c^2*d^4 + b^14*d^2*e^2 - 2*b^13*c*d^3*e) - ((-c^3*(b*e - c*d)^3)^(1/2)*(d + e*x)^(1/2)*(35*b^2*e^2 + 48*c^2*d^2 - 84*b*c*d*e)*(128*b^10*c^5*d^5*e^2 - 320*b^11*c^4*d^4*e^3 + 256*b^12*c^3*d^3*e^4 - 64*b^13*c^2*d^2*e^5))/(64*(b^8*c^2*d^4 + b^10*d^2*e^2 - 2*b^9*c*d^3*e)*(b^8*e^3 - b^5*c^3*d^3 + 3*b^6*c^2*d^2*e - 3*b^7*c*d*e^2)))*(35*b^2*e^2 + 48*c^2*d^2 - 84*b*c*d*e))/(8*(b^8*e^3 - b^5*c^3*d^3 + 3*b^6*c^2*d^2*e - 3*b^7*c*d*e^2)))*(35*b^2*e^2 + 48*c^2*d^2 - 84*b*c*d*e)*1i)/(8*(b^8*e^3 - b^5*c^3*d^3 + 3*b^6*c^2*d^2*e - 3*b^7*c*d*e^2)) + ((-c^3*(b*e - c*d)^3)^(1/2)*(((d + e*x)^(1/2)*(b^6*c^3*e^8 + 4608*c^9*d^6*e^2 - 13824*b*c^8*d^5*e^3 + 22*b^5*c^4*d*e^7 + 15072*b^2*c^7*d^4*e^4 - 7104*b^3*c^6*d^3*e^5 + 1226*b^4*c^5*d^2*e^6))/(8*(b^8*c^2*d^4 + b^10*d^2*e^2 - 2*b^9*c*d^3*e)) - ((-c^3*(b*e - c*d)^3)^(1/2)*((b^14*c^2*d*e^7 - 24*b^10*c^6*d^5*e^3 + 60*b^11*c^5*d^4*e^4 - 46*b^12*c^4*d^3*e^5 + 9*b^13*c^3*d^2*e^6)/(b^12*c^2*d^4 + b^14*d^2*e^2 - 2*b^13*c*d^3*e) + ((-c^3*(b*e - c*d)^3)^(1/2)*(d + e*x)^(1/2)*(35*b^2*e^2 + 48*c^2*d^2 - 84*b*c*d*e)*(128*b^10*c^5*d^5*e^2 - 320*b^11*c^4*d^4*e^3 + 256*b^12*c^3*d^3*e^4 - 64*b^13*c^2*d^2*e^5))/(64*(b^8*c^2*d^4 + b^10*d^2*e^2 - 2*b^9*c*d^3*e)*(b^8*e^3 - b^5*c^3*d^3 + 3*b^6*c^2*d^2*e - 3*b^7*c*d*e^2)))*(35*b^2*e^2 + 48*c^2*d^2 - 84*b*c*d*e))/(8*(b^8*e^3 - b^5*c^3*d^3 + 3*b^6*c^2*d^2*e - 3*b^7*c*d*e^2)))*(35*b^2*e^2 + 48*c^2*d^2 - 84*b*c*d*e)*1i)/(8*(b^8*e^3 - b^5*c^3*d^3 + 3*b^6*c^2*d^2*e - 3*b^7*c*d*e^2)))/((1728*c^10*d^6*e^3 - (35*b^6*c^4*e^9)/32 - 5184*b*c^9*d^5*e^4 + (63*b^5*c^5*d*e^8)/4 + 5508*b^2*c^8*d^4*e^5 - 2376*b^3*c^7*d^3*e^6 + (1233*b^4*c^6*d^2*e^7)/4)/(b^12*c^2*d^4 + b^14*d^2*e^2 - 2*b^13*c*d^3*e) + ((-c^3*(b*e - c*d)^3)^(1/2)*(((d + e*x)^(1/2)*(b^6*c^3*e^8 + 4608*c^9*d^6*e^2 - 13824*b*c^8*d^5*e^3 + 22*b^5*c^4*d*e^7 + 15072*b^2*c^7*d^4*e^4 - 7104*b^3*c^6*d^3*e^5 + 1226*b^4*c^5*d^2*e^6))/(8*(b^8*c^2*d^4 + b^10*d^2*e^2 - 2*b^9*c*d^3*e)) + ((-c^3*(b*e - c*d)^3)^(1/2)*((b^14*c^2*d*e^7 - 24*b^10*c^6*d^5*e^3 + 60*b^11*c^5*d^4*e^4 - 46*b^12*c^4*d^3*e^5 + 9*b^13*c^3*d^2*e^6)/(b^12*c^2*d^4 + b^14*d^2*e^2 - 2*b^13*c*d^3*e) - ((-c^3*(b*e - c*d)^3)^(1/2)*(d + e*x)^(1/2)*(35*b^2*e^2 + 48*c^2*d^2 - 84*b*c*d*e)*(128*b^10*c^5*d^5*e^2 - 320*b^11*c^4*d^4*e^3 + 256*b^12*c^3*d^3*e^4 - 64*b^13*c^2*d^2*e^5))/(64*(b^8*c^2*d^4 + b^10*d^2*e^2 - 2*b^9*c*d^3*e)*(b^8*e^3 - b^5*c^3*d^3 + 3*b^6*c^2*d^2*e - 3*b^7*c*d*e^2)))*(35*b^2*e^2 + 48*c^2*d^2 - 84*b*c*d*e))/(8*(b^8*e^3 - b^5*c^3*d^3 + 3*b^6*c^2*d^2*e - 3*b^7*c*d*e^2)))*(35*b^2*e^2 + 48*c^2*d^2 - 84*b*c*d*e))/(8*(b^8*e^3 - b^5*c^3*d^3 + 3*b^6*c^2*d^2*e - 3*b^7*c*d*e^2)) - ((-c^3*(b*e - c*d)^3)^(1/2)*(((d + e*x)^(1/2)*(b^6*c^3*e^8 + 4608*c^9*d^6*e^2 - 13824*b*c^8*d^5*e^3 + 22*b^5*c^4*d*e^7 + 15072*b^2*c^7*d^4*e^4 - 7104*b^3*c^6*d^3*e^5 + 1226*b^4*c^5*d^2*e^6))/(8*(b^8*c^2*d^4 + b^10*d^2*e^2 - 2*b^9*c*d^3*e)) - ((-c^3*(b*e - c*d)^3)^(1/2)*((b^14*c^2*d*e^7 - 24*b^10*c^6*d^5*e^3 + 60*b^11*c^5*d^4*e^4 - 46*b^12*c^4*d^3*e^5 + 9*b^13*c^3*d^2*e^6)/(b^12*c^2*d^4 + b^14*d^2*e^2 - 2*b^13*c*d^3*e) + ((-c^3*(b*e - c*d)^3)^(1/2)*(d + e*x)^(1/2)*(35*b^2*e^2 + 48*c^2*d^2 - 84*b*c*d*e)*(128*b^10*c^5*d^5*e^2 - 320*b^11*c^4*d^4*e^3 + 256*b^12*c^3*d^3*e^4 - 64*b^13*c^2*d^2*e^5))/(64*(b^8*c^2*d^4 + b^10*d^2*e^2 - 2*b^9*c*d^3*e)*(b^8*e^3 - b^5*c^3*d^3 + 3*b^6*c^2*d^2*e - 3*b^7*c*d*e^2)))*(35*b^2*e^2 + 48*c^2*d^2 - 84*b*c*d*e))/(8*(b^8*e^3 - b^5*c^3*d^3 + 3*b^6*c^2*d^2*e - 3*b^7*c*d*e^2)))*(35*b^2*e^2 + 48*c^2*d^2 - 84*b*c*d*e))/(8*(b^8*e^3 - b^5*c^3*d^3 + 3*b^6*c^2*d^2*e - 3*b^7*c*d*e^2))))*(-c^3*(b*e - c*d)^3)^(1/2)*(35*b^2*e^2 + 48*c^2*d^2 - 84*b*c*d*e)*1i)/(4*(b^8*e^3 - b^5*c^3*d^3 + 3*b^6*c^2*d^2*e - 3*b^7*c*d*e^2))","B"
383,1,6715,299,2.877076,"\text{Not used}","int(1/((b*x + c*x^2)^3*(d + e*x)^(1/2)),x)","\frac{\frac{e\,{\left(d+e\,x\right)}^{3/2}\,\left(3\,b^5\,e^5-10\,b^4\,c\,d\,e^4-24\,b^3\,c^2\,d^2\,e^3+136\,b^2\,c^3\,d^3\,e^2-180\,b\,c^4\,d^4\,e+72\,c^5\,d^5\right)}{4\,b^4\,{\left(c\,d^2-b\,d\,e\right)}^2}-\frac{\sqrt{d+e\,x}\,\left(-5\,b^4\,e^5+3\,b^3\,c\,d\,e^4+21\,b^2\,c^2\,d^2\,e^3-48\,b\,c^3\,d^3\,e^2+24\,c^4\,d^4\,e\right)}{4\,b^4\,\left(c\,d^2-b\,d\,e\right)}+\frac{e\,{\left(d+e\,x\right)}^{5/2}\,\left(6\,b^4\,c\,e^4+b^3\,c^2\,d\,e^3-73\,b^2\,c^3\,d^2\,e^2+144\,b\,c^4\,d^3\,e-72\,c^5\,d^4\right)}{4\,b^4\,{\left(c\,d^2-b\,d\,e\right)}^2}+\frac{3\,c\,e\,{\left(d+e\,x\right)}^{7/2}\,\left(b^3\,c\,e^3+2\,b^2\,c^2\,d\,e^2-12\,b\,c^3\,d^2\,e+8\,c^4\,d^3\right)}{4\,b^4\,{\left(c\,d^2-b\,d\,e\right)}^2}}{c^2\,{\left(d+e\,x\right)}^4-\left(d+e\,x\right)\,\left(2\,b^2\,d\,e^2-6\,b\,c\,d^2\,e+4\,c^2\,d^3\right)-\left(4\,c^2\,d-2\,b\,c\,e\right)\,{\left(d+e\,x\right)}^3+{\left(d+e\,x\right)}^2\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2\right)+c^2\,d^4+b^2\,d^2\,e^2-2\,b\,c\,d^3\,e}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{\sqrt{d+e\,x}\,\left(9\,b^8\,c^3\,e^{10}+36\,b^7\,c^4\,d\,e^9+198\,b^6\,c^5\,d^2\,e^8-180\,b^5\,c^6\,d^3\,e^7+3978\,b^4\,c^7\,d^4\,e^6-17568\,b^3\,c^8\,d^5\,e^5+27360\,b^2\,c^9\,d^6\,e^4-18432\,b\,c^{10}\,d^7\,e^3+4608\,c^{11}\,d^8\,e^2\right)}{8\,\left(b^{12}\,d^4\,e^4-4\,b^{11}\,c\,d^5\,e^3+6\,b^{10}\,c^2\,d^6\,e^2-4\,b^9\,c^3\,d^7\,e+b^8\,c^4\,d^8\right)}+\frac{3\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{3\,b^{16}\,c^2\,d^2\,e^9-3\,b^{15}\,c^3\,d^3\,e^8+18\,b^{14}\,c^4\,d^4\,e^7-87\,b^{13}\,c^5\,d^5\,e^6+141\,b^{12}\,c^6\,d^6\,e^5-96\,b^{11}\,c^7\,d^7\,e^4+24\,b^{10}\,c^8\,d^8\,e^3}{b^{16}\,d^4\,e^4-4\,b^{15}\,c\,d^5\,e^3+6\,b^{14}\,c^2\,d^6\,e^2-4\,b^{13}\,c^3\,d^7\,e+b^{12}\,c^4\,d^8}-\frac{3\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\sqrt{d+e\,x}\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(-64\,b^{15}\,c^2\,d^4\,e^7+384\,b^{14}\,c^3\,d^5\,e^6-896\,b^{13}\,c^4\,d^6\,e^5+1024\,b^{12}\,c^5\,d^7\,e^4-576\,b^{11}\,c^6\,d^8\,e^3+128\,b^{10}\,c^7\,d^9\,e^2\right)}{64\,\left(b^{12}\,d^4\,e^4-4\,b^{11}\,c\,d^5\,e^3+6\,b^{10}\,c^2\,d^6\,e^2-4\,b^9\,c^3\,d^7\,e+b^8\,c^4\,d^8\right)\,\left(b^{10}\,e^5-5\,b^9\,c\,d\,e^4+10\,b^8\,c^2\,d^2\,e^3-10\,b^7\,c^3\,d^3\,e^2+5\,b^6\,c^4\,d^4\,e-b^5\,c^5\,d^5\right)}\right)\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,\left(b^{10}\,e^5-5\,b^9\,c\,d\,e^4+10\,b^8\,c^2\,d^2\,e^3-10\,b^7\,c^3\,d^3\,e^2+5\,b^6\,c^4\,d^4\,e-b^5\,c^5\,d^5\right)}\right)\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{8\,\left(b^{10}\,e^5-5\,b^9\,c\,d\,e^4+10\,b^8\,c^2\,d^2\,e^3-10\,b^7\,c^3\,d^3\,e^2+5\,b^6\,c^4\,d^4\,e-b^5\,c^5\,d^5\right)}+\frac{\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{\sqrt{d+e\,x}\,\left(9\,b^8\,c^3\,e^{10}+36\,b^7\,c^4\,d\,e^9+198\,b^6\,c^5\,d^2\,e^8-180\,b^5\,c^6\,d^3\,e^7+3978\,b^4\,c^7\,d^4\,e^6-17568\,b^3\,c^8\,d^5\,e^5+27360\,b^2\,c^9\,d^6\,e^4-18432\,b\,c^{10}\,d^7\,e^3+4608\,c^{11}\,d^8\,e^2\right)}{8\,\left(b^{12}\,d^4\,e^4-4\,b^{11}\,c\,d^5\,e^3+6\,b^{10}\,c^2\,d^6\,e^2-4\,b^9\,c^3\,d^7\,e+b^8\,c^4\,d^8\right)}-\frac{3\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{3\,b^{16}\,c^2\,d^2\,e^9-3\,b^{15}\,c^3\,d^3\,e^8+18\,b^{14}\,c^4\,d^4\,e^7-87\,b^{13}\,c^5\,d^5\,e^6+141\,b^{12}\,c^6\,d^6\,e^5-96\,b^{11}\,c^7\,d^7\,e^4+24\,b^{10}\,c^8\,d^8\,e^3}{b^{16}\,d^4\,e^4-4\,b^{15}\,c\,d^5\,e^3+6\,b^{14}\,c^2\,d^6\,e^2-4\,b^{13}\,c^3\,d^7\,e+b^{12}\,c^4\,d^8}+\frac{3\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\sqrt{d+e\,x}\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(-64\,b^{15}\,c^2\,d^4\,e^7+384\,b^{14}\,c^3\,d^5\,e^6-896\,b^{13}\,c^4\,d^6\,e^5+1024\,b^{12}\,c^5\,d^7\,e^4-576\,b^{11}\,c^6\,d^8\,e^3+128\,b^{10}\,c^7\,d^9\,e^2\right)}{64\,\left(b^{12}\,d^4\,e^4-4\,b^{11}\,c\,d^5\,e^3+6\,b^{10}\,c^2\,d^6\,e^2-4\,b^9\,c^3\,d^7\,e+b^8\,c^4\,d^8\right)\,\left(b^{10}\,e^5-5\,b^9\,c\,d\,e^4+10\,b^8\,c^2\,d^2\,e^3-10\,b^7\,c^3\,d^3\,e^2+5\,b^6\,c^4\,d^4\,e-b^5\,c^5\,d^5\right)}\right)\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,\left(b^{10}\,e^5-5\,b^9\,c\,d\,e^4+10\,b^8\,c^2\,d^2\,e^3-10\,b^7\,c^3\,d^3\,e^2+5\,b^6\,c^4\,d^4\,e-b^5\,c^5\,d^5\right)}\right)\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{8\,\left(b^{10}\,e^5-5\,b^9\,c\,d\,e^4+10\,b^8\,c^2\,d^2\,e^3-10\,b^7\,c^3\,d^3\,e^2+5\,b^6\,c^4\,d^4\,e-b^5\,c^5\,d^5\right)}}{\frac{\frac{567\,b^7\,c^5\,e^{10}}{32}+\frac{1215\,b^6\,c^6\,d\,e^9}{16}+\frac{351\,b^5\,c^7\,d^2\,e^8}{8}-\frac{1701\,b^4\,c^8\,d^3\,e^7}{4}-2430\,b^3\,c^9\,d^4\,e^6+7020\,b^2\,c^{10}\,d^5\,e^5-6048\,b\,c^{11}\,d^6\,e^4+1728\,c^{12}\,d^7\,e^3}{b^{16}\,d^4\,e^4-4\,b^{15}\,c\,d^5\,e^3+6\,b^{14}\,c^2\,d^6\,e^2-4\,b^{13}\,c^3\,d^7\,e+b^{12}\,c^4\,d^8}-\frac{3\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{\sqrt{d+e\,x}\,\left(9\,b^8\,c^3\,e^{10}+36\,b^7\,c^4\,d\,e^9+198\,b^6\,c^5\,d^2\,e^8-180\,b^5\,c^6\,d^3\,e^7+3978\,b^4\,c^7\,d^4\,e^6-17568\,b^3\,c^8\,d^5\,e^5+27360\,b^2\,c^9\,d^6\,e^4-18432\,b\,c^{10}\,d^7\,e^3+4608\,c^{11}\,d^8\,e^2\right)}{8\,\left(b^{12}\,d^4\,e^4-4\,b^{11}\,c\,d^5\,e^3+6\,b^{10}\,c^2\,d^6\,e^2-4\,b^9\,c^3\,d^7\,e+b^8\,c^4\,d^8\right)}+\frac{3\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{3\,b^{16}\,c^2\,d^2\,e^9-3\,b^{15}\,c^3\,d^3\,e^8+18\,b^{14}\,c^4\,d^4\,e^7-87\,b^{13}\,c^5\,d^5\,e^6+141\,b^{12}\,c^6\,d^6\,e^5-96\,b^{11}\,c^7\,d^7\,e^4+24\,b^{10}\,c^8\,d^8\,e^3}{b^{16}\,d^4\,e^4-4\,b^{15}\,c\,d^5\,e^3+6\,b^{14}\,c^2\,d^6\,e^2-4\,b^{13}\,c^3\,d^7\,e+b^{12}\,c^4\,d^8}-\frac{3\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\sqrt{d+e\,x}\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(-64\,b^{15}\,c^2\,d^4\,e^7+384\,b^{14}\,c^3\,d^5\,e^6-896\,b^{13}\,c^4\,d^6\,e^5+1024\,b^{12}\,c^5\,d^7\,e^4-576\,b^{11}\,c^6\,d^8\,e^3+128\,b^{10}\,c^7\,d^9\,e^2\right)}{64\,\left(b^{12}\,d^4\,e^4-4\,b^{11}\,c\,d^5\,e^3+6\,b^{10}\,c^2\,d^6\,e^2-4\,b^9\,c^3\,d^7\,e+b^8\,c^4\,d^8\right)\,\left(b^{10}\,e^5-5\,b^9\,c\,d\,e^4+10\,b^8\,c^2\,d^2\,e^3-10\,b^7\,c^3\,d^3\,e^2+5\,b^6\,c^4\,d^4\,e-b^5\,c^5\,d^5\right)}\right)\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,\left(b^{10}\,e^5-5\,b^9\,c\,d\,e^4+10\,b^8\,c^2\,d^2\,e^3-10\,b^7\,c^3\,d^3\,e^2+5\,b^6\,c^4\,d^4\,e-b^5\,c^5\,d^5\right)}\right)\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,\left(b^{10}\,e^5-5\,b^9\,c\,d\,e^4+10\,b^8\,c^2\,d^2\,e^3-10\,b^7\,c^3\,d^3\,e^2+5\,b^6\,c^4\,d^4\,e-b^5\,c^5\,d^5\right)}+\frac{3\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{\sqrt{d+e\,x}\,\left(9\,b^8\,c^3\,e^{10}+36\,b^7\,c^4\,d\,e^9+198\,b^6\,c^5\,d^2\,e^8-180\,b^5\,c^6\,d^3\,e^7+3978\,b^4\,c^7\,d^4\,e^6-17568\,b^3\,c^8\,d^5\,e^5+27360\,b^2\,c^9\,d^6\,e^4-18432\,b\,c^{10}\,d^7\,e^3+4608\,c^{11}\,d^8\,e^2\right)}{8\,\left(b^{12}\,d^4\,e^4-4\,b^{11}\,c\,d^5\,e^3+6\,b^{10}\,c^2\,d^6\,e^2-4\,b^9\,c^3\,d^7\,e+b^8\,c^4\,d^8\right)}-\frac{3\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(\frac{3\,b^{16}\,c^2\,d^2\,e^9-3\,b^{15}\,c^3\,d^3\,e^8+18\,b^{14}\,c^4\,d^4\,e^7-87\,b^{13}\,c^5\,d^5\,e^6+141\,b^{12}\,c^6\,d^6\,e^5-96\,b^{11}\,c^7\,d^7\,e^4+24\,b^{10}\,c^8\,d^8\,e^3}{b^{16}\,d^4\,e^4-4\,b^{15}\,c\,d^5\,e^3+6\,b^{14}\,c^2\,d^6\,e^2-4\,b^{13}\,c^3\,d^7\,e+b^{12}\,c^4\,d^8}+\frac{3\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\sqrt{d+e\,x}\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(-64\,b^{15}\,c^2\,d^4\,e^7+384\,b^{14}\,c^3\,d^5\,e^6-896\,b^{13}\,c^4\,d^6\,e^5+1024\,b^{12}\,c^5\,d^7\,e^4-576\,b^{11}\,c^6\,d^8\,e^3+128\,b^{10}\,c^7\,d^9\,e^2\right)}{64\,\left(b^{12}\,d^4\,e^4-4\,b^{11}\,c\,d^5\,e^3+6\,b^{10}\,c^2\,d^6\,e^2-4\,b^9\,c^3\,d^7\,e+b^8\,c^4\,d^8\right)\,\left(b^{10}\,e^5-5\,b^9\,c\,d\,e^4+10\,b^8\,c^2\,d^2\,e^3-10\,b^7\,c^3\,d^3\,e^2+5\,b^6\,c^4\,d^4\,e-b^5\,c^5\,d^5\right)}\right)\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,\left(b^{10}\,e^5-5\,b^9\,c\,d\,e^4+10\,b^8\,c^2\,d^2\,e^3-10\,b^7\,c^3\,d^3\,e^2+5\,b^6\,c^4\,d^4\,e-b^5\,c^5\,d^5\right)}\right)\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,\left(b^{10}\,e^5-5\,b^9\,c\,d\,e^4+10\,b^8\,c^2\,d^2\,e^3-10\,b^7\,c^3\,d^3\,e^2+5\,b^6\,c^4\,d^4\,e-b^5\,c^5\,d^5\right)}}\right)\,\sqrt{-c^5\,{\left(b\,e-c\,d\right)}^5}\,\left(21\,b^2\,e^2-36\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{4\,\left(b^{10}\,e^5-5\,b^9\,c\,d\,e^4+10\,b^8\,c^2\,d^2\,e^3-10\,b^7\,c^3\,d^3\,e^2+5\,b^6\,c^4\,d^4\,e-b^5\,c^5\,d^5\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{d+e\,x}\,\left(9\,b^8\,c^3\,e^{10}+36\,b^7\,c^4\,d\,e^9+198\,b^6\,c^5\,d^2\,e^8-180\,b^5\,c^6\,d^3\,e^7+3978\,b^4\,c^7\,d^4\,e^6-17568\,b^3\,c^8\,d^5\,e^5+27360\,b^2\,c^9\,d^6\,e^4-18432\,b\,c^{10}\,d^7\,e^3+4608\,c^{11}\,d^8\,e^2\right)}{8\,\left(b^{12}\,d^4\,e^4-4\,b^{11}\,c\,d^5\,e^3+6\,b^{10}\,c^2\,d^6\,e^2-4\,b^9\,c^3\,d^7\,e+b^8\,c^4\,d^8\right)}+\frac{3\,\left(\frac{3\,b^{16}\,c^2\,d^2\,e^9-3\,b^{15}\,c^3\,d^3\,e^8+18\,b^{14}\,c^4\,d^4\,e^7-87\,b^{13}\,c^5\,d^5\,e^6+141\,b^{12}\,c^6\,d^6\,e^5-96\,b^{11}\,c^7\,d^7\,e^4+24\,b^{10}\,c^8\,d^8\,e^3}{b^{16}\,d^4\,e^4-4\,b^{15}\,c\,d^5\,e^3+6\,b^{14}\,c^2\,d^6\,e^2-4\,b^{13}\,c^3\,d^7\,e+b^{12}\,c^4\,d^8}-\frac{3\,\sqrt{d+e\,x}\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(-64\,b^{15}\,c^2\,d^4\,e^7+384\,b^{14}\,c^3\,d^5\,e^6-896\,b^{13}\,c^4\,d^6\,e^5+1024\,b^{12}\,c^5\,d^7\,e^4-576\,b^{11}\,c^6\,d^8\,e^3+128\,b^{10}\,c^7\,d^9\,e^2\right)}{64\,b^5\,\sqrt{d^5}\,\left(b^{12}\,d^4\,e^4-4\,b^{11}\,c\,d^5\,e^3+6\,b^{10}\,c^2\,d^6\,e^2-4\,b^9\,c^3\,d^7\,e+b^8\,c^4\,d^8\right)}\right)\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5\,\sqrt{d^5}}\right)\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{8\,b^5\,\sqrt{d^5}}+\frac{\left(\frac{\sqrt{d+e\,x}\,\left(9\,b^8\,c^3\,e^{10}+36\,b^7\,c^4\,d\,e^9+198\,b^6\,c^5\,d^2\,e^8-180\,b^5\,c^6\,d^3\,e^7+3978\,b^4\,c^7\,d^4\,e^6-17568\,b^3\,c^8\,d^5\,e^5+27360\,b^2\,c^9\,d^6\,e^4-18432\,b\,c^{10}\,d^7\,e^3+4608\,c^{11}\,d^8\,e^2\right)}{8\,\left(b^{12}\,d^4\,e^4-4\,b^{11}\,c\,d^5\,e^3+6\,b^{10}\,c^2\,d^6\,e^2-4\,b^9\,c^3\,d^7\,e+b^8\,c^4\,d^8\right)}-\frac{3\,\left(\frac{3\,b^{16}\,c^2\,d^2\,e^9-3\,b^{15}\,c^3\,d^3\,e^8+18\,b^{14}\,c^4\,d^4\,e^7-87\,b^{13}\,c^5\,d^5\,e^6+141\,b^{12}\,c^6\,d^6\,e^5-96\,b^{11}\,c^7\,d^7\,e^4+24\,b^{10}\,c^8\,d^8\,e^3}{b^{16}\,d^4\,e^4-4\,b^{15}\,c\,d^5\,e^3+6\,b^{14}\,c^2\,d^6\,e^2-4\,b^{13}\,c^3\,d^7\,e+b^{12}\,c^4\,d^8}+\frac{3\,\sqrt{d+e\,x}\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(-64\,b^{15}\,c^2\,d^4\,e^7+384\,b^{14}\,c^3\,d^5\,e^6-896\,b^{13}\,c^4\,d^6\,e^5+1024\,b^{12}\,c^5\,d^7\,e^4-576\,b^{11}\,c^6\,d^8\,e^3+128\,b^{10}\,c^7\,d^9\,e^2\right)}{64\,b^5\,\sqrt{d^5}\,\left(b^{12}\,d^4\,e^4-4\,b^{11}\,c\,d^5\,e^3+6\,b^{10}\,c^2\,d^6\,e^2-4\,b^9\,c^3\,d^7\,e+b^8\,c^4\,d^8\right)}\right)\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5\,\sqrt{d^5}}\right)\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{8\,b^5\,\sqrt{d^5}}}{\frac{\frac{567\,b^7\,c^5\,e^{10}}{32}+\frac{1215\,b^6\,c^6\,d\,e^9}{16}+\frac{351\,b^5\,c^7\,d^2\,e^8}{8}-\frac{1701\,b^4\,c^8\,d^3\,e^7}{4}-2430\,b^3\,c^9\,d^4\,e^6+7020\,b^2\,c^{10}\,d^5\,e^5-6048\,b\,c^{11}\,d^6\,e^4+1728\,c^{12}\,d^7\,e^3}{b^{16}\,d^4\,e^4-4\,b^{15}\,c\,d^5\,e^3+6\,b^{14}\,c^2\,d^6\,e^2-4\,b^{13}\,c^3\,d^7\,e+b^{12}\,c^4\,d^8}-\frac{3\,\left(\frac{\sqrt{d+e\,x}\,\left(9\,b^8\,c^3\,e^{10}+36\,b^7\,c^4\,d\,e^9+198\,b^6\,c^5\,d^2\,e^8-180\,b^5\,c^6\,d^3\,e^7+3978\,b^4\,c^7\,d^4\,e^6-17568\,b^3\,c^8\,d^5\,e^5+27360\,b^2\,c^9\,d^6\,e^4-18432\,b\,c^{10}\,d^7\,e^3+4608\,c^{11}\,d^8\,e^2\right)}{8\,\left(b^{12}\,d^4\,e^4-4\,b^{11}\,c\,d^5\,e^3+6\,b^{10}\,c^2\,d^6\,e^2-4\,b^9\,c^3\,d^7\,e+b^8\,c^4\,d^8\right)}+\frac{3\,\left(\frac{3\,b^{16}\,c^2\,d^2\,e^9-3\,b^{15}\,c^3\,d^3\,e^8+18\,b^{14}\,c^4\,d^4\,e^7-87\,b^{13}\,c^5\,d^5\,e^6+141\,b^{12}\,c^6\,d^6\,e^5-96\,b^{11}\,c^7\,d^7\,e^4+24\,b^{10}\,c^8\,d^8\,e^3}{b^{16}\,d^4\,e^4-4\,b^{15}\,c\,d^5\,e^3+6\,b^{14}\,c^2\,d^6\,e^2-4\,b^{13}\,c^3\,d^7\,e+b^{12}\,c^4\,d^8}-\frac{3\,\sqrt{d+e\,x}\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(-64\,b^{15}\,c^2\,d^4\,e^7+384\,b^{14}\,c^3\,d^5\,e^6-896\,b^{13}\,c^4\,d^6\,e^5+1024\,b^{12}\,c^5\,d^7\,e^4-576\,b^{11}\,c^6\,d^8\,e^3+128\,b^{10}\,c^7\,d^9\,e^2\right)}{64\,b^5\,\sqrt{d^5}\,\left(b^{12}\,d^4\,e^4-4\,b^{11}\,c\,d^5\,e^3+6\,b^{10}\,c^2\,d^6\,e^2-4\,b^9\,c^3\,d^7\,e+b^8\,c^4\,d^8\right)}\right)\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5\,\sqrt{d^5}}\right)\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5\,\sqrt{d^5}}+\frac{3\,\left(\frac{\sqrt{d+e\,x}\,\left(9\,b^8\,c^3\,e^{10}+36\,b^7\,c^4\,d\,e^9+198\,b^6\,c^5\,d^2\,e^8-180\,b^5\,c^6\,d^3\,e^7+3978\,b^4\,c^7\,d^4\,e^6-17568\,b^3\,c^8\,d^5\,e^5+27360\,b^2\,c^9\,d^6\,e^4-18432\,b\,c^{10}\,d^7\,e^3+4608\,c^{11}\,d^8\,e^2\right)}{8\,\left(b^{12}\,d^4\,e^4-4\,b^{11}\,c\,d^5\,e^3+6\,b^{10}\,c^2\,d^6\,e^2-4\,b^9\,c^3\,d^7\,e+b^8\,c^4\,d^8\right)}-\frac{3\,\left(\frac{3\,b^{16}\,c^2\,d^2\,e^9-3\,b^{15}\,c^3\,d^3\,e^8+18\,b^{14}\,c^4\,d^4\,e^7-87\,b^{13}\,c^5\,d^5\,e^6+141\,b^{12}\,c^6\,d^6\,e^5-96\,b^{11}\,c^7\,d^7\,e^4+24\,b^{10}\,c^8\,d^8\,e^3}{b^{16}\,d^4\,e^4-4\,b^{15}\,c\,d^5\,e^3+6\,b^{14}\,c^2\,d^6\,e^2-4\,b^{13}\,c^3\,d^7\,e+b^{12}\,c^4\,d^8}+\frac{3\,\sqrt{d+e\,x}\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(-64\,b^{15}\,c^2\,d^4\,e^7+384\,b^{14}\,c^3\,d^5\,e^6-896\,b^{13}\,c^4\,d^6\,e^5+1024\,b^{12}\,c^5\,d^7\,e^4-576\,b^{11}\,c^6\,d^8\,e^3+128\,b^{10}\,c^7\,d^9\,e^2\right)}{64\,b^5\,\sqrt{d^5}\,\left(b^{12}\,d^4\,e^4-4\,b^{11}\,c\,d^5\,e^3+6\,b^{10}\,c^2\,d^6\,e^2-4\,b^9\,c^3\,d^7\,e+b^8\,c^4\,d^8\right)}\right)\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5\,\sqrt{d^5}}\right)\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5\,\sqrt{d^5}}}\right)\,\left(b^2\,e^2+4\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{4\,b^5\,\sqrt{d^5}}","Not used",1,"((e*(d + e*x)^(3/2)*(3*b^5*e^5 + 72*c^5*d^5 + 136*b^2*c^3*d^3*e^2 - 24*b^3*c^2*d^2*e^3 - 180*b*c^4*d^4*e - 10*b^4*c*d*e^4))/(4*b^4*(c*d^2 - b*d*e)^2) - ((d + e*x)^(1/2)*(24*c^4*d^4*e - 5*b^4*e^5 - 48*b*c^3*d^3*e^2 + 21*b^2*c^2*d^2*e^3 + 3*b^3*c*d*e^4))/(4*b^4*(c*d^2 - b*d*e)) + (e*(d + e*x)^(5/2)*(6*b^4*c*e^4 - 72*c^5*d^4 + b^3*c^2*d*e^3 - 73*b^2*c^3*d^2*e^2 + 144*b*c^4*d^3*e))/(4*b^4*(c*d^2 - b*d*e)^2) + (3*c*e*(d + e*x)^(7/2)*(8*c^4*d^3 + b^3*c*e^3 + 2*b^2*c^2*d*e^2 - 12*b*c^3*d^2*e))/(4*b^4*(c*d^2 - b*d*e)^2))/(c^2*(d + e*x)^4 - (d + e*x)*(4*c^2*d^3 + 2*b^2*d*e^2 - 6*b*c*d^2*e) - (4*c^2*d - 2*b*c*e)*(d + e*x)^3 + (d + e*x)^2*(b^2*e^2 + 6*c^2*d^2 - 6*b*c*d*e) + c^2*d^4 + b^2*d^2*e^2 - 2*b*c*d^3*e) - (atan((((-c^5*(b*e - c*d)^5)^(1/2)*(((d + e*x)^(1/2)*(9*b^8*c^3*e^10 + 4608*c^11*d^8*e^2 - 18432*b*c^10*d^7*e^3 + 36*b^7*c^4*d*e^9 + 27360*b^2*c^9*d^6*e^4 - 17568*b^3*c^8*d^5*e^5 + 3978*b^4*c^7*d^4*e^6 - 180*b^5*c^6*d^3*e^7 + 198*b^6*c^5*d^2*e^8))/(8*(b^8*c^4*d^8 + b^12*d^4*e^4 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 6*b^10*c^2*d^6*e^2)) + (3*(-c^5*(b*e - c*d)^5)^(1/2)*((24*b^10*c^8*d^8*e^3 - 96*b^11*c^7*d^7*e^4 + 141*b^12*c^6*d^6*e^5 - 87*b^13*c^5*d^5*e^6 + 18*b^14*c^4*d^4*e^7 - 3*b^15*c^3*d^3*e^8 + 3*b^16*c^2*d^2*e^9)/(b^12*c^4*d^8 + b^16*d^4*e^4 - 4*b^13*c^3*d^7*e - 4*b^15*c*d^5*e^3 + 6*b^14*c^2*d^6*e^2) - (3*(-c^5*(b*e - c*d)^5)^(1/2)*(d + e*x)^(1/2)*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e)*(128*b^10*c^7*d^9*e^2 - 576*b^11*c^6*d^8*e^3 + 1024*b^12*c^5*d^7*e^4 - 896*b^13*c^4*d^6*e^5 + 384*b^14*c^3*d^5*e^6 - 64*b^15*c^2*d^4*e^7))/(64*(b^8*c^4*d^8 + b^12*d^4*e^4 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 6*b^10*c^2*d^6*e^2)*(b^10*e^5 - b^5*c^5*d^5 + 5*b^6*c^4*d^4*e - 10*b^7*c^3*d^3*e^2 + 10*b^8*c^2*d^2*e^3 - 5*b^9*c*d*e^4)))*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e))/(8*(b^10*e^5 - b^5*c^5*d^5 + 5*b^6*c^4*d^4*e - 10*b^7*c^3*d^3*e^2 + 10*b^8*c^2*d^2*e^3 - 5*b^9*c*d*e^4)))*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e)*3i)/(8*(b^10*e^5 - b^5*c^5*d^5 + 5*b^6*c^4*d^4*e - 10*b^7*c^3*d^3*e^2 + 10*b^8*c^2*d^2*e^3 - 5*b^9*c*d*e^4)) + ((-c^5*(b*e - c*d)^5)^(1/2)*(((d + e*x)^(1/2)*(9*b^8*c^3*e^10 + 4608*c^11*d^8*e^2 - 18432*b*c^10*d^7*e^3 + 36*b^7*c^4*d*e^9 + 27360*b^2*c^9*d^6*e^4 - 17568*b^3*c^8*d^5*e^5 + 3978*b^4*c^7*d^4*e^6 - 180*b^5*c^6*d^3*e^7 + 198*b^6*c^5*d^2*e^8))/(8*(b^8*c^4*d^8 + b^12*d^4*e^4 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 6*b^10*c^2*d^6*e^2)) - (3*(-c^5*(b*e - c*d)^5)^(1/2)*((24*b^10*c^8*d^8*e^3 - 96*b^11*c^7*d^7*e^4 + 141*b^12*c^6*d^6*e^5 - 87*b^13*c^5*d^5*e^6 + 18*b^14*c^4*d^4*e^7 - 3*b^15*c^3*d^3*e^8 + 3*b^16*c^2*d^2*e^9)/(b^12*c^4*d^8 + b^16*d^4*e^4 - 4*b^13*c^3*d^7*e - 4*b^15*c*d^5*e^3 + 6*b^14*c^2*d^6*e^2) + (3*(-c^5*(b*e - c*d)^5)^(1/2)*(d + e*x)^(1/2)*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e)*(128*b^10*c^7*d^9*e^2 - 576*b^11*c^6*d^8*e^3 + 1024*b^12*c^5*d^7*e^4 - 896*b^13*c^4*d^6*e^5 + 384*b^14*c^3*d^5*e^6 - 64*b^15*c^2*d^4*e^7))/(64*(b^8*c^4*d^8 + b^12*d^4*e^4 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 6*b^10*c^2*d^6*e^2)*(b^10*e^5 - b^5*c^5*d^5 + 5*b^6*c^4*d^4*e - 10*b^7*c^3*d^3*e^2 + 10*b^8*c^2*d^2*e^3 - 5*b^9*c*d*e^4)))*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e))/(8*(b^10*e^5 - b^5*c^5*d^5 + 5*b^6*c^4*d^4*e - 10*b^7*c^3*d^3*e^2 + 10*b^8*c^2*d^2*e^3 - 5*b^9*c*d*e^4)))*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e)*3i)/(8*(b^10*e^5 - b^5*c^5*d^5 + 5*b^6*c^4*d^4*e - 10*b^7*c^3*d^3*e^2 + 10*b^8*c^2*d^2*e^3 - 5*b^9*c*d*e^4)))/(((567*b^7*c^5*e^10)/32 + 1728*c^12*d^7*e^3 - 6048*b*c^11*d^6*e^4 + (1215*b^6*c^6*d*e^9)/16 + 7020*b^2*c^10*d^5*e^5 - 2430*b^3*c^9*d^4*e^6 - (1701*b^4*c^8*d^3*e^7)/4 + (351*b^5*c^7*d^2*e^8)/8)/(b^12*c^4*d^8 + b^16*d^4*e^4 - 4*b^13*c^3*d^7*e - 4*b^15*c*d^5*e^3 + 6*b^14*c^2*d^6*e^2) - (3*(-c^5*(b*e - c*d)^5)^(1/2)*(((d + e*x)^(1/2)*(9*b^8*c^3*e^10 + 4608*c^11*d^8*e^2 - 18432*b*c^10*d^7*e^3 + 36*b^7*c^4*d*e^9 + 27360*b^2*c^9*d^6*e^4 - 17568*b^3*c^8*d^5*e^5 + 3978*b^4*c^7*d^4*e^6 - 180*b^5*c^6*d^3*e^7 + 198*b^6*c^5*d^2*e^8))/(8*(b^8*c^4*d^8 + b^12*d^4*e^4 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 6*b^10*c^2*d^6*e^2)) + (3*(-c^5*(b*e - c*d)^5)^(1/2)*((24*b^10*c^8*d^8*e^3 - 96*b^11*c^7*d^7*e^4 + 141*b^12*c^6*d^6*e^5 - 87*b^13*c^5*d^5*e^6 + 18*b^14*c^4*d^4*e^7 - 3*b^15*c^3*d^3*e^8 + 3*b^16*c^2*d^2*e^9)/(b^12*c^4*d^8 + b^16*d^4*e^4 - 4*b^13*c^3*d^7*e - 4*b^15*c*d^5*e^3 + 6*b^14*c^2*d^6*e^2) - (3*(-c^5*(b*e - c*d)^5)^(1/2)*(d + e*x)^(1/2)*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e)*(128*b^10*c^7*d^9*e^2 - 576*b^11*c^6*d^8*e^3 + 1024*b^12*c^5*d^7*e^4 - 896*b^13*c^4*d^6*e^5 + 384*b^14*c^3*d^5*e^6 - 64*b^15*c^2*d^4*e^7))/(64*(b^8*c^4*d^8 + b^12*d^4*e^4 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 6*b^10*c^2*d^6*e^2)*(b^10*e^5 - b^5*c^5*d^5 + 5*b^6*c^4*d^4*e - 10*b^7*c^3*d^3*e^2 + 10*b^8*c^2*d^2*e^3 - 5*b^9*c*d*e^4)))*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e))/(8*(b^10*e^5 - b^5*c^5*d^5 + 5*b^6*c^4*d^4*e - 10*b^7*c^3*d^3*e^2 + 10*b^8*c^2*d^2*e^3 - 5*b^9*c*d*e^4)))*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e))/(8*(b^10*e^5 - b^5*c^5*d^5 + 5*b^6*c^4*d^4*e - 10*b^7*c^3*d^3*e^2 + 10*b^8*c^2*d^2*e^3 - 5*b^9*c*d*e^4)) + (3*(-c^5*(b*e - c*d)^5)^(1/2)*(((d + e*x)^(1/2)*(9*b^8*c^3*e^10 + 4608*c^11*d^8*e^2 - 18432*b*c^10*d^7*e^3 + 36*b^7*c^4*d*e^9 + 27360*b^2*c^9*d^6*e^4 - 17568*b^3*c^8*d^5*e^5 + 3978*b^4*c^7*d^4*e^6 - 180*b^5*c^6*d^3*e^7 + 198*b^6*c^5*d^2*e^8))/(8*(b^8*c^4*d^8 + b^12*d^4*e^4 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 6*b^10*c^2*d^6*e^2)) - (3*(-c^5*(b*e - c*d)^5)^(1/2)*((24*b^10*c^8*d^8*e^3 - 96*b^11*c^7*d^7*e^4 + 141*b^12*c^6*d^6*e^5 - 87*b^13*c^5*d^5*e^6 + 18*b^14*c^4*d^4*e^7 - 3*b^15*c^3*d^3*e^8 + 3*b^16*c^2*d^2*e^9)/(b^12*c^4*d^8 + b^16*d^4*e^4 - 4*b^13*c^3*d^7*e - 4*b^15*c*d^5*e^3 + 6*b^14*c^2*d^6*e^2) + (3*(-c^5*(b*e - c*d)^5)^(1/2)*(d + e*x)^(1/2)*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e)*(128*b^10*c^7*d^9*e^2 - 576*b^11*c^6*d^8*e^3 + 1024*b^12*c^5*d^7*e^4 - 896*b^13*c^4*d^6*e^5 + 384*b^14*c^3*d^5*e^6 - 64*b^15*c^2*d^4*e^7))/(64*(b^8*c^4*d^8 + b^12*d^4*e^4 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 6*b^10*c^2*d^6*e^2)*(b^10*e^5 - b^5*c^5*d^5 + 5*b^6*c^4*d^4*e - 10*b^7*c^3*d^3*e^2 + 10*b^8*c^2*d^2*e^3 - 5*b^9*c*d*e^4)))*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e))/(8*(b^10*e^5 - b^5*c^5*d^5 + 5*b^6*c^4*d^4*e - 10*b^7*c^3*d^3*e^2 + 10*b^8*c^2*d^2*e^3 - 5*b^9*c*d*e^4)))*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e))/(8*(b^10*e^5 - b^5*c^5*d^5 + 5*b^6*c^4*d^4*e - 10*b^7*c^3*d^3*e^2 + 10*b^8*c^2*d^2*e^3 - 5*b^9*c*d*e^4))))*(-c^5*(b*e - c*d)^5)^(1/2)*(21*b^2*e^2 + 16*c^2*d^2 - 36*b*c*d*e)*3i)/(4*(b^10*e^5 - b^5*c^5*d^5 + 5*b^6*c^4*d^4*e - 10*b^7*c^3*d^3*e^2 + 10*b^8*c^2*d^2*e^3 - 5*b^9*c*d*e^4)) - (atan((((((d + e*x)^(1/2)*(9*b^8*c^3*e^10 + 4608*c^11*d^8*e^2 - 18432*b*c^10*d^7*e^3 + 36*b^7*c^4*d*e^9 + 27360*b^2*c^9*d^6*e^4 - 17568*b^3*c^8*d^5*e^5 + 3978*b^4*c^7*d^4*e^6 - 180*b^5*c^6*d^3*e^7 + 198*b^6*c^5*d^2*e^8))/(8*(b^8*c^4*d^8 + b^12*d^4*e^4 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 6*b^10*c^2*d^6*e^2)) + (3*((24*b^10*c^8*d^8*e^3 - 96*b^11*c^7*d^7*e^4 + 141*b^12*c^6*d^6*e^5 - 87*b^13*c^5*d^5*e^6 + 18*b^14*c^4*d^4*e^7 - 3*b^15*c^3*d^3*e^8 + 3*b^16*c^2*d^2*e^9)/(b^12*c^4*d^8 + b^16*d^4*e^4 - 4*b^13*c^3*d^7*e - 4*b^15*c*d^5*e^3 + 6*b^14*c^2*d^6*e^2) - (3*(d + e*x)^(1/2)*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e)*(128*b^10*c^7*d^9*e^2 - 576*b^11*c^6*d^8*e^3 + 1024*b^12*c^5*d^7*e^4 - 896*b^13*c^4*d^6*e^5 + 384*b^14*c^3*d^5*e^6 - 64*b^15*c^2*d^4*e^7))/(64*b^5*(d^5)^(1/2)*(b^8*c^4*d^8 + b^12*d^4*e^4 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 6*b^10*c^2*d^6*e^2)))*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e))/(8*b^5*(d^5)^(1/2)))*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e)*3i)/(8*b^5*(d^5)^(1/2)) + ((((d + e*x)^(1/2)*(9*b^8*c^3*e^10 + 4608*c^11*d^8*e^2 - 18432*b*c^10*d^7*e^3 + 36*b^7*c^4*d*e^9 + 27360*b^2*c^9*d^6*e^4 - 17568*b^3*c^8*d^5*e^5 + 3978*b^4*c^7*d^4*e^6 - 180*b^5*c^6*d^3*e^7 + 198*b^6*c^5*d^2*e^8))/(8*(b^8*c^4*d^8 + b^12*d^4*e^4 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 6*b^10*c^2*d^6*e^2)) - (3*((24*b^10*c^8*d^8*e^3 - 96*b^11*c^7*d^7*e^4 + 141*b^12*c^6*d^6*e^5 - 87*b^13*c^5*d^5*e^6 + 18*b^14*c^4*d^4*e^7 - 3*b^15*c^3*d^3*e^8 + 3*b^16*c^2*d^2*e^9)/(b^12*c^4*d^8 + b^16*d^4*e^4 - 4*b^13*c^3*d^7*e - 4*b^15*c*d^5*e^3 + 6*b^14*c^2*d^6*e^2) + (3*(d + e*x)^(1/2)*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e)*(128*b^10*c^7*d^9*e^2 - 576*b^11*c^6*d^8*e^3 + 1024*b^12*c^5*d^7*e^4 - 896*b^13*c^4*d^6*e^5 + 384*b^14*c^3*d^5*e^6 - 64*b^15*c^2*d^4*e^7))/(64*b^5*(d^5)^(1/2)*(b^8*c^4*d^8 + b^12*d^4*e^4 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 6*b^10*c^2*d^6*e^2)))*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e))/(8*b^5*(d^5)^(1/2)))*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e)*3i)/(8*b^5*(d^5)^(1/2)))/(((567*b^7*c^5*e^10)/32 + 1728*c^12*d^7*e^3 - 6048*b*c^11*d^6*e^4 + (1215*b^6*c^6*d*e^9)/16 + 7020*b^2*c^10*d^5*e^5 - 2430*b^3*c^9*d^4*e^6 - (1701*b^4*c^8*d^3*e^7)/4 + (351*b^5*c^7*d^2*e^8)/8)/(b^12*c^4*d^8 + b^16*d^4*e^4 - 4*b^13*c^3*d^7*e - 4*b^15*c*d^5*e^3 + 6*b^14*c^2*d^6*e^2) - (3*(((d + e*x)^(1/2)*(9*b^8*c^3*e^10 + 4608*c^11*d^8*e^2 - 18432*b*c^10*d^7*e^3 + 36*b^7*c^4*d*e^9 + 27360*b^2*c^9*d^6*e^4 - 17568*b^3*c^8*d^5*e^5 + 3978*b^4*c^7*d^4*e^6 - 180*b^5*c^6*d^3*e^7 + 198*b^6*c^5*d^2*e^8))/(8*(b^8*c^4*d^8 + b^12*d^4*e^4 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 6*b^10*c^2*d^6*e^2)) + (3*((24*b^10*c^8*d^8*e^3 - 96*b^11*c^7*d^7*e^4 + 141*b^12*c^6*d^6*e^5 - 87*b^13*c^5*d^5*e^6 + 18*b^14*c^4*d^4*e^7 - 3*b^15*c^3*d^3*e^8 + 3*b^16*c^2*d^2*e^9)/(b^12*c^4*d^8 + b^16*d^4*e^4 - 4*b^13*c^3*d^7*e - 4*b^15*c*d^5*e^3 + 6*b^14*c^2*d^6*e^2) - (3*(d + e*x)^(1/2)*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e)*(128*b^10*c^7*d^9*e^2 - 576*b^11*c^6*d^8*e^3 + 1024*b^12*c^5*d^7*e^4 - 896*b^13*c^4*d^6*e^5 + 384*b^14*c^3*d^5*e^6 - 64*b^15*c^2*d^4*e^7))/(64*b^5*(d^5)^(1/2)*(b^8*c^4*d^8 + b^12*d^4*e^4 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 6*b^10*c^2*d^6*e^2)))*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e))/(8*b^5*(d^5)^(1/2)))*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e))/(8*b^5*(d^5)^(1/2)) + (3*(((d + e*x)^(1/2)*(9*b^8*c^3*e^10 + 4608*c^11*d^8*e^2 - 18432*b*c^10*d^7*e^3 + 36*b^7*c^4*d*e^9 + 27360*b^2*c^9*d^6*e^4 - 17568*b^3*c^8*d^5*e^5 + 3978*b^4*c^7*d^4*e^6 - 180*b^5*c^6*d^3*e^7 + 198*b^6*c^5*d^2*e^8))/(8*(b^8*c^4*d^8 + b^12*d^4*e^4 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 6*b^10*c^2*d^6*e^2)) - (3*((24*b^10*c^8*d^8*e^3 - 96*b^11*c^7*d^7*e^4 + 141*b^12*c^6*d^6*e^5 - 87*b^13*c^5*d^5*e^6 + 18*b^14*c^4*d^4*e^7 - 3*b^15*c^3*d^3*e^8 + 3*b^16*c^2*d^2*e^9)/(b^12*c^4*d^8 + b^16*d^4*e^4 - 4*b^13*c^3*d^7*e - 4*b^15*c*d^5*e^3 + 6*b^14*c^2*d^6*e^2) + (3*(d + e*x)^(1/2)*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e)*(128*b^10*c^7*d^9*e^2 - 576*b^11*c^6*d^8*e^3 + 1024*b^12*c^5*d^7*e^4 - 896*b^13*c^4*d^6*e^5 + 384*b^14*c^3*d^5*e^6 - 64*b^15*c^2*d^4*e^7))/(64*b^5*(d^5)^(1/2)*(b^8*c^4*d^8 + b^12*d^4*e^4 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 6*b^10*c^2*d^6*e^2)))*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e))/(8*b^5*(d^5)^(1/2)))*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e))/(8*b^5*(d^5)^(1/2))))*(b^2*e^2 + 16*c^2*d^2 + 4*b*c*d*e)*3i)/(4*b^5*(d^5)^(1/2))","B"
384,1,9635,370,4.065762,"\text{Not used}","int(1/((b*x + c*x^2)^3*(d + e*x)^(3/2)),x)","-\frac{\frac{2\,e^5}{c\,d^2-b\,d\,e}+\frac{e\,{\left(d+e\,x\right)}^2\,\left(15\,b^6\,e^6-89\,b^5\,c\,d\,e^5+106\,b^4\,c^2\,d^2\,e^4+38\,b^3\,c^3\,d^3\,e^3-199\,b^2\,c^4\,d^4\,e^2+216\,b\,c^5\,d^5\,e-72\,c^6\,d^6\right)}{4\,b^4\,{\left(c\,d^2-b\,d\,e\right)}^3}+\frac{e\,\left(d+e\,x\right)\,\left(25\,b^5\,e^5-56\,b^4\,c\,d\,e^4+6\,b^3\,c^2\,d^2\,e^3+36\,b^2\,c^3\,d^3\,e^2-60\,b\,c^4\,d^4\,e+24\,c^5\,d^5\right)}{4\,b^4\,{\left(c\,d^2-b\,d\,e\right)}^2}-\frac{3\,e\,{\left(d+e\,x\right)}^4\,\left(-5\,b^4\,c^2\,e^4+3\,b^3\,c^3\,d\,e^3+5\,b^2\,c^4\,d^2\,e^2-16\,b\,c^5\,d^3\,e+8\,c^6\,d^4\right)}{4\,b^4\,{\left(c\,d^2-b\,d\,e\right)}^3}+\frac{e\,{\left(d+e\,x\right)}^3\,\left(30\,b^5\,c\,e^5-73\,b^4\,c^2\,d\,e^4+3\,b^3\,c^3\,d^2\,e^3+118\,b^2\,c^4\,d^3\,e^2-180\,b\,c^5\,d^4\,e+72\,c^6\,d^5\right)}{4\,b^4\,{\left(c\,d^2-b\,d\,e\right)}^3}}{c^2\,{\left(d+e\,x\right)}^{9/2}-\left(4\,c^2\,d-2\,b\,c\,e\right)\,{\left(d+e\,x\right)}^{7/2}-{\left(d+e\,x\right)}^{3/2}\,\left(2\,b^2\,d\,e^2-6\,b\,c\,d^2\,e+4\,c^2\,d^3\right)+{\left(d+e\,x\right)}^{5/2}\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2\right)+\sqrt{d+e\,x}\,\left(b^2\,d^2\,e^2-2\,b\,c\,d^3\,e+c^2\,d^4\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(\sqrt{d+e\,x}\,\left(-28800\,b^{31}\,c^3\,d^9\,e^{21}+293760\,b^{30}\,c^4\,d^{10}\,e^{20}-1300608\,b^{29}\,c^5\,d^{11}\,e^{19}+3399552\,b^{28}\,c^6\,d^{12}\,e^{18}-6844032\,b^{27}\,c^7\,d^{13}\,e^{17}+15108480\,b^{26}\,c^8\,d^{14}\,e^{16}-37986048\,b^{25}\,c^9\,d^{15}\,e^{15}+90100224\,b^{24}\,c^{10}\,d^{16}\,e^{14}-201386880\,b^{23}\,c^{11}\,d^{17}\,e^{13}+438185088\,b^{22}\,c^{12}\,d^{18}\,e^{12}-855642240\,b^{21}\,c^{13}\,d^{19}\,e^{11}+1358257536\,b^{20}\,c^{14}\,d^{20}\,e^{10}-1667850624\,b^{19}\,c^{15}\,d^{21}\,e^9+1555380864\,b^{18}\,c^{16}\,d^{22}\,e^8-1089838080\,b^{17}\,c^{17}\,d^{23}\,e^7+564860160\,b^{16}\,c^{18}\,d^{24}\,e^6-210382848\,b^{15}\,c^{19}\,d^{25}\,e^5+53342208\,b^{14}\,c^{20}\,d^{26}\,e^4-8257536\,b^{13}\,c^{21}\,d^{27}\,e^3+589824\,b^{12}\,c^{22}\,d^{28}\,e^2\right)-\frac{3\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(33\,b^2\,e^2-44\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(356352\,b^{19}\,c^{18}\,d^{28}\,e^4-24576\,b^{18}\,c^{19}\,d^{29}\,e^3-2396160\,b^{20}\,c^{17}\,d^{27}\,e^5+9897984\,b^{21}\,c^{16}\,d^{26}\,e^6-28065792\,b^{22}\,c^{15}\,d^{25}\,e^7+57891840\,b^{23}\,c^{14}\,d^{24}\,e^8-90071040\,b^{24}\,c^{13}\,d^{23}\,e^9+108810240\,b^{25}\,c^{12}\,d^{22}\,e^{10}-105566208\,b^{26}\,c^{11}\,d^{21}\,e^{11}+86406144\,b^{27}\,c^{10}\,d^{20}\,e^{12}-63393792\,b^{28}\,c^9\,d^{19}\,e^{13}+43075584\,b^{29}\,c^8\,d^{18}\,e^{14}-26173440\,b^{30}\,c^7\,d^{17}\,e^{15}+13108224\,b^{31}\,c^6\,d^{16}\,e^{16}-4964352\,b^{32}\,c^5\,d^{15}\,e^{17}+1302528\,b^{33}\,c^4\,d^{14}\,e^{18}-208896\,b^{34}\,c^3\,d^{13}\,e^{19}+15360\,b^{35}\,c^2\,d^{12}\,e^{20}+\frac{3\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\sqrt{d+e\,x}\,\left(33\,b^2\,e^2-44\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(8192\,b^{38}\,c^2\,d^{15}\,e^{18}-139264\,b^{37}\,c^3\,d^{16}\,e^{17}+1105920\,b^{36}\,c^4\,d^{17}\,e^{16}-5447680\,b^{35}\,c^5\,d^{18}\,e^{15}+18636800\,b^{34}\,c^6\,d^{19}\,e^{14}-46964736\,b^{33}\,c^7\,d^{20}\,e^{13}+90202112\,b^{32}\,c^8\,d^{21}\,e^{12}-134717440\,b^{31}\,c^9\,d^{22}\,e^{11}+158146560\,b^{30}\,c^{10}\,d^{23}\,e^{10}-146432000\,b^{29}\,c^{11}\,d^{24}\,e^9+106602496\,b^{28}\,c^{12}\,d^{25}\,e^8-60383232\,b^{27}\,c^{13}\,d^{26}\,e^7+26091520\,b^{26}\,c^{14}\,d^{27}\,e^6-8314880\,b^{25}\,c^{15}\,d^{28}\,e^5+1843200\,b^{24}\,c^{16}\,d^{29}\,e^4-253952\,b^{23}\,c^{17}\,d^{30}\,e^3+16384\,b^{22}\,c^{18}\,d^{31}\,e^2\right)}{8\,\left(b^{12}\,e^7-7\,b^{11}\,c\,d\,e^6+21\,b^{10}\,c^2\,d^2\,e^5-35\,b^9\,c^3\,d^3\,e^4+35\,b^8\,c^4\,d^4\,e^3-21\,b^7\,c^5\,d^5\,e^2+7\,b^6\,c^6\,d^6\,e-b^5\,c^7\,d^7\right)}\right)}{8\,\left(b^{12}\,e^7-7\,b^{11}\,c\,d\,e^6+21\,b^{10}\,c^2\,d^2\,e^5-35\,b^9\,c^3\,d^3\,e^4+35\,b^8\,c^4\,d^4\,e^3-21\,b^7\,c^5\,d^5\,e^2+7\,b^6\,c^6\,d^6\,e-b^5\,c^7\,d^7\right)}\right)\,\left(33\,b^2\,e^2-44\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{8\,\left(b^{12}\,e^7-7\,b^{11}\,c\,d\,e^6+21\,b^{10}\,c^2\,d^2\,e^5-35\,b^9\,c^3\,d^3\,e^4+35\,b^8\,c^4\,d^4\,e^3-21\,b^7\,c^5\,d^5\,e^2+7\,b^6\,c^6\,d^6\,e-b^5\,c^7\,d^7\right)}+\frac{\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(\sqrt{d+e\,x}\,\left(-28800\,b^{31}\,c^3\,d^9\,e^{21}+293760\,b^{30}\,c^4\,d^{10}\,e^{20}-1300608\,b^{29}\,c^5\,d^{11}\,e^{19}+3399552\,b^{28}\,c^6\,d^{12}\,e^{18}-6844032\,b^{27}\,c^7\,d^{13}\,e^{17}+15108480\,b^{26}\,c^8\,d^{14}\,e^{16}-37986048\,b^{25}\,c^9\,d^{15}\,e^{15}+90100224\,b^{24}\,c^{10}\,d^{16}\,e^{14}-201386880\,b^{23}\,c^{11}\,d^{17}\,e^{13}+438185088\,b^{22}\,c^{12}\,d^{18}\,e^{12}-855642240\,b^{21}\,c^{13}\,d^{19}\,e^{11}+1358257536\,b^{20}\,c^{14}\,d^{20}\,e^{10}-1667850624\,b^{19}\,c^{15}\,d^{21}\,e^9+1555380864\,b^{18}\,c^{16}\,d^{22}\,e^8-1089838080\,b^{17}\,c^{17}\,d^{23}\,e^7+564860160\,b^{16}\,c^{18}\,d^{24}\,e^6-210382848\,b^{15}\,c^{19}\,d^{25}\,e^5+53342208\,b^{14}\,c^{20}\,d^{26}\,e^4-8257536\,b^{13}\,c^{21}\,d^{27}\,e^3+589824\,b^{12}\,c^{22}\,d^{28}\,e^2\right)-\frac{3\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(33\,b^2\,e^2-44\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(24576\,b^{18}\,c^{19}\,d^{29}\,e^3-356352\,b^{19}\,c^{18}\,d^{28}\,e^4+2396160\,b^{20}\,c^{17}\,d^{27}\,e^5-9897984\,b^{21}\,c^{16}\,d^{26}\,e^6+28065792\,b^{22}\,c^{15}\,d^{25}\,e^7-57891840\,b^{23}\,c^{14}\,d^{24}\,e^8+90071040\,b^{24}\,c^{13}\,d^{23}\,e^9-108810240\,b^{25}\,c^{12}\,d^{22}\,e^{10}+105566208\,b^{26}\,c^{11}\,d^{21}\,e^{11}-86406144\,b^{27}\,c^{10}\,d^{20}\,e^{12}+63393792\,b^{28}\,c^9\,d^{19}\,e^{13}-43075584\,b^{29}\,c^8\,d^{18}\,e^{14}+26173440\,b^{30}\,c^7\,d^{17}\,e^{15}-13108224\,b^{31}\,c^6\,d^{16}\,e^{16}+4964352\,b^{32}\,c^5\,d^{15}\,e^{17}-1302528\,b^{33}\,c^4\,d^{14}\,e^{18}+208896\,b^{34}\,c^3\,d^{13}\,e^{19}-15360\,b^{35}\,c^2\,d^{12}\,e^{20}+\frac{3\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\sqrt{d+e\,x}\,\left(33\,b^2\,e^2-44\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(8192\,b^{38}\,c^2\,d^{15}\,e^{18}-139264\,b^{37}\,c^3\,d^{16}\,e^{17}+1105920\,b^{36}\,c^4\,d^{17}\,e^{16}-5447680\,b^{35}\,c^5\,d^{18}\,e^{15}+18636800\,b^{34}\,c^6\,d^{19}\,e^{14}-46964736\,b^{33}\,c^7\,d^{20}\,e^{13}+90202112\,b^{32}\,c^8\,d^{21}\,e^{12}-134717440\,b^{31}\,c^9\,d^{22}\,e^{11}+158146560\,b^{30}\,c^{10}\,d^{23}\,e^{10}-146432000\,b^{29}\,c^{11}\,d^{24}\,e^9+106602496\,b^{28}\,c^{12}\,d^{25}\,e^8-60383232\,b^{27}\,c^{13}\,d^{26}\,e^7+26091520\,b^{26}\,c^{14}\,d^{27}\,e^6-8314880\,b^{25}\,c^{15}\,d^{28}\,e^5+1843200\,b^{24}\,c^{16}\,d^{29}\,e^4-253952\,b^{23}\,c^{17}\,d^{30}\,e^3+16384\,b^{22}\,c^{18}\,d^{31}\,e^2\right)}{8\,\left(b^{12}\,e^7-7\,b^{11}\,c\,d\,e^6+21\,b^{10}\,c^2\,d^2\,e^5-35\,b^9\,c^3\,d^3\,e^4+35\,b^8\,c^4\,d^4\,e^3-21\,b^7\,c^5\,d^5\,e^2+7\,b^6\,c^6\,d^6\,e-b^5\,c^7\,d^7\right)}\right)}{8\,\left(b^{12}\,e^7-7\,b^{11}\,c\,d\,e^6+21\,b^{10}\,c^2\,d^2\,e^5-35\,b^9\,c^3\,d^3\,e^4+35\,b^8\,c^4\,d^4\,e^3-21\,b^7\,c^5\,d^5\,e^2+7\,b^6\,c^6\,d^6\,e-b^5\,c^7\,d^7\right)}\right)\,\left(33\,b^2\,e^2-44\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{8\,\left(b^{12}\,e^7-7\,b^{11}\,c\,d\,e^6+21\,b^{10}\,c^2\,d^2\,e^5-35\,b^9\,c^3\,d^3\,e^4+35\,b^8\,c^4\,d^4\,e^3-21\,b^7\,c^5\,d^5\,e^2+7\,b^6\,c^6\,d^6\,e-b^5\,c^7\,d^7\right)}}{1769472\,b^8\,c^{23}\,d^{26}\,e^3-23003136\,b^9\,c^{22}\,d^{25}\,e^4+136138752\,b^{10}\,c^{21}\,d^{24}\,e^5-483508224\,b^{11}\,c^{20}\,d^{23}\,e^6+1141579008\,b^{12}\,c^{19}\,d^{22}\,e^7-1869094656\,b^{13}\,c^{18}\,d^{21}\,e^8+2133106272\,b^{14}\,c^{17}\,d^{20}\,e^9-1631703744\,b^{15}\,c^{16}\,d^{19}\,e^{10}+716335488\,b^{16}\,c^{15}\,d^{18}\,e^{11}-36390816\,b^{17}\,c^{14}\,d^{17}\,e^{12}-153641664\,b^{18}\,c^{13}\,d^{16}\,e^{13}+89697024\,b^{19}\,c^{12}\,d^{15}\,e^{14}-40065408\,b^{20}\,c^{11}\,d^{14}\,e^{15}+43695936\,b^{21}\,c^{10}\,d^{13}\,e^{16}-41388192\,b^{22}\,c^9\,d^{12}\,e^{17}+21843648\,b^{23}\,c^8\,d^{11}\,e^{18}-6082560\,b^{24}\,c^7\,d^{10}\,e^{19}+712800\,b^{25}\,c^6\,d^9\,e^{20}-\frac{3\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(\sqrt{d+e\,x}\,\left(-28800\,b^{31}\,c^3\,d^9\,e^{21}+293760\,b^{30}\,c^4\,d^{10}\,e^{20}-1300608\,b^{29}\,c^5\,d^{11}\,e^{19}+3399552\,b^{28}\,c^6\,d^{12}\,e^{18}-6844032\,b^{27}\,c^7\,d^{13}\,e^{17}+15108480\,b^{26}\,c^8\,d^{14}\,e^{16}-37986048\,b^{25}\,c^9\,d^{15}\,e^{15}+90100224\,b^{24}\,c^{10}\,d^{16}\,e^{14}-201386880\,b^{23}\,c^{11}\,d^{17}\,e^{13}+438185088\,b^{22}\,c^{12}\,d^{18}\,e^{12}-855642240\,b^{21}\,c^{13}\,d^{19}\,e^{11}+1358257536\,b^{20}\,c^{14}\,d^{20}\,e^{10}-1667850624\,b^{19}\,c^{15}\,d^{21}\,e^9+1555380864\,b^{18}\,c^{16}\,d^{22}\,e^8-1089838080\,b^{17}\,c^{17}\,d^{23}\,e^7+564860160\,b^{16}\,c^{18}\,d^{24}\,e^6-210382848\,b^{15}\,c^{19}\,d^{25}\,e^5+53342208\,b^{14}\,c^{20}\,d^{26}\,e^4-8257536\,b^{13}\,c^{21}\,d^{27}\,e^3+589824\,b^{12}\,c^{22}\,d^{28}\,e^2\right)-\frac{3\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\left(33\,b^2\,e^2-44\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(356352\,b^{19}\,c^{18}\,d^{28}\,e^4-24576\,b^{18}\,c^{19}\,d^{29}\,e^3-2396160\,b^{20}\,c^{17}\,d^{27}\,e^5+9897984\,b^{21}\,c^{16}\,d^{26}\,e^6-28065792\,b^{22}\,c^{15}\,d^{25}\,e^7+57891840\,b^{23}\,c^{14}\,d^{24}\,e^8-90071040\,b^{24}\,c^{13}\,d^{23}\,e^9+108810240\,b^{25}\,c^{12}\,d^{22}\,e^{10}-105566208\,b^{26}\,c^{11}\,d^{21}\,e^{11}+86406144\,b^{27}\,c^{10}\,d^{20}\,e^{12}-63393792\,b^{28}\,c^9\,d^{19}\,e^{13}+43075584\,b^{29}\,c^8\,d^{18}\,e^{14}-26173440\,b^{30}\,c^7\,d^{17}\,e^{15}+13108224\,b^{31}\,c^6\,d^{16}\,e^{16}-4964352\,b^{32}\,c^5\,d^{15}\,e^{17}+1302528\,b^{33}\,c^4\,d^{14}\,e^{18}-208896\,b^{34}\,c^3\,d^{13}\,e^{19}+15360\,b^{35}\,c^2\,d^{12}\,e^{20}+\frac{3\,\sqrt{-c^7\,{\left(b\,e-c\,d\right)}^7}\,\sqrt{d+e\,x}\,\left(33\,b^2\,e^2-44\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(8192\,b^{38}\,c^2\,d^{15}\,e^{18}-139264\,b^{37}\,c^3\,d^{16}\,e^{17}+1105920\,b^{36}\,c^4\,d^{17}\,e^{16}-5447680\,b^{35}\,c^5\,d^{18}\,e^{15}+18636800\,b^{34}\,c^6\,d^{19}\,e^{14}-46964736\,b^{33}\,c^7\,d^{20}\,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,c^{17}\,d^{23}\,e^7+564860160\,b^{16}\,c^{18}\,d^{24}\,e^6-210382848\,b^{15}\,c^{19}\,d^{25}\,e^5+53342208\,b^{14}\,c^{20}\,d^{26}\,e^4-8257536\,b^{13}\,c^{21}\,d^{27}\,e^3+589824\,b^{12}\,c^{22}\,d^{28}\,e^2\right)-\frac{3\,\left(5\,b^2\,e^2+12\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(356352\,b^{19}\,c^{18}\,d^{28}\,e^4-24576\,b^{18}\,c^{19}\,d^{29}\,e^3-2396160\,b^{20}\,c^{17}\,d^{27}\,e^5+9897984\,b^{21}\,c^{16}\,d^{26}\,e^6-28065792\,b^{22}\,c^{15}\,d^{25}\,e^7+57891840\,b^{23}\,c^{14}\,d^{24}\,e^8-90071040\,b^{24}\,c^{13}\,d^{23}\,e^9+108810240\,b^{25}\,c^{12}\,d^{22}\,e^{10}-105566208\,b^{26}\,c^{11}\,d^{21}\,e^{11}+86406144\,b^{27}\,c^{10}\,d^{20}\,e^{12}-63393792\,b^{28}\,c^9\,d^{19}\,e^{13}+43075584\,b^{29}\,c^8\,d^{18}\,e^{14}-26173440\,b^{30}\,c^7\,d^{17}\,e^{15}+13108224\,b^{31}\,c^6\,d^{16}\,e^{16}-4964352\,b^{32}\,c^5\,d^{15}\,e^{17}+1302528\,b^{33}\,c^4\,d^{14}\,e^{18}-208896\,b^{34}\,c^3\,d^{13}\,e^{19}+15360\,b^{35}\,c^2\,d^{12}\,e^{20}+\frac{3\,\sqrt{d+e\,x}\,\left(5\,b^2\,e^2+12\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(8192\,b^{38}\,c^2\,d^{15}\,e^{18}-139264\,b^{37}\,c^3\,d^{16}\,e^{17}+1105920\,b^{36}\,c^4\,d^{17}\,e^{16}-5447680\,b^{35}\,c^5\,d^{18}\,e^{15}+18636800\,b^{34}\,c^6\,d^{19}\,e^{14}-46964736\,b^{33}\,c^7\,d^{20}\,e^{13}+90202112\,b^{32}\,c^8\,d^{21}\,e^{12}-134717440\,b^{31}\,c^9\,d^{22}\,e^{11}+158146560\,b^{30}\,c^{10}\,d^{23}\,e^{10}-146432000\,b^{29}\,c^{11}\,d^{24}\,e^9+106602496\,b^{28}\,c^{12}\,d^{25}\,e^8-60383232\,b^{27}\,c^{13}\,d^{26}\,e^7+26091520\,b^{26}\,c^{14}\,d^{27}\,e^6-8314880\,b^{25}\,c^{15}\,d^{28}\,e^5+1843200\,b^{24}\,c^{16}\,d^{29}\,e^4-253952\,b^{23}\,c^{17}\,d^{30}\,e^3+16384\,b^{22}\,c^{18}\,d^{31}\,e^2\right)}{8\,b^5\,\sqrt{d^7}}\right)}{8\,b^5\,\sqrt{d^7}}\right)\,\left(5\,b^2\,e^2+12\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{8\,b^5\,\sqrt{d^7}}+\frac{\left(\sqrt{d+e\,x}\,\left(-28800\,b^{31}\,c^3\,d^9\,e^{21}+293760\,b^{30}\,c^4\,d^{10}\,e^{20}-1300608\,b^{29}\,c^5\,d^{11}\,e^{19}+3399552\,b^{28}\,c^6\,d^{12}\,e^{18}-6844032\,b^{27}\,c^7\,d^{13}\,e^{17}+15108480\,b^{26}\,c^8\,d^{14}\,e^{16}-37986048\,b^{25}\,c^9\,d^{15}\,e^{15}+90100224\,b^{24}\,c^{10}\,d^{16}\,e^{14}-201386880\,b^{23}\,c^{11}\,d^{17}\,e^{13}+438185088\,b^{22}\,c^{12}\,d^{18}\,e^{12}-855642240\,b^{21}\,c^{13}\,d^{19}\,e^{11}+1358257536\,b^{20}\,c^{14}\,d^{20}\,e^{10}-1667850624\,b^{19}\,c^{15}\,d^{21}\,e^9+1555380864\,b^{18}\,c^{16}\,d^{22}\,e^8-1089838080\,b^{17}\,c^{17}\,d^{23}\,e^7+564860160\,b^{16}\,c^{18}\,d^{24}\,e^6-210382848\,b^{15}\,c^{19}\,d^{25}\,e^5+53342208\,b^{14}\,c^{20}\,d^{26}\,e^4-8257536\,b^{13}\,c^{21}\,d^{27}\,e^3+589824\,b^{12}\,c^{22}\,d^{28}\,e^2\right)-\frac{3\,\left(5\,b^2\,e^2+12\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(24576\,b^{18}\,c^{19}\,d^{29}\,e^3-356352\,b^{19}\,c^{18}\,d^{28}\,e^4+2396160\,b^{20}\,c^{17}\,d^{27}\,e^5-9897984\,b^{21}\,c^{16}\,d^{26}\,e^6+28065792\,b^{22}\,c^{15}\,d^{25}\,e^7-57891840\,b^{23}\,c^{14}\,d^{24}\,e^8+90071040\,b^{24}\,c^{13}\,d^{23}\,e^9-108810240\,b^{25}\,c^{12}\,d^{22}\,e^{10}+105566208\,b^{26}\,c^{11}\,d^{21}\,e^{11}-86406144\,b^{27}\,c^{10}\,d^{20}\,e^{12}+63393792\,b^{28}\,c^9\,d^{19}\,e^{13}-43075584\,b^{29}\,c^8\,d^{18}\,e^{14}+26173440\,b^{30}\,c^7\,d^{17}\,e^{15}-13108224\,b^{31}\,c^6\,d^{16}\,e^{16}+4964352\,b^{32}\,c^5\,d^{15}\,e^{17}-1302528\,b^{33}\,c^4\,d^{14}\,e^{18}+208896\,b^{34}\,c^3\,d^{13}\,e^{19}-15360\,b^{35}\,c^2\,d^{12}\,e^{20}+\frac{3\,\sqrt{d+e\,x}\,\left(5\,b^2\,e^2+12\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(8192\,b^{38}\,c^2\,d^{15}\,e^{18}-139264\,b^{37}\,c^3\,d^{16}\,e^{17}+1105920\,b^{36}\,c^4\,d^{17}\,e^{16}-5447680\,b^{35}\,c^5\,d^{18}\,e^{15}+18636800\,b^{34}\,c^6\,d^{19}\,e^{14}-46964736\,b^{33}\,c^7\,d^{20}\,e^{13}+90202112\,b^{32}\,c^8\,d^{21}\,e^{12}-134717440\,b^{31}\,c^9\,d^{22}\,e^{11}+158146560\,b^{30}\,c^{10}\,d^{23}\,e^{10}-146432000\,b^{29}\,c^{11}\,d^{24}\,e^9+106602496\,b^{28}\,c^{12}\,d^{25}\,e^8-60383232\,b^{27}\,c^{13}\,d^{26}\,e^7+26091520\,b^{26}\,c^{14}\,d^{27}\,e^6-8314880\,b^{25}\,c^{15}\,d^{28}\,e^5+1843200\,b^{24}\,c^{16}\,d^{29}\,e^4-253952\,b^{23}\,c^{17}\,d^{30}\,e^3+16384\,b^{22}\,c^{18}\,d^{31}\,e^2\right)}{8\,b^5\,\sqrt{d^7}}\right)}{8\,b^5\,\sqrt{d^7}}\right)\,\left(5\,b^2\,e^2+12\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{8\,b^5\,\sqrt{d^7}}}{1769472\,b^8\,c^{23}\,d^{26}\,e^3-23003136\,b^9\,c^{22}\,d^{25}\,e^4+136138752\,b^{10}\,c^{21}\,d^{24}\,e^5-483508224\,b^{11}\,c^{20}\,d^{23}\,e^6+1141579008\,b^{12}\,c^{19}\,d^{22}\,e^7-1869094656\,b^{13}\,c^{18}\,d^{21}\,e^8+2133106272\,b^{14}\,c^{17}\,d^{20}\,e^9-1631703744\,b^{15}\,c^{16}\,d^{19}\,e^{10}+716335488\,b^{16}\,c^{15}\,d^{18}\,e^{11}-36390816\,b^{17}\,c^{14}\,d^{17}\,e^{12}-153641664\,b^{18}\,c^{13}\,d^{16}\,e^{13}+89697024\,b^{19}\,c^{12}\,d^{15}\,e^{14}-40065408\,b^{20}\,c^{11}\,d^{14}\,e^{15}+43695936\,b^{21}\,c^{10}\,d^{13}\,e^{16}-41388192\,b^{22}\,c^9\,d^{12}\,e^{17}+21843648\,b^{23}\,c^8\,d^{11}\,e^{18}-6082560\,b^{24}\,c^7\,d^{10}\,e^{19}+712800\,b^{25}\,c^6\,d^9\,e^{20}-\frac{3\,\left(\sqrt{d+e\,x}\,\left(-28800\,b^{31}\,c^3\,d^9\,e^{21}+293760\,b^{30}\,c^4\,d^{10}\,e^{20}-1300608\,b^{29}\,c^5\,d^{11}\,e^{19}+3399552\,b^{28}\,c^6\,d^{12}\,e^{18}-6844032\,b^{27}\,c^7\,d^{13}\,e^{17}+15108480\,b^{26}\,c^8\,d^{14}\,e^{16}-37986048\,b^{25}\,c^9\,d^{15}\,e^{15}+90100224\,b^{24}\,c^{10}\,d^{16}\,e^{14}-201386880\,b^{23}\,c^{11}\,d^{17}\,e^{13}+438185088\,b^{22}\,c^{12}\,d^{18}\,e^{12}-855642240\,b^{21}\,c^{13}\,d^{19}\,e^{11}+1358257536\,b^{20}\,c^{14}\,d^{20}\,e^{10}-1667850624\,b^{19}\,c^{15}\,d^{21}\,e^9+1555380864\,b^{18}\,c^{16}\,d^{22}\,e^8-1089838080\,b^{17}\,c^{17}\,d^{23}\,e^7+564860160\,b^{16}\,c^{18}\,d^{24}\,e^6-210382848\,b^{15}\,c^{19}\,d^{25}\,e^5+53342208\,b^{14}\,c^{20}\,d^{26}\,e^4-8257536\,b^{13}\,c^{21}\,d^{27}\,e^3+589824\,b^{12}\,c^{22}\,d^{28}\,e^2\right)-\frac{3\,\left(5\,b^2\,e^2+12\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(356352\,b^{19}\,c^{18}\,d^{28}\,e^4-24576\,b^{18}\,c^{19}\,d^{29}\,e^3-2396160\,b^{20}\,c^{17}\,d^{27}\,e^5+9897984\,b^{21}\,c^{16}\,d^{26}\,e^6-28065792\,b^{22}\,c^{15}\,d^{25}\,e^7+57891840\,b^{23}\,c^{14}\,d^{24}\,e^8-90071040\,b^{24}\,c^{13}\,d^{23}\,e^9+108810240\,b^{25}\,c^{12}\,d^{22}\,e^{10}-105566208\,b^{26}\,c^{11}\,d^{21}\,e^{11}+86406144\,b^{27}\,c^{10}\,d^{20}\,e^{12}-63393792\,b^{28}\,c^9\,d^{19}\,e^{13}+43075584\,b^{29}\,c^8\,d^{18}\,e^{14}-26173440\,b^{30}\,c^7\,d^{17}\,e^{15}+13108224\,b^{31}\,c^6\,d^{16}\,e^{16}-4964352\,b^{32}\,c^5\,d^{15}\,e^{17}+1302528\,b^{33}\,c^4\,d^{14}\,e^{18}-208896\,b^{34}\,c^3\,d^{13}\,e^{19}+15360\,b^{35}\,c^2\,d^{12}\,e^{20}+\frac{3\,\sqrt{d+e\,x}\,\left(5\,b^2\,e^2+12\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(8192\,b^{38}\,c^2\,d^{15}\,e^{18}-139264\,b^{37}\,c^3\,d^{16}\,e^{17}+1105920\,b^{36}\,c^4\,d^{17}\,e^{16}-5447680\,b^{35}\,c^5\,d^{18}\,e^{15}+18636800\,b^{34}\,c^6\,d^{19}\,e^{14}-46964736\,b^{33}\,c^7\,d^{20}\,e^{13}+90202112\,b^{32}\,c^8\,d^{21}\,e^{12}-134717440\,b^{31}\,c^9\,d^{22}\,e^{11}+158146560\,b^{30}\,c^{10}\,d^{23}\,e^{10}-146432000\,b^{29}\,c^{11}\,d^{24}\,e^9+106602496\,b^{28}\,c^{12}\,d^{25}\,e^8-60383232\,b^{27}\,c^{13}\,d^{26}\,e^7+26091520\,b^{26}\,c^{14}\,d^{27}\,e^6-8314880\,b^{25}\,c^{15}\,d^{28}\,e^5+1843200\,b^{24}\,c^{16}\,d^{29}\,e^4-253952\,b^{23}\,c^{17}\,d^{30}\,e^3+16384\,b^{22}\,c^{18}\,d^{31}\,e^2\right)}{8\,b^5\,\sqrt{d^7}}\right)}{8\,b^5\,\sqrt{d^7}}\right)\,\left(5\,b^2\,e^2+12\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5\,\sqrt{d^7}}+\frac{3\,\left(\sqrt{d+e\,x}\,\left(-28800\,b^{31}\,c^3\,d^9\,e^{21}+293760\,b^{30}\,c^4\,d^{10}\,e^{20}-1300608\,b^{29}\,c^5\,d^{11}\,e^{19}+3399552\,b^{28}\,c^6\,d^{12}\,e^{18}-6844032\,b^{27}\,c^7\,d^{13}\,e^{17}+15108480\,b^{26}\,c^8\,d^{14}\,e^{16}-37986048\,b^{25}\,c^9\,d^{15}\,e^{15}+90100224\,b^{24}\,c^{10}\,d^{16}\,e^{14}-201386880\,b^{23}\,c^{11}\,d^{17}\,e^{13}+438185088\,b^{22}\,c^{12}\,d^{18}\,e^{12}-855642240\,b^{21}\,c^{13}\,d^{19}\,e^{11}+1358257536\,b^{20}\,c^{14}\,d^{20}\,e^{10}-1667850624\,b^{19}\,c^{15}\,d^{21}\,e^9+1555380864\,b^{18}\,c^{16}\,d^{22}\,e^8-1089838080\,b^{17}\,c^{17}\,d^{23}\,e^7+564860160\,b^{16}\,c^{18}\,d^{24}\,e^6-210382848\,b^{15}\,c^{19}\,d^{25}\,e^5+53342208\,b^{14}\,c^{20}\,d^{26}\,e^4-8257536\,b^{13}\,c^{21}\,d^{27}\,e^3+589824\,b^{12}\,c^{22}\,d^{28}\,e^2\right)-\frac{3\,\left(5\,b^2\,e^2+12\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(24576\,b^{18}\,c^{19}\,d^{29}\,e^3-356352\,b^{19}\,c^{18}\,d^{28}\,e^4+2396160\,b^{20}\,c^{17}\,d^{27}\,e^5-9897984\,b^{21}\,c^{16}\,d^{26}\,e^6+28065792\,b^{22}\,c^{15}\,d^{25}\,e^7-57891840\,b^{23}\,c^{14}\,d^{24}\,e^8+90071040\,b^{24}\,c^{13}\,d^{23}\,e^9-108810240\,b^{25}\,c^{12}\,d^{22}\,e^{10}+105566208\,b^{26}\,c^{11}\,d^{21}\,e^{11}-86406144\,b^{27}\,c^{10}\,d^{20}\,e^{12}+63393792\,b^{28}\,c^9\,d^{19}\,e^{13}-43075584\,b^{29}\,c^8\,d^{18}\,e^{14}+26173440\,b^{30}\,c^7\,d^{17}\,e^{15}-13108224\,b^{31}\,c^6\,d^{16}\,e^{16}+4964352\,b^{32}\,c^5\,d^{15}\,e^{17}-1302528\,b^{33}\,c^4\,d^{14}\,e^{18}+208896\,b^{34}\,c^3\,d^{13}\,e^{19}-15360\,b^{35}\,c^2\,d^{12}\,e^{20}+\frac{3\,\sqrt{d+e\,x}\,\left(5\,b^2\,e^2+12\,b\,c\,d\,e+16\,c^2\,d^2\right)\,\left(8192\,b^{38}\,c^2\,d^{15}\,e^{18}-139264\,b^{37}\,c^3\,d^{16}\,e^{17}+1105920\,b^{36}\,c^4\,d^{17}\,e^{16}-5447680\,b^{35}\,c^5\,d^{18}\,e^{15}+18636800\,b^{34}\,c^6\,d^{19}\,e^{14}-46964736\,b^{33}\,c^7\,d^{20}\,e^{13}+90202112\,b^{32}\,c^8\,d^{21}\,e^{12}-134717440\,b^{31}\,c^9\,d^{22}\,e^{11}+158146560\,b^{30}\,c^{10}\,d^{23}\,e^{10}-146432000\,b^{29}\,c^{11}\,d^{24}\,e^9+106602496\,b^{28}\,c^{12}\,d^{25}\,e^8-60383232\,b^{27}\,c^{13}\,d^{26}\,e^7+26091520\,b^{26}\,c^{14}\,d^{27}\,e^6-8314880\,b^{25}\,c^{15}\,d^{28}\,e^5+1843200\,b^{24}\,c^{16}\,d^{29}\,e^4-253952\,b^{23}\,c^{17}\,d^{30}\,e^3+16384\,b^{22}\,c^{18}\,d^{31}\,e^2\right)}{8\,b^5\,\sqrt{d^7}}\right)}{8\,b^5\,\sqrt{d^7}}\right)\,\left(5\,b^2\,e^2+12\,b\,c\,d\,e+16\,c^2\,d^2\right)}{8\,b^5\,\sqrt{d^7}}}\right)\,\left(5\,b^2\,e^2+12\,b\,c\,d\,e+16\,c^2\,d^2\right)\,3{}\mathrm{i}}{4\,b^5\,\sqrt{d^7}}","Not used",1,"- ((2*e^5)/(c*d^2 - b*d*e) + (e*(d + e*x)^2*(15*b^6*e^6 - 72*c^6*d^6 - 199*b^2*c^4*d^4*e^2 + 38*b^3*c^3*d^3*e^3 + 106*b^4*c^2*d^2*e^4 + 216*b*c^5*d^5*e - 89*b^5*c*d*e^5))/(4*b^4*(c*d^2 - b*d*e)^3) + (e*(d + e*x)*(25*b^5*e^5 + 24*c^5*d^5 + 36*b^2*c^3*d^3*e^2 + 6*b^3*c^2*d^2*e^3 - 60*b*c^4*d^4*e - 56*b^4*c*d*e^4))/(4*b^4*(c*d^2 - b*d*e)^2) - (3*e*(d + e*x)^4*(8*c^6*d^4 - 5*b^4*c^2*e^4 + 3*b^3*c^3*d*e^3 + 5*b^2*c^4*d^2*e^2 - 16*b*c^5*d^3*e))/(4*b^4*(c*d^2 - b*d*e)^3) + (e*(d + e*x)^3*(72*c^6*d^5 + 30*b^5*c*e^5 - 73*b^4*c^2*d*e^4 + 118*b^2*c^4*d^3*e^2 + 3*b^3*c^3*d^2*e^3 - 180*b*c^5*d^4*e))/(4*b^4*(c*d^2 - b*d*e)^3))/(c^2*(d + e*x)^(9/2) - (4*c^2*d - 2*b*c*e)*(d + e*x)^(7/2) - (d + e*x)^(3/2)*(4*c^2*d^3 + 2*b^2*d*e^2 - 6*b*c*d^2*e) + (d + e*x)^(5/2)*(b^2*e^2 + 6*c^2*d^2 - 6*b*c*d*e) + (d + e*x)^(1/2)*(c^2*d^4 + b^2*d^2*e^2 - 2*b*c*d^3*e)) - (atan((((-c^7*(b*e - c*d)^7)^(1/2)*((d + e*x)^(1/2)*(589824*b^12*c^22*d^28*e^2 - 8257536*b^13*c^21*d^27*e^3 + 53342208*b^14*c^20*d^26*e^4 - 210382848*b^15*c^19*d^25*e^5 + 564860160*b^16*c^18*d^24*e^6 - 1089838080*b^17*c^17*d^23*e^7 + 1555380864*b^18*c^16*d^22*e^8 - 1667850624*b^19*c^15*d^21*e^9 + 1358257536*b^20*c^14*d^20*e^10 - 855642240*b^21*c^13*d^19*e^11 + 438185088*b^22*c^12*d^18*e^12 - 201386880*b^23*c^11*d^17*e^13 + 90100224*b^24*c^10*d^16*e^14 - 37986048*b^25*c^9*d^15*e^15 + 15108480*b^26*c^8*d^14*e^16 - 6844032*b^27*c^7*d^13*e^17 + 3399552*b^28*c^6*d^12*e^18 - 1300608*b^29*c^5*d^11*e^19 + 293760*b^30*c^4*d^10*e^20 - 28800*b^31*c^3*d^9*e^21) - (3*(-c^7*(b*e - c*d)^7)^(1/2)*(33*b^2*e^2 + 16*c^2*d^2 - 44*b*c*d*e)*(356352*b^19*c^18*d^28*e^4 - 24576*b^18*c^19*d^29*e^3 - 2396160*b^20*c^17*d^27*e^5 + 9897984*b^21*c^16*d^26*e^6 - 28065792*b^22*c^15*d^25*e^7 + 57891840*b^23*c^14*d^24*e^8 - 90071040*b^24*c^13*d^23*e^9 + 108810240*b^25*c^12*d^22*e^10 - 105566208*b^26*c^11*d^21*e^11 + 86406144*b^27*c^10*d^20*e^12 - 63393792*b^28*c^9*d^19*e^13 + 43075584*b^29*c^8*d^18*e^14 - 26173440*b^30*c^7*d^17*e^15 + 13108224*b^31*c^6*d^16*e^16 - 4964352*b^32*c^5*d^15*e^17 + 1302528*b^33*c^4*d^14*e^18 - 208896*b^34*c^3*d^13*e^19 + 15360*b^35*c^2*d^12*e^20 + (3*(-c^7*(b*e - c*d)^7)^(1/2)*(d + e*x)^(1/2)*(33*b^2*e^2 + 16*c^2*d^2 - 44*b*c*d*e)*(16384*b^22*c^18*d^31*e^2 - 253952*b^23*c^17*d^30*e^3 + 1843200*b^24*c^16*d^29*e^4 - 8314880*b^25*c^15*d^28*e^5 + 26091520*b^26*c^14*d^27*e^6 - 60383232*b^27*c^13*d^26*e^7 + 106602496*b^28*c^12*d^25*e^8 - 146432000*b^29*c^11*d^24*e^9 + 158146560*b^30*c^10*d^23*e^10 - 134717440*b^31*c^9*d^22*e^11 + 90202112*b^32*c^8*d^21*e^12 - 46964736*b^33*c^7*d^20*e^13 + 18636800*b^34*c^6*d^19*e^14 - 5447680*b^35*c^5*d^18*e^15 + 1105920*b^36*c^4*d^17*e^16 - 139264*b^37*c^3*d^16*e^17 + 8192*b^38*c^2*d^15*e^18))/(8*(b^12*e^7 - b^5*c^7*d^7 + 7*b^6*c^6*d^6*e - 21*b^7*c^5*d^5*e^2 + 35*b^8*c^4*d^4*e^3 - 35*b^9*c^3*d^3*e^4 + 21*b^10*c^2*d^2*e^5 - 7*b^11*c*d*e^6))))/(8*(b^12*e^7 - b^5*c^7*d^7 + 7*b^6*c^6*d^6*e - 21*b^7*c^5*d^5*e^2 + 35*b^8*c^4*d^4*e^3 - 35*b^9*c^3*d^3*e^4 + 21*b^10*c^2*d^2*e^5 - 7*b^11*c*d*e^6)))*(33*b^2*e^2 + 16*c^2*d^2 - 44*b*c*d*e)*3i)/(8*(b^12*e^7 - b^5*c^7*d^7 + 7*b^6*c^6*d^6*e - 21*b^7*c^5*d^5*e^2 + 35*b^8*c^4*d^4*e^3 - 35*b^9*c^3*d^3*e^4 + 21*b^10*c^2*d^2*e^5 - 7*b^11*c*d*e^6)) + ((-c^7*(b*e - c*d)^7)^(1/2)*((d + e*x)^(1/2)*(589824*b^12*c^22*d^28*e^2 - 8257536*b^13*c^21*d^27*e^3 + 53342208*b^14*c^20*d^26*e^4 - 210382848*b^15*c^19*d^25*e^5 + 564860160*b^16*c^18*d^24*e^6 - 1089838080*b^17*c^17*d^23*e^7 + 1555380864*b^18*c^16*d^22*e^8 - 1667850624*b^19*c^15*d^21*e^9 + 1358257536*b^20*c^14*d^20*e^10 - 855642240*b^21*c^13*d^19*e^11 + 438185088*b^22*c^12*d^18*e^12 - 201386880*b^23*c^11*d^17*e^13 + 90100224*b^24*c^10*d^16*e^14 - 37986048*b^25*c^9*d^15*e^15 + 15108480*b^26*c^8*d^14*e^16 - 6844032*b^27*c^7*d^13*e^17 + 3399552*b^28*c^6*d^12*e^18 - 1300608*b^29*c^5*d^11*e^19 + 293760*b^30*c^4*d^10*e^20 - 28800*b^31*c^3*d^9*e^21) - (3*(-c^7*(b*e - c*d)^7)^(1/2)*(33*b^2*e^2 + 16*c^2*d^2 - 44*b*c*d*e)*(24576*b^18*c^19*d^29*e^3 - 356352*b^19*c^18*d^28*e^4 + 2396160*b^20*c^17*d^27*e^5 - 9897984*b^21*c^16*d^26*e^6 + 28065792*b^22*c^15*d^25*e^7 - 57891840*b^23*c^14*d^24*e^8 + 90071040*b^24*c^13*d^23*e^9 - 108810240*b^25*c^12*d^22*e^10 + 105566208*b^26*c^11*d^21*e^11 - 86406144*b^27*c^10*d^20*e^12 + 63393792*b^28*c^9*d^19*e^13 - 43075584*b^29*c^8*d^18*e^14 + 26173440*b^30*c^7*d^17*e^15 - 13108224*b^31*c^6*d^16*e^16 + 4964352*b^32*c^5*d^15*e^17 - 1302528*b^33*c^4*d^14*e^18 + 208896*b^34*c^3*d^13*e^19 - 15360*b^35*c^2*d^12*e^20 + (3*(-c^7*(b*e - c*d)^7)^(1/2)*(d + e*x)^(1/2)*(33*b^2*e^2 + 16*c^2*d^2 - 44*b*c*d*e)*(16384*b^22*c^18*d^31*e^2 - 253952*b^23*c^17*d^30*e^3 + 1843200*b^24*c^16*d^29*e^4 - 8314880*b^25*c^15*d^28*e^5 + 26091520*b^26*c^14*d^27*e^6 - 60383232*b^27*c^13*d^26*e^7 + 106602496*b^28*c^12*d^25*e^8 - 146432000*b^29*c^11*d^24*e^9 + 158146560*b^30*c^10*d^23*e^10 - 134717440*b^31*c^9*d^22*e^11 + 90202112*b^32*c^8*d^21*e^12 - 46964736*b^33*c^7*d^20*e^13 + 18636800*b^34*c^6*d^19*e^14 - 5447680*b^35*c^5*d^18*e^15 + 1105920*b^36*c^4*d^17*e^16 - 139264*b^37*c^3*d^16*e^17 + 8192*b^38*c^2*d^15*e^18))/(8*(b^12*e^7 - b^5*c^7*d^7 + 7*b^6*c^6*d^6*e - 21*b^7*c^5*d^5*e^2 + 35*b^8*c^4*d^4*e^3 - 35*b^9*c^3*d^3*e^4 + 21*b^10*c^2*d^2*e^5 - 7*b^11*c*d*e^6))))/(8*(b^12*e^7 - b^5*c^7*d^7 + 7*b^6*c^6*d^6*e - 21*b^7*c^5*d^5*e^2 + 35*b^8*c^4*d^4*e^3 - 35*b^9*c^3*d^3*e^4 + 21*b^10*c^2*d^2*e^5 - 7*b^11*c*d*e^6)))*(33*b^2*e^2 + 16*c^2*d^2 - 44*b*c*d*e)*3i)/(8*(b^12*e^7 - b^5*c^7*d^7 + 7*b^6*c^6*d^6*e - 21*b^7*c^5*d^5*e^2 + 35*b^8*c^4*d^4*e^3 - 35*b^9*c^3*d^3*e^4 + 21*b^10*c^2*d^2*e^5 - 7*b^11*c*d*e^6)))/(1769472*b^8*c^23*d^26*e^3 - 23003136*b^9*c^22*d^25*e^4 + 136138752*b^10*c^21*d^24*e^5 - 483508224*b^11*c^20*d^23*e^6 + 1141579008*b^12*c^19*d^22*e^7 - 1869094656*b^13*c^18*d^21*e^8 + 2133106272*b^14*c^17*d^20*e^9 - 1631703744*b^15*c^16*d^19*e^10 + 716335488*b^16*c^15*d^18*e^11 - 36390816*b^17*c^14*d^17*e^12 - 153641664*b^18*c^13*d^16*e^13 + 89697024*b^19*c^12*d^15*e^14 - 40065408*b^20*c^11*d^14*e^15 + 43695936*b^21*c^10*d^13*e^16 - 41388192*b^22*c^9*d^12*e^17 + 21843648*b^23*c^8*d^11*e^18 - 6082560*b^24*c^7*d^10*e^19 + 712800*b^25*c^6*d^9*e^20 - (3*(-c^7*(b*e - c*d)^7)^(1/2)*((d + e*x)^(1/2)*(589824*b^12*c^22*d^28*e^2 - 8257536*b^13*c^21*d^27*e^3 + 53342208*b^14*c^20*d^26*e^4 - 210382848*b^15*c^19*d^25*e^5 + 564860160*b^16*c^18*d^24*e^6 - 1089838080*b^17*c^17*d^23*e^7 + 1555380864*b^18*c^16*d^22*e^8 - 1667850624*b^19*c^15*d^21*e^9 + 1358257536*b^20*c^14*d^20*e^10 - 855642240*b^21*c^13*d^19*e^11 + 438185088*b^22*c^12*d^18*e^12 - 201386880*b^23*c^11*d^17*e^13 + 90100224*b^24*c^10*d^16*e^14 - 37986048*b^25*c^9*d^15*e^15 + 15108480*b^26*c^8*d^14*e^16 - 6844032*b^27*c^7*d^13*e^17 + 3399552*b^28*c^6*d^12*e^18 - 1300608*b^29*c^5*d^11*e^19 + 293760*b^30*c^4*d^10*e^20 - 28800*b^31*c^3*d^9*e^21) - (3*(-c^7*(b*e - c*d)^7)^(1/2)*(33*b^2*e^2 + 16*c^2*d^2 - 44*b*c*d*e)*(356352*b^19*c^18*d^28*e^4 - 24576*b^18*c^19*d^29*e^3 - 2396160*b^20*c^17*d^27*e^5 + 9897984*b^21*c^16*d^26*e^6 - 28065792*b^22*c^15*d^25*e^7 + 57891840*b^23*c^14*d^24*e^8 - 90071040*b^24*c^13*d^23*e^9 + 108810240*b^25*c^12*d^22*e^10 - 105566208*b^26*c^11*d^21*e^11 + 86406144*b^27*c^10*d^20*e^12 - 63393792*b^28*c^9*d^19*e^13 + 43075584*b^29*c^8*d^18*e^14 - 26173440*b^30*c^7*d^17*e^15 + 13108224*b^31*c^6*d^16*e^16 - 4964352*b^32*c^5*d^15*e^17 + 1302528*b^33*c^4*d^14*e^18 - 208896*b^34*c^3*d^13*e^19 + 15360*b^35*c^2*d^12*e^20 + (3*(-c^7*(b*e - c*d)^7)^(1/2)*(d + e*x)^(1/2)*(33*b^2*e^2 + 16*c^2*d^2 - 44*b*c*d*e)*(16384*b^22*c^18*d^31*e^2 - 253952*b^23*c^17*d^30*e^3 + 1843200*b^24*c^16*d^29*e^4 - 8314880*b^25*c^15*d^28*e^5 + 26091520*b^26*c^14*d^27*e^6 - 60383232*b^27*c^13*d^26*e^7 + 106602496*b^28*c^12*d^25*e^8 - 146432000*b^29*c^11*d^24*e^9 + 158146560*b^30*c^10*d^23*e^10 - 134717440*b^31*c^9*d^22*e^11 + 90202112*b^32*c^8*d^21*e^12 - 46964736*b^33*c^7*d^20*e^13 + 18636800*b^34*c^6*d^19*e^14 - 5447680*b^35*c^5*d^18*e^15 + 1105920*b^36*c^4*d^17*e^16 - 139264*b^37*c^3*d^16*e^17 + 8192*b^38*c^2*d^15*e^18))/(8*(b^12*e^7 - b^5*c^7*d^7 + 7*b^6*c^6*d^6*e - 21*b^7*c^5*d^5*e^2 + 35*b^8*c^4*d^4*e^3 - 35*b^9*c^3*d^3*e^4 + 21*b^10*c^2*d^2*e^5 - 7*b^11*c*d*e^6))))/(8*(b^12*e^7 - b^5*c^7*d^7 + 7*b^6*c^6*d^6*e - 21*b^7*c^5*d^5*e^2 + 35*b^8*c^4*d^4*e^3 - 35*b^9*c^3*d^3*e^4 + 21*b^10*c^2*d^2*e^5 - 7*b^11*c*d*e^6)))*(33*b^2*e^2 + 16*c^2*d^2 - 44*b*c*d*e))/(8*(b^12*e^7 - b^5*c^7*d^7 + 7*b^6*c^6*d^6*e - 21*b^7*c^5*d^5*e^2 + 35*b^8*c^4*d^4*e^3 - 35*b^9*c^3*d^3*e^4 + 21*b^10*c^2*d^2*e^5 - 7*b^11*c*d*e^6)) + (3*(-c^7*(b*e - c*d)^7)^(1/2)*((d + e*x)^(1/2)*(589824*b^12*c^22*d^28*e^2 - 8257536*b^13*c^21*d^27*e^3 + 53342208*b^14*c^20*d^26*e^4 - 210382848*b^15*c^19*d^25*e^5 + 564860160*b^16*c^18*d^24*e^6 - 1089838080*b^17*c^17*d^23*e^7 + 1555380864*b^18*c^16*d^22*e^8 - 1667850624*b^19*c^15*d^21*e^9 + 1358257536*b^20*c^14*d^20*e^10 - 855642240*b^21*c^13*d^19*e^11 + 438185088*b^22*c^12*d^18*e^12 - 201386880*b^23*c^11*d^17*e^13 + 90100224*b^24*c^10*d^16*e^14 - 37986048*b^25*c^9*d^15*e^15 + 15108480*b^26*c^8*d^14*e^16 - 6844032*b^27*c^7*d^13*e^17 + 3399552*b^28*c^6*d^12*e^18 - 1300608*b^29*c^5*d^11*e^19 + 293760*b^30*c^4*d^10*e^20 - 28800*b^31*c^3*d^9*e^21) - (3*(-c^7*(b*e - c*d)^7)^(1/2)*(33*b^2*e^2 + 16*c^2*d^2 - 44*b*c*d*e)*(24576*b^18*c^19*d^29*e^3 - 356352*b^19*c^18*d^28*e^4 + 2396160*b^20*c^17*d^27*e^5 - 9897984*b^21*c^16*d^26*e^6 + 28065792*b^22*c^15*d^25*e^7 - 57891840*b^23*c^14*d^24*e^8 + 90071040*b^24*c^13*d^23*e^9 - 108810240*b^25*c^12*d^22*e^10 + 105566208*b^26*c^11*d^21*e^11 - 86406144*b^27*c^10*d^20*e^12 + 63393792*b^28*c^9*d^19*e^13 - 43075584*b^29*c^8*d^18*e^14 + 26173440*b^30*c^7*d^17*e^15 - 13108224*b^31*c^6*d^16*e^16 + 4964352*b^32*c^5*d^15*e^17 - 1302528*b^33*c^4*d^14*e^18 + 208896*b^34*c^3*d^13*e^19 - 15360*b^35*c^2*d^12*e^20 + (3*(-c^7*(b*e - c*d)^7)^(1/2)*(d + e*x)^(1/2)*(33*b^2*e^2 + 16*c^2*d^2 - 44*b*c*d*e)*(16384*b^22*c^18*d^31*e^2 - 253952*b^23*c^17*d^30*e^3 + 1843200*b^24*c^16*d^29*e^4 - 8314880*b^25*c^15*d^28*e^5 + 26091520*b^26*c^14*d^27*e^6 - 60383232*b^27*c^13*d^26*e^7 + 106602496*b^28*c^12*d^25*e^8 - 146432000*b^29*c^11*d^24*e^9 + 158146560*b^30*c^10*d^23*e^10 - 134717440*b^31*c^9*d^22*e^11 + 90202112*b^32*c^8*d^21*e^12 - 46964736*b^33*c^7*d^20*e^13 + 18636800*b^34*c^6*d^19*e^14 - 5447680*b^35*c^5*d^18*e^15 + 1105920*b^36*c^4*d^17*e^16 - 139264*b^37*c^3*d^16*e^17 + 8192*b^38*c^2*d^15*e^18))/(8*(b^12*e^7 - b^5*c^7*d^7 + 7*b^6*c^6*d^6*e - 21*b^7*c^5*d^5*e^2 + 35*b^8*c^4*d^4*e^3 - 35*b^9*c^3*d^3*e^4 + 21*b^10*c^2*d^2*e^5 - 7*b^11*c*d*e^6))))/(8*(b^12*e^7 - b^5*c^7*d^7 + 7*b^6*c^6*d^6*e - 21*b^7*c^5*d^5*e^2 + 35*b^8*c^4*d^4*e^3 - 35*b^9*c^3*d^3*e^4 + 21*b^10*c^2*d^2*e^5 - 7*b^11*c*d*e^6)))*(33*b^2*e^2 + 16*c^2*d^2 - 44*b*c*d*e))/(8*(b^12*e^7 - b^5*c^7*d^7 + 7*b^6*c^6*d^6*e - 21*b^7*c^5*d^5*e^2 + 35*b^8*c^4*d^4*e^3 - 35*b^9*c^3*d^3*e^4 + 21*b^10*c^2*d^2*e^5 - 7*b^11*c*d*e^6))))*(-c^7*(b*e - c*d)^7)^(1/2)*(33*b^2*e^2 + 16*c^2*d^2 - 44*b*c*d*e)*3i)/(4*(b^12*e^7 - b^5*c^7*d^7 + 7*b^6*c^6*d^6*e - 21*b^7*c^5*d^5*e^2 + 35*b^8*c^4*d^4*e^3 - 35*b^9*c^3*d^3*e^4 + 21*b^10*c^2*d^2*e^5 - 7*b^11*c*d*e^6)) - (atan(((((d + e*x)^(1/2)*(589824*b^12*c^22*d^28*e^2 - 8257536*b^13*c^21*d^27*e^3 + 53342208*b^14*c^20*d^26*e^4 - 210382848*b^15*c^19*d^25*e^5 + 564860160*b^16*c^18*d^24*e^6 - 1089838080*b^17*c^17*d^23*e^7 + 1555380864*b^18*c^16*d^22*e^8 - 1667850624*b^19*c^15*d^21*e^9 + 1358257536*b^20*c^14*d^20*e^10 - 855642240*b^21*c^13*d^19*e^11 + 438185088*b^22*c^12*d^18*e^12 - 201386880*b^23*c^11*d^17*e^13 + 90100224*b^24*c^10*d^16*e^14 - 37986048*b^25*c^9*d^15*e^15 + 15108480*b^26*c^8*d^14*e^16 - 6844032*b^27*c^7*d^13*e^17 + 3399552*b^28*c^6*d^12*e^18 - 1300608*b^29*c^5*d^11*e^19 + 293760*b^30*c^4*d^10*e^20 - 28800*b^31*c^3*d^9*e^21) - (3*(5*b^2*e^2 + 16*c^2*d^2 + 12*b*c*d*e)*(356352*b^19*c^18*d^28*e^4 - 24576*b^18*c^19*d^29*e^3 - 2396160*b^20*c^17*d^27*e^5 + 9897984*b^21*c^16*d^26*e^6 - 28065792*b^22*c^15*d^25*e^7 + 57891840*b^23*c^14*d^24*e^8 - 90071040*b^24*c^13*d^23*e^9 + 108810240*b^25*c^12*d^22*e^10 - 105566208*b^26*c^11*d^21*e^11 + 86406144*b^27*c^10*d^20*e^12 - 63393792*b^28*c^9*d^19*e^13 + 43075584*b^29*c^8*d^18*e^14 - 26173440*b^30*c^7*d^17*e^15 + 13108224*b^31*c^6*d^16*e^16 - 4964352*b^32*c^5*d^15*e^17 + 1302528*b^33*c^4*d^14*e^18 - 208896*b^34*c^3*d^13*e^19 + 15360*b^35*c^2*d^12*e^20 + (3*(d + e*x)^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 + 12*b*c*d*e)*(16384*b^22*c^18*d^31*e^2 - 253952*b^23*c^17*d^30*e^3 + 1843200*b^24*c^16*d^29*e^4 - 8314880*b^25*c^15*d^28*e^5 + 26091520*b^26*c^14*d^27*e^6 - 60383232*b^27*c^13*d^26*e^7 + 106602496*b^28*c^12*d^25*e^8 - 146432000*b^29*c^11*d^24*e^9 + 158146560*b^30*c^10*d^23*e^10 - 134717440*b^31*c^9*d^22*e^11 + 90202112*b^32*c^8*d^21*e^12 - 46964736*b^33*c^7*d^20*e^13 + 18636800*b^34*c^6*d^19*e^14 - 5447680*b^35*c^5*d^18*e^15 + 1105920*b^36*c^4*d^17*e^16 - 139264*b^37*c^3*d^16*e^17 + 8192*b^38*c^2*d^15*e^18))/(8*b^5*(d^7)^(1/2))))/(8*b^5*(d^7)^(1/2)))*(5*b^2*e^2 + 16*c^2*d^2 + 12*b*c*d*e)*3i)/(8*b^5*(d^7)^(1/2)) + (((d + e*x)^(1/2)*(589824*b^12*c^22*d^28*e^2 - 8257536*b^13*c^21*d^27*e^3 + 53342208*b^14*c^20*d^26*e^4 - 210382848*b^15*c^19*d^25*e^5 + 564860160*b^16*c^18*d^24*e^6 - 1089838080*b^17*c^17*d^23*e^7 + 1555380864*b^18*c^16*d^22*e^8 - 1667850624*b^19*c^15*d^21*e^9 + 1358257536*b^20*c^14*d^20*e^10 - 855642240*b^21*c^13*d^19*e^11 + 438185088*b^22*c^12*d^18*e^12 - 201386880*b^23*c^11*d^17*e^13 + 90100224*b^24*c^10*d^16*e^14 - 37986048*b^25*c^9*d^15*e^15 + 15108480*b^26*c^8*d^14*e^16 - 6844032*b^27*c^7*d^13*e^17 + 3399552*b^28*c^6*d^12*e^18 - 1300608*b^29*c^5*d^11*e^19 + 293760*b^30*c^4*d^10*e^20 - 28800*b^31*c^3*d^9*e^21) - (3*(5*b^2*e^2 + 16*c^2*d^2 + 12*b*c*d*e)*(24576*b^18*c^19*d^29*e^3 - 356352*b^19*c^18*d^28*e^4 + 2396160*b^20*c^17*d^27*e^5 - 9897984*b^21*c^16*d^26*e^6 + 28065792*b^22*c^15*d^25*e^7 - 57891840*b^23*c^14*d^24*e^8 + 90071040*b^24*c^13*d^23*e^9 - 108810240*b^25*c^12*d^22*e^10 + 105566208*b^26*c^11*d^21*e^11 - 86406144*b^27*c^10*d^20*e^12 + 63393792*b^28*c^9*d^19*e^13 - 43075584*b^29*c^8*d^18*e^14 + 26173440*b^30*c^7*d^17*e^15 - 13108224*b^31*c^6*d^16*e^16 + 4964352*b^32*c^5*d^15*e^17 - 1302528*b^33*c^4*d^14*e^18 + 208896*b^34*c^3*d^13*e^19 - 15360*b^35*c^2*d^12*e^20 + (3*(d + e*x)^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 + 12*b*c*d*e)*(16384*b^22*c^18*d^31*e^2 - 253952*b^23*c^17*d^30*e^3 + 1843200*b^24*c^16*d^29*e^4 - 8314880*b^25*c^15*d^28*e^5 + 26091520*b^26*c^14*d^27*e^6 - 60383232*b^27*c^13*d^26*e^7 + 106602496*b^28*c^12*d^25*e^8 - 146432000*b^29*c^11*d^24*e^9 + 158146560*b^30*c^10*d^23*e^10 - 134717440*b^31*c^9*d^22*e^11 + 90202112*b^32*c^8*d^21*e^12 - 46964736*b^33*c^7*d^20*e^13 + 18636800*b^34*c^6*d^19*e^14 - 5447680*b^35*c^5*d^18*e^15 + 1105920*b^36*c^4*d^17*e^16 - 139264*b^37*c^3*d^16*e^17 + 8192*b^38*c^2*d^15*e^18))/(8*b^5*(d^7)^(1/2))))/(8*b^5*(d^7)^(1/2)))*(5*b^2*e^2 + 16*c^2*d^2 + 12*b*c*d*e)*3i)/(8*b^5*(d^7)^(1/2)))/(1769472*b^8*c^23*d^26*e^3 - 23003136*b^9*c^22*d^25*e^4 + 136138752*b^10*c^21*d^24*e^5 - 483508224*b^11*c^20*d^23*e^6 + 1141579008*b^12*c^19*d^22*e^7 - 1869094656*b^13*c^18*d^21*e^8 + 2133106272*b^14*c^17*d^20*e^9 - 1631703744*b^15*c^16*d^19*e^10 + 716335488*b^16*c^15*d^18*e^11 - 36390816*b^17*c^14*d^17*e^12 - 153641664*b^18*c^13*d^16*e^13 + 89697024*b^19*c^12*d^15*e^14 - 40065408*b^20*c^11*d^14*e^15 + 43695936*b^21*c^10*d^13*e^16 - 41388192*b^22*c^9*d^12*e^17 + 21843648*b^23*c^8*d^11*e^18 - 6082560*b^24*c^7*d^10*e^19 + 712800*b^25*c^6*d^9*e^20 - (3*((d + e*x)^(1/2)*(589824*b^12*c^22*d^28*e^2 - 8257536*b^13*c^21*d^27*e^3 + 53342208*b^14*c^20*d^26*e^4 - 210382848*b^15*c^19*d^25*e^5 + 564860160*b^16*c^18*d^24*e^6 - 1089838080*b^17*c^17*d^23*e^7 + 1555380864*b^18*c^16*d^22*e^8 - 1667850624*b^19*c^15*d^21*e^9 + 1358257536*b^20*c^14*d^20*e^10 - 855642240*b^21*c^13*d^19*e^11 + 438185088*b^22*c^12*d^18*e^12 - 201386880*b^23*c^11*d^17*e^13 + 90100224*b^24*c^10*d^16*e^14 - 37986048*b^25*c^9*d^15*e^15 + 15108480*b^26*c^8*d^14*e^16 - 6844032*b^27*c^7*d^13*e^17 + 3399552*b^28*c^6*d^12*e^18 - 1300608*b^29*c^5*d^11*e^19 + 293760*b^30*c^4*d^10*e^20 - 28800*b^31*c^3*d^9*e^21) - (3*(5*b^2*e^2 + 16*c^2*d^2 + 12*b*c*d*e)*(356352*b^19*c^18*d^28*e^4 - 24576*b^18*c^19*d^29*e^3 - 2396160*b^20*c^17*d^27*e^5 + 9897984*b^21*c^16*d^26*e^6 - 28065792*b^22*c^15*d^25*e^7 + 57891840*b^23*c^14*d^24*e^8 - 90071040*b^24*c^13*d^23*e^9 + 108810240*b^25*c^12*d^22*e^10 - 105566208*b^26*c^11*d^21*e^11 + 86406144*b^27*c^10*d^20*e^12 - 63393792*b^28*c^9*d^19*e^13 + 43075584*b^29*c^8*d^18*e^14 - 26173440*b^30*c^7*d^17*e^15 + 13108224*b^31*c^6*d^16*e^16 - 4964352*b^32*c^5*d^15*e^17 + 1302528*b^33*c^4*d^14*e^18 - 208896*b^34*c^3*d^13*e^19 + 15360*b^35*c^2*d^12*e^20 + (3*(d + e*x)^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 + 12*b*c*d*e)*(16384*b^22*c^18*d^31*e^2 - 253952*b^23*c^17*d^30*e^3 + 1843200*b^24*c^16*d^29*e^4 - 8314880*b^25*c^15*d^28*e^5 + 26091520*b^26*c^14*d^27*e^6 - 60383232*b^27*c^13*d^26*e^7 + 106602496*b^28*c^12*d^25*e^8 - 146432000*b^29*c^11*d^24*e^9 + 158146560*b^30*c^10*d^23*e^10 - 134717440*b^31*c^9*d^22*e^11 + 90202112*b^32*c^8*d^21*e^12 - 46964736*b^33*c^7*d^20*e^13 + 18636800*b^34*c^6*d^19*e^14 - 5447680*b^35*c^5*d^18*e^15 + 1105920*b^36*c^4*d^17*e^16 - 139264*b^37*c^3*d^16*e^17 + 8192*b^38*c^2*d^15*e^18))/(8*b^5*(d^7)^(1/2))))/(8*b^5*(d^7)^(1/2)))*(5*b^2*e^2 + 16*c^2*d^2 + 12*b*c*d*e))/(8*b^5*(d^7)^(1/2)) + (3*((d + e*x)^(1/2)*(589824*b^12*c^22*d^28*e^2 - 8257536*b^13*c^21*d^27*e^3 + 53342208*b^14*c^20*d^26*e^4 - 210382848*b^15*c^19*d^25*e^5 + 564860160*b^16*c^18*d^24*e^6 - 1089838080*b^17*c^17*d^23*e^7 + 1555380864*b^18*c^16*d^22*e^8 - 1667850624*b^19*c^15*d^21*e^9 + 1358257536*b^20*c^14*d^20*e^10 - 855642240*b^21*c^13*d^19*e^11 + 438185088*b^22*c^12*d^18*e^12 - 201386880*b^23*c^11*d^17*e^13 + 90100224*b^24*c^10*d^16*e^14 - 37986048*b^25*c^9*d^15*e^15 + 15108480*b^26*c^8*d^14*e^16 - 6844032*b^27*c^7*d^13*e^17 + 3399552*b^28*c^6*d^12*e^18 - 1300608*b^29*c^5*d^11*e^19 + 293760*b^30*c^4*d^10*e^20 - 28800*b^31*c^3*d^9*e^21) - (3*(5*b^2*e^2 + 16*c^2*d^2 + 12*b*c*d*e)*(24576*b^18*c^19*d^29*e^3 - 356352*b^19*c^18*d^28*e^4 + 2396160*b^20*c^17*d^27*e^5 - 9897984*b^21*c^16*d^26*e^6 + 28065792*b^22*c^15*d^25*e^7 - 57891840*b^23*c^14*d^24*e^8 + 90071040*b^24*c^13*d^23*e^9 - 108810240*b^25*c^12*d^22*e^10 + 105566208*b^26*c^11*d^21*e^11 - 86406144*b^27*c^10*d^20*e^12 + 63393792*b^28*c^9*d^19*e^13 - 43075584*b^29*c^8*d^18*e^14 + 26173440*b^30*c^7*d^17*e^15 - 13108224*b^31*c^6*d^16*e^16 + 4964352*b^32*c^5*d^15*e^17 - 1302528*b^33*c^4*d^14*e^18 + 208896*b^34*c^3*d^13*e^19 - 15360*b^35*c^2*d^12*e^20 + (3*(d + e*x)^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 + 12*b*c*d*e)*(16384*b^22*c^18*d^31*e^2 - 253952*b^23*c^17*d^30*e^3 + 1843200*b^24*c^16*d^29*e^4 - 8314880*b^25*c^15*d^28*e^5 + 26091520*b^26*c^14*d^27*e^6 - 60383232*b^27*c^13*d^26*e^7 + 106602496*b^28*c^12*d^25*e^8 - 146432000*b^29*c^11*d^24*e^9 + 158146560*b^30*c^10*d^23*e^10 - 134717440*b^31*c^9*d^22*e^11 + 90202112*b^32*c^8*d^21*e^12 - 46964736*b^33*c^7*d^20*e^13 + 18636800*b^34*c^6*d^19*e^14 - 5447680*b^35*c^5*d^18*e^15 + 1105920*b^36*c^4*d^17*e^16 - 139264*b^37*c^3*d^16*e^17 + 8192*b^38*c^2*d^15*e^18))/(8*b^5*(d^7)^(1/2))))/(8*b^5*(d^7)^(1/2)))*(5*b^2*e^2 + 16*c^2*d^2 + 12*b*c*d*e))/(8*b^5*(d^7)^(1/2))))*(5*b^2*e^2 + 16*c^2*d^2 + 12*b*c*d*e)*3i)/(4*b^5*(d^7)^(1/2))","B"
385,1,11876,470,4.820687,"\text{Not used}","int(1/((b*x + c*x^2)^3*(d + e*x)^(5/2)),x)","-\frac{\frac{2\,e^5}{3\,\left(c\,d^2-b\,d\,e\right)}-\frac{14\,e^5\,\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)}{3\,{\left(c\,d^2-b\,d\,e\right)}^2}-\frac{e\,{\left(d+e\,x\right)}^5\,\left(35\,b^5\,c^2\,e^5-80\,b^4\,c^3\,d\,e^4+18\,b^3\,c^4\,d^2\,e^3+28\,b^2\,c^5\,d^3\,e^2-60\,b\,c^6\,d^4\,e+24\,c^7\,d^5\right)}{4\,b^4\,{\left(c\,d^2-b\,d\,e\right)}^4}+\frac{e\,{\left(d+e\,x\right)}^4\,\left(-210\,b^6\,c\,e^6+865\,b^5\,c^2\,d\,e^5-988\,b^4\,c^3\,d^2\,e^4+30\,b^3\,c^4\,d^3\,e^3+525\,b^2\,c^5\,d^4\,e^2-648\,b\,c^6\,d^5\,e+216\,c^7\,d^6\right)}{12\,b^4\,{\left(c\,d^2-b\,d\,e\right)}^4}+\frac{e\,{\left(d+e\,x\right)}^2\,\left(-175\,b^6\,e^6+687\,b^5\,c\,d\,e^5-738\,b^4\,c^2\,d^2\,e^4+30\,b^3\,c^3\,d^3\,e^3+165\,b^2\,c^4\,d^4\,e^2-216\,b\,c^5\,d^5\,e+72\,c^6\,d^6\right)}{12\,b^4\,{\left(c\,d^2-b\,d\,e\right)}^3}-\frac{e\,{\left(d+e\,x\right)}^3\,\left(105\,b^7\,e^7-800\,b^6\,c\,d\,e^6+1845\,b^5\,c^2\,d^2\,e^5-1372\,b^4\,c^3\,d^3\,e^4-165\,b^3\,c^4\,d^4\,e^3+822\,b^2\,c^5\,d^5\,e^2-756\,b\,c^6\,d^6\,e+216\,c^7\,d^7\right)}{12\,b^4\,{\left(c\,d^2-b\,d\,e\right)}^4}}{c^2\,{\left(d+e\,x\right)}^{11/2}-\left(4\,c^2\,d-2\,b\,c\,e\right)\,{\left(d+e\,x\right)}^{9/2}-{\left(d+e\,x\right)}^{5/2}\,\left(2\,b^2\,d\,e^2-6\,b\,c\,d^2\,e+4\,c^2\,d^3\right)+{\left(d+e\,x\right)}^{7/2}\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2\right)+{\left(d+e\,x\right)}^{3/2}\,\left(b^2\,d^2\,e^2-2\,b\,c\,d^3\,e+c^2\,d^4\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{d+e\,x}\,\left(156800\,b^{36}\,c^3\,d^{12}\,e^{26}-2598400\,b^{35}\,c^4\,d^{13}\,e^{25}+19930880\,b^{34}\,c^5\,d^{14}\,e^{24}-93688320\,b^{33}\,c^6\,d^{15}\,e^{23}+301648512\,b^{32}\,c^7\,d^{16}\,e^{22}-707773440\,b^{31}\,c^8\,d^{17}\,e^{21}+1274465280\,b^{30}\,c^9\,d^{18}\,e^{20}-1894041600\,b^{29}\,c^{10}\,d^{19}\,e^{19}+2608529792\,b^{28}\,c^{11}\,d^{20}\,e^{18}-3708136960\,b^{27}\,c^{12}\,d^{21}\,e^{17}+5421597440\,b^{26}\,c^{13}\,d^{22}\,e^{16}-7643066880\,b^{25}\,c^{14}\,d^{23}\,e^{15}+10265639040\,b^{24}\,c^{15}\,d^{24}\,e^{14}-13484230656\,b^{23}\,c^{16}\,d^{25}\,e^{13}+17074641408\,b^{22}\,c^{17}\,d^{26}\,e^{12}-19535324160\,b^{21}\,c^{18}\,d^{27}\,e^{11}+18936107520\,b^{20}\,c^{19}\,d^{28}\,e^{10}-14937190400\,b^{19}\,c^{20}\,d^{29}\,e^9+9364822016\,b^{18}\,c^{21}\,d^{30}\,e^8-4579446784\,b^{17}\,c^{22}\,d^{31}\,e^7+1707439360\,b^{16}\,c^{23}\,d^{32}\,e^6-468971520\,b^{15}\,c^{24}\,d^{33}\,e^5+89518080\,b^{14}\,c^{25}\,d^{34}\,e^4-10616832\,b^{13}\,c^{26}\,d^{35}\,e^3+589824\,b^{12}\,c^{27}\,d^{36}\,e^2\right)+\frac{\left(35\,b^2\,e^2+60\,b\,c\,d\,e+48\,c^2\,d^2\right)\,\left(24576\,b^{18}\,c^{24}\,d^{38}\,e^3-466944\,b^{19}\,c^{23}\,d^{37}\,e^4+4185088\,b^{20}\,c^{22}\,d^{36}\,e^5-23500800\,b^{21}\,c^{21}\,d^{35}\,e^6+92710912\,b^{22}\,c^{20}\,d^{34}\,e^7-273566720\,b^{23}\,c^{19}\,d^{33}\,e^8+629578752\,b^{24}\,c^{18}\,d^{32}\,e^9-1169833984\,b^{25}\,c^{17}\,d^{31}\,e^{10}+1818910720\,b^{26}\,c^{16}\,d^{30}\,e^{11}-2465058816\,b^{27}\,c^{15}\,d^{29}\,e^{12}+3031169024\,b^{28}\,c^{14}\,d^{28}\,e^{13}-3457871872\,b^{29}\,c^{13}\,d^{27}\,e^{14}+3626348544\,b^{30}\,c^{12}\,d^{26}\,e^{15}-3385559040\,b^{31}\,c^{11}\,d^{25}\,e^{16}+2714064896\,b^{32}\,c^{10}\,d^{24}\,e^{17}-1813512192\,b^{33}\,c^9\,d^{23}\,e^{18}+986251264\,b^{34}\,c^8\,d^{22}\,e^{19}-426815488\,b^{35}\,c^7\,d^{21}\,e^{20}+143109120\,b^{36}\,c^6\,d^{20}\,e^{21}-35796992\,b^{37}\,c^5\,d^{19}\,e^{22}+6285312\,b^{38}\,c^4\,d^{18}\,e^{23}-691200\,b^{39}\,c^3\,d^{17}\,e^{24}+35840\,b^{40}\,c^2\,d^{16}\,e^{25}-\frac{\sqrt{d+e\,x}\,\left(35\,b^2\,e^2+60\,b\,c\,d\,e+48\,c^2\,d^2\right)\,\left(-8192\,b^{43}\,c^2\,d^{20}\,e^{23}+180224\,b^{42}\,c^3\,d^{21}\,e^{22}-1884160\,b^{41}\,c^4\,d^{22}\,e^{21}+12451840\,b^{40}\,c^5\,d^{23}\,e^{20}-58368000\,b^{39}\,c^6\,d^{24}\,e^{19}+206389248\,b^{38}\,c^7\,d^{25}\,e^{18}-571539456\,b^{37}\,c^8\,d^{26}\,e^{17}+1270087680\,b^{36}\,c^9\,d^{27}\,e^{16}-2302033920\,b^{35}\,c^{10}\,d^{28}\,e^{15}+3439820800\,b^{34}\,c^{11}\,d^{29}\,e^{14}-4265377792\,b^{33}\,c^{12}\,d^{30}\,e^{13}+4402970624\,b^{32}\,c^{13}\,d^{31}\,e^{12}-3783802880\,b^{31}\,c^{14}\,d^{32}\,e^{11}+2698936320\,b^{30}\,c^{15}\,d^{33}\,e^{10}-1587609600\,b^{29}\,c^{16}\,d^{34}\,e^9+762052608\,b^{28}\,c^{17}\,d^{35}\,e^8-293707776\,b^{27}\,c^{18}\,d^{36}\,e^7+88719360\,b^{26}\,c^{19}\,d^{37}\,e^6-20234240\,b^{25}\,c^{20}\,d^{38}\,e^5+3276800\,b^{24}\,c^{21}\,d^{39}\,e^4-335872\,b^{23}\,c^{22}\,d^{40}\,e^3+16384\,b^{22}\,c^{23}\,d^{41}\,e^2\right)}{8\,b^5\,\sqrt{d^9}}\right)}{8\,b^5\,\sqrt{d^9}}\right)\,\left(35\,b^2\,e^2+60\,b\,c\,d\,e+48\,c^2\,d^2\right)\,1{}\mathrm{i}}{8\,b^5\,\sqrt{d^9}}+\frac{\left(\sqrt{d+e\,x}\,\left(156800\,b^{36}\,c^3\,d^{12}\,e^{26}-2598400\,b^{35}\,c^4\,d^{13}\,e^{25}+19930880\,b^{34}\,c^5\,d^{14}\,e^{24}-93688320\,b^{33}\,c^6\,d^{15}\,e^{23}+301648512\,b^{32}\,c^7\,d^{16}\,e^{22}-707773440\,b^{31}\,c^8\,d^{17}\,e^{21}+1274465280\,b^{30}\,c^9\,d^{18}\,e^{20}-1894041600\,b^{29}\,c^{10}\,d^{19}\,e^{19}+2608529792\,b^{28}\,c^{11}\,d^{20}\,e^{18}-3708136960\,b^{27}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21}\,c^{21}\,d^{35}\,e^6+92710912\,b^{22}\,c^{20}\,d^{34}\,e^7-273566720\,b^{23}\,c^{19}\,d^{33}\,e^8+629578752\,b^{24}\,c^{18}\,d^{32}\,e^9-1169833984\,b^{25}\,c^{17}\,d^{31}\,e^{10}+1818910720\,b^{26}\,c^{16}\,d^{30}\,e^{11}-2465058816\,b^{27}\,c^{15}\,d^{29}\,e^{12}+3031169024\,b^{28}\,c^{14}\,d^{28}\,e^{13}-3457871872\,b^{29}\,c^{13}\,d^{27}\,e^{14}+3626348544\,b^{30}\,c^{12}\,d^{26}\,e^{15}-3385559040\,b^{31}\,c^{11}\,d^{25}\,e^{16}+2714064896\,b^{32}\,c^{10}\,d^{24}\,e^{17}-1813512192\,b^{33}\,c^9\,d^{23}\,e^{18}+986251264\,b^{34}\,c^8\,d^{22}\,e^{19}-426815488\,b^{35}\,c^7\,d^{21}\,e^{20}+143109120\,b^{36}\,c^6\,d^{20}\,e^{21}-35796992\,b^{37}\,c^5\,d^{19}\,e^{22}+6285312\,b^{38}\,c^4\,d^{18}\,e^{23}-691200\,b^{39}\,c^3\,d^{17}\,e^{24}+35840\,b^{40}\,c^2\,d^{16}\,e^{25}-\frac{\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\sqrt{d+e\,x}\,\left(143\,b^2\,e^2-156\,b\,c\,d\,e+48\,c^2\,d^2\right)\,\left(-8192\,b^{43}\,c^2\,d^{20}\,e^{23}+180224\,b^{42}\,c^3\,d^{21}\,e^{22}-1884160\,b^{41}\,c^4\,d^{22}\,e^{21}+12451840\,b^{40}\,c^5\,d^{23}\,e^{20}-58368000\,b^{39}\,c^6\,d^{24}\,e^{19}+206389248\,b^{38}\,c^7\,d^{25}\,e^{18}-571539456\,b^{37}\,c^8\,d^{26}\,e^{17}+1270087680\,b^{36}\,c^9\,d^{27}\,e^{16}-2302033920\,b^{35}\,c^{10}\,d^{28}\,e^{15}+3439820800\,b^{34}\,c^{11}\,d^{29}\,e^{14}-4265377792\,b^{33}\,c^{12}\,d^{30}\,e^{13}+4402970624\,b^{32}\,c^{13}\,d^{31}\,e^{12}-3783802880\,b^{31}\,c^{14}\,d^{32}\,e^{11}+2698936320\,b^{30}\,c^{15}\,d^{33}\,e^{10}-1587609600\,b^{29}\,c^{16}\,d^{34}\,e^9+762052608\,b^{28}\,c^{17}\,d^{35}\,e^8-293707776\,b^{27}\,c^{18}\,d^{36}\,e^7+88719360\,b^{26}\,c^{19}\,d^{37}\,e^6-20234240\,b^{25}\,c^{20}\,d^{38}\,e^5+3276800\,b^{24}\,c^{21}\,d^{39}\,e^4-335872\,b^{23}\,c^{22}\,d^{40}\,e^3+16384\,b^{22}\,c^{23}\,d^{41}\,e^2\right)}{8\,\left(b^{14}\,e^9-9\,b^{13}\,c\,d\,e^8+36\,b^{12}\,c^2\,d^2\,e^7-84\,b^{11}\,c^3\,d^3\,e^6+126\,b^{10}\,c^4\,d^4\,e^5-126\,b^9\,c^5\,d^5\,e^4+84\,b^8\,c^6\,d^6\,e^3-36\,b^7\,c^7\,d^7\,e^2+9\,b^6\,c^8\,d^8\,e-b^5\,c^9\,d^9\right)}\right)}{8\,\left(b^{14}\,e^9-9\,b^{13}\,c\,d\,e^8+36\,b^{12}\,c^2\,d^2\,e^7-84\,b^{11}\,c^3\,d^3\,e^6+126\,b^{10}\,c^4\,d^4\,e^5-126\,b^9\,c^5\,d^5\,e^4+84\,b^8\,c^6\,d^6\,e^3-36\,b^7\,c^7\,d^7\,e^2+9\,b^6\,c^8\,d^8\,e-b^5\,c^9\,d^9\right)}\right)\,\left(143\,b^2\,e^2-156\,b\,c\,d\,e+48\,c^2\,d^2\right)}{8\,\left(b^{14}\,e^9-9\,b^{13}\,c\,d\,e^8+36\,b^{12}\,c^2\,d^2\,e^7-84\,b^{11}\,c^3\,d^3\,e^6+126\,b^{10}\,c^4\,d^4\,e^5-126\,b^9\,c^5\,d^5\,e^4+84\,b^8\,c^6\,d^6\,e^3-36\,b^7\,c^7\,d^7\,e^2+9\,b^6\,c^8\,d^8\,e-b^5\,c^9\,d^9\right)}+\frac{\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\left(\sqrt{d+e\,x}\,\left(156800\,b^{36}\,c^3\,d^{12}\,e^{26}-2598400\,b^{35}\,c^4\,d^{13}\,e^{25}+19930880\,b^{34}\,c^5\,d^{14}\,e^{24}-93688320\,b^{33}\,c^6\,d^{15}\,e^{23}+301648512\,b^{32}\,c^7\,d^{16}\,e^{22}-707773440\,b^{31}\,c^8\,d^{17}\,e^{21}+1274465280\,b^{30}\,c^9\,d^{18}\,e^{20}-1894041600\,b^{29}\,c^{10}\,d^{19}\,e^{19}+2608529792\,b^{28}\,c^{11}\,d^{20}\,e^{18}-3708136960\,b^{27}\,c^{12}\,d^{21}\,e^{17}+5421597440\,b^{26}\,c^{13}\,d^{22}\,e^{16}-7643066880\,b^{25}\,c^{14}\,d^{23}\,e^{15}+10265639040\,b^{24}\,c^{15}\,d^{24}\,e^{14}-13484230656\,b^{23}\,c^{16}\,d^{25}\,e^{13}+17074641408\,b^{22}\,c^{17}\,d^{26}\,e^{12}-19535324160\,b^{21}\,c^{18}\,d^{27}\,e^{11}+18936107520\,b^{20}\,c^{19}\,d^{28}\,e^{10}-14937190400\,b^{19}\,c^{20}\,d^{29}\,e^9+9364822016\,b^{18}\,c^{21}\,d^{30}\,e^8-4579446784\,b^{17}\,c^{22}\,d^{31}\,e^7+1707439360\,b^{16}\,c^{23}\,d^{32}\,e^6-468971520\,b^{15}\,c^{24}\,d^{33}\,e^5+89518080\,b^{14}\,c^{25}\,d^{34}\,e^4-10616832\,b^{13}\,c^{26}\,d^{35}\,e^3+589824\,b^{12}\,c^{27}\,d^{36}\,e^2\right)-\frac{\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\left(143\,b^2\,e^2-156\,b\,c\,d\,e+48\,c^2\,d^2\right)\,\left(24576\,b^{18}\,c^{24}\,d^{38}\,e^3-466944\,b^{19}\,c^{23}\,d^{37}\,e^4+4185088\,b^{20}\,c^{22}\,d^{36}\,e^5-23500800\,b^{21}\,c^{21}\,d^{35}\,e^6+92710912\,b^{22}\,c^{20}\,d^{34}\,e^7-273566720\,b^{23}\,c^{19}\,d^{33}\,e^8+629578752\,b^{24}\,c^{18}\,d^{32}\,e^9-1169833984\,b^{25}\,c^{17}\,d^{31}\,e^{10}+1818910720\,b^{26}\,c^{16}\,d^{30}\,e^{11}-2465058816\,b^{27}\,c^{15}\,d^{29}\,e^{12}+3031169024\,b^{28}\,c^{14}\,d^{28}\,e^{13}-3457871872\,b^{29}\,c^{13}\,d^{27}\,e^{14}+3626348544\,b^{30}\,c^{12}\,d^{26}\,e^{15}-3385559040\,b^{31}\,c^{11}\,d^{25}\,e^{16}+2714064896\,b^{32}\,c^{10}\,d^{24}\,e^{17}-1813512192\,b^{33}\,c^9\,d^{23}\,e^{18}+986251264\,b^{34}\,c^8\,d^{22}\,e^{19}-426815488\,b^{35}\,c^7\,d^{21}\,e^{20}+143109120\,b^{36}\,c^6\,d^{20}\,e^{21}-35796992\,b^{37}\,c^5\,d^{19}\,e^{22}+6285312\,b^{38}\,c^4\,d^{18}\,e^{23}-691200\,b^{39}\,c^3\,d^{17}\,e^{24}+35840\,b^{40}\,c^2\,d^{16}\,e^{25}+\frac{\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\sqrt{d+e\,x}\,\left(143\,b^2\,e^2-156\,b\,c\,d\,e+48\,c^2\,d^2\right)\,\left(-8192\,b^{43}\,c^2\,d^{20}\,e^{23}+180224\,b^{42}\,c^3\,d^{21}\,e^{22}-1884160\,b^{41}\,c^4\,d^{22}\,e^{21}+12451840\,b^{40}\,c^5\,d^{23}\,e^{20}-58368000\,b^{39}\,c^6\,d^{24}\,e^{19}+206389248\,b^{38}\,c^7\,d^{25}\,e^{18}-571539456\,b^{37}\,c^8\,d^{26}\,e^{17}+1270087680\,b^{36}\,c^9\,d^{27}\,e^{16}-2302033920\,b^{35}\,c^{10}\,d^{28}\,e^{15}+3439820800\,b^{34}\,c^{11}\,d^{29}\,e^{14}-4265377792\,b^{33}\,c^{12}\,d^{30}\,e^{13}+4402970624\,b^{32}\,c^{13}\,d^{31}\,e^{12}-3783802880\,b^{31}\,c^{14}\,d^{32}\,e^{11}+2698936320\,b^{30}\,c^{15}\,d^{33}\,e^{10}-1587609600\,b^{29}\,c^{16}\,d^{34}\,e^9+762052608\,b^{28}\,c^{17}\,d^{35}\,e^8-293707776\,b^{27}\,c^{18}\,d^{36}\,e^7+88719360\,b^{26}\,c^{19}\,d^{37}\,e^6-20234240\,b^{25}\,c^{20}\,d^{38}\,e^5+3276800\,b^{24}\,c^{21}\,d^{39}\,e^4-335872\,b^{23}\,c^{22}\,d^{40}\,e^3+16384\,b^{22}\,c^{23}\,d^{41}\,e^2\right)}{8\,\left(b^{14}\,e^9-9\,b^{13}\,c\,d\,e^8+36\,b^{12}\,c^2\,d^2\,e^7-84\,b^{11}\,c^3\,d^3\,e^6+126\,b^{10}\,c^4\,d^4\,e^5-126\,b^9\,c^5\,d^5\,e^4+84\,b^8\,c^6\,d^6\,e^3-36\,b^7\,c^7\,d^7\,e^2+9\,b^6\,c^8\,d^8\,e-b^5\,c^9\,d^9\right)}\right)}{8\,\left(b^{14}\,e^9-9\,b^{13}\,c\,d\,e^8+36\,b^{12}\,c^2\,d^2\,e^7-84\,b^{11}\,c^3\,d^3\,e^6+126\,b^{10}\,c^4\,d^4\,e^5-126\,b^9\,c^5\,d^5\,e^4+84\,b^8\,c^6\,d^6\,e^3-36\,b^7\,c^7\,d^7\,e^2+9\,b^6\,c^8\,d^8\,e-b^5\,c^9\,d^9\right)}\right)\,\left(143\,b^2\,e^2-156\,b\,c\,d\,e+48\,c^2\,d^2\right)}{8\,\left(b^{14}\,e^9-9\,b^{13}\,c\,d\,e^8+36\,b^{12}\,c^2\,d^2\,e^7-84\,b^{11}\,c^3\,d^3\,e^6+126\,b^{10}\,c^4\,d^4\,e^5-126\,b^9\,c^5\,d^5\,e^4+84\,b^8\,c^6\,d^6\,e^3-36\,b^7\,c^7\,d^7\,e^2+9\,b^6\,c^8\,d^8\,e-b^5\,c^9\,d^9\right)}}\right)\,\sqrt{-c^9\,{\left(b\,e-c\,d\right)}^9}\,\left(143\,b^2\,e^2-156\,b\,c\,d\,e+48\,c^2\,d^2\right)\,1{}\mathrm{i}}{4\,\left(b^{14}\,e^9-9\,b^{13}\,c\,d\,e^8+36\,b^{12}\,c^2\,d^2\,e^7-84\,b^{11}\,c^3\,d^3\,e^6+126\,b^{10}\,c^4\,d^4\,e^5-126\,b^9\,c^5\,d^5\,e^4+84\,b^8\,c^6\,d^6\,e^3-36\,b^7\,c^7\,d^7\,e^2+9\,b^6\,c^8\,d^8\,e-b^5\,c^9\,d^9\right)}","Not used",1,"- ((2*e^5)/(3*(c*d^2 - b*d*e)) - (14*e^5*(b*e - 2*c*d)*(d + e*x))/(3*(c*d^2 - b*d*e)^2) - (e*(d + e*x)^5*(24*c^7*d^5 + 35*b^5*c^2*e^5 - 80*b^4*c^3*d*e^4 + 28*b^2*c^5*d^3*e^2 + 18*b^3*c^4*d^2*e^3 - 60*b*c^6*d^4*e))/(4*b^4*(c*d^2 - b*d*e)^4) + (e*(d + e*x)^4*(216*c^7*d^6 - 210*b^6*c*e^6 + 865*b^5*c^2*d*e^5 + 525*b^2*c^5*d^4*e^2 + 30*b^3*c^4*d^3*e^3 - 988*b^4*c^3*d^2*e^4 - 648*b*c^6*d^5*e))/(12*b^4*(c*d^2 - b*d*e)^4) + (e*(d + e*x)^2*(72*c^6*d^6 - 175*b^6*e^6 + 165*b^2*c^4*d^4*e^2 + 30*b^3*c^3*d^3*e^3 - 738*b^4*c^2*d^2*e^4 - 216*b*c^5*d^5*e + 687*b^5*c*d*e^5))/(12*b^4*(c*d^2 - b*d*e)^3) - (e*(d + e*x)^3*(105*b^7*e^7 + 216*c^7*d^7 + 822*b^2*c^5*d^5*e^2 - 165*b^3*c^4*d^4*e^3 - 1372*b^4*c^3*d^3*e^4 + 1845*b^5*c^2*d^2*e^5 - 756*b*c^6*d^6*e - 800*b^6*c*d*e^6))/(12*b^4*(c*d^2 - b*d*e)^4))/(c^2*(d + e*x)^(11/2) - (4*c^2*d - 2*b*c*e)*(d + e*x)^(9/2) - (d + e*x)^(5/2)*(4*c^2*d^3 + 2*b^2*d*e^2 - 6*b*c*d^2*e) + (d + e*x)^(7/2)*(b^2*e^2 + 6*c^2*d^2 - 6*b*c*d*e) + (d + e*x)^(3/2)*(c^2*d^4 + b^2*d^2*e^2 - 2*b*c*d^3*e)) - (atan(((((d + e*x)^(1/2)*(589824*b^12*c^27*d^36*e^2 - 10616832*b^13*c^26*d^35*e^3 + 89518080*b^14*c^25*d^34*e^4 - 468971520*b^15*c^24*d^33*e^5 + 1707439360*b^16*c^23*d^32*e^6 - 4579446784*b^17*c^22*d^31*e^7 + 9364822016*b^18*c^21*d^30*e^8 - 14937190400*b^19*c^20*d^29*e^9 + 18936107520*b^20*c^19*d^28*e^10 - 19535324160*b^21*c^18*d^27*e^11 + 17074641408*b^22*c^17*d^26*e^12 - 13484230656*b^23*c^16*d^25*e^13 + 10265639040*b^24*c^15*d^24*e^14 - 7643066880*b^25*c^14*d^23*e^15 + 5421597440*b^26*c^13*d^22*e^16 - 3708136960*b^27*c^12*d^21*e^17 + 2608529792*b^28*c^11*d^20*e^18 - 1894041600*b^29*c^10*d^19*e^19 + 1274465280*b^30*c^9*d^18*e^20 - 707773440*b^31*c^8*d^17*e^21 + 301648512*b^32*c^7*d^16*e^22 - 93688320*b^33*c^6*d^15*e^23 + 19930880*b^34*c^5*d^14*e^24 - 2598400*b^35*c^4*d^13*e^25 + 156800*b^36*c^3*d^12*e^26) + ((35*b^2*e^2 + 48*c^2*d^2 + 60*b*c*d*e)*(24576*b^18*c^24*d^38*e^3 - 466944*b^19*c^23*d^37*e^4 + 4185088*b^20*c^22*d^36*e^5 - 23500800*b^21*c^21*d^35*e^6 + 92710912*b^22*c^20*d^34*e^7 - 273566720*b^23*c^19*d^33*e^8 + 629578752*b^24*c^18*d^32*e^9 - 1169833984*b^25*c^17*d^31*e^10 + 1818910720*b^26*c^16*d^30*e^11 - 2465058816*b^27*c^15*d^29*e^12 + 3031169024*b^28*c^14*d^28*e^13 - 3457871872*b^29*c^13*d^27*e^14 + 3626348544*b^30*c^12*d^26*e^15 - 3385559040*b^31*c^11*d^25*e^16 + 2714064896*b^32*c^10*d^24*e^17 - 1813512192*b^33*c^9*d^23*e^18 + 986251264*b^34*c^8*d^22*e^19 - 426815488*b^35*c^7*d^21*e^20 + 143109120*b^36*c^6*d^20*e^21 - 35796992*b^37*c^5*d^19*e^22 + 6285312*b^38*c^4*d^18*e^23 - 691200*b^39*c^3*d^17*e^24 + 35840*b^40*c^2*d^16*e^25 - ((d + e*x)^(1/2)*(35*b^2*e^2 + 48*c^2*d^2 + 60*b*c*d*e)*(16384*b^22*c^23*d^41*e^2 - 335872*b^23*c^22*d^40*e^3 + 3276800*b^24*c^21*d^39*e^4 - 20234240*b^25*c^20*d^38*e^5 + 88719360*b^26*c^19*d^37*e^6 - 293707776*b^27*c^18*d^36*e^7 + 762052608*b^28*c^17*d^35*e^8 - 1587609600*b^29*c^16*d^34*e^9 + 2698936320*b^30*c^15*d^33*e^10 - 3783802880*b^31*c^14*d^32*e^11 + 4402970624*b^32*c^13*d^31*e^12 - 4265377792*b^33*c^12*d^30*e^13 + 3439820800*b^34*c^11*d^29*e^14 - 2302033920*b^35*c^10*d^28*e^15 + 1270087680*b^36*c^9*d^27*e^16 - 571539456*b^37*c^8*d^26*e^17 + 206389248*b^38*c^7*d^25*e^18 - 58368000*b^39*c^6*d^24*e^19 + 12451840*b^40*c^5*d^23*e^20 - 1884160*b^41*c^4*d^22*e^21 + 180224*b^42*c^3*d^21*e^22 - 8192*b^43*c^2*d^20*e^23))/(8*b^5*(d^9)^(1/2))))/(8*b^5*(d^9)^(1/2)))*(35*b^2*e^2 + 48*c^2*d^2 + 60*b*c*d*e)*1i)/(8*b^5*(d^9)^(1/2)) + (((d + e*x)^(1/2)*(589824*b^12*c^27*d^36*e^2 - 10616832*b^13*c^26*d^35*e^3 + 89518080*b^14*c^25*d^34*e^4 - 468971520*b^15*c^24*d^33*e^5 + 1707439360*b^16*c^23*d^32*e^6 - 4579446784*b^17*c^22*d^31*e^7 + 9364822016*b^18*c^21*d^30*e^8 - 14937190400*b^19*c^20*d^29*e^9 + 18936107520*b^20*c^19*d^28*e^10 - 19535324160*b^21*c^18*d^27*e^11 + 17074641408*b^22*c^17*d^26*e^12 - 13484230656*b^23*c^16*d^25*e^13 + 10265639040*b^24*c^15*d^24*e^14 - 7643066880*b^25*c^14*d^23*e^15 + 5421597440*b^26*c^13*d^22*e^16 - 3708136960*b^27*c^12*d^21*e^17 + 2608529792*b^28*c^11*d^20*e^18 - 1894041600*b^29*c^10*d^19*e^19 + 1274465280*b^30*c^9*d^18*e^20 - 707773440*b^31*c^8*d^17*e^21 + 301648512*b^32*c^7*d^16*e^22 - 93688320*b^33*c^6*d^15*e^23 + 19930880*b^34*c^5*d^14*e^24 - 2598400*b^35*c^4*d^13*e^25 + 156800*b^36*c^3*d^12*e^26) - ((35*b^2*e^2 + 48*c^2*d^2 + 60*b*c*d*e)*(24576*b^18*c^24*d^38*e^3 - 466944*b^19*c^23*d^37*e^4 + 4185088*b^20*c^22*d^36*e^5 - 23500800*b^21*c^21*d^35*e^6 + 92710912*b^22*c^20*d^34*e^7 - 273566720*b^23*c^19*d^33*e^8 + 629578752*b^24*c^18*d^32*e^9 - 1169833984*b^25*c^17*d^31*e^10 + 1818910720*b^26*c^16*d^30*e^11 - 2465058816*b^27*c^15*d^29*e^12 + 3031169024*b^28*c^14*d^28*e^13 - 3457871872*b^29*c^13*d^27*e^14 + 3626348544*b^30*c^12*d^26*e^15 - 3385559040*b^31*c^11*d^25*e^16 + 2714064896*b^32*c^10*d^24*e^17 - 1813512192*b^33*c^9*d^23*e^18 + 986251264*b^34*c^8*d^22*e^19 - 426815488*b^35*c^7*d^21*e^20 + 143109120*b^36*c^6*d^20*e^21 - 35796992*b^37*c^5*d^19*e^22 + 6285312*b^38*c^4*d^18*e^23 - 691200*b^39*c^3*d^17*e^24 + 35840*b^40*c^2*d^16*e^25 + ((d + e*x)^(1/2)*(35*b^2*e^2 + 48*c^2*d^2 + 60*b*c*d*e)*(16384*b^22*c^23*d^41*e^2 - 335872*b^23*c^22*d^40*e^3 + 3276800*b^24*c^21*d^39*e^4 - 20234240*b^25*c^20*d^38*e^5 + 88719360*b^26*c^19*d^37*e^6 - 293707776*b^27*c^18*d^36*e^7 + 762052608*b^28*c^17*d^35*e^8 - 1587609600*b^29*c^16*d^34*e^9 + 2698936320*b^30*c^15*d^33*e^10 - 3783802880*b^31*c^14*d^32*e^11 + 4402970624*b^32*c^13*d^31*e^12 - 4265377792*b^33*c^12*d^30*e^13 + 3439820800*b^34*c^11*d^29*e^14 - 2302033920*b^35*c^10*d^28*e^15 + 1270087680*b^36*c^9*d^27*e^16 - 571539456*b^37*c^8*d^26*e^17 + 206389248*b^38*c^7*d^25*e^18 - 58368000*b^39*c^6*d^24*e^19 + 12451840*b^40*c^5*d^23*e^20 - 1884160*b^41*c^4*d^22*e^21 + 180224*b^42*c^3*d^21*e^22 - 8192*b^43*c^2*d^20*e^23))/(8*b^5*(d^9)^(1/2))))/(8*b^5*(d^9)^(1/2)))*(35*b^2*e^2 + 48*c^2*d^2 + 60*b*c*d*e)*1i)/(8*b^5*(d^9)^(1/2)))/((((d + e*x)^(1/2)*(589824*b^12*c^27*d^36*e^2 - 10616832*b^13*c^26*d^35*e^3 + 89518080*b^14*c^25*d^34*e^4 - 468971520*b^15*c^24*d^33*e^5 + 1707439360*b^16*c^23*d^32*e^6 - 4579446784*b^17*c^22*d^31*e^7 + 9364822016*b^18*c^21*d^30*e^8 - 14937190400*b^19*c^20*d^29*e^9 + 18936107520*b^20*c^19*d^28*e^10 - 19535324160*b^21*c^18*d^27*e^11 + 17074641408*b^22*c^17*d^26*e^12 - 13484230656*b^23*c^16*d^25*e^13 + 10265639040*b^24*c^15*d^24*e^14 - 7643066880*b^25*c^14*d^23*e^15 + 5421597440*b^26*c^13*d^22*e^16 - 3708136960*b^27*c^12*d^21*e^17 + 2608529792*b^28*c^11*d^20*e^18 - 1894041600*b^29*c^10*d^19*e^19 + 1274465280*b^30*c^9*d^18*e^20 - 707773440*b^31*c^8*d^17*e^21 + 301648512*b^32*c^7*d^16*e^22 - 93688320*b^33*c^6*d^15*e^23 + 19930880*b^34*c^5*d^14*e^24 - 2598400*b^35*c^4*d^13*e^25 + 156800*b^36*c^3*d^12*e^26) - ((35*b^2*e^2 + 48*c^2*d^2 + 60*b*c*d*e)*(24576*b^18*c^24*d^38*e^3 - 466944*b^19*c^23*d^37*e^4 + 4185088*b^20*c^22*d^36*e^5 - 23500800*b^21*c^21*d^35*e^6 + 92710912*b^22*c^20*d^34*e^7 - 273566720*b^23*c^19*d^33*e^8 + 629578752*b^24*c^18*d^32*e^9 - 1169833984*b^25*c^17*d^31*e^10 + 1818910720*b^26*c^16*d^30*e^11 - 2465058816*b^27*c^15*d^29*e^12 + 3031169024*b^28*c^14*d^28*e^13 - 3457871872*b^29*c^13*d^27*e^14 + 3626348544*b^30*c^12*d^26*e^15 - 3385559040*b^31*c^11*d^25*e^16 + 2714064896*b^32*c^10*d^24*e^17 - 1813512192*b^33*c^9*d^23*e^18 + 986251264*b^34*c^8*d^22*e^19 - 426815488*b^35*c^7*d^21*e^20 + 143109120*b^36*c^6*d^20*e^21 - 35796992*b^37*c^5*d^19*e^22 + 6285312*b^38*c^4*d^18*e^23 - 691200*b^39*c^3*d^17*e^24 + 35840*b^40*c^2*d^16*e^25 + ((d + e*x)^(1/2)*(35*b^2*e^2 + 48*c^2*d^2 + 60*b*c*d*e)*(16384*b^22*c^23*d^41*e^2 - 335872*b^23*c^22*d^40*e^3 + 3276800*b^24*c^21*d^39*e^4 - 20234240*b^25*c^20*d^38*e^5 + 88719360*b^26*c^19*d^37*e^6 - 293707776*b^27*c^18*d^36*e^7 + 762052608*b^28*c^17*d^35*e^8 - 1587609600*b^29*c^16*d^34*e^9 + 2698936320*b^30*c^15*d^33*e^10 - 3783802880*b^31*c^14*d^32*e^11 + 4402970624*b^32*c^13*d^31*e^12 - 4265377792*b^33*c^12*d^30*e^13 + 3439820800*b^34*c^11*d^29*e^14 - 2302033920*b^35*c^10*d^28*e^15 + 1270087680*b^36*c^9*d^27*e^16 - 571539456*b^37*c^8*d^26*e^17 + 206389248*b^38*c^7*d^25*e^18 - 58368000*b^39*c^6*d^24*e^19 + 12451840*b^40*c^5*d^23*e^20 - 1884160*b^41*c^4*d^22*e^21 + 180224*b^42*c^3*d^21*e^22 - 8192*b^43*c^2*d^20*e^23))/(8*b^5*(d^9)^(1/2))))/(8*b^5*(d^9)^(1/2)))*(35*b^2*e^2 + 48*c^2*d^2 + 60*b*c*d*e))/(8*b^5*(d^9)^(1/2)) - (((d + e*x)^(1/2)*(589824*b^12*c^27*d^36*e^2 - 10616832*b^13*c^26*d^35*e^3 + 89518080*b^14*c^25*d^34*e^4 - 468971520*b^15*c^24*d^33*e^5 + 1707439360*b^16*c^23*d^32*e^6 - 4579446784*b^17*c^22*d^31*e^7 + 9364822016*b^18*c^21*d^30*e^8 - 14937190400*b^19*c^20*d^29*e^9 + 18936107520*b^20*c^19*d^28*e^10 - 19535324160*b^21*c^18*d^27*e^11 + 17074641408*b^22*c^17*d^26*e^12 - 13484230656*b^23*c^16*d^25*e^13 + 10265639040*b^24*c^15*d^24*e^14 - 7643066880*b^25*c^14*d^23*e^15 + 5421597440*b^26*c^13*d^22*e^16 - 3708136960*b^27*c^12*d^21*e^17 + 2608529792*b^28*c^11*d^20*e^18 - 1894041600*b^29*c^10*d^19*e^19 + 1274465280*b^30*c^9*d^18*e^20 - 707773440*b^31*c^8*d^17*e^21 + 301648512*b^32*c^7*d^16*e^22 - 93688320*b^33*c^6*d^15*e^23 + 19930880*b^34*c^5*d^14*e^24 - 2598400*b^35*c^4*d^13*e^25 + 156800*b^36*c^3*d^12*e^26) + ((35*b^2*e^2 + 48*c^2*d^2 + 60*b*c*d*e)*(24576*b^18*c^24*d^38*e^3 - 466944*b^19*c^23*d^37*e^4 + 4185088*b^20*c^22*d^36*e^5 - 23500800*b^21*c^21*d^35*e^6 + 92710912*b^22*c^20*d^34*e^7 - 273566720*b^23*c^19*d^33*e^8 + 629578752*b^24*c^18*d^32*e^9 - 1169833984*b^25*c^17*d^31*e^10 + 1818910720*b^26*c^16*d^30*e^11 - 2465058816*b^27*c^15*d^29*e^12 + 3031169024*b^28*c^14*d^28*e^13 - 3457871872*b^29*c^13*d^27*e^14 + 3626348544*b^30*c^12*d^26*e^15 - 3385559040*b^31*c^11*d^25*e^16 + 2714064896*b^32*c^10*d^24*e^17 - 1813512192*b^33*c^9*d^23*e^18 + 986251264*b^34*c^8*d^22*e^19 - 426815488*b^35*c^7*d^21*e^20 + 143109120*b^36*c^6*d^20*e^21 - 35796992*b^37*c^5*d^19*e^22 + 6285312*b^38*c^4*d^18*e^23 - 691200*b^39*c^3*d^17*e^24 + 35840*b^40*c^2*d^16*e^25 - ((d + e*x)^(1/2)*(35*b^2*e^2 + 48*c^2*d^2 + 60*b*c*d*e)*(16384*b^22*c^23*d^41*e^2 - 335872*b^23*c^22*d^40*e^3 + 3276800*b^24*c^21*d^39*e^4 - 20234240*b^25*c^20*d^38*e^5 + 88719360*b^26*c^19*d^37*e^6 - 293707776*b^27*c^18*d^36*e^7 + 762052608*b^28*c^17*d^35*e^8 - 1587609600*b^29*c^16*d^34*e^9 + 2698936320*b^30*c^15*d^33*e^10 - 3783802880*b^31*c^14*d^32*e^11 + 4402970624*b^32*c^13*d^31*e^12 - 4265377792*b^33*c^12*d^30*e^13 + 3439820800*b^34*c^11*d^29*e^14 - 2302033920*b^35*c^10*d^28*e^15 + 1270087680*b^36*c^9*d^27*e^16 - 571539456*b^37*c^8*d^26*e^17 + 206389248*b^38*c^7*d^25*e^18 - 58368000*b^39*c^6*d^24*e^19 + 12451840*b^40*c^5*d^23*e^20 - 1884160*b^41*c^4*d^22*e^21 + 180224*b^42*c^3*d^21*e^22 - 8192*b^43*c^2*d^20*e^23))/(8*b^5*(d^9)^(1/2))))/(8*b^5*(d^9)^(1/2)))*(35*b^2*e^2 + 48*c^2*d^2 + 60*b*c*d*e))/(8*b^5*(d^9)^(1/2)) + 1769472*b^8*c^28*d^33*e^3 - 29196288*b^9*c^27*d^32*e^4 + 222621696*b^10*c^26*d^31*e^5 - 1037076480*b^11*c^25*d^30*e^6 + 3281114880*b^12*c^24*d^29*e^7 - 7384738176*b^13*c^23*d^28*e^8 + 11940731264*b^14*c^22*d^27*e^9 - 13391621568*b^15*c^21*d^26*e^10 + 8822378240*b^16*c^20*d^25*e^11 + 174168800*b^17*c^19*d^24*e^12 - 7908536064*b^18*c^18*d^23*e^13 + 10270788736*b^19*c^17*d^22*e^14 - 8868525952*b^20*c^16*d^21*e^15 + 8022944160*b^21*c^15*d^20*e^16 - 9013107840*b^22*c^14*d^19*e^17 + 9481058368*b^23*c^13*d^18*e^18 - 7612941312*b^24*c^12*d^17*e^19 + 4396193824*b^25*c^11*d^16*e^20 - 1772817920*b^26*c^10*d^15*e^21 + 475772160*b^27*c^9*d^14*e^22 - 76585600*b^28*c^8*d^13*e^23 + 5605600*b^29*c^7*d^12*e^24))*(35*b^2*e^2 + 48*c^2*d^2 + 60*b*c*d*e)*1i)/(4*b^5*(d^9)^(1/2)) - (atan((((-c^9*(b*e - c*d)^9)^(1/2)*((d + e*x)^(1/2)*(589824*b^12*c^27*d^36*e^2 - 10616832*b^13*c^26*d^35*e^3 + 89518080*b^14*c^25*d^34*e^4 - 468971520*b^15*c^24*d^33*e^5 + 1707439360*b^16*c^23*d^32*e^6 - 4579446784*b^17*c^22*d^31*e^7 + 9364822016*b^18*c^21*d^30*e^8 - 14937190400*b^19*c^20*d^29*e^9 + 18936107520*b^20*c^19*d^28*e^10 - 19535324160*b^21*c^18*d^27*e^11 + 17074641408*b^22*c^17*d^26*e^12 - 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8192*b^43*c^2*d^20*e^23))/(8*(b^14*e^9 - b^5*c^9*d^9 + 9*b^6*c^8*d^8*e - 36*b^7*c^7*d^7*e^2 + 84*b^8*c^6*d^6*e^3 - 126*b^9*c^5*d^5*e^4 + 126*b^10*c^4*d^4*e^5 - 84*b^11*c^3*d^3*e^6 + 36*b^12*c^2*d^2*e^7 - 9*b^13*c*d*e^8))))/(8*(b^14*e^9 - b^5*c^9*d^9 + 9*b^6*c^8*d^8*e - 36*b^7*c^7*d^7*e^2 + 84*b^8*c^6*d^6*e^3 - 126*b^9*c^5*d^5*e^4 + 126*b^10*c^4*d^4*e^5 - 84*b^11*c^3*d^3*e^6 + 36*b^12*c^2*d^2*e^7 - 9*b^13*c*d*e^8)))*(143*b^2*e^2 + 48*c^2*d^2 - 156*b*c*d*e)*1i)/(8*(b^14*e^9 - b^5*c^9*d^9 + 9*b^6*c^8*d^8*e - 36*b^7*c^7*d^7*e^2 + 84*b^8*c^6*d^6*e^3 - 126*b^9*c^5*d^5*e^4 + 126*b^10*c^4*d^4*e^5 - 84*b^11*c^3*d^3*e^6 + 36*b^12*c^2*d^2*e^7 - 9*b^13*c*d*e^8)) + ((-c^9*(b*e - c*d)^9)^(1/2)*((d + e*x)^(1/2)*(589824*b^12*c^27*d^36*e^2 - 10616832*b^13*c^26*d^35*e^3 + 89518080*b^14*c^25*d^34*e^4 - 468971520*b^15*c^24*d^33*e^5 + 1707439360*b^16*c^23*d^32*e^6 - 4579446784*b^17*c^22*d^31*e^7 + 9364822016*b^18*c^21*d^30*e^8 - 14937190400*b^19*c^20*d^29*e^9 + 18936107520*b^20*c^19*d^28*e^10 - 19535324160*b^21*c^18*d^27*e^11 + 17074641408*b^22*c^17*d^26*e^12 - 13484230656*b^23*c^16*d^25*e^13 + 10265639040*b^24*c^15*d^24*e^14 - 7643066880*b^25*c^14*d^23*e^15 + 5421597440*b^26*c^13*d^22*e^16 - 3708136960*b^27*c^12*d^21*e^17 + 2608529792*b^28*c^11*d^20*e^18 - 1894041600*b^29*c^10*d^19*e^19 + 1274465280*b^30*c^9*d^18*e^20 - 707773440*b^31*c^8*d^17*e^21 + 301648512*b^32*c^7*d^16*e^22 - 93688320*b^33*c^6*d^15*e^23 + 19930880*b^34*c^5*d^14*e^24 - 2598400*b^35*c^4*d^13*e^25 + 156800*b^36*c^3*d^12*e^26) - ((-c^9*(b*e - c*d)^9)^(1/2)*(143*b^2*e^2 + 48*c^2*d^2 - 156*b*c*d*e)*(24576*b^18*c^24*d^38*e^3 - 466944*b^19*c^23*d^37*e^4 + 4185088*b^20*c^22*d^36*e^5 - 23500800*b^21*c^21*d^35*e^6 + 92710912*b^22*c^20*d^34*e^7 - 273566720*b^23*c^19*d^33*e^8 + 629578752*b^24*c^18*d^32*e^9 - 1169833984*b^25*c^17*d^31*e^10 + 1818910720*b^26*c^16*d^30*e^11 - 2465058816*b^27*c^15*d^29*e^12 + 3031169024*b^28*c^14*d^28*e^13 - 3457871872*b^29*c^13*d^27*e^14 + 3626348544*b^30*c^12*d^26*e^15 - 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1884160*b^41*c^4*d^22*e^21 + 180224*b^42*c^3*d^21*e^22 - 8192*b^43*c^2*d^20*e^23))/(8*(b^14*e^9 - b^5*c^9*d^9 + 9*b^6*c^8*d^8*e - 36*b^7*c^7*d^7*e^2 + 84*b^8*c^6*d^6*e^3 - 126*b^9*c^5*d^5*e^4 + 126*b^10*c^4*d^4*e^5 - 84*b^11*c^3*d^3*e^6 + 36*b^12*c^2*d^2*e^7 - 9*b^13*c*d*e^8))))/(8*(b^14*e^9 - b^5*c^9*d^9 + 9*b^6*c^8*d^8*e - 36*b^7*c^7*d^7*e^2 + 84*b^8*c^6*d^6*e^3 - 126*b^9*c^5*d^5*e^4 + 126*b^10*c^4*d^4*e^5 - 84*b^11*c^3*d^3*e^6 + 36*b^12*c^2*d^2*e^7 - 9*b^13*c*d*e^8)))*(143*b^2*e^2 + 48*c^2*d^2 - 156*b*c*d*e)*1i)/(8*(b^14*e^9 - b^5*c^9*d^9 + 9*b^6*c^8*d^8*e - 36*b^7*c^7*d^7*e^2 + 84*b^8*c^6*d^6*e^3 - 126*b^9*c^5*d^5*e^4 + 126*b^10*c^4*d^4*e^5 - 84*b^11*c^3*d^3*e^6 + 36*b^12*c^2*d^2*e^7 - 9*b^13*c*d*e^8)))/(1769472*b^8*c^28*d^33*e^3 - 29196288*b^9*c^27*d^32*e^4 + 222621696*b^10*c^26*d^31*e^5 - 1037076480*b^11*c^25*d^30*e^6 + 3281114880*b^12*c^24*d^29*e^7 - 7384738176*b^13*c^23*d^28*e^8 + 11940731264*b^14*c^22*d^27*e^9 - 13391621568*b^15*c^21*d^26*e^10 + 8822378240*b^16*c^20*d^25*e^11 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2608529792*b^28*c^11*d^20*e^18 - 1894041600*b^29*c^10*d^19*e^19 + 1274465280*b^30*c^9*d^18*e^20 - 707773440*b^31*c^8*d^17*e^21 + 301648512*b^32*c^7*d^16*e^22 - 93688320*b^33*c^6*d^15*e^23 + 19930880*b^34*c^5*d^14*e^24 - 2598400*b^35*c^4*d^13*e^25 + 156800*b^36*c^3*d^12*e^26) + ((-c^9*(b*e - c*d)^9)^(1/2)*(143*b^2*e^2 + 48*c^2*d^2 - 156*b*c*d*e)*(24576*b^18*c^24*d^38*e^3 - 466944*b^19*c^23*d^37*e^4 + 4185088*b^20*c^22*d^36*e^5 - 23500800*b^21*c^21*d^35*e^6 + 92710912*b^22*c^20*d^34*e^7 - 273566720*b^23*c^19*d^33*e^8 + 629578752*b^24*c^18*d^32*e^9 - 1169833984*b^25*c^17*d^31*e^10 + 1818910720*b^26*c^16*d^30*e^11 - 2465058816*b^27*c^15*d^29*e^12 + 3031169024*b^28*c^14*d^28*e^13 - 3457871872*b^29*c^13*d^27*e^14 + 3626348544*b^30*c^12*d^26*e^15 - 3385559040*b^31*c^11*d^25*e^16 + 2714064896*b^32*c^10*d^24*e^17 - 1813512192*b^33*c^9*d^23*e^18 + 986251264*b^34*c^8*d^22*e^19 - 426815488*b^35*c^7*d^21*e^20 + 143109120*b^36*c^6*d^20*e^21 - 35796992*b^37*c^5*d^19*e^22 + 6285312*b^38*c^4*d^18*e^23 - 691200*b^39*c^3*d^17*e^24 + 35840*b^40*c^2*d^16*e^25 - ((-c^9*(b*e - c*d)^9)^(1/2)*(d + e*x)^(1/2)*(143*b^2*e^2 + 48*c^2*d^2 - 156*b*c*d*e)*(16384*b^22*c^23*d^41*e^2 - 335872*b^23*c^22*d^40*e^3 + 3276800*b^24*c^21*d^39*e^4 - 20234240*b^25*c^20*d^38*e^5 + 88719360*b^26*c^19*d^37*e^6 - 293707776*b^27*c^18*d^36*e^7 + 762052608*b^28*c^17*d^35*e^8 - 1587609600*b^29*c^16*d^34*e^9 + 2698936320*b^30*c^15*d^33*e^10 - 3783802880*b^31*c^14*d^32*e^11 + 4402970624*b^32*c^13*d^31*e^12 - 4265377792*b^33*c^12*d^30*e^13 + 3439820800*b^34*c^11*d^29*e^14 - 2302033920*b^35*c^10*d^28*e^15 + 1270087680*b^36*c^9*d^27*e^16 - 571539456*b^37*c^8*d^26*e^17 + 206389248*b^38*c^7*d^25*e^18 - 58368000*b^39*c^6*d^24*e^19 + 12451840*b^40*c^5*d^23*e^20 - 1884160*b^41*c^4*d^22*e^21 + 180224*b^42*c^3*d^21*e^22 - 8192*b^43*c^2*d^20*e^23))/(8*(b^14*e^9 - b^5*c^9*d^9 + 9*b^6*c^8*d^8*e - 36*b^7*c^7*d^7*e^2 + 84*b^8*c^6*d^6*e^3 - 126*b^9*c^5*d^5*e^4 + 126*b^10*c^4*d^4*e^5 - 84*b^11*c^3*d^3*e^6 + 36*b^12*c^2*d^2*e^7 - 9*b^13*c*d*e^8))))/(8*(b^14*e^9 - b^5*c^9*d^9 + 9*b^6*c^8*d^8*e - 36*b^7*c^7*d^7*e^2 + 84*b^8*c^6*d^6*e^3 - 126*b^9*c^5*d^5*e^4 + 126*b^10*c^4*d^4*e^5 - 84*b^11*c^3*d^3*e^6 + 36*b^12*c^2*d^2*e^7 - 9*b^13*c*d*e^8)))*(143*b^2*e^2 + 48*c^2*d^2 - 156*b*c*d*e))/(8*(b^14*e^9 - b^5*c^9*d^9 + 9*b^6*c^8*d^8*e - 36*b^7*c^7*d^7*e^2 + 84*b^8*c^6*d^6*e^3 - 126*b^9*c^5*d^5*e^4 + 126*b^10*c^4*d^4*e^5 - 84*b^11*c^3*d^3*e^6 + 36*b^12*c^2*d^2*e^7 - 9*b^13*c*d*e^8)) + ((-c^9*(b*e - c*d)^9)^(1/2)*((d + e*x)^(1/2)*(589824*b^12*c^27*d^36*e^2 - 10616832*b^13*c^26*d^35*e^3 + 89518080*b^14*c^25*d^34*e^4 - 468971520*b^15*c^24*d^33*e^5 + 1707439360*b^16*c^23*d^32*e^6 - 4579446784*b^17*c^22*d^31*e^7 + 9364822016*b^18*c^21*d^30*e^8 - 14937190400*b^19*c^20*d^29*e^9 + 18936107520*b^20*c^19*d^28*e^10 - 19535324160*b^21*c^18*d^27*e^11 + 17074641408*b^22*c^17*d^26*e^12 - 13484230656*b^23*c^16*d^25*e^13 + 10265639040*b^24*c^15*d^24*e^14 - 7643066880*b^25*c^14*d^23*e^15 + 5421597440*b^26*c^13*d^22*e^16 - 3708136960*b^27*c^12*d^21*e^17 + 2608529792*b^28*c^11*d^20*e^18 - 1894041600*b^29*c^10*d^19*e^19 + 1274465280*b^30*c^9*d^18*e^20 - 707773440*b^31*c^8*d^17*e^21 + 301648512*b^32*c^7*d^16*e^22 - 93688320*b^33*c^6*d^15*e^23 + 19930880*b^34*c^5*d^14*e^24 - 2598400*b^35*c^4*d^13*e^25 + 156800*b^36*c^3*d^12*e^26) - ((-c^9*(b*e - c*d)^9)^(1/2)*(143*b^2*e^2 + 48*c^2*d^2 - 156*b*c*d*e)*(24576*b^18*c^24*d^38*e^3 - 466944*b^19*c^23*d^37*e^4 + 4185088*b^20*c^22*d^36*e^5 - 23500800*b^21*c^21*d^35*e^6 + 92710912*b^22*c^20*d^34*e^7 - 273566720*b^23*c^19*d^33*e^8 + 629578752*b^24*c^18*d^32*e^9 - 1169833984*b^25*c^17*d^31*e^10 + 1818910720*b^26*c^16*d^30*e^11 - 2465058816*b^27*c^15*d^29*e^12 + 3031169024*b^28*c^14*d^28*e^13 - 3457871872*b^29*c^13*d^27*e^14 + 3626348544*b^30*c^12*d^26*e^15 - 3385559040*b^31*c^11*d^25*e^16 + 2714064896*b^32*c^10*d^24*e^17 - 1813512192*b^33*c^9*d^23*e^18 + 986251264*b^34*c^8*d^22*e^19 - 426815488*b^35*c^7*d^21*e^20 + 143109120*b^36*c^6*d^20*e^21 - 35796992*b^37*c^5*d^19*e^22 + 6285312*b^38*c^4*d^18*e^23 - 691200*b^39*c^3*d^17*e^24 + 35840*b^40*c^2*d^16*e^25 + ((-c^9*(b*e - c*d)^9)^(1/2)*(d + e*x)^(1/2)*(143*b^2*e^2 + 48*c^2*d^2 - 156*b*c*d*e)*(16384*b^22*c^23*d^41*e^2 - 335872*b^23*c^22*d^40*e^3 + 3276800*b^24*c^21*d^39*e^4 - 20234240*b^25*c^20*d^38*e^5 + 88719360*b^26*c^19*d^37*e^6 - 293707776*b^27*c^18*d^36*e^7 + 762052608*b^28*c^17*d^35*e^8 - 1587609600*b^29*c^16*d^34*e^9 + 2698936320*b^30*c^15*d^33*e^10 - 3783802880*b^31*c^14*d^32*e^11 + 4402970624*b^32*c^13*d^31*e^12 - 4265377792*b^33*c^12*d^30*e^13 + 3439820800*b^34*c^11*d^29*e^14 - 2302033920*b^35*c^10*d^28*e^15 + 1270087680*b^36*c^9*d^27*e^16 - 571539456*b^37*c^8*d^26*e^17 + 206389248*b^38*c^7*d^25*e^18 - 58368000*b^39*c^6*d^24*e^19 + 12451840*b^40*c^5*d^23*e^20 - 1884160*b^41*c^4*d^22*e^21 + 180224*b^42*c^3*d^21*e^22 - 8192*b^43*c^2*d^20*e^23))/(8*(b^14*e^9 - b^5*c^9*d^9 + 9*b^6*c^8*d^8*e - 36*b^7*c^7*d^7*e^2 + 84*b^8*c^6*d^6*e^3 - 126*b^9*c^5*d^5*e^4 + 126*b^10*c^4*d^4*e^5 - 84*b^11*c^3*d^3*e^6 + 36*b^12*c^2*d^2*e^7 - 9*b^13*c*d*e^8))))/(8*(b^14*e^9 - b^5*c^9*d^9 + 9*b^6*c^8*d^8*e - 36*b^7*c^7*d^7*e^2 + 84*b^8*c^6*d^6*e^3 - 126*b^9*c^5*d^5*e^4 + 126*b^10*c^4*d^4*e^5 - 84*b^11*c^3*d^3*e^6 + 36*b^12*c^2*d^2*e^7 - 9*b^13*c*d*e^8)))*(143*b^2*e^2 + 48*c^2*d^2 - 156*b*c*d*e))/(8*(b^14*e^9 - b^5*c^9*d^9 + 9*b^6*c^8*d^8*e - 36*b^7*c^7*d^7*e^2 + 84*b^8*c^6*d^6*e^3 - 126*b^9*c^5*d^5*e^4 + 126*b^10*c^4*d^4*e^5 - 84*b^11*c^3*d^3*e^6 + 36*b^12*c^2*d^2*e^7 - 9*b^13*c*d*e^8))))*(-c^9*(b*e - c*d)^9)^(1/2)*(143*b^2*e^2 + 48*c^2*d^2 - 156*b*c*d*e)*1i)/(4*(b^14*e^9 - b^5*c^9*d^9 + 9*b^6*c^8*d^8*e - 36*b^7*c^7*d^7*e^2 + 84*b^8*c^6*d^6*e^3 - 126*b^9*c^5*d^5*e^4 + 126*b^10*c^4*d^4*e^5 - 84*b^11*c^3*d^3*e^6 + 36*b^12*c^2*d^2*e^7 - 9*b^13*c*d*e^8))","B"
386,0,-1,362,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)*(d + e*x)^(3/2),x)","\int \sqrt{c\,x^2+b\,x}\,{\left(d+e\,x\right)}^{3/2} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)*(d + e*x)^(3/2), x)","F"
387,0,-1,308,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)*(d + e*x)^(1/2),x)","\int \sqrt{c\,x^2+b\,x}\,\sqrt{d+e\,x} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)*(d + e*x)^(1/2), x)","F"
388,0,-1,246,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/(d + e*x)^(1/2),x)","\int \frac{\sqrt{c\,x^2+b\,x}}{\sqrt{d+e\,x}} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/(d + e*x)^(1/2), x)","F"
389,0,-1,231,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/(d + e*x)^(3/2),x)","\int \frac{\sqrt{c\,x^2+b\,x}}{{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/(d + e*x)^(3/2), x)","F"
390,0,-1,301,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/(d + e*x)^(5/2),x)","\int \frac{\sqrt{c\,x^2+b\,x}}{{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/(d + e*x)^(5/2), x)","F"
391,0,-1,398,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)/(d + e*x)^(7/2),x)","\int \frac{\sqrt{c\,x^2+b\,x}}{{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)/(d + e*x)^(7/2), x)","F"
392,0,-1,521,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)*(d + e*x)^(3/2),x)","\int {\left(c\,x^2+b\,x\right)}^{3/2}\,{\left(d+e\,x\right)}^{3/2} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)*(d + e*x)^(3/2), x)","F"
393,0,-1,457,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)*(d + e*x)^(1/2),x)","\int {\left(c\,x^2+b\,x\right)}^{3/2}\,\sqrt{d+e\,x} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)*(d + e*x)^(1/2), x)","F"
394,0,-1,360,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/(d + e*x)^(1/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{\sqrt{d+e\,x}} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/(d + e*x)^(1/2), x)","F"
395,0,-1,309,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/(d + e*x)^(3/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/(d + e*x)^(3/2), x)","F"
396,0,-1,298,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/(d + e*x)^(5/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/(d + e*x)^(5/2), x)","F"
397,0,-1,354,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/(d + e*x)^(7/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/(d + e*x)^(7/2), x)","F"
398,0,-1,476,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)/(d + e*x)^(9/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{3/2}}{{\left(d+e\,x\right)}^{9/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)/(d + e*x)^(9/2), x)","F"
399,0,-1,666,0.000000,"\text{Not used}","int((b*x + c*x^2)^(5/2)*(d + e*x)^(1/2),x)","\int {\left(c\,x^2+b\,x\right)}^{5/2}\,\sqrt{d+e\,x} \,d x","Not used",1,"int((b*x + c*x^2)^(5/2)*(d + e*x)^(1/2), x)","F"
400,0,-1,537,0.000000,"\text{Not used}","int((b*x + c*x^2)^(5/2)/(d + e*x)^(1/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{5/2}}{\sqrt{d+e\,x}} \,d x","Not used",1,"int((b*x + c*x^2)^(5/2)/(d + e*x)^(1/2), x)","F"
401,0,-1,457,0.000000,"\text{Not used}","int((b*x + c*x^2)^(5/2)/(d + e*x)^(3/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{5/2}}{{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(5/2)/(d + e*x)^(3/2), x)","F"
402,0,-1,401,0.000000,"\text{Not used}","int((b*x + c*x^2)^(5/2)/(d + e*x)^(5/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{5/2}}{{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(5/2)/(d + e*x)^(5/2), x)","F"
403,0,-1,392,0.000000,"\text{Not used}","int((b*x + c*x^2)^(5/2)/(d + e*x)^(7/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{5/2}}{{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(5/2)/(d + e*x)^(7/2), x)","F"
404,0,-1,474,0.000000,"\text{Not used}","int((b*x + c*x^2)^(5/2)/(d + e*x)^(9/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{5/2}}{{\left(d+e\,x\right)}^{9/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(5/2)/(d + e*x)^(9/2), x)","F"
405,0,-1,570,0.000000,"\text{Not used}","int((b*x + c*x^2)^(5/2)/(d + e*x)^(11/2),x)","\int \frac{{\left(c\,x^2+b\,x\right)}^{5/2}}{{\left(d+e\,x\right)}^{11/2}} \,d x","Not used",1,"int((b*x + c*x^2)^(5/2)/(d + e*x)^(11/2), x)","F"
406,0,-1,379,0.000000,"\text{Not used}","int((d + e*x)^(7/2)/(b*x + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^{7/2}}{\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int((d + e*x)^(7/2)/(b*x + c*x^2)^(1/2), x)","F"
407,0,-1,303,0.000000,"\text{Not used}","int((d + e*x)^(5/2)/(b*x + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^{5/2}}{\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int((d + e*x)^(5/2)/(b*x + c*x^2)^(1/2), x)","F"
408,0,-1,241,0.000000,"\text{Not used}","int((d + e*x)^(3/2)/(b*x + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^{3/2}}{\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int((d + e*x)^(3/2)/(b*x + c*x^2)^(1/2), x)","F"
409,0,-1,94,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/(b*x + c*x^2)^(1/2),x)","\int \frac{\sqrt{d+e\,x}}{\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int((d + e*x)^(1/2)/(b*x + c*x^2)^(1/2), x)","F"
410,0,-1,94,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(1/2)*(d + e*x)^(1/2)),x)","\int \frac{1}{\sqrt{c\,x^2+b\,x}\,\sqrt{d+e\,x}} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(1/2)*(d + e*x)^(1/2)), x)","F"
411,0,-1,146,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(1/2)*(d + e*x)^(3/2)),x)","\int \frac{1}{\sqrt{c\,x^2+b\,x}\,{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(1/2)*(d + e*x)^(3/2)), x)","F"
412,0,-1,317,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(1/2)*(d + e*x)^(5/2)),x)","\int \frac{1}{\sqrt{c\,x^2+b\,x}\,{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(1/2)*(d + e*x)^(5/2)), x)","F"
413,0,-1,403,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(1/2)*(d + e*x)^(7/2)),x)","\int \frac{1}{\sqrt{c\,x^2+b\,x}\,{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(1/2)*(d + e*x)^(7/2)), x)","F"
414,0,-1,395,0.000000,"\text{Not used}","int((d + e*x)^(7/2)/(b*x + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^{7/2}}{{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(7/2)/(b*x + c*x^2)^(3/2), x)","F"
415,0,-1,310,0.000000,"\text{Not used}","int((d + e*x)^(5/2)/(b*x + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^{5/2}}{{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(5/2)/(b*x + c*x^2)^(3/2), x)","F"
416,0,-1,249,0.000000,"\text{Not used}","int((d + e*x)^(3/2)/(b*x + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^{3/2}}{{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(3/2)/(b*x + c*x^2)^(3/2), x)","F"
417,0,-1,231,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/(b*x + c*x^2)^(3/2),x)","\int \frac{\sqrt{d+e\,x}}{{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(1/2)/(b*x + c*x^2)^(3/2), x)","F"
418,0,-1,274,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(3/2)*(d + e*x)^(1/2)),x)","\int \frac{1}{{\left(c\,x^2+b\,x\right)}^{3/2}\,\sqrt{d+e\,x}} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(3/2)*(d + e*x)^(1/2)), x)","F"
419,0,-1,370,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(3/2)*(d + e*x)^(3/2)),x)","\int \frac{1}{{\left(c\,x^2+b\,x\right)}^{3/2}\,{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(3/2)*(d + e*x)^(3/2)), x)","F"
420,0,-1,478,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(3/2)*(d + e*x)^(5/2)),x)","\int \frac{1}{{\left(c\,x^2+b\,x\right)}^{3/2}\,{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(3/2)*(d + e*x)^(5/2)), x)","F"
421,0,-1,470,0.000000,"\text{Not used}","int((d + e*x)^(9/2)/(b*x + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{9/2}}{{\left(c\,x^2+b\,x\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(9/2)/(b*x + c*x^2)^(5/2), x)","F"
422,0,-1,383,0.000000,"\text{Not used}","int((d + e*x)^(7/2)/(b*x + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{7/2}}{{\left(c\,x^2+b\,x\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(7/2)/(b*x + c*x^2)^(5/2), x)","F"
423,0,-1,343,0.000000,"\text{Not used}","int((d + e*x)^(5/2)/(b*x + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{5/2}}{{\left(c\,x^2+b\,x\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(5/2)/(b*x + c*x^2)^(5/2), x)","F"
424,0,-1,344,0.000000,"\text{Not used}","int((d + e*x)^(3/2)/(b*x + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{3/2}}{{\left(c\,x^2+b\,x\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(3/2)/(b*x + c*x^2)^(5/2), x)","F"
425,0,-1,359,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/(b*x + c*x^2)^(5/2),x)","\int \frac{\sqrt{d+e\,x}}{{\left(c\,x^2+b\,x\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(1/2)/(b*x + c*x^2)^(5/2), x)","F"
426,0,-1,451,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(5/2)*(d + e*x)^(1/2)),x)","\int \frac{1}{{\left(c\,x^2+b\,x\right)}^{5/2}\,\sqrt{d+e\,x}} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(5/2)*(d + e*x)^(1/2)), x)","F"
427,0,-1,567,0.000000,"\text{Not used}","int(1/((b*x + c*x^2)^(5/2)*(d + e*x)^(3/2)),x)","\int \frac{1}{{\left(c\,x^2+b\,x\right)}^{5/2}\,{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int(1/((b*x + c*x^2)^(5/2)*(d + e*x)^(3/2)), x)","F"
428,0,-1,51,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/(2*x - 3*x^2)^(1/2),x)","\int \frac{\sqrt{d+e\,x}}{\sqrt{2\,x-3\,x^2}} \,d x","Not used",1,"int((d + e*x)^(1/2)/(2*x - 3*x^2)^(1/2), x)","F"
429,0,-1,51,0.000000,"\text{Not used}","int(1/((2*x - 3*x^2)^(1/2)*(d + e*x)^(1/2)),x)","\int \frac{1}{\sqrt{2\,x-3\,x^2}\,\sqrt{d+e\,x}} \,d x","Not used",1,"int(1/((2*x - 3*x^2)^(1/2)*(d + e*x)^(1/2)), x)","F"
430,0,-1,53,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/(- 2*x - 3*x^2)^(1/2),x)","\int \frac{\sqrt{d+e\,x}}{\sqrt{-3\,x^2-2\,x}} \,d x","Not used",1,"int((d + e*x)^(1/2)/(- 2*x - 3*x^2)^(1/2), x)","F"
431,0,-1,53,0.000000,"\text{Not used}","int(1/((- 2*x - 3*x^2)^(1/2)*(d + e*x)^(1/2)),x)","\int \frac{1}{\sqrt{-3\,x^2-2\,x}\,\sqrt{d+e\,x}} \,d x","Not used",1,"int(1/((- 2*x - 3*x^2)^(1/2)*(d + e*x)^(1/2)), x)","F"
432,0,-1,12,0.000000,"\text{Not used}","int((1 - x)^(1/2)/((-x)^(1/2)*(x + 1)^(1/2)),x)","\int \frac{\sqrt{1-x}}{\sqrt{-x}\,\sqrt{x+1}} \,d x","Not used",1,"int((1 - x)^(1/2)/((-x)^(1/2)*(x + 1)^(1/2)), x)","F"
433,0,-1,12,0.000000,"\text{Not used}","int((1 - x)^(1/2)/(- x - x^2)^(1/2),x)","\int \frac{\sqrt{1-x}}{\sqrt{-x^2-x}} \,d x","Not used",1,"int((1 - x)^(1/2)/(- x - x^2)^(1/2), x)","F"
434,1,333,95,0.585970,"\text{Not used}","int((c*d*x + c*e*x^2)^3*(d + e*x)^m,x)","{\left(d+e\,x\right)}^m\,\left(\frac{c^3\,e^3\,x^7\,\left(m^3+15\,m^2+74\,m+120\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}-\frac{6\,c^3\,d^7}{e^4\,\left(m^4+22\,m^3+179\,m^2+638\,m+840\right)}+\frac{2\,c^3\,d^3\,x^4\,\left(2\,m^3+21\,m^2+79\,m+105\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}+\frac{6\,c^3\,d^6\,m\,x}{e^3\,\left(m^4+22\,m^3+179\,m^2+638\,m+840\right)}+\frac{c^3\,d\,e^2\,x^6\,\left(4\,m^3+57\,m^2+269\,m+420\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}+\frac{6\,c^3\,d^2\,e\,x^5\,\left(m^3+13\,m^2+57\,m+84\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}-\frac{3\,c^3\,d^5\,m\,x^2\,\left(m+1\right)}{e^2\,\left(m^4+22\,m^3+179\,m^2+638\,m+840\right)}+\frac{c^3\,d^4\,m\,x^3\,\left(m^2+3\,m+2\right)}{e\,\left(m^4+22\,m^3+179\,m^2+638\,m+840\right)}\right)","Not used",1,"(d + e*x)^m*((c^3*e^3*x^7*(74*m + 15*m^2 + m^3 + 120))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840) - (6*c^3*d^7)/(e^4*(638*m + 179*m^2 + 22*m^3 + m^4 + 840)) + (2*c^3*d^3*x^4*(79*m + 21*m^2 + 2*m^3 + 105))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840) + (6*c^3*d^6*m*x)/(e^3*(638*m + 179*m^2 + 22*m^3 + m^4 + 840)) + (c^3*d*e^2*x^6*(269*m + 57*m^2 + 4*m^3 + 420))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840) + (6*c^3*d^2*e*x^5*(57*m + 13*m^2 + m^3 + 84))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840) - (3*c^3*d^5*m*x^2*(m + 1))/(e^2*(638*m + 179*m^2 + 22*m^3 + m^4 + 840)) + (c^3*d^4*m*x^3*(3*m + m^2 + 2))/(e*(638*m + 179*m^2 + 22*m^3 + m^4 + 840)))","B"
435,1,197,69,0.423712,"\text{Not used}","int((c*d*x + c*e*x^2)^2*(d + e*x)^m,x)","{\left(d+e\,x\right)}^m\,\left(\frac{2\,c^2\,d^5}{e^3\,\left(m^3+12\,m^2+47\,m+60\right)}+\frac{c^2\,e^2\,x^5\,\left(m^2+7\,m+12\right)}{m^3+12\,m^2+47\,m+60}+\frac{c^2\,d^2\,x^3\,\left(3\,m^2+15\,m+20\right)}{m^3+12\,m^2+47\,m+60}-\frac{2\,c^2\,d^4\,m\,x}{e^2\,\left(m^3+12\,m^2+47\,m+60\right)}+\frac{c^2\,d\,e\,x^4\,\left(3\,m^2+19\,m+30\right)}{m^3+12\,m^2+47\,m+60}+\frac{c^2\,d^3\,m\,x^2\,\left(m+1\right)}{e\,\left(m^3+12\,m^2+47\,m+60\right)}\right)","Not used",1,"(d + e*x)^m*((2*c^2*d^5)/(e^3*(47*m + 12*m^2 + m^3 + 60)) + (c^2*e^2*x^5*(7*m + m^2 + 12))/(47*m + 12*m^2 + m^3 + 60) + (c^2*d^2*x^3*(15*m + 3*m^2 + 20))/(47*m + 12*m^2 + m^3 + 60) - (2*c^2*d^4*m*x)/(e^2*(47*m + 12*m^2 + m^3 + 60)) + (c^2*d*e*x^4*(19*m + 3*m^2 + 30))/(47*m + 12*m^2 + m^3 + 60) + (c^2*d^3*m*x^2*(m + 1))/(e*(47*m + 12*m^2 + m^3 + 60)))","B"
436,1,88,41,0.333321,"\text{Not used}","int((c*d*x + c*e*x^2)*(d + e*x)^m,x)","{\left(d+e\,x\right)}^m\,\left(\frac{c\,e\,x^3\,\left(m+2\right)}{m^2+5\,m+6}-\frac{c\,d^3}{e^2\,\left(m^2+5\,m+6\right)}+\frac{c\,d\,x^2\,\left(2\,m+3\right)}{m^2+5\,m+6}+\frac{c\,d^2\,m\,x}{e\,\left(m^2+5\,m+6\right)}\right)","Not used",1,"(d + e*x)^m*((c*e*x^3*(m + 2))/(5*m + m^2 + 6) - (c*d^3)/(e^2*(5*m + m^2 + 6)) + (c*d*x^2*(2*m + 3))/(5*m + m^2 + 6) + (c*d^2*m*x)/(e*(5*m + m^2 + 6)))","B"
437,1,18,18,0.361613,"\text{Not used}","int((d + e*x)^m,x)","\frac{{\left(d+e\,x\right)}^{m+1}}{e\,\left(m+1\right)}","Not used",1,"(d + e*x)^(m + 1)/(e*(m + 1))","B"
438,0,-1,32,0.000000,"\text{Not used}","int((d + e*x)^m/(c*d*x + c*e*x^2),x)","\int \frac{{\left(d+e\,x\right)}^m}{c\,e\,x^2+c\,d\,x} \,d x","Not used",1,"int((d + e*x)^m/(c*d*x + c*e*x^2), x)","F"
439,0,-1,39,0.000000,"\text{Not used}","int((d + e*x)^m/(c*d*x + c*e*x^2)^2,x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(c\,e\,x^2+c\,d\,x\right)}^2} \,d x","Not used",1,"int((d + e*x)^m/(c*d*x + c*e*x^2)^2, x)","F"
440,1,1085,267,1.017502,"\text{Not used}","int((b*x + c*x^2)^3*(d + e*x)^m,x)","\frac{c^3\,x^7\,{\left(d+e\,x\right)}^m\,\left(m^6+21\,m^5+175\,m^4+735\,m^3+1624\,m^2+1764\,m+720\right)}{m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040}-\frac{6\,d^4\,{\left(d+e\,x\right)}^m\,\left(b^3\,e^3\,m^3+18\,b^3\,e^3\,m^2+107\,b^3\,e^3\,m+210\,b^3\,e^3-12\,b^2\,c\,d\,e^2\,m^2-156\,b^2\,c\,d\,e^2\,m-504\,b^2\,c\,d\,e^2+60\,b\,c^2\,d^2\,e\,m+420\,b\,c^2\,d^2\,e-120\,c^3\,d^3\right)}{e^7\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{x^4\,{\left(d+e\,x\right)}^m\,\left(m^3+6\,m^2+11\,m+6\right)\,\left(b^3\,e^3\,m^3+18\,b^3\,e^3\,m^2+107\,b^3\,e^3\,m+210\,b^3\,e^3+3\,b^2\,c\,d\,e^2\,m^3+39\,b^2\,c\,d\,e^2\,m^2+126\,b^2\,c\,d\,e^2\,m-15\,b\,c^2\,d^2\,e\,m^2-105\,b\,c^2\,d^2\,e\,m+30\,c^3\,d^3\,m\right)}{e^3\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{3\,c\,x^5\,{\left(d+e\,x\right)}^m\,\left(m^4+10\,m^3+35\,m^2+50\,m+24\right)\,\left(b^2\,e^2\,m^2+13\,b^2\,e^2\,m+42\,b^2\,e^2+b\,c\,d\,e\,m^2+7\,b\,c\,d\,e\,m-2\,c^2\,d^2\,m\right)}{e^2\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{6\,d^3\,m\,x\,{\left(d+e\,x\right)}^m\,\left(b^3\,e^3\,m^3+18\,b^3\,e^3\,m^2+107\,b^3\,e^3\,m+210\,b^3\,e^3-12\,b^2\,c\,d\,e^2\,m^2-156\,b^2\,c\,d\,e^2\,m-504\,b^2\,c\,d\,e^2+60\,b\,c^2\,d^2\,e\,m+420\,b\,c^2\,d^2\,e-120\,c^3\,d^3\right)}{e^6\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{c^2\,x^6\,{\left(d+e\,x\right)}^m\,\left(21\,b\,e+3\,b\,e\,m+c\,d\,m\right)\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}{e\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{d\,m\,x^3\,{\left(d+e\,x\right)}^m\,\left(m^2+3\,m+2\right)\,\left(b^3\,e^3\,m^3+18\,b^3\,e^3\,m^2+107\,b^3\,e^3\,m+210\,b^3\,e^3-12\,b^2\,c\,d\,e^2\,m^2-156\,b^2\,c\,d\,e^2\,m-504\,b^2\,c\,d\,e^2+60\,b\,c^2\,d^2\,e\,m+420\,b\,c^2\,d^2\,e-120\,c^3\,d^3\right)}{e^4\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}-\frac{3\,d^2\,m\,x^2\,\left(m+1\right)\,{\left(d+e\,x\right)}^m\,\left(b^3\,e^3\,m^3+18\,b^3\,e^3\,m^2+107\,b^3\,e^3\,m+210\,b^3\,e^3-12\,b^2\,c\,d\,e^2\,m^2-156\,b^2\,c\,d\,e^2\,m-504\,b^2\,c\,d\,e^2+60\,b\,c^2\,d^2\,e\,m+420\,b\,c^2\,d^2\,e-120\,c^3\,d^3\right)}{e^5\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}","Not used",1,"(c^3*x^7*(d + e*x)^m*(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720))/(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040) - (6*d^4*(d + e*x)^m*(210*b^3*e^3 - 120*c^3*d^3 + 107*b^3*e^3*m + 18*b^3*e^3*m^2 + b^3*e^3*m^3 + 420*b*c^2*d^2*e - 504*b^2*c*d*e^2 + 60*b*c^2*d^2*e*m - 156*b^2*c*d*e^2*m - 12*b^2*c*d*e^2*m^2))/(e^7*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (x^4*(d + e*x)^m*(11*m + 6*m^2 + m^3 + 6)*(210*b^3*e^3 + 107*b^3*e^3*m + 30*c^3*d^3*m + 18*b^3*e^3*m^2 + b^3*e^3*m^3 - 105*b*c^2*d^2*e*m + 126*b^2*c*d*e^2*m - 15*b*c^2*d^2*e*m^2 + 39*b^2*c*d*e^2*m^2 + 3*b^2*c*d*e^2*m^3))/(e^3*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (3*c*x^5*(d + e*x)^m*(50*m + 35*m^2 + 10*m^3 + m^4 + 24)*(42*b^2*e^2 + 13*b^2*e^2*m - 2*c^2*d^2*m + b^2*e^2*m^2 + 7*b*c*d*e*m + b*c*d*e*m^2))/(e^2*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (6*d^3*m*x*(d + e*x)^m*(210*b^3*e^3 - 120*c^3*d^3 + 107*b^3*e^3*m + 18*b^3*e^3*m^2 + b^3*e^3*m^3 + 420*b*c^2*d^2*e - 504*b^2*c*d*e^2 + 60*b*c^2*d^2*e*m - 156*b^2*c*d*e^2*m - 12*b^2*c*d*e^2*m^2))/(e^6*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (c^2*x^6*(d + e*x)^m*(21*b*e + 3*b*e*m + c*d*m)*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120))/(e*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (d*m*x^3*(d + e*x)^m*(3*m + m^2 + 2)*(210*b^3*e^3 - 120*c^3*d^3 + 107*b^3*e^3*m + 18*b^3*e^3*m^2 + b^3*e^3*m^3 + 420*b*c^2*d^2*e - 504*b^2*c*d*e^2 + 60*b*c^2*d^2*e*m - 156*b^2*c*d*e^2*m - 12*b^2*c*d*e^2*m^2))/(e^4*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) - (3*d^2*m*x^2*(m + 1)*(d + e*x)^m*(210*b^3*e^3 - 120*c^3*d^3 + 107*b^3*e^3*m + 18*b^3*e^3*m^2 + b^3*e^3*m^3 + 420*b*c^2*d^2*e - 504*b^2*c*d*e^2 + 60*b*c^2*d^2*e*m - 156*b^2*c*d*e^2*m - 12*b^2*c*d*e^2*m^2))/(e^5*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040))","B"
441,1,464,159,0.605715,"\text{Not used}","int((b*x + c*x^2)^2*(d + e*x)^m,x)","{\left(d+e\,x\right)}^m\,\left(\frac{c^2\,x^5\,\left(m^4+10\,m^3+35\,m^2+50\,m+24\right)}{m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120}+\frac{2\,d^3\,\left(b^2\,e^2\,m^2+9\,b^2\,e^2\,m+20\,b^2\,e^2-6\,b\,c\,d\,e\,m-30\,b\,c\,d\,e+12\,c^2\,d^2\right)}{e^5\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}+\frac{x^3\,\left(m^2+3\,m+2\right)\,\left(b^2\,e^2\,m^2+9\,b^2\,e^2\,m+20\,b^2\,e^2+2\,b\,c\,d\,e\,m^2+10\,b\,c\,d\,e\,m-4\,c^2\,d^2\,m\right)}{e^2\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}+\frac{c\,x^4\,\left(10\,b\,e+2\,b\,e\,m+c\,d\,m\right)\,\left(m^3+6\,m^2+11\,m+6\right)}{e\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}-\frac{2\,d^2\,m\,x\,\left(b^2\,e^2\,m^2+9\,b^2\,e^2\,m+20\,b^2\,e^2-6\,b\,c\,d\,e\,m-30\,b\,c\,d\,e+12\,c^2\,d^2\right)}{e^4\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}+\frac{d\,m\,x^2\,\left(m+1\right)\,\left(b^2\,e^2\,m^2+9\,b^2\,e^2\,m+20\,b^2\,e^2-6\,b\,c\,d\,e\,m-30\,b\,c\,d\,e+12\,c^2\,d^2\right)}{e^3\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}\right)","Not used",1,"(d + e*x)^m*((c^2*x^5*(50*m + 35*m^2 + 10*m^3 + m^4 + 24))/(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120) + (2*d^3*(20*b^2*e^2 + 12*c^2*d^2 + 9*b^2*e^2*m + b^2*e^2*m^2 - 30*b*c*d*e - 6*b*c*d*e*m))/(e^5*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)) + (x^3*(3*m + m^2 + 2)*(20*b^2*e^2 + 9*b^2*e^2*m - 4*c^2*d^2*m + b^2*e^2*m^2 + 10*b*c*d*e*m + 2*b*c*d*e*m^2))/(e^2*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)) + (c*x^4*(10*b*e + 2*b*e*m + c*d*m)*(11*m + 6*m^2 + m^3 + 6))/(e*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)) - (2*d^2*m*x*(20*b^2*e^2 + 12*c^2*d^2 + 9*b^2*e^2*m + b^2*e^2*m^2 - 30*b*c*d*e - 6*b*c*d*e*m))/(e^4*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)) + (d*m*x^2*(m + 1)*(20*b^2*e^2 + 12*c^2*d^2 + 9*b^2*e^2*m + b^2*e^2*m^2 - 30*b*c*d*e - 6*b*c*d*e*m))/(e^3*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)))","B"
442,1,146,75,0.367151,"\text{Not used}","int((b*x + c*x^2)*(d + e*x)^m,x)","{\left(d+e\,x\right)}^m\,\left(\frac{c\,x^3\,\left(m^2+3\,m+2\right)}{m^3+6\,m^2+11\,m+6}-\frac{d^2\,\left(3\,b\,e-2\,c\,d+b\,e\,m\right)}{e^3\,\left(m^3+6\,m^2+11\,m+6\right)}+\frac{x^2\,\left(m+1\right)\,\left(3\,b\,e+b\,e\,m+c\,d\,m\right)}{e\,\left(m^3+6\,m^2+11\,m+6\right)}+\frac{d\,m\,x\,\left(3\,b\,e-2\,c\,d+b\,e\,m\right)}{e^2\,\left(m^3+6\,m^2+11\,m+6\right)}\right)","Not used",1,"(d + e*x)^m*((c*x^3*(3*m + m^2 + 2))/(11*m + 6*m^2 + m^3 + 6) - (d^2*(3*b*e - 2*c*d + b*e*m))/(e^3*(11*m + 6*m^2 + m^3 + 6)) + (x^2*(m + 1)*(3*b*e + b*e*m + c*d*m))/(e*(11*m + 6*m^2 + m^3 + 6)) + (d*m*x*(3*b*e - 2*c*d + b*e*m))/(e^2*(11*m + 6*m^2 + m^3 + 6)))","B"
443,0,-1,93,0.000000,"\text{Not used}","int((d + e*x)^m/(b*x + c*x^2),x)","\int \frac{{\left(d+e\,x\right)}^m}{c\,x^2+b\,x} \,d x","Not used",1,"int((d + e*x)^m/(b*x + c*x^2), x)","F"
444,0,-1,180,0.000000,"\text{Not used}","int((d + e*x)^m/(b*x + c*x^2)^2,x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(c\,x^2+b\,x\right)}^2} \,d x","Not used",1,"int((d + e*x)^m/(b*x + c*x^2)^2, x)","F"
445,0,-1,350,0.000000,"\text{Not used}","int((d + e*x)^m/(b*x + c*x^2)^3,x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(c\,x^2+b\,x\right)}^3} \,d x","Not used",1,"int((d + e*x)^m/(b*x + c*x^2)^3, x)","F"
446,0,-1,105,0.000000,"\text{Not used}","int((b*x + c*x^2)^(3/2)*(d + e*x)^m,x)","\int {\left(c\,x^2+b\,x\right)}^{3/2}\,{\left(d+e\,x\right)}^m \,d x","Not used",1,"int((b*x + c*x^2)^(3/2)*(d + e*x)^m, x)","F"
447,0,-1,105,0.000000,"\text{Not used}","int((b*x + c*x^2)^(1/2)*(d + e*x)^m,x)","\int \sqrt{c\,x^2+b\,x}\,{\left(d+e\,x\right)}^m \,d x","Not used",1,"int((b*x + c*x^2)^(1/2)*(d + e*x)^m, x)","F"
448,0,-1,105,0.000000,"\text{Not used}","int((d + e*x)^m/(b*x + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^m}{\sqrt{c\,x^2+b\,x}} \,d x","Not used",1,"int((d + e*x)^m/(b*x + c*x^2)^(1/2), x)","F"
449,0,-1,105,0.000000,"\text{Not used}","int((d + e*x)^m/(b*x + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(c\,x^2+b\,x\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^m/(b*x + c*x^2)^(3/2), x)","F"
450,0,-1,103,0.000000,"\text{Not used}","int((b*x + c*x^2)^p*(d + e*x)^m,x)","\int {\left(c\,x^2+b\,x\right)}^p\,{\left(d+e\,x\right)}^m \,d x","Not used",1,"int((b*x + c*x^2)^p*(d + e*x)^m, x)","F"
451,1,93,57,0.274851,"\text{Not used}","int((a + c*x^2)*(d + e*x)^4,x)","x^3\,\left(\frac{c\,d^4}{3}+2\,a\,d^2\,e^2\right)+x^5\,\left(\frac{6\,c\,d^2\,e^2}{5}+\frac{a\,e^4}{5}\right)+x^4\,\left(c\,d^3\,e+a\,d\,e^3\right)+\frac{c\,e^4\,x^7}{7}+a\,d^4\,x+2\,a\,d^3\,e\,x^2+\frac{2\,c\,d\,e^3\,x^6}{3}","Not used",1,"x^3*((c*d^4)/3 + 2*a*d^2*e^2) + x^5*((a*e^4)/5 + (6*c*d^2*e^2)/5) + x^4*(a*d*e^3 + c*d^3*e) + (c*e^4*x^7)/7 + a*d^4*x + 2*a*d^3*e*x^2 + (2*c*d*e^3*x^6)/3","B"
452,1,71,57,0.031712,"\text{Not used}","int((a + c*x^2)*(d + e*x)^3,x)","x^3\,\left(\frac{c\,d^3}{3}+a\,d\,e^2\right)+x^4\,\left(\frac{3\,c\,d^2\,e}{4}+\frac{a\,e^3}{4}\right)+\frac{c\,e^3\,x^6}{6}+a\,d^3\,x+\frac{3\,a\,d^2\,e\,x^2}{2}+\frac{3\,c\,d\,e^2\,x^5}{5}","Not used",1,"x^3*((c*d^3)/3 + a*d*e^2) + x^4*((a*e^3)/4 + (3*c*d^2*e)/4) + (c*e^3*x^6)/6 + a*d^3*x + (3*a*d^2*e*x^2)/2 + (3*c*d*e^2*x^5)/5","B"
453,1,48,57,0.024868,"\text{Not used}","int((a + c*x^2)*(d + e*x)^2,x)","x^3\,\left(\frac{c\,d^2}{3}+\frac{a\,e^2}{3}\right)+\frac{c\,e^2\,x^5}{5}+a\,d^2\,x+a\,d\,e\,x^2+\frac{c\,d\,e\,x^4}{2}","Not used",1,"x^3*((a*e^2)/3 + (c*d^2)/3) + (c*e^2*x^5)/5 + a*d^2*x + a*d*e*x^2 + (c*d*e*x^4)/2","B"
454,1,26,31,0.044346,"\text{Not used}","int((a + c*x^2)*(d + e*x),x)","\frac{c\,e\,x^4}{4}+\frac{c\,d\,x^3}{3}+\frac{a\,e\,x^2}{2}+a\,d\,x","Not used",1,"a*d*x + (a*e*x^2)/2 + (c*d*x^3)/3 + (c*e*x^4)/4","B"
455,1,39,41,0.054669,"\text{Not used}","int((a + c*x^2)/(d + e*x),x)","\frac{c\,x^2}{2\,e}+\frac{\ln\left(d+e\,x\right)\,\left(c\,d^2+a\,e^2\right)}{e^3}-\frac{c\,d\,x}{e^2}","Not used",1,"(c*x^2)/(2*e) + (log(d + e*x)*(a*e^2 + c*d^2))/e^3 - (c*d*x)/e^2","B"
456,1,49,43,0.063337,"\text{Not used}","int((a + c*x^2)/(d + e*x)^2,x)","\frac{c\,x}{e^2}-\frac{c\,d^2+a\,e^2}{e\,\left(x\,e^3+d\,e^2\right)}-\frac{2\,c\,d\,\ln\left(d+e\,x\right)}{e^3}","Not used",1,"(c*x)/e^2 - (a*e^2 + c*d^2)/(e*(d*e^2 + e^3*x)) - (2*c*d*log(d + e*x))/e^3","B"
457,1,58,53,0.283685,"\text{Not used}","int((a + c*x^2)/(d + e*x)^3,x)","\frac{c\,\ln\left(d+e\,x\right)}{e^3}-\frac{\frac{a\,e^2-3\,c\,d^2}{2\,e^3}-\frac{2\,c\,d\,x}{e^2}}{d^2+2\,d\,e\,x+e^2\,x^2}","Not used",1,"(c*log(d + e*x))/e^3 - ((a*e^2 - 3*c*d^2)/(2*e^3) - (2*c*d*x)/e^2)/(d^2 + e^2*x^2 + 2*d*e*x)","B"
458,1,63,54,0.039744,"\text{Not used}","int((a + c*x^2)/(d + e*x)^4,x)","-\frac{\frac{c\,d^2+a\,e^2}{3\,e^3}+\frac{c\,x^2}{e}+\frac{c\,d\,x}{e^2}}{d^3+3\,d^2\,e\,x+3\,d\,e^2\,x^2+e^3\,x^3}","Not used",1,"-((a*e^2 + c*d^2)/(3*e^3) + (c*x^2)/e + (c*d*x)/e^2)/(d^3 + e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x)","B"
459,1,77,59,0.049571,"\text{Not used}","int((a + c*x^2)/(d + e*x)^5,x)","-\frac{\frac{c\,d^2+3\,a\,e^2}{12\,e^3}+\frac{c\,x^2}{2\,e}+\frac{c\,d\,x}{3\,e^2}}{d^4+4\,d^3\,e\,x+6\,d^2\,e^2\,x^2+4\,d\,e^3\,x^3+e^4\,x^4}","Not used",1,"-((3*a*e^2 + c*d^2)/(12*e^3) + (c*x^2)/(2*e) + (c*d*x)/(3*e^2))/(d^4 + e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x)","B"
460,1,160,117,0.069401,"\text{Not used}","int((a + c*x^2)^2*(d + e*x)^4,x)","x^5\,\left(\frac{a^2\,e^4}{5}+\frac{12\,a\,c\,d^2\,e^2}{5}+\frac{c^2\,d^4}{5}\right)+x^3\,\left(2\,a^2\,d^2\,e^2+\frac{2\,c\,a\,d^4}{3}\right)+x^7\,\left(\frac{6\,c^2\,d^2\,e^2}{7}+\frac{2\,a\,c\,e^4}{7}\right)+a^2\,d^4\,x+\frac{c^2\,e^4\,x^9}{9}+2\,a^2\,d^3\,e\,x^2+\frac{c^2\,d\,e^3\,x^8}{2}+a\,d\,e\,x^4\,\left(2\,c\,d^2+a\,e^2\right)+\frac{2\,c\,d\,e\,x^6\,\left(c\,d^2+2\,a\,e^2\right)}{3}","Not used",1,"x^5*((a^2*e^4)/5 + (c^2*d^4)/5 + (12*a*c*d^2*e^2)/5) + x^3*(2*a^2*d^2*e^2 + (2*a*c*d^4)/3) + x^7*((6*c^2*d^2*e^2)/7 + (2*a*c*e^4)/7) + a^2*d^4*x + (c^2*e^4*x^9)/9 + 2*a^2*d^3*e*x^2 + (c^2*d*e^3*x^8)/2 + a*d*e*x^4*(a*e^2 + 2*c*d^2) + (2*c*d*e*x^6*(2*a*e^2 + c*d^2))/3","B"
461,1,127,117,0.054728,"\text{Not used}","int((a + c*x^2)^2*(d + e*x)^3,x)","x^3\,\left(a^2\,d\,e^2+\frac{2\,c\,a\,d^3}{3}\right)+x^4\,\left(\frac{a^2\,e^3}{4}+\frac{3\,c\,a\,d^2\,e}{2}\right)+x^5\,\left(\frac{c^2\,d^3}{5}+\frac{6\,a\,c\,d\,e^2}{5}\right)+x^6\,\left(\frac{c^2\,d^2\,e}{2}+\frac{a\,c\,e^3}{3}\right)+a^2\,d^3\,x+\frac{c^2\,e^3\,x^8}{8}+\frac{3\,a^2\,d^2\,e\,x^2}{2}+\frac{3\,c^2\,d\,e^2\,x^7}{7}","Not used",1,"x^3*(a^2*d*e^2 + (2*a*c*d^3)/3) + x^4*((a^2*e^3)/4 + (3*a*c*d^2*e)/2) + x^5*((c^2*d^3)/5 + (6*a*c*d*e^2)/5) + x^6*((c^2*d^2*e)/2 + (a*c*e^3)/3) + a^2*d^3*x + (c^2*e^3*x^8)/8 + (3*a^2*d^2*e*x^2)/2 + (3*c^2*d*e^2*x^7)/7","B"
462,1,87,80,0.272762,"\text{Not used}","int((a + c*x^2)^2*(d + e*x)^2,x)","x^3\,\left(\frac{a^2\,e^2}{3}+\frac{2\,c\,a\,d^2}{3}\right)+x^5\,\left(\frac{c^2\,d^2}{5}+\frac{2\,a\,c\,e^2}{5}\right)+a^2\,d^2\,x+\frac{c^2\,e^2\,x^7}{7}+a^2\,d\,e\,x^2+\frac{c^2\,d\,e\,x^6}{3}+a\,c\,d\,e\,x^4","Not used",1,"x^3*((a^2*e^2)/3 + (2*a*c*d^2)/3) + x^5*((c^2*d^2)/5 + (2*a*c*e^2)/5) + a^2*d^2*x + (c^2*e^2*x^7)/7 + a^2*d*e*x^2 + (c^2*d*e*x^6)/3 + a*c*d*e*x^4","B"
463,1,50,45,0.024451,"\text{Not used}","int((a + c*x^2)^2*(d + e*x),x)","\frac{e\,a^2\,x^2}{2}+d\,a^2\,x+\frac{e\,a\,c\,x^4}{2}+\frac{2\,d\,a\,c\,x^3}{3}+\frac{e\,c^2\,x^6}{6}+\frac{d\,c^2\,x^5}{5}","Not used",1,"(a^2*e*x^2)/2 + (c^2*d*x^5)/5 + (c^2*e*x^6)/6 + a^2*d*x + (2*a*c*d*x^3)/3 + (a*c*e*x^4)/2","B"
464,1,106,94,0.043406,"\text{Not used}","int((a + c*x^2)^2/(d + e*x),x)","x^2\,\left(\frac{c^2\,d^2}{2\,e^3}+\frac{a\,c}{e}\right)+\frac{\ln\left(d+e\,x\right)\,\left(a^2\,e^4+2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{e^5}+\frac{c^2\,x^4}{4\,e}-\frac{c^2\,d\,x^3}{3\,e^2}-\frac{d\,x\,\left(\frac{c^2\,d^2}{e^3}+\frac{2\,a\,c}{e}\right)}{e}","Not used",1,"x^2*((c^2*d^2)/(2*e^3) + (a*c)/e) + (log(d + e*x)*(a^2*e^4 + c^2*d^4 + 2*a*c*d^2*e^2))/e^5 + (c^2*x^4)/(4*e) - (c^2*d*x^3)/(3*e^2) - (d*x*((c^2*d^2)/e^3 + (2*a*c)/e))/e","B"
465,1,116,94,0.055538,"\text{Not used}","int((a + c*x^2)^2/(d + e*x)^2,x)","x\,\left(\frac{3\,c^2\,d^2}{e^4}+\frac{2\,a\,c}{e^2}\right)-\frac{\ln\left(d+e\,x\right)\,\left(4\,c^2\,d^3+4\,a\,c\,d\,e^2\right)}{e^5}+\frac{c^2\,x^3}{3\,e^2}-\frac{a^2\,e^4+2\,a\,c\,d^2\,e^2+c^2\,d^4}{e\,\left(x\,e^5+d\,e^4\right)}-\frac{c^2\,d\,x^2}{e^3}","Not used",1,"x*((3*c^2*d^2)/e^4 + (2*a*c)/e^2) - (log(d + e*x)*(4*c^2*d^3 + 4*a*c*d*e^2))/e^5 + (c^2*x^3)/(3*e^2) - (a^2*e^4 + c^2*d^4 + 2*a*c*d^2*e^2)/(e*(d*e^4 + e^5*x)) - (c^2*d*x^2)/e^3","B"
466,1,125,100,0.065360,"\text{Not used}","int((a + c*x^2)^2/(d + e*x)^3,x)","\frac{x\,\left(4\,c^2\,d^3+4\,a\,c\,d\,e^2\right)+\frac{-a^2\,e^4+6\,a\,c\,d^2\,e^2+7\,c^2\,d^4}{2\,e}}{d^2\,e^4+2\,d\,e^5\,x+e^6\,x^2}+\frac{\ln\left(d+e\,x\right)\,\left(6\,c^2\,d^2+2\,a\,c\,e^2\right)}{e^5}+\frac{c^2\,x^2}{2\,e^3}-\frac{3\,c^2\,d\,x}{e^4}","Not used",1,"(x*(4*c^2*d^3 + 4*a*c*d*e^2) + (7*c^2*d^4 - a^2*e^4 + 6*a*c*d^2*e^2)/(2*e))/(d^2*e^4 + e^6*x^2 + 2*d*e^5*x) + (log(d + e*x)*(6*c^2*d^2 + 2*a*c*e^2))/e^5 + (c^2*x^2)/(2*e^3) - (3*c^2*d*x)/e^4","B"
467,1,133,101,0.309839,"\text{Not used}","int((a + c*x^2)^2/(d + e*x)^4,x)","\frac{c^2\,x}{e^4}-\frac{x\,\left(10\,c^2\,d^3+2\,a\,c\,d\,e^2\right)+x^2\,\left(6\,c^2\,d^2\,e+2\,a\,c\,e^3\right)+\frac{a^2\,e^4+2\,a\,c\,d^2\,e^2+13\,c^2\,d^4}{3\,e}}{d^3\,e^4+3\,d^2\,e^5\,x+3\,d\,e^6\,x^2+e^7\,x^3}-\frac{4\,c^2\,d\,\ln\left(d+e\,x\right)}{e^5}","Not used",1,"(c^2*x)/e^4 - (x*(10*c^2*d^3 + 2*a*c*d*e^2) + x^2*(6*c^2*d^2*e + 2*a*c*e^3) + (a^2*e^4 + 13*c^2*d^4 + 2*a*c*d^2*e^2)/(3*e))/(d^3*e^4 + e^7*x^3 + 3*d^2*e^5*x + 3*d*e^6*x^2) - (4*c^2*d*log(d + e*x))/e^5","B"
468,1,144,109,0.318029,"\text{Not used}","int((a + c*x^2)^2/(d + e*x)^5,x)","\frac{c^2\,\ln\left(d+e\,x\right)}{e^5}-\frac{\frac{3\,a^2\,e^4+2\,a\,c\,d^2\,e^2-25\,c^2\,d^4}{12\,e^5}-\frac{2\,x\,\left(11\,c^2\,d^3-a\,c\,d\,e^2\right)}{3\,e^4}-\frac{4\,c^2\,d\,x^3}{e^2}+\frac{c\,x^2\,\left(a\,e^2-9\,c\,d^2\right)}{e^3}}{d^4+4\,d^3\,e\,x+6\,d^2\,e^2\,x^2+4\,d\,e^3\,x^3+e^4\,x^4}","Not used",1,"(c^2*log(d + e*x))/e^5 - ((3*a^2*e^4 - 25*c^2*d^4 + 2*a*c*d^2*e^2)/(12*e^5) - (2*x*(11*c^2*d^3 - a*c*d*e^2))/(3*e^4) - (4*c^2*d*x^3)/e^2 + (c*x^2*(a*e^2 - 9*c*d^2))/e^3)/(d^4 + e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x)","B"
469,1,148,110,0.073688,"\text{Not used}","int((a + c*x^2)^2/(d + e*x)^6,x)","-\frac{\frac{3\,a^2\,e^4+a\,c\,d^2\,e^2+3\,c^2\,d^4}{15\,e^5}+\frac{c^2\,x^4}{e}+\frac{2\,c^2\,d\,x^3}{e^2}+\frac{2\,c\,x^2\,\left(3\,c\,d^2+a\,e^2\right)}{3\,e^3}+\frac{c\,d\,x\,\left(3\,c\,d^2+a\,e^2\right)}{3\,e^4}}{d^5+5\,d^4\,e\,x+10\,d^3\,e^2\,x^2+10\,d^2\,e^3\,x^3+5\,d\,e^4\,x^4+e^5\,x^5}","Not used",1,"-((3*a^2*e^4 + 3*c^2*d^4 + a*c*d^2*e^2)/(15*e^5) + (c^2*x^4)/e + (2*c^2*d*x^3)/e^2 + (2*c*x^2*(a*e^2 + 3*c*d^2))/(3*e^3) + (c*d*x*(a*e^2 + 3*c*d^2))/(3*e^4))/(d^5 + e^5*x^5 + 5*d*e^4*x^4 + 10*d^3*e^2*x^2 + 10*d^2*e^3*x^3 + 5*d^4*e*x)","B"
470,1,157,117,0.310540,"\text{Not used}","int((a + c*x^2)^2/(d + e*x)^7,x)","-\frac{\frac{5\,a^2\,e^4+a\,c\,d^2\,e^2+c^2\,d^4}{30\,e^5}+\frac{c^2\,x^4}{2\,e}+\frac{2\,c^2\,d\,x^3}{3\,e^2}+\frac{c\,x^2\,\left(c\,d^2+a\,e^2\right)}{2\,e^3}+\frac{c\,d\,x\,\left(c\,d^2+a\,e^2\right)}{5\,e^4}}{d^6+6\,d^5\,e\,x+15\,d^4\,e^2\,x^2+20\,d^3\,e^3\,x^3+15\,d^2\,e^4\,x^4+6\,d\,e^5\,x^5+e^6\,x^6}","Not used",1,"-((5*a^2*e^4 + c^2*d^4 + a*c*d^2*e^2)/(30*e^5) + (c^2*x^4)/(2*e) + (2*c^2*d*x^3)/(3*e^2) + (c*x^2*(a*e^2 + c*d^2))/(2*e^3) + (c*d*x*(a*e^2 + c*d^2))/(5*e^4))/(d^6 + e^6*x^6 + 6*d*e^5*x^5 + 15*d^4*e^2*x^2 + 20*d^3*e^3*x^3 + 15*d^2*e^4*x^4 + 6*d^5*e*x)","B"
471,1,171,114,0.073197,"\text{Not used}","int((a + c*x^2)^2/(d + e*x)^8,x)","-\frac{\frac{15\,a^2\,e^4+2\,a\,c\,d^2\,e^2+c^2\,d^4}{105\,e^5}+\frac{c^2\,x^4}{3\,e}+\frac{c^2\,d\,x^3}{3\,e^2}+\frac{c\,x^2\,\left(c\,d^2+2\,a\,e^2\right)}{5\,e^3}+\frac{c\,d\,x\,\left(c\,d^2+2\,a\,e^2\right)}{15\,e^4}}{d^7+7\,d^6\,e\,x+21\,d^5\,e^2\,x^2+35\,d^4\,e^3\,x^3+35\,d^3\,e^4\,x^4+21\,d^2\,e^5\,x^5+7\,d\,e^6\,x^6+e^7\,x^7}","Not used",1,"-((15*a^2*e^4 + c^2*d^4 + 2*a*c*d^2*e^2)/(105*e^5) + (c^2*x^4)/(3*e) + (c^2*d*x^3)/(3*e^2) + (c*x^2*(2*a*e^2 + c*d^2))/(5*e^3) + (c*d*x*(2*a*e^2 + c*d^2))/(15*e^4))/(d^7 + e^7*x^7 + 7*d*e^6*x^6 + 21*d^5*e^2*x^2 + 35*d^4*e^3*x^3 + 35*d^3*e^4*x^4 + 21*d^2*e^5*x^5 + 7*d^6*e*x)","B"
472,1,329,190,0.154633,"\text{Not used}","int((a + c*x^2)^3*(d + e*x)^6,x)","x^7\,\left(\frac{a^3\,e^6}{7}+\frac{45\,a^2\,c\,d^2\,e^4}{7}+\frac{45\,a\,c^2\,d^4\,e^2}{7}+\frac{c^3\,d^6}{7}\right)+x^3\,\left(5\,a^3\,d^4\,e^2+c\,a^2\,d^6\right)+x^{11}\,\left(\frac{15\,c^3\,d^2\,e^4}{11}+\frac{3\,a\,c^2\,e^6}{11}\right)+x^5\,\left(3\,a^3\,d^2\,e^4+9\,a^2\,c\,d^4\,e^2+\frac{3\,a\,c^2\,d^6}{5}\right)+x^9\,\left(\frac{a^2\,c\,e^6}{3}+5\,a\,c^2\,d^2\,e^4+\frac{5\,c^3\,d^4\,e^2}{3}\right)+a^3\,d^6\,x+\frac{c^3\,e^6\,x^{13}}{13}+3\,a^3\,d^5\,e\,x^2+\frac{c^3\,d\,e^5\,x^{12}}{2}+a\,d\,e\,x^6\,\left(a^2\,e^4+10\,a\,c\,d^2\,e^2+3\,c^2\,d^4\right)+\frac{3\,c\,d\,e\,x^8\,\left(3\,a^2\,e^4+10\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{4}+\frac{a^2\,d^3\,e\,x^4\,\left(9\,c\,d^2+10\,a\,e^2\right)}{2}+\frac{c^2\,d\,e^3\,x^{10}\,\left(10\,c\,d^2+9\,a\,e^2\right)}{5}","Not used",1,"x^7*((a^3*e^6)/7 + (c^3*d^6)/7 + (45*a*c^2*d^4*e^2)/7 + (45*a^2*c*d^2*e^4)/7) + x^3*(a^2*c*d^6 + 5*a^3*d^4*e^2) + x^11*((3*a*c^2*e^6)/11 + (15*c^3*d^2*e^4)/11) + x^5*((3*a*c^2*d^6)/5 + 3*a^3*d^2*e^4 + 9*a^2*c*d^4*e^2) + x^9*((a^2*c*e^6)/3 + (5*c^3*d^4*e^2)/3 + 5*a*c^2*d^2*e^4) + a^3*d^6*x + (c^3*e^6*x^13)/13 + 3*a^3*d^5*e*x^2 + (c^3*d*e^5*x^12)/2 + a*d*e*x^6*(a^2*e^4 + 3*c^2*d^4 + 10*a*c*d^2*e^2) + (3*c*d*e*x^8*(3*a^2*e^4 + c^2*d^4 + 10*a*c*d^2*e^2))/4 + (a^2*d^3*e*x^4*(10*a*e^2 + 9*c*d^2))/2 + (c^2*d*e^3*x^10*(9*a*e^2 + 10*c*d^2))/5","B"
473,1,281,190,0.362532,"\text{Not used}","int((a + c*x^2)^3*(d + e*x)^5,x)","x^5\,\left(a^3\,d\,e^4+6\,a^2\,c\,d^3\,e^2+\frac{3\,a\,c^2\,d^5}{5}\right)+x^6\,\left(\frac{a^3\,e^5}{6}+5\,a^2\,c\,d^2\,e^3+\frac{5\,a\,c^2\,d^4\,e}{2}\right)+x^7\,\left(\frac{15\,a^2\,c\,d\,e^4}{7}+\frac{30\,a\,c^2\,d^3\,e^2}{7}+\frac{c^3\,d^5}{7}\right)+x^8\,\left(\frac{3\,a^2\,c\,e^5}{8}+\frac{15\,a\,c^2\,d^2\,e^3}{4}+\frac{5\,c^3\,d^4\,e}{8}\right)+x^3\,\left(\frac{10\,a^3\,d^3\,e^2}{3}+c\,a^2\,d^5\right)+x^{10}\,\left(c^3\,d^2\,e^3+\frac{3\,a\,c^2\,e^5}{10}\right)+a^3\,d^5\,x+\frac{c^3\,e^5\,x^{12}}{12}+\frac{5\,a^3\,d^4\,e\,x^2}{2}+\frac{5\,c^3\,d\,e^4\,x^{11}}{11}+\frac{5\,a^2\,d^2\,e\,x^4\,\left(3\,c\,d^2+2\,a\,e^2\right)}{4}+\frac{5\,c^2\,d\,e^2\,x^9\,\left(2\,c\,d^2+3\,a\,e^2\right)}{9}","Not used",1,"x^5*((3*a*c^2*d^5)/5 + a^3*d*e^4 + 6*a^2*c*d^3*e^2) + x^6*((a^3*e^5)/6 + 5*a^2*c*d^2*e^3 + (5*a*c^2*d^4*e)/2) + x^7*((c^3*d^5)/7 + (30*a*c^2*d^3*e^2)/7 + (15*a^2*c*d*e^4)/7) + x^8*((3*a^2*c*e^5)/8 + (5*c^3*d^4*e)/8 + (15*a*c^2*d^2*e^3)/4) + x^3*(a^2*c*d^5 + (10*a^3*d^3*e^2)/3) + x^10*((3*a*c^2*e^5)/10 + c^3*d^2*e^3) + a^3*d^5*x + (c^3*e^5*x^12)/12 + (5*a^3*d^4*e*x^2)/2 + (5*c^3*d*e^4*x^11)/11 + (5*a^2*d^2*e*x^4*(2*a*e^2 + 3*c*d^2))/4 + (5*c^2*d*e^2*x^9*(3*a*e^2 + 2*c*d^2))/9","B"
474,1,224,188,0.322763,"\text{Not used}","int((a + c*x^2)^3*(d + e*x)^4,x)","x^3\,\left(2\,a^3\,d^2\,e^2+c\,a^2\,d^4\right)+x^9\,\left(\frac{2\,c^3\,d^2\,e^2}{3}+\frac{a\,c^2\,e^4}{3}\right)+x^5\,\left(\frac{a^3\,e^4}{5}+\frac{18\,a^2\,c\,d^2\,e^2}{5}+\frac{3\,a\,c^2\,d^4}{5}\right)+x^7\,\left(\frac{3\,a^2\,c\,e^4}{7}+\frac{18\,a\,c^2\,d^2\,e^2}{7}+\frac{c^3\,d^4}{7}\right)+a^3\,d^4\,x+\frac{c^3\,e^4\,x^{11}}{11}+2\,a^3\,d^3\,e\,x^2+\frac{2\,c^3\,d\,e^3\,x^{10}}{5}+a^2\,d\,e\,x^4\,\left(3\,c\,d^2+a\,e^2\right)+\frac{c^2\,d\,e\,x^8\,\left(c\,d^2+3\,a\,e^2\right)}{2}+2\,a\,c\,d\,e\,x^6\,\left(c\,d^2+a\,e^2\right)","Not used",1,"x^3*(a^2*c*d^4 + 2*a^3*d^2*e^2) + x^9*((a*c^2*e^4)/3 + (2*c^3*d^2*e^2)/3) + x^5*((a^3*e^4)/5 + (3*a*c^2*d^4)/5 + (18*a^2*c*d^2*e^2)/5) + x^7*((c^3*d^4)/7 + (3*a^2*c*e^4)/7 + (18*a*c^2*d^2*e^2)/7) + a^3*d^4*x + (c^3*e^4*x^11)/11 + 2*a^3*d^3*e*x^2 + (2*c^3*d*e^3*x^10)/5 + a^2*d*e*x^4*(a*e^2 + 3*c*d^2) + (c^2*d*e*x^8*(3*a*e^2 + c*d^2))/2 + 2*a*c*d*e*x^6*(a*e^2 + c*d^2)","B"
475,1,174,161,0.072885,"\text{Not used}","int((a + c*x^2)^3*(d + e*x)^3,x)","x^3\,\left(a^3\,d\,e^2+c\,a^2\,d^3\right)+x^4\,\left(\frac{a^3\,e^3}{4}+\frac{9\,c\,a^2\,d^2\,e}{4}\right)+x^7\,\left(\frac{c^3\,d^3}{7}+\frac{9\,a\,c^2\,d\,e^2}{7}\right)+x^8\,\left(\frac{3\,c^3\,d^2\,e}{8}+\frac{3\,a\,c^2\,e^3}{8}\right)+a^3\,d^3\,x+\frac{c^3\,e^3\,x^{10}}{10}+\frac{3\,a^3\,d^2\,e\,x^2}{2}+\frac{c^3\,d\,e^2\,x^9}{3}+\frac{3\,a\,c\,d\,x^5\,\left(c\,d^2+3\,a\,e^2\right)}{5}+\frac{a\,c\,e\,x^6\,\left(3\,c\,d^2+a\,e^2\right)}{2}","Not used",1,"x^3*(a^2*c*d^3 + a^3*d*e^2) + x^4*((a^3*e^3)/4 + (9*a^2*c*d^2*e)/4) + x^7*((c^3*d^3)/7 + (9*a*c^2*d*e^2)/7) + x^8*((3*a*c^2*e^3)/8 + (3*c^3*d^2*e)/8) + a^3*d^3*x + (c^3*e^3*x^10)/10 + (3*a^3*d^2*e*x^2)/2 + (c^3*d*e^2*x^9)/3 + (3*a*c*d*x^5*(3*a*e^2 + c*d^2))/5 + (a*c*e*x^6*(a*e^2 + 3*c*d^2))/2","B"
476,1,121,104,0.053472,"\text{Not used}","int((a + c*x^2)^3*(d + e*x)^2,x)","x^3\,\left(\frac{a^3\,e^2}{3}+c\,a^2\,d^2\right)+x^7\,\left(\frac{c^3\,d^2}{7}+\frac{3\,a\,c^2\,e^2}{7}\right)+a^3\,d^2\,x+\frac{c^3\,e^2\,x^9}{9}+\frac{3\,a\,c\,x^5\,\left(c\,d^2+a\,e^2\right)}{5}+a^3\,d\,e\,x^2+\frac{c^3\,d\,e\,x^8}{4}+\frac{3\,a^2\,c\,d\,e\,x^4}{2}+a\,c^2\,d\,e\,x^6","Not used",1,"x^3*((a^3*e^2)/3 + a^2*c*d^2) + x^7*((c^3*d^2)/7 + (3*a*c^2*e^2)/7) + a^3*d^2*x + (c^3*e^2*x^9)/9 + (3*a*c*x^5*(a*e^2 + c*d^2))/5 + a^3*d*e*x^2 + (c^3*d*e*x^8)/4 + (3*a^2*c*d*e*x^4)/2 + a*c^2*d*e*x^6","B"
477,1,73,56,0.035056,"\text{Not used}","int((a + c*x^2)^3*(d + e*x),x)","\frac{e\,a^3\,x^2}{2}+d\,a^3\,x+\frac{3\,e\,a^2\,c\,x^4}{4}+d\,a^2\,c\,x^3+\frac{e\,a\,c^2\,x^6}{2}+\frac{3\,d\,a\,c^2\,x^5}{5}+\frac{e\,c^3\,x^8}{8}+\frac{d\,c^3\,x^7}{7}","Not used",1,"(a^3*e*x^2)/2 + (c^3*d*x^7)/7 + (c^3*e*x^8)/8 + a^3*d*x + a^2*c*d*x^3 + (3*a*c^2*d*x^5)/5 + (3*a^2*c*e*x^4)/4 + (a*c^2*e*x^6)/2","B"
478,1,213,173,0.286314,"\text{Not used}","int((a + c*x^2)^3/(d + e*x),x)","x^2\,\left(\frac{d^2\,\left(\frac{3\,a\,c^2}{e}+\frac{c^3\,d^2}{e^3}\right)}{2\,e^2}+\frac{3\,a^2\,c}{2\,e}\right)+x^4\,\left(\frac{3\,a\,c^2}{4\,e}+\frac{c^3\,d^2}{4\,e^3}\right)+\frac{c^3\,x^6}{6\,e}+\frac{\ln\left(d+e\,x\right)\,\left(a^3\,e^6+3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6\right)}{e^7}-\frac{c^3\,d\,x^5}{5\,e^2}-\frac{d\,x^3\,\left(\frac{3\,a\,c^2}{e}+\frac{c^3\,d^2}{e^3}\right)}{3\,e}-\frac{d\,x\,\left(\frac{d^2\,\left(\frac{3\,a\,c^2}{e}+\frac{c^3\,d^2}{e^3}\right)}{e^2}+\frac{3\,a^2\,c}{e}\right)}{e}","Not used",1,"x^2*((d^2*((3*a*c^2)/e + (c^3*d^2)/e^3))/(2*e^2) + (3*a^2*c)/(2*e)) + x^4*((3*a*c^2)/(4*e) + (c^3*d^2)/(4*e^3)) + (c^3*x^6)/(6*e) + (log(d + e*x)*(a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4))/e^7 - (c^3*d*x^5)/(5*e^2) - (d*x^3*((3*a*c^2)/e + (c^3*d^2)/e^3))/(3*e) - (d*x*((d^2*((3*a*c^2)/e + (c^3*d^2)/e^3))/e^2 + (3*a^2*c)/e))/e","B"
479,1,274,158,0.306253,"\text{Not used}","int((a + c*x^2)^3/(d + e*x)^2,x)","x^2\,\left(\frac{c^3\,d^3}{e^5}-\frac{d\,\left(\frac{3\,a\,c^2}{e^2}+\frac{3\,c^3\,d^2}{e^4}\right)}{e}\right)-x\,\left(\frac{d^2\,\left(\frac{3\,a\,c^2}{e^2}+\frac{3\,c^3\,d^2}{e^4}\right)}{e^2}-\frac{3\,a^2\,c}{e^2}+\frac{2\,d\,\left(\frac{2\,c^3\,d^3}{e^5}-\frac{2\,d\,\left(\frac{3\,a\,c^2}{e^2}+\frac{3\,c^3\,d^2}{e^4}\right)}{e}\right)}{e}\right)+x^3\,\left(\frac{a\,c^2}{e^2}+\frac{c^3\,d^2}{e^4}\right)-\frac{a^3\,e^6+3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6}{e\,\left(x\,e^7+d\,e^6\right)}-\frac{\ln\left(d+e\,x\right)\,\left(6\,a^2\,c\,d\,e^4+12\,a\,c^2\,d^3\,e^2+6\,c^3\,d^5\right)}{e^7}+\frac{c^3\,x^5}{5\,e^2}-\frac{c^3\,d\,x^4}{2\,e^3}","Not used",1,"x^2*((c^3*d^3)/e^5 - (d*((3*a*c^2)/e^2 + (3*c^3*d^2)/e^4))/e) - x*((d^2*((3*a*c^2)/e^2 + (3*c^3*d^2)/e^4))/e^2 - (3*a^2*c)/e^2 + (2*d*((2*c^3*d^3)/e^5 - (2*d*((3*a*c^2)/e^2 + (3*c^3*d^2)/e^4))/e))/e) + x^3*((a*c^2)/e^2 + (c^3*d^2)/e^4) - (a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)/(e*(d*e^6 + e^7*x)) - (log(d + e*x)*(6*c^3*d^5 + 12*a*c^2*d^3*e^2 + 6*a^2*c*d*e^4))/e^7 + (c^3*x^5)/(5*e^2) - (c^3*d*x^4)/(2*e^3)","B"
480,1,235,163,0.082909,"\text{Not used}","int((a + c*x^2)^3/(d + e*x)^3,x)","x^2\,\left(\frac{3\,a\,c^2}{2\,e^3}+\frac{3\,c^3\,d^2}{e^5}\right)+\frac{\frac{-a^3\,e^6+9\,a^2\,c\,d^2\,e^4+21\,a\,c^2\,d^4\,e^2+11\,c^3\,d^6}{2\,e}+x\,\left(6\,a^2\,c\,d\,e^4+12\,a\,c^2\,d^3\,e^2+6\,c^3\,d^5\right)}{d^2\,e^6+2\,d\,e^7\,x+e^8\,x^2}+x\,\left(\frac{8\,c^3\,d^3}{e^6}-\frac{3\,d\,\left(\frac{3\,a\,c^2}{e^3}+\frac{6\,c^3\,d^2}{e^5}\right)}{e}\right)+\frac{\ln\left(d+e\,x\right)\,\left(3\,a^2\,c\,e^4+18\,a\,c^2\,d^2\,e^2+15\,c^3\,d^4\right)}{e^7}+\frac{c^3\,x^4}{4\,e^3}-\frac{c^3\,d\,x^3}{e^4}","Not used",1,"x^2*((3*a*c^2)/(2*e^3) + (3*c^3*d^2)/e^5) + ((11*c^3*d^6 - a^3*e^6 + 21*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4)/(2*e) + x*(6*c^3*d^5 + 12*a*c^2*d^3*e^2 + 6*a^2*c*d*e^4))/(d^2*e^6 + e^8*x^2 + 2*d*e^7*x) + x*((8*c^3*d^3)/e^6 - (3*d*((3*a*c^2)/e^3 + (6*c^3*d^2)/e^5))/e) + (log(d + e*x)*(15*c^3*d^4 + 3*a^2*c*e^4 + 18*a*c^2*d^2*e^2))/e^7 + (c^3*x^4)/(4*e^3) - (c^3*d*x^3)/e^4","B"
481,1,228,165,0.320894,"\text{Not used}","int((a + c*x^2)^3/(d + e*x)^4,x)","x\,\left(\frac{3\,a\,c^2}{e^4}+\frac{10\,c^3\,d^2}{e^6}\right)-\frac{x^2\,\left(3\,a^2\,c\,e^5+18\,a\,c^2\,d^2\,e^3+15\,c^3\,d^4\,e\right)+\frac{a^3\,e^6+3\,a^2\,c\,d^2\,e^4+39\,a\,c^2\,d^4\,e^2+37\,c^3\,d^6}{3\,e}+x\,\left(3\,a^2\,c\,d\,e^4+30\,a\,c^2\,d^3\,e^2+27\,c^3\,d^5\right)}{d^3\,e^6+3\,d^2\,e^7\,x+3\,d\,e^8\,x^2+e^9\,x^3}-\frac{\ln\left(d+e\,x\right)\,\left(20\,c^3\,d^3+12\,a\,c^2\,d\,e^2\right)}{e^7}+\frac{c^3\,x^3}{3\,e^4}-\frac{2\,c^3\,d\,x^2}{e^5}","Not used",1,"x*((3*a*c^2)/e^4 + (10*c^3*d^2)/e^6) - (x^2*(3*a^2*c*e^5 + 15*c^3*d^4*e + 18*a*c^2*d^2*e^3) + (a^3*e^6 + 37*c^3*d^6 + 39*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)/(3*e) + x*(27*c^3*d^5 + 30*a*c^2*d^3*e^2 + 3*a^2*c*d*e^4))/(d^3*e^6 + e^9*x^3 + 3*d^2*e^7*x + 3*d*e^8*x^2) - (log(d + e*x)*(20*c^3*d^3 + 12*a*c^2*d*e^2))/e^7 + (c^3*x^3)/(3*e^4) - (2*c^3*d*x^2)/e^5","B"
482,1,236,171,0.086445,"\text{Not used}","int((a + c*x^2)^3/(d + e*x)^5,x)","\frac{x^2\,\left(-\frac{3\,a^2\,c\,e^5}{2}+27\,a\,c^2\,d^2\,e^3+\frac{105\,c^3\,d^4\,e}{2}\right)-\frac{a^3\,e^6+a^2\,c\,d^2\,e^4-25\,a\,c^2\,d^4\,e^2-57\,c^3\,d^6}{4\,e}+x\,\left(-a^2\,c\,d\,e^4+22\,a\,c^2\,d^3\,e^2+47\,c^3\,d^5\right)+x^3\,\left(20\,c^3\,d^3\,e^2+12\,a\,c^2\,d\,e^4\right)}{d^4\,e^6+4\,d^3\,e^7\,x+6\,d^2\,e^8\,x^2+4\,d\,e^9\,x^3+e^{10}\,x^4}+\frac{\ln\left(d+e\,x\right)\,\left(15\,c^3\,d^2+3\,a\,c^2\,e^2\right)}{e^7}+\frac{c^3\,x^2}{2\,e^5}-\frac{5\,c^3\,d\,x}{e^6}","Not used",1,"(x^2*((105*c^3*d^4*e)/2 - (3*a^2*c*e^5)/2 + 27*a*c^2*d^2*e^3) - (a^3*e^6 - 57*c^3*d^6 - 25*a*c^2*d^4*e^2 + a^2*c*d^2*e^4)/(4*e) + x*(47*c^3*d^5 + 22*a*c^2*d^3*e^2 - a^2*c*d*e^4) + x^3*(20*c^3*d^3*e^2 + 12*a*c^2*d*e^4))/(d^4*e^6 + e^10*x^4 + 4*d^3*e^7*x + 4*d*e^9*x^3 + 6*d^2*e^8*x^2) + (log(d + e*x)*(15*c^3*d^2 + 3*a*c^2*e^2))/e^7 + (c^3*x^2)/(2*e^5) - (5*c^3*d*x)/e^6","B"
483,1,247,172,0.358689,"\text{Not used}","int((a + c*x^2)^3/(d + e*x)^6,x)","\frac{c^3\,x}{e^6}-\frac{x^2\,\left(a^2\,c\,e^5+6\,a\,c^2\,d^2\,e^3+65\,c^3\,d^4\,e\right)+\frac{2\,a^3\,e^6+a^2\,c\,d^2\,e^4+6\,a\,c^2\,d^4\,e^2+87\,c^3\,d^6}{10\,e}+x^4\,\left(15\,c^3\,d^2\,e^3+3\,a\,c^2\,e^5\right)+x\,\left(\frac{a^2\,c\,d\,e^4}{2}+3\,a\,c^2\,d^3\,e^2+\frac{77\,c^3\,d^5}{2}\right)+x^3\,\left(50\,c^3\,d^3\,e^2+6\,a\,c^2\,d\,e^4\right)}{d^5\,e^6+5\,d^4\,e^7\,x+10\,d^3\,e^8\,x^2+10\,d^2\,e^9\,x^3+5\,d\,e^{10}\,x^4+e^{11}\,x^5}-\frac{6\,c^3\,d\,\ln\left(d+e\,x\right)}{e^7}","Not used",1,"(c^3*x)/e^6 - (x^2*(a^2*c*e^5 + 65*c^3*d^4*e + 6*a*c^2*d^2*e^3) + (2*a^3*e^6 + 87*c^3*d^6 + 6*a*c^2*d^4*e^2 + a^2*c*d^2*e^4)/(10*e) + x^4*(3*a*c^2*e^5 + 15*c^3*d^2*e^3) + x*((77*c^3*d^5)/2 + 3*a*c^2*d^3*e^2 + (a^2*c*d*e^4)/2) + x^3*(50*c^3*d^3*e^2 + 6*a*c^2*d*e^4))/(d^5*e^6 + e^11*x^5 + 5*d^4*e^7*x + 5*d*e^10*x^4 + 10*d^3*e^8*x^2 + 10*d^2*e^9*x^3) - (6*c^3*d*log(d + e*x))/e^7","B"
484,1,262,184,0.370812,"\text{Not used}","int((a + c*x^2)^3/(d + e*x)^7,x)","\frac{c^3\,\ln\left(d+e\,x\right)}{e^7}-\frac{\frac{10\,a^3\,e^6+3\,a^2\,c\,d^2\,e^4+6\,a\,c^2\,d^4\,e^2-147\,c^3\,d^6}{60\,e^7}+\frac{x^2\,\left(3\,a^2\,c\,e^4+6\,a\,c^2\,d^2\,e^2-125\,c^3\,d^4\right)}{4\,e^5}+\frac{x\,\left(3\,a^2\,c\,d\,e^4+6\,a\,c^2\,d^3\,e^2-137\,c^3\,d^5\right)}{10\,e^6}-\frac{2\,x^3\,\left(55\,c^3\,d^3-3\,a\,c^2\,d\,e^2\right)}{3\,e^4}-\frac{6\,c^3\,d\,x^5}{e^2}+\frac{3\,c^2\,x^4\,\left(a\,e^2-15\,c\,d^2\right)}{2\,e^3}}{d^6+6\,d^5\,e\,x+15\,d^4\,e^2\,x^2+20\,d^3\,e^3\,x^3+15\,d^2\,e^4\,x^4+6\,d\,e^5\,x^5+e^6\,x^6}","Not used",1,"(c^3*log(d + e*x))/e^7 - ((10*a^3*e^6 - 147*c^3*d^6 + 6*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)/(60*e^7) + (x^2*(3*a^2*c*e^4 - 125*c^3*d^4 + 6*a*c^2*d^2*e^2))/(4*e^5) + (x*(6*a*c^2*d^3*e^2 - 137*c^3*d^5 + 3*a^2*c*d*e^4))/(10*e^6) - (2*x^3*(55*c^3*d^3 - 3*a*c^2*d*e^2))/(3*e^4) - (6*c^3*d*x^5)/e^2 + (3*c^2*x^4*(a*e^2 - 15*c*d^2))/(2*e^3))/(d^6 + e^6*x^6 + 6*d*e^5*x^5 + 15*d^4*e^2*x^2 + 20*d^3*e^3*x^3 + 15*d^2*e^4*x^4 + 6*d^5*e*x)","B"
485,1,254,178,0.082917,"\text{Not used}","int((a + c*x^2)^3/(d + e*x)^8,x)","-\frac{\frac{5\,a^3\,e^6+a^2\,c\,d^2\,e^4+a\,c^2\,d^4\,e^2+5\,c^3\,d^6}{35\,e^7}+\frac{c^3\,x^6}{e}+\frac{3\,c^3\,d\,x^5}{e^2}+\frac{c^2\,x^4\,\left(5\,c\,d^2+a\,e^2\right)}{e^3}+\frac{3\,c\,x^2\,\left(a^2\,e^4+a\,c\,d^2\,e^2+5\,c^2\,d^4\right)}{5\,e^5}+\frac{c\,d\,x\,\left(a^2\,e^4+a\,c\,d^2\,e^2+5\,c^2\,d^4\right)}{5\,e^6}+\frac{c^2\,d\,x^3\,\left(5\,c\,d^2+a\,e^2\right)}{e^4}}{d^7+7\,d^6\,e\,x+21\,d^5\,e^2\,x^2+35\,d^4\,e^3\,x^3+35\,d^3\,e^4\,x^4+21\,d^2\,e^5\,x^5+7\,d\,e^6\,x^6+e^7\,x^7}","Not used",1,"-((5*a^3*e^6 + 5*c^3*d^6 + a*c^2*d^4*e^2 + a^2*c*d^2*e^4)/(35*e^7) + (c^3*x^6)/e + (3*c^3*d*x^5)/e^2 + (c^2*x^4*(a*e^2 + 5*c*d^2))/e^3 + (3*c*x^2*(a^2*e^4 + 5*c^2*d^4 + a*c*d^2*e^2))/(5*e^5) + (c*d*x*(a^2*e^4 + 5*c^2*d^4 + a*c*d^2*e^2))/(5*e^6) + (c^2*d*x^3*(a*e^2 + 5*c*d^2))/e^4)/(d^7 + e^7*x^7 + 7*d*e^6*x^6 + 21*d^5*e^2*x^2 + 35*d^4*e^3*x^3 + 35*d^3*e^4*x^4 + 21*d^2*e^5*x^5 + 7*d^6*e*x)","B"
486,1,275,188,0.328089,"\text{Not used}","int((a + c*x^2)^3/(d + e*x)^9,x)","-\frac{\frac{35\,a^3\,e^6+5\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+5\,c^3\,d^6}{280\,e^7}+\frac{c^3\,x^6}{2\,e}+\frac{c^3\,d\,x^5}{e^2}+\frac{c^2\,x^4\,\left(5\,c\,d^2+3\,a\,e^2\right)}{4\,e^3}+\frac{c\,x^2\,\left(5\,a^2\,e^4+3\,a\,c\,d^2\,e^2+5\,c^2\,d^4\right)}{10\,e^5}+\frac{c\,d\,x\,\left(5\,a^2\,e^4+3\,a\,c\,d^2\,e^2+5\,c^2\,d^4\right)}{35\,e^6}+\frac{c^2\,d\,x^3\,\left(5\,c\,d^2+3\,a\,e^2\right)}{5\,e^4}}{d^8+8\,d^7\,e\,x+28\,d^6\,e^2\,x^2+56\,d^5\,e^3\,x^3+70\,d^4\,e^4\,x^4+56\,d^3\,e^5\,x^5+28\,d^2\,e^6\,x^6+8\,d\,e^7\,x^7+e^8\,x^8}","Not used",1,"-((35*a^3*e^6 + 5*c^3*d^6 + 3*a*c^2*d^4*e^2 + 5*a^2*c*d^2*e^4)/(280*e^7) + (c^3*x^6)/(2*e) + (c^3*d*x^5)/e^2 + (c^2*x^4*(3*a*e^2 + 5*c*d^2))/(4*e^3) + (c*x^2*(5*a^2*e^4 + 5*c^2*d^4 + 3*a*c*d^2*e^2))/(10*e^5) + (c*d*x*(5*a^2*e^4 + 5*c^2*d^4 + 3*a*c*d^2*e^2))/(35*e^6) + (c^2*d*x^3*(3*a*e^2 + 5*c*d^2))/(5*e^4))/(d^8 + e^8*x^8 + 8*d*e^7*x^7 + 28*d^6*e^2*x^2 + 56*d^5*e^3*x^3 + 70*d^4*e^4*x^4 + 56*d^3*e^5*x^5 + 28*d^2*e^6*x^6 + 8*d^7*e*x)","B"
487,1,287,190,0.342244,"\text{Not used}","int((a + c*x^2)^3/(d + e*x)^10,x)","-\frac{\frac{140\,a^3\,e^6+15\,a^2\,c\,d^2\,e^4+6\,a\,c^2\,d^4\,e^2+5\,c^3\,d^6}{1260\,e^7}+\frac{c^3\,x^6}{3\,e}+\frac{c^3\,d\,x^5}{2\,e^2}+\frac{c^2\,x^4\,\left(5\,c\,d^2+6\,a\,e^2\right)}{10\,e^3}+\frac{c\,x^2\,\left(15\,a^2\,e^4+6\,a\,c\,d^2\,e^2+5\,c^2\,d^4\right)}{35\,e^5}+\frac{c\,d\,x\,\left(15\,a^2\,e^4+6\,a\,c\,d^2\,e^2+5\,c^2\,d^4\right)}{140\,e^6}+\frac{c^2\,d\,x^3\,\left(5\,c\,d^2+6\,a\,e^2\right)}{15\,e^4}}{d^9+9\,d^8\,e\,x+36\,d^7\,e^2\,x^2+84\,d^6\,e^3\,x^3+126\,d^5\,e^4\,x^4+126\,d^4\,e^5\,x^5+84\,d^3\,e^6\,x^6+36\,d^2\,e^7\,x^7+9\,d\,e^8\,x^8+e^9\,x^9}","Not used",1,"-((140*a^3*e^6 + 5*c^3*d^6 + 6*a*c^2*d^4*e^2 + 15*a^2*c*d^2*e^4)/(1260*e^7) + (c^3*x^6)/(3*e) + (c^3*d*x^5)/(2*e^2) + (c^2*x^4*(6*a*e^2 + 5*c*d^2))/(10*e^3) + (c*x^2*(15*a^2*e^4 + 5*c^2*d^4 + 6*a*c*d^2*e^2))/(35*e^5) + (c*d*x*(15*a^2*e^4 + 5*c^2*d^4 + 6*a*c*d^2*e^2))/(140*e^6) + (c^2*d*x^3*(6*a*e^2 + 5*c*d^2))/(15*e^4))/(d^9 + e^9*x^9 + 9*d*e^8*x^8 + 36*d^7*e^2*x^2 + 84*d^6*e^3*x^3 + 126*d^5*e^4*x^4 + 126*d^4*e^5*x^5 + 84*d^3*e^6*x^6 + 36*d^2*e^7*x^7 + 9*d^8*e*x)","B"
488,1,495,278,0.487178,"\text{Not used}","int((a + c*x^2)^4*(d + e*x)^7,x)","x^3\,\left(7\,a^4\,d^5\,e^2+\frac{4\,c\,a^3\,d^7}{3}\right)+x^{14}\,\left(\frac{3\,c^4\,d^2\,e^5}{2}+\frac{2\,a\,c^3\,e^7}{7}\right)+x^7\,\left(a^4\,d\,e^6+20\,a^3\,c\,d^3\,e^4+18\,a^2\,c^2\,d^5\,e^2+\frac{4\,a\,c^3\,d^7}{7}\right)+x^8\,\left(\frac{a^4\,e^7}{8}+\frac{21\,a^3\,c\,d^2\,e^5}{2}+\frac{105\,a^2\,c^2\,d^4\,e^3}{4}+\frac{7\,a\,c^3\,d^6\,e}{2}\right)+x^9\,\left(\frac{28\,a^3\,c\,d\,e^6}{9}+\frac{70\,a^2\,c^2\,d^3\,e^4}{3}+\frac{28\,a\,c^3\,d^5\,e^2}{3}+\frac{c^4\,d^7}{9}\right)+x^{10}\,\left(\frac{2\,a^3\,c\,e^7}{5}+\frac{63\,a^2\,c^2\,d^2\,e^5}{5}+14\,a\,c^3\,d^4\,e^3+\frac{7\,c^4\,d^6\,e}{10}\right)+x^5\,\left(7\,a^4\,d^3\,e^4+\frac{84\,a^3\,c\,d^5\,e^2}{5}+\frac{6\,a^2\,c^2\,d^7}{5}\right)+x^{12}\,\left(\frac{a^2\,c^2\,e^7}{2}+7\,a\,c^3\,d^2\,e^5+\frac{35\,c^4\,d^4\,e^3}{12}\right)+a^4\,d^7\,x+\frac{c^4\,e^7\,x^{16}}{16}+\frac{7\,a^4\,d^6\,e\,x^2}{2}+\frac{7\,c^4\,d\,e^6\,x^{15}}{15}+\frac{7\,a^3\,d^4\,e\,x^4\,\left(4\,c\,d^2+5\,a\,e^2\right)}{4}+\frac{7\,c^3\,d\,e^4\,x^{13}\,\left(5\,c\,d^2+4\,a\,e^2\right)}{13}+\frac{7\,a^2\,d^2\,e\,x^6\,\left(3\,a^2\,e^4+20\,a\,c\,d^2\,e^2+6\,c^2\,d^4\right)}{6}+\frac{7\,c^2\,d\,e^2\,x^{11}\,\left(6\,a^2\,e^4+20\,a\,c\,d^2\,e^2+3\,c^2\,d^4\right)}{11}","Not used",1,"x^3*((4*a^3*c*d^7)/3 + 7*a^4*d^5*e^2) + x^14*((2*a*c^3*e^7)/7 + (3*c^4*d^2*e^5)/2) + x^7*((4*a*c^3*d^7)/7 + a^4*d*e^6 + 20*a^3*c*d^3*e^4 + 18*a^2*c^2*d^5*e^2) + x^8*((a^4*e^7)/8 + (21*a^3*c*d^2*e^5)/2 + (105*a^2*c^2*d^4*e^3)/4 + (7*a*c^3*d^6*e)/2) + x^9*((c^4*d^7)/9 + (28*a*c^3*d^5*e^2)/3 + (70*a^2*c^2*d^3*e^4)/3 + (28*a^3*c*d*e^6)/9) + x^10*((2*a^3*c*e^7)/5 + (7*c^4*d^6*e)/10 + 14*a*c^3*d^4*e^3 + (63*a^2*c^2*d^2*e^5)/5) + x^5*((6*a^2*c^2*d^7)/5 + 7*a^4*d^3*e^4 + (84*a^3*c*d^5*e^2)/5) + x^12*((a^2*c^2*e^7)/2 + (35*c^4*d^4*e^3)/12 + 7*a*c^3*d^2*e^5) + a^4*d^7*x + (c^4*e^7*x^16)/16 + (7*a^4*d^6*e*x^2)/2 + (7*c^4*d*e^6*x^15)/15 + (7*a^3*d^4*e*x^4*(5*a*e^2 + 4*c*d^2))/4 + (7*c^3*d*e^4*x^13*(4*a*e^2 + 5*c*d^2))/13 + (7*a^2*d^2*e*x^6*(3*a^2*e^4 + 6*c^2*d^4 + 20*a*c*d^2*e^2))/6 + (7*c^2*d*e^2*x^11*(6*a^2*e^4 + 3*c^2*d^4 + 20*a*c*d^2*e^2))/11","B"
489,1,425,276,0.221062,"\text{Not used}","int((a + c*x^2)^4*(d + e*x)^6,x)","x^7\,\left(\frac{a^4\,e^6}{7}+\frac{60\,a^3\,c\,d^2\,e^4}{7}+\frac{90\,a^2\,c^2\,d^4\,e^2}{7}+\frac{4\,a\,c^3\,d^6}{7}\right)+x^9\,\left(\frac{4\,a^3\,c\,e^6}{9}+10\,a^2\,c^2\,d^2\,e^4+\frac{20\,a\,c^3\,d^4\,e^2}{3}+\frac{c^4\,d^6}{9}\right)+x^3\,\left(5\,a^4\,d^4\,e^2+\frac{4\,c\,a^3\,d^6}{3}\right)+x^{13}\,\left(\frac{15\,c^4\,d^2\,e^4}{13}+\frac{4\,a\,c^3\,e^6}{13}\right)+x^5\,\left(3\,a^4\,d^2\,e^4+12\,a^3\,c\,d^4\,e^2+\frac{6\,a^2\,c^2\,d^6}{5}\right)+x^{11}\,\left(\frac{6\,a^2\,c^2\,e^6}{11}+\frac{60\,a\,c^3\,d^2\,e^4}{11}+\frac{15\,c^4\,d^4\,e^2}{11}\right)+a^4\,d^6\,x+\frac{c^4\,e^6\,x^{15}}{15}+3\,a^4\,d^5\,e\,x^2+\frac{3\,c^4\,d\,e^5\,x^{14}}{7}+a^3\,d^3\,e\,x^4\,\left(6\,c\,d^2+5\,a\,e^2\right)+\frac{c^3\,d\,e^3\,x^{12}\,\left(5\,c\,d^2+6\,a\,e^2\right)}{3}+\frac{a^2\,d\,e\,x^6\,\left(3\,a^2\,e^4+40\,a\,c\,d^2\,e^2+18\,c^2\,d^4\right)}{3}+\frac{c^2\,d\,e\,x^{10}\,\left(18\,a^2\,e^4+40\,a\,c\,d^2\,e^2+3\,c^2\,d^4\right)}{5}+3\,a\,c\,d\,e\,x^8\,\left(a^2\,e^4+5\,a\,c\,d^2\,e^2+c^2\,d^4\right)","Not used",1,"x^7*((a^4*e^6)/7 + (4*a*c^3*d^6)/7 + (60*a^3*c*d^2*e^4)/7 + (90*a^2*c^2*d^4*e^2)/7) + x^9*((c^4*d^6)/9 + (4*a^3*c*e^6)/9 + (20*a*c^3*d^4*e^2)/3 + 10*a^2*c^2*d^2*e^4) + x^3*((4*a^3*c*d^6)/3 + 5*a^4*d^4*e^2) + x^13*((4*a*c^3*e^6)/13 + (15*c^4*d^2*e^4)/13) + x^5*((6*a^2*c^2*d^6)/5 + 3*a^4*d^2*e^4 + 12*a^3*c*d^4*e^2) + x^11*((6*a^2*c^2*e^6)/11 + (15*c^4*d^4*e^2)/11 + (60*a*c^3*d^2*e^4)/11) + a^4*d^6*x + (c^4*e^6*x^15)/15 + 3*a^4*d^5*e*x^2 + (3*c^4*d*e^5*x^14)/7 + a^3*d^3*e*x^4*(5*a*e^2 + 6*c*d^2) + (c^3*d*e^3*x^12*(6*a*e^2 + 5*c*d^2))/3 + (a^2*d*e*x^6*(3*a^2*e^4 + 18*c^2*d^4 + 40*a*c*d^2*e^2))/3 + (c^2*d*e*x^10*(18*a^2*e^4 + 3*c^2*d^4 + 40*a*c*d^2*e^2))/5 + 3*a*c*d*e*x^8*(a^2*e^4 + c^2*d^4 + 5*a*c*d^2*e^2)","B"
490,1,357,278,0.174547,"\text{Not used}","int((a + c*x^2)^4*(d + e*x)^5,x)","x^3\,\left(\frac{10\,a^4\,d^3\,e^2}{3}+\frac{4\,c\,a^3\,d^5}{3}\right)+x^{12}\,\left(\frac{5\,c^4\,d^2\,e^3}{6}+\frac{a\,c^3\,e^5}{3}\right)+x^5\,\left(a^4\,d\,e^4+8\,a^3\,c\,d^3\,e^2+\frac{6\,a^2\,c^2\,d^5}{5}\right)+x^6\,\left(\frac{a^4\,e^5}{6}+\frac{20\,a^3\,c\,d^2\,e^3}{3}+5\,a^2\,c^2\,d^4\,e\right)+x^9\,\left(\frac{10\,a^2\,c^2\,d\,e^4}{3}+\frac{40\,a\,c^3\,d^3\,e^2}{9}+\frac{c^4\,d^5}{9}\right)+x^{10}\,\left(\frac{3\,a^2\,c^2\,e^5}{5}+4\,a\,c^3\,d^2\,e^3+\frac{c^4\,d^4\,e}{2}\right)+a^4\,d^5\,x+\frac{c^4\,e^5\,x^{14}}{14}+\frac{5\,a^4\,d^4\,e\,x^2}{2}+\frac{5\,c^4\,d\,e^4\,x^{13}}{13}+\frac{4\,a\,c\,d\,x^7\,\left(5\,a^2\,e^4+15\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{7}+\frac{a\,c\,e\,x^8\,\left(a^2\,e^4+15\,a\,c\,d^2\,e^2+5\,c^2\,d^4\right)}{2}+\frac{5\,a^3\,d^2\,e\,x^4\,\left(2\,c\,d^2+a\,e^2\right)}{2}+\frac{10\,c^3\,d\,e^2\,x^{11}\,\left(c\,d^2+2\,a\,e^2\right)}{11}","Not used",1,"x^3*((4*a^3*c*d^5)/3 + (10*a^4*d^3*e^2)/3) + x^12*((a*c^3*e^5)/3 + (5*c^4*d^2*e^3)/6) + x^5*(a^4*d*e^4 + (6*a^2*c^2*d^5)/5 + 8*a^3*c*d^3*e^2) + x^6*((a^4*e^5)/6 + 5*a^2*c^2*d^4*e + (20*a^3*c*d^2*e^3)/3) + x^9*((c^4*d^5)/9 + (40*a*c^3*d^3*e^2)/9 + (10*a^2*c^2*d*e^4)/3) + x^10*((c^4*d^4*e)/2 + (3*a^2*c^2*e^5)/5 + 4*a*c^3*d^2*e^3) + a^4*d^5*x + (c^4*e^5*x^14)/14 + (5*a^4*d^4*e*x^2)/2 + (5*c^4*d*e^4*x^13)/13 + (4*a*c*d*x^7*(5*a^2*e^4 + c^2*d^4 + 15*a*c*d^2*e^2))/7 + (a*c*e*x^8*(a^2*e^4 + 5*c^2*d^4 + 15*a*c*d^2*e^2))/2 + (5*a^3*d^2*e*x^4*(a*e^2 + 2*c*d^2))/2 + (10*c^3*d*e^2*x^11*(2*a*e^2 + c*d^2))/11","B"
491,1,288,270,0.139653,"\text{Not used}","int((a + c*x^2)^4*(d + e*x)^4,x)","x^5\,\left(\frac{a^4\,e^4}{5}+\frac{24\,a^3\,c\,d^2\,e^2}{5}+\frac{6\,a^2\,c^2\,d^4}{5}\right)+x^9\,\left(\frac{2\,a^2\,c^2\,e^4}{3}+\frac{8\,a\,c^3\,d^2\,e^2}{3}+\frac{c^4\,d^4}{9}\right)+x^3\,\left(2\,a^4\,d^2\,e^2+\frac{4\,c\,a^3\,d^4}{3}\right)+x^{11}\,\left(\frac{6\,c^4\,d^2\,e^2}{11}+\frac{4\,a\,c^3\,e^4}{11}\right)+a^4\,d^4\,x+\frac{c^4\,e^4\,x^{13}}{13}+2\,a^4\,d^3\,e\,x^2+\frac{c^4\,d\,e^3\,x^{12}}{3}+\frac{4\,a\,c\,x^7\,\left(a^2\,e^4+9\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{7}+a^3\,d\,e\,x^4\,\left(4\,c\,d^2+a\,e^2\right)+\frac{2\,c^3\,d\,e\,x^{10}\,\left(c\,d^2+4\,a\,e^2\right)}{5}+\frac{4\,a^2\,c\,d\,e\,x^6\,\left(3\,c\,d^2+2\,a\,e^2\right)}{3}+a\,c^2\,d\,e\,x^8\,\left(2\,c\,d^2+3\,a\,e^2\right)","Not used",1,"x^5*((a^4*e^4)/5 + (6*a^2*c^2*d^4)/5 + (24*a^3*c*d^2*e^2)/5) + x^9*((c^4*d^4)/9 + (2*a^2*c^2*e^4)/3 + (8*a*c^3*d^2*e^2)/3) + x^3*((4*a^3*c*d^4)/3 + 2*a^4*d^2*e^2) + x^11*((4*a*c^3*e^4)/11 + (6*c^4*d^2*e^2)/11) + a^4*d^4*x + (c^4*e^4*x^13)/13 + 2*a^4*d^3*e*x^2 + (c^4*d*e^3*x^12)/3 + (4*a*c*x^7*(a^2*e^4 + c^2*d^4 + 9*a*c*d^2*e^2))/7 + a^3*d*e*x^4*(a*e^2 + 4*c*d^2) + (2*c^3*d*e*x^10*(4*a*e^2 + c*d^2))/5 + (4*a^2*c*d*e*x^6*(2*a*e^2 + 3*c*d^2))/3 + a*c^2*d*e*x^8*(3*a*e^2 + 2*c*d^2)","B"
492,1,225,209,0.331470,"\text{Not used}","int((a + c*x^2)^4*(d + e*x)^3,x)","x^3\,\left(a^4\,d\,e^2+\frac{4\,c\,a^3\,d^3}{3}\right)+x^4\,\left(\frac{a^4\,e^3}{4}+3\,c\,a^3\,d^2\,e\right)+x^9\,\left(\frac{c^4\,d^3}{9}+\frac{4\,a\,c^3\,d\,e^2}{3}\right)+x^{10}\,\left(\frac{3\,c^4\,d^2\,e}{10}+\frac{2\,a\,c^3\,e^3}{5}\right)+a^4\,d^3\,x+\frac{c^4\,e^3\,x^{12}}{12}+\frac{3\,a^4\,d^2\,e\,x^2}{2}+\frac{3\,c^4\,d\,e^2\,x^{11}}{11}+\frac{6\,a^2\,c\,d\,x^5\,\left(c\,d^2+2\,a\,e^2\right)}{5}+\frac{2\,a\,c^2\,d\,x^7\,\left(2\,c\,d^2+9\,a\,e^2\right)}{7}+\frac{3\,a\,c^2\,e\,x^8\,\left(2\,c\,d^2+a\,e^2\right)}{4}+\frac{a^2\,c\,e\,x^6\,\left(9\,c\,d^2+2\,a\,e^2\right)}{3}","Not used",1,"x^3*((4*a^3*c*d^3)/3 + a^4*d*e^2) + x^4*((a^4*e^3)/4 + 3*a^3*c*d^2*e) + x^9*((c^4*d^3)/9 + (4*a*c^3*d*e^2)/3) + x^10*((2*a*c^3*e^3)/5 + (3*c^4*d^2*e)/10) + a^4*d^3*x + (c^4*e^3*x^12)/12 + (3*a^4*d^2*e*x^2)/2 + (3*c^4*d*e^2*x^11)/11 + (6*a^2*c*d*x^5*(2*a*e^2 + c*d^2))/5 + (2*a*c^2*d*x^7*(9*a*e^2 + 2*c*d^2))/7 + (3*a*c^2*e*x^8*(a*e^2 + 2*c*d^2))/4 + (a^2*c*e*x^6*(2*a*e^2 + 9*c*d^2))/3","B"
493,1,161,132,0.072507,"\text{Not used}","int((a + c*x^2)^4*(d + e*x)^2,x)","x^3\,\left(\frac{a^4\,e^2}{3}+\frac{4\,c\,a^3\,d^2}{3}\right)+x^9\,\left(\frac{c^4\,d^2}{9}+\frac{4\,a\,c^3\,e^2}{9}\right)+a^4\,d^2\,x+\frac{c^4\,e^2\,x^{11}}{11}+a^4\,d\,e\,x^2+\frac{c^4\,d\,e\,x^{10}}{5}+\frac{2\,a^2\,c\,x^5\,\left(3\,c\,d^2+2\,a\,e^2\right)}{5}+\frac{2\,a\,c^2\,x^7\,\left(2\,c\,d^2+3\,a\,e^2\right)}{7}+2\,a^3\,c\,d\,e\,x^4+a\,c^3\,d\,e\,x^8+2\,a^2\,c^2\,d\,e\,x^6","Not used",1,"x^3*((a^4*e^2)/3 + (4*a^3*c*d^2)/3) + x^9*((c^4*d^2)/9 + (4*a*c^3*e^2)/9) + a^4*d^2*x + (c^4*e^2*x^11)/11 + a^4*d*e*x^2 + (c^4*d*e*x^10)/5 + (2*a^2*c*x^5*(2*a*e^2 + 3*c*d^2))/5 + (2*a*c^2*x^7*(3*a*e^2 + 2*c*d^2))/7 + 2*a^3*c*d*e*x^4 + a*c^3*d*e*x^8 + 2*a^2*c^2*d*e*x^6","B"
494,1,96,73,0.049568,"\text{Not used}","int((a + c*x^2)^4*(d + e*x),x)","\frac{e\,a^4\,x^2}{2}+d\,a^4\,x+e\,a^3\,c\,x^4+\frac{4\,d\,a^3\,c\,x^3}{3}+e\,a^2\,c^2\,x^6+\frac{6\,d\,a^2\,c^2\,x^5}{5}+\frac{e\,a\,c^3\,x^8}{2}+\frac{4\,d\,a\,c^3\,x^7}{7}+\frac{e\,c^4\,x^{10}}{10}+\frac{d\,c^4\,x^9}{9}","Not used",1,"(a^4*e*x^2)/2 + (c^4*d*x^9)/9 + (c^4*e*x^10)/10 + a^4*d*x + (6*a^2*c^2*d*x^5)/5 + a^2*c^2*e*x^6 + (4*a^3*c*d*x^3)/3 + (4*a*c^3*d*x^7)/7 + a^3*c*e*x^4 + (a*c^3*e*x^8)/2","B"
495,1,357,264,0.070486,"\text{Not used}","int((a + c*x^2)^4/(d + e*x),x)","x^2\,\left(\frac{d^2\,\left(\frac{d^2\,\left(\frac{4\,a\,c^3}{e}+\frac{c^4\,d^2}{e^3}\right)}{e^2}+\frac{6\,a^2\,c^2}{e}\right)}{2\,e^2}+\frac{2\,a^3\,c}{e}\right)+x^4\,\left(\frac{d^2\,\left(\frac{4\,a\,c^3}{e}+\frac{c^4\,d^2}{e^3}\right)}{4\,e^2}+\frac{3\,a^2\,c^2}{2\,e}\right)+x^6\,\left(\frac{2\,a\,c^3}{3\,e}+\frac{c^4\,d^2}{6\,e^3}\right)+\frac{\ln\left(d+e\,x\right)\,\left(a^4\,e^8+4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4+4\,a\,c^3\,d^6\,e^2+c^4\,d^8\right)}{e^9}+\frac{c^4\,x^8}{8\,e}-\frac{c^4\,d\,x^7}{7\,e^2}-\frac{d\,x^3\,\left(\frac{d^2\,\left(\frac{4\,a\,c^3}{e}+\frac{c^4\,d^2}{e^3}\right)}{e^2}+\frac{6\,a^2\,c^2}{e}\right)}{3\,e}-\frac{d\,x^5\,\left(\frac{4\,a\,c^3}{e}+\frac{c^4\,d^2}{e^3}\right)}{5\,e}-\frac{d\,x\,\left(\frac{d^2\,\left(\frac{d^2\,\left(\frac{4\,a\,c^3}{e}+\frac{c^4\,d^2}{e^3}\right)}{e^2}+\frac{6\,a^2\,c^2}{e}\right)}{e^2}+\frac{4\,a^3\,c}{e}\right)}{e}","Not used",1,"x^2*((d^2*((d^2*((4*a*c^3)/e + (c^4*d^2)/e^3))/e^2 + (6*a^2*c^2)/e))/(2*e^2) + (2*a^3*c)/e) + x^4*((d^2*((4*a*c^3)/e + (c^4*d^2)/e^3))/(4*e^2) + (3*a^2*c^2)/(2*e)) + x^6*((2*a*c^3)/(3*e) + (c^4*d^2)/(6*e^3)) + (log(d + e*x)*(a^4*e^8 + c^4*d^8 + 4*a*c^3*d^6*e^2 + 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4))/e^9 + (c^4*x^8)/(8*e) - (c^4*d*x^7)/(7*e^2) - (d*x^3*((d^2*((4*a*c^3)/e + (c^4*d^2)/e^3))/e^2 + (6*a^2*c^2)/e))/(3*e) - (d*x^5*((4*a*c^3)/e + (c^4*d^2)/e^3))/(5*e) - (d*x*((d^2*((d^2*((4*a*c^3)/e + (c^4*d^2)/e^3))/e^2 + (6*a^2*c^2)/e))/e^2 + (4*a^3*c)/e))/e","B"
496,1,701,255,0.324431,"\text{Not used}","int((a + c*x^2)^4/(d + e*x)^2,x)","x^4\,\left(\frac{c^4\,d^3}{2\,e^5}-\frac{d\,\left(\frac{4\,a\,c^3}{e^2}+\frac{3\,c^4\,d^2}{e^4}\right)}{2\,e}\right)+x^5\,\left(\frac{4\,a\,c^3}{5\,e^2}+\frac{3\,c^4\,d^2}{5\,e^4}\right)+x^2\,\left(\frac{d\,\left(\frac{d^2\,\left(\frac{4\,a\,c^3}{e^2}+\frac{3\,c^4\,d^2}{e^4}\right)}{e^2}+\frac{2\,d\,\left(\frac{2\,c^4\,d^3}{e^5}-\frac{2\,d\,\left(\frac{4\,a\,c^3}{e^2}+\frac{3\,c^4\,d^2}{e^4}\right)}{e}\right)}{e}-\frac{6\,a^2\,c^2}{e^2}\right)}{e}-\frac{d^2\,\left(\frac{2\,c^4\,d^3}{e^5}-\frac{2\,d\,\left(\frac{4\,a\,c^3}{e^2}+\frac{3\,c^4\,d^2}{e^4}\right)}{e}\right)}{2\,e^2}\right)-x^3\,\left(\frac{d^2\,\left(\frac{4\,a\,c^3}{e^2}+\frac{3\,c^4\,d^2}{e^4}\right)}{3\,e^2}+\frac{2\,d\,\left(\frac{2\,c^4\,d^3}{e^5}-\frac{2\,d\,\left(\frac{4\,a\,c^3}{e^2}+\frac{3\,c^4\,d^2}{e^4}\right)}{e}\right)}{3\,e}-\frac{2\,a^2\,c^2}{e^2}\right)+x\,\left(\frac{4\,a^3\,c}{e^2}+\frac{d^2\,\left(\frac{d^2\,\left(\frac{4\,a\,c^3}{e^2}+\frac{3\,c^4\,d^2}{e^4}\right)}{e^2}+\frac{2\,d\,\left(\frac{2\,c^4\,d^3}{e^5}-\frac{2\,d\,\left(\frac{4\,a\,c^3}{e^2}+\frac{3\,c^4\,d^2}{e^4}\right)}{e}\right)}{e}-\frac{6\,a^2\,c^2}{e^2}\right)}{e^2}-\frac{2\,d\,\left(\frac{2\,d\,\left(\frac{d^2\,\left(\frac{4\,a\,c^3}{e^2}+\frac{3\,c^4\,d^2}{e^4}\right)}{e^2}+\frac{2\,d\,\left(\frac{2\,c^4\,d^3}{e^5}-\frac{2\,d\,\left(\frac{4\,a\,c^3}{e^2}+\frac{3\,c^4\,d^2}{e^4}\right)}{e}\right)}{e}-\frac{6\,a^2\,c^2}{e^2}\right)}{e}-\frac{d^2\,\left(\frac{2\,c^4\,d^3}{e^5}-\frac{2\,d\,\left(\frac{4\,a\,c^3}{e^2}+\frac{3\,c^4\,d^2}{e^4}\right)}{e}\right)}{e^2}\right)}{e}\right)-\frac{a^4\,e^8+4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4+4\,a\,c^3\,d^6\,e^2+c^4\,d^8}{e\,\left(x\,e^9+d\,e^8\right)}+\frac{c^4\,x^7}{7\,e^2}-\frac{\ln\left(d+e\,x\right)\,\left(8\,a^3\,c\,d\,e^6+24\,a^2\,c^2\,d^3\,e^4+24\,a\,c^3\,d^5\,e^2+8\,c^4\,d^7\right)}{e^9}-\frac{c^4\,d\,x^6}{3\,e^3}","Not used",1,"x^4*((c^4*d^3)/(2*e^5) - (d*((4*a*c^3)/e^2 + (3*c^4*d^2)/e^4))/(2*e)) + x^5*((4*a*c^3)/(5*e^2) + (3*c^4*d^2)/(5*e^4)) + x^2*((d*((d^2*((4*a*c^3)/e^2 + (3*c^4*d^2)/e^4))/e^2 + (2*d*((2*c^4*d^3)/e^5 - (2*d*((4*a*c^3)/e^2 + (3*c^4*d^2)/e^4))/e))/e - (6*a^2*c^2)/e^2))/e - (d^2*((2*c^4*d^3)/e^5 - (2*d*((4*a*c^3)/e^2 + (3*c^4*d^2)/e^4))/e))/(2*e^2)) - x^3*((d^2*((4*a*c^3)/e^2 + (3*c^4*d^2)/e^4))/(3*e^2) + (2*d*((2*c^4*d^3)/e^5 - (2*d*((4*a*c^3)/e^2 + (3*c^4*d^2)/e^4))/e))/(3*e) - (2*a^2*c^2)/e^2) + x*((4*a^3*c)/e^2 + (d^2*((d^2*((4*a*c^3)/e^2 + (3*c^4*d^2)/e^4))/e^2 + (2*d*((2*c^4*d^3)/e^5 - (2*d*((4*a*c^3)/e^2 + (3*c^4*d^2)/e^4))/e))/e - (6*a^2*c^2)/e^2))/e^2 - (2*d*((2*d*((d^2*((4*a*c^3)/e^2 + (3*c^4*d^2)/e^4))/e^2 + (2*d*((2*c^4*d^3)/e^5 - (2*d*((4*a*c^3)/e^2 + (3*c^4*d^2)/e^4))/e))/e - (6*a^2*c^2)/e^2))/e - (d^2*((2*c^4*d^3)/e^5 - (2*d*((4*a*c^3)/e^2 + (3*c^4*d^2)/e^4))/e))/e^2))/e) - (a^4*e^8 + c^4*d^8 + 4*a*c^3*d^6*e^2 + 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4)/(e*(d*e^8 + e^9*x)) + (c^4*x^7)/(7*e^2) - (log(d + e*x)*(8*c^4*d^7 + 24*a*c^3*d^5*e^2 + 24*a^2*c^2*d^3*e^4 + 8*a^3*c*d*e^6))/e^9 - (c^4*d*x^6)/(3*e^3)","B"
497,1,96,73,0.276068,"\text{Not used}","int((a + b*x^2)^4*(c + d*x),x)","\frac{d\,a^4\,x^2}{2}+c\,a^4\,x+d\,a^3\,b\,x^4+\frac{4\,c\,a^3\,b\,x^3}{3}+d\,a^2\,b^2\,x^6+\frac{6\,c\,a^2\,b^2\,x^5}{5}+\frac{d\,a\,b^3\,x^8}{2}+\frac{4\,c\,a\,b^3\,x^7}{7}+\frac{d\,b^4\,x^{10}}{10}+\frac{c\,b^4\,x^9}{9}","Not used",1,"(a^4*d*x^2)/2 + (b^4*c*x^9)/9 + (b^4*d*x^10)/10 + a^4*c*x + (6*a^2*b^2*c*x^5)/5 + a^2*b^2*d*x^6 + (4*a^3*b*c*x^3)/3 + (4*a*b^3*c*x^7)/7 + a^3*b*d*x^4 + (a*b^3*d*x^8)/2","B"
498,1,127,123,0.113830,"\text{Not used}","int((d + e*x)^4/(a + c*x^2),x)","\frac{e^4\,x^3}{3\,c}-x\,\left(\frac{a\,e^4}{c^2}-\frac{6\,d^2\,e^2}{c}\right)+\frac{2\,d\,e^3\,x^2}{c}+\frac{\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)\,\left(a^2\,e^4-6\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{\sqrt{a}\,c^{5/2}}-\frac{\ln\left(c\,x^2+a\right)\,\left(16\,a^2\,c^3\,d\,e^3-16\,a\,c^4\,d^3\,e\right)}{8\,a\,c^5}","Not used",1,"(e^4*x^3)/(3*c) - x*((a*e^4)/c^2 - (6*d^2*e^2)/c) + (2*d*e^3*x^2)/c + (atan((c^(1/2)*x)/a^(1/2))*(a^2*e^4 + c^2*d^4 - 6*a*c*d^2*e^2))/(a^(1/2)*c^(5/2)) - (log(a + c*x^2)*(16*a^2*c^3*d*e^3 - 16*a*c^4*d^3*e))/(8*a*c^5)","B"
499,1,91,90,0.130686,"\text{Not used}","int((d + e*x)^3/(a + c*x^2),x)","\frac{e^3\,x^2}{2\,c}-\frac{\ln\left(c\,x^2+a\right)\,\left(4\,a^2\,c^2\,e^3-12\,a\,c^3\,d^2\,e\right)}{8\,a\,c^4}+\frac{3\,d\,e^2\,x}{c}-\frac{d\,\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)\,\left(3\,a\,e^2-c\,d^2\right)}{\sqrt{a}\,c^{3/2}}","Not used",1,"(e^3*x^2)/(2*c) - (log(a + c*x^2)*(4*a^2*c^2*e^3 - 12*a*c^3*d^2*e))/(8*a*c^4) + (3*d*e^2*x)/c - (d*atan((c^(1/2)*x)/a^(1/2))*(3*a*e^2 - c*d^2))/(a^(1/2)*c^(3/2))","B"
500,1,62,59,0.299932,"\text{Not used}","int((d + e*x)^2/(a + c*x^2),x)","\frac{e^2\,x}{c}+\frac{d^2\,\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)}{\sqrt{a}\,\sqrt{c}}-\frac{\sqrt{a}\,e^2\,\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)}{c^{3/2}}+\frac{d\,e\,\ln\left(c\,x^2+a\right)}{c}","Not used",1,"(e^2*x)/c + (d^2*atan((c^(1/2)*x)/a^(1/2)))/(a^(1/2)*c^(1/2)) - (a^(1/2)*e^2*atan((c^(1/2)*x)/a^(1/2)))/c^(3/2) + (d*e*log(a + c*x^2))/c","B"
501,1,32,42,0.278508,"\text{Not used}","int((d + e*x)/(a + c*x^2),x)","\frac{e\,\ln\left(c\,x^2+a\right)}{2\,c}+\frac{d\,\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)}{\sqrt{a}\,\sqrt{c}}","Not used",1,"(e*log(a + c*x^2))/(2*c) + (d*atan((c^(1/2)*x)/a^(1/2)))/(a^(1/2)*c^(1/2))","B"
502,1,230,86,0.820051,"\text{Not used}","int(1/((a + c*x^2)*(d + e*x)),x)","\frac{e\,\ln\left(d+e\,x\right)}{c\,d^2+a\,e^2}-\frac{\ln\left(3\,c^2\,e^2\,x+c^2\,d\,e-\frac{c^2\,e\,\left(a\,e-d\,\sqrt{-a\,c}\right)\,\left(-c\,x\,d^2+4\,a\,d\,e+3\,a\,x\,e^2\right)}{a^2\,e^2+c\,a\,d^2}\right)\,\left(a\,e-d\,\sqrt{-a\,c}\right)}{2\,\left(a^2\,e^2+c\,a\,d^2\right)}-\frac{\ln\left(3\,c^2\,e^2\,x+c^2\,d\,e-\frac{c^2\,e\,\left(a\,e+d\,\sqrt{-a\,c}\right)\,\left(-c\,x\,d^2+4\,a\,d\,e+3\,a\,x\,e^2\right)}{a^2\,e^2+c\,a\,d^2}\right)\,\left(a\,e+d\,\sqrt{-a\,c}\right)}{2\,\left(a^2\,e^2+c\,a\,d^2\right)}","Not used",1,"(e*log(d + e*x))/(a*e^2 + c*d^2) - (log(3*c^2*e^2*x + c^2*d*e - (c^2*e*(a*e - d*(-a*c)^(1/2))*(4*a*d*e + 3*a*e^2*x - c*d^2*x))/(a^2*e^2 + a*c*d^2))*(a*e - d*(-a*c)^(1/2)))/(2*(a^2*e^2 + a*c*d^2)) - (log(3*c^2*e^2*x + c^2*d*e - (c^2*e*(a*e + d*(-a*c)^(1/2))*(4*a*d*e + 3*a*e^2*x - c*d^2*x))/(a^2*e^2 + a*c*d^2))*(a*e + d*(-a*c)^(1/2)))/(2*(a^2*e^2 + a*c*d^2))","B"
503,1,452,123,0.908468,"\text{Not used}","int(1/((a + c*x^2)*(d + e*x)^2),x)","\frac{\ln\left(a^5\,e^8\,\sqrt{-a\,c}-c^3\,d^8\,{\left(-a\,c\right)}^{3/2}-36\,a^3\,d^2\,e^6\,{\left(-a\,c\right)}^{3/2}+a\,c^5\,d^8\,x+a^5\,c\,e^8\,x+70\,a\,d^4\,e^4\,{\left(-a\,c\right)}^{5/2}+36\,c\,d^6\,e^2\,{\left(-a\,c\right)}^{5/2}+36\,a^2\,c^4\,d^6\,e^2\,x+70\,a^3\,c^3\,d^4\,e^4\,x+36\,a^4\,c^2\,d^2\,e^6\,x\right)\,\left(c\,\left(\frac{d^2\,\sqrt{-a\,c}}{2}-a\,d\,e\right)-\frac{a\,e^2\,\sqrt{-a\,c}}{2}\right)}{a^3\,e^4+2\,a^2\,c\,d^2\,e^2+a\,c^2\,d^4}+\frac{\ln\left(c^3\,d^8\,{\left(-a\,c\right)}^{3/2}-a^5\,e^8\,\sqrt{-a\,c}+36\,a^3\,d^2\,e^6\,{\left(-a\,c\right)}^{3/2}+a\,c^5\,d^8\,x+a^5\,c\,e^8\,x-70\,a\,d^4\,e^4\,{\left(-a\,c\right)}^{5/2}-36\,c\,d^6\,e^2\,{\left(-a\,c\right)}^{5/2}+36\,a^2\,c^4\,d^6\,e^2\,x+70\,a^3\,c^3\,d^4\,e^4\,x+36\,a^4\,c^2\,d^2\,e^6\,x\right)\,\left(a\,\left(\frac{e^2\,\sqrt{-a\,c}}{2}-c\,d\,e\right)-\frac{c\,d^2\,\sqrt{-a\,c}}{2}\right)}{a^3\,e^4+2\,a^2\,c\,d^2\,e^2+a\,c^2\,d^4}-\frac{e}{\left(c\,d^2+a\,e^2\right)\,\left(d+e\,x\right)}+\frac{2\,c\,d\,e\,\ln\left(d+e\,x\right)}{{\left(c\,d^2+a\,e^2\right)}^2}","Not used",1,"(log(a^5*e^8*(-a*c)^(1/2) - c^3*d^8*(-a*c)^(3/2) - 36*a^3*d^2*e^6*(-a*c)^(3/2) + a*c^5*d^8*x + a^5*c*e^8*x + 70*a*d^4*e^4*(-a*c)^(5/2) + 36*c*d^6*e^2*(-a*c)^(5/2) + 36*a^2*c^4*d^6*e^2*x + 70*a^3*c^3*d^4*e^4*x + 36*a^4*c^2*d^2*e^6*x)*(c*((d^2*(-a*c)^(1/2))/2 - a*d*e) - (a*e^2*(-a*c)^(1/2))/2))/(a^3*e^4 + a*c^2*d^4 + 2*a^2*c*d^2*e^2) + (log(c^3*d^8*(-a*c)^(3/2) - a^5*e^8*(-a*c)^(1/2) + 36*a^3*d^2*e^6*(-a*c)^(3/2) + a*c^5*d^8*x + a^5*c*e^8*x - 70*a*d^4*e^4*(-a*c)^(5/2) - 36*c*d^6*e^2*(-a*c)^(5/2) + 36*a^2*c^4*d^6*e^2*x + 70*a^3*c^3*d^4*e^4*x + 36*a^4*c^2*d^2*e^6*x)*(a*((e^2*(-a*c)^(1/2))/2 - c*d*e) - (c*d^2*(-a*c)^(1/2))/2))/(a^3*e^4 + a*c^2*d^4 + 2*a^2*c*d^2*e^2) - e/((a*e^2 + c*d^2)*(d + e*x)) + (2*c*d*e*log(d + e*x))/(a*e^2 + c*d^2)^2","B"
504,1,745,176,1.139951,"\text{Not used}","int(1/((a + c*x^2)*(d + e*x)^3),x)","\frac{\ln\left(d+e\,x\right)\,\left(3\,c^2\,d^2\,e-a\,c\,e^3\right)}{a^3\,e^6+3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6}-\frac{\ln\left(c^2\,d^{10}\,{\left(-a\,c^3\right)}^{3/2}-9\,a^6\,e^{10}\,\sqrt{-a\,c^3}+9\,a^6\,c^2\,e^{10}\,x+106\,a^2\,d^6\,e^4\,{\left(-a\,c^3\right)}^{3/2}+a\,c^7\,d^{10}\,x+6\,a^4\,c^2\,d^4\,e^6\,\sqrt{-a\,c^3}+77\,a\,c\,d^8\,e^2\,{\left(-a\,c^3\right)}^{3/2}+77\,a^2\,c^6\,d^8\,e^2\,x+106\,a^3\,c^5\,d^6\,e^4\,x-6\,a^4\,c^4\,d^4\,e^6\,x-27\,a^5\,c^3\,d^2\,e^8\,x+27\,a^5\,c\,d^2\,e^8\,\sqrt{-a\,c^3}\right)\,\left(c\,\left(\frac{d^3\,\sqrt{-a\,c^3}}{2}-\frac{a^2\,e^3}{2}\right)+\frac{3\,a\,c^2\,d^2\,e}{2}-\frac{3\,a\,d\,e^2\,\sqrt{-a\,c^3}}{2}\right)}{a^4\,e^6+3\,a^3\,c\,d^2\,e^4+3\,a^2\,c^2\,d^4\,e^2+a\,c^3\,d^6}-\frac{\ln\left(c^2\,d^{10}\,{\left(-a\,c^3\right)}^{3/2}-9\,a^6\,e^{10}\,\sqrt{-a\,c^3}-9\,a^6\,c^2\,e^{10}\,x+106\,a^2\,d^6\,e^4\,{\left(-a\,c^3\right)}^{3/2}-a\,c^7\,d^{10}\,x+6\,a^4\,c^2\,d^4\,e^6\,\sqrt{-a\,c^3}+77\,a\,c\,d^8\,e^2\,{\left(-a\,c^3\right)}^{3/2}-77\,a^2\,c^6\,d^8\,e^2\,x-106\,a^3\,c^5\,d^6\,e^4\,x+6\,a^4\,c^4\,d^4\,e^6\,x+27\,a^5\,c^3\,d^2\,e^8\,x+27\,a^5\,c\,d^2\,e^8\,\sqrt{-a\,c^3}\right)\,\left(\frac{3\,a\,c^2\,d^2\,e}{2}-c\,\left(\frac{d^3\,\sqrt{-a\,c^3}}{2}+\frac{a^2\,e^3}{2}\right)+\frac{3\,a\,d\,e^2\,\sqrt{-a\,c^3}}{2}\right)}{a^4\,e^6+3\,a^3\,c\,d^2\,e^4+3\,a^2\,c^2\,d^4\,e^2+a\,c^3\,d^6}-\frac{\frac{5\,c\,d^2\,e+a\,e^3}{2\,\left(a^2\,e^4+2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}+\frac{2\,c\,d\,e^2\,x}{a^2\,e^4+2\,a\,c\,d^2\,e^2+c^2\,d^4}}{d^2+2\,d\,e\,x+e^2\,x^2}","Not used",1,"(log(d + e*x)*(3*c^2*d^2*e - a*c*e^3))/(a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4) - (log(c^2*d^10*(-a*c^3)^(3/2) - 9*a^6*e^10*(-a*c^3)^(1/2) + 9*a^6*c^2*e^10*x + 106*a^2*d^6*e^4*(-a*c^3)^(3/2) + a*c^7*d^10*x + 6*a^4*c^2*d^4*e^6*(-a*c^3)^(1/2) + 77*a*c*d^8*e^2*(-a*c^3)^(3/2) + 77*a^2*c^6*d^8*e^2*x + 106*a^3*c^5*d^6*e^4*x - 6*a^4*c^4*d^4*e^6*x - 27*a^5*c^3*d^2*e^8*x + 27*a^5*c*d^2*e^8*(-a*c^3)^(1/2))*(c*((d^3*(-a*c^3)^(1/2))/2 - (a^2*e^3)/2) + (3*a*c^2*d^2*e)/2 - (3*a*d*e^2*(-a*c^3)^(1/2))/2))/(a^4*e^6 + a*c^3*d^6 + 3*a^3*c*d^2*e^4 + 3*a^2*c^2*d^4*e^2) - (log(c^2*d^10*(-a*c^3)^(3/2) - 9*a^6*e^10*(-a*c^3)^(1/2) - 9*a^6*c^2*e^10*x + 106*a^2*d^6*e^4*(-a*c^3)^(3/2) - a*c^7*d^10*x + 6*a^4*c^2*d^4*e^6*(-a*c^3)^(1/2) + 77*a*c*d^8*e^2*(-a*c^3)^(3/2) - 77*a^2*c^6*d^8*e^2*x - 106*a^3*c^5*d^6*e^4*x + 6*a^4*c^4*d^4*e^6*x + 27*a^5*c^3*d^2*e^8*x + 27*a^5*c*d^2*e^8*(-a*c^3)^(1/2))*((3*a*c^2*d^2*e)/2 - c*((d^3*(-a*c^3)^(1/2))/2 + (a^2*e^3)/2) + (3*a*d*e^2*(-a*c^3)^(1/2))/2))/(a^4*e^6 + a*c^3*d^6 + 3*a^3*c*d^2*e^4 + 3*a^2*c^2*d^4*e^2) - ((a*e^3 + 5*c*d^2*e)/(2*(a^2*e^4 + c^2*d^4 + 2*a*c*d^2*e^2)) + (2*c*d*e^2*x)/(a^2*e^4 + c^2*d^4 + 2*a*c*d^2*e^2))/(d^2 + e^2*x^2 + 2*d*e*x)","B"
505,1,191,190,0.159030,"\text{Not used}","int((d + e*x)^5/(a + c*x^2)^2,x)","\frac{e^5\,x^2}{2\,c^2}-\frac{\frac{a^2\,e^5-10\,a\,c\,d^2\,e^3+5\,c^2\,d^4\,e}{2\,c}-\frac{x\,\left(5\,a^2\,d\,e^4-10\,a\,c\,d^3\,e^2+c^2\,d^5\right)}{2\,a}}{c^3\,x^2+a\,c^2}-\frac{\ln\left(c\,x^2+a\right)\,\left(32\,a^4\,c^3\,e^5-160\,a^3\,c^4\,d^2\,e^3\right)}{32\,a^3\,c^6}+\frac{5\,d\,e^4\,x}{c^2}+\frac{d\,\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)\,\left(-15\,a^2\,e^4+10\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{2\,a^{3/2}\,c^{5/2}}","Not used",1,"(e^5*x^2)/(2*c^2) - ((a^2*e^5 + 5*c^2*d^4*e - 10*a*c*d^2*e^3)/(2*c) - (x*(c^2*d^5 + 5*a^2*d*e^4 - 10*a*c*d^3*e^2))/(2*a))/(a*c^2 + c^3*x^2) - (log(a + c*x^2)*(32*a^4*c^3*e^5 - 160*a^3*c^4*d^2*e^3))/(32*a^3*c^6) + (5*d*e^4*x)/c^2 + (d*atan((c^(1/2)*x)/a^(1/2))*(c^2*d^4 - 15*a^2*e^4 + 10*a*c*d^2*e^2))/(2*a^(3/2)*c^(5/2))","B"
506,1,131,149,0.337923,"\text{Not used}","int((d + e*x)^4/(a + c*x^2)^2,x)","\frac{\frac{x\,\left(a^2\,e^4-6\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{2\,a}+2\,a\,d\,e^3-2\,c\,d^3\,e}{c^3\,x^2+a\,c^2}+\frac{e^4\,x}{c^2}+\frac{2\,d\,e^3\,\ln\left(c\,x^2+a\right)}{c^2}+\frac{\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)\,\left(-3\,a^2\,e^4+6\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{2\,a^{3/2}\,c^{5/2}}","Not used",1,"((x*(a^2*e^4 + c^2*d^4 - 6*a*c*d^2*e^2))/(2*a) + 2*a*d*e^3 - 2*c*d^3*e)/(a*c^2 + c^3*x^2) + (e^4*x)/c^2 + (2*d*e^3*log(a + c*x^2))/c^2 + (atan((c^(1/2)*x)/a^(1/2))*(c^2*d^4 - 3*a^2*e^4 + 6*a*c*d^2*e^2))/(2*a^(3/2)*c^(5/2))","B"
507,1,143,109,0.327294,"\text{Not used}","int((d + e*x)^3/(a + c*x^2)^2,x)","\frac{d^3\,x}{2\,\left(a^2+c\,a\,x^2\right)}-\frac{3\,d^2\,e}{2\,\left(c^2\,x^2+a\,c\right)}+\frac{e^3\,\ln\left(c\,x^2+a\right)}{2\,c^2}+\frac{a\,e^3}{2\,\left(c^3\,x^2+a\,c^2\right)}+\frac{d^3\,\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)}{2\,a^{3/2}\,\sqrt{c}}-\frac{3\,d\,e^2\,x}{2\,\left(c^2\,x^2+a\,c\right)}+\frac{3\,d\,e^2\,\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)}{2\,\sqrt{a}\,c^{3/2}}","Not used",1,"(d^3*x)/(2*(a^2 + a*c*x^2)) - (3*d^2*e)/(2*(a*c + c^2*x^2)) + (e^3*log(a + c*x^2))/(2*c^2) + (a*e^3)/(2*(a*c^2 + c^3*x^2)) + (d^3*atan((c^(1/2)*x)/a^(1/2)))/(2*a^(3/2)*c^(1/2)) - (3*d*e^2*x)/(2*(a*c + c^2*x^2)) + (3*d*e^2*atan((c^(1/2)*x)/a^(1/2)))/(2*a^(1/2)*c^(3/2))","B"
508,1,68,72,0.323069,"\text{Not used}","int((d + e*x)^2/(a + c*x^2)^2,x)","\frac{\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)\,\left(c\,d^2+a\,e^2\right)}{2\,a^{3/2}\,c^{3/2}}-\frac{\frac{d\,e}{c}+\frac{x\,\left(a\,e^2-c\,d^2\right)}{2\,a\,c}}{c\,x^2+a}","Not used",1,"(atan((c^(1/2)*x)/a^(1/2))*(a*e^2 + c*d^2))/(2*a^(3/2)*c^(3/2)) - ((d*e)/c + (x*(a*e^2 - c*d^2))/(2*a*c))/(a + c*x^2)","B"
509,1,44,57,0.312383,"\text{Not used}","int((d + e*x)/(a + c*x^2)^2,x)","\frac{d\,\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)}{2\,a^{3/2}\,\sqrt{c}}-\frac{\frac{e}{2\,c}-\frac{d\,x}{2\,a}}{c\,x^2+a}","Not used",1,"(d*atan((c^(1/2)*x)/a^(1/2)))/(2*a^(3/2)*c^(1/2)) - (e/(2*c) - (d*x)/(2*a))/(a + c*x^2)","B"
510,1,609,142,1.040388,"\text{Not used}","int(1/((a + c*x^2)^2*(d + e*x)),x)","\frac{\frac{e}{2\,\left(c\,d^2+a\,e^2\right)}+\frac{c\,d\,x}{2\,a\,\left(c\,d^2+a\,e^2\right)}}{c\,x^2+a}+\frac{e^3\,\ln\left(d+e\,x\right)}{{\left(c\,d^2+a\,e^2\right)}^2}+\frac{\ln\left(36\,a^7\,e^{10}\,\sqrt{-a^3\,c}+a^3\,c^6\,d^{10}\,x+a^2\,c^5\,d^{10}\,\sqrt{-a^3\,c}-81\,a^3\,d^2\,e^8\,{\left(-a^3\,c\right)}^{3/2}-8\,c^3\,d^8\,e^2\,{\left(-a^3\,c\right)}^{3/2}+36\,a^8\,c\,e^{10}\,x+8\,a^4\,c^5\,d^8\,e^2\,x+22\,a^5\,c^4\,d^6\,e^4\,x+60\,a^6\,c^3\,d^4\,e^6\,x+81\,a^7\,c^2\,d^2\,e^8\,x-22\,a\,c^2\,d^6\,e^4\,{\left(-a^3\,c\right)}^{3/2}-60\,a^2\,c\,d^4\,e^6\,{\left(-a^3\,c\right)}^{3/2}\right)\,\left(c\,d^3\,\sqrt{-a^3\,c}-2\,a^3\,e^3+3\,a\,d\,e^2\,\sqrt{-a^3\,c}\right)}{4\,\left(a^5\,e^4+2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}-\frac{\ln\left(a^3\,c^6\,d^{10}\,x-36\,a^7\,e^{10}\,\sqrt{-a^3\,c}-a^2\,c^5\,d^{10}\,\sqrt{-a^3\,c}+81\,a^3\,d^2\,e^8\,{\left(-a^3\,c\right)}^{3/2}+8\,c^3\,d^8\,e^2\,{\left(-a^3\,c\right)}^{3/2}+36\,a^8\,c\,e^{10}\,x+8\,a^4\,c^5\,d^8\,e^2\,x+22\,a^5\,c^4\,d^6\,e^4\,x+60\,a^6\,c^3\,d^4\,e^6\,x+81\,a^7\,c^2\,d^2\,e^8\,x+22\,a\,c^2\,d^6\,e^4\,{\left(-a^3\,c\right)}^{3/2}+60\,a^2\,c\,d^4\,e^6\,{\left(-a^3\,c\right)}^{3/2}\right)\,\left(2\,a^3\,e^3+c\,d^3\,\sqrt{-a^3\,c}+3\,a\,d\,e^2\,\sqrt{-a^3\,c}\right)}{4\,\left(a^5\,e^4+2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}","Not used",1,"(e/(2*(a*e^2 + c*d^2)) + (c*d*x)/(2*a*(a*e^2 + c*d^2)))/(a + c*x^2) + (e^3*log(d + e*x))/(a*e^2 + c*d^2)^2 + (log(36*a^7*e^10*(-a^3*c)^(1/2) + a^3*c^6*d^10*x + a^2*c^5*d^10*(-a^3*c)^(1/2) - 81*a^3*d^2*e^8*(-a^3*c)^(3/2) - 8*c^3*d^8*e^2*(-a^3*c)^(3/2) + 36*a^8*c*e^10*x + 8*a^4*c^5*d^8*e^2*x + 22*a^5*c^4*d^6*e^4*x + 60*a^6*c^3*d^4*e^6*x + 81*a^7*c^2*d^2*e^8*x - 22*a*c^2*d^6*e^4*(-a^3*c)^(3/2) - 60*a^2*c*d^4*e^6*(-a^3*c)^(3/2))*(c*d^3*(-a^3*c)^(1/2) - 2*a^3*e^3 + 3*a*d*e^2*(-a^3*c)^(1/2)))/(4*(a^5*e^4 + a^3*c^2*d^4 + 2*a^4*c*d^2*e^2)) - (log(a^3*c^6*d^10*x - 36*a^7*e^10*(-a^3*c)^(1/2) - a^2*c^5*d^10*(-a^3*c)^(1/2) + 81*a^3*d^2*e^8*(-a^3*c)^(3/2) + 8*c^3*d^8*e^2*(-a^3*c)^(3/2) + 36*a^8*c*e^10*x + 8*a^4*c^5*d^8*e^2*x + 22*a^5*c^4*d^6*e^4*x + 60*a^6*c^3*d^4*e^6*x + 81*a^7*c^2*d^2*e^8*x + 22*a*c^2*d^6*e^4*(-a^3*c)^(3/2) + 60*a^2*c*d^4*e^6*(-a^3*c)^(3/2))*(2*a^3*e^3 + c*d^3*(-a^3*c)^(1/2) + 3*a*d*e^2*(-a^3*c)^(1/2)))/(4*(a^5*e^4 + a^3*c^2*d^4 + 2*a^4*c*d^2*e^2))","B"
511,1,819,205,1.314497,"\text{Not used}","int(1/((a + c*x^2)^2*(d + e*x)^2),x)","\frac{4\,c\,d\,e^3\,\ln\left(d+e\,x\right)}{{\left(c\,d^2+a\,e^2\right)}^3}-\frac{\ln\left(c^5\,d^{12}\,{\left(-a^3\,c\right)}^{3/2}-9\,a^9\,e^{12}\,\sqrt{-a^3\,c}+a^4\,c^7\,d^{12}\,x-1119\,a\,d^4\,e^8\,{\left(-a^3\,c\right)}^{5/2}-612\,c\,d^6\,e^6\,{\left(-a^3\,c\right)}^{5/2}+558\,a^5\,d^2\,e^{10}\,{\left(-a^3\,c\right)}^{3/2}+9\,a^{10}\,c\,e^{12}\,x+55\,a^2\,c^3\,d^8\,e^4\,{\left(-a^3\,c\right)}^{3/2}+14\,a^5\,c^6\,d^{10}\,e^2\,x+55\,a^6\,c^5\,d^8\,e^4\,x+612\,a^7\,c^4\,d^6\,e^6\,x+1119\,a^8\,c^3\,d^4\,e^8\,x+558\,a^9\,c^2\,d^2\,e^{10}\,x+14\,a\,c^4\,d^{10}\,e^2\,{\left(-a^3\,c\right)}^{3/2}\right)\,\left(c\,\left(2\,a^3\,d\,e^3+\frac{3\,a\,d^2\,e^2\,\sqrt{-a^3\,c}}{2}\right)-\frac{3\,a^2\,e^4\,\sqrt{-a^3\,c}}{4}+\frac{c^2\,d^4\,\sqrt{-a^3\,c}}{4}\right)}{a^6\,e^6+3\,a^5\,c\,d^2\,e^4+3\,a^4\,c^2\,d^4\,e^2+a^3\,c^3\,d^6}-\frac{\ln\left(9\,a^9\,e^{12}\,\sqrt{-a^3\,c}-c^5\,d^{12}\,{\left(-a^3\,c\right)}^{3/2}+a^4\,c^7\,d^{12}\,x+1119\,a\,d^4\,e^8\,{\left(-a^3\,c\right)}^{5/2}+612\,c\,d^6\,e^6\,{\left(-a^3\,c\right)}^{5/2}-558\,a^5\,d^2\,e^{10}\,{\left(-a^3\,c\right)}^{3/2}+9\,a^{10}\,c\,e^{12}\,x-55\,a^2\,c^3\,d^8\,e^4\,{\left(-a^3\,c\right)}^{3/2}+14\,a^5\,c^6\,d^{10}\,e^2\,x+55\,a^6\,c^5\,d^8\,e^4\,x+612\,a^7\,c^4\,d^6\,e^6\,x+1119\,a^8\,c^3\,d^4\,e^8\,x+558\,a^9\,c^2\,d^2\,e^{10}\,x-14\,a\,c^4\,d^{10}\,e^2\,{\left(-a^3\,c\right)}^{3/2}\right)\,\left(c\,\left(2\,a^3\,d\,e^3-\frac{3\,a\,d^2\,e^2\,\sqrt{-a^3\,c}}{2}\right)+\frac{3\,a^2\,e^4\,\sqrt{-a^3\,c}}{4}-\frac{c^2\,d^4\,\sqrt{-a^3\,c}}{4}\right)}{a^6\,e^6+3\,a^5\,c\,d^2\,e^4+3\,a^4\,c^2\,d^4\,e^2+a^3\,c^3\,d^6}-\frac{\frac{a\,e^3-c\,d^2\,e}{{\left(c\,d^2+a\,e^2\right)}^2}-\frac{c\,d\,x}{2\,a\,\left(c\,d^2+a\,e^2\right)}+\frac{c\,x^2\,\left(3\,a\,e^3-c\,d^2\,e\right)}{2\,a\,\left(a^2\,e^4+2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}}{c\,e\,x^3+c\,d\,x^2+a\,e\,x+a\,d}","Not used",1,"(4*c*d*e^3*log(d + e*x))/(a*e^2 + c*d^2)^3 - (log(c^5*d^12*(-a^3*c)^(3/2) - 9*a^9*e^12*(-a^3*c)^(1/2) + a^4*c^7*d^12*x - 1119*a*d^4*e^8*(-a^3*c)^(5/2) - 612*c*d^6*e^6*(-a^3*c)^(5/2) + 558*a^5*d^2*e^10*(-a^3*c)^(3/2) + 9*a^10*c*e^12*x + 55*a^2*c^3*d^8*e^4*(-a^3*c)^(3/2) + 14*a^5*c^6*d^10*e^2*x + 55*a^6*c^5*d^8*e^4*x + 612*a^7*c^4*d^6*e^6*x + 1119*a^8*c^3*d^4*e^8*x + 558*a^9*c^2*d^2*e^10*x + 14*a*c^4*d^10*e^2*(-a^3*c)^(3/2))*(c*(2*a^3*d*e^3 + (3*a*d^2*e^2*(-a^3*c)^(1/2))/2) - (3*a^2*e^4*(-a^3*c)^(1/2))/4 + (c^2*d^4*(-a^3*c)^(1/2))/4))/(a^6*e^6 + a^3*c^3*d^6 + 3*a^5*c*d^2*e^4 + 3*a^4*c^2*d^4*e^2) - (log(9*a^9*e^12*(-a^3*c)^(1/2) - c^5*d^12*(-a^3*c)^(3/2) + a^4*c^7*d^12*x + 1119*a*d^4*e^8*(-a^3*c)^(5/2) + 612*c*d^6*e^6*(-a^3*c)^(5/2) - 558*a^5*d^2*e^10*(-a^3*c)^(3/2) + 9*a^10*c*e^12*x - 55*a^2*c^3*d^8*e^4*(-a^3*c)^(3/2) + 14*a^5*c^6*d^10*e^2*x + 55*a^6*c^5*d^8*e^4*x + 612*a^7*c^4*d^6*e^6*x + 1119*a^8*c^3*d^4*e^8*x + 558*a^9*c^2*d^2*e^10*x - 14*a*c^4*d^10*e^2*(-a^3*c)^(3/2))*(c*(2*a^3*d*e^3 - (3*a*d^2*e^2*(-a^3*c)^(1/2))/2) + (3*a^2*e^4*(-a^3*c)^(1/2))/4 - (c^2*d^4*(-a^3*c)^(1/2))/4))/(a^6*e^6 + a^3*c^3*d^6 + 3*a^5*c*d^2*e^4 + 3*a^4*c^2*d^4*e^2) - ((a*e^3 - c*d^2*e)/(a*e^2 + c*d^2)^2 - (c*d*x)/(2*a*(a*e^2 + c*d^2)) + (c*x^2*(3*a*e^3 - c*d^2*e))/(2*a*(a^2*e^4 + c^2*d^4 + 2*a*c*d^2*e^2)))/(a*d + a*e*x + c*d*x^2 + c*e*x^3)","B"
512,1,467,198,0.243436,"\text{Not used}","int((d + e*x)^5/(a + c*x^2)^3,x)","\frac{e^5\,\ln\left(c\,x^2+a\right)}{2\,c^3}-\frac{5\,d^4\,e}{4\,\left(a^2\,c+2\,a\,c^2\,x^2+c^3\,x^4\right)}+\frac{5\,d^5\,x}{8\,\left(a^3+2\,a^2\,c\,x^2+a\,c^2\,x^4\right)}+\frac{3\,a^2\,e^5}{4\,\left(a^2\,c^3+2\,a\,c^4\,x^2+c^5\,x^4\right)}-\frac{5\,a\,d^2\,e^3}{2\,\left(a^2\,c^2+2\,a\,c^3\,x^2+c^4\,x^4\right)}+\frac{a\,e^5\,x^2}{a^2\,c^2+2\,a\,c^3\,x^2+c^4\,x^4}-\frac{5\,d^2\,e^3\,x^2}{a^2\,c+2\,a\,c^2\,x^2+c^3\,x^4}+\frac{3\,d^5\,\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)}{8\,a^{5/2}\,\sqrt{c}}+\frac{3\,c\,d^5\,x^3}{8\,\left(a^4+2\,a^3\,c\,x^2+a^2\,c^2\,x^4\right)}+\frac{5\,d^3\,e^2\,x^3}{4\,\left(a^3+2\,a^2\,c\,x^2+a\,c^2\,x^4\right)}-\frac{5\,d^3\,e^2\,x}{4\,\left(a^2\,c+2\,a\,c^2\,x^2+c^3\,x^4\right)}-\frac{25\,d\,e^4\,x^3}{8\,\left(a^2\,c+2\,a\,c^2\,x^2+c^3\,x^4\right)}+\frac{5\,d^3\,e^2\,\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)}{4\,a^{3/2}\,c^{3/2}}-\frac{15\,a\,d\,e^4\,x}{8\,\left(a^2\,c^2+2\,a\,c^3\,x^2+c^4\,x^4\right)}+\frac{15\,d\,e^4\,\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)}{8\,\sqrt{a}\,c^{5/2}}","Not used",1,"(e^5*log(a + c*x^2))/(2*c^3) - (5*d^4*e)/(4*(a^2*c + c^3*x^4 + 2*a*c^2*x^2)) + (5*d^5*x)/(8*(a^3 + 2*a^2*c*x^2 + a*c^2*x^4)) + (3*a^2*e^5)/(4*(a^2*c^3 + c^5*x^4 + 2*a*c^4*x^2)) - (5*a*d^2*e^3)/(2*(a^2*c^2 + c^4*x^4 + 2*a*c^3*x^2)) + (a*e^5*x^2)/(a^2*c^2 + c^4*x^4 + 2*a*c^3*x^2) - (5*d^2*e^3*x^2)/(a^2*c + c^3*x^4 + 2*a*c^2*x^2) + (3*d^5*atan((c^(1/2)*x)/a^(1/2)))/(8*a^(5/2)*c^(1/2)) + (3*c*d^5*x^3)/(8*(a^4 + 2*a^3*c*x^2 + a^2*c^2*x^4)) + (5*d^3*e^2*x^3)/(4*(a^3 + 2*a^2*c*x^2 + a*c^2*x^4)) - (5*d^3*e^2*x)/(4*(a^2*c + c^3*x^4 + 2*a*c^2*x^2)) - (25*d*e^4*x^3)/(8*(a^2*c + c^3*x^4 + 2*a*c^2*x^2)) + (5*d^3*e^2*atan((c^(1/2)*x)/a^(1/2)))/(4*a^(3/2)*c^(3/2)) - (15*a*d*e^4*x)/(8*(a^2*c^2 + c^4*x^4 + 2*a*c^3*x^2)) + (15*d*e^4*atan((c^(1/2)*x)/a^(1/2)))/(8*a^(1/2)*c^(5/2))","B"
513,1,197,120,0.163287,"\text{Not used}","int((d + e*x)^4/(a + c*x^2)^3,x)","\frac{3\,\mathrm{atan}\left(\frac{\sqrt{c}\,x\,{\left(c\,d^2+a\,e^2\right)}^2}{\sqrt{a}\,\left(a^2\,e^4+2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}\right)\,{\left(c\,d^2+a\,e^2\right)}^2}{8\,a^{5/2}\,c^{5/2}}-\frac{\frac{2\,d\,e^3\,x^2}{c}+\frac{x\,\left(3\,a^2\,e^4+6\,a\,c\,d^2\,e^2-5\,c^2\,d^4\right)}{8\,a\,c^2}+\frac{d\,e\,\left(c\,d^2+a\,e^2\right)}{c^2}-\frac{x^3\,\left(-5\,a^2\,e^4+6\,a\,c\,d^2\,e^2+3\,c^2\,d^4\right)}{8\,a^2\,c}}{a^2+2\,a\,c\,x^2+c^2\,x^4}","Not used",1,"(3*atan((c^(1/2)*x*(a*e^2 + c*d^2)^2)/(a^(1/2)*(a^2*e^4 + c^2*d^4 + 2*a*c*d^2*e^2)))*(a*e^2 + c*d^2)^2)/(8*a^(5/2)*c^(5/2)) - ((2*d*e^3*x^2)/c + (x*(3*a^2*e^4 - 5*c^2*d^4 + 6*a*c*d^2*e^2))/(8*a*c^2) + (d*e*(a*e^2 + c*d^2))/c^2 - (x^3*(3*c^2*d^4 - 5*a^2*e^4 + 6*a*c*d^2*e^2))/(8*a^2*c))/(a^2 + c^2*x^4 + 2*a*c*x^2)","B"
514,1,125,98,0.132180,"\text{Not used}","int((d + e*x)^3/(a + c*x^2)^3,x)","\frac{3\,d\,\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)\,\left(c\,d^2+a\,e^2\right)}{8\,a^{5/2}\,c^{3/2}}-\frac{\frac{e^3\,x^2}{2\,c}+\frac{e\,\left(3\,c\,d^2+a\,e^2\right)}{4\,c^2}-\frac{3\,d\,x^3\,\left(c\,d^2+a\,e^2\right)}{8\,a^2}+\frac{d\,x\,\left(3\,a\,e^2-5\,c\,d^2\right)}{8\,a\,c}}{a^2+2\,a\,c\,x^2+c^2\,x^4}","Not used",1,"(3*d*atan((c^(1/2)*x)/a^(1/2))*(a*e^2 + c*d^2))/(8*a^(5/2)*c^(3/2)) - ((e^3*x^2)/(2*c) + (e*(a*e^2 + 3*c*d^2))/(4*c^2) - (3*d*x^3*(a*e^2 + c*d^2))/(8*a^2) + (d*x*(3*a*e^2 - 5*c*d^2))/(8*a*c))/(a^2 + c^2*x^4 + 2*a*c*x^2)","B"
515,1,101,113,0.350129,"\text{Not used}","int((d + e*x)^2/(a + c*x^2)^3,x)","\frac{\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)\,\left(3\,c\,d^2+a\,e^2\right)}{8\,a^{5/2}\,c^{3/2}}-\frac{\frac{d\,e}{2\,c}-\frac{x^3\,\left(3\,c\,d^2+a\,e^2\right)}{8\,a^2}+\frac{x\,\left(a\,e^2-5\,c\,d^2\right)}{8\,a\,c}}{a^2+2\,a\,c\,x^2+c^2\,x^4}","Not used",1,"(atan((c^(1/2)*x)/a^(1/2))*(a*e^2 + 3*c*d^2))/(8*a^(5/2)*c^(3/2)) - ((d*e)/(2*c) - (x^3*(a*e^2 + 3*c*d^2))/(8*a^2) + (x*(a*e^2 - 5*c*d^2))/(8*a*c))/(a^2 + c^2*x^4 + 2*a*c*x^2)","B"
516,1,64,75,0.324894,"\text{Not used}","int((d + e*x)/(a + c*x^2)^3,x)","\frac{\frac{5\,d\,x}{8\,a}-\frac{e}{4\,c}+\frac{3\,c\,d\,x^3}{8\,a^2}}{a^2+2\,a\,c\,x^2+c^2\,x^4}+\frac{3\,d\,\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)}{8\,a^{5/2}\,\sqrt{c}}","Not used",1,"((5*d*x)/(8*a) - e/(4*c) + (3*c*d*x^3)/(8*a^2))/(a^2 + c^2*x^4 + 2*a*c*x^2) + (3*d*atan((c^(1/2)*x)/a^(1/2)))/(8*a^(5/2)*c^(1/2))","B"
517,1,987,212,1.430886,"\text{Not used}","int(1/((a + c*x^2)^3*(d + e*x)),x)","\frac{\frac{c\,d^2\,e+3\,a\,e^3}{4\,\left(a^2\,e^4+2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}+\frac{x^3\,\left(3\,c^3\,d^3+7\,a\,c^2\,d\,e^2\right)}{8\,a^2\,\left(a^2\,e^4+2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}+\frac{x\,\left(5\,c^2\,d^3+9\,a\,c\,d\,e^2\right)}{8\,a\,\left(a^2\,e^4+2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}+\frac{c\,e^3\,x^2}{2\,\left(a^2\,e^4+2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}}{a^2+2\,a\,c\,x^2+c^2\,x^4}+\frac{e^5\,\ln\left(d+e\,x\right)}{{\left(c\,d^2+a\,e^2\right)}^3}-\frac{\ln\left(9\,c^6\,d^{14}\,{\left(-a^5\,c\right)}^{3/2}-576\,a^{12}\,e^{14}\,\sqrt{-a^5\,c}-1326\,d^4\,e^{10}\,{\left(-a^5\,c\right)}^{5/2}+9\,a^7\,c^8\,d^{14}\,x+1377\,a^6\,d^2\,e^{12}\,{\left(-a^5\,c\right)}^{3/2}+576\,a^{14}\,c\,e^{14}\,x+319\,a^2\,c^4\,d^{10}\,e^4\,{\left(-a^5\,c\right)}^{3/2}+740\,a^3\,c^3\,d^8\,e^6\,{\left(-a^5\,c\right)}^{3/2}+1015\,a^4\,c^2\,d^6\,e^8\,{\left(-a^5\,c\right)}^{3/2}+78\,a^8\,c^7\,d^{12}\,e^2\,x+319\,a^9\,c^6\,d^{10}\,e^4\,x+740\,a^{10}\,c^5\,d^8\,e^6\,x+1015\,a^{11}\,c^4\,d^6\,e^8\,x+1326\,a^{12}\,c^3\,d^4\,e^{10}\,x+1377\,a^{13}\,c^2\,d^2\,e^{12}\,x+78\,a\,c^5\,d^{12}\,e^2\,{\left(-a^5\,c\right)}^{3/2}\right)\,\left(8\,a^5\,e^5+3\,c^2\,d^5\,\sqrt{-a^5\,c}+15\,a^2\,d\,e^4\,\sqrt{-a^5\,c}+10\,a\,c\,d^3\,e^2\,\sqrt{-a^5\,c}\right)}{16\,\left(a^8\,e^6+3\,a^7\,c\,d^2\,e^4+3\,a^6\,c^2\,d^4\,e^2+a^5\,c^3\,d^6\right)}+\frac{\ln\left(576\,a^{10}\,e^{14}\,\sqrt{-a^5\,c}+9\,a^5\,c^8\,d^{14}\,x+9\,a^3\,c^7\,d^{14}\,\sqrt{-a^5\,c}-1377\,a^4\,d^2\,e^{12}\,{\left(-a^5\,c\right)}^{3/2}-319\,c^4\,d^{10}\,e^4\,{\left(-a^5\,c\right)}^{3/2}+576\,a^{12}\,c\,e^{14}\,x-1015\,a^2\,c^2\,d^6\,e^8\,{\left(-a^5\,c\right)}^{3/2}+78\,a^4\,c^6\,d^{12}\,e^2\,\sqrt{-a^5\,c}+78\,a^6\,c^7\,d^{12}\,e^2\,x+319\,a^7\,c^6\,d^{10}\,e^4\,x+740\,a^8\,c^5\,d^8\,e^6\,x+1015\,a^9\,c^4\,d^6\,e^8\,x+1326\,a^{10}\,c^3\,d^4\,e^{10}\,x+1377\,a^{11}\,c^2\,d^2\,e^{12}\,x-740\,a\,c^3\,d^8\,e^6\,{\left(-a^5\,c\right)}^{3/2}-1326\,a^3\,c\,d^4\,e^{10}\,{\left(-a^5\,c\right)}^{3/2}\right)\,\left(3\,c^2\,d^5\,\sqrt{-a^5\,c}-8\,a^5\,e^5+15\,a^2\,d\,e^4\,\sqrt{-a^5\,c}+10\,a\,c\,d^3\,e^2\,\sqrt{-a^5\,c}\right)}{16\,\left(a^8\,e^6+3\,a^7\,c\,d^2\,e^4+3\,a^6\,c^2\,d^4\,e^2+a^5\,c^3\,d^6\right)}","Not used",1,"((3*a*e^3 + c*d^2*e)/(4*(a^2*e^4 + c^2*d^4 + 2*a*c*d^2*e^2)) + (x^3*(3*c^3*d^3 + 7*a*c^2*d*e^2))/(8*a^2*(a^2*e^4 + c^2*d^4 + 2*a*c*d^2*e^2)) + (x*(5*c^2*d^3 + 9*a*c*d*e^2))/(8*a*(a^2*e^4 + c^2*d^4 + 2*a*c*d^2*e^2)) + (c*e^3*x^2)/(2*(a^2*e^4 + c^2*d^4 + 2*a*c*d^2*e^2)))/(a^2 + c^2*x^4 + 2*a*c*x^2) + (e^5*log(d + e*x))/(a*e^2 + c*d^2)^3 - (log(9*c^6*d^14*(-a^5*c)^(3/2) - 576*a^12*e^14*(-a^5*c)^(1/2) - 1326*d^4*e^10*(-a^5*c)^(5/2) + 9*a^7*c^8*d^14*x + 1377*a^6*d^2*e^12*(-a^5*c)^(3/2) + 576*a^14*c*e^14*x + 319*a^2*c^4*d^10*e^4*(-a^5*c)^(3/2) + 740*a^3*c^3*d^8*e^6*(-a^5*c)^(3/2) + 1015*a^4*c^2*d^6*e^8*(-a^5*c)^(3/2) + 78*a^8*c^7*d^12*e^2*x + 319*a^9*c^6*d^10*e^4*x + 740*a^10*c^5*d^8*e^6*x + 1015*a^11*c^4*d^6*e^8*x + 1326*a^12*c^3*d^4*e^10*x + 1377*a^13*c^2*d^2*e^12*x + 78*a*c^5*d^12*e^2*(-a^5*c)^(3/2))*(8*a^5*e^5 + 3*c^2*d^5*(-a^5*c)^(1/2) + 15*a^2*d*e^4*(-a^5*c)^(1/2) + 10*a*c*d^3*e^2*(-a^5*c)^(1/2)))/(16*(a^8*e^6 + a^5*c^3*d^6 + 3*a^7*c*d^2*e^4 + 3*a^6*c^2*d^4*e^2)) + (log(576*a^10*e^14*(-a^5*c)^(1/2) + 9*a^5*c^8*d^14*x + 9*a^3*c^7*d^14*(-a^5*c)^(1/2) - 1377*a^4*d^2*e^12*(-a^5*c)^(3/2) - 319*c^4*d^10*e^4*(-a^5*c)^(3/2) + 576*a^12*c*e^14*x - 1015*a^2*c^2*d^6*e^8*(-a^5*c)^(3/2) + 78*a^4*c^6*d^12*e^2*(-a^5*c)^(1/2) + 78*a^6*c^7*d^12*e^2*x + 319*a^7*c^6*d^10*e^4*x + 740*a^8*c^5*d^8*e^6*x + 1015*a^9*c^4*d^6*e^8*x + 1326*a^10*c^3*d^4*e^10*x + 1377*a^11*c^2*d^2*e^12*x - 740*a*c^3*d^8*e^6*(-a^5*c)^(3/2) - 1326*a^3*c*d^4*e^10*(-a^5*c)^(3/2))*(3*c^2*d^5*(-a^5*c)^(1/2) - 8*a^5*e^5 + 15*a^2*d*e^4*(-a^5*c)^(1/2) + 10*a*c*d^3*e^2*(-a^5*c)^(1/2)))/(16*(a^8*e^6 + a^5*c^3*d^6 + 3*a^7*c*d^2*e^4 + 3*a^6*c^2*d^4*e^2))","B"
518,1,1296,300,1.842667,"\text{Not used}","int(1/((a + c*x^2)^3*(d + e*x)^2),x)","\frac{\frac{-2\,a^2\,e^5+5\,a\,c\,d^2\,e^3+c^2\,d^4\,e}{2\,\left(c\,d^2+a\,e^2\right)\,\left(a^2\,e^4+2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}+\frac{3\,x^3\,\left(c^3\,d^3+3\,a\,c^2\,d\,e^2\right)}{8\,a^2\,\left(a^2\,e^4+2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}+\frac{x\,\left(5\,c^2\,d^3+11\,a\,c\,d\,e^2\right)}{8\,a\,\left(a^2\,e^4+2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}+\frac{3\,x^4\,\left(-5\,a^2\,c^2\,e^5+4\,a\,c^3\,d^2\,e^3+c^4\,d^4\,e\right)}{8\,a^2\,\left(a^3\,e^6+3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6\right)}+\frac{x^2\,\left(-25\,a^2\,c\,e^5+28\,a\,c^2\,d^2\,e^3+5\,c^3\,d^4\,e\right)}{8\,a\,\left(c\,d^2+a\,e^2\right)\,\left(a^2\,e^4+2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}}{e\,a^2\,x+d\,a^2+2\,e\,a\,c\,x^3+2\,d\,a\,c\,x^2+e\,c^2\,x^5+d\,c^2\,x^4}-\frac{\ln\left(c^7\,d^{16}\,{\left(-a^5\,c\right)}^{3/2}-25\,a^{13}\,e^{16}\,\sqrt{-a^5\,c}+a^7\,c^9\,d^{16}\,x-4508\,a\,d^4\,e^{12}\,{\left(-a^5\,c\right)}^{5/2}-2644\,c\,d^6\,e^{10}\,{\left(-a^5\,c\right)}^{5/2}+2204\,a^7\,d^2\,e^{14}\,{\left(-a^5\,c\right)}^{3/2}+25\,a^{15}\,c\,e^{16}\,x+76\,a^2\,c^5\,d^{12}\,e^4\,{\left(-a^5\,c\right)}^{3/2}+260\,a^3\,c^4\,d^{10}\,e^6\,{\left(-a^5\,c\right)}^{3/2}+510\,a^4\,c^3\,d^8\,e^8\,{\left(-a^5\,c\right)}^{3/2}+12\,a^8\,c^8\,d^{14}\,e^2\,x+76\,a^9\,c^7\,d^{12}\,e^4\,x+260\,a^{10}\,c^6\,d^{10}\,e^6\,x+510\,a^{11}\,c^5\,d^8\,e^8\,x+2644\,a^{12}\,c^4\,d^6\,e^{10}\,x+4508\,a^{13}\,c^3\,d^4\,e^{12}\,x+2204\,a^{14}\,c^2\,d^2\,e^{14}\,x+12\,a\,c^6\,d^{14}\,e^2\,{\left(-a^5\,c\right)}^{3/2}\right)\,\left(c\,\left(3\,a^5\,d\,e^5+\frac{45\,a^2\,d^2\,e^4\,\sqrt{-a^5\,c}}{16}\right)-\frac{15\,a^3\,e^6\,\sqrt{-a^5\,c}}{16}+\frac{3\,c^3\,d^6\,\sqrt{-a^5\,c}}{16}+\frac{15\,a\,c^2\,d^4\,e^2\,\sqrt{-a^5\,c}}{16}\right)}{a^9\,e^8+4\,a^8\,c\,d^2\,e^6+6\,a^7\,c^2\,d^4\,e^4+4\,a^6\,c^3\,d^6\,e^2+a^5\,c^4\,d^8}-\frac{\ln\left(25\,a^{13}\,e^{16}\,\sqrt{-a^5\,c}-c^7\,d^{16}\,{\left(-a^5\,c\right)}^{3/2}+a^7\,c^9\,d^{16}\,x+4508\,a\,d^4\,e^{12}\,{\left(-a^5\,c\right)}^{5/2}+2644\,c\,d^6\,e^{10}\,{\left(-a^5\,c\right)}^{5/2}-2204\,a^7\,d^2\,e^{14}\,{\left(-a^5\,c\right)}^{3/2}+25\,a^{15}\,c\,e^{16}\,x-76\,a^2\,c^5\,d^{12}\,e^4\,{\left(-a^5\,c\right)}^{3/2}-260\,a^3\,c^4\,d^{10}\,e^6\,{\left(-a^5\,c\right)}^{3/2}-510\,a^4\,c^3\,d^8\,e^8\,{\left(-a^5\,c\right)}^{3/2}+12\,a^8\,c^8\,d^{14}\,e^2\,x+76\,a^9\,c^7\,d^{12}\,e^4\,x+260\,a^{10}\,c^6\,d^{10}\,e^6\,x+510\,a^{11}\,c^5\,d^8\,e^8\,x+2644\,a^{12}\,c^4\,d^6\,e^{10}\,x+4508\,a^{13}\,c^3\,d^4\,e^{12}\,x+2204\,a^{14}\,c^2\,d^2\,e^{14}\,x-12\,a\,c^6\,d^{14}\,e^2\,{\left(-a^5\,c\right)}^{3/2}\right)\,\left(c\,\left(3\,a^5\,d\,e^5-\frac{45\,a^2\,d^2\,e^4\,\sqrt{-a^5\,c}}{16}\right)+\frac{15\,a^3\,e^6\,\sqrt{-a^5\,c}}{16}-\frac{3\,c^3\,d^6\,\sqrt{-a^5\,c}}{16}-\frac{15\,a\,c^2\,d^4\,e^2\,\sqrt{-a^5\,c}}{16}\right)}{a^9\,e^8+4\,a^8\,c\,d^2\,e^6+6\,a^7\,c^2\,d^4\,e^4+4\,a^6\,c^3\,d^6\,e^2+a^5\,c^4\,d^8}+\frac{6\,c\,d\,e^5\,\ln\left(d+e\,x\right)}{{\left(c\,d^2+a\,e^2\right)}^4}","Not used",1,"((c^2*d^4*e - 2*a^2*e^5 + 5*a*c*d^2*e^3)/(2*(a*e^2 + c*d^2)*(a^2*e^4 + c^2*d^4 + 2*a*c*d^2*e^2)) + (3*x^3*(c^3*d^3 + 3*a*c^2*d*e^2))/(8*a^2*(a^2*e^4 + c^2*d^4 + 2*a*c*d^2*e^2)) + (x*(5*c^2*d^3 + 11*a*c*d*e^2))/(8*a*(a^2*e^4 + c^2*d^4 + 2*a*c*d^2*e^2)) + (3*x^4*(c^4*d^4*e - 5*a^2*c^2*e^5 + 4*a*c^3*d^2*e^3))/(8*a^2*(a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)) + (x^2*(5*c^3*d^4*e - 25*a^2*c*e^5 + 28*a*c^2*d^2*e^3))/(8*a*(a*e^2 + c*d^2)*(a^2*e^4 + c^2*d^4 + 2*a*c*d^2*e^2)))/(a^2*d + c^2*d*x^4 + c^2*e*x^5 + a^2*e*x + 2*a*c*d*x^2 + 2*a*c*e*x^3) - (log(c^7*d^16*(-a^5*c)^(3/2) - 25*a^13*e^16*(-a^5*c)^(1/2) + a^7*c^9*d^16*x - 4508*a*d^4*e^12*(-a^5*c)^(5/2) - 2644*c*d^6*e^10*(-a^5*c)^(5/2) + 2204*a^7*d^2*e^14*(-a^5*c)^(3/2) + 25*a^15*c*e^16*x + 76*a^2*c^5*d^12*e^4*(-a^5*c)^(3/2) + 260*a^3*c^4*d^10*e^6*(-a^5*c)^(3/2) + 510*a^4*c^3*d^8*e^8*(-a^5*c)^(3/2) + 12*a^8*c^8*d^14*e^2*x + 76*a^9*c^7*d^12*e^4*x + 260*a^10*c^6*d^10*e^6*x + 510*a^11*c^5*d^8*e^8*x + 2644*a^12*c^4*d^6*e^10*x + 4508*a^13*c^3*d^4*e^12*x + 2204*a^14*c^2*d^2*e^14*x + 12*a*c^6*d^14*e^2*(-a^5*c)^(3/2))*(c*(3*a^5*d*e^5 + (45*a^2*d^2*e^4*(-a^5*c)^(1/2))/16) - (15*a^3*e^6*(-a^5*c)^(1/2))/16 + (3*c^3*d^6*(-a^5*c)^(1/2))/16 + (15*a*c^2*d^4*e^2*(-a^5*c)^(1/2))/16))/(a^9*e^8 + a^5*c^4*d^8 + 4*a^8*c*d^2*e^6 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4) - (log(25*a^13*e^16*(-a^5*c)^(1/2) - c^7*d^16*(-a^5*c)^(3/2) + a^7*c^9*d^16*x + 4508*a*d^4*e^12*(-a^5*c)^(5/2) + 2644*c*d^6*e^10*(-a^5*c)^(5/2) - 2204*a^7*d^2*e^14*(-a^5*c)^(3/2) + 25*a^15*c*e^16*x - 76*a^2*c^5*d^12*e^4*(-a^5*c)^(3/2) - 260*a^3*c^4*d^10*e^6*(-a^5*c)^(3/2) - 510*a^4*c^3*d^8*e^8*(-a^5*c)^(3/2) + 12*a^8*c^8*d^14*e^2*x + 76*a^9*c^7*d^12*e^4*x + 260*a^10*c^6*d^10*e^6*x + 510*a^11*c^5*d^8*e^8*x + 2644*a^12*c^4*d^6*e^10*x + 4508*a^13*c^3*d^4*e^12*x + 2204*a^14*c^2*d^2*e^14*x - 12*a*c^6*d^14*e^2*(-a^5*c)^(3/2))*(c*(3*a^5*d*e^5 - (45*a^2*d^2*e^4*(-a^5*c)^(1/2))/16) + (15*a^3*e^6*(-a^5*c)^(1/2))/16 - (3*c^3*d^6*(-a^5*c)^(1/2))/16 - (15*a*c^2*d^4*e^2*(-a^5*c)^(1/2))/16))/(a^9*e^8 + a^5*c^4*d^8 + 4*a^8*c*d^2*e^6 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4) + (6*c*d*e^5*log(d + e*x))/(a*e^2 + c*d^2)^4","B"
519,1,263,155,0.438273,"\text{Not used}","int((d + e*x)^4/(a + c*x^2)^4,x)","\frac{\mathrm{atan}\left(\frac{\sqrt{c}\,x\,\left(c\,d^2+a\,e^2\right)\,\left(5\,c\,d^2+a\,e^2\right)}{\sqrt{a}\,\left(a^2\,e^4+6\,a\,c\,d^2\,e^2+5\,c^2\,d^4\right)}\right)\,\left(c\,d^2+a\,e^2\right)\,\left(5\,c\,d^2+a\,e^2\right)}{16\,a^{7/2}\,c^{5/2}}-\frac{\frac{d\,e^3\,x^2}{c}-\frac{x^5\,\left(a^2\,e^4+6\,a\,c\,d^2\,e^2+5\,c^2\,d^4\right)}{16\,a^3}+\frac{x\,\left(a^2\,e^4+6\,a\,c\,d^2\,e^2-11\,c^2\,d^4\right)}{16\,a\,c^2}+\frac{d\,e\,\left(2\,c\,d^2+a\,e^2\right)}{3\,c^2}-\frac{x^3\,\left(-a^2\,e^4+6\,a\,c\,d^2\,e^2+5\,c^2\,d^4\right)}{6\,a^2\,c}}{a^3+3\,a^2\,c\,x^2+3\,a\,c^2\,x^4+c^3\,x^6}","Not used",1,"(atan((c^(1/2)*x*(a*e^2 + c*d^2)*(a*e^2 + 5*c*d^2))/(a^(1/2)*(a^2*e^4 + 5*c^2*d^4 + 6*a*c*d^2*e^2)))*(a*e^2 + c*d^2)*(a*e^2 + 5*c*d^2))/(16*a^(7/2)*c^(5/2)) - ((d*e^3*x^2)/c - (x^5*(a^2*e^4 + 5*c^2*d^4 + 6*a*c*d^2*e^2))/(16*a^3) + (x*(a^2*e^4 - 11*c^2*d^4 + 6*a*c*d^2*e^2))/(16*a*c^2) + (d*e*(a*e^2 + 2*c*d^2))/(3*c^2) - (x^3*(5*c^2*d^4 - a^2*e^4 + 6*a*c*d^2*e^2))/(6*a^2*c))/(a^3 + c^3*x^6 + 3*a^2*c*x^2 + 3*a*c^2*x^4)","B"
520,1,163,156,0.133916,"\text{Not used}","int((d + e*x)^3/(a + c*x^2)^4,x)","\frac{d\,\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)\,\left(5\,c\,d^2+3\,a\,e^2\right)}{16\,a^{7/2}\,c^{3/2}}-\frac{\frac{e^3\,x^2}{4\,c}+\frac{e\,\left(6\,c\,d^2+a\,e^2\right)}{12\,c^2}-\frac{d\,x^3\,\left(5\,c\,d^2+3\,a\,e^2\right)}{6\,a^2}+\frac{d\,x\,\left(3\,a\,e^2-11\,c\,d^2\right)}{16\,a\,c}-\frac{c\,d\,x^5\,\left(5\,c\,d^2+3\,a\,e^2\right)}{16\,a^3}}{a^3+3\,a^2\,c\,x^2+3\,a\,c^2\,x^4+c^3\,x^6}","Not used",1,"(d*atan((c^(1/2)*x)/a^(1/2))*(3*a*e^2 + 5*c*d^2))/(16*a^(7/2)*c^(3/2)) - ((e^3*x^2)/(4*c) + (e*(a*e^2 + 6*c*d^2))/(12*c^2) - (d*x^3*(3*a*e^2 + 5*c*d^2))/(6*a^2) + (d*x*(3*a*e^2 - 11*c*d^2))/(16*a*c) - (c*d*x^5*(3*a*e^2 + 5*c*d^2))/(16*a^3))/(a^3 + c^3*x^6 + 3*a^2*c*x^2 + 3*a*c^2*x^4)","B"
521,1,132,145,0.356485,"\text{Not used}","int((d + e*x)^2/(a + c*x^2)^4,x)","\frac{\frac{x^3\,\left(5\,c\,d^2+a\,e^2\right)}{6\,a^2}-\frac{d\,e}{3\,c}-\frac{x\,\left(a\,e^2-11\,c\,d^2\right)}{16\,a\,c}+\frac{c\,x^5\,\left(5\,c\,d^2+a\,e^2\right)}{16\,a^3}}{a^3+3\,a^2\,c\,x^2+3\,a\,c^2\,x^4+c^3\,x^6}+\frac{\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)\,\left(5\,c\,d^2+a\,e^2\right)}{16\,a^{7/2}\,c^{3/2}}","Not used",1,"((x^3*(a*e^2 + 5*c*d^2))/(6*a^2) - (d*e)/(3*c) - (x*(a*e^2 - 11*c*d^2))/(16*a*c) + (c*x^5*(a*e^2 + 5*c*d^2))/(16*a^3))/(a^3 + c^3*x^6 + 3*a^2*c*x^2 + 3*a*c^2*x^4) + (atan((c^(1/2)*x)/a^(1/2))*(a*e^2 + 5*c*d^2))/(16*a^(7/2)*c^(3/2))","B"
522,1,87,93,0.090110,"\text{Not used}","int((d + e*x)/(a + c*x^2)^4,x)","\frac{\frac{11\,d\,x}{16\,a}-\frac{e}{6\,c}+\frac{5\,c^2\,d\,x^5}{16\,a^3}+\frac{5\,c\,d\,x^3}{6\,a^2}}{a^3+3\,a^2\,c\,x^2+3\,a\,c^2\,x^4+c^3\,x^6}+\frac{5\,d\,\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{a}}\right)}{16\,a^{7/2}\,\sqrt{c}}","Not used",1,"((11*d*x)/(16*a) - e/(6*c) + (5*c^2*d*x^5)/(16*a^3) + (5*c*d*x^3)/(6*a^2))/(a^3 + c^3*x^6 + 3*a^2*c*x^2 + 3*a*c^2*x^4) + (5*d*atan((c^(1/2)*x)/a^(1/2)))/(16*a^(7/2)*c^(1/2))","B"
523,1,1470,295,1.816389,"\text{Not used}","int(1/((a + c*x^2)^4*(d + e*x)),x)","\frac{\frac{11\,a^2\,e^5+7\,a\,c\,d^2\,e^3+2\,c^2\,d^4\,e}{12\,\left(a^3\,e^6+3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6\right)}+\frac{x^2\,\left(c^2\,d^2\,e^3+5\,a\,c\,e^5\right)}{4\,\left(a^3\,e^6+3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6\right)}+\frac{x\,\left(29\,a^2\,c\,d\,e^4+32\,a\,c^2\,d^3\,e^2+11\,c^3\,d^5\right)}{16\,a\,\left(a^3\,e^6+3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6\right)}+\frac{c^2\,e^5\,x^4}{2\,\left(a^3\,e^6+3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6\right)}+\frac{x^3\,\left(17\,a^2\,c^2\,d\,e^4+16\,a\,c^3\,d^3\,e^2+5\,c^4\,d^5\right)}{6\,a^2\,\left(a^3\,e^6+3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6\right)}+\frac{x^5\,\left(19\,a^2\,c^3\,d\,e^4+16\,a\,c^4\,d^3\,e^2+5\,c^5\,d^5\right)}{16\,a^3\,\left(a^3\,e^6+3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6\right)}}{a^3+3\,a^2\,c\,x^2+3\,a\,c^2\,x^4+c^3\,x^6}+\frac{e^7\,\ln\left(d+e\,x\right)}{{\left(c\,d^2+a\,e^2\right)}^4}-\frac{\ln\left(25\,a^7\,c^{10}\,d^{18}\,x-2304\,a^{13}\,e^{18}\,\sqrt{-a^7\,c}-25\,a^4\,c^9\,d^{18}\,\sqrt{-a^7\,c}+5833\,a^5\,d^2\,e^{16}\,{\left(-a^7\,c\right)}^{3/2}+3612\,c^5\,d^{12}\,e^6\,{\left(-a^7\,c\right)}^{3/2}+2304\,a^{16}\,c\,e^{18}\,x+9660\,a^2\,c^3\,d^8\,e^{10}\,{\left(-a^7\,c\right)}^{3/2}+8820\,a^3\,c^2\,d^6\,e^{12}\,{\left(-a^7\,c\right)}^{3/2}-260\,a^5\,c^8\,d^{16}\,e^2\,\sqrt{-a^7\,c}-1236\,a^6\,c^7\,d^{14}\,e^4\,\sqrt{-a^7\,c}+260\,a^8\,c^9\,d^{16}\,e^2\,x+1236\,a^9\,c^8\,d^{14}\,e^4\,x+3612\,a^{10}\,c^7\,d^{12}\,e^6\,x+7126\,a^{11}\,c^6\,d^{10}\,e^8\,x+9660\,a^{12}\,c^5\,d^8\,e^{10}\,x+8820\,a^{13}\,c^4\,d^6\,e^{12}\,x+7204\,a^{14}\,c^3\,d^4\,e^{14}\,x+5833\,a^{15}\,c^2\,d^2\,e^{16}\,x+7126\,a\,c^4\,d^{10}\,e^8\,{\left(-a^7\,c\right)}^{3/2}+7204\,a^4\,c\,d^4\,e^{14}\,{\left(-a^7\,c\right)}^{3/2}\right)\,\left(16\,a^7\,e^7+5\,c^3\,d^7\,\sqrt{-a^7\,c}+35\,a^3\,d\,e^6\,\sqrt{-a^7\,c}+21\,a\,c^2\,d^5\,e^2\,\sqrt{-a^7\,c}+35\,a^2\,c\,d^3\,e^4\,\sqrt{-a^7\,c}\right)}{32\,\left(a^{11}\,e^8+4\,a^{10}\,c\,d^2\,e^6+6\,a^9\,c^2\,d^4\,e^4+4\,a^8\,c^3\,d^6\,e^2+a^7\,c^4\,d^8\right)}+\frac{\ln\left(2304\,a^{13}\,e^{18}\,\sqrt{-a^7\,c}+25\,a^7\,c^{10}\,d^{18}\,x+25\,a^4\,c^9\,d^{18}\,\sqrt{-a^7\,c}-5833\,a^5\,d^2\,e^{16}\,{\left(-a^7\,c\right)}^{3/2}-3612\,c^5\,d^{12}\,e^6\,{\left(-a^7\,c\right)}^{3/2}+2304\,a^{16}\,c\,e^{18}\,x-9660\,a^2\,c^3\,d^8\,e^{10}\,{\left(-a^7\,c\right)}^{3/2}-8820\,a^3\,c^2\,d^6\,e^{12}\,{\left(-a^7\,c\right)}^{3/2}+260\,a^5\,c^8\,d^{16}\,e^2\,\sqrt{-a^7\,c}+1236\,a^6\,c^7\,d^{14}\,e^4\,\sqrt{-a^7\,c}+260\,a^8\,c^9\,d^{16}\,e^2\,x+1236\,a^9\,c^8\,d^{14}\,e^4\,x+3612\,a^{10}\,c^7\,d^{12}\,e^6\,x+7126\,a^{11}\,c^6\,d^{10}\,e^8\,x+9660\,a^{12}\,c^5\,d^8\,e^{10}\,x+8820\,a^{13}\,c^4\,d^6\,e^{12}\,x+7204\,a^{14}\,c^3\,d^4\,e^{14}\,x+5833\,a^{15}\,c^2\,d^2\,e^{16}\,x-7126\,a\,c^4\,d^{10}\,e^8\,{\left(-a^7\,c\right)}^{3/2}-7204\,a^4\,c\,d^4\,e^{14}\,{\left(-a^7\,c\right)}^{3/2}\right)\,\left(5\,c^3\,d^7\,\sqrt{-a^7\,c}-16\,a^7\,e^7+35\,a^3\,d\,e^6\,\sqrt{-a^7\,c}+21\,a\,c^2\,d^5\,e^2\,\sqrt{-a^7\,c}+35\,a^2\,c\,d^3\,e^4\,\sqrt{-a^7\,c}\right)}{32\,\left(a^{11}\,e^8+4\,a^{10}\,c\,d^2\,e^6+6\,a^9\,c^2\,d^4\,e^4+4\,a^8\,c^3\,d^6\,e^2+a^7\,c^4\,d^8\right)}","Not used",1,"((11*a^2*e^5 + 2*c^2*d^4*e + 7*a*c*d^2*e^3)/(12*(a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)) + (x^2*(c^2*d^2*e^3 + 5*a*c*e^5))/(4*(a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)) + (x*(11*c^3*d^5 + 32*a*c^2*d^3*e^2 + 29*a^2*c*d*e^4))/(16*a*(a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)) + (c^2*e^5*x^4)/(2*(a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)) + (x^3*(5*c^4*d^5 + 16*a*c^3*d^3*e^2 + 17*a^2*c^2*d*e^4))/(6*a^2*(a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)) + (x^5*(5*c^5*d^5 + 16*a*c^4*d^3*e^2 + 19*a^2*c^3*d*e^4))/(16*a^3*(a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)))/(a^3 + c^3*x^6 + 3*a^2*c*x^2 + 3*a*c^2*x^4) + (e^7*log(d + e*x))/(a*e^2 + c*d^2)^4 - (log(25*a^7*c^10*d^18*x - 2304*a^13*e^18*(-a^7*c)^(1/2) - 25*a^4*c^9*d^18*(-a^7*c)^(1/2) + 5833*a^5*d^2*e^16*(-a^7*c)^(3/2) + 3612*c^5*d^12*e^6*(-a^7*c)^(3/2) + 2304*a^16*c*e^18*x + 9660*a^2*c^3*d^8*e^10*(-a^7*c)^(3/2) + 8820*a^3*c^2*d^6*e^12*(-a^7*c)^(3/2) - 260*a^5*c^8*d^16*e^2*(-a^7*c)^(1/2) - 1236*a^6*c^7*d^14*e^4*(-a^7*c)^(1/2) + 260*a^8*c^9*d^16*e^2*x + 1236*a^9*c^8*d^14*e^4*x + 3612*a^10*c^7*d^12*e^6*x + 7126*a^11*c^6*d^10*e^8*x + 9660*a^12*c^5*d^8*e^10*x + 8820*a^13*c^4*d^6*e^12*x + 7204*a^14*c^3*d^4*e^14*x + 5833*a^15*c^2*d^2*e^16*x + 7126*a*c^4*d^10*e^8*(-a^7*c)^(3/2) + 7204*a^4*c*d^4*e^14*(-a^7*c)^(3/2))*(16*a^7*e^7 + 5*c^3*d^7*(-a^7*c)^(1/2) + 35*a^3*d*e^6*(-a^7*c)^(1/2) + 21*a*c^2*d^5*e^2*(-a^7*c)^(1/2) + 35*a^2*c*d^3*e^4*(-a^7*c)^(1/2)))/(32*(a^11*e^8 + a^7*c^4*d^8 + 4*a^10*c*d^2*e^6 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4)) + (log(2304*a^13*e^18*(-a^7*c)^(1/2) + 25*a^7*c^10*d^18*x + 25*a^4*c^9*d^18*(-a^7*c)^(1/2) - 5833*a^5*d^2*e^16*(-a^7*c)^(3/2) - 3612*c^5*d^12*e^6*(-a^7*c)^(3/2) + 2304*a^16*c*e^18*x - 9660*a^2*c^3*d^8*e^10*(-a^7*c)^(3/2) - 8820*a^3*c^2*d^6*e^12*(-a^7*c)^(3/2) + 260*a^5*c^8*d^16*e^2*(-a^7*c)^(1/2) + 1236*a^6*c^7*d^14*e^4*(-a^7*c)^(1/2) + 260*a^8*c^9*d^16*e^2*x + 1236*a^9*c^8*d^14*e^4*x + 3612*a^10*c^7*d^12*e^6*x + 7126*a^11*c^6*d^10*e^8*x + 9660*a^12*c^5*d^8*e^10*x + 8820*a^13*c^4*d^6*e^12*x + 7204*a^14*c^3*d^4*e^14*x + 5833*a^15*c^2*d^2*e^16*x - 7126*a*c^4*d^10*e^8*(-a^7*c)^(3/2) - 7204*a^4*c*d^4*e^14*(-a^7*c)^(3/2))*(5*c^3*d^7*(-a^7*c)^(1/2) - 16*a^7*e^7 + 35*a^3*d*e^6*(-a^7*c)^(1/2) + 21*a*c^2*d^5*e^2*(-a^7*c)^(1/2) + 35*a^2*c*d^3*e^4*(-a^7*c)^(1/2)))/(32*(a^11*e^8 + a^7*c^4*d^8 + 4*a^10*c*d^2*e^6 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4))","B"
524,1,1876,430,2.487503,"\text{Not used}","int(1/((a + c*x^2)^4*(d + e*x)^2),x)","\frac{\frac{-3\,a^3\,e^7+13\,a^2\,c\,d^2\,e^5+5\,a\,c^2\,d^4\,e^3+c^3\,d^6\,e}{3\,\left(c\,d^2+a\,e^2\right)\,\left(a^3\,e^6+3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6\right)}+\frac{x\,\left(121\,a^2\,c\,d\,e^4+106\,a\,c^2\,d^3\,e^2+33\,c^3\,d^5\right)}{48\,a\,\left(a^3\,e^6+3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6\right)}+\frac{x^6\,\left(-35\,a^3\,c^3\,e^7+47\,a^2\,c^4\,d^2\,e^5+23\,a\,c^5\,d^4\,e^3+5\,c^6\,d^6\,e\right)}{16\,a^3\,\left(a^4\,e^8+4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4+4\,a\,c^3\,d^6\,e^2+c^4\,d^8\right)}+\frac{x^3\,\left(25\,a^2\,c^2\,d\,e^4+18\,a\,c^3\,d^3\,e^2+5\,c^4\,d^5\right)}{6\,a^2\,\left(a^3\,e^6+3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6\right)}+\frac{x^5\,\left(29\,a^2\,c^3\,d\,e^4+18\,a\,c^4\,d^3\,e^2+5\,c^5\,d^5\right)}{16\,a^3\,\left(a^3\,e^6+3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6\right)}+\frac{x^4\,\left(-35\,a^3\,c^2\,e^7+55\,a^2\,c^3\,d^2\,e^5+23\,a\,c^4\,d^4\,e^3+5\,c^5\,d^6\,e\right)}{6\,a^2\,\left(c\,d^2+a\,e^2\right)\,\left(a^3\,e^6+3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6\right)}+\frac{x^2\,\left(-77\,a^3\,c\,e^7+161\,a^2\,c^2\,d^2\,e^5+57\,a\,c^3\,d^4\,e^3+11\,c^4\,d^6\,e\right)}{16\,a\,\left(c\,d^2+a\,e^2\right)\,\left(a^3\,e^6+3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6\right)}}{e\,a^3\,x+d\,a^3+3\,e\,a^2\,c\,x^3+3\,d\,a^2\,c\,x^2+3\,e\,a\,c^2\,x^5+3\,d\,a\,c^2\,x^4+e\,c^3\,x^7+d\,c^3\,x^6}-\frac{\ln\left(25\,c^9\,d^{20}\,{\left(-a^7\,c\right)}^{3/2}-1225\,a^{17}\,e^{20}\,\sqrt{-a^7\,c}+25\,a^{10}\,c^{11}\,d^{20}\,x-291237\,a\,d^4\,e^{16}\,{\left(-a^7\,c\right)}^{5/2}-184696\,c\,d^6\,e^{14}\,{\left(-a^7\,c\right)}^{5/2}+140106\,a^9\,d^2\,e^{18}\,{\left(-a^7\,c\right)}^{3/2}+1225\,a^{20}\,c\,e^{20}\,x+2069\,a^2\,c^7\,d^{16}\,e^4\,{\left(-a^7\,c\right)}^{3/2}+8568\,a^3\,c^6\,d^{14}\,e^6\,{\left(-a^7\,c\right)}^{3/2}+24514\,a^4\,c^5\,d^{12}\,e^8\,{\left(-a^7\,c\right)}^{3/2}+47740\,a^5\,c^4\,d^{10}\,e^{10}\,{\left(-a^7\,c\right)}^{3/2}+62370\,a^6\,c^3\,d^8\,e^{12}\,{\left(-a^7\,c\right)}^{3/2}+330\,a^{11}\,c^{10}\,d^{18}\,e^2\,x+2069\,a^{12}\,c^9\,d^{16}\,e^4\,x+8568\,a^{13}\,c^8\,d^{14}\,e^6\,x+24514\,a^{14}\,c^7\,d^{12}\,e^8\,x+47740\,a^{15}\,c^6\,d^{10}\,e^{10}\,x+62370\,a^{16}\,c^5\,d^8\,e^{12}\,x+184696\,a^{17}\,c^4\,d^6\,e^{14}\,x+291237\,a^{18}\,c^3\,d^4\,e^{16}\,x+140106\,a^{19}\,c^2\,d^2\,e^{18}\,x+330\,a\,c^8\,d^{18}\,e^2\,{\left(-a^7\,c\right)}^{3/2}\right)\,\left(c\,\left(4\,a^7\,d\,e^7+\frac{35\,a^3\,d^2\,e^6\,\sqrt{-a^7\,c}}{8}\right)-\frac{35\,a^4\,e^8\,\sqrt{-a^7\,c}}{32}+\frac{5\,c^4\,d^8\,\sqrt{-a^7\,c}}{32}+\frac{35\,a^2\,c^2\,d^4\,e^4\,\sqrt{-a^7\,c}}{16}+\frac{7\,a\,c^3\,d^6\,e^2\,\sqrt{-a^7\,c}}{8}\right)}{a^{12}\,e^{10}+5\,a^{11}\,c\,d^2\,e^8+10\,a^{10}\,c^2\,d^4\,e^6+10\,a^9\,c^3\,d^6\,e^4+5\,a^8\,c^4\,d^8\,e^2+a^7\,c^5\,d^{10}}+\frac{\ln\left(1225\,a^{17}\,e^{20}\,\sqrt{-a^7\,c}-25\,c^9\,d^{20}\,{\left(-a^7\,c\right)}^{3/2}+25\,a^{10}\,c^{11}\,d^{20}\,x+291237\,a\,d^4\,e^{16}\,{\left(-a^7\,c\right)}^{5/2}+184696\,c\,d^6\,e^{14}\,{\left(-a^7\,c\right)}^{5/2}-140106\,a^9\,d^2\,e^{18}\,{\left(-a^7\,c\right)}^{3/2}+1225\,a^{20}\,c\,e^{20}\,x-2069\,a^2\,c^7\,d^{16}\,e^4\,{\left(-a^7\,c\right)}^{3/2}-8568\,a^3\,c^6\,d^{14}\,e^6\,{\left(-a^7\,c\right)}^{3/2}-24514\,a^4\,c^5\,d^{12}\,e^8\,{\left(-a^7\,c\right)}^{3/2}-47740\,a^5\,c^4\,d^{10}\,e^{10}\,{\left(-a^7\,c\right)}^{3/2}-62370\,a^6\,c^3\,d^8\,e^{12}\,{\left(-a^7\,c\right)}^{3/2}+330\,a^{11}\,c^{10}\,d^{18}\,e^2\,x+2069\,a^{12}\,c^9\,d^{16}\,e^4\,x+8568\,a^{13}\,c^8\,d^{14}\,e^6\,x+24514\,a^{14}\,c^7\,d^{12}\,e^8\,x+47740\,a^{15}\,c^6\,d^{10}\,e^{10}\,x+62370\,a^{16}\,c^5\,d^8\,e^{12}\,x+184696\,a^{17}\,c^4\,d^6\,e^{14}\,x+291237\,a^{18}\,c^3\,d^4\,e^{16}\,x+140106\,a^{19}\,c^2\,d^2\,e^{18}\,x-330\,a\,c^8\,d^{18}\,e^2\,{\left(-a^7\,c\right)}^{3/2}\right)\,\left(\frac{5\,c^4\,d^8\,\sqrt{-a^7\,c}}{32}-\frac{35\,a^4\,e^8\,\sqrt{-a^7\,c}}{32}-c\,\left(4\,a^7\,d\,e^7-\frac{35\,a^3\,d^2\,e^6\,\sqrt{-a^7\,c}}{8}\right)+\frac{35\,a^2\,c^2\,d^4\,e^4\,\sqrt{-a^7\,c}}{16}+\frac{7\,a\,c^3\,d^6\,e^2\,\sqrt{-a^7\,c}}{8}\right)}{a^{12}\,e^{10}+5\,a^{11}\,c\,d^2\,e^8+10\,a^{10}\,c^2\,d^4\,e^6+10\,a^9\,c^3\,d^6\,e^4+5\,a^8\,c^4\,d^8\,e^2+a^7\,c^5\,d^{10}}+\frac{8\,c\,d\,e^7\,\ln\left(d+e\,x\right)}{{\left(c\,d^2+a\,e^2\right)}^5}","Not used",1,"((c^3*d^6*e - 3*a^3*e^7 + 5*a*c^2*d^4*e^3 + 13*a^2*c*d^2*e^5)/(3*(a*e^2 + c*d^2)*(a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)) + (x*(33*c^3*d^5 + 106*a*c^2*d^3*e^2 + 121*a^2*c*d*e^4))/(48*a*(a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)) + (x^6*(5*c^6*d^6*e - 35*a^3*c^3*e^7 + 23*a*c^5*d^4*e^3 + 47*a^2*c^4*d^2*e^5))/(16*a^3*(a^4*e^8 + c^4*d^8 + 4*a*c^3*d^6*e^2 + 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4)) + (x^3*(5*c^4*d^5 + 18*a*c^3*d^3*e^2 + 25*a^2*c^2*d*e^4))/(6*a^2*(a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)) + (x^5*(5*c^5*d^5 + 18*a*c^4*d^3*e^2 + 29*a^2*c^3*d*e^4))/(16*a^3*(a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)) + (x^4*(5*c^5*d^6*e - 35*a^3*c^2*e^7 + 23*a*c^4*d^4*e^3 + 55*a^2*c^3*d^2*e^5))/(6*a^2*(a*e^2 + c*d^2)*(a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)) + (x^2*(11*c^4*d^6*e - 77*a^3*c*e^7 + 57*a*c^3*d^4*e^3 + 161*a^2*c^2*d^2*e^5))/(16*a*(a*e^2 + c*d^2)*(a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)))/(a^3*d + c^3*d*x^6 + c^3*e*x^7 + a^3*e*x + 3*a^2*c*d*x^2 + 3*a*c^2*d*x^4 + 3*a^2*c*e*x^3 + 3*a*c^2*e*x^5) - (log(25*c^9*d^20*(-a^7*c)^(3/2) - 1225*a^17*e^20*(-a^7*c)^(1/2) + 25*a^10*c^11*d^20*x - 291237*a*d^4*e^16*(-a^7*c)^(5/2) - 184696*c*d^6*e^14*(-a^7*c)^(5/2) + 140106*a^9*d^2*e^18*(-a^7*c)^(3/2) + 1225*a^20*c*e^20*x + 2069*a^2*c^7*d^16*e^4*(-a^7*c)^(3/2) + 8568*a^3*c^6*d^14*e^6*(-a^7*c)^(3/2) + 24514*a^4*c^5*d^12*e^8*(-a^7*c)^(3/2) + 47740*a^5*c^4*d^10*e^10*(-a^7*c)^(3/2) + 62370*a^6*c^3*d^8*e^12*(-a^7*c)^(3/2) + 330*a^11*c^10*d^18*e^2*x + 2069*a^12*c^9*d^16*e^4*x + 8568*a^13*c^8*d^14*e^6*x + 24514*a^14*c^7*d^12*e^8*x + 47740*a^15*c^6*d^10*e^10*x + 62370*a^16*c^5*d^8*e^12*x + 184696*a^17*c^4*d^6*e^14*x + 291237*a^18*c^3*d^4*e^16*x + 140106*a^19*c^2*d^2*e^18*x + 330*a*c^8*d^18*e^2*(-a^7*c)^(3/2))*(c*(4*a^7*d*e^7 + (35*a^3*d^2*e^6*(-a^7*c)^(1/2))/8) - (35*a^4*e^8*(-a^7*c)^(1/2))/32 + (5*c^4*d^8*(-a^7*c)^(1/2))/32 + (35*a^2*c^2*d^4*e^4*(-a^7*c)^(1/2))/16 + (7*a*c^3*d^6*e^2*(-a^7*c)^(1/2))/8))/(a^12*e^10 + a^7*c^5*d^10 + 5*a^11*c*d^2*e^8 + 5*a^8*c^4*d^8*e^2 + 10*a^9*c^3*d^6*e^4 + 10*a^10*c^2*d^4*e^6) + (log(1225*a^17*e^20*(-a^7*c)^(1/2) - 25*c^9*d^20*(-a^7*c)^(3/2) + 25*a^10*c^11*d^20*x + 291237*a*d^4*e^16*(-a^7*c)^(5/2) + 184696*c*d^6*e^14*(-a^7*c)^(5/2) - 140106*a^9*d^2*e^18*(-a^7*c)^(3/2) + 1225*a^20*c*e^20*x - 2069*a^2*c^7*d^16*e^4*(-a^7*c)^(3/2) - 8568*a^3*c^6*d^14*e^6*(-a^7*c)^(3/2) - 24514*a^4*c^5*d^12*e^8*(-a^7*c)^(3/2) - 47740*a^5*c^4*d^10*e^10*(-a^7*c)^(3/2) - 62370*a^6*c^3*d^8*e^12*(-a^7*c)^(3/2) + 330*a^11*c^10*d^18*e^2*x + 2069*a^12*c^9*d^16*e^4*x + 8568*a^13*c^8*d^14*e^6*x + 24514*a^14*c^7*d^12*e^8*x + 47740*a^15*c^6*d^10*e^10*x + 62370*a^16*c^5*d^8*e^12*x + 184696*a^17*c^4*d^6*e^14*x + 291237*a^18*c^3*d^4*e^16*x + 140106*a^19*c^2*d^2*e^18*x - 330*a*c^8*d^18*e^2*(-a^7*c)^(3/2))*((5*c^4*d^8*(-a^7*c)^(1/2))/32 - (35*a^4*e^8*(-a^7*c)^(1/2))/32 - c*(4*a^7*d*e^7 - (35*a^3*d^2*e^6*(-a^7*c)^(1/2))/8) + (35*a^2*c^2*d^4*e^4*(-a^7*c)^(1/2))/16 + (7*a*c^3*d^6*e^2*(-a^7*c)^(1/2))/8))/(a^12*e^10 + a^7*c^5*d^10 + 5*a^11*c*d^2*e^8 + 5*a^8*c^4*d^8*e^2 + 10*a^9*c^3*d^6*e^4 + 10*a^10*c^2*d^4*e^6) + (8*c*d*e^7*log(d + e*x))/(a*e^2 + c*d^2)^5","B"
525,0,-1,207,0.000000,"\text{Not used}","int((a + c*x^2)^(1/2)*(d + e*x)^4,x)","\int \sqrt{c\,x^2+a}\,{\left(d+e\,x\right)}^4 \,d x","Not used",1,"int((a + c*x^2)^(1/2)*(d + e*x)^4, x)","F"
526,0,-1,144,0.000000,"\text{Not used}","int((a + c*x^2)^(1/2)*(d + e*x)^3,x)","\int \sqrt{c\,x^2+a}\,{\left(d+e\,x\right)}^3 \,d x","Not used",1,"int((a + c*x^2)^(1/2)*(d + e*x)^3, x)","F"
527,0,-1,119,0.000000,"\text{Not used}","int((a + c*x^2)^(1/2)*(d + e*x)^2,x)","\int \sqrt{c\,x^2+a}\,{\left(d+e\,x\right)}^2 \,d x","Not used",1,"int((a + c*x^2)^(1/2)*(d + e*x)^2, x)","F"
528,1,52,67,0.531225,"\text{Not used}","int((a + c*x^2)^(1/2)*(d + e*x),x)","\frac{e\,{\left(c\,x^2+a\right)}^{3/2}}{3\,c}+\frac{d\,x\,\sqrt{c\,x^2+a}}{2}+\frac{a\,d\,\ln\left(\sqrt{c}\,x+\sqrt{c\,x^2+a}\right)}{2\,\sqrt{c}}","Not used",1,"(e*(a + c*x^2)^(3/2))/(3*c) + (d*x*(a + c*x^2)^(1/2))/2 + (a*d*log(c^(1/2)*x + (a + c*x^2)^(1/2)))/(2*c^(1/2))","B"
529,0,-1,103,0.000000,"\text{Not used}","int((a + c*x^2)^(1/2)/(d + e*x),x)","\int \frac{\sqrt{c\,x^2+a}}{d+e\,x} \,d x","Not used",1,"int((a + c*x^2)^(1/2)/(d + e*x), x)","F"
530,0,-1,110,0.000000,"\text{Not used}","int((a + c*x^2)^(1/2)/(d + e*x)^2,x)","\int \frac{\sqrt{c\,x^2+a}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a + c*x^2)^(1/2)/(d + e*x)^2, x)","F"
531,0,-1,103,0.000000,"\text{Not used}","int((a + c*x^2)^(1/2)/(d + e*x)^3,x)","\int \frac{\sqrt{c\,x^2+a}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((a + c*x^2)^(1/2)/(d + e*x)^3, x)","F"
532,0,-1,144,0.000000,"\text{Not used}","int((a + c*x^2)^(1/2)/(d + e*x)^4,x)","\int \frac{\sqrt{c\,x^2+a}}{{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int((a + c*x^2)^(1/2)/(d + e*x)^4, x)","F"
533,0,-1,206,0.000000,"\text{Not used}","int((a + c*x^2)^(1/2)/(d + e*x)^5,x)","\int \frac{\sqrt{c\,x^2+a}}{{\left(d+e\,x\right)}^5} \,d x","Not used",1,"int((a + c*x^2)^(1/2)/(d + e*x)^5, x)","F"
534,0,-1,255,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)*(d + e*x)^4,x)","\int {\left(c\,x^2+a\right)}^{3/2}\,{\left(d+e\,x\right)}^4 \,d x","Not used",1,"int((a + c*x^2)^(3/2)*(d + e*x)^4, x)","F"
535,0,-1,180,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)*(d + e*x)^3,x)","\int {\left(c\,x^2+a\right)}^{3/2}\,{\left(d+e\,x\right)}^3 \,d x","Not used",1,"int((a + c*x^2)^(3/2)*(d + e*x)^3, x)","F"
536,0,-1,154,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)*(d + e*x)^2,x)","\int {\left(c\,x^2+a\right)}^{3/2}\,{\left(d+e\,x\right)}^2 \,d x","Not used",1,"int((a + c*x^2)^(3/2)*(d + e*x)^2, x)","F"
537,1,54,87,0.541374,"\text{Not used}","int((a + c*x^2)^(3/2)*(d + e*x),x)","\frac{e\,{\left(c\,x^2+a\right)}^{5/2}}{5\,c}+\frac{d\,x\,{\left(c\,x^2+a\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{2},\frac{1}{2};\ \frac{3}{2};\ -\frac{c\,x^2}{a}\right)}{{\left(\frac{c\,x^2}{a}+1\right)}^{3/2}}","Not used",1,"(e*(a + c*x^2)^(5/2))/(5*c) + (d*x*(a + c*x^2)^(3/2)*hypergeom([-3/2, 1/2], 3/2, -(c*x^2)/a))/((c*x^2)/a + 1)^(3/2)","B"
538,0,-1,159,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)/(d + e*x),x)","\int \frac{{\left(c\,x^2+a\right)}^{3/2}}{d+e\,x} \,d x","Not used",1,"int((a + c*x^2)^(3/2)/(d + e*x), x)","F"
539,0,-1,153,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)/(d + e*x)^2,x)","\int \frac{{\left(c\,x^2+a\right)}^{3/2}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a + c*x^2)^(3/2)/(d + e*x)^2, x)","F"
540,0,-1,161,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)/(d + e*x)^3,x)","\int \frac{{\left(c\,x^2+a\right)}^{3/2}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((a + c*x^2)^(3/2)/(d + e*x)^3, x)","F"
541,0,-1,200,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)/(d + e*x)^4,x)","\int \frac{{\left(c\,x^2+a\right)}^{3/2}}{{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int((a + c*x^2)^(3/2)/(d + e*x)^4, x)","F"
542,0,-1,153,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)/(d + e*x)^5,x)","\int \frac{{\left(c\,x^2+a\right)}^{3/2}}{{\left(d+e\,x\right)}^5} \,d x","Not used",1,"int((a + c*x^2)^(3/2)/(d + e*x)^5, x)","F"
543,0,-1,195,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)/(d + e*x)^6,x)","\int \frac{{\left(c\,x^2+a\right)}^{3/2}}{{\left(d+e\,x\right)}^6} \,d x","Not used",1,"int((a + c*x^2)^(3/2)/(d + e*x)^6, x)","F"
544,0,-1,269,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)/(d + e*x)^7,x)","\int \frac{{\left(c\,x^2+a\right)}^{3/2}}{{\left(d+e\,x\right)}^7} \,d x","Not used",1,"int((a + c*x^2)^(3/2)/(d + e*x)^7, x)","F"
545,0,-1,307,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)*(d + e*x)^4,x)","\int {\left(c\,x^2+a\right)}^{5/2}\,{\left(d+e\,x\right)}^4 \,d x","Not used",1,"int((a + c*x^2)^(5/2)*(d + e*x)^4, x)","F"
546,0,-1,216,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)*(d + e*x)^3,x)","\int {\left(c\,x^2+a\right)}^{5/2}\,{\left(d+e\,x\right)}^3 \,d x","Not used",1,"int((a + c*x^2)^(5/2)*(d + e*x)^3, x)","F"
547,0,-1,189,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)*(d + e*x)^2,x)","\int {\left(c\,x^2+a\right)}^{5/2}\,{\left(d+e\,x\right)}^2 \,d x","Not used",1,"int((a + c*x^2)^(5/2)*(d + e*x)^2, x)","F"
548,1,54,107,0.591935,"\text{Not used}","int((a + c*x^2)^(5/2)*(d + e*x),x)","\frac{e\,{\left(c\,x^2+a\right)}^{7/2}}{7\,c}+\frac{d\,x\,{\left(c\,x^2+a\right)}^{5/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{2},\frac{1}{2};\ \frac{3}{2};\ -\frac{c\,x^2}{a}\right)}{{\left(\frac{c\,x^2}{a}+1\right)}^{5/2}}","Not used",1,"(e*(a + c*x^2)^(7/2))/(7*c) + (d*x*(a + c*x^2)^(5/2)*hypergeom([-5/2, 1/2], 3/2, -(c*x^2)/a))/((c*x^2)/a + 1)^(5/2)","B"
549,0,-1,226,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)/(d + e*x),x)","\int \frac{{\left(c\,x^2+a\right)}^{5/2}}{d+e\,x} \,d x","Not used",1,"int((a + c*x^2)^(5/2)/(d + e*x), x)","F"
550,0,-1,219,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)/(d + e*x)^2,x)","\int \frac{{\left(c\,x^2+a\right)}^{5/2}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a + c*x^2)^(5/2)/(d + e*x)^2, x)","F"
551,0,-1,213,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)/(d + e*x)^3,x)","\int \frac{{\left(c\,x^2+a\right)}^{5/2}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((a + c*x^2)^(5/2)/(d + e*x)^3, x)","F"
552,0,-1,222,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)/(d + e*x)^4,x)","\int \frac{{\left(c\,x^2+a\right)}^{5/2}}{{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int((a + c*x^2)^(5/2)/(d + e*x)^4, x)","F"
553,0,-1,287,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)/(d + e*x)^5,x)","\int \frac{{\left(c\,x^2+a\right)}^{5/2}}{{\left(d+e\,x\right)}^5} \,d x","Not used",1,"int((a + c*x^2)^(5/2)/(d + e*x)^5, x)","F"
554,0,-1,314,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)/(d + e*x)^6,x)","\int \frac{{\left(c\,x^2+a\right)}^{5/2}}{{\left(d+e\,x\right)}^6} \,d x","Not used",1,"int((a + c*x^2)^(5/2)/(d + e*x)^6, x)","F"
555,0,-1,203,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)/(d + e*x)^7,x)","\int \frac{{\left(c\,x^2+a\right)}^{5/2}}{{\left(d+e\,x\right)}^7} \,d x","Not used",1,"int((a + c*x^2)^(5/2)/(d + e*x)^7, x)","F"
556,0,-1,246,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)/(d + e*x)^8,x)","\int \frac{{\left(c\,x^2+a\right)}^{5/2}}{{\left(d+e\,x\right)}^8} \,d x","Not used",1,"int((a + c*x^2)^(5/2)/(d + e*x)^8, x)","F"
557,0,-1,332,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)/(d + e*x)^9,x)","\int \frac{{\left(c\,x^2+a\right)}^{5/2}}{{\left(d+e\,x\right)}^9} \,d x","Not used",1,"int((a + c*x^2)^(5/2)/(d + e*x)^9, x)","F"
558,1,49,56,0.405203,"\text{Not used}","int((x^2 + 2)^(1/2)/(4*x + 1),x)","\frac{\sqrt{x^2+2}}{4}-\frac{\mathrm{asinh}\left(\frac{\sqrt{2}\,x}{2}\right)}{16}+\frac{\sqrt{33}\,\left(132\,\ln\left(x+\frac{1}{4}\right)-132\,\ln\left(x-\sqrt{33}\,\sqrt{x^2+2}-8\right)\right)}{2112}","Not used",1,"(x^2 + 2)^(1/2)/4 - asinh((2^(1/2)*x)/2)/16 + (33^(1/2)*(132*log(x + 1/4) - 132*log(x - 33^(1/2)*(x^2 + 2)^(1/2) - 8)))/2112","B"
559,1,48,67,0.155238,"\text{Not used}","int((4*x^2 + 2)^(1/2)/(4*x + 5),x)","\frac{\sqrt{x^2+\frac{1}{2}}}{2}-\frac{5\,\mathrm{asinh}\left(\sqrt{2}\,x\right)}{8}+\frac{\sqrt{33}\,\left(132\,\ln\left(x+\frac{5}{4}\right)-132\,\ln\left(x-\frac{\sqrt{33}\,\sqrt{x^2+\frac{1}{2}}}{5}-\frac{2}{5}\right)\right)}{1056}","Not used",1,"(x^2 + 1/2)^(1/2)/2 - (5*asinh(2^(1/2)*x))/8 + (33^(1/2)*(132*log(x + 5/4) - 132*log(x - (33^(1/2)*(x^2 + 1/2)^(1/2))/5 - 2/5)))/1056","B"
560,1,44,55,0.353878,"\text{Not used}","int((3*x + 2)*(7*x^2 - 5)^(1/2),x)","x\,\sqrt{7\,x^2-5}-\frac{5\,\sqrt{7}\,\ln\left(\sqrt{7}\,x+\sqrt{7\,x^2-5}\right)}{7}+\frac{{\left(7\,x^2-5\right)}^{3/2}}{7}","Not used",1,"x*(7*x^2 - 5)^(1/2) - (5*7^(1/2)*log(7^(1/2)*x + (7*x^2 - 5)^(1/2)))/7 + (7*x^2 - 5)^(3/2)/7","B"
561,0,-1,161,0.000000,"\text{Not used}","int((d + e*x)^4/(a + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{\sqrt{c\,x^2+a}} \,d x","Not used",1,"int((d + e*x)^4/(a + c*x^2)^(1/2), x)","F"
562,0,-1,110,0.000000,"\text{Not used}","int((d + e*x)^3/(a + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^3}{\sqrt{c\,x^2+a}} \,d x","Not used",1,"int((d + e*x)^3/(a + c*x^2)^(1/2), x)","F"
563,0,-1,86,0.000000,"\text{Not used}","int((d + e*x)^2/(a + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^2}{\sqrt{c\,x^2+a}} \,d x","Not used",1,"int((d + e*x)^2/(a + c*x^2)^(1/2), x)","F"
564,1,36,43,0.618939,"\text{Not used}","int((d + e*x)/(a + c*x^2)^(1/2),x)","\frac{e\,\sqrt{c\,x^2+a}}{c}+\frac{d\,\ln\left(\sqrt{c}\,x+\sqrt{c\,x^2+a}\right)}{\sqrt{c}}","Not used",1,"(e*(a + c*x^2)^(1/2))/c + (d*log(c^(1/2)*x + (a + c*x^2)^(1/2)))/c^(1/2)","B"
565,0,-1,54,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(1/2)*(d + e*x)),x)","\int \frac{1}{\sqrt{c\,x^2+a}\,\left(d+e\,x\right)} \,d x","Not used",1,"int(1/((a + c*x^2)^(1/2)*(d + e*x)), x)","F"
566,0,-1,91,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(1/2)*(d + e*x)^2),x)","\int \frac{1}{\sqrt{c\,x^2+a}\,{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int(1/((a + c*x^2)^(1/2)*(d + e*x)^2), x)","F"
567,0,-1,145,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(1/2)*(d + e*x)^3),x)","\int \frac{1}{\sqrt{c\,x^2+a}\,{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int(1/((a + c*x^2)^(1/2)*(d + e*x)^3), x)","F"
568,0,-1,198,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(1/2)*(d + e*x)^4),x)","\int \frac{1}{\sqrt{c\,x^2+a}\,{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int(1/((a + c*x^2)^(1/2)*(d + e*x)^4), x)","F"
569,0,-1,162,0.000000,"\text{Not used}","int((d + e*x)^4/(a + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{{\left(c\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^4/(a + c*x^2)^(3/2), x)","F"
570,0,-1,106,0.000000,"\text{Not used}","int((d + e*x)^3/(a + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^3}{{\left(c\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^3/(a + c*x^2)^(3/2), x)","F"
571,1,75,83,0.629772,"\text{Not used}","int((d + e*x)^2/(a + c*x^2)^(3/2),x)","\frac{e^2\,\ln\left(\sqrt{c}\,x+\sqrt{c\,x^2+a}\right)}{c^{3/2}}+\frac{d^2\,x}{a\,\sqrt{c\,x^2+a}}-\frac{e^2\,x}{c\,\sqrt{c\,x^2+a}}-\frac{2\,d\,e}{c\,\sqrt{c\,x^2+a}}","Not used",1,"(e^2*log(c^(1/2)*x + (a + c*x^2)^(1/2)))/c^(3/2) + (d^2*x)/(a*(a + c*x^2)^(1/2)) - (e^2*x)/(c*(a + c*x^2)^(1/2)) - (2*d*e)/(c*(a + c*x^2)^(1/2))","B"
572,1,24,28,0.370697,"\text{Not used}","int((d + e*x)/(a + c*x^2)^(3/2),x)","-\frac{\frac{e}{c}-\frac{d\,x}{a}}{\sqrt{c\,x^2+a}}","Not used",1,"-(e/c - (d*x)/a)/(a + c*x^2)^(1/2)","B"
573,0,-1,94,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(3/2)*(d + e*x)),x)","\int \frac{1}{{\left(c\,x^2+a\right)}^{3/2}\,\left(d+e\,x\right)} \,d x","Not used",1,"int(1/((a + c*x^2)^(3/2)*(d + e*x)), x)","F"
574,0,-1,151,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(3/2)*(d + e*x)^2),x)","\int \frac{1}{{\left(c\,x^2+a\right)}^{3/2}\,{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int(1/((a + c*x^2)^(3/2)*(d + e*x)^2), x)","F"
575,0,-1,223,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(3/2)*(d + e*x)^3),x)","\int \frac{1}{{\left(c\,x^2+a\right)}^{3/2}\,{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int(1/((a + c*x^2)^(3/2)*(d + e*x)^3), x)","F"
576,0,-1,293,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(3/2)*(d + e*x)^4),x)","\int \frac{1}{{\left(c\,x^2+a\right)}^{3/2}\,{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int(1/((a + c*x^2)^(3/2)*(d + e*x)^4), x)","F"
577,0,-1,191,0.000000,"\text{Not used}","int((d + e*x)^5/(a + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^5}{{\left(c\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^5/(a + c*x^2)^(5/2), x)","F"
578,0,-1,161,0.000000,"\text{Not used}","int((d + e*x)^4/(a + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{{\left(c\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^4/(a + c*x^2)^(5/2), x)","F"
579,1,82,79,0.506143,"\text{Not used}","int((d + e*x)^3/(a + c*x^2)^(5/2),x)","-\frac{2\,a^3\,e^3+3\,a^2\,c\,d^2\,e+3\,a^2\,c\,e^3\,x^2-3\,a\,c^2\,d^3\,x-3\,a\,c^2\,d\,e^2\,x^3-2\,c^3\,d^3\,x^3}{3\,a^2\,c^2\,{\left(c\,x^2+a\right)}^{3/2}}","Not used",1,"-(2*a^3*e^3 - 2*c^3*d^3*x^3 + 3*a^2*c*e^3*x^2 + 3*a^2*c*d^2*e - 3*a*c^2*d^3*x - 3*a*c^2*d*e^2*x^3)/(3*a^2*c^2*(a + c*x^2)^(3/2))","B"
580,1,68,58,0.441611,"\text{Not used}","int((d + e*x)^2/(a + c*x^2)^(5/2),x)","\frac{a\,e^2\,x\,\left(c\,x^2+a\right)-2\,a^2\,d\,e-a^2\,e^2\,x+2\,c\,d^2\,x\,\left(c\,x^2+a\right)+a\,c\,d^2\,x}{3\,a^2\,c\,{\left(c\,x^2+a\right)}^{3/2}}","Not used",1,"(a*e^2*x*(a + c*x^2) - 2*a^2*d*e - a^2*e^2*x + 2*c*d^2*x*(a + c*x^2) + a*c*d^2*x)/(3*a^2*c*(a + c*x^2)^(3/2))","B"
581,1,41,51,0.394695,"\text{Not used}","int((d + e*x)/(a + c*x^2)^(5/2),x)","\frac{2\,c\,d\,x\,\left(c\,x^2+a\right)-a^2\,e+a\,c\,d\,x}{3\,a^2\,c\,{\left(c\,x^2+a\right)}^{3/2}}","Not used",1,"(2*c*d*x*(a + c*x^2) - a^2*e + a*c*d*x)/(3*a^2*c*(a + c*x^2)^(3/2))","B"
582,0,-1,154,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(5/2)*(d + e*x)),x)","\int \frac{1}{{\left(c\,x^2+a\right)}^{5/2}\,\left(d+e\,x\right)} \,d x","Not used",1,"int(1/((a + c*x^2)^(5/2)*(d + e*x)), x)","F"
583,0,-1,244,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(5/2)*(d + e*x)^2),x)","\int \frac{1}{{\left(c\,x^2+a\right)}^{5/2}\,{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int(1/((a + c*x^2)^(5/2)*(d + e*x)^2), x)","F"
584,0,-1,327,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(5/2)*(d + e*x)^3),x)","\int \frac{1}{{\left(c\,x^2+a\right)}^{5/2}\,{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int(1/((a + c*x^2)^(5/2)*(d + e*x)^3), x)","F"
585,1,16,18,0.325188,"\text{Not used}","int((x + 3)/(1 - x^2)^(1/2),x)","3\,\mathrm{asin}\left(x\right)-\sqrt{1-x^2}","Not used",1,"3*asin(x) - (1 - x^2)^(1/2)","B"
586,1,16,20,0.033832,"\text{Not used}","int((x + 1)/(4 - x^2)^(1/2),x)","\mathrm{asin}\left(\frac{x}{2}\right)-\sqrt{4-x^2}","Not used",1,"asin(x/2) - (4 - x^2)^(1/2)","B"
587,1,14,18,0.043069,"\text{Not used}","int((x + 2)/(x^2 + 9)^(1/2),x)","2\,\mathrm{asinh}\left(\frac{x}{3}\right)+\sqrt{x^2+9}","Not used",1,"2*asinh(x/3) + (x^2 + 9)^(1/2)","B"
588,1,35,54,0.033689,"\text{Not used}","int((a + b*x)^2/(1 - x^2)^(1/2),x)","\mathrm{asin}\left(x\right)\,\left(a^2+\frac{b^2}{2}\right)-\left(\frac{x\,b^2}{2}+2\,a\,b\right)\,\sqrt{1-x^2}","Not used",1,"asin(x)*(a^2 + b^2/2) - (2*a*b + (b^2*x)/2)*(1 - x^2)^(1/2)","B"
589,1,32,52,0.034823,"\text{Not used}","int((a + b*x)^2/(x^2 + 1)^(1/2),x)","\left(\frac{x\,b^2}{2}+2\,a\,b\right)\,\sqrt{x^2+1}+\mathrm{asinh}\left(x\right)\,\left(a^2-\frac{b^2}{2}\right)","Not used",1,"(2*a*b + (b^2*x)/2)*(x^2 + 1)^(1/2) + asinh(x)*(a^2 - b^2/2)","B"
590,1,12,18,0.338375,"\text{Not used}","int((3*x + 2)/(x^2 + 4)^(3/2),x)","\frac{x-6}{2\,\sqrt{x^2+4}}","Not used",1,"(x - 6)/(2*(x^2 + 4)^(1/2))","B"
591,1,44,63,0.064809,"\text{Not used}","int((a + c*x^2)*(d + e*x)^(5/2),x)","\frac{2\,{\left(d+e\,x\right)}^{7/2}\,\left(63\,c\,{\left(d+e\,x\right)}^2+99\,a\,e^2+99\,c\,d^2-154\,c\,d\,\left(d+e\,x\right)\right)}{693\,e^3}","Not used",1,"(2*(d + e*x)^(7/2)*(63*c*(d + e*x)^2 + 99*a*e^2 + 99*c*d^2 - 154*c*d*(d + e*x)))/(693*e^3)","B"
592,1,44,63,0.344660,"\text{Not used}","int((a + c*x^2)*(d + e*x)^(3/2),x)","\frac{2\,{\left(d+e\,x\right)}^{5/2}\,\left(35\,c\,{\left(d+e\,x\right)}^2+63\,a\,e^2+63\,c\,d^2-90\,c\,d\,\left(d+e\,x\right)\right)}{315\,e^3}","Not used",1,"(2*(d + e*x)^(5/2)*(35*c*(d + e*x)^2 + 63*a*e^2 + 63*c*d^2 - 90*c*d*(d + e*x)))/(315*e^3)","B"
593,1,44,63,0.053221,"\text{Not used}","int((a + c*x^2)*(d + e*x)^(1/2),x)","\frac{2\,{\left(d+e\,x\right)}^{3/2}\,\left(15\,c\,{\left(d+e\,x\right)}^2+35\,a\,e^2+35\,c\,d^2-42\,c\,d\,\left(d+e\,x\right)\right)}{105\,e^3}","Not used",1,"(2*(d + e*x)^(3/2)*(15*c*(d + e*x)^2 + 35*a*e^2 + 35*c*d^2 - 42*c*d*(d + e*x)))/(105*e^3)","B"
594,1,44,61,0.048226,"\text{Not used}","int((a + c*x^2)/(d + e*x)^(1/2),x)","\frac{2\,\sqrt{d+e\,x}\,\left(3\,c\,{\left(d+e\,x\right)}^2+15\,a\,e^2+15\,c\,d^2-10\,c\,d\,\left(d+e\,x\right)\right)}{15\,e^3}","Not used",1,"(2*(d + e*x)^(1/2)*(3*c*(d + e*x)^2 + 15*a*e^2 + 15*c*d^2 - 10*c*d*(d + e*x)))/(15*e^3)","B"
595,1,44,59,0.051265,"\text{Not used}","int((a + c*x^2)/(d + e*x)^(3/2),x)","-\frac{6\,a\,e^2-2\,c\,{\left(d+e\,x\right)}^2+6\,c\,d^2+12\,c\,d\,\left(d+e\,x\right)}{3\,e^3\,\sqrt{d+e\,x}}","Not used",1,"-(6*a*e^2 - 2*c*(d + e*x)^2 + 6*c*d^2 + 12*c*d*(d + e*x))/(3*e^3*(d + e*x)^(1/2))","B"
596,1,44,59,0.042870,"\text{Not used}","int((a + c*x^2)/(d + e*x)^(5/2),x)","\frac{6\,c\,{\left(d+e\,x\right)}^2-2\,a\,e^2-2\,c\,d^2+12\,c\,d\,\left(d+e\,x\right)}{3\,e^3\,{\left(d+e\,x\right)}^{3/2}}","Not used",1,"(6*c*(d + e*x)^2 - 2*a*e^2 - 2*c*d^2 + 12*c*d*(d + e*x))/(3*e^3*(d + e*x)^(3/2))","B"
597,1,44,61,0.055616,"\text{Not used}","int((a + c*x^2)/(d + e*x)^(7/2),x)","-\frac{30\,c\,{\left(d+e\,x\right)}^2+6\,a\,e^2+6\,c\,d^2-20\,c\,d\,\left(d+e\,x\right)}{15\,e^3\,{\left(d+e\,x\right)}^{5/2}}","Not used",1,"-(30*c*(d + e*x)^2 + 6*a*e^2 + 6*c*d^2 - 20*c*d*(d + e*x))/(15*e^3*(d + e*x)^(5/2))","B"
598,1,114,127,0.354769,"\text{Not used}","int((a + c*x^2)^2*(d + e*x)^(5/2),x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{15/2}}{15\,e^5}-\frac{\left(8\,c^2\,d^3+8\,a\,c\,d\,e^2\right)\,{\left(d+e\,x\right)}^{9/2}}{9\,e^5}+\frac{2\,{\left(c\,d^2+a\,e^2\right)}^2\,{\left(d+e\,x\right)}^{7/2}}{7\,e^5}+\frac{\left(12\,c^2\,d^2+4\,a\,c\,e^2\right)\,{\left(d+e\,x\right)}^{11/2}}{11\,e^5}-\frac{8\,c^2\,d\,{\left(d+e\,x\right)}^{13/2}}{13\,e^5}","Not used",1,"(2*c^2*(d + e*x)^(15/2))/(15*e^5) - ((8*c^2*d^3 + 8*a*c*d*e^2)*(d + e*x)^(9/2))/(9*e^5) + (2*(a*e^2 + c*d^2)^2*(d + e*x)^(7/2))/(7*e^5) + ((12*c^2*d^2 + 4*a*c*e^2)*(d + e*x)^(11/2))/(11*e^5) - (8*c^2*d*(d + e*x)^(13/2))/(13*e^5)","B"
599,1,114,127,0.038320,"\text{Not used}","int((a + c*x^2)^2*(d + e*x)^(3/2),x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{13/2}}{13\,e^5}-\frac{\left(8\,c^2\,d^3+8\,a\,c\,d\,e^2\right)\,{\left(d+e\,x\right)}^{7/2}}{7\,e^5}+\frac{2\,{\left(c\,d^2+a\,e^2\right)}^2\,{\left(d+e\,x\right)}^{5/2}}{5\,e^5}+\frac{\left(12\,c^2\,d^2+4\,a\,c\,e^2\right)\,{\left(d+e\,x\right)}^{9/2}}{9\,e^5}-\frac{8\,c^2\,d\,{\left(d+e\,x\right)}^{11/2}}{11\,e^5}","Not used",1,"(2*c^2*(d + e*x)^(13/2))/(13*e^5) - ((8*c^2*d^3 + 8*a*c*d*e^2)*(d + e*x)^(7/2))/(7*e^5) + (2*(a*e^2 + c*d^2)^2*(d + e*x)^(5/2))/(5*e^5) + ((12*c^2*d^2 + 4*a*c*e^2)*(d + e*x)^(9/2))/(9*e^5) - (8*c^2*d*(d + e*x)^(11/2))/(11*e^5)","B"
600,1,114,127,0.043991,"\text{Not used}","int((a + c*x^2)^2*(d + e*x)^(1/2),x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{11/2}}{11\,e^5}-\frac{\left(8\,c^2\,d^3+8\,a\,c\,d\,e^2\right)\,{\left(d+e\,x\right)}^{5/2}}{5\,e^5}+\frac{2\,{\left(c\,d^2+a\,e^2\right)}^2\,{\left(d+e\,x\right)}^{3/2}}{3\,e^5}+\frac{\left(12\,c^2\,d^2+4\,a\,c\,e^2\right)\,{\left(d+e\,x\right)}^{7/2}}{7\,e^5}-\frac{8\,c^2\,d\,{\left(d+e\,x\right)}^{9/2}}{9\,e^5}","Not used",1,"(2*c^2*(d + e*x)^(11/2))/(11*e^5) - ((8*c^2*d^3 + 8*a*c*d*e^2)*(d + e*x)^(5/2))/(5*e^5) + (2*(a*e^2 + c*d^2)^2*(d + e*x)^(3/2))/(3*e^5) + ((12*c^2*d^2 + 4*a*c*e^2)*(d + e*x)^(7/2))/(7*e^5) - (8*c^2*d*(d + e*x)^(9/2))/(9*e^5)","B"
601,1,114,125,0.037097,"\text{Not used}","int((a + c*x^2)^2/(d + e*x)^(1/2),x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{9/2}}{9\,e^5}-\frac{\left(8\,c^2\,d^3+8\,a\,c\,d\,e^2\right)\,{\left(d+e\,x\right)}^{3/2}}{3\,e^5}+\frac{2\,{\left(c\,d^2+a\,e^2\right)}^2\,\sqrt{d+e\,x}}{e^5}+\frac{\left(12\,c^2\,d^2+4\,a\,c\,e^2\right)\,{\left(d+e\,x\right)}^{5/2}}{5\,e^5}-\frac{8\,c^2\,d\,{\left(d+e\,x\right)}^{7/2}}{7\,e^5}","Not used",1,"(2*c^2*(d + e*x)^(9/2))/(9*e^5) - ((8*c^2*d^3 + 8*a*c*d*e^2)*(d + e*x)^(3/2))/(3*e^5) + (2*(a*e^2 + c*d^2)^2*(d + e*x)^(1/2))/e^5 + ((12*c^2*d^2 + 4*a*c*e^2)*(d + e*x)^(5/2))/(5*e^5) - (8*c^2*d*(d + e*x)^(7/2))/(7*e^5)","B"
602,1,128,123,0.045554,"\text{Not used}","int((a + c*x^2)^2/(d + e*x)^(3/2),x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{7/2}}{7\,e^5}-\frac{\left(8\,c^2\,d^3+8\,a\,c\,d\,e^2\right)\,\sqrt{d+e\,x}}{e^5}-\frac{2\,a^2\,e^4+4\,a\,c\,d^2\,e^2+2\,c^2\,d^4}{e^5\,\sqrt{d+e\,x}}+\frac{\left(12\,c^2\,d^2+4\,a\,c\,e^2\right)\,{\left(d+e\,x\right)}^{3/2}}{3\,e^5}-\frac{8\,c^2\,d\,{\left(d+e\,x\right)}^{5/2}}{5\,e^5}","Not used",1,"(2*c^2*(d + e*x)^(7/2))/(7*e^5) - ((8*c^2*d^3 + 8*a*c*d*e^2)*(d + e*x)^(1/2))/e^5 - (2*a^2*e^4 + 2*c^2*d^4 + 4*a*c*d^2*e^2)/(e^5*(d + e*x)^(1/2)) + ((12*c^2*d^2 + 4*a*c*e^2)*(d + e*x)^(3/2))/(3*e^5) - (8*c^2*d*(d + e*x)^(5/2))/(5*e^5)","B"
603,1,122,123,0.403655,"\text{Not used}","int((a + c*x^2)^2/(d + e*x)^(5/2),x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{5/2}}{5\,e^5}-\frac{\frac{2\,a^2\,e^4}{3}+\frac{2\,c^2\,d^4}{3}-\left(8\,c^2\,d^3+8\,a\,c\,d\,e^2\right)\,\left(d+e\,x\right)+\frac{4\,a\,c\,d^2\,e^2}{3}}{e^5\,{\left(d+e\,x\right)}^{3/2}}+\frac{\left(12\,c^2\,d^2+4\,a\,c\,e^2\right)\,\sqrt{d+e\,x}}{e^5}-\frac{8\,c^2\,d\,{\left(d+e\,x\right)}^{3/2}}{3\,e^5}","Not used",1,"(2*c^2*(d + e*x)^(5/2))/(5*e^5) - ((2*a^2*e^4)/3 + (2*c^2*d^4)/3 - (8*c^2*d^3 + 8*a*c*d*e^2)*(d + e*x) + (4*a*c*d^2*e^2)/3)/(e^5*(d + e*x)^(3/2)) + ((12*c^2*d^2 + 4*a*c*e^2)*(d + e*x)^(1/2))/e^5 - (8*c^2*d*(d + e*x)^(3/2))/(3*e^5)","B"
604,1,105,123,0.416809,"\text{Not used}","int((a + c*x^2)^2/(d + e*x)^(7/2),x)","-\frac{2\,\left(3\,a^2\,e^4+16\,a\,c\,d^2\,e^2+40\,a\,c\,d\,e^3\,x+30\,a\,c\,e^4\,x^2+128\,c^2\,d^4+320\,c^2\,d^3\,e\,x+240\,c^2\,d^2\,e^2\,x^2+40\,c^2\,d\,e^3\,x^3-5\,c^2\,e^4\,x^4\right)}{15\,e^5\,{\left(d+e\,x\right)}^{5/2}}","Not used",1,"-(2*(3*a^2*e^4 + 128*c^2*d^4 - 5*c^2*e^4*x^4 + 40*c^2*d*e^3*x^3 + 240*c^2*d^2*e^2*x^2 + 16*a*c*d^2*e^2 + 30*a*c*e^4*x^2 + 320*c^2*d^3*e*x + 40*a*c*d*e^3*x))/(15*e^5*(d + e*x)^(5/2))","B"
605,1,187,204,0.072598,"\text{Not used}","int((a + c*x^2)^3*(d + e*x)^(5/2),x)","\frac{\left(30\,c^3\,d^2+6\,a\,c^2\,e^2\right)\,{\left(d+e\,x\right)}^{15/2}}{15\,e^7}+\frac{{\left(d+e\,x\right)}^{11/2}\,\left(6\,a^2\,c\,e^4+36\,a\,c^2\,d^2\,e^2+30\,c^3\,d^4\right)}{11\,e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{19/2}}{19\,e^7}+\frac{2\,{\left(c\,d^2+a\,e^2\right)}^3\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}-\frac{\left(40\,c^3\,d^3+24\,a\,c^2\,d\,e^2\right)\,{\left(d+e\,x\right)}^{13/2}}{13\,e^7}-\frac{12\,c^3\,d\,{\left(d+e\,x\right)}^{17/2}}{17\,e^7}-\frac{4\,c\,d\,{\left(c\,d^2+a\,e^2\right)}^2\,{\left(d+e\,x\right)}^{9/2}}{3\,e^7}","Not used",1,"((30*c^3*d^2 + 6*a*c^2*e^2)*(d + e*x)^(15/2))/(15*e^7) + ((d + e*x)^(11/2)*(30*c^3*d^4 + 6*a^2*c*e^4 + 36*a*c^2*d^2*e^2))/(11*e^7) + (2*c^3*(d + e*x)^(19/2))/(19*e^7) + (2*(a*e^2 + c*d^2)^3*(d + e*x)^(7/2))/(7*e^7) - ((40*c^3*d^3 + 24*a*c^2*d*e^2)*(d + e*x)^(13/2))/(13*e^7) - (12*c^3*d*(d + e*x)^(17/2))/(17*e^7) - (4*c*d*(a*e^2 + c*d^2)^2*(d + e*x)^(9/2))/(3*e^7)","B"
606,1,187,204,0.366800,"\text{Not used}","int((a + c*x^2)^3*(d + e*x)^(3/2),x)","\frac{\left(30\,c^3\,d^2+6\,a\,c^2\,e^2\right)\,{\left(d+e\,x\right)}^{13/2}}{13\,e^7}+\frac{{\left(d+e\,x\right)}^{9/2}\,\left(6\,a^2\,c\,e^4+36\,a\,c^2\,d^2\,e^2+30\,c^3\,d^4\right)}{9\,e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{17/2}}{17\,e^7}+\frac{2\,{\left(c\,d^2+a\,e^2\right)}^3\,{\left(d+e\,x\right)}^{5/2}}{5\,e^7}-\frac{\left(40\,c^3\,d^3+24\,a\,c^2\,d\,e^2\right)\,{\left(d+e\,x\right)}^{11/2}}{11\,e^7}-\frac{4\,c^3\,d\,{\left(d+e\,x\right)}^{15/2}}{5\,e^7}-\frac{12\,c\,d\,{\left(c\,d^2+a\,e^2\right)}^2\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}","Not used",1,"((30*c^3*d^2 + 6*a*c^2*e^2)*(d + e*x)^(13/2))/(13*e^7) + ((d + e*x)^(9/2)*(30*c^3*d^4 + 6*a^2*c*e^4 + 36*a*c^2*d^2*e^2))/(9*e^7) + (2*c^3*(d + e*x)^(17/2))/(17*e^7) + (2*(a*e^2 + c*d^2)^3*(d + e*x)^(5/2))/(5*e^7) - ((40*c^3*d^3 + 24*a*c^2*d*e^2)*(d + e*x)^(11/2))/(11*e^7) - (4*c^3*d*(d + e*x)^(15/2))/(5*e^7) - (12*c*d*(a*e^2 + c*d^2)^2*(d + e*x)^(7/2))/(7*e^7)","B"
607,1,187,204,0.052489,"\text{Not used}","int((a + c*x^2)^3*(d + e*x)^(1/2),x)","\frac{\left(30\,c^3\,d^2+6\,a\,c^2\,e^2\right)\,{\left(d+e\,x\right)}^{11/2}}{11\,e^7}+\frac{{\left(d+e\,x\right)}^{7/2}\,\left(6\,a^2\,c\,e^4+36\,a\,c^2\,d^2\,e^2+30\,c^3\,d^4\right)}{7\,e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{15/2}}{15\,e^7}+\frac{2\,{\left(c\,d^2+a\,e^2\right)}^3\,{\left(d+e\,x\right)}^{3/2}}{3\,e^7}-\frac{\left(40\,c^3\,d^3+24\,a\,c^2\,d\,e^2\right)\,{\left(d+e\,x\right)}^{9/2}}{9\,e^7}-\frac{12\,c^3\,d\,{\left(d+e\,x\right)}^{13/2}}{13\,e^7}-\frac{12\,c\,d\,{\left(c\,d^2+a\,e^2\right)}^2\,{\left(d+e\,x\right)}^{5/2}}{5\,e^7}","Not used",1,"((30*c^3*d^2 + 6*a*c^2*e^2)*(d + e*x)^(11/2))/(11*e^7) + ((d + e*x)^(7/2)*(30*c^3*d^4 + 6*a^2*c*e^4 + 36*a*c^2*d^2*e^2))/(7*e^7) + (2*c^3*(d + e*x)^(15/2))/(15*e^7) + (2*(a*e^2 + c*d^2)^3*(d + e*x)^(3/2))/(3*e^7) - ((40*c^3*d^3 + 24*a*c^2*d*e^2)*(d + e*x)^(9/2))/(9*e^7) - (12*c^3*d*(d + e*x)^(13/2))/(13*e^7) - (12*c*d*(a*e^2 + c*d^2)^2*(d + e*x)^(5/2))/(5*e^7)","B"
608,1,187,200,0.051507,"\text{Not used}","int((a + c*x^2)^3/(d + e*x)^(1/2),x)","\frac{\left(30\,c^3\,d^2+6\,a\,c^2\,e^2\right)\,{\left(d+e\,x\right)}^{9/2}}{9\,e^7}+\frac{{\left(d+e\,x\right)}^{5/2}\,\left(6\,a^2\,c\,e^4+36\,a\,c^2\,d^2\,e^2+30\,c^3\,d^4\right)}{5\,e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{13/2}}{13\,e^7}+\frac{2\,{\left(c\,d^2+a\,e^2\right)}^3\,\sqrt{d+e\,x}}{e^7}-\frac{\left(40\,c^3\,d^3+24\,a\,c^2\,d\,e^2\right)\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}-\frac{12\,c^3\,d\,{\left(d+e\,x\right)}^{11/2}}{11\,e^7}-\frac{4\,c\,d\,{\left(c\,d^2+a\,e^2\right)}^2\,{\left(d+e\,x\right)}^{3/2}}{e^7}","Not used",1,"((30*c^3*d^2 + 6*a*c^2*e^2)*(d + e*x)^(9/2))/(9*e^7) + ((d + e*x)^(5/2)*(30*c^3*d^4 + 6*a^2*c*e^4 + 36*a*c^2*d^2*e^2))/(5*e^7) + (2*c^3*(d + e*x)^(13/2))/(13*e^7) + (2*(a*e^2 + c*d^2)^3*(d + e*x)^(1/2))/e^7 - ((40*c^3*d^3 + 24*a*c^2*d*e^2)*(d + e*x)^(7/2))/(7*e^7) - (12*c^3*d*(d + e*x)^(11/2))/(11*e^7) - (4*c*d*(a*e^2 + c*d^2)^2*(d + e*x)^(3/2))/e^7","B"
609,1,215,198,0.354295,"\text{Not used}","int((a + c*x^2)^3/(d + e*x)^(3/2),x)","\frac{\left(30\,c^3\,d^2+6\,a\,c^2\,e^2\right)\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}+\frac{{\left(d+e\,x\right)}^{3/2}\,\left(6\,a^2\,c\,e^4+36\,a\,c^2\,d^2\,e^2+30\,c^3\,d^4\right)}{3\,e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{11/2}}{11\,e^7}-\frac{\left(40\,c^3\,d^3+24\,a\,c^2\,d\,e^2\right)\,{\left(d+e\,x\right)}^{5/2}}{5\,e^7}-\frac{2\,a^3\,e^6+6\,a^2\,c\,d^2\,e^4+6\,a\,c^2\,d^4\,e^2+2\,c^3\,d^6}{e^7\,\sqrt{d+e\,x}}-\frac{4\,c^3\,d\,{\left(d+e\,x\right)}^{9/2}}{3\,e^7}-\frac{12\,c\,d\,{\left(c\,d^2+a\,e^2\right)}^2\,\sqrt{d+e\,x}}{e^7}","Not used",1,"((30*c^3*d^2 + 6*a*c^2*e^2)*(d + e*x)^(7/2))/(7*e^7) + ((d + e*x)^(3/2)*(30*c^3*d^4 + 6*a^2*c*e^4 + 36*a*c^2*d^2*e^2))/(3*e^7) + (2*c^3*(d + e*x)^(11/2))/(11*e^7) - ((40*c^3*d^3 + 24*a*c^2*d*e^2)*(d + e*x)^(5/2))/(5*e^7) - (2*a^3*e^6 + 2*c^3*d^6 + 6*a*c^2*d^4*e^2 + 6*a^2*c*d^2*e^4)/(e^7*(d + e*x)^(1/2)) - (4*c^3*d*(d + e*x)^(9/2))/(3*e^7) - (12*c*d*(a*e^2 + c*d^2)^2*(d + e*x)^(1/2))/e^7","B"
610,1,225,200,0.347069,"\text{Not used}","int((a + c*x^2)^3/(d + e*x)^(5/2),x)","\frac{\left(30\,c^3\,d^2+6\,a\,c^2\,e^2\right)\,{\left(d+e\,x\right)}^{5/2}}{5\,e^7}+\frac{\sqrt{d+e\,x}\,\left(6\,a^2\,c\,e^4+36\,a\,c^2\,d^2\,e^2+30\,c^3\,d^4\right)}{e^7}-\frac{\frac{2\,a^3\,e^6}{3}-\left(d+e\,x\right)\,\left(12\,a^2\,c\,d\,e^4+24\,a\,c^2\,d^3\,e^2+12\,c^3\,d^5\right)+\frac{2\,c^3\,d^6}{3}+2\,a\,c^2\,d^4\,e^2+2\,a^2\,c\,d^2\,e^4}{e^7\,{\left(d+e\,x\right)}^{3/2}}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{9/2}}{9\,e^7}-\frac{\left(40\,c^3\,d^3+24\,a\,c^2\,d\,e^2\right)\,{\left(d+e\,x\right)}^{3/2}}{3\,e^7}-\frac{12\,c^3\,d\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}","Not used",1,"((30*c^3*d^2 + 6*a*c^2*e^2)*(d + e*x)^(5/2))/(5*e^7) + ((d + e*x)^(1/2)*(30*c^3*d^4 + 6*a^2*c*e^4 + 36*a*c^2*d^2*e^2))/e^7 - ((2*a^3*e^6)/3 - (d + e*x)*(12*c^3*d^5 + 24*a*c^2*d^3*e^2 + 12*a^2*c*d*e^4) + (2*c^3*d^6)/3 + 2*a*c^2*d^4*e^2 + 2*a^2*c*d^2*e^4)/(e^7*(d + e*x)^(3/2)) + (2*c^3*(d + e*x)^(9/2))/(9*e^7) - ((40*c^3*d^3 + 24*a*c^2*d*e^2)*(d + e*x)^(3/2))/(3*e^7) - (12*c^3*d*(d + e*x)^(7/2))/(7*e^7)","B"
611,1,222,196,0.064326,"\text{Not used}","int((a + c*x^2)^3/(d + e*x)^(7/2),x)","\frac{\left(30\,c^3\,d^2+6\,a\,c^2\,e^2\right)\,{\left(d+e\,x\right)}^{3/2}}{3\,e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}-\frac{{\left(d+e\,x\right)}^2\,\left(6\,a^2\,c\,e^4+36\,a\,c^2\,d^2\,e^2+30\,c^3\,d^4\right)-\left(d+e\,x\right)\,\left(4\,a^2\,c\,d\,e^4+8\,a\,c^2\,d^3\,e^2+4\,c^3\,d^5\right)+\frac{2\,a^3\,e^6}{5}+\frac{2\,c^3\,d^6}{5}+\frac{6\,a\,c^2\,d^4\,e^2}{5}+\frac{6\,a^2\,c\,d^2\,e^4}{5}}{e^7\,{\left(d+e\,x\right)}^{5/2}}-\frac{\left(40\,c^3\,d^3+24\,a\,c^2\,d\,e^2\right)\,\sqrt{d+e\,x}}{e^7}-\frac{12\,c^3\,d\,{\left(d+e\,x\right)}^{5/2}}{5\,e^7}","Not used",1,"((30*c^3*d^2 + 6*a*c^2*e^2)*(d + e*x)^(3/2))/(3*e^7) + (2*c^3*(d + e*x)^(7/2))/(7*e^7) - ((d + e*x)^2*(30*c^3*d^4 + 6*a^2*c*e^4 + 36*a*c^2*d^2*e^2) - (d + e*x)*(4*c^3*d^5 + 8*a*c^2*d^3*e^2 + 4*a^2*c*d*e^4) + (2*a^3*e^6)/5 + (2*c^3*d^6)/5 + (6*a*c^2*d^4*e^2)/5 + (6*a^2*c*d^2*e^4)/5)/(e^7*(d + e*x)^(5/2)) - ((40*c^3*d^3 + 24*a*c^2*d*e^2)*(d + e*x)^(1/2))/e^7 - (12*c^3*d*(d + e*x)^(5/2))/(5*e^7)","B"
612,1,3385,167,0.806743,"\text{Not used}","int((d + e*x)^(5/2)/(a - c*x^2),x)","-\frac{2\,e\,{\left(d+e\,x\right)}^{3/2}}{3\,c}-\frac{4\,d\,e\,\sqrt{d+e\,x}}{c}-\mathrm{atan}\left(\frac{a^3\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{e^5\,\sqrt{a^3\,c^7}}{4\,c^7}+\frac{d^5}{4\,a\,c}+\frac{5\,d^3\,e^2}{2\,c^2}+\frac{5\,a\,d\,e^4}{4\,c^3}+\frac{5\,d^4\,e\,\sqrt{a^3\,c^7}}{4\,a^2\,c^5}+\frac{5\,d^2\,e^3\,\sqrt{a^3\,c^7}}{2\,a\,c^6}}\,32{}\mathrm{i}}{\frac{16\,a^4\,e^{11}}{c^2}+64\,a^2\,d^4\,e^7-80\,c^2\,d^8\,e^3+\frac{160\,a^3\,d^2\,e^9}{c}-160\,a\,c\,d^6\,e^5-\frac{160\,d^5\,e^6\,\sqrt{a^3\,c^7}}{c^3}+\frac{288\,a\,d^3\,e^8\,\sqrt{a^3\,c^7}}{c^4}+\frac{32\,a^2\,d\,e^{10}\,\sqrt{a^3\,c^7}}{c^5}-\frac{160\,d^7\,e^4\,\sqrt{a^3\,c^7}}{a\,c^2}}-\frac{d^5\,e^3\,\sqrt{a^3\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{e^5\,\sqrt{a^3\,c^7}}{4\,c^7}+\frac{d^5}{4\,a\,c}+\frac{5\,d^3\,e^2}{2\,c^2}+\frac{5\,a\,d\,e^4}{4\,c^3}+\frac{5\,d^4\,e\,\sqrt{a^3\,c^7}}{4\,a^2\,c^5}+\frac{5\,d^2\,e^3\,\sqrt{a^3\,c^7}}{2\,a\,c^6}}\,160{}\mathrm{i}}{\frac{16\,a^5\,e^{11}}{c}+160\,a^4\,d^2\,e^9-80\,a\,c^3\,d^8\,e^3+64\,a^3\,c\,d^4\,e^7-160\,a^2\,c^2\,d^6\,e^5-\frac{160\,d^7\,e^4\,\sqrt{a^3\,c^7}}{c}-\frac{160\,a\,d^5\,e^6\,\sqrt{a^3\,c^7}}{c^2}+\frac{32\,a^3\,d\,e^{10}\,\sqrt{a^3\,c^7}}{c^4}+\frac{288\,a^2\,d^3\,e^8\,\sqrt{a^3\,c^7}}{c^3}}-\frac{d^3\,e^5\,\sqrt{a^3\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{e^5\,\sqrt{a^3\,c^7}}{4\,c^7}+\frac{d^5}{4\,a\,c}+\frac{5\,d^3\,e^2}{2\,c^2}+\frac{5\,a\,d\,e^4}{4\,c^3}+\frac{5\,d^4\,e\,\sqrt{a^3\,c^7}}{4\,a^2\,c^5}+\frac{5\,d^2\,e^3\,\sqrt{a^3\,c^7}}{2\,a\,c^6}}\,320{}\mathrm{i}}{16\,a^4\,e^{11}-80\,c^4\,d^8\,e^3-160\,a\,c^3\,d^6\,e^5+160\,a^3\,c\,d^2\,e^9+64\,a^2\,c^2\,d^4\,e^7-\frac{160\,d^7\,e^4\,\sqrt{a^3\,c^7}}{a}-\frac{160\,d^5\,e^6\,\sqrt{a^3\,c^7}}{c}+\frac{288\,a\,d^3\,e^8\,\sqrt{a^3\,c^7}}{c^2}+\frac{32\,a^2\,d\,e^{10}\,\sqrt{a^3\,c^7}}{c^3}}-\frac{a\,d\,e^7\,\sqrt{a^3\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{e^5\,\sqrt{a^3\,c^7}}{4\,c^7}+\frac{d^5}{4\,a\,c}+\frac{5\,d^3\,e^2}{2\,c^2}+\frac{5\,a\,d\,e^4}{4\,c^3}+\frac{5\,d^4\,e\,\sqrt{a^3\,c^7}}{4\,a^2\,c^5}+\frac{5\,d^2\,e^3\,\sqrt{a^3\,c^7}}{2\,a\,c^6}}\,32{}\mathrm{i}}{16\,a^4\,c\,e^{11}-160\,d^5\,e^6\,\sqrt{a^3\,c^7}-80\,c^5\,d^8\,e^3-160\,a\,c^4\,d^6\,e^5+64\,a^2\,c^3\,d^4\,e^7+160\,a^3\,c^2\,d^2\,e^9+\frac{288\,a\,d^3\,e^8\,\sqrt{a^3\,c^7}}{c}-\frac{160\,c\,d^7\,e^4\,\sqrt{a^3\,c^7}}{a}+\frac{32\,a^2\,d\,e^{10}\,\sqrt{a^3\,c^7}}{c^2}}+\frac{a\,c^2\,d^4\,e^4\,\sqrt{d+e\,x}\,\sqrt{\frac{e^5\,\sqrt{a^3\,c^7}}{4\,c^7}+\frac{d^5}{4\,a\,c}+\frac{5\,d^3\,e^2}{2\,c^2}+\frac{5\,a\,d\,e^4}{4\,c^3}+\frac{5\,d^4\,e\,\sqrt{a^3\,c^7}}{4\,a^2\,c^5}+\frac{5\,d^2\,e^3\,\sqrt{a^3\,c^7}}{2\,a\,c^6}}\,160{}\mathrm{i}}{\frac{16\,a^4\,e^{11}}{c^2}+64\,a^2\,d^4\,e^7-80\,c^2\,d^8\,e^3+\frac{160\,a^3\,d^2\,e^9}{c}-160\,a\,c\,d^6\,e^5-\frac{160\,d^5\,e^6\,\sqrt{a^3\,c^7}}{c^3}+\frac{288\,a\,d^3\,e^8\,\sqrt{a^3\,c^7}}{c^4}+\frac{32\,a^2\,d\,e^{10}\,\sqrt{a^3\,c^7}}{c^5}-\frac{160\,d^7\,e^4\,\sqrt{a^3\,c^7}}{a\,c^2}}+\frac{a^2\,c\,d^2\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{e^5\,\sqrt{a^3\,c^7}}{4\,c^7}+\frac{d^5}{4\,a\,c}+\frac{5\,d^3\,e^2}{2\,c^2}+\frac{5\,a\,d\,e^4}{4\,c^3}+\frac{5\,d^4\,e\,\sqrt{a^3\,c^7}}{4\,a^2\,c^5}+\frac{5\,d^2\,e^3\,\sqrt{a^3\,c^7}}{2\,a\,c^6}}\,320{}\mathrm{i}}{\frac{16\,a^4\,e^{11}}{c^2}+64\,a^2\,d^4\,e^7-80\,c^2\,d^8\,e^3+\frac{160\,a^3\,d^2\,e^9}{c}-160\,a\,c\,d^6\,e^5-\frac{160\,d^5\,e^6\,\sqrt{a^3\,c^7}}{c^3}+\frac{288\,a\,d^3\,e^8\,\sqrt{a^3\,c^7}}{c^4}+\frac{32\,a^2\,d\,e^{10}\,\sqrt{a^3\,c^7}}{c^5}-\frac{160\,d^7\,e^4\,\sqrt{a^3\,c^7}}{a\,c^2}}\right)\,\sqrt{\frac{a^2\,e^5\,\sqrt{a^3\,c^7}+a\,c^6\,d^5+5\,a^3\,c^4\,d\,e^4+10\,a^2\,c^5\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^7}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^7}}{4\,a^2\,c^7}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{a^3\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{d^5}{4\,a\,c}-\frac{e^5\,\sqrt{a^3\,c^7}}{4\,c^7}+\frac{5\,d^3\,e^2}{2\,c^2}+\frac{5\,a\,d\,e^4}{4\,c^3}-\frac{5\,d^4\,e\,\sqrt{a^3\,c^7}}{4\,a^2\,c^5}-\frac{5\,d^2\,e^3\,\sqrt{a^3\,c^7}}{2\,a\,c^6}}\,32{}\mathrm{i}}{\frac{16\,a^4\,e^{11}}{c^2}+64\,a^2\,d^4\,e^7-80\,c^2\,d^8\,e^3+\frac{160\,a^3\,d^2\,e^9}{c}-160\,a\,c\,d^6\,e^5+\frac{160\,d^5\,e^6\,\sqrt{a^3\,c^7}}{c^3}-\frac{288\,a\,d^3\,e^8\,\sqrt{a^3\,c^7}}{c^4}-\frac{32\,a^2\,d\,e^{10}\,\sqrt{a^3\,c^7}}{c^5}+\frac{160\,d^7\,e^4\,\sqrt{a^3\,c^7}}{a\,c^2}}+\frac{d^5\,e^3\,\sqrt{a^3\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{d^5}{4\,a\,c}-\frac{e^5\,\sqrt{a^3\,c^7}}{4\,c^7}+\frac{5\,d^3\,e^2}{2\,c^2}+\frac{5\,a\,d\,e^4}{4\,c^3}-\frac{5\,d^4\,e\,\sqrt{a^3\,c^7}}{4\,a^2\,c^5}-\frac{5\,d^2\,e^3\,\sqrt{a^3\,c^7}}{2\,a\,c^6}}\,160{}\mathrm{i}}{\frac{16\,a^5\,e^{11}}{c}+160\,a^4\,d^2\,e^9-80\,a\,c^3\,d^8\,e^3+64\,a^3\,c\,d^4\,e^7-160\,a^2\,c^2\,d^6\,e^5+\frac{160\,d^7\,e^4\,\sqrt{a^3\,c^7}}{c}+\frac{160\,a\,d^5\,e^6\,\sqrt{a^3\,c^7}}{c^2}-\frac{32\,a^3\,d\,e^{10}\,\sqrt{a^3\,c^7}}{c^4}-\frac{288\,a^2\,d^3\,e^8\,\sqrt{a^3\,c^7}}{c^3}}+\frac{d^3\,e^5\,\sqrt{a^3\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{d^5}{4\,a\,c}-\frac{e^5\,\sqrt{a^3\,c^7}}{4\,c^7}+\frac{5\,d^3\,e^2}{2\,c^2}+\frac{5\,a\,d\,e^4}{4\,c^3}-\frac{5\,d^4\,e\,\sqrt{a^3\,c^7}}{4\,a^2\,c^5}-\frac{5\,d^2\,e^3\,\sqrt{a^3\,c^7}}{2\,a\,c^6}}\,320{}\mathrm{i}}{16\,a^4\,e^{11}-80\,c^4\,d^8\,e^3-160\,a\,c^3\,d^6\,e^5+160\,a^3\,c\,d^2\,e^9+64\,a^2\,c^2\,d^4\,e^7+\frac{160\,d^7\,e^4\,\sqrt{a^3\,c^7}}{a}+\frac{160\,d^5\,e^6\,\sqrt{a^3\,c^7}}{c}-\frac{288\,a\,d^3\,e^8\,\sqrt{a^3\,c^7}}{c^2}-\frac{32\,a^2\,d\,e^{10}\,\sqrt{a^3\,c^7}}{c^3}}+\frac{a\,d\,e^7\,\sqrt{a^3\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{d^5}{4\,a\,c}-\frac{e^5\,\sqrt{a^3\,c^7}}{4\,c^7}+\frac{5\,d^3\,e^2}{2\,c^2}+\frac{5\,a\,d\,e^4}{4\,c^3}-\frac{5\,d^4\,e\,\sqrt{a^3\,c^7}}{4\,a^2\,c^5}-\frac{5\,d^2\,e^3\,\sqrt{a^3\,c^7}}{2\,a\,c^6}}\,32{}\mathrm{i}}{160\,d^5\,e^6\,\sqrt{a^3\,c^7}+16\,a^4\,c\,e^{11}-80\,c^5\,d^8\,e^3-160\,a\,c^4\,d^6\,e^5+64\,a^2\,c^3\,d^4\,e^7+160\,a^3\,c^2\,d^2\,e^9-\frac{288\,a\,d^3\,e^8\,\sqrt{a^3\,c^7}}{c}+\frac{160\,c\,d^7\,e^4\,\sqrt{a^3\,c^7}}{a}-\frac{32\,a^2\,d\,e^{10}\,\sqrt{a^3\,c^7}}{c^2}}+\frac{a\,c^2\,d^4\,e^4\,\sqrt{d+e\,x}\,\sqrt{\frac{d^5}{4\,a\,c}-\frac{e^5\,\sqrt{a^3\,c^7}}{4\,c^7}+\frac{5\,d^3\,e^2}{2\,c^2}+\frac{5\,a\,d\,e^4}{4\,c^3}-\frac{5\,d^4\,e\,\sqrt{a^3\,c^7}}{4\,a^2\,c^5}-\frac{5\,d^2\,e^3\,\sqrt{a^3\,c^7}}{2\,a\,c^6}}\,160{}\mathrm{i}}{\frac{16\,a^4\,e^{11}}{c^2}+64\,a^2\,d^4\,e^7-80\,c^2\,d^8\,e^3+\frac{160\,a^3\,d^2\,e^9}{c}-160\,a\,c\,d^6\,e^5+\frac{160\,d^5\,e^6\,\sqrt{a^3\,c^7}}{c^3}-\frac{288\,a\,d^3\,e^8\,\sqrt{a^3\,c^7}}{c^4}-\frac{32\,a^2\,d\,e^{10}\,\sqrt{a^3\,c^7}}{c^5}+\frac{160\,d^7\,e^4\,\sqrt{a^3\,c^7}}{a\,c^2}}+\frac{a^2\,c\,d^2\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{d^5}{4\,a\,c}-\frac{e^5\,\sqrt{a^3\,c^7}}{4\,c^7}+\frac{5\,d^3\,e^2}{2\,c^2}+\frac{5\,a\,d\,e^4}{4\,c^3}-\frac{5\,d^4\,e\,\sqrt{a^3\,c^7}}{4\,a^2\,c^5}-\frac{5\,d^2\,e^3\,\sqrt{a^3\,c^7}}{2\,a\,c^6}}\,320{}\mathrm{i}}{\frac{16\,a^4\,e^{11}}{c^2}+64\,a^2\,d^4\,e^7-80\,c^2\,d^8\,e^3+\frac{160\,a^3\,d^2\,e^9}{c}-160\,a\,c\,d^6\,e^5+\frac{160\,d^5\,e^6\,\sqrt{a^3\,c^7}}{c^3}-\frac{288\,a\,d^3\,e^8\,\sqrt{a^3\,c^7}}{c^4}-\frac{32\,a^2\,d\,e^{10}\,\sqrt{a^3\,c^7}}{c^5}+\frac{160\,d^7\,e^4\,\sqrt{a^3\,c^7}}{a\,c^2}}\right)\,\sqrt{-\frac{a^2\,e^5\,\sqrt{a^3\,c^7}-a\,c^6\,d^5-5\,a^3\,c^4\,d\,e^4-10\,a^2\,c^5\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^7}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^7}}{4\,a^2\,c^7}}\,2{}\mathrm{i}","Not used",1,"- atan((a^3*e^8*(d + e*x)^(1/2)*((e^5*(a^3*c^7)^(1/2))/(4*c^7) + d^5/(4*a*c) + (5*d^3*e^2)/(2*c^2) + (5*a*d*e^4)/(4*c^3) + (5*d^4*e*(a^3*c^7)^(1/2))/(4*a^2*c^5) + (5*d^2*e^3*(a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*32i)/((16*a^4*e^11)/c^2 + 64*a^2*d^4*e^7 - 80*c^2*d^8*e^3 + (160*a^3*d^2*e^9)/c - 160*a*c*d^6*e^5 - (160*d^5*e^6*(a^3*c^7)^(1/2))/c^3 + (288*a*d^3*e^8*(a^3*c^7)^(1/2))/c^4 + (32*a^2*d*e^10*(a^3*c^7)^(1/2))/c^5 - (160*d^7*e^4*(a^3*c^7)^(1/2))/(a*c^2)) - (d^5*e^3*(a^3*c^7)^(1/2)*(d + e*x)^(1/2)*((e^5*(a^3*c^7)^(1/2))/(4*c^7) + d^5/(4*a*c) + (5*d^3*e^2)/(2*c^2) + (5*a*d*e^4)/(4*c^3) + (5*d^4*e*(a^3*c^7)^(1/2))/(4*a^2*c^5) + (5*d^2*e^3*(a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*160i)/((16*a^5*e^11)/c + 160*a^4*d^2*e^9 - 80*a*c^3*d^8*e^3 + 64*a^3*c*d^4*e^7 - 160*a^2*c^2*d^6*e^5 - (160*d^7*e^4*(a^3*c^7)^(1/2))/c - (160*a*d^5*e^6*(a^3*c^7)^(1/2))/c^2 + (32*a^3*d*e^10*(a^3*c^7)^(1/2))/c^4 + (288*a^2*d^3*e^8*(a^3*c^7)^(1/2))/c^3) - (d^3*e^5*(a^3*c^7)^(1/2)*(d + e*x)^(1/2)*((e^5*(a^3*c^7)^(1/2))/(4*c^7) + d^5/(4*a*c) + (5*d^3*e^2)/(2*c^2) + (5*a*d*e^4)/(4*c^3) + (5*d^4*e*(a^3*c^7)^(1/2))/(4*a^2*c^5) + (5*d^2*e^3*(a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*320i)/(16*a^4*e^11 - 80*c^4*d^8*e^3 - 160*a*c^3*d^6*e^5 + 160*a^3*c*d^2*e^9 + 64*a^2*c^2*d^4*e^7 - (160*d^7*e^4*(a^3*c^7)^(1/2))/a - (160*d^5*e^6*(a^3*c^7)^(1/2))/c + (288*a*d^3*e^8*(a^3*c^7)^(1/2))/c^2 + (32*a^2*d*e^10*(a^3*c^7)^(1/2))/c^3) - (a*d*e^7*(a^3*c^7)^(1/2)*(d + e*x)^(1/2)*((e^5*(a^3*c^7)^(1/2))/(4*c^7) + d^5/(4*a*c) + (5*d^3*e^2)/(2*c^2) + (5*a*d*e^4)/(4*c^3) + (5*d^4*e*(a^3*c^7)^(1/2))/(4*a^2*c^5) + (5*d^2*e^3*(a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*32i)/(16*a^4*c*e^11 - 160*d^5*e^6*(a^3*c^7)^(1/2) - 80*c^5*d^8*e^3 - 160*a*c^4*d^6*e^5 + 64*a^2*c^3*d^4*e^7 + 160*a^3*c^2*d^2*e^9 + (288*a*d^3*e^8*(a^3*c^7)^(1/2))/c - (160*c*d^7*e^4*(a^3*c^7)^(1/2))/a + (32*a^2*d*e^10*(a^3*c^7)^(1/2))/c^2) + (a*c^2*d^4*e^4*(d + e*x)^(1/2)*((e^5*(a^3*c^7)^(1/2))/(4*c^7) + d^5/(4*a*c) + (5*d^3*e^2)/(2*c^2) + (5*a*d*e^4)/(4*c^3) + (5*d^4*e*(a^3*c^7)^(1/2))/(4*a^2*c^5) + (5*d^2*e^3*(a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*160i)/((16*a^4*e^11)/c^2 + 64*a^2*d^4*e^7 - 80*c^2*d^8*e^3 + (160*a^3*d^2*e^9)/c - 160*a*c*d^6*e^5 - (160*d^5*e^6*(a^3*c^7)^(1/2))/c^3 + (288*a*d^3*e^8*(a^3*c^7)^(1/2))/c^4 + (32*a^2*d*e^10*(a^3*c^7)^(1/2))/c^5 - (160*d^7*e^4*(a^3*c^7)^(1/2))/(a*c^2)) + (a^2*c*d^2*e^6*(d + e*x)^(1/2)*((e^5*(a^3*c^7)^(1/2))/(4*c^7) + d^5/(4*a*c) + (5*d^3*e^2)/(2*c^2) + (5*a*d*e^4)/(4*c^3) + (5*d^4*e*(a^3*c^7)^(1/2))/(4*a^2*c^5) + (5*d^2*e^3*(a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*320i)/((16*a^4*e^11)/c^2 + 64*a^2*d^4*e^7 - 80*c^2*d^8*e^3 + (160*a^3*d^2*e^9)/c - 160*a*c*d^6*e^5 - (160*d^5*e^6*(a^3*c^7)^(1/2))/c^3 + (288*a*d^3*e^8*(a^3*c^7)^(1/2))/c^4 + (32*a^2*d*e^10*(a^3*c^7)^(1/2))/c^5 - (160*d^7*e^4*(a^3*c^7)^(1/2))/(a*c^2)))*((a^2*e^5*(a^3*c^7)^(1/2) + a*c^6*d^5 + 5*a^3*c^4*d*e^4 + 10*a^2*c^5*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^7)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^7)^(1/2))/(4*a^2*c^7))^(1/2)*2i - atan((a^3*e^8*(d + e*x)^(1/2)*(d^5/(4*a*c) - (e^5*(a^3*c^7)^(1/2))/(4*c^7) + (5*d^3*e^2)/(2*c^2) + (5*a*d*e^4)/(4*c^3) - (5*d^4*e*(a^3*c^7)^(1/2))/(4*a^2*c^5) - (5*d^2*e^3*(a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*32i)/((16*a^4*e^11)/c^2 + 64*a^2*d^4*e^7 - 80*c^2*d^8*e^3 + (160*a^3*d^2*e^9)/c - 160*a*c*d^6*e^5 + (160*d^5*e^6*(a^3*c^7)^(1/2))/c^3 - (288*a*d^3*e^8*(a^3*c^7)^(1/2))/c^4 - (32*a^2*d*e^10*(a^3*c^7)^(1/2))/c^5 + (160*d^7*e^4*(a^3*c^7)^(1/2))/(a*c^2)) + (d^5*e^3*(a^3*c^7)^(1/2)*(d + e*x)^(1/2)*(d^5/(4*a*c) - (e^5*(a^3*c^7)^(1/2))/(4*c^7) + (5*d^3*e^2)/(2*c^2) + (5*a*d*e^4)/(4*c^3) - (5*d^4*e*(a^3*c^7)^(1/2))/(4*a^2*c^5) - (5*d^2*e^3*(a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*160i)/((16*a^5*e^11)/c + 160*a^4*d^2*e^9 - 80*a*c^3*d^8*e^3 + 64*a^3*c*d^4*e^7 - 160*a^2*c^2*d^6*e^5 + (160*d^7*e^4*(a^3*c^7)^(1/2))/c + (160*a*d^5*e^6*(a^3*c^7)^(1/2))/c^2 - (32*a^3*d*e^10*(a^3*c^7)^(1/2))/c^4 - (288*a^2*d^3*e^8*(a^3*c^7)^(1/2))/c^3) + (d^3*e^5*(a^3*c^7)^(1/2)*(d + e*x)^(1/2)*(d^5/(4*a*c) - (e^5*(a^3*c^7)^(1/2))/(4*c^7) + (5*d^3*e^2)/(2*c^2) + (5*a*d*e^4)/(4*c^3) - (5*d^4*e*(a^3*c^7)^(1/2))/(4*a^2*c^5) - (5*d^2*e^3*(a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*320i)/(16*a^4*e^11 - 80*c^4*d^8*e^3 - 160*a*c^3*d^6*e^5 + 160*a^3*c*d^2*e^9 + 64*a^2*c^2*d^4*e^7 + (160*d^7*e^4*(a^3*c^7)^(1/2))/a + (160*d^5*e^6*(a^3*c^7)^(1/2))/c - (288*a*d^3*e^8*(a^3*c^7)^(1/2))/c^2 - (32*a^2*d*e^10*(a^3*c^7)^(1/2))/c^3) + (a*d*e^7*(a^3*c^7)^(1/2)*(d + e*x)^(1/2)*(d^5/(4*a*c) - (e^5*(a^3*c^7)^(1/2))/(4*c^7) + (5*d^3*e^2)/(2*c^2) + (5*a*d*e^4)/(4*c^3) - (5*d^4*e*(a^3*c^7)^(1/2))/(4*a^2*c^5) - (5*d^2*e^3*(a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*32i)/(160*d^5*e^6*(a^3*c^7)^(1/2) + 16*a^4*c*e^11 - 80*c^5*d^8*e^3 - 160*a*c^4*d^6*e^5 + 64*a^2*c^3*d^4*e^7 + 160*a^3*c^2*d^2*e^9 - (288*a*d^3*e^8*(a^3*c^7)^(1/2))/c + (160*c*d^7*e^4*(a^3*c^7)^(1/2))/a - (32*a^2*d*e^10*(a^3*c^7)^(1/2))/c^2) + (a*c^2*d^4*e^4*(d + e*x)^(1/2)*(d^5/(4*a*c) - (e^5*(a^3*c^7)^(1/2))/(4*c^7) + (5*d^3*e^2)/(2*c^2) + (5*a*d*e^4)/(4*c^3) - (5*d^4*e*(a^3*c^7)^(1/2))/(4*a^2*c^5) - (5*d^2*e^3*(a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*160i)/((16*a^4*e^11)/c^2 + 64*a^2*d^4*e^7 - 80*c^2*d^8*e^3 + (160*a^3*d^2*e^9)/c - 160*a*c*d^6*e^5 + (160*d^5*e^6*(a^3*c^7)^(1/2))/c^3 - (288*a*d^3*e^8*(a^3*c^7)^(1/2))/c^4 - (32*a^2*d*e^10*(a^3*c^7)^(1/2))/c^5 + (160*d^7*e^4*(a^3*c^7)^(1/2))/(a*c^2)) + (a^2*c*d^2*e^6*(d + e*x)^(1/2)*(d^5/(4*a*c) - (e^5*(a^3*c^7)^(1/2))/(4*c^7) + (5*d^3*e^2)/(2*c^2) + (5*a*d*e^4)/(4*c^3) - (5*d^4*e*(a^3*c^7)^(1/2))/(4*a^2*c^5) - (5*d^2*e^3*(a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*320i)/((16*a^4*e^11)/c^2 + 64*a^2*d^4*e^7 - 80*c^2*d^8*e^3 + (160*a^3*d^2*e^9)/c - 160*a*c*d^6*e^5 + (160*d^5*e^6*(a^3*c^7)^(1/2))/c^3 - (288*a*d^3*e^8*(a^3*c^7)^(1/2))/c^4 - (32*a^2*d*e^10*(a^3*c^7)^(1/2))/c^5 + (160*d^7*e^4*(a^3*c^7)^(1/2))/(a*c^2)))*(-(a^2*e^5*(a^3*c^7)^(1/2) - a*c^6*d^5 - 5*a^3*c^4*d*e^4 - 10*a^2*c^5*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^7)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^7)^(1/2))/(4*a^2*c^7))^(1/2)*2i - (2*e*(d + e*x)^(3/2))/(3*c) - (4*d*e*(d + e*x)^(1/2))/c","B"
613,1,1581,149,0.676644,"\text{Not used}","int((d + e*x)^(3/2)/(a - c*x^2),x)","2\,\mathrm{atanh}\left(\frac{32\,a^2\,c\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{3\,d\,e^2}{4\,c^2}+\frac{d^3}{4\,a\,c}-\frac{e^3\,\sqrt{a^3\,c^5}}{4\,a\,c^5}-\frac{3\,d^2\,e\,\sqrt{a^3\,c^5}}{4\,a^2\,c^4}}}{16\,a^2\,d\,e^7-48\,c^2\,d^5\,e^3-\frac{16\,a\,e^8\,\sqrt{a^3\,c^5}}{c^3}+32\,a\,c\,d^3\,e^5-\frac{32\,d^2\,e^6\,\sqrt{a^3\,c^5}}{c^2}+\frac{48\,d^4\,e^4\,\sqrt{a^3\,c^5}}{a\,c}}-\frac{32\,d\,e^5\,\sqrt{a^3\,c^5}\,\sqrt{d+e\,x}\,\sqrt{\frac{3\,d\,e^2}{4\,c^2}+\frac{d^3}{4\,a\,c}-\frac{e^3\,\sqrt{a^3\,c^5}}{4\,a\,c^5}-\frac{3\,d^2\,e\,\sqrt{a^3\,c^5}}{4\,a^2\,c^4}}}{48\,c^3\,d^5\,e^3-32\,a\,c^2\,d^3\,e^5+\frac{16\,a\,e^8\,\sqrt{a^3\,c^5}}{c^2}-16\,a^2\,c\,d\,e^7-\frac{48\,d^4\,e^4\,\sqrt{a^3\,c^5}}{a}+\frac{32\,d^2\,e^6\,\sqrt{a^3\,c^5}}{c}}+\frac{96\,d^3\,e^3\,\sqrt{a^3\,c^5}\,\sqrt{d+e\,x}\,\sqrt{\frac{3\,d\,e^2}{4\,c^2}+\frac{d^3}{4\,a\,c}-\frac{e^3\,\sqrt{a^3\,c^5}}{4\,a\,c^5}-\frac{3\,d^2\,e\,\sqrt{a^3\,c^5}}{4\,a^2\,c^4}}}{16\,a^3\,d\,e^7-48\,a\,c^2\,d^5\,e^3+32\,a^2\,c\,d^3\,e^5-\frac{16\,a^2\,e^8\,\sqrt{a^3\,c^5}}{c^3}+\frac{48\,d^4\,e^4\,\sqrt{a^3\,c^5}}{c}-\frac{32\,a\,d^2\,e^6\,\sqrt{a^3\,c^5}}{c^2}}+\frac{96\,a\,c^2\,d^2\,e^4\,\sqrt{d+e\,x}\,\sqrt{\frac{3\,d\,e^2}{4\,c^2}+\frac{d^3}{4\,a\,c}-\frac{e^3\,\sqrt{a^3\,c^5}}{4\,a\,c^5}-\frac{3\,d^2\,e\,\sqrt{a^3\,c^5}}{4\,a^2\,c^4}}}{16\,a^2\,d\,e^7-48\,c^2\,d^5\,e^3-\frac{16\,a\,e^8\,\sqrt{a^3\,c^5}}{c^3}+32\,a\,c\,d^3\,e^5-\frac{32\,d^2\,e^6\,\sqrt{a^3\,c^5}}{c^2}+\frac{48\,d^4\,e^4\,\sqrt{a^3\,c^5}}{a\,c}}\right)\,\sqrt{\frac{a\,c^4\,d^3-a\,e^3\,\sqrt{a^3\,c^5}+3\,a^2\,c^3\,d\,e^2-3\,c\,d^2\,e\,\sqrt{a^3\,c^5}}{4\,a^2\,c^5}}-2\,\mathrm{atanh}\left(\frac{32\,d\,e^5\,\sqrt{a^3\,c^5}\,\sqrt{d+e\,x}\,\sqrt{\frac{3\,d\,e^2}{4\,c^2}+\frac{d^3}{4\,a\,c}+\frac{e^3\,\sqrt{a^3\,c^5}}{4\,a\,c^5}+\frac{3\,d^2\,e\,\sqrt{a^3\,c^5}}{4\,a^2\,c^4}}}{32\,a\,c^2\,d^3\,e^5-48\,c^3\,d^5\,e^3+\frac{16\,a\,e^8\,\sqrt{a^3\,c^5}}{c^2}+16\,a^2\,c\,d\,e^7-\frac{48\,d^4\,e^4\,\sqrt{a^3\,c^5}}{a}+\frac{32\,d^2\,e^6\,\sqrt{a^3\,c^5}}{c}}-\frac{32\,a^2\,c\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{3\,d\,e^2}{4\,c^2}+\frac{d^3}{4\,a\,c}+\frac{e^3\,\sqrt{a^3\,c^5}}{4\,a\,c^5}+\frac{3\,d^2\,e\,\sqrt{a^3\,c^5}}{4\,a^2\,c^4}}}{16\,a^2\,d\,e^7-48\,c^2\,d^5\,e^3+\frac{16\,a\,e^8\,\sqrt{a^3\,c^5}}{c^3}+32\,a\,c\,d^3\,e^5+\frac{32\,d^2\,e^6\,\sqrt{a^3\,c^5}}{c^2}-\frac{48\,d^4\,e^4\,\sqrt{a^3\,c^5}}{a\,c}}+\frac{96\,d^3\,e^3\,\sqrt{a^3\,c^5}\,\sqrt{d+e\,x}\,\sqrt{\frac{3\,d\,e^2}{4\,c^2}+\frac{d^3}{4\,a\,c}+\frac{e^3\,\sqrt{a^3\,c^5}}{4\,a\,c^5}+\frac{3\,d^2\,e\,\sqrt{a^3\,c^5}}{4\,a^2\,c^4}}}{16\,a^3\,d\,e^7-48\,a\,c^2\,d^5\,e^3+32\,a^2\,c\,d^3\,e^5+\frac{16\,a^2\,e^8\,\sqrt{a^3\,c^5}}{c^3}-\frac{48\,d^4\,e^4\,\sqrt{a^3\,c^5}}{c}+\frac{32\,a\,d^2\,e^6\,\sqrt{a^3\,c^5}}{c^2}}-\frac{96\,a\,c^2\,d^2\,e^4\,\sqrt{d+e\,x}\,\sqrt{\frac{3\,d\,e^2}{4\,c^2}+\frac{d^3}{4\,a\,c}+\frac{e^3\,\sqrt{a^3\,c^5}}{4\,a\,c^5}+\frac{3\,d^2\,e\,\sqrt{a^3\,c^5}}{4\,a^2\,c^4}}}{16\,a^2\,d\,e^7-48\,c^2\,d^5\,e^3+\frac{16\,a\,e^8\,\sqrt{a^3\,c^5}}{c^3}+32\,a\,c\,d^3\,e^5+\frac{32\,d^2\,e^6\,\sqrt{a^3\,c^5}}{c^2}-\frac{48\,d^4\,e^4\,\sqrt{a^3\,c^5}}{a\,c}}\right)\,\sqrt{\frac{a\,c^4\,d^3+a\,e^3\,\sqrt{a^3\,c^5}+3\,a^2\,c^3\,d\,e^2+3\,c\,d^2\,e\,\sqrt{a^3\,c^5}}{4\,a^2\,c^5}}-\frac{2\,e\,\sqrt{d+e\,x}}{c}","Not used",1,"2*atanh((32*a^2*c*e^6*(d + e*x)^(1/2)*((3*d*e^2)/(4*c^2) + d^3/(4*a*c) - (e^3*(a^3*c^5)^(1/2))/(4*a*c^5) - (3*d^2*e*(a^3*c^5)^(1/2))/(4*a^2*c^4))^(1/2))/(16*a^2*d*e^7 - 48*c^2*d^5*e^3 - (16*a*e^8*(a^3*c^5)^(1/2))/c^3 + 32*a*c*d^3*e^5 - (32*d^2*e^6*(a^3*c^5)^(1/2))/c^2 + (48*d^4*e^4*(a^3*c^5)^(1/2))/(a*c)) - (32*d*e^5*(a^3*c^5)^(1/2)*(d + e*x)^(1/2)*((3*d*e^2)/(4*c^2) + d^3/(4*a*c) - (e^3*(a^3*c^5)^(1/2))/(4*a*c^5) - (3*d^2*e*(a^3*c^5)^(1/2))/(4*a^2*c^4))^(1/2))/(48*c^3*d^5*e^3 - 32*a*c^2*d^3*e^5 + (16*a*e^8*(a^3*c^5)^(1/2))/c^2 - 16*a^2*c*d*e^7 - (48*d^4*e^4*(a^3*c^5)^(1/2))/a + (32*d^2*e^6*(a^3*c^5)^(1/2))/c) + (96*d^3*e^3*(a^3*c^5)^(1/2)*(d + e*x)^(1/2)*((3*d*e^2)/(4*c^2) + d^3/(4*a*c) - (e^3*(a^3*c^5)^(1/2))/(4*a*c^5) - (3*d^2*e*(a^3*c^5)^(1/2))/(4*a^2*c^4))^(1/2))/(16*a^3*d*e^7 - 48*a*c^2*d^5*e^3 + 32*a^2*c*d^3*e^5 - (16*a^2*e^8*(a^3*c^5)^(1/2))/c^3 + (48*d^4*e^4*(a^3*c^5)^(1/2))/c - (32*a*d^2*e^6*(a^3*c^5)^(1/2))/c^2) + (96*a*c^2*d^2*e^4*(d + e*x)^(1/2)*((3*d*e^2)/(4*c^2) + d^3/(4*a*c) - (e^3*(a^3*c^5)^(1/2))/(4*a*c^5) - (3*d^2*e*(a^3*c^5)^(1/2))/(4*a^2*c^4))^(1/2))/(16*a^2*d*e^7 - 48*c^2*d^5*e^3 - (16*a*e^8*(a^3*c^5)^(1/2))/c^3 + 32*a*c*d^3*e^5 - (32*d^2*e^6*(a^3*c^5)^(1/2))/c^2 + (48*d^4*e^4*(a^3*c^5)^(1/2))/(a*c)))*((a*c^4*d^3 - a*e^3*(a^3*c^5)^(1/2) + 3*a^2*c^3*d*e^2 - 3*c*d^2*e*(a^3*c^5)^(1/2))/(4*a^2*c^5))^(1/2) - 2*atanh((32*d*e^5*(a^3*c^5)^(1/2)*(d + e*x)^(1/2)*((3*d*e^2)/(4*c^2) + d^3/(4*a*c) + (e^3*(a^3*c^5)^(1/2))/(4*a*c^5) + (3*d^2*e*(a^3*c^5)^(1/2))/(4*a^2*c^4))^(1/2))/(32*a*c^2*d^3*e^5 - 48*c^3*d^5*e^3 + (16*a*e^8*(a^3*c^5)^(1/2))/c^2 + 16*a^2*c*d*e^7 - (48*d^4*e^4*(a^3*c^5)^(1/2))/a + (32*d^2*e^6*(a^3*c^5)^(1/2))/c) - (32*a^2*c*e^6*(d + e*x)^(1/2)*((3*d*e^2)/(4*c^2) + d^3/(4*a*c) + (e^3*(a^3*c^5)^(1/2))/(4*a*c^5) + (3*d^2*e*(a^3*c^5)^(1/2))/(4*a^2*c^4))^(1/2))/(16*a^2*d*e^7 - 48*c^2*d^5*e^3 + (16*a*e^8*(a^3*c^5)^(1/2))/c^3 + 32*a*c*d^3*e^5 + (32*d^2*e^6*(a^3*c^5)^(1/2))/c^2 - (48*d^4*e^4*(a^3*c^5)^(1/2))/(a*c)) + (96*d^3*e^3*(a^3*c^5)^(1/2)*(d + e*x)^(1/2)*((3*d*e^2)/(4*c^2) + d^3/(4*a*c) + (e^3*(a^3*c^5)^(1/2))/(4*a*c^5) + (3*d^2*e*(a^3*c^5)^(1/2))/(4*a^2*c^4))^(1/2))/(16*a^3*d*e^7 - 48*a*c^2*d^5*e^3 + 32*a^2*c*d^3*e^5 + (16*a^2*e^8*(a^3*c^5)^(1/2))/c^3 - (48*d^4*e^4*(a^3*c^5)^(1/2))/c + (32*a*d^2*e^6*(a^3*c^5)^(1/2))/c^2) - (96*a*c^2*d^2*e^4*(d + e*x)^(1/2)*((3*d*e^2)/(4*c^2) + d^3/(4*a*c) + (e^3*(a^3*c^5)^(1/2))/(4*a*c^5) + (3*d^2*e*(a^3*c^5)^(1/2))/(4*a^2*c^4))^(1/2))/(16*a^2*d*e^7 - 48*c^2*d^5*e^3 + (16*a*e^8*(a^3*c^5)^(1/2))/c^3 + 32*a*c*d^3*e^5 + (32*d^2*e^6*(a^3*c^5)^(1/2))/c^2 - (48*d^4*e^4*(a^3*c^5)^(1/2))/(a*c)))*((a*c^4*d^3 + a*e^3*(a^3*c^5)^(1/2) + 3*a^2*c^3*d*e^2 + 3*c*d^2*e*(a^3*c^5)^(1/2))/(4*a^2*c^5))^(1/2) - (2*e*(d + e*x)^(1/2))/c","B"
614,1,302,134,0.338329,"\text{Not used}","int((d + e*x)^(1/2)/(a - c*x^2),x)","-2\,\mathrm{atanh}\left(\frac{2\,\left(\left(16\,c^3\,d^2\,e^2+16\,a\,c^2\,e^4\right)\,\sqrt{d+e\,x}-\frac{16\,c\,d\,e^2\,\left(e\,\sqrt{a^3\,c^3}+a\,c^2\,d\right)\,\sqrt{d+e\,x}}{a}\right)\,\sqrt{\frac{e\,\sqrt{a^3\,c^3}+a\,c^2\,d}{4\,a^2\,c^3}}}{16\,c^2\,d^2\,e^3-16\,a\,c\,e^5}\right)\,\sqrt{\frac{e\,\sqrt{a^3\,c^3}+a\,c^2\,d}{4\,a^2\,c^3}}-2\,\mathrm{atanh}\left(\frac{2\,\left(\left(16\,c^3\,d^2\,e^2+16\,a\,c^2\,e^4\right)\,\sqrt{d+e\,x}+\frac{16\,c\,d\,e^2\,\left(e\,\sqrt{a^3\,c^3}-a\,c^2\,d\right)\,\sqrt{d+e\,x}}{a}\right)\,\sqrt{-\frac{e\,\sqrt{a^3\,c^3}-a\,c^2\,d}{4\,a^2\,c^3}}}{16\,c^2\,d^2\,e^3-16\,a\,c\,e^5}\right)\,\sqrt{-\frac{e\,\sqrt{a^3\,c^3}-a\,c^2\,d}{4\,a^2\,c^3}}","Not used",1,"- 2*atanh((2*((16*a*c^2*e^4 + 16*c^3*d^2*e^2)*(d + e*x)^(1/2) - (16*c*d*e^2*(e*(a^3*c^3)^(1/2) + a*c^2*d)*(d + e*x)^(1/2))/a)*((e*(a^3*c^3)^(1/2) + a*c^2*d)/(4*a^2*c^3))^(1/2))/(16*c^2*d^2*e^3 - 16*a*c*e^5))*((e*(a^3*c^3)^(1/2) + a*c^2*d)/(4*a^2*c^3))^(1/2) - 2*atanh((2*((16*a*c^2*e^4 + 16*c^3*d^2*e^2)*(d + e*x)^(1/2) + (16*c*d*e^2*(e*(a^3*c^3)^(1/2) - a*c^2*d)*(d + e*x)^(1/2))/a)*(-(e*(a^3*c^3)^(1/2) - a*c^2*d)/(4*a^2*c^3))^(1/2))/(16*c^2*d^2*e^3 - 16*a*c*e^5))*(-(e*(a^3*c^3)^(1/2) - a*c^2*d)/(4*a^2*c^3))^(1/2)","B"
615,1,1366,134,0.652139,"\text{Not used}","int(1/((a - c*x^2)*(d + e*x)^(1/2)),x)","2\,\mathrm{atanh}\left(\frac{32\,a^2\,c^5\,d^2\,e^2\,\sqrt{-\frac{e\,\sqrt{a^3\,c}}{4\,\left(a^3\,c\,e^2-a^2\,c^2\,d^2\right)}-\frac{a\,c\,d}{4\,\left(a^3\,c\,e^2-a^2\,c^2\,d^2\right)}}\,\sqrt{d+e\,x}}{\frac{16\,a^4\,c^6\,d^3\,e^3}{a^3\,c\,e^2-a^2\,c^2\,d^2}-\frac{16\,a^4\,c^4\,e^6\,\sqrt{a^3\,c}}{a^3\,c\,e^2-a^2\,c^2\,d^2}-\frac{16\,a^5\,c^5\,d\,e^5}{a^3\,c\,e^2-a^2\,c^2\,d^2}+\frac{16\,a^3\,c^5\,d^2\,e^4\,\sqrt{a^3\,c}}{a^3\,c\,e^2-a^2\,c^2\,d^2}}-\frac{32\,c^3\,e^2\,\sqrt{-\frac{e\,\sqrt{a^3\,c}}{4\,\left(a^3\,c\,e^2-a^2\,c^2\,d^2\right)}-\frac{a\,c\,d}{4\,\left(a^3\,c\,e^2-a^2\,c^2\,d^2\right)}}\,\sqrt{d+e\,x}}{\frac{16\,a^2\,c^4\,d\,e^3}{a^3\,c\,e^2-a^2\,c^2\,d^2}+\frac{16\,a\,c^3\,e^4\,\sqrt{a^3\,c}}{a^3\,c\,e^2-a^2\,c^2\,d^2}}+\frac{32\,a\,c^4\,d\,e^3\,\sqrt{a^3\,c}\,\sqrt{-\frac{e\,\sqrt{a^3\,c}}{4\,\left(a^3\,c\,e^2-a^2\,c^2\,d^2\right)}-\frac{a\,c\,d}{4\,\left(a^3\,c\,e^2-a^2\,c^2\,d^2\right)}}\,\sqrt{d+e\,x}}{\frac{16\,a^4\,c^6\,d^3\,e^3}{a^3\,c\,e^2-a^2\,c^2\,d^2}-\frac{16\,a^4\,c^4\,e^6\,\sqrt{a^3\,c}}{a^3\,c\,e^2-a^2\,c^2\,d^2}-\frac{16\,a^5\,c^5\,d\,e^5}{a^3\,c\,e^2-a^2\,c^2\,d^2}+\frac{16\,a^3\,c^5\,d^2\,e^4\,\sqrt{a^3\,c}}{a^3\,c\,e^2-a^2\,c^2\,d^2}}\right)\,\sqrt{-\frac{e\,\sqrt{a^3\,c}+a\,c\,d}{4\,\left(a^3\,c\,e^2-a^2\,c^2\,d^2\right)}}-2\,\mathrm{atanh}\left(\frac{32\,c^3\,e^2\,\sqrt{\frac{e\,\sqrt{a^3\,c}}{4\,\left(a^3\,c\,e^2-a^2\,c^2\,d^2\right)}-\frac{a\,c\,d}{4\,\left(a^3\,c\,e^2-a^2\,c^2\,d^2\right)}}\,\sqrt{d+e\,x}}{\frac{16\,a^2\,c^4\,d\,e^3}{a^3\,c\,e^2-a^2\,c^2\,d^2}-\frac{16\,a\,c^3\,e^4\,\sqrt{a^3\,c}}{a^3\,c\,e^2-a^2\,c^2\,d^2}}-\frac{32\,a^2\,c^5\,d^2\,e^2\,\sqrt{\frac{e\,\sqrt{a^3\,c}}{4\,\left(a^3\,c\,e^2-a^2\,c^2\,d^2\right)}-\frac{a\,c\,d}{4\,\left(a^3\,c\,e^2-a^2\,c^2\,d^2\right)}}\,\sqrt{d+e\,x}}{\frac{16\,a^4\,c^6\,d^3\,e^3}{a^3\,c\,e^2-a^2\,c^2\,d^2}+\frac{16\,a^4\,c^4\,e^6\,\sqrt{a^3\,c}}{a^3\,c\,e^2-a^2\,c^2\,d^2}-\frac{16\,a^5\,c^5\,d\,e^5}{a^3\,c\,e^2-a^2\,c^2\,d^2}-\frac{16\,a^3\,c^5\,d^2\,e^4\,\sqrt{a^3\,c}}{a^3\,c\,e^2-a^2\,c^2\,d^2}}+\frac{32\,a\,c^4\,d\,e^3\,\sqrt{a^3\,c}\,\sqrt{\frac{e\,\sqrt{a^3\,c}}{4\,\left(a^3\,c\,e^2-a^2\,c^2\,d^2\right)}-\frac{a\,c\,d}{4\,\left(a^3\,c\,e^2-a^2\,c^2\,d^2\right)}}\,\sqrt{d+e\,x}}{\frac{16\,a^4\,c^6\,d^3\,e^3}{a^3\,c\,e^2-a^2\,c^2\,d^2}+\frac{16\,a^4\,c^4\,e^6\,\sqrt{a^3\,c}}{a^3\,c\,e^2-a^2\,c^2\,d^2}-\frac{16\,a^5\,c^5\,d\,e^5}{a^3\,c\,e^2-a^2\,c^2\,d^2}-\frac{16\,a^3\,c^5\,d^2\,e^4\,\sqrt{a^3\,c}}{a^3\,c\,e^2-a^2\,c^2\,d^2}}\right)\,\sqrt{\frac{e\,\sqrt{a^3\,c}-a\,c\,d}{4\,\left(a^3\,c\,e^2-a^2\,c^2\,d^2\right)}}","Not used",1,"2*atanh((32*a^2*c^5*d^2*e^2*(- (e*(a^3*c)^(1/2))/(4*(a^3*c*e^2 - a^2*c^2*d^2)) - (a*c*d)/(4*(a^3*c*e^2 - a^2*c^2*d^2)))^(1/2)*(d + e*x)^(1/2))/((16*a^4*c^6*d^3*e^3)/(a^3*c*e^2 - a^2*c^2*d^2) - (16*a^4*c^4*e^6*(a^3*c)^(1/2))/(a^3*c*e^2 - a^2*c^2*d^2) - (16*a^5*c^5*d*e^5)/(a^3*c*e^2 - a^2*c^2*d^2) + (16*a^3*c^5*d^2*e^4*(a^3*c)^(1/2))/(a^3*c*e^2 - a^2*c^2*d^2)) - (32*c^3*e^2*(- (e*(a^3*c)^(1/2))/(4*(a^3*c*e^2 - a^2*c^2*d^2)) - (a*c*d)/(4*(a^3*c*e^2 - a^2*c^2*d^2)))^(1/2)*(d + e*x)^(1/2))/((16*a^2*c^4*d*e^3)/(a^3*c*e^2 - a^2*c^2*d^2) + (16*a*c^3*e^4*(a^3*c)^(1/2))/(a^3*c*e^2 - a^2*c^2*d^2)) + (32*a*c^4*d*e^3*(a^3*c)^(1/2)*(- (e*(a^3*c)^(1/2))/(4*(a^3*c*e^2 - a^2*c^2*d^2)) - (a*c*d)/(4*(a^3*c*e^2 - a^2*c^2*d^2)))^(1/2)*(d + e*x)^(1/2))/((16*a^4*c^6*d^3*e^3)/(a^3*c*e^2 - a^2*c^2*d^2) - (16*a^4*c^4*e^6*(a^3*c)^(1/2))/(a^3*c*e^2 - a^2*c^2*d^2) - (16*a^5*c^5*d*e^5)/(a^3*c*e^2 - a^2*c^2*d^2) + (16*a^3*c^5*d^2*e^4*(a^3*c)^(1/2))/(a^3*c*e^2 - a^2*c^2*d^2)))*(-(e*(a^3*c)^(1/2) + a*c*d)/(4*(a^3*c*e^2 - a^2*c^2*d^2)))^(1/2) - 2*atanh((32*c^3*e^2*((e*(a^3*c)^(1/2))/(4*(a^3*c*e^2 - a^2*c^2*d^2)) - (a*c*d)/(4*(a^3*c*e^2 - a^2*c^2*d^2)))^(1/2)*(d + e*x)^(1/2))/((16*a^2*c^4*d*e^3)/(a^3*c*e^2 - a^2*c^2*d^2) - (16*a*c^3*e^4*(a^3*c)^(1/2))/(a^3*c*e^2 - a^2*c^2*d^2)) - (32*a^2*c^5*d^2*e^2*((e*(a^3*c)^(1/2))/(4*(a^3*c*e^2 - a^2*c^2*d^2)) - (a*c*d)/(4*(a^3*c*e^2 - a^2*c^2*d^2)))^(1/2)*(d + e*x)^(1/2))/((16*a^4*c^6*d^3*e^3)/(a^3*c*e^2 - a^2*c^2*d^2) + (16*a^4*c^4*e^6*(a^3*c)^(1/2))/(a^3*c*e^2 - a^2*c^2*d^2) - (16*a^5*c^5*d*e^5)/(a^3*c*e^2 - a^2*c^2*d^2) - (16*a^3*c^5*d^2*e^4*(a^3*c)^(1/2))/(a^3*c*e^2 - a^2*c^2*d^2)) + (32*a*c^4*d*e^3*(a^3*c)^(1/2)*((e*(a^3*c)^(1/2))/(4*(a^3*c*e^2 - a^2*c^2*d^2)) - (a*c*d)/(4*(a^3*c*e^2 - a^2*c^2*d^2)))^(1/2)*(d + e*x)^(1/2))/((16*a^4*c^6*d^3*e^3)/(a^3*c*e^2 - a^2*c^2*d^2) + (16*a^4*c^4*e^6*(a^3*c)^(1/2))/(a^3*c*e^2 - a^2*c^2*d^2) - (16*a^5*c^5*d*e^5)/(a^3*c*e^2 - a^2*c^2*d^2) - (16*a^3*c^5*d^2*e^4*(a^3*c)^(1/2))/(a^3*c*e^2 - a^2*c^2*d^2)))*((e*(a^3*c)^(1/2) - a*c*d)/(4*(a^3*c*e^2 - a^2*c^2*d^2)))^(1/2)","B"
616,1,4412,160,1.330630,"\text{Not used}","int(1/((a - c*x^2)*(d + e*x)^(3/2)),x)","-\frac{2\,e}{\left(a\,e^2-c\,d^2\right)\,\sqrt{d+e\,x}}-\mathrm{atan}\left(\frac{\left(\sqrt{d+e\,x}\,\left(16\,a^4\,c^4\,e^{10}-32\,a^3\,c^5\,d^2\,e^8+32\,a\,c^7\,d^6\,e^4-16\,c^8\,d^8\,e^2\right)+\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,\left(-64\,a^6\,c^4\,d\,e^{12}+320\,a^5\,c^5\,d^3\,e^{10}-640\,a^4\,c^6\,d^5\,e^8+640\,a^3\,c^7\,d^7\,e^6-320\,a^2\,c^8\,d^9\,e^4+64\,a\,c^9\,d^{11}\,e^2\right)-64\,a\,c^8\,d^9\,e^3-64\,a^5\,c^4\,d\,e^{11}+256\,a^2\,c^7\,d^7\,e^5-384\,a^3\,c^6\,d^5\,e^7+256\,a^4\,c^5\,d^3\,e^9\right)\right)\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,1{}\mathrm{i}+\left(\sqrt{d+e\,x}\,\left(16\,a^4\,c^4\,e^{10}-32\,a^3\,c^5\,d^2\,e^8+32\,a\,c^7\,d^6\,e^4-16\,c^8\,d^8\,e^2\right)+\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,\left(-64\,a^6\,c^4\,d\,e^{12}+320\,a^5\,c^5\,d^3\,e^{10}-640\,a^4\,c^6\,d^5\,e^8+640\,a^3\,c^7\,d^7\,e^6-320\,a^2\,c^8\,d^9\,e^4+64\,a\,c^9\,d^{11}\,e^2\right)+64\,a\,c^8\,d^9\,e^3+64\,a^5\,c^4\,d\,e^{11}-256\,a^2\,c^7\,d^7\,e^5+384\,a^3\,c^6\,d^5\,e^7-256\,a^4\,c^5\,d^3\,e^9\right)\right)\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,1{}\mathrm{i}}{\left(\sqrt{d+e\,x}\,\left(16\,a^4\,c^4\,e^{10}-32\,a^3\,c^5\,d^2\,e^8+32\,a\,c^7\,d^6\,e^4-16\,c^8\,d^8\,e^2\right)+\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,\left(-64\,a^6\,c^4\,d\,e^{12}+320\,a^5\,c^5\,d^3\,e^{10}-640\,a^4\,c^6\,d^5\,e^8+640\,a^3\,c^7\,d^7\,e^6-320\,a^2\,c^8\,d^9\,e^4+64\,a\,c^9\,d^{11}\,e^2\right)-64\,a\,c^8\,d^9\,e^3-64\,a^5\,c^4\,d\,e^{11}+256\,a^2\,c^7\,d^7\,e^5-384\,a^3\,c^6\,d^5\,e^7+256\,a^4\,c^5\,d^3\,e^9\right)\right)\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}-\left(\sqrt{d+e\,x}\,\left(16\,a^4\,c^4\,e^{10}-32\,a^3\,c^5\,d^2\,e^8+32\,a\,c^7\,d^6\,e^4-16\,c^8\,d^8\,e^2\right)+\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,\left(-64\,a^6\,c^4\,d\,e^{12}+320\,a^5\,c^5\,d^3\,e^{10}-640\,a^4\,c^6\,d^5\,e^8+640\,a^3\,c^7\,d^7\,e^6-320\,a^2\,c^8\,d^9\,e^4+64\,a\,c^9\,d^{11}\,e^2\right)+64\,a\,c^8\,d^9\,e^3+64\,a^5\,c^4\,d\,e^{11}-256\,a^2\,c^7\,d^7\,e^5+384\,a^3\,c^6\,d^5\,e^7-256\,a^4\,c^5\,d^3\,e^9\right)\right)\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}+16\,a^3\,c^4\,e^9-16\,c^7\,d^6\,e^3+48\,a\,c^6\,d^4\,e^5-48\,a^2\,c^5\,d^2\,e^7}\right)\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\sqrt{d+e\,x}\,\left(16\,a^4\,c^4\,e^{10}-32\,a^3\,c^5\,d^2\,e^8+32\,a\,c^7\,d^6\,e^4-16\,c^8\,d^8\,e^2\right)+\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,\left(-64\,a^6\,c^4\,d\,e^{12}+320\,a^5\,c^5\,d^3\,e^{10}-640\,a^4\,c^6\,d^5\,e^8+640\,a^3\,c^7\,d^7\,e^6-320\,a^2\,c^8\,d^9\,e^4+64\,a\,c^9\,d^{11}\,e^2\right)-64\,a\,c^8\,d^9\,e^3-64\,a^5\,c^4\,d\,e^{11}+256\,a^2\,c^7\,d^7\,e^5-384\,a^3\,c^6\,d^5\,e^7+256\,a^4\,c^5\,d^3\,e^9\right)\right)\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,1{}\mathrm{i}+\left(\sqrt{d+e\,x}\,\left(16\,a^4\,c^4\,e^{10}-32\,a^3\,c^5\,d^2\,e^8+32\,a\,c^7\,d^6\,e^4-16\,c^8\,d^8\,e^2\right)+\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,\left(-64\,a^6\,c^4\,d\,e^{12}+320\,a^5\,c^5\,d^3\,e^{10}-640\,a^4\,c^6\,d^5\,e^8+640\,a^3\,c^7\,d^7\,e^6-320\,a^2\,c^8\,d^9\,e^4+64\,a\,c^9\,d^{11}\,e^2\right)+64\,a\,c^8\,d^9\,e^3+64\,a^5\,c^4\,d\,e^{11}-256\,a^2\,c^7\,d^7\,e^5+384\,a^3\,c^6\,d^5\,e^7-256\,a^4\,c^5\,d^3\,e^9\right)\right)\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,1{}\mathrm{i}}{\left(\sqrt{d+e\,x}\,\left(16\,a^4\,c^4\,e^{10}-32\,a^3\,c^5\,d^2\,e^8+32\,a\,c^7\,d^6\,e^4-16\,c^8\,d^8\,e^2\right)+\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,\left(-64\,a^6\,c^4\,d\,e^{12}+320\,a^5\,c^5\,d^3\,e^{10}-640\,a^4\,c^6\,d^5\,e^8+640\,a^3\,c^7\,d^7\,e^6-320\,a^2\,c^8\,d^9\,e^4+64\,a\,c^9\,d^{11}\,e^2\right)-64\,a\,c^8\,d^9\,e^3-64\,a^5\,c^4\,d\,e^{11}+256\,a^2\,c^7\,d^7\,e^5-384\,a^3\,c^6\,d^5\,e^7+256\,a^4\,c^5\,d^3\,e^9\right)\right)\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}-\left(\sqrt{d+e\,x}\,\left(16\,a^4\,c^4\,e^{10}-32\,a^3\,c^5\,d^2\,e^8+32\,a\,c^7\,d^6\,e^4-16\,c^8\,d^8\,e^2\right)+\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,\left(-64\,a^6\,c^4\,d\,e^{12}+320\,a^5\,c^5\,d^3\,e^{10}-640\,a^4\,c^6\,d^5\,e^8+640\,a^3\,c^7\,d^7\,e^6-320\,a^2\,c^8\,d^9\,e^4+64\,a\,c^9\,d^{11}\,e^2\right)+64\,a\,c^8\,d^9\,e^3+64\,a^5\,c^4\,d\,e^{11}-256\,a^2\,c^7\,d^7\,e^5+384\,a^3\,c^6\,d^5\,e^7-256\,a^4\,c^5\,d^3\,e^9\right)\right)\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}+16\,a^3\,c^4\,e^9-16\,c^7\,d^6\,e^3+48\,a\,c^6\,d^4\,e^5-48\,a^2\,c^5\,d^2\,e^7}\right)\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{a^3\,c}+3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{a^3\,c}}{4\,\left(a^5\,e^6-3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2-a^2\,c^3\,d^6\right)}}\,2{}\mathrm{i}","Not used",1,"- atan((((d + e*x)^(1/2)*(16*a^4*c^4*e^10 - 16*c^8*d^8*e^2 + 32*a*c^7*d^6*e^4 - 32*a^3*c^5*d^2*e^8) + (-(a*c^2*d^3 + a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 + 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*((d + e*x)^(1/2)*(-(a*c^2*d^3 + a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 + 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^9*d^11*e^2 - 64*a^6*c^4*d*e^12 - 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 - 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10) - 64*a*c^8*d^9*e^3 - 64*a^5*c^4*d*e^11 + 256*a^2*c^7*d^7*e^5 - 384*a^3*c^6*d^5*e^7 + 256*a^4*c^5*d^3*e^9))*(-(a*c^2*d^3 + a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 + 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*1i + ((d + e*x)^(1/2)*(16*a^4*c^4*e^10 - 16*c^8*d^8*e^2 + 32*a*c^7*d^6*e^4 - 32*a^3*c^5*d^2*e^8) + (-(a*c^2*d^3 + a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 + 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*((d + e*x)^(1/2)*(-(a*c^2*d^3 + a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 + 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^9*d^11*e^2 - 64*a^6*c^4*d*e^12 - 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 - 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10) + 64*a*c^8*d^9*e^3 + 64*a^5*c^4*d*e^11 - 256*a^2*c^7*d^7*e^5 + 384*a^3*c^6*d^5*e^7 - 256*a^4*c^5*d^3*e^9))*(-(a*c^2*d^3 + a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 + 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*1i)/(((d + e*x)^(1/2)*(16*a^4*c^4*e^10 - 16*c^8*d^8*e^2 + 32*a*c^7*d^6*e^4 - 32*a^3*c^5*d^2*e^8) + (-(a*c^2*d^3 + a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 + 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*((d + e*x)^(1/2)*(-(a*c^2*d^3 + a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 + 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^9*d^11*e^2 - 64*a^6*c^4*d*e^12 - 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 - 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10) - 64*a*c^8*d^9*e^3 - 64*a^5*c^4*d*e^11 + 256*a^2*c^7*d^7*e^5 - 384*a^3*c^6*d^5*e^7 + 256*a^4*c^5*d^3*e^9))*(-(a*c^2*d^3 + a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 + 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2) - ((d + e*x)^(1/2)*(16*a^4*c^4*e^10 - 16*c^8*d^8*e^2 + 32*a*c^7*d^6*e^4 - 32*a^3*c^5*d^2*e^8) + (-(a*c^2*d^3 + a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 + 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*((d + e*x)^(1/2)*(-(a*c^2*d^3 + a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 + 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^9*d^11*e^2 - 64*a^6*c^4*d*e^12 - 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 - 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10) + 64*a*c^8*d^9*e^3 + 64*a^5*c^4*d*e^11 - 256*a^2*c^7*d^7*e^5 + 384*a^3*c^6*d^5*e^7 - 256*a^4*c^5*d^3*e^9))*(-(a*c^2*d^3 + a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 + 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2) + 16*a^3*c^4*e^9 - 16*c^7*d^6*e^3 + 48*a*c^6*d^4*e^5 - 48*a^2*c^5*d^2*e^7))*(-(a*c^2*d^3 + a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 + 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*2i - atan((((d + e*x)^(1/2)*(16*a^4*c^4*e^10 - 16*c^8*d^8*e^2 + 32*a*c^7*d^6*e^4 - 32*a^3*c^5*d^2*e^8) + (-(a*c^2*d^3 - a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 - 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*((d + e*x)^(1/2)*(-(a*c^2*d^3 - a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 - 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^9*d^11*e^2 - 64*a^6*c^4*d*e^12 - 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 - 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10) - 64*a*c^8*d^9*e^3 - 64*a^5*c^4*d*e^11 + 256*a^2*c^7*d^7*e^5 - 384*a^3*c^6*d^5*e^7 + 256*a^4*c^5*d^3*e^9))*(-(a*c^2*d^3 - a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 - 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*1i + ((d + e*x)^(1/2)*(16*a^4*c^4*e^10 - 16*c^8*d^8*e^2 + 32*a*c^7*d^6*e^4 - 32*a^3*c^5*d^2*e^8) + (-(a*c^2*d^3 - a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 - 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*((d + e*x)^(1/2)*(-(a*c^2*d^3 - a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 - 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^9*d^11*e^2 - 64*a^6*c^4*d*e^12 - 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 - 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10) + 64*a*c^8*d^9*e^3 + 64*a^5*c^4*d*e^11 - 256*a^2*c^7*d^7*e^5 + 384*a^3*c^6*d^5*e^7 - 256*a^4*c^5*d^3*e^9))*(-(a*c^2*d^3 - a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 - 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*1i)/(((d + e*x)^(1/2)*(16*a^4*c^4*e^10 - 16*c^8*d^8*e^2 + 32*a*c^7*d^6*e^4 - 32*a^3*c^5*d^2*e^8) + (-(a*c^2*d^3 - a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 - 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*((d + e*x)^(1/2)*(-(a*c^2*d^3 - a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 - 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^9*d^11*e^2 - 64*a^6*c^4*d*e^12 - 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 - 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10) - 64*a*c^8*d^9*e^3 - 64*a^5*c^4*d*e^11 + 256*a^2*c^7*d^7*e^5 - 384*a^3*c^6*d^5*e^7 + 256*a^4*c^5*d^3*e^9))*(-(a*c^2*d^3 - a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 - 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2) - ((d + e*x)^(1/2)*(16*a^4*c^4*e^10 - 16*c^8*d^8*e^2 + 32*a*c^7*d^6*e^4 - 32*a^3*c^5*d^2*e^8) + (-(a*c^2*d^3 - a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 - 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*((d + e*x)^(1/2)*(-(a*c^2*d^3 - a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 - 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^9*d^11*e^2 - 64*a^6*c^4*d*e^12 - 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 - 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10) + 64*a*c^8*d^9*e^3 + 64*a^5*c^4*d*e^11 - 256*a^2*c^7*d^7*e^5 + 384*a^3*c^6*d^5*e^7 - 256*a^4*c^5*d^3*e^9))*(-(a*c^2*d^3 - a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 - 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2) + 16*a^3*c^4*e^9 - 16*c^7*d^6*e^3 + 48*a*c^6*d^4*e^5 - 48*a^2*c^5*d^2*e^7))*(-(a*c^2*d^3 - a*e^3*(a^3*c)^(1/2) + 3*a^2*c*d*e^2 - 3*c*d^2*e*(a^3*c)^(1/2))/(4*(a^5*e^6 - a^2*c^3*d^6 - 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*2i - (2*e)/((a*e^2 - c*d^2)*(d + e*x)^(1/2))","B"
617,1,7831,190,2.660455,"\text{Not used}","int(1/((a - c*x^2)*(d + e*x)^(5/2)),x)","-\frac{\frac{2\,e}{3\,\left(a\,e^2-c\,d^2\right)}-\frac{4\,c\,d\,e\,\left(d+e\,x\right)}{{\left(a\,e^2-c\,d^2\right)}^2}}{{\left(d+e\,x\right)}^{3/2}}-\mathrm{atan}\left(\frac{\left(\sqrt{d+e\,x}\,\left(16\,a^8\,c^5\,e^{18}-320\,a^6\,c^7\,d^4\,e^{14}+1024\,a^5\,c^8\,d^6\,e^{12}-1440\,a^4\,c^9\,d^8\,e^{10}+1024\,a^3\,c^{10}\,d^{10}\,e^8-320\,a^2\,c^{11}\,d^{12}\,e^6+16\,c^{13}\,d^{16}\,e^2\right)+\sqrt{-\frac{a^2\,e^5\,\sqrt{a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,\left(32\,a^{10}\,c^4\,e^{21}-\sqrt{d+e\,x}\,\sqrt{-\frac{a^2\,e^5\,\sqrt{a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,\left(64\,a^{11}\,c^4\,d\,e^{22}-640\,a^{10}\,c^5\,d^3\,e^{20}+2880\,a^9\,c^6\,d^5\,e^{18}-7680\,a^8\,c^7\,d^7\,e^{16}+13440\,a^7\,c^8\,d^9\,e^{14}-16128\,a^6\,c^9\,d^{11}\,e^{12}+13440\,a^5\,c^{10}\,d^{13}\,e^{10}-7680\,a^4\,c^{11}\,d^{15}\,e^8+2880\,a^3\,c^{12}\,d^{17}\,e^6-640\,a^2\,c^{13}\,d^{19}\,e^4+64\,a\,c^{14}\,d^{21}\,e^2\right)+96\,a\,c^{13}\,d^{18}\,e^3-736\,a^2\,c^{12}\,d^{16}\,e^5+2432\,a^3\,c^{11}\,d^{14}\,e^7-4480\,a^4\,c^{10}\,d^{12}\,e^9+4928\,a^5\,c^9\,d^{10}\,e^{11}-3136\,a^6\,c^8\,d^8\,e^{13}+896\,a^7\,c^7\,d^6\,e^{15}+128\,a^8\,c^6\,d^4\,e^{17}-160\,a^9\,c^5\,d^2\,e^{19}\right)\right)\,\sqrt{-\frac{a^2\,e^5\,\sqrt{a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,1{}\mathrm{i}+\left(\sqrt{d+e\,x}\,\left(16\,a^8\,c^5\,e^{18}-320\,a^6\,c^7\,d^4\,e^{14}+1024\,a^5\,c^8\,d^6\,e^{12}-1440\,a^4\,c^9\,d^8\,e^{10}+1024\,a^3\,c^{10}\,d^{10}\,e^8-320\,a^2\,c^{11}\,d^{12}\,e^6+16\,c^{13}\,d^{16}\,e^2\right)-\sqrt{-\frac{a^2\,e^5\,\sqrt{a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,\left(32\,a^{10}\,c^4\,e^{21}+\sqrt{d+e\,x}\,\sqrt{-\frac{a^2\,e^5\,\sqrt{a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,\left(64\,a^{11}\,c^4\,d\,e^{22}-640\,a^{10}\,c^5\,d^3\,e^{20}+2880\,a^9\,c^6\,d^5\,e^{18}-7680\,a^8\,c^7\,d^7\,e^{16}+13440\,a^7\,c^8\,d^9\,e^{14}-16128\,a^6\,c^9\,d^{11}\,e^{12}+13440\,a^5\,c^{10}\,d^{13}\,e^{10}-7680\,a^4\,c^{11}\,d^{15}\,e^8+2880\,a^3\,c^{12}\,d^{17}\,e^6-640\,a^2\,c^{13}\,d^{19}\,e^4+64\,a\,c^{14}\,d^{21}\,e^2\right)+96\,a\,c^{13}\,d^{18}\,e^3-736\,a^2\,c^{12}\,d^{16}\,e^5+2432\,a^3\,c^{11}\,d^{14}\,e^7-4480\,a^4\,c^{10}\,d^{12}\,e^9+4928\,a^5\,c^9\,d^{10}\,e^{11}-3136\,a^6\,c^8\,d^8\,e^{13}+896\,a^7\,c^7\,d^6\,e^{15}+128\,a^8\,c^6\,d^4\,e^{17}-160\,a^9\,c^5\,d^2\,e^{19}\right)\right)\,\sqrt{-\frac{a^2\,e^5\,\sqrt{a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,1{}\mathrm{i}}{\left(\sqrt{d+e\,x}\,\left(16\,a^8\,c^5\,e^{18}-320\,a^6\,c^7\,d^4\,e^{14}+1024\,a^5\,c^8\,d^6\,e^{12}-1440\,a^4\,c^9\,d^8\,e^{10}+1024\,a^3\,c^{10}\,d^{10}\,e^8-320\,a^2\,c^{11}\,d^{12}\,e^6+16\,c^{13}\,d^{16}\,e^2\right)+\sqrt{-\frac{a^2\,e^5\,\sqrt{a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,\left(32\,a^{10}\,c^4\,e^{21}-\sqrt{d+e\,x}\,\sqrt{-\frac{a^2\,e^5\,\sqrt{a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,\left(64\,a^{11}\,c^4\,d\,e^{22}-640\,a^{10}\,c^5\,d^3\,e^{20}+2880\,a^9\,c^6\,d^5\,e^{18}-7680\,a^8\,c^7\,d^7\,e^{16}+13440\,a^7\,c^8\,d^9\,e^{14}-16128\,a^6\,c^9\,d^{11}\,e^{12}+13440\,a^5\,c^{10}\,d^{13}\,e^{10}-7680\,a^4\,c^{11}\,d^{15}\,e^8+2880\,a^3\,c^{12}\,d^{17}\,e^6-640\,a^2\,c^{13}\,d^{19}\,e^4+64\,a\,c^{14}\,d^{21}\,e^2\right)+96\,a\,c^{13}\,d^{18}\,e^3-736\,a^2\,c^{12}\,d^{16}\,e^5+2432\,a^3\,c^{11}\,d^{14}\,e^7-4480\,a^4\,c^{10}\,d^{12}\,e^9+4928\,a^5\,c^9\,d^{10}\,e^{11}-3136\,a^6\,c^8\,d^8\,e^{13}+896\,a^7\,c^7\,d^6\,e^{15}+128\,a^8\,c^6\,d^4\,e^{17}-160\,a^9\,c^5\,d^2\,e^{19}\right)\right)\,\sqrt{-\frac{a^2\,e^5\,\sqrt{a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}-\left(\sqrt{d+e\,x}\,\left(16\,a^8\,c^5\,e^{18}-320\,a^6\,c^7\,d^4\,e^{14}+1024\,a^5\,c^8\,d^6\,e^{12}-1440\,a^4\,c^9\,d^8\,e^{10}+1024\,a^3\,c^{10}\,d^{10}\,e^8-320\,a^2\,c^{11}\,d^{12}\,e^6+16\,c^{13}\,d^{16}\,e^2\right)-\sqrt{-\frac{a^2\,e^5\,\sqrt{a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,\left(32\,a^{10}\,c^4\,e^{21}+\sqrt{d+e\,x}\,\sqrt{-\frac{a^2\,e^5\,\sqrt{a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,\left(64\,a^{11}\,c^4\,d\,e^{22}-640\,a^{10}\,c^5\,d^3\,e^{20}+2880\,a^9\,c^6\,d^5\,e^{18}-7680\,a^8\,c^7\,d^7\,e^{16}+13440\,a^7\,c^8\,d^9\,e^{14}-16128\,a^6\,c^9\,d^{11}\,e^{12}+13440\,a^5\,c^{10}\,d^{13}\,e^{10}-7680\,a^4\,c^{11}\,d^{15}\,e^8+2880\,a^3\,c^{12}\,d^{17}\,e^6-640\,a^2\,c^{13}\,d^{19}\,e^4+64\,a\,c^{14}\,d^{21}\,e^2\right)+96\,a\,c^{13}\,d^{18}\,e^3-736\,a^2\,c^{12}\,d^{16}\,e^5+2432\,a^3\,c^{11}\,d^{14}\,e^7-4480\,a^4\,c^{10}\,d^{12}\,e^9+4928\,a^5\,c^9\,d^{10}\,e^{11}-3136\,a^6\,c^8\,d^8\,e^{13}+896\,a^7\,c^7\,d^6\,e^{15}+128\,a^8\,c^6\,d^4\,e^{17}-160\,a^9\,c^5\,d^2\,e^{19}\right)\right)\,\sqrt{-\frac{a^2\,e^5\,\sqrt{a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}+32\,c^{12}\,d^{13}\,e^3-192\,a\,c^{11}\,d^{11}\,e^5+32\,a^6\,c^6\,d\,e^{15}+480\,a^2\,c^{10}\,d^9\,e^7-640\,a^3\,c^9\,d^7\,e^9+480\,a^4\,c^8\,d^5\,e^{11}-192\,a^5\,c^7\,d^3\,e^{13}}\right)\,\sqrt{-\frac{a^2\,e^5\,\sqrt{a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\sqrt{d+e\,x}\,\left(16\,a^8\,c^5\,e^{18}-320\,a^6\,c^7\,d^4\,e^{14}+1024\,a^5\,c^8\,d^6\,e^{12}-1440\,a^4\,c^9\,d^8\,e^{10}+1024\,a^3\,c^{10}\,d^{10}\,e^8-320\,a^2\,c^{11}\,d^{12}\,e^6+16\,c^{13}\,d^{16}\,e^2\right)+\sqrt{\frac{a^2\,e^5\,\sqrt{a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,\left(32\,a^{10}\,c^4\,e^{21}-\sqrt{d+e\,x}\,\sqrt{\frac{a^2\,e^5\,\sqrt{a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,\left(64\,a^{11}\,c^4\,d\,e^{22}-640\,a^{10}\,c^5\,d^3\,e^{20}+2880\,a^9\,c^6\,d^5\,e^{18}-7680\,a^8\,c^7\,d^7\,e^{16}+13440\,a^7\,c^8\,d^9\,e^{14}-16128\,a^6\,c^9\,d^{11}\,e^{12}+13440\,a^5\,c^{10}\,d^{13}\,e^{10}-7680\,a^4\,c^{11}\,d^{15}\,e^8+2880\,a^3\,c^{12}\,d^{17}\,e^6-640\,a^2\,c^{13}\,d^{19}\,e^4+64\,a\,c^{14}\,d^{21}\,e^2\right)+96\,a\,c^{13}\,d^{18}\,e^3-736\,a^2\,c^{12}\,d^{16}\,e^5+2432\,a^3\,c^{11}\,d^{14}\,e^7-4480\,a^4\,c^{10}\,d^{12}\,e^9+4928\,a^5\,c^9\,d^{10}\,e^{11}-3136\,a^6\,c^8\,d^8\,e^{13}+896\,a^7\,c^7\,d^6\,e^{15}+128\,a^8\,c^6\,d^4\,e^{17}-160\,a^9\,c^5\,d^2\,e^{19}\right)\right)\,\sqrt{\frac{a^2\,e^5\,\sqrt{a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,1{}\mathrm{i}+\left(\sqrt{d+e\,x}\,\left(16\,a^8\,c^5\,e^{18}-320\,a^6\,c^7\,d^4\,e^{14}+1024\,a^5\,c^8\,d^6\,e^{12}-1440\,a^4\,c^9\,d^8\,e^{10}+1024\,a^3\,c^{10}\,d^{10}\,e^8-320\,a^2\,c^{11}\,d^{12}\,e^6+16\,c^{13}\,d^{16}\,e^2\right)-\sqrt{\frac{a^2\,e^5\,\sqrt{a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,\left(32\,a^{10}\,c^4\,e^{21}+\sqrt{d+e\,x}\,\sqrt{\frac{a^2\,e^5\,\sqrt{a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,\left(64\,a^{11}\,c^4\,d\,e^{22}-640\,a^{10}\,c^5\,d^3\,e^{20}+2880\,a^9\,c^6\,d^5\,e^{18}-7680\,a^8\,c^7\,d^7\,e^{16}+13440\,a^7\,c^8\,d^9\,e^{14}-16128\,a^6\,c^9\,d^{11}\,e^{12}+13440\,a^5\,c^{10}\,d^{13}\,e^{10}-7680\,a^4\,c^{11}\,d^{15}\,e^8+2880\,a^3\,c^{12}\,d^{17}\,e^6-640\,a^2\,c^{13}\,d^{19}\,e^4+64\,a\,c^{14}\,d^{21}\,e^2\right)+96\,a\,c^{13}\,d^{18}\,e^3-736\,a^2\,c^{12}\,d^{16}\,e^5+2432\,a^3\,c^{11}\,d^{14}\,e^7-4480\,a^4\,c^{10}\,d^{12}\,e^9+4928\,a^5\,c^9\,d^{10}\,e^{11}-3136\,a^6\,c^8\,d^8\,e^{13}+896\,a^7\,c^7\,d^6\,e^{15}+128\,a^8\,c^6\,d^4\,e^{17}-160\,a^9\,c^5\,d^2\,e^{19}\right)\right)\,\sqrt{\frac{a^2\,e^5\,\sqrt{a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,1{}\mathrm{i}}{\left(\sqrt{d+e\,x}\,\left(16\,a^8\,c^5\,e^{18}-320\,a^6\,c^7\,d^4\,e^{14}+1024\,a^5\,c^8\,d^6\,e^{12}-1440\,a^4\,c^9\,d^8\,e^{10}+1024\,a^3\,c^{10}\,d^{10}\,e^8-320\,a^2\,c^{11}\,d^{12}\,e^6+16\,c^{13}\,d^{16}\,e^2\right)+\sqrt{\frac{a^2\,e^5\,\sqrt{a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,\left(32\,a^{10}\,c^4\,e^{21}-\sqrt{d+e\,x}\,\sqrt{\frac{a^2\,e^5\,\sqrt{a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,\left(64\,a^{11}\,c^4\,d\,e^{22}-640\,a^{10}\,c^5\,d^3\,e^{20}+2880\,a^9\,c^6\,d^5\,e^{18}-7680\,a^8\,c^7\,d^7\,e^{16}+13440\,a^7\,c^8\,d^9\,e^{14}-16128\,a^6\,c^9\,d^{11}\,e^{12}+13440\,a^5\,c^{10}\,d^{13}\,e^{10}-7680\,a^4\,c^{11}\,d^{15}\,e^8+2880\,a^3\,c^{12}\,d^{17}\,e^6-640\,a^2\,c^{13}\,d^{19}\,e^4+64\,a\,c^{14}\,d^{21}\,e^2\right)+96\,a\,c^{13}\,d^{18}\,e^3-736\,a^2\,c^{12}\,d^{16}\,e^5+2432\,a^3\,c^{11}\,d^{14}\,e^7-4480\,a^4\,c^{10}\,d^{12}\,e^9+4928\,a^5\,c^9\,d^{10}\,e^{11}-3136\,a^6\,c^8\,d^8\,e^{13}+896\,a^7\,c^7\,d^6\,e^{15}+128\,a^8\,c^6\,d^4\,e^{17}-160\,a^9\,c^5\,d^2\,e^{19}\right)\right)\,\sqrt{\frac{a^2\,e^5\,\sqrt{a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}-\left(\sqrt{d+e\,x}\,\left(16\,a^8\,c^5\,e^{18}-320\,a^6\,c^7\,d^4\,e^{14}+1024\,a^5\,c^8\,d^6\,e^{12}-1440\,a^4\,c^9\,d^8\,e^{10}+1024\,a^3\,c^{10}\,d^{10}\,e^8-320\,a^2\,c^{11}\,d^{12}\,e^6+16\,c^{13}\,d^{16}\,e^2\right)-\sqrt{\frac{a^2\,e^5\,\sqrt{a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,\left(32\,a^{10}\,c^4\,e^{21}+\sqrt{d+e\,x}\,\sqrt{\frac{a^2\,e^5\,\sqrt{a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,\left(64\,a^{11}\,c^4\,d\,e^{22}-640\,a^{10}\,c^5\,d^3\,e^{20}+2880\,a^9\,c^6\,d^5\,e^{18}-7680\,a^8\,c^7\,d^7\,e^{16}+13440\,a^7\,c^8\,d^9\,e^{14}-16128\,a^6\,c^9\,d^{11}\,e^{12}+13440\,a^5\,c^{10}\,d^{13}\,e^{10}-7680\,a^4\,c^{11}\,d^{15}\,e^8+2880\,a^3\,c^{12}\,d^{17}\,e^6-640\,a^2\,c^{13}\,d^{19}\,e^4+64\,a\,c^{14}\,d^{21}\,e^2\right)+96\,a\,c^{13}\,d^{18}\,e^3-736\,a^2\,c^{12}\,d^{16}\,e^5+2432\,a^3\,c^{11}\,d^{14}\,e^7-4480\,a^4\,c^{10}\,d^{12}\,e^9+4928\,a^5\,c^9\,d^{10}\,e^{11}-3136\,a^6\,c^8\,d^8\,e^{13}+896\,a^7\,c^7\,d^6\,e^{15}+128\,a^8\,c^6\,d^4\,e^{17}-160\,a^9\,c^5\,d^2\,e^{19}\right)\right)\,\sqrt{\frac{a^2\,e^5\,\sqrt{a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}+32\,c^{12}\,d^{13}\,e^3-192\,a\,c^{11}\,d^{11}\,e^5+32\,a^6\,c^6\,d\,e^{15}+480\,a^2\,c^{10}\,d^9\,e^7-640\,a^3\,c^9\,d^7\,e^9+480\,a^4\,c^8\,d^5\,e^{11}-192\,a^5\,c^7\,d^3\,e^{13}}\right)\,\sqrt{\frac{a^2\,e^5\,\sqrt{a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{a^3\,c^3}+10\,a\,c\,d^2\,e^3\,\sqrt{a^3\,c^3}}{4\,\left(a^7\,e^{10}-5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6-10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2-a^2\,c^5\,d^{10}\right)}}\,2{}\mathrm{i}","Not used",1,"- ((2*e)/(3*(a*e^2 - c*d^2)) - (4*c*d*e*(d + e*x))/(a*e^2 - c*d^2)^2)/(d + e*x)^(3/2) - atan((((d + e*x)^(1/2)*(16*a^8*c^5*e^18 + 16*c^13*d^16*e^2 - 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 - 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 - 320*a^6*c^7*d^4*e^14) + (-(a^2*e^5*(a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(32*a^10*c^4*e^21 - (d + e*x)^(1/2)*(-(a^2*e^5*(a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 + 64*a^11*c^4*d*e^22 - 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 - 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 - 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 - 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 - 640*a^10*c^5*d^3*e^20) + 96*a*c^13*d^18*e^3 - 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 - 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 - 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 + 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19))*(-(a^2*e^5*(a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*1i + ((d + e*x)^(1/2)*(16*a^8*c^5*e^18 + 16*c^13*d^16*e^2 - 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 - 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 - 320*a^6*c^7*d^4*e^14) - (-(a^2*e^5*(a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(32*a^10*c^4*e^21 + (d + e*x)^(1/2)*(-(a^2*e^5*(a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 + 64*a^11*c^4*d*e^22 - 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 - 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 - 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 - 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 - 640*a^10*c^5*d^3*e^20) + 96*a*c^13*d^18*e^3 - 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 - 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 - 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 + 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19))*(-(a^2*e^5*(a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*1i)/(((d + e*x)^(1/2)*(16*a^8*c^5*e^18 + 16*c^13*d^16*e^2 - 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 - 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 - 320*a^6*c^7*d^4*e^14) + (-(a^2*e^5*(a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(32*a^10*c^4*e^21 - (d + e*x)^(1/2)*(-(a^2*e^5*(a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 + 64*a^11*c^4*d*e^22 - 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 - 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 - 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 - 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 - 640*a^10*c^5*d^3*e^20) + 96*a*c^13*d^18*e^3 - 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 - 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 - 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 + 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19))*(-(a^2*e^5*(a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2) - ((d + e*x)^(1/2)*(16*a^8*c^5*e^18 + 16*c^13*d^16*e^2 - 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 - 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 - 320*a^6*c^7*d^4*e^14) - (-(a^2*e^5*(a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(32*a^10*c^4*e^21 + (d + e*x)^(1/2)*(-(a^2*e^5*(a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 + 64*a^11*c^4*d*e^22 - 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 - 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 - 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 - 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 - 640*a^10*c^5*d^3*e^20) + 96*a*c^13*d^18*e^3 - 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 - 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 - 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 + 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19))*(-(a^2*e^5*(a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2) + 32*c^12*d^13*e^3 - 192*a*c^11*d^11*e^5 + 32*a^6*c^6*d*e^15 + 480*a^2*c^10*d^9*e^7 - 640*a^3*c^9*d^7*e^9 + 480*a^4*c^8*d^5*e^11 - 192*a^5*c^7*d^3*e^13))*(-(a^2*e^5*(a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*2i - atan((((d + e*x)^(1/2)*(16*a^8*c^5*e^18 + 16*c^13*d^16*e^2 - 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 - 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 - 320*a^6*c^7*d^4*e^14) + ((a^2*e^5*(a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(32*a^10*c^4*e^21 - (d + e*x)^(1/2)*((a^2*e^5*(a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 + 64*a^11*c^4*d*e^22 - 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 - 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 - 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 - 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 - 640*a^10*c^5*d^3*e^20) + 96*a*c^13*d^18*e^3 - 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 - 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 - 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 + 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19))*((a^2*e^5*(a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*1i + ((d + e*x)^(1/2)*(16*a^8*c^5*e^18 + 16*c^13*d^16*e^2 - 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 - 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 - 320*a^6*c^7*d^4*e^14) - ((a^2*e^5*(a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(32*a^10*c^4*e^21 + (d + e*x)^(1/2)*((a^2*e^5*(a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 + 64*a^11*c^4*d*e^22 - 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 - 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 - 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 - 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 - 640*a^10*c^5*d^3*e^20) + 96*a*c^13*d^18*e^3 - 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 - 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 - 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 + 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19))*((a^2*e^5*(a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*1i)/(((d + e*x)^(1/2)*(16*a^8*c^5*e^18 + 16*c^13*d^16*e^2 - 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 - 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 - 320*a^6*c^7*d^4*e^14) + ((a^2*e^5*(a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(32*a^10*c^4*e^21 - (d + e*x)^(1/2)*((a^2*e^5*(a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 + 64*a^11*c^4*d*e^22 - 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 - 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 - 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 - 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 - 640*a^10*c^5*d^3*e^20) + 96*a*c^13*d^18*e^3 - 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 - 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 - 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 + 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19))*((a^2*e^5*(a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2) - ((d + e*x)^(1/2)*(16*a^8*c^5*e^18 + 16*c^13*d^16*e^2 - 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 - 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 - 320*a^6*c^7*d^4*e^14) - ((a^2*e^5*(a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(32*a^10*c^4*e^21 + (d + e*x)^(1/2)*((a^2*e^5*(a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 + 64*a^11*c^4*d*e^22 - 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 - 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 - 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 - 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 - 640*a^10*c^5*d^3*e^20) + 96*a*c^13*d^18*e^3 - 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 - 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 - 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 + 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19))*((a^2*e^5*(a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2) + 32*c^12*d^13*e^3 - 192*a*c^11*d^11*e^5 + 32*a^6*c^6*d*e^15 + 480*a^2*c^10*d^9*e^7 - 640*a^3*c^9*d^7*e^9 + 480*a^4*c^8*d^5*e^11 - 192*a^5*c^7*d^3*e^13))*((a^2*e^5*(a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(a^3*c^3)^(1/2) + 10*a*c*d^2*e^3*(a^3*c^3)^(1/2))/(4*(a^7*e^10 - a^2*c^5*d^10 - 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 - 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*2i","B"
618,1,3481,781,0.483808,"\text{Not used}","int((d + e*x)^(5/2)/(a + c*x^2),x)","\frac{2\,e\,{\left(d+e\,x\right)}^{3/2}}{3\,c}+\frac{4\,d\,e\,\sqrt{d+e\,x}}{c}-\mathrm{atan}\left(\frac{a^3\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{5\,d^3\,e^2}{2\,c^2}-\frac{d^5}{4\,a\,c}-\frac{e^5\,\sqrt{-a^3\,c^7}}{4\,c^7}-\frac{5\,a\,d\,e^4}{4\,c^3}-\frac{5\,d^4\,e\,\sqrt{-a^3\,c^7}}{4\,a^2\,c^5}+\frac{5\,d^2\,e^3\,\sqrt{-a^3\,c^7}}{2\,a\,c^6}}\,32{}\mathrm{i}}{\frac{16\,a^4\,e^{11}}{c^2}+64\,a^2\,d^4\,e^7-80\,c^2\,d^8\,e^3-\frac{160\,a^3\,d^2\,e^9}{c}+160\,a\,c\,d^6\,e^5+\frac{160\,d^5\,e^6\,\sqrt{-a^3\,c^7}}{c^3}+\frac{288\,a\,d^3\,e^8\,\sqrt{-a^3\,c^7}}{c^4}-\frac{32\,a^2\,d\,e^{10}\,\sqrt{-a^3\,c^7}}{c^5}-\frac{160\,d^7\,e^4\,\sqrt{-a^3\,c^7}}{a\,c^2}}+\frac{d^5\,e^3\,\sqrt{-a^3\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{5\,d^3\,e^2}{2\,c^2}-\frac{d^5}{4\,a\,c}-\frac{e^5\,\sqrt{-a^3\,c^7}}{4\,c^7}-\frac{5\,a\,d\,e^4}{4\,c^3}-\frac{5\,d^4\,e\,\sqrt{-a^3\,c^7}}{4\,a^2\,c^5}+\frac{5\,d^2\,e^3\,\sqrt{-a^3\,c^7}}{2\,a\,c^6}}\,160{}\mathrm{i}}{\frac{16\,a^5\,e^{11}}{c}-160\,a^4\,d^2\,e^9-80\,a\,c^3\,d^8\,e^3+64\,a^3\,c\,d^4\,e^7+160\,a^2\,c^2\,d^6\,e^5-\frac{160\,d^7\,e^4\,\sqrt{-a^3\,c^7}}{c}+\frac{160\,a\,d^5\,e^6\,\sqrt{-a^3\,c^7}}{c^2}-\frac{32\,a^3\,d\,e^{10}\,\sqrt{-a^3\,c^7}}{c^4}+\frac{288\,a^2\,d^3\,e^8\,\sqrt{-a^3\,c^7}}{c^3}}-\frac{d^3\,e^5\,\sqrt{-a^3\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{5\,d^3\,e^2}{2\,c^2}-\frac{d^5}{4\,a\,c}-\frac{e^5\,\sqrt{-a^3\,c^7}}{4\,c^7}-\frac{5\,a\,d\,e^4}{4\,c^3}-\frac{5\,d^4\,e\,\sqrt{-a^3\,c^7}}{4\,a^2\,c^5}+\frac{5\,d^2\,e^3\,\sqrt{-a^3\,c^7}}{2\,a\,c^6}}\,320{}\mathrm{i}}{16\,a^4\,e^{11}-80\,c^4\,d^8\,e^3+160\,a\,c^3\,d^6\,e^5-160\,a^3\,c\,d^2\,e^9+64\,a^2\,c^2\,d^4\,e^7-\frac{160\,d^7\,e^4\,\sqrt{-a^3\,c^7}}{a}+\frac{160\,d^5\,e^6\,\sqrt{-a^3\,c^7}}{c}+\frac{288\,a\,d^3\,e^8\,\sqrt{-a^3\,c^7}}{c^2}-\frac{32\,a^2\,d\,e^{10}\,\sqrt{-a^3\,c^7}}{c^3}}+\frac{a\,d\,e^7\,\sqrt{-a^3\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{5\,d^3\,e^2}{2\,c^2}-\frac{d^5}{4\,a\,c}-\frac{e^5\,\sqrt{-a^3\,c^7}}{4\,c^7}-\frac{5\,a\,d\,e^4}{4\,c^3}-\frac{5\,d^4\,e\,\sqrt{-a^3\,c^7}}{4\,a^2\,c^5}+\frac{5\,d^2\,e^3\,\sqrt{-a^3\,c^7}}{2\,a\,c^6}}\,32{}\mathrm{i}}{160\,d^5\,e^6\,\sqrt{-a^3\,c^7}+16\,a^4\,c\,e^{11}-80\,c^5\,d^8\,e^3+160\,a\,c^4\,d^6\,e^5+64\,a^2\,c^3\,d^4\,e^7-160\,a^3\,c^2\,d^2\,e^9+\frac{288\,a\,d^3\,e^8\,\sqrt{-a^3\,c^7}}{c}-\frac{160\,c\,d^7\,e^4\,\sqrt{-a^3\,c^7}}{a}-\frac{32\,a^2\,d\,e^{10}\,\sqrt{-a^3\,c^7}}{c^2}}+\frac{a\,c^2\,d^4\,e^4\,\sqrt{d+e\,x}\,\sqrt{\frac{5\,d^3\,e^2}{2\,c^2}-\frac{d^5}{4\,a\,c}-\frac{e^5\,\sqrt{-a^3\,c^7}}{4\,c^7}-\frac{5\,a\,d\,e^4}{4\,c^3}-\frac{5\,d^4\,e\,\sqrt{-a^3\,c^7}}{4\,a^2\,c^5}+\frac{5\,d^2\,e^3\,\sqrt{-a^3\,c^7}}{2\,a\,c^6}}\,160{}\mathrm{i}}{\frac{16\,a^4\,e^{11}}{c^2}+64\,a^2\,d^4\,e^7-80\,c^2\,d^8\,e^3-\frac{160\,a^3\,d^2\,e^9}{c}+160\,a\,c\,d^6\,e^5+\frac{160\,d^5\,e^6\,\sqrt{-a^3\,c^7}}{c^3}+\frac{288\,a\,d^3\,e^8\,\sqrt{-a^3\,c^7}}{c^4}-\frac{32\,a^2\,d\,e^{10}\,\sqrt{-a^3\,c^7}}{c^5}-\frac{160\,d^7\,e^4\,\sqrt{-a^3\,c^7}}{a\,c^2}}-\frac{a^2\,c\,d^2\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{5\,d^3\,e^2}{2\,c^2}-\frac{d^5}{4\,a\,c}-\frac{e^5\,\sqrt{-a^3\,c^7}}{4\,c^7}-\frac{5\,a\,d\,e^4}{4\,c^3}-\frac{5\,d^4\,e\,\sqrt{-a^3\,c^7}}{4\,a^2\,c^5}+\frac{5\,d^2\,e^3\,\sqrt{-a^3\,c^7}}{2\,a\,c^6}}\,320{}\mathrm{i}}{\frac{16\,a^4\,e^{11}}{c^2}+64\,a^2\,d^4\,e^7-80\,c^2\,d^8\,e^3-\frac{160\,a^3\,d^2\,e^9}{c}+160\,a\,c\,d^6\,e^5+\frac{160\,d^5\,e^6\,\sqrt{-a^3\,c^7}}{c^3}+\frac{288\,a\,d^3\,e^8\,\sqrt{-a^3\,c^7}}{c^4}-\frac{32\,a^2\,d\,e^{10}\,\sqrt{-a^3\,c^7}}{c^5}-\frac{160\,d^7\,e^4\,\sqrt{-a^3\,c^7}}{a\,c^2}}\right)\,\sqrt{-\frac{a^2\,e^5\,\sqrt{-a^3\,c^7}+a\,c^6\,d^5+5\,a^3\,c^4\,d\,e^4-10\,a^2\,c^5\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^7}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^7}}{4\,a^2\,c^7}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{a^3\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{e^5\,\sqrt{-a^3\,c^7}}{4\,c^7}-\frac{d^5}{4\,a\,c}+\frac{5\,d^3\,e^2}{2\,c^2}-\frac{5\,a\,d\,e^4}{4\,c^3}+\frac{5\,d^4\,e\,\sqrt{-a^3\,c^7}}{4\,a^2\,c^5}-\frac{5\,d^2\,e^3\,\sqrt{-a^3\,c^7}}{2\,a\,c^6}}\,32{}\mathrm{i}}{\frac{16\,a^4\,e^{11}}{c^2}+64\,a^2\,d^4\,e^7-80\,c^2\,d^8\,e^3-\frac{160\,a^3\,d^2\,e^9}{c}+160\,a\,c\,d^6\,e^5-\frac{160\,d^5\,e^6\,\sqrt{-a^3\,c^7}}{c^3}-\frac{288\,a\,d^3\,e^8\,\sqrt{-a^3\,c^7}}{c^4}+\frac{32\,a^2\,d\,e^{10}\,\sqrt{-a^3\,c^7}}{c^5}+\frac{160\,d^7\,e^4\,\sqrt{-a^3\,c^7}}{a\,c^2}}-\frac{d^5\,e^3\,\sqrt{-a^3\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{e^5\,\sqrt{-a^3\,c^7}}{4\,c^7}-\frac{d^5}{4\,a\,c}+\frac{5\,d^3\,e^2}{2\,c^2}-\frac{5\,a\,d\,e^4}{4\,c^3}+\frac{5\,d^4\,e\,\sqrt{-a^3\,c^7}}{4\,a^2\,c^5}-\frac{5\,d^2\,e^3\,\sqrt{-a^3\,c^7}}{2\,a\,c^6}}\,160{}\mathrm{i}}{\frac{16\,a^5\,e^{11}}{c}-160\,a^4\,d^2\,e^9-80\,a\,c^3\,d^8\,e^3+64\,a^3\,c\,d^4\,e^7+160\,a^2\,c^2\,d^6\,e^5+\frac{160\,d^7\,e^4\,\sqrt{-a^3\,c^7}}{c}-\frac{160\,a\,d^5\,e^6\,\sqrt{-a^3\,c^7}}{c^2}+\frac{32\,a^3\,d\,e^{10}\,\sqrt{-a^3\,c^7}}{c^4}-\frac{288\,a^2\,d^3\,e^8\,\sqrt{-a^3\,c^7}}{c^3}}+\frac{d^3\,e^5\,\sqrt{-a^3\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{e^5\,\sqrt{-a^3\,c^7}}{4\,c^7}-\frac{d^5}{4\,a\,c}+\frac{5\,d^3\,e^2}{2\,c^2}-\frac{5\,a\,d\,e^4}{4\,c^3}+\frac{5\,d^4\,e\,\sqrt{-a^3\,c^7}}{4\,a^2\,c^5}-\frac{5\,d^2\,e^3\,\sqrt{-a^3\,c^7}}{2\,a\,c^6}}\,320{}\mathrm{i}}{16\,a^4\,e^{11}-80\,c^4\,d^8\,e^3+160\,a\,c^3\,d^6\,e^5-160\,a^3\,c\,d^2\,e^9+64\,a^2\,c^2\,d^4\,e^7+\frac{160\,d^7\,e^4\,\sqrt{-a^3\,c^7}}{a}-\frac{160\,d^5\,e^6\,\sqrt{-a^3\,c^7}}{c}-\frac{288\,a\,d^3\,e^8\,\sqrt{-a^3\,c^7}}{c^2}+\frac{32\,a^2\,d\,e^{10}\,\sqrt{-a^3\,c^7}}{c^3}}-\frac{a\,d\,e^7\,\sqrt{-a^3\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{e^5\,\sqrt{-a^3\,c^7}}{4\,c^7}-\frac{d^5}{4\,a\,c}+\frac{5\,d^3\,e^2}{2\,c^2}-\frac{5\,a\,d\,e^4}{4\,c^3}+\frac{5\,d^4\,e\,\sqrt{-a^3\,c^7}}{4\,a^2\,c^5}-\frac{5\,d^2\,e^3\,\sqrt{-a^3\,c^7}}{2\,a\,c^6}}\,32{}\mathrm{i}}{16\,a^4\,c\,e^{11}-160\,d^5\,e^6\,\sqrt{-a^3\,c^7}-80\,c^5\,d^8\,e^3+160\,a\,c^4\,d^6\,e^5+64\,a^2\,c^3\,d^4\,e^7-160\,a^3\,c^2\,d^2\,e^9-\frac{288\,a\,d^3\,e^8\,\sqrt{-a^3\,c^7}}{c}+\frac{160\,c\,d^7\,e^4\,\sqrt{-a^3\,c^7}}{a}+\frac{32\,a^2\,d\,e^{10}\,\sqrt{-a^3\,c^7}}{c^2}}+\frac{a\,c^2\,d^4\,e^4\,\sqrt{d+e\,x}\,\sqrt{\frac{e^5\,\sqrt{-a^3\,c^7}}{4\,c^7}-\frac{d^5}{4\,a\,c}+\frac{5\,d^3\,e^2}{2\,c^2}-\frac{5\,a\,d\,e^4}{4\,c^3}+\frac{5\,d^4\,e\,\sqrt{-a^3\,c^7}}{4\,a^2\,c^5}-\frac{5\,d^2\,e^3\,\sqrt{-a^3\,c^7}}{2\,a\,c^6}}\,160{}\mathrm{i}}{\frac{16\,a^4\,e^{11}}{c^2}+64\,a^2\,d^4\,e^7-80\,c^2\,d^8\,e^3-\frac{160\,a^3\,d^2\,e^9}{c}+160\,a\,c\,d^6\,e^5-\frac{160\,d^5\,e^6\,\sqrt{-a^3\,c^7}}{c^3}-\frac{288\,a\,d^3\,e^8\,\sqrt{-a^3\,c^7}}{c^4}+\frac{32\,a^2\,d\,e^{10}\,\sqrt{-a^3\,c^7}}{c^5}+\frac{160\,d^7\,e^4\,\sqrt{-a^3\,c^7}}{a\,c^2}}-\frac{a^2\,c\,d^2\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{e^5\,\sqrt{-a^3\,c^7}}{4\,c^7}-\frac{d^5}{4\,a\,c}+\frac{5\,d^3\,e^2}{2\,c^2}-\frac{5\,a\,d\,e^4}{4\,c^3}+\frac{5\,d^4\,e\,\sqrt{-a^3\,c^7}}{4\,a^2\,c^5}-\frac{5\,d^2\,e^3\,\sqrt{-a^3\,c^7}}{2\,a\,c^6}}\,320{}\mathrm{i}}{\frac{16\,a^4\,e^{11}}{c^2}+64\,a^2\,d^4\,e^7-80\,c^2\,d^8\,e^3-\frac{160\,a^3\,d^2\,e^9}{c}+160\,a\,c\,d^6\,e^5-\frac{160\,d^5\,e^6\,\sqrt{-a^3\,c^7}}{c^3}-\frac{288\,a\,d^3\,e^8\,\sqrt{-a^3\,c^7}}{c^4}+\frac{32\,a^2\,d\,e^{10}\,\sqrt{-a^3\,c^7}}{c^5}+\frac{160\,d^7\,e^4\,\sqrt{-a^3\,c^7}}{a\,c^2}}\right)\,\sqrt{\frac{a^2\,e^5\,\sqrt{-a^3\,c^7}-a\,c^6\,d^5-5\,a^3\,c^4\,d\,e^4+10\,a^2\,c^5\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^7}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^7}}{4\,a^2\,c^7}}\,2{}\mathrm{i}","Not used",1,"(2*e*(d + e*x)^(3/2))/(3*c) - atan((a^3*e^8*(d + e*x)^(1/2)*((e^5*(-a^3*c^7)^(1/2))/(4*c^7) - d^5/(4*a*c) + (5*d^3*e^2)/(2*c^2) - (5*a*d*e^4)/(4*c^3) + (5*d^4*e*(-a^3*c^7)^(1/2))/(4*a^2*c^5) - (5*d^2*e^3*(-a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*32i)/((16*a^4*e^11)/c^2 + 64*a^2*d^4*e^7 - 80*c^2*d^8*e^3 - (160*a^3*d^2*e^9)/c + 160*a*c*d^6*e^5 - (160*d^5*e^6*(-a^3*c^7)^(1/2))/c^3 - (288*a*d^3*e^8*(-a^3*c^7)^(1/2))/c^4 + (32*a^2*d*e^10*(-a^3*c^7)^(1/2))/c^5 + (160*d^7*e^4*(-a^3*c^7)^(1/2))/(a*c^2)) - (d^5*e^3*(-a^3*c^7)^(1/2)*(d + e*x)^(1/2)*((e^5*(-a^3*c^7)^(1/2))/(4*c^7) - d^5/(4*a*c) + (5*d^3*e^2)/(2*c^2) - (5*a*d*e^4)/(4*c^3) + (5*d^4*e*(-a^3*c^7)^(1/2))/(4*a^2*c^5) - (5*d^2*e^3*(-a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*160i)/((16*a^5*e^11)/c - 160*a^4*d^2*e^9 - 80*a*c^3*d^8*e^3 + 64*a^3*c*d^4*e^7 + 160*a^2*c^2*d^6*e^5 + (160*d^7*e^4*(-a^3*c^7)^(1/2))/c - (160*a*d^5*e^6*(-a^3*c^7)^(1/2))/c^2 + (32*a^3*d*e^10*(-a^3*c^7)^(1/2))/c^4 - (288*a^2*d^3*e^8*(-a^3*c^7)^(1/2))/c^3) + (d^3*e^5*(-a^3*c^7)^(1/2)*(d + e*x)^(1/2)*((e^5*(-a^3*c^7)^(1/2))/(4*c^7) - d^5/(4*a*c) + (5*d^3*e^2)/(2*c^2) - (5*a*d*e^4)/(4*c^3) + (5*d^4*e*(-a^3*c^7)^(1/2))/(4*a^2*c^5) - (5*d^2*e^3*(-a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*320i)/(16*a^4*e^11 - 80*c^4*d^8*e^3 + 160*a*c^3*d^6*e^5 - 160*a^3*c*d^2*e^9 + 64*a^2*c^2*d^4*e^7 + (160*d^7*e^4*(-a^3*c^7)^(1/2))/a - (160*d^5*e^6*(-a^3*c^7)^(1/2))/c - (288*a*d^3*e^8*(-a^3*c^7)^(1/2))/c^2 + (32*a^2*d*e^10*(-a^3*c^7)^(1/2))/c^3) - (a*d*e^7*(-a^3*c^7)^(1/2)*(d + e*x)^(1/2)*((e^5*(-a^3*c^7)^(1/2))/(4*c^7) - d^5/(4*a*c) + (5*d^3*e^2)/(2*c^2) - (5*a*d*e^4)/(4*c^3) + (5*d^4*e*(-a^3*c^7)^(1/2))/(4*a^2*c^5) - (5*d^2*e^3*(-a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*32i)/(16*a^4*c*e^11 - 160*d^5*e^6*(-a^3*c^7)^(1/2) - 80*c^5*d^8*e^3 + 160*a*c^4*d^6*e^5 + 64*a^2*c^3*d^4*e^7 - 160*a^3*c^2*d^2*e^9 - (288*a*d^3*e^8*(-a^3*c^7)^(1/2))/c + (160*c*d^7*e^4*(-a^3*c^7)^(1/2))/a + (32*a^2*d*e^10*(-a^3*c^7)^(1/2))/c^2) + (a*c^2*d^4*e^4*(d + e*x)^(1/2)*((e^5*(-a^3*c^7)^(1/2))/(4*c^7) - d^5/(4*a*c) + (5*d^3*e^2)/(2*c^2) - (5*a*d*e^4)/(4*c^3) + (5*d^4*e*(-a^3*c^7)^(1/2))/(4*a^2*c^5) - (5*d^2*e^3*(-a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*160i)/((16*a^4*e^11)/c^2 + 64*a^2*d^4*e^7 - 80*c^2*d^8*e^3 - (160*a^3*d^2*e^9)/c + 160*a*c*d^6*e^5 - (160*d^5*e^6*(-a^3*c^7)^(1/2))/c^3 - (288*a*d^3*e^8*(-a^3*c^7)^(1/2))/c^4 + (32*a^2*d*e^10*(-a^3*c^7)^(1/2))/c^5 + (160*d^7*e^4*(-a^3*c^7)^(1/2))/(a*c^2)) - (a^2*c*d^2*e^6*(d + e*x)^(1/2)*((e^5*(-a^3*c^7)^(1/2))/(4*c^7) - d^5/(4*a*c) + (5*d^3*e^2)/(2*c^2) - (5*a*d*e^4)/(4*c^3) + (5*d^4*e*(-a^3*c^7)^(1/2))/(4*a^2*c^5) - (5*d^2*e^3*(-a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*320i)/((16*a^4*e^11)/c^2 + 64*a^2*d^4*e^7 - 80*c^2*d^8*e^3 - (160*a^3*d^2*e^9)/c + 160*a*c*d^6*e^5 - (160*d^5*e^6*(-a^3*c^7)^(1/2))/c^3 - (288*a*d^3*e^8*(-a^3*c^7)^(1/2))/c^4 + (32*a^2*d*e^10*(-a^3*c^7)^(1/2))/c^5 + (160*d^7*e^4*(-a^3*c^7)^(1/2))/(a*c^2)))*((a^2*e^5*(-a^3*c^7)^(1/2) - a*c^6*d^5 - 5*a^3*c^4*d*e^4 + 10*a^2*c^5*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^7)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^7)^(1/2))/(4*a^2*c^7))^(1/2)*2i - atan((a^3*e^8*(d + e*x)^(1/2)*((5*d^3*e^2)/(2*c^2) - d^5/(4*a*c) - (e^5*(-a^3*c^7)^(1/2))/(4*c^7) - (5*a*d*e^4)/(4*c^3) - (5*d^4*e*(-a^3*c^7)^(1/2))/(4*a^2*c^5) + (5*d^2*e^3*(-a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*32i)/((16*a^4*e^11)/c^2 + 64*a^2*d^4*e^7 - 80*c^2*d^8*e^3 - (160*a^3*d^2*e^9)/c + 160*a*c*d^6*e^5 + (160*d^5*e^6*(-a^3*c^7)^(1/2))/c^3 + (288*a*d^3*e^8*(-a^3*c^7)^(1/2))/c^4 - (32*a^2*d*e^10*(-a^3*c^7)^(1/2))/c^5 - (160*d^7*e^4*(-a^3*c^7)^(1/2))/(a*c^2)) + (d^5*e^3*(-a^3*c^7)^(1/2)*(d + e*x)^(1/2)*((5*d^3*e^2)/(2*c^2) - d^5/(4*a*c) - (e^5*(-a^3*c^7)^(1/2))/(4*c^7) - (5*a*d*e^4)/(4*c^3) - (5*d^4*e*(-a^3*c^7)^(1/2))/(4*a^2*c^5) + (5*d^2*e^3*(-a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*160i)/((16*a^5*e^11)/c - 160*a^4*d^2*e^9 - 80*a*c^3*d^8*e^3 + 64*a^3*c*d^4*e^7 + 160*a^2*c^2*d^6*e^5 - (160*d^7*e^4*(-a^3*c^7)^(1/2))/c + (160*a*d^5*e^6*(-a^3*c^7)^(1/2))/c^2 - (32*a^3*d*e^10*(-a^3*c^7)^(1/2))/c^4 + (288*a^2*d^3*e^8*(-a^3*c^7)^(1/2))/c^3) - (d^3*e^5*(-a^3*c^7)^(1/2)*(d + e*x)^(1/2)*((5*d^3*e^2)/(2*c^2) - d^5/(4*a*c) - (e^5*(-a^3*c^7)^(1/2))/(4*c^7) - (5*a*d*e^4)/(4*c^3) - (5*d^4*e*(-a^3*c^7)^(1/2))/(4*a^2*c^5) + (5*d^2*e^3*(-a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*320i)/(16*a^4*e^11 - 80*c^4*d^8*e^3 + 160*a*c^3*d^6*e^5 - 160*a^3*c*d^2*e^9 + 64*a^2*c^2*d^4*e^7 - (160*d^7*e^4*(-a^3*c^7)^(1/2))/a + (160*d^5*e^6*(-a^3*c^7)^(1/2))/c + (288*a*d^3*e^8*(-a^3*c^7)^(1/2))/c^2 - (32*a^2*d*e^10*(-a^3*c^7)^(1/2))/c^3) + (a*d*e^7*(-a^3*c^7)^(1/2)*(d + e*x)^(1/2)*((5*d^3*e^2)/(2*c^2) - d^5/(4*a*c) - (e^5*(-a^3*c^7)^(1/2))/(4*c^7) - (5*a*d*e^4)/(4*c^3) - (5*d^4*e*(-a^3*c^7)^(1/2))/(4*a^2*c^5) + (5*d^2*e^3*(-a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*32i)/(160*d^5*e^6*(-a^3*c^7)^(1/2) + 16*a^4*c*e^11 - 80*c^5*d^8*e^3 + 160*a*c^4*d^6*e^5 + 64*a^2*c^3*d^4*e^7 - 160*a^3*c^2*d^2*e^9 + (288*a*d^3*e^8*(-a^3*c^7)^(1/2))/c - (160*c*d^7*e^4*(-a^3*c^7)^(1/2))/a - (32*a^2*d*e^10*(-a^3*c^7)^(1/2))/c^2) + (a*c^2*d^4*e^4*(d + e*x)^(1/2)*((5*d^3*e^2)/(2*c^2) - d^5/(4*a*c) - (e^5*(-a^3*c^7)^(1/2))/(4*c^7) - (5*a*d*e^4)/(4*c^3) - (5*d^4*e*(-a^3*c^7)^(1/2))/(4*a^2*c^5) + (5*d^2*e^3*(-a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*160i)/((16*a^4*e^11)/c^2 + 64*a^2*d^4*e^7 - 80*c^2*d^8*e^3 - (160*a^3*d^2*e^9)/c + 160*a*c*d^6*e^5 + (160*d^5*e^6*(-a^3*c^7)^(1/2))/c^3 + (288*a*d^3*e^8*(-a^3*c^7)^(1/2))/c^4 - (32*a^2*d*e^10*(-a^3*c^7)^(1/2))/c^5 - (160*d^7*e^4*(-a^3*c^7)^(1/2))/(a*c^2)) - (a^2*c*d^2*e^6*(d + e*x)^(1/2)*((5*d^3*e^2)/(2*c^2) - d^5/(4*a*c) - (e^5*(-a^3*c^7)^(1/2))/(4*c^7) - (5*a*d*e^4)/(4*c^3) - (5*d^4*e*(-a^3*c^7)^(1/2))/(4*a^2*c^5) + (5*d^2*e^3*(-a^3*c^7)^(1/2))/(2*a*c^6))^(1/2)*320i)/((16*a^4*e^11)/c^2 + 64*a^2*d^4*e^7 - 80*c^2*d^8*e^3 - (160*a^3*d^2*e^9)/c + 160*a*c*d^6*e^5 + (160*d^5*e^6*(-a^3*c^7)^(1/2))/c^3 + (288*a*d^3*e^8*(-a^3*c^7)^(1/2))/c^4 - (32*a^2*d*e^10*(-a^3*c^7)^(1/2))/c^5 - (160*d^7*e^4*(-a^3*c^7)^(1/2))/(a*c^2)))*(-(a^2*e^5*(-a^3*c^7)^(1/2) + a*c^6*d^5 + 5*a^3*c^4*d*e^4 - 10*a^2*c^5*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^7)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^7)^(1/2))/(4*a^2*c^7))^(1/2)*2i + (4*d*e*(d + e*x)^(1/2))/c","B"
619,1,1625,689,0.677084,"\text{Not used}","int((d + e*x)^(3/2)/(a + c*x^2),x)","2\,\mathrm{atanh}\left(\frac{32\,a^2\,c\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{3\,d\,e^2}{4\,c^2}-\frac{d^3}{4\,a\,c}+\frac{e^3\,\sqrt{-a^3\,c^5}}{4\,a\,c^5}-\frac{3\,d^2\,e\,\sqrt{-a^3\,c^5}}{4\,a^2\,c^4}}}{48\,c^2\,d^5\,e^3-16\,a^2\,d\,e^7-\frac{16\,a\,e^8\,\sqrt{-a^3\,c^5}}{c^3}+32\,a\,c\,d^3\,e^5+\frac{32\,d^2\,e^6\,\sqrt{-a^3\,c^5}}{c^2}+\frac{48\,d^4\,e^4\,\sqrt{-a^3\,c^5}}{a\,c}}+\frac{32\,d\,e^5\,\sqrt{-a^3\,c^5}\,\sqrt{d+e\,x}\,\sqrt{\frac{3\,d\,e^2}{4\,c^2}-\frac{d^3}{4\,a\,c}+\frac{e^3\,\sqrt{-a^3\,c^5}}{4\,a\,c^5}-\frac{3\,d^2\,e\,\sqrt{-a^3\,c^5}}{4\,a^2\,c^4}}}{48\,c^3\,d^5\,e^3+32\,a\,c^2\,d^3\,e^5-\frac{16\,a\,e^8\,\sqrt{-a^3\,c^5}}{c^2}-16\,a^2\,c\,d\,e^7+\frac{48\,d^4\,e^4\,\sqrt{-a^3\,c^5}}{a}+\frac{32\,d^2\,e^6\,\sqrt{-a^3\,c^5}}{c}}-\frac{96\,d^3\,e^3\,\sqrt{-a^3\,c^5}\,\sqrt{d+e\,x}\,\sqrt{\frac{3\,d\,e^2}{4\,c^2}-\frac{d^3}{4\,a\,c}+\frac{e^3\,\sqrt{-a^3\,c^5}}{4\,a\,c^5}-\frac{3\,d^2\,e\,\sqrt{-a^3\,c^5}}{4\,a^2\,c^4}}}{48\,a\,c^2\,d^5\,e^3-16\,a^3\,d\,e^7+32\,a^2\,c\,d^3\,e^5-\frac{16\,a^2\,e^8\,\sqrt{-a^3\,c^5}}{c^3}+\frac{48\,d^4\,e^4\,\sqrt{-a^3\,c^5}}{c}+\frac{32\,a\,d^2\,e^6\,\sqrt{-a^3\,c^5}}{c^2}}-\frac{96\,a\,c^2\,d^2\,e^4\,\sqrt{d+e\,x}\,\sqrt{\frac{3\,d\,e^2}{4\,c^2}-\frac{d^3}{4\,a\,c}+\frac{e^3\,\sqrt{-a^3\,c^5}}{4\,a\,c^5}-\frac{3\,d^2\,e\,\sqrt{-a^3\,c^5}}{4\,a^2\,c^4}}}{48\,c^2\,d^5\,e^3-16\,a^2\,d\,e^7-\frac{16\,a\,e^8\,\sqrt{-a^3\,c^5}}{c^3}+32\,a\,c\,d^3\,e^5+\frac{32\,d^2\,e^6\,\sqrt{-a^3\,c^5}}{c^2}+\frac{48\,d^4\,e^4\,\sqrt{-a^3\,c^5}}{a\,c}}\right)\,\sqrt{-\frac{a\,c^4\,d^3-a\,e^3\,\sqrt{-a^3\,c^5}-3\,a^2\,c^3\,d\,e^2+3\,c\,d^2\,e\,\sqrt{-a^3\,c^5}}{4\,a^2\,c^5}}-2\,\mathrm{atanh}\left(\frac{32\,a^2\,c\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{3\,d\,e^2}{4\,c^2}-\frac{d^3}{4\,a\,c}-\frac{e^3\,\sqrt{-a^3\,c^5}}{4\,a\,c^5}+\frac{3\,d^2\,e\,\sqrt{-a^3\,c^5}}{4\,a^2\,c^4}}}{16\,a^2\,d\,e^7-48\,c^2\,d^5\,e^3-\frac{16\,a\,e^8\,\sqrt{-a^3\,c^5}}{c^3}-32\,a\,c\,d^3\,e^5+\frac{32\,d^2\,e^6\,\sqrt{-a^3\,c^5}}{c^2}+\frac{48\,d^4\,e^4\,\sqrt{-a^3\,c^5}}{a\,c}}+\frac{32\,d\,e^5\,\sqrt{-a^3\,c^5}\,\sqrt{d+e\,x}\,\sqrt{\frac{3\,d\,e^2}{4\,c^2}-\frac{d^3}{4\,a\,c}-\frac{e^3\,\sqrt{-a^3\,c^5}}{4\,a\,c^5}+\frac{3\,d^2\,e\,\sqrt{-a^3\,c^5}}{4\,a^2\,c^4}}}{48\,c^3\,d^5\,e^3+32\,a\,c^2\,d^3\,e^5+\frac{16\,a\,e^8\,\sqrt{-a^3\,c^5}}{c^2}-16\,a^2\,c\,d\,e^7-\frac{48\,d^4\,e^4\,\sqrt{-a^3\,c^5}}{a}-\frac{32\,d^2\,e^6\,\sqrt{-a^3\,c^5}}{c}}+\frac{96\,d^3\,e^3\,\sqrt{-a^3\,c^5}\,\sqrt{d+e\,x}\,\sqrt{\frac{3\,d\,e^2}{4\,c^2}-\frac{d^3}{4\,a\,c}-\frac{e^3\,\sqrt{-a^3\,c^5}}{4\,a\,c^5}+\frac{3\,d^2\,e\,\sqrt{-a^3\,c^5}}{4\,a^2\,c^4}}}{16\,a^3\,d\,e^7-48\,a\,c^2\,d^5\,e^3-32\,a^2\,c\,d^3\,e^5-\frac{16\,a^2\,e^8\,\sqrt{-a^3\,c^5}}{c^3}+\frac{48\,d^4\,e^4\,\sqrt{-a^3\,c^5}}{c}+\frac{32\,a\,d^2\,e^6\,\sqrt{-a^3\,c^5}}{c^2}}-\frac{96\,a\,c^2\,d^2\,e^4\,\sqrt{d+e\,x}\,\sqrt{\frac{3\,d\,e^2}{4\,c^2}-\frac{d^3}{4\,a\,c}-\frac{e^3\,\sqrt{-a^3\,c^5}}{4\,a\,c^5}+\frac{3\,d^2\,e\,\sqrt{-a^3\,c^5}}{4\,a^2\,c^4}}}{16\,a^2\,d\,e^7-48\,c^2\,d^5\,e^3-\frac{16\,a\,e^8\,\sqrt{-a^3\,c^5}}{c^3}-32\,a\,c\,d^3\,e^5+\frac{32\,d^2\,e^6\,\sqrt{-a^3\,c^5}}{c^2}+\frac{48\,d^4\,e^4\,\sqrt{-a^3\,c^5}}{a\,c}}\right)\,\sqrt{-\frac{a\,c^4\,d^3+a\,e^3\,\sqrt{-a^3\,c^5}-3\,a^2\,c^3\,d\,e^2-3\,c\,d^2\,e\,\sqrt{-a^3\,c^5}}{4\,a^2\,c^5}}+\frac{2\,e\,\sqrt{d+e\,x}}{c}","Not used",1,"2*atanh((32*a^2*c*e^6*(d + e*x)^(1/2)*((3*d*e^2)/(4*c^2) - d^3/(4*a*c) + (e^3*(-a^3*c^5)^(1/2))/(4*a*c^5) - (3*d^2*e*(-a^3*c^5)^(1/2))/(4*a^2*c^4))^(1/2))/(48*c^2*d^5*e^3 - 16*a^2*d*e^7 - (16*a*e^8*(-a^3*c^5)^(1/2))/c^3 + 32*a*c*d^3*e^5 + (32*d^2*e^6*(-a^3*c^5)^(1/2))/c^2 + (48*d^4*e^4*(-a^3*c^5)^(1/2))/(a*c)) + (32*d*e^5*(-a^3*c^5)^(1/2)*(d + e*x)^(1/2)*((3*d*e^2)/(4*c^2) - d^3/(4*a*c) + (e^3*(-a^3*c^5)^(1/2))/(4*a*c^5) - (3*d^2*e*(-a^3*c^5)^(1/2))/(4*a^2*c^4))^(1/2))/(48*c^3*d^5*e^3 + 32*a*c^2*d^3*e^5 - (16*a*e^8*(-a^3*c^5)^(1/2))/c^2 - 16*a^2*c*d*e^7 + (48*d^4*e^4*(-a^3*c^5)^(1/2))/a + (32*d^2*e^6*(-a^3*c^5)^(1/2))/c) - (96*d^3*e^3*(-a^3*c^5)^(1/2)*(d + e*x)^(1/2)*((3*d*e^2)/(4*c^2) - d^3/(4*a*c) + (e^3*(-a^3*c^5)^(1/2))/(4*a*c^5) - (3*d^2*e*(-a^3*c^5)^(1/2))/(4*a^2*c^4))^(1/2))/(48*a*c^2*d^5*e^3 - 16*a^3*d*e^7 + 32*a^2*c*d^3*e^5 - (16*a^2*e^8*(-a^3*c^5)^(1/2))/c^3 + (48*d^4*e^4*(-a^3*c^5)^(1/2))/c + (32*a*d^2*e^6*(-a^3*c^5)^(1/2))/c^2) - (96*a*c^2*d^2*e^4*(d + e*x)^(1/2)*((3*d*e^2)/(4*c^2) - d^3/(4*a*c) + (e^3*(-a^3*c^5)^(1/2))/(4*a*c^5) - (3*d^2*e*(-a^3*c^5)^(1/2))/(4*a^2*c^4))^(1/2))/(48*c^2*d^5*e^3 - 16*a^2*d*e^7 - (16*a*e^8*(-a^3*c^5)^(1/2))/c^3 + 32*a*c*d^3*e^5 + (32*d^2*e^6*(-a^3*c^5)^(1/2))/c^2 + (48*d^4*e^4*(-a^3*c^5)^(1/2))/(a*c)))*(-(a*c^4*d^3 - a*e^3*(-a^3*c^5)^(1/2) - 3*a^2*c^3*d*e^2 + 3*c*d^2*e*(-a^3*c^5)^(1/2))/(4*a^2*c^5))^(1/2) - 2*atanh((32*a^2*c*e^6*(d + e*x)^(1/2)*((3*d*e^2)/(4*c^2) - d^3/(4*a*c) - (e^3*(-a^3*c^5)^(1/2))/(4*a*c^5) + (3*d^2*e*(-a^3*c^5)^(1/2))/(4*a^2*c^4))^(1/2))/(16*a^2*d*e^7 - 48*c^2*d^5*e^3 - (16*a*e^8*(-a^3*c^5)^(1/2))/c^3 - 32*a*c*d^3*e^5 + (32*d^2*e^6*(-a^3*c^5)^(1/2))/c^2 + (48*d^4*e^4*(-a^3*c^5)^(1/2))/(a*c)) + (32*d*e^5*(-a^3*c^5)^(1/2)*(d + e*x)^(1/2)*((3*d*e^2)/(4*c^2) - d^3/(4*a*c) - (e^3*(-a^3*c^5)^(1/2))/(4*a*c^5) + (3*d^2*e*(-a^3*c^5)^(1/2))/(4*a^2*c^4))^(1/2))/(48*c^3*d^5*e^3 + 32*a*c^2*d^3*e^5 + (16*a*e^8*(-a^3*c^5)^(1/2))/c^2 - 16*a^2*c*d*e^7 - (48*d^4*e^4*(-a^3*c^5)^(1/2))/a - (32*d^2*e^6*(-a^3*c^5)^(1/2))/c) + (96*d^3*e^3*(-a^3*c^5)^(1/2)*(d + e*x)^(1/2)*((3*d*e^2)/(4*c^2) - d^3/(4*a*c) - (e^3*(-a^3*c^5)^(1/2))/(4*a*c^5) + (3*d^2*e*(-a^3*c^5)^(1/2))/(4*a^2*c^4))^(1/2))/(16*a^3*d*e^7 - 48*a*c^2*d^5*e^3 - 32*a^2*c*d^3*e^5 - (16*a^2*e^8*(-a^3*c^5)^(1/2))/c^3 + (48*d^4*e^4*(-a^3*c^5)^(1/2))/c + (32*a*d^2*e^6*(-a^3*c^5)^(1/2))/c^2) - (96*a*c^2*d^2*e^4*(d + e*x)^(1/2)*((3*d*e^2)/(4*c^2) - d^3/(4*a*c) - (e^3*(-a^3*c^5)^(1/2))/(4*a*c^5) + (3*d^2*e*(-a^3*c^5)^(1/2))/(4*a^2*c^4))^(1/2))/(16*a^2*d*e^7 - 48*c^2*d^5*e^3 - (16*a*e^8*(-a^3*c^5)^(1/2))/c^3 - 32*a*c*d^3*e^5 + (32*d^2*e^6*(-a^3*c^5)^(1/2))/c^2 + (48*d^4*e^4*(-a^3*c^5)^(1/2))/(a*c)))*(-(a*c^4*d^3 + a*e^3*(-a^3*c^5)^(1/2) - 3*a^2*c^3*d*e^2 - 3*c*d^2*e*(-a^3*c^5)^(1/2))/(4*a^2*c^5))^(1/2) + (2*e*(d + e*x)^(1/2))/c","B"
620,1,308,478,0.629835,"\text{Not used}","int((d + e*x)^(1/2)/(a + c*x^2),x)","-2\,\mathrm{atanh}\left(\frac{2\,\left(\left(16\,a\,c^2\,e^4-16\,c^3\,d^2\,e^2\right)\,\sqrt{d+e\,x}+\frac{16\,c\,d\,e^2\,\left(e\,\sqrt{-a^3\,c^3}+a\,c^2\,d\right)\,\sqrt{d+e\,x}}{a}\right)\,\sqrt{-\frac{e\,\sqrt{-a^3\,c^3}+a\,c^2\,d}{4\,a^2\,c^3}}}{16\,c^2\,d^2\,e^3+16\,a\,c\,e^5}\right)\,\sqrt{-\frac{e\,\sqrt{-a^3\,c^3}+a\,c^2\,d}{4\,a^2\,c^3}}-2\,\mathrm{atanh}\left(\frac{2\,\left(\left(16\,a\,c^2\,e^4-16\,c^3\,d^2\,e^2\right)\,\sqrt{d+e\,x}-\frac{16\,c\,d\,e^2\,\left(e\,\sqrt{-a^3\,c^3}-a\,c^2\,d\right)\,\sqrt{d+e\,x}}{a}\right)\,\sqrt{\frac{e\,\sqrt{-a^3\,c^3}-a\,c^2\,d}{4\,a^2\,c^3}}}{16\,c^2\,d^2\,e^3+16\,a\,c\,e^5}\right)\,\sqrt{\frac{e\,\sqrt{-a^3\,c^3}-a\,c^2\,d}{4\,a^2\,c^3}}","Not used",1,"- 2*atanh((2*((16*a*c^2*e^4 - 16*c^3*d^2*e^2)*(d + e*x)^(1/2) + (16*c*d*e^2*(e*(-a^3*c^3)^(1/2) + a*c^2*d)*(d + e*x)^(1/2))/a)*(-(e*(-a^3*c^3)^(1/2) + a*c^2*d)/(4*a^2*c^3))^(1/2))/(16*c^2*d^2*e^3 + 16*a*c*e^5))*(-(e*(-a^3*c^3)^(1/2) + a*c^2*d)/(4*a^2*c^3))^(1/2) - 2*atanh((2*((16*a*c^2*e^4 - 16*c^3*d^2*e^2)*(d + e*x)^(1/2) - (16*c*d*e^2*(e*(-a^3*c^3)^(1/2) - a*c^2*d)*(d + e*x)^(1/2))/a)*((e*(-a^3*c^3)^(1/2) - a*c^2*d)/(4*a^2*c^3))^(1/2))/(16*c^2*d^2*e^3 + 16*a*c*e^5))*((e*(-a^3*c^3)^(1/2) - a*c^2*d)/(4*a^2*c^3))^(1/2)","B"
621,1,1366,538,0.650978,"\text{Not used}","int(1/((a + c*x^2)*(d + e*x)^(1/2)),x)","2\,\mathrm{atanh}\left(\frac{32\,a^2\,c^5\,d^2\,e^2\,\sqrt{-\frac{e\,\sqrt{-a^3\,c}}{4\,\left(a^3\,c\,e^2+a^2\,c^2\,d^2\right)}-\frac{a\,c\,d}{4\,\left(a^3\,c\,e^2+a^2\,c^2\,d^2\right)}}\,\sqrt{d+e\,x}}{\frac{16\,a^4\,c^6\,d^3\,e^3}{a^3\,c\,e^2+a^2\,c^2\,d^2}+\frac{16\,a^4\,c^4\,e^6\,\sqrt{-a^3\,c}}{a^3\,c\,e^2+a^2\,c^2\,d^2}+\frac{16\,a^5\,c^5\,d\,e^5}{a^3\,c\,e^2+a^2\,c^2\,d^2}+\frac{16\,a^3\,c^5\,d^2\,e^4\,\sqrt{-a^3\,c}}{a^3\,c\,e^2+a^2\,c^2\,d^2}}-\frac{32\,c^3\,e^2\,\sqrt{-\frac{e\,\sqrt{-a^3\,c}}{4\,\left(a^3\,c\,e^2+a^2\,c^2\,d^2\right)}-\frac{a\,c\,d}{4\,\left(a^3\,c\,e^2+a^2\,c^2\,d^2\right)}}\,\sqrt{d+e\,x}}{\frac{16\,a^2\,c^4\,d\,e^3}{a^3\,c\,e^2+a^2\,c^2\,d^2}+\frac{16\,a\,c^3\,e^4\,\sqrt{-a^3\,c}}{a^3\,c\,e^2+a^2\,c^2\,d^2}}+\frac{32\,a\,c^4\,d\,e^3\,\sqrt{-a^3\,c}\,\sqrt{-\frac{e\,\sqrt{-a^3\,c}}{4\,\left(a^3\,c\,e^2+a^2\,c^2\,d^2\right)}-\frac{a\,c\,d}{4\,\left(a^3\,c\,e^2+a^2\,c^2\,d^2\right)}}\,\sqrt{d+e\,x}}{\frac{16\,a^4\,c^6\,d^3\,e^3}{a^3\,c\,e^2+a^2\,c^2\,d^2}+\frac{16\,a^4\,c^4\,e^6\,\sqrt{-a^3\,c}}{a^3\,c\,e^2+a^2\,c^2\,d^2}+\frac{16\,a^5\,c^5\,d\,e^5}{a^3\,c\,e^2+a^2\,c^2\,d^2}+\frac{16\,a^3\,c^5\,d^2\,e^4\,\sqrt{-a^3\,c}}{a^3\,c\,e^2+a^2\,c^2\,d^2}}\right)\,\sqrt{-\frac{e\,\sqrt{-a^3\,c}+a\,c\,d}{4\,\left(a^3\,c\,e^2+a^2\,c^2\,d^2\right)}}-2\,\mathrm{atanh}\left(\frac{32\,c^3\,e^2\,\sqrt{\frac{e\,\sqrt{-a^3\,c}}{4\,\left(a^3\,c\,e^2+a^2\,c^2\,d^2\right)}-\frac{a\,c\,d}{4\,\left(a^3\,c\,e^2+a^2\,c^2\,d^2\right)}}\,\sqrt{d+e\,x}}{\frac{16\,a^2\,c^4\,d\,e^3}{a^3\,c\,e^2+a^2\,c^2\,d^2}-\frac{16\,a\,c^3\,e^4\,\sqrt{-a^3\,c}}{a^3\,c\,e^2+a^2\,c^2\,d^2}}-\frac{32\,a^2\,c^5\,d^2\,e^2\,\sqrt{\frac{e\,\sqrt{-a^3\,c}}{4\,\left(a^3\,c\,e^2+a^2\,c^2\,d^2\right)}-\frac{a\,c\,d}{4\,\left(a^3\,c\,e^2+a^2\,c^2\,d^2\right)}}\,\sqrt{d+e\,x}}{\frac{16\,a^4\,c^6\,d^3\,e^3}{a^3\,c\,e^2+a^2\,c^2\,d^2}-\frac{16\,a^4\,c^4\,e^6\,\sqrt{-a^3\,c}}{a^3\,c\,e^2+a^2\,c^2\,d^2}+\frac{16\,a^5\,c^5\,d\,e^5}{a^3\,c\,e^2+a^2\,c^2\,d^2}-\frac{16\,a^3\,c^5\,d^2\,e^4\,\sqrt{-a^3\,c}}{a^3\,c\,e^2+a^2\,c^2\,d^2}}+\frac{32\,a\,c^4\,d\,e^3\,\sqrt{-a^3\,c}\,\sqrt{\frac{e\,\sqrt{-a^3\,c}}{4\,\left(a^3\,c\,e^2+a^2\,c^2\,d^2\right)}-\frac{a\,c\,d}{4\,\left(a^3\,c\,e^2+a^2\,c^2\,d^2\right)}}\,\sqrt{d+e\,x}}{\frac{16\,a^4\,c^6\,d^3\,e^3}{a^3\,c\,e^2+a^2\,c^2\,d^2}-\frac{16\,a^4\,c^4\,e^6\,\sqrt{-a^3\,c}}{a^3\,c\,e^2+a^2\,c^2\,d^2}+\frac{16\,a^5\,c^5\,d\,e^5}{a^3\,c\,e^2+a^2\,c^2\,d^2}-\frac{16\,a^3\,c^5\,d^2\,e^4\,\sqrt{-a^3\,c}}{a^3\,c\,e^2+a^2\,c^2\,d^2}}\right)\,\sqrt{\frac{e\,\sqrt{-a^3\,c}-a\,c\,d}{4\,\left(a^3\,c\,e^2+a^2\,c^2\,d^2\right)}}","Not used",1,"2*atanh((32*a^2*c^5*d^2*e^2*(- (e*(-a^3*c)^(1/2))/(4*(a^3*c*e^2 + a^2*c^2*d^2)) - (a*c*d)/(4*(a^3*c*e^2 + a^2*c^2*d^2)))^(1/2)*(d + e*x)^(1/2))/((16*a^4*c^6*d^3*e^3)/(a^3*c*e^2 + a^2*c^2*d^2) + (16*a^4*c^4*e^6*(-a^3*c)^(1/2))/(a^3*c*e^2 + a^2*c^2*d^2) + (16*a^5*c^5*d*e^5)/(a^3*c*e^2 + a^2*c^2*d^2) + (16*a^3*c^5*d^2*e^4*(-a^3*c)^(1/2))/(a^3*c*e^2 + a^2*c^2*d^2)) - (32*c^3*e^2*(- (e*(-a^3*c)^(1/2))/(4*(a^3*c*e^2 + a^2*c^2*d^2)) - (a*c*d)/(4*(a^3*c*e^2 + a^2*c^2*d^2)))^(1/2)*(d + e*x)^(1/2))/((16*a^2*c^4*d*e^3)/(a^3*c*e^2 + a^2*c^2*d^2) + (16*a*c^3*e^4*(-a^3*c)^(1/2))/(a^3*c*e^2 + a^2*c^2*d^2)) + (32*a*c^4*d*e^3*(-a^3*c)^(1/2)*(- (e*(-a^3*c)^(1/2))/(4*(a^3*c*e^2 + a^2*c^2*d^2)) - (a*c*d)/(4*(a^3*c*e^2 + a^2*c^2*d^2)))^(1/2)*(d + e*x)^(1/2))/((16*a^4*c^6*d^3*e^3)/(a^3*c*e^2 + a^2*c^2*d^2) + (16*a^4*c^4*e^6*(-a^3*c)^(1/2))/(a^3*c*e^2 + a^2*c^2*d^2) + (16*a^5*c^5*d*e^5)/(a^3*c*e^2 + a^2*c^2*d^2) + (16*a^3*c^5*d^2*e^4*(-a^3*c)^(1/2))/(a^3*c*e^2 + a^2*c^2*d^2)))*(-(e*(-a^3*c)^(1/2) + a*c*d)/(4*(a^3*c*e^2 + a^2*c^2*d^2)))^(1/2) - 2*atanh((32*c^3*e^2*((e*(-a^3*c)^(1/2))/(4*(a^3*c*e^2 + a^2*c^2*d^2)) - (a*c*d)/(4*(a^3*c*e^2 + a^2*c^2*d^2)))^(1/2)*(d + e*x)^(1/2))/((16*a^2*c^4*d*e^3)/(a^3*c*e^2 + a^2*c^2*d^2) - (16*a*c^3*e^4*(-a^3*c)^(1/2))/(a^3*c*e^2 + a^2*c^2*d^2)) - (32*a^2*c^5*d^2*e^2*((e*(-a^3*c)^(1/2))/(4*(a^3*c*e^2 + a^2*c^2*d^2)) - (a*c*d)/(4*(a^3*c*e^2 + a^2*c^2*d^2)))^(1/2)*(d + e*x)^(1/2))/((16*a^4*c^6*d^3*e^3)/(a^3*c*e^2 + a^2*c^2*d^2) - (16*a^4*c^4*e^6*(-a^3*c)^(1/2))/(a^3*c*e^2 + a^2*c^2*d^2) + (16*a^5*c^5*d*e^5)/(a^3*c*e^2 + a^2*c^2*d^2) - (16*a^3*c^5*d^2*e^4*(-a^3*c)^(1/2))/(a^3*c*e^2 + a^2*c^2*d^2)) + (32*a*c^4*d*e^3*(-a^3*c)^(1/2)*((e*(-a^3*c)^(1/2))/(4*(a^3*c*e^2 + a^2*c^2*d^2)) - (a*c*d)/(4*(a^3*c*e^2 + a^2*c^2*d^2)))^(1/2)*(d + e*x)^(1/2))/((16*a^4*c^6*d^3*e^3)/(a^3*c*e^2 + a^2*c^2*d^2) - (16*a^4*c^4*e^6*(-a^3*c)^(1/2))/(a^3*c*e^2 + a^2*c^2*d^2) + (16*a^5*c^5*d*e^5)/(a^3*c*e^2 + a^2*c^2*d^2) - (16*a^3*c^5*d^2*e^4*(-a^3*c)^(1/2))/(a^3*c*e^2 + a^2*c^2*d^2)))*((e*(-a^3*c)^(1/2) - a*c*d)/(4*(a^3*c*e^2 + a^2*c^2*d^2)))^(1/2)","B"
622,1,4471,663,1.302824,"\text{Not used}","int(1/((a + c*x^2)*(d + e*x)^(3/2)),x)","-\frac{2\,e}{\left(c\,d^2+a\,e^2\right)\,\sqrt{d+e\,x}}-\mathrm{atan}\left(\frac{\left(\sqrt{d+e\,x}\,\left(16\,a^4\,c^4\,e^{10}+32\,a^3\,c^5\,d^2\,e^8-32\,a\,c^7\,d^6\,e^4-16\,c^8\,d^8\,e^2\right)+\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,\left(64\,a\,c^8\,d^9\,e^3-\sqrt{d+e\,x}\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,\left(64\,a^6\,c^4\,d\,e^{12}+320\,a^5\,c^5\,d^3\,e^{10}+640\,a^4\,c^6\,d^5\,e^8+640\,a^3\,c^7\,d^7\,e^6+320\,a^2\,c^8\,d^9\,e^4+64\,a\,c^9\,d^{11}\,e^2\right)+64\,a^5\,c^4\,d\,e^{11}+256\,a^2\,c^7\,d^7\,e^5+384\,a^3\,c^6\,d^5\,e^7+256\,a^4\,c^5\,d^3\,e^9\right)\right)\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,1{}\mathrm{i}+\left(\sqrt{d+e\,x}\,\left(16\,a^4\,c^4\,e^{10}+32\,a^3\,c^5\,d^2\,e^8-32\,a\,c^7\,d^6\,e^4-16\,c^8\,d^8\,e^2\right)-\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,\left(64\,a^6\,c^4\,d\,e^{12}+320\,a^5\,c^5\,d^3\,e^{10}+640\,a^4\,c^6\,d^5\,e^8+640\,a^3\,c^7\,d^7\,e^6+320\,a^2\,c^8\,d^9\,e^4+64\,a\,c^9\,d^{11}\,e^2\right)+64\,a\,c^8\,d^9\,e^3+64\,a^5\,c^4\,d\,e^{11}+256\,a^2\,c^7\,d^7\,e^5+384\,a^3\,c^6\,d^5\,e^7+256\,a^4\,c^5\,d^3\,e^9\right)\right)\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,1{}\mathrm{i}}{\left(\sqrt{d+e\,x}\,\left(16\,a^4\,c^4\,e^{10}+32\,a^3\,c^5\,d^2\,e^8-32\,a\,c^7\,d^6\,e^4-16\,c^8\,d^8\,e^2\right)-\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,\left(64\,a^6\,c^4\,d\,e^{12}+320\,a^5\,c^5\,d^3\,e^{10}+640\,a^4\,c^6\,d^5\,e^8+640\,a^3\,c^7\,d^7\,e^6+320\,a^2\,c^8\,d^9\,e^4+64\,a\,c^9\,d^{11}\,e^2\right)+64\,a\,c^8\,d^9\,e^3+64\,a^5\,c^4\,d\,e^{11}+256\,a^2\,c^7\,d^7\,e^5+384\,a^3\,c^6\,d^5\,e^7+256\,a^4\,c^5\,d^3\,e^9\right)\right)\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}-\left(\sqrt{d+e\,x}\,\left(16\,a^4\,c^4\,e^{10}+32\,a^3\,c^5\,d^2\,e^8-32\,a\,c^7\,d^6\,e^4-16\,c^8\,d^8\,e^2\right)+\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,\left(64\,a\,c^8\,d^9\,e^3-\sqrt{d+e\,x}\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,\left(64\,a^6\,c^4\,d\,e^{12}+320\,a^5\,c^5\,d^3\,e^{10}+640\,a^4\,c^6\,d^5\,e^8+640\,a^3\,c^7\,d^7\,e^6+320\,a^2\,c^8\,d^9\,e^4+64\,a\,c^9\,d^{11}\,e^2\right)+64\,a^5\,c^4\,d\,e^{11}+256\,a^2\,c^7\,d^7\,e^5+384\,a^3\,c^6\,d^5\,e^7+256\,a^4\,c^5\,d^3\,e^9\right)\right)\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}+16\,a^3\,c^4\,e^9+16\,c^7\,d^6\,e^3+48\,a\,c^6\,d^4\,e^5+48\,a^2\,c^5\,d^2\,e^7}\right)\,\sqrt{-\frac{a\,c^2\,d^3+a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2-3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\sqrt{d+e\,x}\,\left(16\,a^4\,c^4\,e^{10}+32\,a^3\,c^5\,d^2\,e^8-32\,a\,c^7\,d^6\,e^4-16\,c^8\,d^8\,e^2\right)+\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,\left(64\,a\,c^8\,d^9\,e^3-\sqrt{d+e\,x}\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,\left(64\,a^6\,c^4\,d\,e^{12}+320\,a^5\,c^5\,d^3\,e^{10}+640\,a^4\,c^6\,d^5\,e^8+640\,a^3\,c^7\,d^7\,e^6+320\,a^2\,c^8\,d^9\,e^4+64\,a\,c^9\,d^{11}\,e^2\right)+64\,a^5\,c^4\,d\,e^{11}+256\,a^2\,c^7\,d^7\,e^5+384\,a^3\,c^6\,d^5\,e^7+256\,a^4\,c^5\,d^3\,e^9\right)\right)\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,1{}\mathrm{i}+\left(\sqrt{d+e\,x}\,\left(16\,a^4\,c^4\,e^{10}+32\,a^3\,c^5\,d^2\,e^8-32\,a\,c^7\,d^6\,e^4-16\,c^8\,d^8\,e^2\right)-\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,\left(64\,a^6\,c^4\,d\,e^{12}+320\,a^5\,c^5\,d^3\,e^{10}+640\,a^4\,c^6\,d^5\,e^8+640\,a^3\,c^7\,d^7\,e^6+320\,a^2\,c^8\,d^9\,e^4+64\,a\,c^9\,d^{11}\,e^2\right)+64\,a\,c^8\,d^9\,e^3+64\,a^5\,c^4\,d\,e^{11}+256\,a^2\,c^7\,d^7\,e^5+384\,a^3\,c^6\,d^5\,e^7+256\,a^4\,c^5\,d^3\,e^9\right)\right)\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,1{}\mathrm{i}}{\left(\sqrt{d+e\,x}\,\left(16\,a^4\,c^4\,e^{10}+32\,a^3\,c^5\,d^2\,e^8-32\,a\,c^7\,d^6\,e^4-16\,c^8\,d^8\,e^2\right)-\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,\left(64\,a^6\,c^4\,d\,e^{12}+320\,a^5\,c^5\,d^3\,e^{10}+640\,a^4\,c^6\,d^5\,e^8+640\,a^3\,c^7\,d^7\,e^6+320\,a^2\,c^8\,d^9\,e^4+64\,a\,c^9\,d^{11}\,e^2\right)+64\,a\,c^8\,d^9\,e^3+64\,a^5\,c^4\,d\,e^{11}+256\,a^2\,c^7\,d^7\,e^5+384\,a^3\,c^6\,d^5\,e^7+256\,a^4\,c^5\,d^3\,e^9\right)\right)\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}-\left(\sqrt{d+e\,x}\,\left(16\,a^4\,c^4\,e^{10}+32\,a^3\,c^5\,d^2\,e^8-32\,a\,c^7\,d^6\,e^4-16\,c^8\,d^8\,e^2\right)+\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,\left(64\,a\,c^8\,d^9\,e^3-\sqrt{d+e\,x}\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,\left(64\,a^6\,c^4\,d\,e^{12}+320\,a^5\,c^5\,d^3\,e^{10}+640\,a^4\,c^6\,d^5\,e^8+640\,a^3\,c^7\,d^7\,e^6+320\,a^2\,c^8\,d^9\,e^4+64\,a\,c^9\,d^{11}\,e^2\right)+64\,a^5\,c^4\,d\,e^{11}+256\,a^2\,c^7\,d^7\,e^5+384\,a^3\,c^6\,d^5\,e^7+256\,a^4\,c^5\,d^3\,e^9\right)\right)\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}+16\,a^3\,c^4\,e^9+16\,c^7\,d^6\,e^3+48\,a\,c^6\,d^4\,e^5+48\,a^2\,c^5\,d^2\,e^7}\right)\,\sqrt{-\frac{a\,c^2\,d^3-a\,e^3\,\sqrt{-a^3\,c}-3\,a^2\,c\,d\,e^2+3\,c\,d^2\,e\,\sqrt{-a^3\,c}}{4\,\left(a^5\,e^6+3\,a^4\,c\,d^2\,e^4+3\,a^3\,c^2\,d^4\,e^2+a^2\,c^3\,d^6\right)}}\,2{}\mathrm{i}","Not used",1,"- atan((((d + e*x)^(1/2)*(16*a^4*c^4*e^10 - 16*c^8*d^8*e^2 - 32*a*c^7*d^6*e^4 + 32*a^3*c^5*d^2*e^8) + (-(a*c^2*d^3 + a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 - 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^8*d^9*e^3 - (d + e*x)^(1/2)*(-(a*c^2*d^3 + a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 - 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^9*d^11*e^2 + 64*a^6*c^4*d*e^12 + 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 + 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10) + 64*a^5*c^4*d*e^11 + 256*a^2*c^7*d^7*e^5 + 384*a^3*c^6*d^5*e^7 + 256*a^4*c^5*d^3*e^9))*(-(a*c^2*d^3 + a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 - 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*1i + ((d + e*x)^(1/2)*(16*a^4*c^4*e^10 - 16*c^8*d^8*e^2 - 32*a*c^7*d^6*e^4 + 32*a^3*c^5*d^2*e^8) - (-(a*c^2*d^3 + a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 - 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*((d + e*x)^(1/2)*(-(a*c^2*d^3 + a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 - 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^9*d^11*e^2 + 64*a^6*c^4*d*e^12 + 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 + 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10) + 64*a*c^8*d^9*e^3 + 64*a^5*c^4*d*e^11 + 256*a^2*c^7*d^7*e^5 + 384*a^3*c^6*d^5*e^7 + 256*a^4*c^5*d^3*e^9))*(-(a*c^2*d^3 + a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 - 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*1i)/(((d + e*x)^(1/2)*(16*a^4*c^4*e^10 - 16*c^8*d^8*e^2 - 32*a*c^7*d^6*e^4 + 32*a^3*c^5*d^2*e^8) - (-(a*c^2*d^3 + a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 - 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*((d + e*x)^(1/2)*(-(a*c^2*d^3 + a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 - 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^9*d^11*e^2 + 64*a^6*c^4*d*e^12 + 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 + 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10) + 64*a*c^8*d^9*e^3 + 64*a^5*c^4*d*e^11 + 256*a^2*c^7*d^7*e^5 + 384*a^3*c^6*d^5*e^7 + 256*a^4*c^5*d^3*e^9))*(-(a*c^2*d^3 + a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 - 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2) - ((d + e*x)^(1/2)*(16*a^4*c^4*e^10 - 16*c^8*d^8*e^2 - 32*a*c^7*d^6*e^4 + 32*a^3*c^5*d^2*e^8) + (-(a*c^2*d^3 + a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 - 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^8*d^9*e^3 - (d + e*x)^(1/2)*(-(a*c^2*d^3 + a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 - 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^9*d^11*e^2 + 64*a^6*c^4*d*e^12 + 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 + 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10) + 64*a^5*c^4*d*e^11 + 256*a^2*c^7*d^7*e^5 + 384*a^3*c^6*d^5*e^7 + 256*a^4*c^5*d^3*e^9))*(-(a*c^2*d^3 + a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 - 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2) + 16*a^3*c^4*e^9 + 16*c^7*d^6*e^3 + 48*a*c^6*d^4*e^5 + 48*a^2*c^5*d^2*e^7))*(-(a*c^2*d^3 + a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 - 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*2i - atan((((d + e*x)^(1/2)*(16*a^4*c^4*e^10 - 16*c^8*d^8*e^2 - 32*a*c^7*d^6*e^4 + 32*a^3*c^5*d^2*e^8) + (-(a*c^2*d^3 - a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 + 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^8*d^9*e^3 - (d + e*x)^(1/2)*(-(a*c^2*d^3 - a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 + 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^9*d^11*e^2 + 64*a^6*c^4*d*e^12 + 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 + 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10) + 64*a^5*c^4*d*e^11 + 256*a^2*c^7*d^7*e^5 + 384*a^3*c^6*d^5*e^7 + 256*a^4*c^5*d^3*e^9))*(-(a*c^2*d^3 - a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 + 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*1i + ((d + e*x)^(1/2)*(16*a^4*c^4*e^10 - 16*c^8*d^8*e^2 - 32*a*c^7*d^6*e^4 + 32*a^3*c^5*d^2*e^8) - (-(a*c^2*d^3 - a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 + 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*((d + e*x)^(1/2)*(-(a*c^2*d^3 - a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 + 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^9*d^11*e^2 + 64*a^6*c^4*d*e^12 + 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 + 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10) + 64*a*c^8*d^9*e^3 + 64*a^5*c^4*d*e^11 + 256*a^2*c^7*d^7*e^5 + 384*a^3*c^6*d^5*e^7 + 256*a^4*c^5*d^3*e^9))*(-(a*c^2*d^3 - a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 + 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*1i)/(((d + e*x)^(1/2)*(16*a^4*c^4*e^10 - 16*c^8*d^8*e^2 - 32*a*c^7*d^6*e^4 + 32*a^3*c^5*d^2*e^8) - (-(a*c^2*d^3 - a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 + 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*((d + e*x)^(1/2)*(-(a*c^2*d^3 - a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 + 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^9*d^11*e^2 + 64*a^6*c^4*d*e^12 + 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 + 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10) + 64*a*c^8*d^9*e^3 + 64*a^5*c^4*d*e^11 + 256*a^2*c^7*d^7*e^5 + 384*a^3*c^6*d^5*e^7 + 256*a^4*c^5*d^3*e^9))*(-(a*c^2*d^3 - a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 + 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2) - ((d + e*x)^(1/2)*(16*a^4*c^4*e^10 - 16*c^8*d^8*e^2 - 32*a*c^7*d^6*e^4 + 32*a^3*c^5*d^2*e^8) + (-(a*c^2*d^3 - a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 + 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^8*d^9*e^3 - (d + e*x)^(1/2)*(-(a*c^2*d^3 - a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 + 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*(64*a*c^9*d^11*e^2 + 64*a^6*c^4*d*e^12 + 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 + 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10) + 64*a^5*c^4*d*e^11 + 256*a^2*c^7*d^7*e^5 + 384*a^3*c^6*d^5*e^7 + 256*a^4*c^5*d^3*e^9))*(-(a*c^2*d^3 - a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 + 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2) + 16*a^3*c^4*e^9 + 16*c^7*d^6*e^3 + 48*a*c^6*d^4*e^5 + 48*a^2*c^5*d^2*e^7))*(-(a*c^2*d^3 - a*e^3*(-a^3*c)^(1/2) - 3*a^2*c*d*e^2 + 3*c*d^2*e*(-a^3*c)^(1/2))/(4*(a^5*e^6 + a^2*c^3*d^6 + 3*a^4*c*d^2*e^4 + 3*a^3*c^2*d^4*e^2)))^(1/2)*2i - (2*e)/((a*e^2 + c*d^2)*(d + e*x)^(1/2))","B"
623,1,7908,736,2.569146,"\text{Not used}","int(1/((a + c*x^2)*(d + e*x)^(5/2)),x)","-\frac{\frac{2\,e}{3\,\left(c\,d^2+a\,e^2\right)}+\frac{4\,c\,d\,e\,\left(d+e\,x\right)}{{\left(c\,d^2+a\,e^2\right)}^2}}{{\left(d+e\,x\right)}^{3/2}}-\mathrm{atan}\left(\frac{\left(\sqrt{d+e\,x}\,\left(-16\,a^8\,c^5\,e^{18}+320\,a^6\,c^7\,d^4\,e^{14}+1024\,a^5\,c^8\,d^6\,e^{12}+1440\,a^4\,c^9\,d^8\,e^{10}+1024\,a^3\,c^{10}\,d^{10}\,e^8+320\,a^2\,c^{11}\,d^{12}\,e^6-16\,c^{13}\,d^{16}\,e^2\right)+\sqrt{-\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,\left(96\,a\,c^{13}\,d^{18}\,e^3-\sqrt{d+e\,x}\,\sqrt{-\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,\left(64\,a^{11}\,c^4\,d\,e^{22}+640\,a^{10}\,c^5\,d^3\,e^{20}+2880\,a^9\,c^6\,d^5\,e^{18}+7680\,a^8\,c^7\,d^7\,e^{16}+13440\,a^7\,c^8\,d^9\,e^{14}+16128\,a^6\,c^9\,d^{11}\,e^{12}+13440\,a^5\,c^{10}\,d^{13}\,e^{10}+7680\,a^4\,c^{11}\,d^{15}\,e^8+2880\,a^3\,c^{12}\,d^{17}\,e^6+640\,a^2\,c^{13}\,d^{19}\,e^4+64\,a\,c^{14}\,d^{21}\,e^2\right)-32\,a^{10}\,c^4\,e^{21}+736\,a^2\,c^{12}\,d^{16}\,e^5+2432\,a^3\,c^{11}\,d^{14}\,e^7+4480\,a^4\,c^{10}\,d^{12}\,e^9+4928\,a^5\,c^9\,d^{10}\,e^{11}+3136\,a^6\,c^8\,d^8\,e^{13}+896\,a^7\,c^7\,d^6\,e^{15}-128\,a^8\,c^6\,d^4\,e^{17}-160\,a^9\,c^5\,d^2\,e^{19}\right)\right)\,\sqrt{-\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,1{}\mathrm{i}+\left(\sqrt{d+e\,x}\,\left(-16\,a^8\,c^5\,e^{18}+320\,a^6\,c^7\,d^4\,e^{14}+1024\,a^5\,c^8\,d^6\,e^{12}+1440\,a^4\,c^9\,d^8\,e^{10}+1024\,a^3\,c^{10}\,d^{10}\,e^8+320\,a^2\,c^{11}\,d^{12}\,e^6-16\,c^{13}\,d^{16}\,e^2\right)-\sqrt{-\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,\left(64\,a^{11}\,c^4\,d\,e^{22}+640\,a^{10}\,c^5\,d^3\,e^{20}+2880\,a^9\,c^6\,d^5\,e^{18}+7680\,a^8\,c^7\,d^7\,e^{16}+13440\,a^7\,c^8\,d^9\,e^{14}+16128\,a^6\,c^9\,d^{11}\,e^{12}+13440\,a^5\,c^{10}\,d^{13}\,e^{10}+7680\,a^4\,c^{11}\,d^{15}\,e^8+2880\,a^3\,c^{12}\,d^{17}\,e^6+640\,a^2\,c^{13}\,d^{19}\,e^4+64\,a\,c^{14}\,d^{21}\,e^2\right)-32\,a^{10}\,c^4\,e^{21}+96\,a\,c^{13}\,d^{18}\,e^3+736\,a^2\,c^{12}\,d^{16}\,e^5+2432\,a^3\,c^{11}\,d^{14}\,e^7+4480\,a^4\,c^{10}\,d^{12}\,e^9+4928\,a^5\,c^9\,d^{10}\,e^{11}+3136\,a^6\,c^8\,d^8\,e^{13}+896\,a^7\,c^7\,d^6\,e^{15}-128\,a^8\,c^6\,d^4\,e^{17}-160\,a^9\,c^5\,d^2\,e^{19}\right)\right)\,\sqrt{-\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,1{}\mathrm{i}}{\left(\sqrt{d+e\,x}\,\left(-16\,a^8\,c^5\,e^{18}+320\,a^6\,c^7\,d^4\,e^{14}+1024\,a^5\,c^8\,d^6\,e^{12}+1440\,a^4\,c^9\,d^8\,e^{10}+1024\,a^3\,c^{10}\,d^{10}\,e^8+320\,a^2\,c^{11}\,d^{12}\,e^6-16\,c^{13}\,d^{16}\,e^2\right)-\sqrt{-\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,\left(64\,a^{11}\,c^4\,d\,e^{22}+640\,a^{10}\,c^5\,d^3\,e^{20}+2880\,a^9\,c^6\,d^5\,e^{18}+7680\,a^8\,c^7\,d^7\,e^{16}+13440\,a^7\,c^8\,d^9\,e^{14}+16128\,a^6\,c^9\,d^{11}\,e^{12}+13440\,a^5\,c^{10}\,d^{13}\,e^{10}+7680\,a^4\,c^{11}\,d^{15}\,e^8+2880\,a^3\,c^{12}\,d^{17}\,e^6+640\,a^2\,c^{13}\,d^{19}\,e^4+64\,a\,c^{14}\,d^{21}\,e^2\right)-32\,a^{10}\,c^4\,e^{21}+96\,a\,c^{13}\,d^{18}\,e^3+736\,a^2\,c^{12}\,d^{16}\,e^5+2432\,a^3\,c^{11}\,d^{14}\,e^7+4480\,a^4\,c^{10}\,d^{12}\,e^9+4928\,a^5\,c^9\,d^{10}\,e^{11}+3136\,a^6\,c^8\,d^8\,e^{13}+896\,a^7\,c^7\,d^6\,e^{15}-128\,a^8\,c^6\,d^4\,e^{17}-160\,a^9\,c^5\,d^2\,e^{19}\right)\right)\,\sqrt{-\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}-\left(\sqrt{d+e\,x}\,\left(-16\,a^8\,c^5\,e^{18}+320\,a^6\,c^7\,d^4\,e^{14}+1024\,a^5\,c^8\,d^6\,e^{12}+1440\,a^4\,c^9\,d^8\,e^{10}+1024\,a^3\,c^{10}\,d^{10}\,e^8+320\,a^2\,c^{11}\,d^{12}\,e^6-16\,c^{13}\,d^{16}\,e^2\right)+\sqrt{-\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,\left(96\,a\,c^{13}\,d^{18}\,e^3-\sqrt{d+e\,x}\,\sqrt{-\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,\left(64\,a^{11}\,c^4\,d\,e^{22}+640\,a^{10}\,c^5\,d^3\,e^{20}+2880\,a^9\,c^6\,d^5\,e^{18}+7680\,a^8\,c^7\,d^7\,e^{16}+13440\,a^7\,c^8\,d^9\,e^{14}+16128\,a^6\,c^9\,d^{11}\,e^{12}+13440\,a^5\,c^{10}\,d^{13}\,e^{10}+7680\,a^4\,c^{11}\,d^{15}\,e^8+2880\,a^3\,c^{12}\,d^{17}\,e^6+640\,a^2\,c^{13}\,d^{19}\,e^4+64\,a\,c^{14}\,d^{21}\,e^2\right)-32\,a^{10}\,c^4\,e^{21}+736\,a^2\,c^{12}\,d^{16}\,e^5+2432\,a^3\,c^{11}\,d^{14}\,e^7+4480\,a^4\,c^{10}\,d^{12}\,e^9+4928\,a^5\,c^9\,d^{10}\,e^{11}+3136\,a^6\,c^8\,d^8\,e^{13}+896\,a^7\,c^7\,d^6\,e^{15}-128\,a^8\,c^6\,d^4\,e^{17}-160\,a^9\,c^5\,d^2\,e^{19}\right)\right)\,\sqrt{-\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}+32\,c^{12}\,d^{13}\,e^3+192\,a\,c^{11}\,d^{11}\,e^5+32\,a^6\,c^6\,d\,e^{15}+480\,a^2\,c^{10}\,d^9\,e^7+640\,a^3\,c^9\,d^7\,e^9+480\,a^4\,c^8\,d^5\,e^{11}+192\,a^5\,c^7\,d^3\,e^{13}}\right)\,\sqrt{-\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}+a\,c^4\,d^5+5\,a^3\,c^2\,d\,e^4-10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\sqrt{d+e\,x}\,\left(-16\,a^8\,c^5\,e^{18}+320\,a^6\,c^7\,d^4\,e^{14}+1024\,a^5\,c^8\,d^6\,e^{12}+1440\,a^4\,c^9\,d^8\,e^{10}+1024\,a^3\,c^{10}\,d^{10}\,e^8+320\,a^2\,c^{11}\,d^{12}\,e^6-16\,c^{13}\,d^{16}\,e^2\right)+\sqrt{\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,\left(96\,a\,c^{13}\,d^{18}\,e^3-\sqrt{d+e\,x}\,\sqrt{\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,\left(64\,a^{11}\,c^4\,d\,e^{22}+640\,a^{10}\,c^5\,d^3\,e^{20}+2880\,a^9\,c^6\,d^5\,e^{18}+7680\,a^8\,c^7\,d^7\,e^{16}+13440\,a^7\,c^8\,d^9\,e^{14}+16128\,a^6\,c^9\,d^{11}\,e^{12}+13440\,a^5\,c^{10}\,d^{13}\,e^{10}+7680\,a^4\,c^{11}\,d^{15}\,e^8+2880\,a^3\,c^{12}\,d^{17}\,e^6+640\,a^2\,c^{13}\,d^{19}\,e^4+64\,a\,c^{14}\,d^{21}\,e^2\right)-32\,a^{10}\,c^4\,e^{21}+736\,a^2\,c^{12}\,d^{16}\,e^5+2432\,a^3\,c^{11}\,d^{14}\,e^7+4480\,a^4\,c^{10}\,d^{12}\,e^9+4928\,a^5\,c^9\,d^{10}\,e^{11}+3136\,a^6\,c^8\,d^8\,e^{13}+896\,a^7\,c^7\,d^6\,e^{15}-128\,a^8\,c^6\,d^4\,e^{17}-160\,a^9\,c^5\,d^2\,e^{19}\right)\right)\,\sqrt{\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,1{}\mathrm{i}+\left(\sqrt{d+e\,x}\,\left(-16\,a^8\,c^5\,e^{18}+320\,a^6\,c^7\,d^4\,e^{14}+1024\,a^5\,c^8\,d^6\,e^{12}+1440\,a^4\,c^9\,d^8\,e^{10}+1024\,a^3\,c^{10}\,d^{10}\,e^8+320\,a^2\,c^{11}\,d^{12}\,e^6-16\,c^{13}\,d^{16}\,e^2\right)-\sqrt{\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,\left(64\,a^{11}\,c^4\,d\,e^{22}+640\,a^{10}\,c^5\,d^3\,e^{20}+2880\,a^9\,c^6\,d^5\,e^{18}+7680\,a^8\,c^7\,d^7\,e^{16}+13440\,a^7\,c^8\,d^9\,e^{14}+16128\,a^6\,c^9\,d^{11}\,e^{12}+13440\,a^5\,c^{10}\,d^{13}\,e^{10}+7680\,a^4\,c^{11}\,d^{15}\,e^8+2880\,a^3\,c^{12}\,d^{17}\,e^6+640\,a^2\,c^{13}\,d^{19}\,e^4+64\,a\,c^{14}\,d^{21}\,e^2\right)-32\,a^{10}\,c^4\,e^{21}+96\,a\,c^{13}\,d^{18}\,e^3+736\,a^2\,c^{12}\,d^{16}\,e^5+2432\,a^3\,c^{11}\,d^{14}\,e^7+4480\,a^4\,c^{10}\,d^{12}\,e^9+4928\,a^5\,c^9\,d^{10}\,e^{11}+3136\,a^6\,c^8\,d^8\,e^{13}+896\,a^7\,c^7\,d^6\,e^{15}-128\,a^8\,c^6\,d^4\,e^{17}-160\,a^9\,c^5\,d^2\,e^{19}\right)\right)\,\sqrt{\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,1{}\mathrm{i}}{\left(\sqrt{d+e\,x}\,\left(-16\,a^8\,c^5\,e^{18}+320\,a^6\,c^7\,d^4\,e^{14}+1024\,a^5\,c^8\,d^6\,e^{12}+1440\,a^4\,c^9\,d^8\,e^{10}+1024\,a^3\,c^{10}\,d^{10}\,e^8+320\,a^2\,c^{11}\,d^{12}\,e^6-16\,c^{13}\,d^{16}\,e^2\right)-\sqrt{\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,\left(64\,a^{11}\,c^4\,d\,e^{22}+640\,a^{10}\,c^5\,d^3\,e^{20}+2880\,a^9\,c^6\,d^5\,e^{18}+7680\,a^8\,c^7\,d^7\,e^{16}+13440\,a^7\,c^8\,d^9\,e^{14}+16128\,a^6\,c^9\,d^{11}\,e^{12}+13440\,a^5\,c^{10}\,d^{13}\,e^{10}+7680\,a^4\,c^{11}\,d^{15}\,e^8+2880\,a^3\,c^{12}\,d^{17}\,e^6+640\,a^2\,c^{13}\,d^{19}\,e^4+64\,a\,c^{14}\,d^{21}\,e^2\right)-32\,a^{10}\,c^4\,e^{21}+96\,a\,c^{13}\,d^{18}\,e^3+736\,a^2\,c^{12}\,d^{16}\,e^5+2432\,a^3\,c^{11}\,d^{14}\,e^7+4480\,a^4\,c^{10}\,d^{12}\,e^9+4928\,a^5\,c^9\,d^{10}\,e^{11}+3136\,a^6\,c^8\,d^8\,e^{13}+896\,a^7\,c^7\,d^6\,e^{15}-128\,a^8\,c^6\,d^4\,e^{17}-160\,a^9\,c^5\,d^2\,e^{19}\right)\right)\,\sqrt{\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}-\left(\sqrt{d+e\,x}\,\left(-16\,a^8\,c^5\,e^{18}+320\,a^6\,c^7\,d^4\,e^{14}+1024\,a^5\,c^8\,d^6\,e^{12}+1440\,a^4\,c^9\,d^8\,e^{10}+1024\,a^3\,c^{10}\,d^{10}\,e^8+320\,a^2\,c^{11}\,d^{12}\,e^6-16\,c^{13}\,d^{16}\,e^2\right)+\sqrt{\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,\left(96\,a\,c^{13}\,d^{18}\,e^3-\sqrt{d+e\,x}\,\sqrt{\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,\left(64\,a^{11}\,c^4\,d\,e^{22}+640\,a^{10}\,c^5\,d^3\,e^{20}+2880\,a^9\,c^6\,d^5\,e^{18}+7680\,a^8\,c^7\,d^7\,e^{16}+13440\,a^7\,c^8\,d^9\,e^{14}+16128\,a^6\,c^9\,d^{11}\,e^{12}+13440\,a^5\,c^{10}\,d^{13}\,e^{10}+7680\,a^4\,c^{11}\,d^{15}\,e^8+2880\,a^3\,c^{12}\,d^{17}\,e^6+640\,a^2\,c^{13}\,d^{19}\,e^4+64\,a\,c^{14}\,d^{21}\,e^2\right)-32\,a^{10}\,c^4\,e^{21}+736\,a^2\,c^{12}\,d^{16}\,e^5+2432\,a^3\,c^{11}\,d^{14}\,e^7+4480\,a^4\,c^{10}\,d^{12}\,e^9+4928\,a^5\,c^9\,d^{10}\,e^{11}+3136\,a^6\,c^8\,d^8\,e^{13}+896\,a^7\,c^7\,d^6\,e^{15}-128\,a^8\,c^6\,d^4\,e^{17}-160\,a^9\,c^5\,d^2\,e^{19}\right)\right)\,\sqrt{\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}+32\,c^{12}\,d^{13}\,e^3+192\,a\,c^{11}\,d^{11}\,e^5+32\,a^6\,c^6\,d\,e^{15}+480\,a^2\,c^{10}\,d^9\,e^7+640\,a^3\,c^9\,d^7\,e^9+480\,a^4\,c^8\,d^5\,e^{11}+192\,a^5\,c^7\,d^3\,e^{13}}\right)\,\sqrt{\frac{a^2\,e^5\,\sqrt{-a^3\,c^3}-a\,c^4\,d^5-5\,a^3\,c^2\,d\,e^4+10\,a^2\,c^3\,d^3\,e^2+5\,c^2\,d^4\,e\,\sqrt{-a^3\,c^3}-10\,a\,c\,d^2\,e^3\,\sqrt{-a^3\,c^3}}{4\,\left(a^7\,e^{10}+5\,a^6\,c\,d^2\,e^8+10\,a^5\,c^2\,d^4\,e^6+10\,a^4\,c^3\,d^6\,e^4+5\,a^3\,c^4\,d^8\,e^2+a^2\,c^5\,d^{10}\right)}}\,2{}\mathrm{i}","Not used",1,"- ((2*e)/(3*(a*e^2 + c*d^2)) + (4*c*d*e*(d + e*x))/(a*e^2 + c*d^2)^2)/(d + e*x)^(3/2) - atan((((d + e*x)^(1/2)*(320*a^2*c^11*d^12*e^6 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14) + (-(a^2*e^5*(-a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(96*a*c^13*d^18*e^3 - (d + e*x)^(1/2)*(-(a^2*e^5*(-a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 + 64*a^11*c^4*d*e^22 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20) - 32*a^10*c^4*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19))*(-(a^2*e^5*(-a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*1i + ((d + e*x)^(1/2)*(320*a^2*c^11*d^12*e^6 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14) - (-(a^2*e^5*(-a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*(-(a^2*e^5*(-a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 + 64*a^11*c^4*d*e^22 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20) - 32*a^10*c^4*e^21 + 96*a*c^13*d^18*e^3 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19))*(-(a^2*e^5*(-a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*1i)/(((d + e*x)^(1/2)*(320*a^2*c^11*d^12*e^6 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14) - (-(a^2*e^5*(-a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*(-(a^2*e^5*(-a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 + 64*a^11*c^4*d*e^22 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20) - 32*a^10*c^4*e^21 + 96*a*c^13*d^18*e^3 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19))*(-(a^2*e^5*(-a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2) - ((d + e*x)^(1/2)*(320*a^2*c^11*d^12*e^6 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14) + (-(a^2*e^5*(-a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(96*a*c^13*d^18*e^3 - (d + e*x)^(1/2)*(-(a^2*e^5*(-a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 + 64*a^11*c^4*d*e^22 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20) - 32*a^10*c^4*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19))*(-(a^2*e^5*(-a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2) + 32*c^12*d^13*e^3 + 192*a*c^11*d^11*e^5 + 32*a^6*c^6*d*e^15 + 480*a^2*c^10*d^9*e^7 + 640*a^3*c^9*d^7*e^9 + 480*a^4*c^8*d^5*e^11 + 192*a^5*c^7*d^3*e^13))*(-(a^2*e^5*(-a^3*c^3)^(1/2) + a*c^4*d^5 + 5*a^3*c^2*d*e^4 - 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*2i - atan((((d + e*x)^(1/2)*(320*a^2*c^11*d^12*e^6 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14) + ((a^2*e^5*(-a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(96*a*c^13*d^18*e^3 - (d + e*x)^(1/2)*((a^2*e^5*(-a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 + 64*a^11*c^4*d*e^22 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20) - 32*a^10*c^4*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19))*((a^2*e^5*(-a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*1i + ((d + e*x)^(1/2)*(320*a^2*c^11*d^12*e^6 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14) - ((a^2*e^5*(-a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*((a^2*e^5*(-a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 + 64*a^11*c^4*d*e^22 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20) - 32*a^10*c^4*e^21 + 96*a*c^13*d^18*e^3 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19))*((a^2*e^5*(-a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*1i)/(((d + e*x)^(1/2)*(320*a^2*c^11*d^12*e^6 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14) - ((a^2*e^5*(-a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*((a^2*e^5*(-a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 + 64*a^11*c^4*d*e^22 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20) - 32*a^10*c^4*e^21 + 96*a*c^13*d^18*e^3 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19))*((a^2*e^5*(-a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2) - ((d + e*x)^(1/2)*(320*a^2*c^11*d^12*e^6 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14) + ((a^2*e^5*(-a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(96*a*c^13*d^18*e^3 - (d + e*x)^(1/2)*((a^2*e^5*(-a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*(64*a*c^14*d^21*e^2 + 64*a^11*c^4*d*e^22 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20) - 32*a^10*c^4*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19))*((a^2*e^5*(-a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2) + 32*c^12*d^13*e^3 + 192*a*c^11*d^11*e^5 + 32*a^6*c^6*d*e^15 + 480*a^2*c^10*d^9*e^7 + 640*a^3*c^9*d^7*e^9 + 480*a^4*c^8*d^5*e^11 + 192*a^5*c^7*d^3*e^13))*((a^2*e^5*(-a^3*c^3)^(1/2) - a*c^4*d^5 - 5*a^3*c^2*d*e^4 + 10*a^2*c^3*d^3*e^2 + 5*c^2*d^4*e*(-a^3*c^3)^(1/2) - 10*a*c*d^2*e^3*(-a^3*c^3)^(1/2))/(4*(a^7*e^10 + a^2*c^5*d^10 + 5*a^6*c*d^2*e^8 + 5*a^3*c^4*d^8*e^2 + 10*a^4*c^3*d^6*e^4 + 10*a^5*c^2*d^4*e^6)))^(1/2)*2i","B"
624,1,4090,263,1.205725,"\text{Not used}","int((d + e*x)^(7/2)/(a - c*x^2)^2,x)","\frac{2\,e^3\,\sqrt{d+e\,x}}{c^2}-\frac{\frac{\left(a^2\,e^5-c^2\,d^4\,e\right)\,\sqrt{d+e\,x}}{2\,a}+\frac{\left(c^2\,d^3\,e+3\,a\,c\,d\,e^3\right)\,{\left(d+e\,x\right)}^{3/2}}{2\,a}}{c^3\,{\left(d+e\,x\right)}^2+c^3\,d^2-a\,c^2\,e^2-2\,c^3\,d\,\left(d+e\,x\right)}-\mathrm{atan}\left(\frac{a^2\,e^{10}\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}+\frac{d^7}{16\,a^3\,c}+\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}-\frac{25\,e^7\,\sqrt{a^9\,c^9}}{64\,a^4\,c^9}-\frac{77\,d^2\,e^5\,\sqrt{a^9\,c^9}}{32\,a^5\,c^8}+\frac{35\,d^4\,e^3\,\sqrt{a^9\,c^9}}{64\,a^6\,c^7}}\,50{}\mathrm{i}}{\frac{885\,d^5\,e^9}{2}-\frac{491\,a\,d^3\,e^{11}}{2\,c}-\frac{329\,c\,d^7\,e^7}{2\,a}-\frac{50\,a^2\,d\,e^{13}}{c^2}+\frac{35\,c^2\,d^9\,e^5}{2\,a^2}+\frac{125\,e^{14}\,\sqrt{a^9\,c^9}}{4\,a^2\,c^7}+\frac{335\,d^2\,e^{12}\,\sqrt{a^9\,c^9}}{2\,a^3\,c^6}-\frac{204\,d^4\,e^{10}\,\sqrt{a^9\,c^9}}{a^4\,c^5}-\frac{7\,d^6\,e^8\,\sqrt{a^9\,c^9}}{2\,a^5\,c^4}+\frac{35\,d^8\,e^6\,\sqrt{a^9\,c^9}}{4\,a^6\,c^3}}+\frac{d^3\,e^7\,\sqrt{a^9\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}+\frac{d^7}{16\,a^3\,c}+\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}-\frac{25\,e^7\,\sqrt{a^9\,c^9}}{64\,a^4\,c^9}-\frac{77\,d^2\,e^5\,\sqrt{a^9\,c^9}}{32\,a^5\,c^8}+\frac{35\,d^4\,e^3\,\sqrt{a^9\,c^9}}{64\,a^6\,c^7}}\,308{}\mathrm{i}}{\frac{35\,a^2\,c^5\,d^9\,e^5}{2}-\frac{329\,a^3\,c^4\,d^7\,e^7}{2}+\frac{885\,a^4\,c^3\,d^5\,e^9}{2}-\frac{491\,a^5\,c^2\,d^3\,e^{11}}{2}-50\,a^6\,c\,d\,e^{13}+\frac{125\,a^2\,e^{14}\,\sqrt{a^9\,c^9}}{4\,c^4}+\frac{35\,d^8\,e^6\,\sqrt{a^9\,c^9}}{4\,a^2}-\frac{204\,d^4\,e^{10}\,\sqrt{a^9\,c^9}}{c^2}+\frac{335\,a\,d^2\,e^{12}\,\sqrt{a^9\,c^9}}{2\,c^3}-\frac{7\,d^6\,e^8\,\sqrt{a^9\,c^9}}{2\,a\,c}}+\frac{d^5\,e^5\,\sqrt{a^9\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}+\frac{d^7}{16\,a^3\,c}+\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}-\frac{25\,e^7\,\sqrt{a^9\,c^9}}{64\,a^4\,c^9}-\frac{77\,d^2\,e^5\,\sqrt{a^9\,c^9}}{32\,a^5\,c^8}+\frac{35\,d^4\,e^3\,\sqrt{a^9\,c^9}}{64\,a^6\,c^7}}\,70{}\mathrm{i}}{50\,a^7\,d\,e^{13}+\frac{491\,a^6\,c\,d^3\,e^{11}}{2}-\frac{35\,a^3\,c^4\,d^9\,e^5}{2}+\frac{329\,a^4\,c^3\,d^7\,e^7}{2}-\frac{885\,a^5\,c^2\,d^5\,e^9}{2}-\frac{125\,a^3\,e^{14}\,\sqrt{a^9\,c^9}}{4\,c^5}+\frac{7\,d^6\,e^8\,\sqrt{a^9\,c^9}}{2\,c^2}+\frac{204\,a\,d^4\,e^{10}\,\sqrt{a^9\,c^9}}{c^3}-\frac{35\,d^8\,e^6\,\sqrt{a^9\,c^9}}{4\,a\,c}-\frac{335\,a^2\,d^2\,e^{12}\,\sqrt{a^9\,c^9}}{2\,c^4}}-\frac{a\,d^2\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}+\frac{d^7}{16\,a^3\,c}+\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}-\frac{25\,e^7\,\sqrt{a^9\,c^9}}{64\,a^4\,c^9}-\frac{77\,d^2\,e^5\,\sqrt{a^9\,c^9}}{32\,a^5\,c^8}+\frac{35\,d^4\,e^3\,\sqrt{a^9\,c^9}}{64\,a^6\,c^7}}\,308{}\mathrm{i}}{\frac{329\,d^7\,e^7}{2\,a}-\frac{885\,d^5\,e^9}{2\,c}+\frac{491\,a\,d^3\,e^{11}}{2\,c^2}-\frac{35\,c\,d^9\,e^5}{2\,a^2}+\frac{50\,a^2\,d\,e^{13}}{c^3}-\frac{125\,e^{14}\,\sqrt{a^9\,c^9}}{4\,a^2\,c^8}-\frac{335\,d^2\,e^{12}\,\sqrt{a^9\,c^9}}{2\,a^3\,c^7}+\frac{204\,d^4\,e^{10}\,\sqrt{a^9\,c^9}}{a^4\,c^6}+\frac{7\,d^6\,e^8\,\sqrt{a^9\,c^9}}{2\,a^5\,c^5}-\frac{35\,d^8\,e^6\,\sqrt{a^9\,c^9}}{4\,a^6\,c^4}}+\frac{c\,d^4\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}+\frac{d^7}{16\,a^3\,c}+\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}-\frac{25\,e^7\,\sqrt{a^9\,c^9}}{64\,a^4\,c^9}-\frac{77\,d^2\,e^5\,\sqrt{a^9\,c^9}}{32\,a^5\,c^8}+\frac{35\,d^4\,e^3\,\sqrt{a^9\,c^9}}{64\,a^6\,c^7}}\,70{}\mathrm{i}}{\frac{329\,d^7\,e^7}{2\,a}-\frac{885\,d^5\,e^9}{2\,c}+\frac{491\,a\,d^3\,e^{11}}{2\,c^2}-\frac{35\,c\,d^9\,e^5}{2\,a^2}+\frac{50\,a^2\,d\,e^{13}}{c^3}-\frac{125\,e^{14}\,\sqrt{a^9\,c^9}}{4\,a^2\,c^8}-\frac{335\,d^2\,e^{12}\,\sqrt{a^9\,c^9}}{2\,a^3\,c^7}+\frac{204\,d^4\,e^{10}\,\sqrt{a^9\,c^9}}{a^4\,c^6}+\frac{7\,d^6\,e^8\,\sqrt{a^9\,c^9}}{2\,a^5\,c^5}-\frac{35\,d^8\,e^6\,\sqrt{a^9\,c^9}}{4\,a^6\,c^4}}+\frac{d\,e^9\,\sqrt{a^9\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}+\frac{d^7}{16\,a^3\,c}+\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}-\frac{25\,e^7\,\sqrt{a^9\,c^9}}{64\,a^4\,c^9}-\frac{77\,d^2\,e^5\,\sqrt{a^9\,c^9}}{32\,a^5\,c^8}+\frac{35\,d^4\,e^3\,\sqrt{a^9\,c^9}}{64\,a^6\,c^7}}\,50{}\mathrm{i}}{\frac{35\,a\,c^6\,d^9\,e^5}{2}-50\,a^5\,c^2\,d\,e^{13}-\frac{329\,a^2\,c^5\,d^7\,e^7}{2}+\frac{885\,a^3\,c^4\,d^5\,e^9}{2}-\frac{491\,a^4\,c^3\,d^3\,e^{11}}{2}+\frac{125\,a\,e^{14}\,\sqrt{a^9\,c^9}}{4\,c^3}-\frac{7\,d^6\,e^8\,\sqrt{a^9\,c^9}}{2\,a^2}+\frac{335\,d^2\,e^{12}\,\sqrt{a^9\,c^9}}{2\,c^2}+\frac{35\,c\,d^8\,e^6\,\sqrt{a^9\,c^9}}{4\,a^3}-\frac{204\,d^4\,e^{10}\,\sqrt{a^9\,c^9}}{a\,c}}\right)\,\sqrt{\frac{4\,a^3\,c^8\,d^7-25\,a^2\,e^7\,\sqrt{a^9\,c^9}+105\,a^6\,c^5\,d\,e^6-35\,a^4\,c^7\,d^5\,e^2+70\,a^5\,c^6\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c^9}-154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c^9}}{64\,a^6\,c^9}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{a^2\,e^{10}\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}+\frac{d^7}{16\,a^3\,c}+\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}+\frac{25\,e^7\,\sqrt{a^9\,c^9}}{64\,a^4\,c^9}+\frac{77\,d^2\,e^5\,\sqrt{a^9\,c^9}}{32\,a^5\,c^8}-\frac{35\,d^4\,e^3\,\sqrt{a^9\,c^9}}{64\,a^6\,c^7}}\,50{}\mathrm{i}}{\frac{491\,a\,d^3\,e^{11}}{2\,c}-\frac{885\,d^5\,e^9}{2}+\frac{329\,c\,d^7\,e^7}{2\,a}+\frac{50\,a^2\,d\,e^{13}}{c^2}-\frac{35\,c^2\,d^9\,e^5}{2\,a^2}+\frac{125\,e^{14}\,\sqrt{a^9\,c^9}}{4\,a^2\,c^7}+\frac{335\,d^2\,e^{12}\,\sqrt{a^9\,c^9}}{2\,a^3\,c^6}-\frac{204\,d^4\,e^{10}\,\sqrt{a^9\,c^9}}{a^4\,c^5}-\frac{7\,d^6\,e^8\,\sqrt{a^9\,c^9}}{2\,a^5\,c^4}+\frac{35\,d^8\,e^6\,\sqrt{a^9\,c^9}}{4\,a^6\,c^3}}-\frac{d^3\,e^7\,\sqrt{a^9\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}+\frac{d^7}{16\,a^3\,c}+\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}+\frac{25\,e^7\,\sqrt{a^9\,c^9}}{64\,a^4\,c^9}+\frac{77\,d^2\,e^5\,\sqrt{a^9\,c^9}}{32\,a^5\,c^8}-\frac{35\,d^4\,e^3\,\sqrt{a^9\,c^9}}{64\,a^6\,c^7}}\,308{}\mathrm{i}}{\frac{329\,a^3\,c^4\,d^7\,e^7}{2}-\frac{35\,a^2\,c^5\,d^9\,e^5}{2}-\frac{885\,a^4\,c^3\,d^5\,e^9}{2}+\frac{491\,a^5\,c^2\,d^3\,e^{11}}{2}+50\,a^6\,c\,d\,e^{13}+\frac{125\,a^2\,e^{14}\,\sqrt{a^9\,c^9}}{4\,c^4}+\frac{35\,d^8\,e^6\,\sqrt{a^9\,c^9}}{4\,a^2}-\frac{204\,d^4\,e^{10}\,\sqrt{a^9\,c^9}}{c^2}+\frac{335\,a\,d^2\,e^{12}\,\sqrt{a^9\,c^9}}{2\,c^3}-\frac{7\,d^6\,e^8\,\sqrt{a^9\,c^9}}{2\,a\,c}}+\frac{d^5\,e^5\,\sqrt{a^9\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}+\frac{d^7}{16\,a^3\,c}+\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}+\frac{25\,e^7\,\sqrt{a^9\,c^9}}{64\,a^4\,c^9}+\frac{77\,d^2\,e^5\,\sqrt{a^9\,c^9}}{32\,a^5\,c^8}-\frac{35\,d^4\,e^3\,\sqrt{a^9\,c^9}}{64\,a^6\,c^7}}\,70{}\mathrm{i}}{50\,a^7\,d\,e^{13}+\frac{491\,a^6\,c\,d^3\,e^{11}}{2}-\frac{35\,a^3\,c^4\,d^9\,e^5}{2}+\frac{329\,a^4\,c^3\,d^7\,e^7}{2}-\frac{885\,a^5\,c^2\,d^5\,e^9}{2}+\frac{125\,a^3\,e^{14}\,\sqrt{a^9\,c^9}}{4\,c^5}-\frac{7\,d^6\,e^8\,\sqrt{a^9\,c^9}}{2\,c^2}-\frac{204\,a\,d^4\,e^{10}\,\sqrt{a^9\,c^9}}{c^3}+\frac{35\,d^8\,e^6\,\sqrt{a^9\,c^9}}{4\,a\,c}+\frac{335\,a^2\,d^2\,e^{12}\,\sqrt{a^9\,c^9}}{2\,c^4}}+\frac{a\,d^2\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}+\frac{d^7}{16\,a^3\,c}+\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}+\frac{25\,e^7\,\sqrt{a^9\,c^9}}{64\,a^4\,c^9}+\frac{77\,d^2\,e^5\,\sqrt{a^9\,c^9}}{32\,a^5\,c^8}-\frac{35\,d^4\,e^3\,\sqrt{a^9\,c^9}}{64\,a^6\,c^7}}\,308{}\mathrm{i}}{\frac{329\,d^7\,e^7}{2\,a}-\frac{885\,d^5\,e^9}{2\,c}+\frac{491\,a\,d^3\,e^{11}}{2\,c^2}-\frac{35\,c\,d^9\,e^5}{2\,a^2}+\frac{50\,a^2\,d\,e^{13}}{c^3}+\frac{125\,e^{14}\,\sqrt{a^9\,c^9}}{4\,a^2\,c^8}+\frac{335\,d^2\,e^{12}\,\sqrt{a^9\,c^9}}{2\,a^3\,c^7}-\frac{204\,d^4\,e^{10}\,\sqrt{a^9\,c^9}}{a^4\,c^6}-\frac{7\,d^6\,e^8\,\sqrt{a^9\,c^9}}{2\,a^5\,c^5}+\frac{35\,d^8\,e^6\,\sqrt{a^9\,c^9}}{4\,a^6\,c^4}}-\frac{c\,d^4\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}+\frac{d^7}{16\,a^3\,c}+\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}+\frac{25\,e^7\,\sqrt{a^9\,c^9}}{64\,a^4\,c^9}+\frac{77\,d^2\,e^5\,\sqrt{a^9\,c^9}}{32\,a^5\,c^8}-\frac{35\,d^4\,e^3\,\sqrt{a^9\,c^9}}{64\,a^6\,c^7}}\,70{}\mathrm{i}}{\frac{329\,d^7\,e^7}{2\,a}-\frac{885\,d^5\,e^9}{2\,c}+\frac{491\,a\,d^3\,e^{11}}{2\,c^2}-\frac{35\,c\,d^9\,e^5}{2\,a^2}+\frac{50\,a^2\,d\,e^{13}}{c^3}+\frac{125\,e^{14}\,\sqrt{a^9\,c^9}}{4\,a^2\,c^8}+\frac{335\,d^2\,e^{12}\,\sqrt{a^9\,c^9}}{2\,a^3\,c^7}-\frac{204\,d^4\,e^{10}\,\sqrt{a^9\,c^9}}{a^4\,c^6}-\frac{7\,d^6\,e^8\,\sqrt{a^9\,c^9}}{2\,a^5\,c^5}+\frac{35\,d^8\,e^6\,\sqrt{a^9\,c^9}}{4\,a^6\,c^4}}-\frac{d\,e^9\,\sqrt{a^9\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}+\frac{d^7}{16\,a^3\,c}+\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}+\frac{25\,e^7\,\sqrt{a^9\,c^9}}{64\,a^4\,c^9}+\frac{77\,d^2\,e^5\,\sqrt{a^9\,c^9}}{32\,a^5\,c^8}-\frac{35\,d^4\,e^3\,\sqrt{a^9\,c^9}}{64\,a^6\,c^7}}\,50{}\mathrm{i}}{50\,a^5\,c^2\,d\,e^{13}-\frac{35\,a\,c^6\,d^9\,e^5}{2}+\frac{329\,a^2\,c^5\,d^7\,e^7}{2}-\frac{885\,a^3\,c^4\,d^5\,e^9}{2}+\frac{491\,a^4\,c^3\,d^3\,e^{11}}{2}+\frac{125\,a\,e^{14}\,\sqrt{a^9\,c^9}}{4\,c^3}-\frac{7\,d^6\,e^8\,\sqrt{a^9\,c^9}}{2\,a^2}+\frac{335\,d^2\,e^{12}\,\sqrt{a^9\,c^9}}{2\,c^2}+\frac{35\,c\,d^8\,e^6\,\sqrt{a^9\,c^9}}{4\,a^3}-\frac{204\,d^4\,e^{10}\,\sqrt{a^9\,c^9}}{a\,c}}\right)\,\sqrt{\frac{25\,a^2\,e^7\,\sqrt{a^9\,c^9}+4\,a^3\,c^8\,d^7+105\,a^6\,c^5\,d\,e^6-35\,a^4\,c^7\,d^5\,e^2+70\,a^5\,c^6\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c^9}+154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c^9}}{64\,a^6\,c^9}}\,2{}\mathrm{i}","Not used",1,"atan((a^2*e^10*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) + d^7/(16*a^3*c) + (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) + (25*e^7*(a^9*c^9)^(1/2))/(64*a^4*c^9) + (77*d^2*e^5*(a^9*c^9)^(1/2))/(32*a^5*c^8) - (35*d^4*e^3*(a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*50i)/((491*a*d^3*e^11)/(2*c) - (885*d^5*e^9)/2 + (329*c*d^7*e^7)/(2*a) + (50*a^2*d*e^13)/c^2 - (35*c^2*d^9*e^5)/(2*a^2) + (125*e^14*(a^9*c^9)^(1/2))/(4*a^2*c^7) + (335*d^2*e^12*(a^9*c^9)^(1/2))/(2*a^3*c^6) - (204*d^4*e^10*(a^9*c^9)^(1/2))/(a^4*c^5) - (7*d^6*e^8*(a^9*c^9)^(1/2))/(2*a^5*c^4) + (35*d^8*e^6*(a^9*c^9)^(1/2))/(4*a^6*c^3)) - (d^3*e^7*(a^9*c^9)^(1/2)*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) + d^7/(16*a^3*c) + (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) + (25*e^7*(a^9*c^9)^(1/2))/(64*a^4*c^9) + (77*d^2*e^5*(a^9*c^9)^(1/2))/(32*a^5*c^8) - (35*d^4*e^3*(a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*308i)/((329*a^3*c^4*d^7*e^7)/2 - (35*a^2*c^5*d^9*e^5)/2 - (885*a^4*c^3*d^5*e^9)/2 + (491*a^5*c^2*d^3*e^11)/2 + 50*a^6*c*d*e^13 + (125*a^2*e^14*(a^9*c^9)^(1/2))/(4*c^4) + (35*d^8*e^6*(a^9*c^9)^(1/2))/(4*a^2) - (204*d^4*e^10*(a^9*c^9)^(1/2))/c^2 + (335*a*d^2*e^12*(a^9*c^9)^(1/2))/(2*c^3) - (7*d^6*e^8*(a^9*c^9)^(1/2))/(2*a*c)) + (d^5*e^5*(a^9*c^9)^(1/2)*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) + d^7/(16*a^3*c) + (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) + (25*e^7*(a^9*c^9)^(1/2))/(64*a^4*c^9) + (77*d^2*e^5*(a^9*c^9)^(1/2))/(32*a^5*c^8) - (35*d^4*e^3*(a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*70i)/(50*a^7*d*e^13 + (491*a^6*c*d^3*e^11)/2 - (35*a^3*c^4*d^9*e^5)/2 + (329*a^4*c^3*d^7*e^7)/2 - (885*a^5*c^2*d^5*e^9)/2 + (125*a^3*e^14*(a^9*c^9)^(1/2))/(4*c^5) - (7*d^6*e^8*(a^9*c^9)^(1/2))/(2*c^2) - (204*a*d^4*e^10*(a^9*c^9)^(1/2))/c^3 + (35*d^8*e^6*(a^9*c^9)^(1/2))/(4*a*c) + (335*a^2*d^2*e^12*(a^9*c^9)^(1/2))/(2*c^4)) + (a*d^2*e^8*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) + d^7/(16*a^3*c) + (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) + (25*e^7*(a^9*c^9)^(1/2))/(64*a^4*c^9) + (77*d^2*e^5*(a^9*c^9)^(1/2))/(32*a^5*c^8) - (35*d^4*e^3*(a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*308i)/((329*d^7*e^7)/(2*a) - (885*d^5*e^9)/(2*c) + (491*a*d^3*e^11)/(2*c^2) - (35*c*d^9*e^5)/(2*a^2) + (50*a^2*d*e^13)/c^3 + (125*e^14*(a^9*c^9)^(1/2))/(4*a^2*c^8) + (335*d^2*e^12*(a^9*c^9)^(1/2))/(2*a^3*c^7) - (204*d^4*e^10*(a^9*c^9)^(1/2))/(a^4*c^6) - (7*d^6*e^8*(a^9*c^9)^(1/2))/(2*a^5*c^5) + (35*d^8*e^6*(a^9*c^9)^(1/2))/(4*a^6*c^4)) - (c*d^4*e^6*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) + d^7/(16*a^3*c) + (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) + (25*e^7*(a^9*c^9)^(1/2))/(64*a^4*c^9) + (77*d^2*e^5*(a^9*c^9)^(1/2))/(32*a^5*c^8) - (35*d^4*e^3*(a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*70i)/((329*d^7*e^7)/(2*a) - (885*d^5*e^9)/(2*c) + (491*a*d^3*e^11)/(2*c^2) - (35*c*d^9*e^5)/(2*a^2) + (50*a^2*d*e^13)/c^3 + (125*e^14*(a^9*c^9)^(1/2))/(4*a^2*c^8) + (335*d^2*e^12*(a^9*c^9)^(1/2))/(2*a^3*c^7) - (204*d^4*e^10*(a^9*c^9)^(1/2))/(a^4*c^6) - (7*d^6*e^8*(a^9*c^9)^(1/2))/(2*a^5*c^5) + (35*d^8*e^6*(a^9*c^9)^(1/2))/(4*a^6*c^4)) - (d*e^9*(a^9*c^9)^(1/2)*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) + d^7/(16*a^3*c) + (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) + (25*e^7*(a^9*c^9)^(1/2))/(64*a^4*c^9) + (77*d^2*e^5*(a^9*c^9)^(1/2))/(32*a^5*c^8) - (35*d^4*e^3*(a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*50i)/(50*a^5*c^2*d*e^13 - (35*a*c^6*d^9*e^5)/2 + (329*a^2*c^5*d^7*e^7)/2 - (885*a^3*c^4*d^5*e^9)/2 + (491*a^4*c^3*d^3*e^11)/2 + (125*a*e^14*(a^9*c^9)^(1/2))/(4*c^3) - (7*d^6*e^8*(a^9*c^9)^(1/2))/(2*a^2) + (335*d^2*e^12*(a^9*c^9)^(1/2))/(2*c^2) + (35*c*d^8*e^6*(a^9*c^9)^(1/2))/(4*a^3) - (204*d^4*e^10*(a^9*c^9)^(1/2))/(a*c)))*((25*a^2*e^7*(a^9*c^9)^(1/2) + 4*a^3*c^8*d^7 + 105*a^6*c^5*d*e^6 - 35*a^4*c^7*d^5*e^2 + 70*a^5*c^6*d^3*e^4 - 35*c^2*d^4*e^3*(a^9*c^9)^(1/2) + 154*a*c*d^2*e^5*(a^9*c^9)^(1/2))/(64*a^6*c^9))^(1/2)*2i - atan((a^2*e^10*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) + d^7/(16*a^3*c) + (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) - (25*e^7*(a^9*c^9)^(1/2))/(64*a^4*c^9) - (77*d^2*e^5*(a^9*c^9)^(1/2))/(32*a^5*c^8) + (35*d^4*e^3*(a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*50i)/((885*d^5*e^9)/2 - (491*a*d^3*e^11)/(2*c) - (329*c*d^7*e^7)/(2*a) - (50*a^2*d*e^13)/c^2 + (35*c^2*d^9*e^5)/(2*a^2) + (125*e^14*(a^9*c^9)^(1/2))/(4*a^2*c^7) + (335*d^2*e^12*(a^9*c^9)^(1/2))/(2*a^3*c^6) - (204*d^4*e^10*(a^9*c^9)^(1/2))/(a^4*c^5) - (7*d^6*e^8*(a^9*c^9)^(1/2))/(2*a^5*c^4) + (35*d^8*e^6*(a^9*c^9)^(1/2))/(4*a^6*c^3)) + (d^3*e^7*(a^9*c^9)^(1/2)*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) + d^7/(16*a^3*c) + (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) - (25*e^7*(a^9*c^9)^(1/2))/(64*a^4*c^9) - (77*d^2*e^5*(a^9*c^9)^(1/2))/(32*a^5*c^8) + (35*d^4*e^3*(a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*308i)/((35*a^2*c^5*d^9*e^5)/2 - (329*a^3*c^4*d^7*e^7)/2 + (885*a^4*c^3*d^5*e^9)/2 - (491*a^5*c^2*d^3*e^11)/2 - 50*a^6*c*d*e^13 + (125*a^2*e^14*(a^9*c^9)^(1/2))/(4*c^4) + (35*d^8*e^6*(a^9*c^9)^(1/2))/(4*a^2) - (204*d^4*e^10*(a^9*c^9)^(1/2))/c^2 + (335*a*d^2*e^12*(a^9*c^9)^(1/2))/(2*c^3) - (7*d^6*e^8*(a^9*c^9)^(1/2))/(2*a*c)) + (d^5*e^5*(a^9*c^9)^(1/2)*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) + d^7/(16*a^3*c) + (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) - (25*e^7*(a^9*c^9)^(1/2))/(64*a^4*c^9) - (77*d^2*e^5*(a^9*c^9)^(1/2))/(32*a^5*c^8) + (35*d^4*e^3*(a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*70i)/(50*a^7*d*e^13 + (491*a^6*c*d^3*e^11)/2 - (35*a^3*c^4*d^9*e^5)/2 + (329*a^4*c^3*d^7*e^7)/2 - (885*a^5*c^2*d^5*e^9)/2 - (125*a^3*e^14*(a^9*c^9)^(1/2))/(4*c^5) + (7*d^6*e^8*(a^9*c^9)^(1/2))/(2*c^2) + (204*a*d^4*e^10*(a^9*c^9)^(1/2))/c^3 - (35*d^8*e^6*(a^9*c^9)^(1/2))/(4*a*c) - (335*a^2*d^2*e^12*(a^9*c^9)^(1/2))/(2*c^4)) - (a*d^2*e^8*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) + d^7/(16*a^3*c) + (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) - (25*e^7*(a^9*c^9)^(1/2))/(64*a^4*c^9) - (77*d^2*e^5*(a^9*c^9)^(1/2))/(32*a^5*c^8) + (35*d^4*e^3*(a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*308i)/((329*d^7*e^7)/(2*a) - (885*d^5*e^9)/(2*c) + (491*a*d^3*e^11)/(2*c^2) - (35*c*d^9*e^5)/(2*a^2) + (50*a^2*d*e^13)/c^3 - (125*e^14*(a^9*c^9)^(1/2))/(4*a^2*c^8) - (335*d^2*e^12*(a^9*c^9)^(1/2))/(2*a^3*c^7) + (204*d^4*e^10*(a^9*c^9)^(1/2))/(a^4*c^6) + (7*d^6*e^8*(a^9*c^9)^(1/2))/(2*a^5*c^5) - (35*d^8*e^6*(a^9*c^9)^(1/2))/(4*a^6*c^4)) + (c*d^4*e^6*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) + d^7/(16*a^3*c) + (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) - (25*e^7*(a^9*c^9)^(1/2))/(64*a^4*c^9) - (77*d^2*e^5*(a^9*c^9)^(1/2))/(32*a^5*c^8) + (35*d^4*e^3*(a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*70i)/((329*d^7*e^7)/(2*a) - (885*d^5*e^9)/(2*c) + (491*a*d^3*e^11)/(2*c^2) - (35*c*d^9*e^5)/(2*a^2) + (50*a^2*d*e^13)/c^3 - (125*e^14*(a^9*c^9)^(1/2))/(4*a^2*c^8) - (335*d^2*e^12*(a^9*c^9)^(1/2))/(2*a^3*c^7) + (204*d^4*e^10*(a^9*c^9)^(1/2))/(a^4*c^6) + (7*d^6*e^8*(a^9*c^9)^(1/2))/(2*a^5*c^5) - (35*d^8*e^6*(a^9*c^9)^(1/2))/(4*a^6*c^4)) + (d*e^9*(a^9*c^9)^(1/2)*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) + d^7/(16*a^3*c) + (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) - (25*e^7*(a^9*c^9)^(1/2))/(64*a^4*c^9) - (77*d^2*e^5*(a^9*c^9)^(1/2))/(32*a^5*c^8) + (35*d^4*e^3*(a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*50i)/((35*a*c^6*d^9*e^5)/2 - 50*a^5*c^2*d*e^13 - (329*a^2*c^5*d^7*e^7)/2 + (885*a^3*c^4*d^5*e^9)/2 - (491*a^4*c^3*d^3*e^11)/2 + (125*a*e^14*(a^9*c^9)^(1/2))/(4*c^3) - (7*d^6*e^8*(a^9*c^9)^(1/2))/(2*a^2) + (335*d^2*e^12*(a^9*c^9)^(1/2))/(2*c^2) + (35*c*d^8*e^6*(a^9*c^9)^(1/2))/(4*a^3) - (204*d^4*e^10*(a^9*c^9)^(1/2))/(a*c)))*((4*a^3*c^8*d^7 - 25*a^2*e^7*(a^9*c^9)^(1/2) + 105*a^6*c^5*d*e^6 - 35*a^4*c^7*d^5*e^2 + 70*a^5*c^6*d^3*e^4 + 35*c^2*d^4*e^3*(a^9*c^9)^(1/2) - 154*a*c*d^2*e^5*(a^9*c^9)^(1/2))/(64*a^6*c^9))^(1/2)*2i - (((a^2*e^5 - c^2*d^4*e)*(d + e*x)^(1/2))/(2*a) + ((c^2*d^3*e + 3*a*c*d*e^3)*(d + e*x)^(3/2))/(2*a))/(c^3*(d + e*x)^2 + c^3*d^2 - a*c^2*e^2 - 2*c^3*d*(d + e*x)) + (2*e^3*(d + e*x)^(1/2))/c^2","B"
625,1,1988,231,0.826719,"\text{Not used}","int((d + e*x)^(5/2)/(a - c*x^2)^2,x)","2\,\mathrm{atanh}\left(\frac{18\,a\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{d^5}{16\,a^3\,c}+\frac{15\,d\,e^4}{64\,a\,c^3}-\frac{15\,d^3\,e^2}{64\,a^2\,c^2}-\frac{9\,e^5\,\sqrt{a^9\,c^7}}{64\,a^5\,c^7}+\frac{5\,d^2\,e^3\,\sqrt{a^9\,c^7}}{64\,a^6\,c^6}}}{\frac{15\,d^2\,e^9}{c}-\frac{43\,d^4\,e^7}{4\,a}-\frac{27\,a\,e^{11}}{4\,c^2}+\frac{5\,c\,d^6\,e^5}{2\,a^2}+\frac{9\,d\,e^{10}\,\sqrt{a^9\,c^7}}{4\,a^4\,c^5}-\frac{7\,d^3\,e^8\,\sqrt{a^9\,c^7}}{2\,a^5\,c^4}+\frac{5\,d^5\,e^6\,\sqrt{a^9\,c^7}}{4\,a^6\,c^3}}-\frac{10\,c\,d^2\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{d^5}{16\,a^3\,c}+\frac{15\,d\,e^4}{64\,a\,c^3}-\frac{15\,d^3\,e^2}{64\,a^2\,c^2}-\frac{9\,e^5\,\sqrt{a^9\,c^7}}{64\,a^5\,c^7}+\frac{5\,d^2\,e^3\,\sqrt{a^9\,c^7}}{64\,a^6\,c^6}}}{\frac{15\,d^2\,e^9}{c}-\frac{43\,d^4\,e^7}{4\,a}-\frac{27\,a\,e^{11}}{4\,c^2}+\frac{5\,c\,d^6\,e^5}{2\,a^2}+\frac{9\,d\,e^{10}\,\sqrt{a^9\,c^7}}{4\,a^4\,c^5}-\frac{7\,d^3\,e^8\,\sqrt{a^9\,c^7}}{2\,a^5\,c^4}+\frac{5\,d^5\,e^6\,\sqrt{a^9\,c^7}}{4\,a^6\,c^3}}+\frac{18\,d\,e^7\,\sqrt{a^9\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{d^5}{16\,a^3\,c}+\frac{15\,d\,e^4}{64\,a\,c^3}-\frac{15\,d^3\,e^2}{64\,a^2\,c^2}-\frac{9\,e^5\,\sqrt{a^9\,c^7}}{64\,a^5\,c^7}+\frac{5\,d^2\,e^3\,\sqrt{a^9\,c^7}}{64\,a^6\,c^6}}}{\frac{5\,a^2\,c^4\,d^6\,e^5}{2}-\frac{27\,a^5\,c\,e^{11}}{4}-\frac{43\,a^3\,c^3\,d^4\,e^7}{4}+15\,a^4\,c^2\,d^2\,e^9+\frac{9\,d\,e^{10}\,\sqrt{a^9\,c^7}}{4\,c^2}+\frac{5\,d^5\,e^6\,\sqrt{a^9\,c^7}}{4\,a^2}-\frac{7\,d^3\,e^8\,\sqrt{a^9\,c^7}}{2\,a\,c}}-\frac{10\,d^3\,e^5\,\sqrt{a^9\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{d^5}{16\,a^3\,c}+\frac{15\,d\,e^4}{64\,a\,c^3}-\frac{15\,d^3\,e^2}{64\,a^2\,c^2}-\frac{9\,e^5\,\sqrt{a^9\,c^7}}{64\,a^5\,c^7}+\frac{5\,d^2\,e^3\,\sqrt{a^9\,c^7}}{64\,a^6\,c^6}}}{15\,a^5\,c\,d^2\,e^9-\frac{27\,a^6\,e^{11}}{4}+\frac{5\,a^3\,c^3\,d^6\,e^5}{2}-\frac{43\,a^4\,c^2\,d^4\,e^7}{4}-\frac{7\,d^3\,e^8\,\sqrt{a^9\,c^7}}{2\,c^2}+\frac{5\,d^5\,e^6\,\sqrt{a^9\,c^7}}{4\,a\,c}+\frac{9\,a\,d\,e^{10}\,\sqrt{a^9\,c^7}}{4\,c^3}}\right)\,\sqrt{\frac{4\,a^3\,c^6\,d^5-9\,a\,e^5\,\sqrt{a^9\,c^7}+15\,a^5\,c^4\,d\,e^4-15\,a^4\,c^5\,d^3\,e^2+5\,c\,d^2\,e^3\,\sqrt{a^9\,c^7}}{64\,a^6\,c^7}}-\frac{\frac{\left(c\,d^2\,e+a\,e^3\right)\,{\left(d+e\,x\right)}^{3/2}}{2\,a\,c}+\frac{\left(a\,d\,e^3-c\,d^3\,e\right)\,\sqrt{d+e\,x}}{2\,a\,c}}{c\,{\left(d+e\,x\right)}^2-a\,e^2+c\,d^2-2\,c\,d\,\left(d+e\,x\right)}-2\,\mathrm{atanh}\left(\frac{18\,a\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{d^5}{16\,a^3\,c}+\frac{15\,d\,e^4}{64\,a\,c^3}-\frac{15\,d^3\,e^2}{64\,a^2\,c^2}+\frac{9\,e^5\,\sqrt{a^9\,c^7}}{64\,a^5\,c^7}-\frac{5\,d^2\,e^3\,\sqrt{a^9\,c^7}}{64\,a^6\,c^6}}}{\frac{27\,a\,e^{11}}{4\,c^2}+\frac{43\,d^4\,e^7}{4\,a}-\frac{15\,d^2\,e^9}{c}-\frac{5\,c\,d^6\,e^5}{2\,a^2}+\frac{9\,d\,e^{10}\,\sqrt{a^9\,c^7}}{4\,a^4\,c^5}-\frac{7\,d^3\,e^8\,\sqrt{a^9\,c^7}}{2\,a^5\,c^4}+\frac{5\,d^5\,e^6\,\sqrt{a^9\,c^7}}{4\,a^6\,c^3}}-\frac{10\,c\,d^2\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{d^5}{16\,a^3\,c}+\frac{15\,d\,e^4}{64\,a\,c^3}-\frac{15\,d^3\,e^2}{64\,a^2\,c^2}+\frac{9\,e^5\,\sqrt{a^9\,c^7}}{64\,a^5\,c^7}-\frac{5\,d^2\,e^3\,\sqrt{a^9\,c^7}}{64\,a^6\,c^6}}}{\frac{27\,a\,e^{11}}{4\,c^2}+\frac{43\,d^4\,e^7}{4\,a}-\frac{15\,d^2\,e^9}{c}-\frac{5\,c\,d^6\,e^5}{2\,a^2}+\frac{9\,d\,e^{10}\,\sqrt{a^9\,c^7}}{4\,a^4\,c^5}-\frac{7\,d^3\,e^8\,\sqrt{a^9\,c^7}}{2\,a^5\,c^4}+\frac{5\,d^5\,e^6\,\sqrt{a^9\,c^7}}{4\,a^6\,c^3}}-\frac{18\,d\,e^7\,\sqrt{a^9\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{d^5}{16\,a^3\,c}+\frac{15\,d\,e^4}{64\,a\,c^3}-\frac{15\,d^3\,e^2}{64\,a^2\,c^2}+\frac{9\,e^5\,\sqrt{a^9\,c^7}}{64\,a^5\,c^7}-\frac{5\,d^2\,e^3\,\sqrt{a^9\,c^7}}{64\,a^6\,c^6}}}{\frac{27\,a^5\,c\,e^{11}}{4}-\frac{5\,a^2\,c^4\,d^6\,e^5}{2}+\frac{43\,a^3\,c^3\,d^4\,e^7}{4}-15\,a^4\,c^2\,d^2\,e^9+\frac{9\,d\,e^{10}\,\sqrt{a^9\,c^7}}{4\,c^2}+\frac{5\,d^5\,e^6\,\sqrt{a^9\,c^7}}{4\,a^2}-\frac{7\,d^3\,e^8\,\sqrt{a^9\,c^7}}{2\,a\,c}}+\frac{10\,d^3\,e^5\,\sqrt{a^9\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{d^5}{16\,a^3\,c}+\frac{15\,d\,e^4}{64\,a\,c^3}-\frac{15\,d^3\,e^2}{64\,a^2\,c^2}+\frac{9\,e^5\,\sqrt{a^9\,c^7}}{64\,a^5\,c^7}-\frac{5\,d^2\,e^3\,\sqrt{a^9\,c^7}}{64\,a^6\,c^6}}}{\frac{27\,a^6\,e^{11}}{4}-15\,a^5\,c\,d^2\,e^9-\frac{5\,a^3\,c^3\,d^6\,e^5}{2}+\frac{43\,a^4\,c^2\,d^4\,e^7}{4}-\frac{7\,d^3\,e^8\,\sqrt{a^9\,c^7}}{2\,c^2}+\frac{5\,d^5\,e^6\,\sqrt{a^9\,c^7}}{4\,a\,c}+\frac{9\,a\,d\,e^{10}\,\sqrt{a^9\,c^7}}{4\,c^3}}\right)\,\sqrt{\frac{4\,a^3\,c^6\,d^5+9\,a\,e^5\,\sqrt{a^9\,c^7}+15\,a^5\,c^4\,d\,e^4-15\,a^4\,c^5\,d^3\,e^2-5\,c\,d^2\,e^3\,\sqrt{a^9\,c^7}}{64\,a^6\,c^7}}","Not used",1,"2*atanh((18*a*e^8*(d + e*x)^(1/2)*(d^5/(16*a^3*c) + (15*d*e^4)/(64*a*c^3) - (15*d^3*e^2)/(64*a^2*c^2) - (9*e^5*(a^9*c^7)^(1/2))/(64*a^5*c^7) + (5*d^2*e^3*(a^9*c^7)^(1/2))/(64*a^6*c^6))^(1/2))/((15*d^2*e^9)/c - (43*d^4*e^7)/(4*a) - (27*a*e^11)/(4*c^2) + (5*c*d^6*e^5)/(2*a^2) + (9*d*e^10*(a^9*c^7)^(1/2))/(4*a^4*c^5) - (7*d^3*e^8*(a^9*c^7)^(1/2))/(2*a^5*c^4) + (5*d^5*e^6*(a^9*c^7)^(1/2))/(4*a^6*c^3)) - (10*c*d^2*e^6*(d + e*x)^(1/2)*(d^5/(16*a^3*c) + (15*d*e^4)/(64*a*c^3) - (15*d^3*e^2)/(64*a^2*c^2) - (9*e^5*(a^9*c^7)^(1/2))/(64*a^5*c^7) + (5*d^2*e^3*(a^9*c^7)^(1/2))/(64*a^6*c^6))^(1/2))/((15*d^2*e^9)/c - (43*d^4*e^7)/(4*a) - (27*a*e^11)/(4*c^2) + (5*c*d^6*e^5)/(2*a^2) + (9*d*e^10*(a^9*c^7)^(1/2))/(4*a^4*c^5) - (7*d^3*e^8*(a^9*c^7)^(1/2))/(2*a^5*c^4) + (5*d^5*e^6*(a^9*c^7)^(1/2))/(4*a^6*c^3)) + (18*d*e^7*(a^9*c^7)^(1/2)*(d + e*x)^(1/2)*(d^5/(16*a^3*c) + (15*d*e^4)/(64*a*c^3) - (15*d^3*e^2)/(64*a^2*c^2) - (9*e^5*(a^9*c^7)^(1/2))/(64*a^5*c^7) + (5*d^2*e^3*(a^9*c^7)^(1/2))/(64*a^6*c^6))^(1/2))/((5*a^2*c^4*d^6*e^5)/2 - (27*a^5*c*e^11)/4 - (43*a^3*c^3*d^4*e^7)/4 + 15*a^4*c^2*d^2*e^9 + (9*d*e^10*(a^9*c^7)^(1/2))/(4*c^2) + (5*d^5*e^6*(a^9*c^7)^(1/2))/(4*a^2) - (7*d^3*e^8*(a^9*c^7)^(1/2))/(2*a*c)) - (10*d^3*e^5*(a^9*c^7)^(1/2)*(d + e*x)^(1/2)*(d^5/(16*a^3*c) + (15*d*e^4)/(64*a*c^3) - (15*d^3*e^2)/(64*a^2*c^2) - (9*e^5*(a^9*c^7)^(1/2))/(64*a^5*c^7) + (5*d^2*e^3*(a^9*c^7)^(1/2))/(64*a^6*c^6))^(1/2))/(15*a^5*c*d^2*e^9 - (27*a^6*e^11)/4 + (5*a^3*c^3*d^6*e^5)/2 - (43*a^4*c^2*d^4*e^7)/4 - (7*d^3*e^8*(a^9*c^7)^(1/2))/(2*c^2) + (5*d^5*e^6*(a^9*c^7)^(1/2))/(4*a*c) + (9*a*d*e^10*(a^9*c^7)^(1/2))/(4*c^3)))*((4*a^3*c^6*d^5 - 9*a*e^5*(a^9*c^7)^(1/2) + 15*a^5*c^4*d*e^4 - 15*a^4*c^5*d^3*e^2 + 5*c*d^2*e^3*(a^9*c^7)^(1/2))/(64*a^6*c^7))^(1/2) - (((a*e^3 + c*d^2*e)*(d + e*x)^(3/2))/(2*a*c) + ((a*d*e^3 - c*d^3*e)*(d + e*x)^(1/2))/(2*a*c))/(c*(d + e*x)^2 - a*e^2 + c*d^2 - 2*c*d*(d + e*x)) - 2*atanh((18*a*e^8*(d + e*x)^(1/2)*(d^5/(16*a^3*c) + (15*d*e^4)/(64*a*c^3) - (15*d^3*e^2)/(64*a^2*c^2) + (9*e^5*(a^9*c^7)^(1/2))/(64*a^5*c^7) - (5*d^2*e^3*(a^9*c^7)^(1/2))/(64*a^6*c^6))^(1/2))/((27*a*e^11)/(4*c^2) + (43*d^4*e^7)/(4*a) - (15*d^2*e^9)/c - (5*c*d^6*e^5)/(2*a^2) + (9*d*e^10*(a^9*c^7)^(1/2))/(4*a^4*c^5) - (7*d^3*e^8*(a^9*c^7)^(1/2))/(2*a^5*c^4) + (5*d^5*e^6*(a^9*c^7)^(1/2))/(4*a^6*c^3)) - (10*c*d^2*e^6*(d + e*x)^(1/2)*(d^5/(16*a^3*c) + (15*d*e^4)/(64*a*c^3) - (15*d^3*e^2)/(64*a^2*c^2) + (9*e^5*(a^9*c^7)^(1/2))/(64*a^5*c^7) - (5*d^2*e^3*(a^9*c^7)^(1/2))/(64*a^6*c^6))^(1/2))/((27*a*e^11)/(4*c^2) + (43*d^4*e^7)/(4*a) - (15*d^2*e^9)/c - (5*c*d^6*e^5)/(2*a^2) + (9*d*e^10*(a^9*c^7)^(1/2))/(4*a^4*c^5) - (7*d^3*e^8*(a^9*c^7)^(1/2))/(2*a^5*c^4) + (5*d^5*e^6*(a^9*c^7)^(1/2))/(4*a^6*c^3)) - (18*d*e^7*(a^9*c^7)^(1/2)*(d + e*x)^(1/2)*(d^5/(16*a^3*c) + (15*d*e^4)/(64*a*c^3) - (15*d^3*e^2)/(64*a^2*c^2) + (9*e^5*(a^9*c^7)^(1/2))/(64*a^5*c^7) - (5*d^2*e^3*(a^9*c^7)^(1/2))/(64*a^6*c^6))^(1/2))/((27*a^5*c*e^11)/4 - (5*a^2*c^4*d^6*e^5)/2 + (43*a^3*c^3*d^4*e^7)/4 - 15*a^4*c^2*d^2*e^9 + (9*d*e^10*(a^9*c^7)^(1/2))/(4*c^2) + (5*d^5*e^6*(a^9*c^7)^(1/2))/(4*a^2) - (7*d^3*e^8*(a^9*c^7)^(1/2))/(2*a*c)) + (10*d^3*e^5*(a^9*c^7)^(1/2)*(d + e*x)^(1/2)*(d^5/(16*a^3*c) + (15*d*e^4)/(64*a*c^3) - (15*d^3*e^2)/(64*a^2*c^2) + (9*e^5*(a^9*c^7)^(1/2))/(64*a^5*c^7) - (5*d^2*e^3*(a^9*c^7)^(1/2))/(64*a^6*c^6))^(1/2))/((27*a^6*e^11)/4 - 15*a^5*c*d^2*e^9 - (5*a^3*c^3*d^6*e^5)/2 + (43*a^4*c^2*d^4*e^7)/4 - (7*d^3*e^8*(a^9*c^7)^(1/2))/(2*c^2) + (5*d^5*e^6*(a^9*c^7)^(1/2))/(4*a*c) + (9*a*d*e^10*(a^9*c^7)^(1/2))/(4*c^3)))*((4*a^3*c^6*d^5 + 9*a*e^5*(a^9*c^7)^(1/2) + 15*a^5*c^4*d*e^4 - 15*a^4*c^5*d^3*e^2 - 5*c*d^2*e^3*(a^9*c^7)^(1/2))/(64*a^6*c^7))^(1/2)","B"
626,1,704,209,0.433210,"\text{Not used}","int((d + e*x)^(3/2)/(a - c*x^2)^2,x)","2\,\mathrm{atanh}\left(\frac{2\,c\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{d^3}{16\,a^3\,c}-\frac{3\,d\,e^2}{64\,a^2\,c^2}-\frac{e^3\,\sqrt{a^9\,c^5}}{64\,a^6\,c^5}}}{\frac{d\,e^7}{2\,a}-\frac{c\,d^3\,e^5}{2\,a^2}+\frac{e^8\,\sqrt{a^9\,c^5}}{4\,a^5\,c^3}-\frac{d^2\,e^6\,\sqrt{a^9\,c^5}}{4\,a^6\,c^2}}+\frac{2\,d\,e^5\,\sqrt{a^9\,c^5}\,\sqrt{d+e\,x}\,\sqrt{\frac{d^3}{16\,a^3\,c}-\frac{3\,d\,e^2}{64\,a^2\,c^2}-\frac{e^3\,\sqrt{a^9\,c^5}}{64\,a^6\,c^5}}}{\frac{e^8\,\sqrt{a^9\,c^5}}{4\,c^2}-\frac{a^3\,c^2\,d^3\,e^5}{2}+\frac{a^4\,c\,d\,e^7}{2}-\frac{d^2\,e^6\,\sqrt{a^9\,c^5}}{4\,a\,c}}\right)\,\sqrt{-\frac{e^3\,\sqrt{a^9\,c^5}-4\,a^3\,c^4\,d^3+3\,a^4\,c^3\,d\,e^2}{64\,a^6\,c^5}}-\frac{\frac{\left(a\,e^3-c\,d^2\,e\right)\,\sqrt{d+e\,x}}{2\,a\,c}+\frac{d\,e\,{\left(d+e\,x\right)}^{3/2}}{2\,a}}{c\,{\left(d+e\,x\right)}^2-a\,e^2+c\,d^2-2\,c\,d\,\left(d+e\,x\right)}+2\,\mathrm{atanh}\left(\frac{2\,c\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{d^3}{16\,a^3\,c}-\frac{3\,d\,e^2}{64\,a^2\,c^2}+\frac{e^3\,\sqrt{a^9\,c^5}}{64\,a^6\,c^5}}}{\frac{d\,e^7}{2\,a}-\frac{c\,d^3\,e^5}{2\,a^2}-\frac{e^8\,\sqrt{a^9\,c^5}}{4\,a^5\,c^3}+\frac{d^2\,e^6\,\sqrt{a^9\,c^5}}{4\,a^6\,c^2}}+\frac{2\,d\,e^5\,\sqrt{a^9\,c^5}\,\sqrt{d+e\,x}\,\sqrt{\frac{d^3}{16\,a^3\,c}-\frac{3\,d\,e^2}{64\,a^2\,c^2}+\frac{e^3\,\sqrt{a^9\,c^5}}{64\,a^6\,c^5}}}{\frac{e^8\,\sqrt{a^9\,c^5}}{4\,c^2}+\frac{a^3\,c^2\,d^3\,e^5}{2}-\frac{a^4\,c\,d\,e^7}{2}-\frac{d^2\,e^6\,\sqrt{a^9\,c^5}}{4\,a\,c}}\right)\,\sqrt{\frac{e^3\,\sqrt{a^9\,c^5}+4\,a^3\,c^4\,d^3-3\,a^4\,c^3\,d\,e^2}{64\,a^6\,c^5}}","Not used",1,"2*atanh((2*c*e^6*(d + e*x)^(1/2)*(d^3/(16*a^3*c) - (3*d*e^2)/(64*a^2*c^2) - (e^3*(a^9*c^5)^(1/2))/(64*a^6*c^5))^(1/2))/((d*e^7)/(2*a) - (c*d^3*e^5)/(2*a^2) + (e^8*(a^9*c^5)^(1/2))/(4*a^5*c^3) - (d^2*e^6*(a^9*c^5)^(1/2))/(4*a^6*c^2)) + (2*d*e^5*(a^9*c^5)^(1/2)*(d + e*x)^(1/2)*(d^3/(16*a^3*c) - (3*d*e^2)/(64*a^2*c^2) - (e^3*(a^9*c^5)^(1/2))/(64*a^6*c^5))^(1/2))/((e^8*(a^9*c^5)^(1/2))/(4*c^2) - (a^3*c^2*d^3*e^5)/2 + (a^4*c*d*e^7)/2 - (d^2*e^6*(a^9*c^5)^(1/2))/(4*a*c)))*(-(e^3*(a^9*c^5)^(1/2) - 4*a^3*c^4*d^3 + 3*a^4*c^3*d*e^2)/(64*a^6*c^5))^(1/2) - (((a*e^3 - c*d^2*e)*(d + e*x)^(1/2))/(2*a*c) + (d*e*(d + e*x)^(3/2))/(2*a))/(c*(d + e*x)^2 - a*e^2 + c*d^2 - 2*c*d*(d + e*x)) + 2*atanh((2*c*e^6*(d + e*x)^(1/2)*(d^3/(16*a^3*c) - (3*d*e^2)/(64*a^2*c^2) + (e^3*(a^9*c^5)^(1/2))/(64*a^6*c^5))^(1/2))/((d*e^7)/(2*a) - (c*d^3*e^5)/(2*a^2) - (e^8*(a^9*c^5)^(1/2))/(4*a^5*c^3) + (d^2*e^6*(a^9*c^5)^(1/2))/(4*a^6*c^2)) + (2*d*e^5*(a^9*c^5)^(1/2)*(d + e*x)^(1/2)*(d^3/(16*a^3*c) - (3*d*e^2)/(64*a^2*c^2) + (e^3*(a^9*c^5)^(1/2))/(64*a^6*c^5))^(1/2))/((e^8*(a^9*c^5)^(1/2))/(4*c^2) + (a^3*c^2*d^3*e^5)/2 - (a^4*c*d*e^7)/2 - (d^2*e^6*(a^9*c^5)^(1/2))/(4*a*c)))*((e^3*(a^9*c^5)^(1/2) + 4*a^3*c^4*d^3 - 3*a^4*c^3*d*e^2)/(64*a^6*c^5))^(1/2)","B"
627,1,2332,194,2.188117,"\text{Not used}","int((d + e*x)^(1/2)/(a - c*x^2)^2,x)","-\frac{\frac{e\,{\left(d+e\,x\right)}^{3/2}}{2\,a}-\frac{d\,e\,\sqrt{d+e\,x}}{2\,a}}{c\,{\left(d+e\,x\right)}^2-a\,e^2+c\,d^2-2\,c\,d\,\left(d+e\,x\right)}-\mathrm{atan}\left(\frac{\left(\left(8\,c^3\,d\,e^3-64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{e^3\,\sqrt{a^9\,c^3}-4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}\right)\,\sqrt{-\frac{e^3\,\sqrt{a^9\,c^3}-4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}+\frac{\left(4\,c^3\,d^2\,e^2+a\,c^2\,e^4\right)\,\sqrt{d+e\,x}}{a^2}\right)\,\sqrt{-\frac{e^3\,\sqrt{a^9\,c^3}-4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}\,1{}\mathrm{i}-\left(\left(8\,c^3\,d\,e^3+64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{e^3\,\sqrt{a^9\,c^3}-4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}\right)\,\sqrt{-\frac{e^3\,\sqrt{a^9\,c^3}-4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}-\frac{\left(4\,c^3\,d^2\,e^2+a\,c^2\,e^4\right)\,\sqrt{d+e\,x}}{a^2}\right)\,\sqrt{-\frac{e^3\,\sqrt{a^9\,c^3}-4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}\,1{}\mathrm{i}}{\left(\left(8\,c^3\,d\,e^3-64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{e^3\,\sqrt{a^9\,c^3}-4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}\right)\,\sqrt{-\frac{e^3\,\sqrt{a^9\,c^3}-4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}+\frac{\left(4\,c^3\,d^2\,e^2+a\,c^2\,e^4\right)\,\sqrt{d+e\,x}}{a^2}\right)\,\sqrt{-\frac{e^3\,\sqrt{a^9\,c^3}-4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}-\frac{4\,c^2\,d^2\,e^3-a\,c\,e^5}{4\,a^3}+\left(\left(8\,c^3\,d\,e^3+64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{e^3\,\sqrt{a^9\,c^3}-4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}\right)\,\sqrt{-\frac{e^3\,\sqrt{a^9\,c^3}-4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}-\frac{\left(4\,c^3\,d^2\,e^2+a\,c^2\,e^4\right)\,\sqrt{d+e\,x}}{a^2}\right)\,\sqrt{-\frac{e^3\,\sqrt{a^9\,c^3}-4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}}\right)\,\sqrt{-\frac{e^3\,\sqrt{a^9\,c^3}-4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(8\,c^3\,d\,e^3-64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{\frac{e^3\,\sqrt{a^9\,c^3}+4\,a^3\,c^3\,d^3-3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}\right)\,\sqrt{\frac{e^3\,\sqrt{a^9\,c^3}+4\,a^3\,c^3\,d^3-3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}+\frac{\left(4\,c^3\,d^2\,e^2+a\,c^2\,e^4\right)\,\sqrt{d+e\,x}}{a^2}\right)\,\sqrt{\frac{e^3\,\sqrt{a^9\,c^3}+4\,a^3\,c^3\,d^3-3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}\,1{}\mathrm{i}-\left(\left(8\,c^3\,d\,e^3+64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{\frac{e^3\,\sqrt{a^9\,c^3}+4\,a^3\,c^3\,d^3-3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}\right)\,\sqrt{\frac{e^3\,\sqrt{a^9\,c^3}+4\,a^3\,c^3\,d^3-3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}-\frac{\left(4\,c^3\,d^2\,e^2+a\,c^2\,e^4\right)\,\sqrt{d+e\,x}}{a^2}\right)\,\sqrt{\frac{e^3\,\sqrt{a^9\,c^3}+4\,a^3\,c^3\,d^3-3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}\,1{}\mathrm{i}}{\left(\left(8\,c^3\,d\,e^3-64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{\frac{e^3\,\sqrt{a^9\,c^3}+4\,a^3\,c^3\,d^3-3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}\right)\,\sqrt{\frac{e^3\,\sqrt{a^9\,c^3}+4\,a^3\,c^3\,d^3-3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}+\frac{\left(4\,c^3\,d^2\,e^2+a\,c^2\,e^4\right)\,\sqrt{d+e\,x}}{a^2}\right)\,\sqrt{\frac{e^3\,\sqrt{a^9\,c^3}+4\,a^3\,c^3\,d^3-3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}-\frac{4\,c^2\,d^2\,e^3-a\,c\,e^5}{4\,a^3}+\left(\left(8\,c^3\,d\,e^3+64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{\frac{e^3\,\sqrt{a^9\,c^3}+4\,a^3\,c^3\,d^3-3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}\right)\,\sqrt{\frac{e^3\,\sqrt{a^9\,c^3}+4\,a^3\,c^3\,d^3-3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}-\frac{\left(4\,c^3\,d^2\,e^2+a\,c^2\,e^4\right)\,\sqrt{d+e\,x}}{a^2}\right)\,\sqrt{\frac{e^3\,\sqrt{a^9\,c^3}+4\,a^3\,c^3\,d^3-3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}}\right)\,\sqrt{\frac{e^3\,\sqrt{a^9\,c^3}+4\,a^3\,c^3\,d^3-3\,a^4\,c^2\,d\,e^2}{64\,\left(a^6\,c^4\,d^2-a^7\,c^3\,e^2\right)}}\,2{}\mathrm{i}","Not used",1,"- atan((((8*c^3*d*e^3 - 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(e^3*(a^9*c^3)^(1/2) - 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2))*(-(e^3*(a^9*c^3)^(1/2) - 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2) + ((a*c^2*e^4 + 4*c^3*d^2*e^2)*(d + e*x)^(1/2))/a^2)*(-(e^3*(a^9*c^3)^(1/2) - 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2)*1i - ((8*c^3*d*e^3 + 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(e^3*(a^9*c^3)^(1/2) - 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2))*(-(e^3*(a^9*c^3)^(1/2) - 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2) - ((a*c^2*e^4 + 4*c^3*d^2*e^2)*(d + e*x)^(1/2))/a^2)*(-(e^3*(a^9*c^3)^(1/2) - 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2)*1i)/(((8*c^3*d*e^3 - 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(e^3*(a^9*c^3)^(1/2) - 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2))*(-(e^3*(a^9*c^3)^(1/2) - 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2) + ((a*c^2*e^4 + 4*c^3*d^2*e^2)*(d + e*x)^(1/2))/a^2)*(-(e^3*(a^9*c^3)^(1/2) - 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2) - (4*c^2*d^2*e^3 - a*c*e^5)/(4*a^3) + ((8*c^3*d*e^3 + 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(e^3*(a^9*c^3)^(1/2) - 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2))*(-(e^3*(a^9*c^3)^(1/2) - 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2) - ((a*c^2*e^4 + 4*c^3*d^2*e^2)*(d + e*x)^(1/2))/a^2)*(-(e^3*(a^9*c^3)^(1/2) - 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2)))*(-(e^3*(a^9*c^3)^(1/2) - 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2)*2i - atan((((8*c^3*d*e^3 - 64*a*c^4*d*e^2*(d + e*x)^(1/2)*((e^3*(a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 - 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2))*((e^3*(a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 - 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2) + ((a*c^2*e^4 + 4*c^3*d^2*e^2)*(d + e*x)^(1/2))/a^2)*((e^3*(a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 - 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2)*1i - ((8*c^3*d*e^3 + 64*a*c^4*d*e^2*(d + e*x)^(1/2)*((e^3*(a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 - 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2))*((e^3*(a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 - 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2) - ((a*c^2*e^4 + 4*c^3*d^2*e^2)*(d + e*x)^(1/2))/a^2)*((e^3*(a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 - 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2)*1i)/(((8*c^3*d*e^3 - 64*a*c^4*d*e^2*(d + e*x)^(1/2)*((e^3*(a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 - 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2))*((e^3*(a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 - 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2) + ((a*c^2*e^4 + 4*c^3*d^2*e^2)*(d + e*x)^(1/2))/a^2)*((e^3*(a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 - 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2) - (4*c^2*d^2*e^3 - a*c*e^5)/(4*a^3) + ((8*c^3*d*e^3 + 64*a*c^4*d*e^2*(d + e*x)^(1/2)*((e^3*(a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 - 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2))*((e^3*(a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 - 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2) - ((a*c^2*e^4 + 4*c^3*d^2*e^2)*(d + e*x)^(1/2))/a^2)*((e^3*(a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 - 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2)))*((e^3*(a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 - 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 - a^7*c^3*e^2)))^(1/2)*2i - ((e*(d + e*x)^(3/2))/(2*a) - (d*e*(d + e*x)^(1/2))/(2*a))/(c*(d + e*x)^2 - a*e^2 + c*d^2 - 2*c*d*(d + e*x))","B"
628,1,5253,222,2.531384,"\text{Not used}","int(1/((a - c*x^2)^2*(d + e*x)^(1/2)),x)","-\frac{\frac{\left(c\,d^2\,e+a\,e^3\right)\,\sqrt{d+e\,x}}{2\,a\,\left(a\,e^2-c\,d^2\right)}-\frac{c\,d\,e\,{\left(d+e\,x\right)}^{3/2}}{2\,a\,\left(a\,e^2-c\,d^2\right)}}{c\,{\left(d+e\,x\right)}^2-a\,e^2+c\,d^2-2\,c\,d\,\left(d+e\,x\right)}+\mathrm{atan}\left(\frac{\left(\left(\frac{192\,a^5\,c^3\,e^7-256\,a^4\,c^4\,d^2\,e^5+64\,a^3\,c^5\,d^4\,e^3}{8\,\left(a^5\,e^4-2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}+\frac{\sqrt{d+e\,x}\,\left(64\,a^5\,c^4\,d\,e^6-128\,a^4\,c^5\,d^3\,e^4+64\,a^3\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{a^9\,c}+5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}}{a^4\,e^4-2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{a^9\,c}+5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}-\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c^3\,e^6-11\,a\,c^4\,d^2\,e^4+4\,c^5\,d^4\,e^2\right)}{a^4\,e^4-2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{a^9\,c}+5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}\,1{}\mathrm{i}-\left(\left(\frac{192\,a^5\,c^3\,e^7-256\,a^4\,c^4\,d^2\,e^5+64\,a^3\,c^5\,d^4\,e^3}{8\,\left(a^5\,e^4-2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}-\frac{\sqrt{d+e\,x}\,\left(64\,a^5\,c^4\,d\,e^6-128\,a^4\,c^5\,d^3\,e^4+64\,a^3\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{a^9\,c}+5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}}{a^4\,e^4-2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{a^9\,c}+5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}+\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c^3\,e^6-11\,a\,c^4\,d^2\,e^4+4\,c^5\,d^4\,e^2\right)}{a^4\,e^4-2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{a^9\,c}+5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{192\,a^5\,c^3\,e^7-256\,a^4\,c^4\,d^2\,e^5+64\,a^3\,c^5\,d^4\,e^3}{8\,\left(a^5\,e^4-2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}+\frac{\sqrt{d+e\,x}\,\left(64\,a^5\,c^4\,d\,e^6-128\,a^4\,c^5\,d^3\,e^4+64\,a^3\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{a^9\,c}+5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}}{a^4\,e^4-2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{a^9\,c}+5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}-\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c^3\,e^6-11\,a\,c^4\,d^2\,e^4+4\,c^5\,d^4\,e^2\right)}{a^4\,e^4-2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{a^9\,c}+5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}-\frac{4\,c^4\,d^3\,e^3-9\,a\,c^3\,d\,e^5}{4\,\left(a^5\,e^4-2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}+\left(\left(\frac{192\,a^5\,c^3\,e^7-256\,a^4\,c^4\,d^2\,e^5+64\,a^3\,c^5\,d^4\,e^3}{8\,\left(a^5\,e^4-2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}-\frac{\sqrt{d+e\,x}\,\left(64\,a^5\,c^4\,d\,e^6-128\,a^4\,c^5\,d^3\,e^4+64\,a^3\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{a^9\,c}+5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}}{a^4\,e^4-2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{a^9\,c}+5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}+\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c^3\,e^6-11\,a\,c^4\,d^2\,e^4+4\,c^5\,d^4\,e^2\right)}{a^4\,e^4-2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{a^9\,c}+5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{a^9\,c}+5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(\frac{192\,a^5\,c^3\,e^7-256\,a^4\,c^4\,d^2\,e^5+64\,a^3\,c^5\,d^4\,e^3}{8\,\left(a^5\,e^4-2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}+\frac{\sqrt{d+e\,x}\,\left(64\,a^5\,c^4\,d\,e^6-128\,a^4\,c^5\,d^3\,e^4+64\,a^3\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{a^9\,c}+4\,a^3\,c^3\,d^5-5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}}{a^4\,e^4-2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{a^9\,c}+4\,a^3\,c^3\,d^5-5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}-\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c^3\,e^6-11\,a\,c^4\,d^2\,e^4+4\,c^5\,d^4\,e^2\right)}{a^4\,e^4-2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{a^9\,c}+4\,a^3\,c^3\,d^5-5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}\,1{}\mathrm{i}-\left(\left(\frac{192\,a^5\,c^3\,e^7-256\,a^4\,c^4\,d^2\,e^5+64\,a^3\,c^5\,d^4\,e^3}{8\,\left(a^5\,e^4-2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}-\frac{\sqrt{d+e\,x}\,\left(64\,a^5\,c^4\,d\,e^6-128\,a^4\,c^5\,d^3\,e^4+64\,a^3\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{a^9\,c}+4\,a^3\,c^3\,d^5-5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}}{a^4\,e^4-2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{a^9\,c}+4\,a^3\,c^3\,d^5-5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}+\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c^3\,e^6-11\,a\,c^4\,d^2\,e^4+4\,c^5\,d^4\,e^2\right)}{a^4\,e^4-2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{a^9\,c}+4\,a^3\,c^3\,d^5-5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{192\,a^5\,c^3\,e^7-256\,a^4\,c^4\,d^2\,e^5+64\,a^3\,c^5\,d^4\,e^3}{8\,\left(a^5\,e^4-2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}+\frac{\sqrt{d+e\,x}\,\left(64\,a^5\,c^4\,d\,e^6-128\,a^4\,c^5\,d^3\,e^4+64\,a^3\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{a^9\,c}+4\,a^3\,c^3\,d^5-5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}}{a^4\,e^4-2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{a^9\,c}+4\,a^3\,c^3\,d^5-5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}-\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c^3\,e^6-11\,a\,c^4\,d^2\,e^4+4\,c^5\,d^4\,e^2\right)}{a^4\,e^4-2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{a^9\,c}+4\,a^3\,c^3\,d^5-5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}-\frac{4\,c^4\,d^3\,e^3-9\,a\,c^3\,d\,e^5}{4\,\left(a^5\,e^4-2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}+\left(\left(\frac{192\,a^5\,c^3\,e^7-256\,a^4\,c^4\,d^2\,e^5+64\,a^3\,c^5\,d^4\,e^3}{8\,\left(a^5\,e^4-2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}-\frac{\sqrt{d+e\,x}\,\left(64\,a^5\,c^4\,d\,e^6-128\,a^4\,c^5\,d^3\,e^4+64\,a^3\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{a^9\,c}+4\,a^3\,c^3\,d^5-5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}}{a^4\,e^4-2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{a^9\,c}+4\,a^3\,c^3\,d^5-5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}+\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c^3\,e^6-11\,a\,c^4\,d^2\,e^4+4\,c^5\,d^4\,e^2\right)}{a^4\,e^4-2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{a^9\,c}+4\,a^3\,c^3\,d^5-5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{a^9\,c}+4\,a^3\,c^3\,d^5-5\,c\,d^2\,e^3\,\sqrt{a^9\,c}-15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6-3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2-a^6\,c^4\,d^6\right)}}\,2{}\mathrm{i}","Not used",1,"atan(((((192*a^5*c^3*e^7 + 64*a^3*c^5*d^4*e^3 - 256*a^4*c^4*d^2*e^5)/(8*(a^5*e^4 + a^3*c^2*d^4 - 2*a^4*c*d^2*e^2)) + ((d + e*x)^(1/2)*(64*a^5*c^4*d*e^6 + 64*a^3*c^6*d^5*e^2 - 128*a^4*c^5*d^3*e^4)*(-(4*a^3*c^3*d^5 - 9*a*e^5*(a^9*c)^(1/2) + 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2))/(a^4*e^4 + a^2*c^2*d^4 - 2*a^3*c*d^2*e^2))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(a^9*c)^(1/2) + 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2) - ((d + e*x)^(1/2)*(9*a^2*c^3*e^6 + 4*c^5*d^4*e^2 - 11*a*c^4*d^2*e^4))/(a^4*e^4 + a^2*c^2*d^4 - 2*a^3*c*d^2*e^2))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(a^9*c)^(1/2) + 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2)*1i - (((192*a^5*c^3*e^7 + 64*a^3*c^5*d^4*e^3 - 256*a^4*c^4*d^2*e^5)/(8*(a^5*e^4 + a^3*c^2*d^4 - 2*a^4*c*d^2*e^2)) - ((d + e*x)^(1/2)*(64*a^5*c^4*d*e^6 + 64*a^3*c^6*d^5*e^2 - 128*a^4*c^5*d^3*e^4)*(-(4*a^3*c^3*d^5 - 9*a*e^5*(a^9*c)^(1/2) + 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2))/(a^4*e^4 + a^2*c^2*d^4 - 2*a^3*c*d^2*e^2))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(a^9*c)^(1/2) + 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2) + ((d + e*x)^(1/2)*(9*a^2*c^3*e^6 + 4*c^5*d^4*e^2 - 11*a*c^4*d^2*e^4))/(a^4*e^4 + a^2*c^2*d^4 - 2*a^3*c*d^2*e^2))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(a^9*c)^(1/2) + 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2)*1i)/((((192*a^5*c^3*e^7 + 64*a^3*c^5*d^4*e^3 - 256*a^4*c^4*d^2*e^5)/(8*(a^5*e^4 + a^3*c^2*d^4 - 2*a^4*c*d^2*e^2)) + ((d + e*x)^(1/2)*(64*a^5*c^4*d*e^6 + 64*a^3*c^6*d^5*e^2 - 128*a^4*c^5*d^3*e^4)*(-(4*a^3*c^3*d^5 - 9*a*e^5*(a^9*c)^(1/2) + 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2))/(a^4*e^4 + a^2*c^2*d^4 - 2*a^3*c*d^2*e^2))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(a^9*c)^(1/2) + 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2) - ((d + e*x)^(1/2)*(9*a^2*c^3*e^6 + 4*c^5*d^4*e^2 - 11*a*c^4*d^2*e^4))/(a^4*e^4 + a^2*c^2*d^4 - 2*a^3*c*d^2*e^2))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(a^9*c)^(1/2) + 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2) - (4*c^4*d^3*e^3 - 9*a*c^3*d*e^5)/(4*(a^5*e^4 + a^3*c^2*d^4 - 2*a^4*c*d^2*e^2)) + (((192*a^5*c^3*e^7 + 64*a^3*c^5*d^4*e^3 - 256*a^4*c^4*d^2*e^5)/(8*(a^5*e^4 + a^3*c^2*d^4 - 2*a^4*c*d^2*e^2)) - ((d + e*x)^(1/2)*(64*a^5*c^4*d*e^6 + 64*a^3*c^6*d^5*e^2 - 128*a^4*c^5*d^3*e^4)*(-(4*a^3*c^3*d^5 - 9*a*e^5*(a^9*c)^(1/2) + 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2))/(a^4*e^4 + a^2*c^2*d^4 - 2*a^3*c*d^2*e^2))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(a^9*c)^(1/2) + 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2) + ((d + e*x)^(1/2)*(9*a^2*c^3*e^6 + 4*c^5*d^4*e^2 - 11*a*c^4*d^2*e^4))/(a^4*e^4 + a^2*c^2*d^4 - 2*a^3*c*d^2*e^2))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(a^9*c)^(1/2) + 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2)))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(a^9*c)^(1/2) + 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2)*2i + atan(((((192*a^5*c^3*e^7 + 64*a^3*c^5*d^4*e^3 - 256*a^4*c^4*d^2*e^5)/(8*(a^5*e^4 + a^3*c^2*d^4 - 2*a^4*c*d^2*e^2)) + ((d + e*x)^(1/2)*(64*a^5*c^4*d*e^6 + 64*a^3*c^6*d^5*e^2 - 128*a^4*c^5*d^3*e^4)*(-(9*a*e^5*(a^9*c)^(1/2) + 4*a^3*c^3*d^5 - 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2))/(a^4*e^4 + a^2*c^2*d^4 - 2*a^3*c*d^2*e^2))*(-(9*a*e^5*(a^9*c)^(1/2) + 4*a^3*c^3*d^5 - 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2) - ((d + e*x)^(1/2)*(9*a^2*c^3*e^6 + 4*c^5*d^4*e^2 - 11*a*c^4*d^2*e^4))/(a^4*e^4 + a^2*c^2*d^4 - 2*a^3*c*d^2*e^2))*(-(9*a*e^5*(a^9*c)^(1/2) + 4*a^3*c^3*d^5 - 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2)*1i - (((192*a^5*c^3*e^7 + 64*a^3*c^5*d^4*e^3 - 256*a^4*c^4*d^2*e^5)/(8*(a^5*e^4 + a^3*c^2*d^4 - 2*a^4*c*d^2*e^2)) - ((d + e*x)^(1/2)*(64*a^5*c^4*d*e^6 + 64*a^3*c^6*d^5*e^2 - 128*a^4*c^5*d^3*e^4)*(-(9*a*e^5*(a^9*c)^(1/2) + 4*a^3*c^3*d^5 - 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2))/(a^4*e^4 + a^2*c^2*d^4 - 2*a^3*c*d^2*e^2))*(-(9*a*e^5*(a^9*c)^(1/2) + 4*a^3*c^3*d^5 - 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2) + ((d + e*x)^(1/2)*(9*a^2*c^3*e^6 + 4*c^5*d^4*e^2 - 11*a*c^4*d^2*e^4))/(a^4*e^4 + a^2*c^2*d^4 - 2*a^3*c*d^2*e^2))*(-(9*a*e^5*(a^9*c)^(1/2) + 4*a^3*c^3*d^5 - 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2)*1i)/((((192*a^5*c^3*e^7 + 64*a^3*c^5*d^4*e^3 - 256*a^4*c^4*d^2*e^5)/(8*(a^5*e^4 + a^3*c^2*d^4 - 2*a^4*c*d^2*e^2)) + ((d + e*x)^(1/2)*(64*a^5*c^4*d*e^6 + 64*a^3*c^6*d^5*e^2 - 128*a^4*c^5*d^3*e^4)*(-(9*a*e^5*(a^9*c)^(1/2) + 4*a^3*c^3*d^5 - 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2))/(a^4*e^4 + a^2*c^2*d^4 - 2*a^3*c*d^2*e^2))*(-(9*a*e^5*(a^9*c)^(1/2) + 4*a^3*c^3*d^5 - 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2) - ((d + e*x)^(1/2)*(9*a^2*c^3*e^6 + 4*c^5*d^4*e^2 - 11*a*c^4*d^2*e^4))/(a^4*e^4 + a^2*c^2*d^4 - 2*a^3*c*d^2*e^2))*(-(9*a*e^5*(a^9*c)^(1/2) + 4*a^3*c^3*d^5 - 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2) - (4*c^4*d^3*e^3 - 9*a*c^3*d*e^5)/(4*(a^5*e^4 + a^3*c^2*d^4 - 2*a^4*c*d^2*e^2)) + (((192*a^5*c^3*e^7 + 64*a^3*c^5*d^4*e^3 - 256*a^4*c^4*d^2*e^5)/(8*(a^5*e^4 + a^3*c^2*d^4 - 2*a^4*c*d^2*e^2)) - ((d + e*x)^(1/2)*(64*a^5*c^4*d*e^6 + 64*a^3*c^6*d^5*e^2 - 128*a^4*c^5*d^3*e^4)*(-(9*a*e^5*(a^9*c)^(1/2) + 4*a^3*c^3*d^5 - 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2))/(a^4*e^4 + a^2*c^2*d^4 - 2*a^3*c*d^2*e^2))*(-(9*a*e^5*(a^9*c)^(1/2) + 4*a^3*c^3*d^5 - 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2) + ((d + e*x)^(1/2)*(9*a^2*c^3*e^6 + 4*c^5*d^4*e^2 - 11*a*c^4*d^2*e^4))/(a^4*e^4 + a^2*c^2*d^4 - 2*a^3*c*d^2*e^2))*(-(9*a*e^5*(a^9*c)^(1/2) + 4*a^3*c^3*d^5 - 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2)))*(-(9*a*e^5*(a^9*c)^(1/2) + 4*a^3*c^3*d^5 - 5*c*d^2*e^3*(a^9*c)^(1/2) - 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 - a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 - 3*a^8*c^2*d^2*e^4)))^(1/2)*2i - (((a*e^3 + c*d^2*e)*(d + e*x)^(1/2))/(2*a*(a*e^2 - c*d^2)) - (c*d*e*(d + e*x)^(3/2))/(2*a*(a*e^2 - c*d^2)))/(c*(d + e*x)^2 - a*e^2 + c*d^2 - 2*c*d*(d + e*x))","B"
629,1,8700,265,3.163367,"\text{Not used}","int(1/((a - c*x^2)^2*(d + e*x)^(3/2)),x)","-\frac{\frac{2\,e^3}{a\,e^2-c\,d^2}-\frac{c\,e\,\left(c\,d^2+5\,a\,e^2\right)\,{\left(d+e\,x\right)}^2}{2\,a\,{\left(a\,e^2-c\,d^2\right)}^2}+\frac{c\,d\,e\,\left(c\,d^2+11\,a\,e^2\right)\,\left(d+e\,x\right)}{2\,a\,{\left(a\,e^2-c\,d^2\right)}^2}}{\left(a\,e^2-c\,d^2\right)\,\sqrt{d+e\,x}-c\,{\left(d+e\,x\right)}^{5/2}+2\,c\,d\,{\left(d+e\,x\right)}^{3/2}}+\mathrm{atan}\left(\frac{\left(\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,\left(2048\,a^{16}\,c^4\,d\,e^{22}-20480\,a^{15}\,c^5\,d^3\,e^{20}+92160\,a^{14}\,c^6\,d^5\,e^{18}-245760\,a^{13}\,c^7\,d^7\,e^{16}+430080\,a^{12}\,c^8\,d^9\,e^{14}-516096\,a^{11}\,c^9\,d^{11}\,e^{12}+430080\,a^{10}\,c^{10}\,d^{13}\,e^{10}-245760\,a^9\,c^{11}\,d^{15}\,e^8+92160\,a^8\,c^{12}\,d^{17}\,e^6-20480\,a^7\,c^{13}\,d^{19}\,e^4+2048\,a^6\,c^{14}\,d^{21}\,e^2\right)-3328\,a^{14}\,c^4\,d\,e^{21}+256\,a^5\,c^{13}\,d^{19}\,e^3-5376\,a^6\,c^{12}\,d^{17}\,e^5+33792\,a^7\,c^{11}\,d^{15}\,e^7-107520\,a^8\,c^{10}\,d^{13}\,e^9+204288\,a^9\,c^9\,d^{11}\,e^{11}-247296\,a^{10}\,c^8\,d^9\,e^{13}+193536\,a^{11}\,c^7\,d^7\,e^{15}-95232\,a^{12}\,c^6\,d^5\,e^{17}+26880\,a^{13}\,c^5\,d^3\,e^{19}\right)-\sqrt{d+e\,x}\,\left(800\,a^{12}\,c^4\,e^{20}-2432\,a^{11}\,c^5\,d^2\,e^{18}-3200\,a^{10}\,c^6\,d^4\,e^{16}+25600\,a^9\,c^7\,d^6\,e^{14}-51008\,a^8\,c^8\,d^8\,e^{12}+52480\,a^7\,c^9\,d^{10}\,e^{10}-30848\,a^6\,c^{10}\,d^{12}\,e^8+10240\,a^5\,c^{11}\,d^{14}\,e^6-1760\,a^4\,c^{12}\,d^{16}\,e^4+128\,a^3\,c^{13}\,d^{18}\,e^2\right)\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,1{}\mathrm{i}+\left(\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,\left(2048\,a^{16}\,c^4\,d\,e^{22}-20480\,a^{15}\,c^5\,d^3\,e^{20}+92160\,a^{14}\,c^6\,d^5\,e^{18}-245760\,a^{13}\,c^7\,d^7\,e^{16}+430080\,a^{12}\,c^8\,d^9\,e^{14}-516096\,a^{11}\,c^9\,d^{11}\,e^{12}+430080\,a^{10}\,c^{10}\,d^{13}\,e^{10}-245760\,a^9\,c^{11}\,d^{15}\,e^8+92160\,a^8\,c^{12}\,d^{17}\,e^6-20480\,a^7\,c^{13}\,d^{19}\,e^4+2048\,a^6\,c^{14}\,d^{21}\,e^2\right)+3328\,a^{14}\,c^4\,d\,e^{21}-256\,a^5\,c^{13}\,d^{19}\,e^3+5376\,a^6\,c^{12}\,d^{17}\,e^5-33792\,a^7\,c^{11}\,d^{15}\,e^7+107520\,a^8\,c^{10}\,d^{13}\,e^9-204288\,a^9\,c^9\,d^{11}\,e^{11}+247296\,a^{10}\,c^8\,d^9\,e^{13}-193536\,a^{11}\,c^7\,d^7\,e^{15}+95232\,a^{12}\,c^6\,d^5\,e^{17}-26880\,a^{13}\,c^5\,d^3\,e^{19}\right)-\sqrt{d+e\,x}\,\left(800\,a^{12}\,c^4\,e^{20}-2432\,a^{11}\,c^5\,d^2\,e^{18}-3200\,a^{10}\,c^6\,d^4\,e^{16}+25600\,a^9\,c^7\,d^6\,e^{14}-51008\,a^8\,c^8\,d^8\,e^{12}+52480\,a^7\,c^9\,d^{10}\,e^{10}-30848\,a^6\,c^{10}\,d^{12}\,e^8+10240\,a^5\,c^{11}\,d^{14}\,e^6-1760\,a^4\,c^{12}\,d^{16}\,e^4+128\,a^3\,c^{13}\,d^{18}\,e^2\right)\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,1{}\mathrm{i}}{\left(\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,\left(2048\,a^{16}\,c^4\,d\,e^{22}-20480\,a^{15}\,c^5\,d^3\,e^{20}+92160\,a^{14}\,c^6\,d^5\,e^{18}-245760\,a^{13}\,c^7\,d^7\,e^{16}+430080\,a^{12}\,c^8\,d^9\,e^{14}-516096\,a^{11}\,c^9\,d^{11}\,e^{12}+430080\,a^{10}\,c^{10}\,d^{13}\,e^{10}-245760\,a^9\,c^{11}\,d^{15}\,e^8+92160\,a^8\,c^{12}\,d^{17}\,e^6-20480\,a^7\,c^{13}\,d^{19}\,e^4+2048\,a^6\,c^{14}\,d^{21}\,e^2\right)-3328\,a^{14}\,c^4\,d\,e^{21}+256\,a^5\,c^{13}\,d^{19}\,e^3-5376\,a^6\,c^{12}\,d^{17}\,e^5+33792\,a^7\,c^{11}\,d^{15}\,e^7-107520\,a^8\,c^{10}\,d^{13}\,e^9+204288\,a^9\,c^9\,d^{11}\,e^{11}-247296\,a^{10}\,c^8\,d^9\,e^{13}+193536\,a^{11}\,c^7\,d^7\,e^{15}-95232\,a^{12}\,c^6\,d^5\,e^{17}+26880\,a^{13}\,c^5\,d^3\,e^{19}\right)-\sqrt{d+e\,x}\,\left(800\,a^{12}\,c^4\,e^{20}-2432\,a^{11}\,c^5\,d^2\,e^{18}-3200\,a^{10}\,c^6\,d^4\,e^{16}+25600\,a^9\,c^7\,d^6\,e^{14}-51008\,a^8\,c^8\,d^8\,e^{12}+52480\,a^7\,c^9\,d^{10}\,e^{10}-30848\,a^6\,c^{10}\,d^{12}\,e^8+10240\,a^5\,c^{11}\,d^{14}\,e^6-1760\,a^4\,c^{12}\,d^{16}\,e^4+128\,a^3\,c^{13}\,d^{18}\,e^2\right)\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}-\left(\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,\left(2048\,a^{16}\,c^4\,d\,e^{22}-20480\,a^{15}\,c^5\,d^3\,e^{20}+92160\,a^{14}\,c^6\,d^5\,e^{18}-245760\,a^{13}\,c^7\,d^7\,e^{16}+430080\,a^{12}\,c^8\,d^9\,e^{14}-516096\,a^{11}\,c^9\,d^{11}\,e^{12}+430080\,a^{10}\,c^{10}\,d^{13}\,e^{10}-245760\,a^9\,c^{11}\,d^{15}\,e^8+92160\,a^8\,c^{12}\,d^{17}\,e^6-20480\,a^7\,c^{13}\,d^{19}\,e^4+2048\,a^6\,c^{14}\,d^{21}\,e^2\right)+3328\,a^{14}\,c^4\,d\,e^{21}-256\,a^5\,c^{13}\,d^{19}\,e^3+5376\,a^6\,c^{12}\,d^{17}\,e^5-33792\,a^7\,c^{11}\,d^{15}\,e^7+107520\,a^8\,c^{10}\,d^{13}\,e^9-204288\,a^9\,c^9\,d^{11}\,e^{11}+247296\,a^{10}\,c^8\,d^9\,e^{13}-193536\,a^{11}\,c^7\,d^7\,e^{15}+95232\,a^{12}\,c^6\,d^5\,e^{17}-26880\,a^{13}\,c^5\,d^3\,e^{19}\right)-\sqrt{d+e\,x}\,\left(800\,a^{12}\,c^4\,e^{20}-2432\,a^{11}\,c^5\,d^2\,e^{18}-3200\,a^{10}\,c^6\,d^4\,e^{16}+25600\,a^9\,c^7\,d^6\,e^{14}-51008\,a^8\,c^8\,d^8\,e^{12}+52480\,a^7\,c^9\,d^{10}\,e^{10}-30848\,a^6\,c^{10}\,d^{12}\,e^8+10240\,a^5\,c^{11}\,d^{14}\,e^6-1760\,a^4\,c^{12}\,d^{16}\,e^4+128\,a^3\,c^{13}\,d^{18}\,e^2\right)\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}+1000\,a^{10}\,c^4\,e^{19}-32\,a^2\,c^{12}\,d^{16}\,e^3+232\,a^3\,c^{11}\,d^{14}\,e^5+280\,a^4\,c^{10}\,d^{12}\,e^7-4760\,a^5\,c^9\,d^{10}\,e^9+13720\,a^6\,c^8\,d^8\,e^{11}-19208\,a^7\,c^7\,d^6\,e^{13}+14728\,a^8\,c^6\,d^4\,e^{15}-5960\,a^9\,c^5\,d^2\,e^{17}}\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,\left(2048\,a^{16}\,c^4\,d\,e^{22}-20480\,a^{15}\,c^5\,d^3\,e^{20}+92160\,a^{14}\,c^6\,d^5\,e^{18}-245760\,a^{13}\,c^7\,d^7\,e^{16}+430080\,a^{12}\,c^8\,d^9\,e^{14}-516096\,a^{11}\,c^9\,d^{11}\,e^{12}+430080\,a^{10}\,c^{10}\,d^{13}\,e^{10}-245760\,a^9\,c^{11}\,d^{15}\,e^8+92160\,a^8\,c^{12}\,d^{17}\,e^6-20480\,a^7\,c^{13}\,d^{19}\,e^4+2048\,a^6\,c^{14}\,d^{21}\,e^2\right)-3328\,a^{14}\,c^4\,d\,e^{21}+256\,a^5\,c^{13}\,d^{19}\,e^3-5376\,a^6\,c^{12}\,d^{17}\,e^5+33792\,a^7\,c^{11}\,d^{15}\,e^7-107520\,a^8\,c^{10}\,d^{13}\,e^9+204288\,a^9\,c^9\,d^{11}\,e^{11}-247296\,a^{10}\,c^8\,d^9\,e^{13}+193536\,a^{11}\,c^7\,d^7\,e^{15}-95232\,a^{12}\,c^6\,d^5\,e^{17}+26880\,a^{13}\,c^5\,d^3\,e^{19}\right)-\sqrt{d+e\,x}\,\left(800\,a^{12}\,c^4\,e^{20}-2432\,a^{11}\,c^5\,d^2\,e^{18}-3200\,a^{10}\,c^6\,d^4\,e^{16}+25600\,a^9\,c^7\,d^6\,e^{14}-51008\,a^8\,c^8\,d^8\,e^{12}+52480\,a^7\,c^9\,d^{10}\,e^{10}-30848\,a^6\,c^{10}\,d^{12}\,e^8+10240\,a^5\,c^{11}\,d^{14}\,e^6-1760\,a^4\,c^{12}\,d^{16}\,e^4+128\,a^3\,c^{13}\,d^{18}\,e^2\right)\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,1{}\mathrm{i}+\left(\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,\left(2048\,a^{16}\,c^4\,d\,e^{22}-20480\,a^{15}\,c^5\,d^3\,e^{20}+92160\,a^{14}\,c^6\,d^5\,e^{18}-245760\,a^{13}\,c^7\,d^7\,e^{16}+430080\,a^{12}\,c^8\,d^9\,e^{14}-516096\,a^{11}\,c^9\,d^{11}\,e^{12}+430080\,a^{10}\,c^{10}\,d^{13}\,e^{10}-245760\,a^9\,c^{11}\,d^{15}\,e^8+92160\,a^8\,c^{12}\,d^{17}\,e^6-20480\,a^7\,c^{13}\,d^{19}\,e^4+2048\,a^6\,c^{14}\,d^{21}\,e^2\right)+3328\,a^{14}\,c^4\,d\,e^{21}-256\,a^5\,c^{13}\,d^{19}\,e^3+5376\,a^6\,c^{12}\,d^{17}\,e^5-33792\,a^7\,c^{11}\,d^{15}\,e^7+107520\,a^8\,c^{10}\,d^{13}\,e^9-204288\,a^9\,c^9\,d^{11}\,e^{11}+247296\,a^{10}\,c^8\,d^9\,e^{13}-193536\,a^{11}\,c^7\,d^7\,e^{15}+95232\,a^{12}\,c^6\,d^5\,e^{17}-26880\,a^{13}\,c^5\,d^3\,e^{19}\right)-\sqrt{d+e\,x}\,\left(800\,a^{12}\,c^4\,e^{20}-2432\,a^{11}\,c^5\,d^2\,e^{18}-3200\,a^{10}\,c^6\,d^4\,e^{16}+25600\,a^9\,c^7\,d^6\,e^{14}-51008\,a^8\,c^8\,d^8\,e^{12}+52480\,a^7\,c^9\,d^{10}\,e^{10}-30848\,a^6\,c^{10}\,d^{12}\,e^8+10240\,a^5\,c^{11}\,d^{14}\,e^6-1760\,a^4\,c^{12}\,d^{16}\,e^4+128\,a^3\,c^{13}\,d^{18}\,e^2\right)\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,1{}\mathrm{i}}{\left(\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,\left(2048\,a^{16}\,c^4\,d\,e^{22}-20480\,a^{15}\,c^5\,d^3\,e^{20}+92160\,a^{14}\,c^6\,d^5\,e^{18}-245760\,a^{13}\,c^7\,d^7\,e^{16}+430080\,a^{12}\,c^8\,d^9\,e^{14}-516096\,a^{11}\,c^9\,d^{11}\,e^{12}+430080\,a^{10}\,c^{10}\,d^{13}\,e^{10}-245760\,a^9\,c^{11}\,d^{15}\,e^8+92160\,a^8\,c^{12}\,d^{17}\,e^6-20480\,a^7\,c^{13}\,d^{19}\,e^4+2048\,a^6\,c^{14}\,d^{21}\,e^2\right)-3328\,a^{14}\,c^4\,d\,e^{21}+256\,a^5\,c^{13}\,d^{19}\,e^3-5376\,a^6\,c^{12}\,d^{17}\,e^5+33792\,a^7\,c^{11}\,d^{15}\,e^7-107520\,a^8\,c^{10}\,d^{13}\,e^9+204288\,a^9\,c^9\,d^{11}\,e^{11}-247296\,a^{10}\,c^8\,d^9\,e^{13}+193536\,a^{11}\,c^7\,d^7\,e^{15}-95232\,a^{12}\,c^6\,d^5\,e^{17}+26880\,a^{13}\,c^5\,d^3\,e^{19}\right)-\sqrt{d+e\,x}\,\left(800\,a^{12}\,c^4\,e^{20}-2432\,a^{11}\,c^5\,d^2\,e^{18}-3200\,a^{10}\,c^6\,d^4\,e^{16}+25600\,a^9\,c^7\,d^6\,e^{14}-51008\,a^8\,c^8\,d^8\,e^{12}+52480\,a^7\,c^9\,d^{10}\,e^{10}-30848\,a^6\,c^{10}\,d^{12}\,e^8+10240\,a^5\,c^{11}\,d^{14}\,e^6-1760\,a^4\,c^{12}\,d^{16}\,e^4+128\,a^3\,c^{13}\,d^{18}\,e^2\right)\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}-\left(\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,\left(2048\,a^{16}\,c^4\,d\,e^{22}-20480\,a^{15}\,c^5\,d^3\,e^{20}+92160\,a^{14}\,c^6\,d^5\,e^{18}-245760\,a^{13}\,c^7\,d^7\,e^{16}+430080\,a^{12}\,c^8\,d^9\,e^{14}-516096\,a^{11}\,c^9\,d^{11}\,e^{12}+430080\,a^{10}\,c^{10}\,d^{13}\,e^{10}-245760\,a^9\,c^{11}\,d^{15}\,e^8+92160\,a^8\,c^{12}\,d^{17}\,e^6-20480\,a^7\,c^{13}\,d^{19}\,e^4+2048\,a^6\,c^{14}\,d^{21}\,e^2\right)+3328\,a^{14}\,c^4\,d\,e^{21}-256\,a^5\,c^{13}\,d^{19}\,e^3+5376\,a^6\,c^{12}\,d^{17}\,e^5-33792\,a^7\,c^{11}\,d^{15}\,e^7+107520\,a^8\,c^{10}\,d^{13}\,e^9-204288\,a^9\,c^9\,d^{11}\,e^{11}+247296\,a^{10}\,c^8\,d^9\,e^{13}-193536\,a^{11}\,c^7\,d^7\,e^{15}+95232\,a^{12}\,c^6\,d^5\,e^{17}-26880\,a^{13}\,c^5\,d^3\,e^{19}\right)-\sqrt{d+e\,x}\,\left(800\,a^{12}\,c^4\,e^{20}-2432\,a^{11}\,c^5\,d^2\,e^{18}-3200\,a^{10}\,c^6\,d^4\,e^{16}+25600\,a^9\,c^7\,d^6\,e^{14}-51008\,a^8\,c^8\,d^8\,e^{12}+52480\,a^7\,c^9\,d^{10}\,e^{10}-30848\,a^6\,c^{10}\,d^{12}\,e^8+10240\,a^5\,c^{11}\,d^{14}\,e^6-1760\,a^4\,c^{12}\,d^{16}\,e^4+128\,a^3\,c^{13}\,d^{18}\,e^2\right)\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}+1000\,a^{10}\,c^4\,e^{19}-32\,a^2\,c^{12}\,d^{16}\,e^3+232\,a^3\,c^{11}\,d^{14}\,e^5+280\,a^4\,c^{10}\,d^{12}\,e^7-4760\,a^5\,c^9\,d^{10}\,e^9+13720\,a^6\,c^8\,d^8\,e^{11}-19208\,a^7\,c^7\,d^6\,e^{13}+14728\,a^8\,c^6\,d^4\,e^{15}-5960\,a^9\,c^5\,d^2\,e^{17}}\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{a^9\,c}-35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{a^9\,c}+105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{a^9\,c}}{64\,\left(a^{11}\,e^{10}-5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6-10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2-a^6\,c^5\,d^{10}\right)}}\,2{}\mathrm{i}","Not used",1,"atan((((-(4*a^3*c^4*d^7 - 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(2048*a^16*c^4*d*e^22 + 2048*a^6*c^14*d^21*e^2 - 20480*a^7*c^13*d^19*e^4 + 92160*a^8*c^12*d^17*e^6 - 245760*a^9*c^11*d^15*e^8 + 430080*a^10*c^10*d^13*e^10 - 516096*a^11*c^9*d^11*e^12 + 430080*a^12*c^8*d^9*e^14 - 245760*a^13*c^7*d^7*e^16 + 92160*a^14*c^6*d^5*e^18 - 20480*a^15*c^5*d^3*e^20) - 3328*a^14*c^4*d*e^21 + 256*a^5*c^13*d^19*e^3 - 5376*a^6*c^12*d^17*e^5 + 33792*a^7*c^11*d^15*e^7 - 107520*a^8*c^10*d^13*e^9 + 204288*a^9*c^9*d^11*e^11 - 247296*a^10*c^8*d^9*e^13 + 193536*a^11*c^7*d^7*e^15 - 95232*a^12*c^6*d^5*e^17 + 26880*a^13*c^5*d^3*e^19) - (d + e*x)^(1/2)*(800*a^12*c^4*e^20 + 128*a^3*c^13*d^18*e^2 - 1760*a^4*c^12*d^16*e^4 + 10240*a^5*c^11*d^14*e^6 - 30848*a^6*c^10*d^12*e^8 + 52480*a^7*c^9*d^10*e^10 - 51008*a^8*c^8*d^8*e^12 + 25600*a^9*c^7*d^6*e^14 - 3200*a^10*c^6*d^4*e^16 - 2432*a^11*c^5*d^2*e^18))*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*1i + ((-(4*a^3*c^4*d^7 - 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(2048*a^16*c^4*d*e^22 + 2048*a^6*c^14*d^21*e^2 - 20480*a^7*c^13*d^19*e^4 + 92160*a^8*c^12*d^17*e^6 - 245760*a^9*c^11*d^15*e^8 + 430080*a^10*c^10*d^13*e^10 - 516096*a^11*c^9*d^11*e^12 + 430080*a^12*c^8*d^9*e^14 - 245760*a^13*c^7*d^7*e^16 + 92160*a^14*c^6*d^5*e^18 - 20480*a^15*c^5*d^3*e^20) + 3328*a^14*c^4*d*e^21 - 256*a^5*c^13*d^19*e^3 + 5376*a^6*c^12*d^17*e^5 - 33792*a^7*c^11*d^15*e^7 + 107520*a^8*c^10*d^13*e^9 - 204288*a^9*c^9*d^11*e^11 + 247296*a^10*c^8*d^9*e^13 - 193536*a^11*c^7*d^7*e^15 + 95232*a^12*c^6*d^5*e^17 - 26880*a^13*c^5*d^3*e^19) - (d + e*x)^(1/2)*(800*a^12*c^4*e^20 + 128*a^3*c^13*d^18*e^2 - 1760*a^4*c^12*d^16*e^4 + 10240*a^5*c^11*d^14*e^6 - 30848*a^6*c^10*d^12*e^8 + 52480*a^7*c^9*d^10*e^10 - 51008*a^8*c^8*d^8*e^12 + 25600*a^9*c^7*d^6*e^14 - 3200*a^10*c^6*d^4*e^16 - 2432*a^11*c^5*d^2*e^18))*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*1i)/(((-(4*a^3*c^4*d^7 - 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(2048*a^16*c^4*d*e^22 + 2048*a^6*c^14*d^21*e^2 - 20480*a^7*c^13*d^19*e^4 + 92160*a^8*c^12*d^17*e^6 - 245760*a^9*c^11*d^15*e^8 + 430080*a^10*c^10*d^13*e^10 - 516096*a^11*c^9*d^11*e^12 + 430080*a^12*c^8*d^9*e^14 - 245760*a^13*c^7*d^7*e^16 + 92160*a^14*c^6*d^5*e^18 - 20480*a^15*c^5*d^3*e^20) - 3328*a^14*c^4*d*e^21 + 256*a^5*c^13*d^19*e^3 - 5376*a^6*c^12*d^17*e^5 + 33792*a^7*c^11*d^15*e^7 - 107520*a^8*c^10*d^13*e^9 + 204288*a^9*c^9*d^11*e^11 - 247296*a^10*c^8*d^9*e^13 + 193536*a^11*c^7*d^7*e^15 - 95232*a^12*c^6*d^5*e^17 + 26880*a^13*c^5*d^3*e^19) - (d + e*x)^(1/2)*(800*a^12*c^4*e^20 + 128*a^3*c^13*d^18*e^2 - 1760*a^4*c^12*d^16*e^4 + 10240*a^5*c^11*d^14*e^6 - 30848*a^6*c^10*d^12*e^8 + 52480*a^7*c^9*d^10*e^10 - 51008*a^8*c^8*d^8*e^12 + 25600*a^9*c^7*d^6*e^14 - 3200*a^10*c^6*d^4*e^16 - 2432*a^11*c^5*d^2*e^18))*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2) - ((-(4*a^3*c^4*d^7 - 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(2048*a^16*c^4*d*e^22 + 2048*a^6*c^14*d^21*e^2 - 20480*a^7*c^13*d^19*e^4 + 92160*a^8*c^12*d^17*e^6 - 245760*a^9*c^11*d^15*e^8 + 430080*a^10*c^10*d^13*e^10 - 516096*a^11*c^9*d^11*e^12 + 430080*a^12*c^8*d^9*e^14 - 245760*a^13*c^7*d^7*e^16 + 92160*a^14*c^6*d^5*e^18 - 20480*a^15*c^5*d^3*e^20) + 3328*a^14*c^4*d*e^21 - 256*a^5*c^13*d^19*e^3 + 5376*a^6*c^12*d^17*e^5 - 33792*a^7*c^11*d^15*e^7 + 107520*a^8*c^10*d^13*e^9 - 204288*a^9*c^9*d^11*e^11 + 247296*a^10*c^8*d^9*e^13 - 193536*a^11*c^7*d^7*e^15 + 95232*a^12*c^6*d^5*e^17 - 26880*a^13*c^5*d^3*e^19) - (d + e*x)^(1/2)*(800*a^12*c^4*e^20 + 128*a^3*c^13*d^18*e^2 - 1760*a^4*c^12*d^16*e^4 + 10240*a^5*c^11*d^14*e^6 - 30848*a^6*c^10*d^12*e^8 + 52480*a^7*c^9*d^10*e^10 - 51008*a^8*c^8*d^8*e^12 + 25600*a^9*c^7*d^6*e^14 - 3200*a^10*c^6*d^4*e^16 - 2432*a^11*c^5*d^2*e^18))*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2) + 1000*a^10*c^4*e^19 - 32*a^2*c^12*d^16*e^3 + 232*a^3*c^11*d^14*e^5 + 280*a^4*c^10*d^12*e^7 - 4760*a^5*c^9*d^10*e^9 + 13720*a^6*c^8*d^8*e^11 - 19208*a^7*c^7*d^6*e^13 + 14728*a^8*c^6*d^4*e^15 - 5960*a^9*c^5*d^2*e^17))*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*2i - ((2*e^3)/(a*e^2 - c*d^2) - (c*e*(5*a*e^2 + c*d^2)*(d + e*x)^2)/(2*a*(a*e^2 - c*d^2)^2) + (c*d*e*(11*a*e^2 + c*d^2)*(d + e*x))/(2*a*(a*e^2 - c*d^2)^2))/((a*e^2 - c*d^2)*(d + e*x)^(1/2) - c*(d + e*x)^(5/2) + 2*c*d*(d + e*x)^(3/2)) + atan((((-(4*a^3*c^4*d^7 + 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(2048*a^16*c^4*d*e^22 + 2048*a^6*c^14*d^21*e^2 - 20480*a^7*c^13*d^19*e^4 + 92160*a^8*c^12*d^17*e^6 - 245760*a^9*c^11*d^15*e^8 + 430080*a^10*c^10*d^13*e^10 - 516096*a^11*c^9*d^11*e^12 + 430080*a^12*c^8*d^9*e^14 - 245760*a^13*c^7*d^7*e^16 + 92160*a^14*c^6*d^5*e^18 - 20480*a^15*c^5*d^3*e^20) - 3328*a^14*c^4*d*e^21 + 256*a^5*c^13*d^19*e^3 - 5376*a^6*c^12*d^17*e^5 + 33792*a^7*c^11*d^15*e^7 - 107520*a^8*c^10*d^13*e^9 + 204288*a^9*c^9*d^11*e^11 - 247296*a^10*c^8*d^9*e^13 + 193536*a^11*c^7*d^7*e^15 - 95232*a^12*c^6*d^5*e^17 + 26880*a^13*c^5*d^3*e^19) - (d + e*x)^(1/2)*(800*a^12*c^4*e^20 + 128*a^3*c^13*d^18*e^2 - 1760*a^4*c^12*d^16*e^4 + 10240*a^5*c^11*d^14*e^6 - 30848*a^6*c^10*d^12*e^8 + 52480*a^7*c^9*d^10*e^10 - 51008*a^8*c^8*d^8*e^12 + 25600*a^9*c^7*d^6*e^14 - 3200*a^10*c^6*d^4*e^16 - 2432*a^11*c^5*d^2*e^18))*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*1i + ((-(4*a^3*c^4*d^7 + 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(2048*a^16*c^4*d*e^22 + 2048*a^6*c^14*d^21*e^2 - 20480*a^7*c^13*d^19*e^4 + 92160*a^8*c^12*d^17*e^6 - 245760*a^9*c^11*d^15*e^8 + 430080*a^10*c^10*d^13*e^10 - 516096*a^11*c^9*d^11*e^12 + 430080*a^12*c^8*d^9*e^14 - 245760*a^13*c^7*d^7*e^16 + 92160*a^14*c^6*d^5*e^18 - 20480*a^15*c^5*d^3*e^20) + 3328*a^14*c^4*d*e^21 - 256*a^5*c^13*d^19*e^3 + 5376*a^6*c^12*d^17*e^5 - 33792*a^7*c^11*d^15*e^7 + 107520*a^8*c^10*d^13*e^9 - 204288*a^9*c^9*d^11*e^11 + 247296*a^10*c^8*d^9*e^13 - 193536*a^11*c^7*d^7*e^15 + 95232*a^12*c^6*d^5*e^17 - 26880*a^13*c^5*d^3*e^19) - (d + e*x)^(1/2)*(800*a^12*c^4*e^20 + 128*a^3*c^13*d^18*e^2 - 1760*a^4*c^12*d^16*e^4 + 10240*a^5*c^11*d^14*e^6 - 30848*a^6*c^10*d^12*e^8 + 52480*a^7*c^9*d^10*e^10 - 51008*a^8*c^8*d^8*e^12 + 25600*a^9*c^7*d^6*e^14 - 3200*a^10*c^6*d^4*e^16 - 2432*a^11*c^5*d^2*e^18))*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*1i)/(((-(4*a^3*c^4*d^7 + 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(2048*a^16*c^4*d*e^22 + 2048*a^6*c^14*d^21*e^2 - 20480*a^7*c^13*d^19*e^4 + 92160*a^8*c^12*d^17*e^6 - 245760*a^9*c^11*d^15*e^8 + 430080*a^10*c^10*d^13*e^10 - 516096*a^11*c^9*d^11*e^12 + 430080*a^12*c^8*d^9*e^14 - 245760*a^13*c^7*d^7*e^16 + 92160*a^14*c^6*d^5*e^18 - 20480*a^15*c^5*d^3*e^20) - 3328*a^14*c^4*d*e^21 + 256*a^5*c^13*d^19*e^3 - 5376*a^6*c^12*d^17*e^5 + 33792*a^7*c^11*d^15*e^7 - 107520*a^8*c^10*d^13*e^9 + 204288*a^9*c^9*d^11*e^11 - 247296*a^10*c^8*d^9*e^13 + 193536*a^11*c^7*d^7*e^15 - 95232*a^12*c^6*d^5*e^17 + 26880*a^13*c^5*d^3*e^19) - (d + e*x)^(1/2)*(800*a^12*c^4*e^20 + 128*a^3*c^13*d^18*e^2 - 1760*a^4*c^12*d^16*e^4 + 10240*a^5*c^11*d^14*e^6 - 30848*a^6*c^10*d^12*e^8 + 52480*a^7*c^9*d^10*e^10 - 51008*a^8*c^8*d^8*e^12 + 25600*a^9*c^7*d^6*e^14 - 3200*a^10*c^6*d^4*e^16 - 2432*a^11*c^5*d^2*e^18))*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2) - ((-(4*a^3*c^4*d^7 + 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(2048*a^16*c^4*d*e^22 + 2048*a^6*c^14*d^21*e^2 - 20480*a^7*c^13*d^19*e^4 + 92160*a^8*c^12*d^17*e^6 - 245760*a^9*c^11*d^15*e^8 + 430080*a^10*c^10*d^13*e^10 - 516096*a^11*c^9*d^11*e^12 + 430080*a^12*c^8*d^9*e^14 - 245760*a^13*c^7*d^7*e^16 + 92160*a^14*c^6*d^5*e^18 - 20480*a^15*c^5*d^3*e^20) + 3328*a^14*c^4*d*e^21 - 256*a^5*c^13*d^19*e^3 + 5376*a^6*c^12*d^17*e^5 - 33792*a^7*c^11*d^15*e^7 + 107520*a^8*c^10*d^13*e^9 - 204288*a^9*c^9*d^11*e^11 + 247296*a^10*c^8*d^9*e^13 - 193536*a^11*c^7*d^7*e^15 + 95232*a^12*c^6*d^5*e^17 - 26880*a^13*c^5*d^3*e^19) - (d + e*x)^(1/2)*(800*a^12*c^4*e^20 + 128*a^3*c^13*d^18*e^2 - 1760*a^4*c^12*d^16*e^4 + 10240*a^5*c^11*d^14*e^6 - 30848*a^6*c^10*d^12*e^8 + 52480*a^7*c^9*d^10*e^10 - 51008*a^8*c^8*d^8*e^12 + 25600*a^9*c^7*d^6*e^14 - 3200*a^10*c^6*d^4*e^16 - 2432*a^11*c^5*d^2*e^18))*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2) + 1000*a^10*c^4*e^19 - 32*a^2*c^12*d^16*e^3 + 232*a^3*c^11*d^14*e^5 + 280*a^4*c^10*d^12*e^7 - 4760*a^5*c^9*d^10*e^9 + 13720*a^6*c^8*d^8*e^11 - 19208*a^7*c^7*d^6*e^13 + 14728*a^8*c^6*d^4*e^15 - 5960*a^9*c^5*d^2*e^17))*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(a^9*c)^(1/2) - 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(a^9*c)^(1/2) + 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(a^9*c)^(1/2))/(64*(a^11*e^10 - a^6*c^5*d^10 - 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 - 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*2i","B"
630,1,12290,311,4.836162,"\text{Not used}","int(1/((a - c*x^2)^2*(d + e*x)^(5/2)),x)","-\frac{\frac{2\,e^3}{3\,\left(a\,e^2-c\,d^2\right)}-\frac{20\,c\,d\,e^3\,\left(d+e\,x\right)}{3\,{\left(a\,e^2-c\,d^2\right)}^2}-\frac{c\,e\,{\left(d+e\,x\right)}^2\,\left(7\,a^2\,e^4+110\,a\,c\,d^2\,e^2+3\,c^2\,d^4\right)}{6\,a\,{\left(a\,e^2-c\,d^2\right)}^3}+\frac{c^2\,d\,e\,\left(c\,d^2+19\,a\,e^2\right)\,{\left(d+e\,x\right)}^3}{2\,a\,{\left(a\,e^2-c\,d^2\right)}^3}}{\left(a\,e^2-c\,d^2\right)\,{\left(d+e\,x\right)}^{3/2}-c\,{\left(d+e\,x\right)}^{7/2}+2\,c\,d\,{\left(d+e\,x\right)}^{5/2}}-\mathrm{atan}\left(\frac{\left(\sqrt{d+e\,x}\,\left(1568\,a^{16}\,c^5\,e^{28}+4160\,a^{15}\,c^6\,d^2\,e^{26}-100480\,a^{14}\,c^7\,d^4\,e^{24}+456512\,a^{13}\,c^8\,d^6\,e^{22}-1049440\,a^{12}\,c^9\,d^8\,e^{20}+1403904\,a^{11}\,c^{10}\,d^{10}\,e^{18}-1059840\,a^{10}\,c^{11}\,d^{12}\,e^{16}+282240\,a^9\,c^{12}\,d^{14}\,e^{14}+242016\,a^8\,c^{13}\,d^{16}\,e^{12}-282560\,a^7\,c^{14}\,d^{18}\,e^{10}+128128\,a^6\,c^{15}\,d^{20}\,e^8-29120\,a^5\,c^{16}\,d^{22}\,e^6+3040\,a^4\,c^{17}\,d^{24}\,e^4-128\,a^3\,c^{18}\,d^{26}\,e^2\right)-\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{a^9\,c^3}+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{a^9\,c^3}+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,\left(2048\,a^{21}\,c^4\,d\,e^{32}-30720\,a^{20}\,c^5\,d^3\,e^{30}+215040\,a^{19}\,c^6\,d^5\,e^{28}-931840\,a^{18}\,c^7\,d^7\,e^{26}+2795520\,a^{17}\,c^8\,d^9\,e^{24}-6150144\,a^{16}\,c^9\,d^{11}\,e^{22}+10250240\,a^{15}\,c^{10}\,d^{13}\,e^{20}-13178880\,a^{14}\,c^{11}\,d^{15}\,e^{18}+13178880\,a^{13}\,c^{12}\,d^{17}\,e^{16}-10250240\,a^{12}\,c^{13}\,d^{19}\,e^{14}+6150144\,a^{11}\,c^{14}\,d^{21}\,e^{12}-2795520\,a^{10}\,c^{15}\,d^{23}\,e^{10}+931840\,a^9\,c^{16}\,d^{25}\,e^8-215040\,a^8\,c^{17}\,d^{27}\,e^6+30720\,a^7\,c^{18}\,d^{29}\,e^4-2048\,a^6\,c^{19}\,d^{31}\,e^2\right)-1792\,a^{19}\,c^4\,e^{31}+256\,a^5\,c^{18}\,d^{28}\,e^3-11776\,a^6\,c^{17}\,d^{26}\,e^5+119552\,a^7\,c^{16}\,d^{24}\,e^7-609280\,a^8\,c^{15}\,d^{22}\,e^9+1923328\,a^9\,c^{14}\,d^{20}\,e^{11}-4116992\,a^{10}\,c^{13}\,d^{18}\,e^{13}+6243072\,a^{11}\,c^{12}\,d^{16}\,e^{15}-6825984\,a^{12}\,c^{11}\,d^{14}\,e^{17}+5364480\,a^{13}\,c^{10}\,d^{12}\,e^{19}-2945536\,a^{14}\,c^9\,d^{10}\,e^{21}+1044736\,a^{15}\,c^8\,d^8\,e^{23}-183296\,a^{16}\,c^7\,d^6\,e^{25}-13568\,a^{17}\,c^6\,d^4\,e^{27}+12800\,a^{18}\,c^5\,d^2\,e^{29}\right)\right)\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{a^9\,c^3}+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,1{}\mathrm{i}+\left(\sqrt{d+e\,x}\,\left(1568\,a^{16}\,c^5\,e^{28}+4160\,a^{15}\,c^6\,d^2\,e^{26}-100480\,a^{14}\,c^7\,d^4\,e^{24}+456512\,a^{13}\,c^8\,d^6\,e^{22}-1049440\,a^{12}\,c^9\,d^8\,e^{20}+1403904\,a^{11}\,c^{10}\,d^{10}\,e^{18}-1059840\,a^{10}\,c^{11}\,d^{12}\,e^{16}+282240\,a^9\,c^{12}\,d^{14}\,e^{14}+242016\,a^8\,c^{13}\,d^{16}\,e^{12}-282560\,a^7\,c^{14}\,d^{18}\,e^{10}+128128\,a^6\,c^{15}\,d^{20}\,e^8-29120\,a^5\,c^{16}\,d^{22}\,e^6+3040\,a^4\,c^{17}\,d^{24}\,e^4-128\,a^3\,c^{18}\,d^{26}\,e^2\right)-\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{a^9\,c^3}+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{a^9\,c^3}+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,\left(2048\,a^{21}\,c^4\,d\,e^{32}-30720\,a^{20}\,c^5\,d^3\,e^{30}+215040\,a^{19}\,c^6\,d^5\,e^{28}-931840\,a^{18}\,c^7\,d^7\,e^{26}+2795520\,a^{17}\,c^8\,d^9\,e^{24}-6150144\,a^{16}\,c^9\,d^{11}\,e^{22}+10250240\,a^{15}\,c^{10}\,d^{13}\,e^{20}-13178880\,a^{14}\,c^{11}\,d^{15}\,e^{18}+13178880\,a^{13}\,c^{12}\,d^{17}\,e^{16}-10250240\,a^{12}\,c^{13}\,d^{19}\,e^{14}+6150144\,a^{11}\,c^{14}\,d^{21}\,e^{12}-2795520\,a^{10}\,c^{15}\,d^{23}\,e^{10}+931840\,a^9\,c^{16}\,d^{25}\,e^8-215040\,a^8\,c^{17}\,d^{27}\,e^6+30720\,a^7\,c^{18}\,d^{29}\,e^4-2048\,a^6\,c^{19}\,d^{31}\,e^2\right)+1792\,a^{19}\,c^4\,e^{31}-256\,a^5\,c^{18}\,d^{28}\,e^3+11776\,a^6\,c^{17}\,d^{26}\,e^5-119552\,a^7\,c^{16}\,d^{24}\,e^7+609280\,a^8\,c^{15}\,d^{22}\,e^9-1923328\,a^9\,c^{14}\,d^{20}\,e^{11}+4116992\,a^{10}\,c^{13}\,d^{18}\,e^{13}-6243072\,a^{11}\,c^{12}\,d^{16}\,e^{15}+6825984\,a^{12}\,c^{11}\,d^{14}\,e^{17}-5364480\,a^{13}\,c^{10}\,d^{12}\,e^{19}+2945536\,a^{14}\,c^9\,d^{10}\,e^{21}-1044736\,a^{15}\,c^8\,d^8\,e^{23}+183296\,a^{16}\,c^7\,d^6\,e^{25}+13568\,a^{17}\,c^6\,d^4\,e^{27}-12800\,a^{18}\,c^5\,d^2\,e^{29}\right)\right)\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{a^9\,c^3}+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,1{}\mathrm{i}}{\left(\sqrt{d+e\,x}\,\left(1568\,a^{16}\,c^5\,e^{28}+4160\,a^{15}\,c^6\,d^2\,e^{26}-100480\,a^{14}\,c^7\,d^4\,e^{24}+456512\,a^{13}\,c^8\,d^6\,e^{22}-1049440\,a^{12}\,c^9\,d^8\,e^{20}+1403904\,a^{11}\,c^{10}\,d^{10}\,e^{18}-1059840\,a^{10}\,c^{11}\,d^{12}\,e^{16}+282240\,a^9\,c^{12}\,d^{14}\,e^{14}+242016\,a^8\,c^{13}\,d^{16}\,e^{12}-282560\,a^7\,c^{14}\,d^{18}\,e^{10}+128128\,a^6\,c^{15}\,d^{20}\,e^8-29120\,a^5\,c^{16}\,d^{22}\,e^6+3040\,a^4\,c^{17}\,d^{24}\,e^4-128\,a^3\,c^{18}\,d^{26}\,e^2\right)-\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{a^9\,c^3}+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{a^9\,c^3}+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,\left(2048\,a^{21}\,c^4\,d\,e^{32}-30720\,a^{20}\,c^5\,d^3\,e^{30}+215040\,a^{19}\,c^6\,d^5\,e^{28}-931840\,a^{18}\,c^7\,d^7\,e^{26}+2795520\,a^{17}\,c^8\,d^9\,e^{24}-6150144\,a^{16}\,c^9\,d^{11}\,e^{22}+10250240\,a^{15}\,c^{10}\,d^{13}\,e^{20}-13178880\,a^{14}\,c^{11}\,d^{15}\,e^{18}+13178880\,a^{13}\,c^{12}\,d^{17}\,e^{16}-10250240\,a^{12}\,c^{13}\,d^{19}\,e^{14}+6150144\,a^{11}\,c^{14}\,d^{21}\,e^{12}-2795520\,a^{10}\,c^{15}\,d^{23}\,e^{10}+931840\,a^9\,c^{16}\,d^{25}\,e^8-215040\,a^8\,c^{17}\,d^{27}\,e^6+30720\,a^7\,c^{18}\,d^{29}\,e^4-2048\,a^6\,c^{19}\,d^{31}\,e^2\right)-1792\,a^{19}\,c^4\,e^{31}+256\,a^5\,c^{18}\,d^{28}\,e^3-11776\,a^6\,c^{17}\,d^{26}\,e^5+119552\,a^7\,c^{16}\,d^{24}\,e^7-609280\,a^8\,c^{15}\,d^{22}\,e^9+1923328\,a^9\,c^{14}\,d^{20}\,e^{11}-4116992\,a^{10}\,c^{13}\,d^{18}\,e^{13}+6243072\,a^{11}\,c^{12}\,d^{16}\,e^{15}-6825984\,a^{12}\,c^{11}\,d^{14}\,e^{17}+5364480\,a^{13}\,c^{10}\,d^{12}\,e^{19}-2945536\,a^{14}\,c^9\,d^{10}\,e^{21}+1044736\,a^{15}\,c^8\,d^8\,e^{23}-183296\,a^{16}\,c^7\,d^6\,e^{25}-13568\,a^{17}\,c^6\,d^4\,e^{27}+12800\,a^{18}\,c^5\,d^2\,e^{29}\right)\right)\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{a^9\,c^3}+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}-\left(\sqrt{d+e\,x}\,\left(1568\,a^{16}\,c^5\,e^{28}+4160\,a^{15}\,c^6\,d^2\,e^{26}-100480\,a^{14}\,c^7\,d^4\,e^{24}+456512\,a^{13}\,c^8\,d^6\,e^{22}-1049440\,a^{12}\,c^9\,d^8\,e^{20}+1403904\,a^{11}\,c^{10}\,d^{10}\,e^{18}-1059840\,a^{10}\,c^{11}\,d^{12}\,e^{16}+282240\,a^9\,c^{12}\,d^{14}\,e^{14}+242016\,a^8\,c^{13}\,d^{16}\,e^{12}-282560\,a^7\,c^{14}\,d^{18}\,e^{10}+128128\,a^6\,c^{15}\,d^{20}\,e^8-29120\,a^5\,c^{16}\,d^{22}\,e^6+3040\,a^4\,c^{17}\,d^{24}\,e^4-128\,a^3\,c^{18}\,d^{26}\,e^2\right)-\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{a^9\,c^3}+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{a^9\,c^3}+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,\left(2048\,a^{21}\,c^4\,d\,e^{32}-30720\,a^{20}\,c^5\,d^3\,e^{30}+215040\,a^{19}\,c^6\,d^5\,e^{28}-931840\,a^{18}\,c^7\,d^7\,e^{26}+2795520\,a^{17}\,c^8\,d^9\,e^{24}-6150144\,a^{16}\,c^9\,d^{11}\,e^{22}+10250240\,a^{15}\,c^{10}\,d^{13}\,e^{20}-13178880\,a^{14}\,c^{11}\,d^{15}\,e^{18}+13178880\,a^{13}\,c^{12}\,d^{17}\,e^{16}-10250240\,a^{12}\,c^{13}\,d^{19}\,e^{14}+6150144\,a^{11}\,c^{14}\,d^{21}\,e^{12}-2795520\,a^{10}\,c^{15}\,d^{23}\,e^{10}+931840\,a^9\,c^{16}\,d^{25}\,e^8-215040\,a^8\,c^{17}\,d^{27}\,e^6+30720\,a^7\,c^{18}\,d^{29}\,e^4-2048\,a^6\,c^{19}\,d^{31}\,e^2\right)+1792\,a^{19}\,c^4\,e^{31}-256\,a^5\,c^{18}\,d^{28}\,e^3+11776\,a^6\,c^{17}\,d^{26}\,e^5-119552\,a^7\,c^{16}\,d^{24}\,e^7+609280\,a^8\,c^{15}\,d^{22}\,e^9-1923328\,a^9\,c^{14}\,d^{20}\,e^{11}+4116992\,a^{10}\,c^{13}\,d^{18}\,e^{13}-6243072\,a^{11}\,c^{12}\,d^{16}\,e^{15}+6825984\,a^{12}\,c^{11}\,d^{14}\,e^{17}-5364480\,a^{13}\,c^{10}\,d^{12}\,e^{19}+2945536\,a^{14}\,c^9\,d^{10}\,e^{21}-1044736\,a^{15}\,c^8\,d^8\,e^{23}+183296\,a^{16}\,c^7\,d^6\,e^{25}+13568\,a^{17}\,c^6\,d^4\,e^{27}-12800\,a^{18}\,c^5\,d^2\,e^{29}\right)\right)\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{a^9\,c^3}+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}+7448\,a^{13}\,c^6\,d\,e^{25}+32\,a^2\,c^{17}\,d^{23}\,e^3-72\,a^3\,c^{16}\,d^{21}\,e^5-8240\,a^4\,c^{15}\,d^{19}\,e^7+72120\,a^5\,c^{14}\,d^{17}\,e^9-282240\,a^6\,c^{13}\,d^{15}\,e^{11}+648816\,a^7\,c^{12}\,d^{13}\,e^{13}-962976\,a^8\,c^{11}\,d^{11}\,e^{15}+955440\,a^9\,c^{10}\,d^9\,e^{17}-633120\,a^{10}\,c^9\,d^7\,e^{19}+270040\,a^{11}\,c^8\,d^5\,e^{21}-67248\,a^{12}\,c^7\,d^3\,e^{23}}\right)\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{a^9\,c^3}+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\sqrt{d+e\,x}\,\left(1568\,a^{16}\,c^5\,e^{28}+4160\,a^{15}\,c^6\,d^2\,e^{26}-100480\,a^{14}\,c^7\,d^4\,e^{24}+456512\,a^{13}\,c^8\,d^6\,e^{22}-1049440\,a^{12}\,c^9\,d^8\,e^{20}+1403904\,a^{11}\,c^{10}\,d^{10}\,e^{18}-1059840\,a^{10}\,c^{11}\,d^{12}\,e^{16}+282240\,a^9\,c^{12}\,d^{14}\,e^{14}+242016\,a^8\,c^{13}\,d^{16}\,e^{12}-282560\,a^7\,c^{14}\,d^{18}\,e^{10}+128128\,a^6\,c^{15}\,d^{20}\,e^8-29120\,a^5\,c^{16}\,d^{22}\,e^6+3040\,a^4\,c^{17}\,d^{24}\,e^4-128\,a^3\,c^{18}\,d^{26}\,e^2\right)-\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,\left(2048\,a^{21}\,c^4\,d\,e^{32}-30720\,a^{20}\,c^5\,d^3\,e^{30}+215040\,a^{19}\,c^6\,d^5\,e^{28}-931840\,a^{18}\,c^7\,d^7\,e^{26}+2795520\,a^{17}\,c^8\,d^9\,e^{24}-6150144\,a^{16}\,c^9\,d^{11}\,e^{22}+10250240\,a^{15}\,c^{10}\,d^{13}\,e^{20}-13178880\,a^{14}\,c^{11}\,d^{15}\,e^{18}+13178880\,a^{13}\,c^{12}\,d^{17}\,e^{16}-10250240\,a^{12}\,c^{13}\,d^{19}\,e^{14}+6150144\,a^{11}\,c^{14}\,d^{21}\,e^{12}-2795520\,a^{10}\,c^{15}\,d^{23}\,e^{10}+931840\,a^9\,c^{16}\,d^{25}\,e^8-215040\,a^8\,c^{17}\,d^{27}\,e^6+30720\,a^7\,c^{18}\,d^{29}\,e^4-2048\,a^6\,c^{19}\,d^{31}\,e^2\right)-1792\,a^{19}\,c^4\,e^{31}+256\,a^5\,c^{18}\,d^{28}\,e^3-11776\,a^6\,c^{17}\,d^{26}\,e^5+119552\,a^7\,c^{16}\,d^{24}\,e^7-609280\,a^8\,c^{15}\,d^{22}\,e^9+1923328\,a^9\,c^{14}\,d^{20}\,e^{11}-4116992\,a^{10}\,c^{13}\,d^{18}\,e^{13}+6243072\,a^{11}\,c^{12}\,d^{16}\,e^{15}-6825984\,a^{12}\,c^{11}\,d^{14}\,e^{17}+5364480\,a^{13}\,c^{10}\,d^{12}\,e^{19}-2945536\,a^{14}\,c^9\,d^{10}\,e^{21}+1044736\,a^{15}\,c^8\,d^8\,e^{23}-183296\,a^{16}\,c^7\,d^6\,e^{25}-13568\,a^{17}\,c^6\,d^4\,e^{27}+12800\,a^{18}\,c^5\,d^2\,e^{29}\right)\right)\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,1{}\mathrm{i}+\left(\sqrt{d+e\,x}\,\left(1568\,a^{16}\,c^5\,e^{28}+4160\,a^{15}\,c^6\,d^2\,e^{26}-100480\,a^{14}\,c^7\,d^4\,e^{24}+456512\,a^{13}\,c^8\,d^6\,e^{22}-1049440\,a^{12}\,c^9\,d^8\,e^{20}+1403904\,a^{11}\,c^{10}\,d^{10}\,e^{18}-1059840\,a^{10}\,c^{11}\,d^{12}\,e^{16}+282240\,a^9\,c^{12}\,d^{14}\,e^{14}+242016\,a^8\,c^{13}\,d^{16}\,e^{12}-282560\,a^7\,c^{14}\,d^{18}\,e^{10}+128128\,a^6\,c^{15}\,d^{20}\,e^8-29120\,a^5\,c^{16}\,d^{22}\,e^6+3040\,a^4\,c^{17}\,d^{24}\,e^4-128\,a^3\,c^{18}\,d^{26}\,e^2\right)-\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,\left(2048\,a^{21}\,c^4\,d\,e^{32}-30720\,a^{20}\,c^5\,d^3\,e^{30}+215040\,a^{19}\,c^6\,d^5\,e^{28}-931840\,a^{18}\,c^7\,d^7\,e^{26}+2795520\,a^{17}\,c^8\,d^9\,e^{24}-6150144\,a^{16}\,c^9\,d^{11}\,e^{22}+10250240\,a^{15}\,c^{10}\,d^{13}\,e^{20}-13178880\,a^{14}\,c^{11}\,d^{15}\,e^{18}+13178880\,a^{13}\,c^{12}\,d^{17}\,e^{16}-10250240\,a^{12}\,c^{13}\,d^{19}\,e^{14}+6150144\,a^{11}\,c^{14}\,d^{21}\,e^{12}-2795520\,a^{10}\,c^{15}\,d^{23}\,e^{10}+931840\,a^9\,c^{16}\,d^{25}\,e^8-215040\,a^8\,c^{17}\,d^{27}\,e^6+30720\,a^7\,c^{18}\,d^{29}\,e^4-2048\,a^6\,c^{19}\,d^{31}\,e^2\right)+1792\,a^{19}\,c^4\,e^{31}-256\,a^5\,c^{18}\,d^{28}\,e^3+11776\,a^6\,c^{17}\,d^{26}\,e^5-119552\,a^7\,c^{16}\,d^{24}\,e^7+609280\,a^8\,c^{15}\,d^{22}\,e^9-1923328\,a^9\,c^{14}\,d^{20}\,e^{11}+4116992\,a^{10}\,c^{13}\,d^{18}\,e^{13}-6243072\,a^{11}\,c^{12}\,d^{16}\,e^{15}+6825984\,a^{12}\,c^{11}\,d^{14}\,e^{17}-5364480\,a^{13}\,c^{10}\,d^{12}\,e^{19}+2945536\,a^{14}\,c^9\,d^{10}\,e^{21}-1044736\,a^{15}\,c^8\,d^8\,e^{23}+183296\,a^{16}\,c^7\,d^6\,e^{25}+13568\,a^{17}\,c^6\,d^4\,e^{27}-12800\,a^{18}\,c^5\,d^2\,e^{29}\right)\right)\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,1{}\mathrm{i}}{\left(\sqrt{d+e\,x}\,\left(1568\,a^{16}\,c^5\,e^{28}+4160\,a^{15}\,c^6\,d^2\,e^{26}-100480\,a^{14}\,c^7\,d^4\,e^{24}+456512\,a^{13}\,c^8\,d^6\,e^{22}-1049440\,a^{12}\,c^9\,d^8\,e^{20}+1403904\,a^{11}\,c^{10}\,d^{10}\,e^{18}-1059840\,a^{10}\,c^{11}\,d^{12}\,e^{16}+282240\,a^9\,c^{12}\,d^{14}\,e^{14}+242016\,a^8\,c^{13}\,d^{16}\,e^{12}-282560\,a^7\,c^{14}\,d^{18}\,e^{10}+128128\,a^6\,c^{15}\,d^{20}\,e^8-29120\,a^5\,c^{16}\,d^{22}\,e^6+3040\,a^4\,c^{17}\,d^{24}\,e^4-128\,a^3\,c^{18}\,d^{26}\,e^2\right)-\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,\left(2048\,a^{21}\,c^4\,d\,e^{32}-30720\,a^{20}\,c^5\,d^3\,e^{30}+215040\,a^{19}\,c^6\,d^5\,e^{28}-931840\,a^{18}\,c^7\,d^7\,e^{26}+2795520\,a^{17}\,c^8\,d^9\,e^{24}-6150144\,a^{16}\,c^9\,d^{11}\,e^{22}+10250240\,a^{15}\,c^{10}\,d^{13}\,e^{20}-13178880\,a^{14}\,c^{11}\,d^{15}\,e^{18}+13178880\,a^{13}\,c^{12}\,d^{17}\,e^{16}-10250240\,a^{12}\,c^{13}\,d^{19}\,e^{14}+6150144\,a^{11}\,c^{14}\,d^{21}\,e^{12}-2795520\,a^{10}\,c^{15}\,d^{23}\,e^{10}+931840\,a^9\,c^{16}\,d^{25}\,e^8-215040\,a^8\,c^{17}\,d^{27}\,e^6+30720\,a^7\,c^{18}\,d^{29}\,e^4-2048\,a^6\,c^{19}\,d^{31}\,e^2\right)-1792\,a^{19}\,c^4\,e^{31}+256\,a^5\,c^{18}\,d^{28}\,e^3-11776\,a^6\,c^{17}\,d^{26}\,e^5+119552\,a^7\,c^{16}\,d^{24}\,e^7-609280\,a^8\,c^{15}\,d^{22}\,e^9+1923328\,a^9\,c^{14}\,d^{20}\,e^{11}-4116992\,a^{10}\,c^{13}\,d^{18}\,e^{13}+6243072\,a^{11}\,c^{12}\,d^{16}\,e^{15}-6825984\,a^{12}\,c^{11}\,d^{14}\,e^{17}+5364480\,a^{13}\,c^{10}\,d^{12}\,e^{19}-2945536\,a^{14}\,c^9\,d^{10}\,e^{21}+1044736\,a^{15}\,c^8\,d^8\,e^{23}-183296\,a^{16}\,c^7\,d^6\,e^{25}-13568\,a^{17}\,c^6\,d^4\,e^{27}+12800\,a^{18}\,c^5\,d^2\,e^{29}\right)\right)\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}-\left(\sqrt{d+e\,x}\,\left(1568\,a^{16}\,c^5\,e^{28}+4160\,a^{15}\,c^6\,d^2\,e^{26}-100480\,a^{14}\,c^7\,d^4\,e^{24}+456512\,a^{13}\,c^8\,d^6\,e^{22}-1049440\,a^{12}\,c^9\,d^8\,e^{20}+1403904\,a^{11}\,c^{10}\,d^{10}\,e^{18}-1059840\,a^{10}\,c^{11}\,d^{12}\,e^{16}+282240\,a^9\,c^{12}\,d^{14}\,e^{14}+242016\,a^8\,c^{13}\,d^{16}\,e^{12}-282560\,a^7\,c^{14}\,d^{18}\,e^{10}+128128\,a^6\,c^{15}\,d^{20}\,e^8-29120\,a^5\,c^{16}\,d^{22}\,e^6+3040\,a^4\,c^{17}\,d^{24}\,e^4-128\,a^3\,c^{18}\,d^{26}\,e^2\right)-\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,\left(2048\,a^{21}\,c^4\,d\,e^{32}-30720\,a^{20}\,c^5\,d^3\,e^{30}+215040\,a^{19}\,c^6\,d^5\,e^{28}-931840\,a^{18}\,c^7\,d^7\,e^{26}+2795520\,a^{17}\,c^8\,d^9\,e^{24}-6150144\,a^{16}\,c^9\,d^{11}\,e^{22}+10250240\,a^{15}\,c^{10}\,d^{13}\,e^{20}-13178880\,a^{14}\,c^{11}\,d^{15}\,e^{18}+13178880\,a^{13}\,c^{12}\,d^{17}\,e^{16}-10250240\,a^{12}\,c^{13}\,d^{19}\,e^{14}+6150144\,a^{11}\,c^{14}\,d^{21}\,e^{12}-2795520\,a^{10}\,c^{15}\,d^{23}\,e^{10}+931840\,a^9\,c^{16}\,d^{25}\,e^8-215040\,a^8\,c^{17}\,d^{27}\,e^6+30720\,a^7\,c^{18}\,d^{29}\,e^4-2048\,a^6\,c^{19}\,d^{31}\,e^2\right)+1792\,a^{19}\,c^4\,e^{31}-256\,a^5\,c^{18}\,d^{28}\,e^3+11776\,a^6\,c^{17}\,d^{26}\,e^5-119552\,a^7\,c^{16}\,d^{24}\,e^7+609280\,a^8\,c^{15}\,d^{22}\,e^9-1923328\,a^9\,c^{14}\,d^{20}\,e^{11}+4116992\,a^{10}\,c^{13}\,d^{18}\,e^{13}-6243072\,a^{11}\,c^{12}\,d^{16}\,e^{15}+6825984\,a^{12}\,c^{11}\,d^{14}\,e^{17}-5364480\,a^{13}\,c^{10}\,d^{12}\,e^{19}+2945536\,a^{14}\,c^9\,d^{10}\,e^{21}-1044736\,a^{15}\,c^8\,d^8\,e^{23}+183296\,a^{16}\,c^7\,d^6\,e^{25}+13568\,a^{17}\,c^6\,d^4\,e^{27}-12800\,a^{18}\,c^5\,d^2\,e^{29}\right)\right)\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}+7448\,a^{13}\,c^6\,d\,e^{25}+32\,a^2\,c^{17}\,d^{23}\,e^3-72\,a^3\,c^{16}\,d^{21}\,e^5-8240\,a^4\,c^{15}\,d^{19}\,e^7+72120\,a^5\,c^{14}\,d^{17}\,e^9-282240\,a^6\,c^{13}\,d^{15}\,e^{11}+648816\,a^7\,c^{12}\,d^{13}\,e^{13}-962976\,a^8\,c^{11}\,d^{11}\,e^{15}+955440\,a^9\,c^{10}\,d^9\,e^{17}-633120\,a^{10}\,c^9\,d^7\,e^{19}+270040\,a^{11}\,c^8\,d^5\,e^{21}-67248\,a^{12}\,c^7\,d^3\,e^{23}}\right)\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8-63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4+1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{a^9\,c^3}}{64\,\left(a^{13}\,e^{14}-7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}-35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6-21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2-a^6\,c^7\,d^{14}\right)}}\,2{}\mathrm{i}","Not used",1,"- ((2*e^3)/(3*(a*e^2 - c*d^2)) - (20*c*d*e^3*(d + e*x))/(3*(a*e^2 - c*d^2)^2) - (c*e*(d + e*x)^2*(7*a^2*e^4 + 3*c^2*d^4 + 110*a*c*d^2*e^2))/(6*a*(a*e^2 - c*d^2)^3) + (c^2*d*e*(19*a*e^2 + c*d^2)*(d + e*x)^3)/(2*a*(a*e^2 - c*d^2)^3))/((a*e^2 - c*d^2)*(d + e*x)^(3/2) - c*(d + e*x)^(7/2) + 2*c*d*(d + e*x)^(5/2)) - atan((((d + e*x)^(1/2)*(1568*a^16*c^5*e^28 - 128*a^3*c^18*d^26*e^2 + 3040*a^4*c^17*d^24*e^4 - 29120*a^5*c^16*d^22*e^6 + 128128*a^6*c^15*d^20*e^8 - 282560*a^7*c^14*d^18*e^10 + 242016*a^8*c^13*d^16*e^12 + 282240*a^9*c^12*d^14*e^14 - 1059840*a^10*c^11*d^12*e^16 + 1403904*a^11*c^10*d^10*e^18 - 1049440*a^12*c^9*d^8*e^20 + 456512*a^13*c^8*d^6*e^22 - 100480*a^14*c^7*d^4*e^24 + 4160*a^15*c^6*d^2*e^26) - (-(4*a^3*c^6*d^9 - 49*a^3*e^9*(a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(2048*a^21*c^4*d*e^32 - 2048*a^6*c^19*d^31*e^2 + 30720*a^7*c^18*d^29*e^4 - 215040*a^8*c^17*d^27*e^6 + 931840*a^9*c^16*d^25*e^8 - 2795520*a^10*c^15*d^23*e^10 + 6150144*a^11*c^14*d^21*e^12 - 10250240*a^12*c^13*d^19*e^14 + 13178880*a^13*c^12*d^17*e^16 - 13178880*a^14*c^11*d^15*e^18 + 10250240*a^15*c^10*d^13*e^20 - 6150144*a^16*c^9*d^11*e^22 + 2795520*a^17*c^8*d^9*e^24 - 931840*a^18*c^7*d^7*e^26 + 215040*a^19*c^6*d^5*e^28 - 30720*a^20*c^5*d^3*e^30) - 1792*a^19*c^4*e^31 + 256*a^5*c^18*d^28*e^3 - 11776*a^6*c^17*d^26*e^5 + 119552*a^7*c^16*d^24*e^7 - 609280*a^8*c^15*d^22*e^9 + 1923328*a^9*c^14*d^20*e^11 - 4116992*a^10*c^13*d^18*e^13 + 6243072*a^11*c^12*d^16*e^15 - 6825984*a^12*c^11*d^14*e^17 + 5364480*a^13*c^10*d^12*e^19 - 2945536*a^14*c^9*d^10*e^21 + 1044736*a^15*c^8*d^8*e^23 - 183296*a^16*c^7*d^6*e^25 - 13568*a^17*c^6*d^4*e^27 + 12800*a^18*c^5*d^2*e^29))*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*1i + ((d + e*x)^(1/2)*(1568*a^16*c^5*e^28 - 128*a^3*c^18*d^26*e^2 + 3040*a^4*c^17*d^24*e^4 - 29120*a^5*c^16*d^22*e^6 + 128128*a^6*c^15*d^20*e^8 - 282560*a^7*c^14*d^18*e^10 + 242016*a^8*c^13*d^16*e^12 + 282240*a^9*c^12*d^14*e^14 - 1059840*a^10*c^11*d^12*e^16 + 1403904*a^11*c^10*d^10*e^18 - 1049440*a^12*c^9*d^8*e^20 + 456512*a^13*c^8*d^6*e^22 - 100480*a^14*c^7*d^4*e^24 + 4160*a^15*c^6*d^2*e^26) - (-(4*a^3*c^6*d^9 - 49*a^3*e^9*(a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(2048*a^21*c^4*d*e^32 - 2048*a^6*c^19*d^31*e^2 + 30720*a^7*c^18*d^29*e^4 - 215040*a^8*c^17*d^27*e^6 + 931840*a^9*c^16*d^25*e^8 - 2795520*a^10*c^15*d^23*e^10 + 6150144*a^11*c^14*d^21*e^12 - 10250240*a^12*c^13*d^19*e^14 + 13178880*a^13*c^12*d^17*e^16 - 13178880*a^14*c^11*d^15*e^18 + 10250240*a^15*c^10*d^13*e^20 - 6150144*a^16*c^9*d^11*e^22 + 2795520*a^17*c^8*d^9*e^24 - 931840*a^18*c^7*d^7*e^26 + 215040*a^19*c^6*d^5*e^28 - 30720*a^20*c^5*d^3*e^30) + 1792*a^19*c^4*e^31 - 256*a^5*c^18*d^28*e^3 + 11776*a^6*c^17*d^26*e^5 - 119552*a^7*c^16*d^24*e^7 + 609280*a^8*c^15*d^22*e^9 - 1923328*a^9*c^14*d^20*e^11 + 4116992*a^10*c^13*d^18*e^13 - 6243072*a^11*c^12*d^16*e^15 + 6825984*a^12*c^11*d^14*e^17 - 5364480*a^13*c^10*d^12*e^19 + 2945536*a^14*c^9*d^10*e^21 - 1044736*a^15*c^8*d^8*e^23 + 183296*a^16*c^7*d^6*e^25 + 13568*a^17*c^6*d^4*e^27 - 12800*a^18*c^5*d^2*e^29))*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*1i)/(((d + e*x)^(1/2)*(1568*a^16*c^5*e^28 - 128*a^3*c^18*d^26*e^2 + 3040*a^4*c^17*d^24*e^4 - 29120*a^5*c^16*d^22*e^6 + 128128*a^6*c^15*d^20*e^8 - 282560*a^7*c^14*d^18*e^10 + 242016*a^8*c^13*d^16*e^12 + 282240*a^9*c^12*d^14*e^14 - 1059840*a^10*c^11*d^12*e^16 + 1403904*a^11*c^10*d^10*e^18 - 1049440*a^12*c^9*d^8*e^20 + 456512*a^13*c^8*d^6*e^22 - 100480*a^14*c^7*d^4*e^24 + 4160*a^15*c^6*d^2*e^26) - (-(4*a^3*c^6*d^9 - 49*a^3*e^9*(a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(2048*a^21*c^4*d*e^32 - 2048*a^6*c^19*d^31*e^2 + 30720*a^7*c^18*d^29*e^4 - 215040*a^8*c^17*d^27*e^6 + 931840*a^9*c^16*d^25*e^8 - 2795520*a^10*c^15*d^23*e^10 + 6150144*a^11*c^14*d^21*e^12 - 10250240*a^12*c^13*d^19*e^14 + 13178880*a^13*c^12*d^17*e^16 - 13178880*a^14*c^11*d^15*e^18 + 10250240*a^15*c^10*d^13*e^20 - 6150144*a^16*c^9*d^11*e^22 + 2795520*a^17*c^8*d^9*e^24 - 931840*a^18*c^7*d^7*e^26 + 215040*a^19*c^6*d^5*e^28 - 30720*a^20*c^5*d^3*e^30) - 1792*a^19*c^4*e^31 + 256*a^5*c^18*d^28*e^3 - 11776*a^6*c^17*d^26*e^5 + 119552*a^7*c^16*d^24*e^7 - 609280*a^8*c^15*d^22*e^9 + 1923328*a^9*c^14*d^20*e^11 - 4116992*a^10*c^13*d^18*e^13 + 6243072*a^11*c^12*d^16*e^15 - 6825984*a^12*c^11*d^14*e^17 + 5364480*a^13*c^10*d^12*e^19 - 2945536*a^14*c^9*d^10*e^21 + 1044736*a^15*c^8*d^8*e^23 - 183296*a^16*c^7*d^6*e^25 - 13568*a^17*c^6*d^4*e^27 + 12800*a^18*c^5*d^2*e^29))*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2) - ((d + e*x)^(1/2)*(1568*a^16*c^5*e^28 - 128*a^3*c^18*d^26*e^2 + 3040*a^4*c^17*d^24*e^4 - 29120*a^5*c^16*d^22*e^6 + 128128*a^6*c^15*d^20*e^8 - 282560*a^7*c^14*d^18*e^10 + 242016*a^8*c^13*d^16*e^12 + 282240*a^9*c^12*d^14*e^14 - 1059840*a^10*c^11*d^12*e^16 + 1403904*a^11*c^10*d^10*e^18 - 1049440*a^12*c^9*d^8*e^20 + 456512*a^13*c^8*d^6*e^22 - 100480*a^14*c^7*d^4*e^24 + 4160*a^15*c^6*d^2*e^26) - (-(4*a^3*c^6*d^9 - 49*a^3*e^9*(a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(2048*a^21*c^4*d*e^32 - 2048*a^6*c^19*d^31*e^2 + 30720*a^7*c^18*d^29*e^4 - 215040*a^8*c^17*d^27*e^6 + 931840*a^9*c^16*d^25*e^8 - 2795520*a^10*c^15*d^23*e^10 + 6150144*a^11*c^14*d^21*e^12 - 10250240*a^12*c^13*d^19*e^14 + 13178880*a^13*c^12*d^17*e^16 - 13178880*a^14*c^11*d^15*e^18 + 10250240*a^15*c^10*d^13*e^20 - 6150144*a^16*c^9*d^11*e^22 + 2795520*a^17*c^8*d^9*e^24 - 931840*a^18*c^7*d^7*e^26 + 215040*a^19*c^6*d^5*e^28 - 30720*a^20*c^5*d^3*e^30) + 1792*a^19*c^4*e^31 - 256*a^5*c^18*d^28*e^3 + 11776*a^6*c^17*d^26*e^5 - 119552*a^7*c^16*d^24*e^7 + 609280*a^8*c^15*d^22*e^9 - 1923328*a^9*c^14*d^20*e^11 + 4116992*a^10*c^13*d^18*e^13 - 6243072*a^11*c^12*d^16*e^15 + 6825984*a^12*c^11*d^14*e^17 - 5364480*a^13*c^10*d^12*e^19 + 2945536*a^14*c^9*d^10*e^21 - 1044736*a^15*c^8*d^8*e^23 + 183296*a^16*c^7*d^6*e^25 + 13568*a^17*c^6*d^4*e^27 - 12800*a^18*c^5*d^2*e^29))*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2) + 7448*a^13*c^6*d*e^25 + 32*a^2*c^17*d^23*e^3 - 72*a^3*c^16*d^21*e^5 - 8240*a^4*c^15*d^19*e^7 + 72120*a^5*c^14*d^17*e^9 - 282240*a^6*c^13*d^15*e^11 + 648816*a^7*c^12*d^13*e^13 - 962976*a^8*c^11*d^11*e^15 + 955440*a^9*c^10*d^9*e^17 - 633120*a^10*c^9*d^7*e^19 + 270040*a^11*c^8*d^5*e^21 - 67248*a^12*c^7*d^3*e^23))*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*2i - atan((((d + e*x)^(1/2)*(1568*a^16*c^5*e^28 - 128*a^3*c^18*d^26*e^2 + 3040*a^4*c^17*d^24*e^4 - 29120*a^5*c^16*d^22*e^6 + 128128*a^6*c^15*d^20*e^8 - 282560*a^7*c^14*d^18*e^10 + 242016*a^8*c^13*d^16*e^12 + 282240*a^9*c^12*d^14*e^14 - 1059840*a^10*c^11*d^12*e^16 + 1403904*a^11*c^10*d^10*e^18 - 1049440*a^12*c^9*d^8*e^20 + 456512*a^13*c^8*d^6*e^22 - 100480*a^14*c^7*d^4*e^24 + 4160*a^15*c^6*d^2*e^26) - (-(49*a^3*e^9*(a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*((d + e*x)^(1/2)*(-(49*a^3*e^9*(a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(2048*a^21*c^4*d*e^32 - 2048*a^6*c^19*d^31*e^2 + 30720*a^7*c^18*d^29*e^4 - 215040*a^8*c^17*d^27*e^6 + 931840*a^9*c^16*d^25*e^8 - 2795520*a^10*c^15*d^23*e^10 + 6150144*a^11*c^14*d^21*e^12 - 10250240*a^12*c^13*d^19*e^14 + 13178880*a^13*c^12*d^17*e^16 - 13178880*a^14*c^11*d^15*e^18 + 10250240*a^15*c^10*d^13*e^20 - 6150144*a^16*c^9*d^11*e^22 + 2795520*a^17*c^8*d^9*e^24 - 931840*a^18*c^7*d^7*e^26 + 215040*a^19*c^6*d^5*e^28 - 30720*a^20*c^5*d^3*e^30) - 1792*a^19*c^4*e^31 + 256*a^5*c^18*d^28*e^3 - 11776*a^6*c^17*d^26*e^5 + 119552*a^7*c^16*d^24*e^7 - 609280*a^8*c^15*d^22*e^9 + 1923328*a^9*c^14*d^20*e^11 - 4116992*a^10*c^13*d^18*e^13 + 6243072*a^11*c^12*d^16*e^15 - 6825984*a^12*c^11*d^14*e^17 + 5364480*a^13*c^10*d^12*e^19 - 2945536*a^14*c^9*d^10*e^21 + 1044736*a^15*c^8*d^8*e^23 - 183296*a^16*c^7*d^6*e^25 - 13568*a^17*c^6*d^4*e^27 + 12800*a^18*c^5*d^2*e^29))*(-(49*a^3*e^9*(a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*1i + ((d + e*x)^(1/2)*(1568*a^16*c^5*e^28 - 128*a^3*c^18*d^26*e^2 + 3040*a^4*c^17*d^24*e^4 - 29120*a^5*c^16*d^22*e^6 + 128128*a^6*c^15*d^20*e^8 - 282560*a^7*c^14*d^18*e^10 + 242016*a^8*c^13*d^16*e^12 + 282240*a^9*c^12*d^14*e^14 - 1059840*a^10*c^11*d^12*e^16 + 1403904*a^11*c^10*d^10*e^18 - 1049440*a^12*c^9*d^8*e^20 + 456512*a^13*c^8*d^6*e^22 - 100480*a^14*c^7*d^4*e^24 + 4160*a^15*c^6*d^2*e^26) - (-(49*a^3*e^9*(a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*((d + e*x)^(1/2)*(-(49*a^3*e^9*(a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(2048*a^21*c^4*d*e^32 - 2048*a^6*c^19*d^31*e^2 + 30720*a^7*c^18*d^29*e^4 - 215040*a^8*c^17*d^27*e^6 + 931840*a^9*c^16*d^25*e^8 - 2795520*a^10*c^15*d^23*e^10 + 6150144*a^11*c^14*d^21*e^12 - 10250240*a^12*c^13*d^19*e^14 + 13178880*a^13*c^12*d^17*e^16 - 13178880*a^14*c^11*d^15*e^18 + 10250240*a^15*c^10*d^13*e^20 - 6150144*a^16*c^9*d^11*e^22 + 2795520*a^17*c^8*d^9*e^24 - 931840*a^18*c^7*d^7*e^26 + 215040*a^19*c^6*d^5*e^28 - 30720*a^20*c^5*d^3*e^30) + 1792*a^19*c^4*e^31 - 256*a^5*c^18*d^28*e^3 + 11776*a^6*c^17*d^26*e^5 - 119552*a^7*c^16*d^24*e^7 + 609280*a^8*c^15*d^22*e^9 - 1923328*a^9*c^14*d^20*e^11 + 4116992*a^10*c^13*d^18*e^13 - 6243072*a^11*c^12*d^16*e^15 + 6825984*a^12*c^11*d^14*e^17 - 5364480*a^13*c^10*d^12*e^19 + 2945536*a^14*c^9*d^10*e^21 - 1044736*a^15*c^8*d^8*e^23 + 183296*a^16*c^7*d^6*e^25 + 13568*a^17*c^6*d^4*e^27 - 12800*a^18*c^5*d^2*e^29))*(-(49*a^3*e^9*(a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*1i)/(((d + e*x)^(1/2)*(1568*a^16*c^5*e^28 - 128*a^3*c^18*d^26*e^2 + 3040*a^4*c^17*d^24*e^4 - 29120*a^5*c^16*d^22*e^6 + 128128*a^6*c^15*d^20*e^8 - 282560*a^7*c^14*d^18*e^10 + 242016*a^8*c^13*d^16*e^12 + 282240*a^9*c^12*d^14*e^14 - 1059840*a^10*c^11*d^12*e^16 + 1403904*a^11*c^10*d^10*e^18 - 1049440*a^12*c^9*d^8*e^20 + 456512*a^13*c^8*d^6*e^22 - 100480*a^14*c^7*d^4*e^24 + 4160*a^15*c^6*d^2*e^26) - (-(49*a^3*e^9*(a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*((d + e*x)^(1/2)*(-(49*a^3*e^9*(a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(2048*a^21*c^4*d*e^32 - 2048*a^6*c^19*d^31*e^2 + 30720*a^7*c^18*d^29*e^4 - 215040*a^8*c^17*d^27*e^6 + 931840*a^9*c^16*d^25*e^8 - 2795520*a^10*c^15*d^23*e^10 + 6150144*a^11*c^14*d^21*e^12 - 10250240*a^12*c^13*d^19*e^14 + 13178880*a^13*c^12*d^17*e^16 - 13178880*a^14*c^11*d^15*e^18 + 10250240*a^15*c^10*d^13*e^20 - 6150144*a^16*c^9*d^11*e^22 + 2795520*a^17*c^8*d^9*e^24 - 931840*a^18*c^7*d^7*e^26 + 215040*a^19*c^6*d^5*e^28 - 30720*a^20*c^5*d^3*e^30) - 1792*a^19*c^4*e^31 + 256*a^5*c^18*d^28*e^3 - 11776*a^6*c^17*d^26*e^5 + 119552*a^7*c^16*d^24*e^7 - 609280*a^8*c^15*d^22*e^9 + 1923328*a^9*c^14*d^20*e^11 - 4116992*a^10*c^13*d^18*e^13 + 6243072*a^11*c^12*d^16*e^15 - 6825984*a^12*c^11*d^14*e^17 + 5364480*a^13*c^10*d^12*e^19 - 2945536*a^14*c^9*d^10*e^21 + 1044736*a^15*c^8*d^8*e^23 - 183296*a^16*c^7*d^6*e^25 - 13568*a^17*c^6*d^4*e^27 + 12800*a^18*c^5*d^2*e^29))*(-(49*a^3*e^9*(a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2) - ((d + e*x)^(1/2)*(1568*a^16*c^5*e^28 - 128*a^3*c^18*d^26*e^2 + 3040*a^4*c^17*d^24*e^4 - 29120*a^5*c^16*d^22*e^6 + 128128*a^6*c^15*d^20*e^8 - 282560*a^7*c^14*d^18*e^10 + 242016*a^8*c^13*d^16*e^12 + 282240*a^9*c^12*d^14*e^14 - 1059840*a^10*c^11*d^12*e^16 + 1403904*a^11*c^10*d^10*e^18 - 1049440*a^12*c^9*d^8*e^20 + 456512*a^13*c^8*d^6*e^22 - 100480*a^14*c^7*d^4*e^24 + 4160*a^15*c^6*d^2*e^26) - (-(49*a^3*e^9*(a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*((d + e*x)^(1/2)*(-(49*a^3*e^9*(a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(2048*a^21*c^4*d*e^32 - 2048*a^6*c^19*d^31*e^2 + 30720*a^7*c^18*d^29*e^4 - 215040*a^8*c^17*d^27*e^6 + 931840*a^9*c^16*d^25*e^8 - 2795520*a^10*c^15*d^23*e^10 + 6150144*a^11*c^14*d^21*e^12 - 10250240*a^12*c^13*d^19*e^14 + 13178880*a^13*c^12*d^17*e^16 - 13178880*a^14*c^11*d^15*e^18 + 10250240*a^15*c^10*d^13*e^20 - 6150144*a^16*c^9*d^11*e^22 + 2795520*a^17*c^8*d^9*e^24 - 931840*a^18*c^7*d^7*e^26 + 215040*a^19*c^6*d^5*e^28 - 30720*a^20*c^5*d^3*e^30) + 1792*a^19*c^4*e^31 - 256*a^5*c^18*d^28*e^3 + 11776*a^6*c^17*d^26*e^5 - 119552*a^7*c^16*d^24*e^7 + 609280*a^8*c^15*d^22*e^9 - 1923328*a^9*c^14*d^20*e^11 + 4116992*a^10*c^13*d^18*e^13 - 6243072*a^11*c^12*d^16*e^15 + 6825984*a^12*c^11*d^14*e^17 - 5364480*a^13*c^10*d^12*e^19 + 2945536*a^14*c^9*d^10*e^21 - 1044736*a^15*c^8*d^8*e^23 + 183296*a^16*c^7*d^6*e^25 + 13568*a^17*c^6*d^4*e^27 - 12800*a^18*c^5*d^2*e^29))*(-(49*a^3*e^9*(a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2) + 7448*a^13*c^6*d*e^25 + 32*a^2*c^17*d^23*e^3 - 72*a^3*c^16*d^21*e^5 - 8240*a^4*c^15*d^19*e^7 + 72120*a^5*c^14*d^17*e^9 - 282240*a^6*c^13*d^15*e^11 + 648816*a^7*c^12*d^13*e^13 - 962976*a^8*c^11*d^11*e^15 + 955440*a^9*c^10*d^9*e^17 - 633120*a^10*c^9*d^7*e^19 + 270040*a^11*c^8*d^5*e^21 - 67248*a^12*c^7*d^3*e^23))*(-(49*a^3*e^9*(a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 - 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 + 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(a^9*c^3)^(1/2))/(64*(a^13*e^14 - a^6*c^7*d^14 - 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 - 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 - 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*2i","B"
631,1,4192,887,0.870772,"\text{Not used}","int((d + e*x)^(7/2)/(a + c*x^2)^2,x)","\frac{\frac{\left(a^2\,e^5-c^2\,d^4\,e\right)\,\sqrt{d+e\,x}}{2\,a}+\frac{\left(c^2\,d^3\,e-3\,a\,c\,d\,e^3\right)\,{\left(d+e\,x\right)}^{3/2}}{2\,a}}{c^3\,{\left(d+e\,x\right)}^2+c^3\,d^2+a\,c^2\,e^2-2\,c^3\,d\,\left(d+e\,x\right)}+\frac{2\,e^3\,\sqrt{d+e\,x}}{c^2}-\mathrm{atan}\left(\frac{a^2\,e^{10}\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}-\frac{d^7}{16\,a^3\,c}-\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}-\frac{25\,e^7\,\sqrt{-a^9\,c^9}}{64\,a^4\,c^9}+\frac{77\,d^2\,e^5\,\sqrt{-a^9\,c^9}}{32\,a^5\,c^8}+\frac{35\,d^4\,e^3\,\sqrt{-a^9\,c^9}}{64\,a^6\,c^7}}\,50{}\mathrm{i}}{\frac{885\,d^5\,e^9}{2}+\frac{491\,a\,d^3\,e^{11}}{2\,c}+\frac{329\,c\,d^7\,e^7}{2\,a}-\frac{50\,a^2\,d\,e^{13}}{c^2}+\frac{35\,c^2\,d^9\,e^5}{2\,a^2}+\frac{125\,e^{14}\,\sqrt{-a^9\,c^9}}{4\,a^2\,c^7}-\frac{335\,d^2\,e^{12}\,\sqrt{-a^9\,c^9}}{2\,a^3\,c^6}-\frac{204\,d^4\,e^{10}\,\sqrt{-a^9\,c^9}}{a^4\,c^5}+\frac{7\,d^6\,e^8\,\sqrt{-a^9\,c^9}}{2\,a^5\,c^4}+\frac{35\,d^8\,e^6\,\sqrt{-a^9\,c^9}}{4\,a^6\,c^3}}+\frac{d^3\,e^7\,\sqrt{-a^9\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}-\frac{d^7}{16\,a^3\,c}-\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}-\frac{25\,e^7\,\sqrt{-a^9\,c^9}}{64\,a^4\,c^9}+\frac{77\,d^2\,e^5\,\sqrt{-a^9\,c^9}}{32\,a^5\,c^8}+\frac{35\,d^4\,e^3\,\sqrt{-a^9\,c^9}}{64\,a^6\,c^7}}\,308{}\mathrm{i}}{\frac{35\,a^2\,c^5\,d^9\,e^5}{2}+\frac{329\,a^3\,c^4\,d^7\,e^7}{2}+\frac{885\,a^4\,c^3\,d^5\,e^9}{2}+\frac{491\,a^5\,c^2\,d^3\,e^{11}}{2}-50\,a^6\,c\,d\,e^{13}+\frac{125\,a^2\,e^{14}\,\sqrt{-a^9\,c^9}}{4\,c^4}+\frac{35\,d^8\,e^6\,\sqrt{-a^9\,c^9}}{4\,a^2}-\frac{204\,d^4\,e^{10}\,\sqrt{-a^9\,c^9}}{c^2}-\frac{335\,a\,d^2\,e^{12}\,\sqrt{-a^9\,c^9}}{2\,c^3}+\frac{7\,d^6\,e^8\,\sqrt{-a^9\,c^9}}{2\,a\,c}}+\frac{d^5\,e^5\,\sqrt{-a^9\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}-\frac{d^7}{16\,a^3\,c}-\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}-\frac{25\,e^7\,\sqrt{-a^9\,c^9}}{64\,a^4\,c^9}+\frac{77\,d^2\,e^5\,\sqrt{-a^9\,c^9}}{32\,a^5\,c^8}+\frac{35\,d^4\,e^3\,\sqrt{-a^9\,c^9}}{64\,a^6\,c^7}}\,70{}\mathrm{i}}{\frac{491\,a^6\,c\,d^3\,e^{11}}{2}-50\,a^7\,d\,e^{13}+\frac{35\,a^3\,c^4\,d^9\,e^5}{2}+\frac{329\,a^4\,c^3\,d^7\,e^7}{2}+\frac{885\,a^5\,c^2\,d^5\,e^9}{2}+\frac{125\,a^3\,e^{14}\,\sqrt{-a^9\,c^9}}{4\,c^5}+\frac{7\,d^6\,e^8\,\sqrt{-a^9\,c^9}}{2\,c^2}-\frac{204\,a\,d^4\,e^{10}\,\sqrt{-a^9\,c^9}}{c^3}+\frac{35\,d^8\,e^6\,\sqrt{-a^9\,c^9}}{4\,a\,c}-\frac{335\,a^2\,d^2\,e^{12}\,\sqrt{-a^9\,c^9}}{2\,c^4}}-\frac{a\,d^2\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}-\frac{d^7}{16\,a^3\,c}-\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}-\frac{25\,e^7\,\sqrt{-a^9\,c^9}}{64\,a^4\,c^9}+\frac{77\,d^2\,e^5\,\sqrt{-a^9\,c^9}}{32\,a^5\,c^8}+\frac{35\,d^4\,e^3\,\sqrt{-a^9\,c^9}}{64\,a^6\,c^7}}\,308{}\mathrm{i}}{\frac{329\,d^7\,e^7}{2\,a}+\frac{885\,d^5\,e^9}{2\,c}+\frac{491\,a\,d^3\,e^{11}}{2\,c^2}+\frac{35\,c\,d^9\,e^5}{2\,a^2}-\frac{50\,a^2\,d\,e^{13}}{c^3}+\frac{125\,e^{14}\,\sqrt{-a^9\,c^9}}{4\,a^2\,c^8}-\frac{335\,d^2\,e^{12}\,\sqrt{-a^9\,c^9}}{2\,a^3\,c^7}-\frac{204\,d^4\,e^{10}\,\sqrt{-a^9\,c^9}}{a^4\,c^6}+\frac{7\,d^6\,e^8\,\sqrt{-a^9\,c^9}}{2\,a^5\,c^5}+\frac{35\,d^8\,e^6\,\sqrt{-a^9\,c^9}}{4\,a^6\,c^4}}-\frac{c\,d^4\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}-\frac{d^7}{16\,a^3\,c}-\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}-\frac{25\,e^7\,\sqrt{-a^9\,c^9}}{64\,a^4\,c^9}+\frac{77\,d^2\,e^5\,\sqrt{-a^9\,c^9}}{32\,a^5\,c^8}+\frac{35\,d^4\,e^3\,\sqrt{-a^9\,c^9}}{64\,a^6\,c^7}}\,70{}\mathrm{i}}{\frac{329\,d^7\,e^7}{2\,a}+\frac{885\,d^5\,e^9}{2\,c}+\frac{491\,a\,d^3\,e^{11}}{2\,c^2}+\frac{35\,c\,d^9\,e^5}{2\,a^2}-\frac{50\,a^2\,d\,e^{13}}{c^3}+\frac{125\,e^{14}\,\sqrt{-a^9\,c^9}}{4\,a^2\,c^8}-\frac{335\,d^2\,e^{12}\,\sqrt{-a^9\,c^9}}{2\,a^3\,c^7}-\frac{204\,d^4\,e^{10}\,\sqrt{-a^9\,c^9}}{a^4\,c^6}+\frac{7\,d^6\,e^8\,\sqrt{-a^9\,c^9}}{2\,a^5\,c^5}+\frac{35\,d^8\,e^6\,\sqrt{-a^9\,c^9}}{4\,a^6\,c^4}}-\frac{d\,e^9\,\sqrt{-a^9\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}-\frac{d^7}{16\,a^3\,c}-\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}-\frac{25\,e^7\,\sqrt{-a^9\,c^9}}{64\,a^4\,c^9}+\frac{77\,d^2\,e^5\,\sqrt{-a^9\,c^9}}{32\,a^5\,c^8}+\frac{35\,d^4\,e^3\,\sqrt{-a^9\,c^9}}{64\,a^6\,c^7}}\,50{}\mathrm{i}}{\frac{35\,a\,c^6\,d^9\,e^5}{2}-50\,a^5\,c^2\,d\,e^{13}+\frac{329\,a^2\,c^5\,d^7\,e^7}{2}+\frac{885\,a^3\,c^4\,d^5\,e^9}{2}+\frac{491\,a^4\,c^3\,d^3\,e^{11}}{2}+\frac{125\,a\,e^{14}\,\sqrt{-a^9\,c^9}}{4\,c^3}+\frac{7\,d^6\,e^8\,\sqrt{-a^9\,c^9}}{2\,a^2}-\frac{335\,d^2\,e^{12}\,\sqrt{-a^9\,c^9}}{2\,c^2}+\frac{35\,c\,d^8\,e^6\,\sqrt{-a^9\,c^9}}{4\,a^3}-\frac{204\,d^4\,e^{10}\,\sqrt{-a^9\,c^9}}{a\,c}}\right)\,\sqrt{-\frac{25\,a^2\,e^7\,\sqrt{-a^9\,c^9}+4\,a^3\,c^8\,d^7-105\,a^6\,c^5\,d\,e^6+35\,a^4\,c^7\,d^5\,e^2+70\,a^5\,c^6\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c^9}-154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c^9}}{64\,a^6\,c^9}}\,2{}\mathrm{i}+\mathrm{atan}\left(-\frac{a^2\,e^{10}\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}-\frac{d^7}{16\,a^3\,c}-\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}+\frac{25\,e^7\,\sqrt{-a^9\,c^9}}{64\,a^4\,c^9}-\frac{77\,d^2\,e^5\,\sqrt{-a^9\,c^9}}{32\,a^5\,c^8}-\frac{35\,d^4\,e^3\,\sqrt{-a^9\,c^9}}{64\,a^6\,c^7}}\,50{}\mathrm{i}}{\frac{885\,d^5\,e^9}{2}+\frac{491\,a\,d^3\,e^{11}}{2\,c}+\frac{329\,c\,d^7\,e^7}{2\,a}-\frac{50\,a^2\,d\,e^{13}}{c^2}+\frac{35\,c^2\,d^9\,e^5}{2\,a^2}-\frac{125\,e^{14}\,\sqrt{-a^9\,c^9}}{4\,a^2\,c^7}+\frac{335\,d^2\,e^{12}\,\sqrt{-a^9\,c^9}}{2\,a^3\,c^6}+\frac{204\,d^4\,e^{10}\,\sqrt{-a^9\,c^9}}{a^4\,c^5}-\frac{7\,d^6\,e^8\,\sqrt{-a^9\,c^9}}{2\,a^5\,c^4}-\frac{35\,d^8\,e^6\,\sqrt{-a^9\,c^9}}{4\,a^6\,c^3}}+\frac{d^3\,e^7\,\sqrt{-a^9\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}-\frac{d^7}{16\,a^3\,c}-\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}+\frac{25\,e^7\,\sqrt{-a^9\,c^9}}{64\,a^4\,c^9}-\frac{77\,d^2\,e^5\,\sqrt{-a^9\,c^9}}{32\,a^5\,c^8}-\frac{35\,d^4\,e^3\,\sqrt{-a^9\,c^9}}{64\,a^6\,c^7}}\,308{}\mathrm{i}}{\frac{35\,a^2\,c^5\,d^9\,e^5}{2}+\frac{329\,a^3\,c^4\,d^7\,e^7}{2}+\frac{885\,a^4\,c^3\,d^5\,e^9}{2}+\frac{491\,a^5\,c^2\,d^3\,e^{11}}{2}-50\,a^6\,c\,d\,e^{13}-\frac{125\,a^2\,e^{14}\,\sqrt{-a^9\,c^9}}{4\,c^4}-\frac{35\,d^8\,e^6\,\sqrt{-a^9\,c^9}}{4\,a^2}+\frac{204\,d^4\,e^{10}\,\sqrt{-a^9\,c^9}}{c^2}+\frac{335\,a\,d^2\,e^{12}\,\sqrt{-a^9\,c^9}}{2\,c^3}-\frac{7\,d^6\,e^8\,\sqrt{-a^9\,c^9}}{2\,a\,c}}+\frac{d^5\,e^5\,\sqrt{-a^9\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}-\frac{d^7}{16\,a^3\,c}-\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}+\frac{25\,e^7\,\sqrt{-a^9\,c^9}}{64\,a^4\,c^9}-\frac{77\,d^2\,e^5\,\sqrt{-a^9\,c^9}}{32\,a^5\,c^8}-\frac{35\,d^4\,e^3\,\sqrt{-a^9\,c^9}}{64\,a^6\,c^7}}\,70{}\mathrm{i}}{\frac{491\,a^6\,c\,d^3\,e^{11}}{2}-50\,a^7\,d\,e^{13}+\frac{35\,a^3\,c^4\,d^9\,e^5}{2}+\frac{329\,a^4\,c^3\,d^7\,e^7}{2}+\frac{885\,a^5\,c^2\,d^5\,e^9}{2}-\frac{125\,a^3\,e^{14}\,\sqrt{-a^9\,c^9}}{4\,c^5}-\frac{7\,d^6\,e^8\,\sqrt{-a^9\,c^9}}{2\,c^2}+\frac{204\,a\,d^4\,e^{10}\,\sqrt{-a^9\,c^9}}{c^3}-\frac{35\,d^8\,e^6\,\sqrt{-a^9\,c^9}}{4\,a\,c}+\frac{335\,a^2\,d^2\,e^{12}\,\sqrt{-a^9\,c^9}}{2\,c^4}}+\frac{a\,d^2\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}-\frac{d^7}{16\,a^3\,c}-\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}+\frac{25\,e^7\,\sqrt{-a^9\,c^9}}{64\,a^4\,c^9}-\frac{77\,d^2\,e^5\,\sqrt{-a^9\,c^9}}{32\,a^5\,c^8}-\frac{35\,d^4\,e^3\,\sqrt{-a^9\,c^9}}{64\,a^6\,c^7}}\,308{}\mathrm{i}}{\frac{329\,d^7\,e^7}{2\,a}+\frac{885\,d^5\,e^9}{2\,c}+\frac{491\,a\,d^3\,e^{11}}{2\,c^2}+\frac{35\,c\,d^9\,e^5}{2\,a^2}-\frac{50\,a^2\,d\,e^{13}}{c^3}-\frac{125\,e^{14}\,\sqrt{-a^9\,c^9}}{4\,a^2\,c^8}+\frac{335\,d^2\,e^{12}\,\sqrt{-a^9\,c^9}}{2\,a^3\,c^7}+\frac{204\,d^4\,e^{10}\,\sqrt{-a^9\,c^9}}{a^4\,c^6}-\frac{7\,d^6\,e^8\,\sqrt{-a^9\,c^9}}{2\,a^5\,c^5}-\frac{35\,d^8\,e^6\,\sqrt{-a^9\,c^9}}{4\,a^6\,c^4}}+\frac{c\,d^4\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}-\frac{d^7}{16\,a^3\,c}-\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}+\frac{25\,e^7\,\sqrt{-a^9\,c^9}}{64\,a^4\,c^9}-\frac{77\,d^2\,e^5\,\sqrt{-a^9\,c^9}}{32\,a^5\,c^8}-\frac{35\,d^4\,e^3\,\sqrt{-a^9\,c^9}}{64\,a^6\,c^7}}\,70{}\mathrm{i}}{\frac{329\,d^7\,e^7}{2\,a}+\frac{885\,d^5\,e^9}{2\,c}+\frac{491\,a\,d^3\,e^{11}}{2\,c^2}+\frac{35\,c\,d^9\,e^5}{2\,a^2}-\frac{50\,a^2\,d\,e^{13}}{c^3}-\frac{125\,e^{14}\,\sqrt{-a^9\,c^9}}{4\,a^2\,c^8}+\frac{335\,d^2\,e^{12}\,\sqrt{-a^9\,c^9}}{2\,a^3\,c^7}+\frac{204\,d^4\,e^{10}\,\sqrt{-a^9\,c^9}}{a^4\,c^6}-\frac{7\,d^6\,e^8\,\sqrt{-a^9\,c^9}}{2\,a^5\,c^5}-\frac{35\,d^8\,e^6\,\sqrt{-a^9\,c^9}}{4\,a^6\,c^4}}-\frac{d\,e^9\,\sqrt{-a^9\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{105\,d\,e^6}{64\,c^4}-\frac{d^7}{16\,a^3\,c}-\frac{35\,d^3\,e^4}{32\,a\,c^3}-\frac{35\,d^5\,e^2}{64\,a^2\,c^2}+\frac{25\,e^7\,\sqrt{-a^9\,c^9}}{64\,a^4\,c^9}-\frac{77\,d^2\,e^5\,\sqrt{-a^9\,c^9}}{32\,a^5\,c^8}-\frac{35\,d^4\,e^3\,\sqrt{-a^9\,c^9}}{64\,a^6\,c^7}}\,50{}\mathrm{i}}{\frac{35\,a\,c^6\,d^9\,e^5}{2}-50\,a^5\,c^2\,d\,e^{13}+\frac{329\,a^2\,c^5\,d^7\,e^7}{2}+\frac{885\,a^3\,c^4\,d^5\,e^9}{2}+\frac{491\,a^4\,c^3\,d^3\,e^{11}}{2}-\frac{125\,a\,e^{14}\,\sqrt{-a^9\,c^9}}{4\,c^3}-\frac{7\,d^6\,e^8\,\sqrt{-a^9\,c^9}}{2\,a^2}+\frac{335\,d^2\,e^{12}\,\sqrt{-a^9\,c^9}}{2\,c^2}-\frac{35\,c\,d^8\,e^6\,\sqrt{-a^9\,c^9}}{4\,a^3}+\frac{204\,d^4\,e^{10}\,\sqrt{-a^9\,c^9}}{a\,c}}\right)\,\sqrt{-\frac{4\,a^3\,c^8\,d^7-25\,a^2\,e^7\,\sqrt{-a^9\,c^9}-105\,a^6\,c^5\,d\,e^6+35\,a^4\,c^7\,d^5\,e^2+70\,a^5\,c^6\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c^9}+154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c^9}}{64\,a^6\,c^9}}\,2{}\mathrm{i}","Not used",1,"(((a^2*e^5 - c^2*d^4*e)*(d + e*x)^(1/2))/(2*a) + ((c^2*d^3*e - 3*a*c*d*e^3)*(d + e*x)^(3/2))/(2*a))/(c^3*(d + e*x)^2 + c^3*d^2 + a*c^2*e^2 - 2*c^3*d*(d + e*x)) - atan((a^2*e^10*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) - d^7/(16*a^3*c) - (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) - (25*e^7*(-a^9*c^9)^(1/2))/(64*a^4*c^9) + (77*d^2*e^5*(-a^9*c^9)^(1/2))/(32*a^5*c^8) + (35*d^4*e^3*(-a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*50i)/((885*d^5*e^9)/2 + (491*a*d^3*e^11)/(2*c) + (329*c*d^7*e^7)/(2*a) - (50*a^2*d*e^13)/c^2 + (35*c^2*d^9*e^5)/(2*a^2) + (125*e^14*(-a^9*c^9)^(1/2))/(4*a^2*c^7) - (335*d^2*e^12*(-a^9*c^9)^(1/2))/(2*a^3*c^6) - (204*d^4*e^10*(-a^9*c^9)^(1/2))/(a^4*c^5) + (7*d^6*e^8*(-a^9*c^9)^(1/2))/(2*a^5*c^4) + (35*d^8*e^6*(-a^9*c^9)^(1/2))/(4*a^6*c^3)) + (d^3*e^7*(-a^9*c^9)^(1/2)*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) - d^7/(16*a^3*c) - (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) - (25*e^7*(-a^9*c^9)^(1/2))/(64*a^4*c^9) + (77*d^2*e^5*(-a^9*c^9)^(1/2))/(32*a^5*c^8) + (35*d^4*e^3*(-a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*308i)/((35*a^2*c^5*d^9*e^5)/2 + (329*a^3*c^4*d^7*e^7)/2 + (885*a^4*c^3*d^5*e^9)/2 + (491*a^5*c^2*d^3*e^11)/2 - 50*a^6*c*d*e^13 + (125*a^2*e^14*(-a^9*c^9)^(1/2))/(4*c^4) + (35*d^8*e^6*(-a^9*c^9)^(1/2))/(4*a^2) - (204*d^4*e^10*(-a^9*c^9)^(1/2))/c^2 - (335*a*d^2*e^12*(-a^9*c^9)^(1/2))/(2*c^3) + (7*d^6*e^8*(-a^9*c^9)^(1/2))/(2*a*c)) + (d^5*e^5*(-a^9*c^9)^(1/2)*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) - d^7/(16*a^3*c) - (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) - (25*e^7*(-a^9*c^9)^(1/2))/(64*a^4*c^9) + (77*d^2*e^5*(-a^9*c^9)^(1/2))/(32*a^5*c^8) + (35*d^4*e^3*(-a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*70i)/((491*a^6*c*d^3*e^11)/2 - 50*a^7*d*e^13 + (35*a^3*c^4*d^9*e^5)/2 + (329*a^4*c^3*d^7*e^7)/2 + (885*a^5*c^2*d^5*e^9)/2 + (125*a^3*e^14*(-a^9*c^9)^(1/2))/(4*c^5) + (7*d^6*e^8*(-a^9*c^9)^(1/2))/(2*c^2) - (204*a*d^4*e^10*(-a^9*c^9)^(1/2))/c^3 + (35*d^8*e^6*(-a^9*c^9)^(1/2))/(4*a*c) - (335*a^2*d^2*e^12*(-a^9*c^9)^(1/2))/(2*c^4)) - (a*d^2*e^8*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) - d^7/(16*a^3*c) - (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) - (25*e^7*(-a^9*c^9)^(1/2))/(64*a^4*c^9) + (77*d^2*e^5*(-a^9*c^9)^(1/2))/(32*a^5*c^8) + (35*d^4*e^3*(-a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*308i)/((329*d^7*e^7)/(2*a) + (885*d^5*e^9)/(2*c) + (491*a*d^3*e^11)/(2*c^2) + (35*c*d^9*e^5)/(2*a^2) - (50*a^2*d*e^13)/c^3 + (125*e^14*(-a^9*c^9)^(1/2))/(4*a^2*c^8) - (335*d^2*e^12*(-a^9*c^9)^(1/2))/(2*a^3*c^7) - (204*d^4*e^10*(-a^9*c^9)^(1/2))/(a^4*c^6) + (7*d^6*e^8*(-a^9*c^9)^(1/2))/(2*a^5*c^5) + (35*d^8*e^6*(-a^9*c^9)^(1/2))/(4*a^6*c^4)) - (c*d^4*e^6*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) - d^7/(16*a^3*c) - (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) - (25*e^7*(-a^9*c^9)^(1/2))/(64*a^4*c^9) + (77*d^2*e^5*(-a^9*c^9)^(1/2))/(32*a^5*c^8) + (35*d^4*e^3*(-a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*70i)/((329*d^7*e^7)/(2*a) + (885*d^5*e^9)/(2*c) + (491*a*d^3*e^11)/(2*c^2) + (35*c*d^9*e^5)/(2*a^2) - (50*a^2*d*e^13)/c^3 + (125*e^14*(-a^9*c^9)^(1/2))/(4*a^2*c^8) - (335*d^2*e^12*(-a^9*c^9)^(1/2))/(2*a^3*c^7) - (204*d^4*e^10*(-a^9*c^9)^(1/2))/(a^4*c^6) + (7*d^6*e^8*(-a^9*c^9)^(1/2))/(2*a^5*c^5) + (35*d^8*e^6*(-a^9*c^9)^(1/2))/(4*a^6*c^4)) - (d*e^9*(-a^9*c^9)^(1/2)*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) - d^7/(16*a^3*c) - (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) - (25*e^7*(-a^9*c^9)^(1/2))/(64*a^4*c^9) + (77*d^2*e^5*(-a^9*c^9)^(1/2))/(32*a^5*c^8) + (35*d^4*e^3*(-a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*50i)/((35*a*c^6*d^9*e^5)/2 - 50*a^5*c^2*d*e^13 + (329*a^2*c^5*d^7*e^7)/2 + (885*a^3*c^4*d^5*e^9)/2 + (491*a^4*c^3*d^3*e^11)/2 + (125*a*e^14*(-a^9*c^9)^(1/2))/(4*c^3) + (7*d^6*e^8*(-a^9*c^9)^(1/2))/(2*a^2) - (335*d^2*e^12*(-a^9*c^9)^(1/2))/(2*c^2) + (35*c*d^8*e^6*(-a^9*c^9)^(1/2))/(4*a^3) - (204*d^4*e^10*(-a^9*c^9)^(1/2))/(a*c)))*(-(25*a^2*e^7*(-a^9*c^9)^(1/2) + 4*a^3*c^8*d^7 - 105*a^6*c^5*d*e^6 + 35*a^4*c^7*d^5*e^2 + 70*a^5*c^6*d^3*e^4 - 35*c^2*d^4*e^3*(-a^9*c^9)^(1/2) - 154*a*c*d^2*e^5*(-a^9*c^9)^(1/2))/(64*a^6*c^9))^(1/2)*2i + atan((d^3*e^7*(-a^9*c^9)^(1/2)*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) - d^7/(16*a^3*c) - (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) + (25*e^7*(-a^9*c^9)^(1/2))/(64*a^4*c^9) - (77*d^2*e^5*(-a^9*c^9)^(1/2))/(32*a^5*c^8) - (35*d^4*e^3*(-a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*308i)/((35*a^2*c^5*d^9*e^5)/2 + (329*a^3*c^4*d^7*e^7)/2 + (885*a^4*c^3*d^5*e^9)/2 + (491*a^5*c^2*d^3*e^11)/2 - 50*a^6*c*d*e^13 - (125*a^2*e^14*(-a^9*c^9)^(1/2))/(4*c^4) - (35*d^8*e^6*(-a^9*c^9)^(1/2))/(4*a^2) + (204*d^4*e^10*(-a^9*c^9)^(1/2))/c^2 + (335*a*d^2*e^12*(-a^9*c^9)^(1/2))/(2*c^3) - (7*d^6*e^8*(-a^9*c^9)^(1/2))/(2*a*c)) - (a^2*e^10*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) - d^7/(16*a^3*c) - (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) + (25*e^7*(-a^9*c^9)^(1/2))/(64*a^4*c^9) - (77*d^2*e^5*(-a^9*c^9)^(1/2))/(32*a^5*c^8) - (35*d^4*e^3*(-a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*50i)/((885*d^5*e^9)/2 + (491*a*d^3*e^11)/(2*c) + (329*c*d^7*e^7)/(2*a) - (50*a^2*d*e^13)/c^2 + (35*c^2*d^9*e^5)/(2*a^2) - (125*e^14*(-a^9*c^9)^(1/2))/(4*a^2*c^7) + (335*d^2*e^12*(-a^9*c^9)^(1/2))/(2*a^3*c^6) + (204*d^4*e^10*(-a^9*c^9)^(1/2))/(a^4*c^5) - (7*d^6*e^8*(-a^9*c^9)^(1/2))/(2*a^5*c^4) - (35*d^8*e^6*(-a^9*c^9)^(1/2))/(4*a^6*c^3)) + (d^5*e^5*(-a^9*c^9)^(1/2)*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) - d^7/(16*a^3*c) - (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) + (25*e^7*(-a^9*c^9)^(1/2))/(64*a^4*c^9) - (77*d^2*e^5*(-a^9*c^9)^(1/2))/(32*a^5*c^8) - (35*d^4*e^3*(-a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*70i)/((491*a^6*c*d^3*e^11)/2 - 50*a^7*d*e^13 + (35*a^3*c^4*d^9*e^5)/2 + (329*a^4*c^3*d^7*e^7)/2 + (885*a^5*c^2*d^5*e^9)/2 - (125*a^3*e^14*(-a^9*c^9)^(1/2))/(4*c^5) - (7*d^6*e^8*(-a^9*c^9)^(1/2))/(2*c^2) + (204*a*d^4*e^10*(-a^9*c^9)^(1/2))/c^3 - (35*d^8*e^6*(-a^9*c^9)^(1/2))/(4*a*c) + (335*a^2*d^2*e^12*(-a^9*c^9)^(1/2))/(2*c^4)) + (a*d^2*e^8*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) - d^7/(16*a^3*c) - (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) + (25*e^7*(-a^9*c^9)^(1/2))/(64*a^4*c^9) - (77*d^2*e^5*(-a^9*c^9)^(1/2))/(32*a^5*c^8) - (35*d^4*e^3*(-a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*308i)/((329*d^7*e^7)/(2*a) + (885*d^5*e^9)/(2*c) + (491*a*d^3*e^11)/(2*c^2) + (35*c*d^9*e^5)/(2*a^2) - (50*a^2*d*e^13)/c^3 - (125*e^14*(-a^9*c^9)^(1/2))/(4*a^2*c^8) + (335*d^2*e^12*(-a^9*c^9)^(1/2))/(2*a^3*c^7) + (204*d^4*e^10*(-a^9*c^9)^(1/2))/(a^4*c^6) - (7*d^6*e^8*(-a^9*c^9)^(1/2))/(2*a^5*c^5) - (35*d^8*e^6*(-a^9*c^9)^(1/2))/(4*a^6*c^4)) + (c*d^4*e^6*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) - d^7/(16*a^3*c) - (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) + (25*e^7*(-a^9*c^9)^(1/2))/(64*a^4*c^9) - (77*d^2*e^5*(-a^9*c^9)^(1/2))/(32*a^5*c^8) - (35*d^4*e^3*(-a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*70i)/((329*d^7*e^7)/(2*a) + (885*d^5*e^9)/(2*c) + (491*a*d^3*e^11)/(2*c^2) + (35*c*d^9*e^5)/(2*a^2) - (50*a^2*d*e^13)/c^3 - (125*e^14*(-a^9*c^9)^(1/2))/(4*a^2*c^8) + (335*d^2*e^12*(-a^9*c^9)^(1/2))/(2*a^3*c^7) + (204*d^4*e^10*(-a^9*c^9)^(1/2))/(a^4*c^6) - (7*d^6*e^8*(-a^9*c^9)^(1/2))/(2*a^5*c^5) - (35*d^8*e^6*(-a^9*c^9)^(1/2))/(4*a^6*c^4)) - (d*e^9*(-a^9*c^9)^(1/2)*(d + e*x)^(1/2)*((105*d*e^6)/(64*c^4) - d^7/(16*a^3*c) - (35*d^3*e^4)/(32*a*c^3) - (35*d^5*e^2)/(64*a^2*c^2) + (25*e^7*(-a^9*c^9)^(1/2))/(64*a^4*c^9) - (77*d^2*e^5*(-a^9*c^9)^(1/2))/(32*a^5*c^8) - (35*d^4*e^3*(-a^9*c^9)^(1/2))/(64*a^6*c^7))^(1/2)*50i)/((35*a*c^6*d^9*e^5)/2 - 50*a^5*c^2*d*e^13 + (329*a^2*c^5*d^7*e^7)/2 + (885*a^3*c^4*d^5*e^9)/2 + (491*a^4*c^3*d^3*e^11)/2 - (125*a*e^14*(-a^9*c^9)^(1/2))/(4*c^3) - (7*d^6*e^8*(-a^9*c^9)^(1/2))/(2*a^2) + (335*d^2*e^12*(-a^9*c^9)^(1/2))/(2*c^2) - (35*c*d^8*e^6*(-a^9*c^9)^(1/2))/(4*a^3) + (204*d^4*e^10*(-a^9*c^9)^(1/2))/(a*c)))*(-(4*a^3*c^8*d^7 - 25*a^2*e^7*(-a^9*c^9)^(1/2) - 105*a^6*c^5*d*e^6 + 35*a^4*c^7*d^5*e^2 + 70*a^5*c^6*d^3*e^4 + 35*c^2*d^4*e^3*(-a^9*c^9)^(1/2) + 154*a*c*d^2*e^5*(-a^9*c^9)^(1/2))/(64*a^6*c^9))^(1/2)*2i + (2*e^3*(d + e*x)^(1/2))/c^2","B"
632,1,2031,811,0.828176,"\text{Not used}","int((d + e*x)^(5/2)/(a + c*x^2)^2,x)","-\frac{\frac{\left(a\,e^3-c\,d^2\,e\right)\,{\left(d+e\,x\right)}^{3/2}}{2\,a\,c}+\frac{\left(c\,d^3\,e+a\,d\,e^3\right)\,\sqrt{d+e\,x}}{2\,a\,c}}{c\,{\left(d+e\,x\right)}^2+a\,e^2+c\,d^2-2\,c\,d\,\left(d+e\,x\right)}-2\,\mathrm{atanh}\left(\frac{18\,a\,e^8\,\sqrt{d+e\,x}\,\sqrt{-\frac{d^5}{16\,a^3\,c}-\frac{15\,d\,e^4}{64\,a\,c^3}-\frac{15\,d^3\,e^2}{64\,a^2\,c^2}-\frac{9\,e^5\,\sqrt{-a^9\,c^7}}{64\,a^5\,c^7}-\frac{5\,d^2\,e^3\,\sqrt{-a^9\,c^7}}{64\,a^6\,c^6}}}{\frac{27\,a\,e^{11}}{4\,c^2}+\frac{43\,d^4\,e^7}{4\,a}+\frac{15\,d^2\,e^9}{c}+\frac{5\,c\,d^6\,e^5}{2\,a^2}-\frac{9\,d\,e^{10}\,\sqrt{-a^9\,c^7}}{4\,a^4\,c^5}-\frac{7\,d^3\,e^8\,\sqrt{-a^9\,c^7}}{2\,a^5\,c^4}-\frac{5\,d^5\,e^6\,\sqrt{-a^9\,c^7}}{4\,a^6\,c^3}}+\frac{10\,c\,d^2\,e^6\,\sqrt{d+e\,x}\,\sqrt{-\frac{d^5}{16\,a^3\,c}-\frac{15\,d\,e^4}{64\,a\,c^3}-\frac{15\,d^3\,e^2}{64\,a^2\,c^2}-\frac{9\,e^5\,\sqrt{-a^9\,c^7}}{64\,a^5\,c^7}-\frac{5\,d^2\,e^3\,\sqrt{-a^9\,c^7}}{64\,a^6\,c^6}}}{\frac{27\,a\,e^{11}}{4\,c^2}+\frac{43\,d^4\,e^7}{4\,a}+\frac{15\,d^2\,e^9}{c}+\frac{5\,c\,d^6\,e^5}{2\,a^2}-\frac{9\,d\,e^{10}\,\sqrt{-a^9\,c^7}}{4\,a^4\,c^5}-\frac{7\,d^3\,e^8\,\sqrt{-a^9\,c^7}}{2\,a^5\,c^4}-\frac{5\,d^5\,e^6\,\sqrt{-a^9\,c^7}}{4\,a^6\,c^3}}+\frac{18\,d\,e^7\,\sqrt{-a^9\,c^7}\,\sqrt{d+e\,x}\,\sqrt{-\frac{d^5}{16\,a^3\,c}-\frac{15\,d\,e^4}{64\,a\,c^3}-\frac{15\,d^3\,e^2}{64\,a^2\,c^2}-\frac{9\,e^5\,\sqrt{-a^9\,c^7}}{64\,a^5\,c^7}-\frac{5\,d^2\,e^3\,\sqrt{-a^9\,c^7}}{64\,a^6\,c^6}}}{\frac{27\,a^5\,c\,e^{11}}{4}+\frac{5\,a^2\,c^4\,d^6\,e^5}{2}+\frac{43\,a^3\,c^3\,d^4\,e^7}{4}+15\,a^4\,c^2\,d^2\,e^9-\frac{9\,d\,e^{10}\,\sqrt{-a^9\,c^7}}{4\,c^2}-\frac{5\,d^5\,e^6\,\sqrt{-a^9\,c^7}}{4\,a^2}-\frac{7\,d^3\,e^8\,\sqrt{-a^9\,c^7}}{2\,a\,c}}+\frac{10\,d^3\,e^5\,\sqrt{-a^9\,c^7}\,\sqrt{d+e\,x}\,\sqrt{-\frac{d^5}{16\,a^3\,c}-\frac{15\,d\,e^4}{64\,a\,c^3}-\frac{15\,d^3\,e^2}{64\,a^2\,c^2}-\frac{9\,e^5\,\sqrt{-a^9\,c^7}}{64\,a^5\,c^7}-\frac{5\,d^2\,e^3\,\sqrt{-a^9\,c^7}}{64\,a^6\,c^6}}}{\frac{27\,a^6\,e^{11}}{4}+15\,a^5\,c\,d^2\,e^9+\frac{5\,a^3\,c^3\,d^6\,e^5}{2}+\frac{43\,a^4\,c^2\,d^4\,e^7}{4}-\frac{7\,d^3\,e^8\,\sqrt{-a^9\,c^7}}{2\,c^2}-\frac{5\,d^5\,e^6\,\sqrt{-a^9\,c^7}}{4\,a\,c}-\frac{9\,a\,d\,e^{10}\,\sqrt{-a^9\,c^7}}{4\,c^3}}\right)\,\sqrt{-\frac{4\,a^3\,c^6\,d^5+9\,a\,e^5\,\sqrt{-a^9\,c^7}+15\,a^5\,c^4\,d\,e^4+15\,a^4\,c^5\,d^3\,e^2+5\,c\,d^2\,e^3\,\sqrt{-a^9\,c^7}}{64\,a^6\,c^7}}-2\,\mathrm{atanh}\left(\frac{18\,a\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,e^5\,\sqrt{-a^9\,c^7}}{64\,a^5\,c^7}-\frac{15\,d\,e^4}{64\,a\,c^3}-\frac{15\,d^3\,e^2}{64\,a^2\,c^2}-\frac{d^5}{16\,a^3\,c}+\frac{5\,d^2\,e^3\,\sqrt{-a^9\,c^7}}{64\,a^6\,c^6}}}{\frac{27\,a\,e^{11}}{4\,c^2}+\frac{43\,d^4\,e^7}{4\,a}+\frac{15\,d^2\,e^9}{c}+\frac{5\,c\,d^6\,e^5}{2\,a^2}+\frac{9\,d\,e^{10}\,\sqrt{-a^9\,c^7}}{4\,a^4\,c^5}+\frac{7\,d^3\,e^8\,\sqrt{-a^9\,c^7}}{2\,a^5\,c^4}+\frac{5\,d^5\,e^6\,\sqrt{-a^9\,c^7}}{4\,a^6\,c^3}}+\frac{10\,c\,d^2\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,e^5\,\sqrt{-a^9\,c^7}}{64\,a^5\,c^7}-\frac{15\,d\,e^4}{64\,a\,c^3}-\frac{15\,d^3\,e^2}{64\,a^2\,c^2}-\frac{d^5}{16\,a^3\,c}+\frac{5\,d^2\,e^3\,\sqrt{-a^9\,c^7}}{64\,a^6\,c^6}}}{\frac{27\,a\,e^{11}}{4\,c^2}+\frac{43\,d^4\,e^7}{4\,a}+\frac{15\,d^2\,e^9}{c}+\frac{5\,c\,d^6\,e^5}{2\,a^2}+\frac{9\,d\,e^{10}\,\sqrt{-a^9\,c^7}}{4\,a^4\,c^5}+\frac{7\,d^3\,e^8\,\sqrt{-a^9\,c^7}}{2\,a^5\,c^4}+\frac{5\,d^5\,e^6\,\sqrt{-a^9\,c^7}}{4\,a^6\,c^3}}-\frac{18\,d\,e^7\,\sqrt{-a^9\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,e^5\,\sqrt{-a^9\,c^7}}{64\,a^5\,c^7}-\frac{15\,d\,e^4}{64\,a\,c^3}-\frac{15\,d^3\,e^2}{64\,a^2\,c^2}-\frac{d^5}{16\,a^3\,c}+\frac{5\,d^2\,e^3\,\sqrt{-a^9\,c^7}}{64\,a^6\,c^6}}}{\frac{27\,a^5\,c\,e^{11}}{4}+\frac{5\,a^2\,c^4\,d^6\,e^5}{2}+\frac{43\,a^3\,c^3\,d^4\,e^7}{4}+15\,a^4\,c^2\,d^2\,e^9+\frac{9\,d\,e^{10}\,\sqrt{-a^9\,c^7}}{4\,c^2}+\frac{5\,d^5\,e^6\,\sqrt{-a^9\,c^7}}{4\,a^2}+\frac{7\,d^3\,e^8\,\sqrt{-a^9\,c^7}}{2\,a\,c}}-\frac{10\,d^3\,e^5\,\sqrt{-a^9\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,e^5\,\sqrt{-a^9\,c^7}}{64\,a^5\,c^7}-\frac{15\,d\,e^4}{64\,a\,c^3}-\frac{15\,d^3\,e^2}{64\,a^2\,c^2}-\frac{d^5}{16\,a^3\,c}+\frac{5\,d^2\,e^3\,\sqrt{-a^9\,c^7}}{64\,a^6\,c^6}}}{\frac{27\,a^6\,e^{11}}{4}+15\,a^5\,c\,d^2\,e^9+\frac{5\,a^3\,c^3\,d^6\,e^5}{2}+\frac{43\,a^4\,c^2\,d^4\,e^7}{4}+\frac{7\,d^3\,e^8\,\sqrt{-a^9\,c^7}}{2\,c^2}+\frac{5\,d^5\,e^6\,\sqrt{-a^9\,c^7}}{4\,a\,c}+\frac{9\,a\,d\,e^{10}\,\sqrt{-a^9\,c^7}}{4\,c^3}}\right)\,\sqrt{-\frac{4\,a^3\,c^6\,d^5-9\,a\,e^5\,\sqrt{-a^9\,c^7}+15\,a^5\,c^4\,d\,e^4+15\,a^4\,c^5\,d^3\,e^2-5\,c\,d^2\,e^3\,\sqrt{-a^9\,c^7}}{64\,a^6\,c^7}}","Not used",1,"- (((a*e^3 - c*d^2*e)*(d + e*x)^(3/2))/(2*a*c) + ((a*d*e^3 + c*d^3*e)*(d + e*x)^(1/2))/(2*a*c))/(c*(d + e*x)^2 + a*e^2 + c*d^2 - 2*c*d*(d + e*x)) - 2*atanh((18*a*e^8*(d + e*x)^(1/2)*(- d^5/(16*a^3*c) - (15*d*e^4)/(64*a*c^3) - (15*d^3*e^2)/(64*a^2*c^2) - (9*e^5*(-a^9*c^7)^(1/2))/(64*a^5*c^7) - (5*d^2*e^3*(-a^9*c^7)^(1/2))/(64*a^6*c^6))^(1/2))/((27*a*e^11)/(4*c^2) + (43*d^4*e^7)/(4*a) + (15*d^2*e^9)/c + (5*c*d^6*e^5)/(2*a^2) - (9*d*e^10*(-a^9*c^7)^(1/2))/(4*a^4*c^5) - (7*d^3*e^8*(-a^9*c^7)^(1/2))/(2*a^5*c^4) - (5*d^5*e^6*(-a^9*c^7)^(1/2))/(4*a^6*c^3)) + (10*c*d^2*e^6*(d + e*x)^(1/2)*(- d^5/(16*a^3*c) - (15*d*e^4)/(64*a*c^3) - (15*d^3*e^2)/(64*a^2*c^2) - (9*e^5*(-a^9*c^7)^(1/2))/(64*a^5*c^7) - (5*d^2*e^3*(-a^9*c^7)^(1/2))/(64*a^6*c^6))^(1/2))/((27*a*e^11)/(4*c^2) + (43*d^4*e^7)/(4*a) + (15*d^2*e^9)/c + (5*c*d^6*e^5)/(2*a^2) - (9*d*e^10*(-a^9*c^7)^(1/2))/(4*a^4*c^5) - (7*d^3*e^8*(-a^9*c^7)^(1/2))/(2*a^5*c^4) - (5*d^5*e^6*(-a^9*c^7)^(1/2))/(4*a^6*c^3)) + (18*d*e^7*(-a^9*c^7)^(1/2)*(d + e*x)^(1/2)*(- d^5/(16*a^3*c) - (15*d*e^4)/(64*a*c^3) - (15*d^3*e^2)/(64*a^2*c^2) - (9*e^5*(-a^9*c^7)^(1/2))/(64*a^5*c^7) - (5*d^2*e^3*(-a^9*c^7)^(1/2))/(64*a^6*c^6))^(1/2))/((27*a^5*c*e^11)/4 + (5*a^2*c^4*d^6*e^5)/2 + (43*a^3*c^3*d^4*e^7)/4 + 15*a^4*c^2*d^2*e^9 - (9*d*e^10*(-a^9*c^7)^(1/2))/(4*c^2) - (5*d^5*e^6*(-a^9*c^7)^(1/2))/(4*a^2) - (7*d^3*e^8*(-a^9*c^7)^(1/2))/(2*a*c)) + (10*d^3*e^5*(-a^9*c^7)^(1/2)*(d + e*x)^(1/2)*(- d^5/(16*a^3*c) - (15*d*e^4)/(64*a*c^3) - (15*d^3*e^2)/(64*a^2*c^2) - (9*e^5*(-a^9*c^7)^(1/2))/(64*a^5*c^7) - (5*d^2*e^3*(-a^9*c^7)^(1/2))/(64*a^6*c^6))^(1/2))/((27*a^6*e^11)/4 + 15*a^5*c*d^2*e^9 + (5*a^3*c^3*d^6*e^5)/2 + (43*a^4*c^2*d^4*e^7)/4 - (7*d^3*e^8*(-a^9*c^7)^(1/2))/(2*c^2) - (5*d^5*e^6*(-a^9*c^7)^(1/2))/(4*a*c) - (9*a*d*e^10*(-a^9*c^7)^(1/2))/(4*c^3)))*(-(4*a^3*c^6*d^5 + 9*a*e^5*(-a^9*c^7)^(1/2) + 15*a^5*c^4*d*e^4 + 15*a^4*c^5*d^3*e^2 + 5*c*d^2*e^3*(-a^9*c^7)^(1/2))/(64*a^6*c^7))^(1/2) - 2*atanh((18*a*e^8*(d + e*x)^(1/2)*((9*e^5*(-a^9*c^7)^(1/2))/(64*a^5*c^7) - (15*d*e^4)/(64*a*c^3) - (15*d^3*e^2)/(64*a^2*c^2) - d^5/(16*a^3*c) + (5*d^2*e^3*(-a^9*c^7)^(1/2))/(64*a^6*c^6))^(1/2))/((27*a*e^11)/(4*c^2) + (43*d^4*e^7)/(4*a) + (15*d^2*e^9)/c + (5*c*d^6*e^5)/(2*a^2) + (9*d*e^10*(-a^9*c^7)^(1/2))/(4*a^4*c^5) + (7*d^3*e^8*(-a^9*c^7)^(1/2))/(2*a^5*c^4) + (5*d^5*e^6*(-a^9*c^7)^(1/2))/(4*a^6*c^3)) + (10*c*d^2*e^6*(d + e*x)^(1/2)*((9*e^5*(-a^9*c^7)^(1/2))/(64*a^5*c^7) - (15*d*e^4)/(64*a*c^3) - (15*d^3*e^2)/(64*a^2*c^2) - d^5/(16*a^3*c) + (5*d^2*e^3*(-a^9*c^7)^(1/2))/(64*a^6*c^6))^(1/2))/((27*a*e^11)/(4*c^2) + (43*d^4*e^7)/(4*a) + (15*d^2*e^9)/c + (5*c*d^6*e^5)/(2*a^2) + (9*d*e^10*(-a^9*c^7)^(1/2))/(4*a^4*c^5) + (7*d^3*e^8*(-a^9*c^7)^(1/2))/(2*a^5*c^4) + (5*d^5*e^6*(-a^9*c^7)^(1/2))/(4*a^6*c^3)) - (18*d*e^7*(-a^9*c^7)^(1/2)*(d + e*x)^(1/2)*((9*e^5*(-a^9*c^7)^(1/2))/(64*a^5*c^7) - (15*d*e^4)/(64*a*c^3) - (15*d^3*e^2)/(64*a^2*c^2) - d^5/(16*a^3*c) + (5*d^2*e^3*(-a^9*c^7)^(1/2))/(64*a^6*c^6))^(1/2))/((27*a^5*c*e^11)/4 + (5*a^2*c^4*d^6*e^5)/2 + (43*a^3*c^3*d^4*e^7)/4 + 15*a^4*c^2*d^2*e^9 + (9*d*e^10*(-a^9*c^7)^(1/2))/(4*c^2) + (5*d^5*e^6*(-a^9*c^7)^(1/2))/(4*a^2) + (7*d^3*e^8*(-a^9*c^7)^(1/2))/(2*a*c)) - (10*d^3*e^5*(-a^9*c^7)^(1/2)*(d + e*x)^(1/2)*((9*e^5*(-a^9*c^7)^(1/2))/(64*a^5*c^7) - (15*d*e^4)/(64*a*c^3) - (15*d^3*e^2)/(64*a^2*c^2) - d^5/(16*a^3*c) + (5*d^2*e^3*(-a^9*c^7)^(1/2))/(64*a^6*c^6))^(1/2))/((27*a^6*e^11)/4 + 15*a^5*c*d^2*e^9 + (5*a^3*c^3*d^6*e^5)/2 + (43*a^4*c^2*d^4*e^7)/4 + (7*d^3*e^8*(-a^9*c^7)^(1/2))/(2*c^2) + (5*d^5*e^6*(-a^9*c^7)^(1/2))/(4*a*c) + (9*a*d*e^10*(-a^9*c^7)^(1/2))/(4*c^3)))*(-(4*a^3*c^6*d^5 - 9*a*e^5*(-a^9*c^7)^(1/2) + 15*a^5*c^4*d*e^4 + 15*a^4*c^5*d^3*e^2 - 5*c*d^2*e^3*(-a^9*c^7)^(1/2))/(64*a^6*c^7))^(1/2)","B"
633,1,717,726,0.437529,"\text{Not used}","int((d + e*x)^(3/2)/(a + c*x^2)^2,x)","-\frac{\frac{\left(c\,d^2\,e+a\,e^3\right)\,\sqrt{d+e\,x}}{2\,a\,c}-\frac{d\,e\,{\left(d+e\,x\right)}^{3/2}}{2\,a}}{c\,{\left(d+e\,x\right)}^2+a\,e^2+c\,d^2-2\,c\,d\,\left(d+e\,x\right)}-2\,\mathrm{atanh}\left(\frac{2\,c\,e^6\,\sqrt{d+e\,x}\,\sqrt{-\frac{d^3}{16\,a^3\,c}-\frac{3\,d\,e^2}{64\,a^2\,c^2}-\frac{e^3\,\sqrt{-a^9\,c^5}}{64\,a^6\,c^5}}}{\frac{d\,e^7}{2\,a}+\frac{c\,d^3\,e^5}{2\,a^2}+\frac{e^8\,\sqrt{-a^9\,c^5}}{4\,a^5\,c^3}+\frac{d^2\,e^6\,\sqrt{-a^9\,c^5}}{4\,a^6\,c^2}}-\frac{2\,d\,e^5\,\sqrt{-a^9\,c^5}\,\sqrt{d+e\,x}\,\sqrt{-\frac{d^3}{16\,a^3\,c}-\frac{3\,d\,e^2}{64\,a^2\,c^2}-\frac{e^3\,\sqrt{-a^9\,c^5}}{64\,a^6\,c^5}}}{\frac{e^8\,\sqrt{-a^9\,c^5}}{4\,c^2}+\frac{a^3\,c^2\,d^3\,e^5}{2}+\frac{a^4\,c\,d\,e^7}{2}+\frac{d^2\,e^6\,\sqrt{-a^9\,c^5}}{4\,a\,c}}\right)\,\sqrt{-\frac{e^3\,\sqrt{-a^9\,c^5}+4\,a^3\,c^4\,d^3+3\,a^4\,c^3\,d\,e^2}{64\,a^6\,c^5}}-2\,\mathrm{atanh}\left(\frac{2\,c\,e^6\,\sqrt{d+e\,x}\,\sqrt{\frac{e^3\,\sqrt{-a^9\,c^5}}{64\,a^6\,c^5}-\frac{3\,d\,e^2}{64\,a^2\,c^2}-\frac{d^3}{16\,a^3\,c}}}{\frac{d\,e^7}{2\,a}+\frac{c\,d^3\,e^5}{2\,a^2}-\frac{e^8\,\sqrt{-a^9\,c^5}}{4\,a^5\,c^3}-\frac{d^2\,e^6\,\sqrt{-a^9\,c^5}}{4\,a^6\,c^2}}-\frac{2\,d\,e^5\,\sqrt{-a^9\,c^5}\,\sqrt{d+e\,x}\,\sqrt{\frac{e^3\,\sqrt{-a^9\,c^5}}{64\,a^6\,c^5}-\frac{3\,d\,e^2}{64\,a^2\,c^2}-\frac{d^3}{16\,a^3\,c}}}{\frac{e^8\,\sqrt{-a^9\,c^5}}{4\,c^2}-\frac{a^3\,c^2\,d^3\,e^5}{2}-\frac{a^4\,c\,d\,e^7}{2}+\frac{d^2\,e^6\,\sqrt{-a^9\,c^5}}{4\,a\,c}}\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^3-e^3\,\sqrt{-a^9\,c^5}+3\,a^4\,c^3\,d\,e^2}{64\,a^6\,c^5}}","Not used",1,"- (((a*e^3 + c*d^2*e)*(d + e*x)^(1/2))/(2*a*c) - (d*e*(d + e*x)^(3/2))/(2*a))/(c*(d + e*x)^2 + a*e^2 + c*d^2 - 2*c*d*(d + e*x)) - 2*atanh((2*c*e^6*(d + e*x)^(1/2)*(- d^3/(16*a^3*c) - (3*d*e^2)/(64*a^2*c^2) - (e^3*(-a^9*c^5)^(1/2))/(64*a^6*c^5))^(1/2))/((d*e^7)/(2*a) + (c*d^3*e^5)/(2*a^2) + (e^8*(-a^9*c^5)^(1/2))/(4*a^5*c^3) + (d^2*e^6*(-a^9*c^5)^(1/2))/(4*a^6*c^2)) - (2*d*e^5*(-a^9*c^5)^(1/2)*(d + e*x)^(1/2)*(- d^3/(16*a^3*c) - (3*d*e^2)/(64*a^2*c^2) - (e^3*(-a^9*c^5)^(1/2))/(64*a^6*c^5))^(1/2))/((e^8*(-a^9*c^5)^(1/2))/(4*c^2) + (a^3*c^2*d^3*e^5)/2 + (a^4*c*d*e^7)/2 + (d^2*e^6*(-a^9*c^5)^(1/2))/(4*a*c)))*(-(e^3*(-a^9*c^5)^(1/2) + 4*a^3*c^4*d^3 + 3*a^4*c^3*d*e^2)/(64*a^6*c^5))^(1/2) - 2*atanh((2*c*e^6*(d + e*x)^(1/2)*((e^3*(-a^9*c^5)^(1/2))/(64*a^6*c^5) - (3*d*e^2)/(64*a^2*c^2) - d^3/(16*a^3*c))^(1/2))/((d*e^7)/(2*a) + (c*d^3*e^5)/(2*a^2) - (e^8*(-a^9*c^5)^(1/2))/(4*a^5*c^3) - (d^2*e^6*(-a^9*c^5)^(1/2))/(4*a^6*c^2)) - (2*d*e^5*(-a^9*c^5)^(1/2)*(d + e*x)^(1/2)*((e^3*(-a^9*c^5)^(1/2))/(64*a^6*c^5) - (3*d*e^2)/(64*a^2*c^2) - d^3/(16*a^3*c))^(1/2))/((e^8*(-a^9*c^5)^(1/2))/(4*c^2) - (a^3*c^2*d^3*e^5)/2 - (a^4*c*d*e^7)/2 + (d^2*e^6*(-a^9*c^5)^(1/2))/(4*a*c)))*(-(4*a^3*c^4*d^3 - e^3*(-a^9*c^5)^(1/2) + 3*a^4*c^3*d*e^2)/(64*a^6*c^5))^(1/2)","B"
634,1,2380,675,2.166889,"\text{Not used}","int((d + e*x)^(1/2)/(a + c*x^2)^2,x)","\frac{\frac{e\,{\left(d+e\,x\right)}^{3/2}}{2\,a}-\frac{d\,e\,\sqrt{d+e\,x}}{2\,a}}{c\,{\left(d+e\,x\right)}^2+a\,e^2+c\,d^2-2\,c\,d\,\left(d+e\,x\right)}+\mathrm{atan}\left(\frac{\left(\left(8\,c^3\,d\,e^3-64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{e^3\,\sqrt{-a^9\,c^3}+4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}\right)\,\sqrt{-\frac{e^3\,\sqrt{-a^9\,c^3}+4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}+\frac{\left(a\,c^2\,e^4-4\,c^3\,d^2\,e^2\right)\,\sqrt{d+e\,x}}{a^2}\right)\,\sqrt{-\frac{e^3\,\sqrt{-a^9\,c^3}+4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(8\,c^3\,d\,e^3+64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{e^3\,\sqrt{-a^9\,c^3}+4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}\right)\,\sqrt{-\frac{e^3\,\sqrt{-a^9\,c^3}+4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}-\frac{\left(a\,c^2\,e^4-4\,c^3\,d^2\,e^2\right)\,\sqrt{d+e\,x}}{a^2}\right)\,\sqrt{-\frac{e^3\,\sqrt{-a^9\,c^3}+4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}\,1{}\mathrm{i}}{\frac{4\,c^2\,d^2\,e^3+a\,c\,e^5}{4\,a^3}+\left(\left(8\,c^3\,d\,e^3-64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{e^3\,\sqrt{-a^9\,c^3}+4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}\right)\,\sqrt{-\frac{e^3\,\sqrt{-a^9\,c^3}+4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}+\frac{\left(a\,c^2\,e^4-4\,c^3\,d^2\,e^2\right)\,\sqrt{d+e\,x}}{a^2}\right)\,\sqrt{-\frac{e^3\,\sqrt{-a^9\,c^3}+4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}+\left(\left(8\,c^3\,d\,e^3+64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{e^3\,\sqrt{-a^9\,c^3}+4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}\right)\,\sqrt{-\frac{e^3\,\sqrt{-a^9\,c^3}+4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}-\frac{\left(a\,c^2\,e^4-4\,c^3\,d^2\,e^2\right)\,\sqrt{d+e\,x}}{a^2}\right)\,\sqrt{-\frac{e^3\,\sqrt{-a^9\,c^3}+4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}}\right)\,\sqrt{-\frac{e^3\,\sqrt{-a^9\,c^3}+4\,a^3\,c^3\,d^3+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(8\,c^3\,d\,e^3-64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^3\,d^3-e^3\,\sqrt{-a^9\,c^3}+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^3-e^3\,\sqrt{-a^9\,c^3}+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}+\frac{\left(a\,c^2\,e^4-4\,c^3\,d^2\,e^2\right)\,\sqrt{d+e\,x}}{a^2}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^3-e^3\,\sqrt{-a^9\,c^3}+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(8\,c^3\,d\,e^3+64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^3\,d^3-e^3\,\sqrt{-a^9\,c^3}+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^3-e^3\,\sqrt{-a^9\,c^3}+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}-\frac{\left(a\,c^2\,e^4-4\,c^3\,d^2\,e^2\right)\,\sqrt{d+e\,x}}{a^2}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^3-e^3\,\sqrt{-a^9\,c^3}+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}\,1{}\mathrm{i}}{\frac{4\,c^2\,d^2\,e^3+a\,c\,e^5}{4\,a^3}+\left(\left(8\,c^3\,d\,e^3-64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^3\,d^3-e^3\,\sqrt{-a^9\,c^3}+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^3-e^3\,\sqrt{-a^9\,c^3}+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}+\frac{\left(a\,c^2\,e^4-4\,c^3\,d^2\,e^2\right)\,\sqrt{d+e\,x}}{a^2}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^3-e^3\,\sqrt{-a^9\,c^3}+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}+\left(\left(8\,c^3\,d\,e^3+64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^3\,d^3-e^3\,\sqrt{-a^9\,c^3}+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^3-e^3\,\sqrt{-a^9\,c^3}+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}-\frac{\left(a\,c^2\,e^4-4\,c^3\,d^2\,e^2\right)\,\sqrt{d+e\,x}}{a^2}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^3-e^3\,\sqrt{-a^9\,c^3}+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^3-e^3\,\sqrt{-a^9\,c^3}+3\,a^4\,c^2\,d\,e^2}{64\,\left(a^7\,c^3\,e^2+a^6\,c^4\,d^2\right)}}\,2{}\mathrm{i}","Not used",1,"atan((((8*c^3*d*e^3 - 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(e^3*(-a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2))*(-(e^3*(-a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2) + ((a*c^2*e^4 - 4*c^3*d^2*e^2)*(d + e*x)^(1/2))/a^2)*(-(e^3*(-a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2)*1i - ((8*c^3*d*e^3 + 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(e^3*(-a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2))*(-(e^3*(-a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2) - ((a*c^2*e^4 - 4*c^3*d^2*e^2)*(d + e*x)^(1/2))/a^2)*(-(e^3*(-a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2)*1i)/((4*c^2*d^2*e^3 + a*c*e^5)/(4*a^3) + ((8*c^3*d*e^3 - 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(e^3*(-a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2))*(-(e^3*(-a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2) + ((a*c^2*e^4 - 4*c^3*d^2*e^2)*(d + e*x)^(1/2))/a^2)*(-(e^3*(-a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2) + ((8*c^3*d*e^3 + 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(e^3*(-a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2))*(-(e^3*(-a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2) - ((a*c^2*e^4 - 4*c^3*d^2*e^2)*(d + e*x)^(1/2))/a^2)*(-(e^3*(-a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2)))*(-(e^3*(-a^9*c^3)^(1/2) + 4*a^3*c^3*d^3 + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2)*2i + atan((((8*c^3*d*e^3 - 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(4*a^3*c^3*d^3 - e^3*(-a^9*c^3)^(1/2) + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2))*(-(4*a^3*c^3*d^3 - e^3*(-a^9*c^3)^(1/2) + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2) + ((a*c^2*e^4 - 4*c^3*d^2*e^2)*(d + e*x)^(1/2))/a^2)*(-(4*a^3*c^3*d^3 - e^3*(-a^9*c^3)^(1/2) + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2)*1i - ((8*c^3*d*e^3 + 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(4*a^3*c^3*d^3 - e^3*(-a^9*c^3)^(1/2) + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2))*(-(4*a^3*c^3*d^3 - e^3*(-a^9*c^3)^(1/2) + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2) - ((a*c^2*e^4 - 4*c^3*d^2*e^2)*(d + e*x)^(1/2))/a^2)*(-(4*a^3*c^3*d^3 - e^3*(-a^9*c^3)^(1/2) + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2)*1i)/((4*c^2*d^2*e^3 + a*c*e^5)/(4*a^3) + ((8*c^3*d*e^3 - 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(4*a^3*c^3*d^3 - e^3*(-a^9*c^3)^(1/2) + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2))*(-(4*a^3*c^3*d^3 - e^3*(-a^9*c^3)^(1/2) + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2) + ((a*c^2*e^4 - 4*c^3*d^2*e^2)*(d + e*x)^(1/2))/a^2)*(-(4*a^3*c^3*d^3 - e^3*(-a^9*c^3)^(1/2) + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2) + ((8*c^3*d*e^3 + 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(4*a^3*c^3*d^3 - e^3*(-a^9*c^3)^(1/2) + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2))*(-(4*a^3*c^3*d^3 - e^3*(-a^9*c^3)^(1/2) + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2) - ((a*c^2*e^4 - 4*c^3*d^2*e^2)*(d + e*x)^(1/2))/a^2)*(-(4*a^3*c^3*d^3 - e^3*(-a^9*c^3)^(1/2) + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2)))*(-(4*a^3*c^3*d^3 - e^3*(-a^9*c^3)^(1/2) + 3*a^4*c^2*d*e^2)/(64*(a^6*c^4*d^2 + a^7*c^3*e^2)))^(1/2)*2i + ((e*(d + e*x)^(3/2))/(2*a) - (d*e*(d + e*x)^(1/2))/(2*a))/(c*(d + e*x)^2 + a*e^2 + c*d^2 - 2*c*d*(d + e*x))","B"
635,1,5300,739,2.223516,"\text{Not used}","int(1/((a + c*x^2)^2*(d + e*x)^(1/2)),x)","\frac{\frac{\left(a\,e^3-c\,d^2\,e\right)\,\sqrt{d+e\,x}}{2\,a\,\left(c\,d^2+a\,e^2\right)}+\frac{c\,d\,e\,{\left(d+e\,x\right)}^{3/2}}{2\,a\,\left(c\,d^2+a\,e^2\right)}}{c\,{\left(d+e\,x\right)}^2+a\,e^2+c\,d^2-2\,c\,d\,\left(d+e\,x\right)}-\mathrm{atan}\left(\frac{\left(\left(\frac{192\,a^5\,c^3\,e^7+256\,a^4\,c^4\,d^2\,e^5+64\,a^3\,c^5\,d^4\,e^3}{8\,\left(a^5\,e^4+2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}+\frac{\sqrt{d+e\,x}\,\left(64\,a^5\,c^4\,d\,e^6+128\,a^4\,c^5\,d^3\,e^4+64\,a^3\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{-a^9\,c}-5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}}{a^4\,e^4+2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{-a^9\,c}-5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}+\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c^3\,e^6+11\,a\,c^4\,d^2\,e^4+4\,c^5\,d^4\,e^2\right)}{a^4\,e^4+2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{-a^9\,c}-5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}\,1{}\mathrm{i}-\left(\left(\frac{192\,a^5\,c^3\,e^7+256\,a^4\,c^4\,d^2\,e^5+64\,a^3\,c^5\,d^4\,e^3}{8\,\left(a^5\,e^4+2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}-\frac{\sqrt{d+e\,x}\,\left(64\,a^5\,c^4\,d\,e^6+128\,a^4\,c^5\,d^3\,e^4+64\,a^3\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{-a^9\,c}-5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}}{a^4\,e^4+2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{-a^9\,c}-5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}-\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c^3\,e^6+11\,a\,c^4\,d^2\,e^4+4\,c^5\,d^4\,e^2\right)}{a^4\,e^4+2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{-a^9\,c}-5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}\,1{}\mathrm{i}}{\frac{4\,c^4\,d^3\,e^3+9\,a\,c^3\,d\,e^5}{4\,\left(a^5\,e^4+2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}+\left(\left(\frac{192\,a^5\,c^3\,e^7+256\,a^4\,c^4\,d^2\,e^5+64\,a^3\,c^5\,d^4\,e^3}{8\,\left(a^5\,e^4+2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}+\frac{\sqrt{d+e\,x}\,\left(64\,a^5\,c^4\,d\,e^6+128\,a^4\,c^5\,d^3\,e^4+64\,a^3\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{-a^9\,c}-5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}}{a^4\,e^4+2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{-a^9\,c}-5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}+\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c^3\,e^6+11\,a\,c^4\,d^2\,e^4+4\,c^5\,d^4\,e^2\right)}{a^4\,e^4+2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{-a^9\,c}-5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}+\left(\left(\frac{192\,a^5\,c^3\,e^7+256\,a^4\,c^4\,d^2\,e^5+64\,a^3\,c^5\,d^4\,e^3}{8\,\left(a^5\,e^4+2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}-\frac{\sqrt{d+e\,x}\,\left(64\,a^5\,c^4\,d\,e^6+128\,a^4\,c^5\,d^3\,e^4+64\,a^3\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{-a^9\,c}-5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}}{a^4\,e^4+2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{-a^9\,c}-5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}-\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c^3\,e^6+11\,a\,c^4\,d^2\,e^4+4\,c^5\,d^4\,e^2\right)}{a^4\,e^4+2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{-a^9\,c}-5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}}\right)\,\sqrt{-\frac{4\,a^3\,c^3\,d^5-9\,a\,e^5\,\sqrt{-a^9\,c}-5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(\frac{192\,a^5\,c^3\,e^7+256\,a^4\,c^4\,d^2\,e^5+64\,a^3\,c^5\,d^4\,e^3}{8\,\left(a^5\,e^4+2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}+\frac{\sqrt{d+e\,x}\,\left(64\,a^5\,c^4\,d\,e^6+128\,a^4\,c^5\,d^3\,e^4+64\,a^3\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{-a^9\,c}+4\,a^3\,c^3\,d^5+5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}}{a^4\,e^4+2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{-a^9\,c}+4\,a^3\,c^3\,d^5+5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}+\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c^3\,e^6+11\,a\,c^4\,d^2\,e^4+4\,c^5\,d^4\,e^2\right)}{a^4\,e^4+2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{-a^9\,c}+4\,a^3\,c^3\,d^5+5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}\,1{}\mathrm{i}-\left(\left(\frac{192\,a^5\,c^3\,e^7+256\,a^4\,c^4\,d^2\,e^5+64\,a^3\,c^5\,d^4\,e^3}{8\,\left(a^5\,e^4+2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}-\frac{\sqrt{d+e\,x}\,\left(64\,a^5\,c^4\,d\,e^6+128\,a^4\,c^5\,d^3\,e^4+64\,a^3\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{-a^9\,c}+4\,a^3\,c^3\,d^5+5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}}{a^4\,e^4+2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{-a^9\,c}+4\,a^3\,c^3\,d^5+5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}-\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c^3\,e^6+11\,a\,c^4\,d^2\,e^4+4\,c^5\,d^4\,e^2\right)}{a^4\,e^4+2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{-a^9\,c}+4\,a^3\,c^3\,d^5+5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}\,1{}\mathrm{i}}{\frac{4\,c^4\,d^3\,e^3+9\,a\,c^3\,d\,e^5}{4\,\left(a^5\,e^4+2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}+\left(\left(\frac{192\,a^5\,c^3\,e^7+256\,a^4\,c^4\,d^2\,e^5+64\,a^3\,c^5\,d^4\,e^3}{8\,\left(a^5\,e^4+2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}+\frac{\sqrt{d+e\,x}\,\left(64\,a^5\,c^4\,d\,e^6+128\,a^4\,c^5\,d^3\,e^4+64\,a^3\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{-a^9\,c}+4\,a^3\,c^3\,d^5+5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}}{a^4\,e^4+2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{-a^9\,c}+4\,a^3\,c^3\,d^5+5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}+\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c^3\,e^6+11\,a\,c^4\,d^2\,e^4+4\,c^5\,d^4\,e^2\right)}{a^4\,e^4+2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{-a^9\,c}+4\,a^3\,c^3\,d^5+5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}+\left(\left(\frac{192\,a^5\,c^3\,e^7+256\,a^4\,c^4\,d^2\,e^5+64\,a^3\,c^5\,d^4\,e^3}{8\,\left(a^5\,e^4+2\,a^4\,c\,d^2\,e^2+a^3\,c^2\,d^4\right)}-\frac{\sqrt{d+e\,x}\,\left(64\,a^5\,c^4\,d\,e^6+128\,a^4\,c^5\,d^3\,e^4+64\,a^3\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{-a^9\,c}+4\,a^3\,c^3\,d^5+5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}}{a^4\,e^4+2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{-a^9\,c}+4\,a^3\,c^3\,d^5+5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}-\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c^3\,e^6+11\,a\,c^4\,d^2\,e^4+4\,c^5\,d^4\,e^2\right)}{a^4\,e^4+2\,a^3\,c\,d^2\,e^2+a^2\,c^2\,d^4}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{-a^9\,c}+4\,a^3\,c^3\,d^5+5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}}\right)\,\sqrt{-\frac{9\,a\,e^5\,\sqrt{-a^9\,c}+4\,a^3\,c^3\,d^5+5\,c\,d^2\,e^3\,\sqrt{-a^9\,c}+15\,a^4\,c^2\,d^3\,e^2+15\,a^5\,c\,d\,e^4}{64\,\left(a^9\,c\,e^6+3\,a^8\,c^2\,d^2\,e^4+3\,a^7\,c^3\,d^4\,e^2+a^6\,c^4\,d^6\right)}}\,2{}\mathrm{i}","Not used",1,"(((a*e^3 - c*d^2*e)*(d + e*x)^(1/2))/(2*a*(a*e^2 + c*d^2)) + (c*d*e*(d + e*x)^(3/2))/(2*a*(a*e^2 + c*d^2)))/(c*(d + e*x)^2 + a*e^2 + c*d^2 - 2*c*d*(d + e*x)) - atan(((((192*a^5*c^3*e^7 + 64*a^3*c^5*d^4*e^3 + 256*a^4*c^4*d^2*e^5)/(8*(a^5*e^4 + a^3*c^2*d^4 + 2*a^4*c*d^2*e^2)) + ((d + e*x)^(1/2)*(64*a^5*c^4*d*e^6 + 64*a^3*c^6*d^5*e^2 + 128*a^4*c^5*d^3*e^4)*(-(9*a*e^5*(-a^9*c)^(1/2) + 4*a^3*c^3*d^5 + 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2))/(a^4*e^4 + a^2*c^2*d^4 + 2*a^3*c*d^2*e^2))*(-(9*a*e^5*(-a^9*c)^(1/2) + 4*a^3*c^3*d^5 + 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2) + ((d + e*x)^(1/2)*(9*a^2*c^3*e^6 + 4*c^5*d^4*e^2 + 11*a*c^4*d^2*e^4))/(a^4*e^4 + a^2*c^2*d^4 + 2*a^3*c*d^2*e^2))*(-(9*a*e^5*(-a^9*c)^(1/2) + 4*a^3*c^3*d^5 + 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2)*1i - (((192*a^5*c^3*e^7 + 64*a^3*c^5*d^4*e^3 + 256*a^4*c^4*d^2*e^5)/(8*(a^5*e^4 + a^3*c^2*d^4 + 2*a^4*c*d^2*e^2)) - ((d + e*x)^(1/2)*(64*a^5*c^4*d*e^6 + 64*a^3*c^6*d^5*e^2 + 128*a^4*c^5*d^3*e^4)*(-(9*a*e^5*(-a^9*c)^(1/2) + 4*a^3*c^3*d^5 + 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2))/(a^4*e^4 + a^2*c^2*d^4 + 2*a^3*c*d^2*e^2))*(-(9*a*e^5*(-a^9*c)^(1/2) + 4*a^3*c^3*d^5 + 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2) - ((d + e*x)^(1/2)*(9*a^2*c^3*e^6 + 4*c^5*d^4*e^2 + 11*a*c^4*d^2*e^4))/(a^4*e^4 + a^2*c^2*d^4 + 2*a^3*c*d^2*e^2))*(-(9*a*e^5*(-a^9*c)^(1/2) + 4*a^3*c^3*d^5 + 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2)*1i)/((4*c^4*d^3*e^3 + 9*a*c^3*d*e^5)/(4*(a^5*e^4 + a^3*c^2*d^4 + 2*a^4*c*d^2*e^2)) + (((192*a^5*c^3*e^7 + 64*a^3*c^5*d^4*e^3 + 256*a^4*c^4*d^2*e^5)/(8*(a^5*e^4 + a^3*c^2*d^4 + 2*a^4*c*d^2*e^2)) + ((d + e*x)^(1/2)*(64*a^5*c^4*d*e^6 + 64*a^3*c^6*d^5*e^2 + 128*a^4*c^5*d^3*e^4)*(-(9*a*e^5*(-a^9*c)^(1/2) + 4*a^3*c^3*d^5 + 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2))/(a^4*e^4 + a^2*c^2*d^4 + 2*a^3*c*d^2*e^2))*(-(9*a*e^5*(-a^9*c)^(1/2) + 4*a^3*c^3*d^5 + 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2) + ((d + e*x)^(1/2)*(9*a^2*c^3*e^6 + 4*c^5*d^4*e^2 + 11*a*c^4*d^2*e^4))/(a^4*e^4 + a^2*c^2*d^4 + 2*a^3*c*d^2*e^2))*(-(9*a*e^5*(-a^9*c)^(1/2) + 4*a^3*c^3*d^5 + 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2) + (((192*a^5*c^3*e^7 + 64*a^3*c^5*d^4*e^3 + 256*a^4*c^4*d^2*e^5)/(8*(a^5*e^4 + a^3*c^2*d^4 + 2*a^4*c*d^2*e^2)) - ((d + e*x)^(1/2)*(64*a^5*c^4*d*e^6 + 64*a^3*c^6*d^5*e^2 + 128*a^4*c^5*d^3*e^4)*(-(9*a*e^5*(-a^9*c)^(1/2) + 4*a^3*c^3*d^5 + 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2))/(a^4*e^4 + a^2*c^2*d^4 + 2*a^3*c*d^2*e^2))*(-(9*a*e^5*(-a^9*c)^(1/2) + 4*a^3*c^3*d^5 + 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2) - ((d + e*x)^(1/2)*(9*a^2*c^3*e^6 + 4*c^5*d^4*e^2 + 11*a*c^4*d^2*e^4))/(a^4*e^4 + a^2*c^2*d^4 + 2*a^3*c*d^2*e^2))*(-(9*a*e^5*(-a^9*c)^(1/2) + 4*a^3*c^3*d^5 + 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2)))*(-(9*a*e^5*(-a^9*c)^(1/2) + 4*a^3*c^3*d^5 + 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2)*2i - atan(((((192*a^5*c^3*e^7 + 64*a^3*c^5*d^4*e^3 + 256*a^4*c^4*d^2*e^5)/(8*(a^5*e^4 + a^3*c^2*d^4 + 2*a^4*c*d^2*e^2)) + ((d + e*x)^(1/2)*(64*a^5*c^4*d*e^6 + 64*a^3*c^6*d^5*e^2 + 128*a^4*c^5*d^3*e^4)*(-(4*a^3*c^3*d^5 - 9*a*e^5*(-a^9*c)^(1/2) - 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2))/(a^4*e^4 + a^2*c^2*d^4 + 2*a^3*c*d^2*e^2))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(-a^9*c)^(1/2) - 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2) + ((d + e*x)^(1/2)*(9*a^2*c^3*e^6 + 4*c^5*d^4*e^2 + 11*a*c^4*d^2*e^4))/(a^4*e^4 + a^2*c^2*d^4 + 2*a^3*c*d^2*e^2))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(-a^9*c)^(1/2) - 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2)*1i - (((192*a^5*c^3*e^7 + 64*a^3*c^5*d^4*e^3 + 256*a^4*c^4*d^2*e^5)/(8*(a^5*e^4 + a^3*c^2*d^4 + 2*a^4*c*d^2*e^2)) - ((d + e*x)^(1/2)*(64*a^5*c^4*d*e^6 + 64*a^3*c^6*d^5*e^2 + 128*a^4*c^5*d^3*e^4)*(-(4*a^3*c^3*d^5 - 9*a*e^5*(-a^9*c)^(1/2) - 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2))/(a^4*e^4 + a^2*c^2*d^4 + 2*a^3*c*d^2*e^2))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(-a^9*c)^(1/2) - 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2) - ((d + e*x)^(1/2)*(9*a^2*c^3*e^6 + 4*c^5*d^4*e^2 + 11*a*c^4*d^2*e^4))/(a^4*e^4 + a^2*c^2*d^4 + 2*a^3*c*d^2*e^2))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(-a^9*c)^(1/2) - 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2)*1i)/((4*c^4*d^3*e^3 + 9*a*c^3*d*e^5)/(4*(a^5*e^4 + a^3*c^2*d^4 + 2*a^4*c*d^2*e^2)) + (((192*a^5*c^3*e^7 + 64*a^3*c^5*d^4*e^3 + 256*a^4*c^4*d^2*e^5)/(8*(a^5*e^4 + a^3*c^2*d^4 + 2*a^4*c*d^2*e^2)) + ((d + e*x)^(1/2)*(64*a^5*c^4*d*e^6 + 64*a^3*c^6*d^5*e^2 + 128*a^4*c^5*d^3*e^4)*(-(4*a^3*c^3*d^5 - 9*a*e^5*(-a^9*c)^(1/2) - 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2))/(a^4*e^4 + a^2*c^2*d^4 + 2*a^3*c*d^2*e^2))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(-a^9*c)^(1/2) - 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2) + ((d + e*x)^(1/2)*(9*a^2*c^3*e^6 + 4*c^5*d^4*e^2 + 11*a*c^4*d^2*e^4))/(a^4*e^4 + a^2*c^2*d^4 + 2*a^3*c*d^2*e^2))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(-a^9*c)^(1/2) - 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2) + (((192*a^5*c^3*e^7 + 64*a^3*c^5*d^4*e^3 + 256*a^4*c^4*d^2*e^5)/(8*(a^5*e^4 + a^3*c^2*d^4 + 2*a^4*c*d^2*e^2)) - ((d + e*x)^(1/2)*(64*a^5*c^4*d*e^6 + 64*a^3*c^6*d^5*e^2 + 128*a^4*c^5*d^3*e^4)*(-(4*a^3*c^3*d^5 - 9*a*e^5*(-a^9*c)^(1/2) - 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2))/(a^4*e^4 + a^2*c^2*d^4 + 2*a^3*c*d^2*e^2))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(-a^9*c)^(1/2) - 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2) - ((d + e*x)^(1/2)*(9*a^2*c^3*e^6 + 4*c^5*d^4*e^2 + 11*a*c^4*d^2*e^4))/(a^4*e^4 + a^2*c^2*d^4 + 2*a^3*c*d^2*e^2))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(-a^9*c)^(1/2) - 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2)))*(-(4*a^3*c^3*d^5 - 9*a*e^5*(-a^9*c)^(1/2) - 5*c*d^2*e^3*(-a^9*c)^(1/2) + 15*a^4*c^2*d^3*e^2 + 15*a^5*c*d*e^4)/(64*(a^9*c*e^6 + a^6*c^4*d^6 + 3*a^7*c^3*d^4*e^2 + 3*a^8*c^2*d^2*e^4)))^(1/2)*2i","B"
636,1,8777,845,3.207459,"\text{Not used}","int(1/((a + c*x^2)^2*(d + e*x)^(3/2)),x)","-\frac{\frac{2\,e^3}{c\,d^2+a\,e^2}+\frac{c\,e\,\left(5\,a\,e^2-c\,d^2\right)\,{\left(d+e\,x\right)}^2}{2\,a\,{\left(c\,d^2+a\,e^2\right)}^2}-\frac{c\,d\,e\,\left(11\,a\,e^2-c\,d^2\right)\,\left(d+e\,x\right)}{2\,a\,{\left(c\,d^2+a\,e^2\right)}^2}}{c\,{\left(d+e\,x\right)}^{5/2}+\left(c\,d^2+a\,e^2\right)\,\sqrt{d+e\,x}-2\,c\,d\,{\left(d+e\,x\right)}^{3/2}}+\mathrm{atan}\left(\frac{\left(\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,\left(2048\,a^{16}\,c^4\,d\,e^{22}+20480\,a^{15}\,c^5\,d^3\,e^{20}+92160\,a^{14}\,c^6\,d^5\,e^{18}+245760\,a^{13}\,c^7\,d^7\,e^{16}+430080\,a^{12}\,c^8\,d^9\,e^{14}+516096\,a^{11}\,c^9\,d^{11}\,e^{12}+430080\,a^{10}\,c^{10}\,d^{13}\,e^{10}+245760\,a^9\,c^{11}\,d^{15}\,e^8+92160\,a^8\,c^{12}\,d^{17}\,e^6+20480\,a^7\,c^{13}\,d^{19}\,e^4+2048\,a^6\,c^{14}\,d^{21}\,e^2\right)+3328\,a^{14}\,c^4\,d\,e^{21}+256\,a^5\,c^{13}\,d^{19}\,e^3+5376\,a^6\,c^{12}\,d^{17}\,e^5+33792\,a^7\,c^{11}\,d^{15}\,e^7+107520\,a^8\,c^{10}\,d^{13}\,e^9+204288\,a^9\,c^9\,d^{11}\,e^{11}+247296\,a^{10}\,c^8\,d^9\,e^{13}+193536\,a^{11}\,c^7\,d^7\,e^{15}+95232\,a^{12}\,c^6\,d^5\,e^{17}+26880\,a^{13}\,c^5\,d^3\,e^{19}\right)+\sqrt{d+e\,x}\,\left(-800\,a^{12}\,c^4\,e^{20}-2432\,a^{11}\,c^5\,d^2\,e^{18}+3200\,a^{10}\,c^6\,d^4\,e^{16}+25600\,a^9\,c^7\,d^6\,e^{14}+51008\,a^8\,c^8\,d^8\,e^{12}+52480\,a^7\,c^9\,d^{10}\,e^{10}+30848\,a^6\,c^{10}\,d^{12}\,e^8+10240\,a^5\,c^{11}\,d^{14}\,e^6+1760\,a^4\,c^{12}\,d^{16}\,e^4+128\,a^3\,c^{13}\,d^{18}\,e^2\right)\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,1{}\mathrm{i}-\left(\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,\left(3328\,a^{14}\,c^4\,d\,e^{21}-\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,\left(2048\,a^{16}\,c^4\,d\,e^{22}+20480\,a^{15}\,c^5\,d^3\,e^{20}+92160\,a^{14}\,c^6\,d^5\,e^{18}+245760\,a^{13}\,c^7\,d^7\,e^{16}+430080\,a^{12}\,c^8\,d^9\,e^{14}+516096\,a^{11}\,c^9\,d^{11}\,e^{12}+430080\,a^{10}\,c^{10}\,d^{13}\,e^{10}+245760\,a^9\,c^{11}\,d^{15}\,e^8+92160\,a^8\,c^{12}\,d^{17}\,e^6+20480\,a^7\,c^{13}\,d^{19}\,e^4+2048\,a^6\,c^{14}\,d^{21}\,e^2\right)+256\,a^5\,c^{13}\,d^{19}\,e^3+5376\,a^6\,c^{12}\,d^{17}\,e^5+33792\,a^7\,c^{11}\,d^{15}\,e^7+107520\,a^8\,c^{10}\,d^{13}\,e^9+204288\,a^9\,c^9\,d^{11}\,e^{11}+247296\,a^{10}\,c^8\,d^9\,e^{13}+193536\,a^{11}\,c^7\,d^7\,e^{15}+95232\,a^{12}\,c^6\,d^5\,e^{17}+26880\,a^{13}\,c^5\,d^3\,e^{19}\right)-\sqrt{d+e\,x}\,\left(-800\,a^{12}\,c^4\,e^{20}-2432\,a^{11}\,c^5\,d^2\,e^{18}+3200\,a^{10}\,c^6\,d^4\,e^{16}+25600\,a^9\,c^7\,d^6\,e^{14}+51008\,a^8\,c^8\,d^8\,e^{12}+52480\,a^7\,c^9\,d^{10}\,e^{10}+30848\,a^6\,c^{10}\,d^{12}\,e^8+10240\,a^5\,c^{11}\,d^{14}\,e^6+1760\,a^4\,c^{12}\,d^{16}\,e^4+128\,a^3\,c^{13}\,d^{18}\,e^2\right)\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,1{}\mathrm{i}}{1000\,a^{10}\,c^4\,e^{19}-\left(\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,\left(3328\,a^{14}\,c^4\,d\,e^{21}-\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,\left(2048\,a^{16}\,c^4\,d\,e^{22}+20480\,a^{15}\,c^5\,d^3\,e^{20}+92160\,a^{14}\,c^6\,d^5\,e^{18}+245760\,a^{13}\,c^7\,d^7\,e^{16}+430080\,a^{12}\,c^8\,d^9\,e^{14}+516096\,a^{11}\,c^9\,d^{11}\,e^{12}+430080\,a^{10}\,c^{10}\,d^{13}\,e^{10}+245760\,a^9\,c^{11}\,d^{15}\,e^8+92160\,a^8\,c^{12}\,d^{17}\,e^6+20480\,a^7\,c^{13}\,d^{19}\,e^4+2048\,a^6\,c^{14}\,d^{21}\,e^2\right)+256\,a^5\,c^{13}\,d^{19}\,e^3+5376\,a^6\,c^{12}\,d^{17}\,e^5+33792\,a^7\,c^{11}\,d^{15}\,e^7+107520\,a^8\,c^{10}\,d^{13}\,e^9+204288\,a^9\,c^9\,d^{11}\,e^{11}+247296\,a^{10}\,c^8\,d^9\,e^{13}+193536\,a^{11}\,c^7\,d^7\,e^{15}+95232\,a^{12}\,c^6\,d^5\,e^{17}+26880\,a^{13}\,c^5\,d^3\,e^{19}\right)-\sqrt{d+e\,x}\,\left(-800\,a^{12}\,c^4\,e^{20}-2432\,a^{11}\,c^5\,d^2\,e^{18}+3200\,a^{10}\,c^6\,d^4\,e^{16}+25600\,a^9\,c^7\,d^6\,e^{14}+51008\,a^8\,c^8\,d^8\,e^{12}+52480\,a^7\,c^9\,d^{10}\,e^{10}+30848\,a^6\,c^{10}\,d^{12}\,e^8+10240\,a^5\,c^{11}\,d^{14}\,e^6+1760\,a^4\,c^{12}\,d^{16}\,e^4+128\,a^3\,c^{13}\,d^{18}\,e^2\right)\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}-\left(\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,\left(2048\,a^{16}\,c^4\,d\,e^{22}+20480\,a^{15}\,c^5\,d^3\,e^{20}+92160\,a^{14}\,c^6\,d^5\,e^{18}+245760\,a^{13}\,c^7\,d^7\,e^{16}+430080\,a^{12}\,c^8\,d^9\,e^{14}+516096\,a^{11}\,c^9\,d^{11}\,e^{12}+430080\,a^{10}\,c^{10}\,d^{13}\,e^{10}+245760\,a^9\,c^{11}\,d^{15}\,e^8+92160\,a^8\,c^{12}\,d^{17}\,e^6+20480\,a^7\,c^{13}\,d^{19}\,e^4+2048\,a^6\,c^{14}\,d^{21}\,e^2\right)+3328\,a^{14}\,c^4\,d\,e^{21}+256\,a^5\,c^{13}\,d^{19}\,e^3+5376\,a^6\,c^{12}\,d^{17}\,e^5+33792\,a^7\,c^{11}\,d^{15}\,e^7+107520\,a^8\,c^{10}\,d^{13}\,e^9+204288\,a^9\,c^9\,d^{11}\,e^{11}+247296\,a^{10}\,c^8\,d^9\,e^{13}+193536\,a^{11}\,c^7\,d^7\,e^{15}+95232\,a^{12}\,c^6\,d^5\,e^{17}+26880\,a^{13}\,c^5\,d^3\,e^{19}\right)+\sqrt{d+e\,x}\,\left(-800\,a^{12}\,c^4\,e^{20}-2432\,a^{11}\,c^5\,d^2\,e^{18}+3200\,a^{10}\,c^6\,d^4\,e^{16}+25600\,a^9\,c^7\,d^6\,e^{14}+51008\,a^8\,c^8\,d^8\,e^{12}+52480\,a^7\,c^9\,d^{10}\,e^{10}+30848\,a^6\,c^{10}\,d^{12}\,e^8+10240\,a^5\,c^{11}\,d^{14}\,e^6+1760\,a^4\,c^{12}\,d^{16}\,e^4+128\,a^3\,c^{13}\,d^{18}\,e^2\right)\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}-32\,a^2\,c^{12}\,d^{16}\,e^3-232\,a^3\,c^{11}\,d^{14}\,e^5+280\,a^4\,c^{10}\,d^{12}\,e^7+4760\,a^5\,c^9\,d^{10}\,e^9+13720\,a^6\,c^8\,d^8\,e^{11}+19208\,a^7\,c^7\,d^6\,e^{13}+14728\,a^8\,c^6\,d^4\,e^{15}+5960\,a^9\,c^5\,d^2\,e^{17}}\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7-25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4+35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6+154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,\left(2048\,a^{16}\,c^4\,d\,e^{22}+20480\,a^{15}\,c^5\,d^3\,e^{20}+92160\,a^{14}\,c^6\,d^5\,e^{18}+245760\,a^{13}\,c^7\,d^7\,e^{16}+430080\,a^{12}\,c^8\,d^9\,e^{14}+516096\,a^{11}\,c^9\,d^{11}\,e^{12}+430080\,a^{10}\,c^{10}\,d^{13}\,e^{10}+245760\,a^9\,c^{11}\,d^{15}\,e^8+92160\,a^8\,c^{12}\,d^{17}\,e^6+20480\,a^7\,c^{13}\,d^{19}\,e^4+2048\,a^6\,c^{14}\,d^{21}\,e^2\right)+3328\,a^{14}\,c^4\,d\,e^{21}+256\,a^5\,c^{13}\,d^{19}\,e^3+5376\,a^6\,c^{12}\,d^{17}\,e^5+33792\,a^7\,c^{11}\,d^{15}\,e^7+107520\,a^8\,c^{10}\,d^{13}\,e^9+204288\,a^9\,c^9\,d^{11}\,e^{11}+247296\,a^{10}\,c^8\,d^9\,e^{13}+193536\,a^{11}\,c^7\,d^7\,e^{15}+95232\,a^{12}\,c^6\,d^5\,e^{17}+26880\,a^{13}\,c^5\,d^3\,e^{19}\right)+\sqrt{d+e\,x}\,\left(-800\,a^{12}\,c^4\,e^{20}-2432\,a^{11}\,c^5\,d^2\,e^{18}+3200\,a^{10}\,c^6\,d^4\,e^{16}+25600\,a^9\,c^7\,d^6\,e^{14}+51008\,a^8\,c^8\,d^8\,e^{12}+52480\,a^7\,c^9\,d^{10}\,e^{10}+30848\,a^6\,c^{10}\,d^{12}\,e^8+10240\,a^5\,c^{11}\,d^{14}\,e^6+1760\,a^4\,c^{12}\,d^{16}\,e^4+128\,a^3\,c^{13}\,d^{18}\,e^2\right)\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,1{}\mathrm{i}-\left(\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,\left(3328\,a^{14}\,c^4\,d\,e^{21}-\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,\left(2048\,a^{16}\,c^4\,d\,e^{22}+20480\,a^{15}\,c^5\,d^3\,e^{20}+92160\,a^{14}\,c^6\,d^5\,e^{18}+245760\,a^{13}\,c^7\,d^7\,e^{16}+430080\,a^{12}\,c^8\,d^9\,e^{14}+516096\,a^{11}\,c^9\,d^{11}\,e^{12}+430080\,a^{10}\,c^{10}\,d^{13}\,e^{10}+245760\,a^9\,c^{11}\,d^{15}\,e^8+92160\,a^8\,c^{12}\,d^{17}\,e^6+20480\,a^7\,c^{13}\,d^{19}\,e^4+2048\,a^6\,c^{14}\,d^{21}\,e^2\right)+256\,a^5\,c^{13}\,d^{19}\,e^3+5376\,a^6\,c^{12}\,d^{17}\,e^5+33792\,a^7\,c^{11}\,d^{15}\,e^7+107520\,a^8\,c^{10}\,d^{13}\,e^9+204288\,a^9\,c^9\,d^{11}\,e^{11}+247296\,a^{10}\,c^8\,d^9\,e^{13}+193536\,a^{11}\,c^7\,d^7\,e^{15}+95232\,a^{12}\,c^6\,d^5\,e^{17}+26880\,a^{13}\,c^5\,d^3\,e^{19}\right)-\sqrt{d+e\,x}\,\left(-800\,a^{12}\,c^4\,e^{20}-2432\,a^{11}\,c^5\,d^2\,e^{18}+3200\,a^{10}\,c^6\,d^4\,e^{16}+25600\,a^9\,c^7\,d^6\,e^{14}+51008\,a^8\,c^8\,d^8\,e^{12}+52480\,a^7\,c^9\,d^{10}\,e^{10}+30848\,a^6\,c^{10}\,d^{12}\,e^8+10240\,a^5\,c^{11}\,d^{14}\,e^6+1760\,a^4\,c^{12}\,d^{16}\,e^4+128\,a^3\,c^{13}\,d^{18}\,e^2\right)\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,1{}\mathrm{i}}{1000\,a^{10}\,c^4\,e^{19}-\left(\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,\left(3328\,a^{14}\,c^4\,d\,e^{21}-\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,\left(2048\,a^{16}\,c^4\,d\,e^{22}+20480\,a^{15}\,c^5\,d^3\,e^{20}+92160\,a^{14}\,c^6\,d^5\,e^{18}+245760\,a^{13}\,c^7\,d^7\,e^{16}+430080\,a^{12}\,c^8\,d^9\,e^{14}+516096\,a^{11}\,c^9\,d^{11}\,e^{12}+430080\,a^{10}\,c^{10}\,d^{13}\,e^{10}+245760\,a^9\,c^{11}\,d^{15}\,e^8+92160\,a^8\,c^{12}\,d^{17}\,e^6+20480\,a^7\,c^{13}\,d^{19}\,e^4+2048\,a^6\,c^{14}\,d^{21}\,e^2\right)+256\,a^5\,c^{13}\,d^{19}\,e^3+5376\,a^6\,c^{12}\,d^{17}\,e^5+33792\,a^7\,c^{11}\,d^{15}\,e^7+107520\,a^8\,c^{10}\,d^{13}\,e^9+204288\,a^9\,c^9\,d^{11}\,e^{11}+247296\,a^{10}\,c^8\,d^9\,e^{13}+193536\,a^{11}\,c^7\,d^7\,e^{15}+95232\,a^{12}\,c^6\,d^5\,e^{17}+26880\,a^{13}\,c^5\,d^3\,e^{19}\right)-\sqrt{d+e\,x}\,\left(-800\,a^{12}\,c^4\,e^{20}-2432\,a^{11}\,c^5\,d^2\,e^{18}+3200\,a^{10}\,c^6\,d^4\,e^{16}+25600\,a^9\,c^7\,d^6\,e^{14}+51008\,a^8\,c^8\,d^8\,e^{12}+52480\,a^7\,c^9\,d^{10}\,e^{10}+30848\,a^6\,c^{10}\,d^{12}\,e^8+10240\,a^5\,c^{11}\,d^{14}\,e^6+1760\,a^4\,c^{12}\,d^{16}\,e^4+128\,a^3\,c^{13}\,d^{18}\,e^2\right)\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}-\left(\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,\left(2048\,a^{16}\,c^4\,d\,e^{22}+20480\,a^{15}\,c^5\,d^3\,e^{20}+92160\,a^{14}\,c^6\,d^5\,e^{18}+245760\,a^{13}\,c^7\,d^7\,e^{16}+430080\,a^{12}\,c^8\,d^9\,e^{14}+516096\,a^{11}\,c^9\,d^{11}\,e^{12}+430080\,a^{10}\,c^{10}\,d^{13}\,e^{10}+245760\,a^9\,c^{11}\,d^{15}\,e^8+92160\,a^8\,c^{12}\,d^{17}\,e^6+20480\,a^7\,c^{13}\,d^{19}\,e^4+2048\,a^6\,c^{14}\,d^{21}\,e^2\right)+3328\,a^{14}\,c^4\,d\,e^{21}+256\,a^5\,c^{13}\,d^{19}\,e^3+5376\,a^6\,c^{12}\,d^{17}\,e^5+33792\,a^7\,c^{11}\,d^{15}\,e^7+107520\,a^8\,c^{10}\,d^{13}\,e^9+204288\,a^9\,c^9\,d^{11}\,e^{11}+247296\,a^{10}\,c^8\,d^9\,e^{13}+193536\,a^{11}\,c^7\,d^7\,e^{15}+95232\,a^{12}\,c^6\,d^5\,e^{17}+26880\,a^{13}\,c^5\,d^3\,e^{19}\right)+\sqrt{d+e\,x}\,\left(-800\,a^{12}\,c^4\,e^{20}-2432\,a^{11}\,c^5\,d^2\,e^{18}+3200\,a^{10}\,c^6\,d^4\,e^{16}+25600\,a^9\,c^7\,d^6\,e^{14}+51008\,a^8\,c^8\,d^8\,e^{12}+52480\,a^7\,c^9\,d^{10}\,e^{10}+30848\,a^6\,c^{10}\,d^{12}\,e^8+10240\,a^5\,c^{11}\,d^{14}\,e^6+1760\,a^4\,c^{12}\,d^{16}\,e^4+128\,a^3\,c^{13}\,d^{18}\,e^2\right)\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}-32\,a^2\,c^{12}\,d^{16}\,e^3-232\,a^3\,c^{11}\,d^{14}\,e^5+280\,a^4\,c^{10}\,d^{12}\,e^7+4760\,a^5\,c^9\,d^{10}\,e^9+13720\,a^6\,c^8\,d^8\,e^{11}+19208\,a^7\,c^7\,d^6\,e^{13}+14728\,a^8\,c^6\,d^4\,e^{15}+5960\,a^9\,c^5\,d^2\,e^{17}}\right)\,\sqrt{-\frac{4\,a^3\,c^4\,d^7+25\,a^2\,e^7\,\sqrt{-a^9\,c}+35\,a^4\,c^3\,d^5\,e^2+70\,a^5\,c^2\,d^3\,e^4-35\,c^2\,d^4\,e^3\,\sqrt{-a^9\,c}-105\,a^6\,c\,d\,e^6-154\,a\,c\,d^2\,e^5\,\sqrt{-a^9\,c}}{64\,\left(a^{11}\,e^{10}+5\,a^{10}\,c\,d^2\,e^8+10\,a^9\,c^2\,d^4\,e^6+10\,a^8\,c^3\,d^6\,e^4+5\,a^7\,c^4\,d^8\,e^2+a^6\,c^5\,d^{10}\right)}}\,2{}\mathrm{i}","Not used",1,"atan((((-(4*a^3*c^4*d^7 - 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(2048*a^16*c^4*d*e^22 + 2048*a^6*c^14*d^21*e^2 + 20480*a^7*c^13*d^19*e^4 + 92160*a^8*c^12*d^17*e^6 + 245760*a^9*c^11*d^15*e^8 + 430080*a^10*c^10*d^13*e^10 + 516096*a^11*c^9*d^11*e^12 + 430080*a^12*c^8*d^9*e^14 + 245760*a^13*c^7*d^7*e^16 + 92160*a^14*c^6*d^5*e^18 + 20480*a^15*c^5*d^3*e^20) + 3328*a^14*c^4*d*e^21 + 256*a^5*c^13*d^19*e^3 + 5376*a^6*c^12*d^17*e^5 + 33792*a^7*c^11*d^15*e^7 + 107520*a^8*c^10*d^13*e^9 + 204288*a^9*c^9*d^11*e^11 + 247296*a^10*c^8*d^9*e^13 + 193536*a^11*c^7*d^7*e^15 + 95232*a^12*c^6*d^5*e^17 + 26880*a^13*c^5*d^3*e^19) + (d + e*x)^(1/2)*(128*a^3*c^13*d^18*e^2 - 800*a^12*c^4*e^20 + 1760*a^4*c^12*d^16*e^4 + 10240*a^5*c^11*d^14*e^6 + 30848*a^6*c^10*d^12*e^8 + 52480*a^7*c^9*d^10*e^10 + 51008*a^8*c^8*d^8*e^12 + 25600*a^9*c^7*d^6*e^14 + 3200*a^10*c^6*d^4*e^16 - 2432*a^11*c^5*d^2*e^18))*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*1i - ((-(4*a^3*c^4*d^7 - 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(3328*a^14*c^4*d*e^21 - (d + e*x)^(1/2)*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(2048*a^16*c^4*d*e^22 + 2048*a^6*c^14*d^21*e^2 + 20480*a^7*c^13*d^19*e^4 + 92160*a^8*c^12*d^17*e^6 + 245760*a^9*c^11*d^15*e^8 + 430080*a^10*c^10*d^13*e^10 + 516096*a^11*c^9*d^11*e^12 + 430080*a^12*c^8*d^9*e^14 + 245760*a^13*c^7*d^7*e^16 + 92160*a^14*c^6*d^5*e^18 + 20480*a^15*c^5*d^3*e^20) + 256*a^5*c^13*d^19*e^3 + 5376*a^6*c^12*d^17*e^5 + 33792*a^7*c^11*d^15*e^7 + 107520*a^8*c^10*d^13*e^9 + 204288*a^9*c^9*d^11*e^11 + 247296*a^10*c^8*d^9*e^13 + 193536*a^11*c^7*d^7*e^15 + 95232*a^12*c^6*d^5*e^17 + 26880*a^13*c^5*d^3*e^19) - (d + e*x)^(1/2)*(128*a^3*c^13*d^18*e^2 - 800*a^12*c^4*e^20 + 1760*a^4*c^12*d^16*e^4 + 10240*a^5*c^11*d^14*e^6 + 30848*a^6*c^10*d^12*e^8 + 52480*a^7*c^9*d^10*e^10 + 51008*a^8*c^8*d^8*e^12 + 25600*a^9*c^7*d^6*e^14 + 3200*a^10*c^6*d^4*e^16 - 2432*a^11*c^5*d^2*e^18))*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*1i)/(1000*a^10*c^4*e^19 - ((-(4*a^3*c^4*d^7 - 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(3328*a^14*c^4*d*e^21 - (d + e*x)^(1/2)*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(2048*a^16*c^4*d*e^22 + 2048*a^6*c^14*d^21*e^2 + 20480*a^7*c^13*d^19*e^4 + 92160*a^8*c^12*d^17*e^6 + 245760*a^9*c^11*d^15*e^8 + 430080*a^10*c^10*d^13*e^10 + 516096*a^11*c^9*d^11*e^12 + 430080*a^12*c^8*d^9*e^14 + 245760*a^13*c^7*d^7*e^16 + 92160*a^14*c^6*d^5*e^18 + 20480*a^15*c^5*d^3*e^20) + 256*a^5*c^13*d^19*e^3 + 5376*a^6*c^12*d^17*e^5 + 33792*a^7*c^11*d^15*e^7 + 107520*a^8*c^10*d^13*e^9 + 204288*a^9*c^9*d^11*e^11 + 247296*a^10*c^8*d^9*e^13 + 193536*a^11*c^7*d^7*e^15 + 95232*a^12*c^6*d^5*e^17 + 26880*a^13*c^5*d^3*e^19) - (d + e*x)^(1/2)*(128*a^3*c^13*d^18*e^2 - 800*a^12*c^4*e^20 + 1760*a^4*c^12*d^16*e^4 + 10240*a^5*c^11*d^14*e^6 + 30848*a^6*c^10*d^12*e^8 + 52480*a^7*c^9*d^10*e^10 + 51008*a^8*c^8*d^8*e^12 + 25600*a^9*c^7*d^6*e^14 + 3200*a^10*c^6*d^4*e^16 - 2432*a^11*c^5*d^2*e^18))*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2) - ((-(4*a^3*c^4*d^7 - 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(2048*a^16*c^4*d*e^22 + 2048*a^6*c^14*d^21*e^2 + 20480*a^7*c^13*d^19*e^4 + 92160*a^8*c^12*d^17*e^6 + 245760*a^9*c^11*d^15*e^8 + 430080*a^10*c^10*d^13*e^10 + 516096*a^11*c^9*d^11*e^12 + 430080*a^12*c^8*d^9*e^14 + 245760*a^13*c^7*d^7*e^16 + 92160*a^14*c^6*d^5*e^18 + 20480*a^15*c^5*d^3*e^20) + 3328*a^14*c^4*d*e^21 + 256*a^5*c^13*d^19*e^3 + 5376*a^6*c^12*d^17*e^5 + 33792*a^7*c^11*d^15*e^7 + 107520*a^8*c^10*d^13*e^9 + 204288*a^9*c^9*d^11*e^11 + 247296*a^10*c^8*d^9*e^13 + 193536*a^11*c^7*d^7*e^15 + 95232*a^12*c^6*d^5*e^17 + 26880*a^13*c^5*d^3*e^19) + (d + e*x)^(1/2)*(128*a^3*c^13*d^18*e^2 - 800*a^12*c^4*e^20 + 1760*a^4*c^12*d^16*e^4 + 10240*a^5*c^11*d^14*e^6 + 30848*a^6*c^10*d^12*e^8 + 52480*a^7*c^9*d^10*e^10 + 51008*a^8*c^8*d^8*e^12 + 25600*a^9*c^7*d^6*e^14 + 3200*a^10*c^6*d^4*e^16 - 2432*a^11*c^5*d^2*e^18))*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2) - 32*a^2*c^12*d^16*e^3 - 232*a^3*c^11*d^14*e^5 + 280*a^4*c^10*d^12*e^7 + 4760*a^5*c^9*d^10*e^9 + 13720*a^6*c^8*d^8*e^11 + 19208*a^7*c^7*d^6*e^13 + 14728*a^8*c^6*d^4*e^15 + 5960*a^9*c^5*d^2*e^17))*(-(4*a^3*c^4*d^7 - 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 + 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 + 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*2i - ((2*e^3)/(a*e^2 + c*d^2) + (c*e*(5*a*e^2 - c*d^2)*(d + e*x)^2)/(2*a*(a*e^2 + c*d^2)^2) - (c*d*e*(11*a*e^2 - c*d^2)*(d + e*x))/(2*a*(a*e^2 + c*d^2)^2))/(c*(d + e*x)^(5/2) + (a*e^2 + c*d^2)*(d + e*x)^(1/2) - 2*c*d*(d + e*x)^(3/2)) + atan((((-(4*a^3*c^4*d^7 + 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(2048*a^16*c^4*d*e^22 + 2048*a^6*c^14*d^21*e^2 + 20480*a^7*c^13*d^19*e^4 + 92160*a^8*c^12*d^17*e^6 + 245760*a^9*c^11*d^15*e^8 + 430080*a^10*c^10*d^13*e^10 + 516096*a^11*c^9*d^11*e^12 + 430080*a^12*c^8*d^9*e^14 + 245760*a^13*c^7*d^7*e^16 + 92160*a^14*c^6*d^5*e^18 + 20480*a^15*c^5*d^3*e^20) + 3328*a^14*c^4*d*e^21 + 256*a^5*c^13*d^19*e^3 + 5376*a^6*c^12*d^17*e^5 + 33792*a^7*c^11*d^15*e^7 + 107520*a^8*c^10*d^13*e^9 + 204288*a^9*c^9*d^11*e^11 + 247296*a^10*c^8*d^9*e^13 + 193536*a^11*c^7*d^7*e^15 + 95232*a^12*c^6*d^5*e^17 + 26880*a^13*c^5*d^3*e^19) + (d + e*x)^(1/2)*(128*a^3*c^13*d^18*e^2 - 800*a^12*c^4*e^20 + 1760*a^4*c^12*d^16*e^4 + 10240*a^5*c^11*d^14*e^6 + 30848*a^6*c^10*d^12*e^8 + 52480*a^7*c^9*d^10*e^10 + 51008*a^8*c^8*d^8*e^12 + 25600*a^9*c^7*d^6*e^14 + 3200*a^10*c^6*d^4*e^16 - 2432*a^11*c^5*d^2*e^18))*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*1i - ((-(4*a^3*c^4*d^7 + 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(3328*a^14*c^4*d*e^21 - (d + e*x)^(1/2)*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(2048*a^16*c^4*d*e^22 + 2048*a^6*c^14*d^21*e^2 + 20480*a^7*c^13*d^19*e^4 + 92160*a^8*c^12*d^17*e^6 + 245760*a^9*c^11*d^15*e^8 + 430080*a^10*c^10*d^13*e^10 + 516096*a^11*c^9*d^11*e^12 + 430080*a^12*c^8*d^9*e^14 + 245760*a^13*c^7*d^7*e^16 + 92160*a^14*c^6*d^5*e^18 + 20480*a^15*c^5*d^3*e^20) + 256*a^5*c^13*d^19*e^3 + 5376*a^6*c^12*d^17*e^5 + 33792*a^7*c^11*d^15*e^7 + 107520*a^8*c^10*d^13*e^9 + 204288*a^9*c^9*d^11*e^11 + 247296*a^10*c^8*d^9*e^13 + 193536*a^11*c^7*d^7*e^15 + 95232*a^12*c^6*d^5*e^17 + 26880*a^13*c^5*d^3*e^19) - (d + e*x)^(1/2)*(128*a^3*c^13*d^18*e^2 - 800*a^12*c^4*e^20 + 1760*a^4*c^12*d^16*e^4 + 10240*a^5*c^11*d^14*e^6 + 30848*a^6*c^10*d^12*e^8 + 52480*a^7*c^9*d^10*e^10 + 51008*a^8*c^8*d^8*e^12 + 25600*a^9*c^7*d^6*e^14 + 3200*a^10*c^6*d^4*e^16 - 2432*a^11*c^5*d^2*e^18))*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*1i)/(1000*a^10*c^4*e^19 - ((-(4*a^3*c^4*d^7 + 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(3328*a^14*c^4*d*e^21 - (d + e*x)^(1/2)*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(2048*a^16*c^4*d*e^22 + 2048*a^6*c^14*d^21*e^2 + 20480*a^7*c^13*d^19*e^4 + 92160*a^8*c^12*d^17*e^6 + 245760*a^9*c^11*d^15*e^8 + 430080*a^10*c^10*d^13*e^10 + 516096*a^11*c^9*d^11*e^12 + 430080*a^12*c^8*d^9*e^14 + 245760*a^13*c^7*d^7*e^16 + 92160*a^14*c^6*d^5*e^18 + 20480*a^15*c^5*d^3*e^20) + 256*a^5*c^13*d^19*e^3 + 5376*a^6*c^12*d^17*e^5 + 33792*a^7*c^11*d^15*e^7 + 107520*a^8*c^10*d^13*e^9 + 204288*a^9*c^9*d^11*e^11 + 247296*a^10*c^8*d^9*e^13 + 193536*a^11*c^7*d^7*e^15 + 95232*a^12*c^6*d^5*e^17 + 26880*a^13*c^5*d^3*e^19) - (d + e*x)^(1/2)*(128*a^3*c^13*d^18*e^2 - 800*a^12*c^4*e^20 + 1760*a^4*c^12*d^16*e^4 + 10240*a^5*c^11*d^14*e^6 + 30848*a^6*c^10*d^12*e^8 + 52480*a^7*c^9*d^10*e^10 + 51008*a^8*c^8*d^8*e^12 + 25600*a^9*c^7*d^6*e^14 + 3200*a^10*c^6*d^4*e^16 - 2432*a^11*c^5*d^2*e^18))*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2) - ((-(4*a^3*c^4*d^7 + 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*(2048*a^16*c^4*d*e^22 + 2048*a^6*c^14*d^21*e^2 + 20480*a^7*c^13*d^19*e^4 + 92160*a^8*c^12*d^17*e^6 + 245760*a^9*c^11*d^15*e^8 + 430080*a^10*c^10*d^13*e^10 + 516096*a^11*c^9*d^11*e^12 + 430080*a^12*c^8*d^9*e^14 + 245760*a^13*c^7*d^7*e^16 + 92160*a^14*c^6*d^5*e^18 + 20480*a^15*c^5*d^3*e^20) + 3328*a^14*c^4*d*e^21 + 256*a^5*c^13*d^19*e^3 + 5376*a^6*c^12*d^17*e^5 + 33792*a^7*c^11*d^15*e^7 + 107520*a^8*c^10*d^13*e^9 + 204288*a^9*c^9*d^11*e^11 + 247296*a^10*c^8*d^9*e^13 + 193536*a^11*c^7*d^7*e^15 + 95232*a^12*c^6*d^5*e^17 + 26880*a^13*c^5*d^3*e^19) + (d + e*x)^(1/2)*(128*a^3*c^13*d^18*e^2 - 800*a^12*c^4*e^20 + 1760*a^4*c^12*d^16*e^4 + 10240*a^5*c^11*d^14*e^6 + 30848*a^6*c^10*d^12*e^8 + 52480*a^7*c^9*d^10*e^10 + 51008*a^8*c^8*d^8*e^12 + 25600*a^9*c^7*d^6*e^14 + 3200*a^10*c^6*d^4*e^16 - 2432*a^11*c^5*d^2*e^18))*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2) - 32*a^2*c^12*d^16*e^3 - 232*a^3*c^11*d^14*e^5 + 280*a^4*c^10*d^12*e^7 + 4760*a^5*c^9*d^10*e^9 + 13720*a^6*c^8*d^8*e^11 + 19208*a^7*c^7*d^6*e^13 + 14728*a^8*c^6*d^4*e^15 + 5960*a^9*c^5*d^2*e^17))*(-(4*a^3*c^4*d^7 + 25*a^2*e^7*(-a^9*c)^(1/2) + 35*a^4*c^3*d^5*e^2 + 70*a^5*c^2*d^3*e^4 - 35*c^2*d^4*e^3*(-a^9*c)^(1/2) - 105*a^6*c*d*e^6 - 154*a*c*d^2*e^5*(-a^9*c)^(1/2))/(64*(a^11*e^10 + a^6*c^5*d^10 + 5*a^10*c*d^2*e^8 + 5*a^7*c^4*d^8*e^2 + 10*a^8*c^3*d^6*e^4 + 10*a^9*c^2*d^4*e^6)))^(1/2)*2i","B"
637,1,12390,930,4.738558,"\text{Not used}","int(1/((a + c*x^2)^2*(d + e*x)^(5/2)),x)","-\frac{\frac{2\,e^3}{3\,\left(c\,d^2+a\,e^2\right)}+\frac{20\,c\,d\,e^3\,\left(d+e\,x\right)}{3\,{\left(c\,d^2+a\,e^2\right)}^2}+\frac{c\,e\,{\left(d+e\,x\right)}^2\,\left(7\,a^2\,e^4-110\,a\,c\,d^2\,e^2+3\,c^2\,d^4\right)}{6\,a\,{\left(c\,d^2+a\,e^2\right)}^3}+\frac{c^2\,d\,e\,\left(19\,a\,e^2-c\,d^2\right)\,{\left(d+e\,x\right)}^3}{2\,a\,{\left(c\,d^2+a\,e^2\right)}^3}}{c\,{\left(d+e\,x\right)}^{7/2}+\left(c\,d^2+a\,e^2\right)\,{\left(d+e\,x\right)}^{3/2}-2\,c\,d\,{\left(d+e\,x\right)}^{5/2}}+\mathrm{atan}\left(\frac{\left(\sqrt{d+e\,x}\,\left(1568\,a^{16}\,c^5\,e^{28}-4160\,a^{15}\,c^6\,d^2\,e^{26}-100480\,a^{14}\,c^7\,d^4\,e^{24}-456512\,a^{13}\,c^8\,d^6\,e^{22}-1049440\,a^{12}\,c^9\,d^8\,e^{20}-1403904\,a^{11}\,c^{10}\,d^{10}\,e^{18}-1059840\,a^{10}\,c^{11}\,d^{12}\,e^{16}-282240\,a^9\,c^{12}\,d^{14}\,e^{14}+242016\,a^8\,c^{13}\,d^{16}\,e^{12}+282560\,a^7\,c^{14}\,d^{18}\,e^{10}+128128\,a^6\,c^{15}\,d^{20}\,e^8+29120\,a^5\,c^{16}\,d^{22}\,e^6+3040\,a^4\,c^{17}\,d^{24}\,e^4+128\,a^3\,c^{18}\,d^{26}\,e^2\right)+\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,\left(2048\,a^{21}\,c^4\,d\,e^{32}+30720\,a^{20}\,c^5\,d^3\,e^{30}+215040\,a^{19}\,c^6\,d^5\,e^{28}+931840\,a^{18}\,c^7\,d^7\,e^{26}+2795520\,a^{17}\,c^8\,d^9\,e^{24}+6150144\,a^{16}\,c^9\,d^{11}\,e^{22}+10250240\,a^{15}\,c^{10}\,d^{13}\,e^{20}+13178880\,a^{14}\,c^{11}\,d^{15}\,e^{18}+13178880\,a^{13}\,c^{12}\,d^{17}\,e^{16}+10250240\,a^{12}\,c^{13}\,d^{19}\,e^{14}+6150144\,a^{11}\,c^{14}\,d^{21}\,e^{12}+2795520\,a^{10}\,c^{15}\,d^{23}\,e^{10}+931840\,a^9\,c^{16}\,d^{25}\,e^8+215040\,a^8\,c^{17}\,d^{27}\,e^6+30720\,a^7\,c^{18}\,d^{29}\,e^4+2048\,a^6\,c^{19}\,d^{31}\,e^2\right)-1792\,a^{19}\,c^4\,e^{31}+256\,a^5\,c^{18}\,d^{28}\,e^3+11776\,a^6\,c^{17}\,d^{26}\,e^5+119552\,a^7\,c^{16}\,d^{24}\,e^7+609280\,a^8\,c^{15}\,d^{22}\,e^9+1923328\,a^9\,c^{14}\,d^{20}\,e^{11}+4116992\,a^{10}\,c^{13}\,d^{18}\,e^{13}+6243072\,a^{11}\,c^{12}\,d^{16}\,e^{15}+6825984\,a^{12}\,c^{11}\,d^{14}\,e^{17}+5364480\,a^{13}\,c^{10}\,d^{12}\,e^{19}+2945536\,a^{14}\,c^9\,d^{10}\,e^{21}+1044736\,a^{15}\,c^8\,d^8\,e^{23}+183296\,a^{16}\,c^7\,d^6\,e^{25}-13568\,a^{17}\,c^6\,d^4\,e^{27}-12800\,a^{18}\,c^5\,d^2\,e^{29}\right)\right)\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,1{}\mathrm{i}+\left(\sqrt{d+e\,x}\,\left(1568\,a^{16}\,c^5\,e^{28}-4160\,a^{15}\,c^6\,d^2\,e^{26}-100480\,a^{14}\,c^7\,d^4\,e^{24}-456512\,a^{13}\,c^8\,d^6\,e^{22}-1049440\,a^{12}\,c^9\,d^8\,e^{20}-1403904\,a^{11}\,c^{10}\,d^{10}\,e^{18}-1059840\,a^{10}\,c^{11}\,d^{12}\,e^{16}-282240\,a^9\,c^{12}\,d^{14}\,e^{14}+242016\,a^8\,c^{13}\,d^{16}\,e^{12}+282560\,a^7\,c^{14}\,d^{18}\,e^{10}+128128\,a^6\,c^{15}\,d^{20}\,e^8+29120\,a^5\,c^{16}\,d^{22}\,e^6+3040\,a^4\,c^{17}\,d^{24}\,e^4+128\,a^3\,c^{18}\,d^{26}\,e^2\right)-\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,\left(256\,a^5\,c^{18}\,d^{28}\,e^3-1792\,a^{19}\,c^4\,e^{31}-\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,\left(2048\,a^{21}\,c^4\,d\,e^{32}+30720\,a^{20}\,c^5\,d^3\,e^{30}+215040\,a^{19}\,c^6\,d^5\,e^{28}+931840\,a^{18}\,c^7\,d^7\,e^{26}+2795520\,a^{17}\,c^8\,d^9\,e^{24}+6150144\,a^{16}\,c^9\,d^{11}\,e^{22}+10250240\,a^{15}\,c^{10}\,d^{13}\,e^{20}+13178880\,a^{14}\,c^{11}\,d^{15}\,e^{18}+13178880\,a^{13}\,c^{12}\,d^{17}\,e^{16}+10250240\,a^{12}\,c^{13}\,d^{19}\,e^{14}+6150144\,a^{11}\,c^{14}\,d^{21}\,e^{12}+2795520\,a^{10}\,c^{15}\,d^{23}\,e^{10}+931840\,a^9\,c^{16}\,d^{25}\,e^8+215040\,a^8\,c^{17}\,d^{27}\,e^6+30720\,a^7\,c^{18}\,d^{29}\,e^4+2048\,a^6\,c^{19}\,d^{31}\,e^2\right)+11776\,a^6\,c^{17}\,d^{26}\,e^5+119552\,a^7\,c^{16}\,d^{24}\,e^7+609280\,a^8\,c^{15}\,d^{22}\,e^9+1923328\,a^9\,c^{14}\,d^{20}\,e^{11}+4116992\,a^{10}\,c^{13}\,d^{18}\,e^{13}+6243072\,a^{11}\,c^{12}\,d^{16}\,e^{15}+6825984\,a^{12}\,c^{11}\,d^{14}\,e^{17}+5364480\,a^{13}\,c^{10}\,d^{12}\,e^{19}+2945536\,a^{14}\,c^9\,d^{10}\,e^{21}+1044736\,a^{15}\,c^8\,d^8\,e^{23}+183296\,a^{16}\,c^7\,d^6\,e^{25}-13568\,a^{17}\,c^6\,d^4\,e^{27}-12800\,a^{18}\,c^5\,d^2\,e^{29}\right)\right)\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,1{}\mathrm{i}}{\left(\sqrt{d+e\,x}\,\left(1568\,a^{16}\,c^5\,e^{28}-4160\,a^{15}\,c^6\,d^2\,e^{26}-100480\,a^{14}\,c^7\,d^4\,e^{24}-456512\,a^{13}\,c^8\,d^6\,e^{22}-1049440\,a^{12}\,c^9\,d^8\,e^{20}-1403904\,a^{11}\,c^{10}\,d^{10}\,e^{18}-1059840\,a^{10}\,c^{11}\,d^{12}\,e^{16}-282240\,a^9\,c^{12}\,d^{14}\,e^{14}+242016\,a^8\,c^{13}\,d^{16}\,e^{12}+282560\,a^7\,c^{14}\,d^{18}\,e^{10}+128128\,a^6\,c^{15}\,d^{20}\,e^8+29120\,a^5\,c^{16}\,d^{22}\,e^6+3040\,a^4\,c^{17}\,d^{24}\,e^4+128\,a^3\,c^{18}\,d^{26}\,e^2\right)-\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,\left(256\,a^5\,c^{18}\,d^{28}\,e^3-1792\,a^{19}\,c^4\,e^{31}-\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,\left(2048\,a^{21}\,c^4\,d\,e^{32}+30720\,a^{20}\,c^5\,d^3\,e^{30}+215040\,a^{19}\,c^6\,d^5\,e^{28}+931840\,a^{18}\,c^7\,d^7\,e^{26}+2795520\,a^{17}\,c^8\,d^9\,e^{24}+6150144\,a^{16}\,c^9\,d^{11}\,e^{22}+10250240\,a^{15}\,c^{10}\,d^{13}\,e^{20}+13178880\,a^{14}\,c^{11}\,d^{15}\,e^{18}+13178880\,a^{13}\,c^{12}\,d^{17}\,e^{16}+10250240\,a^{12}\,c^{13}\,d^{19}\,e^{14}+6150144\,a^{11}\,c^{14}\,d^{21}\,e^{12}+2795520\,a^{10}\,c^{15}\,d^{23}\,e^{10}+931840\,a^9\,c^{16}\,d^{25}\,e^8+215040\,a^8\,c^{17}\,d^{27}\,e^6+30720\,a^7\,c^{18}\,d^{29}\,e^4+2048\,a^6\,c^{19}\,d^{31}\,e^2\right)+11776\,a^6\,c^{17}\,d^{26}\,e^5+119552\,a^7\,c^{16}\,d^{24}\,e^7+609280\,a^8\,c^{15}\,d^{22}\,e^9+1923328\,a^9\,c^{14}\,d^{20}\,e^{11}+4116992\,a^{10}\,c^{13}\,d^{18}\,e^{13}+6243072\,a^{11}\,c^{12}\,d^{16}\,e^{15}+6825984\,a^{12}\,c^{11}\,d^{14}\,e^{17}+5364480\,a^{13}\,c^{10}\,d^{12}\,e^{19}+2945536\,a^{14}\,c^9\,d^{10}\,e^{21}+1044736\,a^{15}\,c^8\,d^8\,e^{23}+183296\,a^{16}\,c^7\,d^6\,e^{25}-13568\,a^{17}\,c^6\,d^4\,e^{27}-12800\,a^{18}\,c^5\,d^2\,e^{29}\right)\right)\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}-\left(\sqrt{d+e\,x}\,\left(1568\,a^{16}\,c^5\,e^{28}-4160\,a^{15}\,c^6\,d^2\,e^{26}-100480\,a^{14}\,c^7\,d^4\,e^{24}-456512\,a^{13}\,c^8\,d^6\,e^{22}-1049440\,a^{12}\,c^9\,d^8\,e^{20}-1403904\,a^{11}\,c^{10}\,d^{10}\,e^{18}-1059840\,a^{10}\,c^{11}\,d^{12}\,e^{16}-282240\,a^9\,c^{12}\,d^{14}\,e^{14}+242016\,a^8\,c^{13}\,d^{16}\,e^{12}+282560\,a^7\,c^{14}\,d^{18}\,e^{10}+128128\,a^6\,c^{15}\,d^{20}\,e^8+29120\,a^5\,c^{16}\,d^{22}\,e^6+3040\,a^4\,c^{17}\,d^{24}\,e^4+128\,a^3\,c^{18}\,d^{26}\,e^2\right)+\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,\left(2048\,a^{21}\,c^4\,d\,e^{32}+30720\,a^{20}\,c^5\,d^3\,e^{30}+215040\,a^{19}\,c^6\,d^5\,e^{28}+931840\,a^{18}\,c^7\,d^7\,e^{26}+2795520\,a^{17}\,c^8\,d^9\,e^{24}+6150144\,a^{16}\,c^9\,d^{11}\,e^{22}+10250240\,a^{15}\,c^{10}\,d^{13}\,e^{20}+13178880\,a^{14}\,c^{11}\,d^{15}\,e^{18}+13178880\,a^{13}\,c^{12}\,d^{17}\,e^{16}+10250240\,a^{12}\,c^{13}\,d^{19}\,e^{14}+6150144\,a^{11}\,c^{14}\,d^{21}\,e^{12}+2795520\,a^{10}\,c^{15}\,d^{23}\,e^{10}+931840\,a^9\,c^{16}\,d^{25}\,e^8+215040\,a^8\,c^{17}\,d^{27}\,e^6+30720\,a^7\,c^{18}\,d^{29}\,e^4+2048\,a^6\,c^{19}\,d^{31}\,e^2\right)-1792\,a^{19}\,c^4\,e^{31}+256\,a^5\,c^{18}\,d^{28}\,e^3+11776\,a^6\,c^{17}\,d^{26}\,e^5+119552\,a^7\,c^{16}\,d^{24}\,e^7+609280\,a^8\,c^{15}\,d^{22}\,e^9+1923328\,a^9\,c^{14}\,d^{20}\,e^{11}+4116992\,a^{10}\,c^{13}\,d^{18}\,e^{13}+6243072\,a^{11}\,c^{12}\,d^{16}\,e^{15}+6825984\,a^{12}\,c^{11}\,d^{14}\,e^{17}+5364480\,a^{13}\,c^{10}\,d^{12}\,e^{19}+2945536\,a^{14}\,c^9\,d^{10}\,e^{21}+1044736\,a^{15}\,c^8\,d^8\,e^{23}+183296\,a^{16}\,c^7\,d^6\,e^{25}-13568\,a^{17}\,c^6\,d^4\,e^{27}-12800\,a^{18}\,c^5\,d^2\,e^{29}\right)\right)\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}+7448\,a^{13}\,c^6\,d\,e^{25}-32\,a^2\,c^{17}\,d^{23}\,e^3-72\,a^3\,c^{16}\,d^{21}\,e^5+8240\,a^4\,c^{15}\,d^{19}\,e^7+72120\,a^5\,c^{14}\,d^{17}\,e^9+282240\,a^6\,c^{13}\,d^{15}\,e^{11}+648816\,a^7\,c^{12}\,d^{13}\,e^{13}+962976\,a^8\,c^{11}\,d^{11}\,e^{15}+955440\,a^9\,c^{10}\,d^9\,e^{17}+633120\,a^{10}\,c^9\,d^7\,e^{19}+270040\,a^{11}\,c^8\,d^5\,e^{21}+67248\,a^{12}\,c^7\,d^3\,e^{23}}\right)\,\sqrt{-\frac{4\,a^3\,c^6\,d^9-49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6-105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}-819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}+837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\sqrt{d+e\,x}\,\left(1568\,a^{16}\,c^5\,e^{28}-4160\,a^{15}\,c^6\,d^2\,e^{26}-100480\,a^{14}\,c^7\,d^4\,e^{24}-456512\,a^{13}\,c^8\,d^6\,e^{22}-1049440\,a^{12}\,c^9\,d^8\,e^{20}-1403904\,a^{11}\,c^{10}\,d^{10}\,e^{18}-1059840\,a^{10}\,c^{11}\,d^{12}\,e^{16}-282240\,a^9\,c^{12}\,d^{14}\,e^{14}+242016\,a^8\,c^{13}\,d^{16}\,e^{12}+282560\,a^7\,c^{14}\,d^{18}\,e^{10}+128128\,a^6\,c^{15}\,d^{20}\,e^8+29120\,a^5\,c^{16}\,d^{22}\,e^6+3040\,a^4\,c^{17}\,d^{24}\,e^4+128\,a^3\,c^{18}\,d^{26}\,e^2\right)+\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,\left(2048\,a^{21}\,c^4\,d\,e^{32}+30720\,a^{20}\,c^5\,d^3\,e^{30}+215040\,a^{19}\,c^6\,d^5\,e^{28}+931840\,a^{18}\,c^7\,d^7\,e^{26}+2795520\,a^{17}\,c^8\,d^9\,e^{24}+6150144\,a^{16}\,c^9\,d^{11}\,e^{22}+10250240\,a^{15}\,c^{10}\,d^{13}\,e^{20}+13178880\,a^{14}\,c^{11}\,d^{15}\,e^{18}+13178880\,a^{13}\,c^{12}\,d^{17}\,e^{16}+10250240\,a^{12}\,c^{13}\,d^{19}\,e^{14}+6150144\,a^{11}\,c^{14}\,d^{21}\,e^{12}+2795520\,a^{10}\,c^{15}\,d^{23}\,e^{10}+931840\,a^9\,c^{16}\,d^{25}\,e^8+215040\,a^8\,c^{17}\,d^{27}\,e^6+30720\,a^7\,c^{18}\,d^{29}\,e^4+2048\,a^6\,c^{19}\,d^{31}\,e^2\right)-1792\,a^{19}\,c^4\,e^{31}+256\,a^5\,c^{18}\,d^{28}\,e^3+11776\,a^6\,c^{17}\,d^{26}\,e^5+119552\,a^7\,c^{16}\,d^{24}\,e^7+609280\,a^8\,c^{15}\,d^{22}\,e^9+1923328\,a^9\,c^{14}\,d^{20}\,e^{11}+4116992\,a^{10}\,c^{13}\,d^{18}\,e^{13}+6243072\,a^{11}\,c^{12}\,d^{16}\,e^{15}+6825984\,a^{12}\,c^{11}\,d^{14}\,e^{17}+5364480\,a^{13}\,c^{10}\,d^{12}\,e^{19}+2945536\,a^{14}\,c^9\,d^{10}\,e^{21}+1044736\,a^{15}\,c^8\,d^8\,e^{23}+183296\,a^{16}\,c^7\,d^6\,e^{25}-13568\,a^{17}\,c^6\,d^4\,e^{27}-12800\,a^{18}\,c^5\,d^2\,e^{29}\right)\right)\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,1{}\mathrm{i}+\left(\sqrt{d+e\,x}\,\left(1568\,a^{16}\,c^5\,e^{28}-4160\,a^{15}\,c^6\,d^2\,e^{26}-100480\,a^{14}\,c^7\,d^4\,e^{24}-456512\,a^{13}\,c^8\,d^6\,e^{22}-1049440\,a^{12}\,c^9\,d^8\,e^{20}-1403904\,a^{11}\,c^{10}\,d^{10}\,e^{18}-1059840\,a^{10}\,c^{11}\,d^{12}\,e^{16}-282240\,a^9\,c^{12}\,d^{14}\,e^{14}+242016\,a^8\,c^{13}\,d^{16}\,e^{12}+282560\,a^7\,c^{14}\,d^{18}\,e^{10}+128128\,a^6\,c^{15}\,d^{20}\,e^8+29120\,a^5\,c^{16}\,d^{22}\,e^6+3040\,a^4\,c^{17}\,d^{24}\,e^4+128\,a^3\,c^{18}\,d^{26}\,e^2\right)-\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,\left(256\,a^5\,c^{18}\,d^{28}\,e^3-1792\,a^{19}\,c^4\,e^{31}-\sqrt{d+e\,x}\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,\left(2048\,a^{21}\,c^4\,d\,e^{32}+30720\,a^{20}\,c^5\,d^3\,e^{30}+215040\,a^{19}\,c^6\,d^5\,e^{28}+931840\,a^{18}\,c^7\,d^7\,e^{26}+2795520\,a^{17}\,c^8\,d^9\,e^{24}+6150144\,a^{16}\,c^9\,d^{11}\,e^{22}+10250240\,a^{15}\,c^{10}\,d^{13}\,e^{20}+13178880\,a^{14}\,c^{11}\,d^{15}\,e^{18}+13178880\,a^{13}\,c^{12}\,d^{17}\,e^{16}+10250240\,a^{12}\,c^{13}\,d^{19}\,e^{14}+6150144\,a^{11}\,c^{14}\,d^{21}\,e^{12}+2795520\,a^{10}\,c^{15}\,d^{23}\,e^{10}+931840\,a^9\,c^{16}\,d^{25}\,e^8+215040\,a^8\,c^{17}\,d^{27}\,e^6+30720\,a^7\,c^{18}\,d^{29}\,e^4+2048\,a^6\,c^{19}\,d^{31}\,e^2\right)+11776\,a^6\,c^{17}\,d^{26}\,e^5+119552\,a^7\,c^{16}\,d^{24}\,e^7+609280\,a^8\,c^{15}\,d^{22}\,e^9+1923328\,a^9\,c^{14}\,d^{20}\,e^{11}+4116992\,a^{10}\,c^{13}\,d^{18}\,e^{13}+6243072\,a^{11}\,c^{12}\,d^{16}\,e^{15}+6825984\,a^{12}\,c^{11}\,d^{14}\,e^{17}+5364480\,a^{13}\,c^{10}\,d^{12}\,e^{19}+2945536\,a^{14}\,c^9\,d^{10}\,e^{21}+1044736\,a^{15}\,c^8\,d^8\,e^{23}+183296\,a^{16}\,c^7\,d^6\,e^{25}-13568\,a^{17}\,c^6\,d^4\,e^{27}-12800\,a^{18}\,c^5\,d^2\,e^{29}\right)\right)\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,1{}\mathrm{i}}{\left(\sqrt{d+e\,x}\,\left(1568\,a^{16}\,c^5\,e^{28}-4160\,a^{15}\,c^6\,d^2\,e^{26}-100480\,a^{14}\,c^7\,d^4\,e^{24}-456512\,a^{13}\,c^8\,d^6\,e^{22}-1049440\,a^{12}\,c^9\,d^8\,e^{20}-1403904\,a^{11}\,c^{10}\,d^{10}\,e^{18}-1059840\,a^{10}\,c^{11}\,d^{12}\,e^{16}-282240\,a^9\,c^{12}\,d^{14}\,e^{14}+242016\,a^8\,c^{13}\,d^{16}\,e^{12}+282560\,a^7\,c^{14}\,d^{18}\,e^{10}+128128\,a^6\,c^{15}\,d^{20}\,e^8+29120\,a^5\,c^{16}\,d^{22}\,e^6+3040\,a^4\,c^{17}\,d^{24}\,e^4+128\,a^3\,c^{18}\,d^{26}\,e^2\right)-\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,\left(256\,a^5\,c^{18}\,d^{28}\,e^3-1792\,a^{19}\,c^4\,e^{31}-\sqrt{d+e\,x}\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,\left(2048\,a^{21}\,c^4\,d\,e^{32}+30720\,a^{20}\,c^5\,d^3\,e^{30}+215040\,a^{19}\,c^6\,d^5\,e^{28}+931840\,a^{18}\,c^7\,d^7\,e^{26}+2795520\,a^{17}\,c^8\,d^9\,e^{24}+6150144\,a^{16}\,c^9\,d^{11}\,e^{22}+10250240\,a^{15}\,c^{10}\,d^{13}\,e^{20}+13178880\,a^{14}\,c^{11}\,d^{15}\,e^{18}+13178880\,a^{13}\,c^{12}\,d^{17}\,e^{16}+10250240\,a^{12}\,c^{13}\,d^{19}\,e^{14}+6150144\,a^{11}\,c^{14}\,d^{21}\,e^{12}+2795520\,a^{10}\,c^{15}\,d^{23}\,e^{10}+931840\,a^9\,c^{16}\,d^{25}\,e^8+215040\,a^8\,c^{17}\,d^{27}\,e^6+30720\,a^7\,c^{18}\,d^{29}\,e^4+2048\,a^6\,c^{19}\,d^{31}\,e^2\right)+11776\,a^6\,c^{17}\,d^{26}\,e^5+119552\,a^7\,c^{16}\,d^{24}\,e^7+609280\,a^8\,c^{15}\,d^{22}\,e^9+1923328\,a^9\,c^{14}\,d^{20}\,e^{11}+4116992\,a^{10}\,c^{13}\,d^{18}\,e^{13}+6243072\,a^{11}\,c^{12}\,d^{16}\,e^{15}+6825984\,a^{12}\,c^{11}\,d^{14}\,e^{17}+5364480\,a^{13}\,c^{10}\,d^{12}\,e^{19}+2945536\,a^{14}\,c^9\,d^{10}\,e^{21}+1044736\,a^{15}\,c^8\,d^8\,e^{23}+183296\,a^{16}\,c^7\,d^6\,e^{25}-13568\,a^{17}\,c^6\,d^4\,e^{27}-12800\,a^{18}\,c^5\,d^2\,e^{29}\right)\right)\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}-\left(\sqrt{d+e\,x}\,\left(1568\,a^{16}\,c^5\,e^{28}-4160\,a^{15}\,c^6\,d^2\,e^{26}-100480\,a^{14}\,c^7\,d^4\,e^{24}-456512\,a^{13}\,c^8\,d^6\,e^{22}-1049440\,a^{12}\,c^9\,d^8\,e^{20}-1403904\,a^{11}\,c^{10}\,d^{10}\,e^{18}-1059840\,a^{10}\,c^{11}\,d^{12}\,e^{16}-282240\,a^9\,c^{12}\,d^{14}\,e^{14}+242016\,a^8\,c^{13}\,d^{16}\,e^{12}+282560\,a^7\,c^{14}\,d^{18}\,e^{10}+128128\,a^6\,c^{15}\,d^{20}\,e^8+29120\,a^5\,c^{16}\,d^{22}\,e^6+3040\,a^4\,c^{17}\,d^{24}\,e^4+128\,a^3\,c^{18}\,d^{26}\,e^2\right)+\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,\left(2048\,a^{21}\,c^4\,d\,e^{32}+30720\,a^{20}\,c^5\,d^3\,e^{30}+215040\,a^{19}\,c^6\,d^5\,e^{28}+931840\,a^{18}\,c^7\,d^7\,e^{26}+2795520\,a^{17}\,c^8\,d^9\,e^{24}+6150144\,a^{16}\,c^9\,d^{11}\,e^{22}+10250240\,a^{15}\,c^{10}\,d^{13}\,e^{20}+13178880\,a^{14}\,c^{11}\,d^{15}\,e^{18}+13178880\,a^{13}\,c^{12}\,d^{17}\,e^{16}+10250240\,a^{12}\,c^{13}\,d^{19}\,e^{14}+6150144\,a^{11}\,c^{14}\,d^{21}\,e^{12}+2795520\,a^{10}\,c^{15}\,d^{23}\,e^{10}+931840\,a^9\,c^{16}\,d^{25}\,e^8+215040\,a^8\,c^{17}\,d^{27}\,e^6+30720\,a^7\,c^{18}\,d^{29}\,e^4+2048\,a^6\,c^{19}\,d^{31}\,e^2\right)-1792\,a^{19}\,c^4\,e^{31}+256\,a^5\,c^{18}\,d^{28}\,e^3+11776\,a^6\,c^{17}\,d^{26}\,e^5+119552\,a^7\,c^{16}\,d^{24}\,e^7+609280\,a^8\,c^{15}\,d^{22}\,e^9+1923328\,a^9\,c^{14}\,d^{20}\,e^{11}+4116992\,a^{10}\,c^{13}\,d^{18}\,e^{13}+6243072\,a^{11}\,c^{12}\,d^{16}\,e^{15}+6825984\,a^{12}\,c^{11}\,d^{14}\,e^{17}+5364480\,a^{13}\,c^{10}\,d^{12}\,e^{19}+2945536\,a^{14}\,c^9\,d^{10}\,e^{21}+1044736\,a^{15}\,c^8\,d^8\,e^{23}+183296\,a^{16}\,c^7\,d^6\,e^{25}-13568\,a^{17}\,c^6\,d^4\,e^{27}-12800\,a^{18}\,c^5\,d^2\,e^{29}\right)\right)\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}+7448\,a^{13}\,c^6\,d\,e^{25}-32\,a^2\,c^{17}\,d^{23}\,e^3-72\,a^3\,c^{16}\,d^{21}\,e^5+8240\,a^4\,c^{15}\,d^{19}\,e^7+72120\,a^5\,c^{14}\,d^{17}\,e^9+282240\,a^6\,c^{13}\,d^{15}\,e^{11}+648816\,a^7\,c^{12}\,d^{13}\,e^{13}+962976\,a^8\,c^{11}\,d^{11}\,e^{15}+955440\,a^9\,c^{10}\,d^9\,e^{17}+633120\,a^{10}\,c^9\,d^7\,e^{19}+270040\,a^{11}\,c^8\,d^5\,e^{21}+67248\,a^{12}\,c^7\,d^3\,e^{23}}\right)\,\sqrt{-\frac{49\,a^3\,e^9\,\sqrt{-a^9\,c^3}+4\,a^3\,c^6\,d^9+315\,a^7\,c^2\,d\,e^8+63\,a^4\,c^5\,d^7\,e^2+189\,a^5\,c^4\,d^5\,e^4-1155\,a^6\,c^3\,d^3\,e^6+105\,c^3\,d^6\,e^3\,\sqrt{-a^9\,c^3}+819\,a\,c^2\,d^4\,e^5\,\sqrt{-a^9\,c^3}-837\,a^2\,c\,d^2\,e^7\,\sqrt{-a^9\,c^3}}{64\,\left(a^{13}\,e^{14}+7\,a^{12}\,c\,d^2\,e^{12}+21\,a^{11}\,c^2\,d^4\,e^{10}+35\,a^{10}\,c^3\,d^6\,e^8+35\,a^9\,c^4\,d^8\,e^6+21\,a^8\,c^5\,d^{10}\,e^4+7\,a^7\,c^6\,d^{12}\,e^2+a^6\,c^7\,d^{14}\right)}}\,2{}\mathrm{i}","Not used",1,"atan((((d + e*x)^(1/2)*(1568*a^16*c^5*e^28 + 128*a^3*c^18*d^26*e^2 + 3040*a^4*c^17*d^24*e^4 + 29120*a^5*c^16*d^22*e^6 + 128128*a^6*c^15*d^20*e^8 + 282560*a^7*c^14*d^18*e^10 + 242016*a^8*c^13*d^16*e^12 - 282240*a^9*c^12*d^14*e^14 - 1059840*a^10*c^11*d^12*e^16 - 1403904*a^11*c^10*d^10*e^18 - 1049440*a^12*c^9*d^8*e^20 - 456512*a^13*c^8*d^6*e^22 - 100480*a^14*c^7*d^4*e^24 - 4160*a^15*c^6*d^2*e^26) + (-(4*a^3*c^6*d^9 - 49*a^3*e^9*(-a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(-a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(2048*a^21*c^4*d*e^32 + 2048*a^6*c^19*d^31*e^2 + 30720*a^7*c^18*d^29*e^4 + 215040*a^8*c^17*d^27*e^6 + 931840*a^9*c^16*d^25*e^8 + 2795520*a^10*c^15*d^23*e^10 + 6150144*a^11*c^14*d^21*e^12 + 10250240*a^12*c^13*d^19*e^14 + 13178880*a^13*c^12*d^17*e^16 + 13178880*a^14*c^11*d^15*e^18 + 10250240*a^15*c^10*d^13*e^20 + 6150144*a^16*c^9*d^11*e^22 + 2795520*a^17*c^8*d^9*e^24 + 931840*a^18*c^7*d^7*e^26 + 215040*a^19*c^6*d^5*e^28 + 30720*a^20*c^5*d^3*e^30) - 1792*a^19*c^4*e^31 + 256*a^5*c^18*d^28*e^3 + 11776*a^6*c^17*d^26*e^5 + 119552*a^7*c^16*d^24*e^7 + 609280*a^8*c^15*d^22*e^9 + 1923328*a^9*c^14*d^20*e^11 + 4116992*a^10*c^13*d^18*e^13 + 6243072*a^11*c^12*d^16*e^15 + 6825984*a^12*c^11*d^14*e^17 + 5364480*a^13*c^10*d^12*e^19 + 2945536*a^14*c^9*d^10*e^21 + 1044736*a^15*c^8*d^8*e^23 + 183296*a^16*c^7*d^6*e^25 - 13568*a^17*c^6*d^4*e^27 - 12800*a^18*c^5*d^2*e^29))*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(-a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*1i + ((d + e*x)^(1/2)*(1568*a^16*c^5*e^28 + 128*a^3*c^18*d^26*e^2 + 3040*a^4*c^17*d^24*e^4 + 29120*a^5*c^16*d^22*e^6 + 128128*a^6*c^15*d^20*e^8 + 282560*a^7*c^14*d^18*e^10 + 242016*a^8*c^13*d^16*e^12 - 282240*a^9*c^12*d^14*e^14 - 1059840*a^10*c^11*d^12*e^16 - 1403904*a^11*c^10*d^10*e^18 - 1049440*a^12*c^9*d^8*e^20 - 456512*a^13*c^8*d^6*e^22 - 100480*a^14*c^7*d^4*e^24 - 4160*a^15*c^6*d^2*e^26) - (-(4*a^3*c^6*d^9 - 49*a^3*e^9*(-a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(256*a^5*c^18*d^28*e^3 - 1792*a^19*c^4*e^31 - (d + e*x)^(1/2)*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(-a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(2048*a^21*c^4*d*e^32 + 2048*a^6*c^19*d^31*e^2 + 30720*a^7*c^18*d^29*e^4 + 215040*a^8*c^17*d^27*e^6 + 931840*a^9*c^16*d^25*e^8 + 2795520*a^10*c^15*d^23*e^10 + 6150144*a^11*c^14*d^21*e^12 + 10250240*a^12*c^13*d^19*e^14 + 13178880*a^13*c^12*d^17*e^16 + 13178880*a^14*c^11*d^15*e^18 + 10250240*a^15*c^10*d^13*e^20 + 6150144*a^16*c^9*d^11*e^22 + 2795520*a^17*c^8*d^9*e^24 + 931840*a^18*c^7*d^7*e^26 + 215040*a^19*c^6*d^5*e^28 + 30720*a^20*c^5*d^3*e^30) + 11776*a^6*c^17*d^26*e^5 + 119552*a^7*c^16*d^24*e^7 + 609280*a^8*c^15*d^22*e^9 + 1923328*a^9*c^14*d^20*e^11 + 4116992*a^10*c^13*d^18*e^13 + 6243072*a^11*c^12*d^16*e^15 + 6825984*a^12*c^11*d^14*e^17 + 5364480*a^13*c^10*d^12*e^19 + 2945536*a^14*c^9*d^10*e^21 + 1044736*a^15*c^8*d^8*e^23 + 183296*a^16*c^7*d^6*e^25 - 13568*a^17*c^6*d^4*e^27 - 12800*a^18*c^5*d^2*e^29))*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(-a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*1i)/(((d + e*x)^(1/2)*(1568*a^16*c^5*e^28 + 128*a^3*c^18*d^26*e^2 + 3040*a^4*c^17*d^24*e^4 + 29120*a^5*c^16*d^22*e^6 + 128128*a^6*c^15*d^20*e^8 + 282560*a^7*c^14*d^18*e^10 + 242016*a^8*c^13*d^16*e^12 - 282240*a^9*c^12*d^14*e^14 - 1059840*a^10*c^11*d^12*e^16 - 1403904*a^11*c^10*d^10*e^18 - 1049440*a^12*c^9*d^8*e^20 - 456512*a^13*c^8*d^6*e^22 - 100480*a^14*c^7*d^4*e^24 - 4160*a^15*c^6*d^2*e^26) - (-(4*a^3*c^6*d^9 - 49*a^3*e^9*(-a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(256*a^5*c^18*d^28*e^3 - 1792*a^19*c^4*e^31 - (d + e*x)^(1/2)*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(-a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(2048*a^21*c^4*d*e^32 + 2048*a^6*c^19*d^31*e^2 + 30720*a^7*c^18*d^29*e^4 + 215040*a^8*c^17*d^27*e^6 + 931840*a^9*c^16*d^25*e^8 + 2795520*a^10*c^15*d^23*e^10 + 6150144*a^11*c^14*d^21*e^12 + 10250240*a^12*c^13*d^19*e^14 + 13178880*a^13*c^12*d^17*e^16 + 13178880*a^14*c^11*d^15*e^18 + 10250240*a^15*c^10*d^13*e^20 + 6150144*a^16*c^9*d^11*e^22 + 2795520*a^17*c^8*d^9*e^24 + 931840*a^18*c^7*d^7*e^26 + 215040*a^19*c^6*d^5*e^28 + 30720*a^20*c^5*d^3*e^30) + 11776*a^6*c^17*d^26*e^5 + 119552*a^7*c^16*d^24*e^7 + 609280*a^8*c^15*d^22*e^9 + 1923328*a^9*c^14*d^20*e^11 + 4116992*a^10*c^13*d^18*e^13 + 6243072*a^11*c^12*d^16*e^15 + 6825984*a^12*c^11*d^14*e^17 + 5364480*a^13*c^10*d^12*e^19 + 2945536*a^14*c^9*d^10*e^21 + 1044736*a^15*c^8*d^8*e^23 + 183296*a^16*c^7*d^6*e^25 - 13568*a^17*c^6*d^4*e^27 - 12800*a^18*c^5*d^2*e^29))*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(-a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2) - ((d + e*x)^(1/2)*(1568*a^16*c^5*e^28 + 128*a^3*c^18*d^26*e^2 + 3040*a^4*c^17*d^24*e^4 + 29120*a^5*c^16*d^22*e^6 + 128128*a^6*c^15*d^20*e^8 + 282560*a^7*c^14*d^18*e^10 + 242016*a^8*c^13*d^16*e^12 - 282240*a^9*c^12*d^14*e^14 - 1059840*a^10*c^11*d^12*e^16 - 1403904*a^11*c^10*d^10*e^18 - 1049440*a^12*c^9*d^8*e^20 - 456512*a^13*c^8*d^6*e^22 - 100480*a^14*c^7*d^4*e^24 - 4160*a^15*c^6*d^2*e^26) + (-(4*a^3*c^6*d^9 - 49*a^3*e^9*(-a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*((d + e*x)^(1/2)*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(-a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(2048*a^21*c^4*d*e^32 + 2048*a^6*c^19*d^31*e^2 + 30720*a^7*c^18*d^29*e^4 + 215040*a^8*c^17*d^27*e^6 + 931840*a^9*c^16*d^25*e^8 + 2795520*a^10*c^15*d^23*e^10 + 6150144*a^11*c^14*d^21*e^12 + 10250240*a^12*c^13*d^19*e^14 + 13178880*a^13*c^12*d^17*e^16 + 13178880*a^14*c^11*d^15*e^18 + 10250240*a^15*c^10*d^13*e^20 + 6150144*a^16*c^9*d^11*e^22 + 2795520*a^17*c^8*d^9*e^24 + 931840*a^18*c^7*d^7*e^26 + 215040*a^19*c^6*d^5*e^28 + 30720*a^20*c^5*d^3*e^30) - 1792*a^19*c^4*e^31 + 256*a^5*c^18*d^28*e^3 + 11776*a^6*c^17*d^26*e^5 + 119552*a^7*c^16*d^24*e^7 + 609280*a^8*c^15*d^22*e^9 + 1923328*a^9*c^14*d^20*e^11 + 4116992*a^10*c^13*d^18*e^13 + 6243072*a^11*c^12*d^16*e^15 + 6825984*a^12*c^11*d^14*e^17 + 5364480*a^13*c^10*d^12*e^19 + 2945536*a^14*c^9*d^10*e^21 + 1044736*a^15*c^8*d^8*e^23 + 183296*a^16*c^7*d^6*e^25 - 13568*a^17*c^6*d^4*e^27 - 12800*a^18*c^5*d^2*e^29))*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(-a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2) + 7448*a^13*c^6*d*e^25 - 32*a^2*c^17*d^23*e^3 - 72*a^3*c^16*d^21*e^5 + 8240*a^4*c^15*d^19*e^7 + 72120*a^5*c^14*d^17*e^9 + 282240*a^6*c^13*d^15*e^11 + 648816*a^7*c^12*d^13*e^13 + 962976*a^8*c^11*d^11*e^15 + 955440*a^9*c^10*d^9*e^17 + 633120*a^10*c^9*d^7*e^19 + 270040*a^11*c^8*d^5*e^21 + 67248*a^12*c^7*d^3*e^23))*(-(4*a^3*c^6*d^9 - 49*a^3*e^9*(-a^9*c^3)^(1/2) + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 - 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) - 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) + 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*2i - ((2*e^3)/(3*(a*e^2 + c*d^2)) + (20*c*d*e^3*(d + e*x))/(3*(a*e^2 + c*d^2)^2) + (c*e*(d + e*x)^2*(7*a^2*e^4 + 3*c^2*d^4 - 110*a*c*d^2*e^2))/(6*a*(a*e^2 + c*d^2)^3) + (c^2*d*e*(19*a*e^2 - c*d^2)*(d + e*x)^3)/(2*a*(a*e^2 + c*d^2)^3))/(c*(d + e*x)^(7/2) + (a*e^2 + c*d^2)*(d + e*x)^(3/2) - 2*c*d*(d + e*x)^(5/2)) + atan((((d + e*x)^(1/2)*(1568*a^16*c^5*e^28 + 128*a^3*c^18*d^26*e^2 + 3040*a^4*c^17*d^24*e^4 + 29120*a^5*c^16*d^22*e^6 + 128128*a^6*c^15*d^20*e^8 + 282560*a^7*c^14*d^18*e^10 + 242016*a^8*c^13*d^16*e^12 - 282240*a^9*c^12*d^14*e^14 - 1059840*a^10*c^11*d^12*e^16 - 1403904*a^11*c^10*d^10*e^18 - 1049440*a^12*c^9*d^8*e^20 - 456512*a^13*c^8*d^6*e^22 - 100480*a^14*c^7*d^4*e^24 - 4160*a^15*c^6*d^2*e^26) + (-(49*a^3*e^9*(-a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*((d + e*x)^(1/2)*(-(49*a^3*e^9*(-a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(2048*a^21*c^4*d*e^32 + 2048*a^6*c^19*d^31*e^2 + 30720*a^7*c^18*d^29*e^4 + 215040*a^8*c^17*d^27*e^6 + 931840*a^9*c^16*d^25*e^8 + 2795520*a^10*c^15*d^23*e^10 + 6150144*a^11*c^14*d^21*e^12 + 10250240*a^12*c^13*d^19*e^14 + 13178880*a^13*c^12*d^17*e^16 + 13178880*a^14*c^11*d^15*e^18 + 10250240*a^15*c^10*d^13*e^20 + 6150144*a^16*c^9*d^11*e^22 + 2795520*a^17*c^8*d^9*e^24 + 931840*a^18*c^7*d^7*e^26 + 215040*a^19*c^6*d^5*e^28 + 30720*a^20*c^5*d^3*e^30) - 1792*a^19*c^4*e^31 + 256*a^5*c^18*d^28*e^3 + 11776*a^6*c^17*d^26*e^5 + 119552*a^7*c^16*d^24*e^7 + 609280*a^8*c^15*d^22*e^9 + 1923328*a^9*c^14*d^20*e^11 + 4116992*a^10*c^13*d^18*e^13 + 6243072*a^11*c^12*d^16*e^15 + 6825984*a^12*c^11*d^14*e^17 + 5364480*a^13*c^10*d^12*e^19 + 2945536*a^14*c^9*d^10*e^21 + 1044736*a^15*c^8*d^8*e^23 + 183296*a^16*c^7*d^6*e^25 - 13568*a^17*c^6*d^4*e^27 - 12800*a^18*c^5*d^2*e^29))*(-(49*a^3*e^9*(-a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*1i + ((d + e*x)^(1/2)*(1568*a^16*c^5*e^28 + 128*a^3*c^18*d^26*e^2 + 3040*a^4*c^17*d^24*e^4 + 29120*a^5*c^16*d^22*e^6 + 128128*a^6*c^15*d^20*e^8 + 282560*a^7*c^14*d^18*e^10 + 242016*a^8*c^13*d^16*e^12 - 282240*a^9*c^12*d^14*e^14 - 1059840*a^10*c^11*d^12*e^16 - 1403904*a^11*c^10*d^10*e^18 - 1049440*a^12*c^9*d^8*e^20 - 456512*a^13*c^8*d^6*e^22 - 100480*a^14*c^7*d^4*e^24 - 4160*a^15*c^6*d^2*e^26) - (-(49*a^3*e^9*(-a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(256*a^5*c^18*d^28*e^3 - 1792*a^19*c^4*e^31 - (d + e*x)^(1/2)*(-(49*a^3*e^9*(-a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(2048*a^21*c^4*d*e^32 + 2048*a^6*c^19*d^31*e^2 + 30720*a^7*c^18*d^29*e^4 + 215040*a^8*c^17*d^27*e^6 + 931840*a^9*c^16*d^25*e^8 + 2795520*a^10*c^15*d^23*e^10 + 6150144*a^11*c^14*d^21*e^12 + 10250240*a^12*c^13*d^19*e^14 + 13178880*a^13*c^12*d^17*e^16 + 13178880*a^14*c^11*d^15*e^18 + 10250240*a^15*c^10*d^13*e^20 + 6150144*a^16*c^9*d^11*e^22 + 2795520*a^17*c^8*d^9*e^24 + 931840*a^18*c^7*d^7*e^26 + 215040*a^19*c^6*d^5*e^28 + 30720*a^20*c^5*d^3*e^30) + 11776*a^6*c^17*d^26*e^5 + 119552*a^7*c^16*d^24*e^7 + 609280*a^8*c^15*d^22*e^9 + 1923328*a^9*c^14*d^20*e^11 + 4116992*a^10*c^13*d^18*e^13 + 6243072*a^11*c^12*d^16*e^15 + 6825984*a^12*c^11*d^14*e^17 + 5364480*a^13*c^10*d^12*e^19 + 2945536*a^14*c^9*d^10*e^21 + 1044736*a^15*c^8*d^8*e^23 + 183296*a^16*c^7*d^6*e^25 - 13568*a^17*c^6*d^4*e^27 - 12800*a^18*c^5*d^2*e^29))*(-(49*a^3*e^9*(-a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*1i)/(((d + e*x)^(1/2)*(1568*a^16*c^5*e^28 + 128*a^3*c^18*d^26*e^2 + 3040*a^4*c^17*d^24*e^4 + 29120*a^5*c^16*d^22*e^6 + 128128*a^6*c^15*d^20*e^8 + 282560*a^7*c^14*d^18*e^10 + 242016*a^8*c^13*d^16*e^12 - 282240*a^9*c^12*d^14*e^14 - 1059840*a^10*c^11*d^12*e^16 - 1403904*a^11*c^10*d^10*e^18 - 1049440*a^12*c^9*d^8*e^20 - 456512*a^13*c^8*d^6*e^22 - 100480*a^14*c^7*d^4*e^24 - 4160*a^15*c^6*d^2*e^26) - (-(49*a^3*e^9*(-a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(256*a^5*c^18*d^28*e^3 - 1792*a^19*c^4*e^31 - (d + e*x)^(1/2)*(-(49*a^3*e^9*(-a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(2048*a^21*c^4*d*e^32 + 2048*a^6*c^19*d^31*e^2 + 30720*a^7*c^18*d^29*e^4 + 215040*a^8*c^17*d^27*e^6 + 931840*a^9*c^16*d^25*e^8 + 2795520*a^10*c^15*d^23*e^10 + 6150144*a^11*c^14*d^21*e^12 + 10250240*a^12*c^13*d^19*e^14 + 13178880*a^13*c^12*d^17*e^16 + 13178880*a^14*c^11*d^15*e^18 + 10250240*a^15*c^10*d^13*e^20 + 6150144*a^16*c^9*d^11*e^22 + 2795520*a^17*c^8*d^9*e^24 + 931840*a^18*c^7*d^7*e^26 + 215040*a^19*c^6*d^5*e^28 + 30720*a^20*c^5*d^3*e^30) + 11776*a^6*c^17*d^26*e^5 + 119552*a^7*c^16*d^24*e^7 + 609280*a^8*c^15*d^22*e^9 + 1923328*a^9*c^14*d^20*e^11 + 4116992*a^10*c^13*d^18*e^13 + 6243072*a^11*c^12*d^16*e^15 + 6825984*a^12*c^11*d^14*e^17 + 5364480*a^13*c^10*d^12*e^19 + 2945536*a^14*c^9*d^10*e^21 + 1044736*a^15*c^8*d^8*e^23 + 183296*a^16*c^7*d^6*e^25 - 13568*a^17*c^6*d^4*e^27 - 12800*a^18*c^5*d^2*e^29))*(-(49*a^3*e^9*(-a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2) - ((d + e*x)^(1/2)*(1568*a^16*c^5*e^28 + 128*a^3*c^18*d^26*e^2 + 3040*a^4*c^17*d^24*e^4 + 29120*a^5*c^16*d^22*e^6 + 128128*a^6*c^15*d^20*e^8 + 282560*a^7*c^14*d^18*e^10 + 242016*a^8*c^13*d^16*e^12 - 282240*a^9*c^12*d^14*e^14 - 1059840*a^10*c^11*d^12*e^16 - 1403904*a^11*c^10*d^10*e^18 - 1049440*a^12*c^9*d^8*e^20 - 456512*a^13*c^8*d^6*e^22 - 100480*a^14*c^7*d^4*e^24 - 4160*a^15*c^6*d^2*e^26) + (-(49*a^3*e^9*(-a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*((d + e*x)^(1/2)*(-(49*a^3*e^9*(-a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*(2048*a^21*c^4*d*e^32 + 2048*a^6*c^19*d^31*e^2 + 30720*a^7*c^18*d^29*e^4 + 215040*a^8*c^17*d^27*e^6 + 931840*a^9*c^16*d^25*e^8 + 2795520*a^10*c^15*d^23*e^10 + 6150144*a^11*c^14*d^21*e^12 + 10250240*a^12*c^13*d^19*e^14 + 13178880*a^13*c^12*d^17*e^16 + 13178880*a^14*c^11*d^15*e^18 + 10250240*a^15*c^10*d^13*e^20 + 6150144*a^16*c^9*d^11*e^22 + 2795520*a^17*c^8*d^9*e^24 + 931840*a^18*c^7*d^7*e^26 + 215040*a^19*c^6*d^5*e^28 + 30720*a^20*c^5*d^3*e^30) - 1792*a^19*c^4*e^31 + 256*a^5*c^18*d^28*e^3 + 11776*a^6*c^17*d^26*e^5 + 119552*a^7*c^16*d^24*e^7 + 609280*a^8*c^15*d^22*e^9 + 1923328*a^9*c^14*d^20*e^11 + 4116992*a^10*c^13*d^18*e^13 + 6243072*a^11*c^12*d^16*e^15 + 6825984*a^12*c^11*d^14*e^17 + 5364480*a^13*c^10*d^12*e^19 + 2945536*a^14*c^9*d^10*e^21 + 1044736*a^15*c^8*d^8*e^23 + 183296*a^16*c^7*d^6*e^25 - 13568*a^17*c^6*d^4*e^27 - 12800*a^18*c^5*d^2*e^29))*(-(49*a^3*e^9*(-a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2) + 7448*a^13*c^6*d*e^25 - 32*a^2*c^17*d^23*e^3 - 72*a^3*c^16*d^21*e^5 + 8240*a^4*c^15*d^19*e^7 + 72120*a^5*c^14*d^17*e^9 + 282240*a^6*c^13*d^15*e^11 + 648816*a^7*c^12*d^13*e^13 + 962976*a^8*c^11*d^11*e^15 + 955440*a^9*c^10*d^9*e^17 + 633120*a^10*c^9*d^7*e^19 + 270040*a^11*c^8*d^5*e^21 + 67248*a^12*c^7*d^3*e^23))*(-(49*a^3*e^9*(-a^9*c^3)^(1/2) + 4*a^3*c^6*d^9 + 315*a^7*c^2*d*e^8 + 63*a^4*c^5*d^7*e^2 + 189*a^5*c^4*d^5*e^4 - 1155*a^6*c^3*d^3*e^6 + 105*c^3*d^6*e^3*(-a^9*c^3)^(1/2) + 819*a*c^2*d^4*e^5*(-a^9*c^3)^(1/2) - 837*a^2*c*d^2*e^7*(-a^9*c^3)^(1/2))/(64*(a^13*e^14 + a^6*c^7*d^14 + 7*a^12*c*d^2*e^12 + 7*a^7*c^6*d^12*e^2 + 21*a^8*c^5*d^10*e^4 + 35*a^9*c^4*d^8*e^6 + 35*a^10*c^3*d^6*e^8 + 21*a^11*c^2*d^4*e^10)))^(1/2)*2i","B"
638,1,2518,294,0.737828,"\text{Not used}","int((d + e*x)^(7/2)/(a - c*x^2)^3,x)","-\frac{\frac{e\,\left(3\,c\,d^3-4\,a\,d\,e^2\right)\,{\left(d+e\,x\right)}^{7/2}}{8\,a^2}+\frac{{\left(d+e\,x\right)}^{3/2}\,\left(7\,a^2\,d\,e^5-16\,a\,c\,d^3\,e^3+9\,c^2\,d^5\,e\right)}{8\,a^2\,c}+\frac{\sqrt{d+e\,x}\,\left(5\,a^3\,e^7-16\,a^2\,c\,d^2\,e^5+17\,a\,c^2\,d^4\,e^3-6\,c^3\,d^6\,e\right)}{16\,a^2\,c^2}-\frac{e\,{\left(d+e\,x\right)}^{5/2}\,\left(9\,a^2\,e^4-23\,a\,c\,d^2\,e^2+18\,c^2\,d^4\right)}{16\,a^2\,c}}{c^2\,{\left(d+e\,x\right)}^4+a^2\,e^4+c^2\,d^4+\left(6\,c^2\,d^2-2\,a\,c\,e^2\right)\,{\left(d+e\,x\right)}^2-\left(4\,c^2\,d^3-4\,a\,c\,d\,e^2\right)\,\left(d+e\,x\right)-4\,c^2\,d\,{\left(d+e\,x\right)}^3-2\,a\,c\,d^2\,e^2}-2\,\mathrm{atanh}\left(\frac{25\,e^{10}\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,d^7}{256\,a^5\,c}-\frac{105\,d\,e^6}{4096\,a^2\,c^4}+\frac{385\,d^3\,e^4}{4096\,a^3\,c^3}-\frac{105\,d^5\,e^2}{1024\,a^4\,c^2}-\frac{25\,e^7\,\sqrt{a^{15}\,c^9}}{4096\,a^9\,c^9}+\frac{21\,d^2\,e^5\,\sqrt{a^{15}\,c^9}}{4096\,a^{10}\,c^8}}}{32\,\left(\frac{825\,d^5\,e^9}{2048\,a^3}+\frac{325\,d\,e^{13}}{2048\,a\,c^2}-\frac{63\,c\,d^7\,e^7}{512\,a^4}-\frac{449\,d^3\,e^{11}}{1024\,a^2\,c}+\frac{125\,e^{14}\,\sqrt{a^{15}\,c^9}}{2048\,a^8\,c^7}-\frac{95\,d^2\,e^{12}\,\sqrt{a^{15}\,c^9}}{512\,a^9\,c^6}+\frac{381\,d^4\,e^{10}\,\sqrt{a^{15}\,c^9}}{2048\,a^{10}\,c^5}-\frac{63\,d^6\,e^8\,\sqrt{a^{15}\,c^9}}{1024\,a^{11}\,c^4}\right)}-\frac{21\,d^2\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,d^7}{256\,a^5\,c}-\frac{105\,d\,e^6}{4096\,a^2\,c^4}+\frac{385\,d^3\,e^4}{4096\,a^3\,c^3}-\frac{105\,d^5\,e^2}{1024\,a^4\,c^2}-\frac{25\,e^7\,\sqrt{a^{15}\,c^9}}{4096\,a^9\,c^9}+\frac{21\,d^2\,e^5\,\sqrt{a^{15}\,c^9}}{4096\,a^{10}\,c^8}}}{32\,\left(\frac{325\,d\,e^{13}}{2048\,c^3}-\frac{63\,d^7\,e^7}{512\,a^3}-\frac{449\,d^3\,e^{11}}{1024\,a\,c^2}+\frac{825\,d^5\,e^9}{2048\,a^2\,c}+\frac{125\,e^{14}\,\sqrt{a^{15}\,c^9}}{2048\,a^7\,c^8}-\frac{95\,d^2\,e^{12}\,\sqrt{a^{15}\,c^9}}{512\,a^8\,c^7}+\frac{381\,d^4\,e^{10}\,\sqrt{a^{15}\,c^9}}{2048\,a^9\,c^6}-\frac{63\,d^6\,e^8\,\sqrt{a^{15}\,c^9}}{1024\,a^{10}\,c^5}\right)}+\frac{25\,d\,e^9\,\sqrt{a^{15}\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,d^7}{256\,a^5\,c}-\frac{105\,d\,e^6}{4096\,a^2\,c^4}+\frac{385\,d^3\,e^4}{4096\,a^3\,c^3}-\frac{105\,d^5\,e^2}{1024\,a^4\,c^2}-\frac{25\,e^7\,\sqrt{a^{15}\,c^9}}{4096\,a^9\,c^9}+\frac{21\,d^2\,e^5\,\sqrt{a^{15}\,c^9}}{4096\,a^{10}\,c^8}}}{32\,\left(\frac{125\,e^{14}\,\sqrt{a^{15}\,c^9}}{2048\,c^3}+\frac{325\,a^7\,c^2\,d\,e^{13}}{2048}-\frac{63\,a^4\,c^5\,d^7\,e^7}{512}+\frac{825\,a^5\,c^4\,d^5\,e^9}{2048}-\frac{449\,a^6\,c^3\,d^3\,e^{11}}{1024}-\frac{63\,d^6\,e^8\,\sqrt{a^{15}\,c^9}}{1024\,a^3}-\frac{95\,d^2\,e^{12}\,\sqrt{a^{15}\,c^9}}{512\,a\,c^2}+\frac{381\,d^4\,e^{10}\,\sqrt{a^{15}\,c^9}}{2048\,a^2\,c}\right)}+\frac{21\,d^3\,e^7\,\sqrt{a^{15}\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,d^7}{256\,a^5\,c}-\frac{105\,d\,e^6}{4096\,a^2\,c^4}+\frac{385\,d^3\,e^4}{4096\,a^3\,c^3}-\frac{105\,d^5\,e^2}{1024\,a^4\,c^2}-\frac{25\,e^7\,\sqrt{a^{15}\,c^9}}{4096\,a^9\,c^9}+\frac{21\,d^2\,e^5\,\sqrt{a^{15}\,c^9}}{4096\,a^{10}\,c^8}}}{32\,\left(\frac{63\,a^5\,c^4\,d^7\,e^7}{512}-\frac{825\,a^6\,c^3\,d^5\,e^9}{2048}+\frac{449\,a^7\,c^2\,d^3\,e^{11}}{1024}-\frac{125\,a\,e^{14}\,\sqrt{a^{15}\,c^9}}{2048\,c^4}-\frac{325\,a^8\,c\,d\,e^{13}}{2048}+\frac{95\,d^2\,e^{12}\,\sqrt{a^{15}\,c^9}}{512\,c^3}-\frac{381\,d^4\,e^{10}\,\sqrt{a^{15}\,c^9}}{2048\,a\,c^2}+\frac{63\,d^6\,e^8\,\sqrt{a^{15}\,c^9}}{1024\,a^2\,c}\right)}\right)\,\sqrt{\frac{144\,a^5\,c^8\,d^7-25\,a\,e^7\,\sqrt{a^{15}\,c^9}-105\,a^8\,c^5\,d\,e^6-420\,a^6\,c^7\,d^5\,e^2+385\,a^7\,c^6\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^9}}{4096\,a^{10}\,c^9}}-2\,\mathrm{atanh}\left(\frac{25\,e^{10}\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,d^7}{256\,a^5\,c}-\frac{105\,d\,e^6}{4096\,a^2\,c^4}+\frac{385\,d^3\,e^4}{4096\,a^3\,c^3}-\frac{105\,d^5\,e^2}{1024\,a^4\,c^2}+\frac{25\,e^7\,\sqrt{a^{15}\,c^9}}{4096\,a^9\,c^9}-\frac{21\,d^2\,e^5\,\sqrt{a^{15}\,c^9}}{4096\,a^{10}\,c^8}}}{32\,\left(\frac{825\,d^5\,e^9}{2048\,a^3}+\frac{325\,d\,e^{13}}{2048\,a\,c^2}-\frac{63\,c\,d^7\,e^7}{512\,a^4}-\frac{449\,d^3\,e^{11}}{1024\,a^2\,c}-\frac{125\,e^{14}\,\sqrt{a^{15}\,c^9}}{2048\,a^8\,c^7}+\frac{95\,d^2\,e^{12}\,\sqrt{a^{15}\,c^9}}{512\,a^9\,c^6}-\frac{381\,d^4\,e^{10}\,\sqrt{a^{15}\,c^9}}{2048\,a^{10}\,c^5}+\frac{63\,d^6\,e^8\,\sqrt{a^{15}\,c^9}}{1024\,a^{11}\,c^4}\right)}-\frac{21\,d^2\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,d^7}{256\,a^5\,c}-\frac{105\,d\,e^6}{4096\,a^2\,c^4}+\frac{385\,d^3\,e^4}{4096\,a^3\,c^3}-\frac{105\,d^5\,e^2}{1024\,a^4\,c^2}+\frac{25\,e^7\,\sqrt{a^{15}\,c^9}}{4096\,a^9\,c^9}-\frac{21\,d^2\,e^5\,\sqrt{a^{15}\,c^9}}{4096\,a^{10}\,c^8}}}{32\,\left(\frac{325\,d\,e^{13}}{2048\,c^3}-\frac{63\,d^7\,e^7}{512\,a^3}-\frac{449\,d^3\,e^{11}}{1024\,a\,c^2}+\frac{825\,d^5\,e^9}{2048\,a^2\,c}-\frac{125\,e^{14}\,\sqrt{a^{15}\,c^9}}{2048\,a^7\,c^8}+\frac{95\,d^2\,e^{12}\,\sqrt{a^{15}\,c^9}}{512\,a^8\,c^7}-\frac{381\,d^4\,e^{10}\,\sqrt{a^{15}\,c^9}}{2048\,a^9\,c^6}+\frac{63\,d^6\,e^8\,\sqrt{a^{15}\,c^9}}{1024\,a^{10}\,c^5}\right)}+\frac{25\,d\,e^9\,\sqrt{a^{15}\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,d^7}{256\,a^5\,c}-\frac{105\,d\,e^6}{4096\,a^2\,c^4}+\frac{385\,d^3\,e^4}{4096\,a^3\,c^3}-\frac{105\,d^5\,e^2}{1024\,a^4\,c^2}+\frac{25\,e^7\,\sqrt{a^{15}\,c^9}}{4096\,a^9\,c^9}-\frac{21\,d^2\,e^5\,\sqrt{a^{15}\,c^9}}{4096\,a^{10}\,c^8}}}{32\,\left(\frac{125\,e^{14}\,\sqrt{a^{15}\,c^9}}{2048\,c^3}-\frac{325\,a^7\,c^2\,d\,e^{13}}{2048}+\frac{63\,a^4\,c^5\,d^7\,e^7}{512}-\frac{825\,a^5\,c^4\,d^5\,e^9}{2048}+\frac{449\,a^6\,c^3\,d^3\,e^{11}}{1024}-\frac{63\,d^6\,e^8\,\sqrt{a^{15}\,c^9}}{1024\,a^3}-\frac{95\,d^2\,e^{12}\,\sqrt{a^{15}\,c^9}}{512\,a\,c^2}+\frac{381\,d^4\,e^{10}\,\sqrt{a^{15}\,c^9}}{2048\,a^2\,c}\right)}-\frac{21\,d^3\,e^7\,\sqrt{a^{15}\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,d^7}{256\,a^5\,c}-\frac{105\,d\,e^6}{4096\,a^2\,c^4}+\frac{385\,d^3\,e^4}{4096\,a^3\,c^3}-\frac{105\,d^5\,e^2}{1024\,a^4\,c^2}+\frac{25\,e^7\,\sqrt{a^{15}\,c^9}}{4096\,a^9\,c^9}-\frac{21\,d^2\,e^5\,\sqrt{a^{15}\,c^9}}{4096\,a^{10}\,c^8}}}{32\,\left(\frac{63\,a^5\,c^4\,d^7\,e^7}{512}-\frac{825\,a^6\,c^3\,d^5\,e^9}{2048}+\frac{449\,a^7\,c^2\,d^3\,e^{11}}{1024}+\frac{125\,a\,e^{14}\,\sqrt{a^{15}\,c^9}}{2048\,c^4}-\frac{325\,a^8\,c\,d\,e^{13}}{2048}-\frac{95\,d^2\,e^{12}\,\sqrt{a^{15}\,c^9}}{512\,c^3}+\frac{381\,d^4\,e^{10}\,\sqrt{a^{15}\,c^9}}{2048\,a\,c^2}-\frac{63\,d^6\,e^8\,\sqrt{a^{15}\,c^9}}{1024\,a^2\,c}\right)}\right)\,\sqrt{\frac{144\,a^5\,c^8\,d^7+25\,a\,e^7\,\sqrt{a^{15}\,c^9}-105\,a^8\,c^5\,d\,e^6-420\,a^6\,c^7\,d^5\,e^2+385\,a^7\,c^6\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^9}}{4096\,a^{10}\,c^9}}","Not used",1,"- ((e*(3*c*d^3 - 4*a*d*e^2)*(d + e*x)^(7/2))/(8*a^2) + ((d + e*x)^(3/2)*(7*a^2*d*e^5 + 9*c^2*d^5*e - 16*a*c*d^3*e^3))/(8*a^2*c) + ((d + e*x)^(1/2)*(5*a^3*e^7 - 6*c^3*d^6*e + 17*a*c^2*d^4*e^3 - 16*a^2*c*d^2*e^5))/(16*a^2*c^2) - (e*(d + e*x)^(5/2)*(9*a^2*e^4 + 18*c^2*d^4 - 23*a*c*d^2*e^2))/(16*a^2*c))/(c^2*(d + e*x)^4 + a^2*e^4 + c^2*d^4 + (6*c^2*d^2 - 2*a*c*e^2)*(d + e*x)^2 - (4*c^2*d^3 - 4*a*c*d*e^2)*(d + e*x) - 4*c^2*d*(d + e*x)^3 - 2*a*c*d^2*e^2) - 2*atanh((25*e^10*(d + e*x)^(1/2)*((9*d^7)/(256*a^5*c) - (105*d*e^6)/(4096*a^2*c^4) + (385*d^3*e^4)/(4096*a^3*c^3) - (105*d^5*e^2)/(1024*a^4*c^2) - (25*e^7*(a^15*c^9)^(1/2))/(4096*a^9*c^9) + (21*d^2*e^5*(a^15*c^9)^(1/2))/(4096*a^10*c^8))^(1/2))/(32*((825*d^5*e^9)/(2048*a^3) + (325*d*e^13)/(2048*a*c^2) - (63*c*d^7*e^7)/(512*a^4) - (449*d^3*e^11)/(1024*a^2*c) + (125*e^14*(a^15*c^9)^(1/2))/(2048*a^8*c^7) - (95*d^2*e^12*(a^15*c^9)^(1/2))/(512*a^9*c^6) + (381*d^4*e^10*(a^15*c^9)^(1/2))/(2048*a^10*c^5) - (63*d^6*e^8*(a^15*c^9)^(1/2))/(1024*a^11*c^4))) - (21*d^2*e^8*(d + e*x)^(1/2)*((9*d^7)/(256*a^5*c) - (105*d*e^6)/(4096*a^2*c^4) + (385*d^3*e^4)/(4096*a^3*c^3) - (105*d^5*e^2)/(1024*a^4*c^2) - (25*e^7*(a^15*c^9)^(1/2))/(4096*a^9*c^9) + (21*d^2*e^5*(a^15*c^9)^(1/2))/(4096*a^10*c^8))^(1/2))/(32*((325*d*e^13)/(2048*c^3) - (63*d^7*e^7)/(512*a^3) - (449*d^3*e^11)/(1024*a*c^2) + (825*d^5*e^9)/(2048*a^2*c) + (125*e^14*(a^15*c^9)^(1/2))/(2048*a^7*c^8) - (95*d^2*e^12*(a^15*c^9)^(1/2))/(512*a^8*c^7) + (381*d^4*e^10*(a^15*c^9)^(1/2))/(2048*a^9*c^6) - (63*d^6*e^8*(a^15*c^9)^(1/2))/(1024*a^10*c^5))) + (25*d*e^9*(a^15*c^9)^(1/2)*(d + e*x)^(1/2)*((9*d^7)/(256*a^5*c) - (105*d*e^6)/(4096*a^2*c^4) + (385*d^3*e^4)/(4096*a^3*c^3) - (105*d^5*e^2)/(1024*a^4*c^2) - (25*e^7*(a^15*c^9)^(1/2))/(4096*a^9*c^9) + (21*d^2*e^5*(a^15*c^9)^(1/2))/(4096*a^10*c^8))^(1/2))/(32*((125*e^14*(a^15*c^9)^(1/2))/(2048*c^3) + (325*a^7*c^2*d*e^13)/2048 - (63*a^4*c^5*d^7*e^7)/512 + (825*a^5*c^4*d^5*e^9)/2048 - (449*a^6*c^3*d^3*e^11)/1024 - (63*d^6*e^8*(a^15*c^9)^(1/2))/(1024*a^3) - (95*d^2*e^12*(a^15*c^9)^(1/2))/(512*a*c^2) + (381*d^4*e^10*(a^15*c^9)^(1/2))/(2048*a^2*c))) + (21*d^3*e^7*(a^15*c^9)^(1/2)*(d + e*x)^(1/2)*((9*d^7)/(256*a^5*c) - (105*d*e^6)/(4096*a^2*c^4) + (385*d^3*e^4)/(4096*a^3*c^3) - (105*d^5*e^2)/(1024*a^4*c^2) - (25*e^7*(a^15*c^9)^(1/2))/(4096*a^9*c^9) + (21*d^2*e^5*(a^15*c^9)^(1/2))/(4096*a^10*c^8))^(1/2))/(32*((63*a^5*c^4*d^7*e^7)/512 - (825*a^6*c^3*d^5*e^9)/2048 + (449*a^7*c^2*d^3*e^11)/1024 - (125*a*e^14*(a^15*c^9)^(1/2))/(2048*c^4) - (325*a^8*c*d*e^13)/2048 + (95*d^2*e^12*(a^15*c^9)^(1/2))/(512*c^3) - (381*d^4*e^10*(a^15*c^9)^(1/2))/(2048*a*c^2) + (63*d^6*e^8*(a^15*c^9)^(1/2))/(1024*a^2*c))))*((144*a^5*c^8*d^7 - 25*a*e^7*(a^15*c^9)^(1/2) - 105*a^8*c^5*d*e^6 - 420*a^6*c^7*d^5*e^2 + 385*a^7*c^6*d^3*e^4 + 21*c*d^2*e^5*(a^15*c^9)^(1/2))/(4096*a^10*c^9))^(1/2) - 2*atanh((25*e^10*(d + e*x)^(1/2)*((9*d^7)/(256*a^5*c) - (105*d*e^6)/(4096*a^2*c^4) + (385*d^3*e^4)/(4096*a^3*c^3) - (105*d^5*e^2)/(1024*a^4*c^2) + (25*e^7*(a^15*c^9)^(1/2))/(4096*a^9*c^9) - (21*d^2*e^5*(a^15*c^9)^(1/2))/(4096*a^10*c^8))^(1/2))/(32*((825*d^5*e^9)/(2048*a^3) + (325*d*e^13)/(2048*a*c^2) - (63*c*d^7*e^7)/(512*a^4) - (449*d^3*e^11)/(1024*a^2*c) - (125*e^14*(a^15*c^9)^(1/2))/(2048*a^8*c^7) + (95*d^2*e^12*(a^15*c^9)^(1/2))/(512*a^9*c^6) - (381*d^4*e^10*(a^15*c^9)^(1/2))/(2048*a^10*c^5) + (63*d^6*e^8*(a^15*c^9)^(1/2))/(1024*a^11*c^4))) - (21*d^2*e^8*(d + e*x)^(1/2)*((9*d^7)/(256*a^5*c) - (105*d*e^6)/(4096*a^2*c^4) + (385*d^3*e^4)/(4096*a^3*c^3) - (105*d^5*e^2)/(1024*a^4*c^2) + (25*e^7*(a^15*c^9)^(1/2))/(4096*a^9*c^9) - (21*d^2*e^5*(a^15*c^9)^(1/2))/(4096*a^10*c^8))^(1/2))/(32*((325*d*e^13)/(2048*c^3) - (63*d^7*e^7)/(512*a^3) - (449*d^3*e^11)/(1024*a*c^2) + (825*d^5*e^9)/(2048*a^2*c) - (125*e^14*(a^15*c^9)^(1/2))/(2048*a^7*c^8) + (95*d^2*e^12*(a^15*c^9)^(1/2))/(512*a^8*c^7) - (381*d^4*e^10*(a^15*c^9)^(1/2))/(2048*a^9*c^6) + (63*d^6*e^8*(a^15*c^9)^(1/2))/(1024*a^10*c^5))) + (25*d*e^9*(a^15*c^9)^(1/2)*(d + e*x)^(1/2)*((9*d^7)/(256*a^5*c) - (105*d*e^6)/(4096*a^2*c^4) + (385*d^3*e^4)/(4096*a^3*c^3) - (105*d^5*e^2)/(1024*a^4*c^2) + (25*e^7*(a^15*c^9)^(1/2))/(4096*a^9*c^9) - (21*d^2*e^5*(a^15*c^9)^(1/2))/(4096*a^10*c^8))^(1/2))/(32*((125*e^14*(a^15*c^9)^(1/2))/(2048*c^3) - (325*a^7*c^2*d*e^13)/2048 + (63*a^4*c^5*d^7*e^7)/512 - (825*a^5*c^4*d^5*e^9)/2048 + (449*a^6*c^3*d^3*e^11)/1024 - (63*d^6*e^8*(a^15*c^9)^(1/2))/(1024*a^3) - (95*d^2*e^12*(a^15*c^9)^(1/2))/(512*a*c^2) + (381*d^4*e^10*(a^15*c^9)^(1/2))/(2048*a^2*c))) - (21*d^3*e^7*(a^15*c^9)^(1/2)*(d + e*x)^(1/2)*((9*d^7)/(256*a^5*c) - (105*d*e^6)/(4096*a^2*c^4) + (385*d^3*e^4)/(4096*a^3*c^3) - (105*d^5*e^2)/(1024*a^4*c^2) + (25*e^7*(a^15*c^9)^(1/2))/(4096*a^9*c^9) - (21*d^2*e^5*(a^15*c^9)^(1/2))/(4096*a^10*c^8))^(1/2))/(32*((63*a^5*c^4*d^7*e^7)/512 - (825*a^6*c^3*d^5*e^9)/2048 + (449*a^7*c^2*d^3*e^11)/1024 + (125*a*e^14*(a^15*c^9)^(1/2))/(2048*c^4) - (325*a^8*c*d*e^13)/2048 - (95*d^2*e^12*(a^15*c^9)^(1/2))/(512*c^3) + (381*d^4*e^10*(a^15*c^9)^(1/2))/(2048*a*c^2) - (63*d^6*e^8*(a^15*c^9)^(1/2))/(1024*a^2*c))))*((144*a^5*c^8*d^7 + 25*a*e^7*(a^15*c^9)^(1/2) - 105*a^8*c^5*d*e^6 - 420*a^6*c^7*d^5*e^2 + 385*a^7*c^6*d^3*e^4 - 21*c*d^2*e^5*(a^15*c^9)^(1/2))/(4096*a^10*c^9))^(1/2)","B"
639,1,1015,279,0.519799,"\text{Not used}","int((d + e*x)^(5/2)/(a - c*x^2)^3,x)","\frac{\frac{3\,e\,\left(a\,e^2-2\,c\,d^2\right)\,{\left(d+e\,x\right)}^{7/2}}{16\,a^2}+\frac{{\left(d+e\,x\right)}^{3/2}\,\left(a^2\,e^5+17\,a\,c\,d^2\,e^3-18\,c^2\,d^4\,e\right)}{16\,a^2\,c}-\frac{d\,\left(4\,a\,e^3-9\,c\,d^2\,e\right)\,{\left(d+e\,x\right)}^{5/2}}{8\,a^2}+\frac{3\,\sqrt{d+e\,x}\,\left(a^2\,d\,e^5-2\,a\,c\,d^3\,e^3+c^2\,d^5\,e\right)}{8\,a^2\,c}}{c^2\,{\left(d+e\,x\right)}^4+a^2\,e^4+c^2\,d^4+\left(6\,c^2\,d^2-2\,a\,c\,e^2\right)\,{\left(d+e\,x\right)}^2-\left(4\,c^2\,d^3-4\,a\,c\,d\,e^2\right)\,\left(d+e\,x\right)-4\,c^2\,d\,{\left(d+e\,x\right)}^3-2\,a\,c\,d^2\,e^2}-2\,\mathrm{atanh}\left(\frac{9\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,d^5}{256\,a^5\,c}+\frac{45\,d\,e^4}{4096\,a^3\,c^3}-\frac{45\,d^3\,e^2}{1024\,a^4\,c^2}-\frac{9\,e^5\,\sqrt{a^{15}\,c^7}}{4096\,a^{10}\,c^7}}}{32\,\left(\frac{27\,e^{11}}{2048\,a\,c^2}+\frac{27\,d^4\,e^7}{512\,a^3}-\frac{135\,d^2\,e^9}{2048\,a^2\,c}-\frac{27\,d\,e^{10}\,\sqrt{a^{15}\,c^7}}{1024\,a^9\,c^5}+\frac{27\,d^3\,e^8\,\sqrt{a^{15}\,c^7}}{1024\,a^{10}\,c^4}\right)}+\frac{9\,d\,e^7\,\sqrt{a^{15}\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,d^5}{256\,a^5\,c}+\frac{45\,d\,e^4}{4096\,a^3\,c^3}-\frac{45\,d^3\,e^2}{1024\,a^4\,c^2}-\frac{9\,e^5\,\sqrt{a^{15}\,c^7}}{4096\,a^{10}\,c^7}}}{32\,\left(\frac{27\,a^7\,c\,e^{11}}{2048}+\frac{27\,a^5\,c^3\,d^4\,e^7}{512}-\frac{135\,a^6\,c^2\,d^2\,e^9}{2048}-\frac{27\,d\,e^{10}\,\sqrt{a^{15}\,c^7}}{1024\,a\,c^2}+\frac{27\,d^3\,e^8\,\sqrt{a^{15}\,c^7}}{1024\,a^2\,c}\right)}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^7}-16\,a^5\,c^6\,d^5-5\,a^7\,c^4\,d\,e^4+20\,a^6\,c^5\,d^3\,e^2\right)}{4096\,a^{10}\,c^7}}-2\,\mathrm{atanh}\left(\frac{9\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,d^5}{256\,a^5\,c}+\frac{45\,d\,e^4}{4096\,a^3\,c^3}-\frac{45\,d^3\,e^2}{1024\,a^4\,c^2}+\frac{9\,e^5\,\sqrt{a^{15}\,c^7}}{4096\,a^{10}\,c^7}}}{32\,\left(\frac{27\,e^{11}}{2048\,a\,c^2}+\frac{27\,d^4\,e^7}{512\,a^3}-\frac{135\,d^2\,e^9}{2048\,a^2\,c}+\frac{27\,d\,e^{10}\,\sqrt{a^{15}\,c^7}}{1024\,a^9\,c^5}-\frac{27\,d^3\,e^8\,\sqrt{a^{15}\,c^7}}{1024\,a^{10}\,c^4}\right)}-\frac{9\,d\,e^7\,\sqrt{a^{15}\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,d^5}{256\,a^5\,c}+\frac{45\,d\,e^4}{4096\,a^3\,c^3}-\frac{45\,d^3\,e^2}{1024\,a^4\,c^2}+\frac{9\,e^5\,\sqrt{a^{15}\,c^7}}{4096\,a^{10}\,c^7}}}{32\,\left(\frac{27\,a^7\,c\,e^{11}}{2048}+\frac{27\,a^5\,c^3\,d^4\,e^7}{512}-\frac{135\,a^6\,c^2\,d^2\,e^9}{2048}+\frac{27\,d\,e^{10}\,\sqrt{a^{15}\,c^7}}{1024\,a\,c^2}-\frac{27\,d^3\,e^8\,\sqrt{a^{15}\,c^7}}{1024\,a^2\,c}\right)}\right)\,\sqrt{\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^7}+16\,a^5\,c^6\,d^5+5\,a^7\,c^4\,d\,e^4-20\,a^6\,c^5\,d^3\,e^2\right)}{4096\,a^{10}\,c^7}}","Not used",1,"((3*e*(a*e^2 - 2*c*d^2)*(d + e*x)^(7/2))/(16*a^2) + ((d + e*x)^(3/2)*(a^2*e^5 - 18*c^2*d^4*e + 17*a*c*d^2*e^3))/(16*a^2*c) - (d*(4*a*e^3 - 9*c*d^2*e)*(d + e*x)^(5/2))/(8*a^2) + (3*(d + e*x)^(1/2)*(a^2*d*e^5 + c^2*d^5*e - 2*a*c*d^3*e^3))/(8*a^2*c))/(c^2*(d + e*x)^4 + a^2*e^4 + c^2*d^4 + (6*c^2*d^2 - 2*a*c*e^2)*(d + e*x)^2 - (4*c^2*d^3 - 4*a*c*d*e^2)*(d + e*x) - 4*c^2*d*(d + e*x)^3 - 2*a*c*d^2*e^2) - 2*atanh((9*e^8*(d + e*x)^(1/2)*((9*d^5)/(256*a^5*c) + (45*d*e^4)/(4096*a^3*c^3) - (45*d^3*e^2)/(1024*a^4*c^2) - (9*e^5*(a^15*c^7)^(1/2))/(4096*a^10*c^7))^(1/2))/(32*((27*e^11)/(2048*a*c^2) + (27*d^4*e^7)/(512*a^3) - (135*d^2*e^9)/(2048*a^2*c) - (27*d*e^10*(a^15*c^7)^(1/2))/(1024*a^9*c^5) + (27*d^3*e^8*(a^15*c^7)^(1/2))/(1024*a^10*c^4))) + (9*d*e^7*(a^15*c^7)^(1/2)*(d + e*x)^(1/2)*((9*d^5)/(256*a^5*c) + (45*d*e^4)/(4096*a^3*c^3) - (45*d^3*e^2)/(1024*a^4*c^2) - (9*e^5*(a^15*c^7)^(1/2))/(4096*a^10*c^7))^(1/2))/(32*((27*a^7*c*e^11)/2048 + (27*a^5*c^3*d^4*e^7)/512 - (135*a^6*c^2*d^2*e^9)/2048 - (27*d*e^10*(a^15*c^7)^(1/2))/(1024*a*c^2) + (27*d^3*e^8*(a^15*c^7)^(1/2))/(1024*a^2*c))))*(-(9*(e^5*(a^15*c^7)^(1/2) - 16*a^5*c^6*d^5 - 5*a^7*c^4*d*e^4 + 20*a^6*c^5*d^3*e^2))/(4096*a^10*c^7))^(1/2) - 2*atanh((9*e^8*(d + e*x)^(1/2)*((9*d^5)/(256*a^5*c) + (45*d*e^4)/(4096*a^3*c^3) - (45*d^3*e^2)/(1024*a^4*c^2) + (9*e^5*(a^15*c^7)^(1/2))/(4096*a^10*c^7))^(1/2))/(32*((27*e^11)/(2048*a*c^2) + (27*d^4*e^7)/(512*a^3) - (135*d^2*e^9)/(2048*a^2*c) + (27*d*e^10*(a^15*c^7)^(1/2))/(1024*a^9*c^5) - (27*d^3*e^8*(a^15*c^7)^(1/2))/(1024*a^10*c^4))) - (9*d*e^7*(a^15*c^7)^(1/2)*(d + e*x)^(1/2)*((9*d^5)/(256*a^5*c) + (45*d*e^4)/(4096*a^3*c^3) - (45*d^3*e^2)/(1024*a^4*c^2) + (9*e^5*(a^15*c^7)^(1/2))/(4096*a^10*c^7))^(1/2))/(32*((27*a^7*c*e^11)/2048 + (27*a^5*c^3*d^4*e^7)/512 - (135*a^6*c^2*d^2*e^9)/2048 + (27*d*e^10*(a^15*c^7)^(1/2))/(1024*a*c^2) - (27*d^3*e^8*(a^15*c^7)^(1/2))/(1024*a^2*c))))*((9*(e^5*(a^15*c^7)^(1/2) + 16*a^5*c^6*d^5 + 5*a^7*c^4*d*e^4 - 20*a^6*c^5*d^3*e^2))/(4096*a^10*c^7))^(1/2)","B"
640,1,3191,268,2.736511,"\text{Not used}","int((d + e*x)^(3/2)/(a - c*x^2)^3,x)","\frac{\frac{\left(4\,a\,d\,e^3-9\,c\,d^3\,e\right)\,{\left(d+e\,x\right)}^{3/2}}{8\,a^2}+\frac{e\,\left(18\,c\,d^2+a\,e^2\right)\,{\left(d+e\,x\right)}^{5/2}}{16\,a^2}+\frac{3\,\sqrt{d+e\,x}\,\left(a^2\,e^5-3\,a\,c\,d^2\,e^3+2\,c^2\,d^4\,e\right)}{16\,a^2\,c}-\frac{3\,c\,d\,e\,{\left(d+e\,x\right)}^{7/2}}{8\,a^2}}{c^2\,{\left(d+e\,x\right)}^4+a^2\,e^4+c^2\,d^4+\left(6\,c^2\,d^2-2\,a\,c\,e^2\right)\,{\left(d+e\,x\right)}^2-\left(4\,c^2\,d^3-4\,a\,c\,d\,e^2\right)\,\left(d+e\,x\right)-4\,c^2\,d\,{\left(d+e\,x\right)}^3-2\,a\,c\,d^2\,e^2}+\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(2048\,a^6\,c^2\,e^5-4096\,a^5\,c^3\,d^2\,e^3\right)}{2048\,a^6}-64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}-16\,a^5\,c^5\,d^5-5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}-16\,a^5\,c^5\,d^5-5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}+\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c\,e^6-36\,a\,c^2\,d^2\,e^4+144\,c^3\,d^4\,e^2\right)}{64\,a^4}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}-16\,a^5\,c^5\,d^5-5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3\,\left(2048\,a^6\,c^2\,e^5-4096\,a^5\,c^3\,d^2\,e^3\right)}{2048\,a^6}+64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}-16\,a^5\,c^5\,d^5-5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}-16\,a^5\,c^5\,d^5-5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}-\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c\,e^6-36\,a\,c^2\,d^2\,e^4+144\,c^3\,d^4\,e^2\right)}{64\,a^4}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}-16\,a^5\,c^5\,d^5-5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}\,1{}\mathrm{i}}{\frac{3\,\left(9\,a^2\,d\,e^7-108\,a\,c\,d^3\,e^5+144\,c^2\,d^5\,e^3\right)}{1024\,a^6}+\left(\left(\frac{3\,\left(2048\,a^6\,c^2\,e^5-4096\,a^5\,c^3\,d^2\,e^3\right)}{2048\,a^6}-64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}-16\,a^5\,c^5\,d^5-5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}-16\,a^5\,c^5\,d^5-5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}+\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c\,e^6-36\,a\,c^2\,d^2\,e^4+144\,c^3\,d^4\,e^2\right)}{64\,a^4}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}-16\,a^5\,c^5\,d^5-5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}+\left(\left(\frac{3\,\left(2048\,a^6\,c^2\,e^5-4096\,a^5\,c^3\,d^2\,e^3\right)}{2048\,a^6}+64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}-16\,a^5\,c^5\,d^5-5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}-16\,a^5\,c^5\,d^5-5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}-\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c\,e^6-36\,a\,c^2\,d^2\,e^4+144\,c^3\,d^4\,e^2\right)}{64\,a^4}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}-16\,a^5\,c^5\,d^5-5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}-16\,a^5\,c^5\,d^5-5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(2048\,a^6\,c^2\,e^5-4096\,a^5\,c^3\,d^2\,e^3\right)}{2048\,a^6}-64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4-20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}\right)\,\sqrt{\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4-20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}+\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c\,e^6-36\,a\,c^2\,d^2\,e^4+144\,c^3\,d^4\,e^2\right)}{64\,a^4}\right)\,\sqrt{\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4-20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3\,\left(2048\,a^6\,c^2\,e^5-4096\,a^5\,c^3\,d^2\,e^3\right)}{2048\,a^6}+64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4-20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}\right)\,\sqrt{\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4-20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}-\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c\,e^6-36\,a\,c^2\,d^2\,e^4+144\,c^3\,d^4\,e^2\right)}{64\,a^4}\right)\,\sqrt{\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4-20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}\,1{}\mathrm{i}}{\frac{3\,\left(9\,a^2\,d\,e^7-108\,a\,c\,d^3\,e^5+144\,c^2\,d^5\,e^3\right)}{1024\,a^6}+\left(\left(\frac{3\,\left(2048\,a^6\,c^2\,e^5-4096\,a^5\,c^3\,d^2\,e^3\right)}{2048\,a^6}-64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4-20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}\right)\,\sqrt{\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4-20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}+\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c\,e^6-36\,a\,c^2\,d^2\,e^4+144\,c^3\,d^4\,e^2\right)}{64\,a^4}\right)\,\sqrt{\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4-20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}+\left(\left(\frac{3\,\left(2048\,a^6\,c^2\,e^5-4096\,a^5\,c^3\,d^2\,e^3\right)}{2048\,a^6}+64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4-20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}\right)\,\sqrt{\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4-20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}-\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c\,e^6-36\,a\,c^2\,d^2\,e^4+144\,c^3\,d^4\,e^2\right)}{64\,a^4}\right)\,\sqrt{\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4-20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}}\right)\,\sqrt{\frac{9\,\left(e^5\,\sqrt{a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4-20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{10}\,c^6\,d^2-a^{11}\,c^5\,e^2\right)}}\,2{}\mathrm{i}","Not used",1,"(((4*a*d*e^3 - 9*c*d^3*e)*(d + e*x)^(3/2))/(8*a^2) + (e*(a*e^2 + 18*c*d^2)*(d + e*x)^(5/2))/(16*a^2) + (3*(d + e*x)^(1/2)*(a^2*e^5 + 2*c^2*d^4*e - 3*a*c*d^2*e^3))/(16*a^2*c) - (3*c*d*e*(d + e*x)^(7/2))/(8*a^2))/(c^2*(d + e*x)^4 + a^2*e^4 + c^2*d^4 + (6*c^2*d^2 - 2*a*c*e^2)*(d + e*x)^2 - (4*c^2*d^3 - 4*a*c*d*e^2)*(d + e*x) - 4*c^2*d*(d + e*x)^3 - 2*a*c*d^2*e^2) + atan(((((3*(2048*a^6*c^2*e^5 - 4096*a^5*c^3*d^2*e^3))/(2048*a^6) - 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(9*(e^5*(a^15*c^5)^(1/2) - 16*a^5*c^5*d^5 - 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2))*(-(9*(e^5*(a^15*c^5)^(1/2) - 16*a^5*c^5*d^5 - 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2) + ((d + e*x)^(1/2)*(9*a^2*c*e^6 + 144*c^3*d^4*e^2 - 36*a*c^2*d^2*e^4))/(64*a^4))*(-(9*(e^5*(a^15*c^5)^(1/2) - 16*a^5*c^5*d^5 - 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2)*1i - (((3*(2048*a^6*c^2*e^5 - 4096*a^5*c^3*d^2*e^3))/(2048*a^6) + 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(9*(e^5*(a^15*c^5)^(1/2) - 16*a^5*c^5*d^5 - 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2))*(-(9*(e^5*(a^15*c^5)^(1/2) - 16*a^5*c^5*d^5 - 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2) - ((d + e*x)^(1/2)*(9*a^2*c*e^6 + 144*c^3*d^4*e^2 - 36*a*c^2*d^2*e^4))/(64*a^4))*(-(9*(e^5*(a^15*c^5)^(1/2) - 16*a^5*c^5*d^5 - 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2)*1i)/((3*(9*a^2*d*e^7 + 144*c^2*d^5*e^3 - 108*a*c*d^3*e^5))/(1024*a^6) + (((3*(2048*a^6*c^2*e^5 - 4096*a^5*c^3*d^2*e^3))/(2048*a^6) - 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(9*(e^5*(a^15*c^5)^(1/2) - 16*a^5*c^5*d^5 - 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2))*(-(9*(e^5*(a^15*c^5)^(1/2) - 16*a^5*c^5*d^5 - 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2) + ((d + e*x)^(1/2)*(9*a^2*c*e^6 + 144*c^3*d^4*e^2 - 36*a*c^2*d^2*e^4))/(64*a^4))*(-(9*(e^5*(a^15*c^5)^(1/2) - 16*a^5*c^5*d^5 - 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2) + (((3*(2048*a^6*c^2*e^5 - 4096*a^5*c^3*d^2*e^3))/(2048*a^6) + 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(9*(e^5*(a^15*c^5)^(1/2) - 16*a^5*c^5*d^5 - 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2))*(-(9*(e^5*(a^15*c^5)^(1/2) - 16*a^5*c^5*d^5 - 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2) - ((d + e*x)^(1/2)*(9*a^2*c*e^6 + 144*c^3*d^4*e^2 - 36*a*c^2*d^2*e^4))/(64*a^4))*(-(9*(e^5*(a^15*c^5)^(1/2) - 16*a^5*c^5*d^5 - 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2)))*(-(9*(e^5*(a^15*c^5)^(1/2) - 16*a^5*c^5*d^5 - 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2)*2i + atan(((((3*(2048*a^6*c^2*e^5 - 4096*a^5*c^3*d^2*e^3))/(2048*a^6) - 64*a*c^4*d*e^2*(d + e*x)^(1/2)*((9*(e^5*(a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 - 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2))*((9*(e^5*(a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 - 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2) + ((d + e*x)^(1/2)*(9*a^2*c*e^6 + 144*c^3*d^4*e^2 - 36*a*c^2*d^2*e^4))/(64*a^4))*((9*(e^5*(a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 - 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2)*1i - (((3*(2048*a^6*c^2*e^5 - 4096*a^5*c^3*d^2*e^3))/(2048*a^6) + 64*a*c^4*d*e^2*(d + e*x)^(1/2)*((9*(e^5*(a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 - 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2))*((9*(e^5*(a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 - 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2) - ((d + e*x)^(1/2)*(9*a^2*c*e^6 + 144*c^3*d^4*e^2 - 36*a*c^2*d^2*e^4))/(64*a^4))*((9*(e^5*(a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 - 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2)*1i)/((3*(9*a^2*d*e^7 + 144*c^2*d^5*e^3 - 108*a*c*d^3*e^5))/(1024*a^6) + (((3*(2048*a^6*c^2*e^5 - 4096*a^5*c^3*d^2*e^3))/(2048*a^6) - 64*a*c^4*d*e^2*(d + e*x)^(1/2)*((9*(e^5*(a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 - 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2))*((9*(e^5*(a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 - 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2) + ((d + e*x)^(1/2)*(9*a^2*c*e^6 + 144*c^3*d^4*e^2 - 36*a*c^2*d^2*e^4))/(64*a^4))*((9*(e^5*(a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 - 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2) + (((3*(2048*a^6*c^2*e^5 - 4096*a^5*c^3*d^2*e^3))/(2048*a^6) + 64*a*c^4*d*e^2*(d + e*x)^(1/2)*((9*(e^5*(a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 - 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2))*((9*(e^5*(a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 - 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2) - ((d + e*x)^(1/2)*(9*a^2*c*e^6 + 144*c^3*d^4*e^2 - 36*a*c^2*d^2*e^4))/(64*a^4))*((9*(e^5*(a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 - 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2)))*((9*(e^5*(a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 - 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 - a^11*c^5*e^2)))^(1/2)*2i","B"
641,1,6163,281,3.300692,"\text{Not used}","int((d + e*x)^(1/2)/(a - c*x^2)^3,x)","-\frac{\frac{\left(4\,a\,d\,e^3-3\,c\,d^3\,e\right)\,\sqrt{d+e\,x}}{8\,a^2}-\frac{{\left(d+e\,x\right)}^{3/2}\,\left(9\,a^2\,e^5-23\,a\,c\,d^2\,e^3+18\,c^2\,d^4\,e\right)}{16\,a^2\,\left(a\,e^2-c\,d^2\right)}+\frac{c\,e\,\left(5\,a\,e^2-6\,c\,d^2\right)\,{\left(d+e\,x\right)}^{7/2}}{16\,a^2\,\left(a\,e^2-c\,d^2\right)}-\frac{c\,d\,\left(7\,a\,e^3-9\,c\,d^2\,e\right)\,{\left(d+e\,x\right)}^{5/2}}{8\,a^2\,\left(a\,e^2-c\,d^2\right)}}{c^2\,{\left(d+e\,x\right)}^4+a^2\,e^4+c^2\,d^4+\left(6\,c^2\,d^2-2\,a\,c\,e^2\right)\,{\left(d+e\,x\right)}^2-\left(4\,c^2\,d^3-4\,a\,c\,d\,e^2\right)\,\left(d+e\,x\right)-4\,c^2\,d\,{\left(d+e\,x\right)}^3-2\,a\,c\,d^2\,e^2}-\mathrm{atan}\left(\frac{\left(\left(\frac{32768\,a^7\,c^3\,d\,e^7-57344\,a^6\,c^4\,d^3\,e^5+24576\,a^5\,c^5\,d^5\,e^3}{4096\,\left(a^8\,e^4-2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}-\frac{\sqrt{d+e\,x}\,\left(4096\,a^7\,c^4\,d\,e^6-8192\,a^6\,c^5\,d^3\,e^4+4096\,a^5\,c^6\,d^5\,e^2\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}}{64\,\left(a^6\,e^4-2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}+\frac{\sqrt{d+e\,x}\,\left(25\,a^3\,c^2\,e^8+109\,a^2\,c^3\,d^2\,e^6-276\,a\,c^4\,d^4\,e^4+144\,c^5\,d^6\,e^2\right)}{64\,\left(a^6\,e^4-2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}\,1{}\mathrm{i}-\left(\left(\frac{32768\,a^7\,c^3\,d\,e^7-57344\,a^6\,c^4\,d^3\,e^5+24576\,a^5\,c^5\,d^5\,e^3}{4096\,\left(a^8\,e^4-2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}+\frac{\sqrt{d+e\,x}\,\left(4096\,a^7\,c^4\,d\,e^6-8192\,a^6\,c^5\,d^3\,e^4+4096\,a^5\,c^6\,d^5\,e^2\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}}{64\,\left(a^6\,e^4-2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}-\frac{\sqrt{d+e\,x}\,\left(25\,a^3\,c^2\,e^8+109\,a^2\,c^3\,d^2\,e^6-276\,a\,c^4\,d^4\,e^4+144\,c^5\,d^6\,e^2\right)}{64\,\left(a^6\,e^4-2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{32768\,a^7\,c^3\,d\,e^7-57344\,a^6\,c^4\,d^3\,e^5+24576\,a^5\,c^5\,d^5\,e^3}{4096\,\left(a^8\,e^4-2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}-\frac{\sqrt{d+e\,x}\,\left(4096\,a^7\,c^4\,d\,e^6-8192\,a^6\,c^5\,d^3\,e^4+4096\,a^5\,c^6\,d^5\,e^2\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}}{64\,\left(a^6\,e^4-2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}+\frac{\sqrt{d+e\,x}\,\left(25\,a^3\,c^2\,e^8+109\,a^2\,c^3\,d^2\,e^6-276\,a\,c^4\,d^4\,e^4+144\,c^5\,d^6\,e^2\right)}{64\,\left(a^6\,e^4-2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}+\left(\left(\frac{32768\,a^7\,c^3\,d\,e^7-57344\,a^6\,c^4\,d^3\,e^5+24576\,a^5\,c^5\,d^5\,e^3}{4096\,\left(a^8\,e^4-2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}+\frac{\sqrt{d+e\,x}\,\left(4096\,a^7\,c^4\,d\,e^6-8192\,a^6\,c^5\,d^3\,e^4+4096\,a^5\,c^6\,d^5\,e^2\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}}{64\,\left(a^6\,e^4-2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}-\frac{\sqrt{d+e\,x}\,\left(25\,a^3\,c^2\,e^8+109\,a^2\,c^3\,d^2\,e^6-276\,a\,c^4\,d^4\,e^4+144\,c^5\,d^6\,e^2\right)}{64\,\left(a^6\,e^4-2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}+\frac{125\,a^3\,c\,e^9-1170\,a^2\,c^2\,d^2\,e^7+1944\,a\,c^3\,d^4\,e^5-864\,c^4\,d^6\,e^3}{2048\,\left(a^8\,e^4-2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(\frac{32768\,a^7\,c^3\,d\,e^7-57344\,a^6\,c^4\,d^3\,e^5+24576\,a^5\,c^5\,d^5\,e^3}{4096\,\left(a^8\,e^4-2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}-\frac{\sqrt{d+e\,x}\,\left(4096\,a^7\,c^4\,d\,e^6-8192\,a^6\,c^5\,d^3\,e^4+4096\,a^5\,c^6\,d^5\,e^2\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}}{64\,\left(a^6\,e^4-2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}+\frac{\sqrt{d+e\,x}\,\left(25\,a^3\,c^2\,e^8+109\,a^2\,c^3\,d^2\,e^6-276\,a\,c^4\,d^4\,e^4+144\,c^5\,d^6\,e^2\right)}{64\,\left(a^6\,e^4-2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}\,1{}\mathrm{i}-\left(\left(\frac{32768\,a^7\,c^3\,d\,e^7-57344\,a^6\,c^4\,d^3\,e^5+24576\,a^5\,c^5\,d^5\,e^3}{4096\,\left(a^8\,e^4-2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}+\frac{\sqrt{d+e\,x}\,\left(4096\,a^7\,c^4\,d\,e^6-8192\,a^6\,c^5\,d^3\,e^4+4096\,a^5\,c^6\,d^5\,e^2\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}}{64\,\left(a^6\,e^4-2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}-\frac{\sqrt{d+e\,x}\,\left(25\,a^3\,c^2\,e^8+109\,a^2\,c^3\,d^2\,e^6-276\,a\,c^4\,d^4\,e^4+144\,c^5\,d^6\,e^2\right)}{64\,\left(a^6\,e^4-2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{32768\,a^7\,c^3\,d\,e^7-57344\,a^6\,c^4\,d^3\,e^5+24576\,a^5\,c^5\,d^5\,e^3}{4096\,\left(a^8\,e^4-2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}-\frac{\sqrt{d+e\,x}\,\left(4096\,a^7\,c^4\,d\,e^6-8192\,a^6\,c^5\,d^3\,e^4+4096\,a^5\,c^6\,d^5\,e^2\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}}{64\,\left(a^6\,e^4-2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}+\frac{\sqrt{d+e\,x}\,\left(25\,a^3\,c^2\,e^8+109\,a^2\,c^3\,d^2\,e^6-276\,a\,c^4\,d^4\,e^4+144\,c^5\,d^6\,e^2\right)}{64\,\left(a^6\,e^4-2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}+\left(\left(\frac{32768\,a^7\,c^3\,d\,e^7-57344\,a^6\,c^4\,d^3\,e^5+24576\,a^5\,c^5\,d^5\,e^3}{4096\,\left(a^8\,e^4-2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}+\frac{\sqrt{d+e\,x}\,\left(4096\,a^7\,c^4\,d\,e^6-8192\,a^6\,c^5\,d^3\,e^4+4096\,a^5\,c^6\,d^5\,e^2\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}}{64\,\left(a^6\,e^4-2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}-\frac{\sqrt{d+e\,x}\,\left(25\,a^3\,c^2\,e^8+109\,a^2\,c^3\,d^2\,e^6-276\,a\,c^4\,d^4\,e^4+144\,c^5\,d^6\,e^2\right)}{64\,\left(a^6\,e^4-2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}+\frac{125\,a^3\,c\,e^9-1170\,a^2\,c^2\,d^2\,e^7+1944\,a\,c^3\,d^4\,e^5-864\,c^4\,d^6\,e^3}{2048\,\left(a^8\,e^4-2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}}\right)\,\sqrt{\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{a^{15}\,c^3}-105\,a^8\,c^2\,d\,e^6-420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{a^{15}\,c^3}}{4096\,\left(-a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4-3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}\,2{}\mathrm{i}","Not used",1,"- atan(((((32768*a^7*c^3*d*e^7 + 24576*a^5*c^5*d^5*e^3 - 57344*a^6*c^4*d^3*e^5)/(4096*(a^8*e^4 + a^6*c^2*d^4 - 2*a^7*c*d^2*e^2)) - ((d + e*x)^(1/2)*(4096*a^7*c^4*d*e^6 + 4096*a^5*c^6*d^5*e^2 - 8192*a^6*c^5*d^3*e^4)*((144*a^5*c^5*d^7 - 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2))/(64*(a^6*e^4 + a^4*c^2*d^4 - 2*a^5*c*d^2*e^2)))*((144*a^5*c^5*d^7 - 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) + ((d + e*x)^(1/2)*(25*a^3*c^2*e^8 + 144*c^5*d^6*e^2 - 276*a*c^4*d^4*e^4 + 109*a^2*c^3*d^2*e^6))/(64*(a^6*e^4 + a^4*c^2*d^4 - 2*a^5*c*d^2*e^2)))*((144*a^5*c^5*d^7 - 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2)*1i - (((32768*a^7*c^3*d*e^7 + 24576*a^5*c^5*d^5*e^3 - 57344*a^6*c^4*d^3*e^5)/(4096*(a^8*e^4 + a^6*c^2*d^4 - 2*a^7*c*d^2*e^2)) + ((d + e*x)^(1/2)*(4096*a^7*c^4*d*e^6 + 4096*a^5*c^6*d^5*e^2 - 8192*a^6*c^5*d^3*e^4)*((144*a^5*c^5*d^7 - 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2))/(64*(a^6*e^4 + a^4*c^2*d^4 - 2*a^5*c*d^2*e^2)))*((144*a^5*c^5*d^7 - 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) - ((d + e*x)^(1/2)*(25*a^3*c^2*e^8 + 144*c^5*d^6*e^2 - 276*a*c^4*d^4*e^4 + 109*a^2*c^3*d^2*e^6))/(64*(a^6*e^4 + a^4*c^2*d^4 - 2*a^5*c*d^2*e^2)))*((144*a^5*c^5*d^7 - 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2)*1i)/((((32768*a^7*c^3*d*e^7 + 24576*a^5*c^5*d^5*e^3 - 57344*a^6*c^4*d^3*e^5)/(4096*(a^8*e^4 + a^6*c^2*d^4 - 2*a^7*c*d^2*e^2)) - ((d + e*x)^(1/2)*(4096*a^7*c^4*d*e^6 + 4096*a^5*c^6*d^5*e^2 - 8192*a^6*c^5*d^3*e^4)*((144*a^5*c^5*d^7 - 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2))/(64*(a^6*e^4 + a^4*c^2*d^4 - 2*a^5*c*d^2*e^2)))*((144*a^5*c^5*d^7 - 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) + ((d + e*x)^(1/2)*(25*a^3*c^2*e^8 + 144*c^5*d^6*e^2 - 276*a*c^4*d^4*e^4 + 109*a^2*c^3*d^2*e^6))/(64*(a^6*e^4 + a^4*c^2*d^4 - 2*a^5*c*d^2*e^2)))*((144*a^5*c^5*d^7 - 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) + (((32768*a^7*c^3*d*e^7 + 24576*a^5*c^5*d^5*e^3 - 57344*a^6*c^4*d^3*e^5)/(4096*(a^8*e^4 + a^6*c^2*d^4 - 2*a^7*c*d^2*e^2)) + ((d + e*x)^(1/2)*(4096*a^7*c^4*d*e^6 + 4096*a^5*c^6*d^5*e^2 - 8192*a^6*c^5*d^3*e^4)*((144*a^5*c^5*d^7 - 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2))/(64*(a^6*e^4 + a^4*c^2*d^4 - 2*a^5*c*d^2*e^2)))*((144*a^5*c^5*d^7 - 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) - ((d + e*x)^(1/2)*(25*a^3*c^2*e^8 + 144*c^5*d^6*e^2 - 276*a*c^4*d^4*e^4 + 109*a^2*c^3*d^2*e^6))/(64*(a^6*e^4 + a^4*c^2*d^4 - 2*a^5*c*d^2*e^2)))*((144*a^5*c^5*d^7 - 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) + (125*a^3*c*e^9 - 864*c^4*d^6*e^3 + 1944*a*c^3*d^4*e^5 - 1170*a^2*c^2*d^2*e^7)/(2048*(a^8*e^4 + a^6*c^2*d^4 - 2*a^7*c*d^2*e^2))))*((144*a^5*c^5*d^7 - 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2)*2i - atan(((((32768*a^7*c^3*d*e^7 + 24576*a^5*c^5*d^5*e^3 - 57344*a^6*c^4*d^3*e^5)/(4096*(a^8*e^4 + a^6*c^2*d^4 - 2*a^7*c*d^2*e^2)) - ((d + e*x)^(1/2)*(4096*a^7*c^4*d*e^6 + 4096*a^5*c^6*d^5*e^2 - 8192*a^6*c^5*d^3*e^4)*((144*a^5*c^5*d^7 + 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2))/(64*(a^6*e^4 + a^4*c^2*d^4 - 2*a^5*c*d^2*e^2)))*((144*a^5*c^5*d^7 + 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) + ((d + e*x)^(1/2)*(25*a^3*c^2*e^8 + 144*c^5*d^6*e^2 - 276*a*c^4*d^4*e^4 + 109*a^2*c^3*d^2*e^6))/(64*(a^6*e^4 + a^4*c^2*d^4 - 2*a^5*c*d^2*e^2)))*((144*a^5*c^5*d^7 + 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2)*1i - (((32768*a^7*c^3*d*e^7 + 24576*a^5*c^5*d^5*e^3 - 57344*a^6*c^4*d^3*e^5)/(4096*(a^8*e^4 + a^6*c^2*d^4 - 2*a^7*c*d^2*e^2)) + ((d + e*x)^(1/2)*(4096*a^7*c^4*d*e^6 + 4096*a^5*c^6*d^5*e^2 - 8192*a^6*c^5*d^3*e^4)*((144*a^5*c^5*d^7 + 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2))/(64*(a^6*e^4 + a^4*c^2*d^4 - 2*a^5*c*d^2*e^2)))*((144*a^5*c^5*d^7 + 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) - ((d + e*x)^(1/2)*(25*a^3*c^2*e^8 + 144*c^5*d^6*e^2 - 276*a*c^4*d^4*e^4 + 109*a^2*c^3*d^2*e^6))/(64*(a^6*e^4 + a^4*c^2*d^4 - 2*a^5*c*d^2*e^2)))*((144*a^5*c^5*d^7 + 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2)*1i)/((((32768*a^7*c^3*d*e^7 + 24576*a^5*c^5*d^5*e^3 - 57344*a^6*c^4*d^3*e^5)/(4096*(a^8*e^4 + a^6*c^2*d^4 - 2*a^7*c*d^2*e^2)) - ((d + e*x)^(1/2)*(4096*a^7*c^4*d*e^6 + 4096*a^5*c^6*d^5*e^2 - 8192*a^6*c^5*d^3*e^4)*((144*a^5*c^5*d^7 + 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2))/(64*(a^6*e^4 + a^4*c^2*d^4 - 2*a^5*c*d^2*e^2)))*((144*a^5*c^5*d^7 + 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) + ((d + e*x)^(1/2)*(25*a^3*c^2*e^8 + 144*c^5*d^6*e^2 - 276*a*c^4*d^4*e^4 + 109*a^2*c^3*d^2*e^6))/(64*(a^6*e^4 + a^4*c^2*d^4 - 2*a^5*c*d^2*e^2)))*((144*a^5*c^5*d^7 + 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) + (((32768*a^7*c^3*d*e^7 + 24576*a^5*c^5*d^5*e^3 - 57344*a^6*c^4*d^3*e^5)/(4096*(a^8*e^4 + a^6*c^2*d^4 - 2*a^7*c*d^2*e^2)) + ((d + e*x)^(1/2)*(4096*a^7*c^4*d*e^6 + 4096*a^5*c^6*d^5*e^2 - 8192*a^6*c^5*d^3*e^4)*((144*a^5*c^5*d^7 + 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2))/(64*(a^6*e^4 + a^4*c^2*d^4 - 2*a^5*c*d^2*e^2)))*((144*a^5*c^5*d^7 + 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) - ((d + e*x)^(1/2)*(25*a^3*c^2*e^8 + 144*c^5*d^6*e^2 - 276*a*c^4*d^4*e^4 + 109*a^2*c^3*d^2*e^6))/(64*(a^6*e^4 + a^4*c^2*d^4 - 2*a^5*c*d^2*e^2)))*((144*a^5*c^5*d^7 + 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) + (125*a^3*c*e^9 - 864*c^4*d^6*e^3 + 1944*a*c^3*d^4*e^5 - 1170*a^2*c^2*d^2*e^7)/(2048*(a^8*e^4 + a^6*c^2*d^4 - 2*a^7*c*d^2*e^2))))*((144*a^5*c^5*d^7 + 25*a*e^7*(a^15*c^3)^(1/2) - 105*a^8*c^2*d*e^6 - 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 - a^13*c^3*e^6 - 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2)*2i - (((4*a*d*e^3 - 3*c*d^3*e)*(d + e*x)^(1/2))/(8*a^2) - ((d + e*x)^(3/2)*(9*a^2*e^5 + 18*c^2*d^4*e - 23*a*c*d^2*e^3))/(16*a^2*(a*e^2 - c*d^2)) + (c*e*(5*a*e^2 - 6*c*d^2)*(d + e*x)^(7/2))/(16*a^2*(a*e^2 - c*d^2)) - (c*d*(7*a*e^3 - 9*c*d^2*e)*(d + e*x)^(5/2))/(8*a^2*(a*e^2 - c*d^2)))/(c^2*(d + e*x)^4 + a^2*e^4 + c^2*d^4 + (6*c^2*d^2 - 2*a*c*e^2)*(d + e*x)^2 - (4*c^2*d^3 - 4*a*c*d*e^2)*(d + e*x) - 4*c^2*d*(d + e*x)^3 - 2*a*c*d^2*e^2)","B"
642,1,8961,315,3.711794,"\text{Not used}","int(1/((a - c*x^2)^3*(d + e*x)^(1/2)),x)","-\frac{\frac{e\,{\left(d+e\,x\right)}^{3/2}\,\left(a^2\,c\,d\,e^4-22\,a\,c^2\,d^3\,e^2+9\,c^3\,d^5\right)}{8\,a^2\,{\left(a\,e^2-c\,d^2\right)}^2}-\frac{e\,\sqrt{d+e\,x}\,\left(11\,a^2\,e^4+15\,a\,c\,d^2\,e^2-6\,c^2\,d^4\right)}{16\,a^2\,\left(a\,e^2-c\,d^2\right)}+\frac{3\,c\,e\,\left(c^2\,d^3-2\,a\,c\,d\,e^2\right)\,{\left(d+e\,x\right)}^{7/2}}{8\,a^2\,{\left(a\,e^2-c\,d^2\right)}^2}+\frac{c\,e\,{\left(d+e\,x\right)}^{5/2}\,\left(7\,a^2\,e^4+35\,a\,c\,d^2\,e^2-18\,c^2\,d^4\right)}{16\,a^2\,{\left(a\,e^2-c\,d^2\right)}^2}}{c^2\,{\left(d+e\,x\right)}^4+a^2\,e^4+c^2\,d^4+\left(6\,c^2\,d^2-2\,a\,c\,e^2\right)\,{\left(d+e\,x\right)}^2-\left(4\,c^2\,d^3-4\,a\,c\,d\,e^2\right)\,\left(d+e\,x\right)-4\,c^2\,d\,{\left(d+e\,x\right)}^3-2\,a\,c\,d^2\,e^2}-\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(14336\,a^9\,c^3\,e^{11}-38912\,a^8\,c^4\,d^2\,e^9+38912\,a^7\,c^5\,d^4\,e^7-18432\,a^6\,c^6\,d^6\,e^5+4096\,a^5\,c^7\,d^8\,e^3\right)}{2048\,\left(a^{10}\,e^8-4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4-4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}-\frac{\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}\,\left(4096\,a^9\,c^4\,d\,e^{10}-16384\,a^8\,c^5\,d^3\,e^8+24576\,a^7\,c^6\,d^5\,e^6-16384\,a^6\,c^7\,d^7\,e^4+4096\,a^5\,c^8\,d^9\,e^2\right)}{64\,\left(a^8\,e^8-4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4-4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}+\frac{\sqrt{d+e\,x}\,\left(441\,a^4\,c^3\,e^{10}-990\,a^3\,c^4\,d^2\,e^8+1089\,a^2\,c^5\,d^4\,e^6-612\,a\,c^6\,d^6\,e^4+144\,c^7\,d^8\,e^2\right)}{64\,\left(a^8\,e^8-4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4-4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3\,\left(14336\,a^9\,c^3\,e^{11}-38912\,a^8\,c^4\,d^2\,e^9+38912\,a^7\,c^5\,d^4\,e^7-18432\,a^6\,c^6\,d^6\,e^5+4096\,a^5\,c^7\,d^8\,e^3\right)}{2048\,\left(a^{10}\,e^8-4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4-4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}+\frac{\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}\,\left(4096\,a^9\,c^4\,d\,e^{10}-16384\,a^8\,c^5\,d^3\,e^8+24576\,a^7\,c^6\,d^5\,e^6-16384\,a^6\,c^7\,d^7\,e^4+4096\,a^5\,c^8\,d^9\,e^2\right)}{64\,\left(a^8\,e^8-4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4-4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}-\frac{\sqrt{d+e\,x}\,\left(441\,a^4\,c^3\,e^{10}-990\,a^3\,c^4\,d^2\,e^8+1089\,a^2\,c^5\,d^4\,e^6-612\,a\,c^6\,d^6\,e^4+144\,c^7\,d^8\,e^2\right)}{64\,\left(a^8\,e^8-4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4-4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{3\,\left(14336\,a^9\,c^3\,e^{11}-38912\,a^8\,c^4\,d^2\,e^9+38912\,a^7\,c^5\,d^4\,e^7-18432\,a^6\,c^6\,d^6\,e^5+4096\,a^5\,c^7\,d^8\,e^3\right)}{2048\,\left(a^{10}\,e^8-4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4-4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}-\frac{\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}\,\left(4096\,a^9\,c^4\,d\,e^{10}-16384\,a^8\,c^5\,d^3\,e^8+24576\,a^7\,c^6\,d^5\,e^6-16384\,a^6\,c^7\,d^7\,e^4+4096\,a^5\,c^8\,d^9\,e^2\right)}{64\,\left(a^8\,e^8-4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4-4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}+\frac{\sqrt{d+e\,x}\,\left(441\,a^4\,c^3\,e^{10}-990\,a^3\,c^4\,d^2\,e^8+1089\,a^2\,c^5\,d^4\,e^6-612\,a\,c^6\,d^6\,e^4+144\,c^7\,d^8\,e^2\right)}{64\,\left(a^8\,e^8-4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4-4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}-\frac{3\,\left(-882\,a^3\,c^3\,d\,e^9+1233\,a^2\,c^4\,d^3\,e^7-684\,a\,c^5\,d^5\,e^5+144\,c^6\,d^7\,e^3\right)}{1024\,\left(a^{10}\,e^8-4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4-4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}+\left(\left(\frac{3\,\left(14336\,a^9\,c^3\,e^{11}-38912\,a^8\,c^4\,d^2\,e^9+38912\,a^7\,c^5\,d^4\,e^7-18432\,a^6\,c^6\,d^6\,e^5+4096\,a^5\,c^7\,d^8\,e^3\right)}{2048\,\left(a^{10}\,e^8-4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4-4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}+\frac{\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}\,\left(4096\,a^9\,c^4\,d\,e^{10}-16384\,a^8\,c^5\,d^3\,e^8+24576\,a^7\,c^6\,d^5\,e^6-16384\,a^6\,c^7\,d^7\,e^4+4096\,a^5\,c^8\,d^9\,e^2\right)}{64\,\left(a^8\,e^8-4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4-4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}-\frac{\sqrt{d+e\,x}\,\left(441\,a^4\,c^3\,e^{10}-990\,a^3\,c^4\,d^2\,e^8+1089\,a^2\,c^5\,d^4\,e^6-612\,a\,c^6\,d^6\,e^4+144\,c^7\,d^8\,e^2\right)}{64\,\left(a^8\,e^8-4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4-4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(14336\,a^9\,c^3\,e^{11}-38912\,a^8\,c^4\,d^2\,e^9+38912\,a^7\,c^5\,d^4\,e^7-18432\,a^6\,c^6\,d^6\,e^5+4096\,a^5\,c^7\,d^8\,e^3\right)}{2048\,\left(a^{10}\,e^8-4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4-4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}-\frac{\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}\,\left(4096\,a^9\,c^4\,d\,e^{10}-16384\,a^8\,c^5\,d^3\,e^8+24576\,a^7\,c^6\,d^5\,e^6-16384\,a^6\,c^7\,d^7\,e^4+4096\,a^5\,c^8\,d^9\,e^2\right)}{64\,\left(a^8\,e^8-4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4-4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}+\frac{\sqrt{d+e\,x}\,\left(441\,a^4\,c^3\,e^{10}-990\,a^3\,c^4\,d^2\,e^8+1089\,a^2\,c^5\,d^4\,e^6-612\,a\,c^6\,d^6\,e^4+144\,c^7\,d^8\,e^2\right)}{64\,\left(a^8\,e^8-4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4-4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3\,\left(14336\,a^9\,c^3\,e^{11}-38912\,a^8\,c^4\,d^2\,e^9+38912\,a^7\,c^5\,d^4\,e^7-18432\,a^6\,c^6\,d^6\,e^5+4096\,a^5\,c^7\,d^8\,e^3\right)}{2048\,\left(a^{10}\,e^8-4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4-4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}+\frac{\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}\,\left(4096\,a^9\,c^4\,d\,e^{10}-16384\,a^8\,c^5\,d^3\,e^8+24576\,a^7\,c^6\,d^5\,e^6-16384\,a^6\,c^7\,d^7\,e^4+4096\,a^5\,c^8\,d^9\,e^2\right)}{64\,\left(a^8\,e^8-4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4-4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}-\frac{\sqrt{d+e\,x}\,\left(441\,a^4\,c^3\,e^{10}-990\,a^3\,c^4\,d^2\,e^8+1089\,a^2\,c^5\,d^4\,e^6-612\,a\,c^6\,d^6\,e^4+144\,c^7\,d^8\,e^2\right)}{64\,\left(a^8\,e^8-4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4-4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{3\,\left(14336\,a^9\,c^3\,e^{11}-38912\,a^8\,c^4\,d^2\,e^9+38912\,a^7\,c^5\,d^4\,e^7-18432\,a^6\,c^6\,d^6\,e^5+4096\,a^5\,c^7\,d^8\,e^3\right)}{2048\,\left(a^{10}\,e^8-4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4-4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}-\frac{\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}\,\left(4096\,a^9\,c^4\,d\,e^{10}-16384\,a^8\,c^5\,d^3\,e^8+24576\,a^7\,c^6\,d^5\,e^6-16384\,a^6\,c^7\,d^7\,e^4+4096\,a^5\,c^8\,d^9\,e^2\right)}{64\,\left(a^8\,e^8-4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4-4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}+\frac{\sqrt{d+e\,x}\,\left(441\,a^4\,c^3\,e^{10}-990\,a^3\,c^4\,d^2\,e^8+1089\,a^2\,c^5\,d^4\,e^6-612\,a\,c^6\,d^6\,e^4+144\,c^7\,d^8\,e^2\right)}{64\,\left(a^8\,e^8-4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4-4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}-\frac{3\,\left(-882\,a^3\,c^3\,d\,e^9+1233\,a^2\,c^4\,d^3\,e^7-684\,a\,c^5\,d^5\,e^5+144\,c^6\,d^7\,e^3\right)}{1024\,\left(a^{10}\,e^8-4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4-4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}+\left(\left(\frac{3\,\left(14336\,a^9\,c^3\,e^{11}-38912\,a^8\,c^4\,d^2\,e^9+38912\,a^7\,c^5\,d^4\,e^7-18432\,a^6\,c^6\,d^6\,e^5+4096\,a^5\,c^7\,d^8\,e^3\right)}{2048\,\left(a^{10}\,e^8-4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4-4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}+\frac{\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}\,\left(4096\,a^9\,c^4\,d\,e^{10}-16384\,a^8\,c^5\,d^3\,e^8+24576\,a^7\,c^6\,d^5\,e^6-16384\,a^6\,c^7\,d^7\,e^4+4096\,a^5\,c^8\,d^9\,e^2\right)}{64\,\left(a^8\,e^8-4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4-4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}-\frac{\sqrt{d+e\,x}\,\left(441\,a^4\,c^3\,e^{10}-990\,a^3\,c^4\,d^2\,e^8+1089\,a^2\,c^5\,d^4\,e^6-612\,a\,c^6\,d^6\,e^4+144\,c^7\,d^8\,e^2\right)}{64\,\left(a^8\,e^8-4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4-4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{a^{15}\,c}-84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4-210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}-5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6-10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2-a^{10}\,c^6\,d^{10}\right)}}\,2{}\mathrm{i}","Not used",1,"- atan(((((3*(14336*a^9*c^3*e^11 + 4096*a^5*c^7*d^8*e^3 - 18432*a^6*c^6*d^6*e^5 + 38912*a^7*c^5*d^4*e^7 - 38912*a^8*c^4*d^2*e^9))/(2048*(a^10*e^8 + a^6*c^4*d^8 - 4*a^9*c*d^2*e^6 - 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) - ((d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2)*(4096*a^9*c^4*d*e^10 + 4096*a^5*c^8*d^9*e^2 - 16384*a^6*c^7*d^7*e^4 + 24576*a^7*c^6*d^5*e^6 - 16384*a^8*c^5*d^3*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 - 4*a^7*c*d^2*e^6 - 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2) + ((d + e*x)^(1/2)*(441*a^4*c^3*e^10 + 144*c^7*d^8*e^2 - 612*a*c^6*d^6*e^4 + 1089*a^2*c^5*d^4*e^6 - 990*a^3*c^4*d^2*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 - 4*a^7*c*d^2*e^6 - 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2)*1i - (((3*(14336*a^9*c^3*e^11 + 4096*a^5*c^7*d^8*e^3 - 18432*a^6*c^6*d^6*e^5 + 38912*a^7*c^5*d^4*e^7 - 38912*a^8*c^4*d^2*e^9))/(2048*(a^10*e^8 + a^6*c^4*d^8 - 4*a^9*c*d^2*e^6 - 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) + ((d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2)*(4096*a^9*c^4*d*e^10 + 4096*a^5*c^8*d^9*e^2 - 16384*a^6*c^7*d^7*e^4 + 24576*a^7*c^6*d^5*e^6 - 16384*a^8*c^5*d^3*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 - 4*a^7*c*d^2*e^6 - 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2) - ((d + e*x)^(1/2)*(441*a^4*c^3*e^10 + 144*c^7*d^8*e^2 - 612*a*c^6*d^6*e^4 + 1089*a^2*c^5*d^4*e^6 - 990*a^3*c^4*d^2*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 - 4*a^7*c*d^2*e^6 - 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2)*1i)/((((3*(14336*a^9*c^3*e^11 + 4096*a^5*c^7*d^8*e^3 - 18432*a^6*c^6*d^6*e^5 + 38912*a^7*c^5*d^4*e^7 - 38912*a^8*c^4*d^2*e^9))/(2048*(a^10*e^8 + a^6*c^4*d^8 - 4*a^9*c*d^2*e^6 - 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) - ((d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2)*(4096*a^9*c^4*d*e^10 + 4096*a^5*c^8*d^9*e^2 - 16384*a^6*c^7*d^7*e^4 + 24576*a^7*c^6*d^5*e^6 - 16384*a^8*c^5*d^3*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 - 4*a^7*c*d^2*e^6 - 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2) + ((d + e*x)^(1/2)*(441*a^4*c^3*e^10 + 144*c^7*d^8*e^2 - 612*a*c^6*d^6*e^4 + 1089*a^2*c^5*d^4*e^6 - 990*a^3*c^4*d^2*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 - 4*a^7*c*d^2*e^6 - 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2) - (3*(144*c^6*d^7*e^3 - 684*a*c^5*d^5*e^5 - 882*a^3*c^3*d*e^9 + 1233*a^2*c^4*d^3*e^7))/(1024*(a^10*e^8 + a^6*c^4*d^8 - 4*a^9*c*d^2*e^6 - 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) + (((3*(14336*a^9*c^3*e^11 + 4096*a^5*c^7*d^8*e^3 - 18432*a^6*c^6*d^6*e^5 + 38912*a^7*c^5*d^4*e^7 - 38912*a^8*c^4*d^2*e^9))/(2048*(a^10*e^8 + a^6*c^4*d^8 - 4*a^9*c*d^2*e^6 - 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) + ((d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2)*(4096*a^9*c^4*d*e^10 + 4096*a^5*c^8*d^9*e^2 - 16384*a^6*c^7*d^7*e^4 + 24576*a^7*c^6*d^5*e^6 - 16384*a^8*c^5*d^3*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 - 4*a^7*c*d^2*e^6 - 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2) - ((d + e*x)^(1/2)*(441*a^4*c^3*e^10 + 144*c^7*d^8*e^2 - 612*a*c^6*d^6*e^4 + 1089*a^2*c^5*d^4*e^6 - 990*a^3*c^4*d^2*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 - 4*a^7*c*d^2*e^6 - 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2)*2i - atan(((((3*(14336*a^9*c^3*e^11 + 4096*a^5*c^7*d^8*e^3 - 18432*a^6*c^6*d^6*e^5 + 38912*a^7*c^5*d^4*e^7 - 38912*a^8*c^4*d^2*e^9))/(2048*(a^10*e^8 + a^6*c^4*d^8 - 4*a^9*c*d^2*e^6 - 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) - ((d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2)*(4096*a^9*c^4*d*e^10 + 4096*a^5*c^8*d^9*e^2 - 16384*a^6*c^7*d^7*e^4 + 24576*a^7*c^6*d^5*e^6 - 16384*a^8*c^5*d^3*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 - 4*a^7*c*d^2*e^6 - 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2) + ((d + e*x)^(1/2)*(441*a^4*c^3*e^10 + 144*c^7*d^8*e^2 - 612*a*c^6*d^6*e^4 + 1089*a^2*c^5*d^4*e^6 - 990*a^3*c^4*d^2*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 - 4*a^7*c*d^2*e^6 - 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2)*1i - (((3*(14336*a^9*c^3*e^11 + 4096*a^5*c^7*d^8*e^3 - 18432*a^6*c^6*d^6*e^5 + 38912*a^7*c^5*d^4*e^7 - 38912*a^8*c^4*d^2*e^9))/(2048*(a^10*e^8 + a^6*c^4*d^8 - 4*a^9*c*d^2*e^6 - 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) + ((d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2)*(4096*a^9*c^4*d*e^10 + 4096*a^5*c^8*d^9*e^2 - 16384*a^6*c^7*d^7*e^4 + 24576*a^7*c^6*d^5*e^6 - 16384*a^8*c^5*d^3*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 - 4*a^7*c*d^2*e^6 - 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2) - ((d + e*x)^(1/2)*(441*a^4*c^3*e^10 + 144*c^7*d^8*e^2 - 612*a*c^6*d^6*e^4 + 1089*a^2*c^5*d^4*e^6 - 990*a^3*c^4*d^2*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 - 4*a^7*c*d^2*e^6 - 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2)*1i)/((((3*(14336*a^9*c^3*e^11 + 4096*a^5*c^7*d^8*e^3 - 18432*a^6*c^6*d^6*e^5 + 38912*a^7*c^5*d^4*e^7 - 38912*a^8*c^4*d^2*e^9))/(2048*(a^10*e^8 + a^6*c^4*d^8 - 4*a^9*c*d^2*e^6 - 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) - ((d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2)*(4096*a^9*c^4*d*e^10 + 4096*a^5*c^8*d^9*e^2 - 16384*a^6*c^7*d^7*e^4 + 24576*a^7*c^6*d^5*e^6 - 16384*a^8*c^5*d^3*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 - 4*a^7*c*d^2*e^6 - 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2) + ((d + e*x)^(1/2)*(441*a^4*c^3*e^10 + 144*c^7*d^8*e^2 - 612*a*c^6*d^6*e^4 + 1089*a^2*c^5*d^4*e^6 - 990*a^3*c^4*d^2*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 - 4*a^7*c*d^2*e^6 - 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2) - (3*(144*c^6*d^7*e^3 - 684*a*c^5*d^5*e^5 - 882*a^3*c^3*d*e^9 + 1233*a^2*c^4*d^3*e^7))/(1024*(a^10*e^8 + a^6*c^4*d^8 - 4*a^9*c*d^2*e^6 - 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) + (((3*(14336*a^9*c^3*e^11 + 4096*a^5*c^7*d^8*e^3 - 18432*a^6*c^6*d^6*e^5 + 38912*a^7*c^5*d^4*e^7 - 38912*a^8*c^4*d^2*e^9))/(2048*(a^10*e^8 + a^6*c^4*d^8 - 4*a^9*c*d^2*e^6 - 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) + ((d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2)*(4096*a^9*c^4*d*e^10 + 4096*a^5*c^8*d^9*e^2 - 16384*a^6*c^7*d^7*e^4 + 24576*a^7*c^6*d^5*e^6 - 16384*a^8*c^5*d^3*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 - 4*a^7*c*d^2*e^6 - 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2) - ((d + e*x)^(1/2)*(441*a^4*c^3*e^10 + 144*c^7*d^8*e^2 - 612*a*c^6*d^6*e^4 + 1089*a^2*c^5*d^4*e^6 - 990*a^3*c^4*d^2*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 - 4*a^7*c*d^2*e^6 - 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(a^15*c)^(1/2) - 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 - 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(a^15*c)^(1/2)))/(4096*(a^15*c*e^10 - a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 - 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 - 5*a^14*c^2*d^2*e^8)))^(1/2)*2i - ((e*(d + e*x)^(3/2)*(9*c^3*d^5 - 22*a*c^2*d^3*e^2 + a^2*c*d*e^4))/(8*a^2*(a*e^2 - c*d^2)^2) - (e*(d + e*x)^(1/2)*(11*a^2*e^4 - 6*c^2*d^4 + 15*a*c*d^2*e^2))/(16*a^2*(a*e^2 - c*d^2)) + (3*c*e*(c^2*d^3 - 2*a*c*d*e^2)*(d + e*x)^(7/2))/(8*a^2*(a*e^2 - c*d^2)^2) + (c*e*(d + e*x)^(5/2)*(7*a^2*e^4 - 18*c^2*d^4 + 35*a*c*d^2*e^2))/(16*a^2*(a*e^2 - c*d^2)^2))/(c^2*(d + e*x)^4 + a^2*e^4 + c^2*d^4 + (6*c^2*d^2 - 2*a*c*e^2)*(d + e*x)^2 - (4*c^2*d^3 - 4*a*c*d*e^2)*(d + e*x) - 4*c^2*d*(d + e*x)^3 - 2*a*c*d^2*e^2)","B"
643,1,2569,905,1.070639,"\text{Not used}","int((d + e*x)^(7/2)/(a + c*x^2)^3,x)","\frac{\frac{e\,\left(3\,c\,d^3+4\,a\,d\,e^2\right)\,{\left(d+e\,x\right)}^{7/2}}{8\,a^2}+\frac{{\left(d+e\,x\right)}^{3/2}\,\left(7\,a^2\,d\,e^5+16\,a\,c\,d^3\,e^3+9\,c^2\,d^5\,e\right)}{8\,a^2\,c}-\frac{\sqrt{d+e\,x}\,\left(5\,a^3\,e^7+16\,a^2\,c\,d^2\,e^5+17\,a\,c^2\,d^4\,e^3+6\,c^3\,d^6\,e\right)}{16\,a^2\,c^2}-\frac{e\,{\left(d+e\,x\right)}^{5/2}\,\left(9\,a^2\,e^4+23\,a\,c\,d^2\,e^2+18\,c^2\,d^4\right)}{16\,a^2\,c}}{c^2\,{\left(d+e\,x\right)}^4+a^2\,e^4+c^2\,d^4+\left(6\,c^2\,d^2+2\,a\,c\,e^2\right)\,{\left(d+e\,x\right)}^2-\left(4\,c^2\,d^3+4\,a\,c\,d\,e^2\right)\,\left(d+e\,x\right)-4\,c^2\,d\,{\left(d+e\,x\right)}^3+2\,a\,c\,d^2\,e^2}-2\,\mathrm{atanh}\left(\frac{25\,e^{10}\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,d^7}{256\,a^5\,c}-\frac{105\,d\,e^6}{4096\,a^2\,c^4}-\frac{385\,d^3\,e^4}{4096\,a^3\,c^3}-\frac{105\,d^5\,e^2}{1024\,a^4\,c^2}-\frac{25\,e^7\,\sqrt{-a^{15}\,c^9}}{4096\,a^9\,c^9}-\frac{21\,d^2\,e^5\,\sqrt{-a^{15}\,c^9}}{4096\,a^{10}\,c^8}}}{32\,\left(\frac{825\,d^5\,e^9}{2048\,a^3}+\frac{325\,d\,e^{13}}{2048\,a\,c^2}+\frac{63\,c\,d^7\,e^7}{512\,a^4}+\frac{449\,d^3\,e^{11}}{1024\,a^2\,c}+\frac{125\,e^{14}\,\sqrt{-a^{15}\,c^9}}{2048\,a^8\,c^7}+\frac{95\,d^2\,e^{12}\,\sqrt{-a^{15}\,c^9}}{512\,a^9\,c^6}+\frac{381\,d^4\,e^{10}\,\sqrt{-a^{15}\,c^9}}{2048\,a^{10}\,c^5}+\frac{63\,d^6\,e^8\,\sqrt{-a^{15}\,c^9}}{1024\,a^{11}\,c^4}\right)}+\frac{21\,d^2\,e^8\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,d^7}{256\,a^5\,c}-\frac{105\,d\,e^6}{4096\,a^2\,c^4}-\frac{385\,d^3\,e^4}{4096\,a^3\,c^3}-\frac{105\,d^5\,e^2}{1024\,a^4\,c^2}-\frac{25\,e^7\,\sqrt{-a^{15}\,c^9}}{4096\,a^9\,c^9}-\frac{21\,d^2\,e^5\,\sqrt{-a^{15}\,c^9}}{4096\,a^{10}\,c^8}}}{32\,\left(\frac{325\,d\,e^{13}}{2048\,c^3}+\frac{63\,d^7\,e^7}{512\,a^3}+\frac{449\,d^3\,e^{11}}{1024\,a\,c^2}+\frac{825\,d^5\,e^9}{2048\,a^2\,c}+\frac{125\,e^{14}\,\sqrt{-a^{15}\,c^9}}{2048\,a^7\,c^8}+\frac{95\,d^2\,e^{12}\,\sqrt{-a^{15}\,c^9}}{512\,a^8\,c^7}+\frac{381\,d^4\,e^{10}\,\sqrt{-a^{15}\,c^9}}{2048\,a^9\,c^6}+\frac{63\,d^6\,e^8\,\sqrt{-a^{15}\,c^9}}{1024\,a^{10}\,c^5}\right)}-\frac{25\,d\,e^9\,\sqrt{-a^{15}\,c^9}\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,d^7}{256\,a^5\,c}-\frac{105\,d\,e^6}{4096\,a^2\,c^4}-\frac{385\,d^3\,e^4}{4096\,a^3\,c^3}-\frac{105\,d^5\,e^2}{1024\,a^4\,c^2}-\frac{25\,e^7\,\sqrt{-a^{15}\,c^9}}{4096\,a^9\,c^9}-\frac{21\,d^2\,e^5\,\sqrt{-a^{15}\,c^9}}{4096\,a^{10}\,c^8}}}{32\,\left(\frac{125\,e^{14}\,\sqrt{-a^{15}\,c^9}}{2048\,c^3}+\frac{325\,a^7\,c^2\,d\,e^{13}}{2048}+\frac{63\,a^4\,c^5\,d^7\,e^7}{512}+\frac{825\,a^5\,c^4\,d^5\,e^9}{2048}+\frac{449\,a^6\,c^3\,d^3\,e^{11}}{1024}+\frac{63\,d^6\,e^8\,\sqrt{-a^{15}\,c^9}}{1024\,a^3}+\frac{95\,d^2\,e^{12}\,\sqrt{-a^{15}\,c^9}}{512\,a\,c^2}+\frac{381\,d^4\,e^{10}\,\sqrt{-a^{15}\,c^9}}{2048\,a^2\,c}\right)}-\frac{21\,d^3\,e^7\,\sqrt{-a^{15}\,c^9}\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,d^7}{256\,a^5\,c}-\frac{105\,d\,e^6}{4096\,a^2\,c^4}-\frac{385\,d^3\,e^4}{4096\,a^3\,c^3}-\frac{105\,d^5\,e^2}{1024\,a^4\,c^2}-\frac{25\,e^7\,\sqrt{-a^{15}\,c^9}}{4096\,a^9\,c^9}-\frac{21\,d^2\,e^5\,\sqrt{-a^{15}\,c^9}}{4096\,a^{10}\,c^8}}}{32\,\left(\frac{63\,a^5\,c^4\,d^7\,e^7}{512}+\frac{825\,a^6\,c^3\,d^5\,e^9}{2048}+\frac{449\,a^7\,c^2\,d^3\,e^{11}}{1024}+\frac{125\,a\,e^{14}\,\sqrt{-a^{15}\,c^9}}{2048\,c^4}+\frac{325\,a^8\,c\,d\,e^{13}}{2048}+\frac{95\,d^2\,e^{12}\,\sqrt{-a^{15}\,c^9}}{512\,c^3}+\frac{381\,d^4\,e^{10}\,\sqrt{-a^{15}\,c^9}}{2048\,a\,c^2}+\frac{63\,d^6\,e^8\,\sqrt{-a^{15}\,c^9}}{1024\,a^2\,c}\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^8\,d^7+25\,a\,e^7\,\sqrt{-a^{15}\,c^9}+105\,a^8\,c^5\,d\,e^6+420\,a^6\,c^7\,d^5\,e^2+385\,a^7\,c^6\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^9}}{4096\,a^{10}\,c^9}}-2\,\mathrm{atanh}\left(\frac{25\,e^{10}\,\sqrt{d+e\,x}\,\sqrt{\frac{25\,e^7\,\sqrt{-a^{15}\,c^9}}{4096\,a^9\,c^9}-\frac{105\,d\,e^6}{4096\,a^2\,c^4}-\frac{385\,d^3\,e^4}{4096\,a^3\,c^3}-\frac{105\,d^5\,e^2}{1024\,a^4\,c^2}-\frac{9\,d^7}{256\,a^5\,c}+\frac{21\,d^2\,e^5\,\sqrt{-a^{15}\,c^9}}{4096\,a^{10}\,c^8}}}{32\,\left(\frac{825\,d^5\,e^9}{2048\,a^3}+\frac{325\,d\,e^{13}}{2048\,a\,c^2}+\frac{63\,c\,d^7\,e^7}{512\,a^4}+\frac{449\,d^3\,e^{11}}{1024\,a^2\,c}-\frac{125\,e^{14}\,\sqrt{-a^{15}\,c^9}}{2048\,a^8\,c^7}-\frac{95\,d^2\,e^{12}\,\sqrt{-a^{15}\,c^9}}{512\,a^9\,c^6}-\frac{381\,d^4\,e^{10}\,\sqrt{-a^{15}\,c^9}}{2048\,a^{10}\,c^5}-\frac{63\,d^6\,e^8\,\sqrt{-a^{15}\,c^9}}{1024\,a^{11}\,c^4}\right)}+\frac{21\,d^2\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{25\,e^7\,\sqrt{-a^{15}\,c^9}}{4096\,a^9\,c^9}-\frac{105\,d\,e^6}{4096\,a^2\,c^4}-\frac{385\,d^3\,e^4}{4096\,a^3\,c^3}-\frac{105\,d^5\,e^2}{1024\,a^4\,c^2}-\frac{9\,d^7}{256\,a^5\,c}+\frac{21\,d^2\,e^5\,\sqrt{-a^{15}\,c^9}}{4096\,a^{10}\,c^8}}}{32\,\left(\frac{325\,d\,e^{13}}{2048\,c^3}+\frac{63\,d^7\,e^7}{512\,a^3}+\frac{449\,d^3\,e^{11}}{1024\,a\,c^2}+\frac{825\,d^5\,e^9}{2048\,a^2\,c}-\frac{125\,e^{14}\,\sqrt{-a^{15}\,c^9}}{2048\,a^7\,c^8}-\frac{95\,d^2\,e^{12}\,\sqrt{-a^{15}\,c^9}}{512\,a^8\,c^7}-\frac{381\,d^4\,e^{10}\,\sqrt{-a^{15}\,c^9}}{2048\,a^9\,c^6}-\frac{63\,d^6\,e^8\,\sqrt{-a^{15}\,c^9}}{1024\,a^{10}\,c^5}\right)}-\frac{25\,d\,e^9\,\sqrt{-a^{15}\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{25\,e^7\,\sqrt{-a^{15}\,c^9}}{4096\,a^9\,c^9}-\frac{105\,d\,e^6}{4096\,a^2\,c^4}-\frac{385\,d^3\,e^4}{4096\,a^3\,c^3}-\frac{105\,d^5\,e^2}{1024\,a^4\,c^2}-\frac{9\,d^7}{256\,a^5\,c}+\frac{21\,d^2\,e^5\,\sqrt{-a^{15}\,c^9}}{4096\,a^{10}\,c^8}}}{32\,\left(\frac{125\,e^{14}\,\sqrt{-a^{15}\,c^9}}{2048\,c^3}-\frac{325\,a^7\,c^2\,d\,e^{13}}{2048}-\frac{63\,a^4\,c^5\,d^7\,e^7}{512}-\frac{825\,a^5\,c^4\,d^5\,e^9}{2048}-\frac{449\,a^6\,c^3\,d^3\,e^{11}}{1024}+\frac{63\,d^6\,e^8\,\sqrt{-a^{15}\,c^9}}{1024\,a^3}+\frac{95\,d^2\,e^{12}\,\sqrt{-a^{15}\,c^9}}{512\,a\,c^2}+\frac{381\,d^4\,e^{10}\,\sqrt{-a^{15}\,c^9}}{2048\,a^2\,c}\right)}+\frac{21\,d^3\,e^7\,\sqrt{-a^{15}\,c^9}\,\sqrt{d+e\,x}\,\sqrt{\frac{25\,e^7\,\sqrt{-a^{15}\,c^9}}{4096\,a^9\,c^9}-\frac{105\,d\,e^6}{4096\,a^2\,c^4}-\frac{385\,d^3\,e^4}{4096\,a^3\,c^3}-\frac{105\,d^5\,e^2}{1024\,a^4\,c^2}-\frac{9\,d^7}{256\,a^5\,c}+\frac{21\,d^2\,e^5\,\sqrt{-a^{15}\,c^9}}{4096\,a^{10}\,c^8}}}{32\,\left(\frac{63\,a^5\,c^4\,d^7\,e^7}{512}+\frac{825\,a^6\,c^3\,d^5\,e^9}{2048}+\frac{449\,a^7\,c^2\,d^3\,e^{11}}{1024}-\frac{125\,a\,e^{14}\,\sqrt{-a^{15}\,c^9}}{2048\,c^4}+\frac{325\,a^8\,c\,d\,e^{13}}{2048}-\frac{95\,d^2\,e^{12}\,\sqrt{-a^{15}\,c^9}}{512\,c^3}-\frac{381\,d^4\,e^{10}\,\sqrt{-a^{15}\,c^9}}{2048\,a\,c^2}-\frac{63\,d^6\,e^8\,\sqrt{-a^{15}\,c^9}}{1024\,a^2\,c}\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^8\,d^7-25\,a\,e^7\,\sqrt{-a^{15}\,c^9}+105\,a^8\,c^5\,d\,e^6+420\,a^6\,c^7\,d^5\,e^2+385\,a^7\,c^6\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^9}}{4096\,a^{10}\,c^9}}","Not used",1,"((e*(3*c*d^3 + 4*a*d*e^2)*(d + e*x)^(7/2))/(8*a^2) + ((d + e*x)^(3/2)*(7*a^2*d*e^5 + 9*c^2*d^5*e + 16*a*c*d^3*e^3))/(8*a^2*c) - ((d + e*x)^(1/2)*(5*a^3*e^7 + 6*c^3*d^6*e + 17*a*c^2*d^4*e^3 + 16*a^2*c*d^2*e^5))/(16*a^2*c^2) - (e*(d + e*x)^(5/2)*(9*a^2*e^4 + 18*c^2*d^4 + 23*a*c*d^2*e^2))/(16*a^2*c))/(c^2*(d + e*x)^4 + a^2*e^4 + c^2*d^4 + (6*c^2*d^2 + 2*a*c*e^2)*(d + e*x)^2 - (4*c^2*d^3 + 4*a*c*d*e^2)*(d + e*x) - 4*c^2*d*(d + e*x)^3 + 2*a*c*d^2*e^2) - 2*atanh((25*e^10*(d + e*x)^(1/2)*(- (9*d^7)/(256*a^5*c) - (105*d*e^6)/(4096*a^2*c^4) - (385*d^3*e^4)/(4096*a^3*c^3) - (105*d^5*e^2)/(1024*a^4*c^2) - (25*e^7*(-a^15*c^9)^(1/2))/(4096*a^9*c^9) - (21*d^2*e^5*(-a^15*c^9)^(1/2))/(4096*a^10*c^8))^(1/2))/(32*((825*d^5*e^9)/(2048*a^3) + (325*d*e^13)/(2048*a*c^2) + (63*c*d^7*e^7)/(512*a^4) + (449*d^3*e^11)/(1024*a^2*c) + (125*e^14*(-a^15*c^9)^(1/2))/(2048*a^8*c^7) + (95*d^2*e^12*(-a^15*c^9)^(1/2))/(512*a^9*c^6) + (381*d^4*e^10*(-a^15*c^9)^(1/2))/(2048*a^10*c^5) + (63*d^6*e^8*(-a^15*c^9)^(1/2))/(1024*a^11*c^4))) + (21*d^2*e^8*(d + e*x)^(1/2)*(- (9*d^7)/(256*a^5*c) - (105*d*e^6)/(4096*a^2*c^4) - (385*d^3*e^4)/(4096*a^3*c^3) - (105*d^5*e^2)/(1024*a^4*c^2) - (25*e^7*(-a^15*c^9)^(1/2))/(4096*a^9*c^9) - (21*d^2*e^5*(-a^15*c^9)^(1/2))/(4096*a^10*c^8))^(1/2))/(32*((325*d*e^13)/(2048*c^3) + (63*d^7*e^7)/(512*a^3) + (449*d^3*e^11)/(1024*a*c^2) + (825*d^5*e^9)/(2048*a^2*c) + (125*e^14*(-a^15*c^9)^(1/2))/(2048*a^7*c^8) + (95*d^2*e^12*(-a^15*c^9)^(1/2))/(512*a^8*c^7) + (381*d^4*e^10*(-a^15*c^9)^(1/2))/(2048*a^9*c^6) + (63*d^6*e^8*(-a^15*c^9)^(1/2))/(1024*a^10*c^5))) - (25*d*e^9*(-a^15*c^9)^(1/2)*(d + e*x)^(1/2)*(- (9*d^7)/(256*a^5*c) - (105*d*e^6)/(4096*a^2*c^4) - (385*d^3*e^4)/(4096*a^3*c^3) - (105*d^5*e^2)/(1024*a^4*c^2) - (25*e^7*(-a^15*c^9)^(1/2))/(4096*a^9*c^9) - (21*d^2*e^5*(-a^15*c^9)^(1/2))/(4096*a^10*c^8))^(1/2))/(32*((125*e^14*(-a^15*c^9)^(1/2))/(2048*c^3) + (325*a^7*c^2*d*e^13)/2048 + (63*a^4*c^5*d^7*e^7)/512 + (825*a^5*c^4*d^5*e^9)/2048 + (449*a^6*c^3*d^3*e^11)/1024 + (63*d^6*e^8*(-a^15*c^9)^(1/2))/(1024*a^3) + (95*d^2*e^12*(-a^15*c^9)^(1/2))/(512*a*c^2) + (381*d^4*e^10*(-a^15*c^9)^(1/2))/(2048*a^2*c))) - (21*d^3*e^7*(-a^15*c^9)^(1/2)*(d + e*x)^(1/2)*(- (9*d^7)/(256*a^5*c) - (105*d*e^6)/(4096*a^2*c^4) - (385*d^3*e^4)/(4096*a^3*c^3) - (105*d^5*e^2)/(1024*a^4*c^2) - (25*e^7*(-a^15*c^9)^(1/2))/(4096*a^9*c^9) - (21*d^2*e^5*(-a^15*c^9)^(1/2))/(4096*a^10*c^8))^(1/2))/(32*((63*a^5*c^4*d^7*e^7)/512 + (825*a^6*c^3*d^5*e^9)/2048 + (449*a^7*c^2*d^3*e^11)/1024 + (125*a*e^14*(-a^15*c^9)^(1/2))/(2048*c^4) + (325*a^8*c*d*e^13)/2048 + (95*d^2*e^12*(-a^15*c^9)^(1/2))/(512*c^3) + (381*d^4*e^10*(-a^15*c^9)^(1/2))/(2048*a*c^2) + (63*d^6*e^8*(-a^15*c^9)^(1/2))/(1024*a^2*c))))*(-(144*a^5*c^8*d^7 + 25*a*e^7*(-a^15*c^9)^(1/2) + 105*a^8*c^5*d*e^6 + 420*a^6*c^7*d^5*e^2 + 385*a^7*c^6*d^3*e^4 + 21*c*d^2*e^5*(-a^15*c^9)^(1/2))/(4096*a^10*c^9))^(1/2) - 2*atanh((25*e^10*(d + e*x)^(1/2)*((25*e^7*(-a^15*c^9)^(1/2))/(4096*a^9*c^9) - (105*d*e^6)/(4096*a^2*c^4) - (385*d^3*e^4)/(4096*a^3*c^3) - (105*d^5*e^2)/(1024*a^4*c^2) - (9*d^7)/(256*a^5*c) + (21*d^2*e^5*(-a^15*c^9)^(1/2))/(4096*a^10*c^8))^(1/2))/(32*((825*d^5*e^9)/(2048*a^3) + (325*d*e^13)/(2048*a*c^2) + (63*c*d^7*e^7)/(512*a^4) + (449*d^3*e^11)/(1024*a^2*c) - (125*e^14*(-a^15*c^9)^(1/2))/(2048*a^8*c^7) - (95*d^2*e^12*(-a^15*c^9)^(1/2))/(512*a^9*c^6) - (381*d^4*e^10*(-a^15*c^9)^(1/2))/(2048*a^10*c^5) - (63*d^6*e^8*(-a^15*c^9)^(1/2))/(1024*a^11*c^4))) + (21*d^2*e^8*(d + e*x)^(1/2)*((25*e^7*(-a^15*c^9)^(1/2))/(4096*a^9*c^9) - (105*d*e^6)/(4096*a^2*c^4) - (385*d^3*e^4)/(4096*a^3*c^3) - (105*d^5*e^2)/(1024*a^4*c^2) - (9*d^7)/(256*a^5*c) + (21*d^2*e^5*(-a^15*c^9)^(1/2))/(4096*a^10*c^8))^(1/2))/(32*((325*d*e^13)/(2048*c^3) + (63*d^7*e^7)/(512*a^3) + (449*d^3*e^11)/(1024*a*c^2) + (825*d^5*e^9)/(2048*a^2*c) - (125*e^14*(-a^15*c^9)^(1/2))/(2048*a^7*c^8) - (95*d^2*e^12*(-a^15*c^9)^(1/2))/(512*a^8*c^7) - (381*d^4*e^10*(-a^15*c^9)^(1/2))/(2048*a^9*c^6) - (63*d^6*e^8*(-a^15*c^9)^(1/2))/(1024*a^10*c^5))) - (25*d*e^9*(-a^15*c^9)^(1/2)*(d + e*x)^(1/2)*((25*e^7*(-a^15*c^9)^(1/2))/(4096*a^9*c^9) - (105*d*e^6)/(4096*a^2*c^4) - (385*d^3*e^4)/(4096*a^3*c^3) - (105*d^5*e^2)/(1024*a^4*c^2) - (9*d^7)/(256*a^5*c) + (21*d^2*e^5*(-a^15*c^9)^(1/2))/(4096*a^10*c^8))^(1/2))/(32*((125*e^14*(-a^15*c^9)^(1/2))/(2048*c^3) - (325*a^7*c^2*d*e^13)/2048 - (63*a^4*c^5*d^7*e^7)/512 - (825*a^5*c^4*d^5*e^9)/2048 - (449*a^6*c^3*d^3*e^11)/1024 + (63*d^6*e^8*(-a^15*c^9)^(1/2))/(1024*a^3) + (95*d^2*e^12*(-a^15*c^9)^(1/2))/(512*a*c^2) + (381*d^4*e^10*(-a^15*c^9)^(1/2))/(2048*a^2*c))) + (21*d^3*e^7*(-a^15*c^9)^(1/2)*(d + e*x)^(1/2)*((25*e^7*(-a^15*c^9)^(1/2))/(4096*a^9*c^9) - (105*d*e^6)/(4096*a^2*c^4) - (385*d^3*e^4)/(4096*a^3*c^3) - (105*d^5*e^2)/(1024*a^4*c^2) - (9*d^7)/(256*a^5*c) + (21*d^2*e^5*(-a^15*c^9)^(1/2))/(4096*a^10*c^8))^(1/2))/(32*((63*a^5*c^4*d^7*e^7)/512 + (825*a^6*c^3*d^5*e^9)/2048 + (449*a^7*c^2*d^3*e^11)/1024 - (125*a*e^14*(-a^15*c^9)^(1/2))/(2048*c^4) + (325*a^8*c*d*e^13)/2048 - (95*d^2*e^12*(-a^15*c^9)^(1/2))/(512*c^3) - (381*d^4*e^10*(-a^15*c^9)^(1/2))/(2048*a*c^2) - (63*d^6*e^8*(-a^15*c^9)^(1/2))/(1024*a^2*c))))*(-(144*a^5*c^8*d^7 - 25*a*e^7*(-a^15*c^9)^(1/2) + 105*a^8*c^5*d*e^6 + 420*a^6*c^7*d^5*e^2 + 385*a^7*c^6*d^3*e^4 - 21*c*d^2*e^5*(-a^15*c^9)^(1/2))/(4096*a^10*c^9))^(1/2)","B"
644,1,1028,846,0.845183,"\text{Not used}","int((d + e*x)^(5/2)/(a + c*x^2)^3,x)","\frac{\frac{3\,e\,\left(2\,c\,d^2+a\,e^2\right)\,{\left(d+e\,x\right)}^{7/2}}{16\,a^2}+\frac{{\left(d+e\,x\right)}^{3/2}\,\left(-a^2\,e^5+17\,a\,c\,d^2\,e^3+18\,c^2\,d^4\,e\right)}{16\,a^2\,c}-\frac{d\,\left(9\,c\,d^2\,e+4\,a\,e^3\right)\,{\left(d+e\,x\right)}^{5/2}}{8\,a^2}-\frac{3\,\sqrt{d+e\,x}\,\left(a^2\,d\,e^5+2\,a\,c\,d^3\,e^3+c^2\,d^5\,e\right)}{8\,a^2\,c}}{c^2\,{\left(d+e\,x\right)}^4+a^2\,e^4+c^2\,d^4+\left(6\,c^2\,d^2+2\,a\,c\,e^2\right)\,{\left(d+e\,x\right)}^2-\left(4\,c^2\,d^3+4\,a\,c\,d\,e^2\right)\,\left(d+e\,x\right)-4\,c^2\,d\,{\left(d+e\,x\right)}^3+2\,a\,c\,d^2\,e^2}-2\,\mathrm{atanh}\left(\frac{9\,e^8\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,d^5}{256\,a^5\,c}-\frac{45\,d\,e^4}{4096\,a^3\,c^3}-\frac{45\,d^3\,e^2}{1024\,a^4\,c^2}-\frac{9\,e^5\,\sqrt{-a^{15}\,c^7}}{4096\,a^{10}\,c^7}}}{32\,\left(\frac{27\,e^{11}}{2048\,a\,c^2}+\frac{27\,d^4\,e^7}{512\,a^3}+\frac{135\,d^2\,e^9}{2048\,a^2\,c}-\frac{27\,d\,e^{10}\,\sqrt{-a^{15}\,c^7}}{1024\,a^9\,c^5}-\frac{27\,d^3\,e^8\,\sqrt{-a^{15}\,c^7}}{1024\,a^{10}\,c^4}\right)}+\frac{9\,d\,e^7\,\sqrt{-a^{15}\,c^7}\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,d^5}{256\,a^5\,c}-\frac{45\,d\,e^4}{4096\,a^3\,c^3}-\frac{45\,d^3\,e^2}{1024\,a^4\,c^2}-\frac{9\,e^5\,\sqrt{-a^{15}\,c^7}}{4096\,a^{10}\,c^7}}}{32\,\left(\frac{27\,a^7\,c\,e^{11}}{2048}+\frac{27\,a^5\,c^3\,d^4\,e^7}{512}+\frac{135\,a^6\,c^2\,d^2\,e^9}{2048}-\frac{27\,d\,e^{10}\,\sqrt{-a^{15}\,c^7}}{1024\,a\,c^2}-\frac{27\,d^3\,e^8\,\sqrt{-a^{15}\,c^7}}{1024\,a^2\,c}\right)}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{-a^{15}\,c^7}+16\,a^5\,c^6\,d^5+5\,a^7\,c^4\,d\,e^4+20\,a^6\,c^5\,d^3\,e^2\right)}{4096\,a^{10}\,c^7}}-2\,\mathrm{atanh}\left(\frac{9\,e^8\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,e^5\,\sqrt{-a^{15}\,c^7}}{4096\,a^{10}\,c^7}-\frac{45\,d\,e^4}{4096\,a^3\,c^3}-\frac{45\,d^3\,e^2}{1024\,a^4\,c^2}-\frac{9\,d^5}{256\,a^5\,c}}}{32\,\left(\frac{27\,e^{11}}{2048\,a\,c^2}+\frac{27\,d^4\,e^7}{512\,a^3}+\frac{135\,d^2\,e^9}{2048\,a^2\,c}+\frac{27\,d\,e^{10}\,\sqrt{-a^{15}\,c^7}}{1024\,a^9\,c^5}+\frac{27\,d^3\,e^8\,\sqrt{-a^{15}\,c^7}}{1024\,a^{10}\,c^4}\right)}-\frac{9\,d\,e^7\,\sqrt{-a^{15}\,c^7}\,\sqrt{d+e\,x}\,\sqrt{\frac{9\,e^5\,\sqrt{-a^{15}\,c^7}}{4096\,a^{10}\,c^7}-\frac{45\,d\,e^4}{4096\,a^3\,c^3}-\frac{45\,d^3\,e^2}{1024\,a^4\,c^2}-\frac{9\,d^5}{256\,a^5\,c}}}{32\,\left(\frac{27\,a^7\,c\,e^{11}}{2048}+\frac{27\,a^5\,c^3\,d^4\,e^7}{512}+\frac{135\,a^6\,c^2\,d^2\,e^9}{2048}+\frac{27\,d\,e^{10}\,\sqrt{-a^{15}\,c^7}}{1024\,a\,c^2}+\frac{27\,d^3\,e^8\,\sqrt{-a^{15}\,c^7}}{1024\,a^2\,c}\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^6\,d^5-e^5\,\sqrt{-a^{15}\,c^7}+5\,a^7\,c^4\,d\,e^4+20\,a^6\,c^5\,d^3\,e^2\right)}{4096\,a^{10}\,c^7}}","Not used",1,"((3*e*(a*e^2 + 2*c*d^2)*(d + e*x)^(7/2))/(16*a^2) + ((d + e*x)^(3/2)*(18*c^2*d^4*e - a^2*e^5 + 17*a*c*d^2*e^3))/(16*a^2*c) - (d*(4*a*e^3 + 9*c*d^2*e)*(d + e*x)^(5/2))/(8*a^2) - (3*(d + e*x)^(1/2)*(a^2*d*e^5 + c^2*d^5*e + 2*a*c*d^3*e^3))/(8*a^2*c))/(c^2*(d + e*x)^4 + a^2*e^4 + c^2*d^4 + (6*c^2*d^2 + 2*a*c*e^2)*(d + e*x)^2 - (4*c^2*d^3 + 4*a*c*d*e^2)*(d + e*x) - 4*c^2*d*(d + e*x)^3 + 2*a*c*d^2*e^2) - 2*atanh((9*e^8*(d + e*x)^(1/2)*(- (9*d^5)/(256*a^5*c) - (45*d*e^4)/(4096*a^3*c^3) - (45*d^3*e^2)/(1024*a^4*c^2) - (9*e^5*(-a^15*c^7)^(1/2))/(4096*a^10*c^7))^(1/2))/(32*((27*e^11)/(2048*a*c^2) + (27*d^4*e^7)/(512*a^3) + (135*d^2*e^9)/(2048*a^2*c) - (27*d*e^10*(-a^15*c^7)^(1/2))/(1024*a^9*c^5) - (27*d^3*e^8*(-a^15*c^7)^(1/2))/(1024*a^10*c^4))) + (9*d*e^7*(-a^15*c^7)^(1/2)*(d + e*x)^(1/2)*(- (9*d^5)/(256*a^5*c) - (45*d*e^4)/(4096*a^3*c^3) - (45*d^3*e^2)/(1024*a^4*c^2) - (9*e^5*(-a^15*c^7)^(1/2))/(4096*a^10*c^7))^(1/2))/(32*((27*a^7*c*e^11)/2048 + (27*a^5*c^3*d^4*e^7)/512 + (135*a^6*c^2*d^2*e^9)/2048 - (27*d*e^10*(-a^15*c^7)^(1/2))/(1024*a*c^2) - (27*d^3*e^8*(-a^15*c^7)^(1/2))/(1024*a^2*c))))*(-(9*(e^5*(-a^15*c^7)^(1/2) + 16*a^5*c^6*d^5 + 5*a^7*c^4*d*e^4 + 20*a^6*c^5*d^3*e^2))/(4096*a^10*c^7))^(1/2) - 2*atanh((9*e^8*(d + e*x)^(1/2)*((9*e^5*(-a^15*c^7)^(1/2))/(4096*a^10*c^7) - (45*d*e^4)/(4096*a^3*c^3) - (45*d^3*e^2)/(1024*a^4*c^2) - (9*d^5)/(256*a^5*c))^(1/2))/(32*((27*e^11)/(2048*a*c^2) + (27*d^4*e^7)/(512*a^3) + (135*d^2*e^9)/(2048*a^2*c) + (27*d*e^10*(-a^15*c^7)^(1/2))/(1024*a^9*c^5) + (27*d^3*e^8*(-a^15*c^7)^(1/2))/(1024*a^10*c^4))) - (9*d*e^7*(-a^15*c^7)^(1/2)*(d + e*x)^(1/2)*((9*e^5*(-a^15*c^7)^(1/2))/(4096*a^10*c^7) - (45*d*e^4)/(4096*a^3*c^3) - (45*d^3*e^2)/(1024*a^4*c^2) - (9*d^5)/(256*a^5*c))^(1/2))/(32*((27*a^7*c*e^11)/2048 + (27*a^5*c^3*d^4*e^7)/512 + (135*a^6*c^2*d^2*e^9)/2048 + (27*d*e^10*(-a^15*c^7)^(1/2))/(1024*a*c^2) + (27*d^3*e^8*(-a^15*c^7)^(1/2))/(1024*a^2*c))))*(-(9*(16*a^5*c^6*d^5 - e^5*(-a^15*c^7)^(1/2) + 5*a^7*c^4*d*e^4 + 20*a^6*c^5*d^3*e^2))/(4096*a^10*c^7))^(1/2)","B"
645,1,3204,769,3.022434,"\text{Not used}","int((d + e*x)^(3/2)/(a + c*x^2)^3,x)","\frac{\frac{\left(9\,c\,d^3\,e+4\,a\,d\,e^3\right)\,{\left(d+e\,x\right)}^{3/2}}{8\,a^2}+\frac{e\,\left(a\,e^2-18\,c\,d^2\right)\,{\left(d+e\,x\right)}^{5/2}}{16\,a^2}-\frac{3\,\sqrt{d+e\,x}\,\left(a^2\,e^5+3\,a\,c\,d^2\,e^3+2\,c^2\,d^4\,e\right)}{16\,a^2\,c}+\frac{3\,c\,d\,e\,{\left(d+e\,x\right)}^{7/2}}{8\,a^2}}{c^2\,{\left(d+e\,x\right)}^4+a^2\,e^4+c^2\,d^4+\left(6\,c^2\,d^2+2\,a\,c\,e^2\right)\,{\left(d+e\,x\right)}^2-\left(4\,c^2\,d^3+4\,a\,c\,d\,e^2\right)\,\left(d+e\,x\right)-4\,c^2\,d\,{\left(d+e\,x\right)}^3+2\,a\,c\,d^2\,e^2}+\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(2048\,a^6\,c^2\,e^5+4096\,a^5\,c^3\,d^2\,e^3\right)}{2048\,a^6}-64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{-a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{-a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}-\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c\,e^6+36\,a\,c^2\,d^2\,e^4+144\,c^3\,d^4\,e^2\right)}{64\,a^4}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{-a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3\,\left(2048\,a^6\,c^2\,e^5+4096\,a^5\,c^3\,d^2\,e^3\right)}{2048\,a^6}+64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{-a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{-a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}+\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c\,e^6+36\,a\,c^2\,d^2\,e^4+144\,c^3\,d^4\,e^2\right)}{64\,a^4}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{-a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}\,1{}\mathrm{i}}{\frac{3\,\left(9\,a^2\,d\,e^7+108\,a\,c\,d^3\,e^5+144\,c^2\,d^5\,e^3\right)}{1024\,a^6}+\left(\left(\frac{3\,\left(2048\,a^6\,c^2\,e^5+4096\,a^5\,c^3\,d^2\,e^3\right)}{2048\,a^6}-64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{-a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{-a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}-\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c\,e^6+36\,a\,c^2\,d^2\,e^4+144\,c^3\,d^4\,e^2\right)}{64\,a^4}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{-a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}+\left(\left(\frac{3\,\left(2048\,a^6\,c^2\,e^5+4096\,a^5\,c^3\,d^2\,e^3\right)}{2048\,a^6}+64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{-a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{-a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}+\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c\,e^6+36\,a\,c^2\,d^2\,e^4+144\,c^3\,d^4\,e^2\right)}{64\,a^4}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{-a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}}\right)\,\sqrt{-\frac{9\,\left(e^5\,\sqrt{-a^{15}\,c^5}+16\,a^5\,c^5\,d^5+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(2048\,a^6\,c^2\,e^5+4096\,a^5\,c^3\,d^2\,e^3\right)}{2048\,a^6}-64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^5-e^5\,\sqrt{-a^{15}\,c^5}+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^5-e^5\,\sqrt{-a^{15}\,c^5}+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}-\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c\,e^6+36\,a\,c^2\,d^2\,e^4+144\,c^3\,d^4\,e^2\right)}{64\,a^4}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^5-e^5\,\sqrt{-a^{15}\,c^5}+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3\,\left(2048\,a^6\,c^2\,e^5+4096\,a^5\,c^3\,d^2\,e^3\right)}{2048\,a^6}+64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^5-e^5\,\sqrt{-a^{15}\,c^5}+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^5-e^5\,\sqrt{-a^{15}\,c^5}+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}+\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c\,e^6+36\,a\,c^2\,d^2\,e^4+144\,c^3\,d^4\,e^2\right)}{64\,a^4}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^5-e^5\,\sqrt{-a^{15}\,c^5}+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}\,1{}\mathrm{i}}{\frac{3\,\left(9\,a^2\,d\,e^7+108\,a\,c\,d^3\,e^5+144\,c^2\,d^5\,e^3\right)}{1024\,a^6}+\left(\left(\frac{3\,\left(2048\,a^6\,c^2\,e^5+4096\,a^5\,c^3\,d^2\,e^3\right)}{2048\,a^6}-64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^5-e^5\,\sqrt{-a^{15}\,c^5}+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^5-e^5\,\sqrt{-a^{15}\,c^5}+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}-\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c\,e^6+36\,a\,c^2\,d^2\,e^4+144\,c^3\,d^4\,e^2\right)}{64\,a^4}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^5-e^5\,\sqrt{-a^{15}\,c^5}+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}+\left(\left(\frac{3\,\left(2048\,a^6\,c^2\,e^5+4096\,a^5\,c^3\,d^2\,e^3\right)}{2048\,a^6}+64\,a\,c^4\,d\,e^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^5-e^5\,\sqrt{-a^{15}\,c^5}+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^5-e^5\,\sqrt{-a^{15}\,c^5}+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}+\frac{\sqrt{d+e\,x}\,\left(9\,a^2\,c\,e^6+36\,a\,c^2\,d^2\,e^4+144\,c^3\,d^4\,e^2\right)}{64\,a^4}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^5-e^5\,\sqrt{-a^{15}\,c^5}+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^5-e^5\,\sqrt{-a^{15}\,c^5}+5\,a^7\,c^3\,d\,e^4+20\,a^6\,c^4\,d^3\,e^2\right)}{4096\,\left(a^{11}\,c^5\,e^2+a^{10}\,c^6\,d^2\right)}}\,2{}\mathrm{i}","Not used",1,"(((4*a*d*e^3 + 9*c*d^3*e)*(d + e*x)^(3/2))/(8*a^2) + (e*(a*e^2 - 18*c*d^2)*(d + e*x)^(5/2))/(16*a^2) - (3*(d + e*x)^(1/2)*(a^2*e^5 + 2*c^2*d^4*e + 3*a*c*d^2*e^3))/(16*a^2*c) + (3*c*d*e*(d + e*x)^(7/2))/(8*a^2))/(c^2*(d + e*x)^4 + a^2*e^4 + c^2*d^4 + (6*c^2*d^2 + 2*a*c*e^2)*(d + e*x)^2 - (4*c^2*d^3 + 4*a*c*d*e^2)*(d + e*x) - 4*c^2*d*(d + e*x)^3 + 2*a*c*d^2*e^2) + atan(((((3*(2048*a^6*c^2*e^5 + 4096*a^5*c^3*d^2*e^3))/(2048*a^6) - 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(9*(e^5*(-a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2))*(-(9*(e^5*(-a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2) - ((d + e*x)^(1/2)*(9*a^2*c*e^6 + 144*c^3*d^4*e^2 + 36*a*c^2*d^2*e^4))/(64*a^4))*(-(9*(e^5*(-a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2)*1i - (((3*(2048*a^6*c^2*e^5 + 4096*a^5*c^3*d^2*e^3))/(2048*a^6) + 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(9*(e^5*(-a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2))*(-(9*(e^5*(-a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2) + ((d + e*x)^(1/2)*(9*a^2*c*e^6 + 144*c^3*d^4*e^2 + 36*a*c^2*d^2*e^4))/(64*a^4))*(-(9*(e^5*(-a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2)*1i)/((3*(9*a^2*d*e^7 + 144*c^2*d^5*e^3 + 108*a*c*d^3*e^5))/(1024*a^6) + (((3*(2048*a^6*c^2*e^5 + 4096*a^5*c^3*d^2*e^3))/(2048*a^6) - 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(9*(e^5*(-a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2))*(-(9*(e^5*(-a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2) - ((d + e*x)^(1/2)*(9*a^2*c*e^6 + 144*c^3*d^4*e^2 + 36*a*c^2*d^2*e^4))/(64*a^4))*(-(9*(e^5*(-a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2) + (((3*(2048*a^6*c^2*e^5 + 4096*a^5*c^3*d^2*e^3))/(2048*a^6) + 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(9*(e^5*(-a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2))*(-(9*(e^5*(-a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2) + ((d + e*x)^(1/2)*(9*a^2*c*e^6 + 144*c^3*d^4*e^2 + 36*a*c^2*d^2*e^4))/(64*a^4))*(-(9*(e^5*(-a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2)))*(-(9*(e^5*(-a^15*c^5)^(1/2) + 16*a^5*c^5*d^5 + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2)*2i + atan(((((3*(2048*a^6*c^2*e^5 + 4096*a^5*c^3*d^2*e^3))/(2048*a^6) - 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^5 - e^5*(-a^15*c^5)^(1/2) + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2))*(-(9*(16*a^5*c^5*d^5 - e^5*(-a^15*c^5)^(1/2) + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2) - ((d + e*x)^(1/2)*(9*a^2*c*e^6 + 144*c^3*d^4*e^2 + 36*a*c^2*d^2*e^4))/(64*a^4))*(-(9*(16*a^5*c^5*d^5 - e^5*(-a^15*c^5)^(1/2) + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2)*1i - (((3*(2048*a^6*c^2*e^5 + 4096*a^5*c^3*d^2*e^3))/(2048*a^6) + 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^5 - e^5*(-a^15*c^5)^(1/2) + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2))*(-(9*(16*a^5*c^5*d^5 - e^5*(-a^15*c^5)^(1/2) + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2) + ((d + e*x)^(1/2)*(9*a^2*c*e^6 + 144*c^3*d^4*e^2 + 36*a*c^2*d^2*e^4))/(64*a^4))*(-(9*(16*a^5*c^5*d^5 - e^5*(-a^15*c^5)^(1/2) + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2)*1i)/((3*(9*a^2*d*e^7 + 144*c^2*d^5*e^3 + 108*a*c*d^3*e^5))/(1024*a^6) + (((3*(2048*a^6*c^2*e^5 + 4096*a^5*c^3*d^2*e^3))/(2048*a^6) - 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^5 - e^5*(-a^15*c^5)^(1/2) + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2))*(-(9*(16*a^5*c^5*d^5 - e^5*(-a^15*c^5)^(1/2) + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2) - ((d + e*x)^(1/2)*(9*a^2*c*e^6 + 144*c^3*d^4*e^2 + 36*a*c^2*d^2*e^4))/(64*a^4))*(-(9*(16*a^5*c^5*d^5 - e^5*(-a^15*c^5)^(1/2) + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2) + (((3*(2048*a^6*c^2*e^5 + 4096*a^5*c^3*d^2*e^3))/(2048*a^6) + 64*a*c^4*d*e^2*(d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^5 - e^5*(-a^15*c^5)^(1/2) + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2))*(-(9*(16*a^5*c^5*d^5 - e^5*(-a^15*c^5)^(1/2) + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2) + ((d + e*x)^(1/2)*(9*a^2*c*e^6 + 144*c^3*d^4*e^2 + 36*a*c^2*d^2*e^4))/(64*a^4))*(-(9*(16*a^5*c^5*d^5 - e^5*(-a^15*c^5)^(1/2) + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2)))*(-(9*(16*a^5*c^5*d^5 - e^5*(-a^15*c^5)^(1/2) + 5*a^7*c^3*d*e^4 + 20*a^6*c^4*d^3*e^2))/(4096*(a^10*c^6*d^2 + a^11*c^5*e^2)))^(1/2)*2i","B"
646,1,6238,849,3.217321,"\text{Not used}","int((d + e*x)^(1/2)/(a + c*x^2)^3,x)","-\frac{\frac{\left(3\,c\,d^3\,e+4\,a\,d\,e^3\right)\,\sqrt{d+e\,x}}{8\,a^2}-\frac{{\left(d+e\,x\right)}^{3/2}\,\left(9\,a^2\,e^5+23\,a\,c\,d^2\,e^3+18\,c^2\,d^4\,e\right)}{16\,a^2\,\left(c\,d^2+a\,e^2\right)}-\frac{c\,e\,\left(6\,c\,d^2+5\,a\,e^2\right)\,{\left(d+e\,x\right)}^{7/2}}{16\,a^2\,\left(c\,d^2+a\,e^2\right)}+\frac{c\,d\,\left(9\,c\,d^2\,e+7\,a\,e^3\right)\,{\left(d+e\,x\right)}^{5/2}}{8\,a^2\,\left(c\,d^2+a\,e^2\right)}}{c^2\,{\left(d+e\,x\right)}^4+a^2\,e^4+c^2\,d^4+\left(6\,c^2\,d^2+2\,a\,c\,e^2\right)\,{\left(d+e\,x\right)}^2-\left(4\,c^2\,d^3+4\,a\,c\,d\,e^2\right)\,\left(d+e\,x\right)-4\,c^2\,d\,{\left(d+e\,x\right)}^3+2\,a\,c\,d^2\,e^2}+\mathrm{atan}\left(\frac{\left(\left(\frac{32768\,a^7\,c^3\,d\,e^7+57344\,a^6\,c^4\,d^3\,e^5+24576\,a^5\,c^5\,d^5\,e^3}{4096\,\left(a^8\,e^4+2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}-\frac{\sqrt{d+e\,x}\,\left(4096\,a^7\,c^4\,d\,e^6+8192\,a^6\,c^5\,d^3\,e^4+4096\,a^5\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}}{64\,\left(a^6\,e^4+2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}-\frac{\sqrt{d+e\,x}\,\left(-25\,a^3\,c^2\,e^8+109\,a^2\,c^3\,d^2\,e^6+276\,a\,c^4\,d^4\,e^4+144\,c^5\,d^6\,e^2\right)}{64\,\left(a^6\,e^4+2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}\,1{}\mathrm{i}-\left(\left(\frac{32768\,a^7\,c^3\,d\,e^7+57344\,a^6\,c^4\,d^3\,e^5+24576\,a^5\,c^5\,d^5\,e^3}{4096\,\left(a^8\,e^4+2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}+\frac{\sqrt{d+e\,x}\,\left(4096\,a^7\,c^4\,d\,e^6+8192\,a^6\,c^5\,d^3\,e^4+4096\,a^5\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}}{64\,\left(a^6\,e^4+2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}+\frac{\sqrt{d+e\,x}\,\left(-25\,a^3\,c^2\,e^8+109\,a^2\,c^3\,d^2\,e^6+276\,a\,c^4\,d^4\,e^4+144\,c^5\,d^6\,e^2\right)}{64\,\left(a^6\,e^4+2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{32768\,a^7\,c^3\,d\,e^7+57344\,a^6\,c^4\,d^3\,e^5+24576\,a^5\,c^5\,d^5\,e^3}{4096\,\left(a^8\,e^4+2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}-\frac{\sqrt{d+e\,x}\,\left(4096\,a^7\,c^4\,d\,e^6+8192\,a^6\,c^5\,d^3\,e^4+4096\,a^5\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}}{64\,\left(a^6\,e^4+2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}-\frac{\sqrt{d+e\,x}\,\left(-25\,a^3\,c^2\,e^8+109\,a^2\,c^3\,d^2\,e^6+276\,a\,c^4\,d^4\,e^4+144\,c^5\,d^6\,e^2\right)}{64\,\left(a^6\,e^4+2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}+\left(\left(\frac{32768\,a^7\,c^3\,d\,e^7+57344\,a^6\,c^4\,d^3\,e^5+24576\,a^5\,c^5\,d^5\,e^3}{4096\,\left(a^8\,e^4+2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}+\frac{\sqrt{d+e\,x}\,\left(4096\,a^7\,c^4\,d\,e^6+8192\,a^6\,c^5\,d^3\,e^4+4096\,a^5\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}}{64\,\left(a^6\,e^4+2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}+\frac{\sqrt{d+e\,x}\,\left(-25\,a^3\,c^2\,e^8+109\,a^2\,c^3\,d^2\,e^6+276\,a\,c^4\,d^4\,e^4+144\,c^5\,d^6\,e^2\right)}{64\,\left(a^6\,e^4+2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}+\frac{125\,a^3\,c\,e^9+1170\,a^2\,c^2\,d^2\,e^7+1944\,a\,c^3\,d^4\,e^5+864\,c^4\,d^6\,e^3}{2048\,\left(a^8\,e^4+2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7-25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4-21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(\frac{32768\,a^7\,c^3\,d\,e^7+57344\,a^6\,c^4\,d^3\,e^5+24576\,a^5\,c^5\,d^5\,e^3}{4096\,\left(a^8\,e^4+2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}-\frac{\sqrt{d+e\,x}\,\left(4096\,a^7\,c^4\,d\,e^6+8192\,a^6\,c^5\,d^3\,e^4+4096\,a^5\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}}{64\,\left(a^6\,e^4+2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}-\frac{\sqrt{d+e\,x}\,\left(-25\,a^3\,c^2\,e^8+109\,a^2\,c^3\,d^2\,e^6+276\,a\,c^4\,d^4\,e^4+144\,c^5\,d^6\,e^2\right)}{64\,\left(a^6\,e^4+2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}\,1{}\mathrm{i}-\left(\left(\frac{32768\,a^7\,c^3\,d\,e^7+57344\,a^6\,c^4\,d^3\,e^5+24576\,a^5\,c^5\,d^5\,e^3}{4096\,\left(a^8\,e^4+2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}+\frac{\sqrt{d+e\,x}\,\left(4096\,a^7\,c^4\,d\,e^6+8192\,a^6\,c^5\,d^3\,e^4+4096\,a^5\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}}{64\,\left(a^6\,e^4+2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}+\frac{\sqrt{d+e\,x}\,\left(-25\,a^3\,c^2\,e^8+109\,a^2\,c^3\,d^2\,e^6+276\,a\,c^4\,d^4\,e^4+144\,c^5\,d^6\,e^2\right)}{64\,\left(a^6\,e^4+2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{32768\,a^7\,c^3\,d\,e^7+57344\,a^6\,c^4\,d^3\,e^5+24576\,a^5\,c^5\,d^5\,e^3}{4096\,\left(a^8\,e^4+2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}-\frac{\sqrt{d+e\,x}\,\left(4096\,a^7\,c^4\,d\,e^6+8192\,a^6\,c^5\,d^3\,e^4+4096\,a^5\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}}{64\,\left(a^6\,e^4+2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}-\frac{\sqrt{d+e\,x}\,\left(-25\,a^3\,c^2\,e^8+109\,a^2\,c^3\,d^2\,e^6+276\,a\,c^4\,d^4\,e^4+144\,c^5\,d^6\,e^2\right)}{64\,\left(a^6\,e^4+2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}+\left(\left(\frac{32768\,a^7\,c^3\,d\,e^7+57344\,a^6\,c^4\,d^3\,e^5+24576\,a^5\,c^5\,d^5\,e^3}{4096\,\left(a^8\,e^4+2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}+\frac{\sqrt{d+e\,x}\,\left(4096\,a^7\,c^4\,d\,e^6+8192\,a^6\,c^5\,d^3\,e^4+4096\,a^5\,c^6\,d^5\,e^2\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}}{64\,\left(a^6\,e^4+2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}+\frac{\sqrt{d+e\,x}\,\left(-25\,a^3\,c^2\,e^8+109\,a^2\,c^3\,d^2\,e^6+276\,a\,c^4\,d^4\,e^4+144\,c^5\,d^6\,e^2\right)}{64\,\left(a^6\,e^4+2\,a^5\,c\,d^2\,e^2+a^4\,c^2\,d^4\right)}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}+\frac{125\,a^3\,c\,e^9+1170\,a^2\,c^2\,d^2\,e^7+1944\,a\,c^3\,d^4\,e^5+864\,c^4\,d^6\,e^3}{2048\,\left(a^8\,e^4+2\,a^7\,c\,d^2\,e^2+a^6\,c^2\,d^4\right)}}\right)\,\sqrt{-\frac{144\,a^5\,c^5\,d^7+25\,a\,e^7\,\sqrt{-a^{15}\,c^3}+105\,a^8\,c^2\,d\,e^6+420\,a^6\,c^4\,d^5\,e^2+385\,a^7\,c^3\,d^3\,e^4+21\,c\,d^2\,e^5\,\sqrt{-a^{15}\,c^3}}{4096\,\left(a^{13}\,c^3\,e^6+3\,a^{12}\,c^4\,d^2\,e^4+3\,a^{11}\,c^5\,d^4\,e^2+a^{10}\,c^6\,d^6\right)}}\,2{}\mathrm{i}","Not used",1,"atan(((((32768*a^7*c^3*d*e^7 + 24576*a^5*c^5*d^5*e^3 + 57344*a^6*c^4*d^3*e^5)/(4096*(a^8*e^4 + a^6*c^2*d^4 + 2*a^7*c*d^2*e^2)) - ((d + e*x)^(1/2)*(4096*a^7*c^4*d*e^6 + 4096*a^5*c^6*d^5*e^2 + 8192*a^6*c^5*d^3*e^4)*(-(144*a^5*c^5*d^7 - 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2))/(64*(a^6*e^4 + a^4*c^2*d^4 + 2*a^5*c*d^2*e^2)))*(-(144*a^5*c^5*d^7 - 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) - ((d + e*x)^(1/2)*(144*c^5*d^6*e^2 - 25*a^3*c^2*e^8 + 276*a*c^4*d^4*e^4 + 109*a^2*c^3*d^2*e^6))/(64*(a^6*e^4 + a^4*c^2*d^4 + 2*a^5*c*d^2*e^2)))*(-(144*a^5*c^5*d^7 - 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2)*1i - (((32768*a^7*c^3*d*e^7 + 24576*a^5*c^5*d^5*e^3 + 57344*a^6*c^4*d^3*e^5)/(4096*(a^8*e^4 + a^6*c^2*d^4 + 2*a^7*c*d^2*e^2)) + ((d + e*x)^(1/2)*(4096*a^7*c^4*d*e^6 + 4096*a^5*c^6*d^5*e^2 + 8192*a^6*c^5*d^3*e^4)*(-(144*a^5*c^5*d^7 - 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2))/(64*(a^6*e^4 + a^4*c^2*d^4 + 2*a^5*c*d^2*e^2)))*(-(144*a^5*c^5*d^7 - 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) + ((d + e*x)^(1/2)*(144*c^5*d^6*e^2 - 25*a^3*c^2*e^8 + 276*a*c^4*d^4*e^4 + 109*a^2*c^3*d^2*e^6))/(64*(a^6*e^4 + a^4*c^2*d^4 + 2*a^5*c*d^2*e^2)))*(-(144*a^5*c^5*d^7 - 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2)*1i)/((((32768*a^7*c^3*d*e^7 + 24576*a^5*c^5*d^5*e^3 + 57344*a^6*c^4*d^3*e^5)/(4096*(a^8*e^4 + a^6*c^2*d^4 + 2*a^7*c*d^2*e^2)) - ((d + e*x)^(1/2)*(4096*a^7*c^4*d*e^6 + 4096*a^5*c^6*d^5*e^2 + 8192*a^6*c^5*d^3*e^4)*(-(144*a^5*c^5*d^7 - 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2))/(64*(a^6*e^4 + a^4*c^2*d^4 + 2*a^5*c*d^2*e^2)))*(-(144*a^5*c^5*d^7 - 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) - ((d + e*x)^(1/2)*(144*c^5*d^6*e^2 - 25*a^3*c^2*e^8 + 276*a*c^4*d^4*e^4 + 109*a^2*c^3*d^2*e^6))/(64*(a^6*e^4 + a^4*c^2*d^4 + 2*a^5*c*d^2*e^2)))*(-(144*a^5*c^5*d^7 - 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) + (((32768*a^7*c^3*d*e^7 + 24576*a^5*c^5*d^5*e^3 + 57344*a^6*c^4*d^3*e^5)/(4096*(a^8*e^4 + a^6*c^2*d^4 + 2*a^7*c*d^2*e^2)) + ((d + e*x)^(1/2)*(4096*a^7*c^4*d*e^6 + 4096*a^5*c^6*d^5*e^2 + 8192*a^6*c^5*d^3*e^4)*(-(144*a^5*c^5*d^7 - 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2))/(64*(a^6*e^4 + a^4*c^2*d^4 + 2*a^5*c*d^2*e^2)))*(-(144*a^5*c^5*d^7 - 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) + ((d + e*x)^(1/2)*(144*c^5*d^6*e^2 - 25*a^3*c^2*e^8 + 276*a*c^4*d^4*e^4 + 109*a^2*c^3*d^2*e^6))/(64*(a^6*e^4 + a^4*c^2*d^4 + 2*a^5*c*d^2*e^2)))*(-(144*a^5*c^5*d^7 - 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) + (125*a^3*c*e^9 + 864*c^4*d^6*e^3 + 1944*a*c^3*d^4*e^5 + 1170*a^2*c^2*d^2*e^7)/(2048*(a^8*e^4 + a^6*c^2*d^4 + 2*a^7*c*d^2*e^2))))*(-(144*a^5*c^5*d^7 - 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 - 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2)*2i + atan(((((32768*a^7*c^3*d*e^7 + 24576*a^5*c^5*d^5*e^3 + 57344*a^6*c^4*d^3*e^5)/(4096*(a^8*e^4 + a^6*c^2*d^4 + 2*a^7*c*d^2*e^2)) - ((d + e*x)^(1/2)*(4096*a^7*c^4*d*e^6 + 4096*a^5*c^6*d^5*e^2 + 8192*a^6*c^5*d^3*e^4)*(-(144*a^5*c^5*d^7 + 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2))/(64*(a^6*e^4 + a^4*c^2*d^4 + 2*a^5*c*d^2*e^2)))*(-(144*a^5*c^5*d^7 + 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) - ((d + e*x)^(1/2)*(144*c^5*d^6*e^2 - 25*a^3*c^2*e^8 + 276*a*c^4*d^4*e^4 + 109*a^2*c^3*d^2*e^6))/(64*(a^6*e^4 + a^4*c^2*d^4 + 2*a^5*c*d^2*e^2)))*(-(144*a^5*c^5*d^7 + 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2)*1i - (((32768*a^7*c^3*d*e^7 + 24576*a^5*c^5*d^5*e^3 + 57344*a^6*c^4*d^3*e^5)/(4096*(a^8*e^4 + a^6*c^2*d^4 + 2*a^7*c*d^2*e^2)) + ((d + e*x)^(1/2)*(4096*a^7*c^4*d*e^6 + 4096*a^5*c^6*d^5*e^2 + 8192*a^6*c^5*d^3*e^4)*(-(144*a^5*c^5*d^7 + 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2))/(64*(a^6*e^4 + a^4*c^2*d^4 + 2*a^5*c*d^2*e^2)))*(-(144*a^5*c^5*d^7 + 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) + ((d + e*x)^(1/2)*(144*c^5*d^6*e^2 - 25*a^3*c^2*e^8 + 276*a*c^4*d^4*e^4 + 109*a^2*c^3*d^2*e^6))/(64*(a^6*e^4 + a^4*c^2*d^4 + 2*a^5*c*d^2*e^2)))*(-(144*a^5*c^5*d^7 + 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2)*1i)/((((32768*a^7*c^3*d*e^7 + 24576*a^5*c^5*d^5*e^3 + 57344*a^6*c^4*d^3*e^5)/(4096*(a^8*e^4 + a^6*c^2*d^4 + 2*a^7*c*d^2*e^2)) - ((d + e*x)^(1/2)*(4096*a^7*c^4*d*e^6 + 4096*a^5*c^6*d^5*e^2 + 8192*a^6*c^5*d^3*e^4)*(-(144*a^5*c^5*d^7 + 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2))/(64*(a^6*e^4 + a^4*c^2*d^4 + 2*a^5*c*d^2*e^2)))*(-(144*a^5*c^5*d^7 + 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) - ((d + e*x)^(1/2)*(144*c^5*d^6*e^2 - 25*a^3*c^2*e^8 + 276*a*c^4*d^4*e^4 + 109*a^2*c^3*d^2*e^6))/(64*(a^6*e^4 + a^4*c^2*d^4 + 2*a^5*c*d^2*e^2)))*(-(144*a^5*c^5*d^7 + 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) + (((32768*a^7*c^3*d*e^7 + 24576*a^5*c^5*d^5*e^3 + 57344*a^6*c^4*d^3*e^5)/(4096*(a^8*e^4 + a^6*c^2*d^4 + 2*a^7*c*d^2*e^2)) + ((d + e*x)^(1/2)*(4096*a^7*c^4*d*e^6 + 4096*a^5*c^6*d^5*e^2 + 8192*a^6*c^5*d^3*e^4)*(-(144*a^5*c^5*d^7 + 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2))/(64*(a^6*e^4 + a^4*c^2*d^4 + 2*a^5*c*d^2*e^2)))*(-(144*a^5*c^5*d^7 + 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) + ((d + e*x)^(1/2)*(144*c^5*d^6*e^2 - 25*a^3*c^2*e^8 + 276*a*c^4*d^4*e^4 + 109*a^2*c^3*d^2*e^6))/(64*(a^6*e^4 + a^4*c^2*d^4 + 2*a^5*c*d^2*e^2)))*(-(144*a^5*c^5*d^7 + 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2) + (125*a^3*c*e^9 + 864*c^4*d^6*e^3 + 1944*a*c^3*d^4*e^5 + 1170*a^2*c^2*d^2*e^7)/(2048*(a^8*e^4 + a^6*c^2*d^4 + 2*a^7*c*d^2*e^2))))*(-(144*a^5*c^5*d^7 + 25*a*e^7*(-a^15*c^3)^(1/2) + 105*a^8*c^2*d*e^6 + 420*a^6*c^4*d^5*e^2 + 385*a^7*c^3*d^3*e^4 + 21*c*d^2*e^5*(-a^15*c^3)^(1/2))/(4096*(a^10*c^6*d^6 + a^13*c^3*e^6 + 3*a^11*c^5*d^4*e^2 + 3*a^12*c^4*d^2*e^4)))^(1/2)*2i - (((4*a*d*e^3 + 3*c*d^3*e)*(d + e*x)^(1/2))/(8*a^2) - ((d + e*x)^(3/2)*(9*a^2*e^5 + 18*c^2*d^4*e + 23*a*c*d^2*e^3))/(16*a^2*(a*e^2 + c*d^2)) - (c*e*(5*a*e^2 + 6*c*d^2)*(d + e*x)^(7/2))/(16*a^2*(a*e^2 + c*d^2)) + (c*d*(7*a*e^3 + 9*c*d^2*e)*(d + e*x)^(5/2))/(8*a^2*(a*e^2 + c*d^2)))/(c^2*(d + e*x)^4 + a^2*e^4 + c^2*d^4 + (6*c^2*d^2 + 2*a*c*e^2)*(d + e*x)^2 - (4*c^2*d^3 + 4*a*c*d*e^2)*(d + e*x) - 4*c^2*d*(d + e*x)^3 + 2*a*c*d^2*e^2)","B"
647,1,9035,920,3.601650,"\text{Not used}","int(1/((a + c*x^2)^3*(d + e*x)^(1/2)),x)","-\frac{\frac{\sqrt{d+e\,x}\,\left(-11\,a^2\,e^5+15\,a\,c\,d^2\,e^3+6\,c^2\,d^4\,e\right)}{16\,a^2\,\left(c\,d^2+a\,e^2\right)}-\frac{e\,{\left(d+e\,x\right)}^{3/2}\,\left(a^2\,c\,d\,e^4+22\,a\,c^2\,d^3\,e^2+9\,c^3\,d^5\right)}{8\,a^2\,{\left(c\,d^2+a\,e^2\right)}^2}-\frac{3\,c\,e\,\left(c^2\,d^3+2\,a\,c\,d\,e^2\right)\,{\left(d+e\,x\right)}^{7/2}}{8\,a^2\,{\left(c\,d^2+a\,e^2\right)}^2}+\frac{c\,e\,{\left(d+e\,x\right)}^{5/2}\,\left(-7\,a^2\,e^4+35\,a\,c\,d^2\,e^2+18\,c^2\,d^4\right)}{16\,a^2\,{\left(c\,d^2+a\,e^2\right)}^2}}{c^2\,{\left(d+e\,x\right)}^4+a^2\,e^4+c^2\,d^4+\left(6\,c^2\,d^2+2\,a\,c\,e^2\right)\,{\left(d+e\,x\right)}^2-\left(4\,c^2\,d^3+4\,a\,c\,d\,e^2\right)\,\left(d+e\,x\right)-4\,c^2\,d\,{\left(d+e\,x\right)}^3+2\,a\,c\,d^2\,e^2}+\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(14336\,a^9\,c^3\,e^{11}+38912\,a^8\,c^4\,d^2\,e^9+38912\,a^7\,c^5\,d^4\,e^7+18432\,a^6\,c^6\,d^6\,e^5+4096\,a^5\,c^7\,d^8\,e^3\right)}{2048\,\left(a^{10}\,e^8+4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4+4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}-\frac{\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}\,\left(4096\,a^9\,c^4\,d\,e^{10}+16384\,a^8\,c^5\,d^3\,e^8+24576\,a^7\,c^6\,d^5\,e^6+16384\,a^6\,c^7\,d^7\,e^4+4096\,a^5\,c^8\,d^9\,e^2\right)}{64\,\left(a^8\,e^8+4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4+4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}-\frac{\sqrt{d+e\,x}\,\left(441\,a^4\,c^3\,e^{10}+990\,a^3\,c^4\,d^2\,e^8+1089\,a^2\,c^5\,d^4\,e^6+612\,a\,c^6\,d^6\,e^4+144\,c^7\,d^8\,e^2\right)}{64\,\left(a^8\,e^8+4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4+4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3\,\left(14336\,a^9\,c^3\,e^{11}+38912\,a^8\,c^4\,d^2\,e^9+38912\,a^7\,c^5\,d^4\,e^7+18432\,a^6\,c^6\,d^6\,e^5+4096\,a^5\,c^7\,d^8\,e^3\right)}{2048\,\left(a^{10}\,e^8+4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4+4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}+\frac{\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}\,\left(4096\,a^9\,c^4\,d\,e^{10}+16384\,a^8\,c^5\,d^3\,e^8+24576\,a^7\,c^6\,d^5\,e^6+16384\,a^6\,c^7\,d^7\,e^4+4096\,a^5\,c^8\,d^9\,e^2\right)}{64\,\left(a^8\,e^8+4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4+4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}+\frac{\sqrt{d+e\,x}\,\left(441\,a^4\,c^3\,e^{10}+990\,a^3\,c^4\,d^2\,e^8+1089\,a^2\,c^5\,d^4\,e^6+612\,a\,c^6\,d^6\,e^4+144\,c^7\,d^8\,e^2\right)}{64\,\left(a^8\,e^8+4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4+4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}\,1{}\mathrm{i}}{\frac{3\,\left(882\,a^3\,c^3\,d\,e^9+1233\,a^2\,c^4\,d^3\,e^7+684\,a\,c^5\,d^5\,e^5+144\,c^6\,d^7\,e^3\right)}{1024\,\left(a^{10}\,e^8+4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4+4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}+\left(\left(\frac{3\,\left(14336\,a^9\,c^3\,e^{11}+38912\,a^8\,c^4\,d^2\,e^9+38912\,a^7\,c^5\,d^4\,e^7+18432\,a^6\,c^6\,d^6\,e^5+4096\,a^5\,c^7\,d^8\,e^3\right)}{2048\,\left(a^{10}\,e^8+4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4+4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}-\frac{\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}\,\left(4096\,a^9\,c^4\,d\,e^{10}+16384\,a^8\,c^5\,d^3\,e^8+24576\,a^7\,c^6\,d^5\,e^6+16384\,a^6\,c^7\,d^7\,e^4+4096\,a^5\,c^8\,d^9\,e^2\right)}{64\,\left(a^8\,e^8+4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4+4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}-\frac{\sqrt{d+e\,x}\,\left(441\,a^4\,c^3\,e^{10}+990\,a^3\,c^4\,d^2\,e^8+1089\,a^2\,c^5\,d^4\,e^6+612\,a\,c^6\,d^6\,e^4+144\,c^7\,d^8\,e^2\right)}{64\,\left(a^8\,e^8+4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4+4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}+\left(\left(\frac{3\,\left(14336\,a^9\,c^3\,e^{11}+38912\,a^8\,c^4\,d^2\,e^9+38912\,a^7\,c^5\,d^4\,e^7+18432\,a^6\,c^6\,d^6\,e^5+4096\,a^5\,c^7\,d^8\,e^3\right)}{2048\,\left(a^{10}\,e^8+4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4+4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}+\frac{\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}\,\left(4096\,a^9\,c^4\,d\,e^{10}+16384\,a^8\,c^5\,d^3\,e^8+24576\,a^7\,c^6\,d^5\,e^6+16384\,a^6\,c^7\,d^7\,e^4+4096\,a^5\,c^8\,d^9\,e^2\right)}{64\,\left(a^8\,e^8+4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4+4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}+\frac{\sqrt{d+e\,x}\,\left(441\,a^4\,c^3\,e^{10}+990\,a^3\,c^4\,d^2\,e^8+1089\,a^2\,c^5\,d^4\,e^6+612\,a\,c^6\,d^6\,e^4+144\,c^7\,d^8\,e^2\right)}{64\,\left(a^8\,e^8+4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4+4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9-49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6-21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8-54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(14336\,a^9\,c^3\,e^{11}+38912\,a^8\,c^4\,d^2\,e^9+38912\,a^7\,c^5\,d^4\,e^7+18432\,a^6\,c^6\,d^6\,e^5+4096\,a^5\,c^7\,d^8\,e^3\right)}{2048\,\left(a^{10}\,e^8+4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4+4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}-\frac{\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}\,\left(4096\,a^9\,c^4\,d\,e^{10}+16384\,a^8\,c^5\,d^3\,e^8+24576\,a^7\,c^6\,d^5\,e^6+16384\,a^6\,c^7\,d^7\,e^4+4096\,a^5\,c^8\,d^9\,e^2\right)}{64\,\left(a^8\,e^8+4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4+4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}-\frac{\sqrt{d+e\,x}\,\left(441\,a^4\,c^3\,e^{10}+990\,a^3\,c^4\,d^2\,e^8+1089\,a^2\,c^5\,d^4\,e^6+612\,a\,c^6\,d^6\,e^4+144\,c^7\,d^8\,e^2\right)}{64\,\left(a^8\,e^8+4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4+4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3\,\left(14336\,a^9\,c^3\,e^{11}+38912\,a^8\,c^4\,d^2\,e^9+38912\,a^7\,c^5\,d^4\,e^7+18432\,a^6\,c^6\,d^6\,e^5+4096\,a^5\,c^7\,d^8\,e^3\right)}{2048\,\left(a^{10}\,e^8+4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4+4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}+\frac{\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}\,\left(4096\,a^9\,c^4\,d\,e^{10}+16384\,a^8\,c^5\,d^3\,e^8+24576\,a^7\,c^6\,d^5\,e^6+16384\,a^6\,c^7\,d^7\,e^4+4096\,a^5\,c^8\,d^9\,e^2\right)}{64\,\left(a^8\,e^8+4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4+4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}+\frac{\sqrt{d+e\,x}\,\left(441\,a^4\,c^3\,e^{10}+990\,a^3\,c^4\,d^2\,e^8+1089\,a^2\,c^5\,d^4\,e^6+612\,a\,c^6\,d^6\,e^4+144\,c^7\,d^8\,e^2\right)}{64\,\left(a^8\,e^8+4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4+4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}\,1{}\mathrm{i}}{\frac{3\,\left(882\,a^3\,c^3\,d\,e^9+1233\,a^2\,c^4\,d^3\,e^7+684\,a\,c^5\,d^5\,e^5+144\,c^6\,d^7\,e^3\right)}{1024\,\left(a^{10}\,e^8+4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4+4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}+\left(\left(\frac{3\,\left(14336\,a^9\,c^3\,e^{11}+38912\,a^8\,c^4\,d^2\,e^9+38912\,a^7\,c^5\,d^4\,e^7+18432\,a^6\,c^6\,d^6\,e^5+4096\,a^5\,c^7\,d^8\,e^3\right)}{2048\,\left(a^{10}\,e^8+4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4+4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}-\frac{\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}\,\left(4096\,a^9\,c^4\,d\,e^{10}+16384\,a^8\,c^5\,d^3\,e^8+24576\,a^7\,c^6\,d^5\,e^6+16384\,a^6\,c^7\,d^7\,e^4+4096\,a^5\,c^8\,d^9\,e^2\right)}{64\,\left(a^8\,e^8+4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4+4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}-\frac{\sqrt{d+e\,x}\,\left(441\,a^4\,c^3\,e^{10}+990\,a^3\,c^4\,d^2\,e^8+1089\,a^2\,c^5\,d^4\,e^6+612\,a\,c^6\,d^6\,e^4+144\,c^7\,d^8\,e^2\right)}{64\,\left(a^8\,e^8+4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4+4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}+\left(\left(\frac{3\,\left(14336\,a^9\,c^3\,e^{11}+38912\,a^8\,c^4\,d^2\,e^9+38912\,a^7\,c^5\,d^4\,e^7+18432\,a^6\,c^6\,d^6\,e^5+4096\,a^5\,c^7\,d^8\,e^3\right)}{2048\,\left(a^{10}\,e^8+4\,a^9\,c\,d^2\,e^6+6\,a^8\,c^2\,d^4\,e^4+4\,a^7\,c^3\,d^6\,e^2+a^6\,c^4\,d^8\right)}+\frac{\sqrt{d+e\,x}\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}\,\left(4096\,a^9\,c^4\,d\,e^{10}+16384\,a^8\,c^5\,d^3\,e^8+24576\,a^7\,c^6\,d^5\,e^6+16384\,a^6\,c^7\,d^7\,e^4+4096\,a^5\,c^8\,d^9\,e^2\right)}{64\,\left(a^8\,e^8+4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4+4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}+\frac{\sqrt{d+e\,x}\,\left(441\,a^4\,c^3\,e^{10}+990\,a^3\,c^4\,d^2\,e^8+1089\,a^2\,c^5\,d^4\,e^6+612\,a\,c^6\,d^6\,e^4+144\,c^7\,d^8\,e^2\right)}{64\,\left(a^8\,e^8+4\,a^7\,c\,d^2\,e^6+6\,a^6\,c^2\,d^4\,e^4+4\,a^5\,c^3\,d^6\,e^2+a^4\,c^4\,d^8\right)}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}}\right)\,\sqrt{-\frac{9\,\left(16\,a^5\,c^5\,d^9+49\,a^2\,e^9\,\sqrt{-a^{15}\,c}+84\,a^6\,c^4\,d^7\,e^2+189\,a^7\,c^3\,d^5\,e^4+210\,a^8\,c^2\,d^3\,e^6+21\,c^2\,d^4\,e^5\,\sqrt{-a^{15}\,c}+105\,a^9\,c\,d\,e^8+54\,a\,c\,d^2\,e^7\,\sqrt{-a^{15}\,c}\right)}{4096\,\left(a^{15}\,c\,e^{10}+5\,a^{14}\,c^2\,d^2\,e^8+10\,a^{13}\,c^3\,d^4\,e^6+10\,a^{12}\,c^4\,d^6\,e^4+5\,a^{11}\,c^5\,d^8\,e^2+a^{10}\,c^6\,d^{10}\right)}}\,2{}\mathrm{i}","Not used",1,"atan(((((3*(14336*a^9*c^3*e^11 + 4096*a^5*c^7*d^8*e^3 + 18432*a^6*c^6*d^6*e^5 + 38912*a^7*c^5*d^4*e^7 + 38912*a^8*c^4*d^2*e^9))/(2048*(a^10*e^8 + a^6*c^4*d^8 + 4*a^9*c*d^2*e^6 + 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) - ((d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2)*(4096*a^9*c^4*d*e^10 + 4096*a^5*c^8*d^9*e^2 + 16384*a^6*c^7*d^7*e^4 + 24576*a^7*c^6*d^5*e^6 + 16384*a^8*c^5*d^3*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 + 4*a^7*c*d^2*e^6 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2) - ((d + e*x)^(1/2)*(441*a^4*c^3*e^10 + 144*c^7*d^8*e^2 + 612*a*c^6*d^6*e^4 + 1089*a^2*c^5*d^4*e^6 + 990*a^3*c^4*d^2*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 + 4*a^7*c*d^2*e^6 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2)*1i - (((3*(14336*a^9*c^3*e^11 + 4096*a^5*c^7*d^8*e^3 + 18432*a^6*c^6*d^6*e^5 + 38912*a^7*c^5*d^4*e^7 + 38912*a^8*c^4*d^2*e^9))/(2048*(a^10*e^8 + a^6*c^4*d^8 + 4*a^9*c*d^2*e^6 + 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) + ((d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2)*(4096*a^9*c^4*d*e^10 + 4096*a^5*c^8*d^9*e^2 + 16384*a^6*c^7*d^7*e^4 + 24576*a^7*c^6*d^5*e^6 + 16384*a^8*c^5*d^3*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 + 4*a^7*c*d^2*e^6 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2) + ((d + e*x)^(1/2)*(441*a^4*c^3*e^10 + 144*c^7*d^8*e^2 + 612*a*c^6*d^6*e^4 + 1089*a^2*c^5*d^4*e^6 + 990*a^3*c^4*d^2*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 + 4*a^7*c*d^2*e^6 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2)*1i)/((3*(144*c^6*d^7*e^3 + 684*a*c^5*d^5*e^5 + 882*a^3*c^3*d*e^9 + 1233*a^2*c^4*d^3*e^7))/(1024*(a^10*e^8 + a^6*c^4*d^8 + 4*a^9*c*d^2*e^6 + 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) + (((3*(14336*a^9*c^3*e^11 + 4096*a^5*c^7*d^8*e^3 + 18432*a^6*c^6*d^6*e^5 + 38912*a^7*c^5*d^4*e^7 + 38912*a^8*c^4*d^2*e^9))/(2048*(a^10*e^8 + a^6*c^4*d^8 + 4*a^9*c*d^2*e^6 + 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) - ((d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2)*(4096*a^9*c^4*d*e^10 + 4096*a^5*c^8*d^9*e^2 + 16384*a^6*c^7*d^7*e^4 + 24576*a^7*c^6*d^5*e^6 + 16384*a^8*c^5*d^3*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 + 4*a^7*c*d^2*e^6 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2) - ((d + e*x)^(1/2)*(441*a^4*c^3*e^10 + 144*c^7*d^8*e^2 + 612*a*c^6*d^6*e^4 + 1089*a^2*c^5*d^4*e^6 + 990*a^3*c^4*d^2*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 + 4*a^7*c*d^2*e^6 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2) + (((3*(14336*a^9*c^3*e^11 + 4096*a^5*c^7*d^8*e^3 + 18432*a^6*c^6*d^6*e^5 + 38912*a^7*c^5*d^4*e^7 + 38912*a^8*c^4*d^2*e^9))/(2048*(a^10*e^8 + a^6*c^4*d^8 + 4*a^9*c*d^2*e^6 + 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) + ((d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2)*(4096*a^9*c^4*d*e^10 + 4096*a^5*c^8*d^9*e^2 + 16384*a^6*c^7*d^7*e^4 + 24576*a^7*c^6*d^5*e^6 + 16384*a^8*c^5*d^3*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 + 4*a^7*c*d^2*e^6 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2) + ((d + e*x)^(1/2)*(441*a^4*c^3*e^10 + 144*c^7*d^8*e^2 + 612*a*c^6*d^6*e^4 + 1089*a^2*c^5*d^4*e^6 + 990*a^3*c^4*d^2*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 + 4*a^7*c*d^2*e^6 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2)))*(-(9*(16*a^5*c^5*d^9 - 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 - 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 - 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2)*2i + atan(((((3*(14336*a^9*c^3*e^11 + 4096*a^5*c^7*d^8*e^3 + 18432*a^6*c^6*d^6*e^5 + 38912*a^7*c^5*d^4*e^7 + 38912*a^8*c^4*d^2*e^9))/(2048*(a^10*e^8 + a^6*c^4*d^8 + 4*a^9*c*d^2*e^6 + 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) - ((d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2)*(4096*a^9*c^4*d*e^10 + 4096*a^5*c^8*d^9*e^2 + 16384*a^6*c^7*d^7*e^4 + 24576*a^7*c^6*d^5*e^6 + 16384*a^8*c^5*d^3*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 + 4*a^7*c*d^2*e^6 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2) - ((d + e*x)^(1/2)*(441*a^4*c^3*e^10 + 144*c^7*d^8*e^2 + 612*a*c^6*d^6*e^4 + 1089*a^2*c^5*d^4*e^6 + 990*a^3*c^4*d^2*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 + 4*a^7*c*d^2*e^6 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2)*1i - (((3*(14336*a^9*c^3*e^11 + 4096*a^5*c^7*d^8*e^3 + 18432*a^6*c^6*d^6*e^5 + 38912*a^7*c^5*d^4*e^7 + 38912*a^8*c^4*d^2*e^9))/(2048*(a^10*e^8 + a^6*c^4*d^8 + 4*a^9*c*d^2*e^6 + 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) + ((d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2)*(4096*a^9*c^4*d*e^10 + 4096*a^5*c^8*d^9*e^2 + 16384*a^6*c^7*d^7*e^4 + 24576*a^7*c^6*d^5*e^6 + 16384*a^8*c^5*d^3*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 + 4*a^7*c*d^2*e^6 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2) + ((d + e*x)^(1/2)*(441*a^4*c^3*e^10 + 144*c^7*d^8*e^2 + 612*a*c^6*d^6*e^4 + 1089*a^2*c^5*d^4*e^6 + 990*a^3*c^4*d^2*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 + 4*a^7*c*d^2*e^6 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2)*1i)/((3*(144*c^6*d^7*e^3 + 684*a*c^5*d^5*e^5 + 882*a^3*c^3*d*e^9 + 1233*a^2*c^4*d^3*e^7))/(1024*(a^10*e^8 + a^6*c^4*d^8 + 4*a^9*c*d^2*e^6 + 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) + (((3*(14336*a^9*c^3*e^11 + 4096*a^5*c^7*d^8*e^3 + 18432*a^6*c^6*d^6*e^5 + 38912*a^7*c^5*d^4*e^7 + 38912*a^8*c^4*d^2*e^9))/(2048*(a^10*e^8 + a^6*c^4*d^8 + 4*a^9*c*d^2*e^6 + 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) - ((d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2)*(4096*a^9*c^4*d*e^10 + 4096*a^5*c^8*d^9*e^2 + 16384*a^6*c^7*d^7*e^4 + 24576*a^7*c^6*d^5*e^6 + 16384*a^8*c^5*d^3*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 + 4*a^7*c*d^2*e^6 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2) - ((d + e*x)^(1/2)*(441*a^4*c^3*e^10 + 144*c^7*d^8*e^2 + 612*a*c^6*d^6*e^4 + 1089*a^2*c^5*d^4*e^6 + 990*a^3*c^4*d^2*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 + 4*a^7*c*d^2*e^6 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2) + (((3*(14336*a^9*c^3*e^11 + 4096*a^5*c^7*d^8*e^3 + 18432*a^6*c^6*d^6*e^5 + 38912*a^7*c^5*d^4*e^7 + 38912*a^8*c^4*d^2*e^9))/(2048*(a^10*e^8 + a^6*c^4*d^8 + 4*a^9*c*d^2*e^6 + 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4)) + ((d + e*x)^(1/2)*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2)*(4096*a^9*c^4*d*e^10 + 4096*a^5*c^8*d^9*e^2 + 16384*a^6*c^7*d^7*e^4 + 24576*a^7*c^6*d^5*e^6 + 16384*a^8*c^5*d^3*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 + 4*a^7*c*d^2*e^6 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2) + ((d + e*x)^(1/2)*(441*a^4*c^3*e^10 + 144*c^7*d^8*e^2 + 612*a*c^6*d^6*e^4 + 1089*a^2*c^5*d^4*e^6 + 990*a^3*c^4*d^2*e^8))/(64*(a^8*e^8 + a^4*c^4*d^8 + 4*a^7*c*d^2*e^6 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2)))*(-(9*(16*a^5*c^5*d^9 + 49*a^2*e^9*(-a^15*c)^(1/2) + 84*a^6*c^4*d^7*e^2 + 189*a^7*c^3*d^5*e^4 + 210*a^8*c^2*d^3*e^6 + 21*c^2*d^4*e^5*(-a^15*c)^(1/2) + 105*a^9*c*d*e^8 + 54*a*c*d^2*e^7*(-a^15*c)^(1/2)))/(4096*(a^15*c*e^10 + a^10*c^6*d^10 + 5*a^11*c^5*d^8*e^2 + 10*a^12*c^4*d^6*e^4 + 10*a^13*c^3*d^4*e^6 + 5*a^14*c^2*d^2*e^8)))^(1/2)*2i - (((d + e*x)^(1/2)*(6*c^2*d^4*e - 11*a^2*e^5 + 15*a*c*d^2*e^3))/(16*a^2*(a*e^2 + c*d^2)) - (e*(d + e*x)^(3/2)*(9*c^3*d^5 + 22*a*c^2*d^3*e^2 + a^2*c*d*e^4))/(8*a^2*(a*e^2 + c*d^2)^2) - (3*c*e*(c^2*d^3 + 2*a*c*d*e^2)*(d + e*x)^(7/2))/(8*a^2*(a*e^2 + c*d^2)^2) + (c*e*(d + e*x)^(5/2)*(18*c^2*d^4 - 7*a^2*e^4 + 35*a*c*d^2*e^2))/(16*a^2*(a*e^2 + c*d^2)^2))/(c^2*(d + e*x)^4 + a^2*e^4 + c^2*d^4 + (6*c^2*d^2 + 2*a*c*e^2)*(d + e*x)^2 - (4*c^2*d^3 + 4*a*c*d*e^2)*(d + e*x) - 4*c^2*d*(d + e*x)^3 + 2*a*c*d^2*e^2)","B"
648,1,179,214,0.127894,"\text{Not used}","int((3*x + 2)^(1/2)/(x^2 + 1),x)","-\mathrm{atanh}\left(-\frac{\left(1152\,\sqrt{3\,x+2}\,{\left(\sqrt{-\frac{\sqrt{13}}{8}-\frac{1}{4}}-\sqrt{\frac{\sqrt{13}}{8}-\frac{1}{4}}\right)}^2-720\,\sqrt{3\,x+2}\right)\,\left(\sqrt{-\frac{\sqrt{13}}{8}-\frac{1}{4}}-\sqrt{\frac{\sqrt{13}}{8}-\frac{1}{4}}\right)}{2808}\right)\,\left(2\,\sqrt{-\frac{\sqrt{13}}{8}-\frac{1}{4}}-2\,\sqrt{\frac{\sqrt{13}}{8}-\frac{1}{4}}\right)-\mathrm{atanh}\left(\frac{\left(720\,\sqrt{3\,x+2}-1152\,\sqrt{3\,x+2}\,{\left(\sqrt{-\frac{\sqrt{13}}{8}-\frac{1}{4}}+\sqrt{\frac{\sqrt{13}}{8}-\frac{1}{4}}\right)}^2\right)\,\left(\sqrt{-\frac{\sqrt{13}}{8}-\frac{1}{4}}+\sqrt{\frac{\sqrt{13}}{8}-\frac{1}{4}}\right)}{2808}\right)\,\left(2\,\sqrt{-\frac{\sqrt{13}}{8}-\frac{1}{4}}+2\,\sqrt{\frac{\sqrt{13}}{8}-\frac{1}{4}}\right)","Not used",1,"- atanh(-((1152*(3*x + 2)^(1/2)*((- 13^(1/2)/8 - 1/4)^(1/2) - (13^(1/2)/8 - 1/4)^(1/2))^2 - 720*(3*x + 2)^(1/2))*((- 13^(1/2)/8 - 1/4)^(1/2) - (13^(1/2)/8 - 1/4)^(1/2)))/2808)*(2*(- 13^(1/2)/8 - 1/4)^(1/2) - 2*(13^(1/2)/8 - 1/4)^(1/2)) - atanh(((720*(3*x + 2)^(1/2) - 1152*(3*x + 2)^(1/2)*((- 13^(1/2)/8 - 1/4)^(1/2) + (13^(1/2)/8 - 1/4)^(1/2))^2)*((- 13^(1/2)/8 - 1/4)^(1/2) + (13^(1/2)/8 - 1/4)^(1/2)))/2808)*(2*(- 13^(1/2)/8 - 1/4)^(1/2) + 2*(13^(1/2)/8 - 1/4)^(1/2))","B"
649,1,133,316,0.156409,"\text{Not used}","int((c + d*x)^(1/2)/(x^2 + 1),x)","-\mathrm{atan}\left(\frac{2\,c\,\sqrt{-\frac{c}{4}-\frac{d\,1{}\mathrm{i}}{4}}\,\sqrt{c+d\,x}-d\,\sqrt{-\frac{c}{4}-\frac{d\,1{}\mathrm{i}}{4}}\,\sqrt{c+d\,x}\,2{}\mathrm{i}}{c^2+d^2}\right)\,\sqrt{-\frac{c}{4}-\frac{d\,1{}\mathrm{i}}{4}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{2\,c\,\sqrt{-\frac{c}{4}+\frac{d\,1{}\mathrm{i}}{4}}\,\sqrt{c+d\,x}+d\,\sqrt{-\frac{c}{4}+\frac{d\,1{}\mathrm{i}}{4}}\,\sqrt{c+d\,x}\,2{}\mathrm{i}}{c^2+d^2}\right)\,\sqrt{-\frac{c}{4}+\frac{d\,1{}\mathrm{i}}{4}}\,2{}\mathrm{i}","Not used",1,"atan((2*c*((d*1i)/4 - c/4)^(1/2)*(c + d*x)^(1/2) + d*((d*1i)/4 - c/4)^(1/2)*(c + d*x)^(1/2)*2i)/(c^2 + d^2))*((d*1i)/4 - c/4)^(1/2)*2i - atan((2*c*(- c/4 - (d*1i)/4)^(1/2)*(c + d*x)^(1/2) - d*(- c/4 - (d*1i)/4)^(1/2)*(c + d*x)^(1/2)*2i)/(c^2 + d^2))*(- c/4 - (d*1i)/4)^(1/2)*2i","B"
650,1,28,35,0.403213,"\text{Not used}","int(-(3*x + 2)^(1/2)/(x^2 - 1),x)","\sqrt{5}\,\mathrm{atanh}\left(\frac{\sqrt{5}\,\sqrt{3\,x+2}}{5}\right)-\mathrm{atan}\left(\sqrt{3\,x+2}\right)","Not used",1,"5^(1/2)*atanh((5^(1/2)*(3*x + 2)^(1/2))/5) - atan((3*x + 2)^(1/2))","B"
651,1,46,58,0.477421,"\text{Not used}","int(-(c + d*x)^(1/2)/(x^2 - 1),x)","\mathrm{atanh}\left(\frac{\sqrt{c+d\,x}}{\sqrt{c+d}}\right)\,\sqrt{c+d}-\mathrm{atanh}\left(\frac{\sqrt{c+d\,x}}{\sqrt{c-d}}\right)\,\sqrt{c-d}","Not used",1,"atanh((c + d*x)^(1/2)/(c + d)^(1/2))*(c + d)^(1/2) - atanh((c + d*x)^(1/2)/(c - d)^(1/2))*(c - d)^(1/2)","B"
652,1,261,427,0.938991,"\text{Not used}","int((3*x + 2)^(1/2)/(a + b*x^2),x)","-2\,\mathrm{atanh}\left(\frac{2\,\left(\left(1296\,a\,b^2-576\,b^3\right)\,\sqrt{3\,x+2}-\frac{288\,b\,\sqrt{3\,x+2}\,\left(3\,\sqrt{-a^3\,b^3}-2\,a\,b^2\right)}{a}\right)\,\sqrt{\frac{3\,\sqrt{-a^3\,b^3}-2\,a\,b^2}{4\,a^2\,b^3}}}{1728\,b^2+3888\,a\,b}\right)\,\sqrt{\frac{3\,\sqrt{-a^3\,b^3}-2\,a\,b^2}{4\,a^2\,b^3}}-2\,\mathrm{atanh}\left(\frac{2\,\left(\left(1296\,a\,b^2-576\,b^3\right)\,\sqrt{3\,x+2}+\frac{288\,b\,\sqrt{3\,x+2}\,\left(3\,\sqrt{-a^3\,b^3}+2\,a\,b^2\right)}{a}\right)\,\sqrt{-\frac{3\,\sqrt{-a^3\,b^3}+2\,a\,b^2}{4\,a^2\,b^3}}}{1728\,b^2+3888\,a\,b}\right)\,\sqrt{-\frac{3\,\sqrt{-a^3\,b^3}+2\,a\,b^2}{4\,a^2\,b^3}}","Not used",1,"- 2*atanh((2*((1296*a*b^2 - 576*b^3)*(3*x + 2)^(1/2) - (288*b*(3*x + 2)^(1/2)*(3*(-a^3*b^3)^(1/2) - 2*a*b^2))/a)*((3*(-a^3*b^3)^(1/2) - 2*a*b^2)/(4*a^2*b^3))^(1/2))/(3888*a*b + 1728*b^2))*((3*(-a^3*b^3)^(1/2) - 2*a*b^2)/(4*a^2*b^3))^(1/2) - 2*atanh((2*((1296*a*b^2 - 576*b^3)*(3*x + 2)^(1/2) + (288*b*(3*x + 2)^(1/2)*(3*(-a^3*b^3)^(1/2) + 2*a*b^2))/a)*(-(3*(-a^3*b^3)^(1/2) + 2*a*b^2)/(4*a^2*b^3))^(1/2))/(3888*a*b + 1728*b^2))*(-(3*(-a^3*b^3)^(1/2) + 2*a*b^2)/(4*a^2*b^3))^(1/2)","B"
653,1,255,132,0.758107,"\text{Not used}","int((3*x + 2)^(1/2)/(a - b*x^2),x)","2\,\mathrm{atanh}\left(\frac{2\,\left(\left(576\,b^3+1296\,a\,b^2\right)\,\sqrt{3\,x+2}+\frac{288\,b\,\sqrt{3\,x+2}\,\left(3\,\sqrt{a^3\,b^3}-2\,a\,b^2\right)}{a}\right)\,\sqrt{-\frac{3\,\sqrt{a^3\,b^3}-2\,a\,b^2}{4\,a^2\,b^3}}}{3888\,a\,b-1728\,b^2}\right)\,\sqrt{-\frac{3\,\sqrt{a^3\,b^3}-2\,a\,b^2}{4\,a^2\,b^3}}+2\,\mathrm{atanh}\left(\frac{2\,\left(\left(576\,b^3+1296\,a\,b^2\right)\,\sqrt{3\,x+2}-\frac{288\,b\,\sqrt{3\,x+2}\,\left(3\,\sqrt{a^3\,b^3}+2\,a\,b^2\right)}{a}\right)\,\sqrt{\frac{3\,\sqrt{a^3\,b^3}+2\,a\,b^2}{4\,a^2\,b^3}}}{3888\,a\,b-1728\,b^2}\right)\,\sqrt{\frac{3\,\sqrt{a^3\,b^3}+2\,a\,b^2}{4\,a^2\,b^3}}","Not used",1,"2*atanh((2*((1296*a*b^2 + 576*b^3)*(3*x + 2)^(1/2) + (288*b*(3*x + 2)^(1/2)*(3*(a^3*b^3)^(1/2) - 2*a*b^2))/a)*(-(3*(a^3*b^3)^(1/2) - 2*a*b^2)/(4*a^2*b^3))^(1/2))/(3888*a*b - 1728*b^2))*(-(3*(a^3*b^3)^(1/2) - 2*a*b^2)/(4*a^2*b^3))^(1/2) + 2*atanh((2*((1296*a*b^2 + 576*b^3)*(3*x + 2)^(1/2) - (288*b*(3*x + 2)^(1/2)*(3*(a^3*b^3)^(1/2) + 2*a*b^2))/a)*((3*(a^3*b^3)^(1/2) + 2*a*b^2)/(4*a^2*b^3))^(1/2))/(3888*a*b - 1728*b^2))*((3*(a^3*b^3)^(1/2) + 2*a*b^2)/(4*a^2*b^3))^(1/2)","B"
654,1,109,205,0.124069,"\text{Not used}","int((x + 1)^(1/2)/(x^2 + 1),x)","\mathrm{atanh}\left(4\,{\left(\sqrt{-\frac{\sqrt{2}}{8}-\frac{1}{8}}+\sqrt{\frac{\sqrt{2}}{8}-\frac{1}{8}}\right)}^3\,\sqrt{x+1}\right)\,\left(2\,\sqrt{-\frac{\sqrt{2}}{8}-\frac{1}{8}}+2\,\sqrt{\frac{\sqrt{2}}{8}-\frac{1}{8}}\right)+\mathrm{atanh}\left(4\,{\left(\sqrt{-\frac{\sqrt{2}}{8}-\frac{1}{8}}-\sqrt{\frac{\sqrt{2}}{8}-\frac{1}{8}}\right)}^3\,\sqrt{x+1}\right)\,\left(2\,\sqrt{-\frac{\sqrt{2}}{8}-\frac{1}{8}}-2\,\sqrt{\frac{\sqrt{2}}{8}-\frac{1}{8}}\right)","Not used",1,"atanh(4*((- 2^(1/2)/8 - 1/8)^(1/2) + (2^(1/2)/8 - 1/8)^(1/2))^3*(x + 1)^(1/2))*(2*(- 2^(1/2)/8 - 1/8)^(1/2) + 2*(2^(1/2)/8 - 1/8)^(1/2)) + atanh(4*((- 2^(1/2)/8 - 1/8)^(1/2) - (2^(1/2)/8 - 1/8)^(1/2))^3*(x + 1)^(1/2))*(2*(- 2^(1/2)/8 - 1/8)^(1/2) - 2*(2^(1/2)/8 - 1/8)^(1/2))","B"
655,1,226,198,0.458084,"\text{Not used}","int(1/((x^2 + 1)*(x + 1)^(1/2)),x)","\mathrm{atanh}\left(\frac{16\,\sqrt{2}\,\sqrt{-\frac{\sqrt{2}}{16}-\frac{1}{16}}\,\sqrt{x+1}}{128\,\sqrt{\frac{\sqrt{2}}{16}-\frac{1}{16}}\,\sqrt{-\frac{\sqrt{2}}{16}-\frac{1}{16}}-8}-\frac{16\,\sqrt{2}\,\sqrt{\frac{\sqrt{2}}{16}-\frac{1}{16}}\,\sqrt{x+1}}{128\,\sqrt{\frac{\sqrt{2}}{16}-\frac{1}{16}}\,\sqrt{-\frac{\sqrt{2}}{16}-\frac{1}{16}}-8}\right)\,\left(2\,\sqrt{-\frac{\sqrt{2}}{16}-\frac{1}{16}}+2\,\sqrt{\frac{\sqrt{2}}{16}-\frac{1}{16}}\right)-\mathrm{atanh}\left(\frac{16\,\sqrt{2}\,\sqrt{-\frac{\sqrt{2}}{16}-\frac{1}{16}}\,\sqrt{x+1}}{128\,\sqrt{\frac{\sqrt{2}}{16}-\frac{1}{16}}\,\sqrt{-\frac{\sqrt{2}}{16}-\frac{1}{16}}+8}+\frac{16\,\sqrt{2}\,\sqrt{\frac{\sqrt{2}}{16}-\frac{1}{16}}\,\sqrt{x+1}}{128\,\sqrt{\frac{\sqrt{2}}{16}-\frac{1}{16}}\,\sqrt{-\frac{\sqrt{2}}{16}-\frac{1}{16}}+8}\right)\,\left(2\,\sqrt{-\frac{\sqrt{2}}{16}-\frac{1}{16}}-2\,\sqrt{\frac{\sqrt{2}}{16}-\frac{1}{16}}\right)","Not used",1,"atanh((16*2^(1/2)*(- 2^(1/2)/16 - 1/16)^(1/2)*(x + 1)^(1/2))/(128*(2^(1/2)/16 - 1/16)^(1/2)*(- 2^(1/2)/16 - 1/16)^(1/2) - 8) - (16*2^(1/2)*(2^(1/2)/16 - 1/16)^(1/2)*(x + 1)^(1/2))/(128*(2^(1/2)/16 - 1/16)^(1/2)*(- 2^(1/2)/16 - 1/16)^(1/2) - 8))*(2*(- 2^(1/2)/16 - 1/16)^(1/2) + 2*(2^(1/2)/16 - 1/16)^(1/2)) - atanh((16*2^(1/2)*(- 2^(1/2)/16 - 1/16)^(1/2)*(x + 1)^(1/2))/(128*(2^(1/2)/16 - 1/16)^(1/2)*(- 2^(1/2)/16 - 1/16)^(1/2) + 8) + (16*2^(1/2)*(2^(1/2)/16 - 1/16)^(1/2)*(x + 1)^(1/2))/(128*(2^(1/2)/16 - 1/16)^(1/2)*(- 2^(1/2)/16 - 1/16)^(1/2) + 8))*(2*(- 2^(1/2)/16 - 1/16)^(1/2) - 2*(2^(1/2)/16 - 1/16)^(1/2))","B"
656,1,440,272,0.119841,"\text{Not used}","int((x - 1)^(1/2)/(x^2 + 1)^3,x)","\mathrm{atanh}\left(\frac{275\,\sqrt{\frac{527}{32768}-\frac{373\,\sqrt{2}}{32768}}\,\sqrt{x-1}}{64\,\left(28\,\sqrt{\frac{527}{32768}-\frac{373\,\sqrt{2}}{32768}}\,\sqrt{\frac{373\,\sqrt{2}}{32768}+\frac{527}{32768}}-\frac{207}{4096}\right)}+\frac{275\,\sqrt{\frac{373\,\sqrt{2}}{32768}+\frac{527}{32768}}\,\sqrt{x-1}}{64\,\left(28\,\sqrt{\frac{527}{32768}-\frac{373\,\sqrt{2}}{32768}}\,\sqrt{\frac{373\,\sqrt{2}}{32768}+\frac{527}{32768}}-\frac{207}{4096}\right)}+\frac{373\,\sqrt{2}\,\sqrt{\frac{527}{32768}-\frac{373\,\sqrt{2}}{32768}}\,\sqrt{x-1}}{128\,\left(28\,\sqrt{\frac{527}{32768}-\frac{373\,\sqrt{2}}{32768}}\,\sqrt{\frac{373\,\sqrt{2}}{32768}+\frac{527}{32768}}-\frac{207}{4096}\right)}-\frac{373\,\sqrt{2}\,\sqrt{\frac{373\,\sqrt{2}}{32768}+\frac{527}{32768}}\,\sqrt{x-1}}{128\,\left(28\,\sqrt{\frac{527}{32768}-\frac{373\,\sqrt{2}}{32768}}\,\sqrt{\frac{373\,\sqrt{2}}{32768}+\frac{527}{32768}}-\frac{207}{4096}\right)}\right)\,\left(2\,\sqrt{\frac{527}{32768}-\frac{373\,\sqrt{2}}{32768}}+2\,\sqrt{\frac{373\,\sqrt{2}}{32768}+\frac{527}{32768}}\right)-\mathrm{atanh}\left(\frac{275\,\sqrt{\frac{527}{32768}-\frac{373\,\sqrt{2}}{32768}}\,\sqrt{x-1}}{64\,\left(28\,\sqrt{\frac{527}{32768}-\frac{373\,\sqrt{2}}{32768}}\,\sqrt{\frac{373\,\sqrt{2}}{32768}+\frac{527}{32768}}+\frac{207}{4096}\right)}-\frac{275\,\sqrt{\frac{373\,\sqrt{2}}{32768}+\frac{527}{32768}}\,\sqrt{x-1}}{64\,\left(28\,\sqrt{\frac{527}{32768}-\frac{373\,\sqrt{2}}{32768}}\,\sqrt{\frac{373\,\sqrt{2}}{32768}+\frac{527}{32768}}+\frac{207}{4096}\right)}+\frac{373\,\sqrt{2}\,\sqrt{\frac{527}{32768}-\frac{373\,\sqrt{2}}{32768}}\,\sqrt{x-1}}{128\,\left(28\,\sqrt{\frac{527}{32768}-\frac{373\,\sqrt{2}}{32768}}\,\sqrt{\frac{373\,\sqrt{2}}{32768}+\frac{527}{32768}}+\frac{207}{4096}\right)}+\frac{373\,\sqrt{2}\,\sqrt{\frac{373\,\sqrt{2}}{32768}+\frac{527}{32768}}\,\sqrt{x-1}}{128\,\left(28\,\sqrt{\frac{527}{32768}-\frac{373\,\sqrt{2}}{32768}}\,\sqrt{\frac{373\,\sqrt{2}}{32768}+\frac{527}{32768}}+\frac{207}{4096}\right)}\right)\,\left(2\,\sqrt{\frac{527}{32768}-\frac{373\,\sqrt{2}}{32768}}-2\,\sqrt{\frac{373\,\sqrt{2}}{32768}+\frac{527}{32768}}\right)+\frac{\frac{7\,\sqrt{x-1}}{8}+\frac{25\,{\left(x-1\right)}^{3/2}}{16}+{\left(x-1\right)}^{5/2}+\frac{11\,{\left(x-1\right)}^{7/2}}{32}}{8\,x+8\,{\left(x-1\right)}^2+4\,{\left(x-1\right)}^3+{\left(x-1\right)}^4-4}","Not used",1,"atanh((275*(527/32768 - (373*2^(1/2))/32768)^(1/2)*(x - 1)^(1/2))/(64*(28*(527/32768 - (373*2^(1/2))/32768)^(1/2)*((373*2^(1/2))/32768 + 527/32768)^(1/2) - 207/4096)) + (275*((373*2^(1/2))/32768 + 527/32768)^(1/2)*(x - 1)^(1/2))/(64*(28*(527/32768 - (373*2^(1/2))/32768)^(1/2)*((373*2^(1/2))/32768 + 527/32768)^(1/2) - 207/4096)) + (373*2^(1/2)*(527/32768 - (373*2^(1/2))/32768)^(1/2)*(x - 1)^(1/2))/(128*(28*(527/32768 - (373*2^(1/2))/32768)^(1/2)*((373*2^(1/2))/32768 + 527/32768)^(1/2) - 207/4096)) - (373*2^(1/2)*((373*2^(1/2))/32768 + 527/32768)^(1/2)*(x - 1)^(1/2))/(128*(28*(527/32768 - (373*2^(1/2))/32768)^(1/2)*((373*2^(1/2))/32768 + 527/32768)^(1/2) - 207/4096)))*(2*(527/32768 - (373*2^(1/2))/32768)^(1/2) + 2*((373*2^(1/2))/32768 + 527/32768)^(1/2)) - atanh((275*(527/32768 - (373*2^(1/2))/32768)^(1/2)*(x - 1)^(1/2))/(64*(28*(527/32768 - (373*2^(1/2))/32768)^(1/2)*((373*2^(1/2))/32768 + 527/32768)^(1/2) + 207/4096)) - (275*((373*2^(1/2))/32768 + 527/32768)^(1/2)*(x - 1)^(1/2))/(64*(28*(527/32768 - (373*2^(1/2))/32768)^(1/2)*((373*2^(1/2))/32768 + 527/32768)^(1/2) + 207/4096)) + (373*2^(1/2)*(527/32768 - (373*2^(1/2))/32768)^(1/2)*(x - 1)^(1/2))/(128*(28*(527/32768 - (373*2^(1/2))/32768)^(1/2)*((373*2^(1/2))/32768 + 527/32768)^(1/2) + 207/4096)) + (373*2^(1/2)*((373*2^(1/2))/32768 + 527/32768)^(1/2)*(x - 1)^(1/2))/(128*(28*(527/32768 - (373*2^(1/2))/32768)^(1/2)*((373*2^(1/2))/32768 + 527/32768)^(1/2) + 207/4096)))*(2*(527/32768 - (373*2^(1/2))/32768)^(1/2) - 2*((373*2^(1/2))/32768 + 527/32768)^(1/2)) + ((7*(x - 1)^(1/2))/8 + (25*(x - 1)^(3/2))/16 + (x - 1)^(5/2) + (11*(x - 1)^(7/2))/32)/(8*x + 8*(x - 1)^2 + 4*(x - 1)^3 + (x - 1)^4 - 4)","B"
657,0,-1,398,0.000000,"\text{Not used}","int((a + c*x^2)^(1/2)*(d + e*x)^(3/2),x)","\int \sqrt{c\,x^2+a}\,{\left(d+e\,x\right)}^{3/2} \,d x","Not used",1,"int((a + c*x^2)^(1/2)*(d + e*x)^(3/2), x)","F"
658,0,-1,362,0.000000,"\text{Not used}","int((a + c*x^2)^(1/2)*(d + e*x)^(1/2),x)","\int \sqrt{c\,x^2+a}\,\sqrt{d+e\,x} \,d x","Not used",1,"int((a + c*x^2)^(1/2)*(d + e*x)^(1/2), x)","F"
659,0,-1,322,0.000000,"\text{Not used}","int((a + c*x^2)^(1/2)/(d + e*x)^(1/2),x)","\int \frac{\sqrt{c\,x^2+a}}{\sqrt{d+e\,x}} \,d x","Not used",1,"int((a + c*x^2)^(1/2)/(d + e*x)^(1/2), x)","F"
660,0,-1,305,0.000000,"\text{Not used}","int((a + c*x^2)^(1/2)/(d + e*x)^(3/2),x)","\int \frac{\sqrt{c\,x^2+a}}{{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int((a + c*x^2)^(1/2)/(d + e*x)^(3/2), x)","F"
661,0,-1,366,0.000000,"\text{Not used}","int((a + c*x^2)^(1/2)/(d + e*x)^(5/2),x)","\int \frac{\sqrt{c\,x^2+a}}{{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int((a + c*x^2)^(1/2)/(d + e*x)^(5/2), x)","F"
662,0,-1,444,0.000000,"\text{Not used}","int((a + c*x^2)^(1/2)/(d + e*x)^(7/2),x)","\int \frac{\sqrt{c\,x^2+a}}{{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int((a + c*x^2)^(1/2)/(d + e*x)^(7/2), x)","F"
663,0,-1,497,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)*(d + e*x)^(3/2),x)","\int {\left(c\,x^2+a\right)}^{3/2}\,{\left(d+e\,x\right)}^{3/2} \,d x","Not used",1,"int((a + c*x^2)^(3/2)*(d + e*x)^(3/2), x)","F"
664,0,-1,448,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)*(d + e*x)^(1/2),x)","\int {\left(c\,x^2+a\right)}^{3/2}\,\sqrt{d+e\,x} \,d x","Not used",1,"int((a + c*x^2)^(3/2)*(d + e*x)^(1/2), x)","F"
665,0,-1,393,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)/(d + e*x)^(1/2),x)","\int \frac{{\left(c\,x^2+a\right)}^{3/2}}{\sqrt{d+e\,x}} \,d x","Not used",1,"int((a + c*x^2)^(3/2)/(d + e*x)^(1/2), x)","F"
666,0,-1,369,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)/(d + e*x)^(3/2),x)","\int \frac{{\left(c\,x^2+a\right)}^{3/2}}{{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int((a + c*x^2)^(3/2)/(d + e*x)^(3/2), x)","F"
667,0,-1,358,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)/(d + e*x)^(5/2),x)","\int \frac{{\left(c\,x^2+a\right)}^{3/2}}{{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int((a + c*x^2)^(3/2)/(d + e*x)^(5/2), x)","F"
668,0,-1,410,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)/(d + e*x)^(7/2),x)","\int \frac{{\left(c\,x^2+a\right)}^{3/2}}{{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int((a + c*x^2)^(3/2)/(d + e*x)^(7/2), x)","F"
669,0,-1,491,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)/(d + e*x)^(9/2),x)","\int \frac{{\left(c\,x^2+a\right)}^{3/2}}{{\left(d+e\,x\right)}^{9/2}} \,d x","Not used",1,"int((a + c*x^2)^(3/2)/(d + e*x)^(9/2), x)","F"
670,0,-1,566,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)*(d + e*x)^(1/2),x)","\int {\left(c\,x^2+a\right)}^{5/2}\,\sqrt{d+e\,x} \,d x","Not used",1,"int((a + c*x^2)^(5/2)*(d + e*x)^(1/2), x)","F"
671,0,-1,494,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)/(d + e*x)^(1/2),x)","\int \frac{{\left(c\,x^2+a\right)}^{5/2}}{\sqrt{d+e\,x}} \,d x","Not used",1,"int((a + c*x^2)^(5/2)/(d + e*x)^(1/2), x)","F"
672,0,-1,457,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)/(d + e*x)^(3/2),x)","\int \frac{{\left(c\,x^2+a\right)}^{5/2}}{{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int((a + c*x^2)^(5/2)/(d + e*x)^(3/2), x)","F"
673,0,-1,430,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)/(d + e*x)^(5/2),x)","\int \frac{{\left(c\,x^2+a\right)}^{5/2}}{{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int((a + c*x^2)^(5/2)/(d + e*x)^(5/2), x)","F"
674,0,-1,420,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)/(d + e*x)^(7/2),x)","\int \frac{{\left(c\,x^2+a\right)}^{5/2}}{{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int((a + c*x^2)^(5/2)/(d + e*x)^(7/2), x)","F"
675,0,-1,498,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)/(d + e*x)^(9/2),x)","\int \frac{{\left(c\,x^2+a\right)}^{5/2}}{{\left(d+e\,x\right)}^{9/2}} \,d x","Not used",1,"int((a + c*x^2)^(5/2)/(d + e*x)^(9/2), x)","F"
676,0,-1,553,0.000000,"\text{Not used}","int((a + c*x^2)^(5/2)/(d + e*x)^(11/2),x)","\int \frac{{\left(c\,x^2+a\right)}^{5/2}}{{\left(d+e\,x\right)}^{11/2}} \,d x","Not used",1,"int((a + c*x^2)^(5/2)/(d + e*x)^(11/2), x)","F"
677,0,-1,413,0.000000,"\text{Not used}","int((d + e*x)^(7/2)/(a + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^{7/2}}{\sqrt{c\,x^2+a}} \,d x","Not used",1,"int((d + e*x)^(7/2)/(a + c*x^2)^(1/2), x)","F"
678,0,-1,359,0.000000,"\text{Not used}","int((d + e*x)^(5/2)/(a + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^{5/2}}{\sqrt{c\,x^2+a}} \,d x","Not used",1,"int((d + e*x)^(5/2)/(a + c*x^2)^(1/2), x)","F"
679,0,-1,317,0.000000,"\text{Not used}","int((d + e*x)^(3/2)/(a + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^{3/2}}{\sqrt{c\,x^2+a}} \,d x","Not used",1,"int((d + e*x)^(3/2)/(a + c*x^2)^(1/2), x)","F"
680,0,-1,136,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/(a + c*x^2)^(1/2),x)","\int \frac{\sqrt{d+e\,x}}{\sqrt{c\,x^2+a}} \,d x","Not used",1,"int((d + e*x)^(1/2)/(a + c*x^2)^(1/2), x)","F"
681,0,-1,136,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(1/2)*(d + e*x)^(1/2)),x)","\int \frac{1}{\sqrt{c\,x^2+a}\,\sqrt{d+e\,x}} \,d x","Not used",1,"int(1/((a + c*x^2)^(1/2)*(d + e*x)^(1/2)), x)","F"
682,0,-1,186,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(1/2)*(d + e*x)^(3/2)),x)","\int \frac{1}{\sqrt{c\,x^2+a}\,{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + c*x^2)^(1/2)*(d + e*x)^(3/2)), x)","F"
683,0,-1,382,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(1/2)*(d + e*x)^(5/2)),x)","\int \frac{1}{\sqrt{c\,x^2+a}\,{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + c*x^2)^(1/2)*(d + e*x)^(5/2)), x)","F"
684,0,-1,447,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(1/2)*(d + e*x)^(7/2)),x)","\int \frac{1}{\sqrt{c\,x^2+a}\,{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int(1/((a + c*x^2)^(1/2)*(d + e*x)^(7/2)), x)","F"
685,0,-1,426,0.000000,"\text{Not used}","int((d + e*x)^(7/2)/(a + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^{7/2}}{{\left(c\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(7/2)/(a + c*x^2)^(3/2), x)","F"
686,0,-1,363,0.000000,"\text{Not used}","int((d + e*x)^(5/2)/(a + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^{5/2}}{{\left(c\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(5/2)/(a + c*x^2)^(3/2), x)","F"
687,0,-1,321,0.000000,"\text{Not used}","int((d + e*x)^(3/2)/(a + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^{3/2}}{{\left(c\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(3/2)/(a + c*x^2)^(3/2), x)","F"
688,0,-1,298,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/(a + c*x^2)^(3/2),x)","\int \frac{\sqrt{d+e\,x}}{{\left(c\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(1/2)/(a + c*x^2)^(3/2), x)","F"
689,0,-1,331,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(3/2)*(d + e*x)^(1/2)),x)","\int \frac{1}{{\left(c\,x^2+a\right)}^{3/2}\,\sqrt{d+e\,x}} \,d x","Not used",1,"int(1/((a + c*x^2)^(3/2)*(d + e*x)^(1/2)), x)","F"
690,0,-1,406,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(3/2)*(d + e*x)^(3/2)),x)","\int \frac{1}{{\left(c\,x^2+a\right)}^{3/2}\,{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + c*x^2)^(3/2)*(d + e*x)^(3/2)), x)","F"
691,0,-1,485,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(3/2)*(d + e*x)^(5/2)),x)","\int \frac{1}{{\left(c\,x^2+a\right)}^{3/2}\,{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + c*x^2)^(3/2)*(d + e*x)^(5/2)), x)","F"
692,0,-1,475,0.000000,"\text{Not used}","int((d + e*x)^(9/2)/(a + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{9/2}}{{\left(c\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(9/2)/(a + c*x^2)^(5/2), x)","F"
693,0,-1,418,0.000000,"\text{Not used}","int((d + e*x)^(7/2)/(a + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{7/2}}{{\left(c\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(7/2)/(a + c*x^2)^(5/2), x)","F"
694,0,-1,392,0.000000,"\text{Not used}","int((d + e*x)^(5/2)/(a + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{5/2}}{{\left(c\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(5/2)/(a + c*x^2)^(5/2), x)","F"
695,0,-1,368,0.000000,"\text{Not used}","int((d + e*x)^(3/2)/(a + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{3/2}}{{\left(c\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(3/2)/(a + c*x^2)^(5/2), x)","F"
696,0,-1,392,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/(a + c*x^2)^(5/2),x)","\int \frac{\sqrt{d+e\,x}}{{\left(c\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(1/2)/(a + c*x^2)^(5/2), x)","F"
697,0,-1,450,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(5/2)*(d + e*x)^(1/2)),x)","\int \frac{1}{{\left(c\,x^2+a\right)}^{5/2}\,\sqrt{d+e\,x}} \,d x","Not used",1,"int(1/((a + c*x^2)^(5/2)*(d + e*x)^(1/2)), x)","F"
698,0,-1,532,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(5/2)*(d + e*x)^(3/2)),x)","\int \frac{1}{{\left(c\,x^2+a\right)}^{5/2}\,{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + c*x^2)^(5/2)*(d + e*x)^(3/2)), x)","F"
699,0,-1,151,0.000000,"\text{Not used}","int(1/((d^2 + 3*e^2*x^2)^(1/3)*(d + e*x)),x)","\int \frac{1}{{\left(d^2+3\,e^2\,x^2\right)}^{1/3}\,\left(d+e\,x\right)} \,d x","Not used",1,"int(1/((d^2 + 3*e^2*x^2)^(1/3)*(d + e*x)), x)","F"
700,0,-1,558,0.000000,"\text{Not used}","int((3*x + 2)^3/(27*x^2 + 4)^(1/3),x)","\int \frac{{\left(3\,x+2\right)}^3}{{\left(27\,x^2+4\right)}^{1/3}} \,d x","Not used",1,"int((3*x + 2)^3/(27*x^2 + 4)^(1/3), x)","F"
701,0,-1,551,0.000000,"\text{Not used}","int((3*x + 2)^2/(27*x^2 + 4)^(1/3),x)","\int \frac{{\left(3\,x+2\right)}^2}{{\left(27\,x^2+4\right)}^{1/3}} \,d x","Not used",1,"int((3*x + 2)^2/(27*x^2 + 4)^(1/3), x)","F"
702,1,27,529,0.253689,"\text{Not used}","int((3*x + 2)/(27*x^2 + 4)^(1/3),x)","\frac{{\left(27\,x^2+4\right)}^{2/3}}{12}+2^{1/3}\,x\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},\frac{1}{2};\ \frac{3}{2};\ -\frac{27\,x^2}{4}\right)","Not used",1,"(27*x^2 + 4)^(2/3)/12 + 2^(1/3)*x*hypergeom([1/3, 1/2], 3/2, -(27*x^2)/4)","B"
703,0,-1,97,0.000000,"\text{Not used}","int(1/((3*x + 2)*(27*x^2 + 4)^(1/3)),x)","\int \frac{1}{\left(3\,x+2\right)\,{\left(27\,x^2+4\right)}^{1/3}} \,d x","Not used",1,"int(1/((3*x + 2)*(27*x^2 + 4)^(1/3)), x)","F"
704,0,-1,634,0.000000,"\text{Not used}","int(1/((3*x + 2)^2*(27*x^2 + 4)^(1/3)),x)","\int \frac{1}{{\left(3\,x+2\right)}^2\,{\left(27\,x^2+4\right)}^{1/3}} \,d x","Not used",1,"int(1/((3*x + 2)^2*(27*x^2 + 4)^(1/3)), x)","F"
705,0,-1,656,0.000000,"\text{Not used}","int(1/((3*x + 2)^3*(27*x^2 + 4)^(1/3)),x)","\int \frac{1}{{\left(3\,x+2\right)}^3\,{\left(27\,x^2+4\right)}^{1/3}} \,d x","Not used",1,"int(1/((3*x + 2)^3*(27*x^2 + 4)^(1/3)), x)","F"
706,0,-1,564,0.000000,"\text{Not used}","int((x*3i + 2)^3/(4 - 27*x^2)^(1/3),x)","\int \frac{{\left(2+x\,3{}\mathrm{i}\right)}^3}{{\left(4-27\,x^2\right)}^{1/3}} \,d x","Not used",1,"int((x*3i + 2)^3/(4 - 27*x^2)^(1/3), x)","F"
707,0,-1,557,0.000000,"\text{Not used}","int((x*3i + 2)^2/(4 - 27*x^2)^(1/3),x)","\int \frac{{\left(2+x\,3{}\mathrm{i}\right)}^2}{{\left(4-27\,x^2\right)}^{1/3}} \,d x","Not used",1,"int((x*3i + 2)^2/(4 - 27*x^2)^(1/3), x)","F"
708,1,28,531,0.770086,"\text{Not used}","int((x*3i + 2)/(4 - 27*x^2)^(1/3),x)","2^{1/3}\,x\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},\frac{1}{2};\ \frac{3}{2};\ \frac{27\,x^2}{4}\right)-\frac{{\left(4-27\,x^2\right)}^{2/3}\,1{}\mathrm{i}}{12}","Not used",1,"2^(1/3)*x*hypergeom([1/3, 1/2], 3/2, (27*x^2)/4) - ((4 - 27*x^2)^(2/3)*1i)/12","B"
709,0,-1,109,0.000000,"\text{Not used}","int(1/((x*3i + 2)*(4 - 27*x^2)^(1/3)),x)","\int \frac{1}{\left(2+x\,3{}\mathrm{i}\right)\,{\left(4-27\,x^2\right)}^{1/3}} \,d x","Not used",1,"int(1/((x*3i + 2)*(4 - 27*x^2)^(1/3)), x)","F"
710,0,-1,650,0.000000,"\text{Not used}","int(1/((x*3i + 2)^2*(4 - 27*x^2)^(1/3)),x)","\int \frac{1}{{\left(2+x\,3{}\mathrm{i}\right)}^2\,{\left(4-27\,x^2\right)}^{1/3}} \,d x","Not used",1,"int(1/((x*3i + 2)^2*(4 - 27*x^2)^(1/3)), x)","F"
711,0,-1,676,0.000000,"\text{Not used}","int(1/((x*3i + 2)^3*(4 - 27*x^2)^(1/3)),x)","\int \frac{1}{{\left(2+x\,3{}\mathrm{i}\right)}^3\,{\left(4-27\,x^2\right)}^{1/3}} \,d x","Not used",1,"int(1/((x*3i + 2)^3*(4 - 27*x^2)^(1/3)), x)","F"
712,0,-1,104,0.000000,"\text{Not used}","int(1/((x^2 + 1)^(1/3)*(x + 3^(1/2))),x)","\int \frac{1}{{\left(x^2+1\right)}^{1/3}\,\left(x+\sqrt{3}\right)} \,d x","Not used",1,"int(1/((x^2 + 1)^(1/3)*(x + 3^(1/2))), x)","F"
713,0,-1,101,0.000000,"\text{Not used}","int(-1/((x^2 + 1)^(1/3)*(x - 3^(1/2))),x)","-\int \frac{1}{{\left(x^2+1\right)}^{1/3}\,\left(x-\sqrt{3}\right)} \,d x","Not used",1,"-int(1/((x^2 + 1)^(1/3)*(x - 3^(1/2))), x)","F"
714,0,-1,78,0.000000,"\text{Not used}","int(-1/((1 - x^2)^(1/3)*(x - 3)),x)","-\int \frac{1}{{\left(1-x^2\right)}^{1/3}\,\left(x-3\right)} \,d x","Not used",1,"-int(1/((1 - x^2)^(1/3)*(x - 3)), x)","F"
715,0,-1,76,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/3)*(x + 3)),x)","\int \frac{1}{{\left(1-x^2\right)}^{1/3}\,\left(x+3\right)} \,d x","Not used",1,"int(1/((1 - x^2)^(1/3)*(x + 3)), x)","F"
716,0,-1,206,0.000000,"\text{Not used}","int(1/((d^2 - 9*e^2*x^2)^(1/3)*(d + e*x)),x)","\int \frac{1}{{\left(d^2-9\,e^2\,x^2\right)}^{1/3}\,\left(d+e\,x\right)} \,d x","Not used",1,"int(1/((d^2 - 9*e^2*x^2)^(1/3)*(d + e*x)), x)","F"
717,0,-1,278,0.000000,"\text{Not used}","int(1/((c + d*x^2)^(1/4)*(a + b*x)),x)","\int \frac{1}{{\left(d\,x^2+c\right)}^{1/4}\,\left(a+b\,x\right)} \,d x","Not used",1,"int(1/((c + d*x^2)^(1/4)*(a + b*x)), x)","F"
718,0,-1,268,0.000000,"\text{Not used}","int(1/((c + d*x^2)^(3/4)*(a + b*x)),x)","\int \frac{1}{{\left(d\,x^2+c\right)}^{3/4}\,\left(a+b\,x\right)} \,d x","Not used",1,"int(1/((c + d*x^2)^(3/4)*(a + b*x)), x)","F"
719,0,-1,200,0.000000,"\text{Not used}","int(1/((a + c*x^2)^(1/4)*(d + e*x)^(3/2)),x)","\int \frac{1}{{\left(c\,x^2+a\right)}^{1/4}\,{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + c*x^2)^(1/4)*(d + e*x)^(3/2)), x)","F"
720,0,-1,203,0.000000,"\text{Not used}","int(1/((x^2 + 1)^(1/6)*(x + 1)),x)","\int \frac{1}{{\left(x^2+1\right)}^{1/6}\,\left(x+1\right)} \,d x","Not used",1,"int(1/((x^2 + 1)^(1/6)*(x + 1)), x)","F"
721,1,1144,223,1.047227,"\text{Not used}","int((a + c*x^2)^3*(d + e*x)^m,x)","\frac{{\left(d+e\,x\right)}^m\,\left(a^3\,d\,e^6\,m^6+27\,a^3\,d\,e^6\,m^5+295\,a^3\,d\,e^6\,m^4+1665\,a^3\,d\,e^6\,m^3+5104\,a^3\,d\,e^6\,m^2+8028\,a^3\,d\,e^6\,m+5040\,a^3\,d\,e^6+6\,a^2\,c\,d^3\,e^4\,m^4+132\,a^2\,c\,d^3\,e^4\,m^3+1074\,a^2\,c\,d^3\,e^4\,m^2+3828\,a^2\,c\,d^3\,e^4\,m+5040\,a^2\,c\,d^3\,e^4+72\,a\,c^2\,d^5\,e^2\,m^2+936\,a\,c^2\,d^5\,e^2\,m+3024\,a\,c^2\,d^5\,e^2+720\,c^3\,d^7\right)}{e^7\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}-\frac{x\,{\left(d+e\,x\right)}^m\,\left(-a^3\,e^7\,m^6-27\,a^3\,e^7\,m^5-295\,a^3\,e^7\,m^4-1665\,a^3\,e^7\,m^3-5104\,a^3\,e^7\,m^2-8028\,a^3\,e^7\,m-5040\,a^3\,e^7+6\,a^2\,c\,d^2\,e^5\,m^5+132\,a^2\,c\,d^2\,e^5\,m^4+1074\,a^2\,c\,d^2\,e^5\,m^3+3828\,a^2\,c\,d^2\,e^5\,m^2+5040\,a^2\,c\,d^2\,e^5\,m+72\,a\,c^2\,d^4\,e^3\,m^3+936\,a\,c^2\,d^4\,e^3\,m^2+3024\,a\,c^2\,d^4\,e^3\,m+720\,c^3\,d^6\,e\,m\right)}{e^7\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{c^3\,x^7\,{\left(d+e\,x\right)}^m\,\left(m^6+21\,m^5+175\,m^4+735\,m^3+1624\,m^2+1764\,m+720\right)}{m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040}+\frac{3\,c^2\,x^5\,{\left(d+e\,x\right)}^m\,\left(-2\,c\,d^2\,m+a\,e^2\,m^2+13\,a\,e^2\,m+42\,a\,e^2\right)\,\left(m^4+10\,m^3+35\,m^2+50\,m+24\right)}{e^2\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{3\,c\,x^3\,{\left(d+e\,x\right)}^m\,\left(m^2+3\,m+2\right)\,\left(a^2\,e^4\,m^4+22\,a^2\,e^4\,m^3+179\,a^2\,e^4\,m^2+638\,a^2\,e^4\,m+840\,a^2\,e^4-4\,a\,c\,d^2\,e^2\,m^3-52\,a\,c\,d^2\,e^2\,m^2-168\,a\,c\,d^2\,e^2\,m-40\,c^2\,d^4\,m\right)}{e^4\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{c^3\,d\,m\,x^6\,{\left(d+e\,x\right)}^m\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}{e\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{3\,c^2\,d\,m\,x^4\,{\left(d+e\,x\right)}^m\,\left(m^3+6\,m^2+11\,m+6\right)\,\left(10\,c\,d^2+a\,e^2\,m^2+13\,a\,e^2\,m+42\,a\,e^2\right)}{e^3\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{3\,c\,d\,m\,x^2\,\left(m+1\right)\,{\left(d+e\,x\right)}^m\,\left(a^2\,e^4\,m^4+22\,a^2\,e^4\,m^3+179\,a^2\,e^4\,m^2+638\,a^2\,e^4\,m+840\,a^2\,e^4+12\,a\,c\,d^2\,e^2\,m^2+156\,a\,c\,d^2\,e^2\,m+504\,a\,c\,d^2\,e^2+120\,c^2\,d^4\right)}{e^5\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}","Not used",1,"((d + e*x)^m*(720*c^3*d^7 + 5040*a^3*d*e^6 + 3024*a*c^2*d^5*e^2 + 5040*a^2*c*d^3*e^4 + 5104*a^3*d*e^6*m^2 + 1665*a^3*d*e^6*m^3 + 295*a^3*d*e^6*m^4 + 27*a^3*d*e^6*m^5 + a^3*d*e^6*m^6 + 8028*a^3*d*e^6*m + 936*a*c^2*d^5*e^2*m + 3828*a^2*c*d^3*e^4*m + 72*a*c^2*d^5*e^2*m^2 + 1074*a^2*c*d^3*e^4*m^2 + 132*a^2*c*d^3*e^4*m^3 + 6*a^2*c*d^3*e^4*m^4))/(e^7*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) - (x*(d + e*x)^m*(720*c^3*d^6*e*m - 8028*a^3*e^7*m - 5104*a^3*e^7*m^2 - 1665*a^3*e^7*m^3 - 295*a^3*e^7*m^4 - 27*a^3*e^7*m^5 - a^3*e^7*m^6 - 5040*a^3*e^7 + 3024*a*c^2*d^4*e^3*m + 5040*a^2*c*d^2*e^5*m + 936*a*c^2*d^4*e^3*m^2 + 3828*a^2*c*d^2*e^5*m^2 + 72*a*c^2*d^4*e^3*m^3 + 1074*a^2*c*d^2*e^5*m^3 + 132*a^2*c*d^2*e^5*m^4 + 6*a^2*c*d^2*e^5*m^5))/(e^7*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (c^3*x^7*(d + e*x)^m*(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720))/(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040) + (3*c^2*x^5*(d + e*x)^m*(42*a*e^2 + a*e^2*m^2 + 13*a*e^2*m - 2*c*d^2*m)*(50*m + 35*m^2 + 10*m^3 + m^4 + 24))/(e^2*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (3*c*x^3*(d + e*x)^m*(3*m + m^2 + 2)*(840*a^2*e^4 + 638*a^2*e^4*m - 40*c^2*d^4*m + 179*a^2*e^4*m^2 + 22*a^2*e^4*m^3 + a^2*e^4*m^4 - 168*a*c*d^2*e^2*m - 52*a*c*d^2*e^2*m^2 - 4*a*c*d^2*e^2*m^3))/(e^4*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (c^3*d*m*x^6*(d + e*x)^m*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120))/(e*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (3*c^2*d*m*x^4*(d + e*x)^m*(11*m + 6*m^2 + m^3 + 6)*(42*a*e^2 + 10*c*d^2 + a*e^2*m^2 + 13*a*e^2*m))/(e^3*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (3*c*d*m*x^2*(m + 1)*(d + e*x)^m*(840*a^2*e^4 + 120*c^2*d^4 + 638*a^2*e^4*m + 179*a^2*e^4*m^2 + 22*a^2*e^4*m^3 + a^2*e^4*m^4 + 504*a*c*d^2*e^2 + 156*a*c*d^2*e^2*m + 12*a*c*d^2*e^2*m^2))/(e^5*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040))","B"
722,1,496,140,0.695331,"\text{Not used}","int((a + c*x^2)^2*(d + e*x)^m,x)","{\left(d+e\,x\right)}^m\,\left(\frac{c^2\,x^5\,\left(m^4+10\,m^3+35\,m^2+50\,m+24\right)}{m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120}+\frac{d\,\left(a^2\,e^4\,m^4+14\,a^2\,e^4\,m^3+71\,a^2\,e^4\,m^2+154\,a^2\,e^4\,m+120\,a^2\,e^4+4\,a\,c\,d^2\,e^2\,m^2+36\,a\,c\,d^2\,e^2\,m+80\,a\,c\,d^2\,e^2+24\,c^2\,d^4\right)}{e^5\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}+\frac{x\,\left(a^2\,e^5\,m^4+14\,a^2\,e^5\,m^3+71\,a^2\,e^5\,m^2+154\,a^2\,e^5\,m+120\,a^2\,e^5-4\,a\,c\,d^2\,e^3\,m^3-36\,a\,c\,d^2\,e^3\,m^2-80\,a\,c\,d^2\,e^3\,m-24\,c^2\,d^4\,e\,m\right)}{e^5\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}+\frac{2\,c\,x^3\,\left(m^2+3\,m+2\right)\,\left(-2\,c\,d^2\,m+a\,e^2\,m^2+9\,a\,e^2\,m+20\,a\,e^2\right)}{e^2\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}+\frac{c^2\,d\,m\,x^4\,\left(m^3+6\,m^2+11\,m+6\right)}{e\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}+\frac{2\,c\,d\,m\,x^2\,\left(m+1\right)\,\left(6\,c\,d^2+a\,e^2\,m^2+9\,a\,e^2\,m+20\,a\,e^2\right)}{e^3\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}\right)","Not used",1,"(d + e*x)^m*((c^2*x^5*(50*m + 35*m^2 + 10*m^3 + m^4 + 24))/(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120) + (d*(120*a^2*e^4 + 24*c^2*d^4 + 154*a^2*e^4*m + 71*a^2*e^4*m^2 + 14*a^2*e^4*m^3 + a^2*e^4*m^4 + 80*a*c*d^2*e^2 + 36*a*c*d^2*e^2*m + 4*a*c*d^2*e^2*m^2))/(e^5*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)) + (x*(120*a^2*e^5 + 154*a^2*e^5*m + 71*a^2*e^5*m^2 + 14*a^2*e^5*m^3 + a^2*e^5*m^4 - 24*c^2*d^4*e*m - 80*a*c*d^2*e^3*m - 36*a*c*d^2*e^3*m^2 - 4*a*c*d^2*e^3*m^3))/(e^5*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)) + (2*c*x^3*(3*m + m^2 + 2)*(20*a*e^2 + a*e^2*m^2 + 9*a*e^2*m - 2*c*d^2*m))/(e^2*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)) + (c^2*d*m*x^4*(11*m + 6*m^2 + m^3 + 6))/(e*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)) + (2*c*d*m*x^2*(m + 1)*(20*a*e^2 + 6*c*d^2 + a*e^2*m^2 + 9*a*e^2*m))/(e^3*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)))","B"
723,1,163,70,0.483079,"\text{Not used}","int((a + c*x^2)*(d + e*x)^m,x)","{\left(d+e\,x\right)}^m\,\left(\frac{c\,x^3\,\left(m^2+3\,m+2\right)}{m^3+6\,m^2+11\,m+6}+\frac{x\,\left(-2\,c\,d^2\,e\,m+a\,e^3\,m^2+5\,a\,e^3\,m+6\,a\,e^3\right)}{e^3\,\left(m^3+6\,m^2+11\,m+6\right)}+\frac{d\,\left(2\,c\,d^2+a\,e^2\,m^2+5\,a\,e^2\,m+6\,a\,e^2\right)}{e^3\,\left(m^3+6\,m^2+11\,m+6\right)}+\frac{c\,d\,m\,x^2\,\left(m+1\right)}{e\,\left(m^3+6\,m^2+11\,m+6\right)}\right)","Not used",1,"(d + e*x)^m*((c*x^3*(3*m + m^2 + 2))/(11*m + 6*m^2 + m^3 + 6) + (x*(6*a*e^3 + a*e^3*m^2 + 5*a*e^3*m - 2*c*d^2*e*m))/(e^3*(11*m + 6*m^2 + m^3 + 6)) + (d*(6*a*e^2 + 2*c*d^2 + a*e^2*m^2 + 5*a*e^2*m))/(e^3*(11*m + 6*m^2 + m^3 + 6)) + (c*d*m*x^2*(m + 1))/(e*(11*m + 6*m^2 + m^3 + 6)))","B"
724,0,-1,167,0.000000,"\text{Not used}","int((d + e*x)^m/(a + c*x^2),x)","\int \frac{{\left(d+e\,x\right)}^m}{c\,x^2+a} \,d x","Not used",1,"int((d + e*x)^m/(a + c*x^2), x)","F"
725,0,-1,304,0.000000,"\text{Not used}","int((d + e*x)^m/(a + c*x^2)^2,x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(c\,x^2+a\right)}^2} \,d x","Not used",1,"int((d + e*x)^m/(a + c*x^2)^2, x)","F"
726,0,-1,472,0.000000,"\text{Not used}","int((d + e*x)^m/(a + c*x^2)^3,x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(c\,x^2+a\right)}^3} \,d x","Not used",1,"int((d + e*x)^m/(a + c*x^2)^3, x)","F"
727,0,-1,154,0.000000,"\text{Not used}","int((a + c*x^2)^(3/2)*(d + e*x)^m,x)","\int {\left(c\,x^2+a\right)}^{3/2}\,{\left(d+e\,x\right)}^m \,d x","Not used",1,"int((a + c*x^2)^(3/2)*(d + e*x)^m, x)","F"
728,0,-1,154,0.000000,"\text{Not used}","int((a + c*x^2)^(1/2)*(d + e*x)^m,x)","\int \sqrt{c\,x^2+a}\,{\left(d+e\,x\right)}^m \,d x","Not used",1,"int((a + c*x^2)^(1/2)*(d + e*x)^m, x)","F"
729,0,-1,154,0.000000,"\text{Not used}","int((d + e*x)^m/(a + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^m}{\sqrt{c\,x^2+a}} \,d x","Not used",1,"int((d + e*x)^m/(a + c*x^2)^(1/2), x)","F"
730,0,-1,154,0.000000,"\text{Not used}","int((d + e*x)^m/(a + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(c\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^m/(a + c*x^2)^(3/2), x)","F"
731,0,-1,152,0.000000,"\text{Not used}","int((a + c*x^2)^p*(d + e*x)^m,x)","\int {\left(c\,x^2+a\right)}^p\,{\left(d+e\,x\right)}^m \,d x","Not used",1,"int((a + c*x^2)^p*(d + e*x)^m, x)","F"
732,0,-1,178,0.000000,"\text{Not used}","int((a + c*x^2)^p*(d + e*x)^3,x)","\int {\left(c\,x^2+a\right)}^p\,{\left(d+e\,x\right)}^3 \,d x","Not used",1,"int((a + c*x^2)^p*(d + e*x)^3, x)","F"
733,0,-1,133,0.000000,"\text{Not used}","int((a + c*x^2)^p*(d + e*x)^2,x)","\int {\left(c\,x^2+a\right)}^p\,{\left(d+e\,x\right)}^2 \,d x","Not used",1,"int((a + c*x^2)^p*(d + e*x)^2, x)","F"
734,1,65,61,1.114824,"\text{Not used}","int((a + c*x^2)^p*(d + e*x),x)","\frac{e\,{\left(c\,x^2+a\right)}^{p+1}}{2\,c\,\left(p+1\right)}+\frac{d\,x\,{\left(c\,x^2+a\right)}^p\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},-p;\ \frac{3}{2};\ -\frac{c\,x^2}{a}\right)}{{\left(\frac{c\,x^2}{a}+1\right)}^p}","Not used",1,"(e*(a + c*x^2)^(p + 1))/(2*c*(p + 1)) + (d*x*(a + c*x^2)^p*hypergeom([1/2, -p], 3/2, -(c*x^2)/a))/((c*x^2)/a + 1)^p","B"
735,1,41,35,0.986275,"\text{Not used}","int((a + c*x^2)^p,x)","\frac{x\,{\left(c\,x^2+a\right)}^p\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},-p;\ \frac{3}{2};\ -\frac{c\,x^2}{a}\right)}{{\left(\frac{c\,x^2}{a}+1\right)}^p}","Not used",1,"(x*(a + c*x^2)^p*hypergeom([1/2, -p], 3/2, -(c*x^2)/a))/((c*x^2)/a + 1)^p","B"
736,0,-1,125,0.000000,"\text{Not used}","int((a + c*x^2)^p/(d + e*x),x)","\int \frac{{\left(c\,x^2+a\right)}^p}{d+e\,x} \,d x","Not used",1,"int((a + c*x^2)^p/(d + e*x), x)","F"
737,0,-1,191,0.000000,"\text{Not used}","int((a + c*x^2)^p/(d + e*x)^2,x)","\int \frac{{\left(c\,x^2+a\right)}^p}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a + c*x^2)^p/(d + e*x)^2, x)","F"
738,0,-1,322,0.000000,"\text{Not used}","int((a + c*x^2)^p/(d + e*x)^3,x)","\int \frac{{\left(c\,x^2+a\right)}^p}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((a + c*x^2)^p/(d + e*x)^3, x)","F"
739,0,-1,160,0.000000,"\text{Not used}","int((a + c*x^2)^p/(d + e*x)^(2*p),x)","\int \frac{{\left(c\,x^2+a\right)}^p}{{\left(d+e\,x\right)}^{2\,p}} \,d x","Not used",1,"int((a + c*x^2)^p/(d + e*x)^(2*p), x)","F"
740,0,-1,155,0.000000,"\text{Not used}","int((a + c*x^2)^p/(d + e*x)^(2*p + 1),x)","\int \frac{{\left(c\,x^2+a\right)}^p}{{\left(d+e\,x\right)}^{2\,p+1}} \,d x","Not used",1,"int((a + c*x^2)^p/(d + e*x)^(2*p + 1), x)","F"
741,0,-1,209,0.000000,"\text{Not used}","int((a + c*x^2)^p/(d + e*x)^(2*p + 2),x)","\int \frac{{\left(c\,x^2+a\right)}^p}{{\left(d+e\,x\right)}^{2\,p+2}} \,d x","Not used",1,"int((a + c*x^2)^p/(d + e*x)^(2*p + 2), x)","F"
742,0,-1,270,0.000000,"\text{Not used}","int((a + c*x^2)^p/(d + e*x)^(2*p + 3),x)","\int \frac{{\left(c\,x^2+a\right)}^p}{{\left(d+e\,x\right)}^{2\,p+3}} \,d x","Not used",1,"int((a + c*x^2)^p/(d + e*x)^(2*p + 3), x)","F"
743,0,-1,347,0.000000,"\text{Not used}","int((a + c*x^2)^p/(d + e*x)^(2*p + 4),x)","\int \frac{{\left(c\,x^2+a\right)}^p}{{\left(d+e\,x\right)}^{2\,p+4}} \,d x","Not used",1,"int((a + c*x^2)^p/(d + e*x)^(2*p + 4), x)","F"
744,0,-1,436,0.000000,"\text{Not used}","int((a + c*x^2)^p/(d + e*x)^(2*p + 5),x)","\int \frac{{\left(c\,x^2+a\right)}^p}{{\left(d+e\,x\right)}^{2\,p+5}} \,d x","Not used",1,"int((a + c*x^2)^p/(d + e*x)^(2*p + 5), x)","F"
745,0,-1,559,0.000000,"\text{Not used}","int((a + c*x^2)^p/(d + e*x)^(2*p + 6),x)","\int \frac{{\left(c\,x^2+a\right)}^p}{{\left(d+e\,x\right)}^{2\,p+6}} \,d x","Not used",1,"int((a + c*x^2)^p/(d + e*x)^(2*p + 6), x)","F"
746,0,-1,43,0.000000,"\text{Not used}","int((3 - 4*x)^n/(1 - x^2)^(1/2),x)","\int \frac{{\left(3-4\,x\right)}^n}{\sqrt{1-x^2}} \,d x","Not used",1,"int((3 - 4*x)^n/(1 - x^2)^(1/2), x)","F"
747,1,60,83,0.397903,"\text{Not used}","int((a + b*x)^6/(a^2 - b^2*x^2),x)","-31\,a^4\,x-\frac{b^4\,x^5}{5}-13\,a^3\,b\,x^2-\frac{3\,a\,b^3\,x^4}{2}-\frac{32\,a^5\,\ln\left(b\,x-a\right)}{b}-\frac{16\,a^2\,b^2\,x^3}{3}","Not used",1,"- 31*a^4*x - (b^4*x^5)/5 - 13*a^3*b*x^2 - (3*a*b^3*x^4)/2 - (32*a^5*log(b*x - a))/b - (16*a^2*b^2*x^3)/3","B"
748,1,49,66,0.379255,"\text{Not used}","int((a + b*x)^5/(a^2 - b^2*x^2),x)","-15\,a^3\,x-\frac{b^3\,x^4}{4}-\frac{11\,a^2\,b\,x^2}{2}-\frac{5\,a\,b^2\,x^3}{3}-\frac{16\,a^4\,\ln\left(b\,x-a\right)}{b}","Not used",1,"- 15*a^3*x - (b^3*x^4)/4 - (11*a^2*b*x^2)/2 - (5*a*b^2*x^3)/3 - (16*a^4*log(b*x - a))/b","B"
749,1,38,49,0.399824,"\text{Not used}","int((a + b*x)^4/(a^2 - b^2*x^2),x)","-7\,a^2\,x-\frac{b^2\,x^3}{3}-\frac{8\,a^3\,\ln\left(b\,x-a\right)}{b}-2\,a\,b\,x^2","Not used",1,"- 7*a^2*x - (b^2*x^3)/3 - (8*a^3*log(b*x - a))/b - 2*a*b*x^2","B"
750,1,27,28,0.405722,"\text{Not used}","int((a + b*x)^3/(a^2 - b^2*x^2),x)","-3\,a\,x-\frac{b\,x^2}{2}-\frac{4\,a^2\,\ln\left(b\,x-a\right)}{b}","Not used",1,"- 3*a*x - (b*x^2)/2 - (4*a^2*log(b*x - a))/b","B"
751,1,18,17,0.396524,"\text{Not used}","int((a + b*x)^2/(a^2 - b^2*x^2),x)","-x-\frac{2\,a\,\ln\left(b\,x-a\right)}{b}","Not used",1,"- x - (2*a*log(b*x - a))/b","B"
752,1,13,12,0.026278,"\text{Not used}","int((a + b*x)/(a^2 - b^2*x^2),x)","-\frac{\ln\left(b\,x-a\right)}{b}","Not used",1,"-log(b*x - a)/b","B"
753,1,31,35,0.076417,"\text{Not used}","int(1/((a^2 - b^2*x^2)*(a + b*x)),x)","\frac{\mathrm{atanh}\left(\frac{b\,x}{a}\right)}{2\,a^2\,b}-\frac{1}{2\,a\,b\,\left(a+b\,x\right)}","Not used",1,"atanh((b*x)/a)/(2*a^2*b) - 1/(2*a*b*(a + b*x))","B"
754,1,51,52,0.068568,"\text{Not used}","int(1/((a^2 - b^2*x^2)*(a + b*x)^2),x)","\frac{\mathrm{atanh}\left(\frac{b\,x}{a}\right)}{4\,a^3\,b}-\frac{\frac{x}{4\,a^2}+\frac{1}{2\,a\,b}}{a^2+2\,a\,b\,x+b^2\,x^2}","Not used",1,"atanh((b*x)/a)/(4*a^3*b) - (x/(4*a^2) + 1/(2*a*b))/(a^2 + b^2*x^2 + 2*a*b*x)","B"
755,1,71,69,0.087005,"\text{Not used}","int(1/((a^2 - b^2*x^2)*(a + b*x)^3),x)","\frac{\mathrm{atanh}\left(\frac{b\,x}{a}\right)}{8\,a^4\,b}-\frac{\frac{3\,x}{8\,a^2}+\frac{5}{12\,a\,b}+\frac{b\,x^2}{8\,a^3}}{a^3+3\,a^2\,b\,x+3\,a\,b^2\,x^2+b^3\,x^3}","Not used",1,"atanh((b*x)/a)/(8*a^4*b) - ((3*x)/(8*a^2) + 5/(12*a*b) + (b*x^2)/(8*a^3))/(a^3 + b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x)","B"
756,1,93,86,0.441976,"\text{Not used}","int(1/((a^2 - b^2*x^2)*(a + b*x)^4),x)","\frac{\mathrm{atanh}\left(\frac{b\,x}{a}\right)}{16\,a^5\,b}-\frac{\frac{19\,x}{48\,a^2}+\frac{1}{3\,a\,b}+\frac{b\,x^2}{4\,a^3}+\frac{b^2\,x^3}{16\,a^4}}{a^4+4\,a^3\,b\,x+6\,a^2\,b^2\,x^2+4\,a\,b^3\,x^3+b^4\,x^4}","Not used",1,"atanh((b*x)/a)/(16*a^5*b) - ((19*x)/(48*a^2) + 1/(3*a*b) + (b*x^2)/(4*a^3) + (b^2*x^3)/(16*a^4))/(a^4 + b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x)","B"
757,1,64,70,0.046373,"\text{Not used}","int((a + b*x)^7/(a^2 - b^2*x^2)^2,x)","49\,a^3\,x+\frac{b^3\,x^4}{4}+\frac{32\,a^5}{b\,\left(a-b\,x\right)}+\frac{80\,a^4\,\ln\left(a-b\,x\right)}{b}+\frac{23\,a^2\,b\,x^2}{2}+\frac{7\,a\,b^2\,x^3}{3}","Not used",1,"49*a^3*x + (b^3*x^4)/4 + (32*a^5)/(b*(a - b*x)) + (80*a^4*log(a - b*x))/b + (23*a^2*b*x^2)/2 + (7*a*b^2*x^3)/3","B"
758,1,53,55,0.391562,"\text{Not used}","int((a + b*x)^6/(a^2 - b^2*x^2)^2,x)","17\,a^2\,x+\frac{b^2\,x^3}{3}+\frac{16\,a^4}{b\,\left(a-b\,x\right)}+\frac{32\,a^3\,\ln\left(a-b\,x\right)}{b}+3\,a\,b\,x^2","Not used",1,"17*a^2*x + (b^2*x^3)/3 + (16*a^4)/(b*(a - b*x)) + (32*a^3*log(a - b*x))/b + 3*a*b*x^2","B"
759,1,42,44,0.046419,"\text{Not used}","int((a + b*x)^5/(a^2 - b^2*x^2)^2,x)","5\,a\,x+\frac{b\,x^2}{2}+\frac{8\,a^3}{b\,\left(a-b\,x\right)}+\frac{12\,a^2\,\ln\left(a-b\,x\right)}{b}","Not used",1,"5*a*x + (b*x^2)/2 + (8*a^3)/(b*(a - b*x)) + (12*a^2*log(a - b*x))/b","B"
760,1,31,31,0.042137,"\text{Not used}","int((a + b*x)^4/(a^2 - b^2*x^2)^2,x)","x+\frac{4\,a^2}{b\,\left(a-b\,x\right)}+\frac{4\,a\,\ln\left(a-b\,x\right)}{b}","Not used",1,"x + (4*a^2)/(b*(a - b*x)) + (4*a*log(a - b*x))/b","B"
761,1,26,26,0.037898,"\text{Not used}","int((a + b*x)^3/(a^2 - b^2*x^2)^2,x)","\frac{\ln\left(a-b\,x\right)}{b}+\frac{2\,a}{b\,\left(a-b\,x\right)}","Not used",1,"log(a - b*x)/b + (2*a)/(b*(a - b*x))","B"
762,1,12,12,0.407988,"\text{Not used}","int((a + b*x)^2/(a^2 - b^2*x^2)^2,x)","\frac{1}{b\,\left(a-b\,x\right)}","Not used",1,"1/(b*(a - b*x))","B"
763,1,32,36,0.053416,"\text{Not used}","int((a + b*x)/(a^2 - b^2*x^2)^2,x)","\frac{1}{2\,a\,b\,\left(a-b\,x\right)}+\frac{\mathrm{atanh}\left(\frac{b\,x}{a}\right)}{2\,a^2\,b}","Not used",1,"1/(2*a*b*(a - b*x)) + atanh((b*x)/a)/(2*a^2*b)","B"
764,1,70,70,0.079205,"\text{Not used}","int(1/((a^2 - b^2*x^2)^2*(a + b*x)),x)","\frac{\frac{3\,x}{8\,a^2}-\frac{1}{4\,a\,b}+\frac{3\,b\,x^2}{8\,a^3}}{a^3+a^2\,b\,x-a\,b^2\,x^2-b^3\,x^3}+\frac{3\,\mathrm{atanh}\left(\frac{b\,x}{a}\right)}{8\,a^4\,b}","Not used",1,"((3*x)/(8*a^2) - 1/(4*a*b) + (3*b*x^2)/(8*a^3))/(a^3 - b^3*x^3 - a*b^2*x^2 + a^2*b*x) + (3*atanh((b*x)/a))/(8*a^4*b)","B"
765,1,82,87,0.083752,"\text{Not used}","int(1/((a^2 - b^2*x^2)^2*(a + b*x)^2),x)","\frac{\frac{x}{12\,a^2}-\frac{1}{3\,a\,b}+\frac{b\,x^2}{2\,a^3}+\frac{b^2\,x^3}{4\,a^4}}{a^4+2\,a^3\,b\,x-2\,a\,b^3\,x^3-b^4\,x^4}+\frac{\mathrm{atanh}\left(\frac{b\,x}{a}\right)}{4\,a^5\,b}","Not used",1,"(x/(12*a^2) - 1/(3*a*b) + (b*x^2)/(2*a^3) + (b^2*x^3)/(4*a^4))/(a^4 - b^4*x^4 - 2*a*b^3*x^3 + 2*a^3*b*x) + atanh((b*x)/a)/(4*a^5*b)","B"
766,1,115,104,0.466418,"\text{Not used}","int(1/((a^2 - b^2*x^2)^2*(a + b*x)^3),x)","\frac{\frac{35\,b\,x^2}{96\,a^3}-\frac{1}{3\,a\,b}-\frac{5\,x}{32\,a^2}+\frac{15\,b^2\,x^3}{32\,a^4}+\frac{5\,b^3\,x^4}{32\,a^5}}{a^5+3\,a^4\,b\,x+2\,a^3\,b^2\,x^2-2\,a^2\,b^3\,x^3-3\,a\,b^4\,x^4-b^5\,x^5}+\frac{5\,\mathrm{atanh}\left(\frac{b\,x}{a}\right)}{32\,a^6\,b}","Not used",1,"((35*b*x^2)/(96*a^3) - 1/(3*a*b) - (5*x)/(32*a^2) + (15*b^2*x^3)/(32*a^4) + (5*b^3*x^4)/(32*a^5))/(a^5 - b^5*x^5 - 3*a*b^4*x^4 + 2*a^3*b^2*x^2 - 2*a^2*b^3*x^3 + 3*a^4*b*x) + (5*atanh((b*x)/a))/(32*a^6*b)","B"
767,1,72,71,0.052306,"\text{Not used}","int((a + b*x)^8/(a^2 - b^2*x^2)^3,x)","\frac{80\,a^4\,x-\frac{64\,a^5}{b}}{a^2-2\,a\,b\,x+b^2\,x^2}-31\,a^2\,x-\frac{b^2\,x^3}{3}-\frac{80\,a^3\,\ln\left(b\,x-a\right)}{b}-4\,a\,b\,x^2","Not used",1,"(80*a^4*x - (64*a^5)/b)/(a^2 + b^2*x^2 - 2*a*b*x) - 31*a^2*x - (b^2*x^3)/3 - (80*a^3*log(b*x - a))/b - 4*a*b*x^2","B"
768,1,61,60,0.049691,"\text{Not used}","int((a + b*x)^7/(a^2 - b^2*x^2)^3,x)","\frac{32\,a^3\,x-\frac{24\,a^4}{b}}{a^2-2\,a\,b\,x+b^2\,x^2}-7\,a\,x-\frac{b\,x^2}{2}-\frac{24\,a^2\,\ln\left(b\,x-a\right)}{b}","Not used",1,"(32*a^3*x - (24*a^4)/b)/(a^2 + b^2*x^2 - 2*a*b*x) - 7*a*x - (b*x^2)/2 - (24*a^2*log(b*x - a))/b","B"
769,1,52,49,0.058109,"\text{Not used}","int((a + b*x)^6/(a^2 - b^2*x^2)^3,x)","\frac{12\,a^2\,x-\frac{8\,a^3}{b}}{a^2-2\,a\,b\,x+b^2\,x^2}-x-\frac{6\,a\,\ln\left(b\,x-a\right)}{b}","Not used",1,"(12*a^2*x - (8*a^3)/b)/(a^2 + b^2*x^2 - 2*a*b*x) - x - (6*a*log(b*x - a))/b","B"
770,1,46,43,0.399130,"\text{Not used}","int((a + b*x)^5/(a^2 - b^2*x^2)^3,x)","\frac{4\,a\,x-\frac{2\,a^2}{b}}{a^2-2\,a\,b\,x+b^2\,x^2}-\frac{\ln\left(b\,x-a\right)}{b}","Not used",1,"(4*a*x - (2*a^2)/b)/(a^2 + b^2*x^2 - 2*a*b*x) - log(b*x - a)/b","B"
771,1,10,10,0.397121,"\text{Not used}","int((a + b*x)^4/(a^2 - b^2*x^2)^3,x)","\frac{x}{{\left(a-b\,x\right)}^2}","Not used",1,"x/(a - b*x)^2","B"
772,1,24,15,0.390096,"\text{Not used}","int((a + b*x)^3/(a^2 - b^2*x^2)^3,x)","\frac{1}{2\,a^2\,b-4\,a\,b^2\,x+2\,b^3\,x^2}","Not used",1,"1/(2*a^2*b + 2*b^3*x^2 - 4*a*b^2*x)","B"
773,1,51,54,0.060861,"\text{Not used}","int((a + b*x)^2/(a^2 - b^2*x^2)^3,x)","\frac{\mathrm{atanh}\left(\frac{b\,x}{a}\right)}{4\,a^3\,b}-\frac{\frac{x}{4\,a^2}-\frac{1}{2\,a\,b}}{a^2-2\,a\,b\,x+b^2\,x^2}","Not used",1,"atanh((b*x)/a)/(4*a^3*b) - (x/(4*a^2) - 1/(2*a*b))/(a^2 + b^2*x^2 - 2*a*b*x)","B"
774,1,70,71,0.431605,"\text{Not used}","int((a + b*x)/(a^2 - b^2*x^2)^3,x)","\frac{\frac{3\,x}{8\,a^2}+\frac{1}{4\,a\,b}-\frac{3\,b\,x^2}{8\,a^3}}{a^3-a^2\,b\,x-a\,b^2\,x^2+b^3\,x^3}+\frac{3\,\mathrm{atanh}\left(\frac{b\,x}{a}\right)}{8\,a^4\,b}","Not used",1,"((3*x)/(8*a^2) + 1/(4*a*b) - (3*b*x^2)/(8*a^3))/(a^3 + b^3*x^3 - a*b^2*x^2 - a^2*b*x) + (3*atanh((b*x)/a))/(8*a^4*b)","B"
775,1,113,105,0.106102,"\text{Not used}","int(1/((a^2 - b^2*x^2)^3*(a + b*x)),x)","\frac{5\,\mathrm{atanh}\left(\frac{b\,x}{a}\right)}{16\,a^6\,b}-\frac{\frac{1}{6\,a\,b}-\frac{25\,x}{48\,a^2}-\frac{25\,b\,x^2}{48\,a^3}+\frac{5\,b^2\,x^3}{16\,a^4}+\frac{5\,b^3\,x^4}{16\,a^5}}{a^5+a^4\,b\,x-2\,a^3\,b^2\,x^2-2\,a^2\,b^3\,x^3+a\,b^4\,x^4+b^5\,x^5}","Not used",1,"(5*atanh((b*x)/a))/(16*a^6*b) - (1/(6*a*b) - (25*x)/(48*a^2) - (25*b*x^2)/(48*a^3) + (5*b^2*x^3)/(16*a^4) + (5*b^3*x^4)/(16*a^5))/(a^5 + b^5*x^5 + a*b^4*x^4 - 2*a^3*b^2*x^2 - 2*a^2*b^3*x^3 + a^4*b*x)","B"
776,1,136,122,0.468815,"\text{Not used}","int(1/((a^2 - b^2*x^2)^3*(a + b*x)^2),x)","\frac{\frac{17\,x}{64\,a^2}-\frac{1}{4\,a\,b}+\frac{25\,b\,x^2}{32\,a^3}+\frac{5\,b^2\,x^3}{32\,a^4}-\frac{15\,b^3\,x^4}{32\,a^5}-\frac{15\,b^4\,x^5}{64\,a^6}}{a^6+2\,a^5\,b\,x-a^4\,b^2\,x^2-4\,a^3\,b^3\,x^3-a^2\,b^4\,x^4+2\,a\,b^5\,x^5+b^6\,x^6}+\frac{15\,\mathrm{atanh}\left(\frac{b\,x}{a}\right)}{64\,a^7\,b}","Not used",1,"((17*x)/(64*a^2) - 1/(4*a*b) + (25*b*x^2)/(32*a^3) + (5*b^2*x^3)/(32*a^4) - (15*b^3*x^4)/(32*a^5) - (15*b^4*x^5)/(64*a^6))/(a^6 + b^6*x^6 + 2*a*b^5*x^5 - a^4*b^2*x^2 - 4*a^3*b^3*x^3 - a^2*b^4*x^4 + 2*a^5*b*x) + (15*atanh((b*x)/a))/(64*a^7*b)","B"
777,0,-1,173,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^(1/2)*(a + b*x)^4,x)","\int \sqrt{a^2-b^2\,x^2}\,{\left(a+b\,x\right)}^4 \,d x","Not used",1,"int((a^2 - b^2*x^2)^(1/2)*(a + b*x)^4, x)","F"
778,0,-1,140,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^(1/2)*(a + b*x)^3,x)","\int \sqrt{a^2-b^2\,x^2}\,{\left(a+b\,x\right)}^3 \,d x","Not used",1,"int((a^2 - b^2*x^2)^(1/2)*(a + b*x)^3, x)","F"
779,0,-1,107,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^(1/2)*(a + b*x)^2,x)","\int \sqrt{a^2-b^2\,x^2}\,{\left(a+b\,x\right)}^2 \,d x","Not used",1,"int((a^2 - b^2*x^2)^(1/2)*(a + b*x)^2, x)","F"
780,1,75,76,0.846977,"\text{Not used}","int((a^2 - b^2*x^2)^(1/2)*(a + b*x),x)","\frac{a^3\,\ln\left(x\,\sqrt{-b^2}+\sqrt{a^2-b^2\,x^2}\right)}{2\,\sqrt{-b^2}}-\frac{{\left(a^2-b^2\,x^2\right)}^{3/2}}{3\,b}+\frac{a\,x\,\sqrt{a^2-b^2\,x^2}}{2}","Not used",1,"(a^3*log(x*(-b^2)^(1/2) + (a^2 - b^2*x^2)^(1/2)))/(2*(-b^2)^(1/2)) - (a^2 - b^2*x^2)^(3/2)/(3*b) + (a*x*(a^2 - b^2*x^2)^(1/2))/2","B"
781,0,-1,46,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^(1/2)/(a + b*x),x)","\int \frac{\sqrt{a^2-b^2\,x^2}}{a+b\,x} \,d x","Not used",1,"int((a^2 - b^2*x^2)^(1/2)/(a + b*x), x)","F"
782,0,-1,54,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^(1/2)/(a + b*x)^2,x)","\int \frac{\sqrt{a^2-b^2\,x^2}}{{\left(a+b\,x\right)}^2} \,d x","Not used",1,"int((a^2 - b^2*x^2)^(1/2)/(a + b*x)^2, x)","F"
783,1,35,33,0.527672,"\text{Not used}","int((a^2 - b^2*x^2)^(1/2)/(a + b*x)^3,x)","-\frac{\sqrt{a^2-b^2\,x^2}\,\left(a-b\,x\right)}{3\,a\,b\,{\left(a+b\,x\right)}^2}","Not used",1,"-((a^2 - b^2*x^2)^(1/2)*(a - b*x))/(3*a*b*(a + b*x)^2)","B"
784,1,47,67,0.617123,"\text{Not used}","int((a^2 - b^2*x^2)^(1/2)/(a + b*x)^4,x)","\frac{\sqrt{a^2-b^2\,x^2}\,\left(-4\,a^2+3\,a\,b\,x+b^2\,x^2\right)}{15\,a^2\,b\,{\left(a+b\,x\right)}^3}","Not used",1,"((a^2 - b^2*x^2)^(1/2)*(b^2*x^2 - 4*a^2 + 3*a*b*x))/(15*a^2*b*(a + b*x)^3)","B"
785,1,114,100,0.723337,"\text{Not used}","int((a^2 - b^2*x^2)^(1/2)/(a + b*x)^5,x)","\frac{\sqrt{a^2-b^2\,x^2}}{35\,a\,b\,{\left(a+b\,x\right)}^3}-\frac{2\,\sqrt{a^2-b^2\,x^2}}{7\,b\,{\left(a+b\,x\right)}^4}+\frac{2\,\sqrt{a^2-b^2\,x^2}}{105\,a^2\,b\,{\left(a+b\,x\right)}^2}+\frac{2\,\sqrt{a^2-b^2\,x^2}}{105\,a^3\,b\,\left(a+b\,x\right)}","Not used",1,"(a^2 - b^2*x^2)^(1/2)/(35*a*b*(a + b*x)^3) - (2*(a^2 - b^2*x^2)^(1/2))/(7*b*(a + b*x)^4) + (2*(a^2 - b^2*x^2)^(1/2))/(105*a^2*b*(a + b*x)^2) + (2*(a^2 - b^2*x^2)^(1/2))/(105*a^3*b*(a + b*x))","B"
786,1,143,133,0.826498,"\text{Not used}","int((a^2 - b^2*x^2)^(1/2)/(a + b*x)^6,x)","\frac{\sqrt{a^2-b^2\,x^2}}{63\,a\,b\,{\left(a+b\,x\right)}^4}-\frac{2\,\sqrt{a^2-b^2\,x^2}}{9\,b\,{\left(a+b\,x\right)}^5}+\frac{\sqrt{a^2-b^2\,x^2}}{105\,a^2\,b\,{\left(a+b\,x\right)}^3}+\frac{2\,\sqrt{a^2-b^2\,x^2}}{315\,a^3\,b\,{\left(a+b\,x\right)}^2}+\frac{2\,\sqrt{a^2-b^2\,x^2}}{315\,a^4\,b\,\left(a+b\,x\right)}","Not used",1,"(a^2 - b^2*x^2)^(1/2)/(63*a*b*(a + b*x)^4) - (2*(a^2 - b^2*x^2)^(1/2))/(9*b*(a + b*x)^5) + (a^2 - b^2*x^2)^(1/2)/(105*a^2*b*(a + b*x)^3) + (2*(a^2 - b^2*x^2)^(1/2))/(315*a^3*b*(a + b*x)^2) + (2*(a^2 - b^2*x^2)^(1/2))/(315*a^4*b*(a + b*x))","B"
787,1,172,166,1.040368,"\text{Not used}","int((a^2 - b^2*x^2)^(1/2)/(a + b*x)^7,x)","\frac{\sqrt{a^2-b^2\,x^2}}{99\,a\,b\,{\left(a+b\,x\right)}^5}-\frac{2\,\sqrt{a^2-b^2\,x^2}}{11\,b\,{\left(a+b\,x\right)}^6}+\frac{4\,\sqrt{a^2-b^2\,x^2}}{693\,a^2\,b\,{\left(a+b\,x\right)}^4}+\frac{4\,\sqrt{a^2-b^2\,x^2}}{1155\,a^3\,b\,{\left(a+b\,x\right)}^3}+\frac{8\,\sqrt{a^2-b^2\,x^2}}{3465\,a^4\,b\,{\left(a+b\,x\right)}^2}+\frac{8\,\sqrt{a^2-b^2\,x^2}}{3465\,a^5\,b\,\left(a+b\,x\right)}","Not used",1,"(a^2 - b^2*x^2)^(1/2)/(99*a*b*(a + b*x)^5) - (2*(a^2 - b^2*x^2)^(1/2))/(11*b*(a + b*x)^6) + (4*(a^2 - b^2*x^2)^(1/2))/(693*a^2*b*(a + b*x)^4) + (4*(a^2 - b^2*x^2)^(1/2))/(1155*a^3*b*(a + b*x)^3) + (8*(a^2 - b^2*x^2)^(1/2))/(3465*a^4*b*(a + b*x)^2) + (8*(a^2 - b^2*x^2)^(1/2))/(3465*a^5*b*(a + b*x))","B"
788,0,-1,164,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^(3/2)*(a + b*x)^3,x)","\int {\left(a^2-b^2\,x^2\right)}^{3/2}\,{\left(a+b\,x\right)}^3 \,d x","Not used",1,"int((a^2 - b^2*x^2)^(3/2)*(a + b*x)^3, x)","F"
789,0,-1,131,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^(3/2)*(a + b*x)^2,x)","\int {\left(a^2-b^2\,x^2\right)}^{3/2}\,{\left(a+b\,x\right)}^2 \,d x","Not used",1,"int((a^2 - b^2*x^2)^(3/2)*(a + b*x)^2, x)","F"
790,1,67,100,0.728025,"\text{Not used}","int((a^2 - b^2*x^2)^(3/2)*(a + b*x),x)","\frac{a\,x\,{\left(a^2-b^2\,x^2\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{2},\frac{1}{2};\ \frac{3}{2};\ \frac{b^2\,x^2}{a^2}\right)}{{\left(1-\frac{b^2\,x^2}{a^2}\right)}^{3/2}}-\frac{{\left(a^2-b^2\,x^2\right)}^{5/2}}{5\,b}","Not used",1,"(a*x*(a^2 - b^2*x^2)^(3/2)*hypergeom([-3/2, 1/2], 3/2, (b^2*x^2)/a^2))/(1 - (b^2*x^2)/a^2)^(3/2) - (a^2 - b^2*x^2)^(5/2)/(5*b)","B"
791,0,-1,76,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^(3/2)/(a + b*x),x)","\int \frac{{\left(a^2-b^2\,x^2\right)}^{3/2}}{a+b\,x} \,d x","Not used",1,"int((a^2 - b^2*x^2)^(3/2)/(a + b*x), x)","F"
792,0,-1,85,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^(3/2)/(a + b*x)^2,x)","\int \frac{{\left(a^2-b^2\,x^2\right)}^{3/2}}{{\left(a+b\,x\right)}^2} \,d x","Not used",1,"int((a^2 - b^2*x^2)^(3/2)/(a + b*x)^2, x)","F"
793,0,-1,76,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^(3/2)/(a + b*x)^3,x)","\int \frac{{\left(a^2-b^2\,x^2\right)}^{3/2}}{{\left(a+b\,x\right)}^3} \,d x","Not used",1,"int((a^2 - b^2*x^2)^(3/2)/(a + b*x)^3, x)","F"
794,0,-1,83,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^(3/2)/(a + b*x)^4,x)","\int \frac{{\left(a^2-b^2\,x^2\right)}^{3/2}}{{\left(a+b\,x\right)}^4} \,d x","Not used",1,"int((a^2 - b^2*x^2)^(3/2)/(a + b*x)^4, x)","F"
795,1,37,33,0.795160,"\text{Not used}","int((a^2 - b^2*x^2)^(3/2)/(a + b*x)^5,x)","-\frac{\sqrt{a^2-b^2\,x^2}\,{\left(a-b\,x\right)}^2}{5\,a\,b\,{\left(a+b\,x\right)}^3}","Not used",1,"-((a^2 - b^2*x^2)^(1/2)*(a - b*x)^2)/(5*a*b*(a + b*x)^3)","B"
796,1,112,67,0.989675,"\text{Not used}","int((a^2 - b^2*x^2)^(3/2)/(a + b*x)^6,x)","\frac{16\,\sqrt{a^2-b^2\,x^2}}{35\,b\,{\left(a+b\,x\right)}^3}-\frac{4\,a\,\sqrt{a^2-b^2\,x^2}}{7\,b\,{\left(a+b\,x\right)}^4}-\frac{\sqrt{a^2-b^2\,x^2}}{35\,a\,b\,{\left(a+b\,x\right)}^2}-\frac{\sqrt{a^2-b^2\,x^2}}{35\,a^2\,b\,\left(a+b\,x\right)}","Not used",1,"(16*(a^2 - b^2*x^2)^(1/2))/(35*b*(a + b*x)^3) - (4*a*(a^2 - b^2*x^2)^(1/2))/(7*b*(a + b*x)^4) - (a^2 - b^2*x^2)^(1/2)/(35*a*b*(a + b*x)^2) - (a^2 - b^2*x^2)^(1/2)/(35*a^2*b*(a + b*x))","B"
797,1,141,100,1.184855,"\text{Not used}","int((a^2 - b^2*x^2)^(3/2)/(a + b*x)^7,x)","\frac{20\,\sqrt{a^2-b^2\,x^2}}{63\,b\,{\left(a+b\,x\right)}^4}-\frac{4\,a\,\sqrt{a^2-b^2\,x^2}}{9\,b\,{\left(a+b\,x\right)}^5}-\frac{\sqrt{a^2-b^2\,x^2}}{105\,a\,b\,{\left(a+b\,x\right)}^3}-\frac{2\,\sqrt{a^2-b^2\,x^2}}{315\,a^2\,b\,{\left(a+b\,x\right)}^2}-\frac{2\,\sqrt{a^2-b^2\,x^2}}{315\,a^3\,b\,\left(a+b\,x\right)}","Not used",1,"(20*(a^2 - b^2*x^2)^(1/2))/(63*b*(a + b*x)^4) - (4*a*(a^2 - b^2*x^2)^(1/2))/(9*b*(a + b*x)^5) - (a^2 - b^2*x^2)^(1/2)/(105*a*b*(a + b*x)^3) - (2*(a^2 - b^2*x^2)^(1/2))/(315*a^2*b*(a + b*x)^2) - (2*(a^2 - b^2*x^2)^(1/2))/(315*a^3*b*(a + b*x))","B"
798,1,170,133,1.423059,"\text{Not used}","int((a^2 - b^2*x^2)^(3/2)/(a + b*x)^8,x)","\frac{8\,\sqrt{a^2-b^2\,x^2}}{33\,b\,{\left(a+b\,x\right)}^5}-\frac{4\,a\,\sqrt{a^2-b^2\,x^2}}{11\,b\,{\left(a+b\,x\right)}^6}-\frac{\sqrt{a^2-b^2\,x^2}}{231\,a\,b\,{\left(a+b\,x\right)}^4}-\frac{\sqrt{a^2-b^2\,x^2}}{385\,a^2\,b\,{\left(a+b\,x\right)}^3}-\frac{2\,\sqrt{a^2-b^2\,x^2}}{1155\,a^3\,b\,{\left(a+b\,x\right)}^2}-\frac{2\,\sqrt{a^2-b^2\,x^2}}{1155\,a^4\,b\,\left(a+b\,x\right)}","Not used",1,"(8*(a^2 - b^2*x^2)^(1/2))/(33*b*(a + b*x)^5) - (4*a*(a^2 - b^2*x^2)^(1/2))/(11*b*(a + b*x)^6) - (a^2 - b^2*x^2)^(1/2)/(231*a*b*(a + b*x)^4) - (a^2 - b^2*x^2)^(1/2)/(385*a^2*b*(a + b*x)^3) - (2*(a^2 - b^2*x^2)^(1/2))/(1155*a^3*b*(a + b*x)^2) - (2*(a^2 - b^2*x^2)^(1/2))/(1155*a^4*b*(a + b*x))","B"
799,1,199,166,1.703432,"\text{Not used}","int((a^2 - b^2*x^2)^(3/2)/(a + b*x)^9,x)","\frac{28\,\sqrt{a^2-b^2\,x^2}}{143\,b\,{\left(a+b\,x\right)}^6}-\frac{4\,a\,\sqrt{a^2-b^2\,x^2}}{13\,b\,{\left(a+b\,x\right)}^7}-\frac{\sqrt{a^2-b^2\,x^2}}{429\,a\,b\,{\left(a+b\,x\right)}^5}-\frac{4\,\sqrt{a^2-b^2\,x^2}}{3003\,a^2\,b\,{\left(a+b\,x\right)}^4}-\frac{4\,\sqrt{a^2-b^2\,x^2}}{5005\,a^3\,b\,{\left(a+b\,x\right)}^3}-\frac{8\,\sqrt{a^2-b^2\,x^2}}{15015\,a^4\,b\,{\left(a+b\,x\right)}^2}-\frac{8\,\sqrt{a^2-b^2\,x^2}}{15015\,a^5\,b\,\left(a+b\,x\right)}","Not used",1,"(28*(a^2 - b^2*x^2)^(1/2))/(143*b*(a + b*x)^6) - (4*a*(a^2 - b^2*x^2)^(1/2))/(13*b*(a + b*x)^7) - (a^2 - b^2*x^2)^(1/2)/(429*a*b*(a + b*x)^5) - (4*(a^2 - b^2*x^2)^(1/2))/(3003*a^2*b*(a + b*x)^4) - (4*(a^2 - b^2*x^2)^(1/2))/(5005*a^3*b*(a + b*x)^3) - (8*(a^2 - b^2*x^2)^(1/2))/(15015*a^4*b*(a + b*x)^2) - (8*(a^2 - b^2*x^2)^(1/2))/(15015*a^5*b*(a + b*x))","B"
800,0,-1,212,0.000000,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)*(d + e*x)^3,x)","\int {\left(d^2-e^2\,x^2\right)}^{7/2}\,{\left(d+e\,x\right)}^3 \,d x","Not used",1,"int((d^2 - e^2*x^2)^(7/2)*(d + e*x)^3, x)","F"
801,0,-1,179,0.000000,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)*(d + e*x)^2,x)","\int {\left(d^2-e^2\,x^2\right)}^{7/2}\,{\left(d+e\,x\right)}^2 \,d x","Not used",1,"int((d^2 - e^2*x^2)^(7/2)*(d + e*x)^2, x)","F"
802,1,67,148,0.851358,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)*(d + e*x),x)","\frac{d\,x\,{\left(d^2-e^2\,x^2\right)}^{7/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{2},\frac{1}{2};\ \frac{3}{2};\ \frac{e^2\,x^2}{d^2}\right)}{{\left(1-\frac{e^2\,x^2}{d^2}\right)}^{7/2}}-\frac{{\left(d^2-e^2\,x^2\right)}^{9/2}}{9\,e}","Not used",1,"(d*x*(d^2 - e^2*x^2)^(7/2)*hypergeom([-7/2, 1/2], 3/2, (e^2*x^2)/d^2))/(1 - (e^2*x^2)/d^2)^(7/2) - (d^2 - e^2*x^2)^(9/2)/(9*e)","B"
803,0,-1,124,0.000000,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)/(d + e*x),x)","\int \frac{{\left(d^2-e^2\,x^2\right)}^{7/2}}{d+e\,x} \,d x","Not used",1,"int((d^2 - e^2*x^2)^(7/2)/(d + e*x), x)","F"
804,0,-1,132,0.000000,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^2,x)","\int \frac{{\left(d^2-e^2\,x^2\right)}^{7/2}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^2, x)","F"
805,0,-1,142,0.000000,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^3,x)","\int \frac{{\left(d^2-e^2\,x^2\right)}^{7/2}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^3, x)","F"
806,0,-1,136,0.000000,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^4,x)","\int \frac{{\left(d^2-e^2\,x^2\right)}^{7/2}}{{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^4, x)","F"
807,0,-1,132,0.000000,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^5,x)","\int \frac{{\left(d^2-e^2\,x^2\right)}^{7/2}}{{\left(d+e\,x\right)}^5} \,d x","Not used",1,"int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^5, x)","F"
808,0,-1,145,0.000000,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^6,x)","\int \frac{{\left(d^2-e^2\,x^2\right)}^{7/2}}{{\left(d+e\,x\right)}^6} \,d x","Not used",1,"int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^6, x)","F"
809,0,-1,138,0.000000,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^7,x)","\int \frac{{\left(d^2-e^2\,x^2\right)}^{7/2}}{{\left(d+e\,x\right)}^7} \,d x","Not used",1,"int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^7, x)","F"
810,0,-1,143,0.000000,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^8,x)","\int \frac{{\left(d^2-e^2\,x^2\right)}^{7/2}}{{\left(d+e\,x\right)}^8} \,d x","Not used",1,"int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^8, x)","F"
811,1,141,33,1.619638,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^9,x)","\frac{8\,\sqrt{d^2-e^2\,x^2}}{9\,e\,{\left(d+e\,x\right)}^2}-\frac{8\,d\,\sqrt{d^2-e^2\,x^2}}{3\,e\,{\left(d+e\,x\right)}^3}-\frac{\sqrt{d^2-e^2\,x^2}}{9\,d\,e\,\left(d+e\,x\right)}+\frac{32\,d^2\,\sqrt{d^2-e^2\,x^2}}{9\,e\,{\left(d+e\,x\right)}^4}-\frac{16\,d^3\,\sqrt{d^2-e^2\,x^2}}{9\,e\,{\left(d+e\,x\right)}^5}","Not used",1,"(8*(d^2 - e^2*x^2)^(1/2))/(9*e*(d + e*x)^2) - (8*d*(d^2 - e^2*x^2)^(1/2))/(3*e*(d + e*x)^3) - (d^2 - e^2*x^2)^(1/2)/(9*d*e*(d + e*x)) + (32*d^2*(d^2 - e^2*x^2)^(1/2))/(9*e*(d + e*x)^4) - (16*d^3*(d^2 - e^2*x^2)^(1/2))/(9*e*(d + e*x)^5)","B"
812,1,170,67,2.116083,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^10,x)","\frac{16\,\sqrt{d^2-e^2\,x^2}}{33\,e\,{\left(d+e\,x\right)}^3}-\frac{184\,d\,\sqrt{d^2-e^2\,x^2}}{99\,e\,{\left(d+e\,x\right)}^4}-\frac{\sqrt{d^2-e^2\,x^2}}{99\,d\,e\,{\left(d+e\,x\right)}^2}-\frac{\sqrt{d^2-e^2\,x^2}}{99\,d^2\,e\,\left(d+e\,x\right)}+\frac{272\,d^2\,\sqrt{d^2-e^2\,x^2}}{99\,e\,{\left(d+e\,x\right)}^5}-\frac{16\,d^3\,\sqrt{d^2-e^2\,x^2}}{11\,e\,{\left(d+e\,x\right)}^6}","Not used",1,"(16*(d^2 - e^2*x^2)^(1/2))/(33*e*(d + e*x)^3) - (184*d*(d^2 - e^2*x^2)^(1/2))/(99*e*(d + e*x)^4) - (d^2 - e^2*x^2)^(1/2)/(99*d*e*(d + e*x)^2) - (d^2 - e^2*x^2)^(1/2)/(99*d^2*e*(d + e*x)) + (272*d^2*(d^2 - e^2*x^2)^(1/2))/(99*e*(d + e*x)^5) - (16*d^3*(d^2 - e^2*x^2)^(1/2))/(11*e*(d + e*x)^6)","B"
813,1,199,100,2.529340,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^11,x)","\frac{424\,\sqrt{d^2-e^2\,x^2}}{1287\,e\,{\left(d+e\,x\right)}^4}-\frac{1832\,d\,\sqrt{d^2-e^2\,x^2}}{1287\,e\,{\left(d+e\,x\right)}^5}-\frac{\sqrt{d^2-e^2\,x^2}}{429\,d\,e\,{\left(d+e\,x\right)}^3}-\frac{2\,\sqrt{d^2-e^2\,x^2}}{1287\,d^2\,e\,{\left(d+e\,x\right)}^2}-\frac{2\,\sqrt{d^2-e^2\,x^2}}{1287\,d^3\,e\,\left(d+e\,x\right)}+\frac{320\,d^2\,\sqrt{d^2-e^2\,x^2}}{143\,e\,{\left(d+e\,x\right)}^6}-\frac{16\,d^3\,\sqrt{d^2-e^2\,x^2}}{13\,e\,{\left(d+e\,x\right)}^7}","Not used",1,"(424*(d^2 - e^2*x^2)^(1/2))/(1287*e*(d + e*x)^4) - (1832*d*(d^2 - e^2*x^2)^(1/2))/(1287*e*(d + e*x)^5) - (d^2 - e^2*x^2)^(1/2)/(429*d*e*(d + e*x)^3) - (2*(d^2 - e^2*x^2)^(1/2))/(1287*d^2*e*(d + e*x)^2) - (2*(d^2 - e^2*x^2)^(1/2))/(1287*d^3*e*(d + e*x)) + (320*d^2*(d^2 - e^2*x^2)^(1/2))/(143*e*(d + e*x)^6) - (16*d^3*(d^2 - e^2*x^2)^(1/2))/(13*e*(d + e*x)^7)","B"
814,1,228,133,3.024665,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^12,x)","\frac{320\,\sqrt{d^2-e^2\,x^2}}{1287\,e\,{\left(d+e\,x\right)}^5}-\frac{824\,d\,\sqrt{d^2-e^2\,x^2}}{715\,e\,{\left(d+e\,x\right)}^6}-\frac{\sqrt{d^2-e^2\,x^2}}{1287\,d\,e\,{\left(d+e\,x\right)}^4}-\frac{\sqrt{d^2-e^2\,x^2}}{2145\,d^2\,e\,{\left(d+e\,x\right)}^3}-\frac{2\,\sqrt{d^2-e^2\,x^2}}{6435\,d^3\,e\,{\left(d+e\,x\right)}^2}-\frac{2\,\sqrt{d^2-e^2\,x^2}}{6435\,d^4\,e\,\left(d+e\,x\right)}+\frac{368\,d^2\,\sqrt{d^2-e^2\,x^2}}{195\,e\,{\left(d+e\,x\right)}^7}-\frac{16\,d^3\,\sqrt{d^2-e^2\,x^2}}{15\,e\,{\left(d+e\,x\right)}^8}","Not used",1,"(320*(d^2 - e^2*x^2)^(1/2))/(1287*e*(d + e*x)^5) - (824*d*(d^2 - e^2*x^2)^(1/2))/(715*e*(d + e*x)^6) - (d^2 - e^2*x^2)^(1/2)/(1287*d*e*(d + e*x)^4) - (d^2 - e^2*x^2)^(1/2)/(2145*d^2*e*(d + e*x)^3) - (2*(d^2 - e^2*x^2)^(1/2))/(6435*d^3*e*(d + e*x)^2) - (2*(d^2 - e^2*x^2)^(1/2))/(6435*d^4*e*(d + e*x)) + (368*d^2*(d^2 - e^2*x^2)^(1/2))/(195*e*(d + e*x)^7) - (16*d^3*(d^2 - e^2*x^2)^(1/2))/(15*e*(d + e*x)^8)","B"
815,1,257,166,3.549841,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)/(d + e*x)^13,x)","\frac{2424\,\sqrt{d^2-e^2\,x^2}}{12155\,e\,{\left(d+e\,x\right)}^6}-\frac{3208\,d\,\sqrt{d^2-e^2\,x^2}}{3315\,e\,{\left(d+e\,x\right)}^7}-\frac{7\,\sqrt{d^2-e^2\,x^2}}{21879\,d\,e\,{\left(d+e\,x\right)}^5}-\frac{4\,\sqrt{d^2-e^2\,x^2}}{21879\,d^2\,e\,{\left(d+e\,x\right)}^4}-\frac{4\,\sqrt{d^2-e^2\,x^2}}{36465\,d^3\,e\,{\left(d+e\,x\right)}^3}-\frac{8\,\sqrt{d^2-e^2\,x^2}}{109395\,d^4\,e\,{\left(d+e\,x\right)}^2}-\frac{8\,\sqrt{d^2-e^2\,x^2}}{109395\,d^5\,e\,\left(d+e\,x\right)}+\frac{416\,d^2\,\sqrt{d^2-e^2\,x^2}}{255\,e\,{\left(d+e\,x\right)}^8}-\frac{16\,d^3\,\sqrt{d^2-e^2\,x^2}}{17\,e\,{\left(d+e\,x\right)}^9}","Not used",1,"(2424*(d^2 - e^2*x^2)^(1/2))/(12155*e*(d + e*x)^6) - (3208*d*(d^2 - e^2*x^2)^(1/2))/(3315*e*(d + e*x)^7) - (7*(d^2 - e^2*x^2)^(1/2))/(21879*d*e*(d + e*x)^5) - (4*(d^2 - e^2*x^2)^(1/2))/(21879*d^2*e*(d + e*x)^4) - (4*(d^2 - e^2*x^2)^(1/2))/(36465*d^3*e*(d + e*x)^3) - (8*(d^2 - e^2*x^2)^(1/2))/(109395*d^4*e*(d + e*x)^2) - (8*(d^2 - e^2*x^2)^(1/2))/(109395*d^5*e*(d + e*x)) + (416*d^2*(d^2 - e^2*x^2)^(1/2))/(255*e*(d + e*x)^8) - (16*d^3*(d^2 - e^2*x^2)^(1/2))/(17*e*(d + e*x)^9)","B"
816,0,-1,47,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^(1/2)/(a - b*x),x)","\int \frac{\sqrt{a^2-b^2\,x^2}}{a-b\,x} \,d x","Not used",1,"int((a^2 - b^2*x^2)^(1/2)/(a - b*x), x)","F"
817,0,-1,130,0.000000,"\text{Not used}","int((c*x^2 - (a^2*c)/b^2)^(1/2)*(a + b*x)^2,x)","\int \sqrt{c\,x^2-\frac{a^2\,c}{b^2}}\,{\left(a+b\,x\right)}^2 \,d x","Not used",1,"int((c*x^2 - (a^2*c)/b^2)^(1/2)*(a + b*x)^2, x)","F"
818,0,-1,167,0.000000,"\text{Not used}","int((c*x^2 - (a^2*c)/b^2)^(1/2)*(a + b*x)^3,x)","\int \sqrt{c\,x^2-\frac{a^2\,c}{b^2}}\,{\left(a+b\,x\right)}^3 \,d x","Not used",1,"int((c*x^2 - (a^2*c)/b^2)^(1/2)*(a + b*x)^3, x)","F"
819,1,32,44,0.561303,"\text{Not used}","int((x^2 - 1)^(1/2)*(x + 1),x)","\frac{x\,\sqrt{x^2-1}}{2}-\frac{\ln\left(x+\sqrt{x^2-1}\right)}{2}+\frac{{\left(x^2-1\right)}^{3/2}}{3}","Not used",1,"(x*(x^2 - 1)^(1/2))/2 - log(x + (x^2 - 1)^(1/2))/2 + (x^2 - 1)^(3/2)/3","B"
820,1,25,38,0.029321,"\text{Not used}","int((1 - x^2)^(1/2)*(x + 1),x)","\frac{\mathrm{asin}\left(x\right)}{2}+\sqrt{1-x^2}\,\left(\frac{x^2}{3}+\frac{x}{2}-\frac{1}{3}\right)","Not used",1,"asin(x)/2 + (1 - x^2)^(1/2)*(x/2 + x^2/3 - 1/3)","B"
821,1,12,14,0.476475,"\text{Not used}","int((1 - x^2)^(1/2)/(x + 1),x)","\mathrm{asin}\left(x\right)+\sqrt{1-x^2}","Not used",1,"asin(x) + (1 - x^2)^(1/2)","B"
822,1,25,38,0.027585,"\text{Not used}","int(-(1 - x^2)^(1/2)*(x - 1),x)","\frac{\mathrm{asin}\left(x\right)}{2}+\sqrt{1-x^2}\,\left(-\frac{x^2}{3}+\frac{x}{2}+\frac{1}{3}\right)","Not used",1,"asin(x)/2 + (1 - x^2)^(1/2)*(x/2 - x^2/3 + 1/3)","B"
823,1,14,16,0.024374,"\text{Not used}","int(-(1 - x^2)^(1/2)/(x - 1),x)","\mathrm{asin}\left(x\right)-\sqrt{1-x^2}","Not used",1,"asin(x) - (1 - x^2)^(1/2)","B"
824,1,21,25,0.038415,"\text{Not used}","int((1 - x^2)^(1/2)/(x - 1)^2,x)","-\mathrm{asin}\left(x\right)-\frac{2\,\sqrt{1-x^2}}{x-1}","Not used",1,"- asin(x) - (2*(1 - x^2)^(1/2))/(x - 1)","B"
825,1,19,22,0.387954,"\text{Not used}","int(-(1 - x^2)^(1/2)/(x - 1)^3,x)","\frac{\sqrt{1-x^2}\,\left(x+1\right)}{3\,{\left(x-1\right)}^2}","Not used",1,"((1 - x^2)^(1/2)*(x + 1))/(3*(x - 1)^2)","B"
826,0,-1,182,0.000000,"\text{Not used}","int((d + e*x)^5/(d^2 - e^2*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^5}{\sqrt{d^2-e^2\,x^2}} \,d x","Not used",1,"int((d + e*x)^5/(d^2 - e^2*x^2)^(1/2), x)","F"
827,0,-1,149,0.000000,"\text{Not used}","int((d + e*x)^4/(d^2 - e^2*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{\sqrt{d^2-e^2\,x^2}} \,d x","Not used",1,"int((d + e*x)^4/(d^2 - e^2*x^2)^(1/2), x)","F"
828,0,-1,116,0.000000,"\text{Not used}","int((d + e*x)^3/(d^2 - e^2*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^3}{\sqrt{d^2-e^2\,x^2}} \,d x","Not used",1,"int((d + e*x)^3/(d^2 - e^2*x^2)^(1/2), x)","F"
829,0,-1,74,0.000000,"\text{Not used}","int((d + e*x)^2/(d^2 - e^2*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^2}{\sqrt{d^2-e^2\,x^2}} \,d x","Not used",1,"int((d + e*x)^2/(d^2 - e^2*x^2)^(1/2), x)","F"
830,1,54,47,0.933111,"\text{Not used}","int((d + e*x)/(d^2 - e^2*x^2)^(1/2),x)","\frac{d\,\ln\left(x\,\sqrt{-e^2}+\sqrt{d^2-e^2\,x^2}\right)}{\sqrt{-e^2}}-\frac{\sqrt{d^2-e^2\,x^2}}{e}","Not used",1,"(d*log(x*(-e^2)^(1/2) + (d^2 - e^2*x^2)^(1/2)))/(-e^2)^(1/2) - (d^2 - e^2*x^2)^(1/2)/e","B"
831,1,29,31,0.435445,"\text{Not used}","int(1/((d^2 - e^2*x^2)^(1/2)*(d + e*x)),x)","-\frac{\sqrt{d^2-e^2\,x^2}}{d\,e\,\left(d+e\,x\right)}","Not used",1,"-(d^2 - e^2*x^2)^(1/2)/(d*e*(d + e*x))","B"
832,1,36,67,0.454066,"\text{Not used}","int(1/((d^2 - e^2*x^2)^(1/2)*(d + e*x)^2),x)","-\frac{\sqrt{d^2-e^2\,x^2}\,\left(2\,d+e\,x\right)}{3\,d^2\,e\,{\left(d+e\,x\right)}^2}","Not used",1,"-((d^2 - e^2*x^2)^(1/2)*(2*d + e*x))/(3*d^2*e*(d + e*x)^2)","B"
833,1,48,100,0.486863,"\text{Not used}","int(1/((d^2 - e^2*x^2)^(1/2)*(d + e*x)^3),x)","-\frac{\sqrt{d^2-e^2\,x^2}\,\left(7\,d^2+6\,d\,e\,x+2\,e^2\,x^2\right)}{15\,d^3\,e\,{\left(d+e\,x\right)}^3}","Not used",1,"-((d^2 - e^2*x^2)^(1/2)*(7*d^2 + 2*e^2*x^2 + 6*d*e*x))/(15*d^3*e*(d + e*x)^3)","B"
834,1,117,133,0.479719,"\text{Not used}","int(1/((d^2 - e^2*x^2)^(1/2)*(d + e*x)^4),x)","-\frac{\sqrt{d^2-e^2\,x^2}}{7\,d\,e\,{\left(d+e\,x\right)}^4}-\frac{3\,\sqrt{d^2-e^2\,x^2}}{35\,d^2\,e\,{\left(d+e\,x\right)}^3}-\frac{2\,\sqrt{d^2-e^2\,x^2}}{35\,d^3\,e\,{\left(d+e\,x\right)}^2}-\frac{2\,\sqrt{d^2-e^2\,x^2}}{35\,d^4\,e\,\left(d+e\,x\right)}","Not used",1,"- (d^2 - e^2*x^2)^(1/2)/(7*d*e*(d + e*x)^4) - (3*(d^2 - e^2*x^2)^(1/2))/(35*d^2*e*(d + e*x)^3) - (2*(d^2 - e^2*x^2)^(1/2))/(35*d^3*e*(d + e*x)^2) - (2*(d^2 - e^2*x^2)^(1/2))/(35*d^4*e*(d + e*x))","B"
835,1,146,166,0.470064,"\text{Not used}","int(1/((d^2 - e^2*x^2)^(1/2)*(d + e*x)^5),x)","-\frac{\sqrt{d^2-e^2\,x^2}}{9\,d\,e\,{\left(d+e\,x\right)}^5}-\frac{4\,\sqrt{d^2-e^2\,x^2}}{63\,d^2\,e\,{\left(d+e\,x\right)}^4}-\frac{4\,\sqrt{d^2-e^2\,x^2}}{105\,d^3\,e\,{\left(d+e\,x\right)}^3}-\frac{8\,\sqrt{d^2-e^2\,x^2}}{315\,d^4\,e\,{\left(d+e\,x\right)}^2}-\frac{8\,\sqrt{d^2-e^2\,x^2}}{315\,d^5\,e\,\left(d+e\,x\right)}","Not used",1,"- (d^2 - e^2*x^2)^(1/2)/(9*d*e*(d + e*x)^5) - (4*(d^2 - e^2*x^2)^(1/2))/(63*d^2*e*(d + e*x)^4) - (4*(d^2 - e^2*x^2)^(1/2))/(105*d^3*e*(d + e*x)^3) - (8*(d^2 - e^2*x^2)^(1/2))/(315*d^4*e*(d + e*x)^2) - (8*(d^2 - e^2*x^2)^(1/2))/(315*d^5*e*(d + e*x))","B"
836,0,-1,143,0.000000,"\text{Not used}","int((d + e*x)^6/(d^2 - e^2*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^6}{{\left(d^2-e^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^6/(d^2 - e^2*x^2)^(5/2), x)","F"
837,0,-1,108,0.000000,"\text{Not used}","int((d + e*x)^5/(d^2 - e^2*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^5}{{\left(d^2-e^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^5/(d^2 - e^2*x^2)^(5/2), x)","F"
838,0,-1,81,0.000000,"\text{Not used}","int((d + e*x)^4/(d^2 - e^2*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{{\left(d^2-e^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^4/(d^2 - e^2*x^2)^(5/2), x)","F"
839,1,35,33,0.570843,"\text{Not used}","int((d + e*x)^3/(d^2 - e^2*x^2)^(5/2),x)","\frac{\sqrt{d^2-e^2\,x^2}\,\left(d+e\,x\right)}{3\,d\,e\,{\left(d-e\,x\right)}^2}","Not used",1,"((d^2 - e^2*x^2)^(1/2)*(d + e*x))/(3*d*e*(d - e*x)^2)","B"
840,1,38,53,0.483317,"\text{Not used}","int((d + e*x)^2/(d^2 - e^2*x^2)^(5/2),x)","\frac{\sqrt{d^2-e^2\,x^2}\,\left(2\,d-e\,x\right)}{3\,d^2\,e\,{\left(d-e\,x\right)}^2}","Not used",1,"((d^2 - e^2*x^2)^(1/2)*(2*d - e*x))/(3*d^2*e*(d - e*x)^2)","B"
841,1,54,56,0.524415,"\text{Not used}","int((d + e*x)/(d^2 - e^2*x^2)^(5/2),x)","\frac{\sqrt{d^2-e^2\,x^2}\,\left(d^2+2\,d\,e\,x-2\,e^2\,x^2\right)}{3\,d^3\,e\,\left(d+e\,x\right)\,{\left(d-e\,x\right)}^2}","Not used",1,"((d^2 - e^2*x^2)^(1/2)*(d^2 - 2*e^2*x^2 + 2*d*e*x))/(3*d^3*e*(d + e*x)*(d - e*x)^2)","B"
842,1,78,82,0.582265,"\text{Not used}","int(1/((d^2 - e^2*x^2)^(5/2)*(d + e*x)),x)","-\frac{\sqrt{d^2-e^2\,x^2}\,\left(3\,d^4-12\,d^3\,e\,x-12\,d^2\,e^2\,x^2+8\,d\,e^3\,x^3+8\,e^4\,x^4\right)}{15\,d^5\,e\,{\left(d+e\,x\right)}^3\,{\left(d-e\,x\right)}^2}","Not used",1,"-((d^2 - e^2*x^2)^(1/2)*(3*d^4 + 8*e^4*x^4 + 8*d*e^3*x^3 - 12*d^2*e^2*x^2 - 12*d^3*e*x))/(15*d^5*e*(d + e*x)^3*(d - e*x)^2)","B"
843,1,139,115,0.643348,"\text{Not used}","int(1/((d^2 - e^2*x^2)^(5/2)*(d + e*x)^2),x)","\frac{\sqrt{d^2-e^2\,x^2}\,\left(\frac{11\,x}{42\,d^4}-\frac{5}{28\,d^3\,e}\right)}{{\left(d+e\,x\right)}^2\,{\left(d-e\,x\right)}^2}-\frac{\sqrt{d^2-e^2\,x^2}}{28\,d^3\,e\,{\left(d+e\,x\right)}^4}-\frac{\sqrt{d^2-e^2\,x^2}}{14\,d^4\,e\,{\left(d+e\,x\right)}^3}+\frac{8\,x\,\sqrt{d^2-e^2\,x^2}}{21\,d^6\,\left(d+e\,x\right)\,\left(d-e\,x\right)}","Not used",1,"((d^2 - e^2*x^2)^(1/2)*((11*x)/(42*d^4) - 5/(28*d^3*e)))/((d + e*x)^2*(d - e*x)^2) - (d^2 - e^2*x^2)^(1/2)/(28*d^3*e*(d + e*x)^4) - (d^2 - e^2*x^2)^(1/2)/(14*d^4*e*(d + e*x)^3) + (8*x*(d^2 - e^2*x^2)^(1/2))/(21*d^6*(d + e*x)*(d - e*x))","B"
844,1,168,148,0.711735,"\text{Not used}","int(1/((d^2 - e^2*x^2)^(5/2)*(d + e*x)^3),x)","\frac{\sqrt{d^2-e^2\,x^2}\,\left(\frac{197\,x}{1008\,d^5}-\frac{155}{1008\,d^4\,e}\right)}{{\left(d+e\,x\right)}^2\,{\left(d-e\,x\right)}^2}-\frac{\sqrt{d^2-e^2\,x^2}}{36\,d^3\,e\,{\left(d+e\,x\right)}^5}-\frac{13\,\sqrt{d^2-e^2\,x^2}}{252\,d^4\,e\,{\left(d+e\,x\right)}^4}-\frac{23\,\sqrt{d^2-e^2\,x^2}}{336\,d^5\,e\,{\left(d+e\,x\right)}^3}+\frac{16\,x\,\sqrt{d^2-e^2\,x^2}}{63\,d^7\,\left(d+e\,x\right)\,\left(d-e\,x\right)}","Not used",1,"((d^2 - e^2*x^2)^(1/2)*((197*x)/(1008*d^5) - 155/(1008*d^4*e)))/((d + e*x)^2*(d - e*x)^2) - (d^2 - e^2*x^2)^(1/2)/(36*d^3*e*(d + e*x)^5) - (13*(d^2 - e^2*x^2)^(1/2))/(252*d^4*e*(d + e*x)^4) - (23*(d^2 - e^2*x^2)^(1/2))/(336*d^5*e*(d + e*x)^3) + (16*x*(d^2 - e^2*x^2)^(1/2))/(63*d^7*(d + e*x)*(d - e*x))","B"
845,1,197,181,0.808037,"\text{Not used}","int(1/((d^2 - e^2*x^2)^(5/2)*(d + e*x)^4),x)","\frac{\sqrt{d^2-e^2\,x^2}\,\left(\frac{215\,x}{1584\,d^6}-\frac{91}{792\,d^5\,e}\right)}{{\left(d+e\,x\right)}^2\,{\left(d-e\,x\right)}^2}-\frac{\sqrt{d^2-e^2\,x^2}}{44\,d^3\,e\,{\left(d+e\,x\right)}^6}-\frac{4\,\sqrt{d^2-e^2\,x^2}}{99\,d^4\,e\,{\left(d+e\,x\right)}^5}-\frac{79\,\sqrt{d^2-e^2\,x^2}}{1584\,d^5\,e\,{\left(d+e\,x\right)}^4}-\frac{29\,\sqrt{d^2-e^2\,x^2}}{528\,d^6\,e\,{\left(d+e\,x\right)}^3}+\frac{16\,x\,\sqrt{d^2-e^2\,x^2}}{99\,d^8\,\left(d+e\,x\right)\,\left(d-e\,x\right)}","Not used",1,"((d^2 - e^2*x^2)^(1/2)*((215*x)/(1584*d^6) - 91/(792*d^5*e)))/((d + e*x)^2*(d - e*x)^2) - (d^2 - e^2*x^2)^(1/2)/(44*d^3*e*(d + e*x)^6) - (4*(d^2 - e^2*x^2)^(1/2))/(99*d^4*e*(d + e*x)^5) - (79*(d^2 - e^2*x^2)^(1/2))/(1584*d^5*e*(d + e*x)^4) - (29*(d^2 - e^2*x^2)^(1/2))/(528*d^6*e*(d + e*x)^3) + (16*x*(d^2 - e^2*x^2)^(1/2))/(99*d^8*(d + e*x)*(d - e*x))","B"
846,0,-1,206,0.000000,"\text{Not used}","int((d + e*x)^9/(d^2 - e^2*x^2)^(7/2),x)","\int \frac{{\left(d+e\,x\right)}^9}{{\left(d^2-e^2\,x^2\right)}^{7/2}} \,d x","Not used",1,"int((d + e*x)^9/(d^2 - e^2*x^2)^(7/2), x)","F"
847,0,-1,173,0.000000,"\text{Not used}","int((d + e*x)^8/(d^2 - e^2*x^2)^(7/2),x)","\int \frac{{\left(d+e\,x\right)}^8}{{\left(d^2-e^2\,x^2\right)}^{7/2}} \,d x","Not used",1,"int((d + e*x)^8/(d^2 - e^2*x^2)^(7/2), x)","F"
848,0,-1,138,0.000000,"\text{Not used}","int((d + e*x)^7/(d^2 - e^2*x^2)^(7/2),x)","\int \frac{{\left(d+e\,x\right)}^7}{{\left(d^2-e^2\,x^2\right)}^{7/2}} \,d x","Not used",1,"int((d + e*x)^7/(d^2 - e^2*x^2)^(7/2), x)","F"
849,0,-1,112,0.000000,"\text{Not used}","int((d + e*x)^6/(d^2 - e^2*x^2)^(7/2),x)","\int \frac{{\left(d+e\,x\right)}^6}{{\left(d^2-e^2\,x^2\right)}^{7/2}} \,d x","Not used",1,"int((d + e*x)^6/(d^2 - e^2*x^2)^(7/2), x)","F"
850,1,37,33,0.865010,"\text{Not used}","int((d + e*x)^5/(d^2 - e^2*x^2)^(7/2),x)","\frac{\sqrt{d^2-e^2\,x^2}\,{\left(d+e\,x\right)}^2}{5\,d\,e\,{\left(d-e\,x\right)}^3}","Not used",1,"((d^2 - e^2*x^2)^(1/2)*(d + e*x)^2)/(5*d*e*(d - e*x)^3)","B"
851,1,49,67,0.682881,"\text{Not used}","int((d + e*x)^4/(d^2 - e^2*x^2)^(7/2),x)","\frac{\sqrt{d^2-e^2\,x^2}\,\left(4\,d^2+3\,d\,e\,x-e^2\,x^2\right)}{15\,d^2\,e\,{\left(d-e\,x\right)}^3}","Not used",1,"((d^2 - e^2*x^2)^(1/2)*(4*d^2 - e^2*x^2 + 3*d*e*x))/(15*d^2*e*(d - e*x)^3)","B"
852,1,49,103,0.516349,"\text{Not used}","int((d + e*x)^3/(d^2 - e^2*x^2)^(7/2),x)","\frac{\sqrt{d^2-e^2\,x^2}\,\left(7\,d^2-6\,d\,e\,x+2\,e^2\,x^2\right)}{15\,d^3\,e\,{\left(d-e\,x\right)}^3}","Not used",1,"((d^2 - e^2*x^2)^(1/2)*(7*d^2 + 2*e^2*x^2 - 6*d*e*x))/(15*d^3*e*(d - e*x)^3)","B"
853,1,66,77,0.603317,"\text{Not used}","int((d + e*x)^2/(d^2 - e^2*x^2)^(7/2),x)","\frac{\sqrt{d^2-e^2\,x^2}\,\left(2\,d^3+d^2\,e\,x-4\,d\,e^2\,x^2+2\,e^3\,x^3\right)}{5\,d^4\,e\,\left(d+e\,x\right)\,{\left(d-e\,x\right)}^3}","Not used",1,"((d^2 - e^2*x^2)^(1/2)*(2*d^3 + 2*e^3*x^3 - 4*d*e^2*x^2 + d^2*e*x))/(5*d^4*e*(d + e*x)*(d - e*x)^3)","B"
854,1,78,80,0.592378,"\text{Not used}","int((d + e*x)/(d^2 - e^2*x^2)^(7/2),x)","\frac{\sqrt{d^2-e^2\,x^2}\,\left(3\,d^4+12\,d^3\,e\,x-12\,d^2\,e^2\,x^2-8\,d\,e^3\,x^3+8\,e^4\,x^4\right)}{15\,d^5\,e\,{\left(d+e\,x\right)}^2\,{\left(d-e\,x\right)}^3}","Not used",1,"((d^2 - e^2*x^2)^(1/2)*(3*d^4 + 8*e^4*x^4 - 8*d*e^3*x^3 - 12*d^2*e^2*x^2 + 12*d^3*e*x))/(15*d^5*e*(d + e*x)^2*(d - e*x)^3)","B"
855,1,155,106,0.631462,"\text{Not used}","int(1/((d^2 - e^2*x^2)^(7/2)*(d + e*x)),x)","\frac{\sqrt{d^2-e^2\,x^2}\,\left(\frac{17\,x}{70\,d^3}-\frac{1}{7\,d^2\,e}\right)}{{\left(d+e\,x\right)}^3\,{\left(d-e\,x\right)}^3}+\frac{\sqrt{d^2-e^2\,x^2}\,\left(\frac{8\,x}{35\,d^5}+\frac{1}{56\,d^4\,e}\right)}{{\left(d+e\,x\right)}^2\,{\left(d-e\,x\right)}^2}-\frac{\sqrt{d^2-e^2\,x^2}}{56\,d^4\,e\,{\left(d+e\,x\right)}^4}+\frac{16\,x\,\sqrt{d^2-e^2\,x^2}}{35\,d^7\,\left(d+e\,x\right)\,\left(d-e\,x\right)}","Not used",1,"((d^2 - e^2*x^2)^(1/2)*((17*x)/(70*d^3) - 1/(7*d^2*e)))/((d + e*x)^3*(d - e*x)^3) + ((d^2 - e^2*x^2)^(1/2)*((8*x)/(35*d^5) + 1/(56*d^4*e)))/((d + e*x)^2*(d - e*x)^2) - (d^2 - e^2*x^2)^(1/2)/(56*d^4*e*(d + e*x)^4) + (16*x*(d^2 - e^2*x^2)^(1/2))/(35*d^7*(d + e*x)*(d - e*x))","B"
856,1,184,139,0.692954,"\text{Not used}","int(1/((d^2 - e^2*x^2)^(7/2)*(d + e*x)^2),x)","\frac{\sqrt{d^2-e^2\,x^2}\,\left(\frac{31\,x}{120\,d^4}-\frac{5}{24\,d^3\,e}\right)}{{\left(d+e\,x\right)}^3\,{\left(d-e\,x\right)}^3}+\frac{\sqrt{d^2-e^2\,x^2}\,\left(\frac{8\,x}{45\,d^6}+\frac{5}{144\,d^5\,e}\right)}{{\left(d+e\,x\right)}^2\,{\left(d-e\,x\right)}^2}-\frac{\sqrt{d^2-e^2\,x^2}}{72\,d^4\,e\,{\left(d+e\,x\right)}^5}-\frac{5\,\sqrt{d^2-e^2\,x^2}}{144\,d^5\,e\,{\left(d+e\,x\right)}^4}+\frac{16\,x\,\sqrt{d^2-e^2\,x^2}}{45\,d^8\,\left(d+e\,x\right)\,\left(d-e\,x\right)}","Not used",1,"((d^2 - e^2*x^2)^(1/2)*((31*x)/(120*d^4) - 5/(24*d^3*e)))/((d + e*x)^3*(d - e*x)^3) + ((d^2 - e^2*x^2)^(1/2)*((8*x)/(45*d^6) + 5/(144*d^5*e)))/((d + e*x)^2*(d - e*x)^2) - (d^2 - e^2*x^2)^(1/2)/(72*d^4*e*(d + e*x)^5) - (5*(d^2 - e^2*x^2)^(1/2))/(144*d^5*e*(d + e*x)^4) + (16*x*(d^2 - e^2*x^2)^(1/2))/(45*d^8*(d + e*x)*(d - e*x))","B"
857,1,213,172,0.819875,"\text{Not used}","int(1/((d^2 - e^2*x^2)^(7/2)*(d + e*x)^3),x)","\frac{\sqrt{d^2-e^2\,x^2}\,\left(\frac{64\,x}{495\,d^7}+\frac{67}{1584\,d^6\,e}\right)}{{\left(d+e\,x\right)}^2\,{\left(d-e\,x\right)}^2}+\frac{\sqrt{d^2-e^2\,x^2}\,\left(\frac{631\,x}{2640\,d^5}-\frac{113}{528\,d^4\,e}\right)}{{\left(d+e\,x\right)}^3\,{\left(d-e\,x\right)}^3}-\frac{\sqrt{d^2-e^2\,x^2}}{88\,d^4\,e\,{\left(d+e\,x\right)}^6}-\frac{43\,\sqrt{d^2-e^2\,x^2}}{1584\,d^5\,e\,{\left(d+e\,x\right)}^5}-\frac{67\,\sqrt{d^2-e^2\,x^2}}{1584\,d^6\,e\,{\left(d+e\,x\right)}^4}+\frac{128\,x\,\sqrt{d^2-e^2\,x^2}}{495\,d^9\,\left(d+e\,x\right)\,\left(d-e\,x\right)}","Not used",1,"((d^2 - e^2*x^2)^(1/2)*((64*x)/(495*d^7) + 67/(1584*d^6*e)))/((d + e*x)^2*(d - e*x)^2) + ((d^2 - e^2*x^2)^(1/2)*((631*x)/(2640*d^5) - 113/(528*d^4*e)))/((d + e*x)^3*(d - e*x)^3) - (d^2 - e^2*x^2)^(1/2)/(88*d^4*e*(d + e*x)^6) - (43*(d^2 - e^2*x^2)^(1/2))/(1584*d^5*e*(d + e*x)^5) - (67*(d^2 - e^2*x^2)^(1/2))/(1584*d^6*e*(d + e*x)^4) + (128*x*(d^2 - e^2*x^2)^(1/2))/(495*d^9*(d + e*x)*(d - e*x))","B"
858,1,242,205,0.964283,"\text{Not used}","int(1/((d^2 - e^2*x^2)^(7/2)*(d + e*x)^4),x)","\frac{\sqrt{d^2-e^2\,x^2}\,\left(\frac{64\,x}{715\,d^8}+\frac{189}{4576\,d^7\,e}\right)}{{\left(d+e\,x\right)}^2\,{\left(d-e\,x\right)}^2}+\frac{\sqrt{d^2-e^2\,x^2}\,\left(\frac{1139\,x}{5720\,d^6}-\frac{427}{2288\,d^5\,e}\right)}{{\left(d+e\,x\right)}^3\,{\left(d-e\,x\right)}^3}-\frac{\sqrt{d^2-e^2\,x^2}}{104\,d^4\,e\,{\left(d+e\,x\right)}^7}-\frac{51\,\sqrt{d^2-e^2\,x^2}}{2288\,d^5\,e\,{\left(d+e\,x\right)}^6}-\frac{19\,\sqrt{d^2-e^2\,x^2}}{572\,d^6\,e\,{\left(d+e\,x\right)}^5}-\frac{189\,\sqrt{d^2-e^2\,x^2}}{4576\,d^7\,e\,{\left(d+e\,x\right)}^4}+\frac{128\,x\,\sqrt{d^2-e^2\,x^2}}{715\,d^{10}\,\left(d+e\,x\right)\,\left(d-e\,x\right)}","Not used",1,"((d^2 - e^2*x^2)^(1/2)*((64*x)/(715*d^8) + 189/(4576*d^7*e)))/((d + e*x)^2*(d - e*x)^2) + ((d^2 - e^2*x^2)^(1/2)*((1139*x)/(5720*d^6) - 427/(2288*d^5*e)))/((d + e*x)^3*(d - e*x)^3) - (d^2 - e^2*x^2)^(1/2)/(104*d^4*e*(d + e*x)^7) - (51*(d^2 - e^2*x^2)^(1/2))/(2288*d^5*e*(d + e*x)^6) - (19*(d^2 - e^2*x^2)^(1/2))/(572*d^6*e*(d + e*x)^5) - (189*(d^2 - e^2*x^2)^(1/2))/(4576*d^7*e*(d + e*x)^4) + (128*x*(d^2 - e^2*x^2)^(1/2))/(715*d^10*(d + e*x)*(d - e*x))","B"
859,1,271,238,1.136545,"\text{Not used}","int(1/((d^2 - e^2*x^2)^(7/2)*(d + e*x)^5),x)","\frac{\sqrt{d^2-e^2\,x^2}\,\left(\frac{128\,x}{2145\,d^9}+\frac{647}{18304\,d^8\,e}\right)}{{\left(d+e\,x\right)}^2\,{\left(d-e\,x\right)}^2}+\frac{\sqrt{d^2-e^2\,x^2}\,\left(\frac{1757\,x}{11440\,d^7}-\frac{3371}{22880\,d^6\,e}\right)}{{\left(d+e\,x\right)}^3\,{\left(d-e\,x\right)}^3}-\frac{\sqrt{d^2-e^2\,x^2}}{120\,d^4\,e\,{\left(d+e\,x\right)}^8}-\frac{59\,\sqrt{d^2-e^2\,x^2}}{3120\,d^5\,e\,{\left(d+e\,x\right)}^7}-\frac{313\,\sqrt{d^2-e^2\,x^2}}{11440\,d^6\,e\,{\left(d+e\,x\right)}^6}-\frac{149\,\sqrt{d^2-e^2\,x^2}}{4576\,d^7\,e\,{\left(d+e\,x\right)}^5}-\frac{647\,\sqrt{d^2-e^2\,x^2}}{18304\,d^8\,e\,{\left(d+e\,x\right)}^4}+\frac{256\,x\,\sqrt{d^2-e^2\,x^2}}{2145\,d^{11}\,\left(d+e\,x\right)\,\left(d-e\,x\right)}","Not used",1,"((d^2 - e^2*x^2)^(1/2)*((128*x)/(2145*d^9) + 647/(18304*d^8*e)))/((d + e*x)^2*(d - e*x)^2) + ((d^2 - e^2*x^2)^(1/2)*((1757*x)/(11440*d^7) - 3371/(22880*d^6*e)))/((d + e*x)^3*(d - e*x)^3) - (d^2 - e^2*x^2)^(1/2)/(120*d^4*e*(d + e*x)^8) - (59*(d^2 - e^2*x^2)^(1/2))/(3120*d^5*e*(d + e*x)^7) - (313*(d^2 - e^2*x^2)^(1/2))/(11440*d^6*e*(d + e*x)^6) - (149*(d^2 - e^2*x^2)^(1/2))/(4576*d^7*e*(d + e*x)^5) - (647*(d^2 - e^2*x^2)^(1/2))/(18304*d^8*e*(d + e*x)^4) + (256*x*(d^2 - e^2*x^2)^(1/2))/(2145*d^11*(d + e*x)*(d - e*x))","B"
860,1,14,16,0.035057,"\text{Not used}","int((x + 1)/(1 - x^2)^(1/2),x)","\mathrm{asin}\left(x\right)-\sqrt{1-x^2}","Not used",1,"asin(x) - (1 - x^2)^(1/2)","B"
861,1,12,14,0.108243,"\text{Not used}","int(-(x - 1)/(1 - x^2)^(1/2),x)","\mathrm{asin}\left(x\right)+\sqrt{1-x^2}","Not used",1,"asin(x) + (1 - x^2)^(1/2)","B"
862,1,103,160,0.631837,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(1/2)*(d + e*x)^(5/2),x)","\frac{\sqrt{c\,d^2-c\,e^2\,x^2}\,\left(\frac{104\,d^2\,x^2\,\sqrt{d+e\,x}}{105}-\frac{638\,d^4\,\sqrt{d+e\,x}}{315\,e^2}+\frac{2\,e^2\,x^4\,\sqrt{d+e\,x}}{9}+\frac{52\,d\,e\,x^3\,\sqrt{d+e\,x}}{63}-\frac{4\,d^3\,x\,\sqrt{d+e\,x}}{315\,e}\right)}{x+\frac{d}{e}}","Not used",1,"((c*d^2 - c*e^2*x^2)^(1/2)*((104*d^2*x^2*(d + e*x)^(1/2))/105 - (638*d^4*(d + e*x)^(1/2))/(315*e^2) + (2*e^2*x^4*(d + e*x)^(1/2))/9 + (52*d*e*x^3*(d + e*x)^(1/2))/63 - (4*d^3*x*(d + e*x)^(1/2))/(315*e)))/(x + d/e)","B"
863,1,85,119,0.545660,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(1/2)*(d + e*x)^(3/2),x)","\frac{\sqrt{c\,d^2-c\,e^2\,x^2}\,\left(\frac{26\,d\,x^2\,\sqrt{d+e\,x}}{35}-\frac{142\,d^3\,\sqrt{d+e\,x}}{105\,e^2}+\frac{2\,e\,x^3\,\sqrt{d+e\,x}}{7}+\frac{34\,d^2\,x\,\sqrt{d+e\,x}}{105\,e}\right)}{x+\frac{d}{e}}","Not used",1,"((c*d^2 - c*e^2*x^2)^(1/2)*((26*d*x^2*(d + e*x)^(1/2))/35 - (142*d^3*(d + e*x)^(1/2))/(105*e^2) + (2*e*x^3*(d + e*x)^(1/2))/7 + (34*d^2*x*(d + e*x)^(1/2))/(105*e)))/(x + d/e)","B"
864,1,69,78,0.516683,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(1/2)*(d + e*x)^(1/2),x)","\frac{\sqrt{c\,d^2-c\,e^2\,x^2}\,\left(\frac{2\,x^2\,\sqrt{d+e\,x}}{5}-\frac{14\,d^2\,\sqrt{d+e\,x}}{15\,e^2}+\frac{8\,d\,x\,\sqrt{d+e\,x}}{15\,e}\right)}{x+\frac{d}{e}}","Not used",1,"((c*d^2 - c*e^2*x^2)^(1/2)*((2*x^2*(d + e*x)^(1/2))/5 - (14*d^2*(d + e*x)^(1/2))/(15*e^2) + (8*d*x*(d + e*x)^(1/2))/(15*e)))/(x + d/e)","B"
865,1,35,38,0.510021,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(1/2)/(d + e*x)^(1/2),x)","\frac{\sqrt{c\,d^2-c\,e^2\,x^2}\,\left(\frac{2\,x}{3}-\frac{2\,d}{3\,e}\right)}{\sqrt{d+e\,x}}","Not used",1,"((c*d^2 - c*e^2*x^2)^(1/2)*((2*x)/3 - (2*d)/(3*e)))/(d + e*x)^(1/2)","B"
866,0,-1,99,0.000000,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(1/2)/(d + e*x)^(3/2),x)","\int \frac{\sqrt{c\,d^2-c\,e^2\,x^2}}{{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int((c*d^2 - c*e^2*x^2)^(1/2)/(d + e*x)^(3/2), x)","F"
867,0,-1,98,0.000000,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(1/2)/(d + e*x)^(5/2),x)","\int \frac{\sqrt{c\,d^2-c\,e^2\,x^2}}{{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int((c*d^2 - c*e^2*x^2)^(1/2)/(d + e*x)^(5/2), x)","F"
868,0,-1,141,0.000000,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(1/2)/(d + e*x)^(7/2),x)","\int \frac{\sqrt{c\,d^2-c\,e^2\,x^2}}{{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int((c*d^2 - c*e^2*x^2)^(1/2)/(d + e*x)^(7/2), x)","F"
869,1,116,201,0.700562,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(3/2)*(d + e*x)^(5/2),x)","-\frac{16384\,c\,d^6\,\sqrt{c\,d^2-c\,e^2\,x^2}}{15015\,e\,\sqrt{d+e\,x}}-\frac{2\,c\,\sqrt{c\,d^2-c\,e^2\,x^2}\,\sqrt{d+e\,x}\,\left(1491\,d^5-4157\,d^4\,e\,x-5350\,d^3\,e^2\,x^2-70\,d^2\,e^3\,x^3+2835\,d\,e^4\,x^4+1155\,e^5\,x^5\right)}{15015\,e}","Not used",1,"- (16384*c*d^6*(c*d^2 - c*e^2*x^2)^(1/2))/(15015*e*(d + e*x)^(1/2)) - (2*c*(c*d^2 - c*e^2*x^2)^(1/2)*(d + e*x)^(1/2)*(1491*d^5 + 1155*e^5*x^5 + 2835*d*e^4*x^4 - 5350*d^3*e^2*x^2 - 70*d^2*e^3*x^3 - 4157*d^4*e*x))/(15015*e)","B"
870,1,128,160,0.635560,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(3/2)*(d + e*x)^(3/2),x)","-\frac{\sqrt{c\,d^2-c\,e^2\,x^2}\,\left(\frac{1066\,c\,d^5\,\sqrt{d+e\,x}}{1155\,e^2}-\frac{348\,c\,d^3\,x^2\,\sqrt{d+e\,x}}{385}+\frac{2\,c\,e^3\,x^5\,\sqrt{d+e\,x}}{11}-\frac{20\,c\,d^2\,e\,x^3\,\sqrt{d+e\,x}}{231}-\frac{622\,c\,d^4\,x\,\sqrt{d+e\,x}}{1155\,e}+\frac{14\,c\,d\,e^2\,x^4\,\sqrt{d+e\,x}}{33}\right)}{x+\frac{d}{e}}","Not used",1,"-((c*d^2 - c*e^2*x^2)^(1/2)*((1066*c*d^5*(d + e*x)^(1/2))/(1155*e^2) - (348*c*d^3*x^2*(d + e*x)^(1/2))/385 + (2*c*e^3*x^5*(d + e*x)^(1/2))/11 - (20*c*d^2*e*x^3*(d + e*x)^(1/2))/231 - (622*c*d^4*x*(d + e*x)^(1/2))/(1155*e) + (14*c*d*e^2*x^4*(d + e*x)^(1/2))/33))/(x + d/e)","B"
871,1,109,119,0.580961,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(3/2)*(d + e*x)^(1/2),x)","-\frac{\sqrt{c\,d^2-c\,e^2\,x^2}\,\left(\frac{214\,c\,d^4\,\sqrt{d+e\,x}}{315\,e^2}-\frac{52\,c\,d^2\,x^2\,\sqrt{d+e\,x}}{105}+\frac{2\,c\,e^2\,x^4\,\sqrt{d+e\,x}}{9}-\frac{208\,c\,d^3\,x\,\sqrt{d+e\,x}}{315\,e}+\frac{16\,c\,d\,e\,x^3\,\sqrt{d+e\,x}}{63}\right)}{x+\frac{d}{e}}","Not used",1,"-((c*d^2 - c*e^2*x^2)^(1/2)*((214*c*d^4*(d + e*x)^(1/2))/(315*e^2) - (52*c*d^2*x^2*(d + e*x)^(1/2))/105 + (2*c*e^2*x^4*(d + e*x)^(1/2))/9 - (208*c*d^3*x*(d + e*x)^(1/2))/(315*e) + (16*c*d*e*x^3*(d + e*x)^(1/2))/63))/(x + d/e)","B"
872,1,60,78,0.590385,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(1/2),x)","-\frac{\sqrt{c\,d^2-c\,e^2\,x^2}\,\left(\frac{18\,c\,d^3}{35\,e}+\frac{2\,c\,e^2\,x^3}{7}-\frac{26\,c\,d^2\,x}{35}-\frac{2\,c\,d\,e\,x^2}{35}\right)}{\sqrt{d+e\,x}}","Not used",1,"-((c*d^2 - c*e^2*x^2)^(1/2)*((18*c*d^3)/(35*e) + (2*c*e^2*x^3)/7 - (26*c*d^2*x)/35 - (2*c*d*e*x^2)/35))/(d + e*x)^(1/2)","B"
873,1,48,38,0.550235,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(3/2),x)","-\frac{\sqrt{c\,d^2-c\,e^2\,x^2}\,\left(\frac{2\,c\,d^2}{5\,e}-\frac{4\,c\,d\,x}{5}+\frac{2\,c\,e\,x^2}{5}\right)}{\sqrt{d+e\,x}}","Not used",1,"-((c*d^2 - c*e^2*x^2)^(1/2)*((2*c*d^2)/(5*e) - (4*c*d*x)/5 + (2*c*e*x^2)/5))/(d + e*x)^(1/2)","B"
874,0,-1,136,0.000000,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(5/2),x)","\int \frac{{\left(c\,d^2-c\,e^2\,x^2\right)}^{3/2}}{{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int((c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(5/2), x)","F"
875,0,-1,133,0.000000,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(7/2),x)","\int \frac{{\left(c\,d^2-c\,e^2\,x^2\right)}^{3/2}}{{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int((c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(7/2), x)","F"
876,0,-1,139,0.000000,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(9/2),x)","\int \frac{{\left(c\,d^2-c\,e^2\,x^2\right)}^{3/2}}{{\left(d+e\,x\right)}^{9/2}} \,d x","Not used",1,"int((c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(9/2), x)","F"
877,0,-1,178,0.000000,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(11/2),x)","\int \frac{{\left(c\,d^2-c\,e^2\,x^2\right)}^{3/2}}{{\left(d+e\,x\right)}^{11/2}} \,d x","Not used",1,"int((c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(11/2), x)","F"
878,0,-1,217,0.000000,"\text{Not used}","int((c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(13/2),x)","\int \frac{{\left(c\,d^2-c\,e^2\,x^2\right)}^{3/2}}{{\left(d+e\,x\right)}^{13/2}} \,d x","Not used",1,"int((c*d^2 - c*e^2*x^2)^(3/2)/(d + e*x)^(13/2), x)","F"
879,1,98,160,0.675568,"\text{Not used}","int((d + e*x)^(7/2)/(c*d^2 - c*e^2*x^2)^(1/2),x)","-\frac{\sqrt{c\,d^2-c\,e^2\,x^2}\,\left(\frac{354\,d^3\,\sqrt{d+e\,x}}{35\,c\,e^2}+\frac{54\,d\,x^2\,\sqrt{d+e\,x}}{35\,c}+\frac{2\,e\,x^3\,\sqrt{d+e\,x}}{7\,c}+\frac{142\,d^2\,x\,\sqrt{d+e\,x}}{35\,c\,e}\right)}{x+\frac{d}{e}}","Not used",1,"-((c*d^2 - c*e^2*x^2)^(1/2)*((354*d^3*(d + e*x)^(1/2))/(35*c*e^2) + (54*d*x^2*(d + e*x)^(1/2))/(35*c) + (2*e*x^3*(d + e*x)^(1/2))/(7*c) + (142*d^2*x*(d + e*x)^(1/2))/(35*c*e)))/(x + d/e)","B"
880,1,79,119,0.614911,"\text{Not used}","int((d + e*x)^(5/2)/(c*d^2 - c*e^2*x^2)^(1/2),x)","-\frac{\sqrt{c\,d^2-c\,e^2\,x^2}\,\left(\frac{2\,x^2\,\sqrt{d+e\,x}}{5\,c}+\frac{86\,d^2\,\sqrt{d+e\,x}}{15\,c\,e^2}+\frac{28\,d\,x\,\sqrt{d+e\,x}}{15\,c\,e}\right)}{x+\frac{d}{e}}","Not used",1,"-((c*d^2 - c*e^2*x^2)^(1/2)*((2*x^2*(d + e*x)^(1/2))/(5*c) + (86*d^2*(d + e*x)^(1/2))/(15*c*e^2) + (28*d*x*(d + e*x)^(1/2))/(15*c*e)))/(x + d/e)","B"
881,1,61,78,0.568261,"\text{Not used}","int((d + e*x)^(3/2)/(c*d^2 - c*e^2*x^2)^(1/2),x)","-\frac{\sqrt{c\,d^2-c\,e^2\,x^2}\,\left(\frac{10\,d\,\sqrt{d+e\,x}}{3\,c\,e^2}+\frac{2\,x\,\sqrt{d+e\,x}}{3\,c\,e}\right)}{x+\frac{d}{e}}","Not used",1,"-((c*d^2 - c*e^2*x^2)^(1/2)*((10*d*(d + e*x)^(1/2))/(3*c*e^2) + (2*x*(d + e*x)^(1/2))/(3*c*e)))/(x + d/e)","B"
882,1,32,36,0.574726,"\text{Not used}","int((d + e*x)^(1/2)/(c*d^2 - c*e^2*x^2)^(1/2),x)","-\frac{2\,\sqrt{c\,d^2-c\,e^2\,x^2}}{c\,e\,\sqrt{d+e\,x}}","Not used",1,"-(2*(c*d^2 - c*e^2*x^2)^(1/2))/(c*e*(d + e*x)^(1/2))","B"
883,0,-1,65,0.000000,"\text{Not used}","int(1/((c*d^2 - c*e^2*x^2)^(1/2)*(d + e*x)^(1/2)),x)","\int \frac{1}{\sqrt{c\,d^2-c\,e^2\,x^2}\,\sqrt{d+e\,x}} \,d x","Not used",1,"int(1/((c*d^2 - c*e^2*x^2)^(1/2)*(d + e*x)^(1/2)), x)","F"
884,0,-1,109,0.000000,"\text{Not used}","int(1/((c*d^2 - c*e^2*x^2)^(1/2)*(d + e*x)^(3/2)),x)","\int \frac{1}{\sqrt{c\,d^2-c\,e^2\,x^2}\,{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int(1/((c*d^2 - c*e^2*x^2)^(1/2)*(d + e*x)^(3/2)), x)","F"
885,0,-1,150,0.000000,"\text{Not used}","int(1/((c*d^2 - c*e^2*x^2)^(1/2)*(d + e*x)^(5/2)),x)","\int \frac{1}{\sqrt{c\,d^2-c\,e^2\,x^2}\,{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int(1/((c*d^2 - c*e^2*x^2)^(1/2)*(d + e*x)^(5/2)), x)","F"
886,1,104,160,0.754297,"\text{Not used}","int((d + e*x)^(9/2)/(c*d^2 - c*e^2*x^2)^(3/2),x)","\frac{\sqrt{c\,d^2-c\,e^2\,x^2}\,\left(\frac{2\,x^3\,\sqrt{d+e\,x}}{5\,c^2}-\frac{182\,d^3\,\sqrt{d+e\,x}}{5\,c^2\,e^3}+\frac{14\,d\,x^2\,\sqrt{d+e\,x}}{5\,c^2\,e}+\frac{86\,d^2\,x\,\sqrt{d+e\,x}}{5\,c^2\,e^2}\right)}{x^2-\frac{d^2}{e^2}}","Not used",1,"((c*d^2 - c*e^2*x^2)^(1/2)*((2*x^3*(d + e*x)^(1/2))/(5*c^2) - (182*d^3*(d + e*x)^(1/2))/(5*c^2*e^3) + (14*d*x^2*(d + e*x)^(1/2))/(5*c^2*e) + (86*d^2*x*(d + e*x)^(1/2))/(5*c^2*e^2)))/(x^2 - d^2/e^2)","B"
887,1,86,119,0.666076,"\text{Not used}","int((d + e*x)^(7/2)/(c*d^2 - c*e^2*x^2)^(3/2),x)","\frac{\sqrt{c\,d^2-c\,e^2\,x^2}\,\left(\frac{2\,x^2\,\sqrt{d+e\,x}}{3\,c^2\,e}-\frac{46\,d^2\,\sqrt{d+e\,x}}{3\,c^2\,e^3}+\frac{20\,d\,x\,\sqrt{d+e\,x}}{3\,c^2\,e^2}\right)}{x^2-\frac{d^2}{e^2}}","Not used",1,"((c*d^2 - c*e^2*x^2)^(1/2)*((2*x^2*(d + e*x)^(1/2))/(3*c^2*e) - (46*d^2*(d + e*x)^(1/2))/(3*c^2*e^3) + (20*d*x*(d + e*x)^(1/2))/(3*c^2*e^2)))/(x^2 - d^2/e^2)","B"
888,1,66,74,0.604832,"\text{Not used}","int((d + e*x)^(5/2)/(c*d^2 - c*e^2*x^2)^(3/2),x)","-\frac{\sqrt{c\,d^2-c\,e^2\,x^2}\,\left(\frac{6\,d\,\sqrt{d+e\,x}}{c^2\,e^3}-\frac{2\,x\,\sqrt{d+e\,x}}{c^2\,e^2}\right)}{x^2-\frac{d^2}{e^2}}","Not used",1,"-((c*d^2 - c*e^2*x^2)^(1/2)*((6*d*(d + e*x)^(1/2))/(c^2*e^3) - (2*x*(d + e*x)^(1/2))/(c^2*e^2)))/(x^2 - d^2/e^2)","B"
889,1,50,36,0.649116,"\text{Not used}","int((d + e*x)^(3/2)/(c*d^2 - c*e^2*x^2)^(3/2),x)","\frac{2\,\sqrt{c\,d^2-c\,e^2\,x^2}\,\sqrt{d+e\,x}}{e\,\left(c^2\,d^2-c^2\,e^2\,x^2\right)}","Not used",1,"(2*(c*d^2 - c*e^2*x^2)^(1/2)*(d + e*x)^(1/2))/(e*(c^2*d^2 - c^2*e^2*x^2))","B"
890,0,-1,104,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/(c*d^2 - c*e^2*x^2)^(3/2),x)","\int \frac{\sqrt{d+e\,x}}{{\left(c\,d^2-c\,e^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(1/2)/(c*d^2 - c*e^2*x^2)^(3/2), x)","F"
891,0,-1,150,0.000000,"\text{Not used}","int(1/((c*d^2 - c*e^2*x^2)^(3/2)*(d + e*x)^(1/2)),x)","\int \frac{1}{{\left(c\,d^2-c\,e^2\,x^2\right)}^{3/2}\,\sqrt{d+e\,x}} \,d x","Not used",1,"int(1/((c*d^2 - c*e^2*x^2)^(3/2)*(d + e*x)^(1/2)), x)","F"
892,0,-1,191,0.000000,"\text{Not used}","int(1/((c*d^2 - c*e^2*x^2)^(3/2)*(d + e*x)^(3/2)),x)","\int \frac{1}{{\left(c\,d^2-c\,e^2\,x^2\right)}^{3/2}\,{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int(1/((c*d^2 - c*e^2*x^2)^(3/2)*(d + e*x)^(3/2)), x)","F"
893,0,-1,31,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/2)*(x - 1)^(1/2)),x)","\int \frac{1}{\sqrt{1-x^2}\,\sqrt{x-1}} \,d x","Not used",1,"int(1/((1 - x^2)^(1/2)*(x - 1)^(1/2)), x)","F"
894,1,54,87,0.310554,"\text{Not used}","int((12 - 3*e^2*x^2)^(1/2)*(e*x + 2)^(5/2),x)","\frac{2\,\sqrt{12-3\,e^2\,x^2}\,\left(35\,e^4\,x^4+260\,e^3\,x^3+624\,e^2\,x^2-16\,e\,x-5104\right)}{315\,e\,\sqrt{e\,x+2}}","Not used",1,"(2*(12 - 3*e^2*x^2)^(1/2)*(624*e^2*x^2 - 16*e*x + 260*e^3*x^3 + 35*e^4*x^4 - 5104))/(315*e*(e*x + 2)^(1/2))","B"
895,1,73,65,0.516381,"\text{Not used}","int((12 - 3*e^2*x^2)^(1/2)*(e*x + 2)^(3/2),x)","\frac{\sqrt{12-3\,e^2\,x^2}\,\left(\frac{52\,x^2\,\sqrt{e\,x+2}}{35}-\frac{1136\,\sqrt{e\,x+2}}{105\,e^2}+\frac{136\,x\,\sqrt{e\,x+2}}{105\,e}+\frac{2\,e\,x^3\,\sqrt{e\,x+2}}{7}\right)}{x+\frac{2}{e}}","Not used",1,"((12 - 3*e^2*x^2)^(1/2)*((52*x^2*(e*x + 2)^(1/2))/35 - (1136*(e*x + 2)^(1/2))/(105*e^2) + (136*x*(e*x + 2)^(1/2))/(105*e) + (2*e*x^3*(e*x + 2)^(1/2))/7))/(x + 2/e)","B"
896,1,60,43,0.493453,"\text{Not used}","int((12 - 3*e^2*x^2)^(1/2)*(e*x + 2)^(1/2),x)","\frac{\sqrt{12-3\,e^2\,x^2}\,\left(\frac{2\,x^2\,\sqrt{e\,x+2}}{5}-\frac{56\,\sqrt{e\,x+2}}{15\,e^2}+\frac{16\,x\,\sqrt{e\,x+2}}{15\,e}\right)}{x+\frac{2}{e}}","Not used",1,"((12 - 3*e^2*x^2)^(1/2)*((2*x^2*(e*x + 2)^(1/2))/5 - (56*(e*x + 2)^(1/2))/(15*e^2) + (16*x*(e*x + 2)^(1/2))/(15*e)))/(x + 2/e)","B"
897,1,29,20,0.109347,"\text{Not used}","int((12 - 3*e^2*x^2)^(1/2)/(e*x + 2)^(1/2),x)","\frac{\left(\frac{2\,x}{3}-\frac{4}{3\,e}\right)\,\sqrt{12-3\,e^2\,x^2}}{\sqrt{e\,x+2}}","Not used",1,"(((2*x)/3 - 4/(3*e))*(12 - 3*e^2*x^2)^(1/2))/(e*x + 2)^(1/2)","B"
898,0,-1,46,0.000000,"\text{Not used}","int((12 - 3*e^2*x^2)^(1/2)/(e*x + 2)^(3/2),x)","\int \frac{\sqrt{12-3\,e^2\,x^2}}{{\left(e\,x+2\right)}^{3/2}} \,d x","Not used",1,"int((12 - 3*e^2*x^2)^(1/2)/(e*x + 2)^(3/2), x)","F"
899,0,-1,55,0.000000,"\text{Not used}","int((12 - 3*e^2*x^2)^(1/2)/(e*x + 2)^(5/2),x)","\int \frac{\sqrt{12-3\,e^2\,x^2}}{{\left(e\,x+2\right)}^{5/2}} \,d x","Not used",1,"int((12 - 3*e^2*x^2)^(1/2)/(e*x + 2)^(5/2), x)","F"
900,0,-1,86,0.000000,"\text{Not used}","int((12 - 3*e^2*x^2)^(1/2)/(e*x + 2)^(7/2),x)","\int \frac{\sqrt{12-3\,e^2\,x^2}}{{\left(e\,x+2\right)}^{7/2}} \,d x","Not used",1,"int((12 - 3*e^2*x^2)^(1/2)/(e*x + 2)^(7/2), x)","F"
901,1,87,109,0.266938,"\text{Not used}","int((12 - 3*e^2*x^2)^(3/2)*(e*x + 2)^(5/2),x)","\frac{2\,\sqrt{12-3\,e^2\,x^2}\,\sqrt{e\,x+2}\,\left(-1155\,e^5\,x^5-5670\,e^4\,x^4+280\,e^3\,x^3+42800\,e^2\,x^2+66512\,e\,x-47712\right)}{5005\,e}-\frac{1048576\,\sqrt{12-3\,e^2\,x^2}}{5005\,e\,\sqrt{e\,x+2}}","Not used",1,"(2*(12 - 3*e^2*x^2)^(1/2)*(e*x + 2)^(1/2)*(66512*e*x + 42800*e^2*x^2 + 280*e^3*x^3 - 5670*e^4*x^4 - 1155*e^5*x^5 - 47712))/(5005*e) - (1048576*(12 - 3*e^2*x^2)^(1/2))/(5005*e*(e*x + 2)^(1/2))","B"
902,1,53,87,0.592257,"\text{Not used}","int((12 - 3*e^2*x^2)^(3/2)*(e*x + 2)^(3/2),x)","-\frac{2\,\sqrt{12-3\,e^2\,x^2}\,{\left(e\,x-2\right)}^2\,\left(105\,e^3\,x^3+910\,e^2\,x^2+3020\,e\,x+4264\right)}{385\,e\,\sqrt{e\,x+2}}","Not used",1,"-(2*(12 - 3*e^2*x^2)^(1/2)*(e*x - 2)^2*(3020*e*x + 910*e^2*x^2 + 105*e^3*x^3 + 4264))/(385*e*(e*x + 2)^(1/2))","B"
903,1,71,65,0.189369,"\text{Not used}","int((12 - 3*e^2*x^2)^(3/2)*(e*x + 2)^(1/2),x)","\frac{2\,\sqrt{12-3\,e^2\,x^2}\,\sqrt{e\,x+2}\,\left(-35\,e^3\,x^3-10\,e^2\,x^2+332\,e\,x+168\right)}{105\,e}-\frac{4096\,\sqrt{12-3\,e^2\,x^2}}{105\,e\,\sqrt{e\,x+2}}","Not used",1,"(2*(12 - 3*e^2*x^2)^(1/2)*(e*x + 2)^(1/2)*(332*e*x - 10*e^2*x^2 - 35*e^3*x^3 + 168))/(105*e) - (4096*(12 - 3*e^2*x^2)^(1/2))/(105*e*(e*x + 2)^(1/2))","B"
904,1,43,45,0.167758,"\text{Not used}","int((12 - 3*e^2*x^2)^(3/2)/(e*x + 2)^(1/2),x)","\frac{\sqrt{12-3\,e^2\,x^2}\,\left(\frac{312\,x}{35}+\frac{12\,e\,x^2}{35}-\frac{432}{35\,e}-\frac{6\,e^2\,x^3}{7}\right)}{\sqrt{e\,x+2}}","Not used",1,"((12 - 3*e^2*x^2)^(1/2)*((312*x)/35 + (12*e*x^2)/35 - 432/(35*e) - (6*e^2*x^3)/7))/(e*x + 2)^(1/2)","B"
905,1,36,22,0.497102,"\text{Not used}","int((12 - 3*e^2*x^2)^(3/2)/(e*x + 2)^(3/2),x)","-\frac{\sqrt{12-3\,e^2\,x^2}\,\left(\frac{6\,e\,x^2}{5}-\frac{24\,x}{5}+\frac{24}{5\,e}\right)}{\sqrt{e\,x+2}}","Not used",1,"-((12 - 3*e^2*x^2)^(1/2)*((6*e*x^2)/5 - (24*x)/5 + 24/(5*e)))/(e*x + 2)^(1/2)","B"
906,0,-1,66,0.000000,"\text{Not used}","int((12 - 3*e^2*x^2)^(3/2)/(e*x + 2)^(5/2),x)","\int \frac{{\left(12-3\,e^2\,x^2\right)}^{3/2}}{{\left(e\,x+2\right)}^{5/2}} \,d x","Not used",1,"int((12 - 3*e^2*x^2)^(3/2)/(e*x + 2)^(5/2), x)","F"
907,0,-1,73,0.000000,"\text{Not used}","int((12 - 3*e^2*x^2)^(3/2)/(e*x + 2)^(7/2),x)","\int \frac{{\left(12-3\,e^2\,x^2\right)}^{3/2}}{{\left(e\,x+2\right)}^{7/2}} \,d x","Not used",1,"int((12 - 3*e^2*x^2)^(3/2)/(e*x + 2)^(7/2), x)","F"
908,0,-1,86,0.000000,"\text{Not used}","int((12 - 3*e^2*x^2)^(3/2)/(e*x + 2)^(9/2),x)","\int \frac{{\left(12-3\,e^2\,x^2\right)}^{3/2}}{{\left(e\,x+2\right)}^{9/2}} \,d x","Not used",1,"int((12 - 3*e^2*x^2)^(3/2)/(e*x + 2)^(9/2), x)","F"
909,0,-1,113,0.000000,"\text{Not used}","int((12 - 3*e^2*x^2)^(3/2)/(e*x + 2)^(11/2),x)","\int \frac{{\left(12-3\,e^2\,x^2\right)}^{3/2}}{{\left(e\,x+2\right)}^{11/2}} \,d x","Not used",1,"int((12 - 3*e^2*x^2)^(3/2)/(e*x + 2)^(11/2), x)","F"
910,0,-1,144,0.000000,"\text{Not used}","int((12 - 3*e^2*x^2)^(3/2)/(e*x + 2)^(13/2),x)","\int \frac{{\left(12-3\,e^2\,x^2\right)}^{3/2}}{{\left(e\,x+2\right)}^{13/2}} \,d x","Not used",1,"int((12 - 3*e^2*x^2)^(3/2)/(e*x + 2)^(13/2), x)","F"
911,1,74,85,0.219190,"\text{Not used}","int((e*x + 2)^(7/2)/(12 - 3*e^2*x^2)^(1/2),x)","-\frac{\sqrt{12-3\,e^2\,x^2}\,\left(\frac{944\,\sqrt{e\,x+2}}{35\,e^2}+\frac{36\,x^2\,\sqrt{e\,x+2}}{35}+\frac{568\,x\,\sqrt{e\,x+2}}{105\,e}+\frac{2\,e\,x^3\,\sqrt{e\,x+2}}{21}\right)}{x+\frac{2}{e}}","Not used",1,"-((12 - 3*e^2*x^2)^(1/2)*((944*(e*x + 2)^(1/2))/(35*e^2) + (36*x^2*(e*x + 2)^(1/2))/35 + (568*x*(e*x + 2)^(1/2))/(105*e) + (2*e*x^3*(e*x + 2)^(1/2))/21))/(x + 2/e)","B"
912,1,61,65,0.546076,"\text{Not used}","int((e*x + 2)^(5/2)/(12 - 3*e^2*x^2)^(1/2),x)","-\frac{\sqrt{12-3\,e^2\,x^2}\,\left(\frac{344\,\sqrt{e\,x+2}}{45\,e^2}+\frac{2\,x^2\,\sqrt{e\,x+2}}{15}+\frac{56\,x\,\sqrt{e\,x+2}}{45\,e}\right)}{x+\frac{2}{e}}","Not used",1,"-((12 - 3*e^2*x^2)^(1/2)*((344*(e*x + 2)^(1/2))/(45*e^2) + (2*x^2*(e*x + 2)^(1/2))/15 + (56*x*(e*x + 2)^(1/2))/(45*e)))/(x + 2/e)","B"
913,1,49,43,0.140571,"\text{Not used}","int((e*x + 2)^(3/2)/(12 - 3*e^2*x^2)^(1/2),x)","-\frac{\left(\frac{20\,\sqrt{e\,x+2}}{9\,e^2}+\frac{2\,x\,\sqrt{e\,x+2}}{9\,e}\right)\,\sqrt{12-3\,e^2\,x^2}}{x+\frac{2}{e}}","Not used",1,"-(((20*(e*x + 2)^(1/2))/(9*e^2) + (2*x*(e*x + 2)^(1/2))/(9*e))*(12 - 3*e^2*x^2)^(1/2))/(x + 2/e)","B"
914,1,24,20,0.148201,"\text{Not used}","int((e*x + 2)^(1/2)/(12 - 3*e^2*x^2)^(1/2),x)","-\frac{2\,\sqrt{12-3\,e^2\,x^2}}{3\,e\,\sqrt{e\,x+2}}","Not used",1,"-(2*(12 - 3*e^2*x^2)^(1/2))/(3*e*(e*x + 2)^(1/2))","B"
915,0,-1,25,0.000000,"\text{Not used}","int(1/((12 - 3*e^2*x^2)^(1/2)*(e*x + 2)^(1/2)),x)","\int \frac{1}{\sqrt{12-3\,e^2\,x^2}\,\sqrt{e\,x+2}} \,d x","Not used",1,"int(1/((12 - 3*e^2*x^2)^(1/2)*(e*x + 2)^(1/2)), x)","F"
916,0,-1,57,0.000000,"\text{Not used}","int(1/((12 - 3*e^2*x^2)^(1/2)*(e*x + 2)^(3/2)),x)","\int \frac{1}{\sqrt{12-3\,e^2\,x^2}\,{\left(e\,x+2\right)}^{3/2}} \,d x","Not used",1,"int(1/((12 - 3*e^2*x^2)^(1/2)*(e*x + 2)^(3/2)), x)","F"
917,0,-1,86,0.000000,"\text{Not used}","int(1/((12 - 3*e^2*x^2)^(1/2)*(e*x + 2)^(5/2)),x)","\int \frac{1}{\sqrt{12-3\,e^2\,x^2}\,{\left(e\,x+2\right)}^{5/2}} \,d x","Not used",1,"int(1/((12 - 3*e^2*x^2)^(1/2)*(e*x + 2)^(5/2)), x)","F"
918,1,93,111,0.300249,"\text{Not used}","int((e*x + 2)^(11/2)/(12 - 3*e^2*x^2)^(3/2),x)","-\frac{\sqrt{12-3\,e^2\,x^2}\,\left(\frac{16\,x^3\,\sqrt{e\,x+2}}{35}-\frac{46432\,\sqrt{e\,x+2}}{315\,e^3}+\frac{3776\,x\,\sqrt{e\,x+2}}{105\,e^2}+\frac{2\,e\,x^4\,\sqrt{e\,x+2}}{63}+\frac{1136\,x^2\,\sqrt{e\,x+2}}{315\,e}\right)}{\frac{4}{e^2}-x^2}","Not used",1,"-((12 - 3*e^2*x^2)^(1/2)*((16*x^3*(e*x + 2)^(1/2))/35 - (46432*(e*x + 2)^(1/2))/(315*e^3) + (3776*x*(e*x + 2)^(1/2))/(105*e^2) + (2*e*x^4*(e*x + 2)^(1/2))/63 + (1136*x^2*(e*x + 2)^(1/2))/(315*e)))/(4/e^2 - x^2)","B"
919,1,80,87,0.624998,"\text{Not used}","int((e*x + 2)^(9/2)/(12 - 3*e^2*x^2)^(3/2),x)","-\frac{\sqrt{12-3\,e^2\,x^2}\,\left(\frac{2\,x^3\,\sqrt{e\,x+2}}{45}-\frac{1456\,\sqrt{e\,x+2}}{45\,e^3}+\frac{344\,x\,\sqrt{e\,x+2}}{45\,e^2}+\frac{28\,x^2\,\sqrt{e\,x+2}}{45\,e}\right)}{\frac{4}{e^2}-x^2}","Not used",1,"-((12 - 3*e^2*x^2)^(1/2)*((2*x^3*(e*x + 2)^(1/2))/45 - (1456*(e*x + 2)^(1/2))/(45*e^3) + (344*x*(e*x + 2)^(1/2))/(45*e^2) + (28*x^2*(e*x + 2)^(1/2))/(45*e)))/(4/e^2 - x^2)","B"
920,1,48,67,0.600127,"\text{Not used}","int((e*x + 2)^(7/2)/(12 - 3*e^2*x^2)^(3/2),x)","\frac{2\,\sqrt{12-3\,e^2\,x^2}\,\sqrt{e\,x+2}\,\left(e^2\,x^2+20\,e\,x-92\right)}{27\,e\,\left(e^2\,x^2-4\right)}","Not used",1,"(2*(12 - 3*e^2*x^2)^(1/2)*(e*x + 2)^(1/2)*(20*e*x + e^2*x^2 - 92))/(27*e*(e^2*x^2 - 4))","B"
921,1,52,45,0.565393,"\text{Not used}","int((e*x + 2)^(5/2)/(12 - 3*e^2*x^2)^(3/2),x)","\frac{\left(\frac{4\,\sqrt{e\,x+2}}{3\,e^3}-\frac{2\,x\,\sqrt{e\,x+2}}{9\,e^2}\right)\,\sqrt{12-3\,e^2\,x^2}}{\frac{4}{e^2}-x^2}","Not used",1,"(((4*(e*x + 2)^(1/2))/(3*e^3) - (2*x*(e*x + 2)^(1/2))/(9*e^2))*(12 - 3*e^2*x^2)^(1/2))/(4/e^2 - x^2)","B"
922,1,24,22,0.207378,"\text{Not used}","int((e*x + 2)^(3/2)/(12 - 3*e^2*x^2)^(3/2),x)","\frac{2\,\sqrt{e\,x+2}}{3\,e\,\sqrt{12-3\,e^2\,x^2}}","Not used",1,"(2*(e*x + 2)^(1/2))/(3*e*(12 - 3*e^2*x^2)^(1/2))","B"
923,0,-1,50,0.000000,"\text{Not used}","int((e*x + 2)^(1/2)/(12 - 3*e^2*x^2)^(3/2),x)","\int \frac{\sqrt{e\,x+2}}{{\left(12-3\,e^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((e*x + 2)^(1/2)/(12 - 3*e^2*x^2)^(3/2), x)","F"
924,0,-1,79,0.000000,"\text{Not used}","int(1/((12 - 3*e^2*x^2)^(3/2)*(e*x + 2)^(1/2)),x)","\int \frac{1}{{\left(12-3\,e^2\,x^2\right)}^{3/2}\,\sqrt{e\,x+2}} \,d x","Not used",1,"int(1/((12 - 3*e^2*x^2)^(3/2)*(e*x + 2)^(1/2)), x)","F"
925,0,-1,108,0.000000,"\text{Not used}","int(1/((12 - 3*e^2*x^2)^(3/2)*(e*x + 2)^(3/2)),x)","\int \frac{1}{{\left(12-3\,e^2\,x^2\right)}^{3/2}\,{\left(e\,x+2\right)}^{3/2}} \,d x","Not used",1,"int(1/((12 - 3*e^2*x^2)^(3/2)*(e*x + 2)^(3/2)), x)","F"
926,1,18,23,0.092160,"\text{Not used}","int(1/((1 - x)^(1/2)*(x + 1)),x)","-\sqrt{2}\,\mathrm{atanh}\left(\frac{\sqrt{2}\,\sqrt{1-x}}{2}\right)","Not used",1,"-2^(1/2)*atanh((2^(1/2)*(1 - x)^(1/2))/2)","B"
927,0,-1,23,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/2)*(x + 1)^(1/2)),x)","\int \frac{1}{\sqrt{1-x^2}\,\sqrt{x+1}} \,d x","Not used",1,"int(1/((1 - x^2)^(1/2)*(x + 1)^(1/2)), x)","F"
928,1,19,27,0.468671,"\text{Not used}","int(1/((1 - a*x)^(1/2)*(a*x + 1)),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{\sqrt{2-2\,a\,x}}{2}\right)}{a}","Not used",1,"-(2^(1/2)*atanh((2 - 2*a*x)^(1/2)/2))/a","B"
929,0,-1,27,0.000000,"\text{Not used}","int(1/((1 - a^2*x^2)^(1/2)*(a*x + 1)^(1/2)),x)","\int \frac{1}{\sqrt{1-a^2\,x^2}\,\sqrt{a\,x+1}} \,d x","Not used",1,"int(1/((1 - a^2*x^2)^(1/2)*(a*x + 1)^(1/2)), x)","F"
930,0,-1,309,0.000000,"\text{Not used}","int((12 - 3*e^2*x^2)^(1/4)*(e*x + 2)^(1/2),x)","\int {\left(12-3\,e^2\,x^2\right)}^{1/4}\,\sqrt{e\,x+2} \,d x","Not used",1,"int((12 - 3*e^2*x^2)^(1/4)*(e*x + 2)^(1/2), x)","F"
931,0,-1,269,0.000000,"\text{Not used}","int((12 - 3*e^2*x^2)^(1/4)/(e*x + 2)^(1/2),x)","\int \frac{{\left(12-3\,e^2\,x^2\right)}^{1/4}}{\sqrt{e\,x+2}} \,d x","Not used",1,"int((12 - 3*e^2*x^2)^(1/4)/(e*x + 2)^(1/2), x)","F"
932,0,-1,270,0.000000,"\text{Not used}","int((12 - 3*e^2*x^2)^(1/4)/(e*x + 2)^(3/2),x)","\int \frac{{\left(12-3\,e^2\,x^2\right)}^{1/4}}{{\left(e\,x+2\right)}^{3/2}} \,d x","Not used",1,"int((12 - 3*e^2*x^2)^(1/4)/(e*x + 2)^(3/2), x)","F"
933,1,49,35,0.640516,"\text{Not used}","int((12 - 3*e^2*x^2)^(1/4)/(e*x + 2)^(5/2),x)","\frac{\left(\frac{x}{5\,e}-\frac{2}{5\,e^2}\right)\,{\left(12-3\,e^2\,x^2\right)}^{1/4}}{\frac{2\,\sqrt{e\,x+2}}{e}+x\,\sqrt{e\,x+2}}","Not used",1,"((x/(5*e) - 2/(5*e^2))*(12 - 3*e^2*x^2)^(1/4))/((2*(e*x + 2)^(1/2))/e + x*(e*x + 2)^(1/2))","B"
934,1,37,71,0.294236,"\text{Not used}","int((12 - 3*e^2*x^2)^(1/4)/(e*x + 2)^(7/2),x)","\frac{{\left(12-3\,e^2\,x^2\right)}^{1/4}\,\left(e^2\,x^2+5\,e\,x-14\right)}{45\,e\,{\left(e\,x+2\right)}^{5/2}}","Not used",1,"((12 - 3*e^2*x^2)^(1/4)*(5*e*x + e^2*x^2 - 14))/(45*e*(e*x + 2)^(5/2))","B"
935,1,46,106,0.695922,"\text{Not used}","int((12 - 3*e^2*x^2)^(1/4)/(e*x + 2)^(9/2),x)","\frac{{\left(12-3\,e^2\,x^2\right)}^{1/4}\,\left(2\,e^3\,x^3+14\,e^2\,x^2+37\,e\,x-146\right)}{585\,e\,{\left(e\,x+2\right)}^{7/2}}","Not used",1,"((12 - 3*e^2*x^2)^(1/4)*(37*e*x + 14*e^2*x^2 + 2*e^3*x^3 - 146))/(585*e*(e*x + 2)^(7/2))","B"
936,1,118,141,0.699305,"\text{Not used}","int((12 - 3*e^2*x^2)^(1/4)/(e*x + 2)^(11/2),x)","\frac{{\left(12-3\,e^2\,x^2\right)}^{1/4}\,\left(\frac{41\,x}{1105\,e^4}-\frac{682}{3315\,e^5}+\frac{2\,x^4}{3315\,e}+\frac{6\,x^3}{1105\,e^2}+\frac{x^2}{51\,e^3}\right)}{\frac{16\,\sqrt{e\,x+2}}{e^4}+x^4\,\sqrt{e\,x+2}+\frac{32\,x\,\sqrt{e\,x+2}}{e^3}+\frac{8\,x^3\,\sqrt{e\,x+2}}{e}+\frac{24\,x^2\,\sqrt{e\,x+2}}{e^2}}","Not used",1,"((12 - 3*e^2*x^2)^(1/4)*((41*x)/(1105*e^4) - 682/(3315*e^5) + (2*x^4)/(3315*e) + (6*x^3)/(1105*e^2) + x^2/(51*e^3)))/((16*(e*x + 2)^(1/2))/e^4 + x^4*(e*x + 2)^(1/2) + (32*x*(e*x + 2)^(1/2))/e^3 + (8*x^3*(e*x + 2)^(1/2))/e + (24*x^2*(e*x + 2)^(1/2))/e^2)","B"
937,0,-1,340,0.000000,"\text{Not used}","int((e*x + 2)^(5/2)/(12 - 3*e^2*x^2)^(1/4),x)","\int \frac{{\left(e\,x+2\right)}^{5/2}}{{\left(12-3\,e^2\,x^2\right)}^{1/4}} \,d x","Not used",1,"int((e*x + 2)^(5/2)/(12 - 3*e^2*x^2)^(1/4), x)","F"
938,0,-1,309,0.000000,"\text{Not used}","int((e*x + 2)^(3/2)/(12 - 3*e^2*x^2)^(1/4),x)","\int \frac{{\left(e\,x+2\right)}^{3/2}}{{\left(12-3\,e^2\,x^2\right)}^{1/4}} \,d x","Not used",1,"int((e*x + 2)^(3/2)/(12 - 3*e^2*x^2)^(1/4), x)","F"
939,0,-1,270,0.000000,"\text{Not used}","int((e*x + 2)^(1/2)/(12 - 3*e^2*x^2)^(1/4),x)","\int \frac{\sqrt{e\,x+2}}{{\left(12-3\,e^2\,x^2\right)}^{1/4}} \,d x","Not used",1,"int((e*x + 2)^(1/2)/(12 - 3*e^2*x^2)^(1/4), x)","F"
940,0,-1,241,0.000000,"\text{Not used}","int(1/((12 - 3*e^2*x^2)^(1/4)*(e*x + 2)^(1/2)),x)","\int \frac{1}{{\left(12-3\,e^2\,x^2\right)}^{1/4}\,\sqrt{e\,x+2}} \,d x","Not used",1,"int(1/((12 - 3*e^2*x^2)^(1/4)*(e*x + 2)^(1/2)), x)","F"
941,1,24,35,0.669002,"\text{Not used}","int(1/((12 - 3*e^2*x^2)^(1/4)*(e*x + 2)^(3/2)),x)","-\frac{{\left(12-3\,e^2\,x^2\right)}^{3/4}}{9\,e\,{\left(e\,x+2\right)}^{3/2}}","Not used",1,"-(12 - 3*e^2*x^2)^(3/4)/(9*e*(e*x + 2)^(3/2))","B"
942,1,65,71,0.678145,"\text{Not used}","int(1/((12 - 3*e^2*x^2)^(1/4)*(e*x + 2)^(5/2)),x)","-\frac{\left(\frac{x}{63\,e^2}+\frac{5}{63\,e^3}\right)\,{\left(12-3\,e^2\,x^2\right)}^{3/4}}{\frac{4\,\sqrt{e\,x+2}}{e^2}+x^2\,\sqrt{e\,x+2}+\frac{4\,x\,\sqrt{e\,x+2}}{e}}","Not used",1,"-((x/(63*e^2) + 5/(63*e^3))*(12 - 3*e^2*x^2)^(3/4))/((4*(e*x + 2)^(1/2))/e^2 + x^2*(e*x + 2)^(1/2) + (4*x*(e*x + 2)^(1/2))/e)","B"
943,1,88,106,0.341533,"\text{Not used}","int(1/((12 - 3*e^2*x^2)^(1/4)*(e*x + 2)^(7/2)),x)","-\frac{{\left(12-3\,e^2\,x^2\right)}^{3/4}\,\left(\frac{2\,x}{99\,e^3}+\frac{41}{693\,e^4}+\frac{2\,x^2}{693\,e^2}\right)}{\frac{8\,\sqrt{e\,x+2}}{e^3}+x^3\,\sqrt{e\,x+2}+\frac{12\,x\,\sqrt{e\,x+2}}{e^2}+\frac{6\,x^2\,\sqrt{e\,x+2}}{e}}","Not used",1,"-((12 - 3*e^2*x^2)^(3/4)*((2*x)/(99*e^3) + 41/(693*e^4) + (2*x^2)/(693*e^2)))/((8*(e*x + 2)^(1/2))/e^3 + x^3*(e*x + 2)^(1/2) + (12*x*(e*x + 2)^(1/2))/e^2 + (6*x^2*(e*x + 2)^(1/2))/e)","B"
944,1,111,141,0.368811,"\text{Not used}","int(1/((12 - 3*e^2*x^2)^(1/4)*(e*x + 2)^(9/2)),x)","-\frac{{\left(12-3\,e^2\,x^2\right)}^{3/4}\,\left(\frac{23\,x}{1155\,e^4}+\frac{53}{1155\,e^5}+\frac{2\,x^3}{3465\,e^2}+\frac{2\,x^2}{385\,e^3}\right)}{\frac{16\,\sqrt{e\,x+2}}{e^4}+x^4\,\sqrt{e\,x+2}+\frac{32\,x\,\sqrt{e\,x+2}}{e^3}+\frac{8\,x^3\,\sqrt{e\,x+2}}{e}+\frac{24\,x^2\,\sqrt{e\,x+2}}{e^2}}","Not used",1,"-((12 - 3*e^2*x^2)^(3/4)*((23*x)/(1155*e^4) + 53/(1155*e^5) + (2*x^3)/(3465*e^2) + (2*x^2)/(385*e^3)))/((16*(e*x + 2)^(1/2))/e^4 + x^4*(e*x + 2)^(1/2) + (32*x*(e*x + 2)^(1/2))/e^3 + (8*x^3*(e*x + 2)^(1/2))/e + (24*x^2*(e*x + 2)^(1/2))/e^2)","B"
945,1,332,84,0.746524,"\text{Not used}","int((a^2 - b^2*x^2)^3*(a + b*x)^m,x)","{\left(a+b\,x\right)}^m\,\left(\frac{a^6\,x\,\left(m^3+27\,m^2+254\,m+840\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}+\frac{a^7\,\left(m^3+21\,m^2+152\,m+384\right)}{b\,\left(m^4+22\,m^3+179\,m^2+638\,m+840\right)}-\frac{b^6\,x^7\,\left(m^3+15\,m^2+74\,m+120\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}+\frac{3\,a^2\,b^4\,x^5\,\left(m^3+19\,m^2+102\,m+168\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}-\frac{3\,a^4\,b^2\,x^3\,\left(m^3+23\,m^2+162\,m+280\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}-\frac{a\,b^5\,m\,x^6\,\left(m^2+9\,m+20\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}-\frac{3\,a^5\,b\,m\,x^2\,\left(m^2+17\,m+76\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}+\frac{3\,a^3\,b^3\,m\,x^4\,\left(m^2+13\,m+32\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}\right)","Not used",1,"(a + b*x)^m*((a^6*x*(254*m + 27*m^2 + m^3 + 840))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840) + (a^7*(152*m + 21*m^2 + m^3 + 384))/(b*(638*m + 179*m^2 + 22*m^3 + m^4 + 840)) - (b^6*x^7*(74*m + 15*m^2 + m^3 + 120))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840) + (3*a^2*b^4*x^5*(102*m + 19*m^2 + m^3 + 168))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840) - (3*a^4*b^2*x^3*(162*m + 23*m^2 + m^3 + 280))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840) - (a*b^5*m*x^6*(9*m + m^2 + 20))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840) - (3*a^5*b*m*x^2*(17*m + m^2 + 76))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840) + (3*a^3*b^3*m*x^4*(13*m + m^2 + 32))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840))","B"
946,1,186,61,0.547842,"\text{Not used}","int((a^2 - b^2*x^2)^2*(a + b*x)^m,x)","{\left(a+b\,x\right)}^m\,\left(\frac{a^4\,x\,\left(m^2+15\,m+60\right)}{m^3+12\,m^2+47\,m+60}+\frac{a^5\,\left(m^2+11\,m+32\right)}{b\,\left(m^3+12\,m^2+47\,m+60\right)}+\frac{b^4\,x^5\,\left(m^2+7\,m+12\right)}{m^3+12\,m^2+47\,m+60}-\frac{2\,a^2\,b^2\,x^3\,\left(m^2+11\,m+20\right)}{m^3+12\,m^2+47\,m+60}+\frac{a\,b^3\,m\,x^4\,\left(m+3\right)}{m^3+12\,m^2+47\,m+60}-\frac{2\,a^3\,b\,m\,x^2\,\left(m+7\right)}{m^3+12\,m^2+47\,m+60}\right)","Not used",1,"(a + b*x)^m*((a^4*x*(15*m + m^2 + 60))/(47*m + 12*m^2 + m^3 + 60) + (a^5*(11*m + m^2 + 32))/(b*(47*m + 12*m^2 + m^3 + 60)) + (b^4*x^5*(7*m + m^2 + 12))/(47*m + 12*m^2 + m^3 + 60) - (2*a^2*b^2*x^3*(11*m + m^2 + 20))/(47*m + 12*m^2 + m^3 + 60) + (a*b^3*m*x^4*(m + 3))/(47*m + 12*m^2 + m^3 + 60) - (2*a^3*b*m*x^2*(m + 7))/(47*m + 12*m^2 + m^3 + 60))","B"
947,1,86,40,0.459847,"\text{Not used}","int((a^2 - b^2*x^2)*(a + b*x)^m,x)","{\left(a+b\,x\right)}^m\,\left(\frac{a^3\,\left(m+4\right)}{b\,\left(m^2+5\,m+6\right)}-\frac{b^2\,x^3\,\left(m+2\right)}{m^2+5\,m+6}+\frac{a^2\,x\,\left(m+6\right)}{m^2+5\,m+6}-\frac{a\,b\,m\,x^2}{m^2+5\,m+6}\right)","Not used",1,"(a + b*x)^m*((a^3*(m + 4))/(b*(5*m + m^2 + 6)) - (b^2*x^3*(m + 2))/(5*m + m^2 + 6) + (a^2*x*(m + 6))/(5*m + m^2 + 6) - (a*b*m*x^2)/(5*m + m^2 + 6))","B"
948,0,-1,38,0.000000,"\text{Not used}","int((a + b*x)^m/(a^2 - b^2*x^2),x)","\int \frac{{\left(a+b\,x\right)}^m}{a^2-b^2\,x^2} \,d x","Not used",1,"int((a + b*x)^m/(a^2 - b^2*x^2), x)","F"
949,0,-1,44,0.000000,"\text{Not used}","int((a + b*x)^m/(a^2 - b^2*x^2)^2,x)","\int \frac{{\left(a+b\,x\right)}^m}{{\left(a^2-b^2\,x^2\right)}^2} \,d x","Not used",1,"int((a + b*x)^m/(a^2 - b^2*x^2)^2, x)","F"
950,0,-1,46,0.000000,"\text{Not used}","int((a + b*x)^m/(a^2 - b^2*x^2)^3,x)","\int \frac{{\left(a+b\,x\right)}^m}{{\left(a^2-b^2\,x^2\right)}^3} \,d x","Not used",1,"int((a + b*x)^m/(a^2 - b^2*x^2)^3, x)","F"
951,0,-1,59,0.000000,"\text{Not used}","int((d^2 - e^2*x^2)^(7/2)*(d + e*x)^m,x)","\int {\left(d^2-e^2\,x^2\right)}^{7/2}\,{\left(d+e\,x\right)}^m \,d x","Not used",1,"int((d^2 - e^2*x^2)^(7/2)*(d + e*x)^m, x)","F"
952,0,-1,83,0.000000,"\text{Not used}","int((d^2 - e^2*x^2)^(5/2)*(d + e*x)^m,x)","\int {\left(d^2-e^2\,x^2\right)}^{5/2}\,{\left(d+e\,x\right)}^m \,d x","Not used",1,"int((d^2 - e^2*x^2)^(5/2)*(d + e*x)^m, x)","F"
953,0,-1,59,0.000000,"\text{Not used}","int((d^2 - e^2*x^2)^(3/2)*(d + e*x)^m,x)","\int {\left(d^2-e^2\,x^2\right)}^{3/2}\,{\left(d+e\,x\right)}^m \,d x","Not used",1,"int((d^2 - e^2*x^2)^(3/2)*(d + e*x)^m, x)","F"
954,0,-1,67,0.000000,"\text{Not used}","int((d^2 - e^2*x^2)^(1/2)*(d + e*x)^m,x)","\int \sqrt{d^2-e^2\,x^2}\,{\left(d+e\,x\right)}^m \,d x","Not used",1,"int((d^2 - e^2*x^2)^(1/2)*(d + e*x)^m, x)","F"
955,0,-1,67,0.000000,"\text{Not used}","int((d + e*x)^m/(d^2 - e^2*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^m}{\sqrt{d^2-e^2\,x^2}} \,d x","Not used",1,"int((d + e*x)^m/(d^2 - e^2*x^2)^(1/2), x)","F"
956,0,-1,80,0.000000,"\text{Not used}","int((d + e*x)^m/(d^2 - e^2*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(d^2-e^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^m/(d^2 - e^2*x^2)^(3/2), x)","F"
957,0,-1,60,0.000000,"\text{Not used}","int((d + e*x)^m/(d^2 - e^2*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(d^2-e^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^m/(d^2 - e^2*x^2)^(5/2), x)","F"
958,0,-1,68,0.000000,"\text{Not used}","int((d + e*x)^m/(d^2 - e^2*x^2)^(7/2),x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(d^2-e^2\,x^2\right)}^{7/2}} \,d x","Not used",1,"int((d + e*x)^m/(d^2 - e^2*x^2)^(7/2), x)","F"
959,0,-1,63,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^p*(a + b*x)^m,x)","\int {\left(a^2-b^2\,x^2\right)}^p\,{\left(a+b\,x\right)}^m \,d x","Not used",1,"int((a^2 - b^2*x^2)^p*(a + b*x)^m, x)","F"
960,0,-1,57,0.000000,"\text{Not used}","int((1 - (e^2*x^2)/d^2)^p*(d + e*x)^3,x)","\int {\left(1-\frac{e^2\,x^2}{d^2}\right)}^p\,{\left(d+e\,x\right)}^3 \,d x","Not used",1,"int((1 - (e^2*x^2)/d^2)^p*(d + e*x)^3, x)","F"
961,0,-1,57,0.000000,"\text{Not used}","int((1 - (e^2*x^2)/d^2)^p*(d + e*x)^2,x)","\int {\left(1-\frac{e^2\,x^2}{d^2}\right)}^p\,{\left(d+e\,x\right)}^2 \,d x","Not used",1,"int((1 - (e^2*x^2)/d^2)^p*(d + e*x)^2, x)","F"
962,1,58,57,1.389782,"\text{Not used}","int((1 - (e^2*x^2)/d^2)^p*(d + e*x),x)","d\,x\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},-p;\ \frac{3}{2};\ \frac{e^2\,x^2}{d^2}\right)-\frac{\left(d^2-e^2\,x^2\right)\,{\left(1-\frac{e^2\,x^2}{d^2}\right)}^p}{2\,e\,\left(p+1\right)}","Not used",1,"d*x*hypergeom([1/2, -p], 3/2, (e^2*x^2)/d^2) - ((d^2 - e^2*x^2)*(1 - (e^2*x^2)/d^2)^p)/(2*e*(p + 1))","B"
963,1,19,22,1.209778,"\text{Not used}","int((1 - (e^2*x^2)/d^2)^p,x)","x\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},-p;\ \frac{3}{2};\ \frac{e^2\,x^2}{d^2}\right)","Not used",1,"x*hypergeom([1/2, -p], 3/2, (e^2*x^2)/d^2)","B"
964,0,-1,41,0.000000,"\text{Not used}","int((1 - (e^2*x^2)/d^2)^p/(d + e*x),x)","\int \frac{{\left(1-\frac{e^2\,x^2}{d^2}\right)}^p}{d+e\,x} \,d x","Not used",1,"int((1 - (e^2*x^2)/d^2)^p/(d + e*x), x)","F"
965,0,-1,57,0.000000,"\text{Not used}","int((1 - (e^2*x^2)/d^2)^p/(d + e*x)^2,x)","\int \frac{{\left(1-\frac{e^2\,x^2}{d^2}\right)}^p}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((1 - (e^2*x^2)/d^2)^p/(d + e*x)^2, x)","F"
966,0,-1,57,0.000000,"\text{Not used}","int((1 - (e^2*x^2)/d^2)^p/(d + e*x)^3,x)","\int \frac{{\left(1-\frac{e^2\,x^2}{d^2}\right)}^p}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((1 - (e^2*x^2)/d^2)^p/(d + e*x)^3, x)","F"
967,0,-1,60,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^p*(a + b*x)^3,x)","\int {\left(a^2-b^2\,x^2\right)}^p\,{\left(a+b\,x\right)}^3 \,d x","Not used",1,"int((a^2 - b^2*x^2)^p*(a + b*x)^3, x)","F"
968,0,-1,60,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^p*(a + b*x)^2,x)","\int {\left(a^2-b^2\,x^2\right)}^p\,{\left(a+b\,x\right)}^2 \,d x","Not used",1,"int((a^2 - b^2*x^2)^p*(a + b*x)^2, x)","F"
969,1,78,83,2.361238,"\text{Not used}","int((a^2 - b^2*x^2)^p*(a + b*x),x)","\frac{a\,x\,{\left(a^2-b^2\,x^2\right)}^p\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},-p;\ \frac{3}{2};\ \frac{b^2\,x^2}{a^2}\right)}{{\left(1-\frac{b^2\,x^2}{a^2}\right)}^p}-\frac{{\left(a^2-b^2\,x^2\right)}^{p+1}}{2\,b\,\left(p+1\right)}","Not used",1,"(a*x*(a^2 - b^2*x^2)^p*hypergeom([1/2, -p], 3/2, (b^2*x^2)/a^2))/(1 - (b^2*x^2)/a^2)^p - (a^2 - b^2*x^2)^(p + 1)/(2*b*(p + 1))","B"
970,0,-1,55,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^p/(a + b*x),x)","\int \frac{{\left(a^2-b^2\,x^2\right)}^p}{a+b\,x} \,d x","Not used",1,"int((a^2 - b^2*x^2)^p/(a + b*x), x)","F"
971,0,-1,58,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^p/(a + b*x)^2,x)","\int \frac{{\left(a^2-b^2\,x^2\right)}^p}{{\left(a+b\,x\right)}^2} \,d x","Not used",1,"int((a^2 - b^2*x^2)^p/(a + b*x)^2, x)","F"
972,0,-1,62,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^p/(a + b*x)^3,x)","\int \frac{{\left(a^2-b^2\,x^2\right)}^p}{{\left(a+b\,x\right)}^3} \,d x","Not used",1,"int((a^2 - b^2*x^2)^p/(a + b*x)^3, x)","F"
973,0,-1,85,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^p*(a + b*x)^(3/2),x)","\int {\left(a^2-b^2\,x^2\right)}^p\,{\left(a+b\,x\right)}^{3/2} \,d x","Not used",1,"int((a^2 - b^2*x^2)^p*(a + b*x)^(3/2), x)","F"
974,0,-1,88,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^p*(a + b*x)^(1/2),x)","\int {\left(a^2-b^2\,x^2\right)}^p\,\sqrt{a+b\,x} \,d x","Not used",1,"int((a^2 - b^2*x^2)^p*(a + b*x)^(1/2), x)","F"
975,0,-1,88,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^p/(a + b*x)^(1/2),x)","\int \frac{{\left(a^2-b^2\,x^2\right)}^p}{\sqrt{a+b\,x}} \,d x","Not used",1,"int((a^2 - b^2*x^2)^p/(a + b*x)^(1/2), x)","F"
976,0,-1,88,0.000000,"\text{Not used}","int((a^2 - b^2*x^2)^p/(a + b*x)^(3/2),x)","\int \frac{{\left(a^2-b^2\,x^2\right)}^p}{{\left(a+b\,x\right)}^{3/2}} \,d x","Not used",1,"int((a^2 - b^2*x^2)^p/(a + b*x)^(3/2), x)","F"
977,1,26,28,0.459446,"\text{Not used}","int((a^2 - b^2*x^2)^p*(a + b*x) - a*(a^2 - b^2*x^2)^p,x)","-\frac{{\left(a^2-b^2\,x^2\right)}^{p+1}}{2\,b\,\left(p+1\right)}","Not used",1,"-(a^2 - b^2*x^2)^(p + 1)/(2*b*(p + 1))","B"
978,1,47,15,0.421397,"\text{Not used}","int((d + e*x)^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x),x)","c\,d^4\,x+2\,c\,d^3\,e\,x^2+2\,c\,d^2\,e^2\,x^3+c\,d\,e^3\,x^4+\frac{c\,e^4\,x^5}{5}","Not used",1,"(c*e^4*x^5)/5 + c*d^4*x + 2*c*d^2*e^2*x^3 + 2*c*d^3*e*x^2 + c*d*e^3*x^4","B"
979,1,35,15,0.046737,"\text{Not used}","int((d + e*x)*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x),x)","c\,d^3\,x+\frac{3\,c\,d^2\,e\,x^2}{2}+c\,d\,e^2\,x^3+\frac{c\,e^3\,x^4}{4}","Not used",1,"(c*e^3*x^4)/4 + c*d^3*x + (3*c*d^2*e*x^2)/2 + c*d*e^2*x^3","B"
980,1,22,25,0.032244,"\text{Not used}","int(c*d^2 + c*e^2*x^2 + 2*c*d*e*x,x)","\frac{c\,x\,\left(3\,d^2+3\,d\,e\,x+e^2\,x^2\right)}{3}","Not used",1,"(c*x*(3*d^2 + e^2*x^2 + 3*d*e*x))/3","B"
981,1,11,14,0.024344,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)/(d + e*x),x)","\frac{c\,x\,\left(2\,d+e\,x\right)}{2}","Not used",1,"(c*x*(2*d + e*x))/2","B"
982,1,3,3,0.006723,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)/(d + e*x)^2,x)","c\,x","Not used",1,"c*x","B"
983,1,11,11,0.425239,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)/(d + e*x)^3,x)","\frac{c\,\ln\left(d+e\,x\right)}{e}","Not used",1,"(c*log(d + e*x))/e","B"
984,1,13,13,0.038608,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)/(d + e*x)^4,x)","-\frac{c}{e\,\left(d+e\,x\right)}","Not used",1,"-c/(e*(d + e*x))","B"
985,1,24,15,0.401317,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)/(d + e*x)^5,x)","-\frac{c}{2\,e\,\left(d^2+2\,d\,e\,x+e^2\,x^2\right)}","Not used",1,"-c/(2*e*(d^2 + e^2*x^2 + 2*d*e*x))","B"
986,1,35,15,0.414299,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)/(d + e*x)^6,x)","-\frac{c}{3\,e\,\left(d^3+3\,d^2\,e\,x+3\,d\,e^2\,x^2+e^3\,x^3\right)}","Not used",1,"-c/(3*e*(d^3 + e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x))","B"
987,1,85,17,0.037927,"\text{Not used}","int((d + e*x)^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2,x)","c^2\,d^6\,x+3\,c^2\,d^5\,e\,x^2+5\,c^2\,d^4\,e^2\,x^3+5\,c^2\,d^3\,e^3\,x^4+3\,c^2\,d^2\,e^4\,x^5+c^2\,d\,e^5\,x^6+\frac{c^2\,e^6\,x^7}{7}","Not used",1,"c^2*d^6*x + (c^2*e^6*x^7)/7 + 3*c^2*d^5*e*x^2 + c^2*d*e^5*x^6 + 5*c^2*d^4*e^2*x^3 + 5*c^2*d^3*e^3*x^4 + 3*c^2*d^2*e^4*x^5","B"
988,1,71,17,0.028207,"\text{Not used}","int((d + e*x)*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2,x)","c^2\,d^5\,x+\frac{5\,c^2\,d^4\,e\,x^2}{2}+\frac{10\,c^2\,d^3\,e^2\,x^3}{3}+\frac{5\,c^2\,d^2\,e^3\,x^4}{2}+c^2\,d\,e^4\,x^5+\frac{c^2\,e^5\,x^6}{6}","Not used",1,"c^2*d^5*x + (c^2*e^5*x^6)/6 + (5*c^2*d^4*e*x^2)/2 + c^2*d*e^4*x^5 + (10*c^2*d^3*e^2*x^3)/3 + (5*c^2*d^2*e^3*x^4)/2","B"
989,1,57,17,0.023858,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2,x)","c^2\,d^4\,x+2\,c^2\,d^3\,e\,x^2+2\,c^2\,d^2\,e^2\,x^3+c^2\,d\,e^3\,x^4+\frac{c^2\,e^4\,x^5}{5}","Not used",1,"c^2*d^4*x + (c^2*e^4*x^5)/5 + 2*c^2*d^3*e*x^2 + c^2*d*e^3*x^4 + 2*c^2*d^2*e^2*x^3","B"
990,1,43,17,0.046940,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2/(d + e*x),x)","c^2\,d^3\,x+\frac{3\,c^2\,d^2\,e\,x^2}{2}+c^2\,d\,e^2\,x^3+\frac{c^2\,e^3\,x^4}{4}","Not used",1,"c^2*d^3*x + (c^2*e^3*x^4)/4 + (3*c^2*d^2*e*x^2)/2 + c^2*d*e^2*x^3","B"
991,1,24,17,0.039395,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2/(d + e*x)^2,x)","\frac{c^2\,x\,\left(3\,d^2+3\,d\,e\,x+e^2\,x^2\right)}{3}","Not used",1,"(c^2*x*(3*d^2 + e^2*x^2 + 3*d*e*x))/3","B"
992,1,13,17,0.021946,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2/(d + e*x)^3,x)","\frac{c^2\,x\,\left(2\,d+e\,x\right)}{2}","Not used",1,"(c^2*x*(2*d + e*x))/2","B"
993,1,5,5,0.006545,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2/(d + e*x)^4,x)","c^2\,x","Not used",1,"c^2*x","B"
994,1,13,13,0.024376,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2/(d + e*x)^5,x)","\frac{c^2\,\ln\left(d+e\,x\right)}{e}","Not used",1,"(c^2*log(d + e*x))/e","B"
995,1,15,15,0.021296,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2/(d + e*x)^6,x)","-\frac{c^2}{e\,\left(d+e\,x\right)}","Not used",1,"-c^2/(e*(d + e*x))","B"
996,1,26,17,0.026995,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2/(d + e*x)^7,x)","-\frac{c^2}{2\,e\,\left(d^2+2\,d\,e\,x+e^2\,x^2\right)}","Not used",1,"-c^2/(2*e*(d^2 + e^2*x^2 + 2*d*e*x))","B"
997,1,37,17,0.028042,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2/(d + e*x)^8,x)","-\frac{c^2}{3\,e\,\left(d^3+3\,d^2\,e\,x+3\,d\,e^2\,x^2+e^3\,x^3\right)}","Not used",1,"-c^2/(3*e*(d^3 + e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x))","B"
998,1,43,17,0.048281,"\text{Not used}","int((d + e*x)^5/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x),x)","\frac{d^3\,x}{c}+\frac{e^3\,x^4}{4\,c}+\frac{3\,d^2\,e\,x^2}{2\,c}+\frac{d\,e^2\,x^3}{c}","Not used",1,"(d^3*x)/c + (e^3*x^4)/(4*c) + (3*d^2*e*x^2)/(2*c) + (d*e^2*x^3)/c","B"
999,1,24,17,0.034492,"\text{Not used}","int((d + e*x)^4/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x),x)","\frac{x\,\left(3\,d^2+3\,d\,e\,x+e^2\,x^2\right)}{3\,c}","Not used",1,"(x*(3*d^2 + e^2*x^2 + 3*d*e*x))/(3*c)","B"
1000,1,13,17,0.024327,"\text{Not used}","int((d + e*x)^3/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x),x)","\frac{x\,\left(2\,d+e\,x\right)}{2\,c}","Not used",1,"(x*(2*d + e*x))/(2*c)","B"
1001,1,5,5,0.008811,"\text{Not used}","int((d + e*x)^2/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x),x)","\frac{x}{c}","Not used",1,"x/c","B"
1002,1,13,13,0.030720,"\text{Not used}","int((d + e*x)/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x),x)","\frac{\ln\left(d+e\,x\right)}{c\,e}","Not used",1,"log(d + e*x)/(c*e)","B"
1003,1,15,15,0.390690,"\text{Not used}","int(1/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x),x)","-\frac{1}{c\,x\,e^2+c\,d\,e}","Not used",1,"-1/(c*d*e + c*e^2*x)","B"
1004,1,29,17,0.034716,"\text{Not used}","int(1/((d + e*x)*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)),x)","-\frac{1}{2\,c\,d^2\,e+4\,c\,d\,e^2\,x+2\,c\,e^3\,x^2}","Not used",1,"-1/(2*c*e^3*x^2 + 2*c*d^2*e + 4*c*d*e^2*x)","B"
1005,1,41,17,0.403936,"\text{Not used}","int(1/((d + e*x)^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)),x)","-\frac{1}{3\,c\,d^3\,e+9\,c\,d^2\,e^2\,x+9\,c\,d\,e^3\,x^2+3\,c\,e^4\,x^3}","Not used",1,"-1/(3*c*e^4*x^3 + 3*c*d^3*e + 9*c*d^2*e^2*x + 9*c*d*e^3*x^2)","B"
1006,1,53,17,0.413866,"\text{Not used}","int(1/((d + e*x)^3*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)),x)","-\frac{1}{4\,c\,d^4\,e+16\,c\,d^3\,e^2\,x+24\,c\,d^2\,e^3\,x^2+16\,c\,d\,e^4\,x^3+4\,c\,e^5\,x^4}","Not used",1,"-1/(4*c*e^5*x^4 + 4*c*d^4*e + 24*c*d^2*e^3*x^2 + 16*c*d^3*e^2*x + 16*c*d*e^4*x^3)","B"
1007,1,43,17,0.047928,"\text{Not used}","int((d + e*x)^7/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2,x)","\frac{d^3\,x}{c^2}+\frac{e^3\,x^4}{4\,c^2}+\frac{3\,d^2\,e\,x^2}{2\,c^2}+\frac{d\,e^2\,x^3}{c^2}","Not used",1,"(d^3*x)/c^2 + (e^3*x^4)/(4*c^2) + (3*d^2*e*x^2)/(2*c^2) + (d*e^2*x^3)/c^2","B"
1008,1,24,17,0.033575,"\text{Not used}","int((d + e*x)^6/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2,x)","\frac{x\,\left(3\,d^2+3\,d\,e\,x+e^2\,x^2\right)}{3\,c^2}","Not used",1,"(x*(3*d^2 + e^2*x^2 + 3*d*e*x))/(3*c^2)","B"
1009,1,13,17,0.024341,"\text{Not used}","int((d + e*x)^5/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2,x)","\frac{x\,\left(2\,d+e\,x\right)}{2\,c^2}","Not used",1,"(x*(2*d + e*x))/(2*c^2)","B"
1010,1,5,5,0.008201,"\text{Not used}","int((d + e*x)^4/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2,x)","\frac{x}{c^2}","Not used",1,"x/c^2","B"
1011,1,13,13,0.035884,"\text{Not used}","int((d + e*x)^3/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2,x)","\frac{\ln\left(d+e\,x\right)}{c^2\,e}","Not used",1,"log(d + e*x)/(c^2*e)","B"
1012,1,19,15,0.036959,"\text{Not used}","int((d + e*x)^2/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2,x)","-\frac{1}{x\,c^2\,e^2+d\,c^2\,e}","Not used",1,"-1/(c^2*e^2*x + c^2*d*e)","B"
1013,1,35,17,0.423795,"\text{Not used}","int((d + e*x)/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2,x)","-\frac{1}{2\,c^2\,d^2\,e+4\,c^2\,d\,e^2\,x+2\,c^2\,e^3\,x^2}","Not used",1,"-1/(2*c^2*d^2*e + 2*c^2*e^3*x^2 + 4*c^2*d*e^2*x)","B"
1014,1,49,17,0.416967,"\text{Not used}","int(1/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2,x)","-\frac{1}{3\,c^2\,d^3\,e+9\,c^2\,d^2\,e^2\,x+9\,c^2\,d\,e^3\,x^2+3\,c^2\,e^4\,x^3}","Not used",1,"-1/(3*c^2*d^3*e + 3*c^2*e^4*x^3 + 9*c^2*d^2*e^2*x + 9*c^2*d*e^3*x^2)","B"
1015,1,63,17,0.053156,"\text{Not used}","int(1/((d + e*x)*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2),x)","-\frac{1}{4\,c^2\,d^4\,e+16\,c^2\,d^3\,e^2\,x+24\,c^2\,d^2\,e^3\,x^2+16\,c^2\,d\,e^4\,x^3+4\,c^2\,e^5\,x^4}","Not used",1,"-1/(4*c^2*d^4*e + 4*c^2*e^5*x^4 + 16*c^2*d^3*e^2*x + 16*c^2*d*e^4*x^3 + 24*c^2*d^2*e^3*x^2)","B"
1016,1,77,17,0.066143,"\text{Not used}","int(1/((d + e*x)^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2),x)","-\frac{1}{5\,c^2\,d^5\,e+25\,c^2\,d^4\,e^2\,x+50\,c^2\,d^3\,e^3\,x^2+50\,c^2\,d^2\,e^4\,x^3+25\,c^2\,d\,e^5\,x^4+5\,c^2\,e^6\,x^5}","Not used",1,"-1/(5*c^2*d^5*e + 5*c^2*e^6*x^5 + 25*c^2*d^4*e^2*x + 25*c^2*d*e^5*x^4 + 50*c^2*d^3*e^3*x^2 + 50*c^2*d^2*e^4*x^3)","B"
1017,1,43,17,0.046004,"\text{Not used}","int((d + e*x)^9/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^3,x)","\frac{d^3\,x}{c^3}+\frac{e^3\,x^4}{4\,c^3}+\frac{3\,d^2\,e\,x^2}{2\,c^3}+\frac{d\,e^2\,x^3}{c^3}","Not used",1,"(d^3*x)/c^3 + (e^3*x^4)/(4*c^3) + (3*d^2*e*x^2)/(2*c^3) + (d*e^2*x^3)/c^3","B"
1018,1,24,17,0.037641,"\text{Not used}","int((d + e*x)^8/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^3,x)","\frac{x\,\left(3\,d^2+3\,d\,e\,x+e^2\,x^2\right)}{3\,c^3}","Not used",1,"(x*(3*d^2 + e^2*x^2 + 3*d*e*x))/(3*c^3)","B"
1019,1,13,17,0.024604,"\text{Not used}","int((d + e*x)^7/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^3,x)","\frac{x\,\left(2\,d+e\,x\right)}{2\,c^3}","Not used",1,"(x*(2*d + e*x))/(2*c^3)","B"
1020,1,5,5,0.007718,"\text{Not used}","int((d + e*x)^6/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^3,x)","\frac{x}{c^3}","Not used",1,"x/c^3","B"
1021,1,13,13,0.409522,"\text{Not used}","int((d + e*x)^5/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^3,x)","\frac{\ln\left(d+e\,x\right)}{c^3\,e}","Not used",1,"log(d + e*x)/(c^3*e)","B"
1022,1,19,15,0.407126,"\text{Not used}","int((d + e*x)^4/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^3,x)","-\frac{1}{x\,c^3\,e^2+d\,c^3\,e}","Not used",1,"-1/(c^3*e^2*x + c^3*d*e)","B"
1023,1,35,17,0.412697,"\text{Not used}","int((d + e*x)^3/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^3,x)","-\frac{1}{2\,c^3\,d^2\,e+4\,c^3\,d\,e^2\,x+2\,c^3\,e^3\,x^2}","Not used",1,"-1/(2*c^3*d^2*e + 2*c^3*e^3*x^2 + 4*c^3*d*e^2*x)","B"
1024,1,49,17,0.406478,"\text{Not used}","int((d + e*x)^2/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^3,x)","-\frac{1}{3\,c^3\,d^3\,e+9\,c^3\,d^2\,e^2\,x+9\,c^3\,d\,e^3\,x^2+3\,c^3\,e^4\,x^3}","Not used",1,"-1/(3*c^3*d^3*e + 3*c^3*e^4*x^3 + 9*c^3*d^2*e^2*x + 9*c^3*d*e^3*x^2)","B"
1025,1,63,17,0.050998,"\text{Not used}","int((d + e*x)/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^3,x)","-\frac{1}{4\,c^3\,d^4\,e+16\,c^3\,d^3\,e^2\,x+24\,c^3\,d^2\,e^3\,x^2+16\,c^3\,d\,e^4\,x^3+4\,c^3\,e^5\,x^4}","Not used",1,"-1/(4*c^3*d^4*e + 4*c^3*e^5*x^4 + 16*c^3*d^3*e^2*x + 16*c^3*d*e^4*x^3 + 24*c^3*d^2*e^3*x^2)","B"
1026,1,77,17,0.433603,"\text{Not used}","int(1/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^3,x)","-\frac{1}{5\,c^3\,d^5\,e+25\,c^3\,d^4\,e^2\,x+50\,c^3\,d^3\,e^3\,x^2+50\,c^3\,d^2\,e^4\,x^3+25\,c^3\,d\,e^5\,x^4+5\,c^3\,e^6\,x^5}","Not used",1,"-1/(5*c^3*d^5*e + 5*c^3*e^6*x^5 + 25*c^3*d^4*e^2*x + 25*c^3*d*e^5*x^4 + 50*c^3*d^3*e^3*x^2 + 50*c^3*d^2*e^4*x^3)","B"
1027,1,91,17,0.454429,"\text{Not used}","int(1/((d + e*x)*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^3),x)","-\frac{1}{6\,c^3\,d^6\,e+36\,c^3\,d^5\,e^2\,x+90\,c^3\,d^4\,e^3\,x^2+120\,c^3\,d^3\,e^4\,x^3+90\,c^3\,d^2\,e^5\,x^4+36\,c^3\,d\,e^6\,x^5+6\,c^3\,e^7\,x^6}","Not used",1,"-1/(6*c^3*d^6*e + 6*c^3*e^7*x^6 + 36*c^3*d^5*e^2*x + 36*c^3*d*e^6*x^5 + 90*c^3*d^4*e^3*x^2 + 120*c^3*d^3*e^4*x^3 + 90*c^3*d^2*e^5*x^4)","B"
1028,1,105,17,0.065509,"\text{Not used}","int(1/((d + e*x)^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^3),x)","-\frac{1}{7\,c^3\,d^7\,e+49\,c^3\,d^6\,e^2\,x+147\,c^3\,d^5\,e^3\,x^2+245\,c^3\,d^4\,e^4\,x^3+245\,c^3\,d^3\,e^5\,x^4+147\,c^3\,d^2\,e^6\,x^5+49\,c^3\,d\,e^7\,x^6+7\,c^3\,e^8\,x^7}","Not used",1,"-1/(7*c^3*d^7*e + 7*c^3*e^8*x^7 + 49*c^3*d^6*e^2*x + 49*c^3*d*e^7*x^6 + 147*c^3*d^5*e^3*x^2 + 245*c^3*d^4*e^4*x^3 + 245*c^3*d^3*e^5*x^4 + 147*c^3*d^2*e^6*x^5)","B"
1029,1,239,34,0.911172,"\text{Not used}","int((d + e*x)^3*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2),x)","\frac{d^3\,\left(\frac{x}{2}+\frac{d}{2\,e}\right)\,\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{4}+\frac{e\,x^2\,{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{3/2}}{5\,c}-\frac{23\,d^2\,\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}\,\left(8\,e^2\,\left(d^2+e^2\,x^2\right)-12\,d^2\,e^2+4\,d\,e^3\,x\right)}{480\,e^3}+\frac{3\,d\,x\,{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{3/2}}{4\,c}-\frac{7\,d\,\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}\,\left(c\,d^3+3\,e\,x\,\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)-4\,c\,d^2\,e\,x-5\,c\,d\,e^2\,x^2\right)}{60\,c\,e}","Not used",1,"(d^3*(x/2 + d/(2*e))*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2))/4 + (e*x^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2))/(5*c) - (23*d^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)*(8*e^2*(d^2 + e^2*x^2) - 12*d^2*e^2 + 4*d*e^3*x))/(480*e^3) + (3*d*x*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2))/(4*c) - (7*d*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)*(c*d^3 + 3*e*x*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x) - 4*c*d^2*e*x - 5*c*d*e^2*x^2))/(60*c*e)","B"
1030,1,76,39,0.701302,"\text{Not used}","int((d + e*x)^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2),x)","\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}\,\left(c\,d^3+e\,x\,\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)+2\,c\,d^2\,e\,x+c\,d\,e^2\,x^2\right)}{4\,c\,e}","Not used",1,"((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)*(c*d^3 + e*x*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x) + 2*c*d^2*e*x + c*d*e^2*x^2))/(4*c*e)","B"
1031,1,34,34,0.533134,"\text{Not used}","int((d + e*x)*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2),x)","\frac{{\left(d+e\,x\right)}^2\,\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{3\,e}","Not used",1,"((d + e*x)^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2))/(3*e)","B"
1032,1,33,36,0.426225,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2),x)","\left(\frac{x}{2}+\frac{d}{2\,e}\right)\,\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}","Not used",1,"(x/2 + d/(2*e))*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)","B"
1033,1,15,28,0.477538,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(d + e*x),x)","\frac{\sqrt{c\,{\left(d+e\,x\right)}^2}}{e}","Not used",1,"(c*(d + e*x)^2)^(1/2)/e","B"
1034,0,-1,40,0.000000,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(d + e*x)^2,x)","\int \frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(d + e*x)^2, x)","F"
1035,1,34,30,0.422173,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(d + e*x)^3,x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{e\,{\left(d+e\,x\right)}^2}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(e*(d + e*x)^2)","B"
1036,1,34,39,0.443937,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(d + e*x)^4,x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{2\,e\,{\left(d+e\,x\right)}^3}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(2*e*(d + e*x)^3)","B"
1037,1,34,34,0.457968,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(d + e*x)^5,x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{3\,e\,{\left(d+e\,x\right)}^4}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(3*e*(d + e*x)^4)","B"
1038,1,34,41,0.485955,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(d + e*x)^6,x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{4\,e\,{\left(d+e\,x\right)}^5}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(4*e*(d + e*x)^5)","B"
1039,0,-1,34,0.000000,"\text{Not used}","int((d + e*x)^3*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2),x)","\int {\left(d+e\,x\right)}^3\,{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^3*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2), x)","F"
1040,0,-1,39,0.000000,"\text{Not used}","int((d + e*x)^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2),x)","\int {\left(d+e\,x\right)}^2\,{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2), x)","F"
1041,1,34,34,0.557383,"\text{Not used}","int((d + e*x)*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2),x)","\frac{{\left(d+e\,x\right)}^2\,{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{3/2}}{5\,e}","Not used",1,"((d + e*x)^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2))/(5*e)","B"
1042,1,36,36,0.413317,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2),x)","\frac{\left(x\,e^2+d\,e\right)\,{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{3/2}}{4\,e^2}","Not used",1,"((d*e + e^2*x)*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2))/(4*e^2)","B"
1043,1,16,31,0.477172,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2)/(d + e*x),x)","\frac{{\left(c\,{\left(d+e\,x\right)}^2\right)}^{3/2}}{3\,e}","Not used",1,"(c*(d + e*x)^2)^(3/2)/(3*e)","B"
1044,0,-1,37,0.000000,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2)/(d + e*x)^2,x)","\int \frac{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{3/2}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2)/(d + e*x)^2, x)","F"
1045,0,-1,29,0.000000,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2)/(d + e*x)^3,x)","\int \frac{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{3/2}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2)/(d + e*x)^3, x)","F"
1046,0,-1,42,0.000000,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2)/(d + e*x)^4,x)","\int \frac{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{3/2}}{{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2)/(d + e*x)^4, x)","F"
1047,1,35,32,0.425311,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2)/(d + e*x)^5,x)","-\frac{c\,\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{e\,{\left(d+e\,x\right)}^2}","Not used",1,"-(c*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2))/(e*(d + e*x)^2)","B"
1048,1,35,41,0.442074,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2)/(d + e*x)^6,x)","-\frac{c\,\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{2\,e\,{\left(d+e\,x\right)}^3}","Not used",1,"-(c*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2))/(2*e*(d + e*x)^3)","B"
1049,1,35,34,0.457365,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2)/(d + e*x)^7,x)","-\frac{c\,\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{3\,e\,{\left(d+e\,x\right)}^4}","Not used",1,"-(c*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2))/(3*e*(d + e*x)^4)","B"
1050,0,-1,34,0.000000,"\text{Not used}","int((d + e*x)^3*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2),x)","\int {\left(d+e\,x\right)}^3\,{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)^3*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2), x)","F"
1051,0,-1,39,0.000000,"\text{Not used}","int((d + e*x)^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2),x)","\int {\left(d+e\,x\right)}^2\,{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2), x)","F"
1052,1,19,34,0.654975,"\text{Not used}","int((d + e*x)*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2),x)","\frac{{\left(c\,{\left(d+e\,x\right)}^2\right)}^{7/2}}{7\,c\,e}","Not used",1,"(c*(d + e*x)^2)^(7/2)/(7*c*e)","B"
1053,1,36,36,0.039129,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2),x)","\frac{\left(x\,e^2+d\,e\right)\,{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{5/2}}{6\,e^2}","Not used",1,"((d*e + e^2*x)*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2))/(6*e^2)","B"
1054,1,16,31,0.476328,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2)/(d + e*x),x)","\frac{{\left(c\,{\left(d+e\,x\right)}^2\right)}^{5/2}}{5\,e}","Not used",1,"(c*(d + e*x)^2)^(5/2)/(5*e)","B"
1055,0,-1,37,0.000000,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2)/(d + e*x)^2,x)","\int \frac{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{5/2}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2)/(d + e*x)^2, x)","F"
1056,0,-1,32,0.000000,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2)/(d + e*x)^3,x)","\int \frac{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{5/2}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2)/(d + e*x)^3, x)","F"
1057,0,-1,39,0.000000,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2)/(d + e*x)^4,x)","\int \frac{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{5/2}}{{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2)/(d + e*x)^4, x)","F"
1058,0,-1,31,0.000000,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2)/(d + e*x)^5,x)","\int \frac{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{5/2}}{{\left(d+e\,x\right)}^5} \,d x","Not used",1,"int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2)/(d + e*x)^5, x)","F"
1059,0,-1,42,0.000000,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2)/(d + e*x)^6,x)","\int \frac{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{5/2}}{{\left(d+e\,x\right)}^6} \,d x","Not used",1,"int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2)/(d + e*x)^6, x)","F"
1060,1,37,32,0.428851,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2)/(d + e*x)^7,x)","-\frac{c^2\,\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{e\,{\left(d+e\,x\right)}^2}","Not used",1,"-(c^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2))/(e*(d + e*x)^2)","B"
1061,1,37,41,0.446331,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2)/(d + e*x)^8,x)","-\frac{c^2\,\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{2\,e\,{\left(d+e\,x\right)}^3}","Not used",1,"-(c^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2))/(2*e*(d + e*x)^3)","B"
1062,0,-1,39,0.000000,"\text{Not used}","int((d + e*x)^4/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}} \,d x","Not used",1,"int((d + e*x)^4/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2), x)","F"
1063,0,-1,34,0.000000,"\text{Not used}","int((d + e*x)^3/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^3}{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}} \,d x","Not used",1,"int((d + e*x)^3/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2), x)","F"
1064,0,-1,39,0.000000,"\text{Not used}","int((d + e*x)^2/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^2}{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}} \,d x","Not used",1,"int((d + e*x)^2/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2), x)","F"
1065,1,109,31,0.734137,"\text{Not used}","int((d + e*x)/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2),x)","\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{c\,e}-\frac{c\,d\,e^2\,\ln\left(\sqrt{c\,{\left(d+e\,x\right)}^2}\,\sqrt{c\,e^2}+c\,d\,e+c\,e^2\,x\right)}{{\left(c\,e^2\right)}^{3/2}}+\frac{c\,d\,e^2\,\ln\left(c\,x\,e^2+c\,d\,e\right)\,\mathrm{sign}\left(c\,e\,\left(d+e\,x\right)\right)}{{\left(c\,e^2\right)}^{3/2}}","Not used",1,"(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(c*e) - (c*d*e^2*log((c*(d + e*x)^2)^(1/2)*(c*e^2)^(1/2) + c*d*e + c*e^2*x))/(c*e^2)^(3/2) + (c*d*e^2*log(c*d*e + c*e^2*x)*sign(c*e*(d + e*x)))/(c*e^2)^(3/2)","B"
1066,1,29,39,0.465501,"\text{Not used}","int(1/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2),x)","\frac{\ln\left(c\,x\,e^2+c\,d\,e\right)\,\mathrm{sign}\left(c\,e\,\left(d+e\,x\right)\right)}{\sqrt{c\,e^2}}","Not used",1,"(log(c*d*e + c*e^2*x)*sign(c*e*(d + e*x)))/(c*e^2)^(1/2)","B"
1067,1,27,29,0.433394,"\text{Not used}","int(1/((d + e*x)*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)),x)","-\frac{1}{e\,\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}","Not used",1,"-1/(e*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2))","B"
1068,1,37,38,0.451056,"\text{Not used}","int(1/((d + e*x)^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)),x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{2\,c\,e\,{\left(d+e\,x\right)}^3}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(2*c*e*(d + e*x)^3)","B"
1069,1,37,32,0.455226,"\text{Not used}","int(1/((d + e*x)^3*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)),x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{3\,c\,e\,{\left(d+e\,x\right)}^4}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(3*c*e*(d + e*x)^4)","B"
1070,1,37,39,0.463372,"\text{Not used}","int(1/((d + e*x)^4*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)),x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{4\,c\,e\,{\left(d+e\,x\right)}^5}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(4*c*e*(d + e*x)^5)","B"
1071,0,-1,39,0.000000,"\text{Not used}","int((d + e*x)^4/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^4/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2), x)","F"
1072,0,-1,31,0.000000,"\text{Not used}","int((d + e*x)^3/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^3}{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^3/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2), x)","F"
1073,0,-1,42,0.000000,"\text{Not used}","int((d + e*x)^2/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^2}{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^2/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2), x)","F"
1074,1,37,32,0.457842,"\text{Not used}","int((d + e*x)/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2),x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{c^2\,e\,{\left(d+e\,x\right)}^2}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(c^2*e*(d + e*x)^2)","B"
1075,1,37,41,0.479910,"\text{Not used}","int(1/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2),x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{2\,c^2\,e\,{\left(d+e\,x\right)}^3}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(2*c^2*e*(d + e*x)^3)","B"
1076,1,37,31,0.473914,"\text{Not used}","int(1/((d + e*x)*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2)),x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{3\,c^2\,e\,{\left(d+e\,x\right)}^4}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(3*c^2*e*(d + e*x)^4)","B"
1077,1,37,38,0.478521,"\text{Not used}","int(1/((d + e*x)^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2)),x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{4\,c^2\,e\,{\left(d+e\,x\right)}^5}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(4*c^2*e*(d + e*x)^5)","B"
1078,1,37,32,0.516719,"\text{Not used}","int(1/((d + e*x)^3*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2)),x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{5\,c^2\,e\,{\left(d+e\,x\right)}^6}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(5*c^2*e*(d + e*x)^6)","B"
1079,0,-1,39,0.000000,"\text{Not used}","int((d + e*x)^6/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^6}{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^6/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2), x)","F"
1080,0,-1,31,0.000000,"\text{Not used}","int((d + e*x)^5/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^5}{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^5/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2), x)","F"
1081,0,-1,42,0.000000,"\text{Not used}","int((d + e*x)^4/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^4/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2), x)","F"
1082,1,37,32,0.481230,"\text{Not used}","int((d + e*x)^3/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2),x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{c^3\,e\,{\left(d+e\,x\right)}^2}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(c^3*e*(d + e*x)^2)","B"
1083,1,37,41,0.490453,"\text{Not used}","int((d + e*x)^2/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2),x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{2\,c^3\,e\,{\left(d+e\,x\right)}^3}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(2*c^3*e*(d + e*x)^3)","B"
1084,1,37,34,0.487682,"\text{Not used}","int((d + e*x)/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2),x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{3\,c^3\,e\,{\left(d+e\,x\right)}^4}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(3*c^3*e*(d + e*x)^4)","B"
1085,1,37,41,0.496665,"\text{Not used}","int(1/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2),x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{4\,c^3\,e\,{\left(d+e\,x\right)}^5}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(4*c^3*e*(d + e*x)^5)","B"
1086,1,37,31,0.538793,"\text{Not used}","int(1/((d + e*x)*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2)),x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{5\,c^3\,e\,{\left(d+e\,x\right)}^6}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(5*c^3*e*(d + e*x)^6)","B"
1087,1,37,38,0.563141,"\text{Not used}","int(1/((d + e*x)^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2)),x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{6\,c^3\,e\,{\left(d+e\,x\right)}^7}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(6*c^3*e*(d + e*x)^7)","B"
1088,1,37,32,0.568727,"\text{Not used}","int(1/((d + e*x)^3*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(5/2)),x)","-\frac{\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{7\,c^3\,e\,{\left(d+e\,x\right)}^8}","Not used",1,"-(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2)/(7*c^3*e*(d + e*x)^8)","B"
1089,1,106,21,0.510247,"\text{Not used}","int((d + e*x)^m*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2,x)","{\left(d+e\,x\right)}^m\,\left(\frac{5\,c^2\,d^4\,x}{m+5}+\frac{c^2\,d^5}{e\,\left(m+5\right)}+\frac{c^2\,e^4\,x^5}{m+5}+\frac{10\,c^2\,d^3\,e\,x^2}{m+5}+\frac{5\,c^2\,d\,e^3\,x^4}{m+5}+\frac{10\,c^2\,d^2\,e^2\,x^3}{m+5}\right)","Not used",1,"(d + e*x)^m*((5*c^2*d^4*x)/(m + 5) + (c^2*d^5)/(e*(m + 5)) + (c^2*e^4*x^5)/(m + 5) + (10*c^2*d^3*e*x^2)/(m + 5) + (5*c^2*d*e^3*x^4)/(m + 5) + (10*c^2*d^2*e^2*x^3)/(m + 5))","B"
1090,1,60,19,0.459435,"\text{Not used}","int((d + e*x)^m*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x),x)","{\left(d+e\,x\right)}^m\,\left(\frac{3\,c\,d^2\,x}{m+3}+\frac{c\,d^3}{e\,\left(m+3\right)}+\frac{c\,e^2\,x^3}{m+3}+\frac{3\,c\,d\,e\,x^2}{m+3}\right)","Not used",1,"(d + e*x)^m*((3*c*d^2*x)/(m + 3) + (c*d^3)/(e*(m + 3)) + (c*e^2*x^3)/(m + 3) + (3*c*d*e*x^2)/(m + 3))","B"
1091,1,28,24,0.468127,"\text{Not used}","int((d + e*x)^m/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x),x)","\frac{{\left(d+e\,x\right)}^m}{c\,e^2\,\left(x+\frac{d}{e}\right)\,\left(m-1\right)}","Not used",1,"(d + e*x)^m/(c*e^2*(x + d/e)*(m - 1))","B"
1092,1,50,24,0.495829,"\text{Not used}","int((d + e*x)^m/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^2,x)","\frac{{\left(d+e\,x\right)}^m}{c^2\,e^4\,\left(m-3\right)\,\left(x^3+\frac{d^3}{e^3}+\frac{3\,d\,x^2}{e}+\frac{3\,d^2\,x}{e^2}\right)}","Not used",1,"(d + e*x)^m/(c^2*e^4*(m - 3)*(x^3 + d^3/e^3 + (3*d*x^2)/e + (3*d^2*x)/e^2))","B"
1093,1,72,24,0.550260,"\text{Not used}","int((d + e*x)^m/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^3,x)","\frac{{\left(d+e\,x\right)}^m}{c^3\,e^6\,\left(m-5\right)\,\left(x^5+\frac{d^5}{e^5}+\frac{5\,d\,x^4}{e}+\frac{5\,d^4\,x}{e^4}+\frac{10\,d^2\,x^3}{e^2}+\frac{10\,d^3\,x^2}{e^3}\right)}","Not used",1,"(d + e*x)^m/(c^3*e^6*(m - 5)*(x^5 + d^5/e^5 + (5*d*x^4)/e + (5*d^4*x)/e^4 + (10*d^2*x^3)/e^2 + (10*d^3*x^2)/e^3))","B"
1094,0,-1,42,0.000000,"\text{Not used}","int((d + e*x)^m*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2),x)","\int {\left(d+e\,x\right)}^m\,{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^m*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2), x)","F"
1095,0,-1,42,0.000000,"\text{Not used}","int((d + e*x)^m*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2),x)","\int {\left(d+e\,x\right)}^m\,\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2} \,d x","Not used",1,"int((d + e*x)^m*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2), x)","F"
1096,1,48,40,0.487631,"\text{Not used}","int((d + e*x)^m/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2),x)","\frac{{\left(d+e\,x\right)}^m\,\sqrt{c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2}}{c\,e^2\,m\,\left(x+\frac{d}{e}\right)}","Not used",1,"((d + e*x)^m*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(1/2))/(c*e^2*m*(x + d/e))","B"
1097,0,-1,45,0.000000,"\text{Not used}","int((d + e*x)^m/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^m/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^(3/2), x)","F"
1098,1,43,43,0.479889,"\text{Not used}","int((d + e*x)^m*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p,x)","\frac{{\left(d+e\,x\right)}^{m+1}\,{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^p}{e\,\left(m+2\,p+1\right)}","Not used",1,"((d + e*x)^(m + 1)*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p)/(e*(m + 2*p + 1))","B"
1099,1,43,44,0.467382,"\text{Not used}","int((d + e*x)^p/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p,x)","-\frac{{\left(d+e\,x\right)}^{p+1}}{e\,\left(p-1\right)\,{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^p}","Not used",1,"-(d + e*x)^(p + 1)/(e*(p - 1)*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p)","B"
1100,1,90,39,0.478475,"\text{Not used}","int((d + e*x)^3*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p,x)","{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^p\,\left(\frac{d^4}{2\,e\,\left(p+2\right)}+\frac{e^3\,x^4}{2\,\left(p+2\right)}+\frac{2\,d^3\,x}{p+2}+\frac{3\,d^2\,e\,x^2}{p+2}+\frac{2\,d\,e^2\,x^3}{p+2}\right)","Not used",1,"(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p*(d^4/(2*e*(p + 2)) + (e^3*x^4)/(2*(p + 2)) + (2*d^3*x)/(p + 2) + (3*d^2*e*x^2)/(p + 2) + (2*d*e^2*x^3)/(p + 2))","B"
1101,1,79,43,0.449259,"\text{Not used}","int((d + e*x)^2*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p,x)","{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^p\,\left(\frac{3\,d^2\,x}{2\,p+3}+\frac{d^3}{e\,\left(2\,p+3\right)}+\frac{e^2\,x^3}{2\,p+3}+\frac{3\,d\,e\,x^2}{2\,p+3}\right)","Not used",1,"(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p*((3*d^2*x)/(2*p + 3) + d^3/(e*(2*p + 3)) + (e^2*x^3)/(2*p + 3) + (3*d*e*x^2)/(2*p + 3))","B"
1102,1,57,39,0.442040,"\text{Not used}","int((d + e*x)*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p,x)","{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^p\,\left(\frac{d^2}{2\,e\,\left(p+1\right)}+\frac{d\,x}{p+1}+\frac{e\,x^2}{2\,\left(p+1\right)}\right)","Not used",1,"(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p*(d^2/(2*e*(p + 1)) + (d*x)/(p + 1) + (e*x^2)/(2*(p + 1)))","B"
1103,1,45,38,0.476331,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p,x)","\left(\frac{x}{2\,p+1}+\frac{d}{e\,\left(2\,p+1\right)}\right)\,{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^p","Not used",1,"(x/(2*p + 1) + d/(e*(2*p + 1)))*(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p","B"
1104,1,30,32,0.414629,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p/(d + e*x),x)","\frac{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^p}{2\,e\,p}","Not used",1,"(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p/(2*e*p)","B"
1105,1,42,42,0.456096,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p/(d + e*x)^2,x)","\frac{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^p}{e^2\,\left(2\,p-1\right)\,\left(x+\frac{d}{e}\right)}","Not used",1,"(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p/(e^2*(2*p - 1)*(x + d/e))","B"
1106,1,52,39,0.485416,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p/(d + e*x)^3,x)","\frac{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^p}{2\,e^3\,\left(p-1\right)\,\left(x^2+\frac{d^2}{e^2}+\frac{2\,d\,x}{e}\right)}","Not used",1,"(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p/(2*e^3*(p - 1)*(x^2 + d^2/e^2 + (2*d*x)/e))","B"
1107,0,-1,41,0.000000,"\text{Not used}","int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p/(d + e*x)^(2*p + 1),x)","\int \frac{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^p}{{\left(d+e\,x\right)}^{2\,p+1}} \,d x","Not used",1,"int((c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p/(d + e*x)^(2*p + 1), x)","F"
1108,0,-1,43,0.000000,"\text{Not used}","int((d + e*x)^(2*p - 1)/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p,x)","\int \frac{{\left(d+e\,x\right)}^{2\,p-1}}{{\left(c\,d^2+2\,c\,d\,e\,x+c\,e^2\,x^2\right)}^p} \,d x","Not used",1,"int((d + e*x)^(2*p - 1)/(c*d^2 + c*e^2*x^2 + 2*c*d*e*x)^p, x)","F"
1109,1,113,45,0.439226,"\text{Not used}","int((b*d + 2*c*d*x)^4*(a + b*x + c*x^2),x)","\frac{16\,c^5\,d^4\,x^7}{7}+\frac{b^3\,d^4\,x^2\,\left(b^2+8\,a\,c\right)}{2}+8\,b\,c^4\,d^4\,x^6+\frac{8\,c^3\,d^4\,x^5\,\left(7\,b^2+2\,a\,c\right)}{5}+a\,b^4\,d^4\,x+8\,b\,c^2\,d^4\,x^4\,\left(b^2+a\,c\right)+b^2\,c\,d^4\,x^3\,\left(3\,b^2+8\,a\,c\right)","Not used",1,"(16*c^5*d^4*x^7)/7 + (b^3*d^4*x^2*(8*a*c + b^2))/2 + 8*b*c^4*d^4*x^6 + (8*c^3*d^4*x^5*(2*a*c + 7*b^2))/5 + a*b^4*d^4*x + 8*b*c^2*d^4*x^4*(a*c + b^2) + b^2*c*d^4*x^3*(8*a*c + 3*b^2)","B"
1110,1,93,45,0.423250,"\text{Not used}","int((b*d + 2*c*d*x)^3*(a + b*x + c*x^2),x)","\frac{4\,c^4\,d^3\,x^6}{3}+\frac{b^2\,d^3\,x^2\,\left(b^2+6\,a\,c\right)}{2}+4\,b\,c^3\,d^3\,x^5+\frac{c^2\,d^3\,x^4\,\left(9\,b^2+4\,a\,c\right)}{2}+a\,b^3\,d^3\,x+\frac{b\,c\,d^3\,x^3\,\left(7\,b^2+12\,a\,c\right)}{3}","Not used",1,"(4*c^4*d^3*x^6)/3 + (b^2*d^3*x^2*(6*a*c + b^2))/2 + 4*b*c^3*d^3*x^5 + (c^2*d^3*x^4*(4*a*c + 9*b^2))/2 + a*b^3*d^3*x + (b*c*d^3*x^3*(12*a*c + 7*b^2))/3","B"
1111,1,69,45,0.036075,"\text{Not used}","int((b*d + 2*c*d*x)^2*(a + b*x + c*x^2),x)","\frac{4\,c^3\,d^2\,x^5}{5}+\frac{c\,d^2\,x^3\,\left(5\,b^2+4\,a\,c\right)}{3}+2\,b\,c^2\,d^2\,x^4+\frac{b\,d^2\,x^2\,\left(b^2+4\,a\,c\right)}{2}+a\,b^2\,d^2\,x","Not used",1,"(4*c^3*d^2*x^5)/5 + (c*d^2*x^3*(4*a*c + 5*b^2))/3 + 2*b*c^2*d^2*x^4 + (b*d^2*x^2*(4*a*c + b^2))/2 + a*b^2*d^2*x","B"
1112,1,36,17,0.048864,"\text{Not used}","int((b*d + 2*c*d*x)*(a + b*x + c*x^2),x)","\frac{c^2\,d\,x^4}{2}+\frac{d\,x^2\,\left(b^2+2\,a\,c\right)}{2}+b\,c\,d\,x^3+a\,b\,d\,x","Not used",1,"(c^2*d*x^4)/2 + (d*x^2*(2*a*c + b^2))/2 + b*c*d*x^3 + a*b*d*x","B"
1113,1,44,48,0.437375,"\text{Not used}","int((a + b*x + c*x^2)/(b*d + 2*c*d*x),x)","\frac{x^2}{4\,d}+\frac{b\,x}{4\,c\,d}+\frac{\ln\left(b+2\,c\,x\right)\,\left(4\,a\,c-b^2\right)}{8\,c^2\,d}","Not used",1,"x^2/(4*d) + (b*x)/(4*c*d) + (log(b + 2*c*x)*(4*a*c - b^2))/(8*c^2*d)","B"
1114,1,36,38,0.429321,"\text{Not used}","int((a + b*x + c*x^2)/(b*d + 2*c*d*x)^2,x)","\frac{x}{4\,c\,d^2}-\frac{\frac{a\,c}{2}-\frac{b^2}{8}}{c^2\,d^2\,\left(b+2\,c\,x\right)}","Not used",1,"x/(4*c*d^2) - ((a*c)/2 - b^2/8)/(c^2*d^2*(b + 2*c*x))","B"
1115,1,42,44,0.447784,"\text{Not used}","int((a + b*x + c*x^2)/(b*d + 2*c*d*x)^3,x)","\frac{\ln\left(b+2\,c\,x\right)}{8\,c^2\,d^3}-\frac{\frac{a\,c}{4}-\frac{b^2}{16}}{c^2\,d^3\,{\left(b+2\,c\,x\right)}^2}","Not used",1,"log(b + 2*c*x)/(8*c^2*d^3) - ((a*c)/4 - b^2/16)/(c^2*d^3*(b + 2*c*x)^2)","B"
1116,1,71,45,0.427120,"\text{Not used}","int((a + b*x + c*x^2)/(b*d + 2*c*d*x)^4,x)","-\frac{\frac{b^2+2\,a\,c}{12\,c^2}+\frac{x^2}{2}+\frac{b\,x}{2\,c}}{b^3\,d^4+6\,b^2\,c\,d^4\,x+12\,b\,c^2\,d^4\,x^2+8\,c^3\,d^4\,x^3}","Not used",1,"-((2*a*c + b^2)/(12*c^2) + x^2/2 + (b*x)/(2*c))/(b^3*d^4 + 8*c^3*d^4*x^3 + 12*b*c^2*d^4*x^2 + 6*b^2*c*d^4*x)","B"
1117,1,85,37,0.065986,"\text{Not used}","int((a + b*x + c*x^2)/(b*d + 2*c*d*x)^5,x)","-\frac{\frac{b^2+4\,a\,c}{32\,c^2}+\frac{x^2}{4}+\frac{b\,x}{4\,c}}{b^4\,d^5+8\,b^3\,c\,d^5\,x+24\,b^2\,c^2\,d^5\,x^2+32\,b\,c^3\,d^5\,x^3+16\,c^4\,d^5\,x^4}","Not used",1,"-((4*a*c + b^2)/(32*c^2) + x^2/4 + (b*x)/(4*c))/(b^4*d^5 + 16*c^4*d^5*x^4 + 32*b*c^3*d^5*x^3 + 24*b^2*c^2*d^5*x^2 + 8*b^3*c*d^5*x)","B"
1118,1,99,45,0.446525,"\text{Not used}","int((a + b*x + c*x^2)/(b*d + 2*c*d*x)^6,x)","-\frac{\frac{b^2+6\,a\,c}{60\,c^2}+\frac{x^2}{6}+\frac{b\,x}{6\,c}}{b^5\,d^6+10\,b^4\,c\,d^6\,x+40\,b^3\,c^2\,d^6\,x^2+80\,b^2\,c^3\,d^6\,x^3+80\,b\,c^4\,d^6\,x^4+32\,c^5\,d^6\,x^5}","Not used",1,"-((6*a*c + b^2)/(60*c^2) + x^2/6 + (b*x)/(6*c))/(b^5*d^6 + 32*c^5*d^6*x^5 + 80*b*c^4*d^6*x^4 + 40*b^3*c^2*d^6*x^2 + 80*b^2*c^3*d^6*x^3 + 10*b^4*c*d^6*x)","B"
1119,1,113,45,0.468731,"\text{Not used}","int((a + b*x + c*x^2)/(b*d + 2*c*d*x)^7,x)","-\frac{\frac{b^2+8\,a\,c}{96\,c^2}+\frac{x^2}{8}+\frac{b\,x}{8\,c}}{b^6\,d^7+12\,b^5\,c\,d^7\,x+60\,b^4\,c^2\,d^7\,x^2+160\,b^3\,c^3\,d^7\,x^3+240\,b^2\,c^4\,d^7\,x^4+192\,b\,c^5\,d^7\,x^5+64\,c^6\,d^7\,x^6}","Not used",1,"-((8*a*c + b^2)/(96*c^2) + x^2/8 + (b*x)/(8*c))/(b^6*d^7 + 64*c^6*d^7*x^6 + 192*b*c^5*d^7*x^5 + 60*b^4*c^2*d^7*x^2 + 160*b^3*c^3*d^7*x^3 + 240*b^2*c^4*d^7*x^4 + 12*b^5*c*d^7*x)","B"
1120,1,127,45,0.486297,"\text{Not used}","int((a + b*x + c*x^2)/(b*d + 2*c*d*x)^8,x)","-\frac{\frac{b^2+10\,a\,c}{140\,c^2}+\frac{x^2}{10}+\frac{b\,x}{10\,c}}{b^7\,d^8+14\,b^6\,c\,d^8\,x+84\,b^5\,c^2\,d^8\,x^2+280\,b^4\,c^3\,d^8\,x^3+560\,b^3\,c^4\,d^8\,x^4+672\,b^2\,c^5\,d^8\,x^5+448\,b\,c^6\,d^8\,x^6+128\,c^7\,d^8\,x^7}","Not used",1,"-((10*a*c + b^2)/(140*c^2) + x^2/10 + (b*x)/(10*c))/(b^7*d^8 + 128*c^7*d^8*x^7 + 448*b*c^6*d^8*x^6 + 84*b^5*c^2*d^8*x^2 + 280*b^4*c^3*d^8*x^3 + 560*b^3*c^4*d^8*x^4 + 672*b^2*c^5*d^8*x^5 + 14*b^6*c*d^8*x)","B"
1121,1,224,73,0.481515,"\text{Not used}","int((b*d + 2*c*d*x)^5*(a + b*x + c*x^2)^2,x)","\frac{16\,c^7\,d^5\,x^{10}}{5}+\frac{c^3\,d^5\,x^6\,\left(16\,a^2\,c^2+160\,a\,b^2\,c+85\,b^4\right)}{3}+a^2\,b^5\,d^5\,x+16\,b\,c^6\,d^5\,x^9+2\,c^5\,d^5\,x^8\,\left(17\,b^2+4\,a\,c\right)+\frac{b^3\,d^5\,x^3\,\left(40\,a^2\,c^2+22\,a\,b^2\,c+b^4\right)}{3}+a\,b^4\,d^5\,x^2\,\left(b^2+5\,a\,c\right)+b^2\,c\,d^5\,x^4\,\left(20\,a^2\,c^2+25\,a\,b^2\,c+3\,b^4\right)+\frac{b\,c^2\,d^5\,x^5\,\left(80\,a^2\,c^2+240\,a\,b^2\,c+61\,b^4\right)}{5}+8\,b\,c^4\,d^5\,x^7\,\left(5\,b^2+4\,a\,c\right)","Not used",1,"(16*c^7*d^5*x^10)/5 + (c^3*d^5*x^6*(85*b^4 + 16*a^2*c^2 + 160*a*b^2*c))/3 + a^2*b^5*d^5*x + 16*b*c^6*d^5*x^9 + 2*c^5*d^5*x^8*(4*a*c + 17*b^2) + (b^3*d^5*x^3*(b^4 + 40*a^2*c^2 + 22*a*b^2*c))/3 + a*b^4*d^5*x^2*(5*a*c + b^2) + b^2*c*d^5*x^4*(3*b^4 + 20*a^2*c^2 + 25*a*b^2*c) + (b*c^2*d^5*x^5*(61*b^4 + 80*a^2*c^2 + 240*a*b^2*c))/5 + 8*b*c^4*d^5*x^7*(4*a*c + 5*b^2)","B"
1122,1,190,73,0.457863,"\text{Not used}","int((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^2,x)","\frac{16\,c^6\,d^4\,x^9}{9}+\frac{c^2\,d^4\,x^5\,\left(16\,a^2\,c^2+112\,a\,b^2\,c+41\,b^4\right)}{5}+a^2\,b^4\,d^4\,x+8\,b\,c^5\,d^4\,x^8+\frac{8\,c^4\,d^4\,x^7\,\left(13\,b^2+4\,a\,c\right)}{7}+\frac{b^2\,d^4\,x^3\,\left(24\,a^2\,c^2+18\,a\,b^2\,c+b^4\right)}{3}+\frac{b\,c\,d^4\,x^4\,\left(16\,a^2\,c^2+32\,a\,b^2\,c+5\,b^4\right)}{2}+a\,b^3\,d^4\,x^2\,\left(b^2+4\,a\,c\right)+\frac{4\,b\,c^3\,d^4\,x^6\,\left(11\,b^2+12\,a\,c\right)}{3}","Not used",1,"(16*c^6*d^4*x^9)/9 + (c^2*d^4*x^5*(41*b^4 + 16*a^2*c^2 + 112*a*b^2*c))/5 + a^2*b^4*d^4*x + 8*b*c^5*d^4*x^8 + (8*c^4*d^4*x^7*(4*a*c + 13*b^2))/7 + (b^2*d^4*x^3*(b^4 + 24*a^2*c^2 + 18*a*b^2*c))/3 + (b*c*d^4*x^4*(5*b^4 + 16*a^2*c^2 + 32*a*b^2*c))/2 + a*b^3*d^4*x^2*(4*a*c + b^2) + (4*b*c^3*d^4*x^6*(12*a*c + 11*b^2))/3","B"
1123,1,152,55,0.071054,"\text{Not used}","int((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^2,x)","c^5\,d^3\,x^8+a^2\,b^3\,d^3\,x+4\,b\,c^4\,d^3\,x^7+\frac{b\,d^3\,x^3\,\left(12\,a^2\,c^2+14\,a\,b^2\,c+b^4\right)}{3}+\frac{c^3\,d^3\,x^6\,\left(19\,b^2+8\,a\,c\right)}{3}+c\,d^3\,x^4\,\left(2\,a^2\,c^2+9\,a\,b^2\,c+2\,b^4\right)+a\,b^2\,d^3\,x^2\,\left(b^2+3\,a\,c\right)+b\,c^2\,d^3\,x^5\,\left(5\,b^2+8\,a\,c\right)","Not used",1,"c^5*d^3*x^8 + a^2*b^3*d^3*x + 4*b*c^4*d^3*x^7 + (b*d^3*x^3*(b^4 + 12*a^2*c^2 + 14*a*b^2*c))/3 + (c^3*d^3*x^6*(8*a*c + 19*b^2))/3 + c*d^3*x^4*(2*b^4 + 2*a^2*c^2 + 9*a*b^2*c) + a*b^2*d^3*x^2*(3*a*c + b^2) + b*c^2*d^3*x^5*(8*a*c + 5*b^2)","B"
1124,1,120,73,0.434316,"\text{Not used}","int((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^2,x)","\frac{4\,c^4\,d^2\,x^7}{7}+\frac{d^2\,x^3\,\left(4\,a^2\,c^2+10\,a\,b^2\,c+b^4\right)}{3}+a^2\,b^2\,d^2\,x+2\,b\,c^3\,d^2\,x^6+\frac{c^2\,d^2\,x^5\,\left(13\,b^2+8\,a\,c\right)}{5}+a\,b\,d^2\,x^2\,\left(b^2+2\,a\,c\right)+\frac{b\,c\,d^2\,x^4\,\left(3\,b^2+8\,a\,c\right)}{2}","Not used",1,"(4*c^4*d^2*x^7)/7 + (d^2*x^3*(b^4 + 4*a^2*c^2 + 10*a*b^2*c))/3 + a^2*b^2*d^2*x + 2*b*c^3*d^2*x^6 + (c^2*d^2*x^5*(8*a*c + 13*b^2))/5 + a*b*d^2*x^2*(2*a*c + b^2) + (b*c*d^2*x^4*(8*a*c + 3*b^2))/2","B"
1125,1,67,17,0.414845,"\text{Not used}","int((b*d + 2*c*d*x)*(a + b*x + c*x^2)^2,x)","\frac{c^3\,d\,x^6}{3}+a\,d\,x^2\,\left(b^2+a\,c\right)+\frac{b\,d\,x^3\,\left(b^2+6\,a\,c\right)}{3}+c\,d\,x^4\,\left(b^2+a\,c\right)+a^2\,b\,d\,x+b\,c^2\,d\,x^5","Not used",1,"(c^3*d*x^6)/3 + a*d*x^2*(a*c + b^2) + (b*d*x^3*(6*a*c + b^2))/3 + c*d*x^4*(a*c + b^2) + a^2*b*d*x + b*c^2*d*x^5","B"
1126,1,133,72,0.054594,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x),x)","x^2\,\left(\frac{b^2+2\,a\,c}{4\,c\,d}-\frac{3\,b^2}{16\,c\,d}\right)-x\,\left(\frac{b\,\left(\frac{b^2+2\,a\,c}{2\,c\,d}-\frac{3\,b^2}{8\,c\,d}\right)}{2\,c}-\frac{a\,b}{c\,d}\right)+\frac{b\,x^3}{4\,d}+\frac{c\,x^4}{8\,d}+\frac{\ln\left(b+2\,c\,x\right)\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}{32\,c^3\,d}","Not used",1,"x^2*((2*a*c + b^2)/(4*c*d) - (3*b^2)/(16*c*d)) - x*((b*((2*a*c + b^2)/(2*c*d) - (3*b^2)/(8*c*d)))/(2*c) - (a*b)/(c*d)) + (b*x^3)/(4*d) + (c*x^4)/(8*d) + (log(b + 2*c*x)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c))/(32*c^3*d)","B"
1127,1,96,72,0.062260,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^2,x)","x\,\left(\frac{b^2+2\,a\,c}{4\,c^2\,d^2}-\frac{5\,b^2}{16\,c^2\,d^2}\right)+\frac{x^3}{12\,d^2}-\frac{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}{2\,c\,\left(32\,x\,c^3\,d^2+16\,b\,c^2\,d^2\right)}+\frac{b\,x^2}{8\,c\,d^2}","Not used",1,"x*((2*a*c + b^2)/(4*c^2*d^2) - (5*b^2)/(16*c^2*d^2)) + x^3/(12*d^2) - (b^4 + 16*a^2*c^2 - 8*a*b^2*c)/(2*c*(16*b*c^2*d^2 + 32*c^3*d^2*x)) + (b*x^2)/(8*c*d^2)","B"
1128,1,106,79,0.086721,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^3,x)","\frac{x^2}{16\,c\,d^3}-\frac{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}{4\,c\,\left(16\,b^2\,c^2\,d^3+64\,b\,c^3\,d^3\,x+64\,c^4\,d^3\,x^2\right)}+\frac{b\,x}{16\,c^2\,d^3}+\frac{\ln\left(b+2\,c\,x\right)\,\left(4\,a\,c-b^2\right)}{16\,c^3\,d^3}","Not used",1,"x^2/(16*c*d^3) - (b^4 + 16*a^2*c^2 - 8*a*b^2*c)/(4*c*(16*b^2*c^2*d^3 + 64*c^4*d^3*x^2 + 64*b*c^3*d^3*x)) + (b*x)/(16*c^2*d^3) + (log(b + 2*c*x)*(4*a*c - b^2))/(16*c^3*d^3)","B"
1129,1,67,66,0.463919,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^4,x)","-\frac{\frac{a^2\,c^2}{6}-b\,\left(\frac{c^3\,x^3}{3}-a\,c^2\,x\right)-\frac{c^4\,x^4}{2}+a\,c^3\,x^2+\frac{a\,b^2\,c}{6}}{c^3\,d^4\,{\left(b+2\,c\,x\right)}^3}","Not used",1,"-((a^2*c^2)/6 - b*((c^3*x^3)/3 - a*c^2*x) - (c^4*x^4)/2 + a*c^3*x^2 + (a*b^2*c)/6)/(c^3*d^4*(b + 2*c*x)^3)","B"
1130,1,135,72,0.489674,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^5,x)","\frac{\ln\left(b+2\,c\,x\right)}{32\,c^3\,d^5}-\frac{\frac{16\,a^2\,c^2+8\,a\,b^2\,c-3\,b^4}{128\,c^3}-\frac{x\,\left(b^3-4\,a\,b\,c\right)}{8\,c^2}+\frac{x^2\,\left(4\,a\,c-b^2\right)}{8\,c}}{b^4\,d^5+8\,b^3\,c\,d^5\,x+24\,b^2\,c^2\,d^5\,x^2+32\,b\,c^3\,d^5\,x^3+16\,c^4\,d^5\,x^4}","Not used",1,"log(b + 2*c*x)/(32*c^3*d^5) - ((16*a^2*c^2 - 3*b^4 + 8*a*b^2*c)/(128*c^3) - (x*(b^3 - 4*a*b*c))/(8*c^2) + (x^2*(4*a*c - b^2))/(8*c))/(b^4*d^5 + 16*c^4*d^5*x^4 + 32*b*c^3*d^5*x^3 + 24*b^2*c^2*d^5*x^2 + 8*b^3*c*d^5*x)","B"
1131,1,141,73,0.082827,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^6,x)","-\frac{\frac{6\,a^2\,c^2+2\,a\,b^2\,c+b^4}{60\,c^3}+b\,x^3+\frac{c\,x^4}{2}+\frac{x^2\,\left(2\,b^2+a\,c\right)}{3\,c}+\frac{b\,x\,\left(b^2+2\,a\,c\right)}{6\,c^2}}{b^5\,d^6+10\,b^4\,c\,d^6\,x+40\,b^3\,c^2\,d^6\,x^2+80\,b^2\,c^3\,d^6\,x^3+80\,b\,c^4\,d^6\,x^4+32\,c^5\,d^6\,x^5}","Not used",1,"-((b^4 + 6*a^2*c^2 + 2*a*b^2*c)/(60*c^3) + b*x^3 + (c*x^4)/2 + (x^2*(a*c + 2*b^2))/(3*c) + (b*x*(2*a*c + b^2))/(6*c^2))/(b^5*d^6 + 32*c^5*d^6*x^5 + 80*b*c^4*d^6*x^4 + 40*b^3*c^2*d^6*x^2 + 80*b^2*c^3*d^6*x^3 + 10*b^4*c*d^6*x)","B"
1132,1,157,37,0.476990,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^7,x)","-\frac{\frac{16\,a^2\,c^2+4\,a\,b^2\,c+b^4}{192\,c^3}+\frac{b\,x^3}{2}+\frac{c\,x^4}{4}+\frac{x^2\,\left(5\,b^2+4\,a\,c\right)}{16\,c}+\frac{b\,x\,\left(b^2+4\,a\,c\right)}{16\,c^2}}{b^6\,d^7+12\,b^5\,c\,d^7\,x+60\,b^4\,c^2\,d^7\,x^2+160\,b^3\,c^3\,d^7\,x^3+240\,b^2\,c^4\,d^7\,x^4+192\,b\,c^5\,d^7\,x^5+64\,c^6\,d^7\,x^6}","Not used",1,"-((b^4 + 16*a^2*c^2 + 4*a*b^2*c)/(192*c^3) + (b*x^3)/2 + (c*x^4)/4 + (x^2*(4*a*c + 5*b^2))/(16*c) + (b*x*(4*a*c + b^2))/(16*c^2))/(b^6*d^7 + 64*c^6*d^7*x^6 + 192*b*c^5*d^7*x^5 + 60*b^4*c^2*d^7*x^2 + 160*b^3*c^3*d^7*x^3 + 240*b^2*c^4*d^7*x^4 + 12*b^5*c*d^7*x)","B"
1133,1,168,73,0.116747,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^8,x)","-\frac{\frac{30\,a^2\,c^2+6\,a\,b^2\,c+b^4}{420\,c^3}+\frac{b\,x^3}{3}+\frac{c\,x^4}{6}+\frac{x^2\,\left(b^2+a\,c\right)}{5\,c}+\frac{b\,x\,\left(b^2+6\,a\,c\right)}{30\,c^2}}{b^7\,d^8+14\,b^6\,c\,d^8\,x+84\,b^5\,c^2\,d^8\,x^2+280\,b^4\,c^3\,d^8\,x^3+560\,b^3\,c^4\,d^8\,x^4+672\,b^2\,c^5\,d^8\,x^5+448\,b\,c^6\,d^8\,x^6+128\,c^7\,d^8\,x^7}","Not used",1,"-((b^4 + 30*a^2*c^2 + 6*a*b^2*c)/(420*c^3) + (b*x^3)/3 + (c*x^4)/6 + (x^2*(a*c + b^2))/(5*c) + (b*x*(6*a*c + b^2))/(30*c^2))/(b^7*d^8 + 128*c^7*d^8*x^7 + 448*b*c^6*d^8*x^6 + 84*b^5*c^2*d^8*x^2 + 280*b^4*c^3*d^8*x^3 + 560*b^3*c^4*d^8*x^4 + 672*b^2*c^5*d^8*x^5 + 14*b^6*c*d^8*x)","B"
1134,1,185,73,0.527080,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^9,x)","-\frac{\frac{48\,a^2\,c^2+8\,a\,b^2\,c+b^4}{768\,c^3}+\frac{b\,x^3}{4}+\frac{c\,x^4}{8}+\frac{x^2\,\left(7\,b^2+8\,a\,c\right)}{48\,c}+\frac{b\,x\,\left(b^2+8\,a\,c\right)}{48\,c^2}}{b^8\,d^9+16\,b^7\,c\,d^9\,x+112\,b^6\,c^2\,d^9\,x^2+448\,b^5\,c^3\,d^9\,x^3+1120\,b^4\,c^4\,d^9\,x^4+1792\,b^3\,c^5\,d^9\,x^5+1792\,b^2\,c^6\,d^9\,x^6+1024\,b\,c^7\,d^9\,x^7+256\,c^8\,d^9\,x^8}","Not used",1,"-((b^4 + 48*a^2*c^2 + 8*a*b^2*c)/(768*c^3) + (b*x^3)/4 + (c*x^4)/8 + (x^2*(8*a*c + 7*b^2))/(48*c) + (b*x*(8*a*c + b^2))/(48*c^2))/(b^8*d^9 + 256*c^8*d^9*x^8 + 1024*b*c^7*d^9*x^7 + 112*b^6*c^2*d^9*x^2 + 448*b^5*c^3*d^9*x^3 + 1120*b^4*c^4*d^9*x^4 + 1792*b^3*c^5*d^9*x^5 + 1792*b^2*c^6*d^9*x^6 + 16*b^7*c*d^9*x)","B"
1135,1,199,73,0.577188,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^10,x)","-\frac{\frac{70\,a^2\,c^2+10\,a\,b^2\,c+b^4}{1260\,c^3}+\frac{b\,x^3}{5}+\frac{c\,x^4}{10}+\frac{x^2\,\left(4\,b^2+5\,a\,c\right)}{35\,c}+\frac{b\,x\,\left(b^2+10\,a\,c\right)}{70\,c^2}}{b^9\,d^{10}+18\,b^8\,c\,d^{10}\,x+144\,b^7\,c^2\,d^{10}\,x^2+672\,b^6\,c^3\,d^{10}\,x^3+2016\,b^5\,c^4\,d^{10}\,x^4+4032\,b^4\,c^5\,d^{10}\,x^5+5376\,b^3\,c^6\,d^{10}\,x^6+4608\,b^2\,c^7\,d^{10}\,x^7+2304\,b\,c^8\,d^{10}\,x^8+512\,c^9\,d^{10}\,x^9}","Not used",1,"-((b^4 + 70*a^2*c^2 + 10*a*b^2*c)/(1260*c^3) + (b*x^3)/5 + (c*x^4)/10 + (x^2*(5*a*c + 4*b^2))/(35*c) + (b*x*(10*a*c + b^2))/(70*c^2))/(b^9*d^10 + 512*c^9*d^10*x^9 + 2304*b*c^8*d^10*x^8 + 144*b^7*c^2*d^10*x^2 + 672*b^6*c^3*d^10*x^3 + 2016*b^5*c^4*d^10*x^4 + 4032*b^4*c^5*d^10*x^5 + 5376*b^3*c^6*d^10*x^6 + 4608*b^2*c^7*d^10*x^7 + 18*b^8*c*d^10*x)","B"
1136,1,213,73,0.638575,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^11,x)","-\frac{\frac{96\,a^2\,c^2+12\,a\,b^2\,c+b^4}{1920\,c^3}+\frac{b\,x^3}{6}+\frac{c\,x^4}{12}+\frac{x^2\,\left(3\,b^2+4\,a\,c\right)}{32\,c}+\frac{b\,x\,\left(b^2+12\,a\,c\right)}{96\,c^2}}{b^{10}\,d^{11}+20\,b^9\,c\,d^{11}\,x+180\,b^8\,c^2\,d^{11}\,x^2+960\,b^7\,c^3\,d^{11}\,x^3+3360\,b^6\,c^4\,d^{11}\,x^4+8064\,b^5\,c^5\,d^{11}\,x^5+13440\,b^4\,c^6\,d^{11}\,x^6+15360\,b^3\,c^7\,d^{11}\,x^7+11520\,b^2\,c^8\,d^{11}\,x^8+5120\,b\,c^9\,d^{11}\,x^9+1024\,c^{10}\,d^{11}\,x^{10}}","Not used",1,"-((b^4 + 96*a^2*c^2 + 12*a*b^2*c)/(1920*c^3) + (b*x^3)/6 + (c*x^4)/12 + (x^2*(4*a*c + 3*b^2))/(32*c) + (b*x*(12*a*c + b^2))/(96*c^2))/(b^10*d^11 + 1024*c^10*d^11*x^10 + 5120*b*c^9*d^11*x^9 + 180*b^8*c^2*d^11*x^2 + 960*b^7*c^3*d^11*x^3 + 3360*b^6*c^4*d^11*x^4 + 8064*b^5*c^5*d^11*x^5 + 13440*b^4*c^6*d^11*x^6 + 15360*b^3*c^7*d^11*x^7 + 11520*b^2*c^8*d^11*x^8 + 20*b^9*c*d^11*x)","B"
1137,1,326,101,0.156290,"\text{Not used}","int((b*d + 2*c*d*x)^5*(a + b*x + c*x^2)^3,x)","\frac{8\,c^8\,d^5\,x^{12}}{3}+\frac{3\,c^4\,d^5\,x^8\,\left(16\,a^2\,c^2+136\,a\,b^2\,c+75\,b^4\right)}{4}+a^3\,b^5\,d^5\,x+16\,b\,c^7\,d^5\,x^{11}+\frac{b^2\,d^5\,x^4\,\left(80\,a^3\,c^3+150\,a^2\,b^2\,c^2+36\,a\,b^4\,c+b^6\right)}{4}+\frac{16\,c^6\,d^5\,x^{10}\,\left(13\,b^2+3\,a\,c\right)}{5}+\frac{c^2\,d^5\,x^6\,\left(32\,a^3\,c^3+480\,a^2\,b^2\,c^2+510\,a\,b^4\,c+73\,b^6\right)}{6}+\frac{a^2\,b^4\,d^5\,x^2\,\left(3\,b^2+10\,a\,c\right)}{2}+\frac{a\,b^3\,d^5\,x^3\,\left(40\,a^2\,c^2+33\,a\,b^2\,c+3\,b^4\right)}{3}+3\,b\,c^3\,d^5\,x^7\,\left(16\,a^2\,c^2+40\,a\,b^2\,c+11\,b^4\right)+\frac{b\,c\,d^5\,x^5\,\left(80\,a^3\,c^3+360\,a^2\,b^2\,c^2+183\,a\,b^4\,c+13\,b^6\right)}{5}+\frac{8\,b\,c^5\,d^5\,x^9\,\left(23\,b^2+18\,a\,c\right)}{3}","Not used",1,"(8*c^8*d^5*x^12)/3 + (3*c^4*d^5*x^8*(75*b^4 + 16*a^2*c^2 + 136*a*b^2*c))/4 + a^3*b^5*d^5*x + 16*b*c^7*d^5*x^11 + (b^2*d^5*x^4*(b^6 + 80*a^3*c^3 + 150*a^2*b^2*c^2 + 36*a*b^4*c))/4 + (16*c^6*d^5*x^10*(3*a*c + 13*b^2))/5 + (c^2*d^5*x^6*(73*b^6 + 32*a^3*c^3 + 480*a^2*b^2*c^2 + 510*a*b^4*c))/6 + (a^2*b^4*d^5*x^2*(10*a*c + 3*b^2))/2 + (a*b^3*d^5*x^3*(3*b^4 + 40*a^2*c^2 + 33*a*b^2*c))/3 + 3*b*c^3*d^5*x^7*(11*b^4 + 16*a^2*c^2 + 40*a*b^2*c) + (b*c*d^5*x^5*(13*b^6 + 80*a^3*c^3 + 360*a^2*b^2*c^2 + 183*a*b^4*c))/5 + (8*b*c^5*d^5*x^9*(18*a*c + 23*b^2))/3","B"
1138,1,274,101,0.121213,"\text{Not used}","int((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^3,x)","\frac{16\,c^7\,d^4\,x^{11}}{11}+\frac{3\,c^3\,d^4\,x^7\,\left(16\,a^2\,c^2+104\,a\,b^2\,c+43\,b^4\right)}{7}+a^3\,b^4\,d^4\,x+8\,b\,c^6\,d^4\,x^{10}+\frac{c\,d^4\,x^5\,\left(16\,a^3\,c^3+168\,a^2\,b^2\,c^2+123\,a\,b^4\,c+11\,b^6\right)}{5}+\frac{8\,c^5\,d^4\,x^9\,\left(7\,b^2+2\,a\,c\right)}{3}+\frac{b\,d^4\,x^4\,\left(32\,a^3\,c^3+96\,a^2\,b^2\,c^2+30\,a\,b^4\,c+b^6\right)}{4}+a\,b^2\,d^4\,x^3\,\left(8\,a^2\,c^2+9\,a\,b^2\,c+b^4\right)+\frac{a^2\,b^3\,d^4\,x^2\,\left(3\,b^2+8\,a\,c\right)}{2}+24\,b\,c^4\,d^4\,x^8\,\left(b^2+a\,c\right)+\frac{b\,c^2\,d^4\,x^6\,\left(48\,a^2\,c^2+88\,a\,b^2\,c+17\,b^4\right)}{2}","Not used",1,"(16*c^7*d^4*x^11)/11 + (3*c^3*d^4*x^7*(43*b^4 + 16*a^2*c^2 + 104*a*b^2*c))/7 + a^3*b^4*d^4*x + 8*b*c^6*d^4*x^10 + (c*d^4*x^5*(11*b^6 + 16*a^3*c^3 + 168*a^2*b^2*c^2 + 123*a*b^4*c))/5 + (8*c^5*d^4*x^9*(2*a*c + 7*b^2))/3 + (b*d^4*x^4*(b^6 + 32*a^3*c^3 + 96*a^2*b^2*c^2 + 30*a*b^4*c))/4 + a*b^2*d^4*x^3*(b^4 + 8*a^2*c^2 + 9*a*b^2*c) + (a^2*b^3*d^4*x^2*(8*a*c + 3*b^2))/2 + 24*b*c^4*d^4*x^8*(a*c + b^2) + (b*c^2*d^4*x^6*(17*b^4 + 48*a^2*c^2 + 88*a*b^2*c))/2","B"
1139,1,229,55,0.483089,"\text{Not used}","int((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^3,x)","\frac{d^3\,x^4\,\left(8\,a^3\,c^3+54\,a^2\,b^2\,c^2+24\,a\,b^4\,c+b^6\right)}{4}+\frac{4\,c^6\,d^3\,x^{10}}{5}+\frac{c^2\,d^3\,x^6\,\left(8\,a^2\,c^2+38\,a\,b^2\,c+11\,b^4\right)}{2}+a^3\,b^3\,d^3\,x+4\,b\,c^5\,d^3\,x^9+\frac{3\,c^4\,d^3\,x^8\,\left(11\,b^2+4\,a\,c\right)}{4}+\frac{3\,b\,c\,d^3\,x^5\,\left(20\,a^2\,c^2+25\,a\,b^2\,c+3\,b^4\right)}{5}+a\,b\,d^3\,x^3\,\left(4\,a^2\,c^2+7\,a\,b^2\,c+b^4\right)+\frac{3\,a^2\,b^2\,d^3\,x^2\,\left(b^2+2\,a\,c\right)}{2}+3\,b\,c^3\,d^3\,x^7\,\left(3\,b^2+4\,a\,c\right)","Not used",1,"(d^3*x^4*(b^6 + 8*a^3*c^3 + 54*a^2*b^2*c^2 + 24*a*b^4*c))/4 + (4*c^6*d^3*x^10)/5 + (c^2*d^3*x^6*(11*b^4 + 8*a^2*c^2 + 38*a*b^2*c))/2 + a^3*b^3*d^3*x + 4*b*c^5*d^3*x^9 + (3*c^4*d^3*x^8*(4*a*c + 11*b^2))/4 + (3*b*c*d^3*x^5*(3*b^4 + 20*a^2*c^2 + 25*a*b^2*c))/5 + a*b*d^3*x^3*(b^4 + 4*a^2*c^2 + 7*a*b^2*c) + (3*a^2*b^2*d^3*x^2*(2*a*c + b^2))/2 + 3*b*c^3*d^3*x^7*(4*a*c + 3*b^2)","B"
1140,1,188,101,0.080562,"\text{Not used}","int((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^3,x)","\frac{4\,c^5\,d^2\,x^9}{9}+a^3\,b^2\,d^2\,x+2\,b\,c^4\,d^2\,x^8+\frac{b\,d^2\,x^4\,\left(24\,a^2\,c^2+18\,a\,b^2\,c+b^4\right)}{4}+\frac{c^3\,d^2\,x^7\,\left(25\,b^2+12\,a\,c\right)}{7}+\frac{a\,d^2\,x^3\,\left(4\,a^2\,c^2+15\,a\,b^2\,c+3\,b^4\right)}{3}+\frac{c\,d^2\,x^5\,\left(12\,a^2\,c^2+39\,a\,b^2\,c+7\,b^4\right)}{5}+\frac{a^2\,b\,d^2\,x^2\,\left(3\,b^2+4\,a\,c\right)}{2}+\frac{b\,c^2\,d^2\,x^6\,\left(19\,b^2+36\,a\,c\right)}{6}","Not used",1,"(4*c^5*d^2*x^9)/9 + a^3*b^2*d^2*x + 2*b*c^4*d^2*x^8 + (b*d^2*x^4*(b^4 + 24*a^2*c^2 + 18*a*b^2*c))/4 + (c^3*d^2*x^7*(12*a*c + 25*b^2))/7 + (a*d^2*x^3*(3*b^4 + 4*a^2*c^2 + 15*a*b^2*c))/3 + (c*d^2*x^5*(7*b^4 + 12*a^2*c^2 + 39*a*b^2*c))/5 + (a^2*b*d^2*x^2*(4*a*c + 3*b^2))/2 + (b*c^2*d^2*x^6*(36*a*c + 19*b^2))/6","B"
1141,1,119,17,0.436503,"\text{Not used}","int((b*d + 2*c*d*x)*(a + b*x + c*x^2)^3,x)","\frac{c^4\,d\,x^8}{4}+\frac{d\,x^4\,\left(6\,a^2\,c^2+12\,a\,b^2\,c+b^4\right)}{4}+\frac{c^2\,d\,x^6\,\left(3\,b^2+2\,a\,c\right)}{2}+a^3\,b\,d\,x+b\,c^3\,d\,x^7+\frac{a^2\,d\,x^2\,\left(3\,b^2+2\,a\,c\right)}{2}+a\,b\,d\,x^3\,\left(b^2+3\,a\,c\right)+b\,c\,d\,x^5\,\left(b^2+3\,a\,c\right)","Not used",1,"(c^4*d*x^8)/4 + (d*x^4*(b^4 + 6*a^2*c^2 + 12*a*b^2*c))/4 + (c^2*d*x^6*(2*a*c + 3*b^2))/2 + a^3*b*d*x + b*c^3*d*x^7 + (a^2*d*x^2*(2*a*c + 3*b^2))/2 + a*b*d*x^3*(3*a*c + b^2) + b*c*d*x^5*(3*a*c + b^2)","B"
1142,1,304,100,0.071995,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x),x)","x^2\,\left(\frac{b\,\left(\frac{b\,\left(\frac{3\,\left(b^2+a\,c\right)}{2\,d}-\frac{5\,b^2}{8\,d}\right)}{2\,c}-\frac{b^3+6\,a\,c\,b}{2\,c\,d}\right)}{4\,c}+\frac{3\,a\,\left(b^2+a\,c\right)}{4\,c\,d}\right)-x^3\,\left(\frac{b\,\left(\frac{3\,\left(b^2+a\,c\right)}{2\,d}-\frac{5\,b^2}{8\,d}\right)}{6\,c}-\frac{b^3+6\,a\,c\,b}{6\,c\,d}\right)-x\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{3\,\left(b^2+a\,c\right)}{2\,d}-\frac{5\,b^2}{8\,d}\right)}{2\,c}-\frac{b^3+6\,a\,c\,b}{2\,c\,d}\right)}{2\,c}+\frac{3\,a\,\left(b^2+a\,c\right)}{2\,c\,d}\right)}{2\,c}-\frac{3\,a^2\,b}{2\,c\,d}\right)+x^4\,\left(\frac{3\,\left(b^2+a\,c\right)}{8\,d}-\frac{5\,b^2}{32\,d}\right)+\frac{c^2\,x^6}{12\,d}+\frac{b\,c\,x^5}{4\,d}-\frac{\ln\left(b+2\,c\,x\right)\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}{128\,c^4\,d}","Not used",1,"x^2*((b*((b*((3*(a*c + b^2))/(2*d) - (5*b^2)/(8*d)))/(2*c) - (b^3 + 6*a*b*c)/(2*c*d)))/(4*c) + (3*a*(a*c + b^2))/(4*c*d)) - x^3*((b*((3*(a*c + b^2))/(2*d) - (5*b^2)/(8*d)))/(6*c) - (b^3 + 6*a*b*c)/(6*c*d)) - x*((b*((b*((b*((3*(a*c + b^2))/(2*d) - (5*b^2)/(8*d)))/(2*c) - (b^3 + 6*a*b*c)/(2*c*d)))/(2*c) + (3*a*(a*c + b^2))/(2*c*d)))/(2*c) - (3*a^2*b)/(2*c*d)) + x^4*((3*(a*c + b^2))/(8*d) - (5*b^2)/(32*d)) + (c^2*x^6)/(12*d) + (b*c*x^5)/(4*d) - (log(b + 2*c*x)*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c))/(128*c^4*d)","B"
1143,1,293,94,0.436927,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^2,x)","x^3\,\left(\frac{b^2+a\,c}{4\,c\,d^2}-\frac{3\,b^2}{16\,c\,d^2}\right)-x^2\,\left(\frac{b^3}{16\,c^2\,d^2}-\frac{b^3+6\,a\,c\,b}{8\,c^2\,d^2}+\frac{b\,\left(\frac{3\,\left(b^2+a\,c\right)}{4\,c\,d^2}-\frac{9\,b^2}{16\,c\,d^2}\right)}{2\,c}\right)+x\,\left(\frac{b\,\left(\frac{b^3}{8\,c^2\,d^2}-\frac{b^3+6\,a\,c\,b}{4\,c^2\,d^2}+\frac{b\,\left(\frac{3\,\left(b^2+a\,c\right)}{4\,c\,d^2}-\frac{9\,b^2}{16\,c\,d^2}\right)}{c}\right)}{c}-\frac{b^2\,\left(\frac{3\,\left(b^2+a\,c\right)}{4\,c\,d^2}-\frac{9\,b^2}{16\,c\,d^2}\right)}{4\,c^2}+\frac{3\,a\,\left(b^2+a\,c\right)}{4\,c^2\,d^2}\right)+\frac{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}{2\,c\,\left(128\,x\,c^4\,d^2+64\,b\,c^3\,d^2\right)}+\frac{b\,x^4}{8\,d^2}+\frac{c\,x^5}{20\,d^2}","Not used",1,"x^3*((a*c + b^2)/(4*c*d^2) - (3*b^2)/(16*c*d^2)) - x^2*(b^3/(16*c^2*d^2) - (b^3 + 6*a*b*c)/(8*c^2*d^2) + (b*((3*(a*c + b^2))/(4*c*d^2) - (9*b^2)/(16*c*d^2)))/(2*c)) + x*((b*(b^3/(8*c^2*d^2) - (b^3 + 6*a*b*c)/(4*c^2*d^2) + (b*((3*(a*c + b^2))/(4*c*d^2) - (9*b^2)/(16*c*d^2)))/c))/c - (b^2*((3*(a*c + b^2))/(4*c*d^2) - (9*b^2)/(16*c*d^2)))/(4*c^2) + (3*a*(a*c + b^2))/(4*c^2*d^2)) + (b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)/(2*c*(64*b*c^3*d^2 + 128*c^4*d^2*x)) + (b*x^4)/(8*d^2) + (c*x^5)/(20*d^2)","B"
1144,1,223,100,0.475923,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^3,x)","x^2\,\left(\frac{3\,\left(b^2+a\,c\right)}{16\,c^2\,d^3}-\frac{3\,b^2}{16\,c^2\,d^3}\right)-x\,\left(\frac{5\,b^3}{32\,c^3\,d^3}-\frac{b^3+6\,a\,c\,b}{8\,c^3\,d^3}+\frac{3\,b\,\left(\frac{3\,\left(b^2+a\,c\right)}{8\,c^2\,d^3}-\frac{3\,b^2}{8\,c^2\,d^3}\right)}{2\,c}\right)+\frac{x^4}{32\,d^3}+\frac{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}{8\,c\,\left(32\,b^2\,c^3\,d^3+128\,b\,c^4\,d^3\,x+128\,c^5\,d^3\,x^2\right)}+\frac{b\,x^3}{16\,c\,d^3}+\frac{\ln\left(b+2\,c\,x\right)\,\left(48\,a^2\,c^2-24\,a\,b^2\,c+3\,b^4\right)}{128\,c^4\,d^3}","Not used",1,"x^2*((3*(a*c + b^2))/(16*c^2*d^3) - (3*b^2)/(16*c^2*d^3)) - x*((5*b^3)/(32*c^3*d^3) - (b^3 + 6*a*b*c)/(8*c^3*d^3) + (3*b*((3*(a*c + b^2))/(8*c^2*d^3) - (3*b^2)/(8*c^2*d^3)))/(2*c)) + x^4/(32*d^3) + (b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)/(8*c*(32*b^2*c^3*d^3 + 128*c^5*d^3*x^2 + 128*b*c^4*d^3*x)) + (b*x^3)/(16*c*d^3) + (log(b + 2*c*x)*(3*b^4 + 48*a^2*c^2 - 24*a*b^2*c))/(128*c^4*d^3)","B"
1145,1,194,103,0.095664,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^4,x)","x\,\left(\frac{3\,\left(b^2+a\,c\right)}{16\,c^3\,d^4}-\frac{7\,b^2}{32\,c^3\,d^4}\right)-\frac{\frac{16\,a^3\,c^3+24\,a^2\,b^2\,c^2-15\,a\,b^4\,c+2\,b^6}{3\,c}+x^2\,\left(48\,a^2\,c^3-24\,a\,b^2\,c^2+3\,b^4\,c\right)+x\,\left(48\,a^2\,b\,c^2-24\,a\,b^3\,c+3\,b^5\right)}{32\,b^3\,c^3\,d^4+192\,b^2\,c^4\,d^4\,x+384\,b\,c^5\,d^4\,x^2+256\,c^6\,d^4\,x^3}+\frac{x^3}{48\,c\,d^4}+\frac{b\,x^2}{32\,c^2\,d^4}","Not used",1,"x*((3*(a*c + b^2))/(16*c^3*d^4) - (7*b^2)/(32*c^3*d^4)) - ((2*b^6 + 16*a^3*c^3 + 24*a^2*b^2*c^2 - 15*a*b^4*c)/(3*c) + x^2*(3*b^4*c + 48*a^2*c^3 - 24*a*b^2*c^2) + x*(3*b^5 + 48*a^2*b*c^2 - 24*a*b^3*c))/(32*b^3*c^3*d^4 + 256*c^6*d^4*x^3 + 192*b^2*c^4*d^4*x + 384*b*c^5*d^4*x^2) + x^3/(48*c*d^4) + (b*x^2)/(32*c^2*d^4)","B"
1146,1,202,107,0.501900,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^5,x)","\frac{x^2}{64\,c^2\,d^5}-\frac{\frac{64\,a^3\,c^3+48\,a^2\,b^2\,c^2-36\,a\,b^4\,c+5\,b^6}{8\,c}+x^2\,\left(48\,a^2\,c^3-24\,a\,b^2\,c^2+3\,b^4\,c\right)+x\,\left(48\,a^2\,b\,c^2-24\,a\,b^3\,c+3\,b^5\right)}{64\,b^4\,c^3\,d^5+512\,b^3\,c^4\,d^5\,x+1536\,b^2\,c^5\,d^5\,x^2+2048\,b\,c^6\,d^5\,x^3+1024\,c^7\,d^5\,x^4}+\frac{b\,x}{64\,c^3\,d^5}+\frac{\ln\left(b+2\,c\,x\right)\,\left(12\,a\,c-3\,b^2\right)}{128\,c^4\,d^5}","Not used",1,"x^2/(64*c^2*d^5) - ((5*b^6 + 64*a^3*c^3 + 48*a^2*b^2*c^2 - 36*a*b^4*c)/(8*c) + x^2*(3*b^4*c + 48*a^2*c^3 - 24*a*b^2*c^2) + x*(3*b^5 + 48*a^2*b*c^2 - 24*a*b^3*c))/(64*b^4*c^3*d^5 + 1024*c^7*d^5*x^4 + 512*b^3*c^4*d^5*x + 2048*b*c^6*d^5*x^3 + 1536*b^2*c^5*d^5*x^2) + (b*x)/(64*c^3*d^5) + (log(b + 2*c*x)*(12*a*c - 3*b^2))/(128*c^4*d^5)","B"
1147,1,129,94,0.527124,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^6,x)","-\frac{b^2\,\left(\frac{a^2\,c^2}{20}+2\,a\,c^3\,x^2-\frac{c^4\,x^4}{4}\right)+b\,\left(\frac{a^2\,c^3\,x}{2}+3\,a\,c^4\,x^3-\frac{7\,c^5\,x^5}{10}\right)+\frac{a^3\,c^3}{10}-\frac{c^6\,x^6}{2}+\frac{3\,a\,c^5\,x^4}{2}+\frac{a^2\,c^4\,x^2}{2}+\frac{a\,b^4\,c}{20}+\frac{a\,b^3\,c^2\,x}{2}}{c^4\,d^6\,{\left(b+2\,c\,x\right)}^5}","Not used",1,"-(b^2*((a^2*c^2)/20 - (c^4*x^4)/4 + 2*a*c^3*x^2) + b*((a^2*c^3*x)/2 - (7*c^5*x^5)/10 + 3*a*c^4*x^3) + (a^3*c^3)/10 - (c^6*x^6)/2 + (3*a*c^5*x^4)/2 + (a^2*c^4*x^2)/2 + (a*b^4*c)/20 + (a*b^3*c^2*x)/2)/(c^4*d^6*(b + 2*c*x)^5)","B"
1148,1,229,100,0.543907,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^7,x)","\frac{\ln\left(b+2\,c\,x\right)}{128\,c^4\,d^7}-\frac{\frac{128\,a^3\,c^3+48\,a^2\,b^2\,c^2+24\,a\,b^4\,c-11\,b^6}{1536\,c^4}+x^4\,\left(\frac{3\,a\,c}{4}-\frac{3\,b^2}{16}\right)+\frac{3\,x^2\,\left(16\,a^2\,c^2+40\,a\,b^2\,c-11\,b^4\right)}{128\,c^2}+\frac{3\,x\,\left(16\,a^2\,b\,c^2+8\,a\,b^3\,c-3\,b^5\right)}{128\,c^3}-\frac{3\,x^3\,\left(b^3-4\,a\,b\,c\right)}{8\,c}}{b^6\,d^7+12\,b^5\,c\,d^7\,x+60\,b^4\,c^2\,d^7\,x^2+160\,b^3\,c^3\,d^7\,x^3+240\,b^2\,c^4\,d^7\,x^4+192\,b\,c^5\,d^7\,x^5+64\,c^6\,d^7\,x^6}","Not used",1,"log(b + 2*c*x)/(128*c^4*d^7) - ((128*a^3*c^3 - 11*b^6 + 48*a^2*b^2*c^2 + 24*a*b^4*c)/(1536*c^4) + x^4*((3*a*c)/4 - (3*b^2)/16) + (3*x^2*(16*a^2*c^2 - 11*b^4 + 40*a*b^2*c))/(128*c^2) + (3*x*(16*a^2*b*c^2 - 3*b^5 + 8*a*b^3*c))/(128*c^3) - (3*x^3*(b^3 - 4*a*b*c))/(8*c))/(b^6*d^7 + 64*c^6*d^7*x^6 + 192*b*c^5*d^7*x^5 + 60*b^4*c^2*d^7*x^2 + 160*b^3*c^3*d^7*x^3 + 240*b^2*c^4*d^7*x^4 + 12*b^5*c*d^7*x)","B"
1149,1,233,101,0.527371,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^8,x)","-\frac{\frac{20\,a^3\,c^3+6\,a^2\,b^2\,c^2+2\,a\,b^4\,c+b^6}{280\,c^4}+x^4\,\left(\frac{7\,b^2}{4}+\frac{a\,c}{2}\right)+\frac{c^2\,x^6}{2}+\frac{x^3\,\left(b^3+a\,c\,b\right)}{c}+\frac{3\,x^2\,\left(a^2\,c^2+2\,a\,b^2\,c+b^4\right)}{10\,c^2}+\frac{3\,b\,c\,x^5}{2}+\frac{b\,x\,\left(6\,a^2\,c^2+2\,a\,b^2\,c+b^4\right)}{20\,c^3}}{b^7\,d^8+14\,b^6\,c\,d^8\,x+84\,b^5\,c^2\,d^8\,x^2+280\,b^4\,c^3\,d^8\,x^3+560\,b^3\,c^4\,d^8\,x^4+672\,b^2\,c^5\,d^8\,x^5+448\,b\,c^6\,d^8\,x^6+128\,c^7\,d^8\,x^7}","Not used",1,"-((b^6 + 20*a^3*c^3 + 6*a^2*b^2*c^2 + 2*a*b^4*c)/(280*c^4) + x^4*((a*c)/2 + (7*b^2)/4) + (c^2*x^6)/2 + (x^3*(b^3 + a*b*c))/c + (3*x^2*(b^4 + a^2*c^2 + 2*a*b^2*c))/(10*c^2) + (3*b*c*x^5)/2 + (b*x*(b^4 + 6*a^2*c^2 + 2*a*b^2*c))/(20*c^3))/(b^7*d^8 + 128*c^7*d^8*x^7 + 448*b*c^6*d^8*x^6 + 84*b^5*c^2*d^8*x^2 + 280*b^4*c^3*d^8*x^3 + 560*b^3*c^4*d^8*x^4 + 672*b^2*c^5*d^8*x^5 + 14*b^6*c*d^8*x)","B"
1150,1,254,37,0.552708,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^9,x)","-\frac{\frac{64\,a^3\,c^3+16\,a^2\,b^2\,c^2+4\,a\,b^4\,c+b^6}{1024\,c^4}+x^4\,\left(\frac{27\,b^2}{32}+\frac{3\,a\,c}{8}\right)+\frac{c^2\,x^6}{4}+\frac{x^2\,\left(16\,a^2\,c^2+28\,a\,b^2\,c+7\,b^4\right)}{64\,c^2}+\frac{3\,b\,c\,x^5}{4}+\frac{x^3\,\left(7\,b^3+12\,a\,c\,b\right)}{16\,c}+\frac{b\,x\,\left(16\,a^2\,c^2+4\,a\,b^2\,c+b^4\right)}{64\,c^3}}{b^8\,d^9+16\,b^7\,c\,d^9\,x+112\,b^6\,c^2\,d^9\,x^2+448\,b^5\,c^3\,d^9\,x^3+1120\,b^4\,c^4\,d^9\,x^4+1792\,b^3\,c^5\,d^9\,x^5+1792\,b^2\,c^6\,d^9\,x^6+1024\,b\,c^7\,d^9\,x^7+256\,c^8\,d^9\,x^8}","Not used",1,"-((b^6 + 64*a^3*c^3 + 16*a^2*b^2*c^2 + 4*a*b^4*c)/(1024*c^4) + x^4*((3*a*c)/8 + (27*b^2)/32) + (c^2*x^6)/4 + (x^2*(7*b^4 + 16*a^2*c^2 + 28*a*b^2*c))/(64*c^2) + (3*b*c*x^5)/4 + (x^3*(7*b^3 + 12*a*b*c))/(16*c) + (b*x*(b^4 + 16*a^2*c^2 + 4*a*b^2*c))/(64*c^3))/(b^8*d^9 + 256*c^8*d^9*x^8 + 1024*b*c^7*d^9*x^7 + 112*b^6*c^2*d^9*x^2 + 448*b^5*c^3*d^9*x^3 + 1120*b^4*c^4*d^9*x^4 + 1792*b^3*c^5*d^9*x^5 + 1792*b^2*c^6*d^9*x^6 + 16*b^7*c*d^9*x)","B"
1151,1,268,101,0.602858,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^10,x)","-\frac{\frac{140\,a^3\,c^3+30\,a^2\,b^2\,c^2+6\,a\,b^4\,c+b^6}{2520\,c^4}+x^4\,\left(\frac{11\,b^2}{20}+\frac{3\,a\,c}{10}\right)+\frac{c^2\,x^6}{6}+\frac{x^2\,\left(15\,a^2\,c^2+24\,a\,b^2\,c+4\,b^4\right)}{70\,c^2}+\frac{b\,c\,x^5}{2}+\frac{x^3\,\left(4\,b^3+9\,a\,c\,b\right)}{15\,c}+\frac{b\,x\,\left(30\,a^2\,c^2+6\,a\,b^2\,c+b^4\right)}{140\,c^3}}{b^9\,d^{10}+18\,b^8\,c\,d^{10}\,x+144\,b^7\,c^2\,d^{10}\,x^2+672\,b^6\,c^3\,d^{10}\,x^3+2016\,b^5\,c^4\,d^{10}\,x^4+4032\,b^4\,c^5\,d^{10}\,x^5+5376\,b^3\,c^6\,d^{10}\,x^6+4608\,b^2\,c^7\,d^{10}\,x^7+2304\,b\,c^8\,d^{10}\,x^8+512\,c^9\,d^{10}\,x^9}","Not used",1,"-((b^6 + 140*a^3*c^3 + 30*a^2*b^2*c^2 + 6*a*b^4*c)/(2520*c^4) + x^4*((3*a*c)/10 + (11*b^2)/20) + (c^2*x^6)/6 + (x^2*(4*b^4 + 15*a^2*c^2 + 24*a*b^2*c))/(70*c^2) + (b*c*x^5)/2 + (x^3*(4*b^3 + 9*a*b*c))/(15*c) + (b*x*(b^4 + 30*a^2*c^2 + 6*a*b^2*c))/(140*c^3))/(b^9*d^10 + 512*c^9*d^10*x^9 + 2304*b*c^8*d^10*x^8 + 144*b^7*c^2*d^10*x^2 + 672*b^6*c^3*d^10*x^3 + 2016*b^5*c^4*d^10*x^4 + 4032*b^4*c^5*d^10*x^5 + 5376*b^3*c^6*d^10*x^6 + 4608*b^2*c^7*d^10*x^7 + 18*b^8*c*d^10*x)","B"
1152,1,282,101,0.653415,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^11,x)","-\frac{\frac{256\,a^3\,c^3+48\,a^2\,b^2\,c^2+8\,a\,b^4\,c+b^6}{5120\,c^4}+x^4\,\left(\frac{13\,b^2}{32}+\frac{a\,c}{4}\right)+\frac{c^2\,x^6}{8}+\frac{3\,x^2\,\left(16\,a^2\,c^2+24\,a\,b^2\,c+3\,b^4\right)}{256\,c^2}+\frac{3\,b\,c\,x^5}{8}+\frac{x^3\,\left(3\,b^3+8\,a\,c\,b\right)}{16\,c}+\frac{b\,x\,\left(48\,a^2\,c^2+8\,a\,b^2\,c+b^4\right)}{256\,c^3}}{b^{10}\,d^{11}+20\,b^9\,c\,d^{11}\,x+180\,b^8\,c^2\,d^{11}\,x^2+960\,b^7\,c^3\,d^{11}\,x^3+3360\,b^6\,c^4\,d^{11}\,x^4+8064\,b^5\,c^5\,d^{11}\,x^5+13440\,b^4\,c^6\,d^{11}\,x^6+15360\,b^3\,c^7\,d^{11}\,x^7+11520\,b^2\,c^8\,d^{11}\,x^8+5120\,b\,c^9\,d^{11}\,x^9+1024\,c^{10}\,d^{11}\,x^{10}}","Not used",1,"-((b^6 + 256*a^3*c^3 + 48*a^2*b^2*c^2 + 8*a*b^4*c)/(5120*c^4) + x^4*((a*c)/4 + (13*b^2)/32) + (c^2*x^6)/8 + (3*x^2*(3*b^4 + 16*a^2*c^2 + 24*a*b^2*c))/(256*c^2) + (3*b*c*x^5)/8 + (x^3*(3*b^3 + 8*a*b*c))/(16*c) + (b*x*(b^4 + 48*a^2*c^2 + 8*a*b^2*c))/(256*c^3))/(b^10*d^11 + 1024*c^10*d^11*x^10 + 5120*b*c^9*d^11*x^9 + 180*b^8*c^2*d^11*x^2 + 960*b^7*c^3*d^11*x^3 + 3360*b^6*c^4*d^11*x^4 + 8064*b^5*c^5*d^11*x^5 + 13440*b^4*c^6*d^11*x^6 + 15360*b^3*c^7*d^11*x^7 + 11520*b^2*c^8*d^11*x^8 + 20*b^9*c*d^11*x)","B"
1153,1,292,101,0.776786,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^12,x)","-\frac{\frac{420\,a^3\,c^3+70\,a^2\,b^2\,c^2+10\,a\,b^4\,c+b^6}{9240\,c^4}+x^4\,\left(\frac{9\,b^2}{28}+\frac{3\,a\,c}{14}\right)+\frac{c^2\,x^6}{10}+\frac{x^3\,\left(b^3+3\,a\,c\,b\right)}{7\,c}+\frac{x^2\,\left(7\,a^2\,c^2+10\,a\,b^2\,c+b^4\right)}{42\,c^2}+\frac{3\,b\,c\,x^5}{10}+\frac{b\,x\,\left(70\,a^2\,c^2+10\,a\,b^2\,c+b^4\right)}{420\,c^3}}{b^{11}\,d^{12}+22\,b^{10}\,c\,d^{12}\,x+220\,b^9\,c^2\,d^{12}\,x^2+1320\,b^8\,c^3\,d^{12}\,x^3+5280\,b^7\,c^4\,d^{12}\,x^4+14784\,b^6\,c^5\,d^{12}\,x^5+29568\,b^5\,c^6\,d^{12}\,x^6+42240\,b^4\,c^7\,d^{12}\,x^7+42240\,b^3\,c^8\,d^{12}\,x^8+28160\,b^2\,c^9\,d^{12}\,x^9+11264\,b\,c^{10}\,d^{12}\,x^{10}+2048\,c^{11}\,d^{12}\,x^{11}}","Not used",1,"-((b^6 + 420*a^3*c^3 + 70*a^2*b^2*c^2 + 10*a*b^4*c)/(9240*c^4) + x^4*((3*a*c)/14 + (9*b^2)/28) + (c^2*x^6)/10 + (x^3*(b^3 + 3*a*b*c))/(7*c) + (x^2*(b^4 + 7*a^2*c^2 + 10*a*b^2*c))/(42*c^2) + (3*b*c*x^5)/10 + (b*x*(b^4 + 70*a^2*c^2 + 10*a*b^2*c))/(420*c^3))/(b^11*d^12 + 2048*c^11*d^12*x^11 + 11264*b*c^10*d^12*x^10 + 220*b^9*c^2*d^12*x^2 + 1320*b^8*c^3*d^12*x^3 + 5280*b^7*c^4*d^12*x^4 + 14784*b^6*c^5*d^12*x^5 + 29568*b^5*c^6*d^12*x^6 + 42240*b^4*c^7*d^12*x^7 + 42240*b^3*c^8*d^12*x^8 + 28160*b^2*c^9*d^12*x^9 + 22*b^10*c*d^12*x)","B"
1154,1,761,122,0.468477,"\text{Not used}","int((b*d + 2*c*d*x)^8/(a + b*x + c*x^2),x)","x^3\,\left(\frac{1120\,b^4\,c^3\,d^8}{3}-\frac{b\,\left(1792\,b^3\,c^4\,d^8+\frac{b\,\left(256\,a\,c^6\,d^8-1024\,b^2\,c^5\,d^8\right)}{c}-768\,a\,b\,c^5\,d^8\right)}{3\,c}+\frac{a\,\left(256\,a\,c^6\,d^8-1024\,b^2\,c^5\,d^8\right)}{3\,c}\right)-x^5\,\left(\frac{256\,a\,c^6\,d^8}{5}-\frac{1024\,b^2\,c^5\,d^8}{5}\right)-x^2\,\left(\frac{a\,\left(1792\,b^3\,c^4\,d^8+\frac{b\,\left(256\,a\,c^6\,d^8-1024\,b^2\,c^5\,d^8\right)}{c}-768\,a\,b\,c^5\,d^8\right)}{2\,c}+\frac{b\,\left(1120\,b^4\,c^3\,d^8-\frac{b\,\left(1792\,b^3\,c^4\,d^8+\frac{b\,\left(256\,a\,c^6\,d^8-1024\,b^2\,c^5\,d^8\right)}{c}-768\,a\,b\,c^5\,d^8\right)}{c}+\frac{a\,\left(256\,a\,c^6\,d^8-1024\,b^2\,c^5\,d^8\right)}{c}\right)}{2\,c}-224\,b^5\,c^2\,d^8\right)+x^4\,\left(448\,b^3\,c^4\,d^8+\frac{b\,\left(256\,a\,c^6\,d^8-1024\,b^2\,c^5\,d^8\right)}{4\,c}-192\,a\,b\,c^5\,d^8\right)+x\,\left(112\,b^6\,c\,d^8-\frac{a\,\left(1120\,b^4\,c^3\,d^8-\frac{b\,\left(1792\,b^3\,c^4\,d^8+\frac{b\,\left(256\,a\,c^6\,d^8-1024\,b^2\,c^5\,d^8\right)}{c}-768\,a\,b\,c^5\,d^8\right)}{c}+\frac{a\,\left(256\,a\,c^6\,d^8-1024\,b^2\,c^5\,d^8\right)}{c}\right)}{c}+\frac{b\,\left(\frac{a\,\left(1792\,b^3\,c^4\,d^8+\frac{b\,\left(256\,a\,c^6\,d^8-1024\,b^2\,c^5\,d^8\right)}{c}-768\,a\,b\,c^5\,d^8\right)}{c}+\frac{b\,\left(1120\,b^4\,c^3\,d^8-\frac{b\,\left(1792\,b^3\,c^4\,d^8+\frac{b\,\left(256\,a\,c^6\,d^8-1024\,b^2\,c^5\,d^8\right)}{c}-768\,a\,b\,c^5\,d^8\right)}{c}+\frac{a\,\left(256\,a\,c^6\,d^8-1024\,b^2\,c^5\,d^8\right)}{c}\right)}{c}-448\,b^5\,c^2\,d^8\right)}{c}\right)+2\,d^8\,\mathrm{atan}\left(\frac{b\,d^8\,{\left(4\,a\,c-b^2\right)}^{7/2}+2\,c\,d^8\,x\,{\left(4\,a\,c-b^2\right)}^{7/2}}{256\,a^4\,c^4\,d^8-256\,a^3\,b^2\,c^3\,d^8+96\,a^2\,b^4\,c^2\,d^8-16\,a\,b^6\,c\,d^8+b^8\,d^8}\right)\,{\left(4\,a\,c-b^2\right)}^{7/2}+\frac{256\,c^7\,d^8\,x^7}{7}+128\,b\,c^6\,d^8\,x^6","Not used",1,"x^3*((1120*b^4*c^3*d^8)/3 - (b*(1792*b^3*c^4*d^8 + (b*(256*a*c^6*d^8 - 1024*b^2*c^5*d^8))/c - 768*a*b*c^5*d^8))/(3*c) + (a*(256*a*c^6*d^8 - 1024*b^2*c^5*d^8))/(3*c)) - x^5*((256*a*c^6*d^8)/5 - (1024*b^2*c^5*d^8)/5) - x^2*((a*(1792*b^3*c^4*d^8 + (b*(256*a*c^6*d^8 - 1024*b^2*c^5*d^8))/c - 768*a*b*c^5*d^8))/(2*c) + (b*(1120*b^4*c^3*d^8 - (b*(1792*b^3*c^4*d^8 + (b*(256*a*c^6*d^8 - 1024*b^2*c^5*d^8))/c - 768*a*b*c^5*d^8))/c + (a*(256*a*c^6*d^8 - 1024*b^2*c^5*d^8))/c))/(2*c) - 224*b^5*c^2*d^8) + x^4*(448*b^3*c^4*d^8 + (b*(256*a*c^6*d^8 - 1024*b^2*c^5*d^8))/(4*c) - 192*a*b*c^5*d^8) + x*(112*b^6*c*d^8 - (a*(1120*b^4*c^3*d^8 - (b*(1792*b^3*c^4*d^8 + (b*(256*a*c^6*d^8 - 1024*b^2*c^5*d^8))/c - 768*a*b*c^5*d^8))/c + (a*(256*a*c^6*d^8 - 1024*b^2*c^5*d^8))/c))/c + (b*((a*(1792*b^3*c^4*d^8 + (b*(256*a*c^6*d^8 - 1024*b^2*c^5*d^8))/c - 768*a*b*c^5*d^8))/c + (b*(1120*b^4*c^3*d^8 - (b*(1792*b^3*c^4*d^8 + (b*(256*a*c^6*d^8 - 1024*b^2*c^5*d^8))/c - 768*a*b*c^5*d^8))/c + (a*(256*a*c^6*d^8 - 1024*b^2*c^5*d^8))/c))/c - 448*b^5*c^2*d^8))/c) + 2*d^8*atan((b*d^8*(4*a*c - b^2)^(7/2) + 2*c*d^8*x*(4*a*c - b^2)^(7/2))/(b^8*d^8 + 256*a^4*c^4*d^8 + 96*a^2*b^4*c^2*d^8 - 256*a^3*b^2*c^3*d^8 - 16*a*b^6*c*d^8))*(4*a*c - b^2)^(7/2) + (256*c^7*d^8*x^7)/7 + 128*b*c^6*d^8*x^6","B"
1155,1,418,86,0.473377,"\text{Not used}","int((b*d + 2*c*d*x)^7/(a + b*x + c*x^2),x)","x^2\,\left(140\,b^4\,c^2\,d^7-\frac{b\,\left(560\,b^3\,c^3\,d^7+\frac{b\,\left(128\,a\,c^5\,d^7-352\,b^2\,c^4\,d^7\right)}{c}-320\,a\,b\,c^4\,d^7\right)}{2\,c}+\frac{a\,\left(128\,a\,c^5\,d^7-352\,b^2\,c^4\,d^7\right)}{2\,c}\right)+\ln\left(c\,x^2+b\,x+a\right)\,\left(-64\,a^3\,c^3\,d^7+48\,a^2\,b^2\,c^2\,d^7-12\,a\,b^4\,c\,d^7+b^6\,d^7\right)-x^4\,\left(32\,a\,c^5\,d^7-88\,b^2\,c^4\,d^7\right)+x^3\,\left(\frac{560\,b^3\,c^3\,d^7}{3}+\frac{b\,\left(128\,a\,c^5\,d^7-352\,b^2\,c^4\,d^7\right)}{3\,c}-\frac{320\,a\,b\,c^4\,d^7}{3}\right)-x\,\left(\frac{a\,\left(560\,b^3\,c^3\,d^7+\frac{b\,\left(128\,a\,c^5\,d^7-352\,b^2\,c^4\,d^7\right)}{c}-320\,a\,b\,c^4\,d^7\right)}{c}-84\,b^5\,c\,d^7+\frac{b\,\left(280\,b^4\,c^2\,d^7-\frac{b\,\left(560\,b^3\,c^3\,d^7+\frac{b\,\left(128\,a\,c^5\,d^7-352\,b^2\,c^4\,d^7\right)}{c}-320\,a\,b\,c^4\,d^7\right)}{c}+\frac{a\,\left(128\,a\,c^5\,d^7-352\,b^2\,c^4\,d^7\right)}{c}\right)}{c}\right)+\frac{64\,c^6\,d^7\,x^6}{3}+64\,b\,c^5\,d^7\,x^5","Not used",1,"x^2*(140*b^4*c^2*d^7 - (b*(560*b^3*c^3*d^7 + (b*(128*a*c^5*d^7 - 352*b^2*c^4*d^7))/c - 320*a*b*c^4*d^7))/(2*c) + (a*(128*a*c^5*d^7 - 352*b^2*c^4*d^7))/(2*c)) + log(a + b*x + c*x^2)*(b^6*d^7 - 64*a^3*c^3*d^7 + 48*a^2*b^2*c^2*d^7 - 12*a*b^4*c*d^7) - x^4*(32*a*c^5*d^7 - 88*b^2*c^4*d^7) + x^3*((560*b^3*c^3*d^7)/3 + (b*(128*a*c^5*d^7 - 352*b^2*c^4*d^7))/(3*c) - (320*a*b*c^4*d^7)/3) - x*((a*(560*b^3*c^3*d^7 + (b*(128*a*c^5*d^7 - 352*b^2*c^4*d^7))/c - 320*a*b*c^4*d^7))/c - 84*b^5*c*d^7 + (b*(280*b^4*c^2*d^7 - (b*(560*b^3*c^3*d^7 + (b*(128*a*c^5*d^7 - 352*b^2*c^4*d^7))/c - 320*a*b*c^4*d^7))/c + (a*(128*a*c^5*d^7 - 352*b^2*c^4*d^7))/c))/c) + (64*c^6*d^7*x^6)/3 + 64*b*c^5*d^7*x^5","B"
1156,1,296,97,0.440678,"\text{Not used}","int((b*d + 2*c*d*x)^6/(a + b*x + c*x^2),x)","x\,\left(60\,b^4\,c\,d^6-\frac{b\,\left(160\,b^3\,c^2\,d^6+\frac{b\,\left(64\,a\,c^4\,d^6-112\,b^2\,c^3\,d^6\right)}{c}-128\,a\,b\,c^3\,d^6\right)}{c}+\frac{a\,\left(64\,a\,c^4\,d^6-112\,b^2\,c^3\,d^6\right)}{c}\right)-x^3\,\left(\frac{64\,a\,c^4\,d^6}{3}-\frac{112\,b^2\,c^3\,d^6}{3}\right)+x^2\,\left(80\,b^3\,c^2\,d^6+\frac{b\,\left(64\,a\,c^4\,d^6-112\,b^2\,c^3\,d^6\right)}{2\,c}-64\,a\,b\,c^3\,d^6\right)+2\,d^6\,\mathrm{atan}\left(\frac{b\,d^6\,{\left(4\,a\,c-b^2\right)}^{5/2}+2\,c\,d^6\,x\,{\left(4\,a\,c-b^2\right)}^{5/2}}{-64\,a^3\,c^3\,d^6+48\,a^2\,b^2\,c^2\,d^6-12\,a\,b^4\,c\,d^6+b^6\,d^6}\right)\,{\left(4\,a\,c-b^2\right)}^{5/2}+\frac{64\,c^5\,d^6\,x^5}{5}+32\,b\,c^4\,d^6\,x^4","Not used",1,"x*(60*b^4*c*d^6 - (b*(160*b^3*c^2*d^6 + (b*(64*a*c^4*d^6 - 112*b^2*c^3*d^6))/c - 128*a*b*c^3*d^6))/c + (a*(64*a*c^4*d^6 - 112*b^2*c^3*d^6))/c) - x^3*((64*a*c^4*d^6)/3 - (112*b^2*c^3*d^6)/3) + x^2*(80*b^3*c^2*d^6 + (b*(64*a*c^4*d^6 - 112*b^2*c^3*d^6))/(2*c) - 64*a*b*c^3*d^6) + 2*d^6*atan((b*d^6*(4*a*c - b^2)^(5/2) + 2*c*d^6*x*(4*a*c - b^2)^(5/2))/(b^6*d^6 - 64*a^3*c^3*d^6 + 48*a^2*b^2*c^2*d^6 - 12*a*b^4*c*d^6))*(4*a*c - b^2)^(5/2) + (64*c^5*d^6*x^5)/5 + 32*b*c^4*d^6*x^4","B"
1157,1,139,61,0.064402,"\text{Not used}","int((b*d + 2*c*d*x)^5/(a + b*x + c*x^2),x)","\ln\left(c\,x^2+b\,x+a\right)\,\left(16\,a^2\,c^2\,d^5-8\,a\,b^2\,c\,d^5+b^4\,d^5\right)-x^2\,\left(16\,a\,c^3\,d^5-16\,b^2\,c^2\,d^5\right)+x\,\left(40\,b^3\,c\,d^5+\frac{b\,\left(32\,a\,c^3\,d^5-32\,b^2\,c^2\,d^5\right)}{c}-48\,a\,b\,c^2\,d^5\right)+8\,c^4\,d^5\,x^4+16\,b\,c^3\,d^5\,x^3","Not used",1,"log(a + b*x + c*x^2)*(b^4*d^5 + 16*a^2*c^2*d^5 - 8*a*b^2*c*d^5) - x^2*(16*a*c^3*d^5 - 16*b^2*c^2*d^5) + x*(40*b^3*c*d^5 + (b*(32*a*c^3*d^5 - 32*b^2*c^2*d^5))/c - 48*a*b*c^2*d^5) + 8*c^4*d^5*x^4 + 16*b*c^3*d^5*x^3","B"
1158,1,133,72,0.074071,"\text{Not used}","int((b*d + 2*c*d*x)^4/(a + b*x + c*x^2),x)","\frac{16\,c^3\,d^4\,x^3}{3}-x\,\left(16\,a\,c^2\,d^4-8\,b^2\,c\,d^4\right)+2\,d^4\,\mathrm{atan}\left(\frac{b\,d^4\,{\left(4\,a\,c-b^2\right)}^{3/2}+2\,c\,d^4\,x\,{\left(4\,a\,c-b^2\right)}^{3/2}}{16\,a^2\,c^2\,d^4-8\,a\,b^2\,c\,d^4+b^4\,d^4}\right)\,{\left(4\,a\,c-b^2\right)}^{3/2}+8\,b\,c^2\,d^4\,x^2","Not used",1,"(16*c^3*d^4*x^3)/3 - x*(16*a*c^2*d^4 - 8*b^2*c*d^4) + 2*d^4*atan((b*d^4*(4*a*c - b^2)^(3/2) + 2*c*d^4*x*(4*a*c - b^2)^(3/2))/(b^4*d^4 + 16*a^2*c^2*d^4 - 8*a*b^2*c*d^4))*(4*a*c - b^2)^(3/2) + 8*b*c^2*d^4*x^2","B"
1159,1,47,36,0.436354,"\text{Not used}","int((b*d + 2*c*d*x)^3/(a + b*x + c*x^2),x)","\ln\left(c\,x^2+b\,x+a\right)\,\left(b^2\,d^3-4\,a\,c\,d^3\right)+4\,c^2\,d^3\,x^2+4\,b\,c\,d^3\,x","Not used",1,"log(a + b*x + c*x^2)*(b^2*d^3 - 4*a*c*d^3) + 4*c^2*d^3*x^2 + 4*b*c*d^3*x","B"
1160,1,81,49,0.067867,"\text{Not used}","int((b*d + 2*c*d*x)^2/(a + b*x + c*x^2),x)","2\,d^2\,\mathrm{atan}\left(\frac{b\,d^2\,\sqrt{4\,a\,c-b^2}+2\,c\,d^2\,x\,\sqrt{4\,a\,c-b^2}}{b^2\,d^2-4\,a\,c\,d^2}\right)\,\sqrt{4\,a\,c-b^2}+4\,c\,d^2\,x","Not used",1,"2*d^2*atan((b*d^2*(4*a*c - b^2)^(1/2) + 2*c*d^2*x*(4*a*c - b^2)^(1/2))/(b^2*d^2 - 4*a*c*d^2))*(4*a*c - b^2)^(1/2) + 4*c*d^2*x","B"
1161,1,13,13,0.036706,"\text{Not used}","int((b*d + 2*c*d*x)/(a + b*x + c*x^2),x)","d\,\ln\left(c\,x^2+b\,x+a\right)","Not used",1,"d*log(a + b*x + c*x^2)","B"
1162,1,47,48,0.531022,"\text{Not used}","int(1/((b*d + 2*c*d*x)*(a + b*x + c*x^2)),x)","\frac{2\,c\,d\,\ln\left(\frac{{\left(b+2\,c\,x\right)}^2}{c\,x^2+b\,x+a}\right)}{8\,a\,c^2\,d^2-2\,b^2\,c\,d^2}","Not used",1,"(2*c*d*log((b + 2*c*x)^2/(a + b*x + c*x^2)))/(8*a*c^2*d^2 - 2*b^2*c*d^2)","B"
1163,1,115,61,0.499983,"\text{Not used}","int(1/((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)),x)","\frac{2\,\mathrm{atan}\left(\frac{b^3\,d^2-4\,a\,b\,c\,d^2}{d^2\,{\left(4\,a\,c-b^2\right)}^{3/2}}+\frac{2\,c\,x\,\left(b^2\,d^2-4\,a\,c\,d^2\right)}{d^2\,{\left(4\,a\,c-b^2\right)}^{3/2}}\right)}{d^2\,{\left(4\,a\,c-b^2\right)}^{3/2}}-\frac{2}{\left(4\,a\,c-b^2\right)\,\left(b\,d^2+2\,c\,d^2\,x\right)}","Not used",1,"(2*atan((b^3*d^2 - 4*a*b*c*d^2)/(d^2*(4*a*c - b^2)^(3/2)) + (2*c*x*(b^2*d^2 - 4*a*c*d^2))/(d^2*(4*a*c - b^2)^(3/2))))/(d^2*(4*a*c - b^2)^(3/2)) - 2/((4*a*c - b^2)*(b*d^2 + 2*c*d^2*x))","B"
1164,1,151,70,0.221145,"\text{Not used}","int(1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)),x)","\frac{\ln\left(c\,x^2+b\,x+a\right)}{16\,a^2\,c^2\,d^3-8\,a\,b^2\,c\,d^3+b^4\,d^3}-\frac{2\,\ln\left(b+2\,c\,x\right)}{16\,a^2\,c^2\,d^3-8\,a\,b^2\,c\,d^3+b^4\,d^3}+\frac{1}{b^4\,d^3+4\,b^3\,c\,d^3\,x+4\,b^2\,c^2\,d^3\,x^2-4\,a\,b^2\,c\,d^3-16\,a\,b\,c^2\,d^3\,x-16\,a\,c^3\,d^3\,x^2}","Not used",1,"log(a + b*x + c*x^2)/(b^4*d^3 + 16*a^2*c^2*d^3 - 8*a*b^2*c*d^3) - (2*log(b + 2*c*x))/(b^4*d^3 + 16*a^2*c^2*d^3 - 8*a*b^2*c*d^3) + 1/(b^4*d^3 - 16*a*c^3*d^3*x^2 + 4*b^2*c^2*d^3*x^2 - 4*a*b^2*c*d^3 + 4*b^3*c*d^3*x - 16*a*b*c^2*d^3*x)","B"
1165,1,219,86,0.591147,"\text{Not used}","int(1/((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)),x)","\frac{\frac{8\,c^2\,x^2}{{\left(4\,a\,c-b^2\right)}^2}-\frac{8\,\left(a\,c-b^2\right)}{3\,{\left(4\,a\,c-b^2\right)}^2}+\frac{8\,b\,c\,x}{{\left(4\,a\,c-b^2\right)}^2}}{b^3\,d^4+6\,b^2\,c\,d^4\,x+12\,b\,c^2\,d^4\,x^2+8\,c^3\,d^4\,x^3}+\frac{2\,\mathrm{atan}\left(\frac{16\,a^2\,b\,c^2\,d^4-8\,a\,b^3\,c\,d^4+b^5\,d^4}{d^4\,{\left(4\,a\,c-b^2\right)}^{5/2}}+\frac{2\,c\,x\,\left(16\,a^2\,c^2\,d^4-8\,a\,b^2\,c\,d^4+b^4\,d^4\right)}{d^4\,{\left(4\,a\,c-b^2\right)}^{5/2}}\right)}{d^4\,{\left(4\,a\,c-b^2\right)}^{5/2}}","Not used",1,"((8*c^2*x^2)/(4*a*c - b^2)^2 - (8*(a*c - b^2))/(3*(4*a*c - b^2)^2) + (8*b*c*x)/(4*a*c - b^2)^2)/(b^3*d^4 + 8*c^3*d^4*x^3 + 12*b*c^2*d^4*x^2 + 6*b^2*c*d^4*x) + (2*atan((b^5*d^4 + 16*a^2*b*c^2*d^4 - 8*a*b^3*c*d^4)/(d^4*(4*a*c - b^2)^(5/2)) + (2*c*x*(b^4*d^4 + 16*a^2*c^2*d^4 - 8*a*b^2*c*d^4))/(d^4*(4*a*c - b^2)^(5/2))))/(d^4*(4*a*c - b^2)^(5/2))","B"
1166,1,508,126,0.115064,"\text{Not used}","int((b*d + 2*c*d*x)^8/(a + b*x + c*x^2)^2,x)","x^2\,\left(896\,b^3\,c^3\,d^8+\frac{b\,\left(256\,c^4\,d^8\,\left(b^2+2\,a\,c\right)-768\,b^2\,c^4\,d^8\right)}{c}-256\,b\,c^3\,d^8\,\left(b^2+2\,a\,c\right)-256\,a\,b\,c^4\,d^8\right)-\frac{x\,\left(-128\,a^3\,c^4\,d^8+96\,a^2\,b^2\,c^3\,d^8-24\,a\,b^4\,c^2\,d^8+2\,b^6\,c\,d^8\right)+b^7\,d^8-64\,a^3\,b\,c^3\,d^8+48\,a^2\,b^3\,c^2\,d^8-12\,a\,b^5\,c\,d^8}{c\,x^2+b\,x+a}-x^3\,\left(\frac{256\,c^4\,d^8\,\left(b^2+2\,a\,c\right)}{3}-256\,b^2\,c^4\,d^8\right)-x\,\left(\frac{2\,b\,\left(1792\,b^3\,c^3\,d^8+\frac{2\,b\,\left(256\,c^4\,d^8\,\left(b^2+2\,a\,c\right)-768\,b^2\,c^4\,d^8\right)}{c}-512\,b\,c^3\,d^8\,\left(b^2+2\,a\,c\right)-512\,a\,b\,c^4\,d^8\right)}{c}-\frac{\left(256\,c^4\,d^8\,\left(b^2+2\,a\,c\right)-768\,b^2\,c^4\,d^8\right)\,\left(b^2+2\,a\,c\right)}{c^2}+256\,a^2\,c^4\,d^8-1120\,b^4\,c^2\,d^8+1024\,a\,b^2\,c^3\,d^8\right)+\frac{256\,c^6\,d^8\,x^5}{5}+28\,c\,d^8\,\mathrm{atan}\left(\frac{28\,c^2\,d^8\,x\,{\left(4\,a\,c-b^2\right)}^{5/2}+14\,b\,c\,d^8\,{\left(4\,a\,c-b^2\right)}^{5/2}}{-896\,a^3\,c^4\,d^8+672\,a^2\,b^2\,c^3\,d^8-168\,a\,b^4\,c^2\,d^8+14\,b^6\,c\,d^8}\right)\,{\left(4\,a\,c-b^2\right)}^{5/2}+128\,b\,c^5\,d^8\,x^4","Not used",1,"x^2*(896*b^3*c^3*d^8 + (b*(256*c^4*d^8*(2*a*c + b^2) - 768*b^2*c^4*d^8))/c - 256*b*c^3*d^8*(2*a*c + b^2) - 256*a*b*c^4*d^8) - (x*(2*b^6*c*d^8 - 128*a^3*c^4*d^8 - 24*a*b^4*c^2*d^8 + 96*a^2*b^2*c^3*d^8) + b^7*d^8 - 64*a^3*b*c^3*d^8 + 48*a^2*b^3*c^2*d^8 - 12*a*b^5*c*d^8)/(a + b*x + c*x^2) - x^3*((256*c^4*d^8*(2*a*c + b^2))/3 - 256*b^2*c^4*d^8) - x*((2*b*(1792*b^3*c^3*d^8 + (2*b*(256*c^4*d^8*(2*a*c + b^2) - 768*b^2*c^4*d^8))/c - 512*b*c^3*d^8*(2*a*c + b^2) - 512*a*b*c^4*d^8))/c - ((256*c^4*d^8*(2*a*c + b^2) - 768*b^2*c^4*d^8)*(2*a*c + b^2))/c^2 + 256*a^2*c^4*d^8 - 1120*b^4*c^2*d^8 + 1024*a*b^2*c^3*d^8) + (256*c^6*d^8*x^5)/5 + 28*c*d^8*atan((28*c^2*d^8*x*(4*a*c - b^2)^(5/2) + 14*b*c*d^8*(4*a*c - b^2)^(5/2))/(14*b^6*c*d^8 - 896*a^3*c^4*d^8 - 168*a*b^4*c^2*d^8 + 672*a^2*b^2*c^3*d^8))*(4*a*c - b^2)^(5/2) + 128*b*c^5*d^8*x^4","B"
1167,1,234,89,0.488087,"\text{Not used}","int((b*d + 2*c*d*x)^7/(a + b*x + c*x^2)^2,x)","\ln\left(c\,x^2+b\,x+a\right)\,\left(192\,a^2\,c^3\,d^7-96\,a\,b^2\,c^2\,d^7+12\,b^4\,c\,d^7\right)-x^2\,\left(64\,c^3\,d^7\,\left(b^2+2\,a\,c\right)-144\,b^2\,c^3\,d^7\right)-\frac{-64\,a^3\,c^3\,d^7+48\,a^2\,b^2\,c^2\,d^7-12\,a\,b^4\,c\,d^7+b^6\,d^7}{c\,x^2+b\,x+a}+x\,\left(560\,b^3\,c^2\,d^7+\frac{2\,b\,\left(128\,c^3\,d^7\,\left(b^2+2\,a\,c\right)-288\,b^2\,c^3\,d^7\right)}{c}-192\,b\,c^2\,d^7\,\left(b^2+2\,a\,c\right)-256\,a\,b\,c^3\,d^7\right)+32\,c^5\,d^7\,x^4+64\,b\,c^4\,d^7\,x^3","Not used",1,"log(a + b*x + c*x^2)*(12*b^4*c*d^7 + 192*a^2*c^3*d^7 - 96*a*b^2*c^2*d^7) - x^2*(64*c^3*d^7*(2*a*c + b^2) - 144*b^2*c^3*d^7) - (b^6*d^7 - 64*a^3*c^3*d^7 + 48*a^2*b^2*c^2*d^7 - 12*a*b^4*c*d^7)/(a + b*x + c*x^2) + x*(560*b^3*c^2*d^7 + (2*b*(128*c^3*d^7*(2*a*c + b^2) - 288*b^2*c^3*d^7))/c - 192*b*c^2*d^7*(2*a*c + b^2) - 256*a*b*c^3*d^7) + 32*c^5*d^7*x^4 + 64*b*c^4*d^7*x^3","B"
1168,1,230,100,0.083163,"\text{Not used}","int((b*d + 2*c*d*x)^6/(a + b*x + c*x^2)^2,x)","\frac{64\,c^4\,d^6\,x^3}{3}-\frac{x\,\left(32\,a^2\,c^3\,d^6-16\,a\,b^2\,c^2\,d^6+2\,b^4\,c\,d^6\right)+b^5\,d^6+16\,a^2\,b\,c^2\,d^6-8\,a\,b^3\,c\,d^6}{c\,x^2+b\,x+a}-x\,\left(64\,c^2\,d^6\,\left(b^2+2\,a\,c\right)-112\,b^2\,c^2\,d^6\right)+32\,b\,c^3\,d^6\,x^2+20\,c\,d^6\,\mathrm{atan}\left(\frac{20\,c^2\,d^6\,x\,{\left(4\,a\,c-b^2\right)}^{3/2}+10\,b\,c\,d^6\,{\left(4\,a\,c-b^2\right)}^{3/2}}{160\,a^2\,c^3\,d^6-80\,a\,b^2\,c^2\,d^6+10\,b^4\,c\,d^6}\right)\,{\left(4\,a\,c-b^2\right)}^{3/2}","Not used",1,"(64*c^4*d^6*x^3)/3 - (x*(2*b^4*c*d^6 + 32*a^2*c^3*d^6 - 16*a*b^2*c^2*d^6) + b^5*d^6 + 16*a^2*b*c^2*d^6 - 8*a*b^3*c*d^6)/(a + b*x + c*x^2) - x*(64*c^2*d^6*(2*a*c + b^2) - 112*b^2*c^2*d^6) + 32*b*c^3*d^6*x^2 + 20*c*d^6*atan((20*c^2*d^6*x*(4*a*c - b^2)^(3/2) + 10*b*c*d^6*(4*a*c - b^2)^(3/2))/(10*b^4*c*d^6 + 160*a^2*c^3*d^6 - 80*a*b^2*c^2*d^6))*(4*a*c - b^2)^(3/2)","B"
1169,1,97,65,0.488088,"\text{Not used}","int((b*d + 2*c*d*x)^5/(a + b*x + c*x^2)^2,x)","16\,c^3\,d^5\,x^2-\frac{16\,a^2\,c^2\,d^5-8\,a\,b^2\,c\,d^5+b^4\,d^5}{c\,x^2+b\,x+a}-\ln\left(c\,x^2+b\,x+a\right)\,\left(32\,a\,c^2\,d^5-8\,b^2\,c\,d^5\right)+16\,b\,c^2\,d^5\,x","Not used",1,"16*c^3*d^5*x^2 - (b^4*d^5 + 16*a^2*c^2*d^5 - 8*a*b^2*c*d^5)/(a + b*x + c*x^2) - log(a + b*x + c*x^2)*(32*a*c^2*d^5 - 8*b^2*c*d^5) + 16*b*c^2*d^5*x","B"
1170,1,143,76,0.490629,"\text{Not used}","int((b*d + 2*c*d*x)^4/(a + b*x + c*x^2)^2,x)","\frac{x\,\left(8\,a\,c^2\,d^4-2\,b^2\,c\,d^4\right)-b^3\,d^4+4\,a\,b\,c\,d^4}{c\,x^2+b\,x+a}+16\,c^2\,d^4\,x-12\,c\,d^4\,\mathrm{atan}\left(\frac{12\,c^2\,d^4\,x\,\sqrt{4\,a\,c-b^2}+6\,b\,c\,d^4\,\sqrt{4\,a\,c-b^2}}{24\,a\,c^2\,d^4-6\,b^2\,c\,d^4}\right)\,\sqrt{4\,a\,c-b^2}","Not used",1,"(x*(8*a*c^2*d^4 - 2*b^2*c*d^4) - b^3*d^4 + 4*a*b*c*d^4)/(a + b*x + c*x^2) + 16*c^2*d^4*x - 12*c*d^4*atan((12*c^2*d^4*x*(4*a*c - b^2)^(1/2) + 6*b*c*d^4*(4*a*c - b^2)^(1/2))/(24*a*c^2*d^4 - 6*b^2*c*d^4))*(4*a*c - b^2)^(1/2)","B"
1171,1,47,43,0.067003,"\text{Not used}","int((b*d + 2*c*d*x)^3/(a + b*x + c*x^2)^2,x)","4\,c\,d^3\,\ln\left(c\,x^2+b\,x+a\right)-\frac{b^2\,d^3-4\,a\,c\,d^3}{c\,x^2+b\,x+a}","Not used",1,"4*c*d^3*log(a + b*x + c*x^2) - (b^2*d^3 - 4*a*c*d^3)/(a + b*x + c*x^2)","B"
1172,1,88,62,0.444919,"\text{Not used}","int((b*d + 2*c*d*x)^2/(a + b*x + c*x^2)^2,x)","\frac{4\,c\,d^2\,\mathrm{atan}\left(\frac{b}{\sqrt{4\,a\,c-b^2}}+\frac{2\,c\,x}{\sqrt{4\,a\,c-b^2}}\right)}{\sqrt{4\,a\,c-b^2}}-\frac{b\,d^2}{c\,x^2+b\,x+a}-\frac{2\,c\,d^2\,x}{c\,x^2+b\,x+a}","Not used",1,"(4*c*d^2*atan(b/(4*a*c - b^2)^(1/2) + (2*c*x)/(4*a*c - b^2)^(1/2)))/(4*a*c - b^2)^(1/2) - (b*d^2)/(a + b*x + c*x^2) - (2*c*d^2*x)/(a + b*x + c*x^2)","B"
1173,1,15,15,0.419750,"\text{Not used}","int((b*d + 2*c*d*x)/(a + b*x + c*x^2)^2,x)","-\frac{d}{c\,x^2+b\,x+a}","Not used",1,"-d/(a + b*x + c*x^2)","B"
1174,1,125,78,0.580035,"\text{Not used}","int(1/((b*d + 2*c*d*x)*(a + b*x + c*x^2)^2),x)","\frac{8\,c\,\ln\left(b+2\,c\,x\right)}{16\,d\,a^2\,c^2-8\,d\,a\,b^2\,c+d\,b^4}-\frac{4\,c\,\ln\left(c\,x^2+b\,x+a\right)}{16\,d\,a^2\,c^2-8\,d\,a\,b^2\,c+d\,b^4}-\frac{1}{-4\,d\,a^2\,c+d\,a\,b^2-4\,d\,a\,b\,c\,x-4\,d\,a\,c^2\,x^2+d\,b^3\,x+d\,b^2\,c\,x^2}","Not used",1,"(8*c*log(b + 2*c*x))/(b^4*d + 16*a^2*c^2*d - 8*a*b^2*c*d) - (4*c*log(a + b*x + c*x^2))/(b^4*d + 16*a^2*c^2*d - 8*a*b^2*c*d) - 1/(a*b^2*d - 4*a^2*c*d + b^3*d*x - 4*a*c^2*d*x^2 + b^2*c*d*x^2 - 4*a*b*c*d*x)","B"
1175,1,232,98,0.646527,"\text{Not used}","int(1/((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^2),x)","-\frac{\frac{b^2+8\,a\,c}{{\left(4\,a\,c-b^2\right)}^2}+\frac{12\,c^2\,x^2}{{\left(4\,a\,c-b^2\right)}^2}+\frac{12\,b\,c\,x}{{\left(4\,a\,c-b^2\right)}^2}}{x\,\left(b^2\,d^2+2\,a\,c\,d^2\right)+2\,c^2\,d^2\,x^3+a\,b\,d^2+3\,b\,c\,d^2\,x^2}-\frac{12\,c\,\mathrm{atan}\left(\frac{\frac{6\,c\,\left(16\,a^2\,b\,c^2\,d^2-8\,a\,b^3\,c\,d^2+b^5\,d^2\right)}{d^2\,{\left(4\,a\,c-b^2\right)}^{5/2}}+\frac{12\,c^2\,x\,\left(16\,a^2\,c^2\,d^2-8\,a\,b^2\,c\,d^2+b^4\,d^2\right)}{d^2\,{\left(4\,a\,c-b^2\right)}^{5/2}}}{6\,c}\right)}{d^2\,{\left(4\,a\,c-b^2\right)}^{5/2}}","Not used",1,"- ((8*a*c + b^2)/(4*a*c - b^2)^2 + (12*c^2*x^2)/(4*a*c - b^2)^2 + (12*b*c*x)/(4*a*c - b^2)^2)/(x*(b^2*d^2 + 2*a*c*d^2) + 2*c^2*d^2*x^3 + a*b*d^2 + 3*b*c*d^2*x^2) - (12*c*atan(((6*c*(b^5*d^2 + 16*a^2*b*c^2*d^2 - 8*a*b^3*c*d^2))/(d^2*(4*a*c - b^2)^(5/2)) + (12*c^2*x*(b^4*d^2 + 16*a^2*c^2*d^2 - 8*a*b^2*c*d^2))/(d^2*(4*a*c - b^2)^(5/2)))/(6*c)))/(d^2*(4*a*c - b^2)^(5/2))","B"
1176,1,278,110,0.778829,"\text{Not used}","int(1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^2),x)","\frac{16\,c\,\ln\left(b+2\,c\,x\right)}{-64\,a^3\,c^3\,d^3+48\,a^2\,b^2\,c^2\,d^3-12\,a\,b^4\,c\,d^3+b^6\,d^3}-\frac{8\,c\,\ln\left(c\,x^2+b\,x+a\right)}{-64\,a^3\,c^3\,d^3+48\,a^2\,b^2\,c^2\,d^3-12\,a\,b^4\,c\,d^3+b^6\,d^3}-\frac{\frac{b^2+4\,a\,c}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}+\frac{8\,c^2\,x^2}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}+\frac{8\,b\,c\,x}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}}{x^2\,\left(5\,b^2\,c\,d^3+4\,a\,c^2\,d^3\right)+x\,\left(b^3\,d^3+4\,a\,c\,b\,d^3\right)+a\,b^2\,d^3+4\,c^3\,d^3\,x^4+8\,b\,c^2\,d^3\,x^3}","Not used",1,"(16*c*log(b + 2*c*x))/(b^6*d^3 - 64*a^3*c^3*d^3 + 48*a^2*b^2*c^2*d^3 - 12*a*b^4*c*d^3) - (8*c*log(a + b*x + c*x^2))/(b^6*d^3 - 64*a^3*c^3*d^3 + 48*a^2*b^2*c^2*d^3 - 12*a*b^4*c*d^3) - ((4*a*c + b^2)/(b^4 + 16*a^2*c^2 - 8*a*b^2*c) + (8*c^2*x^2)/(b^4 + 16*a^2*c^2 - 8*a*b^2*c) + (8*b*c*x)/(b^4 + 16*a^2*c^2 - 8*a*b^2*c))/(x^2*(4*a*c^2*d^3 + 5*b^2*c*d^3) + x*(b^3*d^3 + 4*a*b*c*d^3) + a*b^2*d^3 + 4*c^3*d^3*x^4 + 8*b*c^2*d^3*x^3)","B"
1177,1,695,160,0.589762,"\text{Not used}","int((b*d + 2*c*d*x)^10/(a + b*x + c*x^2)^3,x)","x\,\left(\frac{3\,b\,\left(1024\,c^4\,d^{10}\,\left(b^3+6\,a\,c\,b\right)-15360\,b^3\,c^4\,d^{10}-\frac{3\,b\,\left(3072\,c^5\,d^{10}\,\left(b^2+a\,c\right)-5376\,b^2\,c^5\,d^{10}\right)}{c}+6144\,b\,c^4\,d^{10}\,\left(b^2+a\,c\right)\right)}{c}+\frac{3\,\left(3072\,c^5\,d^{10}\,\left(b^2+a\,c\right)-5376\,b^2\,c^5\,d^{10}\right)\,\left(b^2+a\,c\right)}{c^2}+13440\,b^4\,c^3\,d^{10}-3072\,a\,c^4\,d^{10}\,\left(b^2+a\,c\right)-2048\,b\,c^3\,d^{10}\,\left(b^3+6\,a\,c\,b\right)\right)-x^2\,\left(512\,c^4\,d^{10}\,\left(b^3+6\,a\,c\,b\right)-7680\,b^3\,c^4\,d^{10}-\frac{3\,b\,\left(3072\,c^5\,d^{10}\,\left(b^2+a\,c\right)-5376\,b^2\,c^5\,d^{10}\right)}{2\,c}+3072\,b\,c^4\,d^{10}\,\left(b^2+a\,c\right)\right)-x^3\,\left(1024\,c^5\,d^{10}\,\left(b^2+a\,c\right)-1792\,b^2\,c^5\,d^{10}\right)-\frac{x^2\,\left(-3264\,a^3\,b\,c^5\,d^{10}+2448\,a^2\,b^3\,c^4\,d^{10}-612\,a\,b^5\,c^3\,d^{10}+51\,b^7\,c^2\,d^{10}\right)-x^3\,\left(2176\,a^3\,c^6\,d^{10}-1632\,a^2\,b^2\,c^5\,d^{10}+408\,a\,b^4\,c^4\,d^{10}-34\,b^6\,c^3\,d^{10}\right)+\frac{b^9\,d^{10}}{2}+x\,\left(-1920\,a^4\,c^5\,d^{10}+288\,a^3\,b^2\,c^4\,d^{10}+504\,a^2\,b^4\,c^3\,d^{10}-186\,a\,b^6\,c^2\,d^{10}+18\,b^8\,c\,d^{10}\right)-960\,a^4\,b\,c^4\,d^{10}-156\,a^2\,b^5\,c^2\,d^{10}+688\,a^3\,b^3\,c^3\,d^{10}+9\,a\,b^7\,c\,d^{10}}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}+\frac{1024\,c^7\,d^{10}\,x^5}{5}+512\,b\,c^6\,d^{10}\,x^4-252\,c^2\,d^{10}\,\mathrm{atan}\left(\frac{126\,b\,c^2\,d^{10}\,{\left(4\,a\,c-b^2\right)}^{5/2}+252\,c^3\,d^{10}\,x\,{\left(4\,a\,c-b^2\right)}^{5/2}}{8064\,a^3\,c^5\,d^{10}-6048\,a^2\,b^2\,c^4\,d^{10}+1512\,a\,b^4\,c^3\,d^{10}-126\,b^6\,c^2\,d^{10}}\right)\,{\left(4\,a\,c-b^2\right)}^{5/2}","Not used",1,"x*((3*b*(1024*c^4*d^10*(b^3 + 6*a*b*c) - 15360*b^3*c^4*d^10 - (3*b*(3072*c^5*d^10*(a*c + b^2) - 5376*b^2*c^5*d^10))/c + 6144*b*c^4*d^10*(a*c + b^2)))/c + (3*(3072*c^5*d^10*(a*c + b^2) - 5376*b^2*c^5*d^10)*(a*c + b^2))/c^2 + 13440*b^4*c^3*d^10 - 3072*a*c^4*d^10*(a*c + b^2) - 2048*b*c^3*d^10*(b^3 + 6*a*b*c)) - x^2*(512*c^4*d^10*(b^3 + 6*a*b*c) - 7680*b^3*c^4*d^10 - (3*b*(3072*c^5*d^10*(a*c + b^2) - 5376*b^2*c^5*d^10))/(2*c) + 3072*b*c^4*d^10*(a*c + b^2)) - x^3*(1024*c^5*d^10*(a*c + b^2) - 1792*b^2*c^5*d^10) - (x^2*(51*b^7*c^2*d^10 - 612*a*b^5*c^3*d^10 - 3264*a^3*b*c^5*d^10 + 2448*a^2*b^3*c^4*d^10) - x^3*(2176*a^3*c^6*d^10 - 34*b^6*c^3*d^10 + 408*a*b^4*c^4*d^10 - 1632*a^2*b^2*c^5*d^10) + (b^9*d^10)/2 + x*(18*b^8*c*d^10 - 1920*a^4*c^5*d^10 - 186*a*b^6*c^2*d^10 + 504*a^2*b^4*c^3*d^10 + 288*a^3*b^2*c^4*d^10) - 960*a^4*b*c^4*d^10 - 156*a^2*b^5*c^2*d^10 + 688*a^3*b^3*c^3*d^10 + 9*a*b^7*c*d^10)/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3) + (1024*c^7*d^10*x^5)/5 + 512*b*c^6*d^10*x^4 - 252*c^2*d^10*atan((126*b*c^2*d^10*(4*a*c - b^2)^(5/2) + 252*c^3*d^10*x*(4*a*c - b^2)^(5/2))/(8064*a^3*c^5*d^10 - 126*b^6*c^2*d^10 + 1512*a*b^4*c^3*d^10 - 6048*a^2*b^2*c^4*d^10))*(4*a*c - b^2)^(5/2)","B"
1178,1,385,123,0.180619,"\text{Not used}","int((b*d + 2*c*d*x)^9/(a + b*x + c*x^2)^3,x)","\ln\left(c\,x^2+b\,x+a\right)\,\left(1536\,a^2\,c^4\,d^9-768\,a\,b^2\,c^3\,d^9+96\,b^4\,c^2\,d^9\right)-x^2\,\left(768\,c^4\,d^9\,\left(b^2+a\,c\right)-1152\,b^2\,c^4\,d^9\right)-\frac{\frac{b^8\,d^9}{2}-x^2\,\left(1024\,a^3\,c^5\,d^9-768\,a^2\,b^2\,c^4\,d^9+192\,a\,b^4\,c^3\,d^9-16\,b^6\,c^2\,d^9\right)-896\,a^4\,c^4\,d^9+16\,b\,x\,\left(-64\,a^3\,c^4\,d^9+48\,a^2\,b^2\,c^3\,d^9-12\,a\,b^4\,c^2\,d^9+b^6\,c\,d^9\right)-144\,a^2\,b^4\,c^2\,d^9+640\,a^3\,b^2\,c^3\,d^9+8\,a\,b^6\,c\,d^9}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}-x\,\left(512\,c^3\,d^9\,\left(b^3+6\,a\,c\,b\right)-5376\,b^3\,c^3\,d^9-\frac{3\,b\,\left(1536\,c^4\,d^9\,\left(b^2+a\,c\right)-2304\,b^2\,c^4\,d^9\right)}{c}+2304\,b\,c^3\,d^9\,\left(b^2+a\,c\right)\right)+128\,c^6\,d^9\,x^4+256\,b\,c^5\,d^9\,x^3","Not used",1,"log(a + b*x + c*x^2)*(1536*a^2*c^4*d^9 + 96*b^4*c^2*d^9 - 768*a*b^2*c^3*d^9) - x^2*(768*c^4*d^9*(a*c + b^2) - 1152*b^2*c^4*d^9) - ((b^8*d^9)/2 - x^2*(1024*a^3*c^5*d^9 - 16*b^6*c^2*d^9 + 192*a*b^4*c^3*d^9 - 768*a^2*b^2*c^4*d^9) - 896*a^4*c^4*d^9 + 16*b*x*(b^6*c*d^9 - 64*a^3*c^4*d^9 - 12*a*b^4*c^2*d^9 + 48*a^2*b^2*c^3*d^9) - 144*a^2*b^4*c^2*d^9 + 640*a^3*b^2*c^3*d^9 + 8*a*b^6*c*d^9)/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3) - x*(512*c^3*d^9*(b^3 + 6*a*b*c) - 5376*b^3*c^3*d^9 - (3*b*(1536*c^4*d^9*(a*c + b^2) - 2304*b^2*c^4*d^9))/c + 2304*b*c^3*d^9*(a*c + b^2)) + 128*c^6*d^9*x^4 + 256*b*c^5*d^9*x^3","B"
1179,1,368,134,0.537657,"\text{Not used}","int((b*d + 2*c*d*x)^8/(a + b*x + c*x^2)^3,x)","\frac{256\,c^5\,d^8\,x^3}{3}-\frac{x^2\,\left(624\,a^2\,b\,c^4\,d^8-312\,a\,b^3\,c^3\,d^8+39\,b^5\,c^2\,d^8\right)+x\,\left(352\,a^3\,c^4\,d^8+48\,a^2\,b^2\,c^3\,d^8-90\,a\,b^4\,c^2\,d^8+14\,b^6\,c\,d^8\right)+\frac{b^7\,d^8}{2}+x^3\,\left(416\,a^2\,c^5\,d^8-208\,a\,b^2\,c^4\,d^8+26\,b^4\,c^3\,d^8\right)+176\,a^3\,b\,c^3\,d^8-80\,a^2\,b^3\,c^2\,d^8+7\,a\,b^5\,c\,d^8}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}-x\,\left(768\,c^3\,d^8\,\left(b^2+a\,c\right)-1024\,b^2\,c^3\,d^8\right)+128\,b\,c^4\,d^8\,x^2+140\,c^2\,d^8\,\mathrm{atan}\left(\frac{70\,b\,c^2\,d^8\,{\left(4\,a\,c-b^2\right)}^{3/2}+140\,c^3\,d^8\,x\,{\left(4\,a\,c-b^2\right)}^{3/2}}{1120\,a^2\,c^4\,d^8-560\,a\,b^2\,c^3\,d^8+70\,b^4\,c^2\,d^8}\right)\,{\left(4\,a\,c-b^2\right)}^{3/2}","Not used",1,"(256*c^5*d^8*x^3)/3 - (x^2*(39*b^5*c^2*d^8 - 312*a*b^3*c^3*d^8 + 624*a^2*b*c^4*d^8) + x*(14*b^6*c*d^8 + 352*a^3*c^4*d^8 - 90*a*b^4*c^2*d^8 + 48*a^2*b^2*c^3*d^8) + (b^7*d^8)/2 + x^3*(416*a^2*c^5*d^8 + 26*b^4*c^3*d^8 - 208*a*b^2*c^4*d^8) + 176*a^3*b*c^3*d^8 - 80*a^2*b^3*c^2*d^8 + 7*a*b^5*c*d^8)/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3) - x*(768*c^3*d^8*(a*c + b^2) - 1024*b^2*c^3*d^8) + 128*b*c^4*d^8*x^2 + 140*c^2*d^8*atan((70*b*c^2*d^8*(4*a*c - b^2)^(3/2) + 140*c^3*d^8*x*(4*a*c - b^2)^(3/2))/(1120*a^2*c^4*d^8 + 70*b^4*c^2*d^8 - 560*a*b^2*c^3*d^8))*(4*a*c - b^2)^(3/2)","B"
1180,1,214,97,0.160183,"\text{Not used}","int((b*d + 2*c*d*x)^7/(a + b*x + c*x^2)^3,x)","64\,c^4\,d^7\,x^2-\ln\left(c\,x^2+b\,x+a\right)\,\left(192\,a\,c^3\,d^7-48\,b^2\,c^2\,d^7\right)-\frac{\frac{b^6\,d^7}{2}+x^2\,\left(192\,a^2\,c^4\,d^7-96\,a\,b^2\,c^3\,d^7+12\,b^4\,c^2\,d^7\right)+12\,b\,x\,\left(16\,a^2\,c^3\,d^7-8\,a\,b^2\,c^2\,d^7+b^4\,c\,d^7\right)+160\,a^3\,c^3\,d^7-72\,a^2\,b^2\,c^2\,d^7+6\,a\,b^4\,c\,d^7}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}+64\,b\,c^3\,d^7\,x","Not used",1,"64*c^4*d^7*x^2 - log(a + b*x + c*x^2)*(192*a*c^3*d^7 - 48*b^2*c^2*d^7) - ((b^6*d^7)/2 + x^2*(192*a^2*c^4*d^7 + 12*b^4*c^2*d^7 - 96*a*b^2*c^3*d^7) + 12*b*x*(b^4*c*d^7 + 16*a^2*c^3*d^7 - 8*a*b^2*c^2*d^7) + 160*a^3*c^3*d^7 - 72*a^2*b^2*c^2*d^7 + 6*a*b^4*c*d^7)/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3) + 64*b*c^3*d^7*x","B"
1181,1,254,108,0.567189,"\text{Not used}","int((b*d + 2*c*d*x)^6/(a + b*x + c*x^2)^3,x)","\frac{x\,\left(56\,a^2\,c^3\,d^6+26\,a\,b^2\,c^2\,d^6-10\,b^4\,c\,d^6\right)+x^3\,\left(72\,a\,c^4\,d^6-18\,b^2\,c^3\,d^6\right)-\frac{b^5\,d^6}{2}-x^2\,\left(27\,b^3\,c^2\,d^6-108\,a\,b\,c^3\,d^6\right)+28\,a^2\,b\,c^2\,d^6-5\,a\,b^3\,c\,d^6}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}+64\,c^3\,d^6\,x-60\,c^2\,d^6\,\mathrm{atan}\left(\frac{30\,b\,c^2\,d^6\,\sqrt{4\,a\,c-b^2}+60\,c^3\,d^6\,x\,\sqrt{4\,a\,c-b^2}}{120\,a\,c^3\,d^6-30\,b^2\,c^2\,d^6}\right)\,\sqrt{4\,a\,c-b^2}","Not used",1,"(x*(56*a^2*c^3*d^6 - 10*b^4*c*d^6 + 26*a*b^2*c^2*d^6) + x^3*(72*a*c^4*d^6 - 18*b^2*c^3*d^6) - (b^5*d^6)/2 - x^2*(27*b^3*c^2*d^6 - 108*a*b*c^3*d^6) + 28*a^2*b*c^2*d^6 - 5*a*b^3*c*d^6)/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3) + 64*c^3*d^6*x - 60*c^2*d^6*atan((30*b*c^2*d^6*(4*a*c - b^2)^(1/2) + 60*c^3*d^6*x*(4*a*c - b^2)^(1/2))/(120*a*c^3*d^6 - 30*b^2*c^2*d^6))*(4*a*c - b^2)^(1/2)","B"
1182,1,136,73,0.526900,"\text{Not used}","int((b*d + 2*c*d*x)^5/(a + b*x + c*x^2)^3,x)","\frac{x^2\,\left(32\,a\,c^3\,d^5-8\,b^2\,c^2\,d^5\right)-\frac{b^4\,d^5}{2}+8\,b\,x\,\left(4\,a\,c^2\,d^5-b^2\,c\,d^5\right)+24\,a^2\,c^2\,d^5-4\,a\,b^2\,c\,d^5}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}+16\,c^2\,d^5\,\ln\left(c\,x^2+b\,x+a\right)","Not used",1,"(x^2*(32*a*c^3*d^5 - 8*b^2*c^2*d^5) - (b^4*d^5)/2 + 8*b*x*(4*a*c^2*d^5 - b^2*c*d^5) + 24*a^2*c^2*d^5 - 4*a*b^2*c*d^5)/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3) + 16*c^2*d^5*log(a + b*x + c*x^2)","B"
1183,1,166,92,0.166112,"\text{Not used}","int((b*d + 2*c*d*x)^4/(a + b*x + c*x^2)^3,x)","\frac{12\,c^2\,d^4\,\mathrm{atan}\left(\frac{\frac{6\,b\,c^2\,d^4}{\sqrt{4\,a\,c-b^2}}+\frac{12\,c^3\,d^4\,x}{\sqrt{4\,a\,c-b^2}}}{6\,c^2\,d^4}\right)}{\sqrt{4\,a\,c-b^2}}-\frac{\frac{b^3\,d^4}{2}+10\,c^3\,d^4\,x^3+15\,b\,c^2\,d^4\,x^2+6\,c\,d^4\,x\,\left(b^2+a\,c\right)+3\,a\,b\,c\,d^4}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}","Not used",1,"(12*c^2*d^4*atan(((6*b*c^2*d^4)/(4*a*c - b^2)^(1/2) + (12*c^3*d^4*x)/(4*a*c - b^2)^(1/2))/(6*c^2*d^4)))/(4*a*c - b^2)^(1/2) - ((b^3*d^4)/2 + 10*c^3*d^4*x^3 + 15*b*c^2*d^4*x^2 + 6*c*d^4*x*(a*c + b^2) + 3*a*b*c*d^4)/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3)","B"
1184,1,74,37,0.070021,"\text{Not used}","int((b*d + 2*c*d*x)^3/(a + b*x + c*x^2)^3,x)","-\frac{\frac{b^2\,d^3}{2}+4\,b\,c\,d^3\,x+4\,c^2\,d^3\,x^2+2\,a\,c\,d^3}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}","Not used",1,"-((b^2*d^3)/2 + 4*c^2*d^3*x^2 + 2*a*c*d^3 + 4*b*c*d^3*x)/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3)","B"
1185,1,233,100,0.571150,"\text{Not used}","int((b*d + 2*c*d*x)^2/(a + b*x + c*x^2)^3,x)","\frac{4\,c^2\,d^2\,\mathrm{atan}\left(\frac{\left(\frac{4\,c^3\,d^2\,x}{{\left(4\,a\,c-b^2\right)}^{3/2}}-\frac{2\,c^2\,d^2\,\left(b^3-4\,a\,b\,c\right)}{{\left(4\,a\,c-b^2\right)}^{5/2}}\right)\,\left(4\,a\,c-b^2\right)}{2\,c^2\,d^2}\right)}{{\left(4\,a\,c-b^2\right)}^{3/2}}-\frac{\frac{b\,d^2\,\left(2\,a\,c-b^2\right)}{2\,\left(4\,a\,c-b^2\right)}-\frac{2\,c^3\,d^2\,x^3}{4\,a\,c-b^2}-\frac{3\,b\,c^2\,d^2\,x^2}{4\,a\,c-b^2}+\frac{2\,c\,d^2\,x\,\left(a\,c-b^2\right)}{4\,a\,c-b^2}}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}","Not used",1,"(4*c^2*d^2*atan((((4*c^3*d^2*x)/(4*a*c - b^2)^(3/2) - (2*c^2*d^2*(b^3 - 4*a*b*c))/(4*a*c - b^2)^(5/2))*(4*a*c - b^2))/(2*c^2*d^2)))/(4*a*c - b^2)^(3/2) - ((b*d^2*(2*a*c - b^2))/(2*(4*a*c - b^2)) - (2*c^3*d^2*x^3)/(4*a*c - b^2) - (3*b*c^2*d^2*x^2)/(4*a*c - b^2) + (2*c*d^2*x*(a*c - b^2))/(4*a*c - b^2))/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3)","B"
1186,1,44,17,0.050681,"\text{Not used}","int((b*d + 2*c*d*x)/(a + b*x + c*x^2)^3,x)","-\frac{d}{2\,\left(x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3\right)}","Not used",1,"-d/(2*(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3))","B"
1187,1,239,112,0.750510,"\text{Not used}","int(1/((b*d + 2*c*d*x)*(a + b*x + c*x^2)^3),x)","\frac{\frac{12\,a\,c-b^2}{2\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{4\,c^2\,x^2}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}+\frac{4\,b\,c\,x}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}}{a^2\,d+x^2\,\left(d\,b^2+2\,a\,c\,d\right)+c^2\,d\,x^4+2\,b\,c\,d\,x^3+2\,a\,b\,d\,x}-\frac{32\,c^2\,\ln\left(b+2\,c\,x\right)}{-64\,d\,a^3\,c^3+48\,d\,a^2\,b^2\,c^2-12\,d\,a\,b^4\,c+d\,b^6}+\frac{16\,c^2\,\ln\left(c\,x^2+b\,x+a\right)}{-64\,d\,a^3\,c^3+48\,d\,a^2\,b^2\,c^2-12\,d\,a\,b^4\,c+d\,b^6}","Not used",1,"((12*a*c - b^2)/(2*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (4*c^2*x^2)/(b^4 + 16*a^2*c^2 - 8*a*b^2*c) + (4*b*c*x)/(b^4 + 16*a^2*c^2 - 8*a*b^2*c))/(a^2*d + x^2*(b^2*d + 2*a*c*d) + c^2*d*x^4 + 2*b*c*d*x^3 + 2*a*b*d*x) - (32*c^2*log(b + 2*c*x))/(b^6*d - 64*a^3*c^3*d + 48*a^2*b^2*c^2*d - 12*a*b^4*c*d) + (16*c^2*log(a + b*x + c*x^2))/(b^6*d - 64*a^3*c^3*d + 48*a^2*b^2*c^2*d - 12*a*b^4*c*d)","B"
1188,1,494,140,0.892181,"\text{Not used}","int(1/((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^3),x)","\frac{60\,c^2\,\mathrm{atan}\left(\frac{\frac{30\,c^2\,\left(-64\,a^3\,b\,c^3\,d^2+48\,a^2\,b^3\,c^2\,d^2-12\,a\,b^5\,c\,d^2+b^7\,d^2\right)}{d^2\,{\left(4\,a\,c-b^2\right)}^{7/2}}+\frac{60\,c^3\,x\,\left(-64\,a^3\,c^3\,d^2+48\,a^2\,b^2\,c^2\,d^2-12\,a\,b^4\,c\,d^2+b^6\,d^2\right)}{d^2\,{\left(4\,a\,c-b^2\right)}^{7/2}}}{30\,c^2}\right)}{d^2\,{\left(4\,a\,c-b^2\right)}^{7/2}}-\frac{\frac{64\,a^2\,c^2+18\,a\,b^2\,c-b^4}{2\,\left(4\,a\,c-b^2\right)\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{60\,c^4\,x^4}{\left(4\,a\,c-b^2\right)\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{5\,c\,x\,\left(b^3+20\,a\,c\,b\right)}{\left(4\,a\,c-b^2\right)\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{5\,c\,x^2\,\left(13\,b^2\,c+20\,a\,c^2\right)}{\left(4\,a\,c-b^2\right)\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{120\,b\,c^3\,x^3}{\left(4\,a\,c-b^2\right)\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}}{x^3\,\left(4\,b^2\,c\,d^2+4\,a\,c^2\,d^2\right)+x\,\left(2\,c\,a^2\,d^2+2\,a\,b^2\,d^2\right)+x^2\,\left(b^3\,d^2+6\,a\,c\,b\,d^2\right)+a^2\,b\,d^2+2\,c^3\,d^2\,x^5+5\,b\,c^2\,d^2\,x^4}","Not used",1,"(60*c^2*atan(((30*c^2*(b^7*d^2 - 64*a^3*b*c^3*d^2 + 48*a^2*b^3*c^2*d^2 - 12*a*b^5*c*d^2))/(d^2*(4*a*c - b^2)^(7/2)) + (60*c^3*x*(b^6*d^2 - 64*a^3*c^3*d^2 + 48*a^2*b^2*c^2*d^2 - 12*a*b^4*c*d^2))/(d^2*(4*a*c - b^2)^(7/2)))/(30*c^2)))/(d^2*(4*a*c - b^2)^(7/2)) - ((64*a^2*c^2 - b^4 + 18*a*b^2*c)/(2*(4*a*c - b^2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (60*c^4*x^4)/((4*a*c - b^2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (5*c*x*(b^3 + 20*a*b*c))/((4*a*c - b^2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (5*c*x^2*(20*a*c^2 + 13*b^2*c))/((4*a*c - b^2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (120*b*c^3*x^3)/((4*a*c - b^2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))/(x^3*(4*a*c^2*d^2 + 4*b^2*c*d^2) + x*(2*a*b^2*d^2 + 2*a^2*c*d^2) + x^2*(b^3*d^2 + 6*a*b*c*d^2) + a^2*b*d^2 + 2*c^3*d^2*x^5 + 5*b*c^2*d^2*x^4)","B"
1189,1,522,154,1.044135,"\text{Not used}","int(1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^3),x)","\frac{\frac{32\,a^2\,c^2+20\,a\,b^2\,c-b^4}{2\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{48\,c^4\,x^4}{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}+\frac{96\,b\,c^3\,x^3}{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}+\frac{18\,c\,x^2\,\left(3\,b^2\,c+4\,a\,c^2\right)}{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}+\frac{6\,b\,c\,x\,\left(b^2+12\,a\,c\right)}{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}}{x\,\left(4\,c\,a^2\,b\,d^3+2\,a\,b^3\,d^3\right)+x^4\,\left(13\,b^2\,c^2\,d^3+8\,a\,c^3\,d^3\right)+x^3\,\left(6\,b^3\,c\,d^3+16\,a\,b\,c^2\,d^3\right)+x^2\,\left(4\,a^2\,c^2\,d^3+10\,a\,b^2\,c\,d^3+b^4\,d^3\right)+a^2\,b^2\,d^3+4\,c^4\,d^3\,x^6+12\,b\,c^3\,d^3\,x^5}-\frac{96\,c^2\,\ln\left(b+2\,c\,x\right)}{256\,a^4\,c^4\,d^3-256\,a^3\,b^2\,c^3\,d^3+96\,a^2\,b^4\,c^2\,d^3-16\,a\,b^6\,c\,d^3+b^8\,d^3}+\frac{48\,c^2\,\ln\left(c\,x^2+b\,x+a\right)}{256\,a^4\,c^4\,d^3-256\,a^3\,b^2\,c^3\,d^3+96\,a^2\,b^4\,c^2\,d^3-16\,a\,b^6\,c\,d^3+b^8\,d^3}","Not used",1,"((32*a^2*c^2 - b^4 + 20*a*b^2*c)/(2*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (48*c^4*x^4)/(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c) + (96*b*c^3*x^3)/(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c) + (18*c*x^2*(4*a*c^2 + 3*b^2*c))/(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c) + (6*b*c*x*(12*a*c + b^2))/(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c))/(x*(2*a*b^3*d^3 + 4*a^2*b*c*d^3) + x^4*(8*a*c^3*d^3 + 13*b^2*c^2*d^3) + x^3*(6*b^3*c*d^3 + 16*a*b*c^2*d^3) + x^2*(b^4*d^3 + 4*a^2*c^2*d^3 + 10*a*b^2*c*d^3) + a^2*b^2*d^3 + 4*c^4*d^3*x^6 + 12*b*c^3*d^3*x^5) - (96*c^2*log(b + 2*c*x))/(b^8*d^3 + 256*a^4*c^4*d^3 + 96*a^2*b^4*c^2*d^3 - 256*a^3*b^2*c^3*d^3 - 16*a*b^6*c*d^3) + (48*c^2*log(a + b*x + c*x^2))/(b^8*d^3 + 256*a^4*c^4*d^3 + 96*a^2*b^4*c^2*d^3 - 256*a^3*b^2*c^3*d^3 - 16*a*b^6*c*d^3)","B"
1190,1,827,168,1.359226,"\text{Not used}","int(1/((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^3),x)","\frac{140\,c^2\,\mathrm{atan}\left(\frac{\frac{70\,c^2\,\left(256\,a^4\,b\,c^4\,d^4-256\,a^3\,b^3\,c^3\,d^4+96\,a^2\,b^5\,c^2\,d^4-16\,a\,b^7\,c\,d^4+b^9\,d^4\right)}{d^4\,{\left(4\,a\,c-b^2\right)}^{9/2}}+\frac{140\,c^3\,x\,\left(256\,a^4\,c^4\,d^4-256\,a^3\,b^2\,c^3\,d^4+96\,a^2\,b^4\,c^2\,d^4-16\,a\,b^6\,c\,d^4+b^8\,d^4\right)}{d^4\,{\left(4\,a\,c-b^2\right)}^{9/2}}}{70\,c^2}\right)}{d^4\,{\left(4\,a\,c-b^2\right)}^{9/2}}-\frac{\frac{2800\,x^3\,\left(b^3\,c^3+2\,a\,b\,c^4\right)}{3\,\left(4\,a\,c-b^2\right)\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}-\frac{256\,a^3\,c^3-640\,a^2\,b^2\,c^2-78\,a\,b^4\,c+3\,b^6}{6\,\left(4\,a\,c-b^2\right)\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{7\,x^2\,\left(128\,a^2\,c^4+536\,a\,b^2\,c^3+83\,b^4\,c^2\right)}{3\,\left(4\,a\,c-b^2\right)\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{560\,c^6\,x^6}{\left(4\,a\,c-b^2\right)\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{7\,b\,x\,\left(128\,a^2\,c^3+136\,a\,b^2\,c^2+3\,b^4\,c\right)}{3\,\left(4\,a\,c-b^2\right)\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{1680\,b\,c^5\,x^5}{\left(4\,a\,c-b^2\right)\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{2800\,c\,x^4\,\left(2\,b^2\,c^3+a\,c^4\right)}{3\,\left(4\,a\,c-b^2\right)\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}}{x^2\,\left(12\,a^2\,b\,c^2\,d^4+14\,a\,b^3\,c\,d^4+b^5\,d^4\right)+x^5\,\left(38\,b^2\,c^3\,d^4+16\,a\,c^4\,d^4\right)+x\,\left(6\,c\,a^2\,b^2\,d^4+2\,a\,b^4\,d^4\right)+x^3\,\left(8\,a^2\,c^3\,d^4+36\,a\,b^2\,c^2\,d^4+8\,b^4\,c\,d^4\right)+x^4\,\left(25\,b^3\,c^2\,d^4+40\,a\,b\,c^3\,d^4\right)+a^2\,b^3\,d^4+8\,c^5\,d^4\,x^7+28\,b\,c^4\,d^4\,x^6}","Not used",1,"(140*c^2*atan(((70*c^2*(b^9*d^4 + 256*a^4*b*c^4*d^4 + 96*a^2*b^5*c^2*d^4 - 256*a^3*b^3*c^3*d^4 - 16*a*b^7*c*d^4))/(d^4*(4*a*c - b^2)^(9/2)) + (140*c^3*x*(b^8*d^4 + 256*a^4*c^4*d^4 + 96*a^2*b^4*c^2*d^4 - 256*a^3*b^2*c^3*d^4 - 16*a*b^6*c*d^4))/(d^4*(4*a*c - b^2)^(9/2)))/(70*c^2)))/(d^4*(4*a*c - b^2)^(9/2)) - ((2800*x^3*(b^3*c^3 + 2*a*b*c^4))/(3*(4*a*c - b^2)*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) - (3*b^6 + 256*a^3*c^3 - 640*a^2*b^2*c^2 - 78*a*b^4*c)/(6*(4*a*c - b^2)*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (7*x^2*(128*a^2*c^4 + 83*b^4*c^2 + 536*a*b^2*c^3))/(3*(4*a*c - b^2)*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (560*c^6*x^6)/((4*a*c - b^2)*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (7*b*x*(3*b^4*c + 128*a^2*c^3 + 136*a*b^2*c^2))/(3*(4*a*c - b^2)*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (1680*b*c^5*x^5)/((4*a*c - b^2)*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (2800*c*x^4*(a*c^4 + 2*b^2*c^3))/(3*(4*a*c - b^2)*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)))/(x^2*(b^5*d^4 + 12*a^2*b*c^2*d^4 + 14*a*b^3*c*d^4) + x^5*(16*a*c^4*d^4 + 38*b^2*c^3*d^4) + x*(2*a*b^4*d^4 + 6*a^2*b^2*c*d^4) + x^3*(8*b^4*c*d^4 + 8*a^2*c^3*d^4 + 36*a*b^2*c^2*d^4) + x^4*(25*b^3*c^2*d^4 + 40*a*b*c^3*d^4) + a^2*b^3*d^4 + 8*c^5*d^4*x^7 + 28*b*c^4*d^4*x^6)","B"
1191,1,1144,165,2.191158,"\text{Not used}","int((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(1/2),x)","8\,a\,c^3\,d^4\,\left(\frac{5\,b\,\left(\frac{\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x+a}\right)\,\left(b^3-4\,a\,b\,c\right)}{16\,c^{5/2}}+\frac{\left(-3\,b^2+2\,c\,x\,b+8\,c\,\left(c\,x^2+a\right)\right)\,\sqrt{c\,x^2+b\,x+a}}{24\,c^2}\right)}{8\,c}-\frac{x\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{4\,c}+\frac{a\,\left(\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}+\frac{\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}\right)}{4\,c}\right)-12\,b\,c^3\,d^4\,\left(\frac{7\,b\,\left(\frac{5\,b\,\left(\frac{\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x+a}\right)\,\left(b^3-4\,a\,b\,c\right)}{16\,c^{5/2}}+\frac{\left(-3\,b^2+2\,c\,x\,b+8\,c\,\left(c\,x^2+a\right)\right)\,\sqrt{c\,x^2+b\,x+a}}{24\,c^2}\right)}{8\,c}-\frac{x\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{4\,c}+\frac{a\,\left(\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}+\frac{\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}\right)}{4\,c}\right)}{10\,c}-\frac{2\,a\,\left(\frac{\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x+a}\right)\,\left(b^3-4\,a\,b\,c\right)}{16\,c^{5/2}}+\frac{\left(-3\,b^2+2\,c\,x\,b+8\,c\,\left(c\,x^2+a\right)\right)\,\sqrt{c\,x^2+b\,x+a}}{24\,c^2}\right)}{5\,c}+\frac{x^2\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{5\,c}\right)+b^4\,d^4\,\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}+\frac{8\,c^3\,d^4\,x^3\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{3}+\frac{112\,b^2\,c^2\,d^4\,\left(\frac{5\,b\,\left(\frac{\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x+a}\right)\,\left(b^3-4\,a\,b\,c\right)}{16\,c^{5/2}}+\frac{\left(-3\,b^2+2\,c\,x\,b+8\,c\,\left(c\,x^2+a\right)\right)\,\sqrt{c\,x^2+b\,x+a}}{24\,c^2}\right)}{8\,c}-\frac{x\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{4\,c}+\frac{a\,\left(\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}+\frac{\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}\right)}{4\,c}\right)}{5}-15\,b^3\,c\,d^4\,\left(\frac{\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x+a}\right)\,\left(b^3-4\,a\,b\,c\right)}{16\,c^{5/2}}+\frac{\left(-3\,b^2+2\,c\,x\,b+8\,c\,\left(c\,x^2+a\right)\right)\,\sqrt{c\,x^2+b\,x+a}}{24\,c^2}\right)+\frac{32\,b\,c^2\,d^4\,x^2\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{5}-6\,a\,b^2\,c\,d^4\,\left(\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}+\frac{\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}\right)-\frac{64\,a\,b\,c^2\,d^4\,\left(\frac{\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x+a}\right)\,\left(b^3-4\,a\,b\,c\right)}{16\,c^{5/2}}+\frac{\left(-3\,b^2+2\,c\,x\,b+8\,c\,\left(c\,x^2+a\right)\right)\,\sqrt{c\,x^2+b\,x+a}}{24\,c^2}\right)}{5}+\frac{b^4\,d^4\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}+\frac{b^3\,d^4\,\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x+a}\right)\,\left(b^3-4\,a\,b\,c\right)}{2\,c^{3/2}}+6\,b^2\,c\,d^4\,x\,{\left(c\,x^2+b\,x+a\right)}^{3/2}+\frac{b^3\,d^4\,\left(-3\,b^2+2\,c\,x\,b+8\,c\,\left(c\,x^2+a\right)\right)\,\sqrt{c\,x^2+b\,x+a}}{3\,c}","Not used",1,"8*a*c^3*d^4*((5*b*((log((b + 2*c*x)/c^(1/2) + 2*(a + b*x + c*x^2)^(1/2))*(b^3 - 4*a*b*c))/(16*c^(5/2)) + ((8*c*(a + c*x^2) - 3*b^2 + 2*b*c*x)*(a + b*x + c*x^2)^(1/2))/(24*c^2)))/(8*c) - (x*(a + b*x + c*x^2)^(3/2))/(4*c) + (a*((x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) + (log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2))))/(4*c)) - 12*b*c^3*d^4*((7*b*((5*b*((log((b + 2*c*x)/c^(1/2) + 2*(a + b*x + c*x^2)^(1/2))*(b^3 - 4*a*b*c))/(16*c^(5/2)) + ((8*c*(a + c*x^2) - 3*b^2 + 2*b*c*x)*(a + b*x + c*x^2)^(1/2))/(24*c^2)))/(8*c) - (x*(a + b*x + c*x^2)^(3/2))/(4*c) + (a*((x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) + (log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2))))/(4*c)))/(10*c) - (2*a*((log((b + 2*c*x)/c^(1/2) + 2*(a + b*x + c*x^2)^(1/2))*(b^3 - 4*a*b*c))/(16*c^(5/2)) + ((8*c*(a + c*x^2) - 3*b^2 + 2*b*c*x)*(a + b*x + c*x^2)^(1/2))/(24*c^2)))/(5*c) + (x^2*(a + b*x + c*x^2)^(3/2))/(5*c)) + b^4*d^4*(x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) + (8*c^3*d^4*x^3*(a + b*x + c*x^2)^(3/2))/3 + (112*b^2*c^2*d^4*((5*b*((log((b + 2*c*x)/c^(1/2) + 2*(a + b*x + c*x^2)^(1/2))*(b^3 - 4*a*b*c))/(16*c^(5/2)) + ((8*c*(a + c*x^2) - 3*b^2 + 2*b*c*x)*(a + b*x + c*x^2)^(1/2))/(24*c^2)))/(8*c) - (x*(a + b*x + c*x^2)^(3/2))/(4*c) + (a*((x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) + (log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2))))/(4*c)))/5 - 15*b^3*c*d^4*((log((b + 2*c*x)/c^(1/2) + 2*(a + b*x + c*x^2)^(1/2))*(b^3 - 4*a*b*c))/(16*c^(5/2)) + ((8*c*(a + c*x^2) - 3*b^2 + 2*b*c*x)*(a + b*x + c*x^2)^(1/2))/(24*c^2)) + (32*b*c^2*d^4*x^2*(a + b*x + c*x^2)^(3/2))/5 - 6*a*b^2*c*d^4*((x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) + (log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2))) - (64*a*b*c^2*d^4*((log((b + 2*c*x)/c^(1/2) + 2*(a + b*x + c*x^2)^(1/2))*(b^3 - 4*a*b*c))/(16*c^(5/2)) + ((8*c*(a + c*x^2) - 3*b^2 + 2*b*c*x)*(a + b*x + c*x^2)^(1/2))/(24*c^2)))/5 + (b^4*d^4*log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2)) + (b^3*d^4*log((b + 2*c*x)/c^(1/2) + 2*(a + b*x + c*x^2)^(1/2))*(b^3 - 4*a*b*c))/(2*c^(3/2)) + 6*b^2*c*d^4*x*(a + b*x + c*x^2)^(3/2) + (b^3*d^4*(8*c*(a + c*x^2) - 3*b^2 + 2*b*c*x)*(a + b*x + c*x^2)^(1/2))/(3*c)","B"
1192,1,89,59,0.581079,"\text{Not used}","int((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(1/2),x)","\sqrt{c\,x^2+b\,x+a}\,\left(\frac{8\,c^3\,d^3\,x^4}{5}-\frac{2\,a\,d^3\,\left(8\,a\,c-5\,b^2\right)}{15}+\frac{2\,c\,d^3\,x^2\,\left(17\,b^2+4\,a\,c\right)}{15}+\frac{16\,b\,c^2\,d^3\,x^3}{5}+\frac{2\,b\,d^3\,x\,\left(5\,b^2+4\,a\,c\right)}{15}\right)","Not used",1,"(a + b*x + c*x^2)^(1/2)*((8*c^3*d^3*x^4)/5 - (2*a*d^3*(8*a*c - 5*b^2))/15 + (2*c*d^3*x^2*(4*a*c + 17*b^2))/15 + (16*b*c^2*d^3*x^3)/5 + (2*b*d^3*x*(4*a*c + 5*b^2))/15)","B"
1193,1,335,123,1.068430,"\text{Not used}","int((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(1/2),x)","b^2\,d^2\,\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}-a\,c\,d^2\,\left(\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}+\frac{\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}\right)-\frac{5\,b\,c\,d^2\,\left(\frac{\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x+a}\right)\,\left(b^3-4\,a\,b\,c\right)}{16\,c^{5/2}}+\frac{\left(-3\,b^2+2\,c\,x\,b+8\,c\,\left(c\,x^2+a\right)\right)\,\sqrt{c\,x^2+b\,x+a}}{24\,c^2}\right)}{2}+c\,d^2\,x\,{\left(c\,x^2+b\,x+a\right)}^{3/2}+\frac{b\,d^2\,\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x+a}\right)\,\left(b^3-4\,a\,b\,c\right)}{4\,c^{3/2}}+\frac{b\,d^2\,\left(-3\,b^2+2\,c\,x\,b+8\,c\,\left(c\,x^2+a\right)\right)\,\sqrt{c\,x^2+b\,x+a}}{6\,c}+\frac{b^2\,d^2\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}","Not used",1,"b^2*d^2*(x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) - a*c*d^2*((x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) + (log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2))) - (5*b*c*d^2*((log((b + 2*c*x)/c^(1/2) + 2*(a + b*x + c*x^2)^(1/2))*(b^3 - 4*a*b*c))/(16*c^(5/2)) + ((8*c*(a + c*x^2) - 3*b^2 + 2*b*c*x)*(a + b*x + c*x^2)^(1/2))/(24*c^2)))/2 + c*d^2*x*(a + b*x + c*x^2)^(3/2) + (b*d^2*log((b + 2*c*x)/c^(1/2) + 2*(a + b*x + c*x^2)^(1/2))*(b^3 - 4*a*b*c))/(4*c^(3/2)) + (b*d^2*(8*c*(a + c*x^2) - 3*b^2 + 2*b*c*x)*(a + b*x + c*x^2)^(1/2))/(6*c) + (b^2*d^2*log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2))","B"
1194,1,15,19,0.478367,"\text{Not used}","int((b*d + 2*c*d*x)*(a + b*x + c*x^2)^(1/2),x)","\frac{2\,d\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{3}","Not used",1,"(2*d*(a + b*x + c*x^2)^(3/2))/3","B"
1195,0,-1,83,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x),x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{b\,d+2\,c\,d\,x} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x), x)","F"
1196,0,-1,75,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^2,x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(b\,d+2\,c\,d\,x\right)}^2} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^2, x)","F"
1197,0,-1,91,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^3,x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(b\,d+2\,c\,d\,x\right)}^3} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^3, x)","F"
1198,1,111,39,0.747113,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^4,x)","\frac{2\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{x\,\left(18\,b^4\,c\,d^4-72\,a\,b^2\,c^2\,d^4\right)-x^3\,\left(96\,a\,c^4\,d^4-24\,b^2\,c^3\,d^4\right)+3\,b^5\,d^4+x^2\,\left(36\,b^3\,c^2\,d^4-144\,a\,b\,c^3\,d^4\right)-12\,a\,b^3\,c\,d^4}","Not used",1,"(2*(a + b*x + c*x^2)^(3/2))/(x*(18*b^4*c*d^4 - 72*a*b^2*c^2*d^4) - x^3*(96*a*c^4*d^4 - 24*b^2*c^3*d^4) + 3*b^5*d^4 + x^2*(36*b^3*c^2*d^4 - 144*a*b*c^3*d^4) - 12*a*b^3*c*d^4)","B"
1199,0,-1,133,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^5,x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(b\,d+2\,c\,d\,x\right)}^5} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^5, x)","F"
1200,1,589,79,0.996336,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^6,x)","\frac{\left(\frac{b\,\left(\frac{4\,c^2\,\left(2\,b^2+4\,a\,c\right)}{15\,d^6\,{\left(4\,a\,c-b^2\right)}^2\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}-\frac{8\,b^2\,c^2}{15\,d^6\,{\left(4\,a\,c-b^2\right)}^2\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8\,a\,b\,c^2}{15\,d^6\,{\left(4\,a\,c-b^2\right)}^2\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^2}-\frac{\left(\frac{2\,a}{15\,d^6\,{\left(4\,a\,c-b^2\right)}^3}-\frac{b^2}{30\,c\,d^6\,{\left(4\,a\,c-b^2\right)}^3}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}+\frac{\left(\frac{b\,\left(\frac{4\,c^2\,\left(2\,b^2+4\,a\,c\right)}{5\,d^6\,\left(4\,a\,c-b^2\right)\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}-\frac{8\,b^2\,c^2}{5\,d^6\,\left(4\,a\,c-b^2\right)\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8\,a\,b\,c^2}{5\,d^6\,\left(4\,a\,c-b^2\right)\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^4}-\frac{\left(\frac{8\,a\,c^2}{d^6\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}-\frac{2\,b^2\,c}{d^6\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^5}-\frac{\left(\frac{8\,a\,c^2}{5\,d^6\,\left(4\,a\,c-b^2\right)\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{2\,b^2\,c}{5\,d^6\,\left(4\,a\,c-b^2\right)\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}+\frac{\sqrt{c\,x^2+b\,x+a}}{10\,c\,d^6\,{\left(4\,a\,c-b^2\right)}^2\,\left(b+2\,c\,x\right)}","Not used",1,"(((b*((4*c^2*(4*a*c + 2*b^2))/(15*d^6*(4*a*c - b^2)^2*(32*a*c^3 - 8*b^2*c^2)) - (8*b^2*c^2)/(15*d^6*(4*a*c - b^2)^2*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (8*a*b*c^2)/(15*d^6*(4*a*c - b^2)^2*(32*a*c^3 - 8*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^2 - (((2*a)/(15*d^6*(4*a*c - b^2)^3) - b^2/(30*c*d^6*(4*a*c - b^2)^3))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) + (((b*((4*c^2*(4*a*c + 2*b^2))/(5*d^6*(4*a*c - b^2)*(64*a*c^3 - 16*b^2*c^2)) - (8*b^2*c^2)/(5*d^6*(4*a*c - b^2)*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (8*a*b*c^2)/(5*d^6*(4*a*c - b^2)*(64*a*c^3 - 16*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^4 - (((8*a*c^2)/(d^6*(80*a*c^3 - 20*b^2*c^2)) - (2*b^2*c)/(d^6*(80*a*c^3 - 20*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^5 - (((8*a*c^2)/(5*d^6*(4*a*c - b^2)*(48*a*c^3 - 12*b^2*c^2)) - (2*b^2*c)/(5*d^6*(4*a*c - b^2)*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 + (a + b*x + c*x^2)^(1/2)/(10*c*d^6*(4*a*c - b^2)^2*(b + 2*c*x))","B"
1201,0,-1,175,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^7,x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(b\,d+2\,c\,d\,x\right)}^7} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^7, x)","F"
1202,1,241,98,0.965775,"\text{Not used}","int((b*d + 2*c*d*x)^5*(a + b*x + c*x^2)^(3/2),x)","\sqrt{c\,x^2+b\,x+a}\,\left(\frac{2\,a^2\,d^5\,\left(128\,a^2\,c^2-144\,a\,b^2\,c+63\,b^4\right)}{315}+\frac{32\,c^6\,d^5\,x^8}{9}+\frac{2\,d^5\,x^2\,\left(-64\,a^3\,c^3+120\,a^2\,b^2\,c^2+702\,a\,b^4\,c+63\,b^6\right)}{315}+\frac{2\,c^2\,d^5\,x^4\,\left(48\,a^2\,c^2+2976\,a\,b^2\,c+1703\,b^4\right)}{315}+\frac{128\,b\,c^5\,d^5\,x^7}{9}+\frac{16\,c^4\,d^5\,x^6\,\left(93\,b^2+20\,a\,c\right)}{63}+\frac{4\,b\,c\,d^5\,x^3\,\left(48\,a^2\,c^2+976\,a\,b^2\,c+243\,b^4\right)}{315}+\frac{4\,a\,b\,d^5\,x\,\left(-32\,a^2\,c^2+36\,a\,b^2\,c+63\,b^4\right)}{315}+\frac{16\,b\,c^3\,d^5\,x^5\,\left(83\,b^2+60\,a\,c\right)}{63}\right)","Not used",1,"(a + b*x + c*x^2)^(1/2)*((2*a^2*d^5*(63*b^4 + 128*a^2*c^2 - 144*a*b^2*c))/315 + (32*c^6*d^5*x^8)/9 + (2*d^5*x^2*(63*b^6 - 64*a^3*c^3 + 120*a^2*b^2*c^2 + 702*a*b^4*c))/315 + (2*c^2*d^5*x^4*(1703*b^4 + 48*a^2*c^2 + 2976*a*b^2*c))/315 + (128*b*c^5*d^5*x^7)/9 + (16*c^4*d^5*x^6*(20*a*c + 93*b^2))/63 + (4*b*c*d^5*x^3*(243*b^4 + 48*a^2*c^2 + 976*a*b^2*c))/315 + (4*a*b*d^5*x*(63*b^4 - 32*a^2*c^2 + 36*a*b^2*c))/315 + (16*b*c^3*d^5*x^5*(60*a*c + 83*b^2))/63)","B"
1203,0,-1,207,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(3/2),x)","\int {\left(b\,d+2\,c\,d\,x\right)}^4\,{\left(c\,x^2+b\,x+a\right)}^{3/2} \,d x","Not used",1,"int((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(3/2), x)","F"
1204,1,58,59,0.748238,"\text{Not used}","int((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(3/2),x)","\frac{8\,c\,d^3\,{\left(c\,x^2+b\,x+a\right)}^{7/2}}{7}+\frac{2\,b^2\,d^3\,{\left(c\,x^2+b\,x+a\right)}^{5/2}}{5}-\frac{8\,a\,c\,d^3\,{\left(c\,x^2+b\,x+a\right)}^{5/2}}{5}","Not used",1,"(8*c*d^3*(a + b*x + c*x^2)^(7/2))/7 + (2*b^2*d^3*(a + b*x + c*x^2)^(5/2))/5 - (8*a*c*d^3*(a + b*x + c*x^2)^(5/2))/5","B"
1205,0,-1,165,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(3/2),x)","\int {\left(b\,d+2\,c\,d\,x\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^{3/2} \,d x","Not used",1,"int((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(3/2), x)","F"
1206,1,15,19,0.554844,"\text{Not used}","int((b*d + 2*c*d*x)*(a + b*x + c*x^2)^(3/2),x)","\frac{2\,d\,{\left(c\,x^2+b\,x+a\right)}^{5/2}}{5}","Not used",1,"(2*d*(a + b*x + c*x^2)^(5/2))/5","B"
1207,0,-1,115,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{b\,d+2\,c\,d\,x} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x), x)","F"
1208,0,-1,113,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^2,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(b\,d+2\,c\,d\,x\right)}^2} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^2, x)","F"
1209,0,-1,115,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^3,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(b\,d+2\,c\,d\,x\right)}^3} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^3, x)","F"
1210,0,-1,107,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^4,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(b\,d+2\,c\,d\,x\right)}^4} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^4, x)","F"
1211,0,-1,123,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^5,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(b\,d+2\,c\,d\,x\right)}^5} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^5, x)","F"
1212,1,1156,39,1.533660,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^6,x)","\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{32\,a\,c^4}{3\,d^6\,{\left(4\,a\,c-b^2\right)}^2\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}-\frac{16\,b^2\,c^3}{15\,d^6\,{\left(4\,a\,c-b^2\right)}^2\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8\,b\,c^2\,\left(6\,a\,c-b^2\right)}{3\,d^6\,{\left(4\,a\,c-b^2\right)}^2\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{4\,c\,\left(36\,a^2\,c^2+12\,a\,b^2\,c-4\,b^4\right)}{15\,d^6\,{\left(4\,a\,c-b^2\right)}^2\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8\,a\,b\,c\,\left(9\,a\,c-2\,b^2\right)}{15\,d^6\,{\left(4\,a\,c-b^2\right)}^2\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^2}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{2\,c^2\,\left(28\,a\,c-b^2\right)}{5\,d^6\,\left(4\,a\,c-b^2\right)\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{6\,b^2\,c^2}{5\,d^6\,\left(4\,a\,c-b^2\right)\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(5\,b^3-28\,a\,b\,c\right)}{5\,d^6\,\left(4\,a\,c-b^2\right)\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2\,c\,\left(5\,a\,b^2-24\,a^2\,c\right)}{5\,d^6\,\left(4\,a\,c-b^2\right)\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}+\frac{\left(\frac{8\,a\,c-b^2}{40\,c^2\,d^6\,{\left(4\,a\,c-b^2\right)}^2}-\frac{b^2}{40\,c^2\,d^6\,{\left(4\,a\,c-b^2\right)}^2}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{2\,\left(10\,a\,c-b^2\right)}{15\,d^6\,{\left(4\,a\,c-b^2\right)}^3}-\frac{b^2}{10\,d^6\,{\left(4\,a\,c-b^2\right)}^3}\right)}{2\,c}+\frac{4\,b^3-20\,a\,b\,c}{15\,c\,d^6\,{\left(4\,a\,c-b^2\right)}^3}\right)}{2\,c}-\frac{4\,a\,b^2-18\,a^2\,c}{15\,c\,d^6\,{\left(4\,a\,c-b^2\right)}^3}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{2\,c\,\left(6\,b^2\,c^2+56\,a\,c^3\right)}{5\,d^6\,\left(4\,a\,c-b^2\right)\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}-\frac{16\,b^2\,c^3}{5\,d^6\,\left(4\,a\,c-b^2\right)\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(11\,b^3\,c-84\,a\,b\,c^2\right)}{5\,d^6\,\left(4\,a\,c-b^2\right)\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(48\,a^2\,c^2+18\,a\,b^2\,c-5\,b^4\right)}{5\,d^6\,\left(4\,a\,c-b^2\right)\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(5\,a\,b^3-24\,a^2\,b\,c\right)}{5\,d^6\,\left(4\,a\,c-b^2\right)\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^4}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{4\,c^2\,\left(2\,b^2+4\,a\,c\right)}{d^6\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}-\frac{6\,b^2\,c^2}{d^6\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}-\frac{16\,a\,b\,c^2}{d^6\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}+\frac{8\,a^2\,c^2}{d^6\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^5}","Not used",1,"(((b*((b*((b*((32*a*c^4)/(3*d^6*(4*a*c - b^2)^2*(32*a*c^3 - 8*b^2*c^2)) - (16*b^2*c^3)/(15*d^6*(4*a*c - b^2)^2*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (8*b*c^2*(6*a*c - b^2))/(3*d^6*(4*a*c - b^2)^2*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (4*c*(36*a^2*c^2 - 4*b^4 + 12*a*b^2*c))/(15*d^6*(4*a*c - b^2)^2*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (8*a*b*c*(9*a*c - 2*b^2))/(15*d^6*(4*a*c - b^2)^2*(32*a*c^3 - 8*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^2 - (((b*((b*((2*c^2*(28*a*c - b^2))/(5*d^6*(4*a*c - b^2)*(48*a*c^3 - 12*b^2*c^2)) - (6*b^2*c^2)/(5*d^6*(4*a*c - b^2)*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (2*c*(5*b^3 - 28*a*b*c))/(5*d^6*(4*a*c - b^2)*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (2*c*(5*a*b^2 - 24*a^2*c))/(5*d^6*(4*a*c - b^2)*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 + (((8*a*c - b^2)/(40*c^2*d^6*(4*a*c - b^2)^2) - b^2/(40*c^2*d^6*(4*a*c - b^2)^2))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) - (((b*((b*((2*(10*a*c - b^2))/(15*d^6*(4*a*c - b^2)^3) - b^2/(10*d^6*(4*a*c - b^2)^3)))/(2*c) + (4*b^3 - 20*a*b*c)/(15*c*d^6*(4*a*c - b^2)^3)))/(2*c) - (4*a*b^2 - 18*a^2*c)/(15*c*d^6*(4*a*c - b^2)^3))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) + (((b*((b*((b*((2*c*(56*a*c^3 + 6*b^2*c^2))/(5*d^6*(4*a*c - b^2)*(64*a*c^3 - 16*b^2*c^2)) - (16*b^2*c^3)/(5*d^6*(4*a*c - b^2)*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (2*c*(11*b^3*c - 84*a*b*c^2))/(5*d^6*(4*a*c - b^2)*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (2*c*(48*a^2*c^2 - 5*b^4 + 18*a*b^2*c))/(5*d^6*(4*a*c - b^2)*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (2*c*(5*a*b^3 - 24*a^2*b*c))/(5*d^6*(4*a*c - b^2)*(64*a*c^3 - 16*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^4 - (((b*((b*((4*c^2*(4*a*c + 2*b^2))/(d^6*(80*a*c^3 - 20*b^2*c^2)) - (6*b^2*c^2)/(d^6*(80*a*c^3 - 20*b^2*c^2))))/(2*c) - (16*a*b*c^2)/(d^6*(80*a*c^3 - 20*b^2*c^2))))/(2*c) + (8*a^2*c^2)/(d^6*(80*a*c^3 - 20*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^5","B"
1213,0,-1,165,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^7,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(b\,d+2\,c\,d\,x\right)}^7} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^7, x)","F"
1214,1,1814,79,2.368348,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^8,x)","\frac{\left(\frac{9\,a\,c-2\,b^2}{70\,c^2\,d^8\,{\left(4\,a\,c-b^2\right)}^3}-\frac{b^2}{280\,c^2\,d^8\,{\left(4\,a\,c-b^2\right)}^3}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{16\,c^2\,\left(7\,a\,c-b^2\right)}{35\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{6\,b^2\,c^2}{35\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{4\,c\,\left(6\,b^3-28\,a\,b\,c\right)}{35\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{4\,c\,\left(6\,a\,b^2-26\,a^2\,c\right)}{35\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{6\,c^2\,\left(12\,a\,c-b^2\right)}{7\,d^8\,\left(4\,a\,c-b^2\right)\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}-\frac{6\,b^2\,c^2}{7\,d^8\,\left(4\,a\,c-b^2\right)\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(7\,b^3-36\,a\,b\,c\right)}{7\,d^8\,\left(4\,a\,c-b^2\right)\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2\,c\,\left(7\,a\,b^2-32\,a^2\,c\right)}{7\,d^8\,\left(4\,a\,c-b^2\right)\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^5}-\frac{\left(\frac{b^2}{14\,d^8\,\left(4\,a\,c-b^2\right)\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{8\,a\,c-b^2}{14\,d^8\,\left(4\,a\,c-b^2\right)\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b^2}{70\,d^8\,{\left(4\,a\,c-b^2\right)}^4}-\frac{68\,a\,c^2-11\,b^2\,c}{210\,c\,d^8\,{\left(4\,a\,c-b^2\right)}^4}\right)}{2\,c}-\frac{15\,b^3-68\,a\,b\,c}{210\,c\,d^8\,{\left(4\,a\,c-b^2\right)}^4}\right)}{2\,c}+\frac{15\,a\,b^2-64\,a^2\,c}{210\,c\,d^8\,{\left(4\,a\,c-b^2\right)}^4}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{16\,c^3\,\left(14\,a\,c-b^2\right)}{35\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}-\frac{16\,b^2\,c^3}{35\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{16\,b\,c^2\,\left(21\,a\,c-4\,b^2\right)}{35\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{4\,c\,\left(52\,a^2\,c^2+16\,a\,b^2\,c-6\,b^4\right)}{35\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8\,a\,b\,c\,\left(13\,a\,c-3\,b^2\right)}{35\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^4}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{4\,c^3\,\left(b^2+36\,a\,c\right)}{7\,d^8\,\left(4\,a\,c-b^2\right)\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}-\frac{16\,b^2\,c^3}{7\,d^8\,\left(4\,a\,c-b^2\right)\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(17\,b^3\,c-108\,a\,b\,c^2\right)}{7\,d^8\,\left(4\,a\,c-b^2\right)\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(64\,a^2\,c^2+22\,a\,b^2\,c-7\,b^4\right)}{7\,d^8\,\left(4\,a\,c-b^2\right)\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(7\,a\,b^3-32\,a^2\,b\,c\right)}{7\,d^8\,\left(4\,a\,c-b^2\right)\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^6}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{2\,c\,\left(136\,a\,c^3-14\,b^2\,c^2\right)}{105\,d^8\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}-\frac{16\,b^2\,c^3}{105\,d^8\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(41\,b^3\,c-204\,a\,b\,c^2\right)}{105\,d^8\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(128\,a^2\,c^2+38\,a\,b^2\,c-15\,b^4\right)}{105\,d^8\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(15\,a\,b^3-64\,a^2\,b\,c\right)}{105\,d^8\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^2}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{4\,c^2\,\left(2\,b^2+4\,a\,c\right)}{d^8\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}-\frac{6\,b^2\,c^2}{d^8\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}-\frac{16\,a\,b\,c^2}{d^8\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}+\frac{8\,a^2\,c^2}{d^8\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^7}-\frac{\sqrt{c\,x^2+b\,x+a}}{168\,c^2\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(b+2\,c\,x\right)}","Not used",1,"(((9*a*c - 2*b^2)/(70*c^2*d^8*(4*a*c - b^2)^3) - b^2/(280*c^2*d^8*(4*a*c - b^2)^3))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) - (((b*((b*((16*c^2*(7*a*c - b^2))/(35*d^8*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2)) - (6*b^2*c^2)/(35*d^8*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (4*c*(6*b^3 - 28*a*b*c))/(35*d^8*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (4*c*(6*a*b^2 - 26*a^2*c))/(35*d^8*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 - (((b*((b*((6*c^2*(12*a*c - b^2))/(7*d^8*(4*a*c - b^2)*(80*a*c^3 - 20*b^2*c^2)) - (6*b^2*c^2)/(7*d^8*(4*a*c - b^2)*(80*a*c^3 - 20*b^2*c^2))))/(2*c) + (2*c*(7*b^3 - 36*a*b*c))/(7*d^8*(4*a*c - b^2)*(80*a*c^3 - 20*b^2*c^2))))/(2*c) - (2*c*(7*a*b^2 - 32*a^2*c))/(7*d^8*(4*a*c - b^2)*(80*a*c^3 - 20*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^5 - ((b^2/(14*d^8*(4*a*c - b^2)*(48*a*c^3 - 12*b^2*c^2)) - (8*a*c - b^2)/(14*d^8*(4*a*c - b^2)*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 + (((b*((b*(b^2/(70*d^8*(4*a*c - b^2)^4) - (68*a*c^2 - 11*b^2*c)/(210*c*d^8*(4*a*c - b^2)^4)))/(2*c) - (15*b^3 - 68*a*b*c)/(210*c*d^8*(4*a*c - b^2)^4)))/(2*c) + (15*a*b^2 - 64*a^2*c)/(210*c*d^8*(4*a*c - b^2)^4))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) + (((b*((b*((b*((16*c^3*(14*a*c - b^2))/(35*d^8*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2)) - (16*b^2*c^3)/(35*d^8*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (16*b*c^2*(21*a*c - 4*b^2))/(35*d^8*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (4*c*(52*a^2*c^2 - 6*b^4 + 16*a*b^2*c))/(35*d^8*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (8*a*b*c*(13*a*c - 3*b^2))/(35*d^8*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^4 + (((b*((b*((b*((4*c^3*(36*a*c + b^2))/(7*d^8*(4*a*c - b^2)*(96*a*c^3 - 24*b^2*c^2)) - (16*b^2*c^3)/(7*d^8*(4*a*c - b^2)*(96*a*c^3 - 24*b^2*c^2))))/(2*c) + (2*c*(17*b^3*c - 108*a*b*c^2))/(7*d^8*(4*a*c - b^2)*(96*a*c^3 - 24*b^2*c^2))))/(2*c) + (2*c*(64*a^2*c^2 - 7*b^4 + 22*a*b^2*c))/(7*d^8*(4*a*c - b^2)*(96*a*c^3 - 24*b^2*c^2))))/(2*c) + (2*c*(7*a*b^3 - 32*a^2*b*c))/(7*d^8*(4*a*c - b^2)*(96*a*c^3 - 24*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^6 + (((b*((b*((b*((2*c*(136*a*c^3 - 14*b^2*c^2))/(105*d^8*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2)) - (16*b^2*c^3)/(105*d^8*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (2*c*(41*b^3*c - 204*a*b*c^2))/(105*d^8*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (2*c*(128*a^2*c^2 - 15*b^4 + 38*a*b^2*c))/(105*d^8*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (2*c*(15*a*b^3 - 64*a^2*b*c))/(105*d^8*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^2 - (((b*((b*((4*c^2*(4*a*c + 2*b^2))/(d^8*(112*a*c^3 - 28*b^2*c^2)) - (6*b^2*c^2)/(d^8*(112*a*c^3 - 28*b^2*c^2))))/(2*c) - (16*a*b*c^2)/(d^8*(112*a*c^3 - 28*b^2*c^2))))/(2*c) + (8*a^2*c^2)/(d^8*(112*a*c^3 - 28*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^7 - (a + b*x + c*x^2)^(1/2)/(168*c^2*d^8*(4*a*c - b^2)^2*(b + 2*c*x))","B"
1215,0,-1,207,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^9,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(b\,d+2\,c\,d\,x\right)}^9} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^9, x)","F"
1216,1,3111,118,4.256805,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^10,x)","\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{4\,c^3\,\left(44\,a\,c-b^2\right)}{9\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}-\frac{16\,b^2\,c^3}{9\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(23\,b^3\,c-132\,a\,b\,c^2\right)}{9\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(80\,a^2\,c^2+26\,a\,b^2\,c-9\,b^4\right)}{9\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(9\,a\,b^3-40\,a^2\,b\,c\right)}{9\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^8}-\frac{\left(\frac{b^2}{18\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}-\frac{8\,a\,c-b^2}{18\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^5}-\frac{\left(\frac{b^2}{126\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{22\,a\,c-5\,b^2}{63\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}-\frac{\left(\frac{b\,\left(\frac{c\,\left(6\,a\,c-b^2\right)}{30\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}-\frac{b^2\,c}{90\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,b^3-9\,a\,b\,c}{90\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^2}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{4\,c\,\left(104\,a\,c^3-16\,b^2\,c^2\right)}{945\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}-\frac{16\,b^2\,c^3}{945\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8\,b\,c^2\,\left(78\,a\,c-17\,b^2\right)}{945\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{4\,c\,\left(100\,a^2\,c^2+28\,a\,b^2\,c-12\,b^4\right)}{945\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8\,a\,b\,c\,\left(25\,a\,c-6\,b^2\right)}{945\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^2}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{8\,c^2\,\left(6\,a\,c-b^2\right)}{21\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}-\frac{2\,b^2\,c^2}{21\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}+\frac{4\,c\,\left(8\,b^3-36\,a\,b\,c\right)}{63\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}-\frac{4\,c\,\left(8\,a\,b^2-34\,a^2\,c\right)}{63\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^5}+\frac{\left(\frac{3\,a\,c-b^2}{360\,c^2\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}+\frac{b^2}{1440\,c^2\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}+\frac{\left(\frac{9\,a\,c-2\,b^2}{360\,c^2\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}-\frac{b^2}{1440\,c^2\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}+\frac{\left(\frac{72\,a\,c-17\,b^2}{2520\,c^2\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}-\frac{b^2}{2520\,c^2\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b^2}{630\,d^{10}\,{\left(4\,a\,c-b^2\right)}^5}-\frac{52\,a\,c^2-10\,b^2\,c}{945\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,c}-\frac{12\,b^3-52\,a\,b\,c}{945\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,c}+\frac{12\,a\,b^2-50\,a^2\,c}{945\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^5}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{32\,c^3\,\left(9\,a\,c-b^2\right)}{63\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}-\frac{16\,b^2\,c^3}{63\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8\,b\,c^2\,\left(54\,a\,c-11\,b^2\right)}{63\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}+\frac{4\,c\,\left(68\,a^2\,c^2+20\,a\,b^2\,c-8\,b^4\right)}{63\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8\,a\,b\,c\,\left(17\,a\,c-4\,b^2\right)}{63\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^6}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{2\,c\,\left(44\,a\,c^2-5\,b^2\,c\right)}{9\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}-\frac{2\,b^2\,c^2}{3\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(9\,b^3-44\,a\,b\,c\right)}{9\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2\,c\,\left(9\,a\,b^2-40\,a^2\,c\right)}{9\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^7}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{2\,c\,\left(92\,a\,c^2-17\,b^2\,c\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{2\,b^2\,c^2}{105\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(21\,b^3-92\,a\,b\,c\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2\,c\,\left(21\,a\,b^2-88\,a^2\,c\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{5\,b^2\,c^2+4\,a\,c^3}{90\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{b^2\,c^2}{30\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{b\,c\,\left(b^2+4\,a\,c\right)}{90\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{48\,a^2\,c^2-25\,a\,b^2\,c+3\,b^4}{90\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}+\frac{\left(\frac{b\,\left(\frac{2\,c\,\left(2\,a\,c-b^2\right)}{15\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}+\frac{2\,b^2\,c}{45\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,\left(b^3-3\,a\,b\,c\right)}{45\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^4}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{2\,c\,\left(184\,a\,c^3-26\,b^2\,c^2\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}-\frac{16\,b^2\,c^3}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(59\,b^3\,c-276\,a\,b\,c^2\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(176\,a^2\,c^2+50\,a\,b^2\,c-21\,b^4\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,c\,\left(21\,a\,b^3-88\,a^2\,b\,c\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^4}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{4\,c^2\,\left(2\,b^2+4\,a\,c\right)}{d^{10}\,\left(144\,a\,c^3-36\,b^2\,c^2\right)}-\frac{6\,b^2\,c^2}{d^{10}\,\left(144\,a\,c^3-36\,b^2\,c^2\right)}\right)}{2\,c}-\frac{16\,a\,b\,c^2}{d^{10}\,\left(144\,a\,c^3-36\,b^2\,c^2\right)}\right)}{2\,c}+\frac{8\,a^2\,c^2}{d^{10}\,\left(144\,a\,c^3-36\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^9}-\frac{29\,\sqrt{c\,x^2+b\,x+a}}{1890\,c^2\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(b+2\,c\,x\right)}","Not used",1,"(((b*((b*((b*((4*c^3*(44*a*c - b^2))/(9*d^10*(4*a*c - b^2)*(128*a*c^3 - 32*b^2*c^2)) - (16*b^2*c^3)/(9*d^10*(4*a*c - b^2)*(128*a*c^3 - 32*b^2*c^2))))/(2*c) + (2*c*(23*b^3*c - 132*a*b*c^2))/(9*d^10*(4*a*c - b^2)*(128*a*c^3 - 32*b^2*c^2))))/(2*c) + (2*c*(80*a^2*c^2 - 9*b^4 + 26*a*b^2*c))/(9*d^10*(4*a*c - b^2)*(128*a*c^3 - 32*b^2*c^2))))/(2*c) + (2*c*(9*a*b^3 - 40*a^2*b*c))/(9*d^10*(4*a*c - b^2)*(128*a*c^3 - 32*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^8 - ((b^2/(18*d^10*(4*a*c - b^2)*(80*a*c^3 - 20*b^2*c^2)) - (8*a*c - b^2)/(18*d^10*(4*a*c - b^2)*(80*a*c^3 - 20*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^5 - ((b^2/(126*d^10*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2)) - (22*a*c - 5*b^2)/(63*d^10*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 - (((b*((c*(6*a*c - b^2))/(30*d^10*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2)) - (b^2*c)/(90*d^10*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (2*b^3 - 9*a*b*c)/(90*d^10*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^2 + (((b*((b*((b*((4*c*(104*a*c^3 - 16*b^2*c^2))/(945*d^10*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2)) - (16*b^2*c^3)/(945*d^10*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (8*b*c^2*(78*a*c - 17*b^2))/(945*d^10*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (4*c*(100*a^2*c^2 - 12*b^4 + 28*a*b^2*c))/(945*d^10*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (8*a*b*c*(25*a*c - 6*b^2))/(945*d^10*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^2 - (((b*((b*((8*c^2*(6*a*c - b^2))/(21*d^10*(4*a*c - b^2)^2*(80*a*c^3 - 20*b^2*c^2)) - (2*b^2*c^2)/(21*d^10*(4*a*c - b^2)^2*(80*a*c^3 - 20*b^2*c^2))))/(2*c) + (4*c*(8*b^3 - 36*a*b*c))/(63*d^10*(4*a*c - b^2)^2*(80*a*c^3 - 20*b^2*c^2))))/(2*c) - (4*c*(8*a*b^2 - 34*a^2*c))/(63*d^10*(4*a*c - b^2)^2*(80*a*c^3 - 20*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^5 + (((3*a*c - b^2)/(360*c^2*d^10*(4*a*c - b^2)^4) + b^2/(1440*c^2*d^10*(4*a*c - b^2)^4))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) + (((9*a*c - 2*b^2)/(360*c^2*d^10*(4*a*c - b^2)^4) - b^2/(1440*c^2*d^10*(4*a*c - b^2)^4))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) + (((72*a*c - 17*b^2)/(2520*c^2*d^10*(4*a*c - b^2)^4) - b^2/(2520*c^2*d^10*(4*a*c - b^2)^4))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) + (((b*((b*(b^2/(630*d^10*(4*a*c - b^2)^5) - (52*a*c^2 - 10*b^2*c)/(945*c*d^10*(4*a*c - b^2)^5)))/(2*c) - (12*b^3 - 52*a*b*c)/(945*c*d^10*(4*a*c - b^2)^5)))/(2*c) + (12*a*b^2 - 50*a^2*c)/(945*c*d^10*(4*a*c - b^2)^5))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) + (((b*((b*((b*((32*c^3*(9*a*c - b^2))/(63*d^10*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2)) - (16*b^2*c^3)/(63*d^10*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2))))/(2*c) - (8*b*c^2*(54*a*c - 11*b^2))/(63*d^10*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2))))/(2*c) + (4*c*(68*a^2*c^2 - 8*b^4 + 20*a*b^2*c))/(63*d^10*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2))))/(2*c) - (8*a*b*c*(17*a*c - 4*b^2))/(63*d^10*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^6 - (((b*((b*((2*c*(44*a*c^2 - 5*b^2*c))/(9*d^10*(4*a*c - b^2)*(112*a*c^3 - 28*b^2*c^2)) - (2*b^2*c^2)/(3*d^10*(4*a*c - b^2)*(112*a*c^3 - 28*b^2*c^2))))/(2*c) + (2*c*(9*b^3 - 44*a*b*c))/(9*d^10*(4*a*c - b^2)*(112*a*c^3 - 28*b^2*c^2))))/(2*c) - (2*c*(9*a*b^2 - 40*a^2*c))/(9*d^10*(4*a*c - b^2)*(112*a*c^3 - 28*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^7 - (((b*((b*((2*c*(92*a*c^2 - 17*b^2*c))/(315*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2)) - (2*b^2*c^2)/(105*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (2*c*(21*b^3 - 92*a*b*c))/(315*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (2*c*(21*a*b^2 - 88*a^2*c))/(315*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 + (((b*((b*((4*a*c^3 + 5*b^2*c^2)/(90*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2)) - (b^2*c^2)/(30*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (b*c*(4*a*c + b^2))/(90*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (3*b^4 + 48*a^2*c^2 - 25*a*b^2*c)/(90*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 + (((b*((2*c*(2*a*c - b^2))/(15*d^10*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2)) + (2*b^2*c)/(45*d^10*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (2*(b^3 - 3*a*b*c))/(45*d^10*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^4 + (((b*((b*((b*((2*c*(184*a*c^3 - 26*b^2*c^2))/(315*d^10*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2)) - (16*b^2*c^3)/(315*d^10*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (2*c*(59*b^3*c - 276*a*b*c^2))/(315*d^10*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (2*c*(176*a^2*c^2 - 21*b^4 + 50*a*b^2*c))/(315*d^10*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (2*c*(21*a*b^3 - 88*a^2*b*c))/(315*d^10*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^4 - (((b*((b*((4*c^2*(4*a*c + 2*b^2))/(d^10*(144*a*c^3 - 36*b^2*c^2)) - (6*b^2*c^2)/(d^10*(144*a*c^3 - 36*b^2*c^2))))/(2*c) - (16*a*b*c^2)/(d^10*(144*a*c^3 - 36*b^2*c^2))))/(2*c) + (8*a^2*c^2)/(d^10*(144*a*c^3 - 36*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^9 - (29*(a + b*x + c*x^2)^(1/2))/(1890*c^2*d^10*(4*a*c - b^2)^3*(b + 2*c*x))","B"
1217,1,128,98,1.405727,"\text{Not used}","int((b*d + 2*c*d*x)^5*(a + b*x + c*x^2)^(5/2),x)","\frac{2\,b^4\,d^5\,{\left(c\,x^2+b\,x+a\right)}^{7/2}}{7}+\frac{32\,c^2\,d^5\,{\left(c\,x^2+b\,x+a\right)}^{11/2}}{11}-\frac{64\,a\,c^2\,d^5\,{\left(c\,x^2+b\,x+a\right)}^{9/2}}{9}+\frac{16\,b^2\,c\,d^5\,{\left(c\,x^2+b\,x+a\right)}^{9/2}}{9}+\frac{32\,a^2\,c^2\,d^5\,{\left(c\,x^2+b\,x+a\right)}^{7/2}}{7}-\frac{16\,a\,b^2\,c\,d^5\,{\left(c\,x^2+b\,x+a\right)}^{7/2}}{7}","Not used",1,"(2*b^4*d^5*(a + b*x + c*x^2)^(7/2))/7 + (32*c^2*d^5*(a + b*x + c*x^2)^(11/2))/11 - (64*a*c^2*d^5*(a + b*x + c*x^2)^(9/2))/9 + (16*b^2*c*d^5*(a + b*x + c*x^2)^(9/2))/9 + (32*a^2*c^2*d^5*(a + b*x + c*x^2)^(7/2))/7 - (16*a*b^2*c*d^5*(a + b*x + c*x^2)^(7/2))/7","B"
1218,0,-1,249,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(5/2),x)","\int {\left(b\,d+2\,c\,d\,x\right)}^4\,{\left(c\,x^2+b\,x+a\right)}^{5/2} \,d x","Not used",1,"int((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(5/2), x)","F"
1219,1,58,59,1.013406,"\text{Not used}","int((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(5/2),x)","\frac{8\,c\,d^3\,{\left(c\,x^2+b\,x+a\right)}^{9/2}}{9}+\frac{2\,b^2\,d^3\,{\left(c\,x^2+b\,x+a\right)}^{7/2}}{7}-\frac{8\,a\,c\,d^3\,{\left(c\,x^2+b\,x+a\right)}^{7/2}}{7}","Not used",1,"(8*c*d^3*(a + b*x + c*x^2)^(9/2))/9 + (2*b^2*d^3*(a + b*x + c*x^2)^(7/2))/7 - (8*a*c*d^3*(a + b*x + c*x^2)^(7/2))/7","B"
1220,0,-1,207,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(5/2),x)","\int {\left(b\,d+2\,c\,d\,x\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^{5/2} \,d x","Not used",1,"int((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(5/2), x)","F"
1221,1,15,19,0.674851,"\text{Not used}","int((b*d + 2*c*d*x)*(a + b*x + c*x^2)^(5/2),x)","\frac{2\,d\,{\left(c\,x^2+b\,x+a\right)}^{7/2}}{7}","Not used",1,"(2*d*(a + b*x + c*x^2)^(7/2))/7","B"
1222,0,-1,149,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{b\,d+2\,c\,d\,x} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x), x)","F"
1223,0,-1,153,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^2,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^2} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^2, x)","F"
1224,0,-1,147,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^3,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^3} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^3, x)","F"
1225,0,-1,145,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^4,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^4} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^4, x)","F"
1226,0,-1,147,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^5,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^5} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^5, x)","F"
1227,0,-1,139,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^6,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^6} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^6, x)","F"
1228,0,-1,155,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^7,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^7} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^7, x)","F"
1229,1,3088,39,3.697602,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^8,x)","\frac{\left(\frac{a}{56\,c^2\,d^8\,{\left(4\,a\,c-b^2\right)}^2}-\frac{b^2}{224\,c^3\,d^8\,{\left(4\,a\,c-b^2\right)}^2}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{4\,c^4\,\left(11\,b^2+40\,a\,c\right)}{7\,d^8\,\left(4\,a\,c-b^2\right)\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}-\frac{24\,b^2\,c^4}{7\,d^8\,\left(4\,a\,c-b^2\right)\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}-\frac{10\,b\,c^3\,\left(40\,a\,c-3\,b^2\right)}{7\,d^8\,\left(4\,a\,c-b^2\right)\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}+\frac{768\,a^2\,c^4+416\,a\,b^2\,c^3-82\,b^4\,c^2}{14\,d^8\,\left(4\,a\,c-b^2\right)\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}+\frac{b\,c\,\left(-1152\,a^2\,c^2+176\,a\,b^2\,c+7\,b^4\right)}{14\,d^8\,\left(4\,a\,c-b^2\right)\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}+\frac{480\,a^3\,c^3+216\,a^2\,b^2\,c^2-98\,a\,b^4\,c+7\,b^6}{14\,d^8\,\left(4\,a\,c-b^2\right)\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}-\frac{240\,a^3\,b\,c^2-84\,a^2\,b^3\,c+7\,a\,b^5}{14\,d^8\,\left(4\,a\,c-b^2\right)\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^6}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{10\,a\,c-b^2}{70\,c\,d^8\,{\left(4\,a\,c-b^2\right)}^3}-\frac{3\,b^2}{280\,c\,d^8\,{\left(4\,a\,c-b^2\right)}^3}\right)}{2\,c}-\frac{b\,\left(5\,a\,c-b^2\right)}{35\,c^2\,d^8\,{\left(4\,a\,c-b^2\right)}^3}\right)}{2\,c}+\frac{384\,a^2\,c^2-152\,a\,b^2\,c+15\,b^4}{1120\,c^3\,d^8\,{\left(4\,a\,c-b^2\right)}^3}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{10\,c^3\,\left(b^2+8\,a\,c\right)}{7\,d^8\,\left(4\,a\,c-b^2\right)\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}-\frac{10\,b^2\,c^3}{7\,d^8\,\left(4\,a\,c-b^2\right)\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}-\frac{20\,b\,c^2\,\left(8\,a\,c-b^2\right)}{7\,d^8\,\left(4\,a\,c-b^2\right)\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}+\frac{384\,a^2\,c^3+48\,a\,b^2\,c^2-21\,b^4\,c}{14\,d^8\,\left(4\,a\,c-b^2\right)\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}-\frac{384\,a^2\,b\,c^2-112\,a\,b^3\,c+7\,b^5}{14\,d^8\,\left(4\,a\,c-b^2\right)\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}+\frac{240\,a^3\,c^2-84\,a^2\,b^2\,c+7\,a\,b^4}{14\,d^8\,\left(4\,a\,c-b^2\right)\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^5}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{24\,c^3\,\left(b^2+a\,c\right)}{d^8\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}-\frac{10\,b^2\,c^3}{d^8\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}-\frac{4\,c^2\,\left(2\,b^3+12\,a\,c\,b\right)}{d^8\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}+\frac{24\,a\,c^2\,\left(b^2+a\,c\right)}{d^8\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}-\frac{24\,a^2\,b\,c^2}{d^8\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}+\frac{8\,a^3\,c^2}{d^8\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^7}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{3\,b^2\,c}{14\,d^8\,\left(4\,a\,c-b^2\right)\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{3\,c\,\left(b^2+4\,a\,c\right)}{14\,d^8\,\left(4\,a\,c-b^2\right)\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{b\,\left(12\,a\,c-b^2\right)}{14\,d^8\,\left(4\,a\,c-b^2\right)\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{48\,a^2\,c^2-12\,a\,b^2\,c+b^4}{56\,c\,d^8\,\left(4\,a\,c-b^2\right)\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{24\,a\,c^4}{7\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{2\,b^2\,c^3}{7\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8\,b\,c^2\,\left(6\,a\,c-b^2\right)}{7\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{-1184\,a^2\,c^3+232\,a\,b^2\,c^2+b^4\,c}{70\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{1184\,a^2\,b\,c^2-472\,a\,b^3\,c+47\,b^5}{70\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{960\,a^3\,c^2-424\,a^2\,b^2\,c+47\,a\,b^4}{70\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}+\frac{\left(\frac{b\,\left(\frac{b^2}{14\,d^8\,\left(4\,a\,c-b^2\right)\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}-\frac{b^2+2\,a\,c}{14\,d^8\,\left(4\,a\,c-b^2\right)\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{a\,b}{14\,d^8\,\left(4\,a\,c-b^2\right)\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^2}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{4\,c^4\,\left(b^2+24\,a\,c\right)}{35\,d^8\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}-\frac{8\,b^2\,c^4}{35\,d^8\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2\,b\,c^3\,\left(72\,a\,c-11\,b^2\right)}{21\,d^8\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{-1904\,a^2\,c^4+232\,a\,b^2\,c^3+26\,b^4\,c^2}{105\,d^8\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{b\,c\,\left(952\,a^2\,c^2-356\,a\,b^2\,c+33\,b^4\right)}{35\,d^8\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{1632\,a^3\,c^3+204\,a^2\,b^2\,c^2-318\,a\,b^4\,c+43\,b^6}{105\,d^8\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{816\,a^3\,b\,c^2-374\,a^2\,b^3\,c+43\,a\,b^5}{105\,d^8\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^2}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{24\,c^4\,\left(b^2+10\,a\,c\right)}{35\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}-\frac{24\,b^2\,c^4}{35\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8\,b\,c^3\,\left(15\,a\,c-2\,b^2\right)}{7\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2368\,a^2\,c^4+16\,a\,b^2\,c^3-82\,b^4\,c^2}{70\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{3\,b\,c\,\left(1184\,a^2\,c^2-392\,a\,b^2\,c+31\,b^4\right)}{70\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{1920\,a^3\,c^3+336\,a^2\,b^2\,c^2-378\,a\,b^4\,c+47\,b^6}{70\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{960\,a^3\,b\,c^2-424\,a^2\,b^3\,c+47\,a\,b^5}{70\,d^8\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^4}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{c\,\left(24\,a\,c-b^2\right)}{70\,d^8\,{\left(4\,a\,c-b^2\right)}^4}-\frac{b^2\,c}{42\,d^8\,{\left(4\,a\,c-b^2\right)}^4}\right)}{2\,c}-\frac{b\,\left(72\,a\,c-13\,b^2\right)}{105\,d^8\,{\left(4\,a\,c-b^2\right)}^4}\right)}{2\,c}+\frac{952\,a^2\,c^3-260\,a\,b^2\,c^2+13\,b^4\,c}{420\,c^2\,d^8\,{\left(4\,a\,c-b^2\right)}^4}\right)}{2\,c}-\frac{952\,a^2\,b\,c^2-404\,a\,b^3\,c+43\,b^5}{420\,c^2\,d^8\,{\left(4\,a\,c-b^2\right)}^4}\right)}{2\,c}+\frac{816\,a^3\,c^2-374\,a^2\,b^2\,c+43\,a\,b^4}{420\,c^2\,d^8\,{\left(4\,a\,c-b^2\right)}^4}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}","Not used",1,"((a/(56*c^2*d^8*(4*a*c - b^2)^2) - b^2/(224*c^3*d^8*(4*a*c - b^2)^2))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) + (((b*((b*((b*((b*((b*((4*c^4*(40*a*c + 11*b^2))/(7*d^8*(4*a*c - b^2)*(96*a*c^3 - 24*b^2*c^2)) - (24*b^2*c^4)/(7*d^8*(4*a*c - b^2)*(96*a*c^3 - 24*b^2*c^2))))/(2*c) - (10*b*c^3*(40*a*c - 3*b^2))/(7*d^8*(4*a*c - b^2)*(96*a*c^3 - 24*b^2*c^2))))/(2*c) + (768*a^2*c^4 - 82*b^4*c^2 + 416*a*b^2*c^3)/(14*d^8*(4*a*c - b^2)*(96*a*c^3 - 24*b^2*c^2))))/(2*c) + (b*c*(7*b^4 - 1152*a^2*c^2 + 176*a*b^2*c))/(14*d^8*(4*a*c - b^2)*(96*a*c^3 - 24*b^2*c^2))))/(2*c) + (7*b^6 + 480*a^3*c^3 + 216*a^2*b^2*c^2 - 98*a*b^4*c)/(14*d^8*(4*a*c - b^2)*(96*a*c^3 - 24*b^2*c^2))))/(2*c) - (7*a*b^5 - 84*a^2*b^3*c + 240*a^3*b*c^2)/(14*d^8*(4*a*c - b^2)*(96*a*c^3 - 24*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^6 + (((b*((b*((10*a*c - b^2)/(70*c*d^8*(4*a*c - b^2)^3) - (3*b^2)/(280*c*d^8*(4*a*c - b^2)^3)))/(2*c) - (b*(5*a*c - b^2))/(35*c^2*d^8*(4*a*c - b^2)^3)))/(2*c) + (15*b^4 + 384*a^2*c^2 - 152*a*b^2*c)/(1120*c^3*d^8*(4*a*c - b^2)^3))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) - (((b*((b*((b*((b*((10*c^3*(8*a*c + b^2))/(7*d^8*(4*a*c - b^2)*(80*a*c^3 - 20*b^2*c^2)) - (10*b^2*c^3)/(7*d^8*(4*a*c - b^2)*(80*a*c^3 - 20*b^2*c^2))))/(2*c) - (20*b*c^2*(8*a*c - b^2))/(7*d^8*(4*a*c - b^2)*(80*a*c^3 - 20*b^2*c^2))))/(2*c) + (384*a^2*c^3 - 21*b^4*c + 48*a*b^2*c^2)/(14*d^8*(4*a*c - b^2)*(80*a*c^3 - 20*b^2*c^2))))/(2*c) - (7*b^5 + 384*a^2*b*c^2 - 112*a*b^3*c)/(14*d^8*(4*a*c - b^2)*(80*a*c^3 - 20*b^2*c^2))))/(2*c) + (7*a*b^4 + 240*a^3*c^2 - 84*a^2*b^2*c)/(14*d^8*(4*a*c - b^2)*(80*a*c^3 - 20*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^5 - (((b*((b*((b*((b*((24*c^3*(a*c + b^2))/(d^8*(112*a*c^3 - 28*b^2*c^2)) - (10*b^2*c^3)/(d^8*(112*a*c^3 - 28*b^2*c^2))))/(2*c) - (4*c^2*(2*b^3 + 12*a*b*c))/(d^8*(112*a*c^3 - 28*b^2*c^2))))/(2*c) + (24*a*c^2*(a*c + b^2))/(d^8*(112*a*c^3 - 28*b^2*c^2))))/(2*c) - (24*a^2*b*c^2)/(d^8*(112*a*c^3 - 28*b^2*c^2))))/(2*c) + (8*a^3*c^2)/(d^8*(112*a*c^3 - 28*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^7 - (((b*((b*((3*b^2*c)/(14*d^8*(4*a*c - b^2)*(48*a*c^3 - 12*b^2*c^2)) - (3*c*(4*a*c + b^2))/(14*d^8*(4*a*c - b^2)*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (b*(12*a*c - b^2))/(14*d^8*(4*a*c - b^2)*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (b^4 + 48*a^2*c^2 - 12*a*b^2*c)/(56*c*d^8*(4*a*c - b^2)*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 - (((b*((b*((b*((b*((24*a*c^4)/(7*d^8*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2)) - (2*b^2*c^3)/(7*d^8*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (8*b*c^2*(6*a*c - b^2))/(7*d^8*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (b^4*c - 1184*a^2*c^3 + 232*a*b^2*c^2)/(70*d^8*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (47*b^5 + 1184*a^2*b*c^2 - 472*a*b^3*c)/(70*d^8*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (47*a*b^4 + 960*a^3*c^2 - 424*a^2*b^2*c)/(70*d^8*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 + (((b*(b^2/(14*d^8*(4*a*c - b^2)*(32*a*c^3 - 8*b^2*c^2)) - (2*a*c + b^2)/(14*d^8*(4*a*c - b^2)*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (a*b)/(14*d^8*(4*a*c - b^2)*(32*a*c^3 - 8*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^2 + (((b*((b*((b*((b*((b*((4*c^4*(24*a*c + b^2))/(35*d^8*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2)) - (8*b^2*c^4)/(35*d^8*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (2*b*c^3*(72*a*c - 11*b^2))/(21*d^8*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (26*b^4*c^2 - 1904*a^2*c^4 + 232*a*b^2*c^3)/(105*d^8*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (b*c*(33*b^4 + 952*a^2*c^2 - 356*a*b^2*c))/(35*d^8*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (43*b^6 + 1632*a^3*c^3 + 204*a^2*b^2*c^2 - 318*a*b^4*c)/(105*d^8*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (43*a*b^5 - 374*a^2*b^3*c + 816*a^3*b*c^2)/(105*d^8*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^2 + (((b*((b*((b*((b*((b*((24*c^4*(10*a*c + b^2))/(35*d^8*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2)) - (24*b^2*c^4)/(35*d^8*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (8*b*c^3*(15*a*c - 2*b^2))/(7*d^8*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (2368*a^2*c^4 - 82*b^4*c^2 + 16*a*b^2*c^3)/(70*d^8*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (3*b*c*(31*b^4 + 1184*a^2*c^2 - 392*a*b^2*c))/(70*d^8*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (47*b^6 + 1920*a^3*c^3 + 336*a^2*b^2*c^2 - 378*a*b^4*c)/(70*d^8*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (47*a*b^5 - 424*a^2*b^3*c + 960*a^3*b*c^2)/(70*d^8*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^4 - (((b*((b*((b*((b*((c*(24*a*c - b^2))/(70*d^8*(4*a*c - b^2)^4) - (b^2*c)/(42*d^8*(4*a*c - b^2)^4)))/(2*c) - (b*(72*a*c - 13*b^2))/(105*d^8*(4*a*c - b^2)^4)))/(2*c) + (13*b^4*c + 952*a^2*c^3 - 260*a*b^2*c^2)/(420*c^2*d^8*(4*a*c - b^2)^4)))/(2*c) - (43*b^5 + 952*a^2*b*c^2 - 404*a*b^3*c)/(420*c^2*d^8*(4*a*c - b^2)^4)))/(2*c) + (43*a*b^4 + 816*a^3*c^2 - 374*a^2*b^2*c)/(420*c^2*d^8*(4*a*c - b^2)^4))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)","B"
1230,0,-1,197,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^9,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^9} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^9, x)","F"
1231,1,5511,79,7.029848,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^10,x)","\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{4\,c^4\,\left(3\,b^2+16\,a\,c\right)}{3\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}-\frac{8\,b^2\,c^4}{3\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}\right)}{2\,c}-\frac{10\,b\,c^3\,\left(48\,a\,c-5\,b^2\right)}{9\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}\right)}{2\,c}+\frac{960\,a^2\,c^4+480\,a\,b^2\,c^3-110\,b^4\,c^2}{18\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}\right)}{2\,c}+\frac{b\,c\,\left(-480\,a^2\,c^2+80\,a\,b^2\,c+3\,b^4\right)}{6\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}\right)}{2\,c}+\frac{608\,a^3\,c^3+264\,a^2\,b^2\,c^2-126\,a\,b^4\,c+9\,b^6}{18\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}\right)}{2\,c}-\frac{304\,a^3\,b\,c^2-108\,a^2\,b^3\,c+9\,a\,b^5}{18\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^8}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{8\,c^4\,\left(18\,a\,c-b^2\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}-\frac{8\,b^2\,c^4}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8\,b\,c^3\,\left(27\,a\,c-5\,b^2\right)}{189\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{4496\,a^2\,c^4-1168\,a\,b^2\,c^3+46\,b^4\,c^2}{945\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{b\,c\,\left(2248\,a^2\,c^2-944\,a\,b^2\,c+99\,b^4\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{4080\,a^3\,c^3+312\,a^2\,b^2\,c^2-786\,a\,b^4\,c+115\,b^6}{945\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2040\,a^3\,b\,c^2-968\,a^2\,b^3\,c+115\,a\,b^5}{945\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^2}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{8\,c^4\,\left(b^2+38\,a\,c\right)}{63\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}-\frac{8\,b^2\,c^4}{21\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}-\frac{40\,b\,c^3\,\left(19\,a\,c-3\,b^2\right)}{63\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}-\frac{-3648\,a^2\,c^4+304\,a\,b^2\,c^3+82\,b^4\,c^2}{126\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}-\frac{5472\,a^2\,b\,c^3-1976\,a\,b^3\,c^2+173\,b^5\,c}{126\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}+\frac{3072\,a^3\,c^3+432\,a^2\,b^2\,c^2-602\,a\,b^4\,c+79\,b^6}{126\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}-\frac{1536\,a^3\,b\,c^2-696\,a^2\,b^3\,c+79\,a\,b^5}{126\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^6}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{8\,a\,c-b^2}{240\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}-\frac{b^2}{480\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}\right)}{2\,c}-\frac{b\,\left(24\,a\,c-5\,b^2\right)}{720\,c^2\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}\right)}{2\,c}+\frac{54\,a^2\,c^2-21\,a\,b^2\,c+2\,b^4}{720\,c^3\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{16\,a\,c-b^2}{720\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}-\frac{b^2}{480\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}\right)}{2\,c}-\frac{b\,\left(16\,a\,c-3\,b^2\right)}{720\,c^2\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}\right)}{2\,c}+\frac{12\,a^2\,c^2+2\,a\,b^2\,c-b^4}{1440\,c^3\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{2\,\left(96\,a\,c^4-9\,b^2\,c^3\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{2\,b^2\,c^3}{63\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{4\,b\,c^2\,\left(96\,a\,c-19\,b^2\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,\left(836\,a^2\,c^3-274\,a\,b^2\,c^2+20\,b^4\,c\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2\,\left(836\,a^2\,b\,c^2-370\,a\,b^3\,c+41\,b^5\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,\left(744\,a^3\,c^2-349\,a^2\,b^2\,c+41\,a\,b^4\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{c^3\,\left(b^2+16\,a\,c\right)}{30\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{b^2\,c^3}{18\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{b\,c^2\,\left(48\,a\,c-7\,b^2\right)}{45\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{560\,a^2\,c^4+8\,a\,b^2\,c^3-22\,b^4\,c^2}{360\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{b\,\left(280\,a^2\,c^2-92\,a\,b^2\,c+7\,b^4\right)}{180\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{192\,a^3\,c^3-4\,a^2\,b^2\,c^2-22\,a\,b^4\,c+3\,b^6}{360\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{c\,\left(8\,a\,c-b^2\right)}{21\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{b^2\,c}{42\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{b\,\left(24\,a\,c-5\,b^2\right)}{63\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{480\,a^2\,c^2-192\,a\,b^2\,c+19\,b^4}{504\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}-\frac{\left(\frac{6\,a\,c-b^2}{720\,c^3\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3}-\frac{b^2}{1440\,c^3\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}-\frac{\left(\frac{32\,a\,c-9\,b^2}{2016\,c^3\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3}+\frac{b^2}{2016\,c^3\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{4\,c^4\,\left(32\,a\,c-b^2\right)}{105\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}-\frac{8\,b^2\,c^4}{105\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2\,b\,c^3\,\left(96\,a\,c-17\,b^2\right)}{63\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{4\,c^2\,\left(836\,a^2\,c^2-178\,a\,b^2\,c+b^4\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{4\,b\,c\,\left(418\,a^2\,c^2-169\,a\,b^2\,c+17\,b^4\right)}{105\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2\,\left(1488\,a^3\,c^3+138\,a^2\,b^2\,c^2-288\,a\,b^4\,c+41\,b^6\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2\,\left(744\,a^3\,b\,c^2-349\,a^2\,b^3\,c+41\,a\,b^5\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^4}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b^2}{840\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}-\frac{76\,a\,c^3-13\,b^2\,c^2}{2520\,c^3\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}\right)}{2\,c}+\frac{b\,\left(76\,a\,c-17\,b^2\right)}{2520\,c^2\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}\right)}{2\,c}-\frac{456\,a^2\,c^2-209\,a\,b^2\,c+24\,b^4}{2520\,c^3\,d^{10}\,{\left(4\,a\,c-b^2\right)}^4}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{2\,c^2\,\left(b^2+16\,a\,c\right)}{45\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}-\frac{4\,b^2\,c^2}{45\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{b\,c\,\left(48\,a\,c-7\,b^2\right)}{45\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{24\,a^2\,c^3+36\,a\,b^2\,c^2-8\,b^4\,c}{90\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{12\,a^2\,b\,c^2+2\,a\,b^3\,c-b^5}{90\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^4}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{2\,c^3\,\left(b^2+16\,a\,c\right)}{3\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}-\frac{10\,b^2\,c^3}{9\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}-\frac{4\,b\,c^2\,\left(48\,a\,c-7\,b^2\right)}{9\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}+\frac{480\,a^2\,c^3+48\,a\,b^2\,c^2-27\,b^4\,c}{18\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}-\frac{480\,a^2\,b\,c^2-144\,a\,b^3\,c+9\,b^5}{18\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}+\frac{304\,a^3\,c^2-108\,a^2\,b^2\,c+9\,a\,b^4}{18\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^7}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{24\,c^3\,\left(b^2+a\,c\right)}{d^{10}\,\left(144\,a\,c^3-36\,b^2\,c^2\right)}-\frac{10\,b^2\,c^3}{d^{10}\,\left(144\,a\,c^3-36\,b^2\,c^2\right)}\right)}{2\,c}-\frac{4\,c^2\,\left(2\,b^3+12\,a\,c\,b\right)}{d^{10}\,\left(144\,a\,c^3-36\,b^2\,c^2\right)}\right)}{2\,c}+\frac{24\,a\,c^2\,\left(b^2+a\,c\right)}{d^{10}\,\left(144\,a\,c^3-36\,b^2\,c^2\right)}\right)}{2\,c}-\frac{24\,a^2\,b\,c^2}{d^{10}\,\left(144\,a\,c^3-36\,b^2\,c^2\right)}\right)}{2\,c}+\frac{8\,a^3\,c^2}{d^{10}\,\left(144\,a\,c^3-36\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^9}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b^2\,c}{6\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}-\frac{c\,\left(b^2+4\,a\,c\right)}{6\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}+\frac{b\,\left(12\,a\,c-b^2\right)}{18\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}-\frac{48\,a^2\,c^2-12\,a\,b^2\,c+b^4}{72\,c\,d^{10}\,\left(4\,a\,c-b^2\right)\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^5}+\frac{\left(\frac{b\,\left(\frac{b^2}{126\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}+\frac{64\,a\,c^2-22\,b^2\,c}{504\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{9\,b^3-32\,a\,b\,c}{504\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^2}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{2\,c\,\left(9\,a\,c-b^2\right)}{315\,d^{10}\,{\left(4\,a\,c-b^2\right)}^5}-\frac{b^2\,c}{378\,d^{10}\,{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,c}-\frac{2\,b\,\left(54\,a\,c-11\,b^2\right)}{945\,d^{10}\,{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,c}+\frac{2248\,a^2\,c^3-800\,a\,b^2\,c^2+67\,b^4\,c}{3780\,c^2\,d^{10}\,{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,c}-\frac{2248\,a^2\,b\,c^2-1016\,a\,b^3\,c+115\,b^5}{3780\,c^2\,d^{10}\,{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,c}+\frac{2040\,a^3\,c^2-968\,a^2\,b^2\,c+115\,a\,b^4}{3780\,c^2\,d^{10}\,{\left(4\,a\,c-b^2\right)}^5}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{c^2\,\left(24\,a\,c-b^2\right)}{90\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}-\frac{b^2\,c^2}{45\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{b\,c\,\left(72\,a\,c-13\,b^2\right)}{180\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{-108\,a^2\,c^3+18\,a\,b^2\,c^2+b^4\,c}{180\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{54\,a^2\,b\,c^2-21\,a\,b^3\,c+2\,b^5}{180\,c\,d^{10}\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^2}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{8\,c^3\,\left(19\,a\,c-b^2\right)}{63\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}-\frac{10\,b^2\,c^3}{63\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8\,b\,c^2\,\left(38\,a\,c-7\,b^2\right)}{63\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}+\frac{1824\,a^2\,c^3-456\,a\,b^2\,c^2+15\,b^4\,c}{126\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}-\frac{1824\,a^2\,b\,c^2-760\,a\,b^3\,c+79\,b^5}{126\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}+\frac{1536\,a^3\,c^2-696\,a^2\,b^2\,c+79\,a\,b^4}{126\,d^{10}\,{\left(4\,a\,c-b^2\right)}^2\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^5}","Not used",1,"(((b*((b*((b*((b*((b*((4*c^4*(16*a*c + 3*b^2))/(3*d^10*(4*a*c - b^2)*(128*a*c^3 - 32*b^2*c^2)) - (8*b^2*c^4)/(3*d^10*(4*a*c - b^2)*(128*a*c^3 - 32*b^2*c^2))))/(2*c) - (10*b*c^3*(48*a*c - 5*b^2))/(9*d^10*(4*a*c - b^2)*(128*a*c^3 - 32*b^2*c^2))))/(2*c) + (960*a^2*c^4 - 110*b^4*c^2 + 480*a*b^2*c^3)/(18*d^10*(4*a*c - b^2)*(128*a*c^3 - 32*b^2*c^2))))/(2*c) + (b*c*(3*b^4 - 480*a^2*c^2 + 80*a*b^2*c))/(6*d^10*(4*a*c - b^2)*(128*a*c^3 - 32*b^2*c^2))))/(2*c) + (9*b^6 + 608*a^3*c^3 + 264*a^2*b^2*c^2 - 126*a*b^4*c)/(18*d^10*(4*a*c - b^2)*(128*a*c^3 - 32*b^2*c^2))))/(2*c) - (9*a*b^5 - 108*a^2*b^3*c + 304*a^3*b*c^2)/(18*d^10*(4*a*c - b^2)*(128*a*c^3 - 32*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^8 + (((b*((b*((b*((b*((b*((8*c^4*(18*a*c - b^2))/(315*d^10*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2)) - (8*b^2*c^4)/(315*d^10*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (8*b*c^3*(27*a*c - 5*b^2))/(189*d^10*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (4496*a^2*c^4 + 46*b^4*c^2 - 1168*a*b^2*c^3)/(945*d^10*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (b*c*(99*b^4 + 2248*a^2*c^2 - 944*a*b^2*c))/(315*d^10*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (115*b^6 + 4080*a^3*c^3 + 312*a^2*b^2*c^2 - 786*a*b^4*c)/(945*d^10*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (115*a*b^5 - 968*a^2*b^3*c + 2040*a^3*b*c^2)/(945*d^10*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^2 + (((b*((b*((b*((b*((b*((8*c^4*(38*a*c + b^2))/(63*d^10*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2)) - (8*b^2*c^4)/(21*d^10*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2))))/(2*c) - (40*b*c^3*(19*a*c - 3*b^2))/(63*d^10*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2))))/(2*c) - (82*b^4*c^2 - 3648*a^2*c^4 + 304*a*b^2*c^3)/(126*d^10*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2))))/(2*c) - (173*b^5*c - 1976*a*b^3*c^2 + 5472*a^2*b*c^3)/(126*d^10*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2))))/(2*c) + (79*b^6 + 3072*a^3*c^3 + 432*a^2*b^2*c^2 - 602*a*b^4*c)/(126*d^10*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2))))/(2*c) - (79*a*b^5 - 696*a^2*b^3*c + 1536*a^3*b*c^2)/(126*d^10*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^6 + (((b*((b*((8*a*c - b^2)/(240*c*d^10*(4*a*c - b^2)^4) - b^2/(480*c*d^10*(4*a*c - b^2)^4)))/(2*c) - (b*(24*a*c - 5*b^2))/(720*c^2*d^10*(4*a*c - b^2)^4)))/(2*c) + (2*b^4 + 54*a^2*c^2 - 21*a*b^2*c)/(720*c^3*d^10*(4*a*c - b^2)^4))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) - (((b*((b*((16*a*c - b^2)/(720*c*d^10*(4*a*c - b^2)^4) - b^2/(480*c*d^10*(4*a*c - b^2)^4)))/(2*c) - (b*(16*a*c - 3*b^2))/(720*c^2*d^10*(4*a*c - b^2)^4)))/(2*c) + (12*a^2*c^2 - b^4 + 2*a*b^2*c)/(1440*c^3*d^10*(4*a*c - b^2)^4))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) - (((b*((b*((b*((b*((2*(96*a*c^4 - 9*b^2*c^3))/(315*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2)) - (2*b^2*c^3)/(63*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (4*b*c^2*(96*a*c - 19*b^2))/(315*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (2*(20*b^4*c + 836*a^2*c^3 - 274*a*b^2*c^2))/(315*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (2*(41*b^5 + 836*a^2*b*c^2 - 370*a*b^3*c))/(315*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (2*(41*a*b^4 + 744*a^3*c^2 - 349*a^2*b^2*c))/(315*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 + (((b*((b*((b*((b*((c^3*(16*a*c + b^2))/(30*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2)) - (b^2*c^3)/(18*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (b*c^2*(48*a*c - 7*b^2))/(45*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (560*a^2*c^4 - 22*b^4*c^2 + 8*a*b^2*c^3)/(360*c*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (b*(7*b^4 + 280*a^2*c^2 - 92*a*b^2*c))/(180*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (3*b^6 + 192*a^3*c^3 - 4*a^2*b^2*c^2 - 22*a*b^4*c)/(360*c*d^10*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 + (((b*((b*((c*(8*a*c - b^2))/(21*d^10*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2)) - (b^2*c)/(42*d^10*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (b*(24*a*c - 5*b^2))/(63*d^10*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (19*b^4 + 480*a^2*c^2 - 192*a*b^2*c)/(504*c*d^10*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 - (((6*a*c - b^2)/(720*c^3*d^10*(4*a*c - b^2)^3) - b^2/(1440*c^3*d^10*(4*a*c - b^2)^3))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) - (((32*a*c - 9*b^2)/(2016*c^3*d^10*(4*a*c - b^2)^3) + b^2/(2016*c^3*d^10*(4*a*c - b^2)^3))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) + (((b*((b*((b*((b*((b*((4*c^4*(32*a*c - b^2))/(105*d^10*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2)) - (8*b^2*c^4)/(105*d^10*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (2*b*c^3*(96*a*c - 17*b^2))/(63*d^10*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (4*c^2*(b^4 + 836*a^2*c^2 - 178*a*b^2*c))/(315*d^10*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (4*b*c*(17*b^4 + 418*a^2*c^2 - 169*a*b^2*c))/(105*d^10*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (2*(41*b^6 + 1488*a^3*c^3 + 138*a^2*b^2*c^2 - 288*a*b^4*c))/(315*d^10*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (2*(41*a*b^5 - 349*a^2*b^3*c + 744*a^3*b*c^2))/(315*d^10*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^4 - (((b*((b*(b^2/(840*c*d^10*(4*a*c - b^2)^4) - (76*a*c^3 - 13*b^2*c^2)/(2520*c^3*d^10*(4*a*c - b^2)^4)))/(2*c) + (b*(76*a*c - 17*b^2))/(2520*c^2*d^10*(4*a*c - b^2)^4)))/(2*c) - (24*b^4 + 456*a^2*c^2 - 209*a*b^2*c)/(2520*c^3*d^10*(4*a*c - b^2)^4))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) - (((b*((b*((b*((2*c^2*(16*a*c + b^2))/(45*d^10*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2)) - (4*b^2*c^2)/(45*d^10*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (b*c*(48*a*c - 7*b^2))/(45*d^10*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (24*a^2*c^3 - 8*b^4*c + 36*a*b^2*c^2)/(90*c*d^10*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (12*a^2*b*c^2 - b^5 + 2*a*b^3*c)/(90*c*d^10*(4*a*c - b^2)^2*(64*a*c^3 - 16*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^4 - (((b*((b*((b*((b*((2*c^3*(16*a*c + b^2))/(3*d^10*(4*a*c - b^2)*(112*a*c^3 - 28*b^2*c^2)) - (10*b^2*c^3)/(9*d^10*(4*a*c - b^2)*(112*a*c^3 - 28*b^2*c^2))))/(2*c) - (4*b*c^2*(48*a*c - 7*b^2))/(9*d^10*(4*a*c - b^2)*(112*a*c^3 - 28*b^2*c^2))))/(2*c) + (480*a^2*c^3 - 27*b^4*c + 48*a*b^2*c^2)/(18*d^10*(4*a*c - b^2)*(112*a*c^3 - 28*b^2*c^2))))/(2*c) - (9*b^5 + 480*a^2*b*c^2 - 144*a*b^3*c)/(18*d^10*(4*a*c - b^2)*(112*a*c^3 - 28*b^2*c^2))))/(2*c) + (9*a*b^4 + 304*a^3*c^2 - 108*a^2*b^2*c)/(18*d^10*(4*a*c - b^2)*(112*a*c^3 - 28*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^7 - (((b*((b*((b*((b*((24*c^3*(a*c + b^2))/(d^10*(144*a*c^3 - 36*b^2*c^2)) - (10*b^2*c^3)/(d^10*(144*a*c^3 - 36*b^2*c^2))))/(2*c) - (4*c^2*(2*b^3 + 12*a*b*c))/(d^10*(144*a*c^3 - 36*b^2*c^2))))/(2*c) + (24*a*c^2*(a*c + b^2))/(d^10*(144*a*c^3 - 36*b^2*c^2))))/(2*c) - (24*a^2*b*c^2)/(d^10*(144*a*c^3 - 36*b^2*c^2))))/(2*c) + (8*a^3*c^2)/(d^10*(144*a*c^3 - 36*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^9 - (((b*((b*((b^2*c)/(6*d^10*(4*a*c - b^2)*(80*a*c^3 - 20*b^2*c^2)) - (c*(4*a*c + b^2))/(6*d^10*(4*a*c - b^2)*(80*a*c^3 - 20*b^2*c^2))))/(2*c) + (b*(12*a*c - b^2))/(18*d^10*(4*a*c - b^2)*(80*a*c^3 - 20*b^2*c^2))))/(2*c) - (b^4 + 48*a^2*c^2 - 12*a*b^2*c)/(72*c*d^10*(4*a*c - b^2)*(80*a*c^3 - 20*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^5 + (((b*(b^2/(126*d^10*(4*a*c - b^2)^2*(32*a*c^3 - 8*b^2*c^2)) + (64*a*c^2 - 22*b^2*c)/(504*c*d^10*(4*a*c - b^2)^2*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (9*b^3 - 32*a*b*c)/(504*c*d^10*(4*a*c - b^2)^2*(32*a*c^3 - 8*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^2 - (((b*((b*((b*((b*((2*c*(9*a*c - b^2))/(315*d^10*(4*a*c - b^2)^5) - (b^2*c)/(378*d^10*(4*a*c - b^2)^5)))/(2*c) - (2*b*(54*a*c - 11*b^2))/(945*d^10*(4*a*c - b^2)^5)))/(2*c) + (67*b^4*c + 2248*a^2*c^3 - 800*a*b^2*c^2)/(3780*c^2*d^10*(4*a*c - b^2)^5)))/(2*c) - (115*b^5 + 2248*a^2*b*c^2 - 1016*a*b^3*c)/(3780*c^2*d^10*(4*a*c - b^2)^5)))/(2*c) + (115*a*b^4 + 2040*a^3*c^2 - 968*a^2*b^2*c)/(3780*c^2*d^10*(4*a*c - b^2)^5))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) - (((b*((b*((b*((c^2*(24*a*c - b^2))/(90*d^10*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2)) - (b^2*c^2)/(45*d^10*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (b*c*(72*a*c - 13*b^2))/(180*d^10*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (b^4*c - 108*a^2*c^3 + 18*a*b^2*c^2)/(180*c*d^10*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (2*b^5 + 54*a^2*b*c^2 - 21*a*b^3*c)/(180*c*d^10*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^2 - (((b*((b*((b*((b*((8*c^3*(19*a*c - b^2))/(63*d^10*(4*a*c - b^2)^2*(80*a*c^3 - 20*b^2*c^2)) - (10*b^2*c^3)/(63*d^10*(4*a*c - b^2)^2*(80*a*c^3 - 20*b^2*c^2))))/(2*c) - (8*b*c^2*(38*a*c - 7*b^2))/(63*d^10*(4*a*c - b^2)^2*(80*a*c^3 - 20*b^2*c^2))))/(2*c) + (15*b^4*c + 1824*a^2*c^3 - 456*a*b^2*c^2)/(126*d^10*(4*a*c - b^2)^2*(80*a*c^3 - 20*b^2*c^2))))/(2*c) - (79*b^5 + 1824*a^2*b*c^2 - 760*a*b^3*c)/(126*d^10*(4*a*c - b^2)^2*(80*a*c^3 - 20*b^2*c^2))))/(2*c) + (79*a*b^4 + 1536*a^3*c^2 - 696*a^2*b^2*c)/(126*d^10*(4*a*c - b^2)^2*(80*a*c^3 - 20*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^5","B"
1232,0,-1,239,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^11,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{11}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^11, x)","F"
1233,1,9995,118,15.666805,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^12,x)","\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{4\,c^4\,\left(40\,a\,c-3\,b^2\right)}{231\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}-\frac{8\,b^2\,c^4}{231\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}-\frac{10\,b\,c^3\,\left(120\,a\,c-23\,b^2\right)}{693\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}+\frac{5168\,a^2\,c^4-1384\,a\,b^2\,c^3+58\,b^4\,c^2}{693\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}-\frac{b\,c\,\left(2584\,a^2\,c^2-1092\,a\,b^2\,c+115\,b^4\right)}{231\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}+\frac{4704\,a^3\,c^3+348\,a^2\,b^2\,c^2-906\,a\,b^4\,c+133\,b^6}{693\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2352\,a^3\,b\,c^2-1118\,a^2\,b^3\,c+133\,a\,b^5}{693\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^6}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b^2}{6160\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5}-\frac{32\,a\,c^3-5\,b^2\,c^2}{9240\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,c}-\frac{7\,b^3\,c-32\,a\,b\,c^2}{9240\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,c}-\frac{126\,a^2\,c^2-55\,a\,b^2\,c+6\,b^4}{9240\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b^2}{5280\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5}-\frac{76\,a\,c^3-13\,b^2\,c^2}{15840\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,c}-\frac{17\,b^3\,c-76\,a\,b\,c^2}{15840\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,c}+\frac{296\,a^2\,c^2-167\,a\,b^2\,c+23\,b^4}{15840\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{5\,a\,c-b^2}{1155\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5}-\frac{b^2}{9240\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,c}-\frac{b\,\left(30\,a\,c-7\,b^2\right)}{6930\,c^2\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,c}+\frac{2584\,a^2\,c^2-1232\,a\,b^2\,c+147\,b^4}{55440\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{368\,a\,c^4-32\,b^2\,c^3}{198\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}-\frac{10\,b^2\,c^3}{99\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8\,b\,c^2\,\left(46\,a\,c-9\,b^2\right)}{99\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2592\,a^2\,c^3-744\,a\,b^2\,c^2+39\,b^4\,c}{198\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2592\,a^2\,b\,c^2-1112\,a\,b^3\,c+119\,b^5}{198\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2240\,a^3\,c^2-1032\,a^2\,b^2\,c+119\,a\,b^4}{198\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^7}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b^2\,c}{4158\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}-\frac{608\,a\,c^4-92\,b^2\,c^3}{83160\,c^2\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}\right)}{2\,c}+\frac{b\,\left(152\,a\,c-33\,b^2\right)}{10395\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}\right)}{2\,c}-\frac{9248\,a^2\,c^3-3712\,a\,b^2\,c^2+365\,b^4\,c}{83160\,c^2\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}\right)}{2\,c}+\frac{9248\,a^2\,b\,c^2-4320\,a\,b^3\,c+505\,b^5}{83160\,c^2\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}\right)}{2\,c}-\frac{8656\,a^3\,c^2-4180\,a^2\,b^2\,c+505\,a\,b^4}{83160\,c^2\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{4\,c\,\left(7\,a\,c-b^2\right)}{99\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}-\frac{b^2\,c}{66\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2\,b\,\left(14\,a\,c-3\,b^2\right)}{99\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}+\frac{576\,a^2\,c^2-232\,a\,b^2\,c+23\,b^4}{792\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^5}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{c\,\left(10\,a\,c-b^2\right)}{231\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{b^2\,c}{308\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2\,b\,\left(5\,a\,c-b^2\right)}{231\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{24\,a^2\,c^2+8\,a\,b^2\,c-3\,b^4}{1848\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}-\frac{\left(\frac{32\,a\,c-7\,b^2}{14784\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4}-\frac{b^2}{14784\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}-\frac{\left(\frac{56\,a\,c-13\,b^2}{15840\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4}-\frac{b^2}{15840\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}-\frac{\left(\frac{170\,a\,c-43\,b^2}{11088\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4}+\frac{b^2}{22176\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b^2}{5280\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5}-\frac{276\,a\,c^3-51\,b^2\,c^2}{47520\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,c}+\frac{b\,\left(92\,a\,c-21\,b^2\right)}{15840\,c^2\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,c}-\frac{2392\,a^2\,c^2-1127\,a\,b^2\,c+133\,b^4}{47520\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{8\,c^4\,\left(46\,a\,c-b^2\right)}{99\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}-\frac{8\,b^2\,c^4}{33\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}\right)}{2\,c}-\frac{40\,b\,c^3\,\left(23\,a\,c-4\,b^2\right)}{99\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}\right)}{2\,c}-\frac{-5184\,a^2\,c^4+752\,a\,b^2\,c^3+66\,b^4\,c^2}{198\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}\right)}{2\,c}-\frac{7776\,a^2\,b\,c^3-2968\,a\,b^3\,c^2+277\,b^5\,c}{198\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}\right)}{2\,c}+\frac{4480\,a^3\,c^3+528\,a^2\,b^2\,c^2-874\,a\,b^4\,c+119\,b^6}{198\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2240\,a^3\,b\,c^2-1032\,a^2\,b^3\,c+119\,a\,b^5}{198\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(128\,a\,c^3-32\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^8}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{8\,c^4\,\left(10\,a\,c-b^2\right)}{495\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}-\frac{8\,b^2\,c^4}{1155\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8\,b\,c^3\,\left(5\,a\,c-b^2\right)}{99\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{7568\,a^2\,c^4-2384\,a\,b^2\,c^3+158\,b^4\,c^2}{3465\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{11352\,a^2\,b\,c^3-4976\,a\,b^3\,c^2+545\,b^5\,c}{3465\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{7024\,a^3\,c^3+408\,a^2\,b^2\,c^2-1346\,a\,b^4\,c+203\,b^6}{3465\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{3512\,a^3\,b\,c^2-1688\,a^2\,b^3\,c+203\,a\,b^5}{3465\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^4}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{4\,c^4\,\left(152\,a\,c-17\,b^2\right)}{10395\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}-\frac{8\,b^2\,c^4}{3465\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2\,b\,c^3\,\left(152\,a\,c-31\,b^2\right)}{2079\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{18496\,a^2\,c^4-6208\,a\,b^2\,c^3+466\,b^4\,c^2}{20790\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{27744\,a^2\,b\,c^3-12352\,a\,b^3\,c^2+1375\,b^5\,c}{20790\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{17312\,a^3\,c^3+888\,a^2\,b^2\,c^2-3310\,a\,b^4\,c+505\,b^6}{20790\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8656\,a^3\,b\,c^2-4180\,a^2\,b^3\,c+505\,a\,b^5}{20790\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^2}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{2\,c^3\,\left(b^2+56\,a\,c\right)}{11\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(144\,a\,c^3-36\,b^2\,c^2\right)}-\frac{10\,b^2\,c^3}{11\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(144\,a\,c^3-36\,b^2\,c^2\right)}\right)}{2\,c}-\frac{4\,b\,c^2\,\left(56\,a\,c-9\,b^2\right)}{11\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(144\,a\,c^3-36\,b^2\,c^2\right)}\right)}{2\,c}+\frac{576\,a^2\,c^3+48\,a\,b^2\,c^2-33\,b^4\,c}{22\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(144\,a\,c^3-36\,b^2\,c^2\right)}\right)}{2\,c}-\frac{576\,a^2\,b\,c^2-176\,a\,b^3\,c+11\,b^5}{22\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(144\,a\,c^3-36\,b^2\,c^2\right)}\right)}{2\,c}+\frac{368\,a^3\,c^2-132\,a^2\,b^2\,c+11\,a\,b^4}{22\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(144\,a\,c^3-36\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^9}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{24\,c^3\,\left(b^2+a\,c\right)}{d^{12}\,\left(176\,a\,c^3-44\,b^2\,c^2\right)}-\frac{10\,b^2\,c^3}{d^{12}\,\left(176\,a\,c^3-44\,b^2\,c^2\right)}\right)}{2\,c}-\frac{4\,c^2\,\left(2\,b^3+12\,a\,c\,b\right)}{d^{12}\,\left(176\,a\,c^3-44\,b^2\,c^2\right)}\right)}{2\,c}+\frac{24\,a\,c^2\,\left(b^2+a\,c\right)}{d^{12}\,\left(176\,a\,c^3-44\,b^2\,c^2\right)}\right)}{2\,c}-\frac{24\,a^2\,b\,c^2}{d^{12}\,\left(176\,a\,c^3-44\,b^2\,c^2\right)}\right)}{2\,c}+\frac{8\,a^3\,c^2}{d^{12}\,\left(176\,a\,c^3-44\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^{11}}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{40\,a\,c^3}{77\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}-\frac{4\,b^2\,c^2}{77\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}-\frac{10\,b\,c\,\left(6\,a\,c-b^2\right)}{77\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}+\frac{48\,a^2\,c^3+96\,a\,b^2\,c^2-22\,b^4\,c}{308\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)}{2\,c}-\frac{24\,a^2\,b\,c^2+8\,a\,b^3\,c-3\,b^5}{308\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(96\,a\,c^3-24\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^6}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{3\,b^2\,c}{22\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}-\frac{3\,c\,\left(b^2+4\,a\,c\right)}{22\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}+\frac{b\,\left(12\,a\,c-b^2\right)}{22\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)}{2\,c}-\frac{48\,a^2\,c^2-12\,a\,b^2\,c+b^4}{88\,c\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(112\,a\,c^3-28\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^7}+\frac{\left(\frac{b\,\left(\frac{b^2}{1386\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}+\frac{340\,a\,c^2-88\,b^2\,c}{2772\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{43\,b^3-170\,a\,b\,c}{2772\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^2}-\frac{\left(\frac{b\,\left(\frac{b^2}{924\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}-\frac{64\,a\,c^2-10\,b^2\,c}{3696\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{7\,b^3-32\,a\,b\,c}{3696\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^2}-\frac{\left(\frac{6\,a\,c-b^2}{308\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{b^2}{616\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^2\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{c^3\,\left(64\,a\,c-b^2\right)}{231\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}-\frac{5\,b^2\,c^3}{231\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2\,b\,c^2\,\left(64\,a\,c-11\,b^2\right)}{231\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}-\frac{-2016\,a^2\,c^4+240\,a\,b^2\,c^3+36\,b^4\,c^2}{1848\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}-\frac{b\,\left(504\,a^2\,c^2-188\,a\,b^2\,c+17\,b^4\right)}{462\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}+\frac{576\,a^3\,c^3+72\,a^2\,b^2\,c^2-112\,a\,b^4\,c+15\,b^6}{1848\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^5}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{2\,c^3\,\left(23\,a\,c-2\,b^2\right)}{495\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{b^2\,c^3}{198\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2\,b\,c^2\,\left(46\,a\,c-9\,b^2\right)}{495\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{32\,a^2\,c^4+536\,a\,b^2\,c^3-121\,b^4\,c^2}{3960\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{b\,\left(32\,a^2\,c^2+168\,a\,b^2\,c-41\,b^4\right)}{3960\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{-4736\,a^3\,c^3+3560\,a^2\,b^2\,c^2-869\,a\,b^4\,c+69\,b^6}{3960\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{28\,c^4\,\left(b^2+8\,a\,c\right)}{11\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(160\,a\,c^3-40\,b^2\,c^2\right)}-\frac{24\,b^2\,c^4}{11\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(160\,a\,c^3-40\,b^2\,c^2\right)}\right)}{2\,c}-\frac{70\,b\,c^3\,\left(8\,a\,c-b^2\right)}{11\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(160\,a\,c^3-40\,b^2\,c^2\right)}\right)}{2\,c}+\frac{1152\,a^2\,c^4+544\,a\,b^2\,c^3-138\,b^4\,c^2}{22\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(160\,a\,c^3-40\,b^2\,c^2\right)}\right)}{2\,c}+\frac{b\,c\,\left(-1728\,a^2\,c^2+304\,a\,b^2\,c+11\,b^4\right)}{22\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(160\,a\,c^3-40\,b^2\,c^2\right)}\right)}{2\,c}+\frac{736\,a^3\,c^3+312\,a^2\,b^2\,c^2-154\,a\,b^4\,c+11\,b^6}{22\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(160\,a\,c^3-40\,b^2\,c^2\right)}\right)}{2\,c}-\frac{368\,a^3\,b\,c^2-132\,a^2\,b^3\,c+11\,a\,b^5}{22\,d^{12}\,\left(4\,a\,c-b^2\right)\,\left(160\,a\,c^3-40\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^{10}}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{8\,a\,c^5}{55\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}-\frac{4\,b^2\,c^4}{385\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2\,b\,c^3\,\left(6\,a\,c-b^2\right)}{33\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{-2288\,a^2\,c^5+304\,a\,b^2\,c^4+32\,b^4\,c^3}{2310\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{4\,b\,c\,\left(143\,a^2\,c^2-54\,a\,b^2\,c+5\,b^4\right)}{385\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{3888\,a^3\,c^4-1200\,a^2\,b^2\,c^3-24\,a\,b^4\,c^2+22\,b^6\,c}{2310\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{-1944\,a^3\,b\,c^3+1172\,a^2\,b^3\,c^2-232\,a\,b^5\,c+15\,b^7}{2310\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^4}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b^2\,c}{462\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{92\,a\,c^3-17\,b^2\,c^2}{1386\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{b\,\left(92\,a\,c-21\,b^2\right)}{1386\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{648\,a^2\,c^2-301\,a\,b^2\,c+35\,b^4}{1386\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{10\,c^3\,\left(8\,a\,c-b^2\right)}{231\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}-\frac{10\,b^2\,c^3}{693\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}-\frac{20\,b\,c^2\,\left(24\,a\,c-5\,b^2\right)}{693\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2584\,a^2\,c^3-932\,a\,b^2\,c^2+79\,b^4\,c}{693\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2584\,a^2\,b\,c^2-1172\,a\,b^3\,c+133\,b^5}{693\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2352\,a^3\,c^2-1118\,a^2\,b^2\,c+133\,a\,b^4}{693\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(80\,a\,c^3-20\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^5}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{8\,c^3\,\left(7\,a\,c-b^2\right)}{693\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{2\,b^2\,c^3}{693\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{8\,b\,c^2\,\left(14\,a\,c-3\,b^2\right)}{693\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{3784\,a^2\,c^3-1472\,a\,b^2\,c^2+139\,b^4\,c}{3465\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{3784\,a^2\,b\,c^2-1752\,a\,b^3\,c+203\,b^5}{3465\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{3512\,a^3\,c^2-1688\,a^2\,b^2\,c+203\,a\,b^4}{3465\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{4\,b^2\,c^2}{495\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}-\frac{152\,a\,c^4-18\,b^2\,c^3}{990\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{b\,c\,\left(228\,a\,c-47\,b^2\right)}{990\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}+\frac{592\,a^2\,c^3-410\,a\,b^2\,c^2+63\,b^4\,c}{990\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)}{2\,c}-\frac{296\,a^2\,b\,c^2-167\,a\,b^3\,c+23\,b^5}{990\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(64\,a\,c^3-16\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^4}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b^2\,c^2}{495\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}-\frac{552\,a\,c^4-78\,b^2\,c^3}{11880\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{b\,c\,\left(276\,a\,c-59\,b^2\right)}{3960\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{4784\,a^2\,c^3-1978\,a\,b^2\,c^2+203\,b^4\,c}{11880\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{2392\,a^2\,b\,c^2-1127\,a\,b^3\,c+133\,b^5}{11880\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^4\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^2}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{c\,\left(14\,a\,c-b^2\right)}{3080\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}-\frac{b^2\,c}{3696\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}\right)}{2\,c}-\frac{b\,\left(21\,a\,c-4\,b^2\right)}{2310\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}\right)}{2\,c}+\frac{1144\,a^2\,c^4-320\,a\,b^2\,c^3+16\,b^4\,c^2}{36960\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}\right)}{2\,c}-\frac{b\,\left(286\,a^2\,c^2-122\,a\,b^2\,c+13\,b^4\right)}{9240\,c^2\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}\right)}{2\,c}-\frac{-1944\,a^3\,c^3+1172\,a^2\,b^2\,c^2-232\,a\,b^4\,c+15\,b^6}{36960\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{c\,\left(10\,a\,c-b^2\right)}{1848\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}-\frac{b^2\,c}{3696\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}\right)}{2\,c}-\frac{b\,\left(5\,a\,c-b^2\right)}{462\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}\right)}{2\,c}+\frac{3632\,a^2\,c^4-1216\,a\,b^2\,c^3+92\,b^4\,c^2}{73920\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}\right)}{2\,c}-\frac{b\,\left(908\,a^2\,c^2-404\,a\,b^2\,c+45\,b^4\right)}{18480\,c^2\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}\right)}{2\,c}+\frac{2672\,a^3\,c^3-1096\,a^2\,b^2\,c^2+72\,a\,b^4\,c+9\,b^6}{73920\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^6}\right)\,\sqrt{c\,x^2+b\,x+a}}{b+2\,c\,x}-\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{2\,c^4\,\left(25\,a\,c-b^2\right)}{1155\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}-\frac{b^2\,c^4}{385\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{b\,c^3\,\left(50\,a\,c-9\,b^2\right)}{462\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{7264\,a^2\,c^5-1632\,a\,b^2\,c^4+24\,b^4\,c^3}{18480\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{b\,c\,\left(2724\,a^2\,c^2-1112\,a\,b^2\,c+113\,b^4\right)}{4620\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}+\frac{5344\,a^3\,c^4+1440\,a^2\,b^2\,c^3-1472\,a\,b^4\,c^2+198\,b^6\,c}{18480\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2672\,a^3\,b\,c^3-1096\,a^2\,b^3\,c^2+72\,a\,b^5\,c+9\,b^7}{18480\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(32\,a\,c^3-8\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^2}+\frac{\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{b\,\left(\frac{c^5\,\left(3\,b^2+100\,a\,c\right)}{1155\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}-\frac{b^2\,c^5}{165\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{b\,c^4\,\left(300\,a\,c-47\,b^2\right)}{1155\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{-7264\,a^2\,c^6+632\,a\,b^2\,c^5+156\,b^4\,c^4}{9240\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}-\frac{2\,b\,c^2\,\left(908\,a^2\,c^2-329\,a\,b^2\,c+29\,b^4\right)}{1155\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{26080\,a^3\,c^5-8664\,a^2\,b^2\,c^4+192\,a\,b^4\,c^3+100\,b^6\,c^2}{9240\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{-26080\,a^3\,b\,c^4+15928\,a^2\,b^3\,c^3-3224\,a\,b^5\,c^2+216\,b^7\,c}{9240\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)}{2\,c}+\frac{31104\,a^4\,c^4-24584\,a^3\,b^2\,c^3+7228\,a^2\,b^4\,c^2-936\,a\,b^6\,c+45\,b^8}{9240\,c\,d^{12}\,{\left(4\,a\,c-b^2\right)}^5\,\left(48\,a\,c^3-12\,b^2\,c^2\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{{\left(b+2\,c\,x\right)}^3}+\frac{\sqrt{c\,x^2+b\,x+a}}{2464\,c^3\,d^{12}\,{\left(4\,a\,c-b^2\right)}^3\,\left(b+2\,c\,x\right)}","Not used",1,"(((b*((b*((b*((b*((b*((4*c^4*(40*a*c - 3*b^2))/(231*d^12*(4*a*c - b^2)^3*(96*a*c^3 - 24*b^2*c^2)) - (8*b^2*c^4)/(231*d^12*(4*a*c - b^2)^3*(96*a*c^3 - 24*b^2*c^2))))/(2*c) - (10*b*c^3*(120*a*c - 23*b^2))/(693*d^12*(4*a*c - b^2)^3*(96*a*c^3 - 24*b^2*c^2))))/(2*c) + (5168*a^2*c^4 + 58*b^4*c^2 - 1384*a*b^2*c^3)/(693*d^12*(4*a*c - b^2)^3*(96*a*c^3 - 24*b^2*c^2))))/(2*c) - (b*c*(115*b^4 + 2584*a^2*c^2 - 1092*a*b^2*c))/(231*d^12*(4*a*c - b^2)^3*(96*a*c^3 - 24*b^2*c^2))))/(2*c) + (133*b^6 + 4704*a^3*c^3 + 348*a^2*b^2*c^2 - 906*a*b^4*c)/(693*d^12*(4*a*c - b^2)^3*(96*a*c^3 - 24*b^2*c^2))))/(2*c) - (133*a*b^5 - 1118*a^2*b^3*c + 2352*a^3*b*c^2)/(693*d^12*(4*a*c - b^2)^3*(96*a*c^3 - 24*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^6 + (((b*((b*(b^2/(6160*c*d^12*(4*a*c - b^2)^5) - (32*a*c^3 - 5*b^2*c^2)/(9240*c^3*d^12*(4*a*c - b^2)^5)))/(2*c) - (7*b^3*c - 32*a*b*c^2)/(9240*c^3*d^12*(4*a*c - b^2)^5)))/(2*c) - (6*b^4 + 126*a^2*c^2 - 55*a*b^2*c)/(9240*c^3*d^12*(4*a*c - b^2)^5))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) + (((b*((b*(b^2/(5280*c*d^12*(4*a*c - b^2)^5) - (76*a*c^3 - 13*b^2*c^2)/(15840*c^3*d^12*(4*a*c - b^2)^5)))/(2*c) - (17*b^3*c - 76*a*b*c^2)/(15840*c^3*d^12*(4*a*c - b^2)^5)))/(2*c) + (23*b^4 + 296*a^2*c^2 - 167*a*b^2*c)/(15840*c^3*d^12*(4*a*c - b^2)^5))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) + (((b*((b*((5*a*c - b^2)/(1155*c*d^12*(4*a*c - b^2)^5) - b^2/(9240*c*d^12*(4*a*c - b^2)^5)))/(2*c) - (b*(30*a*c - 7*b^2))/(6930*c^2*d^12*(4*a*c - b^2)^5)))/(2*c) + (147*b^4 + 2584*a^2*c^2 - 1232*a*b^2*c)/(55440*c^3*d^12*(4*a*c - b^2)^5))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) - (((b*((b*((b*((b*((368*a*c^4 - 32*b^2*c^3)/(198*d^12*(4*a*c - b^2)^2*(112*a*c^3 - 28*b^2*c^2)) - (10*b^2*c^3)/(99*d^12*(4*a*c - b^2)^2*(112*a*c^3 - 28*b^2*c^2))))/(2*c) - (8*b*c^2*(46*a*c - 9*b^2))/(99*d^12*(4*a*c - b^2)^2*(112*a*c^3 - 28*b^2*c^2))))/(2*c) + (39*b^4*c + 2592*a^2*c^3 - 744*a*b^2*c^2)/(198*d^12*(4*a*c - b^2)^2*(112*a*c^3 - 28*b^2*c^2))))/(2*c) - (119*b^5 + 2592*a^2*b*c^2 - 1112*a*b^3*c)/(198*d^12*(4*a*c - b^2)^2*(112*a*c^3 - 28*b^2*c^2))))/(2*c) + (119*a*b^4 + 2240*a^3*c^2 - 1032*a^2*b^2*c)/(198*d^12*(4*a*c - b^2)^2*(112*a*c^3 - 28*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^7 + (((b*((b*((b*((b*((b^2*c)/(4158*d^12*(4*a*c - b^2)^6) - (608*a*c^4 - 92*b^2*c^3)/(83160*c^2*d^12*(4*a*c - b^2)^6)))/(2*c) + (b*(152*a*c - 33*b^2))/(10395*d^12*(4*a*c - b^2)^6)))/(2*c) - (365*b^4*c + 9248*a^2*c^3 - 3712*a*b^2*c^2)/(83160*c^2*d^12*(4*a*c - b^2)^6)))/(2*c) + (505*b^5 + 9248*a^2*b*c^2 - 4320*a*b^3*c)/(83160*c^2*d^12*(4*a*c - b^2)^6)))/(2*c) - (505*a*b^4 + 8656*a^3*c^2 - 4180*a^2*b^2*c)/(83160*c^2*d^12*(4*a*c - b^2)^6))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) + (((b*((b*((4*c*(7*a*c - b^2))/(99*d^12*(4*a*c - b^2)^2*(80*a*c^3 - 20*b^2*c^2)) - (b^2*c)/(66*d^12*(4*a*c - b^2)^2*(80*a*c^3 - 20*b^2*c^2))))/(2*c) - (2*b*(14*a*c - 3*b^2))/(99*d^12*(4*a*c - b^2)^2*(80*a*c^3 - 20*b^2*c^2))))/(2*c) + (23*b^4 + 576*a^2*c^2 - 232*a*b^2*c)/(792*c*d^12*(4*a*c - b^2)^2*(80*a*c^3 - 20*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^5 - (((b*((b*((c*(10*a*c - b^2))/(231*d^12*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2)) - (b^2*c)/(308*d^12*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (2*b*(5*a*c - b^2))/(231*d^12*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (24*a^2*c^2 - 3*b^4 + 8*a*b^2*c)/(1848*c*d^12*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 - (((32*a*c - 7*b^2)/(14784*c^3*d^12*(4*a*c - b^2)^4) - b^2/(14784*c^3*d^12*(4*a*c - b^2)^4))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) - (((56*a*c - 13*b^2)/(15840*c^3*d^12*(4*a*c - b^2)^4) - b^2/(15840*c^3*d^12*(4*a*c - b^2)^4))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) - (((170*a*c - 43*b^2)/(11088*c^3*d^12*(4*a*c - b^2)^4) + b^2/(22176*c^3*d^12*(4*a*c - b^2)^4))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) - (((b*((b*(b^2/(5280*c*d^12*(4*a*c - b^2)^5) - (276*a*c^3 - 51*b^2*c^2)/(47520*c^3*d^12*(4*a*c - b^2)^5)))/(2*c) + (b*(92*a*c - 21*b^2))/(15840*c^2*d^12*(4*a*c - b^2)^5)))/(2*c) - (133*b^4 + 2392*a^2*c^2 - 1127*a*b^2*c)/(47520*c^3*d^12*(4*a*c - b^2)^5))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) + (((b*((b*((b*((b*((b*((8*c^4*(46*a*c - b^2))/(99*d^12*(4*a*c - b^2)^2*(128*a*c^3 - 32*b^2*c^2)) - (8*b^2*c^4)/(33*d^12*(4*a*c - b^2)^2*(128*a*c^3 - 32*b^2*c^2))))/(2*c) - (40*b*c^3*(23*a*c - 4*b^2))/(99*d^12*(4*a*c - b^2)^2*(128*a*c^3 - 32*b^2*c^2))))/(2*c) - (66*b^4*c^2 - 5184*a^2*c^4 + 752*a*b^2*c^3)/(198*d^12*(4*a*c - b^2)^2*(128*a*c^3 - 32*b^2*c^2))))/(2*c) - (277*b^5*c - 2968*a*b^3*c^2 + 7776*a^2*b*c^3)/(198*d^12*(4*a*c - b^2)^2*(128*a*c^3 - 32*b^2*c^2))))/(2*c) + (119*b^6 + 4480*a^3*c^3 + 528*a^2*b^2*c^2 - 874*a*b^4*c)/(198*d^12*(4*a*c - b^2)^2*(128*a*c^3 - 32*b^2*c^2))))/(2*c) - (119*a*b^5 - 1032*a^2*b^3*c + 2240*a^3*b*c^2)/(198*d^12*(4*a*c - b^2)^2*(128*a*c^3 - 32*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^8 + (((b*((b*((b*((b*((b*((8*c^4*(10*a*c - b^2))/(495*d^12*(4*a*c - b^2)^4*(64*a*c^3 - 16*b^2*c^2)) - (8*b^2*c^4)/(1155*d^12*(4*a*c - b^2)^4*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (8*b*c^3*(5*a*c - b^2))/(99*d^12*(4*a*c - b^2)^4*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (7568*a^2*c^4 + 158*b^4*c^2 - 2384*a*b^2*c^3)/(3465*d^12*(4*a*c - b^2)^4*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (545*b^5*c - 4976*a*b^3*c^2 + 11352*a^2*b*c^3)/(3465*d^12*(4*a*c - b^2)^4*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (203*b^6 + 7024*a^3*c^3 + 408*a^2*b^2*c^2 - 1346*a*b^4*c)/(3465*d^12*(4*a*c - b^2)^4*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (203*a*b^5 - 1688*a^2*b^3*c + 3512*a^3*b*c^2)/(3465*d^12*(4*a*c - b^2)^4*(64*a*c^3 - 16*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^4 + (((b*((b*((b*((b*((b*((4*c^4*(152*a*c - 17*b^2))/(10395*d^12*(4*a*c - b^2)^5*(32*a*c^3 - 8*b^2*c^2)) - (8*b^2*c^4)/(3465*d^12*(4*a*c - b^2)^5*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (2*b*c^3*(152*a*c - 31*b^2))/(2079*d^12*(4*a*c - b^2)^5*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (18496*a^2*c^4 + 466*b^4*c^2 - 6208*a*b^2*c^3)/(20790*d^12*(4*a*c - b^2)^5*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (1375*b^5*c - 12352*a*b^3*c^2 + 27744*a^2*b*c^3)/(20790*d^12*(4*a*c - b^2)^5*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (505*b^6 + 17312*a^3*c^3 + 888*a^2*b^2*c^2 - 3310*a*b^4*c)/(20790*d^12*(4*a*c - b^2)^5*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (505*a*b^5 - 4180*a^2*b^3*c + 8656*a^3*b*c^2)/(20790*d^12*(4*a*c - b^2)^5*(32*a*c^3 - 8*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^2 - (((b*((b*((b*((b*((2*c^3*(56*a*c + b^2))/(11*d^12*(4*a*c - b^2)*(144*a*c^3 - 36*b^2*c^2)) - (10*b^2*c^3)/(11*d^12*(4*a*c - b^2)*(144*a*c^3 - 36*b^2*c^2))))/(2*c) - (4*b*c^2*(56*a*c - 9*b^2))/(11*d^12*(4*a*c - b^2)*(144*a*c^3 - 36*b^2*c^2))))/(2*c) + (576*a^2*c^3 - 33*b^4*c + 48*a*b^2*c^2)/(22*d^12*(4*a*c - b^2)*(144*a*c^3 - 36*b^2*c^2))))/(2*c) - (11*b^5 + 576*a^2*b*c^2 - 176*a*b^3*c)/(22*d^12*(4*a*c - b^2)*(144*a*c^3 - 36*b^2*c^2))))/(2*c) + (11*a*b^4 + 368*a^3*c^2 - 132*a^2*b^2*c)/(22*d^12*(4*a*c - b^2)*(144*a*c^3 - 36*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^9 - (((b*((b*((b*((b*((24*c^3*(a*c + b^2))/(d^12*(176*a*c^3 - 44*b^2*c^2)) - (10*b^2*c^3)/(d^12*(176*a*c^3 - 44*b^2*c^2))))/(2*c) - (4*c^2*(2*b^3 + 12*a*b*c))/(d^12*(176*a*c^3 - 44*b^2*c^2))))/(2*c) + (24*a*c^2*(a*c + b^2))/(d^12*(176*a*c^3 - 44*b^2*c^2))))/(2*c) - (24*a^2*b*c^2)/(d^12*(176*a*c^3 - 44*b^2*c^2))))/(2*c) + (8*a^3*c^2)/(d^12*(176*a*c^3 - 44*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^11 - (((b*((b*((b*((40*a*c^3)/(77*d^12*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2)) - (4*b^2*c^2)/(77*d^12*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2))))/(2*c) - (10*b*c*(6*a*c - b^2))/(77*d^12*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2))))/(2*c) + (48*a^2*c^3 - 22*b^4*c + 96*a*b^2*c^2)/(308*c*d^12*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2))))/(2*c) - (24*a^2*b*c^2 - 3*b^5 + 8*a*b^3*c)/(308*c*d^12*(4*a*c - b^2)^2*(96*a*c^3 - 24*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^6 - (((b*((b*((3*b^2*c)/(22*d^12*(4*a*c - b^2)*(112*a*c^3 - 28*b^2*c^2)) - (3*c*(4*a*c + b^2))/(22*d^12*(4*a*c - b^2)*(112*a*c^3 - 28*b^2*c^2))))/(2*c) + (b*(12*a*c - b^2))/(22*d^12*(4*a*c - b^2)*(112*a*c^3 - 28*b^2*c^2))))/(2*c) - (b^4 + 48*a^2*c^2 - 12*a*b^2*c)/(88*c*d^12*(4*a*c - b^2)*(112*a*c^3 - 28*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^7 + (((b*(b^2/(1386*d^12*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2)) + (340*a*c^2 - 88*b^2*c)/(2772*c*d^12*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (43*b^3 - 170*a*b*c)/(2772*c*d^12*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^2 - (((b*(b^2/(924*d^12*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2)) - (64*a*c^2 - 10*b^2*c)/(3696*c*d^12*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (7*b^3 - 32*a*b*c)/(3696*c*d^12*(4*a*c - b^2)^3*(32*a*c^3 - 8*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^2 - (((6*a*c - b^2)/(308*c*d^12*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2)) - b^2/(616*c*d^12*(4*a*c - b^2)^2*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 + (((b*((b*((b*((b*((c^3*(64*a*c - b^2))/(231*d^12*(4*a*c - b^2)^3*(80*a*c^3 - 20*b^2*c^2)) - (5*b^2*c^3)/(231*d^12*(4*a*c - b^2)^3*(80*a*c^3 - 20*b^2*c^2))))/(2*c) - (2*b*c^2*(64*a*c - 11*b^2))/(231*d^12*(4*a*c - b^2)^3*(80*a*c^3 - 20*b^2*c^2))))/(2*c) - (36*b^4*c^2 - 2016*a^2*c^4 + 240*a*b^2*c^3)/(1848*c*d^12*(4*a*c - b^2)^3*(80*a*c^3 - 20*b^2*c^2))))/(2*c) - (b*(17*b^4 + 504*a^2*c^2 - 188*a*b^2*c))/(462*d^12*(4*a*c - b^2)^3*(80*a*c^3 - 20*b^2*c^2))))/(2*c) + (15*b^6 + 576*a^3*c^3 + 72*a^2*b^2*c^2 - 112*a*b^4*c)/(1848*c*d^12*(4*a*c - b^2)^3*(80*a*c^3 - 20*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^5 + (((b*((b*((b*((b*((2*c^3*(23*a*c - 2*b^2))/(495*d^12*(4*a*c - b^2)^4*(48*a*c^3 - 12*b^2*c^2)) - (b^2*c^3)/(198*d^12*(4*a*c - b^2)^4*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (2*b*c^2*(46*a*c - 9*b^2))/(495*d^12*(4*a*c - b^2)^4*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (32*a^2*c^4 - 121*b^4*c^2 + 536*a*b^2*c^3)/(3960*c*d^12*(4*a*c - b^2)^4*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (b*(32*a^2*c^2 - 41*b^4 + 168*a*b^2*c))/(3960*d^12*(4*a*c - b^2)^4*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (69*b^6 - 4736*a^3*c^3 + 3560*a^2*b^2*c^2 - 869*a*b^4*c)/(3960*c*d^12*(4*a*c - b^2)^4*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 + (((b*((b*((b*((b*((b*((28*c^4*(8*a*c + b^2))/(11*d^12*(4*a*c - b^2)*(160*a*c^3 - 40*b^2*c^2)) - (24*b^2*c^4)/(11*d^12*(4*a*c - b^2)*(160*a*c^3 - 40*b^2*c^2))))/(2*c) - (70*b*c^3*(8*a*c - b^2))/(11*d^12*(4*a*c - b^2)*(160*a*c^3 - 40*b^2*c^2))))/(2*c) + (1152*a^2*c^4 - 138*b^4*c^2 + 544*a*b^2*c^3)/(22*d^12*(4*a*c - b^2)*(160*a*c^3 - 40*b^2*c^2))))/(2*c) + (b*c*(11*b^4 - 1728*a^2*c^2 + 304*a*b^2*c))/(22*d^12*(4*a*c - b^2)*(160*a*c^3 - 40*b^2*c^2))))/(2*c) + (11*b^6 + 736*a^3*c^3 + 312*a^2*b^2*c^2 - 154*a*b^4*c)/(22*d^12*(4*a*c - b^2)*(160*a*c^3 - 40*b^2*c^2))))/(2*c) - (11*a*b^5 - 132*a^2*b^3*c + 368*a^3*b*c^2)/(22*d^12*(4*a*c - b^2)*(160*a*c^3 - 40*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^10 - (((b*((b*((b*((b*((b*((8*a*c^5)/(55*d^12*(4*a*c - b^2)^4*(64*a*c^3 - 16*b^2*c^2)) - (4*b^2*c^4)/(385*d^12*(4*a*c - b^2)^4*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (2*b*c^3*(6*a*c - b^2))/(33*d^12*(4*a*c - b^2)^4*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (32*b^4*c^3 - 2288*a^2*c^5 + 304*a*b^2*c^4)/(2310*c*d^12*(4*a*c - b^2)^4*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (4*b*c*(5*b^4 + 143*a^2*c^2 - 54*a*b^2*c))/(385*d^12*(4*a*c - b^2)^4*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (22*b^6*c + 3888*a^3*c^4 - 24*a*b^4*c^2 - 1200*a^2*b^2*c^3)/(2310*c*d^12*(4*a*c - b^2)^4*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (15*b^7 - 1944*a^3*b*c^3 + 1172*a^2*b^3*c^2 - 232*a*b^5*c)/(2310*c*d^12*(4*a*c - b^2)^4*(64*a*c^3 - 16*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^4 - (((b*((b*((b^2*c)/(462*d^12*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2)) - (92*a*c^3 - 17*b^2*c^2)/(1386*c*d^12*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (b*(92*a*c - 21*b^2))/(1386*d^12*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (35*b^4 + 648*a^2*c^2 - 301*a*b^2*c)/(1386*c*d^12*(4*a*c - b^2)^3*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 - (((b*((b*((b*((b*((10*c^3*(8*a*c - b^2))/(231*d^12*(4*a*c - b^2)^3*(80*a*c^3 - 20*b^2*c^2)) - (10*b^2*c^3)/(693*d^12*(4*a*c - b^2)^3*(80*a*c^3 - 20*b^2*c^2))))/(2*c) - (20*b*c^2*(24*a*c - 5*b^2))/(693*d^12*(4*a*c - b^2)^3*(80*a*c^3 - 20*b^2*c^2))))/(2*c) + (79*b^4*c + 2584*a^2*c^3 - 932*a*b^2*c^2)/(693*d^12*(4*a*c - b^2)^3*(80*a*c^3 - 20*b^2*c^2))))/(2*c) - (133*b^5 + 2584*a^2*b*c^2 - 1172*a*b^3*c)/(693*d^12*(4*a*c - b^2)^3*(80*a*c^3 - 20*b^2*c^2))))/(2*c) + (133*a*b^4 + 2352*a^3*c^2 - 1118*a^2*b^2*c)/(693*d^12*(4*a*c - b^2)^3*(80*a*c^3 - 20*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^5 - (((b*((b*((b*((b*((8*c^3*(7*a*c - b^2))/(693*d^12*(4*a*c - b^2)^4*(48*a*c^3 - 12*b^2*c^2)) - (2*b^2*c^3)/(693*d^12*(4*a*c - b^2)^4*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (8*b*c^2*(14*a*c - 3*b^2))/(693*d^12*(4*a*c - b^2)^4*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (139*b^4*c + 3784*a^2*c^3 - 1472*a*b^2*c^2)/(3465*d^12*(4*a*c - b^2)^4*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (203*b^5 + 3784*a^2*b*c^2 - 1752*a*b^3*c)/(3465*d^12*(4*a*c - b^2)^4*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (203*a*b^4 + 3512*a^3*c^2 - 1688*a^2*b^2*c)/(3465*d^12*(4*a*c - b^2)^4*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 + (((b*((b*((b*((4*b^2*c^2)/(495*d^12*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2)) - (152*a*c^4 - 18*b^2*c^3)/(990*c*d^12*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (b*c*(228*a*c - 47*b^2))/(990*d^12*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2))))/(2*c) + (63*b^4*c + 592*a^2*c^3 - 410*a*b^2*c^2)/(990*c*d^12*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2))))/(2*c) - (23*b^5 + 296*a^2*b*c^2 - 167*a*b^3*c)/(990*c*d^12*(4*a*c - b^2)^3*(64*a*c^3 - 16*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^4 + (((b*((b*((b*((b^2*c^2)/(495*d^12*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2)) - (552*a*c^4 - 78*b^2*c^3)/(11880*c*d^12*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (b*c*(276*a*c - 59*b^2))/(3960*d^12*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (203*b^4*c + 4784*a^2*c^3 - 1978*a*b^2*c^2)/(11880*c*d^12*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (133*b^5 + 2392*a^2*b*c^2 - 1127*a*b^3*c)/(11880*c*d^12*(4*a*c - b^2)^4*(32*a*c^3 - 8*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^2 - (((b*((b*((b*((b*((c*(14*a*c - b^2))/(3080*d^12*(4*a*c - b^2)^6) - (b^2*c)/(3696*d^12*(4*a*c - b^2)^6)))/(2*c) - (b*(21*a*c - 4*b^2))/(2310*d^12*(4*a*c - b^2)^6)))/(2*c) + (1144*a^2*c^4 + 16*b^4*c^2 - 320*a*b^2*c^3)/(36960*c^3*d^12*(4*a*c - b^2)^6)))/(2*c) - (b*(13*b^4 + 286*a^2*c^2 - 122*a*b^2*c))/(9240*c^2*d^12*(4*a*c - b^2)^6)))/(2*c) - (15*b^6 - 1944*a^3*c^3 + 1172*a^2*b^2*c^2 - 232*a*b^4*c)/(36960*c^3*d^12*(4*a*c - b^2)^6))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) + (((b*((b*((b*((b*((c*(10*a*c - b^2))/(1848*d^12*(4*a*c - b^2)^6) - (b^2*c)/(3696*d^12*(4*a*c - b^2)^6)))/(2*c) - (b*(5*a*c - b^2))/(462*d^12*(4*a*c - b^2)^6)))/(2*c) + (3632*a^2*c^4 + 92*b^4*c^2 - 1216*a*b^2*c^3)/(73920*c^3*d^12*(4*a*c - b^2)^6)))/(2*c) - (b*(45*b^4 + 908*a^2*c^2 - 404*a*b^2*c))/(18480*c^2*d^12*(4*a*c - b^2)^6)))/(2*c) + (9*b^6 + 2672*a^3*c^3 - 1096*a^2*b^2*c^2 + 72*a*b^4*c)/(73920*c^3*d^12*(4*a*c - b^2)^6))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x) - (((b*((b*((b*((b*((b*((2*c^4*(25*a*c - b^2))/(1155*d^12*(4*a*c - b^2)^5*(32*a*c^3 - 8*b^2*c^2)) - (b^2*c^4)/(385*d^12*(4*a*c - b^2)^5*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (b*c^3*(50*a*c - 9*b^2))/(462*d^12*(4*a*c - b^2)^5*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (7264*a^2*c^5 + 24*b^4*c^3 - 1632*a*b^2*c^4)/(18480*c*d^12*(4*a*c - b^2)^5*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (b*c*(113*b^4 + 2724*a^2*c^2 - 1112*a*b^2*c))/(4620*d^12*(4*a*c - b^2)^5*(32*a*c^3 - 8*b^2*c^2))))/(2*c) + (198*b^6*c + 5344*a^3*c^4 - 1472*a*b^4*c^2 + 1440*a^2*b^2*c^3)/(18480*c*d^12*(4*a*c - b^2)^5*(32*a*c^3 - 8*b^2*c^2))))/(2*c) - (9*b^7 + 2672*a^3*b*c^3 - 1096*a^2*b^3*c^2 + 72*a*b^5*c)/(18480*c*d^12*(4*a*c - b^2)^5*(32*a*c^3 - 8*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^2 + (((b*((b*((b*((b*((b*((b*((c^5*(100*a*c + 3*b^2))/(1155*d^12*(4*a*c - b^2)^5*(48*a*c^3 - 12*b^2*c^2)) - (b^2*c^5)/(165*d^12*(4*a*c - b^2)^5*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (b*c^4*(300*a*c - 47*b^2))/(1155*d^12*(4*a*c - b^2)^5*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (156*b^4*c^4 - 7264*a^2*c^6 + 632*a*b^2*c^5)/(9240*c*d^12*(4*a*c - b^2)^5*(48*a*c^3 - 12*b^2*c^2))))/(2*c) - (2*b*c^2*(29*b^4 + 908*a^2*c^2 - 329*a*b^2*c))/(1155*d^12*(4*a*c - b^2)^5*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (26080*a^3*c^5 + 100*b^6*c^2 + 192*a*b^4*c^3 - 8664*a^2*b^2*c^4)/(9240*c*d^12*(4*a*c - b^2)^5*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (216*b^7*c - 3224*a*b^5*c^2 - 26080*a^3*b*c^4 + 15928*a^2*b^3*c^3)/(9240*c*d^12*(4*a*c - b^2)^5*(48*a*c^3 - 12*b^2*c^2))))/(2*c) + (45*b^8 + 31104*a^4*c^4 + 7228*a^2*b^4*c^2 - 24584*a^3*b^2*c^3 - 936*a*b^6*c)/(9240*c*d^12*(4*a*c - b^2)^5*(48*a*c^3 - 12*b^2*c^2)))*(a + b*x + c*x^2)^(1/2))/(b + 2*c*x)^3 + (a + b*x + c*x^2)^(1/2)/(2464*c^3*d^12*(4*a*c - b^2)^3*(b + 2*c*x))","B"
1234,0,-1,117,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^4/(a + b*x + c*x^2)^(1/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^4}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^4/(a + b*x + c*x^2)^(1/2), x)","F"
1235,1,48,59,0.584285,"\text{Not used}","int((b*d + 2*c*d*x)^3/(a + b*x + c*x^2)^(1/2),x)","\left(\frac{8\,c^2\,d^3\,x^2}{3}-\frac{2\,d^3\,\left(8\,a\,c-3\,b^2\right)}{3}+\frac{8\,b\,c\,d^3\,x}{3}\right)\,\sqrt{c\,x^2+b\,x+a}","Not used",1,"((8*c^2*d^3*x^2)/3 - (2*d^3*(8*a*c - 3*b^2))/3 + (8*b*c*d^3*x)/3)*(a + b*x + c*x^2)^(1/2)","B"
1236,0,-1,75,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^2/(a + b*x + c*x^2)^(1/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^2}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^2/(a + b*x + c*x^2)^(1/2), x)","F"
1237,1,15,17,0.527820,"\text{Not used}","int((b*d + 2*c*d*x)/(a + b*x + c*x^2)^(1/2),x)","2\,d\,\sqrt{c\,x^2+b\,x+a}","Not used",1,"2*d*(a + b*x + c*x^2)^(1/2)","B"
1238,0,-1,55,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)*(a + b*x + c*x^2)^(1/2)),x)","\int \frac{1}{\left(b\,d+2\,c\,d\,x\right)\,\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)*(a + b*x + c*x^2)^(1/2)), x)","F"
1239,1,37,37,0.520072,"\text{Not used}","int(1/((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(1/2)),x)","-\frac{2\,\sqrt{c\,x^2+b\,x+a}}{d^2\,\left(4\,a\,c-b^2\right)\,\left(b+2\,c\,x\right)}","Not used",1,"-(2*(a + b*x + c*x^2)^(1/2))/(d^2*(4*a*c - b^2)*(b + 2*c*x))","B"
1240,0,-1,95,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(1/2)),x)","\int \frac{1}{{\left(b\,d+2\,c\,d\,x\right)}^3\,\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(1/2)), x)","F"
1241,1,60,79,0.653366,"\text{Not used}","int(1/((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(1/2)),x)","\frac{2\,\sqrt{c\,x^2+b\,x+a}\,\left(3\,b^2+8\,b\,c\,x+8\,c^2\,x^2-4\,a\,c\right)}{3\,d^4\,{\left(4\,a\,c-b^2\right)}^2\,{\left(b+2\,c\,x\right)}^3}","Not used",1,"(2*(a + b*x + c*x^2)^(1/2)*(3*b^2 - 4*a*c + 8*c^2*x^2 + 8*b*c*x))/(3*d^4*(4*a*c - b^2)^2*(b + 2*c*x)^3)","B"
1242,0,-1,102,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^4/(a + b*x + c*x^2)^(3/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^4}{{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^4/(a + b*x + c*x^2)^(3/2), x)","F"
1243,1,40,48,0.665069,"\text{Not used}","int((b*d + 2*c*d*x)^3/(a + b*x + c*x^2)^(3/2),x)","\frac{2\,d^3\,\left(-b^2+4\,b\,c\,x+4\,c^2\,x^2+8\,a\,c\right)}{\sqrt{c\,x^2+b\,x+a}}","Not used",1,"(2*d^3*(8*a*c - b^2 + 4*c^2*x^2 + 4*b*c*x))/(a + b*x + c*x^2)^(1/2)","B"
1244,1,156,66,0.789714,"\text{Not used}","int((b*d + 2*c*d*x)^2/(a + b*x + c*x^2)^(3/2),x)","4\,\sqrt{c}\,d^2\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)+\frac{b^2\,d^2\,\left(\frac{b}{2}+c\,x\right)}{\left(a\,c-\frac{b^2}{4}\right)\,\sqrt{c\,x^2+b\,x+a}}+\frac{4\,c\,d^2\,\left(\frac{a\,b}{2}-x\,\left(a\,c-\frac{b^2}{2}\right)\right)}{\left(a\,c-\frac{b^2}{4}\right)\,\sqrt{c\,x^2+b\,x+a}}-\frac{4\,b\,c\,d^2\,\left(4\,a+2\,b\,x\right)}{\left(4\,a\,c-b^2\right)\,\sqrt{c\,x^2+b\,x+a}}","Not used",1,"4*c^(1/2)*d^2*log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2)) + (b^2*d^2*(b/2 + c*x))/((a*c - b^2/4)*(a + b*x + c*x^2)^(1/2)) + (4*c*d^2*((a*b)/2 - x*(a*c - b^2/2)))/((a*c - b^2/4)*(a + b*x + c*x^2)^(1/2)) - (4*b*c*d^2*(4*a + 2*b*x))/((4*a*c - b^2)*(a + b*x + c*x^2)^(1/2))","B"
1245,1,15,17,0.527133,"\text{Not used}","int((b*d + 2*c*d*x)/(a + b*x + c*x^2)^(3/2),x)","-\frac{2\,d}{\sqrt{c\,x^2+b\,x+a}}","Not used",1,"-(2*d)/(a + b*x + c*x^2)^(1/2)","B"
1246,0,-1,86,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)*(a + b*x + c*x^2)^(3/2)),x)","\int \frac{1}{\left(b\,d+2\,c\,d\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)*(a + b*x + c*x^2)^(3/2)), x)","F"
1247,1,188,76,0.718887,"\text{Not used}","int(1/((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(3/2)),x)","-\frac{\left(\frac{2\,\left(4\,c^2+\frac{64\,b^2\,c^5}{32\,a\,c^4-8\,b^2\,c^3}\right)}{d^2\,\left(16\,a\,c^3-4\,b^2\,c^2\right)}+\frac{512\,c^7\,x^2}{d^2\,\left(16\,a\,c^3-4\,b^2\,c^2\right)\,\left(32\,a\,c^4-8\,b^2\,c^3\right)}+\frac{512\,b\,c^6\,x}{d^2\,\left(16\,a\,c^3-4\,b^2\,c^2\right)\,\left(32\,a\,c^4-8\,b^2\,c^3\right)}\right)\,\sqrt{c\,x^2+b\,x+a}}{x\,\left(b^2+2\,a\,c\right)+a\,b+2\,c^2\,x^3+3\,b\,c\,x^2}","Not used",1,"-(((2*(4*c^2 + (64*b^2*c^5)/(32*a*c^4 - 8*b^2*c^3)))/(d^2*(16*a*c^3 - 4*b^2*c^2)) + (512*c^7*x^2)/(d^2*(16*a*c^3 - 4*b^2*c^2)*(32*a*c^4 - 8*b^2*c^3)) + (512*b*c^6*x)/(d^2*(16*a*c^3 - 4*b^2*c^2)*(32*a*c^4 - 8*b^2*c^3)))*(a + b*x + c*x^2)^(1/2))/(x*(2*a*c + b^2) + a*b + 2*c^2*x^3 + 3*b*c*x^2)","B"
1248,0,-1,132,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(3/2)),x)","\int \frac{1}{{\left(b\,d+2\,c\,d\,x\right)}^3\,{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(3/2)), x)","F"
1249,1,4588,118,2.232891,"\text{Not used}","int(1/((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(3/2)),x)","\frac{8\,b^6\,c^2}{\sqrt{c\,x^2+b\,x+a}\,\left(-4096\,a^5\,b\,c^7\,d^4-8192\,x\,a^5\,c^8\,d^4+5120\,a^4\,b^3\,c^6\,d^4+10240\,x\,a^4\,b^2\,c^7\,d^4-2560\,a^3\,b^5\,c^5\,d^4-5120\,x\,a^3\,b^4\,c^6\,d^4+640\,a^2\,b^7\,c^4\,d^4+1280\,x\,a^2\,b^6\,c^5\,d^4-80\,a\,b^9\,c^3\,d^4-160\,x\,a\,b^8\,c^4\,d^4+4\,b^{11}\,c^2\,d^4+8\,x\,b^{10}\,c^3\,d^4\right)}-\frac{128\,b^8\,c^5}{\sqrt{c\,x^2+b\,x+a}\,\left(131072\,a^6\,b\,c^{11}\,d^4+262144\,x\,a^6\,c^{12}\,d^4-196608\,a^5\,b^3\,c^{10}\,d^4-393216\,x\,a^5\,b^2\,c^{11}\,d^4+122880\,a^4\,b^5\,c^9\,d^4+245760\,x\,a^4\,b^4\,c^{10}\,d^4-40960\,a^3\,b^7\,c^8\,d^4-81920\,x\,a^3\,b^6\,c^9\,d^4+7680\,a^2\,b^9\,c^7\,d^4+15360\,x\,a^2\,b^8\,c^8\,d^4-768\,a\,b^{11}\,c^6\,d^4-1536\,x\,a\,b^{10}\,c^7\,d^4+32\,b^{13}\,c^5\,d^4+64\,x\,b^{12}\,c^6\,d^4\right)}-\frac{2560\,a^3\,c^5}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(-4096\,a^5\,b\,c^7\,d^4-8192\,x\,a^5\,c^8\,d^4+5120\,a^4\,b^3\,c^6\,d^4+10240\,x\,a^4\,b^2\,c^7\,d^4-2560\,a^3\,b^5\,c^5\,d^4-5120\,x\,a^3\,b^4\,c^6\,d^4+640\,a^2\,b^7\,c^4\,d^4+1280\,x\,a^2\,b^6\,c^5\,d^4-80\,a\,b^9\,c^3\,d^4-160\,x\,a\,b^8\,c^4\,d^4+4\,b^{11}\,c^2\,d^4+8\,x\,b^{10}\,c^3\,d^4\right)}-\frac{32\,c^4\,\sqrt{c\,x^2+b\,x+a}}{192\,a^2\,b^3\,c^5\,d^4+1152\,a^2\,b^2\,c^6\,d^4\,x+2304\,a^2\,b\,c^7\,d^4\,x^2+1536\,a^2\,c^8\,d^4\,x^3-96\,a\,b^5\,c^4\,d^4-576\,a\,b^4\,c^5\,d^4\,x-1152\,a\,b^3\,c^6\,d^4\,x^2-768\,a\,b^2\,c^7\,d^4\,x^3+12\,b^7\,c^3\,d^4+72\,b^6\,c^4\,d^4\,x+144\,b^5\,c^5\,d^4\,x^2+96\,b^4\,c^6\,d^4\,x^3}-\frac{352\,a\,b^4\,c^3}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(-4096\,a^5\,b\,c^7\,d^4-8192\,x\,a^5\,c^8\,d^4+5120\,a^4\,b^3\,c^6\,d^4+10240\,x\,a^4\,b^2\,c^7\,d^4-2560\,a^3\,b^5\,c^5\,d^4-5120\,x\,a^3\,b^4\,c^6\,d^4+640\,a^2\,b^7\,c^4\,d^4+1280\,x\,a^2\,b^6\,c^5\,d^4-80\,a\,b^9\,c^3\,d^4-160\,x\,a\,b^8\,c^4\,d^4+4\,b^{11}\,c^2\,d^4+8\,x\,b^{10}\,c^3\,d^4\right)}-\frac{64\,b^5\,c^3\,x}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(-4096\,a^5\,b\,c^7\,d^4-8192\,x\,a^5\,c^8\,d^4+5120\,a^4\,b^3\,c^6\,d^4+10240\,x\,a^4\,b^2\,c^7\,d^4-2560\,a^3\,b^5\,c^5\,d^4-5120\,x\,a^3\,b^4\,c^6\,d^4+640\,a^2\,b^7\,c^4\,d^4+1280\,x\,a^2\,b^6\,c^5\,d^4-80\,a\,b^9\,c^3\,d^4-160\,x\,a\,b^8\,c^4\,d^4+4\,b^{11}\,c^2\,d^4+8\,x\,b^{10}\,c^3\,d^4\right)}+\frac{1536\,a\,b^6\,c^6}{\sqrt{c\,x^2+b\,x+a}\,\left(131072\,a^6\,b\,c^{11}\,d^4+262144\,x\,a^6\,c^{12}\,d^4-196608\,a^5\,b^3\,c^{10}\,d^4-393216\,x\,a^5\,b^2\,c^{11}\,d^4+122880\,a^4\,b^5\,c^9\,d^4+245760\,x\,a^4\,b^4\,c^{10}\,d^4-40960\,a^3\,b^7\,c^8\,d^4-81920\,x\,a^3\,b^6\,c^9\,d^4+7680\,a^2\,b^9\,c^7\,d^4+15360\,x\,a^2\,b^8\,c^8\,d^4-768\,a\,b^{11}\,c^6\,d^4-1536\,x\,a\,b^{10}\,c^7\,d^4+32\,b^{13}\,c^5\,d^4+64\,x\,b^{12}\,c^6\,d^4\right)}-\frac{512\,b^7\,c^6\,x}{\sqrt{c\,x^2+b\,x+a}\,\left(131072\,a^6\,b\,c^{11}\,d^4+262144\,x\,a^6\,c^{12}\,d^4-196608\,a^5\,b^3\,c^{10}\,d^4-393216\,x\,a^5\,b^2\,c^{11}\,d^4+122880\,a^4\,b^5\,c^9\,d^4+245760\,x\,a^4\,b^4\,c^{10}\,d^4-40960\,a^3\,b^7\,c^8\,d^4-81920\,x\,a^3\,b^6\,c^9\,d^4+7680\,a^2\,b^9\,c^7\,d^4+15360\,x\,a^2\,b^8\,c^8\,d^4-768\,a\,b^{11}\,c^6\,d^4-1536\,x\,a\,b^{10}\,c^7\,d^4+32\,b^{13}\,c^5\,d^4+64\,x\,b^{12}\,c^6\,d^4\right)}+\frac{1664\,a^2\,b^2\,c^4}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(-4096\,a^5\,b\,c^7\,d^4-8192\,x\,a^5\,c^8\,d^4+5120\,a^4\,b^3\,c^6\,d^4+10240\,x\,a^4\,b^2\,c^7\,d^4-2560\,a^3\,b^5\,c^5\,d^4-5120\,x\,a^3\,b^4\,c^6\,d^4+640\,a^2\,b^7\,c^4\,d^4+1280\,x\,a^2\,b^6\,c^5\,d^4-80\,a\,b^9\,c^3\,d^4-160\,x\,a\,b^8\,c^4\,d^4+4\,b^{11}\,c^2\,d^4+8\,x\,b^{10}\,c^3\,d^4\right)}-\frac{1024\,a^2\,c^6\,x^2}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(-4096\,a^5\,b\,c^7\,d^4-8192\,x\,a^5\,c^8\,d^4+5120\,a^4\,b^3\,c^6\,d^4+10240\,x\,a^4\,b^2\,c^7\,d^4-2560\,a^3\,b^5\,c^5\,d^4-5120\,x\,a^3\,b^4\,c^6\,d^4+640\,a^2\,b^7\,c^4\,d^4+1280\,x\,a^2\,b^6\,c^5\,d^4-80\,a\,b^9\,c^3\,d^4-160\,x\,a\,b^8\,c^4\,d^4+4\,b^{11}\,c^2\,d^4+8\,x\,b^{10}\,c^3\,d^4\right)}-\frac{64\,b^4\,c^4\,x^2}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(-4096\,a^5\,b\,c^7\,d^4-8192\,x\,a^5\,c^8\,d^4+5120\,a^4\,b^3\,c^6\,d^4+10240\,x\,a^4\,b^2\,c^7\,d^4-2560\,a^3\,b^5\,c^5\,d^4-5120\,x\,a^3\,b^4\,c^6\,d^4+640\,a^2\,b^7\,c^4\,d^4+1280\,x\,a^2\,b^6\,c^5\,d^4-80\,a\,b^9\,c^3\,d^4-160\,x\,a\,b^8\,c^4\,d^4+4\,b^{11}\,c^2\,d^4+8\,x\,b^{10}\,c^3\,d^4\right)}-\frac{6144\,a^2\,b^4\,c^7}{\sqrt{c\,x^2+b\,x+a}\,\left(131072\,a^6\,b\,c^{11}\,d^4+262144\,x\,a^6\,c^{12}\,d^4-196608\,a^5\,b^3\,c^{10}\,d^4-393216\,x\,a^5\,b^2\,c^{11}\,d^4+122880\,a^4\,b^5\,c^9\,d^4+245760\,x\,a^4\,b^4\,c^{10}\,d^4-40960\,a^3\,b^7\,c^8\,d^4-81920\,x\,a^3\,b^6\,c^9\,d^4+7680\,a^2\,b^9\,c^7\,d^4+15360\,x\,a^2\,b^8\,c^8\,d^4-768\,a\,b^{11}\,c^6\,d^4-1536\,x\,a\,b^{10}\,c^7\,d^4+32\,b^{13}\,c^5\,d^4+64\,x\,b^{12}\,c^6\,d^4\right)}+\frac{8192\,a^3\,b^2\,c^8}{\sqrt{c\,x^2+b\,x+a}\,\left(131072\,a^6\,b\,c^{11}\,d^4+262144\,x\,a^6\,c^{12}\,d^4-196608\,a^5\,b^3\,c^{10}\,d^4-393216\,x\,a^5\,b^2\,c^{11}\,d^4+122880\,a^4\,b^5\,c^9\,d^4+245760\,x\,a^4\,b^4\,c^{10}\,d^4-40960\,a^3\,b^7\,c^8\,d^4-81920\,x\,a^3\,b^6\,c^9\,d^4+7680\,a^2\,b^9\,c^7\,d^4+15360\,x\,a^2\,b^8\,c^8\,d^4-768\,a\,b^{11}\,c^6\,d^4-1536\,x\,a\,b^{10}\,c^7\,d^4+32\,b^{13}\,c^5\,d^4+64\,x\,b^{12}\,c^6\,d^4\right)}+\frac{32768\,a^3\,c^{10}\,x^2}{\sqrt{c\,x^2+b\,x+a}\,\left(131072\,a^6\,b\,c^{11}\,d^4+262144\,x\,a^6\,c^{12}\,d^4-196608\,a^5\,b^3\,c^{10}\,d^4-393216\,x\,a^5\,b^2\,c^{11}\,d^4+122880\,a^4\,b^5\,c^9\,d^4+245760\,x\,a^4\,b^4\,c^{10}\,d^4-40960\,a^3\,b^7\,c^8\,d^4-81920\,x\,a^3\,b^6\,c^9\,d^4+7680\,a^2\,b^9\,c^7\,d^4+15360\,x\,a^2\,b^8\,c^8\,d^4-768\,a\,b^{11}\,c^6\,d^4-1536\,x\,a\,b^{10}\,c^7\,d^4+32\,b^{13}\,c^5\,d^4+64\,x\,b^{12}\,c^6\,d^4\right)}-\frac{512\,b^6\,c^7\,x^2}{\sqrt{c\,x^2+b\,x+a}\,\left(131072\,a^6\,b\,c^{11}\,d^4+262144\,x\,a^6\,c^{12}\,d^4-196608\,a^5\,b^3\,c^{10}\,d^4-393216\,x\,a^5\,b^2\,c^{11}\,d^4+122880\,a^4\,b^5\,c^9\,d^4+245760\,x\,a^4\,b^4\,c^{10}\,d^4-40960\,a^3\,b^7\,c^8\,d^4-81920\,x\,a^3\,b^6\,c^9\,d^4+7680\,a^2\,b^9\,c^7\,d^4+15360\,x\,a^2\,b^8\,c^8\,d^4-768\,a\,b^{11}\,c^6\,d^4-1536\,x\,a\,b^{10}\,c^7\,d^4+32\,b^{13}\,c^5\,d^4+64\,x\,b^{12}\,c^6\,d^4\right)}+\frac{512\,a\,b^2\,c^5\,x^2}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(-4096\,a^5\,b\,c^7\,d^4-8192\,x\,a^5\,c^8\,d^4+5120\,a^4\,b^3\,c^6\,d^4+10240\,x\,a^4\,b^2\,c^7\,d^4-2560\,a^3\,b^5\,c^5\,d^4-5120\,x\,a^3\,b^4\,c^6\,d^4+640\,a^2\,b^7\,c^4\,d^4+1280\,x\,a^2\,b^6\,c^5\,d^4-80\,a\,b^9\,c^3\,d^4-160\,x\,a\,b^8\,c^4\,d^4+4\,b^{11}\,c^2\,d^4+8\,x\,b^{10}\,c^3\,d^4\right)}-\frac{24576\,a^2\,b^3\,c^8\,x}{\sqrt{c\,x^2+b\,x+a}\,\left(131072\,a^6\,b\,c^{11}\,d^4+262144\,x\,a^6\,c^{12}\,d^4-196608\,a^5\,b^3\,c^{10}\,d^4-393216\,x\,a^5\,b^2\,c^{11}\,d^4+122880\,a^4\,b^5\,c^9\,d^4+245760\,x\,a^4\,b^4\,c^{10}\,d^4-40960\,a^3\,b^7\,c^8\,d^4-81920\,x\,a^3\,b^6\,c^9\,d^4+7680\,a^2\,b^9\,c^7\,d^4+15360\,x\,a^2\,b^8\,c^8\,d^4-768\,a\,b^{11}\,c^6\,d^4-1536\,x\,a\,b^{10}\,c^7\,d^4+32\,b^{13}\,c^5\,d^4+64\,x\,b^{12}\,c^6\,d^4\right)}+\frac{6144\,a\,b^4\,c^8\,x^2}{\sqrt{c\,x^2+b\,x+a}\,\left(131072\,a^6\,b\,c^{11}\,d^4+262144\,x\,a^6\,c^{12}\,d^4-196608\,a^5\,b^3\,c^{10}\,d^4-393216\,x\,a^5\,b^2\,c^{11}\,d^4+122880\,a^4\,b^5\,c^9\,d^4+245760\,x\,a^4\,b^4\,c^{10}\,d^4-40960\,a^3\,b^7\,c^8\,d^4-81920\,x\,a^3\,b^6\,c^9\,d^4+7680\,a^2\,b^9\,c^7\,d^4+15360\,x\,a^2\,b^8\,c^8\,d^4-768\,a\,b^{11}\,c^6\,d^4-1536\,x\,a\,b^{10}\,c^7\,d^4+32\,b^{13}\,c^5\,d^4+64\,x\,b^{12}\,c^6\,d^4\right)}+\frac{512\,a\,b^3\,c^4\,x}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(-4096\,a^5\,b\,c^7\,d^4-8192\,x\,a^5\,c^8\,d^4+5120\,a^4\,b^3\,c^6\,d^4+10240\,x\,a^4\,b^2\,c^7\,d^4-2560\,a^3\,b^5\,c^5\,d^4-5120\,x\,a^3\,b^4\,c^6\,d^4+640\,a^2\,b^7\,c^4\,d^4+1280\,x\,a^2\,b^6\,c^5\,d^4-80\,a\,b^9\,c^3\,d^4-160\,x\,a\,b^8\,c^4\,d^4+4\,b^{11}\,c^2\,d^4+8\,x\,b^{10}\,c^3\,d^4\right)}-\frac{1024\,a^2\,b\,c^5\,x}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(-4096\,a^5\,b\,c^7\,d^4-8192\,x\,a^5\,c^8\,d^4+5120\,a^4\,b^3\,c^6\,d^4+10240\,x\,a^4\,b^2\,c^7\,d^4-2560\,a^3\,b^5\,c^5\,d^4-5120\,x\,a^3\,b^4\,c^6\,d^4+640\,a^2\,b^7\,c^4\,d^4+1280\,x\,a^2\,b^6\,c^5\,d^4-80\,a\,b^9\,c^3\,d^4-160\,x\,a\,b^8\,c^4\,d^4+4\,b^{11}\,c^2\,d^4+8\,x\,b^{10}\,c^3\,d^4\right)}-\frac{24576\,a^2\,b^2\,c^9\,x^2}{\sqrt{c\,x^2+b\,x+a}\,\left(131072\,a^6\,b\,c^{11}\,d^4+262144\,x\,a^6\,c^{12}\,d^4-196608\,a^5\,b^3\,c^{10}\,d^4-393216\,x\,a^5\,b^2\,c^{11}\,d^4+122880\,a^4\,b^5\,c^9\,d^4+245760\,x\,a^4\,b^4\,c^{10}\,d^4-40960\,a^3\,b^7\,c^8\,d^4-81920\,x\,a^3\,b^6\,c^9\,d^4+7680\,a^2\,b^9\,c^7\,d^4+15360\,x\,a^2\,b^8\,c^8\,d^4-768\,a\,b^{11}\,c^6\,d^4-1536\,x\,a\,b^{10}\,c^7\,d^4+32\,b^{13}\,c^5\,d^4+64\,x\,b^{12}\,c^6\,d^4\right)}+\frac{6144\,a\,b^5\,c^7\,x}{\sqrt{c\,x^2+b\,x+a}\,\left(131072\,a^6\,b\,c^{11}\,d^4+262144\,x\,a^6\,c^{12}\,d^4-196608\,a^5\,b^3\,c^{10}\,d^4-393216\,x\,a^5\,b^2\,c^{11}\,d^4+122880\,a^4\,b^5\,c^9\,d^4+245760\,x\,a^4\,b^4\,c^{10}\,d^4-40960\,a^3\,b^7\,c^8\,d^4-81920\,x\,a^3\,b^6\,c^9\,d^4+7680\,a^2\,b^9\,c^7\,d^4+15360\,x\,a^2\,b^8\,c^8\,d^4-768\,a\,b^{11}\,c^6\,d^4-1536\,x\,a\,b^{10}\,c^7\,d^4+32\,b^{13}\,c^5\,d^4+64\,x\,b^{12}\,c^6\,d^4\right)}+\frac{32768\,a^3\,b\,c^9\,x}{\sqrt{c\,x^2+b\,x+a}\,\left(131072\,a^6\,b\,c^{11}\,d^4+262144\,x\,a^6\,c^{12}\,d^4-196608\,a^5\,b^3\,c^{10}\,d^4-393216\,x\,a^5\,b^2\,c^{11}\,d^4+122880\,a^4\,b^5\,c^9\,d^4+245760\,x\,a^4\,b^4\,c^{10}\,d^4-40960\,a^3\,b^7\,c^8\,d^4-81920\,x\,a^3\,b^6\,c^9\,d^4+7680\,a^2\,b^9\,c^7\,d^4+15360\,x\,a^2\,b^8\,c^8\,d^4-768\,a\,b^{11}\,c^6\,d^4-1536\,x\,a\,b^{10}\,c^7\,d^4+32\,b^{13}\,c^5\,d^4+64\,x\,b^{12}\,c^6\,d^4\right)}","Not used",1,"(8*b^6*c^2)/((a + b*x + c*x^2)^(1/2)*(4*b^11*c^2*d^4 - 80*a*b^9*c^3*d^4 - 4096*a^5*b*c^7*d^4 - 8192*a^5*c^8*d^4*x + 8*b^10*c^3*d^4*x + 640*a^2*b^7*c^4*d^4 - 2560*a^3*b^5*c^5*d^4 + 5120*a^4*b^3*c^6*d^4 - 160*a*b^8*c^4*d^4*x + 1280*a^2*b^6*c^5*d^4*x - 5120*a^3*b^4*c^6*d^4*x + 10240*a^4*b^2*c^7*d^4*x)) - (128*b^8*c^5)/((a + b*x + c*x^2)^(1/2)*(32*b^13*c^5*d^4 - 768*a*b^11*c^6*d^4 + 131072*a^6*b*c^11*d^4 + 262144*a^6*c^12*d^4*x + 64*b^12*c^6*d^4*x + 7680*a^2*b^9*c^7*d^4 - 40960*a^3*b^7*c^8*d^4 + 122880*a^4*b^5*c^9*d^4 - 196608*a^5*b^3*c^10*d^4 - 1536*a*b^10*c^7*d^4*x + 15360*a^2*b^8*c^8*d^4*x - 81920*a^3*b^6*c^9*d^4*x + 245760*a^4*b^4*c^10*d^4*x - 393216*a^5*b^2*c^11*d^4*x)) - (2560*a^3*c^5)/(3*(a + b*x + c*x^2)^(1/2)*(4*b^11*c^2*d^4 - 80*a*b^9*c^3*d^4 - 4096*a^5*b*c^7*d^4 - 8192*a^5*c^8*d^4*x + 8*b^10*c^3*d^4*x + 640*a^2*b^7*c^4*d^4 - 2560*a^3*b^5*c^5*d^4 + 5120*a^4*b^3*c^6*d^4 - 160*a*b^8*c^4*d^4*x + 1280*a^2*b^6*c^5*d^4*x - 5120*a^3*b^4*c^6*d^4*x + 10240*a^4*b^2*c^7*d^4*x)) - (32*c^4*(a + b*x + c*x^2)^(1/2))/(12*b^7*c^3*d^4 - 96*a*b^5*c^4*d^4 + 72*b^6*c^4*d^4*x + 192*a^2*b^3*c^5*d^4 + 1536*a^2*c^8*d^4*x^3 + 144*b^5*c^5*d^4*x^2 + 96*b^4*c^6*d^4*x^3 - 576*a*b^4*c^5*d^4*x + 1152*a^2*b^2*c^6*d^4*x - 1152*a*b^3*c^6*d^4*x^2 + 2304*a^2*b*c^7*d^4*x^2 - 768*a*b^2*c^7*d^4*x^3) - (352*a*b^4*c^3)/(3*(a + b*x + c*x^2)^(1/2)*(4*b^11*c^2*d^4 - 80*a*b^9*c^3*d^4 - 4096*a^5*b*c^7*d^4 - 8192*a^5*c^8*d^4*x + 8*b^10*c^3*d^4*x + 640*a^2*b^7*c^4*d^4 - 2560*a^3*b^5*c^5*d^4 + 5120*a^4*b^3*c^6*d^4 - 160*a*b^8*c^4*d^4*x + 1280*a^2*b^6*c^5*d^4*x - 5120*a^3*b^4*c^6*d^4*x + 10240*a^4*b^2*c^7*d^4*x)) - (64*b^5*c^3*x)/(3*(a + b*x + c*x^2)^(1/2)*(4*b^11*c^2*d^4 - 80*a*b^9*c^3*d^4 - 4096*a^5*b*c^7*d^4 - 8192*a^5*c^8*d^4*x + 8*b^10*c^3*d^4*x + 640*a^2*b^7*c^4*d^4 - 2560*a^3*b^5*c^5*d^4 + 5120*a^4*b^3*c^6*d^4 - 160*a*b^8*c^4*d^4*x + 1280*a^2*b^6*c^5*d^4*x - 5120*a^3*b^4*c^6*d^4*x + 10240*a^4*b^2*c^7*d^4*x)) + (1536*a*b^6*c^6)/((a + b*x + c*x^2)^(1/2)*(32*b^13*c^5*d^4 - 768*a*b^11*c^6*d^4 + 131072*a^6*b*c^11*d^4 + 262144*a^6*c^12*d^4*x + 64*b^12*c^6*d^4*x + 7680*a^2*b^9*c^7*d^4 - 40960*a^3*b^7*c^8*d^4 + 122880*a^4*b^5*c^9*d^4 - 196608*a^5*b^3*c^10*d^4 - 1536*a*b^10*c^7*d^4*x + 15360*a^2*b^8*c^8*d^4*x - 81920*a^3*b^6*c^9*d^4*x + 245760*a^4*b^4*c^10*d^4*x - 393216*a^5*b^2*c^11*d^4*x)) - (512*b^7*c^6*x)/((a + b*x + c*x^2)^(1/2)*(32*b^13*c^5*d^4 - 768*a*b^11*c^6*d^4 + 131072*a^6*b*c^11*d^4 + 262144*a^6*c^12*d^4*x + 64*b^12*c^6*d^4*x + 7680*a^2*b^9*c^7*d^4 - 40960*a^3*b^7*c^8*d^4 + 122880*a^4*b^5*c^9*d^4 - 196608*a^5*b^3*c^10*d^4 - 1536*a*b^10*c^7*d^4*x + 15360*a^2*b^8*c^8*d^4*x - 81920*a^3*b^6*c^9*d^4*x + 245760*a^4*b^4*c^10*d^4*x - 393216*a^5*b^2*c^11*d^4*x)) + (1664*a^2*b^2*c^4)/(3*(a + b*x + c*x^2)^(1/2)*(4*b^11*c^2*d^4 - 80*a*b^9*c^3*d^4 - 4096*a^5*b*c^7*d^4 - 8192*a^5*c^8*d^4*x + 8*b^10*c^3*d^4*x + 640*a^2*b^7*c^4*d^4 - 2560*a^3*b^5*c^5*d^4 + 5120*a^4*b^3*c^6*d^4 - 160*a*b^8*c^4*d^4*x + 1280*a^2*b^6*c^5*d^4*x - 5120*a^3*b^4*c^6*d^4*x + 10240*a^4*b^2*c^7*d^4*x)) - (1024*a^2*c^6*x^2)/(3*(a + b*x + c*x^2)^(1/2)*(4*b^11*c^2*d^4 - 80*a*b^9*c^3*d^4 - 4096*a^5*b*c^7*d^4 - 8192*a^5*c^8*d^4*x + 8*b^10*c^3*d^4*x + 640*a^2*b^7*c^4*d^4 - 2560*a^3*b^5*c^5*d^4 + 5120*a^4*b^3*c^6*d^4 - 160*a*b^8*c^4*d^4*x + 1280*a^2*b^6*c^5*d^4*x - 5120*a^3*b^4*c^6*d^4*x + 10240*a^4*b^2*c^7*d^4*x)) - (64*b^4*c^4*x^2)/(3*(a + b*x + c*x^2)^(1/2)*(4*b^11*c^2*d^4 - 80*a*b^9*c^3*d^4 - 4096*a^5*b*c^7*d^4 - 8192*a^5*c^8*d^4*x + 8*b^10*c^3*d^4*x + 640*a^2*b^7*c^4*d^4 - 2560*a^3*b^5*c^5*d^4 + 5120*a^4*b^3*c^6*d^4 - 160*a*b^8*c^4*d^4*x + 1280*a^2*b^6*c^5*d^4*x - 5120*a^3*b^4*c^6*d^4*x + 10240*a^4*b^2*c^7*d^4*x)) - (6144*a^2*b^4*c^7)/((a + b*x + c*x^2)^(1/2)*(32*b^13*c^5*d^4 - 768*a*b^11*c^6*d^4 + 131072*a^6*b*c^11*d^4 + 262144*a^6*c^12*d^4*x + 64*b^12*c^6*d^4*x + 7680*a^2*b^9*c^7*d^4 - 40960*a^3*b^7*c^8*d^4 + 122880*a^4*b^5*c^9*d^4 - 196608*a^5*b^3*c^10*d^4 - 1536*a*b^10*c^7*d^4*x + 15360*a^2*b^8*c^8*d^4*x - 81920*a^3*b^6*c^9*d^4*x + 245760*a^4*b^4*c^10*d^4*x - 393216*a^5*b^2*c^11*d^4*x)) + (8192*a^3*b^2*c^8)/((a + b*x + c*x^2)^(1/2)*(32*b^13*c^5*d^4 - 768*a*b^11*c^6*d^4 + 131072*a^6*b*c^11*d^4 + 262144*a^6*c^12*d^4*x + 64*b^12*c^6*d^4*x + 7680*a^2*b^9*c^7*d^4 - 40960*a^3*b^7*c^8*d^4 + 122880*a^4*b^5*c^9*d^4 - 196608*a^5*b^3*c^10*d^4 - 1536*a*b^10*c^7*d^4*x + 15360*a^2*b^8*c^8*d^4*x - 81920*a^3*b^6*c^9*d^4*x + 245760*a^4*b^4*c^10*d^4*x - 393216*a^5*b^2*c^11*d^4*x)) + (32768*a^3*c^10*x^2)/((a + b*x + c*x^2)^(1/2)*(32*b^13*c^5*d^4 - 768*a*b^11*c^6*d^4 + 131072*a^6*b*c^11*d^4 + 262144*a^6*c^12*d^4*x + 64*b^12*c^6*d^4*x + 7680*a^2*b^9*c^7*d^4 - 40960*a^3*b^7*c^8*d^4 + 122880*a^4*b^5*c^9*d^4 - 196608*a^5*b^3*c^10*d^4 - 1536*a*b^10*c^7*d^4*x + 15360*a^2*b^8*c^8*d^4*x - 81920*a^3*b^6*c^9*d^4*x + 245760*a^4*b^4*c^10*d^4*x - 393216*a^5*b^2*c^11*d^4*x)) - (512*b^6*c^7*x^2)/((a + b*x + c*x^2)^(1/2)*(32*b^13*c^5*d^4 - 768*a*b^11*c^6*d^4 + 131072*a^6*b*c^11*d^4 + 262144*a^6*c^12*d^4*x + 64*b^12*c^6*d^4*x + 7680*a^2*b^9*c^7*d^4 - 40960*a^3*b^7*c^8*d^4 + 122880*a^4*b^5*c^9*d^4 - 196608*a^5*b^3*c^10*d^4 - 1536*a*b^10*c^7*d^4*x + 15360*a^2*b^8*c^8*d^4*x - 81920*a^3*b^6*c^9*d^4*x + 245760*a^4*b^4*c^10*d^4*x - 393216*a^5*b^2*c^11*d^4*x)) + (512*a*b^2*c^5*x^2)/(3*(a + b*x + c*x^2)^(1/2)*(4*b^11*c^2*d^4 - 80*a*b^9*c^3*d^4 - 4096*a^5*b*c^7*d^4 - 8192*a^5*c^8*d^4*x + 8*b^10*c^3*d^4*x + 640*a^2*b^7*c^4*d^4 - 2560*a^3*b^5*c^5*d^4 + 5120*a^4*b^3*c^6*d^4 - 160*a*b^8*c^4*d^4*x + 1280*a^2*b^6*c^5*d^4*x - 5120*a^3*b^4*c^6*d^4*x + 10240*a^4*b^2*c^7*d^4*x)) - (24576*a^2*b^3*c^8*x)/((a + b*x + c*x^2)^(1/2)*(32*b^13*c^5*d^4 - 768*a*b^11*c^6*d^4 + 131072*a^6*b*c^11*d^4 + 262144*a^6*c^12*d^4*x + 64*b^12*c^6*d^4*x + 7680*a^2*b^9*c^7*d^4 - 40960*a^3*b^7*c^8*d^4 + 122880*a^4*b^5*c^9*d^4 - 196608*a^5*b^3*c^10*d^4 - 1536*a*b^10*c^7*d^4*x + 15360*a^2*b^8*c^8*d^4*x - 81920*a^3*b^6*c^9*d^4*x + 245760*a^4*b^4*c^10*d^4*x - 393216*a^5*b^2*c^11*d^4*x)) + (6144*a*b^4*c^8*x^2)/((a + b*x + c*x^2)^(1/2)*(32*b^13*c^5*d^4 - 768*a*b^11*c^6*d^4 + 131072*a^6*b*c^11*d^4 + 262144*a^6*c^12*d^4*x + 64*b^12*c^6*d^4*x + 7680*a^2*b^9*c^7*d^4 - 40960*a^3*b^7*c^8*d^4 + 122880*a^4*b^5*c^9*d^4 - 196608*a^5*b^3*c^10*d^4 - 1536*a*b^10*c^7*d^4*x + 15360*a^2*b^8*c^8*d^4*x - 81920*a^3*b^6*c^9*d^4*x + 245760*a^4*b^4*c^10*d^4*x - 393216*a^5*b^2*c^11*d^4*x)) + (512*a*b^3*c^4*x)/(3*(a + b*x + c*x^2)^(1/2)*(4*b^11*c^2*d^4 - 80*a*b^9*c^3*d^4 - 4096*a^5*b*c^7*d^4 - 8192*a^5*c^8*d^4*x + 8*b^10*c^3*d^4*x + 640*a^2*b^7*c^4*d^4 - 2560*a^3*b^5*c^5*d^4 + 5120*a^4*b^3*c^6*d^4 - 160*a*b^8*c^4*d^4*x + 1280*a^2*b^6*c^5*d^4*x - 5120*a^3*b^4*c^6*d^4*x + 10240*a^4*b^2*c^7*d^4*x)) - (1024*a^2*b*c^5*x)/(3*(a + b*x + c*x^2)^(1/2)*(4*b^11*c^2*d^4 - 80*a*b^9*c^3*d^4 - 4096*a^5*b*c^7*d^4 - 8192*a^5*c^8*d^4*x + 8*b^10*c^3*d^4*x + 640*a^2*b^7*c^4*d^4 - 2560*a^3*b^5*c^5*d^4 + 5120*a^4*b^3*c^6*d^4 - 160*a*b^8*c^4*d^4*x + 1280*a^2*b^6*c^5*d^4*x - 5120*a^3*b^4*c^6*d^4*x + 10240*a^4*b^2*c^7*d^4*x)) - (24576*a^2*b^2*c^9*x^2)/((a + b*x + c*x^2)^(1/2)*(32*b^13*c^5*d^4 - 768*a*b^11*c^6*d^4 + 131072*a^6*b*c^11*d^4 + 262144*a^6*c^12*d^4*x + 64*b^12*c^6*d^4*x + 7680*a^2*b^9*c^7*d^4 - 40960*a^3*b^7*c^8*d^4 + 122880*a^4*b^5*c^9*d^4 - 196608*a^5*b^3*c^10*d^4 - 1536*a*b^10*c^7*d^4*x + 15360*a^2*b^8*c^8*d^4*x - 81920*a^3*b^6*c^9*d^4*x + 245760*a^4*b^4*c^10*d^4*x - 393216*a^5*b^2*c^11*d^4*x)) + (6144*a*b^5*c^7*x)/((a + b*x + c*x^2)^(1/2)*(32*b^13*c^5*d^4 - 768*a*b^11*c^6*d^4 + 131072*a^6*b*c^11*d^4 + 262144*a^6*c^12*d^4*x + 64*b^12*c^6*d^4*x + 7680*a^2*b^9*c^7*d^4 - 40960*a^3*b^7*c^8*d^4 + 122880*a^4*b^5*c^9*d^4 - 196608*a^5*b^3*c^10*d^4 - 1536*a*b^10*c^7*d^4*x + 15360*a^2*b^8*c^8*d^4*x - 81920*a^3*b^6*c^9*d^4*x + 245760*a^4*b^4*c^10*d^4*x - 393216*a^5*b^2*c^11*d^4*x)) + (32768*a^3*b*c^9*x)/((a + b*x + c*x^2)^(1/2)*(32*b^13*c^5*d^4 - 768*a*b^11*c^6*d^4 + 131072*a^6*b*c^11*d^4 + 262144*a^6*c^12*d^4*x + 64*b^12*c^6*d^4*x + 7680*a^2*b^9*c^7*d^4 - 40960*a^3*b^7*c^8*d^4 + 122880*a^4*b^5*c^9*d^4 - 196608*a^5*b^3*c^10*d^4 - 1536*a*b^10*c^7*d^4*x + 15360*a^2*b^8*c^8*d^4*x - 81920*a^3*b^6*c^9*d^4*x + 245760*a^4*b^4*c^10*d^4*x - 393216*a^5*b^2*c^11*d^4*x))","B"
1250,0,-1,136,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^6/(a + b*x + c*x^2)^(5/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^6}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^6/(a + b*x + c*x^2)^(5/2), x)","F"
1251,1,118,84,0.912165,"\text{Not used}","int((b*d + 2*c*d*x)^5/(a + b*x + c*x^2)^(5/2),x)","-\frac{2\,b^4\,d^5+32\,a^2\,c^2\,d^5-96\,c^2\,d^5\,{\left(c\,x^2+b\,x+a\right)}^2-16\,a\,b^2\,c\,d^5-192\,a\,c^2\,d^5\,\left(c\,x^2+b\,x+a\right)+48\,b^2\,c\,d^5\,\left(c\,x^2+b\,x+a\right)}{\sqrt{c\,x^2+b\,x+a}\,\left(3\,c\,x^2+3\,b\,x+3\,a\right)}","Not used",1,"-(2*b^4*d^5 + 32*a^2*c^2*d^5 - 96*c^2*d^5*(a + b*x + c*x^2)^2 - 16*a*b^2*c*d^5 - 192*a*c^2*d^5*(a + b*x + c*x^2) + 48*b^2*c*d^5*(a + b*x + c*x^2))/((a + b*x + c*x^2)^(1/2)*(3*a + 3*b*x + 3*c*x^2))","B"
1252,0,-1,96,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^4/(a + b*x + c*x^2)^(5/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^4}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^4/(a + b*x + c*x^2)^(5/2), x)","F"
1253,1,62,52,0.696448,"\text{Not used}","int((b*d + 2*c*d*x)^3/(a + b*x + c*x^2)^(5/2),x)","-\frac{2\,b^2\,d^3+24\,c\,d^3\,\left(c\,x^2+b\,x+a\right)-8\,a\,c\,d^3}{\sqrt{c\,x^2+b\,x+a}\,\left(3\,c\,x^2+3\,b\,x+3\,a\right)}","Not used",1,"-(2*b^2*d^3 + 24*c*d^3*(a + b*x + c*x^2) - 8*a*c*d^3)/((a + b*x + c*x^2)^(1/2)*(3*a + 3*b*x + 3*c*x^2))","B"
1254,1,67,39,0.641344,"\text{Not used}","int((b*d + 2*c*d*x)^2/(a + b*x + c*x^2)^(5/2),x)","\frac{2\,b^3\,d^2+12\,b^2\,c\,d^2\,x+24\,b\,c^2\,d^2\,x^2+16\,c^3\,d^2\,x^3}{\left(12\,a\,c-3\,b^2\right)\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}","Not used",1,"(2*b^3*d^2 + 16*c^3*d^2*x^3 + 24*b*c^2*d^2*x^2 + 12*b^2*c*d^2*x)/((12*a*c - 3*b^2)*(a + b*x + c*x^2)^(3/2))","B"
1255,1,15,19,0.582797,"\text{Not used}","int((b*d + 2*c*d*x)/(a + b*x + c*x^2)^(5/2),x)","-\frac{2\,d}{3\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}","Not used",1,"-(2*d)/(3*(a + b*x + c*x^2)^(3/2))","B"
1256,0,-1,118,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)*(a + b*x + c*x^2)^(5/2)),x)","\int \frac{1}{\left(b\,d+2\,c\,d\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)*(a + b*x + c*x^2)^(5/2)), x)","F"
1257,1,110,122,1.042064,"\text{Not used}","int(1/((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(5/2)),x)","-\frac{2\,\left(48\,a^2\,c^2+24\,a\,b^2\,c+192\,a\,b\,c^2\,x+192\,a\,c^3\,x^2-b^4+16\,b^3\,c\,x+144\,b^2\,c^2\,x^2+256\,b\,c^3\,x^3+128\,c^4\,x^4\right)}{3\,d^2\,{\left(4\,a\,c-b^2\right)}^3\,\left(b+2\,c\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}","Not used",1,"-(2*(48*a^2*c^2 - b^4 + 128*c^4*x^4 + 192*a*c^3*x^2 + 256*b*c^3*x^3 + 144*b^2*c^2*x^2 + 24*a*b^2*c + 16*b^3*c*x + 192*a*b*c^2*x))/(3*d^2*(4*a*c - b^2)^3*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))","B"
1258,0,-1,176,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(5/2)),x)","\int \frac{1}{{\left(b\,d+2\,c\,d\,x\right)}^3\,{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(5/2)), x)","F"
1259,1,5604,162,2.375348,"\text{Not used}","int(1/((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(5/2)),x)","\frac{128\,c^6\,\sqrt{c\,x^2+b\,x+a}}{-768\,a^3\,b^3\,c^7\,d^4-4608\,a^3\,b^2\,c^8\,d^4\,x-9216\,a^3\,b\,c^9\,d^4\,x^2-6144\,a^3\,c^{10}\,d^4\,x^3+576\,a^2\,b^5\,c^6\,d^4+3456\,a^2\,b^4\,c^7\,d^4\,x+6912\,a^2\,b^3\,c^8\,d^4\,x^2+4608\,a^2\,b^2\,c^9\,d^4\,x^3-144\,a\,b^7\,c^5\,d^4-864\,a\,b^6\,c^6\,d^4\,x-1728\,a\,b^5\,c^7\,d^4\,x^2-1152\,a\,b^4\,c^8\,d^4\,x^3+12\,b^9\,c^4\,d^4+72\,b^8\,c^5\,d^4\,x+144\,b^7\,c^6\,d^4\,x^2+96\,b^6\,c^7\,d^4\,x^3}-\frac{800\,b^7\,c^5}{{\left(c\,x^2+b\,x+a\right)}^{3/2}\,\left(-491520\,a^5\,b^2\,c^{10}\,d^4-1966080\,a^5\,b\,c^{11}\,d^4\,x-1966080\,a^5\,c^{12}\,d^4\,x^2+614400\,a^4\,b^4\,c^9\,d^4+2457600\,a^4\,b^3\,c^{10}\,d^4\,x+2457600\,a^4\,b^2\,c^{11}\,d^4\,x^2-307200\,a^3\,b^6\,c^8\,d^4-1228800\,a^3\,b^5\,c^9\,d^4\,x-1228800\,a^3\,b^4\,c^{10}\,d^4\,x^2+76800\,a^2\,b^8\,c^7\,d^4+307200\,a^2\,b^7\,c^8\,d^4\,x+307200\,a^2\,b^6\,c^9\,d^4\,x^2-9600\,a\,b^{10}\,c^6\,d^4-38400\,a\,b^9\,c^7\,d^4\,x-38400\,a\,b^8\,c^8\,d^4\,x^2+480\,b^{12}\,c^5\,d^4+1920\,b^{11}\,c^6\,d^4\,x+1920\,b^{10}\,c^7\,d^4\,x^2\right)}+\frac{384\,a\,c^4}{\sqrt{c\,x^2+b\,x+a}\,\left(1024\,a^4\,b\,c^6\,d^4+2048\,x\,a^4\,c^7\,d^4-1024\,a^3\,b^3\,c^5\,d^4-2048\,x\,a^3\,b^2\,c^6\,d^4+384\,a^2\,b^5\,c^4\,d^4+768\,x\,a^2\,b^4\,c^5\,d^4-64\,a\,b^7\,c^3\,d^4-128\,x\,a\,b^6\,c^4\,d^4+4\,b^9\,c^2\,d^4+8\,x\,b^8\,c^3\,d^4\right)}-\frac{224\,b^2\,c^3}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(1024\,a^4\,b\,c^6\,d^4+2048\,x\,a^4\,c^7\,d^4-1024\,a^3\,b^3\,c^5\,d^4-2048\,x\,a^3\,b^2\,c^6\,d^4+384\,a^2\,b^5\,c^4\,d^4+768\,x\,a^2\,b^4\,c^5\,d^4-64\,a\,b^7\,c^3\,d^4-128\,x\,a\,b^6\,c^4\,d^4+4\,b^9\,c^2\,d^4+8\,x\,b^8\,c^3\,d^4\right)}+\frac{256\,c^5\,x^2}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(1024\,a^4\,b\,c^6\,d^4+2048\,x\,a^4\,c^7\,d^4-1024\,a^3\,b^3\,c^5\,d^4-2048\,x\,a^3\,b^2\,c^6\,d^4+384\,a^2\,b^5\,c^4\,d^4+768\,x\,a^2\,b^4\,c^5\,d^4-64\,a\,b^7\,c^3\,d^4-128\,x\,a\,b^6\,c^4\,d^4+4\,b^9\,c^2\,d^4+8\,x\,b^8\,c^3\,d^4\right)}+\frac{8\,b^5\,c^2}{{\left(c\,x^2+b\,x+a\right)}^{3/2}\,\left(2048\,a^4\,b^2\,c^6\,d^4+8192\,a^4\,b\,c^7\,d^4\,x+8192\,a^4\,c^8\,d^4\,x^2-2048\,a^3\,b^4\,c^5\,d^4-8192\,a^3\,b^3\,c^6\,d^4\,x-8192\,a^3\,b^2\,c^7\,d^4\,x^2+768\,a^2\,b^6\,c^4\,d^4+3072\,a^2\,b^5\,c^5\,d^4\,x+3072\,a^2\,b^4\,c^6\,d^4\,x^2-128\,a\,b^8\,c^3\,d^4-512\,a\,b^7\,c^4\,d^4\,x-512\,a\,b^6\,c^5\,d^4\,x^2+8\,b^{10}\,c^2\,d^4+32\,b^9\,c^3\,d^4\,x+32\,b^8\,c^4\,d^4\,x^2\right)}+\frac{3584\,b^4\,c^6}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(-32768\,a^5\,b\,c^{10}\,d^4-65536\,x\,a^5\,c^{11}\,d^4+40960\,a^4\,b^3\,c^9\,d^4+81920\,x\,a^4\,b^2\,c^{10}\,d^4-20480\,a^3\,b^5\,c^8\,d^4-40960\,x\,a^3\,b^4\,c^9\,d^4+5120\,a^2\,b^7\,c^7\,d^4+10240\,x\,a^2\,b^6\,c^8\,d^4-640\,a\,b^9\,c^6\,d^4-1280\,x\,a\,b^8\,c^7\,d^4+32\,b^{11}\,c^5\,d^4+64\,x\,b^{10}\,c^6\,d^4\right)}-\frac{64\,a\,b^3\,c^3}{{\left(c\,x^2+b\,x+a\right)}^{3/2}\,\left(2048\,a^4\,b^2\,c^6\,d^4+8192\,a^4\,b\,c^7\,d^4\,x+8192\,a^4\,c^8\,d^4\,x^2-2048\,a^3\,b^4\,c^5\,d^4-8192\,a^3\,b^3\,c^6\,d^4\,x-8192\,a^3\,b^2\,c^7\,d^4\,x^2+768\,a^2\,b^6\,c^4\,d^4+3072\,a^2\,b^5\,c^5\,d^4\,x+3072\,a^2\,b^4\,c^6\,d^4\,x^2-128\,a\,b^8\,c^3\,d^4-512\,a\,b^7\,c^4\,d^4\,x-512\,a\,b^6\,c^5\,d^4\,x^2+8\,b^{10}\,c^2\,d^4+32\,b^9\,c^3\,d^4\,x+32\,b^8\,c^4\,d^4\,x^2\right)}+\frac{128\,a^2\,b\,c^4}{{\left(c\,x^2+b\,x+a\right)}^{3/2}\,\left(2048\,a^4\,b^2\,c^6\,d^4+8192\,a^4\,b\,c^7\,d^4\,x+8192\,a^4\,c^8\,d^4\,x^2-2048\,a^3\,b^4\,c^5\,d^4-8192\,a^3\,b^3\,c^6\,d^4\,x-8192\,a^3\,b^2\,c^7\,d^4\,x^2+768\,a^2\,b^6\,c^4\,d^4+3072\,a^2\,b^5\,c^5\,d^4\,x+3072\,a^2\,b^4\,c^6\,d^4\,x^2-128\,a\,b^8\,c^3\,d^4-512\,a\,b^7\,c^4\,d^4\,x-512\,a\,b^6\,c^5\,d^4\,x^2+8\,b^{10}\,c^2\,d^4+32\,b^9\,c^3\,d^4\,x+32\,b^8\,c^4\,d^4\,x^2\right)}+\frac{256\,a^2\,c^5\,x}{{\left(c\,x^2+b\,x+a\right)}^{3/2}\,\left(2048\,a^4\,b^2\,c^6\,d^4+8192\,a^4\,b\,c^7\,d^4\,x+8192\,a^4\,c^8\,d^4\,x^2-2048\,a^3\,b^4\,c^5\,d^4-8192\,a^3\,b^3\,c^6\,d^4\,x-8192\,a^3\,b^2\,c^7\,d^4\,x^2+768\,a^2\,b^6\,c^4\,d^4+3072\,a^2\,b^5\,c^5\,d^4\,x+3072\,a^2\,b^4\,c^6\,d^4\,x^2-128\,a\,b^8\,c^3\,d^4-512\,a\,b^7\,c^4\,d^4\,x-512\,a\,b^6\,c^5\,d^4\,x^2+8\,b^{10}\,c^2\,d^4+32\,b^9\,c^3\,d^4\,x+32\,b^8\,c^4\,d^4\,x^2\right)}+\frac{16\,b^4\,c^3\,x}{{\left(c\,x^2+b\,x+a\right)}^{3/2}\,\left(2048\,a^4\,b^2\,c^6\,d^4+8192\,a^4\,b\,c^7\,d^4\,x+8192\,a^4\,c^8\,d^4\,x^2-2048\,a^3\,b^4\,c^5\,d^4-8192\,a^3\,b^3\,c^6\,d^4\,x-8192\,a^3\,b^2\,c^7\,d^4\,x^2+768\,a^2\,b^6\,c^4\,d^4+3072\,a^2\,b^5\,c^5\,d^4\,x+3072\,a^2\,b^4\,c^6\,d^4\,x^2-128\,a\,b^8\,c^3\,d^4-512\,a\,b^7\,c^4\,d^4\,x-512\,a\,b^6\,c^5\,d^4\,x^2+8\,b^{10}\,c^2\,d^4+32\,b^9\,c^3\,d^4\,x+32\,b^8\,c^4\,d^4\,x^2\right)}-\frac{14336\,a\,b^2\,c^7}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(-32768\,a^5\,b\,c^{10}\,d^4-65536\,x\,a^5\,c^{11}\,d^4+40960\,a^4\,b^3\,c^9\,d^4+81920\,x\,a^4\,b^2\,c^{10}\,d^4-20480\,a^3\,b^5\,c^8\,d^4-40960\,x\,a^3\,b^4\,c^9\,d^4+5120\,a^2\,b^7\,c^7\,d^4+10240\,x\,a^2\,b^6\,c^8\,d^4-640\,a\,b^9\,c^6\,d^4-1280\,x\,a\,b^8\,c^7\,d^4+32\,b^{11}\,c^5\,d^4+64\,x\,b^{10}\,c^6\,d^4\right)}-\frac{57344\,a\,c^9\,x^2}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(-32768\,a^5\,b\,c^{10}\,d^4-65536\,x\,a^5\,c^{11}\,d^4+40960\,a^4\,b^3\,c^9\,d^4+81920\,x\,a^4\,b^2\,c^{10}\,d^4-20480\,a^3\,b^5\,c^8\,d^4-40960\,x\,a^3\,b^4\,c^9\,d^4+5120\,a^2\,b^7\,c^7\,d^4+10240\,x\,a^2\,b^6\,c^8\,d^4-640\,a\,b^9\,c^6\,d^4-1280\,x\,a\,b^8\,c^7\,d^4+32\,b^{11}\,c^5\,d^4+64\,x\,b^{10}\,c^6\,d^4\right)}+\frac{14336\,b^3\,c^7\,x}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(-32768\,a^5\,b\,c^{10}\,d^4-65536\,x\,a^5\,c^{11}\,d^4+40960\,a^4\,b^3\,c^9\,d^4+81920\,x\,a^4\,b^2\,c^{10}\,d^4-20480\,a^3\,b^5\,c^8\,d^4-40960\,x\,a^3\,b^4\,c^9\,d^4+5120\,a^2\,b^7\,c^7\,d^4+10240\,x\,a^2\,b^6\,c^8\,d^4-640\,a\,b^9\,c^6\,d^4-1280\,x\,a\,b^8\,c^7\,d^4+32\,b^{11}\,c^5\,d^4+64\,x\,b^{10}\,c^6\,d^4\right)}+\frac{9600\,a\,b^5\,c^6}{{\left(c\,x^2+b\,x+a\right)}^{3/2}\,\left(-491520\,a^5\,b^2\,c^{10}\,d^4-1966080\,a^5\,b\,c^{11}\,d^4\,x-1966080\,a^5\,c^{12}\,d^4\,x^2+614400\,a^4\,b^4\,c^9\,d^4+2457600\,a^4\,b^3\,c^{10}\,d^4\,x+2457600\,a^4\,b^2\,c^{11}\,d^4\,x^2-307200\,a^3\,b^6\,c^8\,d^4-1228800\,a^3\,b^5\,c^9\,d^4\,x-1228800\,a^3\,b^4\,c^{10}\,d^4\,x^2+76800\,a^2\,b^8\,c^7\,d^4+307200\,a^2\,b^7\,c^8\,d^4\,x+307200\,a^2\,b^6\,c^9\,d^4\,x^2-9600\,a\,b^{10}\,c^6\,d^4-38400\,a\,b^9\,c^7\,d^4\,x-38400\,a\,b^8\,c^8\,d^4\,x^2+480\,b^{12}\,c^5\,d^4+1920\,b^{11}\,c^6\,d^4\,x+1920\,b^{10}\,c^7\,d^4\,x^2\right)}+\frac{51200\,a^3\,b\,c^8}{{\left(c\,x^2+b\,x+a\right)}^{3/2}\,\left(-491520\,a^5\,b^2\,c^{10}\,d^4-1966080\,a^5\,b\,c^{11}\,d^4\,x-1966080\,a^5\,c^{12}\,d^4\,x^2+614400\,a^4\,b^4\,c^9\,d^4+2457600\,a^4\,b^3\,c^{10}\,d^4\,x+2457600\,a^4\,b^2\,c^{11}\,d^4\,x^2-307200\,a^3\,b^6\,c^8\,d^4-1228800\,a^3\,b^5\,c^9\,d^4\,x-1228800\,a^3\,b^4\,c^{10}\,d^4\,x^2+76800\,a^2\,b^8\,c^7\,d^4+307200\,a^2\,b^7\,c^8\,d^4\,x+307200\,a^2\,b^6\,c^9\,d^4\,x^2-9600\,a\,b^{10}\,c^6\,d^4-38400\,a\,b^9\,c^7\,d^4\,x-38400\,a\,b^8\,c^8\,d^4\,x^2+480\,b^{12}\,c^5\,d^4+1920\,b^{11}\,c^6\,d^4\,x+1920\,b^{10}\,c^7\,d^4\,x^2\right)}+\frac{102400\,a^3\,c^9\,x}{{\left(c\,x^2+b\,x+a\right)}^{3/2}\,\left(-491520\,a^5\,b^2\,c^{10}\,d^4-1966080\,a^5\,b\,c^{11}\,d^4\,x-1966080\,a^5\,c^{12}\,d^4\,x^2+614400\,a^4\,b^4\,c^9\,d^4+2457600\,a^4\,b^3\,c^{10}\,d^4\,x+2457600\,a^4\,b^2\,c^{11}\,d^4\,x^2-307200\,a^3\,b^6\,c^8\,d^4-1228800\,a^3\,b^5\,c^9\,d^4\,x-1228800\,a^3\,b^4\,c^{10}\,d^4\,x^2+76800\,a^2\,b^8\,c^7\,d^4+307200\,a^2\,b^7\,c^8\,d^4\,x+307200\,a^2\,b^6\,c^9\,d^4\,x^2-9600\,a\,b^{10}\,c^6\,d^4-38400\,a\,b^9\,c^7\,d^4\,x-38400\,a\,b^8\,c^8\,d^4\,x^2+480\,b^{12}\,c^5\,d^4+1920\,b^{11}\,c^6\,d^4\,x+1920\,b^{10}\,c^7\,d^4\,x^2\right)}-\frac{1600\,b^6\,c^6\,x}{{\left(c\,x^2+b\,x+a\right)}^{3/2}\,\left(-491520\,a^5\,b^2\,c^{10}\,d^4-1966080\,a^5\,b\,c^{11}\,d^4\,x-1966080\,a^5\,c^{12}\,d^4\,x^2+614400\,a^4\,b^4\,c^9\,d^4+2457600\,a^4\,b^3\,c^{10}\,d^4\,x+2457600\,a^4\,b^2\,c^{11}\,d^4\,x^2-307200\,a^3\,b^6\,c^8\,d^4-1228800\,a^3\,b^5\,c^9\,d^4\,x-1228800\,a^3\,b^4\,c^{10}\,d^4\,x^2+76800\,a^2\,b^8\,c^7\,d^4+307200\,a^2\,b^7\,c^8\,d^4\,x+307200\,a^2\,b^6\,c^9\,d^4\,x^2-9600\,a\,b^{10}\,c^6\,d^4-38400\,a\,b^9\,c^7\,d^4\,x-38400\,a\,b^8\,c^8\,d^4\,x^2+480\,b^{12}\,c^5\,d^4+1920\,b^{11}\,c^6\,d^4\,x+1920\,b^{10}\,c^7\,d^4\,x^2\right)}+\frac{256\,b\,c^4\,x}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(1024\,a^4\,b\,c^6\,d^4+2048\,x\,a^4\,c^7\,d^4-1024\,a^3\,b^3\,c^5\,d^4-2048\,x\,a^3\,b^2\,c^6\,d^4+384\,a^2\,b^5\,c^4\,d^4+768\,x\,a^2\,b^4\,c^5\,d^4-64\,a\,b^7\,c^3\,d^4-128\,x\,a\,b^6\,c^4\,d^4+4\,b^9\,c^2\,d^4+8\,x\,b^8\,c^3\,d^4\right)}+\frac{14336\,b^2\,c^8\,x^2}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(-32768\,a^5\,b\,c^{10}\,d^4-65536\,x\,a^5\,c^{11}\,d^4+40960\,a^4\,b^3\,c^9\,d^4+81920\,x\,a^4\,b^2\,c^{10}\,d^4-20480\,a^3\,b^5\,c^8\,d^4-40960\,x\,a^3\,b^4\,c^9\,d^4+5120\,a^2\,b^7\,c^7\,d^4+10240\,x\,a^2\,b^6\,c^8\,d^4-640\,a\,b^9\,c^6\,d^4-1280\,x\,a\,b^8\,c^7\,d^4+32\,b^{11}\,c^5\,d^4+64\,x\,b^{10}\,c^6\,d^4\right)}-\frac{38400\,a^2\,b^3\,c^7}{{\left(c\,x^2+b\,x+a\right)}^{3/2}\,\left(-491520\,a^5\,b^2\,c^{10}\,d^4-1966080\,a^5\,b\,c^{11}\,d^4\,x-1966080\,a^5\,c^{12}\,d^4\,x^2+614400\,a^4\,b^4\,c^9\,d^4+2457600\,a^4\,b^3\,c^{10}\,d^4\,x+2457600\,a^4\,b^2\,c^{11}\,d^4\,x^2-307200\,a^3\,b^6\,c^8\,d^4-1228800\,a^3\,b^5\,c^9\,d^4\,x-1228800\,a^3\,b^4\,c^{10}\,d^4\,x^2+76800\,a^2\,b^8\,c^7\,d^4+307200\,a^2\,b^7\,c^8\,d^4\,x+307200\,a^2\,b^6\,c^9\,d^4\,x^2-9600\,a\,b^{10}\,c^6\,d^4-38400\,a\,b^9\,c^7\,d^4\,x-38400\,a\,b^8\,c^8\,d^4\,x^2+480\,b^{12}\,c^5\,d^4+1920\,b^{11}\,c^6\,d^4\,x+1920\,b^{10}\,c^7\,d^4\,x^2\right)}+\frac{19200\,a\,b^4\,c^7\,x}{{\left(c\,x^2+b\,x+a\right)}^{3/2}\,\left(-491520\,a^5\,b^2\,c^{10}\,d^4-1966080\,a^5\,b\,c^{11}\,d^4\,x-1966080\,a^5\,c^{12}\,d^4\,x^2+614400\,a^4\,b^4\,c^9\,d^4+2457600\,a^4\,b^3\,c^{10}\,d^4\,x+2457600\,a^4\,b^2\,c^{11}\,d^4\,x^2-307200\,a^3\,b^6\,c^8\,d^4-1228800\,a^3\,b^5\,c^9\,d^4\,x-1228800\,a^3\,b^4\,c^{10}\,d^4\,x^2+76800\,a^2\,b^8\,c^7\,d^4+307200\,a^2\,b^7\,c^8\,d^4\,x+307200\,a^2\,b^6\,c^9\,d^4\,x^2-9600\,a\,b^{10}\,c^6\,d^4-38400\,a\,b^9\,c^7\,d^4\,x-38400\,a\,b^8\,c^8\,d^4\,x^2+480\,b^{12}\,c^5\,d^4+1920\,b^{11}\,c^6\,d^4\,x+1920\,b^{10}\,c^7\,d^4\,x^2\right)}-\frac{57344\,a\,b\,c^8\,x}{3\,\sqrt{c\,x^2+b\,x+a}\,\left(-32768\,a^5\,b\,c^{10}\,d^4-65536\,x\,a^5\,c^{11}\,d^4+40960\,a^4\,b^3\,c^9\,d^4+81920\,x\,a^4\,b^2\,c^{10}\,d^4-20480\,a^3\,b^5\,c^8\,d^4-40960\,x\,a^3\,b^4\,c^9\,d^4+5120\,a^2\,b^7\,c^7\,d^4+10240\,x\,a^2\,b^6\,c^8\,d^4-640\,a\,b^9\,c^6\,d^4-1280\,x\,a\,b^8\,c^7\,d^4+32\,b^{11}\,c^5\,d^4+64\,x\,b^{10}\,c^6\,d^4\right)}-\frac{76800\,a^2\,b^2\,c^8\,x}{{\left(c\,x^2+b\,x+a\right)}^{3/2}\,\left(-491520\,a^5\,b^2\,c^{10}\,d^4-1966080\,a^5\,b\,c^{11}\,d^4\,x-1966080\,a^5\,c^{12}\,d^4\,x^2+614400\,a^4\,b^4\,c^9\,d^4+2457600\,a^4\,b^3\,c^{10}\,d^4\,x+2457600\,a^4\,b^2\,c^{11}\,d^4\,x^2-307200\,a^3\,b^6\,c^8\,d^4-1228800\,a^3\,b^5\,c^9\,d^4\,x-1228800\,a^3\,b^4\,c^{10}\,d^4\,x^2+76800\,a^2\,b^8\,c^7\,d^4+307200\,a^2\,b^7\,c^8\,d^4\,x+307200\,a^2\,b^6\,c^9\,d^4\,x^2-9600\,a\,b^{10}\,c^6\,d^4-38400\,a\,b^9\,c^7\,d^4\,x-38400\,a\,b^8\,c^8\,d^4\,x^2+480\,b^{12}\,c^5\,d^4+1920\,b^{11}\,c^6\,d^4\,x+1920\,b^{10}\,c^7\,d^4\,x^2\right)}-\frac{128\,a\,b^2\,c^4\,x}{{\left(c\,x^2+b\,x+a\right)}^{3/2}\,\left(2048\,a^4\,b^2\,c^6\,d^4+8192\,a^4\,b\,c^7\,d^4\,x+8192\,a^4\,c^8\,d^4\,x^2-2048\,a^3\,b^4\,c^5\,d^4-8192\,a^3\,b^3\,c^6\,d^4\,x-8192\,a^3\,b^2\,c^7\,d^4\,x^2+768\,a^2\,b^6\,c^4\,d^4+3072\,a^2\,b^5\,c^5\,d^4\,x+3072\,a^2\,b^4\,c^6\,d^4\,x^2-128\,a\,b^8\,c^3\,d^4-512\,a\,b^7\,c^4\,d^4\,x-512\,a\,b^6\,c^5\,d^4\,x^2+8\,b^{10}\,c^2\,d^4+32\,b^9\,c^3\,d^4\,x+32\,b^8\,c^4\,d^4\,x^2\right)}","Not used",1,"(128*c^6*(a + b*x + c*x^2)^(1/2))/(12*b^9*c^4*d^4 - 144*a*b^7*c^5*d^4 + 72*b^8*c^5*d^4*x + 576*a^2*b^5*c^6*d^4 - 768*a^3*b^3*c^7*d^4 - 6144*a^3*c^10*d^4*x^3 + 144*b^7*c^6*d^4*x^2 + 96*b^6*c^7*d^4*x^3 + 6912*a^2*b^3*c^8*d^4*x^2 + 4608*a^2*b^2*c^9*d^4*x^3 - 864*a*b^6*c^6*d^4*x + 3456*a^2*b^4*c^7*d^4*x - 4608*a^3*b^2*c^8*d^4*x - 1728*a*b^5*c^7*d^4*x^2 - 9216*a^3*b*c^9*d^4*x^2 - 1152*a*b^4*c^8*d^4*x^3) - (800*b^7*c^5)/((a + b*x + c*x^2)^(3/2)*(480*b^12*c^5*d^4 - 9600*a*b^10*c^6*d^4 + 1920*b^11*c^6*d^4*x + 76800*a^2*b^8*c^7*d^4 - 307200*a^3*b^6*c^8*d^4 + 614400*a^4*b^4*c^9*d^4 - 491520*a^5*b^2*c^10*d^4 - 1966080*a^5*c^12*d^4*x^2 + 1920*b^10*c^7*d^4*x^2 + 307200*a^2*b^6*c^9*d^4*x^2 - 1228800*a^3*b^4*c^10*d^4*x^2 + 2457600*a^4*b^2*c^11*d^4*x^2 - 38400*a*b^9*c^7*d^4*x - 1966080*a^5*b*c^11*d^4*x + 307200*a^2*b^7*c^8*d^4*x - 1228800*a^3*b^5*c^9*d^4*x + 2457600*a^4*b^3*c^10*d^4*x - 38400*a*b^8*c^8*d^4*x^2)) + (384*a*c^4)/((a + b*x + c*x^2)^(1/2)*(4*b^9*c^2*d^4 - 64*a*b^7*c^3*d^4 + 1024*a^4*b*c^6*d^4 + 2048*a^4*c^7*d^4*x + 8*b^8*c^3*d^4*x + 384*a^2*b^5*c^4*d^4 - 1024*a^3*b^3*c^5*d^4 - 128*a*b^6*c^4*d^4*x + 768*a^2*b^4*c^5*d^4*x - 2048*a^3*b^2*c^6*d^4*x)) - (224*b^2*c^3)/(3*(a + b*x + c*x^2)^(1/2)*(4*b^9*c^2*d^4 - 64*a*b^7*c^3*d^4 + 1024*a^4*b*c^6*d^4 + 2048*a^4*c^7*d^4*x + 8*b^8*c^3*d^4*x + 384*a^2*b^5*c^4*d^4 - 1024*a^3*b^3*c^5*d^4 - 128*a*b^6*c^4*d^4*x + 768*a^2*b^4*c^5*d^4*x - 2048*a^3*b^2*c^6*d^4*x)) + (256*c^5*x^2)/(3*(a + b*x + c*x^2)^(1/2)*(4*b^9*c^2*d^4 - 64*a*b^7*c^3*d^4 + 1024*a^4*b*c^6*d^4 + 2048*a^4*c^7*d^4*x + 8*b^8*c^3*d^4*x + 384*a^2*b^5*c^4*d^4 - 1024*a^3*b^3*c^5*d^4 - 128*a*b^6*c^4*d^4*x + 768*a^2*b^4*c^5*d^4*x - 2048*a^3*b^2*c^6*d^4*x)) + (8*b^5*c^2)/((a + b*x + c*x^2)^(3/2)*(8*b^10*c^2*d^4 - 128*a*b^8*c^3*d^4 + 32*b^9*c^3*d^4*x + 768*a^2*b^6*c^4*d^4 - 2048*a^3*b^4*c^5*d^4 + 2048*a^4*b^2*c^6*d^4 + 8192*a^4*c^8*d^4*x^2 + 32*b^8*c^4*d^4*x^2 + 3072*a^2*b^4*c^6*d^4*x^2 - 8192*a^3*b^2*c^7*d^4*x^2 - 512*a*b^7*c^4*d^4*x + 8192*a^4*b*c^7*d^4*x + 3072*a^2*b^5*c^5*d^4*x - 8192*a^3*b^3*c^6*d^4*x - 512*a*b^6*c^5*d^4*x^2)) + (3584*b^4*c^6)/(3*(a + b*x + c*x^2)^(1/2)*(32*b^11*c^5*d^4 - 640*a*b^9*c^6*d^4 - 32768*a^5*b*c^10*d^4 - 65536*a^5*c^11*d^4*x + 64*b^10*c^6*d^4*x + 5120*a^2*b^7*c^7*d^4 - 20480*a^3*b^5*c^8*d^4 + 40960*a^4*b^3*c^9*d^4 - 1280*a*b^8*c^7*d^4*x + 10240*a^2*b^6*c^8*d^4*x - 40960*a^3*b^4*c^9*d^4*x + 81920*a^4*b^2*c^10*d^4*x)) - (64*a*b^3*c^3)/((a + b*x + c*x^2)^(3/2)*(8*b^10*c^2*d^4 - 128*a*b^8*c^3*d^4 + 32*b^9*c^3*d^4*x + 768*a^2*b^6*c^4*d^4 - 2048*a^3*b^4*c^5*d^4 + 2048*a^4*b^2*c^6*d^4 + 8192*a^4*c^8*d^4*x^2 + 32*b^8*c^4*d^4*x^2 + 3072*a^2*b^4*c^6*d^4*x^2 - 8192*a^3*b^2*c^7*d^4*x^2 - 512*a*b^7*c^4*d^4*x + 8192*a^4*b*c^7*d^4*x + 3072*a^2*b^5*c^5*d^4*x - 8192*a^3*b^3*c^6*d^4*x - 512*a*b^6*c^5*d^4*x^2)) + (128*a^2*b*c^4)/((a + b*x + c*x^2)^(3/2)*(8*b^10*c^2*d^4 - 128*a*b^8*c^3*d^4 + 32*b^9*c^3*d^4*x + 768*a^2*b^6*c^4*d^4 - 2048*a^3*b^4*c^5*d^4 + 2048*a^4*b^2*c^6*d^4 + 8192*a^4*c^8*d^4*x^2 + 32*b^8*c^4*d^4*x^2 + 3072*a^2*b^4*c^6*d^4*x^2 - 8192*a^3*b^2*c^7*d^4*x^2 - 512*a*b^7*c^4*d^4*x + 8192*a^4*b*c^7*d^4*x + 3072*a^2*b^5*c^5*d^4*x - 8192*a^3*b^3*c^6*d^4*x - 512*a*b^6*c^5*d^4*x^2)) + (256*a^2*c^5*x)/((a + b*x + c*x^2)^(3/2)*(8*b^10*c^2*d^4 - 128*a*b^8*c^3*d^4 + 32*b^9*c^3*d^4*x + 768*a^2*b^6*c^4*d^4 - 2048*a^3*b^4*c^5*d^4 + 2048*a^4*b^2*c^6*d^4 + 8192*a^4*c^8*d^4*x^2 + 32*b^8*c^4*d^4*x^2 + 3072*a^2*b^4*c^6*d^4*x^2 - 8192*a^3*b^2*c^7*d^4*x^2 - 512*a*b^7*c^4*d^4*x + 8192*a^4*b*c^7*d^4*x + 3072*a^2*b^5*c^5*d^4*x - 8192*a^3*b^3*c^6*d^4*x - 512*a*b^6*c^5*d^4*x^2)) + (16*b^4*c^3*x)/((a + b*x + c*x^2)^(3/2)*(8*b^10*c^2*d^4 - 128*a*b^8*c^3*d^4 + 32*b^9*c^3*d^4*x + 768*a^2*b^6*c^4*d^4 - 2048*a^3*b^4*c^5*d^4 + 2048*a^4*b^2*c^6*d^4 + 8192*a^4*c^8*d^4*x^2 + 32*b^8*c^4*d^4*x^2 + 3072*a^2*b^4*c^6*d^4*x^2 - 8192*a^3*b^2*c^7*d^4*x^2 - 512*a*b^7*c^4*d^4*x + 8192*a^4*b*c^7*d^4*x + 3072*a^2*b^5*c^5*d^4*x - 8192*a^3*b^3*c^6*d^4*x - 512*a*b^6*c^5*d^4*x^2)) - (14336*a*b^2*c^7)/(3*(a + b*x + c*x^2)^(1/2)*(32*b^11*c^5*d^4 - 640*a*b^9*c^6*d^4 - 32768*a^5*b*c^10*d^4 - 65536*a^5*c^11*d^4*x + 64*b^10*c^6*d^4*x + 5120*a^2*b^7*c^7*d^4 - 20480*a^3*b^5*c^8*d^4 + 40960*a^4*b^3*c^9*d^4 - 1280*a*b^8*c^7*d^4*x + 10240*a^2*b^6*c^8*d^4*x - 40960*a^3*b^4*c^9*d^4*x + 81920*a^4*b^2*c^10*d^4*x)) - (57344*a*c^9*x^2)/(3*(a + b*x + c*x^2)^(1/2)*(32*b^11*c^5*d^4 - 640*a*b^9*c^6*d^4 - 32768*a^5*b*c^10*d^4 - 65536*a^5*c^11*d^4*x + 64*b^10*c^6*d^4*x + 5120*a^2*b^7*c^7*d^4 - 20480*a^3*b^5*c^8*d^4 + 40960*a^4*b^3*c^9*d^4 - 1280*a*b^8*c^7*d^4*x + 10240*a^2*b^6*c^8*d^4*x - 40960*a^3*b^4*c^9*d^4*x + 81920*a^4*b^2*c^10*d^4*x)) + (14336*b^3*c^7*x)/(3*(a + b*x + c*x^2)^(1/2)*(32*b^11*c^5*d^4 - 640*a*b^9*c^6*d^4 - 32768*a^5*b*c^10*d^4 - 65536*a^5*c^11*d^4*x + 64*b^10*c^6*d^4*x + 5120*a^2*b^7*c^7*d^4 - 20480*a^3*b^5*c^8*d^4 + 40960*a^4*b^3*c^9*d^4 - 1280*a*b^8*c^7*d^4*x + 10240*a^2*b^6*c^8*d^4*x - 40960*a^3*b^4*c^9*d^4*x + 81920*a^4*b^2*c^10*d^4*x)) + (9600*a*b^5*c^6)/((a + b*x + c*x^2)^(3/2)*(480*b^12*c^5*d^4 - 9600*a*b^10*c^6*d^4 + 1920*b^11*c^6*d^4*x + 76800*a^2*b^8*c^7*d^4 - 307200*a^3*b^6*c^8*d^4 + 614400*a^4*b^4*c^9*d^4 - 491520*a^5*b^2*c^10*d^4 - 1966080*a^5*c^12*d^4*x^2 + 1920*b^10*c^7*d^4*x^2 + 307200*a^2*b^6*c^9*d^4*x^2 - 1228800*a^3*b^4*c^10*d^4*x^2 + 2457600*a^4*b^2*c^11*d^4*x^2 - 38400*a*b^9*c^7*d^4*x - 1966080*a^5*b*c^11*d^4*x + 307200*a^2*b^7*c^8*d^4*x - 1228800*a^3*b^5*c^9*d^4*x + 2457600*a^4*b^3*c^10*d^4*x - 38400*a*b^8*c^8*d^4*x^2)) + (51200*a^3*b*c^8)/((a + b*x + c*x^2)^(3/2)*(480*b^12*c^5*d^4 - 9600*a*b^10*c^6*d^4 + 1920*b^11*c^6*d^4*x + 76800*a^2*b^8*c^7*d^4 - 307200*a^3*b^6*c^8*d^4 + 614400*a^4*b^4*c^9*d^4 - 491520*a^5*b^2*c^10*d^4 - 1966080*a^5*c^12*d^4*x^2 + 1920*b^10*c^7*d^4*x^2 + 307200*a^2*b^6*c^9*d^4*x^2 - 1228800*a^3*b^4*c^10*d^4*x^2 + 2457600*a^4*b^2*c^11*d^4*x^2 - 38400*a*b^9*c^7*d^4*x - 1966080*a^5*b*c^11*d^4*x + 307200*a^2*b^7*c^8*d^4*x - 1228800*a^3*b^5*c^9*d^4*x + 2457600*a^4*b^3*c^10*d^4*x - 38400*a*b^8*c^8*d^4*x^2)) + (102400*a^3*c^9*x)/((a + b*x + c*x^2)^(3/2)*(480*b^12*c^5*d^4 - 9600*a*b^10*c^6*d^4 + 1920*b^11*c^6*d^4*x + 76800*a^2*b^8*c^7*d^4 - 307200*a^3*b^6*c^8*d^4 + 614400*a^4*b^4*c^9*d^4 - 491520*a^5*b^2*c^10*d^4 - 1966080*a^5*c^12*d^4*x^2 + 1920*b^10*c^7*d^4*x^2 + 307200*a^2*b^6*c^9*d^4*x^2 - 1228800*a^3*b^4*c^10*d^4*x^2 + 2457600*a^4*b^2*c^11*d^4*x^2 - 38400*a*b^9*c^7*d^4*x - 1966080*a^5*b*c^11*d^4*x + 307200*a^2*b^7*c^8*d^4*x - 1228800*a^3*b^5*c^9*d^4*x + 2457600*a^4*b^3*c^10*d^4*x - 38400*a*b^8*c^8*d^4*x^2)) - (1600*b^6*c^6*x)/((a + b*x + c*x^2)^(3/2)*(480*b^12*c^5*d^4 - 9600*a*b^10*c^6*d^4 + 1920*b^11*c^6*d^4*x + 76800*a^2*b^8*c^7*d^4 - 307200*a^3*b^6*c^8*d^4 + 614400*a^4*b^4*c^9*d^4 - 491520*a^5*b^2*c^10*d^4 - 1966080*a^5*c^12*d^4*x^2 + 1920*b^10*c^7*d^4*x^2 + 307200*a^2*b^6*c^9*d^4*x^2 - 1228800*a^3*b^4*c^10*d^4*x^2 + 2457600*a^4*b^2*c^11*d^4*x^2 - 38400*a*b^9*c^7*d^4*x - 1966080*a^5*b*c^11*d^4*x + 307200*a^2*b^7*c^8*d^4*x - 1228800*a^3*b^5*c^9*d^4*x + 2457600*a^4*b^3*c^10*d^4*x - 38400*a*b^8*c^8*d^4*x^2)) + (256*b*c^4*x)/(3*(a + b*x + c*x^2)^(1/2)*(4*b^9*c^2*d^4 - 64*a*b^7*c^3*d^4 + 1024*a^4*b*c^6*d^4 + 2048*a^4*c^7*d^4*x + 8*b^8*c^3*d^4*x + 384*a^2*b^5*c^4*d^4 - 1024*a^3*b^3*c^5*d^4 - 128*a*b^6*c^4*d^4*x + 768*a^2*b^4*c^5*d^4*x - 2048*a^3*b^2*c^6*d^4*x)) + (14336*b^2*c^8*x^2)/(3*(a + b*x + c*x^2)^(1/2)*(32*b^11*c^5*d^4 - 640*a*b^9*c^6*d^4 - 32768*a^5*b*c^10*d^4 - 65536*a^5*c^11*d^4*x + 64*b^10*c^6*d^4*x + 5120*a^2*b^7*c^7*d^4 - 20480*a^3*b^5*c^8*d^4 + 40960*a^4*b^3*c^9*d^4 - 1280*a*b^8*c^7*d^4*x + 10240*a^2*b^6*c^8*d^4*x - 40960*a^3*b^4*c^9*d^4*x + 81920*a^4*b^2*c^10*d^4*x)) - (38400*a^2*b^3*c^7)/((a + b*x + c*x^2)^(3/2)*(480*b^12*c^5*d^4 - 9600*a*b^10*c^6*d^4 + 1920*b^11*c^6*d^4*x + 76800*a^2*b^8*c^7*d^4 - 307200*a^3*b^6*c^8*d^4 + 614400*a^4*b^4*c^9*d^4 - 491520*a^5*b^2*c^10*d^4 - 1966080*a^5*c^12*d^4*x^2 + 1920*b^10*c^7*d^4*x^2 + 307200*a^2*b^6*c^9*d^4*x^2 - 1228800*a^3*b^4*c^10*d^4*x^2 + 2457600*a^4*b^2*c^11*d^4*x^2 - 38400*a*b^9*c^7*d^4*x - 1966080*a^5*b*c^11*d^4*x + 307200*a^2*b^7*c^8*d^4*x - 1228800*a^3*b^5*c^9*d^4*x + 2457600*a^4*b^3*c^10*d^4*x - 38400*a*b^8*c^8*d^4*x^2)) + (19200*a*b^4*c^7*x)/((a + b*x + c*x^2)^(3/2)*(480*b^12*c^5*d^4 - 9600*a*b^10*c^6*d^4 + 1920*b^11*c^6*d^4*x + 76800*a^2*b^8*c^7*d^4 - 307200*a^3*b^6*c^8*d^4 + 614400*a^4*b^4*c^9*d^4 - 491520*a^5*b^2*c^10*d^4 - 1966080*a^5*c^12*d^4*x^2 + 1920*b^10*c^7*d^4*x^2 + 307200*a^2*b^6*c^9*d^4*x^2 - 1228800*a^3*b^4*c^10*d^4*x^2 + 2457600*a^4*b^2*c^11*d^4*x^2 - 38400*a*b^9*c^7*d^4*x - 1966080*a^5*b*c^11*d^4*x + 307200*a^2*b^7*c^8*d^4*x - 1228800*a^3*b^5*c^9*d^4*x + 2457600*a^4*b^3*c^10*d^4*x - 38400*a*b^8*c^8*d^4*x^2)) - (57344*a*b*c^8*x)/(3*(a + b*x + c*x^2)^(1/2)*(32*b^11*c^5*d^4 - 640*a*b^9*c^6*d^4 - 32768*a^5*b*c^10*d^4 - 65536*a^5*c^11*d^4*x + 64*b^10*c^6*d^4*x + 5120*a^2*b^7*c^7*d^4 - 20480*a^3*b^5*c^8*d^4 + 40960*a^4*b^3*c^9*d^4 - 1280*a*b^8*c^7*d^4*x + 10240*a^2*b^6*c^8*d^4*x - 40960*a^3*b^4*c^9*d^4*x + 81920*a^4*b^2*c^10*d^4*x)) - (76800*a^2*b^2*c^8*x)/((a + b*x + c*x^2)^(3/2)*(480*b^12*c^5*d^4 - 9600*a*b^10*c^6*d^4 + 1920*b^11*c^6*d^4*x + 76800*a^2*b^8*c^7*d^4 - 307200*a^3*b^6*c^8*d^4 + 614400*a^4*b^4*c^9*d^4 - 491520*a^5*b^2*c^10*d^4 - 1966080*a^5*c^12*d^4*x^2 + 1920*b^10*c^7*d^4*x^2 + 307200*a^2*b^6*c^9*d^4*x^2 - 1228800*a^3*b^4*c^10*d^4*x^2 + 2457600*a^4*b^2*c^11*d^4*x^2 - 38400*a*b^9*c^7*d^4*x - 1966080*a^5*b*c^11*d^4*x + 307200*a^2*b^7*c^8*d^4*x - 1228800*a^3*b^5*c^9*d^4*x + 2457600*a^4*b^3*c^10*d^4*x - 38400*a*b^8*c^8*d^4*x^2)) - (128*a*b^2*c^4*x)/((a + b*x + c*x^2)^(3/2)*(8*b^10*c^2*d^4 - 128*a*b^8*c^3*d^4 + 32*b^9*c^3*d^4*x + 768*a^2*b^6*c^4*d^4 - 2048*a^3*b^4*c^5*d^4 + 2048*a^4*b^2*c^6*d^4 + 8192*a^4*c^8*d^4*x^2 + 32*b^8*c^4*d^4*x^2 + 3072*a^2*b^4*c^6*d^4*x^2 - 8192*a^3*b^2*c^7*d^4*x^2 - 512*a*b^7*c^4*d^4*x + 8192*a^4*b*c^7*d^4*x + 3072*a^2*b^5*c^5*d^4*x - 8192*a^3*b^3*c^6*d^4*x - 512*a*b^6*c^5*d^4*x^2))","B"
1260,0,-1,27,0.000000,"\text{Not used}","int(1/((a + b*x)*(a^2 + b^2*x^2 + 2*a*b*x + 1)^(1/2)),x)","\int \frac{1}{\left(a+b\,x\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2+1}} \,d x","Not used",1,"int(1/((a + b*x)*(a^2 + b^2*x^2 + 2*a*b*x + 1)^(1/2)), x)","F"
1261,1,39,55,0.061921,"\text{Not used}","int((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2),x)","\frac{{\left(b\,d+2\,c\,d\,x\right)}^{7/2}\,\left(44\,a\,c+7\,{\left(b+2\,c\,x\right)}^2-11\,b^2\right)}{308\,c^2\,d}","Not used",1,"((b*d + 2*c*d*x)^(7/2)*(44*a*c + 7*(b + 2*c*x)^2 - 11*b^2))/(308*c^2*d)","B"
1262,1,39,55,0.046402,"\text{Not used}","int((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2),x)","\frac{{\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,\left(36\,a\,c+5\,{\left(b+2\,c\,x\right)}^2-9\,b^2\right)}{180\,c^2\,d}","Not used",1,"((b*d + 2*c*d*x)^(5/2)*(36*a*c + 5*(b + 2*c*x)^2 - 9*b^2))/(180*c^2*d)","B"
1263,1,39,55,0.477789,"\text{Not used}","int((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2),x)","\frac{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,\left(28\,a\,c+3\,{\left(b+2\,c\,x\right)}^2-7\,b^2\right)}{84\,c^2\,d}","Not used",1,"((b*d + 2*c*d*x)^(3/2)*(28*a*c + 3*(b + 2*c*x)^2 - 7*b^2))/(84*c^2*d)","B"
1264,1,37,55,0.042436,"\text{Not used}","int((a + b*x + c*x^2)/(b*d + 2*c*d*x)^(1/2),x)","\frac{\sqrt{b\,d+2\,c\,d\,x}\,\left(20\,a\,c+{\left(b+2\,c\,x\right)}^2-5\,b^2\right)}{20\,c^2\,d}","Not used",1,"((b*d + 2*c*d*x)^(1/2)*(20*a*c + (b + 2*c*x)^2 - 5*b^2))/(20*c^2*d)","B"
1265,1,37,55,0.476821,"\text{Not used}","int((a + b*x + c*x^2)/(b*d + 2*c*d*x)^(3/2),x)","\frac{{\left(b+2\,c\,x\right)}^2-12\,a\,c+3\,b^2}{12\,c^2\,d\,\sqrt{b\,d+2\,c\,d\,x}}","Not used",1,"((b + 2*c*x)^2 - 12*a*c + 3*b^2)/(12*c^2*d*(b*d + 2*c*d*x)^(1/2))","B"
1266,1,37,55,0.479626,"\text{Not used}","int((a + b*x + c*x^2)/(b*d + 2*c*d*x)^(5/2),x)","\frac{3\,{\left(b+2\,c\,x\right)}^2-4\,a\,c+b^2}{12\,c^2\,d\,{\left(b\,d+2\,c\,d\,x\right)}^{3/2}}","Not used",1,"(3*(b + 2*c*x)^2 - 4*a*c + b^2)/(12*c^2*d*(b*d + 2*c*d*x)^(3/2))","B"
1267,1,37,55,0.038896,"\text{Not used}","int((a + b*x + c*x^2)/(b*d + 2*c*d*x)^(7/2),x)","-\frac{\frac{4\,a\,c}{5}+{\left(b+2\,c\,x\right)}^2-\frac{b^2}{5}}{4\,c^2\,d\,{\left(b\,d+2\,c\,d\,x\right)}^{5/2}}","Not used",1,"-((4*a*c)/5 + (b + 2*c*x)^2 - b^2/5)/(4*c^2*d*(b*d + 2*c*d*x)^(5/2))","B"
1268,1,39,55,0.468218,"\text{Not used}","int((a + b*x + c*x^2)/(b*d + 2*c*d*x)^(9/2),x)","-\frac{\frac{4\,a\,c}{7}+\frac{{\left(b+2\,c\,x\right)}^2}{3}-\frac{b^2}{7}}{4\,c^2\,d\,{\left(b\,d+2\,c\,d\,x\right)}^{7/2}}","Not used",1,"-((4*a*c)/7 + (b + 2*c*x)^2/3 - b^2/7)/(4*c^2*d*(b*d + 2*c*d*x)^(7/2))","B"
1269,1,99,88,0.515286,"\text{Not used}","int((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^2,x)","\frac{{\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,\left(45\,{\left(b\,d+2\,c\,d\,x\right)}^4+117\,b^4\,d^4-130\,b^2\,d^2\,{\left(b\,d+2\,c\,d\,x\right)}^2+1872\,a^2\,c^2\,d^4+520\,a\,c\,d^2\,{\left(b\,d+2\,c\,d\,x\right)}^2-936\,a\,b^2\,c\,d^4\right)}{9360\,c^3\,d^5}","Not used",1,"((b*d + 2*c*d*x)^(5/2)*(45*(b*d + 2*c*d*x)^4 + 117*b^4*d^4 - 130*b^2*d^2*(b*d + 2*c*d*x)^2 + 1872*a^2*c^2*d^4 + 520*a*c*d^2*(b*d + 2*c*d*x)^2 - 936*a*b^2*c*d^4))/(9360*c^3*d^5)","B"
1270,1,99,88,0.496044,"\text{Not used}","int((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^2,x)","\frac{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,\left(21\,{\left(b\,d+2\,c\,d\,x\right)}^4+77\,b^4\,d^4-66\,b^2\,d^2\,{\left(b\,d+2\,c\,d\,x\right)}^2+1232\,a^2\,c^2\,d^4+264\,a\,c\,d^2\,{\left(b\,d+2\,c\,d\,x\right)}^2-616\,a\,b^2\,c\,d^4\right)}{3696\,c^3\,d^5}","Not used",1,"((b*d + 2*c*d*x)^(3/2)*(21*(b*d + 2*c*d*x)^4 + 77*b^4*d^4 - 66*b^2*d^2*(b*d + 2*c*d*x)^2 + 1232*a^2*c^2*d^4 + 264*a*c*d^2*(b*d + 2*c*d*x)^2 - 616*a*b^2*c*d^4))/(3696*c^3*d^5)","B"
1271,1,99,88,0.490605,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(1/2),x)","\frac{\sqrt{b\,d+2\,c\,d\,x}\,\left(5\,{\left(b\,d+2\,c\,d\,x\right)}^4+45\,b^4\,d^4-18\,b^2\,d^2\,{\left(b\,d+2\,c\,d\,x\right)}^2+720\,a^2\,c^2\,d^4+72\,a\,c\,d^2\,{\left(b\,d+2\,c\,d\,x\right)}^2-360\,a\,b^2\,c\,d^4\right)}{720\,c^3\,d^5}","Not used",1,"((b*d + 2*c*d*x)^(1/2)*(5*(b*d + 2*c*d*x)^4 + 45*b^4*d^4 - 18*b^2*d^2*(b*d + 2*c*d*x)^2 + 720*a^2*c^2*d^4 + 72*a*c*d^2*(b*d + 2*c*d*x)^2 - 360*a*b^2*c*d^4))/(720*c^3*d^5)","B"
1272,1,99,88,0.493344,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(3/2),x)","\frac{3\,{\left(b\,d+2\,c\,d\,x\right)}^4-21\,b^4\,d^4-14\,b^2\,d^2\,{\left(b\,d+2\,c\,d\,x\right)}^2-336\,a^2\,c^2\,d^4+56\,a\,c\,d^2\,{\left(b\,d+2\,c\,d\,x\right)}^2+168\,a\,b^2\,c\,d^4}{336\,c^3\,d^5\,\sqrt{b\,d+2\,c\,d\,x}}","Not used",1,"(3*(b*d + 2*c*d*x)^4 - 21*b^4*d^4 - 14*b^2*d^2*(b*d + 2*c*d*x)^2 - 336*a^2*c^2*d^4 + 56*a*c*d^2*(b*d + 2*c*d*x)^2 + 168*a*b^2*c*d^4)/(336*c^3*d^5*(b*d + 2*c*d*x)^(1/2))","B"
1273,1,99,88,0.488375,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(5/2),x)","\frac{3\,{\left(b\,d+2\,c\,d\,x\right)}^4-5\,b^4\,d^4-30\,b^2\,d^2\,{\left(b\,d+2\,c\,d\,x\right)}^2-80\,a^2\,c^2\,d^4+120\,a\,c\,d^2\,{\left(b\,d+2\,c\,d\,x\right)}^2+40\,a\,b^2\,c\,d^4}{240\,c^3\,d^5\,{\left(b\,d+2\,c\,d\,x\right)}^{3/2}}","Not used",1,"(3*(b*d + 2*c*d*x)^4 - 5*b^4*d^4 - 30*b^2*d^2*(b*d + 2*c*d*x)^2 - 80*a^2*c^2*d^4 + 120*a*c*d^2*(b*d + 2*c*d*x)^2 + 40*a*b^2*c*d^4)/(240*c^3*d^5*(b*d + 2*c*d*x)^(3/2))","B"
1274,1,92,88,0.497583,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(7/2),x)","\frac{-3\,a^2\,c^2-6\,a\,b^2\,c-30\,a\,b\,c^2\,x-30\,a\,c^3\,x^2+2\,b^4+10\,b^3\,c\,x+15\,b^2\,c^2\,x^2+10\,b\,c^3\,x^3+5\,c^4\,x^4}{15\,c^3\,d\,{\left(b\,d+2\,c\,d\,x\right)}^{5/2}}","Not used",1,"(2*b^4 - 3*a^2*c^2 + 5*c^4*x^4 - 30*a*c^3*x^2 + 10*b*c^3*x^3 + 15*b^2*c^2*x^2 - 6*a*b^2*c + 10*b^3*c*x - 30*a*b*c^2*x)/(15*c^3*d*(b*d + 2*c*d*x)^(5/2))","B"
1275,1,92,88,0.061267,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(9/2),x)","\frac{-3\,a^2\,c^2-2\,a\,b^2\,c-14\,a\,b\,c^2\,x-14\,a\,c^3\,x^2+2\,b^4+14\,b^3\,c\,x+35\,b^2\,c^2\,x^2+42\,b\,c^3\,x^3+21\,c^4\,x^4}{21\,c^3\,d\,{\left(b\,d+2\,c\,d\,x\right)}^{7/2}}","Not used",1,"(2*b^4 - 3*a^2*c^2 + 21*c^4*x^4 - 14*a*c^3*x^2 + 42*b*c^3*x^3 + 35*b^2*c^2*x^2 - 2*a*b^2*c + 14*b^3*c*x - 14*a*b*c^2*x)/(21*c^3*d*(b*d + 2*c*d*x)^(7/2))","B"
1276,1,67,88,0.057694,"\text{Not used}","int((a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(11/2),x)","-\frac{{\left(b+2\,c\,x\right)}^4+\left(\frac{8\,a\,c}{5}-\frac{2\,b^2}{5}\right)\,{\left(b+2\,c\,x\right)}^2+\frac{b^4}{9}+\frac{16\,a^2\,c^2}{9}-\frac{8\,a\,b^2\,c}{9}}{16\,c^3\,d\,{\left(b\,d+2\,c\,d\,x\right)}^{9/2}}","Not used",1,"-((b + 2*c*x)^4 + ((8*a*c)/5 - (2*b^2)/5)*(b + 2*c*x)^2 + b^4/9 + (16*a^2*c^2)/9 - (8*a*b^2*c)/9)/(16*c^3*d*(b*d + 2*c*d*x)^(9/2))","B"
1277,1,111,121,0.499649,"\text{Not used}","int((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^3,x)","\frac{{\left(b\,d+2\,c\,d\,x\right)}^{15/2}}{960\,c^4\,d^7}+\frac{3\,{\left(b\,d+2\,c\,d\,x\right)}^{11/2}\,\left(4\,a\,c-b^2\right)}{704\,c^4\,d^5}+\frac{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,{\left(4\,a\,c-b^2\right)}^3}{192\,c^4\,d}+\frac{3\,{\left(b\,d+2\,c\,d\,x\right)}^{7/2}\,{\left(4\,a\,c-b^2\right)}^2}{448\,c^4\,d^3}","Not used",1,"(b*d + 2*c*d*x)^(15/2)/(960*c^4*d^7) + (3*(b*d + 2*c*d*x)^(11/2)*(4*a*c - b^2))/(704*c^4*d^5) + ((b*d + 2*c*d*x)^(3/2)*(4*a*c - b^2)^3)/(192*c^4*d) + (3*(b*d + 2*c*d*x)^(7/2)*(4*a*c - b^2)^2)/(448*c^4*d^3)","B"
1278,1,111,121,0.068046,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(1/2),x)","\frac{{\left(b\,d+2\,c\,d\,x\right)}^{13/2}}{832\,c^4\,d^7}+\frac{{\left(b\,d+2\,c\,d\,x\right)}^{9/2}\,\left(4\,a\,c-b^2\right)}{192\,c^4\,d^5}+\frac{\sqrt{b\,d+2\,c\,d\,x}\,{\left(4\,a\,c-b^2\right)}^3}{64\,c^4\,d}+\frac{3\,{\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,{\left(4\,a\,c-b^2\right)}^2}{320\,c^4\,d^3}","Not used",1,"(b*d + 2*c*d*x)^(13/2)/(832*c^4*d^7) + ((b*d + 2*c*d*x)^(9/2)*(4*a*c - b^2))/(192*c^4*d^5) + ((b*d + 2*c*d*x)^(1/2)*(4*a*c - b^2)^3)/(64*c^4*d) + (3*(b*d + 2*c*d*x)^(5/2)*(4*a*c - b^2)^2)/(320*c^4*d^3)","B"
1279,1,129,121,0.503505,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(3/2),x)","\frac{{\left(b\,d+2\,c\,d\,x\right)}^{11/2}}{704\,c^4\,d^7}+\frac{3\,{\left(b\,d+2\,c\,d\,x\right)}^{7/2}\,\left(4\,a\,c-b^2\right)}{448\,c^4\,d^5}+\frac{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,{\left(4\,a\,c-b^2\right)}^2}{64\,c^4\,d^3}+\frac{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}{64\,c^4\,d\,\sqrt{b\,d+2\,c\,d\,x}}","Not used",1,"(b*d + 2*c*d*x)^(11/2)/(704*c^4*d^7) + (3*(b*d + 2*c*d*x)^(7/2)*(4*a*c - b^2))/(448*c^4*d^5) + ((b*d + 2*c*d*x)^(3/2)*(4*a*c - b^2)^2)/(64*c^4*d^3) + (b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)/(64*c^4*d*(b*d + 2*c*d*x)^(1/2))","B"
1280,1,131,121,0.068494,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(5/2),x)","\frac{{\left(b\,d+2\,c\,d\,x\right)}^{9/2}}{576\,c^4\,d^7}+\frac{3\,{\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,\left(4\,a\,c-b^2\right)}{320\,c^4\,d^5}+\frac{-\frac{64\,a^3\,c^3}{3}+16\,a^2\,b^2\,c^2-4\,a\,b^4\,c+\frac{b^6}{3}}{64\,c^4\,d\,{\left(b\,d+2\,c\,d\,x\right)}^{3/2}}+\frac{3\,\sqrt{b\,d+2\,c\,d\,x}\,{\left(4\,a\,c-b^2\right)}^2}{64\,c^4\,d^3}","Not used",1,"(b*d + 2*c*d*x)^(9/2)/(576*c^4*d^7) + (3*(b*d + 2*c*d*x)^(5/2)*(4*a*c - b^2))/(320*c^4*d^5) + (b^6/3 - (64*a^3*c^3)/3 + 16*a^2*b^2*c^2 - 4*a*b^4*c)/(64*c^4*d*(b*d + 2*c*d*x)^(3/2)) + (3*(b*d + 2*c*d*x)^(1/2)*(4*a*c - b^2)^2)/(64*c^4*d^3)","B"
1281,1,170,121,0.518070,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(7/2),x)","-\frac{7\,a^3\,c^3+21\,a^2\,b^2\,c^2+105\,a^2\,b\,c^3\,x+105\,a^2\,c^4\,x^2-14\,a\,b^4\,c-70\,a\,b^3\,c^2\,x-105\,a\,b^2\,c^3\,x^2-70\,a\,b\,c^4\,x^3-35\,a\,c^5\,x^4+2\,b^6+10\,b^5\,c\,x+15\,b^4\,c^2\,x^2+5\,b^3\,c^3\,x^3-10\,b^2\,c^4\,x^4-15\,b\,c^5\,x^5-5\,c^6\,x^6}{35\,c^4\,d\,{\left(b\,d+2\,c\,d\,x\right)}^{5/2}}","Not used",1,"-(2*b^6 + 7*a^3*c^3 - 5*c^6*x^6 - 35*a*c^5*x^4 - 15*b*c^5*x^5 + 21*a^2*b^2*c^2 + 105*a^2*c^4*x^2 + 15*b^4*c^2*x^2 + 5*b^3*c^3*x^3 - 10*b^2*c^4*x^4 - 14*a*b^4*c + 10*b^5*c*x - 105*a*b^2*c^3*x^2 - 70*a*b^3*c^2*x + 105*a^2*b*c^3*x - 70*a*b*c^4*x^3)/(35*c^4*d*(b*d + 2*c*d*x)^(5/2))","B"
1282,1,159,121,0.507855,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(9/2),x)","-\frac{5\,a^3\,c^3+5\,a^2\,b^2\,c^2+35\,a^2\,b\,c^3\,x+35\,a^2\,c^4\,x^2-10\,a\,b^4\,c-70\,a\,b^3\,c^2\,x-175\,a\,b^2\,c^3\,x^2-210\,a\,b\,c^4\,x^3-105\,a\,c^5\,x^4+2\,b^6+14\,b^5\,c\,x+35\,b^4\,c^2\,x^2+35\,b^3\,c^3\,x^3-21\,b\,c^5\,x^5-7\,c^6\,x^6}{35\,c^4\,d\,{\left(b\,d+2\,c\,d\,x\right)}^{7/2}}","Not used",1,"-(2*b^6 + 5*a^3*c^3 - 7*c^6*x^6 - 105*a*c^5*x^4 - 21*b*c^5*x^5 + 5*a^2*b^2*c^2 + 35*a^2*c^4*x^2 + 35*b^4*c^2*x^2 + 35*b^3*c^3*x^3 - 10*a*b^4*c + 14*b^5*c*x - 175*a*b^2*c^3*x^2 - 70*a*b^3*c^2*x + 35*a^2*b*c^3*x - 210*a*b*c^4*x^3)/(35*c^4*d*(b*d + 2*c*d*x)^(7/2))","B"
1283,1,147,121,0.514290,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(11/2),x)","\frac{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}}{192\,c^4\,d^7}-\frac{{\left(b\,d+2\,c\,d\,x\right)}^2\,\left(\frac{48\,a^2\,c^2\,d^2}{5}-\frac{24\,a\,b^2\,c\,d^2}{5}+\frac{3\,b^4\,d^2}{5}\right)+{\left(b\,d+2\,c\,d\,x\right)}^4\,\left(12\,a\,c-3\,b^2\right)-\frac{b^6\,d^4}{9}+\frac{64\,a^3\,c^3\,d^4}{9}-\frac{16\,a^2\,b^2\,c^2\,d^4}{3}+\frac{4\,a\,b^4\,c\,d^4}{3}}{64\,c^4\,d^5\,{\left(b\,d+2\,c\,d\,x\right)}^{9/2}}","Not used",1,"(b*d + 2*c*d*x)^(3/2)/(192*c^4*d^7) - ((b*d + 2*c*d*x)^2*((3*b^4*d^2)/5 + (48*a^2*c^2*d^2)/5 - (24*a*b^2*c*d^2)/5) + (b*d + 2*c*d*x)^4*(12*a*c - 3*b^2) - (b^6*d^4)/9 + (64*a^3*c^3*d^4)/9 - (16*a^2*b^2*c^2*d^4)/3 + (4*a*b^4*c*d^4)/3)/(64*c^4*d^5*(b*d + 2*c*d*x)^(9/2))","B"
1284,1,147,121,0.079319,"\text{Not used}","int((a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(13/2),x)","\frac{\sqrt{b\,d+2\,c\,d\,x}}{64\,c^4\,d^7}-\frac{{\left(b\,d+2\,c\,d\,x\right)}^2\,\left(\frac{48\,a^2\,c^2\,d^2}{7}-\frac{24\,a\,b^2\,c\,d^2}{7}+\frac{3\,b^4\,d^2}{7}\right)+{\left(b\,d+2\,c\,d\,x\right)}^4\,\left(4\,a\,c-b^2\right)-\frac{b^6\,d^4}{11}+\frac{64\,a^3\,c^3\,d^4}{11}-\frac{48\,a^2\,b^2\,c^2\,d^4}{11}+\frac{12\,a\,b^4\,c\,d^4}{11}}{64\,c^4\,d^5\,{\left(b\,d+2\,c\,d\,x\right)}^{11/2}}","Not used",1,"(b*d + 2*c*d*x)^(1/2)/(64*c^4*d^7) - ((b*d + 2*c*d*x)^2*((3*b^4*d^2)/7 + (48*a^2*c^2*d^2)/7 - (24*a*b^2*c*d^2)/7) + (b*d + 2*c*d*x)^4*(4*a*c - b^2) - (b^6*d^4)/11 + (64*a^3*c^3*d^4)/11 - (48*a^2*b^2*c^2*d^4)/11 + (12*a*b^4*c*d^4)/11)/(64*c^4*d^5*(b*d + 2*c*d*x)^(11/2))","B"
1285,1,240,175,0.649801,"\text{Not used}","int((b*d + 2*c*d*x)^(11/2)/(a + b*x + c*x^2),x)","\frac{4\,d\,{\left(b\,d+2\,c\,d\,x\right)}^{9/2}}{9}-\frac{4\,d^3\,{\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,\left(4\,a\,c-b^2\right)}{5}+4\,d^5\,\sqrt{b\,d+2\,c\,d\,x}\,{\left(4\,a\,c-b^2\right)}^2-2\,d^{11/2}\,\mathrm{atan}\left(\frac{b^4\,\sqrt{b\,d+2\,c\,d\,x}+16\,a^2\,c^2\,\sqrt{b\,d+2\,c\,d\,x}-8\,a\,b^2\,c\,\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{9/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{9/4}+d^{11/2}\,\mathrm{atan}\left(\frac{b^4\,\sqrt{b\,d+2\,c\,d\,x}\,1{}\mathrm{i}+a^2\,c^2\,\sqrt{b\,d+2\,c\,d\,x}\,16{}\mathrm{i}-a\,b^2\,c\,\sqrt{b\,d+2\,c\,d\,x}\,8{}\mathrm{i}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{9/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{9/4}\,2{}\mathrm{i}","Not used",1,"(4*d*(b*d + 2*c*d*x)^(9/2))/9 - (4*d^3*(b*d + 2*c*d*x)^(5/2)*(4*a*c - b^2))/5 + 4*d^5*(b*d + 2*c*d*x)^(1/2)*(4*a*c - b^2)^2 - 2*d^(11/2)*atan((b^4*(b*d + 2*c*d*x)^(1/2) + 16*a^2*c^2*(b*d + 2*c*d*x)^(1/2) - 8*a*b^2*c*(b*d + 2*c*d*x)^(1/2))/(d^(1/2)*(b^2 - 4*a*c)^(9/4)))*(b^2 - 4*a*c)^(9/4) + d^(11/2)*atan((b^4*(b*d + 2*c*d*x)^(1/2)*1i + a^2*c^2*(b*d + 2*c*d*x)^(1/2)*16i - a*b^2*c*(b*d + 2*c*d*x)^(1/2)*8i)/(d^(1/2)*(b^2 - 4*a*c)^(9/4)))*(b^2 - 4*a*c)^(9/4)*2i","B"
1286,1,168,147,0.582096,"\text{Not used}","int((b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2),x)","\frac{4\,d\,{\left(b\,d+2\,c\,d\,x\right)}^{7/2}}{7}-\frac{4\,d^3\,{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,\left(4\,a\,c-b^2\right)}{3}+2\,d^{9/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,{\left(b^2-4\,a\,c\right)}^{7/4}}{\sqrt{d}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}\right)\,{\left(b^2-4\,a\,c\right)}^{7/4}+d^{9/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,{\left(b^2-4\,a\,c\right)}^{7/4}\,1{}\mathrm{i}}{\sqrt{d}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}\right)\,{\left(b^2-4\,a\,c\right)}^{7/4}\,2{}\mathrm{i}","Not used",1,"(4*d*(b*d + 2*c*d*x)^(7/2))/7 - (4*d^3*(b*d + 2*c*d*x)^(3/2)*(4*a*c - b^2))/3 + 2*d^(9/2)*atan(((b*d + 2*c*d*x)^(1/2)*(b^2 - 4*a*c)^(7/4))/(d^(1/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))*(b^2 - 4*a*c)^(7/4) + d^(9/2)*atan(((b*d + 2*c*d*x)^(1/2)*(b^2 - 4*a*c)^(7/4)*1i)/(d^(1/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))*(b^2 - 4*a*c)^(7/4)*2i","B"
1287,1,167,145,0.636725,"\text{Not used}","int((b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2),x)","\frac{4\,d\,{\left(b\,d+2\,c\,d\,x\right)}^{5/2}}{5}-4\,d^3\,\sqrt{b\,d+2\,c\,d\,x}\,\left(4\,a\,c-b^2\right)-2\,d^{7/2}\,\mathrm{atan}\left(\frac{b^2\,\sqrt{b\,d+2\,c\,d\,x}-4\,a\,c\,\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{5/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{5/4}+d^{7/2}\,\mathrm{atan}\left(\frac{b^2\,\sqrt{b\,d+2\,c\,d\,x}\,1{}\mathrm{i}-a\,c\,\sqrt{b\,d+2\,c\,d\,x}\,4{}\mathrm{i}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{5/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{5/4}\,2{}\mathrm{i}","Not used",1,"(4*d*(b*d + 2*c*d*x)^(5/2))/5 - 4*d^3*(b*d + 2*c*d*x)^(1/2)*(4*a*c - b^2) - 2*d^(7/2)*atan((b^2*(b*d + 2*c*d*x)^(1/2) - 4*a*c*(b*d + 2*c*d*x)^(1/2))/(d^(1/2)*(b^2 - 4*a*c)^(5/4)))*(b^2 - 4*a*c)^(5/4) + d^(7/2)*atan((b^2*(b*d + 2*c*d*x)^(1/2)*1i - a*c*(b*d + 2*c*d*x)^(1/2)*4i)/(d^(1/2)*(b^2 - 4*a*c)^(5/4)))*(b^2 - 4*a*c)^(5/4)*2i","B"
1288,1,97,119,0.128516,"\text{Not used}","int((b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2),x)","\frac{4\,d\,{\left(b\,d+2\,c\,d\,x\right)}^{3/2}}{3}+2\,d^{5/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{3/4}-2\,d^{5/2}\,\mathrm{atanh}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{3/4}","Not used",1,"(4*d*(b*d + 2*c*d*x)^(3/2))/3 + 2*d^(5/2)*atan((b*d + 2*c*d*x)^(1/2)/(d^(1/2)*(b^2 - 4*a*c)^(1/4)))*(b^2 - 4*a*c)^(3/4) - 2*d^(5/2)*atanh((b*d + 2*c*d*x)^(1/2)/(d^(1/2)*(b^2 - 4*a*c)^(1/4)))*(b^2 - 4*a*c)^(3/4)","B"
1289,1,97,117,0.588091,"\text{Not used}","int((b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2),x)","4\,d\,\sqrt{b\,d+2\,c\,d\,x}-2\,d^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{1/4}-2\,d^{3/2}\,\mathrm{atanh}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{1/4}","Not used",1,"4*d*(b*d + 2*c*d*x)^(1/2) - 2*d^(3/2)*atan((b*d + 2*c*d*x)^(1/2)/(d^(1/2)*(b^2 - 4*a*c)^(1/4)))*(b^2 - 4*a*c)^(1/4) - 2*d^(3/2)*atanh((b*d + 2*c*d*x)^(1/2)/(d^(1/2)*(b^2 - 4*a*c)^(1/4)))*(b^2 - 4*a*c)^(1/4)","B"
1290,1,83,101,0.106577,"\text{Not used}","int((b*d + 2*c*d*x)^(1/2)/(a + b*x + c*x^2),x)","\frac{2\,\sqrt{d}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)}{{\left(b^2-4\,a\,c\right)}^{1/4}}-\frac{2\,\sqrt{d}\,\mathrm{atanh}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)}{{\left(b^2-4\,a\,c\right)}^{1/4}}","Not used",1,"(2*d^(1/2)*atan((b*d + 2*c*d*x)^(1/2)/(d^(1/2)*(b^2 - 4*a*c)^(1/4))))/(b^2 - 4*a*c)^(1/4) - (2*d^(1/2)*atanh((b*d + 2*c*d*x)^(1/2)/(d^(1/2)*(b^2 - 4*a*c)^(1/4))))/(b^2 - 4*a*c)^(1/4)","B"
1291,1,161,101,0.541917,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)),x)","-\frac{2\,\mathrm{atan}\left(\frac{128\,d^{3/2}\,\sqrt{b\,d+2\,c\,d\,x}}{\left(\frac{128\,b^2\,d^2}{{\left(b^2-4\,a\,c\right)}^{3/2}}-\frac{512\,a\,c\,d^2}{{\left(b^2-4\,a\,c\right)}^{3/2}}\right)\,{\left(b^2-4\,a\,c\right)}^{3/4}}\right)}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{3/4}}-\frac{2\,\mathrm{atanh}\left(\frac{128\,d^{3/2}\,\sqrt{b\,d+2\,c\,d\,x}}{\left(\frac{128\,b^2\,d^2}{{\left(b^2-4\,a\,c\right)}^{3/2}}-\frac{512\,a\,c\,d^2}{{\left(b^2-4\,a\,c\right)}^{3/2}}\right)\,{\left(b^2-4\,a\,c\right)}^{3/4}}\right)}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{3/4}}","Not used",1,"- (2*atan((128*d^(3/2)*(b*d + 2*c*d*x)^(1/2))/(((128*b^2*d^2)/(b^2 - 4*a*c)^(3/2) - (512*a*c*d^2)/(b^2 - 4*a*c)^(3/2))*(b^2 - 4*a*c)^(3/4))))/(d^(1/2)*(b^2 - 4*a*c)^(3/4)) - (2*atanh((128*d^(3/2)*(b*d + 2*c*d*x)^(1/2))/(((128*b^2*d^2)/(b^2 - 4*a*c)^(3/2) - (512*a*c*d^2)/(b^2 - 4*a*c)^(3/2))*(b^2 - 4*a*c)^(3/4))))/(d^(1/2)*(b^2 - 4*a*c)^(3/4))","B"
1292,1,153,129,0.606780,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)),x)","\frac{4}{\sqrt{b\,d+2\,c\,d\,x}\,\left(b^2\,d-4\,a\,c\,d\right)}+\frac{2\,\mathrm{atan}\left(\frac{b^2\,\sqrt{b\,d+2\,c\,d\,x}-4\,a\,c\,\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{5/4}}\right)}{d^{3/2}\,{\left(b^2-4\,a\,c\right)}^{5/4}}+\frac{\mathrm{atan}\left(\frac{b^2\,\sqrt{b\,d+2\,c\,d\,x}\,1{}\mathrm{i}-a\,c\,\sqrt{b\,d+2\,c\,d\,x}\,4{}\mathrm{i}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{5/4}}\right)\,2{}\mathrm{i}}{d^{3/2}\,{\left(b^2-4\,a\,c\right)}^{5/4}}","Not used",1,"4/((b*d + 2*c*d*x)^(1/2)*(b^2*d - 4*a*c*d)) + (2*atan((b^2*(b*d + 2*c*d*x)^(1/2) - 4*a*c*(b*d + 2*c*d*x)^(1/2))/(d^(1/2)*(b^2 - 4*a*c)^(5/4))))/(d^(3/2)*(b^2 - 4*a*c)^(5/4)) + (atan((b^2*(b*d + 2*c*d*x)^(1/2)*1i - a*c*(b*d + 2*c*d*x)^(1/2)*4i)/(d^(1/2)*(b^2 - 4*a*c)^(5/4)))*2i)/(d^(3/2)*(b^2 - 4*a*c)^(5/4))","B"
1293,1,1345,131,0.701567,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)),x)","\frac{4}{3\,{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,\left(b^2\,d-4\,a\,c\,d\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(-4096\,a^3\,c^3\,d^3+3072\,a^2\,b^2\,c^2\,d^3-768\,a\,b^4\,c\,d^3+64\,b^6\,d^3\right)+\frac{-65536\,a^5\,c^5\,d^6+81920\,a^4\,b^2\,c^4\,d^6-40960\,a^3\,b^4\,c^3\,d^6+10240\,a^2\,b^6\,c^2\,d^6-1280\,a\,b^8\,c\,d^6+64\,b^{10}\,d^6}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}\right)\,1{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}+\frac{\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(-4096\,a^3\,c^3\,d^3+3072\,a^2\,b^2\,c^2\,d^3-768\,a\,b^4\,c\,d^3+64\,b^6\,d^3\right)-\frac{-65536\,a^5\,c^5\,d^6+81920\,a^4\,b^2\,c^4\,d^6-40960\,a^3\,b^4\,c^3\,d^6+10240\,a^2\,b^6\,c^2\,d^6-1280\,a\,b^8\,c\,d^6+64\,b^{10}\,d^6}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}\right)\,1{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}}{\frac{\sqrt{b\,d+2\,c\,d\,x}\,\left(-4096\,a^3\,c^3\,d^3+3072\,a^2\,b^2\,c^2\,d^3-768\,a\,b^4\,c\,d^3+64\,b^6\,d^3\right)+\frac{-65536\,a^5\,c^5\,d^6+81920\,a^4\,b^2\,c^4\,d^6-40960\,a^3\,b^4\,c^3\,d^6+10240\,a^2\,b^6\,c^2\,d^6-1280\,a\,b^8\,c\,d^6+64\,b^{10}\,d^6}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}-\frac{\sqrt{b\,d+2\,c\,d\,x}\,\left(-4096\,a^3\,c^3\,d^3+3072\,a^2\,b^2\,c^2\,d^3-768\,a\,b^4\,c\,d^3+64\,b^6\,d^3\right)-\frac{-65536\,a^5\,c^5\,d^6+81920\,a^4\,b^2\,c^4\,d^6-40960\,a^3\,b^4\,c^3\,d^6+10240\,a^2\,b^6\,c^2\,d^6-1280\,a\,b^8\,c\,d^6+64\,b^{10}\,d^6}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}}\right)\,2{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}-\frac{2\,\mathrm{atan}\left(\frac{\frac{\sqrt{b\,d+2\,c\,d\,x}\,\left(-4096\,a^3\,c^3\,d^3+3072\,a^2\,b^2\,c^2\,d^3-768\,a\,b^4\,c\,d^3+64\,b^6\,d^3\right)-\frac{\left(-65536\,a^5\,c^5\,d^6+81920\,a^4\,b^2\,c^4\,d^6-40960\,a^3\,b^4\,c^3\,d^6+10240\,a^2\,b^6\,c^2\,d^6-1280\,a\,b^8\,c\,d^6+64\,b^{10}\,d^6\right)\,1{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}+\frac{\sqrt{b\,d+2\,c\,d\,x}\,\left(-4096\,a^3\,c^3\,d^3+3072\,a^2\,b^2\,c^2\,d^3-768\,a\,b^4\,c\,d^3+64\,b^6\,d^3\right)+\frac{\left(-65536\,a^5\,c^5\,d^6+81920\,a^4\,b^2\,c^4\,d^6-40960\,a^3\,b^4\,c^3\,d^6+10240\,a^2\,b^6\,c^2\,d^6-1280\,a\,b^8\,c\,d^6+64\,b^{10}\,d^6\right)\,1{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}}{\frac{\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(-4096\,a^3\,c^3\,d^3+3072\,a^2\,b^2\,c^2\,d^3-768\,a\,b^4\,c\,d^3+64\,b^6\,d^3\right)-\frac{\left(-65536\,a^5\,c^5\,d^6+81920\,a^4\,b^2\,c^4\,d^6-40960\,a^3\,b^4\,c^3\,d^6+10240\,a^2\,b^6\,c^2\,d^6-1280\,a\,b^8\,c\,d^6+64\,b^{10}\,d^6\right)\,1{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}\right)\,1{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}-\frac{\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(-4096\,a^3\,c^3\,d^3+3072\,a^2\,b^2\,c^2\,d^3-768\,a\,b^4\,c\,d^3+64\,b^6\,d^3\right)+\frac{\left(-65536\,a^5\,c^5\,d^6+81920\,a^4\,b^2\,c^4\,d^6-40960\,a^3\,b^4\,c^3\,d^6+10240\,a^2\,b^6\,c^2\,d^6-1280\,a\,b^8\,c\,d^6+64\,b^{10}\,d^6\right)\,1{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}\right)\,1{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}}\right)}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{7/4}}","Not used",1,"4/(3*(b*d + 2*c*d*x)^(3/2)*(b^2*d - 4*a*c*d)) + (atan(((((b*d + 2*c*d*x)^(1/2)*(64*b^6*d^3 - 4096*a^3*c^3*d^3 + 3072*a^2*b^2*c^2*d^3 - 768*a*b^4*c*d^3) + (64*b^10*d^6 - 65536*a^5*c^5*d^6 + 10240*a^2*b^6*c^2*d^6 - 40960*a^3*b^4*c^3*d^6 + 81920*a^4*b^2*c^4*d^6 - 1280*a*b^8*c*d^6)/(d^(5/2)*(b^2 - 4*a*c)^(7/4)))*1i)/(d^(5/2)*(b^2 - 4*a*c)^(7/4)) + (((b*d + 2*c*d*x)^(1/2)*(64*b^6*d^3 - 4096*a^3*c^3*d^3 + 3072*a^2*b^2*c^2*d^3 - 768*a*b^4*c*d^3) - (64*b^10*d^6 - 65536*a^5*c^5*d^6 + 10240*a^2*b^6*c^2*d^6 - 40960*a^3*b^4*c^3*d^6 + 81920*a^4*b^2*c^4*d^6 - 1280*a*b^8*c*d^6)/(d^(5/2)*(b^2 - 4*a*c)^(7/4)))*1i)/(d^(5/2)*(b^2 - 4*a*c)^(7/4)))/(((b*d + 2*c*d*x)^(1/2)*(64*b^6*d^3 - 4096*a^3*c^3*d^3 + 3072*a^2*b^2*c^2*d^3 - 768*a*b^4*c*d^3) + (64*b^10*d^6 - 65536*a^5*c^5*d^6 + 10240*a^2*b^6*c^2*d^6 - 40960*a^3*b^4*c^3*d^6 + 81920*a^4*b^2*c^4*d^6 - 1280*a*b^8*c*d^6)/(d^(5/2)*(b^2 - 4*a*c)^(7/4)))/(d^(5/2)*(b^2 - 4*a*c)^(7/4)) - ((b*d + 2*c*d*x)^(1/2)*(64*b^6*d^3 - 4096*a^3*c^3*d^3 + 3072*a^2*b^2*c^2*d^3 - 768*a*b^4*c*d^3) - (64*b^10*d^6 - 65536*a^5*c^5*d^6 + 10240*a^2*b^6*c^2*d^6 - 40960*a^3*b^4*c^3*d^6 + 81920*a^4*b^2*c^4*d^6 - 1280*a*b^8*c*d^6)/(d^(5/2)*(b^2 - 4*a*c)^(7/4)))/(d^(5/2)*(b^2 - 4*a*c)^(7/4))))*2i)/(d^(5/2)*(b^2 - 4*a*c)^(7/4)) - (2*atan((((b*d + 2*c*d*x)^(1/2)*(64*b^6*d^3 - 4096*a^3*c^3*d^3 + 3072*a^2*b^2*c^2*d^3 - 768*a*b^4*c*d^3) - ((64*b^10*d^6 - 65536*a^5*c^5*d^6 + 10240*a^2*b^6*c^2*d^6 - 40960*a^3*b^4*c^3*d^6 + 81920*a^4*b^2*c^4*d^6 - 1280*a*b^8*c*d^6)*1i)/(d^(5/2)*(b^2 - 4*a*c)^(7/4)))/(d^(5/2)*(b^2 - 4*a*c)^(7/4)) + ((b*d + 2*c*d*x)^(1/2)*(64*b^6*d^3 - 4096*a^3*c^3*d^3 + 3072*a^2*b^2*c^2*d^3 - 768*a*b^4*c*d^3) + ((64*b^10*d^6 - 65536*a^5*c^5*d^6 + 10240*a^2*b^6*c^2*d^6 - 40960*a^3*b^4*c^3*d^6 + 81920*a^4*b^2*c^4*d^6 - 1280*a*b^8*c*d^6)*1i)/(d^(5/2)*(b^2 - 4*a*c)^(7/4)))/(d^(5/2)*(b^2 - 4*a*c)^(7/4)))/((((b*d + 2*c*d*x)^(1/2)*(64*b^6*d^3 - 4096*a^3*c^3*d^3 + 3072*a^2*b^2*c^2*d^3 - 768*a*b^4*c*d^3) - ((64*b^10*d^6 - 65536*a^5*c^5*d^6 + 10240*a^2*b^6*c^2*d^6 - 40960*a^3*b^4*c^3*d^6 + 81920*a^4*b^2*c^4*d^6 - 1280*a*b^8*c*d^6)*1i)/(d^(5/2)*(b^2 - 4*a*c)^(7/4)))*1i)/(d^(5/2)*(b^2 - 4*a*c)^(7/4)) - (((b*d + 2*c*d*x)^(1/2)*(64*b^6*d^3 - 4096*a^3*c^3*d^3 + 3072*a^2*b^2*c^2*d^3 - 768*a*b^4*c*d^3) + ((64*b^10*d^6 - 65536*a^5*c^5*d^6 + 10240*a^2*b^6*c^2*d^6 - 40960*a^3*b^4*c^3*d^6 + 81920*a^4*b^2*c^4*d^6 - 1280*a*b^8*c*d^6)*1i)/(d^(5/2)*(b^2 - 4*a*c)^(7/4)))*1i)/(d^(5/2)*(b^2 - 4*a*c)^(7/4)))))/(d^(5/2)*(b^2 - 4*a*c)^(7/4))","B"
1294,1,230,159,0.259414,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)),x)","\frac{\frac{4}{5\,\left(b^2\,d-4\,a\,c\,d\right)}+\frac{4\,{\left(b\,d+2\,c\,d\,x\right)}^2}{d\,{\left(b^2\,d-4\,a\,c\,d\right)}^2}}{{\left(b\,d+2\,c\,d\,x\right)}^{5/2}}+\frac{2\,\mathrm{atan}\left(\frac{b^4\,\sqrt{b\,d+2\,c\,d\,x}+16\,a^2\,c^2\,\sqrt{b\,d+2\,c\,d\,x}-8\,a\,b^2\,c\,\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{9/4}}\right)}{d^{7/2}\,{\left(b^2-4\,a\,c\right)}^{9/4}}+\frac{\mathrm{atan}\left(\frac{b^4\,\sqrt{b\,d+2\,c\,d\,x}\,1{}\mathrm{i}+a^2\,c^2\,\sqrt{b\,d+2\,c\,d\,x}\,16{}\mathrm{i}-a\,b^2\,c\,\sqrt{b\,d+2\,c\,d\,x}\,8{}\mathrm{i}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{9/4}}\right)\,2{}\mathrm{i}}{d^{7/2}\,{\left(b^2-4\,a\,c\right)}^{9/4}}","Not used",1,"(4/(5*(b^2*d - 4*a*c*d)) + (4*(b*d + 2*c*d*x)^2)/(d*(b^2*d - 4*a*c*d)^2))/(b*d + 2*c*d*x)^(5/2) + (2*atan((b^4*(b*d + 2*c*d*x)^(1/2) + 16*a^2*c^2*(b*d + 2*c*d*x)^(1/2) - 8*a*b^2*c*(b*d + 2*c*d*x)^(1/2))/(d^(1/2)*(b^2 - 4*a*c)^(9/4))))/(d^(7/2)*(b^2 - 4*a*c)^(9/4)) + (atan((b^4*(b*d + 2*c*d*x)^(1/2)*1i + a^2*c^2*(b*d + 2*c*d*x)^(1/2)*16i - a*b^2*c*(b*d + 2*c*d*x)^(1/2)*8i)/(d^(1/2)*(b^2 - 4*a*c)^(9/4)))*2i)/(d^(7/2)*(b^2 - 4*a*c)^(9/4))","B"
1295,1,1060,210,0.692146,"\text{Not used}","int((b*d + 2*c*d*x)^(15/2)/(a + b*x + c*x^2)^2,x)","\frac{16\,c\,d^3\,{\left(b\,d+2\,c\,d\,x\right)}^{9/2}}{9}-\frac{\sqrt{b\,d+2\,c\,d\,x}\,\left(-256\,a^3\,c^4\,d^9+192\,a^2\,b^2\,c^3\,d^9-48\,a\,b^4\,c^2\,d^9+4\,b^6\,c\,d^9\right)}{{\left(b\,d+2\,c\,d\,x\right)}^2-b^2\,d^2+4\,a\,c\,d^2}+48\,c\,d^7\,\sqrt{b\,d+2\,c\,d\,x}\,{\left(4\,a\,c-b^2\right)}^2-26\,c\,d^{15/2}\,\mathrm{atan}\left(\frac{b^4\,\sqrt{b\,d+2\,c\,d\,x}+16\,a^2\,c^2\,\sqrt{b\,d+2\,c\,d\,x}-8\,a\,b^2\,c\,\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{9/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{9/4}-\frac{32\,c\,d^5\,{\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,\left(4\,a\,c-b^2\right)}{5}-c\,d^{15/2}\,\mathrm{atan}\left(\frac{c\,d^{15/2}\,{\left(b^2-4\,a\,c\right)}^{9/4}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(44302336\,a^6\,c^8\,d^{18}-66453504\,a^5\,b^2\,c^7\,d^{18}+41533440\,a^4\,b^4\,c^6\,d^{18}-13844480\,a^3\,b^6\,c^5\,d^{18}+2595840\,a^2\,b^8\,c^4\,d^{18}-259584\,a\,b^{10}\,c^3\,d^{18}+10816\,b^{12}\,c^2\,d^{18}\right)-13\,c\,d^{15/2}\,{\left(b^2-4\,a\,c\right)}^{9/4}\,\left(212992\,a^4\,c^5\,d^{11}-212992\,a^3\,b^2\,c^4\,d^{11}+79872\,a^2\,b^4\,c^3\,d^{11}-13312\,a\,b^6\,c^2\,d^{11}+832\,b^8\,c\,d^{11}\right)\right)\,13{}\mathrm{i}+c\,d^{15/2}\,{\left(b^2-4\,a\,c\right)}^{9/4}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(44302336\,a^6\,c^8\,d^{18}-66453504\,a^5\,b^2\,c^7\,d^{18}+41533440\,a^4\,b^4\,c^6\,d^{18}-13844480\,a^3\,b^6\,c^5\,d^{18}+2595840\,a^2\,b^8\,c^4\,d^{18}-259584\,a\,b^{10}\,c^3\,d^{18}+10816\,b^{12}\,c^2\,d^{18}\right)+13\,c\,d^{15/2}\,{\left(b^2-4\,a\,c\right)}^{9/4}\,\left(212992\,a^4\,c^5\,d^{11}-212992\,a^3\,b^2\,c^4\,d^{11}+79872\,a^2\,b^4\,c^3\,d^{11}-13312\,a\,b^6\,c^2\,d^{11}+832\,b^8\,c\,d^{11}\right)\right)\,13{}\mathrm{i}}{13\,c\,d^{15/2}\,{\left(b^2-4\,a\,c\right)}^{9/4}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(44302336\,a^6\,c^8\,d^{18}-66453504\,a^5\,b^2\,c^7\,d^{18}+41533440\,a^4\,b^4\,c^6\,d^{18}-13844480\,a^3\,b^6\,c^5\,d^{18}+2595840\,a^2\,b^8\,c^4\,d^{18}-259584\,a\,b^{10}\,c^3\,d^{18}+10816\,b^{12}\,c^2\,d^{18}\right)-13\,c\,d^{15/2}\,{\left(b^2-4\,a\,c\right)}^{9/4}\,\left(212992\,a^4\,c^5\,d^{11}-212992\,a^3\,b^2\,c^4\,d^{11}+79872\,a^2\,b^4\,c^3\,d^{11}-13312\,a\,b^6\,c^2\,d^{11}+832\,b^8\,c\,d^{11}\right)\right)-13\,c\,d^{15/2}\,{\left(b^2-4\,a\,c\right)}^{9/4}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(44302336\,a^6\,c^8\,d^{18}-66453504\,a^5\,b^2\,c^7\,d^{18}+41533440\,a^4\,b^4\,c^6\,d^{18}-13844480\,a^3\,b^6\,c^5\,d^{18}+2595840\,a^2\,b^8\,c^4\,d^{18}-259584\,a\,b^{10}\,c^3\,d^{18}+10816\,b^{12}\,c^2\,d^{18}\right)+13\,c\,d^{15/2}\,{\left(b^2-4\,a\,c\right)}^{9/4}\,\left(212992\,a^4\,c^5\,d^{11}-212992\,a^3\,b^2\,c^4\,d^{11}+79872\,a^2\,b^4\,c^3\,d^{11}-13312\,a\,b^6\,c^2\,d^{11}+832\,b^8\,c\,d^{11}\right)\right)}\right)\,{\left(b^2-4\,a\,c\right)}^{9/4}\,26{}\mathrm{i}","Not used",1,"(16*c*d^3*(b*d + 2*c*d*x)^(9/2))/9 - ((b*d + 2*c*d*x)^(1/2)*(4*b^6*c*d^9 - 256*a^3*c^4*d^9 - 48*a*b^4*c^2*d^9 + 192*a^2*b^2*c^3*d^9))/((b*d + 2*c*d*x)^2 - b^2*d^2 + 4*a*c*d^2) + 48*c*d^7*(b*d + 2*c*d*x)^(1/2)*(4*a*c - b^2)^2 - 26*c*d^(15/2)*atan((b^4*(b*d + 2*c*d*x)^(1/2) + 16*a^2*c^2*(b*d + 2*c*d*x)^(1/2) - 8*a*b^2*c*(b*d + 2*c*d*x)^(1/2))/(d^(1/2)*(b^2 - 4*a*c)^(9/4)))*(b^2 - 4*a*c)^(9/4) - c*d^(15/2)*atan((c*d^(15/2)*(b^2 - 4*a*c)^(9/4)*((b*d + 2*c*d*x)^(1/2)*(44302336*a^6*c^8*d^18 + 10816*b^12*c^2*d^18 - 259584*a*b^10*c^3*d^18 + 2595840*a^2*b^8*c^4*d^18 - 13844480*a^3*b^6*c^5*d^18 + 41533440*a^4*b^4*c^6*d^18 - 66453504*a^5*b^2*c^7*d^18) - 13*c*d^(15/2)*(b^2 - 4*a*c)^(9/4)*(832*b^8*c*d^11 + 212992*a^4*c^5*d^11 - 13312*a*b^6*c^2*d^11 + 79872*a^2*b^4*c^3*d^11 - 212992*a^3*b^2*c^4*d^11))*13i + c*d^(15/2)*(b^2 - 4*a*c)^(9/4)*((b*d + 2*c*d*x)^(1/2)*(44302336*a^6*c^8*d^18 + 10816*b^12*c^2*d^18 - 259584*a*b^10*c^3*d^18 + 2595840*a^2*b^8*c^4*d^18 - 13844480*a^3*b^6*c^5*d^18 + 41533440*a^4*b^4*c^6*d^18 - 66453504*a^5*b^2*c^7*d^18) + 13*c*d^(15/2)*(b^2 - 4*a*c)^(9/4)*(832*b^8*c*d^11 + 212992*a^4*c^5*d^11 - 13312*a*b^6*c^2*d^11 + 79872*a^2*b^4*c^3*d^11 - 212992*a^3*b^2*c^4*d^11))*13i)/(13*c*d^(15/2)*(b^2 - 4*a*c)^(9/4)*((b*d + 2*c*d*x)^(1/2)*(44302336*a^6*c^8*d^18 + 10816*b^12*c^2*d^18 - 259584*a*b^10*c^3*d^18 + 2595840*a^2*b^8*c^4*d^18 - 13844480*a^3*b^6*c^5*d^18 + 41533440*a^4*b^4*c^6*d^18 - 66453504*a^5*b^2*c^7*d^18) - 13*c*d^(15/2)*(b^2 - 4*a*c)^(9/4)*(832*b^8*c*d^11 + 212992*a^4*c^5*d^11 - 13312*a*b^6*c^2*d^11 + 79872*a^2*b^4*c^3*d^11 - 212992*a^3*b^2*c^4*d^11)) - 13*c*d^(15/2)*(b^2 - 4*a*c)^(9/4)*((b*d + 2*c*d*x)^(1/2)*(44302336*a^6*c^8*d^18 + 10816*b^12*c^2*d^18 - 259584*a*b^10*c^3*d^18 + 2595840*a^2*b^8*c^4*d^18 - 13844480*a^3*b^6*c^5*d^18 + 41533440*a^4*b^4*c^6*d^18 - 66453504*a^5*b^2*c^7*d^18) + 13*c*d^(15/2)*(b^2 - 4*a*c)^(9/4)*(832*b^8*c*d^11 + 212992*a^4*c^5*d^11 - 13312*a*b^6*c^2*d^11 + 79872*a^2*b^4*c^3*d^11 - 212992*a^3*b^2*c^4*d^11))))*(b^2 - 4*a*c)^(9/4)*26i - (32*c*d^5*(b*d + 2*c*d*x)^(5/2)*(4*a*c - b^2))/5","B"
1296,1,249,181,0.596027,"\text{Not used}","int((b*d + 2*c*d*x)^(13/2)/(a + b*x + c*x^2)^2,x)","\frac{16\,c\,d^3\,{\left(b\,d+2\,c\,d\,x\right)}^{7/2}}{7}-\frac{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,\left(64\,a^2\,c^3\,d^7-32\,a\,b^2\,c^2\,d^7+4\,b^4\,c\,d^7\right)}{{\left(b\,d+2\,c\,d\,x\right)}^2-b^2\,d^2+4\,a\,c\,d^2}+22\,c\,d^{13/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,{\left(b^2-4\,a\,c\right)}^{7/4}}{\sqrt{d}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}\right)\,{\left(b^2-4\,a\,c\right)}^{7/4}-\frac{32\,c\,d^5\,{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,\left(4\,a\,c-b^2\right)}{3}+c\,d^{13/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,{\left(b^2-4\,a\,c\right)}^{7/4}\,1{}\mathrm{i}}{\sqrt{d}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}\right)\,{\left(b^2-4\,a\,c\right)}^{7/4}\,22{}\mathrm{i}","Not used",1,"(16*c*d^3*(b*d + 2*c*d*x)^(7/2))/7 - ((b*d + 2*c*d*x)^(3/2)*(4*b^4*c*d^7 + 64*a^2*c^3*d^7 - 32*a*b^2*c^2*d^7))/((b*d + 2*c*d*x)^2 - b^2*d^2 + 4*a*c*d^2) + 22*c*d^(13/2)*atan(((b*d + 2*c*d*x)^(1/2)*(b^2 - 4*a*c)^(7/4))/(d^(1/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))*(b^2 - 4*a*c)^(7/4) + c*d^(13/2)*atan(((b*d + 2*c*d*x)^(1/2)*(b^2 - 4*a*c)^(7/4)*1i)/(d^(1/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))*(b^2 - 4*a*c)^(7/4)*22i - (32*c*d^5*(b*d + 2*c*d*x)^(3/2)*(4*a*c - b^2))/3","B"
1297,1,834,179,0.197565,"\text{Not used}","int((b*d + 2*c*d*x)^(11/2)/(a + b*x + c*x^2)^2,x)","\frac{16\,c\,d^3\,{\left(b\,d+2\,c\,d\,x\right)}^{5/2}}{5}-\frac{\sqrt{b\,d+2\,c\,d\,x}\,\left(64\,a^2\,c^3\,d^7-32\,a\,b^2\,c^2\,d^7+4\,b^4\,c\,d^7\right)}{{\left(b\,d+2\,c\,d\,x\right)}^2-b^2\,d^2+4\,a\,c\,d^2}-18\,c\,d^{11/2}\,\mathrm{atan}\left(\frac{9\,c\,d^{11/2}\,{\left(b^2-4\,a\,c\right)}^{5/4}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(1327104\,a^4\,c^6\,d^{14}-1327104\,a^3\,b^2\,c^5\,d^{14}+497664\,a^2\,b^4\,c^4\,d^{14}-82944\,a\,b^6\,c^3\,d^{14}+5184\,b^8\,c^2\,d^{14}\right)-c\,d^{11/2}\,{\left(b^2-4\,a\,c\right)}^{5/4}\,\left(-36864\,a^3\,c^4\,d^9+27648\,a^2\,b^2\,c^3\,d^9-6912\,a\,b^4\,c^2\,d^9+576\,b^6\,c\,d^9\right)\,9{}\mathrm{i}\right)+9\,c\,d^{11/2}\,{\left(b^2-4\,a\,c\right)}^{5/4}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(1327104\,a^4\,c^6\,d^{14}-1327104\,a^3\,b^2\,c^5\,d^{14}+497664\,a^2\,b^4\,c^4\,d^{14}-82944\,a\,b^6\,c^3\,d^{14}+5184\,b^8\,c^2\,d^{14}\right)+c\,d^{11/2}\,{\left(b^2-4\,a\,c\right)}^{5/4}\,\left(-36864\,a^3\,c^4\,d^9+27648\,a^2\,b^2\,c^3\,d^9-6912\,a\,b^4\,c^2\,d^9+576\,b^6\,c\,d^9\right)\,9{}\mathrm{i}\right)}{c\,d^{11/2}\,{\left(b^2-4\,a\,c\right)}^{5/4}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(1327104\,a^4\,c^6\,d^{14}-1327104\,a^3\,b^2\,c^5\,d^{14}+497664\,a^2\,b^4\,c^4\,d^{14}-82944\,a\,b^6\,c^3\,d^{14}+5184\,b^8\,c^2\,d^{14}\right)-c\,d^{11/2}\,{\left(b^2-4\,a\,c\right)}^{5/4}\,\left(-36864\,a^3\,c^4\,d^9+27648\,a^2\,b^2\,c^3\,d^9-6912\,a\,b^4\,c^2\,d^9+576\,b^6\,c\,d^9\right)\,9{}\mathrm{i}\right)\,9{}\mathrm{i}-c\,d^{11/2}\,{\left(b^2-4\,a\,c\right)}^{5/4}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(1327104\,a^4\,c^6\,d^{14}-1327104\,a^3\,b^2\,c^5\,d^{14}+497664\,a^2\,b^4\,c^4\,d^{14}-82944\,a\,b^6\,c^3\,d^{14}+5184\,b^8\,c^2\,d^{14}\right)+c\,d^{11/2}\,{\left(b^2-4\,a\,c\right)}^{5/4}\,\left(-36864\,a^3\,c^4\,d^9+27648\,a^2\,b^2\,c^3\,d^9-6912\,a\,b^4\,c^2\,d^9+576\,b^6\,c\,d^9\right)\,9{}\mathrm{i}\right)\,9{}\mathrm{i}}\right)\,{\left(b^2-4\,a\,c\right)}^{5/4}-32\,c\,d^5\,\sqrt{b\,d+2\,c\,d\,x}\,\left(4\,a\,c-b^2\right)+c\,d^{11/2}\,\mathrm{atan}\left(\frac{b^2\,\sqrt{b\,d+2\,c\,d\,x}\,1{}\mathrm{i}-a\,c\,\sqrt{b\,d+2\,c\,d\,x}\,4{}\mathrm{i}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{5/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{5/4}\,18{}\mathrm{i}","Not used",1,"(16*c*d^3*(b*d + 2*c*d*x)^(5/2))/5 - ((b*d + 2*c*d*x)^(1/2)*(4*b^4*c*d^7 + 64*a^2*c^3*d^7 - 32*a*b^2*c^2*d^7))/((b*d + 2*c*d*x)^2 - b^2*d^2 + 4*a*c*d^2) - 18*c*d^(11/2)*atan((9*c*d^(11/2)*(b^2 - 4*a*c)^(5/4)*((b*d + 2*c*d*x)^(1/2)*(1327104*a^4*c^6*d^14 + 5184*b^8*c^2*d^14 - 82944*a*b^6*c^3*d^14 + 497664*a^2*b^4*c^4*d^14 - 1327104*a^3*b^2*c^5*d^14) - c*d^(11/2)*(b^2 - 4*a*c)^(5/4)*(576*b^6*c*d^9 - 36864*a^3*c^4*d^9 - 6912*a*b^4*c^2*d^9 + 27648*a^2*b^2*c^3*d^9)*9i) + 9*c*d^(11/2)*(b^2 - 4*a*c)^(5/4)*((b*d + 2*c*d*x)^(1/2)*(1327104*a^4*c^6*d^14 + 5184*b^8*c^2*d^14 - 82944*a*b^6*c^3*d^14 + 497664*a^2*b^4*c^4*d^14 - 1327104*a^3*b^2*c^5*d^14) + c*d^(11/2)*(b^2 - 4*a*c)^(5/4)*(576*b^6*c*d^9 - 36864*a^3*c^4*d^9 - 6912*a*b^4*c^2*d^9 + 27648*a^2*b^2*c^3*d^9)*9i))/(c*d^(11/2)*(b^2 - 4*a*c)^(5/4)*((b*d + 2*c*d*x)^(1/2)*(1327104*a^4*c^6*d^14 + 5184*b^8*c^2*d^14 - 82944*a*b^6*c^3*d^14 + 497664*a^2*b^4*c^4*d^14 - 1327104*a^3*b^2*c^5*d^14) - c*d^(11/2)*(b^2 - 4*a*c)^(5/4)*(576*b^6*c*d^9 - 36864*a^3*c^4*d^9 - 6912*a*b^4*c^2*d^9 + 27648*a^2*b^2*c^3*d^9)*9i)*9i - c*d^(11/2)*(b^2 - 4*a*c)^(5/4)*((b*d + 2*c*d*x)^(1/2)*(1327104*a^4*c^6*d^14 + 5184*b^8*c^2*d^14 - 82944*a*b^6*c^3*d^14 + 497664*a^2*b^4*c^4*d^14 - 1327104*a^3*b^2*c^5*d^14) + c*d^(11/2)*(b^2 - 4*a*c)^(5/4)*(576*b^6*c*d^9 - 36864*a^3*c^4*d^9 - 6912*a*b^4*c^2*d^9 + 27648*a^2*b^2*c^3*d^9)*9i)*9i))*(b^2 - 4*a*c)^(5/4) - 32*c*d^5*(b*d + 2*c*d*x)^(1/2)*(4*a*c - b^2) + c*d^(11/2)*atan((b^2*(b*d + 2*c*d*x)^(1/2)*1i - a*c*(b*d + 2*c*d*x)^(1/2)*4i)/(d^(1/2)*(b^2 - 4*a*c)^(5/4)))*(b^2 - 4*a*c)^(5/4)*18i","B"
1298,1,165,152,0.160352,"\text{Not used}","int((b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^2,x)","\frac{16\,c\,d^3\,{\left(b\,d+2\,c\,d\,x\right)}^{3/2}}{3}+\frac{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,\left(16\,a\,c^2\,d^5-4\,b^2\,c\,d^5\right)}{{\left(b\,d+2\,c\,d\,x\right)}^2-b^2\,d^2+4\,a\,c\,d^2}+14\,c\,d^{9/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{3/4}+c\,d^{9/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,1{}\mathrm{i}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{3/4}\,14{}\mathrm{i}","Not used",1,"(16*c*d^3*(b*d + 2*c*d*x)^(3/2))/3 + ((b*d + 2*c*d*x)^(3/2)*(16*a*c^2*d^5 - 4*b^2*c*d^5))/((b*d + 2*c*d*x)^2 - b^2*d^2 + 4*a*c*d^2) + 14*c*d^(9/2)*atan((b*d + 2*c*d*x)^(1/2)/(d^(1/2)*(b^2 - 4*a*c)^(1/4)))*(b^2 - 4*a*c)^(3/4) + c*d^(9/2)*atan(((b*d + 2*c*d*x)^(1/2)*1i)/(d^(1/2)*(b^2 - 4*a*c)^(1/4)))*(b^2 - 4*a*c)^(3/4)*14i","B"
1299,1,597,150,0.620640,"\text{Not used}","int((b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^2,x)","16\,c\,d^3\,\sqrt{b\,d+2\,c\,d\,x}+\frac{\sqrt{b\,d+2\,c\,d\,x}\,\left(16\,a\,c^2\,d^5-4\,b^2\,c\,d^5\right)}{{\left(b\,d+2\,c\,d\,x\right)}^2-b^2\,d^2+4\,a\,c\,d^2}-10\,c\,d^{7/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{1/4}-c\,d^{7/2}\,\mathrm{atan}\left(\frac{c\,d^{7/2}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(25600\,a^2\,c^4\,d^{10}-12800\,a\,b^2\,c^3\,d^{10}+1600\,b^4\,c^2\,d^{10}\right)-5\,c\,d^{7/2}\,{\left(b^2-4\,a\,c\right)}^{1/4}\,\left(5120\,a^2\,c^3\,d^7-2560\,a\,b^2\,c^2\,d^7+320\,b^4\,c\,d^7\right)\right)\,{\left(b^2-4\,a\,c\right)}^{1/4}\,5{}\mathrm{i}+c\,d^{7/2}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(25600\,a^2\,c^4\,d^{10}-12800\,a\,b^2\,c^3\,d^{10}+1600\,b^4\,c^2\,d^{10}\right)+5\,c\,d^{7/2}\,{\left(b^2-4\,a\,c\right)}^{1/4}\,\left(5120\,a^2\,c^3\,d^7-2560\,a\,b^2\,c^2\,d^7+320\,b^4\,c\,d^7\right)\right)\,{\left(b^2-4\,a\,c\right)}^{1/4}\,5{}\mathrm{i}}{5\,c\,d^{7/2}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(25600\,a^2\,c^4\,d^{10}-12800\,a\,b^2\,c^3\,d^{10}+1600\,b^4\,c^2\,d^{10}\right)-5\,c\,d^{7/2}\,{\left(b^2-4\,a\,c\right)}^{1/4}\,\left(5120\,a^2\,c^3\,d^7-2560\,a\,b^2\,c^2\,d^7+320\,b^4\,c\,d^7\right)\right)\,{\left(b^2-4\,a\,c\right)}^{1/4}-5\,c\,d^{7/2}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(25600\,a^2\,c^4\,d^{10}-12800\,a\,b^2\,c^3\,d^{10}+1600\,b^4\,c^2\,d^{10}\right)+5\,c\,d^{7/2}\,{\left(b^2-4\,a\,c\right)}^{1/4}\,\left(5120\,a^2\,c^3\,d^7-2560\,a\,b^2\,c^2\,d^7+320\,b^4\,c\,d^7\right)\right)\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{1/4}\,10{}\mathrm{i}","Not used",1,"16*c*d^3*(b*d + 2*c*d*x)^(1/2) + ((b*d + 2*c*d*x)^(1/2)*(16*a*c^2*d^5 - 4*b^2*c*d^5))/((b*d + 2*c*d*x)^2 - b^2*d^2 + 4*a*c*d^2) - c*d^(7/2)*atan((c*d^(7/2)*((b*d + 2*c*d*x)^(1/2)*(25600*a^2*c^4*d^10 + 1600*b^4*c^2*d^10 - 12800*a*b^2*c^3*d^10) - 5*c*d^(7/2)*(b^2 - 4*a*c)^(1/4)*(320*b^4*c*d^7 + 5120*a^2*c^3*d^7 - 2560*a*b^2*c^2*d^7))*(b^2 - 4*a*c)^(1/4)*5i + c*d^(7/2)*((b*d + 2*c*d*x)^(1/2)*(25600*a^2*c^4*d^10 + 1600*b^4*c^2*d^10 - 12800*a*b^2*c^3*d^10) + 5*c*d^(7/2)*(b^2 - 4*a*c)^(1/4)*(320*b^4*c*d^7 + 5120*a^2*c^3*d^7 - 2560*a*b^2*c^2*d^7))*(b^2 - 4*a*c)^(1/4)*5i)/(5*c*d^(7/2)*((b*d + 2*c*d*x)^(1/2)*(25600*a^2*c^4*d^10 + 1600*b^4*c^2*d^10 - 12800*a*b^2*c^3*d^10) - 5*c*d^(7/2)*(b^2 - 4*a*c)^(1/4)*(320*b^4*c*d^7 + 5120*a^2*c^3*d^7 - 2560*a*b^2*c^2*d^7))*(b^2 - 4*a*c)^(1/4) - 5*c*d^(7/2)*((b*d + 2*c*d*x)^(1/2)*(25600*a^2*c^4*d^10 + 1600*b^4*c^2*d^10 - 12800*a*b^2*c^3*d^10) + 5*c*d^(7/2)*(b^2 - 4*a*c)^(1/4)*(320*b^4*c*d^7 + 5120*a^2*c^3*d^7 - 2560*a*b^2*c^2*d^7))*(b^2 - 4*a*c)^(1/4)))*(b^2 - 4*a*c)^(1/4)*10i - 10*c*d^(7/2)*atan((b*d + 2*c*d*x)^(1/2)/(d^(1/2)*(b^2 - 4*a*c)^(1/4)))*(b^2 - 4*a*c)^(1/4)","B"
1300,1,131,131,0.177917,"\text{Not used}","int((b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^2,x)","\frac{6\,c\,d^{5/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)}{{\left(b^2-4\,a\,c\right)}^{1/4}}-\frac{4\,c\,d^3\,{\left(b\,d+2\,c\,d\,x\right)}^{3/2}}{{\left(b\,d+2\,c\,d\,x\right)}^2-b^2\,d^2+4\,a\,c\,d^2}-\frac{6\,c\,d^{5/2}\,\mathrm{atanh}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)}{{\left(b^2-4\,a\,c\right)}^{1/4}}","Not used",1,"(6*c*d^(5/2)*atan((b*d + 2*c*d*x)^(1/2)/(d^(1/2)*(b^2 - 4*a*c)^(1/4))))/(b^2 - 4*a*c)^(1/4) - (4*c*d^3*(b*d + 2*c*d*x)^(3/2))/((b*d + 2*c*d*x)^2 - b^2*d^2 + 4*a*c*d^2) - (6*c*d^(5/2)*atanh((b*d + 2*c*d*x)^(1/2)/(d^(1/2)*(b^2 - 4*a*c)^(1/4))))/(b^2 - 4*a*c)^(1/4)","B"
1301,1,225,131,0.622639,"\text{Not used}","int((b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^2,x)","-\frac{4\,c\,d^3\,\sqrt{b\,d+2\,c\,d\,x}}{{\left(b\,d+2\,c\,d\,x\right)}^2-b^2\,d^2+4\,a\,c\,d^2}-\frac{2\,c\,d^{3/2}\,\mathrm{atan}\left(\frac{128\,c^3\,d^{15/2}\,\sqrt{b\,d+2\,c\,d\,x}}{\left(\frac{128\,b^2\,c^3\,d^8}{{\left(b^2-4\,a\,c\right)}^{3/2}}-\frac{512\,a\,c^4\,d^8}{{\left(b^2-4\,a\,c\right)}^{3/2}}\right)\,{\left(b^2-4\,a\,c\right)}^{3/4}}\right)}{{\left(b^2-4\,a\,c\right)}^{3/4}}-\frac{2\,c\,d^{3/2}\,\mathrm{atanh}\left(\frac{128\,c^3\,d^{15/2}\,\sqrt{b\,d+2\,c\,d\,x}}{\left(\frac{128\,b^2\,c^3\,d^8}{{\left(b^2-4\,a\,c\right)}^{3/2}}-\frac{512\,a\,c^4\,d^8}{{\left(b^2-4\,a\,c\right)}^{3/2}}\right)\,{\left(b^2-4\,a\,c\right)}^{3/4}}\right)}{{\left(b^2-4\,a\,c\right)}^{3/4}}","Not used",1,"- (4*c*d^3*(b*d + 2*c*d*x)^(1/2))/((b*d + 2*c*d*x)^2 - b^2*d^2 + 4*a*c*d^2) - (2*c*d^(3/2)*atan((128*c^3*d^(15/2)*(b*d + 2*c*d*x)^(1/2))/(((128*b^2*c^3*d^8)/(b^2 - 4*a*c)^(3/2) - (512*a*c^4*d^8)/(b^2 - 4*a*c)^(3/2))*(b^2 - 4*a*c)^(3/4))))/(b^2 - 4*a*c)^(3/4) - (2*c*d^(3/2)*atanh((128*c^3*d^(15/2)*(b*d + 2*c*d*x)^(1/2))/(((128*b^2*c^3*d^8)/(b^2 - 4*a*c)^(3/2) - (512*a*c^4*d^8)/(b^2 - 4*a*c)^(3/2))*(b^2 - 4*a*c)^(3/4))))/(b^2 - 4*a*c)^(3/4)","B"
1302,1,179,143,0.137977,"\text{Not used}","int((b*d + 2*c*d*x)^(1/2)/(a + b*x + c*x^2)^2,x)","\frac{2\,c\,\sqrt{d}\,\mathrm{atanh}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{9/4}}\right)}{{\left(b^2-4\,a\,c\right)}^{5/4}}-\frac{2\,c\,\sqrt{d}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{9/4}}\right)}{{\left(b^2-4\,a\,c\right)}^{5/4}}+\frac{4\,c\,d\,{\left(b\,d+2\,c\,d\,x\right)}^{3/2}}{\left(4\,a\,c-b^2\right)\,\left({\left(b\,d+2\,c\,d\,x\right)}^2-b^2\,d^2+4\,a\,c\,d^2\right)}","Not used",1,"(2*c*d^(1/2)*atanh(((b*d + 2*c*d*x)^(1/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c))/(d^(1/2)*(b^2 - 4*a*c)^(9/4))))/(b^2 - 4*a*c)^(5/4) - (2*c*d^(1/2)*atan(((b*d + 2*c*d*x)^(1/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c))/(d^(1/2)*(b^2 - 4*a*c)^(9/4))))/(b^2 - 4*a*c)^(5/4) + (4*c*d*(b*d + 2*c*d*x)^(3/2))/((4*a*c - b^2)*((b*d + 2*c*d*x)^2 - b^2*d^2 + 4*a*c*d^2))","B"
1303,1,183,143,0.581579,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^2),x)","\frac{6\,c\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,{\left(b^2-4\,a\,c\right)}^{7/4}}{\sqrt{d}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}\right)}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{7/4}}+\frac{6\,c\,\mathrm{atanh}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,{\left(b^2-4\,a\,c\right)}^{7/4}}{\sqrt{d}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}\right)}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{7/4}}+\frac{4\,c\,d\,\sqrt{b\,d+2\,c\,d\,x}}{\left(4\,a\,c-b^2\right)\,\left({\left(b\,d+2\,c\,d\,x\right)}^2-b^2\,d^2+4\,a\,c\,d^2\right)}","Not used",1,"(6*c*atan(((b*d + 2*c*d*x)^(1/2)*(b^2 - 4*a*c)^(7/4))/(d^(1/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c))))/(d^(1/2)*(b^2 - 4*a*c)^(7/4)) + (6*c*atanh(((b*d + 2*c*d*x)^(1/2)*(b^2 - 4*a*c)^(7/4))/(d^(1/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c))))/(d^(1/2)*(b^2 - 4*a*c)^(7/4)) + (4*c*d*(b*d + 2*c*d*x)^(1/2))/((4*a*c - b^2)*((b*d + 2*c*d*x)^2 - b^2*d^2 + 4*a*c*d^2))","B"
1304,1,264,172,0.737717,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^2),x)","\frac{\frac{16\,c\,d}{4\,a\,c-b^2}+\frac{20\,c\,{\left(b\,d+2\,c\,d\,x\right)}^2}{d\,{\left(4\,a\,c-b^2\right)}^2}}{\sqrt{b\,d+2\,c\,d\,x}\,\left(b^2\,d^2-4\,a\,c\,d^2\right)-{\left(b\,d+2\,c\,d\,x\right)}^{5/2}}-\frac{10\,c\,\mathrm{atan}\left(\frac{b^4\,\sqrt{b\,d+2\,c\,d\,x}+16\,a^2\,c^2\,\sqrt{b\,d+2\,c\,d\,x}-8\,a\,b^2\,c\,\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{9/4}}\right)}{d^{3/2}\,{\left(b^2-4\,a\,c\right)}^{9/4}}-\frac{c\,\mathrm{atan}\left(\frac{b^4\,\sqrt{b\,d+2\,c\,d\,x}\,1{}\mathrm{i}+a^2\,c^2\,\sqrt{b\,d+2\,c\,d\,x}\,16{}\mathrm{i}-a\,b^2\,c\,\sqrt{b\,d+2\,c\,d\,x}\,8{}\mathrm{i}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{9/4}}\right)\,10{}\mathrm{i}}{d^{3/2}\,{\left(b^2-4\,a\,c\right)}^{9/4}}","Not used",1,"((16*c*d)/(4*a*c - b^2) + (20*c*(b*d + 2*c*d*x)^2)/(d*(4*a*c - b^2)^2))/((b*d + 2*c*d*x)^(1/2)*(b^2*d^2 - 4*a*c*d^2) - (b*d + 2*c*d*x)^(5/2)) - (10*c*atan((b^4*(b*d + 2*c*d*x)^(1/2) + 16*a^2*c^2*(b*d + 2*c*d*x)^(1/2) - 8*a*b^2*c*(b*d + 2*c*d*x)^(1/2))/(d^(1/2)*(b^2 - 4*a*c)^(9/4))))/(d^(3/2)*(b^2 - 4*a*c)^(9/4)) - (c*atan((b^4*(b*d + 2*c*d*x)^(1/2)*1i + a^2*c^2*(b*d + 2*c*d*x)^(1/2)*16i - a*b^2*c*(b*d + 2*c*d*x)^(1/2)*8i)/(d^(1/2)*(b^2 - 4*a*c)^(9/4)))*10i)/(d^(3/2)*(b^2 - 4*a*c)^(9/4))","B"
1305,1,2280,174,0.899796,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^2),x)","\frac{\frac{16\,c\,d}{3\,\left(4\,a\,c-b^2\right)}+\frac{28\,c\,{\left(b\,d+2\,c\,d\,x\right)}^2}{3\,d\,{\left(4\,a\,c-b^2\right)}^2}}{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,\left(b^2\,d^2-4\,a\,c\,d^2\right)-{\left(b\,d+2\,c\,d\,x\right)}^{7/2}}+\frac{c\,\mathrm{atan}\left(\frac{\frac{c\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(12845056\,a^6\,c^8\,d^3-19267584\,a^5\,b^2\,c^7\,d^3+12042240\,a^4\,b^4\,c^6\,d^3-4014080\,a^3\,b^6\,c^5\,d^3+752640\,a^2\,b^8\,c^4\,d^3-75264\,a\,b^{10}\,c^3\,d^3+3136\,b^{12}\,c^2\,d^3\right)-\frac{7\,c\,\left(-117440512\,a^9\,c^{10}\,d^6+264241152\,a^8\,b^2\,c^9\,d^6-264241152\,a^7\,b^4\,c^8\,d^6+154140672\,a^6\,b^6\,c^7\,d^6-57802752\,a^5\,b^8\,c^6\,d^6+14450688\,a^4\,b^{10}\,c^5\,d^6-2408448\,a^3\,b^{12}\,c^4\,d^6+258048\,a^2\,b^{14}\,c^3\,d^6-16128\,a\,b^{16}\,c^2\,d^6+448\,b^{18}\,c\,d^6\right)}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}\right)\,7{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}+\frac{c\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(12845056\,a^6\,c^8\,d^3-19267584\,a^5\,b^2\,c^7\,d^3+12042240\,a^4\,b^4\,c^6\,d^3-4014080\,a^3\,b^6\,c^5\,d^3+752640\,a^2\,b^8\,c^4\,d^3-75264\,a\,b^{10}\,c^3\,d^3+3136\,b^{12}\,c^2\,d^3\right)+\frac{7\,c\,\left(-117440512\,a^9\,c^{10}\,d^6+264241152\,a^8\,b^2\,c^9\,d^6-264241152\,a^7\,b^4\,c^8\,d^6+154140672\,a^6\,b^6\,c^7\,d^6-57802752\,a^5\,b^8\,c^6\,d^6+14450688\,a^4\,b^{10}\,c^5\,d^6-2408448\,a^3\,b^{12}\,c^4\,d^6+258048\,a^2\,b^{14}\,c^3\,d^6-16128\,a\,b^{16}\,c^2\,d^6+448\,b^{18}\,c\,d^6\right)}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}\right)\,7{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}}{\frac{7\,c\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(12845056\,a^6\,c^8\,d^3-19267584\,a^5\,b^2\,c^7\,d^3+12042240\,a^4\,b^4\,c^6\,d^3-4014080\,a^3\,b^6\,c^5\,d^3+752640\,a^2\,b^8\,c^4\,d^3-75264\,a\,b^{10}\,c^3\,d^3+3136\,b^{12}\,c^2\,d^3\right)-\frac{7\,c\,\left(-117440512\,a^9\,c^{10}\,d^6+264241152\,a^8\,b^2\,c^9\,d^6-264241152\,a^7\,b^4\,c^8\,d^6+154140672\,a^6\,b^6\,c^7\,d^6-57802752\,a^5\,b^8\,c^6\,d^6+14450688\,a^4\,b^{10}\,c^5\,d^6-2408448\,a^3\,b^{12}\,c^4\,d^6+258048\,a^2\,b^{14}\,c^3\,d^6-16128\,a\,b^{16}\,c^2\,d^6+448\,b^{18}\,c\,d^6\right)}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}\right)}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}-\frac{7\,c\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(12845056\,a^6\,c^8\,d^3-19267584\,a^5\,b^2\,c^7\,d^3+12042240\,a^4\,b^4\,c^6\,d^3-4014080\,a^3\,b^6\,c^5\,d^3+752640\,a^2\,b^8\,c^4\,d^3-75264\,a\,b^{10}\,c^3\,d^3+3136\,b^{12}\,c^2\,d^3\right)+\frac{7\,c\,\left(-117440512\,a^9\,c^{10}\,d^6+264241152\,a^8\,b^2\,c^9\,d^6-264241152\,a^7\,b^4\,c^8\,d^6+154140672\,a^6\,b^6\,c^7\,d^6-57802752\,a^5\,b^8\,c^6\,d^6+14450688\,a^4\,b^{10}\,c^5\,d^6-2408448\,a^3\,b^{12}\,c^4\,d^6+258048\,a^2\,b^{14}\,c^3\,d^6-16128\,a\,b^{16}\,c^2\,d^6+448\,b^{18}\,c\,d^6\right)}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}\right)}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}}\right)\,14{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}+\frac{14\,c\,\mathrm{atan}\left(\frac{\frac{7\,c\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(12845056\,a^6\,c^8\,d^3-19267584\,a^5\,b^2\,c^7\,d^3+12042240\,a^4\,b^4\,c^6\,d^3-4014080\,a^3\,b^6\,c^5\,d^3+752640\,a^2\,b^8\,c^4\,d^3-75264\,a\,b^{10}\,c^3\,d^3+3136\,b^{12}\,c^2\,d^3\right)-\frac{c\,\left(-117440512\,a^9\,c^{10}\,d^6+264241152\,a^8\,b^2\,c^9\,d^6-264241152\,a^7\,b^4\,c^8\,d^6+154140672\,a^6\,b^6\,c^7\,d^6-57802752\,a^5\,b^8\,c^6\,d^6+14450688\,a^4\,b^{10}\,c^5\,d^6-2408448\,a^3\,b^{12}\,c^4\,d^6+258048\,a^2\,b^{14}\,c^3\,d^6-16128\,a\,b^{16}\,c^2\,d^6+448\,b^{18}\,c\,d^6\right)\,7{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}\right)}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}+\frac{7\,c\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(12845056\,a^6\,c^8\,d^3-19267584\,a^5\,b^2\,c^7\,d^3+12042240\,a^4\,b^4\,c^6\,d^3-4014080\,a^3\,b^6\,c^5\,d^3+752640\,a^2\,b^8\,c^4\,d^3-75264\,a\,b^{10}\,c^3\,d^3+3136\,b^{12}\,c^2\,d^3\right)+\frac{c\,\left(-117440512\,a^9\,c^{10}\,d^6+264241152\,a^8\,b^2\,c^9\,d^6-264241152\,a^7\,b^4\,c^8\,d^6+154140672\,a^6\,b^6\,c^7\,d^6-57802752\,a^5\,b^8\,c^6\,d^6+14450688\,a^4\,b^{10}\,c^5\,d^6-2408448\,a^3\,b^{12}\,c^4\,d^6+258048\,a^2\,b^{14}\,c^3\,d^6-16128\,a\,b^{16}\,c^2\,d^6+448\,b^{18}\,c\,d^6\right)\,7{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}\right)}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}}{\frac{c\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(12845056\,a^6\,c^8\,d^3-19267584\,a^5\,b^2\,c^7\,d^3+12042240\,a^4\,b^4\,c^6\,d^3-4014080\,a^3\,b^6\,c^5\,d^3+752640\,a^2\,b^8\,c^4\,d^3-75264\,a\,b^{10}\,c^3\,d^3+3136\,b^{12}\,c^2\,d^3\right)-\frac{c\,\left(-117440512\,a^9\,c^{10}\,d^6+264241152\,a^8\,b^2\,c^9\,d^6-264241152\,a^7\,b^4\,c^8\,d^6+154140672\,a^6\,b^6\,c^7\,d^6-57802752\,a^5\,b^8\,c^6\,d^6+14450688\,a^4\,b^{10}\,c^5\,d^6-2408448\,a^3\,b^{12}\,c^4\,d^6+258048\,a^2\,b^{14}\,c^3\,d^6-16128\,a\,b^{16}\,c^2\,d^6+448\,b^{18}\,c\,d^6\right)\,7{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}\right)\,7{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}-\frac{c\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(12845056\,a^6\,c^8\,d^3-19267584\,a^5\,b^2\,c^7\,d^3+12042240\,a^4\,b^4\,c^6\,d^3-4014080\,a^3\,b^6\,c^5\,d^3+752640\,a^2\,b^8\,c^4\,d^3-75264\,a\,b^{10}\,c^3\,d^3+3136\,b^{12}\,c^2\,d^3\right)+\frac{c\,\left(-117440512\,a^9\,c^{10}\,d^6+264241152\,a^8\,b^2\,c^9\,d^6-264241152\,a^7\,b^4\,c^8\,d^6+154140672\,a^6\,b^6\,c^7\,d^6-57802752\,a^5\,b^8\,c^6\,d^6+14450688\,a^4\,b^{10}\,c^5\,d^6-2408448\,a^3\,b^{12}\,c^4\,d^6+258048\,a^2\,b^{14}\,c^3\,d^6-16128\,a\,b^{16}\,c^2\,d^6+448\,b^{18}\,c\,d^6\right)\,7{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}\right)\,7{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}}\right)}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{11/4}}","Not used",1,"((16*c*d)/(3*(4*a*c - b^2)) + (28*c*(b*d + 2*c*d*x)^2)/(3*d*(4*a*c - b^2)^2))/((b*d + 2*c*d*x)^(3/2)*(b^2*d^2 - 4*a*c*d^2) - (b*d + 2*c*d*x)^(7/2)) + (c*atan(((c*((b*d + 2*c*d*x)^(1/2)*(12845056*a^6*c^8*d^3 + 3136*b^12*c^2*d^3 - 75264*a*b^10*c^3*d^3 + 752640*a^2*b^8*c^4*d^3 - 4014080*a^3*b^6*c^5*d^3 + 12042240*a^4*b^4*c^6*d^3 - 19267584*a^5*b^2*c^7*d^3) - (7*c*(448*b^18*c*d^6 - 117440512*a^9*c^10*d^6 - 16128*a*b^16*c^2*d^6 + 258048*a^2*b^14*c^3*d^6 - 2408448*a^3*b^12*c^4*d^6 + 14450688*a^4*b^10*c^5*d^6 - 57802752*a^5*b^8*c^6*d^6 + 154140672*a^6*b^6*c^7*d^6 - 264241152*a^7*b^4*c^8*d^6 + 264241152*a^8*b^2*c^9*d^6))/(d^(5/2)*(b^2 - 4*a*c)^(11/4)))*7i)/(d^(5/2)*(b^2 - 4*a*c)^(11/4)) + (c*((b*d + 2*c*d*x)^(1/2)*(12845056*a^6*c^8*d^3 + 3136*b^12*c^2*d^3 - 75264*a*b^10*c^3*d^3 + 752640*a^2*b^8*c^4*d^3 - 4014080*a^3*b^6*c^5*d^3 + 12042240*a^4*b^4*c^6*d^3 - 19267584*a^5*b^2*c^7*d^3) + (7*c*(448*b^18*c*d^6 - 117440512*a^9*c^10*d^6 - 16128*a*b^16*c^2*d^6 + 258048*a^2*b^14*c^3*d^6 - 2408448*a^3*b^12*c^4*d^6 + 14450688*a^4*b^10*c^5*d^6 - 57802752*a^5*b^8*c^6*d^6 + 154140672*a^6*b^6*c^7*d^6 - 264241152*a^7*b^4*c^8*d^6 + 264241152*a^8*b^2*c^9*d^6))/(d^(5/2)*(b^2 - 4*a*c)^(11/4)))*7i)/(d^(5/2)*(b^2 - 4*a*c)^(11/4)))/((7*c*((b*d + 2*c*d*x)^(1/2)*(12845056*a^6*c^8*d^3 + 3136*b^12*c^2*d^3 - 75264*a*b^10*c^3*d^3 + 752640*a^2*b^8*c^4*d^3 - 4014080*a^3*b^6*c^5*d^3 + 12042240*a^4*b^4*c^6*d^3 - 19267584*a^5*b^2*c^7*d^3) - (7*c*(448*b^18*c*d^6 - 117440512*a^9*c^10*d^6 - 16128*a*b^16*c^2*d^6 + 258048*a^2*b^14*c^3*d^6 - 2408448*a^3*b^12*c^4*d^6 + 14450688*a^4*b^10*c^5*d^6 - 57802752*a^5*b^8*c^6*d^6 + 154140672*a^6*b^6*c^7*d^6 - 264241152*a^7*b^4*c^8*d^6 + 264241152*a^8*b^2*c^9*d^6))/(d^(5/2)*(b^2 - 4*a*c)^(11/4))))/(d^(5/2)*(b^2 - 4*a*c)^(11/4)) - (7*c*((b*d + 2*c*d*x)^(1/2)*(12845056*a^6*c^8*d^3 + 3136*b^12*c^2*d^3 - 75264*a*b^10*c^3*d^3 + 752640*a^2*b^8*c^4*d^3 - 4014080*a^3*b^6*c^5*d^3 + 12042240*a^4*b^4*c^6*d^3 - 19267584*a^5*b^2*c^7*d^3) + (7*c*(448*b^18*c*d^6 - 117440512*a^9*c^10*d^6 - 16128*a*b^16*c^2*d^6 + 258048*a^2*b^14*c^3*d^6 - 2408448*a^3*b^12*c^4*d^6 + 14450688*a^4*b^10*c^5*d^6 - 57802752*a^5*b^8*c^6*d^6 + 154140672*a^6*b^6*c^7*d^6 - 264241152*a^7*b^4*c^8*d^6 + 264241152*a^8*b^2*c^9*d^6))/(d^(5/2)*(b^2 - 4*a*c)^(11/4))))/(d^(5/2)*(b^2 - 4*a*c)^(11/4))))*14i)/(d^(5/2)*(b^2 - 4*a*c)^(11/4)) + (14*c*atan(((7*c*((b*d + 2*c*d*x)^(1/2)*(12845056*a^6*c^8*d^3 + 3136*b^12*c^2*d^3 - 75264*a*b^10*c^3*d^3 + 752640*a^2*b^8*c^4*d^3 - 4014080*a^3*b^6*c^5*d^3 + 12042240*a^4*b^4*c^6*d^3 - 19267584*a^5*b^2*c^7*d^3) - (c*(448*b^18*c*d^6 - 117440512*a^9*c^10*d^6 - 16128*a*b^16*c^2*d^6 + 258048*a^2*b^14*c^3*d^6 - 2408448*a^3*b^12*c^4*d^6 + 14450688*a^4*b^10*c^5*d^6 - 57802752*a^5*b^8*c^6*d^6 + 154140672*a^6*b^6*c^7*d^6 - 264241152*a^7*b^4*c^8*d^6 + 264241152*a^8*b^2*c^9*d^6)*7i)/(d^(5/2)*(b^2 - 4*a*c)^(11/4))))/(d^(5/2)*(b^2 - 4*a*c)^(11/4)) + (7*c*((b*d + 2*c*d*x)^(1/2)*(12845056*a^6*c^8*d^3 + 3136*b^12*c^2*d^3 - 75264*a*b^10*c^3*d^3 + 752640*a^2*b^8*c^4*d^3 - 4014080*a^3*b^6*c^5*d^3 + 12042240*a^4*b^4*c^6*d^3 - 19267584*a^5*b^2*c^7*d^3) + (c*(448*b^18*c*d^6 - 117440512*a^9*c^10*d^6 - 16128*a*b^16*c^2*d^6 + 258048*a^2*b^14*c^3*d^6 - 2408448*a^3*b^12*c^4*d^6 + 14450688*a^4*b^10*c^5*d^6 - 57802752*a^5*b^8*c^6*d^6 + 154140672*a^6*b^6*c^7*d^6 - 264241152*a^7*b^4*c^8*d^6 + 264241152*a^8*b^2*c^9*d^6)*7i)/(d^(5/2)*(b^2 - 4*a*c)^(11/4))))/(d^(5/2)*(b^2 - 4*a*c)^(11/4)))/((c*((b*d + 2*c*d*x)^(1/2)*(12845056*a^6*c^8*d^3 + 3136*b^12*c^2*d^3 - 75264*a*b^10*c^3*d^3 + 752640*a^2*b^8*c^4*d^3 - 4014080*a^3*b^6*c^5*d^3 + 12042240*a^4*b^4*c^6*d^3 - 19267584*a^5*b^2*c^7*d^3) - (c*(448*b^18*c*d^6 - 117440512*a^9*c^10*d^6 - 16128*a*b^16*c^2*d^6 + 258048*a^2*b^14*c^3*d^6 - 2408448*a^3*b^12*c^4*d^6 + 14450688*a^4*b^10*c^5*d^6 - 57802752*a^5*b^8*c^6*d^6 + 154140672*a^6*b^6*c^7*d^6 - 264241152*a^7*b^4*c^8*d^6 + 264241152*a^8*b^2*c^9*d^6)*7i)/(d^(5/2)*(b^2 - 4*a*c)^(11/4)))*7i)/(d^(5/2)*(b^2 - 4*a*c)^(11/4)) - (c*((b*d + 2*c*d*x)^(1/2)*(12845056*a^6*c^8*d^3 + 3136*b^12*c^2*d^3 - 75264*a*b^10*c^3*d^3 + 752640*a^2*b^8*c^4*d^3 - 4014080*a^3*b^6*c^5*d^3 + 12042240*a^4*b^4*c^6*d^3 - 19267584*a^5*b^2*c^7*d^3) + (c*(448*b^18*c*d^6 - 117440512*a^9*c^10*d^6 - 16128*a*b^16*c^2*d^6 + 258048*a^2*b^14*c^3*d^6 - 2408448*a^3*b^12*c^4*d^6 + 14450688*a^4*b^10*c^5*d^6 - 57802752*a^5*b^8*c^6*d^6 + 154140672*a^6*b^6*c^7*d^6 - 264241152*a^7*b^4*c^8*d^6 + 264241152*a^8*b^2*c^9*d^6)*7i)/(d^(5/2)*(b^2 - 4*a*c)^(11/4)))*7i)/(d^(5/2)*(b^2 - 4*a*c)^(11/4)))))/(d^(5/2)*(b^2 - 4*a*c)^(11/4))","B"
1306,1,336,203,0.892676,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^2),x)","\frac{\frac{36\,c\,{\left(b\,d+2\,c\,d\,x\right)}^4}{{\left(b^2\,d-4\,a\,c\,d\right)}^3}+\frac{16\,c\,d}{5\,\left(4\,a\,c-b^2\right)}-\frac{144\,c\,{\left(b\,d+2\,c\,d\,x\right)}^2}{5\,d\,{\left(4\,a\,c-b^2\right)}^2}}{{\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,\left(b^2\,d^2-4\,a\,c\,d^2\right)-{\left(b\,d+2\,c\,d\,x\right)}^{9/2}}-\frac{18\,c\,\mathrm{atan}\left(\frac{b^6\,\sqrt{b\,d+2\,c\,d\,x}-64\,a^3\,c^3\,\sqrt{b\,d+2\,c\,d\,x}+48\,a^2\,b^2\,c^2\,\sqrt{b\,d+2\,c\,d\,x}-12\,a\,b^4\,c\,\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{13/4}}\right)}{d^{7/2}\,{\left(b^2-4\,a\,c\right)}^{13/4}}-\frac{c\,\mathrm{atan}\left(\frac{b^6\,\sqrt{b\,d+2\,c\,d\,x}\,1{}\mathrm{i}-a^3\,c^3\,\sqrt{b\,d+2\,c\,d\,x}\,64{}\mathrm{i}+a^2\,b^2\,c^2\,\sqrt{b\,d+2\,c\,d\,x}\,48{}\mathrm{i}-a\,b^4\,c\,\sqrt{b\,d+2\,c\,d\,x}\,12{}\mathrm{i}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{13/4}}\right)\,18{}\mathrm{i}}{d^{7/2}\,{\left(b^2-4\,a\,c\right)}^{13/4}}","Not used",1,"((36*c*(b*d + 2*c*d*x)^4)/(b^2*d - 4*a*c*d)^3 + (16*c*d)/(5*(4*a*c - b^2)) - (144*c*(b*d + 2*c*d*x)^2)/(5*d*(4*a*c - b^2)^2))/((b*d + 2*c*d*x)^(5/2)*(b^2*d^2 - 4*a*c*d^2) - (b*d + 2*c*d*x)^(9/2)) - (18*c*atan((b^6*(b*d + 2*c*d*x)^(1/2) - 64*a^3*c^3*(b*d + 2*c*d*x)^(1/2) + 48*a^2*b^2*c^2*(b*d + 2*c*d*x)^(1/2) - 12*a*b^4*c*(b*d + 2*c*d*x)^(1/2))/(d^(1/2)*(b^2 - 4*a*c)^(13/4))))/(d^(7/2)*(b^2 - 4*a*c)^(13/4)) - (c*atan((b^6*(b*d + 2*c*d*x)^(1/2)*1i - a^3*c^3*(b*d + 2*c*d*x)^(1/2)*64i + a^2*b^2*c^2*(b*d + 2*c*d*x)^(1/2)*48i - a*b^4*c*(b*d + 2*c*d*x)^(1/2)*12i)/(d^(1/2)*(b^2 - 4*a*c)^(13/4)))*18i)/(d^(7/2)*(b^2 - 4*a*c)^(13/4))","B"
1307,1,364,222,0.650542,"\text{Not used}","int((b*d + 2*c*d*x)^(17/2)/(a + b*x + c*x^2)^3,x)","\frac{64\,c^2\,d^5\,{\left(b\,d+2\,c\,d\,x\right)}^{7/2}}{7}-\frac{{\left(b\,d+2\,c\,d\,x\right)}^{7/2}\,\left(864\,a^2\,c^4\,d^9-432\,a\,b^2\,c^3\,d^9+54\,b^4\,c^2\,d^9\right)+{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,\left(2944\,a^3\,c^5\,d^{11}-2208\,a^2\,b^2\,c^4\,d^{11}+552\,a\,b^4\,c^3\,d^{11}-46\,b^6\,c^2\,d^{11}\right)}{{\left(b\,d+2\,c\,d\,x\right)}^4-{\left(b\,d+2\,c\,d\,x\right)}^2\,\left(2\,b^2\,d^2-8\,a\,c\,d^2\right)+b^4\,d^4+16\,a^2\,c^2\,d^4-8\,a\,b^2\,c\,d^4}-64\,c^2\,d^7\,{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,\left(4\,a\,c-b^2\right)+165\,c^2\,d^{17/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,{\left(b^2-4\,a\,c\right)}^{7/4}}{\sqrt{d}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}\right)\,{\left(b^2-4\,a\,c\right)}^{7/4}+c^2\,d^{17/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,{\left(b^2-4\,a\,c\right)}^{7/4}\,1{}\mathrm{i}}{\sqrt{d}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}\right)\,{\left(b^2-4\,a\,c\right)}^{7/4}\,165{}\mathrm{i}","Not used",1,"(64*c^2*d^5*(b*d + 2*c*d*x)^(7/2))/7 - ((b*d + 2*c*d*x)^(7/2)*(864*a^2*c^4*d^9 + 54*b^4*c^2*d^9 - 432*a*b^2*c^3*d^9) + (b*d + 2*c*d*x)^(3/2)*(2944*a^3*c^5*d^11 - 46*b^6*c^2*d^11 + 552*a*b^4*c^3*d^11 - 2208*a^2*b^2*c^4*d^11))/((b*d + 2*c*d*x)^4 - (b*d + 2*c*d*x)^2*(2*b^2*d^2 - 8*a*c*d^2) + b^4*d^4 + 16*a^2*c^2*d^4 - 8*a*b^2*c*d^4) - 64*c^2*d^7*(b*d + 2*c*d*x)^(3/2)*(4*a*c - b^2) + 165*c^2*d^(17/2)*atan(((b*d + 2*c*d*x)^(1/2)*(b^2 - 4*a*c)^(7/4))/(d^(1/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))*(b^2 - 4*a*c)^(7/4) + c^2*d^(17/2)*atan(((b*d + 2*c*d*x)^(1/2)*(b^2 - 4*a*c)^(7/4)*1i)/(d^(1/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))*(b^2 - 4*a*c)^(7/4)*165i","B"
1308,1,966,222,0.218801,"\text{Not used}","int((b*d + 2*c*d*x)^(15/2)/(a + b*x + c*x^2)^3,x)","\frac{64\,c^2\,d^5\,{\left(b\,d+2\,c\,d\,x\right)}^{5/2}}{5}-\frac{{\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,\left(800\,a^2\,c^4\,d^9-400\,a\,b^2\,c^3\,d^9+50\,b^4\,c^2\,d^9\right)+\sqrt{b\,d+2\,c\,d\,x}\,\left(2688\,a^3\,c^5\,d^{11}-2016\,a^2\,b^2\,c^4\,d^{11}+504\,a\,b^4\,c^3\,d^{11}-42\,b^6\,c^2\,d^{11}\right)}{{\left(b\,d+2\,c\,d\,x\right)}^4-{\left(b\,d+2\,c\,d\,x\right)}^2\,\left(2\,b^2\,d^2-8\,a\,c\,d^2\right)+b^4\,d^4+16\,a^2\,c^2\,d^4-8\,a\,b^2\,c\,d^4}-192\,c^2\,d^7\,\sqrt{b\,d+2\,c\,d\,x}\,\left(4\,a\,c-b^2\right)-117\,c^2\,d^{15/2}\,\mathrm{atan}\left(\frac{b^2\,\sqrt{b\,d+2\,c\,d\,x}-4\,a\,c\,\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{5/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{5/4}+c^2\,d^{15/2}\,\mathrm{atan}\left(\frac{\frac{c^2\,d^{15/2}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(56070144\,a^4\,c^8\,d^{18}-56070144\,a^3\,b^2\,c^7\,d^{18}+21026304\,a^2\,b^4\,c^6\,d^{18}-3504384\,a\,b^6\,c^5\,d^{18}+219024\,b^8\,c^4\,d^{18}\right)-\frac{117\,c^2\,d^{15/2}\,{\left(b^2-4\,a\,c\right)}^{5/4}\,\left(239616\,a^3\,c^5\,d^{11}-179712\,a^2\,b^2\,c^4\,d^{11}+44928\,a\,b^4\,c^3\,d^{11}-3744\,b^6\,c^2\,d^{11}\right)}{2}\right)\,{\left(b^2-4\,a\,c\right)}^{5/4}\,117{}\mathrm{i}}{2}+\frac{c^2\,d^{15/2}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(56070144\,a^4\,c^8\,d^{18}-56070144\,a^3\,b^2\,c^7\,d^{18}+21026304\,a^2\,b^4\,c^6\,d^{18}-3504384\,a\,b^6\,c^5\,d^{18}+219024\,b^8\,c^4\,d^{18}\right)+\frac{117\,c^2\,d^{15/2}\,{\left(b^2-4\,a\,c\right)}^{5/4}\,\left(239616\,a^3\,c^5\,d^{11}-179712\,a^2\,b^2\,c^4\,d^{11}+44928\,a\,b^4\,c^3\,d^{11}-3744\,b^6\,c^2\,d^{11}\right)}{2}\right)\,{\left(b^2-4\,a\,c\right)}^{5/4}\,117{}\mathrm{i}}{2}}{\frac{117\,c^2\,d^{15/2}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(56070144\,a^4\,c^8\,d^{18}-56070144\,a^3\,b^2\,c^7\,d^{18}+21026304\,a^2\,b^4\,c^6\,d^{18}-3504384\,a\,b^6\,c^5\,d^{18}+219024\,b^8\,c^4\,d^{18}\right)-\frac{117\,c^2\,d^{15/2}\,{\left(b^2-4\,a\,c\right)}^{5/4}\,\left(239616\,a^3\,c^5\,d^{11}-179712\,a^2\,b^2\,c^4\,d^{11}+44928\,a\,b^4\,c^3\,d^{11}-3744\,b^6\,c^2\,d^{11}\right)}{2}\right)\,{\left(b^2-4\,a\,c\right)}^{5/4}}{2}-\frac{117\,c^2\,d^{15/2}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(56070144\,a^4\,c^8\,d^{18}-56070144\,a^3\,b^2\,c^7\,d^{18}+21026304\,a^2\,b^4\,c^6\,d^{18}-3504384\,a\,b^6\,c^5\,d^{18}+219024\,b^8\,c^4\,d^{18}\right)+\frac{117\,c^2\,d^{15/2}\,{\left(b^2-4\,a\,c\right)}^{5/4}\,\left(239616\,a^3\,c^5\,d^{11}-179712\,a^2\,b^2\,c^4\,d^{11}+44928\,a\,b^4\,c^3\,d^{11}-3744\,b^6\,c^2\,d^{11}\right)}{2}\right)\,{\left(b^2-4\,a\,c\right)}^{5/4}}{2}}\right)\,{\left(b^2-4\,a\,c\right)}^{5/4}\,117{}\mathrm{i}","Not used",1,"(64*c^2*d^5*(b*d + 2*c*d*x)^(5/2))/5 - ((b*d + 2*c*d*x)^(5/2)*(800*a^2*c^4*d^9 + 50*b^4*c^2*d^9 - 400*a*b^2*c^3*d^9) + (b*d + 2*c*d*x)^(1/2)*(2688*a^3*c^5*d^11 - 42*b^6*c^2*d^11 + 504*a*b^4*c^3*d^11 - 2016*a^2*b^2*c^4*d^11))/((b*d + 2*c*d*x)^4 - (b*d + 2*c*d*x)^2*(2*b^2*d^2 - 8*a*c*d^2) + b^4*d^4 + 16*a^2*c^2*d^4 - 8*a*b^2*c*d^4) - 192*c^2*d^7*(b*d + 2*c*d*x)^(1/2)*(4*a*c - b^2) + c^2*d^(15/2)*atan(((c^2*d^(15/2)*((b*d + 2*c*d*x)^(1/2)*(56070144*a^4*c^8*d^18 + 219024*b^8*c^4*d^18 - 3504384*a*b^6*c^5*d^18 + 21026304*a^2*b^4*c^6*d^18 - 56070144*a^3*b^2*c^7*d^18) - (117*c^2*d^(15/2)*(b^2 - 4*a*c)^(5/4)*(239616*a^3*c^5*d^11 - 3744*b^6*c^2*d^11 + 44928*a*b^4*c^3*d^11 - 179712*a^2*b^2*c^4*d^11))/2)*(b^2 - 4*a*c)^(5/4)*117i)/2 + (c^2*d^(15/2)*((b*d + 2*c*d*x)^(1/2)*(56070144*a^4*c^8*d^18 + 219024*b^8*c^4*d^18 - 3504384*a*b^6*c^5*d^18 + 21026304*a^2*b^4*c^6*d^18 - 56070144*a^3*b^2*c^7*d^18) + (117*c^2*d^(15/2)*(b^2 - 4*a*c)^(5/4)*(239616*a^3*c^5*d^11 - 3744*b^6*c^2*d^11 + 44928*a*b^4*c^3*d^11 - 179712*a^2*b^2*c^4*d^11))/2)*(b^2 - 4*a*c)^(5/4)*117i)/2)/((117*c^2*d^(15/2)*((b*d + 2*c*d*x)^(1/2)*(56070144*a^4*c^8*d^18 + 219024*b^8*c^4*d^18 - 3504384*a*b^6*c^5*d^18 + 21026304*a^2*b^4*c^6*d^18 - 56070144*a^3*b^2*c^7*d^18) - (117*c^2*d^(15/2)*(b^2 - 4*a*c)^(5/4)*(239616*a^3*c^5*d^11 - 3744*b^6*c^2*d^11 + 44928*a*b^4*c^3*d^11 - 179712*a^2*b^2*c^4*d^11))/2)*(b^2 - 4*a*c)^(5/4))/2 - (117*c^2*d^(15/2)*((b*d + 2*c*d*x)^(1/2)*(56070144*a^4*c^8*d^18 + 219024*b^8*c^4*d^18 - 3504384*a*b^6*c^5*d^18 + 21026304*a^2*b^4*c^6*d^18 - 56070144*a^3*b^2*c^7*d^18) + (117*c^2*d^(15/2)*(b^2 - 4*a*c)^(5/4)*(239616*a^3*c^5*d^11 - 3744*b^6*c^2*d^11 + 44928*a*b^4*c^3*d^11 - 179712*a^2*b^2*c^4*d^11))/2)*(b^2 - 4*a*c)^(5/4))/2))*(b^2 - 4*a*c)^(5/4)*117i - 117*c^2*d^(15/2)*atan((b^2*(b*d + 2*c*d*x)^(1/2) - 4*a*c*(b*d + 2*c*d*x)^(1/2))/(d^(1/2)*(b^2 - 4*a*c)^(5/4)))*(b^2 - 4*a*c)^(5/4)","B"
1309,1,264,193,0.625059,"\text{Not used}","int((b*d + 2*c*d*x)^(13/2)/(a + b*x + c*x^2)^3,x)","\frac{{\left(b\,d+2\,c\,d\,x\right)}^{7/2}\,\left(152\,a\,c^3\,d^7-38\,b^2\,c^2\,d^7\right)+{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,\left(480\,a^2\,c^4\,d^9-240\,a\,b^2\,c^3\,d^9+30\,b^4\,c^2\,d^9\right)}{{\left(b\,d+2\,c\,d\,x\right)}^4-{\left(b\,d+2\,c\,d\,x\right)}^2\,\left(2\,b^2\,d^2-8\,a\,c\,d^2\right)+b^4\,d^4+16\,a^2\,c^2\,d^4-8\,a\,b^2\,c\,d^4}+\frac{64\,c^2\,d^5\,{\left(b\,d+2\,c\,d\,x\right)}^{3/2}}{3}+77\,c^2\,d^{13/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{3/4}+c^2\,d^{13/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,1{}\mathrm{i}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{3/4}\,77{}\mathrm{i}","Not used",1,"((b*d + 2*c*d*x)^(7/2)*(152*a*c^3*d^7 - 38*b^2*c^2*d^7) + (b*d + 2*c*d*x)^(3/2)*(480*a^2*c^4*d^9 + 30*b^4*c^2*d^9 - 240*a*b^2*c^3*d^9))/((b*d + 2*c*d*x)^4 - (b*d + 2*c*d*x)^2*(2*b^2*d^2 - 8*a*c*d^2) + b^4*d^4 + 16*a^2*c^2*d^4 - 8*a*b^2*c*d^4) + (64*c^2*d^5*(b*d + 2*c*d*x)^(3/2))/3 + 77*c^2*d^(13/2)*atan((b*d + 2*c*d*x)^(1/2)/(d^(1/2)*(b^2 - 4*a*c)^(1/4)))*(b^2 - 4*a*c)^(3/4) + c^2*d^(13/2)*atan(((b*d + 2*c*d*x)^(1/2)*1i)/(d^(1/2)*(b^2 - 4*a*c)^(1/4)))*(b^2 - 4*a*c)^(3/4)*77i","B"
1310,1,720,191,0.205230,"\text{Not used}","int((b*d + 2*c*d*x)^(11/2)/(a + b*x + c*x^2)^3,x)","\frac{{\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,\left(136\,a\,c^3\,d^7-34\,b^2\,c^2\,d^7\right)+\sqrt{b\,d+2\,c\,d\,x}\,\left(416\,a^2\,c^4\,d^9-208\,a\,b^2\,c^3\,d^9+26\,b^4\,c^2\,d^9\right)}{{\left(b\,d+2\,c\,d\,x\right)}^4-{\left(b\,d+2\,c\,d\,x\right)}^2\,\left(2\,b^2\,d^2-8\,a\,c\,d^2\right)+b^4\,d^4+16\,a^2\,c^2\,d^4-8\,a\,b^2\,c\,d^4}+64\,c^2\,d^5\,\sqrt{b\,d+2\,c\,d\,x}-45\,c^2\,d^{11/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)\,{\left(b^2-4\,a\,c\right)}^{1/4}-c^2\,d^{11/2}\,\mathrm{atan}\left(\frac{\frac{c^2\,d^{11/2}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(518400\,a^2\,c^6\,d^{14}-259200\,a\,b^2\,c^5\,d^{14}+32400\,b^4\,c^4\,d^{14}\right)-\frac{45\,c^2\,d^{11/2}\,{\left(b^2-4\,a\,c\right)}^{1/4}\,\left(23040\,a^2\,c^4\,d^9-11520\,a\,b^2\,c^3\,d^9+1440\,b^4\,c^2\,d^9\right)}{2}\right)\,{\left(b^2-4\,a\,c\right)}^{1/4}\,45{}\mathrm{i}}{2}+\frac{c^2\,d^{11/2}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(518400\,a^2\,c^6\,d^{14}-259200\,a\,b^2\,c^5\,d^{14}+32400\,b^4\,c^4\,d^{14}\right)+\frac{45\,c^2\,d^{11/2}\,{\left(b^2-4\,a\,c\right)}^{1/4}\,\left(23040\,a^2\,c^4\,d^9-11520\,a\,b^2\,c^3\,d^9+1440\,b^4\,c^2\,d^9\right)}{2}\right)\,{\left(b^2-4\,a\,c\right)}^{1/4}\,45{}\mathrm{i}}{2}}{\frac{45\,c^2\,d^{11/2}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(518400\,a^2\,c^6\,d^{14}-259200\,a\,b^2\,c^5\,d^{14}+32400\,b^4\,c^4\,d^{14}\right)-\frac{45\,c^2\,d^{11/2}\,{\left(b^2-4\,a\,c\right)}^{1/4}\,\left(23040\,a^2\,c^4\,d^9-11520\,a\,b^2\,c^3\,d^9+1440\,b^4\,c^2\,d^9\right)}{2}\right)\,{\left(b^2-4\,a\,c\right)}^{1/4}}{2}-\frac{45\,c^2\,d^{11/2}\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(518400\,a^2\,c^6\,d^{14}-259200\,a\,b^2\,c^5\,d^{14}+32400\,b^4\,c^4\,d^{14}\right)+\frac{45\,c^2\,d^{11/2}\,{\left(b^2-4\,a\,c\right)}^{1/4}\,\left(23040\,a^2\,c^4\,d^9-11520\,a\,b^2\,c^3\,d^9+1440\,b^4\,c^2\,d^9\right)}{2}\right)\,{\left(b^2-4\,a\,c\right)}^{1/4}}{2}}\right)\,{\left(b^2-4\,a\,c\right)}^{1/4}\,45{}\mathrm{i}","Not used",1,"((b*d + 2*c*d*x)^(5/2)*(136*a*c^3*d^7 - 34*b^2*c^2*d^7) + (b*d + 2*c*d*x)^(1/2)*(416*a^2*c^4*d^9 + 26*b^4*c^2*d^9 - 208*a*b^2*c^3*d^9))/((b*d + 2*c*d*x)^4 - (b*d + 2*c*d*x)^2*(2*b^2*d^2 - 8*a*c*d^2) + b^4*d^4 + 16*a^2*c^2*d^4 - 8*a*b^2*c*d^4) + 64*c^2*d^5*(b*d + 2*c*d*x)^(1/2) - 45*c^2*d^(11/2)*atan((b*d + 2*c*d*x)^(1/2)/(d^(1/2)*(b^2 - 4*a*c)^(1/4)))*(b^2 - 4*a*c)^(1/4) - c^2*d^(11/2)*atan(((c^2*d^(11/2)*((b*d + 2*c*d*x)^(1/2)*(518400*a^2*c^6*d^14 + 32400*b^4*c^4*d^14 - 259200*a*b^2*c^5*d^14) - (45*c^2*d^(11/2)*(b^2 - 4*a*c)^(1/4)*(23040*a^2*c^4*d^9 + 1440*b^4*c^2*d^9 - 11520*a*b^2*c^3*d^9))/2)*(b^2 - 4*a*c)^(1/4)*45i)/2 + (c^2*d^(11/2)*((b*d + 2*c*d*x)^(1/2)*(518400*a^2*c^6*d^14 + 32400*b^4*c^4*d^14 - 259200*a*b^2*c^5*d^14) + (45*c^2*d^(11/2)*(b^2 - 4*a*c)^(1/4)*(23040*a^2*c^4*d^9 + 1440*b^4*c^2*d^9 - 11520*a*b^2*c^3*d^9))/2)*(b^2 - 4*a*c)^(1/4)*45i)/2)/((45*c^2*d^(11/2)*((b*d + 2*c*d*x)^(1/2)*(518400*a^2*c^6*d^14 + 32400*b^4*c^4*d^14 - 259200*a*b^2*c^5*d^14) - (45*c^2*d^(11/2)*(b^2 - 4*a*c)^(1/4)*(23040*a^2*c^4*d^9 + 1440*b^4*c^2*d^9 - 11520*a*b^2*c^3*d^9))/2)*(b^2 - 4*a*c)^(1/4))/2 - (45*c^2*d^(11/2)*((b*d + 2*c*d*x)^(1/2)*(518400*a^2*c^6*d^14 + 32400*b^4*c^4*d^14 - 259200*a*b^2*c^5*d^14) + (45*c^2*d^(11/2)*(b^2 - 4*a*c)^(1/4)*(23040*a^2*c^4*d^9 + 1440*b^4*c^2*d^9 - 11520*a*b^2*c^3*d^9))/2)*(b^2 - 4*a*c)^(1/4))/2))*(b^2 - 4*a*c)^(1/4)*45i","B"
1311,1,215,170,0.593760,"\text{Not used}","int((b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^3,x)","\frac{21\,c^2\,d^{9/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)}{{\left(b^2-4\,a\,c\right)}^{1/4}}-\frac{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,\left(56\,a\,c^3\,d^7-14\,b^2\,c^2\,d^7\right)+22\,c^2\,d^5\,{\left(b\,d+2\,c\,d\,x\right)}^{7/2}}{{\left(b\,d+2\,c\,d\,x\right)}^4-{\left(b\,d+2\,c\,d\,x\right)}^2\,\left(2\,b^2\,d^2-8\,a\,c\,d^2\right)+b^4\,d^4+16\,a^2\,c^2\,d^4-8\,a\,b^2\,c\,d^4}-\frac{21\,c^2\,d^{9/2}\,\mathrm{atanh}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{1/4}}\right)}{{\left(b^2-4\,a\,c\right)}^{1/4}}","Not used",1,"(21*c^2*d^(9/2)*atan((b*d + 2*c*d*x)^(1/2)/(d^(1/2)*(b^2 - 4*a*c)^(1/4))))/(b^2 - 4*a*c)^(1/4) - ((b*d + 2*c*d*x)^(3/2)*(56*a*c^3*d^7 - 14*b^2*c^2*d^7) + 22*c^2*d^5*(b*d + 2*c*d*x)^(7/2))/((b*d + 2*c*d*x)^4 - (b*d + 2*c*d*x)^2*(2*b^2*d^2 - 8*a*c*d^2) + b^4*d^4 + 16*a^2*c^2*d^4 - 8*a*b^2*c*d^4) - (21*c^2*d^(9/2)*atanh((b*d + 2*c*d*x)^(1/2)/(d^(1/2)*(b^2 - 4*a*c)^(1/4))))/(b^2 - 4*a*c)^(1/4)","B"
1312,1,309,170,0.593375,"\text{Not used}","int((b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^3,x)","-\frac{\sqrt{b\,d+2\,c\,d\,x}\,\left(40\,a\,c^3\,d^7-10\,b^2\,c^2\,d^7\right)+18\,c^2\,d^5\,{\left(b\,d+2\,c\,d\,x\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^4-{\left(b\,d+2\,c\,d\,x\right)}^2\,\left(2\,b^2\,d^2-8\,a\,c\,d^2\right)+b^4\,d^4+16\,a^2\,c^2\,d^4-8\,a\,b^2\,c\,d^4}-\frac{5\,c^2\,d^{7/2}\,\mathrm{atan}\left(\frac{2000\,c^6\,d^{27/2}\,\sqrt{b\,d+2\,c\,d\,x}}{\left(\frac{2000\,b^2\,c^6\,d^{14}}{{\left(b^2-4\,a\,c\right)}^{3/2}}-\frac{8000\,a\,c^7\,d^{14}}{{\left(b^2-4\,a\,c\right)}^{3/2}}\right)\,{\left(b^2-4\,a\,c\right)}^{3/4}}\right)}{{\left(b^2-4\,a\,c\right)}^{3/4}}-\frac{5\,c^2\,d^{7/2}\,\mathrm{atanh}\left(\frac{2000\,c^6\,d^{27/2}\,\sqrt{b\,d+2\,c\,d\,x}}{\left(\frac{2000\,b^2\,c^6\,d^{14}}{{\left(b^2-4\,a\,c\right)}^{3/2}}-\frac{8000\,a\,c^7\,d^{14}}{{\left(b^2-4\,a\,c\right)}^{3/2}}\right)\,{\left(b^2-4\,a\,c\right)}^{3/4}}\right)}{{\left(b^2-4\,a\,c\right)}^{3/4}}","Not used",1,"- ((b*d + 2*c*d*x)^(1/2)*(40*a*c^3*d^7 - 10*b^2*c^2*d^7) + 18*c^2*d^5*(b*d + 2*c*d*x)^(5/2))/((b*d + 2*c*d*x)^4 - (b*d + 2*c*d*x)^2*(2*b^2*d^2 - 8*a*c*d^2) + b^4*d^4 + 16*a^2*c^2*d^4 - 8*a*b^2*c*d^4) - (5*c^2*d^(7/2)*atan((2000*c^6*d^(27/2)*(b*d + 2*c*d*x)^(1/2))/(((2000*b^2*c^6*d^14)/(b^2 - 4*a*c)^(3/2) - (8000*a*c^7*d^14)/(b^2 - 4*a*c)^(3/2))*(b^2 - 4*a*c)^(3/4))))/(b^2 - 4*a*c)^(3/4) - (5*c^2*d^(7/2)*atanh((2000*c^6*d^(27/2)*(b*d + 2*c*d*x)^(1/2))/(((2000*b^2*c^6*d^14)/(b^2 - 4*a*c)^(3/2) - (8000*a*c^7*d^14)/(b^2 - 4*a*c)^(3/2))*(b^2 - 4*a*c)^(3/4))))/(b^2 - 4*a*c)^(3/4)","B"
1313,1,251,178,0.136540,"\text{Not used}","int((b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^3,x)","\frac{3\,c^2\,d^{5/2}\,\mathrm{atanh}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{9/4}}\right)}{{\left(b^2-4\,a\,c\right)}^{5/4}}-\frac{3\,c^2\,d^{5/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{9/4}}\right)}{{\left(b^2-4\,a\,c\right)}^{5/4}}-\frac{2\,c^2\,d^5\,{\left(b\,d+2\,c\,d\,x\right)}^{3/2}-\frac{6\,c^2\,d^3\,{\left(b\,d+2\,c\,d\,x\right)}^{7/2}}{4\,a\,c-b^2}}{{\left(b\,d+2\,c\,d\,x\right)}^4-{\left(b\,d+2\,c\,d\,x\right)}^2\,\left(2\,b^2\,d^2-8\,a\,c\,d^2\right)+b^4\,d^4+16\,a^2\,c^2\,d^4-8\,a\,b^2\,c\,d^4}","Not used",1,"(3*c^2*d^(5/2)*atanh(((b*d + 2*c*d*x)^(1/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c))/(d^(1/2)*(b^2 - 4*a*c)^(9/4))))/(b^2 - 4*a*c)^(5/4) - (3*c^2*d^(5/2)*atan(((b*d + 2*c*d*x)^(1/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c))/(d^(1/2)*(b^2 - 4*a*c)^(9/4))))/(b^2 - 4*a*c)^(5/4) - (2*c^2*d^5*(b*d + 2*c*d*x)^(3/2) - (6*c^2*d^3*(b*d + 2*c*d*x)^(7/2))/(4*a*c - b^2))/((b*d + 2*c*d*x)^4 - (b*d + 2*c*d*x)^2*(2*b^2*d^2 - 8*a*c*d^2) + b^4*d^4 + 16*a^2*c^2*d^4 - 8*a*b^2*c*d^4)","B"
1314,1,255,178,0.601079,"\text{Not used}","int((b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^3,x)","\frac{3\,c^2\,d^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,{\left(b^2-4\,a\,c\right)}^{7/4}}{\sqrt{d}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}\right)}{{\left(b^2-4\,a\,c\right)}^{7/4}}-\frac{6\,c^2\,d^5\,\sqrt{b\,d+2\,c\,d\,x}-\frac{2\,c^2\,d^3\,{\left(b\,d+2\,c\,d\,x\right)}^{5/2}}{4\,a\,c-b^2}}{{\left(b\,d+2\,c\,d\,x\right)}^4-{\left(b\,d+2\,c\,d\,x\right)}^2\,\left(2\,b^2\,d^2-8\,a\,c\,d^2\right)+b^4\,d^4+16\,a^2\,c^2\,d^4-8\,a\,b^2\,c\,d^4}+\frac{3\,c^2\,d^{3/2}\,\mathrm{atanh}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,{\left(b^2-4\,a\,c\right)}^{7/4}}{\sqrt{d}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}\right)}{{\left(b^2-4\,a\,c\right)}^{7/4}}","Not used",1,"(3*c^2*d^(3/2)*atan(((b*d + 2*c*d*x)^(1/2)*(b^2 - 4*a*c)^(7/4))/(d^(1/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c))))/(b^2 - 4*a*c)^(7/4) - (6*c^2*d^5*(b*d + 2*c*d*x)^(1/2) - (2*c^2*d^3*(b*d + 2*c*d*x)^(5/2))/(4*a*c - b^2))/((b*d + 2*c*d*x)^4 - (b*d + 2*c*d*x)^2*(2*b^2*d^2 - 8*a*c*d^2) + b^4*d^4 + 16*a^2*c^2*d^4 - 8*a*b^2*c*d^4) + (3*c^2*d^(3/2)*atanh(((b*d + 2*c*d*x)^(1/2)*(b^2 - 4*a*c)^(7/4))/(d^(1/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c))))/(b^2 - 4*a*c)^(7/4)","B"
1315,1,320,192,0.688823,"\text{Not used}","int((b*d + 2*c*d*x)^(1/2)/(a + b*x + c*x^2)^3,x)","\frac{\frac{10\,c^2\,d\,{\left(b\,d+2\,c\,d\,x\right)}^{7/2}}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}+\frac{18\,c^2\,d^3\,{\left(b\,d+2\,c\,d\,x\right)}^{3/2}}{4\,a\,c-b^2}}{{\left(b\,d+2\,c\,d\,x\right)}^4-{\left(b\,d+2\,c\,d\,x\right)}^2\,\left(2\,b^2\,d^2-8\,a\,c\,d^2\right)+b^4\,d^4+16\,a^2\,c^2\,d^4-8\,a\,b^2\,c\,d^4}+\frac{5\,c^2\,\sqrt{d}\,\mathrm{atan}\left(\frac{b^4\,\sqrt{b\,d+2\,c\,d\,x}+16\,a^2\,c^2\,\sqrt{b\,d+2\,c\,d\,x}-8\,a\,b^2\,c\,\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{9/4}}\right)}{{\left(b^2-4\,a\,c\right)}^{9/4}}+\frac{c^2\,\sqrt{d}\,\mathrm{atan}\left(\frac{b^4\,\sqrt{b\,d+2\,c\,d\,x}\,1{}\mathrm{i}+a^2\,c^2\,\sqrt{b\,d+2\,c\,d\,x}\,16{}\mathrm{i}-a\,b^2\,c\,\sqrt{b\,d+2\,c\,d\,x}\,8{}\mathrm{i}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{9/4}}\right)\,5{}\mathrm{i}}{{\left(b^2-4\,a\,c\right)}^{9/4}}","Not used",1,"((10*c^2*d*(b*d + 2*c*d*x)^(7/2))/(b^4 + 16*a^2*c^2 - 8*a*b^2*c) + (18*c^2*d^3*(b*d + 2*c*d*x)^(3/2))/(4*a*c - b^2))/((b*d + 2*c*d*x)^4 - (b*d + 2*c*d*x)^2*(2*b^2*d^2 - 8*a*c*d^2) + b^4*d^4 + 16*a^2*c^2*d^4 - 8*a*b^2*c*d^4) + (5*c^2*d^(1/2)*atan((b^4*(b*d + 2*c*d*x)^(1/2) + 16*a^2*c^2*(b*d + 2*c*d*x)^(1/2) - 8*a*b^2*c*(b*d + 2*c*d*x)^(1/2))/(d^(1/2)*(b^2 - 4*a*c)^(9/4))))/(b^2 - 4*a*c)^(9/4) + (c^2*d^(1/2)*atan((b^4*(b*d + 2*c*d*x)^(1/2)*1i + a^2*c^2*(b*d + 2*c*d*x)^(1/2)*16i - a*b^2*c*(b*d + 2*c*d*x)^(1/2)*8i)/(d^(1/2)*(b^2 - 4*a*c)^(9/4)))*5i)/(b^2 - 4*a*c)^(9/4)","B"
1316,1,317,192,0.176602,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^3),x)","\frac{\frac{14\,c^2\,d\,{\left(b\,d+2\,c\,d\,x\right)}^{5/2}}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}+\frac{22\,c^2\,d^3\,\sqrt{b\,d+2\,c\,d\,x}}{4\,a\,c-b^2}}{{\left(b\,d+2\,c\,d\,x\right)}^4-{\left(b\,d+2\,c\,d\,x\right)}^2\,\left(2\,b^2\,d^2-8\,a\,c\,d^2\right)+b^4\,d^4+16\,a^2\,c^2\,d^4-8\,a\,b^2\,c\,d^4}-\frac{21\,c^2\,\mathrm{atan}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,{\left(b^2-4\,a\,c\right)}^{15/4}}{\sqrt{d}\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}\right)}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{11/4}}-\frac{21\,c^2\,\mathrm{atanh}\left(\frac{\sqrt{b\,d+2\,c\,d\,x}\,{\left(b^2-4\,a\,c\right)}^{15/4}}{\sqrt{d}\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}\right)}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{11/4}}","Not used",1,"((14*c^2*d*(b*d + 2*c*d*x)^(5/2))/(b^4 + 16*a^2*c^2 - 8*a*b^2*c) + (22*c^2*d^3*(b*d + 2*c*d*x)^(1/2))/(4*a*c - b^2))/((b*d + 2*c*d*x)^4 - (b*d + 2*c*d*x)^2*(2*b^2*d^2 - 8*a*c*d^2) + b^4*d^4 + 16*a^2*c^2*d^4 - 8*a*b^2*c*d^4) - (21*c^2*atan(((b*d + 2*c*d*x)^(1/2)*(b^2 - 4*a*c)^(15/4))/(d^(1/2)*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c))))/(d^(1/2)*(b^2 - 4*a*c)^(11/4)) - (21*c^2*atanh(((b*d + 2*c*d*x)^(1/2)*(b^2 - 4*a*c)^(15/4))/(d^(1/2)*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c))))/(d^(1/2)*(b^2 - 4*a*c)^(11/4))","B"
1317,1,421,223,0.878168,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^3),x)","\frac{45\,c^2\,\mathrm{atan}\left(\frac{b^6\,\sqrt{b\,d+2\,c\,d\,x}-64\,a^3\,c^3\,\sqrt{b\,d+2\,c\,d\,x}+48\,a^2\,b^2\,c^2\,\sqrt{b\,d+2\,c\,d\,x}-12\,a\,b^4\,c\,\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{13/4}}\right)}{d^{3/2}\,{\left(b^2-4\,a\,c\right)}^{13/4}}-\frac{\frac{64\,c^2\,d^3}{4\,a\,c-b^2}-\frac{90\,c^2\,{\left(b\,d+2\,c\,d\,x\right)}^4}{-64\,d\,a^3\,c^3+48\,d\,a^2\,b^2\,c^2-12\,d\,a\,b^4\,c+d\,b^6}+\frac{162\,c^2\,d\,{\left(b\,d+2\,c\,d\,x\right)}^2}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}}{\sqrt{b\,d+2\,c\,d\,x}\,\left(16\,a^2\,c^2\,d^4-8\,a\,b^2\,c\,d^4+b^4\,d^4\right)-{\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,\left(2\,b^2\,d^2-8\,a\,c\,d^2\right)+{\left(b\,d+2\,c\,d\,x\right)}^{9/2}}+\frac{c^2\,\mathrm{atan}\left(\frac{b^6\,\sqrt{b\,d+2\,c\,d\,x}\,1{}\mathrm{i}-a^3\,c^3\,\sqrt{b\,d+2\,c\,d\,x}\,64{}\mathrm{i}+a^2\,b^2\,c^2\,\sqrt{b\,d+2\,c\,d\,x}\,48{}\mathrm{i}-a\,b^4\,c\,\sqrt{b\,d+2\,c\,d\,x}\,12{}\mathrm{i}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{13/4}}\right)\,45{}\mathrm{i}}{d^{3/2}\,{\left(b^2-4\,a\,c\right)}^{13/4}}","Not used",1,"(45*c^2*atan((b^6*(b*d + 2*c*d*x)^(1/2) - 64*a^3*c^3*(b*d + 2*c*d*x)^(1/2) + 48*a^2*b^2*c^2*(b*d + 2*c*d*x)^(1/2) - 12*a*b^4*c*(b*d + 2*c*d*x)^(1/2))/(d^(1/2)*(b^2 - 4*a*c)^(13/4))))/(d^(3/2)*(b^2 - 4*a*c)^(13/4)) - ((64*c^2*d^3)/(4*a*c - b^2) - (90*c^2*(b*d + 2*c*d*x)^4)/(b^6*d - 64*a^3*c^3*d + 48*a^2*b^2*c^2*d - 12*a*b^4*c*d) + (162*c^2*d*(b*d + 2*c*d*x)^2)/(b^4 + 16*a^2*c^2 - 8*a*b^2*c))/((b*d + 2*c*d*x)^(1/2)*(b^4*d^4 + 16*a^2*c^2*d^4 - 8*a*b^2*c*d^4) - (b*d + 2*c*d*x)^(5/2)*(2*b^2*d^2 - 8*a*c*d^2) + (b*d + 2*c*d*x)^(9/2)) + (c^2*atan((b^6*(b*d + 2*c*d*x)^(1/2)*1i - a^3*c^3*(b*d + 2*c*d*x)^(1/2)*64i + a^2*b^2*c^2*(b*d + 2*c*d*x)^(1/2)*48i - a*b^4*c*(b*d + 2*c*d*x)^(1/2)*12i)/(d^(1/2)*(b^2 - 4*a*c)^(13/4)))*45i)/(d^(3/2)*(b^2 - 4*a*c)^(13/4))","B"
1318,1,3227,225,1.111559,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^3),x)","-\frac{\frac{64\,c^2\,d^3}{3\,\left(4\,a\,c-b^2\right)}-\frac{154\,c^2\,{\left(b\,d+2\,c\,d\,x\right)}^4}{3\,\left(-64\,d\,a^3\,c^3+48\,d\,a^2\,b^2\,c^2-12\,d\,a\,b^4\,c+d\,b^6\right)}+\frac{242\,c^2\,d\,{\left(b\,d+2\,c\,d\,x\right)}^2}{3\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}}{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,\left(16\,a^2\,c^2\,d^4-8\,a\,b^2\,c\,d^4+b^4\,d^4\right)-{\left(b\,d+2\,c\,d\,x\right)}^{7/2}\,\left(2\,b^2\,d^2-8\,a\,c\,d^2\right)+{\left(b\,d+2\,c\,d\,x\right)}^{11/2}}-\frac{c^2\,\mathrm{atan}\left(\frac{\frac{c^2\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(24868028416\,a^9\,c^{13}\,d^3-55953063936\,a^8\,b^2\,c^{12}\,d^3+55953063936\,a^7\,b^4\,c^{11}\,d^3-32639287296\,a^6\,b^6\,c^{10}\,d^3+12239732736\,a^5\,b^8\,c^9\,d^3-3059933184\,a^4\,b^{10}\,c^8\,d^3+509988864\,a^3\,b^{12}\,c^7\,d^3-54641664\,a^2\,b^{14}\,c^6\,d^3+3415104\,a\,b^{16}\,c^5\,d^3-94864\,b^{18}\,c^4\,d^3\right)-\frac{77\,c^2\,\left(165356240896\,a^{13}\,c^{15}\,d^6-537407782912\,a^{12}\,b^2\,c^{14}\,d^6+806111674368\,a^{11}\,b^4\,c^{13}\,d^6-738935701504\,a^{10}\,b^6\,c^{12}\,d^6+461834813440\,a^9\,b^8\,c^{11}\,d^6-207825666048\,a^8\,b^{10}\,c^{10}\,d^6+69275222016\,a^7\,b^{12}\,c^9\,d^6-17318805504\,a^6\,b^{14}\,c^8\,d^6+3247276032\,a^5\,b^{16}\,c^7\,d^6-451010560\,a^4\,b^{18}\,c^6\,d^6+45101056\,a^3\,b^{20}\,c^5\,d^6-3075072\,a^2\,b^{22}\,c^4\,d^6+128128\,a\,b^{24}\,c^3\,d^6-2464\,b^{26}\,c^2\,d^6\right)}{2\,d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}\right)\,77{}\mathrm{i}}{2\,d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}+\frac{c^2\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(24868028416\,a^9\,c^{13}\,d^3-55953063936\,a^8\,b^2\,c^{12}\,d^3+55953063936\,a^7\,b^4\,c^{11}\,d^3-32639287296\,a^6\,b^6\,c^{10}\,d^3+12239732736\,a^5\,b^8\,c^9\,d^3-3059933184\,a^4\,b^{10}\,c^8\,d^3+509988864\,a^3\,b^{12}\,c^7\,d^3-54641664\,a^2\,b^{14}\,c^6\,d^3+3415104\,a\,b^{16}\,c^5\,d^3-94864\,b^{18}\,c^4\,d^3\right)+\frac{77\,c^2\,\left(165356240896\,a^{13}\,c^{15}\,d^6-537407782912\,a^{12}\,b^2\,c^{14}\,d^6+806111674368\,a^{11}\,b^4\,c^{13}\,d^6-738935701504\,a^{10}\,b^6\,c^{12}\,d^6+461834813440\,a^9\,b^8\,c^{11}\,d^6-207825666048\,a^8\,b^{10}\,c^{10}\,d^6+69275222016\,a^7\,b^{12}\,c^9\,d^6-17318805504\,a^6\,b^{14}\,c^8\,d^6+3247276032\,a^5\,b^{16}\,c^7\,d^6-451010560\,a^4\,b^{18}\,c^6\,d^6+45101056\,a^3\,b^{20}\,c^5\,d^6-3075072\,a^2\,b^{22}\,c^4\,d^6+128128\,a\,b^{24}\,c^3\,d^6-2464\,b^{26}\,c^2\,d^6\right)}{2\,d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}\right)\,77{}\mathrm{i}}{2\,d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}}{\frac{77\,c^2\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(24868028416\,a^9\,c^{13}\,d^3-55953063936\,a^8\,b^2\,c^{12}\,d^3+55953063936\,a^7\,b^4\,c^{11}\,d^3-32639287296\,a^6\,b^6\,c^{10}\,d^3+12239732736\,a^5\,b^8\,c^9\,d^3-3059933184\,a^4\,b^{10}\,c^8\,d^3+509988864\,a^3\,b^{12}\,c^7\,d^3-54641664\,a^2\,b^{14}\,c^6\,d^3+3415104\,a\,b^{16}\,c^5\,d^3-94864\,b^{18}\,c^4\,d^3\right)-\frac{77\,c^2\,\left(165356240896\,a^{13}\,c^{15}\,d^6-537407782912\,a^{12}\,b^2\,c^{14}\,d^6+806111674368\,a^{11}\,b^4\,c^{13}\,d^6-738935701504\,a^{10}\,b^6\,c^{12}\,d^6+461834813440\,a^9\,b^8\,c^{11}\,d^6-207825666048\,a^8\,b^{10}\,c^{10}\,d^6+69275222016\,a^7\,b^{12}\,c^9\,d^6-17318805504\,a^6\,b^{14}\,c^8\,d^6+3247276032\,a^5\,b^{16}\,c^7\,d^6-451010560\,a^4\,b^{18}\,c^6\,d^6+45101056\,a^3\,b^{20}\,c^5\,d^6-3075072\,a^2\,b^{22}\,c^4\,d^6+128128\,a\,b^{24}\,c^3\,d^6-2464\,b^{26}\,c^2\,d^6\right)}{2\,d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}\right)}{2\,d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}-\frac{77\,c^2\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(24868028416\,a^9\,c^{13}\,d^3-55953063936\,a^8\,b^2\,c^{12}\,d^3+55953063936\,a^7\,b^4\,c^{11}\,d^3-32639287296\,a^6\,b^6\,c^{10}\,d^3+12239732736\,a^5\,b^8\,c^9\,d^3-3059933184\,a^4\,b^{10}\,c^8\,d^3+509988864\,a^3\,b^{12}\,c^7\,d^3-54641664\,a^2\,b^{14}\,c^6\,d^3+3415104\,a\,b^{16}\,c^5\,d^3-94864\,b^{18}\,c^4\,d^3\right)+\frac{77\,c^2\,\left(165356240896\,a^{13}\,c^{15}\,d^6-537407782912\,a^{12}\,b^2\,c^{14}\,d^6+806111674368\,a^{11}\,b^4\,c^{13}\,d^6-738935701504\,a^{10}\,b^6\,c^{12}\,d^6+461834813440\,a^9\,b^8\,c^{11}\,d^6-207825666048\,a^8\,b^{10}\,c^{10}\,d^6+69275222016\,a^7\,b^{12}\,c^9\,d^6-17318805504\,a^6\,b^{14}\,c^8\,d^6+3247276032\,a^5\,b^{16}\,c^7\,d^6-451010560\,a^4\,b^{18}\,c^6\,d^6+45101056\,a^3\,b^{20}\,c^5\,d^6-3075072\,a^2\,b^{22}\,c^4\,d^6+128128\,a\,b^{24}\,c^3\,d^6-2464\,b^{26}\,c^2\,d^6\right)}{2\,d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}\right)}{2\,d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}}\right)\,77{}\mathrm{i}}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}-\frac{77\,c^2\,\mathrm{atan}\left(\frac{\frac{77\,c^2\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(24868028416\,a^9\,c^{13}\,d^3-55953063936\,a^8\,b^2\,c^{12}\,d^3+55953063936\,a^7\,b^4\,c^{11}\,d^3-32639287296\,a^6\,b^6\,c^{10}\,d^3+12239732736\,a^5\,b^8\,c^9\,d^3-3059933184\,a^4\,b^{10}\,c^8\,d^3+509988864\,a^3\,b^{12}\,c^7\,d^3-54641664\,a^2\,b^{14}\,c^6\,d^3+3415104\,a\,b^{16}\,c^5\,d^3-94864\,b^{18}\,c^4\,d^3\right)-\frac{c^2\,\left(165356240896\,a^{13}\,c^{15}\,d^6-537407782912\,a^{12}\,b^2\,c^{14}\,d^6+806111674368\,a^{11}\,b^4\,c^{13}\,d^6-738935701504\,a^{10}\,b^6\,c^{12}\,d^6+461834813440\,a^9\,b^8\,c^{11}\,d^6-207825666048\,a^8\,b^{10}\,c^{10}\,d^6+69275222016\,a^7\,b^{12}\,c^9\,d^6-17318805504\,a^6\,b^{14}\,c^8\,d^6+3247276032\,a^5\,b^{16}\,c^7\,d^6-451010560\,a^4\,b^{18}\,c^6\,d^6+45101056\,a^3\,b^{20}\,c^5\,d^6-3075072\,a^2\,b^{22}\,c^4\,d^6+128128\,a\,b^{24}\,c^3\,d^6-2464\,b^{26}\,c^2\,d^6\right)\,77{}\mathrm{i}}{2\,d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}\right)}{2\,d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}+\frac{77\,c^2\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(24868028416\,a^9\,c^{13}\,d^3-55953063936\,a^8\,b^2\,c^{12}\,d^3+55953063936\,a^7\,b^4\,c^{11}\,d^3-32639287296\,a^6\,b^6\,c^{10}\,d^3+12239732736\,a^5\,b^8\,c^9\,d^3-3059933184\,a^4\,b^{10}\,c^8\,d^3+509988864\,a^3\,b^{12}\,c^7\,d^3-54641664\,a^2\,b^{14}\,c^6\,d^3+3415104\,a\,b^{16}\,c^5\,d^3-94864\,b^{18}\,c^4\,d^3\right)+\frac{c^2\,\left(165356240896\,a^{13}\,c^{15}\,d^6-537407782912\,a^{12}\,b^2\,c^{14}\,d^6+806111674368\,a^{11}\,b^4\,c^{13}\,d^6-738935701504\,a^{10}\,b^6\,c^{12}\,d^6+461834813440\,a^9\,b^8\,c^{11}\,d^6-207825666048\,a^8\,b^{10}\,c^{10}\,d^6+69275222016\,a^7\,b^{12}\,c^9\,d^6-17318805504\,a^6\,b^{14}\,c^8\,d^6+3247276032\,a^5\,b^{16}\,c^7\,d^6-451010560\,a^4\,b^{18}\,c^6\,d^6+45101056\,a^3\,b^{20}\,c^5\,d^6-3075072\,a^2\,b^{22}\,c^4\,d^6+128128\,a\,b^{24}\,c^3\,d^6-2464\,b^{26}\,c^2\,d^6\right)\,77{}\mathrm{i}}{2\,d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}\right)}{2\,d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}}{\frac{c^2\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(24868028416\,a^9\,c^{13}\,d^3-55953063936\,a^8\,b^2\,c^{12}\,d^3+55953063936\,a^7\,b^4\,c^{11}\,d^3-32639287296\,a^6\,b^6\,c^{10}\,d^3+12239732736\,a^5\,b^8\,c^9\,d^3-3059933184\,a^4\,b^{10}\,c^8\,d^3+509988864\,a^3\,b^{12}\,c^7\,d^3-54641664\,a^2\,b^{14}\,c^6\,d^3+3415104\,a\,b^{16}\,c^5\,d^3-94864\,b^{18}\,c^4\,d^3\right)-\frac{c^2\,\left(165356240896\,a^{13}\,c^{15}\,d^6-537407782912\,a^{12}\,b^2\,c^{14}\,d^6+806111674368\,a^{11}\,b^4\,c^{13}\,d^6-738935701504\,a^{10}\,b^6\,c^{12}\,d^6+461834813440\,a^9\,b^8\,c^{11}\,d^6-207825666048\,a^8\,b^{10}\,c^{10}\,d^6+69275222016\,a^7\,b^{12}\,c^9\,d^6-17318805504\,a^6\,b^{14}\,c^8\,d^6+3247276032\,a^5\,b^{16}\,c^7\,d^6-451010560\,a^4\,b^{18}\,c^6\,d^6+45101056\,a^3\,b^{20}\,c^5\,d^6-3075072\,a^2\,b^{22}\,c^4\,d^6+128128\,a\,b^{24}\,c^3\,d^6-2464\,b^{26}\,c^2\,d^6\right)\,77{}\mathrm{i}}{2\,d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}\right)\,77{}\mathrm{i}}{2\,d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}-\frac{c^2\,\left(\sqrt{b\,d+2\,c\,d\,x}\,\left(24868028416\,a^9\,c^{13}\,d^3-55953063936\,a^8\,b^2\,c^{12}\,d^3+55953063936\,a^7\,b^4\,c^{11}\,d^3-32639287296\,a^6\,b^6\,c^{10}\,d^3+12239732736\,a^5\,b^8\,c^9\,d^3-3059933184\,a^4\,b^{10}\,c^8\,d^3+509988864\,a^3\,b^{12}\,c^7\,d^3-54641664\,a^2\,b^{14}\,c^6\,d^3+3415104\,a\,b^{16}\,c^5\,d^3-94864\,b^{18}\,c^4\,d^3\right)+\frac{c^2\,\left(165356240896\,a^{13}\,c^{15}\,d^6-537407782912\,a^{12}\,b^2\,c^{14}\,d^6+806111674368\,a^{11}\,b^4\,c^{13}\,d^6-738935701504\,a^{10}\,b^6\,c^{12}\,d^6+461834813440\,a^9\,b^8\,c^{11}\,d^6-207825666048\,a^8\,b^{10}\,c^{10}\,d^6+69275222016\,a^7\,b^{12}\,c^9\,d^6-17318805504\,a^6\,b^{14}\,c^8\,d^6+3247276032\,a^5\,b^{16}\,c^7\,d^6-451010560\,a^4\,b^{18}\,c^6\,d^6+45101056\,a^3\,b^{20}\,c^5\,d^6-3075072\,a^2\,b^{22}\,c^4\,d^6+128128\,a\,b^{24}\,c^3\,d^6-2464\,b^{26}\,c^2\,d^6\right)\,77{}\mathrm{i}}{2\,d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}\right)\,77{}\mathrm{i}}{2\,d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}}\right)}{d^{5/2}\,{\left(b^2-4\,a\,c\right)}^{15/4}}","Not used",1,"- ((64*c^2*d^3)/(3*(4*a*c - b^2)) - (154*c^2*(b*d + 2*c*d*x)^4)/(3*(b^6*d - 64*a^3*c^3*d + 48*a^2*b^2*c^2*d - 12*a*b^4*c*d)) + (242*c^2*d*(b*d + 2*c*d*x)^2)/(3*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))/((b*d + 2*c*d*x)^(3/2)*(b^4*d^4 + 16*a^2*c^2*d^4 - 8*a*b^2*c*d^4) - (b*d + 2*c*d*x)^(7/2)*(2*b^2*d^2 - 8*a*c*d^2) + (b*d + 2*c*d*x)^(11/2)) - (c^2*atan(((c^2*((b*d + 2*c*d*x)^(1/2)*(24868028416*a^9*c^13*d^3 - 94864*b^18*c^4*d^3 + 3415104*a*b^16*c^5*d^3 - 54641664*a^2*b^14*c^6*d^3 + 509988864*a^3*b^12*c^7*d^3 - 3059933184*a^4*b^10*c^8*d^3 + 12239732736*a^5*b^8*c^9*d^3 - 32639287296*a^6*b^6*c^10*d^3 + 55953063936*a^7*b^4*c^11*d^3 - 55953063936*a^8*b^2*c^12*d^3) - (77*c^2*(165356240896*a^13*c^15*d^6 - 2464*b^26*c^2*d^6 + 128128*a*b^24*c^3*d^6 - 3075072*a^2*b^22*c^4*d^6 + 45101056*a^3*b^20*c^5*d^6 - 451010560*a^4*b^18*c^6*d^6 + 3247276032*a^5*b^16*c^7*d^6 - 17318805504*a^6*b^14*c^8*d^6 + 69275222016*a^7*b^12*c^9*d^6 - 207825666048*a^8*b^10*c^10*d^6 + 461834813440*a^9*b^8*c^11*d^6 - 738935701504*a^10*b^6*c^12*d^6 + 806111674368*a^11*b^4*c^13*d^6 - 537407782912*a^12*b^2*c^14*d^6))/(2*d^(5/2)*(b^2 - 4*a*c)^(15/4)))*77i)/(2*d^(5/2)*(b^2 - 4*a*c)^(15/4)) + (c^2*((b*d + 2*c*d*x)^(1/2)*(24868028416*a^9*c^13*d^3 - 94864*b^18*c^4*d^3 + 3415104*a*b^16*c^5*d^3 - 54641664*a^2*b^14*c^6*d^3 + 509988864*a^3*b^12*c^7*d^3 - 3059933184*a^4*b^10*c^8*d^3 + 12239732736*a^5*b^8*c^9*d^3 - 32639287296*a^6*b^6*c^10*d^3 + 55953063936*a^7*b^4*c^11*d^3 - 55953063936*a^8*b^2*c^12*d^3) + (77*c^2*(165356240896*a^13*c^15*d^6 - 2464*b^26*c^2*d^6 + 128128*a*b^24*c^3*d^6 - 3075072*a^2*b^22*c^4*d^6 + 45101056*a^3*b^20*c^5*d^6 - 451010560*a^4*b^18*c^6*d^6 + 3247276032*a^5*b^16*c^7*d^6 - 17318805504*a^6*b^14*c^8*d^6 + 69275222016*a^7*b^12*c^9*d^6 - 207825666048*a^8*b^10*c^10*d^6 + 461834813440*a^9*b^8*c^11*d^6 - 738935701504*a^10*b^6*c^12*d^6 + 806111674368*a^11*b^4*c^13*d^6 - 537407782912*a^12*b^2*c^14*d^6))/(2*d^(5/2)*(b^2 - 4*a*c)^(15/4)))*77i)/(2*d^(5/2)*(b^2 - 4*a*c)^(15/4)))/((77*c^2*((b*d + 2*c*d*x)^(1/2)*(24868028416*a^9*c^13*d^3 - 94864*b^18*c^4*d^3 + 3415104*a*b^16*c^5*d^3 - 54641664*a^2*b^14*c^6*d^3 + 509988864*a^3*b^12*c^7*d^3 - 3059933184*a^4*b^10*c^8*d^3 + 12239732736*a^5*b^8*c^9*d^3 - 32639287296*a^6*b^6*c^10*d^3 + 55953063936*a^7*b^4*c^11*d^3 - 55953063936*a^8*b^2*c^12*d^3) - (77*c^2*(165356240896*a^13*c^15*d^6 - 2464*b^26*c^2*d^6 + 128128*a*b^24*c^3*d^6 - 3075072*a^2*b^22*c^4*d^6 + 45101056*a^3*b^20*c^5*d^6 - 451010560*a^4*b^18*c^6*d^6 + 3247276032*a^5*b^16*c^7*d^6 - 17318805504*a^6*b^14*c^8*d^6 + 69275222016*a^7*b^12*c^9*d^6 - 207825666048*a^8*b^10*c^10*d^6 + 461834813440*a^9*b^8*c^11*d^6 - 738935701504*a^10*b^6*c^12*d^6 + 806111674368*a^11*b^4*c^13*d^6 - 537407782912*a^12*b^2*c^14*d^6))/(2*d^(5/2)*(b^2 - 4*a*c)^(15/4))))/(2*d^(5/2)*(b^2 - 4*a*c)^(15/4)) - (77*c^2*((b*d + 2*c*d*x)^(1/2)*(24868028416*a^9*c^13*d^3 - 94864*b^18*c^4*d^3 + 3415104*a*b^16*c^5*d^3 - 54641664*a^2*b^14*c^6*d^3 + 509988864*a^3*b^12*c^7*d^3 - 3059933184*a^4*b^10*c^8*d^3 + 12239732736*a^5*b^8*c^9*d^3 - 32639287296*a^6*b^6*c^10*d^3 + 55953063936*a^7*b^4*c^11*d^3 - 55953063936*a^8*b^2*c^12*d^3) + (77*c^2*(165356240896*a^13*c^15*d^6 - 2464*b^26*c^2*d^6 + 128128*a*b^24*c^3*d^6 - 3075072*a^2*b^22*c^4*d^6 + 45101056*a^3*b^20*c^5*d^6 - 451010560*a^4*b^18*c^6*d^6 + 3247276032*a^5*b^16*c^7*d^6 - 17318805504*a^6*b^14*c^8*d^6 + 69275222016*a^7*b^12*c^9*d^6 - 207825666048*a^8*b^10*c^10*d^6 + 461834813440*a^9*b^8*c^11*d^6 - 738935701504*a^10*b^6*c^12*d^6 + 806111674368*a^11*b^4*c^13*d^6 - 537407782912*a^12*b^2*c^14*d^6))/(2*d^(5/2)*(b^2 - 4*a*c)^(15/4))))/(2*d^(5/2)*(b^2 - 4*a*c)^(15/4))))*77i)/(d^(5/2)*(b^2 - 4*a*c)^(15/4)) - (77*c^2*atan(((77*c^2*((b*d + 2*c*d*x)^(1/2)*(24868028416*a^9*c^13*d^3 - 94864*b^18*c^4*d^3 + 3415104*a*b^16*c^5*d^3 - 54641664*a^2*b^14*c^6*d^3 + 509988864*a^3*b^12*c^7*d^3 - 3059933184*a^4*b^10*c^8*d^3 + 12239732736*a^5*b^8*c^9*d^3 - 32639287296*a^6*b^6*c^10*d^3 + 55953063936*a^7*b^4*c^11*d^3 - 55953063936*a^8*b^2*c^12*d^3) - (c^2*(165356240896*a^13*c^15*d^6 - 2464*b^26*c^2*d^6 + 128128*a*b^24*c^3*d^6 - 3075072*a^2*b^22*c^4*d^6 + 45101056*a^3*b^20*c^5*d^6 - 451010560*a^4*b^18*c^6*d^6 + 3247276032*a^5*b^16*c^7*d^6 - 17318805504*a^6*b^14*c^8*d^6 + 69275222016*a^7*b^12*c^9*d^6 - 207825666048*a^8*b^10*c^10*d^6 + 461834813440*a^9*b^8*c^11*d^6 - 738935701504*a^10*b^6*c^12*d^6 + 806111674368*a^11*b^4*c^13*d^6 - 537407782912*a^12*b^2*c^14*d^6)*77i)/(2*d^(5/2)*(b^2 - 4*a*c)^(15/4))))/(2*d^(5/2)*(b^2 - 4*a*c)^(15/4)) + (77*c^2*((b*d + 2*c*d*x)^(1/2)*(24868028416*a^9*c^13*d^3 - 94864*b^18*c^4*d^3 + 3415104*a*b^16*c^5*d^3 - 54641664*a^2*b^14*c^6*d^3 + 509988864*a^3*b^12*c^7*d^3 - 3059933184*a^4*b^10*c^8*d^3 + 12239732736*a^5*b^8*c^9*d^3 - 32639287296*a^6*b^6*c^10*d^3 + 55953063936*a^7*b^4*c^11*d^3 - 55953063936*a^8*b^2*c^12*d^3) + (c^2*(165356240896*a^13*c^15*d^6 - 2464*b^26*c^2*d^6 + 128128*a*b^24*c^3*d^6 - 3075072*a^2*b^22*c^4*d^6 + 45101056*a^3*b^20*c^5*d^6 - 451010560*a^4*b^18*c^6*d^6 + 3247276032*a^5*b^16*c^7*d^6 - 17318805504*a^6*b^14*c^8*d^6 + 69275222016*a^7*b^12*c^9*d^6 - 207825666048*a^8*b^10*c^10*d^6 + 461834813440*a^9*b^8*c^11*d^6 - 738935701504*a^10*b^6*c^12*d^6 + 806111674368*a^11*b^4*c^13*d^6 - 537407782912*a^12*b^2*c^14*d^6)*77i)/(2*d^(5/2)*(b^2 - 4*a*c)^(15/4))))/(2*d^(5/2)*(b^2 - 4*a*c)^(15/4)))/((c^2*((b*d + 2*c*d*x)^(1/2)*(24868028416*a^9*c^13*d^3 - 94864*b^18*c^4*d^3 + 3415104*a*b^16*c^5*d^3 - 54641664*a^2*b^14*c^6*d^3 + 509988864*a^3*b^12*c^7*d^3 - 3059933184*a^4*b^10*c^8*d^3 + 12239732736*a^5*b^8*c^9*d^3 - 32639287296*a^6*b^6*c^10*d^3 + 55953063936*a^7*b^4*c^11*d^3 - 55953063936*a^8*b^2*c^12*d^3) - (c^2*(165356240896*a^13*c^15*d^6 - 2464*b^26*c^2*d^6 + 128128*a*b^24*c^3*d^6 - 3075072*a^2*b^22*c^4*d^6 + 45101056*a^3*b^20*c^5*d^6 - 451010560*a^4*b^18*c^6*d^6 + 3247276032*a^5*b^16*c^7*d^6 - 17318805504*a^6*b^14*c^8*d^6 + 69275222016*a^7*b^12*c^9*d^6 - 207825666048*a^8*b^10*c^10*d^6 + 461834813440*a^9*b^8*c^11*d^6 - 738935701504*a^10*b^6*c^12*d^6 + 806111674368*a^11*b^4*c^13*d^6 - 537407782912*a^12*b^2*c^14*d^6)*77i)/(2*d^(5/2)*(b^2 - 4*a*c)^(15/4)))*77i)/(2*d^(5/2)*(b^2 - 4*a*c)^(15/4)) - (c^2*((b*d + 2*c*d*x)^(1/2)*(24868028416*a^9*c^13*d^3 - 94864*b^18*c^4*d^3 + 3415104*a*b^16*c^5*d^3 - 54641664*a^2*b^14*c^6*d^3 + 509988864*a^3*b^12*c^7*d^3 - 3059933184*a^4*b^10*c^8*d^3 + 12239732736*a^5*b^8*c^9*d^3 - 32639287296*a^6*b^6*c^10*d^3 + 55953063936*a^7*b^4*c^11*d^3 - 55953063936*a^8*b^2*c^12*d^3) + (c^2*(165356240896*a^13*c^15*d^6 - 2464*b^26*c^2*d^6 + 128128*a*b^24*c^3*d^6 - 3075072*a^2*b^22*c^4*d^6 + 45101056*a^3*b^20*c^5*d^6 - 451010560*a^4*b^18*c^6*d^6 + 3247276032*a^5*b^16*c^7*d^6 - 17318805504*a^6*b^14*c^8*d^6 + 69275222016*a^7*b^12*c^9*d^6 - 207825666048*a^8*b^10*c^10*d^6 + 461834813440*a^9*b^8*c^11*d^6 - 738935701504*a^10*b^6*c^12*d^6 + 806111674368*a^11*b^4*c^13*d^6 - 537407782912*a^12*b^2*c^14*d^6)*77i)/(2*d^(5/2)*(b^2 - 4*a*c)^(15/4)))*77i)/(2*d^(5/2)*(b^2 - 4*a*c)^(15/4)))))/(d^(5/2)*(b^2 - 4*a*c)^(15/4))","B"
1319,1,543,256,0.997037,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^3),x)","\frac{\frac{234\,c^2\,{\left(b\,d+2\,c\,d\,x\right)}^6}{256\,a^4\,c^4\,d^3-256\,a^3\,b^2\,c^3\,d^3+96\,a^2\,b^4\,c^2\,d^3-16\,a\,b^6\,c\,d^3+b^8\,d^3}-\frac{2106\,c^2\,{\left(b\,d+2\,c\,d\,x\right)}^4}{5\,\left(-64\,d\,a^3\,c^3+48\,d\,a^2\,b^2\,c^2-12\,d\,a\,b^4\,c+d\,b^6\right)}-\frac{64\,c^2\,d^3}{5\,\left(4\,a\,c-b^2\right)}+\frac{832\,c^2\,d\,{\left(b\,d+2\,c\,d\,x\right)}^2}{5\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}}{{\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,\left(16\,a^2\,c^2\,d^4-8\,a\,b^2\,c\,d^4+b^4\,d^4\right)-{\left(b\,d+2\,c\,d\,x\right)}^{9/2}\,\left(2\,b^2\,d^2-8\,a\,c\,d^2\right)+{\left(b\,d+2\,c\,d\,x\right)}^{13/2}}+\frac{117\,c^2\,\mathrm{atan}\left(\frac{b^8\,\sqrt{b\,d+2\,c\,d\,x}+256\,a^4\,c^4\,\sqrt{b\,d+2\,c\,d\,x}+96\,a^2\,b^4\,c^2\,\sqrt{b\,d+2\,c\,d\,x}-256\,a^3\,b^2\,c^3\,\sqrt{b\,d+2\,c\,d\,x}-16\,a\,b^6\,c\,\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{17/4}}\right)}{d^{7/2}\,{\left(b^2-4\,a\,c\right)}^{17/4}}+\frac{c^2\,\mathrm{atan}\left(\frac{b^8\,\sqrt{b\,d+2\,c\,d\,x}\,1{}\mathrm{i}+a^4\,c^4\,\sqrt{b\,d+2\,c\,d\,x}\,256{}\mathrm{i}+a^2\,b^4\,c^2\,\sqrt{b\,d+2\,c\,d\,x}\,96{}\mathrm{i}-a^3\,b^2\,c^3\,\sqrt{b\,d+2\,c\,d\,x}\,256{}\mathrm{i}-a\,b^6\,c\,\sqrt{b\,d+2\,c\,d\,x}\,16{}\mathrm{i}}{\sqrt{d}\,{\left(b^2-4\,a\,c\right)}^{17/4}}\right)\,117{}\mathrm{i}}{d^{7/2}\,{\left(b^2-4\,a\,c\right)}^{17/4}}","Not used",1,"((234*c^2*(b*d + 2*c*d*x)^6)/(b^8*d^3 + 256*a^4*c^4*d^3 + 96*a^2*b^4*c^2*d^3 - 256*a^3*b^2*c^3*d^3 - 16*a*b^6*c*d^3) - (2106*c^2*(b*d + 2*c*d*x)^4)/(5*(b^6*d - 64*a^3*c^3*d + 48*a^2*b^2*c^2*d - 12*a*b^4*c*d)) - (64*c^2*d^3)/(5*(4*a*c - b^2)) + (832*c^2*d*(b*d + 2*c*d*x)^2)/(5*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))/((b*d + 2*c*d*x)^(5/2)*(b^4*d^4 + 16*a^2*c^2*d^4 - 8*a*b^2*c*d^4) - (b*d + 2*c*d*x)^(9/2)*(2*b^2*d^2 - 8*a*c*d^2) + (b*d + 2*c*d*x)^(13/2)) + (117*c^2*atan((b^8*(b*d + 2*c*d*x)^(1/2) + 256*a^4*c^4*(b*d + 2*c*d*x)^(1/2) + 96*a^2*b^4*c^2*(b*d + 2*c*d*x)^(1/2) - 256*a^3*b^2*c^3*(b*d + 2*c*d*x)^(1/2) - 16*a*b^6*c*(b*d + 2*c*d*x)^(1/2))/(d^(1/2)*(b^2 - 4*a*c)^(17/4))))/(d^(7/2)*(b^2 - 4*a*c)^(17/4)) + (c^2*atan((b^8*(b*d + 2*c*d*x)^(1/2)*1i + a^4*c^4*(b*d + 2*c*d*x)^(1/2)*256i + a^2*b^4*c^2*(b*d + 2*c*d*x)^(1/2)*96i - a^3*b^2*c^3*(b*d + 2*c*d*x)^(1/2)*256i - a*b^6*c*(b*d + 2*c*d*x)^(1/2)*16i)/(d^(1/2)*(b^2 - 4*a*c)^(17/4)))*117i)/(d^(7/2)*(b^2 - 4*a*c)^(17/4))","B"
1320,1,75,183,0.104210,"\text{Not used}","int((2*x + 1)^(7/2)/(x + x^2 + 1),x)","\frac{4\,{\left(2\,x+1\right)}^{5/2}}{5}-12\,\sqrt{2\,x+1}+\sqrt{2}\,3^{1/4}\,\mathrm{atan}\left(\sqrt{2}\,3^{3/4}\,\sqrt{2\,x+1}\,\left(\frac{1}{6}-\frac{1}{6}{}\mathrm{i}\right)\right)\,\left(3+3{}\mathrm{i}\right)+\sqrt{2}\,3^{1/4}\,\mathrm{atan}\left(\sqrt{2}\,3^{3/4}\,\sqrt{2\,x+1}\,\left(\frac{1}{6}+\frac{1}{6}{}\mathrm{i}\right)\right)\,\left(3-3{}\mathrm{i}\right)","Not used",1,"(4*(2*x + 1)^(5/2))/5 - 12*(2*x + 1)^(1/2) + 2^(1/2)*3^(1/4)*atan(2^(1/2)*3^(3/4)*(2*x + 1)^(1/2)*(1/6 - 1i/6))*(3 + 3i) + 2^(1/2)*3^(1/4)*atan(2^(1/2)*3^(3/4)*(2*x + 1)^(1/2)*(1/6 + 1i/6))*(3 - 3i)","B"
1321,1,66,170,0.093665,"\text{Not used}","int((2*x + 1)^(5/2)/(x + x^2 + 1),x)","\frac{4\,{\left(2\,x+1\right)}^{3/2}}{3}+\sqrt{2}\,3^{3/4}\,\mathrm{atan}\left(\sqrt{2}\,3^{3/4}\,\sqrt{2\,x+1}\,\left(\frac{1}{6}-\frac{1}{6}{}\mathrm{i}\right)\right)\,\left(-1+1{}\mathrm{i}\right)+\sqrt{2}\,3^{3/4}\,\mathrm{atan}\left(\sqrt{2}\,3^{3/4}\,\sqrt{2\,x+1}\,\left(\frac{1}{6}+\frac{1}{6}{}\mathrm{i}\right)\right)\,\left(-1-\mathrm{i}\right)","Not used",1,"(4*(2*x + 1)^(3/2))/3 - 2^(1/2)*3^(3/4)*atan(2^(1/2)*3^(3/4)*(2*x + 1)^(1/2)*(1/6 - 1i/6))*(1 - 1i) - 2^(1/2)*3^(3/4)*atan(2^(1/2)*3^(3/4)*(2*x + 1)^(1/2)*(1/6 + 1i/6))*(1 + 1i)","B"
1322,1,66,168,0.517697,"\text{Not used}","int((2*x + 1)^(3/2)/(x + x^2 + 1),x)","4\,\sqrt{2\,x+1}+\sqrt{2}\,3^{1/4}\,\mathrm{atan}\left(\sqrt{2}\,3^{3/4}\,\sqrt{2\,x+1}\,\left(\frac{1}{6}-\frac{1}{6}{}\mathrm{i}\right)\right)\,\left(-1-\mathrm{i}\right)+\sqrt{2}\,3^{1/4}\,\mathrm{atan}\left(\sqrt{2}\,3^{3/4}\,\sqrt{2\,x+1}\,\left(\frac{1}{6}+\frac{1}{6}{}\mathrm{i}\right)\right)\,\left(-1+1{}\mathrm{i}\right)","Not used",1,"4*(2*x + 1)^(1/2) - 2^(1/2)*3^(1/4)*atan(2^(1/2)*3^(3/4)*(2*x + 1)^(1/2)*(1/6 - 1i/6))*(1 + 1i) - 2^(1/2)*3^(1/4)*atan(2^(1/2)*3^(3/4)*(2*x + 1)^(1/2)*(1/6 + 1i/6))*(1 - 1i)","B"
1323,1,57,157,0.516549,"\text{Not used}","int((2*x + 1)^(1/2)/(x + x^2 + 1),x)","\sqrt{2}\,3^{3/4}\,\mathrm{atan}\left(\sqrt{2}\,3^{3/4}\,\sqrt{2\,x+1}\,\left(\frac{1}{6}-\frac{1}{6}{}\mathrm{i}\right)\right)\,\left(\frac{1}{3}-\frac{1}{3}{}\mathrm{i}\right)+\sqrt{2}\,3^{3/4}\,\mathrm{atan}\left(\sqrt{2}\,3^{3/4}\,\sqrt{2\,x+1}\,\left(\frac{1}{6}+\frac{1}{6}{}\mathrm{i}\right)\right)\,\left(\frac{1}{3}+\frac{1}{3}{}\mathrm{i}\right)","Not used",1,"2^(1/2)*3^(3/4)*atan(2^(1/2)*3^(3/4)*(2*x + 1)^(1/2)*(1/6 - 1i/6))*(1/3 - 1i/3) + 2^(1/2)*3^(3/4)*atan(2^(1/2)*3^(3/4)*(2*x + 1)^(1/2)*(1/6 + 1i/6))*(1/3 + 1i/3)","B"
1324,1,57,157,0.083666,"\text{Not used}","int(1/((2*x + 1)^(1/2)*(x + x^2 + 1)),x)","\sqrt{2}\,3^{1/4}\,\mathrm{atan}\left(\sqrt{2}\,3^{3/4}\,\sqrt{2\,x+1}\,\left(\frac{1}{6}-\frac{1}{6}{}\mathrm{i}\right)\right)\,\left(\frac{1}{3}+\frac{1}{3}{}\mathrm{i}\right)+\sqrt{2}\,3^{1/4}\,\mathrm{atan}\left(\sqrt{2}\,3^{3/4}\,\sqrt{2\,x+1}\,\left(\frac{1}{6}+\frac{1}{6}{}\mathrm{i}\right)\right)\,\left(\frac{1}{3}-\frac{1}{3}{}\mathrm{i}\right)","Not used",1,"2^(1/2)*3^(1/4)*atan(2^(1/2)*3^(3/4)*(2*x + 1)^(1/2)*(1/6 - 1i/6))*(1/3 + 1i/3) + 2^(1/2)*3^(1/4)*atan(2^(1/2)*3^(3/4)*(2*x + 1)^(1/2)*(1/6 + 1i/6))*(1/3 - 1i/3)","B"
1325,1,66,180,0.531906,"\text{Not used}","int(1/((2*x + 1)^(3/2)*(x + x^2 + 1)),x)","-\frac{4}{3\,\sqrt{2\,x+1}}+\sqrt{2}\,3^{3/4}\,\mathrm{atan}\left(\sqrt{2}\,3^{3/4}\,\sqrt{2\,x+1}\,\left(\frac{1}{6}-\frac{1}{6}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{9}+\frac{1}{9}{}\mathrm{i}\right)+\sqrt{2}\,3^{3/4}\,\mathrm{atan}\left(\sqrt{2}\,3^{3/4}\,\sqrt{2\,x+1}\,\left(\frac{1}{6}+\frac{1}{6}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{9}-\frac{1}{9}{}\mathrm{i}\right)","Not used",1,"- 4/(3*(2*x + 1)^(1/2)) - 2^(1/2)*3^(3/4)*atan(2^(1/2)*3^(3/4)*(2*x + 1)^(1/2)*(1/6 - 1i/6))*(1/9 - 1i/9) - 2^(1/2)*3^(3/4)*atan(2^(1/2)*3^(3/4)*(2*x + 1)^(1/2)*(1/6 + 1i/6))*(1/9 + 1i/9)","B"
1326,1,66,180,0.095644,"\text{Not used}","int(1/((2*x + 1)^(5/2)*(x + x^2 + 1)),x)","-\frac{4}{9\,{\left(2\,x+1\right)}^{3/2}}+\sqrt{2}\,3^{1/4}\,\mathrm{atan}\left(\sqrt{2}\,3^{3/4}\,\sqrt{2\,x+1}\,\left(\frac{1}{6}-\frac{1}{6}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{9}-\frac{1}{9}{}\mathrm{i}\right)+\sqrt{2}\,3^{1/4}\,\mathrm{atan}\left(\sqrt{2}\,3^{3/4}\,\sqrt{2\,x+1}\,\left(\frac{1}{6}+\frac{1}{6}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{9}+\frac{1}{9}{}\mathrm{i}\right)","Not used",1,"- 4/(9*(2*x + 1)^(3/2)) - 2^(1/2)*3^(1/4)*atan(2^(1/2)*3^(3/4)*(2*x + 1)^(1/2)*(1/6 - 1i/6))*(1/9 + 1i/9) - 2^(1/2)*3^(1/4)*atan(2^(1/2)*3^(3/4)*(2*x + 1)^(1/2)*(1/6 + 1i/6))*(1/9 - 1i/9)","B"
1327,0,-1,227,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(1/2),x)","\int {\left(b\,d+2\,c\,d\,x\right)}^{7/2}\,\sqrt{c\,x^2+b\,x+a} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(1/2), x)","F"
1328,0,-1,180,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(1/2),x)","\int {\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,\sqrt{c\,x^2+b\,x+a} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(1/2), x)","F"
1329,0,-1,137,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(1/2),x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{\sqrt{b\,d+2\,c\,d\,x}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(1/2), x)","F"
1330,0,-1,137,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(5/2),x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(b\,d+2\,c\,d\,x\right)}^{5/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(5/2), x)","F"
1331,0,-1,184,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(9/2),x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(b\,d+2\,c\,d\,x\right)}^{9/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(9/2), x)","F"
1332,0,-1,231,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(13/2),x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(b\,d+2\,c\,d\,x\right)}^{13/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(13/2), x)","F"
1333,0,-1,279,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(1/2),x)","\int {\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,\sqrt{c\,x^2+b\,x+a} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(1/2), x)","F"
1334,0,-1,236,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(1/2),x)","\int \sqrt{b\,d+2\,c\,d\,x}\,\sqrt{c\,x^2+b\,x+a} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(1/2), x)","F"
1335,0,-1,229,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(3/2),x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(3/2), x)","F"
1336,0,-1,283,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(7/2),x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(b\,d+2\,c\,d\,x\right)}^{7/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(7/2), x)","F"
1337,0,-1,274,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(3/2),x)","\int {\left(b\,d+2\,c\,d\,x\right)}^{7/2}\,{\left(c\,x^2+b\,x+a\right)}^{3/2} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(3/2), x)","F"
1338,0,-1,227,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(3/2),x)","\int {\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,{\left(c\,x^2+b\,x+a\right)}^{3/2} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(3/2), x)","F"
1339,0,-1,182,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(1/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{\sqrt{b\,d+2\,c\,d\,x}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(1/2), x)","F"
1340,0,-1,174,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(5/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{5/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(5/2), x)","F"
1341,0,-1,174,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(9/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{9/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(9/2), x)","F"
1342,0,-1,221,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(13/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{13/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(13/2), x)","F"
1343,0,-1,268,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(17/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{17/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(17/2), x)","F"
1344,0,-1,326,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(3/2),x)","\int {\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,{\left(c\,x^2+b\,x+a\right)}^{3/2} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(3/2), x)","F"
1345,0,-1,281,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(3/2),x)","\int \sqrt{b\,d+2\,c\,d\,x}\,{\left(c\,x^2+b\,x+a\right)}^{3/2} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(3/2), x)","F"
1346,0,-1,271,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(3/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(3/2), x)","F"
1347,0,-1,273,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(7/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{7/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(7/2), x)","F"
1348,0,-1,320,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(11/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{11/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(11/2), x)","F"
1349,0,-1,321,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(5/2),x)","\int {\left(b\,d+2\,c\,d\,x\right)}^{7/2}\,{\left(c\,x^2+b\,x+a\right)}^{5/2} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(5/2), x)","F"
1350,0,-1,274,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(5/2),x)","\int {\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,{\left(c\,x^2+b\,x+a\right)}^{5/2} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(5/2), x)","F"
1351,0,-1,229,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(1/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{\sqrt{b\,d+2\,c\,d\,x}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(1/2), x)","F"
1352,0,-1,219,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(5/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{5/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(5/2), x)","F"
1353,0,-1,211,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(9/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{9/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(9/2), x)","F"
1354,0,-1,211,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(13/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{13/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(13/2), x)","F"
1355,0,-1,258,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(17/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{17/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(17/2), x)","F"
1356,0,-1,305,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(21/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{21/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(21/2), x)","F"
1357,0,-1,373,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(5/2),x)","\int {\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,{\left(c\,x^2+b\,x+a\right)}^{5/2} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(5/2), x)","F"
1358,0,-1,328,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(5/2),x)","\int \sqrt{b\,d+2\,c\,d\,x}\,{\left(c\,x^2+b\,x+a\right)}^{5/2} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(5/2), x)","F"
1359,0,-1,316,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(3/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(3/2), x)","F"
1360,0,-1,310,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(7/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{7/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(7/2), x)","F"
1361,0,-1,310,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(11/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{11/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(11/2), x)","F"
1362,0,-1,357,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(15/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(b\,d+2\,c\,d\,x\right)}^{15/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(15/2), x)","F"
1363,0,-1,174,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^(1/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^{7/2}}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^(1/2), x)","F"
1364,0,-1,132,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^(1/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^(1/2), x)","F"
1365,0,-1,97,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{b\,d+2\,c\,d\,x}\,\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(1/2)), x)","F"
1366,0,-1,144,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(1/2)),x)","\int \frac{1}{{\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(1/2)), x)","F"
1367,0,-1,188,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(9/2)*(a + b*x + c*x^2)^(1/2)),x)","\int \frac{1}{{\left(b\,d+2\,c\,d\,x\right)}^{9/2}\,\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)^(9/2)*(a + b*x + c*x^2)^(1/2)), x)","F"
1368,0,-1,273,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^(1/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^{9/2}}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^(1/2), x)","F"
1369,0,-1,231,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^(1/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^{5/2}}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^(1/2), x)","F"
1370,0,-1,195,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(1/2)/(a + b*x + c*x^2)^(1/2),x)","\int \frac{\sqrt{b\,d+2\,c\,d\,x}}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(1/2)/(a + b*x + c*x^2)^(1/2), x)","F"
1371,0,-1,237,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(1/2)),x)","\int \frac{1}{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(1/2)), x)","F"
1372,0,-1,287,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(1/2)),x)","\int \frac{1}{{\left(b\,d+2\,c\,d\,x\right)}^{7/2}\,\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(1/2)), x)","F"
1373,0,-1,79,0.000000,"\text{Not used}","int((3 - 2*x)^(3/2)/(x^2 - 3*x + 1)^(1/2),x)","\int \frac{{\left(3-2\,x\right)}^{3/2}}{\sqrt{x^2-3\,x+1}} \,d x","Not used",1,"int((3 - 2*x)^(3/2)/(x^2 - 3*x + 1)^(1/2), x)","F"
1374,0,-1,51,0.000000,"\text{Not used}","int(1/((3 - 2*x)^(1/2)*(x^2 - 3*x + 1)^(1/2)),x)","\int \frac{1}{\sqrt{3-2\,x}\,\sqrt{x^2-3\,x+1}} \,d x","Not used",1,"int(1/((3 - 2*x)^(1/2)*(x^2 - 3*x + 1)^(1/2)), x)","F"
1375,0,-1,79,0.000000,"\text{Not used}","int(1/((3 - 2*x)^(5/2)*(x^2 - 3*x + 1)^(1/2)),x)","\int \frac{1}{{\left(3-2\,x\right)}^{5/2}\,\sqrt{x^2-3\,x+1}} \,d x","Not used",1,"int(1/((3 - 2*x)^(5/2)*(x^2 - 3*x + 1)^(1/2)), x)","F"
1376,0,-1,128,0.000000,"\text{Not used}","int((3 - 2*x)^(5/2)/(x^2 - 3*x + 1)^(1/2),x)","\int \frac{{\left(3-2\,x\right)}^{5/2}}{\sqrt{x^2-3\,x+1}} \,d x","Not used",1,"int((3 - 2*x)^(5/2)/(x^2 - 3*x + 1)^(1/2), x)","F"
1377,0,-1,103,0.000000,"\text{Not used}","int((3 - 2*x)^(1/2)/(x^2 - 3*x + 1)^(1/2),x)","\int \frac{\sqrt{3-2\,x}}{\sqrt{x^2-3\,x+1}} \,d x","Not used",1,"int((3 - 2*x)^(1/2)/(x^2 - 3*x + 1)^(1/2), x)","F"
1378,0,-1,128,0.000000,"\text{Not used}","int(1/((3 - 2*x)^(3/2)*(x^2 - 3*x + 1)^(1/2)),x)","\int \frac{1}{{\left(3-2\,x\right)}^{3/2}\,\sqrt{x^2-3\,x+1}} \,d x","Not used",1,"int(1/((3 - 2*x)^(3/2)*(x^2 - 3*x + 1)^(1/2)), x)","F"
1379,0,-1,205,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(11/2)/(a + b*x + c*x^2)^(3/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^{11/2}}{{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(11/2)/(a + b*x + c*x^2)^(3/2), x)","F"
1380,0,-1,162,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^(3/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^{7/2}}{{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^(3/2), x)","F"
1381,0,-1,125,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^(3/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}}{{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^(3/2), x)","F"
1382,0,-1,137,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(3/2)),x)","\int \frac{1}{\sqrt{b\,d+2\,c\,d\,x}\,{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(3/2)), x)","F"
1383,0,-1,184,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(3/2)),x)","\int \frac{1}{{\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(3/2)), x)","F"
1384,0,-1,258,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^(3/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^{9/2}}{{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^(3/2), x)","F"
1385,0,-1,219,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^(3/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^{5/2}}{{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^(3/2), x)","F"
1386,0,-1,231,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(1/2)/(a + b*x + c*x^2)^(3/2),x)","\int \frac{\sqrt{b\,d+2\,c\,d\,x}}{{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(1/2)/(a + b*x + c*x^2)^(3/2), x)","F"
1387,0,-1,274,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(3/2)),x)","\int \frac{1}{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(3/2)), x)","F"
1388,0,-1,325,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(3/2)),x)","\int \frac{1}{{\left(b\,d+2\,c\,d\,x\right)}^{7/2}\,{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(3/2)), x)","F"
1389,0,-1,247,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(15/2)/(a + b*x + c*x^2)^(5/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^{15/2}}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(15/2)/(a + b*x + c*x^2)^(5/2), x)","F"
1390,0,-1,196,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(11/2)/(a + b*x + c*x^2)^(5/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^{11/2}}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(11/2)/(a + b*x + c*x^2)^(5/2), x)","F"
1391,0,-1,165,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^(5/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^{7/2}}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^(5/2), x)","F"
1392,0,-1,173,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^(5/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^(5/2), x)","F"
1393,0,-1,187,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(5/2)),x)","\int \frac{1}{\sqrt{b\,d+2\,c\,d\,x}\,{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(5/2)), x)","F"
1394,0,-1,228,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(5/2)),x)","\int \frac{1}{{\left(b\,d+2\,c\,d\,x\right)}^{5/2}\,{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(5/2)), x)","F"
1395,0,-1,299,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(13/2)/(a + b*x + c*x^2)^(5/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^{13/2}}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(13/2)/(a + b*x + c*x^2)^(5/2), x)","F"
1396,0,-1,258,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^(5/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^{9/2}}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^(5/2), x)","F"
1397,0,-1,264,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^(5/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^{5/2}}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^(5/2), x)","F"
1398,0,-1,278,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^(1/2)/(a + b*x + c*x^2)^(5/2),x)","\int \frac{\sqrt{b\,d+2\,c\,d\,x}}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^(1/2)/(a + b*x + c*x^2)^(5/2), x)","F"
1399,0,-1,325,0.000000,"\text{Not used}","int(1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(5/2)),x)","\int \frac{1}{{\left(b\,d+2\,c\,d\,x\right)}^{3/2}\,{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int(1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(5/2)), x)","F"
1400,0,-1,170,0.000000,"\text{Not used}","int((c*e + d*e*x)^(11/2)/(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2),x)","\int \frac{{\left(c\,e+d\,e\,x\right)}^{11/2}}{\sqrt{-c^2-2\,c\,d\,x-d^2\,x^2+1}} \,d x","Not used",1,"int((c*e + d*e*x)^(11/2)/(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2), x)","F"
1401,0,-1,124,0.000000,"\text{Not used}","int((c*e + d*e*x)^(7/2)/(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2),x)","\int \frac{{\left(c\,e+d\,e\,x\right)}^{7/2}}{\sqrt{-c^2-2\,c\,d\,x-d^2\,x^2+1}} \,d x","Not used",1,"int((c*e + d*e*x)^(7/2)/(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2), x)","F"
1402,0,-1,78,0.000000,"\text{Not used}","int((c*e + d*e*x)^(3/2)/(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2),x)","\int \frac{{\left(c\,e+d\,e\,x\right)}^{3/2}}{\sqrt{-c^2-2\,c\,d\,x-d^2\,x^2+1}} \,d x","Not used",1,"int((c*e + d*e*x)^(3/2)/(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2), x)","F"
1403,0,-1,31,0.000000,"\text{Not used}","int(1/((c*e + d*e*x)^(1/2)*(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2)),x)","\int \frac{1}{\sqrt{c\,e+d\,e\,x}\,\sqrt{-c^2-2\,c\,d\,x-d^2\,x^2+1}} \,d x","Not used",1,"int(1/((c*e + d*e*x)^(1/2)*(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2)), x)","F"
1404,0,-1,80,0.000000,"\text{Not used}","int(1/((c*e + d*e*x)^(5/2)*(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2)),x)","\int \frac{1}{{\left(c\,e+d\,e\,x\right)}^{5/2}\,\sqrt{-c^2-2\,c\,d\,x-d^2\,x^2+1}} \,d x","Not used",1,"int(1/((c*e + d*e*x)^(5/2)*(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2)), x)","F"
1405,0,-1,126,0.000000,"\text{Not used}","int(1/((c*e + d*e*x)^(9/2)*(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2)),x)","\int \frac{1}{{\left(c\,e+d\,e\,x\right)}^{9/2}\,\sqrt{-c^2-2\,c\,d\,x-d^2\,x^2+1}} \,d x","Not used",1,"int(1/((c*e + d*e*x)^(9/2)*(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2)), x)","F"
1406,0,-1,172,0.000000,"\text{Not used}","int(1/((c*e + d*e*x)^(13/2)*(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2)),x)","\int \frac{1}{{\left(c\,e+d\,e\,x\right)}^{13/2}\,\sqrt{-c^2-2\,c\,d\,x-d^2\,x^2+1}} \,d x","Not used",1,"int(1/((c*e + d*e*x)^(13/2)*(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2)), x)","F"
1407,0,-1,157,0.000000,"\text{Not used}","int((c*e + d*e*x)^(9/2)/(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2),x)","\int \frac{{\left(c\,e+d\,e\,x\right)}^{9/2}}{\sqrt{-c^2-2\,c\,d\,x-d^2\,x^2+1}} \,d x","Not used",1,"int((c*e + d*e*x)^(9/2)/(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2), x)","F"
1408,0,-1,111,0.000000,"\text{Not used}","int((c*e + d*e*x)^(5/2)/(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2),x)","\int \frac{{\left(c\,e+d\,e\,x\right)}^{5/2}}{\sqrt{-c^2-2\,c\,d\,x-d^2\,x^2+1}} \,d x","Not used",1,"int((c*e + d*e*x)^(5/2)/(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2), x)","F"
1409,0,-1,63,0.000000,"\text{Not used}","int((c*e + d*e*x)^(1/2)/(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2),x)","\int \frac{\sqrt{c\,e+d\,e\,x}}{\sqrt{-c^2-2\,c\,d\,x-d^2\,x^2+1}} \,d x","Not used",1,"int((c*e + d*e*x)^(1/2)/(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2), x)","F"
1410,0,-1,107,0.000000,"\text{Not used}","int(1/((c*e + d*e*x)^(3/2)*(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2)),x)","\int \frac{1}{{\left(c\,e+d\,e\,x\right)}^{3/2}\,\sqrt{-c^2-2\,c\,d\,x-d^2\,x^2+1}} \,d x","Not used",1,"int(1/((c*e + d*e*x)^(3/2)*(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2)), x)","F"
1411,0,-1,159,0.000000,"\text{Not used}","int(1/((c*e + d*e*x)^(7/2)*(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2)),x)","\int \frac{1}{{\left(c\,e+d\,e\,x\right)}^{7/2}\,\sqrt{-c^2-2\,c\,d\,x-d^2\,x^2+1}} \,d x","Not used",1,"int(1/((c*e + d*e*x)^(7/2)*(1 - d^2*x^2 - 2*c*d*x - c^2)^(1/2)), x)","F"
1412,0,-1,320,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(11/3),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{4/3}}{{\left(b\,d+2\,c\,d\,x\right)}^{11/3}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(11/3), x)","F"
1413,0,-1,44,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(17/3),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{4/3}}{{\left(b\,d+2\,c\,d\,x\right)}^{17/3}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(17/3), x)","F"
1414,0,-1,89,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(23/3),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{4/3}}{{\left(b\,d+2\,c\,d\,x\right)}^{23/3}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(23/3), x)","F"
1415,0,-1,133,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(29/3),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{4/3}}{{\left(b\,d+2\,c\,d\,x\right)}^{29/3}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(29/3), x)","F"
1416,0,-1,597,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(2/3),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{4/3}}{{\left(b\,d+2\,c\,d\,x\right)}^{2/3}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(2/3), x)","F"
1417,0,-1,581,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(8/3),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{4/3}}{{\left(b\,d+2\,c\,d\,x\right)}^{8/3}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(8/3), x)","F"
1418,0,-1,591,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(14/3),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{4/3}}{{\left(b\,d+2\,c\,d\,x\right)}^{14/3}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(14/3), x)","F"
1419,0,-1,637,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(20/3),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{4/3}}{{\left(b\,d+2\,c\,d\,x\right)}^{20/3}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(20/3), x)","F"
1420,0,-1,99,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(4/3),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{4/3}}{{\left(b\,d+2\,c\,d\,x\right)}^{4/3}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(4/3), x)","F"
1421,0,-1,99,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(10/3),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{4/3}}{{\left(b\,d+2\,c\,d\,x\right)}^{10/3}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(10/3), x)","F"
1422,0,-1,99,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(16/3),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{4/3}}{{\left(b\,d+2\,c\,d\,x\right)}^{16/3}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(16/3), x)","F"
1423,1,655,141,1.113812,"\text{Not used}","int((b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^3,x)","{\left(b\,d+2\,c\,d\,x\right)}^m\,\left(\frac{4\,a^3\,b\,c^3\,m^3+60\,a^3\,b\,c^3\,m^2+284\,a^3\,b\,c^3\,m+420\,a^3\,b\,c^3-6\,a^2\,b^3\,c^2\,m^2-72\,a^2\,b^3\,c^2\,m-210\,a^2\,b^3\,c^2+6\,a\,b^5\,c\,m+42\,a\,b^5\,c-3\,b^7}{8\,c^4\,\left(m^4+16\,m^3+86\,m^2+176\,m+105\right)}+\frac{c^3\,x^7\,\left(m^3+9\,m^2+23\,m+15\right)}{m^4+16\,m^3+86\,m^2+176\,m+105}+\frac{x\,\left(8\,a^3\,c^4\,m^3+120\,a^3\,c^4\,m^2+568\,a^3\,c^4\,m+840\,a^3\,c^4+12\,a^2\,b^2\,c^3\,m^3+144\,a^2\,b^2\,c^3\,m^2+420\,a^2\,b^2\,c^3\,m-12\,a\,b^4\,c^2\,m^2-84\,a\,b^4\,c^2\,m+6\,b^6\,c\,m\right)}{8\,c^4\,\left(m^4+16\,m^3+86\,m^2+176\,m+105\right)}+\frac{5\,b\,x^4\,\left(m^2+4\,m+3\right)\,\left(42\,a\,c+2\,b^2\,m+7\,b^2+6\,a\,c\,m\right)}{4\,\left(m^4+16\,m^3+86\,m^2+176\,m+105\right)}+\frac{3\,c\,x^5\,\left(m^2+4\,m+3\right)\,\left(14\,a\,c+3\,b^2\,m+14\,b^2+2\,a\,c\,m\right)}{2\,\left(m^4+16\,m^3+86\,m^2+176\,m+105\right)}+\frac{x^3\,\left(m+1\right)\,\left(6\,a^2\,c^2\,m^2+72\,a^2\,c^2\,m+210\,a^2\,c^2+12\,a\,b^2\,c\,m^2+114\,a\,b^2\,c\,m+210\,a\,b^2\,c+b^4\,m^2+2\,b^4\,m\right)}{2\,c\,\left(m^4+16\,m^3+86\,m^2+176\,m+105\right)}+\frac{7\,b\,c^2\,x^6\,\left(m^3+9\,m^2+23\,m+15\right)}{2\,\left(m^4+16\,m^3+86\,m^2+176\,m+105\right)}+\frac{3\,b\,x^2\,\left(m+1\right)\,\left(6\,a^2\,c^2\,m^2+72\,a^2\,c^2\,m+210\,a^2\,c^2+2\,a\,b^2\,c\,m^2+14\,a\,b^2\,c\,m-b^4\,m\right)}{4\,c^2\,\left(m^4+16\,m^3+86\,m^2+176\,m+105\right)}\right)","Not used",1,"(b*d + 2*c*d*x)^m*((420*a^3*b*c^3 - 3*b^7 - 210*a^2*b^3*c^2 + 42*a*b^5*c - 72*a^2*b^3*c^2*m + 60*a^3*b*c^3*m^2 + 4*a^3*b*c^3*m^3 + 6*a*b^5*c*m - 6*a^2*b^3*c^2*m^2 + 284*a^3*b*c^3*m)/(8*c^4*(176*m + 86*m^2 + 16*m^3 + m^4 + 105)) + (c^3*x^7*(23*m + 9*m^2 + m^3 + 15))/(176*m + 86*m^2 + 16*m^3 + m^4 + 105) + (x*(840*a^3*c^4 + 568*a^3*c^4*m + 120*a^3*c^4*m^2 + 8*a^3*c^4*m^3 + 6*b^6*c*m + 420*a^2*b^2*c^3*m - 12*a*b^4*c^2*m^2 + 144*a^2*b^2*c^3*m^2 + 12*a^2*b^2*c^3*m^3 - 84*a*b^4*c^2*m))/(8*c^4*(176*m + 86*m^2 + 16*m^3 + m^4 + 105)) + (5*b*x^4*(4*m + m^2 + 3)*(42*a*c + 2*b^2*m + 7*b^2 + 6*a*c*m))/(4*(176*m + 86*m^2 + 16*m^3 + m^4 + 105)) + (3*c*x^5*(4*m + m^2 + 3)*(14*a*c + 3*b^2*m + 14*b^2 + 2*a*c*m))/(2*(176*m + 86*m^2 + 16*m^3 + m^4 + 105)) + (x^3*(m + 1)*(2*b^4*m + 210*a^2*c^2 + b^4*m^2 + 72*a^2*c^2*m + 6*a^2*c^2*m^2 + 210*a*b^2*c + 114*a*b^2*c*m + 12*a*b^2*c*m^2))/(2*c*(176*m + 86*m^2 + 16*m^3 + m^4 + 105)) + (7*b*c^2*x^6*(23*m + 9*m^2 + m^3 + 15))/(2*(176*m + 86*m^2 + 16*m^3 + m^4 + 105)) + (3*b*x^2*(m + 1)*(210*a^2*c^2 - b^4*m + 72*a^2*c^2*m + 6*a^2*c^2*m^2 + 14*a*b^2*c*m + 2*a*b^2*c*m^2))/(4*c^2*(176*m + 86*m^2 + 16*m^3 + m^4 + 105)))","B"
1424,1,307,103,0.753555,"\text{Not used}","int((b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^2,x)","{\left(b\,d+2\,c\,d\,x\right)}^m\,\left(\frac{x\,\left(4\,a^2\,c^3\,m^2+32\,a^2\,c^3\,m+60\,a^2\,c^3+4\,a\,b^2\,c^2\,m^2+20\,a\,b^2\,c^2\,m-2\,b^4\,c\,m\right)}{4\,c^3\,\left(m^3+9\,m^2+23\,m+15\right)}+\frac{b\,\left(2\,a^2\,c^2\,m^2+16\,a^2\,c^2\,m+30\,a^2\,c^2-2\,a\,b^2\,c\,m-10\,a\,b^2\,c+b^4\right)}{4\,c^3\,\left(m^3+9\,m^2+23\,m+15\right)}+\frac{x^3\,\left(m+1\right)\,\left(10\,a\,c+2\,b^2\,m+5\,b^2+2\,a\,c\,m\right)}{m^3+9\,m^2+23\,m+15}+\frac{c^2\,x^5\,\left(m^2+4\,m+3\right)}{m^3+9\,m^2+23\,m+15}+\frac{5\,b\,c\,x^4\,\left(m^2+4\,m+3\right)}{2\,\left(m^3+9\,m^2+23\,m+15\right)}+\frac{b\,x^2\,\left(m+1\right)\,\left(m\,b^2+30\,a\,c+6\,a\,c\,m\right)}{2\,c\,\left(m^3+9\,m^2+23\,m+15\right)}\right)","Not used",1,"(b*d + 2*c*d*x)^m*((x*(60*a^2*c^3 + 32*a^2*c^3*m + 4*a^2*c^3*m^2 - 2*b^4*c*m + 4*a*b^2*c^2*m^2 + 20*a*b^2*c^2*m))/(4*c^3*(23*m + 9*m^2 + m^3 + 15)) + (b*(b^4 + 30*a^2*c^2 + 16*a^2*c^2*m + 2*a^2*c^2*m^2 - 10*a*b^2*c - 2*a*b^2*c*m))/(4*c^3*(23*m + 9*m^2 + m^3 + 15)) + (x^3*(m + 1)*(10*a*c + 2*b^2*m + 5*b^2 + 2*a*c*m))/(23*m + 9*m^2 + m^3 + 15) + (c^2*x^5*(4*m + m^2 + 3))/(23*m + 9*m^2 + m^3 + 15) + (5*b*c*x^4*(4*m + m^2 + 3))/(2*(23*m + 9*m^2 + m^3 + 15)) + (b*x^2*(m + 1)*(30*a*c + b^2*m + 6*a*c*m))/(2*c*(23*m + 9*m^2 + m^3 + 15)))","B"
1425,1,120,65,0.579083,"\text{Not used}","int((b*d + 2*c*d*x)^m*(a + b*x + c*x^2),x)","{\left(b\,d+2\,c\,d\,x\right)}^m\,\left(\frac{b\,\left(-b^2+6\,a\,c+2\,a\,c\,m\right)}{4\,c^2\,\left(m^2+4\,m+3\right)}+\frac{x\,\left(12\,a\,c^2+4\,a\,c^2\,m+2\,b^2\,c\,m\right)}{4\,c^2\,\left(m^2+4\,m+3\right)}+\frac{3\,b\,x^2\,\left(m+1\right)}{2\,\left(m^2+4\,m+3\right)}+\frac{c\,x^3\,\left(m+1\right)}{m^2+4\,m+3}\right)","Not used",1,"(b*d + 2*c*d*x)^m*((b*(6*a*c - b^2 + 2*a*c*m))/(4*c^2*(4*m + m^2 + 3)) + (x*(12*a*c^2 + 4*a*c^2*m + 2*b^2*c*m))/(4*c^2*(4*m + m^2 + 3)) + (3*b*x^2*(m + 1))/(2*(4*m + m^2 + 3)) + (c*x^3*(m + 1))/(4*m + m^2 + 3))","B"
1426,0,-1,67,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^m/(a + b*x + c*x^2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^m}{c\,x^2+b\,x+a} \,d x","Not used",1,"int((b*d + 2*c*d*x)^m/(a + b*x + c*x^2), x)","F"
1427,0,-1,68,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^2,x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^m}{{\left(c\,x^2+b\,x+a\right)}^2} \,d x","Not used",1,"int((b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^2, x)","F"
1428,0,-1,70,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^3,x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^m}{{\left(c\,x^2+b\,x+a\right)}^3} \,d x","Not used",1,"int((b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^3, x)","F"
1429,0,-1,82,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^(5/2),x)","\int {\left(b\,d+2\,c\,d\,x\right)}^m\,{\left(c\,x^2+b\,x+a\right)}^{5/2} \,d x","Not used",1,"int((b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^(5/2), x)","F"
1430,0,-1,98,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^(3/2),x)","\int {\left(b\,d+2\,c\,d\,x\right)}^m\,{\left(c\,x^2+b\,x+a\right)}^{3/2} \,d x","Not used",1,"int((b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^(3/2), x)","F"
1431,0,-1,98,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^(1/2),x)","\int {\left(b\,d+2\,c\,d\,x\right)}^m\,\sqrt{c\,x^2+b\,x+a} \,d x","Not used",1,"int((b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^(1/2), x)","F"
1432,0,-1,96,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^(1/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^m}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^(1/2), x)","F"
1433,0,-1,94,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^(3/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^m}{{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^(3/2), x)","F"
1434,0,-1,96,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^(5/2),x)","\int \frac{{\left(b\,d+2\,c\,d\,x\right)}^m}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^(5/2), x)","F"
1435,0,-1,107,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^p,x)","\int {\left(b\,d+2\,c\,d\,x\right)}^m\,{\left(c\,x^2+b\,x+a\right)}^p \,d x","Not used",1,"int((b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^p, x)","F"
1436,1,375,121,0.831091,"\text{Not used}","int((b*d + 2*c*d*x)^5*(a + b*x + c*x^2)^p,x)","{\left(c\,x^2+b\,x+a\right)}^p\,\left(\frac{a\,d^5\,\left(32\,a^2\,c^2-8\,a\,b^2\,c\,p-24\,a\,b^2\,c+b^4\,p^2+5\,b^4\,p+6\,b^4\right)}{p^3+6\,p^2+11\,p+6}+\frac{c\,d^5\,x^2\,\left(-32\,a^2\,c^2\,p+24\,a\,b^2\,c\,p^2+40\,a\,b^2\,c\,p+9\,b^4\,p^2+37\,b^4\,p+30\,b^4\right)}{p^3+6\,p^2+11\,p+6}+\frac{16\,c^5\,d^5\,x^6\,\left(p^2+3\,p+2\right)}{p^3+6\,p^2+11\,p+6}+\frac{b\,d^5\,x\,\left(-32\,a^2\,c^2\,p+8\,a\,b^2\,c\,p^2+24\,a\,b^2\,c\,p+b^4\,p^2+5\,b^4\,p+6\,b^4\right)}{p^3+6\,p^2+11\,p+6}+\frac{48\,b\,c^4\,d^5\,x^5\,\left(p^2+3\,p+2\right)}{p^3+6\,p^2+11\,p+6}+\frac{8\,c^3\,d^5\,x^4\,\left(p+1\right)\,\left(7\,b^2\,p+15\,b^2+2\,a\,c\,p\right)}{p^3+6\,p^2+11\,p+6}+\frac{16\,b\,c^2\,d^5\,x^3\,\left(p+1\right)\,\left(2\,b^2\,p+5\,b^2+2\,a\,c\,p\right)}{p^3+6\,p^2+11\,p+6}\right)","Not used",1,"(a + b*x + c*x^2)^p*((a*d^5*(5*b^4*p + 6*b^4 + 32*a^2*c^2 + b^4*p^2 - 24*a*b^2*c - 8*a*b^2*c*p))/(11*p + 6*p^2 + p^3 + 6) + (c*d^5*x^2*(37*b^4*p + 30*b^4 + 9*b^4*p^2 - 32*a^2*c^2*p + 40*a*b^2*c*p + 24*a*b^2*c*p^2))/(11*p + 6*p^2 + p^3 + 6) + (16*c^5*d^5*x^6*(3*p + p^2 + 2))/(11*p + 6*p^2 + p^3 + 6) + (b*d^5*x*(5*b^4*p + 6*b^4 + b^4*p^2 - 32*a^2*c^2*p + 24*a*b^2*c*p + 8*a*b^2*c*p^2))/(11*p + 6*p^2 + p^3 + 6) + (48*b*c^4*d^5*x^5*(3*p + p^2 + 2))/(11*p + 6*p^2 + p^3 + 6) + (8*c^3*d^5*x^4*(p + 1)*(7*b^2*p + 15*b^2 + 2*a*c*p))/(11*p + 6*p^2 + p^3 + 6) + (16*b*c^2*d^5*x^3*(p + 1)*(2*b^2*p + 5*b^2 + 2*a*c*p))/(11*p + 6*p^2 + p^3 + 6))","B"
1437,0,-1,90,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^p,x)","\int {\left(b\,d+2\,c\,d\,x\right)}^4\,{\left(c\,x^2+b\,x+a\right)}^p \,d x","Not used",1,"int((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^p, x)","F"
1438,1,160,68,0.653346,"\text{Not used}","int((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^p,x)","{\left(c\,x^2+b\,x+a\right)}^p\,\left(\frac{a\,d^3\,\left(b^2\,p-4\,a\,c+2\,b^2\right)}{p^2+3\,p+2}+\frac{c\,d^3\,x^2\,\left(5\,b^2\,p+6\,b^2+4\,a\,c\,p\right)}{p^2+3\,p+2}+\frac{4\,c^3\,d^3\,x^4\,\left(p+1\right)}{p^2+3\,p+2}+\frac{b\,d^3\,x\,\left(b^2\,p+2\,b^2+4\,a\,c\,p\right)}{p^2+3\,p+2}+\frac{8\,b\,c^2\,d^3\,x^3\,\left(p+1\right)}{p^2+3\,p+2}\right)","Not used",1,"(a + b*x + c*x^2)^p*((a*d^3*(b^2*p - 4*a*c + 2*b^2))/(3*p + p^2 + 2) + (c*d^3*x^2*(5*b^2*p + 6*b^2 + 4*a*c*p))/(3*p + p^2 + 2) + (4*c^3*d^3*x^4*(p + 1))/(3*p + p^2 + 2) + (b*d^3*x*(b^2*p + 2*b^2 + 4*a*c*p))/(3*p + p^2 + 2) + (8*b*c^2*d^3*x^3*(p + 1))/(3*p + p^2 + 2))","B"
1439,0,-1,90,0.000000,"\text{Not used}","int((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^p,x)","\int {\left(b\,d+2\,c\,d\,x\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^p \,d x","Not used",1,"int((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^p, x)","F"
1440,1,42,21,0.520425,"\text{Not used}","int((b*d + 2*c*d*x)*(a + b*x + c*x^2)^p,x)","{\left(c\,x^2+b\,x+a\right)}^p\,\left(\frac{a\,d}{p+1}+\frac{c\,d\,x^2}{p+1}+\frac{b\,d\,x}{p+1}\right)","Not used",1,"(a + b*x + c*x^2)^p*((a*d)/(p + 1) + (c*d*x^2)/(p + 1) + (b*d*x)/(p + 1))","B"
1441,0,-1,63,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(b*d + 2*c*d*x),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{b\,d+2\,c\,d\,x} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(b*d + 2*c*d*x), x)","F"
1442,0,-1,88,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^2,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{{\left(b\,d+2\,c\,d\,x\right)}^2} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^2, x)","F"
1443,0,-1,63,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^3,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{{\left(b\,d+2\,c\,d\,x\right)}^3} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^3, x)","F"
1444,0,-1,90,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^4,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{{\left(b\,d+2\,c\,d\,x\right)}^4} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^4, x)","F"
1445,0,-1,63,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^5,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{{\left(b\,d+2\,c\,d\,x\right)}^5} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^5, x)","F"
1446,0,-1,90,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^6,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{{\left(b\,d+2\,c\,d\,x\right)}^6} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^6, x)","F"
1447,1,11,16,0.601061,"\text{Not used}","int((x + 1)/(2*x + x^2 - 3)^(2/3),x)","\frac{3\,{\left(\left(x-1\right)\,\left(x+3\right)\right)}^{1/3}}{2}","Not used",1,"(3*((x - 1)*(x + 3))^(1/3))/2","B"
1448,1,15,19,0.601149,"\text{Not used}","int((b + c*x)/(a + 2*b*x + c*x^2)^(3/7),x)","\frac{7\,{\left(c\,x^2+2\,b\,x+a\right)}^{4/7}}{8}","Not used",1,"(7*(a + 2*b*x + c*x^2)^(4/7))/8","B"
1449,1,26,26,0.585881,"\text{Not used}","int((x + 1)^m*(2*x + x^2 + 1)^n,x)","\frac{{\left(x+1\right)}^{m+1}\,{\left(x^2+2\,x+1\right)}^n}{m+2\,n+1}","Not used",1,"((x + 1)^(m + 1)*(2*x + x^2 + 1)^n)/(m + 2*n + 1)","B"
1450,1,51,50,0.666905,"\text{Not used}","int((e*x + (b*e)/(2*c))^m*(b*x + c*x^2 + b^2/(4*c))^n,x)","\frac{{\left(e\,x+\frac{b\,e}{2\,c}\right)}^m\,\left(b+2\,c\,x\right)\,{\left(b\,x+c\,x^2+\frac{b^2}{4\,c}\right)}^n}{2\,c\,\left(m+2\,n+1\right)}","Not used",1,"((e*x + (b*e)/(2*c))^m*(b + 2*c*x)*(b*x + c*x^2 + b^2/(4*c))^n)/(2*c*(m + 2*n + 1))","B"
1451,1,144,65,0.531076,"\text{Not used}","int((d + e*x)^4*(a^2 + b^2*x^2 + 2*a*b*x),x)","x^3\,\left(2\,a^2\,d^2\,e^2+\frac{8\,a\,b\,d^3\,e}{3}+\frac{b^2\,d^4}{3}\right)+x^5\,\left(\frac{a^2\,e^4}{5}+\frac{8\,a\,b\,d\,e^3}{5}+\frac{6\,b^2\,d^2\,e^2}{5}\right)+a^2\,d^4\,x+\frac{b^2\,e^4\,x^7}{7}+a\,d^3\,x^2\,\left(2\,a\,e+b\,d\right)+\frac{b\,e^3\,x^6\,\left(a\,e+2\,b\,d\right)}{3}+d\,e\,x^4\,\left(a^2\,e^2+3\,a\,b\,d\,e+b^2\,d^2\right)","Not used",1,"x^3*((b^2*d^4)/3 + 2*a^2*d^2*e^2 + (8*a*b*d^3*e)/3) + x^5*((a^2*e^4)/5 + (6*b^2*d^2*e^2)/5 + (8*a*b*d*e^3)/5) + a^2*d^4*x + (b^2*e^4*x^7)/7 + a*d^3*x^2*(2*a*e + b*d) + (b*e^3*x^6*(a*e + 2*b*d))/3 + d*e*x^4*(a^2*e^2 + b^2*d^2 + 3*a*b*d*e)","B"
1452,1,115,65,0.505310,"\text{Not used}","int((d + e*x)^3*(a^2 + b^2*x^2 + 2*a*b*x),x)","x^3\,\left(a^2\,d\,e^2+2\,a\,b\,d^2\,e+\frac{b^2\,d^3}{3}\right)+x^4\,\left(\frac{a^2\,e^3}{4}+\frac{3\,a\,b\,d\,e^2}{2}+\frac{3\,b^2\,d^2\,e}{4}\right)+a^2\,d^3\,x+\frac{b^2\,e^3\,x^6}{6}+\frac{a\,d^2\,x^2\,\left(3\,a\,e+2\,b\,d\right)}{2}+\frac{b\,e^2\,x^5\,\left(2\,a\,e+3\,b\,d\right)}{5}","Not used",1,"x^3*((b^2*d^3)/3 + a^2*d*e^2 + 2*a*b*d^2*e) + x^4*((a^2*e^3)/4 + (3*b^2*d^2*e)/4 + (3*a*b*d*e^2)/2) + a^2*d^3*x + (b^2*e^3*x^6)/6 + (a*d^2*x^2*(3*a*e + 2*b*d))/2 + (b*e^2*x^5*(2*a*e + 3*b*d))/5","B"
1453,1,74,65,0.043174,"\text{Not used}","int((d + e*x)^2*(a^2 + b^2*x^2 + 2*a*b*x),x)","x^3\,\left(\frac{a^2\,e^2}{3}+\frac{4\,a\,b\,d\,e}{3}+\frac{b^2\,d^2}{3}\right)+a^2\,d^2\,x+\frac{b^2\,e^2\,x^5}{5}+a\,d\,x^2\,\left(a\,e+b\,d\right)+\frac{b\,e\,x^4\,\left(a\,e+b\,d\right)}{2}","Not used",1,"x^3*((a^2*e^2)/3 + (b^2*d^2)/3 + (4*a*b*d*e)/3) + a^2*d^2*x + (b^2*e^2*x^5)/5 + a*d*x^2*(a*e + b*d) + (b*e*x^4*(a*e + b*d))/2","B"
1454,1,47,38,0.047171,"\text{Not used}","int((d + e*x)*(a^2 + b^2*x^2 + 2*a*b*x),x)","x^2\,\left(\frac{e\,a^2}{2}+b\,d\,a\right)+x^3\,\left(\frac{d\,b^2}{3}+\frac{2\,a\,e\,b}{3}\right)+\frac{b^2\,e\,x^4}{4}+a^2\,d\,x","Not used",1,"x^2*((a^2*e)/2 + a*b*d) + x^3*((b^2*d)/3 + (2*a*b*e)/3) + (b^2*e*x^4)/4 + a^2*d*x","B"
1455,1,20,22,0.028310,"\text{Not used}","int(a^2 + b^2*x^2 + 2*a*b*x,x)","a^2\,x+a\,b\,x^2+\frac{b^2\,x^3}{3}","Not used",1,"a^2*x + (b^2*x^3)/3 + a*b*x^2","B"
1456,1,62,50,0.523170,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)/(d + e*x),x)","\frac{\ln\left(d+e\,x\right)\,\left(a^2\,e^2-2\,a\,b\,d\,e+b^2\,d^2\right)}{e^3}-x\,\left(\frac{b^2\,d}{e^2}-\frac{2\,a\,b}{e}\right)+\frac{b^2\,x^2}{2\,e}","Not used",1,"(log(d + e*x)*(a^2*e^2 + b^2*d^2 - 2*a*b*d*e))/e^3 - x*((b^2*d)/e^2 - (2*a*b)/e) + (b^2*x^2)/(2*e)","B"
1457,1,71,51,0.080559,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)/(d + e*x)^2,x)","\frac{b^2\,x}{e^2}-\frac{a^2\,e^2-2\,a\,b\,d\,e+b^2\,d^2}{e\,\left(x\,e^3+d\,e^2\right)}-\frac{\ln\left(d+e\,x\right)\,\left(2\,b^2\,d-2\,a\,b\,e\right)}{e^3}","Not used",1,"(b^2*x)/e^2 - (a^2*e^2 + b^2*d^2 - 2*a*b*d*e)/(e*(d*e^2 + e^3*x)) - (log(d + e*x)*(2*b^2*d - 2*a*b*e))/e^3","B"
1458,1,77,59,0.078078,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)/(d + e*x)^3,x)","\frac{b^2\,\ln\left(d+e\,x\right)}{e^3}-\frac{\frac{a^2\,e^2+2\,a\,b\,d\,e-3\,b^2\,d^2}{2\,e^3}+\frac{2\,b\,x\,\left(a\,e-b\,d\right)}{e^2}}{d^2+2\,d\,e\,x+e^2\,x^2}","Not used",1,"(b^2*log(d + e*x))/e^3 - ((a^2*e^2 - 3*b^2*d^2 + 2*a*b*d*e)/(2*e^3) + (2*b*x*(a*e - b*d))/e^2)/(d^2 + e^2*x^2 + 2*d*e*x)","B"
1459,1,80,28,0.047844,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)/(d + e*x)^4,x)","-\frac{\frac{a^2\,e^2+a\,b\,d\,e+b^2\,d^2}{3\,e^3}+\frac{b^2\,x^2}{e}+\frac{b\,x\,\left(a\,e+b\,d\right)}{e^2}}{d^3+3\,d^2\,e\,x+3\,d\,e^2\,x^2+e^3\,x^3}","Not used",1,"-((a^2*e^2 + b^2*d^2 + a*b*d*e)/(3*e^3) + (b^2*x^2)/e + (b*x*(a*e + b*d))/e^2)/(d^3 + e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x)","B"
1460,1,96,65,0.058067,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)/(d + e*x)^5,x)","-\frac{\frac{3\,a^2\,e^2+2\,a\,b\,d\,e+b^2\,d^2}{12\,e^3}+\frac{b^2\,x^2}{2\,e}+\frac{b\,x\,\left(2\,a\,e+b\,d\right)}{3\,e^2}}{d^4+4\,d^3\,e\,x+6\,d^2\,e^2\,x^2+4\,d\,e^3\,x^3+e^4\,x^4}","Not used",1,"-((3*a^2*e^2 + b^2*d^2 + 2*a*b*d*e)/(12*e^3) + (b^2*x^2)/(2*e) + (b*x*(2*a*e + b*d))/(3*e^2))/(d^4 + e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x)","B"
1461,1,107,65,0.533606,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)/(d + e*x)^6,x)","-\frac{\frac{6\,a^2\,e^2+3\,a\,b\,d\,e+b^2\,d^2}{30\,e^3}+\frac{b^2\,x^2}{3\,e}+\frac{b\,x\,\left(3\,a\,e+b\,d\right)}{6\,e^2}}{d^5+5\,d^4\,e\,x+10\,d^3\,e^2\,x^2+10\,d^2\,e^3\,x^3+5\,d\,e^4\,x^4+e^5\,x^5}","Not used",1,"-((6*a^2*e^2 + b^2*d^2 + 3*a*b*d*e)/(30*e^3) + (b^2*x^2)/(3*e) + (b*x*(3*a*e + b*d))/(6*e^2))/(d^5 + e^5*x^5 + 5*d*e^4*x^4 + 10*d^3*e^2*x^2 + 10*d^2*e^3*x^3 + 5*d^4*e*x)","B"
1462,1,118,65,0.545272,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)/(d + e*x)^7,x)","-\frac{\frac{10\,a^2\,e^2+4\,a\,b\,d\,e+b^2\,d^2}{60\,e^3}+\frac{b^2\,x^2}{4\,e}+\frac{b\,x\,\left(4\,a\,e+b\,d\right)}{10\,e^2}}{d^6+6\,d^5\,e\,x+15\,d^4\,e^2\,x^2+20\,d^3\,e^3\,x^3+15\,d^2\,e^4\,x^4+6\,d\,e^5\,x^5+e^6\,x^6}","Not used",1,"-((10*a^2*e^2 + b^2*d^2 + 4*a*b*d*e)/(60*e^3) + (b^2*x^2)/(4*e) + (b*x*(4*a*e + b*d))/(10*e^2))/(d^6 + e^6*x^6 + 6*d*e^5*x^5 + 15*d^4*e^2*x^2 + 20*d^3*e^3*x^3 + 15*d^2*e^4*x^4 + 6*d^5*e*x)","B"
1463,1,402,119,0.618217,"\text{Not used}","int((d + e*x)^6*(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","x^5\,\left(3\,a^4\,d^2\,e^4+16\,a^3\,b\,d^3\,e^3+18\,a^2\,b^2\,d^4\,e^2+\frac{24\,a\,b^3\,d^5\,e}{5}+\frac{b^4\,d^6}{5}\right)+x^7\,\left(\frac{a^4\,e^6}{7}+\frac{24\,a^3\,b\,d\,e^5}{7}+\frac{90\,a^2\,b^2\,d^2\,e^4}{7}+\frac{80\,a\,b^3\,d^3\,e^3}{7}+\frac{15\,b^4\,d^4\,e^2}{7}\right)+x^4\,\left(5\,a^4\,d^3\,e^3+15\,a^3\,b\,d^4\,e^2+9\,a^2\,b^2\,d^5\,e+a\,b^3\,d^6\right)+x^8\,\left(\frac{a^3\,b\,e^6}{2}+\frac{9\,a^2\,b^2\,d\,e^5}{2}+\frac{15\,a\,b^3\,d^2\,e^4}{2}+\frac{5\,b^4\,d^3\,e^3}{2}\right)+x^6\,\left(a^4\,d\,e^5+10\,a^3\,b\,d^2\,e^4+20\,a^2\,b^2\,d^3\,e^3+10\,a\,b^3\,d^4\,e^2+b^4\,d^5\,e\right)+a^4\,d^6\,x+\frac{b^4\,e^6\,x^{11}}{11}+a^3\,d^5\,x^2\,\left(3\,a\,e+2\,b\,d\right)+\frac{b^3\,e^5\,x^{10}\,\left(2\,a\,e+3\,b\,d\right)}{5}+a^2\,d^4\,x^3\,\left(5\,a^2\,e^2+8\,a\,b\,d\,e+2\,b^2\,d^2\right)+\frac{b^2\,e^4\,x^9\,\left(2\,a^2\,e^2+8\,a\,b\,d\,e+5\,b^2\,d^2\right)}{3}","Not used",1,"x^5*((b^4*d^6)/5 + 3*a^4*d^2*e^4 + 16*a^3*b*d^3*e^3 + 18*a^2*b^2*d^4*e^2 + (24*a*b^3*d^5*e)/5) + x^7*((a^4*e^6)/7 + (15*b^4*d^4*e^2)/7 + (80*a*b^3*d^3*e^3)/7 + (90*a^2*b^2*d^2*e^4)/7 + (24*a^3*b*d*e^5)/7) + x^4*(a*b^3*d^6 + 5*a^4*d^3*e^3 + 9*a^2*b^2*d^5*e + 15*a^3*b*d^4*e^2) + x^8*((a^3*b*e^6)/2 + (5*b^4*d^3*e^3)/2 + (15*a*b^3*d^2*e^4)/2 + (9*a^2*b^2*d*e^5)/2) + x^6*(a^4*d*e^5 + b^4*d^5*e + 10*a*b^3*d^4*e^2 + 10*a^3*b*d^2*e^4 + 20*a^2*b^2*d^3*e^3) + a^4*d^6*x + (b^4*e^6*x^11)/11 + a^3*d^5*x^2*(3*a*e + 2*b*d) + (b^3*e^5*x^10*(2*a*e + 3*b*d))/5 + a^2*d^4*x^3*(5*a^2*e^2 + 2*b^2*d^2 + 8*a*b*d*e) + (b^2*e^4*x^9*(2*a^2*e^2 + 5*b^2*d^2 + 8*a*b*d*e))/3","B"
1464,1,340,119,0.128209,"\text{Not used}","int((d + e*x)^5*(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","x^4\,\left(\frac{5\,a^4\,d^2\,e^3}{2}+10\,a^3\,b\,d^3\,e^2+\frac{15\,a^2\,b^2\,d^4\,e}{2}+a\,b^3\,d^5\right)+x^7\,\left(\frac{4\,a^3\,b\,e^5}{7}+\frac{30\,a^2\,b^2\,d\,e^4}{7}+\frac{40\,a\,b^3\,d^2\,e^3}{7}+\frac{10\,b^4\,d^3\,e^2}{7}\right)+x^5\,\left(a^4\,d\,e^4+8\,a^3\,b\,d^2\,e^3+12\,a^2\,b^2\,d^3\,e^2+4\,a\,b^3\,d^4\,e+\frac{b^4\,d^5}{5}\right)+x^6\,\left(\frac{a^4\,e^5}{6}+\frac{10\,a^3\,b\,d\,e^4}{3}+10\,a^2\,b^2\,d^2\,e^3+\frac{20\,a\,b^3\,d^3\,e^2}{3}+\frac{5\,b^4\,d^4\,e}{6}\right)+a^4\,d^5\,x+\frac{b^4\,e^5\,x^{10}}{10}+\frac{a^3\,d^4\,x^2\,\left(5\,a\,e+4\,b\,d\right)}{2}+\frac{b^3\,e^4\,x^9\,\left(4\,a\,e+5\,b\,d\right)}{9}+\frac{2\,a^2\,d^3\,x^3\,\left(5\,a^2\,e^2+10\,a\,b\,d\,e+3\,b^2\,d^2\right)}{3}+\frac{b^2\,e^3\,x^8\,\left(3\,a^2\,e^2+10\,a\,b\,d\,e+5\,b^2\,d^2\right)}{4}","Not used",1,"x^4*(a*b^3*d^5 + (5*a^4*d^2*e^3)/2 + (15*a^2*b^2*d^4*e)/2 + 10*a^3*b*d^3*e^2) + x^7*((4*a^3*b*e^5)/7 + (10*b^4*d^3*e^2)/7 + (40*a*b^3*d^2*e^3)/7 + (30*a^2*b^2*d*e^4)/7) + x^5*((b^4*d^5)/5 + a^4*d*e^4 + 8*a^3*b*d^2*e^3 + 12*a^2*b^2*d^3*e^2 + 4*a*b^3*d^4*e) + x^6*((a^4*e^5)/6 + (5*b^4*d^4*e)/6 + (20*a*b^3*d^3*e^2)/3 + 10*a^2*b^2*d^2*e^3 + (10*a^3*b*d*e^4)/3) + a^4*d^5*x + (b^4*e^5*x^10)/10 + (a^3*d^4*x^2*(5*a*e + 4*b*d))/2 + (b^3*e^4*x^9*(4*a*e + 5*b*d))/9 + (2*a^2*d^3*x^3*(5*a^2*e^2 + 3*b^2*d^2 + 10*a*b*d*e))/3 + (b^2*e^3*x^8*(3*a^2*e^2 + 5*b^2*d^2 + 10*a*b*d*e))/4","B"
1465,1,271,119,0.092788,"\text{Not used}","int((d + e*x)^4*(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","x^5\,\left(\frac{a^4\,e^4}{5}+\frac{16\,a^3\,b\,d\,e^3}{5}+\frac{36\,a^2\,b^2\,d^2\,e^2}{5}+\frac{16\,a\,b^3\,d^3\,e}{5}+\frac{b^4\,d^4}{5}\right)+x^4\,\left(a^4\,d\,e^3+6\,a^3\,b\,d^2\,e^2+6\,a^2\,b^2\,d^3\,e+a\,b^3\,d^4\right)+x^6\,\left(\frac{2\,a^3\,b\,e^4}{3}+4\,a^2\,b^2\,d\,e^3+4\,a\,b^3\,d^2\,e^2+\frac{2\,b^4\,d^3\,e}{3}\right)+a^4\,d^4\,x+\frac{b^4\,e^4\,x^9}{9}+2\,a^3\,d^3\,x^2\,\left(a\,e+b\,d\right)+\frac{b^3\,e^3\,x^8\,\left(a\,e+b\,d\right)}{2}+\frac{2\,a^2\,d^2\,x^3\,\left(3\,a^2\,e^2+8\,a\,b\,d\,e+3\,b^2\,d^2\right)}{3}+\frac{2\,b^2\,e^2\,x^7\,\left(3\,a^2\,e^2+8\,a\,b\,d\,e+3\,b^2\,d^2\right)}{7}","Not used",1,"x^5*((a^4*e^4)/5 + (b^4*d^4)/5 + (36*a^2*b^2*d^2*e^2)/5 + (16*a*b^3*d^3*e)/5 + (16*a^3*b*d*e^3)/5) + x^4*(a*b^3*d^4 + a^4*d*e^3 + 6*a^2*b^2*d^3*e + 6*a^3*b*d^2*e^2) + x^6*((2*a^3*b*e^4)/3 + (2*b^4*d^3*e)/3 + 4*a*b^3*d^2*e^2 + 4*a^2*b^2*d*e^3) + a^4*d^4*x + (b^4*e^4*x^9)/9 + 2*a^3*d^3*x^2*(a*e + b*d) + (b^3*e^3*x^8*(a*e + b*d))/2 + (2*a^2*d^2*x^3*(3*a^2*e^2 + 3*b^2*d^2 + 8*a*b*d*e))/3 + (2*b^2*e^2*x^7*(3*a^2*e^2 + 3*b^2*d^2 + 8*a*b*d*e))/7","B"
1466,1,208,92,0.548947,"\text{Not used}","int((d + e*x)^3*(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","x^4\,\left(\frac{a^4\,e^3}{4}+3\,a^3\,b\,d\,e^2+\frac{9\,a^2\,b^2\,d^2\,e}{2}+a\,b^3\,d^3\right)+x^5\,\left(\frac{4\,a^3\,b\,e^3}{5}+\frac{18\,a^2\,b^2\,d\,e^2}{5}+\frac{12\,a\,b^3\,d^2\,e}{5}+\frac{b^4\,d^3}{5}\right)+a^4\,d^3\,x+\frac{b^4\,e^3\,x^8}{8}+\frac{a^3\,d^2\,x^2\,\left(3\,a\,e+4\,b\,d\right)}{2}+\frac{b^3\,e^2\,x^7\,\left(4\,a\,e+3\,b\,d\right)}{7}+a^2\,d\,x^3\,\left(a^2\,e^2+4\,a\,b\,d\,e+2\,b^2\,d^2\right)+\frac{b^2\,e\,x^6\,\left(2\,a^2\,e^2+4\,a\,b\,d\,e+b^2\,d^2\right)}{2}","Not used",1,"x^4*((a^4*e^3)/4 + a*b^3*d^3 + (9*a^2*b^2*d^2*e)/2 + 3*a^3*b*d*e^2) + x^5*((b^4*d^3)/5 + (4*a^3*b*e^3)/5 + (18*a^2*b^2*d*e^2)/5 + (12*a*b^3*d^2*e)/5) + a^4*d^3*x + (b^4*e^3*x^8)/8 + (a^3*d^2*x^2*(3*a*e + 4*b*d))/2 + (b^3*e^2*x^7*(4*a*e + 3*b*d))/7 + a^2*d*x^3*(a^2*e^2 + 2*b^2*d^2 + 4*a*b*d*e) + (b^2*e*x^6*(2*a^2*e^2 + b^2*d^2 + 4*a*b*d*e))/2","B"
1467,1,144,65,0.521158,"\text{Not used}","int((d + e*x)^2*(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","x^3\,\left(\frac{a^4\,e^2}{3}+\frac{8\,a^3\,b\,d\,e}{3}+2\,a^2\,b^2\,d^2\right)+x^5\,\left(\frac{6\,a^2\,b^2\,e^2}{5}+\frac{8\,a\,b^3\,d\,e}{5}+\frac{b^4\,d^2}{5}\right)+a^4\,d^2\,x+\frac{b^4\,e^2\,x^7}{7}+a^3\,d\,x^2\,\left(a\,e+2\,b\,d\right)+\frac{b^3\,e\,x^6\,\left(2\,a\,e+b\,d\right)}{3}+a\,b\,x^4\,\left(a^2\,e^2+3\,a\,b\,d\,e+b^2\,d^2\right)","Not used",1,"x^3*((a^4*e^2)/3 + 2*a^2*b^2*d^2 + (8*a^3*b*d*e)/3) + x^5*((b^4*d^2)/5 + (6*a^2*b^2*e^2)/5 + (8*a*b^3*d*e)/5) + a^4*d^2*x + (b^4*e^2*x^7)/7 + a^3*d*x^2*(a*e + 2*b*d) + (b^3*e*x^6*(2*a*e + b*d))/3 + a*b*x^4*(a^2*e^2 + b^2*d^2 + 3*a*b*d*e)","B"
1468,1,88,38,0.505321,"\text{Not used}","int((d + e*x)*(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","x^2\,\left(\frac{e\,a^4}{2}+2\,b\,d\,a^3\right)+x^5\,\left(\frac{d\,b^4}{5}+\frac{4\,a\,e\,b^3}{5}\right)+\frac{b^4\,e\,x^6}{6}+a^4\,d\,x+\frac{2\,a^2\,b\,x^3\,\left(2\,a\,e+3\,b\,d\right)}{3}+\frac{a\,b^2\,x^4\,\left(3\,a\,e+2\,b\,d\right)}{2}","Not used",1,"x^2*((a^4*e)/2 + 2*a^3*b*d) + x^5*((b^4*d)/5 + (4*a*b^3*e)/5) + (b^4*e*x^6)/6 + a^4*d*x + (2*a^2*b*x^3*(2*a*e + 3*b*d))/3 + (a*b^2*x^4*(3*a*e + 2*b*d))/2","B"
1469,1,42,14,0.021104,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^2,x)","a^4\,x+2\,a^3\,b\,x^2+2\,a^2\,b^2\,x^3+a\,b^3\,x^4+\frac{b^4\,x^5}{5}","Not used",1,"a^4*x + (b^4*x^5)/5 + 2*a^3*b*x^2 + a*b^3*x^4 + 2*a^2*b^2*x^3","B"
1470,1,189,98,0.054101,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^2/(d + e*x),x)","x^3\,\left(\frac{4\,a\,b^3}{3\,e}-\frac{b^4\,d}{3\,e^2}\right)+x\,\left(\frac{d\,\left(\frac{d\,\left(\frac{4\,a\,b^3}{e}-\frac{b^4\,d}{e^2}\right)}{e}-\frac{6\,a^2\,b^2}{e}\right)}{e}+\frac{4\,a^3\,b}{e}\right)-x^2\,\left(\frac{d\,\left(\frac{4\,a\,b^3}{e}-\frac{b^4\,d}{e^2}\right)}{2\,e}-\frac{3\,a^2\,b^2}{e}\right)+\frac{\ln\left(d+e\,x\right)\,\left(a^4\,e^4-4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-4\,a\,b^3\,d^3\,e+b^4\,d^4\right)}{e^5}+\frac{b^4\,x^4}{4\,e}","Not used",1,"x^3*((4*a*b^3)/(3*e) - (b^4*d)/(3*e^2)) + x*((d*((d*((4*a*b^3)/e - (b^4*d)/e^2))/e - (6*a^2*b^2)/e))/e + (4*a^3*b)/e) - x^2*((d*((4*a*b^3)/e - (b^4*d)/e^2))/(2*e) - (3*a^2*b^2)/e) + (log(d + e*x)*(a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 4*a*b^3*d^3*e - 4*a^3*b*d*e^3))/e^5 + (b^4*x^4)/(4*e)","B"
1471,1,203,104,0.546689,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^2/(d + e*x)^2,x)","x^2\,\left(\frac{2\,a\,b^3}{e^2}-\frac{b^4\,d}{e^3}\right)-x\,\left(\frac{2\,d\,\left(\frac{4\,a\,b^3}{e^2}-\frac{2\,b^4\,d}{e^3}\right)}{e}-\frac{6\,a^2\,b^2}{e^2}+\frac{b^4\,d^2}{e^4}\right)+\frac{b^4\,x^3}{3\,e^2}-\frac{\ln\left(d+e\,x\right)\,\left(-4\,a^3\,b\,e^3+12\,a^2\,b^2\,d\,e^2-12\,a\,b^3\,d^2\,e+4\,b^4\,d^3\right)}{e^5}-\frac{a^4\,e^4-4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-4\,a\,b^3\,d^3\,e+b^4\,d^4}{e\,\left(x\,e^5+d\,e^4\right)}","Not used",1,"x^2*((2*a*b^3)/e^2 - (b^4*d)/e^3) - x*((2*d*((4*a*b^3)/e^2 - (2*b^4*d)/e^3))/e - (6*a^2*b^2)/e^2 + (b^4*d^2)/e^4) + (b^4*x^3)/(3*e^2) - (log(d + e*x)*(4*b^4*d^3 - 4*a^3*b*e^3 + 12*a^2*b^2*d*e^2 - 12*a*b^3*d^2*e))/e^5 - (a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 4*a*b^3*d^3*e - 4*a^3*b*d*e^3)/(e*(d*e^4 + e^5*x))","B"
1472,1,196,103,0.096434,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^2/(d + e*x)^3,x)","x\,\left(\frac{4\,a\,b^3}{e^3}-\frac{3\,b^4\,d}{e^4}\right)-\frac{\frac{a^4\,e^4+4\,a^3\,b\,d\,e^3-18\,a^2\,b^2\,d^2\,e^2+20\,a\,b^3\,d^3\,e-7\,b^4\,d^4}{2\,e}-x\,\left(-4\,a^3\,b\,e^3+12\,a^2\,b^2\,d\,e^2-12\,a\,b^3\,d^2\,e+4\,b^4\,d^3\right)}{d^2\,e^4+2\,d\,e^5\,x+e^6\,x^2}+\frac{b^4\,x^2}{2\,e^3}+\frac{\ln\left(d+e\,x\right)\,\left(6\,a^2\,b^2\,e^2-12\,a\,b^3\,d\,e+6\,b^4\,d^2\right)}{e^5}","Not used",1,"x*((4*a*b^3)/e^3 - (3*b^4*d)/e^4) - ((a^4*e^4 - 7*b^4*d^4 - 18*a^2*b^2*d^2*e^2 + 20*a*b^3*d^3*e + 4*a^3*b*d*e^3)/(2*e) - x*(4*b^4*d^3 - 4*a^3*b*e^3 + 12*a^2*b^2*d*e^2 - 12*a*b^3*d^2*e))/(d^2*e^4 + e^6*x^2 + 2*d*e^5*x) + (b^4*x^2)/(2*e^3) + (log(d + e*x)*(6*b^4*d^2 + 6*a^2*b^2*e^2 - 12*a*b^3*d*e))/e^5","B"
1473,1,204,103,0.595955,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^2/(d + e*x)^4,x)","\frac{b^4\,x}{e^4}-\frac{\ln\left(d+e\,x\right)\,\left(4\,b^4\,d-4\,a\,b^3\,e\right)}{e^5}-\frac{\frac{a^4\,e^4+2\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-22\,a\,b^3\,d^3\,e+13\,b^4\,d^4}{3\,e}+x\,\left(2\,a^3\,b\,e^3+6\,a^2\,b^2\,d\,e^2-18\,a\,b^3\,d^2\,e+10\,b^4\,d^3\right)+x^2\,\left(6\,a^2\,b^2\,e^3-12\,a\,b^3\,d\,e^2+6\,b^4\,d^2\,e\right)}{d^3\,e^4+3\,d^2\,e^5\,x+3\,d\,e^6\,x^2+e^7\,x^3}","Not used",1,"(b^4*x)/e^4 - (log(d + e*x)*(4*b^4*d - 4*a*b^3*e))/e^5 - ((a^4*e^4 + 13*b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 22*a*b^3*d^3*e + 2*a^3*b*d*e^3)/(3*e) + x*(10*b^4*d^3 + 2*a^3*b*e^3 + 6*a^2*b^2*d*e^2 - 18*a*b^3*d^2*e) + x^2*(6*b^4*d^2*e + 6*a^2*b^2*e^3 - 12*a*b^3*d*e^2))/(d^3*e^4 + e^7*x^3 + 3*d^2*e^5*x + 3*d*e^6*x^2)","B"
1474,1,213,111,0.611564,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^2/(d + e*x)^5,x)","\frac{b^4\,\ln\left(d+e\,x\right)}{e^5}-\frac{\frac{3\,a^4\,e^4+4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2+12\,a\,b^3\,d^3\,e-25\,b^4\,d^4}{12\,e^5}+\frac{3\,x^2\,\left(a^2\,b^2\,e^2+2\,a\,b^3\,d\,e-3\,b^4\,d^2\right)}{e^3}+\frac{2\,x\,\left(2\,a^3\,b\,e^3+3\,a^2\,b^2\,d\,e^2+6\,a\,b^3\,d^2\,e-11\,b^4\,d^3\right)}{3\,e^4}+\frac{4\,b^3\,x^3\,\left(a\,e-b\,d\right)}{e^2}}{d^4+4\,d^3\,e\,x+6\,d^2\,e^2\,x^2+4\,d\,e^3\,x^3+e^4\,x^4}","Not used",1,"(b^4*log(d + e*x))/e^5 - ((3*a^4*e^4 - 25*b^4*d^4 + 6*a^2*b^2*d^2*e^2 + 12*a*b^3*d^3*e + 4*a^3*b*d*e^3)/(12*e^5) + (3*x^2*(a^2*b^2*e^2 - 3*b^4*d^2 + 2*a*b^3*d*e))/e^3 + (2*x*(2*a^3*b*e^3 - 11*b^4*d^3 + 3*a^2*b^2*d*e^2 + 6*a*b^3*d^2*e))/(3*e^4) + (4*b^3*x^3*(a*e - b*d))/e^2)/(d^4 + e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x)","B"
1475,1,203,28,0.095924,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^2/(d + e*x)^6,x)","-\frac{\frac{a^4\,e^4+a^3\,b\,d\,e^3+a^2\,b^2\,d^2\,e^2+a\,b^3\,d^3\,e+b^4\,d^4}{5\,e^5}+\frac{b^4\,x^4}{e}+\frac{2\,b^3\,x^3\,\left(a\,e+b\,d\right)}{e^2}+\frac{b\,x\,\left(a^3\,e^3+a^2\,b\,d\,e^2+a\,b^2\,d^2\,e+b^3\,d^3\right)}{e^4}+\frac{2\,b^2\,x^2\,\left(a^2\,e^2+a\,b\,d\,e+b^2\,d^2\right)}{e^3}}{d^5+5\,d^4\,e\,x+10\,d^3\,e^2\,x^2+10\,d^2\,e^3\,x^3+5\,d\,e^4\,x^4+e^5\,x^5}","Not used",1,"-((a^4*e^4 + b^4*d^4 + a^2*b^2*d^2*e^2 + a*b^3*d^3*e + a^3*b*d*e^3)/(5*e^5) + (b^4*x^4)/e + (2*b^3*x^3*(a*e + b*d))/e^2 + (b*x*(a^3*e^3 + b^3*d^3 + a*b^2*d^2*e + a^2*b*d*e^2))/e^4 + (2*b^2*x^2*(a^2*e^2 + b^2*d^2 + a*b*d*e))/e^3)/(d^5 + e^5*x^5 + 5*d*e^4*x^4 + 10*d^3*e^2*x^2 + 10*d^2*e^3*x^3 + 5*d^4*e*x)","B"
1476,1,226,58,0.106021,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^2/(d + e*x)^7,x)","-\frac{\frac{5\,a^4\,e^4+4\,a^3\,b\,d\,e^3+3\,a^2\,b^2\,d^2\,e^2+2\,a\,b^3\,d^3\,e+b^4\,d^4}{30\,e^5}+\frac{b^4\,x^4}{2\,e}+\frac{2\,b^3\,x^3\,\left(2\,a\,e+b\,d\right)}{3\,e^2}+\frac{b\,x\,\left(4\,a^3\,e^3+3\,a^2\,b\,d\,e^2+2\,a\,b^2\,d^2\,e+b^3\,d^3\right)}{5\,e^4}+\frac{b^2\,x^2\,\left(3\,a^2\,e^2+2\,a\,b\,d\,e+b^2\,d^2\right)}{2\,e^3}}{d^6+6\,d^5\,e\,x+15\,d^4\,e^2\,x^2+20\,d^3\,e^3\,x^3+15\,d^2\,e^4\,x^4+6\,d\,e^5\,x^5+e^6\,x^6}","Not used",1,"-((5*a^4*e^4 + b^4*d^4 + 3*a^2*b^2*d^2*e^2 + 2*a*b^3*d^3*e + 4*a^3*b*d*e^3)/(30*e^5) + (b^4*x^4)/(2*e) + (2*b^3*x^3*(2*a*e + b*d))/(3*e^2) + (b*x*(4*a^3*e^3 + b^3*d^3 + 2*a*b^2*d^2*e + 3*a^2*b*d*e^2))/(5*e^4) + (b^2*x^2*(3*a^2*e^2 + b^2*d^2 + 2*a*b*d*e))/(2*e^3))/(d^6 + e^6*x^6 + 6*d*e^5*x^5 + 15*d^4*e^2*x^2 + 20*d^3*e^3*x^3 + 15*d^2*e^4*x^4 + 6*d^5*e*x)","B"
1477,1,237,89,0.596948,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^2/(d + e*x)^8,x)","-\frac{\frac{15\,a^4\,e^4+10\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2+3\,a\,b^3\,d^3\,e+b^4\,d^4}{105\,e^5}+\frac{b^4\,x^4}{3\,e}+\frac{b^3\,x^3\,\left(3\,a\,e+b\,d\right)}{3\,e^2}+\frac{b\,x\,\left(10\,a^3\,e^3+6\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e+b^3\,d^3\right)}{15\,e^4}+\frac{b^2\,x^2\,\left(6\,a^2\,e^2+3\,a\,b\,d\,e+b^2\,d^2\right)}{5\,e^3}}{d^7+7\,d^6\,e\,x+21\,d^5\,e^2\,x^2+35\,d^4\,e^3\,x^3+35\,d^3\,e^4\,x^4+21\,d^2\,e^5\,x^5+7\,d\,e^6\,x^6+e^7\,x^7}","Not used",1,"-((15*a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 + 3*a*b^3*d^3*e + 10*a^3*b*d*e^3)/(105*e^5) + (b^4*x^4)/(3*e) + (b^3*x^3*(3*a*e + b*d))/(3*e^2) + (b*x*(10*a^3*e^3 + b^3*d^3 + 3*a*b^2*d^2*e + 6*a^2*b*d*e^2))/(15*e^4) + (b^2*x^2*(6*a^2*e^2 + b^2*d^2 + 3*a*b*d*e))/(5*e^3))/(d^7 + e^7*x^7 + 7*d*e^6*x^6 + 21*d^5*e^2*x^2 + 35*d^4*e^3*x^3 + 35*d^3*e^4*x^4 + 21*d^2*e^5*x^5 + 7*d^6*e*x)","B"
1478,1,248,117,0.615665,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^2/(d + e*x)^9,x)","-\frac{\frac{35\,a^4\,e^4+20\,a^3\,b\,d\,e^3+10\,a^2\,b^2\,d^2\,e^2+4\,a\,b^3\,d^3\,e+b^4\,d^4}{280\,e^5}+\frac{b^4\,x^4}{4\,e}+\frac{b^3\,x^3\,\left(4\,a\,e+b\,d\right)}{5\,e^2}+\frac{b\,x\,\left(20\,a^3\,e^3+10\,a^2\,b\,d\,e^2+4\,a\,b^2\,d^2\,e+b^3\,d^3\right)}{35\,e^4}+\frac{b^2\,x^2\,\left(10\,a^2\,e^2+4\,a\,b\,d\,e+b^2\,d^2\right)}{10\,e^3}}{d^8+8\,d^7\,e\,x+28\,d^6\,e^2\,x^2+56\,d^5\,e^3\,x^3+70\,d^4\,e^4\,x^4+56\,d^3\,e^5\,x^5+28\,d^2\,e^6\,x^6+8\,d\,e^7\,x^7+e^8\,x^8}","Not used",1,"-((35*a^4*e^4 + b^4*d^4 + 10*a^2*b^2*d^2*e^2 + 4*a*b^3*d^3*e + 20*a^3*b*d*e^3)/(280*e^5) + (b^4*x^4)/(4*e) + (b^3*x^3*(4*a*e + b*d))/(5*e^2) + (b*x*(20*a^3*e^3 + b^3*d^3 + 4*a*b^2*d^2*e + 10*a^2*b*d*e^2))/(35*e^4) + (b^2*x^2*(10*a^2*e^2 + b^2*d^2 + 4*a*b*d*e))/(10*e^3))/(d^8 + e^8*x^8 + 8*d*e^7*x^7 + 28*d^6*e^2*x^2 + 56*d^5*e^3*x^3 + 70*d^4*e^4*x^4 + 56*d^3*e^5*x^5 + 28*d^2*e^6*x^6 + 8*d^7*e*x)","B"
1479,1,259,119,0.610749,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^2/(d + e*x)^10,x)","-\frac{\frac{70\,a^4\,e^4+35\,a^3\,b\,d\,e^3+15\,a^2\,b^2\,d^2\,e^2+5\,a\,b^3\,d^3\,e+b^4\,d^4}{630\,e^5}+\frac{b^4\,x^4}{5\,e}+\frac{2\,b^3\,x^3\,\left(5\,a\,e+b\,d\right)}{15\,e^2}+\frac{b\,x\,\left(35\,a^3\,e^3+15\,a^2\,b\,d\,e^2+5\,a\,b^2\,d^2\,e+b^3\,d^3\right)}{70\,e^4}+\frac{2\,b^2\,x^2\,\left(15\,a^2\,e^2+5\,a\,b\,d\,e+b^2\,d^2\right)}{35\,e^3}}{d^9+9\,d^8\,e\,x+36\,d^7\,e^2\,x^2+84\,d^6\,e^3\,x^3+126\,d^5\,e^4\,x^4+126\,d^4\,e^5\,x^5+84\,d^3\,e^6\,x^6+36\,d^2\,e^7\,x^7+9\,d\,e^8\,x^8+e^9\,x^9}","Not used",1,"-((70*a^4*e^4 + b^4*d^4 + 15*a^2*b^2*d^2*e^2 + 5*a*b^3*d^3*e + 35*a^3*b*d*e^3)/(630*e^5) + (b^4*x^4)/(5*e) + (2*b^3*x^3*(5*a*e + b*d))/(15*e^2) + (b*x*(35*a^3*e^3 + b^3*d^3 + 5*a*b^2*d^2*e + 15*a^2*b*d*e^2))/(70*e^4) + (2*b^2*x^2*(15*a^2*e^2 + b^2*d^2 + 5*a*b*d*e))/(35*e^3))/(d^9 + e^9*x^9 + 9*d*e^8*x^8 + 36*d^7*e^2*x^2 + 84*d^6*e^3*x^3 + 126*d^5*e^4*x^4 + 126*d^4*e^5*x^5 + 84*d^3*e^6*x^6 + 36*d^2*e^7*x^7 + 9*d^8*e*x)","B"
1480,1,270,119,0.237867,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^2/(d + e*x)^11,x)","-\frac{\frac{126\,a^4\,e^4+56\,a^3\,b\,d\,e^3+21\,a^2\,b^2\,d^2\,e^2+6\,a\,b^3\,d^3\,e+b^4\,d^4}{1260\,e^5}+\frac{b^4\,x^4}{6\,e}+\frac{2\,b^3\,x^3\,\left(6\,a\,e+b\,d\right)}{21\,e^2}+\frac{b\,x\,\left(56\,a^3\,e^3+21\,a^2\,b\,d\,e^2+6\,a\,b^2\,d^2\,e+b^3\,d^3\right)}{126\,e^4}+\frac{b^2\,x^2\,\left(21\,a^2\,e^2+6\,a\,b\,d\,e+b^2\,d^2\right)}{28\,e^3}}{d^{10}+10\,d^9\,e\,x+45\,d^8\,e^2\,x^2+120\,d^7\,e^3\,x^3+210\,d^6\,e^4\,x^4+252\,d^5\,e^5\,x^5+210\,d^4\,e^6\,x^6+120\,d^3\,e^7\,x^7+45\,d^2\,e^8\,x^8+10\,d\,e^9\,x^9+e^{10}\,x^{10}}","Not used",1,"-((126*a^4*e^4 + b^4*d^4 + 21*a^2*b^2*d^2*e^2 + 6*a*b^3*d^3*e + 56*a^3*b*d*e^3)/(1260*e^5) + (b^4*x^4)/(6*e) + (2*b^3*x^3*(6*a*e + b*d))/(21*e^2) + (b*x*(56*a^3*e^3 + b^3*d^3 + 6*a*b^2*d^2*e + 21*a^2*b*d*e^2))/(126*e^4) + (b^2*x^2*(21*a^2*e^2 + b^2*d^2 + 6*a*b*d*e))/(28*e^3))/(d^10 + e^10*x^10 + 10*d*e^9*x^9 + 45*d^8*e^2*x^2 + 120*d^7*e^3*x^3 + 210*d^6*e^4*x^4 + 252*d^5*e^5*x^5 + 210*d^4*e^6*x^6 + 120*d^3*e^7*x^7 + 45*d^2*e^8*x^8 + 10*d^9*e*x)","B"
1481,1,768,173,0.774073,"\text{Not used}","int((d + e*x)^8*(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","x^7\,\left(4\,a^6\,d^2\,e^6+48\,a^5\,b\,d^3\,e^5+150\,a^4\,b^2\,d^4\,e^4+160\,a^3\,b^3\,d^5\,e^3+60\,a^2\,b^4\,d^6\,e^2+\frac{48\,a\,b^5\,d^7\,e}{7}+\frac{b^6\,d^8}{7}\right)+x^9\,\left(\frac{a^6\,e^8}{9}+\frac{16\,a^5\,b\,d\,e^7}{3}+\frac{140\,a^4\,b^2\,d^2\,e^6}{3}+\frac{1120\,a^3\,b^3\,d^3\,e^5}{9}+\frac{350\,a^2\,b^4\,d^4\,e^4}{3}+\frac{112\,a\,b^5\,d^5\,e^3}{3}+\frac{28\,b^6\,d^6\,e^2}{9}\right)+x^5\,\left(14\,a^6\,d^4\,e^4+\frac{336\,a^5\,b\,d^5\,e^3}{5}+84\,a^4\,b^2\,d^6\,e^2+32\,a^3\,b^3\,d^7\,e+3\,a^2\,b^4\,d^8\right)+x^{11}\,\left(\frac{15\,a^4\,b^2\,e^8}{11}+\frac{160\,a^3\,b^3\,d\,e^7}{11}+\frac{420\,a^2\,b^4\,d^2\,e^6}{11}+\frac{336\,a\,b^5\,d^3\,e^5}{11}+\frac{70\,b^6\,d^4\,e^4}{11}\right)+x^6\,\left(\frac{28\,a^6\,d^3\,e^5}{3}+70\,a^5\,b\,d^4\,e^4+140\,a^4\,b^2\,d^5\,e^3+\frac{280\,a^3\,b^3\,d^6\,e^2}{3}+20\,a^2\,b^4\,d^7\,e+a\,b^5\,d^8\right)+x^{10}\,\left(\frac{3\,a^5\,b\,e^8}{5}+12\,a^4\,b^2\,d\,e^7+56\,a^3\,b^3\,d^2\,e^6+84\,a^2\,b^4\,d^3\,e^5+42\,a\,b^5\,d^4\,e^4+\frac{28\,b^6\,d^5\,e^3}{5}\right)+x^8\,\left(a^6\,d\,e^7+21\,a^5\,b\,d^2\,e^6+105\,a^4\,b^2\,d^3\,e^5+175\,a^3\,b^3\,d^4\,e^4+105\,a^2\,b^4\,d^5\,e^3+21\,a\,b^5\,d^6\,e^2+b^6\,d^7\,e\right)+a^6\,d^8\,x+\frac{b^6\,e^8\,x^{15}}{15}+a^3\,d^5\,x^4\,\left(14\,a^3\,e^3+42\,a^2\,b\,d\,e^2+30\,a\,b^2\,d^2\,e+5\,b^3\,d^3\right)+\frac{b^3\,e^5\,x^{12}\,\left(5\,a^3\,e^3+30\,a^2\,b\,d\,e^2+42\,a\,b^2\,d^2\,e+14\,b^3\,d^3\right)}{3}+a^5\,d^7\,x^2\,\left(4\,a\,e+3\,b\,d\right)+\frac{b^5\,e^7\,x^{14}\,\left(3\,a\,e+4\,b\,d\right)}{7}+\frac{a^4\,d^6\,x^3\,\left(28\,a^2\,e^2+48\,a\,b\,d\,e+15\,b^2\,d^2\right)}{3}+\frac{b^4\,e^6\,x^{13}\,\left(15\,a^2\,e^2+48\,a\,b\,d\,e+28\,b^2\,d^2\right)}{13}","Not used",1,"x^7*((b^6*d^8)/7 + 4*a^6*d^2*e^6 + 48*a^5*b*d^3*e^5 + 60*a^2*b^4*d^6*e^2 + 160*a^3*b^3*d^5*e^3 + 150*a^4*b^2*d^4*e^4 + (48*a*b^5*d^7*e)/7) + x^9*((a^6*e^8)/9 + (28*b^6*d^6*e^2)/9 + (112*a*b^5*d^5*e^3)/3 + (350*a^2*b^4*d^4*e^4)/3 + (1120*a^3*b^3*d^3*e^5)/9 + (140*a^4*b^2*d^2*e^6)/3 + (16*a^5*b*d*e^7)/3) + x^5*(3*a^2*b^4*d^8 + 14*a^6*d^4*e^4 + 32*a^3*b^3*d^7*e + (336*a^5*b*d^5*e^3)/5 + 84*a^4*b^2*d^6*e^2) + x^11*((15*a^4*b^2*e^8)/11 + (70*b^6*d^4*e^4)/11 + (336*a*b^5*d^3*e^5)/11 + (160*a^3*b^3*d*e^7)/11 + (420*a^2*b^4*d^2*e^6)/11) + x^6*(a*b^5*d^8 + (28*a^6*d^3*e^5)/3 + 20*a^2*b^4*d^7*e + 70*a^5*b*d^4*e^4 + (280*a^3*b^3*d^6*e^2)/3 + 140*a^4*b^2*d^5*e^3) + x^10*((3*a^5*b*e^8)/5 + (28*b^6*d^5*e^3)/5 + 42*a*b^5*d^4*e^4 + 12*a^4*b^2*d*e^7 + 84*a^2*b^4*d^3*e^5 + 56*a^3*b^3*d^2*e^6) + x^8*(a^6*d*e^7 + b^6*d^7*e + 21*a*b^5*d^6*e^2 + 21*a^5*b*d^2*e^6 + 105*a^2*b^4*d^5*e^3 + 175*a^3*b^3*d^4*e^4 + 105*a^4*b^2*d^3*e^5) + a^6*d^8*x + (b^6*e^8*x^15)/15 + a^3*d^5*x^4*(14*a^3*e^3 + 5*b^3*d^3 + 30*a*b^2*d^2*e + 42*a^2*b*d*e^2) + (b^3*e^5*x^12*(5*a^3*e^3 + 14*b^3*d^3 + 42*a*b^2*d^2*e + 30*a^2*b*d*e^2))/3 + a^5*d^7*x^2*(4*a*e + 3*b*d) + (b^5*e^7*x^14*(3*a*e + 4*b*d))/7 + (a^4*d^6*x^3*(28*a^2*e^2 + 15*b^2*d^2 + 48*a*b*d*e))/3 + (b^4*e^6*x^13*(15*a^2*e^2 + 28*b^2*d^2 + 48*a*b*d*e))/13","B"
1482,1,683,173,0.268471,"\text{Not used}","int((d + e*x)^7*(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","x^5\,\left(7\,a^6\,d^3\,e^4+42\,a^5\,b\,d^4\,e^3+63\,a^4\,b^2\,d^5\,e^2+28\,a^3\,b^3\,d^6\,e+3\,a^2\,b^4\,d^7\right)+x^{10}\,\left(\frac{3\,a^4\,b^2\,e^7}{2}+14\,a^3\,b^3\,d\,e^6+\frac{63\,a^2\,b^4\,d^2\,e^5}{2}+21\,a\,b^5\,d^3\,e^4+\frac{7\,b^6\,d^4\,e^3}{2}\right)+x^6\,\left(\frac{7\,a^6\,d^2\,e^5}{2}+35\,a^5\,b\,d^3\,e^4+\frac{175\,a^4\,b^2\,d^4\,e^3}{2}+70\,a^3\,b^3\,d^5\,e^2+\frac{35\,a^2\,b^4\,d^6\,e}{2}+a\,b^5\,d^7\right)+x^9\,\left(\frac{2\,a^5\,b\,e^7}{3}+\frac{35\,a^4\,b^2\,d\,e^6}{3}+\frac{140\,a^3\,b^3\,d^2\,e^5}{3}+\frac{175\,a^2\,b^4\,d^3\,e^4}{3}+\frac{70\,a\,b^5\,d^4\,e^3}{3}+\frac{7\,b^6\,d^5\,e^2}{3}\right)+x^7\,\left(a^6\,d\,e^6+18\,a^5\,b\,d^2\,e^5+75\,a^4\,b^2\,d^3\,e^4+100\,a^3\,b^3\,d^4\,e^3+45\,a^2\,b^4\,d^5\,e^2+6\,a\,b^5\,d^6\,e+\frac{b^6\,d^7}{7}\right)+x^8\,\left(\frac{a^6\,e^7}{8}+\frac{21\,a^5\,b\,d\,e^6}{4}+\frac{315\,a^4\,b^2\,d^2\,e^5}{8}+\frac{175\,a^3\,b^3\,d^3\,e^4}{2}+\frac{525\,a^2\,b^4\,d^4\,e^3}{8}+\frac{63\,a\,b^5\,d^5\,e^2}{4}+\frac{7\,b^6\,d^6\,e}{8}\right)+x^4\,\left(\frac{35\,a^6\,d^4\,e^3}{4}+\frac{63\,a^5\,b\,d^5\,e^2}{2}+\frac{105\,a^4\,b^2\,d^6\,e}{4}+5\,a^3\,b^3\,d^7\right)+x^{11}\,\left(\frac{20\,a^3\,b^3\,e^7}{11}+\frac{105\,a^2\,b^4\,d\,e^6}{11}+\frac{126\,a\,b^5\,d^2\,e^5}{11}+\frac{35\,b^6\,d^3\,e^4}{11}\right)+a^6\,d^7\,x+\frac{b^6\,e^7\,x^{14}}{14}+\frac{a^5\,d^6\,x^2\,\left(7\,a\,e+6\,b\,d\right)}{2}+\frac{b^5\,e^6\,x^{13}\,\left(6\,a\,e+7\,b\,d\right)}{13}+a^4\,d^5\,x^3\,\left(7\,a^2\,e^2+14\,a\,b\,d\,e+5\,b^2\,d^2\right)+\frac{b^4\,e^5\,x^{12}\,\left(5\,a^2\,e^2+14\,a\,b\,d\,e+7\,b^2\,d^2\right)}{4}","Not used",1,"x^5*(3*a^2*b^4*d^7 + 7*a^6*d^3*e^4 + 28*a^3*b^3*d^6*e + 42*a^5*b*d^4*e^3 + 63*a^4*b^2*d^5*e^2) + x^10*((3*a^4*b^2*e^7)/2 + (7*b^6*d^4*e^3)/2 + 21*a*b^5*d^3*e^4 + 14*a^3*b^3*d*e^6 + (63*a^2*b^4*d^2*e^5)/2) + x^6*(a*b^5*d^7 + (7*a^6*d^2*e^5)/2 + (35*a^2*b^4*d^6*e)/2 + 35*a^5*b*d^3*e^4 + 70*a^3*b^3*d^5*e^2 + (175*a^4*b^2*d^4*e^3)/2) + x^9*((2*a^5*b*e^7)/3 + (7*b^6*d^5*e^2)/3 + (70*a*b^5*d^4*e^3)/3 + (35*a^4*b^2*d*e^6)/3 + (175*a^2*b^4*d^3*e^4)/3 + (140*a^3*b^3*d^2*e^5)/3) + x^7*((b^6*d^7)/7 + a^6*d*e^6 + 18*a^5*b*d^2*e^5 + 45*a^2*b^4*d^5*e^2 + 100*a^3*b^3*d^4*e^3 + 75*a^4*b^2*d^3*e^4 + 6*a*b^5*d^6*e) + x^8*((a^6*e^7)/8 + (7*b^6*d^6*e)/8 + (63*a*b^5*d^5*e^2)/4 + (525*a^2*b^4*d^4*e^3)/8 + (175*a^3*b^3*d^3*e^4)/2 + (315*a^4*b^2*d^2*e^5)/8 + (21*a^5*b*d*e^6)/4) + x^4*(5*a^3*b^3*d^7 + (35*a^6*d^4*e^3)/4 + (105*a^4*b^2*d^6*e)/4 + (63*a^5*b*d^5*e^2)/2) + x^11*((20*a^3*b^3*e^7)/11 + (35*b^6*d^3*e^4)/11 + (126*a*b^5*d^2*e^5)/11 + (105*a^2*b^4*d*e^6)/11) + a^6*d^7*x + (b^6*e^7*x^14)/14 + (a^5*d^6*x^2*(7*a*e + 6*b*d))/2 + (b^5*e^6*x^13*(6*a*e + 7*b*d))/13 + a^4*d^5*x^3*(7*a^2*e^2 + 5*b^2*d^2 + 14*a*b*d*e) + (b^4*e^5*x^12*(5*a^2*e^2 + 7*b^2*d^2 + 14*a*b*d*e))/4","B"
1483,1,579,171,0.647104,"\text{Not used}","int((d + e*x)^6*(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","x^6\,\left(a^6\,d\,e^5+15\,a^5\,b\,d^2\,e^4+50\,a^4\,b^2\,d^3\,e^3+50\,a^3\,b^3\,d^4\,e^2+15\,a^2\,b^4\,d^5\,e+a\,b^5\,d^6\right)+x^8\,\left(\frac{3\,a^5\,b\,e^6}{4}+\frac{45\,a^4\,b^2\,d\,e^5}{4}+\frac{75\,a^3\,b^3\,d^2\,e^4}{2}+\frac{75\,a^2\,b^4\,d^3\,e^3}{2}+\frac{45\,a\,b^5\,d^4\,e^2}{4}+\frac{3\,b^6\,d^5\,e}{4}\right)+x^5\,\left(3\,a^6\,d^2\,e^4+24\,a^5\,b\,d^3\,e^3+45\,a^4\,b^2\,d^4\,e^2+24\,a^3\,b^3\,d^5\,e+3\,a^2\,b^4\,d^6\right)+x^9\,\left(\frac{5\,a^4\,b^2\,e^6}{3}+\frac{40\,a^3\,b^3\,d\,e^5}{3}+25\,a^2\,b^4\,d^2\,e^4+\frac{40\,a\,b^5\,d^3\,e^3}{3}+\frac{5\,b^6\,d^4\,e^2}{3}\right)+x^7\,\left(\frac{a^6\,e^6}{7}+\frac{36\,a^5\,b\,d\,e^5}{7}+\frac{225\,a^4\,b^2\,d^2\,e^4}{7}+\frac{400\,a^3\,b^3\,d^3\,e^3}{7}+\frac{225\,a^2\,b^4\,d^4\,e^2}{7}+\frac{36\,a\,b^5\,d^5\,e}{7}+\frac{b^6\,d^6}{7}\right)+a^6\,d^6\,x+\frac{b^6\,e^6\,x^{13}}{13}+\frac{5\,a^3\,d^3\,x^4\,\left(2\,a^3\,e^3+9\,a^2\,b\,d\,e^2+9\,a\,b^2\,d^2\,e+2\,b^3\,d^3\right)}{2}+b^3\,e^3\,x^{10}\,\left(2\,a^3\,e^3+9\,a^2\,b\,d\,e^2+9\,a\,b^2\,d^2\,e+2\,b^3\,d^3\right)+3\,a^5\,d^5\,x^2\,\left(a\,e+b\,d\right)+\frac{b^5\,e^5\,x^{12}\,\left(a\,e+b\,d\right)}{2}+a^4\,d^4\,x^3\,\left(5\,a^2\,e^2+12\,a\,b\,d\,e+5\,b^2\,d^2\right)+\frac{3\,b^4\,e^4\,x^{11}\,\left(5\,a^2\,e^2+12\,a\,b\,d\,e+5\,b^2\,d^2\right)}{11}","Not used",1,"x^6*(a*b^5*d^6 + a^6*d*e^5 + 15*a^2*b^4*d^5*e + 15*a^5*b*d^2*e^4 + 50*a^3*b^3*d^4*e^2 + 50*a^4*b^2*d^3*e^3) + x^8*((3*a^5*b*e^6)/4 + (3*b^6*d^5*e)/4 + (45*a*b^5*d^4*e^2)/4 + (45*a^4*b^2*d*e^5)/4 + (75*a^2*b^4*d^3*e^3)/2 + (75*a^3*b^3*d^2*e^4)/2) + x^5*(3*a^2*b^4*d^6 + 3*a^6*d^2*e^4 + 24*a^3*b^3*d^5*e + 24*a^5*b*d^3*e^3 + 45*a^4*b^2*d^4*e^2) + x^9*((5*a^4*b^2*e^6)/3 + (5*b^6*d^4*e^2)/3 + (40*a*b^5*d^3*e^3)/3 + (40*a^3*b^3*d*e^5)/3 + 25*a^2*b^4*d^2*e^4) + x^7*((a^6*e^6)/7 + (b^6*d^6)/7 + (225*a^2*b^4*d^4*e^2)/7 + (400*a^3*b^3*d^3*e^3)/7 + (225*a^4*b^2*d^2*e^4)/7 + (36*a*b^5*d^5*e)/7 + (36*a^5*b*d*e^5)/7) + a^6*d^6*x + (b^6*e^6*x^13)/13 + (5*a^3*d^3*x^4*(2*a^3*e^3 + 2*b^3*d^3 + 9*a*b^2*d^2*e + 9*a^2*b*d*e^2))/2 + b^3*e^3*x^10*(2*a^3*e^3 + 2*b^3*d^3 + 9*a*b^2*d^2*e + 9*a^2*b*d*e^2) + 3*a^5*d^5*x^2*(a*e + b*d) + (b^5*e^5*x^12*(a*e + b*d))/2 + a^4*d^4*x^3*(5*a^2*e^2 + 5*b^2*d^2 + 12*a*b*d*e) + (3*b^4*e^4*x^11*(5*a^2*e^2 + 5*b^2*d^2 + 12*a*b*d*e))/11","B"
1484,1,492,143,0.188269,"\text{Not used}","int((d + e*x)^5*(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","x^5\,\left(a^6\,d\,e^4+12\,a^5\,b\,d^2\,e^3+30\,a^4\,b^2\,d^3\,e^2+20\,a^3\,b^3\,d^4\,e+3\,a^2\,b^4\,d^5\right)+x^8\,\left(\frac{15\,a^4\,b^2\,e^5}{8}+\frac{25\,a^3\,b^3\,d\,e^4}{2}+\frac{75\,a^2\,b^4\,d^2\,e^3}{4}+\frac{15\,a\,b^5\,d^3\,e^2}{2}+\frac{5\,b^6\,d^4\,e}{8}\right)+x^6\,\left(\frac{a^6\,e^5}{6}+5\,a^5\,b\,d\,e^4+25\,a^4\,b^2\,d^2\,e^3+\frac{100\,a^3\,b^3\,d^3\,e^2}{3}+\frac{25\,a^2\,b^4\,d^4\,e}{2}+a\,b^5\,d^5\right)+x^7\,\left(\frac{6\,a^5\,b\,e^5}{7}+\frac{75\,a^4\,b^2\,d\,e^4}{7}+\frac{200\,a^3\,b^3\,d^2\,e^3}{7}+\frac{150\,a^2\,b^4\,d^3\,e^2}{7}+\frac{30\,a\,b^5\,d^4\,e}{7}+\frac{b^6\,d^5}{7}\right)+a^6\,d^5\,x+\frac{b^6\,e^5\,x^{12}}{12}+\frac{5\,a^3\,d^2\,x^4\,\left(2\,a^3\,e^3+12\,a^2\,b\,d\,e^2+15\,a\,b^2\,d^2\,e+4\,b^3\,d^3\right)}{4}+\frac{5\,b^3\,e^2\,x^9\,\left(4\,a^3\,e^3+15\,a^2\,b\,d\,e^2+12\,a\,b^2\,d^2\,e+2\,b^3\,d^3\right)}{9}+\frac{a^5\,d^4\,x^2\,\left(5\,a\,e+6\,b\,d\right)}{2}+\frac{b^5\,e^4\,x^{11}\,\left(6\,a\,e+5\,b\,d\right)}{11}+\frac{5\,a^4\,d^3\,x^3\,\left(2\,a^2\,e^2+6\,a\,b\,d\,e+3\,b^2\,d^2\right)}{3}+\frac{b^4\,e^3\,x^{10}\,\left(3\,a^2\,e^2+6\,a\,b\,d\,e+2\,b^2\,d^2\right)}{2}","Not used",1,"x^5*(a^6*d*e^4 + 3*a^2*b^4*d^5 + 20*a^3*b^3*d^4*e + 12*a^5*b*d^2*e^3 + 30*a^4*b^2*d^3*e^2) + x^8*((5*b^6*d^4*e)/8 + (15*a^4*b^2*e^5)/8 + (15*a*b^5*d^3*e^2)/2 + (25*a^3*b^3*d*e^4)/2 + (75*a^2*b^4*d^2*e^3)/4) + x^6*((a^6*e^5)/6 + a*b^5*d^5 + (25*a^2*b^4*d^4*e)/2 + (100*a^3*b^3*d^3*e^2)/3 + 25*a^4*b^2*d^2*e^3 + 5*a^5*b*d*e^4) + x^7*((b^6*d^5)/7 + (6*a^5*b*e^5)/7 + (75*a^4*b^2*d*e^4)/7 + (150*a^2*b^4*d^3*e^2)/7 + (200*a^3*b^3*d^2*e^3)/7 + (30*a*b^5*d^4*e)/7) + a^6*d^5*x + (b^6*e^5*x^12)/12 + (5*a^3*d^2*x^4*(2*a^3*e^3 + 4*b^3*d^3 + 15*a*b^2*d^2*e + 12*a^2*b*d*e^2))/4 + (5*b^3*e^2*x^9*(4*a^3*e^3 + 2*b^3*d^3 + 12*a*b^2*d^2*e + 15*a^2*b*d*e^2))/9 + (a^5*d^4*x^2*(5*a*e + 6*b*d))/2 + (b^5*e^4*x^11*(6*a*e + 5*b*d))/11 + (5*a^4*d^3*x^3*(2*a^2*e^2 + 3*b^2*d^2 + 6*a*b*d*e))/3 + (b^4*e^3*x^10*(3*a^2*e^2 + 2*b^2*d^2 + 6*a*b*d*e))/2","B"
1485,1,402,119,0.614016,"\text{Not used}","int((d + e*x)^4*(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","x^5\,\left(\frac{a^6\,e^4}{5}+\frac{24\,a^5\,b\,d\,e^3}{5}+18\,a^4\,b^2\,d^2\,e^2+16\,a^3\,b^3\,d^3\,e+3\,a^2\,b^4\,d^4\right)+x^7\,\left(\frac{15\,a^4\,b^2\,e^4}{7}+\frac{80\,a^3\,b^3\,d\,e^3}{7}+\frac{90\,a^2\,b^4\,d^2\,e^2}{7}+\frac{24\,a\,b^5\,d^3\,e}{7}+\frac{b^6\,d^4}{7}\right)+x^4\,\left(a^6\,d\,e^3+9\,a^5\,b\,d^2\,e^2+15\,a^4\,b^2\,d^3\,e+5\,a^3\,b^3\,d^4\right)+x^8\,\left(\frac{5\,a^3\,b^3\,e^4}{2}+\frac{15\,a^2\,b^4\,d\,e^3}{2}+\frac{9\,a\,b^5\,d^2\,e^2}{2}+\frac{b^6\,d^3\,e}{2}\right)+x^6\,\left(a^5\,b\,e^4+10\,a^4\,b^2\,d\,e^3+20\,a^3\,b^3\,d^2\,e^2+10\,a^2\,b^4\,d^3\,e+a\,b^5\,d^4\right)+a^6\,d^4\,x+\frac{b^6\,e^4\,x^{11}}{11}+a^5\,d^3\,x^2\,\left(2\,a\,e+3\,b\,d\right)+\frac{b^5\,e^3\,x^{10}\,\left(3\,a\,e+2\,b\,d\right)}{5}+a^4\,d^2\,x^3\,\left(2\,a^2\,e^2+8\,a\,b\,d\,e+5\,b^2\,d^2\right)+\frac{b^4\,e^2\,x^9\,\left(5\,a^2\,e^2+8\,a\,b\,d\,e+2\,b^2\,d^2\right)}{3}","Not used",1,"x^5*((a^6*e^4)/5 + 3*a^2*b^4*d^4 + 16*a^3*b^3*d^3*e + 18*a^4*b^2*d^2*e^2 + (24*a^5*b*d*e^3)/5) + x^7*((b^6*d^4)/7 + (15*a^4*b^2*e^4)/7 + (80*a^3*b^3*d*e^3)/7 + (90*a^2*b^4*d^2*e^2)/7 + (24*a*b^5*d^3*e)/7) + x^4*(a^6*d*e^3 + 5*a^3*b^3*d^4 + 15*a^4*b^2*d^3*e + 9*a^5*b*d^2*e^2) + x^8*((b^6*d^3*e)/2 + (5*a^3*b^3*e^4)/2 + (9*a*b^5*d^2*e^2)/2 + (15*a^2*b^4*d*e^3)/2) + x^6*(a*b^5*d^4 + a^5*b*e^4 + 10*a^2*b^4*d^3*e + 10*a^4*b^2*d*e^3 + 20*a^3*b^3*d^2*e^2) + a^6*d^4*x + (b^6*e^4*x^11)/11 + a^5*d^3*x^2*(2*a*e + 3*b*d) + (b^5*e^3*x^10*(3*a*e + 2*b*d))/5 + a^4*d^2*x^3*(2*a^2*e^2 + 5*b^2*d^2 + 8*a*b*d*e) + (b^4*e^2*x^9*(5*a^2*e^2 + 2*b^2*d^2 + 8*a*b*d*e))/3","B"
1486,1,308,92,0.576021,"\text{Not used}","int((d + e*x)^3*(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","x^5\,\left(\frac{6\,a^5\,b\,e^3}{5}+9\,a^4\,b^2\,d\,e^2+12\,a^3\,b^3\,d^2\,e+3\,a^2\,b^4\,d^3\right)+x^6\,\left(\frac{5\,a^4\,b^2\,e^3}{2}+10\,a^3\,b^3\,d\,e^2+\frac{15\,a^2\,b^4\,d^2\,e}{2}+a\,b^5\,d^3\right)+x^4\,\left(\frac{a^6\,e^3}{4}+\frac{9\,a^5\,b\,d\,e^2}{2}+\frac{45\,a^4\,b^2\,d^2\,e}{4}+5\,a^3\,b^3\,d^3\right)+x^7\,\left(\frac{20\,a^3\,b^3\,e^3}{7}+\frac{45\,a^2\,b^4\,d\,e^2}{7}+\frac{18\,a\,b^5\,d^2\,e}{7}+\frac{b^6\,d^3}{7}\right)+a^6\,d^3\,x+\frac{b^6\,e^3\,x^{10}}{10}+\frac{3\,a^5\,d^2\,x^2\,\left(a\,e+2\,b\,d\right)}{2}+\frac{b^5\,e^2\,x^9\,\left(2\,a\,e+b\,d\right)}{3}+a^4\,d\,x^3\,\left(a^2\,e^2+6\,a\,b\,d\,e+5\,b^2\,d^2\right)+\frac{3\,b^4\,e\,x^8\,\left(5\,a^2\,e^2+6\,a\,b\,d\,e+b^2\,d^2\right)}{8}","Not used",1,"x^5*((6*a^5*b*e^3)/5 + 3*a^2*b^4*d^3 + 12*a^3*b^3*d^2*e + 9*a^4*b^2*d*e^2) + x^6*(a*b^5*d^3 + (5*a^4*b^2*e^3)/2 + (15*a^2*b^4*d^2*e)/2 + 10*a^3*b^3*d*e^2) + x^4*((a^6*e^3)/4 + 5*a^3*b^3*d^3 + (45*a^4*b^2*d^2*e)/4 + (9*a^5*b*d*e^2)/2) + x^7*((b^6*d^3)/7 + (20*a^3*b^3*e^3)/7 + (45*a^2*b^4*d*e^2)/7 + (18*a*b^5*d^2*e)/7) + a^6*d^3*x + (b^6*e^3*x^10)/10 + (3*a^5*d^2*x^2*(a*e + 2*b*d))/2 + (b^5*e^2*x^9*(2*a*e + b*d))/3 + a^4*d*x^3*(a^2*e^2 + 5*b^2*d^2 + 6*a*b*d*e) + (3*b^4*e*x^8*(5*a^2*e^2 + b^2*d^2 + 6*a*b*d*e))/8","B"
1487,1,214,65,0.091028,"\text{Not used}","int((d + e*x)^2*(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","x^3\,\left(\frac{a^6\,e^2}{3}+4\,a^5\,b\,d\,e+5\,a^4\,b^2\,d^2\right)+x^7\,\left(\frac{15\,a^2\,b^4\,e^2}{7}+\frac{12\,a\,b^5\,d\,e}{7}+\frac{b^6\,d^2}{7}\right)+a^6\,d^2\,x+\frac{b^6\,e^2\,x^9}{9}+a^5\,d\,x^2\,\left(a\,e+3\,b\,d\right)+\frac{b^5\,e\,x^8\,\left(3\,a\,e+b\,d\right)}{4}+\frac{a^3\,b\,x^4\,\left(3\,a^2\,e^2+15\,a\,b\,d\,e+10\,b^2\,d^2\right)}{2}+\frac{a\,b^3\,x^6\,\left(10\,a^2\,e^2+15\,a\,b\,d\,e+3\,b^2\,d^2\right)}{3}+a^2\,b^2\,x^5\,\left(3\,a^2\,e^2+8\,a\,b\,d\,e+3\,b^2\,d^2\right)","Not used",1,"x^3*((a^6*e^2)/3 + 5*a^4*b^2*d^2 + 4*a^5*b*d*e) + x^7*((b^6*d^2)/7 + (15*a^2*b^4*e^2)/7 + (12*a*b^5*d*e)/7) + a^6*d^2*x + (b^6*e^2*x^9)/9 + a^5*d*x^2*(a*e + 3*b*d) + (b^5*e*x^8*(3*a*e + b*d))/4 + (a^3*b*x^4*(3*a^2*e^2 + 10*b^2*d^2 + 15*a*b*d*e))/2 + (a*b^3*x^6*(10*a^2*e^2 + 3*b^2*d^2 + 15*a*b*d*e))/3 + a^2*b^2*x^5*(3*a^2*e^2 + 3*b^2*d^2 + 8*a*b*d*e)","B"
1488,1,126,38,0.063577,"\text{Not used}","int((d + e*x)*(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","x^2\,\left(\frac{e\,a^6}{2}+3\,b\,d\,a^5\right)+x^7\,\left(\frac{d\,b^6}{7}+\frac{6\,a\,e\,b^5}{7}\right)+\frac{b^6\,e\,x^8}{8}+a^6\,d\,x+a^4\,b\,x^3\,\left(2\,a\,e+5\,b\,d\right)+\frac{a\,b^4\,x^6\,\left(5\,a\,e+2\,b\,d\right)}{2}+\frac{5\,a^3\,b^2\,x^4\,\left(3\,a\,e+4\,b\,d\right)}{4}+a^2\,b^3\,x^5\,\left(4\,a\,e+3\,b\,d\right)","Not used",1,"x^2*((a^6*e)/2 + 3*a^5*b*d) + x^7*((b^6*d)/7 + (6*a*b^5*e)/7) + (b^6*e*x^8)/8 + a^6*d*x + a^4*b*x^3*(2*a*e + 5*b*d) + (a*b^4*x^6*(5*a*e + 2*b*d))/2 + (5*a^3*b^2*x^4*(3*a*e + 4*b*d))/4 + a^2*b^3*x^5*(4*a*e + 3*b*d)","B"
1489,1,64,14,0.029179,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3,x)","a^6\,x+3\,a^5\,b\,x^2+5\,a^4\,b^2\,x^3+5\,a^3\,b^3\,x^4+3\,a^2\,b^4\,x^5+a\,b^5\,x^6+\frac{b^6\,x^7}{7}","Not used",1,"a^6*x + (b^6*x^7)/7 + 3*a^5*b*x^2 + a*b^5*x^6 + 5*a^4*b^2*x^3 + 5*a^3*b^3*x^4 + 3*a^2*b^4*x^5","B"
1490,1,385,146,0.521153,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x),x)","x^5\,\left(\frac{6\,a\,b^5}{5\,e}-\frac{b^6\,d}{5\,e^2}\right)+x^3\,\left(\frac{d\,\left(\frac{d\,\left(\frac{6\,a\,b^5}{e}-\frac{b^6\,d}{e^2}\right)}{e}-\frac{15\,a^2\,b^4}{e}\right)}{3\,e}+\frac{20\,a^3\,b^3}{3\,e}\right)+x\,\left(\frac{d\,\left(\frac{d\,\left(\frac{d\,\left(\frac{d\,\left(\frac{6\,a\,b^5}{e}-\frac{b^6\,d}{e^2}\right)}{e}-\frac{15\,a^2\,b^4}{e}\right)}{e}+\frac{20\,a^3\,b^3}{e}\right)}{e}-\frac{15\,a^4\,b^2}{e}\right)}{e}+\frac{6\,a^5\,b}{e}\right)-x^4\,\left(\frac{d\,\left(\frac{6\,a\,b^5}{e}-\frac{b^6\,d}{e^2}\right)}{4\,e}-\frac{15\,a^2\,b^4}{4\,e}\right)-x^2\,\left(\frac{d\,\left(\frac{d\,\left(\frac{d\,\left(\frac{6\,a\,b^5}{e}-\frac{b^6\,d}{e^2}\right)}{e}-\frac{15\,a^2\,b^4}{e}\right)}{e}+\frac{20\,a^3\,b^3}{e}\right)}{2\,e}-\frac{15\,a^4\,b^2}{2\,e}\right)+\frac{\ln\left(d+e\,x\right)\,\left(a^6\,e^6-6\,a^5\,b\,d\,e^5+15\,a^4\,b^2\,d^2\,e^4-20\,a^3\,b^3\,d^3\,e^3+15\,a^2\,b^4\,d^4\,e^2-6\,a\,b^5\,d^5\,e+b^6\,d^6\right)}{e^7}+\frac{b^6\,x^6}{6\,e}","Not used",1,"x^5*((6*a*b^5)/(5*e) - (b^6*d)/(5*e^2)) + x^3*((d*((d*((6*a*b^5)/e - (b^6*d)/e^2))/e - (15*a^2*b^4)/e))/(3*e) + (20*a^3*b^3)/(3*e)) + x*((d*((d*((d*((d*((6*a*b^5)/e - (b^6*d)/e^2))/e - (15*a^2*b^4)/e))/e + (20*a^3*b^3)/e))/e - (15*a^4*b^2)/e))/e + (6*a^5*b)/e) - x^4*((d*((6*a*b^5)/e - (b^6*d)/e^2))/(4*e) - (15*a^2*b^4)/(4*e)) - x^2*((d*((d*((d*((6*a*b^5)/e - (b^6*d)/e^2))/e - (15*a^2*b^4)/e))/e + (20*a^3*b^3)/e))/(2*e) - (15*a^4*b^2)/(2*e)) + (log(d + e*x)*(a^6*e^6 + b^6*d^6 + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a*b^5*d^5*e - 6*a^5*b*d*e^5))/e^7 + (b^6*x^6)/(6*e)","B"
1491,1,523,156,0.089238,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^2,x)","x^4\,\left(\frac{3\,a\,b^5}{2\,e^2}-\frac{b^6\,d}{2\,e^3}\right)-x^3\,\left(\frac{2\,d\,\left(\frac{6\,a\,b^5}{e^2}-\frac{2\,b^6\,d}{e^3}\right)}{3\,e}-\frac{5\,a^2\,b^4}{e^2}+\frac{b^6\,d^2}{3\,e^4}\right)+x^2\,\left(\frac{10\,a^3\,b^3}{e^2}+\frac{d\,\left(\frac{2\,d\,\left(\frac{6\,a\,b^5}{e^2}-\frac{2\,b^6\,d}{e^3}\right)}{e}-\frac{15\,a^2\,b^4}{e^2}+\frac{b^6\,d^2}{e^4}\right)}{e}-\frac{d^2\,\left(\frac{6\,a\,b^5}{e^2}-\frac{2\,b^6\,d}{e^3}\right)}{2\,e^2}\right)+x\,\left(\frac{d^2\,\left(\frac{2\,d\,\left(\frac{6\,a\,b^5}{e^2}-\frac{2\,b^6\,d}{e^3}\right)}{e}-\frac{15\,a^2\,b^4}{e^2}+\frac{b^6\,d^2}{e^4}\right)}{e^2}-\frac{2\,d\,\left(\frac{20\,a^3\,b^3}{e^2}+\frac{2\,d\,\left(\frac{2\,d\,\left(\frac{6\,a\,b^5}{e^2}-\frac{2\,b^6\,d}{e^3}\right)}{e}-\frac{15\,a^2\,b^4}{e^2}+\frac{b^6\,d^2}{e^4}\right)}{e}-\frac{d^2\,\left(\frac{6\,a\,b^5}{e^2}-\frac{2\,b^6\,d}{e^3}\right)}{e^2}\right)}{e}+\frac{15\,a^4\,b^2}{e^2}\right)-\frac{\ln\left(d+e\,x\right)\,\left(-6\,a^5\,b\,e^5+30\,a^4\,b^2\,d\,e^4-60\,a^3\,b^3\,d^2\,e^3+60\,a^2\,b^4\,d^3\,e^2-30\,a\,b^5\,d^4\,e+6\,b^6\,d^5\right)}{e^7}+\frac{b^6\,x^5}{5\,e^2}-\frac{a^6\,e^6-6\,a^5\,b\,d\,e^5+15\,a^4\,b^2\,d^2\,e^4-20\,a^3\,b^3\,d^3\,e^3+15\,a^2\,b^4\,d^4\,e^2-6\,a\,b^5\,d^5\,e+b^6\,d^6}{e\,\left(x\,e^7+d\,e^6\right)}","Not used",1,"x^4*((3*a*b^5)/(2*e^2) - (b^6*d)/(2*e^3)) - x^3*((2*d*((6*a*b^5)/e^2 - (2*b^6*d)/e^3))/(3*e) - (5*a^2*b^4)/e^2 + (b^6*d^2)/(3*e^4)) + x^2*((10*a^3*b^3)/e^2 + (d*((2*d*((6*a*b^5)/e^2 - (2*b^6*d)/e^3))/e - (15*a^2*b^4)/e^2 + (b^6*d^2)/e^4))/e - (d^2*((6*a*b^5)/e^2 - (2*b^6*d)/e^3))/(2*e^2)) + x*((d^2*((2*d*((6*a*b^5)/e^2 - (2*b^6*d)/e^3))/e - (15*a^2*b^4)/e^2 + (b^6*d^2)/e^4))/e^2 - (2*d*((20*a^3*b^3)/e^2 + (2*d*((2*d*((6*a*b^5)/e^2 - (2*b^6*d)/e^3))/e - (15*a^2*b^4)/e^2 + (b^6*d^2)/e^4))/e - (d^2*((6*a*b^5)/e^2 - (2*b^6*d)/e^3))/e^2))/e + (15*a^4*b^2)/e^2) - (log(d + e*x)*(6*b^6*d^5 - 6*a^5*b*e^5 + 30*a^4*b^2*d*e^4 + 60*a^2*b^4*d^3*e^2 - 60*a^3*b^3*d^2*e^3 - 30*a*b^5*d^4*e))/e^7 + (b^6*x^5)/(5*e^2) - (a^6*e^6 + b^6*d^6 + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a*b^5*d^5*e - 6*a^5*b*d*e^5)/(e*(d*e^6 + e^7*x))","B"
1492,1,441,158,0.568510,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^3,x)","x\,\left(\frac{20\,a^3\,b^3}{e^3}-\frac{b^6\,d^3}{e^6}+\frac{3\,d\,\left(\frac{3\,d\,\left(\frac{6\,a\,b^5}{e^3}-\frac{3\,b^6\,d}{e^4}\right)}{e}-\frac{15\,a^2\,b^4}{e^3}+\frac{3\,b^6\,d^2}{e^5}\right)}{e}-\frac{3\,d^2\,\left(\frac{6\,a\,b^5}{e^3}-\frac{3\,b^6\,d}{e^4}\right)}{e^2}\right)-\frac{\frac{a^6\,e^6+6\,a^5\,b\,d\,e^5-45\,a^4\,b^2\,d^2\,e^4+100\,a^3\,b^3\,d^3\,e^3-105\,a^2\,b^4\,d^4\,e^2+54\,a\,b^5\,d^5\,e-11\,b^6\,d^6}{2\,e}-x\,\left(-6\,a^5\,b\,e^5+30\,a^4\,b^2\,d\,e^4-60\,a^3\,b^3\,d^2\,e^3+60\,a^2\,b^4\,d^3\,e^2-30\,a\,b^5\,d^4\,e+6\,b^6\,d^5\right)}{d^2\,e^6+2\,d\,e^7\,x+e^8\,x^2}+x^3\,\left(\frac{2\,a\,b^5}{e^3}-\frac{b^6\,d}{e^4}\right)-x^2\,\left(\frac{3\,d\,\left(\frac{6\,a\,b^5}{e^3}-\frac{3\,b^6\,d}{e^4}\right)}{2\,e}-\frac{15\,a^2\,b^4}{2\,e^3}+\frac{3\,b^6\,d^2}{2\,e^5}\right)+\frac{\ln\left(d+e\,x\right)\,\left(15\,a^4\,b^2\,e^4-60\,a^3\,b^3\,d\,e^3+90\,a^2\,b^4\,d^2\,e^2-60\,a\,b^5\,d^3\,e+15\,b^6\,d^4\right)}{e^7}+\frac{b^6\,x^4}{4\,e^3}","Not used",1,"x*((20*a^3*b^3)/e^3 - (b^6*d^3)/e^6 + (3*d*((3*d*((6*a*b^5)/e^3 - (3*b^6*d)/e^4))/e - (15*a^2*b^4)/e^3 + (3*b^6*d^2)/e^5))/e - (3*d^2*((6*a*b^5)/e^3 - (3*b^6*d)/e^4))/e^2) - ((a^6*e^6 - 11*b^6*d^6 - 105*a^2*b^4*d^4*e^2 + 100*a^3*b^3*d^3*e^3 - 45*a^4*b^2*d^2*e^4 + 54*a*b^5*d^5*e + 6*a^5*b*d*e^5)/(2*e) - x*(6*b^6*d^5 - 6*a^5*b*e^5 + 30*a^4*b^2*d*e^4 + 60*a^2*b^4*d^3*e^2 - 60*a^3*b^3*d^2*e^3 - 30*a*b^5*d^4*e))/(d^2*e^6 + e^8*x^2 + 2*d*e^7*x) + x^3*((2*a*b^5)/e^3 - (b^6*d)/e^4) - x^2*((3*d*((6*a*b^5)/e^3 - (3*b^6*d)/e^4))/(2*e) - (15*a^2*b^4)/(2*e^3) + (3*b^6*d^2)/(2*e^5)) + (log(d + e*x)*(15*b^6*d^4 + 15*a^4*b^2*e^4 - 60*a^3*b^3*d*e^3 + 90*a^2*b^4*d^2*e^2 - 60*a*b^5*d^3*e))/e^7 + (b^6*x^4)/(4*e^3)","B"
1493,1,393,156,0.581011,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^4,x)","x^2\,\left(\frac{3\,a\,b^5}{e^4}-\frac{2\,b^6\,d}{e^5}\right)-\frac{x^2\,\left(15\,a^4\,b^2\,e^5-60\,a^3\,b^3\,d\,e^4+90\,a^2\,b^4\,d^2\,e^3-60\,a\,b^5\,d^3\,e^2+15\,b^6\,d^4\,e\right)+\frac{a^6\,e^6+3\,a^5\,b\,d\,e^5+15\,a^4\,b^2\,d^2\,e^4-110\,a^3\,b^3\,d^3\,e^3+195\,a^2\,b^4\,d^4\,e^2-141\,a\,b^5\,d^5\,e+37\,b^6\,d^6}{3\,e}+x\,\left(3\,a^5\,b\,e^5+15\,a^4\,b^2\,d\,e^4-90\,a^3\,b^3\,d^2\,e^3+150\,a^2\,b^4\,d^3\,e^2-105\,a\,b^5\,d^4\,e+27\,b^6\,d^5\right)}{d^3\,e^6+3\,d^2\,e^7\,x+3\,d\,e^8\,x^2+e^9\,x^3}-x\,\left(\frac{4\,d\,\left(\frac{6\,a\,b^5}{e^4}-\frac{4\,b^6\,d}{e^5}\right)}{e}-\frac{15\,a^2\,b^4}{e^4}+\frac{6\,b^6\,d^2}{e^6}\right)-\frac{\ln\left(d+e\,x\right)\,\left(-20\,a^3\,b^3\,e^3+60\,a^2\,b^4\,d\,e^2-60\,a\,b^5\,d^2\,e+20\,b^6\,d^3\right)}{e^7}+\frac{b^6\,x^3}{3\,e^4}","Not used",1,"x^2*((3*a*b^5)/e^4 - (2*b^6*d)/e^5) - (x^2*(15*b^6*d^4*e + 15*a^4*b^2*e^5 - 60*a*b^5*d^3*e^2 - 60*a^3*b^3*d*e^4 + 90*a^2*b^4*d^2*e^3) + (a^6*e^6 + 37*b^6*d^6 + 195*a^2*b^4*d^4*e^2 - 110*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 141*a*b^5*d^5*e + 3*a^5*b*d*e^5)/(3*e) + x*(27*b^6*d^5 + 3*a^5*b*e^5 + 15*a^4*b^2*d*e^4 + 150*a^2*b^4*d^3*e^2 - 90*a^3*b^3*d^2*e^3 - 105*a*b^5*d^4*e))/(d^3*e^6 + e^9*x^3 + 3*d^2*e^7*x + 3*d*e^8*x^2) - x*((4*d*((6*a*b^5)/e^4 - (4*b^6*d)/e^5))/e - (15*a^2*b^4)/e^4 + (6*b^6*d^2)/e^6) - (log(d + e*x)*(20*b^6*d^3 - 20*a^3*b^3*e^3 + 60*a^2*b^4*d*e^2 - 60*a*b^5*d^2*e))/e^7 + (b^6*x^3)/(3*e^4)","B"
1494,1,387,155,0.147779,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^5,x)","x\,\left(\frac{6\,a\,b^5}{e^5}-\frac{5\,b^6\,d}{e^6}\right)-\frac{x^2\,\left(\frac{15\,a^4\,b^2\,e^5}{2}+30\,a^3\,b^3\,d\,e^4-135\,a^2\,b^4\,d^2\,e^3+150\,a\,b^5\,d^3\,e^2-\frac{105\,b^6\,d^4\,e}{2}\right)+\frac{a^6\,e^6+2\,a^5\,b\,d\,e^5+5\,a^4\,b^2\,d^2\,e^4+20\,a^3\,b^3\,d^3\,e^3-125\,a^2\,b^4\,d^4\,e^2+154\,a\,b^5\,d^5\,e-57\,b^6\,d^6}{4\,e}+x\,\left(2\,a^5\,b\,e^5+5\,a^4\,b^2\,d\,e^4+20\,a^3\,b^3\,d^2\,e^3-110\,a^2\,b^4\,d^3\,e^2+130\,a\,b^5\,d^4\,e-47\,b^6\,d^5\right)+x^3\,\left(20\,a^3\,b^3\,e^5-60\,a^2\,b^4\,d\,e^4+60\,a\,b^5\,d^2\,e^3-20\,b^6\,d^3\,e^2\right)}{d^4\,e^6+4\,d^3\,e^7\,x+6\,d^2\,e^8\,x^2+4\,d\,e^9\,x^3+e^{10}\,x^4}+\frac{b^6\,x^2}{2\,e^5}+\frac{\ln\left(d+e\,x\right)\,\left(15\,a^2\,b^4\,e^2-30\,a\,b^5\,d\,e+15\,b^6\,d^2\right)}{e^7}","Not used",1,"x*((6*a*b^5)/e^5 - (5*b^6*d)/e^6) - (x^2*((15*a^4*b^2*e^5)/2 - (105*b^6*d^4*e)/2 + 150*a*b^5*d^3*e^2 + 30*a^3*b^3*d*e^4 - 135*a^2*b^4*d^2*e^3) + (a^6*e^6 - 57*b^6*d^6 - 125*a^2*b^4*d^4*e^2 + 20*a^3*b^3*d^3*e^3 + 5*a^4*b^2*d^2*e^4 + 154*a*b^5*d^5*e + 2*a^5*b*d*e^5)/(4*e) + x*(2*a^5*b*e^5 - 47*b^6*d^5 + 5*a^4*b^2*d*e^4 - 110*a^2*b^4*d^3*e^2 + 20*a^3*b^3*d^2*e^3 + 130*a*b^5*d^4*e) + x^3*(20*a^3*b^3*e^5 - 20*b^6*d^3*e^2 + 60*a*b^5*d^2*e^3 - 60*a^2*b^4*d*e^4))/(d^4*e^6 + e^10*x^4 + 4*d^3*e^7*x + 4*d*e^9*x^3 + 6*d^2*e^8*x^2) + (b^6*x^2)/(2*e^5) + (log(d + e*x)*(15*b^6*d^2 + 15*a^2*b^4*e^2 - 30*a*b^5*d*e))/e^7","B"
1495,1,399,155,0.650514,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^6,x)","\frac{b^6\,x}{e^6}-\frac{\ln\left(d+e\,x\right)\,\left(6\,b^6\,d-6\,a\,b^5\,e\right)}{e^7}-\frac{x^2\,\left(5\,a^4\,b^2\,e^5+10\,a^3\,b^3\,d\,e^4+30\,a^2\,b^4\,d^2\,e^3-110\,a\,b^5\,d^3\,e^2+65\,b^6\,d^4\,e\right)+x^4\,\left(15\,a^2\,b^4\,e^5-30\,a\,b^5\,d\,e^4+15\,b^6\,d^2\,e^3\right)+\frac{2\,a^6\,e^6+3\,a^5\,b\,d\,e^5+5\,a^4\,b^2\,d^2\,e^4+10\,a^3\,b^3\,d^3\,e^3+30\,a^2\,b^4\,d^4\,e^2-137\,a\,b^5\,d^5\,e+87\,b^6\,d^6}{10\,e}+x\,\left(\frac{3\,a^5\,b\,e^5}{2}+\frac{5\,a^4\,b^2\,d\,e^4}{2}+5\,a^3\,b^3\,d^2\,e^3+15\,a^2\,b^4\,d^3\,e^2-\frac{125\,a\,b^5\,d^4\,e}{2}+\frac{77\,b^6\,d^5}{2}\right)+x^3\,\left(10\,a^3\,b^3\,e^5+30\,a^2\,b^4\,d\,e^4-90\,a\,b^5\,d^2\,e^3+50\,b^6\,d^3\,e^2\right)}{d^5\,e^6+5\,d^4\,e^7\,x+10\,d^3\,e^8\,x^2+10\,d^2\,e^9\,x^3+5\,d\,e^{10}\,x^4+e^{11}\,x^5}","Not used",1,"(b^6*x)/e^6 - (log(d + e*x)*(6*b^6*d - 6*a*b^5*e))/e^7 - (x^2*(65*b^6*d^4*e + 5*a^4*b^2*e^5 - 110*a*b^5*d^3*e^2 + 10*a^3*b^3*d*e^4 + 30*a^2*b^4*d^2*e^3) + x^4*(15*a^2*b^4*e^5 + 15*b^6*d^2*e^3 - 30*a*b^5*d*e^4) + (2*a^6*e^6 + 87*b^6*d^6 + 30*a^2*b^4*d^4*e^2 + 10*a^3*b^3*d^3*e^3 + 5*a^4*b^2*d^2*e^4 - 137*a*b^5*d^5*e + 3*a^5*b*d*e^5)/(10*e) + x*((77*b^6*d^5)/2 + (3*a^5*b*e^5)/2 + (5*a^4*b^2*d*e^4)/2 + 15*a^2*b^4*d^3*e^2 + 5*a^3*b^3*d^2*e^3 - (125*a*b^5*d^4*e)/2) + x^3*(10*a^3*b^3*e^5 + 50*b^6*d^3*e^2 - 90*a*b^5*d^2*e^3 + 30*a^2*b^4*d*e^4))/(d^5*e^6 + e^11*x^5 + 5*d^4*e^7*x + 5*d*e^10*x^4 + 10*d^3*e^8*x^2 + 10*d^2*e^9*x^3)","B"
1496,1,353,167,0.636567,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^7,x)","\frac{b^6\,\ln\left(d+e\,x\right)}{e^7}-\frac{x^5\,\left(6\,a\,b^5\,e^6-6\,b^6\,d\,e^5\right)+x^2\,\left(\frac{15\,a^4\,b^2\,e^6}{4}+5\,a^3\,b^3\,d\,e^5+\frac{15\,a^2\,b^4\,d^2\,e^4}{2}+15\,a\,b^5\,d^3\,e^3-\frac{125\,b^6\,d^4\,e^2}{4}\right)+x^4\,\left(\frac{15\,a^2\,b^4\,e^6}{2}+15\,a\,b^5\,d\,e^5-\frac{45\,b^6\,d^2\,e^4}{2}\right)+x\,\left(\frac{6\,a^5\,b\,e^6}{5}+\frac{3\,a^4\,b^2\,d\,e^5}{2}+2\,a^3\,b^3\,d^2\,e^4+3\,a^2\,b^4\,d^3\,e^3+6\,a\,b^5\,d^4\,e^2-\frac{137\,b^6\,d^5\,e}{10}\right)+\frac{a^6\,e^6}{6}-\frac{49\,b^6\,d^6}{20}+x^3\,\left(\frac{20\,a^3\,b^3\,e^6}{3}+10\,a^2\,b^4\,d\,e^5+20\,a\,b^5\,d^2\,e^4-\frac{110\,b^6\,d^3\,e^3}{3}\right)+\frac{a^2\,b^4\,d^4\,e^2}{2}+\frac{a^3\,b^3\,d^3\,e^3}{3}+\frac{a^4\,b^2\,d^2\,e^4}{4}+a\,b^5\,d^5\,e+\frac{a^5\,b\,d\,e^5}{5}}{e^7\,{\left(d+e\,x\right)}^6}","Not used",1,"(b^6*log(d + e*x))/e^7 - (x^5*(6*a*b^5*e^6 - 6*b^6*d*e^5) + x^2*((15*a^4*b^2*e^6)/4 - (125*b^6*d^4*e^2)/4 + 15*a*b^5*d^3*e^3 + 5*a^3*b^3*d*e^5 + (15*a^2*b^4*d^2*e^4)/2) + x^4*((15*a^2*b^4*e^6)/2 - (45*b^6*d^2*e^4)/2 + 15*a*b^5*d*e^5) + x*((6*a^5*b*e^6)/5 - (137*b^6*d^5*e)/10 + 6*a*b^5*d^4*e^2 + (3*a^4*b^2*d*e^5)/2 + 3*a^2*b^4*d^3*e^3 + 2*a^3*b^3*d^2*e^4) + (a^6*e^6)/6 - (49*b^6*d^6)/20 + x^3*((20*a^3*b^3*e^6)/3 - (110*b^6*d^3*e^3)/3 + 20*a*b^5*d^2*e^4 + 10*a^2*b^4*d*e^5) + (a^2*b^4*d^4*e^2)/2 + (a^3*b^3*d^3*e^3)/3 + (a^4*b^2*d^2*e^4)/4 + a*b^5*d^5*e + (a^5*b*d*e^5)/5)/(e^7*(d + e*x)^6)","B"
1497,1,378,28,0.589246,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^8,x)","-\frac{\frac{a^6\,e^6+a^5\,b\,d\,e^5+a^4\,b^2\,d^2\,e^4+a^3\,b^3\,d^3\,e^3+a^2\,b^4\,d^4\,e^2+a\,b^5\,d^5\,e+b^6\,d^6}{7\,e^7}+\frac{b^6\,x^6}{e}+\frac{5\,b^3\,x^3\,\left(a^3\,e^3+a^2\,b\,d\,e^2+a\,b^2\,d^2\,e+b^3\,d^3\right)}{e^4}+\frac{b\,x\,\left(a^5\,e^5+a^4\,b\,d\,e^4+a^3\,b^2\,d^2\,e^3+a^2\,b^3\,d^3\,e^2+a\,b^4\,d^4\,e+b^5\,d^5\right)}{e^6}+\frac{3\,b^5\,x^5\,\left(a\,e+b\,d\right)}{e^2}+\frac{3\,b^2\,x^2\,\left(a^4\,e^4+a^3\,b\,d\,e^3+a^2\,b^2\,d^2\,e^2+a\,b^3\,d^3\,e+b^4\,d^4\right)}{e^5}+\frac{5\,b^4\,x^4\,\left(a^2\,e^2+a\,b\,d\,e+b^2\,d^2\right)}{e^3}}{d^7+7\,d^6\,e\,x+21\,d^5\,e^2\,x^2+35\,d^4\,e^3\,x^3+35\,d^3\,e^4\,x^4+21\,d^2\,e^5\,x^5+7\,d\,e^6\,x^6+e^7\,x^7}","Not used",1,"-((a^6*e^6 + b^6*d^6 + a^2*b^4*d^4*e^2 + a^3*b^3*d^3*e^3 + a^4*b^2*d^2*e^4 + a*b^5*d^5*e + a^5*b*d*e^5)/(7*e^7) + (b^6*x^6)/e + (5*b^3*x^3*(a^3*e^3 + b^3*d^3 + a*b^2*d^2*e + a^2*b*d*e^2))/e^4 + (b*x*(a^5*e^5 + b^5*d^5 + a^2*b^3*d^3*e^2 + a^3*b^2*d^2*e^3 + a*b^4*d^4*e + a^4*b*d*e^4))/e^6 + (3*b^5*x^5*(a*e + b*d))/e^2 + (3*b^2*x^2*(a^4*e^4 + b^4*d^4 + a^2*b^2*d^2*e^2 + a*b^3*d^3*e + a^3*b*d*e^3))/e^5 + (5*b^4*x^4*(a^2*e^2 + b^2*d^2 + a*b*d*e))/e^3)/(d^7 + e^7*x^7 + 7*d*e^6*x^6 + 21*d^5*e^2*x^2 + 35*d^4*e^3*x^3 + 35*d^3*e^4*x^4 + 21*d^2*e^5*x^5 + 7*d^6*e*x)","B"
1498,1,410,58,0.135592,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^9,x)","-\frac{\frac{7\,a^6\,e^6+6\,a^5\,b\,d\,e^5+5\,a^4\,b^2\,d^2\,e^4+4\,a^3\,b^3\,d^3\,e^3+3\,a^2\,b^4\,d^4\,e^2+2\,a\,b^5\,d^5\,e+b^6\,d^6}{56\,e^7}+\frac{b^6\,x^6}{2\,e}+\frac{b^3\,x^3\,\left(4\,a^3\,e^3+3\,a^2\,b\,d\,e^2+2\,a\,b^2\,d^2\,e+b^3\,d^3\right)}{e^4}+\frac{b\,x\,\left(6\,a^5\,e^5+5\,a^4\,b\,d\,e^4+4\,a^3\,b^2\,d^2\,e^3+3\,a^2\,b^3\,d^3\,e^2+2\,a\,b^4\,d^4\,e+b^5\,d^5\right)}{7\,e^6}+\frac{b^5\,x^5\,\left(2\,a\,e+b\,d\right)}{e^2}+\frac{b^2\,x^2\,\left(5\,a^4\,e^4+4\,a^3\,b\,d\,e^3+3\,a^2\,b^2\,d^2\,e^2+2\,a\,b^3\,d^3\,e+b^4\,d^4\right)}{2\,e^5}+\frac{5\,b^4\,x^4\,\left(3\,a^2\,e^2+2\,a\,b\,d\,e+b^2\,d^2\right)}{4\,e^3}}{d^8+8\,d^7\,e\,x+28\,d^6\,e^2\,x^2+56\,d^5\,e^3\,x^3+70\,d^4\,e^4\,x^4+56\,d^3\,e^5\,x^5+28\,d^2\,e^6\,x^6+8\,d\,e^7\,x^7+e^8\,x^8}","Not used",1,"-((7*a^6*e^6 + b^6*d^6 + 3*a^2*b^4*d^4*e^2 + 4*a^3*b^3*d^3*e^3 + 5*a^4*b^2*d^2*e^4 + 2*a*b^5*d^5*e + 6*a^5*b*d*e^5)/(56*e^7) + (b^6*x^6)/(2*e) + (b^3*x^3*(4*a^3*e^3 + b^3*d^3 + 2*a*b^2*d^2*e + 3*a^2*b*d*e^2))/e^4 + (b*x*(6*a^5*e^5 + b^5*d^5 + 3*a^2*b^3*d^3*e^2 + 4*a^3*b^2*d^2*e^3 + 2*a*b^4*d^4*e + 5*a^4*b*d*e^4))/(7*e^6) + (b^5*x^5*(2*a*e + b*d))/e^2 + (b^2*x^2*(5*a^4*e^4 + b^4*d^4 + 3*a^2*b^2*d^2*e^2 + 2*a*b^3*d^3*e + 4*a^3*b*d*e^3))/(2*e^5) + (5*b^4*x^4*(3*a^2*e^2 + b^2*d^2 + 2*a*b*d*e))/(4*e^3))/(d^8 + e^8*x^8 + 8*d*e^7*x^7 + 28*d^6*e^2*x^2 + 56*d^5*e^3*x^3 + 70*d^4*e^4*x^4 + 56*d^3*e^5*x^5 + 28*d^2*e^6*x^6 + 8*d^7*e*x)","B"
1499,1,423,89,0.611969,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^10,x)","-\frac{\frac{28\,a^6\,e^6+21\,a^5\,b\,d\,e^5+15\,a^4\,b^2\,d^2\,e^4+10\,a^3\,b^3\,d^3\,e^3+6\,a^2\,b^4\,d^4\,e^2+3\,a\,b^5\,d^5\,e+b^6\,d^6}{252\,e^7}+\frac{b^6\,x^6}{3\,e}+\frac{b^3\,x^3\,\left(10\,a^3\,e^3+6\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e+b^3\,d^3\right)}{3\,e^4}+\frac{b\,x\,\left(21\,a^5\,e^5+15\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3+6\,a^2\,b^3\,d^3\,e^2+3\,a\,b^4\,d^4\,e+b^5\,d^5\right)}{28\,e^6}+\frac{b^5\,x^5\,\left(3\,a\,e+b\,d\right)}{2\,e^2}+\frac{b^2\,x^2\,\left(15\,a^4\,e^4+10\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2+3\,a\,b^3\,d^3\,e+b^4\,d^4\right)}{7\,e^5}+\frac{b^4\,x^4\,\left(6\,a^2\,e^2+3\,a\,b\,d\,e+b^2\,d^2\right)}{2\,e^3}}{d^9+9\,d^8\,e\,x+36\,d^7\,e^2\,x^2+84\,d^6\,e^3\,x^3+126\,d^5\,e^4\,x^4+126\,d^4\,e^5\,x^5+84\,d^3\,e^6\,x^6+36\,d^2\,e^7\,x^7+9\,d\,e^8\,x^8+e^9\,x^9}","Not used",1,"-((28*a^6*e^6 + b^6*d^6 + 6*a^2*b^4*d^4*e^2 + 10*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 + 3*a*b^5*d^5*e + 21*a^5*b*d*e^5)/(252*e^7) + (b^6*x^6)/(3*e) + (b^3*x^3*(10*a^3*e^3 + b^3*d^3 + 3*a*b^2*d^2*e + 6*a^2*b*d*e^2))/(3*e^4) + (b*x*(21*a^5*e^5 + b^5*d^5 + 6*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 3*a*b^4*d^4*e + 15*a^4*b*d*e^4))/(28*e^6) + (b^5*x^5*(3*a*e + b*d))/(2*e^2) + (b^2*x^2*(15*a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 + 3*a*b^3*d^3*e + 10*a^3*b*d*e^3))/(7*e^5) + (b^4*x^4*(6*a^2*e^2 + b^2*d^2 + 3*a*b*d*e))/(2*e^3))/(d^9 + e^9*x^9 + 9*d*e^8*x^8 + 36*d^7*e^2*x^2 + 84*d^6*e^3*x^3 + 126*d^5*e^4*x^4 + 126*d^4*e^5*x^5 + 84*d^3*e^6*x^6 + 36*d^2*e^7*x^7 + 9*d^8*e*x)","B"
1500,1,434,120,0.716512,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^11,x)","-\frac{\frac{84\,a^6\,e^6+56\,a^5\,b\,d\,e^5+35\,a^4\,b^2\,d^2\,e^4+20\,a^3\,b^3\,d^3\,e^3+10\,a^2\,b^4\,d^4\,e^2+4\,a\,b^5\,d^5\,e+b^6\,d^6}{840\,e^7}+\frac{b^6\,x^6}{4\,e}+\frac{b^3\,x^3\,\left(20\,a^3\,e^3+10\,a^2\,b\,d\,e^2+4\,a\,b^2\,d^2\,e+b^3\,d^3\right)}{7\,e^4}+\frac{b\,x\,\left(56\,a^5\,e^5+35\,a^4\,b\,d\,e^4+20\,a^3\,b^2\,d^2\,e^3+10\,a^2\,b^3\,d^3\,e^2+4\,a\,b^4\,d^4\,e+b^5\,d^5\right)}{84\,e^6}+\frac{3\,b^5\,x^5\,\left(4\,a\,e+b\,d\right)}{10\,e^2}+\frac{3\,b^2\,x^2\,\left(35\,a^4\,e^4+20\,a^3\,b\,d\,e^3+10\,a^2\,b^2\,d^2\,e^2+4\,a\,b^3\,d^3\,e+b^4\,d^4\right)}{56\,e^5}+\frac{b^4\,x^4\,\left(10\,a^2\,e^2+4\,a\,b\,d\,e+b^2\,d^2\right)}{4\,e^3}}{d^{10}+10\,d^9\,e\,x+45\,d^8\,e^2\,x^2+120\,d^7\,e^3\,x^3+210\,d^6\,e^4\,x^4+252\,d^5\,e^5\,x^5+210\,d^4\,e^6\,x^6+120\,d^3\,e^7\,x^7+45\,d^2\,e^8\,x^8+10\,d\,e^9\,x^9+e^{10}\,x^{10}}","Not used",1,"-((84*a^6*e^6 + b^6*d^6 + 10*a^2*b^4*d^4*e^2 + 20*a^3*b^3*d^3*e^3 + 35*a^4*b^2*d^2*e^4 + 4*a*b^5*d^5*e + 56*a^5*b*d*e^5)/(840*e^7) + (b^6*x^6)/(4*e) + (b^3*x^3*(20*a^3*e^3 + b^3*d^3 + 4*a*b^2*d^2*e + 10*a^2*b*d*e^2))/(7*e^4) + (b*x*(56*a^5*e^5 + b^5*d^5 + 10*a^2*b^3*d^3*e^2 + 20*a^3*b^2*d^2*e^3 + 4*a*b^4*d^4*e + 35*a^4*b*d*e^4))/(84*e^6) + (3*b^5*x^5*(4*a*e + b*d))/(10*e^2) + (3*b^2*x^2*(35*a^4*e^4 + b^4*d^4 + 10*a^2*b^2*d^2*e^2 + 4*a*b^3*d^3*e + 20*a^3*b*d*e^3))/(56*e^5) + (b^4*x^4*(10*a^2*e^2 + b^2*d^2 + 4*a*b*d*e))/(4*e^3))/(d^10 + e^10*x^10 + 10*d*e^9*x^9 + 45*d^8*e^2*x^2 + 120*d^7*e^3*x^3 + 210*d^6*e^4*x^4 + 252*d^5*e^5*x^5 + 210*d^4*e^6*x^6 + 120*d^3*e^7*x^7 + 45*d^2*e^8*x^8 + 10*d^9*e*x)","B"
1501,1,445,170,0.664236,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^12,x)","-\frac{\frac{210\,a^6\,e^6+126\,a^5\,b\,d\,e^5+70\,a^4\,b^2\,d^2\,e^4+35\,a^3\,b^3\,d^3\,e^3+15\,a^2\,b^4\,d^4\,e^2+5\,a\,b^5\,d^5\,e+b^6\,d^6}{2310\,e^7}+\frac{b^6\,x^6}{5\,e}+\frac{b^3\,x^3\,\left(35\,a^3\,e^3+15\,a^2\,b\,d\,e^2+5\,a\,b^2\,d^2\,e+b^3\,d^3\right)}{14\,e^4}+\frac{b\,x\,\left(126\,a^5\,e^5+70\,a^4\,b\,d\,e^4+35\,a^3\,b^2\,d^2\,e^3+15\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e+b^5\,d^5\right)}{210\,e^6}+\frac{b^5\,x^5\,\left(5\,a\,e+b\,d\right)}{5\,e^2}+\frac{b^2\,x^2\,\left(70\,a^4\,e^4+35\,a^3\,b\,d\,e^3+15\,a^2\,b^2\,d^2\,e^2+5\,a\,b^3\,d^3\,e+b^4\,d^4\right)}{42\,e^5}+\frac{b^4\,x^4\,\left(15\,a^2\,e^2+5\,a\,b\,d\,e+b^2\,d^2\right)}{7\,e^3}}{d^{11}+11\,d^{10}\,e\,x+55\,d^9\,e^2\,x^2+165\,d^8\,e^3\,x^3+330\,d^7\,e^4\,x^4+462\,d^6\,e^5\,x^5+462\,d^5\,e^6\,x^6+330\,d^4\,e^7\,x^7+165\,d^3\,e^8\,x^8+55\,d^2\,e^9\,x^9+11\,d\,e^{10}\,x^{10}+e^{11}\,x^{11}}","Not used",1,"-((210*a^6*e^6 + b^6*d^6 + 15*a^2*b^4*d^4*e^2 + 35*a^3*b^3*d^3*e^3 + 70*a^4*b^2*d^2*e^4 + 5*a*b^5*d^5*e + 126*a^5*b*d*e^5)/(2310*e^7) + (b^6*x^6)/(5*e) + (b^3*x^3*(35*a^3*e^3 + b^3*d^3 + 5*a*b^2*d^2*e + 15*a^2*b*d*e^2))/(14*e^4) + (b*x*(126*a^5*e^5 + b^5*d^5 + 15*a^2*b^3*d^3*e^2 + 35*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e + 70*a^4*b*d*e^4))/(210*e^6) + (b^5*x^5*(5*a*e + b*d))/(5*e^2) + (b^2*x^2*(70*a^4*e^4 + b^4*d^4 + 15*a^2*b^2*d^2*e^2 + 5*a*b^3*d^3*e + 35*a^3*b*d*e^3))/(42*e^5) + (b^4*x^4*(15*a^2*e^2 + b^2*d^2 + 5*a*b*d*e))/(7*e^3))/(d^11 + e^11*x^11 + 11*d*e^10*x^10 + 55*d^9*e^2*x^2 + 165*d^8*e^3*x^3 + 330*d^7*e^4*x^4 + 462*d^6*e^5*x^5 + 462*d^5*e^6*x^6 + 330*d^4*e^7*x^7 + 165*d^3*e^8*x^8 + 55*d^2*e^9*x^9 + 11*d^10*e*x)","B"
1502,1,456,173,0.958609,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^13,x)","-\frac{\frac{462\,a^6\,e^6+252\,a^5\,b\,d\,e^5+126\,a^4\,b^2\,d^2\,e^4+56\,a^3\,b^3\,d^3\,e^3+21\,a^2\,b^4\,d^4\,e^2+6\,a\,b^5\,d^5\,e+b^6\,d^6}{5544\,e^7}+\frac{b^6\,x^6}{6\,e}+\frac{5\,b^3\,x^3\,\left(56\,a^3\,e^3+21\,a^2\,b\,d\,e^2+6\,a\,b^2\,d^2\,e+b^3\,d^3\right)}{126\,e^4}+\frac{b\,x\,\left(252\,a^5\,e^5+126\,a^4\,b\,d\,e^4+56\,a^3\,b^2\,d^2\,e^3+21\,a^2\,b^3\,d^3\,e^2+6\,a\,b^4\,d^4\,e+b^5\,d^5\right)}{462\,e^6}+\frac{b^5\,x^5\,\left(6\,a\,e+b\,d\right)}{7\,e^2}+\frac{b^2\,x^2\,\left(126\,a^4\,e^4+56\,a^3\,b\,d\,e^3+21\,a^2\,b^2\,d^2\,e^2+6\,a\,b^3\,d^3\,e+b^4\,d^4\right)}{84\,e^5}+\frac{5\,b^4\,x^4\,\left(21\,a^2\,e^2+6\,a\,b\,d\,e+b^2\,d^2\right)}{56\,e^3}}{d^{12}+12\,d^{11}\,e\,x+66\,d^{10}\,e^2\,x^2+220\,d^9\,e^3\,x^3+495\,d^8\,e^4\,x^4+792\,d^7\,e^5\,x^5+924\,d^6\,e^6\,x^6+792\,d^5\,e^7\,x^7+495\,d^4\,e^8\,x^8+220\,d^3\,e^9\,x^9+66\,d^2\,e^{10}\,x^{10}+12\,d\,e^{11}\,x^{11}+e^{12}\,x^{12}}","Not used",1,"-((462*a^6*e^6 + b^6*d^6 + 21*a^2*b^4*d^4*e^2 + 56*a^3*b^3*d^3*e^3 + 126*a^4*b^2*d^2*e^4 + 6*a*b^5*d^5*e + 252*a^5*b*d*e^5)/(5544*e^7) + (b^6*x^6)/(6*e) + (5*b^3*x^3*(56*a^3*e^3 + b^3*d^3 + 6*a*b^2*d^2*e + 21*a^2*b*d*e^2))/(126*e^4) + (b*x*(252*a^5*e^5 + b^5*d^5 + 21*a^2*b^3*d^3*e^2 + 56*a^3*b^2*d^2*e^3 + 6*a*b^4*d^4*e + 126*a^4*b*d*e^4))/(462*e^6) + (b^5*x^5*(6*a*e + b*d))/(7*e^2) + (b^2*x^2*(126*a^4*e^4 + b^4*d^4 + 21*a^2*b^2*d^2*e^2 + 6*a*b^3*d^3*e + 56*a^3*b*d*e^3))/(84*e^5) + (5*b^4*x^4*(21*a^2*e^2 + b^2*d^2 + 6*a*b*d*e))/(56*e^3))/(d^12 + e^12*x^12 + 12*d*e^11*x^11 + 66*d^10*e^2*x^2 + 220*d^9*e^3*x^3 + 495*d^8*e^4*x^4 + 792*d^7*e^5*x^5 + 924*d^6*e^6*x^6 + 792*d^5*e^7*x^7 + 495*d^4*e^8*x^8 + 220*d^3*e^9*x^9 + 66*d^2*e^10*x^10 + 12*d^11*e*x)","B"
1503,1,467,171,1.173337,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^14,x)","-\frac{\frac{924\,a^6\,e^6+462\,a^5\,b\,d\,e^5+210\,a^4\,b^2\,d^2\,e^4+84\,a^3\,b^3\,d^3\,e^3+28\,a^2\,b^4\,d^4\,e^2+7\,a\,b^5\,d^5\,e+b^6\,d^6}{12012\,e^7}+\frac{b^6\,x^6}{7\,e}+\frac{b^3\,x^3\,\left(84\,a^3\,e^3+28\,a^2\,b\,d\,e^2+7\,a\,b^2\,d^2\,e+b^3\,d^3\right)}{42\,e^4}+\frac{b\,x\,\left(462\,a^5\,e^5+210\,a^4\,b\,d\,e^4+84\,a^3\,b^2\,d^2\,e^3+28\,a^2\,b^3\,d^3\,e^2+7\,a\,b^4\,d^4\,e+b^5\,d^5\right)}{924\,e^6}+\frac{3\,b^5\,x^5\,\left(7\,a\,e+b\,d\right)}{28\,e^2}+\frac{b^2\,x^2\,\left(210\,a^4\,e^4+84\,a^3\,b\,d\,e^3+28\,a^2\,b^2\,d^2\,e^2+7\,a\,b^3\,d^3\,e+b^4\,d^4\right)}{154\,e^5}+\frac{5\,b^4\,x^4\,\left(28\,a^2\,e^2+7\,a\,b\,d\,e+b^2\,d^2\right)}{84\,e^3}}{d^{13}+13\,d^{12}\,e\,x+78\,d^{11}\,e^2\,x^2+286\,d^{10}\,e^3\,x^3+715\,d^9\,e^4\,x^4+1287\,d^8\,e^5\,x^5+1716\,d^7\,e^6\,x^6+1716\,d^6\,e^7\,x^7+1287\,d^5\,e^8\,x^8+715\,d^4\,e^9\,x^9+286\,d^3\,e^{10}\,x^{10}+78\,d^2\,e^{11}\,x^{11}+13\,d\,e^{12}\,x^{12}+e^{13}\,x^{13}}","Not used",1,"-((924*a^6*e^6 + b^6*d^6 + 28*a^2*b^4*d^4*e^2 + 84*a^3*b^3*d^3*e^3 + 210*a^4*b^2*d^2*e^4 + 7*a*b^5*d^5*e + 462*a^5*b*d*e^5)/(12012*e^7) + (b^6*x^6)/(7*e) + (b^3*x^3*(84*a^3*e^3 + b^3*d^3 + 7*a*b^2*d^2*e + 28*a^2*b*d*e^2))/(42*e^4) + (b*x*(462*a^5*e^5 + b^5*d^5 + 28*a^2*b^3*d^3*e^2 + 84*a^3*b^2*d^2*e^3 + 7*a*b^4*d^4*e + 210*a^4*b*d*e^4))/(924*e^6) + (3*b^5*x^5*(7*a*e + b*d))/(28*e^2) + (b^2*x^2*(210*a^4*e^4 + b^4*d^4 + 28*a^2*b^2*d^2*e^2 + 7*a*b^3*d^3*e + 84*a^3*b*d*e^3))/(154*e^5) + (5*b^4*x^4*(28*a^2*e^2 + b^2*d^2 + 7*a*b*d*e))/(84*e^3))/(d^13 + e^13*x^13 + 13*d*e^12*x^12 + 78*d^11*e^2*x^2 + 286*d^10*e^3*x^3 + 715*d^9*e^4*x^4 + 1287*d^8*e^5*x^5 + 1716*d^7*e^6*x^6 + 1716*d^6*e^7*x^7 + 1287*d^5*e^8*x^8 + 715*d^4*e^9*x^9 + 286*d^3*e^10*x^10 + 78*d^2*e^11*x^11 + 13*d^12*e*x)","B"
1504,1,478,173,1.586735,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^15,x)","-\frac{\frac{1716\,a^6\,e^6+792\,a^5\,b\,d\,e^5+330\,a^4\,b^2\,d^2\,e^4+120\,a^3\,b^3\,d^3\,e^3+36\,a^2\,b^4\,d^4\,e^2+8\,a\,b^5\,d^5\,e+b^6\,d^6}{24024\,e^7}+\frac{b^6\,x^6}{8\,e}+\frac{b^3\,x^3\,\left(120\,a^3\,e^3+36\,a^2\,b\,d\,e^2+8\,a\,b^2\,d^2\,e+b^3\,d^3\right)}{66\,e^4}+\frac{b\,x\,\left(792\,a^5\,e^5+330\,a^4\,b\,d\,e^4+120\,a^3\,b^2\,d^2\,e^3+36\,a^2\,b^3\,d^3\,e^2+8\,a\,b^4\,d^4\,e+b^5\,d^5\right)}{1716\,e^6}+\frac{b^5\,x^5\,\left(8\,a\,e+b\,d\right)}{12\,e^2}+\frac{b^2\,x^2\,\left(330\,a^4\,e^4+120\,a^3\,b\,d\,e^3+36\,a^2\,b^2\,d^2\,e^2+8\,a\,b^3\,d^3\,e+b^4\,d^4\right)}{264\,e^5}+\frac{b^4\,x^4\,\left(36\,a^2\,e^2+8\,a\,b\,d\,e+b^2\,d^2\right)}{24\,e^3}}{d^{14}+14\,d^{13}\,e\,x+91\,d^{12}\,e^2\,x^2+364\,d^{11}\,e^3\,x^3+1001\,d^{10}\,e^4\,x^4+2002\,d^9\,e^5\,x^5+3003\,d^8\,e^6\,x^6+3432\,d^7\,e^7\,x^7+3003\,d^6\,e^8\,x^8+2002\,d^5\,e^9\,x^9+1001\,d^4\,e^{10}\,x^{10}+364\,d^3\,e^{11}\,x^{11}+91\,d^2\,e^{12}\,x^{12}+14\,d\,e^{13}\,x^{13}+e^{14}\,x^{14}}","Not used",1,"-((1716*a^6*e^6 + b^6*d^6 + 36*a^2*b^4*d^4*e^2 + 120*a^3*b^3*d^3*e^3 + 330*a^4*b^2*d^2*e^4 + 8*a*b^5*d^5*e + 792*a^5*b*d*e^5)/(24024*e^7) + (b^6*x^6)/(8*e) + (b^3*x^3*(120*a^3*e^3 + b^3*d^3 + 8*a*b^2*d^2*e + 36*a^2*b*d*e^2))/(66*e^4) + (b*x*(792*a^5*e^5 + b^5*d^5 + 36*a^2*b^3*d^3*e^2 + 120*a^3*b^2*d^2*e^3 + 8*a*b^4*d^4*e + 330*a^4*b*d*e^4))/(1716*e^6) + (b^5*x^5*(8*a*e + b*d))/(12*e^2) + (b^2*x^2*(330*a^4*e^4 + b^4*d^4 + 36*a^2*b^2*d^2*e^2 + 8*a*b^3*d^3*e + 120*a^3*b*d*e^3))/(264*e^5) + (b^4*x^4*(36*a^2*e^2 + b^2*d^2 + 8*a*b*d*e))/(24*e^3))/(d^14 + e^14*x^14 + 14*d*e^13*x^13 + 91*d^12*e^2*x^2 + 364*d^11*e^3*x^3 + 1001*d^10*e^4*x^4 + 2002*d^9*e^5*x^5 + 3003*d^8*e^6*x^6 + 3432*d^7*e^7*x^7 + 3003*d^6*e^8*x^8 + 2002*d^5*e^9*x^9 + 1001*d^4*e^10*x^10 + 364*d^3*e^11*x^11 + 91*d^2*e^12*x^12 + 14*d^13*e*x)","B"
1505,1,326,131,0.552937,"\text{Not used}","int((d + e*x)^5/(a^2 + b^2*x^2 + 2*a*b*x),x)","x\,\left(\frac{10\,d^3\,e^2}{b^2}-\frac{2\,a\,\left(\frac{2\,a\,\left(\frac{2\,a\,e^5}{b^3}-\frac{5\,d\,e^4}{b^2}\right)}{b}-\frac{a^2\,e^5}{b^4}+\frac{10\,d^2\,e^3}{b^2}\right)}{b}+\frac{a^2\,\left(\frac{2\,a\,e^5}{b^3}-\frac{5\,d\,e^4}{b^2}\right)}{b^2}\right)-x^3\,\left(\frac{2\,a\,e^5}{3\,b^3}-\frac{5\,d\,e^4}{3\,b^2}\right)+x^2\,\left(\frac{a\,\left(\frac{2\,a\,e^5}{b^3}-\frac{5\,d\,e^4}{b^2}\right)}{b}-\frac{a^2\,e^5}{2\,b^4}+\frac{5\,d^2\,e^3}{b^2}\right)+\frac{\ln\left(a+b\,x\right)\,\left(5\,a^4\,e^5-20\,a^3\,b\,d\,e^4+30\,a^2\,b^2\,d^2\,e^3-20\,a\,b^3\,d^3\,e^2+5\,b^4\,d^4\,e\right)}{b^6}+\frac{a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5}{b\,\left(x\,b^6+a\,b^5\right)}+\frac{e^5\,x^4}{4\,b^2}","Not used",1,"x*((10*d^3*e^2)/b^2 - (2*a*((2*a*((2*a*e^5)/b^3 - (5*d*e^4)/b^2))/b - (a^2*e^5)/b^4 + (10*d^2*e^3)/b^2))/b + (a^2*((2*a*e^5)/b^3 - (5*d*e^4)/b^2))/b^2) - x^3*((2*a*e^5)/(3*b^3) - (5*d*e^4)/(3*b^2)) + x^2*((a*((2*a*e^5)/b^3 - (5*d*e^4)/b^2))/b - (a^2*e^5)/(2*b^4) + (5*d^2*e^3)/b^2) + (log(a + b*x)*(5*a^4*e^5 + 5*b^4*d^4*e - 20*a*b^3*d^3*e^2 + 30*a^2*b^2*d^2*e^3 - 20*a^3*b*d*e^4))/b^6 + (a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4)/(b*(a*b^5 + b^6*x)) + (e^5*x^4)/(4*b^2)","B"
1506,1,203,104,0.538117,"\text{Not used}","int((d + e*x)^4/(a^2 + b^2*x^2 + 2*a*b*x),x)","x\,\left(\frac{2\,a\,\left(\frac{2\,a\,e^4}{b^3}-\frac{4\,d\,e^3}{b^2}\right)}{b}-\frac{a^2\,e^4}{b^4}+\frac{6\,d^2\,e^2}{b^2}\right)-x^2\,\left(\frac{a\,e^4}{b^3}-\frac{2\,d\,e^3}{b^2}\right)+\frac{e^4\,x^3}{3\,b^2}-\frac{\ln\left(a+b\,x\right)\,\left(4\,a^3\,e^4-12\,a^2\,b\,d\,e^3+12\,a\,b^2\,d^2\,e^2-4\,b^3\,d^3\,e\right)}{b^5}-\frac{a^4\,e^4-4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-4\,a\,b^3\,d^3\,e+b^4\,d^4}{b\,\left(x\,b^5+a\,b^4\right)}","Not used",1,"x*((2*a*((2*a*e^4)/b^3 - (4*d*e^3)/b^2))/b - (a^2*e^4)/b^4 + (6*d^2*e^2)/b^2) - x^2*((a*e^4)/b^3 - (2*d*e^3)/b^2) + (e^4*x^3)/(3*b^2) - (log(a + b*x)*(4*a^3*e^4 - 4*b^3*d^3*e + 12*a*b^2*d^2*e^2 - 12*a^2*b*d*e^3))/b^5 - (a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 4*a*b^3*d^3*e - 4*a^3*b*d*e^3)/(b*(a*b^4 + b^5*x))","B"
1507,1,123,75,0.072843,"\text{Not used}","int((d + e*x)^3/(a^2 + b^2*x^2 + 2*a*b*x),x)","\frac{\ln\left(a+b\,x\right)\,\left(3\,a^2\,e^3-6\,a\,b\,d\,e^2+3\,b^2\,d^2\,e\right)}{b^4}-x\,\left(\frac{2\,a\,e^3}{b^3}-\frac{3\,d\,e^2}{b^2}\right)+\frac{a^3\,e^3-3\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e-b^3\,d^3}{b\,\left(x\,b^4+a\,b^3\right)}+\frac{e^3\,x^2}{2\,b^2}","Not used",1,"(log(a + b*x)*(3*a^2*e^3 + 3*b^2*d^2*e - 6*a*b*d*e^2))/b^4 - x*((2*a*e^3)/b^3 - (3*d*e^2)/b^2) + (a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2)/(b*(a*b^3 + b^4*x)) + (e^3*x^2)/(2*b^2)","B"
1508,1,71,51,0.082299,"\text{Not used}","int((d + e*x)^2/(a^2 + b^2*x^2 + 2*a*b*x),x)","\frac{e^2\,x}{b^2}-\frac{a^2\,e^2-2\,a\,b\,d\,e+b^2\,d^2}{b\,\left(x\,b^3+a\,b^2\right)}-\frac{\ln\left(a+b\,x\right)\,\left(2\,a\,e^2-2\,b\,d\,e\right)}{b^3}","Not used",1,"(e^2*x)/b^2 - (a^2*e^2 + b^2*d^2 - 2*a*b*d*e)/(b*(a*b^2 + b^3*x)) - (log(a + b*x)*(2*a*e^2 - 2*b*d*e))/b^3","B"
1509,1,31,32,0.504147,"\text{Not used}","int((d + e*x)/(a^2 + b^2*x^2 + 2*a*b*x),x)","\frac{a\,e-b\,d}{b^2\,\left(a+b\,x\right)}+\frac{e\,\ln\left(a+b\,x\right)}{b^2}","Not used",1,"(a*e - b*d)/(b^2*(a + b*x)) + (e*log(a + b*x))/b^2","B"
1510,1,12,12,0.025430,"\text{Not used}","int(1/(a^2 + b^2*x^2 + 2*a*b*x),x)","-\frac{1}{b\,\left(a+b\,x\right)}","Not used",1,"-1/(b*(a + b*x))","B"
1511,1,76,57,0.580945,"\text{Not used}","int(1/((d + e*x)*(a^2 + b^2*x^2 + 2*a*b*x)),x)","\frac{1}{\left(a\,e-b\,d\right)\,\left(a+b\,x\right)}-\frac{2\,e\,\mathrm{atanh}\left(\frac{a^2\,e^2-b^2\,d^2}{{\left(a\,e-b\,d\right)}^2}+\frac{2\,b\,e\,x}{a\,e-b\,d}\right)}{{\left(a\,e-b\,d\right)}^2}","Not used",1,"1/((a*e - b*d)*(a + b*x)) - (2*e*atanh((a^2*e^2 - b^2*d^2)/(a*e - b*d)^2 + (2*b*e*x)/(a*e - b*d)))/(a*e - b*d)^2","B"
1512,1,182,81,0.614888,"\text{Not used}","int(1/((d + e*x)^2*(a^2 + b^2*x^2 + 2*a*b*x)),x)","\frac{4\,b\,e\,\mathrm{atanh}\left(\frac{a^3\,e^3-a^2\,b\,d\,e^2-a\,b^2\,d^2\,e+b^3\,d^3}{{\left(a\,e-b\,d\right)}^3}+\frac{2\,b\,e\,x\,\left(a^2\,e^2-2\,a\,b\,d\,e+b^2\,d^2\right)}{{\left(a\,e-b\,d\right)}^3}\right)}{{\left(a\,e-b\,d\right)}^3}-\frac{\frac{a\,e+b\,d}{a^2\,e^2-2\,a\,b\,d\,e+b^2\,d^2}+\frac{2\,b\,e\,x}{a^2\,e^2-2\,a\,b\,d\,e+b^2\,d^2}}{b\,e\,x^2+\left(a\,e+b\,d\right)\,x+a\,d}","Not used",1,"(4*b*e*atanh((a^3*e^3 + b^3*d^3 - a*b^2*d^2*e - a^2*b*d*e^2)/(a*e - b*d)^3 + (2*b*e*x*(a^2*e^2 + b^2*d^2 - 2*a*b*d*e))/(a*e - b*d)^3))/(a*e - b*d)^3 - ((a*e + b*d)/(a^2*e^2 + b^2*d^2 - 2*a*b*d*e) + (2*b*e*x)/(a^2*e^2 + b^2*d^2 - 2*a*b*d*e))/(a*d + x*(a*e + b*d) + b*e*x^2)","B"
1513,1,329,110,0.692144,"\text{Not used}","int(1/((d + e*x)^3*(a^2 + b^2*x^2 + 2*a*b*x)),x)","\frac{\frac{-a^2\,e^2+5\,a\,b\,d\,e+2\,b^2\,d^2}{2\,\left(a^3\,e^3-3\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e-b^3\,d^3\right)}+\frac{3\,b\,x\,\left(a\,e^2+3\,b\,d\,e\right)}{2\,\left(a^3\,e^3-3\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e-b^3\,d^3\right)}+\frac{3\,b^2\,e^2\,x^2}{a^3\,e^3-3\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e-b^3\,d^3}}{x\,\left(b\,d^2+2\,a\,e\,d\right)+a\,d^2+x^2\,\left(a\,e^2+2\,b\,d\,e\right)+b\,e^2\,x^3}-\frac{6\,b^2\,e\,\mathrm{atanh}\left(\frac{a^4\,e^4-2\,a^3\,b\,d\,e^3+2\,a\,b^3\,d^3\,e-b^4\,d^4}{{\left(a\,e-b\,d\right)}^4}+\frac{2\,b\,e\,x\,\left(a^3\,e^3-3\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e-b^3\,d^3\right)}{{\left(a\,e-b\,d\right)}^4}\right)}{{\left(a\,e-b\,d\right)}^4}","Not used",1,"((2*b^2*d^2 - a^2*e^2 + 5*a*b*d*e)/(2*(a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2)) + (3*b*x*(a*e^2 + 3*b*d*e))/(2*(a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2)) + (3*b^2*e^2*x^2)/(a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2))/(x*(b*d^2 + 2*a*d*e) + a*d^2 + x^2*(a*e^2 + 2*b*d*e) + b*e^2*x^3) - (6*b^2*e*atanh((a^4*e^4 - b^4*d^4 + 2*a*b^3*d^3*e - 2*a^3*b*d*e^3)/(a*e - b*d)^4 + (2*b*e*x*(a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2))/(a*e - b*d)^4))/(a*e - b*d)^4","B"
1514,1,534,133,0.854783,"\text{Not used}","int(1/((d + e*x)^4*(a^2 + b^2*x^2 + 2*a*b*x)),x)","\frac{8\,b^3\,e\,\mathrm{atanh}\left(\frac{a^5\,e^5-3\,a^4\,b\,d\,e^4+2\,a^3\,b^2\,d^2\,e^3+2\,a^2\,b^3\,d^3\,e^2-3\,a\,b^4\,d^4\,e+b^5\,d^5}{{\left(a\,e-b\,d\right)}^5}+\frac{2\,b\,e\,x\,\left(a^4\,e^4-4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-4\,a\,b^3\,d^3\,e+b^4\,d^4\right)}{{\left(a\,e-b\,d\right)}^5}\right)}{{\left(a\,e-b\,d\right)}^5}-\frac{\frac{a^3\,e^3-5\,a^2\,b\,d\,e^2+13\,a\,b^2\,d^2\,e+3\,b^3\,d^3}{3\,\left(a^4\,e^4-4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-4\,a\,b^3\,d^3\,e+b^4\,d^4\right)}+\frac{4\,b^3\,e^3\,x^3}{a^4\,e^4-4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-4\,a\,b^3\,d^3\,e+b^4\,d^4}+\frac{2\,b^2\,x^2\,\left(a\,e^3+5\,b\,d\,e^2\right)}{a^4\,e^4-4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-4\,a\,b^3\,d^3\,e+b^4\,d^4}+\frac{2\,b\,x\,\left(-a^2\,e^3+8\,a\,b\,d\,e^2+11\,b^2\,d^2\,e\right)}{3\,\left(a^4\,e^4-4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-4\,a\,b^3\,d^3\,e+b^4\,d^4\right)}}{x^3\,\left(a\,e^3+3\,b\,d\,e^2\right)+x^2\,\left(3\,b\,d^2\,e+3\,a\,d\,e^2\right)+a\,d^3+x\,\left(b\,d^3+3\,a\,e\,d^2\right)+b\,e^3\,x^4}","Not used",1,"(8*b^3*e*atanh((a^5*e^5 + b^5*d^5 + 2*a^2*b^3*d^3*e^2 + 2*a^3*b^2*d^2*e^3 - 3*a*b^4*d^4*e - 3*a^4*b*d*e^4)/(a*e - b*d)^5 + (2*b*e*x*(a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 4*a*b^3*d^3*e - 4*a^3*b*d*e^3))/(a*e - b*d)^5))/(a*e - b*d)^5 - ((a^3*e^3 + 3*b^3*d^3 + 13*a*b^2*d^2*e - 5*a^2*b*d*e^2)/(3*(a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 4*a*b^3*d^3*e - 4*a^3*b*d*e^3)) + (4*b^3*e^3*x^3)/(a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 4*a*b^3*d^3*e - 4*a^3*b*d*e^3) + (2*b^2*x^2*(a*e^3 + 5*b*d*e^2))/(a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 4*a*b^3*d^3*e - 4*a^3*b*d*e^3) + (2*b*x*(11*b^2*d^2*e - a^2*e^3 + 8*a*b*d*e^2))/(3*(a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 4*a*b^3*d^3*e - 4*a^3*b*d*e^3)))/(x^3*(a*e^3 + 3*b*d*e^2) + x^2*(3*a*d*e^2 + 3*b*d^2*e) + a*d^3 + x*(b*d^3 + 3*a*d^2*e) + b*e^3*x^4)","B"
1515,1,393,156,0.128241,"\text{Not used}","int((d + e*x)^6/(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","x\,\left(\frac{4\,a\,\left(\frac{4\,a\,e^6}{b^5}-\frac{6\,d\,e^5}{b^4}\right)}{b}-\frac{6\,a^2\,e^6}{b^6}+\frac{15\,d^2\,e^4}{b^4}\right)-\frac{x^2\,\left(15\,a^4\,b\,e^6-60\,a^3\,b^2\,d\,e^5+90\,a^2\,b^3\,d^2\,e^4-60\,a\,b^4\,d^3\,e^3+15\,b^5\,d^4\,e^2\right)+\frac{37\,a^6\,e^6-141\,a^5\,b\,d\,e^5+195\,a^4\,b^2\,d^2\,e^4-110\,a^3\,b^3\,d^3\,e^3+15\,a^2\,b^4\,d^4\,e^2+3\,a\,b^5\,d^5\,e+b^6\,d^6}{3\,b}+x\,\left(27\,a^5\,e^6-105\,a^4\,b\,d\,e^5+150\,a^3\,b^2\,d^2\,e^4-90\,a^2\,b^3\,d^3\,e^3+15\,a\,b^4\,d^4\,e^2+3\,b^5\,d^5\,e\right)}{a^3\,b^6+3\,a^2\,b^7\,x+3\,a\,b^8\,x^2+b^9\,x^3}-x^2\,\left(\frac{2\,a\,e^6}{b^5}-\frac{3\,d\,e^5}{b^4}\right)-\frac{\ln\left(a+b\,x\right)\,\left(20\,a^3\,e^6-60\,a^2\,b\,d\,e^5+60\,a\,b^2\,d^2\,e^4-20\,b^3\,d^3\,e^3\right)}{b^7}+\frac{e^6\,x^3}{3\,b^4}","Not used",1,"x*((4*a*((4*a*e^6)/b^5 - (6*d*e^5)/b^4))/b - (6*a^2*e^6)/b^6 + (15*d^2*e^4)/b^4) - (x^2*(15*a^4*b*e^6 + 15*b^5*d^4*e^2 - 60*a*b^4*d^3*e^3 - 60*a^3*b^2*d*e^5 + 90*a^2*b^3*d^2*e^4) + (37*a^6*e^6 + b^6*d^6 + 15*a^2*b^4*d^4*e^2 - 110*a^3*b^3*d^3*e^3 + 195*a^4*b^2*d^2*e^4 + 3*a*b^5*d^5*e - 141*a^5*b*d*e^5)/(3*b) + x*(27*a^5*e^6 + 3*b^5*d^5*e + 15*a*b^4*d^4*e^2 - 90*a^2*b^3*d^3*e^3 + 150*a^3*b^2*d^2*e^4 - 105*a^4*b*d*e^5))/(a^3*b^6 + b^9*x^3 + 3*a^2*b^7*x + 3*a*b^8*x^2) - x^2*((2*a*e^6)/b^5 - (3*d*e^5)/b^4) - (log(a + b*x)*(20*a^3*e^6 - 20*b^3*d^3*e^3 + 60*a*b^2*d^2*e^4 - 60*a^2*b*d*e^5))/b^7 + (e^6*x^3)/(3*b^4)","B"
1516,1,286,129,0.655536,"\text{Not used}","int((d + e*x)^5/(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","\frac{e^5\,x^2}{2\,b^4}-x\,\left(\frac{4\,a\,e^5}{b^5}-\frac{5\,d\,e^4}{b^4}\right)-\frac{\frac{-47\,a^5\,e^5+130\,a^4\,b\,d\,e^4-110\,a^3\,b^2\,d^2\,e^3+20\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e+2\,b^5\,d^5}{6\,b}+x\,\left(-\frac{35\,a^4\,e^5}{2}+50\,a^3\,b\,d\,e^4-45\,a^2\,b^2\,d^2\,e^3+10\,a\,b^3\,d^3\,e^2+\frac{5\,b^4\,d^4\,e}{2}\right)-x^2\,\left(10\,a^3\,b\,e^5-30\,a^2\,b^2\,d\,e^4+30\,a\,b^3\,d^2\,e^3-10\,b^4\,d^3\,e^2\right)}{a^3\,b^5+3\,a^2\,b^6\,x+3\,a\,b^7\,x^2+b^8\,x^3}+\frac{\ln\left(a+b\,x\right)\,\left(10\,a^2\,e^5-20\,a\,b\,d\,e^4+10\,b^2\,d^2\,e^3\right)}{b^6}","Not used",1,"(e^5*x^2)/(2*b^4) - x*((4*a*e^5)/b^5 - (5*d*e^4)/b^4) - ((2*b^5*d^5 - 47*a^5*e^5 + 20*a^2*b^3*d^3*e^2 - 110*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e + 130*a^4*b*d*e^4)/(6*b) + x*((5*b^4*d^4*e)/2 - (35*a^4*e^5)/2 + 10*a*b^3*d^3*e^2 - 45*a^2*b^2*d^2*e^3 + 50*a^3*b*d*e^4) - x^2*(10*a^3*b*e^5 - 10*b^4*d^3*e^2 + 30*a*b^3*d^2*e^3 - 30*a^2*b^2*d*e^4))/(a^3*b^5 + b^8*x^3 + 3*a^2*b^6*x + 3*a*b^7*x^2) + (log(a + b*x)*(10*a^2*e^5 + 10*b^2*d^2*e^3 - 20*a*b*d*e^4))/b^6","B"
1517,1,204,103,0.661077,"\text{Not used}","int((d + e*x)^4/(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","\frac{e^4\,x}{b^4}-\frac{\ln\left(a+b\,x\right)\,\left(4\,a\,e^4-4\,b\,d\,e^3\right)}{b^5}-\frac{\frac{13\,a^4\,e^4-22\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2+2\,a\,b^3\,d^3\,e+b^4\,d^4}{3\,b}+x\,\left(10\,a^3\,e^4-18\,a^2\,b\,d\,e^3+6\,a\,b^2\,d^2\,e^2+2\,b^3\,d^3\,e\right)+x^2\,\left(6\,a^2\,b\,e^4-12\,a\,b^2\,d\,e^3+6\,b^3\,d^2\,e^2\right)}{a^3\,b^4+3\,a^2\,b^5\,x+3\,a\,b^6\,x^2+b^7\,x^3}","Not used",1,"(e^4*x)/b^4 - (log(a + b*x)*(4*a*e^4 - 4*b*d*e^3))/b^5 - ((13*a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 + 2*a*b^3*d^3*e - 22*a^3*b*d*e^3)/(3*b) + x*(10*a^3*e^4 + 2*b^3*d^3*e + 6*a*b^2*d^2*e^2 - 18*a^2*b*d*e^3) + x^2*(6*a^2*b*e^4 + 6*b^3*d^2*e^2 - 12*a*b^2*d*e^3))/(a^3*b^4 + b^7*x^3 + 3*a^2*b^5*x + 3*a*b^6*x^2)","B"
1518,1,138,86,0.567133,"\text{Not used}","int((d + e*x)^3/(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","\frac{e^3\,\ln\left(a+b\,x\right)}{b^4}-\frac{\frac{-11\,a^3\,e^3+6\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e+2\,b^3\,d^3}{6\,b^4}+\frac{3\,x\,\left(-3\,a^2\,e^3+2\,a\,b\,d\,e^2+b^2\,d^2\,e\right)}{2\,b^3}-\frac{3\,e^2\,x^2\,\left(a\,e-b\,d\right)}{b^2}}{a^3+3\,a^2\,b\,x+3\,a\,b^2\,x^2+b^3\,x^3}","Not used",1,"(e^3*log(a + b*x))/b^4 - ((2*b^3*d^3 - 11*a^3*e^3 + 3*a*b^2*d^2*e + 6*a^2*b*d*e^2)/(6*b^4) + (3*x*(b^2*d^2*e - 3*a^2*e^3 + 2*a*b*d*e^2))/(2*b^3) - (3*e^2*x^2*(a*e - b*d))/b^2)/(a^3 + b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x)","B"
1519,1,80,28,0.043715,"\text{Not used}","int((d + e*x)^2/(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","-\frac{\frac{a^2\,e^2+a\,b\,d\,e+b^2\,d^2}{3\,b^3}+\frac{e^2\,x^2}{b}+\frac{e\,x\,\left(a\,e+b\,d\right)}{b^2}}{a^3+3\,a^2\,b\,x+3\,a\,b^2\,x^2+b^3\,x^3}","Not used",1,"-((a^2*e^2 + b^2*d^2 + a*b*d*e)/(3*b^3) + (e^2*x^2)/b + (e*x*(a*e + b*d))/b^2)/(a^3 + b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x)","B"
1520,1,52,38,0.032842,"\text{Not used}","int((d + e*x)/(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","-\frac{\frac{a\,e+2\,b\,d}{6\,b^2}+\frac{e\,x}{2\,b}}{a^3+3\,a^2\,b\,x+3\,a\,b^2\,x^2+b^3\,x^3}","Not used",1,"-((a*e + 2*b*d)/(6*b^2) + (e*x)/(2*b))/(a^3 + b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x)","B"
1521,1,37,14,0.029502,"\text{Not used}","int(1/(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","-\frac{1}{3\,a^3\,b+9\,a^2\,b^2\,x+9\,a\,b^3\,x^2+3\,b^4\,x^3}","Not used",1,"-1/(3*a^3*b + 3*b^4*x^3 + 9*a^2*b^2*x + 9*a*b^3*x^2)","B"
1522,1,312,107,0.697511,"\text{Not used}","int(1/((d + e*x)*(a^2 + b^2*x^2 + 2*a*b*x)^2),x)","\frac{\frac{11\,a^2\,e^2-7\,a\,b\,d\,e+2\,b^2\,d^2}{6\,\left(a^3\,e^3-3\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e-b^3\,d^3\right)}-\frac{e\,x\,\left(b^2\,d-5\,a\,b\,e\right)}{2\,\left(a^3\,e^3-3\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e-b^3\,d^3\right)}+\frac{b^2\,e^2\,x^2}{a^3\,e^3-3\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e-b^3\,d^3}}{a^3+3\,a^2\,b\,x+3\,a\,b^2\,x^2+b^3\,x^3}-\frac{2\,e^3\,\mathrm{atanh}\left(\frac{a^4\,e^4-2\,a^3\,b\,d\,e^3+2\,a\,b^3\,d^3\,e-b^4\,d^4}{{\left(a\,e-b\,d\right)}^4}+\frac{2\,b\,e\,x\,\left(a^3\,e^3-3\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e-b^3\,d^3\right)}{{\left(a\,e-b\,d\right)}^4}\right)}{{\left(a\,e-b\,d\right)}^4}","Not used",1,"((11*a^2*e^2 + 2*b^2*d^2 - 7*a*b*d*e)/(6*(a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2)) - (e*x*(b^2*d - 5*a*b*e))/(2*(a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2)) + (b^2*e^2*x^2)/(a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2))/(a^3 + b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x) - (2*e^3*atanh((a^4*e^4 - b^4*d^4 + 2*a*b^3*d^3*e - 2*a^3*b*d*e^3)/(a*e - b*d)^4 + (2*b*e*x*(a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2))/(a*e - b*d)^4))/(a*e - b*d)^4","B"
1523,1,534,132,0.831095,"\text{Not used}","int(1/((d + e*x)^2*(a^2 + b^2*x^2 + 2*a*b*x)^2),x)","\frac{8\,b\,e^3\,\mathrm{atanh}\left(\frac{a^5\,e^5-3\,a^4\,b\,d\,e^4+2\,a^3\,b^2\,d^2\,e^3+2\,a^2\,b^3\,d^3\,e^2-3\,a\,b^4\,d^4\,e+b^5\,d^5}{{\left(a\,e-b\,d\right)}^5}+\frac{2\,b\,e\,x\,\left(a^4\,e^4-4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-4\,a\,b^3\,d^3\,e+b^4\,d^4\right)}{{\left(a\,e-b\,d\right)}^5}\right)}{{\left(a\,e-b\,d\right)}^5}-\frac{\frac{3\,a^3\,e^3+13\,a^2\,b\,d\,e^2-5\,a\,b^2\,d^2\,e+b^3\,d^3}{3\,\left(a^4\,e^4-4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-4\,a\,b^3\,d^3\,e+b^4\,d^4\right)}+\frac{4\,b^3\,e^3\,x^3}{a^4\,e^4-4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-4\,a\,b^3\,d^3\,e+b^4\,d^4}+\frac{2\,e^2\,x^2\,\left(d\,b^3+5\,a\,e\,b^2\right)}{a^4\,e^4-4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-4\,a\,b^3\,d^3\,e+b^4\,d^4}+\frac{2\,e\,x\,\left(11\,a^2\,b\,e^2+8\,a\,b^2\,d\,e-b^3\,d^2\right)}{3\,\left(a^4\,e^4-4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-4\,a\,b^3\,d^3\,e+b^4\,d^4\right)}}{x^3\,\left(d\,b^3+3\,a\,e\,b^2\right)+x^2\,\left(3\,e\,a^2\,b+3\,d\,a\,b^2\right)+a^3\,d+x\,\left(e\,a^3+3\,b\,d\,a^2\right)+b^3\,e\,x^4}","Not used",1,"(8*b*e^3*atanh((a^5*e^5 + b^5*d^5 + 2*a^2*b^3*d^3*e^2 + 2*a^3*b^2*d^2*e^3 - 3*a*b^4*d^4*e - 3*a^4*b*d*e^4)/(a*e - b*d)^5 + (2*b*e*x*(a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 4*a*b^3*d^3*e - 4*a^3*b*d*e^3))/(a*e - b*d)^5))/(a*e - b*d)^5 - ((3*a^3*e^3 + b^3*d^3 - 5*a*b^2*d^2*e + 13*a^2*b*d*e^2)/(3*(a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 4*a*b^3*d^3*e - 4*a^3*b*d*e^3)) + (4*b^3*e^3*x^3)/(a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 4*a*b^3*d^3*e - 4*a^3*b*d*e^3) + (2*e^2*x^2*(b^3*d + 5*a*b^2*e))/(a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 4*a*b^3*d^3*e - 4*a^3*b*d*e^3) + (2*e*x*(11*a^2*b*e^2 - b^3*d^2 + 8*a*b^2*d*e))/(3*(a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 4*a*b^3*d^3*e - 4*a^3*b*d*e^3)))/(x^3*(b^3*d + 3*a*b^2*e) + x^2*(3*a*b^2*d + 3*a^2*b*e) + a^3*d + x*(a^3*e + 3*a^2*b*d) + b^3*e*x^4)","B"
1524,1,797,170,1.000456,"\text{Not used}","int(1/((d + e*x)^3*(a^2 + b^2*x^2 + 2*a*b*x)^2),x)","\frac{\frac{-3\,a^4\,e^4+27\,a^3\,b\,d\,e^3+47\,a^2\,b^2\,d^2\,e^2-13\,a\,b^3\,d^3\,e+2\,b^4\,d^4}{6\,\left(a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5\right)}+\frac{5\,e\,x\,\left(3\,a^3\,b\,e^3+35\,a^2\,b^2\,d\,e^2+11\,a\,b^3\,d^2\,e-b^4\,d^3\right)}{6\,\left(a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5\right)}+\frac{10\,b^4\,e^4\,x^4}{a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5}+\frac{5\,e^2\,x^2\,\left(11\,a^2\,b^2\,e^2+23\,a\,b^3\,d\,e+2\,b^4\,d^2\right)}{3\,\left(a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5\right)}+\frac{5\,b\,e^2\,x^3\,\left(3\,d\,b^3\,e+5\,a\,b^2\,e^2\right)}{a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5}}{x^2\,\left(a^3\,e^2+6\,a^2\,b\,d\,e+3\,a\,b^2\,d^2\right)+x^3\,\left(3\,a^2\,b\,e^2+6\,a\,b^2\,d\,e+b^3\,d^2\right)+x\,\left(2\,e\,a^3\,d+3\,b\,a^2\,d^2\right)+x^4\,\left(2\,d\,b^3\,e+3\,a\,b^2\,e^2\right)+a^3\,d^2+b^3\,e^2\,x^5}-\frac{20\,b^2\,e^3\,\mathrm{atanh}\left(\frac{a^6\,e^6-4\,a^5\,b\,d\,e^5+5\,a^4\,b^2\,d^2\,e^4-5\,a^2\,b^4\,d^4\,e^2+4\,a\,b^5\,d^5\,e-b^6\,d^6}{{\left(a\,e-b\,d\right)}^6}+\frac{2\,b\,e\,x\,\left(a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5\right)}{{\left(a\,e-b\,d\right)}^6}\right)}{{\left(a\,e-b\,d\right)}^6}","Not used",1,"((2*b^4*d^4 - 3*a^4*e^4 + 47*a^2*b^2*d^2*e^2 - 13*a*b^3*d^3*e + 27*a^3*b*d*e^3)/(6*(a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4)) + (5*e*x*(3*a^3*b*e^3 - b^4*d^3 + 35*a^2*b^2*d*e^2 + 11*a*b^3*d^2*e))/(6*(a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4)) + (10*b^4*e^4*x^4)/(a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4) + (5*e^2*x^2*(2*b^4*d^2 + 11*a^2*b^2*e^2 + 23*a*b^3*d*e))/(3*(a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4)) + (5*b*e^2*x^3*(5*a*b^2*e^2 + 3*b^3*d*e))/(a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4))/(x^2*(a^3*e^2 + 3*a*b^2*d^2 + 6*a^2*b*d*e) + x^3*(b^3*d^2 + 3*a^2*b*e^2 + 6*a*b^2*d*e) + x*(3*a^2*b*d^2 + 2*a^3*d*e) + x^4*(3*a*b^2*e^2 + 2*b^3*d*e) + a^3*d^2 + b^3*e^2*x^5) - (20*b^2*e^3*atanh((a^6*e^6 - b^6*d^6 - 5*a^2*b^4*d^4*e^2 + 5*a^4*b^2*d^2*e^4 + 4*a*b^5*d^5*e - 4*a^5*b*d*e^5)/(a*e - b*d)^6 + (2*b*e*x*(a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4))/(a*e - b*d)^6))/(a*e - b*d)^6","B"
1525,1,644,208,0.196980,"\text{Not used}","int((d + e*x)^8/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","x\,\left(\frac{6\,a\,\left(\frac{6\,a\,e^8}{b^7}-\frac{8\,d\,e^7}{b^6}\right)}{b}-\frac{15\,a^2\,e^8}{b^8}+\frac{28\,d^2\,e^6}{b^6}\right)-\frac{x^4\,\left(70\,a^4\,b^3\,e^8-280\,a^3\,b^4\,d\,e^7+420\,a^2\,b^5\,d^2\,e^6-280\,a\,b^6\,d^3\,e^5+70\,b^7\,d^4\,e^4\right)+\frac{743\,a^8\,e^8-2754\,a^7\,b\,d\,e^7+3654\,a^6\,b^2\,d^2\,e^6-1918\,a^5\,b^3\,d^3\,e^5+210\,a^4\,b^4\,d^4\,e^4+42\,a^3\,b^5\,d^5\,e^3+14\,a^2\,b^6\,d^6\,e^2+6\,a\,b^7\,d^7\,e+3\,b^8\,d^8}{15\,b}+x\,\left(\frac{638\,a^7\,e^8}{3}-798\,a^6\,b\,d\,e^7+1078\,a^5\,b^2\,d^2\,e^6-\frac{1750\,a^4\,b^3\,d^3\,e^5}{3}+70\,a^3\,b^4\,d^4\,e^4+14\,a^2\,b^5\,d^5\,e^3+\frac{14\,a\,b^6\,d^6\,e^2}{3}+2\,b^7\,d^7\,e\right)+x^3\,\left(252\,a^5\,b^2\,e^8-980\,a^4\,b^3\,d\,e^7+1400\,a^3\,b^4\,d^2\,e^6-840\,a^2\,b^5\,d^3\,e^5+140\,a\,b^6\,d^4\,e^4+28\,b^7\,d^5\,e^3\right)+x^2\,\left(\frac{1036\,a^6\,b\,e^8}{3}-1316\,a^5\,b^2\,d\,e^7+1820\,a^4\,b^3\,d^2\,e^6-\frac{3080\,a^3\,b^4\,d^3\,e^5}{3}+140\,a^2\,b^5\,d^4\,e^4+28\,a\,b^6\,d^5\,e^3+\frac{28\,b^7\,d^6\,e^2}{3}\right)}{a^5\,b^8+5\,a^4\,b^9\,x+10\,a^3\,b^{10}\,x^2+10\,a^2\,b^{11}\,x^3+5\,a\,b^{12}\,x^4+b^{13}\,x^5}-x^2\,\left(\frac{3\,a\,e^8}{b^7}-\frac{4\,d\,e^7}{b^6}\right)-\frac{\ln\left(a+b\,x\right)\,\left(56\,a^3\,e^8-168\,a^2\,b\,d\,e^7+168\,a\,b^2\,d^2\,e^6-56\,b^3\,d^3\,e^5\right)}{b^9}+\frac{e^8\,x^3}{3\,b^6}","Not used",1,"x*((6*a*((6*a*e^8)/b^7 - (8*d*e^7)/b^6))/b - (15*a^2*e^8)/b^8 + (28*d^2*e^6)/b^6) - (x^4*(70*a^4*b^3*e^8 + 70*b^7*d^4*e^4 - 280*a*b^6*d^3*e^5 - 280*a^3*b^4*d*e^7 + 420*a^2*b^5*d^2*e^6) + (743*a^8*e^8 + 3*b^8*d^8 + 14*a^2*b^6*d^6*e^2 + 42*a^3*b^5*d^5*e^3 + 210*a^4*b^4*d^4*e^4 - 1918*a^5*b^3*d^3*e^5 + 3654*a^6*b^2*d^2*e^6 + 6*a*b^7*d^7*e - 2754*a^7*b*d*e^7)/(15*b) + x*((638*a^7*e^8)/3 + 2*b^7*d^7*e + (14*a*b^6*d^6*e^2)/3 + 14*a^2*b^5*d^5*e^3 + 70*a^3*b^4*d^4*e^4 - (1750*a^4*b^3*d^3*e^5)/3 + 1078*a^5*b^2*d^2*e^6 - 798*a^6*b*d*e^7) + x^3*(252*a^5*b^2*e^8 + 28*b^7*d^5*e^3 + 140*a*b^6*d^4*e^4 - 980*a^4*b^3*d*e^7 - 840*a^2*b^5*d^3*e^5 + 1400*a^3*b^4*d^2*e^6) + x^2*((1036*a^6*b*e^8)/3 + (28*b^7*d^6*e^2)/3 + 28*a*b^6*d^5*e^3 - 1316*a^5*b^2*d*e^7 + 140*a^2*b^5*d^4*e^4 - (3080*a^3*b^4*d^3*e^5)/3 + 1820*a^4*b^3*d^2*e^6))/(a^5*b^8 + b^13*x^5 + 5*a^4*b^9*x + 5*a*b^12*x^4 + 10*a^3*b^10*x^2 + 10*a^2*b^11*x^3) - x^2*((3*a*e^8)/b^7 - (4*d*e^7)/b^6) - (log(a + b*x)*(56*a^3*e^8 - 56*b^3*d^3*e^5 + 168*a*b^2*d^2*e^6 - 168*a^2*b*d*e^7))/b^9 + (e^8*x^3)/(3*b^6)","B"
1526,1,508,181,0.637835,"\text{Not used}","int((d + e*x)^7/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\frac{e^7\,x^2}{2\,b^6}-\frac{\frac{-459\,a^7\,e^7+1218\,a^6\,b\,d\,e^6-959\,a^5\,b^2\,d^2\,e^5+140\,a^4\,b^3\,d^3\,e^4+35\,a^3\,b^4\,d^4\,e^3+14\,a^2\,b^5\,d^5\,e^2+7\,a\,b^6\,d^6\,e+4\,b^7\,d^7}{20\,b}+x\,\left(-\frac{399\,a^6\,e^7}{4}+\frac{539\,a^5\,b\,d\,e^6}{2}-\frac{875\,a^4\,b^2\,d^2\,e^5}{4}+35\,a^3\,b^3\,d^3\,e^4+\frac{35\,a^2\,b^4\,d^4\,e^3}{4}+\frac{7\,a\,b^5\,d^5\,e^2}{2}+\frac{7\,b^6\,d^6\,e}{4}\right)+x^3\,\left(-\frac{245\,a^4\,b^2\,e^7}{2}+350\,a^3\,b^3\,d\,e^6-315\,a^2\,b^4\,d^2\,e^5+70\,a\,b^5\,d^3\,e^4+\frac{35\,b^6\,d^4\,e^3}{2}\right)+x^2\,\left(-\frac{329\,a^5\,b\,e^7}{2}+455\,a^4\,b^2\,d\,e^6-385\,a^3\,b^3\,d^2\,e^5+70\,a^2\,b^4\,d^3\,e^4+\frac{35\,a\,b^5\,d^4\,e^3}{2}+7\,b^6\,d^5\,e^2\right)-x^4\,\left(35\,a^3\,b^3\,e^7-105\,a^2\,b^4\,d\,e^6+105\,a\,b^5\,d^2\,e^5-35\,b^6\,d^3\,e^4\right)}{a^5\,b^7+5\,a^4\,b^8\,x+10\,a^3\,b^9\,x^2+10\,a^2\,b^{10}\,x^3+5\,a\,b^{11}\,x^4+b^{12}\,x^5}-x\,\left(\frac{6\,a\,e^7}{b^7}-\frac{7\,d\,e^6}{b^6}\right)+\frac{\ln\left(a+b\,x\right)\,\left(21\,a^2\,e^7-42\,a\,b\,d\,e^6+21\,b^2\,d^2\,e^5\right)}{b^8}","Not used",1,"(e^7*x^2)/(2*b^6) - ((4*b^7*d^7 - 459*a^7*e^7 + 14*a^2*b^5*d^5*e^2 + 35*a^3*b^4*d^4*e^3 + 140*a^4*b^3*d^3*e^4 - 959*a^5*b^2*d^2*e^5 + 7*a*b^6*d^6*e + 1218*a^6*b*d*e^6)/(20*b) + x*((7*b^6*d^6*e)/4 - (399*a^6*e^7)/4 + (7*a*b^5*d^5*e^2)/2 + (35*a^2*b^4*d^4*e^3)/4 + 35*a^3*b^3*d^3*e^4 - (875*a^4*b^2*d^2*e^5)/4 + (539*a^5*b*d*e^6)/2) + x^3*((35*b^6*d^4*e^3)/2 - (245*a^4*b^2*e^7)/2 + 70*a*b^5*d^3*e^4 + 350*a^3*b^3*d*e^6 - 315*a^2*b^4*d^2*e^5) + x^2*(7*b^6*d^5*e^2 - (329*a^5*b*e^7)/2 + (35*a*b^5*d^4*e^3)/2 + 455*a^4*b^2*d*e^6 + 70*a^2*b^4*d^3*e^4 - 385*a^3*b^3*d^2*e^5) - x^4*(35*a^3*b^3*e^7 - 35*b^6*d^3*e^4 + 105*a*b^5*d^2*e^5 - 105*a^2*b^4*d*e^6))/(a^5*b^7 + b^12*x^5 + 5*a^4*b^8*x + 5*a*b^11*x^4 + 10*a^3*b^9*x^2 + 10*a^2*b^10*x^3) - x*((6*a*e^7)/b^7 - (7*d*e^6)/b^6) + (log(a + b*x)*(21*a^2*e^7 + 21*b^2*d^2*e^5 - 42*a*b*d*e^6))/b^8","B"
1527,1,399,155,0.644148,"\text{Not used}","int((d + e*x)^6/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\frac{e^6\,x}{b^6}-\frac{\ln\left(a+b\,x\right)\,\left(6\,a\,e^6-6\,b\,d\,e^5\right)}{b^7}-\frac{x^2\,\left(65\,a^4\,b\,e^6-110\,a^3\,b^2\,d\,e^5+30\,a^2\,b^3\,d^2\,e^4+10\,a\,b^4\,d^3\,e^3+5\,b^5\,d^4\,e^2\right)+x^4\,\left(15\,a^2\,b^3\,e^6-30\,a\,b^4\,d\,e^5+15\,b^5\,d^2\,e^4\right)+\frac{87\,a^6\,e^6-137\,a^5\,b\,d\,e^5+30\,a^4\,b^2\,d^2\,e^4+10\,a^3\,b^3\,d^3\,e^3+5\,a^2\,b^4\,d^4\,e^2+3\,a\,b^5\,d^5\,e+2\,b^6\,d^6}{10\,b}+x\,\left(\frac{77\,a^5\,e^6}{2}-\frac{125\,a^4\,b\,d\,e^5}{2}+15\,a^3\,b^2\,d^2\,e^4+5\,a^2\,b^3\,d^3\,e^3+\frac{5\,a\,b^4\,d^4\,e^2}{2}+\frac{3\,b^5\,d^5\,e}{2}\right)+x^3\,\left(50\,a^3\,b^2\,e^6-90\,a^2\,b^3\,d\,e^5+30\,a\,b^4\,d^2\,e^4+10\,b^5\,d^3\,e^3\right)}{a^5\,b^6+5\,a^4\,b^7\,x+10\,a^3\,b^8\,x^2+10\,a^2\,b^9\,x^3+5\,a\,b^{10}\,x^4+b^{11}\,x^5}","Not used",1,"(e^6*x)/b^6 - (log(a + b*x)*(6*a*e^6 - 6*b*d*e^5))/b^7 - (x^2*(65*a^4*b*e^6 + 5*b^5*d^4*e^2 + 10*a*b^4*d^3*e^3 - 110*a^3*b^2*d*e^5 + 30*a^2*b^3*d^2*e^4) + x^4*(15*a^2*b^3*e^6 + 15*b^5*d^2*e^4 - 30*a*b^4*d*e^5) + (87*a^6*e^6 + 2*b^6*d^6 + 5*a^2*b^4*d^4*e^2 + 10*a^3*b^3*d^3*e^3 + 30*a^4*b^2*d^2*e^4 + 3*a*b^5*d^5*e - 137*a^5*b*d*e^5)/(10*b) + x*((77*a^5*e^6)/2 + (3*b^5*d^5*e)/2 + (5*a*b^4*d^4*e^2)/2 + 5*a^2*b^3*d^3*e^3 + 15*a^3*b^2*d^2*e^4 - (125*a^4*b*d*e^5)/2) + x^3*(50*a^3*b^2*e^6 + 10*b^5*d^3*e^3 + 30*a*b^4*d^2*e^4 - 90*a^2*b^3*d*e^5))/(a^5*b^6 + b^11*x^5 + 5*a^4*b^7*x + 5*a*b^10*x^4 + 10*a^3*b^8*x^2 + 10*a^2*b^9*x^3)","B"
1528,1,261,138,0.604542,"\text{Not used}","int((d + e*x)^5/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\frac{e^5\,\ln\left(a+b\,x\right)}{b^6}-\frac{x\,\left(-\frac{125\,a^4\,b\,e^5}{12}+5\,a^3\,b^2\,d\,e^4+\frac{5\,a^2\,b^3\,d^2\,e^3}{2}+\frac{5\,a\,b^4\,d^3\,e^2}{3}+\frac{5\,b^5\,d^4\,e}{4}\right)-x^4\,\left(5\,a\,b^4\,e^5-5\,b^5\,d\,e^4\right)+x^3\,\left(-15\,a^2\,b^3\,e^5+10\,a\,b^4\,d\,e^4+5\,b^5\,d^2\,e^3\right)-\frac{137\,a^5\,e^5}{60}+\frac{b^5\,d^5}{5}+x^2\,\left(-\frac{55\,a^3\,b^2\,e^5}{3}+10\,a^2\,b^3\,d\,e^4+5\,a\,b^4\,d^2\,e^3+\frac{10\,b^5\,d^3\,e^2}{3}\right)+\frac{a^2\,b^3\,d^3\,e^2}{3}+\frac{a^3\,b^2\,d^2\,e^3}{2}+\frac{a\,b^4\,d^4\,e}{4}+a^4\,b\,d\,e^4}{b^6\,{\left(a+b\,x\right)}^5}","Not used",1,"(e^5*log(a + b*x))/b^6 - (x*((5*b^5*d^4*e)/4 - (125*a^4*b*e^5)/12 + (5*a*b^4*d^3*e^2)/3 + 5*a^3*b^2*d*e^4 + (5*a^2*b^3*d^2*e^3)/2) - x^4*(5*a*b^4*e^5 - 5*b^5*d*e^4) + x^3*(5*b^5*d^2*e^3 - 15*a^2*b^3*e^5 + 10*a*b^4*d*e^4) - (137*a^5*e^5)/60 + (b^5*d^5)/5 + x^2*((10*b^5*d^3*e^2)/3 - (55*a^3*b^2*e^5)/3 + 5*a*b^4*d^2*e^3 + 10*a^2*b^3*d*e^4) + (a^2*b^3*d^3*e^2)/3 + (a^3*b^2*d^2*e^3)/2 + (a*b^4*d^4*e)/4 + a^4*b*d*e^4)/(b^6*(a + b*x)^5)","B"
1529,1,203,28,0.084782,"\text{Not used}","int((d + e*x)^4/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","-\frac{\frac{a^4\,e^4+a^3\,b\,d\,e^3+a^2\,b^2\,d^2\,e^2+a\,b^3\,d^3\,e+b^4\,d^4}{5\,b^5}+\frac{e^4\,x^4}{b}+\frac{2\,e^3\,x^3\,\left(a\,e+b\,d\right)}{b^2}+\frac{e\,x\,\left(a^3\,e^3+a^2\,b\,d\,e^2+a\,b^2\,d^2\,e+b^3\,d^3\right)}{b^4}+\frac{2\,e^2\,x^2\,\left(a^2\,e^2+a\,b\,d\,e+b^2\,d^2\right)}{b^3}}{a^5+5\,a^4\,b\,x+10\,a^3\,b^2\,x^2+10\,a^2\,b^3\,x^3+5\,a\,b^4\,x^4+b^5\,x^5}","Not used",1,"-((a^4*e^4 + b^4*d^4 + a^2*b^2*d^2*e^2 + a*b^3*d^3*e + a^3*b*d*e^3)/(5*b^5) + (e^4*x^4)/b + (2*e^3*x^3*(a*e + b*d))/b^2 + (e*x*(a^3*e^3 + b^3*d^3 + a*b^2*d^2*e + a^2*b*d*e^2))/b^4 + (2*e^2*x^2*(a^2*e^2 + b^2*d^2 + a*b*d*e))/b^3)/(a^5 + b^5*x^5 + 5*a*b^4*x^4 + 10*a^3*b^2*x^2 + 10*a^2*b^3*x^3 + 5*a^4*b*x)","B"
1530,1,154,58,0.530688,"\text{Not used}","int((d + e*x)^3/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","-\frac{\frac{a^3\,e^3+2\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e+4\,b^3\,d^3}{20\,b^4}+\frac{e^3\,x^3}{2\,b}+\frac{e\,x\,\left(a^2\,e^2+2\,a\,b\,d\,e+3\,b^2\,d^2\right)}{4\,b^3}+\frac{e^2\,x^2\,\left(a\,e+2\,b\,d\right)}{2\,b^2}}{a^5+5\,a^4\,b\,x+10\,a^3\,b^2\,x^2+10\,a^2\,b^3\,x^3+5\,a\,b^4\,x^4+b^5\,x^5}","Not used",1,"-((a^3*e^3 + 4*b^3*d^3 + 3*a*b^2*d^2*e + 2*a^2*b*d*e^2)/(20*b^4) + (e^3*x^3)/(2*b) + (e*x*(a^2*e^2 + 3*b^2*d^2 + 2*a*b*d*e))/(4*b^3) + (e^2*x^2*(a*e + 2*b*d))/(2*b^2))/(a^5 + b^5*x^5 + 5*a*b^4*x^4 + 10*a^3*b^2*x^2 + 10*a^2*b^3*x^3 + 5*a^4*b*x)","B"
1531,1,107,65,0.058011,"\text{Not used}","int((d + e*x)^2/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","-\frac{\frac{a^2\,e^2+3\,a\,b\,d\,e+6\,b^2\,d^2}{30\,b^3}+\frac{e^2\,x^2}{3\,b}+\frac{e\,x\,\left(a\,e+3\,b\,d\right)}{6\,b^2}}{a^5+5\,a^4\,b\,x+10\,a^3\,b^2\,x^2+10\,a^2\,b^3\,x^3+5\,a\,b^4\,x^4+b^5\,x^5}","Not used",1,"-((a^2*e^2 + 6*b^2*d^2 + 3*a*b*d*e)/(30*b^3) + (e^2*x^2)/(3*b) + (e*x*(a*e + 3*b*d))/(6*b^2))/(a^5 + b^5*x^5 + 5*a*b^4*x^4 + 10*a^3*b^2*x^2 + 10*a^2*b^3*x^3 + 5*a^4*b*x)","B"
1532,1,74,38,0.046091,"\text{Not used}","int((d + e*x)/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","-\frac{\frac{a\,e+4\,b\,d}{20\,b^2}+\frac{e\,x}{4\,b}}{a^5+5\,a^4\,b\,x+10\,a^3\,b^2\,x^2+10\,a^2\,b^3\,x^3+5\,a\,b^4\,x^4+b^5\,x^5}","Not used",1,"-((a*e + 4*b*d)/(20*b^2) + (e*x)/(4*b))/(a^5 + b^5*x^5 + 5*a*b^4*x^4 + 10*a^3*b^2*x^2 + 10*a^2*b^3*x^3 + 5*a^4*b*x)","B"
1533,1,59,14,0.516548,"\text{Not used}","int(1/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","-\frac{1}{5\,a^5\,b+25\,a^4\,b^2\,x+50\,a^3\,b^3\,x^2+50\,a^2\,b^4\,x^3+25\,a\,b^5\,x^4+5\,b^6\,x^5}","Not used",1,"-1/(5*a^5*b + 5*b^6*x^5 + 25*a^4*b^2*x + 25*a*b^5*x^4 + 50*a^3*b^3*x^2 + 50*a^2*b^4*x^3)","B"
1534,1,721,155,0.887655,"\text{Not used}","int(1/((d + e*x)*(a^2 + b^2*x^2 + 2*a*b*x)^3),x)","\frac{\frac{137\,a^4\,e^4-163\,a^3\,b\,d\,e^3+137\,a^2\,b^2\,d^2\,e^2-63\,a\,b^3\,d^3\,e+12\,b^4\,d^4}{60\,\left(a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5\right)}-\frac{e\,x\,\left(-77\,a^3\,b\,e^3+43\,a^2\,b^2\,d\,e^2-17\,a\,b^3\,d^2\,e+3\,b^4\,d^3\right)}{12\,\left(a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5\right)}+\frac{b^4\,e^4\,x^4}{a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5}-\frac{e^3\,x^3\,\left(b^4\,d-9\,a\,b^3\,e\right)}{2\,\left(a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5\right)}+\frac{e^2\,x^2\,\left(47\,a^2\,b^2\,e^2-13\,a\,b^3\,d\,e+2\,b^4\,d^2\right)}{6\,\left(a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5\right)}}{a^5+5\,a^4\,b\,x+10\,a^3\,b^2\,x^2+10\,a^2\,b^3\,x^3+5\,a\,b^4\,x^4+b^5\,x^5}-\frac{2\,e^5\,\mathrm{atanh}\left(\frac{a^6\,e^6-4\,a^5\,b\,d\,e^5+5\,a^4\,b^2\,d^2\,e^4-5\,a^2\,b^4\,d^4\,e^2+4\,a\,b^5\,d^5\,e-b^6\,d^6}{{\left(a\,e-b\,d\right)}^6}+\frac{2\,b\,e\,x\,\left(a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5\right)}{{\left(a\,e-b\,d\right)}^6}\right)}{{\left(a\,e-b\,d\right)}^6}","Not used",1,"((137*a^4*e^4 + 12*b^4*d^4 + 137*a^2*b^2*d^2*e^2 - 63*a*b^3*d^3*e - 163*a^3*b*d*e^3)/(60*(a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4)) - (e*x*(3*b^4*d^3 - 77*a^3*b*e^3 + 43*a^2*b^2*d*e^2 - 17*a*b^3*d^2*e))/(12*(a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4)) + (b^4*e^4*x^4)/(a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4) - (e^3*x^3*(b^4*d - 9*a*b^3*e))/(2*(a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4)) + (e^2*x^2*(2*b^4*d^2 + 47*a^2*b^2*e^2 - 13*a*b^3*d*e))/(6*(a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4)))/(a^5 + b^5*x^5 + 5*a*b^4*x^4 + 10*a^3*b^2*x^2 + 10*a^2*b^3*x^3 + 5*a^4*b*x) - (2*e^5*atanh((a^6*e^6 - b^6*d^6 - 5*a^2*b^4*d^4*e^2 + 5*a^4*b^2*d^2*e^4 + 4*a*b^5*d^5*e - 4*a^5*b*d*e^5)/(a*e - b*d)^6 + (2*b*e*x*(a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4))/(a*e - b*d)^6))/(a*e - b*d)^6","B"
1535,1,1047,181,1.182285,"\text{Not used}","int(1/((d + e*x)^2*(a^2 + b^2*x^2 + 2*a*b*x)^3),x)","\frac{12\,b\,e^5\,\mathrm{atanh}\left(\frac{a^7\,e^7-5\,a^6\,b\,d\,e^6+9\,a^5\,b^2\,d^2\,e^5-5\,a^4\,b^3\,d^3\,e^4-5\,a^3\,b^4\,d^4\,e^3+9\,a^2\,b^5\,d^5\,e^2-5\,a\,b^6\,d^6\,e+b^7\,d^7}{{\left(a\,e-b\,d\right)}^7}+\frac{2\,b\,e\,x\,\left(a^6\,e^6-6\,a^5\,b\,d\,e^5+15\,a^4\,b^2\,d^2\,e^4-20\,a^3\,b^3\,d^3\,e^3+15\,a^2\,b^4\,d^4\,e^2-6\,a\,b^5\,d^5\,e+b^6\,d^6\right)}{{\left(a\,e-b\,d\right)}^7}\right)}{{\left(a\,e-b\,d\right)}^7}-\frac{\frac{10\,a^5\,e^5+87\,a^4\,b\,d\,e^4-63\,a^3\,b^2\,d^2\,e^3+37\,a^2\,b^3\,d^3\,e^2-13\,a\,b^4\,d^4\,e+2\,b^5\,d^5}{10\,\left(a^6\,e^6-6\,a^5\,b\,d\,e^5+15\,a^4\,b^2\,d^2\,e^4-20\,a^3\,b^3\,d^3\,e^3+15\,a^2\,b^4\,d^4\,e^2-6\,a\,b^5\,d^5\,e+b^6\,d^6\right)}+\frac{e^3\,x^3\,\left(47\,a^2\,b^3\,e^2+14\,a\,b^4\,d\,e-b^5\,d^2\right)}{a^6\,e^6-6\,a^5\,b\,d\,e^5+15\,a^4\,b^2\,d^2\,e^4-20\,a^3\,b^3\,d^3\,e^3+15\,a^2\,b^4\,d^4\,e^2-6\,a\,b^5\,d^5\,e+b^6\,d^6}+\frac{e^2\,x^2\,\left(77\,a^3\,b^2\,e^3+51\,a^2\,b^3\,d\,e^2-9\,a\,b^4\,d^2\,e+b^5\,d^3\right)}{2\,\left(a^6\,e^6-6\,a^5\,b\,d\,e^5+15\,a^4\,b^2\,d^2\,e^4-20\,a^3\,b^3\,d^3\,e^3+15\,a^2\,b^4\,d^4\,e^2-6\,a\,b^5\,d^5\,e+b^6\,d^6\right)}+\frac{6\,b^5\,e^5\,x^5}{a^6\,e^6-6\,a^5\,b\,d\,e^5+15\,a^4\,b^2\,d^2\,e^4-20\,a^3\,b^3\,d^3\,e^3+15\,a^2\,b^4\,d^4\,e^2-6\,a\,b^5\,d^5\,e+b^6\,d^6}+\frac{3\,e^4\,x^4\,\left(d\,b^5+9\,a\,e\,b^4\right)}{a^6\,e^6-6\,a^5\,b\,d\,e^5+15\,a^4\,b^2\,d^2\,e^4-20\,a^3\,b^3\,d^3\,e^3+15\,a^2\,b^4\,d^4\,e^2-6\,a\,b^5\,d^5\,e+b^6\,d^6}+\frac{e\,x\,\left(137\,a^4\,b\,e^4+222\,a^3\,b^2\,d\,e^3-78\,a^2\,b^3\,d^2\,e^2+22\,a\,b^4\,d^3\,e-3\,b^5\,d^4\right)}{10\,\left(a^6\,e^6-6\,a^5\,b\,d\,e^5+15\,a^4\,b^2\,d^2\,e^4-20\,a^3\,b^3\,d^3\,e^3+15\,a^2\,b^4\,d^4\,e^2-6\,a\,b^5\,d^5\,e+b^6\,d^6\right)}}{x^5\,\left(d\,b^5+5\,a\,e\,b^4\right)+x^3\,\left(10\,e\,a^3\,b^2+10\,d\,a^2\,b^3\right)+a^5\,d+x\,\left(e\,a^5+5\,b\,d\,a^4\right)+x^2\,\left(5\,e\,a^4\,b+10\,d\,a^3\,b^2\right)+x^4\,\left(10\,e\,a^2\,b^3+5\,d\,a\,b^4\right)+b^5\,e\,x^6}","Not used",1,"(12*b*e^5*atanh((a^7*e^7 + b^7*d^7 + 9*a^2*b^5*d^5*e^2 - 5*a^3*b^4*d^4*e^3 - 5*a^4*b^3*d^3*e^4 + 9*a^5*b^2*d^2*e^5 - 5*a*b^6*d^6*e - 5*a^6*b*d*e^6)/(a*e - b*d)^7 + (2*b*e*x*(a^6*e^6 + b^6*d^6 + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a*b^5*d^5*e - 6*a^5*b*d*e^5))/(a*e - b*d)^7))/(a*e - b*d)^7 - ((10*a^5*e^5 + 2*b^5*d^5 + 37*a^2*b^3*d^3*e^2 - 63*a^3*b^2*d^2*e^3 - 13*a*b^4*d^4*e + 87*a^4*b*d*e^4)/(10*(a^6*e^6 + b^6*d^6 + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a*b^5*d^5*e - 6*a^5*b*d*e^5)) + (e^3*x^3*(47*a^2*b^3*e^2 - b^5*d^2 + 14*a*b^4*d*e))/(a^6*e^6 + b^6*d^6 + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a*b^5*d^5*e - 6*a^5*b*d*e^5) + (e^2*x^2*(b^5*d^3 + 77*a^3*b^2*e^3 + 51*a^2*b^3*d*e^2 - 9*a*b^4*d^2*e))/(2*(a^6*e^6 + b^6*d^6 + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a*b^5*d^5*e - 6*a^5*b*d*e^5)) + (6*b^5*e^5*x^5)/(a^6*e^6 + b^6*d^6 + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a*b^5*d^5*e - 6*a^5*b*d*e^5) + (3*e^4*x^4*(b^5*d + 9*a*b^4*e))/(a^6*e^6 + b^6*d^6 + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a*b^5*d^5*e - 6*a^5*b*d*e^5) + (e*x*(137*a^4*b*e^4 - 3*b^5*d^4 + 222*a^3*b^2*d*e^3 - 78*a^2*b^3*d^2*e^2 + 22*a*b^4*d^3*e))/(10*(a^6*e^6 + b^6*d^6 + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a*b^5*d^5*e - 6*a^5*b*d*e^5)))/(x^5*(b^5*d + 5*a*b^4*e) + x^3*(10*a^2*b^3*d + 10*a^3*b^2*e) + a^5*d + x*(a^5*e + 5*a^4*b*d) + x^2*(10*a^3*b^2*d + 5*a^4*b*e) + x^4*(10*a^2*b^3*e + 5*a*b^4*d) + b^5*e*x^6)","B"
1536,1,1427,220,1.468451,"\text{Not used}","int(1/((d + e*x)^3*(a^2 + b^2*x^2 + 2*a*b*x)^3),x)","\frac{\frac{-10\,a^6\,e^6+130\,a^5\,b\,d\,e^5+459\,a^4\,b^2\,d^2\,e^4-241\,a^3\,b^3\,d^3\,e^3+109\,a^2\,b^4\,d^4\,e^2-31\,a\,b^5\,d^5\,e+4\,b^6\,d^6}{20\,\left(a^7\,e^7-7\,a^6\,b\,d\,e^6+21\,a^5\,b^2\,d^2\,e^5-35\,a^4\,b^3\,d^3\,e^4+35\,a^3\,b^4\,d^4\,e^3-21\,a^2\,b^5\,d^5\,e^2+7\,a\,b^6\,d^6\,e-b^7\,d^7\right)}+\frac{7\,e^3\,x^3\,\left(77\,a^3\,b^3\,e^3+145\,a^2\,b^4\,d\,e^2+19\,a\,b^5\,d^2\,e-b^6\,d^3\right)}{4\,\left(a^7\,e^7-7\,a^6\,b\,d\,e^6+21\,a^5\,b^2\,d^2\,e^5-35\,a^4\,b^3\,d^3\,e^4+35\,a^3\,b^4\,d^4\,e^3-21\,a^2\,b^5\,d^5\,e^2+7\,a\,b^6\,d^6\,e-b^7\,d^7\right)}+\frac{21\,b^6\,e^6\,x^6}{a^7\,e^7-7\,a^6\,b\,d\,e^6+21\,a^5\,b^2\,d^2\,e^5-35\,a^4\,b^3\,d^3\,e^4+35\,a^3\,b^4\,d^4\,e^3-21\,a^2\,b^5\,d^5\,e^2+7\,a\,b^6\,d^6\,e-b^7\,d^7}+\frac{7\,e^2\,x^2\,\left(137\,a^4\,b^2\,e^4+607\,a^3\,b^3\,d\,e^3+177\,a^2\,b^4\,d^2\,e^2-23\,a\,b^5\,d^3\,e+2\,b^6\,d^4\right)}{20\,\left(a^7\,e^7-7\,a^6\,b\,d\,e^6+21\,a^5\,b^2\,d^2\,e^5-35\,a^4\,b^3\,d^3\,e^4+35\,a^3\,b^4\,d^4\,e^3-21\,a^2\,b^5\,d^5\,e^2+7\,a\,b^6\,d^6\,e-b^7\,d^7\right)}+\frac{7\,e^4\,x^4\,\left(47\,a^2\,b^4\,e^2+41\,a\,b^5\,d\,e+2\,b^6\,d^2\right)}{2\,\left(a^7\,e^7-7\,a^6\,b\,d\,e^6+21\,a^5\,b^2\,d^2\,e^5-35\,a^4\,b^3\,d^3\,e^4+35\,a^3\,b^4\,d^4\,e^3-21\,a^2\,b^5\,d^5\,e^2+7\,a\,b^6\,d^6\,e-b^7\,d^7\right)}+\frac{7\,e\,x\,\left(10\,a^5\,b\,e^5+224\,a^4\,b^2\,d\,e^4+159\,a^3\,b^3\,d^2\,e^3-41\,a^2\,b^4\,d^3\,e^2+9\,a\,b^5\,d^4\,e-b^6\,d^5\right)}{20\,\left(a^7\,e^7-7\,a^6\,b\,d\,e^6+21\,a^5\,b^2\,d^2\,e^5-35\,a^4\,b^3\,d^3\,e^4+35\,a^3\,b^4\,d^4\,e^3-21\,a^2\,b^5\,d^5\,e^2+7\,a\,b^6\,d^6\,e-b^7\,d^7\right)}+\frac{63\,b\,e^4\,x^5\,\left(d\,b^5\,e+3\,a\,b^4\,e^2\right)}{2\,\left(a^7\,e^7-7\,a^6\,b\,d\,e^6+21\,a^5\,b^2\,d^2\,e^5-35\,a^4\,b^3\,d^3\,e^4+35\,a^3\,b^4\,d^4\,e^3-21\,a^2\,b^5\,d^5\,e^2+7\,a\,b^6\,d^6\,e-b^7\,d^7\right)}}{x^3\,\left(5\,a^4\,b\,e^2+20\,a^3\,b^2\,d\,e+10\,a^2\,b^3\,d^2\right)+x^4\,\left(10\,a^3\,b^2\,e^2+20\,a^2\,b^3\,d\,e+5\,a\,b^4\,d^2\right)+x\,\left(2\,e\,a^5\,d+5\,b\,a^4\,d^2\right)+x^2\,\left(a^5\,e^2+10\,a^4\,b\,d\,e+10\,a^3\,b^2\,d^2\right)+x^5\,\left(10\,a^2\,b^3\,e^2+10\,a\,b^4\,d\,e+b^5\,d^2\right)+x^6\,\left(2\,d\,b^5\,e+5\,a\,b^4\,e^2\right)+a^5\,d^2+b^5\,e^2\,x^7}-\frac{42\,b^2\,e^5\,\mathrm{atanh}\left(\frac{a^8\,e^8-6\,a^7\,b\,d\,e^7+14\,a^6\,b^2\,d^2\,e^6-14\,a^5\,b^3\,d^3\,e^5+14\,a^3\,b^5\,d^5\,e^3-14\,a^2\,b^6\,d^6\,e^2+6\,a\,b^7\,d^7\,e-b^8\,d^8}{{\left(a\,e-b\,d\right)}^8}+\frac{2\,b\,e\,x\,\left(a^7\,e^7-7\,a^6\,b\,d\,e^6+21\,a^5\,b^2\,d^2\,e^5-35\,a^4\,b^3\,d^3\,e^4+35\,a^3\,b^4\,d^4\,e^3-21\,a^2\,b^5\,d^5\,e^2+7\,a\,b^6\,d^6\,e-b^7\,d^7\right)}{{\left(a\,e-b\,d\right)}^8}\right)}{{\left(a\,e-b\,d\right)}^8}","Not used",1,"((4*b^6*d^6 - 10*a^6*e^6 + 109*a^2*b^4*d^4*e^2 - 241*a^3*b^3*d^3*e^3 + 459*a^4*b^2*d^2*e^4 - 31*a*b^5*d^5*e + 130*a^5*b*d*e^5)/(20*(a^7*e^7 - b^7*d^7 - 21*a^2*b^5*d^5*e^2 + 35*a^3*b^4*d^4*e^3 - 35*a^4*b^3*d^3*e^4 + 21*a^5*b^2*d^2*e^5 + 7*a*b^6*d^6*e - 7*a^6*b*d*e^6)) + (7*e^3*x^3*(77*a^3*b^3*e^3 - b^6*d^3 + 145*a^2*b^4*d*e^2 + 19*a*b^5*d^2*e))/(4*(a^7*e^7 - b^7*d^7 - 21*a^2*b^5*d^5*e^2 + 35*a^3*b^4*d^4*e^3 - 35*a^4*b^3*d^3*e^4 + 21*a^5*b^2*d^2*e^5 + 7*a*b^6*d^6*e - 7*a^6*b*d*e^6)) + (21*b^6*e^6*x^6)/(a^7*e^7 - b^7*d^7 - 21*a^2*b^5*d^5*e^2 + 35*a^3*b^4*d^4*e^3 - 35*a^4*b^3*d^3*e^4 + 21*a^5*b^2*d^2*e^5 + 7*a*b^6*d^6*e - 7*a^6*b*d*e^6) + (7*e^2*x^2*(2*b^6*d^4 + 137*a^4*b^2*e^4 + 607*a^3*b^3*d*e^3 + 177*a^2*b^4*d^2*e^2 - 23*a*b^5*d^3*e))/(20*(a^7*e^7 - b^7*d^7 - 21*a^2*b^5*d^5*e^2 + 35*a^3*b^4*d^4*e^3 - 35*a^4*b^3*d^3*e^4 + 21*a^5*b^2*d^2*e^5 + 7*a*b^6*d^6*e - 7*a^6*b*d*e^6)) + (7*e^4*x^4*(2*b^6*d^2 + 47*a^2*b^4*e^2 + 41*a*b^5*d*e))/(2*(a^7*e^7 - b^7*d^7 - 21*a^2*b^5*d^5*e^2 + 35*a^3*b^4*d^4*e^3 - 35*a^4*b^3*d^3*e^4 + 21*a^5*b^2*d^2*e^5 + 7*a*b^6*d^6*e - 7*a^6*b*d*e^6)) + (7*e*x*(10*a^5*b*e^5 - b^6*d^5 + 224*a^4*b^2*d*e^4 - 41*a^2*b^4*d^3*e^2 + 159*a^3*b^3*d^2*e^3 + 9*a*b^5*d^4*e))/(20*(a^7*e^7 - b^7*d^7 - 21*a^2*b^5*d^5*e^2 + 35*a^3*b^4*d^4*e^3 - 35*a^4*b^3*d^3*e^4 + 21*a^5*b^2*d^2*e^5 + 7*a*b^6*d^6*e - 7*a^6*b*d*e^6)) + (63*b*e^4*x^5*(3*a*b^4*e^2 + b^5*d*e))/(2*(a^7*e^7 - b^7*d^7 - 21*a^2*b^5*d^5*e^2 + 35*a^3*b^4*d^4*e^3 - 35*a^4*b^3*d^3*e^4 + 21*a^5*b^2*d^2*e^5 + 7*a*b^6*d^6*e - 7*a^6*b*d*e^6)))/(x^3*(5*a^4*b*e^2 + 10*a^2*b^3*d^2 + 20*a^3*b^2*d*e) + x^4*(5*a*b^4*d^2 + 10*a^3*b^2*e^2 + 20*a^2*b^3*d*e) + x*(5*a^4*b*d^2 + 2*a^5*d*e) + x^2*(a^5*e^2 + 10*a^3*b^2*d^2 + 10*a^4*b*d*e) + x^5*(b^5*d^2 + 10*a^2*b^3*e^2 + 10*a*b^4*d*e) + x^6*(5*a*b^4*e^2 + 2*b^5*d*e) + a^5*d^2 + b^5*e^2*x^7) - (42*b^2*e^5*atanh((a^8*e^8 - b^8*d^8 - 14*a^2*b^6*d^6*e^2 + 14*a^3*b^5*d^5*e^3 - 14*a^5*b^3*d^3*e^5 + 14*a^6*b^2*d^2*e^6 + 6*a*b^7*d^7*e - 6*a^7*b*d*e^7)/(a*e - b*d)^8 + (2*b*e*x*(a^7*e^7 - b^7*d^7 - 21*a^2*b^5*d^5*e^2 + 35*a^3*b^4*d^4*e^3 - 35*a^4*b^3*d^3*e^4 + 21*a^5*b^2*d^2*e^5 + 7*a*b^6*d^6*e - 7*a^6*b*d*e^6))/(a*e - b*d)^8))/(a*e - b*d)^8","B"
1537,1,77,31,0.062560,"\text{Not used}","int((d + e*x)*(12*x + 4*x^2 + 9)^3,x)","8\,e\,x^8+\left(\frac{64\,d}{7}+\frac{576\,e}{7}\right)\,x^7+\left(96\,d+360\,e\right)\,x^6+\left(432\,d+864\,e\right)\,x^5+\left(1080\,d+1215\,e\right)\,x^4+\left(1620\,d+972\,e\right)\,x^3+\left(1458\,d+\frac{729\,e}{2}\right)\,x^2+729\,d\,x","Not used",1,"x^6*(96*d + 360*e) + x^7*((64*d)/7 + (576*e)/7) + x^5*(432*d + 864*e) + x^2*(1458*d + (729*e)/2) + x^4*(1080*d + 1215*e) + x^3*(1620*d + 972*e) + 729*d*x + 8*e*x^8","B"
1538,1,55,31,0.514240,"\text{Not used}","int((d + e*x)*(12*x + 4*x^2 + 9)^2,x)","\frac{8\,e\,x^6}{3}+\left(\frac{16\,d}{5}+\frac{96\,e}{5}\right)\,x^5+\left(24\,d+54\,e\right)\,x^4+\left(72\,d+72\,e\right)\,x^3+\left(108\,d+\frac{81\,e}{2}\right)\,x^2+81\,d\,x","Not used",1,"x^4*(24*d + 54*e) + x^5*((16*d)/5 + (96*e)/5) + x^3*(72*d + 72*e) + x^2*(108*d + (81*e)/2) + 81*d*x + (8*e*x^6)/3","B"
1539,1,32,31,0.043550,"\text{Not used}","int((d + e*x)*(12*x + 4*x^2 + 9),x)","e\,x^4+\left(\frac{4\,d}{3}+4\,e\right)\,x^3+\left(6\,d+\frac{9\,e}{2}\right)\,x^2+9\,d\,x","Not used",1,"x^3*((4*d)/3 + 4*e) + x^2*(6*d + (9*e)/2) + 9*d*x + e*x^4","B"
1540,1,24,30,0.043564,"\text{Not used}","int((d + e*x)/(12*x + 4*x^2 + 9),x)","\frac{e\,\ln\left(x+\frac{3}{2}\right)}{4}-\frac{\frac{d}{2}-\frac{3\,e}{4}}{2\,x+3}","Not used",1,"(e*log(x + 3/2))/4 - (d/2 - (3*e)/4)/(2*x + 3)","B"
1541,1,20,31,0.040364,"\text{Not used}","int((d + e*x)/(12*x + 4*x^2 + 9)^2,x)","-\frac{4\,d+3\,e+6\,e\,x}{24\,{\left(2\,x+3\right)}^3}","Not used",1,"-(4*d + 3*e + 6*e*x)/(24*(2*x + 3)^3)","B"
1542,1,20,31,0.045879,"\text{Not used}","int((d + e*x)/(12*x + 4*x^2 + 9)^3,x)","-\frac{8\,d+3\,e+10\,e\,x}{80\,{\left(2\,x+3\right)}^5}","Not used",1,"-(8*d + 3*e + 10*e*x)/(80*(2*x + 3)^5)","B"
1543,1,580,92,1.310820,"\text{Not used}","int(((a + b*x)^2)^(1/2)*(d + e*x)^4,x)","d^4\,\left(\frac{x}{2}+\frac{a}{2\,b}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}+\frac{e^4\,x^3\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{6\,b^2}-\frac{a^2\,e^4\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(a^3-5\,a\,b^2\,x^2+3\,b\,x\,\left(a^2+2\,a\,b\,x+b^2\,x^2\right)-4\,a^2\,b\,x\right)}{24\,b^5}+\frac{3\,d^2\,e^2\,x\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{2\,b^2}+\frac{4\,d\,e^3\,x^2\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{5\,b^2}-\frac{3\,a\,e^4\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(4\,b^2\,x^2\,\left(a^2+2\,a\,b\,x+b^2\,x^2\right)-a^4+9\,a^2\,b^2\,x^2+8\,a^3\,b\,x-7\,a\,b\,x\,\left(a^2+2\,a\,b\,x+b^2\,x^2\right)\right)}{40\,b^5}+\frac{d^3\,e\,\left(8\,b^2\,\left(a^2+b^2\,x^2\right)-12\,a^2\,b^2+4\,a\,b^3\,x\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{6\,b^4}-\frac{7\,a\,d\,e^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(a^3-5\,a\,b^2\,x^2+3\,b\,x\,\left(a^2+2\,a\,b\,x+b^2\,x^2\right)-4\,a^2\,b\,x\right)}{15\,b^4}-\frac{3\,a^2\,d^2\,e^2\,\left(\frac{x}{2}+\frac{a}{2\,b}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,b^2}-\frac{5\,a\,d^2\,e^2\,\left(8\,b^2\,\left(a^2+b^2\,x^2\right)-12\,a^2\,b^2+4\,a\,b^3\,x\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{16\,b^5}-\frac{a^2\,d\,e^3\,\left(8\,b^2\,\left(a^2+b^2\,x^2\right)-12\,a^2\,b^2+4\,a\,b^3\,x\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{15\,b^6}","Not used",1,"d^4*(x/2 + a/(2*b))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2) + (e^4*x^3*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2))/(6*b^2) - (a^2*e^4*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*(a^3 - 5*a*b^2*x^2 + 3*b*x*(a^2 + b^2*x^2 + 2*a*b*x) - 4*a^2*b*x))/(24*b^5) + (3*d^2*e^2*x*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2))/(2*b^2) + (4*d*e^3*x^2*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2))/(5*b^2) - (3*a*e^4*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*(4*b^2*x^2*(a^2 + b^2*x^2 + 2*a*b*x) - a^4 + 9*a^2*b^2*x^2 + 8*a^3*b*x - 7*a*b*x*(a^2 + b^2*x^2 + 2*a*b*x)))/(40*b^5) + (d^3*e*(8*b^2*(a^2 + b^2*x^2) - 12*a^2*b^2 + 4*a*b^3*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(6*b^4) - (7*a*d*e^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*(a^3 - 5*a*b^2*x^2 + 3*b*x*(a^2 + b^2*x^2 + 2*a*b*x) - 4*a^2*b*x))/(15*b^4) - (3*a^2*d^2*e^2*(x/2 + a/(2*b))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(2*b^2) - (5*a*d^2*e^2*(8*b^2*(a^2 + b^2*x^2) - 12*a^2*b^2 + 4*a*b^3*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(16*b^5) - (a^2*d*e^3*(8*b^2*(a^2 + b^2*x^2) - 12*a^2*b^2 + 4*a*b^3*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(15*b^6)","B"
1544,1,377,92,0.922796,"\text{Not used}","int(((a + b*x)^2)^(1/2)*(d + e*x)^3,x)","d^3\,\left(\frac{x}{2}+\frac{a}{2\,b}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}+\frac{e^3\,x^2\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{5\,b^2}-\frac{a^2\,e^3\,\left(8\,b^2\,\left(a^2+b^2\,x^2\right)-12\,a^2\,b^2+4\,a\,b^3\,x\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{60\,b^6}-\frac{7\,a\,e^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(a^3-5\,a\,b^2\,x^2+3\,b\,x\,\left(a^2+2\,a\,b\,x+b^2\,x^2\right)-4\,a^2\,b\,x\right)}{60\,b^4}+\frac{d^2\,e\,\left(8\,b^2\,\left(a^2+b^2\,x^2\right)-12\,a^2\,b^2+4\,a\,b^3\,x\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{8\,b^4}+\frac{3\,d\,e^2\,x\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{4\,b^2}-\frac{5\,a\,d\,e^2\,\left(8\,b^2\,\left(a^2+b^2\,x^2\right)-12\,a^2\,b^2+4\,a\,b^3\,x\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{32\,b^5}-\frac{3\,a^2\,d\,e^2\,\left(\frac{x}{2}+\frac{a}{2\,b}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{4\,b^2}","Not used",1,"d^3*(x/2 + a/(2*b))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2) + (e^3*x^2*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2))/(5*b^2) - (a^2*e^3*(8*b^2*(a^2 + b^2*x^2) - 12*a^2*b^2 + 4*a*b^3*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(60*b^6) - (7*a*e^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*(a^3 - 5*a*b^2*x^2 + 3*b*x*(a^2 + b^2*x^2 + 2*a*b*x) - 4*a^2*b*x))/(60*b^4) + (d^2*e*(8*b^2*(a^2 + b^2*x^2) - 12*a^2*b^2 + 4*a*b^3*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(8*b^4) + (3*d*e^2*x*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2))/(4*b^2) - (5*a*d*e^2*(8*b^2*(a^2 + b^2*x^2) - 12*a^2*b^2 + 4*a*b^3*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(32*b^5) - (3*a^2*d*e^2*(x/2 + a/(2*b))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(4*b^2)","B"
1545,1,215,92,0.782362,"\text{Not used}","int(((a + b*x)^2)^(1/2)*(d + e*x)^2,x)","d^2\,\left(\frac{x}{2}+\frac{a}{2\,b}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}+\frac{e^2\,x\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{4\,b^2}+\frac{d\,e\,\left(8\,b^2\,\left(a^2+b^2\,x^2\right)-12\,a^2\,b^2+4\,a\,b^3\,x\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{12\,b^4}-\frac{a^2\,e^2\,\left(\frac{x}{2}+\frac{a}{2\,b}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{4\,b^2}-\frac{5\,a\,e^2\,\left(8\,b^2\,\left(a^2+b^2\,x^2\right)-12\,a^2\,b^2+4\,a\,b^3\,x\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{96\,b^5}","Not used",1,"d^2*(x/2 + a/(2*b))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2) + (e^2*x*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2))/(4*b^2) + (d*e*(8*b^2*(a^2 + b^2*x^2) - 12*a^2*b^2 + 4*a*b^3*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(12*b^4) - (a^2*e^2*(x/2 + a/(2*b))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(4*b^2) - (5*a*e^2*(8*b^2*(a^2 + b^2*x^2) - 12*a^2*b^2 + 4*a*b^3*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(96*b^5)","B"
1546,1,77,69,0.715345,"\text{Not used}","int(((a + b*x)^2)^(1/2)*(d + e*x),x)","\frac{e\,\left(8\,b^2\,\left(a^2+b^2\,x^2\right)-12\,a^2\,b^2+4\,a\,b^3\,x\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{24\,b^4}+\frac{d\,\sqrt{{\left(a+b\,x\right)}^2}\,\left(a+b\,x\right)}{2\,b}","Not used",1,"(e*(8*b^2*(a^2 + b^2*x^2) - 12*a^2*b^2 + 4*a*b^3*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(24*b^4) + (d*((a + b*x)^2)^(1/2)*(a + b*x))/(2*b)","B"
1547,1,19,32,0.560024,"\text{Not used}","int(((a + b*x)^2)^(1/2),x)","\frac{\sqrt{{\left(a+b\,x\right)}^2}\,\left(a+b\,x\right)}{2\,b}","Not used",1,"(((a + b*x)^2)^(1/2)*(a + b*x))/(2*b)","B"
1548,0,-1,80,0.000000,"\text{Not used}","int(((a + b*x)^2)^(1/2)/(d + e*x),x)","\int \frac{\sqrt{{\left(a+b\,x\right)}^2}}{d+e\,x} \,d x","Not used",1,"int(((a + b*x)^2)^(1/2)/(d + e*x), x)","F"
1549,0,-1,85,0.000000,"\text{Not used}","int(((a + b*x)^2)^(1/2)/(d + e*x)^2,x)","\int \frac{\sqrt{{\left(a+b\,x\right)}^2}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int(((a + b*x)^2)^(1/2)/(d + e*x)^2, x)","F"
1550,1,40,46,0.566593,"\text{Not used}","int(((a + b*x)^2)^(1/2)/(d + e*x)^3,x)","-\frac{\sqrt{{\left(a+b\,x\right)}^2}\,\left(a\,e+b\,d+2\,b\,e\,x\right)}{2\,e^2\,\left(a+b\,x\right)\,{\left(d+e\,x\right)}^2}","Not used",1,"-(((a + b*x)^2)^(1/2)*(a*e + b*d + 2*b*e*x))/(2*e^2*(a + b*x)*(d + e*x)^2)","B"
1551,1,41,92,0.568289,"\text{Not used}","int(((a + b*x)^2)^(1/2)/(d + e*x)^4,x)","-\frac{\sqrt{{\left(a+b\,x\right)}^2}\,\left(2\,a\,e+b\,d+3\,b\,e\,x\right)}{6\,e^2\,\left(a+b\,x\right)\,{\left(d+e\,x\right)}^3}","Not used",1,"-(((a + b*x)^2)^(1/2)*(2*a*e + b*d + 3*b*e*x))/(6*e^2*(a + b*x)*(d + e*x)^3)","B"
1552,1,41,92,0.585070,"\text{Not used}","int(((a + b*x)^2)^(1/2)/(d + e*x)^5,x)","-\frac{\sqrt{{\left(a+b\,x\right)}^2}\,\left(3\,a\,e+b\,d+4\,b\,e\,x\right)}{12\,e^2\,\left(a+b\,x\right)\,{\left(d+e\,x\right)}^4}","Not used",1,"-(((a + b*x)^2)^(1/2)*(3*a*e + b*d + 4*b*e*x))/(12*e^2*(a + b*x)*(d + e*x)^4)","B"
1553,1,41,92,0.595736,"\text{Not used}","int(((a + b*x)^2)^(1/2)/(d + e*x)^6,x)","-\frac{\sqrt{{\left(a+b\,x\right)}^2}\,\left(4\,a\,e+b\,d+5\,b\,e\,x\right)}{20\,e^2\,\left(a+b\,x\right)\,{\left(d+e\,x\right)}^5}","Not used",1,"-(((a + b*x)^2)^(1/2)*(4*a*e + b*d + 5*b*e*x))/(20*e^2*(a + b*x)*(d + e*x)^5)","B"
1554,0,-1,200,0.000000,"\text{Not used}","int((d + e*x)^5*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int {\left(d+e\,x\right)}^5\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^5*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1555,0,-1,200,0.000000,"\text{Not used}","int((d + e*x)^4*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int {\left(d+e\,x\right)}^4\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^4*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1556,0,-1,172,0.000000,"\text{Not used}","int((d + e*x)^3*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int {\left(d+e\,x\right)}^3\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^3*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1557,0,-1,114,0.000000,"\text{Not used}","int((d + e*x)^2*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int {\left(d+e\,x\right)}^2\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^2*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1558,1,42,69,0.670314,"\text{Not used}","int((d + e*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\frac{\left(a+b\,x\right)\,\left(5\,b\,d-a\,e+4\,b\,e\,x\right)\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{20\,b^2}","Not used",1,"((a + b*x)*(5*b*d - a*e + 4*b*e*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2))/(20*b^2)","B"
1559,1,32,32,0.047327,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\frac{\left(x\,b^2+a\,b\right)\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{4\,b^2}","Not used",1,"((a*b + b^2*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2))/(4*b^2)","B"
1560,0,-1,166,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x),x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{d+e\,x} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x), x)","F"
1561,0,-1,183,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^2,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^2, x)","F"
1562,0,-1,186,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^3,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^3, x)","F"
1563,0,-1,194,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^4,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}}{{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^4, x)","F"
1564,1,284,48,0.633695,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^5,x)","\frac{\left(\frac{2\,b^3\,d-3\,a\,b^2\,e}{2\,e^4}+\frac{b^3\,d}{2\,e^4}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^2}-\frac{\left(\frac{3\,a^2\,b\,e^2-3\,a\,b^2\,d\,e+b^3\,d^2}{3\,e^4}+\frac{d\,\left(\frac{b^3\,d}{3\,e^3}-\frac{b^2\,\left(3\,a\,e-b\,d\right)}{3\,e^3}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^3}-\frac{\left(\frac{a^3}{4\,e}-\frac{d\,\left(\frac{3\,a^2\,b}{4\,e}-\frac{d\,\left(\frac{3\,a\,b^2}{4\,e}-\frac{b^3\,d}{4\,e^2}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^4}-\frac{b^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{e^4\,\left(a+b\,x\right)\,\left(d+e\,x\right)}","Not used",1,"(((2*b^3*d - 3*a*b^2*e)/(2*e^4) + (b^3*d)/(2*e^4))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^2) - (((b^3*d^2 + 3*a^2*b*e^2 - 3*a*b^2*d*e)/(3*e^4) + (d*((b^3*d)/(3*e^3) - (b^2*(3*a*e - b*d))/(3*e^3)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^3) - ((a^3/(4*e) - (d*((3*a^2*b)/(4*e) - (d*((3*a*b^2)/(4*e) - (b^3*d)/(4*e^2)))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^4) - (b^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(e^4*(a + b*x)*(d + e*x))","B"
1565,1,284,98,0.625809,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^6,x)","\frac{\left(\frac{2\,b^3\,d-3\,a\,b^2\,e}{3\,e^4}+\frac{b^3\,d}{3\,e^4}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^3}-\frac{\left(\frac{3\,a^2\,b\,e^2-3\,a\,b^2\,d\,e+b^3\,d^2}{4\,e^4}+\frac{d\,\left(\frac{b^3\,d}{4\,e^3}-\frac{b^2\,\left(3\,a\,e-b\,d\right)}{4\,e^3}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^4}-\frac{\left(\frac{a^3}{5\,e}-\frac{d\,\left(\frac{3\,a^2\,b}{5\,e}-\frac{d\,\left(\frac{3\,a\,b^2}{5\,e}-\frac{b^3\,d}{5\,e^2}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^5}-\frac{b^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,e^4\,\left(a+b\,x\right)\,{\left(d+e\,x\right)}^2}","Not used",1,"(((2*b^3*d - 3*a*b^2*e)/(3*e^4) + (b^3*d)/(3*e^4))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^3) - (((b^3*d^2 + 3*a^2*b*e^2 - 3*a*b^2*d*e)/(4*e^4) + (d*((b^3*d)/(4*e^3) - (b^2*(3*a*e - b*d))/(4*e^3)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^4) - ((a^3/(5*e) - (d*((3*a^2*b)/(5*e) - (d*((3*a*b^2)/(5*e) - (b^3*d)/(5*e^2)))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^5) - (b^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(2*e^4*(a + b*x)*(d + e*x)^2)","B"
1566,1,284,143,0.641372,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^7,x)","\frac{\left(\frac{2\,b^3\,d-3\,a\,b^2\,e}{4\,e^4}+\frac{b^3\,d}{4\,e^4}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^4}-\frac{\left(\frac{3\,a^2\,b\,e^2-3\,a\,b^2\,d\,e+b^3\,d^2}{5\,e^4}+\frac{d\,\left(\frac{b^3\,d}{5\,e^3}-\frac{b^2\,\left(3\,a\,e-b\,d\right)}{5\,e^3}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^5}-\frac{\left(\frac{a^3}{6\,e}-\frac{d\,\left(\frac{a^2\,b}{2\,e}-\frac{d\,\left(\frac{a\,b^2}{2\,e}-\frac{b^3\,d}{6\,e^2}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^6}-\frac{b^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{3\,e^4\,\left(a+b\,x\right)\,{\left(d+e\,x\right)}^3}","Not used",1,"(((2*b^3*d - 3*a*b^2*e)/(4*e^4) + (b^3*d)/(4*e^4))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^4) - (((b^3*d^2 + 3*a^2*b*e^2 - 3*a*b^2*d*e)/(5*e^4) + (d*((b^3*d)/(5*e^3) - (b^2*(3*a*e - b*d))/(5*e^3)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^5) - ((a^3/(6*e) - (d*((a^2*b)/(2*e) - (d*((a*b^2)/(2*e) - (b^3*d)/(6*e^2)))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^6) - (b^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(3*e^4*(a + b*x)*(d + e*x)^3)","B"
1567,1,284,200,0.647162,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^8,x)","\frac{\left(\frac{2\,b^3\,d-3\,a\,b^2\,e}{5\,e^4}+\frac{b^3\,d}{5\,e^4}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^5}-\frac{\left(\frac{3\,a^2\,b\,e^2-3\,a\,b^2\,d\,e+b^3\,d^2}{6\,e^4}+\frac{d\,\left(\frac{b^3\,d}{6\,e^3}-\frac{b^2\,\left(3\,a\,e-b\,d\right)}{6\,e^3}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^6}-\frac{\left(\frac{a^3}{7\,e}-\frac{d\,\left(\frac{3\,a^2\,b}{7\,e}-\frac{d\,\left(\frac{3\,a\,b^2}{7\,e}-\frac{b^3\,d}{7\,e^2}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^7}-\frac{b^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{4\,e^4\,\left(a+b\,x\right)\,{\left(d+e\,x\right)}^4}","Not used",1,"(((2*b^3*d - 3*a*b^2*e)/(5*e^4) + (b^3*d)/(5*e^4))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^5) - (((b^3*d^2 + 3*a^2*b*e^2 - 3*a*b^2*d*e)/(6*e^4) + (d*((b^3*d)/(6*e^3) - (b^2*(3*a*e - b*d))/(6*e^3)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^6) - ((a^3/(7*e) - (d*((3*a^2*b)/(7*e) - (d*((3*a*b^2)/(7*e) - (b^3*d)/(7*e^2)))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^7) - (b^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(4*e^4*(a + b*x)*(d + e*x)^4)","B"
1568,1,284,200,0.663952,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^9,x)","\frac{\left(\frac{2\,b^3\,d-3\,a\,b^2\,e}{6\,e^4}+\frac{b^3\,d}{6\,e^4}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^6}-\frac{\left(\frac{3\,a^2\,b\,e^2-3\,a\,b^2\,d\,e+b^3\,d^2}{7\,e^4}+\frac{d\,\left(\frac{b^3\,d}{7\,e^3}-\frac{b^2\,\left(3\,a\,e-b\,d\right)}{7\,e^3}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^7}-\frac{\left(\frac{a^3}{8\,e}-\frac{d\,\left(\frac{3\,a^2\,b}{8\,e}-\frac{d\,\left(\frac{3\,a\,b^2}{8\,e}-\frac{b^3\,d}{8\,e^2}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^8}-\frac{b^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{5\,e^4\,\left(a+b\,x\right)\,{\left(d+e\,x\right)}^5}","Not used",1,"(((2*b^3*d - 3*a*b^2*e)/(6*e^4) + (b^3*d)/(6*e^4))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^6) - (((b^3*d^2 + 3*a^2*b*e^2 - 3*a*b^2*d*e)/(7*e^4) + (d*((b^3*d)/(7*e^3) - (b^2*(3*a*e - b*d))/(7*e^3)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^7) - ((a^3/(8*e) - (d*((3*a^2*b)/(8*e) - (d*((3*a*b^2)/(8*e) - (b^3*d)/(8*e^2)))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^8) - (b^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(5*e^4*(a + b*x)*(d + e*x)^5)","B"
1569,0,-1,266,0.000000,"\text{Not used}","int((d + e*x)^5*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int {\left(d+e\,x\right)}^5\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)^5*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1570,0,-1,219,0.000000,"\text{Not used}","int((d + e*x)^4*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int {\left(d+e\,x\right)}^4\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)^4*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1571,0,-1,172,0.000000,"\text{Not used}","int((d + e*x)^3*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int {\left(d+e\,x\right)}^3\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)^3*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1572,0,-1,125,0.000000,"\text{Not used}","int((d + e*x)^2*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int {\left(d+e\,x\right)}^2\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)^2*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1573,0,-1,69,0.000000,"\text{Not used}","int((d + e*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int \left(d+e\,x\right)\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1574,1,32,32,0.514865,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\frac{\left(x\,b^2+a\,b\right)\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}}{6\,b^2}","Not used",1,"((a*b + b^2*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2))/(6*b^2)","B"
1575,0,-1,254,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x),x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}}{d+e\,x} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x), x)","F"
1576,0,-1,292,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^2,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^2, x)","F"
1577,0,-1,295,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^3,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^3, x)","F"
1578,0,-1,292,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^4,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}}{{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^4, x)","F"
1579,0,-1,292,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^5,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}}{{\left(d+e\,x\right)}^5} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^5, x)","F"
1580,0,-1,300,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^6,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}}{{\left(d+e\,x\right)}^6} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^6, x)","F"
1581,1,687,48,0.736307,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^7,x)","\frac{\left(\frac{4\,b^5\,d-5\,a\,b^4\,e}{2\,e^6}+\frac{b^5\,d}{2\,e^6}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^2}-\frac{\left(\frac{5\,a^4\,b\,e^4-10\,a^3\,b^2\,d\,e^3+10\,a^2\,b^3\,d^2\,e^2-5\,a\,b^4\,d^3\,e+b^5\,d^4}{5\,e^6}+\frac{d\,\left(\frac{-10\,a^3\,b^2\,e^4+10\,a^2\,b^3\,d\,e^3-5\,a\,b^4\,d^2\,e^2+b^5\,d^3\,e}{5\,e^6}+\frac{d\,\left(\frac{d\,\left(\frac{b^5\,d}{5\,e^3}-\frac{b^4\,\left(5\,a\,e-b\,d\right)}{5\,e^3}\right)}{e}+\frac{b^3\,\left(10\,a^2\,e^2-5\,a\,b\,d\,e+b^2\,d^2\right)}{5\,e^4}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^5}-\frac{\left(\frac{10\,a^2\,b^3\,e^2-15\,a\,b^4\,d\,e+6\,b^5\,d^2}{3\,e^6}+\frac{d\,\left(\frac{b^5\,d}{3\,e^5}-\frac{b^4\,\left(5\,a\,e-3\,b\,d\right)}{3\,e^5}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^3}-\frac{\left(\frac{a^5}{6\,e}-\frac{d\,\left(\frac{5\,a^4\,b}{6\,e}-\frac{d\,\left(\frac{d\,\left(\frac{d\,\left(\frac{5\,a\,b^4}{6\,e}-\frac{b^5\,d}{6\,e^2}\right)}{e}-\frac{5\,a^2\,b^3}{3\,e}\right)}{e}+\frac{5\,a^3\,b^2}{3\,e}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^6}+\frac{\left(\frac{-10\,a^3\,b^2\,e^3+20\,a^2\,b^3\,d\,e^2-15\,a\,b^4\,d^2\,e+4\,b^5\,d^3}{4\,e^6}+\frac{d\,\left(\frac{d\,\left(\frac{b^5\,d}{4\,e^4}-\frac{b^4\,\left(5\,a\,e-2\,b\,d\right)}{4\,e^4}\right)}{e}+\frac{b^3\,\left(10\,a^2\,e^2-10\,a\,b\,d\,e+3\,b^2\,d^2\right)}{4\,e^5}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^4}-\frac{b^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{e^6\,\left(a+b\,x\right)\,\left(d+e\,x\right)}","Not used",1,"(((4*b^5*d - 5*a*b^4*e)/(2*e^6) + (b^5*d)/(2*e^6))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^2) - (((b^5*d^4 + 5*a^4*b*e^4 - 10*a^3*b^2*d*e^3 + 10*a^2*b^3*d^2*e^2 - 5*a*b^4*d^3*e)/(5*e^6) + (d*((b^5*d^3*e - 10*a^3*b^2*e^4 - 5*a*b^4*d^2*e^2 + 10*a^2*b^3*d*e^3)/(5*e^6) + (d*((d*((b^5*d)/(5*e^3) - (b^4*(5*a*e - b*d))/(5*e^3)))/e + (b^3*(10*a^2*e^2 + b^2*d^2 - 5*a*b*d*e))/(5*e^4)))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^5) - (((6*b^5*d^2 + 10*a^2*b^3*e^2 - 15*a*b^4*d*e)/(3*e^6) + (d*((b^5*d)/(3*e^5) - (b^4*(5*a*e - 3*b*d))/(3*e^5)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^3) - ((a^5/(6*e) - (d*((5*a^4*b)/(6*e) - (d*((d*((d*((5*a*b^4)/(6*e) - (b^5*d)/(6*e^2)))/e - (5*a^2*b^3)/(3*e)))/e + (5*a^3*b^2)/(3*e)))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^6) + (((4*b^5*d^3 - 10*a^3*b^2*e^3 + 20*a^2*b^3*d*e^2 - 15*a*b^4*d^2*e)/(4*e^6) + (d*((d*((b^5*d)/(4*e^4) - (b^4*(5*a*e - 2*b*d))/(4*e^4)))/e + (b^3*(10*a^2*e^2 + 3*b^2*d^2 - 10*a*b*d*e))/(4*e^5)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^4) - (b^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(e^6*(a + b*x)*(d + e*x))","B"
1582,1,687,98,0.738409,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^8,x)","\frac{\left(\frac{4\,b^5\,d-5\,a\,b^4\,e}{3\,e^6}+\frac{b^5\,d}{3\,e^6}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^3}-\frac{\left(\frac{5\,a^4\,b\,e^4-10\,a^3\,b^2\,d\,e^3+10\,a^2\,b^3\,d^2\,e^2-5\,a\,b^4\,d^3\,e+b^5\,d^4}{6\,e^6}+\frac{d\,\left(\frac{-10\,a^3\,b^2\,e^4+10\,a^2\,b^3\,d\,e^3-5\,a\,b^4\,d^2\,e^2+b^5\,d^3\,e}{6\,e^6}+\frac{d\,\left(\frac{d\,\left(\frac{b^5\,d}{6\,e^3}-\frac{b^4\,\left(5\,a\,e-b\,d\right)}{6\,e^3}\right)}{e}+\frac{b^3\,\left(10\,a^2\,e^2-5\,a\,b\,d\,e+b^2\,d^2\right)}{6\,e^4}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^6}-\frac{\left(\frac{10\,a^2\,b^3\,e^2-15\,a\,b^4\,d\,e+6\,b^5\,d^2}{4\,e^6}+\frac{d\,\left(\frac{b^5\,d}{4\,e^5}-\frac{b^4\,\left(5\,a\,e-3\,b\,d\right)}{4\,e^5}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^4}-\frac{\left(\frac{a^5}{7\,e}-\frac{d\,\left(\frac{5\,a^4\,b}{7\,e}-\frac{d\,\left(\frac{d\,\left(\frac{d\,\left(\frac{5\,a\,b^4}{7\,e}-\frac{b^5\,d}{7\,e^2}\right)}{e}-\frac{10\,a^2\,b^3}{7\,e}\right)}{e}+\frac{10\,a^3\,b^2}{7\,e}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^7}+\frac{\left(\frac{-10\,a^3\,b^2\,e^3+20\,a^2\,b^3\,d\,e^2-15\,a\,b^4\,d^2\,e+4\,b^5\,d^3}{5\,e^6}+\frac{d\,\left(\frac{d\,\left(\frac{b^5\,d}{5\,e^4}-\frac{b^4\,\left(5\,a\,e-2\,b\,d\right)}{5\,e^4}\right)}{e}+\frac{b^3\,\left(10\,a^2\,e^2-10\,a\,b\,d\,e+3\,b^2\,d^2\right)}{5\,e^5}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^5}-\frac{b^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,e^6\,\left(a+b\,x\right)\,{\left(d+e\,x\right)}^2}","Not used",1,"(((4*b^5*d - 5*a*b^4*e)/(3*e^6) + (b^5*d)/(3*e^6))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^3) - (((b^5*d^4 + 5*a^4*b*e^4 - 10*a^3*b^2*d*e^3 + 10*a^2*b^3*d^2*e^2 - 5*a*b^4*d^3*e)/(6*e^6) + (d*((b^5*d^3*e - 10*a^3*b^2*e^4 - 5*a*b^4*d^2*e^2 + 10*a^2*b^3*d*e^3)/(6*e^6) + (d*((d*((b^5*d)/(6*e^3) - (b^4*(5*a*e - b*d))/(6*e^3)))/e + (b^3*(10*a^2*e^2 + b^2*d^2 - 5*a*b*d*e))/(6*e^4)))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^6) - (((6*b^5*d^2 + 10*a^2*b^3*e^2 - 15*a*b^4*d*e)/(4*e^6) + (d*((b^5*d)/(4*e^5) - (b^4*(5*a*e - 3*b*d))/(4*e^5)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^4) - ((a^5/(7*e) - (d*((5*a^4*b)/(7*e) - (d*((d*((d*((5*a*b^4)/(7*e) - (b^5*d)/(7*e^2)))/e - (10*a^2*b^3)/(7*e)))/e + (10*a^3*b^2)/(7*e)))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^7) + (((4*b^5*d^3 - 10*a^3*b^2*e^3 + 20*a^2*b^3*d*e^2 - 15*a*b^4*d^2*e)/(5*e^6) + (d*((d*((b^5*d)/(5*e^4) - (b^4*(5*a*e - 2*b*d))/(5*e^4)))/e + (b^3*(10*a^2*e^2 + 3*b^2*d^2 - 10*a*b*d*e))/(5*e^5)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^5) - (b^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(2*e^6*(a + b*x)*(d + e*x)^2)","B"
1583,1,687,149,0.742158,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^9,x)","\frac{\left(\frac{4\,b^5\,d-5\,a\,b^4\,e}{4\,e^6}+\frac{b^5\,d}{4\,e^6}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^4}-\frac{\left(\frac{5\,a^4\,b\,e^4-10\,a^3\,b^2\,d\,e^3+10\,a^2\,b^3\,d^2\,e^2-5\,a\,b^4\,d^3\,e+b^5\,d^4}{7\,e^6}+\frac{d\,\left(\frac{-10\,a^3\,b^2\,e^4+10\,a^2\,b^3\,d\,e^3-5\,a\,b^4\,d^2\,e^2+b^5\,d^3\,e}{7\,e^6}+\frac{d\,\left(\frac{d\,\left(\frac{b^5\,d}{7\,e^3}-\frac{b^4\,\left(5\,a\,e-b\,d\right)}{7\,e^3}\right)}{e}+\frac{b^3\,\left(10\,a^2\,e^2-5\,a\,b\,d\,e+b^2\,d^2\right)}{7\,e^4}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^7}-\frac{\left(\frac{10\,a^2\,b^3\,e^2-15\,a\,b^4\,d\,e+6\,b^5\,d^2}{5\,e^6}+\frac{d\,\left(\frac{b^5\,d}{5\,e^5}-\frac{b^4\,\left(5\,a\,e-3\,b\,d\right)}{5\,e^5}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^5}-\frac{\left(\frac{a^5}{8\,e}-\frac{d\,\left(\frac{5\,a^4\,b}{8\,e}-\frac{d\,\left(\frac{d\,\left(\frac{d\,\left(\frac{5\,a\,b^4}{8\,e}-\frac{b^5\,d}{8\,e^2}\right)}{e}-\frac{5\,a^2\,b^3}{4\,e}\right)}{e}+\frac{5\,a^3\,b^2}{4\,e}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^8}+\frac{\left(\frac{-10\,a^3\,b^2\,e^3+20\,a^2\,b^3\,d\,e^2-15\,a\,b^4\,d^2\,e+4\,b^5\,d^3}{6\,e^6}+\frac{d\,\left(\frac{d\,\left(\frac{b^5\,d}{6\,e^4}-\frac{b^4\,\left(5\,a\,e-2\,b\,d\right)}{6\,e^4}\right)}{e}+\frac{b^3\,\left(10\,a^2\,e^2-10\,a\,b\,d\,e+3\,b^2\,d^2\right)}{6\,e^5}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^6}-\frac{b^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{3\,e^6\,\left(a+b\,x\right)\,{\left(d+e\,x\right)}^3}","Not used",1,"(((4*b^5*d - 5*a*b^4*e)/(4*e^6) + (b^5*d)/(4*e^6))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^4) - (((b^5*d^4 + 5*a^4*b*e^4 - 10*a^3*b^2*d*e^3 + 10*a^2*b^3*d^2*e^2 - 5*a*b^4*d^3*e)/(7*e^6) + (d*((b^5*d^3*e - 10*a^3*b^2*e^4 - 5*a*b^4*d^2*e^2 + 10*a^2*b^3*d*e^3)/(7*e^6) + (d*((d*((b^5*d)/(7*e^3) - (b^4*(5*a*e - b*d))/(7*e^3)))/e + (b^3*(10*a^2*e^2 + b^2*d^2 - 5*a*b*d*e))/(7*e^4)))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^7) - (((6*b^5*d^2 + 10*a^2*b^3*e^2 - 15*a*b^4*d*e)/(5*e^6) + (d*((b^5*d)/(5*e^5) - (b^4*(5*a*e - 3*b*d))/(5*e^5)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^5) - ((a^5/(8*e) - (d*((5*a^4*b)/(8*e) - (d*((d*((d*((5*a*b^4)/(8*e) - (b^5*d)/(8*e^2)))/e - (5*a^2*b^3)/(4*e)))/e + (5*a^3*b^2)/(4*e)))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^8) + (((4*b^5*d^3 - 10*a^3*b^2*e^3 + 20*a^2*b^3*d*e^2 - 15*a*b^4*d^2*e)/(6*e^6) + (d*((d*((b^5*d)/(6*e^4) - (b^4*(5*a*e - 2*b*d))/(6*e^4)))/e + (b^3*(10*a^2*e^2 + 3*b^2*d^2 - 10*a*b*d*e))/(6*e^5)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^6) - (b^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(3*e^6*(a + b*x)*(d + e*x)^3)","B"
1584,1,687,200,0.756892,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^10,x)","\frac{\left(\frac{4\,b^5\,d-5\,a\,b^4\,e}{5\,e^6}+\frac{b^5\,d}{5\,e^6}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^5}-\frac{\left(\frac{5\,a^4\,b\,e^4-10\,a^3\,b^2\,d\,e^3+10\,a^2\,b^3\,d^2\,e^2-5\,a\,b^4\,d^3\,e+b^5\,d^4}{8\,e^6}+\frac{d\,\left(\frac{-10\,a^3\,b^2\,e^4+10\,a^2\,b^3\,d\,e^3-5\,a\,b^4\,d^2\,e^2+b^5\,d^3\,e}{8\,e^6}+\frac{d\,\left(\frac{d\,\left(\frac{b^5\,d}{8\,e^3}-\frac{b^4\,\left(5\,a\,e-b\,d\right)}{8\,e^3}\right)}{e}+\frac{b^3\,\left(10\,a^2\,e^2-5\,a\,b\,d\,e+b^2\,d^2\right)}{8\,e^4}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^8}-\frac{\left(\frac{10\,a^2\,b^3\,e^2-15\,a\,b^4\,d\,e+6\,b^5\,d^2}{6\,e^6}+\frac{d\,\left(\frac{b^5\,d}{6\,e^5}-\frac{b^4\,\left(5\,a\,e-3\,b\,d\right)}{6\,e^5}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^6}-\frac{\left(\frac{a^5}{9\,e}-\frac{d\,\left(\frac{5\,a^4\,b}{9\,e}-\frac{d\,\left(\frac{d\,\left(\frac{d\,\left(\frac{5\,a\,b^4}{9\,e}-\frac{b^5\,d}{9\,e^2}\right)}{e}-\frac{10\,a^2\,b^3}{9\,e}\right)}{e}+\frac{10\,a^3\,b^2}{9\,e}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^9}+\frac{\left(\frac{-10\,a^3\,b^2\,e^3+20\,a^2\,b^3\,d\,e^2-15\,a\,b^4\,d^2\,e+4\,b^5\,d^3}{7\,e^6}+\frac{d\,\left(\frac{d\,\left(\frac{b^5\,d}{7\,e^4}-\frac{b^4\,\left(5\,a\,e-2\,b\,d\right)}{7\,e^4}\right)}{e}+\frac{b^3\,\left(10\,a^2\,e^2-10\,a\,b\,d\,e+3\,b^2\,d^2\right)}{7\,e^5}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^7}-\frac{b^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{4\,e^6\,\left(a+b\,x\right)\,{\left(d+e\,x\right)}^4}","Not used",1,"(((4*b^5*d - 5*a*b^4*e)/(5*e^6) + (b^5*d)/(5*e^6))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^5) - (((b^5*d^4 + 5*a^4*b*e^4 - 10*a^3*b^2*d*e^3 + 10*a^2*b^3*d^2*e^2 - 5*a*b^4*d^3*e)/(8*e^6) + (d*((b^5*d^3*e - 10*a^3*b^2*e^4 - 5*a*b^4*d^2*e^2 + 10*a^2*b^3*d*e^3)/(8*e^6) + (d*((d*((b^5*d)/(8*e^3) - (b^4*(5*a*e - b*d))/(8*e^3)))/e + (b^3*(10*a^2*e^2 + b^2*d^2 - 5*a*b*d*e))/(8*e^4)))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^8) - (((6*b^5*d^2 + 10*a^2*b^3*e^2 - 15*a*b^4*d*e)/(6*e^6) + (d*((b^5*d)/(6*e^5) - (b^4*(5*a*e - 3*b*d))/(6*e^5)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^6) - ((a^5/(9*e) - (d*((5*a^4*b)/(9*e) - (d*((d*((d*((5*a*b^4)/(9*e) - (b^5*d)/(9*e^2)))/e - (10*a^2*b^3)/(9*e)))/e + (10*a^3*b^2)/(9*e)))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^9) + (((4*b^5*d^3 - 10*a^3*b^2*e^3 + 20*a^2*b^3*d*e^2 - 15*a*b^4*d^2*e)/(7*e^6) + (d*((d*((b^5*d)/(7*e^4) - (b^4*(5*a*e - 2*b*d))/(7*e^4)))/e + (b^3*(10*a^2*e^2 + 3*b^2*d^2 - 10*a*b*d*e))/(7*e^5)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^7) - (b^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(4*e^6*(a + b*x)*(d + e*x)^4)","B"
1585,1,686,308,0.757367,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^11,x)","\frac{\left(\frac{4\,b^5\,d-5\,a\,b^4\,e}{6\,e^6}+\frac{b^5\,d}{6\,e^6}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^6}-\frac{\left(\frac{5\,a^4\,b\,e^4-10\,a^3\,b^2\,d\,e^3+10\,a^2\,b^3\,d^2\,e^2-5\,a\,b^4\,d^3\,e+b^5\,d^4}{9\,e^6}+\frac{d\,\left(\frac{-10\,a^3\,b^2\,e^4+10\,a^2\,b^3\,d\,e^3-5\,a\,b^4\,d^2\,e^2+b^5\,d^3\,e}{9\,e^6}+\frac{d\,\left(\frac{d\,\left(\frac{b^5\,d}{9\,e^3}-\frac{b^4\,\left(5\,a\,e-b\,d\right)}{9\,e^3}\right)}{e}+\frac{b^3\,\left(10\,a^2\,e^2-5\,a\,b\,d\,e+b^2\,d^2\right)}{9\,e^4}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^9}-\frac{\left(\frac{10\,a^2\,b^3\,e^2-15\,a\,b^4\,d\,e+6\,b^5\,d^2}{7\,e^6}+\frac{d\,\left(\frac{b^5\,d}{7\,e^5}-\frac{b^4\,\left(5\,a\,e-3\,b\,d\right)}{7\,e^5}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^7}-\frac{\left(\frac{a^5}{10\,e}-\frac{d\,\left(\frac{a^4\,b}{2\,e}-\frac{d\,\left(\frac{d\,\left(\frac{d\,\left(\frac{a\,b^4}{2\,e}-\frac{b^5\,d}{10\,e^2}\right)}{e}-\frac{a^2\,b^3}{e}\right)}{e}+\frac{a^3\,b^2}{e}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^{10}}+\frac{\left(\frac{-10\,a^3\,b^2\,e^3+20\,a^2\,b^3\,d\,e^2-15\,a\,b^4\,d^2\,e+4\,b^5\,d^3}{8\,e^6}+\frac{d\,\left(\frac{d\,\left(\frac{b^5\,d}{8\,e^4}-\frac{b^4\,\left(5\,a\,e-2\,b\,d\right)}{8\,e^4}\right)}{e}+\frac{b^3\,\left(10\,a^2\,e^2-10\,a\,b\,d\,e+3\,b^2\,d^2\right)}{8\,e^5}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^8}-\frac{b^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{5\,e^6\,\left(a+b\,x\right)\,{\left(d+e\,x\right)}^5}","Not used",1,"(((4*b^5*d - 5*a*b^4*e)/(6*e^6) + (b^5*d)/(6*e^6))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^6) - (((b^5*d^4 + 5*a^4*b*e^4 - 10*a^3*b^2*d*e^3 + 10*a^2*b^3*d^2*e^2 - 5*a*b^4*d^3*e)/(9*e^6) + (d*((b^5*d^3*e - 10*a^3*b^2*e^4 - 5*a*b^4*d^2*e^2 + 10*a^2*b^3*d*e^3)/(9*e^6) + (d*((d*((b^5*d)/(9*e^3) - (b^4*(5*a*e - b*d))/(9*e^3)))/e + (b^3*(10*a^2*e^2 + b^2*d^2 - 5*a*b*d*e))/(9*e^4)))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^9) - (((6*b^5*d^2 + 10*a^2*b^3*e^2 - 15*a*b^4*d*e)/(7*e^6) + (d*((b^5*d)/(7*e^5) - (b^4*(5*a*e - 3*b*d))/(7*e^5)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^7) - ((a^5/(10*e) - (d*((a^4*b)/(2*e) - (d*((d*((d*((a*b^4)/(2*e) - (b^5*d)/(10*e^2)))/e - (a^2*b^3)/e))/e + (a^3*b^2)/e))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^10) + (((4*b^5*d^3 - 10*a^3*b^2*e^3 + 20*a^2*b^3*d*e^2 - 15*a*b^4*d^2*e)/(8*e^6) + (d*((d*((b^5*d)/(8*e^4) - (b^4*(5*a*e - 2*b*d))/(8*e^4)))/e + (b^3*(10*a^2*e^2 + 3*b^2*d^2 - 10*a*b*d*e))/(8*e^5)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^8) - (b^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(5*e^6*(a + b*x)*(d + e*x)^5)","B"
1586,1,687,308,0.772711,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^12,x)","\frac{\left(\frac{4\,b^5\,d-5\,a\,b^4\,e}{7\,e^6}+\frac{b^5\,d}{7\,e^6}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^7}-\frac{\left(\frac{5\,a^4\,b\,e^4-10\,a^3\,b^2\,d\,e^3+10\,a^2\,b^3\,d^2\,e^2-5\,a\,b^4\,d^3\,e+b^5\,d^4}{10\,e^6}+\frac{d\,\left(\frac{-10\,a^3\,b^2\,e^4+10\,a^2\,b^3\,d\,e^3-5\,a\,b^4\,d^2\,e^2+b^5\,d^3\,e}{10\,e^6}+\frac{d\,\left(\frac{d\,\left(\frac{b^5\,d}{10\,e^3}-\frac{b^4\,\left(5\,a\,e-b\,d\right)}{10\,e^3}\right)}{e}+\frac{b^3\,\left(10\,a^2\,e^2-5\,a\,b\,d\,e+b^2\,d^2\right)}{10\,e^4}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^{10}}-\frac{\left(\frac{10\,a^2\,b^3\,e^2-15\,a\,b^4\,d\,e+6\,b^5\,d^2}{8\,e^6}+\frac{d\,\left(\frac{b^5\,d}{8\,e^5}-\frac{b^4\,\left(5\,a\,e-3\,b\,d\right)}{8\,e^5}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^8}-\frac{\left(\frac{a^5}{11\,e}-\frac{d\,\left(\frac{5\,a^4\,b}{11\,e}-\frac{d\,\left(\frac{d\,\left(\frac{d\,\left(\frac{5\,a\,b^4}{11\,e}-\frac{b^5\,d}{11\,e^2}\right)}{e}-\frac{10\,a^2\,b^3}{11\,e}\right)}{e}+\frac{10\,a^3\,b^2}{11\,e}\right)}{e}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^{11}}+\frac{\left(\frac{-10\,a^3\,b^2\,e^3+20\,a^2\,b^3\,d\,e^2-15\,a\,b^4\,d^2\,e+4\,b^5\,d^3}{9\,e^6}+\frac{d\,\left(\frac{d\,\left(\frac{b^5\,d}{9\,e^4}-\frac{b^4\,\left(5\,a\,e-2\,b\,d\right)}{9\,e^4}\right)}{e}+\frac{b^3\,\left(10\,a^2\,e^2-10\,a\,b\,d\,e+3\,b^2\,d^2\right)}{9\,e^5}\right)}{e}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{\left(a+b\,x\right)\,{\left(d+e\,x\right)}^9}-\frac{b^5\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{6\,e^6\,\left(a+b\,x\right)\,{\left(d+e\,x\right)}^6}","Not used",1,"(((4*b^5*d - 5*a*b^4*e)/(7*e^6) + (b^5*d)/(7*e^6))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^7) - (((b^5*d^4 + 5*a^4*b*e^4 - 10*a^3*b^2*d*e^3 + 10*a^2*b^3*d^2*e^2 - 5*a*b^4*d^3*e)/(10*e^6) + (d*((b^5*d^3*e - 10*a^3*b^2*e^4 - 5*a*b^4*d^2*e^2 + 10*a^2*b^3*d*e^3)/(10*e^6) + (d*((d*((b^5*d)/(10*e^3) - (b^4*(5*a*e - b*d))/(10*e^3)))/e + (b^3*(10*a^2*e^2 + b^2*d^2 - 5*a*b*d*e))/(10*e^4)))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^10) - (((6*b^5*d^2 + 10*a^2*b^3*e^2 - 15*a*b^4*d*e)/(8*e^6) + (d*((b^5*d)/(8*e^5) - (b^4*(5*a*e - 3*b*d))/(8*e^5)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^8) - ((a^5/(11*e) - (d*((5*a^4*b)/(11*e) - (d*((d*((d*((5*a*b^4)/(11*e) - (b^5*d)/(11*e^2)))/e - (10*a^2*b^3)/(11*e)))/e + (10*a^3*b^2)/(11*e)))/e))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^11) + (((4*b^5*d^3 - 10*a^3*b^2*e^3 + 20*a^2*b^3*d*e^2 - 15*a*b^4*d^2*e)/(9*e^6) + (d*((d*((b^5*d)/(9*e^4) - (b^4*(5*a*e - 2*b*d))/(9*e^4)))/e + (b^3*(10*a^2*e^2 + 3*b^2*d^2 - 10*a*b*d*e))/(9*e^5)))/e)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/((a + b*x)*(d + e*x)^9) - (b^5*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(6*e^6*(a + b*x)*(d + e*x)^6)","B"
1587,0,-1,222,0.000000,"\text{Not used}","int((d + e*x)^4/((a + b*x)^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{\sqrt{{\left(a+b\,x\right)}^2}} \,d x","Not used",1,"int((d + e*x)^4/((a + b*x)^2)^(1/2), x)","F"
1588,0,-1,173,0.000000,"\text{Not used}","int((d + e*x)^3/((a + b*x)^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^3}{\sqrt{{\left(a+b\,x\right)}^2}} \,d x","Not used",1,"int((d + e*x)^3/((a + b*x)^2)^(1/2), x)","F"
1589,0,-1,124,0.000000,"\text{Not used}","int((d + e*x)^2/((a + b*x)^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^2}{\sqrt{{\left(a+b\,x\right)}^2}} \,d x","Not used",1,"int((d + e*x)^2/((a + b*x)^2)^(1/2), x)","F"
1590,1,79,69,0.939986,"\text{Not used}","int((d + e*x)/((a + b*x)^2)^(1/2),x)","\frac{e\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{b^2}+\frac{d\,\ln\left(a+b\,x+\sqrt{{\left(a+b\,x\right)}^2}\right)}{b}-\frac{a\,b\,e\,\ln\left(a\,b+\sqrt{{\left(a+b\,x\right)}^2}\,\sqrt{b^2}+b^2\,x\right)}{{\left(b^2\right)}^{3/2}}","Not used",1,"(e*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/b^2 + (d*log(a + b*x + ((a + b*x)^2)^(1/2)))/b - (a*b*e*log(a*b + ((a + b*x)^2)^(1/2)*(b^2)^(1/2) + b^2*x))/(b^2)^(3/2)","B"
1591,1,19,35,0.582220,"\text{Not used}","int(1/((a + b*x)^2)^(1/2),x)","\frac{\ln\left(a+b\,x+\sqrt{{\left(a+b\,x\right)}^2}\right)}{b}","Not used",1,"log(a + b*x + ((a + b*x)^2)^(1/2))/b","B"
1592,0,-1,86,0.000000,"\text{Not used}","int(1/(((a + b*x)^2)^(1/2)*(d + e*x)),x)","\int \frac{1}{\sqrt{{\left(a+b\,x\right)}^2}\,\left(d+e\,x\right)} \,d x","Not used",1,"int(1/(((a + b*x)^2)^(1/2)*(d + e*x)), x)","F"
1593,0,-1,131,0.000000,"\text{Not used}","int(1/(((a + b*x)^2)^(1/2)*(d + e*x)^2),x)","\int \frac{1}{\sqrt{{\left(a+b\,x\right)}^2}\,{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int(1/(((a + b*x)^2)^(1/2)*(d + e*x)^2), x)","F"
1594,0,-1,182,0.000000,"\text{Not used}","int(1/(((a + b*x)^2)^(1/2)*(d + e*x)^3),x)","\int \frac{1}{\sqrt{{\left(a+b\,x\right)}^2}\,{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int(1/(((a + b*x)^2)^(1/2)*(d + e*x)^3), x)","F"
1595,0,-1,231,0.000000,"\text{Not used}","int(1/(((a + b*x)^2)^(1/2)*(d + e*x)^4),x)","\int \frac{1}{\sqrt{{\left(a+b\,x\right)}^2}\,{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int(1/(((a + b*x)^2)^(1/2)*(d + e*x)^4), x)","F"
1596,0,-1,210,0.000000,"\text{Not used}","int((d + e*x)^4/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^4/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1597,0,-1,161,0.000000,"\text{Not used}","int((d + e*x)^3/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^3}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^3/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1598,0,-1,117,0.000000,"\text{Not used}","int((d + e*x)^2/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^2}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^2/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1599,1,42,69,0.622487,"\text{Not used}","int((d + e*x)/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","-\frac{\left(a\,e+b\,d+2\,b\,e\,x\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,b^2\,{\left(a+b\,x\right)}^3}","Not used",1,"-((a*e + b*d + 2*b*e*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(2*b^2*(a + b*x)^3)","B"
1600,1,30,34,0.588289,"\text{Not used}","int(1/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{2\,b\,{\left(a+b\,x\right)}^3}","Not used",1,"-(a^2 + b^2*x^2 + 2*a*b*x)^(1/2)/(2*b*(a + b*x)^3)","B"
1601,0,-1,165,0.000000,"\text{Not used}","int(1/((d + e*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)),x)","\int \frac{1}{\left(d+e\,x\right)\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)), x)","F"
1602,0,-1,217,0.000000,"\text{Not used}","int(1/((d + e*x)^2*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^2\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)^2*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)), x)","F"
1603,0,-1,276,0.000000,"\text{Not used}","int(1/((d + e*x)^3*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^3\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)^3*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)), x)","F"
1604,0,-1,302,0.000000,"\text{Not used}","int((d + e*x)^6/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^6}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^6/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1605,0,-1,253,0.000000,"\text{Not used}","int((d + e*x)^5/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^5}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^5/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1606,0,-1,209,0.000000,"\text{Not used}","int((d + e*x)^4/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^4/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1607,1,254,48,0.748071,"\text{Not used}","int((d + e*x)^3/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\frac{\left(\frac{2\,a\,e^3-3\,b\,d\,e^2}{2\,b^4}+\frac{a\,e^3}{2\,b^4}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{{\left(a+b\,x\right)}^3}-\frac{\left(\frac{d^3}{4\,b}-\frac{a\,\left(\frac{3\,d^2\,e}{4\,b}+\frac{a\,\left(\frac{a\,e^3}{4\,b^2}-\frac{3\,d\,e^2}{4\,b}\right)}{b}\right)}{b}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{{\left(a+b\,x\right)}^5}-\frac{\left(\frac{a^2\,e^3-3\,a\,b\,d\,e^2+3\,b^2\,d^2\,e}{3\,b^4}+\frac{a\,\left(\frac{a\,e^3}{3\,b^3}+\frac{e^2\,\left(a\,e-3\,b\,d\right)}{3\,b^3}\right)}{b}\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{{\left(a+b\,x\right)}^4}-\frac{e^3\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{b^4\,{\left(a+b\,x\right)}^2}","Not used",1,"(((2*a*e^3 - 3*b*d*e^2)/(2*b^4) + (a*e^3)/(2*b^4))*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(a + b*x)^3 - ((d^3/(4*b) - (a*((3*d^2*e)/(4*b) + (a*((a*e^3)/(4*b^2) - (3*d*e^2)/(4*b)))/b))/b)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(a + b*x)^5 - (((a^2*e^3 + 3*b^2*d^2*e - 3*a*b*d*e^2)/(3*b^4) + (a*((a*e^3)/(3*b^3) + (e^2*(a*e - 3*b*d))/(3*b^3)))/b)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(a + b*x)^4 - (e^3*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(b^4*(a + b*x)^2)","B"
1608,1,79,125,0.712979,"\text{Not used}","int((d + e*x)^2/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(a^2\,e^2+2\,a\,b\,d\,e+4\,a\,b\,e^2\,x+3\,b^2\,d^2+8\,b^2\,d\,e\,x+6\,b^2\,e^2\,x^2\right)}{12\,b^3\,{\left(a+b\,x\right)}^5}","Not used",1,"-((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*(a^2*e^2 + 3*b^2*d^2 + 6*b^2*e^2*x^2 + 4*a*b*e^2*x + 8*b^2*d*e*x + 2*a*b*d*e))/(12*b^3*(a + b*x)^5)","B"
1609,1,43,71,0.647832,"\text{Not used}","int((d + e*x)/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","-\frac{\left(a\,e+3\,b\,d+4\,b\,e\,x\right)\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{12\,b^2\,{\left(a+b\,x\right)}^5}","Not used",1,"-((a*e + 3*b*d + 4*b*e*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/(12*b^2*(a + b*x)^5)","B"
1610,1,30,34,0.623274,"\text{Not used}","int(1/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{4\,b\,{\left(a+b\,x\right)}^5}","Not used",1,"-(a^2 + b^2*x^2 + 2*a*b*x)^(1/2)/(4*b*(a + b*x)^5)","B"
1611,0,-1,253,0.000000,"\text{Not used}","int(1/((d + e*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)),x)","\int \frac{1}{\left(d+e\,x\right)\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int(1/((d + e*x)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)), x)","F"
1612,0,-1,307,0.000000,"\text{Not used}","int(1/((d + e*x)^2*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^2\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int(1/((d + e*x)^2*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)), x)","F"
1613,0,-1,365,0.000000,"\text{Not used}","int(1/((d + e*x)^3*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^3\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int(1/((d + e*x)^3*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)), x)","F"
1614,0,-1,50,0.000000,"\text{Not used}","int((d + e*x)*(12*x + 4*x^2 + 9)^(5/2),x)","\int \left(d+e\,x\right)\,{\left(4\,x^2+12\,x+9\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)*(12*x + 4*x^2 + 9)^(5/2), x)","F"
1615,1,67,50,0.620863,"\text{Not used}","int((d + e*x)*(12*x + 4*x^2 + 9)^(3/2),x)","\frac{e\,{\left(4\,x^2+12\,x+9\right)}^{5/2}}{20}-\frac{9\,e\,{\left(4\,x^2+12\,x+9\right)}^{3/2}}{16}-\frac{3\,e\,x\,{\left(4\,x^2+12\,x+9\right)}^{3/2}}{8}+\frac{d\,\left(2\,x+3\right)\,{\left(4\,x^2+12\,x+9\right)}^{3/2}}{8}","Not used",1,"(e*(12*x + 4*x^2 + 9)^(5/2))/20 - (9*e*(12*x + 4*x^2 + 9)^(3/2))/16 - (3*e*x*(12*x + 4*x^2 + 9)^(3/2))/8 + (d*(2*x + 3)*(12*x + 4*x^2 + 9)^(3/2))/8","B"
1616,1,30,50,0.614380,"\text{Not used}","int((d + e*x)*(12*x + 4*x^2 + 9)^(1/2),x)","\frac{\left(2\,x+3\right)\,\left(6\,d-3\,e+4\,e\,x\right)\,\sqrt{4\,x^2+12\,x+9}}{24}","Not used",1,"((2*x + 3)*(6*d - 3*e + 4*e*x)*(12*x + 4*x^2 + 9)^(1/2))/24","B"
1617,1,46,56,1.504631,"\text{Not used}","int((d + e*x)/(12*x + 4*x^2 + 9)^(1/2),x)","\frac{e\,\sqrt{4\,x^2+12\,x+9}}{4}-\frac{3\,e\,\ln\left(x+\frac{\left|2\,x+3\right|}{2}+\frac{3}{2}\right)}{4}+\frac{d\,\ln\left(4\,x+6\right)\,\mathrm{sign}\left(8\,x+12\right)}{2}","Not used",1,"(e*(12*x + 4*x^2 + 9)^(1/2))/4 - (3*e*log(x + abs(2*x + 3)/2 + 3/2))/4 + (d*log(4*x + 6)*sign(8*x + 12))/2","B"
1618,1,32,52,0.092877,"\text{Not used}","int((d + e*x)/(12*x + 4*x^2 + 9)^(3/2),x)","-\frac{\left(2\,d+3\,e+4\,e\,x\right)\,\sqrt{4\,x^2+12\,x+9}}{8\,{\left(2\,x+3\right)}^3}","Not used",1,"-((2*d + 3*e + 4*e*x)*(12*x + 4*x^2 + 9)^(1/2))/(8*(2*x + 3)^3)","B"
1619,1,32,52,0.096584,"\text{Not used}","int((d + e*x)/(12*x + 4*x^2 + 9)^(5/2),x)","-\frac{\left(6\,d+3\,e+8\,e\,x\right)\,\sqrt{4\,x^2+12\,x+9}}{48\,{\left(2\,x+3\right)}^5}","Not used",1,"-((6*d + 3*e + 8*e*x)*(12*x + 4*x^2 + 9)^(1/2))/(48*(2*x + 3)^5)","B"
1620,1,32,52,0.581411,"\text{Not used}","int((d + e*x)/(12*x + 4*x^2 + 9)^(7/2),x)","-\frac{\left(10\,d+3\,e+12\,e\,x\right)\,\sqrt{4\,x^2+12\,x+9}}{120\,{\left(2\,x+3\right)}^7}","Not used",1,"-((10*d + 3*e + 12*e*x)*(12*x + 4*x^2 + 9)^(1/2))/(120*(2*x + 3)^7)","B"
1621,1,68,71,0.090436,"\text{Not used}","int((d + e*x)^(7/2)*(a^2 + b^2*x^2 + 2*a*b*x),x)","\frac{2\,{\left(d+e\,x\right)}^{9/2}\,\left(99\,b^2\,{\left(d+e\,x\right)}^2+143\,a^2\,e^2+143\,b^2\,d^2-234\,b^2\,d\,\left(d+e\,x\right)+234\,a\,b\,e\,\left(d+e\,x\right)-286\,a\,b\,d\,e\right)}{1287\,e^3}","Not used",1,"(2*(d + e*x)^(9/2)*(99*b^2*(d + e*x)^2 + 143*a^2*e^2 + 143*b^2*d^2 - 234*b^2*d*(d + e*x) + 234*a*b*e*(d + e*x) - 286*a*b*d*e))/(1287*e^3)","B"
1622,1,68,71,0.056392,"\text{Not used}","int((d + e*x)^(5/2)*(a^2 + b^2*x^2 + 2*a*b*x),x)","\frac{2\,{\left(d+e\,x\right)}^{7/2}\,\left(63\,b^2\,{\left(d+e\,x\right)}^2+99\,a^2\,e^2+99\,b^2\,d^2-154\,b^2\,d\,\left(d+e\,x\right)+154\,a\,b\,e\,\left(d+e\,x\right)-198\,a\,b\,d\,e\right)}{693\,e^3}","Not used",1,"(2*(d + e*x)^(7/2)*(63*b^2*(d + e*x)^2 + 99*a^2*e^2 + 99*b^2*d^2 - 154*b^2*d*(d + e*x) + 154*a*b*e*(d + e*x) - 198*a*b*d*e))/(693*e^3)","B"
1623,1,68,71,0.548892,"\text{Not used}","int((d + e*x)^(3/2)*(a^2 + b^2*x^2 + 2*a*b*x),x)","\frac{2\,{\left(d+e\,x\right)}^{5/2}\,\left(35\,b^2\,{\left(d+e\,x\right)}^2+63\,a^2\,e^2+63\,b^2\,d^2-90\,b^2\,d\,\left(d+e\,x\right)+90\,a\,b\,e\,\left(d+e\,x\right)-126\,a\,b\,d\,e\right)}{315\,e^3}","Not used",1,"(2*(d + e*x)^(5/2)*(35*b^2*(d + e*x)^2 + 63*a^2*e^2 + 63*b^2*d^2 - 90*b^2*d*(d + e*x) + 90*a*b*e*(d + e*x) - 126*a*b*d*e))/(315*e^3)","B"
1624,1,68,71,0.555189,"\text{Not used}","int((d + e*x)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x),x)","\frac{2\,{\left(d+e\,x\right)}^{3/2}\,\left(15\,b^2\,{\left(d+e\,x\right)}^2+35\,a^2\,e^2+35\,b^2\,d^2-42\,b^2\,d\,\left(d+e\,x\right)+42\,a\,b\,e\,\left(d+e\,x\right)-70\,a\,b\,d\,e\right)}{105\,e^3}","Not used",1,"(2*(d + e*x)^(3/2)*(15*b^2*(d + e*x)^2 + 35*a^2*e^2 + 35*b^2*d^2 - 42*b^2*d*(d + e*x) + 42*a*b*e*(d + e*x) - 70*a*b*d*e))/(105*e^3)","B"
1625,1,68,69,0.055534,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)/(d + e*x)^(1/2),x)","\frac{2\,\sqrt{d+e\,x}\,\left(3\,b^2\,{\left(d+e\,x\right)}^2+15\,a^2\,e^2+15\,b^2\,d^2-10\,b^2\,d\,\left(d+e\,x\right)+10\,a\,b\,e\,\left(d+e\,x\right)-30\,a\,b\,d\,e\right)}{15\,e^3}","Not used",1,"(2*(d + e*x)^(1/2)*(3*b^2*(d + e*x)^2 + 15*a^2*e^2 + 15*b^2*d^2 - 10*b^2*d*(d + e*x) + 10*a*b*e*(d + e*x) - 30*a*b*d*e))/(15*e^3)","B"
1626,1,67,67,0.555748,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)/(d + e*x)^(3/2),x)","\frac{\frac{2\,b^2\,{\left(d+e\,x\right)}^2}{3}-2\,a^2\,e^2-2\,b^2\,d^2-4\,b^2\,d\,\left(d+e\,x\right)+4\,a\,b\,e\,\left(d+e\,x\right)+4\,a\,b\,d\,e}{e^3\,\sqrt{d+e\,x}}","Not used",1,"((2*b^2*(d + e*x)^2)/3 - 2*a^2*e^2 - 2*b^2*d^2 - 4*b^2*d*(d + e*x) + 4*a*b*e*(d + e*x) + 4*a*b*d*e)/(e^3*(d + e*x)^(1/2))","B"
1627,1,68,67,0.053901,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)/(d + e*x)^(5/2),x)","\frac{6\,b^2\,{\left(d+e\,x\right)}^2-2\,a^2\,e^2-2\,b^2\,d^2+12\,b^2\,d\,\left(d+e\,x\right)-12\,a\,b\,e\,\left(d+e\,x\right)+4\,a\,b\,d\,e}{3\,e^3\,{\left(d+e\,x\right)}^{3/2}}","Not used",1,"(6*b^2*(d + e*x)^2 - 2*a^2*e^2 - 2*b^2*d^2 + 12*b^2*d*(d + e*x) - 12*a*b*e*(d + e*x) + 4*a*b*d*e)/(3*e^3*(d + e*x)^(3/2))","B"
1628,1,62,69,0.565624,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)/(d + e*x)^(7/2),x)","-\frac{6\,a^2\,e^2+8\,a\,b\,d\,e+20\,a\,b\,e^2\,x+16\,b^2\,d^2+40\,b^2\,d\,e\,x+30\,b^2\,e^2\,x^2}{15\,e^3\,{\left(d+e\,x\right)}^{5/2}}","Not used",1,"-(6*a^2*e^2 + 16*b^2*d^2 + 30*b^2*e^2*x^2 + 20*a*b*e^2*x + 40*b^2*d*e*x + 8*a*b*d*e)/(15*e^3*(d + e*x)^(5/2))","B"
1629,1,112,129,0.058815,"\text{Not used}","int((d + e*x)^(7/2)*(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","\frac{2\,b^4\,{\left(d+e\,x\right)}^{17/2}}{17\,e^5}-\frac{\left(8\,b^4\,d-8\,a\,b^3\,e\right)\,{\left(d+e\,x\right)}^{15/2}}{15\,e^5}+\frac{2\,{\left(a\,e-b\,d\right)}^4\,{\left(d+e\,x\right)}^{9/2}}{9\,e^5}+\frac{12\,b^2\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{13/2}}{13\,e^5}+\frac{8\,b\,{\left(a\,e-b\,d\right)}^3\,{\left(d+e\,x\right)}^{11/2}}{11\,e^5}","Not used",1,"(2*b^4*(d + e*x)^(17/2))/(17*e^5) - ((8*b^4*d - 8*a*b^3*e)*(d + e*x)^(15/2))/(15*e^5) + (2*(a*e - b*d)^4*(d + e*x)^(9/2))/(9*e^5) + (12*b^2*(a*e - b*d)^2*(d + e*x)^(13/2))/(13*e^5) + (8*b*(a*e - b*d)^3*(d + e*x)^(11/2))/(11*e^5)","B"
1630,1,112,129,0.539274,"\text{Not used}","int((d + e*x)^(5/2)*(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","\frac{2\,b^4\,{\left(d+e\,x\right)}^{15/2}}{15\,e^5}-\frac{\left(8\,b^4\,d-8\,a\,b^3\,e\right)\,{\left(d+e\,x\right)}^{13/2}}{13\,e^5}+\frac{2\,{\left(a\,e-b\,d\right)}^4\,{\left(d+e\,x\right)}^{7/2}}{7\,e^5}+\frac{12\,b^2\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{11/2}}{11\,e^5}+\frac{8\,b\,{\left(a\,e-b\,d\right)}^3\,{\left(d+e\,x\right)}^{9/2}}{9\,e^5}","Not used",1,"(2*b^4*(d + e*x)^(15/2))/(15*e^5) - ((8*b^4*d - 8*a*b^3*e)*(d + e*x)^(13/2))/(13*e^5) + (2*(a*e - b*d)^4*(d + e*x)^(7/2))/(7*e^5) + (12*b^2*(a*e - b*d)^2*(d + e*x)^(11/2))/(11*e^5) + (8*b*(a*e - b*d)^3*(d + e*x)^(9/2))/(9*e^5)","B"
1631,1,112,129,0.042613,"\text{Not used}","int((d + e*x)^(3/2)*(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","\frac{2\,b^4\,{\left(d+e\,x\right)}^{13/2}}{13\,e^5}-\frac{\left(8\,b^4\,d-8\,a\,b^3\,e\right)\,{\left(d+e\,x\right)}^{11/2}}{11\,e^5}+\frac{2\,{\left(a\,e-b\,d\right)}^4\,{\left(d+e\,x\right)}^{5/2}}{5\,e^5}+\frac{4\,b^2\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{9/2}}{3\,e^5}+\frac{8\,b\,{\left(a\,e-b\,d\right)}^3\,{\left(d+e\,x\right)}^{7/2}}{7\,e^5}","Not used",1,"(2*b^4*(d + e*x)^(13/2))/(13*e^5) - ((8*b^4*d - 8*a*b^3*e)*(d + e*x)^(11/2))/(11*e^5) + (2*(a*e - b*d)^4*(d + e*x)^(5/2))/(5*e^5) + (4*b^2*(a*e - b*d)^2*(d + e*x)^(9/2))/(3*e^5) + (8*b*(a*e - b*d)^3*(d + e*x)^(7/2))/(7*e^5)","B"
1632,1,112,129,0.041416,"\text{Not used}","int((d + e*x)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","\frac{2\,b^4\,{\left(d+e\,x\right)}^{11/2}}{11\,e^5}-\frac{\left(8\,b^4\,d-8\,a\,b^3\,e\right)\,{\left(d+e\,x\right)}^{9/2}}{9\,e^5}+\frac{2\,{\left(a\,e-b\,d\right)}^4\,{\left(d+e\,x\right)}^{3/2}}{3\,e^5}+\frac{12\,b^2\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{7/2}}{7\,e^5}+\frac{8\,b\,{\left(a\,e-b\,d\right)}^3\,{\left(d+e\,x\right)}^{5/2}}{5\,e^5}","Not used",1,"(2*b^4*(d + e*x)^(11/2))/(11*e^5) - ((8*b^4*d - 8*a*b^3*e)*(d + e*x)^(9/2))/(9*e^5) + (2*(a*e - b*d)^4*(d + e*x)^(3/2))/(3*e^5) + (12*b^2*(a*e - b*d)^2*(d + e*x)^(7/2))/(7*e^5) + (8*b*(a*e - b*d)^3*(d + e*x)^(5/2))/(5*e^5)","B"
1633,1,112,127,0.040576,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^2/(d + e*x)^(1/2),x)","\frac{2\,b^4\,{\left(d+e\,x\right)}^{9/2}}{9\,e^5}-\frac{\left(8\,b^4\,d-8\,a\,b^3\,e\right)\,{\left(d+e\,x\right)}^{7/2}}{7\,e^5}+\frac{2\,{\left(a\,e-b\,d\right)}^4\,\sqrt{d+e\,x}}{e^5}+\frac{12\,b^2\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{5/2}}{5\,e^5}+\frac{8\,b\,{\left(a\,e-b\,d\right)}^3\,{\left(d+e\,x\right)}^{3/2}}{3\,e^5}","Not used",1,"(2*b^4*(d + e*x)^(9/2))/(9*e^5) - ((8*b^4*d - 8*a*b^3*e)*(d + e*x)^(7/2))/(7*e^5) + (2*(a*e - b*d)^4*(d + e*x)^(1/2))/e^5 + (12*b^2*(a*e - b*d)^2*(d + e*x)^(5/2))/(5*e^5) + (8*b*(a*e - b*d)^3*(d + e*x)^(3/2))/(3*e^5)","B"
1634,1,153,123,0.542944,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^2/(d + e*x)^(3/2),x)","\frac{2\,b^4\,{\left(d+e\,x\right)}^{7/2}}{7\,e^5}-\frac{\left(8\,b^4\,d-8\,a\,b^3\,e\right)\,{\left(d+e\,x\right)}^{5/2}}{5\,e^5}-\frac{2\,a^4\,e^4-8\,a^3\,b\,d\,e^3+12\,a^2\,b^2\,d^2\,e^2-8\,a\,b^3\,d^3\,e+2\,b^4\,d^4}{e^5\,\sqrt{d+e\,x}}+\frac{4\,b^2\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{3/2}}{e^5}+\frac{8\,b\,{\left(a\,e-b\,d\right)}^3\,\sqrt{d+e\,x}}{e^5}","Not used",1,"(2*b^4*(d + e*x)^(7/2))/(7*e^5) - ((8*b^4*d - 8*a*b^3*e)*(d + e*x)^(5/2))/(5*e^5) - (2*a^4*e^4 + 2*b^4*d^4 + 12*a^2*b^2*d^2*e^2 - 8*a*b^3*d^3*e - 8*a^3*b*d*e^3)/(e^5*(d + e*x)^(1/2)) + (4*b^2*(a*e - b*d)^2*(d + e*x)^(3/2))/e^5 + (8*b*(a*e - b*d)^3*(d + e*x)^(1/2))/e^5","B"
1635,1,175,125,0.072416,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^2/(d + e*x)^(5/2),x)","\frac{\left(d+e\,x\right)\,\left(-8\,a^3\,b\,e^3+24\,a^2\,b^2\,d\,e^2-24\,a\,b^3\,d^2\,e+8\,b^4\,d^3\right)-\frac{2\,a^4\,e^4}{3}-\frac{2\,b^4\,d^4}{3}-4\,a^2\,b^2\,d^2\,e^2+\frac{8\,a\,b^3\,d^3\,e}{3}+\frac{8\,a^3\,b\,d\,e^3}{3}}{e^5\,{\left(d+e\,x\right)}^{3/2}}+\frac{2\,b^4\,{\left(d+e\,x\right)}^{5/2}}{5\,e^5}-\frac{\left(8\,b^4\,d-8\,a\,b^3\,e\right)\,{\left(d+e\,x\right)}^{3/2}}{3\,e^5}+\frac{12\,b^2\,{\left(a\,e-b\,d\right)}^2\,\sqrt{d+e\,x}}{e^5}","Not used",1,"((d + e*x)*(8*b^4*d^3 - 8*a^3*b*e^3 + 24*a^2*b^2*d*e^2 - 24*a*b^3*d^2*e) - (2*a^4*e^4)/3 - (2*b^4*d^4)/3 - 4*a^2*b^2*d^2*e^2 + (8*a*b^3*d^3*e)/3 + (8*a^3*b*d*e^3)/3)/(e^5*(d + e*x)^(3/2)) + (2*b^4*(d + e*x)^(5/2))/(5*e^5) - ((8*b^4*d - 8*a*b^3*e)*(d + e*x)^(3/2))/(3*e^5) + (12*b^2*(a*e - b*d)^2*(d + e*x)^(1/2))/e^5","B"
1636,1,185,125,0.586086,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^2/(d + e*x)^(7/2),x)","-\frac{2\,\left(3\,a^4\,e^4+8\,a^3\,b\,d\,e^3+20\,a^3\,b\,e^4\,x+48\,a^2\,b^2\,d^2\,e^2+120\,a^2\,b^2\,d\,e^3\,x+90\,a^2\,b^2\,e^4\,x^2-192\,a\,b^3\,d^3\,e-480\,a\,b^3\,d^2\,e^2\,x-360\,a\,b^3\,d\,e^3\,x^2-60\,a\,b^3\,e^4\,x^3+128\,b^4\,d^4+320\,b^4\,d^3\,e\,x+240\,b^4\,d^2\,e^2\,x^2+40\,b^4\,d\,e^3\,x^3-5\,b^4\,e^4\,x^4\right)}{15\,e^5\,{\left(d+e\,x\right)}^{5/2}}","Not used",1,"-(2*(3*a^4*e^4 + 128*b^4*d^4 - 5*b^4*e^4*x^4 - 60*a*b^3*e^4*x^3 + 40*b^4*d*e^3*x^3 + 48*a^2*b^2*d^2*e^2 + 90*a^2*b^2*e^4*x^2 + 240*b^4*d^2*e^2*x^2 - 192*a*b^3*d^3*e + 8*a^3*b*d*e^3 + 20*a^3*b*e^4*x + 320*b^4*d^3*e*x - 480*a*b^3*d^2*e^2*x + 120*a^2*b^2*d*e^3*x - 360*a*b^3*d*e^3*x^2))/(15*e^5*(d + e*x)^(5/2))","B"
1637,1,162,187,0.577107,"\text{Not used}","int((d + e*x)^(7/2)*(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\frac{2\,b^6\,{\left(d+e\,x\right)}^{21/2}}{21\,e^7}-\frac{\left(12\,b^6\,d-12\,a\,b^5\,e\right)\,{\left(d+e\,x\right)}^{19/2}}{19\,e^7}+\frac{2\,{\left(a\,e-b\,d\right)}^6\,{\left(d+e\,x\right)}^{9/2}}{9\,e^7}+\frac{30\,b^2\,{\left(a\,e-b\,d\right)}^4\,{\left(d+e\,x\right)}^{13/2}}{13\,e^7}+\frac{8\,b^3\,{\left(a\,e-b\,d\right)}^3\,{\left(d+e\,x\right)}^{15/2}}{3\,e^7}+\frac{30\,b^4\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{17/2}}{17\,e^7}+\frac{12\,b\,{\left(a\,e-b\,d\right)}^5\,{\left(d+e\,x\right)}^{11/2}}{11\,e^7}","Not used",1,"(2*b^6*(d + e*x)^(21/2))/(21*e^7) - ((12*b^6*d - 12*a*b^5*e)*(d + e*x)^(19/2))/(19*e^7) + (2*(a*e - b*d)^6*(d + e*x)^(9/2))/(9*e^7) + (30*b^2*(a*e - b*d)^4*(d + e*x)^(13/2))/(13*e^7) + (8*b^3*(a*e - b*d)^3*(d + e*x)^(15/2))/(3*e^7) + (30*b^4*(a*e - b*d)^2*(d + e*x)^(17/2))/(17*e^7) + (12*b*(a*e - b*d)^5*(d + e*x)^(11/2))/(11*e^7)","B"
1638,1,162,185,0.055401,"\text{Not used}","int((d + e*x)^(5/2)*(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\frac{2\,b^6\,{\left(d+e\,x\right)}^{19/2}}{19\,e^7}-\frac{\left(12\,b^6\,d-12\,a\,b^5\,e\right)\,{\left(d+e\,x\right)}^{17/2}}{17\,e^7}+\frac{2\,{\left(a\,e-b\,d\right)}^6\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}+\frac{30\,b^2\,{\left(a\,e-b\,d\right)}^4\,{\left(d+e\,x\right)}^{11/2}}{11\,e^7}+\frac{40\,b^3\,{\left(a\,e-b\,d\right)}^3\,{\left(d+e\,x\right)}^{13/2}}{13\,e^7}+\frac{2\,b^4\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{15/2}}{e^7}+\frac{4\,b\,{\left(a\,e-b\,d\right)}^5\,{\left(d+e\,x\right)}^{9/2}}{3\,e^7}","Not used",1,"(2*b^6*(d + e*x)^(19/2))/(19*e^7) - ((12*b^6*d - 12*a*b^5*e)*(d + e*x)^(17/2))/(17*e^7) + (2*(a*e - b*d)^6*(d + e*x)^(7/2))/(7*e^7) + (30*b^2*(a*e - b*d)^4*(d + e*x)^(11/2))/(11*e^7) + (40*b^3*(a*e - b*d)^3*(d + e*x)^(13/2))/(13*e^7) + (2*b^4*(a*e - b*d)^2*(d + e*x)^(15/2))/e^7 + (4*b*(a*e - b*d)^5*(d + e*x)^(9/2))/(3*e^7)","B"
1639,1,162,187,0.548624,"\text{Not used}","int((d + e*x)^(3/2)*(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\frac{2\,b^6\,{\left(d+e\,x\right)}^{17/2}}{17\,e^7}-\frac{\left(12\,b^6\,d-12\,a\,b^5\,e\right)\,{\left(d+e\,x\right)}^{15/2}}{15\,e^7}+\frac{2\,{\left(a\,e-b\,d\right)}^6\,{\left(d+e\,x\right)}^{5/2}}{5\,e^7}+\frac{10\,b^2\,{\left(a\,e-b\,d\right)}^4\,{\left(d+e\,x\right)}^{9/2}}{3\,e^7}+\frac{40\,b^3\,{\left(a\,e-b\,d\right)}^3\,{\left(d+e\,x\right)}^{11/2}}{11\,e^7}+\frac{30\,b^4\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{13/2}}{13\,e^7}+\frac{12\,b\,{\left(a\,e-b\,d\right)}^5\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}","Not used",1,"(2*b^6*(d + e*x)^(17/2))/(17*e^7) - ((12*b^6*d - 12*a*b^5*e)*(d + e*x)^(15/2))/(15*e^7) + (2*(a*e - b*d)^6*(d + e*x)^(5/2))/(5*e^7) + (10*b^2*(a*e - b*d)^4*(d + e*x)^(9/2))/(3*e^7) + (40*b^3*(a*e - b*d)^3*(d + e*x)^(11/2))/(11*e^7) + (30*b^4*(a*e - b*d)^2*(d + e*x)^(13/2))/(13*e^7) + (12*b*(a*e - b*d)^5*(d + e*x)^(7/2))/(7*e^7)","B"
1640,1,162,187,0.549419,"\text{Not used}","int((d + e*x)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\frac{2\,b^6\,{\left(d+e\,x\right)}^{15/2}}{15\,e^7}-\frac{\left(12\,b^6\,d-12\,a\,b^5\,e\right)\,{\left(d+e\,x\right)}^{13/2}}{13\,e^7}+\frac{2\,{\left(a\,e-b\,d\right)}^6\,{\left(d+e\,x\right)}^{3/2}}{3\,e^7}+\frac{30\,b^2\,{\left(a\,e-b\,d\right)}^4\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}+\frac{40\,b^3\,{\left(a\,e-b\,d\right)}^3\,{\left(d+e\,x\right)}^{9/2}}{9\,e^7}+\frac{30\,b^4\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{11/2}}{11\,e^7}+\frac{12\,b\,{\left(a\,e-b\,d\right)}^5\,{\left(d+e\,x\right)}^{5/2}}{5\,e^7}","Not used",1,"(2*b^6*(d + e*x)^(15/2))/(15*e^7) - ((12*b^6*d - 12*a*b^5*e)*(d + e*x)^(13/2))/(13*e^7) + (2*(a*e - b*d)^6*(d + e*x)^(3/2))/(3*e^7) + (30*b^2*(a*e - b*d)^4*(d + e*x)^(7/2))/(7*e^7) + (40*b^3*(a*e - b*d)^3*(d + e*x)^(9/2))/(9*e^7) + (30*b^4*(a*e - b*d)^2*(d + e*x)^(11/2))/(11*e^7) + (12*b*(a*e - b*d)^5*(d + e*x)^(5/2))/(5*e^7)","B"
1641,1,162,181,0.554288,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^(1/2),x)","\frac{2\,b^6\,{\left(d+e\,x\right)}^{13/2}}{13\,e^7}-\frac{\left(12\,b^6\,d-12\,a\,b^5\,e\right)\,{\left(d+e\,x\right)}^{11/2}}{11\,e^7}+\frac{2\,{\left(a\,e-b\,d\right)}^6\,\sqrt{d+e\,x}}{e^7}+\frac{6\,b^2\,{\left(a\,e-b\,d\right)}^4\,{\left(d+e\,x\right)}^{5/2}}{e^7}+\frac{40\,b^3\,{\left(a\,e-b\,d\right)}^3\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}+\frac{10\,b^4\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{9/2}}{3\,e^7}+\frac{4\,b\,{\left(a\,e-b\,d\right)}^5\,{\left(d+e\,x\right)}^{3/2}}{e^7}","Not used",1,"(2*b^6*(d + e*x)^(13/2))/(13*e^7) - ((12*b^6*d - 12*a*b^5*e)*(d + e*x)^(11/2))/(11*e^7) + (2*(a*e - b*d)^6*(d + e*x)^(1/2))/e^7 + (6*b^2*(a*e - b*d)^4*(d + e*x)^(5/2))/e^7 + (40*b^3*(a*e - b*d)^3*(d + e*x)^(7/2))/(7*e^7) + (10*b^4*(a*e - b*d)^2*(d + e*x)^(9/2))/(3*e^7) + (4*b*(a*e - b*d)^5*(d + e*x)^(3/2))/e^7","B"
1642,1,231,179,0.554599,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^(3/2),x)","\frac{2\,b^6\,{\left(d+e\,x\right)}^{11/2}}{11\,e^7}-\frac{2\,a^6\,e^6-12\,a^5\,b\,d\,e^5+30\,a^4\,b^2\,d^2\,e^4-40\,a^3\,b^3\,d^3\,e^3+30\,a^2\,b^4\,d^4\,e^2-12\,a\,b^5\,d^5\,e+2\,b^6\,d^6}{e^7\,\sqrt{d+e\,x}}-\frac{\left(12\,b^6\,d-12\,a\,b^5\,e\right)\,{\left(d+e\,x\right)}^{9/2}}{9\,e^7}+\frac{10\,b^2\,{\left(a\,e-b\,d\right)}^4\,{\left(d+e\,x\right)}^{3/2}}{e^7}+\frac{8\,b^3\,{\left(a\,e-b\,d\right)}^3\,{\left(d+e\,x\right)}^{5/2}}{e^7}+\frac{30\,b^4\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}+\frac{12\,b\,{\left(a\,e-b\,d\right)}^5\,\sqrt{d+e\,x}}{e^7}","Not used",1,"(2*b^6*(d + e*x)^(11/2))/(11*e^7) - (2*a^6*e^6 + 2*b^6*d^6 + 30*a^2*b^4*d^4*e^2 - 40*a^3*b^3*d^3*e^3 + 30*a^4*b^2*d^2*e^4 - 12*a*b^5*d^5*e - 12*a^5*b*d*e^5)/(e^7*(d + e*x)^(1/2)) - ((12*b^6*d - 12*a*b^5*e)*(d + e*x)^(9/2))/(9*e^7) + (10*b^2*(a*e - b*d)^4*(d + e*x)^(3/2))/e^7 + (8*b^3*(a*e - b*d)^3*(d + e*x)^(5/2))/e^7 + (30*b^4*(a*e - b*d)^2*(d + e*x)^(7/2))/(7*e^7) + (12*b*(a*e - b*d)^5*(d + e*x)^(1/2))/e^7","B"
1643,1,281,181,0.555556,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^(5/2),x)","\frac{2\,b^6\,{\left(d+e\,x\right)}^{9/2}}{9\,e^7}-\frac{\left(12\,b^6\,d-12\,a\,b^5\,e\right)\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}+\frac{\left(d+e\,x\right)\,\left(-12\,a^5\,b\,e^5+60\,a^4\,b^2\,d\,e^4-120\,a^3\,b^3\,d^2\,e^3+120\,a^2\,b^4\,d^3\,e^2-60\,a\,b^5\,d^4\,e+12\,b^6\,d^5\right)-\frac{2\,a^6\,e^6}{3}-\frac{2\,b^6\,d^6}{3}-10\,a^2\,b^4\,d^4\,e^2+\frac{40\,a^3\,b^3\,d^3\,e^3}{3}-10\,a^4\,b^2\,d^2\,e^4+4\,a\,b^5\,d^5\,e+4\,a^5\,b\,d\,e^5}{e^7\,{\left(d+e\,x\right)}^{3/2}}+\frac{30\,b^2\,{\left(a\,e-b\,d\right)}^4\,\sqrt{d+e\,x}}{e^7}+\frac{40\,b^3\,{\left(a\,e-b\,d\right)}^3\,{\left(d+e\,x\right)}^{3/2}}{3\,e^7}+\frac{6\,b^4\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{5/2}}{e^7}","Not used",1,"(2*b^6*(d + e*x)^(9/2))/(9*e^7) - ((12*b^6*d - 12*a*b^5*e)*(d + e*x)^(7/2))/(7*e^7) + ((d + e*x)*(12*b^6*d^5 - 12*a^5*b*e^5 + 60*a^4*b^2*d*e^4 + 120*a^2*b^4*d^3*e^2 - 120*a^3*b^3*d^2*e^3 - 60*a*b^5*d^4*e) - (2*a^6*e^6)/3 - (2*b^6*d^6)/3 - 10*a^2*b^4*d^4*e^2 + (40*a^3*b^3*d^3*e^3)/3 - 10*a^4*b^2*d^2*e^4 + 4*a*b^5*d^5*e + 4*a^5*b*d*e^5)/(e^7*(d + e*x)^(3/2)) + (30*b^2*(a*e - b*d)^4*(d + e*x)^(1/2))/e^7 + (40*b^3*(a*e - b*d)^3*(d + e*x)^(3/2))/(3*e^7) + (6*b^4*(a*e - b*d)^2*(d + e*x)^(5/2))/e^7","B"
1644,1,322,179,0.554751,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^(7/2),x)","\frac{2\,b^6\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}-\frac{\left(12\,b^6\,d-12\,a\,b^5\,e\right)\,{\left(d+e\,x\right)}^{5/2}}{5\,e^7}-\frac{{\left(d+e\,x\right)}^2\,\left(30\,a^4\,b^2\,e^4-120\,a^3\,b^3\,d\,e^3+180\,a^2\,b^4\,d^2\,e^2-120\,a\,b^5\,d^3\,e+30\,b^6\,d^4\right)-\left(d+e\,x\right)\,\left(-4\,a^5\,b\,e^5+20\,a^4\,b^2\,d\,e^4-40\,a^3\,b^3\,d^2\,e^3+40\,a^2\,b^4\,d^3\,e^2-20\,a\,b^5\,d^4\,e+4\,b^6\,d^5\right)+\frac{2\,a^6\,e^6}{5}+\frac{2\,b^6\,d^6}{5}+6\,a^2\,b^4\,d^4\,e^2-8\,a^3\,b^3\,d^3\,e^3+6\,a^4\,b^2\,d^2\,e^4-\frac{12\,a\,b^5\,d^5\,e}{5}-\frac{12\,a^5\,b\,d\,e^5}{5}}{e^7\,{\left(d+e\,x\right)}^{5/2}}+\frac{40\,b^3\,{\left(a\,e-b\,d\right)}^3\,\sqrt{d+e\,x}}{e^7}+\frac{10\,b^4\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{3/2}}{e^7}","Not used",1,"(2*b^6*(d + e*x)^(7/2))/(7*e^7) - ((12*b^6*d - 12*a*b^5*e)*(d + e*x)^(5/2))/(5*e^7) - ((d + e*x)^2*(30*b^6*d^4 + 30*a^4*b^2*e^4 - 120*a^3*b^3*d*e^3 + 180*a^2*b^4*d^2*e^2 - 120*a*b^5*d^3*e) - (d + e*x)*(4*b^6*d^5 - 4*a^5*b*e^5 + 20*a^4*b^2*d*e^4 + 40*a^2*b^4*d^3*e^2 - 40*a^3*b^3*d^2*e^3 - 20*a*b^5*d^4*e) + (2*a^6*e^6)/5 + (2*b^6*d^6)/5 + 6*a^2*b^4*d^4*e^2 - 8*a^3*b^3*d^3*e^3 + 6*a^4*b^2*d^2*e^4 - (12*a*b^5*d^5*e)/5 - (12*a^5*b*d*e^5)/5)/(e^7*(d + e*x)^(5/2)) + (40*b^3*(a*e - b*d)^3*(d + e*x)^(1/2))/e^7 + (10*b^4*(a*e - b*d)^2*(d + e*x)^(3/2))/e^7","B"
1645,1,352,162,0.606556,"\text{Not used}","int((d + e*x)^(9/2)/(a^2 + b^2*x^2 + 2*a*b*x),x)","\left(\frac{\left(\frac{2\,e\,{\left(2\,b^2\,d-2\,a\,b\,e\right)}^2}{b^6}-\frac{2\,e\,{\left(a\,e-b\,d\right)}^2}{b^4}\right)\,\left(2\,b^2\,d-2\,a\,b\,e\right)}{b^2}-\frac{2\,e\,\left(2\,b^2\,d-2\,a\,b\,e\right)\,{\left(a\,e-b\,d\right)}^2}{b^6}\right)\,\sqrt{d+e\,x}+\left(\frac{2\,e\,{\left(2\,b^2\,d-2\,a\,b\,e\right)}^2}{3\,b^6}-\frac{2\,e\,{\left(a\,e-b\,d\right)}^2}{3\,b^4}\right)\,{\left(d+e\,x\right)}^{3/2}-\frac{\sqrt{d+e\,x}\,\left(a^4\,e^5-4\,a^3\,b\,d\,e^4+6\,a^2\,b^2\,d^2\,e^3-4\,a\,b^3\,d^3\,e^2+b^4\,d^4\,e\right)}{b^6\,\left(d+e\,x\right)-b^6\,d+a\,b^5\,e}+\frac{2\,e\,{\left(d+e\,x\right)}^{7/2}}{7\,b^2}+\frac{2\,e\,\left(2\,b^2\,d-2\,a\,b\,e\right)\,{\left(d+e\,x\right)}^{5/2}}{5\,b^4}+\frac{9\,e\,\mathrm{atan}\left(\frac{\sqrt{b}\,e\,{\left(a\,e-b\,d\right)}^{7/2}\,\sqrt{d+e\,x}}{a^4\,e^5-4\,a^3\,b\,d\,e^4+6\,a^2\,b^2\,d^2\,e^3-4\,a\,b^3\,d^3\,e^2+b^4\,d^4\,e}\right)\,{\left(a\,e-b\,d\right)}^{7/2}}{b^{11/2}}","Not used",1,"((((2*e*(2*b^2*d - 2*a*b*e)^2)/b^6 - (2*e*(a*e - b*d)^2)/b^4)*(2*b^2*d - 2*a*b*e))/b^2 - (2*e*(2*b^2*d - 2*a*b*e)*(a*e - b*d)^2)/b^6)*(d + e*x)^(1/2) + ((2*e*(2*b^2*d - 2*a*b*e)^2)/(3*b^6) - (2*e*(a*e - b*d)^2)/(3*b^4))*(d + e*x)^(3/2) - ((d + e*x)^(1/2)*(a^4*e^5 + b^4*d^4*e - 4*a*b^3*d^3*e^2 + 6*a^2*b^2*d^2*e^3 - 4*a^3*b*d*e^4))/(b^6*(d + e*x) - b^6*d + a*b^5*e) + (2*e*(d + e*x)^(7/2))/(7*b^2) + (2*e*(2*b^2*d - 2*a*b*e)*(d + e*x)^(5/2))/(5*b^4) + (9*e*atan((b^(1/2)*e*(a*e - b*d)^(7/2)*(d + e*x)^(1/2))/(a^4*e^5 + b^4*d^4*e - 4*a*b^3*d^3*e^2 + 6*a^2*b^2*d^2*e^3 - 4*a^3*b*d*e^4))*(a*e - b*d)^(7/2))/b^(11/2)","B"
1646,1,235,137,0.092712,"\text{Not used}","int((d + e*x)^(7/2)/(a^2 + b^2*x^2 + 2*a*b*x),x)","\left(\frac{2\,e\,{\left(2\,b^2\,d-2\,a\,b\,e\right)}^2}{b^6}-\frac{2\,e\,{\left(a\,e-b\,d\right)}^2}{b^4}\right)\,\sqrt{d+e\,x}+\frac{\sqrt{d+e\,x}\,\left(a^3\,e^4-3\,a^2\,b\,d\,e^3+3\,a\,b^2\,d^2\,e^2-b^3\,d^3\,e\right)}{b^5\,\left(d+e\,x\right)-b^5\,d+a\,b^4\,e}+\frac{2\,e\,{\left(d+e\,x\right)}^{5/2}}{5\,b^2}+\frac{2\,e\,\left(2\,b^2\,d-2\,a\,b\,e\right)\,{\left(d+e\,x\right)}^{3/2}}{3\,b^4}-\frac{7\,e\,\mathrm{atan}\left(\frac{\sqrt{b}\,e\,{\left(a\,e-b\,d\right)}^{5/2}\,\sqrt{d+e\,x}}{a^3\,e^4-3\,a^2\,b\,d\,e^3+3\,a\,b^2\,d^2\,e^2-b^3\,d^3\,e}\right)\,{\left(a\,e-b\,d\right)}^{5/2}}{b^{9/2}}","Not used",1,"((2*e*(2*b^2*d - 2*a*b*e)^2)/b^6 - (2*e*(a*e - b*d)^2)/b^4)*(d + e*x)^(1/2) + ((d + e*x)^(1/2)*(a^3*e^4 - b^3*d^3*e + 3*a*b^2*d^2*e^2 - 3*a^2*b*d*e^3))/(b^5*(d + e*x) - b^5*d + a*b^4*e) + (2*e*(d + e*x)^(5/2))/(5*b^2) + (2*e*(2*b^2*d - 2*a*b*e)*(d + e*x)^(3/2))/(3*b^4) - (7*e*atan((b^(1/2)*e*(a*e - b*d)^(5/2)*(d + e*x)^(1/2))/(a^3*e^4 - b^3*d^3*e + 3*a*b^2*d^2*e^2 - 3*a^2*b*d*e^3))*(a*e - b*d)^(5/2))/b^(9/2)","B"
1647,1,161,110,0.593337,"\text{Not used}","int((d + e*x)^(5/2)/(a^2 + b^2*x^2 + 2*a*b*x),x)","\frac{2\,e\,{\left(d+e\,x\right)}^{3/2}}{3\,b^2}-\frac{\sqrt{d+e\,x}\,\left(a^2\,e^3-2\,a\,b\,d\,e^2+b^2\,d^2\,e\right)}{b^4\,\left(d+e\,x\right)-b^4\,d+a\,b^3\,e}+\frac{5\,e\,\mathrm{atan}\left(\frac{\sqrt{b}\,e\,{\left(a\,e-b\,d\right)}^{3/2}\,\sqrt{d+e\,x}}{a^2\,e^3-2\,a\,b\,d\,e^2+b^2\,d^2\,e}\right)\,{\left(a\,e-b\,d\right)}^{3/2}}{b^{7/2}}+\frac{2\,e\,\left(2\,b^2\,d-2\,a\,b\,e\right)\,\sqrt{d+e\,x}}{b^4}","Not used",1,"(2*e*(d + e*x)^(3/2))/(3*b^2) - ((d + e*x)^(1/2)*(a^2*e^3 + b^2*d^2*e - 2*a*b*d*e^2))/(b^4*(d + e*x) - b^4*d + a*b^3*e) + (5*e*atan((b^(1/2)*e*(a*e - b*d)^(3/2)*(d + e*x)^(1/2))/(a^2*e^3 + b^2*d^2*e - 2*a*b*d*e^2))*(a*e - b*d)^(3/2))/b^(7/2) + (2*e*(2*b^2*d - 2*a*b*e)*(d + e*x)^(1/2))/b^4","B"
1648,1,109,85,0.105095,"\text{Not used}","int((d + e*x)^(3/2)/(a^2 + b^2*x^2 + 2*a*b*x),x)","\frac{\left(a\,e^2-b\,d\,e\right)\,\sqrt{d+e\,x}}{b^3\,\left(d+e\,x\right)-b^3\,d+a\,b^2\,e}+\frac{2\,e\,\sqrt{d+e\,x}}{b^2}-\frac{3\,e\,\mathrm{atan}\left(\frac{\sqrt{b}\,e\,\sqrt{a\,e-b\,d}\,\sqrt{d+e\,x}}{a\,e^2-b\,d\,e}\right)\,\sqrt{a\,e-b\,d}}{b^{5/2}}","Not used",1,"((a*e^2 - b*d*e)*(d + e*x)^(1/2))/(b^3*(d + e*x) - b^3*d + a*b^2*e) + (2*e*(d + e*x)^(1/2))/b^2 - (3*e*atan((b^(1/2)*e*(a*e - b*d)^(1/2)*(d + e*x)^(1/2))/(a*e^2 - b*d*e))*(a*e - b*d)^(1/2))/b^(5/2)","B"
1649,1,61,70,0.069942,"\text{Not used}","int((d + e*x)^(1/2)/(a^2 + b^2*x^2 + 2*a*b*x),x)","\frac{e\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}}{\sqrt{a\,e-b\,d}}\right)}{b^{3/2}\,\sqrt{a\,e-b\,d}}-\frac{e\,\sqrt{d+e\,x}}{e\,x\,b^2+a\,e\,b}","Not used",1,"(e*atan((b^(1/2)*(d + e*x)^(1/2))/(a*e - b*d)^(1/2)))/(b^(3/2)*(a*e - b*d)^(1/2)) - (e*(d + e*x)^(1/2))/(a*b*e + b^2*e*x)","B"
1650,1,74,76,0.569180,"\text{Not used}","int(1/((d + e*x)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)),x)","\frac{e\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}}{\sqrt{a\,e-b\,d}}\right)}{\sqrt{b}\,{\left(a\,e-b\,d\right)}^{3/2}}+\frac{e\,\sqrt{d+e\,x}}{\left(a\,e-b\,d\right)\,\left(a\,e-b\,d+b\,\left(d+e\,x\right)\right)}","Not used",1,"(e*atan((b^(1/2)*(d + e*x)^(1/2))/(a*e - b*d)^(1/2)))/(b^(1/2)*(a*e - b*d)^(3/2)) + (e*(d + e*x)^(1/2))/((a*e - b*d)*(a*e - b*d + b*(d + e*x)))","B"
1651,1,123,99,0.158730,"\text{Not used}","int(1/((d + e*x)^(3/2)*(a^2 + b^2*x^2 + 2*a*b*x)),x)","-\frac{\frac{2\,e}{a\,e-b\,d}+\frac{3\,b\,e\,\left(d+e\,x\right)}{{\left(a\,e-b\,d\right)}^2}}{b\,{\left(d+e\,x\right)}^{3/2}+\left(a\,e-b\,d\right)\,\sqrt{d+e\,x}}-\frac{3\,\sqrt{b}\,e\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}\,\left(a^2\,e^2-2\,a\,b\,d\,e+b^2\,d^2\right)}{{\left(a\,e-b\,d\right)}^{5/2}}\right)}{{\left(a\,e-b\,d\right)}^{5/2}}","Not used",1,"- ((2*e)/(a*e - b*d) + (3*b*e*(d + e*x))/(a*e - b*d)^2)/(b*(d + e*x)^(3/2) + (a*e - b*d)*(d + e*x)^(1/2)) - (3*b^(1/2)*e*atan((b^(1/2)*(d + e*x)^(1/2)*(a^2*e^2 + b^2*d^2 - 2*a*b*d*e))/(a*e - b*d)^(5/2)))/(a*e - b*d)^(5/2)","B"
1652,1,161,124,0.666821,"\text{Not used}","int(1/((d + e*x)^(5/2)*(a^2 + b^2*x^2 + 2*a*b*x)),x)","\frac{\frac{10\,b\,e\,\left(d+e\,x\right)}{3\,{\left(a\,e-b\,d\right)}^2}-\frac{2\,e}{3\,\left(a\,e-b\,d\right)}+\frac{5\,b^2\,e\,{\left(d+e\,x\right)}^2}{{\left(a\,e-b\,d\right)}^3}}{b\,{\left(d+e\,x\right)}^{5/2}+\left(a\,e-b\,d\right)\,{\left(d+e\,x\right)}^{3/2}}+\frac{5\,b^{3/2}\,e\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}\,\left(a^3\,e^3-3\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e-b^3\,d^3\right)}{{\left(a\,e-b\,d\right)}^{7/2}}\right)}{{\left(a\,e-b\,d\right)}^{7/2}}","Not used",1,"((10*b*e*(d + e*x))/(3*(a*e - b*d)^2) - (2*e)/(3*(a*e - b*d)) + (5*b^2*e*(d + e*x)^2)/(a*e - b*d)^3)/(b*(d + e*x)^(5/2) + (a*e - b*d)*(d + e*x)^(3/2)) + (5*b^(3/2)*e*atan((b^(1/2)*(d + e*x)^(1/2)*(a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2))/(a*e - b*d)^(7/2)))/(a*e - b*d)^(7/2)","B"
1653,1,198,151,0.717865,"\text{Not used}","int(1/((d + e*x)^(7/2)*(a^2 + b^2*x^2 + 2*a*b*x)),x)","-\frac{\frac{2\,e}{5\,\left(a\,e-b\,d\right)}-\frac{14\,b\,e\,\left(d+e\,x\right)}{15\,{\left(a\,e-b\,d\right)}^2}+\frac{14\,b^2\,e\,{\left(d+e\,x\right)}^2}{3\,{\left(a\,e-b\,d\right)}^3}+\frac{7\,b^3\,e\,{\left(d+e\,x\right)}^3}{{\left(a\,e-b\,d\right)}^4}}{b\,{\left(d+e\,x\right)}^{7/2}+\left(a\,e-b\,d\right)\,{\left(d+e\,x\right)}^{5/2}}-\frac{7\,b^{5/2}\,e\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}\,\left(a^4\,e^4-4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-4\,a\,b^3\,d^3\,e+b^4\,d^4\right)}{{\left(a\,e-b\,d\right)}^{9/2}}\right)}{{\left(a\,e-b\,d\right)}^{9/2}}","Not used",1,"- ((2*e)/(5*(a*e - b*d)) - (14*b*e*(d + e*x))/(15*(a*e - b*d)^2) + (14*b^2*e*(d + e*x)^2)/(3*(a*e - b*d)^3) + (7*b^3*e*(d + e*x)^3)/(a*e - b*d)^4)/(b*(d + e*x)^(7/2) + (a*e - b*d)*(d + e*x)^(5/2)) - (7*b^(5/2)*e*atan((b^(1/2)*(d + e*x)^(1/2)*(a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 4*a*b^3*d^3*e - 4*a^3*b*d*e^3))/(a*e - b*d)^(9/2)))/(a*e - b*d)^(9/2)","B"
1654,1,495,201,0.681812,"\text{Not used}","int((d + e*x)^(11/2)/(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","\left(\frac{2\,e^3\,{\left(4\,b^4\,d-4\,a\,b^3\,e\right)}^2}{b^{12}}-\frac{12\,e^3\,{\left(a\,e-b\,d\right)}^2}{b^6}\right)\,\sqrt{d+e\,x}+\frac{\sqrt{d+e\,x}\,\left(\frac{71\,a^5\,e^8}{8}-\frac{355\,a^4\,b\,d\,e^7}{8}+\frac{355\,a^3\,b^2\,d^2\,e^6}{4}-\frac{355\,a^2\,b^3\,d^3\,e^5}{4}+\frac{355\,a\,b^4\,d^4\,e^4}{8}-\frac{71\,b^5\,d^5\,e^3}{8}\right)+{\left(d+e\,x\right)}^{5/2}\,\left(\frac{89\,a^3\,b^2\,e^6}{8}-\frac{267\,a^2\,b^3\,d\,e^5}{8}+\frac{267\,a\,b^4\,d^2\,e^4}{8}-\frac{89\,b^5\,d^3\,e^3}{8}\right)+{\left(d+e\,x\right)}^{3/2}\,\left(\frac{59\,a^4\,b\,e^7}{3}-\frac{236\,a^3\,b^2\,d\,e^6}{3}+118\,a^2\,b^3\,d^2\,e^5-\frac{236\,a\,b^4\,d^3\,e^4}{3}+\frac{59\,b^5\,d^4\,e^3}{3}\right)}{b^9\,{\left(d+e\,x\right)}^3-\left(3\,b^9\,d-3\,a\,b^8\,e\right)\,{\left(d+e\,x\right)}^2+\left(d+e\,x\right)\,\left(3\,a^2\,b^7\,e^2-6\,a\,b^8\,d\,e+3\,b^9\,d^2\right)-b^9\,d^3+a^3\,b^6\,e^3-3\,a^2\,b^7\,d\,e^2+3\,a\,b^8\,d^2\,e}+\frac{2\,e^3\,{\left(d+e\,x\right)}^{5/2}}{5\,b^4}+\frac{2\,e^3\,\left(4\,b^4\,d-4\,a\,b^3\,e\right)\,{\left(d+e\,x\right)}^{3/2}}{3\,b^8}-\frac{231\,e^3\,\mathrm{atan}\left(\frac{\sqrt{b}\,e^3\,{\left(a\,e-b\,d\right)}^{5/2}\,\sqrt{d+e\,x}}{a^3\,e^6-3\,a^2\,b\,d\,e^5+3\,a\,b^2\,d^2\,e^4-b^3\,d^3\,e^3}\right)\,{\left(a\,e-b\,d\right)}^{5/2}}{8\,b^{13/2}}","Not used",1,"((2*e^3*(4*b^4*d - 4*a*b^3*e)^2)/b^12 - (12*e^3*(a*e - b*d)^2)/b^6)*(d + e*x)^(1/2) + ((d + e*x)^(1/2)*((71*a^5*e^8)/8 - (71*b^5*d^5*e^3)/8 + (355*a*b^4*d^4*e^4)/8 - (355*a^2*b^3*d^3*e^5)/4 + (355*a^3*b^2*d^2*e^6)/4 - (355*a^4*b*d*e^7)/8) + (d + e*x)^(5/2)*((89*a^3*b^2*e^6)/8 - (89*b^5*d^3*e^3)/8 + (267*a*b^4*d^2*e^4)/8 - (267*a^2*b^3*d*e^5)/8) + (d + e*x)^(3/2)*((59*a^4*b*e^7)/3 + (59*b^5*d^4*e^3)/3 - (236*a*b^4*d^3*e^4)/3 - (236*a^3*b^2*d*e^6)/3 + 118*a^2*b^3*d^2*e^5))/(b^9*(d + e*x)^3 - (3*b^9*d - 3*a*b^8*e)*(d + e*x)^2 + (d + e*x)*(3*b^9*d^2 + 3*a^2*b^7*e^2 - 6*a*b^8*d*e) - b^9*d^3 + a^3*b^6*e^3 - 3*a^2*b^7*d*e^2 + 3*a*b^8*d^2*e) + (2*e^3*(d + e*x)^(5/2))/(5*b^4) + (2*e^3*(4*b^4*d - 4*a*b^3*e)*(d + e*x)^(3/2))/(3*b^8) - (231*e^3*atan((b^(1/2)*e^3*(a*e - b*d)^(5/2)*(d + e*x)^(1/2))/(a^3*e^6 - b^3*d^3*e^3 + 3*a*b^2*d^2*e^4 - 3*a^2*b*d*e^5))*(a*e - b*d)^(5/2))/(8*b^(13/2))","B"
1655,1,388,172,0.678890,"\text{Not used}","int((d + e*x)^(9/2)/(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","\frac{2\,e^3\,{\left(d+e\,x\right)}^{3/2}}{3\,b^4}-\frac{{\left(d+e\,x\right)}^{5/2}\,\left(\frac{55\,a^2\,b^2\,e^5}{8}-\frac{55\,a\,b^3\,d\,e^4}{4}+\frac{55\,b^4\,d^2\,e^3}{8}\right)+{\left(d+e\,x\right)}^{3/2}\,\left(\frac{35\,a^3\,b\,e^6}{3}-35\,a^2\,b^2\,d\,e^5+35\,a\,b^3\,d^2\,e^4-\frac{35\,b^4\,d^3\,e^3}{3}\right)+\sqrt{d+e\,x}\,\left(\frac{41\,a^4\,e^7}{8}-\frac{41\,a^3\,b\,d\,e^6}{2}+\frac{123\,a^2\,b^2\,d^2\,e^5}{4}-\frac{41\,a\,b^3\,d^3\,e^4}{2}+\frac{41\,b^4\,d^4\,e^3}{8}\right)}{b^8\,{\left(d+e\,x\right)}^3-\left(3\,b^8\,d-3\,a\,b^7\,e\right)\,{\left(d+e\,x\right)}^2+\left(d+e\,x\right)\,\left(3\,a^2\,b^6\,e^2-6\,a\,b^7\,d\,e+3\,b^8\,d^2\right)-b^8\,d^3+a^3\,b^5\,e^3-3\,a^2\,b^6\,d\,e^2+3\,a\,b^7\,d^2\,e}+\frac{2\,e^3\,\left(4\,b^4\,d-4\,a\,b^3\,e\right)\,\sqrt{d+e\,x}}{b^8}+\frac{105\,e^3\,\mathrm{atan}\left(\frac{\sqrt{b}\,e^3\,{\left(a\,e-b\,d\right)}^{3/2}\,\sqrt{d+e\,x}}{a^2\,e^5-2\,a\,b\,d\,e^4+b^2\,d^2\,e^3}\right)\,{\left(a\,e-b\,d\right)}^{3/2}}{8\,b^{11/2}}","Not used",1,"(2*e^3*(d + e*x)^(3/2))/(3*b^4) - ((d + e*x)^(5/2)*((55*a^2*b^2*e^5)/8 + (55*b^4*d^2*e^3)/8 - (55*a*b^3*d*e^4)/4) + (d + e*x)^(3/2)*((35*a^3*b*e^6)/3 - (35*b^4*d^3*e^3)/3 + 35*a*b^3*d^2*e^4 - 35*a^2*b^2*d*e^5) + (d + e*x)^(1/2)*((41*a^4*e^7)/8 + (41*b^4*d^4*e^3)/8 - (41*a*b^3*d^3*e^4)/2 + (123*a^2*b^2*d^2*e^5)/4 - (41*a^3*b*d*e^6)/2))/(b^8*(d + e*x)^3 - (3*b^8*d - 3*a*b^7*e)*(d + e*x)^2 + (d + e*x)*(3*b^8*d^2 + 3*a^2*b^6*e^2 - 6*a*b^7*d*e) - b^8*d^3 + a^3*b^5*e^3 - 3*a^2*b^6*d*e^2 + 3*a*b^7*d^2*e) + (2*e^3*(4*b^4*d - 4*a*b^3*e)*(d + e*x)^(1/2))/b^8 + (105*e^3*atan((b^(1/2)*e^3*(a*e - b*d)^(3/2)*(d + e*x)^(1/2))/(a^2*e^5 + b^2*d^2*e^3 - 2*a*b*d*e^4))*(a*e - b*d)^(3/2))/(8*b^(11/2))","B"
1656,1,303,145,0.686239,"\text{Not used}","int((d + e*x)^(7/2)/(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","\frac{\sqrt{d+e\,x}\,\left(\frac{19\,a^3\,e^6}{8}-\frac{57\,a^2\,b\,d\,e^5}{8}+\frac{57\,a\,b^2\,d^2\,e^4}{8}-\frac{19\,b^3\,d^3\,e^3}{8}\right)+\left(\frac{29\,a\,b^2\,e^4}{8}-\frac{29\,b^3\,d\,e^3}{8}\right)\,{\left(d+e\,x\right)}^{5/2}+{\left(d+e\,x\right)}^{3/2}\,\left(\frac{17\,a^2\,b\,e^5}{3}-\frac{34\,a\,b^2\,d\,e^4}{3}+\frac{17\,b^3\,d^2\,e^3}{3}\right)}{b^7\,{\left(d+e\,x\right)}^3-\left(3\,b^7\,d-3\,a\,b^6\,e\right)\,{\left(d+e\,x\right)}^2+\left(d+e\,x\right)\,\left(3\,a^2\,b^5\,e^2-6\,a\,b^6\,d\,e+3\,b^7\,d^2\right)-b^7\,d^3+a^3\,b^4\,e^3-3\,a^2\,b^5\,d\,e^2+3\,a\,b^6\,d^2\,e}+\frac{2\,e^3\,\sqrt{d+e\,x}}{b^4}-\frac{35\,e^3\,\mathrm{atan}\left(\frac{\sqrt{b}\,e^3\,\sqrt{a\,e-b\,d}\,\sqrt{d+e\,x}}{a\,e^4-b\,d\,e^3}\right)\,\sqrt{a\,e-b\,d}}{8\,b^{9/2}}","Not used",1,"((d + e*x)^(1/2)*((19*a^3*e^6)/8 - (19*b^3*d^3*e^3)/8 + (57*a*b^2*d^2*e^4)/8 - (57*a^2*b*d*e^5)/8) + ((29*a*b^2*e^4)/8 - (29*b^3*d*e^3)/8)*(d + e*x)^(5/2) + (d + e*x)^(3/2)*((17*a^2*b*e^5)/3 + (17*b^3*d^2*e^3)/3 - (34*a*b^2*d*e^4)/3))/(b^7*(d + e*x)^3 - (3*b^7*d - 3*a*b^6*e)*(d + e*x)^2 + (d + e*x)*(3*b^7*d^2 + 3*a^2*b^5*e^2 - 6*a*b^6*d*e) - b^7*d^3 + a^3*b^4*e^3 - 3*a^2*b^5*d*e^2 + 3*a*b^6*d^2*e) + (2*e^3*(d + e*x)^(1/2))/b^4 - (35*e^3*atan((b^(1/2)*e^3*(a*e - b*d)^(1/2)*(d + e*x)^(1/2))/(a*e^4 - b*d*e^3))*(a*e - b*d)^(1/2))/(8*b^(9/2))","B"
1657,1,222,126,0.174740,"\text{Not used}","int((d + e*x)^(5/2)/(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","\frac{5\,e^3\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}}{\sqrt{a\,e-b\,d}}\right)}{8\,b^{7/2}\,\sqrt{a\,e-b\,d}}-\frac{\frac{11\,e^3\,{\left(d+e\,x\right)}^{5/2}}{8\,b}+\frac{5\,e^3\,\sqrt{d+e\,x}\,\left(a^2\,e^2-2\,a\,b\,d\,e+b^2\,d^2\right)}{8\,b^3}+\frac{5\,e^3\,\left(a\,e-b\,d\right)\,{\left(d+e\,x\right)}^{3/2}}{3\,b^2}}{\left(d+e\,x\right)\,\left(3\,a^2\,b\,e^2-6\,a\,b^2\,d\,e+3\,b^3\,d^2\right)+b^3\,{\left(d+e\,x\right)}^3-\left(3\,b^3\,d-3\,a\,b^2\,e\right)\,{\left(d+e\,x\right)}^2+a^3\,e^3-b^3\,d^3+3\,a\,b^2\,d^2\,e-3\,a^2\,b\,d\,e^2}","Not used",1,"(5*e^3*atan((b^(1/2)*(d + e*x)^(1/2))/(a*e - b*d)^(1/2)))/(8*b^(7/2)*(a*e - b*d)^(1/2)) - ((11*e^3*(d + e*x)^(5/2))/(8*b) + (5*e^3*(d + e*x)^(1/2)*(a^2*e^2 + b^2*d^2 - 2*a*b*d*e))/(8*b^3) + (5*e^3*(a*e - b*d)*(d + e*x)^(3/2))/(3*b^2))/((d + e*x)*(3*b^3*d^2 + 3*a^2*b*e^2 - 6*a*b^2*d*e) + b^3*(d + e*x)^3 - (3*b^3*d - 3*a*b^2*e)*(d + e*x)^2 + a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2)","B"
1658,1,209,136,0.135399,"\text{Not used}","int((d + e*x)^(3/2)/(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","\frac{e^3\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}}{\sqrt{a\,e-b\,d}}\right)}{8\,b^{5/2}\,{\left(a\,e-b\,d\right)}^{3/2}}-\frac{\frac{e^3\,{\left(d+e\,x\right)}^{3/2}}{3\,b}-\frac{e^3\,{\left(d+e\,x\right)}^{5/2}}{8\,\left(a\,e-b\,d\right)}+\frac{e^3\,\left(a\,e-b\,d\right)\,\sqrt{d+e\,x}}{8\,b^2}}{\left(d+e\,x\right)\,\left(3\,a^2\,b\,e^2-6\,a\,b^2\,d\,e+3\,b^3\,d^2\right)+b^3\,{\left(d+e\,x\right)}^3-\left(3\,b^3\,d-3\,a\,b^2\,e\right)\,{\left(d+e\,x\right)}^2+a^3\,e^3-b^3\,d^3+3\,a\,b^2\,d^2\,e-3\,a^2\,b\,d\,e^2}","Not used",1,"(e^3*atan((b^(1/2)*(d + e*x)^(1/2))/(a*e - b*d)^(1/2)))/(8*b^(5/2)*(a*e - b*d)^(3/2)) - ((e^3*(d + e*x)^(3/2))/(3*b) - (e^3*(d + e*x)^(5/2))/(8*(a*e - b*d)) + (e^3*(a*e - b*d)*(d + e*x)^(1/2))/(8*b^2))/((d + e*x)*(3*b^3*d^2 + 3*a^2*b*e^2 - 6*a*b^2*d*e) + b^3*(d + e*x)^3 - (3*b^3*d - 3*a*b^2*e)*(d + e*x)^2 + a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2)","B"
1659,1,207,146,0.650799,"\text{Not used}","int((d + e*x)^(1/2)/(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","\frac{\frac{e^3\,{\left(d+e\,x\right)}^{3/2}}{3\,\left(a\,e-b\,d\right)}-\frac{e^3\,\sqrt{d+e\,x}}{8\,b}+\frac{b\,e^3\,{\left(d+e\,x\right)}^{5/2}}{8\,{\left(a\,e-b\,d\right)}^2}}{\left(d+e\,x\right)\,\left(3\,a^2\,b\,e^2-6\,a\,b^2\,d\,e+3\,b^3\,d^2\right)+b^3\,{\left(d+e\,x\right)}^3-\left(3\,b^3\,d-3\,a\,b^2\,e\right)\,{\left(d+e\,x\right)}^2+a^3\,e^3-b^3\,d^3+3\,a\,b^2\,d^2\,e-3\,a^2\,b\,d\,e^2}+\frac{e^3\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}}{\sqrt{a\,e-b\,d}}\right)}{8\,b^{3/2}\,{\left(a\,e-b\,d\right)}^{5/2}}","Not used",1,"((e^3*(d + e*x)^(3/2))/(3*(a*e - b*d)) - (e^3*(d + e*x)^(1/2))/(8*b) + (b*e^3*(d + e*x)^(5/2))/(8*(a*e - b*d)^2))/((d + e*x)*(3*b^3*d^2 + 3*a^2*b*e^2 - 6*a*b^2*d*e) + b^3*(d + e*x)^3 - (3*b^3*d - 3*a*b^2*e)*(d + e*x)^2 + a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2) + (e^3*atan((b^(1/2)*(d + e*x)^(1/2))/(a*e - b*d)^(1/2)))/(8*b^(3/2)*(a*e - b*d)^(5/2))","B"
1660,1,218,147,0.653750,"\text{Not used}","int(1/((d + e*x)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^2),x)","\frac{\frac{11\,e^3\,\sqrt{d+e\,x}}{8\,\left(a\,e-b\,d\right)}+\frac{5\,b^2\,e^3\,{\left(d+e\,x\right)}^{5/2}}{8\,{\left(a\,e-b\,d\right)}^3}+\frac{5\,b\,e^3\,{\left(d+e\,x\right)}^{3/2}}{3\,{\left(a\,e-b\,d\right)}^2}}{\left(d+e\,x\right)\,\left(3\,a^2\,b\,e^2-6\,a\,b^2\,d\,e+3\,b^3\,d^2\right)+b^3\,{\left(d+e\,x\right)}^3-\left(3\,b^3\,d-3\,a\,b^2\,e\right)\,{\left(d+e\,x\right)}^2+a^3\,e^3-b^3\,d^3+3\,a\,b^2\,d^2\,e-3\,a^2\,b\,d\,e^2}+\frac{5\,e^3\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}}{\sqrt{a\,e-b\,d}}\right)}{8\,\sqrt{b}\,{\left(a\,e-b\,d\right)}^{7/2}}","Not used",1,"((11*e^3*(d + e*x)^(1/2))/(8*(a*e - b*d)) + (5*b^2*e^3*(d + e*x)^(5/2))/(8*(a*e - b*d)^3) + (5*b*e^3*(d + e*x)^(3/2))/(3*(a*e - b*d)^2))/((d + e*x)*(3*b^3*d^2 + 3*a^2*b*e^2 - 6*a*b^2*d*e) + b^3*(d + e*x)^3 - (3*b^3*d - 3*a*b^2*e)*(d + e*x)^2 + a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2) + (5*e^3*atan((b^(1/2)*(d + e*x)^(1/2))/(a*e - b*d)^(1/2)))/(8*b^(1/2)*(a*e - b*d)^(7/2))","B"
1661,1,294,173,0.776516,"\text{Not used}","int(1/((d + e*x)^(3/2)*(a^2 + b^2*x^2 + 2*a*b*x)^2),x)","-\frac{\frac{2\,e^3}{a\,e-b\,d}+\frac{35\,b^2\,e^3\,{\left(d+e\,x\right)}^2}{3\,{\left(a\,e-b\,d\right)}^3}+\frac{35\,b^3\,e^3\,{\left(d+e\,x\right)}^3}{8\,{\left(a\,e-b\,d\right)}^4}+\frac{77\,b\,e^3\,\left(d+e\,x\right)}{8\,{\left(a\,e-b\,d\right)}^2}}{\sqrt{d+e\,x}\,\left(a^3\,e^3-3\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e-b^3\,d^3\right)+b^3\,{\left(d+e\,x\right)}^{7/2}-\left(3\,b^3\,d-3\,a\,b^2\,e\right)\,{\left(d+e\,x\right)}^{5/2}+{\left(d+e\,x\right)}^{3/2}\,\left(3\,a^2\,b\,e^2-6\,a\,b^2\,d\,e+3\,b^3\,d^2\right)}-\frac{35\,\sqrt{b}\,e^3\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}\,\left(a^4\,e^4-4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-4\,a\,b^3\,d^3\,e+b^4\,d^4\right)}{{\left(a\,e-b\,d\right)}^{9/2}}\right)}{8\,{\left(a\,e-b\,d\right)}^{9/2}}","Not used",1,"- ((2*e^3)/(a*e - b*d) + (35*b^2*e^3*(d + e*x)^2)/(3*(a*e - b*d)^3) + (35*b^3*e^3*(d + e*x)^3)/(8*(a*e - b*d)^4) + (77*b*e^3*(d + e*x))/(8*(a*e - b*d)^2))/((d + e*x)^(1/2)*(a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2) + b^3*(d + e*x)^(7/2) - (3*b^3*d - 3*a*b^2*e)*(d + e*x)^(5/2) + (d + e*x)^(3/2)*(3*b^3*d^2 + 3*a^2*b*e^2 - 6*a*b^2*d*e)) - (35*b^(1/2)*e^3*atan((b^(1/2)*(d + e*x)^(1/2)*(a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 4*a*b^3*d^3*e - 4*a^3*b*d*e^3))/(a*e - b*d)^(9/2)))/(8*(a*e - b*d)^(9/2))","B"
1662,1,334,200,0.873088,"\text{Not used}","int(1/((d + e*x)^(5/2)*(a^2 + b^2*x^2 + 2*a*b*x)^2),x)","\frac{\frac{231\,b^2\,e^3\,{\left(d+e\,x\right)}^2}{8\,{\left(a\,e-b\,d\right)}^3}-\frac{2\,e^3}{3\,\left(a\,e-b\,d\right)}+\frac{35\,b^3\,e^3\,{\left(d+e\,x\right)}^3}{{\left(a\,e-b\,d\right)}^4}+\frac{105\,b^4\,e^3\,{\left(d+e\,x\right)}^4}{8\,{\left(a\,e-b\,d\right)}^5}+\frac{6\,b\,e^3\,\left(d+e\,x\right)}{{\left(a\,e-b\,d\right)}^2}}{{\left(d+e\,x\right)}^{3/2}\,\left(a^3\,e^3-3\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e-b^3\,d^3\right)+b^3\,{\left(d+e\,x\right)}^{9/2}-\left(3\,b^3\,d-3\,a\,b^2\,e\right)\,{\left(d+e\,x\right)}^{7/2}+{\left(d+e\,x\right)}^{5/2}\,\left(3\,a^2\,b\,e^2-6\,a\,b^2\,d\,e+3\,b^3\,d^2\right)}+\frac{105\,b^{3/2}\,e^3\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}\,\left(a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5\right)}{{\left(a\,e-b\,d\right)}^{11/2}}\right)}{8\,{\left(a\,e-b\,d\right)}^{11/2}}","Not used",1,"((231*b^2*e^3*(d + e*x)^2)/(8*(a*e - b*d)^3) - (2*e^3)/(3*(a*e - b*d)) + (35*b^3*e^3*(d + e*x)^3)/(a*e - b*d)^4 + (105*b^4*e^3*(d + e*x)^4)/(8*(a*e - b*d)^5) + (6*b*e^3*(d + e*x))/(a*e - b*d)^2)/((d + e*x)^(3/2)*(a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2) + b^3*(d + e*x)^(9/2) - (3*b^3*d - 3*a*b^2*e)*(d + e*x)^(7/2) + (d + e*x)^(5/2)*(3*b^3*d^2 + 3*a^2*b*e^2 - 6*a*b^2*d*e)) + (105*b^(3/2)*e^3*atan((b^(1/2)*(d + e*x)^(1/2)*(a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4))/(a*e - b*d)^(11/2)))/(8*(a*e - b*d)^(11/2))","B"
1663,1,373,229,0.970188,"\text{Not used}","int(1/((d + e*x)^(7/2)*(a^2 + b^2*x^2 + 2*a*b*x)^2),x)","-\frac{\frac{2\,e^3}{5\,\left(a\,e-b\,d\right)}+\frac{66\,b^2\,e^3\,{\left(d+e\,x\right)}^2}{5\,{\left(a\,e-b\,d\right)}^3}+\frac{2541\,b^3\,e^3\,{\left(d+e\,x\right)}^3}{40\,{\left(a\,e-b\,d\right)}^4}+\frac{77\,b^4\,e^3\,{\left(d+e\,x\right)}^4}{{\left(a\,e-b\,d\right)}^5}+\frac{231\,b^5\,e^3\,{\left(d+e\,x\right)}^5}{8\,{\left(a\,e-b\,d\right)}^6}-\frac{22\,b\,e^3\,\left(d+e\,x\right)}{15\,{\left(a\,e-b\,d\right)}^2}}{{\left(d+e\,x\right)}^{5/2}\,\left(a^3\,e^3-3\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e-b^3\,d^3\right)+b^3\,{\left(d+e\,x\right)}^{11/2}-\left(3\,b^3\,d-3\,a\,b^2\,e\right)\,{\left(d+e\,x\right)}^{9/2}+{\left(d+e\,x\right)}^{7/2}\,\left(3\,a^2\,b\,e^2-6\,a\,b^2\,d\,e+3\,b^3\,d^2\right)}-\frac{231\,b^{5/2}\,e^3\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}\,\left(a^6\,e^6-6\,a^5\,b\,d\,e^5+15\,a^4\,b^2\,d^2\,e^4-20\,a^3\,b^3\,d^3\,e^3+15\,a^2\,b^4\,d^4\,e^2-6\,a\,b^5\,d^5\,e+b^6\,d^6\right)}{{\left(a\,e-b\,d\right)}^{13/2}}\right)}{8\,{\left(a\,e-b\,d\right)}^{13/2}}","Not used",1,"- ((2*e^3)/(5*(a*e - b*d)) + (66*b^2*e^3*(d + e*x)^2)/(5*(a*e - b*d)^3) + (2541*b^3*e^3*(d + e*x)^3)/(40*(a*e - b*d)^4) + (77*b^4*e^3*(d + e*x)^4)/(a*e - b*d)^5 + (231*b^5*e^3*(d + e*x)^5)/(8*(a*e - b*d)^6) - (22*b*e^3*(d + e*x))/(15*(a*e - b*d)^2))/((d + e*x)^(5/2)*(a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2) + b^3*(d + e*x)^(11/2) - (3*b^3*d - 3*a*b^2*e)*(d + e*x)^(9/2) + (d + e*x)^(7/2)*(3*b^3*d^2 + 3*a^2*b*e^2 - 6*a*b^2*d*e)) - (231*b^(5/2)*e^3*atan((b^(1/2)*(d + e*x)^(1/2)*(a^6*e^6 + b^6*d^6 + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a*b^5*d^5*e - 6*a^5*b*d*e^5))/(a*e - b*d)^(13/2)))/(8*(a*e - b*d)^(13/2))","B"
1664,1,846,253,0.832346,"\text{Not used}","int((d + e*x)^(15/2)/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\left(\frac{2\,e^5\,{\left(6\,b^6\,d-6\,a\,b^5\,e\right)}^2}{b^{18}}-\frac{30\,e^5\,{\left(a\,e-b\,d\right)}^2}{b^8}\right)\,\sqrt{d+e\,x}+\frac{\sqrt{d+e\,x}\,\left(\frac{3633\,a^7\,e^{12}}{128}-\frac{25431\,a^6\,b\,d\,e^{11}}{128}+\frac{76293\,a^5\,b^2\,d^2\,e^{10}}{128}-\frac{127155\,a^4\,b^3\,d^3\,e^9}{128}+\frac{127155\,a^3\,b^4\,d^4\,e^8}{128}-\frac{76293\,a^2\,b^5\,d^5\,e^7}{128}+\frac{25431\,a\,b^6\,d^6\,e^6}{128}-\frac{3633\,b^7\,d^7\,e^5}{128}\right)+{\left(d+e\,x\right)}^{5/2}\,\left(\frac{1001\,a^5\,b^2\,e^{10}}{5}-1001\,a^4\,b^3\,d\,e^9+2002\,a^3\,b^4\,d^2\,e^8-2002\,a^2\,b^5\,d^3\,e^7+1001\,a\,b^6\,d^4\,e^6-\frac{1001\,b^7\,d^5\,e^5}{5}\right)+{\left(d+e\,x\right)}^{3/2}\,\left(\frac{7837\,a^6\,b\,e^{11}}{64}-\frac{23511\,a^5\,b^2\,d\,e^{10}}{32}+\frac{117555\,a^4\,b^3\,d^2\,e^9}{64}-\frac{39185\,a^3\,b^4\,d^3\,e^8}{16}+\frac{117555\,a^2\,b^5\,d^4\,e^7}{64}-\frac{23511\,a\,b^6\,d^5\,e^6}{32}+\frac{7837\,b^7\,d^6\,e^5}{64}\right)+{\left(d+e\,x\right)}^{9/2}\,\left(\frac{5327\,a^3\,b^4\,e^8}{128}-\frac{15981\,a^2\,b^5\,d\,e^7}{128}+\frac{15981\,a\,b^6\,d^2\,e^6}{128}-\frac{5327\,b^7\,d^3\,e^5}{128}\right)+{\left(d+e\,x\right)}^{7/2}\,\left(\frac{9443\,a^4\,b^3\,e^9}{64}-\frac{9443\,a^3\,b^4\,d\,e^8}{16}+\frac{28329\,a^2\,b^5\,d^2\,e^7}{32}-\frac{9443\,a\,b^6\,d^3\,e^6}{16}+\frac{9443\,b^7\,d^4\,e^5}{64}\right)}{\left(d+e\,x\right)\,\left(5\,a^4\,b^9\,e^4-20\,a^3\,b^{10}\,d\,e^3+30\,a^2\,b^{11}\,d^2\,e^2-20\,a\,b^{12}\,d^3\,e+5\,b^{13}\,d^4\right)-{\left(d+e\,x\right)}^2\,\left(-10\,a^3\,b^{10}\,e^3+30\,a^2\,b^{11}\,d\,e^2-30\,a\,b^{12}\,d^2\,e+10\,b^{13}\,d^3\right)+b^{13}\,{\left(d+e\,x\right)}^5-\left(5\,b^{13}\,d-5\,a\,b^{12}\,e\right)\,{\left(d+e\,x\right)}^4-b^{13}\,d^5+{\left(d+e\,x\right)}^3\,\left(10\,a^2\,b^{11}\,e^2-20\,a\,b^{12}\,d\,e+10\,b^{13}\,d^2\right)+a^5\,b^8\,e^5-5\,a^4\,b^9\,d\,e^4-10\,a^2\,b^{11}\,d^3\,e^2+10\,a^3\,b^{10}\,d^2\,e^3+5\,a\,b^{12}\,d^4\,e}+\frac{2\,e^5\,{\left(d+e\,x\right)}^{5/2}}{5\,b^6}+\frac{2\,e^5\,\left(6\,b^6\,d-6\,a\,b^5\,e\right)\,{\left(d+e\,x\right)}^{3/2}}{3\,b^{12}}-\frac{9009\,e^5\,\mathrm{atan}\left(\frac{\sqrt{b}\,e^5\,{\left(a\,e-b\,d\right)}^{5/2}\,\sqrt{d+e\,x}}{a^3\,e^8-3\,a^2\,b\,d\,e^7+3\,a\,b^2\,d^2\,e^6-b^3\,d^3\,e^5}\right)\,{\left(a\,e-b\,d\right)}^{5/2}}{128\,b^{17/2}}","Not used",1,"((2*e^5*(6*b^6*d - 6*a*b^5*e)^2)/b^18 - (30*e^5*(a*e - b*d)^2)/b^8)*(d + e*x)^(1/2) + ((d + e*x)^(1/2)*((3633*a^7*e^12)/128 - (3633*b^7*d^7*e^5)/128 + (25431*a*b^6*d^6*e^6)/128 - (76293*a^2*b^5*d^5*e^7)/128 + (127155*a^3*b^4*d^4*e^8)/128 - (127155*a^4*b^3*d^3*e^9)/128 + (76293*a^5*b^2*d^2*e^10)/128 - (25431*a^6*b*d*e^11)/128) + (d + e*x)^(5/2)*((1001*a^5*b^2*e^10)/5 - (1001*b^7*d^5*e^5)/5 + 1001*a*b^6*d^4*e^6 - 1001*a^4*b^3*d*e^9 - 2002*a^2*b^5*d^3*e^7 + 2002*a^3*b^4*d^2*e^8) + (d + e*x)^(3/2)*((7837*a^6*b*e^11)/64 + (7837*b^7*d^6*e^5)/64 - (23511*a*b^6*d^5*e^6)/32 - (23511*a^5*b^2*d*e^10)/32 + (117555*a^2*b^5*d^4*e^7)/64 - (39185*a^3*b^4*d^3*e^8)/16 + (117555*a^4*b^3*d^2*e^9)/64) + (d + e*x)^(9/2)*((5327*a^3*b^4*e^8)/128 - (5327*b^7*d^3*e^5)/128 + (15981*a*b^6*d^2*e^6)/128 - (15981*a^2*b^5*d*e^7)/128) + (d + e*x)^(7/2)*((9443*a^4*b^3*e^9)/64 + (9443*b^7*d^4*e^5)/64 - (9443*a*b^6*d^3*e^6)/16 - (9443*a^3*b^4*d*e^8)/16 + (28329*a^2*b^5*d^2*e^7)/32))/((d + e*x)*(5*b^13*d^4 + 5*a^4*b^9*e^4 - 20*a^3*b^10*d*e^3 + 30*a^2*b^11*d^2*e^2 - 20*a*b^12*d^3*e) - (d + e*x)^2*(10*b^13*d^3 - 10*a^3*b^10*e^3 + 30*a^2*b^11*d*e^2 - 30*a*b^12*d^2*e) + b^13*(d + e*x)^5 - (5*b^13*d - 5*a*b^12*e)*(d + e*x)^4 - b^13*d^5 + (d + e*x)^3*(10*b^13*d^2 + 10*a^2*b^11*e^2 - 20*a*b^12*d*e) + a^5*b^8*e^5 - 5*a^4*b^9*d*e^4 - 10*a^2*b^11*d^3*e^2 + 10*a^3*b^10*d^2*e^3 + 5*a*b^12*d^4*e) + (2*e^5*(d + e*x)^(5/2))/(5*b^6) + (2*e^5*(6*b^6*d - 6*a*b^5*e)*(d + e*x)^(3/2))/(3*b^12) - (9009*e^5*atan((b^(1/2)*e^5*(a*e - b*d)^(5/2)*(d + e*x)^(1/2))/(a^3*e^8 - b^3*d^3*e^5 + 3*a*b^2*d^2*e^6 - 3*a^2*b*d*e^7))*(a*e - b*d)^(5/2))/(128*b^(17/2))","B"
1665,1,711,224,0.810570,"\text{Not used}","int((d + e*x)^(13/2)/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\frac{2\,e^5\,{\left(d+e\,x\right)}^{3/2}}{3\,b^6}-\frac{{\left(d+e\,x\right)}^{9/2}\,\left(\frac{2373\,a^2\,b^4\,e^7}{128}-\frac{2373\,a\,b^5\,d\,e^6}{64}+\frac{2373\,b^6\,d^2\,e^5}{128}\right)+{\left(d+e\,x\right)}^{7/2}\,\left(\frac{12131\,a^3\,b^3\,e^8}{192}-\frac{12131\,a^2\,b^4\,d\,e^7}{64}+\frac{12131\,a\,b^5\,d^2\,e^6}{64}-\frac{12131\,b^6\,d^3\,e^5}{192}\right)+\sqrt{d+e\,x}\,\left(\frac{1467\,a^6\,e^{11}}{128}-\frac{4401\,a^5\,b\,d\,e^{10}}{64}+\frac{22005\,a^4\,b^2\,d^2\,e^9}{128}-\frac{7335\,a^3\,b^3\,d^3\,e^8}{32}+\frac{22005\,a^2\,b^4\,d^4\,e^7}{128}-\frac{4401\,a\,b^5\,d^5\,e^6}{64}+\frac{1467\,b^6\,d^6\,e^5}{128}\right)+{\left(d+e\,x\right)}^{5/2}\,\left(\frac{1253\,a^4\,b^2\,e^9}{15}-\frac{5012\,a^3\,b^3\,d\,e^8}{15}+\frac{2506\,a^2\,b^4\,d^2\,e^7}{5}-\frac{5012\,a\,b^5\,d^3\,e^6}{15}+\frac{1253\,b^6\,d^4\,e^5}{15}\right)+{\left(d+e\,x\right)}^{3/2}\,\left(\frac{9629\,a^5\,b\,e^{10}}{192}-\frac{48145\,a^4\,b^2\,d\,e^9}{192}+\frac{48145\,a^3\,b^3\,d^2\,e^8}{96}-\frac{48145\,a^2\,b^4\,d^3\,e^7}{96}+\frac{48145\,a\,b^5\,d^4\,e^6}{192}-\frac{9629\,b^6\,d^5\,e^5}{192}\right)}{\left(d+e\,x\right)\,\left(5\,a^4\,b^8\,e^4-20\,a^3\,b^9\,d\,e^3+30\,a^2\,b^{10}\,d^2\,e^2-20\,a\,b^{11}\,d^3\,e+5\,b^{12}\,d^4\right)-{\left(d+e\,x\right)}^2\,\left(-10\,a^3\,b^9\,e^3+30\,a^2\,b^{10}\,d\,e^2-30\,a\,b^{11}\,d^2\,e+10\,b^{12}\,d^3\right)+b^{12}\,{\left(d+e\,x\right)}^5-\left(5\,b^{12}\,d-5\,a\,b^{11}\,e\right)\,{\left(d+e\,x\right)}^4-b^{12}\,d^5+{\left(d+e\,x\right)}^3\,\left(10\,a^2\,b^{10}\,e^2-20\,a\,b^{11}\,d\,e+10\,b^{12}\,d^2\right)+a^5\,b^7\,e^5-5\,a^4\,b^8\,d\,e^4-10\,a^2\,b^{10}\,d^3\,e^2+10\,a^3\,b^9\,d^2\,e^3+5\,a\,b^{11}\,d^4\,e}+\frac{2\,e^5\,\left(6\,b^6\,d-6\,a\,b^5\,e\right)\,\sqrt{d+e\,x}}{b^{12}}+\frac{3003\,e^5\,\mathrm{atan}\left(\frac{\sqrt{b}\,e^5\,{\left(a\,e-b\,d\right)}^{3/2}\,\sqrt{d+e\,x}}{a^2\,e^7-2\,a\,b\,d\,e^6+b^2\,d^2\,e^5}\right)\,{\left(a\,e-b\,d\right)}^{3/2}}{128\,b^{15/2}}","Not used",1,"(2*e^5*(d + e*x)^(3/2))/(3*b^6) - ((d + e*x)^(9/2)*((2373*a^2*b^4*e^7)/128 + (2373*b^6*d^2*e^5)/128 - (2373*a*b^5*d*e^6)/64) + (d + e*x)^(7/2)*((12131*a^3*b^3*e^8)/192 - (12131*b^6*d^3*e^5)/192 + (12131*a*b^5*d^2*e^6)/64 - (12131*a^2*b^4*d*e^7)/64) + (d + e*x)^(1/2)*((1467*a^6*e^11)/128 + (1467*b^6*d^6*e^5)/128 - (4401*a*b^5*d^5*e^6)/64 + (22005*a^2*b^4*d^4*e^7)/128 - (7335*a^3*b^3*d^3*e^8)/32 + (22005*a^4*b^2*d^2*e^9)/128 - (4401*a^5*b*d*e^10)/64) + (d + e*x)^(5/2)*((1253*a^4*b^2*e^9)/15 + (1253*b^6*d^4*e^5)/15 - (5012*a*b^5*d^3*e^6)/15 - (5012*a^3*b^3*d*e^8)/15 + (2506*a^2*b^4*d^2*e^7)/5) + (d + e*x)^(3/2)*((9629*a^5*b*e^10)/192 - (9629*b^6*d^5*e^5)/192 + (48145*a*b^5*d^4*e^6)/192 - (48145*a^4*b^2*d*e^9)/192 - (48145*a^2*b^4*d^3*e^7)/96 + (48145*a^3*b^3*d^2*e^8)/96))/((d + e*x)*(5*b^12*d^4 + 5*a^4*b^8*e^4 - 20*a^3*b^9*d*e^3 + 30*a^2*b^10*d^2*e^2 - 20*a*b^11*d^3*e) - (d + e*x)^2*(10*b^12*d^3 - 10*a^3*b^9*e^3 + 30*a^2*b^10*d*e^2 - 30*a*b^11*d^2*e) + b^12*(d + e*x)^5 - (5*b^12*d - 5*a*b^11*e)*(d + e*x)^4 - b^12*d^5 + (d + e*x)^3*(10*b^12*d^2 + 10*a^2*b^10*e^2 - 20*a*b^11*d*e) + a^5*b^7*e^5 - 5*a^4*b^8*d*e^4 - 10*a^2*b^10*d^3*e^2 + 10*a^3*b^9*d^2*e^3 + 5*a*b^11*d^4*e) + (2*e^5*(6*b^6*d - 6*a*b^5*e)*(d + e*x)^(1/2))/b^12 + (3003*e^5*atan((b^(1/2)*e^5*(a*e - b*d)^(3/2)*(d + e*x)^(1/2))/(a^2*e^7 + b^2*d^2*e^5 - 2*a*b*d*e^6))*(a*e - b*d)^(3/2))/(128*b^(15/2))","B"
1666,1,598,197,0.321649,"\text{Not used}","int((d + e*x)^(11/2)/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\frac{{\left(d+e\,x\right)}^{7/2}\,\left(\frac{1327\,a^2\,b^3\,e^7}{64}-\frac{1327\,a\,b^4\,d\,e^6}{32}+\frac{1327\,b^5\,d^2\,e^5}{64}\right)+\sqrt{d+e\,x}\,\left(\frac{437\,a^5\,e^{10}}{128}-\frac{2185\,a^4\,b\,d\,e^9}{128}+\frac{2185\,a^3\,b^2\,d^2\,e^8}{64}-\frac{2185\,a^2\,b^3\,d^3\,e^7}{64}+\frac{2185\,a\,b^4\,d^4\,e^6}{128}-\frac{437\,b^5\,d^5\,e^5}{128}\right)+{\left(d+e\,x\right)}^{5/2}\,\left(\frac{131\,a^3\,b^2\,e^8}{5}-\frac{393\,a^2\,b^3\,d\,e^7}{5}+\frac{393\,a\,b^4\,d^2\,e^6}{5}-\frac{131\,b^5\,d^3\,e^5}{5}\right)+{\left(d+e\,x\right)}^{3/2}\,\left(\frac{977\,a^4\,b\,e^9}{64}-\frac{977\,a^3\,b^2\,d\,e^8}{16}+\frac{2931\,a^2\,b^3\,d^2\,e^7}{32}-\frac{977\,a\,b^4\,d^3\,e^6}{16}+\frac{977\,b^5\,d^4\,e^5}{64}\right)+\left(\frac{843\,a\,b^4\,e^6}{128}-\frac{843\,b^5\,d\,e^5}{128}\right)\,{\left(d+e\,x\right)}^{9/2}}{\left(d+e\,x\right)\,\left(5\,a^4\,b^7\,e^4-20\,a^3\,b^8\,d\,e^3+30\,a^2\,b^9\,d^2\,e^2-20\,a\,b^{10}\,d^3\,e+5\,b^{11}\,d^4\right)-{\left(d+e\,x\right)}^2\,\left(-10\,a^3\,b^8\,e^3+30\,a^2\,b^9\,d\,e^2-30\,a\,b^{10}\,d^2\,e+10\,b^{11}\,d^3\right)+b^{11}\,{\left(d+e\,x\right)}^5-\left(5\,b^{11}\,d-5\,a\,b^{10}\,e\right)\,{\left(d+e\,x\right)}^4-b^{11}\,d^5+{\left(d+e\,x\right)}^3\,\left(10\,a^2\,b^9\,e^2-20\,a\,b^{10}\,d\,e+10\,b^{11}\,d^2\right)+a^5\,b^6\,e^5-5\,a^4\,b^7\,d\,e^4-10\,a^2\,b^9\,d^3\,e^2+10\,a^3\,b^8\,d^2\,e^3+5\,a\,b^{10}\,d^4\,e}+\frac{2\,e^5\,\sqrt{d+e\,x}}{b^6}-\frac{693\,e^5\,\mathrm{atan}\left(\frac{\sqrt{b}\,e^5\,\sqrt{a\,e-b\,d}\,\sqrt{d+e\,x}}{a\,e^6-b\,d\,e^5}\right)\,\sqrt{a\,e-b\,d}}{128\,b^{13/2}}","Not used",1,"((d + e*x)^(7/2)*((1327*a^2*b^3*e^7)/64 + (1327*b^5*d^2*e^5)/64 - (1327*a*b^4*d*e^6)/32) + (d + e*x)^(1/2)*((437*a^5*e^10)/128 - (437*b^5*d^5*e^5)/128 + (2185*a*b^4*d^4*e^6)/128 - (2185*a^2*b^3*d^3*e^7)/64 + (2185*a^3*b^2*d^2*e^8)/64 - (2185*a^4*b*d*e^9)/128) + (d + e*x)^(5/2)*((131*a^3*b^2*e^8)/5 - (131*b^5*d^3*e^5)/5 + (393*a*b^4*d^2*e^6)/5 - (393*a^2*b^3*d*e^7)/5) + (d + e*x)^(3/2)*((977*a^4*b*e^9)/64 + (977*b^5*d^4*e^5)/64 - (977*a*b^4*d^3*e^6)/16 - (977*a^3*b^2*d*e^8)/16 + (2931*a^2*b^3*d^2*e^7)/32) + ((843*a*b^4*e^6)/128 - (843*b^5*d*e^5)/128)*(d + e*x)^(9/2))/((d + e*x)*(5*b^11*d^4 + 5*a^4*b^7*e^4 - 20*a^3*b^8*d*e^3 + 30*a^2*b^9*d^2*e^2 - 20*a*b^10*d^3*e) - (d + e*x)^2*(10*b^11*d^3 - 10*a^3*b^8*e^3 + 30*a^2*b^9*d*e^2 - 30*a*b^10*d^2*e) + b^11*(d + e*x)^5 - (5*b^11*d - 5*a*b^10*e)*(d + e*x)^4 - b^11*d^5 + (d + e*x)^3*(10*b^11*d^2 + 10*a^2*b^9*e^2 - 20*a*b^10*d*e) + a^5*b^6*e^5 - 5*a^4*b^7*d*e^4 - 10*a^2*b^9*d^3*e^2 + 10*a^3*b^8*d^2*e^3 + 5*a*b^10*d^4*e) + (2*e^5*(d + e*x)^(1/2))/b^6 - (693*e^5*atan((b^(1/2)*e^5*(a*e - b*d)^(1/2)*(d + e*x)^(1/2))/(a*e^6 - b*d*e^5))*(a*e - b*d)^(1/2))/(128*b^(13/2))","B"
1667,1,480,178,0.741216,"\text{Not used}","int((d + e*x)^(9/2)/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\frac{63\,e^5\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}}{\sqrt{a\,e-b\,d}}\right)}{128\,b^{11/2}\,\sqrt{a\,e-b\,d}}-\frac{\frac{193\,e^5\,{\left(d+e\,x\right)}^{9/2}}{128\,b}+\frac{63\,e^5\,\sqrt{d+e\,x}\,\left(a^4\,e^4-4\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2-4\,a\,b^3\,d^3\,e+b^4\,d^4\right)}{128\,b^5}+\frac{21\,e^5\,{\left(d+e\,x\right)}^{5/2}\,\left(a^2\,e^2-2\,a\,b\,d\,e+b^2\,d^2\right)}{5\,b^3}+\frac{147\,e^5\,{\left(d+e\,x\right)}^{3/2}\,\left(a^3\,e^3-3\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e-b^3\,d^3\right)}{64\,b^4}+\frac{237\,e^5\,\left(a\,e-b\,d\right)\,{\left(d+e\,x\right)}^{7/2}}{64\,b^2}}{\left(d+e\,x\right)\,\left(5\,a^4\,b\,e^4-20\,a^3\,b^2\,d\,e^3+30\,a^2\,b^3\,d^2\,e^2-20\,a\,b^4\,d^3\,e+5\,b^5\,d^4\right)-{\left(d+e\,x\right)}^2\,\left(-10\,a^3\,b^2\,e^3+30\,a^2\,b^3\,d\,e^2-30\,a\,b^4\,d^2\,e+10\,b^5\,d^3\right)+b^5\,{\left(d+e\,x\right)}^5-\left(5\,b^5\,d-5\,a\,b^4\,e\right)\,{\left(d+e\,x\right)}^4+a^5\,e^5-b^5\,d^5+{\left(d+e\,x\right)}^3\,\left(10\,a^2\,b^3\,e^2-20\,a\,b^4\,d\,e+10\,b^5\,d^2\right)-10\,a^2\,b^3\,d^3\,e^2+10\,a^3\,b^2\,d^2\,e^3+5\,a\,b^4\,d^4\,e-5\,a^4\,b\,d\,e^4}","Not used",1,"(63*e^5*atan((b^(1/2)*(d + e*x)^(1/2))/(a*e - b*d)^(1/2)))/(128*b^(11/2)*(a*e - b*d)^(1/2)) - ((193*e^5*(d + e*x)^(9/2))/(128*b) + (63*e^5*(d + e*x)^(1/2)*(a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 - 4*a*b^3*d^3*e - 4*a^3*b*d*e^3))/(128*b^5) + (21*e^5*(d + e*x)^(5/2)*(a^2*e^2 + b^2*d^2 - 2*a*b*d*e))/(5*b^3) + (147*e^5*(d + e*x)^(3/2)*(a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2))/(64*b^4) + (237*e^5*(a*e - b*d)*(d + e*x)^(7/2))/(64*b^2))/((d + e*x)*(5*b^5*d^4 + 5*a^4*b*e^4 - 20*a^3*b^2*d*e^3 + 30*a^2*b^3*d^2*e^2 - 20*a*b^4*d^3*e) - (d + e*x)^2*(10*b^5*d^3 - 10*a^3*b^2*e^3 + 30*a^2*b^3*d*e^2 - 30*a*b^4*d^2*e) + b^5*(d + e*x)^5 - (5*b^5*d - 5*a*b^4*e)*(d + e*x)^4 + a^5*e^5 - b^5*d^5 + (d + e*x)^3*(10*b^5*d^2 + 10*a^2*b^3*e^2 - 20*a*b^4*d*e) - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4)","B"
1668,1,439,188,0.663077,"\text{Not used}","int((d + e*x)^(7/2)/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\frac{7\,e^5\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}}{\sqrt{a\,e-b\,d}}\right)}{128\,b^{9/2}\,{\left(a\,e-b\,d\right)}^{3/2}}-\frac{\frac{79\,e^5\,{\left(d+e\,x\right)}^{7/2}}{192\,b}-\frac{7\,e^5\,{\left(d+e\,x\right)}^{9/2}}{128\,\left(a\,e-b\,d\right)}+\frac{49\,e^5\,{\left(d+e\,x\right)}^{3/2}\,\left(a^2\,e^2-2\,a\,b\,d\,e+b^2\,d^2\right)}{192\,b^3}+\frac{7\,e^5\,\sqrt{d+e\,x}\,\left(a^3\,e^3-3\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e-b^3\,d^3\right)}{128\,b^4}+\frac{7\,e^5\,\left(a\,e-b\,d\right)\,{\left(d+e\,x\right)}^{5/2}}{15\,b^2}}{\left(d+e\,x\right)\,\left(5\,a^4\,b\,e^4-20\,a^3\,b^2\,d\,e^3+30\,a^2\,b^3\,d^2\,e^2-20\,a\,b^4\,d^3\,e+5\,b^5\,d^4\right)-{\left(d+e\,x\right)}^2\,\left(-10\,a^3\,b^2\,e^3+30\,a^2\,b^3\,d\,e^2-30\,a\,b^4\,d^2\,e+10\,b^5\,d^3\right)+b^5\,{\left(d+e\,x\right)}^5-\left(5\,b^5\,d-5\,a\,b^4\,e\right)\,{\left(d+e\,x\right)}^4+a^5\,e^5-b^5\,d^5+{\left(d+e\,x\right)}^3\,\left(10\,a^2\,b^3\,e^2-20\,a\,b^4\,d\,e+10\,b^5\,d^2\right)-10\,a^2\,b^3\,d^3\,e^2+10\,a^3\,b^2\,d^2\,e^3+5\,a\,b^4\,d^4\,e-5\,a^4\,b\,d\,e^4}","Not used",1,"(7*e^5*atan((b^(1/2)*(d + e*x)^(1/2))/(a*e - b*d)^(1/2)))/(128*b^(9/2)*(a*e - b*d)^(3/2)) - ((79*e^5*(d + e*x)^(7/2))/(192*b) - (7*e^5*(d + e*x)^(9/2))/(128*(a*e - b*d)) + (49*e^5*(d + e*x)^(3/2)*(a^2*e^2 + b^2*d^2 - 2*a*b*d*e))/(192*b^3) + (7*e^5*(d + e*x)^(1/2)*(a^3*e^3 - b^3*d^3 + 3*a*b^2*d^2*e - 3*a^2*b*d*e^2))/(128*b^4) + (7*e^5*(a*e - b*d)*(d + e*x)^(5/2))/(15*b^2))/((d + e*x)*(5*b^5*d^4 + 5*a^4*b*e^4 - 20*a^3*b^2*d*e^3 + 30*a^2*b^3*d^2*e^2 - 20*a*b^4*d^3*e) - (d + e*x)^2*(10*b^5*d^3 - 10*a^3*b^2*e^3 + 30*a^2*b^3*d*e^2 - 30*a*b^4*d^2*e) + b^5*(d + e*x)^5 - (5*b^5*d - 5*a*b^4*e)*(d + e*x)^4 + a^5*e^5 - b^5*d^5 + (d + e*x)^3*(10*b^5*d^2 + 10*a^2*b^3*e^2 - 20*a*b^4*d*e) - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4)","B"
1669,1,411,198,0.171096,"\text{Not used}","int((d + e*x)^(5/2)/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\frac{3\,e^5\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}}{\sqrt{a\,e-b\,d}}\right)}{128\,b^{7/2}\,{\left(a\,e-b\,d\right)}^{5/2}}-\frac{\frac{e^5\,{\left(d+e\,x\right)}^{5/2}}{5\,b}-\frac{7\,e^5\,{\left(d+e\,x\right)}^{7/2}}{64\,\left(a\,e-b\,d\right)}+\frac{3\,e^5\,\sqrt{d+e\,x}\,\left(a^2\,e^2-2\,a\,b\,d\,e+b^2\,d^2\right)}{128\,b^3}+\frac{7\,e^5\,\left(a\,e-b\,d\right)\,{\left(d+e\,x\right)}^{3/2}}{64\,b^2}-\frac{3\,b\,e^5\,{\left(d+e\,x\right)}^{9/2}}{128\,{\left(a\,e-b\,d\right)}^2}}{\left(d+e\,x\right)\,\left(5\,a^4\,b\,e^4-20\,a^3\,b^2\,d\,e^3+30\,a^2\,b^3\,d^2\,e^2-20\,a\,b^4\,d^3\,e+5\,b^5\,d^4\right)-{\left(d+e\,x\right)}^2\,\left(-10\,a^3\,b^2\,e^3+30\,a^2\,b^3\,d\,e^2-30\,a\,b^4\,d^2\,e+10\,b^5\,d^3\right)+b^5\,{\left(d+e\,x\right)}^5-\left(5\,b^5\,d-5\,a\,b^4\,e\right)\,{\left(d+e\,x\right)}^4+a^5\,e^5-b^5\,d^5+{\left(d+e\,x\right)}^3\,\left(10\,a^2\,b^3\,e^2-20\,a\,b^4\,d\,e+10\,b^5\,d^2\right)-10\,a^2\,b^3\,d^3\,e^2+10\,a^3\,b^2\,d^2\,e^3+5\,a\,b^4\,d^4\,e-5\,a^4\,b\,d\,e^4}","Not used",1,"(3*e^5*atan((b^(1/2)*(d + e*x)^(1/2))/(a*e - b*d)^(1/2)))/(128*b^(7/2)*(a*e - b*d)^(5/2)) - ((e^5*(d + e*x)^(5/2))/(5*b) - (7*e^5*(d + e*x)^(7/2))/(64*(a*e - b*d)) + (3*e^5*(d + e*x)^(1/2)*(a^2*e^2 + b^2*d^2 - 2*a*b*d*e))/(128*b^3) + (7*e^5*(a*e - b*d)*(d + e*x)^(3/2))/(64*b^2) - (3*b*e^5*(d + e*x)^(9/2))/(128*(a*e - b*d)^2))/((d + e*x)*(5*b^5*d^4 + 5*a^4*b*e^4 - 20*a^3*b^2*d*e^3 + 30*a^2*b^3*d^2*e^2 - 20*a*b^4*d^3*e) - (d + e*x)^2*(10*b^5*d^3 - 10*a^3*b^2*e^3 + 30*a^2*b^3*d*e^2 - 30*a*b^4*d^2*e) + b^5*(d + e*x)^5 - (5*b^5*d - 5*a*b^4*e)*(d + e*x)^4 + a^5*e^5 - b^5*d^5 + (d + e*x)^3*(10*b^5*d^2 + 10*a^2*b^3*e^2 - 20*a*b^4*d*e) - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4)","B"
1670,1,398,208,0.660555,"\text{Not used}","int((d + e*x)^(3/2)/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\frac{\frac{e^5\,{\left(d+e\,x\right)}^{5/2}}{5\,\left(a\,e-b\,d\right)}-\frac{7\,e^5\,{\left(d+e\,x\right)}^{3/2}}{64\,b}+\frac{3\,b^2\,e^5\,{\left(d+e\,x\right)}^{9/2}}{128\,{\left(a\,e-b\,d\right)}^3}-\frac{3\,e^5\,\left(a\,e-b\,d\right)\,\sqrt{d+e\,x}}{128\,b^2}+\frac{7\,b\,e^5\,{\left(d+e\,x\right)}^{7/2}}{64\,{\left(a\,e-b\,d\right)}^2}}{\left(d+e\,x\right)\,\left(5\,a^4\,b\,e^4-20\,a^3\,b^2\,d\,e^3+30\,a^2\,b^3\,d^2\,e^2-20\,a\,b^4\,d^3\,e+5\,b^5\,d^4\right)-{\left(d+e\,x\right)}^2\,\left(-10\,a^3\,b^2\,e^3+30\,a^2\,b^3\,d\,e^2-30\,a\,b^4\,d^2\,e+10\,b^5\,d^3\right)+b^5\,{\left(d+e\,x\right)}^5-\left(5\,b^5\,d-5\,a\,b^4\,e\right)\,{\left(d+e\,x\right)}^4+a^5\,e^5-b^5\,d^5+{\left(d+e\,x\right)}^3\,\left(10\,a^2\,b^3\,e^2-20\,a\,b^4\,d\,e+10\,b^5\,d^2\right)-10\,a^2\,b^3\,d^3\,e^2+10\,a^3\,b^2\,d^2\,e^3+5\,a\,b^4\,d^4\,e-5\,a^4\,b\,d\,e^4}+\frac{3\,e^5\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}}{\sqrt{a\,e-b\,d}}\right)}{128\,b^{5/2}\,{\left(a\,e-b\,d\right)}^{7/2}}","Not used",1,"((e^5*(d + e*x)^(5/2))/(5*(a*e - b*d)) - (7*e^5*(d + e*x)^(3/2))/(64*b) + (3*b^2*e^5*(d + e*x)^(9/2))/(128*(a*e - b*d)^3) - (3*e^5*(a*e - b*d)*(d + e*x)^(1/2))/(128*b^2) + (7*b*e^5*(d + e*x)^(7/2))/(64*(a*e - b*d)^2))/((d + e*x)*(5*b^5*d^4 + 5*a^4*b*e^4 - 20*a^3*b^2*d*e^3 + 30*a^2*b^3*d^2*e^2 - 20*a*b^4*d^3*e) - (d + e*x)^2*(10*b^5*d^3 - 10*a^3*b^2*e^3 + 30*a^2*b^3*d*e^2 - 30*a*b^4*d^2*e) + b^5*(d + e*x)^5 - (5*b^5*d - 5*a*b^4*e)*(d + e*x)^4 + a^5*e^5 - b^5*d^5 + (d + e*x)^3*(10*b^5*d^2 + 10*a^2*b^3*e^2 - 20*a*b^4*d*e) - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4) + (3*e^5*atan((b^(1/2)*(d + e*x)^(1/2))/(a*e - b*d)^(1/2)))/(128*b^(5/2)*(a*e - b*d)^(7/2))","B"
1671,1,401,218,0.695917,"\text{Not used}","int((d + e*x)^(1/2)/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\frac{\frac{79\,e^5\,{\left(d+e\,x\right)}^{3/2}}{192\,\left(a\,e-b\,d\right)}-\frac{7\,e^5\,\sqrt{d+e\,x}}{128\,b}+\frac{49\,b^2\,e^5\,{\left(d+e\,x\right)}^{7/2}}{192\,{\left(a\,e-b\,d\right)}^3}+\frac{7\,b^3\,e^5\,{\left(d+e\,x\right)}^{9/2}}{128\,{\left(a\,e-b\,d\right)}^4}+\frac{7\,b\,e^5\,{\left(d+e\,x\right)}^{5/2}}{15\,{\left(a\,e-b\,d\right)}^2}}{\left(d+e\,x\right)\,\left(5\,a^4\,b\,e^4-20\,a^3\,b^2\,d\,e^3+30\,a^2\,b^3\,d^2\,e^2-20\,a\,b^4\,d^3\,e+5\,b^5\,d^4\right)-{\left(d+e\,x\right)}^2\,\left(-10\,a^3\,b^2\,e^3+30\,a^2\,b^3\,d\,e^2-30\,a\,b^4\,d^2\,e+10\,b^5\,d^3\right)+b^5\,{\left(d+e\,x\right)}^5-\left(5\,b^5\,d-5\,a\,b^4\,e\right)\,{\left(d+e\,x\right)}^4+a^5\,e^5-b^5\,d^5+{\left(d+e\,x\right)}^3\,\left(10\,a^2\,b^3\,e^2-20\,a\,b^4\,d\,e+10\,b^5\,d^2\right)-10\,a^2\,b^3\,d^3\,e^2+10\,a^3\,b^2\,d^2\,e^3+5\,a\,b^4\,d^4\,e-5\,a^4\,b\,d\,e^4}+\frac{7\,e^5\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}}{\sqrt{a\,e-b\,d}}\right)}{128\,b^{3/2}\,{\left(a\,e-b\,d\right)}^{9/2}}","Not used",1,"((79*e^5*(d + e*x)^(3/2))/(192*(a*e - b*d)) - (7*e^5*(d + e*x)^(1/2))/(128*b) + (49*b^2*e^5*(d + e*x)^(7/2))/(192*(a*e - b*d)^3) + (7*b^3*e^5*(d + e*x)^(9/2))/(128*(a*e - b*d)^4) + (7*b*e^5*(d + e*x)^(5/2))/(15*(a*e - b*d)^2))/((d + e*x)*(5*b^5*d^4 + 5*a^4*b*e^4 - 20*a^3*b^2*d*e^3 + 30*a^2*b^3*d^2*e^2 - 20*a*b^4*d^3*e) - (d + e*x)^2*(10*b^5*d^3 - 10*a^3*b^2*e^3 + 30*a^2*b^3*d*e^2 - 30*a*b^4*d^2*e) + b^5*(d + e*x)^5 - (5*b^5*d - 5*a*b^4*e)*(d + e*x)^4 + a^5*e^5 - b^5*d^5 + (d + e*x)^3*(10*b^5*d^2 + 10*a^2*b^3*e^2 - 20*a*b^4*d*e) - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4) + (7*e^5*atan((b^(1/2)*(d + e*x)^(1/2))/(a*e - b*d)^(1/2)))/(128*b^(3/2)*(a*e - b*d)^(9/2))","B"
1672,1,252,213,0.738990,"\text{Not used}","int(1/((d + e*x)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^3),x)","\frac{\frac{965\,\sqrt{b}\,{\left(a\,e-b\,d\right)}^{9/2}\,\sqrt{d+e\,x}+2370\,b^{3/2}\,{\left(a\,e-b\,d\right)}^{7/2}\,{\left(d+e\,x\right)}^{3/2}+2688\,b^{5/2}\,{\left(a\,e-b\,d\right)}^{5/2}\,{\left(d+e\,x\right)}^{5/2}+1470\,b^{7/2}\,{\left(a\,e-b\,d\right)}^{3/2}\,{\left(d+e\,x\right)}^{7/2}+315\,b^{9/2}\,\sqrt{a\,e-b\,d}\,{\left(d+e\,x\right)}^{9/2}+315\,b^5\,e^5\,x^5\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}}{\sqrt{a\,e-b\,d}}\right)}{640\,\sqrt{b}\,{\left(a\,e-b\,d\right)}^{11/2}}-\frac{63\,b^{9/2}\,e^5\,x^5\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}}{\sqrt{a\,e-b\,d}}\right)}{128\,{\left(a\,e-b\,d\right)}^{11/2}}}{{\left(a+b\,x\right)}^5}+\frac{63\,e^5\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}}{\sqrt{a\,e-b\,d}}\right)}{128\,\sqrt{b}\,{\left(a\,e-b\,d\right)}^{11/2}}","Not used",1,"((965*b^(1/2)*(a*e - b*d)^(9/2)*(d + e*x)^(1/2) + 2370*b^(3/2)*(a*e - b*d)^(7/2)*(d + e*x)^(3/2) + 2688*b^(5/2)*(a*e - b*d)^(5/2)*(d + e*x)^(5/2) + 1470*b^(7/2)*(a*e - b*d)^(3/2)*(d + e*x)^(7/2) + 315*b^(9/2)*(a*e - b*d)^(1/2)*(d + e*x)^(9/2) + 315*b^5*e^5*x^5*atan((b^(1/2)*(d + e*x)^(1/2))/(a*e - b*d)^(1/2)))/(640*b^(1/2)*(a*e - b*d)^(11/2)) - (63*b^(9/2)*e^5*x^5*atan((b^(1/2)*(d + e*x)^(1/2))/(a*e - b*d)^(1/2)))/(128*(a*e - b*d)^(11/2)))/(a + b*x)^5 + (63*e^5*atan((b^(1/2)*(d + e*x)^(1/2))/(a*e - b*d)^(1/2)))/(128*b^(1/2)*(a*e - b*d)^(11/2))","B"
1673,1,515,239,1.103669,"\text{Not used}","int(1/((d + e*x)^(3/2)*(a^2 + b^2*x^2 + 2*a*b*x)^3),x)","-\frac{\frac{2\,e^5}{a\,e-b\,d}+\frac{2607\,b^2\,e^5\,{\left(d+e\,x\right)}^2}{64\,{\left(a\,e-b\,d\right)}^3}+\frac{231\,b^3\,e^5\,{\left(d+e\,x\right)}^3}{5\,{\left(a\,e-b\,d\right)}^4}+\frac{1617\,b^4\,e^5\,{\left(d+e\,x\right)}^4}{64\,{\left(a\,e-b\,d\right)}^5}+\frac{693\,b^5\,e^5\,{\left(d+e\,x\right)}^5}{128\,{\left(a\,e-b\,d\right)}^6}+\frac{2123\,b\,e^5\,\left(d+e\,x\right)}{128\,{\left(a\,e-b\,d\right)}^2}}{\sqrt{d+e\,x}\,\left(a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5\right)-{\left(d+e\,x\right)}^{5/2}\,\left(-10\,a^3\,b^2\,e^3+30\,a^2\,b^3\,d\,e^2-30\,a\,b^4\,d^2\,e+10\,b^5\,d^3\right)+{\left(d+e\,x\right)}^{3/2}\,\left(5\,a^4\,b\,e^4-20\,a^3\,b^2\,d\,e^3+30\,a^2\,b^3\,d^2\,e^2-20\,a\,b^4\,d^3\,e+5\,b^5\,d^4\right)+b^5\,{\left(d+e\,x\right)}^{11/2}-\left(5\,b^5\,d-5\,a\,b^4\,e\right)\,{\left(d+e\,x\right)}^{9/2}+{\left(d+e\,x\right)}^{7/2}\,\left(10\,a^2\,b^3\,e^2-20\,a\,b^4\,d\,e+10\,b^5\,d^2\right)}-\frac{693\,\sqrt{b}\,e^5\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}\,\left(a^6\,e^6-6\,a^5\,b\,d\,e^5+15\,a^4\,b^2\,d^2\,e^4-20\,a^3\,b^3\,d^3\,e^3+15\,a^2\,b^4\,d^4\,e^2-6\,a\,b^5\,d^5\,e+b^6\,d^6\right)}{{\left(a\,e-b\,d\right)}^{13/2}}\right)}{128\,{\left(a\,e-b\,d\right)}^{13/2}}","Not used",1,"- ((2*e^5)/(a*e - b*d) + (2607*b^2*e^5*(d + e*x)^2)/(64*(a*e - b*d)^3) + (231*b^3*e^5*(d + e*x)^3)/(5*(a*e - b*d)^4) + (1617*b^4*e^5*(d + e*x)^4)/(64*(a*e - b*d)^5) + (693*b^5*e^5*(d + e*x)^5)/(128*(a*e - b*d)^6) + (2123*b*e^5*(d + e*x))/(128*(a*e - b*d)^2))/((d + e*x)^(1/2)*(a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4) - (d + e*x)^(5/2)*(10*b^5*d^3 - 10*a^3*b^2*e^3 + 30*a^2*b^3*d*e^2 - 30*a*b^4*d^2*e) + (d + e*x)^(3/2)*(5*b^5*d^4 + 5*a^4*b*e^4 - 20*a^3*b^2*d*e^3 + 30*a^2*b^3*d^2*e^2 - 20*a*b^4*d^3*e) + b^5*(d + e*x)^(11/2) - (5*b^5*d - 5*a*b^4*e)*(d + e*x)^(9/2) + (d + e*x)^(7/2)*(10*b^5*d^2 + 10*a^2*b^3*e^2 - 20*a*b^4*d*e)) - (693*b^(1/2)*e^5*atan((b^(1/2)*(d + e*x)^(1/2)*(a^6*e^6 + b^6*d^6 + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a*b^5*d^5*e - 6*a^5*b*d*e^5))/(a*e - b*d)^(13/2)))/(128*(a*e - b*d)^(13/2))","B"
1674,1,555,266,1.259487,"\text{Not used}","int(1/((d + e*x)^(5/2)*(a^2 + b^2*x^2 + 2*a*b*x)^3),x)","\frac{\frac{27599\,b^2\,e^5\,{\left(d+e\,x\right)}^2}{384\,{\left(a\,e-b\,d\right)}^3}-\frac{2\,e^5}{3\,\left(a\,e-b\,d\right)}+\frac{11297\,b^3\,e^5\,{\left(d+e\,x\right)}^3}{64\,{\left(a\,e-b\,d\right)}^4}+\frac{1001\,b^4\,e^5\,{\left(d+e\,x\right)}^4}{5\,{\left(a\,e-b\,d\right)}^5}+\frac{7007\,b^5\,e^5\,{\left(d+e\,x\right)}^5}{64\,{\left(a\,e-b\,d\right)}^6}+\frac{3003\,b^6\,e^5\,{\left(d+e\,x\right)}^6}{128\,{\left(a\,e-b\,d\right)}^7}+\frac{26\,b\,e^5\,\left(d+e\,x\right)}{3\,{\left(a\,e-b\,d\right)}^2}}{{\left(d+e\,x\right)}^{3/2}\,\left(a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5\right)-{\left(d+e\,x\right)}^{7/2}\,\left(-10\,a^3\,b^2\,e^3+30\,a^2\,b^3\,d\,e^2-30\,a\,b^4\,d^2\,e+10\,b^5\,d^3\right)+{\left(d+e\,x\right)}^{5/2}\,\left(5\,a^4\,b\,e^4-20\,a^3\,b^2\,d\,e^3+30\,a^2\,b^3\,d^2\,e^2-20\,a\,b^4\,d^3\,e+5\,b^5\,d^4\right)+b^5\,{\left(d+e\,x\right)}^{13/2}-\left(5\,b^5\,d-5\,a\,b^4\,e\right)\,{\left(d+e\,x\right)}^{11/2}+{\left(d+e\,x\right)}^{9/2}\,\left(10\,a^2\,b^3\,e^2-20\,a\,b^4\,d\,e+10\,b^5\,d^2\right)}+\frac{3003\,b^{3/2}\,e^5\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}\,\left(a^7\,e^7-7\,a^6\,b\,d\,e^6+21\,a^5\,b^2\,d^2\,e^5-35\,a^4\,b^3\,d^3\,e^4+35\,a^3\,b^4\,d^4\,e^3-21\,a^2\,b^5\,d^5\,e^2+7\,a\,b^6\,d^6\,e-b^7\,d^7\right)}{{\left(a\,e-b\,d\right)}^{15/2}}\right)}{128\,{\left(a\,e-b\,d\right)}^{15/2}}","Not used",1,"((27599*b^2*e^5*(d + e*x)^2)/(384*(a*e - b*d)^3) - (2*e^5)/(3*(a*e - b*d)) + (11297*b^3*e^5*(d + e*x)^3)/(64*(a*e - b*d)^4) + (1001*b^4*e^5*(d + e*x)^4)/(5*(a*e - b*d)^5) + (7007*b^5*e^5*(d + e*x)^5)/(64*(a*e - b*d)^6) + (3003*b^6*e^5*(d + e*x)^6)/(128*(a*e - b*d)^7) + (26*b*e^5*(d + e*x))/(3*(a*e - b*d)^2))/((d + e*x)^(3/2)*(a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4) - (d + e*x)^(7/2)*(10*b^5*d^3 - 10*a^3*b^2*e^3 + 30*a^2*b^3*d*e^2 - 30*a*b^4*d^2*e) + (d + e*x)^(5/2)*(5*b^5*d^4 + 5*a^4*b*e^4 - 20*a^3*b^2*d*e^3 + 30*a^2*b^3*d^2*e^2 - 20*a*b^4*d^3*e) + b^5*(d + e*x)^(13/2) - (5*b^5*d - 5*a*b^4*e)*(d + e*x)^(11/2) + (d + e*x)^(9/2)*(10*b^5*d^2 + 10*a^2*b^3*e^2 - 20*a*b^4*d*e)) + (3003*b^(3/2)*e^5*atan((b^(1/2)*(d + e*x)^(1/2)*(a^7*e^7 - b^7*d^7 - 21*a^2*b^5*d^5*e^2 + 35*a^3*b^4*d^4*e^3 - 35*a^4*b^3*d^3*e^4 + 21*a^5*b^2*d^2*e^5 + 7*a*b^6*d^6*e - 7*a^6*b*d*e^6))/(a*e - b*d)^(15/2)))/(128*(a*e - b*d)^(15/2))","B"
1675,1,594,295,1.514187,"\text{Not used}","int(1/((d + e*x)^(7/2)*(a^2 + b^2*x^2 + 2*a*b*x)^3),x)","-\frac{\frac{2\,e^5}{5\,\left(a\,e-b\,d\right)}+\frac{26\,b^2\,e^5\,{\left(d+e\,x\right)}^2}{{\left(a\,e-b\,d\right)}^3}+\frac{27599\,b^3\,e^5\,{\left(d+e\,x\right)}^3}{128\,{\left(a\,e-b\,d\right)}^4}+\frac{33891\,b^4\,e^5\,{\left(d+e\,x\right)}^4}{64\,{\left(a\,e-b\,d\right)}^5}+\frac{3003\,b^5\,e^5\,{\left(d+e\,x\right)}^5}{5\,{\left(a\,e-b\,d\right)}^6}+\frac{21021\,b^6\,e^5\,{\left(d+e\,x\right)}^6}{64\,{\left(a\,e-b\,d\right)}^7}+\frac{9009\,b^7\,e^5\,{\left(d+e\,x\right)}^7}{128\,{\left(a\,e-b\,d\right)}^8}-\frac{2\,b\,e^5\,\left(d+e\,x\right)}{{\left(a\,e-b\,d\right)}^2}}{{\left(d+e\,x\right)}^{5/2}\,\left(a^5\,e^5-5\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3-10\,a^2\,b^3\,d^3\,e^2+5\,a\,b^4\,d^4\,e-b^5\,d^5\right)-{\left(d+e\,x\right)}^{9/2}\,\left(-10\,a^3\,b^2\,e^3+30\,a^2\,b^3\,d\,e^2-30\,a\,b^4\,d^2\,e+10\,b^5\,d^3\right)+{\left(d+e\,x\right)}^{7/2}\,\left(5\,a^4\,b\,e^4-20\,a^3\,b^2\,d\,e^3+30\,a^2\,b^3\,d^2\,e^2-20\,a\,b^4\,d^3\,e+5\,b^5\,d^4\right)+b^5\,{\left(d+e\,x\right)}^{15/2}-\left(5\,b^5\,d-5\,a\,b^4\,e\right)\,{\left(d+e\,x\right)}^{13/2}+{\left(d+e\,x\right)}^{11/2}\,\left(10\,a^2\,b^3\,e^2-20\,a\,b^4\,d\,e+10\,b^5\,d^2\right)}-\frac{9009\,b^{5/2}\,e^5\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d+e\,x}\,\left(a^8\,e^8-8\,a^7\,b\,d\,e^7+28\,a^6\,b^2\,d^2\,e^6-56\,a^5\,b^3\,d^3\,e^5+70\,a^4\,b^4\,d^4\,e^4-56\,a^3\,b^5\,d^5\,e^3+28\,a^2\,b^6\,d^6\,e^2-8\,a\,b^7\,d^7\,e+b^8\,d^8\right)}{{\left(a\,e-b\,d\right)}^{17/2}}\right)}{128\,{\left(a\,e-b\,d\right)}^{17/2}}","Not used",1,"- ((2*e^5)/(5*(a*e - b*d)) + (26*b^2*e^5*(d + e*x)^2)/(a*e - b*d)^3 + (27599*b^3*e^5*(d + e*x)^3)/(128*(a*e - b*d)^4) + (33891*b^4*e^5*(d + e*x)^4)/(64*(a*e - b*d)^5) + (3003*b^5*e^5*(d + e*x)^5)/(5*(a*e - b*d)^6) + (21021*b^6*e^5*(d + e*x)^6)/(64*(a*e - b*d)^7) + (9009*b^7*e^5*(d + e*x)^7)/(128*(a*e - b*d)^8) - (2*b*e^5*(d + e*x))/(a*e - b*d)^2)/((d + e*x)^(5/2)*(a^5*e^5 - b^5*d^5 - 10*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 5*a*b^4*d^4*e - 5*a^4*b*d*e^4) - (d + e*x)^(9/2)*(10*b^5*d^3 - 10*a^3*b^2*e^3 + 30*a^2*b^3*d*e^2 - 30*a*b^4*d^2*e) + (d + e*x)^(7/2)*(5*b^5*d^4 + 5*a^4*b*e^4 - 20*a^3*b^2*d*e^3 + 30*a^2*b^3*d^2*e^2 - 20*a*b^4*d^3*e) + b^5*(d + e*x)^(15/2) - (5*b^5*d - 5*a*b^4*e)*(d + e*x)^(13/2) + (d + e*x)^(11/2)*(10*b^5*d^2 + 10*a^2*b^3*e^2 - 20*a*b^4*d*e)) - (9009*b^(5/2)*e^5*atan((b^(1/2)*(d + e*x)^(1/2)*(a^8*e^8 + b^8*d^8 + 28*a^2*b^6*d^6*e^2 - 56*a^3*b^5*d^5*e^3 + 70*a^4*b^4*d^4*e^4 - 56*a^5*b^3*d^3*e^5 + 28*a^6*b^2*d^2*e^6 - 8*a*b^7*d^7*e - 8*a^7*b*d*e^7))/(a*e - b*d)^(17/2)))/(128*(a*e - b*d)^(17/2))","B"
1676,0,-1,96,0.000000,"\text{Not used}","int(((a + b*x)^2)^(1/2)*(d + e*x)^(5/2),x)","\int \sqrt{{\left(a+b\,x\right)}^2}\,{\left(d+e\,x\right)}^{5/2} \,d x","Not used",1,"int(((a + b*x)^2)^(1/2)*(d + e*x)^(5/2), x)","F"
1677,0,-1,96,0.000000,"\text{Not used}","int(((a + b*x)^2)^(1/2)*(d + e*x)^(3/2),x)","\int \sqrt{{\left(a+b\,x\right)}^2}\,{\left(d+e\,x\right)}^{3/2} \,d x","Not used",1,"int(((a + b*x)^2)^(1/2)*(d + e*x)^(3/2), x)","F"
1678,0,-1,96,0.000000,"\text{Not used}","int(((a + b*x)^2)^(1/2)*(d + e*x)^(1/2),x)","\int \sqrt{{\left(a+b\,x\right)}^2}\,\sqrt{d+e\,x} \,d x","Not used",1,"int(((a + b*x)^2)^(1/2)*(d + e*x)^(1/2), x)","F"
1679,1,81,94,0.753516,"\text{Not used}","int(((a + b*x)^2)^(1/2)/(d + e*x)^(1/2),x)","\frac{\sqrt{{\left(a+b\,x\right)}^2}\,\left(\frac{2\,x^2}{3}-\frac{4\,b\,d^2-6\,a\,d\,e}{3\,b\,e^2}+\frac{x\,\left(6\,a\,e^2-2\,b\,d\,e\right)}{3\,b\,e^2}\right)}{x\,\sqrt{d+e\,x}+\frac{a\,\sqrt{d+e\,x}}{b}}","Not used",1,"(((a + b*x)^2)^(1/2)*((2*x^2)/3 - (4*b*d^2 - 6*a*d*e)/(3*b*e^2) + (x*(6*a*e^2 - 2*b*d*e))/(3*b*e^2)))/(x*(d + e*x)^(1/2) + (a*(d + e*x)^(1/2))/b)","B"
1680,1,58,92,0.850748,"\text{Not used}","int(((a + b*x)^2)^(1/2)/(d + e*x)^(3/2),x)","\frac{\sqrt{{\left(a+b\,x\right)}^2}\,\left(\frac{2\,x}{e}-\frac{2\,a\,e-4\,b\,d}{b\,e^2}\right)}{x\,\sqrt{d+e\,x}+\frac{a\,\sqrt{d+e\,x}}{b}}","Not used",1,"(((a + b*x)^2)^(1/2)*((2*x)/e - (2*a*e - 4*b*d)/(b*e^2)))/(x*(d + e*x)^(1/2) + (a*(d + e*x)^(1/2))/b)","B"
1681,1,95,94,0.901215,"\text{Not used}","int(((a + b*x)^2)^(1/2)/(d + e*x)^(5/2),x)","-\frac{\sqrt{{\left(a+b\,x\right)}^2}\,\left(\frac{2\,x}{e^2}+\frac{2\,a\,e+4\,b\,d}{3\,b\,e^3}\right)}{x^2\,\sqrt{d+e\,x}+\frac{a\,d\,\sqrt{d+e\,x}}{b\,e}+\frac{x\,\left(3\,a\,e^3+3\,b\,d\,e^2\right)\,\sqrt{d+e\,x}}{3\,b\,e^3}}","Not used",1,"-(((a + b*x)^2)^(1/2)*((2*x)/e^2 + (2*a*e + 4*b*d)/(3*b*e^3)))/(x^2*(d + e*x)^(1/2) + (a*d*(d + e*x)^(1/2))/(b*e) + (x*(3*a*e^3 + 3*b*d*e^2)*(d + e*x)^(1/2))/(3*b*e^3))","B"
1682,1,120,96,0.940573,"\text{Not used}","int(((a + b*x)^2)^(1/2)/(d + e*x)^(7/2),x)","-\frac{\sqrt{{\left(a+b\,x\right)}^2}\,\left(\frac{2\,x}{3\,e^3}+\frac{\frac{2\,a\,e}{5}+\frac{4\,b\,d}{15}}{b\,e^4}\right)}{x^3\,\sqrt{d+e\,x}+\frac{a\,d^2\,\sqrt{d+e\,x}}{b\,e^2}+\frac{x^2\,\left(a\,e^4+2\,b\,d\,e^3\right)\,\sqrt{d+e\,x}}{b\,e^4}+\frac{d\,x\,\left(2\,a\,e+b\,d\right)\,\sqrt{d+e\,x}}{b\,e^2}}","Not used",1,"-(((a + b*x)^2)^(1/2)*((2*x)/(3*e^3) + ((2*a*e)/5 + (4*b*d)/15)/(b*e^4)))/(x^3*(d + e*x)^(1/2) + (a*d^2*(d + e*x)^(1/2))/(b*e^2) + (x^2*(a*e^4 + 2*b*d*e^3)*(d + e*x)^(1/2))/(b*e^4) + (d*x*(2*a*e + b*d)*(d + e*x)^(1/2))/(b*e^2))","B"
1683,0,-1,208,0.000000,"\text{Not used}","int((d + e*x)^(5/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int {\left(d+e\,x\right)}^{5/2}\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^(5/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1684,0,-1,208,0.000000,"\text{Not used}","int((d + e*x)^(3/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int {\left(d+e\,x\right)}^{3/2}\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^(3/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1685,0,-1,208,0.000000,"\text{Not used}","int((d + e*x)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int \sqrt{d+e\,x}\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1686,1,198,204,0.982163,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^(1/2),x)","\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(\frac{2\,b^2\,x^4}{7}+\frac{2\,x^2\,\left(35\,a^2\,e^2-7\,a\,b\,d\,e+2\,b^2\,d^2\right)}{35\,e^2}-\frac{-70\,a^3\,d\,e^3+140\,a^2\,b\,d^2\,e^2-112\,a\,b^2\,d^3\,e+32\,b^3\,d^4}{35\,b\,e^4}+\frac{2\,b\,x^3\,\left(21\,a\,e-b\,d\right)}{35\,e}+\frac{x\,\left(70\,a^3\,e^4-70\,a^2\,b\,d\,e^3+56\,a\,b^2\,d^2\,e^2-16\,b^3\,d^3\,e\right)}{35\,b\,e^4}\right)}{x\,\sqrt{d+e\,x}+\frac{a\,\sqrt{d+e\,x}}{b}}","Not used",1,"((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*((2*b^2*x^4)/7 + (2*x^2*(35*a^2*e^2 + 2*b^2*d^2 - 7*a*b*d*e))/(35*e^2) - (32*b^3*d^4 - 70*a^3*d*e^3 + 140*a^2*b*d^2*e^2 - 112*a*b^2*d^3*e)/(35*b*e^4) + (2*b*x^3*(21*a*e - b*d))/(35*e) + (x*(70*a^3*e^4 - 16*b^3*d^3*e + 56*a*b^2*d^2*e^2 - 70*a^2*b*d*e^3))/(35*b*e^4)))/(x*(d + e*x)^(1/2) + (a*(d + e*x)^(1/2))/b)","B"
1687,1,147,202,1.148216,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^(3/2),x)","\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(\frac{2\,x\,\left(15\,a^2\,e^2-20\,a\,b\,d\,e+8\,b^2\,d^2\right)}{5\,e^3}-\frac{2\,a^3\,e^3-12\,a^2\,b\,d\,e^2+16\,a\,b^2\,d^2\,e-\frac{32\,b^3\,d^3}{5}}{b\,e^4}+\frac{2\,b^2\,x^3}{5\,e}+\frac{2\,b\,x^2\,\left(5\,a\,e-2\,b\,d\right)}{5\,e^2}\right)}{x\,\sqrt{d+e\,x}+\frac{a\,\sqrt{d+e\,x}}{b}}","Not used",1,"((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*((2*x*(15*a^2*e^2 + 8*b^2*d^2 - 20*a*b*d*e))/(5*e^3) - (2*a^3*e^3 - (32*b^3*d^3)/5 + 16*a*b^2*d^2*e - 12*a^2*b*d*e^2)/(b*e^4) + (2*b^2*x^3)/(5*e) + (2*b*x^2*(5*a*e - 2*b*d))/(5*e^2)))/(x*(d + e*x)^(1/2) + (a*(d + e*x)^(1/2))/b)","B"
1688,1,184,204,1.233846,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^(5/2),x)","-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(\frac{2\,a^3\,e^3+12\,a^2\,b\,d\,e^2-48\,a\,b^2\,d^2\,e+32\,b^3\,d^3}{3\,b\,e^5}+\frac{2\,x\,\left(3\,a^2\,e^2-12\,a\,b\,d\,e+8\,b^2\,d^2\right)}{e^4}-\frac{2\,b^2\,x^3}{3\,e^2}-\frac{2\,b\,x^2\,\left(3\,a\,e-2\,b\,d\right)}{e^3}\right)}{x^2\,\sqrt{d+e\,x}+\frac{a\,d\,\sqrt{d+e\,x}}{b\,e}+\frac{x\,\left(3\,a\,e^5+3\,b\,d\,e^4\right)\,\sqrt{d+e\,x}}{3\,b\,e^5}}","Not used",1,"-((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*((2*a^3*e^3 + 32*b^3*d^3 - 48*a*b^2*d^2*e + 12*a^2*b*d*e^2)/(3*b*e^5) + (2*x*(3*a^2*e^2 + 8*b^2*d^2 - 12*a*b*d*e))/e^4 - (2*b^2*x^3)/(3*e^2) - (2*b*x^2*(3*a*e - 2*b*d))/e^3))/(x^2*(d + e*x)^(1/2) + (a*d*(d + e*x)^(1/2))/(b*e) + (x*(3*a*e^5 + 3*b*d*e^4)*(d + e*x)^(1/2))/(3*b*e^5))","B"
1689,1,210,202,1.290953,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^(7/2),x)","-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(\frac{2\,a^3\,e^3+4\,a^2\,b\,d\,e^2+16\,a\,b^2\,d^2\,e-32\,b^3\,d^3}{5\,b\,e^6}+\frac{2\,x\,\left(a^2\,e^2+4\,a\,b\,d\,e-8\,b^2\,d^2\right)}{e^5}-\frac{2\,b^2\,x^3}{e^3}+\frac{6\,b\,x^2\,\left(a\,e-2\,b\,d\right)}{e^4}\right)}{x^3\,\sqrt{d+e\,x}+\frac{a\,d^2\,\sqrt{d+e\,x}}{b\,e^2}+\frac{x^2\,\left(5\,a\,e^6+10\,b\,d\,e^5\right)\,\sqrt{d+e\,x}}{5\,b\,e^6}+\frac{d\,x\,\left(2\,a\,e+b\,d\right)\,\sqrt{d+e\,x}}{b\,e^2}}","Not used",1,"-((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*((2*a^3*e^3 - 32*b^3*d^3 + 16*a*b^2*d^2*e + 4*a^2*b*d*e^2)/(5*b*e^6) + (2*x*(a^2*e^2 - 8*b^2*d^2 + 4*a*b*d*e))/e^5 - (2*b^2*x^3)/e^3 + (6*b*x^2*(a*e - 2*b*d))/e^4))/(x^3*(d + e*x)^(1/2) + (a*d^2*(d + e*x)^(1/2))/(b*e^2) + (x^2*(5*a*e^6 + 10*b*d*e^5)*(d + e*x)^(1/2))/(5*b*e^6) + (d*x*(2*a*e + b*d)*(d + e*x)^(1/2))/(b*e^2))","B"
1690,1,239,204,1.327051,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^(9/2),x)","-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(\frac{10\,a^3\,e^3+12\,a^2\,b\,d\,e^2+16\,a\,b^2\,d^2\,e+32\,b^3\,d^3}{35\,b\,e^7}+\frac{2\,x\,\left(3\,a^2\,e^2+4\,a\,b\,d\,e+8\,b^2\,d^2\right)}{5\,e^6}+\frac{2\,b^2\,x^3}{e^4}+\frac{2\,b\,x^2\,\left(a\,e+2\,b\,d\right)}{e^5}\right)}{x^4\,\sqrt{d+e\,x}+\frac{a\,d^3\,\sqrt{d+e\,x}}{b\,e^3}+\frac{x^3\,\left(35\,a\,e^7+105\,b\,d\,e^6\right)\,\sqrt{d+e\,x}}{35\,b\,e^7}+\frac{3\,d\,x^2\,\left(a\,e+b\,d\right)\,\sqrt{d+e\,x}}{b\,e^2}+\frac{d^2\,x\,\left(3\,a\,e+b\,d\right)\,\sqrt{d+e\,x}}{b\,e^3}}","Not used",1,"-((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*((10*a^3*e^3 + 32*b^3*d^3 + 16*a*b^2*d^2*e + 12*a^2*b*d*e^2)/(35*b*e^7) + (2*x*(3*a^2*e^2 + 8*b^2*d^2 + 4*a*b*d*e))/(5*e^6) + (2*b^2*x^3)/e^4 + (2*b*x^2*(a*e + 2*b*d))/e^5))/(x^4*(d + e*x)^(1/2) + (a*d^3*(d + e*x)^(1/2))/(b*e^3) + (x^3*(35*a*e^7 + 105*b*d*e^6)*(d + e*x)^(1/2))/(35*b*e^7) + (3*d*x^2*(a*e + b*d)*(d + e*x)^(1/2))/(b*e^2) + (d^2*x*(3*a*e + b*d)*(d + e*x)^(1/2))/(b*e^3))","B"
1691,1,268,208,1.365261,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(3/2)/(d + e*x)^(11/2),x)","-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(\frac{\frac{2\,a^3\,e^3}{9}+\frac{4\,a^2\,b\,d\,e^2}{21}+\frac{16\,a\,b^2\,d^2\,e}{105}+\frac{32\,b^3\,d^3}{315}}{b\,e^8}+\frac{2\,x\,\left(15\,a^2\,e^2+12\,a\,b\,d\,e+8\,b^2\,d^2\right)}{35\,e^7}+\frac{2\,b^2\,x^3}{3\,e^5}+\frac{2\,b\,x^2\,\left(3\,a\,e+2\,b\,d\right)}{5\,e^6}\right)}{x^5\,\sqrt{d+e\,x}+\frac{a\,d^4\,\sqrt{d+e\,x}}{b\,e^4}+\frac{x^4\,\left(a\,e^8+4\,b\,d\,e^7\right)\,\sqrt{d+e\,x}}{b\,e^8}+\frac{2\,d\,x^3\,\left(2\,a\,e+3\,b\,d\right)\,\sqrt{d+e\,x}}{b\,e^2}+\frac{d^3\,x\,\left(4\,a\,e+b\,d\right)\,\sqrt{d+e\,x}}{b\,e^4}+\frac{d^2\,x^2\,\left(6\,a\,e+4\,b\,d\right)\,\sqrt{d+e\,x}}{b\,e^3}}","Not used",1,"-((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*(((2*a^3*e^3)/9 + (32*b^3*d^3)/315 + (16*a*b^2*d^2*e)/105 + (4*a^2*b*d*e^2)/21)/(b*e^8) + (2*x*(15*a^2*e^2 + 8*b^2*d^2 + 12*a*b*d*e))/(35*e^7) + (2*b^2*x^3)/(3*e^5) + (2*b*x^2*(3*a*e + 2*b*d))/(5*e^6)))/(x^5*(d + e*x)^(1/2) + (a*d^4*(d + e*x)^(1/2))/(b*e^4) + (x^4*(a*e^8 + 4*b*d*e^7)*(d + e*x)^(1/2))/(b*e^8) + (2*d*x^3*(2*a*e + 3*b*d)*(d + e*x)^(1/2))/(b*e^2) + (d^3*x*(4*a*e + b*d)*(d + e*x)^(1/2))/(b*e^4) + (d^2*x^2*(6*a*e + 4*b*d)*(d + e*x)^(1/2))/(b*e^3))","B"
1692,0,-1,320,0.000000,"\text{Not used}","int((d + e*x)^(5/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int {\left(d+e\,x\right)}^{5/2}\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)^(5/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1693,0,-1,320,0.000000,"\text{Not used}","int((d + e*x)^(3/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int {\left(d+e\,x\right)}^{3/2}\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)^(3/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1694,0,-1,318,0.000000,"\text{Not used}","int((d + e*x)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int \sqrt{d+e\,x}\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1695,1,375,316,1.187528,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^(1/2),x)","\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(\frac{2\,b^4\,x^6}{11}-\frac{-1386\,a^5\,d\,e^5+4620\,a^4\,b\,d^2\,e^4-7392\,a^3\,b^2\,d^3\,e^3+6336\,a^2\,b^3\,d^4\,e^2-2816\,a\,b^4\,d^5\,e+512\,b^5\,d^6}{693\,b\,e^6}+\frac{2\,b^3\,x^5\,\left(55\,a\,e-b\,d\right)}{99\,e}+\frac{x\,\left(1386\,a^5\,e^6-2310\,a^4\,b\,d\,e^5+3696\,a^3\,b^2\,d^2\,e^4-3168\,a^2\,b^3\,d^3\,e^3+1408\,a\,b^4\,d^4\,e^2-256\,b^5\,d^5\,e\right)}{693\,b\,e^6}+\frac{x^2\,\left(2310\,a^4\,b\,e^6-924\,a^3\,b^2\,d\,e^5+792\,a^2\,b^3\,d^2\,e^4-352\,a\,b^4\,d^3\,e^3+64\,b^5\,d^4\,e^2\right)}{693\,b\,e^6}+\frac{10\,b^2\,x^4\,\left(198\,a^2\,e^2-11\,a\,b\,d\,e+2\,b^2\,d^2\right)}{693\,e^2}+\frac{4\,b\,x^3\,\left(693\,a^3\,e^3-99\,a^2\,b\,d\,e^2+44\,a\,b^2\,d^2\,e-8\,b^3\,d^3\right)}{693\,e^3}\right)}{x\,\sqrt{d+e\,x}+\frac{a\,\sqrt{d+e\,x}}{b}}","Not used",1,"((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*((2*b^4*x^6)/11 - (512*b^5*d^6 - 1386*a^5*d*e^5 + 4620*a^4*b*d^2*e^4 + 6336*a^2*b^3*d^4*e^2 - 7392*a^3*b^2*d^3*e^3 - 2816*a*b^4*d^5*e)/(693*b*e^6) + (2*b^3*x^5*(55*a*e - b*d))/(99*e) + (x*(1386*a^5*e^6 - 256*b^5*d^5*e + 1408*a*b^4*d^4*e^2 - 3168*a^2*b^3*d^3*e^3 + 3696*a^3*b^2*d^2*e^4 - 2310*a^4*b*d*e^5))/(693*b*e^6) + (x^2*(2310*a^4*b*e^6 + 64*b^5*d^4*e^2 - 352*a*b^4*d^3*e^3 - 924*a^3*b^2*d*e^5 + 792*a^2*b^3*d^2*e^4))/(693*b*e^6) + (10*b^2*x^4*(198*a^2*e^2 + 2*b^2*d^2 - 11*a*b*d*e))/(693*e^2) + (4*b*x^3*(693*a^3*e^3 - 8*b^3*d^3 + 44*a*b^2*d^2*e - 99*a^2*b*d*e^2))/(693*e^3)))/(x*(d + e*x)^(1/2) + (a*(d + e*x)^(1/2))/b)","B"
1696,1,294,314,1.489608,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^(3/2),x)","\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(\frac{2\,b^4\,x^5}{9\,e}-\frac{126\,a^5\,e^5-1260\,a^4\,b\,d\,e^4+3360\,a^3\,b^2\,d^2\,e^3-4032\,a^2\,b^3\,d^3\,e^2+2304\,a\,b^4\,d^4\,e-512\,b^5\,d^5}{63\,b\,e^6}+\frac{10\,b^3\,x^4\,\left(9\,a\,e-2\,b\,d\right)}{63\,e^2}+\frac{x\,\left(630\,a^4\,b\,e^5-1680\,a^3\,b^2\,d\,e^4+2016\,a^2\,b^3\,d^2\,e^3-1152\,a\,b^4\,d^3\,e^2+256\,b^5\,d^4\,e\right)}{63\,b\,e^6}+\frac{4\,b^2\,x^3\,\left(63\,a^2\,e^2-36\,a\,b\,d\,e+8\,b^2\,d^2\right)}{63\,e^3}+\frac{4\,b\,x^2\,\left(105\,a^3\,e^3-126\,a^2\,b\,d\,e^2+72\,a\,b^2\,d^2\,e-16\,b^3\,d^3\right)}{63\,e^4}\right)}{x\,\sqrt{d+e\,x}+\frac{a\,\sqrt{d+e\,x}}{b}}","Not used",1,"((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*((2*b^4*x^5)/(9*e) - (126*a^5*e^5 - 512*b^5*d^5 - 4032*a^2*b^3*d^3*e^2 + 3360*a^3*b^2*d^2*e^3 + 2304*a*b^4*d^4*e - 1260*a^4*b*d*e^4)/(63*b*e^6) + (10*b^3*x^4*(9*a*e - 2*b*d))/(63*e^2) + (x*(630*a^4*b*e^5 + 256*b^5*d^4*e - 1152*a*b^4*d^3*e^2 - 1680*a^3*b^2*d*e^4 + 2016*a^2*b^3*d^2*e^3))/(63*b*e^6) + (4*b^2*x^3*(63*a^2*e^2 + 8*b^2*d^2 - 36*a*b*d*e))/(63*e^3) + (4*b*x^2*(105*a^3*e^3 - 16*b^3*d^3 + 72*a*b^2*d^2*e - 126*a^2*b*d*e^2))/(63*e^4)))/(x*(d + e*x)^(1/2) + (a*(d + e*x)^(1/2))/b)","B"
1697,1,330,314,1.572651,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^(5/2),x)","\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(\frac{2\,b^4\,x^5}{7\,e^2}-\frac{14\,a^5\,e^5+140\,a^4\,b\,d\,e^4-1120\,a^3\,b^2\,d^2\,e^3+2240\,a^2\,b^3\,d^3\,e^2-1792\,a\,b^4\,d^4\,e+512\,b^5\,d^5}{21\,b\,e^7}+\frac{2\,b^3\,x^4\,\left(7\,a\,e-2\,b\,d\right)}{7\,e^3}-\frac{x\,\left(210\,a^4\,b\,e^5-1680\,a^3\,b^2\,d\,e^4+3360\,a^2\,b^3\,d^2\,e^3-2688\,a\,b^4\,d^3\,e^2+768\,b^5\,d^4\,e\right)}{21\,b\,e^7}+\frac{4\,b^2\,x^3\,\left(35\,a^2\,e^2-28\,a\,b\,d\,e+8\,b^2\,d^2\right)}{21\,e^4}+\frac{4\,b\,x^2\,\left(35\,a^3\,e^3-70\,a^2\,b\,d\,e^2+56\,a\,b^2\,d^2\,e-16\,b^3\,d^3\right)}{7\,e^5}\right)}{x^2\,\sqrt{d+e\,x}+\frac{a\,d\,\sqrt{d+e\,x}}{b\,e}+\frac{x\,\left(21\,a\,e^7+21\,b\,d\,e^6\right)\,\sqrt{d+e\,x}}{21\,b\,e^7}}","Not used",1,"((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*((2*b^4*x^5)/(7*e^2) - (14*a^5*e^5 + 512*b^5*d^5 + 2240*a^2*b^3*d^3*e^2 - 1120*a^3*b^2*d^2*e^3 - 1792*a*b^4*d^4*e + 140*a^4*b*d*e^4)/(21*b*e^7) + (2*b^3*x^4*(7*a*e - 2*b*d))/(7*e^3) - (x*(210*a^4*b*e^5 + 768*b^5*d^4*e - 2688*a*b^4*d^3*e^2 - 1680*a^3*b^2*d*e^4 + 3360*a^2*b^3*d^2*e^3))/(21*b*e^7) + (4*b^2*x^3*(35*a^2*e^2 + 8*b^2*d^2 - 28*a*b*d*e))/(21*e^4) + (4*b*x^2*(35*a^3*e^3 - 16*b^3*d^3 + 56*a*b^2*d^2*e - 70*a^2*b*d*e^2))/(7*e^5)))/(x^2*(d + e*x)^(1/2) + (a*d*(d + e*x)^(1/2))/(b*e) + (x*(21*a*e^7 + 21*b*d*e^6)*(d + e*x)^(1/2))/(21*b*e^7))","B"
1698,1,359,316,1.595692,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^(7/2),x)","-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(\frac{6\,a^5\,e^5+20\,a^4\,b\,d\,e^4+160\,a^3\,b^2\,d^2\,e^3-960\,a^2\,b^3\,d^3\,e^2+1280\,a\,b^4\,d^4\,e-512\,b^5\,d^5}{15\,b\,e^8}-\frac{2\,b^4\,x^5}{5\,e^3}-\frac{2\,b^3\,x^4\,\left(5\,a\,e-2\,b\,d\right)}{3\,e^4}+\frac{x\,\left(50\,a^4\,b\,e^5+400\,a^3\,b^2\,d\,e^4-2400\,a^2\,b^3\,d^2\,e^3+3200\,a\,b^4\,d^3\,e^2-1280\,b^5\,d^4\,e\right)}{15\,b\,e^8}-\frac{4\,b^2\,x^3\,\left(15\,a^2\,e^2-20\,a\,b\,d\,e+8\,b^2\,d^2\right)}{3\,e^5}+\frac{4\,b\,x^2\,\left(5\,a^3\,e^3-30\,a^2\,b\,d\,e^2+40\,a\,b^2\,d^2\,e-16\,b^3\,d^3\right)}{e^6}\right)}{x^3\,\sqrt{d+e\,x}+\frac{a\,d^2\,\sqrt{d+e\,x}}{b\,e^2}+\frac{x^2\,\left(15\,a\,e^8+30\,b\,d\,e^7\right)\,\sqrt{d+e\,x}}{15\,b\,e^8}+\frac{d\,x\,\left(2\,a\,e+b\,d\right)\,\sqrt{d+e\,x}}{b\,e^2}}","Not used",1,"-((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*((6*a^5*e^5 - 512*b^5*d^5 - 960*a^2*b^3*d^3*e^2 + 160*a^3*b^2*d^2*e^3 + 1280*a*b^4*d^4*e + 20*a^4*b*d*e^4)/(15*b*e^8) - (2*b^4*x^5)/(5*e^3) - (2*b^3*x^4*(5*a*e - 2*b*d))/(3*e^4) + (x*(50*a^4*b*e^5 - 1280*b^5*d^4*e + 3200*a*b^4*d^3*e^2 + 400*a^3*b^2*d*e^4 - 2400*a^2*b^3*d^2*e^3))/(15*b*e^8) - (4*b^2*x^3*(15*a^2*e^2 + 8*b^2*d^2 - 20*a*b*d*e))/(3*e^5) + (4*b*x^2*(5*a^3*e^3 - 16*b^3*d^3 + 40*a*b^2*d^2*e - 30*a^2*b*d*e^2))/e^6))/(x^3*(d + e*x)^(1/2) + (a*d^2*(d + e*x)^(1/2))/(b*e^2) + (x^2*(15*a*e^8 + 30*b*d*e^7)*(d + e*x)^(1/2))/(15*b*e^8) + (d*x*(2*a*e + b*d)*(d + e*x)^(1/2))/(b*e^2))","B"
1699,1,386,314,1.659164,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^(9/2),x)","-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(\frac{6\,a^5\,e^5+12\,a^4\,b\,d\,e^4+32\,a^3\,b^2\,d^2\,e^3+192\,a^2\,b^3\,d^3\,e^2-768\,a\,b^4\,d^4\,e+512\,b^5\,d^5}{21\,b\,e^9}-\frac{2\,b^4\,x^5}{3\,e^4}-\frac{10\,b^3\,x^4\,\left(3\,a\,e-2\,b\,d\right)}{3\,e^5}+\frac{x\,\left(42\,a^4\,b\,e^5+112\,a^3\,b^2\,d\,e^4+672\,a^2\,b^3\,d^2\,e^3-2688\,a\,b^4\,d^3\,e^2+1792\,b^5\,d^4\,e\right)}{21\,b\,e^9}+\frac{20\,b^2\,x^3\,\left(3\,a^2\,e^2-12\,a\,b\,d\,e+8\,b^2\,d^2\right)}{3\,e^6}+\frac{20\,b\,x^2\,\left(a^3\,e^3+6\,a^2\,b\,d\,e^2-24\,a\,b^2\,d^2\,e+16\,b^3\,d^3\right)}{3\,e^7}\right)}{x^4\,\sqrt{d+e\,x}+\frac{a\,d^3\,\sqrt{d+e\,x}}{b\,e^3}+\frac{x^3\,\left(21\,a\,e^9+63\,b\,d\,e^8\right)\,\sqrt{d+e\,x}}{21\,b\,e^9}+\frac{3\,d\,x^2\,\left(a\,e+b\,d\right)\,\sqrt{d+e\,x}}{b\,e^2}+\frac{d^2\,x\,\left(3\,a\,e+b\,d\right)\,\sqrt{d+e\,x}}{b\,e^3}}","Not used",1,"-((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*((6*a^5*e^5 + 512*b^5*d^5 + 192*a^2*b^3*d^3*e^2 + 32*a^3*b^2*d^2*e^3 - 768*a*b^4*d^4*e + 12*a^4*b*d*e^4)/(21*b*e^9) - (2*b^4*x^5)/(3*e^4) - (10*b^3*x^4*(3*a*e - 2*b*d))/(3*e^5) + (x*(42*a^4*b*e^5 + 1792*b^5*d^4*e - 2688*a*b^4*d^3*e^2 + 112*a^3*b^2*d*e^4 + 672*a^2*b^3*d^2*e^3))/(21*b*e^9) + (20*b^2*x^3*(3*a^2*e^2 + 8*b^2*d^2 - 12*a*b*d*e))/(3*e^6) + (20*b*x^2*(a^3*e^3 + 16*b^3*d^3 - 24*a*b^2*d^2*e + 6*a^2*b*d*e^2))/(3*e^7)))/(x^4*(d + e*x)^(1/2) + (a*d^3*(d + e*x)^(1/2))/(b*e^3) + (x^3*(21*a*e^9 + 63*b*d*e^8)*(d + e*x)^(1/2))/(21*b*e^9) + (3*d*x^2*(a*e + b*d)*(d + e*x)^(1/2))/(b*e^2) + (d^2*x*(3*a*e + b*d)*(d + e*x)^(1/2))/(b*e^3))","B"
1700,1,416,314,1.688421,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^(11/2),x)","-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(\frac{14\,a^5\,e^5+20\,a^4\,b\,d\,e^4+32\,a^3\,b^2\,d^2\,e^3+64\,a^2\,b^3\,d^3\,e^2+256\,a\,b^4\,d^4\,e-512\,b^5\,d^5}{63\,b\,e^{10}}-\frac{2\,b^4\,x^5}{e^5}+\frac{10\,b^3\,x^4\,\left(a\,e-2\,b\,d\right)}{e^6}+\frac{x\,\left(90\,a^4\,b\,e^5+144\,a^3\,b^2\,d\,e^4+288\,a^2\,b^3\,d^2\,e^3+1152\,a\,b^4\,d^3\,e^2-2304\,b^5\,d^4\,e\right)}{63\,b\,e^{10}}+\frac{20\,b^2\,x^3\,\left(a^2\,e^2+4\,a\,b\,d\,e-8\,b^2\,d^2\right)}{3\,e^7}+\frac{4\,b\,x^2\,\left(a^3\,e^3+2\,a^2\,b\,d\,e^2+8\,a\,b^2\,d^2\,e-16\,b^3\,d^3\right)}{e^8}\right)}{x^5\,\sqrt{d+e\,x}+\frac{a\,d^4\,\sqrt{d+e\,x}}{b\,e^4}+\frac{x^4\,\left(63\,a\,e^{10}+252\,b\,d\,e^9\right)\,\sqrt{d+e\,x}}{63\,b\,e^{10}}+\frac{2\,d\,x^3\,\left(2\,a\,e+3\,b\,d\right)\,\sqrt{d+e\,x}}{b\,e^2}+\frac{d^3\,x\,\left(4\,a\,e+b\,d\right)\,\sqrt{d+e\,x}}{b\,e^4}+\frac{2\,d^2\,x^2\,\left(3\,a\,e+2\,b\,d\right)\,\sqrt{d+e\,x}}{b\,e^3}}","Not used",1,"-((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*((14*a^5*e^5 - 512*b^5*d^5 + 64*a^2*b^3*d^3*e^2 + 32*a^3*b^2*d^2*e^3 + 256*a*b^4*d^4*e + 20*a^4*b*d*e^4)/(63*b*e^10) - (2*b^4*x^5)/e^5 + (10*b^3*x^4*(a*e - 2*b*d))/e^6 + (x*(90*a^4*b*e^5 - 2304*b^5*d^4*e + 1152*a*b^4*d^3*e^2 + 144*a^3*b^2*d*e^4 + 288*a^2*b^3*d^2*e^3))/(63*b*e^10) + (20*b^2*x^3*(a^2*e^2 - 8*b^2*d^2 + 4*a*b*d*e))/(3*e^7) + (4*b*x^2*(a^3*e^3 - 16*b^3*d^3 + 8*a*b^2*d^2*e + 2*a^2*b*d*e^2))/e^8))/(x^5*(d + e*x)^(1/2) + (a*d^4*(d + e*x)^(1/2))/(b*e^4) + (x^4*(63*a*e^10 + 252*b*d*e^9)*(d + e*x)^(1/2))/(63*b*e^10) + (2*d*x^3*(2*a*e + 3*b*d)*(d + e*x)^(1/2))/(b*e^2) + (d^3*x*(4*a*e + b*d)*(d + e*x)^(1/2))/(b*e^4) + (2*d^2*x^2*(3*a*e + 2*b*d)*(d + e*x)^(1/2))/(b*e^3))","B"
1701,1,437,316,1.733657,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^(13/2),x)","-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(\frac{126\,a^5\,e^5+140\,a^4\,b\,d\,e^4+160\,a^3\,b^2\,d^2\,e^3+192\,a^2\,b^3\,d^3\,e^2+256\,a\,b^4\,d^4\,e+512\,b^5\,d^5}{693\,b\,e^{11}}+\frac{2\,b^4\,x^5}{e^6}+\frac{10\,b^3\,x^4\,\left(a\,e+2\,b\,d\right)}{3\,e^7}+\frac{x\,\left(770\,a^4\,b\,e^5+880\,a^3\,b^2\,d\,e^4+1056\,a^2\,b^3\,d^2\,e^3+1408\,a\,b^4\,d^3\,e^2+2816\,b^5\,d^4\,e\right)}{693\,b\,e^{11}}+\frac{4\,b^2\,x^3\,\left(3\,a^2\,e^2+4\,a\,b\,d\,e+8\,b^2\,d^2\right)}{3\,e^8}+\frac{4\,b\,x^2\,\left(5\,a^3\,e^3+6\,a^2\,b\,d\,e^2+8\,a\,b^2\,d^2\,e+16\,b^3\,d^3\right)}{7\,e^9}\right)}{x^6\,\sqrt{d+e\,x}+\frac{a\,d^5\,\sqrt{d+e\,x}}{b\,e^5}+\frac{x^5\,\left(a\,e+5\,b\,d\right)\,\sqrt{d+e\,x}}{b\,e}+\frac{5\,d\,x^4\,\left(a\,e+2\,b\,d\right)\,\sqrt{d+e\,x}}{b\,e^2}+\frac{d^4\,x\,\left(5\,a\,e+b\,d\right)\,\sqrt{d+e\,x}}{b\,e^5}+\frac{10\,d^2\,x^3\,\left(a\,e+b\,d\right)\,\sqrt{d+e\,x}}{b\,e^3}+\frac{5\,d^3\,x^2\,\left(2\,a\,e+b\,d\right)\,\sqrt{d+e\,x}}{b\,e^4}}","Not used",1,"-((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*((126*a^5*e^5 + 512*b^5*d^5 + 192*a^2*b^3*d^3*e^2 + 160*a^3*b^2*d^2*e^3 + 256*a*b^4*d^4*e + 140*a^4*b*d*e^4)/(693*b*e^11) + (2*b^4*x^5)/e^6 + (10*b^3*x^4*(a*e + 2*b*d))/(3*e^7) + (x*(770*a^4*b*e^5 + 2816*b^5*d^4*e + 1408*a*b^4*d^3*e^2 + 880*a^3*b^2*d*e^4 + 1056*a^2*b^3*d^2*e^3))/(693*b*e^11) + (4*b^2*x^3*(3*a^2*e^2 + 8*b^2*d^2 + 4*a*b*d*e))/(3*e^8) + (4*b*x^2*(5*a^3*e^3 + 16*b^3*d^3 + 8*a*b^2*d^2*e + 6*a^2*b*d*e^2))/(7*e^9)))/(x^6*(d + e*x)^(1/2) + (a*d^5*(d + e*x)^(1/2))/(b*e^5) + (x^5*(a*e + 5*b*d)*(d + e*x)^(1/2))/(b*e) + (5*d*x^4*(a*e + 2*b*d)*(d + e*x)^(1/2))/(b*e^2) + (d^4*x*(5*a*e + b*d)*(d + e*x)^(1/2))/(b*e^5) + (10*d^2*x^3*(a*e + b*d)*(d + e*x)^(1/2))/(b*e^3) + (5*d^3*x^2*(2*a*e + b*d)*(d + e*x)^(1/2))/(b*e^4))","B"
1702,1,472,318,1.769502,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^(5/2)/(d + e*x)^(15/2),x)","-\frac{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}\,\left(\frac{1386\,a^5\,e^5+1260\,a^4\,b\,d\,e^4+1120\,a^3\,b^2\,d^2\,e^3+960\,a^2\,b^3\,d^3\,e^2+768\,a\,b^4\,d^4\,e+512\,b^5\,d^5}{9009\,b\,e^{12}}+\frac{2\,b^4\,x^5}{3\,e^7}+\frac{2\,b^3\,x^4\,\left(3\,a\,e+2\,b\,d\right)}{3\,e^8}+\frac{x\,\left(8190\,a^4\,b\,e^5+7280\,a^3\,b^2\,d\,e^4+6240\,a^2\,b^3\,d^2\,e^3+4992\,a\,b^4\,d^3\,e^2+3328\,b^5\,d^4\,e\right)}{9009\,b\,e^{12}}+\frac{4\,b^2\,x^3\,\left(15\,a^2\,e^2+12\,a\,b\,d\,e+8\,b^2\,d^2\right)}{21\,e^9}+\frac{4\,b\,x^2\,\left(35\,a^3\,e^3+30\,a^2\,b\,d\,e^2+24\,a\,b^2\,d^2\,e+16\,b^3\,d^3\right)}{63\,e^{10}}\right)}{x^7\,\sqrt{d+e\,x}+\frac{a\,d^6\,\sqrt{d+e\,x}}{b\,e^6}+\frac{x^6\,\left(a\,e+6\,b\,d\right)\,\sqrt{d+e\,x}}{b\,e}+\frac{3\,d\,x^5\,\left(2\,a\,e+5\,b\,d\right)\,\sqrt{d+e\,x}}{b\,e^2}+\frac{d^5\,x\,\left(6\,a\,e+b\,d\right)\,\sqrt{d+e\,x}}{b\,e^6}+\frac{5\,d^2\,x^4\,\left(3\,a\,e+4\,b\,d\right)\,\sqrt{d+e\,x}}{b\,e^3}+\frac{5\,d^3\,x^3\,\left(4\,a\,e+3\,b\,d\right)\,\sqrt{d+e\,x}}{b\,e^4}+\frac{3\,d^4\,x^2\,\left(5\,a\,e+2\,b\,d\right)\,\sqrt{d+e\,x}}{b\,e^5}}","Not used",1,"-((a^2 + b^2*x^2 + 2*a*b*x)^(1/2)*((1386*a^5*e^5 + 512*b^5*d^5 + 960*a^2*b^3*d^3*e^2 + 1120*a^3*b^2*d^2*e^3 + 768*a*b^4*d^4*e + 1260*a^4*b*d*e^4)/(9009*b*e^12) + (2*b^4*x^5)/(3*e^7) + (2*b^3*x^4*(3*a*e + 2*b*d))/(3*e^8) + (x*(8190*a^4*b*e^5 + 3328*b^5*d^4*e + 4992*a*b^4*d^3*e^2 + 7280*a^3*b^2*d*e^4 + 6240*a^2*b^3*d^2*e^3))/(9009*b*e^12) + (4*b^2*x^3*(15*a^2*e^2 + 8*b^2*d^2 + 12*a*b*d*e))/(21*e^9) + (4*b*x^2*(35*a^3*e^3 + 16*b^3*d^3 + 24*a*b^2*d^2*e + 30*a^2*b*d*e^2))/(63*e^10)))/(x^7*(d + e*x)^(1/2) + (a*d^6*(d + e*x)^(1/2))/(b*e^6) + (x^6*(a*e + 6*b*d)*(d + e*x)^(1/2))/(b*e) + (3*d*x^5*(2*a*e + 5*b*d)*(d + e*x)^(1/2))/(b*e^2) + (d^5*x*(6*a*e + b*d)*(d + e*x)^(1/2))/(b*e^6) + (5*d^2*x^4*(3*a*e + 4*b*d)*(d + e*x)^(1/2))/(b*e^3) + (5*d^3*x^3*(4*a*e + 3*b*d)*(d + e*x)^(1/2))/(b*e^4) + (3*d^4*x^2*(5*a*e + 2*b*d)*(d + e*x)^(1/2))/(b*e^5))","B"
1703,0,-1,263,0.000000,"\text{Not used}","int((d + e*x)^(7/2)/((a + b*x)^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^{7/2}}{\sqrt{{\left(a+b\,x\right)}^2}} \,d x","Not used",1,"int((d + e*x)^(7/2)/((a + b*x)^2)^(1/2), x)","F"
1704,0,-1,212,0.000000,"\text{Not used}","int((d + e*x)^(5/2)/((a + b*x)^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^{5/2}}{\sqrt{{\left(a+b\,x\right)}^2}} \,d x","Not used",1,"int((d + e*x)^(5/2)/((a + b*x)^2)^(1/2), x)","F"
1705,0,-1,161,0.000000,"\text{Not used}","int((d + e*x)^(3/2)/((a + b*x)^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^{3/2}}{\sqrt{{\left(a+b\,x\right)}^2}} \,d x","Not used",1,"int((d + e*x)^(3/2)/((a + b*x)^2)^(1/2), x)","F"
1706,0,-1,112,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/((a + b*x)^2)^(1/2),x)","\int \frac{\sqrt{d+e\,x}}{\sqrt{{\left(a+b\,x\right)}^2}} \,d x","Not used",1,"int((d + e*x)^(1/2)/((a + b*x)^2)^(1/2), x)","F"
1707,0,-1,72,0.000000,"\text{Not used}","int(1/(((a + b*x)^2)^(1/2)*(d + e*x)^(1/2)),x)","\int \frac{1}{\sqrt{{\left(a+b\,x\right)}^2}\,\sqrt{d+e\,x}} \,d x","Not used",1,"int(1/(((a + b*x)^2)^(1/2)*(d + e*x)^(1/2)), x)","F"
1708,0,-1,119,0.000000,"\text{Not used}","int(1/(((a + b*x)^2)^(1/2)*(d + e*x)^(3/2)),x)","\int \frac{1}{\sqrt{{\left(a+b\,x\right)}^2}\,{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int(1/(((a + b*x)^2)^(1/2)*(d + e*x)^(3/2)), x)","F"
1709,0,-1,168,0.000000,"\text{Not used}","int(1/(((a + b*x)^2)^(1/2)*(d + e*x)^(5/2)),x)","\int \frac{1}{\sqrt{{\left(a+b\,x\right)}^2}\,{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int(1/(((a + b*x)^2)^(1/2)*(d + e*x)^(5/2)), x)","F"
1710,0,-1,219,0.000000,"\text{Not used}","int(1/(((a + b*x)^2)^(1/2)*(d + e*x)^(7/2)),x)","\int \frac{1}{\sqrt{{\left(a+b\,x\right)}^2}\,{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int(1/(((a + b*x)^2)^(1/2)*(d + e*x)^(7/2)), x)","F"
1711,0,-1,308,0.000000,"\text{Not used}","int((d + e*x)^(9/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^{9/2}}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(9/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1712,0,-1,254,0.000000,"\text{Not used}","int((d + e*x)^(7/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^{7/2}}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(7/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1713,0,-1,202,0.000000,"\text{Not used}","int((d + e*x)^(5/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^{5/2}}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(5/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1714,0,-1,158,0.000000,"\text{Not used}","int((d + e*x)^(3/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^{3/2}}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(3/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1715,0,-1,168,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int \frac{\sqrt{d+e\,x}}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(1/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1716,0,-1,172,0.000000,"\text{Not used}","int(1/((d + e*x)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)),x)","\int \frac{1}{\sqrt{d+e\,x}\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)), x)","F"
1717,0,-1,223,0.000000,"\text{Not used}","int(1/((d + e*x)^(3/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{3/2}\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)^(3/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)), x)","F"
1718,0,-1,275,0.000000,"\text{Not used}","int(1/((d + e*x)^(5/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{5/2}\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)^(5/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)), x)","F"
1719,0,-1,329,0.000000,"\text{Not used}","int(1/((d + e*x)^(7/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{7/2}\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)^(7/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2)), x)","F"
1720,0,-1,400,0.000000,"\text{Not used}","int((d + e*x)^(13/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{13/2}}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(13/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1721,0,-1,346,0.000000,"\text{Not used}","int((d + e*x)^(11/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{11/2}}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(11/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1722,0,-1,294,0.000000,"\text{Not used}","int((d + e*x)^(9/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{9/2}}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(9/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1723,0,-1,250,0.000000,"\text{Not used}","int((d + e*x)^(7/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{7/2}}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(7/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1724,0,-1,260,0.000000,"\text{Not used}","int((d + e*x)^(5/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{5/2}}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(5/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1725,0,-1,270,0.000000,"\text{Not used}","int((d + e*x)^(3/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{3/2}}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(3/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1726,0,-1,280,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int \frac{\sqrt{d+e\,x}}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(1/2)/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1727,0,-1,278,0.000000,"\text{Not used}","int(1/((d + e*x)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)),x)","\int \frac{1}{\sqrt{d+e\,x}\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int(1/((d + e*x)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)), x)","F"
1728,0,-1,329,0.000000,"\text{Not used}","int(1/((d + e*x)^(3/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{3/2}\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int(1/((d + e*x)^(3/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)), x)","F"
1729,0,-1,381,0.000000,"\text{Not used}","int(1/((d + e*x)^(5/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{5/2}\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int(1/((d + e*x)^(5/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)), x)","F"
1730,0,-1,435,0.000000,"\text{Not used}","int(1/((d + e*x)^(7/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{7/2}\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int(1/((d + e*x)^(7/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2)), x)","F"
1731,1,1898,206,1.641964,"\text{Not used}","int((d + e*x)^m*(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\frac{{\left(d+e\,x\right)}^m\,\left(a^6\,d\,e^6\,m^6+27\,a^6\,d\,e^6\,m^5+295\,a^6\,d\,e^6\,m^4+1665\,a^6\,d\,e^6\,m^3+5104\,a^6\,d\,e^6\,m^2+8028\,a^6\,d\,e^6\,m+5040\,a^6\,d\,e^6-6\,a^5\,b\,d^2\,e^5\,m^5-150\,a^5\,b\,d^2\,e^5\,m^4-1470\,a^5\,b\,d^2\,e^5\,m^3-7050\,a^5\,b\,d^2\,e^5\,m^2-16524\,a^5\,b\,d^2\,e^5\,m-15120\,a^5\,b\,d^2\,e^5+30\,a^4\,b^2\,d^3\,e^4\,m^4+660\,a^4\,b^2\,d^3\,e^4\,m^3+5370\,a^4\,b^2\,d^3\,e^4\,m^2+19140\,a^4\,b^2\,d^3\,e^4\,m+25200\,a^4\,b^2\,d^3\,e^4-120\,a^3\,b^3\,d^4\,e^3\,m^3-2160\,a^3\,b^3\,d^4\,e^3\,m^2-12840\,a^3\,b^3\,d^4\,e^3\,m-25200\,a^3\,b^3\,d^4\,e^3+360\,a^2\,b^4\,d^5\,e^2\,m^2+4680\,a^2\,b^4\,d^5\,e^2\,m+15120\,a^2\,b^4\,d^5\,e^2-720\,a\,b^5\,d^6\,e\,m-5040\,a\,b^5\,d^6\,e+720\,b^6\,d^7\right)}{e^7\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{x\,{\left(d+e\,x\right)}^m\,\left(a^6\,e^7\,m^6+27\,a^6\,e^7\,m^5+295\,a^6\,e^7\,m^4+1665\,a^6\,e^7\,m^3+5104\,a^6\,e^7\,m^2+8028\,a^6\,e^7\,m+5040\,a^6\,e^7+6\,a^5\,b\,d\,e^6\,m^6+150\,a^5\,b\,d\,e^6\,m^5+1470\,a^5\,b\,d\,e^6\,m^4+7050\,a^5\,b\,d\,e^6\,m^3+16524\,a^5\,b\,d\,e^6\,m^2+15120\,a^5\,b\,d\,e^6\,m-30\,a^4\,b^2\,d^2\,e^5\,m^5-660\,a^4\,b^2\,d^2\,e^5\,m^4-5370\,a^4\,b^2\,d^2\,e^5\,m^3-19140\,a^4\,b^2\,d^2\,e^5\,m^2-25200\,a^4\,b^2\,d^2\,e^5\,m+120\,a^3\,b^3\,d^3\,e^4\,m^4+2160\,a^3\,b^3\,d^3\,e^4\,m^3+12840\,a^3\,b^3\,d^3\,e^4\,m^2+25200\,a^3\,b^3\,d^3\,e^4\,m-360\,a^2\,b^4\,d^4\,e^3\,m^3-4680\,a^2\,b^4\,d^4\,e^3\,m^2-15120\,a^2\,b^4\,d^4\,e^3\,m+720\,a\,b^5\,d^5\,e^2\,m^2+5040\,a\,b^5\,d^5\,e^2\,m-720\,b^6\,d^6\,e\,m\right)}{e^7\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{b^6\,x^7\,{\left(d+e\,x\right)}^m\,\left(m^6+21\,m^5+175\,m^4+735\,m^3+1624\,m^2+1764\,m+720\right)}{m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040}+\frac{3\,b\,x^2\,\left(m+1\right)\,{\left(d+e\,x\right)}^m\,\left(2\,a^5\,e^5\,m^5+50\,a^5\,e^5\,m^4+490\,a^5\,e^5\,m^3+2350\,a^5\,e^5\,m^2+5508\,a^5\,e^5\,m+5040\,a^5\,e^5+5\,a^4\,b\,d\,e^4\,m^5+110\,a^4\,b\,d\,e^4\,m^4+895\,a^4\,b\,d\,e^4\,m^3+3190\,a^4\,b\,d\,e^4\,m^2+4200\,a^4\,b\,d\,e^4\,m-20\,a^3\,b^2\,d^2\,e^3\,m^4-360\,a^3\,b^2\,d^2\,e^3\,m^3-2140\,a^3\,b^2\,d^2\,e^3\,m^2-4200\,a^3\,b^2\,d^2\,e^3\,m+60\,a^2\,b^3\,d^3\,e^2\,m^3+780\,a^2\,b^3\,d^3\,e^2\,m^2+2520\,a^2\,b^3\,d^3\,e^2\,m-120\,a\,b^4\,d^4\,e\,m^2-840\,a\,b^4\,d^4\,e\,m+120\,b^5\,d^5\,m\right)}{e^5\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{3\,b^4\,x^5\,{\left(d+e\,x\right)}^m\,\left(m^4+10\,m^3+35\,m^2+50\,m+24\right)\,\left(5\,a^2\,e^2\,m^2+65\,a^2\,e^2\,m+210\,a^2\,e^2+2\,a\,b\,d\,e\,m^2+14\,a\,b\,d\,e\,m-2\,b^2\,d^2\,m\right)}{e^2\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{5\,b^3\,x^4\,{\left(d+e\,x\right)}^m\,\left(m^3+6\,m^2+11\,m+6\right)\,\left(4\,a^3\,e^3\,m^3+72\,a^3\,e^3\,m^2+428\,a^3\,e^3\,m+840\,a^3\,e^3+3\,a^2\,b\,d\,e^2\,m^3+39\,a^2\,b\,d\,e^2\,m^2+126\,a^2\,b\,d\,e^2\,m-6\,a\,b^2\,d^2\,e\,m^2-42\,a\,b^2\,d^2\,e\,m+6\,b^3\,d^3\,m\right)}{e^3\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{b^5\,x^6\,{\left(d+e\,x\right)}^m\,\left(42\,a\,e+6\,a\,e\,m+b\,d\,m\right)\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}{e\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{5\,b^2\,x^3\,{\left(d+e\,x\right)}^m\,\left(m^2+3\,m+2\right)\,\left(3\,a^4\,e^4\,m^4+66\,a^4\,e^4\,m^3+537\,a^4\,e^4\,m^2+1914\,a^4\,e^4\,m+2520\,a^4\,e^4+4\,a^3\,b\,d\,e^3\,m^4+72\,a^3\,b\,d\,e^3\,m^3+428\,a^3\,b\,d\,e^3\,m^2+840\,a^3\,b\,d\,e^3\,m-12\,a^2\,b^2\,d^2\,e^2\,m^3-156\,a^2\,b^2\,d^2\,e^2\,m^2-504\,a^2\,b^2\,d^2\,e^2\,m+24\,a\,b^3\,d^3\,e\,m^2+168\,a\,b^3\,d^3\,e\,m-24\,b^4\,d^4\,m\right)}{e^4\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}","Not used",1,"((d + e*x)^m*(720*b^6*d^7 + 5040*a^6*d*e^6 - 15120*a^5*b*d^2*e^5 + 5104*a^6*d*e^6*m^2 + 1665*a^6*d*e^6*m^3 + 295*a^6*d*e^6*m^4 + 27*a^6*d*e^6*m^5 + a^6*d*e^6*m^6 + 15120*a^2*b^4*d^5*e^2 - 25200*a^3*b^3*d^4*e^3 + 25200*a^4*b^2*d^3*e^4 - 5040*a*b^5*d^6*e + 8028*a^6*d*e^6*m - 720*a*b^5*d^6*e*m + 360*a^2*b^4*d^5*e^2*m^2 - 2160*a^3*b^3*d^4*e^3*m^2 + 5370*a^4*b^2*d^3*e^4*m^2 - 120*a^3*b^3*d^4*e^3*m^3 + 660*a^4*b^2*d^3*e^4*m^3 + 30*a^4*b^2*d^3*e^4*m^4 - 16524*a^5*b*d^2*e^5*m + 4680*a^2*b^4*d^5*e^2*m - 12840*a^3*b^3*d^4*e^3*m + 19140*a^4*b^2*d^3*e^4*m - 7050*a^5*b*d^2*e^5*m^2 - 1470*a^5*b*d^2*e^5*m^3 - 150*a^5*b*d^2*e^5*m^4 - 6*a^5*b*d^2*e^5*m^5))/(e^7*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (x*(d + e*x)^m*(5040*a^6*e^7 + 8028*a^6*e^7*m + 5104*a^6*e^7*m^2 + 1665*a^6*e^7*m^3 + 295*a^6*e^7*m^4 + 27*a^6*e^7*m^5 + a^6*e^7*m^6 - 720*b^6*d^6*e*m + 15120*a^5*b*d*e^6*m - 4680*a^2*b^4*d^4*e^3*m^2 + 12840*a^3*b^3*d^3*e^4*m^2 - 19140*a^4*b^2*d^2*e^5*m^2 - 360*a^2*b^4*d^4*e^3*m^3 + 2160*a^3*b^3*d^3*e^4*m^3 - 5370*a^4*b^2*d^2*e^5*m^3 + 120*a^3*b^3*d^3*e^4*m^4 - 660*a^4*b^2*d^2*e^5*m^4 - 30*a^4*b^2*d^2*e^5*m^5 + 5040*a*b^5*d^5*e^2*m + 16524*a^5*b*d*e^6*m^2 + 7050*a^5*b*d*e^6*m^3 + 1470*a^5*b*d*e^6*m^4 + 150*a^5*b*d*e^6*m^5 + 6*a^5*b*d*e^6*m^6 - 15120*a^2*b^4*d^4*e^3*m + 25200*a^3*b^3*d^3*e^4*m - 25200*a^4*b^2*d^2*e^5*m + 720*a*b^5*d^5*e^2*m^2))/(e^7*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (b^6*x^7*(d + e*x)^m*(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720))/(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040) + (3*b*x^2*(m + 1)*(d + e*x)^m*(5040*a^5*e^5 + 5508*a^5*e^5*m + 120*b^5*d^5*m + 2350*a^5*e^5*m^2 + 490*a^5*e^5*m^3 + 50*a^5*e^5*m^4 + 2*a^5*e^5*m^5 - 840*a*b^4*d^4*e*m + 4200*a^4*b*d*e^4*m + 780*a^2*b^3*d^3*e^2*m^2 - 2140*a^3*b^2*d^2*e^3*m^2 + 60*a^2*b^3*d^3*e^2*m^3 - 360*a^3*b^2*d^2*e^3*m^3 - 20*a^3*b^2*d^2*e^3*m^4 - 120*a*b^4*d^4*e*m^2 + 3190*a^4*b*d*e^4*m^2 + 895*a^4*b*d*e^4*m^3 + 110*a^4*b*d*e^4*m^4 + 5*a^4*b*d*e^4*m^5 + 2520*a^2*b^3*d^3*e^2*m - 4200*a^3*b^2*d^2*e^3*m))/(e^5*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (3*b^4*x^5*(d + e*x)^m*(50*m + 35*m^2 + 10*m^3 + m^4 + 24)*(210*a^2*e^2 + 65*a^2*e^2*m - 2*b^2*d^2*m + 5*a^2*e^2*m^2 + 14*a*b*d*e*m + 2*a*b*d*e*m^2))/(e^2*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (5*b^3*x^4*(d + e*x)^m*(11*m + 6*m^2 + m^3 + 6)*(840*a^3*e^3 + 428*a^3*e^3*m + 6*b^3*d^3*m + 72*a^3*e^3*m^2 + 4*a^3*e^3*m^3 - 42*a*b^2*d^2*e*m + 126*a^2*b*d*e^2*m - 6*a*b^2*d^2*e*m^2 + 39*a^2*b*d*e^2*m^2 + 3*a^2*b*d*e^2*m^3))/(e^3*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (b^5*x^6*(d + e*x)^m*(42*a*e + 6*a*e*m + b*d*m)*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120))/(e*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (5*b^2*x^3*(d + e*x)^m*(3*m + m^2 + 2)*(2520*a^4*e^4 + 1914*a^4*e^4*m - 24*b^4*d^4*m + 537*a^4*e^4*m^2 + 66*a^4*e^4*m^3 + 3*a^4*e^4*m^4 + 168*a*b^3*d^3*e*m + 840*a^3*b*d*e^3*m - 156*a^2*b^2*d^2*e^2*m^2 - 12*a^2*b^2*d^2*e^2*m^3 + 24*a*b^3*d^3*e*m^2 + 428*a^3*b*d*e^3*m^2 + 72*a^3*b*d*e^3*m^3 + 4*a^3*b*d*e^3*m^4 - 504*a^2*b^2*d^2*e^2*m))/(e^4*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040))","B"
1732,1,831,142,1.038738,"\text{Not used}","int((d + e*x)^m*(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","\frac{{\left(d+e\,x\right)}^m\,\left(a^4\,d\,e^4\,m^4+14\,a^4\,d\,e^4\,m^3+71\,a^4\,d\,e^4\,m^2+154\,a^4\,d\,e^4\,m+120\,a^4\,d\,e^4-4\,a^3\,b\,d^2\,e^3\,m^3-48\,a^3\,b\,d^2\,e^3\,m^2-188\,a^3\,b\,d^2\,e^3\,m-240\,a^3\,b\,d^2\,e^3+12\,a^2\,b^2\,d^3\,e^2\,m^2+108\,a^2\,b^2\,d^3\,e^2\,m+240\,a^2\,b^2\,d^3\,e^2-24\,a\,b^3\,d^4\,e\,m-120\,a\,b^3\,d^4\,e+24\,b^4\,d^5\right)}{e^5\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}+\frac{x\,{\left(d+e\,x\right)}^m\,\left(a^4\,e^5\,m^4+14\,a^4\,e^5\,m^3+71\,a^4\,e^5\,m^2+154\,a^4\,e^5\,m+120\,a^4\,e^5+4\,a^3\,b\,d\,e^4\,m^4+48\,a^3\,b\,d\,e^4\,m^3+188\,a^3\,b\,d\,e^4\,m^2+240\,a^3\,b\,d\,e^4\,m-12\,a^2\,b^2\,d^2\,e^3\,m^3-108\,a^2\,b^2\,d^2\,e^3\,m^2-240\,a^2\,b^2\,d^2\,e^3\,m+24\,a\,b^3\,d^3\,e^2\,m^2+120\,a\,b^3\,d^3\,e^2\,m-24\,b^4\,d^4\,e\,m\right)}{e^5\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}+\frac{b^4\,x^5\,{\left(d+e\,x\right)}^m\,\left(m^4+10\,m^3+35\,m^2+50\,m+24\right)}{m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120}+\frac{2\,b^2\,x^3\,{\left(d+e\,x\right)}^m\,\left(m^2+3\,m+2\right)\,\left(3\,a^2\,e^2\,m^2+27\,a^2\,e^2\,m+60\,a^2\,e^2+2\,a\,b\,d\,e\,m^2+10\,a\,b\,d\,e\,m-2\,b^2\,d^2\,m\right)}{e^2\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}+\frac{b^3\,x^4\,{\left(d+e\,x\right)}^m\,\left(20\,a\,e+4\,a\,e\,m+b\,d\,m\right)\,\left(m^3+6\,m^2+11\,m+6\right)}{e\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}+\frac{2\,b\,x^2\,\left(m+1\right)\,{\left(d+e\,x\right)}^m\,\left(2\,a^3\,e^3\,m^3+24\,a^3\,e^3\,m^2+94\,a^3\,e^3\,m+120\,a^3\,e^3+3\,a^2\,b\,d\,e^2\,m^3+27\,a^2\,b\,d\,e^2\,m^2+60\,a^2\,b\,d\,e^2\,m-6\,a\,b^2\,d^2\,e\,m^2-30\,a\,b^2\,d^2\,e\,m+6\,b^3\,d^3\,m\right)}{e^3\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}","Not used",1,"((d + e*x)^m*(24*b^4*d^5 + 120*a^4*d*e^4 - 240*a^3*b*d^2*e^3 + 71*a^4*d*e^4*m^2 + 14*a^4*d*e^4*m^3 + a^4*d*e^4*m^4 + 240*a^2*b^2*d^3*e^2 - 120*a*b^3*d^4*e + 154*a^4*d*e^4*m - 24*a*b^3*d^4*e*m + 12*a^2*b^2*d^3*e^2*m^2 - 188*a^3*b*d^2*e^3*m + 108*a^2*b^2*d^3*e^2*m - 48*a^3*b*d^2*e^3*m^2 - 4*a^3*b*d^2*e^3*m^3))/(e^5*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)) + (x*(d + e*x)^m*(120*a^4*e^5 + 154*a^4*e^5*m + 71*a^4*e^5*m^2 + 14*a^4*e^5*m^3 + a^4*e^5*m^4 - 24*b^4*d^4*e*m + 240*a^3*b*d*e^4*m - 108*a^2*b^2*d^2*e^3*m^2 - 12*a^2*b^2*d^2*e^3*m^3 + 120*a*b^3*d^3*e^2*m + 188*a^3*b*d*e^4*m^2 + 48*a^3*b*d*e^4*m^3 + 4*a^3*b*d*e^4*m^4 - 240*a^2*b^2*d^2*e^3*m + 24*a*b^3*d^3*e^2*m^2))/(e^5*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)) + (b^4*x^5*(d + e*x)^m*(50*m + 35*m^2 + 10*m^3 + m^4 + 24))/(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120) + (2*b^2*x^3*(d + e*x)^m*(3*m + m^2 + 2)*(60*a^2*e^2 + 27*a^2*e^2*m - 2*b^2*d^2*m + 3*a^2*e^2*m^2 + 10*a*b*d*e*m + 2*a*b*d*e*m^2))/(e^2*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)) + (b^3*x^4*(d + e*x)^m*(20*a*e + 4*a*e*m + b*d*m)*(11*m + 6*m^2 + m^3 + 6))/(e*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)) + (2*b*x^2*(m + 1)*(d + e*x)^m*(120*a^3*e^3 + 94*a^3*e^3*m + 6*b^3*d^3*m + 24*a^3*e^3*m^2 + 2*a^3*e^3*m^3 - 30*a*b^2*d^2*e*m + 60*a^2*b*d*e^2*m - 6*a*b^2*d^2*e*m^2 + 27*a^2*b*d*e^2*m^2 + 3*a^2*b*d*e^2*m^3))/(e^3*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120))","B"
1733,1,226,78,0.717519,"\text{Not used}","int((d + e*x)^m*(a^2 + b^2*x^2 + 2*a*b*x),x)","{\left(d+e\,x\right)}^m\,\left(\frac{b^2\,x^3\,\left(m^2+3\,m+2\right)}{m^3+6\,m^2+11\,m+6}+\frac{d\,\left(a^2\,e^2\,m^2+5\,a^2\,e^2\,m+6\,a^2\,e^2-2\,a\,b\,d\,e\,m-6\,a\,b\,d\,e+2\,b^2\,d^2\right)}{e^3\,\left(m^3+6\,m^2+11\,m+6\right)}+\frac{x\,\left(a^2\,e^3\,m^2+5\,a^2\,e^3\,m+6\,a^2\,e^3+2\,a\,b\,d\,e^2\,m^2+6\,a\,b\,d\,e^2\,m-2\,b^2\,d^2\,e\,m\right)}{e^3\,\left(m^3+6\,m^2+11\,m+6\right)}+\frac{b\,x^2\,\left(m+1\right)\,\left(6\,a\,e+2\,a\,e\,m+b\,d\,m\right)}{e\,\left(m^3+6\,m^2+11\,m+6\right)}\right)","Not used",1,"(d + e*x)^m*((b^2*x^3*(3*m + m^2 + 2))/(11*m + 6*m^2 + m^3 + 6) + (d*(6*a^2*e^2 + 2*b^2*d^2 + 5*a^2*e^2*m + a^2*e^2*m^2 - 6*a*b*d*e - 2*a*b*d*e*m))/(e^3*(11*m + 6*m^2 + m^3 + 6)) + (x*(6*a^2*e^3 + 5*a^2*e^3*m + a^2*e^3*m^2 - 2*b^2*d^2*e*m + 2*a*b*d*e^2*m^2 + 6*a*b*d*e^2*m))/(e^3*(11*m + 6*m^2 + m^3 + 6)) + (b*x^2*(m + 1)*(6*a*e + 2*a*e*m + b*d*m))/(e*(11*m + 6*m^2 + m^3 + 6)))","B"
1734,0,-1,51,0.000000,"\text{Not used}","int((d + e*x)^m/(a^2 + b^2*x^2 + 2*a*b*x),x)","\int \frac{{\left(d+e\,x\right)}^m}{a^2+2\,a\,b\,x+b^2\,x^2} \,d x","Not used",1,"int((d + e*x)^m/(a^2 + b^2*x^2 + 2*a*b*x), x)","F"
1735,0,-1,53,0.000000,"\text{Not used}","int((d + e*x)^m/(a^2 + b^2*x^2 + 2*a*b*x)^2,x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^2} \,d x","Not used",1,"int((d + e*x)^m/(a^2 + b^2*x^2 + 2*a*b*x)^2, x)","F"
1736,0,-1,53,0.000000,"\text{Not used}","int((d + e*x)^m/(a^2 + b^2*x^2 + 2*a*b*x)^3,x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^3} \,d x","Not used",1,"int((d + e*x)^m/(a^2 + b^2*x^2 + 2*a*b*x)^3, x)","F"
1737,0,-1,337,0.000000,"\text{Not used}","int((d + e*x)^m*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int {\left(d+e\,x\right)}^m\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)^m*(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1738,0,-1,219,0.000000,"\text{Not used}","int((d + e*x)^m*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int {\left(d+e\,x\right)}^m\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^m*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1739,0,-1,101,0.000000,"\text{Not used}","int((d + e*x)^m*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2),x)","\int {\left(d+e\,x\right)}^m\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2} \,d x","Not used",1,"int((d + e*x)^m*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2), x)","F"
1740,0,-1,76,0.000000,"\text{Not used}","int((d + e*x)^m/(a^2 + b^2*x^2 + 2*a*b*x)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^m}{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}} \,d x","Not used",1,"int((d + e*x)^m/(a^2 + b^2*x^2 + 2*a*b*x)^(1/2), x)","F"
1741,0,-1,79,0.000000,"\text{Not used}","int((d + e*x)^m/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^m/(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)","F"
1742,0,-1,79,0.000000,"\text{Not used}","int((d + e*x)^m/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^m/(a^2 + b^2*x^2 + 2*a*b*x)^(5/2), x)","F"
1743,0,-1,85,0.000000,"\text{Not used}","int((d + e*x)^m*(a^2 + b^2*x^2 + 2*a*b*x)^p,x)","\int {\left(d+e\,x\right)}^m\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^p \,d x","Not used",1,"int((d + e*x)^m*(a^2 + b^2*x^2 + 2*a*b*x)^p, x)","F"
1744,1,484,181,0.904250,"\text{Not used}","int((d + e*x)^3*(a^2 + b^2*x^2 + 2*a*b*x)^p,x)","{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^p\,\left(\frac{a\,\left(-3\,a^3\,e^3+6\,a^2\,b\,d\,e^2\,p+12\,a^2\,b\,d\,e^2-6\,a\,b^2\,d^2\,e\,p^2-21\,a\,b^2\,d^2\,e\,p-18\,a\,b^2\,d^2\,e+4\,b^3\,d^3\,p^3+18\,b^3\,d^3\,p^2+26\,b^3\,d^3\,p+12\,b^3\,d^3\right)}{2\,b^4\,\left(4\,p^4+20\,p^3+35\,p^2+25\,p+6\right)}+\frac{e^3\,x^4\,\left(4\,p^3+12\,p^2+11\,p+3\right)}{2\,\left(4\,p^4+20\,p^3+35\,p^2+25\,p+6\right)}+\frac{x\,\left(6\,a^3\,b\,e^3\,p-12\,a^2\,b^2\,d\,e^2\,p^2-24\,a^2\,b^2\,d\,e^2\,p+12\,a\,b^3\,d^2\,e\,p^3+42\,a\,b^3\,d^2\,e\,p^2+36\,a\,b^3\,d^2\,e\,p+4\,b^4\,d^3\,p^3+18\,b^4\,d^3\,p^2+26\,b^4\,d^3\,p+12\,b^4\,d^3\right)}{2\,b^4\,\left(4\,p^4+20\,p^3+35\,p^2+25\,p+6\right)}+\frac{3\,e\,x^2\,\left(2\,p+1\right)\,\left(-a^2\,e^2\,p+2\,a\,b\,d\,e\,p^2+4\,a\,b\,d\,e\,p+2\,b^2\,d^2\,p^2+7\,b^2\,d^2\,p+6\,b^2\,d^2\right)}{2\,b^2\,\left(4\,p^4+20\,p^3+35\,p^2+25\,p+6\right)}+\frac{e^2\,x^3\,\left(2\,p^2+3\,p+1\right)\,\left(6\,b\,d+a\,e\,p+3\,b\,d\,p\right)}{b\,\left(4\,p^4+20\,p^3+35\,p^2+25\,p+6\right)}\right)","Not used",1,"(a^2 + b^2*x^2 + 2*a*b*x)^p*((a*(12*b^3*d^3 - 3*a^3*e^3 + 26*b^3*d^3*p + 18*b^3*d^3*p^2 + 4*b^3*d^3*p^3 - 18*a*b^2*d^2*e + 12*a^2*b*d*e^2 - 21*a*b^2*d^2*e*p + 6*a^2*b*d*e^2*p - 6*a*b^2*d^2*e*p^2))/(2*b^4*(25*p + 35*p^2 + 20*p^3 + 4*p^4 + 6)) + (e^3*x^4*(11*p + 12*p^2 + 4*p^3 + 3))/(2*(25*p + 35*p^2 + 20*p^3 + 4*p^4 + 6)) + (x*(12*b^4*d^3 + 26*b^4*d^3*p + 18*b^4*d^3*p^2 + 4*b^4*d^3*p^3 + 6*a^3*b*e^3*p + 36*a*b^3*d^2*e*p - 24*a^2*b^2*d*e^2*p + 42*a*b^3*d^2*e*p^2 + 12*a*b^3*d^2*e*p^3 - 12*a^2*b^2*d*e^2*p^2))/(2*b^4*(25*p + 35*p^2 + 20*p^3 + 4*p^4 + 6)) + (3*e*x^2*(2*p + 1)*(6*b^2*d^2 - a^2*e^2*p + 7*b^2*d^2*p + 2*b^2*d^2*p^2 + 4*a*b*d*e*p + 2*a*b*d*e*p^2))/(2*b^2*(25*p + 35*p^2 + 20*p^3 + 4*p^4 + 6)) + (e^2*x^3*(3*p + 2*p^2 + 1)*(6*b*d + a*e*p + 3*b*d*p))/(b*(25*p + 35*p^2 + 20*p^3 + 4*p^4 + 6)))","B"
1745,1,250,127,0.710340,"\text{Not used}","int((d + e*x)^2*(a^2 + b^2*x^2 + 2*a*b*x)^p,x)","{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^p\,\left(\frac{e^2\,x^3\,\left(2\,p^2+3\,p+1\right)}{4\,p^3+12\,p^2+11\,p+3}+\frac{x\,\left(-2\,a^2\,b\,e^2\,p+4\,a\,b^2\,d\,e\,p^2+6\,a\,b^2\,d\,e\,p+2\,b^3\,d^2\,p^2+5\,b^3\,d^2\,p+3\,b^3\,d^2\right)}{b^3\,\left(4\,p^3+12\,p^2+11\,p+3\right)}+\frac{a\,\left(a^2\,e^2-2\,a\,b\,d\,e\,p-3\,a\,b\,d\,e+2\,b^2\,d^2\,p^2+5\,b^2\,d^2\,p+3\,b^2\,d^2\right)}{b^3\,\left(4\,p^3+12\,p^2+11\,p+3\right)}+\frac{e\,x^2\,\left(2\,p+1\right)\,\left(3\,b\,d+a\,e\,p+2\,b\,d\,p\right)}{b\,\left(4\,p^3+12\,p^2+11\,p+3\right)}\right)","Not used",1,"(a^2 + b^2*x^2 + 2*a*b*x)^p*((e^2*x^3*(3*p + 2*p^2 + 1))/(11*p + 12*p^2 + 4*p^3 + 3) + (x*(3*b^3*d^2 + 5*b^3*d^2*p + 2*b^3*d^2*p^2 - 2*a^2*b*e^2*p + 4*a*b^2*d*e*p^2 + 6*a*b^2*d*e*p))/(b^3*(11*p + 12*p^2 + 4*p^3 + 3)) + (a*(a^2*e^2 + 3*b^2*d^2 + 5*b^2*d^2*p + 2*b^2*d^2*p^2 - 3*a*b*d*e - 2*a*b*d*e*p))/(b^3*(11*p + 12*p^2 + 4*p^3 + 3)) + (e*x^2*(2*p + 1)*(3*b*d + a*e*p + 2*b*d*p))/(b*(11*p + 12*p^2 + 4*p^3 + 3)))","B"
1746,1,112,76,0.624598,"\text{Not used}","int((d + e*x)*(a^2 + b^2*x^2 + 2*a*b*x)^p,x)","\left(\frac{x\,\left(2\,b^2\,d+2\,b^2\,d\,p+2\,a\,b\,e\,p\right)}{2\,b^2\,\left(2\,p^2+3\,p+1\right)}+\frac{a\,\left(2\,b\,d-a\,e+2\,b\,d\,p\right)}{2\,b^2\,\left(2\,p^2+3\,p+1\right)}+\frac{e\,x^2\,\left(2\,p+1\right)}{2\,\left(2\,p^2+3\,p+1\right)}\right)\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^p","Not used",1,"((x*(2*b^2*d + 2*b^2*d*p + 2*a*b*e*p))/(2*b^2*(3*p + 2*p^2 + 1)) + (a*(2*b*d - a*e + 2*b*d*p))/(2*b^2*(3*p + 2*p^2 + 1)) + (e*x^2*(2*p + 1))/(2*(3*p + 2*p^2 + 1)))*(a^2 + b^2*x^2 + 2*a*b*x)^p","B"
1747,1,41,34,0.656236,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^p,x)","\left(\frac{x}{2\,p+1}+\frac{a}{b\,\left(2\,p+1\right)}\right)\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^p","Not used",1,"(x/(2*p + 1) + a/(b*(2*p + 1)))*(a^2 + b^2*x^2 + 2*a*b*x)^p","B"
1748,0,-1,71,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^p/(d + e*x),x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^p}{d+e\,x} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^p/(d + e*x), x)","F"
1749,0,-1,72,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^p/(d + e*x)^2,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^p}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^p/(d + e*x)^2, x)","F"
1750,0,-1,74,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^p/(d + e*x)^3,x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^p}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^p/(d + e*x)^3, x)","F"
1751,0,-1,83,0.000000,"\text{Not used}","int((d + e*x)^(3/2)*(a^2 + b^2*x^2 + 2*a*b*x)^p,x)","\int {\left(d+e\,x\right)}^{3/2}\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^p \,d x","Not used",1,"int((d + e*x)^(3/2)*(a^2 + b^2*x^2 + 2*a*b*x)^p, x)","F"
1752,0,-1,83,0.000000,"\text{Not used}","int((d + e*x)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^p,x)","\int \sqrt{d+e\,x}\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^p \,d x","Not used",1,"int((d + e*x)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^p, x)","F"
1753,0,-1,81,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^p/(d + e*x)^(1/2),x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^p}{\sqrt{d+e\,x}} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^p/(d + e*x)^(1/2), x)","F"
1754,0,-1,81,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^p/(d + e*x)^(3/2),x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^p}{{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^p/(d + e*x)^(3/2), x)","F"
1755,0,-1,83,0.000000,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^p/(d + e*x)^(5/2),x)","\int \frac{{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^p}{{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int((a^2 + b^2*x^2 + 2*a*b*x)^p/(d + e*x)^(5/2), x)","F"
1756,0,-1,97,0.000000,"\text{Not used}","int((d + e*x)^m*(a^2 + b^2*x^2 + 2*a*b*x)^(p + 5),x)","\int {\left(d+e\,x\right)}^m\,{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^{p+5} \,d x","Not used",1,"int((d + e*x)^m*(a^2 + b^2*x^2 + 2*a*b*x)^(p + 5), x)","F"
1757,1,259,115,0.833295,"\text{Not used}","int((a^2 + b^2*x^2 + 2*a*b*x)^p/(d + e*x)^(2*p + 3),x)","{\left(a^2+2\,a\,b\,x+b^2\,x^2\right)}^p\,\left(\frac{x\,\left(2\,b^2\,d^2-a^2\,e^2-2\,a^2\,e^2\,p+2\,b^2\,d^2\,p+2\,a\,b\,d\,e\right)}{2\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{2\,p+3}\,\left(2\,p^2+3\,p+1\right)}+\frac{b^2\,e^2\,x^3}{2\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{2\,p+3}\,\left(2\,p^2+3\,p+1\right)}-\frac{a\,d\,\left(a\,e-2\,b\,d+2\,a\,e\,p-2\,b\,d\,p\right)}{2\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{2\,p+3}\,\left(2\,p^2+3\,p+1\right)}+\frac{b\,e\,x^2\,\left(3\,b\,d-2\,a\,e\,p+2\,b\,d\,p\right)}{2\,{\left(a\,e-b\,d\right)}^2\,{\left(d+e\,x\right)}^{2\,p+3}\,\left(2\,p^2+3\,p+1\right)}\right)","Not used",1,"(a^2 + b^2*x^2 + 2*a*b*x)^p*((x*(2*b^2*d^2 - a^2*e^2 - 2*a^2*e^2*p + 2*b^2*d^2*p + 2*a*b*d*e))/(2*(a*e - b*d)^2*(d + e*x)^(2*p + 3)*(3*p + 2*p^2 + 1)) + (b^2*e^2*x^3)/(2*(a*e - b*d)^2*(d + e*x)^(2*p + 3)*(3*p + 2*p^2 + 1)) - (a*d*(a*e - 2*b*d + 2*a*e*p - 2*b*d*p))/(2*(a*e - b*d)^2*(d + e*x)^(2*p + 3)*(3*p + 2*p^2 + 1)) + (b*e*x^2*(3*b*d - 2*a*e*p + 2*b*d*p))/(2*(a*e - b*d)^2*(d + e*x)^(2*p + 3)*(3*p + 2*p^2 + 1)))","B"
1758,1,87,60,0.109914,"\text{Not used}","int((d + e*x)*(12*x + 4*x^2 + 9)^p,x)","\left(\frac{12\,d-9\,e+12\,d\,p}{16\,p^2+24\,p+8}+\frac{x\,\left(8\,d+8\,d\,p+12\,e\,p\right)}{16\,p^2+24\,p+8}+\frac{4\,e\,x^2\,\left(2\,p+1\right)}{16\,p^2+24\,p+8}\right)\,{\left(4\,x^2+12\,x+9\right)}^p","Not used",1,"((12*d - 9*e + 12*d*p)/(24*p + 16*p^2 + 8) + (x*(8*d + 8*d*p + 12*e*p))/(24*p + 16*p^2 + 8) + (4*e*x^2*(2*p + 1))/(24*p + 16*p^2 + 8))*(12*x + 4*x^2 + 9)^p","B"
1759,1,88,38,0.053859,"\text{Not used}","int((a + b*x)^3*(a*c + x*(a*d + b*c) + b*d*x^2),x)","x^5\,\left(\frac{c\,b^4}{5}+\frac{4\,a\,d\,b^3}{5}\right)+x^2\,\left(\frac{d\,a^4}{2}+2\,b\,c\,a^3\right)+\frac{b^4\,d\,x^6}{6}+a^4\,c\,x+\frac{2\,a^2\,b\,x^3\,\left(2\,a\,d+3\,b\,c\right)}{3}+\frac{a\,b^2\,x^4\,\left(3\,a\,d+2\,b\,c\right)}{2}","Not used",1,"x^5*((b^4*c)/5 + (4*a*b^3*d)/5) + x^2*((a^4*d)/2 + 2*a^3*b*c) + (b^4*d*x^6)/6 + a^4*c*x + (2*a^2*b*x^3*(2*a*d + 3*b*c))/3 + (a*b^2*x^4*(3*a*d + 2*b*c))/2","B"
1760,1,65,38,0.551255,"\text{Not used}","int((a + b*x)^2*(a*c + x*(a*d + b*c) + b*d*x^2),x)","x^4\,\left(\frac{c\,b^3}{4}+\frac{3\,a\,d\,b^2}{4}\right)+x^2\,\left(\frac{d\,a^3}{2}+\frac{3\,b\,c\,a^2}{2}\right)+\frac{b^3\,d\,x^5}{5}+a^3\,c\,x+a\,b\,x^3\,\left(a\,d+b\,c\right)","Not used",1,"x^4*((b^3*c)/4 + (3*a*b^2*d)/4) + x^2*((a^3*d)/2 + (3*a^2*b*c)/2) + (b^3*d*x^5)/5 + a^3*c*x + a*b*x^3*(a*d + b*c)","B"
1761,1,47,38,0.049407,"\text{Not used}","int((a + b*x)*(a*c + x*(a*d + b*c) + b*d*x^2),x)","x^2\,\left(\frac{d\,a^2}{2}+b\,c\,a\right)+x^3\,\left(\frac{c\,b^2}{3}+\frac{2\,a\,d\,b}{3}\right)+\frac{b^2\,d\,x^4}{4}+a^2\,c\,x","Not used",1,"x^2*((a^2*d)/2 + a*b*c) + x^3*((b^2*c)/3 + (2*a*b*d)/3) + (b^2*d*x^4)/4 + a^2*c*x","B"
1762,1,25,28,0.036142,"\text{Not used}","int(a*c + x*(a*d + b*c) + b*d*x^2,x)","\frac{b\,d\,x^3}{3}+\left(\frac{a\,d}{2}+\frac{b\,c}{2}\right)\,x^2+a\,c\,x","Not used",1,"x^2*((a*d)/2 + (b*c)/2) + a*c*x + (b*d*x^3)/3","B"
1763,1,10,12,0.018008,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)/(a + b*x),x)","\frac{d\,x^2}{2}+c\,x","Not used",1,"c*x + (d*x^2)/2","B"
1764,1,26,25,0.052520,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)/(a + b*x)^2,x)","\frac{d\,x}{b}-\frac{\ln\left(a+b\,x\right)\,\left(a\,d-b\,c\right)}{b^2}","Not used",1,"(d*x)/b - (log(a + b*x)*(a*d - b*c))/b^2","B"
1765,1,31,32,0.563293,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)/(a + b*x)^3,x)","\frac{a\,d-b\,c}{b^2\,\left(a+b\,x\right)}+\frac{d\,\ln\left(a+b\,x\right)}{b^2}","Not used",1,"(a*d - b*c)/(b^2*(a + b*x)) + (d*log(a + b*x))/b^2","B"
1766,1,39,28,0.549081,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)/(a + b*x)^4,x)","-\frac{\frac{a\,d+b\,c}{2\,b^2}+\frac{d\,x}{b}}{a^2+2\,a\,b\,x+b^2\,x^2}","Not used",1,"-((a*d + b*c)/(2*b^2) + (d*x)/b)/(a^2 + b^2*x^2 + 2*a*b*x)","B"
1767,1,52,38,0.554473,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)/(a + b*x)^5,x)","-\frac{\frac{a\,d+2\,b\,c}{6\,b^2}+\frac{d\,x}{2\,b}}{a^3+3\,a^2\,b\,x+3\,a\,b^2\,x^2+b^3\,x^3}","Not used",1,"-((a*d + 2*b*c)/(6*b^2) + (d*x)/(2*b))/(a^3 + b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x)","B"
1768,1,63,38,0.046516,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)/(a + b*x)^6,x)","-\frac{\frac{a\,d+3\,b\,c}{12\,b^2}+\frac{d\,x}{3\,b}}{a^4+4\,a^3\,b\,x+6\,a^2\,b^2\,x^2+4\,a\,b^3\,x^3+b^4\,x^4}","Not used",1,"-((a*d + 3*b*c)/(12*b^2) + (d*x)/(3*b))/(a^4 + b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x)","B"
1769,1,181,65,0.091385,"\text{Not used}","int((a + b*x)^3*(a*c + x*(a*d + b*c) + b*d*x^2)^2,x)","x^3\,\left(\frac{a^5\,d^2}{3}+\frac{10\,a^4\,b\,c\,d}{3}+\frac{10\,a^3\,b^2\,c^2}{3}\right)+x^6\,\left(\frac{5\,a^2\,b^3\,d^2}{3}+\frac{5\,a\,b^4\,c\,d}{3}+\frac{b^5\,c^2}{6}\right)+a^5\,c^2\,x+\frac{b^5\,d^2\,x^8}{8}+\frac{a^4\,c\,x^2\,\left(2\,a\,d+5\,b\,c\right)}{2}+\frac{b^4\,d\,x^7\,\left(5\,a\,d+2\,b\,c\right)}{7}+\frac{5\,a^2\,b\,x^4\,\left(a^2\,d^2+4\,a\,b\,c\,d+2\,b^2\,c^2\right)}{4}+a\,b^2\,x^5\,\left(2\,a^2\,d^2+4\,a\,b\,c\,d+b^2\,c^2\right)","Not used",1,"x^3*((a^5*d^2)/3 + (10*a^3*b^2*c^2)/3 + (10*a^4*b*c*d)/3) + x^6*((b^5*c^2)/6 + (5*a^2*b^3*d^2)/3 + (5*a*b^4*c*d)/3) + a^5*c^2*x + (b^5*d^2*x^8)/8 + (a^4*c*x^2*(2*a*d + 5*b*c))/2 + (b^4*d*x^7*(5*a*d + 2*b*c))/7 + (5*a^2*b*x^4*(a^2*d^2 + 2*b^2*c^2 + 4*a*b*c*d))/4 + a*b^2*x^5*(2*a^2*d^2 + b^2*c^2 + 4*a*b*c*d)","B"
1770,1,144,65,0.064235,"\text{Not used}","int((a + b*x)^2*(a*c + x*(a*d + b*c) + b*d*x^2)^2,x)","x^3\,\left(\frac{a^4\,d^2}{3}+\frac{8\,a^3\,b\,c\,d}{3}+2\,a^2\,b^2\,c^2\right)+x^5\,\left(\frac{6\,a^2\,b^2\,d^2}{5}+\frac{8\,a\,b^3\,c\,d}{5}+\frac{b^4\,c^2}{5}\right)+a^4\,c^2\,x+\frac{b^4\,d^2\,x^7}{7}+a^3\,c\,x^2\,\left(a\,d+2\,b\,c\right)+\frac{b^3\,d\,x^6\,\left(2\,a\,d+b\,c\right)}{3}+a\,b\,x^4\,\left(a^2\,d^2+3\,a\,b\,c\,d+b^2\,c^2\right)","Not used",1,"x^3*((a^4*d^2)/3 + 2*a^2*b^2*c^2 + (8*a^3*b*c*d)/3) + x^5*((b^4*c^2)/5 + (6*a^2*b^2*d^2)/5 + (8*a*b^3*c*d)/5) + a^4*c^2*x + (b^4*d^2*x^7)/7 + a^3*c*x^2*(a*d + 2*b*c) + (b^3*d*x^6*(2*a*d + b*c))/3 + a*b*x^4*(a^2*d^2 + b^2*c^2 + 3*a*b*c*d)","B"
1771,1,115,65,0.575750,"\text{Not used}","int((a + b*x)*(a*c + x*(a*d + b*c) + b*d*x^2)^2,x)","x^3\,\left(\frac{a^3\,d^2}{3}+2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)+x^4\,\left(\frac{3\,a^2\,b\,d^2}{4}+\frac{3\,a\,b^2\,c\,d}{2}+\frac{b^3\,c^2}{4}\right)+a^3\,c^2\,x+\frac{b^3\,d^2\,x^6}{6}+\frac{a^2\,c\,x^2\,\left(2\,a\,d+3\,b\,c\right)}{2}+\frac{b^2\,d\,x^5\,\left(3\,a\,d+2\,b\,c\right)}{5}","Not used",1,"x^3*((a^3*d^2)/3 + a*b^2*c^2 + 2*a^2*b*c*d) + x^4*((b^3*c^2)/4 + (3*a^2*b*d^2)/4 + (3*a*b^2*c*d)/2) + a^3*c^2*x + (b^3*d^2*x^6)/6 + (a^2*c*x^2*(2*a*d + 3*b*c))/2 + (b^2*d*x^5*(3*a*d + 2*b*c))/5","B"
1772,1,74,65,0.043038,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^2,x)","x^3\,\left(\frac{a^2\,d^2}{3}+\frac{4\,a\,b\,c\,d}{3}+\frac{b^2\,c^2}{3}\right)+a^2\,c^2\,x+\frac{b^2\,d^2\,x^5}{5}+a\,c\,x^2\,\left(a\,d+b\,c\right)+\frac{b\,d\,x^4\,\left(a\,d+b\,c\right)}{2}","Not used",1,"x^3*((a^2*d^2)/3 + (b^2*c^2)/3 + (4*a*b*c*d)/3) + a^2*c^2*x + (b^2*d^2*x^5)/5 + a*c*x^2*(a*d + b*c) + (b*d*x^4*(a*d + b*c))/2","B"
1773,1,47,38,0.049692,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^2/(a + b*x),x)","x^2\,\left(\frac{b\,c^2}{2}+a\,d\,c\right)+x^3\,\left(\frac{a\,d^2}{3}+\frac{2\,b\,c\,d}{3}\right)+\frac{b\,d^2\,x^4}{4}+a\,c^2\,x","Not used",1,"x^2*((b*c^2)/2 + a*c*d) + x^3*((a*d^2)/3 + (2*b*c*d)/3) + (b*d^2*x^4)/4 + a*c^2*x","B"
1774,1,20,14,0.031605,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^2/(a + b*x)^2,x)","c^2\,x+c\,d\,x^2+\frac{d^2\,x^3}{3}","Not used",1,"c^2*x + (d^2*x^3)/3 + c*d*x^2","B"
1775,1,62,49,0.069268,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^2/(a + b*x)^3,x)","\frac{\ln\left(a+b\,x\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{b^3}-x\,\left(\frac{a\,d^2}{b^2}-\frac{2\,c\,d}{b}\right)+\frac{d^2\,x^2}{2\,b}","Not used",1,"(log(a + b*x)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/b^3 - x*((a*d^2)/b^2 - (2*c*d)/b) + (d^2*x^2)/(2*b)","B"
1776,1,71,51,0.081063,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^2/(a + b*x)^4,x)","\frac{d^2\,x}{b^2}-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{b\,\left(x\,b^3+a\,b^2\right)}-\frac{\ln\left(a+b\,x\right)\,\left(2\,a\,d^2-2\,b\,c\,d\right)}{b^3}","Not used",1,"(d^2*x)/b^2 - (a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(b*(a*b^2 + b^3*x)) - (log(a + b*x)*(2*a*d^2 - 2*b*c*d))/b^3","B"
1777,1,77,59,0.585248,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^2/(a + b*x)^5,x)","\frac{d^2\,\ln\left(a+b\,x\right)}{b^3}-\frac{\frac{-3\,a^2\,d^2+2\,a\,b\,c\,d+b^2\,c^2}{2\,b^3}-\frac{2\,d\,x\,\left(a\,d-b\,c\right)}{b^2}}{a^2+2\,a\,b\,x+b^2\,x^2}","Not used",1,"(d^2*log(a + b*x))/b^3 - ((b^2*c^2 - 3*a^2*d^2 + 2*a*b*c*d)/(2*b^3) - (2*d*x*(a*d - b*c))/b^2)/(a^2 + b^2*x^2 + 2*a*b*x)","B"
1778,1,80,28,0.558681,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^2/(a + b*x)^6,x)","-\frac{\frac{a^2\,d^2+a\,b\,c\,d+b^2\,c^2}{3\,b^3}+\frac{d^2\,x^2}{b}+\frac{d\,x\,\left(a\,d+b\,c\right)}{b^2}}{a^3+3\,a^2\,b\,x+3\,a\,b^2\,x^2+b^3\,x^3}","Not used",1,"-((a^2*d^2 + b^2*c^2 + a*b*c*d)/(3*b^3) + (d^2*x^2)/b + (d*x*(a*d + b*c))/b^2)/(a^3 + b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x)","B"
1779,1,96,65,0.047845,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^2/(a + b*x)^7,x)","-\frac{\frac{a^2\,d^2+2\,a\,b\,c\,d+3\,b^2\,c^2}{12\,b^3}+\frac{d^2\,x^2}{2\,b}+\frac{d\,x\,\left(a\,d+2\,b\,c\right)}{3\,b^2}}{a^4+4\,a^3\,b\,x+6\,a^2\,b^2\,x^2+4\,a\,b^3\,x^3+b^4\,x^4}","Not used",1,"-((a^2*d^2 + 3*b^2*c^2 + 2*a*b*c*d)/(12*b^3) + (d^2*x^2)/(2*b) + (d*x*(a*d + 2*b*c))/(3*b^2))/(a^4 + b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x)","B"
1780,1,107,65,0.586266,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^2/(a + b*x)^8,x)","-\frac{\frac{a^2\,d^2+3\,a\,b\,c\,d+6\,b^2\,c^2}{30\,b^3}+\frac{d^2\,x^2}{3\,b}+\frac{d\,x\,\left(a\,d+3\,b\,c\right)}{6\,b^2}}{a^5+5\,a^4\,b\,x+10\,a^3\,b^2\,x^2+10\,a^2\,b^3\,x^3+5\,a\,b^4\,x^4+b^5\,x^5}","Not used",1,"-((a^2*d^2 + 6*b^2*c^2 + 3*a*b*c*d)/(30*b^3) + (d^2*x^2)/(3*b) + (d*x*(a*d + 3*b*c))/(6*b^2))/(a^5 + b^5*x^5 + 5*a*b^4*x^4 + 10*a^3*b^2*x^2 + 10*a^2*b^3*x^3 + 5*a^4*b*x)","B"
1781,1,118,65,0.629625,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^2/(a + b*x)^9,x)","-\frac{\frac{a^2\,d^2+4\,a\,b\,c\,d+10\,b^2\,c^2}{60\,b^3}+\frac{d^2\,x^2}{4\,b}+\frac{d\,x\,\left(a\,d+4\,b\,c\right)}{10\,b^2}}{a^6+6\,a^5\,b\,x+15\,a^4\,b^2\,x^2+20\,a^3\,b^3\,x^3+15\,a^2\,b^4\,x^4+6\,a\,b^5\,x^5+b^6\,x^6}","Not used",1,"-((a^2*d^2 + 10*b^2*c^2 + 4*a*b*c*d)/(60*b^3) + (d^2*x^2)/(4*b) + (d*x*(a*d + 4*b*c))/(10*b^2))/(a^6 + b^6*x^6 + 6*a*b^5*x^5 + 15*a^4*b^2*x^2 + 20*a^3*b^3*x^3 + 15*a^2*b^4*x^4 + 6*a^5*b*x)","B"
1782,1,129,65,0.104228,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^2/(a + b*x)^10,x)","-\frac{\frac{a^2\,d^2+5\,a\,b\,c\,d+15\,b^2\,c^2}{105\,b^3}+\frac{d^2\,x^2}{5\,b}+\frac{d\,x\,\left(a\,d+5\,b\,c\right)}{15\,b^2}}{a^7+7\,a^6\,b\,x+21\,a^5\,b^2\,x^2+35\,a^4\,b^3\,x^3+35\,a^3\,b^4\,x^4+21\,a^2\,b^5\,x^5+7\,a\,b^6\,x^6+b^7\,x^7}","Not used",1,"-((a^2*d^2 + 15*b^2*c^2 + 5*a*b*c*d)/(105*b^3) + (d^2*x^2)/(5*b) + (d*x*(a*d + 5*b*c))/(15*b^2))/(a^7 + b^7*x^7 + 7*a*b^6*x^6 + 21*a^5*b^2*x^2 + 35*a^4*b^3*x^3 + 35*a^3*b^4*x^4 + 21*a^2*b^5*x^5 + 7*a^6*b*x)","B"
1783,1,308,92,0.670175,"\text{Not used}","int((a + b*x)^3*(a*c + x*(a*d + b*c) + b*d*x^2)^3,x)","x^5\,\left(\frac{6\,a^5\,b\,d^3}{5}+9\,a^4\,b^2\,c\,d^2+12\,a^3\,b^3\,c^2\,d+3\,a^2\,b^4\,c^3\right)+x^6\,\left(\frac{5\,a^4\,b^2\,d^3}{2}+10\,a^3\,b^3\,c\,d^2+\frac{15\,a^2\,b^4\,c^2\,d}{2}+a\,b^5\,c^3\right)+x^4\,\left(\frac{a^6\,d^3}{4}+\frac{9\,a^5\,b\,c\,d^2}{2}+\frac{45\,a^4\,b^2\,c^2\,d}{4}+5\,a^3\,b^3\,c^3\right)+x^7\,\left(\frac{20\,a^3\,b^3\,d^3}{7}+\frac{45\,a^2\,b^4\,c\,d^2}{7}+\frac{18\,a\,b^5\,c^2\,d}{7}+\frac{b^6\,c^3}{7}\right)+a^6\,c^3\,x+\frac{b^6\,d^3\,x^{10}}{10}+\frac{3\,a^5\,c^2\,x^2\,\left(a\,d+2\,b\,c\right)}{2}+\frac{b^5\,d^2\,x^9\,\left(2\,a\,d+b\,c\right)}{3}+a^4\,c\,x^3\,\left(a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)+\frac{3\,b^4\,d\,x^8\,\left(5\,a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}{8}","Not used",1,"x^5*((6*a^5*b*d^3)/5 + 3*a^2*b^4*c^3 + 12*a^3*b^3*c^2*d + 9*a^4*b^2*c*d^2) + x^6*(a*b^5*c^3 + (5*a^4*b^2*d^3)/2 + (15*a^2*b^4*c^2*d)/2 + 10*a^3*b^3*c*d^2) + x^4*((a^6*d^3)/4 + 5*a^3*b^3*c^3 + (45*a^4*b^2*c^2*d)/4 + (9*a^5*b*c*d^2)/2) + x^7*((b^6*c^3)/7 + (20*a^3*b^3*d^3)/7 + (45*a^2*b^4*c*d^2)/7 + (18*a*b^5*c^2*d)/7) + a^6*c^3*x + (b^6*d^3*x^10)/10 + (3*a^5*c^2*x^2*(a*d + 2*b*c))/2 + (b^5*d^2*x^9*(2*a*d + b*c))/3 + a^4*c*x^3*(a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d) + (3*b^4*d*x^8*(5*a^2*d^2 + b^2*c^2 + 6*a*b*c*d))/8","B"
1784,1,261,92,0.657473,"\text{Not used}","int((a + b*x)^2*(a*c + x*(a*d + b*c) + b*d*x^2)^3,x)","x^5\,\left(a^4\,b\,d^3+6\,a^3\,b^2\,c\,d^2+6\,a^2\,b^3\,c^2\,d+a\,b^4\,c^3\right)+x^4\,\left(\frac{a^5\,d^3}{4}+\frac{15\,a^4\,b\,c\,d^2}{4}+\frac{15\,a^3\,b^2\,c^2\,d}{2}+\frac{5\,a^2\,b^3\,c^3}{2}\right)+x^6\,\left(\frac{5\,a^3\,b^2\,d^3}{3}+5\,a^2\,b^3\,c\,d^2+\frac{5\,a\,b^4\,c^2\,d}{2}+\frac{b^5\,c^3}{6}\right)+a^5\,c^3\,x+\frac{b^5\,d^3\,x^9}{9}+\frac{a^4\,c^2\,x^2\,\left(3\,a\,d+5\,b\,c\right)}{2}+\frac{b^4\,d^2\,x^8\,\left(5\,a\,d+3\,b\,c\right)}{8}+\frac{a^3\,c\,x^3\,\left(3\,a^2\,d^2+15\,a\,b\,c\,d+10\,b^2\,c^2\right)}{3}+\frac{b^3\,d\,x^7\,\left(10\,a^2\,d^2+15\,a\,b\,c\,d+3\,b^2\,c^2\right)}{7}","Not used",1,"x^5*(a*b^4*c^3 + a^4*b*d^3 + 6*a^2*b^3*c^2*d + 6*a^3*b^2*c*d^2) + x^4*((a^5*d^3)/4 + (5*a^2*b^3*c^3)/2 + (15*a^3*b^2*c^2*d)/2 + (15*a^4*b*c*d^2)/4) + x^6*((b^5*c^3)/6 + (5*a^3*b^2*d^3)/3 + 5*a^2*b^3*c*d^2 + (5*a*b^4*c^2*d)/2) + a^5*c^3*x + (b^5*d^3*x^9)/9 + (a^4*c^2*x^2*(3*a*d + 5*b*c))/2 + (b^4*d^2*x^8*(5*a*d + 3*b*c))/8 + (a^3*c*x^3*(3*a^2*d^2 + 10*b^2*c^2 + 15*a*b*c*d))/3 + (b^3*d*x^7*(10*a^2*d^2 + 3*b^2*c^2 + 15*a*b*c*d))/7","B"
1785,1,208,92,0.090387,"\text{Not used}","int((a + b*x)*(a*c + x*(a*d + b*c) + b*d*x^2)^3,x)","x^4\,\left(\frac{a^4\,d^3}{4}+3\,a^3\,b\,c\,d^2+\frac{9\,a^2\,b^2\,c^2\,d}{2}+a\,b^3\,c^3\right)+x^5\,\left(\frac{4\,a^3\,b\,d^3}{5}+\frac{18\,a^2\,b^2\,c\,d^2}{5}+\frac{12\,a\,b^3\,c^2\,d}{5}+\frac{b^4\,c^3}{5}\right)+a^4\,c^3\,x+\frac{b^4\,d^3\,x^8}{8}+\frac{a^3\,c^2\,x^2\,\left(3\,a\,d+4\,b\,c\right)}{2}+\frac{b^3\,d^2\,x^7\,\left(4\,a\,d+3\,b\,c\right)}{7}+a^2\,c\,x^3\,\left(a^2\,d^2+4\,a\,b\,c\,d+2\,b^2\,c^2\right)+\frac{b^2\,d\,x^6\,\left(2\,a^2\,d^2+4\,a\,b\,c\,d+b^2\,c^2\right)}{2}","Not used",1,"x^4*((a^4*d^3)/4 + a*b^3*c^3 + (9*a^2*b^2*c^2*d)/2 + 3*a^3*b*c*d^2) + x^5*((b^4*c^3)/5 + (4*a^3*b*d^3)/5 + (18*a^2*b^2*c*d^2)/5 + (12*a*b^3*c^2*d)/5) + a^4*c^3*x + (b^4*d^3*x^8)/8 + (a^3*c^2*x^2*(3*a*d + 4*b*c))/2 + (b^3*d^2*x^7*(4*a*d + 3*b*c))/7 + a^2*c*x^3*(a^2*d^2 + 2*b^2*c^2 + 4*a*b*c*d) + (b^2*d*x^6*(2*a^2*d^2 + b^2*c^2 + 4*a*b*c*d))/2","B"
1786,1,152,92,0.604290,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^3,x)","x^4\,\left(\frac{a^3\,d^3}{4}+\frac{9\,a^2\,b\,c\,d^2}{4}+\frac{9\,a\,b^2\,c^2\,d}{4}+\frac{b^3\,c^3}{4}\right)+a^3\,c^3\,x+\frac{b^3\,d^3\,x^7}{7}+a\,c\,x^3\,\left(a^2\,d^2+3\,a\,b\,c\,d+b^2\,c^2\right)+\frac{3\,b\,d\,x^5\,\left(a^2\,d^2+3\,a\,b\,c\,d+b^2\,c^2\right)}{5}+\frac{3\,a^2\,c^2\,x^2\,\left(a\,d+b\,c\right)}{2}+\frac{b^2\,d^2\,x^6\,\left(a\,d+b\,c\right)}{2}","Not used",1,"x^4*((a^3*d^3)/4 + (b^3*c^3)/4 + (9*a*b^2*c^2*d)/4 + (9*a^2*b*c*d^2)/4) + a^3*c^3*x + (b^3*d^3*x^7)/7 + a*c*x^3*(a^2*d^2 + b^2*c^2 + 3*a*b*c*d) + (3*b*d*x^5*(a^2*d^2 + b^2*c^2 + 3*a*b*c*d))/5 + (3*a^2*c^2*x^2*(a*d + b*c))/2 + (b^2*d^2*x^6*(a*d + b*c))/2","B"
1787,1,115,65,0.594696,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^3/(a + b*x),x)","x^3\,\left(a^2\,c\,d^2+2\,a\,b\,c^2\,d+\frac{b^2\,c^3}{3}\right)+x^4\,\left(\frac{a^2\,d^3}{4}+\frac{3\,a\,b\,c\,d^2}{2}+\frac{3\,b^2\,c^2\,d}{4}\right)+a^2\,c^3\,x+\frac{b^2\,d^3\,x^6}{6}+\frac{a\,c^2\,x^2\,\left(3\,a\,d+2\,b\,c\right)}{2}+\frac{b\,d^2\,x^5\,\left(2\,a\,d+3\,b\,c\right)}{5}","Not used",1,"x^3*((b^2*c^3)/3 + a^2*c*d^2 + 2*a*b*c^2*d) + x^4*((a^2*d^3)/4 + (3*b^2*c^2*d)/4 + (3*a*b*c*d^2)/2) + a^2*c^3*x + (b^2*d^3*x^6)/6 + (a*c^2*x^2*(3*a*d + 2*b*c))/2 + (b*d^2*x^5*(2*a*d + 3*b*c))/5","B"
1788,1,65,38,0.038853,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^3/(a + b*x)^2,x)","x^2\,\left(\frac{b\,c^3}{2}+\frac{3\,a\,d\,c^2}{2}\right)+x^4\,\left(\frac{a\,d^3}{4}+\frac{3\,b\,c\,d^2}{4}\right)+\frac{b\,d^3\,x^5}{5}+a\,c^3\,x+c\,d\,x^3\,\left(a\,d+b\,c\right)","Not used",1,"x^2*((b*c^3)/2 + (3*a*c^2*d)/2) + x^4*((a*d^3)/4 + (3*b*c*d^2)/4) + (b*d^3*x^5)/5 + a*c^3*x + c*d*x^3*(a*d + b*c)","B"
1789,1,31,14,0.045283,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^3/(a + b*x)^3,x)","c^3\,x+\frac{3\,c^2\,d\,x^2}{2}+c\,d^2\,x^3+\frac{d^3\,x^4}{4}","Not used",1,"c^3*x + (d^3*x^4)/4 + (3*c^2*d*x^2)/2 + c*d^2*x^3","B"
1790,1,118,73,0.062034,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^3/(a + b*x)^4,x)","x\,\left(\frac{3\,c^2\,d}{b}+\frac{a\,\left(\frac{a\,d^3}{b^2}-\frac{3\,c\,d^2}{b}\right)}{b}\right)-x^2\,\left(\frac{a\,d^3}{2\,b^2}-\frac{3\,c\,d^2}{2\,b}\right)+\frac{d^3\,x^3}{3\,b}-\frac{\ln\left(a+b\,x\right)\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{b^4}","Not used",1,"x*((3*c^2*d)/b + (a*((a*d^3)/b^2 - (3*c*d^2)/b))/b) - x^2*((a*d^3)/(2*b^2) - (3*c*d^2)/(2*b)) + (d^3*x^3)/(3*b) - (log(a + b*x)*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/b^4","B"
1791,1,123,75,0.626885,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^3/(a + b*x)^5,x)","\frac{\ln\left(a+b\,x\right)\,\left(3\,a^2\,d^3-6\,a\,b\,c\,d^2+3\,b^2\,c^2\,d\right)}{b^4}-x\,\left(\frac{2\,a\,d^3}{b^3}-\frac{3\,c\,d^2}{b^2}\right)+\frac{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}{b\,\left(x\,b^4+a\,b^3\right)}+\frac{d^3\,x^2}{2\,b^2}","Not used",1,"(log(a + b*x)*(3*a^2*d^3 + 3*b^2*c^2*d - 6*a*b*c*d^2))/b^4 - x*((2*a*d^3)/b^3 - (3*c*d^2)/b^2) + (a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)/(b*(a*b^3 + b^4*x)) + (d^3*x^2)/(2*b^2)","B"
1792,1,130,78,0.643638,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^3/(a + b*x)^6,x)","\frac{d^3\,x}{b^3}-\frac{\ln\left(a+b\,x\right)\,\left(3\,a\,d^3-3\,b\,c\,d^2\right)}{b^4}-\frac{\frac{5\,a^3\,d^3-9\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d+b^3\,c^3}{2\,b}+x\,\left(3\,a^2\,d^3-6\,a\,b\,c\,d^2+3\,b^2\,c^2\,d\right)}{a^2\,b^3+2\,a\,b^4\,x+b^5\,x^2}","Not used",1,"(d^3*x)/b^3 - (log(a + b*x)*(3*a*d^3 - 3*b*c*d^2))/b^4 - ((5*a^3*d^3 + b^3*c^3 + 3*a*b^2*c^2*d - 9*a^2*b*c*d^2)/(2*b) + x*(3*a^2*d^3 + 3*b^2*c^2*d - 6*a*b*c*d^2))/(a^2*b^3 + b^5*x^2 + 2*a*b^4*x)","B"
1793,1,138,86,0.098141,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^3/(a + b*x)^7,x)","\frac{d^3\,\ln\left(a+b\,x\right)}{b^4}-\frac{\frac{-11\,a^3\,d^3+6\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d+2\,b^3\,c^3}{6\,b^4}+\frac{3\,x\,\left(-3\,a^2\,d^3+2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{2\,b^3}-\frac{3\,d^2\,x^2\,\left(a\,d-b\,c\right)}{b^2}}{a^3+3\,a^2\,b\,x+3\,a\,b^2\,x^2+b^3\,x^3}","Not used",1,"(d^3*log(a + b*x))/b^4 - ((2*b^3*c^3 - 11*a^3*d^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2)/(6*b^4) + (3*x*(b^2*c^2*d - 3*a^2*d^3 + 2*a*b*c*d^2))/(2*b^3) - (3*d^2*x^2*(a*d - b*c))/b^2)/(a^3 + b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x)","B"
1794,1,135,28,0.601547,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^3/(a + b*x)^8,x)","-\frac{\frac{a^3\,d^3+a^2\,b\,c\,d^2+a\,b^2\,c^2\,d+b^3\,c^3}{4\,b^4}+\frac{d^3\,x^3}{b}+\frac{d\,x\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)}{b^3}+\frac{3\,d^2\,x^2\,\left(a\,d+b\,c\right)}{2\,b^2}}{a^4+4\,a^3\,b\,x+6\,a^2\,b^2\,x^2+4\,a\,b^3\,x^3+b^4\,x^4}","Not used",1,"-((a^3*d^3 + b^3*c^3 + a*b^2*c^2*d + a^2*b*c*d^2)/(4*b^4) + (d^3*x^3)/b + (d*x*(a^2*d^2 + b^2*c^2 + a*b*c*d))/b^3 + (3*d^2*x^2*(a*d + b*c))/(2*b^2))/(a^4 + b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x)","B"
1795,1,154,58,0.624332,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^3/(a + b*x)^9,x)","-\frac{\frac{a^3\,d^3+2\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d+4\,b^3\,c^3}{20\,b^4}+\frac{d^3\,x^3}{2\,b}+\frac{d\,x\,\left(a^2\,d^2+2\,a\,b\,c\,d+3\,b^2\,c^2\right)}{4\,b^3}+\frac{d^2\,x^2\,\left(a\,d+2\,b\,c\right)}{2\,b^2}}{a^5+5\,a^4\,b\,x+10\,a^3\,b^2\,x^2+10\,a^2\,b^3\,x^3+5\,a\,b^4\,x^4+b^5\,x^5}","Not used",1,"-((a^3*d^3 + 4*b^3*c^3 + 3*a*b^2*c^2*d + 2*a^2*b*c*d^2)/(20*b^4) + (d^3*x^3)/(2*b) + (d*x*(a^2*d^2 + 3*b^2*c^2 + 2*a*b*c*d))/(4*b^3) + (d^2*x^2*(a*d + 2*b*c))/(2*b^2))/(a^5 + b^5*x^5 + 5*a*b^4*x^4 + 10*a^3*b^2*x^2 + 10*a^2*b^3*x^3 + 5*a^4*b*x)","B"
1796,1,165,92,0.629862,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^3/(a + b*x)^10,x)","-\frac{\frac{a^3\,d^3+3\,a^2\,b\,c\,d^2+6\,a\,b^2\,c^2\,d+10\,b^3\,c^3}{60\,b^4}+\frac{d^3\,x^3}{3\,b}+\frac{d\,x\,\left(a^2\,d^2+3\,a\,b\,c\,d+6\,b^2\,c^2\right)}{10\,b^3}+\frac{d^2\,x^2\,\left(a\,d+3\,b\,c\right)}{4\,b^2}}{a^6+6\,a^5\,b\,x+15\,a^4\,b^2\,x^2+20\,a^3\,b^3\,x^3+15\,a^2\,b^4\,x^4+6\,a\,b^5\,x^5+b^6\,x^6}","Not used",1,"-((a^3*d^3 + 10*b^3*c^3 + 6*a*b^2*c^2*d + 3*a^2*b*c*d^2)/(60*b^4) + (d^3*x^3)/(3*b) + (d*x*(a^2*d^2 + 6*b^2*c^2 + 3*a*b*c*d))/(10*b^3) + (d^2*x^2*(a*d + 3*b*c))/(4*b^2))/(a^6 + b^6*x^6 + 6*a*b^5*x^5 + 15*a^4*b^2*x^2 + 20*a^3*b^3*x^3 + 15*a^2*b^4*x^4 + 6*a^5*b*x)","B"
1797,1,176,92,0.639015,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^3/(a + b*x)^11,x)","-\frac{\frac{a^3\,d^3+4\,a^2\,b\,c\,d^2+10\,a\,b^2\,c^2\,d+20\,b^3\,c^3}{140\,b^4}+\frac{d^3\,x^3}{4\,b}+\frac{d\,x\,\left(a^2\,d^2+4\,a\,b\,c\,d+10\,b^2\,c^2\right)}{20\,b^3}+\frac{3\,d^2\,x^2\,\left(a\,d+4\,b\,c\right)}{20\,b^2}}{a^7+7\,a^6\,b\,x+21\,a^5\,b^2\,x^2+35\,a^4\,b^3\,x^3+35\,a^3\,b^4\,x^4+21\,a^2\,b^5\,x^5+7\,a\,b^6\,x^6+b^7\,x^7}","Not used",1,"-((a^3*d^3 + 20*b^3*c^3 + 10*a*b^2*c^2*d + 4*a^2*b*c*d^2)/(140*b^4) + (d^3*x^3)/(4*b) + (d*x*(a^2*d^2 + 10*b^2*c^2 + 4*a*b*c*d))/(20*b^3) + (3*d^2*x^2*(a*d + 4*b*c))/(20*b^2))/(a^7 + b^7*x^7 + 7*a*b^6*x^6 + 21*a^5*b^2*x^2 + 35*a^4*b^3*x^3 + 35*a^3*b^4*x^4 + 21*a^2*b^5*x^5 + 7*a^6*b*x)","B"
1798,1,187,92,0.097814,"\text{Not used}","int((a*c + x*(a*d + b*c) + b*d*x^2)^3/(a + b*x)^12,x)","-\frac{\frac{a^3\,d^3+5\,a^2\,b\,c\,d^2+15\,a\,b^2\,c^2\,d+35\,b^3\,c^3}{280\,b^4}+\frac{d^3\,x^3}{5\,b}+\frac{d\,x\,\left(a^2\,d^2+5\,a\,b\,c\,d+15\,b^2\,c^2\right)}{35\,b^3}+\frac{d^2\,x^2\,\left(a\,d+5\,b\,c\right)}{10\,b^2}}{a^8+8\,a^7\,b\,x+28\,a^6\,b^2\,x^2+56\,a^5\,b^3\,x^3+70\,a^4\,b^4\,x^4+56\,a^3\,b^5\,x^5+28\,a^2\,b^6\,x^6+8\,a\,b^7\,x^7+b^8\,x^8}","Not used",1,"-((a^3*d^3 + 35*b^3*c^3 + 15*a*b^2*c^2*d + 5*a^2*b*c*d^2)/(280*b^4) + (d^3*x^3)/(5*b) + (d*x*(a^2*d^2 + 15*b^2*c^2 + 5*a*b*c*d))/(35*b^3) + (d^2*x^2*(a*d + 5*b*c))/(10*b^2))/(a^8 + b^8*x^8 + 8*a*b^7*x^7 + 28*a^6*b^2*x^2 + 56*a^5*b^3*x^3 + 70*a^4*b^4*x^4 + 56*a^3*b^5*x^5 + 28*a^2*b^6*x^6 + 8*a^7*b*x)","B"
1799,1,280,122,0.597051,"\text{Not used}","int((a + b*x)^6/(a*c + x*(a*d + b*c) + b*d*x^2),x)","x\,\left(\frac{5\,a^4\,b}{d}-\frac{c\,\left(\frac{10\,a^3\,b^2}{d}+\frac{c\,\left(\frac{c\,\left(\frac{5\,a\,b^4}{d}-\frac{b^5\,c}{d^2}\right)}{d}-\frac{10\,a^2\,b^3}{d}\right)}{d}\right)}{d}\right)+x^4\,\left(\frac{5\,a\,b^4}{4\,d}-\frac{b^5\,c}{4\,d^2}\right)+x^2\,\left(\frac{5\,a^3\,b^2}{d}+\frac{c\,\left(\frac{c\,\left(\frac{5\,a\,b^4}{d}-\frac{b^5\,c}{d^2}\right)}{d}-\frac{10\,a^2\,b^3}{d}\right)}{2\,d}\right)-x^3\,\left(\frac{c\,\left(\frac{5\,a\,b^4}{d}-\frac{b^5\,c}{d^2}\right)}{3\,d}-\frac{10\,a^2\,b^3}{3\,d}\right)+\frac{b^5\,x^5}{5\,d}+\frac{\ln\left(c+d\,x\right)\,\left(a^5\,d^5-5\,a^4\,b\,c\,d^4+10\,a^3\,b^2\,c^2\,d^3-10\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d-b^5\,c^5\right)}{d^6}","Not used",1,"x*((5*a^4*b)/d - (c*((10*a^3*b^2)/d + (c*((c*((5*a*b^4)/d - (b^5*c)/d^2))/d - (10*a^2*b^3)/d))/d))/d) + x^4*((5*a*b^4)/(4*d) - (b^5*c)/(4*d^2)) + x^2*((5*a^3*b^2)/d + (c*((c*((5*a*b^4)/d - (b^5*c)/d^2))/d - (10*a^2*b^3)/d))/(2*d)) - x^3*((c*((5*a*b^4)/d - (b^5*c)/d^2))/(3*d) - (10*a^2*b^3)/(3*d)) + (b^5*x^5)/(5*d) + (log(c + d*x)*(a^5*d^5 - b^5*c^5 - 10*a^2*b^3*c^3*d^2 + 10*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 5*a^4*b*c*d^4))/d^6","B"
1800,1,189,98,0.052605,"\text{Not used}","int((a + b*x)^5/(a*c + x*(a*d + b*c) + b*d*x^2),x)","x^3\,\left(\frac{4\,a\,b^3}{3\,d}-\frac{b^4\,c}{3\,d^2}\right)+x\,\left(\frac{4\,a^3\,b}{d}+\frac{c\,\left(\frac{c\,\left(\frac{4\,a\,b^3}{d}-\frac{b^4\,c}{d^2}\right)}{d}-\frac{6\,a^2\,b^2}{d}\right)}{d}\right)-x^2\,\left(\frac{c\,\left(\frac{4\,a\,b^3}{d}-\frac{b^4\,c}{d^2}\right)}{2\,d}-\frac{3\,a^2\,b^2}{d}\right)+\frac{\ln\left(c+d\,x\right)\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{d^5}+\frac{b^4\,x^4}{4\,d}","Not used",1,"x^3*((4*a*b^3)/(3*d) - (b^4*c)/(3*d^2)) + x*((4*a^3*b)/d + (c*((c*((4*a*b^3)/d - (b^4*c)/d^2))/d - (6*a^2*b^2)/d))/d) - x^2*((c*((4*a*b^3)/d - (b^4*c)/d^2))/(2*d) - (3*a^2*b^2)/d) + (log(c + d*x)*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/d^5 + (b^4*x^4)/(4*d)","B"
1801,1,118,74,0.574144,"\text{Not used}","int((a + b*x)^4/(a*c + x*(a*d + b*c) + b*d*x^2),x)","x^2\,\left(\frac{3\,a\,b^2}{2\,d}-\frac{b^3\,c}{2\,d^2}\right)+x\,\left(\frac{3\,a^2\,b}{d}-\frac{c\,\left(\frac{3\,a\,b^2}{d}-\frac{b^3\,c}{d^2}\right)}{d}\right)+\frac{\ln\left(c+d\,x\right)\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{d^4}+\frac{b^3\,x^3}{3\,d}","Not used",1,"x^2*((3*a*b^2)/(2*d) - (b^3*c)/(2*d^2)) + x*((3*a^2*b)/d - (c*((3*a*b^2)/d - (b^3*c)/d^2))/d) + (log(c + d*x)*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/d^4 + (b^3*x^3)/(3*d)","B"
1802,1,62,50,0.598732,"\text{Not used}","int((a + b*x)^3/(a*c + x*(a*d + b*c) + b*d*x^2),x)","\frac{\ln\left(c+d\,x\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{d^3}-x\,\left(\frac{b^2\,c}{d^2}-\frac{2\,a\,b}{d}\right)+\frac{b^2\,x^2}{2\,d}","Not used",1,"(log(c + d*x)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/d^3 - x*((b^2*c)/d^2 - (2*a*b)/d) + (b^2*x^2)/(2*d)","B"
1803,1,25,26,0.044311,"\text{Not used}","int((a + b*x)^2/(a*c + x*(a*d + b*c) + b*d*x^2),x)","\frac{\ln\left(c+d\,x\right)\,\left(a\,d-b\,c\right)}{d^2}+\frac{b\,x}{d}","Not used",1,"(log(c + d*x)*(a*d - b*c))/d^2 + (b*x)/d","B"
1804,1,10,10,0.022194,"\text{Not used}","int((a + b*x)/(a*c + x*(a*d + b*c) + b*d*x^2),x)","\frac{\ln\left(c+d\,x\right)}{d}","Not used",1,"log(c + d*x)/d","B"
1805,1,40,36,0.078019,"\text{Not used}","int(1/(a*c + x*(a*d + b*c) + b*d*x^2),x)","\frac{\mathrm{atan}\left(\frac{b\,c\,2{}\mathrm{i}+b\,d\,x\,2{}\mathrm{i}}{a\,d-b\,c}+1{}\mathrm{i}\right)\,2{}\mathrm{i}}{a\,d-b\,c}","Not used",1,"(atan((b*c*2i + b*d*x*2i)/(a*d - b*c) + 1i)*2i)/(a*d - b*c)","B"
1806,1,76,57,0.645918,"\text{Not used}","int(1/((a + b*x)*(a*c + x*(a*d + b*c) + b*d*x^2)),x)","\frac{1}{\left(a\,d-b\,c\right)\,\left(a+b\,x\right)}-\frac{2\,d\,\mathrm{atanh}\left(\frac{a^2\,d^2-b^2\,c^2}{{\left(a\,d-b\,c\right)}^2}+\frac{2\,b\,d\,x}{a\,d-b\,c}\right)}{{\left(a\,d-b\,c\right)}^2}","Not used",1,"1/((a*d - b*c)*(a + b*x)) - (2*d*atanh((a^2*d^2 - b^2*c^2)/(a*d - b*c)^2 + (2*b*d*x)/(a*d - b*c)))/(a*d - b*c)^2","B"
1807,1,182,82,0.693920,"\text{Not used}","int(1/((a + b*x)^2*(a*c + x*(a*d + b*c) + b*d*x^2)),x)","\frac{\frac{3\,a\,d-b\,c}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{b\,d\,x}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}}{a^2+2\,a\,b\,x+b^2\,x^2}-\frac{2\,d^2\,\mathrm{atanh}\left(\frac{a^3\,d^3-a^2\,b\,c\,d^2-a\,b^2\,c^2\,d+b^3\,c^3}{{\left(a\,d-b\,c\right)}^3}+\frac{2\,b\,d\,x\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{{\left(a\,d-b\,c\right)}^3}\right)}{{\left(a\,d-b\,c\right)}^3}","Not used",1,"((3*a*d - b*c)/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*d*x)/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(a^2 + b^2*x^2 + 2*a*b*x) - (2*d^2*atanh((a^3*d^3 + b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2)/(a*d - b*c)^3 + (2*b*d*x*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(a*d - b*c)^3))/(a*d - b*c)^3","B"
1808,1,312,107,0.744996,"\text{Not used}","int(1/((a + b*x)^3*(a*c + x*(a*d + b*c) + b*d*x^2)),x)","\frac{\frac{11\,a^2\,d^2-7\,a\,b\,c\,d+2\,b^2\,c^2}{6\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}-\frac{d\,x\,\left(b^2\,c-5\,a\,b\,d\right)}{2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{b^2\,d^2\,x^2}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}}{a^3+3\,a^2\,b\,x+3\,a\,b^2\,x^2+b^3\,x^3}-\frac{2\,d^3\,\mathrm{atanh}\left(\frac{a^4\,d^4-2\,a^3\,b\,c\,d^3+2\,a\,b^3\,c^3\,d-b^4\,c^4}{{\left(a\,d-b\,c\right)}^4}+\frac{2\,b\,d\,x\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{{\left(a\,d-b\,c\right)}^4}\right)}{{\left(a\,d-b\,c\right)}^4}","Not used",1,"((11*a^2*d^2 + 2*b^2*c^2 - 7*a*b*c*d)/(6*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) - (d*x*(b^2*c - 5*a*b*d))/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (b^2*d^2*x^2)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(a^3 + b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x) - (2*d^3*atanh((a^4*d^4 - b^4*c^4 + 2*a*b^3*c^3*d - 2*a^3*b*c*d^3)/(a*d - b*c)^4 + (2*b*d*x*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(a*d - b*c)^4))/(a*d - b*c)^4","B"
1809,1,505,130,0.829939,"\text{Not used}","int(1/((a + b*x)^4*(a*c + x*(a*d + b*c) + b*d*x^2)),x)","\frac{\frac{25\,a^3\,d^3-23\,a^2\,b\,c\,d^2+13\,a\,b^2\,c^2\,d-3\,b^3\,c^3}{12\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}-\frac{d^2\,x^2\,\left(b^3\,c-7\,a\,b^2\,d\right)}{2\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}+\frac{d\,x\,\left(13\,a^2\,b\,d^2-5\,a\,b^2\,c\,d+b^3\,c^2\right)}{3\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}+\frac{b^3\,d^3\,x^3}{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}}{a^4+4\,a^3\,b\,x+6\,a^2\,b^2\,x^2+4\,a\,b^3\,x^3+b^4\,x^4}-\frac{2\,d^4\,\mathrm{atanh}\left(\frac{a^5\,d^5-3\,a^4\,b\,c\,d^4+2\,a^3\,b^2\,c^2\,d^3+2\,a^2\,b^3\,c^3\,d^2-3\,a\,b^4\,c^4\,d+b^5\,c^5}{{\left(a\,d-b\,c\right)}^5}+\frac{2\,b\,d\,x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{{\left(a\,d-b\,c\right)}^5}\right)}{{\left(a\,d-b\,c\right)}^5}","Not used",1,"((25*a^3*d^3 - 3*b^3*c^3 + 13*a*b^2*c^2*d - 23*a^2*b*c*d^2)/(12*(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^2*x^2*(b^3*c - 7*a*b^2*d))/(2*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3)) + (d*x*(b^3*c^2 + 13*a^2*b*d^2 - 5*a*b^2*c*d))/(3*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3)) + (b^3*d^3*x^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))/(a^4 + b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x) - (2*d^4*atanh((a^5*d^5 + b^5*c^5 + 2*a^2*b^3*c^3*d^2 + 2*a^3*b^2*c^2*d^3 - 3*a*b^4*c^4*d - 3*a^4*b*c*d^4)/(a*d - b*c)^5 + (2*b*d*x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/(a*d - b*c)^5))/(a*d - b*c)^5","B"
1810,1,203,104,0.077842,"\text{Not used}","int((a + b*x)^6/(a*c + x*(a*d + b*c) + b*d*x^2)^2,x)","x^2\,\left(\frac{2\,a\,b^3}{d^2}-\frac{b^4\,c}{d^3}\right)-x\,\left(\frac{2\,c\,\left(\frac{4\,a\,b^3}{d^2}-\frac{2\,b^4\,c}{d^3}\right)}{d}-\frac{6\,a^2\,b^2}{d^2}+\frac{b^4\,c^2}{d^4}\right)+\frac{b^4\,x^3}{3\,d^2}-\frac{\ln\left(c+d\,x\right)\,\left(-4\,a^3\,b\,d^3+12\,a^2\,b^2\,c\,d^2-12\,a\,b^3\,c^2\,d+4\,b^4\,c^3\right)}{d^5}-\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}{d\,\left(x\,d^5+c\,d^4\right)}","Not used",1,"x^2*((2*a*b^3)/d^2 - (b^4*c)/d^3) - x*((2*c*((4*a*b^3)/d^2 - (2*b^4*c)/d^3))/d - (6*a^2*b^2)/d^2 + (b^4*c^2)/d^4) + (b^4*x^3)/(3*d^2) - (log(c + d*x)*(4*b^4*c^3 - 4*a^3*b*d^3 + 12*a^2*b^2*c*d^2 - 12*a*b^3*c^2*d))/d^5 - (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*(c*d^4 + d^5*x))","B"
1811,1,123,75,0.592884,"\text{Not used}","int((a + b*x)^5/(a*c + x*(a*d + b*c) + b*d*x^2)^2,x)","x\,\left(\frac{3\,a\,b^2}{d^2}-\frac{2\,b^3\,c}{d^3}\right)+\frac{\ln\left(c+d\,x\right)\,\left(3\,a^2\,b\,d^2-6\,a\,b^2\,c\,d+3\,b^3\,c^2\right)}{d^4}-\frac{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}{d\,\left(x\,d^4+c\,d^3\right)}+\frac{b^3\,x^2}{2\,d^2}","Not used",1,"x*((3*a*b^2)/d^2 - (2*b^3*c)/d^3) + (log(c + d*x)*(3*b^3*c^2 + 3*a^2*b*d^2 - 6*a*b^2*c*d))/d^4 - (a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)/(d*(c*d^3 + d^4*x)) + (b^3*x^2)/(2*d^2)","B"
1812,1,71,51,0.606556,"\text{Not used}","int((a + b*x)^4/(a*c + x*(a*d + b*c) + b*d*x^2)^2,x)","\frac{b^2\,x}{d^2}-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{d\,\left(x\,d^3+c\,d^2\right)}-\frac{\ln\left(c+d\,x\right)\,\left(2\,b^2\,c-2\,a\,b\,d\right)}{d^3}","Not used",1,"(b^2*x)/d^2 - (a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(d*(c*d^2 + d^3*x)) - (log(c + d*x)*(2*b^2*c - 2*a*b*d))/d^3","B"
1813,1,32,31,0.049687,"\text{Not used}","int((a + b*x)^3/(a*c + x*(a*d + b*c) + b*d*x^2)^2,x)","\frac{b\,\ln\left(c+d\,x\right)}{d^2}-\frac{a\,d-b\,c}{d^2\,\left(c+d\,x\right)}","Not used",1,"(b*log(c + d*x))/d^2 - (a*d - b*c)/(d^2*(c + d*x))","B"
1814,1,12,12,0.536052,"\text{Not used}","int((a + b*x)^2/(a*c + x*(a*d + b*c) + b*d*x^2)^2,x)","-\frac{1}{d\,\left(c+d\,x\right)}","Not used",1,"-1/(d*(c + d*x))","B"
1815,1,77,56,0.109737,"\text{Not used}","int((a + b*x)/(a*c + x*(a*d + b*c) + b*d*x^2)^2,x)","\frac{2\,b\,\mathrm{atanh}\left(\frac{a^2\,d^2-b^2\,c^2}{{\left(a\,d-b\,c\right)}^2}+\frac{2\,b\,d\,x}{a\,d-b\,c}\right)}{{\left(a\,d-b\,c\right)}^2}-\frac{1}{\left(a\,d-b\,c\right)\,\left(c+d\,x\right)}","Not used",1,"(2*b*atanh((a^2*d^2 - b^2*c^2)/(a*d - b*c)^2 + (2*b*d*x)/(a*d - b*c)))/(a*d - b*c)^2 - 1/((a*d - b*c)*(c + d*x))","B"
1816,1,182,86,0.768217,"\text{Not used}","int(1/(a*c + x*(a*d + b*c) + b*d*x^2)^2,x)","\frac{4\,b\,d\,\mathrm{atanh}\left(\frac{a^3\,d^3-a^2\,b\,c\,d^2-a\,b^2\,c^2\,d+b^3\,c^3}{{\left(a\,d-b\,c\right)}^3}+\frac{2\,b\,d\,x\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{{\left(a\,d-b\,c\right)}^3}\right)}{{\left(a\,d-b\,c\right)}^3}-\frac{\frac{a\,d+b\,c}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}+\frac{2\,b\,d\,x}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}}{b\,d\,x^2+\left(a\,d+b\,c\right)\,x+a\,c}","Not used",1,"(4*b*d*atanh((a^3*d^3 + b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2)/(a*d - b*c)^3 + (2*b*d*x*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(a*d - b*c)^3))/(a*d - b*c)^3 - ((a*d + b*c)/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d) + (2*b*d*x)/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(a*c + x*(a*d + b*c) + b*d*x^2)","B"
1817,1,330,109,0.238677,"\text{Not used}","int(1/((a + b*x)*(a*c + x*(a*d + b*c) + b*d*x^2)^2),x)","\frac{6\,b\,d^2\,\mathrm{atanh}\left(\frac{a^4\,d^4-2\,a^3\,b\,c\,d^3+2\,a\,b^3\,c^3\,d-b^4\,c^4}{{\left(a\,d-b\,c\right)}^4}+\frac{2\,b\,d\,x\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{{\left(a\,d-b\,c\right)}^4}\right)}{{\left(a\,d-b\,c\right)}^4}-\frac{\frac{2\,a^2\,d^2+5\,a\,b\,c\,d-b^2\,c^2}{2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{3\,d\,x\,\left(c\,b^2+3\,a\,d\,b\right)}{2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{3\,b^2\,d^2\,x^2}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}}{x\,\left(d\,a^2+2\,b\,c\,a\right)+a^2\,c+x^2\,\left(c\,b^2+2\,a\,d\,b\right)+b^2\,d\,x^3}","Not used",1,"(6*b*d^2*atanh((a^4*d^4 - b^4*c^4 + 2*a*b^3*c^3*d - 2*a^3*b*c*d^3)/(a*d - b*c)^4 + (2*b*d*x*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(a*d - b*c)^4))/(a*d - b*c)^4 - ((2*a^2*d^2 - b^2*c^2 + 5*a*b*c*d)/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (3*d*x*(b^2*c + 3*a*b*d))/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (3*b^2*d^2*x^2)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(x*(a^2*d + 2*a*b*c) + a^2*c + x^2*(b^2*c + 2*a*b*d) + b^2*d*x^3)","B"
1818,1,291,133,0.616007,"\text{Not used}","int((a + b*x)^8/(a*c + x*(a*d + b*c) + b*d*x^2)^3,x)","x^2\,\left(\frac{5\,a\,b^4}{2\,d^3}-\frac{3\,b^5\,c}{2\,d^4}\right)-\frac{\frac{a^5\,d^5+5\,a^4\,b\,c\,d^4-30\,a^3\,b^2\,c^2\,d^3+50\,a^2\,b^3\,c^3\,d^2-35\,a\,b^4\,c^4\,d+9\,b^5\,c^5}{2\,d}+x\,\left(5\,a^4\,b\,d^4-20\,a^3\,b^2\,c\,d^3+30\,a^2\,b^3\,c^2\,d^2-20\,a\,b^4\,c^3\,d+5\,b^5\,c^4\right)}{c^2\,d^5+2\,c\,d^6\,x+d^7\,x^2}-x\,\left(\frac{3\,c\,\left(\frac{5\,a\,b^4}{d^3}-\frac{3\,b^5\,c}{d^4}\right)}{d}-\frac{10\,a^2\,b^3}{d^3}+\frac{3\,b^5\,c^2}{d^5}\right)-\frac{\ln\left(c+d\,x\right)\,\left(-10\,a^3\,b^2\,d^3+30\,a^2\,b^3\,c\,d^2-30\,a\,b^4\,c^2\,d+10\,b^5\,c^3\right)}{d^6}+\frac{b^5\,x^3}{3\,d^3}","Not used",1,"x^2*((5*a*b^4)/(2*d^3) - (3*b^5*c)/(2*d^4)) - ((a^5*d^5 + 9*b^5*c^5 + 50*a^2*b^3*c^3*d^2 - 30*a^3*b^2*c^2*d^3 - 35*a*b^4*c^4*d + 5*a^4*b*c*d^4)/(2*d) + x*(5*b^5*c^4 + 5*a^4*b*d^4 - 20*a^3*b^2*c*d^3 + 30*a^2*b^3*c^2*d^2 - 20*a*b^4*c^3*d))/(c^2*d^5 + d^7*x^2 + 2*c*d^6*x) - x*((3*c*((5*a*b^4)/d^3 - (3*b^5*c)/d^4))/d - (10*a^2*b^3)/d^3 + (3*b^5*c^2)/d^5) - (log(c + d*x)*(10*b^5*c^3 - 10*a^3*b^2*d^3 + 30*a^2*b^3*c*d^2 - 30*a*b^4*c^2*d))/d^6 + (b^5*x^3)/(3*d^3)","B"
1819,1,196,103,0.092176,"\text{Not used}","int((a + b*x)^7/(a*c + x*(a*d + b*c) + b*d*x^2)^3,x)","x\,\left(\frac{4\,a\,b^3}{d^3}-\frac{3\,b^4\,c}{d^4}\right)-\frac{\frac{a^4\,d^4+4\,a^3\,b\,c\,d^3-18\,a^2\,b^2\,c^2\,d^2+20\,a\,b^3\,c^3\,d-7\,b^4\,c^4}{2\,d}-x\,\left(-4\,a^3\,b\,d^3+12\,a^2\,b^2\,c\,d^2-12\,a\,b^3\,c^2\,d+4\,b^4\,c^3\right)}{c^2\,d^4+2\,c\,d^5\,x+d^6\,x^2}+\frac{b^4\,x^2}{2\,d^3}+\frac{\ln\left(c+d\,x\right)\,\left(6\,a^2\,b^2\,d^2-12\,a\,b^3\,c\,d+6\,b^4\,c^2\right)}{d^5}","Not used",1,"x*((4*a*b^3)/d^3 - (3*b^4*c)/d^4) - ((a^4*d^4 - 7*b^4*c^4 - 18*a^2*b^2*c^2*d^2 + 20*a*b^3*c^3*d + 4*a^3*b*c*d^3)/(2*d) - x*(4*b^4*c^3 - 4*a^3*b*d^3 + 12*a^2*b^2*c*d^2 - 12*a*b^3*c^2*d))/(c^2*d^4 + d^6*x^2 + 2*c*d^5*x) + (b^4*x^2)/(2*d^3) + (log(c + d*x)*(6*b^4*c^2 + 6*a^2*b^2*d^2 - 12*a*b^3*c*d))/d^5","B"
1820,1,130,78,0.617367,"\text{Not used}","int((a + b*x)^6/(a*c + x*(a*d + b*c) + b*d*x^2)^3,x)","\frac{b^3\,x}{d^3}-\frac{\ln\left(c+d\,x\right)\,\left(3\,b^3\,c-3\,a\,b^2\,d\right)}{d^4}-\frac{\frac{a^3\,d^3+3\,a^2\,b\,c\,d^2-9\,a\,b^2\,c^2\,d+5\,b^3\,c^3}{2\,d}+x\,\left(3\,a^2\,b\,d^2-6\,a\,b^2\,c\,d+3\,b^3\,c^2\right)}{c^2\,d^3+2\,c\,d^4\,x+d^5\,x^2}","Not used",1,"(b^3*x)/d^3 - (log(c + d*x)*(3*b^3*c - 3*a*b^2*d))/d^4 - ((a^3*d^3 + 5*b^3*c^3 - 9*a*b^2*c^2*d + 3*a^2*b*c*d^2)/(2*d) + x*(3*b^3*c^2 + 3*a^2*b*d^2 - 6*a*b^2*c*d))/(c^2*d^3 + d^5*x^2 + 2*c*d^4*x)","B"
1821,1,77,59,0.589998,"\text{Not used}","int((a + b*x)^5/(a*c + x*(a*d + b*c) + b*d*x^2)^3,x)","\frac{b^2\,\ln\left(c+d\,x\right)}{d^3}-\frac{\frac{a^2\,d^2+2\,a\,b\,c\,d-3\,b^2\,c^2}{2\,d^3}+\frac{2\,b\,x\,\left(a\,d-b\,c\right)}{d^2}}{c^2+2\,c\,d\,x+d^2\,x^2}","Not used",1,"(b^2*log(c + d*x))/d^3 - ((a^2*d^2 - 3*b^2*c^2 + 2*a*b*c*d)/(2*d^3) + (2*b*x*(a*d - b*c))/d^2)/(c^2 + d^2*x^2 + 2*c*d*x)","B"
1822,1,39,28,0.032888,"\text{Not used}","int((a + b*x)^4/(a*c + x*(a*d + b*c) + b*d*x^2)^3,x)","-\frac{\frac{a\,d+b\,c}{2\,d^2}+\frac{b\,x}{d}}{c^2+2\,c\,d\,x+d^2\,x^2}","Not used",1,"-((a*d + b*c)/(2*d^2) + (b*x)/d)/(c^2 + d^2*x^2 + 2*c*d*x)","B"
1823,1,26,14,0.553312,"\text{Not used}","int((a + b*x)^3/(a*c + x*(a*d + b*c) + b*d*x^2)^3,x)","-\frac{1}{2\,c^2\,d+4\,c\,d^2\,x+2\,d^3\,x^2}","Not used",1,"-1/(2*c^2*d + 2*d^3*x^2 + 4*c*d^2*x)","B"
1824,1,183,82,0.666462,"\text{Not used}","int((a + b*x)^2/(a*c + x*(a*d + b*c) + b*d*x^2)^3,x)","-\frac{\frac{a\,d-3\,b\,c}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}-\frac{b\,d\,x}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}}{c^2+2\,c\,d\,x+d^2\,x^2}-\frac{2\,b^2\,\mathrm{atanh}\left(\frac{a^3\,d^3-a^2\,b\,c\,d^2-a\,b^2\,c^2\,d+b^3\,c^3}{{\left(a\,d-b\,c\right)}^3}+\frac{2\,b\,d\,x\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{{\left(a\,d-b\,c\right)}^3}\right)}{{\left(a\,d-b\,c\right)}^3}","Not used",1,"- ((a*d - 3*b*c)/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) - (b*d*x)/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(c^2 + d^2*x^2 + 2*c*d*x) - (2*b^2*atanh((a^3*d^3 + b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2)/(a*d - b*c)^3 + (2*b*d*x*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(a*d - b*c)^3))/(a*d - b*c)^3","B"
1825,1,329,110,0.750402,"\text{Not used}","int((a + b*x)/(a*c + x*(a*d + b*c) + b*d*x^2)^3,x)","\frac{\frac{-a^2\,d^2+5\,a\,b\,c\,d+2\,b^2\,c^2}{2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{3\,b\,x\,\left(a\,d^2+3\,b\,c\,d\right)}{2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{3\,b^2\,d^2\,x^2}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}}{x\,\left(b\,c^2+2\,a\,d\,c\right)+a\,c^2+x^2\,\left(a\,d^2+2\,b\,c\,d\right)+b\,d^2\,x^3}-\frac{6\,b^2\,d\,\mathrm{atanh}\left(\frac{a^4\,d^4-2\,a^3\,b\,c\,d^3+2\,a\,b^3\,c^3\,d-b^4\,c^4}{{\left(a\,d-b\,c\right)}^4}+\frac{2\,b\,d\,x\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{{\left(a\,d-b\,c\right)}^4}\right)}{{\left(a\,d-b\,c\right)}^4}","Not used",1,"((2*b^2*c^2 - a^2*d^2 + 5*a*b*c*d)/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (3*b*x*(a*d^2 + 3*b*c*d))/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (3*b^2*d^2*x^2)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(x*(b*c^2 + 2*a*c*d) + a*c^2 + x^2*(a*d^2 + 2*b*c*d) + b*d^2*x^3) - (6*b^2*d*atanh((a^4*d^4 - b^4*c^4 + 2*a*b^3*c^3*d - 2*a^3*b*c*d^3)/(a*d - b*c)^4 + (2*b*d*x*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(a*d - b*c)^4))/(a*d - b*c)^4","B"
1826,1,542,143,0.928033,"\text{Not used}","int(1/(a*c + x*(a*d + b*c) + b*d*x^2)^3,x)","\frac{\frac{6\,b^3\,d^3\,x^3}{a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4}-\frac{a^3\,d^3-7\,a^2\,b\,c\,d^2-7\,a\,b^2\,c^2\,d+b^3\,c^3}{2\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}+\frac{9\,b\,d\,x^2\,\left(c\,b^2\,d+a\,b\,d^2\right)}{a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4}+\frac{2\,b\,d\,x\,\left(a^2\,d^2+7\,a\,b\,c\,d+b^2\,c^2\right)}{a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4}}{x\,\left(2\,d\,a^2\,c+2\,b\,a\,c^2\right)+x^2\,\left(a^2\,d^2+4\,a\,b\,c\,d+b^2\,c^2\right)+x^3\,\left(2\,c\,b^2\,d+2\,a\,b\,d^2\right)+a^2\,c^2+b^2\,d^2\,x^4}-\frac{12\,b^2\,d^2\,\mathrm{atanh}\left(\frac{a^5\,d^5-3\,a^4\,b\,c\,d^4+2\,a^3\,b^2\,c^2\,d^3+2\,a^2\,b^3\,c^3\,d^2-3\,a\,b^4\,c^4\,d+b^5\,c^5}{{\left(a\,d-b\,c\right)}^5}+\frac{2\,b\,d\,x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{{\left(a\,d-b\,c\right)}^5}\right)}{{\left(a\,d-b\,c\right)}^5}","Not used",1,"((6*b^3*d^3*x^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) - (a^3*d^3 + b^3*c^3 - 7*a*b^2*c^2*d - 7*a^2*b*c*d^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)) + (9*b*d*x^2*(a*b*d^2 + b^2*c*d))/(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3) + (2*b*d*x*(a^2*d^2 + b^2*c^2 + 7*a*b*c*d))/(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/(x*(2*a*b*c^2 + 2*a^2*c*d) + x^2*(a^2*d^2 + b^2*c^2 + 4*a*b*c*d) + x^3*(2*a*b*d^2 + 2*b^2*c*d) + a^2*c^2 + b^2*d^2*x^4) - (12*b^2*d^2*atanh((a^5*d^5 + b^5*c^5 + 2*a^2*b^3*c^3*d^2 + 2*a^3*b^2*c^2*d^3 - 3*a*b^4*c^4*d - 3*a^4*b*c*d^4)/(a*d - b*c)^5 + (2*b*d*x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/(a*d - b*c)^5))/(a*d - b*c)^5","B"
1827,1,797,170,1.056698,"\text{Not used}","int(1/((a + b*x)*(a*c + x*(a*d + b*c) + b*d*x^2)^3),x)","\frac{\frac{-3\,a^4\,d^4+27\,a^3\,b\,c\,d^3+47\,a^2\,b^2\,c^2\,d^2-13\,a\,b^3\,c^3\,d+2\,b^4\,c^4}{6\,\left(a^5\,d^5-5\,a^4\,b\,c\,d^4+10\,a^3\,b^2\,c^2\,d^3-10\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d-b^5\,c^5\right)}+\frac{5\,d\,x\,\left(3\,a^3\,b\,d^3+35\,a^2\,b^2\,c\,d^2+11\,a\,b^3\,c^2\,d-b^4\,c^3\right)}{6\,\left(a^5\,d^5-5\,a^4\,b\,c\,d^4+10\,a^3\,b^2\,c^2\,d^3-10\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d-b^5\,c^5\right)}+\frac{10\,b^4\,d^4\,x^4}{a^5\,d^5-5\,a^4\,b\,c\,d^4+10\,a^3\,b^2\,c^2\,d^3-10\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d-b^5\,c^5}+\frac{5\,d^2\,x^2\,\left(11\,a^2\,b^2\,d^2+23\,a\,b^3\,c\,d+2\,b^4\,c^2\right)}{3\,\left(a^5\,d^5-5\,a^4\,b\,c\,d^4+10\,a^3\,b^2\,c^2\,d^3-10\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d-b^5\,c^5\right)}+\frac{5\,b\,d^2\,x^3\,\left(3\,c\,b^3\,d+5\,a\,b^2\,d^2\right)}{a^5\,d^5-5\,a^4\,b\,c\,d^4+10\,a^3\,b^2\,c^2\,d^3-10\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d-b^5\,c^5}}{x^2\,\left(a^3\,d^2+6\,a^2\,b\,c\,d+3\,a\,b^2\,c^2\right)+x^3\,\left(3\,a^2\,b\,d^2+6\,a\,b^2\,c\,d+b^3\,c^2\right)+x\,\left(2\,d\,a^3\,c+3\,b\,a^2\,c^2\right)+x^4\,\left(2\,c\,b^3\,d+3\,a\,b^2\,d^2\right)+a^3\,c^2+b^3\,d^2\,x^5}-\frac{20\,b^2\,d^3\,\mathrm{atanh}\left(\frac{a^6\,d^6-4\,a^5\,b\,c\,d^5+5\,a^4\,b^2\,c^2\,d^4-5\,a^2\,b^4\,c^4\,d^2+4\,a\,b^5\,c^5\,d-b^6\,c^6}{{\left(a\,d-b\,c\right)}^6}+\frac{2\,b\,d\,x\,\left(a^5\,d^5-5\,a^4\,b\,c\,d^4+10\,a^3\,b^2\,c^2\,d^3-10\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d-b^5\,c^5\right)}{{\left(a\,d-b\,c\right)}^6}\right)}{{\left(a\,d-b\,c\right)}^6}","Not used",1,"((2*b^4*c^4 - 3*a^4*d^4 + 47*a^2*b^2*c^2*d^2 - 13*a*b^3*c^3*d + 27*a^3*b*c*d^3)/(6*(a^5*d^5 - b^5*c^5 - 10*a^2*b^3*c^3*d^2 + 10*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 5*a^4*b*c*d^4)) + (5*d*x*(3*a^3*b*d^3 - b^4*c^3 + 35*a^2*b^2*c*d^2 + 11*a*b^3*c^2*d))/(6*(a^5*d^5 - b^5*c^5 - 10*a^2*b^3*c^3*d^2 + 10*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 5*a^4*b*c*d^4)) + (10*b^4*d^4*x^4)/(a^5*d^5 - b^5*c^5 - 10*a^2*b^3*c^3*d^2 + 10*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 5*a^4*b*c*d^4) + (5*d^2*x^2*(2*b^4*c^2 + 11*a^2*b^2*d^2 + 23*a*b^3*c*d))/(3*(a^5*d^5 - b^5*c^5 - 10*a^2*b^3*c^3*d^2 + 10*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 5*a^4*b*c*d^4)) + (5*b*d^2*x^3*(5*a*b^2*d^2 + 3*b^3*c*d))/(a^5*d^5 - b^5*c^5 - 10*a^2*b^3*c^3*d^2 + 10*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 5*a^4*b*c*d^4))/(x^2*(a^3*d^2 + 3*a*b^2*c^2 + 6*a^2*b*c*d) + x^3*(b^3*c^2 + 3*a^2*b*d^2 + 6*a*b^2*c*d) + x*(3*a^2*b*c^2 + 2*a^3*c*d) + x^4*(3*a*b^2*d^2 + 2*b^3*c*d) + a^3*c^2 + b^3*d^2*x^5) - (20*b^2*d^3*atanh((a^6*d^6 - b^6*c^6 - 5*a^2*b^4*c^4*d^2 + 5*a^4*b^2*c^2*d^4 + 4*a*b^5*c^5*d - 4*a^5*b*c*d^5)/(a*d - b*c)^6 + (2*b*d*x*(a^5*d^5 - b^5*c^5 - 10*a^2*b^3*c^3*d^2 + 10*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 5*a^4*b*c*d^4))/(a*d - b*c)^6))/(a*d - b*c)^6","B"
1828,1,122,39,0.060049,"\text{Not used}","int((d + e*x)^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","x^4\,\left(\frac{5\,c\,d^4\,e^2}{2}+\frac{5\,a\,d^2\,e^4}{2}\right)+x^2\,\left(\frac{c\,d^6}{2}+\frac{5\,a\,d^4\,e^2}{2}\right)+x^6\,\left(\frac{5\,c\,d^2\,e^4}{6}+\frac{a\,e^6}{6}\right)+x^5\,\left(2\,c\,d^3\,e^3+a\,d\,e^5\right)+x^3\,\left(\frac{5\,c\,d^5\,e}{3}+\frac{10\,a\,d^3\,e^3}{3}\right)+a\,d^5\,e\,x+\frac{c\,d\,e^5\,x^7}{7}","Not used",1,"x^4*((5*a*d^2*e^4)/2 + (5*c*d^4*e^2)/2) + x^2*((c*d^6)/2 + (5*a*d^4*e^2)/2) + x^6*((a*e^6)/6 + (5*c*d^2*e^4)/6) + x^5*(2*c*d^3*e^3 + a*d*e^5) + x^3*((10*a*d^3*e^3)/3 + (5*c*d^5*e)/3) + a*d^5*e*x + (c*d*e^5*x^7)/7","B"
1829,1,99,39,0.043214,"\text{Not used}","int((d + e*x)^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","x^2\,\left(\frac{c\,d^5}{2}+2\,a\,d^3\,e^2\right)+x^5\,\left(\frac{4\,c\,d^2\,e^3}{5}+\frac{a\,e^5}{5}\right)+x^4\,\left(\frac{3\,c\,d^3\,e^2}{2}+a\,d\,e^4\right)+x^3\,\left(\frac{4\,c\,d^4\,e}{3}+2\,a\,d^2\,e^3\right)+a\,d^4\,e\,x+\frac{c\,d\,e^4\,x^6}{6}","Not used",1,"x^2*((c*d^5)/2 + 2*a*d^3*e^2) + x^5*((a*e^5)/5 + (4*c*d^2*e^3)/5) + x^4*((3*c*d^3*e^2)/2 + a*d*e^4) + x^3*(2*a*d^2*e^3 + (4*c*d^4*e)/3) + a*d^4*e*x + (c*d*e^4*x^6)/6","B"
1830,1,75,39,0.549438,"\text{Not used}","int((d + e*x)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","x^2\,\left(\frac{c\,d^4}{2}+\frac{3\,a\,d^2\,e^2}{2}\right)+x^4\,\left(\frac{3\,c\,d^2\,e^2}{4}+\frac{a\,e^4}{4}\right)+x^3\,\left(c\,d^3\,e+a\,d\,e^3\right)+a\,d^3\,e\,x+\frac{c\,d\,e^3\,x^5}{5}","Not used",1,"x^2*((c*d^4)/2 + (3*a*d^2*e^2)/2) + x^4*((a*e^4)/4 + (3*c*d^2*e^2)/4) + x^3*(a*d*e^3 + c*d^3*e) + a*d^3*e*x + (c*d*e^3*x^5)/5","B"
1831,1,53,39,0.048190,"\text{Not used}","int((d + e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","x^2\,\left(\frac{c\,d^3}{2}+a\,d\,e^2\right)+x^3\,\left(\frac{2\,c\,d^2\,e}{3}+\frac{a\,e^3}{3}\right)+a\,d^2\,e\,x+\frac{c\,d\,e^2\,x^4}{4}","Not used",1,"x^2*((c*d^3)/2 + a*d*e^2) + x^3*((a*e^3)/3 + (2*c*d^2*e)/3) + a*d^2*e*x + (c*d*e^2*x^4)/4","B"
1832,1,31,34,0.039051,"\text{Not used}","int(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2,x)","\frac{c\,d\,e\,x^3}{3}+\left(\frac{c\,d^2}{2}+\frac{a\,e^2}{2}\right)\,x^2+a\,d\,e\,x","Not used",1,"x^2*((a*e^2)/2 + (c*d^2)/2) + a*d*e*x + (c*d*e*x^3)/3","B"
1833,1,12,14,0.019269,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)/(d + e*x),x)","\frac{c\,d\,x^2}{2}+a\,e\,x","Not used",1,"a*e*x + (c*d*x^2)/2","B"
1834,1,30,26,0.052339,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)/(d + e*x)^2,x)","\frac{\ln\left(d+e\,x\right)\,\left(a\,e^2-c\,d^2\right)}{e^2}+\frac{c\,d\,x}{e}","Not used",1,"(log(d + e*x)*(a*e^2 - c*d^2))/e^2 + (c*d*x)/e","B"
1835,1,37,33,0.575975,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)/(d + e*x)^3,x)","\frac{c\,d\,\ln\left(d+e\,x\right)}{e^2}-\frac{a\,e^2-c\,d^2}{e^2\,\left(d+e\,x\right)}","Not used",1,"(c*d*log(d + e*x))/e^2 - (a*e^2 - c*d^2)/(e^2*(d + e*x))","B"
1836,1,30,35,0.042544,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)/(d + e*x)^4,x)","-\frac{\frac{a}{2}-\frac{c\,x^2}{2}}{d^2+2\,d\,e\,x+e^2\,x^2}","Not used",1,"-(a/2 - (c*x^2)/2)/(d^2 + e^2*x^2 + 2*d*e*x)","B"
1837,1,57,39,0.043918,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)/(d + e*x)^5,x)","-\frac{\frac{c\,d^2+2\,a\,e^2}{6\,e^2}+\frac{c\,d\,x}{2\,e}}{d^3+3\,d^2\,e\,x+3\,d\,e^2\,x^2+e^3\,x^3}","Not used",1,"-((2*a*e^2 + c*d^2)/(6*e^2) + (c*d*x)/(2*e))/(d^3 + e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x)","B"
1838,1,68,39,0.575443,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)/(d + e*x)^6,x)","-\frac{\frac{c\,d^2+3\,a\,e^2}{12\,e^2}+\frac{c\,d\,x}{3\,e}}{d^4+4\,d^3\,e\,x+6\,d^2\,e^2\,x^2+4\,d\,e^3\,x^3+e^4\,x^4}","Not used",1,"-((3*a*e^2 + c*d^2)/(12*e^2) + (c*d*x)/(3*e))/(d^4 + e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x)","B"
1839,1,168,77,0.597928,"\text{Not used}","int((d + e*x)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","x^3\,\left(2\,a^2\,d^2\,e^4+\frac{8\,a\,c\,d^4\,e^2}{3}+\frac{c^2\,d^6}{3}\right)+x^5\,\left(\frac{a^2\,e^6}{5}+\frac{8\,a\,c\,d^2\,e^4}{5}+\frac{6\,c^2\,d^4\,e^2}{5}\right)+x^4\,\left(a^2\,d\,e^5+3\,a\,c\,d^3\,e^3+c^2\,d^5\,e\right)+a^2\,d^4\,e^2\,x+\frac{c^2\,d^2\,e^4\,x^7}{7}+a\,d^3\,e\,x^2\,\left(c\,d^2+2\,a\,e^2\right)+\frac{c\,d\,e^3\,x^6\,\left(2\,c\,d^2+a\,e^2\right)}{3}","Not used",1,"x^3*((c^2*d^6)/3 + 2*a^2*d^2*e^4 + (8*a*c*d^4*e^2)/3) + x^5*((a^2*e^6)/5 + (6*c^2*d^4*e^2)/5 + (8*a*c*d^2*e^4)/5) + x^4*(a^2*d*e^5 + c^2*d^5*e + 3*a*c*d^3*e^3) + a^2*d^4*e^2*x + (c^2*d^2*e^4*x^7)/7 + a*d^3*e*x^2*(2*a*e^2 + c*d^2) + (c*d*e^3*x^6*(a*e^2 + 2*c*d^2))/3","B"
1840,1,135,77,0.051898,"\text{Not used}","int((d + e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","x^3\,\left(a^2\,d\,e^4+2\,a\,c\,d^3\,e^2+\frac{c^2\,d^5}{3}\right)+x^4\,\left(\frac{a^2\,e^5}{4}+\frac{3\,a\,c\,d^2\,e^3}{2}+\frac{3\,c^2\,d^4\,e}{4}\right)+a^2\,d^3\,e^2\,x+\frac{c^2\,d^2\,e^3\,x^6}{6}+\frac{a\,d^2\,e\,x^2\,\left(2\,c\,d^2+3\,a\,e^2\right)}{2}+\frac{c\,d\,e^2\,x^5\,\left(3\,c\,d^2+2\,a\,e^2\right)}{5}","Not used",1,"x^3*((c^2*d^5)/3 + a^2*d*e^4 + 2*a*c*d^3*e^2) + x^4*((a^2*e^5)/4 + (3*c^2*d^4*e)/4 + (3*a*c*d^2*e^3)/2) + a^2*d^3*e^2*x + (c^2*d^2*e^3*x^6)/6 + (a*d^2*e*x^2*(3*a*e^2 + 2*c*d^2))/2 + (c*d*e^2*x^5*(2*a*e^2 + 3*c*d^2))/5","B"
1841,1,99,77,0.566651,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","x^3\,\left(\frac{a^2\,e^4}{3}+\frac{4\,a\,c\,d^2\,e^2}{3}+\frac{c^2\,d^4}{3}\right)+x^2\,\left(a^2\,d\,e^3+c\,a\,d^3\,e\right)+x^4\,\left(\frac{c^2\,d^3\,e}{2}+\frac{a\,c\,d\,e^3}{2}\right)+a^2\,d^2\,e^2\,x+\frac{c^2\,d^2\,e^2\,x^5}{5}","Not used",1,"x^3*((a^2*e^4)/3 + (c^2*d^4)/3 + (4*a*c*d^2*e^2)/3) + x^2*(a^2*d*e^3 + a*c*d^3*e) + x^4*((c^2*d^3*e)/2 + (a*c*d*e^3)/2) + a^2*d^2*e^2*x + (c^2*d^2*e^2*x^5)/5","B"
1842,1,63,54,0.575062,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2/(d + e*x),x)","x^2\,\left(\frac{a^2\,e^3}{2}+c\,a\,d^2\,e\right)+x^3\,\left(\frac{c^2\,d^3}{3}+\frac{2\,a\,c\,d\,e^2}{3}\right)+\frac{c^2\,d^2\,e\,x^4}{4}+a^2\,d\,e^2\,x","Not used",1,"x^2*((a^2*e^3)/2 + a*c*d^2*e) + x^3*((c^2*d^3)/3 + (2*a*c*d*e^2)/3) + (c^2*d^2*e*x^4)/4 + a^2*d*e^2*x","B"
1843,1,28,20,0.039941,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2/(d + e*x)^2,x)","a^2\,e^2\,x+a\,c\,d\,e\,x^2+\frac{c^2\,d^2\,x^3}{3}","Not used",1,"a^2*e^2*x + (c^2*d^2*x^3)/3 + a*c*d*e*x^2","B"
1844,1,69,62,0.071758,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2/(d + e*x)^3,x)","x\,\left(2\,a\,c\,d-\frac{c^2\,d^3}{e^2}\right)+\frac{\ln\left(d+e\,x\right)\,\left(a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{e^3}+\frac{c^2\,d^2\,x^2}{2\,e}","Not used",1,"x*(2*a*c*d - (c^2*d^3)/e^2) + (log(d + e*x)*(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2))/e^3 + (c^2*d^2*x^2)/(2*e)","B"
1845,1,83,63,0.606473,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2/(d + e*x)^4,x)","\frac{c^2\,d^2\,x}{e^2}-\frac{a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4}{e\,\left(x\,e^3+d\,e^2\right)}-\frac{\ln\left(d+e\,x\right)\,\left(2\,c^2\,d^3-2\,a\,c\,d\,e^2\right)}{e^3}","Not used",1,"(c^2*d^2*x)/e^2 - (a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2)/(e*(d*e^2 + e^3*x)) - (log(d + e*x)*(2*c^2*d^3 - 2*a*c*d*e^2))/e^3","B"
1846,1,89,71,0.595336,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2/(d + e*x)^5,x)","\frac{c^2\,d^2\,\ln\left(d+e\,x\right)}{e^3}-\frac{\frac{a^2\,e^4+2\,a\,c\,d^2\,e^2-3\,c^2\,d^4}{2\,e^3}+\frac{2\,c\,d\,x\,\left(a\,e^2-c\,d^2\right)}{e^2}}{d^2+2\,d\,e\,x+e^2\,x^2}","Not used",1,"(c^2*d^2*log(d + e*x))/e^3 - ((a^2*e^4 - 3*c^2*d^4 + 2*a*c*d^2*e^2)/(2*e^3) + (2*c*d*x*(a*e^2 - c*d^2))/e^2)/(d^2 + e^2*x^2 + 2*d*e*x)","B"
1847,1,65,35,0.571043,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2/(d + e*x)^6,x)","-\frac{\frac{a^2\,e}{3}-d\,\left(\frac{c^2\,x^3}{3}-a\,c\,x\right)+\frac{a\,c\,d^2}{3\,e}}{d^3+3\,d^2\,e\,x+3\,d\,e^2\,x^2+e^3\,x^3}","Not used",1,"-((a^2*e)/3 - d*((c^2*x^3)/3 - a*c*x) + (a*c*d^2)/(3*e))/(d^3 + e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x)","B"
1848,1,85,77,0.579720,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2/(d + e*x)^7,x)","-\frac{\frac{a^2\,e}{4}-d\,\left(\frac{c^2\,x^3}{3}-\frac{2\,a\,c\,x}{3}\right)-\frac{c^2\,e\,x^4}{12}+\frac{a\,c\,d^2}{6\,e}}{d^4+4\,d^3\,e\,x+6\,d^2\,e^2\,x^2+4\,d\,e^3\,x^3+e^4\,x^4}","Not used",1,"-((a^2*e)/4 - d*((c^2*x^3)/3 - (2*a*c*x)/3) - (c^2*e*x^4)/12 + (a*c*d^2)/(6*e))/(d^4 + e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x)","B"
1849,1,119,77,0.611890,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2/(d + e*x)^8,x)","-\frac{\frac{6\,a^2\,e^4+3\,a\,c\,d^2\,e^2+c^2\,d^4}{30\,e^3}+\frac{c^2\,d^2\,x^2}{3\,e}+\frac{c\,d\,x\,\left(c\,d^2+3\,a\,e^2\right)}{6\,e^2}}{d^5+5\,d^4\,e\,x+10\,d^3\,e^2\,x^2+10\,d^2\,e^3\,x^3+5\,d\,e^4\,x^4+e^5\,x^5}","Not used",1,"-((6*a^2*e^4 + c^2*d^4 + 3*a*c*d^2*e^2)/(30*e^3) + (c^2*d^2*x^2)/(3*e) + (c*d*x*(3*a*e^2 + c*d^2))/(6*e^2))/(d^5 + e^5*x^5 + 5*d*e^4*x^4 + 10*d^3*e^2*x^2 + 10*d^2*e^3*x^3 + 5*d^4*e*x)","B"
1850,1,130,77,0.085682,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2/(d + e*x)^9,x)","-\frac{\frac{10\,a^2\,e^4+4\,a\,c\,d^2\,e^2+c^2\,d^4}{60\,e^3}+\frac{c^2\,d^2\,x^2}{4\,e}+\frac{c\,d\,x\,\left(c\,d^2+4\,a\,e^2\right)}{10\,e^2}}{d^6+6\,d^5\,e\,x+15\,d^4\,e^2\,x^2+20\,d^3\,e^3\,x^3+15\,d^2\,e^4\,x^4+6\,d\,e^5\,x^5+e^6\,x^6}","Not used",1,"-((10*a^2*e^4 + c^2*d^4 + 4*a*c*d^2*e^2)/(60*e^3) + (c^2*d^2*x^2)/(4*e) + (c*d*x*(4*a*e^2 + c*d^2))/(10*e^2))/(d^6 + e^6*x^6 + 6*d*e^5*x^5 + 15*d^4*e^2*x^2 + 20*d^3*e^3*x^3 + 15*d^2*e^4*x^4 + 6*d^5*e*x)","B"
1851,1,295,111,0.110521,"\text{Not used}","int((d + e*x)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","x^4\,\left(\frac{5\,a^3\,d^2\,e^6}{2}+\frac{15\,a^2\,c\,d^4\,e^4}{2}+\frac{15\,a\,c^2\,d^6\,e^2}{4}+\frac{c^3\,d^8}{4}\right)+x^6\,\left(\frac{a^3\,e^8}{6}+\frac{5\,a^2\,c\,d^2\,e^6}{2}+5\,a\,c^2\,d^4\,e^4+\frac{5\,c^3\,d^6\,e^2}{3}\right)+x^5\,\left(a^3\,d\,e^7+6\,a^2\,c\,d^3\,e^5+6\,a\,c^2\,d^5\,e^3+c^3\,d^7\,e\right)+a^3\,d^5\,e^3\,x+\frac{c^3\,d^3\,e^5\,x^9}{9}+\frac{a\,d^3\,e\,x^3\,\left(10\,a^2\,e^4+15\,a\,c\,d^2\,e^2+3\,c^2\,d^4\right)}{3}+\frac{c\,d\,e^3\,x^7\,\left(3\,a^2\,e^4+15\,a\,c\,d^2\,e^2+10\,c^2\,d^4\right)}{7}+\frac{a^2\,d^4\,e^2\,x^2\,\left(3\,c\,d^2+5\,a\,e^2\right)}{2}+\frac{c^2\,d^2\,e^4\,x^8\,\left(5\,c\,d^2+3\,a\,e^2\right)}{8}","Not used",1,"x^4*((c^3*d^8)/4 + (5*a^3*d^2*e^6)/2 + (15*a*c^2*d^6*e^2)/4 + (15*a^2*c*d^4*e^4)/2) + x^6*((a^3*e^8)/6 + (5*c^3*d^6*e^2)/3 + 5*a*c^2*d^4*e^4 + (5*a^2*c*d^2*e^6)/2) + x^5*(a^3*d*e^7 + c^3*d^7*e + 6*a*c^2*d^5*e^3 + 6*a^2*c*d^3*e^5) + a^3*d^5*e^3*x + (c^3*d^3*e^5*x^9)/9 + (a*d^3*e*x^3*(10*a^2*e^4 + 3*c^2*d^4 + 15*a*c*d^2*e^2))/3 + (c*d*e^3*x^7*(3*a^2*e^4 + 10*c^2*d^4 + 15*a*c*d^2*e^2))/7 + (a^2*d^4*e^2*x^2*(5*a*e^2 + 3*c*d^2))/2 + (c^2*d^2*e^4*x^8*(3*a*e^2 + 5*c*d^2))/8","B"
1852,1,242,111,0.587141,"\text{Not used}","int((d + e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","x^4\,\left(a^3\,d\,e^6+\frac{9\,a^2\,c\,d^3\,e^4}{2}+3\,a\,c^2\,d^5\,e^2+\frac{c^3\,d^7}{4}\right)+x^5\,\left(\frac{a^3\,e^7}{5}+\frac{12\,a^2\,c\,d^2\,e^5}{5}+\frac{18\,a\,c^2\,d^4\,e^3}{5}+\frac{4\,c^3\,d^6\,e}{5}\right)+a^3\,d^4\,e^3\,x+\frac{c^3\,d^3\,e^4\,x^8}{8}+a\,d^2\,e\,x^3\,\left(2\,a^2\,e^4+4\,a\,c\,d^2\,e^2+c^2\,d^4\right)+\frac{c\,d\,e^2\,x^6\,\left(a^2\,e^4+4\,a\,c\,d^2\,e^2+2\,c^2\,d^4\right)}{2}+\frac{a^2\,d^3\,e^2\,x^2\,\left(3\,c\,d^2+4\,a\,e^2\right)}{2}+\frac{c^2\,d^2\,e^3\,x^7\,\left(4\,c\,d^2+3\,a\,e^2\right)}{7}","Not used",1,"x^4*((c^3*d^7)/4 + a^3*d*e^6 + 3*a*c^2*d^5*e^2 + (9*a^2*c*d^3*e^4)/2) + x^5*((a^3*e^7)/5 + (4*c^3*d^6*e)/5 + (18*a*c^2*d^4*e^3)/5 + (12*a^2*c*d^2*e^5)/5) + a^3*d^4*e^3*x + (c^3*d^3*e^4*x^8)/8 + a*d^2*e*x^3*(2*a^2*e^4 + c^2*d^4 + 4*a*c*d^2*e^2) + (c*d*e^2*x^6*(a^2*e^4 + 2*c^2*d^4 + 4*a*c*d^2*e^2))/2 + (a^2*d^3*e^2*x^2*(4*a*e^2 + 3*c*d^2))/2 + (c^2*d^2*e^3*x^7*(3*a*e^2 + 4*c*d^2))/7","B"
1853,1,186,111,0.599004,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","x^4\,\left(\frac{a^3\,e^6}{4}+\frac{9\,a^2\,c\,d^2\,e^4}{4}+\frac{9\,a\,c^2\,d^4\,e^2}{4}+\frac{c^3\,d^6}{4}\right)+a^3\,d^3\,e^3\,x+\frac{c^3\,d^3\,e^3\,x^7}{7}+a\,d\,e\,x^3\,\left(a^2\,e^4+3\,a\,c\,d^2\,e^2+c^2\,d^4\right)+\frac{3\,c\,d\,e\,x^5\,\left(a^2\,e^4+3\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{5}+\frac{3\,a^2\,d^2\,e^2\,x^2\,\left(c\,d^2+a\,e^2\right)}{2}+\frac{c^2\,d^2\,e^2\,x^6\,\left(c\,d^2+a\,e^2\right)}{2}","Not used",1,"x^4*((a^3*e^6)/4 + (c^3*d^6)/4 + (9*a*c^2*d^4*e^2)/4 + (9*a^2*c*d^2*e^4)/4) + a^3*d^3*e^3*x + (c^3*d^3*e^3*x^7)/7 + a*d*e*x^3*(a^2*e^4 + c^2*d^4 + 3*a*c*d^2*e^2) + (3*c*d*e*x^5*(a^2*e^4 + c^2*d^4 + 3*a*c*d^2*e^2))/5 + (3*a^2*d^2*e^2*x^2*(a*e^2 + c*d^2))/2 + (c^2*d^2*e^2*x^6*(a*e^2 + c*d^2))/2","B"
1854,1,145,91,0.055257,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x),x)","x^3\,\left(\frac{a^3\,e^5}{3}+2\,a^2\,c\,d^2\,e^3+a\,c^2\,d^4\,e\right)+x^4\,\left(\frac{3\,a^2\,c\,d\,e^4}{4}+\frac{3\,a\,c^2\,d^3\,e^2}{2}+\frac{c^3\,d^5}{4}\right)+a^3\,d^2\,e^3\,x+\frac{c^3\,d^3\,e^2\,x^6}{6}+\frac{a^2\,d\,e^2\,x^2\,\left(3\,c\,d^2+2\,a\,e^2\right)}{2}+\frac{c^2\,d^2\,e\,x^5\,\left(2\,c\,d^2+3\,a\,e^2\right)}{5}","Not used",1,"x^3*((a^3*e^5)/3 + 2*a^2*c*d^2*e^3 + a*c^2*d^4*e) + x^4*((c^3*d^5)/4 + (3*a*c^2*d^3*e^2)/2 + (3*a^2*c*d*e^4)/4) + a^3*d^2*e^3*x + (c^3*d^3*e^2*x^6)/6 + (a^2*d*e^2*x^2*(2*a*e^2 + 3*c*d^2))/2 + (c^2*d^2*e*x^5*(3*a*e^2 + 2*c*d^2))/5","B"
1855,1,91,54,0.560732,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^2,x)","x^2\,\left(\frac{a^3\,e^4}{2}+\frac{3\,c\,a^2\,d^2\,e^2}{2}\right)+x^4\,\left(\frac{c^3\,d^4}{4}+\frac{3\,a\,c^2\,d^2\,e^2}{4}\right)+\frac{c^3\,d^3\,e\,x^5}{5}+a^3\,d\,e^3\,x+a\,c\,d\,e\,x^3\,\left(c\,d^2+a\,e^2\right)","Not used",1,"x^2*((a^3*e^4)/2 + (3*a^2*c*d^2*e^2)/2) + x^4*((c^3*d^4)/4 + (3*a*c^2*d^2*e^2)/4) + (c^3*d^3*e*x^5)/5 + a^3*d*e^3*x + a*c*d*e*x^3*(a*e^2 + c*d^2)","B"
1856,1,45,20,0.054005,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^3,x)","a^3\,e^3\,x+\frac{3\,a^2\,c\,d\,e^2\,x^2}{2}+a\,c^2\,d^2\,e\,x^3+\frac{c^3\,d^3\,x^4}{4}","Not used",1,"a^3*e^3*x + (c^3*d^3*x^4)/4 + (3*a^2*c*d*e^2*x^2)/2 + a*c^2*d^2*e*x^3","B"
1857,1,128,89,0.059990,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^4,x)","x^2\,\left(\frac{3\,a\,c^2\,d^2}{2}-\frac{c^3\,d^4}{2\,e^2}\right)-x\,\left(\frac{d\,\left(3\,a\,c^2\,d^2-\frac{c^3\,d^4}{e^2}\right)}{e}-3\,a^2\,c\,d\,e\right)+\frac{\ln\left(d+e\,x\right)\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}{e^4}+\frac{c^3\,d^3\,x^3}{3\,e}","Not used",1,"x^2*((3*a*c^2*d^2)/2 - (c^3*d^4)/(2*e^2)) - x*((d*(3*a*c^2*d^2 - (c^3*d^4)/e^2))/e - 3*a^2*c*d*e) + (log(d + e*x)*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4))/e^4 + (c^3*d^3*x^3)/(3*e)","B"
1858,1,141,94,0.077920,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^5,x)","\frac{\ln\left(d+e\,x\right)\,\left(3\,a^2\,c\,d\,e^4-6\,a\,c^2\,d^3\,e^2+3\,c^3\,d^5\right)}{e^4}-\frac{a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6}{e\,\left(x\,e^4+d\,e^3\right)}-x\,\left(\frac{2\,c^3\,d^4}{e^3}-\frac{3\,a\,c^2\,d^2}{e}\right)+\frac{c^3\,d^3\,x^2}{2\,e^2}","Not used",1,"(log(d + e*x)*(3*c^3*d^5 - 6*a*c^2*d^3*e^2 + 3*a^2*c*d*e^4))/e^4 - (a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4)/(e*(d*e^3 + e^4*x)) - x*((2*c^3*d^4)/e^3 - (3*a*c^2*d^2)/e) + (c^3*d^3*x^2)/(2*e^2)","B"
1859,1,149,97,0.119401,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^6,x)","\frac{c^3\,d^3\,x}{e^3}-\frac{\ln\left(d+e\,x\right)\,\left(3\,c^3\,d^4-3\,a\,c^2\,d^2\,e^2\right)}{e^4}-\frac{\frac{a^3\,e^6+3\,a^2\,c\,d^2\,e^4-9\,a\,c^2\,d^4\,e^2+5\,c^3\,d^6}{2\,e}+x\,\left(3\,a^2\,c\,d\,e^4-6\,a\,c^2\,d^3\,e^2+3\,c^3\,d^5\right)}{d^2\,e^3+2\,d\,e^4\,x+e^5\,x^2}","Not used",1,"(c^3*d^3*x)/e^3 - (log(d + e*x)*(3*c^3*d^4 - 3*a*c^2*d^2*e^2))/e^4 - ((a^3*e^6 + 5*c^3*d^6 - 9*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)/(2*e) + x*(3*c^3*d^5 - 6*a*c^2*d^3*e^2 + 3*a^2*c*d*e^4))/(d^2*e^3 + e^5*x^2 + 2*d*e^4*x)","B"
1860,1,157,105,0.626516,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^7,x)","\frac{c^3\,d^3\,\ln\left(d+e\,x\right)}{e^4}-\frac{\frac{2\,a^3\,e^6+3\,a^2\,c\,d^2\,e^4+6\,a\,c^2\,d^4\,e^2-11\,c^3\,d^6}{6\,e^4}+\frac{3\,x\,\left(a^2\,c\,d\,e^4+2\,a\,c^2\,d^3\,e^2-3\,c^3\,d^5\right)}{2\,e^3}+\frac{3\,c^2\,d^2\,x^2\,\left(a\,e^2-c\,d^2\right)}{e^2}}{d^3+3\,d^2\,e\,x+3\,d\,e^2\,x^2+e^3\,x^3}","Not used",1,"(c^3*d^3*log(d + e*x))/e^4 - ((2*a^3*e^6 - 11*c^3*d^6 + 6*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4)/(6*e^4) + (3*x*(2*a*c^2*d^3*e^2 - 3*c^3*d^5 + a^2*c*d*e^4))/(2*e^3) + (3*c^2*d^2*x^2*(a*e^2 - c*d^2))/e^2)/(d^3 + e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x)","B"
1861,1,102,35,0.609905,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^8,x)","-\frac{d\,\left(a^2\,c\,e\,x-a\,c^2\,e\,x^3\right)+\frac{a^3\,e^2}{4}+d^2\,\left(\frac{a^2\,c}{4}-\frac{c^3\,x^4}{4}\right)-\frac{a\,c^2\,e^2\,x^4}{4}}{d^4+4\,d^3\,e\,x+6\,d^2\,e^2\,x^2+4\,d\,e^3\,x^3+e^4\,x^4}","Not used",1,"-(d*(a^2*c*e*x - a*c^2*e*x^3) + (a^3*e^2)/4 + d^2*((a^2*c)/4 - (c^3*x^4)/4) - (a*c^2*e^2*x^4)/4)/(d^4 + e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x)","B"
1862,1,135,73,0.603506,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^9,x)","-\frac{d^2\,\left(\frac{3\,a^2\,c}{20}+a\,c^2\,x^2-\frac{c^3\,x^4}{4}\right)-d\,\left(\frac{c^3\,e\,x^5}{20}-\frac{3\,a^2\,c\,e\,x}{4}\right)+\frac{a^3\,e^2}{5}+\frac{a\,c^2\,d^4}{10\,e^2}+\frac{a\,c^2\,d^3\,x}{2\,e}}{d^5+5\,d^4\,e\,x+10\,d^3\,e^2\,x^2+10\,d^2\,e^3\,x^3+5\,d\,e^4\,x^4+e^5\,x^5}","Not used",1,"-(d^2*((3*a^2*c)/20 - (c^3*x^4)/4 + a*c^2*x^2) - d*((c^3*e*x^5)/20 - (3*a^2*c*e*x)/4) + (a^3*e^2)/5 + (a*c^2*d^4)/(10*e^2) + (a*c^2*d^3*x)/(2*e))/(d^5 + e^5*x^5 + 5*d*e^4*x^4 + 10*d^3*e^2*x^2 + 10*d^2*e^3*x^3 + 5*d^4*e*x)","B"
1863,1,184,111,0.624879,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^10,x)","-\frac{\frac{10\,a^3\,e^6+6\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6}{60\,e^4}+\frac{c^3\,d^3\,x^3}{3\,e}+\frac{c\,d\,x\,\left(6\,a^2\,e^4+3\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{10\,e^3}+\frac{c^2\,d^2\,x^2\,\left(c\,d^2+3\,a\,e^2\right)}{4\,e^2}}{d^6+6\,d^5\,e\,x+15\,d^4\,e^2\,x^2+20\,d^3\,e^3\,x^3+15\,d^2\,e^4\,x^4+6\,d\,e^5\,x^5+e^6\,x^6}","Not used",1,"-((10*a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 6*a^2*c*d^2*e^4)/(60*e^4) + (c^3*d^3*x^3)/(3*e) + (c*d*x*(6*a^2*e^4 + c^2*d^4 + 3*a*c*d^2*e^2))/(10*e^3) + (c^2*d^2*x^2*(3*a*e^2 + c*d^2))/(4*e^2))/(d^6 + e^6*x^6 + 6*d*e^5*x^5 + 15*d^4*e^2*x^2 + 20*d^3*e^3*x^3 + 15*d^2*e^4*x^4 + 6*d^5*e*x)","B"
1864,1,195,111,0.082998,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^11,x)","-\frac{\frac{20\,a^3\,e^6+10\,a^2\,c\,d^2\,e^4+4\,a\,c^2\,d^4\,e^2+c^3\,d^6}{140\,e^4}+\frac{c^3\,d^3\,x^3}{4\,e}+\frac{c\,d\,x\,\left(10\,a^2\,e^4+4\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{20\,e^3}+\frac{3\,c^2\,d^2\,x^2\,\left(c\,d^2+4\,a\,e^2\right)}{20\,e^2}}{d^7+7\,d^6\,e\,x+21\,d^5\,e^2\,x^2+35\,d^4\,e^3\,x^3+35\,d^3\,e^4\,x^4+21\,d^2\,e^5\,x^5+7\,d\,e^6\,x^6+e^7\,x^7}","Not used",1,"-((20*a^3*e^6 + c^3*d^6 + 4*a*c^2*d^4*e^2 + 10*a^2*c*d^2*e^4)/(140*e^4) + (c^3*d^3*x^3)/(4*e) + (c*d*x*(10*a^2*e^4 + c^2*d^4 + 4*a*c*d^2*e^2))/(20*e^3) + (3*c^2*d^2*x^2*(4*a*e^2 + c*d^2))/(20*e^2))/(d^7 + e^7*x^7 + 7*d*e^6*x^6 + 21*d^5*e^2*x^2 + 35*d^4*e^3*x^3 + 35*d^3*e^4*x^4 + 21*d^2*e^5*x^5 + 7*d^6*e*x)","B"
1865,1,217,131,0.594357,"\text{Not used}","int((d + e*x)^5/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","x^3\,\left(\frac{4\,e^3}{3\,c}-\frac{a\,e^5}{3\,c^2\,d^2}\right)+x\,\left(\frac{4\,d^2\,e}{c}-\frac{a\,e\,\left(\frac{6\,d\,e^2}{c}-\frac{a\,e\,\left(\frac{4\,e^3}{c}-\frac{a\,e^5}{c^2\,d^2}\right)}{c\,d}\right)}{c\,d}\right)+x^2\,\left(\frac{3\,d\,e^2}{c}-\frac{a\,e\,\left(\frac{4\,e^3}{c}-\frac{a\,e^5}{c^2\,d^2}\right)}{2\,c\,d}\right)+\frac{\ln\left(a\,e+c\,d\,x\right)\,\left(a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8\right)}{c^5\,d^5}+\frac{e^4\,x^4}{4\,c\,d}","Not used",1,"x^3*((4*e^3)/(3*c) - (a*e^5)/(3*c^2*d^2)) + x*((4*d^2*e)/c - (a*e*((6*d*e^2)/c - (a*e*((4*e^3)/c - (a*e^5)/(c^2*d^2)))/(c*d)))/(c*d)) + x^2*((3*d*e^2)/c - (a*e*((4*e^3)/c - (a*e^5)/(c^2*d^2)))/(2*c*d)) + (log(a*e + c*d*x)*(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4))/(c^5*d^5) + (e^4*x^4)/(4*c*d)","B"
1866,1,138,100,0.592565,"\text{Not used}","int((d + e*x)^4/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","x\,\left(\frac{3\,d\,e}{c}-\frac{a\,e\,\left(\frac{3\,e^2}{c}-\frac{a\,e^4}{c^2\,d^2}\right)}{c\,d}\right)+x^2\,\left(\frac{3\,e^2}{2\,c}-\frac{a\,e^4}{2\,c^2\,d^2}\right)+\frac{e^3\,x^3}{3\,c\,d}-\frac{\ln\left(a\,e+c\,d\,x\right)\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}{c^4\,d^4}","Not used",1,"x*((3*d*e)/c - (a*e*((3*e^2)/c - (a*e^4)/(c^2*d^2)))/(c*d)) + x^2*((3*e^2)/(2*c) - (a*e^4)/(2*c^2*d^2)) + (e^3*x^3)/(3*c*d) - (log(a*e + c*d*x)*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4))/(c^4*d^4)","B"
1867,1,77,69,0.071320,"\text{Not used}","int((d + e*x)^3/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","x\,\left(\frac{2\,e}{c}-\frac{a\,e^3}{c^2\,d^2}\right)+\frac{\ln\left(a\,e+c\,d\,x\right)\,\left(a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{c^3\,d^3}+\frac{e^2\,x^2}{2\,c\,d}","Not used",1,"x*((2*e)/c - (a*e^3)/(c^2*d^2)) + (log(a*e + c*d*x)*(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2))/(c^3*d^3) + (e^2*x^2)/(2*c*d)","B"
1868,1,39,38,0.057012,"\text{Not used}","int((d + e*x)^2/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","\frac{e\,x}{c\,d}-\frac{\ln\left(a\,e+c\,d\,x\right)\,\left(a\,e^2-c\,d^2\right)}{c^2\,d^2}","Not used",1,"(e*x)/(c*d) - (log(a*e + c*d*x)*(a*e^2 - c*d^2))/(c^2*d^2)","B"
1869,1,16,16,0.564624,"\text{Not used}","int((d + e*x)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","\frac{\ln\left(a\,e+c\,d\,x\right)}{c\,d}","Not used",1,"log(a*e + c*d*x)/(c*d)","B"
1870,1,51,47,0.086917,"\text{Not used}","int(1/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","\frac{\mathrm{atan}\left(\frac{2{}\mathrm{i}\,c\,d^2+2{}\mathrm{i}\,c\,e\,x\,d}{a\,e^2-c\,d^2}+1{}\mathrm{i}\right)\,2{}\mathrm{i}}{a\,e^2-c\,d^2}","Not used",1,"(atan((c*d^2*2i + c*d*e*x*2i)/(a*e^2 - c*d^2) + 1i)*2i)/(a*e^2 - c*d^2)","B"
1871,1,95,73,0.133221,"\text{Not used}","int(1/((d + e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)),x)","\frac{2\,c\,d\,\mathrm{atanh}\left(\frac{a^2\,e^4-c^2\,d^4}{{\left(a\,e^2-c\,d^2\right)}^2}+\frac{2\,c\,d\,e\,x}{a\,e^2-c\,d^2}\right)}{{\left(a\,e^2-c\,d^2\right)}^2}-\frac{1}{\left(a\,e^2-c\,d^2\right)\,\left(d+e\,x\right)}","Not used",1,"(2*c*d*atanh((a^2*e^4 - c^2*d^4)/(a*e^2 - c*d^2)^2 + (2*c*d*e*x)/(a*e^2 - c*d^2)))/(a*e^2 - c*d^2)^2 - 1/((a*e^2 - c*d^2)*(d + e*x))","B"
1872,1,220,108,0.699487,"\text{Not used}","int(1/((d + e*x)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)),x)","-\frac{\frac{a\,e^2-3\,c\,d^2}{2\,\left(a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}-\frac{c\,d\,e\,x}{a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4}}{d^2+2\,d\,e\,x+e^2\,x^2}-\frac{2\,c^2\,d^2\,\mathrm{atanh}\left(\frac{a^3\,e^6-a^2\,c\,d^2\,e^4-a\,c^2\,d^4\,e^2+c^3\,d^6}{{\left(a\,e^2-c\,d^2\right)}^3}+\frac{2\,c\,d\,e\,x\,\left(a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{{\left(a\,e^2-c\,d^2\right)}^3}\right)}{{\left(a\,e^2-c\,d^2\right)}^3}","Not used",1,"- ((a*e^2 - 3*c*d^2)/(2*(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2)) - (c*d*e*x)/(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2))/(d^2 + e^2*x^2 + 2*d*e*x) - (2*c^2*d^2*atanh((a^3*e^6 + c^3*d^6 - a*c^2*d^4*e^2 - a^2*c*d^2*e^4)/(a*e^2 - c*d^2)^3 + (2*c*d*e*x*(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2))/(a*e^2 - c*d^2)^3))/(a*e^2 - c*d^2)^3","B"
1873,1,359,139,0.760896,"\text{Not used}","int(1/((d + e*x)^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)),x)","\frac{2\,c^3\,d^3\,\mathrm{atanh}\left(\frac{a^4\,e^8-2\,a^3\,c\,d^2\,e^6+2\,a\,c^3\,d^6\,e^2-c^4\,d^8}{{\left(a\,e^2-c\,d^2\right)}^4}+\frac{2\,c\,d\,e\,x\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}{{\left(a\,e^2-c\,d^2\right)}^4}\right)}{{\left(a\,e^2-c\,d^2\right)}^4}-\frac{\frac{2\,a^2\,e^4-7\,a\,c\,d^2\,e^2+11\,c^2\,d^4}{6\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}-\frac{c\,d\,x\,\left(a\,e^3-5\,c\,d^2\,e\right)}{2\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}+\frac{c^2\,d^2\,e^2\,x^2}{a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6}}{d^3+3\,d^2\,e\,x+3\,d\,e^2\,x^2+e^3\,x^3}","Not used",1,"(2*c^3*d^3*atanh((a^4*e^8 - c^4*d^8 + 2*a*c^3*d^6*e^2 - 2*a^3*c*d^2*e^6)/(a*e^2 - c*d^2)^4 + (2*c*d*e*x*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4))/(a*e^2 - c*d^2)^4))/(a*e^2 - c*d^2)^4 - ((2*a^2*e^4 + 11*c^2*d^4 - 7*a*c*d^2*e^2)/(6*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4)) - (c*d*x*(a*e^3 - 5*c*d^2*e))/(2*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4)) + (c^2*d^2*e^2*x^2)/(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4))/(d^3 + e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x)","B"
1874,1,625,219,0.107701,"\text{Not used}","int((d + e*x)^8/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","x^4\,\left(\frac{3\,e^5}{2\,c^2\,d}-\frac{a\,e^7}{2\,c^3\,d^3}\right)+x^2\,\left(\frac{10\,d\,e^3}{c^2}+\frac{a\,e\,\left(\frac{a^2\,e^8}{c^4\,d^4}-\frac{15\,e^4}{c^2}+\frac{2\,a\,e\,\left(\frac{6\,e^5}{c^2\,d}-\frac{2\,a\,e^7}{c^3\,d^3}\right)}{c\,d}\right)}{c\,d}-\frac{a^2\,e^2\,\left(\frac{6\,e^5}{c^2\,d}-\frac{2\,a\,e^7}{c^3\,d^3}\right)}{2\,c^2\,d^2}\right)-x^3\,\left(\frac{a^2\,e^8}{3\,c^4\,d^4}-\frac{5\,e^4}{c^2}+\frac{2\,a\,e\,\left(\frac{6\,e^5}{c^2\,d}-\frac{2\,a\,e^7}{c^3\,d^3}\right)}{3\,c\,d}\right)+x\,\left(\frac{15\,d^2\,e^2}{c^2}+\frac{a^2\,e^2\,\left(\frac{a^2\,e^8}{c^4\,d^4}-\frac{15\,e^4}{c^2}+\frac{2\,a\,e\,\left(\frac{6\,e^5}{c^2\,d}-\frac{2\,a\,e^7}{c^3\,d^3}\right)}{c\,d}\right)}{c^2\,d^2}-\frac{2\,a\,e\,\left(\frac{20\,d\,e^3}{c^2}+\frac{2\,a\,e\,\left(\frac{a^2\,e^8}{c^4\,d^4}-\frac{15\,e^4}{c^2}+\frac{2\,a\,e\,\left(\frac{6\,e^5}{c^2\,d}-\frac{2\,a\,e^7}{c^3\,d^3}\right)}{c\,d}\right)}{c\,d}-\frac{a^2\,e^2\,\left(\frac{6\,e^5}{c^2\,d}-\frac{2\,a\,e^7}{c^3\,d^3}\right)}{c^2\,d^2}\right)}{c\,d}\right)-\frac{a^6\,e^{12}-6\,a^5\,c\,d^2\,e^{10}+15\,a^4\,c^2\,d^4\,e^8-20\,a^3\,c^3\,d^6\,e^6+15\,a^2\,c^4\,d^8\,e^4-6\,a\,c^5\,d^{10}\,e^2+c^6\,d^{12}}{c\,d\,\left(x\,c^7\,d^7+a\,e\,c^6\,d^6\right)}+\frac{e^6\,x^5}{5\,c^2\,d^2}-\frac{\ln\left(a\,e+c\,d\,x\right)\,\left(6\,a^5\,e^{11}-30\,a^4\,c\,d^2\,e^9+60\,a^3\,c^2\,d^4\,e^7-60\,a^2\,c^3\,d^6\,e^5+30\,a\,c^4\,d^8\,e^3-6\,c^5\,d^{10}\,e\right)}{c^7\,d^7}","Not used",1,"x^4*((3*e^5)/(2*c^2*d) - (a*e^7)/(2*c^3*d^3)) + x^2*((10*d*e^3)/c^2 + (a*e*((a^2*e^8)/(c^4*d^4) - (15*e^4)/c^2 + (2*a*e*((6*e^5)/(c^2*d) - (2*a*e^7)/(c^3*d^3)))/(c*d)))/(c*d) - (a^2*e^2*((6*e^5)/(c^2*d) - (2*a*e^7)/(c^3*d^3)))/(2*c^2*d^2)) - x^3*((a^2*e^8)/(3*c^4*d^4) - (5*e^4)/c^2 + (2*a*e*((6*e^5)/(c^2*d) - (2*a*e^7)/(c^3*d^3)))/(3*c*d)) + x*((15*d^2*e^2)/c^2 + (a^2*e^2*((a^2*e^8)/(c^4*d^4) - (15*e^4)/c^2 + (2*a*e*((6*e^5)/(c^2*d) - (2*a*e^7)/(c^3*d^3)))/(c*d)))/(c^2*d^2) - (2*a*e*((20*d*e^3)/c^2 + (2*a*e*((a^2*e^8)/(c^4*d^4) - (15*e^4)/c^2 + (2*a*e*((6*e^5)/(c^2*d) - (2*a*e^7)/(c^3*d^3)))/(c*d)))/(c*d) - (a^2*e^2*((6*e^5)/(c^2*d) - (2*a*e^7)/(c^3*d^3)))/(c^2*d^2)))/(c*d)) - (a^6*e^12 + c^6*d^12 - 6*a*c^5*d^10*e^2 - 6*a^5*c*d^2*e^10 + 15*a^2*c^4*d^8*e^4 - 20*a^3*c^3*d^6*e^6 + 15*a^4*c^2*d^4*e^8)/(c*d*(c^7*d^7*x + a*c^6*d^6*e)) + (e^6*x^5)/(5*c^2*d^2) - (log(a*e + c*d*x)*(6*a^5*e^11 - 6*c^5*d^10*e + 30*a*c^4*d^8*e^3 - 30*a^4*c*d^2*e^9 - 60*a^2*c^3*d^6*e^5 + 60*a^3*c^2*d^4*e^7))/(c^7*d^7)","B"
1875,1,387,184,0.603255,"\text{Not used}","int((d + e*x)^7/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","x\,\left(\frac{10\,d\,e^2}{c^2}+\frac{2\,a\,e\,\left(\frac{a^2\,e^7}{c^4\,d^4}-\frac{10\,e^3}{c^2}+\frac{2\,a\,e\,\left(\frac{5\,e^4}{c^2\,d}-\frac{2\,a\,e^6}{c^3\,d^3}\right)}{c\,d}\right)}{c\,d}-\frac{a^2\,e^2\,\left(\frac{5\,e^4}{c^2\,d}-\frac{2\,a\,e^6}{c^3\,d^3}\right)}{c^2\,d^2}\right)+x^3\,\left(\frac{5\,e^4}{3\,c^2\,d}-\frac{2\,a\,e^6}{3\,c^3\,d^3}\right)-x^2\,\left(\frac{a^2\,e^7}{2\,c^4\,d^4}-\frac{5\,e^3}{c^2}+\frac{a\,e\,\left(\frac{5\,e^4}{c^2\,d}-\frac{2\,a\,e^6}{c^3\,d^3}\right)}{c\,d}\right)+\frac{e^5\,x^4}{4\,c^2\,d^2}+\frac{\ln\left(a\,e+c\,d\,x\right)\,\left(5\,a^4\,e^9-20\,a^3\,c\,d^2\,e^7+30\,a^2\,c^2\,d^4\,e^5-20\,a\,c^3\,d^6\,e^3+5\,c^4\,d^8\,e\right)}{c^6\,d^6}+\frac{a^5\,e^{10}-5\,a^4\,c\,d^2\,e^8+10\,a^3\,c^2\,d^4\,e^6-10\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2-c^5\,d^{10}}{c\,d\,\left(x\,c^6\,d^6+a\,e\,c^5\,d^5\right)}","Not used",1,"x*((10*d*e^2)/c^2 + (2*a*e*((a^2*e^7)/(c^4*d^4) - (10*e^3)/c^2 + (2*a*e*((5*e^4)/(c^2*d) - (2*a*e^6)/(c^3*d^3)))/(c*d)))/(c*d) - (a^2*e^2*((5*e^4)/(c^2*d) - (2*a*e^6)/(c^3*d^3)))/(c^2*d^2)) + x^3*((5*e^4)/(3*c^2*d) - (2*a*e^6)/(3*c^3*d^3)) - x^2*((a^2*e^7)/(2*c^4*d^4) - (5*e^3)/c^2 + (a*e*((5*e^4)/(c^2*d) - (2*a*e^6)/(c^3*d^3)))/(c*d)) + (e^5*x^4)/(4*c^2*d^2) + (log(a*e + c*d*x)*(5*a^4*e^9 + 5*c^4*d^8*e - 20*a*c^3*d^6*e^3 - 20*a^3*c*d^2*e^7 + 30*a^2*c^2*d^4*e^5))/(c^6*d^6) + (a^5*e^10 - c^5*d^10 + 5*a*c^4*d^8*e^2 - 5*a^4*c*d^2*e^8 - 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6)/(c*d*(c^6*d^6*x + a*c^5*d^5*e))","B"
1876,1,242,145,0.598380,"\text{Not used}","int((d + e*x)^6/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","x^2\,\left(\frac{2\,e^3}{c^2\,d}-\frac{a\,e^5}{c^3\,d^3}\right)-x\,\left(\frac{a^2\,e^6}{c^4\,d^4}-\frac{6\,e^2}{c^2}+\frac{2\,a\,e\,\left(\frac{4\,e^3}{c^2\,d}-\frac{2\,a\,e^5}{c^3\,d^3}\right)}{c\,d}\right)-\frac{\ln\left(a\,e+c\,d\,x\right)\,\left(4\,a^3\,e^7-12\,a^2\,c\,d^2\,e^5+12\,a\,c^2\,d^4\,e^3-4\,c^3\,d^6\,e\right)}{c^5\,d^5}-\frac{a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8}{c\,d\,\left(x\,c^5\,d^5+a\,e\,c^4\,d^4\right)}+\frac{e^4\,x^3}{3\,c^2\,d^2}","Not used",1,"x^2*((2*e^3)/(c^2*d) - (a*e^5)/(c^3*d^3)) - x*((a^2*e^6)/(c^4*d^4) - (6*e^2)/c^2 + (2*a*e*((4*e^3)/(c^2*d) - (2*a*e^5)/(c^3*d^3)))/(c*d)) - (log(a*e + c*d*x)*(4*a^3*e^7 - 4*c^3*d^6*e + 12*a*c^2*d^4*e^3 - 12*a^2*c*d^2*e^5))/(c^5*d^5) - (a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4)/(c*d*(c^5*d^5*x + a*c^4*d^4*e)) + (e^4*x^3)/(3*c^2*d^2)","B"
1877,1,152,105,0.080036,"\text{Not used}","int((d + e*x)^5/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","x\,\left(\frac{3\,e^2}{c^2\,d}-\frac{2\,a\,e^4}{c^3\,d^3}\right)+\frac{e^3\,x^2}{2\,c^2\,d^2}+\frac{\ln\left(a\,e+c\,d\,x\right)\,\left(3\,a^2\,e^5-6\,a\,c\,d^2\,e^3+3\,c^2\,d^4\,e\right)}{c^4\,d^4}+\frac{a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6}{c\,d\,\left(x\,c^4\,d^4+a\,e\,c^3\,d^3\right)}","Not used",1,"x*((3*e^2)/(c^2*d) - (2*a*e^4)/(c^3*d^3)) + (e^3*x^2)/(2*c^2*d^2) + (log(a*e + c*d*x)*(3*a^2*e^5 + 3*c^2*d^4*e - 6*a*c*d^2*e^3))/(c^4*d^4) + (a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4)/(c*d*(c^4*d^4*x + a*c^3*d^3*e))","B"
1878,1,96,74,0.615161,"\text{Not used}","int((d + e*x)^4/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","\frac{e^2\,x}{c^2\,d^2}-\frac{\ln\left(a\,e+c\,d\,x\right)\,\left(2\,a\,e^3-2\,c\,d^2\,e\right)}{c^3\,d^3}-\frac{a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4}{c\,d\,\left(x\,c^3\,d^3+a\,e\,c^2\,d^2\right)}","Not used",1,"(e^2*x)/(c^2*d^2) - (log(a*e + c*d*x)*(2*a*e^3 - 2*c*d^2*e))/(c^3*d^3) - (a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2)/(c*d*(c^3*d^3*x + a*c^2*d^2*e))","B"
1879,1,47,48,0.065532,"\text{Not used}","int((d + e*x)^3/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","\frac{a\,e^2-c\,d^2}{c^2\,d^2\,\left(a\,e+c\,d\,x\right)}+\frac{e\,\ln\left(a\,e+c\,d\,x\right)}{c^2\,d^2}","Not used",1,"(a*e^2 - c*d^2)/(c^2*d^2*(a*e + c*d*x)) + (e*log(a*e + c*d*x))/(c^2*d^2)","B"
1880,1,18,18,0.546110,"\text{Not used}","int((d + e*x)^2/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","-\frac{1}{c\,d\,\left(a\,e+c\,d\,x\right)}","Not used",1,"-1/(c*d*(a*e + c*d*x))","B"
1881,1,96,75,0.634038,"\text{Not used}","int((d + e*x)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","\frac{1}{\left(a\,e+c\,d\,x\right)\,\left(a\,e^2-c\,d^2\right)}-\frac{2\,e\,\mathrm{atanh}\left(\frac{a^2\,e^4-c^2\,d^4}{{\left(a\,e^2-c\,d^2\right)}^2}+\frac{2\,c\,d\,e\,x}{a\,e^2-c\,d^2}\right)}{{\left(a\,e^2-c\,d^2\right)}^2}","Not used",1,"1/((a*e + c*d*x)*(a*e^2 - c*d^2)) - (2*e*atanh((a^2*e^4 - c^2*d^4)/(a*e^2 - c*d^2)^2 + (2*c*d*e*x)/(a*e^2 - c*d^2)))/(a*e^2 - c*d^2)^2","B"
1882,1,223,114,0.787103,"\text{Not used}","int(1/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","\frac{4\,c\,d\,e\,\mathrm{atanh}\left(\frac{a^3\,e^6-a^2\,c\,d^2\,e^4-a\,c^2\,d^4\,e^2+c^3\,d^6}{{\left(a\,e^2-c\,d^2\right)}^3}+\frac{2\,c\,d\,e\,x\,\left(a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{{\left(a\,e^2-c\,d^2\right)}^3}\right)}{{\left(a\,e^2-c\,d^2\right)}^3}-\frac{\frac{c\,d^2+a\,e^2}{a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4}+\frac{2\,c\,d\,e\,x}{a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4}}{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}","Not used",1,"(4*c*d*e*atanh((a^3*e^6 + c^3*d^6 - a*c^2*d^4*e^2 - a^2*c*d^2*e^4)/(a*e^2 - c*d^2)^3 + (2*c*d*e*x*(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2))/(a*e^2 - c*d^2)^3))/(a*e^2 - c*d^2)^3 - ((a*e^2 + c*d^2)/(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2) + (2*c*d*e*x)/(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2))/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)","B"
1883,1,381,146,0.780030,"\text{Not used}","int(1/((d + e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2),x)","\frac{\frac{-a^2\,e^4+5\,a\,c\,d^2\,e^2+2\,c^2\,d^4}{2\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}+\frac{3\,c\,d\,x\,\left(3\,c\,d^2\,e+a\,e^3\right)}{2\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}+\frac{3\,c^2\,d^2\,e^2\,x^2}{a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6}}{x^2\,\left(2\,c\,d^2\,e+a\,e^3\right)+x\,\left(c\,d^3+2\,a\,d\,e^2\right)+a\,d^2\,e+c\,d\,e^2\,x^3}-\frac{6\,c^2\,d^2\,e\,\mathrm{atanh}\left(\frac{a^4\,e^8-2\,a^3\,c\,d^2\,e^6+2\,a\,c^3\,d^6\,e^2-c^4\,d^8}{{\left(a\,e^2-c\,d^2\right)}^4}+\frac{2\,c\,d\,e\,x\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}{{\left(a\,e^2-c\,d^2\right)}^4}\right)}{{\left(a\,e^2-c\,d^2\right)}^4}","Not used",1,"((2*c^2*d^4 - a^2*e^4 + 5*a*c*d^2*e^2)/(2*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4)) + (3*c*d*x*(a*e^3 + 3*c*d^2*e))/(2*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4)) + (3*c^2*d^2*e^2*x^2)/(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4))/(x^2*(a*e^3 + 2*c*d^2*e) + x*(c*d^3 + 2*a*d*e^2) + a*d^2*e + c*d*e^2*x^3) - (6*c^2*d^2*e*atanh((a^4*e^8 - c^4*d^8 + 2*a*c^3*d^6*e^2 - 2*a^3*c*d^2*e^6)/(a*e^2 - c*d^2)^4 + (2*c*d*e*x*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4))/(a*e^2 - c*d^2)^4))/(a*e^2 - c*d^2)^4","B"
1884,1,595,176,0.960407,"\text{Not used}","int(1/((d + e*x)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2),x)","\frac{8\,c^3\,d^3\,e\,\mathrm{atanh}\left(\frac{a^5\,e^{10}-3\,a^4\,c\,d^2\,e^8+2\,a^3\,c^2\,d^4\,e^6+2\,a^2\,c^3\,d^6\,e^4-3\,a\,c^4\,d^8\,e^2+c^5\,d^{10}}{{\left(a\,e^2-c\,d^2\right)}^5}+\frac{2\,c\,d\,e\,x\,\left(a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8\right)}{{\left(a\,e^2-c\,d^2\right)}^5}\right)}{{\left(a\,e^2-c\,d^2\right)}^5}-\frac{\frac{a^3\,e^6-5\,a^2\,c\,d^2\,e^4+13\,a\,c^2\,d^4\,e^2+3\,c^3\,d^6}{3\,\left(a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8\right)}+\frac{4\,c^3\,d^3\,e^3\,x^3}{a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8}+\frac{2\,c\,d\,x\,\left(-a^2\,e^5+8\,a\,c\,d^2\,e^3+11\,c^2\,d^4\,e\right)}{3\,\left(a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8\right)}+\frac{2\,c^2\,d^2\,x^2\,\left(5\,c\,d^2\,e^2+a\,e^4\right)}{a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8}}{x\,\left(c\,d^4+3\,a\,d^2\,e^2\right)+x^3\,\left(3\,c\,d^2\,e^2+a\,e^4\right)+x^2\,\left(3\,c\,d^3\,e+3\,a\,d\,e^3\right)+a\,d^3\,e+c\,d\,e^3\,x^4}","Not used",1,"(8*c^3*d^3*e*atanh((a^5*e^10 + c^5*d^10 - 3*a*c^4*d^8*e^2 - 3*a^4*c*d^2*e^8 + 2*a^2*c^3*d^6*e^4 + 2*a^3*c^2*d^4*e^6)/(a*e^2 - c*d^2)^5 + (2*c*d*e*x*(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4))/(a*e^2 - c*d^2)^5))/(a*e^2 - c*d^2)^5 - ((a^3*e^6 + 3*c^3*d^6 + 13*a*c^2*d^4*e^2 - 5*a^2*c*d^2*e^4)/(3*(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4)) + (4*c^3*d^3*e^3*x^3)/(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4) + (2*c*d*x*(11*c^2*d^4*e - a^2*e^5 + 8*a*c*d^2*e^3))/(3*(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4)) + (2*c^2*d^2*x^2*(a*e^4 + 5*c*d^2*e^2))/(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4))/(x*(c*d^4 + 3*a*d^2*e^2) + x^3*(a*e^4 + 3*c*d^2*e^2) + x^2*(3*a*d*e^3 + 3*c*d^3*e) + a*d^3*e + c*d*e^3*x^4)","B"
1885,1,516,221,0.133820,"\text{Not used}","int((d + e*x)^9/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","x^3\,\left(\frac{2\,e^5}{c^3\,d^2}-\frac{a\,e^7}{c^4\,d^4}\right)-x^2\,\left(\frac{3\,a^2\,e^8}{2\,c^5\,d^5}-\frac{15\,e^4}{2\,c^3\,d}+\frac{3\,a\,e\,\left(\frac{6\,e^5}{c^3\,d^2}-\frac{3\,a\,e^7}{c^4\,d^4}\right)}{2\,c\,d}\right)+\frac{x\,\left(6\,a^5\,e^{11}-30\,a^4\,c\,d^2\,e^9+60\,a^3\,c^2\,d^4\,e^7-60\,a^2\,c^3\,d^6\,e^5+30\,a\,c^4\,d^8\,e^3-6\,c^5\,d^{10}\,e\right)-\frac{-11\,a^6\,e^{12}+54\,a^5\,c\,d^2\,e^{10}-105\,a^4\,c^2\,d^4\,e^8+100\,a^3\,c^3\,d^6\,e^6-45\,a^2\,c^4\,d^8\,e^4+6\,a\,c^5\,d^{10}\,e^2+c^6\,d^{12}}{2\,c\,d}}{a^2\,c^6\,d^6\,e^2+2\,a\,c^7\,d^7\,e\,x+c^8\,d^8\,x^2}+x\,\left(\frac{20\,e^3}{c^3}-\frac{a^3\,e^9}{c^6\,d^6}-\frac{3\,a^2\,e^2\,\left(\frac{6\,e^5}{c^3\,d^2}-\frac{3\,a\,e^7}{c^4\,d^4}\right)}{c^2\,d^2}+\frac{3\,a\,e\,\left(\frac{3\,a^2\,e^8}{c^5\,d^5}-\frac{15\,e^4}{c^3\,d}+\frac{3\,a\,e\,\left(\frac{6\,e^5}{c^3\,d^2}-\frac{3\,a\,e^7}{c^4\,d^4}\right)}{c\,d}\right)}{c\,d}\right)+\frac{e^6\,x^4}{4\,c^3\,d^3}+\frac{\ln\left(a\,e+c\,d\,x\right)\,\left(15\,a^4\,e^{10}-60\,a^3\,c\,d^2\,e^8+90\,a^2\,c^2\,d^4\,e^6-60\,a\,c^3\,d^6\,e^4+15\,c^4\,d^8\,e^2\right)}{c^7\,d^7}","Not used",1,"x^3*((2*e^5)/(c^3*d^2) - (a*e^7)/(c^4*d^4)) - x^2*((3*a^2*e^8)/(2*c^5*d^5) - (15*e^4)/(2*c^3*d) + (3*a*e*((6*e^5)/(c^3*d^2) - (3*a*e^7)/(c^4*d^4)))/(2*c*d)) + (x*(6*a^5*e^11 - 6*c^5*d^10*e + 30*a*c^4*d^8*e^3 - 30*a^4*c*d^2*e^9 - 60*a^2*c^3*d^6*e^5 + 60*a^3*c^2*d^4*e^7) - (c^6*d^12 - 11*a^6*e^12 + 6*a*c^5*d^10*e^2 + 54*a^5*c*d^2*e^10 - 45*a^2*c^4*d^8*e^4 + 100*a^3*c^3*d^6*e^6 - 105*a^4*c^2*d^4*e^8)/(2*c*d))/(c^8*d^8*x^2 + a^2*c^6*d^6*e^2 + 2*a*c^7*d^7*e*x) + x*((20*e^3)/c^3 - (a^3*e^9)/(c^6*d^6) - (3*a^2*e^2*((6*e^5)/(c^3*d^2) - (3*a*e^7)/(c^4*d^4)))/(c^2*d^2) + (3*a*e*((3*a^2*e^8)/(c^5*d^5) - (15*e^4)/(c^3*d) + (3*a*e*((6*e^5)/(c^3*d^2) - (3*a*e^7)/(c^4*d^4)))/(c*d)))/(c*d)) + (e^6*x^4)/(4*c^3*d^3) + (log(a*e + c*d*x)*(15*a^4*e^10 + 15*c^4*d^8*e^2 - 60*a*c^3*d^6*e^4 - 60*a^3*c*d^2*e^8 + 90*a^2*c^2*d^4*e^6))/(c^7*d^7)","B"
1886,1,341,185,0.621692,"\text{Not used}","int((d + e*x)^8/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","x^2\,\left(\frac{5\,e^4}{2\,c^3\,d^2}-\frac{3\,a\,e^6}{2\,c^4\,d^4}\right)-x\,\left(\frac{3\,a^2\,e^7}{c^5\,d^5}-\frac{10\,e^3}{c^3\,d}+\frac{3\,a\,e\,\left(\frac{5\,e^4}{c^3\,d^2}-\frac{3\,a\,e^6}{c^4\,d^4}\right)}{c\,d}\right)-\frac{x\,\left(5\,a^4\,e^9-20\,a^3\,c\,d^2\,e^7+30\,a^2\,c^2\,d^4\,e^5-20\,a\,c^3\,d^6\,e^3+5\,c^4\,d^8\,e\right)+\frac{9\,a^5\,e^{10}-35\,a^4\,c\,d^2\,e^8+50\,a^3\,c^2\,d^4\,e^6-30\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2+c^5\,d^{10}}{2\,c\,d}}{a^2\,c^5\,d^5\,e^2+2\,a\,c^6\,d^6\,e\,x+c^7\,d^7\,x^2}-\frac{\ln\left(a\,e+c\,d\,x\right)\,\left(10\,a^3\,e^8-30\,a^2\,c\,d^2\,e^6+30\,a\,c^2\,d^4\,e^4-10\,c^3\,d^6\,e^2\right)}{c^6\,d^6}+\frac{e^5\,x^3}{3\,c^3\,d^3}","Not used",1,"x^2*((5*e^4)/(2*c^3*d^2) - (3*a*e^6)/(2*c^4*d^4)) - x*((3*a^2*e^7)/(c^5*d^5) - (10*e^3)/(c^3*d) + (3*a*e*((5*e^4)/(c^3*d^2) - (3*a*e^6)/(c^4*d^4)))/(c*d)) - (x*(5*a^4*e^9 + 5*c^4*d^8*e - 20*a*c^3*d^6*e^3 - 20*a^3*c*d^2*e^7 + 30*a^2*c^2*d^4*e^5) + (9*a^5*e^10 + c^5*d^10 + 5*a*c^4*d^8*e^2 - 35*a^4*c*d^2*e^8 - 30*a^2*c^3*d^6*e^4 + 50*a^3*c^2*d^4*e^6)/(2*c*d))/(c^7*d^7*x^2 + a^2*c^5*d^5*e^2 + 2*a*c^6*d^6*e*x) - (log(a*e + c*d*x)*(10*a^3*e^8 - 10*c^3*d^6*e^2 + 30*a*c^2*d^4*e^4 - 30*a^2*c*d^2*e^6))/(c^6*d^6) + (e^5*x^3)/(3*c^3*d^3)","B"
1887,1,232,142,0.111739,"\text{Not used}","int((d + e*x)^7/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","\frac{x\,\left(4\,a^3\,e^7-12\,a^2\,c\,d^2\,e^5+12\,a\,c^2\,d^4\,e^3-4\,c^3\,d^6\,e\right)-\frac{-7\,a^4\,e^8+20\,a^3\,c\,d^2\,e^6-18\,a^2\,c^2\,d^4\,e^4+4\,a\,c^3\,d^6\,e^2+c^4\,d^8}{2\,c\,d}}{a^2\,c^4\,d^4\,e^2+2\,a\,c^5\,d^5\,e\,x+c^6\,d^6\,x^2}+x\,\left(\frac{4\,e^3}{c^3\,d^2}-\frac{3\,a\,e^5}{c^4\,d^4}\right)+\frac{\ln\left(a\,e+c\,d\,x\right)\,\left(6\,a^2\,e^6-12\,a\,c\,d^2\,e^4+6\,c^2\,d^4\,e^2\right)}{c^5\,d^5}+\frac{e^4\,x^2}{2\,c^3\,d^3}","Not used",1,"(x*(4*a^3*e^7 - 4*c^3*d^6*e + 12*a*c^2*d^4*e^3 - 12*a^2*c*d^2*e^5) - (c^4*d^8 - 7*a^4*e^8 + 4*a*c^3*d^6*e^2 + 20*a^3*c*d^2*e^6 - 18*a^2*c^2*d^4*e^4)/(2*c*d))/(c^6*d^6*x^2 + a^2*c^4*d^4*e^2 + 2*a*c^5*d^5*e*x) + x*((4*e^3)/(c^3*d^2) - (3*a*e^5)/(c^4*d^4)) + (log(a*e + c*d*x)*(6*a^2*e^6 + 6*c^2*d^4*e^2 - 12*a*c*d^2*e^4))/(c^5*d^5) + (e^4*x^2)/(2*c^3*d^3)","B"
1888,1,163,111,0.651250,"\text{Not used}","int((d + e*x)^6/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","\frac{e^3\,x}{c^3\,d^3}-\frac{x\,\left(3\,a^2\,e^5-6\,a\,c\,d^2\,e^3+3\,c^2\,d^4\,e\right)+\frac{5\,a^3\,e^6-9\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+c^3\,d^6}{2\,c\,d}}{a^2\,c^3\,d^3\,e^2+2\,a\,c^4\,d^4\,e\,x+c^5\,d^5\,x^2}-\frac{\ln\left(a\,e+c\,d\,x\right)\,\left(3\,a\,e^4-3\,c\,d^2\,e^2\right)}{c^4\,d^4}","Not used",1,"(e^3*x)/(c^3*d^3) - (x*(3*a^2*e^5 + 3*c^2*d^4*e - 6*a*c*d^2*e^3) + (5*a^3*e^6 + c^3*d^6 + 3*a*c^2*d^4*e^2 - 9*a^2*c*d^2*e^4)/(2*c*d))/(c^5*d^5*x^2 + a^2*c^3*d^3*e^2 + 2*a*c^4*d^4*e*x) - (log(a*e + c*d*x)*(3*a*e^4 - 3*c*d^2*e^2))/(c^4*d^4)","B"
1889,1,106,85,0.093469,"\text{Not used}","int((d + e*x)^5/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","\frac{e^2\,\ln\left(a\,e+c\,d\,x\right)}{c^3\,d^3}-\frac{\frac{-3\,a^2\,e^4+2\,a\,c\,d^2\,e^2+c^2\,d^4}{2\,c^3\,d^3}-\frac{2\,e\,x\,\left(a\,e^2-c\,d^2\right)}{c^2\,d^2}}{a^2\,e^2+2\,a\,c\,d\,e\,x+c^2\,d^2\,x^2}","Not used",1,"(e^2*log(a*e + c*d*x))/(c^3*d^3) - ((c^2*d^4 - 3*a^2*e^4 + 2*a*c*d^2*e^2)/(2*c^3*d^3) - (2*e*x*(a*e^2 - c*d^2))/(c^2*d^2))/(a^2*e^2 + c^2*d^2*x^2 + 2*a*c*d*e*x)","B"
1890,1,43,35,0.045860,"\text{Not used}","int((d + e*x)^4/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","-\frac{\frac{1}{2\,c}-\frac{x^2}{2\,a}}{a^2\,e^2+2\,a\,c\,d\,e\,x+c^2\,d^2\,x^2}","Not used",1,"-(1/(2*c) - x^2/(2*a))/(a^2*e^2 + c^2*d^2*x^2 + 2*a*c*d*e*x)","B"
1891,1,37,20,0.030403,"\text{Not used}","int((d + e*x)^3/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","-\frac{1}{2\,a^2\,c\,d\,e^2+4\,a\,c^2\,d^2\,e\,x+2\,c^3\,d^3\,x^2}","Not used",1,"-1/(2*c^3*d^3*x^2 + 2*a^2*c*d*e^2 + 4*a*c^2*d^2*e*x)","B"
1892,1,225,107,0.690501,"\text{Not used}","int((d + e*x)^2/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","\frac{\frac{3\,a\,e^2-c\,d^2}{2\,\left(a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}+\frac{c\,d\,e\,x}{a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4}}{a^2\,e^2+2\,a\,c\,d\,e\,x+c^2\,d^2\,x^2}-\frac{2\,e^2\,\mathrm{atanh}\left(\frac{a^3\,e^6-a^2\,c\,d^2\,e^4-a\,c^2\,d^4\,e^2+c^3\,d^6}{{\left(a\,e^2-c\,d^2\right)}^3}+\frac{2\,c\,d\,e\,x\,\left(a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{{\left(a\,e^2-c\,d^2\right)}^3}\right)}{{\left(a\,e^2-c\,d^2\right)}^3}","Not used",1,"((3*a*e^2 - c*d^2)/(2*(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2)) + (c*d*e*x)/(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2))/(a^2*e^2 + c^2*d^2*x^2 + 2*a*c*d*e*x) - (2*e^2*atanh((a^3*e^6 + c^3*d^6 - a*c^2*d^4*e^2 - a^2*c*d^2*e^4)/(a*e^2 - c*d^2)^3 + (2*c*d*e*x*(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2))/(a*e^2 - c*d^2)^3))/(a*e^2 - c*d^2)^3","B"
1893,1,392,142,0.783257,"\text{Not used}","int((d + e*x)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","\frac{6\,c\,d\,e^2\,\mathrm{atanh}\left(\frac{a^4\,e^8-2\,a^3\,c\,d^2\,e^6+2\,a\,c^3\,d^6\,e^2-c^4\,d^8}{{\left(a\,e^2-c\,d^2\right)}^4}+\frac{2\,c\,d\,e\,x\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}{{\left(a\,e^2-c\,d^2\right)}^4}\right)}{{\left(a\,e^2-c\,d^2\right)}^4}-\frac{\frac{2\,a^2\,e^4+5\,a\,c\,d^2\,e^2-c^2\,d^4}{2\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}+\frac{3\,e\,x\,\left(c^2\,d^3+3\,a\,c\,d\,e^2\right)}{2\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}+\frac{3\,c^2\,d^2\,e^2\,x^2}{a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6}}{x\,\left(a^2\,e^3+2\,c\,a\,d^2\,e\right)+x^2\,\left(c^2\,d^3+2\,a\,c\,d\,e^2\right)+a^2\,d\,e^2+c^2\,d^2\,e\,x^3}","Not used",1,"(6*c*d*e^2*atanh((a^4*e^8 - c^4*d^8 + 2*a*c^3*d^6*e^2 - 2*a^3*c*d^2*e^6)/(a*e^2 - c*d^2)^4 + (2*c*d*e*x*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4))/(a*e^2 - c*d^2)^4))/(a*e^2 - c*d^2)^4 - ((2*a^2*e^4 - c^2*d^4 + 5*a*c*d^2*e^2)/(2*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4)) + (3*e*x*(c^2*d^3 + 3*a*c*d*e^2))/(2*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4)) + (3*c^2*d^2*e^2*x^2)/(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4))/(x*(a^2*e^3 + 2*a*c*d^2*e) + x^2*(c^2*d^3 + 2*a*c*d*e^2) + a^2*d*e^2 + c^2*d^2*e*x^3)","B"
1894,1,616,191,0.987936,"\text{Not used}","int(1/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","\frac{\frac{9\,c\,x^2\,\left(c^2\,d^4\,e^2+a\,c\,d^2\,e^4\right)}{a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8}-\frac{a^3\,e^6-7\,a^2\,c\,d^2\,e^4-7\,a\,c^2\,d^4\,e^2+c^3\,d^6}{2\,\left(a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8\right)}+\frac{6\,c^3\,d^3\,e^3\,x^3}{a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8}+\frac{2\,c\,d\,e\,x\,\left(a^2\,e^4+7\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8}}{x^2\,\left(a^2\,e^4+4\,a\,c\,d^2\,e^2+c^2\,d^4\right)+x^3\,\left(2\,c^2\,d^3\,e+2\,a\,c\,d\,e^3\right)+x\,\left(2\,a^2\,d\,e^3+2\,c\,a\,d^3\,e\right)+a^2\,d^2\,e^2+c^2\,d^2\,e^2\,x^4}-\frac{12\,c^2\,d^2\,e^2\,\mathrm{atanh}\left(\frac{a^5\,e^{10}-3\,a^4\,c\,d^2\,e^8+2\,a^3\,c^2\,d^4\,e^6+2\,a^2\,c^3\,d^6\,e^4-3\,a\,c^4\,d^8\,e^2+c^5\,d^{10}}{{\left(a\,e^2-c\,d^2\right)}^5}+\frac{2\,c\,d\,e\,x\,\left(a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8\right)}{{\left(a\,e^2-c\,d^2\right)}^5}\right)}{{\left(a\,e^2-c\,d^2\right)}^5}","Not used",1,"((9*c*x^2*(c^2*d^4*e^2 + a*c*d^2*e^4))/(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4) - (a^3*e^6 + c^3*d^6 - 7*a*c^2*d^4*e^2 - 7*a^2*c*d^2*e^4)/(2*(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4)) + (6*c^3*d^3*e^3*x^3)/(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4) + (2*c*d*e*x*(a^2*e^4 + c^2*d^4 + 7*a*c*d^2*e^2))/(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4))/(x^2*(a^2*e^4 + c^2*d^4 + 4*a*c*d^2*e^2) + x^3*(2*c^2*d^3*e + 2*a*c*d*e^3) + x*(2*a^2*d*e^3 + 2*a*c*d^3*e) + a^2*d^2*e^2 + c^2*d^2*e^2*x^4) - (12*c^2*d^2*e^2*atanh((a^5*e^10 + c^5*d^10 - 3*a*c^4*d^8*e^2 - 3*a^4*c*d^2*e^8 + 2*a^2*c^3*d^6*e^4 + 2*a^3*c^2*d^4*e^6)/(a*e^2 - c*d^2)^5 + (2*c*d*e*x*(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4))/(a*e^2 - c*d^2)^5))/(a*e^2 - c*d^2)^5","B"
1895,1,878,223,1.132665,"\text{Not used}","int(1/((d + e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3),x)","\frac{20\,c^3\,d^3\,e^2\,\mathrm{atanh}\left(\frac{a^6\,e^{12}-4\,a^5\,c\,d^2\,e^{10}+5\,a^4\,c^2\,d^4\,e^8-5\,a^2\,c^4\,d^8\,e^4+4\,a\,c^5\,d^{10}\,e^2-c^6\,d^{12}}{{\left(a\,e^2-c\,d^2\right)}^6}+\frac{2\,c\,d\,e\,x\,\left(a^5\,e^{10}-5\,a^4\,c\,d^2\,e^8+10\,a^3\,c^2\,d^4\,e^6-10\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2-c^5\,d^{10}\right)}{{\left(a\,e^2-c\,d^2\right)}^6}\right)}{{\left(a\,e^2-c\,d^2\right)}^6}-\frac{\frac{2\,a^4\,e^8-13\,a^3\,c\,d^2\,e^6+47\,a^2\,c^2\,d^4\,e^4+27\,a\,c^3\,d^6\,e^2-3\,c^4\,d^8}{6\,\left(a^5\,e^{10}-5\,a^4\,c\,d^2\,e^8+10\,a^3\,c^2\,d^4\,e^6-10\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2-c^5\,d^{10}\right)}+\frac{5\,c^2\,d\,x^3\,\left(5\,c^2\,d^4\,e^3+3\,a\,c\,d^2\,e^5\right)}{a^5\,e^{10}-5\,a^4\,c\,d^2\,e^8+10\,a^3\,c^2\,d^4\,e^6-10\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2-c^5\,d^{10}}+\frac{5\,c^2\,d^2\,x^2\,\left(2\,a^2\,e^6+23\,a\,c\,d^2\,e^4+11\,c^2\,d^4\,e^2\right)}{3\,\left(a^5\,e^{10}-5\,a^4\,c\,d^2\,e^8+10\,a^3\,c^2\,d^4\,e^6-10\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2-c^5\,d^{10}\right)}+\frac{10\,c^4\,d^4\,e^4\,x^4}{a^5\,e^{10}-5\,a^4\,c\,d^2\,e^8+10\,a^3\,c^2\,d^4\,e^6-10\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2-c^5\,d^{10}}+\frac{5\,c\,d\,e\,x\,\left(-a^3\,e^6+11\,a^2\,c\,d^2\,e^4+35\,a\,c^2\,d^4\,e^2+3\,c^3\,d^6\right)}{6\,\left(a^5\,e^{10}-5\,a^4\,c\,d^2\,e^8+10\,a^3\,c^2\,d^4\,e^6-10\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2-c^5\,d^{10}\right)}}{x\,\left(3\,a^2\,d^2\,e^3+2\,c\,a\,d^4\,e\right)+x^2\,\left(3\,a^2\,d\,e^4+6\,a\,c\,d^3\,e^2+c^2\,d^5\right)+x^3\,\left(a^2\,e^5+6\,a\,c\,d^2\,e^3+3\,c^2\,d^4\,e\right)+x^4\,\left(3\,c^2\,d^3\,e^2+2\,a\,c\,d\,e^4\right)+a^2\,d^3\,e^2+c^2\,d^2\,e^3\,x^5}","Not used",1,"(20*c^3*d^3*e^2*atanh((a^6*e^12 - c^6*d^12 + 4*a*c^5*d^10*e^2 - 4*a^5*c*d^2*e^10 - 5*a^2*c^4*d^8*e^4 + 5*a^4*c^2*d^4*e^8)/(a*e^2 - c*d^2)^6 + (2*c*d*e*x*(a^5*e^10 - c^5*d^10 + 5*a*c^4*d^8*e^2 - 5*a^4*c*d^2*e^8 - 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6))/(a*e^2 - c*d^2)^6))/(a*e^2 - c*d^2)^6 - ((2*a^4*e^8 - 3*c^4*d^8 + 27*a*c^3*d^6*e^2 - 13*a^3*c*d^2*e^6 + 47*a^2*c^2*d^4*e^4)/(6*(a^5*e^10 - c^5*d^10 + 5*a*c^4*d^8*e^2 - 5*a^4*c*d^2*e^8 - 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6)) + (5*c^2*d*x^3*(5*c^2*d^4*e^3 + 3*a*c*d^2*e^5))/(a^5*e^10 - c^5*d^10 + 5*a*c^4*d^8*e^2 - 5*a^4*c*d^2*e^8 - 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6) + (5*c^2*d^2*x^2*(2*a^2*e^6 + 11*c^2*d^4*e^2 + 23*a*c*d^2*e^4))/(3*(a^5*e^10 - c^5*d^10 + 5*a*c^4*d^8*e^2 - 5*a^4*c*d^2*e^8 - 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6)) + (10*c^4*d^4*e^4*x^4)/(a^5*e^10 - c^5*d^10 + 5*a*c^4*d^8*e^2 - 5*a^4*c*d^2*e^8 - 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6) + (5*c*d*e*x*(3*c^3*d^6 - a^3*e^6 + 35*a*c^2*d^4*e^2 + 11*a^2*c*d^2*e^4))/(6*(a^5*e^10 - c^5*d^10 + 5*a*c^4*d^8*e^2 - 5*a^4*c*d^2*e^8 - 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6)))/(x*(3*a^2*d^2*e^3 + 2*a*c*d^4*e) + x^2*(c^2*d^5 + 3*a^2*d*e^4 + 6*a*c*d^3*e^2) + x^3*(a^2*e^5 + 3*c^2*d^4*e + 6*a*c*d^2*e^3) + x^4*(3*c^2*d^3*e^2 + 2*a*c*d*e^4) + a^2*d^3*e^2 + c^2*d^2*e^3*x^5)","B"
1896,1,452,217,0.154274,"\text{Not used}","int((d + e*x)^10/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^4,x)","x^2\,\left(\frac{3\,e^5}{c^4\,d^3}-\frac{2\,a\,e^7}{c^5\,d^5}\right)-x\,\left(\frac{6\,a^2\,e^8}{c^6\,d^6}-\frac{15\,e^4}{c^4\,d^2}+\frac{4\,a\,e\,\left(\frac{6\,e^5}{c^4\,d^3}-\frac{4\,a\,e^7}{c^5\,d^5}\right)}{c\,d}\right)-\frac{x\,\left(27\,a^5\,e^{11}-105\,a^4\,c\,d^2\,e^9+150\,a^3\,c^2\,d^4\,e^7-90\,a^2\,c^3\,d^6\,e^5+15\,a\,c^4\,d^8\,e^3+3\,c^5\,d^{10}\,e\right)+x^2\,\left(15\,a^4\,c\,d\,e^{10}-60\,a^3\,c^2\,d^3\,e^8+90\,a^2\,c^3\,d^5\,e^6-60\,a\,c^4\,d^7\,e^4+15\,c^5\,d^9\,e^2\right)+\frac{37\,a^6\,e^{12}-141\,a^5\,c\,d^2\,e^{10}+195\,a^4\,c^2\,d^4\,e^8-110\,a^3\,c^3\,d^6\,e^6+15\,a^2\,c^4\,d^8\,e^4+3\,a\,c^5\,d^{10}\,e^2+c^6\,d^{12}}{3\,c\,d}}{a^3\,c^6\,d^6\,e^3+3\,a^2\,c^7\,d^7\,e^2\,x+3\,a\,c^8\,d^8\,e\,x^2+c^9\,d^9\,x^3}-\frac{\ln\left(a\,e+c\,d\,x\right)\,\left(20\,a^3\,e^9-60\,a^2\,c\,d^2\,e^7+60\,a\,c^2\,d^4\,e^5-20\,c^3\,d^6\,e^3\right)}{c^7\,d^7}+\frac{e^6\,x^3}{3\,c^4\,d^4}","Not used",1,"x^2*((3*e^5)/(c^4*d^3) - (2*a*e^7)/(c^5*d^5)) - x*((6*a^2*e^8)/(c^6*d^6) - (15*e^4)/(c^4*d^2) + (4*a*e*((6*e^5)/(c^4*d^3) - (4*a*e^7)/(c^5*d^5)))/(c*d)) - (x*(27*a^5*e^11 + 3*c^5*d^10*e + 15*a*c^4*d^8*e^3 - 105*a^4*c*d^2*e^9 - 90*a^2*c^3*d^6*e^5 + 150*a^3*c^2*d^4*e^7) + x^2*(15*c^5*d^9*e^2 - 60*a*c^4*d^7*e^4 + 90*a^2*c^3*d^5*e^6 - 60*a^3*c^2*d^3*e^8 + 15*a^4*c*d*e^10) + (37*a^6*e^12 + c^6*d^12 + 3*a*c^5*d^10*e^2 - 141*a^5*c*d^2*e^10 + 15*a^2*c^4*d^8*e^4 - 110*a^3*c^3*d^6*e^6 + 195*a^4*c^2*d^4*e^8)/(3*c*d))/(c^9*d^9*x^3 + a^3*c^6*d^6*e^3 + 3*a*c^8*d^8*e*x^2 + 3*a^2*c^7*d^7*e^2*x) - (log(a*e + c*d*x)*(20*a^3*e^9 - 20*c^3*d^6*e^3 + 60*a*c^2*d^4*e^5 - 60*a^2*c*d^2*e^7))/(c^7*d^7) + (e^6*x^3)/(3*c^4*d^4)","B"
1897,1,331,179,0.141625,"\text{Not used}","int((d + e*x)^9/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^4,x)","x\,\left(\frac{5\,e^4}{c^4\,d^3}-\frac{4\,a\,e^6}{c^5\,d^5}\right)-\frac{x^2\,\left(-10\,a^3\,c\,d\,e^8+30\,a^2\,c^2\,d^3\,e^6-30\,a\,c^3\,d^5\,e^4+10\,c^4\,d^7\,e^2\right)+x\,\left(-\frac{35\,a^4\,e^9}{2}+50\,a^3\,c\,d^2\,e^7-45\,a^2\,c^2\,d^4\,e^5+10\,a\,c^3\,d^6\,e^3+\frac{5\,c^4\,d^8\,e}{2}\right)+\frac{-47\,a^5\,e^{10}+130\,a^4\,c\,d^2\,e^8-110\,a^3\,c^2\,d^4\,e^6+20\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2+2\,c^5\,d^{10}}{6\,c\,d}}{a^3\,c^5\,d^5\,e^3+3\,a^2\,c^6\,d^6\,e^2\,x+3\,a\,c^7\,d^7\,e\,x^2+c^8\,d^8\,x^3}+\frac{\ln\left(a\,e+c\,d\,x\right)\,\left(10\,a^2\,e^7-20\,a\,c\,d^2\,e^5+10\,c^2\,d^4\,e^3\right)}{c^6\,d^6}+\frac{e^5\,x^2}{2\,c^4\,d^4}","Not used",1,"x*((5*e^4)/(c^4*d^3) - (4*a*e^6)/(c^5*d^5)) - (x^2*(10*c^4*d^7*e^2 - 30*a*c^3*d^5*e^4 + 30*a^2*c^2*d^3*e^6 - 10*a^3*c*d*e^8) + x*((5*c^4*d^8*e)/2 - (35*a^4*e^9)/2 + 10*a*c^3*d^6*e^3 + 50*a^3*c*d^2*e^7 - 45*a^2*c^2*d^4*e^5) + (2*c^5*d^10 - 47*a^5*e^10 + 5*a*c^4*d^8*e^2 + 130*a^4*c*d^2*e^8 + 20*a^2*c^3*d^6*e^4 - 110*a^3*c^2*d^4*e^6)/(6*c*d))/(c^8*d^8*x^3 + a^3*c^5*d^5*e^3 + 3*a*c^7*d^7*e*x^2 + 3*a^2*c^6*d^6*e^2*x) + (log(a*e + c*d*x)*(10*a^2*e^7 + 10*c^2*d^4*e^3 - 20*a*c*d^2*e^5))/(c^6*d^6) + (e^5*x^2)/(2*c^4*d^4)","B"
1898,1,246,146,0.167953,"\text{Not used}","int((d + e*x)^8/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^4,x)","\frac{e^4\,x}{c^4\,d^4}-\frac{x\,\left(10\,a^3\,e^7-18\,a^2\,c\,d^2\,e^5+6\,a\,c^2\,d^4\,e^3+2\,c^3\,d^6\,e\right)+x^2\,\left(6\,a^2\,c\,d\,e^6-12\,a\,c^2\,d^3\,e^4+6\,c^3\,d^5\,e^2\right)+\frac{13\,a^4\,e^8-22\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4+2\,a\,c^3\,d^6\,e^2+c^4\,d^8}{3\,c\,d}}{a^3\,c^4\,d^4\,e^3+3\,a^2\,c^5\,d^5\,e^2\,x+3\,a\,c^6\,d^6\,e\,x^2+c^7\,d^7\,x^3}-\frac{\ln\left(a\,e+c\,d\,x\right)\,\left(4\,a\,e^5-4\,c\,d^2\,e^3\right)}{c^5\,d^5}","Not used",1,"(e^4*x)/(c^4*d^4) - (x*(10*a^3*e^7 + 2*c^3*d^6*e + 6*a*c^2*d^4*e^3 - 18*a^2*c*d^2*e^5) + x^2*(6*c^3*d^5*e^2 - 12*a*c^2*d^3*e^4 + 6*a^2*c*d*e^6) + (13*a^4*e^8 + c^4*d^8 + 2*a*c^3*d^6*e^2 - 22*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4)/(3*c*d))/(c^7*d^7*x^3 + a^3*c^4*d^4*e^3 + 3*a*c^6*d^6*e*x^2 + 3*a^2*c^5*d^5*e^2*x) - (log(a*e + c*d*x)*(4*a*e^5 - 4*c*d^2*e^3))/(c^5*d^5)","B"
1899,1,178,122,0.658633,"\text{Not used}","int((d + e*x)^7/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^4,x)","\frac{e^3\,\ln\left(a\,e+c\,d\,x\right)}{c^4\,d^4}-\frac{\frac{-11\,a^3\,e^6+6\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2+2\,c^3\,d^6}{6\,c^4\,d^4}+\frac{3\,x\,\left(-3\,a^2\,e^5+2\,a\,c\,d^2\,e^3+c^2\,d^4\,e\right)}{2\,c^3\,d^3}-\frac{3\,e^2\,x^2\,\left(a\,e^2-c\,d^2\right)}{c^2\,d^2}}{a^3\,e^3+3\,a^2\,c\,d\,e^2\,x+3\,a\,c^2\,d^2\,e\,x^2+c^3\,d^3\,x^3}","Not used",1,"(e^3*log(a*e + c*d*x))/(c^4*d^4) - ((2*c^3*d^6 - 11*a^3*e^6 + 3*a*c^2*d^4*e^2 + 6*a^2*c*d^2*e^4)/(6*c^4*d^4) + (3*x*(c^2*d^4*e - 3*a^2*e^5 + 2*a*c*d^2*e^3))/(2*c^3*d^3) - (3*e^2*x^2*(a*e^2 - c*d^2))/(c^2*d^2))/(a^3*e^3 + c^3*d^3*x^3 + 3*a^2*c*d*e^2*x + 3*a*c^2*d^2*e*x^2)","B"
1900,1,81,35,0.064724,"\text{Not used}","int((d + e*x)^6/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^4,x)","-\frac{\frac{d}{3\,c}+e\,\left(\frac{x}{c}-\frac{x^3}{3\,a}\right)+\frac{a\,e^2}{3\,c^2\,d}}{a^3\,e^3+3\,a^2\,c\,d\,e^2\,x+3\,a\,c^2\,d^2\,e\,x^2+c^3\,d^3\,x^3}","Not used",1,"-(d/(3*c) + e*(x/c - x^3/(3*a)) + (a*e^2)/(3*c^2*d))/(a^3*e^3 + c^3*d^3*x^3 + 3*a^2*c*d*e^2*x + 3*a*c^2*d^2*e*x^2)","B"
1901,1,77,54,0.570874,"\text{Not used}","int((d + e*x)^5/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^4,x)","-\frac{\frac{2\,c\,d^2+a\,e^2}{6\,c^2\,d^2}+\frac{e\,x}{2\,c\,d}}{a^3\,e^3+3\,a^2\,c\,d\,e^2\,x+3\,a\,c^2\,d^2\,e\,x^2+c^3\,d^3\,x^3}","Not used",1,"-((a*e^2 + 2*c*d^2)/(6*c^2*d^2) + (e*x)/(2*c*d))/(a^3*e^3 + c^3*d^3*x^3 + 3*a^2*c*d*e^2*x + 3*a*c^2*d^2*e*x^2)","B"
1902,1,54,20,0.570195,"\text{Not used}","int((d + e*x)^4/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^4,x)","-\frac{1}{3\,a^3\,c\,d\,e^3+9\,a^2\,c^2\,d^2\,e^2\,x+9\,a\,c^3\,d^3\,e\,x^2+3\,c^4\,d^4\,x^3}","Not used",1,"-1/(3*c^4*d^4*x^3 + 3*a^3*c*d*e^3 + 9*a*c^3*d^3*e*x^2 + 9*a^2*c^2*d^2*e^2*x)","B"
1903,1,372,139,0.758580,"\text{Not used}","int((d + e*x)^3/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^4,x)","\frac{\frac{11\,a^2\,e^4-7\,a\,c\,d^2\,e^2+2\,c^2\,d^4}{6\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}-\frac{e\,x\,\left(c^2\,d^3-5\,a\,c\,d\,e^2\right)}{2\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}+\frac{c^2\,d^2\,e^2\,x^2}{a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6}}{a^3\,e^3+3\,a^2\,c\,d\,e^2\,x+3\,a\,c^2\,d^2\,e\,x^2+c^3\,d^3\,x^3}-\frac{2\,e^3\,\mathrm{atanh}\left(\frac{a^4\,e^8-2\,a^3\,c\,d^2\,e^6+2\,a\,c^3\,d^6\,e^2-c^4\,d^8}{{\left(a\,e^2-c\,d^2\right)}^4}+\frac{2\,c\,d\,e\,x\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}{{\left(a\,e^2-c\,d^2\right)}^4}\right)}{{\left(a\,e^2-c\,d^2\right)}^4}","Not used",1,"((11*a^2*e^4 + 2*c^2*d^4 - 7*a*c*d^2*e^2)/(6*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4)) - (e*x*(c^2*d^3 - 5*a*c*d*e^2))/(2*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4)) + (c^2*d^2*e^2*x^2)/(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4))/(a^3*e^3 + c^3*d^3*x^3 + 3*a^2*c*d*e^2*x + 3*a*c^2*d^2*e*x^2) - (2*e^3*atanh((a^4*e^8 - c^4*d^8 + 2*a*c^3*d^6*e^2 - 2*a^3*c*d^2*e^6)/(a*e^2 - c*d^2)^4 + (2*c*d*e*x*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4))/(a*e^2 - c*d^2)^4))/(a*e^2 - c*d^2)^4","B"
1904,1,617,173,0.978370,"\text{Not used}","int((d + e*x)^2/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^4,x)","\frac{8\,c\,d\,e^3\,\mathrm{atanh}\left(\frac{a^5\,e^{10}-3\,a^4\,c\,d^2\,e^8+2\,a^3\,c^2\,d^4\,e^6+2\,a^2\,c^3\,d^6\,e^4-3\,a\,c^4\,d^8\,e^2+c^5\,d^{10}}{{\left(a\,e^2-c\,d^2\right)}^5}+\frac{2\,c\,d\,e\,x\,\left(a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8\right)}{{\left(a\,e^2-c\,d^2\right)}^5}\right)}{{\left(a\,e^2-c\,d^2\right)}^5}-\frac{\frac{3\,a^3\,e^6+13\,a^2\,c\,d^2\,e^4-5\,a\,c^2\,d^4\,e^2+c^3\,d^6}{3\,\left(a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8\right)}+\frac{2\,e\,x\,\left(11\,a^2\,c\,d\,e^4+8\,a\,c^2\,d^3\,e^2-c^3\,d^5\right)}{3\,\left(a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8\right)}+\frac{2\,e^2\,x^2\,\left(c^3\,d^4+5\,a\,c^2\,d^2\,e^2\right)}{a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8}+\frac{4\,c^3\,d^3\,e^3\,x^3}{a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8}}{x\,\left(a^3\,e^4+3\,c\,a^2\,d^2\,e^2\right)+x^3\,\left(c^3\,d^4+3\,a\,c^2\,d^2\,e^2\right)+x^2\,\left(3\,a^2\,c\,d\,e^3+3\,a\,c^2\,d^3\,e\right)+a^3\,d\,e^3+c^3\,d^3\,e\,x^4}","Not used",1,"(8*c*d*e^3*atanh((a^5*e^10 + c^5*d^10 - 3*a*c^4*d^8*e^2 - 3*a^4*c*d^2*e^8 + 2*a^2*c^3*d^6*e^4 + 2*a^3*c^2*d^4*e^6)/(a*e^2 - c*d^2)^5 + (2*c*d*e*x*(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4))/(a*e^2 - c*d^2)^5))/(a*e^2 - c*d^2)^5 - ((3*a^3*e^6 + c^3*d^6 - 5*a*c^2*d^4*e^2 + 13*a^2*c*d^2*e^4)/(3*(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4)) + (2*e*x*(8*a*c^2*d^3*e^2 - c^3*d^5 + 11*a^2*c*d*e^4))/(3*(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4)) + (2*e^2*x^2*(c^3*d^4 + 5*a*c^2*d^2*e^2))/(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4) + (4*c^3*d^3*e^3*x^3)/(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4))/(x*(a^3*e^4 + 3*a^2*c*d^2*e^2) + x^3*(c^3*d^4 + 3*a*c^2*d^2*e^2) + x^2*(3*a*c^2*d^3*e + 3*a^2*c*d*e^3) + a^3*d*e^3 + c^3*d^3*e*x^4)","B"
1905,1,891,226,1.153499,"\text{Not used}","int((d + e*x)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^4,x)","\frac{\frac{-3\,a^4\,e^8+27\,a^3\,c\,d^2\,e^6+47\,a^2\,c^2\,d^4\,e^4-13\,a\,c^3\,d^6\,e^2+2\,c^4\,d^8}{6\,\left(a^5\,e^{10}-5\,a^4\,c\,d^2\,e^8+10\,a^3\,c^2\,d^4\,e^6-10\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2-c^5\,d^{10}\right)}+\frac{5\,e^2\,x^2\,\left(11\,a^2\,c^2\,d^2\,e^4+23\,a\,c^3\,d^4\,e^2+2\,c^4\,d^6\right)}{3\,\left(a^5\,e^{10}-5\,a^4\,c\,d^2\,e^8+10\,a^3\,c^2\,d^4\,e^6-10\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2-c^5\,d^{10}\right)}+\frac{5\,d\,e\,x\,\left(3\,a^3\,c\,e^6+35\,a^2\,c^2\,d^2\,e^4+11\,a\,c^3\,d^4\,e^2-c^4\,d^6\right)}{6\,\left(a^5\,e^{10}-5\,a^4\,c\,d^2\,e^8+10\,a^3\,c^2\,d^4\,e^6-10\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2-c^5\,d^{10}\right)}+\frac{5\,c\,e\,x^3\,\left(3\,c^3\,d^5\,e^2+5\,a\,c^2\,d^3\,e^4\right)}{a^5\,e^{10}-5\,a^4\,c\,d^2\,e^8+10\,a^3\,c^2\,d^4\,e^6-10\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2-c^5\,d^{10}}+\frac{10\,c^4\,d^4\,e^4\,x^4}{a^5\,e^{10}-5\,a^4\,c\,d^2\,e^8+10\,a^3\,c^2\,d^4\,e^6-10\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2-c^5\,d^{10}}}{x^2\,\left(a^3\,e^5+6\,a^2\,c\,d^2\,e^3+3\,a\,c^2\,d^4\,e\right)+x^3\,\left(3\,a^2\,c\,d\,e^4+6\,a\,c^2\,d^3\,e^2+c^3\,d^5\right)+x\,\left(2\,a^3\,d\,e^4+3\,c\,a^2\,d^3\,e^2\right)+x^4\,\left(2\,c^3\,d^4\,e+3\,a\,c^2\,d^2\,e^3\right)+a^3\,d^2\,e^3+c^3\,d^3\,e^2\,x^5}-\frac{20\,c^2\,d^2\,e^3\,\mathrm{atanh}\left(\frac{a^6\,e^{12}-4\,a^5\,c\,d^2\,e^{10}+5\,a^4\,c^2\,d^4\,e^8-5\,a^2\,c^4\,d^8\,e^4+4\,a\,c^5\,d^{10}\,e^2-c^6\,d^{12}}{{\left(a\,e^2-c\,d^2\right)}^6}+\frac{2\,c\,d\,e\,x\,\left(a^5\,e^{10}-5\,a^4\,c\,d^2\,e^8+10\,a^3\,c^2\,d^4\,e^6-10\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2-c^5\,d^{10}\right)}{{\left(a\,e^2-c\,d^2\right)}^6}\right)}{{\left(a\,e^2-c\,d^2\right)}^6}","Not used",1,"((2*c^4*d^8 - 3*a^4*e^8 - 13*a*c^3*d^6*e^2 + 27*a^3*c*d^2*e^6 + 47*a^2*c^2*d^4*e^4)/(6*(a^5*e^10 - c^5*d^10 + 5*a*c^4*d^8*e^2 - 5*a^4*c*d^2*e^8 - 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6)) + (5*e^2*x^2*(2*c^4*d^6 + 23*a*c^3*d^4*e^2 + 11*a^2*c^2*d^2*e^4))/(3*(a^5*e^10 - c^5*d^10 + 5*a*c^4*d^8*e^2 - 5*a^4*c*d^2*e^8 - 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6)) + (5*d*e*x*(3*a^3*c*e^6 - c^4*d^6 + 11*a*c^3*d^4*e^2 + 35*a^2*c^2*d^2*e^4))/(6*(a^5*e^10 - c^5*d^10 + 5*a*c^4*d^8*e^2 - 5*a^4*c*d^2*e^8 - 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6)) + (5*c*e*x^3*(3*c^3*d^5*e^2 + 5*a*c^2*d^3*e^4))/(a^5*e^10 - c^5*d^10 + 5*a*c^4*d^8*e^2 - 5*a^4*c*d^2*e^8 - 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6) + (10*c^4*d^4*e^4*x^4)/(a^5*e^10 - c^5*d^10 + 5*a*c^4*d^8*e^2 - 5*a^4*c*d^2*e^8 - 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6))/(x^2*(a^3*e^5 + 6*a^2*c*d^2*e^3 + 3*a*c^2*d^4*e) + x^3*(c^3*d^5 + 6*a*c^2*d^3*e^2 + 3*a^2*c*d*e^4) + x*(2*a^3*d*e^4 + 3*a^2*c*d^3*e^2) + x^4*(2*c^3*d^4*e + 3*a*c^2*d^2*e^3) + a^3*d^2*e^3 + c^3*d^3*e^2*x^5) - (20*c^2*d^2*e^3*atanh((a^6*e^12 - c^6*d^12 + 4*a*c^5*d^10*e^2 - 4*a^5*c*d^2*e^10 - 5*a^2*c^4*d^8*e^4 + 5*a^4*c^2*d^4*e^8)/(a*e^2 - c*d^2)^6 + (2*c*d*e*x*(a^5*e^10 - c^5*d^10 + 5*a*c^4*d^8*e^2 - 5*a^4*c*d^2*e^8 - 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6))/(a*e^2 - c*d^2)^6))/(a*e^2 - c*d^2)^6","B"
1906,0,-1,262,0.000000,"\text{Not used}","int(1/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^4,x)","\left\{\begin{array}{cl} -\frac{20\,c^3\,d^3\,e^3\,\ln\left(\frac{\frac{a\,e^2}{2}+\frac{c\,d^2}{2}-\sqrt{\frac{{\left(c\,d^2+a\,e^2\right)}^2}{4}-a\,c\,d^2\,e^2}+c\,d\,e\,x}{\frac{a\,e^2}{2}+\frac{c\,d^2}{2}+\sqrt{\frac{{\left(c\,d^2+a\,e^2\right)}^2}{4}-a\,c\,d^2\,e^2}+c\,d\,e\,x}\right)}{{\left({\left(c\,d^2+a\,e^2\right)}^2-4\,a\,c\,d^2\,e^2\right)}^{7/2}}-\frac{20\,\left(\frac{c\,d^2}{2}+c\,x\,d\,e+\frac{a\,e^2}{2}\right)\,\left(\frac{c\,d\,e}{30\,\left({\left(c\,d^2+a\,e^2\right)}^2-4\,a\,c\,d^2\,e^2\right)\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^3}-\frac{c^2\,d^2\,e^2}{6\,{\left({\left(c\,d^2+a\,e^2\right)}^2-4\,a\,c\,d^2\,e^2\right)}^2\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^2}+\frac{c^3\,d^3\,e^3}{{\left({\left(c\,d^2+a\,e^2\right)}^2-4\,a\,c\,d^2\,e^2\right)}^3\,\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}\right)}{c\,d\,e} & \text{\ if\ \ }0<{\left(c\,d^2+a\,e^2\right)}^2-4\,a\,c\,d^2\,e^2\\ -\frac{20\,\left(\frac{c\,d^2}{2}+c\,x\,d\,e+\frac{a\,e^2}{2}\right)\,\left(\frac{c\,d\,e}{30\,\left({\left(c\,d^2+a\,e^2\right)}^2-4\,a\,c\,d^2\,e^2\right)\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^3}-\frac{c^2\,d^2\,e^2}{6\,{\left({\left(c\,d^2+a\,e^2\right)}^2-4\,a\,c\,d^2\,e^2\right)}^2\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^2}+\frac{c^3\,d^3\,e^3}{{\left({\left(c\,d^2+a\,e^2\right)}^2-4\,a\,c\,d^2\,e^2\right)}^3\,\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}\right)}{c\,d\,e}-\frac{20\,c^3\,d^3\,e^3\,\mathrm{atan}\left(\frac{\frac{c\,d^2}{2}+c\,x\,d\,e+\frac{a\,e^2}{2}}{\sqrt{a\,c\,d^2\,e^2-\frac{{\left(c\,d^2+a\,e^2\right)}^2}{4}}}\right)}{\sqrt{a\,c\,d^2\,e^2-\frac{{\left(c\,d^2+a\,e^2\right)}^2}{4}}\,{\left({\left(c\,d^2+a\,e^2\right)}^2-4\,a\,c\,d^2\,e^2\right)}^3} & \text{\ if\ \ }{\left(c\,d^2+a\,e^2\right)}^2-4\,a\,c\,d^2\,e^2<0\\ \int \frac{1}{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^4} \,d x & \text{\ if\ \ }{\left(c\,d^2+a\,e^2\right)}^2-4\,a\,c\,d^2\,e^2\notin \mathbb{R}\vee {\left(c\,d^2+a\,e^2\right)}^2=4\,a\,c\,d^2\,e^2 \end{array}\right.","Not used",1,"piecewise(0 < (a*e^2 + c*d^2)^2 - 4*a*c*d^2*e^2, - (20*c^3*d^3*e^3*log(((a*e^2)/2 + (c*d^2)/2 - ((a*e^2 + c*d^2)^2/4 - a*c*d^2*e^2)^(1/2) + c*d*e*x)/((a*e^2)/2 + (c*d^2)/2 + ((a*e^2 + c*d^2)^2/4 - a*c*d^2*e^2)^(1/2) + c*d*e*x)))/((a*e^2 + c*d^2)^2 - 4*a*c*d^2*e^2)^(7/2) - (20*((a*e^2)/2 + (c*d^2)/2 + c*d*e*x)*((c*d*e)/(30*((a*e^2 + c*d^2)^2 - 4*a*c*d^2*e^2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3) - (c^2*d^2*e^2)/(6*((a*e^2 + c*d^2)^2 - 4*a*c*d^2*e^2)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2) + (c^3*d^3*e^3)/(((a*e^2 + c*d^2)^2 - 4*a*c*d^2*e^2)^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2))))/(c*d*e), (a*e^2 + c*d^2)^2 - 4*a*c*d^2*e^2 < 0, - (20*((a*e^2)/2 + (c*d^2)/2 + c*d*e*x)*((c*d*e)/(30*((a*e^2 + c*d^2)^2 - 4*a*c*d^2*e^2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3) - (c^2*d^2*e^2)/(6*((a*e^2 + c*d^2)^2 - 4*a*c*d^2*e^2)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2) + (c^3*d^3*e^3)/(((a*e^2 + c*d^2)^2 - 4*a*c*d^2*e^2)^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2))))/(c*d*e) - (20*c^3*d^3*e^3*atan(((a*e^2)/2 + (c*d^2)/2 + c*d*e*x)/(- (a*e^2 + c*d^2)^2/4 + a*c*d^2*e^2)^(1/2)))/((- (a*e^2 + c*d^2)^2/4 + a*c*d^2*e^2)^(1/2)*((a*e^2 + c*d^2)^2 - 4*a*c*d^2*e^2)^3), ~in((a*e^2 + c*d^2)^2 - 4*a*c*d^2*e^2, 'real') | (a*e^2 + c*d^2)^2 == 4*a*c*d^2*e^2, int(1/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^4, x))","F"
1907,0,-1,388,0.000000,"\text{Not used}","int((d + e*x)^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","\int {\left(d+e\,x\right)}^4\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e} \,d x","Not used",1,"int((d + e*x)^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2), x)","F"
1908,0,-1,328,0.000000,"\text{Not used}","int((d + e*x)^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","\int {\left(d+e\,x\right)}^3\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e} \,d x","Not used",1,"int((d + e*x)^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2), x)","F"
1909,0,-1,268,0.000000,"\text{Not used}","int((d + e*x)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","\int {\left(d+e\,x\right)}^2\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e} \,d x","Not used",1,"int((d + e*x)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2), x)","F"
1910,1,307,210,1.036567,"\text{Not used}","int((d + e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","d\,\left(\frac{x}{2}+\frac{c\,d^2+a\,e^2}{4\,c\,d\,e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}-\frac{d\,\ln\left(2\,\sqrt{\left(a\,e+c\,d\,x\right)\,\left(d+e\,x\right)}\,\sqrt{c\,d\,e}+a\,e^2+c\,d^2+2\,c\,d\,e\,x\right)\,\left(\frac{{\left(c\,d^2+a\,e^2\right)}^2}{4}-a\,c\,d^2\,e^2\right)}{2\,{\left(c\,d\,e\right)}^{3/2}}+\frac{e\,\ln\left(2\,\sqrt{\left(a\,e+c\,d\,x\right)\,\left(d+e\,x\right)}\,\sqrt{c\,d\,e}+a\,e^2+c\,d^2+2\,c\,d\,e\,x\right)\,\left({\left(c\,d^2+a\,e^2\right)}^3-4\,a\,c\,d^2\,e^2\,\left(c\,d^2+a\,e^2\right)\right)}{16\,{\left(c\,d\,e\right)}^{5/2}}+\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(8\,c\,d\,e\,\left(c\,d\,e\,x^2+a\,d\,e\right)-3\,{\left(c\,d^2+a\,e^2\right)}^2+2\,c\,d\,e\,x\,\left(c\,d^2+a\,e^2\right)\right)}{24\,c^2\,d^2\,e}","Not used",1,"d*(x/2 + (a*e^2 + c*d^2)/(4*c*d*e))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2) - (d*log(2*((a*e + c*d*x)*(d + e*x))^(1/2)*(c*d*e)^(1/2) + a*e^2 + c*d^2 + 2*c*d*e*x)*((a*e^2 + c*d^2)^2/4 - a*c*d^2*e^2))/(2*(c*d*e)^(3/2)) + (e*log(2*((a*e + c*d*x)*(d + e*x))^(1/2)*(c*d*e)^(1/2) + a*e^2 + c*d^2 + 2*c*d*e*x)*((a*e^2 + c*d^2)^3 - 4*a*c*d^2*e^2*(a*e^2 + c*d^2)))/(16*(c*d*e)^(5/2)) + ((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*(8*c*d*e*(a*d*e + c*d*e*x^2) - 3*(a*e^2 + c*d^2)^2 + 2*c*d*e*x*(a*e^2 + c*d^2)))/(24*c^2*d^2*e)","B"
1911,1,131,159,0.178421,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","\left(\frac{x}{2}+\frac{c\,d^2+a\,e^2}{4\,c\,d\,e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}-\frac{\ln\left(2\,\sqrt{\left(a\,e+c\,d\,x\right)\,\left(d+e\,x\right)}\,\sqrt{c\,d\,e}+a\,e^2+c\,d^2+2\,c\,d\,e\,x\right)\,\left(\frac{{\left(c\,d^2+a\,e^2\right)}^2}{4}-a\,c\,d^2\,e^2\right)}{2\,{\left(c\,d\,e\right)}^{3/2}}","Not used",1,"(x/2 + (a*e^2 + c*d^2)/(4*c*d*e))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2) - (log(2*((a*e + c*d*x)*(d + e*x))^(1/2)*(c*d*e)^(1/2) + a*e^2 + c*d^2 + 2*c*d*e*x)*((a*e^2 + c*d^2)^2/4 - a*c*d^2*e^2))/(2*(c*d*e)^(3/2))","B"
1912,0,-1,131,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x),x)","\int \frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x), x)","F"
1913,0,-1,124,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x)^2,x)","\int \frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x)^2, x)","F"
1914,1,58,54,1.077410,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x)^3,x)","-\frac{2\,\left(a\,e+c\,d\,x\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{3\,\left(a\,e^2-c\,d^2\right)\,{\left(d+e\,x\right)}^2}","Not used",1,"-(2*(a*e + c*d*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(3*(a*e^2 - c*d^2)*(d + e*x)^2)","B"
1915,1,562,111,1.403413,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x)^4,x)","\frac{\left(\frac{4\,c^2\,d^3}{5\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{4\,a\,c\,d\,e^2}{5\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{\left(\frac{2\,a\,e^2}{5\,a\,e^3-5\,c\,d^2\,e}-\frac{2\,c\,d^2}{5\,a\,e^3-5\,c\,d^2\,e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{4\,c^3\,d^4+4\,a\,c^2\,d^2\,e^2}{15\,e\,{\left(a\,e^2-c\,d^2\right)}^3}-\frac{8\,c^3\,d^4}{15\,e\,{\left(a\,e^2-c\,d^2\right)}^3}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}+\frac{\left(\frac{2\,c^2\,d^3+2\,a\,c\,d\,e^2}{5\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{4\,c^2\,d^3}{5\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{8\,c^3\,d^4}{15\,e\,{\left(a\,e^2-c\,d^2\right)}^3}-\frac{8\,a\,c^2\,d^2\,e}{15\,{\left(a\,e^2-c\,d^2\right)}^3}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}+\frac{8\,c^2\,d^2\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{15\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(d+e\,x\right)}","Not used",1,"(((4*c^2*d^3)/(5*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)) - (4*a*c*d*e^2)/(5*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (((2*a*e^2)/(5*a*e^3 - 5*c*d^2*e) - (2*c*d^2)/(5*a*e^3 - 5*c*d^2*e))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((4*c^3*d^4 + 4*a*c^2*d^2*e^2)/(15*e*(a*e^2 - c*d^2)^3) - (8*c^3*d^4)/(15*e*(a*e^2 - c*d^2)^3))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (((2*c^2*d^3 + 2*a*c*d*e^2)/(5*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)) - (4*c^2*d^3)/(5*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((8*c^3*d^4)/(15*e*(a*e^2 - c*d^2)^3) - (8*a*c^2*d^2*e)/(15*(a*e^2 - c*d^2)^3))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (8*c^2*d^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(15*e*(a*e^2 - c*d^2)^2*(d + e*x))","B"
1916,1,877,171,1.953235,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x)^5,x)","\frac{\left(\frac{4\,c^2\,d^3}{7\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{4\,a\,c\,d\,e^2}{7\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}-\frac{\left(\frac{2\,a\,e^2}{7\,a\,e^3-7\,c\,d^2\,e}-\frac{2\,c\,d^2}{7\,a\,e^3-7\,c\,d^2\,e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}+\frac{\left(\frac{4\,c^3\,d^4+4\,a\,c^2\,d^2\,e^2}{35\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{8\,c^3\,d^4}{35\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{8\,c^4\,d^5+8\,a\,c^3\,d^3\,e^2}{105\,e\,{\left(a\,e^2-c\,d^2\right)}^4}-\frac{16\,c^4\,d^5}{105\,e\,{\left(a\,e^2-c\,d^2\right)}^4}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}+\frac{\left(\frac{2\,c^2\,d^3+2\,a\,c\,d\,e^2}{7\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{4\,c^2\,d^3}{7\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{8\,c^3\,d^4}{35\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{8\,a\,c^2\,d^2\,e^2}{35\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{16\,c^4\,d^5}{105\,e\,{\left(a\,e^2-c\,d^2\right)}^4}-\frac{16\,a\,c^3\,d^3\,e}{105\,{\left(a\,e^2-c\,d^2\right)}^4}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}+\frac{12\,c^2\,d^2\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{35\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)\,{\left(d+e\,x\right)}^2}-\frac{8\,c^3\,d^3\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{105\,e\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(d+e\,x\right)}","Not used",1,"(((4*c^2*d^3)/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)) - (4*a*c*d*e^2)/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 - (((2*a*e^2)/(7*a*e^3 - 7*c*d^2*e) - (2*c*d^2)/(7*a*e^3 - 7*c*d^2*e))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 + (((4*c^3*d^4 + 4*a*c^2*d^2*e^2)/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)) - (8*c^3*d^4)/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((8*c^4*d^5 + 8*a*c^3*d^3*e^2)/(105*e*(a*e^2 - c*d^2)^4) - (16*c^4*d^5)/(105*e*(a*e^2 - c*d^2)^4))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (((2*c^2*d^3 + 2*a*c*d*e^2)/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)) - (4*c^2*d^3)/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((8*c^3*d^4)/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)) - (8*a*c^2*d^2*e^2)/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((16*c^4*d^5)/(105*e*(a*e^2 - c*d^2)^4) - (16*a*c^3*d^3*e)/(105*(a*e^2 - c*d^2)^4))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (12*c^2*d^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(35*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)*(d + e*x)^2) - (8*c^3*d^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(105*e*(a*e^2 - c*d^2)^3*(d + e*x))","B"
1917,1,1192,231,2.577001,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x)^6,x)","\frac{\left(\frac{4\,c^2\,d^3}{9\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}-\frac{4\,a\,c\,d\,e^2}{9\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}-\frac{\left(\frac{2\,a\,e^2}{9\,a\,e^3-9\,c\,d^2\,e}-\frac{2\,c\,d^2}{9\,a\,e^3-9\,c\,d^2\,e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^5}+\frac{\left(\frac{4\,c^3\,d^4+4\,a\,c^2\,d^2\,e^2}{63\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{8\,c^3\,d^4}{63\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{8\,c^4\,d^5+8\,a\,c^3\,d^3\,e^2}{315\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{16\,c^4\,d^5}{315\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{16\,c^5\,d^6+16\,a\,c^4\,d^4\,e^2}{945\,e\,{\left(a\,e^2-c\,d^2\right)}^5}-\frac{32\,c^5\,d^6}{945\,e\,{\left(a\,e^2-c\,d^2\right)}^5}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}+\frac{\left(\frac{2\,c^2\,d^3+2\,a\,c\,d\,e^2}{9\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}-\frac{4\,c^2\,d^3}{9\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}+\frac{\left(\frac{8\,c^3\,d^4}{63\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{8\,a\,c^2\,d^2\,e^2}{63\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{16\,c^4\,d^5}{315\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{16\,a\,c^3\,d^3\,e^2}{315\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{32\,c^5\,d^6}{945\,e\,{\left(a\,e^2-c\,d^2\right)}^5}-\frac{32\,a\,c^4\,d^4\,e}{945\,{\left(a\,e^2-c\,d^2\right)}^5}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{8\,c^3\,d^3\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{63\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)\,{\left(d+e\,x\right)}^2}+\frac{16\,c^2\,d^2\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{63\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)\,{\left(d+e\,x\right)}^3}+\frac{16\,c^4\,d^4\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{135\,e\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(d+e\,x\right)}","Not used",1,"(((4*c^2*d^3)/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)) - (4*a*c*d*e^2)/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 - (((2*a*e^2)/(9*a*e^3 - 9*c*d^2*e) - (2*c*d^2)/(9*a*e^3 - 9*c*d^2*e))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^5 + (((4*c^3*d^4 + 4*a*c^2*d^2*e^2)/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)) - (8*c^3*d^4)/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((8*c^4*d^5 + 8*a*c^3*d^3*e^2)/(315*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)) - (16*c^4*d^5)/(315*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((16*c^5*d^6 + 16*a*c^4*d^4*e^2)/(945*e*(a*e^2 - c*d^2)^5) - (32*c^5*d^6)/(945*e*(a*e^2 - c*d^2)^5))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (((2*c^2*d^3 + 2*a*c*d*e^2)/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)) - (4*c^2*d^3)/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 + (((8*c^3*d^4)/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)) - (8*a*c^2*d^2*e^2)/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((16*c^4*d^5)/(315*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)) - (16*a*c^3*d^3*e^2)/(315*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((32*c^5*d^6)/(945*e*(a*e^2 - c*d^2)^5) - (32*a*c^4*d^4*e)/(945*(a*e^2 - c*d^2)^5))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (8*c^3*d^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(63*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)*(d + e*x)^2) + (16*c^2*d^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(63*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)*(d + e*x)^3) + (16*c^4*d^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(135*e*(a*e^2 - c*d^2)^4*(d + e*x))","B"
1918,0,-1,461,0.000000,"\text{Not used}","int((d + e*x)^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","\int {\left(d+e\,x\right)}^4\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2), x)","F"
1919,0,-1,401,0.000000,"\text{Not used}","int((d + e*x)^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","\int {\left(d+e\,x\right)}^3\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2), x)","F"
1920,0,-1,341,0.000000,"\text{Not used}","int((d + e*x)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","\int {\left(d+e\,x\right)}^2\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2), x)","F"
1921,1,646,283,1.425680,"\text{Not used}","int((d + e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","\frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}}{5\,c\,d}+\frac{\left(\frac{c\,d^2}{2}+c\,x\,d\,e+\frac{a\,e^2}{2}\right)\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}}{4\,c\,e}-\frac{\left(\frac{3\,{\left(c\,d^2+a\,e^2\right)}^2}{4}-3\,a\,c\,d^2\,e^2\right)\,\left(\left(\frac{x}{2}+\frac{c\,d^2+a\,e^2}{4\,c\,d\,e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}-\frac{\ln\left(2\,\sqrt{\left(a\,e+c\,d\,x\right)\,\left(d+e\,x\right)}\,\sqrt{c\,d\,e}+a\,e^2+c\,d^2+2\,c\,d\,e\,x\right)\,\left(\frac{{\left(c\,d^2+a\,e^2\right)}^2}{4}-a\,c\,d^2\,e^2\right)}{2\,{\left(c\,d\,e\right)}^{3/2}}\right)}{4\,c\,e}-\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{x\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}}{4}-\frac{3\,a\,d\,e\,\left(\ln\left(2\,\sqrt{\left(a\,e+c\,d\,x\right)\,\left(d+e\,x\right)}\,\sqrt{c\,d\,e}+a\,e^2+c\,d^2+2\,c\,d\,e\,x\right)\,\left(\frac{{\left(c\,d^2+a\,e^2\right)}^2}{8\,{\left(c\,d\,e\right)}^{3/2}}-\frac{a\,d\,e}{2\,\sqrt{c\,d\,e}}\right)-\frac{\left(c\,d^2+2\,c\,x\,d\,e+a\,e^2\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{4\,c\,d\,e}\right)}{4}+\frac{\left(c\,d^2+a\,e^2\right)\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}}{8\,c\,d\,e}+\frac{3\,{\left(c\,d^2+a\,e^2\right)}^2\,\left(\ln\left(2\,\sqrt{\left(a\,e+c\,d\,x\right)\,\left(d+e\,x\right)}\,\sqrt{c\,d\,e}+a\,e^2+c\,d^2+2\,c\,d\,e\,x\right)\,\left(\frac{{\left(c\,d^2+a\,e^2\right)}^2}{8\,{\left(c\,d\,e\right)}^{3/2}}-\frac{a\,d\,e}{2\,\sqrt{c\,d\,e}}\right)-\frac{\left(c\,d^2+2\,c\,x\,d\,e+a\,e^2\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{4\,c\,d\,e}\right)}{16\,c\,d\,e}\right)}{2\,c\,d}","Not used",1,"(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(5*c*d) + (((a*e^2)/2 + (c*d^2)/2 + c*d*e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2))/(4*c*e) - (((3*(a*e^2 + c*d^2)^2)/4 - 3*a*c*d^2*e^2)*((x/2 + (a*e^2 + c*d^2)/(4*c*d*e))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2) - (log(2*((a*e + c*d*x)*(d + e*x))^(1/2)*(c*d*e)^(1/2) + a*e^2 + c*d^2 + 2*c*d*e*x)*((a*e^2 + c*d^2)^2/4 - a*c*d^2*e^2))/(2*(c*d*e)^(3/2))))/(4*c*e) - ((a*e^2 + c*d^2)*((x*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2))/4 - (3*a*d*e*(log(2*((a*e + c*d*x)*(d + e*x))^(1/2)*(c*d*e)^(1/2) + a*e^2 + c*d^2 + 2*c*d*e*x)*((a*e^2 + c*d^2)^2/(8*(c*d*e)^(3/2)) - (a*d*e)/(2*(c*d*e)^(1/2))) - ((a*e^2 + c*d^2 + 2*c*d*e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(4*c*d*e)))/4 + ((a*e^2 + c*d^2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2))/(8*c*d*e) + (3*(a*e^2 + c*d^2)^2*(log(2*((a*e + c*d*x)*(d + e*x))^(1/2)*(c*d*e)^(1/2) + a*e^2 + c*d^2 + 2*c*d*e*x)*((a*e^2 + c*d^2)^2/(8*(c*d*e)^(3/2)) - (a*d*e)/(2*(c*d*e)^(1/2))) - ((a*e^2 + c*d^2 + 2*c*d*e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(4*c*d*e)))/(16*c*d*e)))/(2*c*d)","B"
1922,1,225,232,0.809913,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","\frac{\left(\frac{c\,d^2}{2}+c\,x\,d\,e+\frac{a\,e^2}{2}\right)\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}}{4\,c\,d\,e}-\frac{\left(\frac{3\,{\left(c\,d^2+a\,e^2\right)}^2}{4}-3\,a\,c\,d^2\,e^2\right)\,\left(\left(\frac{x}{2}+\frac{c\,d^2+a\,e^2}{4\,c\,d\,e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}-\frac{\ln\left(2\,\sqrt{\left(a\,e+c\,d\,x\right)\,\left(d+e\,x\right)}\,\sqrt{c\,d\,e}+a\,e^2+c\,d^2+2\,c\,d\,e\,x\right)\,\left(\frac{{\left(c\,d^2+a\,e^2\right)}^2}{4}-a\,c\,d^2\,e^2\right)}{2\,{\left(c\,d\,e\right)}^{3/2}}\right)}{4\,c\,d\,e}","Not used",1,"(((a*e^2)/2 + (c*d^2)/2 + c*d*e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2))/(4*c*d*e) - (((3*(a*e^2 + c*d^2)^2)/4 - 3*a*c*d^2*e^2)*((x/2 + (a*e^2 + c*d^2)/(4*c*d*e))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2) - (log(2*((a*e + c*d*x)*(d + e*x))^(1/2)*(c*d*e)^(1/2) + a*e^2 + c*d^2 + 2*c*d*e*x)*((a*e^2 + c*d^2)^2/4 - a*c*d^2*e^2))/(2*(c*d*e)^(3/2))))/(4*c*d*e)","B"
1923,0,-1,201,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x),x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}}{d+e\,x} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x), x)","F"
1924,0,-1,187,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^2,x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^2, x)","F"
1925,0,-1,175,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^3,x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^3, x)","F"
1926,0,-1,169,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^4,x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}}{{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^4, x)","F"
1927,1,901,54,1.926967,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^5,x)","\frac{\left(\frac{d\,\left(\frac{4\,c^3\,d^4}{5\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{2\,c^2\,d^2\,\left(5\,a\,e^2-c\,d^2\right)}{5\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{4\,a^2\,c\,d\,e^4+2\,a\,c^2\,d^3\,e^2-2\,c^3\,d^5}{5\,e\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{\left(\frac{d\,\left(\frac{40\,c^4\,d^5-56\,a\,c^3\,d^3\,e^2}{15\,e\,{\left(a\,e^2-c\,d^2\right)}^3}+\frac{8\,c^4\,d^5}{15\,e\,{\left(a\,e^2-c\,d^2\right)}^3}\right)}{e}+\frac{8\,a\,c^2\,d^2\,\left(6\,a\,e^2-5\,c\,d^2\right)}{15\,{\left(a\,e^2-c\,d^2\right)}^3}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{2\,a^2\,e^3}{5\,a\,e^3-5\,c\,d^2\,e}+\frac{d\,\left(\frac{2\,c^2\,d^3}{5\,a\,e^3-5\,c\,d^2\,e}-\frac{4\,a\,c\,d\,e^2}{5\,a\,e^3-5\,c\,d^2\,e}\right)}{e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}-\frac{\left(\frac{10\,c^3\,d^4-22\,a\,c^2\,d^2\,e^2}{15\,e^2\,{\left(a\,e^2-c\,d^2\right)}^2}+\frac{4\,c^3\,d^4}{5\,e^2\,{\left(a\,e^2-c\,d^2\right)}^2}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{d\,\left(\frac{12\,c^3\,d^4-20\,a\,c^2\,d^2\,e^2}{5\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}+\frac{4\,c^3\,d^4}{5\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{4\,a\,c\,d\,e\,\left(4\,a\,e^2-3\,c\,d^2\right)}{5\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{d\,\left(\frac{8\,c^4\,d^5}{15\,e\,{\left(a\,e^2-c\,d^2\right)}^3}-\frac{4\,c^3\,d^3\,\left(11\,a\,e^2-7\,c\,d^2\right)}{15\,e\,{\left(a\,e^2-c\,d^2\right)}^3}\right)}{e}+\frac{20\,a^2\,c^2\,d^2\,e^4+4\,a\,c^3\,d^4\,e^2-16\,c^4\,d^6}{15\,e^2\,{\left(a\,e^2-c\,d^2\right)}^3}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}","Not used",1,"(((d*((4*c^3*d^4)/(5*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)) - (2*c^2*d^2*(5*a*e^2 - c*d^2))/(5*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e))))/e + (2*a*c^2*d^3*e^2 - 2*c^3*d^5 + 4*a^2*c*d*e^4)/(5*e*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (((d*((40*c^4*d^5 - 56*a*c^3*d^3*e^2)/(15*e*(a*e^2 - c*d^2)^3) + (8*c^4*d^5)/(15*e*(a*e^2 - c*d^2)^3)))/e + (8*a*c^2*d^2*(6*a*e^2 - 5*c*d^2))/(15*(a*e^2 - c*d^2)^3))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((2*a^2*e^3)/(5*a*e^3 - 5*c*d^2*e) + (d*((2*c^2*d^3)/(5*a*e^3 - 5*c*d^2*e) - (4*a*c*d*e^2)/(5*a*e^3 - 5*c*d^2*e)))/e)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 - (((10*c^3*d^4 - 22*a*c^2*d^2*e^2)/(15*e^2*(a*e^2 - c*d^2)^2) + (4*c^3*d^4)/(5*e^2*(a*e^2 - c*d^2)^2))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((d*((12*c^3*d^4 - 20*a*c^2*d^2*e^2)/(5*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)) + (4*c^3*d^4)/(5*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e))))/e + (4*a*c*d*e*(4*a*e^2 - 3*c*d^2))/(5*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((d*((8*c^4*d^5)/(15*e*(a*e^2 - c*d^2)^3) - (4*c^3*d^3*(11*a*e^2 - 7*c*d^2))/(15*e*(a*e^2 - c*d^2)^3)))/e + (4*a*c^3*d^4*e^2 - 16*c^4*d^6 + 20*a^2*c^2*d^2*e^4)/(15*e^2*(a*e^2 - c*d^2)^3))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)","B"
1928,1,1477,111,2.769341,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^6,x)","\frac{\left(\frac{d\,\left(\frac{4\,c^3\,d^4}{7\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{2\,c^2\,d^2\,\left(5\,a\,e^2-c\,d^2\right)}{7\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{4\,a^2\,c\,d\,e^4+2\,a\,c^2\,d^3\,e^2-2\,c^3\,d^5}{7\,e\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}-\frac{\left(\frac{14\,c^3\,d^4-34\,a\,c^2\,d^2\,e^2}{35\,e\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}+\frac{4\,c^3\,d^4}{7\,e\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{\left(\frac{d\,\left(\frac{56\,c^4\,d^5-72\,a\,c^3\,d^3\,e^2}{35\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}+\frac{8\,c^4\,d^5}{35\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{8\,a\,c^2\,d^2\,e\,\left(8\,a\,e^2-7\,c\,d^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{d\,\left(\frac{16\,c^5\,d^6}{105\,e\,{\left(a\,e^2-c\,d^2\right)}^4}-\frac{8\,c^4\,d^4\,\left(19\,a\,e^2-15\,c\,d^2\right)}{105\,e\,{\left(a\,e^2-c\,d^2\right)}^4}\right)}{e}+\frac{8\,c^3\,d^3\,\left(9\,a^2\,e^4+a\,c\,d^2\,e^2-8\,c^2\,d^4\right)}{105\,e^2\,{\left(a\,e^2-c\,d^2\right)}^4}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{2\,a^2\,e^3}{7\,a\,e^3-7\,c\,d^2\,e}+\frac{d\,\left(\frac{2\,c^2\,d^3}{7\,a\,e^3-7\,c\,d^2\,e}-\frac{4\,a\,c\,d\,e^2}{7\,a\,e^3-7\,c\,d^2\,e}\right)}{e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}-\frac{\left(\frac{28\,c^4\,d^5-36\,a\,c^3\,d^3\,e^2}{35\,e^2\,{\left(a\,e^2-c\,d^2\right)}^3}+\frac{8\,c^4\,d^5}{35\,e^2\,{\left(a\,e^2-c\,d^2\right)}^3}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{d\,\left(\frac{16\,c^5\,d^6}{105\,e\,{\left(a\,e^2-c\,d^2\right)}^4}-\frac{16\,c^4\,d^4\,\left(11\,a\,e^2-9\,c\,d^2\right)}{105\,e\,{\left(a\,e^2-c\,d^2\right)}^4}\right)}{e}+\frac{16\,a\,c^3\,d^3\,\left(10\,a\,e^2-9\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^4}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{d\,\left(\frac{16\,c^3\,d^4-24\,a\,c^2\,d^2\,e^2}{7\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}+\frac{4\,c^3\,d^4}{7\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{4\,a\,c\,d\,e\,\left(5\,a\,e^2-4\,c\,d^2\right)}{7\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{d\,\left(\frac{8\,c^4\,d^5}{35\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{4\,c^3\,d^3\,\left(13\,a\,e^2-9\,c\,d^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{24\,a^2\,c^2\,d^2\,e^4+4\,a\,c^3\,d^4\,e^2-20\,c^4\,d^6}{35\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{8\,c^3\,d^3\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{105\,e^2\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(d+e\,x\right)}","Not used",1,"(((d*((4*c^3*d^4)/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)) - (2*c^2*d^2*(5*a*e^2 - c*d^2))/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e))))/e + (2*a*c^2*d^3*e^2 - 2*c^3*d^5 + 4*a^2*c*d*e^4)/(7*e*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 - (((14*c^3*d^4 - 34*a*c^2*d^2*e^2)/(35*e*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)) + (4*c^3*d^4)/(7*e*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (((d*((56*c^4*d^5 - 72*a*c^3*d^3*e^2)/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)) + (8*c^4*d^5)/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e))))/e + (8*a*c^2*d^2*e*(8*a*e^2 - 7*c*d^2))/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((d*((16*c^5*d^6)/(105*e*(a*e^2 - c*d^2)^4) - (8*c^4*d^4*(19*a*e^2 - 15*c*d^2))/(105*e*(a*e^2 - c*d^2)^4)))/e + (8*c^3*d^3*(9*a^2*e^4 - 8*c^2*d^4 + a*c*d^2*e^2))/(105*e^2*(a*e^2 - c*d^2)^4))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((2*a^2*e^3)/(7*a*e^3 - 7*c*d^2*e) + (d*((2*c^2*d^3)/(7*a*e^3 - 7*c*d^2*e) - (4*a*c*d*e^2)/(7*a*e^3 - 7*c*d^2*e)))/e)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 - (((28*c^4*d^5 - 36*a*c^3*d^3*e^2)/(35*e^2*(a*e^2 - c*d^2)^3) + (8*c^4*d^5)/(35*e^2*(a*e^2 - c*d^2)^3))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((d*((16*c^5*d^6)/(105*e*(a*e^2 - c*d^2)^4) - (16*c^4*d^4*(11*a*e^2 - 9*c*d^2))/(105*e*(a*e^2 - c*d^2)^4)))/e + (16*a*c^3*d^3*(10*a*e^2 - 9*c*d^2))/(105*(a*e^2 - c*d^2)^4))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((d*((16*c^3*d^4 - 24*a*c^2*d^2*e^2)/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)) + (4*c^3*d^4)/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e))))/e + (4*a*c*d*e*(5*a*e^2 - 4*c*d^2))/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((d*((8*c^4*d^5)/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)) - (4*c^3*d^3*(13*a*e^2 - 9*c*d^2))/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e))))/e + (4*a*c^3*d^4*e^2 - 20*c^4*d^6 + 24*a^2*c^2*d^2*e^4)/(35*e*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (8*c^3*d^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(105*e^2*(a*e^2 - c*d^2)^2*(d + e*x))","B"
1929,1,2067,171,3.853530,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^7,x)","\frac{\left(\frac{d\,\left(\frac{4\,c^3\,d^4}{9\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}-\frac{2\,c^2\,d^2\,\left(5\,a\,e^2-c\,d^2\right)}{9\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}+\frac{4\,a^2\,c\,d\,e^4+2\,a\,c^2\,d^3\,e^2-2\,c^3\,d^5}{9\,e\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}-\frac{\left(\frac{148\,c^4\,d^5-188\,a\,c^3\,d^3\,e^2}{315\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}+\frac{8\,c^4\,d^5}{63\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{\left(\frac{d\,\left(\frac{16\,c^5\,d^6}{315\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{32\,c^4\,d^4\,\left(7\,a\,e^2-6\,c\,d^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{16\,a\,c^3\,d^3\,e\,\left(13\,a\,e^2-12\,c\,d^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{\left(\frac{18\,c^3\,d^4-46\,a\,c^2\,d^2\,e^2}{63\,e\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}+\frac{4\,c^3\,d^4}{9\,e\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}-\frac{\left(\frac{16\,c^5\,d^6}{315\,e^2\,{\left(a\,e^2-c\,d^2\right)}^4}-\frac{8\,c^4\,d^4\,\left(47\,a\,e^2-41\,c\,d^2\right)}{945\,e^2\,{\left(a\,e^2-c\,d^2\right)}^4}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{d\,\left(\frac{72\,c^4\,d^5-88\,a\,c^3\,d^3\,e^2}{63\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}+\frac{8\,c^4\,d^5}{63\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{8\,a\,c^2\,d^2\,e\,\left(10\,a\,e^2-9\,c\,d^2\right)}{63\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{d\,\left(\frac{32\,c^6\,d^7}{945\,e\,{\left(a\,e^2-c\,d^2\right)}^5}-\frac{16\,c^5\,d^5\,\left(29\,a\,e^2-25\,c\,d^2\right)}{945\,e\,{\left(a\,e^2-c\,d^2\right)}^5}\right)}{e}+\frac{16\,c^4\,d^4\,\left(14\,a^2\,e^4+a\,c\,d^2\,e^2-13\,c^2\,d^4\right)}{945\,e^2\,{\left(a\,e^2-c\,d^2\right)}^5}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}+\frac{\left(\frac{d\,\left(\frac{16\,c^5\,d^6}{315\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{8\,c^4\,d^4\,\left(23\,a\,e^2-19\,c\,d^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{8\,c^3\,d^3\,\left(11\,a^2\,e^4+a\,c\,d^2\,e^2-10\,c^2\,d^4\right)}{315\,e\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{\left(\frac{2\,a^2\,e^3}{9\,a\,e^3-9\,c\,d^2\,e}+\frac{d\,\left(\frac{2\,c^2\,d^3}{9\,a\,e^3-9\,c\,d^2\,e}-\frac{4\,a\,c\,d\,e^2}{9\,a\,e^3-9\,c\,d^2\,e}\right)}{e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^5}-\frac{\left(\frac{d\,\left(\frac{32\,c^6\,d^7}{945\,e\,{\left(a\,e^2-c\,d^2\right)}^5}-\frac{64\,c^5\,d^5\,\left(8\,a\,e^2-7\,c\,d^2\right)}{945\,e\,{\left(a\,e^2-c\,d^2\right)}^5}\right)}{e}+\frac{32\,a\,c^4\,d^4\,\left(15\,a\,e^2-14\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^5}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{d\,\left(\frac{20\,c^3\,d^4-28\,a\,c^2\,d^2\,e^2}{9\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}+\frac{4\,c^3\,d^4}{9\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}+\frac{4\,a\,c\,d\,e\,\left(6\,a\,e^2-5\,c\,d^2\right)}{9\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}+\frac{\left(\frac{d\,\left(\frac{8\,c^4\,d^5}{63\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{4\,c^3\,d^3\,\left(15\,a\,e^2-11\,c\,d^2\right)}{63\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{28\,a^2\,c^2\,d^2\,e^4+4\,a\,c^3\,d^4\,e^2-24\,c^4\,d^6}{63\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}-\frac{8\,c^4\,d^4\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{45\,e^2\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(d+e\,x\right)}-\frac{44\,c^3\,d^3\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{315\,e\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)\,{\left(d+e\,x\right)}^2}","Not used",1,"(((d*((4*c^3*d^4)/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)) - (2*c^2*d^2*(5*a*e^2 - c*d^2))/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e))))/e + (2*a*c^2*d^3*e^2 - 2*c^3*d^5 + 4*a^2*c*d*e^4)/(9*e*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 - (((148*c^4*d^5 - 188*a*c^3*d^3*e^2)/(315*e*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)) + (8*c^4*d^5)/(63*e*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (((d*((16*c^5*d^6)/(315*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)) - (32*c^4*d^4*(7*a*e^2 - 6*c*d^2))/(315*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e))))/e + (16*a*c^3*d^3*e*(13*a*e^2 - 12*c*d^2))/(315*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (((18*c^3*d^4 - 46*a*c^2*d^2*e^2)/(63*e*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)) + (4*c^3*d^4)/(9*e*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 - (((16*c^5*d^6)/(315*e^2*(a*e^2 - c*d^2)^4) - (8*c^4*d^4*(47*a*e^2 - 41*c*d^2))/(945*e^2*(a*e^2 - c*d^2)^4))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((d*((72*c^4*d^5 - 88*a*c^3*d^3*e^2)/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)) + (8*c^4*d^5)/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e))))/e + (8*a*c^2*d^2*e*(10*a*e^2 - 9*c*d^2))/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((d*((32*c^6*d^7)/(945*e*(a*e^2 - c*d^2)^5) - (16*c^5*d^5*(29*a*e^2 - 25*c*d^2))/(945*e*(a*e^2 - c*d^2)^5)))/e + (16*c^4*d^4*(14*a^2*e^4 - 13*c^2*d^4 + a*c*d^2*e^2))/(945*e^2*(a*e^2 - c*d^2)^5))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (((d*((16*c^5*d^6)/(315*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)) - (8*c^4*d^4*(23*a*e^2 - 19*c*d^2))/(315*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e))))/e + (8*c^3*d^3*(11*a^2*e^4 - 10*c^2*d^4 + a*c*d^2*e^2))/(315*e*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (((2*a^2*e^3)/(9*a*e^3 - 9*c*d^2*e) + (d*((2*c^2*d^3)/(9*a*e^3 - 9*c*d^2*e) - (4*a*c*d*e^2)/(9*a*e^3 - 9*c*d^2*e)))/e)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^5 - (((d*((32*c^6*d^7)/(945*e*(a*e^2 - c*d^2)^5) - (64*c^5*d^5*(8*a*e^2 - 7*c*d^2))/(945*e*(a*e^2 - c*d^2)^5)))/e + (32*a*c^4*d^4*(15*a*e^2 - 14*c*d^2))/(945*(a*e^2 - c*d^2)^5))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((d*((20*c^3*d^4 - 28*a*c^2*d^2*e^2)/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)) + (4*c^3*d^4)/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e))))/e + (4*a*c*d*e*(6*a*e^2 - 5*c*d^2))/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 + (((d*((8*c^4*d^5)/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)) - (4*c^3*d^3*(15*a*e^2 - 11*c*d^2))/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e))))/e + (4*a*c^3*d^4*e^2 - 24*c^4*d^6 + 28*a^2*c^2*d^2*e^4)/(63*e*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 - (8*c^4*d^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(45*e^2*(a*e^2 - c*d^2)^3*(d + e*x)) - (44*c^3*d^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(315*e*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)*(d + e*x)^2)","B"
1930,1,2657,231,5.152794,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^8,x)","\frac{\left(\frac{d\,\left(\frac{4\,c^3\,d^4}{11\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}-\frac{2\,c^2\,d^2\,\left(5\,a\,e^2-c\,d^2\right)}{11\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)}{e}+\frac{4\,a^2\,c\,d\,e^4+2\,a\,c^2\,d^3\,e^2-2\,c^3\,d^5}{11\,e\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^5}-\frac{\left(\frac{228\,c^4\,d^5-284\,a\,c^3\,d^3\,e^2}{693\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}+\frac{8\,c^4\,d^5}{99\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}-\frac{\left(\frac{d\,\left(\frac{16\,c^5\,d^6}{693\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{16\,c^4\,d^4\,\left(17\,a\,e^2-15\,c\,d^2\right)}{693\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{16\,a\,c^3\,d^3\,e\,\left(16\,a\,e^2-15\,c\,d^2\right)}{693\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}-\frac{\left(\frac{d\,\left(\frac{32\,c^6\,d^7}{3465\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{64\,c^5\,d^5\,\left(10\,a\,e^2-9\,c\,d^2\right)}{3465\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{32\,a\,c^4\,d^4\,e\,\left(19\,a\,e^2-18\,c\,d^2\right)}{3465\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{\left(\frac{22\,c^3\,d^4-58\,a\,c^2\,d^2\,e^2}{99\,e\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}+\frac{4\,c^3\,d^4}{11\,e\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}-\frac{\left(\frac{32\,c^6\,d^7}{3465\,e^2\,{\left(a\,e^2-c\,d^2\right)}^5}-\frac{16\,c^5\,d^5\,\left(71\,a\,e^2-65\,c\,d^2\right)}{10395\,e^2\,{\left(a\,e^2-c\,d^2\right)}^5}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{d\,\left(\frac{88\,c^4\,d^5-104\,a\,c^3\,d^3\,e^2}{99\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}+\frac{8\,c^4\,d^5}{99\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}+\frac{8\,a\,c^2\,d^2\,e\,\left(12\,a\,e^2-11\,c\,d^2\right)}{99\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}+\frac{\left(\frac{d\,\left(\frac{64\,c^7\,d^8}{10395\,e\,{\left(a\,e^2-c\,d^2\right)}^6}-\frac{32\,c^6\,d^6\,\left(41\,a\,e^2-37\,c\,d^2\right)}{10395\,e\,{\left(a\,e^2-c\,d^2\right)}^6}\right)}{e}+\frac{32\,c^5\,d^5\,\left(20\,a^2\,e^4+a\,c\,d^2\,e^2-19\,c^2\,d^4\right)}{10395\,e^2\,{\left(a\,e^2-c\,d^2\right)}^6}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}+\frac{\left(\frac{d\,\left(\frac{16\,c^5\,d^6}{693\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{8\,c^4\,d^4\,\left(27\,a\,e^2-23\,c\,d^2\right)}{693\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{8\,c^3\,d^3\,\left(13\,a^2\,e^4+a\,c\,d^2\,e^2-12\,c^2\,d^4\right)}{693\,e\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{d\,\left(\frac{32\,c^6\,d^7}{3465\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{16\,c^5\,d^5\,\left(35\,a\,e^2-31\,c\,d^2\right)}{3465\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{16\,c^4\,d^4\,\left(17\,a^2\,e^4+a\,c\,d^2\,e^2-16\,c^2\,d^4\right)}{3465\,e\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{\left(\frac{2\,a^2\,e^3}{11\,a\,e^3-11\,c\,d^2\,e}+\frac{d\,\left(\frac{2\,c^2\,d^3}{11\,a\,e^3-11\,c\,d^2\,e}-\frac{4\,a\,c\,d\,e^2}{11\,a\,e^3-11\,c\,d^2\,e}\right)}{e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^6}-\frac{\left(\frac{16\,c^5\,d^6}{693\,e\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{8\,c^4\,d^4\,\left(83\,a\,e^2-73\,c\,d^2\right)}{3465\,e\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{\left(\frac{d\,\left(\frac{64\,c^7\,d^8}{10395\,e\,{\left(a\,e^2-c\,d^2\right)}^6}-\frac{128\,c^6\,d^6\,\left(11\,a\,e^2-10\,c\,d^2\right)}{10395\,e\,{\left(a\,e^2-c\,d^2\right)}^6}\right)}{e}+\frac{64\,a\,c^5\,d^5\,\left(21\,a\,e^2-20\,c\,d^2\right)}{10395\,{\left(a\,e^2-c\,d^2\right)}^6}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{d\,\left(\frac{24\,c^3\,d^4-32\,a\,c^2\,d^2\,e^2}{11\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}+\frac{4\,c^3\,d^4}{11\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)}{e}+\frac{4\,a\,c\,d\,e\,\left(7\,a\,e^2-6\,c\,d^2\right)}{11\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^5}+\frac{\left(\frac{d\,\left(\frac{8\,c^4\,d^5}{99\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}-\frac{4\,c^3\,d^3\,\left(17\,a\,e^2-13\,c\,d^2\right)}{99\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}+\frac{32\,a^2\,c^2\,d^2\,e^4+4\,a\,c^3\,d^4\,e^2-28\,c^4\,d^6}{99\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}-\frac{16\,c^5\,d^5\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{1155\,e^2\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(d+e\,x\right)}-\frac{472\,c^4\,d^4\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{3465\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)\,{\left(d+e\,x\right)}^2}-\frac{32\,c^3\,d^3\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{231\,e\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)\,{\left(d+e\,x\right)}^3}","Not used",1,"(((d*((4*c^3*d^4)/(11*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e)) - (2*c^2*d^2*(5*a*e^2 - c*d^2))/(11*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e))))/e + (2*a*c^2*d^3*e^2 - 2*c^3*d^5 + 4*a^2*c*d*e^4)/(11*e*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^5 - (((228*c^4*d^5 - 284*a*c^3*d^3*e^2)/(693*e*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)) + (8*c^4*d^5)/(99*e*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 - (((d*((16*c^5*d^6)/(693*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e)) - (16*c^4*d^4*(17*a*e^2 - 15*c*d^2))/(693*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e))))/e + (16*a*c^3*d^3*e*(16*a*e^2 - 15*c*d^2))/(693*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 - (((d*((32*c^6*d^7)/(3465*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e)) - (64*c^5*d^5*(10*a*e^2 - 9*c*d^2))/(3465*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e))))/e + (32*a*c^4*d^4*e*(19*a*e^2 - 18*c*d^2))/(3465*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (((22*c^3*d^4 - 58*a*c^2*d^2*e^2)/(99*e*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)) + (4*c^3*d^4)/(11*e*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 - (((32*c^6*d^7)/(3465*e^2*(a*e^2 - c*d^2)^5) - (16*c^5*d^5*(71*a*e^2 - 65*c*d^2))/(10395*e^2*(a*e^2 - c*d^2)^5))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((d*((88*c^4*d^5 - 104*a*c^3*d^3*e^2)/(99*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e)) + (8*c^4*d^5)/(99*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e))))/e + (8*a*c^2*d^2*e*(12*a*e^2 - 11*c*d^2))/(99*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 + (((d*((64*c^7*d^8)/(10395*e*(a*e^2 - c*d^2)^6) - (32*c^6*d^6*(41*a*e^2 - 37*c*d^2))/(10395*e*(a*e^2 - c*d^2)^6)))/e + (32*c^5*d^5*(20*a^2*e^4 - 19*c^2*d^4 + a*c*d^2*e^2))/(10395*e^2*(a*e^2 - c*d^2)^6))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (((d*((16*c^5*d^6)/(693*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e)) - (8*c^4*d^4*(27*a*e^2 - 23*c*d^2))/(693*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e))))/e + (8*c^3*d^3*(13*a^2*e^4 - 12*c^2*d^4 + a*c*d^2*e^2))/(693*e*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((d*((32*c^6*d^7)/(3465*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e)) - (16*c^5*d^5*(35*a*e^2 - 31*c*d^2))/(3465*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e))))/e + (16*c^4*d^4*(17*a^2*e^4 - 16*c^2*d^4 + a*c*d^2*e^2))/(3465*e*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (((2*a^2*e^3)/(11*a*e^3 - 11*c*d^2*e) + (d*((2*c^2*d^3)/(11*a*e^3 - 11*c*d^2*e) - (4*a*c*d*e^2)/(11*a*e^3 - 11*c*d^2*e)))/e)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^6 - (((16*c^5*d^6)/(693*e*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)) - (8*c^4*d^4*(83*a*e^2 - 73*c*d^2))/(3465*e*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (((d*((64*c^7*d^8)/(10395*e*(a*e^2 - c*d^2)^6) - (128*c^6*d^6*(11*a*e^2 - 10*c*d^2))/(10395*e*(a*e^2 - c*d^2)^6)))/e + (64*a*c^5*d^5*(21*a*e^2 - 20*c*d^2))/(10395*(a*e^2 - c*d^2)^6))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((d*((24*c^3*d^4 - 32*a*c^2*d^2*e^2)/(11*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e)) + (4*c^3*d^4)/(11*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e))))/e + (4*a*c*d*e*(7*a*e^2 - 6*c*d^2))/(11*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^5 + (((d*((8*c^4*d^5)/(99*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e)) - (4*c^3*d^3*(17*a*e^2 - 13*c*d^2))/(99*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e))))/e + (4*a*c^3*d^4*e^2 - 28*c^4*d^6 + 32*a^2*c^2*d^2*e^4)/(99*e*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 - (16*c^5*d^5*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(1155*e^2*(a*e^2 - c*d^2)^4*(d + e*x)) - (472*c^4*d^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(3465*e*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)*(d + e*x)^2) - (32*c^3*d^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(231*e*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)*(d + e*x)^3)","B"
1931,0,-1,534,0.000000,"\text{Not used}","int((d + e*x)^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","\int {\left(d+e\,x\right)}^4\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2), x)","F"
1932,0,-1,474,0.000000,"\text{Not used}","int((d + e*x)^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","\int {\left(d+e\,x\right)}^3\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2), x)","F"
1933,0,-1,414,0.000000,"\text{Not used}","int((d + e*x)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","\int {\left(d+e\,x\right)}^2\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2), x)","F"
1934,0,-1,356,0.000000,"\text{Not used}","int((d + e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","\int \left(d+e\,x\right)\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2), x)","F"
1935,1,319,305,0.794748,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","\frac{\left(\frac{c\,d^2}{2}+c\,x\,d\,e+\frac{a\,e^2}{2}\right)\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}}{6\,c\,d\,e}-\frac{\left(\frac{5\,{\left(c\,d^2+a\,e^2\right)}^2}{4}-5\,a\,c\,d^2\,e^2\right)\,\left(\frac{\left(\frac{c\,d^2}{2}+c\,x\,d\,e+\frac{a\,e^2}{2}\right)\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}}{4\,c\,d\,e}-\frac{\left(\frac{3\,{\left(c\,d^2+a\,e^2\right)}^2}{4}-3\,a\,c\,d^2\,e^2\right)\,\left(\left(\frac{x}{2}+\frac{c\,d^2+a\,e^2}{4\,c\,d\,e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}-\frac{\ln\left(2\,\sqrt{\left(a\,e+c\,d\,x\right)\,\left(d+e\,x\right)}\,\sqrt{c\,d\,e}+a\,e^2+c\,d^2+2\,c\,d\,e\,x\right)\,\left(\frac{{\left(c\,d^2+a\,e^2\right)}^2}{4}-a\,c\,d^2\,e^2\right)}{2\,{\left(c\,d\,e\right)}^{3/2}}\right)}{4\,c\,d\,e}\right)}{6\,c\,d\,e}","Not used",1,"(((a*e^2)/2 + (c*d^2)/2 + c*d*e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2))/(6*c*d*e) - (((5*(a*e^2 + c*d^2)^2)/4 - 5*a*c*d^2*e^2)*((((a*e^2)/2 + (c*d^2)/2 + c*d*e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2))/(4*c*d*e) - (((3*(a*e^2 + c*d^2)^2)/4 - 3*a*c*d^2*e^2)*((x/2 + (a*e^2 + c*d^2)/(4*c*d*e))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2) - (log(2*((a*e + c*d*x)*(d + e*x))^(1/2)*(c*d*e)^(1/2) + a*e^2 + c*d^2 + 2*c*d*e*x)*((a*e^2 + c*d^2)^2/4 - a*c*d^2*e^2))/(2*(c*d*e)^(3/2))))/(4*c*d*e)))/(6*c*d*e)","B"
1936,0,-1,274,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x),x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}}{d+e\,x} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x), x)","F"
1937,0,-1,261,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^2,x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^2, x)","F"
1938,0,-1,244,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^3,x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^3, x)","F"
1939,0,-1,235,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^4,x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}}{{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^4, x)","F"
1940,0,-1,226,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^5,x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}}{{\left(d+e\,x\right)}^5} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^5, x)","F"
1941,0,-1,218,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^6,x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}}{{\left(d+e\,x\right)}^6} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^6, x)","F"
1942,1,2156,54,3.756184,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^7,x)","\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{16\,c^6\,d^7}{105\,e\,{\left(a\,e^2-c\,d^2\right)}^4}-\frac{16\,c^5\,d^5\,\left(4\,a\,e^2-3\,c\,d^2\right)}{35\,e\,{\left(a\,e^2-c\,d^2\right)}^4}\right)}{e}+\frac{16\,c^4\,d^4\,\left(56\,a^2\,e^4-88\,a\,c\,d^2\,e^2+35\,c^2\,d^4\right)}{105\,e^2\,{\left(a\,e^2-c\,d^2\right)}^4}\right)}{e}-\frac{16\,a\,c^3\,d^3\,\left(45\,a^2\,e^4-79\,a\,c\,d^2\,e^2+35\,c^2\,d^4\right)}{105\,e\,{\left(a\,e^2-c\,d^2\right)}^4}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{2\,a^3\,e^4}{7\,a\,e^3-7\,c\,d^2\,e}-\frac{d\,\left(\frac{d\,\left(\frac{2\,c^3\,d^4}{7\,a\,e^3-7\,c\,d^2\,e}-\frac{6\,a\,c^2\,d^2\,e^2}{7\,a\,e^3-7\,c\,d^2\,e}\right)}{e}+\frac{6\,a^2\,c\,d\,e^3}{7\,a\,e^3-7\,c\,d^2\,e}\right)}{e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{4\,c^4\,d^5}{7\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{4\,c^3\,d^3\,\left(7\,a\,e^2-4\,c\,d^2\right)}{7\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{60\,a^2\,c^2\,d^2\,e^4-64\,a\,c^3\,d^4\,e^2+16\,c^4\,d^6}{7\,e\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}-\frac{4\,a\,c\,d\,{\left(3\,a\,e^2-2\,c\,d^2\right)}^2}{7\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{d\,\left(\frac{4\,c^4\,d^5}{7\,e\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{2\,c^3\,d^3\,\left(7\,a\,e^2-3\,c\,d^2\right)}{7\,e\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{66\,a^2\,c^2\,d^2\,e^4-62\,a\,c^3\,d^4\,e^2+16\,c^4\,d^6}{35\,e^2\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{288\,a^3\,c^3\,d^3\,e^6-208\,a^2\,c^4\,d^5\,e^4-280\,a\,c^5\,d^7\,e^2+216\,c^6\,d^9}{105\,e^3\,{\left(a\,e^2-c\,d^2\right)}^4}-\frac{d\,\left(\frac{d\,\left(\frac{16\,c^6\,d^7}{105\,e\,{\left(a\,e^2-c\,d^2\right)}^4}-\frac{8\,c^5\,d^5\,\left(7\,a\,e^2-5\,c\,d^2\right)}{35\,e\,{\left(a\,e^2-c\,d^2\right)}^4}\right)}{e}+\frac{16\,c^4\,d^4\,\left(41\,a^2\,e^4-61\,a\,c\,d^2\,e^2+23\,c^2\,d^4\right)}{105\,e^2\,{\left(a\,e^2-c\,d^2\right)}^4}\right)}{e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{8\,c^5\,d^6}{35\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{8\,c^4\,d^4\,\left(10\,a\,e^2-7\,c\,d^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{8\,c^3\,d^3\,\left(36\,a^2\,e^4-52\,a\,c\,d^2\,e^2+19\,c^2\,d^4\right)}{35\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}-\frac{8\,a\,c^2\,d^2\,\left(27\,a^2\,e^4-45\,a\,c\,d^2\,e^2+19\,c^2\,d^4\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{d\,\left(\frac{8\,c^5\,d^6}{35\,e^2\,{\left(a\,e^2-c\,d^2\right)}^3}-\frac{4\,c^4\,d^4\,\left(15\,a\,e^2-11\,c\,d^2\right)}{35\,e^2\,{\left(a\,e^2-c\,d^2\right)}^3}\right)}{e}+\frac{4\,c^3\,d^3\,\left(27\,a^2\,e^4-39\,a\,c\,d^2\,e^2+14\,c^2\,d^4\right)}{35\,e^3\,{\left(a\,e^2-c\,d^2\right)}^3}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{4\,c^4\,d^5}{7\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{2\,c^3\,d^3\,\left(7\,a\,e^2-c\,d^2\right)}{7\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{2\,c^2\,d^2\,\left(9\,a^2\,e^4-4\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{7\,e\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}-\frac{6\,a^3\,c\,d\,e^6-4\,a\,c^3\,d^5\,e^2+2\,c^4\,d^7}{7\,e^2\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{8\,c^5\,d^6}{35\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{12\,c^4\,d^4\,\left(5\,a\,e^2-3\,c\,d^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{4\,c^3\,d^3\,\left(37\,a^2\,e^4-44\,a\,c\,d^2\,e^2+13\,c^2\,d^4\right)}{35\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}-\frac{60\,a^3\,c^2\,d^2\,e^6-32\,a^2\,c^3\,d^4\,e^4-56\,a\,c^4\,d^6\,e^2+36\,c^5\,d^8}{35\,e^2\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{\left(\frac{6\,c^4\,d^5-26\,a\,c^3\,d^3\,e^2}{35\,e^3\,{\left(a\,e^2-c\,d^2\right)}^2}+\frac{4\,c^4\,d^5}{7\,e^3\,{\left(a\,e^2-c\,d^2\right)}^2}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}","Not used",1,"(((d*((d*((16*c^6*d^7)/(105*e*(a*e^2 - c*d^2)^4) - (16*c^5*d^5*(4*a*e^2 - 3*c*d^2))/(35*e*(a*e^2 - c*d^2)^4)))/e + (16*c^4*d^4*(56*a^2*e^4 + 35*c^2*d^4 - 88*a*c*d^2*e^2))/(105*e^2*(a*e^2 - c*d^2)^4)))/e - (16*a*c^3*d^3*(45*a^2*e^4 + 35*c^2*d^4 - 79*a*c*d^2*e^2))/(105*e*(a*e^2 - c*d^2)^4))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((2*a^3*e^4)/(7*a*e^3 - 7*c*d^2*e) - (d*((d*((2*c^3*d^4)/(7*a*e^3 - 7*c*d^2*e) - (6*a*c^2*d^2*e^2)/(7*a*e^3 - 7*c*d^2*e)))/e + (6*a^2*c*d*e^3)/(7*a*e^3 - 7*c*d^2*e)))/e)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 + (((d*((d*((4*c^4*d^5)/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)) - (4*c^3*d^3*(7*a*e^2 - 4*c*d^2))/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e))))/e + (16*c^4*d^6 - 64*a*c^3*d^4*e^2 + 60*a^2*c^2*d^2*e^4)/(7*e*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e))))/e - (4*a*c*d*(3*a*e^2 - 2*c*d^2)^2)/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((d*((4*c^4*d^5)/(7*e*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)) - (2*c^3*d^3*(7*a*e^2 - 3*c*d^2))/(7*e*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e))))/e + (16*c^4*d^6 - 62*a*c^3*d^4*e^2 + 66*a^2*c^2*d^2*e^4)/(35*e^2*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((216*c^6*d^9 - 280*a*c^5*d^7*e^2 - 208*a^2*c^4*d^5*e^4 + 288*a^3*c^3*d^3*e^6)/(105*e^3*(a*e^2 - c*d^2)^4) - (d*((d*((16*c^6*d^7)/(105*e*(a*e^2 - c*d^2)^4) - (8*c^5*d^5*(7*a*e^2 - 5*c*d^2))/(35*e*(a*e^2 - c*d^2)^4)))/e + (16*c^4*d^4*(41*a^2*e^4 + 23*c^2*d^4 - 61*a*c*d^2*e^2))/(105*e^2*(a*e^2 - c*d^2)^4)))/e)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (((d*((d*((8*c^5*d^6)/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)) - (8*c^4*d^4*(10*a*e^2 - 7*c*d^2))/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e))))/e + (8*c^3*d^3*(36*a^2*e^4 + 19*c^2*d^4 - 52*a*c*d^2*e^2))/(35*e*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e))))/e - (8*a*c^2*d^2*(27*a^2*e^4 + 19*c^2*d^4 - 45*a*c*d^2*e^2))/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((d*((8*c^5*d^6)/(35*e^2*(a*e^2 - c*d^2)^3) - (4*c^4*d^4*(15*a*e^2 - 11*c*d^2))/(35*e^2*(a*e^2 - c*d^2)^3)))/e + (4*c^3*d^3*(27*a^2*e^4 + 14*c^2*d^4 - 39*a*c*d^2*e^2))/(35*e^3*(a*e^2 - c*d^2)^3))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((d*((d*((4*c^4*d^5)/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)) - (2*c^3*d^3*(7*a*e^2 - c*d^2))/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e))))/e + (2*c^2*d^2*(9*a^2*e^4 + c^2*d^4 - 4*a*c*d^2*e^2))/(7*e*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e))))/e - (2*c^4*d^7 - 4*a*c^3*d^5*e^2 + 6*a^3*c*d*e^6)/(7*e^2*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 - (((d*((d*((8*c^5*d^6)/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)) - (12*c^4*d^4*(5*a*e^2 - 3*c*d^2))/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e))))/e + (4*c^3*d^3*(37*a^2*e^4 + 13*c^2*d^4 - 44*a*c*d^2*e^2))/(35*e*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e))))/e - (36*c^5*d^8 - 56*a*c^4*d^6*e^2 - 32*a^2*c^3*d^4*e^4 + 60*a^3*c^2*d^2*e^6)/(35*e^2*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (((6*c^4*d^5 - 26*a*c^3*d^3*e^2)/(35*e^3*(a*e^2 - c*d^2)^2) + (4*c^4*d^5)/(7*e^3*(a*e^2 - c*d^2)^2))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)","B"
1943,1,3125,111,5.290622,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^8,x)","\frac{\left(\frac{d\,\left(\frac{8\,c^5\,d^6}{63\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{4\,c^4\,d^4\,\left(17\,a\,e^2-13\,c\,d^2\right)}{63\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{4\,c^3\,d^3\,\left(148\,a^2\,e^4-211\,a\,c\,d^2\,e^2+73\,c^2\,d^4\right)}{315\,e^2\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{\left(\frac{2\,a^3\,e^4}{9\,a\,e^3-9\,c\,d^2\,e}-\frac{d\,\left(\frac{d\,\left(\frac{2\,c^3\,d^4}{9\,a\,e^3-9\,c\,d^2\,e}-\frac{6\,a\,c^2\,d^2\,e^2}{9\,a\,e^3-9\,c\,d^2\,e}\right)}{e}+\frac{6\,a^2\,c\,d\,e^3}{9\,a\,e^3-9\,c\,d^2\,e}\right)}{e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^5}+\frac{\left(\frac{2\,c^4\,d^5+26\,a\,c^3\,d^3\,e^2}{63\,e^2\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{4\,c^4\,d^5}{9\,e^2\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{32\,c^7\,d^8}{945\,e\,{\left(a\,e^2-c\,d^2\right)}^5}-\frac{32\,c^6\,d^6\,\left(17\,a\,e^2-14\,c\,d^2\right)}{945\,e\,{\left(a\,e^2-c\,d^2\right)}^5}\right)}{e}+\frac{32\,c^5\,d^5\,\left(116\,a^2\,e^4-198\,a\,c\,d^2\,e^2+85\,c^2\,d^4\right)}{945\,e^2\,{\left(a\,e^2-c\,d^2\right)}^5}\right)}{e}-\frac{32\,a\,c^4\,d^4\,\left(100\,a^2\,e^4-184\,a\,c\,d^2\,e^2+85\,c^2\,d^4\right)}{945\,e\,{\left(a\,e^2-c\,d^2\right)}^5}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{4\,c^4\,d^5}{9\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}-\frac{4\,c^3\,d^3\,\left(8\,a\,e^2-5\,c\,d^2\right)}{9\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}+\frac{72\,a^2\,c^2\,d^2\,e^4-80\,a\,c^3\,d^4\,e^2+20\,c^4\,d^6}{9\,e\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}-\frac{4\,a\,c\,d\,\left(11\,a^2\,e^4-15\,a\,c\,d^2\,e^2+5\,c^2\,d^4\right)}{9\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}+\frac{\left(\frac{d\,\left(\frac{4\,c^4\,d^5}{9\,e\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{2\,c^3\,d^3\,\left(7\,a\,e^2-3\,c\,d^2\right)}{9\,e\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{90\,a^2\,c^2\,d^2\,e^4-82\,a\,c^3\,d^4\,e^2+20\,c^4\,d^6}{63\,e^2\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{1376\,a^3\,c^4\,d^4\,e^6-1136\,a^2\,c^5\,d^6\,e^4-1360\,a\,c^6\,d^8\,e^2+1152\,c^7\,d^{10}}{945\,e^3\,{\left(a\,e^2-c\,d^2\right)}^5}-\frac{d\,\left(\frac{d\,\left(\frac{32\,c^7\,d^8}{945\,e\,{\left(a\,e^2-c\,d^2\right)}^5}-\frac{16\,c^6\,d^6\,\left(31\,a\,e^2-25\,c\,d^2\right)}{945\,e\,{\left(a\,e^2-c\,d^2\right)}^5}\right)}{e}+\frac{16\,c^5\,d^5\,\left(187\,a^2\,e^4-312\,a\,c\,d^2\,e^2+131\,c^2\,d^4\right)}{945\,e^2\,{\left(a\,e^2-c\,d^2\right)}^5}\right)}{e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{8\,c^5\,d^6}{63\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{8\,c^4\,d^4\,\left(4\,a\,e^2-3\,c\,d^2\right)}{21\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{8\,c^3\,d^3\,\left(50\,a^2\,e^4-76\,a\,c\,d^2\,e^2+29\,c^2\,d^4\right)}{63\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}-\frac{8\,a\,c^2\,d^2\,\left(39\,a^2\,e^4-67\,a\,c\,d^2\,e^2+29\,c^2\,d^4\right)}{63\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{16\,c^6\,d^7}{315\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{16\,c^5\,d^5\,\left(5\,a\,e^2-4\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{16\,c^4\,d^4\,\left(86\,a^2\,e^4-142\,a\,c\,d^2\,e^2+59\,c^2\,d^4\right)}{315\,e\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}-\frac{16\,a\,c^3\,d^3\,\left(72\,a^2\,e^4-130\,a\,c\,d^2\,e^2+59\,c^2\,d^4\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{d\,\left(\frac{16\,c^6\,d^7}{315\,e^2\,{\left(a\,e^2-c\,d^2\right)}^4}-\frac{8\,c^5\,d^5\,\left(25\,a\,e^2-21\,c\,d^2\right)}{315\,e^2\,{\left(a\,e^2-c\,d^2\right)}^4}\right)}{e}+\frac{8\,c^4\,d^4\,\left(236\,a^2\,e^4-397\,a\,c\,d^2\,e^2+167\,c^2\,d^4\right)}{945\,e^3\,{\left(a\,e^2-c\,d^2\right)}^4}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{4\,c^4\,d^5}{9\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}-\frac{2\,c^3\,d^3\,\left(7\,a\,e^2-c\,d^2\right)}{9\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}+\frac{2\,c^2\,d^2\,\left(9\,a^2\,e^4-4\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{9\,e\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}-\frac{6\,a^3\,c\,d\,e^6-4\,a\,c^3\,d^5\,e^2+2\,c^4\,d^7}{9\,e^2\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{8\,c^5\,d^6}{63\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{4\,c^4\,d^4\,\left(17\,a\,e^2-11\,c\,d^2\right)}{63\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{8\,c^3\,d^3\,\left(22\,a^2\,e^4-27\,a\,c\,d^2\,e^2+8\,c^2\,d^4\right)}{63\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}-\frac{72\,a^3\,c^2\,d^2\,e^6-40\,a^2\,c^3\,d^4\,e^4-68\,a\,c^4\,d^6\,e^2+44\,c^5\,d^8}{63\,e^2\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{16\,c^6\,d^7}{315\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{8\,c^5\,d^5\,\left(25\,a\,e^2-19\,c\,d^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{16\,c^4\,d^4\,\left(56\,a^2\,e^4-87\,a\,c\,d^2\,e^2+34\,c^2\,d^4\right)}{315\,e\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}-\frac{400\,a^3\,c^3\,d^3\,e^6-304\,a^2\,c^4\,d^5\,e^4-392\,a\,c^5\,d^7\,e^2+312\,c^6\,d^9}{315\,e^2\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{284\,c^5\,d^6-164\,a\,c^4\,d^4\,e^2}{945\,e^3\,{\left(a\,e^2-c\,d^2\right)}^3}-\frac{8\,c^5\,d^6}{63\,e^3\,{\left(a\,e^2-c\,d^2\right)}^3}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}+\frac{32\,c^4\,d^4\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{189\,e^3\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(d+e\,x\right)}","Not used",1,"(((d*((8*c^5*d^6)/(63*e*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)) - (4*c^4*d^4*(17*a*e^2 - 13*c*d^2))/(63*e*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e))))/e + (4*c^3*d^3*(148*a^2*e^4 + 73*c^2*d^4 - 211*a*c*d^2*e^2))/(315*e^2*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (((2*a^3*e^4)/(9*a*e^3 - 9*c*d^2*e) - (d*((d*((2*c^3*d^4)/(9*a*e^3 - 9*c*d^2*e) - (6*a*c^2*d^2*e^2)/(9*a*e^3 - 9*c*d^2*e)))/e + (6*a^2*c*d*e^3)/(9*a*e^3 - 9*c*d^2*e)))/e)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^5 + (((2*c^4*d^5 + 26*a*c^3*d^3*e^2)/(63*e^2*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)) - (4*c^4*d^5)/(9*e^2*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((d*((d*((32*c^7*d^8)/(945*e*(a*e^2 - c*d^2)^5) - (32*c^6*d^6*(17*a*e^2 - 14*c*d^2))/(945*e*(a*e^2 - c*d^2)^5)))/e + (32*c^5*d^5*(116*a^2*e^4 + 85*c^2*d^4 - 198*a*c*d^2*e^2))/(945*e^2*(a*e^2 - c*d^2)^5)))/e - (32*a*c^4*d^4*(100*a^2*e^4 + 85*c^2*d^4 - 184*a*c*d^2*e^2))/(945*e*(a*e^2 - c*d^2)^5))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (((d*((d*((4*c^4*d^5)/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)) - (4*c^3*d^3*(8*a*e^2 - 5*c*d^2))/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e))))/e + (20*c^4*d^6 - 80*a*c^3*d^4*e^2 + 72*a^2*c^2*d^2*e^4)/(9*e*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e))))/e - (4*a*c*d*(11*a^2*e^4 + 5*c^2*d^4 - 15*a*c*d^2*e^2))/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 + (((d*((4*c^4*d^5)/(9*e*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)) - (2*c^3*d^3*(7*a*e^2 - 3*c*d^2))/(9*e*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e))))/e + (20*c^4*d^6 - 82*a*c^3*d^4*e^2 + 90*a^2*c^2*d^2*e^4)/(63*e^2*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((1152*c^7*d^10 - 1360*a*c^6*d^8*e^2 - 1136*a^2*c^5*d^6*e^4 + 1376*a^3*c^4*d^4*e^6)/(945*e^3*(a*e^2 - c*d^2)^5) - (d*((d*((32*c^7*d^8)/(945*e*(a*e^2 - c*d^2)^5) - (16*c^6*d^6*(31*a*e^2 - 25*c*d^2))/(945*e*(a*e^2 - c*d^2)^5)))/e + (16*c^5*d^5*(187*a^2*e^4 + 131*c^2*d^4 - 312*a*c*d^2*e^2))/(945*e^2*(a*e^2 - c*d^2)^5)))/e)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (((d*((d*((8*c^5*d^6)/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)) - (8*c^4*d^4*(4*a*e^2 - 3*c*d^2))/(21*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e))))/e + (8*c^3*d^3*(50*a^2*e^4 + 29*c^2*d^4 - 76*a*c*d^2*e^2))/(63*e*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e))))/e - (8*a*c^2*d^2*(39*a^2*e^4 + 29*c^2*d^4 - 67*a*c*d^2*e^2))/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((d*((d*((16*c^6*d^7)/(315*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)) - (16*c^5*d^5*(5*a*e^2 - 4*c*d^2))/(105*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e))))/e + (16*c^4*d^4*(86*a^2*e^4 + 59*c^2*d^4 - 142*a*c*d^2*e^2))/(315*e*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e))))/e - (16*a*c^3*d^3*(72*a^2*e^4 + 59*c^2*d^4 - 130*a*c*d^2*e^2))/(315*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((d*((16*c^6*d^7)/(315*e^2*(a*e^2 - c*d^2)^4) - (8*c^5*d^5*(25*a*e^2 - 21*c*d^2))/(315*e^2*(a*e^2 - c*d^2)^4)))/e + (8*c^4*d^4*(236*a^2*e^4 + 167*c^2*d^4 - 397*a*c*d^2*e^2))/(945*e^3*(a*e^2 - c*d^2)^4))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((d*((d*((4*c^4*d^5)/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)) - (2*c^3*d^3*(7*a*e^2 - c*d^2))/(9*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e))))/e + (2*c^2*d^2*(9*a^2*e^4 + c^2*d^4 - 4*a*c*d^2*e^2))/(9*e*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e))))/e - (2*c^4*d^7 - 4*a*c^3*d^5*e^2 + 6*a^3*c*d*e^6)/(9*e^2*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 - (((d*((d*((8*c^5*d^6)/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)) - (4*c^4*d^4*(17*a*e^2 - 11*c*d^2))/(63*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e))))/e + (8*c^3*d^3*(22*a^2*e^4 + 8*c^2*d^4 - 27*a*c*d^2*e^2))/(63*e*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e))))/e - (44*c^5*d^8 - 68*a*c^4*d^6*e^2 - 40*a^2*c^3*d^4*e^4 + 72*a^3*c^2*d^2*e^6)/(63*e^2*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 - (((d*((d*((16*c^6*d^7)/(315*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)) - (8*c^5*d^5*(25*a*e^2 - 19*c*d^2))/(315*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e))))/e + (16*c^4*d^4*(56*a^2*e^4 + 34*c^2*d^4 - 87*a*c*d^2*e^2))/(315*e*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e))))/e - (312*c^6*d^9 - 392*a*c^5*d^7*e^2 - 304*a^2*c^4*d^5*e^4 + 400*a^3*c^3*d^3*e^6)/(315*e^2*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((284*c^5*d^6 - 164*a*c^4*d^4*e^2)/(945*e^3*(a*e^2 - c*d^2)^3) - (8*c^5*d^6)/(63*e^3*(a*e^2 - c*d^2)^3))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (32*c^4*d^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(189*e^3*(a*e^2 - c*d^2)^2*(d + e*x))","B"
1944,1,4096,171,7.208587,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^9,x)","\frac{\left(\frac{d\,\left(\frac{8\,c^5\,d^6}{99\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{4\,c^4\,d^4\,\left(19\,a\,e^2-15\,c\,d^2\right)}{99\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{4\,c^3\,d^3\,\left(33\,a^2\,e^4-47\,a\,c\,d^2\,e^2+16\,c^2\,d^4\right)}{99\,e^2\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}-\frac{\left(\frac{2\,a^3\,e^4}{11\,a\,e^3-11\,c\,d^2\,e}-\frac{d\,\left(\frac{d\,\left(\frac{2\,c^3\,d^4}{11\,a\,e^3-11\,c\,d^2\,e}-\frac{6\,a\,c^2\,d^2\,e^2}{11\,a\,e^3-11\,c\,d^2\,e}\right)}{e}+\frac{6\,a^2\,c\,d\,e^3}{11\,a\,e^3-11\,c\,d^2\,e}\right)}{e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^6}+\frac{\left(\frac{d\,\left(\frac{16\,c^6\,d^7}{693\,e\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{8\,c^5\,d^5\,\left(29\,a\,e^2-25\,c\,d^2\right)}{693\,e\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{8\,c^4\,d^4\,\left(466\,a^2\,e^4-787\,a\,c\,d^2\,e^2+331\,c^2\,d^4\right)}{3465\,e^2\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{6\,c^4\,d^5+22\,a\,c^3\,d^3\,e^2}{77\,e^2\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{4\,c^4\,d^5}{11\,e^2\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{188\,c^5\,d^6-148\,a\,c^4\,d^4\,e^2}{495\,e^2\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{8\,c^5\,d^6}{99\,e^2\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{64\,c^8\,d^9}{10395\,e\,{\left(a\,e^2-c\,d^2\right)}^6}-\frac{64\,c^7\,d^7\,\left(23\,a\,e^2-20\,c\,d^2\right)}{10395\,e\,{\left(a\,e^2-c\,d^2\right)}^6}\right)}{e}+\frac{64\,c^6\,d^6\,\left(218\,a^2\,e^4-390\,a\,c\,d^2\,e^2+175\,c^2\,d^4\right)}{10395\,e^2\,{\left(a\,e^2-c\,d^2\right)}^6}\right)}{e}-\frac{64\,a\,c^5\,d^5\,\left(196\,a^2\,e^4-370\,a\,c\,d^2\,e^2+175\,c^2\,d^4\right)}{10395\,e\,{\left(a\,e^2-c\,d^2\right)}^6}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{16\,c^6\,d^7}{693\,e^3\,{\left(a\,e^2-c\,d^2\right)}^4}+\frac{8\,c^5\,d^5\,\left(497\,a\,e^2-527\,c\,d^2\right)}{10395\,e^3\,{\left(a\,e^2-c\,d^2\right)}^4}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}+\frac{\left(\frac{d\,\left(\frac{4\,c^4\,d^5}{11\,e\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}-\frac{2\,c^3\,d^3\,\left(7\,a\,e^2-3\,c\,d^2\right)}{11\,e\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}+\frac{38\,a^2\,c^2\,d^2\,e^4-34\,a\,c^3\,d^4\,e^2+8\,c^4\,d^6}{33\,e^2\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}+\frac{\left(\frac{5632\,a^3\,c^5\,d^5\,e^6-4960\,a^2\,c^6\,d^7\,e^4-5600\,a\,c^7\,d^9\,e^2+4992\,c^8\,d^{11}}{10395\,e^3\,{\left(a\,e^2-c\,d^2\right)}^6}-\frac{d\,\left(\frac{d\,\left(\frac{64\,c^8\,d^9}{10395\,e\,{\left(a\,e^2-c\,d^2\right)}^6}-\frac{32\,c^7\,d^7\,\left(43\,a\,e^2-37\,c\,d^2\right)}{10395\,e\,{\left(a\,e^2-c\,d^2\right)}^6}\right)}{e}+\frac{32\,c^6\,d^6\,\left(373\,a^2\,e^4-660\,a\,c\,d^2\,e^2+293\,c^2\,d^4\right)}{10395\,e^2\,{\left(a\,e^2-c\,d^2\right)}^6}\right)}{e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{8\,c^5\,d^6}{99\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}-\frac{8\,c^4\,d^4\,\left(14\,a\,e^2-11\,c\,d^2\right)}{99\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}+\frac{8\,c^3\,d^3\,\left(66\,a^2\,e^4-104\,a\,c\,d^2\,e^2+41\,c^2\,d^4\right)}{99\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}-\frac{8\,a\,c^2\,d^2\,\left(53\,a^2\,e^4-93\,a\,c\,d^2\,e^2+41\,c^2\,d^4\right)}{99\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{16\,c^6\,d^7}{693\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{16\,c^5\,d^5\,\left(6\,a\,e^2-5\,c\,d^2\right)}{231\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{16\,c^4\,d^4\,\left(122\,a^2\,e^4-208\,a\,c\,d^2\,e^2+89\,c^2\,d^4\right)}{693\,e\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}-\frac{16\,a\,c^3\,d^3\,\left(105\,a^2\,e^4-193\,a\,c\,d^2\,e^2+89\,c^2\,d^4\right)}{693\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{32\,c^7\,d^8}{3465\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{32\,c^6\,d^6\,\left(7\,a\,e^2-6\,c\,d^2\right)}{1155\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{32\,c^5\,d^5\,\left(176\,a^2\,e^4-310\,a\,c\,d^2\,e^2+137\,c^2\,d^4\right)}{3465\,e\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}-\frac{32\,a\,c^4\,d^4\,\left(156\,a^2\,e^4-292\,a\,c\,d^2\,e^2+137\,c^2\,d^4\right)}{3465\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{d\,\left(\frac{32\,c^7\,d^8}{3465\,e^2\,{\left(a\,e^2-c\,d^2\right)}^5}-\frac{16\,c^6\,d^6\,\left(37\,a\,e^2-33\,c\,d^2\right)}{3465\,e^2\,{\left(a\,e^2-c\,d^2\right)}^5}\right)}{e}+\frac{16\,c^5\,d^5\,\left(542\,a^2\,e^4-973\,a\,c\,d^2\,e^2+437\,c^2\,d^4\right)}{10395\,e^3\,{\left(a\,e^2-c\,d^2\right)}^5}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{4\,c^4\,d^5}{11\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}-\frac{2\,c^3\,d^3\,\left(7\,a\,e^2-c\,d^2\right)}{11\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)}{e}+\frac{2\,c^2\,d^2\,\left(9\,a^2\,e^4-4\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{11\,e\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)}{e}-\frac{6\,a^3\,c\,d\,e^6-4\,a\,c^3\,d^5\,e^2+2\,c^4\,d^7}{11\,e^2\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^5}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{8\,c^5\,d^6}{99\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}-\frac{4\,c^4\,d^4\,\left(19\,a\,e^2-13\,c\,d^2\right)}{99\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}+\frac{4\,c^3\,d^3\,\left(51\,a^2\,e^4-64\,a\,c\,d^2\,e^2+19\,c^2\,d^4\right)}{99\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}-\frac{84\,a^3\,c^2\,d^2\,e^6-48\,a^2\,c^3\,d^4\,e^4-80\,a\,c^4\,d^6\,e^2+52\,c^5\,d^8}{99\,e^2\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{16\,c^6\,d^7}{693\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{8\,c^5\,d^5\,\left(29\,a\,e^2-23\,c\,d^2\right)}{693\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{16\,c^4\,d^4\,\left(73\,a^2\,e^4-117\,a\,c\,d^2\,e^2+47\,c^2\,d^4\right)}{693\,e\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}-\frac{528\,a^3\,c^3\,d^3\,e^6-416\,a^2\,c^4\,d^5\,e^4-520\,a\,c^5\,d^7\,e^2+424\,c^6\,d^9}{693\,e^2\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{32\,c^7\,d^8}{3465\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{16\,c^6\,d^6\,\left(37\,a\,e^2-31\,c\,d^2\right)}{3465\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{32\,c^5\,d^5\,\left(131\,a^2\,e^4-225\,a\,c\,d^2\,e^2+97\,c^2\,d^4\right)}{3465\,e\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}-\frac{1952\,a^3\,c^4\,d^4\,e^6-1664\,a^2\,c^5\,d^6\,e^4-1936\,a\,c^6\,d^8\,e^2+1680\,c^7\,d^{10}}{3465\,e^2\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{4\,c^4\,d^5}{11\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}-\frac{12\,c^3\,d^3\,\left(3\,a\,e^2-2\,c\,d^2\right)}{11\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)}{e}+\frac{12\,c^2\,d^2\,\left(7\,a^2\,e^4-8\,a\,c\,d^2\,e^2+2\,c^2\,d^4\right)}{11\,e\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)}{e}-\frac{4\,a\,c\,d\,\left(13\,a^2\,e^4-18\,a\,c\,d^2\,e^2+6\,c^2\,d^4\right)}{11\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^5}+\frac{1976\,c^5\,d^5\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{10395\,e^3\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(d+e\,x\right)}+\frac{52\,c^4\,d^4\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{385\,e^2\,\left(a\,e^2-c\,d^2\right)\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)\,{\left(d+e\,x\right)}^2}","Not used",1,"(((d*((8*c^5*d^6)/(99*e*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)) - (4*c^4*d^4*(19*a*e^2 - 15*c*d^2))/(99*e*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e))))/e + (4*c^3*d^3*(33*a^2*e^4 + 16*c^2*d^4 - 47*a*c*d^2*e^2))/(99*e^2*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 - (((2*a^3*e^4)/(11*a*e^3 - 11*c*d^2*e) - (d*((d*((2*c^3*d^4)/(11*a*e^3 - 11*c*d^2*e) - (6*a*c^2*d^2*e^2)/(11*a*e^3 - 11*c*d^2*e)))/e + (6*a^2*c*d*e^3)/(11*a*e^3 - 11*c*d^2*e)))/e)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^6 + (((d*((16*c^6*d^7)/(693*e*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)) - (8*c^5*d^5*(29*a*e^2 - 25*c*d^2))/(693*e*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e))))/e + (8*c^4*d^4*(466*a^2*e^4 + 331*c^2*d^4 - 787*a*c*d^2*e^2))/(3465*e^2*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((6*c^4*d^5 + 22*a*c^3*d^3*e^2)/(77*e^2*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)) - (4*c^4*d^5)/(11*e^2*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((188*c^5*d^6 - 148*a*c^4*d^4*e^2)/(495*e^2*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)) - (8*c^5*d^6)/(99*e^2*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((d*((d*((64*c^8*d^9)/(10395*e*(a*e^2 - c*d^2)^6) - (64*c^7*d^7*(23*a*e^2 - 20*c*d^2))/(10395*e*(a*e^2 - c*d^2)^6)))/e + (64*c^6*d^6*(218*a^2*e^4 + 175*c^2*d^4 - 390*a*c*d^2*e^2))/(10395*e^2*(a*e^2 - c*d^2)^6)))/e - (64*a*c^5*d^5*(196*a^2*e^4 + 175*c^2*d^4 - 370*a*c*d^2*e^2))/(10395*e*(a*e^2 - c*d^2)^6))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((16*c^6*d^7)/(693*e^3*(a*e^2 - c*d^2)^4) + (8*c^5*d^5*(497*a*e^2 - 527*c*d^2))/(10395*e^3*(a*e^2 - c*d^2)^4))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (((d*((4*c^4*d^5)/(11*e*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)) - (2*c^3*d^3*(7*a*e^2 - 3*c*d^2))/(11*e*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e))))/e + (8*c^4*d^6 - 34*a*c^3*d^4*e^2 + 38*a^2*c^2*d^2*e^4)/(33*e^2*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 + (((4992*c^8*d^11 - 5600*a*c^7*d^9*e^2 - 4960*a^2*c^6*d^7*e^4 + 5632*a^3*c^5*d^5*e^6)/(10395*e^3*(a*e^2 - c*d^2)^6) - (d*((d*((64*c^8*d^9)/(10395*e*(a*e^2 - c*d^2)^6) - (32*c^7*d^7*(43*a*e^2 - 37*c*d^2))/(10395*e*(a*e^2 - c*d^2)^6)))/e + (32*c^6*d^6*(373*a^2*e^4 + 293*c^2*d^4 - 660*a*c*d^2*e^2))/(10395*e^2*(a*e^2 - c*d^2)^6)))/e)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (((d*((d*((8*c^5*d^6)/(99*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e)) - (8*c^4*d^4*(14*a*e^2 - 11*c*d^2))/(99*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e))))/e + (8*c^3*d^3*(66*a^2*e^4 + 41*c^2*d^4 - 104*a*c*d^2*e^2))/(99*e*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e))))/e - (8*a*c^2*d^2*(53*a^2*e^4 + 41*c^2*d^4 - 93*a*c*d^2*e^2))/(99*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 + (((d*((d*((16*c^6*d^7)/(693*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e)) - (16*c^5*d^5*(6*a*e^2 - 5*c*d^2))/(231*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e))))/e + (16*c^4*d^4*(122*a^2*e^4 + 89*c^2*d^4 - 208*a*c*d^2*e^2))/(693*e*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e))))/e - (16*a*c^3*d^3*(105*a^2*e^4 + 89*c^2*d^4 - 193*a*c*d^2*e^2))/(693*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((d*((d*((32*c^7*d^8)/(3465*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e)) - (32*c^6*d^6*(7*a*e^2 - 6*c*d^2))/(1155*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e))))/e + (32*c^5*d^5*(176*a^2*e^4 + 137*c^2*d^4 - 310*a*c*d^2*e^2))/(3465*e*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e))))/e - (32*a*c^4*d^4*(156*a^2*e^4 + 137*c^2*d^4 - 292*a*c*d^2*e^2))/(3465*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((d*((32*c^7*d^8)/(3465*e^2*(a*e^2 - c*d^2)^5) - (16*c^6*d^6*(37*a*e^2 - 33*c*d^2))/(3465*e^2*(a*e^2 - c*d^2)^5)))/e + (16*c^5*d^5*(542*a^2*e^4 + 437*c^2*d^4 - 973*a*c*d^2*e^2))/(10395*e^3*(a*e^2 - c*d^2)^5))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((d*((d*((4*c^4*d^5)/(11*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e)) - (2*c^3*d^3*(7*a*e^2 - c*d^2))/(11*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e))))/e + (2*c^2*d^2*(9*a^2*e^4 + c^2*d^4 - 4*a*c*d^2*e^2))/(11*e*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e))))/e - (2*c^4*d^7 - 4*a*c^3*d^5*e^2 + 6*a^3*c*d*e^6)/(11*e^2*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^5 - (((d*((d*((8*c^5*d^6)/(99*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e)) - (4*c^4*d^4*(19*a*e^2 - 13*c*d^2))/(99*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e))))/e + (4*c^3*d^3*(51*a^2*e^4 + 19*c^2*d^4 - 64*a*c*d^2*e^2))/(99*e*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e))))/e - (52*c^5*d^8 - 80*a*c^4*d^6*e^2 - 48*a^2*c^3*d^4*e^4 + 84*a^3*c^2*d^2*e^6)/(99*e^2*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 - (((d*((d*((16*c^6*d^7)/(693*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e)) - (8*c^5*d^5*(29*a*e^2 - 23*c*d^2))/(693*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e))))/e + (16*c^4*d^4*(73*a^2*e^4 + 47*c^2*d^4 - 117*a*c*d^2*e^2))/(693*e*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e))))/e - (424*c^6*d^9 - 520*a*c^5*d^7*e^2 - 416*a^2*c^4*d^5*e^4 + 528*a^3*c^3*d^3*e^6)/(693*e^2*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 - (((d*((d*((32*c^7*d^8)/(3465*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e)) - (16*c^6*d^6*(37*a*e^2 - 31*c*d^2))/(3465*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e))))/e + (32*c^5*d^5*(131*a^2*e^4 + 97*c^2*d^4 - 225*a*c*d^2*e^2))/(3465*e*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e))))/e - (1680*c^7*d^10 - 1936*a*c^6*d^8*e^2 - 1664*a^2*c^5*d^6*e^4 + 1952*a^3*c^4*d^4*e^6)/(3465*e^2*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((d*((d*((4*c^4*d^5)/(11*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e)) - (12*c^3*d^3*(3*a*e^2 - 2*c*d^2))/(11*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e))))/e + (12*c^2*d^2*(7*a^2*e^4 + 2*c^2*d^4 - 8*a*c*d^2*e^2))/(11*e*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e))))/e - (4*a*c*d*(13*a^2*e^4 + 6*c^2*d^4 - 18*a*c*d^2*e^2))/(11*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^5 + (1976*c^5*d^5*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(10395*e^3*(a*e^2 - c*d^2)^3*(d + e*x)) + (52*c^4*d^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(385*e^2*(a*e^2 - c*d^2)*(3*a*e^3 - 3*c*d^2*e)*(d + e*x)^2)","B"
1945,1,5069,231,9.572788,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^10,x)","\frac{\left(\frac{d\,\left(\frac{8\,c^5\,d^6}{143\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}-\frac{4\,c^4\,d^4\,\left(21\,a\,e^2-17\,c\,d^2\right)}{143\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}+\frac{4\,c^3\,d^3\,\left(110\,a^2\,e^4-157\,a\,c\,d^2\,e^2+53\,c^2\,d^4\right)}{429\,e^2\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}-\frac{\left(\frac{2\,a^3\,e^4}{13\,a\,e^3-13\,c\,d^2\,e}-\frac{d\,\left(\frac{d\,\left(\frac{2\,c^3\,d^4}{13\,a\,e^3-13\,c\,d^2\,e}-\frac{6\,a\,c^2\,d^2\,e^2}{13\,a\,e^3-13\,c\,d^2\,e}\right)}{e}+\frac{6\,a^2\,c\,d\,e^3}{13\,a\,e^3-13\,c\,d^2\,e}\right)}{e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^7}+\frac{\left(\frac{d\,\left(\frac{16\,c^6\,d^7}{1287\,e\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{8\,c^5\,d^5\,\left(33\,a\,e^2-29\,c\,d^2\right)}{1287\,e\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{8\,c^4\,d^4\,\left(112\,a^2\,e^4-191\,a\,c\,d^2\,e^2+81\,c^2\,d^4\right)}{1287\,e^2\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{d\,\left(\frac{32\,c^7\,d^8}{9009\,e\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{16\,c^6\,d^6\,\left(43\,a\,e^2-39\,c\,d^2\right)}{9009\,e\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{16\,c^5\,d^5\,\left(1089\,a^2\,e^4-1963\,a\,c\,d^2\,e^2+884\,c^2\,d^4\right)}{45045\,e^2\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{38\,c^4\,d^5+94\,a\,c^3\,d^3\,e^2}{429\,e^2\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}-\frac{4\,c^4\,d^5}{13\,e^2\,\left(a\,e^2-c\,d^2\right)\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}+\frac{\left(\frac{348\,c^5\,d^6-292\,a\,c^4\,d^4\,e^2}{1001\,e^2\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{8\,c^5\,d^6}{143\,e^2\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{128\,c^9\,d^{10}}{135135\,e\,{\left(a\,e^2-c\,d^2\right)}^7}-\frac{128\,c^8\,d^8\,\left(10\,a\,e^2-9\,c\,d^2\right)}{45045\,e\,{\left(a\,e^2-c\,d^2\right)}^7}\right)}{e}+\frac{128\,c^7\,d^7\,\left(379\,a^2\,e^4-698\,a\,c\,d^2\,e^2+322\,c^2\,d^4\right)}{135135\,e^2\,{\left(a\,e^2-c\,d^2\right)}^7}\right)}{e}-\frac{128\,a\,c^6\,d^6\,\left(350\,a^2\,e^4-671\,a\,c\,d^2\,e^2+322\,c^2\,d^4\right)}{135135\,e\,{\left(a\,e^2-c\,d^2\right)}^7}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{128\,c^9\,d^{10}}{135135\,e\,{\left(a\,e^2-c\,d^2\right)}^7}-\frac{64\,c^8\,d^8\,\left(19\,a\,e^2-17\,c\,d^2\right)}{45045\,e\,{\left(a\,e^2-c\,d^2\right)}^7}\right)}{e}+\frac{128\,c^7\,d^7\,\left(337\,a^2\,e^4-617\,a\,c\,d^2\,e^2+283\,c^2\,d^4\right)}{135135\,e^2\,{\left(a\,e^2-c\,d^2\right)}^7}\right)}{e}-\frac{64\,c^6\,d^6\,\left(323\,a^3\,e^6-295\,a^2\,c\,d^2\,e^4-322\,a\,c^2\,d^4\,e^2+296\,c^3\,d^6\right)}{135135\,e^3\,{\left(a\,e^2-c\,d^2\right)}^7}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{4\,c^4\,d^5}{13\,\left(a\,e^2-c\,d^2\right)\,\left(11\,a\,e^3-11\,c\,d^2\,e\right)}-\frac{4\,c^3\,d^3\,\left(10\,a\,e^2-7\,c\,d^2\right)}{13\,\left(a\,e^2-c\,d^2\right)\,\left(11\,a\,e^3-11\,c\,d^2\,e\right)}\right)}{e}+\frac{96\,a^2\,c^2\,d^2\,e^4-112\,a\,c^3\,d^4\,e^2+28\,c^4\,d^6}{13\,e\,\left(a\,e^2-c\,d^2\right)\,\left(11\,a\,e^3-11\,c\,d^2\,e\right)}\right)}{e}-\frac{4\,a\,c\,d\,\left(15\,a^2\,e^4-21\,a\,c\,d^2\,e^2+7\,c^2\,d^4\right)}{13\,\left(a\,e^2-c\,d^2\right)\,\left(11\,a\,e^3-11\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^6}-\frac{\left(\frac{32\,c^7\,d^8}{9009\,e^3\,{\left(a\,e^2-c\,d^2\right)}^5}+\frac{16\,c^6\,d^6\,\left(511\,a\,e^2-521\,c\,d^2\right)}{45045\,e^3\,{\left(a\,e^2-c\,d^2\right)}^5}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}+\frac{\left(\frac{d\,\left(\frac{4\,c^4\,d^5}{13\,e\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}-\frac{2\,c^3\,d^3\,\left(7\,a\,e^2-3\,c\,d^2\right)}{13\,e\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)}{e}+\frac{138\,a^2\,c^2\,d^2\,e^4-122\,a\,c^3\,d^4\,e^2+28\,c^4\,d^6}{143\,e^2\,\left(a\,e^2-c\,d^2\right)\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^5}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{8\,c^5\,d^6}{143\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}-\frac{8\,c^4\,d^4\,\left(16\,a\,e^2-13\,c\,d^2\right)}{143\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)}{e}+\frac{8\,c^3\,d^3\,\left(84\,a^2\,e^4-136\,a\,c\,d^2\,e^2+55\,c^2\,d^4\right)}{143\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)}{e}-\frac{8\,a\,c^2\,d^2\,\left(69\,a^2\,e^4-123\,a\,c\,d^2\,e^2+55\,c^2\,d^4\right)}{143\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^5}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{16\,c^6\,d^7}{1287\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}-\frac{16\,c^5\,d^5\,\left(7\,a\,e^2-6\,c\,d^2\right)}{429\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}+\frac{16\,c^4\,d^4\,\left(164\,a^2\,e^4-286\,a\,c\,d^2\,e^2+125\,c^2\,d^4\right)}{1287\,e\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}-\frac{16\,a\,c^3\,d^3\,\left(144\,a^2\,e^4-268\,a\,c\,d^2\,e^2+125\,c^2\,d^4\right)}{1287\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{32\,c^7\,d^8}{9009\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{32\,c^6\,d^6\,\left(25\,a\,e^2-22\,c\,d^2\right)}{9009\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{32\,c^5\,d^5\,\left(248\,a^2\,e^4-446\,a\,c\,d^2\,e^2+201\,c^2\,d^4\right)}{9009\,e\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}-\frac{32\,a\,c^4\,d^4\,\left(224\,a^2\,e^4-424\,a\,c\,d^2\,e^2+201\,c^2\,d^4\right)}{9009\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{64\,c^8\,d^9}{45045\,{\left(a\,e^2-c\,d^2\right)}^5\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{64\,c^7\,d^7\,\left(28\,a\,e^2-25\,c\,d^2\right)}{45045\,{\left(a\,e^2-c\,d^2\right)}^5\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{64\,c^6\,d^6\,\left(323\,a^2\,e^4-590\,a\,c\,d^2\,e^2+270\,c^2\,d^4\right)}{45045\,e\,{\left(a\,e^2-c\,d^2\right)}^5\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}-\frac{64\,a\,c^5\,d^5\,\left(296\,a^2\,e^4-565\,a\,c\,d^2\,e^2+270\,c^2\,d^4\right)}{45045\,{\left(a\,e^2-c\,d^2\right)}^5\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{d\,\left(\frac{64\,c^8\,d^9}{45045\,e^2\,{\left(a\,e^2-c\,d^2\right)}^6}-\frac{32\,c^7\,d^7\,\left(51\,a\,e^2-47\,c\,d^2\right)}{45045\,e^2\,{\left(a\,e^2-c\,d^2\right)}^6}\right)}{e}+\frac{32\,c^6\,d^6\,\left(1067\,a^2\,e^4-1981\,a\,c\,d^2\,e^2+920\,c^2\,d^4\right)}{135135\,e^3\,{\left(a\,e^2-c\,d^2\right)}^6}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{4\,c^4\,d^5}{13\,\left(a\,e^2-c\,d^2\right)\,\left(11\,a\,e^3-11\,c\,d^2\,e\right)}-\frac{2\,c^3\,d^3\,\left(7\,a\,e^2-c\,d^2\right)}{13\,\left(a\,e^2-c\,d^2\right)\,\left(11\,a\,e^3-11\,c\,d^2\,e\right)}\right)}{e}+\frac{2\,c^2\,d^2\,\left(9\,a^2\,e^4-4\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{13\,e\,\left(a\,e^2-c\,d^2\right)\,\left(11\,a\,e^3-11\,c\,d^2\,e\right)}\right)}{e}-\frac{6\,a^3\,c\,d\,e^6-4\,a\,c^3\,d^5\,e^2+2\,c^4\,d^7}{13\,e^2\,\left(a\,e^2-c\,d^2\right)\,\left(11\,a\,e^3-11\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^6}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{8\,c^5\,d^6}{143\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}-\frac{12\,c^4\,d^4\,\left(7\,a\,e^2-5\,c\,d^2\right)}{143\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)}{e}+\frac{8\,c^3\,d^3\,\left(29\,a^2\,e^4-37\,a\,c\,d^2\,e^2+11\,c^2\,d^4\right)}{143\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)}{e}-\frac{96\,a^3\,c^2\,d^2\,e^6-56\,a^2\,c^3\,d^4\,e^4-92\,a\,c^4\,d^6\,e^2+60\,c^5\,d^8}{143\,e^2\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(9\,a\,e^3-9\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^5}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{16\,c^6\,d^7}{1287\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}-\frac{8\,c^5\,d^5\,\left(11\,a\,e^2-9\,c\,d^2\right)}{429\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}+\frac{16\,c^4\,d^4\,\left(92\,a^2\,e^4-151\,a\,c\,d^2\,e^2+62\,c^2\,d^4\right)}{1287\,e\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)}{e}-\frac{672\,a^3\,c^3\,d^3\,e^6-544\,a^2\,c^4\,d^5\,e^4-664\,a\,c^5\,d^7\,e^2+552\,c^6\,d^9}{1287\,e^2\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(7\,a\,e^3-7\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{32\,c^7\,d^8}{9009\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{16\,c^6\,d^6\,\left(43\,a\,e^2-37\,c\,d^2\right)}{9009\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{16\,c^5\,d^5\,\left(349\,a^2\,e^4-612\,a\,c\,d^2\,e^2+269\,c^2\,d^4\right)}{9009\,e\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}-\frac{2624\,a^3\,c^4\,d^4\,e^6-2288\,a^2\,c^5\,d^6\,e^4-2608\,a\,c^6\,d^8\,e^2+2304\,c^7\,d^{10}}{9009\,e^2\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{64\,c^8\,d^9}{45045\,{\left(a\,e^2-c\,d^2\right)}^5\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{32\,c^7\,d^7\,\left(17\,a\,e^2-15\,c\,d^2\right)}{15015\,{\left(a\,e^2-c\,d^2\right)}^5\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{32\,c^6\,d^6\,\left(521\,a^2\,e^4-940\,a\,c\,d^2\,e^2+425\,c^2\,d^4\right)}{45045\,e\,{\left(a\,e^2-c\,d^2\right)}^5\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}-\frac{7936\,a^3\,c^5\,d^5\,e^6-7136\,a^2\,c^6\,d^7\,e^4-7904\,a\,c^7\,d^9\,e^2+7168\,c^8\,d^{11}}{45045\,e^2\,{\left(a\,e^2-c\,d^2\right)}^5\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{\left(\frac{16\,c^6\,d^7}{1287\,e^2\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}+\frac{8\,c^5\,d^5\,\left(283\,a\,e^2-293\,c\,d^2\right)}{6435\,e^2\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{15952\,c^6\,d^6\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{135135\,e^3\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(d+e\,x\right)}+\frac{88\,c^5\,d^5\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{455\,e^2\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)\,{\left(d+e\,x\right)}^2}+\frac{120\,c^4\,d^4\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{1001\,e^2\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)\,{\left(d+e\,x\right)}^3}","Not used",1,"(((d*((8*c^5*d^6)/(143*e*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e)) - (4*c^4*d^4*(21*a*e^2 - 17*c*d^2))/(143*e*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e))))/e + (4*c^3*d^3*(110*a^2*e^4 + 53*c^2*d^4 - 157*a*c*d^2*e^2))/(429*e^2*(a*e^2 - c*d^2)^2*(7*a*e^3 - 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 - (((2*a^3*e^4)/(13*a*e^3 - 13*c*d^2*e) - (d*((d*((2*c^3*d^4)/(13*a*e^3 - 13*c*d^2*e) - (6*a*c^2*d^2*e^2)/(13*a*e^3 - 13*c*d^2*e)))/e + (6*a^2*c*d*e^3)/(13*a*e^3 - 13*c*d^2*e)))/e)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^7 + (((d*((16*c^6*d^7)/(1287*e*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e)) - (8*c^5*d^5*(33*a*e^2 - 29*c*d^2))/(1287*e*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e))))/e + (8*c^4*d^4*(112*a^2*e^4 + 81*c^2*d^4 - 191*a*c*d^2*e^2))/(1287*e^2*(a*e^2 - c*d^2)^3*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((d*((32*c^7*d^8)/(9009*e*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e)) - (16*c^6*d^6*(43*a*e^2 - 39*c*d^2))/(9009*e*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e))))/e + (16*c^5*d^5*(1089*a^2*e^4 + 884*c^2*d^4 - 1963*a*c*d^2*e^2))/(45045*e^2*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((38*c^4*d^5 + 94*a*c^3*d^3*e^2)/(429*e^2*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)) - (4*c^4*d^5)/(13*e^2*(a*e^2 - c*d^2)*(7*a*e^3 - 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 + (((348*c^5*d^6 - 292*a*c^4*d^4*e^2)/(1001*e^2*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)) - (8*c^5*d^6)/(143*e^2*(a*e^2 - c*d^2)^2*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((d*((d*((128*c^9*d^10)/(135135*e*(a*e^2 - c*d^2)^7) - (128*c^8*d^8*(10*a*e^2 - 9*c*d^2))/(45045*e*(a*e^2 - c*d^2)^7)))/e + (128*c^7*d^7*(379*a^2*e^4 + 322*c^2*d^4 - 698*a*c*d^2*e^2))/(135135*e^2*(a*e^2 - c*d^2)^7)))/e - (128*a*c^6*d^6*(350*a^2*e^4 + 322*c^2*d^4 - 671*a*c*d^2*e^2))/(135135*e*(a*e^2 - c*d^2)^7))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((d*((d*((128*c^9*d^10)/(135135*e*(a*e^2 - c*d^2)^7) - (64*c^8*d^8*(19*a*e^2 - 17*c*d^2))/(45045*e*(a*e^2 - c*d^2)^7)))/e + (128*c^7*d^7*(337*a^2*e^4 + 283*c^2*d^4 - 617*a*c*d^2*e^2))/(135135*e^2*(a*e^2 - c*d^2)^7)))/e - (64*c^6*d^6*(323*a^3*e^6 + 296*c^3*d^6 - 322*a*c^2*d^4*e^2 - 295*a^2*c*d^2*e^4))/(135135*e^3*(a*e^2 - c*d^2)^7))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (((d*((d*((4*c^4*d^5)/(13*(a*e^2 - c*d^2)*(11*a*e^3 - 11*c*d^2*e)) - (4*c^3*d^3*(10*a*e^2 - 7*c*d^2))/(13*(a*e^2 - c*d^2)*(11*a*e^3 - 11*c*d^2*e))))/e + (28*c^4*d^6 - 112*a*c^3*d^4*e^2 + 96*a^2*c^2*d^2*e^4)/(13*e*(a*e^2 - c*d^2)*(11*a*e^3 - 11*c*d^2*e))))/e - (4*a*c*d*(15*a^2*e^4 + 7*c^2*d^4 - 21*a*c*d^2*e^2))/(13*(a*e^2 - c*d^2)*(11*a*e^3 - 11*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^6 - (((32*c^7*d^8)/(9009*e^3*(a*e^2 - c*d^2)^5) + (16*c^6*d^6*(511*a*e^2 - 521*c*d^2))/(45045*e^3*(a*e^2 - c*d^2)^5))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (((d*((4*c^4*d^5)/(13*e*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e)) - (2*c^3*d^3*(7*a*e^2 - 3*c*d^2))/(13*e*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e))))/e + (28*c^4*d^6 - 122*a*c^3*d^4*e^2 + 138*a^2*c^2*d^2*e^4)/(143*e^2*(a*e^2 - c*d^2)*(9*a*e^3 - 9*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^5 + (((d*((d*((8*c^5*d^6)/(143*(a*e^2 - c*d^2)^2*(9*a*e^3 - 9*c*d^2*e)) - (8*c^4*d^4*(16*a*e^2 - 13*c*d^2))/(143*(a*e^2 - c*d^2)^2*(9*a*e^3 - 9*c*d^2*e))))/e + (8*c^3*d^3*(84*a^2*e^4 + 55*c^2*d^4 - 136*a*c*d^2*e^2))/(143*e*(a*e^2 - c*d^2)^2*(9*a*e^3 - 9*c*d^2*e))))/e - (8*a*c^2*d^2*(69*a^2*e^4 + 55*c^2*d^4 - 123*a*c*d^2*e^2))/(143*(a*e^2 - c*d^2)^2*(9*a*e^3 - 9*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^5 + (((d*((d*((16*c^6*d^7)/(1287*(a*e^2 - c*d^2)^3*(7*a*e^3 - 7*c*d^2*e)) - (16*c^5*d^5*(7*a*e^2 - 6*c*d^2))/(429*(a*e^2 - c*d^2)^3*(7*a*e^3 - 7*c*d^2*e))))/e + (16*c^4*d^4*(164*a^2*e^4 + 125*c^2*d^4 - 286*a*c*d^2*e^2))/(1287*e*(a*e^2 - c*d^2)^3*(7*a*e^3 - 7*c*d^2*e))))/e - (16*a*c^3*d^3*(144*a^2*e^4 + 125*c^2*d^4 - 268*a*c*d^2*e^2))/(1287*(a*e^2 - c*d^2)^3*(7*a*e^3 - 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 + (((d*((d*((32*c^7*d^8)/(9009*(a*e^2 - c*d^2)^4*(5*a*e^3 - 5*c*d^2*e)) - (32*c^6*d^6*(25*a*e^2 - 22*c*d^2))/(9009*(a*e^2 - c*d^2)^4*(5*a*e^3 - 5*c*d^2*e))))/e + (32*c^5*d^5*(248*a^2*e^4 + 201*c^2*d^4 - 446*a*c*d^2*e^2))/(9009*e*(a*e^2 - c*d^2)^4*(5*a*e^3 - 5*c*d^2*e))))/e - (32*a*c^4*d^4*(224*a^2*e^4 + 201*c^2*d^4 - 424*a*c*d^2*e^2))/(9009*(a*e^2 - c*d^2)^4*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((d*((d*((64*c^8*d^9)/(45045*(a*e^2 - c*d^2)^5*(3*a*e^3 - 3*c*d^2*e)) - (64*c^7*d^7*(28*a*e^2 - 25*c*d^2))/(45045*(a*e^2 - c*d^2)^5*(3*a*e^3 - 3*c*d^2*e))))/e + (64*c^6*d^6*(323*a^2*e^4 + 270*c^2*d^4 - 590*a*c*d^2*e^2))/(45045*e*(a*e^2 - c*d^2)^5*(3*a*e^3 - 3*c*d^2*e))))/e - (64*a*c^5*d^5*(296*a^2*e^4 + 270*c^2*d^4 - 565*a*c*d^2*e^2))/(45045*(a*e^2 - c*d^2)^5*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((d*((64*c^8*d^9)/(45045*e^2*(a*e^2 - c*d^2)^6) - (32*c^7*d^7*(51*a*e^2 - 47*c*d^2))/(45045*e^2*(a*e^2 - c*d^2)^6)))/e + (32*c^6*d^6*(1067*a^2*e^4 + 920*c^2*d^4 - 1981*a*c*d^2*e^2))/(135135*e^3*(a*e^2 - c*d^2)^6))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((d*((d*((4*c^4*d^5)/(13*(a*e^2 - c*d^2)*(11*a*e^3 - 11*c*d^2*e)) - (2*c^3*d^3*(7*a*e^2 - c*d^2))/(13*(a*e^2 - c*d^2)*(11*a*e^3 - 11*c*d^2*e))))/e + (2*c^2*d^2*(9*a^2*e^4 + c^2*d^4 - 4*a*c*d^2*e^2))/(13*e*(a*e^2 - c*d^2)*(11*a*e^3 - 11*c*d^2*e))))/e - (2*c^4*d^7 - 4*a*c^3*d^5*e^2 + 6*a^3*c*d*e^6)/(13*e^2*(a*e^2 - c*d^2)*(11*a*e^3 - 11*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^6 - (((d*((d*((8*c^5*d^6)/(143*(a*e^2 - c*d^2)^2*(9*a*e^3 - 9*c*d^2*e)) - (12*c^4*d^4*(7*a*e^2 - 5*c*d^2))/(143*(a*e^2 - c*d^2)^2*(9*a*e^3 - 9*c*d^2*e))))/e + (8*c^3*d^3*(29*a^2*e^4 + 11*c^2*d^4 - 37*a*c*d^2*e^2))/(143*e*(a*e^2 - c*d^2)^2*(9*a*e^3 - 9*c*d^2*e))))/e - (60*c^5*d^8 - 92*a*c^4*d^6*e^2 - 56*a^2*c^3*d^4*e^4 + 96*a^3*c^2*d^2*e^6)/(143*e^2*(a*e^2 - c*d^2)^2*(9*a*e^3 - 9*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^5 - (((d*((d*((16*c^6*d^7)/(1287*(a*e^2 - c*d^2)^3*(7*a*e^3 - 7*c*d^2*e)) - (8*c^5*d^5*(11*a*e^2 - 9*c*d^2))/(429*(a*e^2 - c*d^2)^3*(7*a*e^3 - 7*c*d^2*e))))/e + (16*c^4*d^4*(92*a^2*e^4 + 62*c^2*d^4 - 151*a*c*d^2*e^2))/(1287*e*(a*e^2 - c*d^2)^3*(7*a*e^3 - 7*c*d^2*e))))/e - (552*c^6*d^9 - 664*a*c^5*d^7*e^2 - 544*a^2*c^4*d^5*e^4 + 672*a^3*c^3*d^3*e^6)/(1287*e^2*(a*e^2 - c*d^2)^3*(7*a*e^3 - 7*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 - (((d*((d*((32*c^7*d^8)/(9009*(a*e^2 - c*d^2)^4*(5*a*e^3 - 5*c*d^2*e)) - (16*c^6*d^6*(43*a*e^2 - 37*c*d^2))/(9009*(a*e^2 - c*d^2)^4*(5*a*e^3 - 5*c*d^2*e))))/e + (16*c^5*d^5*(349*a^2*e^4 + 269*c^2*d^4 - 612*a*c*d^2*e^2))/(9009*e*(a*e^2 - c*d^2)^4*(5*a*e^3 - 5*c*d^2*e))))/e - (2304*c^7*d^10 - 2608*a*c^6*d^8*e^2 - 2288*a^2*c^5*d^6*e^4 + 2624*a^3*c^4*d^4*e^6)/(9009*e^2*(a*e^2 - c*d^2)^4*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 - (((d*((d*((64*c^8*d^9)/(45045*(a*e^2 - c*d^2)^5*(3*a*e^3 - 3*c*d^2*e)) - (32*c^7*d^7*(17*a*e^2 - 15*c*d^2))/(15015*(a*e^2 - c*d^2)^5*(3*a*e^3 - 3*c*d^2*e))))/e + (32*c^6*d^6*(521*a^2*e^4 + 425*c^2*d^4 - 940*a*c*d^2*e^2))/(45045*e*(a*e^2 - c*d^2)^5*(3*a*e^3 - 3*c*d^2*e))))/e - (7168*c^8*d^11 - 7904*a*c^7*d^9*e^2 - 7136*a^2*c^6*d^7*e^4 + 7936*a^3*c^5*d^5*e^6)/(45045*e^2*(a*e^2 - c*d^2)^5*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (((16*c^6*d^7)/(1287*e^2*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)) + (8*c^5*d^5*(283*a*e^2 - 293*c*d^2))/(6435*e^2*(a*e^2 - c*d^2)^3*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (15952*c^6*d^6*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(135135*e^3*(a*e^2 - c*d^2)^4*(d + e*x)) + (88*c^5*d^5*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(455*e^2*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)*(d + e*x)^2) + (120*c^4*d^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(1001*e^2*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)*(d + e*x)^3)","B"
1946,0,-1,255,0.000000,"\text{Not used}","int((d + e*x)^3/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^3}{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}} \,d x","Not used",1,"int((d + e*x)^3/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2), x)","F"
1947,0,-1,195,0.000000,"\text{Not used}","int((d + e*x)^2/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^2}{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}} \,d x","Not used",1,"int((d + e*x)^2/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2), x)","F"
1948,1,144,134,1.068804,"\text{Not used}","int((d + e*x)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{c\,d}-\frac{a\,e^3\,\ln\left(2\,\sqrt{\left(a\,e+c\,d\,x\right)\,\left(d+e\,x\right)}\,\sqrt{c\,d\,e}+a\,e^2+c\,d^2+2\,c\,d\,e\,x\right)}{2\,{\left(c\,d\,e\right)}^{3/2}}+\frac{c\,d^2\,e\,\ln\left(2\,\sqrt{\left(a\,e+c\,d\,x\right)\,\left(d+e\,x\right)}\,\sqrt{c\,d\,e}+a\,e^2+c\,d^2+2\,c\,d\,e\,x\right)}{2\,{\left(c\,d\,e\right)}^{3/2}}","Not used",1,"(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(c*d) - (a*e^3*log(2*((a*e + c*d*x)*(d + e*x))^(1/2)*(c*d*e)^(1/2) + a*e^2 + c*d^2 + 2*c*d*e*x))/(2*(c*d*e)^(3/2)) + (c*d^2*e*log(2*((a*e + c*d*x)*(d + e*x))^(1/2)*(c*d*e)^(1/2) + a*e^2 + c*d^2 + 2*c*d*e*x))/(2*(c*d*e)^(3/2))","B"
1949,1,49,82,0.743780,"\text{Not used}","int(1/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","\frac{\ln\left(2\,\sqrt{\left(a\,e+c\,d\,x\right)\,\left(d+e\,x\right)}\,\sqrt{c\,d\,e}+a\,e^2+c\,d^2+2\,c\,d\,e\,x\right)}{\sqrt{c\,d\,e}}","Not used",1,"log(2*((a*e + c*d*x)*(d + e*x))^(1/2)*(c*d*e)^(1/2) + a*e^2 + c*d^2 + 2*c*d*e*x)/(c*d*e)^(1/2)","B"
1950,1,50,52,0.693884,"\text{Not used}","int(1/((d + e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)),x)","-\frac{2\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{\left(a\,e^2-c\,d^2\right)\,\left(d+e\,x\right)}","Not used",1,"-(2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/((a*e^2 - c*d^2)*(d + e*x))","B"
1951,1,69,111,0.723310,"\text{Not used}","int(1/((d + e*x)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)),x)","\frac{2\,\left(3\,c\,d^2+2\,c\,x\,d\,e-a\,e^2\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{3\,{\left(a\,e^2-c\,d^2\right)}^2\,{\left(d+e\,x\right)}^2}","Not used",1,"(2*(3*c*d^2 - a*e^2 + 2*c*d*e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(3*(a*e^2 - c*d^2)^2*(d + e*x)^2)","B"
1952,1,110,171,0.779041,"\text{Not used}","int(1/((d + e*x)^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)),x)","-\frac{2\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(3\,a^2\,e^4-10\,a\,c\,d^2\,e^2-4\,a\,c\,d\,e^3\,x+15\,c^2\,d^4+20\,c^2\,d^3\,e\,x+8\,c^2\,d^2\,e^2\,x^2\right)}{15\,{\left(a\,e^2-c\,d^2\right)}^3\,{\left(d+e\,x\right)}^3}","Not used",1,"-(2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*(3*a^2*e^4 + 15*c^2*d^4 + 8*c^2*d^2*e^2*x^2 - 10*a*c*d^2*e^2 + 20*c^2*d^3*e*x - 4*a*c*d*e^3*x))/(15*(a*e^2 - c*d^2)^3*(d + e*x)^3)","B"
1953,1,252,231,0.809647,"\text{Not used}","int(1/((d + e*x)^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)),x)","\frac{32\,c^3\,d^3\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{35\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(d+e\,x\right)}-\frac{2\,e\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{\left(7\,a\,e^3-7\,c\,d^2\,e\right)\,{\left(d+e\,x\right)}^4}-\frac{48\,c^2\,d^2\,e\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{35\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)\,{\left(d+e\,x\right)}^2}+\frac{12\,c\,d\,e\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{7\,\left(a\,e^2-c\,d^2\right)\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)\,{\left(d+e\,x\right)}^3}","Not used",1,"(32*c^3*d^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(35*(a*e^2 - c*d^2)^4*(d + e*x)) - (2*e*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/((7*a*e^3 - 7*c*d^2*e)*(d + e*x)^4) - (48*c^2*d^2*e*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(35*(a*e^2 - c*d^2)^2*(3*a*e^3 - 3*c*d^2*e)*(d + e*x)^2) + (12*c*d*e*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(7*(a*e^2 - c*d^2)*(5*a*e^3 - 5*c*d^2*e)*(d + e*x)^3)","B"
1954,0,-1,302,0.000000,"\text{Not used}","int((d + e*x)^5/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^5}{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^5/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2), x)","F"
1955,0,-1,241,0.000000,"\text{Not used}","int((d + e*x)^4/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^4/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2), x)","F"
1956,0,-1,180,0.000000,"\text{Not used}","int((d + e*x)^3/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^3}{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^3/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2), x)","F"
1957,0,-1,125,0.000000,"\text{Not used}","int((d + e*x)^2/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^2}{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^2/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2), x)","F"
1958,1,53,50,0.763672,"\text{Not used}","int((d + e*x)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","\frac{2\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{\left(a\,e+c\,d\,x\right)\,\left(a\,e^2-c\,d^2\right)}","Not used",1,"(2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/((a*e + c*d*x)*(a*e^2 - c*d^2))","B"
1959,1,75,62,0.607523,"\text{Not used}","int(1/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","-\frac{\frac{c\,d^2}{2}+c\,x\,d\,e+\frac{a\,e^2}{2}}{\left(\frac{{\left(c\,d^2+a\,e^2\right)}^2}{4}-a\,c\,d^2\,e^2\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}","Not used",1,"-((a*e^2)/2 + (c*d^2)/2 + c*d*e*x)/(((a*e^2 + c*d^2)^2/4 - a*c*d^2*e^2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))","B"
1960,1,120,121,1.017284,"\text{Not used}","int(1/((d + e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)),x)","\frac{2\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(-a^2\,e^4+6\,a\,c\,d^2\,e^2+4\,a\,c\,d\,e^3\,x+3\,c^2\,d^4+12\,c^2\,d^3\,e\,x+8\,c^2\,d^2\,e^2\,x^2\right)}{3\,\left(a\,e+c\,d\,x\right)\,{\left(a\,e^2-c\,d^2\right)}^3\,{\left(d+e\,x\right)}^2}","Not used",1,"(2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*(3*c^2*d^4 - a^2*e^4 + 8*c^2*d^2*e^2*x^2 + 6*a*c*d^2*e^2 + 12*c^2*d^3*e*x + 4*a*c*d*e^3*x))/(3*(a*e + c*d*x)*(a*e^2 - c*d^2)^3*(d + e*x)^2)","B"
1961,1,1005,181,1.522534,"\text{Not used}","int(1/((d + e*x)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)),x)","\frac{\left(\frac{16\,c^3\,d^4\,e}{15\,{\left(a\,e^2-c\,d^2\right)}^5}-\frac{8\,c^2\,d^2\,e\,\left(c\,d^2+a\,e^2\right)}{15\,{\left(a\,e^2-c\,d^2\right)}^5}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{e^2\,\left(10\,c^2\,d^3-18\,a\,c\,d\,e^2\right)}{5\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a^2\,e^5-6\,a\,c\,d^2\,e^3+3\,c^2\,d^4\,e\right)}+\frac{8\,c^2\,d^3\,e^2}{5\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(3\,a^2\,e^5-6\,a\,c\,d^2\,e^3+3\,c^2\,d^4\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{2\,e^2\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3\,\left(5\,a^2\,e^5-10\,a\,c\,d^2\,e^3+5\,c^2\,d^4\,e\right)}-\frac{\left(x\,\left(\frac{32\,a\,c^5\,d^6\,e^4}{15\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{16\,c^5\,d^5\,e^3\,\left(c\,d^2+a\,e^2\right)}{15\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^5\,d^5\,e^3\,\left(3\,a\,e^2-11\,c\,d^2\right)}{15\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{2\,c^2\,d^2\,e^2\,\left(58\,a^2\,c^2\,d^2\,e^4-104\,a\,c^3\,d^4\,e^2+30\,c^4\,d^6\right)}{15\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{4\,c^4\,d^4\,e^2\,\left(c\,d^2+a\,e^2\right)\,\left(3\,a\,e^2-11\,c\,d^2\right)}{15\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)-\frac{a\,\left(\frac{16\,c^5\,d^5\,e^3\,\left(c\,d^2+a\,e^2\right)}{15\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^5\,d^5\,e^3\,\left(3\,a\,e^2-11\,c\,d^2\right)}{15\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}+\frac{c\,d\,e\,\left(c\,d^2+a\,e^2\right)\,\left(58\,a^2\,c^2\,d^2\,e^4-104\,a\,c^3\,d^4\,e^2+30\,c^4\,d^6\right)}{15\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{\left(a\,e+c\,d\,x\right)\,\left(d+e\,x\right)}","Not used",1,"(((16*c^3*d^4*e)/(15*(a*e^2 - c*d^2)^5) - (8*c^2*d^2*e*(a*e^2 + c*d^2))/(15*(a*e^2 - c*d^2)^5))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((e^2*(10*c^2*d^3 - 18*a*c*d*e^2))/(5*(a*e^2 - c*d^2)^2*(3*a^2*e^5 + 3*c^2*d^4*e - 6*a*c*d^2*e^3)) + (8*c^2*d^3*e^2)/(5*(a*e^2 - c*d^2)^2*(3*a^2*e^5 + 3*c^2*d^4*e - 6*a*c*d^2*e^3)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (2*e^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/((d + e*x)^3*(5*a^2*e^5 + 5*c^2*d^4*e - 10*a*c*d^2*e^3)) - ((x*((32*a*c^5*d^6*e^4)/(15*(a*e^2 - c*d^2)^4*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - ((a*e^2 + c*d^2)*((16*c^5*d^5*e^3*(a*e^2 + c*d^2))/(15*(a*e^2 - c*d^2)^4*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^5*d^5*e^3*(3*a*e^2 - 11*c*d^2))/(15*(a*e^2 - c*d^2)^4*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (2*c^2*d^2*e^2*(30*c^4*d^6 - 104*a*c^3*d^4*e^2 + 58*a^2*c^2*d^2*e^4))/(15*(a*e^2 - c*d^2)^4*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (4*c^4*d^4*e^2*(a*e^2 + c*d^2)*(3*a*e^2 - 11*c*d^2))/(15*(a*e^2 - c*d^2)^4*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))) - (a*((16*c^5*d^5*e^3*(a*e^2 + c*d^2))/(15*(a*e^2 - c*d^2)^4*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^5*d^5*e^3*(3*a*e^2 - 11*c*d^2))/(15*(a*e^2 - c*d^2)^4*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c + (c*d*e*(a*e^2 + c*d^2)*(30*c^4*d^6 - 104*a*c^3*d^4*e^2 + 58*a^2*c^2*d^2*e^4))/(15*(a*e^2 - c*d^2)^4*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/((a*e + c*d*x)*(d + e*x))","B"
1962,1,2121,241,2.589329,"\text{Not used}","int(1/((d + e*x)^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)),x)","\frac{\left(\frac{d\,\left(\frac{24\,c^4\,d^5\,e^3}{35\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a^2\,e^5-6\,a\,c\,d^2\,e^3+3\,c^2\,d^4\,e\right)}+\frac{4\,c^3\,d^3\,e^3\,\left(17\,a\,e^2-29\,c\,d^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a^2\,e^5-6\,a\,c\,d^2\,e^3+3\,c^2\,d^4\,e\right)}\right)}{e}-\frac{e^2\,\left(162\,a^2\,c^2\,d^2\,e^4-256\,a\,c^3\,d^4\,e^2+70\,c^4\,d^6\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a^2\,e^5-6\,a\,c\,d^2\,e^3+3\,c^2\,d^4\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{\left(\frac{e^2\,\left(14\,c^2\,d^3-26\,a\,c\,d\,e^2\right)}{7\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a^2\,e^5-10\,a\,c\,d^2\,e^3+5\,c^2\,d^4\,e\right)}+\frac{12\,c^2\,d^3\,e^2}{7\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(5\,a^2\,e^5-10\,a\,c\,d^2\,e^3+5\,c^2\,d^4\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}-\frac{\left(\frac{d\,\left(\frac{16\,c^5\,d^6\,e^2}{35\,{\left(a\,e^2-c\,d^2\right)}^7}+\frac{16\,c^4\,d^4\,e^2\,\left(7\,a\,e^2-13\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^7}\right)}{e}+\frac{4\,c^3\,d^3\,e\,\left(-17\,a^2\,e^4+6\,a\,c\,d^2\,e^2+23\,c^2\,d^4\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^7}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}+\frac{\left(\frac{24\,c^3\,d^4\,e^2}{35\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{12\,c^2\,d^2\,e^2\,\left(c\,d^2+a\,e^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{2\,e^2\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4\,\left(7\,a^2\,e^5-14\,a\,c\,d^2\,e^3+7\,c^2\,d^4\,e\right)}-\frac{\left(\frac{a\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{16\,c^7\,d^7\,e^4\,\left(c\,d^2+a\,e^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{32\,c^7\,d^7\,e^4\,\left(4\,a\,e^2-13\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{16\,c^6\,d^6\,e^3\,\left(27\,a^2\,e^4-70\,a\,c\,d^2\,e^2+61\,c^2\,d^4\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{32\,a\,c^7\,d^8\,e^5}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^6\,d^6\,e^3\,\left(c\,d^2+a\,e^2\right)\,\left(4\,a\,e^2-13\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}-x\,\left(\frac{a\,\left(\frac{16\,c^7\,d^7\,e^4\,\left(c\,d^2+a\,e^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{32\,c^7\,d^7\,e^4\,\left(4\,a\,e^2-13\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}-\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{16\,c^7\,d^7\,e^4\,\left(c\,d^2+a\,e^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{32\,c^7\,d^7\,e^4\,\left(4\,a\,e^2-13\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{16\,c^6\,d^6\,e^3\,\left(27\,a^2\,e^4-70\,a\,c\,d^2\,e^2+61\,c^2\,d^4\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{32\,a\,c^7\,d^8\,e^5}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^6\,d^6\,e^3\,\left(c\,d^2+a\,e^2\right)\,\left(4\,a\,e^2-13\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}-\frac{2\,c^2\,d^2\,e^2\,\left(-538\,a^3\,c^3\,d^3\,e^6+1398\,a^2\,c^4\,d^5\,e^4-1118\,a\,c^5\,d^7\,e^2+210\,c^6\,d^9\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^5\,d^5\,e^2\,\left(c\,d^2+a\,e^2\right)\,\left(27\,a^2\,e^4-70\,a\,c\,d^2\,e^2+61\,c^2\,d^4\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)+\frac{c\,d\,e\,\left(c\,d^2+a\,e^2\right)\,\left(-538\,a^3\,c^3\,d^3\,e^6+1398\,a^2\,c^4\,d^5\,e^4-1118\,a\,c^5\,d^7\,e^2+210\,c^6\,d^9\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{\left(a\,e+c\,d\,x\right)\,\left(d+e\,x\right)}-\frac{16\,c^3\,d^3\,e\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{35\,{\left(a\,e^2-c\,d^2\right)}^5\,\left(d+e\,x\right)}","Not used",1,"(((d*((24*c^4*d^5*e^3)/(35*(a*e^2 - c*d^2)^4*(3*a^2*e^5 + 3*c^2*d^4*e - 6*a*c*d^2*e^3)) + (4*c^3*d^3*e^3*(17*a*e^2 - 29*c*d^2))/(35*(a*e^2 - c*d^2)^4*(3*a^2*e^5 + 3*c^2*d^4*e - 6*a*c*d^2*e^3))))/e - (e^2*(70*c^4*d^6 - 256*a*c^3*d^4*e^2 + 162*a^2*c^2*d^2*e^4))/(35*(a*e^2 - c*d^2)^4*(3*a^2*e^5 + 3*c^2*d^4*e - 6*a*c*d^2*e^3)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (((e^2*(14*c^2*d^3 - 26*a*c*d*e^2))/(7*(a*e^2 - c*d^2)^2*(5*a^2*e^5 + 5*c^2*d^4*e - 10*a*c*d^2*e^3)) + (12*c^2*d^3*e^2)/(7*(a*e^2 - c*d^2)^2*(5*a^2*e^5 + 5*c^2*d^4*e - 10*a*c*d^2*e^3)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 - (((d*((16*c^5*d^6*e^2)/(35*(a*e^2 - c*d^2)^7) + (16*c^4*d^4*e^2*(7*a*e^2 - 13*c*d^2))/(105*(a*e^2 - c*d^2)^7)))/e + (4*c^3*d^3*e*(23*c^2*d^4 - 17*a^2*e^4 + 6*a*c*d^2*e^2))/(105*(a*e^2 - c*d^2)^7))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) + (((24*c^3*d^4*e^2)/(35*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e)) - (12*c^2*d^2*e^2*(a*e^2 + c*d^2))/(35*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (2*e^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/((d + e*x)^4*(7*a^2*e^5 + 7*c^2*d^4*e - 14*a*c*d^2*e^3)) - (((a*(((a*e^2 + c*d^2)*((16*c^7*d^7*e^4*(a*e^2 + c*d^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (32*c^7*d^7*e^4*(4*a*e^2 - 13*c*d^2))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (16*c^6*d^6*e^3*(27*a^2*e^4 + 61*c^2*d^4 - 70*a*c*d^2*e^2))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (32*a*c^7*d^8*e^5)/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^6*d^6*e^3*(a*e^2 + c*d^2)*(4*a*e^2 - 13*c*d^2))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c - x*((a*((16*c^7*d^7*e^4*(a*e^2 + c*d^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (32*c^7*d^7*e^4*(4*a*e^2 - 13*c*d^2))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c - ((a*e^2 + c*d^2)*(((a*e^2 + c*d^2)*((16*c^7*d^7*e^4*(a*e^2 + c*d^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (32*c^7*d^7*e^4*(4*a*e^2 - 13*c*d^2))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (16*c^6*d^6*e^3*(27*a^2*e^4 + 61*c^2*d^4 - 70*a*c*d^2*e^2))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (32*a*c^7*d^8*e^5)/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^6*d^6*e^3*(a*e^2 + c*d^2)*(4*a*e^2 - 13*c*d^2))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) - (2*c^2*d^2*e^2*(210*c^6*d^9 - 1118*a*c^5*d^7*e^2 + 1398*a^2*c^4*d^5*e^4 - 538*a^3*c^3*d^3*e^6))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^5*d^5*e^2*(a*e^2 + c*d^2)*(27*a^2*e^4 + 61*c^2*d^4 - 70*a*c*d^2*e^2))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))) + (c*d*e*(a*e^2 + c*d^2)*(210*c^6*d^9 - 1118*a*c^5*d^7*e^2 + 1398*a^2*c^4*d^5*e^4 - 538*a^3*c^3*d^3*e^6))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/((a*e + c*d*x)*(d + e*x)) - (16*c^3*d^3*e*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(35*(a*e^2 - c*d^2)^5*(d + e*x))","B"
1963,1,3925,301,4.357589,"\text{Not used}","int(1/((d + e*x)^4*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)),x)","\frac{\left(\frac{64\,c^5\,d^6\,e}{315\,{\left(a\,e^2-c\,d^2\right)}^7}+\frac{16\,c^4\,d^4\,e\,\left(11\,a\,e^2-15\,c\,d^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^7}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{e^2\,\left(18\,c^2\,d^3-34\,a\,c\,d\,e^2\right)}{9\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a^2\,e^5-14\,a\,c\,d^2\,e^3+7\,c^2\,d^4\,e\right)}+\frac{16\,c^2\,d^3\,e^2}{9\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(7\,a^2\,e^5-14\,a\,c\,d^2\,e^3+7\,c^2\,d^4\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}-\frac{\left(\frac{d\,\left(\frac{64\,c^5\,d^6\,e^3}{315\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}+\frac{8\,c^4\,d^4\,e^3\,\left(35\,a\,e^2-51\,c\,d^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{4\,c^3\,d^3\,e^2\,\left(-39\,a^2\,e^4+8\,a\,c\,d^2\,e^2+47\,c^2\,d^4\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{d\,\left(\frac{32\,c^4\,d^5\,e^3}{63\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(5\,a^2\,e^5-10\,a\,c\,d^2\,e^3+5\,c^2\,d^4\,e\right)}+\frac{4\,c^3\,d^3\,e^3\,\left(39\,a\,e^2-55\,c\,d^2\right)}{63\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(5\,a^2\,e^5-10\,a\,c\,d^2\,e^3+5\,c^2\,d^4\,e\right)}\right)}{e}-\frac{e^2\,\left(314\,a^2\,c^2\,d^2\,e^4-472\,a\,c^3\,d^4\,e^2+126\,c^4\,d^6\right)}{63\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(5\,a^2\,e^5-10\,a\,c\,d^2\,e^3+5\,c^2\,d^4\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{32\,c^3\,d^4\,e^2}{63\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{16\,c^2\,d^2\,e^2\,\left(c\,d^2+a\,e^2\right)}{63\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{128\,c^7\,d^8\,e^3}{945\,{\left(a\,e^2-c\,d^2\right)}^9}+\frac{16\,c^6\,d^6\,e^3\,\left(23\,a\,e^2-47\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9}\right)}{e}+\frac{16\,c^5\,d^5\,e^2\,\left(109\,a^2\,e^4-264\,a\,c\,d^2\,e^2+179\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9}\right)}{e}-\frac{4\,c^4\,d^4\,e\,\left(245\,a^3\,e^6-299\,a^2\,c\,d^2\,e^4-229\,a\,c^2\,d^4\,e^2+315\,c^3\,d^6\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{64\,c^6\,d^7\,e^4}{315\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(3\,a^2\,e^5-6\,a\,c\,d^2\,e^3+3\,c^2\,d^4\,e\right)}+\frac{8\,c^5\,d^5\,e^4\,\left(9\,a\,e^2-17\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(3\,a^2\,e^5-6\,a\,c\,d^2\,e^3+3\,c^2\,d^4\,e\right)}\right)}{e}+\frac{4\,c^4\,d^4\,e^3\,\left(245\,a^2\,e^4-598\,a\,c\,d^2\,e^2+401\,c^2\,d^4\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(3\,a^2\,e^5-6\,a\,c\,d^2\,e^3+3\,c^2\,d^4\,e\right)}\right)}{e}+\frac{e^2\,\left(-1890\,a^3\,c^3\,d^3\,e^6+4690\,a^2\,c^4\,d^5\,e^4-3494\,a\,c^5\,d^7\,e^2+630\,c^6\,d^9\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(3\,a^2\,e^5-6\,a\,c\,d^2\,e^3+3\,c^2\,d^4\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{2\,e^2\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^5\,\left(9\,a^2\,e^5-18\,a\,c\,d^2\,e^3+9\,c^2\,d^4\,e\right)}-\frac{\left(x\,\left(\frac{a\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{128\,c^9\,d^9\,e^5\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{32\,c^9\,d^9\,e^5\,\left(15\,a\,e^2-47\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{32\,c^8\,d^8\,e^4\,\left(98\,a^2\,e^4-241\,a\,c\,d^2\,e^2+191\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{256\,a\,c^9\,d^{10}\,e^6}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^8\,d^8\,e^4\,\left(c\,d^2+a\,e^2\right)\,\left(15\,a\,e^2-47\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}+\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{a\,\left(\frac{128\,c^9\,d^9\,e^5\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{32\,c^9\,d^9\,e^5\,\left(15\,a\,e^2-47\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}-\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{128\,c^9\,d^9\,e^5\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{32\,c^9\,d^9\,e^5\,\left(15\,a\,e^2-47\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{32\,c^8\,d^8\,e^4\,\left(98\,a^2\,e^4-241\,a\,c\,d^2\,e^2+191\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{256\,a\,c^9\,d^{10}\,e^6}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^8\,d^8\,e^4\,\left(c\,d^2+a\,e^2\right)\,\left(15\,a\,e^2-47\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}-\frac{16\,c^7\,d^7\,e^3\,\left(213\,a^3\,e^6-1031\,a^2\,c\,d^2\,e^4+1513\,a\,c^2\,d^4\,e^2-759\,c^3\,d^6\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{16\,c^7\,d^7\,e^3\,\left(c\,d^2+a\,e^2\right)\,\left(98\,a^2\,e^4-241\,a\,c\,d^2\,e^2+191\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{2\,c^2\,d^2\,e^2\,\left(5530\,a^4\,c^4\,d^4\,e^8-20416\,a^3\,c^5\,d^6\,e^6+26500\,a^2\,c^6\,d^8\,e^4-13632\,a\,c^7\,d^{10}\,e^2+1890\,c^8\,d^{12}\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^6\,d^6\,e^2\,\left(c\,d^2+a\,e^2\right)\,\left(213\,a^3\,e^6-1031\,a^2\,c\,d^2\,e^4+1513\,a\,c^2\,d^4\,e^2-759\,c^3\,d^6\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)+\frac{a\,\left(\frac{a\,\left(\frac{128\,c^9\,d^9\,e^5\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{32\,c^9\,d^9\,e^5\,\left(15\,a\,e^2-47\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}-\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{128\,c^9\,d^9\,e^5\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{32\,c^9\,d^9\,e^5\,\left(15\,a\,e^2-47\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{32\,c^8\,d^8\,e^4\,\left(98\,a^2\,e^4-241\,a\,c\,d^2\,e^2+191\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{256\,a\,c^9\,d^{10}\,e^6}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^8\,d^8\,e^4\,\left(c\,d^2+a\,e^2\right)\,\left(15\,a\,e^2-47\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}-\frac{16\,c^7\,d^7\,e^3\,\left(213\,a^3\,e^6-1031\,a^2\,c\,d^2\,e^4+1513\,a\,c^2\,d^4\,e^2-759\,c^3\,d^6\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{16\,c^7\,d^7\,e^3\,\left(c\,d^2+a\,e^2\right)\,\left(98\,a^2\,e^4-241\,a\,c\,d^2\,e^2+191\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}+\frac{c\,d\,e\,\left(c\,d^2+a\,e^2\right)\,\left(5530\,a^4\,c^4\,d^4\,e^8-20416\,a^3\,c^5\,d^6\,e^6+26500\,a^2\,c^6\,d^8\,e^4-13632\,a\,c^7\,d^{10}\,e^2+1890\,c^8\,d^{12}\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^8\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{\left(a\,e+c\,d\,x\right)\,\left(d+e\,x\right)}+\frac{64\,c^4\,d^4\,e\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{315\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(d+e\,x\right)}-\frac{32\,c^3\,d^3\,e^2\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{105\,{\left(a\,e^2-c\,d^2\right)}^4\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)\,{\left(d+e\,x\right)}^2}","Not used",1,"(((64*c^5*d^6*e)/(315*(a*e^2 - c*d^2)^7) + (16*c^4*d^4*e*(11*a*e^2 - 15*c*d^2))/(315*(a*e^2 - c*d^2)^7))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((e^2*(18*c^2*d^3 - 34*a*c*d*e^2))/(9*(a*e^2 - c*d^2)^2*(7*a^2*e^5 + 7*c^2*d^4*e - 14*a*c*d^2*e^3)) + (16*c^2*d^3*e^2)/(9*(a*e^2 - c*d^2)^2*(7*a^2*e^5 + 7*c^2*d^4*e - 14*a*c*d^2*e^3)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 - (((d*((64*c^5*d^6*e^3)/(315*(a*e^2 - c*d^2)^6*(3*a*e^3 - 3*c*d^2*e)) + (8*c^4*d^4*e^3*(35*a*e^2 - 51*c*d^2))/(315*(a*e^2 - c*d^2)^6*(3*a*e^3 - 3*c*d^2*e))))/e + (4*c^3*d^3*e^2*(47*c^2*d^4 - 39*a^2*e^4 + 8*a*c*d^2*e^2))/(315*(a*e^2 - c*d^2)^6*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((d*((32*c^4*d^5*e^3)/(63*(a*e^2 - c*d^2)^4*(5*a^2*e^5 + 5*c^2*d^4*e - 10*a*c*d^2*e^3)) + (4*c^3*d^3*e^3*(39*a*e^2 - 55*c*d^2))/(63*(a*e^2 - c*d^2)^4*(5*a^2*e^5 + 5*c^2*d^4*e - 10*a*c*d^2*e^3))))/e - (e^2*(126*c^4*d^6 - 472*a*c^3*d^4*e^2 + 314*a^2*c^2*d^2*e^4))/(63*(a*e^2 - c*d^2)^4*(5*a^2*e^5 + 5*c^2*d^4*e - 10*a*c*d^2*e^3)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((32*c^3*d^4*e^2)/(63*(a*e^2 - c*d^2)^4*(5*a*e^3 - 5*c*d^2*e)) - (16*c^2*d^2*e^2*(a*e^2 + c*d^2))/(63*(a*e^2 - c*d^2)^4*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((d*((d*((128*c^7*d^8*e^3)/(945*(a*e^2 - c*d^2)^9) + (16*c^6*d^6*e^3*(23*a*e^2 - 47*c*d^2))/(945*(a*e^2 - c*d^2)^9)))/e + (16*c^5*d^5*e^2*(109*a^2*e^4 + 179*c^2*d^4 - 264*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^9)))/e - (4*c^4*d^4*e*(245*a^3*e^6 + 315*c^3*d^6 - 229*a*c^2*d^4*e^2 - 299*a^2*c*d^2*e^4))/(945*(a*e^2 - c*d^2)^9))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((d*((d*((64*c^6*d^7*e^4)/(315*(a*e^2 - c*d^2)^6*(3*a^2*e^5 + 3*c^2*d^4*e - 6*a*c*d^2*e^3)) + (8*c^5*d^5*e^4*(9*a*e^2 - 17*c*d^2))/(105*(a*e^2 - c*d^2)^6*(3*a^2*e^5 + 3*c^2*d^4*e - 6*a*c*d^2*e^3))))/e + (4*c^4*d^4*e^3*(245*a^2*e^4 + 401*c^2*d^4 - 598*a*c*d^2*e^2))/(315*(a*e^2 - c*d^2)^6*(3*a^2*e^5 + 3*c^2*d^4*e - 6*a*c*d^2*e^3))))/e + (e^2*(630*c^6*d^9 - 3494*a*c^5*d^7*e^2 + 4690*a^2*c^4*d^5*e^4 - 1890*a^3*c^3*d^3*e^6))/(315*(a*e^2 - c*d^2)^6*(3*a^2*e^5 + 3*c^2*d^4*e - 6*a*c*d^2*e^3)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (2*e^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/((d + e*x)^5*(9*a^2*e^5 + 9*c^2*d^4*e - 18*a*c*d^2*e^3)) - ((x*((a*(((a*e^2 + c*d^2)*((128*c^9*d^9*e^5*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (32*c^9*d^9*e^5*(15*a*e^2 - 47*c*d^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (32*c^8*d^8*e^4*(98*a^2*e^4 + 191*c^2*d^4 - 241*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (256*a*c^9*d^10*e^6)/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^8*d^8*e^4*(a*e^2 + c*d^2)*(15*a*e^2 - 47*c*d^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c + ((a*e^2 + c*d^2)*((a*((128*c^9*d^9*e^5*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (32*c^9*d^9*e^5*(15*a*e^2 - 47*c*d^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c - ((a*e^2 + c*d^2)*(((a*e^2 + c*d^2)*((128*c^9*d^9*e^5*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (32*c^9*d^9*e^5*(15*a*e^2 - 47*c*d^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (32*c^8*d^8*e^4*(98*a^2*e^4 + 191*c^2*d^4 - 241*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (256*a*c^9*d^10*e^6)/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^8*d^8*e^4*(a*e^2 + c*d^2)*(15*a*e^2 - 47*c*d^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) - (16*c^7*d^7*e^3*(213*a^3*e^6 - 759*c^3*d^6 + 1513*a*c^2*d^4*e^2 - 1031*a^2*c*d^2*e^4))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (16*c^7*d^7*e^3*(a*e^2 + c*d^2)*(98*a^2*e^4 + 191*c^2*d^4 - 241*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (2*c^2*d^2*e^2*(1890*c^8*d^12 - 13632*a*c^7*d^10*e^2 + 26500*a^2*c^6*d^8*e^4 - 20416*a^3*c^5*d^6*e^6 + 5530*a^4*c^4*d^4*e^8))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^6*d^6*e^2*(a*e^2 + c*d^2)*(213*a^3*e^6 - 759*c^3*d^6 + 1513*a*c^2*d^4*e^2 - 1031*a^2*c*d^2*e^4))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))) + (a*((a*((128*c^9*d^9*e^5*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (32*c^9*d^9*e^5*(15*a*e^2 - 47*c*d^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c - ((a*e^2 + c*d^2)*(((a*e^2 + c*d^2)*((128*c^9*d^9*e^5*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (32*c^9*d^9*e^5*(15*a*e^2 - 47*c*d^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (32*c^8*d^8*e^4*(98*a^2*e^4 + 191*c^2*d^4 - 241*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (256*a*c^9*d^10*e^6)/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^8*d^8*e^4*(a*e^2 + c*d^2)*(15*a*e^2 - 47*c*d^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) - (16*c^7*d^7*e^3*(213*a^3*e^6 - 759*c^3*d^6 + 1513*a*c^2*d^4*e^2 - 1031*a^2*c*d^2*e^4))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (16*c^7*d^7*e^3*(a*e^2 + c*d^2)*(98*a^2*e^4 + 191*c^2*d^4 - 241*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c + (c*d*e*(a*e^2 + c*d^2)*(1890*c^8*d^12 - 13632*a*c^7*d^10*e^2 + 26500*a^2*c^6*d^8*e^4 - 20416*a^3*c^5*d^6*e^6 + 5530*a^4*c^4*d^4*e^8))/(945*(a*e^2 - c*d^2)^8*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/((a*e + c*d*x)*(d + e*x)) + (64*c^4*d^4*e*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(315*(a*e^2 - c*d^2)^6*(d + e*x)) - (32*c^3*d^3*e^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(105*(a*e^2 - c*d^2)^4*(3*a*e^3 - 3*c*d^2*e)*(d + e*x)^2)","B"
1964,0,-1,294,0.000000,"\text{Not used}","int((d + e*x)^6/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^6}{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^6/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2), x)","F"
1965,0,-1,231,0.000000,"\text{Not used}","int((d + e*x)^5/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^5}{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^5/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2), x)","F"
1966,0,-1,172,0.000000,"\text{Not used}","int((d + e*x)^4/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^4/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2), x)","F"
1967,1,58,54,1.426096,"\text{Not used}","int((d + e*x)^3/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","\frac{2\,\left(d+e\,x\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{3\,{\left(a\,e+c\,d\,x\right)}^2\,\left(a\,e^2-c\,d^2\right)}","Not used",1,"(2*(d + e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(3*(a*e + c*d*x)^2*(a*e^2 - c*d^2))","B"
1968,1,72,116,0.947812,"\text{Not used}","int((d + e*x)^2/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","\frac{2\,\left(-c\,d^2+2\,c\,x\,d\,e+3\,a\,e^2\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{3\,{\left(a\,e+c\,d\,x\right)}^2\,{\left(a\,e^2-c\,d^2\right)}^2}","Not used",1,"(2*(3*a*e^2 - c*d^2 + 2*c*d*e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(3*(a*e + c*d*x)^2*(a*e^2 - c*d^2)^2)","B"
1969,1,120,118,1.144469,"\text{Not used}","int((d + e*x)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","-\frac{2\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(3\,a^2\,e^4+6\,a\,c\,d^2\,e^2+12\,a\,c\,d\,e^3\,x-c^2\,d^4+4\,c^2\,d^3\,e\,x+8\,c^2\,d^2\,e^2\,x^2\right)}{3\,{\left(a\,e+c\,d\,x\right)}^2\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(d+e\,x\right)}","Not used",1,"-(2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*(3*a^2*e^4 - c^2*d^4 + 8*c^2*d^2*e^2*x^2 + 6*a*c*d^2*e^2 + 4*c^2*d^3*e*x + 12*a*c*d*e^3*x))/(3*(a*e + c*d*x)^2*(a*e^2 - c*d^2)^3*(d + e*x))","B"
1970,1,131,132,0.724753,"\text{Not used}","int(1/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","\frac{\left(2\,c\,d^2+4\,c\,x\,d\,e+2\,a\,e^2\right)\,\left(8\,c^2\,d^2\,e^2\,x^2-{\left(c\,d^2+a\,e^2\right)}^2+12\,a\,c\,d^2\,e^2+8\,c\,d\,e\,x\,\left(c\,d^2+a\,e^2\right)\right)}{3\,{\left({\left(c\,d^2+a\,e^2\right)}^2-4\,a\,c\,d^2\,e^2\right)}^2\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}}","Not used",1,"((2*a*e^2 + 2*c*d^2 + 4*c*d*e*x)*(8*c^2*d^2*e^2*x^2 - (a*e^2 + c*d^2)^2 + 12*a*c*d^2*e^2 + 8*c*d*e*x*(a*e^2 + c*d^2)))/(3*((a*e^2 + c*d^2)^2 - 4*a*c*d^2*e^2)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2))","B"
1971,1,253,192,1.648544,"\text{Not used}","int(1/((d + e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)),x)","-\frac{2\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(3\,a^4\,e^8-20\,a^3\,c\,d^2\,e^6-8\,a^3\,c\,d\,e^7\,x+90\,a^2\,c^2\,d^4\,e^4+120\,a^2\,c^2\,d^3\,e^5\,x+48\,a^2\,c^2\,d^2\,e^6\,x^2+60\,a\,c^3\,d^6\,e^2+360\,a\,c^3\,d^5\,e^3\,x+480\,a\,c^3\,d^4\,e^4\,x^2+192\,a\,c^3\,d^3\,e^5\,x^3-5\,c^4\,d^8+40\,c^4\,d^7\,e\,x+240\,c^4\,d^6\,e^2\,x^2+320\,c^4\,d^5\,e^3\,x^3+128\,c^4\,d^4\,e^4\,x^4\right)}{15\,{\left(a\,e+c\,d\,x\right)}^2\,{\left(a\,e^2-c\,d^2\right)}^5\,{\left(d+e\,x\right)}^3}","Not used",1,"-(2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*(3*a^4*e^8 - 5*c^4*d^8 + 60*a*c^3*d^6*e^2 - 20*a^3*c*d^2*e^6 + 90*a^2*c^2*d^4*e^4 + 240*c^4*d^6*e^2*x^2 + 320*c^4*d^5*e^3*x^3 + 128*c^4*d^4*e^4*x^4 + 40*c^4*d^7*e*x - 8*a^3*c*d*e^7*x + 48*a^2*c^2*d^2*e^6*x^2 + 360*a*c^3*d^5*e^3*x + 120*a^2*c^2*d^3*e^5*x + 480*a*c^3*d^4*e^4*x^2 + 192*a*c^3*d^3*e^5*x^3))/(15*(a*e + c*d*x)^2*(a*e^2 - c*d^2)^5*(d + e*x)^3)","B"
1972,1,3654,252,3.097363,"\text{Not used}","int(1/((d + e*x)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)),x)","\frac{\left(\frac{d\,\left(\frac{12\,c^3\,d^4\,e^4}{7\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a^3\,e^7-15\,a^2\,c\,d^2\,e^5+15\,a\,c^2\,d^4\,e^3-5\,c^3\,d^6\,e\right)}-\frac{2\,c^2\,d^2\,e^4\,\left(19\,a\,e^2-7\,c\,d^2\right)}{7\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a^3\,e^7-15\,a^2\,c\,d^2\,e^5+15\,a\,c^2\,d^4\,e^3-5\,c^3\,d^6\,e\right)}\right)}{e}+\frac{e^3\,\left(40\,a^2\,c\,d\,e^4-42\,a\,c^2\,d^3\,e^2+14\,c^3\,d^5\right)}{7\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(5\,a^3\,e^7-15\,a^2\,c\,d^2\,e^5+15\,a\,c^2\,d^4\,e^3-5\,c^3\,d^6\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}-\frac{\left(\frac{d\,\left(\frac{24\,c^4\,d^5\,e^4}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{8\,c^3\,d^3\,e^4\,\left(11\,a\,e^2-5\,c\,d^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{2\,c^2\,d^2\,e^3\,\left(19\,a^2\,e^4+6\,a\,c\,d^2\,e^2-13\,c^2\,d^4\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}+\frac{\left(\frac{24\,c^4\,d^5\,e^2}{35\,{\left(a\,e^2-c\,d^2\right)}^7}-\frac{4\,c^3\,d^3\,e^2\,\left(47\,a\,e^2-29\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^7}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{2\,e^3\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4\,\left(7\,a^3\,e^7-21\,a^2\,c\,d^2\,e^5+21\,a\,c^2\,d^4\,e^3-7\,c^3\,d^6\,e\right)}-\frac{\left(x\,\left(\frac{a\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{8\,c^7\,d^7\,e^5\,\left(c\,d^2+a\,e^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^7\,d^7\,e^5\,\left(17\,a\,e^2-5\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{4\,c^6\,d^6\,e^4\,\left(13\,a^2\,e^4+42\,a\,c\,d^2\,e^2-31\,c^2\,d^4\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,a\,c^7\,d^8\,e^6}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^6\,d^6\,e^4\,\left(c\,d^2+a\,e^2\right)\,\left(17\,a\,e^2-5\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}+\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{a\,\left(\frac{8\,c^7\,d^7\,e^5\,\left(c\,d^2+a\,e^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^7\,d^7\,e^5\,\left(17\,a\,e^2-5\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}-\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{8\,c^7\,d^7\,e^5\,\left(c\,d^2+a\,e^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^7\,d^7\,e^5\,\left(17\,a\,e^2-5\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{4\,c^6\,d^6\,e^4\,\left(13\,a^2\,e^4+42\,a\,c\,d^2\,e^2-31\,c^2\,d^4\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,a\,c^7\,d^8\,e^6}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^6\,d^6\,e^4\,\left(c\,d^2+a\,e^2\right)\,\left(17\,a\,e^2-5\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}-\frac{8\,c^5\,d^5\,e^3\,\left(74\,a^3\,e^6-261\,a^2\,c\,d^2\,e^4+198\,a\,c^2\,d^4\,e^2-35\,c^3\,d^6\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{2\,c^5\,d^5\,e^3\,\left(c\,d^2+a\,e^2\right)\,\left(13\,a^2\,e^4+42\,a\,c\,d^2\,e^2-31\,c^2\,d^4\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{2\,c^2\,d^2\,e^2\,\left(332\,a^4\,c^2\,d^2\,e^8-1032\,a^3\,c^3\,d^4\,e^6+1026\,a^2\,c^4\,d^6\,e^4-420\,a\,c^5\,d^8\,e^2+70\,c^6\,d^{10}\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{4\,c^4\,d^4\,e^2\,\left(c\,d^2+a\,e^2\right)\,\left(74\,a^3\,e^6-261\,a^2\,c\,d^2\,e^4+198\,a\,c^2\,d^4\,e^2-35\,c^3\,d^6\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)+\frac{a\,\left(\frac{a\,\left(\frac{8\,c^7\,d^7\,e^5\,\left(c\,d^2+a\,e^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^7\,d^7\,e^5\,\left(17\,a\,e^2-5\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}-\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{8\,c^7\,d^7\,e^5\,\left(c\,d^2+a\,e^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^7\,d^7\,e^5\,\left(17\,a\,e^2-5\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{4\,c^6\,d^6\,e^4\,\left(13\,a^2\,e^4+42\,a\,c\,d^2\,e^2-31\,c^2\,d^4\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,a\,c^7\,d^8\,e^6}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^6\,d^6\,e^4\,\left(c\,d^2+a\,e^2\right)\,\left(17\,a\,e^2-5\,c\,d^2\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}-\frac{8\,c^5\,d^5\,e^3\,\left(74\,a^3\,e^6-261\,a^2\,c\,d^2\,e^4+198\,a\,c^2\,d^4\,e^2-35\,c^3\,d^6\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{2\,c^5\,d^5\,e^3\,\left(c\,d^2+a\,e^2\right)\,\left(13\,a^2\,e^4+42\,a\,c\,d^2\,e^2-31\,c^2\,d^4\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}+\frac{c\,d\,e\,\left(c\,d^2+a\,e^2\right)\,\left(332\,a^4\,c^2\,d^2\,e^8-1032\,a^3\,c^3\,d^4\,e^6+1026\,a^2\,c^4\,d^6\,e^4-420\,a\,c^5\,d^8\,e^2+70\,c^6\,d^{10}\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(a\,e+c\,d\,x\right)}^2\,{\left(d+e\,x\right)}^2}+\frac{\left(x\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{24\,c^6\,d^6\,e^4\,\left(c\,d^2+a\,e^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{32\,c^6\,d^6\,e^4\,\left(7\,a\,e^2-4\,c\,d^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{4\,c^5\,d^5\,e^3\,\left(251\,a^2\,e^4-446\,a\,c\,d^2\,e^2+207\,c^2\,d^4\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{48\,a\,c^6\,d^7\,e^5}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{16\,c^5\,d^5\,e^3\,\left(c\,d^2+a\,e^2\right)\,\left(7\,a\,e^2-4\,c\,d^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)+\frac{a\,\left(\frac{24\,c^6\,d^6\,e^4\,\left(c\,d^2+a\,e^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{32\,c^6\,d^6\,e^4\,\left(7\,a\,e^2-4\,c\,d^2\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}+\frac{2\,c^4\,d^4\,e^2\,\left(c\,d^2+a\,e^2\right)\,\left(251\,a^2\,e^4-446\,a\,c\,d^2\,e^2+207\,c^2\,d^4\right)}{35\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{\left(a\,e+c\,d\,x\right)\,\left(d+e\,x\right)}","Not used",1,"(((d*((12*c^3*d^4*e^4)/(7*(a*e^2 - c*d^2)^3*(5*a^3*e^7 - 5*c^3*d^6*e + 15*a*c^2*d^4*e^3 - 15*a^2*c*d^2*e^5)) - (2*c^2*d^2*e^4*(19*a*e^2 - 7*c*d^2))/(7*(a*e^2 - c*d^2)^3*(5*a^3*e^7 - 5*c^3*d^6*e + 15*a*c^2*d^4*e^3 - 15*a^2*c*d^2*e^5))))/e + (e^3*(14*c^3*d^5 - 42*a*c^2*d^3*e^2 + 40*a^2*c*d*e^4))/(7*(a*e^2 - c*d^2)^3*(5*a^3*e^7 - 5*c^3*d^6*e + 15*a*c^2*d^4*e^3 - 15*a^2*c*d^2*e^5)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 - (((d*((24*c^4*d^5*e^4)/(35*(a*e^2 - c*d^2)^6*(3*a*e^3 - 3*c*d^2*e)) - (8*c^3*d^3*e^4*(11*a*e^2 - 5*c*d^2))/(35*(a*e^2 - c*d^2)^6*(3*a*e^3 - 3*c*d^2*e))))/e + (2*c^2*d^2*e^3*(19*a^2*e^4 - 13*c^2*d^4 + 6*a*c*d^2*e^2))/(35*(a*e^2 - c*d^2)^6*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 + (((24*c^4*d^5*e^2)/(35*(a*e^2 - c*d^2)^7) - (4*c^3*d^3*e^2*(47*a*e^2 - 29*c*d^2))/(105*(a*e^2 - c*d^2)^7))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (2*e^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/((d + e*x)^4*(7*a^3*e^7 - 7*c^3*d^6*e + 21*a*c^2*d^4*e^3 - 21*a^2*c*d^2*e^5)) - ((x*((a*(((a*e^2 + c*d^2)*((8*c^7*d^7*e^5*(a*e^2 + c*d^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^7*d^7*e^5*(17*a*e^2 - 5*c*d^2))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (4*c^6*d^6*e^4*(13*a^2*e^4 - 31*c^2*d^4 + 42*a*c*d^2*e^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*a*c^7*d^8*e^6)/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^6*d^6*e^4*(a*e^2 + c*d^2)*(17*a*e^2 - 5*c*d^2))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c + ((a*e^2 + c*d^2)*((a*((8*c^7*d^7*e^5*(a*e^2 + c*d^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^7*d^7*e^5*(17*a*e^2 - 5*c*d^2))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c - ((a*e^2 + c*d^2)*(((a*e^2 + c*d^2)*((8*c^7*d^7*e^5*(a*e^2 + c*d^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^7*d^7*e^5*(17*a*e^2 - 5*c*d^2))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (4*c^6*d^6*e^4*(13*a^2*e^4 - 31*c^2*d^4 + 42*a*c*d^2*e^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*a*c^7*d^8*e^6)/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^6*d^6*e^4*(a*e^2 + c*d^2)*(17*a*e^2 - 5*c*d^2))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) - (8*c^5*d^5*e^3*(74*a^3*e^6 - 35*c^3*d^6 + 198*a*c^2*d^4*e^2 - 261*a^2*c*d^2*e^4))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (2*c^5*d^5*e^3*(a*e^2 + c*d^2)*(13*a^2*e^4 - 31*c^2*d^4 + 42*a*c*d^2*e^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (2*c^2*d^2*e^2*(70*c^6*d^10 - 420*a*c^5*d^8*e^2 + 1026*a^2*c^4*d^6*e^4 - 1032*a^3*c^3*d^4*e^6 + 332*a^4*c^2*d^2*e^8))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (4*c^4*d^4*e^2*(a*e^2 + c*d^2)*(74*a^3*e^6 - 35*c^3*d^6 + 198*a*c^2*d^4*e^2 - 261*a^2*c*d^2*e^4))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))) + (a*((a*((8*c^7*d^7*e^5*(a*e^2 + c*d^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^7*d^7*e^5*(17*a*e^2 - 5*c*d^2))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c - ((a*e^2 + c*d^2)*(((a*e^2 + c*d^2)*((8*c^7*d^7*e^5*(a*e^2 + c*d^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^7*d^7*e^5*(17*a*e^2 - 5*c*d^2))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (4*c^6*d^6*e^4*(13*a^2*e^4 - 31*c^2*d^4 + 42*a*c*d^2*e^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*a*c^7*d^8*e^6)/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^6*d^6*e^4*(a*e^2 + c*d^2)*(17*a*e^2 - 5*c*d^2))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) - (8*c^5*d^5*e^3*(74*a^3*e^6 - 35*c^3*d^6 + 198*a*c^2*d^4*e^2 - 261*a^2*c*d^2*e^4))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (2*c^5*d^5*e^3*(a*e^2 + c*d^2)*(13*a^2*e^4 - 31*c^2*d^4 + 42*a*c*d^2*e^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c + (c*d*e*(a*e^2 + c*d^2)*(70*c^6*d^10 - 420*a*c^5*d^8*e^2 + 1026*a^2*c^4*d^6*e^4 - 1032*a^3*c^3*d^4*e^6 + 332*a^4*c^2*d^2*e^8))/(105*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/((a*e + c*d*x)^2*(d + e*x)^2) + ((x*(((a*e^2 + c*d^2)*((24*c^6*d^6*e^4*(a*e^2 + c*d^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (32*c^6*d^6*e^4*(7*a*e^2 - 4*c*d^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (4*c^5*d^5*e^3*(251*a^2*e^4 + 207*c^2*d^4 - 446*a*c*d^2*e^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (48*a*c^6*d^7*e^5)/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (16*c^5*d^5*e^3*(a*e^2 + c*d^2)*(7*a*e^2 - 4*c*d^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))) + (a*((24*c^6*d^6*e^4*(a*e^2 + c*d^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (32*c^6*d^6*e^4*(7*a*e^2 - 4*c*d^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c + (2*c^4*d^4*e^2*(a*e^2 + c*d^2)*(251*a^2*e^4 + 207*c^2*d^4 - 446*a*c*d^2*e^2))/(35*(a*e^2 - c*d^2)^6*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/((a*e + c*d*x)*(d + e*x))","B"
1973,1,10949,312,6.191060,"\text{Not used}","int(1/((d + e*x)^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)),x)","\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{64\,c^7\,d^8\,e^4}{315\,{\left(a\,e^2-c\,d^2\right)}^{10}}-\frac{8\,c^6\,d^6\,e^4\,\left(49\,a\,e^2-25\,c\,d^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^{10}}\right)}{e}+\frac{8\,c^5\,d^5\,e^3\,\left(23\,a^2\,e^4+52\,a\,c\,d^2\,e^2-51\,c^2\,d^4\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^{10}}\right)}{e}+\frac{2\,c^4\,d^4\,e^2\,\left(439\,a^3\,e^6-1409\,a^2\,c\,d^2\,e^4+1305\,a\,c^2\,d^4\,e^2-367\,c^3\,d^6\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^{10}}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{d+e\,x}-\frac{\left(\frac{d\,\left(\frac{32\,c^4\,d^5\,e^4}{63\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}-\frac{4\,c^3\,d^3\,e^4\,\left(29\,a\,e^2-13\,c\,d^2\right)}{63\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)}{e}+\frac{2\,c^2\,d^2\,e^3\,\left(25\,a^2\,e^4+8\,a\,c\,d^2\,e^2-17\,c^2\,d^4\right)}{63\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(5\,a\,e^3-5\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{d\,\left(\frac{16\,c^3\,d^4\,e^4}{9\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(7\,a^3\,e^7-21\,a^2\,c\,d^2\,e^5+21\,a\,c^2\,d^4\,e^3-7\,c^3\,d^6\,e\right)}-\frac{2\,c^2\,d^2\,e^4\,\left(25\,a\,e^2-9\,c\,d^2\right)}{9\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(7\,a^3\,e^7-21\,a^2\,c\,d^2\,e^5+21\,a\,c^2\,d^4\,e^3-7\,c^3\,d^6\,e\right)}\right)}{e}+\frac{e^3\,\left(52\,a^2\,c\,d\,e^4-54\,a\,c^2\,d^3\,e^2+18\,c^3\,d^5\right)}{9\,{\left(a\,e^2-c\,d^2\right)}^3\,\left(7\,a^3\,e^7-21\,a^2\,c\,d^2\,e^5+21\,a\,c^2\,d^4\,e^3-7\,c^3\,d^6\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^4}+\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{d\,\left(\frac{32\,c^6\,d^7\,e^6}{63\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(5\,a^3\,e^7-15\,a^2\,c\,d^2\,e^5+15\,a\,c^2\,d^4\,e^3-5\,c^3\,d^6\,e\right)}-\frac{4\,c^5\,d^5\,e^6\,\left(45\,a\,e^2-13\,c\,d^2\right)}{63\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(5\,a^3\,e^7-15\,a^2\,c\,d^2\,e^5+15\,a\,c^2\,d^4\,e^3-5\,c^3\,d^6\,e\right)}\right)}{e}+\frac{2\,c^4\,d^4\,e^5\,\left(a^2\,e^4+268\,a\,c\,d^2\,e^2-173\,c^2\,d^4\right)}{63\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(5\,a^3\,e^7-15\,a^2\,c\,d^2\,e^5+15\,a\,c^2\,d^4\,e^3-5\,c^3\,d^6\,e\right)}\right)}{e}+\frac{4\,c^3\,d^3\,e^4\,\left(165\,a^3\,e^6-496\,a^2\,c\,d^2\,e^4+362\,a\,c^2\,d^4\,e^2-63\,c^3\,d^6\right)}{63\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(5\,a^3\,e^7-15\,a^2\,c\,d^2\,e^5+15\,a\,c^2\,d^4\,e^3-5\,c^3\,d^6\,e\right)}\right)}{e}-\frac{e^3\,\left(640\,a^4\,c^2\,d^2\,e^8-1900\,a^3\,c^3\,d^4\,e^6+1858\,a^2\,c^4\,d^6\,e^4-756\,a\,c^5\,d^8\,e^2+126\,c^6\,d^{10}\right)}{63\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(5\,a^3\,e^7-15\,a^2\,c\,d^2\,e^5+15\,a\,c^2\,d^4\,e^3-5\,c^3\,d^6\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^3}+\frac{\left(\frac{32\,c^4\,d^5\,e^3}{63\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{4\,c^3\,d^3\,e^3\,\left(19\,a\,e^2-11\,c\,d^2\right)}{63\,{\left(a\,e^2-c\,d^2\right)}^6\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{\left(\frac{d\,\left(\frac{d\,\left(\frac{d\,\left(\frac{64\,c^7\,d^8\,e^6}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}-\frac{8\,c^6\,d^6\,e^6\,\left(49\,a\,e^2-17\,c\,d^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{8\,c^5\,d^5\,e^5\,\left(23\,a^2\,e^4+101\,a\,c\,d^2\,e^2-76\,c^2\,d^4\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{2\,c^4\,d^4\,e^4\,\left(659\,a^3\,e^6-2161\,a^2\,c\,d^2\,e^4+1757\,a\,c^2\,d^4\,e^2-383\,c^3\,d^6\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)}{e}+\frac{e\,\left(-660\,a^4\,c^3\,d^3\,e^{10}+1322\,a^3\,c^4\,d^5\,e^8+178\,a^2\,c^5\,d^7\,e^6-1290\,a\,c^6\,d^9\,e^4+514\,c^7\,d^{11}\,e^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(3\,a\,e^3-3\,c\,d^2\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^2}-\frac{\left(x\,\left(\frac{a\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{64\,c^9\,d^9\,e^6\,\left(c\,d^2+a\,e^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^9\,d^9\,e^6\,\left(57\,a\,e^2-25\,c\,d^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{16\,c^8\,d^8\,e^5\,\left(24\,a^2\,e^4+9\,a\,c\,d^2\,e^2-17\,c^2\,d^4\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{128\,a\,c^9\,d^{10}\,e^7}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^8\,d^8\,e^5\,\left(c\,d^2+a\,e^2\right)\,\left(57\,a\,e^2-25\,c\,d^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}+\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{a\,\left(\frac{64\,c^9\,d^9\,e^6\,\left(c\,d^2+a\,e^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^9\,d^9\,e^6\,\left(57\,a\,e^2-25\,c\,d^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}-\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{64\,c^9\,d^9\,e^6\,\left(c\,d^2+a\,e^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^9\,d^9\,e^6\,\left(57\,a\,e^2-25\,c\,d^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{16\,c^8\,d^8\,e^5\,\left(24\,a^2\,e^4+9\,a\,c\,d^2\,e^2-17\,c^2\,d^4\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{128\,a\,c^9\,d^{10}\,e^7}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^8\,d^8\,e^5\,\left(c\,d^2+a\,e^2\right)\,\left(57\,a\,e^2-25\,c\,d^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}-\frac{4\,c^7\,d^7\,e^4\,\left(487\,a^3\,e^6-2037\,a^2\,c\,d^2\,e^4+1929\,a\,c^2\,d^4\,e^2-507\,c^3\,d^6\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^7\,d^7\,e^4\,\left(c\,d^2+a\,e^2\right)\,\left(24\,a^2\,e^4+9\,a\,c\,d^2\,e^2-17\,c^2\,d^4\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{2\,c^2\,d^2\,e^2\,\left(18554\,a^4\,c^4\,d^4\,e^9-71294\,a^3\,c^5\,d^6\,e^7+100830\,a^2\,c^6\,d^8\,e^5-63362\,a\,c^7\,d^{10}\,e^3+15080\,c^8\,d^{12}\,e\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{2\,c^6\,d^6\,e^3\,\left(c\,d^2+a\,e^2\right)\,\left(487\,a^3\,e^6-2037\,a^2\,c\,d^2\,e^4+1929\,a\,c^2\,d^4\,e^2-507\,c^3\,d^6\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)+\frac{a\,\left(\frac{a\,\left(\frac{64\,c^9\,d^9\,e^6\,\left(c\,d^2+a\,e^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^9\,d^9\,e^6\,\left(57\,a\,e^2-25\,c\,d^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}-\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{64\,c^9\,d^9\,e^6\,\left(c\,d^2+a\,e^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^9\,d^9\,e^6\,\left(57\,a\,e^2-25\,c\,d^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{16\,c^8\,d^8\,e^5\,\left(24\,a^2\,e^4+9\,a\,c\,d^2\,e^2-17\,c^2\,d^4\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{128\,a\,c^9\,d^{10}\,e^7}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^8\,d^8\,e^5\,\left(c\,d^2+a\,e^2\right)\,\left(57\,a\,e^2-25\,c\,d^2\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}-\frac{4\,c^7\,d^7\,e^4\,\left(487\,a^3\,e^6-2037\,a^2\,c\,d^2\,e^4+1929\,a\,c^2\,d^4\,e^2-507\,c^3\,d^6\right)}{315\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^7\,d^7\,e^4\,\left(c\,d^2+a\,e^2\right)\,\left(24\,a^2\,e^4+9\,a\,c\,d^2\,e^2-17\,c^2\,d^4\right)}{105\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}+\frac{c\,d\,e\,\left(c\,d^2+a\,e^2\right)\,\left(18554\,a^4\,c^4\,d^4\,e^9-71294\,a^3\,c^5\,d^6\,e^7+100830\,a^2\,c^6\,d^8\,e^5-63362\,a\,c^7\,d^{10}\,e^3+15080\,c^8\,d^{12}\,e\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{\left(a\,e+c\,d\,x\right)\,\left(d+e\,x\right)}-\frac{2\,e^3\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^5\,\left(9\,a^3\,e^7-27\,a^2\,c\,d^2\,e^5+27\,a\,c^2\,d^4\,e^3-9\,c^3\,d^6\,e\right)}+\frac{\left(x\,\left(\frac{a\,\left(\frac{a\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{64\,c^{10}\,d^{10}\,e^7\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^{10}\,d^{10}\,e^7\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{16\,c^9\,d^9\,e^6\,\left(129\,a^2\,e^4+67\,a\,c\,d^2\,e^2-76\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{128\,a\,c^{10}\,d^{11}\,e^8}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^9\,d^9\,e^6\,\left(c\,d^2+a\,e^2\right)\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}+\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{a\,\left(\frac{64\,c^{10}\,d^{10}\,e^7\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^{10}\,d^{10}\,e^7\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}-\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{64\,c^{10}\,d^{10}\,e^7\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^{10}\,d^{10}\,e^7\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{16\,c^9\,d^9\,e^6\,\left(129\,a^2\,e^4+67\,a\,c\,d^2\,e^2-76\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{128\,a\,c^{10}\,d^{11}\,e^8}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^9\,d^9\,e^6\,\left(c\,d^2+a\,e^2\right)\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}-\frac{4\,c^8\,d^8\,e^5\,\left(199\,a^3\,e^6-2661\,a^2\,c\,d^2\,e^4+2125\,a\,c^2\,d^4\,e^2-303\,c^3\,d^6\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^8\,d^8\,e^5\,\left(c\,d^2+a\,e^2\right)\,\left(129\,a^2\,e^4+67\,a\,c\,d^2\,e^2-76\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}-\frac{4\,c^7\,d^7\,e^4\,\left(174\,a^4\,e^8-1293\,a^3\,c\,d^2\,e^6+5931\,a^2\,c^2\,d^4\,e^4-6079\,a\,c^3\,d^6\,e^2+1747\,c^4\,d^8\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{2\,c^7\,d^7\,e^4\,\left(c\,d^2+a\,e^2\right)\,\left(199\,a^3\,e^6-2661\,a^2\,c\,d^2\,e^4+2125\,a\,c^2\,d^4\,e^2-303\,c^3\,d^6\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}+\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{a\,\left(\frac{a\,\left(\frac{64\,c^{10}\,d^{10}\,e^7\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^{10}\,d^{10}\,e^7\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}-\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{64\,c^{10}\,d^{10}\,e^7\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^{10}\,d^{10}\,e^7\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{16\,c^9\,d^9\,e^6\,\left(129\,a^2\,e^4+67\,a\,c\,d^2\,e^2-76\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{128\,a\,c^{10}\,d^{11}\,e^8}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^9\,d^9\,e^6\,\left(c\,d^2+a\,e^2\right)\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}-\frac{4\,c^8\,d^8\,e^5\,\left(199\,a^3\,e^6-2661\,a^2\,c\,d^2\,e^4+2125\,a\,c^2\,d^4\,e^2-303\,c^3\,d^6\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^8\,d^8\,e^5\,\left(c\,d^2+a\,e^2\right)\,\left(129\,a^2\,e^4+67\,a\,c\,d^2\,e^2-76\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}-\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{a\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{64\,c^{10}\,d^{10}\,e^7\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^{10}\,d^{10}\,e^7\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{16\,c^9\,d^9\,e^6\,\left(129\,a^2\,e^4+67\,a\,c\,d^2\,e^2-76\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{128\,a\,c^{10}\,d^{11}\,e^8}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^9\,d^9\,e^6\,\left(c\,d^2+a\,e^2\right)\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}+\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{a\,\left(\frac{64\,c^{10}\,d^{10}\,e^7\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^{10}\,d^{10}\,e^7\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}-\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{64\,c^{10}\,d^{10}\,e^7\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^{10}\,d^{10}\,e^7\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{16\,c^9\,d^9\,e^6\,\left(129\,a^2\,e^4+67\,a\,c\,d^2\,e^2-76\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{128\,a\,c^{10}\,d^{11}\,e^8}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^9\,d^9\,e^6\,\left(c\,d^2+a\,e^2\right)\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}-\frac{4\,c^8\,d^8\,e^5\,\left(199\,a^3\,e^6-2661\,a^2\,c\,d^2\,e^4+2125\,a\,c^2\,d^4\,e^2-303\,c^3\,d^6\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^8\,d^8\,e^5\,\left(c\,d^2+a\,e^2\right)\,\left(129\,a^2\,e^4+67\,a\,c\,d^2\,e^2-76\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}-\frac{4\,c^7\,d^7\,e^4\,\left(174\,a^4\,e^8-1293\,a^3\,c\,d^2\,e^6+5931\,a^2\,c^2\,d^4\,e^4-6079\,a\,c^3\,d^6\,e^2+1747\,c^4\,d^8\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{2\,c^7\,d^7\,e^4\,\left(c\,d^2+a\,e^2\right)\,\left(199\,a^3\,e^6-2661\,a^2\,c\,d^2\,e^4+2125\,a\,c^2\,d^4\,e^2-303\,c^3\,d^6\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{2\,c^2\,d^2\,e^2\,\left(-5692\,a^5\,c^4\,d^4\,e^{11}+27764\,a^4\,c^5\,d^6\,e^9-52942\,a^3\,c^6\,d^8\,e^7+45034\,a^2\,c^7\,d^{10}\,e^5-16438\,a\,c^8\,d^{12}\,e^3+1890\,c^9\,d^{14}\,e\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{2\,c^6\,d^6\,e^3\,\left(c\,d^2+a\,e^2\right)\,\left(174\,a^4\,e^8-1293\,a^3\,c\,d^2\,e^6+5931\,a^2\,c^2\,d^4\,e^4-6079\,a\,c^3\,d^6\,e^2+1747\,c^4\,d^8\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{2\,c^2\,d^2\,e^2\,\left(5000\,a^6\,c^3\,d^3\,e^{12}-24308\,a^5\,c^4\,d^5\,e^{10}+46888\,a^4\,c^5\,d^7\,e^8-44870\,a^3\,c^6\,d^9\,e^6+22394\,a^2\,c^7\,d^{11}\,e^4-5670\,a\,c^8\,d^{13}\,e^2+630\,c^9\,d^{15}\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{c\,d\,e\,\left(c\,d^2+a\,e^2\right)\,\left(-5692\,a^5\,c^4\,d^4\,e^{11}+27764\,a^4\,c^5\,d^6\,e^9-52942\,a^3\,c^6\,d^8\,e^7+45034\,a^2\,c^7\,d^{10}\,e^5-16438\,a\,c^8\,d^{12}\,e^3+1890\,c^9\,d^{14}\,e\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)+\frac{a\,\left(\frac{a\,\left(\frac{a\,\left(\frac{64\,c^{10}\,d^{10}\,e^7\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^{10}\,d^{10}\,e^7\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}-\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{64\,c^{10}\,d^{10}\,e^7\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^{10}\,d^{10}\,e^7\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{16\,c^9\,d^9\,e^6\,\left(129\,a^2\,e^4+67\,a\,c\,d^2\,e^2-76\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{128\,a\,c^{10}\,d^{11}\,e^8}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^9\,d^9\,e^6\,\left(c\,d^2+a\,e^2\right)\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}-\frac{4\,c^8\,d^8\,e^5\,\left(199\,a^3\,e^6-2661\,a^2\,c\,d^2\,e^4+2125\,a\,c^2\,d^4\,e^2-303\,c^3\,d^6\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^8\,d^8\,e^5\,\left(c\,d^2+a\,e^2\right)\,\left(129\,a^2\,e^4+67\,a\,c\,d^2\,e^2-76\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}-\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{a\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{64\,c^{10}\,d^{10}\,e^7\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^{10}\,d^{10}\,e^7\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{16\,c^9\,d^9\,e^6\,\left(129\,a^2\,e^4+67\,a\,c\,d^2\,e^2-76\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{128\,a\,c^{10}\,d^{11}\,e^8}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^9\,d^9\,e^6\,\left(c\,d^2+a\,e^2\right)\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}+\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{a\,\left(\frac{64\,c^{10}\,d^{10}\,e^7\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^{10}\,d^{10}\,e^7\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}-\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{\left(c\,d^2+a\,e^2\right)\,\left(\frac{64\,c^{10}\,d^{10}\,e^7\,\left(c\,d^2+a\,e^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{16\,c^{10}\,d^{10}\,e^7\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{16\,c^9\,d^9\,e^6\,\left(129\,a^2\,e^4+67\,a\,c\,d^2\,e^2-76\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{128\,a\,c^{10}\,d^{11}\,e^8}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^9\,d^9\,e^6\,\left(c\,d^2+a\,e^2\right)\,\left(65\,a\,e^2-17\,c\,d^2\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}-\frac{4\,c^8\,d^8\,e^5\,\left(199\,a^3\,e^6-2661\,a^2\,c\,d^2\,e^4+2125\,a\,c^2\,d^4\,e^2-303\,c^3\,d^6\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{8\,c^8\,d^8\,e^5\,\left(c\,d^2+a\,e^2\right)\,\left(129\,a^2\,e^4+67\,a\,c\,d^2\,e^2-76\,c^2\,d^4\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}-\frac{4\,c^7\,d^7\,e^4\,\left(174\,a^4\,e^8-1293\,a^3\,c\,d^2\,e^6+5931\,a^2\,c^2\,d^4\,e^4-6079\,a\,c^3\,d^6\,e^2+1747\,c^4\,d^8\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}+\frac{2\,c^7\,d^7\,e^4\,\left(c\,d^2+a\,e^2\right)\,\left(199\,a^3\,e^6-2661\,a^2\,c\,d^2\,e^4+2125\,a\,c^2\,d^4\,e^2-303\,c^3\,d^6\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c\,d\,e}+\frac{2\,c^2\,d^2\,e^2\,\left(-5692\,a^5\,c^4\,d^4\,e^{11}+27764\,a^4\,c^5\,d^6\,e^9-52942\,a^3\,c^6\,d^8\,e^7+45034\,a^2\,c^7\,d^{10}\,e^5-16438\,a\,c^8\,d^{12}\,e^3+1890\,c^9\,d^{14}\,e\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}-\frac{2\,c^6\,d^6\,e^3\,\left(c\,d^2+a\,e^2\right)\,\left(174\,a^4\,e^8-1293\,a^3\,c\,d^2\,e^6+5931\,a^2\,c^2\,d^4\,e^4-6079\,a\,c^3\,d^6\,e^2+1747\,c^4\,d^8\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)}{c}+\frac{c\,d\,e\,\left(c\,d^2+a\,e^2\right)\,\left(5000\,a^6\,c^3\,d^3\,e^{12}-24308\,a^5\,c^4\,d^5\,e^{10}+46888\,a^4\,c^5\,d^7\,e^8-44870\,a^3\,c^6\,d^9\,e^6+22394\,a^2\,c^7\,d^{11}\,e^4-5670\,a\,c^8\,d^{13}\,e^2+630\,c^9\,d^{15}\right)}{945\,{\left(a\,e^2-c\,d^2\right)}^9\,\left(a^2\,c\,d\,e^5-2\,a\,c^2\,d^3\,e^3+c^3\,d^5\,e\right)}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(a\,e+c\,d\,x\right)}^2\,{\left(d+e\,x\right)}^2}+\frac{8\,c^4\,d^4\,e^2\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{27\,{\left(a\,e^2-c\,d^2\right)}^7\,\left(d+e\,x\right)}","Not used",1,"(((d*((d*((64*c^7*d^8*e^4)/(315*(a*e^2 - c*d^2)^10) - (8*c^6*d^6*e^4*(49*a*e^2 - 25*c*d^2))/(315*(a*e^2 - c*d^2)^10)))/e + (8*c^5*d^5*e^3*(23*a^2*e^4 - 51*c^2*d^4 + 52*a*c*d^2*e^2))/(315*(a*e^2 - c*d^2)^10)))/e + (2*c^4*d^4*e^2*(439*a^3*e^6 - 367*c^3*d^6 + 1305*a*c^2*d^4*e^2 - 1409*a^2*c*d^2*e^4))/(315*(a*e^2 - c*d^2)^10))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x) - (((d*((32*c^4*d^5*e^4)/(63*(a*e^2 - c*d^2)^6*(5*a*e^3 - 5*c*d^2*e)) - (4*c^3*d^3*e^4*(29*a*e^2 - 13*c*d^2))/(63*(a*e^2 - c*d^2)^6*(5*a*e^3 - 5*c*d^2*e))))/e + (2*c^2*d^2*e^3*(25*a^2*e^4 - 17*c^2*d^4 + 8*a*c*d^2*e^2))/(63*(a*e^2 - c*d^2)^6*(5*a*e^3 - 5*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((d*((16*c^3*d^4*e^4)/(9*(a*e^2 - c*d^2)^3*(7*a^3*e^7 - 7*c^3*d^6*e + 21*a*c^2*d^4*e^3 - 21*a^2*c*d^2*e^5)) - (2*c^2*d^2*e^4*(25*a*e^2 - 9*c*d^2))/(9*(a*e^2 - c*d^2)^3*(7*a^3*e^7 - 7*c^3*d^6*e + 21*a*c^2*d^4*e^3 - 21*a^2*c*d^2*e^5))))/e + (e^3*(18*c^3*d^5 - 54*a*c^2*d^3*e^2 + 52*a^2*c*d*e^4))/(9*(a*e^2 - c*d^2)^3*(7*a^3*e^7 - 7*c^3*d^6*e + 21*a*c^2*d^4*e^3 - 21*a^2*c*d^2*e^5)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^4 + (((d*((d*((d*((32*c^6*d^7*e^6)/(63*(a*e^2 - c*d^2)^6*(5*a^3*e^7 - 5*c^3*d^6*e + 15*a*c^2*d^4*e^3 - 15*a^2*c*d^2*e^5)) - (4*c^5*d^5*e^6*(45*a*e^2 - 13*c*d^2))/(63*(a*e^2 - c*d^2)^6*(5*a^3*e^7 - 5*c^3*d^6*e + 15*a*c^2*d^4*e^3 - 15*a^2*c*d^2*e^5))))/e + (2*c^4*d^4*e^5*(a^2*e^4 - 173*c^2*d^4 + 268*a*c*d^2*e^2))/(63*(a*e^2 - c*d^2)^6*(5*a^3*e^7 - 5*c^3*d^6*e + 15*a*c^2*d^4*e^3 - 15*a^2*c*d^2*e^5))))/e + (4*c^3*d^3*e^4*(165*a^3*e^6 - 63*c^3*d^6 + 362*a*c^2*d^4*e^2 - 496*a^2*c*d^2*e^4))/(63*(a*e^2 - c*d^2)^6*(5*a^3*e^7 - 5*c^3*d^6*e + 15*a*c^2*d^4*e^3 - 15*a^2*c*d^2*e^5))))/e - (e^3*(126*c^6*d^10 - 756*a*c^5*d^8*e^2 + 1858*a^2*c^4*d^6*e^4 - 1900*a^3*c^3*d^4*e^6 + 640*a^4*c^2*d^2*e^8))/(63*(a*e^2 - c*d^2)^6*(5*a^3*e^7 - 5*c^3*d^6*e + 15*a*c^2*d^4*e^3 - 15*a^2*c*d^2*e^5)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^3 + (((32*c^4*d^5*e^3)/(63*(a*e^2 - c*d^2)^6*(3*a*e^3 - 3*c*d^2*e)) - (4*c^3*d^3*e^3*(19*a*e^2 - 11*c*d^2))/(63*(a*e^2 - c*d^2)^6*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - (((d*((d*((d*((64*c^7*d^8*e^6)/(315*(a*e^2 - c*d^2)^9*(3*a*e^3 - 3*c*d^2*e)) - (8*c^6*d^6*e^6*(49*a*e^2 - 17*c*d^2))/(315*(a*e^2 - c*d^2)^9*(3*a*e^3 - 3*c*d^2*e))))/e + (8*c^5*d^5*e^5*(23*a^2*e^4 - 76*c^2*d^4 + 101*a*c*d^2*e^2))/(315*(a*e^2 - c*d^2)^9*(3*a*e^3 - 3*c*d^2*e))))/e + (2*c^4*d^4*e^4*(659*a^3*e^6 - 383*c^3*d^6 + 1757*a*c^2*d^4*e^2 - 2161*a^2*c*d^2*e^4))/(315*(a*e^2 - c*d^2)^9*(3*a*e^3 - 3*c*d^2*e))))/e + (e*(514*c^7*d^11*e^2 - 1290*a*c^6*d^9*e^4 + 178*a^2*c^5*d^7*e^6 + 1322*a^3*c^4*d^5*e^8 - 660*a^4*c^3*d^3*e^10))/(315*(a*e^2 - c*d^2)^9*(3*a*e^3 - 3*c*d^2*e)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^2 - ((x*((a*(((a*e^2 + c*d^2)*((64*c^9*d^9*e^6*(a*e^2 + c*d^2))/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^9*d^9*e^6*(57*a*e^2 - 25*c*d^2))/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (16*c^8*d^8*e^5*(24*a^2*e^4 - 17*c^2*d^4 + 9*a*c*d^2*e^2))/(105*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (128*a*c^9*d^10*e^7)/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^8*d^8*e^5*(a*e^2 + c*d^2)*(57*a*e^2 - 25*c*d^2))/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c + ((a*e^2 + c*d^2)*((a*((64*c^9*d^9*e^6*(a*e^2 + c*d^2))/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^9*d^9*e^6*(57*a*e^2 - 25*c*d^2))/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c - ((a*e^2 + c*d^2)*(((a*e^2 + c*d^2)*((64*c^9*d^9*e^6*(a*e^2 + c*d^2))/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^9*d^9*e^6*(57*a*e^2 - 25*c*d^2))/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (16*c^8*d^8*e^5*(24*a^2*e^4 - 17*c^2*d^4 + 9*a*c*d^2*e^2))/(105*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (128*a*c^9*d^10*e^7)/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^8*d^8*e^5*(a*e^2 + c*d^2)*(57*a*e^2 - 25*c*d^2))/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) - (4*c^7*d^7*e^4*(487*a^3*e^6 - 507*c^3*d^6 + 1929*a*c^2*d^4*e^2 - 2037*a^2*c*d^2*e^4))/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^7*d^7*e^4*(a*e^2 + c*d^2)*(24*a^2*e^4 - 17*c^2*d^4 + 9*a*c*d^2*e^2))/(105*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (2*c^2*d^2*e^2*(15080*c^8*d^12*e - 63362*a*c^7*d^10*e^3 + 100830*a^2*c^6*d^8*e^5 - 71294*a^3*c^5*d^6*e^7 + 18554*a^4*c^4*d^4*e^9))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (2*c^6*d^6*e^3*(a*e^2 + c*d^2)*(487*a^3*e^6 - 507*c^3*d^6 + 1929*a*c^2*d^4*e^2 - 2037*a^2*c*d^2*e^4))/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))) + (a*((a*((64*c^9*d^9*e^6*(a*e^2 + c*d^2))/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^9*d^9*e^6*(57*a*e^2 - 25*c*d^2))/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c - ((a*e^2 + c*d^2)*(((a*e^2 + c*d^2)*((64*c^9*d^9*e^6*(a*e^2 + c*d^2))/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^9*d^9*e^6*(57*a*e^2 - 25*c*d^2))/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (16*c^8*d^8*e^5*(24*a^2*e^4 - 17*c^2*d^4 + 9*a*c*d^2*e^2))/(105*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (128*a*c^9*d^10*e^7)/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^8*d^8*e^5*(a*e^2 + c*d^2)*(57*a*e^2 - 25*c*d^2))/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) - (4*c^7*d^7*e^4*(487*a^3*e^6 - 507*c^3*d^6 + 1929*a*c^2*d^4*e^2 - 2037*a^2*c*d^2*e^4))/(315*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^7*d^7*e^4*(a*e^2 + c*d^2)*(24*a^2*e^4 - 17*c^2*d^4 + 9*a*c*d^2*e^2))/(105*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c + (c*d*e*(a*e^2 + c*d^2)*(15080*c^8*d^12*e - 63362*a*c^7*d^10*e^3 + 100830*a^2*c^6*d^8*e^5 - 71294*a^3*c^5*d^6*e^7 + 18554*a^4*c^4*d^4*e^9))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/((a*e + c*d*x)*(d + e*x)) - (2*e^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/((d + e*x)^5*(9*a^3*e^7 - 9*c^3*d^6*e + 27*a*c^2*d^4*e^3 - 27*a^2*c*d^2*e^5)) + ((x*((a*((a*(((a*e^2 + c*d^2)*((64*c^10*d^10*e^7*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^10*d^10*e^7*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (16*c^9*d^9*e^6*(129*a^2*e^4 - 76*c^2*d^4 + 67*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (128*a*c^10*d^11*e^8)/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^9*d^9*e^6*(a*e^2 + c*d^2)*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c + ((a*e^2 + c*d^2)*((a*((64*c^10*d^10*e^7*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^10*d^10*e^7*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c - ((a*e^2 + c*d^2)*(((a*e^2 + c*d^2)*((64*c^10*d^10*e^7*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^10*d^10*e^7*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (16*c^9*d^9*e^6*(129*a^2*e^4 - 76*c^2*d^4 + 67*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (128*a*c^10*d^11*e^8)/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^9*d^9*e^6*(a*e^2 + c*d^2)*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) - (4*c^8*d^8*e^5*(199*a^3*e^6 - 303*c^3*d^6 + 2125*a*c^2*d^4*e^2 - 2661*a^2*c*d^2*e^4))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^8*d^8*e^5*(a*e^2 + c*d^2)*(129*a^2*e^4 - 76*c^2*d^4 + 67*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) - (4*c^7*d^7*e^4*(174*a^4*e^8 + 1747*c^4*d^8 - 6079*a*c^3*d^6*e^2 - 1293*a^3*c*d^2*e^6 + 5931*a^2*c^2*d^4*e^4))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (2*c^7*d^7*e^4*(a*e^2 + c*d^2)*(199*a^3*e^6 - 303*c^3*d^6 + 2125*a*c^2*d^4*e^2 - 2661*a^2*c*d^2*e^4))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c + ((a*e^2 + c*d^2)*((a*((a*((64*c^10*d^10*e^7*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^10*d^10*e^7*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c - ((a*e^2 + c*d^2)*(((a*e^2 + c*d^2)*((64*c^10*d^10*e^7*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^10*d^10*e^7*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (16*c^9*d^9*e^6*(129*a^2*e^4 - 76*c^2*d^4 + 67*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (128*a*c^10*d^11*e^8)/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^9*d^9*e^6*(a*e^2 + c*d^2)*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) - (4*c^8*d^8*e^5*(199*a^3*e^6 - 303*c^3*d^6 + 2125*a*c^2*d^4*e^2 - 2661*a^2*c*d^2*e^4))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^8*d^8*e^5*(a*e^2 + c*d^2)*(129*a^2*e^4 - 76*c^2*d^4 + 67*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c - ((a*e^2 + c*d^2)*((a*(((a*e^2 + c*d^2)*((64*c^10*d^10*e^7*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^10*d^10*e^7*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (16*c^9*d^9*e^6*(129*a^2*e^4 - 76*c^2*d^4 + 67*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (128*a*c^10*d^11*e^8)/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^9*d^9*e^6*(a*e^2 + c*d^2)*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c + ((a*e^2 + c*d^2)*((a*((64*c^10*d^10*e^7*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^10*d^10*e^7*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c - ((a*e^2 + c*d^2)*(((a*e^2 + c*d^2)*((64*c^10*d^10*e^7*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^10*d^10*e^7*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (16*c^9*d^9*e^6*(129*a^2*e^4 - 76*c^2*d^4 + 67*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (128*a*c^10*d^11*e^8)/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^9*d^9*e^6*(a*e^2 + c*d^2)*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) - (4*c^8*d^8*e^5*(199*a^3*e^6 - 303*c^3*d^6 + 2125*a*c^2*d^4*e^2 - 2661*a^2*c*d^2*e^4))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^8*d^8*e^5*(a*e^2 + c*d^2)*(129*a^2*e^4 - 76*c^2*d^4 + 67*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) - (4*c^7*d^7*e^4*(174*a^4*e^8 + 1747*c^4*d^8 - 6079*a*c^3*d^6*e^2 - 1293*a^3*c*d^2*e^6 + 5931*a^2*c^2*d^4*e^4))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (2*c^7*d^7*e^4*(a*e^2 + c*d^2)*(199*a^3*e^6 - 303*c^3*d^6 + 2125*a*c^2*d^4*e^2 - 2661*a^2*c*d^2*e^4))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (2*c^2*d^2*e^2*(1890*c^9*d^14*e - 16438*a*c^8*d^12*e^3 + 45034*a^2*c^7*d^10*e^5 - 52942*a^3*c^6*d^8*e^7 + 27764*a^4*c^5*d^6*e^9 - 5692*a^5*c^4*d^4*e^11))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (2*c^6*d^6*e^3*(a*e^2 + c*d^2)*(174*a^4*e^8 + 1747*c^4*d^8 - 6079*a*c^3*d^6*e^2 - 1293*a^3*c*d^2*e^6 + 5931*a^2*c^2*d^4*e^4))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (2*c^2*d^2*e^2*(630*c^9*d^15 - 5670*a*c^8*d^13*e^2 + 22394*a^2*c^7*d^11*e^4 - 44870*a^3*c^6*d^9*e^6 + 46888*a^4*c^5*d^7*e^8 - 24308*a^5*c^4*d^5*e^10 + 5000*a^6*c^3*d^3*e^12))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (c*d*e*(a*e^2 + c*d^2)*(1890*c^9*d^14*e - 16438*a*c^8*d^12*e^3 + 45034*a^2*c^7*d^10*e^5 - 52942*a^3*c^6*d^8*e^7 + 27764*a^4*c^5*d^6*e^9 - 5692*a^5*c^4*d^4*e^11))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))) + (a*((a*((a*((64*c^10*d^10*e^7*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^10*d^10*e^7*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c - ((a*e^2 + c*d^2)*(((a*e^2 + c*d^2)*((64*c^10*d^10*e^7*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^10*d^10*e^7*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (16*c^9*d^9*e^6*(129*a^2*e^4 - 76*c^2*d^4 + 67*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (128*a*c^10*d^11*e^8)/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^9*d^9*e^6*(a*e^2 + c*d^2)*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) - (4*c^8*d^8*e^5*(199*a^3*e^6 - 303*c^3*d^6 + 2125*a*c^2*d^4*e^2 - 2661*a^2*c*d^2*e^4))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^8*d^8*e^5*(a*e^2 + c*d^2)*(129*a^2*e^4 - 76*c^2*d^4 + 67*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c - ((a*e^2 + c*d^2)*((a*(((a*e^2 + c*d^2)*((64*c^10*d^10*e^7*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^10*d^10*e^7*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (16*c^9*d^9*e^6*(129*a^2*e^4 - 76*c^2*d^4 + 67*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (128*a*c^10*d^11*e^8)/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^9*d^9*e^6*(a*e^2 + c*d^2)*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c + ((a*e^2 + c*d^2)*((a*((64*c^10*d^10*e^7*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^10*d^10*e^7*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c - ((a*e^2 + c*d^2)*(((a*e^2 + c*d^2)*((64*c^10*d^10*e^7*(a*e^2 + c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (16*c^10*d^10*e^7*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (16*c^9*d^9*e^6*(129*a^2*e^4 - 76*c^2*d^4 + 67*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (128*a*c^10*d^11*e^8)/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^9*d^9*e^6*(a*e^2 + c*d^2)*(65*a*e^2 - 17*c*d^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) - (4*c^8*d^8*e^5*(199*a^3*e^6 - 303*c^3*d^6 + 2125*a*c^2*d^4*e^2 - 2661*a^2*c*d^2*e^4))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (8*c^8*d^8*e^5*(a*e^2 + c*d^2)*(129*a^2*e^4 - 76*c^2*d^4 + 67*a*c*d^2*e^2))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) - (4*c^7*d^7*e^4*(174*a^4*e^8 + 1747*c^4*d^8 - 6079*a*c^3*d^6*e^2 - 1293*a^3*c*d^2*e^6 + 5931*a^2*c^2*d^4*e^4))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) + (2*c^7*d^7*e^4*(a*e^2 + c*d^2)*(199*a^3*e^6 - 303*c^3*d^6 + 2125*a*c^2*d^4*e^2 - 2661*a^2*c*d^2*e^4))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/(c*d*e) + (2*c^2*d^2*e^2*(1890*c^9*d^14*e - 16438*a*c^8*d^12*e^3 + 45034*a^2*c^7*d^10*e^5 - 52942*a^3*c^6*d^8*e^7 + 27764*a^4*c^5*d^6*e^9 - 5692*a^5*c^4*d^4*e^11))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)) - (2*c^6*d^6*e^3*(a*e^2 + c*d^2)*(174*a^4*e^8 + 1747*c^4*d^8 - 6079*a*c^3*d^6*e^2 - 1293*a^3*c*d^2*e^6 + 5931*a^2*c^2*d^4*e^4))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5))))/c + (c*d*e*(a*e^2 + c*d^2)*(630*c^9*d^15 - 5670*a*c^8*d^13*e^2 + 22394*a^2*c^7*d^11*e^4 - 44870*a^3*c^6*d^9*e^6 + 46888*a^4*c^5*d^7*e^8 - 24308*a^5*c^4*d^5*e^10 + 5000*a^6*c^3*d^3*e^12))/(945*(a*e^2 - c*d^2)^9*(c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/((a*e + c*d*x)^2*(d + e*x)^2) + (8*c^4*d^4*e^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(27*(a*e^2 - c*d^2)^7*(d + e*x))","B"
1974,0,-1,1485,0.000000,"\text{Not used}","int((d + e*x)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/3),x)","\int \frac{d+e\,x}{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{1/3}} \,d x","Not used",1,"int((d + e*x)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/3), x)","F"
1975,0,-1,1432,0.000000,"\text{Not used}","int(1/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/3),x)","\int \frac{1}{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{1/3}} \,d x","Not used",1,"int(1/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/3), x)","F"
1976,1,34,43,0.610376,"\text{Not used}","int((d + e*x)^(3/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","\frac{2\,{\left(d+e\,x\right)}^{7/2}\,\left(9\,a\,e^2-9\,c\,d^2+7\,c\,d\,\left(d+e\,x\right)\right)}{63\,e^2}","Not used",1,"(2*(d + e*x)^(7/2)*(9*a*e^2 - 9*c*d^2 + 7*c*d*(d + e*x)))/(63*e^2)","B"
1977,1,34,43,0.043364,"\text{Not used}","int((d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","\frac{2\,{\left(d+e\,x\right)}^{5/2}\,\left(7\,a\,e^2-7\,c\,d^2+5\,c\,d\,\left(d+e\,x\right)\right)}{35\,e^2}","Not used",1,"(2*(d + e*x)^(5/2)*(7*a*e^2 - 7*c*d^2 + 5*c*d*(d + e*x)))/(35*e^2)","B"
1978,1,34,43,0.045374,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)/(d + e*x)^(1/2),x)","\frac{2\,{\left(d+e\,x\right)}^{3/2}\,\left(5\,a\,e^2-5\,c\,d^2+3\,c\,d\,\left(d+e\,x\right)\right)}{15\,e^2}","Not used",1,"(2*(d + e*x)^(3/2)*(5*a*e^2 - 5*c*d^2 + 3*c*d*(d + e*x)))/(15*e^2)","B"
1979,1,33,41,0.603715,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)/(d + e*x)^(3/2),x)","\frac{2\,\sqrt{d+e\,x}\,\left(3\,a\,e^2-3\,c\,d^2+c\,d\,\left(d+e\,x\right)\right)}{3\,e^2}","Not used",1,"(2*(d + e*x)^(1/2)*(3*a*e^2 - 3*c*d^2 + c*d*(d + e*x)))/(3*e^2)","B"
1980,1,30,39,0.054086,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)/(d + e*x)^(5/2),x)","\frac{4\,c\,d^2+2\,c\,x\,d\,e-2\,a\,e^2}{e^2\,\sqrt{d+e\,x}}","Not used",1,"(4*c*d^2 - 2*a*e^2 + 2*c*d*e*x)/(e^2*(d + e*x)^(1/2))","B"
1981,1,34,41,0.598765,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)/(d + e*x)^(7/2),x)","-\frac{2\,a\,e^2-2\,c\,d^2+6\,c\,d\,\left(d+e\,x\right)}{3\,e^2\,{\left(d+e\,x\right)}^{3/2}}","Not used",1,"-(2*a*e^2 - 2*c*d^2 + 6*c*d*(d + e*x))/(3*e^2*(d + e*x)^(3/2))","B"
1982,1,34,43,0.042425,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)/(d + e*x)^(9/2),x)","-\frac{6\,a\,e^2-6\,c\,d^2+10\,c\,d\,\left(d+e\,x\right)}{15\,e^2\,{\left(d+e\,x\right)}^{5/2}}","Not used",1,"-(6*a*e^2 - 6*c*d^2 + 10*c*d*(d + e*x))/(15*e^2*(d + e*x)^(5/2))","B"
1983,1,31,43,0.594533,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)/(d + e*x)^(11/2),x)","-\frac{4\,c\,d^2+14\,c\,x\,d\,e+10\,a\,e^2}{35\,e^2\,{\left(d+e\,x\right)}^{7/2}}","Not used",1,"-(10*a*e^2 + 4*c*d^2 + 14*c*d*e*x)/(35*e^2*(d + e*x)^(7/2))","B"
1984,1,80,83,0.642821,"\text{Not used}","int((d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","\frac{2\,{\left(d+e\,x\right)}^{7/2}\,\left(99\,a^2\,e^4+99\,c^2\,d^4+63\,c^2\,d^2\,{\left(d+e\,x\right)}^2-154\,c^2\,d^3\,\left(d+e\,x\right)-198\,a\,c\,d^2\,e^2+154\,a\,c\,d\,e^2\,\left(d+e\,x\right)\right)}{693\,e^3}","Not used",1,"(2*(d + e*x)^(7/2)*(99*a^2*e^4 + 99*c^2*d^4 + 63*c^2*d^2*(d + e*x)^2 - 154*c^2*d^3*(d + e*x) - 198*a*c*d^2*e^2 + 154*a*c*d*e^2*(d + e*x)))/(693*e^3)","B"
1985,1,80,83,0.057644,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2/(d + e*x)^(1/2),x)","\frac{2\,{\left(d+e\,x\right)}^{5/2}\,\left(63\,a^2\,e^4+63\,c^2\,d^4+35\,c^2\,d^2\,{\left(d+e\,x\right)}^2-90\,c^2\,d^3\,\left(d+e\,x\right)-126\,a\,c\,d^2\,e^2+90\,a\,c\,d\,e^2\,\left(d+e\,x\right)\right)}{315\,e^3}","Not used",1,"(2*(d + e*x)^(5/2)*(63*a^2*e^4 + 63*c^2*d^4 + 35*c^2*d^2*(d + e*x)^2 - 90*c^2*d^3*(d + e*x) - 126*a*c*d^2*e^2 + 90*a*c*d*e^2*(d + e*x)))/(315*e^3)","B"
1986,1,80,83,0.626204,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2/(d + e*x)^(3/2),x)","\frac{2\,{\left(d+e\,x\right)}^{3/2}\,\left(35\,a^2\,e^4+35\,c^2\,d^4+15\,c^2\,d^2\,{\left(d+e\,x\right)}^2-42\,c^2\,d^3\,\left(d+e\,x\right)-70\,a\,c\,d^2\,e^2+42\,a\,c\,d\,e^2\,\left(d+e\,x\right)\right)}{105\,e^3}","Not used",1,"(2*(d + e*x)^(3/2)*(35*a^2*e^4 + 35*c^2*d^4 + 15*c^2*d^2*(d + e*x)^2 - 42*c^2*d^3*(d + e*x) - 70*a*c*d^2*e^2 + 42*a*c*d*e^2*(d + e*x)))/(105*e^3)","B"
1987,1,80,81,0.055951,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2/(d + e*x)^(5/2),x)","\frac{2\,\sqrt{d+e\,x}\,\left(15\,a^2\,e^4+15\,c^2\,d^4+3\,c^2\,d^2\,{\left(d+e\,x\right)}^2-10\,c^2\,d^3\,\left(d+e\,x\right)-30\,a\,c\,d^2\,e^2+10\,a\,c\,d\,e^2\,\left(d+e\,x\right)\right)}{15\,e^3}","Not used",1,"(2*(d + e*x)^(1/2)*(15*a^2*e^4 + 15*c^2*d^4 + 3*c^2*d^2*(d + e*x)^2 - 10*c^2*d^3*(d + e*x) - 30*a*c*d^2*e^2 + 10*a*c*d*e^2*(d + e*x)))/(15*e^3)","B"
1988,1,80,79,0.630156,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2/(d + e*x)^(7/2),x)","-\frac{6\,a^2\,e^4+6\,c^2\,d^4-2\,c^2\,d^2\,{\left(d+e\,x\right)}^2+12\,c^2\,d^3\,\left(d+e\,x\right)-12\,a\,c\,d^2\,e^2-12\,a\,c\,d\,e^2\,\left(d+e\,x\right)}{3\,e^3\,\sqrt{d+e\,x}}","Not used",1,"-(6*a^2*e^4 + 6*c^2*d^4 - 2*c^2*d^2*(d + e*x)^2 + 12*c^2*d^3*(d + e*x) - 12*a*c*d^2*e^2 - 12*a*c*d*e^2*(d + e*x))/(3*e^3*(d + e*x)^(1/2))","B"
1989,1,80,79,0.625625,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2/(d + e*x)^(9/2),x)","-\frac{2\,a^2\,e^4+2\,c^2\,d^4-6\,c^2\,d^2\,{\left(d+e\,x\right)}^2-12\,c^2\,d^3\,\left(d+e\,x\right)-4\,a\,c\,d^2\,e^2+12\,a\,c\,d\,e^2\,\left(d+e\,x\right)}{3\,e^3\,{\left(d+e\,x\right)}^{3/2}}","Not used",1,"-(2*a^2*e^4 + 2*c^2*d^4 - 6*c^2*d^2*(d + e*x)^2 - 12*c^2*d^3*(d + e*x) - 4*a*c*d^2*e^2 + 12*a*c*d*e^2*(d + e*x))/(3*e^3*(d + e*x)^(3/2))","B"
1990,1,78,81,0.076665,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2/(d + e*x)^(11/2),x)","-\frac{\frac{2\,a^2\,e^4}{5}+\frac{2\,c^2\,d^4}{5}-\left(\frac{4\,c^2\,d^3}{3}-\frac{4\,a\,c\,d\,e^2}{3}\right)\,\left(d+e\,x\right)+2\,c^2\,d^2\,{\left(d+e\,x\right)}^2-\frac{4\,a\,c\,d^2\,e^2}{5}}{e^3\,{\left(d+e\,x\right)}^{5/2}}","Not used",1,"-((2*a^2*e^4)/5 + (2*c^2*d^4)/5 - ((4*c^2*d^3)/3 - (4*a*c*d*e^2)/3)*(d + e*x) + 2*c^2*d^2*(d + e*x)^2 - (4*a*c*d^2*e^2)/5)/(e^3*(d + e*x)^(5/2))","B"
1991,1,78,83,0.636009,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2/(d + e*x)^(13/2),x)","-\frac{\frac{2\,a^2\,e^4}{7}+\frac{2\,c^2\,d^4}{7}-\left(\frac{4\,c^2\,d^3}{5}-\frac{4\,a\,c\,d\,e^2}{5}\right)\,\left(d+e\,x\right)+\frac{2\,c^2\,d^2\,{\left(d+e\,x\right)}^2}{3}-\frac{4\,a\,c\,d^2\,e^2}{7}}{e^3\,{\left(d+e\,x\right)}^{7/2}}","Not used",1,"-((2*a^2*e^4)/7 + (2*c^2*d^4)/7 - ((4*c^2*d^3)/5 - (4*a*c*d*e^2)/5)*(d + e*x) + (2*c^2*d^2*(d + e*x)^2)/3 - (4*a*c*d^2*e^2)/7)/(e^3*(d + e*x)^(7/2))","B"
1992,1,106,119,0.073404,"\text{Not used}","int((d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","\frac{2\,{\left(a\,e^2-c\,d^2\right)}^3\,{\left(d+e\,x\right)}^{9/2}}{9\,e^4}-\frac{\left(6\,c^3\,d^4-6\,a\,c^2\,d^2\,e^2\right)\,{\left(d+e\,x\right)}^{13/2}}{13\,e^4}+\frac{2\,c^3\,d^3\,{\left(d+e\,x\right)}^{15/2}}{15\,e^4}+\frac{6\,c\,d\,{\left(a\,e^2-c\,d^2\right)}^2\,{\left(d+e\,x\right)}^{11/2}}{11\,e^4}","Not used",1,"(2*(a*e^2 - c*d^2)^3*(d + e*x)^(9/2))/(9*e^4) - ((6*c^3*d^4 - 6*a*c^2*d^2*e^2)*(d + e*x)^(13/2))/(13*e^4) + (2*c^3*d^3*(d + e*x)^(15/2))/(15*e^4) + (6*c*d*(a*e^2 - c*d^2)^2*(d + e*x)^(11/2))/(11*e^4)","B"
1993,1,106,119,0.064382,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^(1/2),x)","\frac{2\,{\left(a\,e^2-c\,d^2\right)}^3\,{\left(d+e\,x\right)}^{7/2}}{7\,e^4}-\frac{\left(6\,c^3\,d^4-6\,a\,c^2\,d^2\,e^2\right)\,{\left(d+e\,x\right)}^{11/2}}{11\,e^4}+\frac{2\,c^3\,d^3\,{\left(d+e\,x\right)}^{13/2}}{13\,e^4}+\frac{2\,c\,d\,{\left(a\,e^2-c\,d^2\right)}^2\,{\left(d+e\,x\right)}^{9/2}}{3\,e^4}","Not used",1,"(2*(a*e^2 - c*d^2)^3*(d + e*x)^(7/2))/(7*e^4) - ((6*c^3*d^4 - 6*a*c^2*d^2*e^2)*(d + e*x)^(11/2))/(11*e^4) + (2*c^3*d^3*(d + e*x)^(13/2))/(13*e^4) + (2*c*d*(a*e^2 - c*d^2)^2*(d + e*x)^(9/2))/(3*e^4)","B"
1994,1,106,119,0.067150,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^(3/2),x)","\frac{2\,{\left(a\,e^2-c\,d^2\right)}^3\,{\left(d+e\,x\right)}^{5/2}}{5\,e^4}-\frac{\left(6\,c^3\,d^4-6\,a\,c^2\,d^2\,e^2\right)\,{\left(d+e\,x\right)}^{9/2}}{9\,e^4}+\frac{2\,c^3\,d^3\,{\left(d+e\,x\right)}^{11/2}}{11\,e^4}+\frac{6\,c\,d\,{\left(a\,e^2-c\,d^2\right)}^2\,{\left(d+e\,x\right)}^{7/2}}{7\,e^4}","Not used",1,"(2*(a*e^2 - c*d^2)^3*(d + e*x)^(5/2))/(5*e^4) - ((6*c^3*d^4 - 6*a*c^2*d^2*e^2)*(d + e*x)^(9/2))/(9*e^4) + (2*c^3*d^3*(d + e*x)^(11/2))/(11*e^4) + (6*c*d*(a*e^2 - c*d^2)^2*(d + e*x)^(7/2))/(7*e^4)","B"
1995,1,106,119,0.067198,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^(5/2),x)","\frac{2\,{\left(a\,e^2-c\,d^2\right)}^3\,{\left(d+e\,x\right)}^{3/2}}{3\,e^4}-\frac{\left(6\,c^3\,d^4-6\,a\,c^2\,d^2\,e^2\right)\,{\left(d+e\,x\right)}^{7/2}}{7\,e^4}+\frac{2\,c^3\,d^3\,{\left(d+e\,x\right)}^{9/2}}{9\,e^4}+\frac{6\,c\,d\,{\left(a\,e^2-c\,d^2\right)}^2\,{\left(d+e\,x\right)}^{5/2}}{5\,e^4}","Not used",1,"(2*(a*e^2 - c*d^2)^3*(d + e*x)^(3/2))/(3*e^4) - ((6*c^3*d^4 - 6*a*c^2*d^2*e^2)*(d + e*x)^(7/2))/(7*e^4) + (2*c^3*d^3*(d + e*x)^(9/2))/(9*e^4) + (6*c*d*(a*e^2 - c*d^2)^2*(d + e*x)^(5/2))/(5*e^4)","B"
1996,1,106,115,0.065624,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^(7/2),x)","\frac{2\,{\left(a\,e^2-c\,d^2\right)}^3\,\sqrt{d+e\,x}}{e^4}-\frac{\left(6\,c^3\,d^4-6\,a\,c^2\,d^2\,e^2\right)\,{\left(d+e\,x\right)}^{5/2}}{5\,e^4}+\frac{2\,c^3\,d^3\,{\left(d+e\,x\right)}^{7/2}}{7\,e^4}+\frac{2\,c\,d\,{\left(a\,e^2-c\,d^2\right)}^2\,{\left(d+e\,x\right)}^{3/2}}{e^4}","Not used",1,"(2*(a*e^2 - c*d^2)^3*(d + e*x)^(1/2))/e^4 - ((6*c^3*d^4 - 6*a*c^2*d^2*e^2)*(d + e*x)^(5/2))/(5*e^4) + (2*c^3*d^3*(d + e*x)^(7/2))/(7*e^4) + (2*c*d*(a*e^2 - c*d^2)^2*(d + e*x)^(3/2))/e^4","B"
1997,1,133,113,0.073467,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^(9/2),x)","\frac{2\,c^3\,d^3\,{\left(d+e\,x\right)}^{5/2}}{5\,e^4}-\frac{\left(6\,c^3\,d^4-6\,a\,c^2\,d^2\,e^2\right)\,{\left(d+e\,x\right)}^{3/2}}{3\,e^4}-\frac{2\,a^3\,e^6-6\,a^2\,c\,d^2\,e^4+6\,a\,c^2\,d^4\,e^2-2\,c^3\,d^6}{e^4\,\sqrt{d+e\,x}}+\frac{6\,c\,d\,{\left(a\,e^2-c\,d^2\right)}^2\,\sqrt{d+e\,x}}{e^4}","Not used",1,"(2*c^3*d^3*(d + e*x)^(5/2))/(5*e^4) - ((6*c^3*d^4 - 6*a*c^2*d^2*e^2)*(d + e*x)^(3/2))/(3*e^4) - (2*a^3*e^6 - 2*c^3*d^6 + 6*a*c^2*d^4*e^2 - 6*a^2*c*d^2*e^4)/(e^4*(d + e*x)^(1/2)) + (6*c*d*(a*e^2 - c*d^2)^2*(d + e*x)^(1/2))/e^4","B"
1998,1,147,115,0.645544,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^(11/2),x)","-\frac{2\,a^3\,e^6-2\,c^3\,d^6-2\,c^3\,d^3\,{\left(d+e\,x\right)}^3+18\,c^3\,d^4\,{\left(d+e\,x\right)}^2+18\,c^3\,d^5\,\left(d+e\,x\right)+6\,a\,c^2\,d^4\,e^2-6\,a^2\,c\,d^2\,e^4-36\,a\,c^2\,d^3\,e^2\,\left(d+e\,x\right)-18\,a\,c^2\,d^2\,e^2\,{\left(d+e\,x\right)}^2+18\,a^2\,c\,d\,e^4\,\left(d+e\,x\right)}{3\,e^4\,{\left(d+e\,x\right)}^{3/2}}","Not used",1,"-(2*a^3*e^6 - 2*c^3*d^6 - 2*c^3*d^3*(d + e*x)^3 + 18*c^3*d^4*(d + e*x)^2 + 18*c^3*d^5*(d + e*x) + 6*a*c^2*d^4*e^2 - 6*a^2*c*d^2*e^4 - 36*a*c^2*d^3*e^2*(d + e*x) - 18*a*c^2*d^2*e^2*(d + e*x)^2 + 18*a^2*c*d*e^4*(d + e*x))/(3*e^4*(d + e*x)^(3/2))","B"
1999,1,129,113,0.654605,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3/(d + e*x)^(13/2),x)","-\frac{2\,\left(a^3\,e^6+2\,a^2\,c\,d^2\,e^4+5\,a^2\,c\,d\,e^5\,x+8\,a\,c^2\,d^4\,e^2+20\,a\,c^2\,d^3\,e^3\,x+15\,a\,c^2\,d^2\,e^4\,x^2-16\,c^3\,d^6-40\,c^3\,d^5\,e\,x-30\,c^3\,d^4\,e^2\,x^2-5\,c^3\,d^3\,e^3\,x^3\right)}{5\,e^4\,{\left(d+e\,x\right)}^{5/2}}","Not used",1,"-(2*(a^3*e^6 - 16*c^3*d^6 + 8*a*c^2*d^4*e^2 + 2*a^2*c*d^2*e^4 - 30*c^3*d^4*e^2*x^2 - 5*c^3*d^3*e^3*x^3 - 40*c^3*d^5*e*x + 5*a^2*c*d*e^5*x + 20*a*c^2*d^3*e^3*x + 15*a*c^2*d^2*e^4*x^2))/(5*e^4*(d + e*x)^(5/2))","B"
2000,1,207,180,0.633370,"\text{Not used}","int((d + e*x)^(9/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","\frac{2\,{\left(d+e\,x\right)}^{7/2}}{7\,c\,d}+\frac{2\,{\left(a\,e^2-c\,d^2\right)}^2\,{\left(d+e\,x\right)}^{3/2}}{3\,c^3\,d^3}-\frac{2\,{\left(a\,e^2-c\,d^2\right)}^3\,\sqrt{d+e\,x}}{c^4\,d^4}+\frac{2\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,{\left(a\,e^2-c\,d^2\right)}^{7/2}\,\sqrt{d+e\,x}}{a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8}\right)\,{\left(a\,e^2-c\,d^2\right)}^{7/2}}{c^{9/2}\,d^{9/2}}-\frac{2\,\left(a\,e^2-c\,d^2\right)\,{\left(d+e\,x\right)}^{5/2}}{5\,c^2\,d^2}","Not used",1,"(2*(d + e*x)^(7/2))/(7*c*d) + (2*(a*e^2 - c*d^2)^2*(d + e*x)^(3/2))/(3*c^3*d^3) - (2*(a*e^2 - c*d^2)^3*(d + e*x)^(1/2))/(c^4*d^4) + (2*atan((c^(1/2)*d^(1/2)*(a*e^2 - c*d^2)^(7/2)*(d + e*x)^(1/2))/(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4))*(a*e^2 - c*d^2)^(7/2))/(c^(9/2)*d^(9/2)) - (2*(a*e^2 - c*d^2)*(d + e*x)^(5/2))/(5*c^2*d^2)","B"
2001,1,165,147,0.653713,"\text{Not used}","int((d + e*x)^(7/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","\frac{2\,{\left(d+e\,x\right)}^{5/2}}{5\,c\,d}+\frac{2\,{\left(a\,e^2-c\,d^2\right)}^2\,\sqrt{d+e\,x}}{c^3\,d^3}-\frac{2\,\left(a\,e^2-c\,d^2\right)\,{\left(d+e\,x\right)}^{3/2}}{3\,c^2\,d^2}-\frac{2\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,{\left(a\,e^2-c\,d^2\right)}^{5/2}\,\sqrt{d+e\,x}}{a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6}\right)\,{\left(a\,e^2-c\,d^2\right)}^{5/2}}{c^{7/2}\,d^{7/2}}","Not used",1,"(2*(d + e*x)^(5/2))/(5*c*d) + (2*(a*e^2 - c*d^2)^2*(d + e*x)^(1/2))/(c^3*d^3) - (2*(a*e^2 - c*d^2)*(d + e*x)^(3/2))/(3*c^2*d^2) - (2*atan((c^(1/2)*d^(1/2)*(a*e^2 - c*d^2)^(5/2)*(d + e*x)^(1/2))/(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4))*(a*e^2 - c*d^2)^(5/2))/(c^(7/2)*d^(7/2))","B"
2002,1,121,114,0.086204,"\text{Not used}","int((d + e*x)^(5/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","\frac{2\,{\left(d+e\,x\right)}^{3/2}}{3\,c\,d}+\frac{2\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,{\left(a\,e^2-c\,d^2\right)}^{3/2}\,\sqrt{d+e\,x}}{a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4}\right)\,{\left(a\,e^2-c\,d^2\right)}^{3/2}}{c^{5/2}\,d^{5/2}}-\frac{2\,\left(a\,e^2-c\,d^2\right)\,\sqrt{d+e\,x}}{c^2\,d^2}","Not used",1,"(2*(d + e*x)^(3/2))/(3*c*d) + (2*atan((c^(1/2)*d^(1/2)*(a*e^2 - c*d^2)^(3/2)*(d + e*x)^(1/2))/(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2))*(a*e^2 - c*d^2)^(3/2))/(c^(5/2)*d^(5/2)) - (2*(a*e^2 - c*d^2)*(d + e*x)^(1/2))/(c^2*d^2)","B"
2003,1,67,83,0.071875,"\text{Not used}","int((d + e*x)^(3/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","\frac{2\,\sqrt{d+e\,x}}{c\,d}-\frac{2\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,\sqrt{d+e\,x}}{\sqrt{a\,e^2-c\,d^2}}\right)\,\sqrt{a\,e^2-c\,d^2}}{c^{3/2}\,d^{3/2}}","Not used",1,"(2*(d + e*x)^(1/2))/(c*d) - (2*atan((c^(1/2)*d^(1/2)*(d + e*x)^(1/2))/(a*e^2 - c*d^2)^(1/2))*(a*e^2 - c*d^2)^(1/2))/(c^(3/2)*d^(3/2))","B"
2004,1,49,65,0.648717,"\text{Not used}","int((d + e*x)^(1/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","\frac{2\,\mathrm{atan}\left(\frac{c\,d\,\sqrt{d+e\,x}}{\sqrt{a\,c\,d\,e^2-c^2\,d^3}}\right)}{\sqrt{a\,c\,d\,e^2-c^2\,d^3}}","Not used",1,"(2*atan((c*d*(d + e*x)^(1/2))/(a*c*d*e^2 - c^2*d^3)^(1/2)))/(a*c*d*e^2 - c^2*d^3)^(1/2)","B"
2005,1,75,91,0.633761,"\text{Not used}","int(1/((d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)),x)","-\frac{2}{\left(a\,e^2-c\,d^2\right)\,\sqrt{d+e\,x}}-\frac{2\,\sqrt{c}\,\sqrt{d}\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,\sqrt{d+e\,x}}{\sqrt{a\,e^2-c\,d^2}}\right)}{{\left(a\,e^2-c\,d^2\right)}^{3/2}}","Not used",1,"- 2/((a*e^2 - c*d^2)*(d + e*x)^(1/2)) - (2*c^(1/2)*d^(1/2)*atan((c^(1/2)*d^(1/2)*(d + e*x)^(1/2))/(a*e^2 - c*d^2)^(1/2)))/(a*e^2 - c*d^2)^(3/2)","B"
2006,1,127,120,0.689600,"\text{Not used}","int(1/((d + e*x)^(3/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)),x)","\frac{2\,c^{3/2}\,d^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,\sqrt{d+e\,x}\,\left(a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{{\left(a\,e^2-c\,d^2\right)}^{5/2}}\right)}{{\left(a\,e^2-c\,d^2\right)}^{5/2}}-\frac{\frac{2}{3\,\left(a\,e^2-c\,d^2\right)}-\frac{2\,c\,d\,\left(d+e\,x\right)}{{\left(a\,e^2-c\,d^2\right)}^2}}{{\left(d+e\,x\right)}^{3/2}}","Not used",1,"(2*c^(3/2)*d^(3/2)*atan((c^(1/2)*d^(1/2)*(d + e*x)^(1/2)*(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2))/(a*e^2 - c*d^2)^(5/2)))/(a*e^2 - c*d^2)^(5/2) - (2/(3*(a*e^2 - c*d^2)) - (2*c*d*(d + e*x))/(a*e^2 - c*d^2)^2)/(d + e*x)^(3/2)","B"
2007,1,171,153,0.137683,"\text{Not used}","int(1/((d + e*x)^(5/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)),x)","-\frac{\frac{2}{5\,\left(a\,e^2-c\,d^2\right)}+\frac{2\,c^2\,d^2\,{\left(d+e\,x\right)}^2}{{\left(a\,e^2-c\,d^2\right)}^3}-\frac{2\,c\,d\,\left(d+e\,x\right)}{3\,{\left(a\,e^2-c\,d^2\right)}^2}}{{\left(d+e\,x\right)}^{5/2}}-\frac{2\,c^{5/2}\,d^{5/2}\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,\sqrt{d+e\,x}\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}{{\left(a\,e^2-c\,d^2\right)}^{7/2}}\right)}{{\left(a\,e^2-c\,d^2\right)}^{7/2}}","Not used",1,"- (2/(5*(a*e^2 - c*d^2)) + (2*c^2*d^2*(d + e*x)^2)/(a*e^2 - c*d^2)^3 - (2*c*d*(d + e*x))/(3*(a*e^2 - c*d^2)^2))/(d + e*x)^(5/2) - (2*c^(5/2)*d^(5/2)*atan((c^(1/2)*d^(1/2)*(d + e*x)^(1/2)*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4))/(a*e^2 - c*d^2)^(7/2)))/(a*e^2 - c*d^2)^(7/2)","B"
2008,1,213,186,0.742803,"\text{Not used}","int(1/((d + e*x)^(7/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)),x)","\frac{2\,c^{7/2}\,d^{7/2}\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,\sqrt{d+e\,x}\,\left(a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8\right)}{{\left(a\,e^2-c\,d^2\right)}^{9/2}}\right)}{{\left(a\,e^2-c\,d^2\right)}^{9/2}}-\frac{\frac{2}{7\,\left(a\,e^2-c\,d^2\right)}+\frac{2\,c^2\,d^2\,{\left(d+e\,x\right)}^2}{3\,{\left(a\,e^2-c\,d^2\right)}^3}-\frac{2\,c^3\,d^3\,{\left(d+e\,x\right)}^3}{{\left(a\,e^2-c\,d^2\right)}^4}-\frac{2\,c\,d\,\left(d+e\,x\right)}{5\,{\left(a\,e^2-c\,d^2\right)}^2}}{{\left(d+e\,x\right)}^{7/2}}","Not used",1,"(2*c^(7/2)*d^(7/2)*atan((c^(1/2)*d^(1/2)*(d + e*x)^(1/2)*(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4))/(a*e^2 - c*d^2)^(9/2)))/(a*e^2 - c*d^2)^(9/2) - (2/(7*(a*e^2 - c*d^2)) + (2*c^2*d^2*(d + e*x)^2)/(3*(a*e^2 - c*d^2)^3) - (2*c^3*d^3*(d + e*x)^3)/(a*e^2 - c*d^2)^4 - (2*c*d*(d + e*x))/(5*(a*e^2 - c*d^2)^2))/(d + e*x)^(7/2)","B"
2009,1,443,210,0.696694,"\text{Not used}","int((d + e*x)^(13/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","\frac{2\,e\,{\left(d+e\,x\right)}^{7/2}}{7\,c^2\,d^2}-\left(\frac{\left(2\,c^2\,d^3-2\,a\,c\,d\,e^2\right)\,\left(\frac{2\,e\,{\left(a\,e^2-c\,d^2\right)}^2}{c^4\,d^4}-\frac{2\,e\,{\left(2\,c^2\,d^3-2\,a\,c\,d\,e^2\right)}^2}{c^6\,d^6}\right)}{c^2\,d^2}+\frac{2\,e\,{\left(a\,e^2-c\,d^2\right)}^2\,\left(2\,c^2\,d^3-2\,a\,c\,d\,e^2\right)}{c^6\,d^6}\right)\,\sqrt{d+e\,x}-\frac{\sqrt{d+e\,x}\,\left(a^4\,e^9-4\,a^3\,c\,d^2\,e^7+6\,a^2\,c^2\,d^4\,e^5-4\,a\,c^3\,d^6\,e^3+c^4\,d^8\,e\right)}{c^6\,d^6\,\left(d+e\,x\right)-c^6\,d^7+a\,c^5\,d^5\,e^2}-\left(\frac{2\,e\,{\left(a\,e^2-c\,d^2\right)}^2}{3\,c^4\,d^4}-\frac{2\,e\,{\left(2\,c^2\,d^3-2\,a\,c\,d\,e^2\right)}^2}{3\,c^6\,d^6}\right)\,{\left(d+e\,x\right)}^{3/2}+\frac{2\,e\,\left(2\,c^2\,d^3-2\,a\,c\,d\,e^2\right)\,{\left(d+e\,x\right)}^{5/2}}{5\,c^4\,d^4}+\frac{9\,e\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,e\,{\left(a\,e^2-c\,d^2\right)}^{7/2}\,\sqrt{d+e\,x}}{a^4\,e^9-4\,a^3\,c\,d^2\,e^7+6\,a^2\,c^2\,d^4\,e^5-4\,a\,c^3\,d^6\,e^3+c^4\,d^8\,e}\right)\,{\left(a\,e^2-c\,d^2\right)}^{7/2}}{c^{11/2}\,d^{11/2}}","Not used",1,"(2*e*(d + e*x)^(7/2))/(7*c^2*d^2) - (((2*c^2*d^3 - 2*a*c*d*e^2)*((2*e*(a*e^2 - c*d^2)^2)/(c^4*d^4) - (2*e*(2*c^2*d^3 - 2*a*c*d*e^2)^2)/(c^6*d^6)))/(c^2*d^2) + (2*e*(a*e^2 - c*d^2)^2*(2*c^2*d^3 - 2*a*c*d*e^2))/(c^6*d^6))*(d + e*x)^(1/2) - ((d + e*x)^(1/2)*(a^4*e^9 + c^4*d^8*e - 4*a*c^3*d^6*e^3 - 4*a^3*c*d^2*e^7 + 6*a^2*c^2*d^4*e^5))/(c^6*d^6*(d + e*x) - c^6*d^7 + a*c^5*d^5*e^2) - ((2*e*(a*e^2 - c*d^2)^2)/(3*c^4*d^4) - (2*e*(2*c^2*d^3 - 2*a*c*d*e^2)^2)/(3*c^6*d^6))*(d + e*x)^(3/2) + (2*e*(2*c^2*d^3 - 2*a*c*d*e^2)*(d + e*x)^(5/2))/(5*c^4*d^4) + (9*e*atan((c^(1/2)*d^(1/2)*e*(a*e^2 - c*d^2)^(7/2)*(d + e*x)^(1/2))/(a^4*e^9 + c^4*d^8*e - 4*a*c^3*d^6*e^3 - 4*a^3*c*d^2*e^7 + 6*a^2*c^2*d^4*e^5))*(a*e^2 - c*d^2)^(7/2))/(c^(11/2)*d^(11/2))","B"
2010,1,290,178,0.676052,"\text{Not used}","int((d + e*x)^(11/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","\frac{\sqrt{d+e\,x}\,\left(a^3\,e^7-3\,a^2\,c\,d^2\,e^5+3\,a\,c^2\,d^4\,e^3-c^3\,d^6\,e\right)}{c^5\,d^5\,\left(d+e\,x\right)-c^5\,d^6+a\,c^4\,d^4\,e^2}-\left(\frac{2\,e\,{\left(a\,e^2-c\,d^2\right)}^2}{c^4\,d^4}-\frac{2\,e\,{\left(2\,c^2\,d^3-2\,a\,c\,d\,e^2\right)}^2}{c^6\,d^6}\right)\,\sqrt{d+e\,x}+\frac{2\,e\,{\left(d+e\,x\right)}^{5/2}}{5\,c^2\,d^2}+\frac{2\,e\,\left(2\,c^2\,d^3-2\,a\,c\,d\,e^2\right)\,{\left(d+e\,x\right)}^{3/2}}{3\,c^4\,d^4}-\frac{7\,e\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,e\,{\left(a\,e^2-c\,d^2\right)}^{5/2}\,\sqrt{d+e\,x}}{a^3\,e^7-3\,a^2\,c\,d^2\,e^5+3\,a\,c^2\,d^4\,e^3-c^3\,d^6\,e}\right)\,{\left(a\,e^2-c\,d^2\right)}^{5/2}}{c^{9/2}\,d^{9/2}}","Not used",1,"((d + e*x)^(1/2)*(a^3*e^7 - c^3*d^6*e + 3*a*c^2*d^4*e^3 - 3*a^2*c*d^2*e^5))/(c^5*d^5*(d + e*x) - c^5*d^6 + a*c^4*d^4*e^2) - ((2*e*(a*e^2 - c*d^2)^2)/(c^4*d^4) - (2*e*(2*c^2*d^3 - 2*a*c*d*e^2)^2)/(c^6*d^6))*(d + e*x)^(1/2) + (2*e*(d + e*x)^(5/2))/(5*c^2*d^2) + (2*e*(2*c^2*d^3 - 2*a*c*d*e^2)*(d + e*x)^(3/2))/(3*c^4*d^4) - (7*e*atan((c^(1/2)*d^(1/2)*e*(a*e^2 - c*d^2)^(5/2)*(d + e*x)^(1/2))/(a^3*e^7 - c^3*d^6*e + 3*a*c^2*d^4*e^3 - 3*a^2*c*d^2*e^5))*(a*e^2 - c*d^2)^(5/2))/(c^(9/2)*d^(9/2))","B"
2011,1,200,144,0.699634,"\text{Not used}","int((d + e*x)^(9/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","\frac{2\,e\,{\left(d+e\,x\right)}^{3/2}}{3\,c^2\,d^2}-\frac{\sqrt{d+e\,x}\,\left(a^2\,e^5-2\,a\,c\,d^2\,e^3+c^2\,d^4\,e\right)}{c^4\,d^4\,\left(d+e\,x\right)-c^4\,d^5+a\,c^3\,d^3\,e^2}+\frac{2\,e\,\left(2\,c^2\,d^3-2\,a\,c\,d\,e^2\right)\,\sqrt{d+e\,x}}{c^4\,d^4}+\frac{5\,e\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,e\,{\left(a\,e^2-c\,d^2\right)}^{3/2}\,\sqrt{d+e\,x}}{a^2\,e^5-2\,a\,c\,d^2\,e^3+c^2\,d^4\,e}\right)\,{\left(a\,e^2-c\,d^2\right)}^{3/2}}{c^{7/2}\,d^{7/2}}","Not used",1,"(2*e*(d + e*x)^(3/2))/(3*c^2*d^2) - ((d + e*x)^(1/2)*(a^2*e^5 + c^2*d^4*e - 2*a*c*d^2*e^3))/(c^4*d^4*(d + e*x) - c^4*d^5 + a*c^3*d^3*e^2) + (2*e*(2*c^2*d^3 - 2*a*c*d*e^2)*(d + e*x)^(1/2))/(c^4*d^4) + (5*e*atan((c^(1/2)*d^(1/2)*e*(a*e^2 - c*d^2)^(3/2)*(d + e*x)^(1/2))/(a^2*e^5 + c^2*d^4*e - 2*a*c*d^2*e^3))*(a*e^2 - c*d^2)^(3/2))/(c^(7/2)*d^(7/2))","B"
2012,1,140,112,0.132990,"\text{Not used}","int((d + e*x)^(7/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","\frac{\left(a\,e^3-c\,d^2\,e\right)\,\sqrt{d+e\,x}}{c^3\,d^3\,\left(d+e\,x\right)-c^3\,d^4+a\,c^2\,d^2\,e^2}+\frac{2\,e\,\sqrt{d+e\,x}}{c^2\,d^2}-\frac{3\,e\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,e\,\sqrt{a\,e^2-c\,d^2}\,\sqrt{d+e\,x}}{a\,e^3-c\,d^2\,e}\right)\,\sqrt{a\,e^2-c\,d^2}}{c^{5/2}\,d^{5/2}}","Not used",1,"((a*e^3 - c*d^2*e)*(d + e*x)^(1/2))/(c^3*d^3*(d + e*x) - c^3*d^4 + a*c^2*d^2*e^2) + (2*e*(d + e*x)^(1/2))/(c^2*d^2) - (3*e*atan((c^(1/2)*d^(1/2)*e*(a*e^2 - c*d^2)^(1/2)*(d + e*x)^(1/2))/(a*e^3 - c*d^2*e))*(a*e^2 - c*d^2)^(1/2))/(c^(5/2)*d^(5/2))","B"
2013,1,81,94,0.649934,"\text{Not used}","int((d + e*x)^(5/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","\frac{e\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,\sqrt{d+e\,x}}{\sqrt{a\,e^2-c\,d^2}}\right)}{c^{3/2}\,d^{3/2}\,\sqrt{a\,e^2-c\,d^2}}-\frac{e\,\sqrt{d+e\,x}}{x\,c^2\,d^2\,e+a\,c\,d\,e^2}","Not used",1,"(e*atan((c^(1/2)*d^(1/2)*(d + e*x)^(1/2))/(a*e^2 - c*d^2)^(1/2)))/(c^(3/2)*d^(3/2)*(a*e^2 - c*d^2)^(1/2)) - (e*(d + e*x)^(1/2))/(a*c*d*e^2 + c^2*d^2*e*x)","B"
2014,1,97,101,0.656199,"\text{Not used}","int((d + e*x)^(3/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","\frac{e\,\mathrm{atan}\left(\frac{c\,d\,\sqrt{d+e\,x}}{\sqrt{c\,d}\,\sqrt{a\,e^2-c\,d^2}}\right)}{\sqrt{c\,d}\,{\left(a\,e^2-c\,d^2\right)}^{3/2}}+\frac{e\,\sqrt{d+e\,x}}{\left(a\,e^2-c\,d^2\right)\,\left(a\,e^2-c\,d^2+c\,d\,\left(d+e\,x\right)\right)}","Not used",1,"(e*atan((c*d*(d + e*x)^(1/2))/((c*d)^(1/2)*(a*e^2 - c*d^2)^(1/2))))/((c*d)^(1/2)*(a*e^2 - c*d^2)^(3/2)) + (e*(d + e*x)^(1/2))/((a*e^2 - c*d^2)*(a*e^2 - c*d^2 + c*d*(d + e*x)))","B"
2015,1,155,128,0.752781,"\text{Not used}","int((d + e*x)^(1/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","-\frac{\frac{2\,e}{a\,e^2-c\,d^2}+\frac{3\,c\,d\,e\,\left(d+e\,x\right)}{{\left(a\,e^2-c\,d^2\right)}^2}}{\left(a\,e^2-c\,d^2\right)\,\sqrt{d+e\,x}+c\,d\,{\left(d+e\,x\right)}^{3/2}}-\frac{3\,\sqrt{c}\,\sqrt{d}\,e\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,\sqrt{d+e\,x}\,\left(a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4\right)}{{\left(a\,e^2-c\,d^2\right)}^{5/2}}\right)}{{\left(a\,e^2-c\,d^2\right)}^{5/2}}","Not used",1,"- ((2*e)/(a*e^2 - c*d^2) + (3*c*d*e*(d + e*x))/(a*e^2 - c*d^2)^2)/((a*e^2 - c*d^2)*(d + e*x)^(1/2) + c*d*(d + e*x)^(3/2)) - (3*c^(1/2)*d^(1/2)*e*atan((c^(1/2)*d^(1/2)*(d + e*x)^(1/2)*(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2))/(a*e^2 - c*d^2)^(5/2)))/(a*e^2 - c*d^2)^(5/2)","B"
2016,1,200,158,0.778194,"\text{Not used}","int(1/((d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2),x)","\frac{\frac{10\,c\,d\,e\,\left(d+e\,x\right)}{3\,{\left(a\,e^2-c\,d^2\right)}^2}-\frac{2\,e}{3\,\left(a\,e^2-c\,d^2\right)}+\frac{5\,c^2\,d^2\,e\,{\left(d+e\,x\right)}^2}{{\left(a\,e^2-c\,d^2\right)}^3}}{\left(a\,e^2-c\,d^2\right)\,{\left(d+e\,x\right)}^{3/2}+c\,d\,{\left(d+e\,x\right)}^{5/2}}+\frac{5\,c^{3/2}\,d^{3/2}\,e\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,\sqrt{d+e\,x}\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}{{\left(a\,e^2-c\,d^2\right)}^{7/2}}\right)}{{\left(a\,e^2-c\,d^2\right)}^{7/2}}","Not used",1,"((10*c*d*e*(d + e*x))/(3*(a*e^2 - c*d^2)^2) - (2*e)/(3*(a*e^2 - c*d^2)) + (5*c^2*d^2*e*(d + e*x)^2)/(a*e^2 - c*d^2)^3)/((a*e^2 - c*d^2)*(d + e*x)^(3/2) + c*d*(d + e*x)^(5/2)) + (5*c^(3/2)*d^(3/2)*e*atan((c^(1/2)*d^(1/2)*(d + e*x)^(1/2)*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4))/(a*e^2 - c*d^2)^(7/2)))/(a*e^2 - c*d^2)^(7/2)","B"
2017,1,244,192,0.832905,"\text{Not used}","int(1/((d + e*x)^(3/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2),x)","-\frac{\frac{2\,e}{5\,\left(a\,e^2-c\,d^2\right)}-\frac{14\,c\,d\,e\,\left(d+e\,x\right)}{15\,{\left(a\,e^2-c\,d^2\right)}^2}+\frac{14\,c^2\,d^2\,e\,{\left(d+e\,x\right)}^2}{3\,{\left(a\,e^2-c\,d^2\right)}^3}+\frac{7\,c^3\,d^3\,e\,{\left(d+e\,x\right)}^3}{{\left(a\,e^2-c\,d^2\right)}^4}}{\left(a\,e^2-c\,d^2\right)\,{\left(d+e\,x\right)}^{5/2}+c\,d\,{\left(d+e\,x\right)}^{7/2}}-\frac{7\,c^{5/2}\,d^{5/2}\,e\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,\sqrt{d+e\,x}\,\left(a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8\right)}{{\left(a\,e^2-c\,d^2\right)}^{9/2}}\right)}{{\left(a\,e^2-c\,d^2\right)}^{9/2}}","Not used",1,"- ((2*e)/(5*(a*e^2 - c*d^2)) - (14*c*d*e*(d + e*x))/(15*(a*e^2 - c*d^2)^2) + (14*c^2*d^2*e*(d + e*x)^2)/(3*(a*e^2 - c*d^2)^3) + (7*c^3*d^3*e*(d + e*x)^3)/(a*e^2 - c*d^2)^4)/((a*e^2 - c*d^2)*(d + e*x)^(5/2) + c*d*(d + e*x)^(7/2)) - (7*c^(5/2)*d^(5/2)*e*atan((c^(1/2)*d^(1/2)*(d + e*x)^(1/2)*(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4))/(a*e^2 - c*d^2)^(9/2)))/(a*e^2 - c*d^2)^(9/2)","B"
2018,1,430,222,0.730781,"\text{Not used}","int((d + e*x)^(15/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","\frac{\sqrt{d+e\,x}\,\left(\frac{15\,a^4\,e^{10}}{4}-15\,a^3\,c\,d^2\,e^8+\frac{45\,a^2\,c^2\,d^4\,e^6}{2}-15\,a\,c^3\,d^6\,e^4+\frac{15\,c^4\,d^8\,e^2}{4}\right)-{\left(d+e\,x\right)}^{3/2}\,\left(-\frac{17\,a^3\,c\,d\,e^8}{4}+\frac{51\,a^2\,c^2\,d^3\,e^6}{4}-\frac{51\,a\,c^3\,d^5\,e^4}{4}+\frac{17\,c^4\,d^7\,e^2}{4}\right)}{c^7\,d^9-\left(2\,c^7\,d^8-2\,a\,c^6\,d^6\,e^2\right)\,\left(d+e\,x\right)+c^7\,d^7\,{\left(d+e\,x\right)}^2-2\,a\,c^6\,d^7\,e^2+a^2\,c^5\,d^5\,e^4}+\left(\frac{2\,e^2\,{\left(3\,c^3\,d^4-3\,a\,c^2\,d^2\,e^2\right)}^2}{c^9\,d^9}-\frac{6\,e^2\,{\left(a\,e^2-c\,d^2\right)}^2}{c^5\,d^5}\right)\,\sqrt{d+e\,x}+\frac{2\,e^2\,{\left(d+e\,x\right)}^{5/2}}{5\,c^3\,d^3}-\frac{63\,e^2\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,e^2\,{\left(a\,e^2-c\,d^2\right)}^{5/2}\,\sqrt{d+e\,x}}{a^3\,e^8-3\,a^2\,c\,d^2\,e^6+3\,a\,c^2\,d^4\,e^4-c^3\,d^6\,e^2}\right)\,{\left(a\,e^2-c\,d^2\right)}^{5/2}}{4\,c^{11/2}\,d^{11/2}}+\frac{2\,e^2\,\left(3\,c^3\,d^4-3\,a\,c^2\,d^2\,e^2\right)\,{\left(d+e\,x\right)}^{3/2}}{3\,c^6\,d^6}","Not used",1,"((d + e*x)^(1/2)*((15*a^4*e^10)/4 + (15*c^4*d^8*e^2)/4 - 15*a*c^3*d^6*e^4 - 15*a^3*c*d^2*e^8 + (45*a^2*c^2*d^4*e^6)/2) - (d + e*x)^(3/2)*((17*c^4*d^7*e^2)/4 - (51*a*c^3*d^5*e^4)/4 + (51*a^2*c^2*d^3*e^6)/4 - (17*a^3*c*d*e^8)/4))/(c^7*d^9 - (2*c^7*d^8 - 2*a*c^6*d^6*e^2)*(d + e*x) + c^7*d^7*(d + e*x)^2 - 2*a*c^6*d^7*e^2 + a^2*c^5*d^5*e^4) + ((2*e^2*(3*c^3*d^4 - 3*a*c^2*d^2*e^2)^2)/(c^9*d^9) - (6*e^2*(a*e^2 - c*d^2)^2)/(c^5*d^5))*(d + e*x)^(1/2) + (2*e^2*(d + e*x)^(5/2))/(5*c^3*d^3) - (63*e^2*atan((c^(1/2)*d^(1/2)*e^2*(a*e^2 - c*d^2)^(5/2)*(d + e*x)^(1/2))/(a^3*e^8 - c^3*d^6*e^2 + 3*a*c^2*d^4*e^4 - 3*a^2*c*d^2*e^6))*(a*e^2 - c*d^2)^(5/2))/(4*c^(11/2)*d^(11/2)) + (2*e^2*(3*c^3*d^4 - 3*a*c^2*d^2*e^2)*(d + e*x)^(3/2))/(3*c^6*d^6)","B"
2019,1,319,186,0.735988,"\text{Not used}","int((d + e*x)^(13/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","\frac{2\,e^2\,{\left(d+e\,x\right)}^{3/2}}{3\,c^3\,d^3}-\frac{{\left(d+e\,x\right)}^{3/2}\,\left(\frac{13\,a^2\,c\,d\,e^6}{4}-\frac{13\,a\,c^2\,d^3\,e^4}{2}+\frac{13\,c^3\,d^5\,e^2}{4}\right)+\sqrt{d+e\,x}\,\left(\frac{11\,a^3\,e^8}{4}-\frac{33\,a^2\,c\,d^2\,e^6}{4}+\frac{33\,a\,c^2\,d^4\,e^4}{4}-\frac{11\,c^3\,d^6\,e^2}{4}\right)}{c^6\,d^8-\left(2\,c^6\,d^7-2\,a\,c^5\,d^5\,e^2\right)\,\left(d+e\,x\right)+c^6\,d^6\,{\left(d+e\,x\right)}^2-2\,a\,c^5\,d^6\,e^2+a^2\,c^4\,d^4\,e^4}+\frac{2\,e^2\,\left(3\,c^3\,d^4-3\,a\,c^2\,d^2\,e^2\right)\,\sqrt{d+e\,x}}{c^6\,d^6}+\frac{35\,e^2\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,e^2\,{\left(a\,e^2-c\,d^2\right)}^{3/2}\,\sqrt{d+e\,x}}{a^2\,e^6-2\,a\,c\,d^2\,e^4+c^2\,d^4\,e^2}\right)\,{\left(a\,e^2-c\,d^2\right)}^{3/2}}{4\,c^{9/2}\,d^{9/2}}","Not used",1,"(2*e^2*(d + e*x)^(3/2))/(3*c^3*d^3) - ((d + e*x)^(3/2)*((13*c^3*d^5*e^2)/4 - (13*a*c^2*d^3*e^4)/2 + (13*a^2*c*d*e^6)/4) + (d + e*x)^(1/2)*((11*a^3*e^8)/4 - (11*c^3*d^6*e^2)/4 + (33*a*c^2*d^4*e^4)/4 - (33*a^2*c*d^2*e^6)/4))/(c^6*d^8 - (2*c^6*d^7 - 2*a*c^5*d^5*e^2)*(d + e*x) + c^6*d^6*(d + e*x)^2 - 2*a*c^5*d^6*e^2 + a^2*c^4*d^4*e^4) + (2*e^2*(3*c^3*d^4 - 3*a*c^2*d^2*e^2)*(d + e*x)^(1/2))/(c^6*d^6) + (35*e^2*atan((c^(1/2)*d^(1/2)*e^2*(a*e^2 - c*d^2)^(3/2)*(d + e*x)^(1/2))/(a^2*e^6 + c^2*d^4*e^2 - 2*a*c*d^2*e^4))*(a*e^2 - c*d^2)^(3/2))/(4*c^(9/2)*d^(9/2))","B"
2020,1,240,152,0.165980,"\text{Not used}","int((d + e*x)^(11/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","\frac{2\,e^2\,\sqrt{d+e\,x}}{c^3\,d^3}-\frac{\left(\frac{9\,c^2\,d^3\,e^2}{4}-\frac{9\,a\,c\,d\,e^4}{4}\right)\,{\left(d+e\,x\right)}^{3/2}-\sqrt{d+e\,x}\,\left(\frac{7\,a^2\,e^6}{4}-\frac{7\,a\,c\,d^2\,e^4}{2}+\frac{7\,c^2\,d^4\,e^2}{4}\right)}{c^5\,d^7-\left(2\,c^5\,d^6-2\,a\,c^4\,d^4\,e^2\right)\,\left(d+e\,x\right)+c^5\,d^5\,{\left(d+e\,x\right)}^2-2\,a\,c^4\,d^5\,e^2+a^2\,c^3\,d^3\,e^4}-\frac{15\,e^2\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,e^2\,\sqrt{a\,e^2-c\,d^2}\,\sqrt{d+e\,x}}{a\,e^4-c\,d^2\,e^2}\right)\,\sqrt{a\,e^2-c\,d^2}}{4\,c^{7/2}\,d^{7/2}}","Not used",1,"(2*e^2*(d + e*x)^(1/2))/(c^3*d^3) - (((9*c^2*d^3*e^2)/4 - (9*a*c*d*e^4)/4)*(d + e*x)^(3/2) - (d + e*x)^(1/2)*((7*a^2*e^6)/4 + (7*c^2*d^4*e^2)/4 - (7*a*c*d^2*e^4)/2))/(c^5*d^7 - (2*c^5*d^6 - 2*a*c^4*d^4*e^2)*(d + e*x) + c^5*d^5*(d + e*x)^2 - 2*a*c^4*d^5*e^2 + a^2*c^3*d^3*e^4) - (15*e^2*atan((c^(1/2)*d^(1/2)*e^2*(a*e^2 - c*d^2)^(1/2)*(d + e*x)^(1/2))/(a*e^4 - c*d^2*e^2))*(a*e^2 - c*d^2)^(1/2))/(4*c^(7/2)*d^(7/2))","B"
2021,1,171,130,0.706500,"\text{Not used}","int((d + e*x)^(9/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","\frac{3\,e^2\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,\sqrt{d+e\,x}}{\sqrt{a\,e^2-c\,d^2}}\right)}{4\,c^{5/2}\,d^{5/2}\,\sqrt{a\,e^2-c\,d^2}}-\frac{\frac{5\,e^2\,{\left(d+e\,x\right)}^{3/2}}{4\,c\,d}+\frac{3\,e^2\,\left(a\,e^2-c\,d^2\right)\,\sqrt{d+e\,x}}{4\,c^2\,d^2}}{a^2\,e^4+c^2\,d^4-\left(2\,c^2\,d^3-2\,a\,c\,d\,e^2\right)\,\left(d+e\,x\right)+c^2\,d^2\,{\left(d+e\,x\right)}^2-2\,a\,c\,d^2\,e^2}","Not used",1,"(3*e^2*atan((c^(1/2)*d^(1/2)*(d + e*x)^(1/2))/(a*e^2 - c*d^2)^(1/2)))/(4*c^(5/2)*d^(5/2)*(a*e^2 - c*d^2)^(1/2)) - ((5*e^2*(d + e*x)^(3/2))/(4*c*d) + (3*e^2*(a*e^2 - c*d^2)*(d + e*x)^(1/2))/(4*c^2*d^2))/(a^2*e^4 + c^2*d^4 - (2*c^2*d^3 - 2*a*c*d*e^2)*(d + e*x) + c^2*d^2*(d + e*x)^2 - 2*a*c*d^2*e^2)","B"
2022,1,166,144,0.103981,"\text{Not used}","int((d + e*x)^(7/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","\frac{\frac{e^2\,{\left(d+e\,x\right)}^{3/2}}{4\,\left(a\,e^2-c\,d^2\right)}-\frac{e^2\,\sqrt{d+e\,x}}{4\,c\,d}}{a^2\,e^4+c^2\,d^4-\left(2\,c^2\,d^3-2\,a\,c\,d\,e^2\right)\,\left(d+e\,x\right)+c^2\,d^2\,{\left(d+e\,x\right)}^2-2\,a\,c\,d^2\,e^2}+\frac{e^2\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,\sqrt{d+e\,x}}{\sqrt{a\,e^2-c\,d^2}}\right)}{4\,c^{3/2}\,d^{3/2}\,{\left(a\,e^2-c\,d^2\right)}^{3/2}}","Not used",1,"((e^2*(d + e*x)^(3/2))/(4*(a*e^2 - c*d^2)) - (e^2*(d + e*x)^(1/2))/(4*c*d))/(a^2*e^4 + c^2*d^4 - (2*c^2*d^3 - 2*a*c*d*e^2)*(d + e*x) + c^2*d^2*(d + e*x)^2 - 2*a*c*d^2*e^2) + (e^2*atan((c^(1/2)*d^(1/2)*(d + e*x)^(1/2))/(a*e^2 - c*d^2)^(1/2)))/(4*c^(3/2)*d^(3/2)*(a*e^2 - c*d^2)^(3/2))","B"
2023,1,177,146,0.720345,"\text{Not used}","int((d + e*x)^(5/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","\frac{\frac{5\,e^2\,\sqrt{d+e\,x}}{4\,\left(a\,e^2-c\,d^2\right)}+\frac{3\,c\,d\,e^2\,{\left(d+e\,x\right)}^{3/2}}{4\,{\left(a\,e^2-c\,d^2\right)}^2}}{a^2\,e^4+c^2\,d^4-\left(2\,c^2\,d^3-2\,a\,c\,d\,e^2\right)\,\left(d+e\,x\right)+c^2\,d^2\,{\left(d+e\,x\right)}^2-2\,a\,c\,d^2\,e^2}+\frac{3\,e^2\,\mathrm{atan}\left(\frac{c\,d\,\sqrt{d+e\,x}}{\sqrt{c\,d}\,\sqrt{a\,e^2-c\,d^2}}\right)}{4\,\sqrt{c\,d}\,{\left(a\,e^2-c\,d^2\right)}^{5/2}}","Not used",1,"((5*e^2*(d + e*x)^(1/2))/(4*(a*e^2 - c*d^2)) + (3*c*d*e^2*(d + e*x)^(3/2))/(4*(a*e^2 - c*d^2)^2))/(a^2*e^4 + c^2*d^4 - (2*c^2*d^3 - 2*a*c*d*e^2)*(d + e*x) + c^2*d^2*(d + e*x)^2 - 2*a*c*d^2*e^2) + (3*e^2*atan((c*d*(d + e*x)^(1/2))/((c*d)^(1/2)*(a*e^2 - c*d^2)^(1/2))))/(4*(c*d)^(1/2)*(a*e^2 - c*d^2)^(5/2))","B"
2024,1,251,176,0.798512,"\text{Not used}","int((d + e*x)^(3/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","-\frac{\frac{2\,e^2}{a\,e^2-c\,d^2}+\frac{25\,c\,d\,e^2\,\left(d+e\,x\right)}{4\,{\left(a\,e^2-c\,d^2\right)}^2}+\frac{15\,c^2\,d^2\,e^2\,{\left(d+e\,x\right)}^2}{4\,{\left(a\,e^2-c\,d^2\right)}^3}}{\sqrt{d+e\,x}\,\left(a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4\right)-\left(2\,c^2\,d^3-2\,a\,c\,d\,e^2\right)\,{\left(d+e\,x\right)}^{3/2}+c^2\,d^2\,{\left(d+e\,x\right)}^{5/2}}-\frac{15\,\sqrt{c}\,\sqrt{d}\,e^2\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,\sqrt{d+e\,x}\,\left(a^3\,e^6-3\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2-c^3\,d^6\right)}{{\left(a\,e^2-c\,d^2\right)}^{7/2}}\right)}{4\,{\left(a\,e^2-c\,d^2\right)}^{7/2}}","Not used",1,"- ((2*e^2)/(a*e^2 - c*d^2) + (25*c*d*e^2*(d + e*x))/(4*(a*e^2 - c*d^2)^2) + (15*c^2*d^2*e^2*(d + e*x)^2)/(4*(a*e^2 - c*d^2)^3))/((d + e*x)^(1/2)*(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2) - (2*c^2*d^3 - 2*a*c*d*e^2)*(d + e*x)^(3/2) + c^2*d^2*(d + e*x)^(5/2)) - (15*c^(1/2)*d^(1/2)*e^2*atan((c^(1/2)*d^(1/2)*(d + e*x)^(1/2)*(a^3*e^6 - c^3*d^6 + 3*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4))/(a*e^2 - c*d^2)^(7/2)))/(4*(a*e^2 - c*d^2)^(7/2))","B"
2025,1,296,208,0.859698,"\text{Not used}","int((d + e*x)^(1/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","\frac{\frac{14\,c\,d\,e^2\,\left(d+e\,x\right)}{3\,{\left(a\,e^2-c\,d^2\right)}^2}-\frac{2\,e^2}{3\,\left(a\,e^2-c\,d^2\right)}+\frac{175\,c^2\,d^2\,e^2\,{\left(d+e\,x\right)}^2}{12\,{\left(a\,e^2-c\,d^2\right)}^3}+\frac{35\,c^3\,d^3\,e^2\,{\left(d+e\,x\right)}^3}{4\,{\left(a\,e^2-c\,d^2\right)}^4}}{{\left(d+e\,x\right)}^{3/2}\,\left(a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4\right)-\left(2\,c^2\,d^3-2\,a\,c\,d\,e^2\right)\,{\left(d+e\,x\right)}^{5/2}+c^2\,d^2\,{\left(d+e\,x\right)}^{7/2}}+\frac{35\,c^{3/2}\,d^{3/2}\,e^2\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,\sqrt{d+e\,x}\,\left(a^4\,e^8-4\,a^3\,c\,d^2\,e^6+6\,a^2\,c^2\,d^4\,e^4-4\,a\,c^3\,d^6\,e^2+c^4\,d^8\right)}{{\left(a\,e^2-c\,d^2\right)}^{9/2}}\right)}{4\,{\left(a\,e^2-c\,d^2\right)}^{9/2}}","Not used",1,"((14*c*d*e^2*(d + e*x))/(3*(a*e^2 - c*d^2)^2) - (2*e^2)/(3*(a*e^2 - c*d^2)) + (175*c^2*d^2*e^2*(d + e*x)^2)/(12*(a*e^2 - c*d^2)^3) + (35*c^3*d^3*e^2*(d + e*x)^3)/(4*(a*e^2 - c*d^2)^4))/((d + e*x)^(3/2)*(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2) - (2*c^2*d^3 - 2*a*c*d*e^2)*(d + e*x)^(5/2) + c^2*d^2*(d + e*x)^(7/2)) + (35*c^(3/2)*d^(3/2)*e^2*atan((c^(1/2)*d^(1/2)*(d + e*x)^(1/2)*(a^4*e^8 + c^4*d^8 - 4*a*c^3*d^6*e^2 - 4*a^3*c*d^2*e^6 + 6*a^2*c^2*d^4*e^4))/(a*e^2 - c*d^2)^(9/2)))/(4*(a*e^2 - c*d^2)^(9/2))","B"
2026,1,344,244,0.950607,"\text{Not used}","int(1/((d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3),x)","-\frac{\frac{2\,e^2}{5\,\left(a\,e^2-c\,d^2\right)}-\frac{6\,c\,d\,e^2\,\left(d+e\,x\right)}{5\,{\left(a\,e^2-c\,d^2\right)}^2}+\frac{42\,c^2\,d^2\,e^2\,{\left(d+e\,x\right)}^2}{5\,{\left(a\,e^2-c\,d^2\right)}^3}+\frac{105\,c^3\,d^3\,e^2\,{\left(d+e\,x\right)}^3}{4\,{\left(a\,e^2-c\,d^2\right)}^4}+\frac{63\,c^4\,d^4\,e^2\,{\left(d+e\,x\right)}^4}{4\,{\left(a\,e^2-c\,d^2\right)}^5}}{{\left(d+e\,x\right)}^{5/2}\,\left(a^2\,e^4-2\,a\,c\,d^2\,e^2+c^2\,d^4\right)-\left(2\,c^2\,d^3-2\,a\,c\,d\,e^2\right)\,{\left(d+e\,x\right)}^{7/2}+c^2\,d^2\,{\left(d+e\,x\right)}^{9/2}}-\frac{63\,c^{5/2}\,d^{5/2}\,e^2\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,\sqrt{d+e\,x}\,\left(a^5\,e^{10}-5\,a^4\,c\,d^2\,e^8+10\,a^3\,c^2\,d^4\,e^6-10\,a^2\,c^3\,d^6\,e^4+5\,a\,c^4\,d^8\,e^2-c^5\,d^{10}\right)}{{\left(a\,e^2-c\,d^2\right)}^{11/2}}\right)}{4\,{\left(a\,e^2-c\,d^2\right)}^{11/2}}","Not used",1,"- ((2*e^2)/(5*(a*e^2 - c*d^2)) - (6*c*d*e^2*(d + e*x))/(5*(a*e^2 - c*d^2)^2) + (42*c^2*d^2*e^2*(d + e*x)^2)/(5*(a*e^2 - c*d^2)^3) + (105*c^3*d^3*e^2*(d + e*x)^3)/(4*(a*e^2 - c*d^2)^4) + (63*c^4*d^4*e^2*(d + e*x)^4)/(4*(a*e^2 - c*d^2)^5))/((d + e*x)^(5/2)*(a^2*e^4 + c^2*d^4 - 2*a*c*d^2*e^2) - (2*c^2*d^3 - 2*a*c*d*e^2)*(d + e*x)^(7/2) + c^2*d^2*(d + e*x)^(9/2)) - (63*c^(5/2)*d^(5/2)*e^2*atan((c^(1/2)*d^(1/2)*(d + e*x)^(1/2)*(a^5*e^10 - c^5*d^10 + 5*a*c^4*d^8*e^2 - 5*a^4*c*d^2*e^8 - 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6))/(a*e^2 - c*d^2)^(11/2)))/(4*(a*e^2 - c*d^2)^(11/2))","B"
2027,1,346,295,1.212418,"\text{Not used}","int((d + e*x)^(7/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(\frac{2\,e^3\,x^5\,\sqrt{d+e\,x}}{11}+\frac{4\,x^2\,\sqrt{d+e\,x}\,\left(8\,a^3\,e^6-44\,a^2\,c\,d^2\,e^4+99\,a\,c^2\,d^4\,e^2+462\,c^3\,d^6\right)}{1155\,c^3\,d^3}+\frac{\sqrt{d+e\,x}\,\left(256\,a^5\,e^9-1408\,a^4\,c\,d^2\,e^7+3168\,a^3\,c^2\,d^4\,e^5-3696\,a^2\,c^3\,d^6\,e^3+2310\,a\,c^4\,d^8\,e\right)}{3465\,c^5\,d^5\,e}+\frac{2\,e^2\,x^4\,\left(44\,c\,d^2+a\,e^2\right)\,\sqrt{d+e\,x}}{99\,c\,d}+\frac{x\,\sqrt{d+e\,x}\,\left(-128\,a^4\,c\,d\,e^8+704\,a^3\,c^2\,d^3\,e^6-1584\,a^2\,c^3\,d^5\,e^4+1848\,a\,c^4\,d^7\,e^2+2310\,c^5\,d^9\right)}{3465\,c^5\,d^5\,e}+\frac{4\,e\,x^3\,\sqrt{d+e\,x}\,\left(-4\,a^2\,e^4+22\,a\,c\,d^2\,e^2+297\,c^2\,d^4\right)}{693\,c^2\,d^2}\right)}{x+\frac{d}{e}}","Not used",1,"((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*((2*e^3*x^5*(d + e*x)^(1/2))/11 + (4*x^2*(d + e*x)^(1/2)*(8*a^3*e^6 + 462*c^3*d^6 + 99*a*c^2*d^4*e^2 - 44*a^2*c*d^2*e^4))/(1155*c^3*d^3) + ((d + e*x)^(1/2)*(256*a^5*e^9 - 1408*a^4*c*d^2*e^7 - 3696*a^2*c^3*d^6*e^3 + 3168*a^3*c^2*d^4*e^5 + 2310*a*c^4*d^8*e))/(3465*c^5*d^5*e) + (2*e^2*x^4*(a*e^2 + 44*c*d^2)*(d + e*x)^(1/2))/(99*c*d) + (x*(d + e*x)^(1/2)*(2310*c^5*d^9 + 1848*a*c^4*d^7*e^2 - 1584*a^2*c^3*d^5*e^4 + 704*a^3*c^2*d^3*e^6 - 128*a^4*c*d*e^8))/(3465*c^5*d^5*e) + (4*e*x^3*(d + e*x)^(1/2)*(297*c^2*d^4 - 4*a^2*e^4 + 22*a*c*d^2*e^2))/(693*c^2*d^2)))/(x + d/e)","B"
2028,1,256,233,1.047429,"\text{Not used}","int((d + e*x)^(5/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(\frac{2\,e^2\,x^4\,\sqrt{d+e\,x}}{9}-\frac{\sqrt{d+e\,x}\,\left(32\,a^4\,e^7-144\,a^3\,c\,d^2\,e^5+252\,a^2\,c^2\,d^4\,e^3-210\,a\,c^3\,d^6\,e\right)}{315\,c^4\,d^4\,e}+\frac{2\,x^2\,\sqrt{d+e\,x}\,\left(-2\,a^2\,e^4+9\,a\,c\,d^2\,e^2+63\,c^2\,d^4\right)}{105\,c^2\,d^2}+\frac{x\,\sqrt{d+e\,x}\,\left(16\,a^3\,c\,d\,e^6-72\,a^2\,c^2\,d^3\,e^4+126\,a\,c^3\,d^5\,e^2+210\,c^4\,d^7\right)}{315\,c^4\,d^4\,e}+\frac{2\,e\,x^3\,\left(27\,c\,d^2+a\,e^2\right)\,\sqrt{d+e\,x}}{63\,c\,d}\right)}{x+\frac{d}{e}}","Not used",1,"((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*((2*e^2*x^4*(d + e*x)^(1/2))/9 - ((d + e*x)^(1/2)*(32*a^4*e^7 - 144*a^3*c*d^2*e^5 + 252*a^2*c^2*d^4*e^3 - 210*a*c^3*d^6*e))/(315*c^4*d^4*e) + (2*x^2*(d + e*x)^(1/2)*(63*c^2*d^4 - 2*a^2*e^4 + 9*a*c*d^2*e^2))/(105*c^2*d^2) + (x*(d + e*x)^(1/2)*(210*c^4*d^7 + 126*a*c^3*d^5*e^2 - 72*a^2*c^2*d^3*e^4 + 16*a^3*c*d*e^6))/(315*c^4*d^4*e) + (2*e*x^3*(a*e^2 + 27*c*d^2)*(d + e*x)^(1/2))/(63*c*d)))/(x + d/e)","B"
2029,1,180,171,0.921606,"\text{Not used}","int((d + e*x)^(3/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(\frac{2\,e\,x^3\,\sqrt{d+e\,x}}{7}+\frac{\sqrt{d+e\,x}\,\left(16\,a^3\,e^5-56\,a^2\,c\,d^2\,e^3+70\,a\,c^2\,d^4\,e\right)}{105\,c^3\,d^3\,e}+\frac{2\,x^2\,\left(14\,c\,d^2+a\,e^2\right)\,\sqrt{d+e\,x}}{35\,c\,d}+\frac{x\,\sqrt{d+e\,x}\,\left(-8\,a^2\,c\,d\,e^4+28\,a\,c^2\,d^3\,e^2+70\,c^3\,d^5\right)}{105\,c^3\,d^3\,e}\right)}{x+\frac{d}{e}}","Not used",1,"((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*((2*e*x^3*(d + e*x)^(1/2))/7 + ((d + e*x)^(1/2)*(16*a^3*e^5 - 56*a^2*c*d^2*e^3 + 70*a*c^2*d^4*e))/(105*c^3*d^3*e) + (2*x^2*(a*e^2 + 14*c*d^2)*(d + e*x)^(1/2))/(35*c*d) + (x*(d + e*x)^(1/2)*(70*c^3*d^5 + 28*a*c^2*d^3*e^2 - 8*a^2*c*d*e^4))/(105*c^3*d^3*e)))/(x + d/e)","B"
2030,1,121,109,0.802058,"\text{Not used}","int((d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(\frac{2\,x^2\,\sqrt{d+e\,x}}{5}-\frac{\left(4\,a^2\,e^3-10\,a\,c\,d^2\,e\right)\,\sqrt{d+e\,x}}{15\,c^2\,d^2\,e}+\frac{x\,\left(10\,c^2\,d^3+2\,a\,c\,d\,e^2\right)\,\sqrt{d+e\,x}}{15\,c^2\,d^2\,e}\right)}{x+\frac{d}{e}}","Not used",1,"((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*((2*x^2*(d + e*x)^(1/2))/5 - ((4*a^2*e^3 - 10*a*c*d^2*e)*(d + e*x)^(1/2))/(15*c^2*d^2*e) + (x*(10*c^2*d^3 + 2*a*c*d*e^2)*(d + e*x)^(1/2))/(15*c^2*d^2*e)))/(x + d/e)","B"
2031,1,49,48,0.750987,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x)^(1/2),x)","\frac{\left(\frac{2\,x}{3}+\frac{2\,a\,e}{3\,c\,d}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{\sqrt{d+e\,x}}","Not used",1,"(((2*x)/3 + (2*a*e)/(3*c*d))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^(1/2)","B"
2032,0,-1,128,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x)^(3/2),x)","\int \frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x)^(3/2), x)","F"
2033,0,-1,129,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x)^(5/2),x)","\int \frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x)^(5/2), x)","F"
2034,0,-1,199,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x)^(7/2),x)","\int \frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x)^(7/2), x)","F"
2035,0,-1,264,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x)^(9/2),x)","\int \frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{{\left(d+e\,x\right)}^{9/2}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)/(d + e*x)^(9/2), x)","F"
2036,1,424,295,1.354230,"\text{Not used}","int((d + e*x)^(5/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(\frac{4\,e^2\,x^5\,\left(26\,c\,d^2+7\,a\,e^2\right)\,\sqrt{d+e\,x}}{143}+\frac{2\,c\,d\,e^3\,x^6\,\sqrt{d+e\,x}}{13}+\frac{8\,x^3\,\sqrt{d+e\,x}\,\left(-2\,a^3\,e^6+13\,a^2\,c\,d^2\,e^4+715\,a\,c^2\,d^4\,e^2+429\,c^3\,d^6\right)}{3003\,c^2\,d^2}+\frac{\sqrt{d+e\,x}\,\left(256\,a^6\,e^{10}-1664\,a^5\,c\,d^2\,e^8+4576\,a^4\,c^2\,d^4\,e^6-6864\,a^3\,c^3\,d^6\,e^4+6006\,a^2\,c^4\,d^8\,e^2\right)}{15015\,c^5\,d^5\,e}+\frac{2\,e\,x^4\,\sqrt{d+e\,x}\,\left(a^2\,e^4+208\,a\,c\,d^2\,e^2+286\,c^2\,d^4\right)}{429\,c\,d}+\frac{x^2\,\sqrt{d+e\,x}\,\left(96\,a^4\,c^2\,d^2\,e^8-624\,a^3\,c^3\,d^4\,e^6+1716\,a^2\,c^4\,d^6\,e^4+27456\,a\,c^5\,d^8\,e^2+6006\,c^6\,d^{10}\right)}{15015\,c^5\,d^5\,e}+\frac{4\,a\,x\,\sqrt{d+e\,x}\,\left(-32\,a^4\,e^8+208\,a^3\,c\,d^2\,e^6-572\,a^2\,c^2\,d^4\,e^4+858\,a\,c^3\,d^6\,e^2+3003\,c^4\,d^8\right)}{15015\,c^4\,d^4}\right)}{x+\frac{d}{e}}","Not used",1,"((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*((4*e^2*x^5*(7*a*e^2 + 26*c*d^2)*(d + e*x)^(1/2))/143 + (2*c*d*e^3*x^6*(d + e*x)^(1/2))/13 + (8*x^3*(d + e*x)^(1/2)*(429*c^3*d^6 - 2*a^3*e^6 + 715*a*c^2*d^4*e^2 + 13*a^2*c*d^2*e^4))/(3003*c^2*d^2) + ((d + e*x)^(1/2)*(256*a^6*e^10 - 1664*a^5*c*d^2*e^8 + 6006*a^2*c^4*d^8*e^2 - 6864*a^3*c^3*d^6*e^4 + 4576*a^4*c^2*d^4*e^6))/(15015*c^5*d^5*e) + (2*e*x^4*(d + e*x)^(1/2)*(a^2*e^4 + 286*c^2*d^4 + 208*a*c*d^2*e^2))/(429*c*d) + (x^2*(d + e*x)^(1/2)*(6006*c^6*d^10 + 27456*a*c^5*d^8*e^2 + 1716*a^2*c^4*d^6*e^4 - 624*a^3*c^3*d^4*e^6 + 96*a^4*c^2*d^2*e^8))/(15015*c^5*d^5*e) + (4*a*x*(d + e*x)^(1/2)*(3003*c^4*d^8 - 32*a^4*e^8 + 858*a*c^3*d^6*e^2 + 208*a^3*c*d^2*e^6 - 572*a^2*c^2*d^4*e^4))/(15015*c^4*d^4)))/(x + d/e)","B"
2037,1,320,233,1.211097,"\text{Not used}","int((d + e*x)^(3/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(\frac{2\,e\,x^4\,\left(11\,c\,d^2+4\,a\,e^2\right)\,\sqrt{d+e\,x}}{33}+\frac{2\,c\,d\,e^2\,x^5\,\sqrt{d+e\,x}}{11}-\frac{\sqrt{d+e\,x}\,\left(32\,a^5\,e^8-176\,a^4\,c\,d^2\,e^6+396\,a^3\,c^2\,d^4\,e^4-462\,a^2\,c^3\,d^6\,e^2\right)}{1155\,c^4\,d^4\,e}+\frac{2\,x^3\,\sqrt{d+e\,x}\,\left(a^2\,e^4+110\,a\,c\,d^2\,e^2+99\,c^2\,d^4\right)}{231\,c\,d}+\frac{x^2\,\sqrt{d+e\,x}\,\left(-12\,a^3\,c^2\,d^2\,e^6+66\,a^2\,c^3\,d^4\,e^4+1584\,a\,c^4\,d^6\,e^2+462\,c^5\,d^8\right)}{1155\,c^4\,d^4\,e}+\frac{2\,a\,x\,\sqrt{d+e\,x}\,\left(8\,a^3\,e^6-44\,a^2\,c\,d^2\,e^4+99\,a\,c^2\,d^4\,e^2+462\,c^3\,d^6\right)}{1155\,c^3\,d^3}\right)}{x+\frac{d}{e}}","Not used",1,"((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*((2*e*x^4*(4*a*e^2 + 11*c*d^2)*(d + e*x)^(1/2))/33 + (2*c*d*e^2*x^5*(d + e*x)^(1/2))/11 - ((d + e*x)^(1/2)*(32*a^5*e^8 - 176*a^4*c*d^2*e^6 - 462*a^2*c^3*d^6*e^2 + 396*a^3*c^2*d^4*e^4))/(1155*c^4*d^4*e) + (2*x^3*(d + e*x)^(1/2)*(a^2*e^4 + 99*c^2*d^4 + 110*a*c*d^2*e^2))/(231*c*d) + (x^2*(d + e*x)^(1/2)*(462*c^5*d^8 + 1584*a*c^4*d^6*e^2 + 66*a^2*c^3*d^4*e^4 - 12*a^3*c^2*d^2*e^6))/(1155*c^4*d^4*e) + (2*a*x*(d + e*x)^(1/2)*(8*a^3*e^6 + 462*c^3*d^6 + 99*a*c^2*d^4*e^2 - 44*a^2*c*d^2*e^4))/(1155*c^3*d^3)))/(x + d/e)","B"
2038,1,230,171,1.018601,"\text{Not used}","int((d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(x^3\,\left(\frac{4\,c\,d^2}{7}+\frac{20\,a\,e^2}{63}\right)\,\sqrt{d+e\,x}+\frac{\sqrt{d+e\,x}\,\left(16\,a^4\,e^6-72\,a^3\,c\,d^2\,e^4+126\,a^2\,c^2\,d^4\,e^2\right)}{315\,c^3\,d^3\,e}+\frac{2\,c\,d\,e\,x^4\,\sqrt{d+e\,x}}{9}+\frac{x^2\,\sqrt{d+e\,x}\,\left(6\,a^2\,c^2\,d^2\,e^4+288\,a\,c^3\,d^4\,e^2+126\,c^4\,d^6\right)}{315\,c^3\,d^3\,e}+\frac{4\,a\,x\,\sqrt{d+e\,x}\,\left(-2\,a^2\,e^4+9\,a\,c\,d^2\,e^2+63\,c^2\,d^4\right)}{315\,c^2\,d^2}\right)}{x+\frac{d}{e}}","Not used",1,"((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*(x^3*((20*a*e^2)/63 + (4*c*d^2)/7)*(d + e*x)^(1/2) + ((d + e*x)^(1/2)*(16*a^4*e^6 - 72*a^3*c*d^2*e^4 + 126*a^2*c^2*d^4*e^2))/(315*c^3*d^3*e) + (2*c*d*e*x^4*(d + e*x)^(1/2))/9 + (x^2*(d + e*x)^(1/2)*(126*c^4*d^6 + 288*a*c^3*d^4*e^2 + 6*a^2*c^2*d^2*e^4))/(315*c^3*d^3*e) + (4*a*x*(d + e*x)^(1/2)*(63*c^2*d^4 - 2*a^2*e^4 + 9*a*c*d^2*e^2))/(315*c^2*d^2)))/(x + d/e)","B"
2039,1,128,109,0.936961,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^(1/2),x)","\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(\frac{x^2\,\left(14\,c^3\,d^4+16\,a\,c^2\,d^2\,e^2\right)}{35\,c^2\,d^2}-\frac{4\,a^3\,e^4-14\,a^2\,c\,d^2\,e^2}{35\,c^2\,d^2}+\frac{2\,c\,d\,e\,x^3}{7}+\frac{2\,a\,e\,x\,\left(14\,c\,d^2+a\,e^2\right)}{35\,c\,d}\right)}{\sqrt{d+e\,x}}","Not used",1,"((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*((x^2*(14*c^3*d^4 + 16*a*c^2*d^2*e^2))/(35*c^2*d^2) - (4*a^3*e^4 - 14*a^2*c*d^2*e^2)/(35*c^2*d^2) + (2*c*d*e*x^3)/7 + (2*a*e*x*(a*e^2 + 14*c*d^2))/(35*c*d)))/(d + e*x)^(1/2)","B"
2040,1,62,48,0.784892,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^(3/2),x)","\frac{\left(\frac{4\,a\,e\,x}{5}+\frac{2\,c\,d\,x^2}{5}+\frac{2\,a^2\,e^2}{5\,c\,d}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{\sqrt{d+e\,x}}","Not used",1,"(((4*a*e*x)/5 + (2*c*d*x^2)/5 + (2*a^2*e^2)/(5*c*d))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(d + e*x)^(1/2)","B"
2041,0,-1,181,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^(5/2),x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}}{{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^(5/2), x)","F"
2042,0,-1,175,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^(7/2),x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}}{{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^(7/2), x)","F"
2043,0,-1,185,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^(9/2),x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}}{{\left(d+e\,x\right)}^{9/2}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^(9/2), x)","F"
2044,0,-1,250,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^(11/2),x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}}{{\left(d+e\,x\right)}^{11/2}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^(11/2), x)","F"
2045,0,-1,315,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^(13/2),x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}}{{\left(d+e\,x\right)}^{13/2}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)/(d + e*x)^(13/2), x)","F"
2046,1,501,295,1.558789,"\text{Not used}","int((d + e*x)^(3/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(\frac{2\,e\,x^5\,\sqrt{d+e\,x}\,\left(71\,a^2\,e^4+540\,a\,c\,d^2\,e^2+390\,c^2\,d^4\right)}{715}+\frac{2\,x^4\,\sqrt{d+e\,x}\,\left(a^3\,e^6+636\,a^2\,c\,d^2\,e^4+1794\,a\,c^2\,d^4\,e^2+572\,c^3\,d^6\right)}{1287\,c\,d}+\frac{\sqrt{d+e\,x}\,\left(256\,a^7\,e^{11}-1920\,a^6\,c\,d^2\,e^9+6240\,a^5\,c^2\,d^4\,e^7-11440\,a^4\,c^3\,d^6\,e^5+12870\,a^3\,c^4\,d^8\,e^3\right)}{45045\,c^5\,d^5\,e}+\frac{2\,c^2\,d^2\,e^3\,x^7\,\sqrt{d+e\,x}}{15}+\frac{2\,a\,x^2\,\sqrt{d+e\,x}\,\left(16\,a^4\,e^8-120\,a^3\,c\,d^2\,e^6+390\,a^2\,c^2\,d^4\,e^4+14300\,a\,c^3\,d^6\,e^2+6435\,c^4\,d^8\right)}{15015\,c^3\,d^3}+\frac{x^3\,\sqrt{d+e\,x}\,\left(-80\,a^4\,c^3\,d^3\,e^8+600\,a^3\,c^4\,d^5\,e^6+88140\,a^2\,c^5\,d^7\,e^4+108680\,a\,c^6\,d^9\,e^2+12870\,c^7\,d^{11}\right)}{45045\,c^5\,d^5\,e}+\frac{2\,c\,d\,e^2\,x^6\,\left(60\,c\,d^2+31\,a\,e^2\right)\,\sqrt{d+e\,x}}{195}+\frac{2\,a^2\,e\,x\,\sqrt{d+e\,x}\,\left(-64\,a^4\,e^8+480\,a^3\,c\,d^2\,e^6-1560\,a^2\,c^2\,d^4\,e^4+2860\,a\,c^3\,d^6\,e^2+19305\,c^4\,d^8\right)}{45045\,c^4\,d^4}\right)}{x+\frac{d}{e}}","Not used",1,"((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*((2*e*x^5*(d + e*x)^(1/2)*(71*a^2*e^4 + 390*c^2*d^4 + 540*a*c*d^2*e^2))/715 + (2*x^4*(d + e*x)^(1/2)*(a^3*e^6 + 572*c^3*d^6 + 1794*a*c^2*d^4*e^2 + 636*a^2*c*d^2*e^4))/(1287*c*d) + ((d + e*x)^(1/2)*(256*a^7*e^11 - 1920*a^6*c*d^2*e^9 + 12870*a^3*c^4*d^8*e^3 - 11440*a^4*c^3*d^6*e^5 + 6240*a^5*c^2*d^4*e^7))/(45045*c^5*d^5*e) + (2*c^2*d^2*e^3*x^7*(d + e*x)^(1/2))/15 + (2*a*x^2*(d + e*x)^(1/2)*(16*a^4*e^8 + 6435*c^4*d^8 + 14300*a*c^3*d^6*e^2 - 120*a^3*c*d^2*e^6 + 390*a^2*c^2*d^4*e^4))/(15015*c^3*d^3) + (x^3*(d + e*x)^(1/2)*(12870*c^7*d^11 + 108680*a*c^6*d^9*e^2 + 88140*a^2*c^5*d^7*e^4 + 600*a^3*c^4*d^5*e^6 - 80*a^4*c^3*d^3*e^8))/(45045*c^5*d^5*e) + (2*c*d*e^2*x^6*(31*a*e^2 + 60*c*d^2)*(d + e*x)^(1/2))/195 + (2*a^2*e*x*(d + e*x)^(1/2)*(19305*c^4*d^8 - 64*a^4*e^8 + 2860*a*c^3*d^6*e^2 + 480*a^3*c*d^2*e^6 - 1560*a^2*c^2*d^4*e^4))/(45045*c^4*d^4)))/(x + d/e)","B"
2047,1,383,233,1.396141,"\text{Not used}","int((d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(x^4\,\sqrt{d+e\,x}\,\left(\frac{106\,a^2\,e^4}{429}+\frac{46\,a\,c\,d^2\,e^2}{33}+\frac{2\,c^2\,d^4}{3}\right)-\frac{\sqrt{d+e\,x}\,\left(32\,a^6\,e^9-208\,a^5\,c\,d^2\,e^7+572\,a^4\,c^2\,d^4\,e^5-858\,a^3\,c^3\,d^6\,e^3\right)}{3003\,c^4\,d^4\,e}+\frac{2\,c^2\,d^2\,e^2\,x^6\,\sqrt{d+e\,x}}{13}+\frac{x^3\,\sqrt{d+e\,x}\,\left(10\,a^3\,c^3\,d^3\,e^6+2938\,a^2\,c^4\,d^5\,e^4+5434\,a\,c^5\,d^7\,e^2+858\,c^6\,d^9\right)}{3003\,c^4\,d^4\,e}+\frac{6\,c\,d\,e\,x^5\,\left(13\,c\,d^2+9\,a\,e^2\right)\,\sqrt{d+e\,x}}{143}+\frac{2\,a\,x^2\,\sqrt{d+e\,x}\,\left(-2\,a^3\,e^6+13\,a^2\,c\,d^2\,e^4+715\,a\,c^2\,d^4\,e^2+429\,c^3\,d^6\right)}{1001\,c^2\,d^2}+\frac{2\,a^2\,e\,x\,\sqrt{d+e\,x}\,\left(8\,a^3\,e^6-52\,a^2\,c\,d^2\,e^4+143\,a\,c^2\,d^4\,e^2+1287\,c^3\,d^6\right)}{3003\,c^3\,d^3}\right)}{x+\frac{d}{e}}","Not used",1,"((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*(x^4*(d + e*x)^(1/2)*((106*a^2*e^4)/429 + (2*c^2*d^4)/3 + (46*a*c*d^2*e^2)/33) - ((d + e*x)^(1/2)*(32*a^6*e^9 - 208*a^5*c*d^2*e^7 - 858*a^3*c^3*d^6*e^3 + 572*a^4*c^2*d^4*e^5))/(3003*c^4*d^4*e) + (2*c^2*d^2*e^2*x^6*(d + e*x)^(1/2))/13 + (x^3*(d + e*x)^(1/2)*(858*c^6*d^9 + 5434*a*c^5*d^7*e^2 + 2938*a^2*c^4*d^5*e^4 + 10*a^3*c^3*d^3*e^6))/(3003*c^4*d^4*e) + (6*c*d*e*x^5*(9*a*e^2 + 13*c*d^2)*(d + e*x)^(1/2))/143 + (2*a*x^2*(d + e*x)^(1/2)*(429*c^3*d^6 - 2*a^3*e^6 + 715*a*c^2*d^4*e^2 + 13*a^2*c*d^2*e^4))/(1001*c^2*d^2) + (2*a^2*e*x*(d + e*x)^(1/2)*(8*a^3*e^6 + 1287*c^3*d^6 + 143*a*c^2*d^4*e^2 - 52*a^2*c*d^2*e^4))/(3003*c^3*d^3)))/(x + d/e)","B"
2048,1,241,171,1.199699,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^(1/2),x)","\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(\frac{16\,a^5\,e^7-88\,a^4\,c\,d^2\,e^5+198\,a^3\,c^2\,d^4\,e^3}{693\,c^3\,d^3}+\frac{x^3\,\left(226\,a^2\,c^3\,d^3\,e^4+836\,a\,c^4\,d^5\,e^2+198\,c^5\,d^7\right)}{693\,c^3\,d^3}+\frac{2\,c^2\,d^2\,e^2\,x^5}{11}+\frac{2\,c\,d\,e\,x^4\,\left(22\,c\,d^2+23\,a\,e^2\right)}{99}+\frac{2\,a\,e\,x^2\,\left(a^2\,e^4+110\,a\,c\,d^2\,e^2+99\,c^2\,d^4\right)}{231\,c\,d}+\frac{2\,a^2\,e^2\,x\,\left(-4\,a^2\,e^4+22\,a\,c\,d^2\,e^2+297\,c^2\,d^4\right)}{693\,c^2\,d^2}\right)}{\sqrt{d+e\,x}}","Not used",1,"((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*((16*a^5*e^7 - 88*a^4*c*d^2*e^5 + 198*a^3*c^2*d^4*e^3)/(693*c^3*d^3) + (x^3*(198*c^5*d^7 + 836*a*c^4*d^5*e^2 + 226*a^2*c^3*d^3*e^4))/(693*c^3*d^3) + (2*c^2*d^2*e^2*x^5)/11 + (2*c*d*e*x^4*(23*a*e^2 + 22*c*d^2))/99 + (2*a*e*x^2*(a^2*e^4 + 99*c^2*d^4 + 110*a*c*d^2*e^2))/(231*c*d) + (2*a^2*e^2*x*(297*c^2*d^4 - 4*a^2*e^4 + 22*a*c*d^2*e^2))/(693*c^2*d^2)))/(d + e*x)^(1/2)","B"
2049,1,156,109,1.028503,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^(3/2),x)","\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(\frac{x^3\,\left(18\,c^4\,d^5+38\,a\,c^3\,d^3\,e^2\right)}{63\,c^2\,d^2}-\frac{4\,a^4\,e^5-18\,a^3\,c\,d^2\,e^3}{63\,c^2\,d^2}+\frac{2\,c^2\,d^2\,e\,x^4}{9}+\frac{2\,a\,e\,x^2\,\left(9\,c\,d^2+5\,a\,e^2\right)}{21}+\frac{2\,a^2\,e^2\,x\,\left(27\,c\,d^2+a\,e^2\right)}{63\,c\,d}\right)}{\sqrt{d+e\,x}}","Not used",1,"((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*((x^3*(18*c^4*d^5 + 38*a*c^3*d^3*e^2))/(63*c^2*d^2) - (4*a^4*e^5 - 18*a^3*c*d^2*e^3)/(63*c^2*d^2) + (2*c^2*d^2*e*x^4)/9 + (2*a*e*x^2*(5*a*e^2 + 9*c*d^2))/21 + (2*a^2*e^2*x*(a*e^2 + 27*c*d^2))/(63*c*d)))/(d + e*x)^(1/2)","B"
2050,1,79,48,0.823860,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^(5/2),x)","\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(\frac{6\,a^2\,e^2\,x}{7}+\frac{2\,c^2\,d^2\,x^3}{7}+\frac{2\,a^3\,e^3}{7\,c\,d}+\frac{6\,a\,c\,d\,e\,x^2}{7}\right)}{\sqrt{d+e\,x}}","Not used",1,"((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*((6*a^2*e^2*x)/7 + (2*c^2*d^2*x^3)/7 + (2*a^3*e^3)/(7*c*d) + (6*a*c*d*e*x^2)/7))/(d + e*x)^(1/2)","B"
2051,0,-1,240,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^(7/2),x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}}{{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^(7/2), x)","F"
2052,0,-1,233,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^(9/2),x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}}{{\left(d+e\,x\right)}^{9/2}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^(9/2), x)","F"
2053,0,-1,236,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^(11/2),x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}}{{\left(d+e\,x\right)}^{11/2}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^(11/2), x)","F"
2054,0,-1,236,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^(13/2),x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}}{{\left(d+e\,x\right)}^{13/2}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^(13/2), x)","F"
2055,0,-1,301,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^(15/2),x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}}{{\left(d+e\,x\right)}^{15/2}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^(15/2), x)","F"
2056,0,-1,366,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^(17/2),x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}}{{\left(d+e\,x\right)}^{17/2}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)/(d + e*x)^(17/2), x)","F"
2057,1,194,233,1.038627,"\text{Not used}","int((d + e*x)^(7/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","-\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(\frac{\sqrt{d+e\,x}\,\left(32\,a^3\,e^6-112\,a^2\,c\,d^2\,e^4+140\,a\,c^2\,d^4\,e^2-70\,c^3\,d^6\right)}{35\,c^4\,d^4\,e}-\frac{2\,x\,\sqrt{d+e\,x}\,\left(8\,a^2\,e^4-28\,a\,c\,d^2\,e^2+35\,c^2\,d^4\right)}{35\,c^3\,d^3}-\frac{2\,e^2\,x^3\,\sqrt{d+e\,x}}{7\,c\,d}+\frac{6\,e\,x^2\,\left(2\,a\,e^2-7\,c\,d^2\right)\,\sqrt{d+e\,x}}{35\,c^2\,d^2}\right)}{x+\frac{d}{e}}","Not used",1,"-((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*(((d + e*x)^(1/2)*(32*a^3*e^6 - 70*c^3*d^6 + 140*a*c^2*d^4*e^2 - 112*a^2*c*d^2*e^4))/(35*c^4*d^4*e) - (2*x*(d + e*x)^(1/2)*(8*a^2*e^4 + 35*c^2*d^4 - 28*a*c*d^2*e^2))/(35*c^3*d^3) - (2*e^2*x^3*(d + e*x)^(1/2))/(7*c*d) + (6*e*x^2*(2*a*e^2 - 7*c*d^2)*(d + e*x)^(1/2))/(35*c^2*d^2)))/(x + d/e)","B"
2058,1,131,171,0.920104,"\text{Not used}","int((d + e*x)^(5/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","\frac{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}\,\left(\frac{2\,e\,x^2\,\sqrt{d+e\,x}}{5\,c\,d}-\frac{4\,x\,\left(2\,a\,e^2-5\,c\,d^2\right)\,\sqrt{d+e\,x}}{15\,c^2\,d^2}+\frac{\sqrt{d+e\,x}\,\left(16\,a^2\,e^4-40\,a\,c\,d^2\,e^2+30\,c^2\,d^4\right)}{15\,c^3\,d^3\,e}\right)}{x+\frac{d}{e}}","Not used",1,"((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)*((2*e*x^2*(d + e*x)^(1/2))/(5*c*d) - (4*x*(2*a*e^2 - 5*c*d^2)*(d + e*x)^(1/2))/(15*c^2*d^2) + ((d + e*x)^(1/2)*(16*a^2*e^4 + 30*c^2*d^4 - 40*a*c*d^2*e^2))/(15*c^3*d^3*e)))/(x + d/e)","B"
2059,1,85,109,0.853171,"\text{Not used}","int((d + e*x)^(3/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","\frac{\left(\frac{2\,x\,\sqrt{d+e\,x}}{3\,c\,d}-\frac{\left(4\,a\,e^2-6\,c\,d^2\right)\,\sqrt{d+e\,x}}{3\,c^2\,d^2\,e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{x+\frac{d}{e}}","Not used",1,"(((2*x*(d + e*x)^(1/2))/(3*c*d) - ((4*a*e^2 - 6*c*d^2)*(d + e*x)^(1/2))/(3*c^2*d^2*e))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(x + d/e)","B"
2060,1,54,46,0.819294,"\text{Not used}","int((d + e*x)^(1/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","\frac{2\,\sqrt{d+e\,x}\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{c\,d\,e\,\left(x+\frac{d}{e}\right)}","Not used",1,"(2*(d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(c*d*e*(x + d/e))","B"
2061,0,-1,84,0.000000,"\text{Not used}","int(1/((d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{d+e\,x}\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}} \,d x","Not used",1,"int(1/((d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)), x)","F"
2062,0,-1,139,0.000000,"\text{Not used}","int(1/((d + e*x)^(3/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{3/2}\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}} \,d x","Not used",1,"int(1/((d + e*x)^(3/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)), x)","F"
2063,0,-1,207,0.000000,"\text{Not used}","int(1/((d + e*x)^(5/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{5/2}\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}} \,d x","Not used",1,"int(1/((d + e*x)^(5/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)), x)","F"
2064,0,-1,269,0.000000,"\text{Not used}","int(1/((d + e*x)^(7/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{7/2}\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}} \,d x","Not used",1,"int(1/((d + e*x)^(7/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2)), x)","F"
2065,1,174,171,1.096696,"\text{Not used}","int((d + e*x)^(7/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","\frac{\left(\frac{2\,e\,x^2\,\sqrt{d+e\,x}}{3\,c^2\,d^2}-\frac{\sqrt{d+e\,x}\,\left(16\,a^2\,e^4-24\,a\,c\,d^2\,e^2+6\,c^2\,d^4\right)}{3\,c^4\,d^4\,e}+\frac{x\,\left(12\,c^2\,d^3\,e-8\,a\,c\,d\,e^3\right)\,\sqrt{d+e\,x}}{3\,c^4\,d^4\,e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{\frac{a}{c}+x^2+\frac{x\,\left(3\,c^4\,d^5+3\,a\,c^3\,d^3\,e^2\right)}{3\,c^4\,d^4\,e}}","Not used",1,"(((2*e*x^2*(d + e*x)^(1/2))/(3*c^2*d^2) - ((d + e*x)^(1/2)*(16*a^2*e^4 + 6*c^2*d^4 - 24*a*c*d^2*e^2))/(3*c^4*d^4*e) + (x*(12*c^2*d^3*e - 8*a*c*d*e^3)*(d + e*x)^(1/2))/(3*c^4*d^4*e))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(a/c + x^2 + (x*(3*c^4*d^5 + 3*a*c^3*d^3*e^2))/(3*c^4*d^4*e))","B"
2066,1,116,105,0.960934,"\text{Not used}","int((d + e*x)^(5/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","\frac{\left(\frac{2\,x\,\sqrt{d+e\,x}}{c^2\,d^2}+\frac{\left(4\,a\,e^2-2\,c\,d^2\right)\,\sqrt{d+e\,x}}{c^3\,d^3\,e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{\frac{a}{c}+x^2+\frac{x\,\left(c^3\,d^4+a\,c^2\,d^2\,e^2\right)}{c^3\,d^3\,e}}","Not used",1,"(((2*x*(d + e*x)^(1/2))/(c^2*d^2) + ((4*a*e^2 - 2*c*d^2)*(d + e*x)^(1/2))/(c^3*d^3*e))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(a/c + x^2 + (x*(c^3*d^4 + a*c^2*d^2*e^2))/(c^3*d^3*e))","B"
2067,1,82,46,0.988483,"\text{Not used}","int((d + e*x)^(3/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","-\frac{2\,\sqrt{d+e\,x}\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{c^2\,d^2\,e\,\left(\frac{a}{c}+x^2+\frac{x\,\left(c^2\,d^3+a\,c\,d\,e^2\right)}{c^2\,d^2\,e}\right)}","Not used",1,"-(2*(d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(c^2*d^2*e*(a/c + x^2 + (x*(c^2*d^3 + a*c*d*e^2))/(c^2*d^2*e)))","B"
2068,0,-1,139,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2),x)","\int \frac{\sqrt{d+e\,x}}{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(1/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2), x)","F"
2069,0,-1,196,0.000000,"\text{Not used}","int(1/((d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)),x)","\int \frac{1}{\sqrt{d+e\,x}\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)), x)","F"
2070,0,-1,269,0.000000,"\text{Not used}","int(1/((d + e*x)^(3/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{3/2}\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)^(3/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)), x)","F"
2071,0,-1,331,0.000000,"\text{Not used}","int(1/((d + e*x)^(5/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{5/2}\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)^(5/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)), x)","F"
2072,0,-1,393,0.000000,"\text{Not used}","int(1/((d + e*x)^(7/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{7/2}\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)^(7/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(3/2)), x)","F"
2073,1,147,107,1.074208,"\text{Not used}","int((d + e*x)^(7/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","-\frac{\left(\frac{2\,x\,\sqrt{d+e\,x}}{c^3\,d^3}+\frac{\left(\frac{2\,c\,d^2}{3}+\frac{4\,a\,e^2}{3}\right)\,\sqrt{d+e\,x}}{c^4\,d^4\,e}\right)\,\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}}{x^3+\frac{a^2\,e}{c^2\,d}+\frac{a\,x\,\left(2\,c\,d^2+a\,e^2\right)}{c^2\,d^2}+\frac{x^2\,\left(c^4\,d^5+2\,a\,c^3\,d^3\,e^2\right)}{c^4\,d^4\,e}}","Not used",1,"-(((2*x*(d + e*x)^(1/2))/(c^3*d^3) + (((4*a*e^2)/3 + (2*c*d^2)/3)*(d + e*x)^(1/2))/(c^4*d^4*e))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2))/(x^3 + (a^2*e)/(c^2*d) + (a*x*(a*e^2 + 2*c*d^2))/(c^2*d^2) + (x^2*(c^4*d^5 + 2*a*c^3*d^3*e^2))/(c^4*d^4*e))","B"
2074,1,110,48,1.062824,"\text{Not used}","int((d + e*x)^(5/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","-\frac{2\,\sqrt{d+e\,x}\,\sqrt{c\,d^2\,x+c\,d\,e\,x^2+a\,d\,e+a\,e^2\,x}}{3\,\left(a^2\,c\,d^2\,e^2+a^2\,c\,d\,e^3\,x+2\,a\,c^2\,d^3\,e\,x+2\,a\,c^2\,d^2\,e^2\,x^2+c^3\,d^4\,x^2+c^3\,d^3\,e\,x^3\right)}","Not used",1,"-(2*(d + e*x)^(1/2)*(a*d*e + a*e^2*x + c*d^2*x + c*d*e*x^2)^(1/2))/(3*(c^3*d^4*x^2 + a^2*c*d^2*e^2 + c^3*d^3*e*x^3 + 2*a*c^2*d^3*e*x + a^2*c*d*e^3*x + 2*a*c^2*d^2*e^2*x^2))","B"
2075,0,-1,251,0.000000,"\text{Not used}","int((d + e*x)^(3/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{3/2}}{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(3/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2), x)","F"
2076,0,-1,257,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2),x)","\int \frac{\sqrt{d+e\,x}}{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(1/2)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2), x)","F"
2077,0,-1,329,0.000000,"\text{Not used}","int(1/((d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)),x)","\int \frac{1}{\sqrt{d+e\,x}\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}} \,d x","Not used",1,"int(1/((d + e*x)^(1/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)), x)","F"
2078,0,-1,395,0.000000,"\text{Not used}","int(1/((d + e*x)^(3/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{3/2}\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}} \,d x","Not used",1,"int(1/((d + e*x)^(3/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)), x)","F"
2079,0,-1,457,0.000000,"\text{Not used}","int(1/((d + e*x)^(5/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{5/2}\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}} \,d x","Not used",1,"int(1/((d + e*x)^(5/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)), x)","F"
2080,0,-1,519,0.000000,"\text{Not used}","int(1/((d + e*x)^(7/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{7/2}\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^{5/2}} \,d x","Not used",1,"int(1/((d + e*x)^(7/2)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(5/2)), x)","F"
2081,0,-1,52,0.000000,"\text{Not used}","int(1/((d^2 - e^2*x^2)^(1/2)*(d + e*x)^(1/2)),x)","\int \frac{1}{\sqrt{d^2-e^2\,x^2}\,\sqrt{d+e\,x}} \,d x","Not used",1,"int(1/((d^2 - e^2*x^2)^(1/2)*(d + e*x)^(1/2)), x)","F"
2082,0,-1,53,0.000000,"\text{Not used}","int(1/((d^2 - e^2*x^2)^(1/2)*(e*x - d)^(1/2)),x)","\int \frac{1}{\sqrt{d^2-e^2\,x^2}\,\sqrt{e\,x-d}} \,d x","Not used",1,"int(1/((d^2 - e^2*x^2)^(1/2)*(e*x - d)^(1/2)), x)","F"
2083,0,-1,566,0.000000,"\text{Not used}","int((d + e*x)^(2/3)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^{2/3}}{\sqrt{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e}} \,d x","Not used",1,"int((d + e*x)^(2/3)/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^(1/2), x)","F"
2084,1,1202,130,1.521437,"\text{Not used}","int((d + e*x)^m*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","\frac{d^4\,{\left(d+e\,x\right)}^m\,\left(a^3\,e^6\,m^3+18\,a^3\,e^6\,m^2+107\,a^3\,e^6\,m+210\,a^3\,e^6-3\,a^2\,c\,d^2\,e^4\,m^2-39\,a^2\,c\,d^2\,e^4\,m-126\,a^2\,c\,d^2\,e^4+6\,a\,c^2\,d^4\,e^2\,m+42\,a\,c^2\,d^4\,e^2-6\,c^3\,d^6\right)}{e^4\,\left(m^4+22\,m^3+179\,m^2+638\,m+840\right)}+\frac{x^4\,{\left(d+e\,x\right)}^m\,\left(a^3\,e^{10}\,m^3+18\,a^3\,e^{10}\,m^2+107\,a^3\,e^{10}\,m+210\,a^3\,e^{10}+12\,a^2\,c\,d^2\,e^8\,m^3+201\,a^2\,c\,d^2\,e^8\,m^2+1089\,a^2\,c\,d^2\,e^8\,m+1890\,a^2\,c\,d^2\,e^8+18\,a\,c^2\,d^4\,e^6\,m^3+264\,a\,c^2\,d^4\,e^6\,m^2+1236\,a\,c^2\,d^4\,e^6\,m+1890\,a\,c^2\,d^4\,e^6+4\,c^3\,d^6\,e^4\,m^3+42\,c^3\,d^6\,e^4\,m^2+158\,c^3\,d^6\,e^4\,m+210\,c^3\,d^6\,e^4\right)}{e^4\,\left(m^4+22\,m^3+179\,m^2+638\,m+840\right)}+\frac{3\,d^2\,x^2\,{\left(d+e\,x\right)}^m\,\left(2\,a^3\,e^6\,m^3+36\,a^3\,e^6\,m^2+214\,a^3\,e^6\,m+420\,a^3\,e^6+4\,a^2\,c\,d^2\,e^4\,m^3+62\,a^2\,c\,d^2\,e^4\,m^2+298\,a^2\,c\,d^2\,e^4\,m+420\,a^2\,c\,d^2\,e^4+a\,c^2\,d^4\,e^2\,m^3+8\,a\,c^2\,d^4\,e^2\,m^2+7\,a\,c^2\,d^4\,e^2\,m-c^3\,d^6\,m^2-c^3\,d^6\,m\right)}{e^2\,\left(m^4+22\,m^3+179\,m^2+638\,m+840\right)}+\frac{d^3\,x\,{\left(d+e\,x\right)}^m\,\left(4\,a^3\,e^6\,m^3+72\,a^3\,e^6\,m^2+428\,a^3\,e^6\,m+840\,a^3\,e^6+3\,a^2\,c\,d^2\,e^4\,m^3+39\,a^2\,c\,d^2\,e^4\,m^2+126\,a^2\,c\,d^2\,e^4\,m-6\,a\,c^2\,d^4\,e^2\,m^2-42\,a\,c^2\,d^4\,e^2\,m+6\,c^3\,d^6\,m\right)}{e^3\,\left(m^4+22\,m^3+179\,m^2+638\,m+840\right)}+\frac{d\,x^3\,{\left(d+e\,x\right)}^m\,\left(4\,a^3\,e^6\,m^3+72\,a^3\,e^6\,m^2+428\,a^3\,e^6\,m+840\,a^3\,e^6+18\,a^2\,c\,d^2\,e^4\,m^3+294\,a^2\,c\,d^2\,e^4\,m^2+1536\,a^2\,c\,d^2\,e^4\,m+2520\,a^2\,c\,d^2\,e^4+12\,a\,c^2\,d^4\,e^2\,m^3+156\,a\,c^2\,d^4\,e^2\,m^2+624\,a\,c^2\,d^4\,e^2\,m+840\,a\,c^2\,d^4\,e^2+c^3\,d^6\,m^3+3\,c^3\,d^6\,m^2+2\,c^3\,d^6\,m\right)}{e\,\left(m^4+22\,m^3+179\,m^2+638\,m+840\right)}+\frac{c^3\,d^3\,e^3\,x^7\,{\left(d+e\,x\right)}^m\,\left(m^3+15\,m^2+74\,m+120\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}+\frac{3\,c\,d\,e\,x^5\,\left(m+4\right)\,{\left(d+e\,x\right)}^m\,\left(a^2\,e^4\,m^2+13\,a^2\,e^4\,m+42\,a^2\,e^4+4\,a\,c\,d^2\,e^2\,m^2+46\,a\,c\,d^2\,e^2\,m+126\,a\,c\,d^2\,e^2+2\,c^2\,d^4\,m^2+18\,c^2\,d^4\,m+42\,c^2\,d^4\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}+\frac{c^2\,d^2\,e^2\,x^6\,{\left(d+e\,x\right)}^m\,\left(m^2+9\,m+20\right)\,\left(21\,a\,e^2+21\,c\,d^2+3\,a\,e^2\,m+4\,c\,d^2\,m\right)}{m^4+22\,m^3+179\,m^2+638\,m+840}","Not used",1,"(d^4*(d + e*x)^m*(210*a^3*e^6 - 6*c^3*d^6 + 107*a^3*e^6*m + 18*a^3*e^6*m^2 + a^3*e^6*m^3 + 42*a*c^2*d^4*e^2 - 126*a^2*c*d^2*e^4 + 6*a*c^2*d^4*e^2*m - 39*a^2*c*d^2*e^4*m - 3*a^2*c*d^2*e^4*m^2))/(e^4*(638*m + 179*m^2 + 22*m^3 + m^4 + 840)) + (x^4*(d + e*x)^m*(210*a^3*e^10 + 107*a^3*e^10*m + 210*c^3*d^6*e^4 + 18*a^3*e^10*m^2 + a^3*e^10*m^3 + 1890*a*c^2*d^4*e^6 + 1890*a^2*c*d^2*e^8 + 158*c^3*d^6*e^4*m + 42*c^3*d^6*e^4*m^2 + 4*c^3*d^6*e^4*m^3 + 1236*a*c^2*d^4*e^6*m + 1089*a^2*c*d^2*e^8*m + 264*a*c^2*d^4*e^6*m^2 + 201*a^2*c*d^2*e^8*m^2 + 18*a*c^2*d^4*e^6*m^3 + 12*a^2*c*d^2*e^8*m^3))/(e^4*(638*m + 179*m^2 + 22*m^3 + m^4 + 840)) + (3*d^2*x^2*(d + e*x)^m*(420*a^3*e^6 + 214*a^3*e^6*m - c^3*d^6*m + 36*a^3*e^6*m^2 + 2*a^3*e^6*m^3 - c^3*d^6*m^2 + 420*a^2*c*d^2*e^4 + 7*a*c^2*d^4*e^2*m + 298*a^2*c*d^2*e^4*m + 8*a*c^2*d^4*e^2*m^2 + 62*a^2*c*d^2*e^4*m^2 + a*c^2*d^4*e^2*m^3 + 4*a^2*c*d^2*e^4*m^3))/(e^2*(638*m + 179*m^2 + 22*m^3 + m^4 + 840)) + (d^3*x*(d + e*x)^m*(840*a^3*e^6 + 428*a^3*e^6*m + 6*c^3*d^6*m + 72*a^3*e^6*m^2 + 4*a^3*e^6*m^3 - 42*a*c^2*d^4*e^2*m + 126*a^2*c*d^2*e^4*m - 6*a*c^2*d^4*e^2*m^2 + 39*a^2*c*d^2*e^4*m^2 + 3*a^2*c*d^2*e^4*m^3))/(e^3*(638*m + 179*m^2 + 22*m^3 + m^4 + 840)) + (d*x^3*(d + e*x)^m*(840*a^3*e^6 + 428*a^3*e^6*m + 2*c^3*d^6*m + 72*a^3*e^6*m^2 + 4*a^3*e^6*m^3 + 3*c^3*d^6*m^2 + c^3*d^6*m^3 + 840*a*c^2*d^4*e^2 + 2520*a^2*c*d^2*e^4 + 624*a*c^2*d^4*e^2*m + 1536*a^2*c*d^2*e^4*m + 156*a*c^2*d^4*e^2*m^2 + 294*a^2*c*d^2*e^4*m^2 + 12*a*c^2*d^4*e^2*m^3 + 18*a^2*c*d^2*e^4*m^3))/(e*(638*m + 179*m^2 + 22*m^3 + m^4 + 840)) + (c^3*d^3*e^3*x^7*(d + e*x)^m*(74*m + 15*m^2 + m^3 + 120))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840) + (3*c*d*e*x^5*(m + 4)*(d + e*x)^m*(42*a^2*e^4 + 42*c^2*d^4 + 13*a^2*e^4*m + 18*c^2*d^4*m + a^2*e^4*m^2 + 2*c^2*d^4*m^2 + 126*a*c*d^2*e^2 + 46*a*c*d^2*e^2*m + 4*a*c*d^2*e^2*m^2))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840) + (c^2*d^2*e^2*x^6*(d + e*x)^m*(9*m + m^2 + 20)*(21*a*e^2 + 21*c*d^2 + 3*a*e^2*m + 4*c*d^2*m))/(638*m + 179*m^2 + 22*m^3 + m^4 + 840)","B"
2085,1,486,90,1.045861,"\text{Not used}","int((d + e*x)^m*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","{\left(d+e\,x\right)}^m\,\left(\frac{x^3\,\left(a^2\,e^7\,m^2+9\,a^2\,e^7\,m+20\,a^2\,e^7+6\,a\,c\,d^2\,e^5\,m^2+46\,a\,c\,d^2\,e^5\,m+80\,a\,c\,d^2\,e^5+3\,c^2\,d^4\,e^3\,m^2+15\,c^2\,d^4\,e^3\,m+20\,c^2\,d^4\,e^3\right)}{e^3\,\left(m^3+12\,m^2+47\,m+60\right)}+\frac{d^3\,\left(a^2\,e^4\,m^2+9\,a^2\,e^4\,m+20\,a^2\,e^4-2\,a\,c\,d^2\,e^2\,m-10\,a\,c\,d^2\,e^2+2\,c^2\,d^4\right)}{e^3\,\left(m^3+12\,m^2+47\,m+60\right)}+\frac{d^2\,x\,\left(3\,a^2\,e^4\,m^2+27\,a^2\,e^4\,m+60\,a^2\,e^4+2\,a\,c\,d^2\,e^2\,m^2+10\,a\,c\,d^2\,e^2\,m-2\,c^2\,d^4\,m\right)}{e^2\,\left(m^3+12\,m^2+47\,m+60\right)}+\frac{d\,x^2\,\left(3\,a^2\,e^4\,m^2+27\,a^2\,e^4\,m+60\,a^2\,e^4+6\,a\,c\,d^2\,e^2\,m^2+42\,a\,c\,d^2\,e^2\,m+60\,a\,c\,d^2\,e^2+c^2\,d^4\,m^2+c^2\,d^4\,m\right)}{e\,\left(m^3+12\,m^2+47\,m+60\right)}+\frac{c^2\,d^2\,e^2\,x^5\,\left(m^2+7\,m+12\right)}{m^3+12\,m^2+47\,m+60}+\frac{c\,d\,e\,x^4\,\left(m+3\right)\,\left(10\,a\,e^2+10\,c\,d^2+2\,a\,e^2\,m+3\,c\,d^2\,m\right)}{m^3+12\,m^2+47\,m+60}\right)","Not used",1,"(d + e*x)^m*((x^3*(20*a^2*e^7 + 9*a^2*e^7*m + 20*c^2*d^4*e^3 + a^2*e^7*m^2 + 15*c^2*d^4*e^3*m + 3*c^2*d^4*e^3*m^2 + 80*a*c*d^2*e^5 + 46*a*c*d^2*e^5*m + 6*a*c*d^2*e^5*m^2))/(e^3*(47*m + 12*m^2 + m^3 + 60)) + (d^3*(20*a^2*e^4 + 2*c^2*d^4 + 9*a^2*e^4*m + a^2*e^4*m^2 - 10*a*c*d^2*e^2 - 2*a*c*d^2*e^2*m))/(e^3*(47*m + 12*m^2 + m^3 + 60)) + (d^2*x*(60*a^2*e^4 + 27*a^2*e^4*m - 2*c^2*d^4*m + 3*a^2*e^4*m^2 + 10*a*c*d^2*e^2*m + 2*a*c*d^2*e^2*m^2))/(e^2*(47*m + 12*m^2 + m^3 + 60)) + (d*x^2*(60*a^2*e^4 + 27*a^2*e^4*m + c^2*d^4*m + 3*a^2*e^4*m^2 + c^2*d^4*m^2 + 60*a*c*d^2*e^2 + 42*a*c*d^2*e^2*m + 6*a*c*d^2*e^2*m^2))/(e*(47*m + 12*m^2 + m^3 + 60)) + (c^2*d^2*e^2*x^5*(7*m + m^2 + 12))/(47*m + 12*m^2 + m^3 + 60) + (c*d*e*x^4*(m + 3)*(10*a*e^2 + 10*c*d^2 + 2*a*e^2*m + 3*c*d^2*m))/(47*m + 12*m^2 + m^3 + 60))","B"
2086,1,141,52,0.744785,"\text{Not used}","int((d + e*x)^m*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","{\left(d+e\,x\right)}^m\,\left(\frac{x^2\,\left(3\,a\,e^2+3\,c\,d^2+a\,e^2\,m+2\,c\,d^2\,m\right)}{m^2+5\,m+6}+\frac{d^2\,\left(3\,a\,e^2-c\,d^2+a\,e^2\,m\right)}{e^2\,\left(m^2+5\,m+6\right)}+\frac{d\,x\,\left(6\,a\,e^2+2\,a\,e^2\,m+c\,d^2\,m\right)}{e\,\left(m^2+5\,m+6\right)}+\frac{c\,d\,e\,x^3\,\left(m+2\right)}{m^2+5\,m+6}\right)","Not used",1,"(d + e*x)^m*((x^2*(3*a*e^2 + 3*c*d^2 + a*e^2*m + 2*c*d^2*m))/(5*m + m^2 + 6) + (d^2*(3*a*e^2 - c*d^2 + a*e^2*m))/(e^2*(5*m + m^2 + 6)) + (d*x*(6*a*e^2 + 2*a*e^2*m + c*d^2*m))/(e*(5*m + m^2 + 6)) + (c*d*e*x^3*(m + 2))/(5*m + m^2 + 6))","B"
2087,0,-1,54,0.000000,"\text{Not used}","int((d + e*x)^m/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2),x)","\int \frac{{\left(d+e\,x\right)}^m}{c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e} \,d x","Not used",1,"int((d + e*x)^m/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2), x)","F"
2088,0,-1,61,0.000000,"\text{Not used}","int((d + e*x)^m/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2,x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^2} \,d x","Not used",1,"int((d + e*x)^m/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^2, x)","F"
2089,0,-1,64,0.000000,"\text{Not used}","int((d + e*x)^m/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3,x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^3} \,d x","Not used",1,"int((d + e*x)^m/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^3, x)","F"
2090,0,-1,65,0.000000,"\text{Not used}","int((d + e*x)^m/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^4,x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^4} \,d x","Not used",1,"int((d + e*x)^m/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^4, x)","F"
2091,0,-1,100,0.000000,"\text{Not used}","int((d + e*x)^m*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p,x)","\int {\left(d+e\,x\right)}^m\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^p \,d x","Not used",1,"int((d + e*x)^m*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p, x)","F"
2092,0,-1,95,0.000000,"\text{Not used}","int((d + e*x)^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p,x)","\int {\left(d+e\,x\right)}^3\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^p \,d x","Not used",1,"int((d + e*x)^3*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p, x)","F"
2093,0,-1,95,0.000000,"\text{Not used}","int((d + e*x)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p,x)","\int {\left(d+e\,x\right)}^2\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^p \,d x","Not used",1,"int((d + e*x)^2*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p, x)","F"
2094,0,-1,95,0.000000,"\text{Not used}","int((d + e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p,x)","\int \left(d+e\,x\right)\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^p \,d x","Not used",1,"int((d + e*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p, x)","F"
2095,0,-1,113,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p,x)","\int {\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^p \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p, x)","F"
2096,0,-1,93,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p/(d + e*x),x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^p}{d+e\,x} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p/(d + e*x), x)","F"
2097,0,-1,92,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p/(d + e*x)^2,x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^p}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p/(d + e*x)^2, x)","F"
2098,0,-1,96,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p/(d + e*x)^3,x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^p}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p/(d + e*x)^3, x)","F"
2099,0,-1,113,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p/(d + e*x)^(2*p),x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^p}{{\left(d+e\,x\right)}^{2\,p}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p/(d + e*x)^(2*p), x)","F"
2100,0,-1,107,0.000000,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p/(d + e*x)^(2*p + 1),x)","\int \frac{{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^p}{{\left(d+e\,x\right)}^{2\,p+1}} \,d x","Not used",1,"int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p/(d + e*x)^(2*p + 1), x)","F"
2101,1,150,60,0.851058,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p/(d + e*x)^(2*p + 2),x)","-\left(\frac{x\,\left(c\,d^2+a\,e^2\right)}{\left(a\,e^2-c\,d^2\right)\,\left(p+1\right)\,{\left(d+e\,x\right)}^{2\,p+2}}+\frac{a\,d\,e}{\left(a\,e^2-c\,d^2\right)\,\left(p+1\right)\,{\left(d+e\,x\right)}^{2\,p+2}}+\frac{c\,d\,e\,x^2}{\left(a\,e^2-c\,d^2\right)\,\left(p+1\right)\,{\left(d+e\,x\right)}^{2\,p+2}}\right)\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^p","Not used",1,"-((x*(a*e^2 + c*d^2))/((a*e^2 - c*d^2)*(p + 1)*(d + e*x)^(2*p + 2)) + (a*d*e)/((a*e^2 - c*d^2)*(p + 1)*(d + e*x)^(2*p + 2)) + (c*d*e*x^2)/((a*e^2 - c*d^2)*(p + 1)*(d + e*x)^(2*p + 2)))*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p","B"
2102,1,293,128,0.978437,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p/(d + e*x)^(2*p + 3),x)","{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^p\,\left(\frac{x\,\left(2\,c^2\,d^4-a^2\,e^4-a^2\,e^4\,p+c^2\,d^4\,p+2\,a\,c\,d^2\,e^2\right)}{{\left(a\,e^2-c\,d^2\right)}^2\,{\left(d+e\,x\right)}^{2\,p+3}\,\left(p^2+3\,p+2\right)}+\frac{c^2\,d^2\,e^2\,x^3}{{\left(a\,e^2-c\,d^2\right)}^2\,{\left(d+e\,x\right)}^{2\,p+3}\,\left(p^2+3\,p+2\right)}-\frac{a\,d\,e\,\left(a\,e^2-2\,c\,d^2+a\,e^2\,p-c\,d^2\,p\right)}{{\left(a\,e^2-c\,d^2\right)}^2\,{\left(d+e\,x\right)}^{2\,p+3}\,\left(p^2+3\,p+2\right)}+\frac{c\,d\,e\,x^2\,\left(3\,c\,d^2-a\,e^2\,p+c\,d^2\,p\right)}{{\left(a\,e^2-c\,d^2\right)}^2\,{\left(d+e\,x\right)}^{2\,p+3}\,\left(p^2+3\,p+2\right)}\right)","Not used",1,"(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p*((x*(2*c^2*d^4 - a^2*e^4 - a^2*e^4*p + c^2*d^4*p + 2*a*c*d^2*e^2))/((a*e^2 - c*d^2)^2*(d + e*x)^(2*p + 3)*(3*p + p^2 + 2)) + (c^2*d^2*e^2*x^3)/((a*e^2 - c*d^2)^2*(d + e*x)^(2*p + 3)*(3*p + p^2 + 2)) - (a*d*e*(a*e^2 - 2*c*d^2 + a*e^2*p - c*d^2*p))/((a*e^2 - c*d^2)^2*(d + e*x)^(2*p + 3)*(3*p + p^2 + 2)) + (c*d*e*x^2*(3*c*d^2 - a*e^2*p + c*d^2*p))/((a*e^2 - c*d^2)^2*(d + e*x)^(2*p + 3)*(3*p + p^2 + 2)))","B"
2103,1,595,206,1.355559,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p/(d + e*x)^(2*p + 4),x)","-{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^p\,\left(\frac{x\,\left(a^3\,e^6\,p^2+3\,a^3\,e^6\,p+2\,a^3\,e^6-a^2\,c\,d^2\,e^4\,p^2-7\,a^2\,c\,d^2\,e^4\,p-6\,a^2\,c\,d^2\,e^4-a\,c^2\,d^4\,e^2\,p^2-a\,c^2\,d^4\,e^2\,p+6\,a\,c^2\,d^4\,e^2+c^3\,d^6\,p^2+5\,c^3\,d^6\,p+6\,c^3\,d^6\right)}{{\left(a\,e^2-c\,d^2\right)}^3\,{\left(d+e\,x\right)}^{2\,p+4}\,\left(p^3+6\,p^2+11\,p+6\right)}+\frac{2\,c^3\,d^3\,e^3\,x^4}{{\left(a\,e^2-c\,d^2\right)}^3\,{\left(d+e\,x\right)}^{2\,p+4}\,\left(p^3+6\,p^2+11\,p+6\right)}+\frac{a\,d\,e\,\left(a^2\,e^4\,p^2+3\,a^2\,e^4\,p+2\,a^2\,e^4-2\,a\,c\,d^2\,e^2\,p^2-8\,a\,c\,d^2\,e^2\,p-6\,a\,c\,d^2\,e^2+c^2\,d^4\,p^2+5\,c^2\,d^4\,p+6\,c^2\,d^4\right)}{{\left(a\,e^2-c\,d^2\right)}^3\,{\left(d+e\,x\right)}^{2\,p+4}\,\left(p^3+6\,p^2+11\,p+6\right)}+\frac{c\,d\,e\,x^2\,\left(a^2\,e^4\,p^2+a^2\,e^4\,p-2\,a\,c\,d^2\,e^2\,p^2-8\,a\,c\,d^2\,e^2\,p+c^2\,d^4\,p^2+7\,c^2\,d^4\,p+12\,c^2\,d^4\right)}{{\left(a\,e^2-c\,d^2\right)}^3\,{\left(d+e\,x\right)}^{2\,p+4}\,\left(p^3+6\,p^2+11\,p+6\right)}+\frac{2\,c^2\,d^2\,e^2\,x^3\,\left(4\,c\,d^2-a\,e^2\,p+c\,d^2\,p\right)}{{\left(a\,e^2-c\,d^2\right)}^3\,{\left(d+e\,x\right)}^{2\,p+4}\,\left(p^3+6\,p^2+11\,p+6\right)}\right)","Not used",1,"-(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p*((x*(2*a^3*e^6 + 6*c^3*d^6 + 3*a^3*e^6*p + 5*c^3*d^6*p + a^3*e^6*p^2 + c^3*d^6*p^2 + 6*a*c^2*d^4*e^2 - 6*a^2*c*d^2*e^4 - a*c^2*d^4*e^2*p - 7*a^2*c*d^2*e^4*p - a*c^2*d^4*e^2*p^2 - a^2*c*d^2*e^4*p^2))/((a*e^2 - c*d^2)^3*(d + e*x)^(2*p + 4)*(11*p + 6*p^2 + p^3 + 6)) + (2*c^3*d^3*e^3*x^4)/((a*e^2 - c*d^2)^3*(d + e*x)^(2*p + 4)*(11*p + 6*p^2 + p^3 + 6)) + (a*d*e*(2*a^2*e^4 + 6*c^2*d^4 + 3*a^2*e^4*p + 5*c^2*d^4*p + a^2*e^4*p^2 + c^2*d^4*p^2 - 6*a*c*d^2*e^2 - 8*a*c*d^2*e^2*p - 2*a*c*d^2*e^2*p^2))/((a*e^2 - c*d^2)^3*(d + e*x)^(2*p + 4)*(11*p + 6*p^2 + p^3 + 6)) + (c*d*e*x^2*(12*c^2*d^4 + a^2*e^4*p + 7*c^2*d^4*p + a^2*e^4*p^2 + c^2*d^4*p^2 - 8*a*c*d^2*e^2*p - 2*a*c*d^2*e^2*p^2))/((a*e^2 - c*d^2)^3*(d + e*x)^(2*p + 4)*(11*p + 6*p^2 + p^3 + 6)) + (2*c^2*d^2*e^2*x^3*(4*c*d^2 - a*e^2*p + c*d^2*p))/((a*e^2 - c*d^2)^3*(d + e*x)^(2*p + 4)*(11*p + 6*p^2 + p^3 + 6)))","B"
2104,1,1036,288,2.064958,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p/(d + e*x)^(2*p + 5),x)","{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^p\,\left(\frac{6\,c^4\,d^4\,e^4\,x^5}{{\left(a\,e^2-c\,d^2\right)}^4\,{\left(d+e\,x\right)}^{2\,p+5}\,\left(p^4+10\,p^3+35\,p^2+50\,p+24\right)}-\frac{x\,\left(a^4\,e^8\,p^3+6\,a^4\,e^8\,p^2+11\,a^4\,e^8\,p+6\,a^4\,e^8-2\,a^3\,c\,d^2\,e^6\,p^3-18\,a^3\,c\,d^2\,e^6\,p^2-40\,a^3\,c\,d^2\,e^6\,p-24\,a^3\,c\,d^2\,e^6+9\,a^2\,c^2\,d^4\,e^4\,p^2+45\,a^2\,c^2\,d^4\,e^4\,p+36\,a^2\,c^2\,d^4\,e^4+2\,a\,c^3\,d^6\,e^2\,p^3+12\,a\,c^3\,d^6\,e^2\,p^2+10\,a\,c^3\,d^6\,e^2\,p-24\,a\,c^3\,d^6\,e^2-c^4\,d^8\,p^3-9\,c^4\,d^8\,p^2-26\,c^4\,d^8\,p-24\,c^4\,d^8\right)}{{\left(a\,e^2-c\,d^2\right)}^4\,{\left(d+e\,x\right)}^{2\,p+5}\,\left(p^4+10\,p^3+35\,p^2+50\,p+24\right)}-\frac{a\,d\,e\,\left(a^3\,e^6\,p^3+6\,a^3\,e^6\,p^2+11\,a^3\,e^6\,p+6\,a^3\,e^6-3\,a^2\,c\,d^2\,e^4\,p^3-21\,a^2\,c\,d^2\,e^4\,p^2-42\,a^2\,c\,d^2\,e^4\,p-24\,a^2\,c\,d^2\,e^4+3\,a\,c^2\,d^4\,e^2\,p^3+24\,a\,c^2\,d^4\,e^2\,p^2+57\,a\,c^2\,d^4\,e^2\,p+36\,a\,c^2\,d^4\,e^2-c^3\,d^6\,p^3-9\,c^3\,d^6\,p^2-26\,c^3\,d^6\,p-24\,c^3\,d^6\right)}{{\left(a\,e^2-c\,d^2\right)}^4\,{\left(d+e\,x\right)}^{2\,p+5}\,\left(p^4+10\,p^3+35\,p^2+50\,p+24\right)}+\frac{6\,c^3\,d^3\,e^3\,x^4\,\left(5\,c\,d^2-a\,e^2\,p+c\,d^2\,p\right)}{{\left(a\,e^2-c\,d^2\right)}^4\,{\left(d+e\,x\right)}^{2\,p+5}\,\left(p^4+10\,p^3+35\,p^2+50\,p+24\right)}+\frac{3\,c^2\,d^2\,e^2\,x^3\,\left(a^2\,e^4\,p^2+a^2\,e^4\,p-2\,a\,c\,d^2\,e^2\,p^2-10\,a\,c\,d^2\,e^2\,p+c^2\,d^4\,p^2+9\,c^2\,d^4\,p+20\,c^2\,d^4\right)}{{\left(a\,e^2-c\,d^2\right)}^4\,{\left(d+e\,x\right)}^{2\,p+5}\,\left(p^4+10\,p^3+35\,p^2+50\,p+24\right)}+\frac{c\,d\,e\,x^2\,\left(-a^3\,e^6\,p^3-3\,a^3\,e^6\,p^2-2\,a^3\,e^6\,p+3\,a^2\,c\,d^2\,e^4\,p^3+18\,a^2\,c\,d^2\,e^4\,p^2+15\,a^2\,c\,d^2\,e^4\,p-3\,a\,c^2\,d^4\,e^2\,p^3-27\,a\,c^2\,d^4\,e^2\,p^2-60\,a\,c^2\,d^4\,e^2\,p+c^3\,d^6\,p^3+12\,c^3\,d^6\,p^2+47\,c^3\,d^6\,p+60\,c^3\,d^6\right)}{{\left(a\,e^2-c\,d^2\right)}^4\,{\left(d+e\,x\right)}^{2\,p+5}\,\left(p^4+10\,p^3+35\,p^2+50\,p+24\right)}\right)","Not used",1,"(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p*((6*c^4*d^4*e^4*x^5)/((a*e^2 - c*d^2)^4*(d + e*x)^(2*p + 5)*(50*p + 35*p^2 + 10*p^3 + p^4 + 24)) - (x*(6*a^4*e^8 - 24*c^4*d^8 + 11*a^4*e^8*p - 26*c^4*d^8*p + 6*a^4*e^8*p^2 + a^4*e^8*p^3 - 9*c^4*d^8*p^2 - c^4*d^8*p^3 - 24*a*c^3*d^6*e^2 - 24*a^3*c*d^2*e^6 + 36*a^2*c^2*d^4*e^4 + 9*a^2*c^2*d^4*e^4*p^2 + 10*a*c^3*d^6*e^2*p - 40*a^3*c*d^2*e^6*p + 45*a^2*c^2*d^4*e^4*p + 12*a*c^3*d^6*e^2*p^2 - 18*a^3*c*d^2*e^6*p^2 + 2*a*c^3*d^6*e^2*p^3 - 2*a^3*c*d^2*e^6*p^3))/((a*e^2 - c*d^2)^4*(d + e*x)^(2*p + 5)*(50*p + 35*p^2 + 10*p^3 + p^4 + 24)) - (a*d*e*(6*a^3*e^6 - 24*c^3*d^6 + 11*a^3*e^6*p - 26*c^3*d^6*p + 6*a^3*e^6*p^2 + a^3*e^6*p^3 - 9*c^3*d^6*p^2 - c^3*d^6*p^3 + 36*a*c^2*d^4*e^2 - 24*a^2*c*d^2*e^4 + 57*a*c^2*d^4*e^2*p - 42*a^2*c*d^2*e^4*p + 24*a*c^2*d^4*e^2*p^2 - 21*a^2*c*d^2*e^4*p^2 + 3*a*c^2*d^4*e^2*p^3 - 3*a^2*c*d^2*e^4*p^3))/((a*e^2 - c*d^2)^4*(d + e*x)^(2*p + 5)*(50*p + 35*p^2 + 10*p^3 + p^4 + 24)) + (6*c^3*d^3*e^3*x^4*(5*c*d^2 - a*e^2*p + c*d^2*p))/((a*e^2 - c*d^2)^4*(d + e*x)^(2*p + 5)*(50*p + 35*p^2 + 10*p^3 + p^4 + 24)) + (3*c^2*d^2*e^2*x^3*(20*c^2*d^4 + a^2*e^4*p + 9*c^2*d^4*p + a^2*e^4*p^2 + c^2*d^4*p^2 - 10*a*c*d^2*e^2*p - 2*a*c*d^2*e^2*p^2))/((a*e^2 - c*d^2)^4*(d + e*x)^(2*p + 5)*(50*p + 35*p^2 + 10*p^3 + p^4 + 24)) + (c*d*e*x^2*(60*c^3*d^6 - 2*a^3*e^6*p + 47*c^3*d^6*p - 3*a^3*e^6*p^2 - a^3*e^6*p^3 + 12*c^3*d^6*p^2 + c^3*d^6*p^3 - 60*a*c^2*d^4*e^2*p + 15*a^2*c*d^2*e^4*p - 27*a*c^2*d^4*e^2*p^2 + 18*a^2*c*d^2*e^4*p^2 - 3*a*c^2*d^4*e^2*p^3 + 3*a^2*c*d^2*e^4*p^3))/((a*e^2 - c*d^2)^4*(d + e*x)^(2*p + 5)*(50*p + 35*p^2 + 10*p^3 + p^4 + 24)))","B"
2105,1,57,54,0.800999,"\text{Not used}","int((d + e*x)^m/(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^m,x)","-\frac{\left(a\,e+c\,d\,x\right)\,{\left(d+e\,x\right)}^m}{c\,d\,\left(m-1\right)\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^m}","Not used",1,"-((a*e + c*d*x)*(d + e*x)^m)/(c*d*(m - 1)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^m)","B"
2106,1,56,52,0.748946,"\text{Not used}","int((x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p/(d + e*x)^p,x)","\frac{\left(a\,e+c\,d\,x\right)\,{\left(c\,d\,e\,x^2+\left(c\,d^2+a\,e^2\right)\,x+a\,d\,e\right)}^p}{c\,d\,\left(p+1\right)\,{\left(d+e\,x\right)}^p}","Not used",1,"((a*e + c*d*x)*(x*(a*e^2 + c*d^2) + a*d*e + c*d*e*x^2)^p)/(c*d*(p + 1)*(d + e*x)^p)","B"
2107,1,131,69,0.652916,"\text{Not used}","int((d + e*x)^4*(a + b*x + c*x^2),x)","x^2\,\left(\frac{b\,d^4}{2}+2\,a\,e\,d^3\right)+x^6\,\left(\frac{b\,e^4}{6}+\frac{2\,c\,d\,e^3}{3}\right)+x^3\,\left(\frac{c\,d^4}{3}+\frac{4\,b\,d^3\,e}{3}+2\,a\,d^2\,e^2\right)+x^5\,\left(\frac{6\,c\,d^2\,e^2}{5}+\frac{4\,b\,d\,e^3}{5}+\frac{a\,e^4}{5}\right)+\frac{c\,e^4\,x^7}{7}+a\,d^4\,x+\frac{d\,e\,x^4\,\left(2\,c\,d^2+3\,b\,d\,e+2\,a\,e^2\right)}{2}","Not used",1,"x^2*((b*d^4)/2 + 2*a*d^3*e) + x^6*((b*e^4)/6 + (2*c*d*e^3)/3) + x^3*((c*d^4)/3 + 2*a*d^2*e^2 + (4*b*d^3*e)/3) + x^5*((a*e^4)/5 + (6*c*d^2*e^2)/5 + (4*b*d*e^3)/5) + (c*e^4*x^7)/7 + a*d^4*x + (d*e*x^4*(2*a*e^2 + 2*c*d^2 + 3*b*d*e))/2","B"
2108,1,100,69,0.045977,"\text{Not used}","int((d + e*x)^3*(a + b*x + c*x^2),x)","x^2\,\left(\frac{b\,d^3}{2}+\frac{3\,a\,e\,d^2}{2}\right)+x^5\,\left(\frac{b\,e^3}{5}+\frac{3\,c\,d\,e^2}{5}\right)+x^3\,\left(\frac{c\,d^3}{3}+b\,d^2\,e+a\,d\,e^2\right)+x^4\,\left(\frac{3\,c\,d^2\,e}{4}+\frac{3\,b\,d\,e^2}{4}+\frac{a\,e^3}{4}\right)+\frac{c\,e^3\,x^6}{6}+a\,d^3\,x","Not used",1,"x^2*((b*d^3)/2 + (3*a*d^2*e)/2) + x^5*((b*e^3)/5 + (3*c*d*e^2)/5) + x^3*((c*d^3)/3 + a*d*e^2 + b*d^2*e) + x^4*((a*e^3)/4 + (3*b*d*e^2)/4 + (3*c*d^2*e)/4) + (c*e^3*x^6)/6 + a*d^3*x","B"
2109,1,69,69,0.622792,"\text{Not used}","int((d + e*x)^2*(a + b*x + c*x^2),x)","x^3\,\left(\frac{c\,d^2}{3}+\frac{2\,b\,d\,e}{3}+\frac{a\,e^2}{3}\right)+x^2\,\left(\frac{b\,d^2}{2}+a\,e\,d\right)+x^4\,\left(\frac{b\,e^2}{4}+\frac{c\,d\,e}{2}\right)+\frac{c\,e^2\,x^5}{5}+a\,d^2\,x","Not used",1,"x^3*((a*e^2)/3 + (c*d^2)/3 + (2*b*d*e)/3) + x^2*((b*d^2)/2 + a*d*e) + x^4*((b*e^2)/4 + (c*d*e)/2) + (c*e^2*x^5)/5 + a*d^2*x","B"
2110,1,38,42,0.044696,"\text{Not used}","int((d + e*x)*(a + b*x + c*x^2),x)","\frac{c\,e\,x^4}{4}+\left(\frac{b\,e}{3}+\frac{c\,d}{3}\right)\,x^3+\left(\frac{a\,e}{2}+\frac{b\,d}{2}\right)\,x^2+a\,d\,x","Not used",1,"x^2*((a*e)/2 + (b*d)/2) + x^3*((b*e)/3 + (c*d)/3) + a*d*x + (c*e*x^4)/4","B"
2111,1,16,20,0.025645,"\text{Not used}","int(a + b*x + c*x^2,x)","\frac{c\,x^3}{3}+\frac{b\,x^2}{2}+a\,x","Not used",1,"a*x + (b*x^2)/2 + (c*x^3)/3","B"
2112,1,51,52,0.658059,"\text{Not used}","int((a + b*x + c*x^2)/(d + e*x),x)","x\,\left(\frac{b}{e}-\frac{c\,d}{e^2}\right)+\frac{c\,x^2}{2\,e}+\frac{\ln\left(d+e\,x\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}{e^3}","Not used",1,"x*(b/e - (c*d)/e^2) + (c*x^2)/(2*e) + (log(d + e*x)*(a*e^2 + c*d^2 - b*d*e))/e^3","B"
2113,1,59,55,0.656121,"\text{Not used}","int((a + b*x + c*x^2)/(d + e*x)^2,x)","\frac{\ln\left(d+e\,x\right)\,\left(b\,e-2\,c\,d\right)}{e^3}-\frac{c\,d^2-b\,d\,e+a\,e^2}{e\,\left(x\,e^3+d\,e^2\right)}+\frac{c\,x}{e^2}","Not used",1,"(log(d + e*x)*(b*e - 2*c*d))/e^3 - (a*e^2 + c*d^2 - b*d*e)/(e*(d*e^2 + e^3*x)) + (c*x)/e^2","B"
2114,1,67,62,0.065317,"\text{Not used}","int((a + b*x + c*x^2)/(d + e*x)^3,x)","\frac{c\,\ln\left(d+e\,x\right)}{e^3}-\frac{\frac{-3\,c\,d^2+b\,d\,e+a\,e^2}{2\,e^3}+\frac{x\,\left(b\,e-2\,c\,d\right)}{e^2}}{d^2+2\,d\,e\,x+e^2\,x^2}","Not used",1,"(c*log(d + e*x))/e^3 - ((a*e^2 - 3*c*d^2 + b*d*e)/(2*e^3) + (x*(b*e - 2*c*d))/e^2)/(d^2 + e^2*x^2 + 2*d*e*x)","B"
2115,1,76,67,0.043051,"\text{Not used}","int((a + b*x + c*x^2)/(d + e*x)^4,x)","-\frac{\frac{2\,c\,d^2+b\,d\,e+2\,a\,e^2}{6\,e^3}+\frac{x\,\left(b\,e+2\,c\,d\right)}{2\,e^2}+\frac{c\,x^2}{e}}{d^3+3\,d^2\,e\,x+3\,d\,e^2\,x^2+e^3\,x^3}","Not used",1,"-((2*a*e^2 + 2*c*d^2 + b*d*e)/(6*e^3) + (x*(b*e + 2*c*d))/(2*e^2) + (c*x^2)/e)/(d^3 + e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x)","B"
2116,1,86,69,0.646791,"\text{Not used}","int((a + b*x + c*x^2)/(d + e*x)^5,x)","-\frac{\frac{c\,d^2+b\,d\,e+3\,a\,e^2}{12\,e^3}+\frac{x\,\left(b\,e+c\,d\right)}{3\,e^2}+\frac{c\,x^2}{2\,e}}{d^4+4\,d^3\,e\,x+6\,d^2\,e^2\,x^2+4\,d\,e^3\,x^3+e^4\,x^4}","Not used",1,"-((3*a*e^2 + c*d^2 + b*d*e)/(12*e^3) + (x*(b*e + c*d))/(3*e^2) + (c*x^2)/(2*e))/(d^4 + e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x)","B"
2117,1,101,69,0.066093,"\text{Not used}","int((a + b*x + c*x^2)/(d + e*x)^6,x)","-\frac{\frac{2\,c\,d^2+3\,b\,d\,e+12\,a\,e^2}{60\,e^3}+\frac{x\,\left(3\,b\,e+2\,c\,d\right)}{12\,e^2}+\frac{c\,x^2}{3\,e}}{d^5+5\,d^4\,e\,x+10\,d^3\,e^2\,x^2+10\,d^2\,e^3\,x^3+5\,d\,e^4\,x^4+e^5\,x^5}","Not used",1,"-((12*a*e^2 + 2*c*d^2 + 3*b*d*e)/(60*e^3) + (x*(3*b*e + 2*c*d))/(12*e^2) + (c*x^2)/(3*e))/(d^5 + e^5*x^5 + 5*d*e^4*x^4 + 10*d^3*e^2*x^2 + 10*d^2*e^3*x^3 + 5*d^4*e*x)","B"
2118,1,283,156,0.106485,"\text{Not used}","int((d + e*x)^4*(a + b*x + c*x^2)^2,x)","x^4\,\left(a^2\,d\,e^3+3\,a\,b\,d^2\,e^2+2\,c\,a\,d^3\,e+b^2\,d^3\,e+\frac{c\,b\,d^4}{2}\right)+x^6\,\left(\frac{2\,b^2\,d\,e^3}{3}+2\,b\,c\,d^2\,e^2+\frac{a\,b\,e^4}{3}+\frac{2\,c^2\,d^3\,e}{3}+\frac{4\,a\,c\,d\,e^3}{3}\right)+x^5\,\left(\frac{a^2\,e^4}{5}+\frac{8\,a\,b\,d\,e^3}{5}+\frac{12\,a\,c\,d^2\,e^2}{5}+\frac{6\,b^2\,d^2\,e^2}{5}+\frac{8\,b\,c\,d^3\,e}{5}+\frac{c^2\,d^4}{5}\right)+x^3\,\left(2\,a^2\,d^2\,e^2+\frac{8\,a\,b\,d^3\,e}{3}+\frac{2\,c\,a\,d^4}{3}+\frac{b^2\,d^4}{3}\right)+x^7\,\left(\frac{b^2\,e^4}{7}+\frac{8\,b\,c\,d\,e^3}{7}+\frac{6\,c^2\,d^2\,e^2}{7}+\frac{2\,a\,c\,e^4}{7}\right)+a^2\,d^4\,x+\frac{c^2\,e^4\,x^9}{9}+a\,d^3\,x^2\,\left(2\,a\,e+b\,d\right)+\frac{c\,e^3\,x^8\,\left(b\,e+2\,c\,d\right)}{4}","Not used",1,"x^4*(a^2*d*e^3 + b^2*d^3*e + (b*c*d^4)/2 + 2*a*c*d^3*e + 3*a*b*d^2*e^2) + x^6*((2*b^2*d*e^3)/3 + (2*c^2*d^3*e)/3 + (a*b*e^4)/3 + (4*a*c*d*e^3)/3 + 2*b*c*d^2*e^2) + x^5*((a^2*e^4)/5 + (c^2*d^4)/5 + (6*b^2*d^2*e^2)/5 + (8*a*b*d*e^3)/5 + (8*b*c*d^3*e)/5 + (12*a*c*d^2*e^2)/5) + x^3*((b^2*d^4)/3 + 2*a^2*d^2*e^2 + (2*a*c*d^4)/3 + (8*a*b*d^3*e)/3) + x^7*((b^2*e^4)/7 + (6*c^2*d^2*e^2)/7 + (2*a*c*e^4)/7 + (8*b*c*d*e^3)/7) + a^2*d^4*x + (c^2*e^4*x^9)/9 + a*d^3*x^2*(2*a*e + b*d) + (c*e^3*x^8*(b*e + 2*c*d))/4","B"
2119,1,218,156,0.672997,"\text{Not used}","int((d + e*x)^3*(a + b*x + c*x^2)^2,x)","x^4\,\left(\frac{a^2\,e^3}{4}+\frac{3\,a\,b\,d\,e^2}{2}+\frac{3\,c\,a\,d^2\,e}{2}+\frac{3\,b^2\,d^2\,e}{4}+\frac{c\,b\,d^3}{2}\right)+x^5\,\left(\frac{3\,b^2\,d\,e^2}{5}+\frac{6\,b\,c\,d^2\,e}{5}+\frac{2\,a\,b\,e^3}{5}+\frac{c^2\,d^3}{5}+\frac{6\,a\,c\,d\,e^2}{5}\right)+x^3\,\left(a^2\,d\,e^2+2\,a\,b\,d^2\,e+\frac{2\,c\,a\,d^3}{3}+\frac{b^2\,d^3}{3}\right)+x^6\,\left(\frac{b^2\,e^3}{6}+b\,c\,d\,e^2+\frac{c^2\,d^2\,e}{2}+\frac{a\,c\,e^3}{3}\right)+a^2\,d^3\,x+\frac{c^2\,e^3\,x^8}{8}+\frac{a\,d^2\,x^2\,\left(3\,a\,e+2\,b\,d\right)}{2}+\frac{c\,e^2\,x^7\,\left(2\,b\,e+3\,c\,d\right)}{7}","Not used",1,"x^4*((a^2*e^3)/4 + (3*b^2*d^2*e)/4 + (b*c*d^3)/2 + (3*a*b*d*e^2)/2 + (3*a*c*d^2*e)/2) + x^5*((c^2*d^3)/5 + (3*b^2*d*e^2)/5 + (2*a*b*e^3)/5 + (6*a*c*d*e^2)/5 + (6*b*c*d^2*e)/5) + x^3*((b^2*d^3)/3 + a^2*d*e^2 + (2*a*c*d^3)/3 + 2*a*b*d^2*e) + x^6*((b^2*e^3)/6 + (c^2*d^2*e)/2 + (a*c*e^3)/3 + b*c*d*e^2) + a^2*d^3*x + (c^2*e^3*x^8)/8 + (a*d^2*x^2*(3*a*e + 2*b*d))/2 + (c*e^2*x^7*(2*b*e + 3*c*d))/7","B"
2120,1,146,156,0.064242,"\text{Not used}","int((d + e*x)^2*(a + b*x + c*x^2)^2,x)","x^3\,\left(\frac{a^2\,e^2}{3}+\frac{4\,a\,b\,d\,e}{3}+\frac{2\,c\,a\,d^2}{3}+\frac{b^2\,d^2}{3}\right)+x^5\,\left(\frac{b^2\,e^2}{5}+\frac{4\,b\,c\,d\,e}{5}+\frac{c^2\,d^2}{5}+\frac{2\,a\,c\,e^2}{5}\right)+x^4\,\left(\frac{b^2\,d\,e}{2}+\frac{c\,b\,d^2}{2}+\frac{a\,b\,e^2}{2}+a\,c\,d\,e\right)+a^2\,d^2\,x+\frac{c^2\,e^2\,x^7}{7}+a\,d\,x^2\,\left(a\,e+b\,d\right)+\frac{c\,e\,x^6\,\left(b\,e+c\,d\right)}{3}","Not used",1,"x^3*((a^2*e^2)/3 + (b^2*d^2)/3 + (2*a*c*d^2)/3 + (4*a*b*d*e)/3) + x^5*((b^2*e^2)/5 + (c^2*d^2)/5 + (2*a*c*e^2)/5 + (4*b*c*d*e)/5) + x^4*((a*b*e^2)/2 + (b*c*d^2)/2 + (b^2*d*e)/2 + a*c*d*e) + a^2*d^2*x + (c^2*e^2*x^7)/7 + a*d*x^2*(a*e + b*d) + (c*e*x^6*(b*e + c*d))/3","B"
2121,1,89,96,0.636099,"\text{Not used}","int((d + e*x)*(a + b*x + c*x^2)^2,x)","x^3\,\left(\frac{d\,b^2}{3}+\frac{2\,a\,e\,b}{3}+\frac{2\,a\,c\,d}{3}\right)+x^4\,\left(\frac{e\,b^2}{4}+\frac{c\,d\,b}{2}+\frac{a\,c\,e}{2}\right)+x^2\,\left(\frac{e\,a^2}{2}+b\,d\,a\right)+x^5\,\left(\frac{d\,c^2}{5}+\frac{2\,b\,e\,c}{5}\right)+\frac{c^2\,e\,x^6}{6}+a^2\,d\,x","Not used",1,"x^3*((b^2*d)/3 + (2*a*b*e)/3 + (2*a*c*d)/3) + x^4*((b^2*e)/4 + (a*c*e)/2 + (b*c*d)/2) + x^2*((a^2*e)/2 + a*b*d) + x^5*((c^2*d)/5 + (2*b*c*e)/5) + (c^2*e*x^6)/6 + a^2*d*x","B"
2122,1,41,46,0.021198,"\text{Not used}","int((a + b*x + c*x^2)^2,x)","a^2\,x+x^3\,\left(\frac{b^2}{3}+\frac{2\,a\,c}{3}\right)+\frac{c^2\,x^5}{5}+a\,b\,x^2+\frac{b\,c\,x^4}{2}","Not used",1,"a^2*x + x^3*((2*a*c)/3 + b^2/3) + (c^2*x^5)/5 + a*b*x^2 + (b*c*x^4)/2","B"
2123,1,185,129,0.052854,"\text{Not used}","int((a + b*x + c*x^2)^2/(d + e*x),x)","x^2\,\left(\frac{b^2+2\,a\,c}{2\,e}+\frac{d\,\left(\frac{c^2\,d}{e^2}-\frac{2\,b\,c}{e}\right)}{2\,e}\right)-x\,\left(\frac{d\,\left(\frac{b^2+2\,a\,c}{e}+\frac{d\,\left(\frac{c^2\,d}{e^2}-\frac{2\,b\,c}{e}\right)}{e}\right)}{e}-\frac{2\,a\,b}{e}\right)-x^3\,\left(\frac{c^2\,d}{3\,e^2}-\frac{2\,b\,c}{3\,e}\right)+\frac{\ln\left(d+e\,x\right)\,\left(a^2\,e^4-2\,a\,b\,d\,e^3+2\,a\,c\,d^2\,e^2+b^2\,d^2\,e^2-2\,b\,c\,d^3\,e+c^2\,d^4\right)}{e^5}+\frac{c^2\,x^4}{4\,e}","Not used",1,"x^2*((2*a*c + b^2)/(2*e) + (d*((c^2*d)/e^2 - (2*b*c)/e))/(2*e)) - x*((d*((2*a*c + b^2)/e + (d*((c^2*d)/e^2 - (2*b*c)/e))/e))/e - (2*a*b)/e) - x^3*((c^2*d)/(3*e^2) - (2*b*c)/(3*e)) + (log(d + e*x)*(a^2*e^4 + c^2*d^4 + b^2*d^2*e^2 - 2*a*b*d*e^3 - 2*b*c*d^3*e + 2*a*c*d^2*e^2))/e^5 + (c^2*x^4)/(4*e)","B"
2124,1,203,131,0.078004,"\text{Not used}","int((a + b*x + c*x^2)^2/(d + e*x)^2,x)","x\,\left(\frac{b^2+2\,a\,c}{e^2}+\frac{2\,d\,\left(\frac{2\,c^2\,d}{e^3}-\frac{2\,b\,c}{e^2}\right)}{e}-\frac{c^2\,d^2}{e^4}\right)-x^2\,\left(\frac{c^2\,d}{e^3}-\frac{b\,c}{e^2}\right)-\frac{a^2\,e^4-2\,a\,b\,d\,e^3+2\,a\,c\,d^2\,e^2+b^2\,d^2\,e^2-2\,b\,c\,d^3\,e+c^2\,d^4}{e\,\left(x\,e^5+d\,e^4\right)}-\frac{\ln\left(d+e\,x\right)\,\left(2\,b^2\,d\,e^2-6\,b\,c\,d^2\,e-2\,a\,b\,e^3+4\,c^2\,d^3+4\,a\,c\,d\,e^2\right)}{e^5}+\frac{c^2\,x^3}{3\,e^2}","Not used",1,"x*((2*a*c + b^2)/e^2 + (2*d*((2*c^2*d)/e^3 - (2*b*c)/e^2))/e - (c^2*d^2)/e^4) - x^2*((c^2*d)/e^3 - (b*c)/e^2) - (a^2*e^4 + c^2*d^4 + b^2*d^2*e^2 - 2*a*b*d*e^3 - 2*b*c*d^3*e + 2*a*c*d^2*e^2)/(e*(d*e^4 + e^5*x)) - (log(d + e*x)*(4*c^2*d^3 + 2*b^2*d*e^2 - 2*a*b*e^3 + 4*a*c*d*e^2 - 6*b*c*d^2*e))/e^5 + (c^2*x^3)/(3*e^2)","B"
2125,1,200,138,0.085964,"\text{Not used}","int((a + b*x + c*x^2)^2/(d + e*x)^3,x)","\frac{\ln\left(d+e\,x\right)\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2+2\,a\,c\,e^2\right)}{e^5}-\frac{\frac{a^2\,e^4+2\,a\,b\,d\,e^3-6\,a\,c\,d^2\,e^2-3\,b^2\,d^2\,e^2+10\,b\,c\,d^3\,e-7\,c^2\,d^4}{2\,e}-x\,\left(2\,b^2\,d\,e^2-6\,b\,c\,d^2\,e-2\,a\,b\,e^3+4\,c^2\,d^3+4\,a\,c\,d\,e^2\right)}{d^2\,e^4+2\,d\,e^5\,x+e^6\,x^2}-x\,\left(\frac{3\,c^2\,d}{e^4}-\frac{2\,b\,c}{e^3}\right)+\frac{c^2\,x^2}{2\,e^3}","Not used",1,"(log(d + e*x)*(b^2*e^2 + 6*c^2*d^2 + 2*a*c*e^2 - 6*b*c*d*e))/e^5 - ((a^2*e^4 - 7*c^2*d^4 - 3*b^2*d^2*e^2 + 2*a*b*d*e^3 + 10*b*c*d^3*e - 6*a*c*d^2*e^2)/(2*e) - x*(4*c^2*d^3 + 2*b^2*d*e^2 - 2*a*b*e^3 + 4*a*c*d*e^2 - 6*b*c*d^2*e))/(d^2*e^4 + e^6*x^2 + 2*d*e^5*x) - x*((3*c^2*d)/e^4 - (2*b*c)/e^3) + (c^2*x^2)/(2*e^3)","B"
2126,1,203,139,0.743353,"\text{Not used}","int((a + b*x + c*x^2)^2/(d + e*x)^4,x)","\frac{c^2\,x}{e^4}-\frac{\frac{a^2\,e^4+a\,b\,d\,e^3+2\,a\,c\,d^2\,e^2+b^2\,d^2\,e^2-11\,b\,c\,d^3\,e+13\,c^2\,d^4}{3\,e}+x\,\left(b^2\,d\,e^2-9\,b\,c\,d^2\,e+a\,b\,e^3+10\,c^2\,d^3+2\,a\,c\,d\,e^2\right)+x^2\,\left(b^2\,e^3-6\,b\,c\,d\,e^2+6\,c^2\,d^2\,e+2\,a\,c\,e^3\right)}{d^3\,e^4+3\,d^2\,e^5\,x+3\,d\,e^6\,x^2+e^7\,x^3}-\frac{\ln\left(d+e\,x\right)\,\left(4\,c^2\,d-2\,b\,c\,e\right)}{e^5}","Not used",1,"(c^2*x)/e^4 - ((a^2*e^4 + 13*c^2*d^4 + b^2*d^2*e^2 + a*b*d*e^3 - 11*b*c*d^3*e + 2*a*c*d^2*e^2)/(3*e) + x*(10*c^2*d^3 + b^2*d*e^2 + a*b*e^3 + 2*a*c*d*e^2 - 9*b*c*d^2*e) + x^2*(b^2*e^3 + 6*c^2*d^2*e + 2*a*c*e^3 - 6*b*c*d*e^2))/(d^3*e^4 + e^7*x^3 + 3*d^2*e^5*x + 3*d*e^6*x^2) - (log(d + e*x)*(4*c^2*d - 2*b*c*e))/e^5","B"
2127,1,186,150,0.713956,"\text{Not used}","int((a + b*x + c*x^2)^2/(d + e*x)^5,x)","\frac{c^2\,\ln\left(d+e\,x\right)}{e^5}-\frac{x^2\,\left(\frac{b^2\,e^4}{2}+3\,b\,c\,d\,e^3-9\,c^2\,d^2\,e^2+a\,c\,e^4\right)+x\,\left(\frac{b^2\,d\,e^3}{3}+2\,b\,c\,d^2\,e^2+\frac{2\,a\,b\,e^4}{3}-\frac{22\,c^2\,d^3\,e}{3}+\frac{2\,a\,c\,d\,e^3}{3}\right)-x^3\,\left(4\,c^2\,d\,e^3-2\,b\,c\,e^4\right)+\frac{a^2\,e^4}{4}-\frac{25\,c^2\,d^4}{12}+\frac{b^2\,d^2\,e^2}{12}+\frac{a\,b\,d\,e^3}{6}+\frac{b\,c\,d^3\,e}{2}+\frac{a\,c\,d^2\,e^2}{6}}{e^5\,{\left(d+e\,x\right)}^4}","Not used",1,"(c^2*log(d + e*x))/e^5 - (x^2*((b^2*e^4)/2 - 9*c^2*d^2*e^2 + a*c*e^4 + 3*b*c*d*e^3) + x*((b^2*d*e^3)/3 - (22*c^2*d^3*e)/3 + (2*a*b*e^4)/3 + (2*a*c*d*e^3)/3 + 2*b*c*d^2*e^2) - x^3*(4*c^2*d*e^3 - 2*b*c*e^4) + (a^2*e^4)/4 - (25*c^2*d^4)/12 + (b^2*d^2*e^2)/12 + (a*b*d*e^3)/6 + (b*c*d^3*e)/2 + (a*c*d^2*e^2)/6)/(e^5*(d + e*x)^4)","B"
2128,1,221,151,0.088031,"\text{Not used}","int((a + b*x + c*x^2)^2/(d + e*x)^6,x)","-\frac{\frac{6\,a^2\,e^4+3\,a\,b\,d\,e^3+2\,a\,c\,d^2\,e^2+b^2\,d^2\,e^2+3\,b\,c\,d^3\,e+6\,c^2\,d^4}{30\,e^5}+\frac{x\,\left(b^2\,d\,e^2+3\,b\,c\,d^2\,e+3\,a\,b\,e^3+6\,c^2\,d^3+2\,a\,c\,d\,e^2\right)}{6\,e^4}+\frac{c^2\,x^4}{e}+\frac{x^2\,\left(b^2\,e^2+3\,b\,c\,d\,e+6\,c^2\,d^2+2\,a\,c\,e^2\right)}{3\,e^3}+\frac{c\,x^3\,\left(b\,e+2\,c\,d\right)}{e^2}}{d^5+5\,d^4\,e\,x+10\,d^3\,e^2\,x^2+10\,d^2\,e^3\,x^3+5\,d\,e^4\,x^4+e^5\,x^5}","Not used",1,"-((6*a^2*e^4 + 6*c^2*d^4 + b^2*d^2*e^2 + 3*a*b*d*e^3 + 3*b*c*d^3*e + 2*a*c*d^2*e^2)/(30*e^5) + (x*(6*c^2*d^3 + b^2*d*e^2 + 3*a*b*e^3 + 2*a*c*d*e^2 + 3*b*c*d^2*e))/(6*e^4) + (c^2*x^4)/e + (x^2*(b^2*e^2 + 6*c^2*d^2 + 2*a*c*e^2 + 3*b*c*d*e))/(3*e^3) + (c*x^3*(b*e + 2*c*d))/e^2)/(d^5 + e^5*x^5 + 5*d*e^4*x^4 + 10*d^3*e^2*x^2 + 10*d^2*e^3*x^3 + 5*d^4*e*x)","B"
2129,1,233,156,0.711461,"\text{Not used}","int((a + b*x + c*x^2)^2/(d + e*x)^7,x)","-\frac{\frac{10\,a^2\,e^4+4\,a\,b\,d\,e^3+2\,a\,c\,d^2\,e^2+b^2\,d^2\,e^2+2\,b\,c\,d^3\,e+2\,c^2\,d^4}{60\,e^5}+\frac{x\,\left(b^2\,d\,e^2+2\,b\,c\,d^2\,e+4\,a\,b\,e^3+2\,c^2\,d^3+2\,a\,c\,d\,e^2\right)}{10\,e^4}+\frac{c^2\,x^4}{2\,e}+\frac{x^2\,\left(b^2\,e^2+2\,b\,c\,d\,e+2\,c^2\,d^2+2\,a\,c\,e^2\right)}{4\,e^3}+\frac{2\,c\,x^3\,\left(b\,e+c\,d\right)}{3\,e^2}}{d^6+6\,d^5\,e\,x+15\,d^4\,e^2\,x^2+20\,d^3\,e^3\,x^3+15\,d^2\,e^4\,x^4+6\,d\,e^5\,x^5+e^6\,x^6}","Not used",1,"-((10*a^2*e^4 + 2*c^2*d^4 + b^2*d^2*e^2 + 4*a*b*d*e^3 + 2*b*c*d^3*e + 2*a*c*d^2*e^2)/(60*e^5) + (x*(2*c^2*d^3 + b^2*d*e^2 + 4*a*b*e^3 + 2*a*c*d*e^2 + 2*b*c*d^2*e))/(10*e^4) + (c^2*x^4)/(2*e) + (x^2*(b^2*e^2 + 2*c^2*d^2 + 2*a*c*e^2 + 2*b*c*d*e))/(4*e^3) + (2*c*x^3*(b*e + c*d))/(3*e^2))/(d^6 + e^6*x^6 + 6*d*e^5*x^5 + 15*d^4*e^2*x^2 + 20*d^3*e^3*x^3 + 15*d^2*e^4*x^4 + 6*d^5*e*x)","B"
2130,1,249,156,0.117023,"\text{Not used}","int((a + b*x + c*x^2)^2/(d + e*x)^8,x)","-\frac{\frac{30\,a^2\,e^4+10\,a\,b\,d\,e^3+4\,a\,c\,d^2\,e^2+2\,b^2\,d^2\,e^2+3\,b\,c\,d^3\,e+2\,c^2\,d^4}{210\,e^5}+\frac{x\,\left(2\,b^2\,d\,e^2+3\,b\,c\,d^2\,e+10\,a\,b\,e^3+2\,c^2\,d^3+4\,a\,c\,d\,e^2\right)}{30\,e^4}+\frac{c^2\,x^4}{3\,e}+\frac{x^2\,\left(2\,b^2\,e^2+3\,b\,c\,d\,e+2\,c^2\,d^2+4\,a\,c\,e^2\right)}{10\,e^3}+\frac{c\,x^3\,\left(3\,b\,e+2\,c\,d\right)}{6\,e^2}}{d^7+7\,d^6\,e\,x+21\,d^5\,e^2\,x^2+35\,d^4\,e^3\,x^3+35\,d^3\,e^4\,x^4+21\,d^2\,e^5\,x^5+7\,d\,e^6\,x^6+e^7\,x^7}","Not used",1,"-((30*a^2*e^4 + 2*c^2*d^4 + 2*b^2*d^2*e^2 + 10*a*b*d*e^3 + 3*b*c*d^3*e + 4*a*c*d^2*e^2)/(210*e^5) + (x*(2*c^2*d^3 + 2*b^2*d*e^2 + 10*a*b*e^3 + 4*a*c*d*e^2 + 3*b*c*d^2*e))/(30*e^4) + (c^2*x^4)/(3*e) + (x^2*(2*b^2*e^2 + 2*c^2*d^2 + 4*a*c*e^2 + 3*b*c*d*e))/(10*e^3) + (c*x^3*(3*b*e + 2*c*d))/(6*e^2))/(d^7 + e^7*x^7 + 7*d*e^6*x^6 + 21*d^5*e^2*x^2 + 35*d^4*e^3*x^3 + 35*d^3*e^4*x^4 + 21*d^2*e^5*x^5 + 7*d^6*e*x)","B"
2131,1,506,272,0.778268,"\text{Not used}","int((d + e*x)^4*(a + b*x + c*x^2)^3,x)","x^4\,\left(a^3\,d\,e^3+\frac{9\,a^2\,b\,d^2\,e^2}{2}+3\,c\,a^2\,d^3\,e+3\,a\,b^2\,d^3\,e+\frac{3\,c\,a\,b\,d^4}{2}+\frac{b^3\,d^4}{4}\right)+x^8\,\left(\frac{b^3\,e^4}{8}+\frac{3\,b^2\,c\,d\,e^3}{2}+\frac{9\,b\,c^2\,d^2\,e^2}{4}+\frac{3\,a\,b\,c\,e^4}{4}+\frac{c^3\,d^3\,e}{2}+\frac{3\,a\,c^2\,d\,e^3}{2}\right)+x^6\,\left(\frac{a^2\,b\,e^4}{2}+2\,a^2\,c\,d\,e^3+2\,a\,b^2\,d\,e^3+6\,a\,b\,c\,d^2\,e^2+2\,a\,c^2\,d^3\,e+b^3\,d^2\,e^2+2\,b^2\,c\,d^3\,e+\frac{b\,c^2\,d^4}{2}\right)+x^5\,\left(\frac{a^3\,e^4}{5}+\frac{12\,a^2\,b\,d\,e^3}{5}+\frac{18\,a^2\,c\,d^2\,e^2}{5}+\frac{18\,a\,b^2\,d^2\,e^2}{5}+\frac{24\,a\,b\,c\,d^3\,e}{5}+\frac{3\,a\,c^2\,d^4}{5}+\frac{4\,b^3\,d^3\,e}{5}+\frac{3\,b^2\,c\,d^4}{5}\right)+x^7\,\left(\frac{3\,a^2\,c\,e^4}{7}+\frac{3\,a\,b^2\,e^4}{7}+\frac{24\,a\,b\,c\,d\,e^3}{7}+\frac{18\,a\,c^2\,d^2\,e^2}{7}+\frac{4\,b^3\,d\,e^3}{7}+\frac{18\,b^2\,c\,d^2\,e^2}{7}+\frac{12\,b\,c^2\,d^3\,e}{7}+\frac{c^3\,d^4}{7}\right)+a^3\,d^4\,x+\frac{c^3\,e^4\,x^{11}}{11}+a\,d^2\,x^3\,\left(2\,a^2\,e^2+4\,a\,b\,d\,e+c\,a\,d^2+b^2\,d^2\right)+\frac{c\,e^2\,x^9\,\left(b^2\,e^2+4\,b\,c\,d\,e+2\,c^2\,d^2+a\,c\,e^2\right)}{3}+\frac{a^2\,d^3\,x^2\,\left(4\,a\,e+3\,b\,d\right)}{2}+\frac{c^2\,e^3\,x^{10}\,\left(3\,b\,e+4\,c\,d\right)}{10}","Not used",1,"x^4*((b^3*d^4)/4 + a^3*d*e^3 + (9*a^2*b*d^2*e^2)/2 + (3*a*b*c*d^4)/2 + 3*a*b^2*d^3*e + 3*a^2*c*d^3*e) + x^8*((b^3*e^4)/8 + (c^3*d^3*e)/2 + (9*b*c^2*d^2*e^2)/4 + (3*a*b*c*e^4)/4 + (3*a*c^2*d*e^3)/2 + (3*b^2*c*d*e^3)/2) + x^6*((a^2*b*e^4)/2 + (b*c^2*d^4)/2 + b^3*d^2*e^2 + 2*a*b^2*d*e^3 + 2*a*c^2*d^3*e + 2*a^2*c*d*e^3 + 2*b^2*c*d^3*e + 6*a*b*c*d^2*e^2) + x^5*((a^3*e^4)/5 + (3*a*c^2*d^4)/5 + (3*b^2*c*d^4)/5 + (4*b^3*d^3*e)/5 + (18*a*b^2*d^2*e^2)/5 + (18*a^2*c*d^2*e^2)/5 + (12*a^2*b*d*e^3)/5 + (24*a*b*c*d^3*e)/5) + x^7*((c^3*d^4)/7 + (3*a*b^2*e^4)/7 + (3*a^2*c*e^4)/7 + (4*b^3*d*e^3)/7 + (18*a*c^2*d^2*e^2)/7 + (18*b^2*c*d^2*e^2)/7 + (12*b*c^2*d^3*e)/7 + (24*a*b*c*d*e^3)/7) + a^3*d^4*x + (c^3*e^4*x^11)/11 + a*d^2*x^3*(2*a^2*e^2 + b^2*d^2 + a*c*d^2 + 4*a*b*d*e) + (c*e^2*x^9*(b^2*e^2 + 2*c^2*d^2 + a*c*e^2 + 4*b*c*d*e))/3 + (a^2*d^3*x^2*(4*a*e + 3*b*d))/2 + (c^2*e^3*x^10*(3*b*e + 4*c*d))/10","B"
2132,1,381,272,0.120893,"\text{Not used}","int((d + e*x)^3*(a + b*x + c*x^2)^3,x)","x^4\,\left(\frac{a^3\,e^3}{4}+\frac{9\,a^2\,b\,d\,e^2}{4}+\frac{9\,c\,a^2\,d^2\,e}{4}+\frac{9\,a\,b^2\,d^2\,e}{4}+\frac{3\,c\,a\,b\,d^3}{2}+\frac{b^3\,d^3}{4}\right)+x^7\,\left(\frac{b^3\,e^3}{7}+\frac{9\,b^2\,c\,d\,e^2}{7}+\frac{9\,b\,c^2\,d^2\,e}{7}+\frac{6\,a\,b\,c\,e^3}{7}+\frac{c^3\,d^3}{7}+\frac{9\,a\,c^2\,d\,e^2}{7}\right)+x^5\,\left(\frac{3\,a^2\,b\,e^3}{5}+\frac{9\,a^2\,c\,d\,e^2}{5}+\frac{9\,a\,b^2\,d\,e^2}{5}+\frac{18\,a\,b\,c\,d^2\,e}{5}+\frac{3\,a\,c^2\,d^3}{5}+\frac{3\,b^3\,d^2\,e}{5}+\frac{3\,b^2\,c\,d^3}{5}\right)+x^6\,\left(\frac{a^2\,c\,e^3}{2}+\frac{a\,b^2\,e^3}{2}+3\,a\,b\,c\,d\,e^2+\frac{3\,a\,c^2\,d^2\,e}{2}+\frac{b^3\,d\,e^2}{2}+\frac{3\,b^2\,c\,d^2\,e}{2}+\frac{b\,c^2\,d^3}{2}\right)+a^3\,d^3\,x+\frac{c^3\,e^3\,x^{10}}{10}+\frac{3\,a^2\,d^2\,x^2\,\left(a\,e+b\,d\right)}{2}+\frac{c^2\,e^2\,x^9\,\left(b\,e+c\,d\right)}{3}+a\,d\,x^3\,\left(a^2\,e^2+3\,a\,b\,d\,e+c\,a\,d^2+b^2\,d^2\right)+\frac{3\,c\,e\,x^8\,\left(b^2\,e^2+3\,b\,c\,d\,e+c^2\,d^2+a\,c\,e^2\right)}{8}","Not used",1,"x^4*((a^3*e^3)/4 + (b^3*d^3)/4 + (3*a*b*c*d^3)/2 + (9*a*b^2*d^2*e)/4 + (9*a^2*b*d*e^2)/4 + (9*a^2*c*d^2*e)/4) + x^7*((b^3*e^3)/7 + (c^3*d^3)/7 + (6*a*b*c*e^3)/7 + (9*a*c^2*d*e^2)/7 + (9*b*c^2*d^2*e)/7 + (9*b^2*c*d*e^2)/7) + x^5*((3*a*c^2*d^3)/5 + (3*a^2*b*e^3)/5 + (3*b^2*c*d^3)/5 + (3*b^3*d^2*e)/5 + (9*a*b^2*d*e^2)/5 + (9*a^2*c*d*e^2)/5 + (18*a*b*c*d^2*e)/5) + x^6*((a*b^2*e^3)/2 + (b*c^2*d^3)/2 + (a^2*c*e^3)/2 + (b^3*d*e^2)/2 + (3*a*c^2*d^2*e)/2 + (3*b^2*c*d^2*e)/2 + 3*a*b*c*d*e^2) + a^3*d^3*x + (c^3*e^3*x^10)/10 + (3*a^2*d^2*x^2*(a*e + b*d))/2 + (c^2*e^2*x^9*(b*e + c*d))/3 + a*d*x^3*(a^2*e^2 + b^2*d^2 + a*c*d^2 + 3*a*b*d*e) + (3*c*e*x^8*(b^2*e^2 + c^2*d^2 + a*c*e^2 + 3*b*c*d*e))/8","B"
2133,1,276,272,0.097525,"\text{Not used}","int((d + e*x)^2*(a + b*x + c*x^2)^3,x)","x^3\,\left(\frac{a^3\,e^2}{3}+2\,a^2\,b\,d\,e+c\,a^2\,d^2+a\,b^2\,d^2\right)+x^7\,\left(\frac{3\,b^2\,c\,e^2}{7}+\frac{6\,b\,c^2\,d\,e}{7}+\frac{c^3\,d^2}{7}+\frac{3\,a\,c^2\,e^2}{7}\right)+x^4\,\left(\frac{3\,a^2\,b\,e^2}{4}+\frac{3\,c\,a^2\,d\,e}{2}+\frac{3\,a\,b^2\,d\,e}{2}+\frac{3\,c\,a\,b\,d^2}{2}+\frac{b^3\,d^2}{4}\right)+x^6\,\left(\frac{b^3\,e^2}{6}+b^2\,c\,d\,e+\frac{b\,c^2\,d^2}{2}+a\,b\,c\,e^2+a\,c^2\,d\,e\right)+x^5\,\left(\frac{3\,a^2\,c\,e^2}{5}+\frac{3\,a\,b^2\,e^2}{5}+\frac{12\,a\,b\,c\,d\,e}{5}+\frac{3\,a\,c^2\,d^2}{5}+\frac{2\,b^3\,d\,e}{5}+\frac{3\,b^2\,c\,d^2}{5}\right)+a^3\,d^2\,x+\frac{c^3\,e^2\,x^9}{9}+\frac{a^2\,d\,x^2\,\left(2\,a\,e+3\,b\,d\right)}{2}+\frac{c^2\,e\,x^8\,\left(3\,b\,e+2\,c\,d\right)}{8}","Not used",1,"x^3*((a^3*e^2)/3 + a*b^2*d^2 + a^2*c*d^2 + 2*a^2*b*d*e) + x^7*((c^3*d^2)/7 + (3*a*c^2*e^2)/7 + (3*b^2*c*e^2)/7 + (6*b*c^2*d*e)/7) + x^4*((b^3*d^2)/4 + (3*a^2*b*e^2)/4 + (3*a*b*c*d^2)/2 + (3*a*b^2*d*e)/2 + (3*a^2*c*d*e)/2) + x^6*((b^3*e^2)/6 + (b*c^2*d^2)/2 + a*b*c*e^2 + a*c^2*d*e + b^2*c*d*e) + x^5*((3*a*b^2*e^2)/5 + (3*a*c^2*d^2)/5 + (3*a^2*c*e^2)/5 + (3*b^2*c*d^2)/5 + (2*b^3*d*e)/5 + (12*a*b*c*d*e)/5) + a^3*d^2*x + (c^3*e^2*x^9)/9 + (a^2*d*x^2*(2*a*e + 3*b*d))/2 + (c^2*e*x^8*(3*b*e + 2*c*d))/8","B"
2134,1,163,161,0.781537,"\text{Not used}","int((d + e*x)*(a + b*x + c*x^2)^3,x)","x^2\,\left(\frac{e\,a^3}{2}+\frac{3\,b\,d\,a^2}{2}\right)+x^7\,\left(\frac{d\,c^3}{7}+\frac{3\,b\,e\,c^2}{7}\right)+x^3\,\left(e\,a^2\,b+c\,d\,a^2+d\,a\,b^2\right)+x^6\,\left(\frac{e\,b^2\,c}{2}+\frac{d\,b\,c^2}{2}+\frac{a\,e\,c^2}{2}\right)+x^4\,\left(\frac{3\,c\,e\,a^2}{4}+\frac{3\,e\,a\,b^2}{4}+\frac{3\,c\,d\,a\,b}{2}+\frac{d\,b^3}{4}\right)+x^5\,\left(\frac{e\,b^3}{5}+\frac{3\,d\,b^2\,c}{5}+\frac{6\,a\,e\,b\,c}{5}+\frac{3\,a\,d\,c^2}{5}\right)+\frac{c^3\,e\,x^8}{8}+a^3\,d\,x","Not used",1,"x^2*((a^3*e)/2 + (3*a^2*b*d)/2) + x^7*((c^3*d)/7 + (3*b*c^2*e)/7) + x^3*(a*b^2*d + a^2*b*e + a^2*c*d) + x^6*((a*c^2*e)/2 + (b*c^2*d)/2 + (b^2*c*e)/2) + x^4*((b^3*d)/4 + (3*a*b^2*e)/4 + (3*a^2*c*e)/4 + (3*a*b*c*d)/2) + x^5*((b^3*e)/5 + (3*a*c^2*d)/5 + (3*b^2*c*d)/5 + (6*a*b*c*e)/5) + (c^3*e*x^8)/8 + a^3*d*x","B"
2135,1,72,81,0.034746,"\text{Not used}","int((a + b*x + c*x^2)^3,x)","x^4\,\left(\frac{b^3}{4}+\frac{3\,a\,c\,b}{2}\right)+a^3\,x+\frac{c^3\,x^7}{7}+\frac{3\,a^2\,b\,x^2}{2}+\frac{b\,c^2\,x^6}{2}+a\,x^3\,\left(b^2+a\,c\right)+\frac{3\,c\,x^5\,\left(b^2+a\,c\right)}{5}","Not used",1,"x^4*(b^3/4 + (3*a*b*c)/2) + a^3*x + (c^3*x^7)/7 + (3*a^2*b*x^2)/2 + (b*c^2*x^6)/2 + a*x^3*(a*c + b^2) + (3*c*x^5*(a*c + b^2))/5","B"
2136,1,433,260,0.681308,"\text{Not used}","int((a + b*x + c*x^2)^3/(d + e*x),x)","x\,\left(\frac{3\,a^2\,b}{e}-\frac{d\,\left(\frac{3\,a\,\left(b^2+a\,c\right)}{e}-\frac{d\,\left(\frac{b^3+6\,a\,c\,b}{e}+\frac{d\,\left(\frac{d\,\left(\frac{3\,b\,c^2}{e}-\frac{c^3\,d}{e^2}\right)}{e}-\frac{3\,c\,\left(b^2+a\,c\right)}{e}\right)}{e}\right)}{e}\right)}{e}\right)+x^5\,\left(\frac{3\,b\,c^2}{5\,e}-\frac{c^3\,d}{5\,e^2}\right)+x^2\,\left(\frac{3\,a\,\left(b^2+a\,c\right)}{2\,e}-\frac{d\,\left(\frac{b^3+6\,a\,c\,b}{e}+\frac{d\,\left(\frac{d\,\left(\frac{3\,b\,c^2}{e}-\frac{c^3\,d}{e^2}\right)}{e}-\frac{3\,c\,\left(b^2+a\,c\right)}{e}\right)}{e}\right)}{2\,e}\right)+x^3\,\left(\frac{b^3+6\,a\,c\,b}{3\,e}+\frac{d\,\left(\frac{d\,\left(\frac{3\,b\,c^2}{e}-\frac{c^3\,d}{e^2}\right)}{e}-\frac{3\,c\,\left(b^2+a\,c\right)}{e}\right)}{3\,e}\right)-x^4\,\left(\frac{d\,\left(\frac{3\,b\,c^2}{e}-\frac{c^3\,d}{e^2}\right)}{4\,e}-\frac{3\,c\,\left(b^2+a\,c\right)}{4\,e}\right)+\frac{c^3\,x^6}{6\,e}+\frac{\ln\left(d+e\,x\right)\,\left(a^3\,e^6-3\,a^2\,b\,d\,e^5+3\,a^2\,c\,d^2\,e^4+3\,a\,b^2\,d^2\,e^4-6\,a\,b\,c\,d^3\,e^3+3\,a\,c^2\,d^4\,e^2-b^3\,d^3\,e^3+3\,b^2\,c\,d^4\,e^2-3\,b\,c^2\,d^5\,e+c^3\,d^6\right)}{e^7}","Not used",1,"x*((3*a^2*b)/e - (d*((3*a*(a*c + b^2))/e - (d*((b^3 + 6*a*b*c)/e + (d*((d*((3*b*c^2)/e - (c^3*d)/e^2))/e - (3*c*(a*c + b^2))/e))/e))/e))/e) + x^5*((3*b*c^2)/(5*e) - (c^3*d)/(5*e^2)) + x^2*((3*a*(a*c + b^2))/(2*e) - (d*((b^3 + 6*a*b*c)/e + (d*((d*((3*b*c^2)/e - (c^3*d)/e^2))/e - (3*c*(a*c + b^2))/e))/e))/(2*e)) + x^3*((b^3 + 6*a*b*c)/(3*e) + (d*((d*((3*b*c^2)/e - (c^3*d)/e^2))/e - (3*c*(a*c + b^2))/e))/(3*e)) - x^4*((d*((3*b*c^2)/e - (c^3*d)/e^2))/(4*e) - (3*c*(a*c + b^2))/(4*e)) + (c^3*x^6)/(6*e) + (log(d + e*x)*(a^3*e^6 + c^3*d^6 - b^3*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + 3*b^2*c*d^4*e^2 - 3*a^2*b*d*e^5 - 3*b*c^2*d^5*e - 6*a*b*c*d^3*e^3))/e^7","B"
2137,1,592,256,0.704858,"\text{Not used}","int((a + b*x + c*x^2)^3/(d + e*x)^2,x)","x^2\,\left(\frac{b^3+6\,a\,c\,b}{2\,e^2}+\frac{d\,\left(\frac{2\,d\,\left(\frac{3\,b\,c^2}{e^2}-\frac{2\,c^3\,d}{e^3}\right)}{e}+\frac{c^3\,d^2}{e^4}-\frac{3\,c\,\left(b^2+a\,c\right)}{e^2}\right)}{e}-\frac{d^2\,\left(\frac{3\,b\,c^2}{e^2}-\frac{2\,c^3\,d}{e^3}\right)}{2\,e^2}\right)+x^4\,\left(\frac{3\,b\,c^2}{4\,e^2}-\frac{c^3\,d}{2\,e^3}\right)-x^3\,\left(\frac{2\,d\,\left(\frac{3\,b\,c^2}{e^2}-\frac{2\,c^3\,d}{e^3}\right)}{3\,e}+\frac{c^3\,d^2}{3\,e^4}-\frac{c\,\left(b^2+a\,c\right)}{e^2}\right)+x\,\left(\frac{d^2\,\left(\frac{2\,d\,\left(\frac{3\,b\,c^2}{e^2}-\frac{2\,c^3\,d}{e^3}\right)}{e}+\frac{c^3\,d^2}{e^4}-\frac{3\,c\,\left(b^2+a\,c\right)}{e^2}\right)}{e^2}-\frac{2\,d\,\left(\frac{b^3+6\,a\,c\,b}{e^2}+\frac{2\,d\,\left(\frac{2\,d\,\left(\frac{3\,b\,c^2}{e^2}-\frac{2\,c^3\,d}{e^3}\right)}{e}+\frac{c^3\,d^2}{e^4}-\frac{3\,c\,\left(b^2+a\,c\right)}{e^2}\right)}{e}-\frac{d^2\,\left(\frac{3\,b\,c^2}{e^2}-\frac{2\,c^3\,d}{e^3}\right)}{e^2}\right)}{e}+\frac{3\,a\,\left(b^2+a\,c\right)}{e^2}\right)-\frac{a^3\,e^6-3\,a^2\,b\,d\,e^5+3\,a^2\,c\,d^2\,e^4+3\,a\,b^2\,d^2\,e^4-6\,a\,b\,c\,d^3\,e^3+3\,a\,c^2\,d^4\,e^2-b^3\,d^3\,e^3+3\,b^2\,c\,d^4\,e^2-3\,b\,c^2\,d^5\,e+c^3\,d^6}{e\,\left(x\,e^7+d\,e^6\right)}+\frac{c^3\,x^5}{5\,e^2}-\frac{\ln\left(d+e\,x\right)\,\left(-3\,a^2\,b\,e^5+6\,a^2\,c\,d\,e^4+6\,a\,b^2\,d\,e^4-18\,a\,b\,c\,d^2\,e^3+12\,a\,c^2\,d^3\,e^2-3\,b^3\,d^2\,e^3+12\,b^2\,c\,d^3\,e^2-15\,b\,c^2\,d^4\,e+6\,c^3\,d^5\right)}{e^7}","Not used",1,"x^2*((b^3 + 6*a*b*c)/(2*e^2) + (d*((2*d*((3*b*c^2)/e^2 - (2*c^3*d)/e^3))/e + (c^3*d^2)/e^4 - (3*c*(a*c + b^2))/e^2))/e - (d^2*((3*b*c^2)/e^2 - (2*c^3*d)/e^3))/(2*e^2)) + x^4*((3*b*c^2)/(4*e^2) - (c^3*d)/(2*e^3)) - x^3*((2*d*((3*b*c^2)/e^2 - (2*c^3*d)/e^3))/(3*e) + (c^3*d^2)/(3*e^4) - (c*(a*c + b^2))/e^2) + x*((d^2*((2*d*((3*b*c^2)/e^2 - (2*c^3*d)/e^3))/e + (c^3*d^2)/e^4 - (3*c*(a*c + b^2))/e^2))/e^2 - (2*d*((b^3 + 6*a*b*c)/e^2 + (2*d*((2*d*((3*b*c^2)/e^2 - (2*c^3*d)/e^3))/e + (c^3*d^2)/e^4 - (3*c*(a*c + b^2))/e^2))/e - (d^2*((3*b*c^2)/e^2 - (2*c^3*d)/e^3))/e^2))/e + (3*a*(a*c + b^2))/e^2) - (a^3*e^6 + c^3*d^6 - b^3*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + 3*b^2*c*d^4*e^2 - 3*a^2*b*d*e^5 - 3*b*c^2*d^5*e - 6*a*b*c*d^3*e^3)/(e*(d*e^6 + e^7*x)) + (c^3*x^5)/(5*e^2) - (log(d + e*x)*(6*c^3*d^5 - 3*a^2*b*e^5 - 3*b^3*d^2*e^3 + 12*a*c^2*d^3*e^2 + 12*b^2*c*d^3*e^2 + 6*a*b^2*d*e^4 + 6*a^2*c*d*e^4 - 15*b*c^2*d^4*e - 18*a*b*c*d^2*e^3))/e^7","B"
2138,1,521,255,0.756090,"\text{Not used}","int((a + b*x + c*x^2)^3/(d + e*x)^3,x)","\frac{x\,\left(-3\,a^2\,b\,e^5+6\,a^2\,c\,d\,e^4+6\,a\,b^2\,d\,e^4-18\,a\,b\,c\,d^2\,e^3+12\,a\,c^2\,d^3\,e^2-3\,b^3\,d^2\,e^3+12\,b^2\,c\,d^3\,e^2-15\,b\,c^2\,d^4\,e+6\,c^3\,d^5\right)-\frac{a^3\,e^6+3\,a^2\,b\,d\,e^5-9\,a^2\,c\,d^2\,e^4-9\,a\,b^2\,d^2\,e^4+30\,a\,b\,c\,d^3\,e^3-21\,a\,c^2\,d^4\,e^2+5\,b^3\,d^3\,e^3-21\,b^2\,c\,d^4\,e^2+27\,b\,c^2\,d^5\,e-11\,c^3\,d^6}{2\,e}}{d^2\,e^6+2\,d\,e^7\,x+e^8\,x^2}+x^3\,\left(\frac{b\,c^2}{e^3}-\frac{c^3\,d}{e^4}\right)+x\,\left(\frac{b^3+6\,a\,c\,b}{e^3}-\frac{c^3\,d^3}{e^6}+\frac{3\,d\,\left(\frac{3\,d\,\left(\frac{3\,b\,c^2}{e^3}-\frac{3\,c^3\,d}{e^4}\right)}{e}+\frac{3\,c^3\,d^2}{e^5}-\frac{3\,c\,\left(b^2+a\,c\right)}{e^3}\right)}{e}-\frac{3\,d^2\,\left(\frac{3\,b\,c^2}{e^3}-\frac{3\,c^3\,d}{e^4}\right)}{e^2}\right)-x^2\,\left(\frac{3\,d\,\left(\frac{3\,b\,c^2}{e^3}-\frac{3\,c^3\,d}{e^4}\right)}{2\,e}+\frac{3\,c^3\,d^2}{2\,e^5}-\frac{3\,c\,\left(b^2+a\,c\right)}{2\,e^3}\right)+\frac{\ln\left(d+e\,x\right)\,\left(3\,a^2\,c\,e^4+3\,a\,b^2\,e^4-18\,a\,b\,c\,d\,e^3+18\,a\,c^2\,d^2\,e^2-3\,b^3\,d\,e^3+18\,b^2\,c\,d^2\,e^2-30\,b\,c^2\,d^3\,e+15\,c^3\,d^4\right)}{e^7}+\frac{c^3\,x^4}{4\,e^3}","Not used",1,"(x*(6*c^3*d^5 - 3*a^2*b*e^5 - 3*b^3*d^2*e^3 + 12*a*c^2*d^3*e^2 + 12*b^2*c*d^3*e^2 + 6*a*b^2*d*e^4 + 6*a^2*c*d*e^4 - 15*b*c^2*d^4*e - 18*a*b*c*d^2*e^3) - (a^3*e^6 - 11*c^3*d^6 + 5*b^3*d^3*e^3 - 9*a*b^2*d^2*e^4 - 21*a*c^2*d^4*e^2 - 9*a^2*c*d^2*e^4 - 21*b^2*c*d^4*e^2 + 3*a^2*b*d*e^5 + 27*b*c^2*d^5*e + 30*a*b*c*d^3*e^3)/(2*e))/(d^2*e^6 + e^8*x^2 + 2*d*e^7*x) + x^3*((b*c^2)/e^3 - (c^3*d)/e^4) + x*((b^3 + 6*a*b*c)/e^3 - (c^3*d^3)/e^6 + (3*d*((3*d*((3*b*c^2)/e^3 - (3*c^3*d)/e^4))/e + (3*c^3*d^2)/e^5 - (3*c*(a*c + b^2))/e^3))/e - (3*d^2*((3*b*c^2)/e^3 - (3*c^3*d)/e^4))/e^2) - x^2*((3*d*((3*b*c^2)/e^3 - (3*c^3*d)/e^4))/(2*e) + (3*c^3*d^2)/(2*e^5) - (3*c*(a*c + b^2))/(2*e^3)) + (log(d + e*x)*(15*c^3*d^4 + 3*a*b^2*e^4 + 3*a^2*c*e^4 - 3*b^3*d*e^3 + 18*a*c^2*d^2*e^2 + 18*b^2*c*d^2*e^2 - 30*b*c^2*d^3*e - 18*a*b*c*d*e^3))/e^7 + (c^3*x^4)/(4*e^3)","B"
2139,1,484,251,0.140758,"\text{Not used}","int((a + b*x + c*x^2)^3/(d + e*x)^4,x)","x^2\,\left(\frac{3\,b\,c^2}{2\,e^4}-\frac{2\,c^3\,d}{e^5}\right)-x\,\left(\frac{4\,d\,\left(\frac{3\,b\,c^2}{e^4}-\frac{4\,c^3\,d}{e^5}\right)}{e}+\frac{6\,c^3\,d^2}{e^6}-\frac{3\,c\,\left(b^2+a\,c\right)}{e^4}\right)-\frac{x\,\left(\frac{3\,a^2\,b\,e^5}{2}+3\,a^2\,c\,d\,e^4+3\,a\,b^2\,d\,e^4-27\,a\,b\,c\,d^2\,e^3+30\,a\,c^2\,d^3\,e^2-\frac{9\,b^3\,d^2\,e^3}{2}+30\,b^2\,c\,d^3\,e^2-\frac{105\,b\,c^2\,d^4\,e}{2}+27\,c^3\,d^5\right)+\frac{2\,a^3\,e^6+3\,a^2\,b\,d\,e^5+6\,a^2\,c\,d^2\,e^4+6\,a\,b^2\,d^2\,e^4-66\,a\,b\,c\,d^3\,e^3+78\,a\,c^2\,d^4\,e^2-11\,b^3\,d^3\,e^3+78\,b^2\,c\,d^4\,e^2-141\,b\,c^2\,d^5\,e+74\,c^3\,d^6}{6\,e}+x^2\,\left(3\,a^2\,c\,e^5+3\,a\,b^2\,e^5-18\,a\,b\,c\,d\,e^4+18\,a\,c^2\,d^2\,e^3-3\,b^3\,d\,e^4+18\,b^2\,c\,d^2\,e^3-30\,b\,c^2\,d^3\,e^2+15\,c^3\,d^4\,e\right)}{d^3\,e^6+3\,d^2\,e^7\,x+3\,d\,e^8\,x^2+e^9\,x^3}+\frac{\ln\left(d+e\,x\right)\,\left(b^3\,e^3-12\,b^2\,c\,d\,e^2+30\,b\,c^2\,d^2\,e+6\,a\,b\,c\,e^3-20\,c^3\,d^3-12\,a\,c^2\,d\,e^2\right)}{e^7}+\frac{c^3\,x^3}{3\,e^4}","Not used",1,"x^2*((3*b*c^2)/(2*e^4) - (2*c^3*d)/e^5) - x*((4*d*((3*b*c^2)/e^4 - (4*c^3*d)/e^5))/e + (6*c^3*d^2)/e^6 - (3*c*(a*c + b^2))/e^4) - (x*(27*c^3*d^5 + (3*a^2*b*e^5)/2 - (9*b^3*d^2*e^3)/2 + 30*a*c^2*d^3*e^2 + 30*b^2*c*d^3*e^2 + 3*a*b^2*d*e^4 + 3*a^2*c*d*e^4 - (105*b*c^2*d^4*e)/2 - 27*a*b*c*d^2*e^3) + (2*a^3*e^6 + 74*c^3*d^6 - 11*b^3*d^3*e^3 + 6*a*b^2*d^2*e^4 + 78*a*c^2*d^4*e^2 + 6*a^2*c*d^2*e^4 + 78*b^2*c*d^4*e^2 + 3*a^2*b*d*e^5 - 141*b*c^2*d^5*e - 66*a*b*c*d^3*e^3)/(6*e) + x^2*(3*a*b^2*e^5 + 3*a^2*c*e^5 - 3*b^3*d*e^4 + 15*c^3*d^4*e + 18*a*c^2*d^2*e^3 - 30*b*c^2*d^3*e^2 + 18*b^2*c*d^2*e^3 - 18*a*b*c*d*e^4))/(d^3*e^6 + e^9*x^3 + 3*d^2*e^7*x + 3*d*e^8*x^2) + (log(d + e*x)*(b^3*e^3 - 20*c^3*d^3 + 6*a*b*c*e^3 - 12*a*c^2*d*e^2 + 30*b*c^2*d^2*e - 12*b^2*c*d*e^2))/e^7 + (c^3*x^3)/(3*e^4)","B"
2140,1,475,251,0.135449,"\text{Not used}","int((a + b*x + c*x^2)^3/(d + e*x)^5,x)","x\,\left(\frac{3\,b\,c^2}{e^5}-\frac{5\,c^3\,d}{e^6}\right)-\frac{x\,\left(a^2\,b\,e^5+a^2\,c\,d\,e^4+a\,b^2\,d\,e^4+6\,a\,b\,c\,d^2\,e^3-22\,a\,c^2\,d^3\,e^2+b^3\,d^2\,e^3-22\,b^2\,c\,d^3\,e^2+65\,b\,c^2\,d^4\,e-47\,c^3\,d^5\right)+\frac{a^3\,e^6+a^2\,b\,d\,e^5+a^2\,c\,d^2\,e^4+a\,b^2\,d^2\,e^4+6\,a\,b\,c\,d^3\,e^3-25\,a\,c^2\,d^4\,e^2+b^3\,d^3\,e^3-25\,b^2\,c\,d^4\,e^2+77\,b\,c^2\,d^5\,e-57\,c^3\,d^6}{4\,e}+x^2\,\left(\frac{3\,a^2\,c\,e^5}{2}+\frac{3\,a\,b^2\,e^5}{2}+9\,a\,b\,c\,d\,e^4-27\,a\,c^2\,d^2\,e^3+\frac{3\,b^3\,d\,e^4}{2}-27\,b^2\,c\,d^2\,e^3+75\,b\,c^2\,d^3\,e^2-\frac{105\,c^3\,d^4\,e}{2}\right)+x^3\,\left(b^3\,e^5-12\,b^2\,c\,d\,e^4+30\,b\,c^2\,d^2\,e^3+6\,a\,b\,c\,e^5-20\,c^3\,d^3\,e^2-12\,a\,c^2\,d\,e^4\right)}{d^4\,e^6+4\,d^3\,e^7\,x+6\,d^2\,e^8\,x^2+4\,d\,e^9\,x^3+e^{10}\,x^4}+\frac{\ln\left(d+e\,x\right)\,\left(3\,b^2\,c\,e^2-15\,b\,c^2\,d\,e+15\,c^3\,d^2+3\,a\,c^2\,e^2\right)}{e^7}+\frac{c^3\,x^2}{2\,e^5}","Not used",1,"x*((3*b*c^2)/e^5 - (5*c^3*d)/e^6) - (x*(a^2*b*e^5 - 47*c^3*d^5 + b^3*d^2*e^3 - 22*a*c^2*d^3*e^2 - 22*b^2*c*d^3*e^2 + a*b^2*d*e^4 + a^2*c*d*e^4 + 65*b*c^2*d^4*e + 6*a*b*c*d^2*e^3) + (a^3*e^6 - 57*c^3*d^6 + b^3*d^3*e^3 + a*b^2*d^2*e^4 - 25*a*c^2*d^4*e^2 + a^2*c*d^2*e^4 - 25*b^2*c*d^4*e^2 + a^2*b*d*e^5 + 77*b*c^2*d^5*e + 6*a*b*c*d^3*e^3)/(4*e) + x^2*((3*a*b^2*e^5)/2 + (3*a^2*c*e^5)/2 + (3*b^3*d*e^4)/2 - (105*c^3*d^4*e)/2 - 27*a*c^2*d^2*e^3 + 75*b*c^2*d^3*e^2 - 27*b^2*c*d^2*e^3 + 9*a*b*c*d*e^4) + x^3*(b^3*e^5 - 20*c^3*d^3*e^2 + 30*b*c^2*d^2*e^3 + 6*a*b*c*e^5 - 12*a*c^2*d*e^4 - 12*b^2*c*d*e^4))/(d^4*e^6 + e^10*x^4 + 4*d^3*e^7*x + 4*d*e^9*x^3 + 6*d^2*e^8*x^2) + (log(d + e*x)*(15*c^3*d^2 + 3*a*c^2*e^2 + 3*b^2*c*e^2 - 15*b*c^2*d*e))/e^7 + (c^3*x^2)/(2*e^5)","B"
2141,1,493,256,0.802789,"\text{Not used}","int((a + b*x + c*x^2)^3/(d + e*x)^6,x)","\frac{c^3\,x}{e^6}-\frac{x\,\left(\frac{3\,a^2\,b\,e^5}{4}+\frac{a^2\,c\,d\,e^4}{2}+\frac{a\,b^2\,d\,e^4}{2}+\frac{3\,a\,b\,c\,d^2\,e^3}{2}+3\,a\,c^2\,d^3\,e^2+\frac{b^3\,d^2\,e^3}{4}+3\,b^2\,c\,d^3\,e^2-\frac{125\,b\,c^2\,d^4\,e}{4}+\frac{77\,c^3\,d^5}{2}\right)+x^4\,\left(3\,b^2\,c\,e^5-15\,b\,c^2\,d\,e^4+15\,c^3\,d^2\,e^3+3\,a\,c^2\,e^5\right)+\frac{4\,a^3\,e^6+3\,a^2\,b\,d\,e^5+2\,a^2\,c\,d^2\,e^4+2\,a\,b^2\,d^2\,e^4+6\,a\,b\,c\,d^3\,e^3+12\,a\,c^2\,d^4\,e^2+b^3\,d^3\,e^3+12\,b^2\,c\,d^4\,e^2-137\,b\,c^2\,d^5\,e+174\,c^3\,d^6}{20\,e}+x^2\,\left(a^2\,c\,e^5+a\,b^2\,e^5+3\,a\,b\,c\,d\,e^4+6\,a\,c^2\,d^2\,e^3+\frac{b^3\,d\,e^4}{2}+6\,b^2\,c\,d^2\,e^3-55\,b\,c^2\,d^3\,e^2+65\,c^3\,d^4\,e\right)+x^3\,\left(\frac{b^3\,e^5}{2}+6\,b^2\,c\,d\,e^4-45\,b\,c^2\,d^2\,e^3+3\,a\,b\,c\,e^5+50\,c^3\,d^3\,e^2+6\,a\,c^2\,d\,e^4\right)}{d^5\,e^6+5\,d^4\,e^7\,x+10\,d^3\,e^8\,x^2+10\,d^2\,e^9\,x^3+5\,d\,e^{10}\,x^4+e^{11}\,x^5}-\frac{\ln\left(d+e\,x\right)\,\left(6\,c^3\,d-3\,b\,c^2\,e\right)}{e^7}","Not used",1,"(c^3*x)/e^6 - (x*((77*c^3*d^5)/2 + (3*a^2*b*e^5)/4 + (b^3*d^2*e^3)/4 + 3*a*c^2*d^3*e^2 + 3*b^2*c*d^3*e^2 + (a*b^2*d*e^4)/2 + (a^2*c*d*e^4)/2 - (125*b*c^2*d^4*e)/4 + (3*a*b*c*d^2*e^3)/2) + x^4*(3*a*c^2*e^5 + 3*b^2*c*e^5 + 15*c^3*d^2*e^3 - 15*b*c^2*d*e^4) + (4*a^3*e^6 + 174*c^3*d^6 + b^3*d^3*e^3 + 2*a*b^2*d^2*e^4 + 12*a*c^2*d^4*e^2 + 2*a^2*c*d^2*e^4 + 12*b^2*c*d^4*e^2 + 3*a^2*b*d*e^5 - 137*b*c^2*d^5*e + 6*a*b*c*d^3*e^3)/(20*e) + x^2*(a*b^2*e^5 + a^2*c*e^5 + (b^3*d*e^4)/2 + 65*c^3*d^4*e + 6*a*c^2*d^2*e^3 - 55*b*c^2*d^3*e^2 + 6*b^2*c*d^2*e^3 + 3*a*b*c*d*e^4) + x^3*((b^3*e^5)/2 + 50*c^3*d^3*e^2 - 45*b*c^2*d^2*e^3 + 3*a*b*c*e^5 + 6*a*c^2*d*e^4 + 6*b^2*c*d*e^4))/(d^5*e^6 + e^11*x^5 + 5*d^4*e^7*x + 5*d*e^10*x^4 + 10*d^3*e^8*x^2 + 10*d^2*e^9*x^3) - (log(d + e*x)*(6*c^3*d - 3*b*c^2*e))/e^7","B"
2142,1,497,266,0.788180,"\text{Not used}","int((a + b*x + c*x^2)^3/(d + e*x)^7,x)","\frac{c^3\,\ln\left(d+e\,x\right)}{e^7}-\frac{\frac{10\,a^3\,e^6+6\,a^2\,b\,d\,e^5+3\,a^2\,c\,d^2\,e^4+3\,a\,b^2\,d^2\,e^4+6\,a\,b\,c\,d^3\,e^3+6\,a\,c^2\,d^4\,e^2+b^3\,d^3\,e^3+6\,b^2\,c\,d^4\,e^2+30\,b\,c^2\,d^5\,e-147\,c^3\,d^6}{60\,e^7}+\frac{3\,x^4\,\left(b^2\,c\,e^2+5\,b\,c^2\,d\,e-15\,c^3\,d^2+a\,c^2\,e^2\right)}{2\,e^3}+\frac{x^3\,\left(b^3\,e^3+6\,b^2\,c\,d\,e^2+30\,b\,c^2\,d^2\,e+6\,a\,b\,c\,e^3-110\,c^3\,d^3+6\,a\,c^2\,d\,e^2\right)}{3\,e^4}+\frac{x^2\,\left(3\,a^2\,c\,e^4+3\,a\,b^2\,e^4+6\,a\,b\,c\,d\,e^3+6\,a\,c^2\,d^2\,e^2+b^3\,d\,e^3+6\,b^2\,c\,d^2\,e^2+30\,b\,c^2\,d^3\,e-125\,c^3\,d^4\right)}{4\,e^5}+\frac{x\,\left(6\,a^2\,b\,e^5+3\,a^2\,c\,d\,e^4+3\,a\,b^2\,d\,e^4+6\,a\,b\,c\,d^2\,e^3+6\,a\,c^2\,d^3\,e^2+b^3\,d^2\,e^3+6\,b^2\,c\,d^3\,e^2+30\,b\,c^2\,d^4\,e-137\,c^3\,d^5\right)}{10\,e^6}+\frac{3\,c^2\,x^5\,\left(b\,e-2\,c\,d\right)}{e^2}}{d^6+6\,d^5\,e\,x+15\,d^4\,e^2\,x^2+20\,d^3\,e^3\,x^3+15\,d^2\,e^4\,x^4+6\,d\,e^5\,x^5+e^6\,x^6}","Not used",1,"(c^3*log(d + e*x))/e^7 - ((10*a^3*e^6 - 147*c^3*d^6 + b^3*d^3*e^3 + 3*a*b^2*d^2*e^4 + 6*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + 6*b^2*c*d^4*e^2 + 6*a^2*b*d*e^5 + 30*b*c^2*d^5*e + 6*a*b*c*d^3*e^3)/(60*e^7) + (3*x^4*(a*c^2*e^2 - 15*c^3*d^2 + b^2*c*e^2 + 5*b*c^2*d*e))/(2*e^3) + (x^3*(b^3*e^3 - 110*c^3*d^3 + 6*a*b*c*e^3 + 6*a*c^2*d*e^2 + 30*b*c^2*d^2*e + 6*b^2*c*d*e^2))/(3*e^4) + (x^2*(3*a*b^2*e^4 - 125*c^3*d^4 + 3*a^2*c*e^4 + b^3*d*e^3 + 6*a*c^2*d^2*e^2 + 6*b^2*c*d^2*e^2 + 30*b*c^2*d^3*e + 6*a*b*c*d*e^3))/(4*e^5) + (x*(6*a^2*b*e^5 - 137*c^3*d^5 + b^3*d^2*e^3 + 6*a*c^2*d^3*e^2 + 6*b^2*c*d^3*e^2 + 3*a*b^2*d*e^4 + 3*a^2*c*d*e^4 + 30*b*c^2*d^4*e + 6*a*b*c*d^2*e^3))/(10*e^6) + (3*c^2*x^5*(b*e - 2*c*d))/e^2)/(d^6 + e^6*x^6 + 6*d*e^5*x^5 + 15*d^4*e^2*x^2 + 20*d^3*e^3*x^3 + 15*d^2*e^4*x^4 + 6*d^5*e*x)","B"
2143,1,502,268,0.168358,"\text{Not used}","int((a + b*x + c*x^2)^3/(d + e*x)^8,x)","-\frac{\frac{20\,a^3\,e^6+10\,a^2\,b\,d\,e^5+4\,a^2\,c\,d^2\,e^4+4\,a\,b^2\,d^2\,e^4+6\,a\,b\,c\,d^3\,e^3+4\,a\,c^2\,d^4\,e^2+b^3\,d^3\,e^3+4\,b^2\,c\,d^4\,e^2+10\,b\,c^2\,d^5\,e+20\,c^3\,d^6}{140\,e^7}+\frac{x^3\,\left(b^3\,e^3+4\,b^2\,c\,d\,e^2+10\,b\,c^2\,d^2\,e+6\,a\,b\,c\,e^3+20\,c^3\,d^3+4\,a\,c^2\,d\,e^2\right)}{4\,e^4}+\frac{3\,x^2\,\left(4\,a^2\,c\,e^4+4\,a\,b^2\,e^4+6\,a\,b\,c\,d\,e^3+4\,a\,c^2\,d^2\,e^2+b^3\,d\,e^3+4\,b^2\,c\,d^2\,e^2+10\,b\,c^2\,d^3\,e+20\,c^3\,d^4\right)}{20\,e^5}+\frac{c^3\,x^6}{e}+\frac{x\,\left(10\,a^2\,b\,e^5+4\,a^2\,c\,d\,e^4+4\,a\,b^2\,d\,e^4+6\,a\,b\,c\,d^2\,e^3+4\,a\,c^2\,d^3\,e^2+b^3\,d^2\,e^3+4\,b^2\,c\,d^3\,e^2+10\,b\,c^2\,d^4\,e+20\,c^3\,d^5\right)}{20\,e^6}+\frac{c\,x^4\,\left(2\,b^2\,e^2+5\,b\,c\,d\,e+10\,c^2\,d^2+2\,a\,c\,e^2\right)}{2\,e^3}+\frac{3\,c^2\,x^5\,\left(b\,e+2\,c\,d\right)}{2\,e^2}}{d^7+7\,d^6\,e\,x+21\,d^5\,e^2\,x^2+35\,d^4\,e^3\,x^3+35\,d^3\,e^4\,x^4+21\,d^2\,e^5\,x^5+7\,d\,e^6\,x^6+e^7\,x^7}","Not used",1,"-((20*a^3*e^6 + 20*c^3*d^6 + b^3*d^3*e^3 + 4*a*b^2*d^2*e^4 + 4*a*c^2*d^4*e^2 + 4*a^2*c*d^2*e^4 + 4*b^2*c*d^4*e^2 + 10*a^2*b*d*e^5 + 10*b*c^2*d^5*e + 6*a*b*c*d^3*e^3)/(140*e^7) + (x^3*(b^3*e^3 + 20*c^3*d^3 + 6*a*b*c*e^3 + 4*a*c^2*d*e^2 + 10*b*c^2*d^2*e + 4*b^2*c*d*e^2))/(4*e^4) + (3*x^2*(20*c^3*d^4 + 4*a*b^2*e^4 + 4*a^2*c*e^4 + b^3*d*e^3 + 4*a*c^2*d^2*e^2 + 4*b^2*c*d^2*e^2 + 10*b*c^2*d^3*e + 6*a*b*c*d*e^3))/(20*e^5) + (c^3*x^6)/e + (x*(20*c^3*d^5 + 10*a^2*b*e^5 + b^3*d^2*e^3 + 4*a*c^2*d^3*e^2 + 4*b^2*c*d^3*e^2 + 4*a*b^2*d*e^4 + 4*a^2*c*d*e^4 + 10*b*c^2*d^4*e + 6*a*b*c*d^2*e^3))/(20*e^6) + (c*x^4*(2*b^2*e^2 + 10*c^2*d^2 + 2*a*c*e^2 + 5*b*c*d*e))/(2*e^3) + (3*c^2*x^5*(b*e + 2*c*d))/(2*e^2))/(d^7 + e^7*x^7 + 7*d*e^6*x^6 + 21*d^5*e^2*x^2 + 35*d^4*e^3*x^3 + 35*d^3*e^4*x^4 + 21*d^2*e^5*x^5 + 7*d^6*e*x)","B"
2144,1,512,269,0.155861,"\text{Not used}","int((a + b*x + c*x^2)^3/(d + e*x)^9,x)","-\frac{\frac{35\,a^3\,e^6+15\,a^2\,b\,d\,e^5+5\,a^2\,c\,d^2\,e^4+5\,a\,b^2\,d^2\,e^4+6\,a\,b\,c\,d^3\,e^3+3\,a\,c^2\,d^4\,e^2+b^3\,d^3\,e^3+3\,b^2\,c\,d^4\,e^2+5\,b\,c^2\,d^5\,e+5\,c^3\,d^6}{280\,e^7}+\frac{x^3\,\left(b^3\,e^3+3\,b^2\,c\,d\,e^2+5\,b\,c^2\,d^2\,e+6\,a\,b\,c\,e^3+5\,c^3\,d^3+3\,a\,c^2\,d\,e^2\right)}{5\,e^4}+\frac{x^2\,\left(5\,a^2\,c\,e^4+5\,a\,b^2\,e^4+6\,a\,b\,c\,d\,e^3+3\,a\,c^2\,d^2\,e^2+b^3\,d\,e^3+3\,b^2\,c\,d^2\,e^2+5\,b\,c^2\,d^3\,e+5\,c^3\,d^4\right)}{10\,e^5}+\frac{c^3\,x^6}{2\,e}+\frac{x\,\left(15\,a^2\,b\,e^5+5\,a^2\,c\,d\,e^4+5\,a\,b^2\,d\,e^4+6\,a\,b\,c\,d^2\,e^3+3\,a\,c^2\,d^3\,e^2+b^3\,d^2\,e^3+3\,b^2\,c\,d^3\,e^2+5\,b\,c^2\,d^4\,e+5\,c^3\,d^5\right)}{35\,e^6}+\frac{c\,x^4\,\left(3\,b^2\,e^2+5\,b\,c\,d\,e+5\,c^2\,d^2+3\,a\,c\,e^2\right)}{4\,e^3}+\frac{c^2\,x^5\,\left(b\,e+c\,d\right)}{e^2}}{d^8+8\,d^7\,e\,x+28\,d^6\,e^2\,x^2+56\,d^5\,e^3\,x^3+70\,d^4\,e^4\,x^4+56\,d^3\,e^5\,x^5+28\,d^2\,e^6\,x^6+8\,d\,e^7\,x^7+e^8\,x^8}","Not used",1,"-((35*a^3*e^6 + 5*c^3*d^6 + b^3*d^3*e^3 + 5*a*b^2*d^2*e^4 + 3*a*c^2*d^4*e^2 + 5*a^2*c*d^2*e^4 + 3*b^2*c*d^4*e^2 + 15*a^2*b*d*e^5 + 5*b*c^2*d^5*e + 6*a*b*c*d^3*e^3)/(280*e^7) + (x^3*(b^3*e^3 + 5*c^3*d^3 + 6*a*b*c*e^3 + 3*a*c^2*d*e^2 + 5*b*c^2*d^2*e + 3*b^2*c*d*e^2))/(5*e^4) + (x^2*(5*c^3*d^4 + 5*a*b^2*e^4 + 5*a^2*c*e^4 + b^3*d*e^3 + 3*a*c^2*d^2*e^2 + 3*b^2*c*d^2*e^2 + 5*b*c^2*d^3*e + 6*a*b*c*d*e^3))/(10*e^5) + (c^3*x^6)/(2*e) + (x*(5*c^3*d^5 + 15*a^2*b*e^5 + b^3*d^2*e^3 + 3*a*c^2*d^3*e^2 + 3*b^2*c*d^3*e^2 + 5*a*b^2*d*e^4 + 5*a^2*c*d*e^4 + 5*b*c^2*d^4*e + 6*a*b*c*d^2*e^3))/(35*e^6) + (c*x^4*(3*b^2*e^2 + 5*c^2*d^2 + 3*a*c*e^2 + 5*b*c*d*e))/(4*e^3) + (c^2*x^5*(b*e + c*d))/e^2)/(d^8 + e^8*x^8 + 8*d*e^7*x^7 + 28*d^6*e^2*x^2 + 56*d^5*e^3*x^3 + 70*d^4*e^4*x^4 + 56*d^3*e^5*x^5 + 28*d^2*e^6*x^6 + 8*d^7*e*x)","B"
2145,1,530,272,0.763768,"\text{Not used}","int((a + b*x + c*x^2)^3/(d + e*x)^10,x)","-\frac{\frac{280\,a^3\,e^6+105\,a^2\,b\,d\,e^5+30\,a^2\,c\,d^2\,e^4+30\,a\,b^2\,d^2\,e^4+30\,a\,b\,c\,d^3\,e^3+12\,a\,c^2\,d^4\,e^2+5\,b^3\,d^3\,e^3+12\,b^2\,c\,d^4\,e^2+15\,b\,c^2\,d^5\,e+10\,c^3\,d^6}{2520\,e^7}+\frac{x^3\,\left(5\,b^3\,e^3+12\,b^2\,c\,d\,e^2+15\,b\,c^2\,d^2\,e+30\,a\,b\,c\,e^3+10\,c^3\,d^3+12\,a\,c^2\,d\,e^2\right)}{30\,e^4}+\frac{x^2\,\left(30\,a^2\,c\,e^4+30\,a\,b^2\,e^4+30\,a\,b\,c\,d\,e^3+12\,a\,c^2\,d^2\,e^2+5\,b^3\,d\,e^3+12\,b^2\,c\,d^2\,e^2+15\,b\,c^2\,d^3\,e+10\,c^3\,d^4\right)}{70\,e^5}+\frac{c^3\,x^6}{3\,e}+\frac{x\,\left(105\,a^2\,b\,e^5+30\,a^2\,c\,d\,e^4+30\,a\,b^2\,d\,e^4+30\,a\,b\,c\,d^2\,e^3+12\,a\,c^2\,d^3\,e^2+5\,b^3\,d^2\,e^3+12\,b^2\,c\,d^3\,e^2+15\,b\,c^2\,d^4\,e+10\,c^3\,d^5\right)}{280\,e^6}+\frac{c\,x^4\,\left(12\,b^2\,e^2+15\,b\,c\,d\,e+10\,c^2\,d^2+12\,a\,c\,e^2\right)}{20\,e^3}+\frac{c^2\,x^5\,\left(3\,b\,e+2\,c\,d\right)}{4\,e^2}}{d^9+9\,d^8\,e\,x+36\,d^7\,e^2\,x^2+84\,d^6\,e^3\,x^3+126\,d^5\,e^4\,x^4+126\,d^4\,e^5\,x^5+84\,d^3\,e^6\,x^6+36\,d^2\,e^7\,x^7+9\,d\,e^8\,x^8+e^9\,x^9}","Not used",1,"-((280*a^3*e^6 + 10*c^3*d^6 + 5*b^3*d^3*e^3 + 30*a*b^2*d^2*e^4 + 12*a*c^2*d^4*e^2 + 30*a^2*c*d^2*e^4 + 12*b^2*c*d^4*e^2 + 105*a^2*b*d*e^5 + 15*b*c^2*d^5*e + 30*a*b*c*d^3*e^3)/(2520*e^7) + (x^3*(5*b^3*e^3 + 10*c^3*d^3 + 30*a*b*c*e^3 + 12*a*c^2*d*e^2 + 15*b*c^2*d^2*e + 12*b^2*c*d*e^2))/(30*e^4) + (x^2*(10*c^3*d^4 + 30*a*b^2*e^4 + 30*a^2*c*e^4 + 5*b^3*d*e^3 + 12*a*c^2*d^2*e^2 + 12*b^2*c*d^2*e^2 + 15*b*c^2*d^3*e + 30*a*b*c*d*e^3))/(70*e^5) + (c^3*x^6)/(3*e) + (x*(10*c^3*d^5 + 105*a^2*b*e^5 + 5*b^3*d^2*e^3 + 12*a*c^2*d^3*e^2 + 12*b^2*c*d^3*e^2 + 30*a*b^2*d*e^4 + 30*a^2*c*d*e^4 + 15*b*c^2*d^4*e + 30*a*b*c*d^2*e^3))/(280*e^6) + (c*x^4*(12*b^2*e^2 + 10*c^2*d^2 + 12*a*c*e^2 + 15*b*c*d*e))/(20*e^3) + (c^2*x^5*(3*b*e + 2*c*d))/(4*e^2))/(d^9 + e^9*x^9 + 9*d*e^8*x^8 + 36*d^7*e^2*x^2 + 84*d^6*e^3*x^3 + 126*d^5*e^4*x^4 + 126*d^4*e^5*x^5 + 84*d^3*e^6*x^6 + 36*d^2*e^7*x^7 + 9*d^8*e*x)","B"
2146,1,817,443,0.847982,"\text{Not used}","int((d + e*x)^4*(a + b*x + c*x^2)^4,x)","x^6\,\left(\frac{2\,a^3\,b\,e^4}{3}+\frac{8\,a^3\,c\,d\,e^3}{3}+4\,a^2\,b^2\,d\,e^3+12\,a^2\,b\,c\,d^2\,e^2+4\,a^2\,c^2\,d^3\,e+4\,a\,b^3\,d^2\,e^2+8\,a\,b^2\,c\,d^3\,e+2\,a\,b\,c^2\,d^4+\frac{2\,b^4\,d^3\,e}{3}+\frac{2\,b^3\,c\,d^4}{3}\right)+x^8\,\left(\frac{3\,a^2\,b\,c\,e^4}{2}+3\,a^2\,c^2\,d\,e^3+\frac{a\,b^3\,e^4}{2}+6\,a\,b^2\,c\,d\,e^3+9\,a\,b\,c^2\,d^2\,e^2+2\,a\,c^3\,d^3\,e+\frac{b^4\,d\,e^3}{2}+3\,b^3\,c\,d^2\,e^2+3\,b^2\,c^2\,d^3\,e+\frac{b\,c^3\,d^4}{2}\right)+x^7\,\left(\frac{4\,a^3\,c\,e^4}{7}+\frac{6\,a^2\,b^2\,e^4}{7}+\frac{48\,a^2\,b\,c\,d\,e^3}{7}+\frac{36\,a^2\,c^2\,d^2\,e^2}{7}+\frac{16\,a\,b^3\,d\,e^3}{7}+\frac{72\,a\,b^2\,c\,d^2\,e^2}{7}+\frac{48\,a\,b\,c^2\,d^3\,e}{7}+\frac{4\,a\,c^3\,d^4}{7}+\frac{6\,b^4\,d^2\,e^2}{7}+\frac{16\,b^3\,c\,d^3\,e}{7}+\frac{6\,b^2\,c^2\,d^4}{7}\right)+x^5\,\left(\frac{a^4\,e^4}{5}+\frac{16\,a^3\,b\,d\,e^3}{5}+\frac{24\,a^3\,c\,d^2\,e^2}{5}+\frac{36\,a^2\,b^2\,d^2\,e^2}{5}+\frac{48\,a^2\,b\,c\,d^3\,e}{5}+\frac{6\,a^2\,c^2\,d^4}{5}+\frac{16\,a\,b^3\,d^3\,e}{5}+\frac{12\,a\,b^2\,c\,d^4}{5}+\frac{b^4\,d^4}{5}\right)+x^4\,\left(a^4\,d\,e^3+6\,a^3\,b\,d^2\,e^2+4\,c\,a^3\,d^3\,e+6\,a^2\,b^2\,d^3\,e+3\,c\,a^2\,b\,d^4+a\,b^3\,d^4\right)+x^9\,\left(\frac{2\,a^2\,c^2\,e^4}{3}+\frac{4\,a\,b^2\,c\,e^4}{3}+\frac{16\,a\,b\,c^2\,d\,e^3}{3}+\frac{8\,a\,c^3\,d^2\,e^2}{3}+\frac{b^4\,e^4}{9}+\frac{16\,b^3\,c\,d\,e^3}{9}+4\,b^2\,c^2\,d^2\,e^2+\frac{16\,b\,c^3\,d^3\,e}{9}+\frac{c^4\,d^4}{9}\right)+x^{10}\,\left(\frac{2\,b^3\,c\,e^4}{5}+\frac{12\,b^2\,c^2\,d\,e^3}{5}+\frac{12\,b\,c^3\,d^2\,e^2}{5}+\frac{6\,a\,b\,c^2\,e^4}{5}+\frac{2\,c^4\,d^3\,e}{5}+\frac{8\,a\,c^3\,d\,e^3}{5}\right)+a^4\,d^4\,x+\frac{c^4\,e^4\,x^{13}}{13}+2\,a^3\,d^3\,x^2\,\left(a\,e+b\,d\right)+\frac{c^3\,e^3\,x^{12}\,\left(b\,e+c\,d\right)}{3}+\frac{2\,a^2\,d^2\,x^3\,\left(3\,a^2\,e^2+8\,a\,b\,d\,e+2\,c\,a\,d^2+3\,b^2\,d^2\right)}{3}+\frac{2\,c^2\,e^2\,x^{11}\,\left(3\,b^2\,e^2+8\,b\,c\,d\,e+3\,c^2\,d^2+2\,a\,c\,e^2\right)}{11}","Not used",1,"x^6*((2*a^3*b*e^4)/3 + (2*b^3*c*d^4)/3 + (2*b^4*d^3*e)/3 + 4*a*b^3*d^2*e^2 + 4*a^2*b^2*d*e^3 + 4*a^2*c^2*d^3*e + 2*a*b*c^2*d^4 + (8*a^3*c*d*e^3)/3 + 8*a*b^2*c*d^3*e + 12*a^2*b*c*d^2*e^2) + x^8*((a*b^3*e^4)/2 + (b*c^3*d^4)/2 + (b^4*d*e^3)/2 + 3*a^2*c^2*d*e^3 + 3*b^2*c^2*d^3*e + 3*b^3*c*d^2*e^2 + (3*a^2*b*c*e^4)/2 + 2*a*c^3*d^3*e + 6*a*b^2*c*d*e^3 + 9*a*b*c^2*d^2*e^2) + x^7*((4*a*c^3*d^4)/7 + (4*a^3*c*e^4)/7 + (6*a^2*b^2*e^4)/7 + (6*b^2*c^2*d^4)/7 + (6*b^4*d^2*e^2)/7 + (36*a^2*c^2*d^2*e^2)/7 + (16*a*b^3*d*e^3)/7 + (16*b^3*c*d^3*e)/7 + (48*a*b*c^2*d^3*e)/7 + (48*a^2*b*c*d*e^3)/7 + (72*a*b^2*c*d^2*e^2)/7) + x^5*((a^4*e^4)/5 + (b^4*d^4)/5 + (6*a^2*c^2*d^4)/5 + (24*a^3*c*d^2*e^2)/5 + (36*a^2*b^2*d^2*e^2)/5 + (12*a*b^2*c*d^4)/5 + (16*a*b^3*d^3*e)/5 + (16*a^3*b*d*e^3)/5 + (48*a^2*b*c*d^3*e)/5) + x^4*(a*b^3*d^4 + a^4*d*e^3 + 6*a^2*b^2*d^3*e + 6*a^3*b*d^2*e^2 + 3*a^2*b*c*d^4 + 4*a^3*c*d^3*e) + x^9*((b^4*e^4)/9 + (c^4*d^4)/9 + (2*a^2*c^2*e^4)/3 + (8*a*c^3*d^2*e^2)/3 + 4*b^2*c^2*d^2*e^2 + (4*a*b^2*c*e^4)/3 + (16*b*c^3*d^3*e)/9 + (16*b^3*c*d*e^3)/9 + (16*a*b*c^2*d*e^3)/3) + x^10*((2*b^3*c*e^4)/5 + (2*c^4*d^3*e)/5 + (12*b*c^3*d^2*e^2)/5 + (12*b^2*c^2*d*e^3)/5 + (6*a*b*c^2*e^4)/5 + (8*a*c^3*d*e^3)/5) + a^4*d^4*x + (c^4*e^4*x^13)/13 + 2*a^3*d^3*x^2*(a*e + b*d) + (c^3*e^3*x^12*(b*e + c*d))/3 + (2*a^2*d^2*x^3*(3*a^2*e^2 + 3*b^2*d^2 + 2*a*c*d^2 + 8*a*b*d*e))/3 + (2*c^2*e^2*x^11*(3*b^2*e^2 + 3*c^2*d^2 + 2*a*c*e^2 + 8*b*c*d*e))/11","B"
2147,1,630,443,0.198508,"\text{Not used}","int((d + e*x)^3*(a + b*x + c*x^2)^4,x)","x^5\,\left(\frac{4\,a^3\,b\,e^3}{5}+\frac{12\,a^3\,c\,d\,e^2}{5}+\frac{18\,a^2\,b^2\,d\,e^2}{5}+\frac{36\,a^2\,b\,c\,d^2\,e}{5}+\frac{6\,a^2\,c^2\,d^3}{5}+\frac{12\,a\,b^3\,d^2\,e}{5}+\frac{12\,a\,b^2\,c\,d^3}{5}+\frac{b^4\,d^3}{5}\right)+x^8\,\left(\frac{3\,a^2\,c^2\,e^3}{4}+\frac{3\,a\,b^2\,c\,e^3}{2}+\frac{9\,a\,b\,c^2\,d\,e^2}{2}+\frac{3\,a\,c^3\,d^2\,e}{2}+\frac{b^4\,e^3}{8}+\frac{3\,b^3\,c\,d\,e^2}{2}+\frac{9\,b^2\,c^2\,d^2\,e}{4}+\frac{b\,c^3\,d^3}{2}\right)+x^6\,\left(\frac{2\,a^3\,c\,e^3}{3}+a^2\,b^2\,e^3+6\,a^2\,b\,c\,d\,e^2+3\,a^2\,c^2\,d^2\,e+2\,a\,b^3\,d\,e^2+6\,a\,b^2\,c\,d^2\,e+2\,a\,b\,c^2\,d^3+\frac{b^4\,d^2\,e}{2}+\frac{2\,b^3\,c\,d^3}{3}\right)+x^7\,\left(\frac{12\,a^2\,b\,c\,e^3}{7}+\frac{18\,a^2\,c^2\,d\,e^2}{7}+\frac{4\,a\,b^3\,e^3}{7}+\frac{36\,a\,b^2\,c\,d\,e^2}{7}+\frac{36\,a\,b\,c^2\,d^2\,e}{7}+\frac{4\,a\,c^3\,d^3}{7}+\frac{3\,b^4\,d\,e^2}{7}+\frac{12\,b^3\,c\,d^2\,e}{7}+\frac{6\,b^2\,c^2\,d^3}{7}\right)+x^4\,\left(\frac{a^4\,e^3}{4}+3\,a^3\,b\,d\,e^2+3\,c\,a^3\,d^2\,e+\frac{9\,a^2\,b^2\,d^2\,e}{2}+3\,c\,a^2\,b\,d^3+a\,b^3\,d^3\right)+x^9\,\left(\frac{4\,b^3\,c\,e^3}{9}+2\,b^2\,c^2\,d\,e^2+\frac{4\,b\,c^3\,d^2\,e}{3}+\frac{4\,a\,b\,c^2\,e^3}{3}+\frac{c^4\,d^3}{9}+\frac{4\,a\,c^3\,d\,e^2}{3}\right)+a^4\,d^3\,x+\frac{c^4\,e^3\,x^{12}}{12}+\frac{a^2\,d\,x^3\,\left(3\,a^2\,e^2+12\,a\,b\,d\,e+4\,c\,a\,d^2+6\,b^2\,d^2\right)}{3}+\frac{c^2\,e\,x^{10}\,\left(6\,b^2\,e^2+12\,b\,c\,d\,e+3\,c^2\,d^2+4\,a\,c\,e^2\right)}{10}+\frac{a^3\,d^2\,x^2\,\left(3\,a\,e+4\,b\,d\right)}{2}+\frac{c^3\,e^2\,x^{11}\,\left(4\,b\,e+3\,c\,d\right)}{11}","Not used",1,"x^5*((b^4*d^3)/5 + (4*a^3*b*e^3)/5 + (6*a^2*c^2*d^3)/5 + (18*a^2*b^2*d*e^2)/5 + (12*a*b^2*c*d^3)/5 + (12*a*b^3*d^2*e)/5 + (12*a^3*c*d*e^2)/5 + (36*a^2*b*c*d^2*e)/5) + x^8*((b^4*e^3)/8 + (b*c^3*d^3)/2 + (3*a^2*c^2*e^3)/4 + (9*b^2*c^2*d^2*e)/4 + (3*a*b^2*c*e^3)/2 + (3*a*c^3*d^2*e)/2 + (3*b^3*c*d*e^2)/2 + (9*a*b*c^2*d*e^2)/2) + x^6*((2*a^3*c*e^3)/3 + (2*b^3*c*d^3)/3 + (b^4*d^2*e)/2 + a^2*b^2*e^3 + 3*a^2*c^2*d^2*e + 2*a*b*c^2*d^3 + 2*a*b^3*d*e^2 + 6*a*b^2*c*d^2*e + 6*a^2*b*c*d*e^2) + x^7*((4*a*b^3*e^3)/7 + (4*a*c^3*d^3)/7 + (3*b^4*d*e^2)/7 + (6*b^2*c^2*d^3)/7 + (18*a^2*c^2*d*e^2)/7 + (12*a^2*b*c*e^3)/7 + (12*b^3*c*d^2*e)/7 + (36*a*b*c^2*d^2*e)/7 + (36*a*b^2*c*d*e^2)/7) + x^4*((a^4*e^3)/4 + a*b^3*d^3 + (9*a^2*b^2*d^2*e)/2 + 3*a^2*b*c*d^3 + 3*a^3*b*d*e^2 + 3*a^3*c*d^2*e) + x^9*((c^4*d^3)/9 + (4*b^3*c*e^3)/9 + 2*b^2*c^2*d*e^2 + (4*a*b*c^2*e^3)/3 + (4*a*c^3*d*e^2)/3 + (4*b*c^3*d^2*e)/3) + a^4*d^3*x + (c^4*e^3*x^12)/12 + (a^2*d*x^3*(3*a^2*e^2 + 6*b^2*d^2 + 4*a*c*d^2 + 12*a*b*d*e))/3 + (c^2*e*x^10*(6*b^2*e^2 + 3*c^2*d^2 + 4*a*c*e^2 + 12*b*c*d*e))/10 + (a^3*d^2*x^2*(3*a*e + 4*b*d))/2 + (c^3*e^2*x^11*(4*b*e + 3*c*d))/11","B"
2148,1,445,441,0.777966,"\text{Not used}","int((d + e*x)^2*(a + b*x + c*x^2)^4,x)","x^5\,\left(\frac{4\,a^3\,c\,e^2}{5}+\frac{6\,a^2\,b^2\,e^2}{5}+\frac{24\,a^2\,b\,c\,d\,e}{5}+\frac{6\,a^2\,c^2\,d^2}{5}+\frac{8\,a\,b^3\,d\,e}{5}+\frac{12\,a\,b^2\,c\,d^2}{5}+\frac{b^4\,d^2}{5}\right)+x^3\,\left(\frac{a^4\,e^2}{3}+\frac{8\,a^3\,b\,d\,e}{3}+\frac{4\,c\,a^3\,d^2}{3}+2\,a^2\,b^2\,d^2\right)+x^7\,\left(\frac{6\,a^2\,c^2\,e^2}{7}+\frac{12\,a\,b^2\,c\,e^2}{7}+\frac{24\,a\,b\,c^2\,d\,e}{7}+\frac{4\,a\,c^3\,d^2}{7}+\frac{b^4\,e^2}{7}+\frac{8\,b^3\,c\,d\,e}{7}+\frac{6\,b^2\,c^2\,d^2}{7}\right)+x^9\,\left(\frac{2\,b^2\,c^2\,e^2}{3}+\frac{8\,b\,c^3\,d\,e}{9}+\frac{c^4\,d^2}{9}+\frac{4\,a\,c^3\,e^2}{9}\right)+x^6\,\left(2\,a^2\,b\,c\,e^2+2\,a^2\,c^2\,d\,e+\frac{2\,a\,b^3\,e^2}{3}+4\,a\,b^2\,c\,d\,e+2\,a\,b\,c^2\,d^2+\frac{b^4\,d\,e}{3}+\frac{2\,b^3\,c\,d^2}{3}\right)+x^4\,\left(a^3\,b\,e^2+2\,c\,a^3\,d\,e+3\,a^2\,b^2\,d\,e+3\,c\,a^2\,b\,d^2+a\,b^3\,d^2\right)+x^8\,\left(\frac{b^3\,c\,e^2}{2}+\frac{3\,b^2\,c^2\,d\,e}{2}+\frac{b\,c^3\,d^2}{2}+\frac{3\,a\,b\,c^2\,e^2}{2}+a\,c^3\,d\,e\right)+a^4\,d^2\,x+\frac{c^4\,e^2\,x^{11}}{11}+a^3\,d\,x^2\,\left(a\,e+2\,b\,d\right)+\frac{c^3\,e\,x^{10}\,\left(2\,b\,e+c\,d\right)}{5}","Not used",1,"x^5*((b^4*d^2)/5 + (4*a^3*c*e^2)/5 + (6*a^2*b^2*e^2)/5 + (6*a^2*c^2*d^2)/5 + (8*a*b^3*d*e)/5 + (12*a*b^2*c*d^2)/5 + (24*a^2*b*c*d*e)/5) + x^3*((a^4*e^2)/3 + (4*a^3*c*d^2)/3 + 2*a^2*b^2*d^2 + (8*a^3*b*d*e)/3) + x^7*((b^4*e^2)/7 + (4*a*c^3*d^2)/7 + (6*a^2*c^2*e^2)/7 + (6*b^2*c^2*d^2)/7 + (8*b^3*c*d*e)/7 + (12*a*b^2*c*e^2)/7 + (24*a*b*c^2*d*e)/7) + x^9*((c^4*d^2)/9 + (4*a*c^3*e^2)/9 + (2*b^2*c^2*e^2)/3 + (8*b*c^3*d*e)/9) + x^6*((2*a*b^3*e^2)/3 + (2*b^3*c*d^2)/3 + (b^4*d*e)/3 + 2*a*b*c^2*d^2 + 2*a^2*b*c*e^2 + 2*a^2*c^2*d*e + 4*a*b^2*c*d*e) + x^4*(a*b^3*d^2 + a^3*b*e^2 + 2*a^3*c*d*e + 3*a^2*b*c*d^2 + 3*a^2*b^2*d*e) + x^8*((b*c^3*d^2)/2 + (b^3*c*e^2)/2 + a*c^3*d*e + (3*a*b*c^2*e^2)/2 + (3*b^2*c^2*d*e)/2) + a^4*d^2*x + (c^4*e^2*x^11)/11 + a^3*d*x^2*(a*e + 2*b*d) + (c^3*e*x^10*(2*b*e + c*d))/5","B"
2149,1,263,268,0.122789,"\text{Not used}","int((d + e*x)*(a + b*x + c*x^2)^4,x)","x^2\,\left(\frac{e\,a^4}{2}+2\,b\,d\,a^3\right)+x^9\,\left(\frac{d\,c^4}{9}+\frac{4\,b\,e\,c^3}{9}\right)+x^3\,\left(\frac{4\,e\,a^3\,b}{3}+\frac{4\,c\,d\,a^3}{3}+2\,d\,a^2\,b^2\right)+x^8\,\left(\frac{3\,e\,b^2\,c^2}{4}+\frac{d\,b\,c^3}{2}+\frac{a\,e\,c^3}{2}\right)+x^5\,\left(\frac{12\,e\,a^2\,b\,c}{5}+\frac{6\,d\,a^2\,c^2}{5}+\frac{4\,e\,a\,b^3}{5}+\frac{12\,d\,a\,b^2\,c}{5}+\frac{d\,b^4}{5}\right)+x^6\,\left(e\,a^2\,c^2+2\,e\,a\,b^2\,c+2\,d\,a\,b\,c^2+\frac{e\,b^4}{6}+\frac{2\,d\,b^3\,c}{3}\right)+x^4\,\left(c\,e\,a^3+\frac{3\,e\,a^2\,b^2}{2}+3\,c\,d\,a^2\,b+d\,a\,b^3\right)+x^7\,\left(\frac{4\,e\,b^3\,c}{7}+\frac{6\,d\,b^2\,c^2}{7}+\frac{12\,a\,e\,b\,c^2}{7}+\frac{4\,a\,d\,c^3}{7}\right)+\frac{c^4\,e\,x^{10}}{10}+a^4\,d\,x","Not used",1,"x^2*((a^4*e)/2 + 2*a^3*b*d) + x^9*((c^4*d)/9 + (4*b*c^3*e)/9) + x^3*(2*a^2*b^2*d + (4*a^3*b*e)/3 + (4*a^3*c*d)/3) + x^8*((3*b^2*c^2*e)/4 + (a*c^3*e)/2 + (b*c^3*d)/2) + x^5*((b^4*d)/5 + (6*a^2*c^2*d)/5 + (4*a*b^3*e)/5 + (12*a*b^2*c*d)/5 + (12*a^2*b*c*e)/5) + x^6*((b^4*e)/6 + a^2*c^2*e + (2*b^3*c*d)/3 + 2*a*b*c^2*d + 2*a*b^2*c*e) + x^4*((3*a^2*b^2*e)/2 + a*b^3*d + a^3*c*e + 3*a^2*b*c*d) + x^7*((6*b^2*c^2*d)/7 + (4*a*c^3*d)/7 + (4*b^3*c*e)/7 + (12*a*b*c^2*e)/7) + (c^4*e*x^10)/10 + a^4*d*x","B"
2150,1,124,133,0.067422,"\text{Not used}","int((a + b*x + c*x^2)^4,x)","x^5\,\left(\frac{6\,a^2\,c^2}{5}+\frac{12\,a\,b^2\,c}{5}+\frac{b^4}{5}\right)+a^4\,x+\frac{c^4\,x^9}{9}+x^3\,\left(\frac{4\,c\,a^3}{3}+2\,a^2\,b^2\right)+x^7\,\left(\frac{6\,b^2\,c^2}{7}+\frac{4\,a\,c^3}{7}\right)+2\,a^3\,b\,x^2+\frac{b\,c^3\,x^8}{2}+a\,b\,x^4\,\left(b^2+3\,a\,c\right)+\frac{2\,b\,c\,x^6\,\left(b^2+3\,a\,c\right)}{3}","Not used",1,"x^5*(b^4/5 + (6*a^2*c^2)/5 + (12*a*b^2*c)/5) + a^4*x + (c^4*x^9)/9 + x^3*((4*a^3*c)/3 + 2*a^2*b^2) + x^7*((4*a*c^3)/7 + (6*b^2*c^2)/7) + 2*a^3*b*x^2 + (b*c^3*x^8)/2 + a*b*x^4*(3*a*c + b^2) + (2*b*c*x^6*(3*a*c + b^2))/3","B"
2151,1,870,428,0.712349,"\text{Not used}","int((a + b*x + c*x^2)^4/(d + e*x),x)","x^4\,\left(\frac{6\,a^2\,c^2+12\,a\,b^2\,c+b^4}{4\,e}+\frac{d\,\left(\frac{d\,\left(\frac{6\,b^2\,c^2+4\,a\,c^3}{e}-\frac{d\,\left(\frac{4\,b\,c^3}{e}-\frac{c^4\,d}{e^2}\right)}{e}\right)}{e}-\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{e}\right)}{4\,e}\right)-x^5\,\left(\frac{d\,\left(\frac{6\,b^2\,c^2+4\,a\,c^3}{e}-\frac{d\,\left(\frac{4\,b\,c^3}{e}-\frac{c^4\,d}{e^2}\right)}{e}\right)}{5\,e}-\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{5\,e}\right)-x^3\,\left(\frac{d\,\left(\frac{6\,a^2\,c^2+12\,a\,b^2\,c+b^4}{e}+\frac{d\,\left(\frac{d\,\left(\frac{6\,b^2\,c^2+4\,a\,c^3}{e}-\frac{d\,\left(\frac{4\,b\,c^3}{e}-\frac{c^4\,d}{e^2}\right)}{e}\right)}{e}-\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{e}\right)}{e}\right)}{3\,e}-\frac{4\,a\,b\,\left(b^2+3\,a\,c\right)}{3\,e}\right)+x^7\,\left(\frac{4\,b\,c^3}{7\,e}-\frac{c^4\,d}{7\,e^2}\right)-x\,\left(\frac{d\,\left(\frac{4\,c\,a^3+6\,a^2\,b^2}{e}+\frac{d\,\left(\frac{d\,\left(\frac{6\,a^2\,c^2+12\,a\,b^2\,c+b^4}{e}+\frac{d\,\left(\frac{d\,\left(\frac{6\,b^2\,c^2+4\,a\,c^3}{e}-\frac{d\,\left(\frac{4\,b\,c^3}{e}-\frac{c^4\,d}{e^2}\right)}{e}\right)}{e}-\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{e}\right)}{e}\right)}{e}-\frac{4\,a\,b\,\left(b^2+3\,a\,c\right)}{e}\right)}{e}\right)}{e}-\frac{4\,a^3\,b}{e}\right)+x^2\,\left(\frac{4\,c\,a^3+6\,a^2\,b^2}{2\,e}+\frac{d\,\left(\frac{d\,\left(\frac{6\,a^2\,c^2+12\,a\,b^2\,c+b^4}{e}+\frac{d\,\left(\frac{d\,\left(\frac{6\,b^2\,c^2+4\,a\,c^3}{e}-\frac{d\,\left(\frac{4\,b\,c^3}{e}-\frac{c^4\,d}{e^2}\right)}{e}\right)}{e}-\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{e}\right)}{e}\right)}{e}-\frac{4\,a\,b\,\left(b^2+3\,a\,c\right)}{e}\right)}{2\,e}\right)+x^6\,\left(\frac{6\,b^2\,c^2+4\,a\,c^3}{6\,e}-\frac{d\,\left(\frac{4\,b\,c^3}{e}-\frac{c^4\,d}{e^2}\right)}{6\,e}\right)+\frac{\ln\left(d+e\,x\right)\,\left(a^4\,e^8-4\,a^3\,b\,d\,e^7+4\,a^3\,c\,d^2\,e^6+6\,a^2\,b^2\,d^2\,e^6-12\,a^2\,b\,c\,d^3\,e^5+6\,a^2\,c^2\,d^4\,e^4-4\,a\,b^3\,d^3\,e^5+12\,a\,b^2\,c\,d^4\,e^4-12\,a\,b\,c^2\,d^5\,e^3+4\,a\,c^3\,d^6\,e^2+b^4\,d^4\,e^4-4\,b^3\,c\,d^5\,e^3+6\,b^2\,c^2\,d^6\,e^2-4\,b\,c^3\,d^7\,e+c^4\,d^8\right)}{e^9}+\frac{c^4\,x^8}{8\,e}","Not used",1,"x^4*((b^4 + 6*a^2*c^2 + 12*a*b^2*c)/(4*e) + (d*((d*((4*a*c^3 + 6*b^2*c^2)/e - (d*((4*b*c^3)/e - (c^4*d)/e^2))/e))/e - (4*b*c*(3*a*c + b^2))/e))/(4*e)) - x^5*((d*((4*a*c^3 + 6*b^2*c^2)/e - (d*((4*b*c^3)/e - (c^4*d)/e^2))/e))/(5*e) - (4*b*c*(3*a*c + b^2))/(5*e)) - x^3*((d*((b^4 + 6*a^2*c^2 + 12*a*b^2*c)/e + (d*((d*((4*a*c^3 + 6*b^2*c^2)/e - (d*((4*b*c^3)/e - (c^4*d)/e^2))/e))/e - (4*b*c*(3*a*c + b^2))/e))/e))/(3*e) - (4*a*b*(3*a*c + b^2))/(3*e)) + x^7*((4*b*c^3)/(7*e) - (c^4*d)/(7*e^2)) - x*((d*((4*a^3*c + 6*a^2*b^2)/e + (d*((d*((b^4 + 6*a^2*c^2 + 12*a*b^2*c)/e + (d*((d*((4*a*c^3 + 6*b^2*c^2)/e - (d*((4*b*c^3)/e - (c^4*d)/e^2))/e))/e - (4*b*c*(3*a*c + b^2))/e))/e))/e - (4*a*b*(3*a*c + b^2))/e))/e))/e - (4*a^3*b)/e) + x^2*((4*a^3*c + 6*a^2*b^2)/(2*e) + (d*((d*((b^4 + 6*a^2*c^2 + 12*a*b^2*c)/e + (d*((d*((4*a*c^3 + 6*b^2*c^2)/e - (d*((4*b*c^3)/e - (c^4*d)/e^2))/e))/e - (4*b*c*(3*a*c + b^2))/e))/e))/e - (4*a*b*(3*a*c + b^2))/e))/(2*e)) + x^6*((4*a*c^3 + 6*b^2*c^2)/(6*e) - (d*((4*b*c^3)/e - (c^4*d)/e^2))/(6*e)) + (log(d + e*x)*(a^4*e^8 + c^4*d^8 + b^4*d^4*e^4 - 4*a*b^3*d^3*e^5 + 4*a*c^3*d^6*e^2 + 4*a^3*c*d^2*e^6 - 4*b^3*c*d^5*e^3 + 6*a^2*b^2*d^2*e^6 + 6*a^2*c^2*d^4*e^4 + 6*b^2*c^2*d^6*e^2 - 4*a^3*b*d*e^7 - 4*b*c^3*d^7*e - 12*a*b*c^2*d^5*e^3 + 12*a*b^2*c*d^4*e^4 - 12*a^2*b*c*d^3*e^5))/e^9 + (c^4*x^8)/(8*e)","B"
2152,1,1679,426,0.746286,"\text{Not used}","int((a + b*x + c*x^2)^4/(d + e*x)^2,x)","x\,\left(\frac{4\,c\,a^3+6\,a^2\,b^2}{e^2}+\frac{2\,d\,\left(\frac{2\,d\,\left(\frac{6\,a^2\,c^2+12\,a\,b^2\,c+b^4}{e^2}+\frac{d^2\,\left(\frac{2\,d\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^2}+\frac{c^4\,d^2}{e^4}\right)}{e^2}-\frac{2\,d\,\left(\frac{2\,d\,\left(\frac{2\,d\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^2}+\frac{c^4\,d^2}{e^4}\right)}{e}-\frac{d^2\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e^2}+\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{e^2}\right)}{e}\right)}{e}+\frac{d^2\,\left(\frac{2\,d\,\left(\frac{2\,d\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^2}+\frac{c^4\,d^2}{e^4}\right)}{e}-\frac{d^2\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e^2}+\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{e^2}\right)}{e^2}-\frac{4\,a\,b\,\left(b^2+3\,a\,c\right)}{e^2}\right)}{e}-\frac{d^2\,\left(\frac{6\,a^2\,c^2+12\,a\,b^2\,c+b^4}{e^2}+\frac{d^2\,\left(\frac{2\,d\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^2}+\frac{c^4\,d^2}{e^4}\right)}{e^2}-\frac{2\,d\,\left(\frac{2\,d\,\left(\frac{2\,d\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^2}+\frac{c^4\,d^2}{e^4}\right)}{e}-\frac{d^2\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e^2}+\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{e^2}\right)}{e}\right)}{e^2}\right)+x^6\,\left(\frac{2\,b\,c^3}{3\,e^2}-\frac{c^4\,d}{3\,e^3}\right)-x^2\,\left(\frac{d\,\left(\frac{6\,a^2\,c^2+12\,a\,b^2\,c+b^4}{e^2}+\frac{d^2\,\left(\frac{2\,d\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^2}+\frac{c^4\,d^2}{e^4}\right)}{e^2}-\frac{2\,d\,\left(\frac{2\,d\,\left(\frac{2\,d\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^2}+\frac{c^4\,d^2}{e^4}\right)}{e}-\frac{d^2\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e^2}+\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{e^2}\right)}{e}\right)}{e}+\frac{d^2\,\left(\frac{2\,d\,\left(\frac{2\,d\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^2}+\frac{c^4\,d^2}{e^4}\right)}{e}-\frac{d^2\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e^2}+\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{e^2}\right)}{2\,e^2}-\frac{2\,a\,b\,\left(b^2+3\,a\,c\right)}{e^2}\right)+x^4\,\left(\frac{d\,\left(\frac{2\,d\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^2}+\frac{c^4\,d^2}{e^4}\right)}{2\,e}-\frac{d^2\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{4\,e^2}+\frac{b\,c\,\left(b^2+3\,a\,c\right)}{e^2}\right)-x^5\,\left(\frac{2\,d\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{5\,e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{5\,e^2}+\frac{c^4\,d^2}{5\,e^4}\right)+x^3\,\left(\frac{6\,a^2\,c^2+12\,a\,b^2\,c+b^4}{3\,e^2}+\frac{d^2\,\left(\frac{2\,d\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^2}+\frac{c^4\,d^2}{e^4}\right)}{3\,e^2}-\frac{2\,d\,\left(\frac{2\,d\,\left(\frac{2\,d\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^2}+\frac{c^4\,d^2}{e^4}\right)}{e}-\frac{d^2\,\left(\frac{4\,b\,c^3}{e^2}-\frac{2\,c^4\,d}{e^3}\right)}{e^2}+\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{e^2}\right)}{3\,e}\right)-\frac{\ln\left(d+e\,x\right)\,\left(-4\,a^3\,b\,e^7+8\,a^3\,c\,d\,e^6+12\,a^2\,b^2\,d\,e^6-36\,a^2\,b\,c\,d^2\,e^5+24\,a^2\,c^2\,d^3\,e^4-12\,a\,b^3\,d^2\,e^5+48\,a\,b^2\,c\,d^3\,e^4-60\,a\,b\,c^2\,d^4\,e^3+24\,a\,c^3\,d^5\,e^2+4\,b^4\,d^3\,e^4-20\,b^3\,c\,d^4\,e^3+36\,b^2\,c^2\,d^5\,e^2-28\,b\,c^3\,d^6\,e+8\,c^4\,d^7\right)}{e^9}+\frac{c^4\,x^7}{7\,e^2}-\frac{a^4\,e^8-4\,a^3\,b\,d\,e^7+4\,a^3\,c\,d^2\,e^6+6\,a^2\,b^2\,d^2\,e^6-12\,a^2\,b\,c\,d^3\,e^5+6\,a^2\,c^2\,d^4\,e^4-4\,a\,b^3\,d^3\,e^5+12\,a\,b^2\,c\,d^4\,e^4-12\,a\,b\,c^2\,d^5\,e^3+4\,a\,c^3\,d^6\,e^2+b^4\,d^4\,e^4-4\,b^3\,c\,d^5\,e^3+6\,b^2\,c^2\,d^6\,e^2-4\,b\,c^3\,d^7\,e+c^4\,d^8}{e\,\left(x\,e^9+d\,e^8\right)}","Not used",1,"x*((4*a^3*c + 6*a^2*b^2)/e^2 + (2*d*((2*d*((b^4 + 6*a^2*c^2 + 12*a*b^2*c)/e^2 + (d^2*((2*d*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e - (4*a*c^3 + 6*b^2*c^2)/e^2 + (c^4*d^2)/e^4))/e^2 - (2*d*((2*d*((2*d*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e - (4*a*c^3 + 6*b^2*c^2)/e^2 + (c^4*d^2)/e^4))/e - (d^2*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e^2 + (4*b*c*(3*a*c + b^2))/e^2))/e))/e + (d^2*((2*d*((2*d*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e - (4*a*c^3 + 6*b^2*c^2)/e^2 + (c^4*d^2)/e^4))/e - (d^2*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e^2 + (4*b*c*(3*a*c + b^2))/e^2))/e^2 - (4*a*b*(3*a*c + b^2))/e^2))/e - (d^2*((b^4 + 6*a^2*c^2 + 12*a*b^2*c)/e^2 + (d^2*((2*d*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e - (4*a*c^3 + 6*b^2*c^2)/e^2 + (c^4*d^2)/e^4))/e^2 - (2*d*((2*d*((2*d*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e - (4*a*c^3 + 6*b^2*c^2)/e^2 + (c^4*d^2)/e^4))/e - (d^2*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e^2 + (4*b*c*(3*a*c + b^2))/e^2))/e))/e^2) + x^6*((2*b*c^3)/(3*e^2) - (c^4*d)/(3*e^3)) - x^2*((d*((b^4 + 6*a^2*c^2 + 12*a*b^2*c)/e^2 + (d^2*((2*d*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e - (4*a*c^3 + 6*b^2*c^2)/e^2 + (c^4*d^2)/e^4))/e^2 - (2*d*((2*d*((2*d*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e - (4*a*c^3 + 6*b^2*c^2)/e^2 + (c^4*d^2)/e^4))/e - (d^2*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e^2 + (4*b*c*(3*a*c + b^2))/e^2))/e))/e + (d^2*((2*d*((2*d*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e - (4*a*c^3 + 6*b^2*c^2)/e^2 + (c^4*d^2)/e^4))/e - (d^2*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e^2 + (4*b*c*(3*a*c + b^2))/e^2))/(2*e^2) - (2*a*b*(3*a*c + b^2))/e^2) + x^4*((d*((2*d*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e - (4*a*c^3 + 6*b^2*c^2)/e^2 + (c^4*d^2)/e^4))/(2*e) - (d^2*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/(4*e^2) + (b*c*(3*a*c + b^2))/e^2) - x^5*((2*d*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/(5*e) - (4*a*c^3 + 6*b^2*c^2)/(5*e^2) + (c^4*d^2)/(5*e^4)) + x^3*((b^4 + 6*a^2*c^2 + 12*a*b^2*c)/(3*e^2) + (d^2*((2*d*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e - (4*a*c^3 + 6*b^2*c^2)/e^2 + (c^4*d^2)/e^4))/(3*e^2) - (2*d*((2*d*((2*d*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e - (4*a*c^3 + 6*b^2*c^2)/e^2 + (c^4*d^2)/e^4))/e - (d^2*((4*b*c^3)/e^2 - (2*c^4*d)/e^3))/e^2 + (4*b*c*(3*a*c + b^2))/e^2))/(3*e)) - (log(d + e*x)*(8*c^4*d^7 - 4*a^3*b*e^7 + 4*b^4*d^3*e^4 - 12*a*b^3*d^2*e^5 + 12*a^2*b^2*d*e^6 + 24*a*c^3*d^5*e^2 - 20*b^3*c*d^4*e^3 + 24*a^2*c^2*d^3*e^4 + 36*b^2*c^2*d^5*e^2 + 8*a^3*c*d*e^6 - 28*b*c^3*d^6*e - 60*a*b*c^2*d^4*e^3 + 48*a*b^2*c*d^3*e^4 - 36*a^2*b*c*d^2*e^5))/e^9 + (c^4*x^7)/(7*e^2) - (a^4*e^8 + c^4*d^8 + b^4*d^4*e^4 - 4*a*b^3*d^3*e^5 + 4*a*c^3*d^6*e^2 + 4*a^3*c*d^2*e^6 - 4*b^3*c*d^5*e^3 + 6*a^2*b^2*d^2*e^6 + 6*a^2*c^2*d^4*e^4 + 6*b^2*c^2*d^6*e^2 - 4*a^3*b*d*e^7 - 4*b*c^3*d^7*e - 12*a*b*c^2*d^5*e^3 + 12*a*b^2*c*d^4*e^4 - 12*a^2*b*c*d^3*e^5)/(e*(d*e^8 + e^9*x))","B"
2153,1,1444,430,0.815824,"\text{Not used}","int((a + b*x + c*x^2)^4/(d + e*x)^3,x)","\frac{x\,\left(-4\,a^3\,b\,e^7+8\,a^3\,c\,d\,e^6+12\,a^2\,b^2\,d\,e^6-36\,a^2\,b\,c\,d^2\,e^5+24\,a^2\,c^2\,d^3\,e^4-12\,a\,b^3\,d^2\,e^5+48\,a\,b^2\,c\,d^3\,e^4-60\,a\,b\,c^2\,d^4\,e^3+24\,a\,c^3\,d^5\,e^2+4\,b^4\,d^3\,e^4-20\,b^3\,c\,d^4\,e^3+36\,b^2\,c^2\,d^5\,e^2-28\,b\,c^3\,d^6\,e+8\,c^4\,d^7\right)+\frac{-a^4\,e^8-4\,a^3\,b\,d\,e^7+12\,a^3\,c\,d^2\,e^6+18\,a^2\,b^2\,d^2\,e^6-60\,a^2\,b\,c\,d^3\,e^5+42\,a^2\,c^2\,d^4\,e^4-20\,a\,b^3\,d^3\,e^5+84\,a\,b^2\,c\,d^4\,e^4-108\,a\,b\,c^2\,d^5\,e^3+44\,a\,c^3\,d^6\,e^2+7\,b^4\,d^4\,e^4-36\,b^3\,c\,d^5\,e^3+66\,b^2\,c^2\,d^6\,e^2-52\,b\,c^3\,d^7\,e+15\,c^4\,d^8}{2\,e}}{d^2\,e^8+2\,d\,e^9\,x+e^{10}\,x^2}+x^5\,\left(\frac{4\,b\,c^3}{5\,e^3}-\frac{3\,c^4\,d}{5\,e^4}\right)-x^3\,\left(\frac{c^4\,d^3}{3\,e^6}+\frac{d^2\,\left(\frac{4\,b\,c^3}{e^3}-\frac{3\,c^4\,d}{e^4}\right)}{e^2}-\frac{d\,\left(\frac{3\,d\,\left(\frac{4\,b\,c^3}{e^3}-\frac{3\,c^4\,d}{e^4}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^3}+\frac{3\,c^4\,d^2}{e^5}\right)}{e}-\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{3\,e^3}\right)+x\,\left(\frac{d^3\,\left(\frac{3\,d\,\left(\frac{4\,b\,c^3}{e^3}-\frac{3\,c^4\,d}{e^4}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^3}+\frac{3\,c^4\,d^2}{e^5}\right)}{e^3}-\frac{3\,d\,\left(\frac{6\,a^2\,c^2+12\,a\,b^2\,c+b^4}{e^3}+\frac{3\,d^2\,\left(\frac{3\,d\,\left(\frac{4\,b\,c^3}{e^3}-\frac{3\,c^4\,d}{e^4}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^3}+\frac{3\,c^4\,d^2}{e^5}\right)}{e^2}+\frac{3\,d\,\left(\frac{c^4\,d^3}{e^6}+\frac{3\,d^2\,\left(\frac{4\,b\,c^3}{e^3}-\frac{3\,c^4\,d}{e^4}\right)}{e^2}-\frac{3\,d\,\left(\frac{3\,d\,\left(\frac{4\,b\,c^3}{e^3}-\frac{3\,c^4\,d}{e^4}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^3}+\frac{3\,c^4\,d^2}{e^5}\right)}{e}-\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{e^3}\right)}{e}-\frac{d^3\,\left(\frac{4\,b\,c^3}{e^3}-\frac{3\,c^4\,d}{e^4}\right)}{e^3}\right)}{e}+\frac{3\,d^2\,\left(\frac{c^4\,d^3}{e^6}+\frac{3\,d^2\,\left(\frac{4\,b\,c^3}{e^3}-\frac{3\,c^4\,d}{e^4}\right)}{e^2}-\frac{3\,d\,\left(\frac{3\,d\,\left(\frac{4\,b\,c^3}{e^3}-\frac{3\,c^4\,d}{e^4}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^3}+\frac{3\,c^4\,d^2}{e^5}\right)}{e}-\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{e^3}\right)}{e^2}+\frac{4\,a\,b\,\left(b^2+3\,a\,c\right)}{e^3}\right)+x^2\,\left(\frac{6\,a^2\,c^2+12\,a\,b^2\,c+b^4}{2\,e^3}+\frac{3\,d^2\,\left(\frac{3\,d\,\left(\frac{4\,b\,c^3}{e^3}-\frac{3\,c^4\,d}{e^4}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^3}+\frac{3\,c^4\,d^2}{e^5}\right)}{2\,e^2}+\frac{3\,d\,\left(\frac{c^4\,d^3}{e^6}+\frac{3\,d^2\,\left(\frac{4\,b\,c^3}{e^3}-\frac{3\,c^4\,d}{e^4}\right)}{e^2}-\frac{3\,d\,\left(\frac{3\,d\,\left(\frac{4\,b\,c^3}{e^3}-\frac{3\,c^4\,d}{e^4}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^3}+\frac{3\,c^4\,d^2}{e^5}\right)}{e}-\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{e^3}\right)}{2\,e}-\frac{d^3\,\left(\frac{4\,b\,c^3}{e^3}-\frac{3\,c^4\,d}{e^4}\right)}{2\,e^3}\right)-x^4\,\left(\frac{3\,d\,\left(\frac{4\,b\,c^3}{e^3}-\frac{3\,c^4\,d}{e^4}\right)}{4\,e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{4\,e^3}+\frac{3\,c^4\,d^2}{4\,e^5}\right)+\frac{\ln\left(d+e\,x\right)\,\left(4\,a^3\,c\,e^6+6\,a^2\,b^2\,e^6-36\,a^2\,b\,c\,d\,e^5+36\,a^2\,c^2\,d^2\,e^4-12\,a\,b^3\,d\,e^5+72\,a\,b^2\,c\,d^2\,e^4-120\,a\,b\,c^2\,d^3\,e^3+60\,a\,c^3\,d^4\,e^2+6\,b^4\,d^2\,e^4-40\,b^3\,c\,d^3\,e^3+90\,b^2\,c^2\,d^4\,e^2-84\,b\,c^3\,d^5\,e+28\,c^4\,d^6\right)}{e^9}+\frac{c^4\,x^6}{6\,e^3}","Not used",1,"(x*(8*c^4*d^7 - 4*a^3*b*e^7 + 4*b^4*d^3*e^4 - 12*a*b^3*d^2*e^5 + 12*a^2*b^2*d*e^6 + 24*a*c^3*d^5*e^2 - 20*b^3*c*d^4*e^3 + 24*a^2*c^2*d^3*e^4 + 36*b^2*c^2*d^5*e^2 + 8*a^3*c*d*e^6 - 28*b*c^3*d^6*e - 60*a*b*c^2*d^4*e^3 + 48*a*b^2*c*d^3*e^4 - 36*a^2*b*c*d^2*e^5) + (15*c^4*d^8 - a^4*e^8 + 7*b^4*d^4*e^4 - 20*a*b^3*d^3*e^5 + 44*a*c^3*d^6*e^2 + 12*a^3*c*d^2*e^6 - 36*b^3*c*d^5*e^3 + 18*a^2*b^2*d^2*e^6 + 42*a^2*c^2*d^4*e^4 + 66*b^2*c^2*d^6*e^2 - 4*a^3*b*d*e^7 - 52*b*c^3*d^7*e - 108*a*b*c^2*d^5*e^3 + 84*a*b^2*c*d^4*e^4 - 60*a^2*b*c*d^3*e^5)/(2*e))/(d^2*e^8 + e^10*x^2 + 2*d*e^9*x) + x^5*((4*b*c^3)/(5*e^3) - (3*c^4*d)/(5*e^4)) - x^3*((c^4*d^3)/(3*e^6) + (d^2*((4*b*c^3)/e^3 - (3*c^4*d)/e^4))/e^2 - (d*((3*d*((4*b*c^3)/e^3 - (3*c^4*d)/e^4))/e - (4*a*c^3 + 6*b^2*c^2)/e^3 + (3*c^4*d^2)/e^5))/e - (4*b*c*(3*a*c + b^2))/(3*e^3)) + x*((d^3*((3*d*((4*b*c^3)/e^3 - (3*c^4*d)/e^4))/e - (4*a*c^3 + 6*b^2*c^2)/e^3 + (3*c^4*d^2)/e^5))/e^3 - (3*d*((b^4 + 6*a^2*c^2 + 12*a*b^2*c)/e^3 + (3*d^2*((3*d*((4*b*c^3)/e^3 - (3*c^4*d)/e^4))/e - (4*a*c^3 + 6*b^2*c^2)/e^3 + (3*c^4*d^2)/e^5))/e^2 + (3*d*((c^4*d^3)/e^6 + (3*d^2*((4*b*c^3)/e^3 - (3*c^4*d)/e^4))/e^2 - (3*d*((3*d*((4*b*c^3)/e^3 - (3*c^4*d)/e^4))/e - (4*a*c^3 + 6*b^2*c^2)/e^3 + (3*c^4*d^2)/e^5))/e - (4*b*c*(3*a*c + b^2))/e^3))/e - (d^3*((4*b*c^3)/e^3 - (3*c^4*d)/e^4))/e^3))/e + (3*d^2*((c^4*d^3)/e^6 + (3*d^2*((4*b*c^3)/e^3 - (3*c^4*d)/e^4))/e^2 - (3*d*((3*d*((4*b*c^3)/e^3 - (3*c^4*d)/e^4))/e - (4*a*c^3 + 6*b^2*c^2)/e^3 + (3*c^4*d^2)/e^5))/e - (4*b*c*(3*a*c + b^2))/e^3))/e^2 + (4*a*b*(3*a*c + b^2))/e^3) + x^2*((b^4 + 6*a^2*c^2 + 12*a*b^2*c)/(2*e^3) + (3*d^2*((3*d*((4*b*c^3)/e^3 - (3*c^4*d)/e^4))/e - (4*a*c^3 + 6*b^2*c^2)/e^3 + (3*c^4*d^2)/e^5))/(2*e^2) + (3*d*((c^4*d^3)/e^6 + (3*d^2*((4*b*c^3)/e^3 - (3*c^4*d)/e^4))/e^2 - (3*d*((3*d*((4*b*c^3)/e^3 - (3*c^4*d)/e^4))/e - (4*a*c^3 + 6*b^2*c^2)/e^3 + (3*c^4*d^2)/e^5))/e - (4*b*c*(3*a*c + b^2))/e^3))/(2*e) - (d^3*((4*b*c^3)/e^3 - (3*c^4*d)/e^4))/(2*e^3)) - x^4*((3*d*((4*b*c^3)/e^3 - (3*c^4*d)/e^4))/(4*e) - (4*a*c^3 + 6*b^2*c^2)/(4*e^3) + (3*c^4*d^2)/(4*e^5)) + (log(d + e*x)*(28*c^4*d^6 + 4*a^3*c*e^6 + 6*a^2*b^2*e^6 + 6*b^4*d^2*e^4 + 60*a*c^3*d^4*e^2 - 40*b^3*c*d^3*e^3 + 36*a^2*c^2*d^2*e^4 + 90*b^2*c^2*d^4*e^2 - 12*a*b^3*d*e^5 - 84*b*c^3*d^5*e - 36*a^2*b*c*d*e^5 - 120*a*b*c^2*d^3*e^3 + 72*a*b^2*c*d^2*e^4))/e^9 + (c^4*x^6)/(6*e^3)","B"
2154,1,1143,417,0.844734,"\text{Not used}","int((a + b*x + c*x^2)^4/(d + e*x)^4,x)","x^4\,\left(\frac{b\,c^3}{e^4}-\frac{c^4\,d}{e^5}\right)-x^2\,\left(\frac{2\,c^4\,d^3}{e^7}+\frac{3\,d^2\,\left(\frac{4\,b\,c^3}{e^4}-\frac{4\,c^4\,d}{e^5}\right)}{e^2}-\frac{2\,d\,\left(\frac{4\,d\,\left(\frac{4\,b\,c^3}{e^4}-\frac{4\,c^4\,d}{e^5}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^4}+\frac{6\,c^4\,d^2}{e^6}\right)}{e}-\frac{2\,b\,c\,\left(b^2+3\,a\,c\right)}{e^4}\right)-x^3\,\left(\frac{4\,d\,\left(\frac{4\,b\,c^3}{e^4}-\frac{4\,c^4\,d}{e^5}\right)}{3\,e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{3\,e^4}+\frac{2\,c^4\,d^2}{e^6}\right)+x\,\left(\frac{6\,a^2\,c^2+12\,a\,b^2\,c+b^4}{e^4}+\frac{6\,d^2\,\left(\frac{4\,d\,\left(\frac{4\,b\,c^3}{e^4}-\frac{4\,c^4\,d}{e^5}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^4}+\frac{6\,c^4\,d^2}{e^6}\right)}{e^2}+\frac{4\,d\,\left(\frac{4\,c^4\,d^3}{e^7}+\frac{6\,d^2\,\left(\frac{4\,b\,c^3}{e^4}-\frac{4\,c^4\,d}{e^5}\right)}{e^2}-\frac{4\,d\,\left(\frac{4\,d\,\left(\frac{4\,b\,c^3}{e^4}-\frac{4\,c^4\,d}{e^5}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^4}+\frac{6\,c^4\,d^2}{e^6}\right)}{e}-\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{e^4}\right)}{e}-\frac{c^4\,d^4}{e^8}-\frac{4\,d^3\,\left(\frac{4\,b\,c^3}{e^4}-\frac{4\,c^4\,d}{e^5}\right)}{e^3}\right)-\frac{x\,\left(2\,a^3\,b\,e^7+4\,a^3\,c\,d\,e^6+6\,a^2\,b^2\,d\,e^6-54\,a^2\,b\,c\,d^2\,e^5+60\,a^2\,c^2\,d^3\,e^4-18\,a\,b^3\,d^2\,e^5+120\,a\,b^2\,c\,d^3\,e^4-210\,a\,b\,c^2\,d^4\,e^3+108\,a\,c^3\,d^5\,e^2+10\,b^4\,d^3\,e^4-70\,b^3\,c\,d^4\,e^3+162\,b^2\,c^2\,d^5\,e^2-154\,b\,c^3\,d^6\,e+52\,c^4\,d^7\right)+\frac{a^4\,e^8+2\,a^3\,b\,d\,e^7+4\,a^3\,c\,d^2\,e^6+6\,a^2\,b^2\,d^2\,e^6-66\,a^2\,b\,c\,d^3\,e^5+78\,a^2\,c^2\,d^4\,e^4-22\,a\,b^3\,d^3\,e^5+156\,a\,b^2\,c\,d^4\,e^4-282\,a\,b\,c^2\,d^5\,e^3+148\,a\,c^3\,d^6\,e^2+13\,b^4\,d^4\,e^4-94\,b^3\,c\,d^5\,e^3+222\,b^2\,c^2\,d^6\,e^2-214\,b\,c^3\,d^7\,e+73\,c^4\,d^8}{3\,e}+x^2\,\left(4\,a^3\,c\,e^7+6\,a^2\,b^2\,e^7-36\,a^2\,b\,c\,d\,e^6+36\,a^2\,c^2\,d^2\,e^5-12\,a\,b^3\,d\,e^6+72\,a\,b^2\,c\,d^2\,e^5-120\,a\,b\,c^2\,d^3\,e^4+60\,a\,c^3\,d^4\,e^3+6\,b^4\,d^2\,e^5-40\,b^3\,c\,d^3\,e^4+90\,b^2\,c^2\,d^4\,e^3-84\,b\,c^3\,d^5\,e^2+28\,c^4\,d^6\,e\right)}{d^3\,e^8+3\,d^2\,e^9\,x+3\,d\,e^{10}\,x^2+e^{11}\,x^3}+\frac{c^4\,x^5}{5\,e^4}-\frac{\ln\left(d+e\,x\right)\,\left(-12\,a^2\,b\,c\,e^5+24\,a^2\,c^2\,d\,e^4-4\,a\,b^3\,e^5+48\,a\,b^2\,c\,d\,e^4-120\,a\,b\,c^2\,d^2\,e^3+80\,a\,c^3\,d^3\,e^2+4\,b^4\,d\,e^4-40\,b^3\,c\,d^2\,e^3+120\,b^2\,c^2\,d^3\,e^2-140\,b\,c^3\,d^4\,e+56\,c^4\,d^5\right)}{e^9}","Not used",1,"x^4*((b*c^3)/e^4 - (c^4*d)/e^5) - x^2*((2*c^4*d^3)/e^7 + (3*d^2*((4*b*c^3)/e^4 - (4*c^4*d)/e^5))/e^2 - (2*d*((4*d*((4*b*c^3)/e^4 - (4*c^4*d)/e^5))/e - (4*a*c^3 + 6*b^2*c^2)/e^4 + (6*c^4*d^2)/e^6))/e - (2*b*c*(3*a*c + b^2))/e^4) - x^3*((4*d*((4*b*c^3)/e^4 - (4*c^4*d)/e^5))/(3*e) - (4*a*c^3 + 6*b^2*c^2)/(3*e^4) + (2*c^4*d^2)/e^6) + x*((b^4 + 6*a^2*c^2 + 12*a*b^2*c)/e^4 + (6*d^2*((4*d*((4*b*c^3)/e^4 - (4*c^4*d)/e^5))/e - (4*a*c^3 + 6*b^2*c^2)/e^4 + (6*c^4*d^2)/e^6))/e^2 + (4*d*((4*c^4*d^3)/e^7 + (6*d^2*((4*b*c^3)/e^4 - (4*c^4*d)/e^5))/e^2 - (4*d*((4*d*((4*b*c^3)/e^4 - (4*c^4*d)/e^5))/e - (4*a*c^3 + 6*b^2*c^2)/e^4 + (6*c^4*d^2)/e^6))/e - (4*b*c*(3*a*c + b^2))/e^4))/e - (c^4*d^4)/e^8 - (4*d^3*((4*b*c^3)/e^4 - (4*c^4*d)/e^5))/e^3) - (x*(52*c^4*d^7 + 2*a^3*b*e^7 + 10*b^4*d^3*e^4 - 18*a*b^3*d^2*e^5 + 6*a^2*b^2*d*e^6 + 108*a*c^3*d^5*e^2 - 70*b^3*c*d^4*e^3 + 60*a^2*c^2*d^3*e^4 + 162*b^2*c^2*d^5*e^2 + 4*a^3*c*d*e^6 - 154*b*c^3*d^6*e - 210*a*b*c^2*d^4*e^3 + 120*a*b^2*c*d^3*e^4 - 54*a^2*b*c*d^2*e^5) + (a^4*e^8 + 73*c^4*d^8 + 13*b^4*d^4*e^4 - 22*a*b^3*d^3*e^5 + 148*a*c^3*d^6*e^2 + 4*a^3*c*d^2*e^6 - 94*b^3*c*d^5*e^3 + 6*a^2*b^2*d^2*e^6 + 78*a^2*c^2*d^4*e^4 + 222*b^2*c^2*d^6*e^2 + 2*a^3*b*d*e^7 - 214*b*c^3*d^7*e - 282*a*b*c^2*d^5*e^3 + 156*a*b^2*c*d^4*e^4 - 66*a^2*b*c*d^3*e^5)/(3*e) + x^2*(4*a^3*c*e^7 + 28*c^4*d^6*e + 6*a^2*b^2*e^7 + 6*b^4*d^2*e^5 + 60*a*c^3*d^4*e^3 - 84*b*c^3*d^5*e^2 - 40*b^3*c*d^3*e^4 + 36*a^2*c^2*d^2*e^5 + 90*b^2*c^2*d^4*e^3 - 12*a*b^3*d*e^6 - 36*a^2*b*c*d*e^6 - 120*a*b*c^2*d^3*e^4 + 72*a*b^2*c*d^2*e^5))/(d^3*e^8 + e^11*x^3 + 3*d^2*e^9*x + 3*d*e^10*x^2) + (c^4*x^5)/(5*e^4) - (log(d + e*x)*(56*c^4*d^5 - 4*a*b^3*e^5 + 4*b^4*d*e^4 + 80*a*c^3*d^3*e^2 + 24*a^2*c^2*d*e^4 - 40*b^3*c*d^2*e^3 + 120*b^2*c^2*d^3*e^2 - 12*a^2*b*c*e^5 - 140*b*c^3*d^4*e + 48*a*b^2*c*d*e^4 - 120*a*b*c^2*d^2*e^3))/e^9","B"
2155,1,1005,426,0.813108,"\text{Not used}","int((a + b*x + c*x^2)^4/(d + e*x)^5,x)","x^3\,\left(\frac{4\,b\,c^3}{3\,e^5}-\frac{5\,c^4\,d}{3\,e^6}\right)-\frac{x\,\left(\frac{4\,a^3\,b\,e^7}{3}+\frac{4\,a^3\,c\,d\,e^6}{3}+2\,a^2\,b^2\,d\,e^6+12\,a^2\,b\,c\,d^2\,e^5-44\,a^2\,c^2\,d^3\,e^4+4\,a\,b^3\,d^2\,e^5-88\,a\,b^2\,c\,d^3\,e^4+260\,a\,b\,c^2\,d^4\,e^3-188\,a\,c^3\,d^5\,e^2-\frac{22\,b^4\,d^3\,e^4}{3}+\frac{260\,b^3\,c\,d^4\,e^3}{3}-282\,b^2\,c^2\,d^5\,e^2+\frac{1036\,b\,c^3\,d^6\,e}{3}-\frac{428\,c^4\,d^7}{3}\right)-x^3\,\left(-12\,a^2\,b\,c\,e^7+24\,a^2\,c^2\,d\,e^6-4\,a\,b^3\,e^7+48\,a\,b^2\,c\,d\,e^6-120\,a\,b\,c^2\,d^2\,e^5+80\,a\,c^3\,d^3\,e^4+4\,b^4\,d\,e^6-40\,b^3\,c\,d^2\,e^5+120\,b^2\,c^2\,d^3\,e^4-140\,b\,c^3\,d^4\,e^3+56\,c^4\,d^5\,e^2\right)+\frac{3\,a^4\,e^8+4\,a^3\,b\,d\,e^7+4\,a^3\,c\,d^2\,e^6+6\,a^2\,b^2\,d^2\,e^6+36\,a^2\,b\,c\,d^3\,e^5-150\,a^2\,c^2\,d^4\,e^4+12\,a\,b^3\,d^3\,e^5-300\,a\,b^2\,c\,d^4\,e^4+924\,a\,b\,c^2\,d^5\,e^3-684\,a\,c^3\,d^6\,e^2-25\,b^4\,d^4\,e^4+308\,b^3\,c\,d^5\,e^3-1026\,b^2\,c^2\,d^6\,e^2+1276\,b\,c^3\,d^7\,e-533\,c^4\,d^8}{12\,e}+x^2\,\left(2\,a^3\,c\,e^7+3\,a^2\,b^2\,e^7+18\,a^2\,b\,c\,d\,e^6-54\,a^2\,c^2\,d^2\,e^5+6\,a\,b^3\,d\,e^6-108\,a\,b^2\,c\,d^2\,e^5+300\,a\,b\,c^2\,d^3\,e^4-210\,a\,c^3\,d^4\,e^3-9\,b^4\,d^2\,e^5+100\,b^3\,c\,d^3\,e^4-315\,b^2\,c^2\,d^4\,e^3+378\,b\,c^3\,d^5\,e^2-154\,c^4\,d^6\,e\right)}{d^4\,e^8+4\,d^3\,e^9\,x+6\,d^2\,e^{10}\,x^2+4\,d\,e^{11}\,x^3+e^{12}\,x^4}-x^2\,\left(\frac{5\,d\,\left(\frac{4\,b\,c^3}{e^5}-\frac{5\,c^4\,d}{e^6}\right)}{2\,e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{2\,e^5}+\frac{5\,c^4\,d^2}{e^7}\right)-x\,\left(\frac{10\,c^4\,d^3}{e^8}+\frac{10\,d^2\,\left(\frac{4\,b\,c^3}{e^5}-\frac{5\,c^4\,d}{e^6}\right)}{e^2}-\frac{5\,d\,\left(\frac{5\,d\,\left(\frac{4\,b\,c^3}{e^5}-\frac{5\,c^4\,d}{e^6}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^5}+\frac{10\,c^4\,d^2}{e^7}\right)}{e}-\frac{4\,b\,c\,\left(b^2+3\,a\,c\right)}{e^5}\right)+\frac{c^4\,x^4}{4\,e^5}+\frac{\ln\left(d+e\,x\right)\,\left(6\,a^2\,c^2\,e^4+12\,a\,b^2\,c\,e^4-60\,a\,b\,c^2\,d\,e^3+60\,a\,c^3\,d^2\,e^2+b^4\,e^4-20\,b^3\,c\,d\,e^3+90\,b^2\,c^2\,d^2\,e^2-140\,b\,c^3\,d^3\,e+70\,c^4\,d^4\right)}{e^9}","Not used",1,"x^3*((4*b*c^3)/(3*e^5) - (5*c^4*d)/(3*e^6)) - (x*((4*a^3*b*e^7)/3 - (428*c^4*d^7)/3 - (22*b^4*d^3*e^4)/3 + 4*a*b^3*d^2*e^5 + 2*a^2*b^2*d*e^6 - 188*a*c^3*d^5*e^2 + (260*b^3*c*d^4*e^3)/3 - 44*a^2*c^2*d^3*e^4 - 282*b^2*c^2*d^5*e^2 + (4*a^3*c*d*e^6)/3 + (1036*b*c^3*d^6*e)/3 + 260*a*b*c^2*d^4*e^3 - 88*a*b^2*c*d^3*e^4 + 12*a^2*b*c*d^2*e^5) - x^3*(4*b^4*d*e^6 - 4*a*b^3*e^7 + 56*c^4*d^5*e^2 + 80*a*c^3*d^3*e^4 + 24*a^2*c^2*d*e^6 - 140*b*c^3*d^4*e^3 - 40*b^3*c*d^2*e^5 + 120*b^2*c^2*d^3*e^4 - 12*a^2*b*c*e^7 + 48*a*b^2*c*d*e^6 - 120*a*b*c^2*d^2*e^5) + (3*a^4*e^8 - 533*c^4*d^8 - 25*b^4*d^4*e^4 + 12*a*b^3*d^3*e^5 - 684*a*c^3*d^6*e^2 + 4*a^3*c*d^2*e^6 + 308*b^3*c*d^5*e^3 + 6*a^2*b^2*d^2*e^6 - 150*a^2*c^2*d^4*e^4 - 1026*b^2*c^2*d^6*e^2 + 4*a^3*b*d*e^7 + 1276*b*c^3*d^7*e + 924*a*b*c^2*d^5*e^3 - 300*a*b^2*c*d^4*e^4 + 36*a^2*b*c*d^3*e^5)/(12*e) + x^2*(2*a^3*c*e^7 - 154*c^4*d^6*e + 3*a^2*b^2*e^7 - 9*b^4*d^2*e^5 - 210*a*c^3*d^4*e^3 + 378*b*c^3*d^5*e^2 + 100*b^3*c*d^3*e^4 - 54*a^2*c^2*d^2*e^5 - 315*b^2*c^2*d^4*e^3 + 6*a*b^3*d*e^6 + 18*a^2*b*c*d*e^6 + 300*a*b*c^2*d^3*e^4 - 108*a*b^2*c*d^2*e^5))/(d^4*e^8 + e^12*x^4 + 4*d^3*e^9*x + 4*d*e^11*x^3 + 6*d^2*e^10*x^2) - x^2*((5*d*((4*b*c^3)/e^5 - (5*c^4*d)/e^6))/(2*e) - (4*a*c^3 + 6*b^2*c^2)/(2*e^5) + (5*c^4*d^2)/e^7) - x*((10*c^4*d^3)/e^8 + (10*d^2*((4*b*c^3)/e^5 - (5*c^4*d)/e^6))/e^2 - (5*d*((5*d*((4*b*c^3)/e^5 - (5*c^4*d)/e^6))/e - (4*a*c^3 + 6*b^2*c^2)/e^5 + (10*c^4*d^2)/e^7))/e - (4*b*c*(3*a*c + b^2))/e^5) + (c^4*x^4)/(4*e^5) + (log(d + e*x)*(b^4*e^4 + 70*c^4*d^4 + 6*a^2*c^2*e^4 + 60*a*c^3*d^2*e^2 + 90*b^2*c^2*d^2*e^2 + 12*a*b^2*c*e^4 - 140*b*c^3*d^3*e - 20*b^3*c*d*e^3 - 60*a*b*c^2*d*e^3))/e^9","B"
2156,1,959,414,0.212257,"\text{Not used}","int((a + b*x + c*x^2)^4/(d + e*x)^6,x)","x^2\,\left(\frac{2\,b\,c^3}{e^6}-\frac{3\,c^4\,d}{e^7}\right)-x\,\left(\frac{6\,d\,\left(\frac{4\,b\,c^3}{e^6}-\frac{6\,c^4\,d}{e^7}\right)}{e}-\frac{6\,b^2\,c^2+4\,a\,c^3}{e^6}+\frac{15\,c^4\,d^2}{e^8}\right)-\frac{x^3\,\left(6\,a^2\,b\,c\,e^7+12\,a^2\,c^2\,d\,e^6+2\,a\,b^3\,e^7+24\,a\,b^2\,c\,d\,e^6-180\,a\,b\,c^2\,d^2\,e^5+200\,a\,c^3\,d^3\,e^4+2\,b^4\,d\,e^6-60\,b^3\,c\,d^2\,e^5+300\,b^2\,c^2\,d^3\,e^4-490\,b\,c^3\,d^4\,e^3+252\,c^4\,d^5\,e^2\right)+x\,\left(a^3\,b\,e^7+\frac{2\,a^3\,c\,d\,e^6}{3}+a^2\,b^2\,d\,e^6+3\,a^2\,b\,c\,d^2\,e^5+6\,a^2\,c^2\,d^3\,e^4+a\,b^3\,d^2\,e^5+12\,a\,b^2\,c\,d^3\,e^4-125\,a\,b\,c^2\,d^4\,e^3+154\,a\,c^3\,d^5\,e^2+b^4\,d^3\,e^4-\frac{125\,b^3\,c\,d^4\,e^3}{3}+231\,b^2\,c^2\,d^5\,e^2-399\,b\,c^3\,d^6\,e+\frac{638\,c^4\,d^7}{3}\right)+x^4\,\left(6\,a^2\,c^2\,e^7+12\,a\,b^2\,c\,e^7-60\,a\,b\,c^2\,d\,e^6+60\,a\,c^3\,d^2\,e^5+b^4\,e^7-20\,b^3\,c\,d\,e^6+90\,b^2\,c^2\,d^2\,e^5-140\,b\,c^3\,d^3\,e^4+70\,c^4\,d^4\,e^3\right)+\frac{3\,a^4\,e^8+3\,a^3\,b\,d\,e^7+2\,a^3\,c\,d^2\,e^6+3\,a^2\,b^2\,d^2\,e^6+9\,a^2\,b\,c\,d^3\,e^5+18\,a^2\,c^2\,d^4\,e^4+3\,a\,b^3\,d^3\,e^5+36\,a\,b^2\,c\,d^4\,e^4-411\,a\,b\,c^2\,d^5\,e^3+522\,a\,c^3\,d^6\,e^2+3\,b^4\,d^4\,e^4-137\,b^3\,c\,d^5\,e^3+783\,b^2\,c^2\,d^6\,e^2-1377\,b\,c^3\,d^7\,e+743\,c^4\,d^8}{15\,e}+x^2\,\left(\frac{4\,a^3\,c\,e^7}{3}+2\,a^2\,b^2\,e^7+6\,a^2\,b\,c\,d\,e^6+12\,a^2\,c^2\,d^2\,e^5+2\,a\,b^3\,d\,e^6+24\,a\,b^2\,c\,d^2\,e^5-220\,a\,b\,c^2\,d^3\,e^4+260\,a\,c^3\,d^4\,e^3+2\,b^4\,d^2\,e^5-\frac{220\,b^3\,c\,d^3\,e^4}{3}+390\,b^2\,c^2\,d^4\,e^3-658\,b\,c^3\,d^5\,e^2+\frac{1036\,c^4\,d^6\,e}{3}\right)}{d^5\,e^8+5\,d^4\,e^9\,x+10\,d^3\,e^{10}\,x^2+10\,d^2\,e^{11}\,x^3+5\,d\,e^{12}\,x^4+e^{13}\,x^5}-\frac{\ln\left(d+e\,x\right)\,\left(-4\,b^3\,c\,e^3+36\,b^2\,c^2\,d\,e^2-84\,b\,c^3\,d^2\,e-12\,a\,b\,c^2\,e^3+56\,c^4\,d^3+24\,a\,c^3\,d\,e^2\right)}{e^9}+\frac{c^4\,x^3}{3\,e^6}","Not used",1,"x^2*((2*b*c^3)/e^6 - (3*c^4*d)/e^7) - x*((6*d*((4*b*c^3)/e^6 - (6*c^4*d)/e^7))/e - (4*a*c^3 + 6*b^2*c^2)/e^6 + (15*c^4*d^2)/e^8) - (x^3*(2*a*b^3*e^7 + 2*b^4*d*e^6 + 252*c^4*d^5*e^2 + 200*a*c^3*d^3*e^4 + 12*a^2*c^2*d*e^6 - 490*b*c^3*d^4*e^3 - 60*b^3*c*d^2*e^5 + 300*b^2*c^2*d^3*e^4 + 6*a^2*b*c*e^7 + 24*a*b^2*c*d*e^6 - 180*a*b*c^2*d^2*e^5) + x*((638*c^4*d^7)/3 + a^3*b*e^7 + b^4*d^3*e^4 + a*b^3*d^2*e^5 + a^2*b^2*d*e^6 + 154*a*c^3*d^5*e^2 - (125*b^3*c*d^4*e^3)/3 + 6*a^2*c^2*d^3*e^4 + 231*b^2*c^2*d^5*e^2 + (2*a^3*c*d*e^6)/3 - 399*b*c^3*d^6*e - 125*a*b*c^2*d^4*e^3 + 12*a*b^2*c*d^3*e^4 + 3*a^2*b*c*d^2*e^5) + x^4*(b^4*e^7 + 6*a^2*c^2*e^7 + 70*c^4*d^4*e^3 + 60*a*c^3*d^2*e^5 - 140*b*c^3*d^3*e^4 + 90*b^2*c^2*d^2*e^5 + 12*a*b^2*c*e^7 - 20*b^3*c*d*e^6 - 60*a*b*c^2*d*e^6) + (3*a^4*e^8 + 743*c^4*d^8 + 3*b^4*d^4*e^4 + 3*a*b^3*d^3*e^5 + 522*a*c^3*d^6*e^2 + 2*a^3*c*d^2*e^6 - 137*b^3*c*d^5*e^3 + 3*a^2*b^2*d^2*e^6 + 18*a^2*c^2*d^4*e^4 + 783*b^2*c^2*d^6*e^2 + 3*a^3*b*d*e^7 - 1377*b*c^3*d^7*e - 411*a*b*c^2*d^5*e^3 + 36*a*b^2*c*d^4*e^4 + 9*a^2*b*c*d^3*e^5)/(15*e) + x^2*((4*a^3*c*e^7)/3 + (1036*c^4*d^6*e)/3 + 2*a^2*b^2*e^7 + 2*b^4*d^2*e^5 + 260*a*c^3*d^4*e^3 - 658*b*c^3*d^5*e^2 - (220*b^3*c*d^3*e^4)/3 + 12*a^2*c^2*d^2*e^5 + 390*b^2*c^2*d^4*e^3 + 2*a*b^3*d*e^6 + 6*a^2*b*c*d*e^6 - 220*a*b*c^2*d^3*e^4 + 24*a*b^2*c*d^2*e^5))/(d^5*e^8 + e^13*x^5 + 5*d^4*e^9*x + 5*d*e^12*x^4 + 10*d^3*e^10*x^2 + 10*d^2*e^11*x^3) - (log(d + e*x)*(56*c^4*d^3 - 4*b^3*c*e^3 + 36*b^2*c^2*d*e^2 - 12*a*b*c^2*e^3 + 24*a*c^3*d*e^2 - 84*b*c^3*d^2*e))/e^9 + (c^4*x^3)/(3*e^6)","B"
2157,1,955,426,0.813451,"\text{Not used}","int((a + b*x + c*x^2)^4/(d + e*x)^7,x)","x\,\left(\frac{4\,b\,c^3}{e^7}-\frac{7\,c^4\,d}{e^8}\right)-\frac{x^3\,\left(4\,a^2\,b\,c\,e^7+4\,a^2\,c^2\,d\,e^6+\frac{4\,a\,b^3\,e^7}{3}+8\,a\,b^2\,c\,d\,e^6+40\,a\,b\,c^2\,d^2\,e^5-\frac{440\,a\,c^3\,d^3\,e^4}{3}+\frac{2\,b^4\,d\,e^6}{3}+\frac{40\,b^3\,c\,d^2\,e^5}{3}-220\,b^2\,c^2\,d^3\,e^4+\frac{1820\,b\,c^3\,d^4\,e^3}{3}-\frac{1316\,c^4\,d^5\,e^2}{3}\right)+x\,\left(\frac{4\,a^3\,b\,e^7}{5}+\frac{2\,a^3\,c\,d\,e^6}{5}+\frac{3\,a^2\,b^2\,d\,e^6}{5}+\frac{6\,a^2\,b\,c\,d^2\,e^5}{5}+\frac{6\,a^2\,c^2\,d^3\,e^4}{5}+\frac{2\,a\,b^3\,d^2\,e^5}{5}+\frac{12\,a\,b^2\,c\,d^3\,e^4}{5}+12\,a\,b\,c^2\,d^4\,e^3-\frac{274\,a\,c^3\,d^5\,e^2}{5}+\frac{b^4\,d^3\,e^4}{5}+4\,b^3\,c\,d^4\,e^3-\frac{411\,b^2\,c^2\,d^5\,e^2}{5}+\frac{1218\,b\,c^3\,d^6\,e}{5}-\frac{918\,c^4\,d^7}{5}\right)+x^4\,\left(3\,a^2\,c^2\,e^7+6\,a\,b^2\,c\,e^7+30\,a\,b\,c^2\,d\,e^6-90\,a\,c^3\,d^2\,e^5+\frac{b^4\,e^7}{2}+10\,b^3\,c\,d\,e^6-135\,b^2\,c^2\,d^2\,e^5+350\,b\,c^3\,d^3\,e^4-245\,c^4\,d^4\,e^3\right)+x^5\,\left(4\,b^3\,c\,e^7-36\,b^2\,c^2\,d\,e^6+84\,b\,c^3\,d^2\,e^5+12\,a\,b\,c^2\,e^7-56\,c^4\,d^3\,e^4-24\,a\,c^3\,d\,e^6\right)+\frac{5\,a^4\,e^8+4\,a^3\,b\,d\,e^7+2\,a^3\,c\,d^2\,e^6+3\,a^2\,b^2\,d^2\,e^6+6\,a^2\,b\,c\,d^3\,e^5+6\,a^2\,c^2\,d^4\,e^4+2\,a\,b^3\,d^3\,e^5+12\,a\,b^2\,c\,d^4\,e^4+60\,a\,b\,c^2\,d^5\,e^3-294\,a\,c^3\,d^6\,e^2+b^4\,d^4\,e^4+20\,b^3\,c\,d^5\,e^3-441\,b^2\,c^2\,d^6\,e^2+1338\,b\,c^3\,d^7\,e-1023\,c^4\,d^8}{30\,e}+x^2\,\left(a^3\,c\,e^7+\frac{3\,a^2\,b^2\,e^7}{2}+3\,a^2\,b\,c\,d\,e^6+3\,a^2\,c^2\,d^2\,e^5+a\,b^3\,d\,e^6+6\,a\,b^2\,c\,d^2\,e^5+30\,a\,b\,c^2\,d^3\,e^4-125\,a\,c^3\,d^4\,e^3+\frac{b^4\,d^2\,e^5}{2}+10\,b^3\,c\,d^3\,e^4-\frac{375\,b^2\,c^2\,d^4\,e^3}{2}+539\,b\,c^3\,d^5\,e^2-399\,c^4\,d^6\,e\right)}{d^6\,e^8+6\,d^5\,e^9\,x+15\,d^4\,e^{10}\,x^2+20\,d^3\,e^{11}\,x^3+15\,d^2\,e^{12}\,x^4+6\,d\,e^{13}\,x^5+e^{14}\,x^6}+\frac{\ln\left(d+e\,x\right)\,\left(6\,b^2\,c^2\,e^2-28\,b\,c^3\,d\,e+28\,c^4\,d^2+4\,a\,c^3\,e^2\right)}{e^9}+\frac{c^4\,x^2}{2\,e^7}","Not used",1,"x*((4*b*c^3)/e^7 - (7*c^4*d)/e^8) - (x^3*((4*a*b^3*e^7)/3 + (2*b^4*d*e^6)/3 - (1316*c^4*d^5*e^2)/3 - (440*a*c^3*d^3*e^4)/3 + 4*a^2*c^2*d*e^6 + (1820*b*c^3*d^4*e^3)/3 + (40*b^3*c*d^2*e^5)/3 - 220*b^2*c^2*d^3*e^4 + 4*a^2*b*c*e^7 + 8*a*b^2*c*d*e^6 + 40*a*b*c^2*d^2*e^5) + x*((4*a^3*b*e^7)/5 - (918*c^4*d^7)/5 + (b^4*d^3*e^4)/5 + (2*a*b^3*d^2*e^5)/5 + (3*a^2*b^2*d*e^6)/5 - (274*a*c^3*d^5*e^2)/5 + 4*b^3*c*d^4*e^3 + (6*a^2*c^2*d^3*e^4)/5 - (411*b^2*c^2*d^5*e^2)/5 + (2*a^3*c*d*e^6)/5 + (1218*b*c^3*d^6*e)/5 + 12*a*b*c^2*d^4*e^3 + (12*a*b^2*c*d^3*e^4)/5 + (6*a^2*b*c*d^2*e^5)/5) + x^4*((b^4*e^7)/2 + 3*a^2*c^2*e^7 - 245*c^4*d^4*e^3 - 90*a*c^3*d^2*e^5 + 350*b*c^3*d^3*e^4 - 135*b^2*c^2*d^2*e^5 + 6*a*b^2*c*e^7 + 10*b^3*c*d*e^6 + 30*a*b*c^2*d*e^6) + x^5*(4*b^3*c*e^7 - 56*c^4*d^3*e^4 + 84*b*c^3*d^2*e^5 - 36*b^2*c^2*d*e^6 + 12*a*b*c^2*e^7 - 24*a*c^3*d*e^6) + (5*a^4*e^8 - 1023*c^4*d^8 + b^4*d^4*e^4 + 2*a*b^3*d^3*e^5 - 294*a*c^3*d^6*e^2 + 2*a^3*c*d^2*e^6 + 20*b^3*c*d^5*e^3 + 3*a^2*b^2*d^2*e^6 + 6*a^2*c^2*d^4*e^4 - 441*b^2*c^2*d^6*e^2 + 4*a^3*b*d*e^7 + 1338*b*c^3*d^7*e + 60*a*b*c^2*d^5*e^3 + 12*a*b^2*c*d^4*e^4 + 6*a^2*b*c*d^3*e^5)/(30*e) + x^2*(a^3*c*e^7 - 399*c^4*d^6*e + (3*a^2*b^2*e^7)/2 + (b^4*d^2*e^5)/2 - 125*a*c^3*d^4*e^3 + 539*b*c^3*d^5*e^2 + 10*b^3*c*d^3*e^4 + 3*a^2*c^2*d^2*e^5 - (375*b^2*c^2*d^4*e^3)/2 + a*b^3*d*e^6 + 3*a^2*b*c*d*e^6 + 30*a*b*c^2*d^3*e^4 + 6*a*b^2*c*d^2*e^5))/(d^6*e^8 + e^14*x^6 + 6*d^5*e^9*x + 6*d*e^13*x^5 + 15*d^4*e^10*x^2 + 20*d^3*e^11*x^3 + 15*d^2*e^12*x^4) + (log(d + e*x)*(28*c^4*d^2 + 4*a*c^3*e^2 + 6*b^2*c^2*e^2 - 28*b*c^3*d*e))/e^9 + (c^4*x^2)/(2*e^7)","B"
2158,1,1306,424,0.951503,"\text{Not used}","int((a + b*x + c*x^2)^4/(d + e*x)^8,x)","-\frac{\frac{a^4\,e^8}{7}+\frac{481\,c^4\,d^8}{35}+8\,c^4\,d^8\,\ln\left(d+e\,x\right)+\frac{b^4\,d^4\,e^4}{105}+\frac{b^4\,e^8\,x^4}{3}-c^4\,e^8\,x^8+\frac{a\,b^3\,d^3\,e^5}{35}+\frac{4\,a\,c^3\,d^6\,e^2}{7}+\frac{4\,a^3\,c\,d^2\,e^6}{105}+\frac{2\,b^3\,c\,d^5\,e^3}{21}+a\,b^3\,e^8\,x^3+\frac{4\,a^3\,c\,e^8\,x^2}{5}+4\,a\,c^3\,e^8\,x^6+2\,b^3\,c\,e^8\,x^5+\frac{b^4\,d^3\,e^5\,x}{15}+\frac{b^4\,d\,e^7\,x^3}{3}-7\,c^4\,d\,e^7\,x^7+\frac{2\,a^2\,b^2\,d^2\,e^6}{35}+\frac{2\,a^2\,c^2\,d^4\,e^4}{35}+\frac{6\,b^2\,c^2\,d^6\,e^2}{7}+\frac{6\,a^2\,b^2\,e^8\,x^2}{5}+2\,a^2\,c^2\,e^8\,x^4+6\,b^2\,c^2\,e^8\,x^6+\frac{b^4\,d^2\,e^6\,x^2}{5}+\frac{1183\,c^4\,d^6\,e^2\,x^2}{5}+\frac{1015\,c^4\,d^5\,e^3\,x^3}{3}+\frac{805\,c^4\,d^4\,e^4\,x^4}{3}+105\,c^4\,d^3\,e^5\,x^5+7\,c^4\,d^2\,e^6\,x^6+\frac{2\,a^3\,b\,d\,e^7}{21}-\frac{363\,b\,c^3\,d^7\,e}{35}+\frac{2\,a^3\,b\,e^8\,x}{3}+\frac{441\,c^4\,d^7\,e\,x}{5}-4\,b\,c^3\,d^7\,e\,\ln\left(d+e\,x\right)+\frac{4\,a^3\,c\,d\,e^7\,x}{15}+56\,c^4\,d^7\,e\,x\,\ln\left(d+e\,x\right)+\frac{6\,a^2\,c^2\,d^2\,e^6\,x^2}{5}+18\,b^2\,c^2\,d^4\,e^4\,x^2+30\,b^2\,c^2\,d^3\,e^5\,x^3+30\,b^2\,c^2\,d^2\,e^6\,x^4+\frac{2\,a\,b\,c^2\,d^5\,e^3}{7}+\frac{4\,a\,b^2\,c\,d^4\,e^4}{35}+\frac{3\,a^2\,b\,c\,d^3\,e^5}{35}+3\,a^2\,b\,c\,e^8\,x^3+4\,a\,b^2\,c\,e^8\,x^4+6\,a\,b\,c^2\,e^8\,x^5+\frac{a\,b^3\,d^2\,e^6\,x}{5}+\frac{2\,a^2\,b^2\,d\,e^7\,x}{5}+\frac{3\,a\,b^3\,d\,e^7\,x^2}{5}+4\,a\,c^3\,d^5\,e^3\,x+12\,a\,c^3\,d\,e^7\,x^5-\frac{343\,b\,c^3\,d^6\,e^2\,x}{5}+\frac{2\,b^3\,c\,d^4\,e^4\,x}{3}+\frac{10\,b^3\,c\,d\,e^7\,x^4}{3}-28\,b\,c^3\,d\,e^7\,x^6-4\,b\,c^3\,e^8\,x^7\,\ln\left(d+e\,x\right)+8\,c^4\,d\,e^7\,x^7\,\ln\left(d+e\,x\right)+\frac{2\,a^2\,c^2\,d^3\,e^5\,x}{5}+12\,a\,c^3\,d^4\,e^4\,x^2+20\,a\,c^3\,d^3\,e^5\,x^3+2\,a^2\,c^2\,d\,e^7\,x^3+20\,a\,c^3\,d^2\,e^6\,x^4+6\,b^2\,c^2\,d^5\,e^3\,x-\frac{959\,b\,c^3\,d^5\,e^3\,x^2}{5}+2\,b^3\,c\,d^3\,e^5\,x^2-\frac{875\,b\,c^3\,d^4\,e^4\,x^3}{3}+\frac{10\,b^3\,c\,d^2\,e^6\,x^3}{3}-\frac{770\,b\,c^3\,d^3\,e^5\,x^4}{3}-126\,b\,c^3\,d^2\,e^6\,x^5+18\,b^2\,c^2\,d\,e^7\,x^5+168\,c^4\,d^6\,e^2\,x^2\,\ln\left(d+e\,x\right)+280\,c^4\,d^5\,e^3\,x^3\,\ln\left(d+e\,x\right)+280\,c^4\,d^4\,e^4\,x^4\,\ln\left(d+e\,x\right)+168\,c^4\,d^3\,e^5\,x^5\,\ln\left(d+e\,x\right)+56\,c^4\,d^2\,e^6\,x^6\,\ln\left(d+e\,x\right)+6\,a\,b\,c^2\,d^3\,e^5\,x^2+\frac{12\,a\,b^2\,c\,d^2\,e^6\,x^2}{5}+10\,a\,b\,c^2\,d^2\,e^6\,x^3-84\,b\,c^3\,d^5\,e^3\,x^2\,\ln\left(d+e\,x\right)-140\,b\,c^3\,d^4\,e^4\,x^3\,\ln\left(d+e\,x\right)-140\,b\,c^3\,d^3\,e^5\,x^4\,\ln\left(d+e\,x\right)-84\,b\,c^3\,d^2\,e^6\,x^5\,\ln\left(d+e\,x\right)+2\,a\,b\,c^2\,d^4\,e^4\,x+\frac{4\,a\,b^2\,c\,d^3\,e^5\,x}{5}+\frac{3\,a^2\,b\,c\,d^2\,e^6\,x}{5}+\frac{9\,a^2\,b\,c\,d\,e^7\,x^2}{5}+4\,a\,b^2\,c\,d\,e^7\,x^3+10\,a\,b\,c^2\,d\,e^7\,x^4-28\,b\,c^3\,d^6\,e^2\,x\,\ln\left(d+e\,x\right)-28\,b\,c^3\,d\,e^7\,x^6\,\ln\left(d+e\,x\right)}{e^9\,{\left(d+e\,x\right)}^7}","Not used",1,"-((a^4*e^8)/7 + (481*c^4*d^8)/35 + 8*c^4*d^8*log(d + e*x) + (b^4*d^4*e^4)/105 + (b^4*e^8*x^4)/3 - c^4*e^8*x^8 + (a*b^3*d^3*e^5)/35 + (4*a*c^3*d^6*e^2)/7 + (4*a^3*c*d^2*e^6)/105 + (2*b^3*c*d^5*e^3)/21 + a*b^3*e^8*x^3 + (4*a^3*c*e^8*x^2)/5 + 4*a*c^3*e^8*x^6 + 2*b^3*c*e^8*x^5 + (b^4*d^3*e^5*x)/15 + (b^4*d*e^7*x^3)/3 - 7*c^4*d*e^7*x^7 + (2*a^2*b^2*d^2*e^6)/35 + (2*a^2*c^2*d^4*e^4)/35 + (6*b^2*c^2*d^6*e^2)/7 + (6*a^2*b^2*e^8*x^2)/5 + 2*a^2*c^2*e^8*x^4 + 6*b^2*c^2*e^8*x^6 + (b^4*d^2*e^6*x^2)/5 + (1183*c^4*d^6*e^2*x^2)/5 + (1015*c^4*d^5*e^3*x^3)/3 + (805*c^4*d^4*e^4*x^4)/3 + 105*c^4*d^3*e^5*x^5 + 7*c^4*d^2*e^6*x^6 + (2*a^3*b*d*e^7)/21 - (363*b*c^3*d^7*e)/35 + (2*a^3*b*e^8*x)/3 + (441*c^4*d^7*e*x)/5 - 4*b*c^3*d^7*e*log(d + e*x) + (4*a^3*c*d*e^7*x)/15 + 56*c^4*d^7*e*x*log(d + e*x) + (6*a^2*c^2*d^2*e^6*x^2)/5 + 18*b^2*c^2*d^4*e^4*x^2 + 30*b^2*c^2*d^3*e^5*x^3 + 30*b^2*c^2*d^2*e^6*x^4 + (2*a*b*c^2*d^5*e^3)/7 + (4*a*b^2*c*d^4*e^4)/35 + (3*a^2*b*c*d^3*e^5)/35 + 3*a^2*b*c*e^8*x^3 + 4*a*b^2*c*e^8*x^4 + 6*a*b*c^2*e^8*x^5 + (a*b^3*d^2*e^6*x)/5 + (2*a^2*b^2*d*e^7*x)/5 + (3*a*b^3*d*e^7*x^2)/5 + 4*a*c^3*d^5*e^3*x + 12*a*c^3*d*e^7*x^5 - (343*b*c^3*d^6*e^2*x)/5 + (2*b^3*c*d^4*e^4*x)/3 + (10*b^3*c*d*e^7*x^4)/3 - 28*b*c^3*d*e^7*x^6 - 4*b*c^3*e^8*x^7*log(d + e*x) + 8*c^4*d*e^7*x^7*log(d + e*x) + (2*a^2*c^2*d^3*e^5*x)/5 + 12*a*c^3*d^4*e^4*x^2 + 20*a*c^3*d^3*e^5*x^3 + 2*a^2*c^2*d*e^7*x^3 + 20*a*c^3*d^2*e^6*x^4 + 6*b^2*c^2*d^5*e^3*x - (959*b*c^3*d^5*e^3*x^2)/5 + 2*b^3*c*d^3*e^5*x^2 - (875*b*c^3*d^4*e^4*x^3)/3 + (10*b^3*c*d^2*e^6*x^3)/3 - (770*b*c^3*d^3*e^5*x^4)/3 - 126*b*c^3*d^2*e^6*x^5 + 18*b^2*c^2*d*e^7*x^5 + 168*c^4*d^6*e^2*x^2*log(d + e*x) + 280*c^4*d^5*e^3*x^3*log(d + e*x) + 280*c^4*d^4*e^4*x^4*log(d + e*x) + 168*c^4*d^3*e^5*x^5*log(d + e*x) + 56*c^4*d^2*e^6*x^6*log(d + e*x) + 6*a*b*c^2*d^3*e^5*x^2 + (12*a*b^2*c*d^2*e^6*x^2)/5 + 10*a*b*c^2*d^2*e^6*x^3 - 84*b*c^3*d^5*e^3*x^2*log(d + e*x) - 140*b*c^3*d^4*e^4*x^3*log(d + e*x) - 140*b*c^3*d^3*e^5*x^4*log(d + e*x) - 84*b*c^3*d^2*e^6*x^5*log(d + e*x) + 2*a*b*c^2*d^4*e^4*x + (4*a*b^2*c*d^3*e^5*x)/5 + (3*a^2*b*c*d^2*e^6*x)/5 + (9*a^2*b*c*d*e^7*x^2)/5 + 4*a*b^2*c*d*e^7*x^3 + 10*a*b*c^2*d*e^7*x^4 - 28*b*c^3*d^6*e^2*x*log(d + e*x) - 28*b*c^3*d*e^7*x^6*log(d + e*x))/(e^9*(d + e*x)^7)","B"
2159,1,1168,435,0.939390,"\text{Not used}","int((a + b*x + c*x^2)^4/(d + e*x)^9,x)","-\frac{\frac{a^4\,e^8}{8}-\frac{761\,c^4\,d^8}{280}-c^4\,d^8\,\ln\left(d+e\,x\right)+\frac{b^4\,d^4\,e^4}{280}+\frac{b^4\,e^8\,x^4}{4}+\frac{a\,b^3\,d^3\,e^5}{70}+\frac{a\,c^3\,d^6\,e^2}{14}+\frac{a^3\,c\,d^2\,e^6}{42}+\frac{b^3\,c\,d^5\,e^3}{42}+\frac{4\,a\,b^3\,e^8\,x^3}{5}+\frac{2\,a^3\,c\,e^8\,x^2}{3}+2\,a\,c^3\,e^8\,x^6+\frac{4\,b^3\,c\,e^8\,x^5}{3}+4\,b\,c^3\,e^8\,x^7+\frac{b^4\,d^3\,e^5\,x}{35}+\frac{b^4\,d\,e^7\,x^3}{5}-8\,c^4\,d\,e^7\,x^7-c^4\,e^8\,x^8\,\ln\left(d+e\,x\right)+\frac{a^2\,b^2\,d^2\,e^6}{28}+\frac{3\,a^2\,c^2\,d^4\,e^4}{140}+\frac{3\,b^2\,c^2\,d^6\,e^2}{28}+a^2\,b^2\,e^8\,x^2+\frac{3\,a^2\,c^2\,e^8\,x^4}{2}+3\,b^2\,c^2\,e^8\,x^6+\frac{b^4\,d^2\,e^6\,x^2}{10}-\frac{343\,c^4\,d^6\,e^2\,x^2}{5}-\frac{1918\,c^4\,d^5\,e^3\,x^3}{15}-\frac{875\,c^4\,d^4\,e^4\,x^4}{6}-\frac{308\,c^4\,d^3\,e^5\,x^5}{3}-42\,c^4\,d^2\,e^6\,x^6+\frac{a^3\,b\,d\,e^7}{14}+\frac{b\,c^3\,d^7\,e}{2}+\frac{4\,a^3\,b\,e^8\,x}{7}-\frac{726\,c^4\,d^7\,e\,x}{35}+\frac{4\,a^3\,c\,d\,e^7\,x}{21}-8\,c^4\,d^7\,e\,x\,\ln\left(d+e\,x\right)+\frac{3\,a^2\,c^2\,d^2\,e^6\,x^2}{5}+3\,b^2\,c^2\,d^4\,e^4\,x^2+6\,b^2\,c^2\,d^3\,e^5\,x^3+\frac{15\,b^2\,c^2\,d^2\,e^6\,x^4}{2}+\frac{a\,b\,c^2\,d^5\,e^3}{14}+\frac{3\,a\,b^2\,c\,d^4\,e^4}{70}+\frac{3\,a^2\,b\,c\,d^3\,e^5}{70}+\frac{12\,a^2\,b\,c\,e^8\,x^3}{5}+3\,a\,b^2\,c\,e^8\,x^4+4\,a\,b\,c^2\,e^8\,x^5+\frac{4\,a\,b^3\,d^2\,e^6\,x}{35}+\frac{2\,a^2\,b^2\,d\,e^7\,x}{7}+\frac{2\,a\,b^3\,d\,e^7\,x^2}{5}+\frac{4\,a\,c^3\,d^5\,e^3\,x}{7}+4\,a\,c^3\,d\,e^7\,x^5+4\,b\,c^3\,d^6\,e^2\,x+\frac{4\,b^3\,c\,d^4\,e^4\,x}{21}+\frac{5\,b^3\,c\,d\,e^7\,x^4}{3}+14\,b\,c^3\,d\,e^7\,x^6-8\,c^4\,d\,e^7\,x^7\,\ln\left(d+e\,x\right)+\frac{6\,a^2\,c^2\,d^3\,e^5\,x}{35}+2\,a\,c^3\,d^4\,e^4\,x^2+4\,a\,c^3\,d^3\,e^5\,x^3+\frac{6\,a^2\,c^2\,d\,e^7\,x^3}{5}+5\,a\,c^3\,d^2\,e^6\,x^4+\frac{6\,b^2\,c^2\,d^5\,e^3\,x}{7}+14\,b\,c^3\,d^5\,e^3\,x^2+\frac{2\,b^3\,c\,d^3\,e^5\,x^2}{3}+28\,b\,c^3\,d^4\,e^4\,x^3+\frac{4\,b^3\,c\,d^2\,e^6\,x^3}{3}+35\,b\,c^3\,d^3\,e^5\,x^4+28\,b\,c^3\,d^2\,e^6\,x^5+6\,b^2\,c^2\,d\,e^7\,x^5-28\,c^4\,d^6\,e^2\,x^2\,\ln\left(d+e\,x\right)-56\,c^4\,d^5\,e^3\,x^3\,\ln\left(d+e\,x\right)-70\,c^4\,d^4\,e^4\,x^4\,\ln\left(d+e\,x\right)-56\,c^4\,d^3\,e^5\,x^5\,\ln\left(d+e\,x\right)-28\,c^4\,d^2\,e^6\,x^6\,\ln\left(d+e\,x\right)+2\,a\,b\,c^2\,d^3\,e^5\,x^2+\frac{6\,a\,b^2\,c\,d^2\,e^6\,x^2}{5}+4\,a\,b\,c^2\,d^2\,e^6\,x^3+\frac{4\,a\,b\,c^2\,d^4\,e^4\,x}{7}+\frac{12\,a\,b^2\,c\,d^3\,e^5\,x}{35}+\frac{12\,a^2\,b\,c\,d^2\,e^6\,x}{35}+\frac{6\,a^2\,b\,c\,d\,e^7\,x^2}{5}+\frac{12\,a\,b^2\,c\,d\,e^7\,x^3}{5}+5\,a\,b\,c^2\,d\,e^7\,x^4}{e^9\,{\left(d+e\,x\right)}^8}","Not used",1,"-((a^4*e^8)/8 - (761*c^4*d^8)/280 - c^4*d^8*log(d + e*x) + (b^4*d^4*e^4)/280 + (b^4*e^8*x^4)/4 + (a*b^3*d^3*e^5)/70 + (a*c^3*d^6*e^2)/14 + (a^3*c*d^2*e^6)/42 + (b^3*c*d^5*e^3)/42 + (4*a*b^3*e^8*x^3)/5 + (2*a^3*c*e^8*x^2)/3 + 2*a*c^3*e^8*x^6 + (4*b^3*c*e^8*x^5)/3 + 4*b*c^3*e^8*x^7 + (b^4*d^3*e^5*x)/35 + (b^4*d*e^7*x^3)/5 - 8*c^4*d*e^7*x^7 - c^4*e^8*x^8*log(d + e*x) + (a^2*b^2*d^2*e^6)/28 + (3*a^2*c^2*d^4*e^4)/140 + (3*b^2*c^2*d^6*e^2)/28 + a^2*b^2*e^8*x^2 + (3*a^2*c^2*e^8*x^4)/2 + 3*b^2*c^2*e^8*x^6 + (b^4*d^2*e^6*x^2)/10 - (343*c^4*d^6*e^2*x^2)/5 - (1918*c^4*d^5*e^3*x^3)/15 - (875*c^4*d^4*e^4*x^4)/6 - (308*c^4*d^3*e^5*x^5)/3 - 42*c^4*d^2*e^6*x^6 + (a^3*b*d*e^7)/14 + (b*c^3*d^7*e)/2 + (4*a^3*b*e^8*x)/7 - (726*c^4*d^7*e*x)/35 + (4*a^3*c*d*e^7*x)/21 - 8*c^4*d^7*e*x*log(d + e*x) + (3*a^2*c^2*d^2*e^6*x^2)/5 + 3*b^2*c^2*d^4*e^4*x^2 + 6*b^2*c^2*d^3*e^5*x^3 + (15*b^2*c^2*d^2*e^6*x^4)/2 + (a*b*c^2*d^5*e^3)/14 + (3*a*b^2*c*d^4*e^4)/70 + (3*a^2*b*c*d^3*e^5)/70 + (12*a^2*b*c*e^8*x^3)/5 + 3*a*b^2*c*e^8*x^4 + 4*a*b*c^2*e^8*x^5 + (4*a*b^3*d^2*e^6*x)/35 + (2*a^2*b^2*d*e^7*x)/7 + (2*a*b^3*d*e^7*x^2)/5 + (4*a*c^3*d^5*e^3*x)/7 + 4*a*c^3*d*e^7*x^5 + 4*b*c^3*d^6*e^2*x + (4*b^3*c*d^4*e^4*x)/21 + (5*b^3*c*d*e^7*x^4)/3 + 14*b*c^3*d*e^7*x^6 - 8*c^4*d*e^7*x^7*log(d + e*x) + (6*a^2*c^2*d^3*e^5*x)/35 + 2*a*c^3*d^4*e^4*x^2 + 4*a*c^3*d^3*e^5*x^3 + (6*a^2*c^2*d*e^7*x^3)/5 + 5*a*c^3*d^2*e^6*x^4 + (6*b^2*c^2*d^5*e^3*x)/7 + 14*b*c^3*d^5*e^3*x^2 + (2*b^3*c*d^3*e^5*x^2)/3 + 28*b*c^3*d^4*e^4*x^3 + (4*b^3*c*d^2*e^6*x^3)/3 + 35*b*c^3*d^3*e^5*x^4 + 28*b*c^3*d^2*e^6*x^5 + 6*b^2*c^2*d*e^7*x^5 - 28*c^4*d^6*e^2*x^2*log(d + e*x) - 56*c^4*d^5*e^3*x^3*log(d + e*x) - 70*c^4*d^4*e^4*x^4*log(d + e*x) - 56*c^4*d^3*e^5*x^5*log(d + e*x) - 28*c^4*d^2*e^6*x^6*log(d + e*x) + 2*a*b*c^2*d^3*e^5*x^2 + (6*a*b^2*c*d^2*e^6*x^2)/5 + 4*a*b*c^2*d^2*e^6*x^3 + (4*a*b*c^2*d^4*e^4*x)/7 + (12*a*b^2*c*d^3*e^5*x)/35 + (12*a^2*b*c*d^2*e^6*x)/35 + (6*a^2*b*c*d*e^7*x^2)/5 + (12*a*b^2*c*d*e^7*x^3)/5 + 5*a*b*c^2*d*e^7*x^4)/(e^9*(d + e*x)^8)","B"
2160,1,966,436,0.263777,"\text{Not used}","int((a + b*x + c*x^2)^4/(d + e*x)^10,x)","-\frac{\frac{70\,a^4\,e^8+35\,a^3\,b\,d\,e^7+10\,a^3\,c\,d^2\,e^6+15\,a^2\,b^2\,d^2\,e^6+15\,a^2\,b\,c\,d^3\,e^5+6\,a^2\,c^2\,d^4\,e^4+5\,a\,b^3\,d^3\,e^5+12\,a\,b^2\,c\,d^4\,e^4+15\,a\,b\,c^2\,d^5\,e^3+10\,a\,c^3\,d^6\,e^2+b^4\,d^4\,e^4+5\,b^3\,c\,d^5\,e^3+15\,b^2\,c^2\,d^6\,e^2+35\,b\,c^3\,d^7\,e+70\,c^4\,d^8}{630\,e^9}+\frac{2\,x^3\,\left(15\,a^2\,b\,c\,e^5+6\,a^2\,c^2\,d\,e^4+5\,a\,b^3\,e^5+12\,a\,b^2\,c\,d\,e^4+15\,a\,b\,c^2\,d^2\,e^3+10\,a\,c^3\,d^3\,e^2+b^4\,d\,e^4+5\,b^3\,c\,d^2\,e^3+15\,b^2\,c^2\,d^3\,e^2+35\,b\,c^3\,d^4\,e+70\,c^4\,d^5\right)}{15\,e^6}+\frac{x^4\,\left(6\,a^2\,c^2\,e^4+12\,a\,b^2\,c\,e^4+15\,a\,b\,c^2\,d\,e^3+10\,a\,c^3\,d^2\,e^2+b^4\,e^4+5\,b^3\,c\,d\,e^3+15\,b^2\,c^2\,d^2\,e^2+35\,b\,c^3\,d^3\,e+70\,c^4\,d^4\right)}{5\,e^5}+\frac{x\,\left(35\,a^3\,b\,e^7+10\,a^3\,c\,d\,e^6+15\,a^2\,b^2\,d\,e^6+15\,a^2\,b\,c\,d^2\,e^5+6\,a^2\,c^2\,d^3\,e^4+5\,a\,b^3\,d^2\,e^5+12\,a\,b^2\,c\,d^3\,e^4+15\,a\,b\,c^2\,d^4\,e^3+10\,a\,c^3\,d^5\,e^2+b^4\,d^3\,e^4+5\,b^3\,c\,d^4\,e^3+15\,b^2\,c^2\,d^5\,e^2+35\,b\,c^3\,d^6\,e+70\,c^4\,d^7\right)}{70\,e^8}+\frac{c^4\,x^8}{e}+\frac{2\,x^2\,\left(10\,a^3\,c\,e^6+15\,a^2\,b^2\,e^6+15\,a^2\,b\,c\,d\,e^5+6\,a^2\,c^2\,d^2\,e^4+5\,a\,b^3\,d\,e^5+12\,a\,b^2\,c\,d^2\,e^4+15\,a\,b\,c^2\,d^3\,e^3+10\,a\,c^3\,d^4\,e^2+b^4\,d^2\,e^4+5\,b^3\,c\,d^3\,e^3+15\,b^2\,c^2\,d^4\,e^2+35\,b\,c^3\,d^5\,e+70\,c^4\,d^6\right)}{35\,e^7}+\frac{2\,c^3\,x^7\,\left(b\,e+2\,c\,d\right)}{e^2}+\frac{2\,c^2\,x^6\,\left(3\,b^2\,e^2+7\,b\,c\,d\,e+14\,c^2\,d^2+2\,a\,c\,e^2\right)}{3\,e^3}+\frac{c\,x^5\,\left(b^3\,e^3+3\,b^2\,c\,d\,e^2+7\,b\,c^2\,d^2\,e+3\,a\,b\,c\,e^3+14\,c^3\,d^3+2\,a\,c^2\,d\,e^2\right)}{e^4}}{d^9+9\,d^8\,e\,x+36\,d^7\,e^2\,x^2+84\,d^6\,e^3\,x^3+126\,d^5\,e^4\,x^4+126\,d^4\,e^5\,x^5+84\,d^3\,e^6\,x^6+36\,d^2\,e^7\,x^7+9\,d\,e^8\,x^8+e^9\,x^9}","Not used",1,"-((70*a^4*e^8 + 70*c^4*d^8 + b^4*d^4*e^4 + 5*a*b^3*d^3*e^5 + 10*a*c^3*d^6*e^2 + 10*a^3*c*d^2*e^6 + 5*b^3*c*d^5*e^3 + 15*a^2*b^2*d^2*e^6 + 6*a^2*c^2*d^4*e^4 + 15*b^2*c^2*d^6*e^2 + 35*a^3*b*d*e^7 + 35*b*c^3*d^7*e + 15*a*b*c^2*d^5*e^3 + 12*a*b^2*c*d^4*e^4 + 15*a^2*b*c*d^3*e^5)/(630*e^9) + (2*x^3*(70*c^4*d^5 + 5*a*b^3*e^5 + b^4*d*e^4 + 10*a*c^3*d^3*e^2 + 6*a^2*c^2*d*e^4 + 5*b^3*c*d^2*e^3 + 15*b^2*c^2*d^3*e^2 + 15*a^2*b*c*e^5 + 35*b*c^3*d^4*e + 12*a*b^2*c*d*e^4 + 15*a*b*c^2*d^2*e^3))/(15*e^6) + (x^4*(b^4*e^4 + 70*c^4*d^4 + 6*a^2*c^2*e^4 + 10*a*c^3*d^2*e^2 + 15*b^2*c^2*d^2*e^2 + 12*a*b^2*c*e^4 + 35*b*c^3*d^3*e + 5*b^3*c*d*e^3 + 15*a*b*c^2*d*e^3))/(5*e^5) + (x*(70*c^4*d^7 + 35*a^3*b*e^7 + b^4*d^3*e^4 + 5*a*b^3*d^2*e^5 + 15*a^2*b^2*d*e^6 + 10*a*c^3*d^5*e^2 + 5*b^3*c*d^4*e^3 + 6*a^2*c^2*d^3*e^4 + 15*b^2*c^2*d^5*e^2 + 10*a^3*c*d*e^6 + 35*b*c^3*d^6*e + 15*a*b*c^2*d^4*e^3 + 12*a*b^2*c*d^3*e^4 + 15*a^2*b*c*d^2*e^5))/(70*e^8) + (c^4*x^8)/e + (2*x^2*(70*c^4*d^6 + 10*a^3*c*e^6 + 15*a^2*b^2*e^6 + b^4*d^2*e^4 + 10*a*c^3*d^4*e^2 + 5*b^3*c*d^3*e^3 + 6*a^2*c^2*d^2*e^4 + 15*b^2*c^2*d^4*e^2 + 5*a*b^3*d*e^5 + 35*b*c^3*d^5*e + 15*a^2*b*c*d*e^5 + 15*a*b*c^2*d^3*e^3 + 12*a*b^2*c*d^2*e^4))/(35*e^7) + (2*c^3*x^7*(b*e + 2*c*d))/e^2 + (2*c^2*x^6*(3*b^2*e^2 + 14*c^2*d^2 + 2*a*c*e^2 + 7*b*c*d*e))/(3*e^3) + (c*x^5*(b^3*e^3 + 14*c^3*d^3 + 3*a*b*c*e^3 + 2*a*c^2*d*e^2 + 7*b*c^2*d^2*e + 3*b^2*c*d*e^2))/e^4)/(d^9 + e^9*x^9 + 9*d*e^8*x^8 + 36*d^7*e^2*x^2 + 84*d^6*e^3*x^3 + 126*d^5*e^4*x^4 + 126*d^4*e^5*x^5 + 84*d^3*e^6*x^6 + 36*d^2*e^7*x^7 + 9*d^8*e*x)","B"
2161,1,979,443,1.083559,"\text{Not used}","int((a + b*x + c*x^2)^4/(d + e*x)^11,x)","-\frac{\frac{126\,a^4\,e^8+56\,a^3\,b\,d\,e^7+14\,a^3\,c\,d^2\,e^6+21\,a^2\,b^2\,d^2\,e^6+18\,a^2\,b\,c\,d^3\,e^5+6\,a^2\,c^2\,d^4\,e^4+6\,a\,b^3\,d^3\,e^5+12\,a\,b^2\,c\,d^4\,e^4+12\,a\,b\,c^2\,d^5\,e^3+6\,a\,c^3\,d^6\,e^2+b^4\,d^4\,e^4+4\,b^3\,c\,d^5\,e^3+9\,b^2\,c^2\,d^6\,e^2+14\,b\,c^3\,d^7\,e+14\,c^4\,d^8}{1260\,e^9}+\frac{2\,x^3\,\left(18\,a^2\,b\,c\,e^5+6\,a^2\,c^2\,d\,e^4+6\,a\,b^3\,e^5+12\,a\,b^2\,c\,d\,e^4+12\,a\,b\,c^2\,d^2\,e^3+6\,a\,c^3\,d^3\,e^2+b^4\,d\,e^4+4\,b^3\,c\,d^2\,e^3+9\,b^2\,c^2\,d^3\,e^2+14\,b\,c^3\,d^4\,e+14\,c^4\,d^5\right)}{21\,e^6}+\frac{x^4\,\left(6\,a^2\,c^2\,e^4+12\,a\,b^2\,c\,e^4+12\,a\,b\,c^2\,d\,e^3+6\,a\,c^3\,d^2\,e^2+b^4\,e^4+4\,b^3\,c\,d\,e^3+9\,b^2\,c^2\,d^2\,e^2+14\,b\,c^3\,d^3\,e+14\,c^4\,d^4\right)}{6\,e^5}+\frac{x\,\left(56\,a^3\,b\,e^7+14\,a^3\,c\,d\,e^6+21\,a^2\,b^2\,d\,e^6+18\,a^2\,b\,c\,d^2\,e^5+6\,a^2\,c^2\,d^3\,e^4+6\,a\,b^3\,d^2\,e^5+12\,a\,b^2\,c\,d^3\,e^4+12\,a\,b\,c^2\,d^4\,e^3+6\,a\,c^3\,d^5\,e^2+b^4\,d^3\,e^4+4\,b^3\,c\,d^4\,e^3+9\,b^2\,c^2\,d^5\,e^2+14\,b\,c^3\,d^6\,e+14\,c^4\,d^7\right)}{126\,e^8}+\frac{c^4\,x^8}{2\,e}+\frac{x^2\,\left(14\,a^3\,c\,e^6+21\,a^2\,b^2\,e^6+18\,a^2\,b\,c\,d\,e^5+6\,a^2\,c^2\,d^2\,e^4+6\,a\,b^3\,d\,e^5+12\,a\,b^2\,c\,d^2\,e^4+12\,a\,b\,c^2\,d^3\,e^3+6\,a\,c^3\,d^4\,e^2+b^4\,d^2\,e^4+4\,b^3\,c\,d^3\,e^3+9\,b^2\,c^2\,d^4\,e^2+14\,b\,c^3\,d^5\,e+14\,c^4\,d^6\right)}{28\,e^7}+\frac{4\,c^3\,x^7\,\left(b\,e+c\,d\right)}{3\,e^2}+\frac{c^2\,x^6\,\left(9\,b^2\,e^2+14\,b\,c\,d\,e+14\,c^2\,d^2+6\,a\,c\,e^2\right)}{6\,e^3}+\frac{c\,x^5\,\left(4\,b^3\,e^3+9\,b^2\,c\,d\,e^2+14\,b\,c^2\,d^2\,e+12\,a\,b\,c\,e^3+14\,c^3\,d^3+6\,a\,c^2\,d\,e^2\right)}{5\,e^4}}{d^{10}+10\,d^9\,e\,x+45\,d^8\,e^2\,x^2+120\,d^7\,e^3\,x^3+210\,d^6\,e^4\,x^4+252\,d^5\,e^5\,x^5+210\,d^4\,e^6\,x^6+120\,d^3\,e^7\,x^7+45\,d^2\,e^8\,x^8+10\,d\,e^9\,x^9+e^{10}\,x^{10}}","Not used",1,"-((126*a^4*e^8 + 14*c^4*d^8 + b^4*d^4*e^4 + 6*a*b^3*d^3*e^5 + 6*a*c^3*d^6*e^2 + 14*a^3*c*d^2*e^6 + 4*b^3*c*d^5*e^3 + 21*a^2*b^2*d^2*e^6 + 6*a^2*c^2*d^4*e^4 + 9*b^2*c^2*d^6*e^2 + 56*a^3*b*d*e^7 + 14*b*c^3*d^7*e + 12*a*b*c^2*d^5*e^3 + 12*a*b^2*c*d^4*e^4 + 18*a^2*b*c*d^3*e^5)/(1260*e^9) + (2*x^3*(14*c^4*d^5 + 6*a*b^3*e^5 + b^4*d*e^4 + 6*a*c^3*d^3*e^2 + 6*a^2*c^2*d*e^4 + 4*b^3*c*d^2*e^3 + 9*b^2*c^2*d^3*e^2 + 18*a^2*b*c*e^5 + 14*b*c^3*d^4*e + 12*a*b^2*c*d*e^4 + 12*a*b*c^2*d^2*e^3))/(21*e^6) + (x^4*(b^4*e^4 + 14*c^4*d^4 + 6*a^2*c^2*e^4 + 6*a*c^3*d^2*e^2 + 9*b^2*c^2*d^2*e^2 + 12*a*b^2*c*e^4 + 14*b*c^3*d^3*e + 4*b^3*c*d*e^3 + 12*a*b*c^2*d*e^3))/(6*e^5) + (x*(14*c^4*d^7 + 56*a^3*b*e^7 + b^4*d^3*e^4 + 6*a*b^3*d^2*e^5 + 21*a^2*b^2*d*e^6 + 6*a*c^3*d^5*e^2 + 4*b^3*c*d^4*e^3 + 6*a^2*c^2*d^3*e^4 + 9*b^2*c^2*d^5*e^2 + 14*a^3*c*d*e^6 + 14*b*c^3*d^6*e + 12*a*b*c^2*d^4*e^3 + 12*a*b^2*c*d^3*e^4 + 18*a^2*b*c*d^2*e^5))/(126*e^8) + (c^4*x^8)/(2*e) + (x^2*(14*c^4*d^6 + 14*a^3*c*e^6 + 21*a^2*b^2*e^6 + b^4*d^2*e^4 + 6*a*c^3*d^4*e^2 + 4*b^3*c*d^3*e^3 + 6*a^2*c^2*d^2*e^4 + 9*b^2*c^2*d^4*e^2 + 6*a*b^3*d*e^5 + 14*b*c^3*d^5*e + 18*a^2*b*c*d*e^5 + 12*a*b*c^2*d^3*e^3 + 12*a*b^2*c*d^2*e^4))/(28*e^7) + (4*c^3*x^7*(b*e + c*d))/(3*e^2) + (c^2*x^6*(9*b^2*e^2 + 14*c^2*d^2 + 6*a*c*e^2 + 14*b*c*d*e))/(6*e^3) + (c*x^5*(4*b^3*e^3 + 14*c^3*d^3 + 12*a*b*c*e^3 + 6*a*c^2*d*e^2 + 14*b*c^2*d^2*e + 9*b^2*c*d*e^2))/(5*e^4))/(d^10 + e^10*x^10 + 10*d*e^9*x^9 + 45*d^8*e^2*x^2 + 120*d^7*e^3*x^3 + 210*d^6*e^4*x^4 + 252*d^5*e^5*x^5 + 210*d^4*e^6*x^6 + 120*d^3*e^7*x^7 + 45*d^2*e^8*x^8 + 10*d^9*e*x)","B"
2162,1,997,440,1.088042,"\text{Not used}","int((a + b*x + c*x^2)^4/(d + e*x)^12,x)","-\frac{\frac{630\,a^4\,e^8+252\,a^3\,b\,d\,e^7+56\,a^3\,c\,d^2\,e^6+84\,a^2\,b^2\,d^2\,e^6+63\,a^2\,b\,c\,d^3\,e^5+18\,a^2\,c^2\,d^4\,e^4+21\,a\,b^3\,d^3\,e^5+36\,a\,b^2\,c\,d^4\,e^4+30\,a\,b\,c^2\,d^5\,e^3+12\,a\,c^3\,d^6\,e^2+3\,b^4\,d^4\,e^4+10\,b^3\,c\,d^5\,e^3+18\,b^2\,c^2\,d^6\,e^2+21\,b\,c^3\,d^7\,e+14\,c^4\,d^8}{6930\,e^9}+\frac{x^3\,\left(63\,a^2\,b\,c\,e^5+18\,a^2\,c^2\,d\,e^4+21\,a\,b^3\,e^5+36\,a\,b^2\,c\,d\,e^4+30\,a\,b\,c^2\,d^2\,e^3+12\,a\,c^3\,d^3\,e^2+3\,b^4\,d\,e^4+10\,b^3\,c\,d^2\,e^3+18\,b^2\,c^2\,d^3\,e^2+21\,b\,c^3\,d^4\,e+14\,c^4\,d^5\right)}{42\,e^6}+\frac{x^4\,\left(18\,a^2\,c^2\,e^4+36\,a\,b^2\,c\,e^4+30\,a\,b\,c^2\,d\,e^3+12\,a\,c^3\,d^2\,e^2+3\,b^4\,e^4+10\,b^3\,c\,d\,e^3+18\,b^2\,c^2\,d^2\,e^2+21\,b\,c^3\,d^3\,e+14\,c^4\,d^4\right)}{21\,e^5}+\frac{x\,\left(252\,a^3\,b\,e^7+56\,a^3\,c\,d\,e^6+84\,a^2\,b^2\,d\,e^6+63\,a^2\,b\,c\,d^2\,e^5+18\,a^2\,c^2\,d^3\,e^4+21\,a\,b^3\,d^2\,e^5+36\,a\,b^2\,c\,d^3\,e^4+30\,a\,b\,c^2\,d^4\,e^3+12\,a\,c^3\,d^5\,e^2+3\,b^4\,d^3\,e^4+10\,b^3\,c\,d^4\,e^3+18\,b^2\,c^2\,d^5\,e^2+21\,b\,c^3\,d^6\,e+14\,c^4\,d^7\right)}{630\,e^8}+\frac{c^4\,x^8}{3\,e}+\frac{x^2\,\left(56\,a^3\,c\,e^6+84\,a^2\,b^2\,e^6+63\,a^2\,b\,c\,d\,e^5+18\,a^2\,c^2\,d^2\,e^4+21\,a\,b^3\,d\,e^5+36\,a\,b^2\,c\,d^2\,e^4+30\,a\,b\,c^2\,d^3\,e^3+12\,a\,c^3\,d^4\,e^2+3\,b^4\,d^2\,e^4+10\,b^3\,c\,d^3\,e^3+18\,b^2\,c^2\,d^4\,e^2+21\,b\,c^3\,d^5\,e+14\,c^4\,d^6\right)}{126\,e^7}+\frac{c^3\,x^7\,\left(3\,b\,e+2\,c\,d\right)}{3\,e^2}+\frac{c^2\,x^6\,\left(18\,b^2\,e^2+21\,b\,c\,d\,e+14\,c^2\,d^2+12\,a\,c\,e^2\right)}{15\,e^3}+\frac{c\,x^5\,\left(10\,b^3\,e^3+18\,b^2\,c\,d\,e^2+21\,b\,c^2\,d^2\,e+30\,a\,b\,c\,e^3+14\,c^3\,d^3+12\,a\,c^2\,d\,e^2\right)}{15\,e^4}}{d^{11}+11\,d^{10}\,e\,x+55\,d^9\,e^2\,x^2+165\,d^8\,e^3\,x^3+330\,d^7\,e^4\,x^4+462\,d^6\,e^5\,x^5+462\,d^5\,e^6\,x^6+330\,d^4\,e^7\,x^7+165\,d^3\,e^8\,x^8+55\,d^2\,e^9\,x^9+11\,d\,e^{10}\,x^{10}+e^{11}\,x^{11}}","Not used",1,"-((630*a^4*e^8 + 14*c^4*d^8 + 3*b^4*d^4*e^4 + 21*a*b^3*d^3*e^5 + 12*a*c^3*d^6*e^2 + 56*a^3*c*d^2*e^6 + 10*b^3*c*d^5*e^3 + 84*a^2*b^2*d^2*e^6 + 18*a^2*c^2*d^4*e^4 + 18*b^2*c^2*d^6*e^2 + 252*a^3*b*d*e^7 + 21*b*c^3*d^7*e + 30*a*b*c^2*d^5*e^3 + 36*a*b^2*c*d^4*e^4 + 63*a^2*b*c*d^3*e^5)/(6930*e^9) + (x^3*(14*c^4*d^5 + 21*a*b^3*e^5 + 3*b^4*d*e^4 + 12*a*c^3*d^3*e^2 + 18*a^2*c^2*d*e^4 + 10*b^3*c*d^2*e^3 + 18*b^2*c^2*d^3*e^2 + 63*a^2*b*c*e^5 + 21*b*c^3*d^4*e + 36*a*b^2*c*d*e^4 + 30*a*b*c^2*d^2*e^3))/(42*e^6) + (x^4*(3*b^4*e^4 + 14*c^4*d^4 + 18*a^2*c^2*e^4 + 12*a*c^3*d^2*e^2 + 18*b^2*c^2*d^2*e^2 + 36*a*b^2*c*e^4 + 21*b*c^3*d^3*e + 10*b^3*c*d*e^3 + 30*a*b*c^2*d*e^3))/(21*e^5) + (x*(14*c^4*d^7 + 252*a^3*b*e^7 + 3*b^4*d^3*e^4 + 21*a*b^3*d^2*e^5 + 84*a^2*b^2*d*e^6 + 12*a*c^3*d^5*e^2 + 10*b^3*c*d^4*e^3 + 18*a^2*c^2*d^3*e^4 + 18*b^2*c^2*d^5*e^2 + 56*a^3*c*d*e^6 + 21*b*c^3*d^6*e + 30*a*b*c^2*d^4*e^3 + 36*a*b^2*c*d^3*e^4 + 63*a^2*b*c*d^2*e^5))/(630*e^8) + (c^4*x^8)/(3*e) + (x^2*(14*c^4*d^6 + 56*a^3*c*e^6 + 84*a^2*b^2*e^6 + 3*b^4*d^2*e^4 + 12*a*c^3*d^4*e^2 + 10*b^3*c*d^3*e^3 + 18*a^2*c^2*d^2*e^4 + 18*b^2*c^2*d^4*e^2 + 21*a*b^3*d*e^5 + 21*b*c^3*d^5*e + 63*a^2*b*c*d*e^5 + 30*a*b*c^2*d^3*e^3 + 36*a*b^2*c*d^2*e^4))/(126*e^7) + (c^3*x^7*(3*b*e + 2*c*d))/(3*e^2) + (c^2*x^6*(18*b^2*e^2 + 14*c^2*d^2 + 12*a*c*e^2 + 21*b*c*d*e))/(15*e^3) + (c*x^5*(10*b^3*e^3 + 14*c^3*d^3 + 30*a*b*c*e^3 + 12*a*c^2*d*e^2 + 21*b*c^2*d^2*e + 18*b^2*c*d*e^2))/(15*e^4))/(d^11 + e^11*x^11 + 11*d*e^10*x^10 + 55*d^9*e^2*x^2 + 165*d^8*e^3*x^3 + 330*d^7*e^4*x^4 + 462*d^6*e^5*x^5 + 462*d^5*e^6*x^6 + 330*d^4*e^7*x^7 + 165*d^3*e^8*x^8 + 55*d^2*e^9*x^9 + 11*d^10*e*x)","B"
2163,1,26,32,0.028373,"\text{Not used}","int(x^4*(x^2 - 4*x + 3)^2,x)","\frac{x^9}{9}-x^8+\frac{22\,x^7}{7}-4\,x^6+\frac{9\,x^5}{5}","Not used",1,"(9*x^5)/5 - 4*x^6 + (22*x^7)/7 - x^8 + x^9/9","B"
2164,1,26,36,0.019197,"\text{Not used}","int(x^3*(x^2 - 4*x + 3)^2,x)","\frac{x^8}{8}-\frac{8\,x^7}{7}+\frac{11\,x^6}{3}-\frac{24\,x^5}{5}+\frac{9\,x^4}{4}","Not used",1,"(9*x^4)/4 - (24*x^5)/5 + (11*x^6)/3 - (8*x^7)/7 + x^8/8","B"
2165,1,26,32,0.019410,"\text{Not used}","int(x^2*(x^2 - 4*x + 3)^2,x)","\frac{x^7}{7}-\frac{4\,x^6}{3}+\frac{22\,x^5}{5}-6\,x^4+3\,x^3","Not used",1,"3*x^3 - 6*x^4 + (22*x^5)/5 - (4*x^6)/3 + x^7/7","B"
2166,1,26,34,0.019294,"\text{Not used}","int(x*(x^2 - 4*x + 3)^2,x)","\frac{x^6}{6}-\frac{8\,x^5}{5}+\frac{11\,x^4}{2}-8\,x^3+\frac{9\,x^2}{2}","Not used",1,"(9*x^2)/2 - 8*x^3 + (11*x^4)/2 - (8*x^5)/5 + x^6/6","B"
2167,1,24,28,0.018474,"\text{Not used}","int((x^2 - 4*x + 3)^2,x)","\frac{x^5}{5}-2\,x^4+\frac{22\,x^3}{3}-12\,x^2+9\,x","Not used",1,"9*x - 12*x^2 + (22*x^3)/3 - 2*x^4 + x^5/5","B"
2168,1,23,27,0.022677,"\text{Not used}","int((x^2 - 4*x + 3)^2/x,x)","9\,\ln\left(x\right)-24\,x+11\,x^2-\frac{8\,x^3}{3}+\frac{x^4}{4}","Not used",1,"9*log(x) - 24*x + 11*x^2 - (8*x^3)/3 + x^4/4","B"
2169,1,23,25,0.022281,"\text{Not used}","int((x^2 - 4*x + 3)^2/x^2,x)","22\,x-24\,\ln\left(x\right)-\frac{9}{x}-4\,x^2+\frac{x^3}{3}","Not used",1,"22*x - 24*log(x) - 9/x - 4*x^2 + x^3/3","B"
2170,1,22,27,0.028671,"\text{Not used}","int((x^2 - 4*x + 3)^2/x^3,x)","22\,\ln\left(x\right)-8\,x+\frac{24\,x-\frac{9}{2}}{x^2}+\frac{x^2}{2}","Not used",1,"22*log(x) - 8*x + (24*x - 9/2)/x^2 + x^2/2","B"
2171,1,21,21,0.028729,"\text{Not used}","int((x^2 - 4*x + 3)^2/x^4,x)","x-8\,\ln\left(x\right)-\frac{22\,x^2-12\,x+3}{x^3}","Not used",1,"x - 8*log(x) - (22*x^2 - 12*x + 3)/x^3","B"
2172,1,22,25,0.025353,"\text{Not used}","int((x^2 - 4*x + 3)^2/x^5,x)","\ln\left(x\right)+\frac{8\,x^3-11\,x^2+8\,x-\frac{9}{4}}{x^4}","Not used",1,"log(x) + (8*x - 11*x^2 + 8*x^3 - 9/4)/x^4","B"
2173,1,23,30,0.021868,"\text{Not used}","int((x^2 - 4*x + 3)^2/x^6,x)","-\frac{x^4-4\,x^3+\frac{22\,x^2}{3}-6\,x+\frac{9}{5}}{x^5}","Not used",1,"-((22*x^2)/3 - 6*x - 4*x^3 + x^4 + 9/5)/x^5","B"
2174,1,25,36,0.022635,"\text{Not used}","int((x^2 - 4*x + 3)^2/x^7,x)","-\frac{15\,x^4-80\,x^3+165\,x^2-144\,x+45}{30\,x^6}","Not used",1,"-(165*x^2 - 144*x - 80*x^3 + 15*x^4 + 45)/(30*x^6)","B"
2175,1,12,14,0.031039,"\text{Not used}","int((2*x + x^2 + 2)/(x + 2),x)","2\,\ln\left(x+2\right)+\frac{x^2}{2}","Not used",1,"2*log(x + 2) + x^2/2","B"
2176,1,15,19,0.651200,"\text{Not used}","int((4*x + x^2 + 5)/(x - 2),x)","6\,x+17\,\ln\left(x-2\right)+\frac{x^2}{2}","Not used",1,"6*x + 17*log(x - 2) + x^2/2","B"
2177,1,12,14,0.030534,"\text{Not used}","int((2*x + x^2 + 2)/(x + 1)^3,x)","\ln\left(x+1\right)-\frac{1}{2\,{\left(x+1\right)}^2}","Not used",1,"log(x + 1) - 1/(2*(x + 1)^2)","B"
2178,1,14,19,0.030110,"\text{Not used}","int((3*x + 2*x^2 + 3)/(x + 1)^3,x)","2\,\ln\left(x+1\right)+\frac{x}{{\left(x+1\right)}^2}","Not used",1,"2*log(x + 1) + x/(x + 1)^2","B"
2179,1,9,11,0.021492,"\text{Not used}","int((x + x^2 + 1)/x,x)","x+\ln\left(x\right)+\frac{x^2}{2}","Not used",1,"x + log(x) + x^2/2","B"
2180,1,11,11,0.028681,"\text{Not used}","int((6*x + x^2 + 9)/x^2,x)","x+6\,\ln\left(x\right)-\frac{9}{x}","Not used",1,"x + 6*log(x) - 9/x","B"
2181,1,11,18,0.020144,"\text{Not used}","int((2*x + x^2 + 1)/x^4,x)","-\frac{x^2+x+\frac{1}{3}}{x^3}","Not used",1,"-(x + x^2 + 1/3)/x^3","B"
2182,1,367,243,0.986076,"\text{Not used}","int((d + e*x)^4/(a + b*x + c*x^2),x)","x\,\left(\frac{b\,\left(\frac{b\,e^4}{c^2}-\frac{4\,d\,e^3}{c}\right)}{c}-\frac{a\,e^4}{c^2}+\frac{6\,d^2\,e^2}{c}\right)-x^2\,\left(\frac{b\,e^4}{2\,c^2}-\frac{2\,d\,e^3}{c}\right)+\frac{\ln\left(c\,x^2+b\,x+a\right)\,\left(8\,a^2\,b\,c^2\,e^4-16\,a^2\,c^3\,d\,e^3-6\,a\,b^3\,c\,e^4+20\,a\,b^2\,c^2\,d\,e^3-24\,a\,b\,c^3\,d^2\,e^2+16\,a\,c^4\,d^3\,e+b^5\,e^4-4\,b^4\,c\,d\,e^3+6\,b^3\,c^2\,d^2\,e^2-4\,b^2\,c^3\,d^3\,e\right)}{2\,\left(4\,a\,c^5-b^2\,c^4\right)}+\frac{e^4\,x^3}{3\,c}+\frac{\mathrm{atan}\left(\frac{b}{\sqrt{4\,a\,c-b^2}}+\frac{2\,c\,x}{\sqrt{4\,a\,c-b^2}}\right)\,\left(2\,a^2\,c^2\,e^4-4\,a\,b^2\,c\,e^4+12\,a\,b\,c^2\,d\,e^3-12\,a\,c^3\,d^2\,e^2+b^4\,e^4-4\,b^3\,c\,d\,e^3+6\,b^2\,c^2\,d^2\,e^2-4\,b\,c^3\,d^3\,e+2\,c^4\,d^4\right)}{c^4\,\sqrt{4\,a\,c-b^2}}","Not used",1,"x*((b*((b*e^4)/c^2 - (4*d*e^3)/c))/c - (a*e^4)/c^2 + (6*d^2*e^2)/c) - x^2*((b*e^4)/(2*c^2) - (2*d*e^3)/c) + (log(a + b*x + c*x^2)*(b^5*e^4 + 8*a^2*b*c^2*e^4 - 16*a^2*c^3*d*e^3 - 4*b^2*c^3*d^3*e + 6*b^3*c^2*d^2*e^2 - 6*a*b^3*c*e^4 + 16*a*c^4*d^3*e - 4*b^4*c*d*e^3 - 24*a*b*c^3*d^2*e^2 + 20*a*b^2*c^2*d*e^3))/(2*(4*a*c^5 - b^2*c^4)) + (e^4*x^3)/(3*c) + (atan(b/(4*a*c - b^2)^(1/2) + (2*c*x)/(4*a*c - b^2)^(1/2))*(b^4*e^4 + 2*c^4*d^4 + 2*a^2*c^2*e^4 - 12*a*c^3*d^2*e^2 + 6*b^2*c^2*d^2*e^2 - 4*a*b^2*c*e^4 - 4*b*c^3*d^3*e - 4*b^3*c*d*e^3 + 12*a*b*c^2*d*e^3))/(c^4*(4*a*c - b^2)^(1/2))","B"
2183,1,208,151,0.242393,"\text{Not used}","int((d + e*x)^3/(a + b*x + c*x^2),x)","\frac{e^3\,x^2}{2\,c}-\frac{\ln\left(c\,x^2+b\,x+a\right)\,\left(4\,a^2\,c^2\,e^3-5\,a\,b^2\,c\,e^3+12\,a\,b\,c^2\,d\,e^2-12\,a\,c^3\,d^2\,e+b^4\,e^3-3\,b^3\,c\,d\,e^2+3\,b^2\,c^2\,d^2\,e\right)}{2\,\left(4\,a\,c^4-b^2\,c^3\right)}-x\,\left(\frac{b\,e^3}{c^2}-\frac{3\,d\,e^2}{c}\right)-\frac{\mathrm{atan}\left(\frac{b+2\,c\,x}{\sqrt{4\,a\,c-b^2}}\right)\,\left(b\,e-2\,c\,d\right)\,\left(b^2\,e^2-b\,c\,d\,e+c^2\,d^2-3\,a\,c\,e^2\right)}{c^3\,\sqrt{4\,a\,c-b^2}}","Not used",1,"(e^3*x^2)/(2*c) - (log(a + b*x + c*x^2)*(b^4*e^3 + 4*a^2*c^2*e^3 + 3*b^2*c^2*d^2*e - 5*a*b^2*c*e^3 - 12*a*c^3*d^2*e - 3*b^3*c*d*e^2 + 12*a*b*c^2*d*e^2))/(2*(4*a*c^4 - b^2*c^3)) - x*((b*e^3)/c^2 - (3*d*e^2)/c) - (atan((b + 2*c*x)/(4*a*c - b^2)^(1/2))*(b*e - 2*c*d)*(b^2*e^2 + c^2*d^2 - 3*a*c*e^2 - b*c*d*e))/(c^3*(4*a*c - b^2)^(1/2))","B"
2184,1,147,101,0.269468,"\text{Not used}","int((d + e*x)^2/(a + b*x + c*x^2),x)","\frac{e^2\,x}{c}+\frac{\ln\left(c\,x^2+b\,x+a\right)\,\left(b^3\,e^2-2\,d\,b^2\,c\,e-4\,a\,b\,c\,e^2+8\,a\,d\,c^2\,e\right)}{2\,\left(4\,a\,c^3-b^2\,c^2\right)}+\frac{\mathrm{atan}\left(\frac{b}{\sqrt{4\,a\,c-b^2}}+\frac{2\,c\,x}{\sqrt{4\,a\,c-b^2}}\right)\,\left(b^2\,e^2-2\,b\,c\,d\,e+2\,c^2\,d^2-2\,a\,c\,e^2\right)}{c^2\,\sqrt{4\,a\,c-b^2}}","Not used",1,"(e^2*x)/c + (log(a + b*x + c*x^2)*(b^3*e^2 - 4*a*b*c*e^2 + 8*a*c^2*d*e - 2*b^2*c*d*e))/(2*(4*a*c^3 - b^2*c^2)) + (atan(b/(4*a*c - b^2)^(1/2) + (2*c*x)/(4*a*c - b^2)^(1/2))*(b^2*e^2 + 2*c^2*d^2 - 2*a*c*e^2 - 2*b*c*d*e))/(c^2*(4*a*c - b^2)^(1/2))","B"
2185,1,162,66,0.117983,"\text{Not used}","int((d + e*x)/(a + b*x + c*x^2),x)","\frac{2\,d\,\mathrm{atan}\left(\frac{b}{\sqrt{4\,a\,c-b^2}}+\frac{2\,c\,x}{\sqrt{4\,a\,c-b^2}}\right)}{\sqrt{4\,a\,c-b^2}}-\frac{b^2\,e\,\ln\left(c\,x^2+b\,x+a\right)}{2\,\left(4\,a\,c^2-b^2\,c\right)}+\frac{2\,a\,c\,e\,\ln\left(c\,x^2+b\,x+a\right)}{4\,a\,c^2-b^2\,c}-\frac{b\,e\,\mathrm{atan}\left(\frac{b}{\sqrt{4\,a\,c-b^2}}+\frac{2\,c\,x}{\sqrt{4\,a\,c-b^2}}\right)}{c\,\sqrt{4\,a\,c-b^2}}","Not used",1,"(2*d*atan(b/(4*a*c - b^2)^(1/2) + (2*c*x)/(4*a*c - b^2)^(1/2)))/(4*a*c - b^2)^(1/2) - (b^2*e*log(a + b*x + c*x^2))/(2*(4*a*c^2 - b^2*c)) + (2*a*c*e*log(a + b*x + c*x^2))/(4*a*c^2 - b^2*c) - (b*e*atan(b/(4*a*c - b^2)^(1/2) + (2*c*x)/(4*a*c - b^2)^(1/2)))/(c*(4*a*c - b^2)^(1/2))","B"
2186,1,46,34,0.722678,"\text{Not used}","int(1/(a + b*x + c*x^2),x)","\frac{2\,\mathrm{atan}\left(\frac{b}{\sqrt{4\,a\,c-b^2}}+\frac{2\,c\,x}{\sqrt{4\,a\,c-b^2}}\right)}{\sqrt{4\,a\,c-b^2}}","Not used",1,"(2*atan(b/(4*a*c - b^2)^(1/2) + (2*c*x)/(4*a*c - b^2)^(1/2)))/(4*a*c - b^2)^(1/2)","B"
2187,1,122,122,0.980747,"\text{Not used}","int(1/((d + e*x)*(a + b*x + c*x^2)),x)","\frac{e\,\ln\left(\frac{{\left(d+e\,x\right)}^2}{c\,x^2+b\,x+a}\right)}{2\,c\,d^2-2\,b\,d\,e+2\,a\,e^2}-\frac{\ln\left(\frac{b+2\,c\,x-\sqrt{b^2-4\,a\,c}}{b+2\,c\,x+\sqrt{b^2-4\,a\,c}}\right)\,\left(b\,e-2\,c\,d\right)}{\sqrt{b^2-4\,a\,c}\,\left(2\,c\,d^2-2\,b\,d\,e+2\,a\,e^2\right)}","Not used",1,"(e*log((d + e*x)^2/(a + b*x + c*x^2)))/(2*a*e^2 + 2*c*d^2 - 2*b*d*e) - (log((b + 2*c*x - (b^2 - 4*a*c)^(1/2))/(b + 2*c*x + (b^2 - 4*a*c)^(1/2)))*(b*e - 2*c*d))/((b^2 - 4*a*c)^(1/2)*(2*a*e^2 + 2*c*d^2 - 2*b*d*e))","B"
2188,1,1786,186,7.093496,"\text{Not used}","int(1/((d + e*x)^2*(a + b*x + c*x^2)),x)","\frac{\ln\left(a\,e^4\,{\left(b^2-4\,a\,c\right)}^{5/2}+8\,a\,b^5\,e^4+8\,b^6\,e^4\,x-4\,c^3\,d^4\,{\left(b^2-4\,a\,c\right)}^{3/2}+4\,b^3\,c^3\,d^4+4\,b^3\,e^4\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}-60\,a^2\,b^3\,c\,e^4+112\,a^3\,b\,c^2\,e^4+256\,a^2\,c^4\,d^3\,e-256\,a^3\,c^3\,d\,e^3+8\,b^4\,c^2\,d^3\,e-4\,b^5\,c\,d^2\,e^2-32\,a^3\,c^3\,e^4\,x+8\,b^2\,c^4\,d^4\,x+10\,b\,d\,e^3\,{\left(b^2-4\,a\,c\right)}^{5/2}+4\,b\,e^4\,x\,{\left(b^2-4\,a\,c\right)}^{5/2}-16\,a\,b\,c^4\,d^4-32\,a\,c^5\,d^4\,x+7\,a\,b^2\,e^4\,{\left(b^2-4\,a\,c\right)}^{3/2}-10\,b^3\,d\,e^3\,{\left(b^2-4\,a\,c\right)}^{3/2}-14\,c\,d^2\,e^2\,{\left(b^2-4\,a\,c\right)}^{5/2}-8\,c\,d\,e^3\,x\,{\left(b^2-4\,a\,c\right)}^{5/2}-24\,a\,b^4\,c\,d\,e^3-64\,a\,b^4\,c\,e^4\,x-32\,b^5\,c\,d\,e^3\,x-8\,b\,c^2\,d^3\,e\,{\left(b^2-4\,a\,c\right)}^{3/2}-32\,c^3\,d^3\,e\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}-96\,a\,b^2\,c^3\,d^3\,e-16\,b^3\,c^3\,d^3\,e\,x+18\,b^2\,c\,d^2\,e^2\,{\left(b^2-4\,a\,c\right)}^{3/2}+56\,a\,b^3\,c^2\,d^2\,e^2-160\,a^2\,b\,c^3\,d^2\,e^2+160\,a^2\,b^2\,c^2\,d\,e^3+136\,a^2\,b^2\,c^2\,e^4\,x+448\,a^2\,c^4\,d^2\,e^2\,x+40\,b^4\,c^2\,d^2\,e^2\,x+48\,b\,c^2\,d^2\,e^2\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}-272\,a\,b^2\,c^3\,d^2\,e^2\,x+64\,a\,b\,c^4\,d^3\,e\,x-24\,b^2\,c\,d\,e^3\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}+240\,a\,b^3\,c^2\,d\,e^3\,x-448\,a^2\,b\,c^3\,d\,e^3\,x\right)\,\left(a\,\left(e^2\,\left(2\,b\,c+c\,\sqrt{b^2-4\,a\,c}\right)-4\,c^2\,d\,e\right)+e\,\left(b^2\,c\,d+b\,c\,d\,\sqrt{b^2-4\,a\,c}\right)-e^2\,\left(\frac{b^3}{2}+\frac{b^2\,\sqrt{b^2-4\,a\,c}}{2}\right)-c^2\,d^2\,\sqrt{b^2-4\,a\,c}\right)}{4\,a^3\,c\,e^4-a^2\,b^2\,e^4-8\,a^2\,b\,c\,d\,e^3+8\,a^2\,c^2\,d^2\,e^2+2\,a\,b^3\,d\,e^3+2\,a\,b^2\,c\,d^2\,e^2-8\,a\,b\,c^2\,d^3\,e+4\,a\,c^3\,d^4-b^4\,d^2\,e^2+2\,b^3\,c\,d^3\,e-b^2\,c^2\,d^4}+\frac{\ln\left(a\,e^4\,{\left(b^2-4\,a\,c\right)}^{5/2}-8\,a\,b^5\,e^4-8\,b^6\,e^4\,x-4\,c^3\,d^4\,{\left(b^2-4\,a\,c\right)}^{3/2}-4\,b^3\,c^3\,d^4+4\,b^3\,e^4\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}+60\,a^2\,b^3\,c\,e^4-112\,a^3\,b\,c^2\,e^4-256\,a^2\,c^4\,d^3\,e+256\,a^3\,c^3\,d\,e^3-8\,b^4\,c^2\,d^3\,e+4\,b^5\,c\,d^2\,e^2+32\,a^3\,c^3\,e^4\,x-8\,b^2\,c^4\,d^4\,x+10\,b\,d\,e^3\,{\left(b^2-4\,a\,c\right)}^{5/2}+4\,b\,e^4\,x\,{\left(b^2-4\,a\,c\right)}^{5/2}+16\,a\,b\,c^4\,d^4+32\,a\,c^5\,d^4\,x+7\,a\,b^2\,e^4\,{\left(b^2-4\,a\,c\right)}^{3/2}-10\,b^3\,d\,e^3\,{\left(b^2-4\,a\,c\right)}^{3/2}-14\,c\,d^2\,e^2\,{\left(b^2-4\,a\,c\right)}^{5/2}-8\,c\,d\,e^3\,x\,{\left(b^2-4\,a\,c\right)}^{5/2}+24\,a\,b^4\,c\,d\,e^3+64\,a\,b^4\,c\,e^4\,x+32\,b^5\,c\,d\,e^3\,x-8\,b\,c^2\,d^3\,e\,{\left(b^2-4\,a\,c\right)}^{3/2}-32\,c^3\,d^3\,e\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}+96\,a\,b^2\,c^3\,d^3\,e+16\,b^3\,c^3\,d^3\,e\,x+18\,b^2\,c\,d^2\,e^2\,{\left(b^2-4\,a\,c\right)}^{3/2}-56\,a\,b^3\,c^2\,d^2\,e^2+160\,a^2\,b\,c^3\,d^2\,e^2-160\,a^2\,b^2\,c^2\,d\,e^3-136\,a^2\,b^2\,c^2\,e^4\,x-448\,a^2\,c^4\,d^2\,e^2\,x-40\,b^4\,c^2\,d^2\,e^2\,x+48\,b\,c^2\,d^2\,e^2\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}+272\,a\,b^2\,c^3\,d^2\,e^2\,x-64\,a\,b\,c^4\,d^3\,e\,x-24\,b^2\,c\,d\,e^3\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}-240\,a\,b^3\,c^2\,d\,e^3\,x+448\,a^2\,b\,c^3\,d\,e^3\,x\right)\,\left(a\,\left(e^2\,\left(2\,b\,c-c\,\sqrt{b^2-4\,a\,c}\right)-4\,c^2\,d\,e\right)+e\,\left(b^2\,c\,d-b\,c\,d\,\sqrt{b^2-4\,a\,c}\right)-e^2\,\left(\frac{b^3}{2}-\frac{b^2\,\sqrt{b^2-4\,a\,c}}{2}\right)+c^2\,d^2\,\sqrt{b^2-4\,a\,c}\right)}{4\,a^3\,c\,e^4-a^2\,b^2\,e^4-8\,a^2\,b\,c\,d\,e^3+8\,a^2\,c^2\,d^2\,e^2+2\,a\,b^3\,d\,e^3+2\,a\,b^2\,c\,d^2\,e^2-8\,a\,b\,c^2\,d^3\,e+4\,a\,c^3\,d^4-b^4\,d^2\,e^2+2\,b^3\,c\,d^3\,e-b^2\,c^2\,d^4}-\frac{e}{\left(d+e\,x\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}-\frac{\ln\left(d+e\,x\right)\,\left(b\,e^2-2\,c\,d\,e\right)}{a^2\,e^4-2\,a\,b\,d\,e^3+2\,a\,c\,d^2\,e^2+b^2\,d^2\,e^2-2\,b\,c\,d^3\,e+c^2\,d^4}","Not used",1,"(log(a*e^4*(b^2 - 4*a*c)^(5/2) + 8*a*b^5*e^4 + 8*b^6*e^4*x - 4*c^3*d^4*(b^2 - 4*a*c)^(3/2) + 4*b^3*c^3*d^4 + 4*b^3*e^4*x*(b^2 - 4*a*c)^(3/2) - 60*a^2*b^3*c*e^4 + 112*a^3*b*c^2*e^4 + 256*a^2*c^4*d^3*e - 256*a^3*c^3*d*e^3 + 8*b^4*c^2*d^3*e - 4*b^5*c*d^2*e^2 - 32*a^3*c^3*e^4*x + 8*b^2*c^4*d^4*x + 10*b*d*e^3*(b^2 - 4*a*c)^(5/2) + 4*b*e^4*x*(b^2 - 4*a*c)^(5/2) - 16*a*b*c^4*d^4 - 32*a*c^5*d^4*x + 7*a*b^2*e^4*(b^2 - 4*a*c)^(3/2) - 10*b^3*d*e^3*(b^2 - 4*a*c)^(3/2) - 14*c*d^2*e^2*(b^2 - 4*a*c)^(5/2) - 8*c*d*e^3*x*(b^2 - 4*a*c)^(5/2) - 24*a*b^4*c*d*e^3 - 64*a*b^4*c*e^4*x - 32*b^5*c*d*e^3*x - 8*b*c^2*d^3*e*(b^2 - 4*a*c)^(3/2) - 32*c^3*d^3*e*x*(b^2 - 4*a*c)^(3/2) - 96*a*b^2*c^3*d^3*e - 16*b^3*c^3*d^3*e*x + 18*b^2*c*d^2*e^2*(b^2 - 4*a*c)^(3/2) + 56*a*b^3*c^2*d^2*e^2 - 160*a^2*b*c^3*d^2*e^2 + 160*a^2*b^2*c^2*d*e^3 + 136*a^2*b^2*c^2*e^4*x + 448*a^2*c^4*d^2*e^2*x + 40*b^4*c^2*d^2*e^2*x + 48*b*c^2*d^2*e^2*x*(b^2 - 4*a*c)^(3/2) - 272*a*b^2*c^3*d^2*e^2*x + 64*a*b*c^4*d^3*e*x - 24*b^2*c*d*e^3*x*(b^2 - 4*a*c)^(3/2) + 240*a*b^3*c^2*d*e^3*x - 448*a^2*b*c^3*d*e^3*x)*(a*(e^2*(2*b*c + c*(b^2 - 4*a*c)^(1/2)) - 4*c^2*d*e) + e*(b^2*c*d + b*c*d*(b^2 - 4*a*c)^(1/2)) - e^2*(b^3/2 + (b^2*(b^2 - 4*a*c)^(1/2))/2) - c^2*d^2*(b^2 - 4*a*c)^(1/2)))/(4*a*c^3*d^4 + 4*a^3*c*e^4 - a^2*b^2*e^4 - b^2*c^2*d^4 - b^4*d^2*e^2 + 8*a^2*c^2*d^2*e^2 + 2*a*b^3*d*e^3 + 2*b^3*c*d^3*e - 8*a*b*c^2*d^3*e - 8*a^2*b*c*d*e^3 + 2*a*b^2*c*d^2*e^2) + (log(a*e^4*(b^2 - 4*a*c)^(5/2) - 8*a*b^5*e^4 - 8*b^6*e^4*x - 4*c^3*d^4*(b^2 - 4*a*c)^(3/2) - 4*b^3*c^3*d^4 + 4*b^3*e^4*x*(b^2 - 4*a*c)^(3/2) + 60*a^2*b^3*c*e^4 - 112*a^3*b*c^2*e^4 - 256*a^2*c^4*d^3*e + 256*a^3*c^3*d*e^3 - 8*b^4*c^2*d^3*e + 4*b^5*c*d^2*e^2 + 32*a^3*c^3*e^4*x - 8*b^2*c^4*d^4*x + 10*b*d*e^3*(b^2 - 4*a*c)^(5/2) + 4*b*e^4*x*(b^2 - 4*a*c)^(5/2) + 16*a*b*c^4*d^4 + 32*a*c^5*d^4*x + 7*a*b^2*e^4*(b^2 - 4*a*c)^(3/2) - 10*b^3*d*e^3*(b^2 - 4*a*c)^(3/2) - 14*c*d^2*e^2*(b^2 - 4*a*c)^(5/2) - 8*c*d*e^3*x*(b^2 - 4*a*c)^(5/2) + 24*a*b^4*c*d*e^3 + 64*a*b^4*c*e^4*x + 32*b^5*c*d*e^3*x - 8*b*c^2*d^3*e*(b^2 - 4*a*c)^(3/2) - 32*c^3*d^3*e*x*(b^2 - 4*a*c)^(3/2) + 96*a*b^2*c^3*d^3*e + 16*b^3*c^3*d^3*e*x + 18*b^2*c*d^2*e^2*(b^2 - 4*a*c)^(3/2) - 56*a*b^3*c^2*d^2*e^2 + 160*a^2*b*c^3*d^2*e^2 - 160*a^2*b^2*c^2*d*e^3 - 136*a^2*b^2*c^2*e^4*x - 448*a^2*c^4*d^2*e^2*x - 40*b^4*c^2*d^2*e^2*x + 48*b*c^2*d^2*e^2*x*(b^2 - 4*a*c)^(3/2) + 272*a*b^2*c^3*d^2*e^2*x - 64*a*b*c^4*d^3*e*x - 24*b^2*c*d*e^3*x*(b^2 - 4*a*c)^(3/2) - 240*a*b^3*c^2*d*e^3*x + 448*a^2*b*c^3*d*e^3*x)*(a*(e^2*(2*b*c - c*(b^2 - 4*a*c)^(1/2)) - 4*c^2*d*e) + e*(b^2*c*d - b*c*d*(b^2 - 4*a*c)^(1/2)) - e^2*(b^3/2 - (b^2*(b^2 - 4*a*c)^(1/2))/2) + c^2*d^2*(b^2 - 4*a*c)^(1/2)))/(4*a*c^3*d^4 + 4*a^3*c*e^4 - a^2*b^2*e^4 - b^2*c^2*d^4 - b^4*d^2*e^2 + 8*a^2*c^2*d^2*e^2 + 2*a*b^3*d*e^3 + 2*b^3*c*d^3*e - 8*a*b*c^2*d^3*e - 8*a^2*b*c*d*e^3 + 2*a*b^2*c*d^2*e^2) - e/((d + e*x)*(a*e^2 + c*d^2 - b*d*e)) - (log(d + e*x)*(b*e^2 - 2*c*d*e))/(a^2*e^4 + c^2*d^4 + b^2*d^2*e^2 - 2*a*b*d*e^3 - 2*b*c*d^3*e + 2*a*c*d^2*e^2)","B"
2189,1,3506,272,7.661108,"\text{Not used}","int(1/((d + e*x)^3*(a + b*x + c*x^2)),x)","\frac{\ln\left(\frac{27\,d\,e^6\,{\left(b^2-4\,a\,c\right)}^{7/2}}{16}+\frac{9\,e^7\,x\,{\left(b^2-4\,a\,c\right)}^{7/2}}{16}-8\,a\,b^6\,e^7+4\,b\,c^6\,d^7-8\,b^7\,e^7\,x+8\,c^7\,d^7\,x+4\,c^6\,d^7\,\sqrt{b^2-4\,a\,c}+72\,a^4\,c^3\,e^7+\frac{57\,b^2\,e^7\,x\,{\left(b^2-4\,a\,c\right)}^{5/2}}{16}+\frac{51\,b^4\,e^7\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}}{16}+\frac{11\,b^6\,e^7\,x\,\sqrt{b^2-4\,a\,c}}{16}+60\,a^2\,b^4\,c\,e^7+8\,b^2\,c^5\,d^6\,e+4\,b^6\,c\,d^2\,e^5+\frac{75\,c^2\,d^3\,e^4\,{\left(b^2-4\,a\,c\right)}^{5/2}}{4}+25\,c^4\,d^5\,e^2\,{\left(b^2-4\,a\,c\right)}^{3/2}-132\,a^3\,b^2\,c^2\,e^7+408\,a^2\,c^5\,d^4\,e^3-456\,a^3\,c^4\,d^2\,e^5-20\,b^3\,c^4\,d^5\,e^2+28\,b^4\,c^3\,d^4\,e^3-16\,b^5\,c^2\,d^3\,e^4+\frac{9\,a\,b\,e^7\,{\left(b^2-4\,a\,c\right)}^{5/2}}{4}-88\,a\,c^6\,d^6\,e+\frac{9\,a\,b^3\,e^7\,{\left(b^2-4\,a\,c\right)}^{3/2}}{2}+\frac{5\,a\,b^5\,e^7\,\sqrt{b^2-4\,a\,c}}{4}+\frac{111\,b^2\,d\,e^6\,{\left(b^2-4\,a\,c\right)}^{5/2}}{16}-\frac{79\,b^4\,d\,e^6\,{\left(b^2-4\,a\,c\right)}^{3/2}}{16}-\frac{59\,b^6\,d\,e^6\,\sqrt{b^2-4\,a\,c}}{16}+40\,a\,b^5\,c\,d\,e^6+\frac{23\,b^2\,c^2\,d^3\,e^4\,{\left(b^2-4\,a\,c\right)}^{3/2}}{2}-45\,b^2\,c^4\,d^5\,e^2\,\sqrt{b^2-4\,a\,c}+65\,b^3\,c^3\,d^4\,e^3\,\sqrt{b^2-4\,a\,c}-\frac{185\,b^4\,c^2\,d^3\,e^4\,\sqrt{b^2-4\,a\,c}}{4}+64\,a\,b^5\,c\,e^7\,x-28\,b\,c^6\,d^6\,e\,x+48\,b^6\,c\,d\,e^6\,x+504\,a^2\,b^2\,c^3\,d^2\,e^5-21\,b\,c\,d^2\,e^5\,{\left(b^2-4\,a\,c\right)}^{5/2}+8\,b\,c^5\,d^6\,e\,\sqrt{b^2-4\,a\,c}+44\,c^6\,d^6\,e\,x\,\sqrt{b^2-4\,a\,c}+164\,a\,b\,c^5\,d^5\,e^2+348\,a^3\,b\,c^3\,d\,e^6+108\,a^3\,b\,c^3\,e^7\,x-200\,a\,c^6\,d^5\,e^2\,x-216\,a^3\,c^4\,d\,e^6\,x-37\,b\,c^3\,d^4\,e^3\,{\left(b^2-4\,a\,c\right)}^{3/2}+7\,b^3\,c\,d^2\,e^5\,{\left(b^2-4\,a\,c\right)}^{3/2}+18\,b^5\,c\,d^2\,e^5\,\sqrt{b^2-4\,a\,c}+\frac{57\,c^2\,d^2\,e^5\,x\,{\left(b^2-4\,a\,c\right)}^{5/2}}{4}+51\,c^4\,d^4\,e^3\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}-284\,a\,b^2\,c^4\,d^4\,e^3+228\,a\,b^3\,c^3\,d^3\,e^4-124\,a\,b^4\,c^2\,d^2\,e^5-516\,a^2\,b\,c^4\,d^3\,e^4-240\,a^2\,b^3\,c^2\,d\,e^6-156\,a^2\,b^3\,c^2\,e^7\,x+600\,a^2\,c^5\,d^3\,e^4\,x+92\,b^2\,c^5\,d^5\,e^2\,x-160\,b^3\,c^4\,d^4\,e^3\,x+180\,b^4\,c^3\,d^3\,e^4\,x-124\,b^5\,c^2\,d^2\,e^5\,x-102\,b\,c^3\,d^3\,e^4\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}-132\,b\,c^5\,d^5\,e^2\,x\,\sqrt{b^2-4\,a\,c}-800\,a\,b^2\,c^4\,d^3\,e^4\,x+700\,a\,b^3\,c^3\,d^2\,e^5\,x-900\,a^2\,b\,c^4\,d^2\,e^5\,x+612\,a^2\,b^2\,c^3\,d\,e^6\,x-\frac{57\,b\,c\,d\,e^6\,x\,{\left(b^2-4\,a\,c\right)}^{5/2}}{4}+\frac{153\,b^2\,c^2\,d^2\,e^5\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}}{2}+165\,b^2\,c^4\,d^4\,e^3\,x\,\sqrt{b^2-4\,a\,c}-110\,b^3\,c^3\,d^3\,e^4\,x\,\sqrt{b^2-4\,a\,c}+\frac{165\,b^4\,c^2\,d^2\,e^5\,x\,\sqrt{b^2-4\,a\,c}}{4}-\frac{51\,b^3\,c\,d\,e^6\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}}{2}-\frac{33\,b^5\,c\,d\,e^6\,x\,\sqrt{b^2-4\,a\,c}}{4}+500\,a\,b\,c^5\,d^4\,e^3\,x-328\,a\,b^4\,c^2\,d\,e^6\,x\right)\,\left(e^2\,\left(\frac{3\,c\,d\,{\left(b^2-4\,a\,c\right)}^{3/2}}{2}+3\,b\,c\,d\,\left(4\,a\,c-b^2\right)+\frac{3\,b^2\,c\,d\,\sqrt{b^2-4\,a\,c}}{2}\right)-e\,\left(3\,c^2\,d^2\,\left(4\,a\,c-b^2\right)+3\,b\,c^2\,d^2\,\sqrt{b^2-4\,a\,c}\right)-e^3\,\left(\frac{3\,b\,{\left(b^2-4\,a\,c\right)}^{3/2}}{4}-\frac{{\left(4\,a\,c-b^2\right)}^2}{4}+\frac{3\,b^2\,\left(4\,a\,c-b^2\right)}{4}+\frac{b^3\,\sqrt{b^2-4\,a\,c}}{4}\right)+2\,c^3\,d^3\,\sqrt{b^2-4\,a\,c}\right)}{\left(4\,a\,c-b^2\right)\,\left(\left(4\,a\,c-b^2\right)\,\left(\frac{3\,c\,d^4\,e^2}{2}-3\,b\,d^3\,e^3+\frac{3\,a\,d^2\,e^4}{2}\right)+2\,a^3\,e^6+2\,c^3\,d^6-5\,b^3\,d^3\,e^3+\frac{15\,a\,b^2\,d^2\,e^4}{2}+\frac{15\,b^2\,c\,d^4\,e^2}{2}-6\,a^2\,b\,d\,e^5-6\,b\,c^2\,d^5\,e\right)}-\frac{\ln\left(d+e\,x\right)\,\left(e^3\,\left(a\,c-b^2\right)-3\,c^2\,d^2\,e+3\,b\,c\,d\,e^2\right)}{a^3\,e^6-3\,a^2\,b\,d\,e^5+3\,a^2\,c\,d^2\,e^4+3\,a\,b^2\,d^2\,e^4-6\,a\,b\,c\,d^3\,e^3+3\,a\,c^2\,d^4\,e^2-b^3\,d^3\,e^3+3\,b^2\,c\,d^4\,e^2-3\,b\,c^2\,d^5\,e+c^3\,d^6}-\frac{\ln\left(\frac{27\,d\,e^6\,{\left(b^2-4\,a\,c\right)}^{7/2}}{16}+\frac{9\,e^7\,x\,{\left(b^2-4\,a\,c\right)}^{7/2}}{16}+8\,a\,b^6\,e^7-4\,b\,c^6\,d^7+8\,b^7\,e^7\,x-8\,c^7\,d^7\,x+4\,c^6\,d^7\,\sqrt{b^2-4\,a\,c}-72\,a^4\,c^3\,e^7+\frac{57\,b^2\,e^7\,x\,{\left(b^2-4\,a\,c\right)}^{5/2}}{16}+\frac{51\,b^4\,e^7\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}}{16}+\frac{11\,b^6\,e^7\,x\,\sqrt{b^2-4\,a\,c}}{16}-60\,a^2\,b^4\,c\,e^7-8\,b^2\,c^5\,d^6\,e-4\,b^6\,c\,d^2\,e^5+\frac{75\,c^2\,d^3\,e^4\,{\left(b^2-4\,a\,c\right)}^{5/2}}{4}+25\,c^4\,d^5\,e^2\,{\left(b^2-4\,a\,c\right)}^{3/2}+132\,a^3\,b^2\,c^2\,e^7-408\,a^2\,c^5\,d^4\,e^3+456\,a^3\,c^4\,d^2\,e^5+20\,b^3\,c^4\,d^5\,e^2-28\,b^4\,c^3\,d^4\,e^3+16\,b^5\,c^2\,d^3\,e^4+\frac{9\,a\,b\,e^7\,{\left(b^2-4\,a\,c\right)}^{5/2}}{4}+88\,a\,c^6\,d^6\,e+\frac{9\,a\,b^3\,e^7\,{\left(b^2-4\,a\,c\right)}^{3/2}}{2}+\frac{5\,a\,b^5\,e^7\,\sqrt{b^2-4\,a\,c}}{4}+\frac{111\,b^2\,d\,e^6\,{\left(b^2-4\,a\,c\right)}^{5/2}}{16}-\frac{79\,b^4\,d\,e^6\,{\left(b^2-4\,a\,c\right)}^{3/2}}{16}-\frac{59\,b^6\,d\,e^6\,\sqrt{b^2-4\,a\,c}}{16}-40\,a\,b^5\,c\,d\,e^6+\frac{23\,b^2\,c^2\,d^3\,e^4\,{\left(b^2-4\,a\,c\right)}^{3/2}}{2}-45\,b^2\,c^4\,d^5\,e^2\,\sqrt{b^2-4\,a\,c}+65\,b^3\,c^3\,d^4\,e^3\,\sqrt{b^2-4\,a\,c}-\frac{185\,b^4\,c^2\,d^3\,e^4\,\sqrt{b^2-4\,a\,c}}{4}-64\,a\,b^5\,c\,e^7\,x+28\,b\,c^6\,d^6\,e\,x-48\,b^6\,c\,d\,e^6\,x-504\,a^2\,b^2\,c^3\,d^2\,e^5-21\,b\,c\,d^2\,e^5\,{\left(b^2-4\,a\,c\right)}^{5/2}+8\,b\,c^5\,d^6\,e\,\sqrt{b^2-4\,a\,c}+44\,c^6\,d^6\,e\,x\,\sqrt{b^2-4\,a\,c}-164\,a\,b\,c^5\,d^5\,e^2-348\,a^3\,b\,c^3\,d\,e^6-108\,a^3\,b\,c^3\,e^7\,x+200\,a\,c^6\,d^5\,e^2\,x+216\,a^3\,c^4\,d\,e^6\,x-37\,b\,c^3\,d^4\,e^3\,{\left(b^2-4\,a\,c\right)}^{3/2}+7\,b^3\,c\,d^2\,e^5\,{\left(b^2-4\,a\,c\right)}^{3/2}+18\,b^5\,c\,d^2\,e^5\,\sqrt{b^2-4\,a\,c}+\frac{57\,c^2\,d^2\,e^5\,x\,{\left(b^2-4\,a\,c\right)}^{5/2}}{4}+51\,c^4\,d^4\,e^3\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}+284\,a\,b^2\,c^4\,d^4\,e^3-228\,a\,b^3\,c^3\,d^3\,e^4+124\,a\,b^4\,c^2\,d^2\,e^5+516\,a^2\,b\,c^4\,d^3\,e^4+240\,a^2\,b^3\,c^2\,d\,e^6+156\,a^2\,b^3\,c^2\,e^7\,x-600\,a^2\,c^5\,d^3\,e^4\,x-92\,b^2\,c^5\,d^5\,e^2\,x+160\,b^3\,c^4\,d^4\,e^3\,x-180\,b^4\,c^3\,d^3\,e^4\,x+124\,b^5\,c^2\,d^2\,e^5\,x-102\,b\,c^3\,d^3\,e^4\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}-132\,b\,c^5\,d^5\,e^2\,x\,\sqrt{b^2-4\,a\,c}+800\,a\,b^2\,c^4\,d^3\,e^4\,x-700\,a\,b^3\,c^3\,d^2\,e^5\,x+900\,a^2\,b\,c^4\,d^2\,e^5\,x-612\,a^2\,b^2\,c^3\,d\,e^6\,x-\frac{57\,b\,c\,d\,e^6\,x\,{\left(b^2-4\,a\,c\right)}^{5/2}}{4}+\frac{153\,b^2\,c^2\,d^2\,e^5\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}}{2}+165\,b^2\,c^4\,d^4\,e^3\,x\,\sqrt{b^2-4\,a\,c}-110\,b^3\,c^3\,d^3\,e^4\,x\,\sqrt{b^2-4\,a\,c}+\frac{165\,b^4\,c^2\,d^2\,e^5\,x\,\sqrt{b^2-4\,a\,c}}{4}-\frac{51\,b^3\,c\,d\,e^6\,x\,{\left(b^2-4\,a\,c\right)}^{3/2}}{2}-\frac{33\,b^5\,c\,d\,e^6\,x\,\sqrt{b^2-4\,a\,c}}{4}-500\,a\,b\,c^5\,d^4\,e^3\,x+328\,a\,b^4\,c^2\,d\,e^6\,x\right)\,\left(e^2\,\left(\frac{3\,c\,d\,{\left(b^2-4\,a\,c\right)}^{3/2}}{2}-3\,b\,c\,d\,\left(4\,a\,c-b^2\right)+\frac{3\,b^2\,c\,d\,\sqrt{b^2-4\,a\,c}}{2}\right)+e\,\left(3\,c^2\,d^2\,\left(4\,a\,c-b^2\right)-3\,b\,c^2\,d^2\,\sqrt{b^2-4\,a\,c}\right)-e^3\,\left(\frac{{\left(4\,a\,c-b^2\right)}^2}{4}+\frac{3\,b\,{\left(b^2-4\,a\,c\right)}^{3/2}}{4}-\frac{3\,b^2\,\left(4\,a\,c-b^2\right)}{4}+\frac{b^3\,\sqrt{b^2-4\,a\,c}}{4}\right)+2\,c^3\,d^3\,\sqrt{b^2-4\,a\,c}\right)}{\left(4\,a\,c-b^2\right)\,\left(\left(4\,a\,c-b^2\right)\,\left(\frac{3\,c\,d^4\,e^2}{2}-3\,b\,d^3\,e^3+\frac{3\,a\,d^2\,e^4}{2}\right)+2\,a^3\,e^6+2\,c^3\,d^6-5\,b^3\,d^3\,e^3+\frac{15\,a\,b^2\,d^2\,e^4}{2}+\frac{15\,b^2\,c\,d^4\,e^2}{2}-6\,a^2\,b\,d\,e^5-6\,b\,c^2\,d^5\,e\right)}-\frac{\frac{5\,c\,d^2\,e-3\,b\,d\,e^2+a\,e^3}{2\,\left(a^2\,e^4-2\,a\,b\,d\,e^3+2\,a\,c\,d^2\,e^2+b^2\,d^2\,e^2-2\,b\,c\,d^3\,e+c^2\,d^4\right)}-\frac{x\,\left(b\,e^3-2\,c\,d\,e^2\right)}{a^2\,e^4-2\,a\,b\,d\,e^3+2\,a\,c\,d^2\,e^2+b^2\,d^2\,e^2-2\,b\,c\,d^3\,e+c^2\,d^4}}{d^2+2\,d\,e\,x+e^2\,x^2}","Not used",1,"(log((27*d*e^6*(b^2 - 4*a*c)^(7/2))/16 + (9*e^7*x*(b^2 - 4*a*c)^(7/2))/16 - 8*a*b^6*e^7 + 4*b*c^6*d^7 - 8*b^7*e^7*x + 8*c^7*d^7*x + 4*c^6*d^7*(b^2 - 4*a*c)^(1/2) + 72*a^4*c^3*e^7 + (57*b^2*e^7*x*(b^2 - 4*a*c)^(5/2))/16 + (51*b^4*e^7*x*(b^2 - 4*a*c)^(3/2))/16 + (11*b^6*e^7*x*(b^2 - 4*a*c)^(1/2))/16 + 60*a^2*b^4*c*e^7 + 8*b^2*c^5*d^6*e + 4*b^6*c*d^2*e^5 + (75*c^2*d^3*e^4*(b^2 - 4*a*c)^(5/2))/4 + 25*c^4*d^5*e^2*(b^2 - 4*a*c)^(3/2) - 132*a^3*b^2*c^2*e^7 + 408*a^2*c^5*d^4*e^3 - 456*a^3*c^4*d^2*e^5 - 20*b^3*c^4*d^5*e^2 + 28*b^4*c^3*d^4*e^3 - 16*b^5*c^2*d^3*e^4 + (9*a*b*e^7*(b^2 - 4*a*c)^(5/2))/4 - 88*a*c^6*d^6*e + (9*a*b^3*e^7*(b^2 - 4*a*c)^(3/2))/2 + (5*a*b^5*e^7*(b^2 - 4*a*c)^(1/2))/4 + (111*b^2*d*e^6*(b^2 - 4*a*c)^(5/2))/16 - (79*b^4*d*e^6*(b^2 - 4*a*c)^(3/2))/16 - (59*b^6*d*e^6*(b^2 - 4*a*c)^(1/2))/16 + 40*a*b^5*c*d*e^6 + (23*b^2*c^2*d^3*e^4*(b^2 - 4*a*c)^(3/2))/2 - 45*b^2*c^4*d^5*e^2*(b^2 - 4*a*c)^(1/2) + 65*b^3*c^3*d^4*e^3*(b^2 - 4*a*c)^(1/2) - (185*b^4*c^2*d^3*e^4*(b^2 - 4*a*c)^(1/2))/4 + 64*a*b^5*c*e^7*x - 28*b*c^6*d^6*e*x + 48*b^6*c*d*e^6*x + 504*a^2*b^2*c^3*d^2*e^5 - 21*b*c*d^2*e^5*(b^2 - 4*a*c)^(5/2) + 8*b*c^5*d^6*e*(b^2 - 4*a*c)^(1/2) + 44*c^6*d^6*e*x*(b^2 - 4*a*c)^(1/2) + 164*a*b*c^5*d^5*e^2 + 348*a^3*b*c^3*d*e^6 + 108*a^3*b*c^3*e^7*x - 200*a*c^6*d^5*e^2*x - 216*a^3*c^4*d*e^6*x - 37*b*c^3*d^4*e^3*(b^2 - 4*a*c)^(3/2) + 7*b^3*c*d^2*e^5*(b^2 - 4*a*c)^(3/2) + 18*b^5*c*d^2*e^5*(b^2 - 4*a*c)^(1/2) + (57*c^2*d^2*e^5*x*(b^2 - 4*a*c)^(5/2))/4 + 51*c^4*d^4*e^3*x*(b^2 - 4*a*c)^(3/2) - 284*a*b^2*c^4*d^4*e^3 + 228*a*b^3*c^3*d^3*e^4 - 124*a*b^4*c^2*d^2*e^5 - 516*a^2*b*c^4*d^3*e^4 - 240*a^2*b^3*c^2*d*e^6 - 156*a^2*b^3*c^2*e^7*x + 600*a^2*c^5*d^3*e^4*x + 92*b^2*c^5*d^5*e^2*x - 160*b^3*c^4*d^4*e^3*x + 180*b^4*c^3*d^3*e^4*x - 124*b^5*c^2*d^2*e^5*x - 102*b*c^3*d^3*e^4*x*(b^2 - 4*a*c)^(3/2) - 132*b*c^5*d^5*e^2*x*(b^2 - 4*a*c)^(1/2) - 800*a*b^2*c^4*d^3*e^4*x + 700*a*b^3*c^3*d^2*e^5*x - 900*a^2*b*c^4*d^2*e^5*x + 612*a^2*b^2*c^3*d*e^6*x - (57*b*c*d*e^6*x*(b^2 - 4*a*c)^(5/2))/4 + (153*b^2*c^2*d^2*e^5*x*(b^2 - 4*a*c)^(3/2))/2 + 165*b^2*c^4*d^4*e^3*x*(b^2 - 4*a*c)^(1/2) - 110*b^3*c^3*d^3*e^4*x*(b^2 - 4*a*c)^(1/2) + (165*b^4*c^2*d^2*e^5*x*(b^2 - 4*a*c)^(1/2))/4 - (51*b^3*c*d*e^6*x*(b^2 - 4*a*c)^(3/2))/2 - (33*b^5*c*d*e^6*x*(b^2 - 4*a*c)^(1/2))/4 + 500*a*b*c^5*d^4*e^3*x - 328*a*b^4*c^2*d*e^6*x)*(e^2*((3*c*d*(b^2 - 4*a*c)^(3/2))/2 + 3*b*c*d*(4*a*c - b^2) + (3*b^2*c*d*(b^2 - 4*a*c)^(1/2))/2) - e*(3*c^2*d^2*(4*a*c - b^2) + 3*b*c^2*d^2*(b^2 - 4*a*c)^(1/2)) - e^3*((3*b*(b^2 - 4*a*c)^(3/2))/4 - (4*a*c - b^2)^2/4 + (3*b^2*(4*a*c - b^2))/4 + (b^3*(b^2 - 4*a*c)^(1/2))/4) + 2*c^3*d^3*(b^2 - 4*a*c)^(1/2)))/((4*a*c - b^2)*((4*a*c - b^2)*((3*a*d^2*e^4)/2 - 3*b*d^3*e^3 + (3*c*d^4*e^2)/2) + 2*a^3*e^6 + 2*c^3*d^6 - 5*b^3*d^3*e^3 + (15*a*b^2*d^2*e^4)/2 + (15*b^2*c*d^4*e^2)/2 - 6*a^2*b*d*e^5 - 6*b*c^2*d^5*e)) - (log(d + e*x)*(e^3*(a*c - b^2) - 3*c^2*d^2*e + 3*b*c*d*e^2))/(a^3*e^6 + c^3*d^6 - b^3*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + 3*b^2*c*d^4*e^2 - 3*a^2*b*d*e^5 - 3*b*c^2*d^5*e - 6*a*b*c*d^3*e^3) - (log((27*d*e^6*(b^2 - 4*a*c)^(7/2))/16 + (9*e^7*x*(b^2 - 4*a*c)^(7/2))/16 + 8*a*b^6*e^7 - 4*b*c^6*d^7 + 8*b^7*e^7*x - 8*c^7*d^7*x + 4*c^6*d^7*(b^2 - 4*a*c)^(1/2) - 72*a^4*c^3*e^7 + (57*b^2*e^7*x*(b^2 - 4*a*c)^(5/2))/16 + (51*b^4*e^7*x*(b^2 - 4*a*c)^(3/2))/16 + (11*b^6*e^7*x*(b^2 - 4*a*c)^(1/2))/16 - 60*a^2*b^4*c*e^7 - 8*b^2*c^5*d^6*e - 4*b^6*c*d^2*e^5 + (75*c^2*d^3*e^4*(b^2 - 4*a*c)^(5/2))/4 + 25*c^4*d^5*e^2*(b^2 - 4*a*c)^(3/2) + 132*a^3*b^2*c^2*e^7 - 408*a^2*c^5*d^4*e^3 + 456*a^3*c^4*d^2*e^5 + 20*b^3*c^4*d^5*e^2 - 28*b^4*c^3*d^4*e^3 + 16*b^5*c^2*d^3*e^4 + (9*a*b*e^7*(b^2 - 4*a*c)^(5/2))/4 + 88*a*c^6*d^6*e + (9*a*b^3*e^7*(b^2 - 4*a*c)^(3/2))/2 + (5*a*b^5*e^7*(b^2 - 4*a*c)^(1/2))/4 + (111*b^2*d*e^6*(b^2 - 4*a*c)^(5/2))/16 - (79*b^4*d*e^6*(b^2 - 4*a*c)^(3/2))/16 - (59*b^6*d*e^6*(b^2 - 4*a*c)^(1/2))/16 - 40*a*b^5*c*d*e^6 + (23*b^2*c^2*d^3*e^4*(b^2 - 4*a*c)^(3/2))/2 - 45*b^2*c^4*d^5*e^2*(b^2 - 4*a*c)^(1/2) + 65*b^3*c^3*d^4*e^3*(b^2 - 4*a*c)^(1/2) - (185*b^4*c^2*d^3*e^4*(b^2 - 4*a*c)^(1/2))/4 - 64*a*b^5*c*e^7*x + 28*b*c^6*d^6*e*x - 48*b^6*c*d*e^6*x - 504*a^2*b^2*c^3*d^2*e^5 - 21*b*c*d^2*e^5*(b^2 - 4*a*c)^(5/2) + 8*b*c^5*d^6*e*(b^2 - 4*a*c)^(1/2) + 44*c^6*d^6*e*x*(b^2 - 4*a*c)^(1/2) - 164*a*b*c^5*d^5*e^2 - 348*a^3*b*c^3*d*e^6 - 108*a^3*b*c^3*e^7*x + 200*a*c^6*d^5*e^2*x + 216*a^3*c^4*d*e^6*x - 37*b*c^3*d^4*e^3*(b^2 - 4*a*c)^(3/2) + 7*b^3*c*d^2*e^5*(b^2 - 4*a*c)^(3/2) + 18*b^5*c*d^2*e^5*(b^2 - 4*a*c)^(1/2) + (57*c^2*d^2*e^5*x*(b^2 - 4*a*c)^(5/2))/4 + 51*c^4*d^4*e^3*x*(b^2 - 4*a*c)^(3/2) + 284*a*b^2*c^4*d^4*e^3 - 228*a*b^3*c^3*d^3*e^4 + 124*a*b^4*c^2*d^2*e^5 + 516*a^2*b*c^4*d^3*e^4 + 240*a^2*b^3*c^2*d*e^6 + 156*a^2*b^3*c^2*e^7*x - 600*a^2*c^5*d^3*e^4*x - 92*b^2*c^5*d^5*e^2*x + 160*b^3*c^4*d^4*e^3*x - 180*b^4*c^3*d^3*e^4*x + 124*b^5*c^2*d^2*e^5*x - 102*b*c^3*d^3*e^4*x*(b^2 - 4*a*c)^(3/2) - 132*b*c^5*d^5*e^2*x*(b^2 - 4*a*c)^(1/2) + 800*a*b^2*c^4*d^3*e^4*x - 700*a*b^3*c^3*d^2*e^5*x + 900*a^2*b*c^4*d^2*e^5*x - 612*a^2*b^2*c^3*d*e^6*x - (57*b*c*d*e^6*x*(b^2 - 4*a*c)^(5/2))/4 + (153*b^2*c^2*d^2*e^5*x*(b^2 - 4*a*c)^(3/2))/2 + 165*b^2*c^4*d^4*e^3*x*(b^2 - 4*a*c)^(1/2) - 110*b^3*c^3*d^3*e^4*x*(b^2 - 4*a*c)^(1/2) + (165*b^4*c^2*d^2*e^5*x*(b^2 - 4*a*c)^(1/2))/4 - (51*b^3*c*d*e^6*x*(b^2 - 4*a*c)^(3/2))/2 - (33*b^5*c*d*e^6*x*(b^2 - 4*a*c)^(1/2))/4 - 500*a*b*c^5*d^4*e^3*x + 328*a*b^4*c^2*d*e^6*x)*(e^2*((3*c*d*(b^2 - 4*a*c)^(3/2))/2 - 3*b*c*d*(4*a*c - b^2) + (3*b^2*c*d*(b^2 - 4*a*c)^(1/2))/2) + e*(3*c^2*d^2*(4*a*c - b^2) - 3*b*c^2*d^2*(b^2 - 4*a*c)^(1/2)) - e^3*((4*a*c - b^2)^2/4 + (3*b*(b^2 - 4*a*c)^(3/2))/4 - (3*b^2*(4*a*c - b^2))/4 + (b^3*(b^2 - 4*a*c)^(1/2))/4) + 2*c^3*d^3*(b^2 - 4*a*c)^(1/2)))/((4*a*c - b^2)*((4*a*c - b^2)*((3*a*d^2*e^4)/2 - 3*b*d^3*e^3 + (3*c*d^4*e^2)/2) + 2*a^3*e^6 + 2*c^3*d^6 - 5*b^3*d^3*e^3 + (15*a*b^2*d^2*e^4)/2 + (15*b^2*c*d^4*e^2)/2 - 6*a^2*b*d*e^5 - 6*b*c^2*d^5*e)) - ((a*e^3 - 3*b*d*e^2 + 5*c*d^2*e)/(2*(a^2*e^4 + c^2*d^4 + b^2*d^2*e^2 - 2*a*b*d*e^3 - 2*b*c*d^3*e + 2*a*c*d^2*e^2)) - (x*(b*e^3 - 2*c*d*e^2))/(a^2*e^4 + c^2*d^4 + b^2*d^2*e^2 - 2*a*b*d*e^3 - 2*b*c*d^3*e + 2*a*c*d^2*e^2))/(d^2 + e^2*x^2 + 2*d*e*x)","B"
2190,1,1083,374,2.122333,"\text{Not used}","int((d + e*x)^5/(a + b*x + c*x^2)^2,x)","\frac{e^5\,x^2}{2\,c^2}-x\,\left(\frac{2\,b\,e^5}{c^3}-\frac{5\,d\,e^4}{c^2}\right)-\frac{\ln\left(c\,x^2+b\,x+a\right)\,\left(128\,a^4\,c^4\,e^5-288\,a^3\,b^2\,c^3\,e^5+640\,a^3\,b\,c^4\,d\,e^4-640\,a^3\,c^5\,d^2\,e^3+168\,a^2\,b^4\,c^2\,e^5-480\,a^2\,b^3\,c^3\,d\,e^4+480\,a^2\,b^2\,c^4\,d^2\,e^3-38\,a\,b^6\,c\,e^5+120\,a\,b^5\,c^2\,d\,e^4-120\,a\,b^4\,c^3\,d^2\,e^3+3\,b^8\,e^5-10\,b^7\,c\,d\,e^4+10\,b^6\,c^2\,d^2\,e^3\right)}{2\,\left(64\,a^3\,c^7-48\,a^2\,b^2\,c^6+12\,a\,b^4\,c^5-b^6\,c^4\right)}-\frac{\frac{2\,a^3\,c^2\,e^5-4\,a^2\,b^2\,c\,e^5+15\,a^2\,b\,c^2\,d\,e^4-20\,a^2\,c^3\,d^2\,e^3+a\,b^4\,e^5-5\,a\,b^3\,c\,d\,e^4+10\,a\,b^2\,c^2\,d^2\,e^3-10\,a\,b\,c^3\,d^3\,e^2+10\,a\,c^4\,d^4\,e-b\,c^4\,d^5}{c\,\left(4\,a\,c-b^2\right)}+\frac{x\,\left(5\,a^2\,b\,c^2\,e^5-10\,a^2\,c^3\,d\,e^4-5\,a\,b^3\,c\,e^5+20\,a\,b^2\,c^2\,d\,e^4-30\,a\,b\,c^3\,d^2\,e^3+20\,a\,c^4\,d^3\,e^2+b^5\,e^5-5\,b^4\,c\,d\,e^4+10\,b^3\,c^2\,d^2\,e^3-10\,b^2\,c^3\,d^3\,e^2+5\,b\,c^4\,d^4\,e-2\,c^5\,d^5\right)}{c\,\left(4\,a\,c-b^2\right)}}{c^4\,x^2+b\,c^3\,x+a\,c^3}-\frac{\mathrm{atan}\left(\frac{c^4\,\left(\frac{\left(b^3\,c^3-4\,a\,b\,c^4\right)\,\left(b\,e-2\,c\,d\right)\,\left(30\,a^2\,c^2\,e^4-20\,a\,b^2\,c\,e^4+20\,a\,b\,c^2\,d\,e^3-20\,a\,c^3\,d^2\,e^2+3\,b^4\,e^4-4\,b^3\,c\,d\,e^3+2\,b^2\,c^2\,d^2\,e^2+4\,b\,c^3\,d^3\,e-2\,c^4\,d^4\right)}{c^7\,{\left(4\,a\,c-b^2\right)}^4}-\frac{2\,x\,\left(b\,e-2\,c\,d\right)\,\left(30\,a^2\,c^2\,e^4-20\,a\,b^2\,c\,e^4+20\,a\,b\,c^2\,d\,e^3-20\,a\,c^3\,d^2\,e^2+3\,b^4\,e^4-4\,b^3\,c\,d\,e^3+2\,b^2\,c^2\,d^2\,e^2+4\,b\,c^3\,d^3\,e-2\,c^4\,d^4\right)}{c^3\,{\left(4\,a\,c-b^2\right)}^3}\right)\,{\left(4\,a\,c-b^2\right)}^{5/2}}{30\,a^2\,b\,c^2\,e^5-60\,a^2\,c^3\,d\,e^4-20\,a\,b^3\,c\,e^5+60\,a\,b^2\,c^2\,d\,e^4-60\,a\,b\,c^3\,d^2\,e^3+40\,a\,c^4\,d^3\,e^2+3\,b^5\,e^5-10\,b^4\,c\,d\,e^4+10\,b^3\,c^2\,d^2\,e^3-10\,b\,c^4\,d^4\,e+4\,c^5\,d^5}\right)\,\left(b\,e-2\,c\,d\right)\,\left(30\,a^2\,c^2\,e^4-20\,a\,b^2\,c\,e^4+20\,a\,b\,c^2\,d\,e^3-20\,a\,c^3\,d^2\,e^2+3\,b^4\,e^4-4\,b^3\,c\,d\,e^3+2\,b^2\,c^2\,d^2\,e^2+4\,b\,c^3\,d^3\,e-2\,c^4\,d^4\right)}{c^4\,{\left(4\,a\,c-b^2\right)}^{3/2}}","Not used",1,"(e^5*x^2)/(2*c^2) - x*((2*b*e^5)/c^3 - (5*d*e^4)/c^2) - (log(a + b*x + c*x^2)*(3*b^8*e^5 + 128*a^4*c^4*e^5 + 168*a^2*b^4*c^2*e^5 - 288*a^3*b^2*c^3*e^5 - 640*a^3*c^5*d^2*e^3 + 10*b^6*c^2*d^2*e^3 - 38*a*b^6*c*e^5 - 10*b^7*c*d*e^4 + 480*a^2*b^2*c^4*d^2*e^3 + 120*a*b^5*c^2*d*e^4 + 640*a^3*b*c^4*d*e^4 - 120*a*b^4*c^3*d^2*e^3 - 480*a^2*b^3*c^3*d*e^4))/(2*(64*a^3*c^7 - b^6*c^4 + 12*a*b^4*c^5 - 48*a^2*b^2*c^6)) - ((a*b^4*e^5 - b*c^4*d^5 + 2*a^3*c^2*e^5 - 4*a^2*b^2*c*e^5 - 20*a^2*c^3*d^2*e^3 + 10*a*c^4*d^4*e - 5*a*b^3*c*d*e^4 - 10*a*b*c^3*d^3*e^2 + 15*a^2*b*c^2*d*e^4 + 10*a*b^2*c^2*d^2*e^3)/(c*(4*a*c - b^2)) + (x*(b^5*e^5 - 2*c^5*d^5 + 5*a^2*b*c^2*e^5 + 20*a*c^4*d^3*e^2 - 10*a^2*c^3*d*e^4 - 10*b^2*c^3*d^3*e^2 + 10*b^3*c^2*d^2*e^3 - 5*a*b^3*c*e^5 + 5*b*c^4*d^4*e - 5*b^4*c*d*e^4 - 30*a*b*c^3*d^2*e^3 + 20*a*b^2*c^2*d*e^4))/(c*(4*a*c - b^2)))/(a*c^3 + c^4*x^2 + b*c^3*x) - (atan((c^4*(((b^3*c^3 - 4*a*b*c^4)*(b*e - 2*c*d)*(3*b^4*e^4 - 2*c^4*d^4 + 30*a^2*c^2*e^4 - 20*a*c^3*d^2*e^2 + 2*b^2*c^2*d^2*e^2 - 20*a*b^2*c*e^4 + 4*b*c^3*d^3*e - 4*b^3*c*d*e^3 + 20*a*b*c^2*d*e^3))/(c^7*(4*a*c - b^2)^4) - (2*x*(b*e - 2*c*d)*(3*b^4*e^4 - 2*c^4*d^4 + 30*a^2*c^2*e^4 - 20*a*c^3*d^2*e^2 + 2*b^2*c^2*d^2*e^2 - 20*a*b^2*c*e^4 + 4*b*c^3*d^3*e - 4*b^3*c*d*e^3 + 20*a*b*c^2*d*e^3))/(c^3*(4*a*c - b^2)^3))*(4*a*c - b^2)^(5/2))/(3*b^5*e^5 + 4*c^5*d^5 + 30*a^2*b*c^2*e^5 + 40*a*c^4*d^3*e^2 - 60*a^2*c^3*d*e^4 + 10*b^3*c^2*d^2*e^3 - 20*a*b^3*c*e^5 - 10*b*c^4*d^4*e - 10*b^4*c*d*e^4 - 60*a*b*c^3*d^2*e^3 + 60*a*b^2*c^2*d*e^4))*(b*e - 2*c*d)*(3*b^4*e^4 - 2*c^4*d^4 + 30*a^2*c^2*e^4 - 20*a*c^3*d^2*e^2 + 2*b^2*c^2*d^2*e^2 - 20*a*b^2*c*e^4 + 4*b*c^3*d^3*e - 4*b^3*c*d*e^3 + 20*a*b*c^2*d*e^3))/(c^4*(4*a*c - b^2)^(3/2))","B"
2191,1,525,260,1.868439,"\text{Not used}","int((d + e*x)^4/(a + b*x + c*x^2)^2,x)","\frac{\frac{-3\,a^2\,b\,c\,e^4+8\,a^2\,c^2\,d\,e^3+a\,b^3\,e^4-4\,a\,b^2\,c\,d\,e^3+6\,a\,b\,c^2\,d^2\,e^2-8\,a\,c^3\,d^3\,e+b\,c^3\,d^4}{c\,\left(4\,a\,c-b^2\right)}+\frac{x\,\left(2\,a^2\,c^2\,e^4-4\,a\,b^2\,c\,e^4+12\,a\,b\,c^2\,d\,e^3-12\,a\,c^3\,d^2\,e^2+b^4\,e^4-4\,b^3\,c\,d\,e^3+6\,b^2\,c^2\,d^2\,e^2-4\,b\,c^3\,d^3\,e+2\,c^4\,d^4\right)}{c\,\left(4\,a\,c-b^2\right)}}{c^3\,x^2+b\,c^2\,x+a\,c^2}+\frac{\ln\left(c\,x^2+b\,x+a\right)\,\left(-128\,a^3\,b\,c^3\,e^4+256\,d\,a^3\,c^4\,e^3+96\,a^2\,b^3\,c^2\,e^4-192\,d\,a^2\,b^2\,c^3\,e^3-24\,a\,b^5\,c\,e^4+48\,d\,a\,b^4\,c^2\,e^3+2\,b^7\,e^4-4\,d\,b^6\,c\,e^3\right)}{2\,\left(64\,a^3\,c^6-48\,a^2\,b^2\,c^5+12\,a\,b^4\,c^4-b^6\,c^3\right)}+\frac{e^4\,x}{c^2}-\frac{2\,\mathrm{atan}\left(\frac{2\,c\,x}{\sqrt{4\,a\,c-b^2}}-\frac{b^3\,c^2-4\,a\,b\,c^3}{c^2\,{\left(4\,a\,c-b^2\right)}^{3/2}}\right)\,\left(6\,a^2\,c^2\,e^4-6\,a\,b^2\,c\,e^4+12\,a\,b\,c^2\,d\,e^3-12\,a\,c^3\,d^2\,e^2+b^4\,e^4-2\,b^3\,c\,d\,e^3+4\,b\,c^3\,d^3\,e-2\,c^4\,d^4\right)}{c^3\,{\left(4\,a\,c-b^2\right)}^{3/2}}","Not used",1,"((a*b^3*e^4 + b*c^3*d^4 + 8*a^2*c^2*d*e^3 - 3*a^2*b*c*e^4 - 8*a*c^3*d^3*e - 4*a*b^2*c*d*e^3 + 6*a*b*c^2*d^2*e^2)/(c*(4*a*c - b^2)) + (x*(b^4*e^4 + 2*c^4*d^4 + 2*a^2*c^2*e^4 - 12*a*c^3*d^2*e^2 + 6*b^2*c^2*d^2*e^2 - 4*a*b^2*c*e^4 - 4*b*c^3*d^3*e - 4*b^3*c*d*e^3 + 12*a*b*c^2*d*e^3))/(c*(4*a*c - b^2)))/(a*c^2 + c^3*x^2 + b*c^2*x) + (log(a + b*x + c*x^2)*(2*b^7*e^4 - 128*a^3*b*c^3*e^4 + 256*a^3*c^4*d*e^3 + 96*a^2*b^3*c^2*e^4 - 24*a*b^5*c*e^4 - 4*b^6*c*d*e^3 + 48*a*b^4*c^2*d*e^3 - 192*a^2*b^2*c^3*d*e^3))/(2*(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5)) + (e^4*x)/c^2 - (2*atan((2*c*x)/(4*a*c - b^2)^(1/2) - (b^3*c^2 - 4*a*b*c^3)/(c^2*(4*a*c - b^2)^(3/2)))*(b^4*e^4 - 2*c^4*d^4 + 6*a^2*c^2*e^4 - 12*a*c^3*d^2*e^2 - 6*a*b^2*c*e^4 + 4*b*c^3*d^3*e - 2*b^3*c*d*e^3 + 12*a*b*c^2*d*e^3))/(c^3*(4*a*c - b^2)^(3/2))","B"
2192,1,483,173,1.633606,"\text{Not used}","int((d + e*x)^3/(a + b*x + c*x^2)^2,x)","\frac{\frac{2\,a^2\,c\,e^3-a\,b^2\,e^3+3\,a\,b\,c\,d\,e^2-6\,a\,c^2\,d^2\,e+b\,c^2\,d^3}{c^2\,\left(4\,a\,c-b^2\right)}-\frac{x\,\left(b^3\,e^3-3\,b^2\,c\,d\,e^2+3\,b\,c^2\,d^2\,e-3\,a\,b\,c\,e^3-2\,c^3\,d^3+6\,a\,c^2\,d\,e^2\right)}{c^2\,\left(4\,a\,c-b^2\right)}}{c\,x^2+b\,x+a}-\frac{\ln\left(c\,x^2+b\,x+a\right)\,\left(-64\,a^3\,c^3\,e^3+48\,a^2\,b^2\,c^2\,e^3-12\,a\,b^4\,c\,e^3+b^6\,e^3\right)}{2\,\left(64\,a^3\,c^5-48\,a^2\,b^2\,c^4+12\,a\,b^4\,c^3-b^6\,c^2\right)}+\frac{\mathrm{atan}\left(\frac{c^2\,\left(\frac{2\,x\,\left(b\,e-2\,c\,d\right)\,\left(b^2\,e^2+2\,b\,c\,d\,e-2\,c^2\,d^2-6\,a\,c\,e^2\right)}{c\,{\left(4\,a\,c-b^2\right)}^3}-\frac{\left(b\,e-2\,c\,d\right)\,\left(b^3\,c-4\,a\,b\,c^2\right)\,\left(b^2\,e^2+2\,b\,c\,d\,e-2\,c^2\,d^2-6\,a\,c\,e^2\right)}{c^3\,{\left(4\,a\,c-b^2\right)}^4}\right)\,{\left(4\,a\,c-b^2\right)}^{5/2}}{b^3\,e^3-6\,b\,c^2\,d^2\,e-6\,a\,b\,c\,e^3+4\,c^3\,d^3+12\,a\,c^2\,d\,e^2}\right)\,\left(b\,e-2\,c\,d\right)\,\left(b^2\,e^2+2\,b\,c\,d\,e-2\,c^2\,d^2-6\,a\,c\,e^2\right)}{c^2\,{\left(4\,a\,c-b^2\right)}^{3/2}}","Not used",1,"((b*c^2*d^3 - a*b^2*e^3 + 2*a^2*c*e^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2)/(c^2*(4*a*c - b^2)) - (x*(b^3*e^3 - 2*c^3*d^3 - 3*a*b*c*e^3 + 6*a*c^2*d*e^2 + 3*b*c^2*d^2*e - 3*b^2*c*d*e^2))/(c^2*(4*a*c - b^2)))/(a + b*x + c*x^2) - (log(a + b*x + c*x^2)*(b^6*e^3 - 64*a^3*c^3*e^3 + 48*a^2*b^2*c^2*e^3 - 12*a*b^4*c*e^3))/(2*(64*a^3*c^5 - b^6*c^2 + 12*a*b^4*c^3 - 48*a^2*b^2*c^4)) + (atan((c^2*((2*x*(b*e - 2*c*d)*(b^2*e^2 - 2*c^2*d^2 - 6*a*c*e^2 + 2*b*c*d*e))/(c*(4*a*c - b^2)^3) - ((b*e - 2*c*d)*(b^3*c - 4*a*b*c^2)*(b^2*e^2 - 2*c^2*d^2 - 6*a*c*e^2 + 2*b*c*d*e))/(c^3*(4*a*c - b^2)^4))*(4*a*c - b^2)^(5/2))/(b^3*e^3 + 4*c^3*d^3 - 6*a*b*c*e^3 + 12*a*c^2*d*e^2 - 6*b*c^2*d^2*e))*(b*e - 2*c*d)*(b^2*e^2 - 2*c^2*d^2 - 6*a*c*e^2 + 2*b*c*d*e))/(c^2*(4*a*c - b^2)^(3/2))","B"
2193,1,230,99,0.162821,"\text{Not used}","int((d + e*x)^2/(a + b*x + c*x^2)^2,x)","\frac{\frac{b\,c\,d^2-4\,a\,c\,d\,e+a\,b\,e^2}{c\,\left(4\,a\,c-b^2\right)}+\frac{x\,\left(b^2\,e^2-2\,b\,c\,d\,e+2\,c^2\,d^2-2\,a\,c\,e^2\right)}{c\,\left(4\,a\,c-b^2\right)}}{c\,x^2+b\,x+a}-\frac{4\,\mathrm{atan}\left(\frac{\left(\frac{2\,\left(b^3-4\,a\,b\,c\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{5/2}}-\frac{4\,c\,x\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{3/2}}\right)\,\left(4\,a\,c-b^2\right)}{2\,c\,d^2-2\,b\,d\,e+2\,a\,e^2}\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{3/2}}","Not used",1,"((a*b*e^2 + b*c*d^2 - 4*a*c*d*e)/(c*(4*a*c - b^2)) + (x*(b^2*e^2 + 2*c^2*d^2 - 2*a*c*e^2 - 2*b*c*d*e))/(c*(4*a*c - b^2)))/(a + b*x + c*x^2) - (4*atan((((2*(b^3 - 4*a*b*c)*(a*e^2 + c*d^2 - b*d*e))/(4*a*c - b^2)^(5/2) - (4*c*x*(a*e^2 + c*d^2 - b*d*e))/(4*a*c - b^2)^(3/2))*(4*a*c - b^2))/(2*a*e^2 + 2*c*d^2 - 2*b*d*e))*(a*e^2 + c*d^2 - b*d*e))/(4*a*c - b^2)^(3/2)","B"
2194,1,159,87,0.116600,"\text{Not used}","int((d + e*x)/(a + b*x + c*x^2)^2,x)","\frac{2\,\mathrm{atan}\left(\frac{\left(4\,a\,c-b^2\right)\,\left(\frac{\left(b^3-4\,a\,b\,c\right)\,\left(b\,e-2\,c\,d\right)}{{\left(4\,a\,c-b^2\right)}^{5/2}}-\frac{2\,c\,x\,\left(b\,e-2\,c\,d\right)}{{\left(4\,a\,c-b^2\right)}^{3/2}}\right)}{b\,e-2\,c\,d}\right)\,\left(b\,e-2\,c\,d\right)}{{\left(4\,a\,c-b^2\right)}^{3/2}}-\frac{\frac{2\,a\,e-b\,d}{4\,a\,c-b^2}+\frac{x\,\left(b\,e-2\,c\,d\right)}{4\,a\,c-b^2}}{c\,x^2+b\,x+a}","Not used",1,"(2*atan(((4*a*c - b^2)*(((b^3 - 4*a*b*c)*(b*e - 2*c*d))/(4*a*c - b^2)^(5/2) - (2*c*x*(b*e - 2*c*d))/(4*a*c - b^2)^(3/2)))/(b*e - 2*c*d))*(b*e - 2*c*d))/(4*a*c - b^2)^(3/2) - ((2*a*e - b*d)/(4*a*c - b^2) + (x*(b*e - 2*c*d))/(4*a*c - b^2))/(a + b*x + c*x^2)","B"
2195,1,119,66,0.145565,"\text{Not used}","int(1/(a + b*x + c*x^2)^2,x)","\frac{\frac{b}{4\,a\,c-b^2}+\frac{2\,c\,x}{4\,a\,c-b^2}}{c\,x^2+b\,x+a}-\frac{4\,c\,\mathrm{atan}\left(\frac{\left(\frac{2\,c\,\left(b^3-4\,a\,b\,c\right)}{{\left(4\,a\,c-b^2\right)}^{5/2}}-\frac{4\,c^2\,x}{{\left(4\,a\,c-b^2\right)}^{3/2}}\right)\,\left(4\,a\,c-b^2\right)}{2\,c}\right)}{{\left(4\,a\,c-b^2\right)}^{3/2}}","Not used",1,"(b/(4*a*c - b^2) + (2*c*x)/(4*a*c - b^2))/(a + b*x + c*x^2) - (4*c*atan((((2*c*(b^3 - 4*a*b*c))/(4*a*c - b^2)^(5/2) - (4*c^2*x)/(4*a*c - b^2)^(3/2))*(4*a*c - b^2))/(2*c)))/(4*a*c - b^2)^(3/2)","B"
2196,1,2953,224,4.772613,"\text{Not used}","int(1/((d + e*x)*(a + b*x + c*x^2)^2),x)","\frac{e^3\,\ln\left(d+e\,x\right)}{a^2\,e^4-2\,a\,b\,d\,e^3+2\,a\,c\,d^2\,e^2+b^2\,d^2\,e^2-2\,b\,c\,d^3\,e+c^2\,d^4}-\frac{\frac{-e\,b^2+c\,d\,b+2\,a\,c\,e}{-4\,a^2\,c\,e^2+a\,b^2\,e^2+4\,a\,b\,c\,d\,e-4\,a\,c^2\,d^2-b^3\,d\,e+b^2\,c\,d^2}+\frac{x\,\left(2\,c^2\,d-b\,c\,e\right)}{-4\,a^2\,c\,e^2+a\,b^2\,e^2+4\,a\,b\,c\,d\,e-4\,a\,c^2\,d^2-b^3\,d\,e+b^2\,c\,d^2}}{c\,x^2+b\,x+a}+\frac{\ln\left(96\,a^4\,c^3\,e^5-2\,b^7\,e^5\,x-2\,a\,b^6\,e^5-2\,b^3\,c^4\,d^5-2\,c^4\,d^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,a\,b^3\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+23\,a^2\,b^4\,c\,e^5-32\,a^2\,c^5\,d^4\,e+3\,b^4\,c^3\,d^4\,e+b^6\,c\,d^2\,e^3-4\,b^2\,c^5\,d^5\,x+2\,b^4\,e^5\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-84\,a^3\,b^2\,c^2\,e^5-192\,a^3\,c^4\,d^2\,e^3+8\,a\,b\,c^5\,d^5+16\,a\,c^6\,d^5\,x+2\,a\,b^5\,c\,d\,e^4+24\,a\,b^5\,c\,e^5\,x+4\,b^6\,c\,d\,e^4\,x+72\,a^2\,b^2\,c^3\,d^2\,e^3-9\,a^2\,b\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-4\,a\,b^2\,c^4\,d^4\,e+72\,a^3\,b\,c^3\,d\,e^4+3\,b\,c^3\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+120\,a^3\,b\,c^3\,e^5\,x-240\,a^3\,c^4\,d\,e^4\,x+10\,b^3\,c^4\,d^4\,e\,x-4\,c^4\,d^4\,e\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a\,b^3\,c^3\,d^3\,e^2-10\,a\,b^4\,c^2\,d^2\,e^3+80\,a^2\,b\,c^4\,d^3\,e^2-26\,a^2\,b^3\,c^2\,d\,e^4-4\,a\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+30\,a^2\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+b^3\,c\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-94\,a^2\,b^3\,c^2\,e^5\,x+12\,a^2\,c^2\,e^5\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+32\,a^2\,c^5\,d^3\,e^2\,x-8\,b^4\,c^3\,d^3\,e^2\,x+2\,b^5\,c^2\,d^2\,e^3\,x-6\,a\,b\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+24\,a\,b^2\,c^4\,d^3\,e^2\,x+4\,a\,b^3\,c^3\,d^2\,e^3\,x-48\,a^2\,b\,c^4\,d^2\,e^3\,x+204\,a^2\,b^2\,c^3\,d\,e^4\,x-24\,a\,c^3\,d^2\,e^3\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,b\,c^3\,d^3\,e^2\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-40\,a\,b\,c^5\,d^4\,e\,x-6\,a\,b^2\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-12\,a\,b^2\,c\,e^5\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-52\,a\,b^4\,c^2\,d\,e^4\,x-4\,b^3\,c\,d\,e^4\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+24\,a\,b\,c^2\,d\,e^4\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}\right)\,\left(c\,\left(6\,a\,b^4\,e^3-3\,a\,b\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}\right)+c^3\,\left(32\,a^3\,e^3+2\,d^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}\right)-c^2\,\left(24\,a^2\,b^2\,e^3-6\,a\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+3\,b\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}\right)-\frac{b^6\,e^3}{2}+\frac{b^3\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2}\right)}{-64\,a^5\,c^3\,e^4+48\,a^4\,b^2\,c^2\,e^4+128\,a^4\,b\,c^3\,d\,e^3-128\,a^4\,c^4\,d^2\,e^2-12\,a^3\,b^4\,c\,e^4-96\,a^3\,b^3\,c^2\,d\,e^3+32\,a^3\,b^2\,c^3\,d^2\,e^2+128\,a^3\,b\,c^4\,d^3\,e-64\,a^3\,c^5\,d^4+a^2\,b^6\,e^4+24\,a^2\,b^5\,c\,d\,e^3+24\,a^2\,b^4\,c^2\,d^2\,e^2-96\,a^2\,b^3\,c^3\,d^3\,e+48\,a^2\,b^2\,c^4\,d^4-2\,a\,b^7\,d\,e^3-10\,a\,b^6\,c\,d^2\,e^2+24\,a\,b^5\,c^2\,d^3\,e-12\,a\,b^4\,c^3\,d^4+b^8\,d^2\,e^2-2\,b^7\,c\,d^3\,e+b^6\,c^2\,d^4}-\frac{\ln\left(96\,a^4\,c^3\,e^5-2\,b^7\,e^5\,x-2\,a\,b^6\,e^5-2\,b^3\,c^4\,d^5+2\,c^4\,d^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-2\,a\,b^3\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+23\,a^2\,b^4\,c\,e^5-32\,a^2\,c^5\,d^4\,e+3\,b^4\,c^3\,d^4\,e+b^6\,c\,d^2\,e^3-4\,b^2\,c^5\,d^5\,x-2\,b^4\,e^5\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-84\,a^3\,b^2\,c^2\,e^5-192\,a^3\,c^4\,d^2\,e^3+8\,a\,b\,c^5\,d^5+16\,a\,c^6\,d^5\,x+2\,a\,b^5\,c\,d\,e^4+24\,a\,b^5\,c\,e^5\,x+4\,b^6\,c\,d\,e^4\,x+72\,a^2\,b^2\,c^3\,d^2\,e^3+9\,a^2\,b\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-4\,a\,b^2\,c^4\,d^4\,e+72\,a^3\,b\,c^3\,d\,e^4-3\,b\,c^3\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+120\,a^3\,b\,c^3\,e^5\,x-240\,a^3\,c^4\,d\,e^4\,x+10\,b^3\,c^4\,d^4\,e\,x+4\,c^4\,d^4\,e\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a\,b^3\,c^3\,d^3\,e^2-10\,a\,b^4\,c^2\,d^2\,e^3+80\,a^2\,b\,c^4\,d^3\,e^2-26\,a^2\,b^3\,c^2\,d\,e^4+4\,a\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-30\,a^2\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,c\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-94\,a^2\,b^3\,c^2\,e^5\,x-12\,a^2\,c^2\,e^5\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+32\,a^2\,c^5\,d^3\,e^2\,x-8\,b^4\,c^3\,d^3\,e^2\,x+2\,b^5\,c^2\,d^2\,e^3\,x+6\,a\,b\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+24\,a\,b^2\,c^4\,d^3\,e^2\,x+4\,a\,b^3\,c^3\,d^2\,e^3\,x-48\,a^2\,b\,c^4\,d^2\,e^3\,x+204\,a^2\,b^2\,c^3\,d\,e^4\,x+24\,a\,c^3\,d^2\,e^3\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-8\,b\,c^3\,d^3\,e^2\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-40\,a\,b\,c^5\,d^4\,e\,x+6\,a\,b^2\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a\,b^2\,c\,e^5\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-52\,a\,b^4\,c^2\,d\,e^4\,x+4\,b^3\,c\,d\,e^4\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-24\,a\,b\,c^2\,d\,e^4\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}\right)\,\left(c^2\,\left(24\,a^2\,b^2\,e^3+6\,a\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}\right)-c^3\,\left(32\,a^3\,e^3-2\,d^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}\right)-c\,\left(6\,a\,b^4\,e^3+3\,a\,b\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}\right)+\frac{b^6\,e^3}{2}+\frac{b^3\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2}\right)}{-64\,a^5\,c^3\,e^4+48\,a^4\,b^2\,c^2\,e^4+128\,a^4\,b\,c^3\,d\,e^3-128\,a^4\,c^4\,d^2\,e^2-12\,a^3\,b^4\,c\,e^4-96\,a^3\,b^3\,c^2\,d\,e^3+32\,a^3\,b^2\,c^3\,d^2\,e^2+128\,a^3\,b\,c^4\,d^3\,e-64\,a^3\,c^5\,d^4+a^2\,b^6\,e^4+24\,a^2\,b^5\,c\,d\,e^3+24\,a^2\,b^4\,c^2\,d^2\,e^2-96\,a^2\,b^3\,c^3\,d^3\,e+48\,a^2\,b^2\,c^4\,d^4-2\,a\,b^7\,d\,e^3-10\,a\,b^6\,c\,d^2\,e^2+24\,a\,b^5\,c^2\,d^3\,e-12\,a\,b^4\,c^3\,d^4+b^8\,d^2\,e^2-2\,b^7\,c\,d^3\,e+b^6\,c^2\,d^4}","Not used",1,"(e^3*log(d + e*x))/(a^2*e^4 + c^2*d^4 + b^2*d^2*e^2 - 2*a*b*d*e^3 - 2*b*c*d^3*e + 2*a*c*d^2*e^2) - ((2*a*c*e - b^2*e + b*c*d)/(a*b^2*e^2 - 4*a*c^2*d^2 - 4*a^2*c*e^2 + b^2*c*d^2 - b^3*d*e + 4*a*b*c*d*e) + (x*(2*c^2*d - b*c*e))/(a*b^2*e^2 - 4*a*c^2*d^2 - 4*a^2*c*e^2 + b^2*c*d^2 - b^3*d*e + 4*a*b*c*d*e))/(a + b*x + c*x^2) + (log(96*a^4*c^3*e^5 - 2*b^7*e^5*x - 2*a*b^6*e^5 - 2*b^3*c^4*d^5 - 2*c^4*d^5*(-(4*a*c - b^2)^3)^(1/2) + 2*a*b^3*e^5*(-(4*a*c - b^2)^3)^(1/2) + 23*a^2*b^4*c*e^5 - 32*a^2*c^5*d^4*e + 3*b^4*c^3*d^4*e + b^6*c*d^2*e^3 - 4*b^2*c^5*d^5*x + 2*b^4*e^5*x*(-(4*a*c - b^2)^3)^(1/2) - 84*a^3*b^2*c^2*e^5 - 192*a^3*c^4*d^2*e^3 + 8*a*b*c^5*d^5 + 16*a*c^6*d^5*x + 2*a*b^5*c*d*e^4 + 24*a*b^5*c*e^5*x + 4*b^6*c*d*e^4*x + 72*a^2*b^2*c^3*d^2*e^3 - 9*a^2*b*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 4*a*b^2*c^4*d^4*e + 72*a^3*b*c^3*d*e^4 + 3*b*c^3*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 120*a^3*b*c^3*e^5*x - 240*a^3*c^4*d*e^4*x + 10*b^3*c^4*d^4*e*x - 4*c^4*d^4*e*x*(-(4*a*c - b^2)^3)^(1/2) - 20*a*b^3*c^3*d^3*e^2 - 10*a*b^4*c^2*d^2*e^3 + 80*a^2*b*c^4*d^3*e^2 - 26*a^2*b^3*c^2*d*e^4 - 4*a*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 30*a^2*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + b^3*c*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 94*a^2*b^3*c^2*e^5*x + 12*a^2*c^2*e^5*x*(-(4*a*c - b^2)^3)^(1/2) + 32*a^2*c^5*d^3*e^2*x - 8*b^4*c^3*d^3*e^2*x + 2*b^5*c^2*d^2*e^3*x - 6*a*b*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a*b^2*c^4*d^3*e^2*x + 4*a*b^3*c^3*d^2*e^3*x - 48*a^2*b*c^4*d^2*e^3*x + 204*a^2*b^2*c^3*d*e^4*x - 24*a*c^3*d^2*e^3*x*(-(4*a*c - b^2)^3)^(1/2) + 8*b*c^3*d^3*e^2*x*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b*c^5*d^4*e*x - 6*a*b^2*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 12*a*b^2*c*e^5*x*(-(4*a*c - b^2)^3)^(1/2) - 52*a*b^4*c^2*d*e^4*x - 4*b^3*c*d*e^4*x*(-(4*a*c - b^2)^3)^(1/2) + 24*a*b*c^2*d*e^4*x*(-(4*a*c - b^2)^3)^(1/2))*(c*(6*a*b^4*e^3 - 3*a*b*e^3*(-(4*a*c - b^2)^3)^(1/2)) + c^3*(32*a^3*e^3 + 2*d^3*(-(4*a*c - b^2)^3)^(1/2)) - c^2*(24*a^2*b^2*e^3 - 6*a*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 3*b*d^2*e*(-(4*a*c - b^2)^3)^(1/2)) - (b^6*e^3)/2 + (b^3*e^3*(-(4*a*c - b^2)^3)^(1/2))/2))/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) - (log(96*a^4*c^3*e^5 - 2*b^7*e^5*x - 2*a*b^6*e^5 - 2*b^3*c^4*d^5 + 2*c^4*d^5*(-(4*a*c - b^2)^3)^(1/2) - 2*a*b^3*e^5*(-(4*a*c - b^2)^3)^(1/2) + 23*a^2*b^4*c*e^5 - 32*a^2*c^5*d^4*e + 3*b^4*c^3*d^4*e + b^6*c*d^2*e^3 - 4*b^2*c^5*d^5*x - 2*b^4*e^5*x*(-(4*a*c - b^2)^3)^(1/2) - 84*a^3*b^2*c^2*e^5 - 192*a^3*c^4*d^2*e^3 + 8*a*b*c^5*d^5 + 16*a*c^6*d^5*x + 2*a*b^5*c*d*e^4 + 24*a*b^5*c*e^5*x + 4*b^6*c*d*e^4*x + 72*a^2*b^2*c^3*d^2*e^3 + 9*a^2*b*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 4*a*b^2*c^4*d^4*e + 72*a^3*b*c^3*d*e^4 - 3*b*c^3*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 120*a^3*b*c^3*e^5*x - 240*a^3*c^4*d*e^4*x + 10*b^3*c^4*d^4*e*x + 4*c^4*d^4*e*x*(-(4*a*c - b^2)^3)^(1/2) - 20*a*b^3*c^3*d^3*e^2 - 10*a*b^4*c^2*d^2*e^3 + 80*a^2*b*c^4*d^3*e^2 - 26*a^2*b^3*c^2*d*e^4 + 4*a*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) - 30*a^2*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - b^3*c*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 94*a^2*b^3*c^2*e^5*x - 12*a^2*c^2*e^5*x*(-(4*a*c - b^2)^3)^(1/2) + 32*a^2*c^5*d^3*e^2*x - 8*b^4*c^3*d^3*e^2*x + 2*b^5*c^2*d^2*e^3*x + 6*a*b*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 24*a*b^2*c^4*d^3*e^2*x + 4*a*b^3*c^3*d^2*e^3*x - 48*a^2*b*c^4*d^2*e^3*x + 204*a^2*b^2*c^3*d*e^4*x + 24*a*c^3*d^2*e^3*x*(-(4*a*c - b^2)^3)^(1/2) - 8*b*c^3*d^3*e^2*x*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b*c^5*d^4*e*x + 6*a*b^2*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b^2*c*e^5*x*(-(4*a*c - b^2)^3)^(1/2) - 52*a*b^4*c^2*d*e^4*x + 4*b^3*c*d*e^4*x*(-(4*a*c - b^2)^3)^(1/2) - 24*a*b*c^2*d*e^4*x*(-(4*a*c - b^2)^3)^(1/2))*(c^2*(24*a^2*b^2*e^3 + 6*a*d*e^2*(-(4*a*c - b^2)^3)^(1/2) - 3*b*d^2*e*(-(4*a*c - b^2)^3)^(1/2)) - c^3*(32*a^3*e^3 - 2*d^3*(-(4*a*c - b^2)^3)^(1/2)) - c*(6*a*b^4*e^3 + 3*a*b*e^3*(-(4*a*c - b^2)^3)^(1/2)) + (b^6*e^3)/2 + (b^3*e^3*(-(4*a*c - b^2)^3)^(1/2))/2))/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3)","B"
2197,1,2239,344,4.482649,"\text{Not used}","int(1/((d + e*x)^2*(a + b*x + c*x^2)^2),x)","\frac{\frac{-4\,a^2\,c\,e^3+a\,b^2\,e^3-3\,a\,b\,c\,d\,e^2+4\,a\,c^2\,d^2\,e+b^3\,d\,e^2-2\,b^2\,c\,d^2\,e+b\,c^2\,d^3}{4\,a^3\,c\,e^4-a^2\,b^2\,e^4-8\,a^2\,b\,c\,d\,e^3+8\,a^2\,c^2\,d^2\,e^2+2\,a\,b^3\,d\,e^3+2\,a\,b^2\,c\,d^2\,e^2-8\,a\,b\,c^2\,d^3\,e+4\,a\,c^3\,d^4-b^4\,d^2\,e^2+2\,b^3\,c\,d^3\,e-b^2\,c^2\,d^4}-\frac{2\,x^2\,\left(-b^2\,c\,e^3+b\,c^2\,d\,e^2-c^3\,d^2\,e+3\,a\,c^2\,e^3\right)}{4\,a^3\,c\,e^4-a^2\,b^2\,e^4-8\,a^2\,b\,c\,d\,e^3+8\,a^2\,c^2\,d^2\,e^2+2\,a\,b^3\,d\,e^3+2\,a\,b^2\,c\,d^2\,e^2-8\,a\,b\,c^2\,d^3\,e+4\,a\,c^3\,d^4-b^4\,d^2\,e^2+2\,b^3\,c\,d^3\,e-b^2\,c^2\,d^4}+\frac{x\,\left(2\,b^3\,e^3-b^2\,c\,d\,e^2-b\,c^2\,d^2\,e-7\,a\,b\,c\,e^3+2\,c^3\,d^3+2\,a\,c^2\,d\,e^2\right)}{4\,a^3\,c\,e^4-a^2\,b^2\,e^4-8\,a^2\,b\,c\,d\,e^3+8\,a^2\,c^2\,d^2\,e^2+2\,a\,b^3\,d\,e^3+2\,a\,b^2\,c\,d^2\,e^2-8\,a\,b\,c^2\,d^3\,e+4\,a\,c^3\,d^4-b^4\,d^2\,e^2+2\,b^3\,c\,d^3\,e-b^2\,c^2\,d^4}}{c\,e\,x^3+\left(b\,e+c\,d\right)\,x^2+\left(a\,e+b\,d\right)\,x+a\,d}-\frac{\ln\left(b^3+\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-4\,a\,b\,c-8\,a\,c^2\,x+2\,b^2\,c\,x\right)\,\left(b^7\,e^4-b^4\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,c^4\,d^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-64\,a^3\,b\,c^3\,e^4+128\,a^3\,c^4\,d\,e^3+48\,a^2\,b^3\,c^2\,e^4-6\,a^2\,c^2\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-12\,a\,b^5\,c\,e^4-2\,b^6\,c\,d\,e^3+6\,a\,b^2\,c\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+24\,a\,b^4\,c^2\,d\,e^3-4\,b\,c^3\,d^3\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+2\,b^3\,c\,d\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-96\,a^2\,b^2\,c^3\,d\,e^3+12\,a\,c^3\,d^2\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-12\,a\,b\,c^2\,d\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}\right)}{64\,a^6\,c^3\,e^6-48\,a^5\,b^2\,c^2\,e^6-192\,a^5\,b\,c^3\,d\,e^5+192\,a^5\,c^4\,d^2\,e^4+12\,a^4\,b^4\,c\,e^6+144\,a^4\,b^3\,c^2\,d\,e^5+48\,a^4\,b^2\,c^3\,d^2\,e^4-384\,a^4\,b\,c^4\,d^3\,e^3+192\,a^4\,c^5\,d^4\,e^2-a^3\,b^6\,e^6-36\,a^3\,b^5\,c\,d\,e^5-108\,a^3\,b^4\,c^2\,d^2\,e^4+224\,a^3\,b^3\,c^3\,d^3\,e^3+48\,a^3\,b^2\,c^4\,d^4\,e^2-192\,a^3\,b\,c^5\,d^5\,e+64\,a^3\,c^6\,d^6+3\,a^2\,b^7\,d\,e^5+33\,a^2\,b^6\,c\,d^2\,e^4-24\,a^2\,b^5\,c^2\,d^3\,e^3-108\,a^2\,b^4\,c^3\,d^4\,e^2+144\,a^2\,b^3\,c^4\,d^5\,e-48\,a^2\,b^2\,c^5\,d^6-3\,a\,b^8\,d^2\,e^4-6\,a\,b^7\,c\,d^3\,e^3+33\,a\,b^6\,c^2\,d^4\,e^2-36\,a\,b^5\,c^3\,d^5\,e+12\,a\,b^4\,c^4\,d^6+b^9\,d^3\,e^3-3\,b^8\,c\,d^4\,e^2+3\,b^7\,c^2\,d^5\,e-b^6\,c^3\,d^6}-\frac{\ln\left(d+e\,x\right)\,\left(2\,b\,e^4-4\,c\,d\,e^3\right)}{a^3\,e^6-3\,a^2\,b\,d\,e^5+3\,a^2\,c\,d^2\,e^4+3\,a\,b^2\,d^2\,e^4-6\,a\,b\,c\,d^3\,e^3+3\,a\,c^2\,d^4\,e^2-b^3\,d^3\,e^3+3\,b^2\,c\,d^4\,e^2-3\,b\,c^2\,d^5\,e+c^3\,d^6}-\frac{\ln\left(\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3+4\,a\,b\,c+8\,a\,c^2\,x-2\,b^2\,c\,x\right)\,\left(b^7\,e^4+b^4\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-2\,c^4\,d^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-64\,a^3\,b\,c^3\,e^4+128\,a^3\,c^4\,d\,e^3+48\,a^2\,b^3\,c^2\,e^4+6\,a^2\,c^2\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-12\,a\,b^5\,c\,e^4-2\,b^6\,c\,d\,e^3-6\,a\,b^2\,c\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+24\,a\,b^4\,c^2\,d\,e^3+4\,b\,c^3\,d^3\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-2\,b^3\,c\,d\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-96\,a^2\,b^2\,c^3\,d\,e^3-12\,a\,c^3\,d^2\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a\,b\,c^2\,d\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}\right)}{64\,a^6\,c^3\,e^6-48\,a^5\,b^2\,c^2\,e^6-192\,a^5\,b\,c^3\,d\,e^5+192\,a^5\,c^4\,d^2\,e^4+12\,a^4\,b^4\,c\,e^6+144\,a^4\,b^3\,c^2\,d\,e^5+48\,a^4\,b^2\,c^3\,d^2\,e^4-384\,a^4\,b\,c^4\,d^3\,e^3+192\,a^4\,c^5\,d^4\,e^2-a^3\,b^6\,e^6-36\,a^3\,b^5\,c\,d\,e^5-108\,a^3\,b^4\,c^2\,d^2\,e^4+224\,a^3\,b^3\,c^3\,d^3\,e^3+48\,a^3\,b^2\,c^4\,d^4\,e^2-192\,a^3\,b\,c^5\,d^5\,e+64\,a^3\,c^6\,d^6+3\,a^2\,b^7\,d\,e^5+33\,a^2\,b^6\,c\,d^2\,e^4-24\,a^2\,b^5\,c^2\,d^3\,e^3-108\,a^2\,b^4\,c^3\,d^4\,e^2+144\,a^2\,b^3\,c^4\,d^5\,e-48\,a^2\,b^2\,c^5\,d^6-3\,a\,b^8\,d^2\,e^4-6\,a\,b^7\,c\,d^3\,e^3+33\,a\,b^6\,c^2\,d^4\,e^2-36\,a\,b^5\,c^3\,d^5\,e+12\,a\,b^4\,c^4\,d^6+b^9\,d^3\,e^3-3\,b^8\,c\,d^4\,e^2+3\,b^7\,c^2\,d^5\,e-b^6\,c^3\,d^6}","Not used",1,"((a*b^2*e^3 + b*c^2*d^3 - 4*a^2*c*e^3 + b^3*d*e^2 + 4*a*c^2*d^2*e - 2*b^2*c*d^2*e - 3*a*b*c*d*e^2)/(4*a*c^3*d^4 + 4*a^3*c*e^4 - a^2*b^2*e^4 - b^2*c^2*d^4 - b^4*d^2*e^2 + 8*a^2*c^2*d^2*e^2 + 2*a*b^3*d*e^3 + 2*b^3*c*d^3*e - 8*a*b*c^2*d^3*e - 8*a^2*b*c*d*e^3 + 2*a*b^2*c*d^2*e^2) - (2*x^2*(3*a*c^2*e^3 - b^2*c*e^3 - c^3*d^2*e + b*c^2*d*e^2))/(4*a*c^3*d^4 + 4*a^3*c*e^4 - a^2*b^2*e^4 - b^2*c^2*d^4 - b^4*d^2*e^2 + 8*a^2*c^2*d^2*e^2 + 2*a*b^3*d*e^3 + 2*b^3*c*d^3*e - 8*a*b*c^2*d^3*e - 8*a^2*b*c*d*e^3 + 2*a*b^2*c*d^2*e^2) + (x*(2*b^3*e^3 + 2*c^3*d^3 - 7*a*b*c*e^3 + 2*a*c^2*d*e^2 - b*c^2*d^2*e - b^2*c*d*e^2))/(4*a*c^3*d^4 + 4*a^3*c*e^4 - a^2*b^2*e^4 - b^2*c^2*d^4 - b^4*d^2*e^2 + 8*a^2*c^2*d^2*e^2 + 2*a*b^3*d*e^3 + 2*b^3*c*d^3*e - 8*a*b*c^2*d^3*e - 8*a^2*b*c*d*e^3 + 2*a*b^2*c*d^2*e^2))/(a*d + x*(a*e + b*d) + x^2*(b*e + c*d) + c*e*x^3) - (log(b^3 + (-(4*a*c - b^2)^3)^(1/2) - 4*a*b*c - 8*a*c^2*x + 2*b^2*c*x)*(b^7*e^4 - b^4*e^4*(-(4*a*c - b^2)^3)^(1/2) + 2*c^4*d^4*(-(4*a*c - b^2)^3)^(1/2) - 64*a^3*b*c^3*e^4 + 128*a^3*c^4*d*e^3 + 48*a^2*b^3*c^2*e^4 - 6*a^2*c^2*e^4*(-(4*a*c - b^2)^3)^(1/2) - 12*a*b^5*c*e^4 - 2*b^6*c*d*e^3 + 6*a*b^2*c*e^4*(-(4*a*c - b^2)^3)^(1/2) + 24*a*b^4*c^2*d*e^3 - 4*b*c^3*d^3*e*(-(4*a*c - b^2)^3)^(1/2) + 2*b^3*c*d*e^3*(-(4*a*c - b^2)^3)^(1/2) - 96*a^2*b^2*c^3*d*e^3 + 12*a*c^3*d^2*e^2*(-(4*a*c - b^2)^3)^(1/2) - 12*a*b*c^2*d*e^3*(-(4*a*c - b^2)^3)^(1/2)))/(64*a^3*c^6*d^6 - a^3*b^6*e^6 + 64*a^6*c^3*e^6 - b^6*c^3*d^6 + b^9*d^3*e^3 + 12*a*b^4*c^4*d^6 + 12*a^4*b^4*c*e^6 - 3*a*b^8*d^2*e^4 + 3*a^2*b^7*d*e^5 + 3*b^7*c^2*d^5*e - 3*b^8*c*d^4*e^2 - 48*a^2*b^2*c^5*d^6 - 48*a^5*b^2*c^2*e^6 + 192*a^4*c^5*d^4*e^2 + 192*a^5*c^4*d^2*e^4 - 108*a^2*b^4*c^3*d^4*e^2 - 24*a^2*b^5*c^2*d^3*e^3 + 48*a^3*b^2*c^4*d^4*e^2 + 224*a^3*b^3*c^3*d^3*e^3 - 108*a^3*b^4*c^2*d^2*e^4 + 48*a^4*b^2*c^3*d^2*e^4 - 36*a*b^5*c^3*d^5*e - 6*a*b^7*c*d^3*e^3 - 192*a^3*b*c^5*d^5*e - 36*a^3*b^5*c*d*e^5 - 192*a^5*b*c^3*d*e^5 + 33*a*b^6*c^2*d^4*e^2 + 144*a^2*b^3*c^4*d^5*e + 33*a^2*b^6*c*d^2*e^4 - 384*a^4*b*c^4*d^3*e^3 + 144*a^4*b^3*c^2*d*e^5) - (log(d + e*x)*(2*b*e^4 - 4*c*d*e^3))/(a^3*e^6 + c^3*d^6 - b^3*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + 3*b^2*c*d^4*e^2 - 3*a^2*b*d*e^5 - 3*b*c^2*d^5*e - 6*a*b*c*d^3*e^3) - (log((-(4*a*c - b^2)^3)^(1/2) - b^3 + 4*a*b*c + 8*a*c^2*x - 2*b^2*c*x)*(b^7*e^4 + b^4*e^4*(-(4*a*c - b^2)^3)^(1/2) - 2*c^4*d^4*(-(4*a*c - b^2)^3)^(1/2) - 64*a^3*b*c^3*e^4 + 128*a^3*c^4*d*e^3 + 48*a^2*b^3*c^2*e^4 + 6*a^2*c^2*e^4*(-(4*a*c - b^2)^3)^(1/2) - 12*a*b^5*c*e^4 - 2*b^6*c*d*e^3 - 6*a*b^2*c*e^4*(-(4*a*c - b^2)^3)^(1/2) + 24*a*b^4*c^2*d*e^3 + 4*b*c^3*d^3*e*(-(4*a*c - b^2)^3)^(1/2) - 2*b^3*c*d*e^3*(-(4*a*c - b^2)^3)^(1/2) - 96*a^2*b^2*c^3*d*e^3 - 12*a*c^3*d^2*e^2*(-(4*a*c - b^2)^3)^(1/2) + 12*a*b*c^2*d*e^3*(-(4*a*c - b^2)^3)^(1/2)))/(64*a^3*c^6*d^6 - a^3*b^6*e^6 + 64*a^6*c^3*e^6 - b^6*c^3*d^6 + b^9*d^3*e^3 + 12*a*b^4*c^4*d^6 + 12*a^4*b^4*c*e^6 - 3*a*b^8*d^2*e^4 + 3*a^2*b^7*d*e^5 + 3*b^7*c^2*d^5*e - 3*b^8*c*d^4*e^2 - 48*a^2*b^2*c^5*d^6 - 48*a^5*b^2*c^2*e^6 + 192*a^4*c^5*d^4*e^2 + 192*a^5*c^4*d^2*e^4 - 108*a^2*b^4*c^3*d^4*e^2 - 24*a^2*b^5*c^2*d^3*e^3 + 48*a^3*b^2*c^4*d^4*e^2 + 224*a^3*b^3*c^3*d^3*e^3 - 108*a^3*b^4*c^2*d^2*e^4 + 48*a^4*b^2*c^3*d^2*e^4 - 36*a*b^5*c^3*d^5*e - 6*a*b^7*c*d^3*e^3 - 192*a^3*b*c^5*d^5*e - 36*a^3*b^5*c*d*e^5 - 192*a^5*b*c^3*d*e^5 + 33*a*b^6*c^2*d^4*e^2 + 144*a^2*b^3*c^4*d^5*e + 33*a^2*b^6*c*d^2*e^4 - 384*a^4*b*c^4*d^3*e^3 + 144*a^4*b^3*c^2*d*e^5)","B"
2198,1,3748,485,7.475638,"\text{Not used}","int(1/((d + e*x)^3*(a + b*x + c*x^2)^2),x)","\frac{\ln\left(b^3+\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-4\,a\,b\,c-8\,a\,c^2\,x+2\,b^2\,c\,x\right)\,\left(\frac{3\,b^8\,e^5}{2}+64\,a^4\,c^4\,e^5-\frac{3\,b^5\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2}-2\,c^5\,d^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+84\,a^2\,b^4\,c^2\,e^5-144\,a^3\,b^2\,c^3\,e^5-320\,a^3\,c^5\,d^2\,e^3+5\,b^6\,c^2\,d^2\,e^3-19\,a\,b^6\,c\,e^5-5\,b^7\,c\,d\,e^4+240\,a^2\,b^2\,c^4\,d^2\,e^3-5\,b^3\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b^3\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^5\,c^2\,d\,e^4+320\,a^3\,b\,c^4\,d\,e^4+5\,b\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+5\,b^4\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-15\,a^2\,b\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-60\,a\,b^4\,c^3\,d^2\,e^3-240\,a^2\,b^3\,c^3\,d\,e^4-20\,a\,c^4\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+30\,a^2\,c^3\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+30\,a\,b\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-30\,a\,b^2\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}\right)}{64\,a^7\,c^3\,e^8-48\,a^6\,b^2\,c^2\,e^8-256\,a^6\,b\,c^3\,d\,e^7+256\,a^6\,c^4\,d^2\,e^6+12\,a^5\,b^4\,c\,e^8+192\,a^5\,b^3\,c^2\,d\,e^7+192\,a^5\,b^2\,c^3\,d^2\,e^6-768\,a^5\,b\,c^4\,d^3\,e^5+384\,a^5\,c^5\,d^4\,e^4-a^4\,b^6\,e^8-48\,a^4\,b^5\,c\,d\,e^7-240\,a^4\,b^4\,c^2\,d^2\,e^6+320\,a^4\,b^3\,c^3\,d^3\,e^5+480\,a^4\,b^2\,c^4\,d^4\,e^4-768\,a^4\,b\,c^5\,d^5\,e^3+256\,a^4\,c^6\,d^6\,e^2+4\,a^3\,b^7\,d\,e^7+68\,a^3\,b^6\,c\,d^2\,e^6+48\,a^3\,b^5\,c^2\,d^3\,e^5-440\,a^3\,b^4\,c^3\,d^4\,e^4+320\,a^3\,b^3\,c^4\,d^5\,e^3+192\,a^3\,b^2\,c^5\,d^6\,e^2-256\,a^3\,b\,c^6\,d^7\,e+64\,a^3\,c^7\,d^8-6\,a^2\,b^8\,d^2\,e^6-36\,a^2\,b^7\,c\,d^3\,e^5+90\,a^2\,b^6\,c^2\,d^4\,e^4+48\,a^2\,b^5\,c^3\,d^5\,e^3-240\,a^2\,b^4\,c^4\,d^6\,e^2+192\,a^2\,b^3\,c^5\,d^7\,e-48\,a^2\,b^2\,c^6\,d^8+4\,a\,b^9\,d^3\,e^5-36\,a\,b^7\,c^2\,d^5\,e^3+68\,a\,b^6\,c^3\,d^6\,e^2-48\,a\,b^5\,c^4\,d^7\,e+12\,a\,b^4\,c^5\,d^8-b^{10}\,d^4\,e^4+4\,b^9\,c\,d^5\,e^3-6\,b^8\,c^2\,d^6\,e^2+4\,b^7\,c^3\,d^7\,e-b^6\,c^4\,d^8}-\frac{\ln\left(d+e\,x\right)\,\left(e^5\,\left(2\,a\,c-3\,b^2\right)-10\,c^2\,d^2\,e^3+10\,b\,c\,d\,e^4\right)}{a^4\,e^8-4\,a^3\,b\,d\,e^7+4\,a^3\,c\,d^2\,e^6+6\,a^2\,b^2\,d^2\,e^6-12\,a^2\,b\,c\,d^3\,e^5+6\,a^2\,c^2\,d^4\,e^4-4\,a\,b^3\,d^3\,e^5+12\,a\,b^2\,c\,d^4\,e^4-12\,a\,b\,c^2\,d^5\,e^3+4\,a\,c^3\,d^6\,e^2+b^4\,d^4\,e^4-4\,b^3\,c\,d^5\,e^3+6\,b^2\,c^2\,d^6\,e^2-4\,b\,c^3\,d^7\,e+c^4\,d^8}-\frac{\frac{x^3\,\left(3\,b^3\,c\,e^5-7\,b^2\,c^2\,d\,e^4+3\,b\,c^3\,d^2\,e^3-11\,a\,b\,c^2\,e^5-2\,c^4\,d^3\,e^2+22\,a\,c^3\,d\,e^4\right)}{4\,a^4\,c\,e^6-a^3\,b^2\,e^6-12\,a^3\,b\,c\,d\,e^5+12\,a^3\,c^2\,d^2\,e^4+3\,a^2\,b^3\,d\,e^5+9\,a^2\,b^2\,c\,d^2\,e^4-24\,a^2\,b\,c^2\,d^3\,e^3+12\,a^2\,c^3\,d^4\,e^2-3\,a\,b^4\,d^2\,e^4+2\,a\,b^3\,c\,d^3\,e^3+9\,a\,b^2\,c^2\,d^4\,e^2-12\,a\,b\,c^3\,d^5\,e+4\,a\,c^4\,d^6+b^5\,d^3\,e^3-3\,b^4\,c\,d^4\,e^2+3\,b^3\,c^2\,d^5\,e-b^2\,c^3\,d^6}-\frac{-4\,a^3\,c\,e^5+a^2\,b^2\,e^5+20\,a^2\,b\,c\,d\,e^4-40\,a^2\,c^2\,d^2\,e^3-5\,a\,b^3\,d\,e^4+17\,a\,b^2\,c\,d^2\,e^3-18\,a\,b\,c^2\,d^3\,e^2+12\,a\,c^3\,d^4\,e-2\,b^4\,d^2\,e^3+6\,b^3\,c\,d^3\,e^2-6\,b^2\,c^2\,d^4\,e+2\,b\,c^3\,d^5}{2\,\left(4\,a^4\,c\,e^6-a^3\,b^2\,e^6-12\,a^3\,b\,c\,d\,e^5+12\,a^3\,c^2\,d^2\,e^4+3\,a^2\,b^3\,d\,e^5+9\,a^2\,b^2\,c\,d^2\,e^4-24\,a^2\,b\,c^2\,d^3\,e^3+12\,a^2\,c^3\,d^4\,e^2-3\,a\,b^4\,d^2\,e^4+2\,a\,b^3\,c\,d^3\,e^3+9\,a\,b^2\,c^2\,d^4\,e^2-12\,a\,b\,c^3\,d^5\,e+4\,a\,c^4\,d^6+b^5\,d^3\,e^3-3\,b^4\,c\,d^4\,e^2+3\,b^3\,c^2\,d^5\,e-b^2\,c^3\,d^6\right)}+\frac{x\,\left(-12\,a^2\,b\,c\,e^5+40\,a^2\,c^2\,d\,e^4+3\,a\,b^3\,e^5-44\,a\,b^2\,c\,d\,e^4+66\,a\,b\,c^2\,d^2\,e^3-12\,a\,c^3\,d^3\,e^2+9\,b^4\,d\,e^4-19\,b^3\,c\,d^2\,e^3+6\,b^2\,c^2\,d^3\,e^2+2\,b\,c^3\,d^4\,e-4\,c^4\,d^5\right)}{2\,\left(4\,a^4\,c\,e^6-a^3\,b^2\,e^6-12\,a^3\,b\,c\,d\,e^5+12\,a^3\,c^2\,d^2\,e^4+3\,a^2\,b^3\,d\,e^5+9\,a^2\,b^2\,c\,d^2\,e^4-24\,a^2\,b\,c^2\,d^3\,e^3+12\,a^2\,c^3\,d^4\,e^2-3\,a\,b^4\,d^2\,e^4+2\,a\,b^3\,c\,d^3\,e^3+9\,a\,b^2\,c^2\,d^4\,e^2-12\,a\,b\,c^3\,d^5\,e+4\,a\,c^4\,d^6+b^5\,d^3\,e^3-3\,b^4\,c\,d^4\,e^2+3\,b^3\,c^2\,d^5\,e-b^2\,c^3\,d^6\right)}+\frac{x^2\,\left(8\,a^2\,c^2\,e^5-25\,a\,b^2\,c\,e^5+18\,a\,b\,c^2\,d\,e^4+48\,a\,c^3\,d^2\,e^3+6\,b^4\,e^5-5\,b^3\,c\,d\,e^4-15\,b^2\,c^2\,d^2\,e^3+10\,b\,c^3\,d^3\,e^2-8\,c^4\,d^4\,e\right)}{2\,\left(4\,a^4\,c\,e^6-a^3\,b^2\,e^6-12\,a^3\,b\,c\,d\,e^5+12\,a^3\,c^2\,d^2\,e^4+3\,a^2\,b^3\,d\,e^5+9\,a^2\,b^2\,c\,d^2\,e^4-24\,a^2\,b\,c^2\,d^3\,e^3+12\,a^2\,c^3\,d^4\,e^2-3\,a\,b^4\,d^2\,e^4+2\,a\,b^3\,c\,d^3\,e^3+9\,a\,b^2\,c^2\,d^4\,e^2-12\,a\,b\,c^3\,d^5\,e+4\,a\,c^4\,d^6+b^5\,d^3\,e^3-3\,b^4\,c\,d^4\,e^2+3\,b^3\,c^2\,d^5\,e-b^2\,c^3\,d^6\right)}}{x^2\,\left(c\,d^2+2\,b\,d\,e+a\,e^2\right)+x\,\left(b\,d^2+2\,a\,e\,d\right)+a\,d^2+x^3\,\left(b\,e^2+2\,c\,d\,e\right)+c\,e^2\,x^4}+\frac{\ln\left(\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3+4\,a\,b\,c+8\,a\,c^2\,x-2\,b^2\,c\,x\right)\,\left(\frac{3\,b^8\,e^5}{2}+64\,a^4\,c^4\,e^5+\frac{3\,b^5\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2}+2\,c^5\,d^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+84\,a^2\,b^4\,c^2\,e^5-144\,a^3\,b^2\,c^3\,e^5-320\,a^3\,c^5\,d^2\,e^3+5\,b^6\,c^2\,d^2\,e^3-19\,a\,b^6\,c\,e^5-5\,b^7\,c\,d\,e^4+240\,a^2\,b^2\,c^4\,d^2\,e^3+5\,b^3\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,a\,b^3\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^5\,c^2\,d\,e^4+320\,a^3\,b\,c^4\,d\,e^4-5\,b\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-5\,b^4\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+15\,a^2\,b\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-60\,a\,b^4\,c^3\,d^2\,e^3-240\,a^2\,b^3\,c^3\,d\,e^4+20\,a\,c^4\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-30\,a^2\,c^3\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-30\,a\,b\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+30\,a\,b^2\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}\right)}{64\,a^7\,c^3\,e^8-48\,a^6\,b^2\,c^2\,e^8-256\,a^6\,b\,c^3\,d\,e^7+256\,a^6\,c^4\,d^2\,e^6+12\,a^5\,b^4\,c\,e^8+192\,a^5\,b^3\,c^2\,d\,e^7+192\,a^5\,b^2\,c^3\,d^2\,e^6-768\,a^5\,b\,c^4\,d^3\,e^5+384\,a^5\,c^5\,d^4\,e^4-a^4\,b^6\,e^8-48\,a^4\,b^5\,c\,d\,e^7-240\,a^4\,b^4\,c^2\,d^2\,e^6+320\,a^4\,b^3\,c^3\,d^3\,e^5+480\,a^4\,b^2\,c^4\,d^4\,e^4-768\,a^4\,b\,c^5\,d^5\,e^3+256\,a^4\,c^6\,d^6\,e^2+4\,a^3\,b^7\,d\,e^7+68\,a^3\,b^6\,c\,d^2\,e^6+48\,a^3\,b^5\,c^2\,d^3\,e^5-440\,a^3\,b^4\,c^3\,d^4\,e^4+320\,a^3\,b^3\,c^4\,d^5\,e^3+192\,a^3\,b^2\,c^5\,d^6\,e^2-256\,a^3\,b\,c^6\,d^7\,e+64\,a^3\,c^7\,d^8-6\,a^2\,b^8\,d^2\,e^6-36\,a^2\,b^7\,c\,d^3\,e^5+90\,a^2\,b^6\,c^2\,d^4\,e^4+48\,a^2\,b^5\,c^3\,d^5\,e^3-240\,a^2\,b^4\,c^4\,d^6\,e^2+192\,a^2\,b^3\,c^5\,d^7\,e-48\,a^2\,b^2\,c^6\,d^8+4\,a\,b^9\,d^3\,e^5-36\,a\,b^7\,c^2\,d^5\,e^3+68\,a\,b^6\,c^3\,d^6\,e^2-48\,a\,b^5\,c^4\,d^7\,e+12\,a\,b^4\,c^5\,d^8-b^{10}\,d^4\,e^4+4\,b^9\,c\,d^5\,e^3-6\,b^8\,c^2\,d^6\,e^2+4\,b^7\,c^3\,d^7\,e-b^6\,c^4\,d^8}","Not used",1,"(log(b^3 + (-(4*a*c - b^2)^3)^(1/2) - 4*a*b*c - 8*a*c^2*x + 2*b^2*c*x)*((3*b^8*e^5)/2 + 64*a^4*c^4*e^5 - (3*b^5*e^5*(-(4*a*c - b^2)^3)^(1/2))/2 - 2*c^5*d^5*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^4*c^2*e^5 - 144*a^3*b^2*c^3*e^5 - 320*a^3*c^5*d^2*e^3 + 5*b^6*c^2*d^2*e^3 - 19*a*b^6*c*e^5 - 5*b^7*c*d*e^4 + 240*a^2*b^2*c^4*d^2*e^3 - 5*b^3*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b^3*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^5*c^2*d*e^4 + 320*a^3*b*c^4*d*e^4 + 5*b*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 5*b^4*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 15*a^2*b*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^4*c^3*d^2*e^3 - 240*a^2*b^3*c^3*d*e^4 - 20*a*c^4*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 30*a^2*c^3*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 30*a*b*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 30*a*b^2*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2)))/(64*a^3*c^7*d^8 - a^4*b^6*e^8 + 64*a^7*c^3*e^8 - b^6*c^4*d^8 - b^10*d^4*e^4 + 12*a*b^4*c^5*d^8 + 12*a^5*b^4*c*e^8 + 4*a*b^9*d^3*e^5 + 4*a^3*b^7*d*e^7 + 4*b^7*c^3*d^7*e + 4*b^9*c*d^5*e^3 - 48*a^2*b^2*c^6*d^8 - 48*a^6*b^2*c^2*e^8 - 6*a^2*b^8*d^2*e^6 + 256*a^4*c^6*d^6*e^2 + 384*a^5*c^5*d^4*e^4 + 256*a^6*c^4*d^2*e^6 - 6*b^8*c^2*d^6*e^2 - 240*a^2*b^4*c^4*d^6*e^2 + 48*a^2*b^5*c^3*d^5*e^3 + 90*a^2*b^6*c^2*d^4*e^4 + 192*a^3*b^2*c^5*d^6*e^2 + 320*a^3*b^3*c^4*d^5*e^3 - 440*a^3*b^4*c^3*d^4*e^4 + 48*a^3*b^5*c^2*d^3*e^5 + 480*a^4*b^2*c^4*d^4*e^4 + 320*a^4*b^3*c^3*d^3*e^5 - 240*a^4*b^4*c^2*d^2*e^6 + 192*a^5*b^2*c^3*d^2*e^6 - 48*a*b^5*c^4*d^7*e - 256*a^3*b*c^6*d^7*e - 48*a^4*b^5*c*d*e^7 - 256*a^6*b*c^3*d*e^7 + 68*a*b^6*c^3*d^6*e^2 - 36*a*b^7*c^2*d^5*e^3 + 192*a^2*b^3*c^5*d^7*e - 36*a^2*b^7*c*d^3*e^5 + 68*a^3*b^6*c*d^2*e^6 - 768*a^4*b*c^5*d^5*e^3 - 768*a^5*b*c^4*d^3*e^5 + 192*a^5*b^3*c^2*d*e^7) - (log(d + e*x)*(e^5*(2*a*c - 3*b^2) - 10*c^2*d^2*e^3 + 10*b*c*d*e^4))/(a^4*e^8 + c^4*d^8 + b^4*d^4*e^4 - 4*a*b^3*d^3*e^5 + 4*a*c^3*d^6*e^2 + 4*a^3*c*d^2*e^6 - 4*b^3*c*d^5*e^3 + 6*a^2*b^2*d^2*e^6 + 6*a^2*c^2*d^4*e^4 + 6*b^2*c^2*d^6*e^2 - 4*a^3*b*d*e^7 - 4*b*c^3*d^7*e - 12*a*b*c^2*d^5*e^3 + 12*a*b^2*c*d^4*e^4 - 12*a^2*b*c*d^3*e^5) - ((x^3*(3*b^3*c*e^5 - 2*c^4*d^3*e^2 + 3*b*c^3*d^2*e^3 - 7*b^2*c^2*d*e^4 - 11*a*b*c^2*e^5 + 22*a*c^3*d*e^4))/(4*a*c^4*d^6 + 4*a^4*c*e^6 - a^3*b^2*e^6 - b^2*c^3*d^6 + b^5*d^3*e^3 - 3*a*b^4*d^2*e^4 + 3*a^2*b^3*d*e^5 + 3*b^3*c^2*d^5*e - 3*b^4*c*d^4*e^2 + 12*a^2*c^3*d^4*e^2 + 12*a^3*c^2*d^2*e^4 - 12*a*b*c^3*d^5*e - 12*a^3*b*c*d*e^5 + 2*a*b^3*c*d^3*e^3 + 9*a*b^2*c^2*d^4*e^2 - 24*a^2*b*c^2*d^3*e^3 + 9*a^2*b^2*c*d^2*e^4) - (2*b*c^3*d^5 - 4*a^3*c*e^5 + a^2*b^2*e^5 - 2*b^4*d^2*e^3 - 6*b^2*c^2*d^4*e + 6*b^3*c*d^3*e^2 - 40*a^2*c^2*d^2*e^3 - 5*a*b^3*d*e^4 + 12*a*c^3*d^4*e + 20*a^2*b*c*d*e^4 - 18*a*b*c^2*d^3*e^2 + 17*a*b^2*c*d^2*e^3)/(2*(4*a*c^4*d^6 + 4*a^4*c*e^6 - a^3*b^2*e^6 - b^2*c^3*d^6 + b^5*d^3*e^3 - 3*a*b^4*d^2*e^4 + 3*a^2*b^3*d*e^5 + 3*b^3*c^2*d^5*e - 3*b^4*c*d^4*e^2 + 12*a^2*c^3*d^4*e^2 + 12*a^3*c^2*d^2*e^4 - 12*a*b*c^3*d^5*e - 12*a^3*b*c*d*e^5 + 2*a*b^3*c*d^3*e^3 + 9*a*b^2*c^2*d^4*e^2 - 24*a^2*b*c^2*d^3*e^3 + 9*a^2*b^2*c*d^2*e^4)) + (x*(3*a*b^3*e^5 - 4*c^4*d^5 + 9*b^4*d*e^4 - 12*a*c^3*d^3*e^2 + 40*a^2*c^2*d*e^4 - 19*b^3*c*d^2*e^3 + 6*b^2*c^2*d^3*e^2 - 12*a^2*b*c*e^5 + 2*b*c^3*d^4*e - 44*a*b^2*c*d*e^4 + 66*a*b*c^2*d^2*e^3))/(2*(4*a*c^4*d^6 + 4*a^4*c*e^6 - a^3*b^2*e^6 - b^2*c^3*d^6 + b^5*d^3*e^3 - 3*a*b^4*d^2*e^4 + 3*a^2*b^3*d*e^5 + 3*b^3*c^2*d^5*e - 3*b^4*c*d^4*e^2 + 12*a^2*c^3*d^4*e^2 + 12*a^3*c^2*d^2*e^4 - 12*a*b*c^3*d^5*e - 12*a^3*b*c*d*e^5 + 2*a*b^3*c*d^3*e^3 + 9*a*b^2*c^2*d^4*e^2 - 24*a^2*b*c^2*d^3*e^3 + 9*a^2*b^2*c*d^2*e^4)) + (x^2*(6*b^4*e^5 - 8*c^4*d^4*e + 8*a^2*c^2*e^5 + 48*a*c^3*d^2*e^3 + 10*b*c^3*d^3*e^2 - 15*b^2*c^2*d^2*e^3 - 25*a*b^2*c*e^5 - 5*b^3*c*d*e^4 + 18*a*b*c^2*d*e^4))/(2*(4*a*c^4*d^6 + 4*a^4*c*e^6 - a^3*b^2*e^6 - b^2*c^3*d^6 + b^5*d^3*e^3 - 3*a*b^4*d^2*e^4 + 3*a^2*b^3*d*e^5 + 3*b^3*c^2*d^5*e - 3*b^4*c*d^4*e^2 + 12*a^2*c^3*d^4*e^2 + 12*a^3*c^2*d^2*e^4 - 12*a*b*c^3*d^5*e - 12*a^3*b*c*d*e^5 + 2*a*b^3*c*d^3*e^3 + 9*a*b^2*c^2*d^4*e^2 - 24*a^2*b*c^2*d^3*e^3 + 9*a^2*b^2*c*d^2*e^4)))/(x^2*(a*e^2 + c*d^2 + 2*b*d*e) + x*(b*d^2 + 2*a*d*e) + a*d^2 + x^3*(b*e^2 + 2*c*d*e) + c*e^2*x^4) + (log((-(4*a*c - b^2)^3)^(1/2) - b^3 + 4*a*b*c + 8*a*c^2*x - 2*b^2*c*x)*((3*b^8*e^5)/2 + 64*a^4*c^4*e^5 + (3*b^5*e^5*(-(4*a*c - b^2)^3)^(1/2))/2 + 2*c^5*d^5*(-(4*a*c - b^2)^3)^(1/2) + 84*a^2*b^4*c^2*e^5 - 144*a^3*b^2*c^3*e^5 - 320*a^3*c^5*d^2*e^3 + 5*b^6*c^2*d^2*e^3 - 19*a*b^6*c*e^5 - 5*b^7*c*d*e^4 + 240*a^2*b^2*c^4*d^2*e^3 + 5*b^3*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*a*b^3*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^5*c^2*d*e^4 + 320*a^3*b*c^4*d*e^4 - 5*b*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 5*b^4*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 15*a^2*b*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^4*c^3*d^2*e^3 - 240*a^2*b^3*c^3*d*e^4 + 20*a*c^4*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) - 30*a^2*c^3*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 30*a*b*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 30*a*b^2*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2)))/(64*a^3*c^7*d^8 - a^4*b^6*e^8 + 64*a^7*c^3*e^8 - b^6*c^4*d^8 - b^10*d^4*e^4 + 12*a*b^4*c^5*d^8 + 12*a^5*b^4*c*e^8 + 4*a*b^9*d^3*e^5 + 4*a^3*b^7*d*e^7 + 4*b^7*c^3*d^7*e + 4*b^9*c*d^5*e^3 - 48*a^2*b^2*c^6*d^8 - 48*a^6*b^2*c^2*e^8 - 6*a^2*b^8*d^2*e^6 + 256*a^4*c^6*d^6*e^2 + 384*a^5*c^5*d^4*e^4 + 256*a^6*c^4*d^2*e^6 - 6*b^8*c^2*d^6*e^2 - 240*a^2*b^4*c^4*d^6*e^2 + 48*a^2*b^5*c^3*d^5*e^3 + 90*a^2*b^6*c^2*d^4*e^4 + 192*a^3*b^2*c^5*d^6*e^2 + 320*a^3*b^3*c^4*d^5*e^3 - 440*a^3*b^4*c^3*d^4*e^4 + 48*a^3*b^5*c^2*d^3*e^5 + 480*a^4*b^2*c^4*d^4*e^4 + 320*a^4*b^3*c^3*d^3*e^5 - 240*a^4*b^4*c^2*d^2*e^6 + 192*a^5*b^2*c^3*d^2*e^6 - 48*a*b^5*c^4*d^7*e - 256*a^3*b*c^6*d^7*e - 48*a^4*b^5*c*d*e^7 - 256*a^6*b*c^3*d*e^7 + 68*a*b^6*c^3*d^6*e^2 - 36*a*b^7*c^2*d^5*e^3 + 192*a^2*b^3*c^5*d^7*e - 36*a^2*b^7*c*d^3*e^5 + 68*a^3*b^6*c*d^2*e^6 - 768*a^4*b*c^5*d^5*e^3 - 768*a^5*b*c^4*d^3*e^5 + 192*a^5*b^3*c^2*d*e^7)","B"
2199,1,762,294,1.472680,"\text{Not used}","int(x^7/(a + b*x + c*x^2)^3,x)","\frac{\frac{a\,\left(-40\,a^4\,c^3+115\,a^3\,b^2\,c^2-55\,a^2\,b^4\,c+7\,a\,b^6\right)}{2\,c\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{b\,x^3\,\left(-63\,a^3\,c^3+91\,a^2\,b^2\,c^2-35\,a\,b^4\,c+4\,b^6\right)}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}+\frac{x^2\,\left(-48\,a^4\,c^4+27\,a^3\,b^2\,c^3+94\,a^2\,b^4\,c^2-53\,a\,b^6\,c+7\,b^8\right)}{2\,c\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{b\,x\,\left(-73\,a^4\,c^3+136\,a^3\,b^2\,c^2-58\,a^2\,b^4\,c+7\,a\,b^6\right)}{c\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}}{a^2\,c^4+c^6\,x^4+x^2\,\left(b^2\,c^4+2\,a\,c^5\right)+2\,b\,c^5\,x^3+2\,a\,b\,c^4\,x}+\frac{x^2}{2\,c^3}-\frac{\ln\left(c\,x^2+b\,x+a\right)\,\left(3072\,a^6\,c^6-9984\,a^5\,b^2\,c^5+9600\,a^4\,b^4\,c^4-4320\,a^3\,b^6\,c^3+1020\,a^2\,b^8\,c^2-123\,a\,b^{10}\,c+6\,b^{12}\right)}{2\,\left(1024\,a^5\,c^{10}-1280\,a^4\,b^2\,c^9+640\,a^3\,b^4\,c^8-160\,a^2\,b^6\,c^7+20\,a\,b^8\,c^6-b^{10}\,c^5\right)}-\frac{3\,b\,x}{c^4}-\frac{3\,b\,\mathrm{atan}\left(\frac{\left(\frac{3\,b\,x\,\left(-70\,a^3\,c^3+70\,a^2\,b^2\,c^2-21\,a\,b^4\,c+2\,b^6\right)}{c^4\,{\left(4\,a\,c-b^2\right)}^5}+\frac{3\,b^2\,\left(16\,a^2\,c^6-8\,a\,b^2\,c^5+b^4\,c^4\right)\,\left(-70\,a^3\,c^3+70\,a^2\,b^2\,c^2-21\,a\,b^4\,c+2\,b^6\right)}{2\,c^9\,{\left(4\,a\,c-b^2\right)}^5\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}\right)\,\left(32\,a^2\,c^7\,{\left(4\,a\,c-b^2\right)}^{5/2}+2\,b^4\,c^5\,{\left(4\,a\,c-b^2\right)}^{5/2}-16\,a\,b^2\,c^6\,{\left(4\,a\,c-b^2\right)}^{5/2}\right)}{-210\,a^3\,b\,c^3+210\,a^2\,b^3\,c^2-63\,a\,b^5\,c+6\,b^7}\right)\,\left(-70\,a^3\,c^3+70\,a^2\,b^2\,c^2-21\,a\,b^4\,c+2\,b^6\right)}{c^5\,{\left(4\,a\,c-b^2\right)}^{5/2}}","Not used",1,"((a*(7*a*b^6 - 40*a^4*c^3 - 55*a^2*b^4*c + 115*a^3*b^2*c^2))/(2*c*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (b*x^3*(4*b^6 - 63*a^3*c^3 + 91*a^2*b^2*c^2 - 35*a*b^4*c))/(b^4 + 16*a^2*c^2 - 8*a*b^2*c) + (x^2*(7*b^8 - 48*a^4*c^4 + 94*a^2*b^4*c^2 + 27*a^3*b^2*c^3 - 53*a*b^6*c))/(2*c*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (b*x*(7*a*b^6 - 73*a^4*c^3 - 58*a^2*b^4*c + 136*a^3*b^2*c^2))/(c*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))/(a^2*c^4 + c^6*x^4 + x^2*(2*a*c^5 + b^2*c^4) + 2*b*c^5*x^3 + 2*a*b*c^4*x) + x^2/(2*c^3) - (log(a + b*x + c*x^2)*(6*b^12 + 3072*a^6*c^6 + 1020*a^2*b^8*c^2 - 4320*a^3*b^6*c^3 + 9600*a^4*b^4*c^4 - 9984*a^5*b^2*c^5 - 123*a*b^10*c))/(2*(1024*a^5*c^10 - b^10*c^5 + 20*a*b^8*c^6 - 160*a^2*b^6*c^7 + 640*a^3*b^4*c^8 - 1280*a^4*b^2*c^9)) - (3*b*x)/c^4 - (3*b*atan((((3*b*x*(2*b^6 - 70*a^3*c^3 + 70*a^2*b^2*c^2 - 21*a*b^4*c))/(c^4*(4*a*c - b^2)^5) + (3*b^2*(16*a^2*c^6 + b^4*c^4 - 8*a*b^2*c^5)*(2*b^6 - 70*a^3*c^3 + 70*a^2*b^2*c^2 - 21*a*b^4*c))/(2*c^9*(4*a*c - b^2)^5*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))*(32*a^2*c^7*(4*a*c - b^2)^(5/2) + 2*b^4*c^5*(4*a*c - b^2)^(5/2) - 16*a*b^2*c^6*(4*a*c - b^2)^(5/2)))/(6*b^7 - 210*a^3*b*c^3 + 210*a^2*b^3*c^2 - 63*a*b^5*c))*(2*b^6 - 70*a^3*c^3 + 70*a^2*b^2*c^2 - 21*a*b^4*c))/(c^5*(4*a*c - b^2)^(5/2))","B"
2200,1,705,238,1.423645,"\text{Not used}","int(x^6/(a + b*x + c*x^2)^3,x)","\frac{x}{c^3}-\frac{\frac{3\,x^3\,\left(-6\,a^3\,c^3+17\,a^2\,b^2\,c^2-8\,a\,b^4\,c+b^6\right)}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}+\frac{x^2\,\left(42\,a^3\,b\,c^3+41\,a^2\,b^3\,c^2-34\,a\,b^5\,c+5\,b^7\right)}{2\,c\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{a^2\,\left(58\,a^2\,b\,c^2-36\,a\,b^3\,c+5\,b^5\right)}{2\,c\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{a\,x\,\left(-14\,a^3\,c^3+71\,a^2\,b^2\,c^2-38\,a\,b^4\,c+5\,b^6\right)}{c\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}}{a^2\,c^3+c^5\,x^4+x^2\,\left(b^2\,c^3+2\,a\,c^4\right)+2\,b\,c^4\,x^3+2\,a\,b\,c^3\,x}+\frac{\ln\left(c\,x^2+b\,x+a\right)\,\left(-3072\,a^5\,b\,c^5+3840\,a^4\,b^3\,c^4-1920\,a^3\,b^5\,c^3+480\,a^2\,b^7\,c^2-60\,a\,b^9\,c+3\,b^{11}\right)}{2\,\left(1024\,a^5\,c^9-1280\,a^4\,b^2\,c^8+640\,a^3\,b^4\,c^7-160\,a^2\,b^6\,c^6+20\,a\,b^8\,c^5-b^{10}\,c^4\right)}+\frac{3\,\mathrm{atan}\left(\frac{\left(\frac{3\,x\,\left(-20\,a^3\,c^3+30\,a^2\,b^2\,c^2-10\,a\,b^4\,c+b^6\right)}{c^3\,{\left(4\,a\,c-b^2\right)}^5}+\frac{3\,\left(16\,a^2\,b\,c^5-8\,a\,b^3\,c^4+b^5\,c^3\right)\,\left(-20\,a^3\,c^3+30\,a^2\,b^2\,c^2-10\,a\,b^4\,c+b^6\right)}{2\,c^7\,{\left(4\,a\,c-b^2\right)}^5\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}\right)\,\left(32\,a^2\,c^6\,{\left(4\,a\,c-b^2\right)}^{5/2}+2\,b^4\,c^4\,{\left(4\,a\,c-b^2\right)}^{5/2}-16\,a\,b^2\,c^5\,{\left(4\,a\,c-b^2\right)}^{5/2}\right)}{-60\,a^3\,c^3+90\,a^2\,b^2\,c^2-30\,a\,b^4\,c+3\,b^6}\right)\,\left(-20\,a^3\,c^3+30\,a^2\,b^2\,c^2-10\,a\,b^4\,c+b^6\right)}{c^4\,{\left(4\,a\,c-b^2\right)}^{5/2}}","Not used",1,"x/c^3 - ((3*x^3*(b^6 - 6*a^3*c^3 + 17*a^2*b^2*c^2 - 8*a*b^4*c))/(b^4 + 16*a^2*c^2 - 8*a*b^2*c) + (x^2*(5*b^7 + 42*a^3*b*c^3 + 41*a^2*b^3*c^2 - 34*a*b^5*c))/(2*c*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (a^2*(5*b^5 + 58*a^2*b*c^2 - 36*a*b^3*c))/(2*c*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (a*x*(5*b^6 - 14*a^3*c^3 + 71*a^2*b^2*c^2 - 38*a*b^4*c))/(c*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))/(a^2*c^3 + c^5*x^4 + x^2*(2*a*c^4 + b^2*c^3) + 2*b*c^4*x^3 + 2*a*b*c^3*x) + (log(a + b*x + c*x^2)*(3*b^11 - 3072*a^5*b*c^5 + 480*a^2*b^7*c^2 - 1920*a^3*b^5*c^3 + 3840*a^4*b^3*c^4 - 60*a*b^9*c))/(2*(1024*a^5*c^9 - b^10*c^4 + 20*a*b^8*c^5 - 160*a^2*b^6*c^6 + 640*a^3*b^4*c^7 - 1280*a^4*b^2*c^8)) + (3*atan((((3*x*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c))/(c^3*(4*a*c - b^2)^5) + (3*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c))/(2*c^7*(4*a*c - b^2)^5*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))*(32*a^2*c^6*(4*a*c - b^2)^(5/2) + 2*b^4*c^4*(4*a*c - b^2)^(5/2) - 16*a*b^2*c^5*(4*a*c - b^2)^(5/2)))/(3*b^6 - 60*a^3*c^3 + 90*a^2*b^2*c^2 - 30*a*b^4*c))*(b^6 - 20*a^3*c^3 + 30*a^2*b^2*c^2 - 10*a*b^4*c))/(c^4*(4*a*c - b^2)^(5/2))","B"
2201,1,1486,388,3.034642,"\text{Not used}","int((d + e*x)^5/(a + b*x + c*x^2)^3,x)","\frac{\mathrm{atan}\left(\frac{\left(\frac{x\,\left(b\,e-2\,c\,d\right)\,\left(30\,a^2\,c^2\,e^4-10\,a\,b^2\,c\,e^4-20\,a\,b\,c^2\,d\,e^3+20\,a\,c^3\,d^2\,e^2+b^4\,e^4+2\,b^3\,c\,d\,e^3+4\,b^2\,c^2\,d^2\,e^2-12\,b\,c^3\,d^3\,e+6\,c^4\,d^4\right)}{c^2\,{\left(4\,a\,c-b^2\right)}^5}+\frac{\left(b\,e-2\,c\,d\right)\,\left(16\,a^2\,b\,c^4-8\,a\,b^3\,c^3+b^5\,c^2\right)\,\left(30\,a^2\,c^2\,e^4-10\,a\,b^2\,c\,e^4-20\,a\,b\,c^2\,d\,e^3+20\,a\,c^3\,d^2\,e^2+b^4\,e^4+2\,b^3\,c\,d\,e^3+4\,b^2\,c^2\,d^2\,e^2-12\,b\,c^3\,d^3\,e+6\,c^4\,d^4\right)}{2\,c^5\,{\left(4\,a\,c-b^2\right)}^5\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}\right)\,\left(32\,a^2\,c^5\,{\left(4\,a\,c-b^2\right)}^{5/2}+2\,b^4\,c^3\,{\left(4\,a\,c-b^2\right)}^{5/2}-16\,a\,b^2\,c^4\,{\left(4\,a\,c-b^2\right)}^{5/2}\right)}{-30\,a^2\,b\,c^2\,e^5+60\,a^2\,c^3\,d\,e^4+10\,a\,b^3\,c\,e^5-60\,a\,b\,c^3\,d^2\,e^3+40\,a\,c^4\,d^3\,e^2-b^5\,e^5+20\,b^2\,c^3\,d^3\,e^2-30\,b\,c^4\,d^4\,e+12\,c^5\,d^5}\right)\,\left(b\,e-2\,c\,d\right)\,\left(30\,a^2\,c^2\,e^4-10\,a\,b^2\,c\,e^4-20\,a\,b\,c^2\,d\,e^3+20\,a\,c^3\,d^2\,e^2+b^4\,e^4+2\,b^3\,c\,d\,e^3+4\,b^2\,c^2\,d^2\,e^2-12\,b\,c^3\,d^3\,e+6\,c^4\,d^4\right)}{c^3\,{\left(4\,a\,c-b^2\right)}^{5/2}}-\frac{\ln\left(c\,x^2+b\,x+a\right)\,\left(-1024\,a^5\,c^5\,e^5+1280\,a^4\,b^2\,c^4\,e^5-640\,a^3\,b^4\,c^3\,e^5+160\,a^2\,b^6\,c^2\,e^5-20\,a\,b^8\,c\,e^5+b^{10}\,e^5\right)}{2\,\left(1024\,a^5\,c^8-1280\,a^4\,b^2\,c^7+640\,a^3\,b^4\,c^6-160\,a^2\,b^6\,c^5+20\,a\,b^8\,c^4-b^{10}\,c^3\right)}-\frac{\frac{-24\,a^4\,c^2\,e^5+21\,a^3\,b^2\,c\,e^5-50\,a^3\,b\,c^2\,d\,e^4+80\,a^3\,c^3\,d^2\,e^3-3\,a^2\,b^4\,e^5+5\,a^2\,b^3\,c\,d\,e^4+10\,a^2\,b^2\,c^2\,d^2\,e^3-60\,a^2\,b\,c^3\,d^3\,e^2+40\,a^2\,c^4\,d^4\,e+5\,a\,b^2\,c^3\,d^4\,e-10\,a\,b\,c^4\,d^5+b^3\,c^3\,d^5}{2\,c^3\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{x\,\left(-31\,a^3\,b\,c^2\,e^5+30\,a^3\,c^3\,d\,e^4+22\,a^2\,b^3\,c\,e^5-50\,a^2\,b^2\,c^2\,d\,e^4+50\,a^2\,b\,c^3\,d^2\,e^3+20\,a^2\,c^4\,d^3\,e^2-3\,a\,b^5\,e^5+5\,a\,b^4\,c\,d\,e^4+10\,a\,b^3\,c^2\,d^2\,e^3-50\,a\,b^2\,c^3\,d^3\,e^2+25\,a\,b\,c^4\,d^4\,e-10\,a\,c^5\,d^5+5\,b^3\,c^3\,d^4\,e-2\,b^2\,c^4\,d^5\right)}{c^3\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}-\frac{x^2\,\left(32\,a^3\,c^3\,e^5+11\,a^2\,b^2\,c^2\,e^5+10\,a^2\,b\,c^3\,d\,e^4-160\,a^2\,c^4\,d^2\,e^3-19\,a\,b^4\,c\,e^5+40\,a\,b^3\,c^2\,d\,e^4-10\,a\,b^2\,c^3\,d^2\,e^3+60\,a\,b\,c^4\,d^3\,e^2+3\,b^6\,e^5-5\,b^5\,c\,d\,e^4-10\,b^4\,c^2\,d^2\,e^3+30\,b^3\,c^3\,d^3\,e^2-45\,b^2\,c^4\,d^4\,e+18\,b\,c^5\,d^5\right)}{2\,c^3\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}-\frac{x^3\,\left(25\,a^2\,b\,c^2\,e^5-50\,a^2\,c^3\,d\,e^4-15\,a\,b^3\,c\,e^5+40\,a\,b^2\,c^2\,d\,e^4-30\,a\,b\,c^3\,d^2\,e^3+20\,a\,c^4\,d^3\,e^2+2\,b^5\,e^5-5\,b^4\,c\,d\,e^4+10\,b^2\,c^3\,d^3\,e^2-15\,b\,c^4\,d^4\,e+6\,c^5\,d^5\right)}{c^2\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}","Not used",1,"(atan((((x*(b*e - 2*c*d)*(b^4*e^4 + 6*c^4*d^4 + 30*a^2*c^2*e^4 + 20*a*c^3*d^2*e^2 + 4*b^2*c^2*d^2*e^2 - 10*a*b^2*c*e^4 - 12*b*c^3*d^3*e + 2*b^3*c*d*e^3 - 20*a*b*c^2*d*e^3))/(c^2*(4*a*c - b^2)^5) + ((b*e - 2*c*d)*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*(b^4*e^4 + 6*c^4*d^4 + 30*a^2*c^2*e^4 + 20*a*c^3*d^2*e^2 + 4*b^2*c^2*d^2*e^2 - 10*a*b^2*c*e^4 - 12*b*c^3*d^3*e + 2*b^3*c*d*e^3 - 20*a*b*c^2*d*e^3))/(2*c^5*(4*a*c - b^2)^5*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))*(32*a^2*c^5*(4*a*c - b^2)^(5/2) + 2*b^4*c^3*(4*a*c - b^2)^(5/2) - 16*a*b^2*c^4*(4*a*c - b^2)^(5/2)))/(12*c^5*d^5 - b^5*e^5 - 30*a^2*b*c^2*e^5 + 40*a*c^4*d^3*e^2 + 60*a^2*c^3*d*e^4 + 20*b^2*c^3*d^3*e^2 + 10*a*b^3*c*e^5 - 30*b*c^4*d^4*e - 60*a*b*c^3*d^2*e^3))*(b*e - 2*c*d)*(b^4*e^4 + 6*c^4*d^4 + 30*a^2*c^2*e^4 + 20*a*c^3*d^2*e^2 + 4*b^2*c^2*d^2*e^2 - 10*a*b^2*c*e^4 - 12*b*c^3*d^3*e + 2*b^3*c*d*e^3 - 20*a*b*c^2*d*e^3))/(c^3*(4*a*c - b^2)^(5/2)) - (log(a + b*x + c*x^2)*(b^10*e^5 - 1024*a^5*c^5*e^5 + 160*a^2*b^6*c^2*e^5 - 640*a^3*b^4*c^3*e^5 + 1280*a^4*b^2*c^4*e^5 - 20*a*b^8*c*e^5))/(2*(1024*a^5*c^8 - b^10*c^3 + 20*a*b^8*c^4 - 160*a^2*b^6*c^5 + 640*a^3*b^4*c^6 - 1280*a^4*b^2*c^7)) - ((b^3*c^3*d^5 - 24*a^4*c^2*e^5 - 3*a^2*b^4*e^5 + 21*a^3*b^2*c*e^5 + 40*a^2*c^4*d^4*e + 80*a^3*c^3*d^2*e^3 - 10*a*b*c^4*d^5 + 10*a^2*b^2*c^2*d^2*e^3 + 5*a*b^2*c^3*d^4*e + 5*a^2*b^3*c*d*e^4 - 50*a^3*b*c^2*d*e^4 - 60*a^2*b*c^3*d^3*e^2)/(2*c^3*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (x*(22*a^2*b^3*c*e^5 - 10*a*c^5*d^5 - 2*b^2*c^4*d^5 - 3*a*b^5*e^5 - 31*a^3*b*c^2*e^5 + 30*a^3*c^3*d*e^4 + 5*b^3*c^3*d^4*e + 20*a^2*c^4*d^3*e^2 + 25*a*b*c^4*d^4*e + 5*a*b^4*c*d*e^4 - 50*a*b^2*c^3*d^3*e^2 + 10*a*b^3*c^2*d^2*e^3 + 50*a^2*b*c^3*d^2*e^3 - 50*a^2*b^2*c^2*d*e^4))/(c^3*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) - (x^2*(3*b^6*e^5 + 18*b*c^5*d^5 + 32*a^3*c^3*e^5 - 45*b^2*c^4*d^4*e + 11*a^2*b^2*c^2*e^5 - 160*a^2*c^4*d^2*e^3 + 30*b^3*c^3*d^3*e^2 - 10*b^4*c^2*d^2*e^3 - 19*a*b^4*c*e^5 - 5*b^5*c*d*e^4 + 60*a*b*c^4*d^3*e^2 + 40*a*b^3*c^2*d*e^4 + 10*a^2*b*c^3*d*e^4 - 10*a*b^2*c^3*d^2*e^3))/(2*c^3*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) - (x^3*(2*b^5*e^5 + 6*c^5*d^5 + 25*a^2*b*c^2*e^5 + 20*a*c^4*d^3*e^2 - 50*a^2*c^3*d*e^4 + 10*b^2*c^3*d^3*e^2 - 15*a*b^3*c*e^5 - 15*b*c^4*d^4*e - 5*b^4*c*d*e^4 - 30*a*b*c^3*d^2*e^3 + 40*a*b^2*c^2*d*e^4))/(c^2*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3)","B"
2202,1,798,169,1.322937,"\text{Not used}","int((d + e*x)^4/(a + b*x + c*x^2)^3,x)","\frac{12\,\mathrm{atan}\left(\frac{\left(\frac{6\,\left(16\,a^2\,b\,c^2-8\,a\,b^3\,c+b^5\right)\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}{{\left(4\,a\,c-b^2\right)}^{5/2}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{12\,c\,x\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}{{\left(4\,a\,c-b^2\right)}^{5/2}}\right)\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}{6\,a^2\,e^4-12\,a\,b\,d\,e^3+12\,a\,c\,d^2\,e^2+6\,b^2\,d^2\,e^2-12\,b\,c\,d^3\,e+6\,c^2\,d^4}\right)\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}{{\left(4\,a\,c-b^2\right)}^{5/2}}-\frac{\frac{-10\,a^3\,b\,c\,e^4+32\,a^3\,c^2\,d\,e^3+a^2\,b^3\,e^4+4\,a^2\,b^2\,c\,d\,e^3-36\,a^2\,b\,c^2\,d^2\,e^2+32\,a^2\,c^3\,d^3\,e+4\,a\,b^2\,c^2\,d^3\,e-10\,a\,b\,c^3\,d^4+b^3\,c^2\,d^4}{2\,c^2\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{x^2\,\left(-2\,a^2\,b\,c^2\,e^4+64\,a^2\,c^3\,d\,e^3-8\,a\,b^3\,c\,e^4+4\,a\,b^2\,c^2\,d\,e^3-36\,a\,b\,c^3\,d^2\,e^2+b^5\,e^4+4\,b^4\,c\,d\,e^3-18\,b^3\,c^2\,d^2\,e^2+36\,b^2\,c^3\,d^3\,e-18\,b\,c^4\,d^4\right)}{2\,c^2\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{x^3\,\left(10\,a^2\,c^2\,e^4-8\,a\,b^2\,c\,e^4+12\,a\,b\,c^2\,d\,e^3-12\,a\,c^3\,d^2\,e^2+b^4\,e^4-6\,b^2\,c^2\,d^2\,e^2+12\,b\,c^3\,d^3\,e-6\,c^4\,d^4\right)}{c\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{x\,\left(6\,a^3\,c^2\,e^4-10\,a^2\,b^2\,c\,e^4+20\,a^2\,b\,c^2\,d\,e^3+12\,a^2\,c^3\,d^2\,e^2+a\,b^4\,e^4+4\,a\,b^3\,c\,d\,e^3-30\,a\,b^2\,c^2\,d^2\,e^2+20\,a\,b\,c^3\,d^3\,e-10\,a\,c^4\,d^4+4\,b^3\,c^2\,d^3\,e-2\,b^2\,c^3\,d^4\right)}{c^2\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}","Not used",1,"(12*atan((((6*(b^5 + 16*a^2*b*c^2 - 8*a*b^3*c)*(a*e^2 + c*d^2 - b*d*e)^2)/((4*a*c - b^2)^(5/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (12*c*x*(a*e^2 + c*d^2 - b*d*e)^2)/(4*a*c - b^2)^(5/2))*(b^4 + 16*a^2*c^2 - 8*a*b^2*c))/(6*a^2*e^4 + 6*c^2*d^4 + 6*b^2*d^2*e^2 - 12*a*b*d*e^3 - 12*b*c*d^3*e + 12*a*c*d^2*e^2))*(a*e^2 + c*d^2 - b*d*e)^2)/(4*a*c - b^2)^(5/2) - ((a^2*b^3*e^4 + b^3*c^2*d^4 + 32*a^2*c^3*d^3*e + 32*a^3*c^2*d*e^3 - 10*a*b*c^3*d^4 - 10*a^3*b*c*e^4 + 4*a*b^2*c^2*d^3*e + 4*a^2*b^2*c*d*e^3 - 36*a^2*b*c^2*d^2*e^2)/(2*c^2*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (x^2*(b^5*e^4 - 18*b*c^4*d^4 - 2*a^2*b*c^2*e^4 + 64*a^2*c^3*d*e^3 + 36*b^2*c^3*d^3*e - 18*b^3*c^2*d^2*e^2 - 8*a*b^3*c*e^4 + 4*b^4*c*d*e^3 - 36*a*b*c^3*d^2*e^2 + 4*a*b^2*c^2*d*e^3))/(2*c^2*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (x^3*(b^4*e^4 - 6*c^4*d^4 + 10*a^2*c^2*e^4 - 12*a*c^3*d^2*e^2 - 6*b^2*c^2*d^2*e^2 - 8*a*b^2*c*e^4 + 12*b*c^3*d^3*e + 12*a*b*c^2*d*e^3))/(c*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (x*(a*b^4*e^4 - 10*a*c^4*d^4 + 6*a^3*c^2*e^4 - 2*b^2*c^3*d^4 - 10*a^2*b^2*c*e^4 + 4*b^3*c^2*d^3*e + 12*a^2*c^3*d^2*e^2 + 20*a*b*c^3*d^3*e + 4*a*b^3*c*d*e^3 + 20*a^2*b*c^2*d*e^3 - 30*a*b^2*c^2*d^2*e^2))/(c^2*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3)","B"
2203,1,636,158,1.364133,"\text{Not used}","int((d + e*x)^3/(a + b*x + c*x^2)^3,x)","\frac{6\,\mathrm{atan}\left(\frac{\left(\frac{3\,\left(b\,e-2\,c\,d\right)\,\left(16\,a^2\,b\,c^2-8\,a\,b^3\,c+b^5\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{5/2}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{6\,c\,x\,\left(b\,e-2\,c\,d\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{5/2}}\right)\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}{3\,b^2\,d\,e^2-9\,b\,c\,d^2\,e-3\,a\,b\,e^3+6\,c^2\,d^3+6\,a\,c\,d\,e^2}\right)\,\left(b\,e-2\,c\,d\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{5/2}}-\frac{\frac{8\,a^3\,c\,e^3+a^2\,b^2\,e^3-18\,a^2\,b\,c\,d\,e^2+24\,a^2\,c^2\,d^2\,e+3\,a\,b^2\,c\,d^2\,e-10\,a\,b\,c^2\,d^3+b^3\,c\,d^3}{2\,c\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{x^2\,\left(16\,a^2\,c^2\,e^3+a\,b^2\,c\,e^3-18\,a\,b\,c^2\,d\,e^2+b^4\,e^3-9\,b^3\,c\,d\,e^2+27\,b^2\,c^2\,d^2\,e-18\,b\,c^3\,d^3\right)}{2\,c\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}-\frac{3\,c\,x^3\,\left(b^2\,d\,e^2-3\,b\,c\,d^2\,e-a\,b\,e^3+2\,c^2\,d^3+2\,a\,c\,d\,e^2\right)}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}+\frac{x\,\left(5\,a^2\,b\,c\,e^3+6\,a^2\,c^2\,d\,e^2+a\,b^3\,e^3-15\,a\,b^2\,c\,d\,e^2+15\,a\,b\,c^2\,d^2\,e-10\,a\,c^3\,d^3+3\,b^3\,c\,d^2\,e-2\,b^2\,c^2\,d^3\right)}{c\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}","Not used",1,"(6*atan((((3*(b*e - 2*c*d)*(b^5 + 16*a^2*b*c^2 - 8*a*b^3*c)*(a*e^2 + c*d^2 - b*d*e))/((4*a*c - b^2)^(5/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (6*c*x*(b*e - 2*c*d)*(a*e^2 + c*d^2 - b*d*e))/(4*a*c - b^2)^(5/2))*(b^4 + 16*a^2*c^2 - 8*a*b^2*c))/(6*c^2*d^3 + 3*b^2*d*e^2 - 3*a*b*e^3 + 6*a*c*d*e^2 - 9*b*c*d^2*e))*(b*e - 2*c*d)*(a*e^2 + c*d^2 - b*d*e))/(4*a*c - b^2)^(5/2) - ((8*a^3*c*e^3 + b^3*c*d^3 + a^2*b^2*e^3 + 24*a^2*c^2*d^2*e - 10*a*b*c^2*d^3 + 3*a*b^2*c*d^2*e - 18*a^2*b*c*d*e^2)/(2*c*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (x^2*(b^4*e^3 - 18*b*c^3*d^3 + 16*a^2*c^2*e^3 + 27*b^2*c^2*d^2*e + a*b^2*c*e^3 - 9*b^3*c*d*e^2 - 18*a*b*c^2*d*e^2))/(2*c*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) - (3*c*x^3*(2*c^2*d^3 + b^2*d*e^2 - a*b*e^3 + 2*a*c*d*e^2 - 3*b*c*d^2*e))/(b^4 + 16*a^2*c^2 - 8*a*b^2*c) + (x*(a*b^3*e^3 - 10*a*c^3*d^3 - 2*b^2*c^2*d^3 + 6*a^2*c^2*d*e^2 + 5*a^2*b*c*e^3 + 3*b^3*c*d^2*e + 15*a*b*c^2*d^2*e - 15*a*b^2*c*d*e^2))/(c*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3)","B"
2204,1,517,198,1.052281,"\text{Not used}","int((d + e*x)^2/(a + b*x + c*x^2)^3,x)","\frac{\frac{x\,\left(-2\,a^2\,c\,e^2+5\,a\,b^2\,e^2-10\,a\,b\,c\,d\,e+10\,a\,c^2\,d^2-2\,b^3\,d\,e+2\,b^2\,c\,d^2\right)}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}-\frac{-6\,a^2\,b\,e^2+16\,c\,a^2\,d\,e+2\,a\,b^2\,d\,e-10\,c\,a\,b\,d^2+b^3\,d^2}{2\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{3\,b\,x^2\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2+2\,a\,c\,e^2\right)}{2\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{c\,x^3\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2+2\,a\,c\,e^2\right)}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}+\frac{2\,\mathrm{atan}\left(\frac{\left(\frac{2\,c\,x\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2+2\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{5/2}}+\frac{\left(16\,a^2\,b\,c^2-8\,a\,b^3\,c+b^5\right)\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2+2\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{5/2}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}\right)\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}{b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2+2\,a\,c\,e^2}\right)\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2+2\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{5/2}}","Not used",1,"((x*(5*a*b^2*e^2 + 10*a*c^2*d^2 - 2*a^2*c*e^2 + 2*b^2*c*d^2 - 2*b^3*d*e - 10*a*b*c*d*e))/(b^4 + 16*a^2*c^2 - 8*a*b^2*c) - (b^3*d^2 - 6*a^2*b*e^2 - 10*a*b*c*d^2 + 2*a*b^2*d*e + 16*a^2*c*d*e)/(2*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (3*b*x^2*(b^2*e^2 + 6*c^2*d^2 + 2*a*c*e^2 - 6*b*c*d*e))/(2*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (c*x^3*(b^2*e^2 + 6*c^2*d^2 + 2*a*c*e^2 - 6*b*c*d*e))/(b^4 + 16*a^2*c^2 - 8*a*b^2*c))/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3) + (2*atan((((2*c*x*(b^2*e^2 + 6*c^2*d^2 + 2*a*c*e^2 - 6*b*c*d*e))/(4*a*c - b^2)^(5/2) + ((b^5 + 16*a^2*b*c^2 - 8*a*b^3*c)*(b^2*e^2 + 6*c^2*d^2 + 2*a*c*e^2 - 6*b*c*d*e))/((4*a*c - b^2)^(5/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))*(b^4 + 16*a^2*c^2 - 8*a*b^2*c))/(b^2*e^2 + 6*c^2*d^2 + 2*a*c*e^2 - 6*b*c*d*e))*(b^2*e^2 + 6*c^2*d^2 + 2*a*c*e^2 - 6*b*c*d*e))/(4*a*c - b^2)^(5/2)","B"
2205,1,353,131,0.304379,"\text{Not used}","int((d + e*x)/(a + b*x + c*x^2)^3,x)","\frac{6\,c\,\mathrm{atan}\left(\frac{\left(\frac{6\,c^2\,x\,\left(b\,e-2\,c\,d\right)}{{\left(4\,a\,c-b^2\right)}^{5/2}}+\frac{3\,c\,\left(b\,e-2\,c\,d\right)\,\left(16\,a^2\,b\,c^2-8\,a\,b^3\,c+b^5\right)}{{\left(4\,a\,c-b^2\right)}^{5/2}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}\right)\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}{6\,c^2\,d-3\,b\,c\,e}\right)\,\left(b\,e-2\,c\,d\right)}{{\left(4\,a\,c-b^2\right)}^{5/2}}-\frac{\frac{8\,c\,e\,a^2+e\,a\,b^2-10\,c\,d\,a\,b+d\,b^3}{2\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{x\,\left(b^2+5\,a\,c\right)\,\left(b\,e-2\,c\,d\right)}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}+\frac{3\,c^2\,x^3\,\left(b\,e-2\,c\,d\right)}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}+\frac{9\,b\,c\,x^2\,\left(b\,e-2\,c\,d\right)}{2\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}","Not used",1,"(6*c*atan((((6*c^2*x*(b*e - 2*c*d))/(4*a*c - b^2)^(5/2) + (3*c*(b*e - 2*c*d)*(b^5 + 16*a^2*b*c^2 - 8*a*b^3*c))/((4*a*c - b^2)^(5/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))*(b^4 + 16*a^2*c^2 - 8*a*b^2*c))/(6*c^2*d - 3*b*c*e))*(b*e - 2*c*d))/(4*a*c - b^2)^(5/2) - ((b^3*d + a*b^2*e + 8*a^2*c*e - 10*a*b*c*d)/(2*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (x*(5*a*c + b^2)*(b*e - 2*c*d))/(b^4 + 16*a^2*c^2 - 8*a*b^2*c) + (3*c^2*x^3*(b*e - 2*c*d))/(b^4 + 16*a^2*c^2 - 8*a*b^2*c) + (9*b*c*x^2*(b*e - 2*c*d))/(2*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3)","B"
2206,1,285,101,0.212697,"\text{Not used}","int(1/(a + b*x + c*x^2)^3,x)","\frac{\frac{6\,c^3\,x^3}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}-\frac{b^3-10\,a\,b\,c}{2\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{9\,b\,c^2\,x^2}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}+\frac{2\,c\,x\,\left(b^2+5\,a\,c\right)}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}+\frac{12\,c^2\,\mathrm{atan}\left(\frac{\left(\frac{12\,c^3\,x}{{\left(4\,a\,c-b^2\right)}^{5/2}}+\frac{6\,c^2\,\left(16\,a^2\,b\,c^2-8\,a\,b^3\,c+b^5\right)}{{\left(4\,a\,c-b^2\right)}^{5/2}\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}\right)\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}{6\,c^2}\right)}{{\left(4\,a\,c-b^2\right)}^{5/2}}","Not used",1,"((6*c^3*x^3)/(b^4 + 16*a^2*c^2 - 8*a*b^2*c) - (b^3 - 10*a*b*c)/(2*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (9*b*c^2*x^2)/(b^4 + 16*a^2*c^2 - 8*a*b^2*c) + (2*c*x*(5*a*c + b^2))/(b^4 + 16*a^2*c^2 - 8*a*b^2*c))/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3) + (12*c^2*atan((((12*c^3*x)/(4*a*c - b^2)^(5/2) + (6*c^2*(b^5 + 16*a^2*b*c^2 - 8*a*b^3*c))/((4*a*c - b^2)^(5/2)*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))*(b^4 + 16*a^2*c^2 - 8*a*b^2*c))/(6*c^2)))/(4*a*c - b^2)^(5/2)","B"
2207,1,3292,429,9.587495,"\text{Not used}","int(1/((d + e*x)*(a + b*x + c*x^2)^3),x)","\frac{\frac{24\,a^3\,c^2\,e^3-21\,a^2\,b^2\,c\,e^3+10\,a^2\,b\,c^2\,d\,e^2+8\,a^2\,c^3\,d^2\,e+3\,a\,b^4\,e^3+6\,a\,b^3\,c\,d\,e^2-19\,a\,b^2\,c^2\,d^2\,e+10\,a\,b\,c^3\,d^3-b^5\,d\,e^2+2\,b^4\,c\,d^2\,e-b^3\,c^2\,d^3}{2\,\left(16\,a^4\,c^2\,e^4-8\,a^3\,b^2\,c\,e^4-32\,a^3\,b\,c^2\,d\,e^3+32\,a^3\,c^3\,d^2\,e^2+a^2\,b^4\,e^4+16\,a^2\,b^3\,c\,d\,e^3-32\,a^2\,b\,c^3\,d^3\,e+16\,a^2\,c^4\,d^4-2\,a\,b^5\,d\,e^3-6\,a\,b^4\,c\,d^2\,e^2+16\,a\,b^3\,c^2\,d^3\,e-8\,a\,b^2\,c^3\,d^4+b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4\right)}+\frac{x^3\,\left(b^3\,c^2\,e^3+b^2\,c^3\,d\,e^2-9\,b\,c^4\,d^2\,e-7\,a\,b\,c^3\,e^3+6\,c^5\,d^3+14\,a\,c^4\,d\,e^2\right)}{16\,a^4\,c^2\,e^4-8\,a^3\,b^2\,c\,e^4-32\,a^3\,b\,c^2\,d\,e^3+32\,a^3\,c^3\,d^2\,e^2+a^2\,b^4\,e^4+16\,a^2\,b^3\,c\,d\,e^3-32\,a^2\,b\,c^3\,d^3\,e+16\,a^2\,c^4\,d^4-2\,a\,b^5\,d\,e^3-6\,a\,b^4\,c\,d^2\,e^2+16\,a\,b^3\,c^2\,d^3\,e-8\,a\,b^2\,c^3\,d^4+b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4}+\frac{x\,\left(-a^2\,b\,c^2\,e^3+18\,a^2\,c^3\,d\,e^2-6\,a\,b^3\,c\,e^3+9\,a\,b^2\,c^2\,d\,e^2-15\,a\,b\,c^3\,d^2\,e+10\,a\,c^4\,d^3+b^5\,e^3-3\,b^3\,c^2\,d^2\,e+2\,b^2\,c^3\,d^3\right)}{16\,a^4\,c^2\,e^4-8\,a^3\,b^2\,c\,e^4-32\,a^3\,b\,c^2\,d\,e^3+32\,a^3\,c^3\,d^2\,e^2+a^2\,b^4\,e^4+16\,a^2\,b^3\,c\,d\,e^3-32\,a^2\,b\,c^3\,d^3\,e+16\,a^2\,c^4\,d^4-2\,a\,b^5\,d\,e^3-6\,a\,b^4\,c\,d^2\,e^2+16\,a\,b^3\,c^2\,d^3\,e-8\,a\,b^2\,c^3\,d^4+b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4}+\frac{x^2\,\left(16\,a^2\,c^3\,e^3-29\,a\,b^2\,c^2\,e^3+42\,a\,b\,c^3\,d\,e^2+4\,b^4\,c\,e^3+3\,b^3\,c^2\,d\,e^2-27\,b^2\,c^3\,d^2\,e+18\,b\,c^4\,d^3\right)}{2\,\left(16\,a^4\,c^2\,e^4-8\,a^3\,b^2\,c\,e^4-32\,a^3\,b\,c^2\,d\,e^3+32\,a^3\,c^3\,d^2\,e^2+a^2\,b^4\,e^4+16\,a^2\,b^3\,c\,d\,e^3-32\,a^2\,b\,c^3\,d^3\,e+16\,a^2\,c^4\,d^4-2\,a\,b^5\,d\,e^3-6\,a\,b^4\,c\,d^2\,e^2+16\,a\,b^3\,c^2\,d^3\,e-8\,a\,b^2\,c^3\,d^4+b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4\right)}}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}+\frac{e^5\,\ln\left(d+e\,x\right)}{a^3\,e^6-3\,a^2\,b\,d\,e^5+3\,a^2\,c\,d^2\,e^4+3\,a\,b^2\,d^2\,e^4-6\,a\,b\,c\,d^3\,e^3+3\,a\,c^2\,d^4\,e^2-b^3\,d^3\,e^3+3\,b^2\,c\,d^4\,e^2-3\,b\,c^2\,d^5\,e+c^3\,d^6}-\frac{\ln\left(b^5+\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+16\,a^2\,b\,c^2+32\,a^2\,c^3\,x-8\,a\,b^3\,c+2\,b^4\,c\,x-16\,a\,b^2\,c^2\,x\right)\,\left(\frac{b^{10}\,e^5}{2}-512\,a^5\,c^5\,e^5-\frac{b^5\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}}{2}+6\,c^5\,d^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+80\,a^2\,b^6\,c^2\,e^5-320\,a^3\,b^4\,c^3\,e^5+640\,a^4\,b^2\,c^4\,e^5-10\,a\,b^8\,c\,e^5+10\,b^2\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+5\,a\,b^3\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-15\,b\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-15\,a^2\,b\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+20\,a\,c^4\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+30\,a^2\,c^3\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-30\,a\,b\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}\right)}{-1024\,a^8\,c^5\,e^6+1280\,a^7\,b^2\,c^4\,e^6+3072\,a^7\,b\,c^5\,d\,e^5-3072\,a^7\,c^6\,d^2\,e^4-640\,a^6\,b^4\,c^3\,e^6-3840\,a^6\,b^3\,c^4\,d\,e^5+768\,a^6\,b^2\,c^5\,d^2\,e^4+6144\,a^6\,b\,c^6\,d^3\,e^3-3072\,a^6\,c^7\,d^4\,e^2+160\,a^5\,b^6\,c^2\,e^6+1920\,a^5\,b^5\,c^3\,d\,e^5+1920\,a^5\,b^4\,c^4\,d^2\,e^4-6656\,a^5\,b^3\,c^5\,d^3\,e^3+768\,a^5\,b^2\,c^6\,d^4\,e^2+3072\,a^5\,b\,c^7\,d^5\,e-1024\,a^5\,c^8\,d^6-20\,a^4\,b^8\,c\,e^6-480\,a^4\,b^7\,c^2\,d\,e^5-1440\,a^4\,b^6\,c^3\,d^2\,e^4+2560\,a^4\,b^5\,c^4\,d^3\,e^3+1920\,a^4\,b^4\,c^5\,d^4\,e^2-3840\,a^4\,b^3\,c^6\,d^5\,e+1280\,a^4\,b^2\,c^7\,d^6+a^3\,b^{10}\,e^6+60\,a^3\,b^9\,c\,d\,e^5+420\,a^3\,b^8\,c^2\,d^2\,e^4-320\,a^3\,b^7\,c^3\,d^3\,e^3-1440\,a^3\,b^6\,c^4\,d^4\,e^2+1920\,a^3\,b^5\,c^5\,d^5\,e-640\,a^3\,b^4\,c^6\,d^6-3\,a^2\,b^{11}\,d\,e^5-57\,a^2\,b^{10}\,c\,d^2\,e^4-40\,a^2\,b^9\,c^2\,d^3\,e^3+420\,a^2\,b^8\,c^3\,d^4\,e^2-480\,a^2\,b^7\,c^4\,d^5\,e+160\,a^2\,b^6\,c^5\,d^6+3\,a\,b^{12}\,d^2\,e^4+14\,a\,b^{11}\,c\,d^3\,e^3-57\,a\,b^{10}\,c^2\,d^4\,e^2+60\,a\,b^9\,c^3\,d^5\,e-20\,a\,b^8\,c^4\,d^6-b^{13}\,d^3\,e^3+3\,b^{12}\,c\,d^4\,e^2-3\,b^{11}\,c^2\,d^5\,e+b^{10}\,c^3\,d^6}+\frac{\ln\left(b^5-\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+16\,a^2\,b\,c^2+32\,a^2\,c^3\,x-8\,a\,b^3\,c+2\,b^4\,c\,x-16\,a\,b^2\,c^2\,x\right)\,\left(512\,a^5\,c^5\,e^5-\frac{b^{10}\,e^5}{2}-\frac{b^5\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}}{2}+6\,c^5\,d^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-80\,a^2\,b^6\,c^2\,e^5+320\,a^3\,b^4\,c^3\,e^5-640\,a^4\,b^2\,c^4\,e^5+10\,a\,b^8\,c\,e^5+10\,b^2\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+5\,a\,b^3\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-15\,b\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-15\,a^2\,b\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+20\,a\,c^4\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+30\,a^2\,c^3\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-30\,a\,b\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}\right)}{-1024\,a^8\,c^5\,e^6+1280\,a^7\,b^2\,c^4\,e^6+3072\,a^7\,b\,c^5\,d\,e^5-3072\,a^7\,c^6\,d^2\,e^4-640\,a^6\,b^4\,c^3\,e^6-3840\,a^6\,b^3\,c^4\,d\,e^5+768\,a^6\,b^2\,c^5\,d^2\,e^4+6144\,a^6\,b\,c^6\,d^3\,e^3-3072\,a^6\,c^7\,d^4\,e^2+160\,a^5\,b^6\,c^2\,e^6+1920\,a^5\,b^5\,c^3\,d\,e^5+1920\,a^5\,b^4\,c^4\,d^2\,e^4-6656\,a^5\,b^3\,c^5\,d^3\,e^3+768\,a^5\,b^2\,c^6\,d^4\,e^2+3072\,a^5\,b\,c^7\,d^5\,e-1024\,a^5\,c^8\,d^6-20\,a^4\,b^8\,c\,e^6-480\,a^4\,b^7\,c^2\,d\,e^5-1440\,a^4\,b^6\,c^3\,d^2\,e^4+2560\,a^4\,b^5\,c^4\,d^3\,e^3+1920\,a^4\,b^4\,c^5\,d^4\,e^2-3840\,a^4\,b^3\,c^6\,d^5\,e+1280\,a^4\,b^2\,c^7\,d^6+a^3\,b^{10}\,e^6+60\,a^3\,b^9\,c\,d\,e^5+420\,a^3\,b^8\,c^2\,d^2\,e^4-320\,a^3\,b^7\,c^3\,d^3\,e^3-1440\,a^3\,b^6\,c^4\,d^4\,e^2+1920\,a^3\,b^5\,c^5\,d^5\,e-640\,a^3\,b^4\,c^6\,d^6-3\,a^2\,b^{11}\,d\,e^5-57\,a^2\,b^{10}\,c\,d^2\,e^4-40\,a^2\,b^9\,c^2\,d^3\,e^3+420\,a^2\,b^8\,c^3\,d^4\,e^2-480\,a^2\,b^7\,c^4\,d^5\,e+160\,a^2\,b^6\,c^5\,d^6+3\,a\,b^{12}\,d^2\,e^4+14\,a\,b^{11}\,c\,d^3\,e^3-57\,a\,b^{10}\,c^2\,d^4\,e^2+60\,a\,b^9\,c^3\,d^5\,e-20\,a\,b^8\,c^4\,d^6-b^{13}\,d^3\,e^3+3\,b^{12}\,c\,d^4\,e^2-3\,b^{11}\,c^2\,d^5\,e+b^{10}\,c^3\,d^6}","Not used",1,"((3*a*b^4*e^3 - b^5*d*e^2 + 24*a^3*c^2*e^3 - b^3*c^2*d^3 - 21*a^2*b^2*c*e^3 + 8*a^2*c^3*d^2*e + 10*a*b*c^3*d^3 + 2*b^4*c*d^2*e + 6*a*b^3*c*d*e^2 - 19*a*b^2*c^2*d^2*e + 10*a^2*b*c^2*d*e^2)/(2*(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3)) + (x^3*(6*c^5*d^3 + b^3*c^2*e^3 + b^2*c^3*d*e^2 - 7*a*b*c^3*e^3 + 14*a*c^4*d*e^2 - 9*b*c^4*d^2*e))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3) + (x*(b^5*e^3 + 10*a*c^4*d^3 + 2*b^2*c^3*d^3 - a^2*b*c^2*e^3 + 18*a^2*c^3*d*e^2 - 3*b^3*c^2*d^2*e - 6*a*b^3*c*e^3 - 15*a*b*c^3*d^2*e + 9*a*b^2*c^2*d*e^2))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3) + (x^2*(18*b*c^4*d^3 + 4*b^4*c*e^3 + 16*a^2*c^3*e^3 - 29*a*b^2*c^2*e^3 - 27*b^2*c^3*d^2*e + 3*b^3*c^2*d*e^2 + 42*a*b*c^3*d*e^2))/(2*(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3)))/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3) + (e^5*log(d + e*x))/(a^3*e^6 + c^3*d^6 - b^3*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + 3*b^2*c*d^4*e^2 - 3*a^2*b*d*e^5 - 3*b*c^2*d^5*e - 6*a*b*c*d^3*e^3) - (log(b^5 + (-(4*a*c - b^2)^5)^(1/2) + 16*a^2*b*c^2 + 32*a^2*c^3*x - 8*a*b^3*c + 2*b^4*c*x - 16*a*b^2*c^2*x)*((b^10*e^5)/2 - 512*a^5*c^5*e^5 - (b^5*e^5*(-(4*a*c - b^2)^5)^(1/2))/2 + 6*c^5*d^5*(-(4*a*c - b^2)^5)^(1/2) + 80*a^2*b^6*c^2*e^5 - 320*a^3*b^4*c^3*e^5 + 640*a^4*b^2*c^4*e^5 - 10*a*b^8*c*e^5 + 10*b^2*c^3*d^3*e^2*(-(4*a*c - b^2)^5)^(1/2) + 5*a*b^3*c*e^5*(-(4*a*c - b^2)^5)^(1/2) - 15*b*c^4*d^4*e*(-(4*a*c - b^2)^5)^(1/2) - 15*a^2*b*c^2*e^5*(-(4*a*c - b^2)^5)^(1/2) + 20*a*c^4*d^3*e^2*(-(4*a*c - b^2)^5)^(1/2) + 30*a^2*c^3*d*e^4*(-(4*a*c - b^2)^5)^(1/2) - 30*a*b*c^3*d^2*e^3*(-(4*a*c - b^2)^5)^(1/2)))/(a^3*b^10*e^6 - 1024*a^5*c^8*d^6 - 1024*a^8*c^5*e^6 + b^10*c^3*d^6 - b^13*d^3*e^3 - 20*a*b^8*c^4*d^6 - 20*a^4*b^8*c*e^6 + 3*a*b^12*d^2*e^4 - 3*a^2*b^11*d*e^5 - 3*b^11*c^2*d^5*e + 3*b^12*c*d^4*e^2 + 160*a^2*b^6*c^5*d^6 - 640*a^3*b^4*c^6*d^6 + 1280*a^4*b^2*c^7*d^6 + 160*a^5*b^6*c^2*e^6 - 640*a^6*b^4*c^3*e^6 + 1280*a^7*b^2*c^4*e^6 - 3072*a^6*c^7*d^4*e^2 - 3072*a^7*c^6*d^2*e^4 + 420*a^2*b^8*c^3*d^4*e^2 - 40*a^2*b^9*c^2*d^3*e^3 - 1440*a^3*b^6*c^4*d^4*e^2 - 320*a^3*b^7*c^3*d^3*e^3 + 420*a^3*b^8*c^2*d^2*e^4 + 1920*a^4*b^4*c^5*d^4*e^2 + 2560*a^4*b^5*c^4*d^3*e^3 - 1440*a^4*b^6*c^3*d^2*e^4 + 768*a^5*b^2*c^6*d^4*e^2 - 6656*a^5*b^3*c^5*d^3*e^3 + 1920*a^5*b^4*c^4*d^2*e^4 + 768*a^6*b^2*c^5*d^2*e^4 + 60*a*b^9*c^3*d^5*e + 14*a*b^11*c*d^3*e^3 + 60*a^3*b^9*c*d*e^5 + 3072*a^5*b*c^7*d^5*e + 3072*a^7*b*c^5*d*e^5 - 57*a*b^10*c^2*d^4*e^2 - 480*a^2*b^7*c^4*d^5*e - 57*a^2*b^10*c*d^2*e^4 + 1920*a^3*b^5*c^5*d^5*e - 3840*a^4*b^3*c^6*d^5*e - 480*a^4*b^7*c^2*d*e^5 + 1920*a^5*b^5*c^3*d*e^5 + 6144*a^6*b*c^6*d^3*e^3 - 3840*a^6*b^3*c^4*d*e^5) + (log(b^5 - (-(4*a*c - b^2)^5)^(1/2) + 16*a^2*b*c^2 + 32*a^2*c^3*x - 8*a*b^3*c + 2*b^4*c*x - 16*a*b^2*c^2*x)*(512*a^5*c^5*e^5 - (b^10*e^5)/2 - (b^5*e^5*(-(4*a*c - b^2)^5)^(1/2))/2 + 6*c^5*d^5*(-(4*a*c - b^2)^5)^(1/2) - 80*a^2*b^6*c^2*e^5 + 320*a^3*b^4*c^3*e^5 - 640*a^4*b^2*c^4*e^5 + 10*a*b^8*c*e^5 + 10*b^2*c^3*d^3*e^2*(-(4*a*c - b^2)^5)^(1/2) + 5*a*b^3*c*e^5*(-(4*a*c - b^2)^5)^(1/2) - 15*b*c^4*d^4*e*(-(4*a*c - b^2)^5)^(1/2) - 15*a^2*b*c^2*e^5*(-(4*a*c - b^2)^5)^(1/2) + 20*a*c^4*d^3*e^2*(-(4*a*c - b^2)^5)^(1/2) + 30*a^2*c^3*d*e^4*(-(4*a*c - b^2)^5)^(1/2) - 30*a*b*c^3*d^2*e^3*(-(4*a*c - b^2)^5)^(1/2)))/(a^3*b^10*e^6 - 1024*a^5*c^8*d^6 - 1024*a^8*c^5*e^6 + b^10*c^3*d^6 - b^13*d^3*e^3 - 20*a*b^8*c^4*d^6 - 20*a^4*b^8*c*e^6 + 3*a*b^12*d^2*e^4 - 3*a^2*b^11*d*e^5 - 3*b^11*c^2*d^5*e + 3*b^12*c*d^4*e^2 + 160*a^2*b^6*c^5*d^6 - 640*a^3*b^4*c^6*d^6 + 1280*a^4*b^2*c^7*d^6 + 160*a^5*b^6*c^2*e^6 - 640*a^6*b^4*c^3*e^6 + 1280*a^7*b^2*c^4*e^6 - 3072*a^6*c^7*d^4*e^2 - 3072*a^7*c^6*d^2*e^4 + 420*a^2*b^8*c^3*d^4*e^2 - 40*a^2*b^9*c^2*d^3*e^3 - 1440*a^3*b^6*c^4*d^4*e^2 - 320*a^3*b^7*c^3*d^3*e^3 + 420*a^3*b^8*c^2*d^2*e^4 + 1920*a^4*b^4*c^5*d^4*e^2 + 2560*a^4*b^5*c^4*d^3*e^3 - 1440*a^4*b^6*c^3*d^2*e^4 + 768*a^5*b^2*c^6*d^4*e^2 - 6656*a^5*b^3*c^5*d^3*e^3 + 1920*a^5*b^4*c^4*d^2*e^4 + 768*a^6*b^2*c^5*d^2*e^4 + 60*a*b^9*c^3*d^5*e + 14*a*b^11*c*d^3*e^3 + 60*a^3*b^9*c*d*e^5 + 3072*a^5*b*c^7*d^5*e + 3072*a^7*b*c^5*d*e^5 - 57*a*b^10*c^2*d^4*e^2 - 480*a^2*b^7*c^4*d^5*e - 57*a^2*b^10*c*d^2*e^4 + 1920*a^3*b^5*c^5*d^5*e - 3840*a^4*b^3*c^6*d^5*e - 480*a^4*b^7*c^2*d*e^5 + 1920*a^5*b^5*c^3*d*e^5 + 6144*a^6*b*c^6*d^3*e^3 - 3840*a^6*b^3*c^4*d*e^5)","B"
2208,1,1255,239,2.024009,"\text{Not used}","int(1/(x^2*(a + b*x + c*x^2)^3),x)","-\frac{\frac{1}{a}+\frac{x^2\,\left(50\,a^3\,c^3+7\,a^2\,b^2\,c^2-18\,a\,b^4\,c+3\,b^6\right)}{a^3\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{x\,\left(122\,a^2\,b\,c^2-68\,a\,b^3\,c+9\,b^5\right)}{2\,a^2\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{3\,x^3\,\left(46\,a^2\,b\,c^3-29\,a\,b^3\,c^2+4\,b^5\,c\right)}{2\,a^3\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{3\,c^2\,x^4\,\left(10\,a^2\,c^2-7\,a\,b^2\,c+b^4\right)}{a^3\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}}{x^3\,\left(b^2+2\,a\,c\right)+a^2\,x+c^2\,x^5+2\,a\,b\,x^2+2\,b\,c\,x^4}-\frac{3\,b\,\ln\left(x\right)}{a^4}-\frac{3\,\ln\left(2\,a\,b^{11}+2\,b^{12}\,x+2\,a\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-39\,a^2\,b^9\,c-1696\,a^6\,b\,c^5+320\,a^6\,c^6\,x+2\,b^7\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+303\,a^3\,b^7\,c^2-1170\,a^4\,b^5\,c^3+2240\,a^5\,b^3\,c^4-10\,a^4\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-17\,a^2\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+321\,a^2\,b^8\,c^2\,x-1296\,a^3\,b^6\,c^3\,x+2660\,a^4\,b^4\,c^4\,x-2336\,a^5\,b^2\,c^5\,x-40\,a\,b^{10}\,c\,x+39\,a^3\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-20\,a\,b^5\,c\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-58\,a^3\,b\,c^3\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+63\,a^2\,b^3\,c^2\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}\right)\,\left(b^{11}+b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-1024\,a^5\,b\,c^5+160\,a^2\,b^7\,c^2-640\,a^3\,b^5\,c^3+1280\,a^4\,b^3\,c^4-20\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-20\,a\,b^9\,c+30\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-10\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,a^4\,{\left(4\,a\,c-b^2\right)}^5}-\frac{3\,\ln\left(2\,a\,b^{11}+2\,b^{12}\,x-2\,a\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-39\,a^2\,b^9\,c-1696\,a^6\,b\,c^5+320\,a^6\,c^6\,x-2\,b^7\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+303\,a^3\,b^7\,c^2-1170\,a^4\,b^5\,c^3+2240\,a^5\,b^3\,c^4+10\,a^4\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+17\,a^2\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+321\,a^2\,b^8\,c^2\,x-1296\,a^3\,b^6\,c^3\,x+2660\,a^4\,b^4\,c^4\,x-2336\,a^5\,b^2\,c^5\,x-40\,a\,b^{10}\,c\,x-39\,a^3\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+20\,a\,b^5\,c\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+58\,a^3\,b\,c^3\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-63\,a^2\,b^3\,c^2\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}\right)\,\left(b^{11}-b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-1024\,a^5\,b\,c^5+160\,a^2\,b^7\,c^2-640\,a^3\,b^5\,c^3+1280\,a^4\,b^3\,c^4+20\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-20\,a\,b^9\,c-30\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+10\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,a^4\,{\left(4\,a\,c-b^2\right)}^5}","Not used",1,"- (1/a + (x^2*(3*b^6 + 50*a^3*c^3 + 7*a^2*b^2*c^2 - 18*a*b^4*c))/(a^3*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (x*(9*b^5 + 122*a^2*b*c^2 - 68*a*b^3*c))/(2*a^2*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (3*x^3*(4*b^5*c - 29*a*b^3*c^2 + 46*a^2*b*c^3))/(2*a^3*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (3*c^2*x^4*(b^4 + 10*a^2*c^2 - 7*a*b^2*c))/(a^3*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))/(x^3*(2*a*c + b^2) + a^2*x + c^2*x^5 + 2*a*b*x^2 + 2*b*c*x^4) - (3*b*log(x))/a^4 - (3*log(2*a*b^11 + 2*b^12*x + 2*a*b^6*(-(4*a*c - b^2)^5)^(1/2) - 39*a^2*b^9*c - 1696*a^6*b*c^5 + 320*a^6*c^6*x + 2*b^7*x*(-(4*a*c - b^2)^5)^(1/2) + 303*a^3*b^7*c^2 - 1170*a^4*b^5*c^3 + 2240*a^5*b^3*c^4 - 10*a^4*c^3*(-(4*a*c - b^2)^5)^(1/2) - 17*a^2*b^4*c*(-(4*a*c - b^2)^5)^(1/2) + 321*a^2*b^8*c^2*x - 1296*a^3*b^6*c^3*x + 2660*a^4*b^4*c^4*x - 2336*a^5*b^2*c^5*x - 40*a*b^10*c*x + 39*a^3*b^2*c^2*(-(4*a*c - b^2)^5)^(1/2) - 20*a*b^5*c*x*(-(4*a*c - b^2)^5)^(1/2) - 58*a^3*b*c^3*x*(-(4*a*c - b^2)^5)^(1/2) + 63*a^2*b^3*c^2*x*(-(4*a*c - b^2)^5)^(1/2))*(b^11 + b^6*(-(4*a*c - b^2)^5)^(1/2) - 1024*a^5*b*c^5 + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 20*a^3*c^3*(-(4*a*c - b^2)^5)^(1/2) - 20*a*b^9*c + 30*a^2*b^2*c^2*(-(4*a*c - b^2)^5)^(1/2) - 10*a*b^4*c*(-(4*a*c - b^2)^5)^(1/2)))/(2*a^4*(4*a*c - b^2)^5) - (3*log(2*a*b^11 + 2*b^12*x - 2*a*b^6*(-(4*a*c - b^2)^5)^(1/2) - 39*a^2*b^9*c - 1696*a^6*b*c^5 + 320*a^6*c^6*x - 2*b^7*x*(-(4*a*c - b^2)^5)^(1/2) + 303*a^3*b^7*c^2 - 1170*a^4*b^5*c^3 + 2240*a^5*b^3*c^4 + 10*a^4*c^3*(-(4*a*c - b^2)^5)^(1/2) + 17*a^2*b^4*c*(-(4*a*c - b^2)^5)^(1/2) + 321*a^2*b^8*c^2*x - 1296*a^3*b^6*c^3*x + 2660*a^4*b^4*c^4*x - 2336*a^5*b^2*c^5*x - 40*a*b^10*c*x - 39*a^3*b^2*c^2*(-(4*a*c - b^2)^5)^(1/2) + 20*a*b^5*c*x*(-(4*a*c - b^2)^5)^(1/2) + 58*a^3*b*c^3*x*(-(4*a*c - b^2)^5)^(1/2) - 63*a^2*b^3*c^2*x*(-(4*a*c - b^2)^5)^(1/2))*(b^11 - b^6*(-(4*a*c - b^2)^5)^(1/2) - 1024*a^5*b*c^5 + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 + 20*a^3*c^3*(-(4*a*c - b^2)^5)^(1/2) - 20*a*b^9*c - 30*a^2*b^2*c^2*(-(4*a*c - b^2)^5)^(1/2) + 10*a*b^4*c*(-(4*a*c - b^2)^5)^(1/2)))/(2*a^4*(4*a*c - b^2)^5)","B"
2209,1,1404,306,2.312866,"\text{Not used}","int(1/(x^3*(a + b*x + c*x^2)^3),x)","\frac{\frac{2\,b\,x}{a^2}-\frac{1}{2\,a}+\frac{x^2\,\left(-72\,a^3\,c^3+307\,a^2\,b^2\,c^2-145\,a\,b^4\,c+18\,b^6\right)}{2\,a^3\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{3\,x^4\,\left(-16\,a^3\,c^4+121\,a^2\,b^2\,c^3-62\,a\,b^4\,c^2+8\,b^6\,c\right)}{2\,a^4\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{b\,x^3\,\left(103\,a^3\,c^3+32\,a^2\,b^2\,c^2-39\,a\,b^4\,c+6\,b^6\right)}{a^4\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{3\,b\,c^2\,x^5\,\left(27\,a^2\,c^2-15\,a\,b^2\,c+2\,b^4\right)}{a^4\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}}{x^4\,\left(b^2+2\,a\,c\right)+a^2\,x^2+c^2\,x^6+2\,a\,b\,x^3+2\,b\,c\,x^5}-\frac{3\,\ln\left(x\right)\,\left(a\,c-2\,b^2\right)}{a^5}+\frac{3\,\ln\left(4\,a\,b^{12}+4\,b^{13}\,x+1536\,a^7\,c^6-4\,a\,b^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-80\,a^2\,b^{10}\,c-4\,b^8\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+645\,a^3\,b^8\,c^2-2643\,a^4\,b^6\,c^3+5640\,a^5\,b^4\,c^4-5552\,a^6\,b^2\,c^5+36\,a^2\,b^5\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+59\,a^4\,b\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+682\,a^2\,b^9\,c^2\,x-2913\,a^3\,b^7\,c^3\,x+6606\,a^4\,b^5\,c^4\,x-7232\,a^5\,b^3\,c^5\,x-48\,a^4\,c^4\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-82\,a\,b^{11}\,c\,x-95\,a^3\,b^3\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+2656\,a^6\,b\,c^6\,x+42\,a\,b^6\,c\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-146\,a^2\,b^4\,c^2\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+179\,a^3\,b^2\,c^3\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}\right)\,\left(2\,b^{12}+1024\,a^6\,c^6-2\,b^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+340\,a^2\,b^8\,c^2-1440\,a^3\,b^6\,c^3+3200\,a^4\,b^4\,c^4-3328\,a^5\,b^2\,c^5-41\,a\,b^{10}\,c+70\,a^3\,b\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-70\,a^2\,b^3\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+21\,a\,b^5\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,a^5\,{\left(4\,a\,c-b^2\right)}^5}+\frac{3\,\ln\left(4\,a\,b^{12}+4\,b^{13}\,x+1536\,a^7\,c^6+4\,a\,b^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-80\,a^2\,b^{10}\,c+4\,b^8\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+645\,a^3\,b^8\,c^2-2643\,a^4\,b^6\,c^3+5640\,a^5\,b^4\,c^4-5552\,a^6\,b^2\,c^5-36\,a^2\,b^5\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-59\,a^4\,b\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+682\,a^2\,b^9\,c^2\,x-2913\,a^3\,b^7\,c^3\,x+6606\,a^4\,b^5\,c^4\,x-7232\,a^5\,b^3\,c^5\,x+48\,a^4\,c^4\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-82\,a\,b^{11}\,c\,x+95\,a^3\,b^3\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+2656\,a^6\,b\,c^6\,x-42\,a\,b^6\,c\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+146\,a^2\,b^4\,c^2\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-179\,a^3\,b^2\,c^3\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}\right)\,\left(2\,b^{12}+1024\,a^6\,c^6+2\,b^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+340\,a^2\,b^8\,c^2-1440\,a^3\,b^6\,c^3+3200\,a^4\,b^4\,c^4-3328\,a^5\,b^2\,c^5-41\,a\,b^{10}\,c-70\,a^3\,b\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}+70\,a^2\,b^3\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}-21\,a\,b^5\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^5}\right)}{2\,a^5\,{\left(4\,a\,c-b^2\right)}^5}","Not used",1,"((2*b*x)/a^2 - 1/(2*a) + (x^2*(18*b^6 - 72*a^3*c^3 + 307*a^2*b^2*c^2 - 145*a*b^4*c))/(2*a^3*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (3*x^4*(8*b^6*c - 16*a^3*c^4 - 62*a*b^4*c^2 + 121*a^2*b^2*c^3))/(2*a^4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (b*x^3*(6*b^6 + 103*a^3*c^3 + 32*a^2*b^2*c^2 - 39*a*b^4*c))/(a^4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (3*b*c^2*x^5*(2*b^4 + 27*a^2*c^2 - 15*a*b^2*c))/(a^4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))/(x^4*(2*a*c + b^2) + a^2*x^2 + c^2*x^6 + 2*a*b*x^3 + 2*b*c*x^5) - (3*log(x)*(a*c - 2*b^2))/a^5 + (3*log(4*a*b^12 + 4*b^13*x + 1536*a^7*c^6 - 4*a*b^7*(-(4*a*c - b^2)^5)^(1/2) - 80*a^2*b^10*c - 4*b^8*x*(-(4*a*c - b^2)^5)^(1/2) + 645*a^3*b^8*c^2 - 2643*a^4*b^6*c^3 + 5640*a^5*b^4*c^4 - 5552*a^6*b^2*c^5 + 36*a^2*b^5*c*(-(4*a*c - b^2)^5)^(1/2) + 59*a^4*b*c^3*(-(4*a*c - b^2)^5)^(1/2) + 682*a^2*b^9*c^2*x - 2913*a^3*b^7*c^3*x + 6606*a^4*b^5*c^4*x - 7232*a^5*b^3*c^5*x - 48*a^4*c^4*x*(-(4*a*c - b^2)^5)^(1/2) - 82*a*b^11*c*x - 95*a^3*b^3*c^2*(-(4*a*c - b^2)^5)^(1/2) + 2656*a^6*b*c^6*x + 42*a*b^6*c*x*(-(4*a*c - b^2)^5)^(1/2) - 146*a^2*b^4*c^2*x*(-(4*a*c - b^2)^5)^(1/2) + 179*a^3*b^2*c^3*x*(-(4*a*c - b^2)^5)^(1/2))*(2*b^12 + 1024*a^6*c^6 - 2*b^7*(-(4*a*c - b^2)^5)^(1/2) + 340*a^2*b^8*c^2 - 1440*a^3*b^6*c^3 + 3200*a^4*b^4*c^4 - 3328*a^5*b^2*c^5 - 41*a*b^10*c + 70*a^3*b*c^3*(-(4*a*c - b^2)^5)^(1/2) - 70*a^2*b^3*c^2*(-(4*a*c - b^2)^5)^(1/2) + 21*a*b^5*c*(-(4*a*c - b^2)^5)^(1/2)))/(2*a^5*(4*a*c - b^2)^5) + (3*log(4*a*b^12 + 4*b^13*x + 1536*a^7*c^6 + 4*a*b^7*(-(4*a*c - b^2)^5)^(1/2) - 80*a^2*b^10*c + 4*b^8*x*(-(4*a*c - b^2)^5)^(1/2) + 645*a^3*b^8*c^2 - 2643*a^4*b^6*c^3 + 5640*a^5*b^4*c^4 - 5552*a^6*b^2*c^5 - 36*a^2*b^5*c*(-(4*a*c - b^2)^5)^(1/2) - 59*a^4*b*c^3*(-(4*a*c - b^2)^5)^(1/2) + 682*a^2*b^9*c^2*x - 2913*a^3*b^7*c^3*x + 6606*a^4*b^5*c^4*x - 7232*a^5*b^3*c^5*x + 48*a^4*c^4*x*(-(4*a*c - b^2)^5)^(1/2) - 82*a*b^11*c*x + 95*a^3*b^3*c^2*(-(4*a*c - b^2)^5)^(1/2) + 2656*a^6*b*c^6*x - 42*a*b^6*c*x*(-(4*a*c - b^2)^5)^(1/2) + 146*a^2*b^4*c^2*x*(-(4*a*c - b^2)^5)^(1/2) - 179*a^3*b^2*c^3*x*(-(4*a*c - b^2)^5)^(1/2))*(2*b^12 + 1024*a^6*c^6 + 2*b^7*(-(4*a*c - b^2)^5)^(1/2) + 340*a^2*b^8*c^2 - 1440*a^3*b^6*c^3 + 3200*a^4*b^4*c^4 - 3328*a^5*b^2*c^5 - 41*a*b^10*c - 70*a^3*b*c^3*(-(4*a*c - b^2)^5)^(1/2) + 70*a^2*b^3*c^2*(-(4*a*c - b^2)^5)^(1/2) - 21*a*b^5*c*(-(4*a*c - b^2)^5)^(1/2)))/(2*a^5*(4*a*c - b^2)^5)","B"
2210,1,1159,349,1.794328,"\text{Not used}","int(x^8/(a + b*x + c*x^2)^4,x)","\frac{x}{c^4}-\frac{\frac{2\,x^5\,\left(58\,a^4\,c^5-212\,a^3\,b^2\,c^4+146\,a^2\,b^4\,c^3-36\,a\,b^6\,c^2+3\,b^8\,c\right)}{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}-\frac{2\,x^4\,\left(47\,a^4\,b\,c^4+226\,a^3\,b^3\,c^3-209\,a^2\,b^5\,c^2+57\,a\,b^7\,c-5\,b^9\right)}{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}+\frac{x^3\,\left(544\,a^5\,c^5-3234\,a^4\,b^2\,c^4+1788\,a^3\,b^4\,c^3-68\,a^2\,b^6\,c^2-96\,a\,b^8\,c+13\,b^{10}\right)}{3\,c\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}-\frac{x^2\,\left(304\,a^5\,b\,c^4+387\,a^4\,b^3\,c^3-486\,a^3\,b^5\,c^2+143\,a^2\,b^7\,c-13\,a\,b^9\right)}{c\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{a^2\,\left(-590\,a^4\,b\,c^3+535\,a^3\,b^3\,c^2-147\,a^2\,b^5\,c+13\,a\,b^7\right)}{3\,c\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{a\,x\,\left(76\,a^5\,c^4-694\,a^4\,b^2\,c^3+567\,a^3\,b^4\,c^2-150\,a^2\,b^6\,c+13\,a\,b^8\right)}{c\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}}{x^3\,\left(b^3\,c^4+6\,a\,b\,c^5\right)+x^2\,\left(3\,a^2\,c^5+3\,a\,b^2\,c^4\right)+a^3\,c^4+c^7\,x^6+x^4\,\left(3\,b^2\,c^5+3\,a\,c^6\right)+3\,b\,c^6\,x^5+3\,a^2\,b\,c^4\,x}+\frac{\ln\left(c\,x^2+b\,x+a\right)\,\left(-65536\,a^7\,b\,c^7+114688\,a^6\,b^3\,c^6-86016\,a^5\,b^5\,c^5+35840\,a^4\,b^7\,c^4-8960\,a^3\,b^9\,c^3+1344\,a^2\,b^{11}\,c^2-112\,a\,b^{13}\,c+4\,b^{15}\right)}{2\,\left(16384\,a^7\,c^{12}-28672\,a^6\,b^2\,c^{11}+21504\,a^5\,b^4\,c^{10}-8960\,a^4\,b^6\,c^9+2240\,a^3\,b^8\,c^8-336\,a^2\,b^{10}\,c^7+28\,a\,b^{12}\,c^6-b^{14}\,c^5\right)}-\frac{4\,\mathrm{atan}\left(\frac{\left(\frac{4\,x\,\left(70\,a^4\,c^4-140\,a^3\,b^2\,c^3+70\,a^2\,b^4\,c^2-14\,a\,b^6\,c+b^8\right)}{c^4\,{\left(4\,a\,c-b^2\right)}^7}+\frac{2\,\left(-64\,a^3\,b\,c^7+48\,a^2\,b^3\,c^6-12\,a\,b^5\,c^5+b^7\,c^4\right)\,\left(70\,a^4\,c^4-140\,a^3\,b^2\,c^3+70\,a^2\,b^4\,c^2-14\,a\,b^6\,c+b^8\right)}{c^9\,{\left(4\,a\,c-b^2\right)}^7\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}\right)\,\left(64\,a^3\,c^8\,{\left(4\,a\,c-b^2\right)}^{7/2}-b^6\,c^5\,{\left(4\,a\,c-b^2\right)}^{7/2}+12\,a\,b^4\,c^6\,{\left(4\,a\,c-b^2\right)}^{7/2}-48\,a^2\,b^2\,c^7\,{\left(4\,a\,c-b^2\right)}^{7/2}\right)}{140\,a^4\,c^4-280\,a^3\,b^2\,c^3+140\,a^2\,b^4\,c^2-28\,a\,b^6\,c+2\,b^8}\right)\,\left(70\,a^4\,c^4-140\,a^3\,b^2\,c^3+70\,a^2\,b^4\,c^2-14\,a\,b^6\,c+b^8\right)}{c^5\,{\left(4\,a\,c-b^2\right)}^{7/2}}","Not used",1,"x/c^4 - ((2*x^5*(3*b^8*c + 58*a^4*c^5 - 36*a*b^6*c^2 + 146*a^2*b^4*c^3 - 212*a^3*b^2*c^4))/(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c) - (2*x^4*(47*a^4*b*c^4 - 5*b^9 - 209*a^2*b^5*c^2 + 226*a^3*b^3*c^3 + 57*a*b^7*c))/(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c) + (x^3*(13*b^10 + 544*a^5*c^5 - 68*a^2*b^6*c^2 + 1788*a^3*b^4*c^3 - 3234*a^4*b^2*c^4 - 96*a*b^8*c))/(3*c*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) - (x^2*(143*a^2*b^7*c - 13*a*b^9 + 304*a^5*b*c^4 - 486*a^3*b^5*c^2 + 387*a^4*b^3*c^3))/(c*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (a^2*(13*a*b^7 - 147*a^2*b^5*c - 590*a^4*b*c^3 + 535*a^3*b^3*c^2))/(3*c*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (a*x*(13*a*b^8 + 76*a^5*c^4 - 150*a^2*b^6*c + 567*a^3*b^4*c^2 - 694*a^4*b^2*c^3))/(c*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)))/(x^3*(b^3*c^4 + 6*a*b*c^5) + x^2*(3*a^2*c^5 + 3*a*b^2*c^4) + a^3*c^4 + c^7*x^6 + x^4*(3*a*c^6 + 3*b^2*c^5) + 3*b*c^6*x^5 + 3*a^2*b*c^4*x) + (log(a + b*x + c*x^2)*(4*b^15 - 65536*a^7*b*c^7 + 1344*a^2*b^11*c^2 - 8960*a^3*b^9*c^3 + 35840*a^4*b^7*c^4 - 86016*a^5*b^5*c^5 + 114688*a^6*b^3*c^6 - 112*a*b^13*c))/(2*(16384*a^7*c^12 - b^14*c^5 + 28*a*b^12*c^6 - 336*a^2*b^10*c^7 + 2240*a^3*b^8*c^8 - 8960*a^4*b^6*c^9 + 21504*a^5*b^4*c^10 - 28672*a^6*b^2*c^11)) - (4*atan((((4*x*(b^8 + 70*a^4*c^4 + 70*a^2*b^4*c^2 - 140*a^3*b^2*c^3 - 14*a*b^6*c))/(c^4*(4*a*c - b^2)^7) + (2*(b^7*c^4 - 12*a*b^5*c^5 - 64*a^3*b*c^7 + 48*a^2*b^3*c^6)*(b^8 + 70*a^4*c^4 + 70*a^2*b^4*c^2 - 140*a^3*b^2*c^3 - 14*a*b^6*c))/(c^9*(4*a*c - b^2)^7*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)))*(64*a^3*c^8*(4*a*c - b^2)^(7/2) - b^6*c^5*(4*a*c - b^2)^(7/2) + 12*a*b^4*c^6*(4*a*c - b^2)^(7/2) - 48*a^2*b^2*c^7*(4*a*c - b^2)^(7/2)))/(2*b^8 + 140*a^4*c^4 + 140*a^2*b^4*c^2 - 280*a^3*b^2*c^3 - 28*a*b^6*c))*(b^8 + 70*a^4*c^4 + 70*a^2*b^4*c^2 - 140*a^3*b^2*c^3 - 14*a*b^6*c))/(c^5*(4*a*c - b^2)^(7/2))","B"
2211,1,1055,291,2.057034,"\text{Not used}","int(x^7/(a + b*x + c*x^2)^4,x)","\frac{b\,\mathrm{atan}\left(\frac{\left(\frac{b\,x\,\left(-140\,a^3\,c^3+70\,a^2\,b^2\,c^2-14\,a\,b^4\,c+b^6\right)}{c^3\,{\left(4\,a\,c-b^2\right)}^7}-\frac{b^2\,\left(64\,a^3\,c^6-48\,a^2\,b^2\,c^5+12\,a\,b^4\,c^4-b^6\,c^3\right)\,\left(-140\,a^3\,c^3+70\,a^2\,b^2\,c^2-14\,a\,b^4\,c+b^6\right)}{2\,c^7\,{\left(4\,a\,c-b^2\right)}^7\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}\right)\,\left(128\,a^3\,c^7\,{\left(4\,a\,c-b^2\right)}^{7/2}-2\,b^6\,c^4\,{\left(4\,a\,c-b^2\right)}^{7/2}+24\,a\,b^4\,c^5\,{\left(4\,a\,c-b^2\right)}^{7/2}-96\,a^2\,b^2\,c^6\,{\left(4\,a\,c-b^2\right)}^{7/2}\right)}{-140\,a^3\,b\,c^3+70\,a^2\,b^3\,c^2-14\,a\,b^5\,c+b^7}\right)\,\left(-140\,a^3\,c^3+70\,a^2\,b^2\,c^2-14\,a\,b^4\,c+b^6\right)}{c^4\,{\left(4\,a\,c-b^2\right)}^{7/2}}-\frac{\ln\left(c\,x^2+b\,x+a\right)\,\left(-16384\,a^7\,c^7+28672\,a^6\,b^2\,c^6-21504\,a^5\,b^4\,c^5+8960\,a^4\,b^6\,c^4-2240\,a^3\,b^8\,c^3+336\,a^2\,b^{10}\,c^2-28\,a\,b^{12}\,c+b^{14}\right)}{2\,\left(16384\,a^7\,c^{11}-28672\,a^6\,b^2\,c^{10}+21504\,a^5\,b^4\,c^9-8960\,a^4\,b^6\,c^8+2240\,a^3\,b^8\,c^7-336\,a^2\,b^{10}\,c^6+28\,a\,b^{12}\,c^5-b^{14}\,c^4\right)}-\frac{\frac{x^4\,\left(192\,a^4\,c^4+242\,a^3\,b^2\,c^3-341\,a^2\,b^4\,c^2+100\,a\,b^6\,c-9\,b^8\right)}{2\,c^3\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}-\frac{a^3\,\left(-352\,a^3\,c^3+438\,a^2\,b^2\,c^2-124\,a\,b^4\,c+11\,b^6\right)}{6\,c^4\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}-\frac{b\,x^5\,\left(-154\,a^3\,c^3+133\,a^2\,b^2\,c^2-35\,a\,b^4\,c+3\,b^6\right)}{c^2\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{a\,x^2\,\left(288\,a^4\,c^4+152\,a^3\,b^2\,c^3-381\,a^2\,b^4\,c^2+119\,a\,b^6\,c-11\,b^8\right)}{2\,c^4\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{b\,x^3\,\left(2272\,a^4\,c^4-1698\,a^3\,b^2\,c^3+117\,a^2\,b^4\,c^2+76\,a\,b^6\,c-11\,b^8\right)}{6\,c^4\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}-\frac{a^2\,b\,x\,\left(-428\,a^3\,c^3+460\,a^2\,b^2\,c^2-126\,a\,b^4\,c+11\,b^6\right)}{2\,c^4\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}}{x^2\,\left(3\,c\,a^2+3\,a\,b^2\right)+x^4\,\left(3\,b^2\,c+3\,a\,c^2\right)+a^3+x^3\,\left(b^3+6\,a\,c\,b\right)+c^3\,x^6+3\,b\,c^2\,x^5+3\,a^2\,b\,x}","Not used",1,"(b*atan((((b*x*(b^6 - 140*a^3*c^3 + 70*a^2*b^2*c^2 - 14*a*b^4*c))/(c^3*(4*a*c - b^2)^7) - (b^2*(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5)*(b^6 - 140*a^3*c^3 + 70*a^2*b^2*c^2 - 14*a*b^4*c))/(2*c^7*(4*a*c - b^2)^7*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)))*(128*a^3*c^7*(4*a*c - b^2)^(7/2) - 2*b^6*c^4*(4*a*c - b^2)^(7/2) + 24*a*b^4*c^5*(4*a*c - b^2)^(7/2) - 96*a^2*b^2*c^6*(4*a*c - b^2)^(7/2)))/(b^7 - 140*a^3*b*c^3 + 70*a^2*b^3*c^2 - 14*a*b^5*c))*(b^6 - 140*a^3*c^3 + 70*a^2*b^2*c^2 - 14*a*b^4*c))/(c^4*(4*a*c - b^2)^(7/2)) - (log(a + b*x + c*x^2)*(b^14 - 16384*a^7*c^7 + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 28*a*b^12*c))/(2*(16384*a^7*c^11 - b^14*c^4 + 28*a*b^12*c^5 - 336*a^2*b^10*c^6 + 2240*a^3*b^8*c^7 - 8960*a^4*b^6*c^8 + 21504*a^5*b^4*c^9 - 28672*a^6*b^2*c^10)) - ((x^4*(192*a^4*c^4 - 9*b^8 - 341*a^2*b^4*c^2 + 242*a^3*b^2*c^3 + 100*a*b^6*c))/(2*c^3*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) - (a^3*(11*b^6 - 352*a^3*c^3 + 438*a^2*b^2*c^2 - 124*a*b^4*c))/(6*c^4*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) - (b*x^5*(3*b^6 - 154*a^3*c^3 + 133*a^2*b^2*c^2 - 35*a*b^4*c))/(c^2*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (a*x^2*(288*a^4*c^4 - 11*b^8 - 381*a^2*b^4*c^2 + 152*a^3*b^2*c^3 + 119*a*b^6*c))/(2*c^4*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (b*x^3*(2272*a^4*c^4 - 11*b^8 + 117*a^2*b^4*c^2 - 1698*a^3*b^2*c^3 + 76*a*b^6*c))/(6*c^4*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) - (a^2*b*x*(11*b^6 - 428*a^3*c^3 + 460*a^2*b^2*c^2 - 126*a*b^4*c))/(2*c^4*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)))/(x^2*(3*a*b^2 + 3*a^2*c) + x^4*(3*a*c^2 + 3*b^2*c) + a^3 + x^3*(b^3 + 6*a*b*c) + c^3*x^6 + 3*b*c^2*x^5 + 3*a^2*b*x)","B"
2212,1,656,146,0.983506,"\text{Not used}","int(x^6/(a + b*x + c*x^2)^4,x)","-\frac{\frac{a^3\,\left(66\,a^2\,b\,c^2-13\,a\,b^3\,c+b^5\right)}{3\,c^3\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{x^5\,\left(-44\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}{c\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}-\frac{x^3\,\left(160\,a^4\,c^4-286\,a^3\,b^2\,c^3+12\,a^2\,b^4\,c^2+7\,a\,b^6\,c-b^8\right)}{3\,c^3\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{x^4\,\left(-14\,a^3\,b\,c^3+48\,a^2\,b^3\,c^2-12\,a\,b^5\,c+b^7\right)}{c^2\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{a\,x^2\,\left(16\,a^3\,b\,c^3+53\,a^2\,b^3\,c^2-12\,a\,b^5\,c+b^7\right)}{c^3\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{a^2\,x\,\left(-20\,a^3\,c^3+66\,a^2\,b^2\,c^2-13\,a\,b^4\,c+b^6\right)}{c^3\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}}{x^2\,\left(3\,c\,a^2+3\,a\,b^2\right)+x^4\,\left(3\,b^2\,c+3\,a\,c^2\right)+a^3+x^3\,\left(b^3+6\,a\,c\,b\right)+c^3\,x^6+3\,b\,c^2\,x^5+3\,a^2\,b\,x}-\frac{40\,a^3\,\mathrm{atan}\left(\frac{\left(\frac{20\,a^3\,\left(-64\,a^3\,b\,c^3+48\,a^2\,b^3\,c^2-12\,a\,b^5\,c+b^7\right)}{{\left(4\,a\,c-b^2\right)}^{7/2}\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{40\,a^3\,c\,x}{{\left(4\,a\,c-b^2\right)}^{7/2}}\right)\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}{20\,a^3}\right)}{{\left(4\,a\,c-b^2\right)}^{7/2}}","Not used",1,"- ((a^3*(b^5 + 66*a^2*b*c^2 - 13*a*b^3*c))/(3*c^3*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (x^5*(b^6 - 44*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c))/(c*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) - (x^3*(160*a^4*c^4 - b^8 + 12*a^2*b^4*c^2 - 286*a^3*b^2*c^3 + 7*a*b^6*c))/(3*c^3*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (x^4*(b^7 - 14*a^3*b*c^3 + 48*a^2*b^3*c^2 - 12*a*b^5*c))/(c^2*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (a*x^2*(b^7 + 16*a^3*b*c^3 + 53*a^2*b^3*c^2 - 12*a*b^5*c))/(c^3*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (a^2*x*(b^6 - 20*a^3*c^3 + 66*a^2*b^2*c^2 - 13*a*b^4*c))/(c^3*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)))/(x^2*(3*a*b^2 + 3*a^2*c) + x^4*(3*a*c^2 + 3*b^2*c) + a^3 + x^3*(b^3 + 6*a*b*c) + c^3*x^6 + 3*b*c^2*x^5 + 3*a^2*b*x) - (40*a^3*atan((((20*a^3*(b^7 - 64*a^3*b*c^3 + 48*a^2*b^3*c^2 - 12*a*b^5*c))/((4*a*c - b^2)^(7/2)*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (40*a^3*c*x)/(4*a*c - b^2)^(7/2))*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c))/(20*a^3)))/(4*a*c - b^2)^(7/2)","B"
2213,1,563,145,0.927226,"\text{Not used}","int(x^5/(a + b*x + c*x^2)^4,x)","\frac{\frac{a^3\,\left(64\,a^2\,c^2+18\,a\,b^2\,c-b^4\right)}{6\,c^2\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{x^4\,\left(64\,a^3\,c^3+2\,a^2\,b^2\,c^2+12\,a\,b^4\,c-b^6\right)}{2\,c\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{10\,a^2\,b\,c^2\,x^5}{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}+\frac{a\,x^2\,\left(64\,a^3\,c^3+32\,a^2\,b^2\,c^2+17\,a\,b^4\,c-b^6\right)}{2\,c^2\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{b\,x^3\,\left(224\,a^3\,c^3+62\,a^2\,b^2\,c^2+12\,a\,b^4\,c-b^6\right)}{6\,c^2\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{a^2\,b\,x\,\left(44\,a^2\,c^2+18\,a\,b^2\,c-b^4\right)}{2\,c^2\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}}{x^2\,\left(3\,c\,a^2+3\,a\,b^2\right)+x^4\,\left(3\,b^2\,c+3\,a\,c^2\right)+a^3+x^3\,\left(b^3+6\,a\,c\,b\right)+c^3\,x^6+3\,b\,c^2\,x^5+3\,a^2\,b\,x}+\frac{20\,a^2\,b\,\mathrm{atan}\left(\frac{\left(\frac{10\,a^2\,b^2}{{\left(4\,a\,c-b^2\right)}^{7/2}}+\frac{20\,a^2\,b\,c\,x}{{\left(4\,a\,c-b^2\right)}^{7/2}}\right)\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}{10\,a^2\,b}\right)}{{\left(4\,a\,c-b^2\right)}^{7/2}}","Not used",1,"((a^3*(64*a^2*c^2 - b^4 + 18*a*b^2*c))/(6*c^2*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (x^4*(64*a^3*c^3 - b^6 + 2*a^2*b^2*c^2 + 12*a*b^4*c))/(2*c*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (10*a^2*b*c^2*x^5)/(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c) + (a*x^2*(64*a^3*c^3 - b^6 + 32*a^2*b^2*c^2 + 17*a*b^4*c))/(2*c^2*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (b*x^3*(224*a^3*c^3 - b^6 + 62*a^2*b^2*c^2 + 12*a*b^4*c))/(6*c^2*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (a^2*b*x*(44*a^2*c^2 - b^4 + 18*a*b^2*c))/(2*c^2*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)))/(x^2*(3*a*b^2 + 3*a^2*c) + x^4*(3*a*c^2 + 3*b^2*c) + a^3 + x^3*(b^3 + 6*a*b*c) + c^3*x^6 + 3*b*c^2*x^5 + 3*a^2*b*x) + (20*a^2*b*atan((((10*a^2*b^2)/(4*a*c - b^2)^(7/2) + (20*a^2*b*c*x)/(4*a*c - b^2)^(7/2))*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c))/(10*a^2*b)))/(4*a*c - b^2)^(7/2)","B"
2214,1,1463,259,1.808594,"\text{Not used}","int((d + e*x)^4/(a + b*x + c*x^2)^4,x)","-\frac{\frac{26\,a^4\,b\,c\,e^4-64\,a^4\,c^2\,d\,e^3+a^3\,b^3\,e^4-44\,a^3\,b^2\,c\,d\,e^3+156\,a^3\,b\,c^2\,d^2\,e^2-128\,a^3\,c^3\,d^3\,e+6\,a^2\,b^3\,c\,d^2\,e^2-36\,a^2\,b^2\,c^2\,d^3\,e+66\,a^2\,b\,c^3\,d^4+2\,a\,b^4\,c\,d^3\,e-13\,a\,b^3\,c^2\,d^4+b^5\,c\,d^4}{3\,c\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{x^3\,\left(-32\,a^3\,c^3\,e^4+102\,a^2\,b^2\,c^2\,e^4-192\,a^2\,b\,c^3\,d\,e^3+192\,a^2\,c^4\,d^2\,e^2+10\,a\,b^4\,c\,e^4-164\,a\,b^3\,c^2\,d\,e^3+324\,a\,b^2\,c^3\,d^2\,e^2-320\,a\,b\,c^4\,d^3\,e+160\,a\,c^5\,d^4+b^6\,e^4-22\,b^5\,c\,d\,e^3+132\,b^4\,c^2\,d^2\,e^2-220\,b^3\,c^3\,d^3\,e+110\,b^2\,c^4\,d^4\right)}{3\,c\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{4\,c^2\,x^5\,\left(a^2\,c\,e^4+a\,b^2\,e^4-6\,a\,b\,c\,d\,e^3+6\,a\,c^2\,d^2\,e^2-b^3\,d\,e^3+6\,b^2\,c\,d^2\,e^2-10\,b\,c^2\,d^3\,e+5\,c^3\,d^4\right)}{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}+\frac{x^2\,\left(16\,a^3\,b\,c^2\,e^4-64\,a^3\,c^3\,d\,e^3+17\,a^2\,b^3\,c\,e^4-48\,a^2\,b^2\,c^2\,d\,e^3+96\,a^2\,b\,c^3\,d^2\,e^2+a\,b^5\,e^4-34\,a\,b^4\,c\,d\,e^3+102\,a\,b^3\,c^2\,d^2\,e^2-160\,a\,b^2\,c^3\,d^3\,e+80\,a\,b\,c^4\,d^4+6\,b^5\,c\,d^2\,e^2-10\,b^4\,c^2\,d^3\,e+5\,b^3\,c^3\,d^4\right)}{c\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{x\,\left(-4\,a^4\,c^2\,e^4+22\,a^3\,b^2\,c\,e^4-40\,a^3\,b\,c^2\,d\,e^3-24\,a^3\,c^3\,d^2\,e^2+a^2\,b^4\,e^4-40\,a^2\,b^3\,c\,d\,e^3+132\,a^2\,b^2\,c^2\,d^2\,e^2-88\,a^2\,b\,c^3\,d^3\,e+44\,a^2\,c^4\,d^4+6\,a\,b^4\,c\,d^2\,e^2-36\,a\,b^3\,c^2\,d^3\,e+18\,a\,b^2\,c^3\,d^4+2\,b^5\,c\,d^3\,e-b^4\,c^2\,d^4\right)}{c\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{10\,b\,c\,x^4\,\left(a^2\,c\,e^4+a\,b^2\,e^4-6\,a\,b\,c\,d\,e^3+6\,a\,c^2\,d^2\,e^2-b^3\,d\,e^3+6\,b^2\,c\,d^2\,e^2-10\,b\,c^2\,d^3\,e+5\,c^3\,d^4\right)}{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}}{x^2\,\left(3\,c\,a^2+3\,a\,b^2\right)+x^4\,\left(3\,b^2\,c+3\,a\,c^2\right)+a^3+x^3\,\left(b^3+6\,a\,c\,b\right)+c^3\,x^6+3\,b\,c^2\,x^5+3\,a^2\,b\,x}-\frac{8\,\mathrm{atan}\left(\frac{\left(\frac{4\,\left(c\,d^2-b\,d\,e+a\,e^2\right)\,\left(-64\,a^3\,b\,c^3+48\,a^2\,b^3\,c^2-12\,a\,b^5\,c+b^7\right)\,\left(b^2\,e^2-5\,b\,c\,d\,e+5\,c^2\,d^2+a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{7/2}\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{8\,c\,x\,\left(c\,d^2-b\,d\,e+a\,e^2\right)\,\left(b^2\,e^2-5\,b\,c\,d\,e+5\,c^2\,d^2+a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{7/2}}\right)\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}{4\,a^2\,c\,e^4+4\,a\,b^2\,e^4-24\,a\,b\,c\,d\,e^3+24\,a\,c^2\,d^2\,e^2-4\,b^3\,d\,e^3+24\,b^2\,c\,d^2\,e^2-40\,b\,c^2\,d^3\,e+20\,c^3\,d^4}\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)\,\left(b^2\,e^2-5\,b\,c\,d\,e+5\,c^2\,d^2+a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{7/2}}","Not used",1,"- ((b^5*c*d^4 + a^3*b^3*e^4 - 13*a*b^3*c^2*d^4 + 66*a^2*b*c^3*d^4 - 128*a^3*c^3*d^3*e - 64*a^4*c^2*d*e^3 + 26*a^4*b*c*e^4 + 2*a*b^4*c*d^3*e - 44*a^3*b^2*c*d*e^3 - 36*a^2*b^2*c^2*d^3*e + 6*a^2*b^3*c*d^2*e^2 + 156*a^3*b*c^2*d^2*e^2)/(3*c*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (x^3*(b^6*e^4 + 160*a*c^5*d^4 - 32*a^3*c^3*e^4 + 110*b^2*c^4*d^4 - 220*b^3*c^3*d^3*e + 102*a^2*b^2*c^2*e^4 + 192*a^2*c^4*d^2*e^2 + 132*b^4*c^2*d^2*e^2 + 10*a*b^4*c*e^4 - 22*b^5*c*d*e^3 - 320*a*b*c^4*d^3*e - 164*a*b^3*c^2*d*e^3 - 192*a^2*b*c^3*d*e^3 + 324*a*b^2*c^3*d^2*e^2))/(3*c*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (4*c^2*x^5*(5*c^3*d^4 + a*b^2*e^4 + a^2*c*e^4 - b^3*d*e^3 + 6*a*c^2*d^2*e^2 + 6*b^2*c*d^2*e^2 - 10*b*c^2*d^3*e - 6*a*b*c*d*e^3))/(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c) + (x^2*(a*b^5*e^4 + 5*b^3*c^3*d^4 + 17*a^2*b^3*c*e^4 + 16*a^3*b*c^2*e^4 - 64*a^3*c^3*d*e^3 - 10*b^4*c^2*d^3*e + 6*b^5*c*d^2*e^2 + 80*a*b*c^4*d^4 - 34*a*b^4*c*d*e^3 - 160*a*b^2*c^3*d^3*e + 102*a*b^3*c^2*d^2*e^2 + 96*a^2*b*c^3*d^2*e^2 - 48*a^2*b^2*c^2*d*e^3))/(c*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (x*(a^2*b^4*e^4 + 44*a^2*c^4*d^4 - 4*a^4*c^2*e^4 - b^4*c^2*d^4 + 18*a*b^2*c^3*d^4 + 22*a^3*b^2*c*e^4 - 24*a^3*c^3*d^2*e^2 + 2*b^5*c*d^3*e + 132*a^2*b^2*c^2*d^2*e^2 - 36*a*b^3*c^2*d^3*e + 6*a*b^4*c*d^2*e^2 - 88*a^2*b*c^3*d^3*e - 40*a^2*b^3*c*d*e^3 - 40*a^3*b*c^2*d*e^3))/(c*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (10*b*c*x^4*(5*c^3*d^4 + a*b^2*e^4 + a^2*c*e^4 - b^3*d*e^3 + 6*a*c^2*d^2*e^2 + 6*b^2*c*d^2*e^2 - 10*b*c^2*d^3*e - 6*a*b*c*d*e^3))/(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c))/(x^2*(3*a*b^2 + 3*a^2*c) + x^4*(3*a*c^2 + 3*b^2*c) + a^3 + x^3*(b^3 + 6*a*b*c) + c^3*x^6 + 3*b*c^2*x^5 + 3*a^2*b*x) - (8*atan((((4*(a*e^2 + c*d^2 - b*d*e)*(b^7 - 64*a^3*b*c^3 + 48*a^2*b^3*c^2 - 12*a*b^5*c)*(b^2*e^2 + 5*c^2*d^2 + a*c*e^2 - 5*b*c*d*e))/((4*a*c - b^2)^(7/2)*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (8*c*x*(a*e^2 + c*d^2 - b*d*e)*(b^2*e^2 + 5*c^2*d^2 + a*c*e^2 - 5*b*c*d*e))/(4*a*c - b^2)^(7/2))*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c))/(20*c^3*d^4 + 4*a*b^2*e^4 + 4*a^2*c*e^4 - 4*b^3*d*e^3 + 24*a*c^2*d^2*e^2 + 24*b^2*c*d^2*e^2 - 40*b*c^2*d^3*e - 24*a*b*c*d*e^3))*(a*e^2 + c*d^2 - b*d*e)*(b^2*e^2 + 5*c^2*d^2 + a*c*e^2 - 5*b*c*d*e))/(4*a*c - b^2)^(7/2)","B"
2215,1,1126,306,1.554165,"\text{Not used}","int((d + e*x)^3/(a + b*x + c*x^2)^4,x)","\frac{\frac{x\,\left(20\,a^3\,b\,c\,e^3+24\,a^3\,c^2\,d\,e^2+20\,a^2\,b^3\,e^3-132\,a^2\,b^2\,c\,d\,e^2+132\,a^2\,b\,c^2\,d^2\,e-88\,a^2\,c^3\,d^3-6\,a\,b^4\,d\,e^2+54\,a\,b^3\,c\,d^2\,e-36\,a\,b^2\,c^2\,d^3-3\,b^5\,d^2\,e+2\,b^4\,c\,d^3\right)}{2\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}-\frac{-32\,a^4\,c\,e^3-22\,a^3\,b^2\,e^3+156\,a^3\,b\,c\,d\,e^2-192\,a^3\,c^2\,d^2\,e+6\,a^2\,b^3\,d\,e^2-54\,a^2\,b^2\,c\,d^2\,e+132\,a^2\,b\,c^2\,d^3+3\,a\,b^4\,d^2\,e-26\,a\,b^3\,c\,d^3+2\,b^5\,d^3}{6\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{x^2\,\left(32\,a^3\,c^2\,e^3+24\,a^2\,b^2\,c\,e^3-96\,a^2\,b\,c^2\,d\,e^2+17\,a\,b^4\,e^3-102\,a\,b^3\,c\,d\,e^2+240\,a\,b^2\,c^2\,d^2\,e-160\,a\,b\,c^3\,d^3-6\,b^5\,d\,e^2+15\,b^4\,c\,d^2\,e-10\,b^3\,c^2\,d^3\right)}{2\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{x^3\,\left(11\,b^2+16\,a\,c\right)\,\left(b^3\,e^3-12\,b^2\,c\,d\,e^2+30\,b\,c^2\,d^2\,e+6\,a\,b\,c\,e^3-20\,c^3\,d^3-12\,a\,c^2\,d\,e^2\right)}{6\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{c^2\,x^5\,\left(b^3\,e^3-12\,b^2\,c\,d\,e^2+30\,b\,c^2\,d^2\,e+6\,a\,b\,c\,e^3-20\,c^3\,d^3-12\,a\,c^2\,d\,e^2\right)}{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}+\frac{5\,b\,c\,x^4\,\left(b^3\,e^3-12\,b^2\,c\,d\,e^2+30\,b\,c^2\,d^2\,e+6\,a\,b\,c\,e^3-20\,c^3\,d^3-12\,a\,c^2\,d\,e^2\right)}{2\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}}{x^2\,\left(3\,c\,a^2+3\,a\,b^2\right)+x^4\,\left(3\,b^2\,c+3\,a\,c^2\right)+a^3+x^3\,\left(b^3+6\,a\,c\,b\right)+c^3\,x^6+3\,b\,c^2\,x^5+3\,a^2\,b\,x}+\frac{2\,\mathrm{atan}\left(\frac{\left(\frac{\left(b\,e-2\,c\,d\right)\,\left(-64\,a^3\,b\,c^3+48\,a^2\,b^3\,c^2-12\,a\,b^5\,c+b^7\right)\,\left(b^2\,e^2-10\,b\,c\,d\,e+10\,c^2\,d^2+6\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{7/2}\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{2\,c\,x\,\left(b\,e-2\,c\,d\right)\,\left(b^2\,e^2-10\,b\,c\,d\,e+10\,c^2\,d^2+6\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{7/2}}\right)\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}{b^3\,e^3-12\,b^2\,c\,d\,e^2+30\,b\,c^2\,d^2\,e+6\,a\,b\,c\,e^3-20\,c^3\,d^3-12\,a\,c^2\,d\,e^2}\right)\,\left(b\,e-2\,c\,d\right)\,\left(b^2\,e^2-10\,b\,c\,d\,e+10\,c^2\,d^2+6\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{7/2}}","Not used",1,"((x*(2*b^4*c*d^3 - 3*b^5*d^2*e + 20*a^2*b^3*e^3 - 88*a^2*c^3*d^3 - 36*a*b^2*c^2*d^3 + 24*a^3*c^2*d*e^2 + 20*a^3*b*c*e^3 - 6*a*b^4*d*e^2 + 54*a*b^3*c*d^2*e + 132*a^2*b*c^2*d^2*e - 132*a^2*b^2*c*d*e^2))/(2*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) - (2*b^5*d^3 - 32*a^4*c*e^3 - 22*a^3*b^2*e^3 + 132*a^2*b*c^2*d^3 + 6*a^2*b^3*d*e^2 - 192*a^3*c^2*d^2*e - 26*a*b^3*c*d^3 + 3*a*b^4*d^2*e + 156*a^3*b*c*d*e^2 - 54*a^2*b^2*c*d^2*e)/(6*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (x^2*(17*a*b^4*e^3 - 6*b^5*d*e^2 + 32*a^3*c^2*e^3 - 10*b^3*c^2*d^3 + 24*a^2*b^2*c*e^3 - 160*a*b*c^3*d^3 + 15*b^4*c*d^2*e - 102*a*b^3*c*d*e^2 + 240*a*b^2*c^2*d^2*e - 96*a^2*b*c^2*d*e^2))/(2*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (x^3*(16*a*c + 11*b^2)*(b^3*e^3 - 20*c^3*d^3 + 6*a*b*c*e^3 - 12*a*c^2*d*e^2 + 30*b*c^2*d^2*e - 12*b^2*c*d*e^2))/(6*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (c^2*x^5*(b^3*e^3 - 20*c^3*d^3 + 6*a*b*c*e^3 - 12*a*c^2*d*e^2 + 30*b*c^2*d^2*e - 12*b^2*c*d*e^2))/(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c) + (5*b*c*x^4*(b^3*e^3 - 20*c^3*d^3 + 6*a*b*c*e^3 - 12*a*c^2*d*e^2 + 30*b*c^2*d^2*e - 12*b^2*c*d*e^2))/(2*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)))/(x^2*(3*a*b^2 + 3*a^2*c) + x^4*(3*a*c^2 + 3*b^2*c) + a^3 + x^3*(b^3 + 6*a*b*c) + c^3*x^6 + 3*b*c^2*x^5 + 3*a^2*b*x) + (2*atan(((((b*e - 2*c*d)*(b^7 - 64*a^3*b*c^3 + 48*a^2*b^3*c^2 - 12*a*b^5*c)*(b^2*e^2 + 10*c^2*d^2 + 6*a*c*e^2 - 10*b*c*d*e))/((4*a*c - b^2)^(7/2)*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (2*c*x*(b*e - 2*c*d)*(b^2*e^2 + 10*c^2*d^2 + 6*a*c*e^2 - 10*b*c*d*e))/(4*a*c - b^2)^(7/2))*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c))/(b^3*e^3 - 20*c^3*d^3 + 6*a*b*c*e^3 - 12*a*c^2*d*e^2 + 30*b*c^2*d^2*e - 12*b^2*c*d*e^2))*(b*e - 2*c*d)*(b^2*e^2 + 10*c^2*d^2 + 6*a*c*e^2 - 10*b*c*d*e))/(4*a*c - b^2)^(7/2)","B"
2216,1,872,260,1.371507,"\text{Not used}","int((d + e*x)^2/(a + b*x + c*x^2)^4,x)","-\frac{\frac{26\,a^3\,b\,c\,e^2-64\,a^3\,c^2\,d\,e+a^2\,b^3\,e^2-18\,a^2\,b^2\,c\,d\,e+66\,a^2\,b\,c^2\,d^2+a\,b^4\,d\,e-13\,a\,b^3\,c\,d^2+b^5\,d^2}{3\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{x\,\left(-4\,a^3\,c^2\,e^2+22\,a^2\,b^2\,c\,e^2-44\,a^2\,b\,c^2\,d\,e+44\,a^2\,c^3\,d^2+a\,b^4\,e^2-18\,a\,b^3\,c\,d\,e+18\,a\,b^2\,c^2\,d^2+b^5\,d\,e-b^4\,c\,d^2\right)}{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}+\frac{2\,x^3\,\left(11\,b^2\,c+16\,a\,c^2\right)\,\left(b^2\,e^2-5\,b\,c\,d\,e+5\,c^2\,d^2+a\,c\,e^2\right)}{3\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{x^2\,\left(b^3+16\,a\,c\,b\right)\,\left(b^2\,e^2-5\,b\,c\,d\,e+5\,c^2\,d^2+a\,c\,e^2\right)}{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}+\frac{4\,c^3\,x^5\,\left(b^2\,e^2-5\,b\,c\,d\,e+5\,c^2\,d^2+a\,c\,e^2\right)}{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}+\frac{10\,b\,c^2\,x^4\,\left(b^2\,e^2-5\,b\,c\,d\,e+5\,c^2\,d^2+a\,c\,e^2\right)}{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}}{x^2\,\left(3\,c\,a^2+3\,a\,b^2\right)+x^4\,\left(3\,b^2\,c+3\,a\,c^2\right)+a^3+x^3\,\left(b^3+6\,a\,c\,b\right)+c^3\,x^6+3\,b\,c^2\,x^5+3\,a^2\,b\,x}-\frac{8\,c\,\mathrm{atan}\left(\frac{\left(\frac{8\,c^2\,x\,\left(b^2\,e^2-5\,b\,c\,d\,e+5\,c^2\,d^2+a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{7/2}}+\frac{4\,c\,\left(-64\,a^3\,b\,c^3+48\,a^2\,b^3\,c^2-12\,a\,b^5\,c+b^7\right)\,\left(b^2\,e^2-5\,b\,c\,d\,e+5\,c^2\,d^2+a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{7/2}\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}\right)\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}{4\,b^2\,c\,e^2-20\,b\,c^2\,d\,e+20\,c^3\,d^2+4\,a\,c^2\,e^2}\right)\,\left(b^2\,e^2-5\,b\,c\,d\,e+5\,c^2\,d^2+a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{7/2}}","Not used",1,"- ((b^5*d^2 + a^2*b^3*e^2 + 66*a^2*b*c^2*d^2 + a*b^4*d*e - 13*a*b^3*c*d^2 + 26*a^3*b*c*e^2 - 64*a^3*c^2*d*e - 18*a^2*b^2*c*d*e)/(3*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (x*(a*b^4*e^2 - b^4*c*d^2 + 44*a^2*c^3*d^2 - 4*a^3*c^2*e^2 + b^5*d*e + 18*a*b^2*c^2*d^2 + 22*a^2*b^2*c*e^2 - 44*a^2*b*c^2*d*e - 18*a*b^3*c*d*e))/(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c) + (2*x^3*(16*a*c^2 + 11*b^2*c)*(b^2*e^2 + 5*c^2*d^2 + a*c*e^2 - 5*b*c*d*e))/(3*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (x^2*(b^3 + 16*a*b*c)*(b^2*e^2 + 5*c^2*d^2 + a*c*e^2 - 5*b*c*d*e))/(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c) + (4*c^3*x^5*(b^2*e^2 + 5*c^2*d^2 + a*c*e^2 - 5*b*c*d*e))/(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c) + (10*b*c^2*x^4*(b^2*e^2 + 5*c^2*d^2 + a*c*e^2 - 5*b*c*d*e))/(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c))/(x^2*(3*a*b^2 + 3*a^2*c) + x^4*(3*a*c^2 + 3*b^2*c) + a^3 + x^3*(b^3 + 6*a*b*c) + c^3*x^6 + 3*b*c^2*x^5 + 3*a^2*b*x) - (8*c*atan((((8*c^2*x*(b^2*e^2 + 5*c^2*d^2 + a*c*e^2 - 5*b*c*d*e))/(4*a*c - b^2)^(7/2) + (4*c*(b^7 - 64*a^3*b*c^3 + 48*a^2*b^3*c^2 - 12*a*b^5*c)*(b^2*e^2 + 5*c^2*d^2 + a*c*e^2 - 5*b*c*d*e))/((4*a*c - b^2)^(7/2)*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)))*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c))/(20*c^3*d^2 + 4*a*c^2*e^2 + 4*b^2*c*e^2 - 20*b*c^2*d*e))*(b^2*e^2 + 5*c^2*d^2 + a*c*e^2 - 5*b*c*d*e))/(4*a*c - b^2)^(7/2)","B"
2217,1,633,173,1.138127,"\text{Not used}","int((d + e*x)/(a + b*x + c*x^2)^4,x)","\frac{\frac{10\,c^4\,x^5\,\left(b\,e-2\,c\,d\right)}{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}-\frac{-64\,e\,a^3\,c^2-18\,e\,a^2\,b^2\,c+132\,d\,a^2\,b\,c^2+e\,a\,b^4-26\,d\,a\,b^3\,c+2\,d\,b^5}{6\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{x\,\left(b\,e-2\,c\,d\right)\,\left(44\,a^2\,c^2+18\,a\,b^2\,c-b^4\right)}{2\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{5\,c\,x^3\,\left(11\,b^2\,c+16\,a\,c^2\right)\,\left(b\,e-2\,c\,d\right)}{3\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{5\,c\,x^2\,\left(b^3+16\,a\,c\,b\right)\,\left(b\,e-2\,c\,d\right)}{2\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{25\,b\,c^3\,x^4\,\left(b\,e-2\,c\,d\right)}{-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6}}{x^2\,\left(3\,c\,a^2+3\,a\,b^2\right)+x^4\,\left(3\,b^2\,c+3\,a\,c^2\right)+a^3+x^3\,\left(b^3+6\,a\,c\,b\right)+c^3\,x^6+3\,b\,c^2\,x^5+3\,a^2\,b\,x}-\frac{20\,c^2\,\mathrm{atan}\left(\frac{\left(\frac{20\,c^3\,x\,\left(b\,e-2\,c\,d\right)}{{\left(4\,a\,c-b^2\right)}^{7/2}}+\frac{10\,c^2\,\left(b\,e-2\,c\,d\right)\,\left(-64\,a^3\,b\,c^3+48\,a^2\,b^3\,c^2-12\,a\,b^5\,c+b^7\right)}{{\left(4\,a\,c-b^2\right)}^{7/2}\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}\right)\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}{20\,c^3\,d-10\,b\,c^2\,e}\right)\,\left(b\,e-2\,c\,d\right)}{{\left(4\,a\,c-b^2\right)}^{7/2}}","Not used",1,"((10*c^4*x^5*(b*e - 2*c*d))/(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c) - (2*b^5*d - 64*a^3*c^2*e + a*b^4*e - 26*a*b^3*c*d + 132*a^2*b*c^2*d - 18*a^2*b^2*c*e)/(6*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (x*(b*e - 2*c*d)*(44*a^2*c^2 - b^4 + 18*a*b^2*c))/(2*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (5*c*x^3*(16*a*c^2 + 11*b^2*c)*(b*e - 2*c*d))/(3*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (5*c*x^2*(b^3 + 16*a*b*c)*(b*e - 2*c*d))/(2*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (25*b*c^3*x^4*(b*e - 2*c*d))/(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c))/(x^2*(3*a*b^2 + 3*a^2*c) + x^4*(3*a*c^2 + 3*b^2*c) + a^3 + x^3*(b^3 + 6*a*b*c) + c^3*x^6 + 3*b*c^2*x^5 + 3*a^2*b*x) - (20*c^2*atan((((20*c^3*x*(b*e - 2*c*d))/(4*a*c - b^2)^(7/2) + (10*c^2*(b*e - 2*c*d)*(b^7 - 64*a^3*b*c^3 + 48*a^2*b^3*c^2 - 12*a*b^5*c))/((4*a*c - b^2)^(7/2)*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)))*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c))/(20*c^3*d - 10*b*c^2*e))*(b*e - 2*c*d))/(4*a*c - b^2)^(7/2)","B"
2218,0,-1,136,0.000000,"\text{Not used}","int(1/(a + b*x + c*x^2)^4,x)","\left\{\begin{array}{cl} \frac{20\,\left(\frac{b}{2}+c\,x\right)\,\left(\frac{c^2}{6\,{\left(4\,a\,c-b^2\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^2}+\frac{c^3}{{\left(4\,a\,c-b^2\right)}^3\,\left(c\,x^2+b\,x+a\right)}+\frac{c}{30\,\left(4\,a\,c-b^2\right)\,{\left(c\,x^2+b\,x+a\right)}^3}\right)}{c}-\frac{20\,c^3\,\ln\left(\frac{\frac{b}{2}-\sqrt{\frac{b^2}{4}-a\,c}+c\,x}{\frac{b}{2}+\sqrt{\frac{b^2}{4}-a\,c}+c\,x}\right)}{{\left(b^2-4\,a\,c\right)}^{7/2}} & \text{\ if\ \ }0<b^2-4\,a\,c\\ \frac{20\,\left(\frac{b}{2}+c\,x\right)\,\left(\frac{c^2}{6\,{\left(4\,a\,c-b^2\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^2}+\frac{c^3}{{\left(4\,a\,c-b^2\right)}^3\,\left(c\,x^2+b\,x+a\right)}+\frac{c}{30\,\left(4\,a\,c-b^2\right)\,{\left(c\,x^2+b\,x+a\right)}^3}\right)}{c}+\frac{20\,c^3\,\mathrm{atan}\left(\frac{\frac{b}{2}+c\,x}{\sqrt{a\,c-\frac{b^2}{4}}}\right)}{\sqrt{a\,c-\frac{b^2}{4}}\,{\left(4\,a\,c-b^2\right)}^3} & \text{\ if\ \ }b^2-4\,a\,c<0\\ \int \frac{1}{{\left(c\,x^2+b\,x+a\right)}^4} \,d x & \text{\ if\ \ }b^2-4\,a\,c\notin \mathbb{R}\vee b^2=4\,a\,c \end{array}\right.","Not used",1,"piecewise(0 < - 4*a*c + b^2, - (20*c^3*log((b/2 - (- a*c + b^2/4)^(1/2) + c*x)/(b/2 + (- a*c + b^2/4)^(1/2) + c*x)))/(- 4*a*c + b^2)^(7/2) + (20*(b/2 + c*x)*(c^2/(6*(4*a*c - b^2)^2*(a + b*x + c*x^2)^2) + c^3/((4*a*c - b^2)^3*(a + b*x + c*x^2)) + c/(30*(4*a*c - b^2)*(a + b*x + c*x^2)^3)))/c, - 4*a*c + b^2 < 0, (20*(b/2 + c*x)*(c^2/(6*(4*a*c - b^2)^2*(a + b*x + c*x^2)^2) + c^3/((4*a*c - b^2)^3*(a + b*x + c*x^2)) + c/(30*(4*a*c - b^2)*(a + b*x + c*x^2)^3)))/c + (20*c^3*atan((b/2 + c*x)/(a*c - b^2/4)^(1/2)))/((a*c - b^2/4)^(1/2)*(4*a*c - b^2)^3), ~in(- 4*a*c + b^2, 'real') | b^2 == 4*a*c, int(1/(a + b*x + c*x^2)^4, x))","F"
2219,1,13834,771,33.195914,"\text{Not used}","int(1/((d + e*x)*(a + b*x + c*x^2)^4),x)","\frac{\frac{352\,a^5\,c^3\,e^5-438\,a^4\,b^2\,c^2\,e^5+124\,a^4\,b\,c^3\,d\,e^4+224\,a^4\,c^4\,d^2\,e^3+124\,a^3\,b^4\,c\,e^5+244\,a^3\,b^3\,c^2\,d\,e^4-680\,a^3\,b^2\,c^3\,d^2\,e^3+256\,a^3\,b\,c^4\,d^3\,e^2+64\,a^3\,c^5\,d^4\,e-11\,a^2\,b^6\,e^5-78\,a^2\,b^5\,c\,d\,e^4+69\,a^2\,b^4\,c^2\,d^2\,e^3+266\,a^2\,b^3\,c^3\,d^3\,e^2-378\,a^2\,b^2\,c^4\,d^4\,e+132\,a^2\,b\,c^5\,d^5+7\,a\,b^7\,d\,e^4+11\,a\,b^6\,c\,d^2\,e^3-69\,a\,b^5\,c^2\,d^3\,e^2+77\,a\,b^4\,c^3\,d^4\,e-26\,a\,b^3\,c^4\,d^5-2\,b^8\,d^2\,e^3+6\,b^7\,c\,d^3\,e^2-6\,b^6\,c^2\,d^4\,e+2\,b^5\,c^3\,d^5}{6\,\left(64\,a^6\,c^3\,e^6-48\,a^5\,b^2\,c^2\,e^6-192\,a^5\,b\,c^3\,d\,e^5+192\,a^5\,c^4\,d^2\,e^4+12\,a^4\,b^4\,c\,e^6+144\,a^4\,b^3\,c^2\,d\,e^5+48\,a^4\,b^2\,c^3\,d^2\,e^4-384\,a^4\,b\,c^4\,d^3\,e^3+192\,a^4\,c^5\,d^4\,e^2-a^3\,b^6\,e^6-36\,a^3\,b^5\,c\,d\,e^5-108\,a^3\,b^4\,c^2\,d^2\,e^4+224\,a^3\,b^3\,c^3\,d^3\,e^3+48\,a^3\,b^2\,c^4\,d^4\,e^2-192\,a^3\,b\,c^5\,d^5\,e+64\,a^3\,c^6\,d^6+3\,a^2\,b^7\,d\,e^5+33\,a^2\,b^6\,c\,d^2\,e^4-24\,a^2\,b^5\,c^2\,d^3\,e^3-108\,a^2\,b^4\,c^3\,d^4\,e^2+144\,a^2\,b^3\,c^4\,d^5\,e-48\,a^2\,b^2\,c^5\,d^6-3\,a\,b^8\,d^2\,e^4-6\,a\,b^7\,c\,d^3\,e^3+33\,a\,b^6\,c^2\,d^4\,e^2-36\,a\,b^5\,c^3\,d^5\,e+12\,a\,b^4\,c^4\,d^6+b^9\,d^3\,e^3-3\,b^8\,c\,d^4\,e^2+3\,b^7\,c^2\,d^5\,e-b^6\,c^3\,d^6\right)}+\frac{x^3\,\left(-160\,a^3\,b\,c^4\,e^5+1088\,a^3\,c^5\,d\,e^4-578\,a^2\,b^3\,c^3\,e^5+1092\,a^2\,b^2\,c^4\,d\,e^4-1536\,a^2\,b\,c^5\,d^2\,e^3+1024\,a^2\,c^6\,d^3\,e^2+189\,a\,b^5\,c^2\,e^5+70\,a\,b^4\,c^3\,d\,e^4-1072\,a\,b^3\,c^4\,d^2\,e^3+1248\,a\,b^2\,c^5\,d^3\,e^2-800\,a\,b\,c^6\,d^4\,e+320\,a\,c^7\,d^5-18\,b^7\,c\,e^5-9\,b^6\,c^2\,d\,e^4-11\,b^5\,c^3\,d^2\,e^3+374\,b^4\,c^4\,d^3\,e^2-550\,b^3\,c^5\,d^4\,e+220\,b^2\,c^6\,d^5\right)}{6\,\left(64\,a^6\,c^3\,e^6-48\,a^5\,b^2\,c^2\,e^6-192\,a^5\,b\,c^3\,d\,e^5+192\,a^5\,c^4\,d^2\,e^4+12\,a^4\,b^4\,c\,e^6+144\,a^4\,b^3\,c^2\,d\,e^5+48\,a^4\,b^2\,c^3\,d^2\,e^4-384\,a^4\,b\,c^4\,d^3\,e^3+192\,a^4\,c^5\,d^4\,e^2-a^3\,b^6\,e^6-36\,a^3\,b^5\,c\,d\,e^5-108\,a^3\,b^4\,c^2\,d^2\,e^4+224\,a^3\,b^3\,c^3\,d^3\,e^3+48\,a^3\,b^2\,c^4\,d^4\,e^2-192\,a^3\,b\,c^5\,d^5\,e+64\,a^3\,c^6\,d^6+3\,a^2\,b^7\,d\,e^5+33\,a^2\,b^6\,c\,d^2\,e^4-24\,a^2\,b^5\,c^2\,d^3\,e^3-108\,a^2\,b^4\,c^3\,d^4\,e^2+144\,a^2\,b^3\,c^4\,d^5\,e-48\,a^2\,b^2\,c^5\,d^6-3\,a\,b^8\,d^2\,e^4-6\,a\,b^7\,c\,d^3\,e^3+33\,a\,b^6\,c^2\,d^4\,e^2-36\,a\,b^5\,c^3\,d^5\,e+12\,a\,b^4\,c^4\,d^6+b^9\,d^3\,e^3-3\,b^8\,c\,d^4\,e^2+3\,b^7\,c^2\,d^5\,e-b^6\,c^3\,d^6\right)}+\frac{x^2\,\left(160\,a^4\,c^4\,e^5-328\,a^3\,b^2\,c^3\,e^5+512\,a^3\,b\,c^4\,d\,e^4+32\,a^3\,c^5\,d^2\,e^3+27\,a^2\,b^4\,c^2\,e^5+190\,a^2\,b^3\,c^3\,d\,e^4-792\,a^2\,b^2\,c^4\,d^2\,e^3+512\,a^2\,b\,c^5\,d^3\,e^2+13\,a\,b^6\,c\,e^5-21\,a\,b^5\,c^2\,d\,e^4-50\,a\,b^4\,c^3\,d^2\,e^3+304\,a\,b^3\,c^4\,d^3\,e^2-400\,a\,b^2\,c^5\,d^4\,e+160\,a\,b\,c^6\,d^5-2\,b^8\,e^5+b^7\,c\,d\,e^4-b^6\,c^2\,d^2\,e^3+17\,b^5\,c^3\,d^3\,e^2-25\,b^4\,c^4\,d^4\,e+10\,b^3\,c^5\,d^5\right)}{2\,\left(64\,a^6\,c^3\,e^6-48\,a^5\,b^2\,c^2\,e^6-192\,a^5\,b\,c^3\,d\,e^5+192\,a^5\,c^4\,d^2\,e^4+12\,a^4\,b^4\,c\,e^6+144\,a^4\,b^3\,c^2\,d\,e^5+48\,a^4\,b^2\,c^3\,d^2\,e^4-384\,a^4\,b\,c^4\,d^3\,e^3+192\,a^4\,c^5\,d^4\,e^2-a^3\,b^6\,e^6-36\,a^3\,b^5\,c\,d\,e^5-108\,a^3\,b^4\,c^2\,d^2\,e^4+224\,a^3\,b^3\,c^3\,d^3\,e^3+48\,a^3\,b^2\,c^4\,d^4\,e^2-192\,a^3\,b\,c^5\,d^5\,e+64\,a^3\,c^6\,d^6+3\,a^2\,b^7\,d\,e^5+33\,a^2\,b^6\,c\,d^2\,e^4-24\,a^2\,b^5\,c^2\,d^3\,e^3-108\,a^2\,b^4\,c^3\,d^4\,e^2+144\,a^2\,b^3\,c^4\,d^5\,e-48\,a^2\,b^2\,c^5\,d^6-3\,a\,b^8\,d^2\,e^4-6\,a\,b^7\,c\,d^3\,e^3+33\,a\,b^6\,c^2\,d^4\,e^2-36\,a\,b^5\,c^3\,d^5\,e+12\,a\,b^4\,c^4\,d^6+b^9\,d^3\,e^3-3\,b^8\,c\,d^4\,e^2+3\,b^7\,c^2\,d^5\,e-b^6\,c^3\,d^6\right)}+\frac{x^4\,\left(64\,a^3\,c^5\,e^5-238\,a^2\,b^2\,c^4\,e^5+380\,a^2\,b\,c^5\,d\,e^4+67\,a\,b^4\,c^3\,e^5+50\,a\,b^3\,c^4\,d\,e^4-480\,a\,b^2\,c^5\,d^2\,e^3+320\,a\,b\,c^6\,d^3\,e^2-6\,b^6\,c^2\,e^5-5\,b^5\,c^3\,d\,e^4-5\,b^4\,c^4\,d^2\,e^3+170\,b^3\,c^5\,d^3\,e^2-250\,b^2\,c^6\,d^4\,e+100\,b\,c^7\,d^5\right)}{2\,\left(64\,a^6\,c^3\,e^6-48\,a^5\,b^2\,c^2\,e^6-192\,a^5\,b\,c^3\,d\,e^5+192\,a^5\,c^4\,d^2\,e^4+12\,a^4\,b^4\,c\,e^6+144\,a^4\,b^3\,c^2\,d\,e^5+48\,a^4\,b^2\,c^3\,d^2\,e^4-384\,a^4\,b\,c^4\,d^3\,e^3+192\,a^4\,c^5\,d^4\,e^2-a^3\,b^6\,e^6-36\,a^3\,b^5\,c\,d\,e^5-108\,a^3\,b^4\,c^2\,d^2\,e^4+224\,a^3\,b^3\,c^3\,d^3\,e^3+48\,a^3\,b^2\,c^4\,d^4\,e^2-192\,a^3\,b\,c^5\,d^5\,e+64\,a^3\,c^6\,d^6+3\,a^2\,b^7\,d\,e^5+33\,a^2\,b^6\,c\,d^2\,e^4-24\,a^2\,b^5\,c^2\,d^3\,e^3-108\,a^2\,b^4\,c^3\,d^4\,e^2+144\,a^2\,b^3\,c^4\,d^5\,e-48\,a^2\,b^2\,c^5\,d^6-3\,a\,b^8\,d^2\,e^4-6\,a\,b^7\,c\,d^3\,e^3+33\,a\,b^6\,c^2\,d^4\,e^2-36\,a\,b^5\,c^3\,d^5\,e+12\,a\,b^4\,c^4\,d^6+b^9\,d^3\,e^3-3\,b^8\,c\,d^4\,e^2+3\,b^7\,c^2\,d^5\,e-b^6\,c^3\,d^6\right)}+\frac{x^5\,\left(-38\,a^2\,b\,c^5\,e^5+76\,a^2\,c^6\,d\,e^4+11\,a\,b^3\,c^4\,e^5+10\,a\,b^2\,c^5\,d\,e^4-96\,a\,b\,c^6\,d^2\,e^3+64\,a\,c^7\,d^3\,e^2-b^5\,c^3\,e^5-b^4\,c^4\,d\,e^4-b^3\,c^5\,d^2\,e^3+34\,b^2\,c^6\,d^3\,e^2-50\,b\,c^7\,d^4\,e+20\,c^8\,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1}\,c^2\,d\,e^7-12096\,a^5\,b^{10}\,c^3\,d^2\,e^6-8960\,a^5\,b^9\,c^4\,d^3\,e^5+72576\,a^5\,b^8\,c^5\,d^4\,e^4-21504\,a^5\,b^7\,c^6\,d^5\,e^3-93184\,a^5\,b^6\,c^7\,d^6\,e^2+86016\,a^5\,b^5\,c^8\,d^7\,e-21504\,a^5\,b^4\,c^9\,d^8+a^4\,b^{14}\,e^8+112\,a^4\,b^{13}\,c\,d\,e^7+1904\,a^4\,b^{12}\,c^2\,d^2\,e^6+4928\,a^4\,b^{11}\,c^3\,d^3\,e^5-15904\,a^4\,b^{10}\,c^4\,d^4\,e^4-8960\,a^4\,b^9\,c^5\,d^5\,e^3+44800\,a^4\,b^8\,c^6\,d^6\,e^2-35840\,a^4\,b^7\,c^7\,d^7\,e+8960\,a^4\,b^6\,c^8\,d^8-4\,a^3\,b^{15}\,d\,e^7-164\,a^3\,b^{14}\,c\,d^2\,e^6-1008\,a^3\,b^{13}\,c^2\,d^3\,e^5+1624\,a^3\,b^{12}\,c^3\,d^4\,e^4+4928\,a^3\,b^{11}\,c^4\,d^5\,e^3-12096\,a^3\,b^{10}\,c^5\,d^6\,e^2+8960\,a^3\,b^9\,c^6\,d^7\,e-2240\,a^3\,b^8\,c^7\,d^8+6\,a^2\,b^{16}\,d^2\,e^6+100\,a^2\,b^{15}\,c\,d^3\,e^5+6\,a^2\,b^{14}\,c^2\,d^4\,e^4-1008\,a^2\,b^{13}\,c^3\,d^5\,e^3+1904\,a^2\,b^{12}\,c^4\,d^6\,e^2-1344\,a^2\,b^{11}\,c^5\,d^7\,e+336\,a^2\,b^{10}\,c^6\,d^8-4\,a\,b^{17}\,d^3\,e^5-16\,a\,b^{16}\,c\,d^4\,e^4+100\,a\,b^{15}\,c^2\,d^5\,e^3-164\,a\,b^{14}\,c^3\,d^6\,e^2+112\,a\,b^{13}\,c^4\,d^7\,e-28\,a\,b^{12}\,c^5\,d^8+b^{18}\,d^4\,e^4-4\,b^{17}\,c\,d^5\,e^3+6\,b^{16}\,c^2\,d^6\,e^2-4\,b^{15}\,c^3\,d^7\,e+b^{14}\,c^4\,d^8}+\frac{e^7\,\ln\left(d+e\,x\right)}{a^4\,e^8-4\,a^3\,b\,d\,e^7+4\,a^3\,c\,d^2\,e^6+6\,a^2\,b^2\,d^2\,e^6-12\,a^2\,b\,c\,d^3\,e^5+6\,a^2\,c^2\,d^4\,e^4-4\,a\,b^3\,d^3\,e^5+12\,a\,b^2\,c\,d^4\,e^4-12\,a\,b\,c^2\,d^5\,e^3+4\,a\,c^3\,d^6\,e^2+b^4\,d^4\,e^4-4\,b^3\,c\,d^5\,e^3+6\,b^2\,c^2\,d^6\,e^2-4\,b\,c^3\,d^7\,e+c^4\,d^8}","Not used",1,"((352*a^5*c^3*e^5 - 11*a^2*b^6*e^5 + 2*b^5*c^3*d^5 - 2*b^8*d^2*e^3 - 26*a*b^3*c^4*d^5 + 132*a^2*b*c^5*d^5 + 124*a^3*b^4*c*e^5 + 64*a^3*c^5*d^4*e - 6*b^6*c^2*d^4*e + 6*b^7*c*d^3*e^2 - 438*a^4*b^2*c^2*e^5 + 224*a^4*c^4*d^2*e^3 + 7*a*b^7*d*e^4 + 266*a^2*b^3*c^3*d^3*e^2 + 69*a^2*b^4*c^2*d^2*e^3 - 680*a^3*b^2*c^3*d^2*e^3 + 77*a*b^4*c^3*d^4*e + 11*a*b^6*c*d^2*e^3 - 78*a^2*b^5*c*d*e^4 + 124*a^4*b*c^3*d*e^4 - 69*a*b^5*c^2*d^3*e^2 - 378*a^2*b^2*c^4*d^4*e + 256*a^3*b*c^4*d^3*e^2 + 244*a^3*b^3*c^2*d*e^4)/(6*(64*a^3*c^6*d^6 - a^3*b^6*e^6 + 64*a^6*c^3*e^6 - b^6*c^3*d^6 + b^9*d^3*e^3 + 12*a*b^4*c^4*d^6 + 12*a^4*b^4*c*e^6 - 3*a*b^8*d^2*e^4 + 3*a^2*b^7*d*e^5 + 3*b^7*c^2*d^5*e - 3*b^8*c*d^4*e^2 - 48*a^2*b^2*c^5*d^6 - 48*a^5*b^2*c^2*e^6 + 192*a^4*c^5*d^4*e^2 + 192*a^5*c^4*d^2*e^4 - 108*a^2*b^4*c^3*d^4*e^2 - 24*a^2*b^5*c^2*d^3*e^3 + 48*a^3*b^2*c^4*d^4*e^2 + 224*a^3*b^3*c^3*d^3*e^3 - 108*a^3*b^4*c^2*d^2*e^4 + 48*a^4*b^2*c^3*d^2*e^4 - 36*a*b^5*c^3*d^5*e - 6*a*b^7*c*d^3*e^3 - 192*a^3*b*c^5*d^5*e - 36*a^3*b^5*c*d*e^5 - 192*a^5*b*c^3*d*e^5 + 33*a*b^6*c^2*d^4*e^2 + 144*a^2*b^3*c^4*d^5*e + 33*a^2*b^6*c*d^2*e^4 - 384*a^4*b*c^4*d^3*e^3 + 144*a^4*b^3*c^2*d*e^5)) + (x^3*(320*a*c^7*d^5 - 18*b^7*c*e^5 + 220*b^2*c^6*d^5 + 189*a*b^5*c^2*e^5 - 160*a^3*b*c^4*e^5 + 1088*a^3*c^5*d*e^4 - 550*b^3*c^5*d^4*e - 9*b^6*c^2*d*e^4 - 578*a^2*b^3*c^3*e^5 + 1024*a^2*c^6*d^3*e^2 + 374*b^4*c^4*d^3*e^2 - 11*b^5*c^3*d^2*e^3 - 800*a*b*c^6*d^4*e + 70*a*b^4*c^3*d*e^4 + 1248*a*b^2*c^5*d^3*e^2 - 1072*a*b^3*c^4*d^2*e^3 - 1536*a^2*b*c^5*d^2*e^3 + 1092*a^2*b^2*c^4*d*e^4))/(6*(64*a^3*c^6*d^6 - a^3*b^6*e^6 + 64*a^6*c^3*e^6 - b^6*c^3*d^6 + b^9*d^3*e^3 + 12*a*b^4*c^4*d^6 + 12*a^4*b^4*c*e^6 - 3*a*b^8*d^2*e^4 + 3*a^2*b^7*d*e^5 + 3*b^7*c^2*d^5*e - 3*b^8*c*d^4*e^2 - 48*a^2*b^2*c^5*d^6 - 48*a^5*b^2*c^2*e^6 + 192*a^4*c^5*d^4*e^2 + 192*a^5*c^4*d^2*e^4 - 108*a^2*b^4*c^3*d^4*e^2 - 24*a^2*b^5*c^2*d^3*e^3 + 48*a^3*b^2*c^4*d^4*e^2 + 224*a^3*b^3*c^3*d^3*e^3 - 108*a^3*b^4*c^2*d^2*e^4 + 48*a^4*b^2*c^3*d^2*e^4 - 36*a*b^5*c^3*d^5*e - 6*a*b^7*c*d^3*e^3 - 192*a^3*b*c^5*d^5*e - 36*a^3*b^5*c*d*e^5 - 192*a^5*b*c^3*d*e^5 + 33*a*b^6*c^2*d^4*e^2 + 144*a^2*b^3*c^4*d^5*e + 33*a^2*b^6*c*d^2*e^4 - 384*a^4*b*c^4*d^3*e^3 + 144*a^4*b^3*c^2*d*e^5)) + (x^2*(160*a^4*c^4*e^5 - 2*b^8*e^5 + 10*b^3*c^5*d^5 - 25*b^4*c^4*d^4*e + 27*a^2*b^4*c^2*e^5 - 328*a^3*b^2*c^3*e^5 + 32*a^3*c^5*d^2*e^3 + 17*b^5*c^3*d^3*e^2 - b^6*c^2*d^2*e^3 + 160*a*b*c^6*d^5 + 13*a*b^6*c*e^5 + b^7*c*d*e^4 - 792*a^2*b^2*c^4*d^2*e^3 - 400*a*b^2*c^5*d^4*e - 21*a*b^5*c^2*d*e^4 + 512*a^3*b*c^4*d*e^4 + 304*a*b^3*c^4*d^3*e^2 - 50*a*b^4*c^3*d^2*e^3 + 512*a^2*b*c^5*d^3*e^2 + 190*a^2*b^3*c^3*d*e^4))/(2*(64*a^3*c^6*d^6 - a^3*b^6*e^6 + 64*a^6*c^3*e^6 - b^6*c^3*d^6 + b^9*d^3*e^3 + 12*a*b^4*c^4*d^6 + 12*a^4*b^4*c*e^6 - 3*a*b^8*d^2*e^4 + 3*a^2*b^7*d*e^5 + 3*b^7*c^2*d^5*e - 3*b^8*c*d^4*e^2 - 48*a^2*b^2*c^5*d^6 - 48*a^5*b^2*c^2*e^6 + 192*a^4*c^5*d^4*e^2 + 192*a^5*c^4*d^2*e^4 - 108*a^2*b^4*c^3*d^4*e^2 - 24*a^2*b^5*c^2*d^3*e^3 + 48*a^3*b^2*c^4*d^4*e^2 + 224*a^3*b^3*c^3*d^3*e^3 - 108*a^3*b^4*c^2*d^2*e^4 + 48*a^4*b^2*c^3*d^2*e^4 - 36*a*b^5*c^3*d^5*e - 6*a*b^7*c*d^3*e^3 - 192*a^3*b*c^5*d^5*e - 36*a^3*b^5*c*d*e^5 - 192*a^5*b*c^3*d*e^5 + 33*a*b^6*c^2*d^4*e^2 + 144*a^2*b^3*c^4*d^5*e + 33*a^2*b^6*c*d^2*e^4 - 384*a^4*b*c^4*d^3*e^3 + 144*a^4*b^3*c^2*d*e^5)) + (x^4*(100*b*c^7*d^5 + 64*a^3*c^5*e^5 - 6*b^6*c^2*e^5 + 67*a*b^4*c^3*e^5 - 250*b^2*c^6*d^4*e - 5*b^5*c^3*d*e^4 - 238*a^2*b^2*c^4*e^5 + 170*b^3*c^5*d^3*e^2 - 5*b^4*c^4*d^2*e^3 + 320*a*b*c^6*d^3*e^2 + 50*a*b^3*c^4*d*e^4 + 380*a^2*b*c^5*d*e^4 - 480*a*b^2*c^5*d^2*e^3))/(2*(64*a^3*c^6*d^6 - a^3*b^6*e^6 + 64*a^6*c^3*e^6 - b^6*c^3*d^6 + b^9*d^3*e^3 + 12*a*b^4*c^4*d^6 + 12*a^4*b^4*c*e^6 - 3*a*b^8*d^2*e^4 + 3*a^2*b^7*d*e^5 + 3*b^7*c^2*d^5*e - 3*b^8*c*d^4*e^2 - 48*a^2*b^2*c^5*d^6 - 48*a^5*b^2*c^2*e^6 + 192*a^4*c^5*d^4*e^2 + 192*a^5*c^4*d^2*e^4 - 108*a^2*b^4*c^3*d^4*e^2 - 24*a^2*b^5*c^2*d^3*e^3 + 48*a^3*b^2*c^4*d^4*e^2 + 224*a^3*b^3*c^3*d^3*e^3 - 108*a^3*b^4*c^2*d^2*e^4 + 48*a^4*b^2*c^3*d^2*e^4 - 36*a*b^5*c^3*d^5*e - 6*a*b^7*c*d^3*e^3 - 192*a^3*b*c^5*d^5*e - 36*a^3*b^5*c*d*e^5 - 192*a^5*b*c^3*d*e^5 + 33*a*b^6*c^2*d^4*e^2 + 144*a^2*b^3*c^4*d^5*e + 33*a^2*b^6*c*d^2*e^4 - 384*a^4*b*c^4*d^3*e^3 + 144*a^4*b^3*c^2*d*e^5)) + (x^5*(20*c^8*d^5 - b^5*c^3*e^5 + 11*a*b^3*c^4*e^5 - 38*a^2*b*c^5*e^5 + 64*a*c^7*d^3*e^2 + 76*a^2*c^6*d*e^4 - b^4*c^4*d*e^4 + 34*b^2*c^6*d^3*e^2 - b^3*c^5*d^2*e^3 - 50*b*c^7*d^4*e - 96*a*b*c^6*d^2*e^3 + 10*a*b^2*c^5*d*e^4))/(64*a^3*c^6*d^6 - a^3*b^6*e^6 + 64*a^6*c^3*e^6 - b^6*c^3*d^6 + b^9*d^3*e^3 + 12*a*b^4*c^4*d^6 + 12*a^4*b^4*c*e^6 - 3*a*b^8*d^2*e^4 + 3*a^2*b^7*d*e^5 + 3*b^7*c^2*d^5*e - 3*b^8*c*d^4*e^2 - 48*a^2*b^2*c^5*d^6 - 48*a^5*b^2*c^2*e^6 + 192*a^4*c^5*d^4*e^2 + 192*a^5*c^4*d^2*e^4 - 108*a^2*b^4*c^3*d^4*e^2 - 24*a^2*b^5*c^2*d^3*e^3 + 48*a^3*b^2*c^4*d^4*e^2 + 224*a^3*b^3*c^3*d^3*e^3 - 108*a^3*b^4*c^2*d^2*e^4 + 48*a^4*b^2*c^3*d^2*e^4 - 36*a*b^5*c^3*d^5*e - 6*a*b^7*c*d^3*e^3 - 192*a^3*b*c^5*d^5*e - 36*a^3*b^5*c*d*e^5 - 192*a^5*b*c^3*d*e^5 + 33*a*b^6*c^2*d^4*e^2 + 144*a^2*b^3*c^4*d^5*e + 33*a^2*b^6*c*d^2*e^4 - 384*a^4*b*c^4*d^3*e^3 + 144*a^4*b^3*c^2*d*e^5) + (x*(b^8*d*e^4 - 5*a*b^7*e^5 + 88*a^2*c^6*d^5 - 2*b^4*c^4*d^5 + 36*a*b^2*c^5*d^5 + 54*a^2*b^5*c*e^5 + 44*a^4*b*c^3*e^5 + 232*a^4*c^4*d*e^4 + 5*b^5*c^3*d^4*e - b^7*c*d^2*e^3 - 172*a^3*b^3*c^2*e^5 + 256*a^3*c^5*d^3*e^2 - 3*b^6*c^2*d^3*e^2 - 12*a*b^6*c*d*e^4 + 284*a^2*b^2*c^4*d^3*e^2 - 230*a^2*b^3*c^3*d^2*e^3 - 90*a*b^3*c^4*d^4*e - 220*a^2*b*c^5*d^4*e + 50*a*b^4*c^3*d^3*e^2 + 21*a*b^5*c^2*d^2*e^3 + 30*a^2*b^4*c^2*d*e^4 - 352*a^3*b*c^4*d^2*e^3 + 200*a^3*b^2*c^3*d*e^4))/(2*(64*a^3*c^6*d^6 - a^3*b^6*e^6 + 64*a^6*c^3*e^6 - b^6*c^3*d^6 + b^9*d^3*e^3 + 12*a*b^4*c^4*d^6 + 12*a^4*b^4*c*e^6 - 3*a*b^8*d^2*e^4 + 3*a^2*b^7*d*e^5 + 3*b^7*c^2*d^5*e - 3*b^8*c*d^4*e^2 - 48*a^2*b^2*c^5*d^6 - 48*a^5*b^2*c^2*e^6 + 192*a^4*c^5*d^4*e^2 + 192*a^5*c^4*d^2*e^4 - 108*a^2*b^4*c^3*d^4*e^2 - 24*a^2*b^5*c^2*d^3*e^3 + 48*a^3*b^2*c^4*d^4*e^2 + 224*a^3*b^3*c^3*d^3*e^3 - 108*a^3*b^4*c^2*d^2*e^4 + 48*a^4*b^2*c^3*d^2*e^4 - 36*a*b^5*c^3*d^5*e - 6*a*b^7*c*d^3*e^3 - 192*a^3*b*c^5*d^5*e - 36*a^3*b^5*c*d*e^5 - 192*a^5*b*c^3*d*e^5 + 33*a*b^6*c^2*d^4*e^2 + 144*a^2*b^3*c^4*d^5*e + 33*a^2*b^6*c*d^2*e^4 - 384*a^4*b*c^4*d^3*e^3 + 144*a^4*b^3*c^2*d*e^5)))/(x^2*(3*a*b^2 + 3*a^2*c) + x^4*(3*a*c^2 + 3*b^2*c) + a^3 + x^3*(b^3 + 6*a*b*c) + c^3*x^6 + 3*b*c^2*x^5 + 3*a^2*b*x) - (log(24576*a^8*c^7*e^9 - 2*b^15*e^9*x - 2*a*b^14*e^9 - 20*b^7*c^8*d^9 + 20*c^8*d^9*(-(4*a*c - b^2)^7)^(1/2) + 240*a*b^5*c^9*d^9 + 1280*a^3*b*c^11*d^9 - 2*a*b^7*e^9*(-(4*a*c - b^2)^7)^(1/2) + 55*a^2*b^12*c*e^9 - 5120*a^4*c^11*d^8*e + 70*b^8*c^7*d^8*e + b^14*c*d^2*e^7 + 2560*a^3*c^12*d^9*x - 40*b^6*c^9*d^9*x - 2*b^8*e^9*x*(-(4*a*c - b^2)^7)^(1/2) - 960*a^2*b^3*c^10*d^9 - 647*a^3*b^10*c^2*e^9 + 4218*a^4*b^8*c^3*e^9 - 16408*a^5*b^6*c^4*e^9 + 37856*a^6*b^4*c^5*e^9 - 47488*a^7*b^2*c^6*e^9 - 21504*a^5*c^10*d^6*e^3 - 35840*a^6*c^9*d^4*e^5 - 60416*a^7*c^8*d^2*e^7 - 84*b^9*c^6*d^7*e^2 + 35*b^10*c^5*d^6*e^3 + 2*a*b^13*c*d*e^8 + 56*a*b^13*c*e^9*x + 4*b^14*c*d*e^8*x - 107*a^3*b^3*c^2*e^9*(-(4*a*c - b^2)^7)^(1/2) + 576*a^2*b^5*c^8*d^7*e^2 - 5376*a^2*b^6*c^7*d^6*e^3 + 3304*a^2*b^7*c^6*d^5*e^4 + 560*a^2*b^8*c^5*d^4*e^5 - 140*a^2*b^9*c^4*d^3*e^6 + 361*a^2*b^10*c^3*d^2*e^7 - 13056*a^3*b^3*c^9*d^7*e^2 + 23296*a^3*b^4*c^8*d^6*e^3 - 4704*a^3*b^5*c^7*d^5*e^4 - 9520*a^3*b^6*c^6*d^4*e^5 + 560*a^3*b^7*c^5*d^3*e^6 - 2292*a^3*b^8*c^4*d^2*e^7 - 23296*a^4*b^2*c^9*d^6*e^3 - 27776*a^4*b^3*c^8*d^5*e^4 + 38080*a^4*b^4*c^7*d^4*e^5 + 6720*a^4*b^5*c^6*d^3*e^6 + 8512*a^4*b^6*c^5*d^2*e^7 - 35840*a^5*b^2*c^8*d^4*e^5 - 44800*a^5*b^3*c^7*d^3*e^6 - 23296*a^5*b^4*c^6*d^2*e^7 + 51968*a^6*b^2*c^7*d^2*e^7 + 56*a^2*c^6*d^5*e^4*(-(4*a*c - b^2)^7)^(1/2) + 84*b^2*c^6*d^7*e^2*(-(4*a*c - b^2)^7)^(1/2) - 35*b^3*c^5*d^6*e^3*(-(4*a*c - b^2)^7)^(1/2) - 760*a*b^6*c^8*d^8*e + 26880*a^7*b*c^7*d*e^8 - 70*b*c^7*d^8*e*(-(4*a*c - b^2)^7)^(1/2) + 480*a*b^4*c^10*d^9*x + 33536*a^7*b*c^7*e^9*x - 67072*a^7*c^8*d*e^8*x + 180*b^7*c^8*d^8*e*x + 40*c^8*d^8*e*x*(-(4*a*c - b^2)^7)^(1/2) + 25*a^2*b^5*c*e^9*(-(4*a*c - b^2)^7)^(1/2) + 166*a^4*b*c^3*e^9*(-(4*a*c - b^2)^7)^(1/2) + 624*a*b^7*c^7*d^7*e^2 + 196*a*b^8*c^6*d^6*e^3 - 364*a*b^9*c^5*d^5*e^4 + 35*a*b^10*c^4*d^4*e^5 - 29*a*b^12*c^2*d^2*e^7 + 2400*a^2*b^4*c^9*d^8*e - 52*a^2*b^11*c^2*d*e^8 - 640*a^3*b^2*c^10*d^8*e + 572*a^3*b^9*c^3*d*e^8 + 24576*a^4*b*c^10*d^7*e^2 - 3572*a^4*b^7*c^4*d*e^8 + 68096*a^5*b*c^9*d^5*e^4 + 13552*a^5*b^5*c^5*d*e^8 + 71680*a^6*b*c^8*d^3*e^6 - 29120*a^6*b^3*c^6*d*e^8 + 64*a*c^7*d^7*e^2*(-(4*a*c - b^2)^7)^(1/2) - 524*a^4*c^4*d*e^8*(-(4*a*c - b^2)^7)^(1/2) - b^7*c*d^2*e^7*(-(4*a*c - b^2)^7)^(1/2) - 1920*a^2*b^2*c^11*d^9*x - 673*a^2*b^11*c^2*e^9*x + 4504*a^3*b^9*c^3*e^9*x - 18124*a^4*b^7*c^4*e^9*x + 43792*a^5*b^5*c^5*e^9*x - 58688*a^6*b^3*c^6*e^9*x - 192*a^4*c^4*e^9*x*(-(4*a*c - b^2)^7)^(1/2) + 8192*a^4*c^11*d^7*e^2*x + 7168*a^5*c^10*d^5*e^4*x - 328*b^8*c^7*d^7*e^2*x + 308*b^9*c^6*d^6*e^3*x - 154*b^10*c^5*d^5*e^4*x + 35*b^11*c^4*d^4*e^5*x - b^13*c^2*d^2*e^7*x - 140*a*b*c^6*d^6*e^3*(-(4*a*c - b^2)^7)^(1/2) + 3808*a*b^6*c^8*d^7*e^2*x - 3248*a*b^7*c^7*d^6*e^3*x + 1232*a*b^8*c^6*d^5*e^4*x - 140*a*b^10*c^4*d^3*e^6*x + 26*a*b^11*c^3*d^2*e^7*x + 8640*a^2*b^3*c^10*d^8*e*x + 1294*a^2*b^10*c^3*d*e^8*x - 8576*a^3*b^8*c^4*d*e^8*x - 28672*a^4*b*c^10*d^6*e^3*x + 34776*a^4*b^6*c^5*d*e^8*x - 17920*a^5*b*c^9*d^4*e^5*x - 85792*a^5*b^4*c^6*d*e^8*x + 117376*a^6*b^2*c^7*d*e^8*x + 168*a*c^7*d^6*e^3*x*(-(4*a*c - b^2)^7)^(1/2) - 160*b*c^7*d^7*e^2*x*(-(4*a*c - b^2)^7)^(1/2) + 56*a*b^2*c^5*d^5*e^4*(-(4*a*c - b^2)^7)^(1/2) + 35*a*b^3*c^4*d^4*e^5*(-(4*a*c - b^2)^7)^(1/2) + 11*a*b^5*c^2*d^2*e^7*(-(4*a*c - b^2)^7)^(1/2) - 72*a^2*b^4*c^2*d*e^8*(-(4*a*c - b^2)^7)^(1/2) + 236*a^3*b*c^4*d^2*e^7*(-(4*a*c - b^2)^7)^(1/2) + 288*a^3*b^2*c^3*d*e^8*(-(4*a*c - b^2)^7)^(1/2) - 143*a^2*b^4*c^2*e^9*x*(-(4*a*c - b^2)^7)^(1/2) + 310*a^3*b^2*c^3*e^9*x*(-(4*a*c - b^2)^7)^(1/2) - 14208*a^2*b^4*c^9*d^7*e^2*x + 9408*a^2*b^5*c^8*d^6*e^3*x - 112*a^2*b^6*c^7*d^5*e^4*x - 3080*a^2*b^7*c^6*d^4*e^5*x + 1400*a^2*b^8*c^5*d^3*e^6*x - 76*a^2*b^9*c^4*d^2*e^7*x + 14848*a^3*b^2*c^10*d^7*e^2*x + 1792*a^3*b^3*c^9*d^6*e^3*x - 18368*a^3*b^4*c^8*d^5*e^4*x + 14560*a^3*b^5*c^7*d^4*e^5*x - 3360*a^3*b^6*c^6*d^3*e^6*x - 944*a^3*b^7*c^5*d^2*e^7*x + 34048*a^4*b^2*c^9*d^5*e^4*x - 13440*a^4*b^3*c^8*d^4*e^5*x - 4480*a^4*b^4*c^7*d^3*e^6*x + 5824*a^4*b^5*c^6*d^2*e^7*x + 17920*a^5*b^2*c^8*d^3*e^6*x - 8960*a^5*b^3*c^7*d^2*e^7*x + 280*a^2*c^6*d^4*e^5*x*(-(4*a*c - b^2)^7)^(1/2) + 472*a^3*c^5*d^2*e^7*x*(-(4*a*c - b^2)^7)^(1/2) + 238*b^2*c^6*d^6*e^3*x*(-(4*a*c - b^2)^7)^(1/2) - 154*b^3*c^5*d^5*e^4*x*(-(4*a*c - b^2)^7)^(1/2) + 35*b^4*c^4*d^4*e^5*x*(-(4*a*c - b^2)^7)^(1/2) - 3*b^6*c^2*d^2*e^7*x*(-(4*a*c - b^2)^7)^(1/2) + 6*a*b^6*c*d*e^8*(-(4*a*c - b^2)^7)^(1/2) + 28*a*b^6*c*e^9*x*(-(4*a*c - b^2)^7)^(1/2) - 2160*a*b^5*c^9*d^8*e*x - 110*a*b^12*c^2*d*e^8*x - 11520*a^3*b*c^11*d^8*e*x + 4*b^7*c*d*e^8*x*(-(4*a*c - b^2)^7)^(1/2) - 140*a^2*b^2*c^4*d^3*e^6*(-(4*a*c - b^2)^7)^(1/2) - 37*a^2*b^3*c^3*d^2*e^7*(-(4*a*c - b^2)^7)^(1/2) + 490*a*b^2*c^5*d^4*e^5*x*(-(4*a*c - b^2)^7)^(1/2) - 140*a*b^3*c^4*d^3*e^6*x*(-(4*a*c - b^2)^7)^(1/2) + 36*a*b^4*c^3*d^2*e^7*x*(-(4*a*c - b^2)^7)^(1/2) - 560*a^2*b*c^5*d^3*e^6*x*(-(4*a*c - b^2)^7)^(1/2) + 214*a^2*b^3*c^3*d*e^8*x*(-(4*a*c - b^2)^7)^(1/2) + 66*a^2*b^2*c^4*d^2*e^7*x*(-(4*a*c - b^2)^7)^(1/2) - 504*a*b*c^6*d^5*e^4*x*(-(4*a*c - b^2)^7)^(1/2) - 50*a*b^5*c^2*d*e^8*x*(-(4*a*c - b^2)^7)^(1/2) - 472*a^3*b*c^4*d*e^8*x*(-(4*a*c - b^2)^7)^(1/2))*((b^14*e^7)/2 - 8192*a^7*c^7*e^7 + (b^7*e^7*(-(4*a*c - b^2)^7)^(1/2))/2 + 20*c^7*d^7*(-(4*a*c - b^2)^7)^(1/2) + 168*a^2*b^10*c^2*e^7 - 1120*a^3*b^8*c^3*e^7 + 4480*a^4*b^6*c^4*e^7 - 10752*a^5*b^4*c^5*e^7 + 14336*a^6*b^2*c^6*e^7 - 14*a*b^12*c*e^7 + 35*a^2*b^3*c^2*e^7*(-(4*a*c - b^2)^7)^(1/2) + 140*a^2*c^5*d^3*e^4*(-(4*a*c - b^2)^7)^(1/2) + 84*b^2*c^5*d^5*e^2*(-(4*a*c - b^2)^7)^(1/2) - 35*b^3*c^4*d^4*e^3*(-(4*a*c - b^2)^7)^(1/2) - 7*a*b^5*c*e^7*(-(4*a*c - b^2)^7)^(1/2) - 70*b*c^6*d^6*e*(-(4*a*c - b^2)^7)^(1/2) - 70*a^3*b*c^3*e^7*(-(4*a*c - b^2)^7)^(1/2) + 84*a*c^6*d^5*e^2*(-(4*a*c - b^2)^7)^(1/2) + 140*a^3*c^4*d*e^6*(-(4*a*c - b^2)^7)^(1/2) - 210*a*b*c^5*d^4*e^3*(-(4*a*c - b^2)^7)^(1/2) + 140*a*b^2*c^4*d^3*e^4*(-(4*a*c - b^2)^7)^(1/2) - 210*a^2*b*c^4*d^2*e^5*(-(4*a*c - b^2)^7)^(1/2)))/(a^4*b^14*e^8 - 16384*a^7*c^11*d^8 - 16384*a^11*c^7*e^8 + b^14*c^4*d^8 + b^18*d^4*e^4 - 28*a*b^12*c^5*d^8 - 28*a^5*b^12*c*e^8 - 4*a*b^17*d^3*e^5 - 4*a^3*b^15*d*e^7 - 4*b^15*c^3*d^7*e - 4*b^17*c*d^5*e^3 + 336*a^2*b^10*c^6*d^8 - 2240*a^3*b^8*c^7*d^8 + 8960*a^4*b^6*c^8*d^8 - 21504*a^5*b^4*c^9*d^8 + 28672*a^6*b^2*c^10*d^8 + 336*a^6*b^10*c^2*e^8 - 2240*a^7*b^8*c^3*e^8 + 8960*a^8*b^6*c^4*e^8 - 21504*a^9*b^4*c^5*e^8 + 28672*a^10*b^2*c^6*e^8 + 6*a^2*b^16*d^2*e^6 - 65536*a^8*c^10*d^6*e^2 - 98304*a^9*c^9*d^4*e^4 - 65536*a^10*c^8*d^2*e^6 + 6*b^16*c^2*d^6*e^2 + 1904*a^2*b^12*c^4*d^6*e^2 - 1008*a^2*b^13*c^3*d^5*e^3 + 6*a^2*b^14*c^2*d^4*e^4 - 12096*a^3*b^10*c^5*d^6*e^2 + 4928*a^3*b^11*c^4*d^5*e^3 + 1624*a^3*b^12*c^3*d^4*e^4 - 1008*a^3*b^13*c^2*d^3*e^5 + 44800*a^4*b^8*c^6*d^6*e^2 - 8960*a^4*b^9*c^5*d^5*e^3 - 15904*a^4*b^10*c^4*d^4*e^4 + 4928*a^4*b^11*c^3*d^3*e^5 + 1904*a^4*b^12*c^2*d^2*e^6 - 93184*a^5*b^6*c^7*d^6*e^2 - 21504*a^5*b^7*c^6*d^5*e^3 + 72576*a^5*b^8*c^5*d^4*e^4 - 8960*a^5*b^9*c^4*d^3*e^5 - 12096*a^5*b^10*c^3*d^2*e^6 + 86016*a^6*b^4*c^8*d^6*e^2 + 143360*a^6*b^5*c^7*d^5*e^3 - 175616*a^6*b^6*c^6*d^4*e^4 - 21504*a^6*b^7*c^5*d^3*e^5 + 44800*a^6*b^8*c^4*d^2*e^6 + 16384*a^7*b^2*c^9*d^6*e^2 - 278528*a^7*b^3*c^8*d^5*e^3 + 198656*a^7*b^4*c^7*d^4*e^4 + 143360*a^7*b^5*c^6*d^3*e^5 - 93184*a^7*b^6*c^5*d^2*e^6 - 24576*a^8*b^2*c^8*d^4*e^4 - 278528*a^8*b^3*c^7*d^3*e^5 + 86016*a^8*b^4*c^6*d^2*e^6 + 16384*a^9*b^2*c^7*d^2*e^6 + 112*a*b^13*c^4*d^7*e - 16*a*b^16*c*d^4*e^4 + 112*a^4*b^13*c*d*e^7 + 65536*a^7*b*c^10*d^7*e + 65536*a^10*b*c^7*d*e^7 - 164*a*b^14*c^3*d^6*e^2 + 100*a*b^15*c^2*d^5*e^3 - 1344*a^2*b^11*c^5*d^7*e + 100*a^2*b^15*c*d^3*e^5 + 8960*a^3*b^9*c^6*d^7*e - 164*a^3*b^14*c*d^2*e^6 - 35840*a^4*b^7*c^7*d^7*e + 86016*a^5*b^5*c^8*d^7*e - 1344*a^5*b^11*c^2*d*e^7 - 114688*a^6*b^3*c^9*d^7*e + 8960*a^6*b^9*c^3*d*e^7 - 35840*a^7*b^7*c^4*d*e^7 + 196608*a^8*b*c^9*d^5*e^3 + 86016*a^8*b^5*c^5*d*e^7 + 196608*a^9*b*c^8*d^3*e^5 - 114688*a^9*b^3*c^6*d*e^7) + (log(2*a*b^14*e^9 + 2*b^15*e^9*x - 24576*a^8*c^7*e^9 + 20*b^7*c^8*d^9 + 20*c^8*d^9*(-(4*a*c - b^2)^7)^(1/2) - 240*a*b^5*c^9*d^9 - 1280*a^3*b*c^11*d^9 - 2*a*b^7*e^9*(-(4*a*c - b^2)^7)^(1/2) - 55*a^2*b^12*c*e^9 + 5120*a^4*c^11*d^8*e - 70*b^8*c^7*d^8*e - b^14*c*d^2*e^7 - 2560*a^3*c^12*d^9*x + 40*b^6*c^9*d^9*x - 2*b^8*e^9*x*(-(4*a*c - b^2)^7)^(1/2) + 960*a^2*b^3*c^10*d^9 + 647*a^3*b^10*c^2*e^9 - 4218*a^4*b^8*c^3*e^9 + 16408*a^5*b^6*c^4*e^9 - 37856*a^6*b^4*c^5*e^9 + 47488*a^7*b^2*c^6*e^9 + 21504*a^5*c^10*d^6*e^3 + 35840*a^6*c^9*d^4*e^5 + 60416*a^7*c^8*d^2*e^7 + 84*b^9*c^6*d^7*e^2 - 35*b^10*c^5*d^6*e^3 - 2*a*b^13*c*d*e^8 - 56*a*b^13*c*e^9*x - 4*b^14*c*d*e^8*x - 107*a^3*b^3*c^2*e^9*(-(4*a*c - b^2)^7)^(1/2) - 576*a^2*b^5*c^8*d^7*e^2 + 5376*a^2*b^6*c^7*d^6*e^3 - 3304*a^2*b^7*c^6*d^5*e^4 - 560*a^2*b^8*c^5*d^4*e^5 + 140*a^2*b^9*c^4*d^3*e^6 - 361*a^2*b^10*c^3*d^2*e^7 + 13056*a^3*b^3*c^9*d^7*e^2 - 23296*a^3*b^4*c^8*d^6*e^3 + 4704*a^3*b^5*c^7*d^5*e^4 + 9520*a^3*b^6*c^6*d^4*e^5 - 560*a^3*b^7*c^5*d^3*e^6 + 2292*a^3*b^8*c^4*d^2*e^7 + 23296*a^4*b^2*c^9*d^6*e^3 + 27776*a^4*b^3*c^8*d^5*e^4 - 38080*a^4*b^4*c^7*d^4*e^5 - 6720*a^4*b^5*c^6*d^3*e^6 - 8512*a^4*b^6*c^5*d^2*e^7 + 35840*a^5*b^2*c^8*d^4*e^5 + 44800*a^5*b^3*c^7*d^3*e^6 + 23296*a^5*b^4*c^6*d^2*e^7 - 51968*a^6*b^2*c^7*d^2*e^7 + 56*a^2*c^6*d^5*e^4*(-(4*a*c - b^2)^7)^(1/2) + 84*b^2*c^6*d^7*e^2*(-(4*a*c - b^2)^7)^(1/2) - 35*b^3*c^5*d^6*e^3*(-(4*a*c - b^2)^7)^(1/2) + 760*a*b^6*c^8*d^8*e - 26880*a^7*b*c^7*d*e^8 - 70*b*c^7*d^8*e*(-(4*a*c - b^2)^7)^(1/2) - 480*a*b^4*c^10*d^9*x - 33536*a^7*b*c^7*e^9*x + 67072*a^7*c^8*d*e^8*x - 180*b^7*c^8*d^8*e*x + 40*c^8*d^8*e*x*(-(4*a*c - b^2)^7)^(1/2) + 25*a^2*b^5*c*e^9*(-(4*a*c - b^2)^7)^(1/2) + 166*a^4*b*c^3*e^9*(-(4*a*c - b^2)^7)^(1/2) - 624*a*b^7*c^7*d^7*e^2 - 196*a*b^8*c^6*d^6*e^3 + 364*a*b^9*c^5*d^5*e^4 - 35*a*b^10*c^4*d^4*e^5 + 29*a*b^12*c^2*d^2*e^7 - 2400*a^2*b^4*c^9*d^8*e + 52*a^2*b^11*c^2*d*e^8 + 640*a^3*b^2*c^10*d^8*e - 572*a^3*b^9*c^3*d*e^8 - 24576*a^4*b*c^10*d^7*e^2 + 3572*a^4*b^7*c^4*d*e^8 - 68096*a^5*b*c^9*d^5*e^4 - 13552*a^5*b^5*c^5*d*e^8 - 71680*a^6*b*c^8*d^3*e^6 + 29120*a^6*b^3*c^6*d*e^8 + 64*a*c^7*d^7*e^2*(-(4*a*c - b^2)^7)^(1/2) - 524*a^4*c^4*d*e^8*(-(4*a*c - b^2)^7)^(1/2) - b^7*c*d^2*e^7*(-(4*a*c - b^2)^7)^(1/2) + 1920*a^2*b^2*c^11*d^9*x + 673*a^2*b^11*c^2*e^9*x - 4504*a^3*b^9*c^3*e^9*x + 18124*a^4*b^7*c^4*e^9*x - 43792*a^5*b^5*c^5*e^9*x + 58688*a^6*b^3*c^6*e^9*x - 192*a^4*c^4*e^9*x*(-(4*a*c - b^2)^7)^(1/2) - 8192*a^4*c^11*d^7*e^2*x - 7168*a^5*c^10*d^5*e^4*x + 328*b^8*c^7*d^7*e^2*x - 308*b^9*c^6*d^6*e^3*x + 154*b^10*c^5*d^5*e^4*x - 35*b^11*c^4*d^4*e^5*x + b^13*c^2*d^2*e^7*x - 140*a*b*c^6*d^6*e^3*(-(4*a*c - b^2)^7)^(1/2) - 3808*a*b^6*c^8*d^7*e^2*x + 3248*a*b^7*c^7*d^6*e^3*x - 1232*a*b^8*c^6*d^5*e^4*x + 140*a*b^10*c^4*d^3*e^6*x - 26*a*b^11*c^3*d^2*e^7*x - 8640*a^2*b^3*c^10*d^8*e*x - 1294*a^2*b^10*c^3*d*e^8*x + 8576*a^3*b^8*c^4*d*e^8*x + 28672*a^4*b*c^10*d^6*e^3*x - 34776*a^4*b^6*c^5*d*e^8*x + 17920*a^5*b*c^9*d^4*e^5*x + 85792*a^5*b^4*c^6*d*e^8*x - 117376*a^6*b^2*c^7*d*e^8*x + 168*a*c^7*d^6*e^3*x*(-(4*a*c - b^2)^7)^(1/2) - 160*b*c^7*d^7*e^2*x*(-(4*a*c - b^2)^7)^(1/2) + 56*a*b^2*c^5*d^5*e^4*(-(4*a*c - b^2)^7)^(1/2) + 35*a*b^3*c^4*d^4*e^5*(-(4*a*c - b^2)^7)^(1/2) + 11*a*b^5*c^2*d^2*e^7*(-(4*a*c - b^2)^7)^(1/2) - 72*a^2*b^4*c^2*d*e^8*(-(4*a*c - b^2)^7)^(1/2) + 236*a^3*b*c^4*d^2*e^7*(-(4*a*c - b^2)^7)^(1/2) + 288*a^3*b^2*c^3*d*e^8*(-(4*a*c - b^2)^7)^(1/2) - 143*a^2*b^4*c^2*e^9*x*(-(4*a*c - b^2)^7)^(1/2) + 310*a^3*b^2*c^3*e^9*x*(-(4*a*c - b^2)^7)^(1/2) + 14208*a^2*b^4*c^9*d^7*e^2*x - 9408*a^2*b^5*c^8*d^6*e^3*x + 112*a^2*b^6*c^7*d^5*e^4*x + 3080*a^2*b^7*c^6*d^4*e^5*x - 1400*a^2*b^8*c^5*d^3*e^6*x + 76*a^2*b^9*c^4*d^2*e^7*x - 14848*a^3*b^2*c^10*d^7*e^2*x - 1792*a^3*b^3*c^9*d^6*e^3*x + 18368*a^3*b^4*c^8*d^5*e^4*x - 14560*a^3*b^5*c^7*d^4*e^5*x + 3360*a^3*b^6*c^6*d^3*e^6*x + 944*a^3*b^7*c^5*d^2*e^7*x - 34048*a^4*b^2*c^9*d^5*e^4*x + 13440*a^4*b^3*c^8*d^4*e^5*x + 4480*a^4*b^4*c^7*d^3*e^6*x - 5824*a^4*b^5*c^6*d^2*e^7*x - 17920*a^5*b^2*c^8*d^3*e^6*x + 8960*a^5*b^3*c^7*d^2*e^7*x + 280*a^2*c^6*d^4*e^5*x*(-(4*a*c - b^2)^7)^(1/2) + 472*a^3*c^5*d^2*e^7*x*(-(4*a*c - b^2)^7)^(1/2) + 238*b^2*c^6*d^6*e^3*x*(-(4*a*c - b^2)^7)^(1/2) - 154*b^3*c^5*d^5*e^4*x*(-(4*a*c - b^2)^7)^(1/2) + 35*b^4*c^4*d^4*e^5*x*(-(4*a*c - b^2)^7)^(1/2) - 3*b^6*c^2*d^2*e^7*x*(-(4*a*c - b^2)^7)^(1/2) + 6*a*b^6*c*d*e^8*(-(4*a*c - b^2)^7)^(1/2) + 28*a*b^6*c*e^9*x*(-(4*a*c - b^2)^7)^(1/2) + 2160*a*b^5*c^9*d^8*e*x + 110*a*b^12*c^2*d*e^8*x + 11520*a^3*b*c^11*d^8*e*x + 4*b^7*c*d*e^8*x*(-(4*a*c - b^2)^7)^(1/2) - 140*a^2*b^2*c^4*d^3*e^6*(-(4*a*c - b^2)^7)^(1/2) - 37*a^2*b^3*c^3*d^2*e^7*(-(4*a*c - b^2)^7)^(1/2) + 490*a*b^2*c^5*d^4*e^5*x*(-(4*a*c - b^2)^7)^(1/2) - 140*a*b^3*c^4*d^3*e^6*x*(-(4*a*c - b^2)^7)^(1/2) + 36*a*b^4*c^3*d^2*e^7*x*(-(4*a*c - b^2)^7)^(1/2) - 560*a^2*b*c^5*d^3*e^6*x*(-(4*a*c - b^2)^7)^(1/2) + 214*a^2*b^3*c^3*d*e^8*x*(-(4*a*c - b^2)^7)^(1/2) + 66*a^2*b^2*c^4*d^2*e^7*x*(-(4*a*c - b^2)^7)^(1/2) - 504*a*b*c^6*d^5*e^4*x*(-(4*a*c - b^2)^7)^(1/2) - 50*a*b^5*c^2*d*e^8*x*(-(4*a*c - b^2)^7)^(1/2) - 472*a^3*b*c^4*d*e^8*x*(-(4*a*c - b^2)^7)^(1/2))*(8192*a^7*c^7*e^7 - (b^14*e^7)/2 + (b^7*e^7*(-(4*a*c - b^2)^7)^(1/2))/2 + 20*c^7*d^7*(-(4*a*c - b^2)^7)^(1/2) - 168*a^2*b^10*c^2*e^7 + 1120*a^3*b^8*c^3*e^7 - 4480*a^4*b^6*c^4*e^7 + 10752*a^5*b^4*c^5*e^7 - 14336*a^6*b^2*c^6*e^7 + 14*a*b^12*c*e^7 + 35*a^2*b^3*c^2*e^7*(-(4*a*c - b^2)^7)^(1/2) + 140*a^2*c^5*d^3*e^4*(-(4*a*c - b^2)^7)^(1/2) + 84*b^2*c^5*d^5*e^2*(-(4*a*c - b^2)^7)^(1/2) - 35*b^3*c^4*d^4*e^3*(-(4*a*c - b^2)^7)^(1/2) - 7*a*b^5*c*e^7*(-(4*a*c - b^2)^7)^(1/2) - 70*b*c^6*d^6*e*(-(4*a*c - b^2)^7)^(1/2) - 70*a^3*b*c^3*e^7*(-(4*a*c - b^2)^7)^(1/2) + 84*a*c^6*d^5*e^2*(-(4*a*c - b^2)^7)^(1/2) + 140*a^3*c^4*d*e^6*(-(4*a*c - b^2)^7)^(1/2) - 210*a*b*c^5*d^4*e^3*(-(4*a*c - b^2)^7)^(1/2) + 140*a*b^2*c^4*d^3*e^4*(-(4*a*c - b^2)^7)^(1/2) - 210*a^2*b*c^4*d^2*e^5*(-(4*a*c - b^2)^7)^(1/2)))/(a^4*b^14*e^8 - 16384*a^7*c^11*d^8 - 16384*a^11*c^7*e^8 + b^14*c^4*d^8 + b^18*d^4*e^4 - 28*a*b^12*c^5*d^8 - 28*a^5*b^12*c*e^8 - 4*a*b^17*d^3*e^5 - 4*a^3*b^15*d*e^7 - 4*b^15*c^3*d^7*e - 4*b^17*c*d^5*e^3 + 336*a^2*b^10*c^6*d^8 - 2240*a^3*b^8*c^7*d^8 + 8960*a^4*b^6*c^8*d^8 - 21504*a^5*b^4*c^9*d^8 + 28672*a^6*b^2*c^10*d^8 + 336*a^6*b^10*c^2*e^8 - 2240*a^7*b^8*c^3*e^8 + 8960*a^8*b^6*c^4*e^8 - 21504*a^9*b^4*c^5*e^8 + 28672*a^10*b^2*c^6*e^8 + 6*a^2*b^16*d^2*e^6 - 65536*a^8*c^10*d^6*e^2 - 98304*a^9*c^9*d^4*e^4 - 65536*a^10*c^8*d^2*e^6 + 6*b^16*c^2*d^6*e^2 + 1904*a^2*b^12*c^4*d^6*e^2 - 1008*a^2*b^13*c^3*d^5*e^3 + 6*a^2*b^14*c^2*d^4*e^4 - 12096*a^3*b^10*c^5*d^6*e^2 + 4928*a^3*b^11*c^4*d^5*e^3 + 1624*a^3*b^12*c^3*d^4*e^4 - 1008*a^3*b^13*c^2*d^3*e^5 + 44800*a^4*b^8*c^6*d^6*e^2 - 8960*a^4*b^9*c^5*d^5*e^3 - 15904*a^4*b^10*c^4*d^4*e^4 + 4928*a^4*b^11*c^3*d^3*e^5 + 1904*a^4*b^12*c^2*d^2*e^6 - 93184*a^5*b^6*c^7*d^6*e^2 - 21504*a^5*b^7*c^6*d^5*e^3 + 72576*a^5*b^8*c^5*d^4*e^4 - 8960*a^5*b^9*c^4*d^3*e^5 - 12096*a^5*b^10*c^3*d^2*e^6 + 86016*a^6*b^4*c^8*d^6*e^2 + 143360*a^6*b^5*c^7*d^5*e^3 - 175616*a^6*b^6*c^6*d^4*e^4 - 21504*a^6*b^7*c^5*d^3*e^5 + 44800*a^6*b^8*c^4*d^2*e^6 + 16384*a^7*b^2*c^9*d^6*e^2 - 278528*a^7*b^3*c^8*d^5*e^3 + 198656*a^7*b^4*c^7*d^4*e^4 + 143360*a^7*b^5*c^6*d^3*e^5 - 93184*a^7*b^6*c^5*d^2*e^6 - 24576*a^8*b^2*c^8*d^4*e^4 - 278528*a^8*b^3*c^7*d^3*e^5 + 86016*a^8*b^4*c^6*d^2*e^6 + 16384*a^9*b^2*c^7*d^2*e^6 + 112*a*b^13*c^4*d^7*e - 16*a*b^16*c*d^4*e^4 + 112*a^4*b^13*c*d*e^7 + 65536*a^7*b*c^10*d^7*e + 65536*a^10*b*c^7*d*e^7 - 164*a*b^14*c^3*d^6*e^2 + 100*a*b^15*c^2*d^5*e^3 - 1344*a^2*b^11*c^5*d^7*e + 100*a^2*b^15*c*d^3*e^5 + 8960*a^3*b^9*c^6*d^7*e - 164*a^3*b^14*c*d^2*e^6 - 35840*a^4*b^7*c^7*d^7*e + 86016*a^5*b^5*c^8*d^7*e - 1344*a^5*b^11*c^2*d*e^7 - 114688*a^6*b^3*c^9*d^7*e + 8960*a^6*b^9*c^3*d*e^7 - 35840*a^7*b^7*c^4*d*e^7 + 196608*a^8*b*c^9*d^5*e^3 + 86016*a^8*b^5*c^5*d*e^7 + 196608*a^9*b*c^8*d^3*e^5 - 114688*a^9*b^3*c^6*d*e^7) + (e^7*log(d + e*x))/(a^4*e^8 + c^4*d^8 + b^4*d^4*e^4 - 4*a*b^3*d^3*e^5 + 4*a*c^3*d^6*e^2 + 4*a^3*c*d^2*e^6 - 4*b^3*c*d^5*e^3 + 6*a^2*b^2*d^2*e^6 + 6*a^2*c^2*d^4*e^4 + 6*b^2*c^2*d^6*e^2 - 4*a^3*b*d*e^7 - 4*b*c^3*d^7*e - 12*a*b*c^2*d^5*e^3 + 12*a*b^2*c*d^4*e^4 - 12*a^2*b*c*d^3*e^5)","B"
2220,1,1856,352,2.742146,"\text{Not used}","int(1/(x^2*(a + b*x + c*x^2)^4),x)","\frac{2\,\ln\left(2\,a\,b^8\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-2\,b^{16}\,x-2\,a\,b^{15}+55\,a^2\,b^{13}\,c+26816\,a^8\,b\,c^7-4480\,a^8\,c^8\,x+2\,b^9\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-647\,a^3\,b^{11}\,c^2+4218\,a^4\,b^9\,c^3-16443\,a^5\,b^7\,c^4+38276\,a^6\,b^5\,c^5-49168\,a^7\,b^3\,c^6+35\,a^5\,c^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-25\,a^2\,b^6\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-673\,a^2\,b^{12}\,c^2\,x+4504\,a^3\,b^{10}\,c^3\,x-18159\,a^4\,b^8\,c^4\,x+44282\,a^5\,b^6\,c^5\,x-61208\,a^6\,b^4\,c^6\,x+39136\,a^7\,b^2\,c^7\,x+56\,a\,b^{14}\,c\,x+107\,a^3\,b^4\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-166\,a^4\,b^2\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-28\,a\,b^7\,c\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}+227\,a^4\,b\,c^4\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}+143\,a^2\,b^5\,c^2\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-310\,a^3\,b^3\,c^3\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}\right)\,\left(b^8\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-b^{15}+16384\,a^7\,b\,c^7-336\,a^2\,b^{11}\,c^2+2240\,a^3\,b^9\,c^3-8960\,a^4\,b^7\,c^4+21504\,a^5\,b^5\,c^5-28672\,a^6\,b^3\,c^6+70\,a^4\,c^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}+28\,a\,b^{13}\,c+70\,a^2\,b^4\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-140\,a^3\,b^2\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-14\,a\,b^6\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}\right)}{a^5\,{\left(4\,a\,c-b^2\right)}^7}-\frac{4\,b\,\ln\left(x\right)}{a^5}-\frac{2\,\ln\left(2\,a\,b^{15}+2\,b^{16}\,x+2\,a\,b^8\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-55\,a^2\,b^{13}\,c-26816\,a^8\,b\,c^7+4480\,a^8\,c^8\,x+2\,b^9\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}+647\,a^3\,b^{11}\,c^2-4218\,a^4\,b^9\,c^3+16443\,a^5\,b^7\,c^4-38276\,a^6\,b^5\,c^5+49168\,a^7\,b^3\,c^6+35\,a^5\,c^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-25\,a^2\,b^6\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}+673\,a^2\,b^{12}\,c^2\,x-4504\,a^3\,b^{10}\,c^3\,x+18159\,a^4\,b^8\,c^4\,x-44282\,a^5\,b^6\,c^5\,x+61208\,a^6\,b^4\,c^6\,x-39136\,a^7\,b^2\,c^7\,x-56\,a\,b^{14}\,c\,x+107\,a^3\,b^4\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-166\,a^4\,b^2\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-28\,a\,b^7\,c\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}+227\,a^4\,b\,c^4\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}+143\,a^2\,b^5\,c^2\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-310\,a^3\,b^3\,c^3\,x\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}\right)\,\left(b^{15}+b^8\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-16384\,a^7\,b\,c^7+336\,a^2\,b^{11}\,c^2-2240\,a^3\,b^9\,c^3+8960\,a^4\,b^7\,c^4-21504\,a^5\,b^5\,c^5+28672\,a^6\,b^3\,c^6+70\,a^4\,c^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-28\,a\,b^{13}\,c+70\,a^2\,b^4\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-140\,a^3\,b^2\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}-14\,a\,b^6\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^7}\right)}{a^5\,{\left(4\,a\,c-b^2\right)}^7}-\frac{\frac{1}{a}-\frac{2\,x^4\,\left(560\,a^4\,c^5+225\,a^3\,b^2\,c^4-578\,a^2\,b^4\,c^3+189\,a\,b^6\,c^2-18\,b^8\,c\right)}{3\,a^4\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{2\,x^5\,\left(-239\,a^3\,b\,c^5+238\,a^2\,b^3\,c^4-67\,a\,b^5\,c^3+6\,b^7\,c^2\right)}{a^4\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}-\frac{x^2\,\left(308\,a^4\,c^4+214\,a^3\,b^2\,c^3-351\,a^2\,b^4\,c^2+108\,a\,b^6\,c-10\,b^8\right)}{a^3\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{x\,\left(-1166\,a^3\,b\,c^3+967\,a^2\,b^3\,c^2-255\,a\,b^5\,c+22\,b^7\right)}{3\,a^2\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}-\frac{x^3\,\left(880\,a^4\,b\,c^4-621\,a^3\,b^3\,c^3+54\,a^2\,b^5\,c^2+26\,a\,b^7\,c-4\,b^9\right)}{a^4\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}+\frac{4\,c^3\,x^6\,\left(-35\,a^3\,c^3+38\,a^2\,b^2\,c^2-11\,a\,b^4\,c+b^6\right)}{a^4\,\left(-64\,a^3\,c^3+48\,a^2\,b^2\,c^2-12\,a\,b^4\,c+b^6\right)}}{a^3\,x+x^3\,\left(3\,c\,a^2+3\,a\,b^2\right)+x^5\,\left(3\,b^2\,c+3\,a\,c^2\right)+x^4\,\left(b^3+6\,a\,c\,b\right)+c^3\,x^7+3\,a^2\,b\,x^2+3\,b\,c^2\,x^6}","Not used",1,"(2*log(2*a*b^8*(-(4*a*c - b^2)^7)^(1/2) - 2*b^16*x - 2*a*b^15 + 55*a^2*b^13*c + 26816*a^8*b*c^7 - 4480*a^8*c^8*x + 2*b^9*x*(-(4*a*c - b^2)^7)^(1/2) - 647*a^3*b^11*c^2 + 4218*a^4*b^9*c^3 - 16443*a^5*b^7*c^4 + 38276*a^6*b^5*c^5 - 49168*a^7*b^3*c^6 + 35*a^5*c^4*(-(4*a*c - b^2)^7)^(1/2) - 25*a^2*b^6*c*(-(4*a*c - b^2)^7)^(1/2) - 673*a^2*b^12*c^2*x + 4504*a^3*b^10*c^3*x - 18159*a^4*b^8*c^4*x + 44282*a^5*b^6*c^5*x - 61208*a^6*b^4*c^6*x + 39136*a^7*b^2*c^7*x + 56*a*b^14*c*x + 107*a^3*b^4*c^2*(-(4*a*c - b^2)^7)^(1/2) - 166*a^4*b^2*c^3*(-(4*a*c - b^2)^7)^(1/2) - 28*a*b^7*c*x*(-(4*a*c - b^2)^7)^(1/2) + 227*a^4*b*c^4*x*(-(4*a*c - b^2)^7)^(1/2) + 143*a^2*b^5*c^2*x*(-(4*a*c - b^2)^7)^(1/2) - 310*a^3*b^3*c^3*x*(-(4*a*c - b^2)^7)^(1/2))*(b^8*(-(4*a*c - b^2)^7)^(1/2) - b^15 + 16384*a^7*b*c^7 - 336*a^2*b^11*c^2 + 2240*a^3*b^9*c^3 - 8960*a^4*b^7*c^4 + 21504*a^5*b^5*c^5 - 28672*a^6*b^3*c^6 + 70*a^4*c^4*(-(4*a*c - b^2)^7)^(1/2) + 28*a*b^13*c + 70*a^2*b^4*c^2*(-(4*a*c - b^2)^7)^(1/2) - 140*a^3*b^2*c^3*(-(4*a*c - b^2)^7)^(1/2) - 14*a*b^6*c*(-(4*a*c - b^2)^7)^(1/2)))/(a^5*(4*a*c - b^2)^7) - (4*b*log(x))/a^5 - (2*log(2*a*b^15 + 2*b^16*x + 2*a*b^8*(-(4*a*c - b^2)^7)^(1/2) - 55*a^2*b^13*c - 26816*a^8*b*c^7 + 4480*a^8*c^8*x + 2*b^9*x*(-(4*a*c - b^2)^7)^(1/2) + 647*a^3*b^11*c^2 - 4218*a^4*b^9*c^3 + 16443*a^5*b^7*c^4 - 38276*a^6*b^5*c^5 + 49168*a^7*b^3*c^6 + 35*a^5*c^4*(-(4*a*c - b^2)^7)^(1/2) - 25*a^2*b^6*c*(-(4*a*c - b^2)^7)^(1/2) + 673*a^2*b^12*c^2*x - 4504*a^3*b^10*c^3*x + 18159*a^4*b^8*c^4*x - 44282*a^5*b^6*c^5*x + 61208*a^6*b^4*c^6*x - 39136*a^7*b^2*c^7*x - 56*a*b^14*c*x + 107*a^3*b^4*c^2*(-(4*a*c - b^2)^7)^(1/2) - 166*a^4*b^2*c^3*(-(4*a*c - b^2)^7)^(1/2) - 28*a*b^7*c*x*(-(4*a*c - b^2)^7)^(1/2) + 227*a^4*b*c^4*x*(-(4*a*c - b^2)^7)^(1/2) + 143*a^2*b^5*c^2*x*(-(4*a*c - b^2)^7)^(1/2) - 310*a^3*b^3*c^3*x*(-(4*a*c - b^2)^7)^(1/2))*(b^15 + b^8*(-(4*a*c - b^2)^7)^(1/2) - 16384*a^7*b*c^7 + 336*a^2*b^11*c^2 - 2240*a^3*b^9*c^3 + 8960*a^4*b^7*c^4 - 21504*a^5*b^5*c^5 + 28672*a^6*b^3*c^6 + 70*a^4*c^4*(-(4*a*c - b^2)^7)^(1/2) - 28*a*b^13*c + 70*a^2*b^4*c^2*(-(4*a*c - b^2)^7)^(1/2) - 140*a^3*b^2*c^3*(-(4*a*c - b^2)^7)^(1/2) - 14*a*b^6*c*(-(4*a*c - b^2)^7)^(1/2)))/(a^5*(4*a*c - b^2)^7) - (1/a - (2*x^4*(560*a^4*c^5 - 18*b^8*c + 189*a*b^6*c^2 - 578*a^2*b^4*c^3 + 225*a^3*b^2*c^4))/(3*a^4*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (2*x^5*(6*b^7*c^2 - 67*a*b^5*c^3 - 239*a^3*b*c^5 + 238*a^2*b^3*c^4))/(a^4*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) - (x^2*(308*a^4*c^4 - 10*b^8 - 351*a^2*b^4*c^2 + 214*a^3*b^2*c^3 + 108*a*b^6*c))/(a^3*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (x*(22*b^7 - 1166*a^3*b*c^3 + 967*a^2*b^3*c^2 - 255*a*b^5*c))/(3*a^2*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) - (x^3*(880*a^4*b*c^4 - 4*b^9 + 54*a^2*b^5*c^2 - 621*a^3*b^3*c^3 + 26*a*b^7*c))/(a^4*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)) + (4*c^3*x^6*(b^6 - 35*a^3*c^3 + 38*a^2*b^2*c^2 - 11*a*b^4*c))/(a^4*(b^6 - 64*a^3*c^3 + 48*a^2*b^2*c^2 - 12*a*b^4*c)))/(a^3*x + x^3*(3*a*b^2 + 3*a^2*c) + x^5*(3*a*c^2 + 3*b^2*c) + x^4*(b^3 + 6*a*b*c) + c^3*x^7 + 3*a^2*b*x^2 + 3*b*c^2*x^6)","B"
2221,1,2722,388,3.346814,"\text{Not used}","int((d + e*x)^5/(a + b*x + c*x^2)^5,x)","\frac{10\,\mathrm{atan}\left(\frac{\left(\frac{5\,\left(b\,e-2\,c\,d\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)\,\left(b^2\,e^2-7\,b\,c\,d\,e+7\,c^2\,d^2+3\,a\,c\,e^2\right)\,\left(256\,a^4\,b\,c^4-256\,a^3\,b^3\,c^3+96\,a^2\,b^5\,c^2-16\,a\,b^7\,c+b^9\right)}{{\left(4\,a\,c-b^2\right)}^{9/2}\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{10\,c\,x\,\left(b\,e-2\,c\,d\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)\,\left(b^2\,e^2-7\,b\,c\,d\,e+7\,c^2\,d^2+3\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{9/2}}\right)\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}{-15\,a^2\,b\,c\,e^5+30\,a^2\,c^2\,d\,e^4-5\,a\,b^3\,e^5+60\,a\,b^2\,c\,d\,e^4-150\,a\,b\,c^2\,d^2\,e^3+100\,a\,c^3\,d^3\,e^2+5\,b^4\,d\,e^4-50\,b^3\,c\,d^2\,e^3+150\,b^2\,c^2\,d^3\,e^2-175\,b\,c^3\,d^4\,e+70\,c^4\,d^5}\right)\,\left(b\,e-2\,c\,d\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)\,\left(b^2\,e^2-7\,b\,c\,d\,e+7\,c^2\,d^2+3\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{9/2}}-\frac{\frac{128\,a^6\,c^2\,e^5+166\,a^5\,b^2\,c\,e^5-1100\,a^5\,b\,c^2\,d\,e^4+1280\,a^5\,c^3\,d^2\,e^3+3\,a^4\,b^4\,e^5-250\,a^4\,b^3\,c\,d\,e^4+1660\,a^4\,b^2\,c^2\,d^2\,e^3-3240\,a^4\,b\,c^3\,d^3\,e^2+1920\,a^4\,c^4\,d^4\,e+30\,a^3\,b^4\,c\,d^2\,e^3-280\,a^3\,b^3\,c^2\,d^3\,e^2+870\,a^3\,b^2\,c^3\,d^4\,e-1116\,a^3\,b\,c^4\,d^5+10\,a^2\,b^5\,c\,d^3\,e^2-95\,a^2\,b^4\,c^2\,d^4\,e+326\,a^2\,b^3\,c^3\,d^5+5\,a\,b^6\,c\,d^4\,e-50\,a\,b^5\,c^2\,d^5+3\,b^7\,c\,d^5}{12\,c\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{x^3\,\left(219\,a^4\,b\,c^3\,e^5+330\,a^4\,c^4\,d\,e^4+376\,a^3\,b^3\,c^2\,e^5-2250\,a^3\,b^2\,c^3\,d\,e^4+2190\,a^3\,b\,c^4\,d^2\,e^3-1460\,a^3\,c^5\,d^3\,e^2+110\,a^2\,b^5\,c\,e^5-1015\,a^2\,b^4\,c^2\,d\,e^4+3760\,a^2\,b^3\,c^3\,d^2\,e^3-4210\,a^2\,b^2\,c^4\,d^3\,e^2+2555\,a^2\,b\,c^5\,d^4\,e-1022\,a^2\,c^6\,d^5+3\,a\,b^7\,e^5-185\,a\,b^6\,c\,d\,e^4+1100\,a\,b^5\,c^2\,d^2\,e^3-3090\,a\,b^4\,c^3\,d^3\,e^2+3535\,a\,b^3\,c^4\,d^4\,e-1414\,a\,b^2\,c^5\,d^5+30\,b^7\,c\,d^2\,e^3-90\,b^6\,c^2\,d^3\,e^2+105\,b^5\,c^3\,d^4\,e-42\,b^4\,c^4\,d^5\right)}{3\,c\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{x^2\,\left(256\,a^5\,c^3\,e^5+401\,a^4\,b^2\,c^2\,e^5-1570\,a^4\,b\,c^3\,d\,e^4+2560\,a^4\,c^4\,d^2\,e^3+399\,a^3\,b^4\,c\,e^5-2540\,a^3\,b^3\,c^2\,d\,e^4+4010\,a^3\,b^2\,c^3\,d^2\,e^3-4380\,a^3\,b\,c^4\,d^3\,e^2+9\,a^2\,b^6\,e^5-645\,a^2\,b^5\,c\,d\,e^4+3990\,a^2\,b^4\,c^2\,d^2\,e^3-7130\,a^2\,b^3\,c^3\,d^3\,e^2+7665\,a^2\,b^2\,c^4\,d^4\,e-3066\,a^2\,b\,c^5\,d^5+90\,a\,b^6\,c\,d^2\,e^3-820\,a\,b^5\,c^2\,d^3\,e^2+980\,a\,b^4\,c^3\,d^4\,e-392\,a\,b^3\,c^4\,d^5+30\,b^7\,c\,d^3\,e^2-35\,b^6\,c^2\,d^4\,e+14\,b^5\,c^3\,d^5\right)}{6\,c\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}-\frac{5\,x^5\,\left(13\,b^2\,c+11\,a\,c^2\right)\,\left(-3\,a^2\,b\,c\,e^5+6\,a^2\,c^2\,d\,e^4-a\,b^3\,e^5+12\,a\,b^2\,c\,d\,e^4-30\,a\,b\,c^2\,d^2\,e^3+20\,a\,c^3\,d^3\,e^2+b^4\,d\,e^4-10\,b^3\,c\,d^2\,e^3+30\,b^2\,c^2\,d^3\,e^2-35\,b\,c^3\,d^4\,e+14\,c^4\,d^5\right)}{3\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{x^4\,\left(768\,a^4\,c^4\,e^5+882\,a^3\,b^2\,c^3\,e^5-3300\,a^3\,b\,c^4\,d\,e^4+1213\,a^2\,b^4\,c^2\,e^5-7350\,a^2\,b^3\,c^3\,d\,e^4+16500\,a^2\,b^2\,c^4\,d^2\,e^3-11000\,a^2\,b\,c^5\,d^3\,e^2+77\,a\,b^6\,c\,e^5-2050\,a\,b^5\,c^2\,d\,e^4+9250\,a\,b^4\,c^3\,d^2\,e^3-19000\,a\,b^3\,c^4\,d^3\,e^2+19250\,a\,b^2\,c^5\,d^4\,e-7700\,a\,b\,c^6\,d^5+3\,b^8\,e^5-125\,b^7\,c\,d\,e^4+1250\,b^6\,c^2\,d^2\,e^3-3750\,b^5\,c^3\,d^3\,e^2+4375\,b^4\,c^4\,d^4\,e-1750\,b^3\,c^5\,d^5\right)}{12\,c\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{x\,\left(83\,a^5\,b\,c^2\,e^5+90\,a^5\,c^3\,d\,e^4+151\,a^4\,b^3\,c\,e^5-920\,a^4\,b^2\,c^2\,d\,e^4+830\,a^4\,b\,c^3\,d^2\,e^3+300\,a^4\,c^4\,d^3\,e^2+3\,a^3\,b^5\,e^5-235\,a^3\,b^4\,c\,d\,e^4+1510\,a^3\,b^3\,c^2\,d^2\,e^3-2790\,a^3\,b^2\,c^3\,d^3\,e^2+1395\,a^3\,b\,c^4\,d^4\,e-558\,a^3\,c^5\,d^5+30\,a^2\,b^5\,c\,d^2\,e^3-280\,a^2\,b^4\,c^2\,d^3\,e^2+870\,a^2\,b^3\,c^3\,d^4\,e-348\,a^2\,b^2\,c^4\,d^5+10\,a\,b^6\,c\,d^3\,e^2-95\,a\,b^5\,c^2\,d^4\,e+38\,a\,b^4\,c^3\,d^5+5\,b^7\,c\,d^4\,e-2\,b^6\,c^2\,d^5\right)}{3\,c\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}-\frac{5\,c^3\,x^7\,\left(-3\,a^2\,b\,c\,e^5+6\,a^2\,c^2\,d\,e^4-a\,b^3\,e^5+12\,a\,b^2\,c\,d\,e^4-30\,a\,b\,c^2\,d^2\,e^3+20\,a\,c^3\,d^3\,e^2+b^4\,d\,e^4-10\,b^3\,c\,d^2\,e^3+30\,b^2\,c^2\,d^3\,e^2-35\,b\,c^3\,d^4\,e+14\,c^4\,d^5\right)}{256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8}-\frac{35\,b\,c^2\,x^6\,\left(-3\,a^2\,b\,c\,e^5+6\,a^2\,c^2\,d\,e^4-a\,b^3\,e^5+12\,a\,b^2\,c\,d\,e^4-30\,a\,b\,c^2\,d^2\,e^3+20\,a\,c^3\,d^3\,e^2+b^4\,d\,e^4-10\,b^3\,c\,d^2\,e^3+30\,b^2\,c^2\,d^3\,e^2-35\,b\,c^3\,d^4\,e+14\,c^4\,d^5\right)}{2\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}}{x^4\,\left(6\,a^2\,c^2+12\,a\,b^2\,c+b^4\right)+a^4+c^4\,x^8+x^2\,\left(4\,c\,a^3+6\,a^2\,b^2\right)+x^6\,\left(6\,b^2\,c^2+4\,a\,c^3\right)+x^3\,\left(12\,c\,a^2\,b+4\,a\,b^3\right)+x^5\,\left(4\,b^3\,c+12\,a\,b\,c^2\right)+4\,b\,c^3\,x^7+4\,a^3\,b\,x}","Not used",1,"(10*atan((((5*(b*e - 2*c*d)*(a*e^2 + c*d^2 - b*d*e)*(b^2*e^2 + 7*c^2*d^2 + 3*a*c*e^2 - 7*b*c*d*e)*(b^9 + 256*a^4*b*c^4 + 96*a^2*b^5*c^2 - 256*a^3*b^3*c^3 - 16*a*b^7*c))/((4*a*c - b^2)^(9/2)*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (10*c*x*(b*e - 2*c*d)*(a*e^2 + c*d^2 - b*d*e)*(b^2*e^2 + 7*c^2*d^2 + 3*a*c*e^2 - 7*b*c*d*e))/(4*a*c - b^2)^(9/2))*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c))/(70*c^4*d^5 - 5*a*b^3*e^5 + 5*b^4*d*e^4 + 100*a*c^3*d^3*e^2 + 30*a^2*c^2*d*e^4 - 50*b^3*c*d^2*e^3 + 150*b^2*c^2*d^3*e^2 - 15*a^2*b*c*e^5 - 175*b*c^3*d^4*e + 60*a*b^2*c*d*e^4 - 150*a*b*c^2*d^2*e^3))*(b*e - 2*c*d)*(a*e^2 + c*d^2 - b*d*e)*(b^2*e^2 + 7*c^2*d^2 + 3*a*c*e^2 - 7*b*c*d*e))/(4*a*c - b^2)^(9/2) - ((3*b^7*c*d^5 + 3*a^4*b^4*e^5 + 128*a^6*c^2*e^5 - 50*a*b^5*c^2*d^5 - 1116*a^3*b*c^4*d^5 + 166*a^5*b^2*c*e^5 + 1920*a^4*c^4*d^4*e + 326*a^2*b^3*c^3*d^5 + 1280*a^5*c^3*d^2*e^3 + 5*a*b^6*c*d^4*e - 280*a^3*b^3*c^2*d^3*e^2 + 1660*a^4*b^2*c^2*d^2*e^3 - 250*a^4*b^3*c*d*e^4 - 1100*a^5*b*c^2*d*e^4 - 95*a^2*b^4*c^2*d^4*e + 10*a^2*b^5*c*d^3*e^2 + 870*a^3*b^2*c^3*d^4*e + 30*a^3*b^4*c*d^2*e^3 - 3240*a^4*b*c^3*d^3*e^2)/(12*c*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (x^3*(3*a*b^7*e^5 - 1022*a^2*c^6*d^5 - 42*b^4*c^4*d^5 - 1414*a*b^2*c^5*d^5 + 110*a^2*b^5*c*e^5 + 219*a^4*b*c^3*e^5 + 330*a^4*c^4*d*e^4 + 105*b^5*c^3*d^4*e + 30*b^7*c*d^2*e^3 + 376*a^3*b^3*c^2*e^5 - 1460*a^3*c^5*d^3*e^2 - 90*b^6*c^2*d^3*e^2 - 185*a*b^6*c*d*e^4 - 4210*a^2*b^2*c^4*d^3*e^2 + 3760*a^2*b^3*c^3*d^2*e^3 + 3535*a*b^3*c^4*d^4*e + 2555*a^2*b*c^5*d^4*e - 3090*a*b^4*c^3*d^3*e^2 + 1100*a*b^5*c^2*d^2*e^3 - 1015*a^2*b^4*c^2*d*e^4 + 2190*a^3*b*c^4*d^2*e^3 - 2250*a^3*b^2*c^3*d*e^4))/(3*c*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (x^2*(9*a^2*b^6*e^5 + 256*a^5*c^3*e^5 + 14*b^5*c^3*d^5 - 392*a*b^3*c^4*d^5 - 3066*a^2*b*c^5*d^5 + 399*a^3*b^4*c*e^5 - 35*b^6*c^2*d^4*e + 30*b^7*c*d^3*e^2 + 401*a^4*b^2*c^2*e^5 + 2560*a^4*c^4*d^2*e^3 - 7130*a^2*b^3*c^3*d^3*e^2 + 3990*a^2*b^4*c^2*d^2*e^3 + 4010*a^3*b^2*c^3*d^2*e^3 + 980*a*b^4*c^3*d^4*e + 90*a*b^6*c*d^2*e^3 - 645*a^2*b^5*c*d*e^4 - 1570*a^4*b*c^3*d*e^4 - 820*a*b^5*c^2*d^3*e^2 + 7665*a^2*b^2*c^4*d^4*e - 4380*a^3*b*c^4*d^3*e^2 - 2540*a^3*b^3*c^2*d*e^4))/(6*c*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) - (5*x^5*(11*a*c^2 + 13*b^2*c)*(14*c^4*d^5 - a*b^3*e^5 + b^4*d*e^4 + 20*a*c^3*d^3*e^2 + 6*a^2*c^2*d*e^4 - 10*b^3*c*d^2*e^3 + 30*b^2*c^2*d^3*e^2 - 3*a^2*b*c*e^5 - 35*b*c^3*d^4*e + 12*a*b^2*c*d*e^4 - 30*a*b*c^2*d^2*e^3))/(3*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (x^4*(3*b^8*e^5 + 768*a^4*c^4*e^5 - 1750*b^3*c^5*d^5 + 4375*b^4*c^4*d^4*e + 1213*a^2*b^4*c^2*e^5 + 882*a^3*b^2*c^3*e^5 - 3750*b^5*c^3*d^3*e^2 + 1250*b^6*c^2*d^2*e^3 - 7700*a*b*c^6*d^5 + 77*a*b^6*c*e^5 - 125*b^7*c*d*e^4 + 16500*a^2*b^2*c^4*d^2*e^3 + 19250*a*b^2*c^5*d^4*e - 2050*a*b^5*c^2*d*e^4 - 3300*a^3*b*c^4*d*e^4 - 19000*a*b^3*c^4*d^3*e^2 + 9250*a*b^4*c^3*d^2*e^3 - 11000*a^2*b*c^5*d^3*e^2 - 7350*a^2*b^3*c^3*d*e^4))/(12*c*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (x*(3*a^3*b^5*e^5 - 558*a^3*c^5*d^5 - 2*b^6*c^2*d^5 + 38*a*b^4*c^3*d^5 + 151*a^4*b^3*c*e^5 + 83*a^5*b*c^2*e^5 + 90*a^5*c^3*d*e^4 - 348*a^2*b^2*c^4*d^5 + 300*a^4*c^4*d^3*e^2 + 5*b^7*c*d^4*e - 280*a^2*b^4*c^2*d^3*e^2 - 2790*a^3*b^2*c^3*d^3*e^2 + 1510*a^3*b^3*c^2*d^2*e^3 - 95*a*b^5*c^2*d^4*e + 10*a*b^6*c*d^3*e^2 + 1395*a^3*b*c^4*d^4*e - 235*a^3*b^4*c*d*e^4 + 870*a^2*b^3*c^3*d^4*e + 30*a^2*b^5*c*d^2*e^3 + 830*a^4*b*c^3*d^2*e^3 - 920*a^4*b^2*c^2*d*e^4))/(3*c*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) - (5*c^3*x^7*(14*c^4*d^5 - a*b^3*e^5 + b^4*d*e^4 + 20*a*c^3*d^3*e^2 + 6*a^2*c^2*d*e^4 - 10*b^3*c*d^2*e^3 + 30*b^2*c^2*d^3*e^2 - 3*a^2*b*c*e^5 - 35*b*c^3*d^4*e + 12*a*b^2*c*d*e^4 - 30*a*b*c^2*d^2*e^3))/(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c) - (35*b*c^2*x^6*(14*c^4*d^5 - a*b^3*e^5 + b^4*d*e^4 + 20*a*c^3*d^3*e^2 + 6*a^2*c^2*d*e^4 - 10*b^3*c*d^2*e^3 + 30*b^2*c^2*d^3*e^2 - 3*a^2*b*c*e^5 - 35*b*c^3*d^4*e + 12*a*b^2*c*d*e^4 - 30*a*b*c^2*d^2*e^3))/(2*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)))/(x^4*(b^4 + 6*a^2*c^2 + 12*a*b^2*c) + a^4 + c^4*x^8 + x^2*(4*a^3*c + 6*a^2*b^2) + x^6*(4*a*c^3 + 6*b^2*c^2) + x^3*(4*a*b^3 + 12*a^2*b*c) + x^5*(4*b^3*c + 12*a*b*c^2) + 4*b*c^3*x^7 + 4*a^3*b*x)","B"
2222,1,2337,545,2.535736,"\text{Not used}","int((d + e*x)^4/(a + b*x + c*x^2)^5,x)","\frac{\frac{x^2\,\left(314\,a^4\,b\,c^2\,e^4-1024\,a^4\,c^3\,d\,e^3+508\,a^3\,b^3\,c\,e^4-1604\,a^3\,b^2\,c^2\,d\,e^3+2628\,a^3\,b\,c^3\,d^2\,e^2+129\,a^2\,b^5\,e^4-1596\,a^2\,b^4\,c\,d\,e^3+4278\,a^2\,b^3\,c^2\,d^2\,e^2-6132\,a^2\,b^2\,c^3\,d^3\,e+3066\,a^2\,b\,c^4\,d^4-36\,a\,b^6\,d\,e^3+492\,a\,b^5\,c\,d^2\,e^2-784\,a\,b^4\,c^2\,d^3\,e+392\,a\,b^3\,c^3\,d^4-18\,b^7\,d^2\,e^2+28\,b^6\,c\,d^3\,e-14\,b^5\,c^2\,d^4\right)}{6\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}-\frac{x\,\left(18\,a^5\,c^2\,e^4-184\,a^4\,b^2\,c\,e^4+332\,a^4\,b\,c^2\,d\,e^3+180\,a^4\,c^3\,d^2\,e^2-47\,a^3\,b^4\,e^4+604\,a^3\,b^3\,c\,d\,e^3-1674\,a^3\,b^2\,c^2\,d^2\,e^2+1116\,a^3\,b\,c^3\,d^3\,e-558\,a^3\,c^4\,d^4+12\,a^2\,b^5\,d\,e^3-168\,a^2\,b^4\,c\,d^2\,e^2+696\,a^2\,b^3\,c^2\,d^3\,e-348\,a^2\,b^2\,c^3\,d^4+6\,a\,b^6\,d^2\,e^2-76\,a\,b^5\,c\,d^3\,e+38\,a\,b^4\,c^2\,d^4+4\,b^7\,d^3\,e-2\,b^6\,c\,d^4\right)}{3\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}-\frac{-220\,a^5\,b\,c\,e^4+512\,a^5\,c^2\,d\,e^3-50\,a^4\,b^3\,e^4+664\,a^4\,b^2\,c\,d\,e^3-1944\,a^4\,b\,c^2\,d^2\,e^2+1536\,a^4\,c^3\,d^3\,e+12\,a^3\,b^4\,d\,e^3-168\,a^3\,b^3\,c\,d^2\,e^2+696\,a^3\,b^2\,c^2\,d^3\,e-1116\,a^3\,b\,c^3\,d^4+6\,a^2\,b^5\,d^2\,e^2-76\,a^2\,b^4\,c\,d^3\,e+326\,a^2\,b^3\,c^2\,d^4+4\,a\,b^6\,d^3\,e-50\,a\,b^5\,c\,d^4+3\,b^7\,d^4}{12\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{x^3\,\left(-66\,a^4\,c^3\,e^4+450\,a^3\,b^2\,c^2\,e^4-876\,a^3\,b\,c^3\,d\,e^3+876\,a^3\,c^4\,d^2\,e^2+203\,a^2\,b^4\,c\,e^4-1504\,a^2\,b^3\,c^2\,d\,e^3+2526\,a^2\,b^2\,c^3\,d^2\,e^2-2044\,a^2\,b\,c^4\,d^3\,e+1022\,a^2\,c^5\,d^4+37\,a\,b^6\,e^4-440\,a\,b^5\,c\,d\,e^3+1854\,a\,b^4\,c^2\,d^2\,e^2-2828\,a\,b^3\,c^3\,d^3\,e+1414\,a\,b^2\,c^4\,d^4-12\,b^7\,d\,e^3+54\,b^6\,c\,d^2\,e^2-84\,b^5\,c^2\,d^3\,e+42\,b^4\,c^3\,d^4\right)}{3\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{5\,x^4\,\left(5\,b^3+22\,a\,c\,b\right)\,\left(6\,a^2\,c^2\,e^4+12\,a\,b^2\,c\,e^4-60\,a\,b\,c^2\,d\,e^3+60\,a\,c^3\,d^2\,e^2+b^4\,e^4-20\,b^3\,c\,d\,e^3+90\,b^2\,c^2\,d^2\,e^2-140\,b\,c^3\,d^3\,e+70\,c^4\,d^4\right)}{12\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{x^5\,\left(13\,b^2\,c+11\,a\,c^2\right)\,\left(6\,a^2\,c^2\,e^4+12\,a\,b^2\,c\,e^4-60\,a\,b\,c^2\,d\,e^3+60\,a\,c^3\,d^2\,e^2+b^4\,e^4-20\,b^3\,c\,d\,e^3+90\,b^2\,c^2\,d^2\,e^2-140\,b\,c^3\,d^3\,e+70\,c^4\,d^4\right)}{3\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{c^3\,x^7\,\left(6\,a^2\,c^2\,e^4+12\,a\,b^2\,c\,e^4-60\,a\,b\,c^2\,d\,e^3+60\,a\,c^3\,d^2\,e^2+b^4\,e^4-20\,b^3\,c\,d\,e^3+90\,b^2\,c^2\,d^2\,e^2-140\,b\,c^3\,d^3\,e+70\,c^4\,d^4\right)}{256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8}+\frac{7\,b\,c^2\,x^6\,\left(6\,a^2\,c^2\,e^4+12\,a\,b^2\,c\,e^4-60\,a\,b\,c^2\,d\,e^3+60\,a\,c^3\,d^2\,e^2+b^4\,e^4-20\,b^3\,c\,d\,e^3+90\,b^2\,c^2\,d^2\,e^2-140\,b\,c^3\,d^3\,e+70\,c^4\,d^4\right)}{2\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}}{x^4\,\left(6\,a^2\,c^2+12\,a\,b^2\,c+b^4\right)+a^4+c^4\,x^8+x^2\,\left(4\,c\,a^3+6\,a^2\,b^2\right)+x^6\,\left(6\,b^2\,c^2+4\,a\,c^3\right)+x^3\,\left(12\,c\,a^2\,b+4\,a\,b^3\right)+x^5\,\left(4\,b^3\,c+12\,a\,b\,c^2\right)+4\,b\,c^3\,x^7+4\,a^3\,b\,x}+\frac{2\,\mathrm{atan}\left(\frac{\left(\frac{2\,c\,x\,\left(6\,a^2\,c^2\,e^4+12\,a\,b^2\,c\,e^4-60\,a\,b\,c^2\,d\,e^3+60\,a\,c^3\,d^2\,e^2+b^4\,e^4-20\,b^3\,c\,d\,e^3+90\,b^2\,c^2\,d^2\,e^2-140\,b\,c^3\,d^3\,e+70\,c^4\,d^4\right)}{{\left(4\,a\,c-b^2\right)}^{9/2}}+\frac{\left(256\,a^4\,b\,c^4-256\,a^3\,b^3\,c^3+96\,a^2\,b^5\,c^2-16\,a\,b^7\,c+b^9\right)\,\left(6\,a^2\,c^2\,e^4+12\,a\,b^2\,c\,e^4-60\,a\,b\,c^2\,d\,e^3+60\,a\,c^3\,d^2\,e^2+b^4\,e^4-20\,b^3\,c\,d\,e^3+90\,b^2\,c^2\,d^2\,e^2-140\,b\,c^3\,d^3\,e+70\,c^4\,d^4\right)}{{\left(4\,a\,c-b^2\right)}^{9/2}\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}\right)\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}{6\,a^2\,c^2\,e^4+12\,a\,b^2\,c\,e^4-60\,a\,b\,c^2\,d\,e^3+60\,a\,c^3\,d^2\,e^2+b^4\,e^4-20\,b^3\,c\,d\,e^3+90\,b^2\,c^2\,d^2\,e^2-140\,b\,c^3\,d^3\,e+70\,c^4\,d^4}\right)\,\left(6\,a^2\,c^2\,e^4+12\,a\,b^2\,c\,e^4-60\,a\,b\,c^2\,d\,e^3+60\,a\,c^3\,d^2\,e^2+b^4\,e^4-20\,b^3\,c\,d\,e^3+90\,b^2\,c^2\,d^2\,e^2-140\,b\,c^3\,d^3\,e+70\,c^4\,d^4\right)}{{\left(4\,a\,c-b^2\right)}^{9/2}}","Not used",1,"((x^2*(129*a^2*b^5*e^4 - 14*b^5*c^2*d^4 - 18*b^7*d^2*e^2 + 392*a*b^3*c^3*d^4 + 3066*a^2*b*c^4*d^4 + 508*a^3*b^3*c*e^4 + 314*a^4*b*c^2*e^4 - 1024*a^4*c^3*d*e^3 - 36*a*b^6*d*e^3 + 28*b^6*c*d^3*e + 4278*a^2*b^3*c^2*d^2*e^2 - 784*a*b^4*c^2*d^3*e + 492*a*b^5*c*d^2*e^2 - 1596*a^2*b^4*c*d*e^3 - 6132*a^2*b^2*c^3*d^3*e + 2628*a^3*b*c^3*d^2*e^2 - 1604*a^3*b^2*c^2*d*e^3))/(6*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) - (x*(4*b^7*d^3*e - 2*b^6*c*d^4 - 47*a^3*b^4*e^4 - 558*a^3*c^4*d^4 + 18*a^5*c^2*e^4 + 38*a*b^4*c^2*d^4 - 184*a^4*b^2*c*e^4 + 6*a*b^6*d^2*e^2 + 12*a^2*b^5*d*e^3 - 348*a^2*b^2*c^3*d^4 + 180*a^4*c^3*d^2*e^2 - 76*a*b^5*c*d^3*e - 1674*a^3*b^2*c^2*d^2*e^2 + 1116*a^3*b*c^3*d^3*e + 604*a^3*b^3*c*d*e^3 + 332*a^4*b*c^2*d*e^3 + 696*a^2*b^3*c^2*d^3*e - 168*a^2*b^4*c*d^2*e^2))/(3*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) - (3*b^7*d^4 - 50*a^4*b^3*e^4 - 1116*a^3*b*c^3*d^4 + 12*a^3*b^4*d*e^3 + 1536*a^4*c^3*d^3*e + 512*a^5*c^2*d*e^3 + 326*a^2*b^3*c^2*d^4 + 6*a^2*b^5*d^2*e^2 - 50*a*b^5*c*d^4 - 220*a^5*b*c*e^4 + 4*a*b^6*d^3*e - 76*a^2*b^4*c*d^3*e + 664*a^4*b^2*c*d*e^3 + 696*a^3*b^2*c^2*d^3*e - 168*a^3*b^3*c*d^2*e^2 - 1944*a^4*b*c^2*d^2*e^2)/(12*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (x^3*(37*a*b^6*e^4 - 12*b^7*d*e^3 + 1022*a^2*c^5*d^4 - 66*a^4*c^3*e^4 + 42*b^4*c^3*d^4 + 1414*a*b^2*c^4*d^4 + 203*a^2*b^4*c*e^4 - 84*b^5*c^2*d^3*e + 54*b^6*c*d^2*e^2 + 450*a^3*b^2*c^2*e^4 + 876*a^3*c^4*d^2*e^2 - 440*a*b^5*c*d*e^3 + 2526*a^2*b^2*c^3*d^2*e^2 - 2828*a*b^3*c^3*d^3*e - 2044*a^2*b*c^4*d^3*e - 876*a^3*b*c^3*d*e^3 + 1854*a*b^4*c^2*d^2*e^2 - 1504*a^2*b^3*c^2*d*e^3))/(3*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (5*x^4*(5*b^3 + 22*a*b*c)*(b^4*e^4 + 70*c^4*d^4 + 6*a^2*c^2*e^4 + 60*a*c^3*d^2*e^2 + 90*b^2*c^2*d^2*e^2 + 12*a*b^2*c*e^4 - 140*b*c^3*d^3*e - 20*b^3*c*d*e^3 - 60*a*b*c^2*d*e^3))/(12*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (x^5*(11*a*c^2 + 13*b^2*c)*(b^4*e^4 + 70*c^4*d^4 + 6*a^2*c^2*e^4 + 60*a*c^3*d^2*e^2 + 90*b^2*c^2*d^2*e^2 + 12*a*b^2*c*e^4 - 140*b*c^3*d^3*e - 20*b^3*c*d*e^3 - 60*a*b*c^2*d*e^3))/(3*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (c^3*x^7*(b^4*e^4 + 70*c^4*d^4 + 6*a^2*c^2*e^4 + 60*a*c^3*d^2*e^2 + 90*b^2*c^2*d^2*e^2 + 12*a*b^2*c*e^4 - 140*b*c^3*d^3*e - 20*b^3*c*d*e^3 - 60*a*b*c^2*d*e^3))/(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c) + (7*b*c^2*x^6*(b^4*e^4 + 70*c^4*d^4 + 6*a^2*c^2*e^4 + 60*a*c^3*d^2*e^2 + 90*b^2*c^2*d^2*e^2 + 12*a*b^2*c*e^4 - 140*b*c^3*d^3*e - 20*b^3*c*d*e^3 - 60*a*b*c^2*d*e^3))/(2*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)))/(x^4*(b^4 + 6*a^2*c^2 + 12*a*b^2*c) + a^4 + c^4*x^8 + x^2*(4*a^3*c + 6*a^2*b^2) + x^6*(4*a*c^3 + 6*b^2*c^2) + x^3*(4*a*b^3 + 12*a^2*b*c) + x^5*(4*b^3*c + 12*a*b*c^2) + 4*b*c^3*x^7 + 4*a^3*b*x) + (2*atan((((2*c*x*(b^4*e^4 + 70*c^4*d^4 + 6*a^2*c^2*e^4 + 60*a*c^3*d^2*e^2 + 90*b^2*c^2*d^2*e^2 + 12*a*b^2*c*e^4 - 140*b*c^3*d^3*e - 20*b^3*c*d*e^3 - 60*a*b*c^2*d*e^3))/(4*a*c - b^2)^(9/2) + ((b^9 + 256*a^4*b*c^4 + 96*a^2*b^5*c^2 - 256*a^3*b^3*c^3 - 16*a*b^7*c)*(b^4*e^4 + 70*c^4*d^4 + 6*a^2*c^2*e^4 + 60*a*c^3*d^2*e^2 + 90*b^2*c^2*d^2*e^2 + 12*a*b^2*c*e^4 - 140*b*c^3*d^3*e - 20*b^3*c*d*e^3 - 60*a*b*c^2*d*e^3))/((4*a*c - b^2)^(9/2)*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)))*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c))/(b^4*e^4 + 70*c^4*d^4 + 6*a^2*c^2*e^4 + 60*a*c^3*d^2*e^2 + 90*b^2*c^2*d^2*e^2 + 12*a*b^2*c*e^4 - 140*b*c^3*d^3*e - 20*b^3*c*d*e^3 - 60*a*b*c^2*d*e^3))*(b^4*e^4 + 70*c^4*d^4 + 6*a^2*c^2*e^4 + 60*a*c^3*d^2*e^2 + 90*b^2*c^2*d^2*e^2 + 12*a*b^2*c*e^4 - 140*b*c^3*d^3*e - 20*b^3*c*d*e^3 - 60*a*b*c^2*d*e^3))/(4*a*c - b^2)^(9/2)","B"
2223,1,1711,378,2.200871,"\text{Not used}","int((d + e*x)^3/(a + b*x + c*x^2)^5,x)","\frac{10\,c\,\mathrm{atan}\left(\frac{\left(\frac{10\,c^2\,x\,\left(b\,e-2\,c\,d\right)\,\left(b^2\,e^2-7\,b\,c\,d\,e+7\,c^2\,d^2+3\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{9/2}}+\frac{5\,c\,\left(b\,e-2\,c\,d\right)\,\left(b^2\,e^2-7\,b\,c\,d\,e+7\,c^2\,d^2+3\,a\,c\,e^2\right)\,\left(256\,a^4\,b\,c^4-256\,a^3\,b^3\,c^3+96\,a^2\,b^5\,c^2-16\,a\,b^7\,c+b^9\right)}{{\left(4\,a\,c-b^2\right)}^{9/2}\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}\right)\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}{-5\,b^3\,c\,e^3+45\,b^2\,c^2\,d\,e^2-105\,b\,c^3\,d^2\,e-15\,a\,b\,c^2\,e^3+70\,c^4\,d^3+30\,a\,c^3\,d\,e^2}\right)\,\left(b\,e-2\,c\,d\right)\,\left(b^2\,e^2-7\,b\,c\,d\,e+7\,c^2\,d^2+3\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{9/2}}-\frac{\frac{128\,a^5\,c^2\,e^3+166\,a^4\,b^2\,c\,e^3-972\,a^4\,b\,c^2\,d\,e^2+1152\,a^4\,c^3\,d^2\,e+3\,a^3\,b^4\,e^3-84\,a^3\,b^3\,c\,d\,e^2+522\,a^3\,b^2\,c^2\,d^2\,e-1116\,a^3\,b\,c^3\,d^3+3\,a^2\,b^5\,d\,e^2-57\,a^2\,b^4\,c\,d^2\,e+326\,a^2\,b^3\,c^2\,d^3+3\,a\,b^6\,d^2\,e-50\,a\,b^5\,c\,d^3+3\,b^7\,d^3}{12\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{x\,\left(83\,a^4\,b\,c^2\,e^3+90\,a^4\,c^3\,d\,e^2+151\,a^3\,b^3\,c\,e^3-837\,a^3\,b^2\,c^2\,d\,e^2+837\,a^3\,b\,c^3\,d^2\,e-558\,a^3\,c^4\,d^3+3\,a^2\,b^5\,e^3-84\,a^2\,b^4\,c\,d\,e^2+522\,a^2\,b^3\,c^2\,d^2\,e-348\,a^2\,b^2\,c^3\,d^3+3\,a\,b^6\,d\,e^2-57\,a\,b^5\,c\,d^2\,e+38\,a\,b^4\,c^2\,d^3+3\,b^7\,d^2\,e-2\,b^6\,c\,d^3\right)}{3\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{x^2\,\left(256\,a^4\,c^3\,e^3+401\,a^3\,b^2\,c^2\,e^3-1314\,a^3\,b\,c^3\,d\,e^2+399\,a^2\,b^4\,c\,e^3-2139\,a^2\,b^3\,c^2\,d\,e^2+4599\,a^2\,b^2\,c^3\,d^2\,e-3066\,a^2\,b\,c^4\,d^3+9\,a\,b^6\,e^3-246\,a\,b^5\,c\,d\,e^2+588\,a\,b^4\,c^2\,d^2\,e-392\,a\,b^3\,c^3\,d^3+9\,b^7\,d\,e^2-21\,b^6\,c\,d^2\,e+14\,b^5\,c^2\,d^3\right)}{6\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{5\,c^4\,x^7\,\left(b^3\,e^3-9\,b^2\,c\,d\,e^2+21\,b\,c^2\,d^2\,e+3\,a\,b\,c\,e^3-14\,c^3\,d^3-6\,a\,c^2\,d\,e^2\right)}{256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8}+\frac{5\,x^5\,\left(13\,b^2\,c^2+11\,a\,c^3\right)\,\left(b^3\,e^3-9\,b^2\,c\,d\,e^2+21\,b\,c^2\,d^2\,e+3\,a\,b\,c\,e^3-14\,c^3\,d^3-6\,a\,c^2\,d\,e^2\right)}{3\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{25\,x^4\,\left(5\,b^3\,c+22\,a\,b\,c^2\right)\,\left(b^3\,e^3-9\,b^2\,c\,d\,e^2+21\,b\,c^2\,d^2\,e+3\,a\,b\,c\,e^3-14\,c^3\,d^3-6\,a\,c^2\,d\,e^2\right)}{12\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{x^3\,\left(73\,a^2\,c^2+101\,a\,b^2\,c+3\,b^4\right)\,\left(b^3\,e^3-9\,b^2\,c\,d\,e^2+21\,b\,c^2\,d^2\,e+3\,a\,b\,c\,e^3-14\,c^3\,d^3-6\,a\,c^2\,d\,e^2\right)}{3\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{35\,b\,c^3\,x^6\,\left(b^3\,e^3-9\,b^2\,c\,d\,e^2+21\,b\,c^2\,d^2\,e+3\,a\,b\,c\,e^3-14\,c^3\,d^3-6\,a\,c^2\,d\,e^2\right)}{2\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}}{x^4\,\left(6\,a^2\,c^2+12\,a\,b^2\,c+b^4\right)+a^4+c^4\,x^8+x^2\,\left(4\,c\,a^3+6\,a^2\,b^2\right)+x^6\,\left(6\,b^2\,c^2+4\,a\,c^3\right)+x^3\,\left(12\,c\,a^2\,b+4\,a\,b^3\right)+x^5\,\left(4\,b^3\,c+12\,a\,b\,c^2\right)+4\,b\,c^3\,x^7+4\,a^3\,b\,x}","Not used",1,"(10*c*atan((((10*c^2*x*(b*e - 2*c*d)*(b^2*e^2 + 7*c^2*d^2 + 3*a*c*e^2 - 7*b*c*d*e))/(4*a*c - b^2)^(9/2) + (5*c*(b*e - 2*c*d)*(b^2*e^2 + 7*c^2*d^2 + 3*a*c*e^2 - 7*b*c*d*e)*(b^9 + 256*a^4*b*c^4 + 96*a^2*b^5*c^2 - 256*a^3*b^3*c^3 - 16*a*b^7*c))/((4*a*c - b^2)^(9/2)*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)))*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c))/(70*c^4*d^3 - 5*b^3*c*e^3 + 45*b^2*c^2*d*e^2 - 15*a*b*c^2*e^3 + 30*a*c^3*d*e^2 - 105*b*c^3*d^2*e))*(b*e - 2*c*d)*(b^2*e^2 + 7*c^2*d^2 + 3*a*c*e^2 - 7*b*c*d*e))/(4*a*c - b^2)^(9/2) - ((3*b^7*d^3 + 3*a^3*b^4*e^3 + 128*a^5*c^2*e^3 - 1116*a^3*b*c^3*d^3 + 166*a^4*b^2*c*e^3 + 3*a^2*b^5*d*e^2 + 1152*a^4*c^3*d^2*e + 326*a^2*b^3*c^2*d^3 - 50*a*b^5*c*d^3 + 3*a*b^6*d^2*e - 57*a^2*b^4*c*d^2*e - 84*a^3*b^3*c*d*e^2 - 972*a^4*b*c^2*d*e^2 + 522*a^3*b^2*c^2*d^2*e)/(12*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (x*(3*b^7*d^2*e - 2*b^6*c*d^3 + 3*a^2*b^5*e^3 - 558*a^3*c^4*d^3 + 38*a*b^4*c^2*d^3 + 151*a^3*b^3*c*e^3 + 83*a^4*b*c^2*e^3 + 90*a^4*c^3*d*e^2 - 348*a^2*b^2*c^3*d^3 + 3*a*b^6*d*e^2 - 57*a*b^5*c*d^2*e - 84*a^2*b^4*c*d*e^2 + 837*a^3*b*c^3*d^2*e + 522*a^2*b^3*c^2*d^2*e - 837*a^3*b^2*c^2*d*e^2))/(3*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (x^2*(9*a*b^6*e^3 + 9*b^7*d*e^2 + 256*a^4*c^3*e^3 + 14*b^5*c^2*d^3 - 392*a*b^3*c^3*d^3 - 3066*a^2*b*c^4*d^3 + 399*a^2*b^4*c*e^3 + 401*a^3*b^2*c^2*e^3 - 21*b^6*c*d^2*e - 246*a*b^5*c*d*e^2 + 588*a*b^4*c^2*d^2*e - 1314*a^3*b*c^3*d*e^2 + 4599*a^2*b^2*c^3*d^2*e - 2139*a^2*b^3*c^2*d*e^2))/(6*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (5*c^4*x^7*(b^3*e^3 - 14*c^3*d^3 + 3*a*b*c*e^3 - 6*a*c^2*d*e^2 + 21*b*c^2*d^2*e - 9*b^2*c*d*e^2))/(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c) + (5*x^5*(11*a*c^3 + 13*b^2*c^2)*(b^3*e^3 - 14*c^3*d^3 + 3*a*b*c*e^3 - 6*a*c^2*d*e^2 + 21*b*c^2*d^2*e - 9*b^2*c*d*e^2))/(3*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (25*x^4*(5*b^3*c + 22*a*b*c^2)*(b^3*e^3 - 14*c^3*d^3 + 3*a*b*c*e^3 - 6*a*c^2*d*e^2 + 21*b*c^2*d^2*e - 9*b^2*c*d*e^2))/(12*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (x^3*(3*b^4 + 73*a^2*c^2 + 101*a*b^2*c)*(b^3*e^3 - 14*c^3*d^3 + 3*a*b*c*e^3 - 6*a*c^2*d*e^2 + 21*b*c^2*d^2*e - 9*b^2*c*d*e^2))/(3*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (35*b*c^3*x^6*(b^3*e^3 - 14*c^3*d^3 + 3*a*b*c*e^3 - 6*a*c^2*d*e^2 + 21*b*c^2*d^2*e - 9*b^2*c*d*e^2))/(2*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)))/(x^4*(b^4 + 6*a^2*c^2 + 12*a*b^2*c) + a^4 + c^4*x^8 + x^2*(4*a^3*c + 6*a^2*b^2) + x^6*(4*a*c^3 + 6*b^2*c^2) + x^3*(4*a*b^3 + 12*a^2*b*c) + x^5*(4*b^3*c + 12*a*b*c^2) + 4*b*c^3*x^7 + 4*a^3*b*x)","B"
2224,1,1348,330,1.866915,"\text{Not used}","int((d + e*x)^2/(a + b*x + c*x^2)^5,x)","\frac{\frac{x^2\,\left(219\,a^2\,b\,c^2+28\,a\,b^3\,c-b^5\right)\,\left(3\,b^2\,e^2-14\,b\,c\,d\,e+14\,c^2\,d^2+2\,a\,c\,e^2\right)}{6\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}-\frac{x\,\left(30\,a^4\,c^3\,e^2-279\,a^3\,b^2\,c^2\,e^2+558\,a^3\,b\,c^3\,d\,e-558\,a^3\,c^4\,d^2-28\,a^2\,b^4\,c\,e^2+348\,a^2\,b^3\,c^2\,d\,e-348\,a^2\,b^2\,c^3\,d^2+a\,b^6\,e^2-38\,a\,b^5\,c\,d\,e+38\,a\,b^4\,c^2\,d^2+2\,b^7\,d\,e-2\,b^6\,c\,d^2\right)}{3\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}-\frac{-324\,a^4\,b\,c^2\,e^2+768\,a^4\,c^3\,d\,e-28\,a^3\,b^3\,c\,e^2+348\,a^3\,b^2\,c^2\,d\,e-1116\,a^3\,b\,c^3\,d^2+a^2\,b^5\,e^2-38\,a^2\,b^4\,c\,d\,e+326\,a^2\,b^3\,c^2\,d^2+2\,a\,b^6\,d\,e-50\,a\,b^5\,c\,d^2+3\,b^7\,d^2}{12\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{5\,c^5\,x^7\,\left(3\,b^2\,e^2-14\,b\,c\,d\,e+14\,c^2\,d^2+2\,a\,c\,e^2\right)}{256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8}+\frac{x^3\,\left(73\,a^2\,c^3+101\,a\,b^2\,c^2+3\,b^4\,c\right)\,\left(3\,b^2\,e^2-14\,b\,c\,d\,e+14\,c^2\,d^2+2\,a\,c\,e^2\right)}{3\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{25\,x^4\,\left(5\,b^3\,c^2+22\,a\,b\,c^3\right)\,\left(3\,b^2\,e^2-14\,b\,c\,d\,e+14\,c^2\,d^2+2\,a\,c\,e^2\right)}{12\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{35\,b\,c^4\,x^6\,\left(3\,b^2\,e^2-14\,b\,c\,d\,e+14\,c^2\,d^2+2\,a\,c\,e^2\right)}{2\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{5\,c\,x^5\,\left(13\,b^2\,c^2+11\,a\,c^3\right)\,\left(3\,b^2\,e^2-14\,b\,c\,d\,e+14\,c^2\,d^2+2\,a\,c\,e^2\right)}{3\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}}{x^4\,\left(6\,a^2\,c^2+12\,a\,b^2\,c+b^4\right)+a^4+c^4\,x^8+x^2\,\left(4\,c\,a^3+6\,a^2\,b^2\right)+x^6\,\left(6\,b^2\,c^2+4\,a\,c^3\right)+x^3\,\left(12\,c\,a^2\,b+4\,a\,b^3\right)+x^5\,\left(4\,b^3\,c+12\,a\,b\,c^2\right)+4\,b\,c^3\,x^7+4\,a^3\,b\,x}+\frac{10\,c^2\,\mathrm{atan}\left(\frac{\left(\frac{10\,c^3\,x\,\left(3\,b^2\,e^2-14\,b\,c\,d\,e+14\,c^2\,d^2+2\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{9/2}}+\frac{5\,c^2\,\left(3\,b^2\,e^2-14\,b\,c\,d\,e+14\,c^2\,d^2+2\,a\,c\,e^2\right)\,\left(256\,a^4\,b\,c^4-256\,a^3\,b^3\,c^3+96\,a^2\,b^5\,c^2-16\,a\,b^7\,c+b^9\right)}{{\left(4\,a\,c-b^2\right)}^{9/2}\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}\right)\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}{15\,b^2\,c^2\,e^2-70\,b\,c^3\,d\,e+70\,c^4\,d^2+10\,a\,c^3\,e^2}\right)\,\left(3\,b^2\,e^2-14\,b\,c\,d\,e+14\,c^2\,d^2+2\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^{9/2}}","Not used",1,"((x^2*(219*a^2*b*c^2 - b^5 + 28*a*b^3*c)*(3*b^2*e^2 + 14*c^2*d^2 + 2*a*c*e^2 - 14*b*c*d*e))/(6*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) - (x*(a*b^6*e^2 - 2*b^6*c*d^2 - 558*a^3*c^4*d^2 + 30*a^4*c^3*e^2 + 2*b^7*d*e + 38*a*b^4*c^2*d^2 - 28*a^2*b^4*c*e^2 - 348*a^2*b^2*c^3*d^2 - 279*a^3*b^2*c^2*e^2 + 558*a^3*b*c^3*d*e + 348*a^2*b^3*c^2*d*e - 38*a*b^5*c*d*e))/(3*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) - (3*b^7*d^2 + a^2*b^5*e^2 - 1116*a^3*b*c^3*d^2 - 28*a^3*b^3*c*e^2 - 324*a^4*b*c^2*e^2 + 2*a*b^6*d*e + 326*a^2*b^3*c^2*d^2 - 50*a*b^5*c*d^2 + 768*a^4*c^3*d*e - 38*a^2*b^4*c*d*e + 348*a^3*b^2*c^2*d*e)/(12*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (5*c^5*x^7*(3*b^2*e^2 + 14*c^2*d^2 + 2*a*c*e^2 - 14*b*c*d*e))/(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c) + (x^3*(3*b^4*c + 73*a^2*c^3 + 101*a*b^2*c^2)*(3*b^2*e^2 + 14*c^2*d^2 + 2*a*c*e^2 - 14*b*c*d*e))/(3*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (25*x^4*(5*b^3*c^2 + 22*a*b*c^3)*(3*b^2*e^2 + 14*c^2*d^2 + 2*a*c*e^2 - 14*b*c*d*e))/(12*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (35*b*c^4*x^6*(3*b^2*e^2 + 14*c^2*d^2 + 2*a*c*e^2 - 14*b*c*d*e))/(2*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (5*c*x^5*(11*a*c^3 + 13*b^2*c^2)*(3*b^2*e^2 + 14*c^2*d^2 + 2*a*c*e^2 - 14*b*c*d*e))/(3*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)))/(x^4*(b^4 + 6*a^2*c^2 + 12*a*b^2*c) + a^4 + c^4*x^8 + x^2*(4*a^3*c + 6*a^2*b^2) + x^6*(4*a*c^3 + 6*b^2*c^2) + x^3*(4*a*b^3 + 12*a^2*b*c) + x^5*(4*b^3*c + 12*a*b*c^2) + 4*b*c^3*x^7 + 4*a^3*b*x) + (10*c^2*atan((((10*c^3*x*(3*b^2*e^2 + 14*c^2*d^2 + 2*a*c*e^2 - 14*b*c*d*e))/(4*a*c - b^2)^(9/2) + (5*c^2*(3*b^2*e^2 + 14*c^2*d^2 + 2*a*c*e^2 - 14*b*c*d*e)*(b^9 + 256*a^4*b*c^4 + 96*a^2*b^5*c^2 - 256*a^3*b^3*c^3 - 16*a*b^7*c))/((4*a*c - b^2)^(9/2)*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)))*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c))/(70*c^4*d^2 + 10*a*c^3*e^2 + 15*b^2*c^2*e^2 - 70*b*c^3*d*e))*(3*b^2*e^2 + 14*c^2*d^2 + 2*a*c*e^2 - 14*b*c*d*e))/(4*a*c - b^2)^(9/2)","B"
2225,1,992,219,0.835722,"\text{Not used}","int((d + e*x)/(a + b*x + c*x^2)^5,x)","\frac{70\,c^3\,\mathrm{atan}\left(\frac{\left(\frac{70\,c^4\,x\,\left(b\,e-2\,c\,d\right)}{{\left(4\,a\,c-b^2\right)}^{9/2}}+\frac{35\,c^3\,\left(b\,e-2\,c\,d\right)\,\left(256\,a^4\,b\,c^4-256\,a^3\,b^3\,c^3+96\,a^2\,b^5\,c^2-16\,a\,b^7\,c+b^9\right)}{{\left(4\,a\,c-b^2\right)}^{9/2}\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}\right)\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}{70\,c^4\,d-35\,b\,c^3\,e}\right)\,\left(b\,e-2\,c\,d\right)}{{\left(4\,a\,c-b^2\right)}^{9/2}}-\frac{\frac{384\,e\,a^4\,c^3+174\,e\,a^3\,b^2\,c^2-1116\,d\,a^3\,b\,c^3-19\,e\,a^2\,b^4\,c+326\,d\,a^2\,b^3\,c^2+e\,a\,b^6-50\,d\,a\,b^5\,c+3\,d\,b^7}{12\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{35\,c^6\,x^7\,\left(b\,e-2\,c\,d\right)}{256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8}+\frac{x\,\left(b\,e-2\,c\,d\right)\,\left(279\,a^3\,c^3+174\,a^2\,b^2\,c^2-19\,a\,b^4\,c+b^6\right)}{3\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{7\,c\,x^2\,\left(b\,e-2\,c\,d\right)\,\left(219\,a^2\,b\,c^2+28\,a\,b^3\,c-b^5\right)}{6\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{245\,b\,c^5\,x^6\,\left(b\,e-2\,c\,d\right)}{2\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{7\,c\,x^3\,\left(b\,e-2\,c\,d\right)\,\left(73\,a^2\,c^3+101\,a\,b^2\,c^2+3\,b^4\,c\right)}{3\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{35\,c^2\,x^5\,\left(b\,e-2\,c\,d\right)\,\left(13\,b^2\,c^2+11\,a\,c^3\right)}{3\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}+\frac{175\,c\,x^4\,\left(5\,b^3\,c^2+22\,a\,b\,c^3\right)\,\left(b\,e-2\,c\,d\right)}{12\,\left(256\,a^4\,c^4-256\,a^3\,b^2\,c^3+96\,a^2\,b^4\,c^2-16\,a\,b^6\,c+b^8\right)}}{x^4\,\left(6\,a^2\,c^2+12\,a\,b^2\,c+b^4\right)+a^4+c^4\,x^8+x^2\,\left(4\,c\,a^3+6\,a^2\,b^2\right)+x^6\,\left(6\,b^2\,c^2+4\,a\,c^3\right)+x^3\,\left(12\,c\,a^2\,b+4\,a\,b^3\right)+x^5\,\left(4\,b^3\,c+12\,a\,b\,c^2\right)+4\,b\,c^3\,x^7+4\,a^3\,b\,x}","Not used",1,"(70*c^3*atan((((70*c^4*x*(b*e - 2*c*d))/(4*a*c - b^2)^(9/2) + (35*c^3*(b*e - 2*c*d)*(b^9 + 256*a^4*b*c^4 + 96*a^2*b^5*c^2 - 256*a^3*b^3*c^3 - 16*a*b^7*c))/((4*a*c - b^2)^(9/2)*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)))*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c))/(70*c^4*d - 35*b*c^3*e))*(b*e - 2*c*d))/(4*a*c - b^2)^(9/2) - ((3*b^7*d + 384*a^4*c^3*e + a*b^6*e + 326*a^2*b^3*c^2*d + 174*a^3*b^2*c^2*e - 50*a*b^5*c*d - 1116*a^3*b*c^3*d - 19*a^2*b^4*c*e)/(12*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (35*c^6*x^7*(b*e - 2*c*d))/(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c) + (x*(b*e - 2*c*d)*(b^6 + 279*a^3*c^3 + 174*a^2*b^2*c^2 - 19*a*b^4*c))/(3*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (7*c*x^2*(b*e - 2*c*d)*(219*a^2*b*c^2 - b^5 + 28*a*b^3*c))/(6*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (245*b*c^5*x^6*(b*e - 2*c*d))/(2*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (7*c*x^3*(b*e - 2*c*d)*(3*b^4*c + 73*a^2*c^3 + 101*a*b^2*c^2))/(3*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (35*c^2*x^5*(b*e - 2*c*d)*(11*a*c^3 + 13*b^2*c^2))/(3*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)) + (175*c*x^4*(5*b^3*c^2 + 22*a*b*c^3)*(b*e - 2*c*d))/(12*(b^8 + 256*a^4*c^4 + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 - 16*a*b^6*c)))/(x^4*(b^4 + 6*a^2*c^2 + 12*a*b^2*c) + a^4 + c^4*x^8 + x^2*(4*a^3*c + 6*a^2*b^2) + x^6*(4*a*c^3 + 6*b^2*c^2) + x^3*(4*a*b^3 + 12*a^2*b*c) + x^5*(4*b^3*c + 12*a*b*c^2) + 4*b*c^3*x^7 + 4*a^3*b*x)","B"
2226,0,-1,171,0.000000,"\text{Not used}","int(1/(a + b*x + c*x^2)^5,x)","\left\{\begin{array}{cl} \frac{70\,c^4\,\ln\left(\frac{\frac{b}{2}-\sqrt{\frac{b^2}{4}-a\,c}+c\,x}{\frac{b}{2}+\sqrt{\frac{b^2}{4}-a\,c}+c\,x}\right)}{{\left(b^2-4\,a\,c\right)}^{9/2}}+\frac{70\,\left(\frac{b}{2}+c\,x\right)\,\left(\frac{c^2}{30\,{\left(4\,a\,c-b^2\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^3}+\frac{c^3}{6\,{\left(4\,a\,c-b^2\right)}^3\,{\left(c\,x^2+b\,x+a\right)}^2}+\frac{c^4}{{\left(4\,a\,c-b^2\right)}^4\,\left(c\,x^2+b\,x+a\right)}+\frac{c}{140\,\left(4\,a\,c-b^2\right)\,{\left(c\,x^2+b\,x+a\right)}^4}\right)}{c} & \text{\ if\ \ }0<b^2-4\,a\,c\\ \frac{70\,\left(\frac{b}{2}+c\,x\right)\,\left(\frac{c^2}{30\,{\left(4\,a\,c-b^2\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^3}+\frac{c^3}{6\,{\left(4\,a\,c-b^2\right)}^3\,{\left(c\,x^2+b\,x+a\right)}^2}+\frac{c^4}{{\left(4\,a\,c-b^2\right)}^4\,\left(c\,x^2+b\,x+a\right)}+\frac{c}{140\,\left(4\,a\,c-b^2\right)\,{\left(c\,x^2+b\,x+a\right)}^4}\right)}{c}+\frac{70\,c^4\,\mathrm{atan}\left(\frac{\frac{b}{2}+c\,x}{\sqrt{a\,c-\frac{b^2}{4}}}\right)}{\sqrt{a\,c-\frac{b^2}{4}}\,{\left(4\,a\,c-b^2\right)}^4} & \text{\ if\ \ }b^2-4\,a\,c<0\\ \int \frac{1}{{\left(c\,x^2+b\,x+a\right)}^5} \,d x & \text{\ if\ \ }b^2-4\,a\,c\notin \mathbb{R}\vee b^2=4\,a\,c \end{array}\right.","Not used",1,"piecewise(0 < - 4*a*c + b^2, (70*c^4*log((b/2 - (- a*c + b^2/4)^(1/2) + c*x)/(b/2 + (- a*c + b^2/4)^(1/2) + c*x)))/(- 4*a*c + b^2)^(9/2) + (70*(b/2 + c*x)*(c^2/(30*(4*a*c - b^2)^2*(a + b*x + c*x^2)^3) + c^3/(6*(4*a*c - b^2)^3*(a + b*x + c*x^2)^2) + c^4/((4*a*c - b^2)^4*(a + b*x + c*x^2)) + c/(140*(4*a*c - b^2)*(a + b*x + c*x^2)^4)))/c, - 4*a*c + b^2 < 0, (70*(b/2 + c*x)*(c^2/(30*(4*a*c - b^2)^2*(a + b*x + c*x^2)^3) + c^3/(6*(4*a*c - b^2)^3*(a + b*x + c*x^2)^2) + c^4/((4*a*c - b^2)^4*(a + b*x + c*x^2)) + c/(140*(4*a*c - b^2)*(a + b*x + c*x^2)^4)))/c + (70*c^4*atan((b/2 + c*x)/(a*c - b^2/4)^(1/2)))/((a*c - b^2/4)^(1/2)*(4*a*c - b^2)^4), ~in(- 4*a*c + b^2, 'real') | b^2 == 4*a*c, int(1/(a + b*x + c*x^2)^5, x))","F"
2227,1,59814,1324,23.603120,"\text{Not used}","int(1/((d + e*x)*(a + b*x + 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used",1,"((25*a^3*b^8*e^7 + 3200*a^7*c^4*e^7 - 3*b^7*c^4*d^7 - 3*b^11*d^3*e^4 + 50*a*b^5*c^5*d^7 + 1116*a^3*b*c^7*d^7 - 385*a^4*b^6*c*e^7 + 13*a*b^10*d^2*e^5 - 23*a^2*b^9*d*e^6 + 384*a^4*c^7*d^6*e + 12*b^8*c^3*d^6*e + 12*b^10*c*d^4*e^3 - 326*a^2*b^3*c^6*d^7 + 2175*a^5*b^4*c^2*e^7 - 5150*a^6*b^2*c^3*e^7 + 1664*a^5*c^6*d^4*e^3 + 2944*a^6*c^5*d^2*e^5 - 18*b^9*c^2*d^5*e^2 - 1681*a^2*b^5*c^4*d^5*e^2 + 598*a^2*b^6*c^3*d^4*e^3 + 314*a^2*b^7*c^2*d^3*e^4 + 4724*a^3*b^3*c^5*d^5*e^2 + 307*a^3*b^4*c^4*d^4*e^3 - 2812*a^3*b^5*c^3*d^3*e^4 + 574*a^3*b^6*c^2*d^2*e^5 - 11522*a^4*b^2*c^5*d^4*e^3 + 9254*a^4*b^3*c^4*d^3*e^4 + 985*a^4*b^4*c^3*d^2*e^5 - 10910*a^5*b^2*c^4*d^2*e^5 - 199*a*b^6*c^4*d^6*e + 10*a*b^9*c*d^3*e^4 + 356*a^3*b^7*c*d*e^6 + 956*a^6*b*c^4*d*e^6 + 284*a*b^7*c^3*d^5*e^2 - 158*a*b^8*c^2*d^4*e^3 + 1285*a^2*b^4*c^5*d^6*e - 167*a^2*b^8*c*d^2*e^5 - 4290*a^3*b^2*c^6*d^6*e + 3252*a^4*b*c^6*d^5*e^2 - 1983*a^4*b^5*c^2*d*e^6 + 3092*a^5*b*c^5*d^3*e^4 + 4204*a^5*b^3*c^3*d*e^6)/(12*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)) + (x^7*(70*c^11*d^7 + b^7*c^4*e^7 - 15*a*b^5*c^5*e^7 - 187*a^3*b*c^7*e^7 + 290*a*c^10*d^5*e^2 + 374*a^3*c^8*d*e^6 + b^6*c^5*d*e^6 + 82*a^2*b^3*c^6*e^7 + 466*a^2*c^9*d^3*e^4 + 295*b^2*c^9*d^5*e^2 - 125*b^3*c^8*d^4*e^3 + b^4*c^7*d^3*e^4 + b^5*c^6*d^2*e^5 - 245*b*c^10*d^6*e - 725*a*b*c^9*d^4*e^3 - 14*a*b^4*c^6*d*e^6 + 492*a*b^2*c^8*d^3*e^4 - 13*a*b^3*c^7*d^2*e^5 - 699*a^2*b*c^8*d^2*e^5 + 69*a^2*b^2*c^7*d*e^6))/(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7) + (x^4*(48*b^10*c*e^7 + 5376*a^5*c^6*e^7 + 1750*b^3*c^8*d^7 - 612*a*b^8*c^2*e^7 - 6125*b^4*c^7*d^6*e + 12*b^9*c^2*d*e^6 + 2272*a^2*b^6*c^3*e^7 + 473*a^3*b^4*c^4*e^7 - 20058*a^4*b^2*c^5*e^7 + 768*a^4*c^7*d^2*e^5 + 7375*b^5*c^6*d^5*e^2 - 3125*b^6*c^5*d^4*e^3 + 25*b^7*c^4*d^3*e^4 + 28*b^8*c^3*d^2*e^5 + 7700*a*b*c^9*d^7 - 79750*a^2*b^2*c^7*d^4*e^3 + 65770*a^2*b^3*c^6*d^3*e^4 - 18617*a^2*b^4*c^5*d^2*e^5 - 77658*a^3*b^2*c^6*d^2*e^5 - 26950*a*b^2*c^8*d^6*e - 32*a*b^7*c^3*d*e^6 + 37812*a^4*b*c^6*d*e^6 + 39700*a*b^3*c^7*d^5*e^2 - 31875*a*b^4*c^6*d^4*e^3 + 12410*a*b^5*c^5*d^3*e^4 - 263*a*b^6*c^4*d^2*e^5 + 31900*a^2*b*c^8*d^5*e^2 - 1063*a^2*b^5*c^4*d*e^6 + 51260*a^3*b*c^7*d^3*e^4 + 20268*a^3*b^3*c^5*d*e^6))/(12*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)) + (x^5*(770*a*c^10*d^7 + 910*b^2*c^9*d^7 + 18*b^9*c^2*e^7 - 264*a*b^7*c^3*e^7 - 777*a^4*b*c^6*e^7 + 3858*a^4*c^7*d*e^6 - 3185*b^3*c^8*d^6*e + 12*b^8*c^3*d*e^6 + 1381*a^2*b^5*c^4*e^7 - 2809*a^3*b^3*c^5*e^7 + 3190*a^2*c^9*d^5*e^2 + 5126*a^3*c^8*d^3*e^4 + 3835*b^4*c^7*d^5*e^2 - 1625*b^5*c^6*d^4*e^3 + 13*b^6*c^5*d^3*e^4 + 13*b^7*c^4*d^2*e^5 - 2695*a*b*c^9*d^6*e + 11470*a^2*b^2*c^7*d^3*e^4 - 9230*a^2*b^3*c^6*d^2*e^5 - 155*a*b^6*c^4*d*e^6 + 7015*a*b^2*c^8*d^5*e^2 - 10800*a*b^3*c^7*d^4*e^3 + 6407*a*b^4*c^6*d^3*e^4 - 158*a*b^5*c^5*d^2*e^5 - 7975*a^2*b*c^8*d^4*e^3 + 647*a^2*b^4*c^5*d*e^6 - 7689*a^3*b*c^7*d^2*e^5 + 5877*a^3*b^2*c^6*d*e^6))/(3*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)) + (x^3*(3*b^11*e^7 + 1022*a^2*c^9*d^7 + 42*b^4*c^7*d^7 + 1414*a*b^2*c^8*d^7 + 393*a^5*b*c^5*e^7 + 4590*a^5*c^6*d*e^6 - 147*b^5*c^6*d^6*e - 204*a^2*b^7*c^2*e^7 + 1882*a^3*b^5*c^3*e^7 - 5089*a^4*b^3*c^4*e^7 + 4234*a^3*c^8*d^5*e^2 + 6650*a^4*c^7*d^3*e^4 + 177*b^6*c^5*d^5*e^2 - 75*b^7*c^4*d^4*e^3 + 3*b^9*c^2*d^2*e^5 - 15*a*b^9*c*e^7 - 3*b^10*c*d*e^6 + 10165*a^2*b^2*c^7*d^5*e^2 - 16470*a^2*b^3*c^6*d^4*e^3 + 10175*a^2*b^4*c^5*d^3*e^4 - 437*a^2*b^5*c^4*d^2*e^5 + 16750*a^3*b^2*c^6*d^3*e^4 - 14924*a^3*b^3*c^5*d^2*e^5 - 4949*a*b^3*c^7*d^6*e + 66*a*b^8*c^2*d*e^6 - 3577*a^2*b*c^8*d^6*e + 6133*a*b^4*c^6*d^5*e^2 - 2960*a*b^5*c^5*d^4*e^3 + 325*a*b^6*c^4*d^3*e^4 - 26*a*b^7*c^3*d^2*e^5 - 518*a^2*b^6*c^3*d*e^6 - 10585*a^3*b*c^7*d^4*e^3 + 2009*a^3*b^4*c^4*d*e^6 - 9591*a^4*b*c^6*d^2*e^5 + 8511*a^4*b^2*c^5*d*e^6))/(3*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)) + (x*(13*a^2*b^9*e^7 + 558*a^3*c^8*d^7 + 2*b^6*c^5*d^7 + b^11*d^2*e^5 - 38*a*b^4*c^6*d^7 - 196*a^3*b^7*c*e^7 + 689*a^6*b*c^4*e^7 + 1950*a^6*c^5*d*e^6 - 7*b^7*c^4*d^6*e - 2*b^10*c*d^3*e^4 + 348*a^2*b^2*c^7*d^7 + 1068*a^4*b^5*c^2*e^7 - 2324*a^5*b^3*c^3*e^7 + 2202*a^4*c^7*d^5*e^2 + 3210*a^5*c^6*d^3*e^4 + 8*b^8*c^3*d^5*e^2 - 2*b^9*c^2*d^4*e^3 - 5*a*b^10*d*e^6 + 1268*a^2*b^4*c^5*d^5*e^2 - 77*a^2*b^5*c^4*d^4*e^3 - 412*a^2*b^6*c^3*d^3*e^4 - 2*a^2*b^7*c^2*d^2*e^5 + 3903*a^3*b^2*c^6*d^5*e^2 - 5003*a^3*b^3*c^5*d^4*e^3 + 2531*a^3*b^4*c^4*d^3*e^4 + 598*a^3*b^5*c^3*d^2*e^5 + 6224*a^4*b^2*c^5*d^3*e^4 - 4727*a^4*b^3*c^4*d^2*e^5 + 133*a*b^5*c^5*d^6*e - 11*a*b^9*c*d^2*e^5 + 80*a^2*b^8*c*d*e^6 - 1953*a^3*b*c^7*d^6*e - 145*a*b^6*c^4*d^5*e^2 + 22*a*b^7*c^3*d^4*e^3 + 44*a*b^8*c^2*d^3*e^4 - 1218*a^2*b^3*c^6*d^6*e - 450*a^3*b^6*c^2*d*e^6 - 5377*a^4*b*c^6*d^4*e^3 + 790*a^4*b^4*c^3*d*e^6 - 4175*a^5*b*c^5*d^2*e^5 + 2285*a^5*b^2*c^4*d*e^6))/(3*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)) + (x^2*(21*a*b^10*e^7 - 3*b^11*d*e^6 + 3328*a^6*c^5*e^7 - 14*b^5*c^6*d^7 + 392*a*b^3*c^7*d^7 + 3066*a^2*b*c^8*d^7 - 274*a^2*b^8*c*e^7 + 49*b^6*c^5*d^6*e + 5*b^10*c*d^2*e^5 + 1078*a^3*b^6*c^2*e^7 - 150*a^4*b^4*c^3*e^7 - 7525*a^5*b^2*c^4*e^7 + 256*a^4*c^7*d^4*e^3 + 1280*a^5*c^6*d^2*e^5 - 59*b^7*c^4*d^5*e^2 + 26*b^8*c^3*d^4*e^3 - 4*b^9*c^2*d^3*e^4 + 38*a*b^9*c*d*e^6 + 14545*a^2*b^3*c^6*d^5*e^2 - 9439*a^2*b^4*c^5*d^4*e^3 + 2341*a^2*b^5*c^4*d^3*e^4 + 530*a^2*b^6*c^3*d^2*e^5 - 32011*a^3*b^2*c^6*d^4*e^3 + 25132*a^3*b^3*c^5*d^3*e^4 - 5335*a^3*b^4*c^4*d^2*e^5 - 30565*a^4*b^2*c^5*d^2*e^5 - 1372*a*b^4*c^6*d^6*e + 12490*a^5*b*c^5*d*e^6 + 1594*a*b^5*c^5*d^5*e^2 - 571*a*b^6*c^4*d^4*e^3 - 32*a*b^7*c^3*d^3*e^4 - 70*a*b^8*c^2*d^2*e^5 - 10731*a^2*b^2*c^7*d^6*e - 74*a^2*b^7*c^2*d*e^6 + 12702*a^3*b*c^7*d^5*e^2 - 1044*a^3*b^5*c^3*d*e^6 + 19438*a^4*b*c^6*d^3*e^4 + 8291*a^4*b^3*c^4*d*e^6))/(6*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)) + (x^6*(490*b*c^10*d^7 + 256*a^4*c^7*e^7 + 8*b^8*c^3*e^7 - 121*a*b^6*c^4*e^7 - 1715*b^2*c^9*d^6*e + 7*b^7*c^4*d*e^6 + 670*a^2*b^4*c^5*e^7 - 1565*a^3*b^2*c^6*e^7 + 2065*b^3*c^8*d^5*e^2 - 875*b^4*c^7*d^4*e^3 + 7*b^5*c^6*d^3*e^4 + 7*b^6*c^5*d^2*e^5 - 4893*a^2*b^2*c^7*d^2*e^5 + 2030*a*b*c^9*d^5*e^2 - 98*a*b^5*c^5*d*e^6 + 2618*a^3*b*c^7*d*e^6 - 5075*a*b^2*c^8*d^4*e^3 + 3444*a*b^3*c^7*d^3*e^4 - 91*a*b^4*c^6*d^2*e^5 + 3262*a^2*b*c^8*d^3*e^4 + 483*a^2*b^3*c^6*d*e^6))/(2*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)))/(x^4*(b^4 + 6*a^2*c^2 + 12*a*b^2*c) + a^4 + c^4*x^8 + x^2*(4*a^3*c + 6*a^2*b^2) + x^6*(4*a*c^3 + 6*b^2*c^2) + x^3*(4*a*b^3 + 12*a^2*b*c) + x^5*(4*b^3*c + 12*a*b*c^2) + 4*b*c^3*x^7 + 4*a^3*b*x) + symsum(log((b^15*c^2*e^17 + 4900*c^17*d^15*e^2 - 31*a*b^13*c^3*e^17 - 47872*a^7*b*c^9*e^17 + 40600*a*c^16*d^13*e^4 + 95744*a^7*c^10*d*e^16 - 34300*b*c^16*d^14*e^3 + 2*b^14*c^3*d*e^16 + 418*a^2*b^11*c^4*e^17 - 3195*a^3*b^9*c^5*e^17 + 14960*a^4*b^7*c^6*e^17 - 42784*a^5*b^5*c^7*e^17 + 68864*a^6*b^3*c^8*e^17 + 149340*a^2*c^15*d^11*e^6 + 322640*a^3*c^14*d^9*e^8 + 451996*a^4*c^13*d^7*e^10 + 422808*a^5*c^12*d^5*e^12 + 259172*a^6*c^11*d^3*e^14 + 101325*b^2*c^15*d^13*e^4 - 162050*b^3*c^14*d^12*e^5 + 148415*b^4*c^13*d^11*e^6 - 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2228,1,78821,1761,26.544632,"\text{Not used}","int(1/((d + e*x)^2*(a + b*x + 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13756*a^7*b*c^4*d*e^8 + 475*a*b^7*c^4*d^7*e^2 - 420*a*b^8*c^3*d^6*e^3 + 140*a*b^9*c^2*d^5*e^4 + 1592*a^2*b^4*c^6*d^8*e + 143*a^2*b^9*c*d^3*e^6 - 5232*a^3*b^2*c^7*d^8*e - 534*a^3*b^8*c*d^2*e^7 + 2712*a^4*b*c^7*d^7*e^2 - 800*a^5*b*c^6*d^5*e^4 - 6717*a^5*b^5*c^2*d*e^8 - 8472*a^6*b*c^5*d^3*e^6 + 16396*a^6*b^3*c^3*d*e^8)/(12*(256*a^4*c^9*d^10 + a^5*b^8*e^10 + 256*a^9*c^4*e^10 + b^8*c^5*d^10 - b^13*d^5*e^5 - 16*a*b^6*c^6*d^10 - 16*a^6*b^6*c*e^10 + 5*a*b^12*d^4*e^6 - 5*a^4*b^9*d*e^9 - 5*b^9*c^4*d^9*e + 5*b^12*c*d^6*e^4 + 96*a^2*b^4*c^7*d^10 - 256*a^3*b^2*c^8*d^10 + 96*a^7*b^4*c^2*e^10 - 256*a^8*b^2*c^3*e^10 - 10*a^2*b^11*d^3*e^7 + 10*a^3*b^10*d^2*e^8 + 1280*a^5*c^8*d^8*e^2 + 2560*a^6*c^7*d^6*e^4 + 2560*a^7*c^6*d^4*e^6 + 1280*a^8*c^5*d^2*e^8 + 10*b^10*c^3*d^8*e^2 - 10*b^11*c^2*d^7*e^3 + 880*a^2*b^6*c^5*d^8*e^2 - 640*a^2*b^7*c^4*d^7*e^3 + 10*a^2*b^8*c^3*d^6*e^4 + 194*a^2*b^9*c^2*d^5*e^5 - 2080*a^3*b^4*c^6*d^8*e^2 + 640*a^3*b^5*c^5*d^7*e^3 + 1440*a^3*b^6*c^4*d^6*e^4 - 1184*a^3*b^7*c^3*d^5*e^5 + 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392*a*b^3*c^8*d^9 + 3066*a^2*b*c^9*d^9 + 1960*a^3*b^8*c*e^9 + 1116*a^3*c^9*d^8*e + 60*b^6*c^6*d^8*e - 15*b^11*c*d^3*e^6 - 10716*a^4*b^6*c^2*e^9 + 23924*a^5*b^4*c^3*e^9 - 13154*a^6*b^2*c^4*e^9 + 6424*a^4*c^8*d^6*e^3 + 16736*a^5*c^7*d^4*e^5 + 32104*a^6*c^6*d^2*e^7 - 95*b^7*c^5*d^7*e^2 + 65*b^8*c^4*d^6*e^3 - 20*b^9*c^3*d^5*e^4 + 14*b^10*c^2*d^4*e^5 - 55*a*b^11*d*e^8 + 16645*a^2*b^3*c^7*d^7*e^2 - 11711*a^2*b^4*c^6*d^6*e^3 + 4059*a^2*b^5*c^5*d^5*e^4 + 453*a^2*b^6*c^4*d^4*e^5 - 858*a^2*b^7*c^3*d^3*e^6 - 966*a^2*b^8*c^2*d^2*e^7 - 40222*a^3*b^2*c^7*d^6*e^3 + 35333*a^3*b^3*c^6*d^5*e^4 - 6756*a^3*b^4*c^5*d^4*e^5 - 931*a^3*b^5*c^4*d^3*e^6 + 4476*a^3*b^6*c^3*d^2*e^7 - 51574*a^4*b^2*c^6*d^4*e^5 + 14623*a^4*b^3*c^5*d^3*e^6 - 621*a^4*b^4*c^4*d^2*e^7 - 25194*a^5*b^2*c^5*d^2*e^7 - 1644*a*b^4*c^7*d^8*e + 30*a*b^10*c*d^2*e^7 + 830*a^2*b^9*c*d*e^8 - 9778*a^6*b*c^5*d*e^8 + 2440*a*b^5*c^6*d^7*e^2 - 1350*a*b^6*c^5*d^6*e^3 + 105*a*b^7*c^4*d^5*e^4 - 132*a*b^8*c^3*d^4*e^5 + 214*a*b^9*c^2*d^3*e^6 - 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1440*a^4*b^6*c^3*d^4*e^6 - 640*a^4*b^7*c^2*d^3*e^7 + 5120*a^5*b^2*c^6*d^6*e^4 + 2560*a^5*b^3*c^5*d^5*e^5 - 5440*a^5*b^4*c^4*d^4*e^6 + 640*a^5*b^5*c^3*d^3*e^7 + 880*a^5*b^6*c^2*d^2*e^8 + 5120*a^6*b^2*c^5*d^4*e^6 + 2560*a^6*b^3*c^4*d^3*e^7 - 2080*a^6*b^4*c^3*d^2*e^8 + 1280*a^7*b^2*c^4*d^2*e^8 + 80*a*b^7*c^5*d^9*e - 4*a*b^11*c*d^5*e^5 - 1280*a^4*b*c^8*d^9*e + 80*a^5*b^7*c*d*e^9 - 1280*a^8*b*c^4*d*e^9 - 155*a*b^8*c^4*d^8*e^2 + 140*a*b^9*c^3*d^7*e^3 - 50*a*b^10*c^2*d^6*e^4 - 480*a^2*b^5*c^6*d^9*e - 50*a^2*b^10*c*d^4*e^6 + 1280*a^3*b^3*c^7*d^9*e + 140*a^3*b^9*c*d^3*e^7 - 155*a^4*b^8*c*d^2*e^8 - 5120*a^5*b*c^7*d^7*e^3 - 7680*a^6*b*c^6*d^5*e^5 - 480*a^6*b^5*c^2*d*e^9 - 5120*a^7*b*c^5*d^3*e^7 + 1280*a^7*b^3*c^3*d*e^9)) + (5*x^6*(294*b*c^11*d^9 - 2772*a^5*c^7*e^9 - 36*b^10*c^2*e^9 + 528*a*b^8*c^3*e^9 - 812*b^2*c^10*d^8*e + 24*b^9*c^3*d*e^8 - 2762*a^2*b^6*c^4*e^9 + 5618*a^3*b^4*c^5*e^9 - 1722*a^4*b^2*c^6*e^9 + 1672*a^2*c^10*d^6*e^3 + 3872*a^3*c^9*d^4*e^5 + 5880*a^4*c^8*d^2*e^7 + 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20204100*a^2*b^4*c^14*d^12*e^8*z + 19230750*a^4*b^4*c^12*d^8*e^12*z - 19026000*a^2*b^3*c^15*d^13*e^7*z + 14553000*a^5*b^5*c^10*d^5*e^15*z - 13173300*a^5*b^8*c^7*d^2*e^18*z - 12127500*a^6*b^4*c^10*d^4*e^16*z - 11806200*a^2*b^5*c^13*d^11*e^9*z + 10296000*a^2*b^2*c^16*d^14*e^6*z + 9563400*a^4*b^5*c^11*d^7*e^13*z - 6699000*a^3*b^5*c^12*d^9*e^11*z + 4851000*a^6*b^5*c^9*d^3*e^17*z - 4365900*a^4*b^6*c^10*d^6*e^14*z + 3395700*a^2*b^6*c^12*d^10*e^10*z - 3326400*a^4*b^7*c^9*d^5*e^15*z + 3241350*a^4*b^10*c^6*d^2*e^18*z - 2910600*a^5*b^4*c^11*d^6*e^14*z - 2079000*a^5*b^7*c^8*d^3*e^17*z + 1940400*a^3*b^8*c^9*d^6*e^14*z - 1940400*a^3*b^7*c^10*d^7*e^13*z - 1386000*a^3*b^6*c^11*d^8*e^12*z + 1039500*a^4*b^8*c^8*d^4*e^16*z - 990000*a^2*b^7*c^11*d^9*e^11*z + 816750*a^2*b^8*c^10*d^8*e^12*z - 537600*a^3*b^12*c^5*d^2*e^18*z + 346500*a^4*b^9*c^7*d^3*e^17*z - 277200*a^2*b^10*c^8*d^6*e^14*z - 231000*a^3*b^10*c^7*d^4*e^16*z + 92400*a^3*b^9*c^8*d^5*e^15*z + 63000*a^2*b^11*c^7*d^5*e^15*z + 57600*a^2*b^14*c^4*d^2*e^18*z - 39600*a^2*b^9*c^9*d^7*e^13*z - 21000*a^3*b^11*c^6*d^3*e^17*z + 15750*a^2*b^12*c^6*d^4*e^16*z + 58260600*a^7*b^5*c^8*d*e^19*z - 56805300*a^8*b^3*c^9*d*e^19*z - 47124000*a^6*b*c^13*d^7*e^13*z - 40194000*a^5*b*c^14*d^9*e^11*z - 34927200*a^7*b*c^12*d^5*e^15*z - 34297200*a^6*b^7*c^7*d*e^19*z - 23511600*a^4*b*c^15*d^11*e^9*z - 14553000*a^8*b*c^11*d^3*e^17*z + 12896100*a^5*b^9*c^6*d*e^19*z - 9996000*a^3*b*c^16*d^13*e^7*z + 6633000*a*b^4*c^15*d^14*e^6*z - 5481000*a*b^5*c^14*d^13*e^7*z - 4910400*a*b^3*c^16*d^15*e^5*z - 3225600*a^4*b^11*c^5*d*e^19*z - 3031200*a^2*b*c^17*d^15*e^5*z + 2570400*a*b^6*c^13*d^12*e^8*z + 2220300*a*b^2*c^17*d^16*e^4*z + 537600*a^3*b^13*c^4*d*e^19*z - 516600*a*b^7*c^12*d^11*e^9*z - 148500*a*b^10*c^9*d^8*e^12*z + 148500*a*b^9*c^10*d^9*e^11*z - 69300*a*b^8*c^11*d^10*e^10*z - 57600*a^2*b^15*c^3*d*e^19*z + 57600*a*b^11*c^8*d^7*e^13*z - 6300*a*b^13*c^6*d^5*e^15*z + 6300*a*b^12*c^7*d^6*e^14*z - 3600*a*b^16*c^3*d^2*e^18*z - 23629800*a^9*c^11*d^2*e^18*z - 957000*b^5*c^15*d^15*e^5*z + 905025*b^4*c^16*d^16*e^4*z + 643500*b^6*c^14*d^14*e^6*z - 556500*b^3*c^17*d^17*e^3*z - 252000*b^7*c^13*d^13*e^7*z + 217000*b^2*c^18*d^18*e^2*z + 44100*b^8*c^12*d^12*e^8*z + 9375*b^12*c^8*d^8*e^12*z - 8500*b^11*c^9*d^9*e^11*z - 5100*b^13*c^7*d^7*e^13*z + 3850*b^10*c^10*d^10*e^10*z + 1050*b^14*c^6*d^6*e^14*z - 700*b^9*c^11*d^11*e^9*z + 100*b^18*c^2*d^2*e^18*z + 11781000*a^6*c^14*d^8*e^12*z + 11642400*a^7*c^13*d^6*e^14*z + 8038800*a^5*c^15*d^10*e^10*z + 7276500*a^8*c^12*d^4*e^16*z + 3918600*a^4*c^16*d^12*e^8*z + 1428000*a^3*c^17*d^14*e^6*z + 378900*a^2*c^18*d^16*e^4*z + 14862825*a^8*b^4*c^8*e^20*z - 14763600*a^7*b^6*c^7*e^20*z + 8602650*a^6*b^8*c^6*e^20*z - 6899700*a^9*b^2*c^9*e^20*z - 3225600*a^5*b^10*c^5*e^20*z + 806400*a^4*b^12*c^4*e^20*z - 134400*a^3*b^14*c^3*e^20*z + 14400*a^2*b^16*c^2*e^20*z + 63000*a*c^19*d^18*e^2*z - 49000*b*c^19*d^19*e*z - 100*b^19*c*d*e^19*z - 900*a*b^18*c*e^20*z + 396900*a^10*c^10*e^20*z + 4900*c^20*d^20*z + 25*b^20*e^20*z + 3048000*a^3*b*c^11*d^2*e^16 + 2595000*a^2*b*c^12*d^4*e^14 + 2445000*a^3*b^2*c^10*d*e^17 - 1245000*a*b^2*c^12*d^5*e^13 - 669750*a^2*b^4*c^9*d*e^17 + 181500*a*b^4*c^10*d^3*e^15 + 172500*a*b^3*c^11*d^4*e^14 + 143250*a*b^5*c^9*d^2*e^16 + 1176000*a*b*c^13*d^6*e^12 + 87750*a*b^6*c^8*d*e^17 - 1071000*a^2*b^2*c^11*d^3*e^15 - 988500*a^2*b^3*c^10*d^2*e^16 - 357000*b^2*c^13*d^7*e^11 + 220500*b^3*c^12*d^6*e^12 - 12375*b^5*c^10*d^4*e^14 - 11000*b^6*c^9*d^3*e^15 - 9750*b^4*c^11*d^5*e^13 - 7875*b^7*c^8*d^2*e^16 - 2032000*a^3*c^12*d^3*e^15 - 1038000*a^2*c^13*d^5*e^13 - 1730500*a^3*b^3*c^9*e^18 + 586125*a^2*b^5*c^8*e^18 + 220500*b*c^14*d^8*e^10 - 4500*b^8*c^7*d*e^17 - 3969000*a^4*c^11*d*e^17 - 336000*a*c^14*d^7*e^11 + 1984500*a^4*b*c^10*e^18 - 90000*a*b^7*c^7*e^18 - 49000*c^15*d^9*e^9 + 5250*b^9*c^6*e^18, z, k), k, 1, 3)","B"
2229,1,82,89,0.133710,"\text{Not used}","int(1/((2*x + 1)*(3*x + 5*x^2 + 2)^3),x)","\frac{32\,\ln\left(x+\frac{1}{2}\right)}{343}-\ln\left(x+\frac{3}{10}-\frac{\sqrt{31}\,1{}\mathrm{i}}{10}\right)\,\left(\frac{16}{343}+\frac{\sqrt{31}\,62812{}\mathrm{i}}{10218313}\right)+\ln\left(x+\frac{3}{10}+\frac{\sqrt{31}\,1{}\mathrm{i}}{10}\right)\,\left(-\frac{16}{343}+\frac{\sqrt{31}\,62812{}\mathrm{i}}{10218313}\right)+\frac{\frac{916\,x^3}{47089}+\frac{1138\,x^2}{33635}+\frac{26984\,x}{1177225}+\frac{28901}{2354450}}{x^4+\frac{6\,x^3}{5}+\frac{29\,x^2}{25}+\frac{12\,x}{25}+\frac{4}{25}}","Not used",1,"(32*log(x + 1/2))/343 - log(x - (31^(1/2)*1i)/10 + 3/10)*((31^(1/2)*62812i)/10218313 + 16/343) + log(x + (31^(1/2)*1i)/10 + 3/10)*((31^(1/2)*62812i)/10218313 - 16/343) + ((26984*x)/1177225 + (1138*x^2)/33635 + (916*x^3)/47089 + 28901/2354450)/((12*x)/25 + (29*x^2)/25 + (6*x^3)/5 + x^4 + 4/25)","B"
2230,1,93,114,0.122113,"\text{Not used}","int(1/((2*x + 1)^2*(3*x + 5*x^2 + 2)^3),x)","\frac{384\,\ln\left(x+\frac{1}{2}\right)}{2401}-\frac{\frac{25758\,x^4}{329623}+\frac{134178\,x^3}{1648115}+\frac{1146799\,x^2}{16481150}+\frac{77311\,x}{3296230}+\frac{175969}{32962300}}{x^5+\frac{17\,x^4}{10}+\frac{44\,x^3}{25}+\frac{53\,x^2}{50}+\frac{2\,x}{5}+\frac{2}{25}}+\ln\left(x+\frac{3}{10}-\frac{\sqrt{31}\,1{}\mathrm{i}}{10}\right)\,\left(-\frac{192}{2401}+\frac{\sqrt{31}\,532506{}\mathrm{i}}{71528191}\right)-\ln\left(x+\frac{3}{10}+\frac{\sqrt{31}\,1{}\mathrm{i}}{10}\right)\,\left(\frac{192}{2401}+\frac{\sqrt{31}\,532506{}\mathrm{i}}{71528191}\right)","Not used",1,"(384*log(x + 1/2))/2401 - ((77311*x)/3296230 + (1146799*x^2)/16481150 + (134178*x^3)/1648115 + (25758*x^4)/329623 + 175969/32962300)/((2*x)/5 + (53*x^2)/50 + (44*x^3)/25 + (17*x^4)/10 + x^5 + 2/25) + log(x - (31^(1/2)*1i)/10 + 3/10)*((31^(1/2)*532506i)/71528191 - 192/2401) - log(x + (31^(1/2)*1i)/10 + 3/10)*((31^(1/2)*532506i)/71528191 + 192/2401)","B"
2231,1,102,110,0.111681,"\text{Not used}","int(1/((2*x + 1)*(3*x + 5*x^2 + 2)^4),x)","\frac{128\,\ln\left(x+\frac{1}{2}\right)}{2401}-\ln\left(x+\frac{3}{10}-\frac{\sqrt{31}\,1{}\mathrm{i}}{10}\right)\,\left(\frac{64}{2401}+\frac{\sqrt{31}\,9503688{}\mathrm{i}}{2217373921}\right)+\ln\left(x+\frac{3}{10}+\frac{\sqrt{31}\,1{}\mathrm{i}}{10}\right)\,\left(-\frac{64}{2401}+\frac{\sqrt{31}\,9503688{}\mathrm{i}}{2217373921}\right)+\frac{\frac{162584\,x^5}{10218313}+\frac{1696036\,x^4}{51091565}+\frac{28681124\,x^3}{766373475}+\frac{35085948\,x^2}{1277289125}+\frac{14977728\,x}{1277289125}+\frac{2766233}{766373475}}{x^6+\frac{9\,x^5}{5}+\frac{57\,x^4}{25}+\frac{207\,x^3}{125}+\frac{114\,x^2}{125}+\frac{36\,x}{125}+\frac{8}{125}}","Not used",1,"(128*log(x + 1/2))/2401 - log(x - (31^(1/2)*1i)/10 + 3/10)*((31^(1/2)*9503688i)/2217373921 + 64/2401) + log(x + (31^(1/2)*1i)/10 + 3/10)*((31^(1/2)*9503688i)/2217373921 - 64/2401) + ((14977728*x)/1277289125 + (35085948*x^2)/1277289125 + (28681124*x^3)/766373475 + (1696036*x^4)/51091565 + (162584*x^5)/10218313 + 2766233/766373475)/((36*x)/125 + (114*x^2)/125 + (207*x^3)/125 + (57*x^4)/25 + (9*x^5)/5 + x^6 + 8/125)","B"
2232,1,113,142,0.113195,"\text{Not used}","int(1/((2*x + 1)^2*(3*x + 5*x^2 + 2)^4),x)","\frac{2048\,\ln\left(x+\frac{1}{2}\right)}{16807}+\ln\left(x+\frac{3}{10}-\frac{\sqrt{31}\,1{}\mathrm{i}}{10}\right)\,\left(-\frac{1024}{16807}+\frac{\sqrt{31}\,58028492{}\mathrm{i}}{15521617447}\right)-\ln\left(x+\frac{3}{10}+\frac{\sqrt{31}\,1{}\mathrm{i}}{10}\right)\,\left(\frac{1024}{16807}+\frac{\sqrt{31}\,58028492{}\mathrm{i}}{15521617447}\right)-\frac{\frac{3401156\,x^6}{71528191}+\frac{26385064\,x^5}{357640955}+\frac{150847357\,x^4}{1788204775}+\frac{464796512\,x^3}{8941023875}+\frac{433131361\,x^2}{17882047750}+\frac{304894531\,x}{53646143250}+\frac{38489903}{53646143250}}{x^7+\frac{23\,x^6}{10}+\frac{159\,x^5}{50}+\frac{699\,x^4}{250}+\frac{87\,x^3}{50}+\frac{93\,x^2}{125}+\frac{26\,x}{125}+\frac{4}{125}}","Not used",1,"(2048*log(x + 1/2))/16807 + log(x - (31^(1/2)*1i)/10 + 3/10)*((31^(1/2)*58028492i)/15521617447 - 1024/16807) - log(x + (31^(1/2)*1i)/10 + 3/10)*((31^(1/2)*58028492i)/15521617447 + 1024/16807) - ((304894531*x)/53646143250 + (433131361*x^2)/17882047750 + (464796512*x^3)/8941023875 + (150847357*x^4)/1788204775 + (26385064*x^5)/357640955 + (3401156*x^6)/71528191 + 38489903/53646143250)/((26*x)/125 + (93*x^2)/125 + (87*x^3)/50 + (699*x^4)/250 + (159*x^5)/50 + (23*x^6)/10 + x^7 + 4/125)","B"
2233,1,34,47,0.127635,"\text{Not used}","int(-(3*x - 7)/(2*x + x^2 - 5),x)","\ln\left(x-\sqrt{6}+1\right)\,\left(\frac{5\,\sqrt{6}}{6}-\frac{3}{2}\right)-\ln\left(x+\sqrt{6}+1\right)\,\left(\frac{5\,\sqrt{6}}{6}+\frac{3}{2}\right)","Not used",1,"log(x - 6^(1/2) + 1)*((5*6^(1/2))/6 - 3/2) - log(x + 6^(1/2) + 1)*((5*6^(1/2))/6 + 3/2)","B"
2234,1,46,41,0.099629,"\text{Not used}","int(1/((x - 1)*(x + x^2 + 1)),x)","\frac{\ln\left(x-1\right)}{3}+\ln\left(x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)-\ln\left(x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)","Not used",1,"log(x - 1)/3 + log(x - (3^(1/2)*1i)/2 + 1/2)*((3^(1/2)*1i)/6 - 1/6) - log(x + (3^(1/2)*1i)/2 + 1/2)*((3^(1/2)*1i)/6 + 1/6)","B"
2235,1,178,114,1.033128,"\text{Not used}","int((2*(a/b)^(1/n) - 2*x*cos((Pi*(2*k - 1))/n))/((a/b)^(2/n) + x^2 - 2*x*cos((Pi*(2*k - 1))/n)*(a/b)^(1/n)),x)","-2\,\mathrm{atan}\left(\frac{2\,x\,\sqrt{1-{\cos\left(\frac{\Pi \,\left(2\,k-1\right)}{n}\right)}^2}-2\,\cos\left(\frac{\Pi \,\left(2\,k-1\right)}{n}\right)\,{\left(\frac{a}{b}\right)}^{1/n}\,\sqrt{1-{\cos\left(\frac{\Pi \,\left(2\,k-1\right)}{n}\right)}^2}}{2\,{\cos\left(\frac{\Pi \,\left(2\,k-1\right)}{n}\right)}^2\,{\left(\frac{a}{b}\right)}^{1/n}-2\,{\left(\frac{a}{b}\right)}^{1/n}}\right)\,\sqrt{1-{\cos\left(\frac{\Pi \,\left(2\,k-1\right)}{n}\right)}^2}-\cos\left(\frac{\Pi \,\left(2\,k-1\right)}{n}\right)\,\ln\left({\left(\frac{a}{b}\right)}^{2/n}+x^2-2\,x\,\cos\left(\frac{\Pi \,\left(2\,k-1\right)}{n}\right)\,{\left(\frac{a}{b}\right)}^{1/n}\right)","Not used",1,"- 2*atan((2*x*(1 - cos((Pi*(2*k - 1))/n)^2)^(1/2) - 2*cos((Pi*(2*k - 1))/n)*(a/b)^(1/n)*(1 - cos((Pi*(2*k - 1))/n)^2)^(1/2))/(2*cos((Pi*(2*k - 1))/n)^2*(a/b)^(1/n) - 2*(a/b)^(1/n)))*(1 - cos((Pi*(2*k - 1))/n)^2)^(1/2) - cos((Pi*(2*k - 1))/n)*log((a/b)^(2/n) + x^2 - 2*x*cos((Pi*(2*k - 1))/n)*(a/b)^(1/n))","B"
2236,1,26,40,0.056975,"\text{Not used}","int(x^4/(13*x + 15*x^2 + 2),x)","\frac{139\,x}{3375}-\frac{16\,\ln\left(x+\frac{2}{3}\right)}{567}+\frac{\ln\left(x+\frac{1}{5}\right)}{4375}-\frac{13\,x^2}{450}+\frac{x^3}{45}","Not used",1,"(139*x)/3375 - (16*log(x + 2/3))/567 + log(x + 1/5)/4375 - (13*x^2)/450 + x^3/45","B"
2237,1,21,33,0.036777,"\text{Not used}","int(x^3/(13*x + 15*x^2 + 2),x)","\frac{8\,\ln\left(x+\frac{2}{3}\right)}{189}-\frac{13\,x}{225}-\frac{\ln\left(x+\frac{1}{5}\right)}{875}+\frac{x^2}{30}","Not used",1,"(8*log(x + 2/3))/189 - (13*x)/225 - log(x + 1/5)/875 + x^2/30","B"
2238,1,16,26,0.074199,"\text{Not used}","int(x^2/(13*x + 15*x^2 + 2),x)","\frac{x}{15}-\frac{4\,\ln\left(x+\frac{2}{3}\right)}{63}+\frac{\ln\left(x+\frac{1}{5}\right)}{175}","Not used",1,"x/15 - (4*log(x + 2/3))/63 + log(x + 1/5)/175","B"
2239,1,13,21,0.872315,"\text{Not used}","int(x/(13*x + 15*x^2 + 2),x)","\frac{2\,\ln\left(x+\frac{2}{3}\right)}{21}-\frac{\ln\left(x+\frac{1}{5}\right)}{35}","Not used",1,"(2*log(x + 2/3))/21 - log(x + 1/5)/35","B"
2240,1,8,21,0.086857,"\text{Not used}","int(1/(13*x + 15*x^2 + 2),x)","-\frac{2\,\mathrm{atanh}\left(\frac{30\,x}{7}+\frac{13}{7}\right)}{7}","Not used",1,"-(2*atanh((30*x)/7 + 13/7))/7","B"
2241,1,17,27,0.881307,"\text{Not used}","int(1/(x*(13*x + 15*x^2 + 2)),x)","\frac{3\,\ln\left(x+\frac{2}{3}\right)}{14}-\frac{5\,\ln\left(x+\frac{1}{5}\right)}{7}+\frac{\ln\left(x\right)}{2}","Not used",1,"(3*log(x + 2/3))/14 - (5*log(x + 1/5))/7 + log(x)/2","B"
2242,1,22,34,0.815819,"\text{Not used}","int(1/(x^2*(13*x + 15*x^2 + 2)),x)","\frac{25\,\ln\left(x+\frac{1}{5}\right)}{7}-\frac{9\,\ln\left(x+\frac{2}{3}\right)}{28}-\frac{13\,\ln\left(x\right)}{4}-\frac{1}{2\,x}","Not used",1,"(25*log(x + 1/5))/7 - (9*log(x + 2/3))/28 - (13*log(x))/4 - 1/(2*x)","B"
2243,1,26,41,0.036305,"\text{Not used}","int(1/(x^3*(13*x + 15*x^2 + 2)),x)","\frac{27\,\ln\left(x+\frac{2}{3}\right)}{56}-\frac{125\,\ln\left(x+\frac{1}{5}\right)}{7}+\frac{139\,\ln\left(x\right)}{8}+\frac{\frac{13\,x}{4}-\frac{1}{4}}{x^2}","Not used",1,"(27*log(x + 2/3))/56 - (125*log(x + 1/5))/7 + (139*log(x))/8 + ((13*x)/4 - 1/4)/x^2","B"
2244,1,32,48,0.040480,"\text{Not used}","int(1/(x^4*(13*x + 15*x^2 + 2)),x)","\frac{625\,\ln\left(x+\frac{1}{5}\right)}{7}-\frac{81\,\ln\left(x+\frac{2}{3}\right)}{112}-\frac{1417\,\ln\left(x\right)}{16}-\frac{\frac{139\,x^2}{8}-\frac{13\,x}{8}+\frac{1}{6}}{x^3}","Not used",1,"(625*log(x + 1/5))/7 - (81*log(x + 2/3))/112 - (1417*log(x))/16 - ((139*x^2)/8 - (13*x)/8 + 1/6)/x^3","B"
2245,1,26,40,0.027880,"\text{Not used}","int(x^5/(2*x + 13*x^2 + 15*x^3),x)","\frac{139\,x}{3375}-\frac{16\,\ln\left(x+\frac{2}{3}\right)}{567}+\frac{\ln\left(x+\frac{1}{5}\right)}{4375}-\frac{13\,x^2}{450}+\frac{x^3}{45}","Not used",1,"(139*x)/3375 - (16*log(x + 2/3))/567 + log(x + 1/5)/4375 - (13*x^2)/450 + x^3/45","B"
2246,1,21,33,0.029082,"\text{Not used}","int(x^4/(2*x + 13*x^2 + 15*x^3),x)","\frac{8\,\ln\left(x+\frac{2}{3}\right)}{189}-\frac{13\,x}{225}-\frac{\ln\left(x+\frac{1}{5}\right)}{875}+\frac{x^2}{30}","Not used",1,"(8*log(x + 2/3))/189 - (13*x)/225 - log(x + 1/5)/875 + x^2/30","B"
2247,1,16,26,0.027714,"\text{Not used}","int(x^3/(2*x + 13*x^2 + 15*x^3),x)","\frac{x}{15}-\frac{4\,\ln\left(x+\frac{2}{3}\right)}{63}+\frac{\ln\left(x+\frac{1}{5}\right)}{175}","Not used",1,"x/15 - (4*log(x + 2/3))/63 + log(x + 1/5)/175","B"
2248,1,13,21,0.027143,"\text{Not used}","int(x^2/(2*x + 13*x^2 + 15*x^3),x)","\frac{2\,\ln\left(x+\frac{2}{3}\right)}{21}-\frac{\ln\left(x+\frac{1}{5}\right)}{35}","Not used",1,"(2*log(x + 2/3))/21 - log(x + 1/5)/35","B"
2249,1,8,21,0.015820,"\text{Not used}","int(x/(2*x + 13*x^2 + 15*x^3),x)","-\frac{2\,\mathrm{atanh}\left(\frac{30\,x}{7}+\frac{13}{7}\right)}{7}","Not used",1,"-(2*atanh((30*x)/7 + 13/7))/7","B"
2250,1,17,27,0.028479,"\text{Not used}","int(1/(2*x + 13*x^2 + 15*x^3),x)","\frac{3\,\ln\left(x+\frac{2}{3}\right)}{14}-\frac{5\,\ln\left(x+\frac{1}{5}\right)}{7}+\frac{\ln\left(x\right)}{2}","Not used",1,"(3*log(x + 2/3))/14 - (5*log(x + 1/5))/7 + log(x)/2","B"
2251,1,22,34,0.038769,"\text{Not used}","int(1/(x*(2*x + 13*x^2 + 15*x^3)),x)","\frac{25\,\ln\left(x+\frac{1}{5}\right)}{7}-\frac{9\,\ln\left(x+\frac{2}{3}\right)}{28}-\frac{13\,\ln\left(x\right)}{4}-\frac{1}{2\,x}","Not used",1,"(25*log(x + 1/5))/7 - (9*log(x + 2/3))/28 - (13*log(x))/4 - 1/(2*x)","B"
2252,1,26,41,0.039166,"\text{Not used}","int(1/(x^2*(2*x + 13*x^2 + 15*x^3)),x)","\frac{27\,\ln\left(x+\frac{2}{3}\right)}{56}-\frac{125\,\ln\left(x+\frac{1}{5}\right)}{7}+\frac{139\,\ln\left(x\right)}{8}+\frac{\frac{13\,x}{4}-\frac{1}{4}}{x^2}","Not used",1,"(27*log(x + 2/3))/56 - (125*log(x + 1/5))/7 + (139*log(x))/8 + ((13*x)/4 - 1/4)/x^2","B"
2253,1,32,48,0.039326,"\text{Not used}","int(1/(x^3*(2*x + 13*x^2 + 15*x^3)),x)","\frac{625\,\ln\left(x+\frac{1}{5}\right)}{7}-\frac{81\,\ln\left(x+\frac{2}{3}\right)}{112}-\frac{1417\,\ln\left(x\right)}{16}-\frac{\frac{139\,x^2}{8}-\frac{13\,x}{8}+\frac{1}{6}}{x^3}","Not used",1,"(625*log(x + 1/5))/7 - (81*log(x + 2/3))/112 - (1417*log(x))/16 - ((139*x^2)/8 - (13*x)/8 + 1/6)/x^3","B"
2254,1,12,12,0.818106,"\text{Not used}","int(x/(4*x + x^2 + 4),x)","\ln\left(x+2\right)+\frac{2}{x+2}","Not used",1,"log(x + 2) + 2/(x + 2)","B"
2255,1,20,26,0.036577,"\text{Not used}","int(x/(2*x + x^2 + 5),x)","\frac{\ln\left(x^2+2\,x+5\right)}{2}-\frac{\mathrm{atan}\left(\frac{x}{2}+\frac{1}{2}\right)}{2}","Not used",1,"log(2*x + x^2 + 5)/2 - atan(x/2 + 1/2)/2","B"
2256,1,13,17,0.056404,"\text{Not used}","int(x/(x^2 - 5*x + 6),x)","3\,\ln\left(x-3\right)-2\,\ln\left(x-2\right)","Not used",1,"3*log(x - 3) - 2*log(x - 2)","B"
2257,1,24,26,0.035642,"\text{Not used}","int(x/(2*x + x^2 + 2)^2,x)","-\frac{\mathrm{atan}\left(x+1\right)}{2}-\frac{\frac{x}{2}+1}{x^2+2\,x+2}","Not used",1,"- atan(x + 1)/2 - (x/2 + 1)/(2*x + x^2 + 2)","B"
2258,1,56,54,0.053385,"\text{Not used}","int(x/(x + x^2 + 1)^3,x)","-\frac{2\,\sqrt{3}\,\mathrm{atan}\left(\frac{2\,\sqrt{3}\,x}{3}+\frac{\sqrt{3}}{3}\right)}{9}-\frac{\frac{x^3}{3}+\frac{x^2}{2}+\frac{2\,x}{3}+\frac{1}{2}}{x^4+2\,x^3+3\,x^2+2\,x+1}","Not used",1,"- (2*3^(1/2)*atan((2*3^(1/2)*x)/3 + 3^(1/2)/3))/9 - ((2*x)/3 + x^2/2 + x^3/3 + 1/2)/(2*x + 3*x^2 + 2*x^3 + x^4 + 1)","B"
2259,1,29,32,0.032091,"\text{Not used}","int(x^2/(x + x^2 + 1),x)","x-\frac{\ln\left(x^2+x+1\right)}{2}-\frac{\sqrt{3}\,\mathrm{atan}\left(\frac{2\,\sqrt{3}\,x}{3}+\frac{\sqrt{3}}{3}\right)}{3}","Not used",1,"x - log(x + x^2 + 1)/2 - (3^(1/2)*atan((2*3^(1/2)*x)/3 + 3^(1/2)/3))/3","B"
2260,1,14,18,0.043818,"\text{Not used}","int(x^2/(x^2 - 3*x + 2),x)","x-\ln\left(x-1\right)+4\,\ln\left(x-2\right)","Not used",1,"x - log(x - 1) + 4*log(x - 2)","B"
2261,1,14,20,0.813486,"\text{Not used}","int(x^2/(x + x^2 - 6),x)","x+\frac{4\,\ln\left(x-2\right)}{5}-\frac{9\,\ln\left(x+3\right)}{5}","Not used",1,"x + (4*log(x - 2))/5 - (9*log(x + 3))/5","B"
2262,1,15,15,0.030991,"\text{Not used}","int(x^2/(2*x + x^2 + 2)^2,x)","\mathrm{atan}\left(x+1\right)+\frac{1}{x^2+2\,x+2}","Not used",1,"atan(x + 1) + 1/(2*x + x^2 + 2)","B"
2263,1,21,27,0.029508,"\text{Not used}","int(x^3/(x^2 - 3*x + 2),x)","3\,x-\ln\left(x-1\right)+8\,\ln\left(x-2\right)+\frac{x^2}{2}","Not used",1,"3*x - log(x - 1) + 8*log(x - 2) + x^2/2","B"
2264,1,20,22,0.038627,"\text{Not used}","int(x^3/(2*x + x^2 + 1),x)","3\,\ln\left(x+1\right)-2\,x+\frac{1}{x+1}+\frac{x^2}{2}","Not used",1,"3*log(x + 1) - 2*x + 1/(x + 1) + x^2/2","B"
2265,1,22,26,0.037974,"\text{Not used}","int(x^3/(x^2 - 2*x + 1),x)","2\,x+3\,\ln\left(x-1\right)-\frac{1}{x-1}+\frac{x^2}{2}","Not used",1,"2*x + 3*log(x - 1) - 1/(x - 1) + x^2/2","B"
2266,1,27,29,0.024390,"\text{Not used}","int(x^4/(4*x + x^2 + 4),x)","12\,x-32\,\ln\left(x+2\right)-\frac{16}{x+2}-2\,x^2+\frac{x^3}{3}","Not used",1,"12*x - 32*log(x + 2) - 16/(x + 2) - 2*x^2 + x^3/3","B"
2267,1,28,33,0.066487,"\text{Not used}","int(1/(x*(x + x^2 + 1)),x)","\ln\left(x\right)-\frac{\ln\left(x^2+x+1\right)}{2}-\frac{\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{3}\,\left(2\,x+1\right)}{3}\right)}{3}","Not used",1,"log(x) - log(x + x^2 + 1)/2 - (3^(1/2)*atan((3^(1/2)*(2*x + 1))/3))/3","B"
2268,1,58,75,0.841650,"\text{Not used}","int((d + e*x)^(5/2)*(a + b*x + c*x^2),x)","\frac{2\,{\left(d+e\,x\right)}^{7/2}\,\left(63\,c\,{\left(d+e\,x\right)}^2+99\,a\,e^2+99\,c\,d^2+77\,b\,e\,\left(d+e\,x\right)-154\,c\,d\,\left(d+e\,x\right)-99\,b\,d\,e\right)}{693\,e^3}","Not used",1,"(2*(d + e*x)^(7/2)*(63*c*(d + e*x)^2 + 99*a*e^2 + 99*c*d^2 + 77*b*e*(d + e*x) - 154*c*d*(d + e*x) - 99*b*d*e))/(693*e^3)","B"
2269,1,58,75,0.814482,"\text{Not used}","int((d + e*x)^(3/2)*(a + b*x + c*x^2),x)","\frac{2\,{\left(d+e\,x\right)}^{5/2}\,\left(35\,c\,{\left(d+e\,x\right)}^2+63\,a\,e^2+63\,c\,d^2+45\,b\,e\,\left(d+e\,x\right)-90\,c\,d\,\left(d+e\,x\right)-63\,b\,d\,e\right)}{315\,e^3}","Not used",1,"(2*(d + e*x)^(5/2)*(35*c*(d + e*x)^2 + 63*a*e^2 + 63*c*d^2 + 45*b*e*(d + e*x) - 90*c*d*(d + e*x) - 63*b*d*e))/(315*e^3)","B"
2270,1,58,75,0.055224,"\text{Not used}","int((d + e*x)^(1/2)*(a + b*x + c*x^2),x)","\frac{2\,{\left(d+e\,x\right)}^{3/2}\,\left(15\,c\,{\left(d+e\,x\right)}^2+35\,a\,e^2+35\,c\,d^2+21\,b\,e\,\left(d+e\,x\right)-42\,c\,d\,\left(d+e\,x\right)-35\,b\,d\,e\right)}{105\,e^3}","Not used",1,"(2*(d + e*x)^(3/2)*(15*c*(d + e*x)^2 + 35*a*e^2 + 35*c*d^2 + 21*b*e*(d + e*x) - 42*c*d*(d + e*x) - 35*b*d*e))/(105*e^3)","B"
2271,1,58,73,0.811183,"\text{Not used}","int((a + b*x + c*x^2)/(d + e*x)^(1/2),x)","\frac{2\,\sqrt{d+e\,x}\,\left(3\,c\,{\left(d+e\,x\right)}^2+15\,a\,e^2+15\,c\,d^2+5\,b\,e\,\left(d+e\,x\right)-10\,c\,d\,\left(d+e\,x\right)-15\,b\,d\,e\right)}{15\,e^3}","Not used",1,"(2*(d + e*x)^(1/2)*(3*c*(d + e*x)^2 + 15*a*e^2 + 15*c*d^2 + 5*b*e*(d + e*x) - 10*c*d*(d + e*x) - 15*b*d*e))/(15*e^3)","B"
2272,1,58,71,0.814390,"\text{Not used}","int((a + b*x + c*x^2)/(d + e*x)^(3/2),x)","\frac{2\,c\,{\left(d+e\,x\right)}^2-6\,a\,e^2-6\,c\,d^2+6\,b\,e\,\left(d+e\,x\right)-12\,c\,d\,\left(d+e\,x\right)+6\,b\,d\,e}{3\,e^3\,\sqrt{d+e\,x}}","Not used",1,"(2*c*(d + e*x)^2 - 6*a*e^2 - 6*c*d^2 + 6*b*e*(d + e*x) - 12*c*d*(d + e*x) + 6*b*d*e)/(3*e^3*(d + e*x)^(1/2))","B"
2273,1,58,71,0.050814,"\text{Not used}","int((a + b*x + c*x^2)/(d + e*x)^(5/2),x)","\frac{6\,c\,{\left(d+e\,x\right)}^2-2\,a\,e^2-2\,c\,d^2-6\,b\,e\,\left(d+e\,x\right)+12\,c\,d\,\left(d+e\,x\right)+2\,b\,d\,e}{3\,e^3\,{\left(d+e\,x\right)}^{3/2}}","Not used",1,"(6*c*(d + e*x)^2 - 2*a*e^2 - 2*c*d^2 - 6*b*e*(d + e*x) + 12*c*d*(d + e*x) + 2*b*d*e)/(3*e^3*(d + e*x)^(3/2))","B"
2274,1,52,73,0.827124,"\text{Not used}","int((a + b*x + c*x^2)/(d + e*x)^(7/2),x)","-\frac{16\,c\,d^2+40\,c\,d\,e\,x+4\,b\,d\,e+30\,c\,e^2\,x^2+10\,b\,e^2\,x+6\,a\,e^2}{15\,e^3\,{\left(d+e\,x\right)}^{5/2}}","Not used",1,"-(6*a*e^2 + 16*c*d^2 + 30*c*e^2*x^2 + 4*b*d*e + 10*b*e^2*x + 40*c*d*e*x)/(15*e^3*(d + e*x)^(5/2))","B"
2275,1,148,166,0.837881,"\text{Not used}","int((d + e*x)^(5/2)*(a + b*x + c*x^2)^2,x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{15/2}}{15\,e^5}+\frac{{\left(d+e\,x\right)}^{11/2}\,\left(2\,b^2\,e^2-12\,b\,c\,d\,e+12\,c^2\,d^2+4\,a\,c\,e^2\right)}{11\,e^5}+\frac{2\,{\left(d+e\,x\right)}^{7/2}\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}{7\,e^5}-\frac{\left(8\,c^2\,d-4\,b\,c\,e\right)\,{\left(d+e\,x\right)}^{13/2}}{13\,e^5}+\frac{4\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{9/2}\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}{9\,e^5}","Not used",1,"(2*c^2*(d + e*x)^(15/2))/(15*e^5) + ((d + e*x)^(11/2)*(2*b^2*e^2 + 12*c^2*d^2 + 4*a*c*e^2 - 12*b*c*d*e))/(11*e^5) + (2*(d + e*x)^(7/2)*(a*e^2 + c*d^2 - b*d*e)^2)/(7*e^5) - ((8*c^2*d - 4*b*c*e)*(d + e*x)^(13/2))/(13*e^5) + (4*(b*e - 2*c*d)*(d + e*x)^(9/2)*(a*e^2 + c*d^2 - b*d*e))/(9*e^5)","B"
2276,1,148,166,0.817329,"\text{Not used}","int((d + e*x)^(3/2)*(a + b*x + c*x^2)^2,x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{13/2}}{13\,e^5}+\frac{{\left(d+e\,x\right)}^{9/2}\,\left(2\,b^2\,e^2-12\,b\,c\,d\,e+12\,c^2\,d^2+4\,a\,c\,e^2\right)}{9\,e^5}+\frac{2\,{\left(d+e\,x\right)}^{5/2}\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}{5\,e^5}-\frac{\left(8\,c^2\,d-4\,b\,c\,e\right)\,{\left(d+e\,x\right)}^{11/2}}{11\,e^5}+\frac{4\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{7/2}\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}{7\,e^5}","Not used",1,"(2*c^2*(d + e*x)^(13/2))/(13*e^5) + ((d + e*x)^(9/2)*(2*b^2*e^2 + 12*c^2*d^2 + 4*a*c*e^2 - 12*b*c*d*e))/(9*e^5) + (2*(d + e*x)^(5/2)*(a*e^2 + c*d^2 - b*d*e)^2)/(5*e^5) - ((8*c^2*d - 4*b*c*e)*(d + e*x)^(11/2))/(11*e^5) + (4*(b*e - 2*c*d)*(d + e*x)^(7/2)*(a*e^2 + c*d^2 - b*d*e))/(7*e^5)","B"
2277,1,148,166,0.046227,"\text{Not used}","int((d + e*x)^(1/2)*(a + b*x + c*x^2)^2,x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{11/2}}{11\,e^5}+\frac{{\left(d+e\,x\right)}^{7/2}\,\left(2\,b^2\,e^2-12\,b\,c\,d\,e+12\,c^2\,d^2+4\,a\,c\,e^2\right)}{7\,e^5}+\frac{2\,{\left(d+e\,x\right)}^{3/2}\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}{3\,e^5}-\frac{\left(8\,c^2\,d-4\,b\,c\,e\right)\,{\left(d+e\,x\right)}^{9/2}}{9\,e^5}+\frac{4\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{5/2}\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}{5\,e^5}","Not used",1,"(2*c^2*(d + e*x)^(11/2))/(11*e^5) + ((d + e*x)^(7/2)*(2*b^2*e^2 + 12*c^2*d^2 + 4*a*c*e^2 - 12*b*c*d*e))/(7*e^5) + (2*(d + e*x)^(3/2)*(a*e^2 + c*d^2 - b*d*e)^2)/(3*e^5) - ((8*c^2*d - 4*b*c*e)*(d + e*x)^(9/2))/(9*e^5) + (4*(b*e - 2*c*d)*(d + e*x)^(5/2)*(a*e^2 + c*d^2 - b*d*e))/(5*e^5)","B"
2278,1,148,164,0.041246,"\text{Not used}","int((a + b*x + c*x^2)^2/(d + e*x)^(1/2),x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{9/2}}{9\,e^5}+\frac{{\left(d+e\,x\right)}^{5/2}\,\left(2\,b^2\,e^2-12\,b\,c\,d\,e+12\,c^2\,d^2+4\,a\,c\,e^2\right)}{5\,e^5}+\frac{2\,\sqrt{d+e\,x}\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}{e^5}-\frac{\left(8\,c^2\,d-4\,b\,c\,e\right)\,{\left(d+e\,x\right)}^{7/2}}{7\,e^5}+\frac{4\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{3/2}\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}{3\,e^5}","Not used",1,"(2*c^2*(d + e*x)^(9/2))/(9*e^5) + ((d + e*x)^(5/2)*(2*b^2*e^2 + 12*c^2*d^2 + 4*a*c*e^2 - 12*b*c*d*e))/(5*e^5) + (2*(d + e*x)^(1/2)*(a*e^2 + c*d^2 - b*d*e)^2)/e^5 - ((8*c^2*d - 4*b*c*e)*(d + e*x)^(7/2))/(7*e^5) + (4*(b*e - 2*c*d)*(d + e*x)^(3/2)*(a*e^2 + c*d^2 - b*d*e))/(3*e^5)","B"
2279,1,184,162,0.828899,"\text{Not used}","int((a + b*x + c*x^2)^2/(d + e*x)^(3/2),x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{7/2}}{7\,e^5}+\frac{{\left(d+e\,x\right)}^{3/2}\,\left(2\,b^2\,e^2-12\,b\,c\,d\,e+12\,c^2\,d^2+4\,a\,c\,e^2\right)}{3\,e^5}-\frac{2\,a^2\,e^4-4\,a\,b\,d\,e^3+4\,a\,c\,d^2\,e^2+2\,b^2\,d^2\,e^2-4\,b\,c\,d^3\,e+2\,c^2\,d^4}{e^5\,\sqrt{d+e\,x}}-\frac{\left(8\,c^2\,d-4\,b\,c\,e\right)\,{\left(d+e\,x\right)}^{5/2}}{5\,e^5}+\frac{4\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}{e^5}","Not used",1,"(2*c^2*(d + e*x)^(7/2))/(7*e^5) + ((d + e*x)^(3/2)*(2*b^2*e^2 + 12*c^2*d^2 + 4*a*c*e^2 - 12*b*c*d*e))/(3*e^5) - (2*a^2*e^4 + 2*c^2*d^4 + 2*b^2*d^2*e^2 - 4*a*b*d*e^3 - 4*b*c*d^3*e + 4*a*c*d^2*e^2)/(e^5*(d + e*x)^(1/2)) - ((8*c^2*d - 4*b*c*e)*(d + e*x)^(5/2))/(5*e^5) + (4*(b*e - 2*c*d)*(d + e*x)^(1/2)*(a*e^2 + c*d^2 - b*d*e))/e^5","B"
2280,1,195,162,0.866340,"\text{Not used}","int((a + b*x + c*x^2)^2/(d + e*x)^(5/2),x)","\frac{2\,c^2\,{\left(d+e\,x\right)}^{5/2}}{5\,e^5}-\frac{\frac{2\,a^2\,e^4}{3}-\left(d+e\,x\right)\,\left(4\,b^2\,d\,e^2-12\,b\,c\,d^2\,e-4\,a\,b\,e^3+8\,c^2\,d^3+8\,a\,c\,d\,e^2\right)+\frac{2\,c^2\,d^4}{3}+\frac{2\,b^2\,d^2\,e^2}{3}-\frac{4\,a\,b\,d\,e^3}{3}-\frac{4\,b\,c\,d^3\,e}{3}+\frac{4\,a\,c\,d^2\,e^2}{3}}{e^5\,{\left(d+e\,x\right)}^{3/2}}+\frac{\sqrt{d+e\,x}\,\left(2\,b^2\,e^2-12\,b\,c\,d\,e+12\,c^2\,d^2+4\,a\,c\,e^2\right)}{e^5}-\frac{\left(8\,c^2\,d-4\,b\,c\,e\right)\,{\left(d+e\,x\right)}^{3/2}}{3\,e^5}","Not used",1,"(2*c^2*(d + e*x)^(5/2))/(5*e^5) - ((2*a^2*e^4)/3 - (d + e*x)*(8*c^2*d^3 + 4*b^2*d*e^2 - 4*a*b*e^3 + 8*a*c*d*e^2 - 12*b*c*d^2*e) + (2*c^2*d^4)/3 + (2*b^2*d^2*e^2)/3 - (4*a*b*d*e^3)/3 - (4*b*c*d^3*e)/3 + (4*a*c*d^2*e^2)/3)/(e^5*(d + e*x)^(3/2)) + ((d + e*x)^(1/2)*(2*b^2*e^2 + 12*c^2*d^2 + 4*a*c*e^2 - 12*b*c*d*e))/e^5 - ((8*c^2*d - 4*b*c*e)*(d + e*x)^(3/2))/(3*e^5)","B"
2281,1,193,162,0.897909,"\text{Not used}","int((a + b*x + c*x^2)^2/(d + e*x)^(7/2),x)","-\frac{2\,\left(3\,a^2\,e^4+4\,a\,b\,d\,e^3+10\,a\,b\,e^4\,x+16\,a\,c\,d^2\,e^2+40\,a\,c\,d\,e^3\,x+30\,a\,c\,e^4\,x^2+8\,b^2\,d^2\,e^2+20\,b^2\,d\,e^3\,x+15\,b^2\,e^4\,x^2-96\,b\,c\,d^3\,e-240\,b\,c\,d^2\,e^2\,x-180\,b\,c\,d\,e^3\,x^2-30\,b\,c\,e^4\,x^3+128\,c^2\,d^4+320\,c^2\,d^3\,e\,x+240\,c^2\,d^2\,e^2\,x^2+40\,c^2\,d\,e^3\,x^3-5\,c^2\,e^4\,x^4\right)}{15\,e^5\,{\left(d+e\,x\right)}^{5/2}}","Not used",1,"-(2*(3*a^2*e^4 + 128*c^2*d^4 + 8*b^2*d^2*e^2 + 15*b^2*e^4*x^2 - 5*c^2*e^4*x^4 + 40*c^2*d*e^3*x^3 + 4*a*b*d*e^3 - 96*b*c*d^3*e + 10*a*b*e^4*x + 240*c^2*d^2*e^2*x^2 + 16*a*c*d^2*e^2 + 30*a*c*e^4*x^2 - 30*b*c*e^4*x^3 + 20*b^2*d*e^3*x + 320*c^2*d^3*e*x - 240*b*c*d^2*e^2*x - 180*b*c*d*e^3*x^2 + 40*a*c*d*e^3*x))/(15*e^5*(d + e*x)^(5/2))","B"
2282,1,297,286,0.100812,"\text{Not used}","int((d + e*x)^(5/2)*(a + b*x + c*x^2)^3,x)","\frac{{\left(d+e\,x\right)}^{11/2}\,\left(6\,a^2\,c\,e^4+6\,a\,b^2\,e^4-36\,a\,b\,c\,d\,e^3+36\,a\,c^2\,d^2\,e^2-6\,b^3\,d\,e^3+36\,b^2\,c\,d^2\,e^2-60\,b\,c^2\,d^3\,e+30\,c^3\,d^4\right)}{11\,e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{19/2}}{19\,e^7}-\frac{\left(12\,c^3\,d-6\,b\,c^2\,e\right)\,{\left(d+e\,x\right)}^{17/2}}{17\,e^7}+\frac{{\left(d+e\,x\right)}^{15/2}\,\left(6\,b^2\,c\,e^2-30\,b\,c^2\,d\,e+30\,c^3\,d^2+6\,a\,c^2\,e^2\right)}{15\,e^7}+\frac{2\,{\left(d+e\,x\right)}^{7/2}\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^3}{7\,e^7}+\frac{2\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{13/2}\,\left(b^2\,e^2-10\,b\,c\,d\,e+10\,c^2\,d^2+6\,a\,c\,e^2\right)}{13\,e^7}+\frac{2\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{9/2}\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}{3\,e^7}","Not used",1,"((d + e*x)^(11/2)*(30*c^3*d^4 + 6*a*b^2*e^4 + 6*a^2*c*e^4 - 6*b^3*d*e^3 + 36*a*c^2*d^2*e^2 + 36*b^2*c*d^2*e^2 - 60*b*c^2*d^3*e - 36*a*b*c*d*e^3))/(11*e^7) + (2*c^3*(d + e*x)^(19/2))/(19*e^7) - ((12*c^3*d - 6*b*c^2*e)*(d + e*x)^(17/2))/(17*e^7) + ((d + e*x)^(15/2)*(30*c^3*d^2 + 6*a*c^2*e^2 + 6*b^2*c*e^2 - 30*b*c^2*d*e))/(15*e^7) + (2*(d + e*x)^(7/2)*(a*e^2 + c*d^2 - b*d*e)^3)/(7*e^7) + (2*(b*e - 2*c*d)*(d + e*x)^(13/2)*(b^2*e^2 + 10*c^2*d^2 + 6*a*c*e^2 - 10*b*c*d*e))/(13*e^7) + (2*(b*e - 2*c*d)*(d + e*x)^(9/2)*(a*e^2 + c*d^2 - b*d*e)^2)/(3*e^7)","B"
2283,1,297,286,0.853169,"\text{Not used}","int((d + e*x)^(3/2)*(a + b*x + c*x^2)^3,x)","\frac{{\left(d+e\,x\right)}^{9/2}\,\left(6\,a^2\,c\,e^4+6\,a\,b^2\,e^4-36\,a\,b\,c\,d\,e^3+36\,a\,c^2\,d^2\,e^2-6\,b^3\,d\,e^3+36\,b^2\,c\,d^2\,e^2-60\,b\,c^2\,d^3\,e+30\,c^3\,d^4\right)}{9\,e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{17/2}}{17\,e^7}-\frac{\left(12\,c^3\,d-6\,b\,c^2\,e\right)\,{\left(d+e\,x\right)}^{15/2}}{15\,e^7}+\frac{{\left(d+e\,x\right)}^{13/2}\,\left(6\,b^2\,c\,e^2-30\,b\,c^2\,d\,e+30\,c^3\,d^2+6\,a\,c^2\,e^2\right)}{13\,e^7}+\frac{2\,{\left(d+e\,x\right)}^{5/2}\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^3}{5\,e^7}+\frac{2\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{11/2}\,\left(b^2\,e^2-10\,b\,c\,d\,e+10\,c^2\,d^2+6\,a\,c\,e^2\right)}{11\,e^7}+\frac{6\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{7/2}\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}{7\,e^7}","Not used",1,"((d + e*x)^(9/2)*(30*c^3*d^4 + 6*a*b^2*e^4 + 6*a^2*c*e^4 - 6*b^3*d*e^3 + 36*a*c^2*d^2*e^2 + 36*b^2*c*d^2*e^2 - 60*b*c^2*d^3*e - 36*a*b*c*d*e^3))/(9*e^7) + (2*c^3*(d + e*x)^(17/2))/(17*e^7) - ((12*c^3*d - 6*b*c^2*e)*(d + e*x)^(15/2))/(15*e^7) + ((d + e*x)^(13/2)*(30*c^3*d^2 + 6*a*c^2*e^2 + 6*b^2*c*e^2 - 30*b*c^2*d*e))/(13*e^7) + (2*(d + e*x)^(5/2)*(a*e^2 + c*d^2 - b*d*e)^3)/(5*e^7) + (2*(b*e - 2*c*d)*(d + e*x)^(11/2)*(b^2*e^2 + 10*c^2*d^2 + 6*a*c*e^2 - 10*b*c*d*e))/(11*e^7) + (6*(b*e - 2*c*d)*(d + e*x)^(7/2)*(a*e^2 + c*d^2 - b*d*e)^2)/(7*e^7)","B"
2284,1,297,286,0.845154,"\text{Not used}","int((d + e*x)^(1/2)*(a + b*x + c*x^2)^3,x)","\frac{{\left(d+e\,x\right)}^{7/2}\,\left(6\,a^2\,c\,e^4+6\,a\,b^2\,e^4-36\,a\,b\,c\,d\,e^3+36\,a\,c^2\,d^2\,e^2-6\,b^3\,d\,e^3+36\,b^2\,c\,d^2\,e^2-60\,b\,c^2\,d^3\,e+30\,c^3\,d^4\right)}{7\,e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{15/2}}{15\,e^7}-\frac{\left(12\,c^3\,d-6\,b\,c^2\,e\right)\,{\left(d+e\,x\right)}^{13/2}}{13\,e^7}+\frac{{\left(d+e\,x\right)}^{11/2}\,\left(6\,b^2\,c\,e^2-30\,b\,c^2\,d\,e+30\,c^3\,d^2+6\,a\,c^2\,e^2\right)}{11\,e^7}+\frac{2\,{\left(d+e\,x\right)}^{3/2}\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^3}{3\,e^7}+\frac{2\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{9/2}\,\left(b^2\,e^2-10\,b\,c\,d\,e+10\,c^2\,d^2+6\,a\,c\,e^2\right)}{9\,e^7}+\frac{6\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{5/2}\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}{5\,e^7}","Not used",1,"((d + e*x)^(7/2)*(30*c^3*d^4 + 6*a*b^2*e^4 + 6*a^2*c*e^4 - 6*b^3*d*e^3 + 36*a*c^2*d^2*e^2 + 36*b^2*c*d^2*e^2 - 60*b*c^2*d^3*e - 36*a*b*c*d*e^3))/(7*e^7) + (2*c^3*(d + e*x)^(15/2))/(15*e^7) - ((12*c^3*d - 6*b*c^2*e)*(d + e*x)^(13/2))/(13*e^7) + ((d + e*x)^(11/2)*(30*c^3*d^2 + 6*a*c^2*e^2 + 6*b^2*c*e^2 - 30*b*c^2*d*e))/(11*e^7) + (2*(d + e*x)^(3/2)*(a*e^2 + c*d^2 - b*d*e)^3)/(3*e^7) + (2*(b*e - 2*c*d)*(d + e*x)^(9/2)*(b^2*e^2 + 10*c^2*d^2 + 6*a*c*e^2 - 10*b*c*d*e))/(9*e^7) + (6*(b*e - 2*c*d)*(d + e*x)^(5/2)*(a*e^2 + c*d^2 - b*d*e)^2)/(5*e^7)","B"
2285,1,297,282,0.067220,"\text{Not used}","int((a + b*x + c*x^2)^3/(d + e*x)^(1/2),x)","\frac{{\left(d+e\,x\right)}^{5/2}\,\left(6\,a^2\,c\,e^4+6\,a\,b^2\,e^4-36\,a\,b\,c\,d\,e^3+36\,a\,c^2\,d^2\,e^2-6\,b^3\,d\,e^3+36\,b^2\,c\,d^2\,e^2-60\,b\,c^2\,d^3\,e+30\,c^3\,d^4\right)}{5\,e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{13/2}}{13\,e^7}-\frac{\left(12\,c^3\,d-6\,b\,c^2\,e\right)\,{\left(d+e\,x\right)}^{11/2}}{11\,e^7}+\frac{{\left(d+e\,x\right)}^{9/2}\,\left(6\,b^2\,c\,e^2-30\,b\,c^2\,d\,e+30\,c^3\,d^2+6\,a\,c^2\,e^2\right)}{9\,e^7}+\frac{2\,\sqrt{d+e\,x}\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^3}{e^7}+\frac{2\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{7/2}\,\left(b^2\,e^2-10\,b\,c\,d\,e+10\,c^2\,d^2+6\,a\,c\,e^2\right)}{7\,e^7}+\frac{2\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{3/2}\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}{e^7}","Not used",1,"((d + e*x)^(5/2)*(30*c^3*d^4 + 6*a*b^2*e^4 + 6*a^2*c*e^4 - 6*b^3*d*e^3 + 36*a*c^2*d^2*e^2 + 36*b^2*c*d^2*e^2 - 60*b*c^2*d^3*e - 36*a*b*c*d*e^3))/(5*e^7) + (2*c^3*(d + e*x)^(13/2))/(13*e^7) - ((12*c^3*d - 6*b*c^2*e)*(d + e*x)^(11/2))/(11*e^7) + ((d + e*x)^(9/2)*(30*c^3*d^2 + 6*a*c^2*e^2 + 6*b^2*c*e^2 - 30*b*c^2*d*e))/(9*e^7) + (2*(d + e*x)^(1/2)*(a*e^2 + c*d^2 - b*d*e)^3)/e^7 + (2*(b*e - 2*c*d)*(d + e*x)^(7/2)*(b^2*e^2 + 10*c^2*d^2 + 6*a*c*e^2 - 10*b*c*d*e))/(7*e^7) + (2*(b*e - 2*c*d)*(d + e*x)^(3/2)*(a*e^2 + c*d^2 - b*d*e)^2)/e^7","B"
2286,1,386,280,0.865962,"\text{Not used}","int((a + b*x + c*x^2)^3/(d + e*x)^(3/2),x)","\frac{{\left(d+e\,x\right)}^{3/2}\,\left(6\,a^2\,c\,e^4+6\,a\,b^2\,e^4-36\,a\,b\,c\,d\,e^3+36\,a\,c^2\,d^2\,e^2-6\,b^3\,d\,e^3+36\,b^2\,c\,d^2\,e^2-60\,b\,c^2\,d^3\,e+30\,c^3\,d^4\right)}{3\,e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{11/2}}{11\,e^7}-\frac{\left(12\,c^3\,d-6\,b\,c^2\,e\right)\,{\left(d+e\,x\right)}^{9/2}}{9\,e^7}+\frac{{\left(d+e\,x\right)}^{7/2}\,\left(6\,b^2\,c\,e^2-30\,b\,c^2\,d\,e+30\,c^3\,d^2+6\,a\,c^2\,e^2\right)}{7\,e^7}-\frac{2\,a^3\,e^6-6\,a^2\,b\,d\,e^5+6\,a^2\,c\,d^2\,e^4+6\,a\,b^2\,d^2\,e^4-12\,a\,b\,c\,d^3\,e^3+6\,a\,c^2\,d^4\,e^2-2\,b^3\,d^3\,e^3+6\,b^2\,c\,d^4\,e^2-6\,b\,c^2\,d^5\,e+2\,c^3\,d^6}{e^7\,\sqrt{d+e\,x}}+\frac{2\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{5/2}\,\left(b^2\,e^2-10\,b\,c\,d\,e+10\,c^2\,d^2+6\,a\,c\,e^2\right)}{5\,e^7}+\frac{6\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}{e^7}","Not used",1,"((d + e*x)^(3/2)*(30*c^3*d^4 + 6*a*b^2*e^4 + 6*a^2*c*e^4 - 6*b^3*d*e^3 + 36*a*c^2*d^2*e^2 + 36*b^2*c*d^2*e^2 - 60*b*c^2*d^3*e - 36*a*b*c*d*e^3))/(3*e^7) + (2*c^3*(d + e*x)^(11/2))/(11*e^7) - ((12*c^3*d - 6*b*c^2*e)*(d + e*x)^(9/2))/(9*e^7) + ((d + e*x)^(7/2)*(30*c^3*d^2 + 6*a*c^2*e^2 + 6*b^2*c*e^2 - 30*b*c^2*d*e))/(7*e^7) - (2*a^3*e^6 + 2*c^3*d^6 - 2*b^3*d^3*e^3 + 6*a*b^2*d^2*e^4 + 6*a*c^2*d^4*e^2 + 6*a^2*c*d^2*e^4 + 6*b^2*c*d^4*e^2 - 6*a^2*b*d*e^5 - 6*b*c^2*d^5*e - 12*a*b*c*d^3*e^3)/(e^7*(d + e*x)^(1/2)) + (2*(b*e - 2*c*d)*(d + e*x)^(5/2)*(b^2*e^2 + 10*c^2*d^2 + 6*a*c*e^2 - 10*b*c*d*e))/(5*e^7) + (6*(b*e - 2*c*d)*(d + e*x)^(1/2)*(a*e^2 + c*d^2 - b*d*e)^2)/e^7","B"
2287,1,448,282,0.081299,"\text{Not used}","int((a + b*x + c*x^2)^3/(d + e*x)^(5/2),x)","\frac{\sqrt{d+e\,x}\,\left(6\,a^2\,c\,e^4+6\,a\,b^2\,e^4-36\,a\,b\,c\,d\,e^3+36\,a\,c^2\,d^2\,e^2-6\,b^3\,d\,e^3+36\,b^2\,c\,d^2\,e^2-60\,b\,c^2\,d^3\,e+30\,c^3\,d^4\right)}{e^7}+\frac{2\,c^3\,{\left(d+e\,x\right)}^{9/2}}{9\,e^7}-\frac{\left(12\,c^3\,d-6\,b\,c^2\,e\right)\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}-\frac{\frac{2\,a^3\,e^6}{3}-\left(d+e\,x\right)\,\left(-6\,a^2\,b\,e^5+12\,a^2\,c\,d\,e^4+12\,a\,b^2\,d\,e^4-36\,a\,b\,c\,d^2\,e^3+24\,a\,c^2\,d^3\,e^2-6\,b^3\,d^2\,e^3+24\,b^2\,c\,d^3\,e^2-30\,b\,c^2\,d^4\,e+12\,c^3\,d^5\right)+\frac{2\,c^3\,d^6}{3}-\frac{2\,b^3\,d^3\,e^3}{3}+2\,a\,b^2\,d^2\,e^4+2\,a\,c^2\,d^4\,e^2+2\,a^2\,c\,d^2\,e^4+2\,b^2\,c\,d^4\,e^2-2\,a^2\,b\,d\,e^5-2\,b\,c^2\,d^5\,e-4\,a\,b\,c\,d^3\,e^3}{e^7\,{\left(d+e\,x\right)}^{3/2}}+\frac{{\left(d+e\,x\right)}^{5/2}\,\left(6\,b^2\,c\,e^2-30\,b\,c^2\,d\,e+30\,c^3\,d^2+6\,a\,c^2\,e^2\right)}{5\,e^7}+\frac{2\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{3/2}\,\left(b^2\,e^2-10\,b\,c\,d\,e+10\,c^2\,d^2+6\,a\,c\,e^2\right)}{3\,e^7}","Not used",1,"((d + e*x)^(1/2)*(30*c^3*d^4 + 6*a*b^2*e^4 + 6*a^2*c*e^4 - 6*b^3*d*e^3 + 36*a*c^2*d^2*e^2 + 36*b^2*c*d^2*e^2 - 60*b*c^2*d^3*e - 36*a*b*c*d*e^3))/e^7 + (2*c^3*(d + e*x)^(9/2))/(9*e^7) - ((12*c^3*d - 6*b*c^2*e)*(d + e*x)^(7/2))/(7*e^7) - ((2*a^3*e^6)/3 - (d + e*x)*(12*c^3*d^5 - 6*a^2*b*e^5 - 6*b^3*d^2*e^3 + 24*a*c^2*d^3*e^2 + 24*b^2*c*d^3*e^2 + 12*a*b^2*d*e^4 + 12*a^2*c*d*e^4 - 30*b*c^2*d^4*e - 36*a*b*c*d^2*e^3) + (2*c^3*d^6)/3 - (2*b^3*d^3*e^3)/3 + 2*a*b^2*d^2*e^4 + 2*a*c^2*d^4*e^2 + 2*a^2*c*d^2*e^4 + 2*b^2*c*d^4*e^2 - 2*a^2*b*d*e^5 - 2*b*c^2*d^5*e - 4*a*b*c*d^3*e^3)/(e^7*(d + e*x)^(3/2)) + ((d + e*x)^(5/2)*(30*c^3*d^2 + 6*a*c^2*e^2 + 6*b^2*c*e^2 - 30*b*c^2*d*e))/(5*e^7) + (2*(b*e - 2*c*d)*(d + e*x)^(3/2)*(b^2*e^2 + 10*c^2*d^2 + 6*a*c*e^2 - 10*b*c*d*e))/(3*e^7)","B"
2288,1,445,278,0.885257,"\text{Not used}","int((a + b*x + c*x^2)^3/(d + e*x)^(7/2),x)","\frac{2\,c^3\,{\left(d+e\,x\right)}^{7/2}}{7\,e^7}-\frac{\left(12\,c^3\,d-6\,b\,c^2\,e\right)\,{\left(d+e\,x\right)}^{5/2}}{5\,e^7}+\frac{{\left(d+e\,x\right)}^{3/2}\,\left(6\,b^2\,c\,e^2-30\,b\,c^2\,d\,e+30\,c^3\,d^2+6\,a\,c^2\,e^2\right)}{3\,e^7}-\frac{{\left(d+e\,x\right)}^2\,\left(6\,a^2\,c\,e^4+6\,a\,b^2\,e^4-36\,a\,b\,c\,d\,e^3+36\,a\,c^2\,d^2\,e^2-6\,b^3\,d\,e^3+36\,b^2\,c\,d^2\,e^2-60\,b\,c^2\,d^3\,e+30\,c^3\,d^4\right)-\left(d+e\,x\right)\,\left(-2\,a^2\,b\,e^5+4\,a^2\,c\,d\,e^4+4\,a\,b^2\,d\,e^4-12\,a\,b\,c\,d^2\,e^3+8\,a\,c^2\,d^3\,e^2-2\,b^3\,d^2\,e^3+8\,b^2\,c\,d^3\,e^2-10\,b\,c^2\,d^4\,e+4\,c^3\,d^5\right)+\frac{2\,a^3\,e^6}{5}+\frac{2\,c^3\,d^6}{5}-\frac{2\,b^3\,d^3\,e^3}{5}+\frac{6\,a\,b^2\,d^2\,e^4}{5}+\frac{6\,a\,c^2\,d^4\,e^2}{5}+\frac{6\,a^2\,c\,d^2\,e^4}{5}+\frac{6\,b^2\,c\,d^4\,e^2}{5}-\frac{6\,a^2\,b\,d\,e^5}{5}-\frac{6\,b\,c^2\,d^5\,e}{5}-\frac{12\,a\,b\,c\,d^3\,e^3}{5}}{e^7\,{\left(d+e\,x\right)}^{5/2}}+\frac{2\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}\,\left(b^2\,e^2-10\,b\,c\,d\,e+10\,c^2\,d^2+6\,a\,c\,e^2\right)}{e^7}","Not used",1,"(2*c^3*(d + e*x)^(7/2))/(7*e^7) - ((12*c^3*d - 6*b*c^2*e)*(d + e*x)^(5/2))/(5*e^7) + ((d + e*x)^(3/2)*(30*c^3*d^2 + 6*a*c^2*e^2 + 6*b^2*c*e^2 - 30*b*c^2*d*e))/(3*e^7) - ((d + e*x)^2*(30*c^3*d^4 + 6*a*b^2*e^4 + 6*a^2*c*e^4 - 6*b^3*d*e^3 + 36*a*c^2*d^2*e^2 + 36*b^2*c*d^2*e^2 - 60*b*c^2*d^3*e - 36*a*b*c*d*e^3) - (d + e*x)*(4*c^3*d^5 - 2*a^2*b*e^5 - 2*b^3*d^2*e^3 + 8*a*c^2*d^3*e^2 + 8*b^2*c*d^3*e^2 + 4*a*b^2*d*e^4 + 4*a^2*c*d*e^4 - 10*b*c^2*d^4*e - 12*a*b*c*d^2*e^3) + (2*a^3*e^6)/5 + (2*c^3*d^6)/5 - (2*b^3*d^3*e^3)/5 + (6*a*b^2*d^2*e^4)/5 + (6*a*c^2*d^4*e^2)/5 + (6*a^2*c*d^2*e^4)/5 + (6*b^2*c*d^4*e^2)/5 - (6*a^2*b*d*e^5)/5 - (6*b*c^2*d^5*e)/5 - (12*a*b*c*d^3*e^3)/5)/(e^7*(d + e*x)^(5/2)) + (2*(b*e - 2*c*d)*(d + e*x)^(1/2)*(b^2*e^2 + 10*c^2*d^2 + 6*a*c*e^2 - 10*b*c*d*e))/e^7","B"
2289,1,16475,459,3.615799,"\text{Not used}","int((d + e*x)^(5/2)/(a + b*x + c*x^2),x)","\frac{2\,e\,{\left(d+e\,x\right)}^{3/2}}{3\,c}-\frac{2\,e\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}}{c^2}-\mathrm{atan}\left(\frac{\left(\left(\frac{8\,\left(-4\,a^2\,b\,c^4\,e^6+8\,a^2\,c^5\,d\,e^5+a\,b^3\,c^3\,e^6+2\,a\,b^2\,c^4\,d\,e^5-12\,a\,b\,c^5\,d^2\,e^4+8\,a\,c^6\,d^3\,e^3-b^4\,c^3\,d\,e^5+3\,b^3\,c^4\,d^2\,e^4-2\,b^2\,c^5\,d^3\,e^3\right)}{c^3}-\frac{8\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^7\,e^5+8\,a\,c^6\,d^5-2\,b^2\,c^5\,d^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a^3\,b\,c^3\,e^5+40\,a^3\,c^4\,d\,e^4+5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-80\,a^2\,c^5\,d^3\,e^2-10\,b^4\,c^3\,d^3\,e^2+10\,b^5\,c^2\,d^2\,e^3-9\,a\,b^5\,c\,e^5-5\,b^6\,c\,d\,e^4-20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^2\,c^4\,d^3\,e^2-70\,a\,b^3\,c^3\,d^2\,e^3+120\,a^2\,b\,c^4\,d^2\,e^3-90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}\,\left(b^3\,c^5\,e^3-2\,d\,b^2\,c^6\,e^2-4\,a\,b\,c^6\,e^3+8\,a\,d\,c^7\,e^2\right)}{c^3}\right)\,\sqrt{-\frac{b^7\,e^5+8\,a\,c^6\,d^5-2\,b^2\,c^5\,d^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a^3\,b\,c^3\,e^5+40\,a^3\,c^4\,d\,e^4+5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-80\,a^2\,c^5\,d^3\,e^2-10\,b^4\,c^3\,d^3\,e^2+10\,b^5\,c^2\,d^2\,e^3-9\,a\,b^5\,c\,e^5-5\,b^6\,c\,d\,e^4-20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^2\,c^4\,d^3\,e^2-70\,a\,b^3\,c^3\,d^2\,e^3+120\,a^2\,b\,c^4\,d^2\,e^3-90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}-\frac{8\,\sqrt{d+e\,x}\,\left(-2\,a^3\,c^3\,e^8+9\,a^2\,b^2\,c^2\,e^8-30\,a^2\,b\,c^3\,d\,e^7+30\,a^2\,c^4\,d^2\,e^6-6\,a\,b^4\,c\,e^8+30\,a\,b^3\,c^2\,d\,e^7-60\,a\,b^2\,c^3\,d^2\,e^6+60\,a\,b\,c^4\,d^3\,e^5-30\,a\,c^5\,d^4\,e^4+b^6\,e^8-6\,b^5\,c\,d\,e^7+15\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+15\,b^2\,c^4\,d^4\,e^4-6\,b\,c^5\,d^5\,e^3+2\,c^6\,d^6\,e^2\right)}{c^3}\right)\,\sqrt{-\frac{b^7\,e^5+8\,a\,c^6\,d^5-2\,b^2\,c^5\,d^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a^3\,b\,c^3\,e^5+40\,a^3\,c^4\,d\,e^4+5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-80\,a^2\,c^5\,d^3\,e^2-10\,b^4\,c^3\,d^3\,e^2+10\,b^5\,c^2\,d^2\,e^3-9\,a\,b^5\,c\,e^5-5\,b^6\,c\,d\,e^4-20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^2\,c^4\,d^3\,e^2-70\,a\,b^3\,c^3\,d^2\,e^3+120\,a^2\,b\,c^4\,d^2\,e^3-90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}\,1{}\mathrm{i}-\left(\left(\frac{8\,\left(-4\,a^2\,b\,c^4\,e^6+8\,a^2\,c^5\,d\,e^5+a\,b^3\,c^3\,e^6+2\,a\,b^2\,c^4\,d\,e^5-12\,a\,b\,c^5\,d^2\,e^4+8\,a\,c^6\,d^3\,e^3-b^4\,c^3\,d\,e^5+3\,b^3\,c^4\,d^2\,e^4-2\,b^2\,c^5\,d^3\,e^3\right)}{c^3}+\frac{8\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^7\,e^5+8\,a\,c^6\,d^5-2\,b^2\,c^5\,d^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a^3\,b\,c^3\,e^5+40\,a^3\,c^4\,d\,e^4+5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-80\,a^2\,c^5\,d^3\,e^2-10\,b^4\,c^3\,d^3\,e^2+10\,b^5\,c^2\,d^2\,e^3-9\,a\,b^5\,c\,e^5-5\,b^6\,c\,d\,e^4-20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^2\,c^4\,d^3\,e^2-70\,a\,b^3\,c^3\,d^2\,e^3+120\,a^2\,b\,c^4\,d^2\,e^3-90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}\,\left(b^3\,c^5\,e^3-2\,d\,b^2\,c^6\,e^2-4\,a\,b\,c^6\,e^3+8\,a\,d\,c^7\,e^2\right)}{c^3}\right)\,\sqrt{-\frac{b^7\,e^5+8\,a\,c^6\,d^5-2\,b^2\,c^5\,d^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a^3\,b\,c^3\,e^5+40\,a^3\,c^4\,d\,e^4+5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-80\,a^2\,c^5\,d^3\,e^2-10\,b^4\,c^3\,d^3\,e^2+10\,b^5\,c^2\,d^2\,e^3-9\,a\,b^5\,c\,e^5-5\,b^6\,c\,d\,e^4-20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^2\,c^4\,d^3\,e^2-70\,a\,b^3\,c^3\,d^2\,e^3+120\,a^2\,b\,c^4\,d^2\,e^3-90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}+\frac{8\,\sqrt{d+e\,x}\,\left(-2\,a^3\,c^3\,e^8+9\,a^2\,b^2\,c^2\,e^8-30\,a^2\,b\,c^3\,d\,e^7+30\,a^2\,c^4\,d^2\,e^6-6\,a\,b^4\,c\,e^8+30\,a\,b^3\,c^2\,d\,e^7-60\,a\,b^2\,c^3\,d^2\,e^6+60\,a\,b\,c^4\,d^3\,e^5-30\,a\,c^5\,d^4\,e^4+b^6\,e^8-6\,b^5\,c\,d\,e^7+15\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+15\,b^2\,c^4\,d^4\,e^4-6\,b\,c^5\,d^5\,e^3+2\,c^6\,d^6\,e^2\right)}{c^3}\right)\,\sqrt{-\frac{b^7\,e^5+8\,a\,c^6\,d^5-2\,b^2\,c^5\,d^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a^3\,b\,c^3\,e^5+40\,a^3\,c^4\,d\,e^4+5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-80\,a^2\,c^5\,d^3\,e^2-10\,b^4\,c^3\,d^3\,e^2+10\,b^5\,c^2\,d^2\,e^3-9\,a\,b^5\,c\,e^5-5\,b^6\,c\,d\,e^4-20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^2\,c^4\,d^3\,e^2-70\,a\,b^3\,c^3\,d^2\,e^3+120\,a^2\,b\,c^4\,d^2\,e^3-90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{8\,\left(-4\,a^2\,b\,c^4\,e^6+8\,a^2\,c^5\,d\,e^5+a\,b^3\,c^3\,e^6+2\,a\,b^2\,c^4\,d\,e^5-12\,a\,b\,c^5\,d^2\,e^4+8\,a\,c^6\,d^3\,e^3-b^4\,c^3\,d\,e^5+3\,b^3\,c^4\,d^2\,e^4-2\,b^2\,c^5\,d^3\,e^3\right)}{c^3}-\frac{8\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^7\,e^5+8\,a\,c^6\,d^5-2\,b^2\,c^5\,d^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a^3\,b\,c^3\,e^5+40\,a^3\,c^4\,d\,e^4+5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-80\,a^2\,c^5\,d^3\,e^2-10\,b^4\,c^3\,d^3\,e^2+10\,b^5\,c^2\,d^2\,e^3-9\,a\,b^5\,c\,e^5-5\,b^6\,c\,d\,e^4-20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^2\,c^4\,d^3\,e^2-70\,a\,b^3\,c^3\,d^2\,e^3+120\,a^2\,b\,c^4\,d^2\,e^3-90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}\,\left(b^3\,c^5\,e^3-2\,d\,b^2\,c^6\,e^2-4\,a\,b\,c^6\,e^3+8\,a\,d\,c^7\,e^2\right)}{c^3}\right)\,\sqrt{-\frac{b^7\,e^5+8\,a\,c^6\,d^5-2\,b^2\,c^5\,d^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a^3\,b\,c^3\,e^5+40\,a^3\,c^4\,d\,e^4+5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-80\,a^2\,c^5\,d^3\,e^2-10\,b^4\,c^3\,d^3\,e^2+10\,b^5\,c^2\,d^2\,e^3-9\,a\,b^5\,c\,e^5-5\,b^6\,c\,d\,e^4-20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^2\,c^4\,d^3\,e^2-70\,a\,b^3\,c^3\,d^2\,e^3+120\,a^2\,b\,c^4\,d^2\,e^3-90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}-\frac{8\,\sqrt{d+e\,x}\,\left(-2\,a^3\,c^3\,e^8+9\,a^2\,b^2\,c^2\,e^8-30\,a^2\,b\,c^3\,d\,e^7+30\,a^2\,c^4\,d^2\,e^6-6\,a\,b^4\,c\,e^8+30\,a\,b^3\,c^2\,d\,e^7-60\,a\,b^2\,c^3\,d^2\,e^6+60\,a\,b\,c^4\,d^3\,e^5-30\,a\,c^5\,d^4\,e^4+b^6\,e^8-6\,b^5\,c\,d\,e^7+15\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+15\,b^2\,c^4\,d^4\,e^4-6\,b\,c^5\,d^5\,e^3+2\,c^6\,d^6\,e^2\right)}{c^3}\right)\,\sqrt{-\frac{b^7\,e^5+8\,a\,c^6\,d^5-2\,b^2\,c^5\,d^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a^3\,b\,c^3\,e^5+40\,a^3\,c^4\,d\,e^4+5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-80\,a^2\,c^5\,d^3\,e^2-10\,b^4\,c^3\,d^3\,e^2+10\,b^5\,c^2\,d^2\,e^3-9\,a\,b^5\,c\,e^5-5\,b^6\,c\,d\,e^4-20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^2\,c^4\,d^3\,e^2-70\,a\,b^3\,c^3\,d^2\,e^3+120\,a^2\,b\,c^4\,d^2\,e^3-90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}-\frac{16\,\left(-a^4\,c\,e^{11}+a^3\,b^2\,e^{11}-3\,a^2\,b^3\,d\,e^{10}+9\,a^2\,b^2\,c\,d^2\,e^9-12\,a^2\,b\,c^2\,d^3\,e^8+6\,a^2\,c^3\,d^4\,e^7+3\,a\,b^4\,d^2\,e^9-14\,a\,b^3\,c\,d^3\,e^8+27\,a\,b^2\,c^2\,d^4\,e^7-24\,a\,b\,c^3\,d^5\,e^6+8\,a\,c^4\,d^6\,e^5-b^5\,d^3\,e^8+6\,b^4\,c\,d^4\,e^7-15\,b^3\,c^2\,d^5\,e^6+19\,b^2\,c^3\,d^6\,e^5-12\,b\,c^4\,d^7\,e^4+3\,c^5\,d^8\,e^3\right)}{c^3}+\left(\left(\frac{8\,\left(-4\,a^2\,b\,c^4\,e^6+8\,a^2\,c^5\,d\,e^5+a\,b^3\,c^3\,e^6+2\,a\,b^2\,c^4\,d\,e^5-12\,a\,b\,c^5\,d^2\,e^4+8\,a\,c^6\,d^3\,e^3-b^4\,c^3\,d\,e^5+3\,b^3\,c^4\,d^2\,e^4-2\,b^2\,c^5\,d^3\,e^3\right)}{c^3}+\frac{8\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^7\,e^5+8\,a\,c^6\,d^5-2\,b^2\,c^5\,d^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a^3\,b\,c^3\,e^5+40\,a^3\,c^4\,d\,e^4+5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-80\,a^2\,c^5\,d^3\,e^2-10\,b^4\,c^3\,d^3\,e^2+10\,b^5\,c^2\,d^2\,e^3-9\,a\,b^5\,c\,e^5-5\,b^6\,c\,d\,e^4-20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^2\,c^4\,d^3\,e^2-70\,a\,b^3\,c^3\,d^2\,e^3+120\,a^2\,b\,c^4\,d^2\,e^3-90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}\,\left(b^3\,c^5\,e^3-2\,d\,b^2\,c^6\,e^2-4\,a\,b\,c^6\,e^3+8\,a\,d\,c^7\,e^2\right)}{c^3}\right)\,\sqrt{-\frac{b^7\,e^5+8\,a\,c^6\,d^5-2\,b^2\,c^5\,d^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a^3\,b\,c^3\,e^5+40\,a^3\,c^4\,d\,e^4+5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-80\,a^2\,c^5\,d^3\,e^2-10\,b^4\,c^3\,d^3\,e^2+10\,b^5\,c^2\,d^2\,e^3-9\,a\,b^5\,c\,e^5-5\,b^6\,c\,d\,e^4-20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^2\,c^4\,d^3\,e^2-70\,a\,b^3\,c^3\,d^2\,e^3+120\,a^2\,b\,c^4\,d^2\,e^3-90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}+\frac{8\,\sqrt{d+e\,x}\,\left(-2\,a^3\,c^3\,e^8+9\,a^2\,b^2\,c^2\,e^8-30\,a^2\,b\,c^3\,d\,e^7+30\,a^2\,c^4\,d^2\,e^6-6\,a\,b^4\,c\,e^8+30\,a\,b^3\,c^2\,d\,e^7-60\,a\,b^2\,c^3\,d^2\,e^6+60\,a\,b\,c^4\,d^3\,e^5-30\,a\,c^5\,d^4\,e^4+b^6\,e^8-6\,b^5\,c\,d\,e^7+15\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+15\,b^2\,c^4\,d^4\,e^4-6\,b\,c^5\,d^5\,e^3+2\,c^6\,d^6\,e^2\right)}{c^3}\right)\,\sqrt{-\frac{b^7\,e^5+8\,a\,c^6\,d^5-2\,b^2\,c^5\,d^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a^3\,b\,c^3\,e^5+40\,a^3\,c^4\,d\,e^4+5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-80\,a^2\,c^5\,d^3\,e^2-10\,b^4\,c^3\,d^3\,e^2+10\,b^5\,c^2\,d^2\,e^3-9\,a\,b^5\,c\,e^5-5\,b^6\,c\,d\,e^4-20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^2\,c^4\,d^3\,e^2-70\,a\,b^3\,c^3\,d^2\,e^3+120\,a^2\,b\,c^4\,d^2\,e^3-90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}}\right)\,\sqrt{-\frac{b^7\,e^5+8\,a\,c^6\,d^5-2\,b^2\,c^5\,d^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a^3\,b\,c^3\,e^5+40\,a^3\,c^4\,d\,e^4+5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-80\,a^2\,c^5\,d^3\,e^2-10\,b^4\,c^3\,d^3\,e^2+10\,b^5\,c^2\,d^2\,e^3-9\,a\,b^5\,c\,e^5-5\,b^6\,c\,d\,e^4-20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^2\,c^4\,d^3\,e^2-70\,a\,b^3\,c^3\,d^2\,e^3+120\,a^2\,b\,c^4\,d^2\,e^3-90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(\frac{8\,\left(-4\,a^2\,b\,c^4\,e^6+8\,a^2\,c^5\,d\,e^5+a\,b^3\,c^3\,e^6+2\,a\,b^2\,c^4\,d\,e^5-12\,a\,b\,c^5\,d^2\,e^4+8\,a\,c^6\,d^3\,e^3-b^4\,c^3\,d\,e^5+3\,b^3\,c^4\,d^2\,e^4-2\,b^2\,c^5\,d^3\,e^3\right)}{c^3}-\frac{8\,\sqrt{d+e\,x}\,\sqrt{\frac{2\,b^2\,c^5\,d^5-8\,a\,c^6\,d^5-b^7\,e^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+20\,a^3\,b\,c^3\,e^5-40\,a^3\,c^4\,d\,e^4-5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+80\,a^2\,c^5\,d^3\,e^2+10\,b^4\,c^3\,d^3\,e^2-10\,b^5\,c^2\,d^2\,e^3+9\,a\,b^5\,c\,e^5+5\,b^6\,c\,d\,e^4+20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-60\,a\,b^2\,c^4\,d^3\,e^2+70\,a\,b^3\,c^3\,d^2\,e^3-120\,a^2\,b\,c^4\,d^2\,e^3+90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}\,\left(b^3\,c^5\,e^3-2\,d\,b^2\,c^6\,e^2-4\,a\,b\,c^6\,e^3+8\,a\,d\,c^7\,e^2\right)}{c^3}\right)\,\sqrt{\frac{2\,b^2\,c^5\,d^5-8\,a\,c^6\,d^5-b^7\,e^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+20\,a^3\,b\,c^3\,e^5-40\,a^3\,c^4\,d\,e^4-5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+80\,a^2\,c^5\,d^3\,e^2+10\,b^4\,c^3\,d^3\,e^2-10\,b^5\,c^2\,d^2\,e^3+9\,a\,b^5\,c\,e^5+5\,b^6\,c\,d\,e^4+20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-60\,a\,b^2\,c^4\,d^3\,e^2+70\,a\,b^3\,c^3\,d^2\,e^3-120\,a^2\,b\,c^4\,d^2\,e^3+90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}-\frac{8\,\sqrt{d+e\,x}\,\left(-2\,a^3\,c^3\,e^8+9\,a^2\,b^2\,c^2\,e^8-30\,a^2\,b\,c^3\,d\,e^7+30\,a^2\,c^4\,d^2\,e^6-6\,a\,b^4\,c\,e^8+30\,a\,b^3\,c^2\,d\,e^7-60\,a\,b^2\,c^3\,d^2\,e^6+60\,a\,b\,c^4\,d^3\,e^5-30\,a\,c^5\,d^4\,e^4+b^6\,e^8-6\,b^5\,c\,d\,e^7+15\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+15\,b^2\,c^4\,d^4\,e^4-6\,b\,c^5\,d^5\,e^3+2\,c^6\,d^6\,e^2\right)}{c^3}\right)\,\sqrt{\frac{2\,b^2\,c^5\,d^5-8\,a\,c^6\,d^5-b^7\,e^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+20\,a^3\,b\,c^3\,e^5-40\,a^3\,c^4\,d\,e^4-5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+80\,a^2\,c^5\,d^3\,e^2+10\,b^4\,c^3\,d^3\,e^2-10\,b^5\,c^2\,d^2\,e^3+9\,a\,b^5\,c\,e^5+5\,b^6\,c\,d\,e^4+20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-60\,a\,b^2\,c^4\,d^3\,e^2+70\,a\,b^3\,c^3\,d^2\,e^3-120\,a^2\,b\,c^4\,d^2\,e^3+90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}\,1{}\mathrm{i}-\left(\left(\frac{8\,\left(-4\,a^2\,b\,c^4\,e^6+8\,a^2\,c^5\,d\,e^5+a\,b^3\,c^3\,e^6+2\,a\,b^2\,c^4\,d\,e^5-12\,a\,b\,c^5\,d^2\,e^4+8\,a\,c^6\,d^3\,e^3-b^4\,c^3\,d\,e^5+3\,b^3\,c^4\,d^2\,e^4-2\,b^2\,c^5\,d^3\,e^3\right)}{c^3}+\frac{8\,\sqrt{d+e\,x}\,\sqrt{\frac{2\,b^2\,c^5\,d^5-8\,a\,c^6\,d^5-b^7\,e^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+20\,a^3\,b\,c^3\,e^5-40\,a^3\,c^4\,d\,e^4-5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+80\,a^2\,c^5\,d^3\,e^2+10\,b^4\,c^3\,d^3\,e^2-10\,b^5\,c^2\,d^2\,e^3+9\,a\,b^5\,c\,e^5+5\,b^6\,c\,d\,e^4+20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-60\,a\,b^2\,c^4\,d^3\,e^2+70\,a\,b^3\,c^3\,d^2\,e^3-120\,a^2\,b\,c^4\,d^2\,e^3+90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}\,\left(b^3\,c^5\,e^3-2\,d\,b^2\,c^6\,e^2-4\,a\,b\,c^6\,e^3+8\,a\,d\,c^7\,e^2\right)}{c^3}\right)\,\sqrt{\frac{2\,b^2\,c^5\,d^5-8\,a\,c^6\,d^5-b^7\,e^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+20\,a^3\,b\,c^3\,e^5-40\,a^3\,c^4\,d\,e^4-5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+80\,a^2\,c^5\,d^3\,e^2+10\,b^4\,c^3\,d^3\,e^2-10\,b^5\,c^2\,d^2\,e^3+9\,a\,b^5\,c\,e^5+5\,b^6\,c\,d\,e^4+20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-60\,a\,b^2\,c^4\,d^3\,e^2+70\,a\,b^3\,c^3\,d^2\,e^3-120\,a^2\,b\,c^4\,d^2\,e^3+90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}+\frac{8\,\sqrt{d+e\,x}\,\left(-2\,a^3\,c^3\,e^8+9\,a^2\,b^2\,c^2\,e^8-30\,a^2\,b\,c^3\,d\,e^7+30\,a^2\,c^4\,d^2\,e^6-6\,a\,b^4\,c\,e^8+30\,a\,b^3\,c^2\,d\,e^7-60\,a\,b^2\,c^3\,d^2\,e^6+60\,a\,b\,c^4\,d^3\,e^5-30\,a\,c^5\,d^4\,e^4+b^6\,e^8-6\,b^5\,c\,d\,e^7+15\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+15\,b^2\,c^4\,d^4\,e^4-6\,b\,c^5\,d^5\,e^3+2\,c^6\,d^6\,e^2\right)}{c^3}\right)\,\sqrt{\frac{2\,b^2\,c^5\,d^5-8\,a\,c^6\,d^5-b^7\,e^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+20\,a^3\,b\,c^3\,e^5-40\,a^3\,c^4\,d\,e^4-5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+80\,a^2\,c^5\,d^3\,e^2+10\,b^4\,c^3\,d^3\,e^2-10\,b^5\,c^2\,d^2\,e^3+9\,a\,b^5\,c\,e^5+5\,b^6\,c\,d\,e^4+20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-60\,a\,b^2\,c^4\,d^3\,e^2+70\,a\,b^3\,c^3\,d^2\,e^3-120\,a^2\,b\,c^4\,d^2\,e^3+90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{8\,\left(-4\,a^2\,b\,c^4\,e^6+8\,a^2\,c^5\,d\,e^5+a\,b^3\,c^3\,e^6+2\,a\,b^2\,c^4\,d\,e^5-12\,a\,b\,c^5\,d^2\,e^4+8\,a\,c^6\,d^3\,e^3-b^4\,c^3\,d\,e^5+3\,b^3\,c^4\,d^2\,e^4-2\,b^2\,c^5\,d^3\,e^3\right)}{c^3}-\frac{8\,\sqrt{d+e\,x}\,\sqrt{\frac{2\,b^2\,c^5\,d^5-8\,a\,c^6\,d^5-b^7\,e^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+20\,a^3\,b\,c^3\,e^5-40\,a^3\,c^4\,d\,e^4-5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+80\,a^2\,c^5\,d^3\,e^2+10\,b^4\,c^3\,d^3\,e^2-10\,b^5\,c^2\,d^2\,e^3+9\,a\,b^5\,c\,e^5+5\,b^6\,c\,d\,e^4+20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-60\,a\,b^2\,c^4\,d^3\,e^2+70\,a\,b^3\,c^3\,d^2\,e^3-120\,a^2\,b\,c^4\,d^2\,e^3+90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}\,\left(b^3\,c^5\,e^3-2\,d\,b^2\,c^6\,e^2-4\,a\,b\,c^6\,e^3+8\,a\,d\,c^7\,e^2\right)}{c^3}\right)\,\sqrt{\frac{2\,b^2\,c^5\,d^5-8\,a\,c^6\,d^5-b^7\,e^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+20\,a^3\,b\,c^3\,e^5-40\,a^3\,c^4\,d\,e^4-5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+80\,a^2\,c^5\,d^3\,e^2+10\,b^4\,c^3\,d^3\,e^2-10\,b^5\,c^2\,d^2\,e^3+9\,a\,b^5\,c\,e^5+5\,b^6\,c\,d\,e^4+20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-60\,a\,b^2\,c^4\,d^3\,e^2+70\,a\,b^3\,c^3\,d^2\,e^3-120\,a^2\,b\,c^4\,d^2\,e^3+90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}-\frac{8\,\sqrt{d+e\,x}\,\left(-2\,a^3\,c^3\,e^8+9\,a^2\,b^2\,c^2\,e^8-30\,a^2\,b\,c^3\,d\,e^7+30\,a^2\,c^4\,d^2\,e^6-6\,a\,b^4\,c\,e^8+30\,a\,b^3\,c^2\,d\,e^7-60\,a\,b^2\,c^3\,d^2\,e^6+60\,a\,b\,c^4\,d^3\,e^5-30\,a\,c^5\,d^4\,e^4+b^6\,e^8-6\,b^5\,c\,d\,e^7+15\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+15\,b^2\,c^4\,d^4\,e^4-6\,b\,c^5\,d^5\,e^3+2\,c^6\,d^6\,e^2\right)}{c^3}\right)\,\sqrt{\frac{2\,b^2\,c^5\,d^5-8\,a\,c^6\,d^5-b^7\,e^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+20\,a^3\,b\,c^3\,e^5-40\,a^3\,c^4\,d\,e^4-5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+80\,a^2\,c^5\,d^3\,e^2+10\,b^4\,c^3\,d^3\,e^2-10\,b^5\,c^2\,d^2\,e^3+9\,a\,b^5\,c\,e^5+5\,b^6\,c\,d\,e^4+20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-60\,a\,b^2\,c^4\,d^3\,e^2+70\,a\,b^3\,c^3\,d^2\,e^3-120\,a^2\,b\,c^4\,d^2\,e^3+90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}-\frac{16\,\left(-a^4\,c\,e^{11}+a^3\,b^2\,e^{11}-3\,a^2\,b^3\,d\,e^{10}+9\,a^2\,b^2\,c\,d^2\,e^9-12\,a^2\,b\,c^2\,d^3\,e^8+6\,a^2\,c^3\,d^4\,e^7+3\,a\,b^4\,d^2\,e^9-14\,a\,b^3\,c\,d^3\,e^8+27\,a\,b^2\,c^2\,d^4\,e^7-24\,a\,b\,c^3\,d^5\,e^6+8\,a\,c^4\,d^6\,e^5-b^5\,d^3\,e^8+6\,b^4\,c\,d^4\,e^7-15\,b^3\,c^2\,d^5\,e^6+19\,b^2\,c^3\,d^6\,e^5-12\,b\,c^4\,d^7\,e^4+3\,c^5\,d^8\,e^3\right)}{c^3}+\left(\left(\frac{8\,\left(-4\,a^2\,b\,c^4\,e^6+8\,a^2\,c^5\,d\,e^5+a\,b^3\,c^3\,e^6+2\,a\,b^2\,c^4\,d\,e^5-12\,a\,b\,c^5\,d^2\,e^4+8\,a\,c^6\,d^3\,e^3-b^4\,c^3\,d\,e^5+3\,b^3\,c^4\,d^2\,e^4-2\,b^2\,c^5\,d^3\,e^3\right)}{c^3}+\frac{8\,\sqrt{d+e\,x}\,\sqrt{\frac{2\,b^2\,c^5\,d^5-8\,a\,c^6\,d^5-b^7\,e^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+20\,a^3\,b\,c^3\,e^5-40\,a^3\,c^4\,d\,e^4-5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+80\,a^2\,c^5\,d^3\,e^2+10\,b^4\,c^3\,d^3\,e^2-10\,b^5\,c^2\,d^2\,e^3+9\,a\,b^5\,c\,e^5+5\,b^6\,c\,d\,e^4+20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-60\,a\,b^2\,c^4\,d^3\,e^2+70\,a\,b^3\,c^3\,d^2\,e^3-120\,a^2\,b\,c^4\,d^2\,e^3+90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}\,\left(b^3\,c^5\,e^3-2\,d\,b^2\,c^6\,e^2-4\,a\,b\,c^6\,e^3+8\,a\,d\,c^7\,e^2\right)}{c^3}\right)\,\sqrt{\frac{2\,b^2\,c^5\,d^5-8\,a\,c^6\,d^5-b^7\,e^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+20\,a^3\,b\,c^3\,e^5-40\,a^3\,c^4\,d\,e^4-5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+80\,a^2\,c^5\,d^3\,e^2+10\,b^4\,c^3\,d^3\,e^2-10\,b^5\,c^2\,d^2\,e^3+9\,a\,b^5\,c\,e^5+5\,b^6\,c\,d\,e^4+20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-60\,a\,b^2\,c^4\,d^3\,e^2+70\,a\,b^3\,c^3\,d^2\,e^3-120\,a^2\,b\,c^4\,d^2\,e^3+90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}+\frac{8\,\sqrt{d+e\,x}\,\left(-2\,a^3\,c^3\,e^8+9\,a^2\,b^2\,c^2\,e^8-30\,a^2\,b\,c^3\,d\,e^7+30\,a^2\,c^4\,d^2\,e^6-6\,a\,b^4\,c\,e^8+30\,a\,b^3\,c^2\,d\,e^7-60\,a\,b^2\,c^3\,d^2\,e^6+60\,a\,b\,c^4\,d^3\,e^5-30\,a\,c^5\,d^4\,e^4+b^6\,e^8-6\,b^5\,c\,d\,e^7+15\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+15\,b^2\,c^4\,d^4\,e^4-6\,b\,c^5\,d^5\,e^3+2\,c^6\,d^6\,e^2\right)}{c^3}\right)\,\sqrt{\frac{2\,b^2\,c^5\,d^5-8\,a\,c^6\,d^5-b^7\,e^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+20\,a^3\,b\,c^3\,e^5-40\,a^3\,c^4\,d\,e^4-5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+80\,a^2\,c^5\,d^3\,e^2+10\,b^4\,c^3\,d^3\,e^2-10\,b^5\,c^2\,d^2\,e^3+9\,a\,b^5\,c\,e^5+5\,b^6\,c\,d\,e^4+20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-60\,a\,b^2\,c^4\,d^3\,e^2+70\,a\,b^3\,c^3\,d^2\,e^3-120\,a^2\,b\,c^4\,d^2\,e^3+90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}}\right)\,\sqrt{\frac{2\,b^2\,c^5\,d^5-8\,a\,c^6\,d^5-b^7\,e^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+20\,a^3\,b\,c^3\,e^5-40\,a^3\,c^4\,d\,e^4-5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+80\,a^2\,c^5\,d^3\,e^2+10\,b^4\,c^3\,d^3\,e^2-10\,b^5\,c^2\,d^2\,e^3+9\,a\,b^5\,c\,e^5+5\,b^6\,c\,d\,e^4+20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-60\,a\,b^2\,c^4\,d^3\,e^2+70\,a\,b^3\,c^3\,d^2\,e^3-120\,a^2\,b\,c^4\,d^2\,e^3+90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^2\,c^7-8\,a\,b^2\,c^6+b^4\,c^5\right)}}\,2{}\mathrm{i}","Not used",1,"(2*e*(d + e*x)^(3/2))/(3*c) - atan(((((8*(a*b^3*c^3*e^6 - 4*a^2*b*c^4*e^6 + 8*a*c^6*d^3*e^3 + 8*a^2*c^5*d*e^5 - b^4*c^3*d*e^5 - 2*b^2*c^5*d^3*e^3 + 3*b^3*c^4*d^2*e^4 - 12*a*b*c^5*d^2*e^4 + 2*a*b^2*c^4*d*e^5))/c^3 - (8*(d + e*x)^(1/2)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2)*(b^3*c^5*e^3 - 2*b^2*c^6*d*e^2 - 4*a*b*c^6*e^3 + 8*a*c^7*d*e^2))/c^3)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2) - (8*(d + e*x)^(1/2)*(b^6*e^8 - 2*a^3*c^3*e^8 + 2*c^6*d^6*e^2 - 30*a*c^5*d^4*e^4 - 6*b*c^5*d^5*e^3 + 9*a^2*b^2*c^2*e^8 + 30*a^2*c^4*d^2*e^6 + 15*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 + 15*b^4*c^2*d^2*e^6 - 6*a*b^4*c*e^8 - 6*b^5*c*d*e^7 + 60*a*b*c^4*d^3*e^5 + 30*a*b^3*c^2*d*e^7 - 30*a^2*b*c^3*d*e^7 - 60*a*b^2*c^3*d^2*e^6))/c^3)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2)*1i - (((8*(a*b^3*c^3*e^6 - 4*a^2*b*c^4*e^6 + 8*a*c^6*d^3*e^3 + 8*a^2*c^5*d*e^5 - b^4*c^3*d*e^5 - 2*b^2*c^5*d^3*e^3 + 3*b^3*c^4*d^2*e^4 - 12*a*b*c^5*d^2*e^4 + 2*a*b^2*c^4*d*e^5))/c^3 + (8*(d + e*x)^(1/2)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2)*(b^3*c^5*e^3 - 2*b^2*c^6*d*e^2 - 4*a*b*c^6*e^3 + 8*a*c^7*d*e^2))/c^3)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2) + (8*(d + e*x)^(1/2)*(b^6*e^8 - 2*a^3*c^3*e^8 + 2*c^6*d^6*e^2 - 30*a*c^5*d^4*e^4 - 6*b*c^5*d^5*e^3 + 9*a^2*b^2*c^2*e^8 + 30*a^2*c^4*d^2*e^6 + 15*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 + 15*b^4*c^2*d^2*e^6 - 6*a*b^4*c*e^8 - 6*b^5*c*d*e^7 + 60*a*b*c^4*d^3*e^5 + 30*a*b^3*c^2*d*e^7 - 30*a^2*b*c^3*d*e^7 - 60*a*b^2*c^3*d^2*e^6))/c^3)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2)*1i)/((((8*(a*b^3*c^3*e^6 - 4*a^2*b*c^4*e^6 + 8*a*c^6*d^3*e^3 + 8*a^2*c^5*d*e^5 - b^4*c^3*d*e^5 - 2*b^2*c^5*d^3*e^3 + 3*b^3*c^4*d^2*e^4 - 12*a*b*c^5*d^2*e^4 + 2*a*b^2*c^4*d*e^5))/c^3 - (8*(d + e*x)^(1/2)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2)*(b^3*c^5*e^3 - 2*b^2*c^6*d*e^2 - 4*a*b*c^6*e^3 + 8*a*c^7*d*e^2))/c^3)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2) - (8*(d + e*x)^(1/2)*(b^6*e^8 - 2*a^3*c^3*e^8 + 2*c^6*d^6*e^2 - 30*a*c^5*d^4*e^4 - 6*b*c^5*d^5*e^3 + 9*a^2*b^2*c^2*e^8 + 30*a^2*c^4*d^2*e^6 + 15*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 + 15*b^4*c^2*d^2*e^6 - 6*a*b^4*c*e^8 - 6*b^5*c*d*e^7 + 60*a*b*c^4*d^3*e^5 + 30*a*b^3*c^2*d*e^7 - 30*a^2*b*c^3*d*e^7 - 60*a*b^2*c^3*d^2*e^6))/c^3)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2) - (16*(a^3*b^2*e^11 - a^4*c*e^11 - b^5*d^3*e^8 + 3*c^5*d^8*e^3 + 3*a*b^4*d^2*e^9 - 3*a^2*b^3*d*e^10 + 8*a*c^4*d^6*e^5 - 12*b*c^4*d^7*e^4 + 6*b^4*c*d^4*e^7 + 6*a^2*c^3*d^4*e^7 + 19*b^2*c^3*d^6*e^5 - 15*b^3*c^2*d^5*e^6 - 24*a*b*c^3*d^5*e^6 - 14*a*b^3*c*d^3*e^8 + 27*a*b^2*c^2*d^4*e^7 - 12*a^2*b*c^2*d^3*e^8 + 9*a^2*b^2*c*d^2*e^9))/c^3 + (((8*(a*b^3*c^3*e^6 - 4*a^2*b*c^4*e^6 + 8*a*c^6*d^3*e^3 + 8*a^2*c^5*d*e^5 - b^4*c^3*d*e^5 - 2*b^2*c^5*d^3*e^3 + 3*b^3*c^4*d^2*e^4 - 12*a*b*c^5*d^2*e^4 + 2*a*b^2*c^4*d*e^5))/c^3 + (8*(d + e*x)^(1/2)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2)*(b^3*c^5*e^3 - 2*b^2*c^6*d*e^2 - 4*a*b*c^6*e^3 + 8*a*c^7*d*e^2))/c^3)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2) + (8*(d + e*x)^(1/2)*(b^6*e^8 - 2*a^3*c^3*e^8 + 2*c^6*d^6*e^2 - 30*a*c^5*d^4*e^4 - 6*b*c^5*d^5*e^3 + 9*a^2*b^2*c^2*e^8 + 30*a^2*c^4*d^2*e^6 + 15*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 + 15*b^4*c^2*d^2*e^6 - 6*a*b^4*c*e^8 - 6*b^5*c*d*e^7 + 60*a*b*c^4*d^3*e^5 + 30*a*b^3*c^2*d*e^7 - 30*a^2*b*c^3*d*e^7 - 60*a*b^2*c^3*d^2*e^6))/c^3)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2)))*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2)*2i - atan(((((8*(a*b^3*c^3*e^6 - 4*a^2*b*c^4*e^6 + 8*a*c^6*d^3*e^3 + 8*a^2*c^5*d*e^5 - b^4*c^3*d*e^5 - 2*b^2*c^5*d^3*e^3 + 3*b^3*c^4*d^2*e^4 - 12*a*b*c^5*d^2*e^4 + 2*a*b^2*c^4*d*e^5))/c^3 - (8*(d + e*x)^(1/2)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2)*(b^3*c^5*e^3 - 2*b^2*c^6*d*e^2 - 4*a*b*c^6*e^3 + 8*a*c^7*d*e^2))/c^3)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2) - (8*(d + e*x)^(1/2)*(b^6*e^8 - 2*a^3*c^3*e^8 + 2*c^6*d^6*e^2 - 30*a*c^5*d^4*e^4 - 6*b*c^5*d^5*e^3 + 9*a^2*b^2*c^2*e^8 + 30*a^2*c^4*d^2*e^6 + 15*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 + 15*b^4*c^2*d^2*e^6 - 6*a*b^4*c*e^8 - 6*b^5*c*d*e^7 + 60*a*b*c^4*d^3*e^5 + 30*a*b^3*c^2*d*e^7 - 30*a^2*b*c^3*d*e^7 - 60*a*b^2*c^3*d^2*e^6))/c^3)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2)*1i - (((8*(a*b^3*c^3*e^6 - 4*a^2*b*c^4*e^6 + 8*a*c^6*d^3*e^3 + 8*a^2*c^5*d*e^5 - b^4*c^3*d*e^5 - 2*b^2*c^5*d^3*e^3 + 3*b^3*c^4*d^2*e^4 - 12*a*b*c^5*d^2*e^4 + 2*a*b^2*c^4*d*e^5))/c^3 + (8*(d + e*x)^(1/2)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2)*(b^3*c^5*e^3 - 2*b^2*c^6*d*e^2 - 4*a*b*c^6*e^3 + 8*a*c^7*d*e^2))/c^3)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2) + (8*(d + e*x)^(1/2)*(b^6*e^8 - 2*a^3*c^3*e^8 + 2*c^6*d^6*e^2 - 30*a*c^5*d^4*e^4 - 6*b*c^5*d^5*e^3 + 9*a^2*b^2*c^2*e^8 + 30*a^2*c^4*d^2*e^6 + 15*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 + 15*b^4*c^2*d^2*e^6 - 6*a*b^4*c*e^8 - 6*b^5*c*d*e^7 + 60*a*b*c^4*d^3*e^5 + 30*a*b^3*c^2*d*e^7 - 30*a^2*b*c^3*d*e^7 - 60*a*b^2*c^3*d^2*e^6))/c^3)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2)*1i)/((((8*(a*b^3*c^3*e^6 - 4*a^2*b*c^4*e^6 + 8*a*c^6*d^3*e^3 + 8*a^2*c^5*d*e^5 - b^4*c^3*d*e^5 - 2*b^2*c^5*d^3*e^3 + 3*b^3*c^4*d^2*e^4 - 12*a*b*c^5*d^2*e^4 + 2*a*b^2*c^4*d*e^5))/c^3 - (8*(d + e*x)^(1/2)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2)*(b^3*c^5*e^3 - 2*b^2*c^6*d*e^2 - 4*a*b*c^6*e^3 + 8*a*c^7*d*e^2))/c^3)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2) - (8*(d + e*x)^(1/2)*(b^6*e^8 - 2*a^3*c^3*e^8 + 2*c^6*d^6*e^2 - 30*a*c^5*d^4*e^4 - 6*b*c^5*d^5*e^3 + 9*a^2*b^2*c^2*e^8 + 30*a^2*c^4*d^2*e^6 + 15*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 + 15*b^4*c^2*d^2*e^6 - 6*a*b^4*c*e^8 - 6*b^5*c*d*e^7 + 60*a*b*c^4*d^3*e^5 + 30*a*b^3*c^2*d*e^7 - 30*a^2*b*c^3*d*e^7 - 60*a*b^2*c^3*d^2*e^6))/c^3)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2) - (16*(a^3*b^2*e^11 - a^4*c*e^11 - b^5*d^3*e^8 + 3*c^5*d^8*e^3 + 3*a*b^4*d^2*e^9 - 3*a^2*b^3*d*e^10 + 8*a*c^4*d^6*e^5 - 12*b*c^4*d^7*e^4 + 6*b^4*c*d^4*e^7 + 6*a^2*c^3*d^4*e^7 + 19*b^2*c^3*d^6*e^5 - 15*b^3*c^2*d^5*e^6 - 24*a*b*c^3*d^5*e^6 - 14*a*b^3*c*d^3*e^8 + 27*a*b^2*c^2*d^4*e^7 - 12*a^2*b*c^2*d^3*e^8 + 9*a^2*b^2*c*d^2*e^9))/c^3 + (((8*(a*b^3*c^3*e^6 - 4*a^2*b*c^4*e^6 + 8*a*c^6*d^3*e^3 + 8*a^2*c^5*d*e^5 - b^4*c^3*d*e^5 - 2*b^2*c^5*d^3*e^3 + 3*b^3*c^4*d^2*e^4 - 12*a*b*c^5*d^2*e^4 + 2*a*b^2*c^4*d*e^5))/c^3 + (8*(d + e*x)^(1/2)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2)*(b^3*c^5*e^3 - 2*b^2*c^6*d*e^2 - 4*a*b*c^6*e^3 + 8*a*c^7*d*e^2))/c^3)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2) + (8*(d + e*x)^(1/2)*(b^6*e^8 - 2*a^3*c^3*e^8 + 2*c^6*d^6*e^2 - 30*a*c^5*d^4*e^4 - 6*b*c^5*d^5*e^3 + 9*a^2*b^2*c^2*e^8 + 30*a^2*c^4*d^2*e^6 + 15*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 + 15*b^4*c^2*d^2*e^6 - 6*a*b^4*c*e^8 - 6*b^5*c*d*e^7 + 60*a*b*c^4*d^3*e^5 + 30*a*b^3*c^2*d*e^7 - 30*a^2*b*c^3*d*e^7 - 60*a*b^2*c^3*d^2*e^6))/c^3)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2)))*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7 + b^4*c^5 - 8*a*b^2*c^6)))^(1/2)*2i - (2*e*(b*e - 2*c*d)*(d + e*x)^(1/2))/c^2","B"
2290,1,8334,322,2.775625,"\text{Not used}","int((d + e*x)^(3/2)/(a + b*x + c*x^2),x)","\frac{2\,e\,\sqrt{d+e\,x}}{c}-\mathrm{atan}\left(\frac{\left(\left(\frac{8\,\left(4\,a^2\,c^3\,e^5-a\,b^2\,c^2\,e^5-4\,a\,b\,c^3\,d\,e^4+4\,a\,c^4\,d^2\,e^3+b^3\,c^2\,d\,e^4-b^2\,c^3\,d^2\,e^3\right)}{c}-\frac{8\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}\,\left(b^3\,c^3\,e^3-2\,d\,b^2\,c^4\,e^2-4\,a\,b\,c^4\,e^3+8\,a\,d\,c^5\,e^2\right)}{c}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}-\frac{8\,\sqrt{d+e\,x}\,\left(2\,a^2\,c^2\,e^6-4\,a\,b^2\,c\,e^6+12\,a\,b\,c^2\,d\,e^5-12\,a\,c^3\,d^2\,e^4+b^4\,e^6-4\,b^3\,c\,d\,e^5+6\,b^2\,c^2\,d^2\,e^4-4\,b\,c^3\,d^3\,e^3+2\,c^4\,d^4\,e^2\right)}{c}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}\,1{}\mathrm{i}-\left(\left(\frac{8\,\left(4\,a^2\,c^3\,e^5-a\,b^2\,c^2\,e^5-4\,a\,b\,c^3\,d\,e^4+4\,a\,c^4\,d^2\,e^3+b^3\,c^2\,d\,e^4-b^2\,c^3\,d^2\,e^3\right)}{c}+\frac{8\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}\,\left(b^3\,c^3\,e^3-2\,d\,b^2\,c^4\,e^2-4\,a\,b\,c^4\,e^3+8\,a\,d\,c^5\,e^2\right)}{c}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}+\frac{8\,\sqrt{d+e\,x}\,\left(2\,a^2\,c^2\,e^6-4\,a\,b^2\,c\,e^6+12\,a\,b\,c^2\,d\,e^5-12\,a\,c^3\,d^2\,e^4+b^4\,e^6-4\,b^3\,c\,d\,e^5+6\,b^2\,c^2\,d^2\,e^4-4\,b\,c^3\,d^3\,e^3+2\,c^4\,d^4\,e^2\right)}{c}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{8\,\left(4\,a^2\,c^3\,e^5-a\,b^2\,c^2\,e^5-4\,a\,b\,c^3\,d\,e^4+4\,a\,c^4\,d^2\,e^3+b^3\,c^2\,d\,e^4-b^2\,c^3\,d^2\,e^3\right)}{c}-\frac{8\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}\,\left(b^3\,c^3\,e^3-2\,d\,b^2\,c^4\,e^2-4\,a\,b\,c^4\,e^3+8\,a\,d\,c^5\,e^2\right)}{c}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}-\frac{8\,\sqrt{d+e\,x}\,\left(2\,a^2\,c^2\,e^6-4\,a\,b^2\,c\,e^6+12\,a\,b\,c^2\,d\,e^5-12\,a\,c^3\,d^2\,e^4+b^4\,e^6-4\,b^3\,c\,d\,e^5+6\,b^2\,c^2\,d^2\,e^4-4\,b\,c^3\,d^3\,e^3+2\,c^4\,d^4\,e^2\right)}{c}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}+\left(\left(\frac{8\,\left(4\,a^2\,c^3\,e^5-a\,b^2\,c^2\,e^5-4\,a\,b\,c^3\,d\,e^4+4\,a\,c^4\,d^2\,e^3+b^3\,c^2\,d\,e^4-b^2\,c^3\,d^2\,e^3\right)}{c}+\frac{8\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}\,\left(b^3\,c^3\,e^3-2\,d\,b^2\,c^4\,e^2-4\,a\,b\,c^4\,e^3+8\,a\,d\,c^5\,e^2\right)}{c}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}+\frac{8\,\sqrt{d+e\,x}\,\left(2\,a^2\,c^2\,e^6-4\,a\,b^2\,c\,e^6+12\,a\,b\,c^2\,d\,e^5-12\,a\,c^3\,d^2\,e^4+b^4\,e^6-4\,b^3\,c\,d\,e^5+6\,b^2\,c^2\,d^2\,e^4-4\,b\,c^3\,d^3\,e^3+2\,c^4\,d^4\,e^2\right)}{c}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}-\frac{16\,\left(-a^2\,b\,e^8+2\,a^2\,c\,d\,e^7+2\,a\,b^2\,d\,e^7-6\,a\,b\,c\,d^2\,e^6+4\,a\,c^2\,d^3\,e^5-b^3\,d^2\,e^6+4\,b^2\,c\,d^3\,e^5-5\,b\,c^2\,d^4\,e^4+2\,c^3\,d^5\,e^3\right)}{c}}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(\frac{8\,\left(4\,a^2\,c^3\,e^5-a\,b^2\,c^2\,e^5-4\,a\,b\,c^3\,d\,e^4+4\,a\,c^4\,d^2\,e^3+b^3\,c^2\,d\,e^4-b^2\,c^3\,d^2\,e^3\right)}{c}-\frac{8\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}\,\left(b^3\,c^3\,e^3-2\,d\,b^2\,c^4\,e^2-4\,a\,b\,c^4\,e^3+8\,a\,d\,c^5\,e^2\right)}{c}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}-\frac{8\,\sqrt{d+e\,x}\,\left(2\,a^2\,c^2\,e^6-4\,a\,b^2\,c\,e^6+12\,a\,b\,c^2\,d\,e^5-12\,a\,c^3\,d^2\,e^4+b^4\,e^6-4\,b^3\,c\,d\,e^5+6\,b^2\,c^2\,d^2\,e^4-4\,b\,c^3\,d^3\,e^3+2\,c^4\,d^4\,e^2\right)}{c}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}\,1{}\mathrm{i}-\left(\left(\frac{8\,\left(4\,a^2\,c^3\,e^5-a\,b^2\,c^2\,e^5-4\,a\,b\,c^3\,d\,e^4+4\,a\,c^4\,d^2\,e^3+b^3\,c^2\,d\,e^4-b^2\,c^3\,d^2\,e^3\right)}{c}+\frac{8\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}\,\left(b^3\,c^3\,e^3-2\,d\,b^2\,c^4\,e^2-4\,a\,b\,c^4\,e^3+8\,a\,d\,c^5\,e^2\right)}{c}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}+\frac{8\,\sqrt{d+e\,x}\,\left(2\,a^2\,c^2\,e^6-4\,a\,b^2\,c\,e^6+12\,a\,b\,c^2\,d\,e^5-12\,a\,c^3\,d^2\,e^4+b^4\,e^6-4\,b^3\,c\,d\,e^5+6\,b^2\,c^2\,d^2\,e^4-4\,b\,c^3\,d^3\,e^3+2\,c^4\,d^4\,e^2\right)}{c}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{8\,\left(4\,a^2\,c^3\,e^5-a\,b^2\,c^2\,e^5-4\,a\,b\,c^3\,d\,e^4+4\,a\,c^4\,d^2\,e^3+b^3\,c^2\,d\,e^4-b^2\,c^3\,d^2\,e^3\right)}{c}-\frac{8\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}\,\left(b^3\,c^3\,e^3-2\,d\,b^2\,c^4\,e^2-4\,a\,b\,c^4\,e^3+8\,a\,d\,c^5\,e^2\right)}{c}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}-\frac{8\,\sqrt{d+e\,x}\,\left(2\,a^2\,c^2\,e^6-4\,a\,b^2\,c\,e^6+12\,a\,b\,c^2\,d\,e^5-12\,a\,c^3\,d^2\,e^4+b^4\,e^6-4\,b^3\,c\,d\,e^5+6\,b^2\,c^2\,d^2\,e^4-4\,b\,c^3\,d^3\,e^3+2\,c^4\,d^4\,e^2\right)}{c}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}+\left(\left(\frac{8\,\left(4\,a^2\,c^3\,e^5-a\,b^2\,c^2\,e^5-4\,a\,b\,c^3\,d\,e^4+4\,a\,c^4\,d^2\,e^3+b^3\,c^2\,d\,e^4-b^2\,c^3\,d^2\,e^3\right)}{c}+\frac{8\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}\,\left(b^3\,c^3\,e^3-2\,d\,b^2\,c^4\,e^2-4\,a\,b\,c^4\,e^3+8\,a\,d\,c^5\,e^2\right)}{c}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}+\frac{8\,\sqrt{d+e\,x}\,\left(2\,a^2\,c^2\,e^6-4\,a\,b^2\,c\,e^6+12\,a\,b\,c^2\,d\,e^5-12\,a\,c^3\,d^2\,e^4+b^4\,e^6-4\,b^3\,c\,d\,e^5+6\,b^2\,c^2\,d^2\,e^4-4\,b\,c^3\,d^3\,e^3+2\,c^4\,d^4\,e^2\right)}{c}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}-\frac{16\,\left(-a^2\,b\,e^8+2\,a^2\,c\,d\,e^7+2\,a\,b^2\,d\,e^7-6\,a\,b\,c\,d^2\,e^6+4\,a\,c^2\,d^3\,e^5-b^3\,d^2\,e^6+4\,b^2\,c\,d^3\,e^5-5\,b\,c^2\,d^4\,e^4+2\,c^3\,d^5\,e^3\right)}{c}}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3\right)}}\,2{}\mathrm{i}","Not used",1,"(2*e*(d + e*x)^(1/2))/c - atan(((((8*(4*a^2*c^3*e^5 - a*b^2*c^2*e^5 + 4*a*c^4*d^2*e^3 + b^3*c^2*d*e^4 - b^2*c^3*d^2*e^3 - 4*a*b*c^3*d*e^4))/c - (8*(d + e*x)^(1/2)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2)*(b^3*c^3*e^3 - 2*b^2*c^4*d*e^2 - 4*a*b*c^4*e^3 + 8*a*c^5*d*e^2))/c)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2) - (8*(d + e*x)^(1/2)*(b^4*e^6 + 2*a^2*c^2*e^6 + 2*c^4*d^4*e^2 - 12*a*c^3*d^2*e^4 - 4*b*c^3*d^3*e^3 + 6*b^2*c^2*d^2*e^4 - 4*a*b^2*c*e^6 - 4*b^3*c*d*e^5 + 12*a*b*c^2*d*e^5))/c)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2)*1i - (((8*(4*a^2*c^3*e^5 - a*b^2*c^2*e^5 + 4*a*c^4*d^2*e^3 + b^3*c^2*d*e^4 - b^2*c^3*d^2*e^3 - 4*a*b*c^3*d*e^4))/c + (8*(d + e*x)^(1/2)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2)*(b^3*c^3*e^3 - 2*b^2*c^4*d*e^2 - 4*a*b*c^4*e^3 + 8*a*c^5*d*e^2))/c)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2) + (8*(d + e*x)^(1/2)*(b^4*e^6 + 2*a^2*c^2*e^6 + 2*c^4*d^4*e^2 - 12*a*c^3*d^2*e^4 - 4*b*c^3*d^3*e^3 + 6*b^2*c^2*d^2*e^4 - 4*a*b^2*c*e^6 - 4*b^3*c*d*e^5 + 12*a*b*c^2*d*e^5))/c)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2)*1i)/((((8*(4*a^2*c^3*e^5 - a*b^2*c^2*e^5 + 4*a*c^4*d^2*e^3 + b^3*c^2*d*e^4 - b^2*c^3*d^2*e^3 - 4*a*b*c^3*d*e^4))/c - (8*(d + e*x)^(1/2)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2)*(b^3*c^3*e^3 - 2*b^2*c^4*d*e^2 - 4*a*b*c^4*e^3 + 8*a*c^5*d*e^2))/c)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2) - (8*(d + e*x)^(1/2)*(b^4*e^6 + 2*a^2*c^2*e^6 + 2*c^4*d^4*e^2 - 12*a*c^3*d^2*e^4 - 4*b*c^3*d^3*e^3 + 6*b^2*c^2*d^2*e^4 - 4*a*b^2*c*e^6 - 4*b^3*c*d*e^5 + 12*a*b*c^2*d*e^5))/c)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2) + (((8*(4*a^2*c^3*e^5 - a*b^2*c^2*e^5 + 4*a*c^4*d^2*e^3 + b^3*c^2*d*e^4 - b^2*c^3*d^2*e^3 - 4*a*b*c^3*d*e^4))/c + (8*(d + e*x)^(1/2)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2)*(b^3*c^3*e^3 - 2*b^2*c^4*d*e^2 - 4*a*b*c^4*e^3 + 8*a*c^5*d*e^2))/c)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2) + (8*(d + e*x)^(1/2)*(b^4*e^6 + 2*a^2*c^2*e^6 + 2*c^4*d^4*e^2 - 12*a*c^3*d^2*e^4 - 4*b*c^3*d^3*e^3 + 6*b^2*c^2*d^2*e^4 - 4*a*b^2*c*e^6 - 4*b^3*c*d*e^5 + 12*a*b*c^2*d*e^5))/c)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2) - (16*(2*c^3*d^5*e^3 - b^3*d^2*e^6 - a^2*b*e^8 + 4*a*c^2*d^3*e^5 - 5*b*c^2*d^4*e^4 + 4*b^2*c*d^3*e^5 + 2*a*b^2*d*e^7 + 2*a^2*c*d*e^7 - 6*a*b*c*d^2*e^6))/c))*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2)*2i - atan(((((8*(4*a^2*c^3*e^5 - a*b^2*c^2*e^5 + 4*a*c^4*d^2*e^3 + b^3*c^2*d*e^4 - b^2*c^3*d^2*e^3 - 4*a*b*c^3*d*e^4))/c - (8*(d + e*x)^(1/2)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2)*(b^3*c^3*e^3 - 2*b^2*c^4*d*e^2 - 4*a*b*c^4*e^3 + 8*a*c^5*d*e^2))/c)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2) - (8*(d + e*x)^(1/2)*(b^4*e^6 + 2*a^2*c^2*e^6 + 2*c^4*d^4*e^2 - 12*a*c^3*d^2*e^4 - 4*b*c^3*d^3*e^3 + 6*b^2*c^2*d^2*e^4 - 4*a*b^2*c*e^6 - 4*b^3*c*d*e^5 + 12*a*b*c^2*d*e^5))/c)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2)*1i - (((8*(4*a^2*c^3*e^5 - a*b^2*c^2*e^5 + 4*a*c^4*d^2*e^3 + b^3*c^2*d*e^4 - b^2*c^3*d^2*e^3 - 4*a*b*c^3*d*e^4))/c + (8*(d + e*x)^(1/2)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2)*(b^3*c^3*e^3 - 2*b^2*c^4*d*e^2 - 4*a*b*c^4*e^3 + 8*a*c^5*d*e^2))/c)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2) + (8*(d + e*x)^(1/2)*(b^4*e^6 + 2*a^2*c^2*e^6 + 2*c^4*d^4*e^2 - 12*a*c^3*d^2*e^4 - 4*b*c^3*d^3*e^3 + 6*b^2*c^2*d^2*e^4 - 4*a*b^2*c*e^6 - 4*b^3*c*d*e^5 + 12*a*b*c^2*d*e^5))/c)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2)*1i)/((((8*(4*a^2*c^3*e^5 - a*b^2*c^2*e^5 + 4*a*c^4*d^2*e^3 + b^3*c^2*d*e^4 - b^2*c^3*d^2*e^3 - 4*a*b*c^3*d*e^4))/c - (8*(d + e*x)^(1/2)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2)*(b^3*c^3*e^3 - 2*b^2*c^4*d*e^2 - 4*a*b*c^4*e^3 + 8*a*c^5*d*e^2))/c)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2) - (8*(d + e*x)^(1/2)*(b^4*e^6 + 2*a^2*c^2*e^6 + 2*c^4*d^4*e^2 - 12*a*c^3*d^2*e^4 - 4*b*c^3*d^3*e^3 + 6*b^2*c^2*d^2*e^4 - 4*a*b^2*c*e^6 - 4*b^3*c*d*e^5 + 12*a*b*c^2*d*e^5))/c)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2) + (((8*(4*a^2*c^3*e^5 - a*b^2*c^2*e^5 + 4*a*c^4*d^2*e^3 + b^3*c^2*d*e^4 - b^2*c^3*d^2*e^3 - 4*a*b*c^3*d*e^4))/c + (8*(d + e*x)^(1/2)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2)*(b^3*c^3*e^3 - 2*b^2*c^4*d*e^2 - 4*a*b*c^4*e^3 + 8*a*c^5*d*e^2))/c)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2) + (8*(d + e*x)^(1/2)*(b^4*e^6 + 2*a^2*c^2*e^6 + 2*c^4*d^4*e^2 - 12*a*c^3*d^2*e^4 - 4*b*c^3*d^3*e^3 + 6*b^2*c^2*d^2*e^4 - 4*a*b^2*c*e^6 - 4*b^3*c*d*e^5 + 12*a*b*c^2*d*e^5))/c)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2) - (16*(2*c^3*d^5*e^3 - b^3*d^2*e^6 - a^2*b*e^8 + 4*a*c^2*d^3*e^5 - 5*b*c^2*d^4*e^4 + 4*b^2*c*d^3*e^5 + 2*a*b^2*d*e^7 + 2*a^2*c*d*e^7 - 6*a*b*c*d^2*e^6))/c))*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4)))^(1/2)*2i","B"
2291,1,709,198,1.177868,"\text{Not used}","int((d + e*x)^(1/2)/(a + b*x + c*x^2),x)","-2\,\mathrm{atanh}\left(\frac{2\,\left(\sqrt{d+e\,x}\,\left(-8\,b^2\,c\,e^4+16\,b\,c^2\,d\,e^3-16\,c^3\,d^2\,e^2+16\,a\,c^2\,e^4\right)+\frac{\sqrt{d+e\,x}\,\left(8\,b^3\,c^2\,e^3-16\,d\,b^2\,c^3\,e^2-32\,a\,b\,c^3\,e^3+64\,a\,d\,c^4\,e^2\right)\,\left(b^3\,e+e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,a\,c^2\,d-2\,b^2\,c\,d-4\,a\,b\,c\,e\right)}{2\,\left(16\,a^2\,c^3-8\,a\,b^2\,c^2+b^4\,c\right)}\right)\,\sqrt{-\frac{b^3\,e+e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,a\,c^2\,d-2\,b^2\,c\,d-4\,a\,b\,c\,e}{2\,\left(16\,a^2\,c^3-8\,a\,b^2\,c^2+b^4\,c\right)}}}{16\,c^2\,d^2\,e^3-16\,b\,c\,d\,e^4+16\,a\,c\,e^5}\right)\,\sqrt{-\frac{b^3\,e+e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,a\,c^2\,d-2\,b^2\,c\,d-4\,a\,b\,c\,e}{2\,\left(16\,a^2\,c^3-8\,a\,b^2\,c^2+b^4\,c\right)}}-2\,\mathrm{atanh}\left(\frac{2\,\left(\sqrt{d+e\,x}\,\left(-8\,b^2\,c\,e^4+16\,b\,c^2\,d\,e^3-16\,c^3\,d^2\,e^2+16\,a\,c^2\,e^4\right)-\frac{\sqrt{d+e\,x}\,\left(8\,b^3\,c^2\,e^3-16\,d\,b^2\,c^3\,e^2-32\,a\,b\,c^3\,e^3+64\,a\,d\,c^4\,e^2\right)\,\left(e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,e-8\,a\,c^2\,d+2\,b^2\,c\,d+4\,a\,b\,c\,e\right)}{2\,\left(16\,a^2\,c^3-8\,a\,b^2\,c^2+b^4\,c\right)}\right)\,\sqrt{\frac{e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,e-8\,a\,c^2\,d+2\,b^2\,c\,d+4\,a\,b\,c\,e}{2\,\left(16\,a^2\,c^3-8\,a\,b^2\,c^2+b^4\,c\right)}}}{16\,c^2\,d^2\,e^3-16\,b\,c\,d\,e^4+16\,a\,c\,e^5}\right)\,\sqrt{\frac{e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,e-8\,a\,c^2\,d+2\,b^2\,c\,d+4\,a\,b\,c\,e}{2\,\left(16\,a^2\,c^3-8\,a\,b^2\,c^2+b^4\,c\right)}}","Not used",1,"- 2*atanh((2*((d + e*x)^(1/2)*(16*a*c^2*e^4 - 8*b^2*c*e^4 - 16*c^3*d^2*e^2 + 16*b*c^2*d*e^3) + ((d + e*x)^(1/2)*(8*b^3*c^2*e^3 - 16*b^2*c^3*d*e^2 - 32*a*b*c^3*e^3 + 64*a*c^4*d*e^2)*(b^3*e + e*(-(4*a*c - b^2)^3)^(1/2) + 8*a*c^2*d - 2*b^2*c*d - 4*a*b*c*e))/(2*(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2)))*(-(b^3*e + e*(-(4*a*c - b^2)^3)^(1/2) + 8*a*c^2*d - 2*b^2*c*d - 4*a*b*c*e)/(2*(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2)))^(1/2))/(16*c^2*d^2*e^3 + 16*a*c*e^5 - 16*b*c*d*e^4))*(-(b^3*e + e*(-(4*a*c - b^2)^3)^(1/2) + 8*a*c^2*d - 2*b^2*c*d - 4*a*b*c*e)/(2*(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2)))^(1/2) - 2*atanh((2*((d + e*x)^(1/2)*(16*a*c^2*e^4 - 8*b^2*c*e^4 - 16*c^3*d^2*e^2 + 16*b*c^2*d*e^3) - ((d + e*x)^(1/2)*(8*b^3*c^2*e^3 - 16*b^2*c^3*d*e^2 - 32*a*b*c^3*e^3 + 64*a*c^4*d*e^2)*(e*(-(4*a*c - b^2)^3)^(1/2) - b^3*e - 8*a*c^2*d + 2*b^2*c*d + 4*a*b*c*e))/(2*(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2)))*((e*(-(4*a*c - b^2)^3)^(1/2) - b^3*e - 8*a*c^2*d + 2*b^2*c*d + 4*a*b*c*e)/(2*(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2)))^(1/2))/(16*c^2*d^2*e^3 + 16*a*c*e^5 - 16*b*c*d*e^4))*((e*(-(4*a*c - b^2)^3)^(1/2) - b^3*e - 8*a*c^2*d + 2*b^2*c*d + 4*a*b*c*e)/(2*(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2)))^(1/2)","B"
2292,1,4449,199,1.928766,"\text{Not used}","int(1/((d + e*x)^(1/2)*(a + b*x + c*x^2)),x)","\mathrm{atan}\left(\frac{\left(\left(\sqrt{d+e\,x}\,\sqrt{-\frac{b^3\,e+e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,a\,c^2\,d-2\,b^2\,c\,d-4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}\,\left(8\,b^3\,c^2\,e^3-16\,d\,b^2\,c^3\,e^2-32\,a\,b\,c^3\,e^3+64\,a\,d\,c^4\,e^2\right)-32\,a\,c^3\,e^3+8\,b^2\,c^2\,e^3\right)\,\sqrt{-\frac{b^3\,e+e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,a\,c^2\,d-2\,b^2\,c\,d-4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}+16\,c^3\,e^2\,\sqrt{d+e\,x}\right)\,\sqrt{-\frac{b^3\,e+e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,a\,c^2\,d-2\,b^2\,c\,d-4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}\,1{}\mathrm{i}+\left(\left(32\,a\,c^3\,e^3+\sqrt{d+e\,x}\,\sqrt{-\frac{b^3\,e+e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,a\,c^2\,d-2\,b^2\,c\,d-4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}\,\left(8\,b^3\,c^2\,e^3-16\,d\,b^2\,c^3\,e^2-32\,a\,b\,c^3\,e^3+64\,a\,d\,c^4\,e^2\right)-8\,b^2\,c^2\,e^3\right)\,\sqrt{-\frac{b^3\,e+e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,a\,c^2\,d-2\,b^2\,c\,d-4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}+16\,c^3\,e^2\,\sqrt{d+e\,x}\right)\,\sqrt{-\frac{b^3\,e+e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,a\,c^2\,d-2\,b^2\,c\,d-4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}\,1{}\mathrm{i}}{\left(\left(\sqrt{d+e\,x}\,\sqrt{-\frac{b^3\,e+e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,a\,c^2\,d-2\,b^2\,c\,d-4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}\,\left(8\,b^3\,c^2\,e^3-16\,d\,b^2\,c^3\,e^2-32\,a\,b\,c^3\,e^3+64\,a\,d\,c^4\,e^2\right)-32\,a\,c^3\,e^3+8\,b^2\,c^2\,e^3\right)\,\sqrt{-\frac{b^3\,e+e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,a\,c^2\,d-2\,b^2\,c\,d-4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}+16\,c^3\,e^2\,\sqrt{d+e\,x}\right)\,\sqrt{-\frac{b^3\,e+e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,a\,c^2\,d-2\,b^2\,c\,d-4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}-\left(\left(32\,a\,c^3\,e^3+\sqrt{d+e\,x}\,\sqrt{-\frac{b^3\,e+e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,a\,c^2\,d-2\,b^2\,c\,d-4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}\,\left(8\,b^3\,c^2\,e^3-16\,d\,b^2\,c^3\,e^2-32\,a\,b\,c^3\,e^3+64\,a\,d\,c^4\,e^2\right)-8\,b^2\,c^2\,e^3\right)\,\sqrt{-\frac{b^3\,e+e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,a\,c^2\,d-2\,b^2\,c\,d-4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}+16\,c^3\,e^2\,\sqrt{d+e\,x}\right)\,\sqrt{-\frac{b^3\,e+e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,a\,c^2\,d-2\,b^2\,c\,d-4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}}\right)\,\sqrt{-\frac{b^3\,e+e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+8\,a\,c^2\,d-2\,b^2\,c\,d-4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(\sqrt{d+e\,x}\,\sqrt{\frac{e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,e-8\,a\,c^2\,d+2\,b^2\,c\,d+4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}\,\left(8\,b^3\,c^2\,e^3-16\,d\,b^2\,c^3\,e^2-32\,a\,b\,c^3\,e^3+64\,a\,d\,c^4\,e^2\right)-32\,a\,c^3\,e^3+8\,b^2\,c^2\,e^3\right)\,\sqrt{\frac{e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,e-8\,a\,c^2\,d+2\,b^2\,c\,d+4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}+16\,c^3\,e^2\,\sqrt{d+e\,x}\right)\,\sqrt{\frac{e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,e-8\,a\,c^2\,d+2\,b^2\,c\,d+4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}\,1{}\mathrm{i}+\left(\left(32\,a\,c^3\,e^3+\sqrt{d+e\,x}\,\sqrt{\frac{e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,e-8\,a\,c^2\,d+2\,b^2\,c\,d+4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}\,\left(8\,b^3\,c^2\,e^3-16\,d\,b^2\,c^3\,e^2-32\,a\,b\,c^3\,e^3+64\,a\,d\,c^4\,e^2\right)-8\,b^2\,c^2\,e^3\right)\,\sqrt{\frac{e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,e-8\,a\,c^2\,d+2\,b^2\,c\,d+4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}+16\,c^3\,e^2\,\sqrt{d+e\,x}\right)\,\sqrt{\frac{e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,e-8\,a\,c^2\,d+2\,b^2\,c\,d+4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}\,1{}\mathrm{i}}{\left(\left(\sqrt{d+e\,x}\,\sqrt{\frac{e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,e-8\,a\,c^2\,d+2\,b^2\,c\,d+4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}\,\left(8\,b^3\,c^2\,e^3-16\,d\,b^2\,c^3\,e^2-32\,a\,b\,c^3\,e^3+64\,a\,d\,c^4\,e^2\right)-32\,a\,c^3\,e^3+8\,b^2\,c^2\,e^3\right)\,\sqrt{\frac{e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,e-8\,a\,c^2\,d+2\,b^2\,c\,d+4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}+16\,c^3\,e^2\,\sqrt{d+e\,x}\right)\,\sqrt{\frac{e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,e-8\,a\,c^2\,d+2\,b^2\,c\,d+4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}-\left(\left(32\,a\,c^3\,e^3+\sqrt{d+e\,x}\,\sqrt{\frac{e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,e-8\,a\,c^2\,d+2\,b^2\,c\,d+4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}\,\left(8\,b^3\,c^2\,e^3-16\,d\,b^2\,c^3\,e^2-32\,a\,b\,c^3\,e^3+64\,a\,d\,c^4\,e^2\right)-8\,b^2\,c^2\,e^3\right)\,\sqrt{\frac{e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,e-8\,a\,c^2\,d+2\,b^2\,c\,d+4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}+16\,c^3\,e^2\,\sqrt{d+e\,x}\right)\,\sqrt{\frac{e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,e-8\,a\,c^2\,d+2\,b^2\,c\,d+4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}}\right)\,\sqrt{\frac{e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-b^3\,e-8\,a\,c^2\,d+2\,b^2\,c\,d+4\,a\,b\,c\,e}{2\,\left(16\,a^3\,c^2\,e^2-8\,a^2\,b^2\,c\,e^2-16\,a^2\,b\,c^2\,d\,e+16\,a^2\,c^3\,d^2+a\,b^4\,e^2+8\,a\,b^3\,c\,d\,e-8\,a\,b^2\,c^2\,d^2-b^5\,d\,e+b^4\,c\,d^2\right)}}\,2{}\mathrm{i}","Not used",1,"atan(((((d + e*x)^(1/2)*(-(b^3*e + e*(-(4*a*c - b^2)^3)^(1/2) + 8*a*c^2*d - 2*b^2*c*d - 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2)*(8*b^3*c^2*e^3 - 16*b^2*c^3*d*e^2 - 32*a*b*c^3*e^3 + 64*a*c^4*d*e^2) - 32*a*c^3*e^3 + 8*b^2*c^2*e^3)*(-(b^3*e + e*(-(4*a*c - b^2)^3)^(1/2) + 8*a*c^2*d - 2*b^2*c*d - 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2) + 16*c^3*e^2*(d + e*x)^(1/2))*(-(b^3*e + e*(-(4*a*c - b^2)^3)^(1/2) + 8*a*c^2*d - 2*b^2*c*d - 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2)*1i + ((32*a*c^3*e^3 + (d + e*x)^(1/2)*(-(b^3*e + e*(-(4*a*c - b^2)^3)^(1/2) + 8*a*c^2*d - 2*b^2*c*d - 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2)*(8*b^3*c^2*e^3 - 16*b^2*c^3*d*e^2 - 32*a*b*c^3*e^3 + 64*a*c^4*d*e^2) - 8*b^2*c^2*e^3)*(-(b^3*e + e*(-(4*a*c - b^2)^3)^(1/2) + 8*a*c^2*d - 2*b^2*c*d - 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2) + 16*c^3*e^2*(d + e*x)^(1/2))*(-(b^3*e + e*(-(4*a*c - b^2)^3)^(1/2) + 8*a*c^2*d - 2*b^2*c*d - 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2)*1i)/((((d + e*x)^(1/2)*(-(b^3*e + e*(-(4*a*c - b^2)^3)^(1/2) + 8*a*c^2*d - 2*b^2*c*d - 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2)*(8*b^3*c^2*e^3 - 16*b^2*c^3*d*e^2 - 32*a*b*c^3*e^3 + 64*a*c^4*d*e^2) - 32*a*c^3*e^3 + 8*b^2*c^2*e^3)*(-(b^3*e + e*(-(4*a*c - b^2)^3)^(1/2) + 8*a*c^2*d - 2*b^2*c*d - 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2) + 16*c^3*e^2*(d + e*x)^(1/2))*(-(b^3*e + e*(-(4*a*c - b^2)^3)^(1/2) + 8*a*c^2*d - 2*b^2*c*d - 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2) - ((32*a*c^3*e^3 + (d + e*x)^(1/2)*(-(b^3*e + e*(-(4*a*c - b^2)^3)^(1/2) + 8*a*c^2*d - 2*b^2*c*d - 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2)*(8*b^3*c^2*e^3 - 16*b^2*c^3*d*e^2 - 32*a*b*c^3*e^3 + 64*a*c^4*d*e^2) - 8*b^2*c^2*e^3)*(-(b^3*e + e*(-(4*a*c - b^2)^3)^(1/2) + 8*a*c^2*d - 2*b^2*c*d - 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2) + 16*c^3*e^2*(d + e*x)^(1/2))*(-(b^3*e + e*(-(4*a*c - b^2)^3)^(1/2) + 8*a*c^2*d - 2*b^2*c*d - 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2)))*(-(b^3*e + e*(-(4*a*c - b^2)^3)^(1/2) + 8*a*c^2*d - 2*b^2*c*d - 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2)*2i + atan(((((d + e*x)^(1/2)*((e*(-(4*a*c - b^2)^3)^(1/2) - b^3*e - 8*a*c^2*d + 2*b^2*c*d + 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2)*(8*b^3*c^2*e^3 - 16*b^2*c^3*d*e^2 - 32*a*b*c^3*e^3 + 64*a*c^4*d*e^2) - 32*a*c^3*e^3 + 8*b^2*c^2*e^3)*((e*(-(4*a*c - b^2)^3)^(1/2) - b^3*e - 8*a*c^2*d + 2*b^2*c*d + 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2) + 16*c^3*e^2*(d + e*x)^(1/2))*((e*(-(4*a*c - b^2)^3)^(1/2) - b^3*e - 8*a*c^2*d + 2*b^2*c*d + 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2)*1i + ((32*a*c^3*e^3 + (d + e*x)^(1/2)*((e*(-(4*a*c - b^2)^3)^(1/2) - b^3*e - 8*a*c^2*d + 2*b^2*c*d + 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2)*(8*b^3*c^2*e^3 - 16*b^2*c^3*d*e^2 - 32*a*b*c^3*e^3 + 64*a*c^4*d*e^2) - 8*b^2*c^2*e^3)*((e*(-(4*a*c - b^2)^3)^(1/2) - b^3*e - 8*a*c^2*d + 2*b^2*c*d + 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2) + 16*c^3*e^2*(d + e*x)^(1/2))*((e*(-(4*a*c - b^2)^3)^(1/2) - b^3*e - 8*a*c^2*d + 2*b^2*c*d + 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2)*1i)/((((d + e*x)^(1/2)*((e*(-(4*a*c - b^2)^3)^(1/2) - b^3*e - 8*a*c^2*d + 2*b^2*c*d + 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2)*(8*b^3*c^2*e^3 - 16*b^2*c^3*d*e^2 - 32*a*b*c^3*e^3 + 64*a*c^4*d*e^2) - 32*a*c^3*e^3 + 8*b^2*c^2*e^3)*((e*(-(4*a*c - b^2)^3)^(1/2) - b^3*e - 8*a*c^2*d + 2*b^2*c*d + 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2) + 16*c^3*e^2*(d + e*x)^(1/2))*((e*(-(4*a*c - b^2)^3)^(1/2) - b^3*e - 8*a*c^2*d + 2*b^2*c*d + 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2) - ((32*a*c^3*e^3 + (d + e*x)^(1/2)*((e*(-(4*a*c - b^2)^3)^(1/2) - b^3*e - 8*a*c^2*d + 2*b^2*c*d + 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2)*(8*b^3*c^2*e^3 - 16*b^2*c^3*d*e^2 - 32*a*b*c^3*e^3 + 64*a*c^4*d*e^2) - 8*b^2*c^2*e^3)*((e*(-(4*a*c - b^2)^3)^(1/2) - b^3*e - 8*a*c^2*d + 2*b^2*c*d + 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2) + 16*c^3*e^2*(d + e*x)^(1/2))*((e*(-(4*a*c - b^2)^3)^(1/2) - b^3*e - 8*a*c^2*d + 2*b^2*c*d + 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2)))*((e*(-(4*a*c - b^2)^3)^(1/2) - b^3*e - 8*a*c^2*d + 2*b^2*c*d + 4*a*b*c*e)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e - 8*a*b^2*c^2*d^2 - 8*a^2*b^2*c*e^2 - 16*a^2*b*c^2*d*e + 8*a*b^3*c*d*e)))^(1/2)*2i","B"
2293,1,23975,310,5.876487,"\text{Not used}","int(1/((d + e*x)^(3/2)*(a + b*x + c*x^2)),x)","-\frac{2\,e}{\sqrt{d+e\,x}\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}+\mathrm{atan}\left(\frac{\left(\sqrt{d+e\,x}\,\left(-16\,a^4\,c^4\,e^{10}+8\,a^3\,b^2\,c^3\,e^{10}+32\,a^3\,b\,c^4\,d\,e^9-32\,a^3\,c^5\,d^2\,e^8-24\,a^2\,b^3\,c^3\,d\,e^9+24\,a^2\,b^2\,c^4\,d^2\,e^8+24\,a\,b^4\,c^3\,d^2\,e^8-80\,a\,b^3\,c^4\,d^3\,e^7+120\,a\,b^2\,c^5\,d^4\,e^6-96\,a\,b\,c^6\,d^5\,e^5+32\,a\,c^7\,d^6\,e^4-8\,b^5\,c^3\,d^3\,e^7+40\,b^4\,c^4\,d^4\,e^6-88\,b^3\,c^5\,d^5\,e^5+104\,b^2\,c^6\,d^6\,e^4-64\,b\,c^7\,d^7\,e^3+16\,c^8\,d^8\,e^2\right)+\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^5\,c^2\,e^6-8\,a^4\,b^2\,c\,e^6-48\,a^4\,b\,c^2\,d\,e^5+48\,a^4\,c^3\,d^2\,e^4+a^3\,b^4\,e^6+24\,a^3\,b^3\,c\,d\,e^5+24\,a^3\,b^2\,c^2\,d^2\,e^4-96\,a^3\,b\,c^3\,d^3\,e^3+48\,a^3\,c^4\,d^4\,e^2-3\,a^2\,b^5\,d\,e^5-21\,a^2\,b^4\,c\,d^2\,e^4+32\,a^2\,b^3\,c^2\,d^3\,e^3+24\,a^2\,b^2\,c^3\,d^4\,e^2-48\,a^2\,b\,c^4\,d^5\,e+16\,a^2\,c^5\,d^6+3\,a\,b^6\,d^2\,e^4+2\,a\,b^5\,c\,d^3\,e^3-21\,a\,b^4\,c^2\,d^4\,e^2+24\,a\,b^3\,c^3\,d^5\,e-8\,a\,b^2\,c^4\,d^6-b^7\,d^3\,e^3+3\,b^6\,c\,d^4\,e^2-3\,b^5\,c^2\,d^5\,e+b^4\,c^3\,d^6\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^5\,c^2\,e^6-8\,a^4\,b^2\,c\,e^6-48\,a^4\,b\,c^2\,d\,e^5+48\,a^4\,c^3\,d^2\,e^4+a^3\,b^4\,e^6+24\,a^3\,b^3\,c\,d\,e^5+24\,a^3\,b^2\,c^2\,d^2\,e^4-96\,a^3\,b\,c^3\,d^3\,e^3+48\,a^3\,c^4\,d^4\,e^2-3\,a^2\,b^5\,d\,e^5-21\,a^2\,b^4\,c\,d^2\,e^4+32\,a^2\,b^3\,c^2\,d^3\,e^3+24\,a^2\,b^2\,c^3\,d^4\,e^2-48\,a^2\,b\,c^4\,d^5\,e+16\,a^2\,c^5\,d^6+3\,a\,b^6\,d^2\,e^4+2\,a\,b^5\,c\,d^3\,e^3-21\,a\,b^4\,c^2\,d^4\,e^2+24\,a\,b^3\,c^3\,d^5\,e-8\,a\,b^2\,c^4\,d^6-b^7\,d^3\,e^3+3\,b^6\,c\,d^4\,e^2-3\,b^5\,c^2\,d^5\,e+b^4\,c^3\,d^6\right)}}\,\left(-32\,a^6\,b\,c^3\,e^{13}+64\,a^6\,c^4\,d\,e^{12}+8\,a^5\,b^3\,c^2\,e^{13}+144\,a^5\,b^2\,c^3\,d\,e^{12}-480\,a^5\,b\,c^4\,d^2\,e^{11}+320\,a^5\,c^5\,d^3\,e^{10}-40\,a^4\,b^4\,c^2\,d\,e^{12}-200\,a^4\,b^3\,c^3\,d^2\,e^{11}+1200\,a^4\,b^2\,c^4\,d^3\,e^{10}-1600\,a^4\,b\,c^5\,d^4\,e^9+640\,a^4\,c^6\,d^5\,e^8+80\,a^3\,b^5\,c^2\,d^2\,e^{11}-1200\,a^3\,b^3\,c^4\,d^4\,e^9+2720\,a^3\,b^2\,c^5\,d^5\,e^8-2240\,a^3\,b\,c^6\,d^6\,e^7+640\,a^3\,c^7\,d^7\,e^6-80\,a^2\,b^6\,c^2\,d^3\,e^{10}+240\,a^2\,b^5\,c^3\,d^4\,e^9+240\,a^2\,b^4\,c^4\,d^5\,e^8-1680\,a^2\,b^3\,c^5\,d^6\,e^7+2400\,a^2\,b^2\,c^6\,d^7\,e^6-1440\,a^2\,b\,c^7\,d^8\,e^5+320\,a^2\,c^8\,d^9\,e^4+40\,a\,b^7\,c^2\,d^4\,e^9-208\,a\,b^6\,c^3\,d^5\,e^8+336\,a\,b^5\,c^4\,d^6\,e^7-600\,a\,b^3\,c^6\,d^8\,e^5+720\,a\,b^2\,c^7\,d^9\,e^4-352\,a\,b\,c^8\,d^{10}\,e^3+64\,a\,c^9\,d^{11}\,e^2-8\,b^8\,c^2\,d^5\,e^8+56\,b^7\,c^3\,d^6\,e^7-160\,b^6\,c^4\,d^7\,e^6+240\,b^5\,c^5\,d^8\,e^5-200\,b^4\,c^6\,d^9\,e^4+88\,b^3\,c^7\,d^{10}\,e^3-16\,b^2\,c^8\,d^{11}\,e^2\right)-32\,a^5\,b\,c^3\,e^{12}+64\,a\,c^8\,d^9\,e^3+64\,a^5\,c^4\,d\,e^{11}+8\,a^4\,b^3\,c^2\,e^{12}+256\,a^2\,c^7\,d^7\,e^5+384\,a^3\,c^6\,d^5\,e^7+256\,a^4\,c^5\,d^3\,e^9-16\,b^2\,c^7\,d^9\,e^3+72\,b^3\,c^6\,d^8\,e^4-128\,b^4\,c^5\,d^7\,e^5+112\,b^5\,c^4\,d^6\,e^6-48\,b^6\,c^3\,d^5\,e^7+8\,b^7\,c^2\,d^4\,e^8+1056\,a^2\,b^2\,c^5\,d^5\,e^7-400\,a^2\,b^3\,c^4\,d^4\,e^8-64\,a^2\,b^4\,c^3\,d^3\,e^9+48\,a^2\,b^5\,c^2\,d^2\,e^{10}+704\,a^3\,b^2\,c^4\,d^3\,e^9-96\,a^3\,b^3\,c^3\,d^2\,e^{10}-288\,a\,b\,c^7\,d^8\,e^4+448\,a\,b^2\,c^6\,d^7\,e^5-224\,a\,b^3\,c^5\,d^6\,e^6-96\,a\,b^4\,c^4\,d^5\,e^7+128\,a\,b^5\,c^3\,d^4\,e^8-32\,a\,b^6\,c^2\,d^3\,e^9-896\,a^2\,b\,c^6\,d^6\,e^6-960\,a^3\,b\,c^5\,d^4\,e^8-32\,a^3\,b^4\,c^2\,d\,e^{11}-384\,a^4\,b\,c^4\,d^2\,e^{10}+112\,a^4\,b^2\,c^3\,d\,e^{11}\right)\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^5\,c^2\,e^6-8\,a^4\,b^2\,c\,e^6-48\,a^4\,b\,c^2\,d\,e^5+48\,a^4\,c^3\,d^2\,e^4+a^3\,b^4\,e^6+24\,a^3\,b^3\,c\,d\,e^5+24\,a^3\,b^2\,c^2\,d^2\,e^4-96\,a^3\,b\,c^3\,d^3\,e^3+48\,a^3\,c^4\,d^4\,e^2-3\,a^2\,b^5\,d\,e^5-21\,a^2\,b^4\,c\,d^2\,e^4+32\,a^2\,b^3\,c^2\,d^3\,e^3+24\,a^2\,b^2\,c^3\,d^4\,e^2-48\,a^2\,b\,c^4\,d^5\,e+16\,a^2\,c^5\,d^6+3\,a\,b^6\,d^2\,e^4+2\,a\,b^5\,c\,d^3\,e^3-21\,a\,b^4\,c^2\,d^4\,e^2+24\,a\,b^3\,c^3\,d^5\,e-8\,a\,b^2\,c^4\,d^6-b^7\,d^3\,e^3+3\,b^6\,c\,d^4\,e^2-3\,b^5\,c^2\,d^5\,e+b^4\,c^3\,d^6\right)}}\,1{}\mathrm{i}+\left(\sqrt{d+e\,x}\,\left(-16\,a^4\,c^4\,e^{10}+8\,a^3\,b^2\,c^3\,e^{10}+32\,a^3\,b\,c^4\,d\,e^9-32\,a^3\,c^5\,d^2\,e^8-24\,a^2\,b^3\,c^3\,d\,e^9+24\,a^2\,b^2\,c^4\,d^2\,e^8+24\,a\,b^4\,c^3\,d^2\,e^8-80\,a\,b^3\,c^4\,d^3\,e^7+120\,a\,b^2\,c^5\,d^4\,e^6-96\,a\,b\,c^6\,d^5\,e^5+32\,a\,c^7\,d^6\,e^4-8\,b^5\,c^3\,d^3\,e^7+40\,b^4\,c^4\,d^4\,e^6-88\,b^3\,c^5\,d^5\,e^5+104\,b^2\,c^6\,d^6\,e^4-64\,b\,c^7\,d^7\,e^3+16\,c^8\,d^8\,e^2\right)+\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^5\,c^2\,e^6-8\,a^4\,b^2\,c\,e^6-48\,a^4\,b\,c^2\,d\,e^5+48\,a^4\,c^3\,d^2\,e^4+a^3\,b^4\,e^6+24\,a^3\,b^3\,c\,d\,e^5+24\,a^3\,b^2\,c^2\,d^2\,e^4-96\,a^3\,b\,c^3\,d^3\,e^3+48\,a^3\,c^4\,d^4\,e^2-3\,a^2\,b^5\,d\,e^5-21\,a^2\,b^4\,c\,d^2\,e^4+32\,a^2\,b^3\,c^2\,d^3\,e^3+24\,a^2\,b^2\,c^3\,d^4\,e^2-48\,a^2\,b\,c^4\,d^5\,e+16\,a^2\,c^5\,d^6+3\,a\,b^6\,d^2\,e^4+2\,a\,b^5\,c\,d^3\,e^3-21\,a\,b^4\,c^2\,d^4\,e^2+24\,a\,b^3\,c^3\,d^5\,e-8\,a\,b^2\,c^4\,d^6-b^7\,d^3\,e^3+3\,b^6\,c\,d^4\,e^2-3\,b^5\,c^2\,d^5\,e+b^4\,c^3\,d^6\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^5\,c^2\,e^6-8\,a^4\,b^2\,c\,e^6-48\,a^4\,b\,c^2\,d\,e^5+48\,a^4\,c^3\,d^2\,e^4+a^3\,b^4\,e^6+24\,a^3\,b^3\,c\,d\,e^5+24\,a^3\,b^2\,c^2\,d^2\,e^4-96\,a^3\,b\,c^3\,d^3\,e^3+48\,a^3\,c^4\,d^4\,e^2-3\,a^2\,b^5\,d\,e^5-21\,a^2\,b^4\,c\,d^2\,e^4+32\,a^2\,b^3\,c^2\,d^3\,e^3+24\,a^2\,b^2\,c^3\,d^4\,e^2-48\,a^2\,b\,c^4\,d^5\,e+16\,a^2\,c^5\,d^6+3\,a\,b^6\,d^2\,e^4+2\,a\,b^5\,c\,d^3\,e^3-21\,a\,b^4\,c^2\,d^4\,e^2+24\,a\,b^3\,c^3\,d^5\,e-8\,a\,b^2\,c^4\,d^6-b^7\,d^3\,e^3+3\,b^6\,c\,d^4\,e^2-3\,b^5\,c^2\,d^5\,e+b^4\,c^3\,d^6\right)}}\,\left(-32\,a^6\,b\,c^3\,e^{13}+64\,a^6\,c^4\,d\,e^{12}+8\,a^5\,b^3\,c^2\,e^{13}+144\,a^5\,b^2\,c^3\,d\,e^{12}-480\,a^5\,b\,c^4\,d^2\,e^{11}+320\,a^5\,c^5\,d^3\,e^{10}-40\,a^4\,b^4\,c^2\,d\,e^{12}-200\,a^4\,b^3\,c^3\,d^2\,e^{11}+1200\,a^4\,b^2\,c^4\,d^3\,e^{10}-1600\,a^4\,b\,c^5\,d^4\,e^9+640\,a^4\,c^6\,d^5\,e^8+80\,a^3\,b^5\,c^2\,d^2\,e^{11}-1200\,a^3\,b^3\,c^4\,d^4\,e^9+2720\,a^3\,b^2\,c^5\,d^5\,e^8-2240\,a^3\,b\,c^6\,d^6\,e^7+640\,a^3\,c^7\,d^7\,e^6-80\,a^2\,b^6\,c^2\,d^3\,e^{10}+240\,a^2\,b^5\,c^3\,d^4\,e^9+240\,a^2\,b^4\,c^4\,d^5\,e^8-1680\,a^2\,b^3\,c^5\,d^6\,e^7+2400\,a^2\,b^2\,c^6\,d^7\,e^6-1440\,a^2\,b\,c^7\,d^8\,e^5+320\,a^2\,c^8\,d^9\,e^4+40\,a\,b^7\,c^2\,d^4\,e^9-208\,a\,b^6\,c^3\,d^5\,e^8+336\,a\,b^5\,c^4\,d^6\,e^7-600\,a\,b^3\,c^6\,d^8\,e^5+720\,a\,b^2\,c^7\,d^9\,e^4-352\,a\,b\,c^8\,d^{10}\,e^3+64\,a\,c^9\,d^{11}\,e^2-8\,b^8\,c^2\,d^5\,e^8+56\,b^7\,c^3\,d^6\,e^7-160\,b^6\,c^4\,d^7\,e^6+240\,b^5\,c^5\,d^8\,e^5-200\,b^4\,c^6\,d^9\,e^4+88\,b^3\,c^7\,d^{10}\,e^3-16\,b^2\,c^8\,d^{11}\,e^2\right)+32\,a^5\,b\,c^3\,e^{12}-64\,a\,c^8\,d^9\,e^3-64\,a^5\,c^4\,d\,e^{11}-8\,a^4\,b^3\,c^2\,e^{12}-256\,a^2\,c^7\,d^7\,e^5-384\,a^3\,c^6\,d^5\,e^7-256\,a^4\,c^5\,d^3\,e^9+16\,b^2\,c^7\,d^9\,e^3-72\,b^3\,c^6\,d^8\,e^4+128\,b^4\,c^5\,d^7\,e^5-112\,b^5\,c^4\,d^6\,e^6+48\,b^6\,c^3\,d^5\,e^7-8\,b^7\,c^2\,d^4\,e^8-1056\,a^2\,b^2\,c^5\,d^5\,e^7+400\,a^2\,b^3\,c^4\,d^4\,e^8+64\,a^2\,b^4\,c^3\,d^3\,e^9-48\,a^2\,b^5\,c^2\,d^2\,e^{10}-704\,a^3\,b^2\,c^4\,d^3\,e^9+96\,a^3\,b^3\,c^3\,d^2\,e^{10}+288\,a\,b\,c^7\,d^8\,e^4-448\,a\,b^2\,c^6\,d^7\,e^5+224\,a\,b^3\,c^5\,d^6\,e^6+96\,a\,b^4\,c^4\,d^5\,e^7-128\,a\,b^5\,c^3\,d^4\,e^8+32\,a\,b^6\,c^2\,d^3\,e^9+896\,a^2\,b\,c^6\,d^6\,e^6+960\,a^3\,b\,c^5\,d^4\,e^8+32\,a^3\,b^4\,c^2\,d\,e^{11}+384\,a^4\,b\,c^4\,d^2\,e^{10}-112\,a^4\,b^2\,c^3\,d\,e^{11}\right)\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3+b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e+3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3-a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e-3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^5\,c^2\,e^6-8\,a^4\,b^2\,c\,e^6-48\,a^4\,b\,c^2\,d\,e^5+48\,a^4\,c^3\,d^2\,e^4+a^3\,b^4\,e^6+24\,a^3\,b^3\,c\,d\,e^5+24\,a^3\,b^2\,c^2\,d^2\,e^4-96\,a^3\,b\,c^3\,d^3\,e^3+48\,a^3\,c^4\,d^4\,e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\,b\,c^7\,d^8\,e^5+320\,a^2\,c^8\,d^9\,e^4+40\,a\,b^7\,c^2\,d^4\,e^9-208\,a\,b^6\,c^3\,d^5\,e^8+336\,a\,b^5\,c^4\,d^6\,e^7-600\,a\,b^3\,c^6\,d^8\,e^5+720\,a\,b^2\,c^7\,d^9\,e^4-352\,a\,b\,c^8\,d^{10}\,e^3+64\,a\,c^9\,d^{11}\,e^2-8\,b^8\,c^2\,d^5\,e^8+56\,b^7\,c^3\,d^6\,e^7-160\,b^6\,c^4\,d^7\,e^6+240\,b^5\,c^5\,d^8\,e^5-200\,b^4\,c^6\,d^9\,e^4+88\,b^3\,c^7\,d^{10}\,e^3-16\,b^2\,c^8\,d^{11}\,e^2\right)+32\,a^5\,b\,c^3\,e^{12}-64\,a\,c^8\,d^9\,e^3-64\,a^5\,c^4\,d\,e^{11}-8\,a^4\,b^3\,c^2\,e^{12}-256\,a^2\,c^7\,d^7\,e^5-384\,a^3\,c^6\,d^5\,e^7-256\,a^4\,c^5\,d^3\,e^9+16\,b^2\,c^7\,d^9\,e^3-72\,b^3\,c^6\,d^8\,e^4+128\,b^4\,c^5\,d^7\,e^5-112\,b^5\,c^4\,d^6\,e^6+48\,b^6\,c^3\,d^5\,e^7-8\,b^7\,c^2\,d^4\,e^8-1056\,a^2\,b^2\,c^5\,d^5\,e^7+400\,a^2\,b^3\,c^4\,d^4\,e^8+64\,a^2\,b^4\,c^3\,d^3\,e^9-48\,a^2\,b^5\,c^2\,d^2\,e^{10}-704\,a^3\,b^2\,c^4\,d^3\,e^9+96\,a^3\,b^3\,c^3\,d^2\,e^{10}+288\,a\,b\,c^7\,d^8\,e^4-448\,a\,b^2\,c^6\,d^7\,e^5+224\,a\,b^3\,c^5\,d^6\,e^6+96\,a\,b^4\,c^4\,d^5\,e^7-128\,a\,b^5\,c^3\,d^4\,e^8+32\,a\,b^6\,c^2\,d^3\,e^9+896\,a^2\,b\,c^6\,d^6\,e^6+960\,a^3\,b\,c^5\,d^4\,e^8+32\,a^3\,b^4\,c^2\,d\,e^{11}+384\,a^4\,b\,c^4\,d^2\,e^{10}-112\,a^4\,b^2\,c^3\,d\,e^{11}\right)\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^5\,c^2\,e^6-8\,a^4\,b^2\,c\,e^6-48\,a^4\,b\,c^2\,d\,e^5+48\,a^4\,c^3\,d^2\,e^4+a^3\,b^4\,e^6+24\,a^3\,b^3\,c\,d\,e^5+24\,a^3\,b^2\,c^2\,d^2\,e^4-96\,a^3\,b\,c^3\,d^3\,e^3+48\,a^3\,c^4\,d^4\,e^2-3\,a^2\,b^5\,d\,e^5-21\,a^2\,b^4\,c\,d^2\,e^4+32\,a^2\,b^3\,c^2\,d^3\,e^3+24\,a^2\,b^2\,c^3\,d^4\,e^2-48\,a^2\,b\,c^4\,d^5\,e+16\,a^2\,c^5\,d^6+3\,a\,b^6\,d^2\,e^4+2\,a\,b^5\,c\,d^3\,e^3-21\,a\,b^4\,c^2\,d^4\,e^2+24\,a\,b^3\,c^3\,d^5\,e-8\,a\,b^2\,c^4\,d^6-b^7\,d^3\,e^3+3\,b^6\,c\,d^4\,e^2-3\,b^5\,c^2\,d^5\,e+b^4\,c^3\,d^6\right)}}-\left(\sqrt{d+e\,x}\,\left(-16\,a^4\,c^4\,e^{10}+8\,a^3\,b^2\,c^3\,e^{10}+32\,a^3\,b\,c^4\,d\,e^9-32\,a^3\,c^5\,d^2\,e^8-24\,a^2\,b^3\,c^3\,d\,e^9+24\,a^2\,b^2\,c^4\,d^2\,e^8+24\,a\,b^4\,c^3\,d^2\,e^8-80\,a\,b^3\,c^4\,d^3\,e^7+120\,a\,b^2\,c^5\,d^4\,e^6-96\,a\,b\,c^6\,d^5\,e^5+32\,a\,c^7\,d^6\,e^4-8\,b^5\,c^3\,d^3\,e^7+40\,b^4\,c^4\,d^4\,e^6-88\,b^3\,c^5\,d^5\,e^5+104\,b^2\,c^6\,d^6\,e^4-64\,b\,c^7\,d^7\,e^3+16\,c^8\,d^8\,e^2\right)+\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^5\,c^2\,e^6-8\,a^4\,b^2\,c\,e^6-48\,a^4\,b\,c^2\,d\,e^5+48\,a^4\,c^3\,d^2\,e^4+a^3\,b^4\,e^6+24\,a^3\,b^3\,c\,d\,e^5+24\,a^3\,b^2\,c^2\,d^2\,e^4-96\,a^3\,b\,c^3\,d^3\,e^3+48\,a^3\,c^4\,d^4\,e^2-3\,a^2\,b^5\,d\,e^5-21\,a^2\,b^4\,c\,d^2\,e^4+32\,a^2\,b^3\,c^2\,d^3\,e^3+24\,a^2\,b^2\,c^3\,d^4\,e^2-48\,a^2\,b\,c^4\,d^5\,e+16\,a^2\,c^5\,d^6+3\,a\,b^6\,d^2\,e^4+2\,a\,b^5\,c\,d^3\,e^3-21\,a\,b^4\,c^2\,d^4\,e^2+24\,a\,b^3\,c^3\,d^5\,e-8\,a\,b^2\,c^4\,d^6-b^7\,d^3\,e^3+3\,b^6\,c\,d^4\,e^2-3\,b^5\,c^2\,d^5\,e+b^4\,c^3\,d^6\right)}}\,\left(\sqrt{d+e\,x}\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^5\,c^2\,e^6-8\,a^4\,b^2\,c\,e^6-48\,a^4\,b\,c^2\,d\,e^5+48\,a^4\,c^3\,d^2\,e^4+a^3\,b^4\,e^6+24\,a^3\,b^3\,c\,d\,e^5+24\,a^3\,b^2\,c^2\,d^2\,e^4-96\,a^3\,b\,c^3\,d^3\,e^3+48\,a^3\,c^4\,d^4\,e^2-3\,a^2\,b^5\,d\,e^5-21\,a^2\,b^4\,c\,d^2\,e^4+32\,a^2\,b^3\,c^2\,d^3\,e^3+24\,a^2\,b^2\,c^3\,d^4\,e^2-48\,a^2\,b\,c^4\,d^5\,e+16\,a^2\,c^5\,d^6+3\,a\,b^6\,d^2\,e^4+2\,a\,b^5\,c\,d^3\,e^3-21\,a\,b^4\,c^2\,d^4\,e^2+24\,a\,b^3\,c^3\,d^5\,e-8\,a\,b^2\,c^4\,d^6-b^7\,d^3\,e^3+3\,b^6\,c\,d^4\,e^2-3\,b^5\,c^2\,d^5\,e+b^4\,c^3\,d^6\right)}}\,\left(-32\,a^6\,b\,c^3\,e^{13}+64\,a^6\,c^4\,d\,e^{12}+8\,a^5\,b^3\,c^2\,e^{13}+144\,a^5\,b^2\,c^3\,d\,e^{12}-480\,a^5\,b\,c^4\,d^2\,e^{11}+320\,a^5\,c^5\,d^3\,e^{10}-40\,a^4\,b^4\,c^2\,d\,e^{12}-200\,a^4\,b^3\,c^3\,d^2\,e^{11}+1200\,a^4\,b^2\,c^4\,d^3\,e^{10}-1600\,a^4\,b\,c^5\,d^4\,e^9+640\,a^4\,c^6\,d^5\,e^8+80\,a^3\,b^5\,c^2\,d^2\,e^{11}-1200\,a^3\,b^3\,c^4\,d^4\,e^9+2720\,a^3\,b^2\,c^5\,d^5\,e^8-2240\,a^3\,b\,c^6\,d^6\,e^7+640\,a^3\,c^7\,d^7\,e^6-80\,a^2\,b^6\,c^2\,d^3\,e^{10}+240\,a^2\,b^5\,c^3\,d^4\,e^9+240\,a^2\,b^4\,c^4\,d^5\,e^8-1680\,a^2\,b^3\,c^5\,d^6\,e^7+2400\,a^2\,b^2\,c^6\,d^7\,e^6-1440\,a^2\,b\,c^7\,d^8\,e^5+320\,a^2\,c^8\,d^9\,e^4+40\,a\,b^7\,c^2\,d^4\,e^9-208\,a\,b^6\,c^3\,d^5\,e^8+336\,a\,b^5\,c^4\,d^6\,e^7-600\,a\,b^3\,c^6\,d^8\,e^5+720\,a\,b^2\,c^7\,d^9\,e^4-352\,a\,b\,c^8\,d^{10}\,e^3+64\,a\,c^9\,d^{11}\,e^2-8\,b^8\,c^2\,d^5\,e^8+56\,b^7\,c^3\,d^6\,e^7-160\,b^6\,c^4\,d^7\,e^6+240\,b^5\,c^5\,d^8\,e^5-200\,b^4\,c^6\,d^9\,e^4+88\,b^3\,c^7\,d^{10}\,e^3-16\,b^2\,c^8\,d^{11}\,e^2\right)-32\,a^5\,b\,c^3\,e^{12}+64\,a\,c^8\,d^9\,e^3+64\,a^5\,c^4\,d\,e^{11}+8\,a^4\,b^3\,c^2\,e^{12}+256\,a^2\,c^7\,d^7\,e^5+384\,a^3\,c^6\,d^5\,e^7+256\,a^4\,c^5\,d^3\,e^9-16\,b^2\,c^7\,d^9\,e^3+72\,b^3\,c^6\,d^8\,e^4-128\,b^4\,c^5\,d^7\,e^5+112\,b^5\,c^4\,d^6\,e^6-48\,b^6\,c^3\,d^5\,e^7+8\,b^7\,c^2\,d^4\,e^8+1056\,a^2\,b^2\,c^5\,d^5\,e^7-400\,a^2\,b^3\,c^4\,d^4\,e^8-64\,a^2\,b^4\,c^3\,d^3\,e^9+48\,a^2\,b^5\,c^2\,d^2\,e^{10}+704\,a^3\,b^2\,c^4\,d^3\,e^9-96\,a^3\,b^3\,c^3\,d^2\,e^{10}-288\,a\,b\,c^7\,d^8\,e^4+448\,a\,b^2\,c^6\,d^7\,e^5-224\,a\,b^3\,c^5\,d^6\,e^6-96\,a\,b^4\,c^4\,d^5\,e^7+128\,a\,b^5\,c^3\,d^4\,e^8-32\,a\,b^6\,c^2\,d^3\,e^9-896\,a^2\,b\,c^6\,d^6\,e^6-960\,a^3\,b\,c^5\,d^4\,e^8-32\,a^3\,b^4\,c^2\,d\,e^{11}-384\,a^4\,b\,c^4\,d^2\,e^{10}+112\,a^4\,b^2\,c^3\,d\,e^{11}\right)\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^5\,c^2\,e^6-8\,a^4\,b^2\,c\,e^6-48\,a^4\,b\,c^2\,d\,e^5+48\,a^4\,c^3\,d^2\,e^4+a^3\,b^4\,e^6+24\,a^3\,b^3\,c\,d\,e^5+24\,a^3\,b^2\,c^2\,d^2\,e^4-96\,a^3\,b\,c^3\,d^3\,e^3+48\,a^3\,c^4\,d^4\,e^2-3\,a^2\,b^5\,d\,e^5-21\,a^2\,b^4\,c\,d^2\,e^4+32\,a^2\,b^3\,c^2\,d^3\,e^3+24\,a^2\,b^2\,c^3\,d^4\,e^2-48\,a^2\,b\,c^4\,d^5\,e+16\,a^2\,c^5\,d^6+3\,a\,b^6\,d^2\,e^4+2\,a\,b^5\,c\,d^3\,e^3-21\,a\,b^4\,c^2\,d^4\,e^2+24\,a\,b^3\,c^3\,d^5\,e-8\,a\,b^2\,c^4\,d^6-b^7\,d^3\,e^3+3\,b^6\,c\,d^4\,e^2-3\,b^5\,c^2\,d^5\,e+b^4\,c^3\,d^6\right)}}+16\,a^3\,c^4\,e^9+16\,c^7\,d^6\,e^3+48\,a\,c^6\,d^4\,e^5-48\,b\,c^6\,d^5\,e^4+48\,a^2\,c^5\,d^2\,e^7+48\,b^2\,c^5\,d^4\,e^5-16\,b^3\,c^4\,d^3\,e^6-96\,a\,b\,c^5\,d^3\,e^6-48\,a^2\,b\,c^4\,d\,e^8+48\,a\,b^2\,c^4\,d^2\,e^7}\right)\,\sqrt{-\frac{b^5\,e^3+8\,a\,c^4\,d^3-2\,b^2\,c^3\,d^3-b^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+12\,a^2\,b\,c^2\,e^3-24\,a^2\,c^3\,d\,e^2+3\,b^3\,c^2\,d^2\,e-3\,c^2\,d^2\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-7\,a\,b^3\,c\,e^3+a\,c\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,b^4\,c\,d\,e^2-12\,a\,b\,c^3\,d^2\,e+3\,b\,c\,d\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+18\,a\,b^2\,c^2\,d\,e^2}{2\,\left(16\,a^5\,c^2\,e^6-8\,a^4\,b^2\,c\,e^6-48\,a^4\,b\,c^2\,d\,e^5+48\,a^4\,c^3\,d^2\,e^4+a^3\,b^4\,e^6+24\,a^3\,b^3\,c\,d\,e^5+24\,a^3\,b^2\,c^2\,d^2\,e^4-96\,a^3\,b\,c^3\,d^3\,e^3+48\,a^3\,c^4\,d^4\,e^2-3\,a^2\,b^5\,d\,e^5-21\,a^2\,b^4\,c\,d^2\,e^4+32\,a^2\,b^3\,c^2\,d^3\,e^3+24\,a^2\,b^2\,c^3\,d^4\,e^2-48\,a^2\,b\,c^4\,d^5\,e+16\,a^2\,c^5\,d^6+3\,a\,b^6\,d^2\,e^4+2\,a\,b^5\,c\,d^3\,e^3-21\,a\,b^4\,c^2\,d^4\,e^2+24\,a\,b^3\,c^3\,d^5\,e-8\,a\,b^2\,c^4\,d^6-b^7\,d^3\,e^3+3\,b^6\,c\,d^4\,e^2-3\,b^5\,c^2\,d^5\,e+b^4\,c^3\,d^6\right)}}\,2{}\mathrm{i}","Not used",1,"atan((((d + e*x)^(1/2)*(16*c^8*d^8*e^2 - 16*a^4*c^4*e^10 + 32*a*c^7*d^6*e^4 - 64*b*c^7*d^7*e^3 + 8*a^3*b^2*c^3*e^10 - 32*a^3*c^5*d^2*e^8 + 104*b^2*c^6*d^6*e^4 - 88*b^3*c^5*d^5*e^5 + 40*b^4*c^4*d^4*e^6 - 8*b^5*c^3*d^3*e^7 + 24*a^2*b^2*c^4*d^2*e^8 - 96*a*b*c^6*d^5*e^5 + 32*a^3*b*c^4*d*e^9 + 120*a*b^2*c^5*d^4*e^6 - 80*a*b^3*c^4*d^3*e^7 + 24*a*b^4*c^3*d^2*e^8 - 24*a^2*b^3*c^3*d*e^9) + (-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*((d + e*x)^(1/2)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*(64*a*c^9*d^11*e^2 - 32*a^6*b*c^3*e^13 + 64*a^6*c^4*d*e^12 + 8*a^5*b^3*c^2*e^13 + 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 + 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10 - 16*b^2*c^8*d^11*e^2 + 88*b^3*c^7*d^10*e^3 - 200*b^4*c^6*d^9*e^4 + 240*b^5*c^5*d^8*e^5 - 160*b^6*c^4*d^7*e^6 + 56*b^7*c^3*d^6*e^7 - 8*b^8*c^2*d^5*e^8 + 2400*a^2*b^2*c^6*d^7*e^6 - 1680*a^2*b^3*c^5*d^6*e^7 + 240*a^2*b^4*c^4*d^5*e^8 + 240*a^2*b^5*c^3*d^4*e^9 - 80*a^2*b^6*c^2*d^3*e^10 + 2720*a^3*b^2*c^5*d^5*e^8 - 1200*a^3*b^3*c^4*d^4*e^9 + 80*a^3*b^5*c^2*d^2*e^11 + 1200*a^4*b^2*c^4*d^3*e^10 - 200*a^4*b^3*c^3*d^2*e^11 - 352*a*b*c^8*d^10*e^3 + 720*a*b^2*c^7*d^9*e^4 - 600*a*b^3*c^6*d^8*e^5 + 336*a*b^5*c^4*d^6*e^7 - 208*a*b^6*c^3*d^5*e^8 + 40*a*b^7*c^2*d^4*e^9 - 1440*a^2*b*c^7*d^8*e^5 - 2240*a^3*b*c^6*d^6*e^7 - 1600*a^4*b*c^5*d^4*e^9 - 40*a^4*b^4*c^2*d*e^12 - 480*a^5*b*c^4*d^2*e^11 + 144*a^5*b^2*c^3*d*e^12) - 32*a^5*b*c^3*e^12 + 64*a*c^8*d^9*e^3 + 64*a^5*c^4*d*e^11 + 8*a^4*b^3*c^2*e^12 + 256*a^2*c^7*d^7*e^5 + 384*a^3*c^6*d^5*e^7 + 256*a^4*c^5*d^3*e^9 - 16*b^2*c^7*d^9*e^3 + 72*b^3*c^6*d^8*e^4 - 128*b^4*c^5*d^7*e^5 + 112*b^5*c^4*d^6*e^6 - 48*b^6*c^3*d^5*e^7 + 8*b^7*c^2*d^4*e^8 + 1056*a^2*b^2*c^5*d^5*e^7 - 400*a^2*b^3*c^4*d^4*e^8 - 64*a^2*b^4*c^3*d^3*e^9 + 48*a^2*b^5*c^2*d^2*e^10 + 704*a^3*b^2*c^4*d^3*e^9 - 96*a^3*b^3*c^3*d^2*e^10 - 288*a*b*c^7*d^8*e^4 + 448*a*b^2*c^6*d^7*e^5 - 224*a*b^3*c^5*d^6*e^6 - 96*a*b^4*c^4*d^5*e^7 + 128*a*b^5*c^3*d^4*e^8 - 32*a*b^6*c^2*d^3*e^9 - 896*a^2*b*c^6*d^6*e^6 - 960*a^3*b*c^5*d^4*e^8 - 32*a^3*b^4*c^2*d*e^11 - 384*a^4*b*c^4*d^2*e^10 + 112*a^4*b^2*c^3*d*e^11))*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*1i + ((d + e*x)^(1/2)*(16*c^8*d^8*e^2 - 16*a^4*c^4*e^10 + 32*a*c^7*d^6*e^4 - 64*b*c^7*d^7*e^3 + 8*a^3*b^2*c^3*e^10 - 32*a^3*c^5*d^2*e^8 + 104*b^2*c^6*d^6*e^4 - 88*b^3*c^5*d^5*e^5 + 40*b^4*c^4*d^4*e^6 - 8*b^5*c^3*d^3*e^7 + 24*a^2*b^2*c^4*d^2*e^8 - 96*a*b*c^6*d^5*e^5 + 32*a^3*b*c^4*d*e^9 + 120*a*b^2*c^5*d^4*e^6 - 80*a*b^3*c^4*d^3*e^7 + 24*a*b^4*c^3*d^2*e^8 - 24*a^2*b^3*c^3*d*e^9) + (-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*((d + e*x)^(1/2)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*(64*a*c^9*d^11*e^2 - 32*a^6*b*c^3*e^13 + 64*a^6*c^4*d*e^12 + 8*a^5*b^3*c^2*e^13 + 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 + 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10 - 16*b^2*c^8*d^11*e^2 + 88*b^3*c^7*d^10*e^3 - 200*b^4*c^6*d^9*e^4 + 240*b^5*c^5*d^8*e^5 - 160*b^6*c^4*d^7*e^6 + 56*b^7*c^3*d^6*e^7 - 8*b^8*c^2*d^5*e^8 + 2400*a^2*b^2*c^6*d^7*e^6 - 1680*a^2*b^3*c^5*d^6*e^7 + 240*a^2*b^4*c^4*d^5*e^8 + 240*a^2*b^5*c^3*d^4*e^9 - 80*a^2*b^6*c^2*d^3*e^10 + 2720*a^3*b^2*c^5*d^5*e^8 - 1200*a^3*b^3*c^4*d^4*e^9 + 80*a^3*b^5*c^2*d^2*e^11 + 1200*a^4*b^2*c^4*d^3*e^10 - 200*a^4*b^3*c^3*d^2*e^11 - 352*a*b*c^8*d^10*e^3 + 720*a*b^2*c^7*d^9*e^4 - 600*a*b^3*c^6*d^8*e^5 + 336*a*b^5*c^4*d^6*e^7 - 208*a*b^6*c^3*d^5*e^8 + 40*a*b^7*c^2*d^4*e^9 - 1440*a^2*b*c^7*d^8*e^5 - 2240*a^3*b*c^6*d^6*e^7 - 1600*a^4*b*c^5*d^4*e^9 - 40*a^4*b^4*c^2*d*e^12 - 480*a^5*b*c^4*d^2*e^11 + 144*a^5*b^2*c^3*d*e^12) + 32*a^5*b*c^3*e^12 - 64*a*c^8*d^9*e^3 - 64*a^5*c^4*d*e^11 - 8*a^4*b^3*c^2*e^12 - 256*a^2*c^7*d^7*e^5 - 384*a^3*c^6*d^5*e^7 - 256*a^4*c^5*d^3*e^9 + 16*b^2*c^7*d^9*e^3 - 72*b^3*c^6*d^8*e^4 + 128*b^4*c^5*d^7*e^5 - 112*b^5*c^4*d^6*e^6 + 48*b^6*c^3*d^5*e^7 - 8*b^7*c^2*d^4*e^8 - 1056*a^2*b^2*c^5*d^5*e^7 + 400*a^2*b^3*c^4*d^4*e^8 + 64*a^2*b^4*c^3*d^3*e^9 - 48*a^2*b^5*c^2*d^2*e^10 - 704*a^3*b^2*c^4*d^3*e^9 + 96*a^3*b^3*c^3*d^2*e^10 + 288*a*b*c^7*d^8*e^4 - 448*a*b^2*c^6*d^7*e^5 + 224*a*b^3*c^5*d^6*e^6 + 96*a*b^4*c^4*d^5*e^7 - 128*a*b^5*c^3*d^4*e^8 + 32*a*b^6*c^2*d^3*e^9 + 896*a^2*b*c^6*d^6*e^6 + 960*a^3*b*c^5*d^4*e^8 + 32*a^3*b^4*c^2*d*e^11 + 384*a^4*b*c^4*d^2*e^10 - 112*a^4*b^2*c^3*d*e^11))*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*1i)/(((d + e*x)^(1/2)*(16*c^8*d^8*e^2 - 16*a^4*c^4*e^10 + 32*a*c^7*d^6*e^4 - 64*b*c^7*d^7*e^3 + 8*a^3*b^2*c^3*e^10 - 32*a^3*c^5*d^2*e^8 + 104*b^2*c^6*d^6*e^4 - 88*b^3*c^5*d^5*e^5 + 40*b^4*c^4*d^4*e^6 - 8*b^5*c^3*d^3*e^7 + 24*a^2*b^2*c^4*d^2*e^8 - 96*a*b*c^6*d^5*e^5 + 32*a^3*b*c^4*d*e^9 + 120*a*b^2*c^5*d^4*e^6 - 80*a*b^3*c^4*d^3*e^7 + 24*a*b^4*c^3*d^2*e^8 - 24*a^2*b^3*c^3*d*e^9) + (-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*((d + e*x)^(1/2)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*(64*a*c^9*d^11*e^2 - 32*a^6*b*c^3*e^13 + 64*a^6*c^4*d*e^12 + 8*a^5*b^3*c^2*e^13 + 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 + 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10 - 16*b^2*c^8*d^11*e^2 + 88*b^3*c^7*d^10*e^3 - 200*b^4*c^6*d^9*e^4 + 240*b^5*c^5*d^8*e^5 - 160*b^6*c^4*d^7*e^6 + 56*b^7*c^3*d^6*e^7 - 8*b^8*c^2*d^5*e^8 + 2400*a^2*b^2*c^6*d^7*e^6 - 1680*a^2*b^3*c^5*d^6*e^7 + 240*a^2*b^4*c^4*d^5*e^8 + 240*a^2*b^5*c^3*d^4*e^9 - 80*a^2*b^6*c^2*d^3*e^10 + 2720*a^3*b^2*c^5*d^5*e^8 - 1200*a^3*b^3*c^4*d^4*e^9 + 80*a^3*b^5*c^2*d^2*e^11 + 1200*a^4*b^2*c^4*d^3*e^10 - 200*a^4*b^3*c^3*d^2*e^11 - 352*a*b*c^8*d^10*e^3 + 720*a*b^2*c^7*d^9*e^4 - 600*a*b^3*c^6*d^8*e^5 + 336*a*b^5*c^4*d^6*e^7 - 208*a*b^6*c^3*d^5*e^8 + 40*a*b^7*c^2*d^4*e^9 - 1440*a^2*b*c^7*d^8*e^5 - 2240*a^3*b*c^6*d^6*e^7 - 1600*a^4*b*c^5*d^4*e^9 - 40*a^4*b^4*c^2*d*e^12 - 480*a^5*b*c^4*d^2*e^11 + 144*a^5*b^2*c^3*d*e^12) + 32*a^5*b*c^3*e^12 - 64*a*c^8*d^9*e^3 - 64*a^5*c^4*d*e^11 - 8*a^4*b^3*c^2*e^12 - 256*a^2*c^7*d^7*e^5 - 384*a^3*c^6*d^5*e^7 - 256*a^4*c^5*d^3*e^9 + 16*b^2*c^7*d^9*e^3 - 72*b^3*c^6*d^8*e^4 + 128*b^4*c^5*d^7*e^5 - 112*b^5*c^4*d^6*e^6 + 48*b^6*c^3*d^5*e^7 - 8*b^7*c^2*d^4*e^8 - 1056*a^2*b^2*c^5*d^5*e^7 + 400*a^2*b^3*c^4*d^4*e^8 + 64*a^2*b^4*c^3*d^3*e^9 - 48*a^2*b^5*c^2*d^2*e^10 - 704*a^3*b^2*c^4*d^3*e^9 + 96*a^3*b^3*c^3*d^2*e^10 + 288*a*b*c^7*d^8*e^4 - 448*a*b^2*c^6*d^7*e^5 + 224*a*b^3*c^5*d^6*e^6 + 96*a*b^4*c^4*d^5*e^7 - 128*a*b^5*c^3*d^4*e^8 + 32*a*b^6*c^2*d^3*e^9 + 896*a^2*b*c^6*d^6*e^6 + 960*a^3*b*c^5*d^4*e^8 + 32*a^3*b^4*c^2*d*e^11 + 384*a^4*b*c^4*d^2*e^10 - 112*a^4*b^2*c^3*d*e^11))*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2) - ((d + e*x)^(1/2)*(16*c^8*d^8*e^2 - 16*a^4*c^4*e^10 + 32*a*c^7*d^6*e^4 - 64*b*c^7*d^7*e^3 + 8*a^3*b^2*c^3*e^10 - 32*a^3*c^5*d^2*e^8 + 104*b^2*c^6*d^6*e^4 - 88*b^3*c^5*d^5*e^5 + 40*b^4*c^4*d^4*e^6 - 8*b^5*c^3*d^3*e^7 + 24*a^2*b^2*c^4*d^2*e^8 - 96*a*b*c^6*d^5*e^5 + 32*a^3*b*c^4*d*e^9 + 120*a*b^2*c^5*d^4*e^6 - 80*a*b^3*c^4*d^3*e^7 + 24*a*b^4*c^3*d^2*e^8 - 24*a^2*b^3*c^3*d*e^9) + (-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*((d + e*x)^(1/2)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*(64*a*c^9*d^11*e^2 - 32*a^6*b*c^3*e^13 + 64*a^6*c^4*d*e^12 + 8*a^5*b^3*c^2*e^13 + 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 + 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10 - 16*b^2*c^8*d^11*e^2 + 88*b^3*c^7*d^10*e^3 - 200*b^4*c^6*d^9*e^4 + 240*b^5*c^5*d^8*e^5 - 160*b^6*c^4*d^7*e^6 + 56*b^7*c^3*d^6*e^7 - 8*b^8*c^2*d^5*e^8 + 2400*a^2*b^2*c^6*d^7*e^6 - 1680*a^2*b^3*c^5*d^6*e^7 + 240*a^2*b^4*c^4*d^5*e^8 + 240*a^2*b^5*c^3*d^4*e^9 - 80*a^2*b^6*c^2*d^3*e^10 + 2720*a^3*b^2*c^5*d^5*e^8 - 1200*a^3*b^3*c^4*d^4*e^9 + 80*a^3*b^5*c^2*d^2*e^11 + 1200*a^4*b^2*c^4*d^3*e^10 - 200*a^4*b^3*c^3*d^2*e^11 - 352*a*b*c^8*d^10*e^3 + 720*a*b^2*c^7*d^9*e^4 - 600*a*b^3*c^6*d^8*e^5 + 336*a*b^5*c^4*d^6*e^7 - 208*a*b^6*c^3*d^5*e^8 + 40*a*b^7*c^2*d^4*e^9 - 1440*a^2*b*c^7*d^8*e^5 - 2240*a^3*b*c^6*d^6*e^7 - 1600*a^4*b*c^5*d^4*e^9 - 40*a^4*b^4*c^2*d*e^12 - 480*a^5*b*c^4*d^2*e^11 + 144*a^5*b^2*c^3*d*e^12) - 32*a^5*b*c^3*e^12 + 64*a*c^8*d^9*e^3 + 64*a^5*c^4*d*e^11 + 8*a^4*b^3*c^2*e^12 + 256*a^2*c^7*d^7*e^5 + 384*a^3*c^6*d^5*e^7 + 256*a^4*c^5*d^3*e^9 - 16*b^2*c^7*d^9*e^3 + 72*b^3*c^6*d^8*e^4 - 128*b^4*c^5*d^7*e^5 + 112*b^5*c^4*d^6*e^6 - 48*b^6*c^3*d^5*e^7 + 8*b^7*c^2*d^4*e^8 + 1056*a^2*b^2*c^5*d^5*e^7 - 400*a^2*b^3*c^4*d^4*e^8 - 64*a^2*b^4*c^3*d^3*e^9 + 48*a^2*b^5*c^2*d^2*e^10 + 704*a^3*b^2*c^4*d^3*e^9 - 96*a^3*b^3*c^3*d^2*e^10 - 288*a*b*c^7*d^8*e^4 + 448*a*b^2*c^6*d^7*e^5 - 224*a*b^3*c^5*d^6*e^6 - 96*a*b^4*c^4*d^5*e^7 + 128*a*b^5*c^3*d^4*e^8 - 32*a*b^6*c^2*d^3*e^9 - 896*a^2*b*c^6*d^6*e^6 - 960*a^3*b*c^5*d^4*e^8 - 32*a^3*b^4*c^2*d*e^11 - 384*a^4*b*c^4*d^2*e^10 + 112*a^4*b^2*c^3*d*e^11))*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2) + 16*a^3*c^4*e^9 + 16*c^7*d^6*e^3 + 48*a*c^6*d^4*e^5 - 48*b*c^6*d^5*e^4 + 48*a^2*c^5*d^2*e^7 + 48*b^2*c^5*d^4*e^5 - 16*b^3*c^4*d^3*e^6 - 96*a*b*c^5*d^3*e^6 - 48*a^2*b*c^4*d*e^8 + 48*a*b^2*c^4*d^2*e^7))*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 + b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e + 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 - a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e - 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*2i + atan((((d + e*x)^(1/2)*(16*c^8*d^8*e^2 - 16*a^4*c^4*e^10 + 32*a*c^7*d^6*e^4 - 64*b*c^7*d^7*e^3 + 8*a^3*b^2*c^3*e^10 - 32*a^3*c^5*d^2*e^8 + 104*b^2*c^6*d^6*e^4 - 88*b^3*c^5*d^5*e^5 + 40*b^4*c^4*d^4*e^6 - 8*b^5*c^3*d^3*e^7 + 24*a^2*b^2*c^4*d^2*e^8 - 96*a*b*c^6*d^5*e^5 + 32*a^3*b*c^4*d*e^9 + 120*a*b^2*c^5*d^4*e^6 - 80*a*b^3*c^4*d^3*e^7 + 24*a*b^4*c^3*d^2*e^8 - 24*a^2*b^3*c^3*d*e^9) + (-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*((d + e*x)^(1/2)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*(64*a*c^9*d^11*e^2 - 32*a^6*b*c^3*e^13 + 64*a^6*c^4*d*e^12 + 8*a^5*b^3*c^2*e^13 + 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 + 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10 - 16*b^2*c^8*d^11*e^2 + 88*b^3*c^7*d^10*e^3 - 200*b^4*c^6*d^9*e^4 + 240*b^5*c^5*d^8*e^5 - 160*b^6*c^4*d^7*e^6 + 56*b^7*c^3*d^6*e^7 - 8*b^8*c^2*d^5*e^8 + 2400*a^2*b^2*c^6*d^7*e^6 - 1680*a^2*b^3*c^5*d^6*e^7 + 240*a^2*b^4*c^4*d^5*e^8 + 240*a^2*b^5*c^3*d^4*e^9 - 80*a^2*b^6*c^2*d^3*e^10 + 2720*a^3*b^2*c^5*d^5*e^8 - 1200*a^3*b^3*c^4*d^4*e^9 + 80*a^3*b^5*c^2*d^2*e^11 + 1200*a^4*b^2*c^4*d^3*e^10 - 200*a^4*b^3*c^3*d^2*e^11 - 352*a*b*c^8*d^10*e^3 + 720*a*b^2*c^7*d^9*e^4 - 600*a*b^3*c^6*d^8*e^5 + 336*a*b^5*c^4*d^6*e^7 - 208*a*b^6*c^3*d^5*e^8 + 40*a*b^7*c^2*d^4*e^9 - 1440*a^2*b*c^7*d^8*e^5 - 2240*a^3*b*c^6*d^6*e^7 - 1600*a^4*b*c^5*d^4*e^9 - 40*a^4*b^4*c^2*d*e^12 - 480*a^5*b*c^4*d^2*e^11 + 144*a^5*b^2*c^3*d*e^12) - 32*a^5*b*c^3*e^12 + 64*a*c^8*d^9*e^3 + 64*a^5*c^4*d*e^11 + 8*a^4*b^3*c^2*e^12 + 256*a^2*c^7*d^7*e^5 + 384*a^3*c^6*d^5*e^7 + 256*a^4*c^5*d^3*e^9 - 16*b^2*c^7*d^9*e^3 + 72*b^3*c^6*d^8*e^4 - 128*b^4*c^5*d^7*e^5 + 112*b^5*c^4*d^6*e^6 - 48*b^6*c^3*d^5*e^7 + 8*b^7*c^2*d^4*e^8 + 1056*a^2*b^2*c^5*d^5*e^7 - 400*a^2*b^3*c^4*d^4*e^8 - 64*a^2*b^4*c^3*d^3*e^9 + 48*a^2*b^5*c^2*d^2*e^10 + 704*a^3*b^2*c^4*d^3*e^9 - 96*a^3*b^3*c^3*d^2*e^10 - 288*a*b*c^7*d^8*e^4 + 448*a*b^2*c^6*d^7*e^5 - 224*a*b^3*c^5*d^6*e^6 - 96*a*b^4*c^4*d^5*e^7 + 128*a*b^5*c^3*d^4*e^8 - 32*a*b^6*c^2*d^3*e^9 - 896*a^2*b*c^6*d^6*e^6 - 960*a^3*b*c^5*d^4*e^8 - 32*a^3*b^4*c^2*d*e^11 - 384*a^4*b*c^4*d^2*e^10 + 112*a^4*b^2*c^3*d*e^11))*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*1i + ((d + e*x)^(1/2)*(16*c^8*d^8*e^2 - 16*a^4*c^4*e^10 + 32*a*c^7*d^6*e^4 - 64*b*c^7*d^7*e^3 + 8*a^3*b^2*c^3*e^10 - 32*a^3*c^5*d^2*e^8 + 104*b^2*c^6*d^6*e^4 - 88*b^3*c^5*d^5*e^5 + 40*b^4*c^4*d^4*e^6 - 8*b^5*c^3*d^3*e^7 + 24*a^2*b^2*c^4*d^2*e^8 - 96*a*b*c^6*d^5*e^5 + 32*a^3*b*c^4*d*e^9 + 120*a*b^2*c^5*d^4*e^6 - 80*a*b^3*c^4*d^3*e^7 + 24*a*b^4*c^3*d^2*e^8 - 24*a^2*b^3*c^3*d*e^9) + (-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*((d + e*x)^(1/2)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*(64*a*c^9*d^11*e^2 - 32*a^6*b*c^3*e^13 + 64*a^6*c^4*d*e^12 + 8*a^5*b^3*c^2*e^13 + 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 + 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10 - 16*b^2*c^8*d^11*e^2 + 88*b^3*c^7*d^10*e^3 - 200*b^4*c^6*d^9*e^4 + 240*b^5*c^5*d^8*e^5 - 160*b^6*c^4*d^7*e^6 + 56*b^7*c^3*d^6*e^7 - 8*b^8*c^2*d^5*e^8 + 2400*a^2*b^2*c^6*d^7*e^6 - 1680*a^2*b^3*c^5*d^6*e^7 + 240*a^2*b^4*c^4*d^5*e^8 + 240*a^2*b^5*c^3*d^4*e^9 - 80*a^2*b^6*c^2*d^3*e^10 + 2720*a^3*b^2*c^5*d^5*e^8 - 1200*a^3*b^3*c^4*d^4*e^9 + 80*a^3*b^5*c^2*d^2*e^11 + 1200*a^4*b^2*c^4*d^3*e^10 - 200*a^4*b^3*c^3*d^2*e^11 - 352*a*b*c^8*d^10*e^3 + 720*a*b^2*c^7*d^9*e^4 - 600*a*b^3*c^6*d^8*e^5 + 336*a*b^5*c^4*d^6*e^7 - 208*a*b^6*c^3*d^5*e^8 + 40*a*b^7*c^2*d^4*e^9 - 1440*a^2*b*c^7*d^8*e^5 - 2240*a^3*b*c^6*d^6*e^7 - 1600*a^4*b*c^5*d^4*e^9 - 40*a^4*b^4*c^2*d*e^12 - 480*a^5*b*c^4*d^2*e^11 + 144*a^5*b^2*c^3*d*e^12) + 32*a^5*b*c^3*e^12 - 64*a*c^8*d^9*e^3 - 64*a^5*c^4*d*e^11 - 8*a^4*b^3*c^2*e^12 - 256*a^2*c^7*d^7*e^5 - 384*a^3*c^6*d^5*e^7 - 256*a^4*c^5*d^3*e^9 + 16*b^2*c^7*d^9*e^3 - 72*b^3*c^6*d^8*e^4 + 128*b^4*c^5*d^7*e^5 - 112*b^5*c^4*d^6*e^6 + 48*b^6*c^3*d^5*e^7 - 8*b^7*c^2*d^4*e^8 - 1056*a^2*b^2*c^5*d^5*e^7 + 400*a^2*b^3*c^4*d^4*e^8 + 64*a^2*b^4*c^3*d^3*e^9 - 48*a^2*b^5*c^2*d^2*e^10 - 704*a^3*b^2*c^4*d^3*e^9 + 96*a^3*b^3*c^3*d^2*e^10 + 288*a*b*c^7*d^8*e^4 - 448*a*b^2*c^6*d^7*e^5 + 224*a*b^3*c^5*d^6*e^6 + 96*a*b^4*c^4*d^5*e^7 - 128*a*b^5*c^3*d^4*e^8 + 32*a*b^6*c^2*d^3*e^9 + 896*a^2*b*c^6*d^6*e^6 + 960*a^3*b*c^5*d^4*e^8 + 32*a^3*b^4*c^2*d*e^11 + 384*a^4*b*c^4*d^2*e^10 - 112*a^4*b^2*c^3*d*e^11))*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*1i)/(((d + e*x)^(1/2)*(16*c^8*d^8*e^2 - 16*a^4*c^4*e^10 + 32*a*c^7*d^6*e^4 - 64*b*c^7*d^7*e^3 + 8*a^3*b^2*c^3*e^10 - 32*a^3*c^5*d^2*e^8 + 104*b^2*c^6*d^6*e^4 - 88*b^3*c^5*d^5*e^5 + 40*b^4*c^4*d^4*e^6 - 8*b^5*c^3*d^3*e^7 + 24*a^2*b^2*c^4*d^2*e^8 - 96*a*b*c^6*d^5*e^5 + 32*a^3*b*c^4*d*e^9 + 120*a*b^2*c^5*d^4*e^6 - 80*a*b^3*c^4*d^3*e^7 + 24*a*b^4*c^3*d^2*e^8 - 24*a^2*b^3*c^3*d*e^9) + (-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*((d + e*x)^(1/2)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*(64*a*c^9*d^11*e^2 - 32*a^6*b*c^3*e^13 + 64*a^6*c^4*d*e^12 + 8*a^5*b^3*c^2*e^13 + 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 + 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10 - 16*b^2*c^8*d^11*e^2 + 88*b^3*c^7*d^10*e^3 - 200*b^4*c^6*d^9*e^4 + 240*b^5*c^5*d^8*e^5 - 160*b^6*c^4*d^7*e^6 + 56*b^7*c^3*d^6*e^7 - 8*b^8*c^2*d^5*e^8 + 2400*a^2*b^2*c^6*d^7*e^6 - 1680*a^2*b^3*c^5*d^6*e^7 + 240*a^2*b^4*c^4*d^5*e^8 + 240*a^2*b^5*c^3*d^4*e^9 - 80*a^2*b^6*c^2*d^3*e^10 + 2720*a^3*b^2*c^5*d^5*e^8 - 1200*a^3*b^3*c^4*d^4*e^9 + 80*a^3*b^5*c^2*d^2*e^11 + 1200*a^4*b^2*c^4*d^3*e^10 - 200*a^4*b^3*c^3*d^2*e^11 - 352*a*b*c^8*d^10*e^3 + 720*a*b^2*c^7*d^9*e^4 - 600*a*b^3*c^6*d^8*e^5 + 336*a*b^5*c^4*d^6*e^7 - 208*a*b^6*c^3*d^5*e^8 + 40*a*b^7*c^2*d^4*e^9 - 1440*a^2*b*c^7*d^8*e^5 - 2240*a^3*b*c^6*d^6*e^7 - 1600*a^4*b*c^5*d^4*e^9 - 40*a^4*b^4*c^2*d*e^12 - 480*a^5*b*c^4*d^2*e^11 + 144*a^5*b^2*c^3*d*e^12) + 32*a^5*b*c^3*e^12 - 64*a*c^8*d^9*e^3 - 64*a^5*c^4*d*e^11 - 8*a^4*b^3*c^2*e^12 - 256*a^2*c^7*d^7*e^5 - 384*a^3*c^6*d^5*e^7 - 256*a^4*c^5*d^3*e^9 + 16*b^2*c^7*d^9*e^3 - 72*b^3*c^6*d^8*e^4 + 128*b^4*c^5*d^7*e^5 - 112*b^5*c^4*d^6*e^6 + 48*b^6*c^3*d^5*e^7 - 8*b^7*c^2*d^4*e^8 - 1056*a^2*b^2*c^5*d^5*e^7 + 400*a^2*b^3*c^4*d^4*e^8 + 64*a^2*b^4*c^3*d^3*e^9 - 48*a^2*b^5*c^2*d^2*e^10 - 704*a^3*b^2*c^4*d^3*e^9 + 96*a^3*b^3*c^3*d^2*e^10 + 288*a*b*c^7*d^8*e^4 - 448*a*b^2*c^6*d^7*e^5 + 224*a*b^3*c^5*d^6*e^6 + 96*a*b^4*c^4*d^5*e^7 - 128*a*b^5*c^3*d^4*e^8 + 32*a*b^6*c^2*d^3*e^9 + 896*a^2*b*c^6*d^6*e^6 + 960*a^3*b*c^5*d^4*e^8 + 32*a^3*b^4*c^2*d*e^11 + 384*a^4*b*c^4*d^2*e^10 - 112*a^4*b^2*c^3*d*e^11))*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2) - ((d + e*x)^(1/2)*(16*c^8*d^8*e^2 - 16*a^4*c^4*e^10 + 32*a*c^7*d^6*e^4 - 64*b*c^7*d^7*e^3 + 8*a^3*b^2*c^3*e^10 - 32*a^3*c^5*d^2*e^8 + 104*b^2*c^6*d^6*e^4 - 88*b^3*c^5*d^5*e^5 + 40*b^4*c^4*d^4*e^6 - 8*b^5*c^3*d^3*e^7 + 24*a^2*b^2*c^4*d^2*e^8 - 96*a*b*c^6*d^5*e^5 + 32*a^3*b*c^4*d*e^9 + 120*a*b^2*c^5*d^4*e^6 - 80*a*b^3*c^4*d^3*e^7 + 24*a*b^4*c^3*d^2*e^8 - 24*a^2*b^3*c^3*d*e^9) + (-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*((d + e*x)^(1/2)*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*(64*a*c^9*d^11*e^2 - 32*a^6*b*c^3*e^13 + 64*a^6*c^4*d*e^12 + 8*a^5*b^3*c^2*e^13 + 320*a^2*c^8*d^9*e^4 + 640*a^3*c^7*d^7*e^6 + 640*a^4*c^6*d^5*e^8 + 320*a^5*c^5*d^3*e^10 - 16*b^2*c^8*d^11*e^2 + 88*b^3*c^7*d^10*e^3 - 200*b^4*c^6*d^9*e^4 + 240*b^5*c^5*d^8*e^5 - 160*b^6*c^4*d^7*e^6 + 56*b^7*c^3*d^6*e^7 - 8*b^8*c^2*d^5*e^8 + 2400*a^2*b^2*c^6*d^7*e^6 - 1680*a^2*b^3*c^5*d^6*e^7 + 240*a^2*b^4*c^4*d^5*e^8 + 240*a^2*b^5*c^3*d^4*e^9 - 80*a^2*b^6*c^2*d^3*e^10 + 2720*a^3*b^2*c^5*d^5*e^8 - 1200*a^3*b^3*c^4*d^4*e^9 + 80*a^3*b^5*c^2*d^2*e^11 + 1200*a^4*b^2*c^4*d^3*e^10 - 200*a^4*b^3*c^3*d^2*e^11 - 352*a*b*c^8*d^10*e^3 + 720*a*b^2*c^7*d^9*e^4 - 600*a*b^3*c^6*d^8*e^5 + 336*a*b^5*c^4*d^6*e^7 - 208*a*b^6*c^3*d^5*e^8 + 40*a*b^7*c^2*d^4*e^9 - 1440*a^2*b*c^7*d^8*e^5 - 2240*a^3*b*c^6*d^6*e^7 - 1600*a^4*b*c^5*d^4*e^9 - 40*a^4*b^4*c^2*d*e^12 - 480*a^5*b*c^4*d^2*e^11 + 144*a^5*b^2*c^3*d*e^12) - 32*a^5*b*c^3*e^12 + 64*a*c^8*d^9*e^3 + 64*a^5*c^4*d*e^11 + 8*a^4*b^3*c^2*e^12 + 256*a^2*c^7*d^7*e^5 + 384*a^3*c^6*d^5*e^7 + 256*a^4*c^5*d^3*e^9 - 16*b^2*c^7*d^9*e^3 + 72*b^3*c^6*d^8*e^4 - 128*b^4*c^5*d^7*e^5 + 112*b^5*c^4*d^6*e^6 - 48*b^6*c^3*d^5*e^7 + 8*b^7*c^2*d^4*e^8 + 1056*a^2*b^2*c^5*d^5*e^7 - 400*a^2*b^3*c^4*d^4*e^8 - 64*a^2*b^4*c^3*d^3*e^9 + 48*a^2*b^5*c^2*d^2*e^10 + 704*a^3*b^2*c^4*d^3*e^9 - 96*a^3*b^3*c^3*d^2*e^10 - 288*a*b*c^7*d^8*e^4 + 448*a*b^2*c^6*d^7*e^5 - 224*a*b^3*c^5*d^6*e^6 - 96*a*b^4*c^4*d^5*e^7 + 128*a*b^5*c^3*d^4*e^8 - 32*a*b^6*c^2*d^3*e^9 - 896*a^2*b*c^6*d^6*e^6 - 960*a^3*b*c^5*d^4*e^8 - 32*a^3*b^4*c^2*d*e^11 - 384*a^4*b*c^4*d^2*e^10 + 112*a^4*b^2*c^3*d*e^11))*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2) + 16*a^3*c^4*e^9 + 16*c^7*d^6*e^3 + 48*a*c^6*d^4*e^5 - 48*b*c^6*d^5*e^4 + 48*a^2*c^5*d^2*e^7 + 48*b^2*c^5*d^4*e^5 - 16*b^3*c^4*d^3*e^6 - 96*a*b*c^5*d^3*e^6 - 48*a^2*b*c^4*d*e^8 + 48*a*b^2*c^4*d^2*e^7))*(-(b^5*e^3 + 8*a*c^4*d^3 - 2*b^2*c^3*d^3 - b^2*e^3*(-(4*a*c - b^2)^3)^(1/2) + 12*a^2*b*c^2*e^3 - 24*a^2*c^3*d*e^2 + 3*b^3*c^2*d^2*e - 3*c^2*d^2*e*(-(4*a*c - b^2)^3)^(1/2) - 7*a*b^3*c*e^3 + a*c*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*b^4*c*d*e^2 - 12*a*b*c^3*d^2*e + 3*b*c*d*e^2*(-(4*a*c - b^2)^3)^(1/2) + 18*a*b^2*c^2*d*e^2)/(2*(16*a^2*c^5*d^6 + a^3*b^4*e^6 + 16*a^5*c^2*e^6 + b^4*c^3*d^6 - b^7*d^3*e^3 - 8*a*b^2*c^4*d^6 - 8*a^4*b^2*c*e^6 + 3*a*b^6*d^2*e^4 - 3*a^2*b^5*d*e^5 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 + 48*a^3*c^4*d^4*e^2 + 48*a^4*c^3*d^2*e^4 + 24*a^2*b^2*c^3*d^4*e^2 + 32*a^2*b^3*c^2*d^3*e^3 + 24*a^3*b^2*c^2*d^2*e^4 + 24*a*b^3*c^3*d^5*e + 2*a*b^5*c*d^3*e^3 - 48*a^2*b*c^4*d^5*e + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 - 21*a*b^4*c^2*d^4*e^2 - 21*a^2*b^4*c*d^2*e^4 - 96*a^3*b*c^3*d^3*e^3)))^(1/2)*2i - (2*e)/((d + e*x)^(1/2)*(a*e^2 + c*d^2 - b*d*e))","B"
2294,1,58096,414,8.643712,"\text{Not used}","int(1/((d + e*x)^(5/2)*(a + b*x + c*x^2)),x)","-\mathrm{atan}\left(\frac{\left(\sqrt{d+e\,x}\,\left(-16\,a^8\,c^5\,e^{18}+32\,a^7\,b^2\,c^4\,e^{18}-8\,a^6\,b^4\,c^3\,e^{18}-160\,a^6\,b^3\,c^4\,d\,e^{17}+480\,a^6\,b^2\,c^5\,d^2\,e^{16}-640\,a^6\,b\,c^6\,d^3\,e^{15}+320\,a^6\,c^7\,d^4\,e^{14}+48\,a^5\,b^5\,c^3\,d\,e^{17}+240\,a^5\,b^4\,c^4\,d^2\,e^{16}-1600\,a^5\,b^3\,c^5\,d^3\,e^{15}+3360\,a^5\,b^2\,c^6\,d^4\,e^{14}-3072\,a^5\,b\,c^7\,d^5\,e^{13}+1024\,a^5\,c^8\,d^6\,e^{12}-120\,a^4\,b^6\,c^3\,d^2\,e^{16}+80\,a^4\,b^5\,c^4\,d^3\,e^{15}+1800\,a^4\,b^4\,c^5\,d^4\,e^{14}-6240\,a^4\,b^3\,c^6\,d^5\,e^{13}+8800\,a^4\,b^2\,c^7\,d^6\,e^{12}-5760\,a^4\,b\,c^8\,d^7\,e^{11}+1440\,a^4\,c^9\,d^8\,e^{10}+160\,a^3\,b^7\,c^3\,d^3\,e^{15}-640\,a^3\,b^6\,c^4\,d^4\,e^{14}+96\,a^3\,b^5\,c^5\,d^5\,e^{13}+4000\,a^3\,b^4\,c^6\,d^6\,e^{12}-9600\,a^3\,b^3\,c^7\,d^7\,e^{11}+10080\,a^3\,b^2\,c^8\,d^8\,e^{10}-5120\,a^3\,b\,c^9\,d^9\,e^9+1024\,a^3\,c^{10}\,d^{10}\,e^8-120\,a^2\,b^8\,c^3\,d^4\,e^{14}+768\,a^2\,b^7\,c^4\,d^5\,e^{13}-1840\,a^2\,b^6\,c^5\,d^6\,e^{12}+1440\,a^2\,b^5\,c^6\,d^7\,e^{11}+1800\,a^2\,b^4\,c^7\,d^8\,e^{10}-4960\,a^2\,b^3\,c^8\,d^9\,e^9+4512\,a^2\,b^2\,c^9\,d^{10}\,e^8-1920\,a^2\,b\,c^{10}\,d^{11}\,e^7+320\,a^2\,c^{11}\,d^{12}\,e^6+48\,a\,b^9\,c^3\,d^5\,e^{13}-400\,a\,b^8\,c^4\,d^6\,e^{12}+1440\,a\,b^7\,c^5\,d^7\,e^{11}-2880\,a\,b^6\,c^6\,d^8\,e^{10}+3440\,a\,b^5\,c^7\,d^9\,e^9-2448\,a\,b^4\,c^8\,d^{10}\,e^8+960\,a\,b^3\,c^9\,d^{11}\,e^7-160\,a\,b^2\,c^{10}\,d^{12}\,e^6-8\,b^{10}\,c^3\,d^6\,e^{12}+80\,b^9\,c^4\,d^7\,e^{11}-360\,b^8\,c^5\,d^8\,e^{10}+960\,b^7\,c^6\,d^9\,e^9-1688\,b^6\,c^7\,d^{10}\,e^8+2064\,b^5\,c^8\,d^{11}\,e^7-1800\,b^4\,c^9\,d^{12}\,e^6+1120\,b^3\,c^{10}\,d^{13}\,e^5-480\,b^2\,c^{11}\,d^{14}\,e^4+128\,b\,c^{12}\,d^{15}\,e^3-16\,c^{13}\,d^{16}\,e^2\right)+\sqrt{-\frac{b^7\,e^5+8\,a\,c^6\,d^5-2\,b^2\,c^5\,d^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a^3\,b\,c^3\,e^5+40\,a^3\,c^4\,d\,e^4+5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-80\,a^2\,c^5\,d^3\,e^2-10\,b^4\,c^3\,d^3\,e^2+10\,b^5\,c^2\,d^2\,e^3-9\,a\,b^5\,c\,e^5-5\,b^6\,c\,d\,e^4-20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^2\,c^4\,d^3\,e^2-70\,a\,b^3\,c^3\,d^2\,e^3+120\,a^2\,b\,c^4\,d^2\,e^3-90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^7\,c^2\,e^{10}-8\,a^6\,b^2\,c\,e^{10}-80\,a^6\,b\,c^2\,d\,e^9+80\,a^6\,c^3\,d^2\,e^8+a^5\,b^4\,e^{10}+40\,a^5\,b^3\,c\,d\,e^9+120\,a^5\,b^2\,c^2\,d^2\,e^8-320\,a^5\,b\,c^3\,d^3\,e^7+160\,a^5\,c^4\,d^4\,e^6-5\,a^4\,b^5\,d\,e^9-75\,a^4\,b^4\,c\,d^2\,e^8+400\,a^4\,b^2\,c^3\,d^4\,e^6-480\,a^4\,b\,c^4\,d^5\,e^5+160\,a^4\,c^5\,d^6\,e^4+10\,a^3\,b^6\,d^2\,e^8+60\,a^3\,b^5\,c\,d^3\,e^7-150\,a^3\,b^4\,c^2\,d^4\,e^6-80\,a^3\,b^3\,c^3\,d^5\,e^5+400\,a^3\,b^2\,c^4\,d^6\,e^4-320\,a^3\,b\,c^5\,d^7\,e^3+80\,a^3\,c^6\,d^8\,e^2-10\,a^2\,b^7\,d^3\,e^7-10\,a^2\,b^6\,c\,d^4\,e^6+114\,a^2\,b^5\,c^2\,d^5\,e^5-150\,a^2\,b^4\,c^3\,d^6\,e^4+120\,a^2\,b^2\,c^5\,d^8\,e^2-80\,a^2\,b\,c^6\,d^9\,e+16\,a^2\,c^7\,d^{10}+5\,a\,b^8\,d^4\,e^6-12\,a\,b^7\,c\,d^5\,e^5-10\,a\,b^6\,c^2\,d^6\,e^4+60\,a\,b^5\,c^3\,d^7\,e^3-75\,a\,b^4\,c^4\,d^8\,e^2+40\,a\,b^3\,c^5\,d^9\,e-8\,a\,b^2\,c^6\,d^{10}-b^9\,d^5\,e^5+5\,b^8\,c\,d^6\,e^4-10\,b^7\,c^2\,d^7\,e^3+10\,b^6\,c^3\,d^8\,e^2-5\,b^5\,c^4\,d^9\,e+b^4\,c^5\,d^{10}\right)}}\,\left(96\,a\,c^{13}\,d^{18}\,e^3-32\,a^{10}\,c^4\,e^{21}-\sqrt{d+e\,x}\,\sqrt{-\frac{b^7\,e^5+8\,a\,c^6\,d^5-2\,b^2\,c^5\,d^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-20\,a^3\,b\,c^3\,e^5+40\,a^3\,c^4\,d\,e^4+5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-80\,a^2\,c^5\,d^3\,e^2-10\,b^4\,c^3\,d^3\,e^2+10\,b^5\,c^2\,d^2\,e^3-9\,a\,b^5\,c\,e^5-5\,b^6\,c\,d\,e^4-20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+60\,a\,b^2\,c^4\,d^3\,e^2-70\,a\,b^3\,c^3\,d^2\,e^3+120\,a^2\,b\,c^4\,d^2\,e^3-90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^7\,c^2\,e^{10}-8\,a^6\,b^2\,c\,e^{10}-80\,a^6\,b\,c^2\,d\,e^9+80\,a^6\,c^3\,d^2\,e^8+a^5\,b^4\,e^{10}+40\,a^5\,b^3\,c\,d\,e^9+120\,a^5\,b^2\,c^2\,d^2\,e^8-320\,a^5\,b\,c^3\,d^3\,e^7+160\,a^5\,c^4\,d^4\,e^6-5\,a^4\,b^5\,d\,e^9-75\,a^4\,b^4\,c\,d^2\,e^8+400\,a^4\,b^2\,c^3\,d^4\,e^6-480\,a^4\,b\,c^4\,d^5\,e^5+160\,a^4\,c^5\,d^6\,e^4+10\,a^3\,b^6\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,b^3\,c^3\,d^5\,e^5+400\,a^3\,b^2\,c^4\,d^6\,e^4-320\,a^3\,b\,c^5\,d^7\,e^3+80\,a^3\,c^6\,d^8\,e^2-10\,a^2\,b^7\,d^3\,e^7-10\,a^2\,b^6\,c\,d^4\,e^6+114\,a^2\,b^5\,c^2\,d^5\,e^5-150\,a^2\,b^4\,c^3\,d^6\,e^4+120\,a^2\,b^2\,c^5\,d^8\,e^2-80\,a^2\,b\,c^6\,d^9\,e+16\,a^2\,c^7\,d^{10}+5\,a\,b^8\,d^4\,e^6-12\,a\,b^7\,c\,d^5\,e^5-10\,a\,b^6\,c^2\,d^6\,e^4+60\,a\,b^5\,c^3\,d^7\,e^3-75\,a\,b^4\,c^4\,d^8\,e^2+40\,a\,b^3\,c^5\,d^9\,e-8\,a\,b^2\,c^6\,d^{10}-b^9\,d^5\,e^5+5\,b^8\,c\,d^6\,e^4-10\,b^7\,c^2\,d^7\,e^3+10\,b^6\,c^3\,d^8\,e^2-5\,b^5\,c^4\,d^9\,e+b^4\,c^5\,d^{10}\right)}}+32\,c^{12}\,d^{13}\,e^3-16\,a^6\,b\,c^5\,e^{16}+192\,a\,c^{11}\,d^{11}\,e^5+32\,a^6\,c^6\,d\,e^{15}-208\,b\,c^{11}\,d^{12}\,e^4+480\,a^2\,c^{10}\,d^9\,e^7+640\,a^3\,c^9\,d^7\,e^9+480\,a^4\,c^8\,d^5\,e^{11}+192\,a^5\,c^7\,d^3\,e^{13}+576\,b^2\,c^{10}\,d^{11}\,e^5-880\,b^3\,c^9\,d^{10}\,e^6+800\,b^4\,c^8\,d^9\,e^7-432\,b^5\,c^7\,d^8\,e^8+128\,b^6\,c^6\,d^7\,e^9-16\,b^7\,c^5\,d^6\,e^{10}+3840\,a^2\,b^2\,c^8\,d^7\,e^9-3360\,a^2\,b^3\,c^7\,d^6\,e^{10}+1440\,a^2\,b^4\,c^6\,d^5\,e^{11}-240\,a^2\,b^5\,c^5\,d^4\,e^{12}+2880\,a^3\,b^2\,c^7\,d^5\,e^{11}-1600\,a^3\,b^3\,c^6\,d^4\,e^{12}+320\,a^3\,b^4\,c^5\,d^3\,e^{13}+960\,a^4\,b^2\,c^6\,d^3\,e^{13}-240\,a^4\,b^3\,c^5\,d^2\,e^{14}-1056\,a\,b\,c^{10}\,d^{10}\,e^6+2400\,a\,b^2\,c^9\,d^9\,e^7-2880\,a\,b^3\,c^8\,d^8\,e^8+1920\,a\,b^4\,c^7\,d^7\,e^9-672\,a\,b^5\,c^6\,d^6\,e^{10}+96\,a\,b^6\,c^5\,d^5\,e^{11}-2160\,a^2\,b\,c^9\,d^8\,e^8-2240\,a^3\,b\,c^8\,d^6\,e^{10}-1200\,a^4\,b\,c^7\,d^4\,e^{12}-288\,a^5\,b\,c^6\,d^2\,e^{14}+96\,a^5\,b^2\,c^5\,d\,e^{15}}\right)\,\sqrt{\frac{2\,b^2\,c^5\,d^5-8\,a\,c^6\,d^5-b^7\,e^5+b^4\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+20\,a^3\,b\,c^3\,e^5-40\,a^3\,c^4\,d\,e^4-5\,b^3\,c^4\,d^4\,e+5\,c^4\,d^4\,e\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-25\,a^2\,b^3\,c^2\,e^5+a^2\,c^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+80\,a^2\,c^5\,d^3\,e^2+10\,b^4\,c^3\,d^3\,e^2-10\,b^5\,c^2\,d^2\,e^3+9\,a\,b^5\,c\,e^5+5\,b^6\,c\,d\,e^4+20\,a\,b\,c^5\,d^4\,e+10\,b^2\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-3\,a\,b^2\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-40\,a\,b^4\,c^2\,d\,e^4-5\,b^3\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-60\,a\,b^2\,c^4\,d^3\,e^2+70\,a\,b^3\,c^3\,d^2\,e^3-120\,a^2\,b\,c^4\,d^2\,e^3+90\,a^2\,b^2\,c^3\,d\,e^4-10\,a\,c^3\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}-10\,b\,c^3\,d^3\,e^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}+10\,a\,b\,c^2\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^3}}{2\,\left(16\,a^7\,c^2\,e^{10}-8\,a^6\,b^2\,c\,e^{10}-80\,a^6\,b\,c^2\,d\,e^9+80\,a^6\,c^3\,d^2\,e^8+a^5\,b^4\,e^{10}+40\,a^5\,b^3\,c\,d\,e^9+120\,a^5\,b^2\,c^2\,d^2\,e^8-320\,a^5\,b\,c^3\,d^3\,e^7+160\,a^5\,c^4\,d^4\,e^6-5\,a^4\,b^5\,d\,e^9-75\,a^4\,b^4\,c\,d^2\,e^8+400\,a^4\,b^2\,c^3\,d^4\,e^6-480\,a^4\,b\,c^4\,d^5\,e^5+160\,a^4\,c^5\,d^6\,e^4+10\,a^3\,b^6\,d^2\,e^8+60\,a^3\,b^5\,c\,d^3\,e^7-150\,a^3\,b^4\,c^2\,d^4\,e^6-80\,a^3\,b^3\,c^3\,d^5\,e^5+400\,a^3\,b^2\,c^4\,d^6\,e^4-320\,a^3\,b\,c^5\,d^7\,e^3+80\,a^3\,c^6\,d^8\,e^2-10\,a^2\,b^7\,d^3\,e^7-10\,a^2\,b^6\,c\,d^4\,e^6+114\,a^2\,b^5\,c^2\,d^5\,e^5-150\,a^2\,b^4\,c^3\,d^6\,e^4+120\,a^2\,b^2\,c^5\,d^8\,e^2-80\,a^2\,b\,c^6\,d^9\,e+16\,a^2\,c^7\,d^{10}+5\,a\,b^8\,d^4\,e^6-12\,a\,b^7\,c\,d^5\,e^5-10\,a\,b^6\,c^2\,d^6\,e^4+60\,a\,b^5\,c^3\,d^7\,e^3-75\,a\,b^4\,c^4\,d^8\,e^2+40\,a\,b^3\,c^5\,d^9\,e-8\,a\,b^2\,c^6\,d^{10}-b^9\,d^5\,e^5+5\,b^8\,c\,d^6\,e^4-10\,b^7\,c^2\,d^7\,e^3+10\,b^6\,c^3\,d^8\,e^2-5\,b^5\,c^4\,d^9\,e+b^4\,c^5\,d^{10}\right)}}\,2{}\mathrm{i}-\frac{\frac{2\,e}{3\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}-\frac{2\,e\,\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)}{{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}}{{\left(d+e\,x\right)}^{3/2}}","Not used",1,"- atan((((d + e*x)^(1/2)*(128*b*c^12*d^15*e^3 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 - 8*a^6*b^4*c^3*e^18 + 32*a^7*b^2*c^4*e^18 + 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14 - 480*b^2*c^11*d^14*e^4 + 1120*b^3*c^10*d^13*e^5 - 1800*b^4*c^9*d^12*e^6 + 2064*b^5*c^8*d^11*e^7 - 1688*b^6*c^7*d^10*e^8 + 960*b^7*c^6*d^9*e^9 - 360*b^8*c^5*d^8*e^10 + 80*b^9*c^4*d^7*e^11 - 8*b^10*c^3*d^6*e^12 + 4512*a^2*b^2*c^9*d^10*e^8 - 4960*a^2*b^3*c^8*d^9*e^9 + 1800*a^2*b^4*c^7*d^8*e^10 + 1440*a^2*b^5*c^6*d^7*e^11 - 1840*a^2*b^6*c^5*d^6*e^12 + 768*a^2*b^7*c^4*d^5*e^13 - 120*a^2*b^8*c^3*d^4*e^14 + 10080*a^3*b^2*c^8*d^8*e^10 - 9600*a^3*b^3*c^7*d^7*e^11 + 4000*a^3*b^4*c^6*d^6*e^12 + 96*a^3*b^5*c^5*d^5*e^13 - 640*a^3*b^6*c^4*d^4*e^14 + 160*a^3*b^7*c^3*d^3*e^15 + 8800*a^4*b^2*c^7*d^6*e^12 - 6240*a^4*b^3*c^6*d^5*e^13 + 1800*a^4*b^4*c^5*d^4*e^14 + 80*a^4*b^5*c^4*d^3*e^15 - 120*a^4*b^6*c^3*d^2*e^16 + 3360*a^5*b^2*c^6*d^4*e^14 - 1600*a^5*b^3*c^5*d^3*e^15 + 240*a^5*b^4*c^4*d^2*e^16 + 480*a^6*b^2*c^5*d^2*e^16 - 160*a*b^2*c^10*d^12*e^6 + 960*a*b^3*c^9*d^11*e^7 - 2448*a*b^4*c^8*d^10*e^8 + 3440*a*b^5*c^7*d^9*e^9 - 2880*a*b^6*c^6*d^8*e^10 + 1440*a*b^7*c^5*d^7*e^11 - 400*a*b^8*c^4*d^6*e^12 + 48*a*b^9*c^3*d^5*e^13 - 1920*a^2*b*c^10*d^11*e^7 - 5120*a^3*b*c^9*d^9*e^9 - 5760*a^4*b*c^8*d^7*e^11 - 3072*a^5*b*c^7*d^5*e^13 + 48*a^5*b^5*c^3*d*e^17 - 640*a^6*b*c^6*d^3*e^15 - 160*a^6*b^3*c^4*d*e^17) + (-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*(96*a*c^13*d^18*e^3 - 32*a^10*c^4*e^21 - (d + e*x)^(1/2)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*(64*a*c^14*d^21*e^2 - 32*a^11*b*c^3*e^23 + 64*a^11*c^4*d*e^22 + 8*a^10*b^3*c^2*e^23 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20 - 16*b^2*c^13*d^21*e^2 + 168*b^3*c^12*d^20*e^3 - 800*b^4*c^11*d^19*e^4 + 2280*b^5*c^10*d^18*e^5 - 4320*b^6*c^9*d^17*e^6 + 5712*b^7*c^8*d^16*e^7 - 5376*b^8*c^7*d^15*e^8 + 3600*b^9*c^6*d^14*e^9 - 1680*b^10*c^5*d^13*e^10 + 520*b^11*c^4*d^12*e^11 - 96*b^12*c^3*d^11*e^12 + 8*b^13*c^2*d^10*e^13 + 25200*a^2*b^2*c^11*d^17*e^6 - 59160*a^2*b^3*c^10*d^16*e^7 + 84480*a^2*b^4*c^9*d^15*e^8 - 70560*a^2*b^5*c^8*d^14*e^9 + 23520*a^2*b^6*c^7*d^13*e^10 + 15600*a^2*b^7*c^6*d^12*e^11 - 23040*a^2*b^8*c^5*d^11*e^12 + 12320*a^2*b^9*c^4*d^10*e^13 - 3280*a^2*b^10*c^3*d^9*e^14 + 360*a^2*b^11*c^2*d^8*e^15 + 90240*a^3*b^2*c^10*d^15*e^8 - 187200*a^3*b^3*c^9*d^14*e^9 + 235200*a^3*b^4*c^8*d^13*e^10 - 174720*a^3*b^5*c^7*d^12*e^11 + 60480*a^3*b^6*c^6*d^11*e^12 + 10560*a^3*b^7*c^5*d^10*e^13 - 19200*a^3*b^8*c^4*d^9*e^14 + 7200*a^3*b^9*c^3*d^8*e^15 - 960*a^3*b^10*c^2*d^7*e^16 + 184800*a^4*b^2*c^9*d^13*e^10 - 327600*a^4*b^3*c^8*d^12*e^11 + 342720*a^4*b^4*c^7*d^11*e^12 - 203280*a^4*b^5*c^6*d^10*e^13 + 50400*a^4*b^6*c^5*d^9*e^14 + 10800*a^4*b^7*c^4*d^8*e^15 - 9600*a^4*b^8*c^3*d^7*e^16 + 1680*a^4*b^9*c^2*d^6*e^17 + 237888*a^5*b^2*c^8*d^11*e^12 - 347424*a^5*b^3*c^7*d^10*e^13 + 285600*a^5*b^4*c^6*d^9*e^14 - 120960*a^5*b^5*c^5*d^8*e^15 + 13440*a^5*b^6*c^4*d^7*e^16 + 7392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^5*e^18 + 198240*a^6*b^2*c^7*d^9*e^14 - 226800*a^6*b^3*c^6*d^8*e^15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b^5*c^4*d^6*e^17 - 2016*a^6*b^6*c^3*d^5*e^18 + 1680*a^6*b^7*c^2*d^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*a^7*b^3*c^5*d^6*e^17 + 31680*a^7*b^4*c^4*d^5*e^18 - 1920*a^7*b^5*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 33840*a^8*b^2*c^5*d^5*e^18 - 17400*a^8*b^3*c^4*d^4*e^19 + 2400*a^8*b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 + 5600*a^9*b^2*c^4*d^3*e^20 - 1200*a^9*b^3*c^3*d^2*e^21 - 672*a*b*c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 7600*a*b^3*c^11*d^18*e^5 + 10800*a*b^4*c^10*d^17*e^6 - 6528*a*b^5*c^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*a*b^7*c^7*d^14*e^9 - 16800*a*b^8*c^6*d^13*e^10 + 10400*a*b^9*c^5*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a*b^11*c^3*d^10*e^13 - 80*a*b^12*c^2*d^9*e^14 - 6080*a^2*b*c^12*d^18*e^5 - 24480*a^3*b*c^11*d^16*e^7 - 57600*a^4*b*c^10*d^14*e^9 - 87360*a^5*b*c^9*d^12*e^11 - 88704*a^6*b*c^8*d^10*e^13 - 60480*a^7*b*c^7*d^8*e^15 - 26880*a^8*b*c^6*d^6*e^17 - 7200*a^9*b*c^5*d^4*e^19 - 80*a^9*b^4*c^2*d*e^22 - 960*a^10*b*c^4*d^2*e^21 + 304*a^10*b^2*c^3*d*e^22) - 8*a^8*b^4*c^2*e^21 + 40*a^9*b^2*c^3*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19 - 24*b^2*c^12*d^18*e^3 + 216*b^3*c^11*d^17*e^4 - 872*b^4*c^10*d^16*e^5 + 2080*b^5*c^9*d^15*e^6 - 3248*b^6*c^8*d^14*e^7 + 3472*b^7*c^7*d^13*e^8 - 2576*b^8*c^6*d^12*e^9 + 1312*b^9*c^5*d^11*e^10 - 440*b^10*c^4*d^10*e^11 + 88*b^11*c^3*d^9*e^12 - 8*b^12*c^2*d^8*e^13 + 20256*a^2*b^2*c^10*d^14*e^7 - 38752*a^2*b^3*c^9*d^13*e^8 + 43904*a^2*b^4*c^8*d^12*e^9 - 27552*a^2*b^5*c^7*d^11*e^10 + 4928*a^2*b^6*c^6*d^10*e^11 + 5984*a^2*b^7*c^5*d^9*e^12 - 5088*a^2*b^8*c^4*d^8*e^13 + 1696*a^2*b^9*c^3*d^7*e^14 - 224*a^2*b^10*c^2*d^6*e^15 + 50848*a^3*b^2*c^9*d^12*e^9 - 83776*a^3*b^3*c^8*d^11*e^10 + 81312*a^3*b^4*c^7*d^10*e^11 - 44352*a^3*b^5*c^6*d^9*e^12 + 9184*a^3*b^6*c^5*d^8*e^13 + 3392*a^3*b^7*c^4*d^7*e^14 - 2464*a^3*b^8*c^3*d^6*e^15 + 448*a^3*b^9*c^2*d^5*e^16 + 67760*a^4*b^2*c^8*d^10*e^11 - 92400*a^4*b^3*c^7*d^9*e^12 + 72240*a^4*b^4*c^6*d^8*e^13 - 30240*a^4*b^5*c^5*d^7*e^14 + 3920*a^4*b^6*c^4*d^6*e^15 + 1680*a^4*b^7*c^3*d^5*e^16 - 560*a^4*b^8*c^2*d^4*e^17 + 50736*a^5*b^2*c^7*d^8*e^13 - 55104*a^5*b^3*c^6*d^7*e^14 + 32928*a^5*b^4*c^5*d^6*e^15 - 9408*a^5*b^5*c^4*d^5*e^16 + 112*a^5*b^6*c^3*d^4*e^17 + 448*a^5*b^7*c^2*d^3*e^18 + 20384*a^6*b^2*c^6*d^6*e^15 - 17248*a^6*b^3*c^5*d^5*e^16 + 7616*a^6*b^4*c^4*d^4*e^17 - 1120*a^6*b^5*c^3*d^3*e^18 - 224*a^6*b^6*c^2*d^2*e^19 + 3616*a^7*b^2*c^5*d^4*e^17 - 2752*a^7*b^3*c^4*d^3*e^18 + 864*a^7*b^4*c^3*d^2*e^19 + 168*a^8*b^2*c^4*d^2*e^19 - 864*a*b*c^12*d^17*e^4 + 160*a^9*b*c^4*d*e^20 + 3304*a*b^2*c^11*d^16*e^5 - 6848*a*b^3*c^10*d^15*e^6 + 7776*a*b^4*c^9*d^14*e^7 - 3136*a*b^5*c^8*d^13*e^8 - 3920*a*b^6*c^7*d^12*e^9 + 7296*a*b^7*c^6*d^11*e^10 - 5632*a*b^8*c^5*d^10*e^11 + 2464*a*b^9*c^4*d^9*e^12 - 600*a*b^10*c^3*d^8*e^13 + 64*a*b^11*c^2*d^7*e^14 - 5888*a^2*b*c^11*d^15*e^6 - 17024*a^3*b*c^10*d^13*e^8 - 26880*a^4*b*c^9*d^11*e^10 - 24640*a^5*b*c^8*d^9*e^12 - 12544*a^6*b*c^7*d^7*e^14 - 2688*a^7*b*c^6*d^5*e^16 + 64*a^7*b^5*c^2*d*e^20 + 256*a^8*b*c^5*d^3*e^18 - 296*a^8*b^3*c^3*d*e^20))*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*1i + ((d + e*x)^(1/2)*(128*b*c^12*d^15*e^3 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 - 8*a^6*b^4*c^3*e^18 + 32*a^7*b^2*c^4*e^18 + 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14 - 480*b^2*c^11*d^14*e^4 + 1120*b^3*c^10*d^13*e^5 - 1800*b^4*c^9*d^12*e^6 + 2064*b^5*c^8*d^11*e^7 - 1688*b^6*c^7*d^10*e^8 + 960*b^7*c^6*d^9*e^9 - 360*b^8*c^5*d^8*e^10 + 80*b^9*c^4*d^7*e^11 - 8*b^10*c^3*d^6*e^12 + 4512*a^2*b^2*c^9*d^10*e^8 - 4960*a^2*b^3*c^8*d^9*e^9 + 1800*a^2*b^4*c^7*d^8*e^10 + 1440*a^2*b^5*c^6*d^7*e^11 - 1840*a^2*b^6*c^5*d^6*e^12 + 768*a^2*b^7*c^4*d^5*e^13 - 120*a^2*b^8*c^3*d^4*e^14 + 10080*a^3*b^2*c^8*d^8*e^10 - 9600*a^3*b^3*c^7*d^7*e^11 + 4000*a^3*b^4*c^6*d^6*e^12 + 96*a^3*b^5*c^5*d^5*e^13 - 640*a^3*b^6*c^4*d^4*e^14 + 160*a^3*b^7*c^3*d^3*e^15 + 8800*a^4*b^2*c^7*d^6*e^12 - 6240*a^4*b^3*c^6*d^5*e^13 + 1800*a^4*b^4*c^5*d^4*e^14 + 80*a^4*b^5*c^4*d^3*e^15 - 120*a^4*b^6*c^3*d^2*e^16 + 3360*a^5*b^2*c^6*d^4*e^14 - 1600*a^5*b^3*c^5*d^3*e^15 + 240*a^5*b^4*c^4*d^2*e^16 + 480*a^6*b^2*c^5*d^2*e^16 - 160*a*b^2*c^10*d^12*e^6 + 960*a*b^3*c^9*d^11*e^7 - 2448*a*b^4*c^8*d^10*e^8 + 3440*a*b^5*c^7*d^9*e^9 - 2880*a*b^6*c^6*d^8*e^10 + 1440*a*b^7*c^5*d^7*e^11 - 400*a*b^8*c^4*d^6*e^12 + 48*a*b^9*c^3*d^5*e^13 - 1920*a^2*b*c^10*d^11*e^7 - 5120*a^3*b*c^9*d^9*e^9 - 5760*a^4*b*c^8*d^7*e^11 - 3072*a^5*b*c^7*d^5*e^13 + 48*a^5*b^5*c^3*d*e^17 - 640*a^6*b*c^6*d^3*e^15 - 160*a^6*b^3*c^4*d*e^17) - (-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*((d + e*x)^(1/2)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*(64*a*c^14*d^21*e^2 - 32*a^11*b*c^3*e^23 + 64*a^11*c^4*d*e^22 + 8*a^10*b^3*c^2*e^23 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20 - 16*b^2*c^13*d^21*e^2 + 168*b^3*c^12*d^20*e^3 - 800*b^4*c^11*d^19*e^4 + 2280*b^5*c^10*d^18*e^5 - 4320*b^6*c^9*d^17*e^6 + 5712*b^7*c^8*d^16*e^7 - 5376*b^8*c^7*d^15*e^8 + 3600*b^9*c^6*d^14*e^9 - 1680*b^10*c^5*d^13*e^10 + 520*b^11*c^4*d^12*e^11 - 96*b^12*c^3*d^11*e^12 + 8*b^13*c^2*d^10*e^13 + 25200*a^2*b^2*c^11*d^17*e^6 - 59160*a^2*b^3*c^10*d^16*e^7 + 84480*a^2*b^4*c^9*d^15*e^8 - 70560*a^2*b^5*c^8*d^14*e^9 + 23520*a^2*b^6*c^7*d^13*e^10 + 15600*a^2*b^7*c^6*d^12*e^11 - 23040*a^2*b^8*c^5*d^11*e^12 + 12320*a^2*b^9*c^4*d^10*e^13 - 3280*a^2*b^10*c^3*d^9*e^14 + 360*a^2*b^11*c^2*d^8*e^15 + 90240*a^3*b^2*c^10*d^15*e^8 - 187200*a^3*b^3*c^9*d^14*e^9 + 235200*a^3*b^4*c^8*d^13*e^10 - 174720*a^3*b^5*c^7*d^12*e^11 + 60480*a^3*b^6*c^6*d^11*e^12 + 10560*a^3*b^7*c^5*d^10*e^13 - 19200*a^3*b^8*c^4*d^9*e^14 + 7200*a^3*b^9*c^3*d^8*e^15 - 960*a^3*b^10*c^2*d^7*e^16 + 184800*a^4*b^2*c^9*d^13*e^10 - 327600*a^4*b^3*c^8*d^12*e^11 + 342720*a^4*b^4*c^7*d^11*e^12 - 203280*a^4*b^5*c^6*d^10*e^13 + 50400*a^4*b^6*c^5*d^9*e^14 + 10800*a^4*b^7*c^4*d^8*e^15 - 9600*a^4*b^8*c^3*d^7*e^16 + 1680*a^4*b^9*c^2*d^6*e^17 + 237888*a^5*b^2*c^8*d^11*e^12 - 347424*a^5*b^3*c^7*d^10*e^13 + 285600*a^5*b^4*c^6*d^9*e^14 - 120960*a^5*b^5*c^5*d^8*e^15 + 13440*a^5*b^6*c^4*d^7*e^16 + 7392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^5*e^18 + 198240*a^6*b^2*c^7*d^9*e^14 - 226800*a^6*b^3*c^6*d^8*e^15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b^5*c^4*d^6*e^17 - 2016*a^6*b^6*c^3*d^5*e^18 + 1680*a^6*b^7*c^2*d^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*a^7*b^3*c^5*d^6*e^17 + 31680*a^7*b^4*c^4*d^5*e^18 - 1920*a^7*b^5*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 33840*a^8*b^2*c^5*d^5*e^18 - 17400*a^8*b^3*c^4*d^4*e^19 + 2400*a^8*b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 + 5600*a^9*b^2*c^4*d^3*e^20 - 1200*a^9*b^3*c^3*d^2*e^21 - 672*a*b*c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 7600*a*b^3*c^11*d^18*e^5 + 10800*a*b^4*c^10*d^17*e^6 - 6528*a*b^5*c^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*a*b^7*c^7*d^14*e^9 - 16800*a*b^8*c^6*d^13*e^10 + 10400*a*b^9*c^5*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a*b^11*c^3*d^10*e^13 - 80*a*b^12*c^2*d^9*e^14 - 6080*a^2*b*c^12*d^18*e^5 - 24480*a^3*b*c^11*d^16*e^7 - 57600*a^4*b*c^10*d^14*e^9 - 87360*a^5*b*c^9*d^12*e^11 - 88704*a^6*b*c^8*d^10*e^13 - 60480*a^7*b*c^7*d^8*e^15 - 26880*a^8*b*c^6*d^6*e^17 - 7200*a^9*b*c^5*d^4*e^19 - 80*a^9*b^4*c^2*d*e^22 - 960*a^10*b*c^4*d^2*e^21 + 304*a^10*b^2*c^3*d*e^22) - 32*a^10*c^4*e^21 + 96*a*c^13*d^18*e^3 - 8*a^8*b^4*c^2*e^21 + 40*a^9*b^2*c^3*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19 - 24*b^2*c^12*d^18*e^3 + 216*b^3*c^11*d^17*e^4 - 872*b^4*c^10*d^16*e^5 + 2080*b^5*c^9*d^15*e^6 - 3248*b^6*c^8*d^14*e^7 + 3472*b^7*c^7*d^13*e^8 - 2576*b^8*c^6*d^12*e^9 + 1312*b^9*c^5*d^11*e^10 - 440*b^10*c^4*d^10*e^11 + 88*b^11*c^3*d^9*e^12 - 8*b^12*c^2*d^8*e^13 + 20256*a^2*b^2*c^10*d^14*e^7 - 38752*a^2*b^3*c^9*d^13*e^8 + 43904*a^2*b^4*c^8*d^12*e^9 - 27552*a^2*b^5*c^7*d^11*e^10 + 4928*a^2*b^6*c^6*d^10*e^11 + 5984*a^2*b^7*c^5*d^9*e^12 - 5088*a^2*b^8*c^4*d^8*e^13 + 1696*a^2*b^9*c^3*d^7*e^14 - 224*a^2*b^10*c^2*d^6*e^15 + 50848*a^3*b^2*c^9*d^12*e^9 - 83776*a^3*b^3*c^8*d^11*e^10 + 81312*a^3*b^4*c^7*d^10*e^11 - 44352*a^3*b^5*c^6*d^9*e^12 + 9184*a^3*b^6*c^5*d^8*e^13 + 3392*a^3*b^7*c^4*d^7*e^14 - 2464*a^3*b^8*c^3*d^6*e^15 + 448*a^3*b^9*c^2*d^5*e^16 + 67760*a^4*b^2*c^8*d^10*e^11 - 92400*a^4*b^3*c^7*d^9*e^12 + 72240*a^4*b^4*c^6*d^8*e^13 - 30240*a^4*b^5*c^5*d^7*e^14 + 3920*a^4*b^6*c^4*d^6*e^15 + 1680*a^4*b^7*c^3*d^5*e^16 - 560*a^4*b^8*c^2*d^4*e^17 + 50736*a^5*b^2*c^7*d^8*e^13 - 55104*a^5*b^3*c^6*d^7*e^14 + 32928*a^5*b^4*c^5*d^6*e^15 - 9408*a^5*b^5*c^4*d^5*e^16 + 112*a^5*b^6*c^3*d^4*e^17 + 448*a^5*b^7*c^2*d^3*e^18 + 20384*a^6*b^2*c^6*d^6*e^15 - 17248*a^6*b^3*c^5*d^5*e^16 + 7616*a^6*b^4*c^4*d^4*e^17 - 1120*a^6*b^5*c^3*d^3*e^18 - 224*a^6*b^6*c^2*d^2*e^19 + 3616*a^7*b^2*c^5*d^4*e^17 - 2752*a^7*b^3*c^4*d^3*e^18 + 864*a^7*b^4*c^3*d^2*e^19 + 168*a^8*b^2*c^4*d^2*e^19 - 864*a*b*c^12*d^17*e^4 + 160*a^9*b*c^4*d*e^20 + 3304*a*b^2*c^11*d^16*e^5 - 6848*a*b^3*c^10*d^15*e^6 + 7776*a*b^4*c^9*d^14*e^7 - 3136*a*b^5*c^8*d^13*e^8 - 3920*a*b^6*c^7*d^12*e^9 + 7296*a*b^7*c^6*d^11*e^10 - 5632*a*b^8*c^5*d^10*e^11 + 2464*a*b^9*c^4*d^9*e^12 - 600*a*b^10*c^3*d^8*e^13 + 64*a*b^11*c^2*d^7*e^14 - 5888*a^2*b*c^11*d^15*e^6 - 17024*a^3*b*c^10*d^13*e^8 - 26880*a^4*b*c^9*d^11*e^10 - 24640*a^5*b*c^8*d^9*e^12 - 12544*a^6*b*c^7*d^7*e^14 - 2688*a^7*b*c^6*d^5*e^16 + 64*a^7*b^5*c^2*d*e^20 + 256*a^8*b*c^5*d^3*e^18 - 296*a^8*b^3*c^3*d*e^20))*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*1i)/(((d + e*x)^(1/2)*(128*b*c^12*d^15*e^3 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 - 8*a^6*b^4*c^3*e^18 + 32*a^7*b^2*c^4*e^18 + 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14 - 480*b^2*c^11*d^14*e^4 + 1120*b^3*c^10*d^13*e^5 - 1800*b^4*c^9*d^12*e^6 + 2064*b^5*c^8*d^11*e^7 - 1688*b^6*c^7*d^10*e^8 + 960*b^7*c^6*d^9*e^9 - 360*b^8*c^5*d^8*e^10 + 80*b^9*c^4*d^7*e^11 - 8*b^10*c^3*d^6*e^12 + 4512*a^2*b^2*c^9*d^10*e^8 - 4960*a^2*b^3*c^8*d^9*e^9 + 1800*a^2*b^4*c^7*d^8*e^10 + 1440*a^2*b^5*c^6*d^7*e^11 - 1840*a^2*b^6*c^5*d^6*e^12 + 768*a^2*b^7*c^4*d^5*e^13 - 120*a^2*b^8*c^3*d^4*e^14 + 10080*a^3*b^2*c^8*d^8*e^10 - 9600*a^3*b^3*c^7*d^7*e^11 + 4000*a^3*b^4*c^6*d^6*e^12 + 96*a^3*b^5*c^5*d^5*e^13 - 640*a^3*b^6*c^4*d^4*e^14 + 160*a^3*b^7*c^3*d^3*e^15 + 8800*a^4*b^2*c^7*d^6*e^12 - 6240*a^4*b^3*c^6*d^5*e^13 + 1800*a^4*b^4*c^5*d^4*e^14 + 80*a^4*b^5*c^4*d^3*e^15 - 120*a^4*b^6*c^3*d^2*e^16 + 3360*a^5*b^2*c^6*d^4*e^14 - 1600*a^5*b^3*c^5*d^3*e^15 + 240*a^5*b^4*c^4*d^2*e^16 + 480*a^6*b^2*c^5*d^2*e^16 - 160*a*b^2*c^10*d^12*e^6 + 960*a*b^3*c^9*d^11*e^7 - 2448*a*b^4*c^8*d^10*e^8 + 3440*a*b^5*c^7*d^9*e^9 - 2880*a*b^6*c^6*d^8*e^10 + 1440*a*b^7*c^5*d^7*e^11 - 400*a*b^8*c^4*d^6*e^12 + 48*a*b^9*c^3*d^5*e^13 - 1920*a^2*b*c^10*d^11*e^7 - 5120*a^3*b*c^9*d^9*e^9 - 5760*a^4*b*c^8*d^7*e^11 - 3072*a^5*b*c^7*d^5*e^13 + 48*a^5*b^5*c^3*d*e^17 - 640*a^6*b*c^6*d^3*e^15 - 160*a^6*b^3*c^4*d*e^17) - (-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*((d + e*x)^(1/2)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*(64*a*c^14*d^21*e^2 - 32*a^11*b*c^3*e^23 + 64*a^11*c^4*d*e^22 + 8*a^10*b^3*c^2*e^23 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20 - 16*b^2*c^13*d^21*e^2 + 168*b^3*c^12*d^20*e^3 - 800*b^4*c^11*d^19*e^4 + 2280*b^5*c^10*d^18*e^5 - 4320*b^6*c^9*d^17*e^6 + 5712*b^7*c^8*d^16*e^7 - 5376*b^8*c^7*d^15*e^8 + 3600*b^9*c^6*d^14*e^9 - 1680*b^10*c^5*d^13*e^10 + 520*b^11*c^4*d^12*e^11 - 96*b^12*c^3*d^11*e^12 + 8*b^13*c^2*d^10*e^13 + 25200*a^2*b^2*c^11*d^17*e^6 - 59160*a^2*b^3*c^10*d^16*e^7 + 84480*a^2*b^4*c^9*d^15*e^8 - 70560*a^2*b^5*c^8*d^14*e^9 + 23520*a^2*b^6*c^7*d^13*e^10 + 15600*a^2*b^7*c^6*d^12*e^11 - 23040*a^2*b^8*c^5*d^11*e^12 + 12320*a^2*b^9*c^4*d^10*e^13 - 3280*a^2*b^10*c^3*d^9*e^14 + 360*a^2*b^11*c^2*d^8*e^15 + 90240*a^3*b^2*c^10*d^15*e^8 - 187200*a^3*b^3*c^9*d^14*e^9 + 235200*a^3*b^4*c^8*d^13*e^10 - 174720*a^3*b^5*c^7*d^12*e^11 + 60480*a^3*b^6*c^6*d^11*e^12 + 10560*a^3*b^7*c^5*d^10*e^13 - 19200*a^3*b^8*c^4*d^9*e^14 + 7200*a^3*b^9*c^3*d^8*e^15 - 960*a^3*b^10*c^2*d^7*e^16 + 184800*a^4*b^2*c^9*d^13*e^10 - 327600*a^4*b^3*c^8*d^12*e^11 + 342720*a^4*b^4*c^7*d^11*e^12 - 203280*a^4*b^5*c^6*d^10*e^13 + 50400*a^4*b^6*c^5*d^9*e^14 + 10800*a^4*b^7*c^4*d^8*e^15 - 9600*a^4*b^8*c^3*d^7*e^16 + 1680*a^4*b^9*c^2*d^6*e^17 + 237888*a^5*b^2*c^8*d^11*e^12 - 347424*a^5*b^3*c^7*d^10*e^13 + 285600*a^5*b^4*c^6*d^9*e^14 - 120960*a^5*b^5*c^5*d^8*e^15 + 13440*a^5*b^6*c^4*d^7*e^16 + 7392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^5*e^18 + 198240*a^6*b^2*c^7*d^9*e^14 - 226800*a^6*b^3*c^6*d^8*e^15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b^5*c^4*d^6*e^17 - 2016*a^6*b^6*c^3*d^5*e^18 + 1680*a^6*b^7*c^2*d^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*a^7*b^3*c^5*d^6*e^17 + 31680*a^7*b^4*c^4*d^5*e^18 - 1920*a^7*b^5*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 33840*a^8*b^2*c^5*d^5*e^18 - 17400*a^8*b^3*c^4*d^4*e^19 + 2400*a^8*b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 + 5600*a^9*b^2*c^4*d^3*e^20 - 1200*a^9*b^3*c^3*d^2*e^21 - 672*a*b*c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 7600*a*b^3*c^11*d^18*e^5 + 10800*a*b^4*c^10*d^17*e^6 - 6528*a*b^5*c^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*a*b^7*c^7*d^14*e^9 - 16800*a*b^8*c^6*d^13*e^10 + 10400*a*b^9*c^5*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a*b^11*c^3*d^10*e^13 - 80*a*b^12*c^2*d^9*e^14 - 6080*a^2*b*c^12*d^18*e^5 - 24480*a^3*b*c^11*d^16*e^7 - 57600*a^4*b*c^10*d^14*e^9 - 87360*a^5*b*c^9*d^12*e^11 - 88704*a^6*b*c^8*d^10*e^13 - 60480*a^7*b*c^7*d^8*e^15 - 26880*a^8*b*c^6*d^6*e^17 - 7200*a^9*b*c^5*d^4*e^19 - 80*a^9*b^4*c^2*d*e^22 - 960*a^10*b*c^4*d^2*e^21 + 304*a^10*b^2*c^3*d*e^22) - 32*a^10*c^4*e^21 + 96*a*c^13*d^18*e^3 - 8*a^8*b^4*c^2*e^21 + 40*a^9*b^2*c^3*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19 - 24*b^2*c^12*d^18*e^3 + 216*b^3*c^11*d^17*e^4 - 872*b^4*c^10*d^16*e^5 + 2080*b^5*c^9*d^15*e^6 - 3248*b^6*c^8*d^14*e^7 + 3472*b^7*c^7*d^13*e^8 - 2576*b^8*c^6*d^12*e^9 + 1312*b^9*c^5*d^11*e^10 - 440*b^10*c^4*d^10*e^11 + 88*b^11*c^3*d^9*e^12 - 8*b^12*c^2*d^8*e^13 + 20256*a^2*b^2*c^10*d^14*e^7 - 38752*a^2*b^3*c^9*d^13*e^8 + 43904*a^2*b^4*c^8*d^12*e^9 - 27552*a^2*b^5*c^7*d^11*e^10 + 4928*a^2*b^6*c^6*d^10*e^11 + 5984*a^2*b^7*c^5*d^9*e^12 - 5088*a^2*b^8*c^4*d^8*e^13 + 1696*a^2*b^9*c^3*d^7*e^14 - 224*a^2*b^10*c^2*d^6*e^15 + 50848*a^3*b^2*c^9*d^12*e^9 - 83776*a^3*b^3*c^8*d^11*e^10 + 81312*a^3*b^4*c^7*d^10*e^11 - 44352*a^3*b^5*c^6*d^9*e^12 + 9184*a^3*b^6*c^5*d^8*e^13 + 3392*a^3*b^7*c^4*d^7*e^14 - 2464*a^3*b^8*c^3*d^6*e^15 + 448*a^3*b^9*c^2*d^5*e^16 + 67760*a^4*b^2*c^8*d^10*e^11 - 92400*a^4*b^3*c^7*d^9*e^12 + 72240*a^4*b^4*c^6*d^8*e^13 - 30240*a^4*b^5*c^5*d^7*e^14 + 3920*a^4*b^6*c^4*d^6*e^15 + 1680*a^4*b^7*c^3*d^5*e^16 - 560*a^4*b^8*c^2*d^4*e^17 + 50736*a^5*b^2*c^7*d^8*e^13 - 55104*a^5*b^3*c^6*d^7*e^14 + 32928*a^5*b^4*c^5*d^6*e^15 - 9408*a^5*b^5*c^4*d^5*e^16 + 112*a^5*b^6*c^3*d^4*e^17 + 448*a^5*b^7*c^2*d^3*e^18 + 20384*a^6*b^2*c^6*d^6*e^15 - 17248*a^6*b^3*c^5*d^5*e^16 + 7616*a^6*b^4*c^4*d^4*e^17 - 1120*a^6*b^5*c^3*d^3*e^18 - 224*a^6*b^6*c^2*d^2*e^19 + 3616*a^7*b^2*c^5*d^4*e^17 - 2752*a^7*b^3*c^4*d^3*e^18 + 864*a^7*b^4*c^3*d^2*e^19 + 168*a^8*b^2*c^4*d^2*e^19 - 864*a*b*c^12*d^17*e^4 + 160*a^9*b*c^4*d*e^20 + 3304*a*b^2*c^11*d^16*e^5 - 6848*a*b^3*c^10*d^15*e^6 + 7776*a*b^4*c^9*d^14*e^7 - 3136*a*b^5*c^8*d^13*e^8 - 3920*a*b^6*c^7*d^12*e^9 + 7296*a*b^7*c^6*d^11*e^10 - 5632*a*b^8*c^5*d^10*e^11 + 2464*a*b^9*c^4*d^9*e^12 - 600*a*b^10*c^3*d^8*e^13 + 64*a*b^11*c^2*d^7*e^14 - 5888*a^2*b*c^11*d^15*e^6 - 17024*a^3*b*c^10*d^13*e^8 - 26880*a^4*b*c^9*d^11*e^10 - 24640*a^5*b*c^8*d^9*e^12 - 12544*a^6*b*c^7*d^7*e^14 - 2688*a^7*b*c^6*d^5*e^16 + 64*a^7*b^5*c^2*d*e^20 + 256*a^8*b*c^5*d^3*e^18 - 296*a^8*b^3*c^3*d*e^20))*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2) - ((d + e*x)^(1/2)*(128*b*c^12*d^15*e^3 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 - 8*a^6*b^4*c^3*e^18 + 32*a^7*b^2*c^4*e^18 + 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14 - 480*b^2*c^11*d^14*e^4 + 1120*b^3*c^10*d^13*e^5 - 1800*b^4*c^9*d^12*e^6 + 2064*b^5*c^8*d^11*e^7 - 1688*b^6*c^7*d^10*e^8 + 960*b^7*c^6*d^9*e^9 - 360*b^8*c^5*d^8*e^10 + 80*b^9*c^4*d^7*e^11 - 8*b^10*c^3*d^6*e^12 + 4512*a^2*b^2*c^9*d^10*e^8 - 4960*a^2*b^3*c^8*d^9*e^9 + 1800*a^2*b^4*c^7*d^8*e^10 + 1440*a^2*b^5*c^6*d^7*e^11 - 1840*a^2*b^6*c^5*d^6*e^12 + 768*a^2*b^7*c^4*d^5*e^13 - 120*a^2*b^8*c^3*d^4*e^14 + 10080*a^3*b^2*c^8*d^8*e^10 - 9600*a^3*b^3*c^7*d^7*e^11 + 4000*a^3*b^4*c^6*d^6*e^12 + 96*a^3*b^5*c^5*d^5*e^13 - 640*a^3*b^6*c^4*d^4*e^14 + 160*a^3*b^7*c^3*d^3*e^15 + 8800*a^4*b^2*c^7*d^6*e^12 - 6240*a^4*b^3*c^6*d^5*e^13 + 1800*a^4*b^4*c^5*d^4*e^14 + 80*a^4*b^5*c^4*d^3*e^15 - 120*a^4*b^6*c^3*d^2*e^16 + 3360*a^5*b^2*c^6*d^4*e^14 - 1600*a^5*b^3*c^5*d^3*e^15 + 240*a^5*b^4*c^4*d^2*e^16 + 480*a^6*b^2*c^5*d^2*e^16 - 160*a*b^2*c^10*d^12*e^6 + 960*a*b^3*c^9*d^11*e^7 - 2448*a*b^4*c^8*d^10*e^8 + 3440*a*b^5*c^7*d^9*e^9 - 2880*a*b^6*c^6*d^8*e^10 + 1440*a*b^7*c^5*d^7*e^11 - 400*a*b^8*c^4*d^6*e^12 + 48*a*b^9*c^3*d^5*e^13 - 1920*a^2*b*c^10*d^11*e^7 - 5120*a^3*b*c^9*d^9*e^9 - 5760*a^4*b*c^8*d^7*e^11 - 3072*a^5*b*c^7*d^5*e^13 + 48*a^5*b^5*c^3*d*e^17 - 640*a^6*b*c^6*d^3*e^15 - 160*a^6*b^3*c^4*d*e^17) + (-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*(96*a*c^13*d^18*e^3 - 32*a^10*c^4*e^21 - (d + e*x)^(1/2)*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*(64*a*c^14*d^21*e^2 - 32*a^11*b*c^3*e^23 + 64*a^11*c^4*d*e^22 + 8*a^10*b^3*c^2*e^23 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20 - 16*b^2*c^13*d^21*e^2 + 168*b^3*c^12*d^20*e^3 - 800*b^4*c^11*d^19*e^4 + 2280*b^5*c^10*d^18*e^5 - 4320*b^6*c^9*d^17*e^6 + 5712*b^7*c^8*d^16*e^7 - 5376*b^8*c^7*d^15*e^8 + 3600*b^9*c^6*d^14*e^9 - 1680*b^10*c^5*d^13*e^10 + 520*b^11*c^4*d^12*e^11 - 96*b^12*c^3*d^11*e^12 + 8*b^13*c^2*d^10*e^13 + 25200*a^2*b^2*c^11*d^17*e^6 - 59160*a^2*b^3*c^10*d^16*e^7 + 84480*a^2*b^4*c^9*d^15*e^8 - 70560*a^2*b^5*c^8*d^14*e^9 + 23520*a^2*b^6*c^7*d^13*e^10 + 15600*a^2*b^7*c^6*d^12*e^11 - 23040*a^2*b^8*c^5*d^11*e^12 + 12320*a^2*b^9*c^4*d^10*e^13 - 3280*a^2*b^10*c^3*d^9*e^14 + 360*a^2*b^11*c^2*d^8*e^15 + 90240*a^3*b^2*c^10*d^15*e^8 - 187200*a^3*b^3*c^9*d^14*e^9 + 235200*a^3*b^4*c^8*d^13*e^10 - 174720*a^3*b^5*c^7*d^12*e^11 + 60480*a^3*b^6*c^6*d^11*e^12 + 10560*a^3*b^7*c^5*d^10*e^13 - 19200*a^3*b^8*c^4*d^9*e^14 + 7200*a^3*b^9*c^3*d^8*e^15 - 960*a^3*b^10*c^2*d^7*e^16 + 184800*a^4*b^2*c^9*d^13*e^10 - 327600*a^4*b^3*c^8*d^12*e^11 + 342720*a^4*b^4*c^7*d^11*e^12 - 203280*a^4*b^5*c^6*d^10*e^13 + 50400*a^4*b^6*c^5*d^9*e^14 + 10800*a^4*b^7*c^4*d^8*e^15 - 9600*a^4*b^8*c^3*d^7*e^16 + 1680*a^4*b^9*c^2*d^6*e^17 + 237888*a^5*b^2*c^8*d^11*e^12 - 347424*a^5*b^3*c^7*d^10*e^13 + 285600*a^5*b^4*c^6*d^9*e^14 - 120960*a^5*b^5*c^5*d^8*e^15 + 13440*a^5*b^6*c^4*d^7*e^16 + 7392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^5*e^18 + 198240*a^6*b^2*c^7*d^9*e^14 - 226800*a^6*b^3*c^6*d^8*e^15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b^5*c^4*d^6*e^17 - 2016*a^6*b^6*c^3*d^5*e^18 + 1680*a^6*b^7*c^2*d^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*a^7*b^3*c^5*d^6*e^17 + 31680*a^7*b^4*c^4*d^5*e^18 - 1920*a^7*b^5*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 33840*a^8*b^2*c^5*d^5*e^18 - 17400*a^8*b^3*c^4*d^4*e^19 + 2400*a^8*b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 + 5600*a^9*b^2*c^4*d^3*e^20 - 1200*a^9*b^3*c^3*d^2*e^21 - 672*a*b*c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 7600*a*b^3*c^11*d^18*e^5 + 10800*a*b^4*c^10*d^17*e^6 - 6528*a*b^5*c^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*a*b^7*c^7*d^14*e^9 - 16800*a*b^8*c^6*d^13*e^10 + 10400*a*b^9*c^5*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a*b^11*c^3*d^10*e^13 - 80*a*b^12*c^2*d^9*e^14 - 6080*a^2*b*c^12*d^18*e^5 - 24480*a^3*b*c^11*d^16*e^7 - 57600*a^4*b*c^10*d^14*e^9 - 87360*a^5*b*c^9*d^12*e^11 - 88704*a^6*b*c^8*d^10*e^13 - 60480*a^7*b*c^7*d^8*e^15 - 26880*a^8*b*c^6*d^6*e^17 - 7200*a^9*b*c^5*d^4*e^19 - 80*a^9*b^4*c^2*d*e^22 - 960*a^10*b*c^4*d^2*e^21 + 304*a^10*b^2*c^3*d*e^22) - 8*a^8*b^4*c^2*e^21 + 40*a^9*b^2*c^3*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19 - 24*b^2*c^12*d^18*e^3 + 216*b^3*c^11*d^17*e^4 - 872*b^4*c^10*d^16*e^5 + 2080*b^5*c^9*d^15*e^6 - 3248*b^6*c^8*d^14*e^7 + 3472*b^7*c^7*d^13*e^8 - 2576*b^8*c^6*d^12*e^9 + 1312*b^9*c^5*d^11*e^10 - 440*b^10*c^4*d^10*e^11 + 88*b^11*c^3*d^9*e^12 - 8*b^12*c^2*d^8*e^13 + 20256*a^2*b^2*c^10*d^14*e^7 - 38752*a^2*b^3*c^9*d^13*e^8 + 43904*a^2*b^4*c^8*d^12*e^9 - 27552*a^2*b^5*c^7*d^11*e^10 + 4928*a^2*b^6*c^6*d^10*e^11 + 5984*a^2*b^7*c^5*d^9*e^12 - 5088*a^2*b^8*c^4*d^8*e^13 + 1696*a^2*b^9*c^3*d^7*e^14 - 224*a^2*b^10*c^2*d^6*e^15 + 50848*a^3*b^2*c^9*d^12*e^9 - 83776*a^3*b^3*c^8*d^11*e^10 + 81312*a^3*b^4*c^7*d^10*e^11 - 44352*a^3*b^5*c^6*d^9*e^12 + 9184*a^3*b^6*c^5*d^8*e^13 + 3392*a^3*b^7*c^4*d^7*e^14 - 2464*a^3*b^8*c^3*d^6*e^15 + 448*a^3*b^9*c^2*d^5*e^16 + 67760*a^4*b^2*c^8*d^10*e^11 - 92400*a^4*b^3*c^7*d^9*e^12 + 72240*a^4*b^4*c^6*d^8*e^13 - 30240*a^4*b^5*c^5*d^7*e^14 + 3920*a^4*b^6*c^4*d^6*e^15 + 1680*a^4*b^7*c^3*d^5*e^16 - 560*a^4*b^8*c^2*d^4*e^17 + 50736*a^5*b^2*c^7*d^8*e^13 - 55104*a^5*b^3*c^6*d^7*e^14 + 32928*a^5*b^4*c^5*d^6*e^15 - 9408*a^5*b^5*c^4*d^5*e^16 + 112*a^5*b^6*c^3*d^4*e^17 + 448*a^5*b^7*c^2*d^3*e^18 + 20384*a^6*b^2*c^6*d^6*e^15 - 17248*a^6*b^3*c^5*d^5*e^16 + 7616*a^6*b^4*c^4*d^4*e^17 - 1120*a^6*b^5*c^3*d^3*e^18 - 224*a^6*b^6*c^2*d^2*e^19 + 3616*a^7*b^2*c^5*d^4*e^17 - 2752*a^7*b^3*c^4*d^3*e^18 + 864*a^7*b^4*c^3*d^2*e^19 + 168*a^8*b^2*c^4*d^2*e^19 - 864*a*b*c^12*d^17*e^4 + 160*a^9*b*c^4*d*e^20 + 3304*a*b^2*c^11*d^16*e^5 - 6848*a*b^3*c^10*d^15*e^6 + 7776*a*b^4*c^9*d^14*e^7 - 3136*a*b^5*c^8*d^13*e^8 - 3920*a*b^6*c^7*d^12*e^9 + 7296*a*b^7*c^6*d^11*e^10 - 5632*a*b^8*c^5*d^10*e^11 + 2464*a*b^9*c^4*d^9*e^12 - 600*a*b^10*c^3*d^8*e^13 + 64*a*b^11*c^2*d^7*e^14 - 5888*a^2*b*c^11*d^15*e^6 - 17024*a^3*b*c^10*d^13*e^8 - 26880*a^4*b*c^9*d^11*e^10 - 24640*a^5*b*c^8*d^9*e^12 - 12544*a^6*b*c^7*d^7*e^14 - 2688*a^7*b*c^6*d^5*e^16 + 64*a^7*b^5*c^2*d*e^20 + 256*a^8*b*c^5*d^3*e^18 - 296*a^8*b^3*c^3*d*e^20))*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2) + 32*c^12*d^13*e^3 - 16*a^6*b*c^5*e^16 + 192*a*c^11*d^11*e^5 + 32*a^6*c^6*d*e^15 - 208*b*c^11*d^12*e^4 + 480*a^2*c^10*d^9*e^7 + 640*a^3*c^9*d^7*e^9 + 480*a^4*c^8*d^5*e^11 + 192*a^5*c^7*d^3*e^13 + 576*b^2*c^10*d^11*e^5 - 880*b^3*c^9*d^10*e^6 + 800*b^4*c^8*d^9*e^7 - 432*b^5*c^7*d^8*e^8 + 128*b^6*c^6*d^7*e^9 - 16*b^7*c^5*d^6*e^10 + 3840*a^2*b^2*c^8*d^7*e^9 - 3360*a^2*b^3*c^7*d^6*e^10 + 1440*a^2*b^4*c^6*d^5*e^11 - 240*a^2*b^5*c^5*d^4*e^12 + 2880*a^3*b^2*c^7*d^5*e^11 - 1600*a^3*b^3*c^6*d^4*e^12 + 320*a^3*b^4*c^5*d^3*e^13 + 960*a^4*b^2*c^6*d^3*e^13 - 240*a^4*b^3*c^5*d^2*e^14 - 1056*a*b*c^10*d^10*e^6 + 2400*a*b^2*c^9*d^9*e^7 - 2880*a*b^3*c^8*d^8*e^8 + 1920*a*b^4*c^7*d^7*e^9 - 672*a*b^5*c^6*d^6*e^10 + 96*a*b^6*c^5*d^5*e^11 - 2160*a^2*b*c^9*d^8*e^8 - 2240*a^3*b*c^8*d^6*e^10 - 1200*a^4*b*c^7*d^4*e^12 - 288*a^5*b*c^6*d^2*e^14 + 96*a^5*b^2*c^5*d*e^15))*(-(b^7*e^5 + 8*a*c^6*d^5 - 2*b^2*c^5*d^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) - 20*a^3*b*c^3*e^5 + 40*a^3*c^4*d*e^4 + 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) + 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) - 80*a^2*c^5*d^3*e^2 - 10*b^4*c^3*d^3*e^2 + 10*b^5*c^2*d^2*e^3 - 9*a*b^5*c*e^5 - 5*b^6*c*d*e^4 - 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) + 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) + 60*a*b^2*c^4*d^3*e^2 - 70*a*b^3*c^3*d^2*e^3 + 120*a^2*b*c^4*d^2*e^3 - 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*2i - atan((((d + e*x)^(1/2)*(128*b*c^12*d^15*e^3 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 - 8*a^6*b^4*c^3*e^18 + 32*a^7*b^2*c^4*e^18 + 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14 - 480*b^2*c^11*d^14*e^4 + 1120*b^3*c^10*d^13*e^5 - 1800*b^4*c^9*d^12*e^6 + 2064*b^5*c^8*d^11*e^7 - 1688*b^6*c^7*d^10*e^8 + 960*b^7*c^6*d^9*e^9 - 360*b^8*c^5*d^8*e^10 + 80*b^9*c^4*d^7*e^11 - 8*b^10*c^3*d^6*e^12 + 4512*a^2*b^2*c^9*d^10*e^8 - 4960*a^2*b^3*c^8*d^9*e^9 + 1800*a^2*b^4*c^7*d^8*e^10 + 1440*a^2*b^5*c^6*d^7*e^11 - 1840*a^2*b^6*c^5*d^6*e^12 + 768*a^2*b^7*c^4*d^5*e^13 - 120*a^2*b^8*c^3*d^4*e^14 + 10080*a^3*b^2*c^8*d^8*e^10 - 9600*a^3*b^3*c^7*d^7*e^11 + 4000*a^3*b^4*c^6*d^6*e^12 + 96*a^3*b^5*c^5*d^5*e^13 - 640*a^3*b^6*c^4*d^4*e^14 + 160*a^3*b^7*c^3*d^3*e^15 + 8800*a^4*b^2*c^7*d^6*e^12 - 6240*a^4*b^3*c^6*d^5*e^13 + 1800*a^4*b^4*c^5*d^4*e^14 + 80*a^4*b^5*c^4*d^3*e^15 - 120*a^4*b^6*c^3*d^2*e^16 + 3360*a^5*b^2*c^6*d^4*e^14 - 1600*a^5*b^3*c^5*d^3*e^15 + 240*a^5*b^4*c^4*d^2*e^16 + 480*a^6*b^2*c^5*d^2*e^16 - 160*a*b^2*c^10*d^12*e^6 + 960*a*b^3*c^9*d^11*e^7 - 2448*a*b^4*c^8*d^10*e^8 + 3440*a*b^5*c^7*d^9*e^9 - 2880*a*b^6*c^6*d^8*e^10 + 1440*a*b^7*c^5*d^7*e^11 - 400*a*b^8*c^4*d^6*e^12 + 48*a*b^9*c^3*d^5*e^13 - 1920*a^2*b*c^10*d^11*e^7 - 5120*a^3*b*c^9*d^9*e^9 - 5760*a^4*b*c^8*d^7*e^11 - 3072*a^5*b*c^7*d^5*e^13 + 48*a^5*b^5*c^3*d*e^17 - 640*a^6*b*c^6*d^3*e^15 - 160*a^6*b^3*c^4*d*e^17) + ((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*(96*a*c^13*d^18*e^3 - 32*a^10*c^4*e^21 - (d + e*x)^(1/2)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*(64*a*c^14*d^21*e^2 - 32*a^11*b*c^3*e^23 + 64*a^11*c^4*d*e^22 + 8*a^10*b^3*c^2*e^23 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20 - 16*b^2*c^13*d^21*e^2 + 168*b^3*c^12*d^20*e^3 - 800*b^4*c^11*d^19*e^4 + 2280*b^5*c^10*d^18*e^5 - 4320*b^6*c^9*d^17*e^6 + 5712*b^7*c^8*d^16*e^7 - 5376*b^8*c^7*d^15*e^8 + 3600*b^9*c^6*d^14*e^9 - 1680*b^10*c^5*d^13*e^10 + 520*b^11*c^4*d^12*e^11 - 96*b^12*c^3*d^11*e^12 + 8*b^13*c^2*d^10*e^13 + 25200*a^2*b^2*c^11*d^17*e^6 - 59160*a^2*b^3*c^10*d^16*e^7 + 84480*a^2*b^4*c^9*d^15*e^8 - 70560*a^2*b^5*c^8*d^14*e^9 + 23520*a^2*b^6*c^7*d^13*e^10 + 15600*a^2*b^7*c^6*d^12*e^11 - 23040*a^2*b^8*c^5*d^11*e^12 + 12320*a^2*b^9*c^4*d^10*e^13 - 3280*a^2*b^10*c^3*d^9*e^14 + 360*a^2*b^11*c^2*d^8*e^15 + 90240*a^3*b^2*c^10*d^15*e^8 - 187200*a^3*b^3*c^9*d^14*e^9 + 235200*a^3*b^4*c^8*d^13*e^10 - 174720*a^3*b^5*c^7*d^12*e^11 + 60480*a^3*b^6*c^6*d^11*e^12 + 10560*a^3*b^7*c^5*d^10*e^13 - 19200*a^3*b^8*c^4*d^9*e^14 + 7200*a^3*b^9*c^3*d^8*e^15 - 960*a^3*b^10*c^2*d^7*e^16 + 184800*a^4*b^2*c^9*d^13*e^10 - 327600*a^4*b^3*c^8*d^12*e^11 + 342720*a^4*b^4*c^7*d^11*e^12 - 203280*a^4*b^5*c^6*d^10*e^13 + 50400*a^4*b^6*c^5*d^9*e^14 + 10800*a^4*b^7*c^4*d^8*e^15 - 9600*a^4*b^8*c^3*d^7*e^16 + 1680*a^4*b^9*c^2*d^6*e^17 + 237888*a^5*b^2*c^8*d^11*e^12 - 347424*a^5*b^3*c^7*d^10*e^13 + 285600*a^5*b^4*c^6*d^9*e^14 - 120960*a^5*b^5*c^5*d^8*e^15 + 13440*a^5*b^6*c^4*d^7*e^16 + 7392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^5*e^18 + 198240*a^6*b^2*c^7*d^9*e^14 - 226800*a^6*b^3*c^6*d^8*e^15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b^5*c^4*d^6*e^17 - 2016*a^6*b^6*c^3*d^5*e^18 + 1680*a^6*b^7*c^2*d^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*a^7*b^3*c^5*d^6*e^17 + 31680*a^7*b^4*c^4*d^5*e^18 - 1920*a^7*b^5*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 33840*a^8*b^2*c^5*d^5*e^18 - 17400*a^8*b^3*c^4*d^4*e^19 + 2400*a^8*b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 + 5600*a^9*b^2*c^4*d^3*e^20 - 1200*a^9*b^3*c^3*d^2*e^21 - 672*a*b*c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 7600*a*b^3*c^11*d^18*e^5 + 10800*a*b^4*c^10*d^17*e^6 - 6528*a*b^5*c^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*a*b^7*c^7*d^14*e^9 - 16800*a*b^8*c^6*d^13*e^10 + 10400*a*b^9*c^5*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a*b^11*c^3*d^10*e^13 - 80*a*b^12*c^2*d^9*e^14 - 6080*a^2*b*c^12*d^18*e^5 - 24480*a^3*b*c^11*d^16*e^7 - 57600*a^4*b*c^10*d^14*e^9 - 87360*a^5*b*c^9*d^12*e^11 - 88704*a^6*b*c^8*d^10*e^13 - 60480*a^7*b*c^7*d^8*e^15 - 26880*a^8*b*c^6*d^6*e^17 - 7200*a^9*b*c^5*d^4*e^19 - 80*a^9*b^4*c^2*d*e^22 - 960*a^10*b*c^4*d^2*e^21 + 304*a^10*b^2*c^3*d*e^22) - 8*a^8*b^4*c^2*e^21 + 40*a^9*b^2*c^3*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19 - 24*b^2*c^12*d^18*e^3 + 216*b^3*c^11*d^17*e^4 - 872*b^4*c^10*d^16*e^5 + 2080*b^5*c^9*d^15*e^6 - 3248*b^6*c^8*d^14*e^7 + 3472*b^7*c^7*d^13*e^8 - 2576*b^8*c^6*d^12*e^9 + 1312*b^9*c^5*d^11*e^10 - 440*b^10*c^4*d^10*e^11 + 88*b^11*c^3*d^9*e^12 - 8*b^12*c^2*d^8*e^13 + 20256*a^2*b^2*c^10*d^14*e^7 - 38752*a^2*b^3*c^9*d^13*e^8 + 43904*a^2*b^4*c^8*d^12*e^9 - 27552*a^2*b^5*c^7*d^11*e^10 + 4928*a^2*b^6*c^6*d^10*e^11 + 5984*a^2*b^7*c^5*d^9*e^12 - 5088*a^2*b^8*c^4*d^8*e^13 + 1696*a^2*b^9*c^3*d^7*e^14 - 224*a^2*b^10*c^2*d^6*e^15 + 50848*a^3*b^2*c^9*d^12*e^9 - 83776*a^3*b^3*c^8*d^11*e^10 + 81312*a^3*b^4*c^7*d^10*e^11 - 44352*a^3*b^5*c^6*d^9*e^12 + 9184*a^3*b^6*c^5*d^8*e^13 + 3392*a^3*b^7*c^4*d^7*e^14 - 2464*a^3*b^8*c^3*d^6*e^15 + 448*a^3*b^9*c^2*d^5*e^16 + 67760*a^4*b^2*c^8*d^10*e^11 - 92400*a^4*b^3*c^7*d^9*e^12 + 72240*a^4*b^4*c^6*d^8*e^13 - 30240*a^4*b^5*c^5*d^7*e^14 + 3920*a^4*b^6*c^4*d^6*e^15 + 1680*a^4*b^7*c^3*d^5*e^16 - 560*a^4*b^8*c^2*d^4*e^17 + 50736*a^5*b^2*c^7*d^8*e^13 - 55104*a^5*b^3*c^6*d^7*e^14 + 32928*a^5*b^4*c^5*d^6*e^15 - 9408*a^5*b^5*c^4*d^5*e^16 + 112*a^5*b^6*c^3*d^4*e^17 + 448*a^5*b^7*c^2*d^3*e^18 + 20384*a^6*b^2*c^6*d^6*e^15 - 17248*a^6*b^3*c^5*d^5*e^16 + 7616*a^6*b^4*c^4*d^4*e^17 - 1120*a^6*b^5*c^3*d^3*e^18 - 224*a^6*b^6*c^2*d^2*e^19 + 3616*a^7*b^2*c^5*d^4*e^17 - 2752*a^7*b^3*c^4*d^3*e^18 + 864*a^7*b^4*c^3*d^2*e^19 + 168*a^8*b^2*c^4*d^2*e^19 - 864*a*b*c^12*d^17*e^4 + 160*a^9*b*c^4*d*e^20 + 3304*a*b^2*c^11*d^16*e^5 - 6848*a*b^3*c^10*d^15*e^6 + 7776*a*b^4*c^9*d^14*e^7 - 3136*a*b^5*c^8*d^13*e^8 - 3920*a*b^6*c^7*d^12*e^9 + 7296*a*b^7*c^6*d^11*e^10 - 5632*a*b^8*c^5*d^10*e^11 + 2464*a*b^9*c^4*d^9*e^12 - 600*a*b^10*c^3*d^8*e^13 + 64*a*b^11*c^2*d^7*e^14 - 5888*a^2*b*c^11*d^15*e^6 - 17024*a^3*b*c^10*d^13*e^8 - 26880*a^4*b*c^9*d^11*e^10 - 24640*a^5*b*c^8*d^9*e^12 - 12544*a^6*b*c^7*d^7*e^14 - 2688*a^7*b*c^6*d^5*e^16 + 64*a^7*b^5*c^2*d*e^20 + 256*a^8*b*c^5*d^3*e^18 - 296*a^8*b^3*c^3*d*e^20))*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*1i + ((d + e*x)^(1/2)*(128*b*c^12*d^15*e^3 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 - 8*a^6*b^4*c^3*e^18 + 32*a^7*b^2*c^4*e^18 + 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14 - 480*b^2*c^11*d^14*e^4 + 1120*b^3*c^10*d^13*e^5 - 1800*b^4*c^9*d^12*e^6 + 2064*b^5*c^8*d^11*e^7 - 1688*b^6*c^7*d^10*e^8 + 960*b^7*c^6*d^9*e^9 - 360*b^8*c^5*d^8*e^10 + 80*b^9*c^4*d^7*e^11 - 8*b^10*c^3*d^6*e^12 + 4512*a^2*b^2*c^9*d^10*e^8 - 4960*a^2*b^3*c^8*d^9*e^9 + 1800*a^2*b^4*c^7*d^8*e^10 + 1440*a^2*b^5*c^6*d^7*e^11 - 1840*a^2*b^6*c^5*d^6*e^12 + 768*a^2*b^7*c^4*d^5*e^13 - 120*a^2*b^8*c^3*d^4*e^14 + 10080*a^3*b^2*c^8*d^8*e^10 - 9600*a^3*b^3*c^7*d^7*e^11 + 4000*a^3*b^4*c^6*d^6*e^12 + 96*a^3*b^5*c^5*d^5*e^13 - 640*a^3*b^6*c^4*d^4*e^14 + 160*a^3*b^7*c^3*d^3*e^15 + 8800*a^4*b^2*c^7*d^6*e^12 - 6240*a^4*b^3*c^6*d^5*e^13 + 1800*a^4*b^4*c^5*d^4*e^14 + 80*a^4*b^5*c^4*d^3*e^15 - 120*a^4*b^6*c^3*d^2*e^16 + 3360*a^5*b^2*c^6*d^4*e^14 - 1600*a^5*b^3*c^5*d^3*e^15 + 240*a^5*b^4*c^4*d^2*e^16 + 480*a^6*b^2*c^5*d^2*e^16 - 160*a*b^2*c^10*d^12*e^6 + 960*a*b^3*c^9*d^11*e^7 - 2448*a*b^4*c^8*d^10*e^8 + 3440*a*b^5*c^7*d^9*e^9 - 2880*a*b^6*c^6*d^8*e^10 + 1440*a*b^7*c^5*d^7*e^11 - 400*a*b^8*c^4*d^6*e^12 + 48*a*b^9*c^3*d^5*e^13 - 1920*a^2*b*c^10*d^11*e^7 - 5120*a^3*b*c^9*d^9*e^9 - 5760*a^4*b*c^8*d^7*e^11 - 3072*a^5*b*c^7*d^5*e^13 + 48*a^5*b^5*c^3*d*e^17 - 640*a^6*b*c^6*d^3*e^15 - 160*a^6*b^3*c^4*d*e^17) - ((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*((d + e*x)^(1/2)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*(64*a*c^14*d^21*e^2 - 32*a^11*b*c^3*e^23 + 64*a^11*c^4*d*e^22 + 8*a^10*b^3*c^2*e^23 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20 - 16*b^2*c^13*d^21*e^2 + 168*b^3*c^12*d^20*e^3 - 800*b^4*c^11*d^19*e^4 + 2280*b^5*c^10*d^18*e^5 - 4320*b^6*c^9*d^17*e^6 + 5712*b^7*c^8*d^16*e^7 - 5376*b^8*c^7*d^15*e^8 + 3600*b^9*c^6*d^14*e^9 - 1680*b^10*c^5*d^13*e^10 + 520*b^11*c^4*d^12*e^11 - 96*b^12*c^3*d^11*e^12 + 8*b^13*c^2*d^10*e^13 + 25200*a^2*b^2*c^11*d^17*e^6 - 59160*a^2*b^3*c^10*d^16*e^7 + 84480*a^2*b^4*c^9*d^15*e^8 - 70560*a^2*b^5*c^8*d^14*e^9 + 23520*a^2*b^6*c^7*d^13*e^10 + 15600*a^2*b^7*c^6*d^12*e^11 - 23040*a^2*b^8*c^5*d^11*e^12 + 12320*a^2*b^9*c^4*d^10*e^13 - 3280*a^2*b^10*c^3*d^9*e^14 + 360*a^2*b^11*c^2*d^8*e^15 + 90240*a^3*b^2*c^10*d^15*e^8 - 187200*a^3*b^3*c^9*d^14*e^9 + 235200*a^3*b^4*c^8*d^13*e^10 - 174720*a^3*b^5*c^7*d^12*e^11 + 60480*a^3*b^6*c^6*d^11*e^12 + 10560*a^3*b^7*c^5*d^10*e^13 - 19200*a^3*b^8*c^4*d^9*e^14 + 7200*a^3*b^9*c^3*d^8*e^15 - 960*a^3*b^10*c^2*d^7*e^16 + 184800*a^4*b^2*c^9*d^13*e^10 - 327600*a^4*b^3*c^8*d^12*e^11 + 342720*a^4*b^4*c^7*d^11*e^12 - 203280*a^4*b^5*c^6*d^10*e^13 + 50400*a^4*b^6*c^5*d^9*e^14 + 10800*a^4*b^7*c^4*d^8*e^15 - 9600*a^4*b^8*c^3*d^7*e^16 + 1680*a^4*b^9*c^2*d^6*e^17 + 237888*a^5*b^2*c^8*d^11*e^12 - 347424*a^5*b^3*c^7*d^10*e^13 + 285600*a^5*b^4*c^6*d^9*e^14 - 120960*a^5*b^5*c^5*d^8*e^15 + 13440*a^5*b^6*c^4*d^7*e^16 + 7392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^5*e^18 + 198240*a^6*b^2*c^7*d^9*e^14 - 226800*a^6*b^3*c^6*d^8*e^15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b^5*c^4*d^6*e^17 - 2016*a^6*b^6*c^3*d^5*e^18 + 1680*a^6*b^7*c^2*d^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*a^7*b^3*c^5*d^6*e^17 + 31680*a^7*b^4*c^4*d^5*e^18 - 1920*a^7*b^5*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 33840*a^8*b^2*c^5*d^5*e^18 - 17400*a^8*b^3*c^4*d^4*e^19 + 2400*a^8*b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 + 5600*a^9*b^2*c^4*d^3*e^20 - 1200*a^9*b^3*c^3*d^2*e^21 - 672*a*b*c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 7600*a*b^3*c^11*d^18*e^5 + 10800*a*b^4*c^10*d^17*e^6 - 6528*a*b^5*c^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*a*b^7*c^7*d^14*e^9 - 16800*a*b^8*c^6*d^13*e^10 + 10400*a*b^9*c^5*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a*b^11*c^3*d^10*e^13 - 80*a*b^12*c^2*d^9*e^14 - 6080*a^2*b*c^12*d^18*e^5 - 24480*a^3*b*c^11*d^16*e^7 - 57600*a^4*b*c^10*d^14*e^9 - 87360*a^5*b*c^9*d^12*e^11 - 88704*a^6*b*c^8*d^10*e^13 - 60480*a^7*b*c^7*d^8*e^15 - 26880*a^8*b*c^6*d^6*e^17 - 7200*a^9*b*c^5*d^4*e^19 - 80*a^9*b^4*c^2*d*e^22 - 960*a^10*b*c^4*d^2*e^21 + 304*a^10*b^2*c^3*d*e^22) - 32*a^10*c^4*e^21 + 96*a*c^13*d^18*e^3 - 8*a^8*b^4*c^2*e^21 + 40*a^9*b^2*c^3*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19 - 24*b^2*c^12*d^18*e^3 + 216*b^3*c^11*d^17*e^4 - 872*b^4*c^10*d^16*e^5 + 2080*b^5*c^9*d^15*e^6 - 3248*b^6*c^8*d^14*e^7 + 3472*b^7*c^7*d^13*e^8 - 2576*b^8*c^6*d^12*e^9 + 1312*b^9*c^5*d^11*e^10 - 440*b^10*c^4*d^10*e^11 + 88*b^11*c^3*d^9*e^12 - 8*b^12*c^2*d^8*e^13 + 20256*a^2*b^2*c^10*d^14*e^7 - 38752*a^2*b^3*c^9*d^13*e^8 + 43904*a^2*b^4*c^8*d^12*e^9 - 27552*a^2*b^5*c^7*d^11*e^10 + 4928*a^2*b^6*c^6*d^10*e^11 + 5984*a^2*b^7*c^5*d^9*e^12 - 5088*a^2*b^8*c^4*d^8*e^13 + 1696*a^2*b^9*c^3*d^7*e^14 - 224*a^2*b^10*c^2*d^6*e^15 + 50848*a^3*b^2*c^9*d^12*e^9 - 83776*a^3*b^3*c^8*d^11*e^10 + 81312*a^3*b^4*c^7*d^10*e^11 - 44352*a^3*b^5*c^6*d^9*e^12 + 9184*a^3*b^6*c^5*d^8*e^13 + 3392*a^3*b^7*c^4*d^7*e^14 - 2464*a^3*b^8*c^3*d^6*e^15 + 448*a^3*b^9*c^2*d^5*e^16 + 67760*a^4*b^2*c^8*d^10*e^11 - 92400*a^4*b^3*c^7*d^9*e^12 + 72240*a^4*b^4*c^6*d^8*e^13 - 30240*a^4*b^5*c^5*d^7*e^14 + 3920*a^4*b^6*c^4*d^6*e^15 + 1680*a^4*b^7*c^3*d^5*e^16 - 560*a^4*b^8*c^2*d^4*e^17 + 50736*a^5*b^2*c^7*d^8*e^13 - 55104*a^5*b^3*c^6*d^7*e^14 + 32928*a^5*b^4*c^5*d^6*e^15 - 9408*a^5*b^5*c^4*d^5*e^16 + 112*a^5*b^6*c^3*d^4*e^17 + 448*a^5*b^7*c^2*d^3*e^18 + 20384*a^6*b^2*c^6*d^6*e^15 - 17248*a^6*b^3*c^5*d^5*e^16 + 7616*a^6*b^4*c^4*d^4*e^17 - 1120*a^6*b^5*c^3*d^3*e^18 - 224*a^6*b^6*c^2*d^2*e^19 + 3616*a^7*b^2*c^5*d^4*e^17 - 2752*a^7*b^3*c^4*d^3*e^18 + 864*a^7*b^4*c^3*d^2*e^19 + 168*a^8*b^2*c^4*d^2*e^19 - 864*a*b*c^12*d^17*e^4 + 160*a^9*b*c^4*d*e^20 + 3304*a*b^2*c^11*d^16*e^5 - 6848*a*b^3*c^10*d^15*e^6 + 7776*a*b^4*c^9*d^14*e^7 - 3136*a*b^5*c^8*d^13*e^8 - 3920*a*b^6*c^7*d^12*e^9 + 7296*a*b^7*c^6*d^11*e^10 - 5632*a*b^8*c^5*d^10*e^11 + 2464*a*b^9*c^4*d^9*e^12 - 600*a*b^10*c^3*d^8*e^13 + 64*a*b^11*c^2*d^7*e^14 - 5888*a^2*b*c^11*d^15*e^6 - 17024*a^3*b*c^10*d^13*e^8 - 26880*a^4*b*c^9*d^11*e^10 - 24640*a^5*b*c^8*d^9*e^12 - 12544*a^6*b*c^7*d^7*e^14 - 2688*a^7*b*c^6*d^5*e^16 + 64*a^7*b^5*c^2*d*e^20 + 256*a^8*b*c^5*d^3*e^18 - 296*a^8*b^3*c^3*d*e^20))*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*1i)/(((d + e*x)^(1/2)*(128*b*c^12*d^15*e^3 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 - 8*a^6*b^4*c^3*e^18 + 32*a^7*b^2*c^4*e^18 + 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14 - 480*b^2*c^11*d^14*e^4 + 1120*b^3*c^10*d^13*e^5 - 1800*b^4*c^9*d^12*e^6 + 2064*b^5*c^8*d^11*e^7 - 1688*b^6*c^7*d^10*e^8 + 960*b^7*c^6*d^9*e^9 - 360*b^8*c^5*d^8*e^10 + 80*b^9*c^4*d^7*e^11 - 8*b^10*c^3*d^6*e^12 + 4512*a^2*b^2*c^9*d^10*e^8 - 4960*a^2*b^3*c^8*d^9*e^9 + 1800*a^2*b^4*c^7*d^8*e^10 + 1440*a^2*b^5*c^6*d^7*e^11 - 1840*a^2*b^6*c^5*d^6*e^12 + 768*a^2*b^7*c^4*d^5*e^13 - 120*a^2*b^8*c^3*d^4*e^14 + 10080*a^3*b^2*c^8*d^8*e^10 - 9600*a^3*b^3*c^7*d^7*e^11 + 4000*a^3*b^4*c^6*d^6*e^12 + 96*a^3*b^5*c^5*d^5*e^13 - 640*a^3*b^6*c^4*d^4*e^14 + 160*a^3*b^7*c^3*d^3*e^15 + 8800*a^4*b^2*c^7*d^6*e^12 - 6240*a^4*b^3*c^6*d^5*e^13 + 1800*a^4*b^4*c^5*d^4*e^14 + 80*a^4*b^5*c^4*d^3*e^15 - 120*a^4*b^6*c^3*d^2*e^16 + 3360*a^5*b^2*c^6*d^4*e^14 - 1600*a^5*b^3*c^5*d^3*e^15 + 240*a^5*b^4*c^4*d^2*e^16 + 480*a^6*b^2*c^5*d^2*e^16 - 160*a*b^2*c^10*d^12*e^6 + 960*a*b^3*c^9*d^11*e^7 - 2448*a*b^4*c^8*d^10*e^8 + 3440*a*b^5*c^7*d^9*e^9 - 2880*a*b^6*c^6*d^8*e^10 + 1440*a*b^7*c^5*d^7*e^11 - 400*a*b^8*c^4*d^6*e^12 + 48*a*b^9*c^3*d^5*e^13 - 1920*a^2*b*c^10*d^11*e^7 - 5120*a^3*b*c^9*d^9*e^9 - 5760*a^4*b*c^8*d^7*e^11 - 3072*a^5*b*c^7*d^5*e^13 + 48*a^5*b^5*c^3*d*e^17 - 640*a^6*b*c^6*d^3*e^15 - 160*a^6*b^3*c^4*d*e^17) - ((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*((d + e*x)^(1/2)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*(64*a*c^14*d^21*e^2 - 32*a^11*b*c^3*e^23 + 64*a^11*c^4*d*e^22 + 8*a^10*b^3*c^2*e^23 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20 - 16*b^2*c^13*d^21*e^2 + 168*b^3*c^12*d^20*e^3 - 800*b^4*c^11*d^19*e^4 + 2280*b^5*c^10*d^18*e^5 - 4320*b^6*c^9*d^17*e^6 + 5712*b^7*c^8*d^16*e^7 - 5376*b^8*c^7*d^15*e^8 + 3600*b^9*c^6*d^14*e^9 - 1680*b^10*c^5*d^13*e^10 + 520*b^11*c^4*d^12*e^11 - 96*b^12*c^3*d^11*e^12 + 8*b^13*c^2*d^10*e^13 + 25200*a^2*b^2*c^11*d^17*e^6 - 59160*a^2*b^3*c^10*d^16*e^7 + 84480*a^2*b^4*c^9*d^15*e^8 - 70560*a^2*b^5*c^8*d^14*e^9 + 23520*a^2*b^6*c^7*d^13*e^10 + 15600*a^2*b^7*c^6*d^12*e^11 - 23040*a^2*b^8*c^5*d^11*e^12 + 12320*a^2*b^9*c^4*d^10*e^13 - 3280*a^2*b^10*c^3*d^9*e^14 + 360*a^2*b^11*c^2*d^8*e^15 + 90240*a^3*b^2*c^10*d^15*e^8 - 187200*a^3*b^3*c^9*d^14*e^9 + 235200*a^3*b^4*c^8*d^13*e^10 - 174720*a^3*b^5*c^7*d^12*e^11 + 60480*a^3*b^6*c^6*d^11*e^12 + 10560*a^3*b^7*c^5*d^10*e^13 - 19200*a^3*b^8*c^4*d^9*e^14 + 7200*a^3*b^9*c^3*d^8*e^15 - 960*a^3*b^10*c^2*d^7*e^16 + 184800*a^4*b^2*c^9*d^13*e^10 - 327600*a^4*b^3*c^8*d^12*e^11 + 342720*a^4*b^4*c^7*d^11*e^12 - 203280*a^4*b^5*c^6*d^10*e^13 + 50400*a^4*b^6*c^5*d^9*e^14 + 10800*a^4*b^7*c^4*d^8*e^15 - 9600*a^4*b^8*c^3*d^7*e^16 + 1680*a^4*b^9*c^2*d^6*e^17 + 237888*a^5*b^2*c^8*d^11*e^12 - 347424*a^5*b^3*c^7*d^10*e^13 + 285600*a^5*b^4*c^6*d^9*e^14 - 120960*a^5*b^5*c^5*d^8*e^15 + 13440*a^5*b^6*c^4*d^7*e^16 + 7392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^5*e^18 + 198240*a^6*b^2*c^7*d^9*e^14 - 226800*a^6*b^3*c^6*d^8*e^15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b^5*c^4*d^6*e^17 - 2016*a^6*b^6*c^3*d^5*e^18 + 1680*a^6*b^7*c^2*d^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*a^7*b^3*c^5*d^6*e^17 + 31680*a^7*b^4*c^4*d^5*e^18 - 1920*a^7*b^5*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 33840*a^8*b^2*c^5*d^5*e^18 - 17400*a^8*b^3*c^4*d^4*e^19 + 2400*a^8*b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 + 5600*a^9*b^2*c^4*d^3*e^20 - 1200*a^9*b^3*c^3*d^2*e^21 - 672*a*b*c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 7600*a*b^3*c^11*d^18*e^5 + 10800*a*b^4*c^10*d^17*e^6 - 6528*a*b^5*c^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*a*b^7*c^7*d^14*e^9 - 16800*a*b^8*c^6*d^13*e^10 + 10400*a*b^9*c^5*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a*b^11*c^3*d^10*e^13 - 80*a*b^12*c^2*d^9*e^14 - 6080*a^2*b*c^12*d^18*e^5 - 24480*a^3*b*c^11*d^16*e^7 - 57600*a^4*b*c^10*d^14*e^9 - 87360*a^5*b*c^9*d^12*e^11 - 88704*a^6*b*c^8*d^10*e^13 - 60480*a^7*b*c^7*d^8*e^15 - 26880*a^8*b*c^6*d^6*e^17 - 7200*a^9*b*c^5*d^4*e^19 - 80*a^9*b^4*c^2*d*e^22 - 960*a^10*b*c^4*d^2*e^21 + 304*a^10*b^2*c^3*d*e^22) - 32*a^10*c^4*e^21 + 96*a*c^13*d^18*e^3 - 8*a^8*b^4*c^2*e^21 + 40*a^9*b^2*c^3*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19 - 24*b^2*c^12*d^18*e^3 + 216*b^3*c^11*d^17*e^4 - 872*b^4*c^10*d^16*e^5 + 2080*b^5*c^9*d^15*e^6 - 3248*b^6*c^8*d^14*e^7 + 3472*b^7*c^7*d^13*e^8 - 2576*b^8*c^6*d^12*e^9 + 1312*b^9*c^5*d^11*e^10 - 440*b^10*c^4*d^10*e^11 + 88*b^11*c^3*d^9*e^12 - 8*b^12*c^2*d^8*e^13 + 20256*a^2*b^2*c^10*d^14*e^7 - 38752*a^2*b^3*c^9*d^13*e^8 + 43904*a^2*b^4*c^8*d^12*e^9 - 27552*a^2*b^5*c^7*d^11*e^10 + 4928*a^2*b^6*c^6*d^10*e^11 + 5984*a^2*b^7*c^5*d^9*e^12 - 5088*a^2*b^8*c^4*d^8*e^13 + 1696*a^2*b^9*c^3*d^7*e^14 - 224*a^2*b^10*c^2*d^6*e^15 + 50848*a^3*b^2*c^9*d^12*e^9 - 83776*a^3*b^3*c^8*d^11*e^10 + 81312*a^3*b^4*c^7*d^10*e^11 - 44352*a^3*b^5*c^6*d^9*e^12 + 9184*a^3*b^6*c^5*d^8*e^13 + 3392*a^3*b^7*c^4*d^7*e^14 - 2464*a^3*b^8*c^3*d^6*e^15 + 448*a^3*b^9*c^2*d^5*e^16 + 67760*a^4*b^2*c^8*d^10*e^11 - 92400*a^4*b^3*c^7*d^9*e^12 + 72240*a^4*b^4*c^6*d^8*e^13 - 30240*a^4*b^5*c^5*d^7*e^14 + 3920*a^4*b^6*c^4*d^6*e^15 + 1680*a^4*b^7*c^3*d^5*e^16 - 560*a^4*b^8*c^2*d^4*e^17 + 50736*a^5*b^2*c^7*d^8*e^13 - 55104*a^5*b^3*c^6*d^7*e^14 + 32928*a^5*b^4*c^5*d^6*e^15 - 9408*a^5*b^5*c^4*d^5*e^16 + 112*a^5*b^6*c^3*d^4*e^17 + 448*a^5*b^7*c^2*d^3*e^18 + 20384*a^6*b^2*c^6*d^6*e^15 - 17248*a^6*b^3*c^5*d^5*e^16 + 7616*a^6*b^4*c^4*d^4*e^17 - 1120*a^6*b^5*c^3*d^3*e^18 - 224*a^6*b^6*c^2*d^2*e^19 + 3616*a^7*b^2*c^5*d^4*e^17 - 2752*a^7*b^3*c^4*d^3*e^18 + 864*a^7*b^4*c^3*d^2*e^19 + 168*a^8*b^2*c^4*d^2*e^19 - 864*a*b*c^12*d^17*e^4 + 160*a^9*b*c^4*d*e^20 + 3304*a*b^2*c^11*d^16*e^5 - 6848*a*b^3*c^10*d^15*e^6 + 7776*a*b^4*c^9*d^14*e^7 - 3136*a*b^5*c^8*d^13*e^8 - 3920*a*b^6*c^7*d^12*e^9 + 7296*a*b^7*c^6*d^11*e^10 - 5632*a*b^8*c^5*d^10*e^11 + 2464*a*b^9*c^4*d^9*e^12 - 600*a*b^10*c^3*d^8*e^13 + 64*a*b^11*c^2*d^7*e^14 - 5888*a^2*b*c^11*d^15*e^6 - 17024*a^3*b*c^10*d^13*e^8 - 26880*a^4*b*c^9*d^11*e^10 - 24640*a^5*b*c^8*d^9*e^12 - 12544*a^6*b*c^7*d^7*e^14 - 2688*a^7*b*c^6*d^5*e^16 + 64*a^7*b^5*c^2*d*e^20 + 256*a^8*b*c^5*d^3*e^18 - 296*a^8*b^3*c^3*d*e^20))*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2) - ((d + e*x)^(1/2)*(128*b*c^12*d^15*e^3 - 16*c^13*d^16*e^2 - 16*a^8*c^5*e^18 - 8*a^6*b^4*c^3*e^18 + 32*a^7*b^2*c^4*e^18 + 320*a^2*c^11*d^12*e^6 + 1024*a^3*c^10*d^10*e^8 + 1440*a^4*c^9*d^8*e^10 + 1024*a^5*c^8*d^6*e^12 + 320*a^6*c^7*d^4*e^14 - 480*b^2*c^11*d^14*e^4 + 1120*b^3*c^10*d^13*e^5 - 1800*b^4*c^9*d^12*e^6 + 2064*b^5*c^8*d^11*e^7 - 1688*b^6*c^7*d^10*e^8 + 960*b^7*c^6*d^9*e^9 - 360*b^8*c^5*d^8*e^10 + 80*b^9*c^4*d^7*e^11 - 8*b^10*c^3*d^6*e^12 + 4512*a^2*b^2*c^9*d^10*e^8 - 4960*a^2*b^3*c^8*d^9*e^9 + 1800*a^2*b^4*c^7*d^8*e^10 + 1440*a^2*b^5*c^6*d^7*e^11 - 1840*a^2*b^6*c^5*d^6*e^12 + 768*a^2*b^7*c^4*d^5*e^13 - 120*a^2*b^8*c^3*d^4*e^14 + 10080*a^3*b^2*c^8*d^8*e^10 - 9600*a^3*b^3*c^7*d^7*e^11 + 4000*a^3*b^4*c^6*d^6*e^12 + 96*a^3*b^5*c^5*d^5*e^13 - 640*a^3*b^6*c^4*d^4*e^14 + 160*a^3*b^7*c^3*d^3*e^15 + 8800*a^4*b^2*c^7*d^6*e^12 - 6240*a^4*b^3*c^6*d^5*e^13 + 1800*a^4*b^4*c^5*d^4*e^14 + 80*a^4*b^5*c^4*d^3*e^15 - 120*a^4*b^6*c^3*d^2*e^16 + 3360*a^5*b^2*c^6*d^4*e^14 - 1600*a^5*b^3*c^5*d^3*e^15 + 240*a^5*b^4*c^4*d^2*e^16 + 480*a^6*b^2*c^5*d^2*e^16 - 160*a*b^2*c^10*d^12*e^6 + 960*a*b^3*c^9*d^11*e^7 - 2448*a*b^4*c^8*d^10*e^8 + 3440*a*b^5*c^7*d^9*e^9 - 2880*a*b^6*c^6*d^8*e^10 + 1440*a*b^7*c^5*d^7*e^11 - 400*a*b^8*c^4*d^6*e^12 + 48*a*b^9*c^3*d^5*e^13 - 1920*a^2*b*c^10*d^11*e^7 - 5120*a^3*b*c^9*d^9*e^9 - 5760*a^4*b*c^8*d^7*e^11 - 3072*a^5*b*c^7*d^5*e^13 + 48*a^5*b^5*c^3*d*e^17 - 640*a^6*b*c^6*d^3*e^15 - 160*a^6*b^3*c^4*d*e^17) + ((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*(96*a*c^13*d^18*e^3 - 32*a^10*c^4*e^21 - (d + e*x)^(1/2)*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*(64*a*c^14*d^21*e^2 - 32*a^11*b*c^3*e^23 + 64*a^11*c^4*d*e^22 + 8*a^10*b^3*c^2*e^23 + 640*a^2*c^13*d^19*e^4 + 2880*a^3*c^12*d^17*e^6 + 7680*a^4*c^11*d^15*e^8 + 13440*a^5*c^10*d^13*e^10 + 16128*a^6*c^9*d^11*e^12 + 13440*a^7*c^8*d^9*e^14 + 7680*a^8*c^7*d^7*e^16 + 2880*a^9*c^6*d^5*e^18 + 640*a^10*c^5*d^3*e^20 - 16*b^2*c^13*d^21*e^2 + 168*b^3*c^12*d^20*e^3 - 800*b^4*c^11*d^19*e^4 + 2280*b^5*c^10*d^18*e^5 - 4320*b^6*c^9*d^17*e^6 + 5712*b^7*c^8*d^16*e^7 - 5376*b^8*c^7*d^15*e^8 + 3600*b^9*c^6*d^14*e^9 - 1680*b^10*c^5*d^13*e^10 + 520*b^11*c^4*d^12*e^11 - 96*b^12*c^3*d^11*e^12 + 8*b^13*c^2*d^10*e^13 + 25200*a^2*b^2*c^11*d^17*e^6 - 59160*a^2*b^3*c^10*d^16*e^7 + 84480*a^2*b^4*c^9*d^15*e^8 - 70560*a^2*b^5*c^8*d^14*e^9 + 23520*a^2*b^6*c^7*d^13*e^10 + 15600*a^2*b^7*c^6*d^12*e^11 - 23040*a^2*b^8*c^5*d^11*e^12 + 12320*a^2*b^9*c^4*d^10*e^13 - 3280*a^2*b^10*c^3*d^9*e^14 + 360*a^2*b^11*c^2*d^8*e^15 + 90240*a^3*b^2*c^10*d^15*e^8 - 187200*a^3*b^3*c^9*d^14*e^9 + 235200*a^3*b^4*c^8*d^13*e^10 - 174720*a^3*b^5*c^7*d^12*e^11 + 60480*a^3*b^6*c^6*d^11*e^12 + 10560*a^3*b^7*c^5*d^10*e^13 - 19200*a^3*b^8*c^4*d^9*e^14 + 7200*a^3*b^9*c^3*d^8*e^15 - 960*a^3*b^10*c^2*d^7*e^16 + 184800*a^4*b^2*c^9*d^13*e^10 - 327600*a^4*b^3*c^8*d^12*e^11 + 342720*a^4*b^4*c^7*d^11*e^12 - 203280*a^4*b^5*c^6*d^10*e^13 + 50400*a^4*b^6*c^5*d^9*e^14 + 10800*a^4*b^7*c^4*d^8*e^15 - 9600*a^4*b^8*c^3*d^7*e^16 + 1680*a^4*b^9*c^2*d^6*e^17 + 237888*a^5*b^2*c^8*d^11*e^12 - 347424*a^5*b^3*c^7*d^10*e^13 + 285600*a^5*b^4*c^6*d^9*e^14 - 120960*a^5*b^5*c^5*d^8*e^15 + 13440*a^5*b^6*c^4*d^7*e^16 + 7392*a^5*b^7*c^3*d^6*e^17 - 2016*a^5*b^8*c^2*d^5*e^18 + 198240*a^6*b^2*c^7*d^9*e^14 - 226800*a^6*b^3*c^6*d^8*e^15 + 134400*a^6*b^4*c^5*d^7*e^16 - 32928*a^6*b^5*c^4*d^6*e^17 - 2016*a^6*b^6*c^3*d^5*e^18 + 1680*a^6*b^7*c^2*d^4*e^19 + 105600*a^7*b^2*c^6*d^7*e^16 - 87360*a^7*b^3*c^5*d^6*e^17 + 31680*a^7*b^4*c^4*d^5*e^18 - 1920*a^7*b^5*c^3*d^4*e^19 - 960*a^7*b^6*c^2*d^3*e^20 + 33840*a^8*b^2*c^5*d^5*e^18 - 17400*a^8*b^3*c^4*d^4*e^19 + 2400*a^8*b^4*c^3*d^3*e^20 + 360*a^8*b^5*c^2*d^2*e^21 + 5600*a^9*b^2*c^4*d^3*e^20 - 1200*a^9*b^3*c^3*d^2*e^21 - 672*a*b*c^13*d^20*e^3 + 3040*a*b^2*c^12*d^19*e^4 - 7600*a*b^3*c^11*d^18*e^5 + 10800*a*b^4*c^10*d^17*e^6 - 6528*a*b^5*c^9*d^16*e^7 - 5376*a*b^6*c^8*d^15*e^8 + 15840*a*b^7*c^7*d^14*e^9 - 16800*a*b^8*c^6*d^13*e^10 + 10400*a*b^9*c^5*d^12*e^11 - 3936*a*b^10*c^4*d^11*e^12 + 848*a*b^11*c^3*d^10*e^13 - 80*a*b^12*c^2*d^9*e^14 - 6080*a^2*b*c^12*d^18*e^5 - 24480*a^3*b*c^11*d^16*e^7 - 57600*a^4*b*c^10*d^14*e^9 - 87360*a^5*b*c^9*d^12*e^11 - 88704*a^6*b*c^8*d^10*e^13 - 60480*a^7*b*c^7*d^8*e^15 - 26880*a^8*b*c^6*d^6*e^17 - 7200*a^9*b*c^5*d^4*e^19 - 80*a^9*b^4*c^2*d*e^22 - 960*a^10*b*c^4*d^2*e^21 + 304*a^10*b^2*c^3*d*e^22) - 8*a^8*b^4*c^2*e^21 + 40*a^9*b^2*c^3*e^21 + 736*a^2*c^12*d^16*e^5 + 2432*a^3*c^11*d^14*e^7 + 4480*a^4*c^10*d^12*e^9 + 4928*a^5*c^9*d^10*e^11 + 3136*a^6*c^8*d^8*e^13 + 896*a^7*c^7*d^6*e^15 - 128*a^8*c^6*d^4*e^17 - 160*a^9*c^5*d^2*e^19 - 24*b^2*c^12*d^18*e^3 + 216*b^3*c^11*d^17*e^4 - 872*b^4*c^10*d^16*e^5 + 2080*b^5*c^9*d^15*e^6 - 3248*b^6*c^8*d^14*e^7 + 3472*b^7*c^7*d^13*e^8 - 2576*b^8*c^6*d^12*e^9 + 1312*b^9*c^5*d^11*e^10 - 440*b^10*c^4*d^10*e^11 + 88*b^11*c^3*d^9*e^12 - 8*b^12*c^2*d^8*e^13 + 20256*a^2*b^2*c^10*d^14*e^7 - 38752*a^2*b^3*c^9*d^13*e^8 + 43904*a^2*b^4*c^8*d^12*e^9 - 27552*a^2*b^5*c^7*d^11*e^10 + 4928*a^2*b^6*c^6*d^10*e^11 + 5984*a^2*b^7*c^5*d^9*e^12 - 5088*a^2*b^8*c^4*d^8*e^13 + 1696*a^2*b^9*c^3*d^7*e^14 - 224*a^2*b^10*c^2*d^6*e^15 + 50848*a^3*b^2*c^9*d^12*e^9 - 83776*a^3*b^3*c^8*d^11*e^10 + 81312*a^3*b^4*c^7*d^10*e^11 - 44352*a^3*b^5*c^6*d^9*e^12 + 9184*a^3*b^6*c^5*d^8*e^13 + 3392*a^3*b^7*c^4*d^7*e^14 - 2464*a^3*b^8*c^3*d^6*e^15 + 448*a^3*b^9*c^2*d^5*e^16 + 67760*a^4*b^2*c^8*d^10*e^11 - 92400*a^4*b^3*c^7*d^9*e^12 + 72240*a^4*b^4*c^6*d^8*e^13 - 30240*a^4*b^5*c^5*d^7*e^14 + 3920*a^4*b^6*c^4*d^6*e^15 + 1680*a^4*b^7*c^3*d^5*e^16 - 560*a^4*b^8*c^2*d^4*e^17 + 50736*a^5*b^2*c^7*d^8*e^13 - 55104*a^5*b^3*c^6*d^7*e^14 + 32928*a^5*b^4*c^5*d^6*e^15 - 9408*a^5*b^5*c^4*d^5*e^16 + 112*a^5*b^6*c^3*d^4*e^17 + 448*a^5*b^7*c^2*d^3*e^18 + 20384*a^6*b^2*c^6*d^6*e^15 - 17248*a^6*b^3*c^5*d^5*e^16 + 7616*a^6*b^4*c^4*d^4*e^17 - 1120*a^6*b^5*c^3*d^3*e^18 - 224*a^6*b^6*c^2*d^2*e^19 + 3616*a^7*b^2*c^5*d^4*e^17 - 2752*a^7*b^3*c^4*d^3*e^18 + 864*a^7*b^4*c^3*d^2*e^19 + 168*a^8*b^2*c^4*d^2*e^19 - 864*a*b*c^12*d^17*e^4 + 160*a^9*b*c^4*d*e^20 + 3304*a*b^2*c^11*d^16*e^5 - 6848*a*b^3*c^10*d^15*e^6 + 7776*a*b^4*c^9*d^14*e^7 - 3136*a*b^5*c^8*d^13*e^8 - 3920*a*b^6*c^7*d^12*e^9 + 7296*a*b^7*c^6*d^11*e^10 - 5632*a*b^8*c^5*d^10*e^11 + 2464*a*b^9*c^4*d^9*e^12 - 600*a*b^10*c^3*d^8*e^13 + 64*a*b^11*c^2*d^7*e^14 - 5888*a^2*b*c^11*d^15*e^6 - 17024*a^3*b*c^10*d^13*e^8 - 26880*a^4*b*c^9*d^11*e^10 - 24640*a^5*b*c^8*d^9*e^12 - 12544*a^6*b*c^7*d^7*e^14 - 2688*a^7*b*c^6*d^5*e^16 + 64*a^7*b^5*c^2*d*e^20 + 256*a^8*b*c^5*d^3*e^18 - 296*a^8*b^3*c^3*d*e^20))*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2) + 32*c^12*d^13*e^3 - 16*a^6*b*c^5*e^16 + 192*a*c^11*d^11*e^5 + 32*a^6*c^6*d*e^15 - 208*b*c^11*d^12*e^4 + 480*a^2*c^10*d^9*e^7 + 640*a^3*c^9*d^7*e^9 + 480*a^4*c^8*d^5*e^11 + 192*a^5*c^7*d^3*e^13 + 576*b^2*c^10*d^11*e^5 - 880*b^3*c^9*d^10*e^6 + 800*b^4*c^8*d^9*e^7 - 432*b^5*c^7*d^8*e^8 + 128*b^6*c^6*d^7*e^9 - 16*b^7*c^5*d^6*e^10 + 3840*a^2*b^2*c^8*d^7*e^9 - 3360*a^2*b^3*c^7*d^6*e^10 + 1440*a^2*b^4*c^6*d^5*e^11 - 240*a^2*b^5*c^5*d^4*e^12 + 2880*a^3*b^2*c^7*d^5*e^11 - 1600*a^3*b^3*c^6*d^4*e^12 + 320*a^3*b^4*c^5*d^3*e^13 + 960*a^4*b^2*c^6*d^3*e^13 - 240*a^4*b^3*c^5*d^2*e^14 - 1056*a*b*c^10*d^10*e^6 + 2400*a*b^2*c^9*d^9*e^7 - 2880*a*b^3*c^8*d^8*e^8 + 1920*a*b^4*c^7*d^7*e^9 - 672*a*b^5*c^6*d^6*e^10 + 96*a*b^6*c^5*d^5*e^11 - 2160*a^2*b*c^9*d^8*e^8 - 2240*a^3*b*c^8*d^6*e^10 - 1200*a^4*b*c^7*d^4*e^12 - 288*a^5*b*c^6*d^2*e^14 + 96*a^5*b^2*c^5*d*e^15))*((2*b^2*c^5*d^5 - 8*a*c^6*d^5 - b^7*e^5 + b^4*e^5*(-(4*a*c - b^2)^3)^(1/2) + 20*a^3*b*c^3*e^5 - 40*a^3*c^4*d*e^4 - 5*b^3*c^4*d^4*e + 5*c^4*d^4*e*(-(4*a*c - b^2)^3)^(1/2) - 25*a^2*b^3*c^2*e^5 + a^2*c^2*e^5*(-(4*a*c - b^2)^3)^(1/2) + 80*a^2*c^5*d^3*e^2 + 10*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 + 9*a*b^5*c*e^5 + 5*b^6*c*d*e^4 + 20*a*b*c^5*d^4*e + 10*b^2*c^2*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 3*a*b^2*c*e^5*(-(4*a*c - b^2)^3)^(1/2) - 40*a*b^4*c^2*d*e^4 - 5*b^3*c*d*e^4*(-(4*a*c - b^2)^3)^(1/2) - 60*a*b^2*c^4*d^3*e^2 + 70*a*b^3*c^3*d^2*e^3 - 120*a^2*b*c^4*d^2*e^3 + 90*a^2*b^2*c^3*d*e^4 - 10*a*c^3*d^2*e^3*(-(4*a*c - b^2)^3)^(1/2) - 10*b*c^3*d^3*e^2*(-(4*a*c - b^2)^3)^(1/2) + 10*a*b*c^2*d*e^4*(-(4*a*c - b^2)^3)^(1/2))/(2*(16*a^2*c^7*d^10 + a^5*b^4*e^10 + 16*a^7*c^2*e^10 + b^4*c^5*d^10 - b^9*d^5*e^5 - 8*a*b^2*c^6*d^10 - 8*a^6*b^2*c*e^10 + 5*a*b^8*d^4*e^6 - 5*a^4*b^5*d*e^9 - 5*b^5*c^4*d^9*e + 5*b^8*c*d^6*e^4 - 10*a^2*b^7*d^3*e^7 + 10*a^3*b^6*d^2*e^8 + 80*a^3*c^6*d^8*e^2 + 160*a^4*c^5*d^6*e^4 + 160*a^5*c^4*d^4*e^6 + 80*a^6*c^3*d^2*e^8 + 10*b^6*c^3*d^8*e^2 - 10*b^7*c^2*d^7*e^3 + 120*a^2*b^2*c^5*d^8*e^2 - 150*a^2*b^4*c^3*d^6*e^4 + 114*a^2*b^5*c^2*d^5*e^5 + 400*a^3*b^2*c^4*d^6*e^4 - 80*a^3*b^3*c^3*d^5*e^5 - 150*a^3*b^4*c^2*d^4*e^6 + 400*a^4*b^2*c^3*d^4*e^6 + 120*a^5*b^2*c^2*d^2*e^8 + 40*a*b^3*c^5*d^9*e - 12*a*b^7*c*d^5*e^5 - 80*a^2*b*c^6*d^9*e + 40*a^5*b^3*c*d*e^9 - 80*a^6*b*c^2*d*e^9 - 75*a*b^4*c^4*d^8*e^2 + 60*a*b^5*c^3*d^7*e^3 - 10*a*b^6*c^2*d^6*e^4 - 10*a^2*b^6*c*d^4*e^6 - 320*a^3*b*c^5*d^7*e^3 + 60*a^3*b^5*c*d^3*e^7 - 480*a^4*b*c^4*d^5*e^5 - 75*a^4*b^4*c*d^2*e^8 - 320*a^5*b*c^3*d^3*e^7)))^(1/2)*2i - ((2*e)/(3*(a*e^2 + c*d^2 - b*d*e)) - (2*e*(b*e - 2*c*d)*(d + e*x))/(a*e^2 + c*d^2 - b*d*e)^2)/(d + e*x)^(3/2)","B"
2295,1,32541,691,3.883754,"\text{Not used}","int((d + e*x)^(7/2)/(a + b*x + c*x^2)^2,x)","-\frac{\frac{\sqrt{d+e\,x}\,\left(-2\,a^2\,c\,e^5+a\,b^2\,e^5-b^3\,d\,e^4+3\,b^2\,c\,d^2\,e^3-4\,b\,c^2\,d^3\,e^2+2\,c^3\,d^4\,e\right)}{4\,a\,c-b^2}+\frac{{\left(d+e\,x\right)}^{3/2}\,\left(b^3\,e^4-3\,b^2\,c\,d\,e^3+3\,b\,c^2\,d^2\,e^2-3\,a\,b\,c\,e^4-2\,c^3\,d^3\,e+6\,a\,c^2\,d\,e^3\right)}{4\,a\,c-b^2}}{c^3\,{\left(d+e\,x\right)}^2-\left(2\,c^3\,d-b\,c^2\,e\right)\,\left(d+e\,x\right)+c^3\,d^2+a\,c^2\,e^2-b\,c^2\,d\,e}-\mathrm{atan}\left(\frac{\left(\left(\frac{2560\,a^5\,c^7\,e^7-2688\,a^4\,b^2\,c^6\,e^7-2048\,a^4\,b\,c^7\,d\,e^6+2048\,a^4\,c^8\,d^2\,e^5+1056\,a^3\,b^4\,c^5\,e^7+2304\,a^3\,b^3\,c^6\,d\,e^6-2816\,a^3\,b^2\,c^7\,d^2\,e^5+1024\,a^3\,b\,c^8\,d^3\,e^4-512\,a^3\,c^9\,d^4\,e^3-184\,a^2\,b^6\,c^4\,e^7-960\,a^2\,b^5\,c^5\,d\,e^6+1344\,a^2\,b^4\,c^6\,d^2\,e^5-768\,a^2\,b^3\,c^7\,d^3\,e^4+384\,a^2\,b^2\,c^8\,d^4\,e^3+12\,a\,b^8\,c^3\,e^7+176\,a\,b^7\,c^4\,d\,e^6-272\,a\,b^6\,c^5\,d^2\,e^5+192\,a\,b^5\,c^6\,d^3\,e^4-96\,a\,b^4\,c^7\,d^4\,e^3-12\,b^9\,c^3\,d\,e^6+20\,b^8\,c^4\,d^2\,e^5-16\,b^7\,c^5\,d^3\,e^4+8\,b^6\,c^6\,d^4\,e^3}{64\,a^3\,c^6-48\,a^2\,b^2\,c^5+12\,a\,b^4\,c^4-b^6\,c^3}-\frac{2\,\sqrt{d+e\,x}\,\sqrt{\frac{32\,b^6\,c^7\,d^7-2048\,a^3\,c^{10}\,d^7-9\,b^{13}\,e^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^8\,d^7-26880\,a^6\,b\,c^6\,e^7+53760\,a^6\,c^7\,d\,e^6-112\,b^7\,c^6\,d^6\,e+1536\,a^2\,b^2\,c^9\,d^7-2077\,a^2\,b^9\,c^2\,e^7+10656\,a^3\,b^7\,c^3\,e^7-30240\,a^4\,b^5\,c^4\,e^7+44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-17920\,a^4\,c^9\,d^5\,e^2-35840\,a^5\,c^8\,d^3\,e^4+98\,b^8\,c^5\,d^5\,e^2+35\,b^9\,c^4\,d^4\,e^3-70\,b^{10}\,c^3\,d^3\,e^4+14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+213\,a\,b^{11}\,c\,e^7+21\,b^{12}\,c\,d\,e^6+1344\,a^2\,b^4\,c^7\,d^5\,e^2+10080\,a^2\,b^5\,c^6\,d^4\,e^3-7840\,a^2\,b^6\,c^5\,d^3\,e^4-1008\,a^2\,b^7\,c^4\,d^2\,e^5+7168\,a^3\,b^2\,c^8\,d^5\,e^2-35840\,a^3\,b^3\,c^7\,d^4\,e^3+17920\,a^3\,b^4\,c^6\,d^3\,e^4+12544\,a^3\,b^5\,c^5\,d^2\,e^5-44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+1344\,a\,b^5\,c^7\,d^6\,e-532\,a\,b^{10}\,c^2\,d\,e^6+7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-896\,a\,b^6\,c^6\,d^5\,e^2-1120\,a\,b^7\,c^5\,d^4\,e^3+1260\,a\,b^8\,c^4\,d^3\,e^4-98\,a\,b^9\,c^3\,d^2\,e^5-5376\,a^2\,b^3\,c^8\,d^6\,e+5418\,a^2\,b^8\,c^3\,d\,e^6-28224\,a^3\,b^6\,c^4\,d\,e^6+44800\,a^4\,b\,c^8\,d^4\,e^3+78400\,a^4\,b^4\,c^5\,d\,e^6+53760\,a^5\,b\,c^7\,d^2\,e^5-107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}\,\left(-256\,a^3\,b\,c^8\,e^3+512\,d\,a^3\,c^9\,e^2+192\,a^2\,b^3\,c^7\,e^3-384\,d\,a^2\,b^2\,c^8\,e^2-48\,a\,b^5\,c^6\,e^3+96\,d\,a\,b^4\,c^7\,e^2+4\,b^7\,c^5\,e^3-8\,d\,b^6\,c^6\,e^2\right)}{16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3}\right)\,\sqrt{\frac{32\,b^6\,c^7\,d^7-2048\,a^3\,c^{10}\,d^7-9\,b^{13}\,e^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^8\,d^7-26880\,a^6\,b\,c^6\,e^7+53760\,a^6\,c^7\,d\,e^6-112\,b^7\,c^6\,d^6\,e+1536\,a^2\,b^2\,c^9\,d^7-2077\,a^2\,b^9\,c^2\,e^7+10656\,a^3\,b^7\,c^3\,e^7-30240\,a^4\,b^5\,c^4\,e^7+44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-17920\,a^4\,c^9\,d^5\,e^2-35840\,a^5\,c^8\,d^3\,e^4+98\,b^8\,c^5\,d^5\,e^2+35\,b^9\,c^4\,d^4\,e^3-70\,b^{10}\,c^3\,d^3\,e^4+14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+213\,a\,b^{11}\,c\,e^7+21\,b^{12}\,c\,d\,e^6+1344\,a^2\,b^4\,c^7\,d^5\,e^2+10080\,a^2\,b^5\,c^6\,d^4\,e^3-7840\,a^2\,b^6\,c^5\,d^3\,e^4-1008\,a^2\,b^7\,c^4\,d^2\,e^5+7168\,a^3\,b^2\,c^8\,d^5\,e^2-35840\,a^3\,b^3\,c^7\,d^4\,e^3+17920\,a^3\,b^4\,c^6\,d^3\,e^4+12544\,a^3\,b^5\,c^5\,d^2\,e^5-44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+1344\,a\,b^5\,c^7\,d^6\,e-532\,a\,b^{10}\,c^2\,d\,e^6+7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-896\,a\,b^6\,c^6\,d^5\,e^2-1120\,a\,b^7\,c^5\,d^4\,e^3+1260\,a\,b^8\,c^4\,d^3\,e^4-98\,a\,b^9\,c^3\,d^2\,e^5-5376\,a^2\,b^3\,c^8\,d^6\,e+5418\,a^2\,b^8\,c^3\,d\,e^6-28224\,a^3\,b^6\,c^4\,d\,e^6+44800\,a^4\,b\,c^8\,d^4\,e^3+78400\,a^4\,b^4\,c^5\,d\,e^6+53760\,a^5\,b\,c^7\,d^2\,e^5-107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}-\frac{2\,\sqrt{d+e\,x}\,\left(200\,a^4\,c^4\,e^{10}-718\,a^3\,b^2\,c^3\,e^{10}+2072\,a^3\,b\,c^4\,d\,e^9-2072\,a^3\,c^5\,d^2\,e^8+481\,a^2\,b^4\,c^2\,e^{10}-1694\,a^2\,b^3\,c^3\,d\,e^9+1974\,a^2\,b^2\,c^4\,d^2\,e^8-560\,a^2\,b\,c^5\,d^3\,e^7+280\,a^2\,c^6\,d^4\,e^6-114\,a\,b^6\,c\,e^{10}+406\,a\,b^5\,c^2\,d\,e^9-336\,a\,b^4\,c^3\,d^2\,e^8-420\,a\,b^3\,c^4\,d^3\,e^7+910\,a\,b^2\,c^5\,d^4\,e^6-840\,a\,b\,c^6\,d^5\,e^5+280\,a\,c^7\,d^6\,e^4+9\,b^8\,e^{10}-30\,b^7\,c\,d\,e^9+7\,b^6\,c^2\,d^2\,e^8+84\,b^5\,c^3\,d^3\,e^7-105\,b^4\,c^4\,d^4\,e^6-14\,b^3\,c^5\,d^5\,e^5+154\,b^2\,c^6\,d^6\,e^4-128\,b\,c^7\,d^7\,e^3+32\,c^8\,d^8\,e^2\right)}{16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3}\right)\,\sqrt{\frac{32\,b^6\,c^7\,d^7-2048\,a^3\,c^{10}\,d^7-9\,b^{13}\,e^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^8\,d^7-26880\,a^6\,b\,c^6\,e^7+53760\,a^6\,c^7\,d\,e^6-112\,b^7\,c^6\,d^6\,e+1536\,a^2\,b^2\,c^9\,d^7-2077\,a^2\,b^9\,c^2\,e^7+10656\,a^3\,b^7\,c^3\,e^7-30240\,a^4\,b^5\,c^4\,e^7+44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-17920\,a^4\,c^9\,d^5\,e^2-35840\,a^5\,c^8\,d^3\,e^4+98\,b^8\,c^5\,d^5\,e^2+35\,b^9\,c^4\,d^4\,e^3-70\,b^{10}\,c^3\,d^3\,e^4+14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+213\,a\,b^{11}\,c\,e^7+21\,b^{12}\,c\,d\,e^6+1344\,a^2\,b^4\,c^7\,d^5\,e^2+10080\,a^2\,b^5\,c^6\,d^4\,e^3-7840\,a^2\,b^6\,c^5\,d^3\,e^4-1008\,a^2\,b^7\,c^4\,d^2\,e^5+7168\,a^3\,b^2\,c^8\,d^5\,e^2-35840\,a^3\,b^3\,c^7\,d^4\,e^3+17920\,a^3\,b^4\,c^6\,d^3\,e^4+12544\,a^3\,b^5\,c^5\,d^2\,e^5-44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+1344\,a\,b^5\,c^7\,d^6\,e-532\,a\,b^{10}\,c^2\,d\,e^6+7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-896\,a\,b^6\,c^6\,d^5\,e^2-1120\,a\,b^7\,c^5\,d^4\,e^3+1260\,a\,b^8\,c^4\,d^3\,e^4-98\,a\,b^9\,c^3\,d^2\,e^5-5376\,a^2\,b^3\,c^8\,d^6\,e+5418\,a^2\,b^8\,c^3\,d\,e^6-28224\,a^3\,b^6\,c^4\,d\,e^6+44800\,a^4\,b\,c^8\,d^4\,e^3+78400\,a^4\,b^4\,c^5\,d\,e^6+53760\,a^5\,b\,c^7\,d^2\,e^5-107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}\,1{}\mathrm{i}-\left(\left(\frac{2560\,a^5\,c^7\,e^7-2688\,a^4\,b^2\,c^6\,e^7-2048\,a^4\,b\,c^7\,d\,e^6+2048\,a^4\,c^8\,d^2\,e^5+1056\,a^3\,b^4\,c^5\,e^7+2304\,a^3\,b^3\,c^6\,d\,e^6-2816\,a^3\,b^2\,c^7\,d^2\,e^5+1024\,a^3\,b\,c^8\,d^3\,e^4-512\,a^3\,c^9\,d^4\,e^3-184\,a^2\,b^6\,c^4\,e^7-960\,a^2\,b^5\,c^5\,d\,e^6+1344\,a^2\,b^4\,c^6\,d^2\,e^5-768\,a^2\,b^3\,c^7\,d^3\,e^4+384\,a^2\,b^2\,c^8\,d^4\,e^3+12\,a\,b^8\,c^3\,e^7+176\,a\,b^7\,c^4\,d\,e^6-272\,a\,b^6\,c^5\,d^2\,e^5+192\,a\,b^5\,c^6\,d^3\,e^4-96\,a\,b^4\,c^7\,d^4\,e^3-12\,b^9\,c^3\,d\,e^6+20\,b^8\,c^4\,d^2\,e^5-16\,b^7\,c^5\,d^3\,e^4+8\,b^6\,c^6\,d^4\,e^3}{64\,a^3\,c^6-48\,a^2\,b^2\,c^5+12\,a\,b^4\,c^4-b^6\,c^3}+\frac{2\,\sqrt{d+e\,x}\,\sqrt{\frac{32\,b^6\,c^7\,d^7-2048\,a^3\,c^{10}\,d^7-9\,b^{13}\,e^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^8\,d^7-26880\,a^6\,b\,c^6\,e^7+53760\,a^6\,c^7\,d\,e^6-112\,b^7\,c^6\,d^6\,e+1536\,a^2\,b^2\,c^9\,d^7-2077\,a^2\,b^9\,c^2\,e^7+10656\,a^3\,b^7\,c^3\,e^7-30240\,a^4\,b^5\,c^4\,e^7+44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-17920\,a^4\,c^9\,d^5\,e^2-35840\,a^5\,c^8\,d^3\,e^4+98\,b^8\,c^5\,d^5\,e^2+35\,b^9\,c^4\,d^4\,e^3-70\,b^{10}\,c^3\,d^3\,e^4+14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+213\,a\,b^{11}\,c\,e^7+21\,b^{12}\,c\,d\,e^6+1344\,a^2\,b^4\,c^7\,d^5\,e^2+10080\,a^2\,b^5\,c^6\,d^4\,e^3-7840\,a^2\,b^6\,c^5\,d^3\,e^4-1008\,a^2\,b^7\,c^4\,d^2\,e^5+7168\,a^3\,b^2\,c^8\,d^5\,e^2-35840\,a^3\,b^3\,c^7\,d^4\,e^3+17920\,a^3\,b^4\,c^6\,d^3\,e^4+12544\,a^3\,b^5\,c^5\,d^2\,e^5-44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+1344\,a\,b^5\,c^7\,d^6\,e-532\,a\,b^{10}\,c^2\,d\,e^6+7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-896\,a\,b^6\,c^6\,d^5\,e^2-1120\,a\,b^7\,c^5\,d^4\,e^3+1260\,a\,b^8\,c^4\,d^3\,e^4-98\,a\,b^9\,c^3\,d^2\,e^5-5376\,a^2\,b^3\,c^8\,d^6\,e+5418\,a^2\,b^8\,c^3\,d\,e^6-28224\,a^3\,b^6\,c^4\,d\,e^6+44800\,a^4\,b\,c^8\,d^4\,e^3+78400\,a^4\,b^4\,c^5\,d\,e^6+53760\,a^5\,b\,c^7\,d^2\,e^5-107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}\,\left(-256\,a^3\,b\,c^8\,e^3+512\,d\,a^3\,c^9\,e^2+192\,a^2\,b^3\,c^7\,e^3-384\,d\,a^2\,b^2\,c^8\,e^2-48\,a\,b^5\,c^6\,e^3+96\,d\,a\,b^4\,c^7\,e^2+4\,b^7\,c^5\,e^3-8\,d\,b^6\,c^6\,e^2\right)}{16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3}\right)\,\sqrt{\frac{32\,b^6\,c^7\,d^7-2048\,a^3\,c^{10}\,d^7-9\,b^{13}\,e^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^8\,d^7-26880\,a^6\,b\,c^6\,e^7+53760\,a^6\,c^7\,d\,e^6-112\,b^7\,c^6\,d^6\,e+1536\,a^2\,b^2\,c^9\,d^7-2077\,a^2\,b^9\,c^2\,e^7+10656\,a^3\,b^7\,c^3\,e^7-30240\,a^4\,b^5\,c^4\,e^7+44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-17920\,a^4\,c^9\,d^5\,e^2-35840\,a^5\,c^8\,d^3\,e^4+98\,b^8\,c^5\,d^5\,e^2+35\,b^9\,c^4\,d^4\,e^3-70\,b^{10}\,c^3\,d^3\,e^4+14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+213\,a\,b^{11}\,c\,e^7+21\,b^{12}\,c\,d\,e^6+1344\,a^2\,b^4\,c^7\,d^5\,e^2+10080\,a^2\,b^5\,c^6\,d^4\,e^3-7840\,a^2\,b^6\,c^5\,d^3\,e^4-1008\,a^2\,b^7\,c^4\,d^2\,e^5+7168\,a^3\,b^2\,c^8\,d^5\,e^2-35840\,a^3\,b^3\,c^7\,d^4\,e^3+17920\,a^3\,b^4\,c^6\,d^3\,e^4+12544\,a^3\,b^5\,c^5\,d^2\,e^5-44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+1344\,a\,b^5\,c^7\,d^6\,e-532\,a\,b^{10}\,c^2\,d\,e^6+7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-896\,a\,b^6\,c^6\,d^5\,e^2-1120\,a\,b^7\,c^5\,d^4\,e^3+1260\,a\,b^8\,c^4\,d^3\,e^4-98\,a\,b^9\,c^3\,d^2\,e^5-5376\,a^2\,b^3\,c^8\,d^6\,e+5418\,a^2\,b^8\,c^3\,d\,e^6-28224\,a^3\,b^6\,c^4\,d\,e^6+44800\,a^4\,b\,c^8\,d^4\,e^3+78400\,a^4\,b^4\,c^5\,d\,e^6+53760\,a^5\,b\,c^7\,d^2\,e^5-107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}+\frac{2\,\sqrt{d+e\,x}\,\left(200\,a^4\,c^4\,e^{10}-718\,a^3\,b^2\,c^3\,e^{10}+2072\,a^3\,b\,c^4\,d\,e^9-2072\,a^3\,c^5\,d^2\,e^8+481\,a^2\,b^4\,c^2\,e^{10}-1694\,a^2\,b^3\,c^3\,d\,e^9+1974\,a^2\,b^2\,c^4\,d^2\,e^8-560\,a^2\,b\,c^5\,d^3\,e^7+280\,a^2\,c^6\,d^4\,e^6-114\,a\,b^6\,c\,e^{10}+406\,a\,b^5\,c^2\,d\,e^9-336\,a\,b^4\,c^3\,d^2\,e^8-420\,a\,b^3\,c^4\,d^3\,e^7+910\,a\,b^2\,c^5\,d^4\,e^6-840\,a\,b\,c^6\,d^5\,e^5+280\,a\,c^7\,d^6\,e^4+9\,b^8\,e^{10}-30\,b^7\,c\,d\,e^9+7\,b^6\,c^2\,d^2\,e^8+84\,b^5\,c^3\,d^3\,e^7-105\,b^4\,c^4\,d^4\,e^6-14\,b^3\,c^5\,d^5\,e^5+154\,b^2\,c^6\,d^6\,e^4-128\,b\,c^7\,d^7\,e^3+32\,c^8\,d^8\,e^2\right)}{16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3}\right)\,\sqrt{\frac{32\,b^6\,c^7\,d^7-2048\,a^3\,c^{10}\,d^7-9\,b^{13}\,e^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^8\,d^7-26880\,a^6\,b\,c^6\,e^7+53760\,a^6\,c^7\,d\,e^6-112\,b^7\,c^6\,d^6\,e+1536\,a^2\,b^2\,c^9\,d^7-2077\,a^2\,b^9\,c^2\,e^7+10656\,a^3\,b^7\,c^3\,e^7-30240\,a^4\,b^5\,c^4\,e^7+44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-17920\,a^4\,c^9\,d^5\,e^2-35840\,a^5\,c^8\,d^3\,e^4+98\,b^8\,c^5\,d^5\,e^2+35\,b^9\,c^4\,d^4\,e^3-70\,b^{10}\,c^3\,d^3\,e^4+14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+213\,a\,b^{11}\,c\,e^7+21\,b^{12}\,c\,d\,e^6+1344\,a^2\,b^4\,c^7\,d^5\,e^2+10080\,a^2\,b^5\,c^6\,d^4\,e^3-7840\,a^2\,b^6\,c^5\,d^3\,e^4-1008\,a^2\,b^7\,c^4\,d^2\,e^5+7168\,a^3\,b^2\,c^8\,d^5\,e^2-35840\,a^3\,b^3\,c^7\,d^4\,e^3+17920\,a^3\,b^4\,c^6\,d^3\,e^4+12544\,a^3\,b^5\,c^5\,d^2\,e^5-44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+1344\,a\,b^5\,c^7\,d^6\,e-532\,a\,b^{10}\,c^2\,d\,e^6+7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-896\,a\,b^6\,c^6\,d^5\,e^2-1120\,a\,b^7\,c^5\,d^4\,e^3+1260\,a\,b^8\,c^4\,d^3\,e^4-98\,a\,b^9\,c^3\,d^2\,e^5-5376\,a^2\,b^3\,c^8\,d^6\,e+5418\,a^2\,b^8\,c^3\,d\,e^6-28224\,a^3\,b^6\,c^4\,d\,e^6+44800\,a^4\,b\,c^8\,d^4\,e^3+78400\,a^4\,b^4\,c^5\,d\,e^6+53760\,a^5\,b\,c^7\,d^2\,e^5-107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{2560\,a^5\,c^7\,e^7-2688\,a^4\,b^2\,c^6\,e^7-2048\,a^4\,b\,c^7\,d\,e^6+2048\,a^4\,c^8\,d^2\,e^5+1056\,a^3\,b^4\,c^5\,e^7+2304\,a^3\,b^3\,c^6\,d\,e^6-2816\,a^3\,b^2\,c^7\,d^2\,e^5+1024\,a^3\,b\,c^8\,d^3\,e^4-512\,a^3\,c^9\,d^4\,e^3-184\,a^2\,b^6\,c^4\,e^7-960\,a^2\,b^5\,c^5\,d\,e^6+1344\,a^2\,b^4\,c^6\,d^2\,e^5-768\,a^2\,b^3\,c^7\,d^3\,e^4+384\,a^2\,b^2\,c^8\,d^4\,e^3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-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}\,\left(-256\,a^3\,b\,c^8\,e^3+512\,d\,a^3\,c^9\,e^2+192\,a^2\,b^3\,c^7\,e^3-384\,d\,a^2\,b^2\,c^8\,e^2-48\,a\,b^5\,c^6\,e^3+96\,d\,a\,b^4\,c^7\,e^2+4\,b^7\,c^5\,e^3-8\,d\,b^6\,c^6\,e^2\right)}{16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3}\right)\,\sqrt{\frac{32\,b^6\,c^7\,d^7-2048\,a^3\,c^{10}\,d^7-9\,b^{13}\,e^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^8\,d^7-26880\,a^6\,b\,c^6\,e^7+53760\,a^6\,c^7\,d\,e^6-112\,b^7\,c^6\,d^6\,e+1536\,a^2\,b^2\,c^9\,d^7-2077\,a^2\,b^9\,c^2\,e^7+10656\,a^3\,b^7\,c^3\,e^7-30240\,a^4\,b^5\,c^4\,e^7+44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-17920\,a^4\,c^9\,d^5\,e^2-35840\,a^5\,c^8\,d^3\,e^4+98\,b^8\,c^5\,d^5\,e^2+35\,b^9\,c^4\,d^4\,e^3-70\,b^{10}\,c^3\,d^3\,e^4+14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+213\,a\,b^{11}\,c\,e^7+21\,b^{12}\,c\,d\,e^6+1344\,a^2\,b^4\,c^7\,d^5\,e^2+10080\,a^2\,b^5\,c^6\,d^4\,e^3-7840\,a^2\,b^6\,c^5\,d^3\,e^4-1008\,a^2\,b^7\,c^4\,d^2\,e^5+7168\,a^3\,b^2\,c^8\,d^5\,e^2-35840\,a^3\,b^3\,c^7\,d^4\,e^3+17920\,a^3\,b^4\,c^6\,d^3\,e^4+12544\,a^3\,b^5\,c^5\,d^2\,e^5-44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+1344\,a\,b^5\,c^7\,d^6\,e-532\,a\,b^{10}\,c^2\,d\,e^6+7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-896\,a\,b^6\,c^6\,d^5\,e^2-1120\,a\,b^7\,c^5\,d^4\,e^3+1260\,a\,b^8\,c^4\,d^3\,e^4-98\,a\,b^9\,c^3\,d^2\,e^5-5376\,a^2\,b^3\,c^8\,d^6\,e+5418\,a^2\,b^8\,c^3\,d\,e^6-28224\,a^3\,b^6\,c^4\,d\,e^6+44800\,a^4\,b\,c^8\,d^4\,e^3+78400\,a^4\,b^4\,c^5\,d\,e^6+53760\,a^5\,b\,c^7\,d^2\,e^5-107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}+\frac{2\,\sqrt{d+e\,x}\,\left(200\,a^4\,c^4\,e^{10}-718\,a^3\,b^2\,c^3\,e^{10}+2072\,a^3\,b\,c^4\,d\,e^9-2072\,a^3\,c^5\,d^2\,e^8+481\,a^2\,b^4\,c^2\,e^{10}-1694\,a^2\,b^3\,c^3\,d\,e^9+1974\,a^2\,b^2\,c^4\,d^2\,e^8-560\,a^2\,b\,c^5\,d^3\,e^7+280\,a^2\,c^6\,d^4\,e^6-114\,a\,b^6\,c\,e^{10}+406\,a\,b^5\,c^2\,d\,e^9-336\,a\,b^4\,c^3\,d^2\,e^8-420\,a\,b^3\,c^4\,d^3\,e^7+910\,a\,b^2\,c^5\,d^4\,e^6-840\,a\,b\,c^6\,d^5\,e^5+280\,a\,c^7\,d^6\,e^4+9\,b^8\,e^{10}-30\,b^7\,c\,d\,e^9+7\,b^6\,c^2\,d^2\,e^8+84\,b^5\,c^3\,d^3\,e^7-105\,b^4\,c^4\,d^4\,e^6-14\,b^3\,c^5\,d^5\,e^5+154\,b^2\,c^6\,d^6\,e^4-128\,b\,c^7\,d^7\,e^3+32\,c^8\,d^8\,e^2\right)}{16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3}\right)\,\sqrt{\frac{32\,b^6\,c^7\,d^7-2048\,a^3\,c^{10}\,d^7-9\,b^{13}\,e^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^8\,d^7-26880\,a^6\,b\,c^6\,e^7+53760\,a^6\,c^7\,d\,e^6-112\,b^7\,c^6\,d^6\,e+1536\,a^2\,b^2\,c^9\,d^7-2077\,a^2\,b^9\,c^2\,e^7+10656\,a^3\,b^7\,c^3\,e^7-30240\,a^4\,b^5\,c^4\,e^7+44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-17920\,a^4\,c^9\,d^5\,e^2-35840\,a^5\,c^8\,d^3\,e^4+98\,b^8\,c^5\,d^5\,e^2+35\,b^9\,c^4\,d^4\,e^3-70\,b^{10}\,c^3\,d^3\,e^4+14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+213\,a\,b^{11}\,c\,e^7+21\,b^{12}\,c\,d\,e^6+1344\,a^2\,b^4\,c^7\,d^5\,e^2+10080\,a^2\,b^5\,c^6\,d^4\,e^3-7840\,a^2\,b^6\,c^5\,d^3\,e^4-1008\,a^2\,b^7\,c^4\,d^2\,e^5+7168\,a^3\,b^2\,c^8\,d^5\,e^2-35840\,a^3\,b^3\,c^7\,d^4\,e^3+17920\,a^3\,b^4\,c^6\,d^3\,e^4+12544\,a^3\,b^5\,c^5\,d^2\,e^5-44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+1344\,a\,b^5\,c^7\,d^6\,e-532\,a\,b^{10}\,c^2\,d\,e^6+7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-896\,a\,b^6\,c^6\,d^5\,e^2-1120\,a\,b^7\,c^5\,d^4\,e^3+1260\,a\,b^8\,c^4\,d^3\,e^4-98\,a\,b^9\,c^3\,d^2\,e^5-5376\,a^2\,b^3\,c^8\,d^6\,e+5418\,a^2\,b^8\,c^3\,d\,e^6-28224\,a^3\,b^6\,c^4\,d\,e^6+44800\,a^4\,b\,c^8\,d^4\,e^3+78400\,a^4\,b^4\,c^5\,d\,e^6+53760\,a^5\,b\,c^7\,d^2\,e^5-107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}}\right)\,\sqrt{\frac{32\,b^6\,c^7\,d^7-2048\,a^3\,c^{10}\,d^7-9\,b^{13}\,e^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^8\,d^7-26880\,a^6\,b\,c^6\,e^7+53760\,a^6\,c^7\,d\,e^6-112\,b^7\,c^6\,d^6\,e+1536\,a^2\,b^2\,c^9\,d^7-2077\,a^2\,b^9\,c^2\,e^7+10656\,a^3\,b^7\,c^3\,e^7-30240\,a^4\,b^5\,c^4\,e^7+44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-17920\,a^4\,c^9\,d^5\,e^2-35840\,a^5\,c^8\,d^3\,e^4+98\,b^8\,c^5\,d^5\,e^2+35\,b^9\,c^4\,d^4\,e^3-70\,b^{10}\,c^3\,d^3\,e^4+14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+213\,a\,b^{11}\,c\,e^7+21\,b^{12}\,c\,d\,e^6+1344\,a^2\,b^4\,c^7\,d^5\,e^2+10080\,a^2\,b^5\,c^6\,d^4\,e^3-7840\,a^2\,b^6\,c^5\,d^3\,e^4-1008\,a^2\,b^7\,c^4\,d^2\,e^5+7168\,a^3\,b^2\,c^8\,d^5\,e^2-35840\,a^3\,b^3\,c^7\,d^4\,e^3+17920\,a^3\,b^4\,c^6\,d^3\,e^4+12544\,a^3\,b^5\,c^5\,d^2\,e^5-44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+1344\,a\,b^5\,c^7\,d^6\,e-532\,a\,b^{10}\,c^2\,d\,e^6+7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-896\,a\,b^6\,c^6\,d^5\,e^2-1120\,a\,b^7\,c^5\,d^4\,e^3+1260\,a\,b^8\,c^4\,d^3\,e^4-98\,a\,b^9\,c^3\,d^2\,e^5-5376\,a^2\,b^3\,c^8\,d^6\,e+5418\,a^2\,b^8\,c^3\,d\,e^6-28224\,a^3\,b^6\,c^4\,d\,e^6+44800\,a^4\,b\,c^8\,d^4\,e^3+78400\,a^4\,b^4\,c^5\,d\,e^6+53760\,a^5\,b\,c^7\,d^2\,e^5-107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(\frac{2560\,a^5\,c^7\,e^7-2688\,a^4\,b^2\,c^6\,e^7-2048\,a^4\,b\,c^7\,d\,e^6+2048\,a^4\,c^8\,d^2\,e^5+1056\,a^3\,b^4\,c^5\,e^7+2304\,a^3\,b^3\,c^6\,d\,e^6-2816\,a^3\,b^2\,c^7\,d^2\,e^5+1024\,a^3\,b\,c^8\,d^3\,e^4-512\,a^3\,c^9\,d^4\,e^3-184\,a^2\,b^6\,c^4\,e^7-960\,a^2\,b^5\,c^5\,d\,e^6+1344\,a^2\,b^4\,c^6\,d^2\,e^5-768\,a^2\,b^3\,c^7\,d^3\,e^4+384\,a^2\,b^2\,c^8\,d^4\,e^3+12\,a\,b^8\,c^3\,e^7+176\,a\,b^7\,c^4\,d\,e^6-272\,a\,b^6\,c^5\,d^2\,e^5+192\,a\,b^5\,c^6\,d^3\,e^4-96\,a\,b^4\,c^7\,d^4\,e^3-12\,b^9\,c^3\,d\,e^6+20\,b^8\,c^4\,d^2\,e^5-16\,b^7\,c^5\,d^3\,e^4+8\,b^6\,c^6\,d^4\,e^3}{64\,a^3\,c^6-48\,a^2\,b^2\,c^5+12\,a\,b^4\,c^4-b^6\,c^3}-\frac{2\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,b^{13}\,e^7+2048\,a^3\,c^{10}\,d^7-32\,b^6\,c^7\,d^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+384\,a\,b^4\,c^8\,d^7+26880\,a^6\,b\,c^6\,e^7-53760\,a^6\,c^7\,d\,e^6+112\,b^7\,c^6\,d^6\,e-1536\,a^2\,b^2\,c^9\,d^7+2077\,a^2\,b^9\,c^2\,e^7-10656\,a^3\,b^7\,c^3\,e^7+30240\,a^4\,b^5\,c^4\,e^7-44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+17920\,a^4\,c^9\,d^5\,e^2+35840\,a^5\,c^8\,d^3\,e^4-98\,b^8\,c^5\,d^5\,e^2-35\,b^9\,c^4\,d^4\,e^3+70\,b^{10}\,c^3\,d^3\,e^4-14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-213\,a\,b^{11}\,c\,e^7-21\,b^{12}\,c\,d\,e^6-1344\,a^2\,b^4\,c^7\,d^5\,e^2-10080\,a^2\,b^5\,c^6\,d^4\,e^3+7840\,a^2\,b^6\,c^5\,d^3\,e^4+1008\,a^2\,b^7\,c^4\,d^2\,e^5-7168\,a^3\,b^2\,c^8\,d^5\,e^2+35840\,a^3\,b^3\,c^7\,d^4\,e^3-17920\,a^3\,b^4\,c^6\,d^3\,e^4-12544\,a^3\,b^5\,c^5\,d^2\,e^5+44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-1344\,a\,b^5\,c^7\,d^6\,e+532\,a\,b^{10}\,c^2\,d\,e^6-7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+896\,a\,b^6\,c^6\,d^5\,e^2+1120\,a\,b^7\,c^5\,d^4\,e^3-1260\,a\,b^8\,c^4\,d^3\,e^4+98\,a\,b^9\,c^3\,d^2\,e^5+5376\,a^2\,b^3\,c^8\,d^6\,e-5418\,a^2\,b^8\,c^3\,d\,e^6+28224\,a^3\,b^6\,c^4\,d\,e^6-44800\,a^4\,b\,c^8\,d^4\,e^3-78400\,a^4\,b^4\,c^5\,d\,e^6-53760\,a^5\,b\,c^7\,d^2\,e^5+107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}\,\left(-256\,a^3\,b\,c^8\,e^3+512\,d\,a^3\,c^9\,e^2+192\,a^2\,b^3\,c^7\,e^3-384\,d\,a^2\,b^2\,c^8\,e^2-48\,a\,b^5\,c^6\,e^3+96\,d\,a\,b^4\,c^7\,e^2+4\,b^7\,c^5\,e^3-8\,d\,b^6\,c^6\,e^2\right)}{16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3}\right)\,\sqrt{-\frac{9\,b^{13}\,e^7+2048\,a^3\,c^{10}\,d^7-32\,b^6\,c^7\,d^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+384\,a\,b^4\,c^8\,d^7+26880\,a^6\,b\,c^6\,e^7-53760\,a^6\,c^7\,d\,e^6+112\,b^7\,c^6\,d^6\,e-1536\,a^2\,b^2\,c^9\,d^7+2077\,a^2\,b^9\,c^2\,e^7-10656\,a^3\,b^7\,c^3\,e^7+30240\,a^4\,b^5\,c^4\,e^7-44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+17920\,a^4\,c^9\,d^5\,e^2+35840\,a^5\,c^8\,d^3\,e^4-98\,b^8\,c^5\,d^5\,e^2-35\,b^9\,c^4\,d^4\,e^3+70\,b^{10}\,c^3\,d^3\,e^4-14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-213\,a\,b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right)}^9}-213\,a\,b^{11}\,c\,e^7-21\,b^{12}\,c\,d\,e^6-1344\,a^2\,b^4\,c^7\,d^5\,e^2-10080\,a^2\,b^5\,c^6\,d^4\,e^3+7840\,a^2\,b^6\,c^5\,d^3\,e^4+1008\,a^2\,b^7\,c^4\,d^2\,e^5-7168\,a^3\,b^2\,c^8\,d^5\,e^2+35840\,a^3\,b^3\,c^7\,d^4\,e^3-17920\,a^3\,b^4\,c^6\,d^3\,e^4-12544\,a^3\,b^5\,c^5\,d^2\,e^5+44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-1344\,a\,b^5\,c^7\,d^6\,e+532\,a\,b^{10}\,c^2\,d\,e^6-7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+896\,a\,b^6\,c^6\,d^5\,e^2+1120\,a\,b^7\,c^5\,d^4\,e^3-1260\,a\,b^8\,c^4\,d^3\,e^4+98\,a\,b^9\,c^3\,d^2\,e^5+5376\,a^2\,b^3\,c^8\,d^6\,e-5418\,a^2\,b^8\,c^3\,d\,e^6+28224\,a^3\,b^6\,c^4\,d\,e^6-44800\,a^4\,b\,c^8\,d^4\,e^3-78400\,a^4\,b^4\,c^5\,d\,e^6-53760\,a^5\,b\,c^7\,d^2\,e^5+107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}\,\left(-256\,a^3\,b\,c^8\,e^3+512\,d\,a^3\,c^9\,e^2+192\,a^2\,b^3\,c^7\,e^3-384\,d\,a^2\,b^2\,c^8\,e^2-48\,a\,b^5\,c^6\,e^3+96\,d\,a\,b^4\,c^7\,e^2+4\,b^7\,c^5\,e^3-8\,d\,b^6\,c^6\,e^2\right)}{16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3}\right)\,\sqrt{-\frac{9\,b^{13}\,e^7+2048\,a^3\,c^{10}\,d^7-32\,b^6\,c^7\,d^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+384\,a\,b^4\,c^8\,d^7+26880\,a^6\,b\,c^6\,e^7-53760\,a^6\,c^7\,d\,e^6+112\,b^7\,c^6\,d^6\,e-1536\,a^2\,b^2\,c^9\,d^7+2077\,a^2\,b^9\,c^2\,e^7-10656\,a^3\,b^7\,c^3\,e^7+30240\,a^4\,b^5\,c^4\,e^7-44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+17920\,a^4\,c^9\,d^5\,e^2+35840\,a^5\,c^8\,d^3\,e^4-98\,b^8\,c^5\,d^5\,e^2-35\,b^9\,c^4\,d^4\,e^3+70\,b^{10}\,c^3\,d^3\,e^4-14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-213\,a\,b^{11}\,c\,e^7-21\,b^{12}\,c\,d\,e^6-1344\,a^2\,b^4\,c^7\,d^5\,e^2-10080\,a^2\,b^5\,c^6\,d^4\,e^3+7840\,a^2\,b^6\,c^5\,d^3\,e^4+1008\,a^2\,b^7\,c^4\,d^2\,e^5-7168\,a^3\,b^2\,c^8\,d^5\,e^2+35840\,a^3\,b^3\,c^7\,d^4\,e^3-17920\,a^3\,b^4\,c^6\,d^3\,e^4-12544\,a^3\,b^5\,c^5\,d^2\,e^5+44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-1344\,a\,b^5\,c^7\,d^6\,e+532\,a\,b^{10}\,c^2\,d\,e^6-7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+896\,a\,b^6\,c^6\,d^5\,e^2+1120\,a\,b^7\,c^5\,d^4\,e^3-1260\,a\,b^8\,c^4\,d^3\,e^4+98\,a\,b^9\,c^3\,d^2\,e^5+5376\,a^2\,b^3\,c^8\,d^6\,e-5418\,a^2\,b^8\,c^3\,d\,e^6+28224\,a^3\,b^6\,c^4\,d\,e^6-44800\,a^4\,b\,c^8\,d^4\,e^3-78400\,a^4\,b^4\,c^5\,d\,e^6-53760\,a^5\,b\,c^7\,d^2\,e^5+107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}+\frac{2\,\sqrt{d+e\,x}\,\left(200\,a^4\,c^4\,e^{10}-718\,a^3\,b^2\,c^3\,e^{10}+2072\,a^3\,b\,c^4\,d\,e^9-2072\,a^3\,c^5\,d^2\,e^8+481\,a^2\,b^4\,c^2\,e^{10}-1694\,a^2\,b^3\,c^3\,d\,e^9+1974\,a^2\,b^2\,c^4\,d^2\,e^8-560\,a^2\,b\,c^5\,d^3\,e^7+280\,a^2\,c^6\,d^4\,e^6-114\,a\,b^6\,c\,e^{10}+406\,a\,b^5\,c^2\,d\,e^9-336\,a\,b^4\,c^3\,d^2\,e^8-420\,a\,b^3\,c^4\,d^3\,e^7+910\,a\,b^2\,c^5\,d^4\,e^6-840\,a\,b\,c^6\,d^5\,e^5+280\,a\,c^7\,d^6\,e^4+9\,b^8\,e^{10}-30\,b^7\,c\,d\,e^9+7\,b^6\,c^2\,d^2\,e^8+84\,b^5\,c^3\,d^3\,e^7-105\,b^4\,c^4\,d^4\,e^6-14\,b^3\,c^5\,d^5\,e^5+154\,b^2\,c^6\,d^6\,e^4-128\,b\,c^7\,d^7\,e^3+32\,c^8\,d^8\,e^2\right)}{16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3}\right)\,\sqrt{-\frac{9\,b^{13}\,e^7+2048\,a^3\,c^{10}\,d^7-32\,b^6\,c^7\,d^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+384\,a\,b^4\,c^8\,d^7+26880\,a^6\,b\,c^6\,e^7-53760\,a^6\,c^7\,d\,e^6+112\,b^7\,c^6\,d^6\,e-1536\,a^2\,b^2\,c^9\,d^7+2077\,a^2\,b^9\,c^2\,e^7-10656\,a^3\,b^7\,c^3\,e^7+30240\,a^4\,b^5\,c^4\,e^7-44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+17920\,a^4\,c^9\,d^5\,e^2+35840\,a^5\,c^8\,d^3\,e^4-98\,b^8\,c^5\,d^5\,e^2-35\,b^9\,c^4\,d^4\,e^3+70\,b^{10}\,c^3\,d^3\,e^4-14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-213\,a\,b^{11}\,c\,e^7-21\,b^{12}\,c\,d\,e^6-1344\,a^2\,b^4\,c^7\,d^5\,e^2-10080\,a^2\,b^5\,c^6\,d^4\,e^3+7840\,a^2\,b^6\,c^5\,d^3\,e^4+1008\,a^2\,b^7\,c^4\,d^2\,e^5-7168\,a^3\,b^2\,c^8\,d^5\,e^2+35840\,a^3\,b^3\,c^7\,d^4\,e^3-17920\,a^3\,b^4\,c^6\,d^3\,e^4-12544\,a^3\,b^5\,c^5\,d^2\,e^5+44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-1344\,a\,b^5\,c^7\,d^6\,e+532\,a\,b^{10}\,c^2\,d\,e^6-7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+896\,a\,b^6\,c^6\,d^5\,e^2+1120\,a\,b^7\,c^5\,d^4\,e^3-1260\,a\,b^8\,c^4\,d^3\,e^4+98\,a\,b^9\,c^3\,d^2\,e^5+5376\,a^2\,b^3\,c^8\,d^6\,e-5418\,a^2\,b^8\,c^3\,d\,e^6+28224\,a^3\,b^6\,c^4\,d\,e^6-44800\,a^4\,b\,c^8\,d^4\,e^3-78400\,a^4\,b^4\,c^5\,d\,e^6-53760\,a^5\,b\,c^7\,d^2\,e^5+107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{2560\,a^5\,c^7\,e^7-2688\,a^4\,b^2\,c^6\,e^7-2048\,a^4\,b\,c^7\,d\,e^6+2048\,a^4\,c^8\,d^2\,e^5+1056\,a^3\,b^4\,c^5\,e^7+2304\,a^3\,b^3\,c^6\,d\,e^6-2816\,a^3\,b^2\,c^7\,d^2\,e^5+1024\,a^3\,b\,c^8\,d^3\,e^4-512\,a^3\,c^9\,d^4\,e^3-184\,a^2\,b^6\,c^4\,e^7-960\,a^2\,b^5\,c^5\,d\,e^6+1344\,a^2\,b^4\,c^6\,d^2\,e^5-768\,a^2\,b^3\,c^7\,d^3\,e^4+384\,a^2\,b^2\,c^8\,d^4\,e^3+12\,a\,b^8\,c^3\,e^7+176\,a\,b^7\,c^4\,d\,e^6-272\,a\,b^6\,c^5\,d^2\,e^5+192\,a\,b^5\,c^6\,d^3\,e^4-96\,a\,b^4\,c^7\,d^4\,e^3-12\,b^9\,c^3\,d\,e^6+20\,b^8\,c^4\,d^2\,e^5-16\,b^7\,c^5\,d^3\,e^4+8\,b^6\,c^6\,d^4\,e^3}{64\,a^3\,c^6-48\,a^2\,b^2\,c^5+12\,a\,b^4\,c^4-b^6\,c^3}-\frac{2\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,b^{13}\,e^7+2048\,a^3\,c^{10}\,d^7-32\,b^6\,c^7\,d^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+384\,a\,b^4\,c^8\,d^7+26880\,a^6\,b\,c^6\,e^7-53760\,a^6\,c^7\,d\,e^6+112\,b^7\,c^6\,d^6\,e-1536\,a^2\,b^2\,c^9\,d^7+2077\,a^2\,b^9\,c^2\,e^7-10656\,a^3\,b^7\,c^3\,e^7+30240\,a^4\,b^5\,c^4\,e^7-44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+17920\,a^4\,c^9\,d^5\,e^2+35840\,a^5\,c^8\,d^3\,e^4-98\,b^8\,c^5\,d^5\,e^2-35\,b^9\,c^4\,d^4\,e^3+70\,b^{10}\,c^3\,d^3\,e^4-14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-213\,a\,b^{11}\,c\,e^7-21\,b^{12}\,c\,d\,e^6-1344\,a^2\,b^4\,c^7\,d^5\,e^2-10080\,a^2\,b^5\,c^6\,d^4\,e^3+7840\,a^2\,b^6\,c^5\,d^3\,e^4+1008\,a^2\,b^7\,c^4\,d^2\,e^5-7168\,a^3\,b^2\,c^8\,d^5\,e^2+35840\,a^3\,b^3\,c^7\,d^4\,e^3-17920\,a^3\,b^4\,c^6\,d^3\,e^4-12544\,a^3\,b^5\,c^5\,d^2\,e^5+44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-1344\,a\,b^5\,c^7\,d^6\,e+532\,a\,b^{10}\,c^2\,d\,e^6-7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+896\,a\,b^6\,c^6\,d^5\,e^2+1120\,a\,b^7\,c^5\,d^4\,e^3-1260\,a\,b^8\,c^4\,d^3\,e^4+98\,a\,b^9\,c^3\,d^2\,e^5+5376\,a^2\,b^3\,c^8\,d^6\,e-5418\,a^2\,b^8\,c^3\,d\,e^6+28224\,a^3\,b^6\,c^4\,d\,e^6-44800\,a^4\,b\,c^8\,d^4\,e^3-78400\,a^4\,b^4\,c^5\,d\,e^6-53760\,a^5\,b\,c^7\,d^2\,e^5+107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}\,\left(-256\,a^3\,b\,c^8\,e^3+512\,d\,a^3\,c^9\,e^2+192\,a^2\,b^3\,c^7\,e^3-384\,d\,a^2\,b^2\,c^8\,e^2-48\,a\,b^5\,c^6\,e^3+96\,d\,a\,b^4\,c^7\,e^2+4\,b^7\,c^5\,e^3-8\,d\,b^6\,c^6\,e^2\right)}{16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3}\right)\,\sqrt{-\frac{9\,b^{13}\,e^7+2048\,a^3\,c^{10}\,d^7-32\,b^6\,c^7\,d^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+384\,a\,b^4\,c^8\,d^7+26880\,a^6\,b\,c^6\,e^7-53760\,a^6\,c^7\,d\,e^6+112\,b^7\,c^6\,d^6\,e-1536\,a^2\,b^2\,c^9\,d^7+2077\,a^2\,b^9\,c^2\,e^7-10656\,a^3\,b^7\,c^3\,e^7+30240\,a^4\,b^5\,c^4\,e^7-44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+17920\,a^4\,c^9\,d^5\,e^2+35840\,a^5\,c^8\,d^3\,e^4-98\,b^8\,c^5\,d^5\,e^2-35\,b^9\,c^4\,d^4\,e^3+70\,b^{10}\,c^3\,d^3\,e^4-14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-213\,a\,b^{11}\,c\,e^7-21\,b^{12}\,c\,d\,e^6-1344\,a^2\,b^4\,c^7\,d^5\,e^2-10080\,a^2\,b^5\,c^6\,d^4\,e^3+7840\,a^2\,b^6\,c^5\,d^3\,e^4+1008\,a^2\,b^7\,c^4\,d^2\,e^5-7168\,a^3\,b^2\,c^8\,d^5\,e^2+35840\,a^3\,b^3\,c^7\,d^4\,e^3-17920\,a^3\,b^4\,c^6\,d^3\,e^4-12544\,a^3\,b^5\,c^5\,d^2\,e^5+44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-1344\,a\,b^5\,c^7\,d^6\,e+532\,a\,b^{10}\,c^2\,d\,e^6-7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+896\,a\,b^6\,c^6\,d^5\,e^2+1120\,a\,b^7\,c^5\,d^4\,e^3-1260\,a\,b^8\,c^4\,d^3\,e^4+98\,a\,b^9\,c^3\,d^2\,e^5+5376\,a^2\,b^3\,c^8\,d^6\,e-5418\,a^2\,b^8\,c^3\,d\,e^6+28224\,a^3\,b^6\,c^4\,d\,e^6-44800\,a^4\,b\,c^8\,d^4\,e^3-78400\,a^4\,b^4\,c^5\,d\,e^6-53760\,a^5\,b\,c^7\,d^2\,e^5+107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}-\frac{2\,\sqrt{d+e\,x}\,\left(200\,a^4\,c^4\,e^{10}-718\,a^3\,b^2\,c^3\,e^{10}+2072\,a^3\,b\,c^4\,d\,e^9-2072\,a^3\,c^5\,d^2\,e^8+481\,a^2\,b^4\,c^2\,e^{10}-1694\,a^2\,b^3\,c^3\,d\,e^9+1974\,a^2\,b^2\,c^4\,d^2\,e^8-560\,a^2\,b\,c^5\,d^3\,e^7+280\,a^2\,c^6\,d^4\,e^6-114\,a\,b^6\,c\,e^{10}+406\,a\,b^5\,c^2\,d\,e^9-336\,a\,b^4\,c^3\,d^2\,e^8-420\,a\,b^3\,c^4\,d^3\,e^7+910\,a\,b^2\,c^5\,d^4\,e^6-840\,a\,b\,c^6\,d^5\,e^5+280\,a\,c^7\,d^6\,e^4+9\,b^8\,e^{10}-30\,b^7\,c\,d\,e^9+7\,b^6\,c^2\,d^2\,e^8+84\,b^5\,c^3\,d^3\,e^7-105\,b^4\,c^4\,d^4\,e^6-14\,b^3\,c^5\,d^5\,e^5+154\,b^2\,c^6\,d^6\,e^4-128\,b\,c^7\,d^7\,e^3+32\,c^8\,d^8\,e^2\right)}{16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3}\right)\,\sqrt{-\frac{9\,b^{13}\,e^7+2048\,a^3\,c^{10}\,d^7-32\,b^6\,c^7\,d^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+384\,a\,b^4\,c^8\,d^7+26880\,a^6\,b\,c^6\,e^7-53760\,a^6\,c^7\,d\,e^6+112\,b^7\,c^6\,d^6\,e-1536\,a^2\,b^2\,c^9\,d^7+2077\,a^2\,b^9\,c^2\,e^7-10656\,a^3\,b^7\,c^3\,e^7+30240\,a^4\,b^5\,c^4\,e^7-44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+17920\,a^4\,c^9\,d^5\,e^2+35840\,a^5\,c^8\,d^3\,e^4-98\,b^8\,c^5\,d^5\,e^2-35\,b^9\,c^4\,d^4\,e^3+70\,b^{10}\,c^3\,d^3\,e^4-14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-213\,a\,b^{11}\,c\,e^7-21\,b^{12}\,c\,d\,e^6-1344\,a^2\,b^4\,c^7\,d^5\,e^2-10080\,a^2\,b^5\,c^6\,d^4\,e^3+7840\,a^2\,b^6\,c^5\,d^3\,e^4+1008\,a^2\,b^7\,c^4\,d^2\,e^5-7168\,a^3\,b^2\,c^8\,d^5\,e^2+35840\,a^3\,b^3\,c^7\,d^4\,e^3-17920\,a^3\,b^4\,c^6\,d^3\,e^4-12544\,a^3\,b^5\,c^5\,d^2\,e^5+44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-1344\,a\,b^5\,c^7\,d^6\,e+532\,a\,b^{10}\,c^2\,d\,e^6-7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+896\,a\,b^6\,c^6\,d^5\,e^2+1120\,a\,b^7\,c^5\,d^4\,e^3-1260\,a\,b^8\,c^4\,d^3\,e^4+98\,a\,b^9\,c^3\,d^2\,e^5+5376\,a^2\,b^3\,c^8\,d^6\,e-5418\,a^2\,b^8\,c^3\,d\,e^6+28224\,a^3\,b^6\,c^4\,d\,e^6-44800\,a^4\,b\,c^8\,d^4\,e^3-78400\,a^4\,b^4\,c^5\,d\,e^6-53760\,a^5\,b\,c^7\,d^2\,e^5+107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}-\frac{2\,\left(-1300\,a^5\,b\,c^2\,e^{14}+2600\,a^5\,c^3\,d\,e^{13}+573\,a^4\,b^3\,c\,e^{14}+3062\,a^4\,b^2\,c^2\,d\,e^{13}-12624\,a^4\,b\,c^3\,d^2\,e^{12}+8416\,a^4\,c^4\,d^3\,e^{11}-63\,a^3\,b^5\,e^{14}-1662\,a^3\,b^4\,c\,d\,e^{13}+524\,a^3\,b^3\,c^2\,d^2\,e^{12}+15784\,a^3\,b^2\,c^3\,d^3\,e^{11}-24200\,a^3\,b\,c^4\,d^4\,e^{10}+9680\,a^3\,c^5\,d^5\,e^9+189\,a^2\,b^6\,d\,e^{13}+1359\,a^2\,b^5\,c\,d^2\,e^{12}-5054\,a^2\,b^4\,c^2\,d^3\,e^{11}-1730\,a^2\,b^3\,c^3\,d^4\,e^{10}+16596\,a^2\,b^2\,c^4\,d^5\,e^9-15904\,a^2\,b\,c^5\,d^6\,e^8+4544\,a^2\,c^6\,d^7\,e^7-189\,a\,b^7\,d^2\,e^{12}-24\,a\,b^6\,c\,d^3\,e^{11}+2599\,a\,b^5\,c^2\,d^4\,e^{10}-4506\,a\,b^4\,c^3\,d^5\,e^9+476\,a\,b^3\,c^4\,d^6\,e^8+4136\,a\,b^2\,c^5\,d^7\,e^7-3204\,a\,b\,c^6\,d^8\,e^6+712\,a\,c^7\,d^9\,e^5+63\,b^8\,d^3\,e^{11}-246\,b^7\,c\,d^4\,e^{10}+169\,b^6\,c^2\,d^5\,e^9+413\,b^5\,c^3\,d^6\,e^8-658\,b^4\,c^4\,d^7\,e^7+141\,b^3\,c^5\,d^8\,e^6+262\,b^2\,c^6\,d^9\,e^5-176\,b\,c^7\,d^{10}\,e^4+32\,c^8\,d^{11}\,e^3\right)}{64\,a^3\,c^6-48\,a^2\,b^2\,c^5+12\,a\,b^4\,c^4-b^6\,c^3}+\left(\left(\frac{2560\,a^5\,c^7\,e^7-2688\,a^4\,b^2\,c^6\,e^7-2048\,a^4\,b\,c^7\,d\,e^6+2048\,a^4\,c^8\,d^2\,e^5+1056\,a^3\,b^4\,c^5\,e^7+2304\,a^3\,b^3\,c^6\,d\,e^6-2816\,a^3\,b^2\,c^7\,d^2\,e^5+1024\,a^3\,b\,c^8\,d^3\,e^4-512\,a^3\,c^9\,d^4\,e^3-184\,a^2\,b^6\,c^4\,e^7-960\,a^2\,b^5\,c^5\,d\,e^6+1344\,a^2\,b^4\,c^6\,d^2\,e^5-768\,a^2\,b^3\,c^7\,d^3\,e^4+384\,a^2\,b^2\,c^8\,d^4\,e^3+12\,a\,b^8\,c^3\,e^7+176\,a\,b^7\,c^4\,d\,e^6-272\,a\,b^6\,c^5\,d^2\,e^5+192\,a\,b^5\,c^6\,d^3\,e^4-96\,a\,b^4\,c^7\,d^4\,e^3-12\,b^9\,c^3\,d\,e^6+20\,b^8\,c^4\,d^2\,e^5-16\,b^7\,c^5\,d^3\,e^4+8\,b^6\,c^6\,d^4\,e^3}{64\,a^3\,c^6-48\,a^2\,b^2\,c^5+12\,a\,b^4\,c^4-b^6\,c^3}+\frac{2\,\sqrt{d+e\,x}\,\sqrt{-\frac{9\,b^{13}\,e^7+2048\,a^3\,c^{10}\,d^7-32\,b^6\,c^7\,d^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+384\,a\,b^4\,c^8\,d^7+26880\,a^6\,b\,c^6\,e^7-53760\,a^6\,c^7\,d\,e^6+112\,b^7\,c^6\,d^6\,e-1536\,a^2\,b^2\,c^9\,d^7+2077\,a^2\,b^9\,c^2\,e^7-10656\,a^3\,b^7\,c^3\,e^7+30240\,a^4\,b^5\,c^4\,e^7-44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+17920\,a^4\,c^9\,d^5\,e^2+35840\,a^5\,c^8\,d^3\,e^4-98\,b^8\,c^5\,d^5\,e^2-35\,b^9\,c^4\,d^4\,e^3+70\,b^{10}\,c^3\,d^3\,e^4-14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-213\,a\,b^{11}\,c\,e^7-21\,b^{12}\,c\,d\,e^6-1344\,a^2\,b^4\,c^7\,d^5\,e^2-10080\,a^2\,b^5\,c^6\,d^4\,e^3+7840\,a^2\,b^6\,c^5\,d^3\,e^4+1008\,a^2\,b^7\,c^4\,d^2\,e^5-7168\,a^3\,b^2\,c^8\,d^5\,e^2+35840\,a^3\,b^3\,c^7\,d^4\,e^3-17920\,a^3\,b^4\,c^6\,d^3\,e^4-12544\,a^3\,b^5\,c^5\,d^2\,e^5+44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-1344\,a\,b^5\,c^7\,d^6\,e+532\,a\,b^{10}\,c^2\,d\,e^6-7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+896\,a\,b^6\,c^6\,d^5\,e^2+1120\,a\,b^7\,c^5\,d^4\,e^3-1260\,a\,b^8\,c^4\,d^3\,e^4+98\,a\,b^9\,c^3\,d^2\,e^5+5376\,a^2\,b^3\,c^8\,d^6\,e-5418\,a^2\,b^8\,c^3\,d\,e^6+28224\,a^3\,b^6\,c^4\,d\,e^6-44800\,a^4\,b\,c^8\,d^4\,e^3-78400\,a^4\,b^4\,c^5\,d\,e^6-53760\,a^5\,b\,c^7\,d^2\,e^5+107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}\,\left(-256\,a^3\,b\,c^8\,e^3+512\,d\,a^3\,c^9\,e^2+192\,a^2\,b^3\,c^7\,e^3-384\,d\,a^2\,b^2\,c^8\,e^2-48\,a\,b^5\,c^6\,e^3+96\,d\,a\,b^4\,c^7\,e^2+4\,b^7\,c^5\,e^3-8\,d\,b^6\,c^6\,e^2\right)}{16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3}\right)\,\sqrt{-\frac{9\,b^{13}\,e^7+2048\,a^3\,c^{10}\,d^7-32\,b^6\,c^7\,d^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+384\,a\,b^4\,c^8\,d^7+26880\,a^6\,b\,c^6\,e^7-53760\,a^6\,c^7\,d\,e^6+112\,b^7\,c^6\,d^6\,e-1536\,a^2\,b^2\,c^9\,d^7+2077\,a^2\,b^9\,c^2\,e^7-10656\,a^3\,b^7\,c^3\,e^7+30240\,a^4\,b^5\,c^4\,e^7-44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+17920\,a^4\,c^9\,d^5\,e^2+35840\,a^5\,c^8\,d^3\,e^4-98\,b^8\,c^5\,d^5\,e^2-35\,b^9\,c^4\,d^4\,e^3+70\,b^{10}\,c^3\,d^3\,e^4-14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-213\,a\,b^{11}\,c\,e^7-21\,b^{12}\,c\,d\,e^6-1344\,a^2\,b^4\,c^7\,d^5\,e^2-10080\,a^2\,b^5\,c^6\,d^4\,e^3+7840\,a^2\,b^6\,c^5\,d^3\,e^4+1008\,a^2\,b^7\,c^4\,d^2\,e^5-7168\,a^3\,b^2\,c^8\,d^5\,e^2+35840\,a^3\,b^3\,c^7\,d^4\,e^3-17920\,a^3\,b^4\,c^6\,d^3\,e^4-12544\,a^3\,b^5\,c^5\,d^2\,e^5+44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-1344\,a\,b^5\,c^7\,d^6\,e+532\,a\,b^{10}\,c^2\,d\,e^6-7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+896\,a\,b^6\,c^6\,d^5\,e^2+1120\,a\,b^7\,c^5\,d^4\,e^3-1260\,a\,b^8\,c^4\,d^3\,e^4+98\,a\,b^9\,c^3\,d^2\,e^5+5376\,a^2\,b^3\,c^8\,d^6\,e-5418\,a^2\,b^8\,c^3\,d\,e^6+28224\,a^3\,b^6\,c^4\,d\,e^6-44800\,a^4\,b\,c^8\,d^4\,e^3-78400\,a^4\,b^4\,c^5\,d\,e^6-53760\,a^5\,b\,c^7\,d^2\,e^5+107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}+\frac{2\,\sqrt{d+e\,x}\,\left(200\,a^4\,c^4\,e^{10}-718\,a^3\,b^2\,c^3\,e^{10}+2072\,a^3\,b\,c^4\,d\,e^9-2072\,a^3\,c^5\,d^2\,e^8+481\,a^2\,b^4\,c^2\,e^{10}-1694\,a^2\,b^3\,c^3\,d\,e^9+1974\,a^2\,b^2\,c^4\,d^2\,e^8-560\,a^2\,b\,c^5\,d^3\,e^7+280\,a^2\,c^6\,d^4\,e^6-114\,a\,b^6\,c\,e^{10}+406\,a\,b^5\,c^2\,d\,e^9-336\,a\,b^4\,c^3\,d^2\,e^8-420\,a\,b^3\,c^4\,d^3\,e^7+910\,a\,b^2\,c^5\,d^4\,e^6-840\,a\,b\,c^6\,d^5\,e^5+280\,a\,c^7\,d^6\,e^4+9\,b^8\,e^{10}-30\,b^7\,c\,d\,e^9+7\,b^6\,c^2\,d^2\,e^8+84\,b^5\,c^3\,d^3\,e^7-105\,b^4\,c^4\,d^4\,e^6-14\,b^3\,c^5\,d^5\,e^5+154\,b^2\,c^6\,d^6\,e^4-128\,b\,c^7\,d^7\,e^3+32\,c^8\,d^8\,e^2\right)}{16\,a^2\,c^5-8\,a\,b^2\,c^4+b^4\,c^3}\right)\,\sqrt{-\frac{9\,b^{13}\,e^7+2048\,a^3\,c^{10}\,d^7-32\,b^6\,c^7\,d^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+384\,a\,b^4\,c^8\,d^7+26880\,a^6\,b\,c^6\,e^7-53760\,a^6\,c^7\,d\,e^6+112\,b^7\,c^6\,d^6\,e-1536\,a^2\,b^2\,c^9\,d^7+2077\,a^2\,b^9\,c^2\,e^7-10656\,a^3\,b^7\,c^3\,e^7+30240\,a^4\,b^5\,c^4\,e^7-44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+17920\,a^4\,c^9\,d^5\,e^2+35840\,a^5\,c^8\,d^3\,e^4-98\,b^8\,c^5\,d^5\,e^2-35\,b^9\,c^4\,d^4\,e^3+70\,b^{10}\,c^3\,d^3\,e^4-14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-213\,a\,b^{11}\,c\,e^7-21\,b^{12}\,c\,d\,e^6-1344\,a^2\,b^4\,c^7\,d^5\,e^2-10080\,a^2\,b^5\,c^6\,d^4\,e^3+7840\,a^2\,b^6\,c^5\,d^3\,e^4+1008\,a^2\,b^7\,c^4\,d^2\,e^5-7168\,a^3\,b^2\,c^8\,d^5\,e^2+35840\,a^3\,b^3\,c^7\,d^4\,e^3-17920\,a^3\,b^4\,c^6\,d^3\,e^4-12544\,a^3\,b^5\,c^5\,d^2\,e^5+44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-1344\,a\,b^5\,c^7\,d^6\,e+532\,a\,b^{10}\,c^2\,d\,e^6-7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+896\,a\,b^6\,c^6\,d^5\,e^2+1120\,a\,b^7\,c^5\,d^4\,e^3-1260\,a\,b^8\,c^4\,d^3\,e^4+98\,a\,b^9\,c^3\,d^2\,e^5+5376\,a^2\,b^3\,c^8\,d^6\,e-5418\,a^2\,b^8\,c^3\,d\,e^6+28224\,a^3\,b^6\,c^4\,d\,e^6-44800\,a^4\,b\,c^8\,d^4\,e^3-78400\,a^4\,b^4\,c^5\,d\,e^6-53760\,a^5\,b\,c^7\,d^2\,e^5+107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}}\right)\,\sqrt{-\frac{9\,b^{13}\,e^7+2048\,a^3\,c^{10}\,d^7-32\,b^6\,c^7\,d^7-9\,b^4\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+384\,a\,b^4\,c^8\,d^7+26880\,a^6\,b\,c^6\,e^7-53760\,a^6\,c^7\,d\,e^6+112\,b^7\,c^6\,d^6\,e-1536\,a^2\,b^2\,c^9\,d^7+2077\,a^2\,b^9\,c^2\,e^7-10656\,a^3\,b^7\,c^3\,e^7+30240\,a^4\,b^5\,c^4\,e^7-44800\,a^5\,b^3\,c^5\,e^7-25\,a^2\,c^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+17920\,a^4\,c^9\,d^5\,e^2+35840\,a^5\,c^8\,d^3\,e^4-98\,b^8\,c^5\,d^5\,e^2-35\,b^9\,c^4\,d^4\,e^3+70\,b^{10}\,c^3\,d^3\,e^4-14\,b^{11}\,c^2\,d^2\,e^5+35\,c^4\,d^4\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-213\,a\,b^{11}\,c\,e^7-21\,b^{12}\,c\,d\,e^6-1344\,a^2\,b^4\,c^7\,d^5\,e^2-10080\,a^2\,b^5\,c^6\,d^4\,e^3+7840\,a^2\,b^6\,c^5\,d^3\,e^4+1008\,a^2\,b^7\,c^4\,d^2\,e^5-7168\,a^3\,b^2\,c^8\,d^5\,e^2+35840\,a^3\,b^3\,c^7\,d^4\,e^3-17920\,a^3\,b^4\,c^6\,d^3\,e^4-12544\,a^3\,b^5\,c^5\,d^2\,e^5+44800\,a^4\,b^3\,c^6\,d^2\,e^5+14\,b^2\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+51\,a\,b^2\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-1344\,a\,b^5\,c^7\,d^6\,e+532\,a\,b^{10}\,c^2\,d\,e^6-7168\,a^3\,b\,c^9\,d^6\,e+21\,b^3\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+896\,a\,b^6\,c^6\,d^5\,e^2+1120\,a\,b^7\,c^5\,d^4\,e^3-1260\,a\,b^8\,c^4\,d^3\,e^4+98\,a\,b^9\,c^3\,d^2\,e^5+5376\,a^2\,b^3\,c^8\,d^6\,e-5418\,a^2\,b^8\,c^3\,d\,e^6+28224\,a^3\,b^6\,c^4\,d\,e^6-44800\,a^4\,b\,c^8\,d^4\,e^3-78400\,a^4\,b^4\,c^5\,d\,e^6-53760\,a^5\,b\,c^7\,d^2\,e^5+107520\,a^5\,b^2\,c^6\,d\,e^6+154\,a\,c^3\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-70\,b\,c^3\,d^3\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-154\,a\,b\,c^2\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^6\,c^{11}-6144\,a^5\,b^2\,c^{10}+3840\,a^4\,b^4\,c^9-1280\,a^3\,b^6\,c^8+240\,a^2\,b^8\,c^7-24\,a\,b^{10}\,c^6+b^{12}\,c^5\right)}}\,2{}\mathrm{i}+\frac{2\,e^3\,\sqrt{d+e\,x}}{c^2}","Not used",1,"(2*e^3*(d + e*x)^(1/2))/c^2 - atan(((((2560*a^5*c^7*e^7 + 12*a*b^8*c^3*e^7 - 12*b^9*c^3*d*e^6 - 184*a^2*b^6*c^4*e^7 + 1056*a^3*b^4*c^5*e^7 - 2688*a^4*b^2*c^6*e^7 - 512*a^3*c^9*d^4*e^3 + 2048*a^4*c^8*d^2*e^5 + 8*b^6*c^6*d^4*e^3 - 16*b^7*c^5*d^3*e^4 + 20*b^8*c^4*d^2*e^5 + 384*a^2*b^2*c^8*d^4*e^3 - 768*a^2*b^3*c^7*d^3*e^4 + 1344*a^2*b^4*c^6*d^2*e^5 - 2816*a^3*b^2*c^7*d^2*e^5 + 176*a*b^7*c^4*d*e^6 - 2048*a^4*b*c^7*d*e^6 - 96*a*b^4*c^7*d^4*e^3 + 192*a*b^5*c^6*d^3*e^4 - 272*a*b^6*c^5*d^2*e^5 - 960*a^2*b^5*c^5*d*e^6 + 1024*a^3*b*c^8*d^3*e^4 + 2304*a^3*b^3*c^6*d*e^6)/(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5) - (2*(d + e*x)^(1/2)*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2)*(4*b^7*c^5*e^3 - 48*a*b^5*c^6*e^3 - 256*a^3*b*c^8*e^3 + 512*a^3*c^9*d*e^2 - 8*b^6*c^6*d*e^2 + 192*a^2*b^3*c^7*e^3 + 96*a*b^4*c^7*d*e^2 - 384*a^2*b^2*c^8*d*e^2))/(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4))*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2) - (2*(d + e*x)^(1/2)*(9*b^8*e^10 + 200*a^4*c^4*e^10 + 32*c^8*d^8*e^2 + 280*a*c^7*d^6*e^4 - 128*b*c^7*d^7*e^3 + 481*a^2*b^4*c^2*e^10 - 718*a^3*b^2*c^3*e^10 + 280*a^2*c^6*d^4*e^6 - 2072*a^3*c^5*d^2*e^8 + 154*b^2*c^6*d^6*e^4 - 14*b^3*c^5*d^5*e^5 - 105*b^4*c^4*d^4*e^6 + 84*b^5*c^3*d^3*e^7 + 7*b^6*c^2*d^2*e^8 - 114*a*b^6*c*e^10 - 30*b^7*c*d*e^9 + 1974*a^2*b^2*c^4*d^2*e^8 - 840*a*b*c^6*d^5*e^5 + 406*a*b^5*c^2*d*e^9 + 2072*a^3*b*c^4*d*e^9 + 910*a*b^2*c^5*d^4*e^6 - 420*a*b^3*c^4*d^3*e^7 - 336*a*b^4*c^3*d^2*e^8 - 560*a^2*b*c^5*d^3*e^7 - 1694*a^2*b^3*c^3*d*e^9))/(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4))*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2)*1i - (((2560*a^5*c^7*e^7 + 12*a*b^8*c^3*e^7 - 12*b^9*c^3*d*e^6 - 184*a^2*b^6*c^4*e^7 + 1056*a^3*b^4*c^5*e^7 - 2688*a^4*b^2*c^6*e^7 - 512*a^3*c^9*d^4*e^3 + 2048*a^4*c^8*d^2*e^5 + 8*b^6*c^6*d^4*e^3 - 16*b^7*c^5*d^3*e^4 + 20*b^8*c^4*d^2*e^5 + 384*a^2*b^2*c^8*d^4*e^3 - 768*a^2*b^3*c^7*d^3*e^4 + 1344*a^2*b^4*c^6*d^2*e^5 - 2816*a^3*b^2*c^7*d^2*e^5 + 176*a*b^7*c^4*d*e^6 - 2048*a^4*b*c^7*d*e^6 - 96*a*b^4*c^7*d^4*e^3 + 192*a*b^5*c^6*d^3*e^4 - 272*a*b^6*c^5*d^2*e^5 - 960*a^2*b^5*c^5*d*e^6 + 1024*a^3*b*c^8*d^3*e^4 + 2304*a^3*b^3*c^6*d*e^6)/(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5) + (2*(d + e*x)^(1/2)*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2)*(4*b^7*c^5*e^3 - 48*a*b^5*c^6*e^3 - 256*a^3*b*c^8*e^3 + 512*a^3*c^9*d*e^2 - 8*b^6*c^6*d*e^2 + 192*a^2*b^3*c^7*e^3 + 96*a*b^4*c^7*d*e^2 - 384*a^2*b^2*c^8*d*e^2))/(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4))*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2) + (2*(d + e*x)^(1/2)*(9*b^8*e^10 + 200*a^4*c^4*e^10 + 32*c^8*d^8*e^2 + 280*a*c^7*d^6*e^4 - 128*b*c^7*d^7*e^3 + 481*a^2*b^4*c^2*e^10 - 718*a^3*b^2*c^3*e^10 + 280*a^2*c^6*d^4*e^6 - 2072*a^3*c^5*d^2*e^8 + 154*b^2*c^6*d^6*e^4 - 14*b^3*c^5*d^5*e^5 - 105*b^4*c^4*d^4*e^6 + 84*b^5*c^3*d^3*e^7 + 7*b^6*c^2*d^2*e^8 - 114*a*b^6*c*e^10 - 30*b^7*c*d*e^9 + 1974*a^2*b^2*c^4*d^2*e^8 - 840*a*b*c^6*d^5*e^5 + 406*a*b^5*c^2*d*e^9 + 2072*a^3*b*c^4*d*e^9 + 910*a*b^2*c^5*d^4*e^6 - 420*a*b^3*c^4*d^3*e^7 - 336*a*b^4*c^3*d^2*e^8 - 560*a^2*b*c^5*d^3*e^7 - 1694*a^2*b^3*c^3*d*e^9))/(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4))*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2)*1i)/((((2560*a^5*c^7*e^7 + 12*a*b^8*c^3*e^7 - 12*b^9*c^3*d*e^6 - 184*a^2*b^6*c^4*e^7 + 1056*a^3*b^4*c^5*e^7 - 2688*a^4*b^2*c^6*e^7 - 512*a^3*c^9*d^4*e^3 + 2048*a^4*c^8*d^2*e^5 + 8*b^6*c^6*d^4*e^3 - 16*b^7*c^5*d^3*e^4 + 20*b^8*c^4*d^2*e^5 + 384*a^2*b^2*c^8*d^4*e^3 - 768*a^2*b^3*c^7*d^3*e^4 + 1344*a^2*b^4*c^6*d^2*e^5 - 2816*a^3*b^2*c^7*d^2*e^5 + 176*a*b^7*c^4*d*e^6 - 2048*a^4*b*c^7*d*e^6 - 96*a*b^4*c^7*d^4*e^3 + 192*a*b^5*c^6*d^3*e^4 - 272*a*b^6*c^5*d^2*e^5 - 960*a^2*b^5*c^5*d*e^6 + 1024*a^3*b*c^8*d^3*e^4 + 2304*a^3*b^3*c^6*d*e^6)/(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5) - (2*(d + e*x)^(1/2)*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2)*(4*b^7*c^5*e^3 - 48*a*b^5*c^6*e^3 - 256*a^3*b*c^8*e^3 + 512*a^3*c^9*d*e^2 - 8*b^6*c^6*d*e^2 + 192*a^2*b^3*c^7*e^3 + 96*a*b^4*c^7*d*e^2 - 384*a^2*b^2*c^8*d*e^2))/(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4))*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2) - (2*(d + e*x)^(1/2)*(9*b^8*e^10 + 200*a^4*c^4*e^10 + 32*c^8*d^8*e^2 + 280*a*c^7*d^6*e^4 - 128*b*c^7*d^7*e^3 + 481*a^2*b^4*c^2*e^10 - 718*a^3*b^2*c^3*e^10 + 280*a^2*c^6*d^4*e^6 - 2072*a^3*c^5*d^2*e^8 + 154*b^2*c^6*d^6*e^4 - 14*b^3*c^5*d^5*e^5 - 105*b^4*c^4*d^4*e^6 + 84*b^5*c^3*d^3*e^7 + 7*b^6*c^2*d^2*e^8 - 114*a*b^6*c*e^10 - 30*b^7*c*d*e^9 + 1974*a^2*b^2*c^4*d^2*e^8 - 840*a*b*c^6*d^5*e^5 + 406*a*b^5*c^2*d*e^9 + 2072*a^3*b*c^4*d*e^9 + 910*a*b^2*c^5*d^4*e^6 - 420*a*b^3*c^4*d^3*e^7 - 336*a*b^4*c^3*d^2*e^8 - 560*a^2*b*c^5*d^3*e^7 - 1694*a^2*b^3*c^3*d*e^9))/(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4))*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2) - (2*(63*b^8*d^3*e^11 - 63*a^3*b^5*e^14 + 32*c^8*d^11*e^3 + 573*a^4*b^3*c*e^14 - 1300*a^5*b*c^2*e^14 - 189*a*b^7*d^2*e^12 + 189*a^2*b^6*d*e^13 + 712*a*c^7*d^9*e^5 + 2600*a^5*c^3*d*e^13 - 176*b*c^7*d^10*e^4 - 246*b^7*c*d^4*e^10 + 4544*a^2*c^6*d^7*e^7 + 9680*a^3*c^5*d^5*e^9 + 8416*a^4*c^4*d^3*e^11 + 262*b^2*c^6*d^9*e^5 + 141*b^3*c^5*d^8*e^6 - 658*b^4*c^4*d^7*e^7 + 413*b^5*c^3*d^6*e^8 + 169*b^6*c^2*d^5*e^9 + 16596*a^2*b^2*c^4*d^5*e^9 - 1730*a^2*b^3*c^3*d^4*e^10 - 5054*a^2*b^4*c^2*d^3*e^11 + 15784*a^3*b^2*c^3*d^3*e^11 + 524*a^3*b^3*c^2*d^2*e^12 - 3204*a*b*c^6*d^8*e^6 - 24*a*b^6*c*d^3*e^11 - 1662*a^3*b^4*c*d*e^13 + 4136*a*b^2*c^5*d^7*e^7 + 476*a*b^3*c^4*d^6*e^8 - 4506*a*b^4*c^3*d^5*e^9 + 2599*a*b^5*c^2*d^4*e^10 - 15904*a^2*b*c^5*d^6*e^8 + 1359*a^2*b^5*c*d^2*e^12 - 24200*a^3*b*c^4*d^4*e^10 - 12624*a^4*b*c^3*d^2*e^12 + 3062*a^4*b^2*c^2*d*e^13))/(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5) + (((2560*a^5*c^7*e^7 + 12*a*b^8*c^3*e^7 - 12*b^9*c^3*d*e^6 - 184*a^2*b^6*c^4*e^7 + 1056*a^3*b^4*c^5*e^7 - 2688*a^4*b^2*c^6*e^7 - 512*a^3*c^9*d^4*e^3 + 2048*a^4*c^8*d^2*e^5 + 8*b^6*c^6*d^4*e^3 - 16*b^7*c^5*d^3*e^4 + 20*b^8*c^4*d^2*e^5 + 384*a^2*b^2*c^8*d^4*e^3 - 768*a^2*b^3*c^7*d^3*e^4 + 1344*a^2*b^4*c^6*d^2*e^5 - 2816*a^3*b^2*c^7*d^2*e^5 + 176*a*b^7*c^4*d*e^6 - 2048*a^4*b*c^7*d*e^6 - 96*a*b^4*c^7*d^4*e^3 + 192*a*b^5*c^6*d^3*e^4 - 272*a*b^6*c^5*d^2*e^5 - 960*a^2*b^5*c^5*d*e^6 + 1024*a^3*b*c^8*d^3*e^4 + 2304*a^3*b^3*c^6*d*e^6)/(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5) + (2*(d + e*x)^(1/2)*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2)*(4*b^7*c^5*e^3 - 48*a*b^5*c^6*e^3 - 256*a^3*b*c^8*e^3 + 512*a^3*c^9*d*e^2 - 8*b^6*c^6*d*e^2 + 192*a^2*b^3*c^7*e^3 + 96*a*b^4*c^7*d*e^2 - 384*a^2*b^2*c^8*d*e^2))/(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4))*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2) + (2*(d + e*x)^(1/2)*(9*b^8*e^10 + 200*a^4*c^4*e^10 + 32*c^8*d^8*e^2 + 280*a*c^7*d^6*e^4 - 128*b*c^7*d^7*e^3 + 481*a^2*b^4*c^2*e^10 - 718*a^3*b^2*c^3*e^10 + 280*a^2*c^6*d^4*e^6 - 2072*a^3*c^5*d^2*e^8 + 154*b^2*c^6*d^6*e^4 - 14*b^3*c^5*d^5*e^5 - 105*b^4*c^4*d^4*e^6 + 84*b^5*c^3*d^3*e^7 + 7*b^6*c^2*d^2*e^8 - 114*a*b^6*c*e^10 - 30*b^7*c*d*e^9 + 1974*a^2*b^2*c^4*d^2*e^8 - 840*a*b*c^6*d^5*e^5 + 406*a*b^5*c^2*d*e^9 + 2072*a^3*b*c^4*d*e^9 + 910*a*b^2*c^5*d^4*e^6 - 420*a*b^3*c^4*d^3*e^7 - 336*a*b^4*c^3*d^2*e^8 - 560*a^2*b*c^5*d^3*e^7 - 1694*a^2*b^3*c^3*d*e^9))/(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4))*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2)))*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2)*2i - atan(((((2560*a^5*c^7*e^7 + 12*a*b^8*c^3*e^7 - 12*b^9*c^3*d*e^6 - 184*a^2*b^6*c^4*e^7 + 1056*a^3*b^4*c^5*e^7 - 2688*a^4*b^2*c^6*e^7 - 512*a^3*c^9*d^4*e^3 + 2048*a^4*c^8*d^2*e^5 + 8*b^6*c^6*d^4*e^3 - 16*b^7*c^5*d^3*e^4 + 20*b^8*c^4*d^2*e^5 + 384*a^2*b^2*c^8*d^4*e^3 - 768*a^2*b^3*c^7*d^3*e^4 + 1344*a^2*b^4*c^6*d^2*e^5 - 2816*a^3*b^2*c^7*d^2*e^5 + 176*a*b^7*c^4*d*e^6 - 2048*a^4*b*c^7*d*e^6 - 96*a*b^4*c^7*d^4*e^3 + 192*a*b^5*c^6*d^3*e^4 - 272*a*b^6*c^5*d^2*e^5 - 960*a^2*b^5*c^5*d*e^6 + 1024*a^3*b*c^8*d^3*e^4 + 2304*a^3*b^3*c^6*d*e^6)/(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5) - (2*(d + e*x)^(1/2)*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2)*(4*b^7*c^5*e^3 - 48*a*b^5*c^6*e^3 - 256*a^3*b*c^8*e^3 + 512*a^3*c^9*d*e^2 - 8*b^6*c^6*d*e^2 + 192*a^2*b^3*c^7*e^3 + 96*a*b^4*c^7*d*e^2 - 384*a^2*b^2*c^8*d*e^2))/(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4))*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2) - (2*(d + e*x)^(1/2)*(9*b^8*e^10 + 200*a^4*c^4*e^10 + 32*c^8*d^8*e^2 + 280*a*c^7*d^6*e^4 - 128*b*c^7*d^7*e^3 + 481*a^2*b^4*c^2*e^10 - 718*a^3*b^2*c^3*e^10 + 280*a^2*c^6*d^4*e^6 - 2072*a^3*c^5*d^2*e^8 + 154*b^2*c^6*d^6*e^4 - 14*b^3*c^5*d^5*e^5 - 105*b^4*c^4*d^4*e^6 + 84*b^5*c^3*d^3*e^7 + 7*b^6*c^2*d^2*e^8 - 114*a*b^6*c*e^10 - 30*b^7*c*d*e^9 + 1974*a^2*b^2*c^4*d^2*e^8 - 840*a*b*c^6*d^5*e^5 + 406*a*b^5*c^2*d*e^9 + 2072*a^3*b*c^4*d*e^9 + 910*a*b^2*c^5*d^4*e^6 - 420*a*b^3*c^4*d^3*e^7 - 336*a*b^4*c^3*d^2*e^8 - 560*a^2*b*c^5*d^3*e^7 - 1694*a^2*b^3*c^3*d*e^9))/(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4))*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2)*1i - (((2560*a^5*c^7*e^7 + 12*a*b^8*c^3*e^7 - 12*b^9*c^3*d*e^6 - 184*a^2*b^6*c^4*e^7 + 1056*a^3*b^4*c^5*e^7 - 2688*a^4*b^2*c^6*e^7 - 512*a^3*c^9*d^4*e^3 + 2048*a^4*c^8*d^2*e^5 + 8*b^6*c^6*d^4*e^3 - 16*b^7*c^5*d^3*e^4 + 20*b^8*c^4*d^2*e^5 + 384*a^2*b^2*c^8*d^4*e^3 - 768*a^2*b^3*c^7*d^3*e^4 + 1344*a^2*b^4*c^6*d^2*e^5 - 2816*a^3*b^2*c^7*d^2*e^5 + 176*a*b^7*c^4*d*e^6 - 2048*a^4*b*c^7*d*e^6 - 96*a*b^4*c^7*d^4*e^3 + 192*a*b^5*c^6*d^3*e^4 - 272*a*b^6*c^5*d^2*e^5 - 960*a^2*b^5*c^5*d*e^6 + 1024*a^3*b*c^8*d^3*e^4 + 2304*a^3*b^3*c^6*d*e^6)/(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5) + (2*(d + e*x)^(1/2)*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2)*(4*b^7*c^5*e^3 - 48*a*b^5*c^6*e^3 - 256*a^3*b*c^8*e^3 + 512*a^3*c^9*d*e^2 - 8*b^6*c^6*d*e^2 + 192*a^2*b^3*c^7*e^3 + 96*a*b^4*c^7*d*e^2 - 384*a^2*b^2*c^8*d*e^2))/(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4))*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2) + (2*(d + e*x)^(1/2)*(9*b^8*e^10 + 200*a^4*c^4*e^10 + 32*c^8*d^8*e^2 + 280*a*c^7*d^6*e^4 - 128*b*c^7*d^7*e^3 + 481*a^2*b^4*c^2*e^10 - 718*a^3*b^2*c^3*e^10 + 280*a^2*c^6*d^4*e^6 - 2072*a^3*c^5*d^2*e^8 + 154*b^2*c^6*d^6*e^4 - 14*b^3*c^5*d^5*e^5 - 105*b^4*c^4*d^4*e^6 + 84*b^5*c^3*d^3*e^7 + 7*b^6*c^2*d^2*e^8 - 114*a*b^6*c*e^10 - 30*b^7*c*d*e^9 + 1974*a^2*b^2*c^4*d^2*e^8 - 840*a*b*c^6*d^5*e^5 + 406*a*b^5*c^2*d*e^9 + 2072*a^3*b*c^4*d*e^9 + 910*a*b^2*c^5*d^4*e^6 - 420*a*b^3*c^4*d^3*e^7 - 336*a*b^4*c^3*d^2*e^8 - 560*a^2*b*c^5*d^3*e^7 - 1694*a^2*b^3*c^3*d*e^9))/(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4))*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2)*1i)/((((2560*a^5*c^7*e^7 + 12*a*b^8*c^3*e^7 - 12*b^9*c^3*d*e^6 - 184*a^2*b^6*c^4*e^7 + 1056*a^3*b^4*c^5*e^7 - 2688*a^4*b^2*c^6*e^7 - 512*a^3*c^9*d^4*e^3 + 2048*a^4*c^8*d^2*e^5 + 8*b^6*c^6*d^4*e^3 - 16*b^7*c^5*d^3*e^4 + 20*b^8*c^4*d^2*e^5 + 384*a^2*b^2*c^8*d^4*e^3 - 768*a^2*b^3*c^7*d^3*e^4 + 1344*a^2*b^4*c^6*d^2*e^5 - 2816*a^3*b^2*c^7*d^2*e^5 + 176*a*b^7*c^4*d*e^6 - 2048*a^4*b*c^7*d*e^6 - 96*a*b^4*c^7*d^4*e^3 + 192*a*b^5*c^6*d^3*e^4 - 272*a*b^6*c^5*d^2*e^5 - 960*a^2*b^5*c^5*d*e^6 + 1024*a^3*b*c^8*d^3*e^4 + 2304*a^3*b^3*c^6*d*e^6)/(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5) - (2*(d + e*x)^(1/2)*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2)*(4*b^7*c^5*e^3 - 48*a*b^5*c^6*e^3 - 256*a^3*b*c^8*e^3 + 512*a^3*c^9*d*e^2 - 8*b^6*c^6*d*e^2 + 192*a^2*b^3*c^7*e^3 + 96*a*b^4*c^7*d*e^2 - 384*a^2*b^2*c^8*d*e^2))/(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4))*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2) - (2*(d + e*x)^(1/2)*(9*b^8*e^10 + 200*a^4*c^4*e^10 + 32*c^8*d^8*e^2 + 280*a*c^7*d^6*e^4 - 128*b*c^7*d^7*e^3 + 481*a^2*b^4*c^2*e^10 - 718*a^3*b^2*c^3*e^10 + 280*a^2*c^6*d^4*e^6 - 2072*a^3*c^5*d^2*e^8 + 154*b^2*c^6*d^6*e^4 - 14*b^3*c^5*d^5*e^5 - 105*b^4*c^4*d^4*e^6 + 84*b^5*c^3*d^3*e^7 + 7*b^6*c^2*d^2*e^8 - 114*a*b^6*c*e^10 - 30*b^7*c*d*e^9 + 1974*a^2*b^2*c^4*d^2*e^8 - 840*a*b*c^6*d^5*e^5 + 406*a*b^5*c^2*d*e^9 + 2072*a^3*b*c^4*d*e^9 + 910*a*b^2*c^5*d^4*e^6 - 420*a*b^3*c^4*d^3*e^7 - 336*a*b^4*c^3*d^2*e^8 - 560*a^2*b*c^5*d^3*e^7 - 1694*a^2*b^3*c^3*d*e^9))/(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4))*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2) - (2*(63*b^8*d^3*e^11 - 63*a^3*b^5*e^14 + 32*c^8*d^11*e^3 + 573*a^4*b^3*c*e^14 - 1300*a^5*b*c^2*e^14 - 189*a*b^7*d^2*e^12 + 189*a^2*b^6*d*e^13 + 712*a*c^7*d^9*e^5 + 2600*a^5*c^3*d*e^13 - 176*b*c^7*d^10*e^4 - 246*b^7*c*d^4*e^10 + 4544*a^2*c^6*d^7*e^7 + 9680*a^3*c^5*d^5*e^9 + 8416*a^4*c^4*d^3*e^11 + 262*b^2*c^6*d^9*e^5 + 141*b^3*c^5*d^8*e^6 - 658*b^4*c^4*d^7*e^7 + 413*b^5*c^3*d^6*e^8 + 169*b^6*c^2*d^5*e^9 + 16596*a^2*b^2*c^4*d^5*e^9 - 1730*a^2*b^3*c^3*d^4*e^10 - 5054*a^2*b^4*c^2*d^3*e^11 + 15784*a^3*b^2*c^3*d^3*e^11 + 524*a^3*b^3*c^2*d^2*e^12 - 3204*a*b*c^6*d^8*e^6 - 24*a*b^6*c*d^3*e^11 - 1662*a^3*b^4*c*d*e^13 + 4136*a*b^2*c^5*d^7*e^7 + 476*a*b^3*c^4*d^6*e^8 - 4506*a*b^4*c^3*d^5*e^9 + 2599*a*b^5*c^2*d^4*e^10 - 15904*a^2*b*c^5*d^6*e^8 + 1359*a^2*b^5*c*d^2*e^12 - 24200*a^3*b*c^4*d^4*e^10 - 12624*a^4*b*c^3*d^2*e^12 + 3062*a^4*b^2*c^2*d*e^13))/(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5) + (((2560*a^5*c^7*e^7 + 12*a*b^8*c^3*e^7 - 12*b^9*c^3*d*e^6 - 184*a^2*b^6*c^4*e^7 + 1056*a^3*b^4*c^5*e^7 - 2688*a^4*b^2*c^6*e^7 - 512*a^3*c^9*d^4*e^3 + 2048*a^4*c^8*d^2*e^5 + 8*b^6*c^6*d^4*e^3 - 16*b^7*c^5*d^3*e^4 + 20*b^8*c^4*d^2*e^5 + 384*a^2*b^2*c^8*d^4*e^3 - 768*a^2*b^3*c^7*d^3*e^4 + 1344*a^2*b^4*c^6*d^2*e^5 - 2816*a^3*b^2*c^7*d^2*e^5 + 176*a*b^7*c^4*d*e^6 - 2048*a^4*b*c^7*d*e^6 - 96*a*b^4*c^7*d^4*e^3 + 192*a*b^5*c^6*d^3*e^4 - 272*a*b^6*c^5*d^2*e^5 - 960*a^2*b^5*c^5*d*e^6 + 1024*a^3*b*c^8*d^3*e^4 + 2304*a^3*b^3*c^6*d*e^6)/(64*a^3*c^6 - b^6*c^3 + 12*a*b^4*c^4 - 48*a^2*b^2*c^5) + (2*(d + e*x)^(1/2)*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2)*(4*b^7*c^5*e^3 - 48*a*b^5*c^6*e^3 - 256*a^3*b*c^8*e^3 + 512*a^3*c^9*d*e^2 - 8*b^6*c^6*d*e^2 + 192*a^2*b^3*c^7*e^3 + 96*a*b^4*c^7*d*e^2 - 384*a^2*b^2*c^8*d*e^2))/(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4))*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2) + (2*(d + e*x)^(1/2)*(9*b^8*e^10 + 200*a^4*c^4*e^10 + 32*c^8*d^8*e^2 + 280*a*c^7*d^6*e^4 - 128*b*c^7*d^7*e^3 + 481*a^2*b^4*c^2*e^10 - 718*a^3*b^2*c^3*e^10 + 280*a^2*c^6*d^4*e^6 - 2072*a^3*c^5*d^2*e^8 + 154*b^2*c^6*d^6*e^4 - 14*b^3*c^5*d^5*e^5 - 105*b^4*c^4*d^4*e^6 + 84*b^5*c^3*d^3*e^7 + 7*b^6*c^2*d^2*e^8 - 114*a*b^6*c*e^10 - 30*b^7*c*d*e^9 + 1974*a^2*b^2*c^4*d^2*e^8 - 840*a*b*c^6*d^5*e^5 + 406*a*b^5*c^2*d*e^9 + 2072*a^3*b*c^4*d*e^9 + 910*a*b^2*c^5*d^4*e^6 - 420*a*b^3*c^4*d^3*e^7 - 336*a*b^4*c^3*d^2*e^8 - 560*a^2*b*c^5*d^3*e^7 - 1694*a^2*b^3*c^3*d*e^9))/(16*a^2*c^5 + b^4*c^3 - 8*a*b^2*c^4))*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2)))*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(4096*a^6*c^11 + b^12*c^5 - 24*a*b^10*c^6 + 240*a^2*b^8*c^7 - 1280*a^3*b^6*c^8 + 3840*a^4*b^4*c^9 - 6144*a^5*b^2*c^10)))^(1/2)*2i - (((d + e*x)^(1/2)*(a*b^2*e^5 - 2*a^2*c*e^5 - b^3*d*e^4 + 2*c^3*d^4*e - 4*b*c^2*d^3*e^2 + 3*b^2*c*d^2*e^3))/(4*a*c - b^2) + ((d + e*x)^(3/2)*(b^3*e^4 - 2*c^3*d^3*e + 3*b*c^2*d^2*e^2 - 3*a*b*c*e^4 + 6*a*c^2*d*e^3 - 3*b^2*c*d*e^3))/(4*a*c - b^2))/(c^3*(d + e*x)^2 - (2*c^3*d - b*c^2*e)*(d + e*x) + c^3*d^2 + a*c^2*e^2 - b*c^2*d*e)","B"
2296,1,21160,504,4.681040,"\text{Not used}","int((d + e*x)^(5/2)/(a + b*x + c*x^2)^2,x)","-\frac{\frac{\sqrt{d+e\,x}\,\left(b^2\,d\,e^3-3\,b\,c\,d^2\,e^2-a\,b\,e^4+2\,c^2\,d^3\,e+2\,a\,c\,d\,e^3\right)}{c\,\left(4\,a\,c-b^2\right)}-\frac{e\,{\left(d+e\,x\right)}^{3/2}\,\left(b^2\,e^2-2\,b\,c\,d\,e+2\,c^2\,d^2-2\,a\,c\,e^2\right)}{c\,\left(4\,a\,c-b^2\right)}}{\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)+c\,{\left(d+e\,x\right)}^2+a\,e^2+c\,d^2-b\,d\,e}+\mathrm{atan}\left(\frac{\left(\left(\frac{256\,a^4\,b\,c^5\,e^6-512\,a^4\,c^6\,d\,e^5-192\,a^3\,b^3\,c^4\,e^6+128\,a^3\,b^2\,c^5\,d\,e^5+768\,a^3\,b\,c^6\,d^2\,e^4-512\,a^3\,c^7\,d^3\,e^3+48\,a^2\,b^5\,c^3\,e^6+96\,a^2\,b^4\,c^4\,d\,e^5-576\,a^2\,b^3\,c^5\,d^2\,e^4+384\,a^2\,b^2\,c^6\,d^3\,e^3-4\,a\,b^7\,c^2\,e^6-40\,a\,b^6\,c^3\,d\,e^5+144\,a\,b^5\,c^4\,d^2\,e^4-96\,a\,b^4\,c^5\,d^3\,e^3+4\,b^8\,c^2\,d\,e^5-12\,b^7\,c^3\,d^2\,e^4+8\,b^6\,c^4\,d^3\,e^3}{-64\,a^3\,c^4+48\,a^2\,b^2\,c^3-12\,a\,b^4\,c^2+b^6\,c}-\frac{2\,\sqrt{d+e\,x}\,\sqrt{\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5+b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3-5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5-9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4+5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}}\,\left(-256\,a^3\,b\,c^6\,e^3+512\,d\,a^3\,c^7\,e^2+192\,a^2\,b^3\,c^5\,e^3-384\,d\,a^2\,b^2\,c^6\,e^2-48\,a\,b^5\,c^4\,e^3+96\,d\,a\,b^4\,c^5\,e^2+4\,b^7\,c^3\,e^3-8\,d\,b^6\,c^4\,e^2\right)}{16\,a^2\,c^3-8\,a\,b^2\,c^2+b^4\,c}\right)\,\sqrt{\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5+b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3-5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5-9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4+5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}}-\frac{2\,\sqrt{d+e\,x}\,\left(-72\,a^3\,c^3\,e^8+74\,a^2\,b^2\,c^2\,e^8-80\,a^2\,b\,c^3\,d\,e^7+80\,a^2\,c^4\,d^2\,e^6-16\,a\,b^4\,c\,e^8-20\,a\,b^3\,c^2\,d\,e^7+140\,a\,b^2\,c^3\,d^2\,e^6-240\,a\,b\,c^4\,d^3\,e^5+120\,a\,c^5\,d^4\,e^4+b^6\,e^8+4\,b^5\,c\,d\,e^7-10\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+90\,b^2\,c^4\,d^4\,e^4-96\,b\,c^5\,d^5\,e^3+32\,c^6\,d^6\,e^2\right)}{16\,a^2\,c^3-8\,a\,b^2\,c^2+b^4\,c}\right)\,\sqrt{\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5+b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3-5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5-9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4+5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}}\,1{}\mathrm{i}-\left(\left(\frac{256\,a^4\,b\,c^5\,e^6-512\,a^4\,c^6\,d\,e^5-192\,a^3\,b^3\,c^4\,e^6+128\,a^3\,b^2\,c^5\,d\,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12}\,c^3\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(\frac{256\,a^4\,b\,c^5\,e^6-512\,a^4\,c^6\,d\,e^5-192\,a^3\,b^3\,c^4\,e^6+128\,a^3\,b^2\,c^5\,d\,e^5+768\,a^3\,b\,c^6\,d^2\,e^4-512\,a^3\,c^7\,d^3\,e^3+48\,a^2\,b^5\,c^3\,e^6+96\,a^2\,b^4\,c^4\,d\,e^5-576\,a^2\,b^3\,c^5\,d^2\,e^4+384\,a^2\,b^2\,c^6\,d^3\,e^3-4\,a\,b^7\,c^2\,e^6-40\,a\,b^6\,c^3\,d\,e^5+144\,a\,b^5\,c^4\,d^2\,e^4-96\,a\,b^4\,c^5\,d^3\,e^3+4\,b^8\,c^2\,d\,e^5-12\,b^7\,c^3\,d^2\,e^4+8\,b^6\,c^4\,d^3\,e^3}{-64\,a^3\,c^4+48\,a^2\,b^2\,c^3-12\,a\,b^4\,c^2+b^6\,c}-\frac{2\,\sqrt{d+e\,x}\,\sqrt{\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5-b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3+5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5+9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4-5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}}\,\left(-256\,a^3\,b\,c^6\,e^3+512\,d\,a^3\,c^7\,e^2+192\,a^2\,b^3\,c^5\,e^3-384\,d\,a^2\,b^2\,c^6\,e^2-48\,a\,b^5\,c^4\,e^3+96\,d\,a\,b^4\,c^5\,e^2+4\,b^7\,c^3\,e^3-8\,d\,b^6\,c^4\,e^2\right)}{16\,a^2\,c^3-8\,a\,b^2\,c^2+b^4\,c}\right)\,\sqrt{\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5-b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3+5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5+9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4-5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}}-\frac{2\,\sqrt{d+e\,x}\,\left(-72\,a^3\,c^3\,e^8+74\,a^2\,b^2\,c^2\,e^8-80\,a^2\,b\,c^3\,d\,e^7+80\,a^2\,c^4\,d^2\,e^6-16\,a\,b^4\,c\,e^8-20\,a\,b^3\,c^2\,d\,e^7+140\,a\,b^2\,c^3\,d^2\,e^6-240\,a\,b\,c^4\,d^3\,e^5+120\,a\,c^5\,d^4\,e^4+b^6\,e^8+4\,b^5\,c\,d\,e^7-10\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+90\,b^2\,c^4\,d^4\,e^4-96\,b\,c^5\,d^5\,e^3+32\,c^6\,d^6\,e^2\right)}{16\,a^2\,c^3-8\,a\,b^2\,c^2+b^4\,c}\right)\,\sqrt{\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5-b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3+5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5+9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4-5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}}\,1{}\mathrm{i}-\left(\left(\frac{256\,a^4\,b\,c^5\,e^6-512\,a^4\,c^6\,d\,e^5-192\,a^3\,b^3\,c^4\,e^6+128\,a^3\,b^2\,c^5\,d\,e^5+768\,a^3\,b\,c^6\,d^2\,e^4-512\,a^3\,c^7\,d^3\,e^3+48\,a^2\,b^5\,c^3\,e^6+96\,a^2\,b^4\,c^4\,d\,e^5-576\,a^2\,b^3\,c^5\,d^2\,e^4+384\,a^2\,b^2\,c^6\,d^3\,e^3-4\,a\,b^7\,c^2\,e^6-40\,a\,b^6\,c^3\,d\,e^5+144\,a\,b^5\,c^4\,d^2\,e^4-96\,a\,b^4\,c^5\,d^3\,e^3+4\,b^8\,c^2\,d\,e^5-12\,b^7\,c^3\,d^2\,e^4+8\,b^6\,c^4\,d^3\,e^3}{-64\,a^3\,c^4+48\,a^2\,b^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-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4-5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}}\,\left(-256\,a^3\,b\,c^6\,e^3+512\,d\,a^3\,c^7\,e^2+192\,a^2\,b^3\,c^5\,e^3-384\,d\,a^2\,b^2\,c^6\,e^2-48\,a\,b^5\,c^4\,e^3+96\,d\,a\,b^4\,c^5\,e^2+4\,b^7\,c^3\,e^3-8\,d\,b^6\,c^4\,e^2\right)}{16\,a^2\,c^3-8\,a\,b^2\,c^2+b^4\,c}\right)\,\sqrt{\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5-b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3+5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5+9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4-5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}}-\frac{2\,\sqrt{d+e\,x}\,\left(-72\,a^3\,c^3\,e^8+74\,a^2\,b^2\,c^2\,e^8-80\,a^2\,b\,c^3\,d\,e^7+80\,a^2\,c^4\,d^2\,e^6-16\,a\,b^4\,c\,e^8-20\,a\,b^3\,c^2\,d\,e^7+140\,a\,b^2\,c^3\,d^2\,e^6-240\,a\,b\,c^4\,d^3\,e^5+120\,a\,c^5\,d^4\,e^4+b^6\,e^8+4\,b^5\,c\,d\,e^7-10\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+90\,b^2\,c^4\,d^4\,e^4-96\,b\,c^5\,d^5\,e^3+32\,c^6\,d^6\,e^2\right)}{16\,a^2\,c^3-8\,a\,b^2\,c^2+b^4\,c}\right)\,\sqrt{\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5-b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3+5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5+9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4-5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}}-\frac{2\,\left(216\,a^4\,c^2\,e^{11}-66\,a^3\,b^2\,c\,e^{11}-600\,a^3\,b\,c^2\,d\,e^{10}+600\,a^3\,c^3\,d^2\,e^9+5\,a^2\,b^4\,e^{11}+158\,a^2\,b^3\,c\,d\,e^{10}+426\,a^2\,b^2\,c^2\,d^2\,e^9-1168\,a^2\,b\,c^3\,d^3\,e^8+584\,a^2\,c^4\,d^4\,e^7-10\,a\,b^5\,d\,e^{10}-108\,a\,b^4\,c\,d^2\,e^9+4\,a\,b^3\,c^2\,d^3\,e^8+578\,a\,b^2\,c^3\,d^4\,e^7-696\,a\,b\,c^4\,d^5\,e^6+232\,a\,c^5\,d^6\,e^5+5\,b^6\,d^2\,e^9+16\,b^5\,c\,d^3\,e^8-41\,b^4\,c^2\,d^4\,e^7-50\,b^3\,c^3\,d^5\,e^6+166\,b^2\,c^4\,d^6\,e^5-128\,b\,c^5\,d^7\,e^4+32\,c^6\,d^8\,e^3\right)}{-64\,a^3\,c^4+48\,a^2\,b^2\,c^3-12\,a\,b^4\,c^2+b^6\,c}+\left(\left(\frac{256\,a^4\,b\,c^5\,e^6-512\,a^4\,c^6\,d\,e^5-192\,a^3\,b^3\,c^4\,e^6+128\,a^3\,b^2\,c^5\,d\,e^5+768\,a^3\,b\,c^6\,d^2\,e^4-512\,a^3\,c^7\,d^3\,e^3+48\,a^2\,b^5\,c^3\,e^6+96\,a^2\,b^4\,c^4\,d\,e^5-576\,a^2\,b^3\,c^5\,d^2\,e^4+384\,a^2\,b^2\,c^6\,d^3\,e^3-4\,a\,b^7\,c^2\,e^6-40\,a\,b^6\,c^3\,d\,e^5+144\,a\,b^5\,c^4\,d^2\,e^4-96\,a\,b^4\,c^5\,d^3\,e^3+4\,b^8\,c^2\,d\,e^5-12\,b^7\,c^3\,d^2\,e^4+8\,b^6\,c^4\,d^3\,e^3}{-64\,a^3\,c^4+48\,a^2\,b^2\,c^3-12\,a\,b^4\,c^2+b^6\,c}+\frac{2\,\sqrt{d+e\,x}\,\sqrt{\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5-b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3+5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5+9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4-5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}}\,\left(-256\,a^3\,b\,c^6\,e^3+512\,d\,a^3\,c^7\,e^2+192\,a^2\,b^3\,c^5\,e^3-384\,d\,a^2\,b^2\,c^6\,e^2-48\,a\,b^5\,c^4\,e^3+96\,d\,a\,b^4\,c^5\,e^2+4\,b^7\,c^3\,e^3-8\,d\,b^6\,c^4\,e^2\right)}{16\,a^2\,c^3-8\,a\,b^2\,c^2+b^4\,c}\right)\,\sqrt{\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5-b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3+5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5+9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4-5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}}+\frac{2\,\sqrt{d+e\,x}\,\left(-72\,a^3\,c^3\,e^8+74\,a^2\,b^2\,c^2\,e^8-80\,a^2\,b\,c^3\,d\,e^7+80\,a^2\,c^4\,d^2\,e^6-16\,a\,b^4\,c\,e^8-20\,a\,b^3\,c^2\,d\,e^7+140\,a\,b^2\,c^3\,d^2\,e^6-240\,a\,b\,c^4\,d^3\,e^5+120\,a\,c^5\,d^4\,e^4+b^6\,e^8+4\,b^5\,c\,d\,e^7-10\,b^4\,c^2\,d^2\,e^6-20\,b^3\,c^3\,d^3\,e^5+90\,b^2\,c^4\,d^4\,e^4-96\,b\,c^5\,d^5\,e^3+32\,c^6\,d^6\,e^2\right)}{16\,a^2\,c^3-8\,a\,b^2\,c^2+b^4\,c}\right)\,\sqrt{\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5-b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3+5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5+9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4-5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}}}\right)\,\sqrt{\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5-b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3+5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5+9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4-5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}}\,2{}\mathrm{i}","Not used",1,"atan(((((256*a^4*b*c^5*e^6 - 4*a*b^7*c^2*e^6 - 512*a^4*c^6*d*e^5 + 4*b^8*c^2*d*e^5 + 48*a^2*b^5*c^3*e^6 - 192*a^3*b^3*c^4*e^6 - 512*a^3*c^7*d^3*e^3 + 8*b^6*c^4*d^3*e^3 - 12*b^7*c^3*d^2*e^4 + 384*a^2*b^2*c^6*d^3*e^3 - 576*a^2*b^3*c^5*d^2*e^4 - 40*a*b^6*c^3*d*e^5 - 96*a*b^4*c^5*d^3*e^3 + 144*a*b^5*c^4*d^2*e^4 + 96*a^2*b^4*c^4*d*e^5 + 768*a^3*b*c^6*d^2*e^4 + 128*a^3*b^2*c^5*d*e^5)/(b^6*c - 64*a^3*c^4 - 12*a*b^4*c^2 + 48*a^2*b^2*c^3) - (2*(d + e*x)^(1/2)*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2)*(4*b^7*c^3*e^3 - 48*a*b^5*c^4*e^3 - 256*a^3*b*c^6*e^3 + 512*a^3*c^7*d*e^2 - 8*b^6*c^4*d*e^2 + 192*a^2*b^3*c^5*e^3 + 96*a*b^4*c^5*d*e^2 - 384*a^2*b^2*c^6*d*e^2))/(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2) - (2*(d + e*x)^(1/2)*(b^6*e^8 - 72*a^3*c^3*e^8 + 32*c^6*d^6*e^2 + 120*a*c^5*d^4*e^4 - 96*b*c^5*d^5*e^3 + 74*a^2*b^2*c^2*e^8 + 80*a^2*c^4*d^2*e^6 + 90*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 - 10*b^4*c^2*d^2*e^6 - 16*a*b^4*c*e^8 + 4*b^5*c*d*e^7 - 240*a*b*c^4*d^3*e^5 - 20*a*b^3*c^2*d*e^7 - 80*a^2*b*c^3*d*e^7 + 140*a*b^2*c^3*d^2*e^6))/(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2)*1i - (((256*a^4*b*c^5*e^6 - 4*a*b^7*c^2*e^6 - 512*a^4*c^6*d*e^5 + 4*b^8*c^2*d*e^5 + 48*a^2*b^5*c^3*e^6 - 192*a^3*b^3*c^4*e^6 - 512*a^3*c^7*d^3*e^3 + 8*b^6*c^4*d^3*e^3 - 12*b^7*c^3*d^2*e^4 + 384*a^2*b^2*c^6*d^3*e^3 - 576*a^2*b^3*c^5*d^2*e^4 - 40*a*b^6*c^3*d*e^5 - 96*a*b^4*c^5*d^3*e^3 + 144*a*b^5*c^4*d^2*e^4 + 96*a^2*b^4*c^4*d*e^5 + 768*a^3*b*c^6*d^2*e^4 + 128*a^3*b^2*c^5*d*e^5)/(b^6*c - 64*a^3*c^4 - 12*a*b^4*c^2 + 48*a^2*b^2*c^3) + (2*(d + e*x)^(1/2)*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2)*(4*b^7*c^3*e^3 - 48*a*b^5*c^4*e^3 - 256*a^3*b*c^6*e^3 + 512*a^3*c^7*d*e^2 - 8*b^6*c^4*d*e^2 + 192*a^2*b^3*c^5*e^3 + 96*a*b^4*c^5*d*e^2 - 384*a^2*b^2*c^6*d*e^2))/(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2) + (2*(d + e*x)^(1/2)*(b^6*e^8 - 72*a^3*c^3*e^8 + 32*c^6*d^6*e^2 + 120*a*c^5*d^4*e^4 - 96*b*c^5*d^5*e^3 + 74*a^2*b^2*c^2*e^8 + 80*a^2*c^4*d^2*e^6 + 90*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 - 10*b^4*c^2*d^2*e^6 - 16*a*b^4*c*e^8 + 4*b^5*c*d*e^7 - 240*a*b*c^4*d^3*e^5 - 20*a*b^3*c^2*d*e^7 - 80*a^2*b*c^3*d*e^7 + 140*a*b^2*c^3*d^2*e^6))/(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2)*1i)/((((256*a^4*b*c^5*e^6 - 4*a*b^7*c^2*e^6 - 512*a^4*c^6*d*e^5 + 4*b^8*c^2*d*e^5 + 48*a^2*b^5*c^3*e^6 - 192*a^3*b^3*c^4*e^6 - 512*a^3*c^7*d^3*e^3 + 8*b^6*c^4*d^3*e^3 - 12*b^7*c^3*d^2*e^4 + 384*a^2*b^2*c^6*d^3*e^3 - 576*a^2*b^3*c^5*d^2*e^4 - 40*a*b^6*c^3*d*e^5 - 96*a*b^4*c^5*d^3*e^3 + 144*a*b^5*c^4*d^2*e^4 + 96*a^2*b^4*c^4*d*e^5 + 768*a^3*b*c^6*d^2*e^4 + 128*a^3*b^2*c^5*d*e^5)/(b^6*c - 64*a^3*c^4 - 12*a*b^4*c^2 + 48*a^2*b^2*c^3) - (2*(d + e*x)^(1/2)*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2)*(4*b^7*c^3*e^3 - 48*a*b^5*c^4*e^3 - 256*a^3*b*c^6*e^3 + 512*a^3*c^7*d*e^2 - 8*b^6*c^4*d*e^2 + 192*a^2*b^3*c^5*e^3 + 96*a*b^4*c^5*d*e^2 - 384*a^2*b^2*c^6*d*e^2))/(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2) - (2*(d + e*x)^(1/2)*(b^6*e^8 - 72*a^3*c^3*e^8 + 32*c^6*d^6*e^2 + 120*a*c^5*d^4*e^4 - 96*b*c^5*d^5*e^3 + 74*a^2*b^2*c^2*e^8 + 80*a^2*c^4*d^2*e^6 + 90*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 - 10*b^4*c^2*d^2*e^6 - 16*a*b^4*c*e^8 + 4*b^5*c*d*e^7 - 240*a*b*c^4*d^3*e^5 - 20*a*b^3*c^2*d*e^7 - 80*a^2*b*c^3*d*e^7 + 140*a*b^2*c^3*d^2*e^6))/(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2) - (2*(5*a^2*b^4*e^11 + 216*a^4*c^2*e^11 + 5*b^6*d^2*e^9 + 32*c^6*d^8*e^3 - 66*a^3*b^2*c*e^11 + 232*a*c^5*d^6*e^5 - 128*b*c^5*d^7*e^4 + 16*b^5*c*d^3*e^8 + 584*a^2*c^4*d^4*e^7 + 600*a^3*c^3*d^2*e^9 + 166*b^2*c^4*d^6*e^5 - 50*b^3*c^3*d^5*e^6 - 41*b^4*c^2*d^4*e^7 - 10*a*b^5*d*e^10 + 426*a^2*b^2*c^2*d^2*e^9 - 696*a*b*c^4*d^5*e^6 - 108*a*b^4*c*d^2*e^9 + 158*a^2*b^3*c*d*e^10 - 600*a^3*b*c^2*d*e^10 + 578*a*b^2*c^3*d^4*e^7 + 4*a*b^3*c^2*d^3*e^8 - 1168*a^2*b*c^3*d^3*e^8))/(b^6*c - 64*a^3*c^4 - 12*a*b^4*c^2 + 48*a^2*b^2*c^3) + (((256*a^4*b*c^5*e^6 - 4*a*b^7*c^2*e^6 - 512*a^4*c^6*d*e^5 + 4*b^8*c^2*d*e^5 + 48*a^2*b^5*c^3*e^6 - 192*a^3*b^3*c^4*e^6 - 512*a^3*c^7*d^3*e^3 + 8*b^6*c^4*d^3*e^3 - 12*b^7*c^3*d^2*e^4 + 384*a^2*b^2*c^6*d^3*e^3 - 576*a^2*b^3*c^5*d^2*e^4 - 40*a*b^6*c^3*d*e^5 - 96*a*b^4*c^5*d^3*e^3 + 144*a*b^5*c^4*d^2*e^4 + 96*a^2*b^4*c^4*d*e^5 + 768*a^3*b*c^6*d^2*e^4 + 128*a^3*b^2*c^5*d*e^5)/(b^6*c - 64*a^3*c^4 - 12*a*b^4*c^2 + 48*a^2*b^2*c^3) + (2*(d + e*x)^(1/2)*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2)*(4*b^7*c^3*e^3 - 48*a*b^5*c^4*e^3 - 256*a^3*b*c^6*e^3 + 512*a^3*c^7*d*e^2 - 8*b^6*c^4*d*e^2 + 192*a^2*b^3*c^5*e^3 + 96*a*b^4*c^5*d*e^2 - 384*a^2*b^2*c^6*d*e^2))/(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2) + (2*(d + e*x)^(1/2)*(b^6*e^8 - 72*a^3*c^3*e^8 + 32*c^6*d^6*e^2 + 120*a*c^5*d^4*e^4 - 96*b*c^5*d^5*e^3 + 74*a^2*b^2*c^2*e^8 + 80*a^2*c^4*d^2*e^6 + 90*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 - 10*b^4*c^2*d^2*e^6 - 16*a*b^4*c*e^8 + 4*b^5*c*d*e^7 - 240*a*b*c^4*d^3*e^5 - 20*a*b^3*c^2*d*e^7 - 80*a^2*b*c^3*d*e^7 + 140*a*b^2*c^3*d^2*e^6))/(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2)))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2)*2i - (((d + e*x)^(1/2)*(b^2*d*e^3 + 2*c^2*d^3*e - a*b*e^4 + 2*a*c*d*e^3 - 3*b*c*d^2*e^2))/(c*(4*a*c - b^2)) - (e*(d + e*x)^(3/2)*(b^2*e^2 + 2*c^2*d^2 - 2*a*c*e^2 - 2*b*c*d*e))/(c*(4*a*c - b^2)))/((b*e - 2*c*d)*(d + e*x) + c*(d + e*x)^2 + a*e^2 + c*d^2 - b*d*e) + atan(((((256*a^4*b*c^5*e^6 - 4*a*b^7*c^2*e^6 - 512*a^4*c^6*d*e^5 + 4*b^8*c^2*d*e^5 + 48*a^2*b^5*c^3*e^6 - 192*a^3*b^3*c^4*e^6 - 512*a^3*c^7*d^3*e^3 + 8*b^6*c^4*d^3*e^3 - 12*b^7*c^3*d^2*e^4 + 384*a^2*b^2*c^6*d^3*e^3 - 576*a^2*b^3*c^5*d^2*e^4 - 40*a*b^6*c^3*d*e^5 - 96*a*b^4*c^5*d^3*e^3 + 144*a*b^5*c^4*d^2*e^4 + 96*a^2*b^4*c^4*d*e^5 + 768*a^3*b*c^6*d^2*e^4 + 128*a^3*b^2*c^5*d*e^5)/(b^6*c - 64*a^3*c^4 - 12*a*b^4*c^2 + 48*a^2*b^2*c^3) - (2*(d + e*x)^(1/2)*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2)*(4*b^7*c^3*e^3 - 48*a*b^5*c^4*e^3 - 256*a^3*b*c^6*e^3 + 512*a^3*c^7*d*e^2 - 8*b^6*c^4*d*e^2 + 192*a^2*b^3*c^5*e^3 + 96*a*b^4*c^5*d*e^2 - 384*a^2*b^2*c^6*d*e^2))/(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2) - (2*(d + e*x)^(1/2)*(b^6*e^8 - 72*a^3*c^3*e^8 + 32*c^6*d^6*e^2 + 120*a*c^5*d^4*e^4 - 96*b*c^5*d^5*e^3 + 74*a^2*b^2*c^2*e^8 + 80*a^2*c^4*d^2*e^6 + 90*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 - 10*b^4*c^2*d^2*e^6 - 16*a*b^4*c*e^8 + 4*b^5*c*d*e^7 - 240*a*b*c^4*d^3*e^5 - 20*a*b^3*c^2*d*e^7 - 80*a^2*b*c^3*d*e^7 + 140*a*b^2*c^3*d^2*e^6))/(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2)*1i - (((256*a^4*b*c^5*e^6 - 4*a*b^7*c^2*e^6 - 512*a^4*c^6*d*e^5 + 4*b^8*c^2*d*e^5 + 48*a^2*b^5*c^3*e^6 - 192*a^3*b^3*c^4*e^6 - 512*a^3*c^7*d^3*e^3 + 8*b^6*c^4*d^3*e^3 - 12*b^7*c^3*d^2*e^4 + 384*a^2*b^2*c^6*d^3*e^3 - 576*a^2*b^3*c^5*d^2*e^4 - 40*a*b^6*c^3*d*e^5 - 96*a*b^4*c^5*d^3*e^3 + 144*a*b^5*c^4*d^2*e^4 + 96*a^2*b^4*c^4*d*e^5 + 768*a^3*b*c^6*d^2*e^4 + 128*a^3*b^2*c^5*d*e^5)/(b^6*c - 64*a^3*c^4 - 12*a*b^4*c^2 + 48*a^2*b^2*c^3) + (2*(d + e*x)^(1/2)*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2)*(4*b^7*c^3*e^3 - 48*a*b^5*c^4*e^3 - 256*a^3*b*c^6*e^3 + 512*a^3*c^7*d*e^2 - 8*b^6*c^4*d*e^2 + 192*a^2*b^3*c^5*e^3 + 96*a*b^4*c^5*d*e^2 - 384*a^2*b^2*c^6*d*e^2))/(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2) + (2*(d + e*x)^(1/2)*(b^6*e^8 - 72*a^3*c^3*e^8 + 32*c^6*d^6*e^2 + 120*a*c^5*d^4*e^4 - 96*b*c^5*d^5*e^3 + 74*a^2*b^2*c^2*e^8 + 80*a^2*c^4*d^2*e^6 + 90*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 - 10*b^4*c^2*d^2*e^6 - 16*a*b^4*c*e^8 + 4*b^5*c*d*e^7 - 240*a*b*c^4*d^3*e^5 - 20*a*b^3*c^2*d*e^7 - 80*a^2*b*c^3*d*e^7 + 140*a*b^2*c^3*d^2*e^6))/(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2)*1i)/((((256*a^4*b*c^5*e^6 - 4*a*b^7*c^2*e^6 - 512*a^4*c^6*d*e^5 + 4*b^8*c^2*d*e^5 + 48*a^2*b^5*c^3*e^6 - 192*a^3*b^3*c^4*e^6 - 512*a^3*c^7*d^3*e^3 + 8*b^6*c^4*d^3*e^3 - 12*b^7*c^3*d^2*e^4 + 384*a^2*b^2*c^6*d^3*e^3 - 576*a^2*b^3*c^5*d^2*e^4 - 40*a*b^6*c^3*d*e^5 - 96*a*b^4*c^5*d^3*e^3 + 144*a*b^5*c^4*d^2*e^4 + 96*a^2*b^4*c^4*d*e^5 + 768*a^3*b*c^6*d^2*e^4 + 128*a^3*b^2*c^5*d*e^5)/(b^6*c - 64*a^3*c^4 - 12*a*b^4*c^2 + 48*a^2*b^2*c^3) - (2*(d + e*x)^(1/2)*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2)*(4*b^7*c^3*e^3 - 48*a*b^5*c^4*e^3 - 256*a^3*b*c^6*e^3 + 512*a^3*c^7*d*e^2 - 8*b^6*c^4*d*e^2 + 192*a^2*b^3*c^5*e^3 + 96*a*b^4*c^5*d*e^2 - 384*a^2*b^2*c^6*d*e^2))/(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2) - (2*(d + e*x)^(1/2)*(b^6*e^8 - 72*a^3*c^3*e^8 + 32*c^6*d^6*e^2 + 120*a*c^5*d^4*e^4 - 96*b*c^5*d^5*e^3 + 74*a^2*b^2*c^2*e^8 + 80*a^2*c^4*d^2*e^6 + 90*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 - 10*b^4*c^2*d^2*e^6 - 16*a*b^4*c*e^8 + 4*b^5*c*d*e^7 - 240*a*b*c^4*d^3*e^5 - 20*a*b^3*c^2*d*e^7 - 80*a^2*b*c^3*d*e^7 + 140*a*b^2*c^3*d^2*e^6))/(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2) - (2*(5*a^2*b^4*e^11 + 216*a^4*c^2*e^11 + 5*b^6*d^2*e^9 + 32*c^6*d^8*e^3 - 66*a^3*b^2*c*e^11 + 232*a*c^5*d^6*e^5 - 128*b*c^5*d^7*e^4 + 16*b^5*c*d^3*e^8 + 584*a^2*c^4*d^4*e^7 + 600*a^3*c^3*d^2*e^9 + 166*b^2*c^4*d^6*e^5 - 50*b^3*c^3*d^5*e^6 - 41*b^4*c^2*d^4*e^7 - 10*a*b^5*d*e^10 + 426*a^2*b^2*c^2*d^2*e^9 - 696*a*b*c^4*d^5*e^6 - 108*a*b^4*c*d^2*e^9 + 158*a^2*b^3*c*d*e^10 - 600*a^3*b*c^2*d*e^10 + 578*a*b^2*c^3*d^4*e^7 + 4*a*b^3*c^2*d^3*e^8 - 1168*a^2*b*c^3*d^3*e^8))/(b^6*c - 64*a^3*c^4 - 12*a*b^4*c^2 + 48*a^2*b^2*c^3) + (((256*a^4*b*c^5*e^6 - 4*a*b^7*c^2*e^6 - 512*a^4*c^6*d*e^5 + 4*b^8*c^2*d*e^5 + 48*a^2*b^5*c^3*e^6 - 192*a^3*b^3*c^4*e^6 - 512*a^3*c^7*d^3*e^3 + 8*b^6*c^4*d^3*e^3 - 12*b^7*c^3*d^2*e^4 + 384*a^2*b^2*c^6*d^3*e^3 - 576*a^2*b^3*c^5*d^2*e^4 - 40*a*b^6*c^3*d*e^5 - 96*a*b^4*c^5*d^3*e^3 + 144*a*b^5*c^4*d^2*e^4 + 96*a^2*b^4*c^4*d*e^5 + 768*a^3*b*c^6*d^2*e^4 + 128*a^3*b^2*c^5*d*e^5)/(b^6*c - 64*a^3*c^4 - 12*a*b^4*c^2 + 48*a^2*b^2*c^3) + (2*(d + e*x)^(1/2)*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2)*(4*b^7*c^3*e^3 - 48*a*b^5*c^4*e^3 - 256*a^3*b*c^6*e^3 + 512*a^3*c^7*d*e^2 - 8*b^6*c^4*d*e^2 + 192*a^2*b^3*c^5*e^3 + 96*a*b^4*c^5*d*e^2 - 384*a^2*b^2*c^6*d*e^2))/(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2) + (2*(d + e*x)^(1/2)*(b^6*e^8 - 72*a^3*c^3*e^8 + 32*c^6*d^6*e^2 + 120*a*c^5*d^4*e^4 - 96*b*c^5*d^5*e^3 + 74*a^2*b^2*c^2*e^8 + 80*a^2*c^4*d^2*e^6 + 90*b^2*c^4*d^4*e^4 - 20*b^3*c^3*d^3*e^5 - 10*b^4*c^2*d^2*e^6 - 16*a*b^4*c*e^8 + 4*b^5*c*d*e^7 - 240*a*b*c^4*d^3*e^5 - 20*a*b^3*c^2*d*e^7 - 80*a^2*b*c^3*d*e^7 + 140*a*b^2*c^3*d^2*e^6))/(b^4*c + 16*a^2*c^3 - 8*a*b^2*c^2))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2)))*((32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)))^(1/2)*2i","B"
2297,1,5326,363,6.324386,"\text{Not used}","int((d + e*x)^(3/2)/(a + b*x + c*x^2)^2,x)","\ln\left(\frac{c\,e^3\,\left(b\,e-2\,c\,d\right)\,\left(4\,a^2\,c\,e^4+3\,a\,b^2\,e^4-20\,a\,b\,c\,d\,e^3+20\,a\,c^2\,d^2\,e^2-3\,b^3\,d\,e^3+19\,b^2\,c\,d^2\,e^2-32\,b\,c^2\,d^3\,e+16\,c^3\,d^4\right)}{{\left(4\,a\,c-b^2\right)}^3}-\frac{\sqrt{2}\,\left(\frac{\sqrt{2}\,\left(8\,c^2\,e^3\,\left(c\,d^2-b\,d\,e+a\,e^2\right)-2\,\sqrt{2}\,c^2\,e^2\,\left(4\,a\,c-b^2\right)\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^9\,e^3+e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+2048\,a^3\,c^6\,d^3-32\,b^6\,c^3\,d^3+384\,a\,b^4\,c^4\,d^3-768\,a^4\,b\,c^4\,e^3+1536\,a^4\,c^5\,d\,e^2+48\,b^7\,c^2\,d^2\,e-1536\,a^2\,b^2\,c^5\,d^3-96\,a^2\,b^5\,c^2\,e^3+512\,a^3\,b^3\,c^3\,e^3-18\,b^8\,c\,d\,e^2-576\,a\,b^5\,c^3\,d^2\,e+192\,a\,b^6\,c^2\,d\,e^2-3072\,a^3\,b\,c^5\,d^2\,e+2304\,a^2\,b^3\,c^4\,d^2\,e-576\,a^2\,b^4\,c^3\,d\,e^2}{c\,{\left(4\,a\,c-b^2\right)}^6}}\right)\,\sqrt{-\frac{b^9\,e^3+e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+2048\,a^3\,c^6\,d^3-32\,b^6\,c^3\,d^3+384\,a\,b^4\,c^4\,d^3-768\,a^4\,b\,c^4\,e^3+1536\,a^4\,c^5\,d\,e^2+48\,b^7\,c^2\,d^2\,e-1536\,a^2\,b^2\,c^5\,d^3-96\,a^2\,b^5\,c^2\,e^3+512\,a^3\,b^3\,c^3\,e^3-18\,b^8\,c\,d\,e^2-576\,a\,b^5\,c^3\,d^2\,e+192\,a\,b^6\,c^2\,d\,e^2-3072\,a^3\,b\,c^5\,d^2\,e+2304\,a^2\,b^3\,c^4\,d^2\,e-576\,a^2\,b^4\,c^3\,d\,e^2}{c\,{\left(4\,a\,c-b^2\right)}^6}}}{4}+\frac{2\,c\,e^2\,\sqrt{d+e\,x}\,\left(8\,a^2\,c^2\,e^4+2\,a\,b^2\,c\,e^4-24\,a\,b\,c^2\,d\,e^3+24\,a\,c^3\,d^2\,e^2+b^4\,e^4-10\,b^3\,c\,d\,e^3+42\,b^2\,c^2\,d^2\,e^2-64\,b\,c^3\,d^3\,e+32\,c^4\,d^4\right)}{{\left(4\,a\,c-b^2\right)}^2}\right)\,\sqrt{-\frac{b^9\,e^3+e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+2048\,a^3\,c^6\,d^3-32\,b^6\,c^3\,d^3+384\,a\,b^4\,c^4\,d^3-768\,a^4\,b\,c^4\,e^3+1536\,a^4\,c^5\,d\,e^2+48\,b^7\,c^2\,d^2\,e-1536\,a^2\,b^2\,c^5\,d^3-96\,a^2\,b^5\,c^2\,e^3+512\,a^3\,b^3\,c^3\,e^3-18\,b^8\,c\,d\,e^2-576\,a\,b^5\,c^3\,d^2\,e+192\,a\,b^6\,c^2\,d\,e^2-3072\,a^3\,b\,c^5\,d^2\,e+2304\,a^2\,b^3\,c^4\,d^2\,e-576\,a^2\,b^4\,c^3\,d\,e^2}{c\,{\left(4\,a\,c-b^2\right)}^6}}}{4}\right)\,\sqrt{-\frac{b^9\,e^3+e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+2048\,a^3\,c^6\,d^3-32\,b^6\,c^3\,d^3+384\,a\,b^4\,c^4\,d^3-768\,a^4\,b\,c^4\,e^3+1536\,a^4\,c^5\,d\,e^2+48\,b^7\,c^2\,d^2\,e-1536\,a^2\,b^2\,c^5\,d^3-96\,a^2\,b^5\,c^2\,e^3+512\,a^3\,b^3\,c^3\,e^3-18\,b^8\,c\,d\,e^2-576\,a\,b^5\,c^3\,d^2\,e+192\,a\,b^6\,c^2\,d\,e^2-3072\,a^3\,b\,c^5\,d^2\,e+2304\,a^2\,b^3\,c^4\,d^2\,e-576\,a^2\,b^4\,c^3\,d\,e^2}{8\,\left(4096\,a^6\,c^7-6144\,a^5\,b^2\,c^6+3840\,a^4\,b^4\,c^5-1280\,a^3\,b^6\,c^4+240\,a^2\,b^8\,c^3-24\,a\,b^{10}\,c^2+b^{12}\,c\right)}}+\ln\left(\frac{c\,e^3\,\left(b\,e-2\,c\,d\right)\,\left(4\,a^2\,c\,e^4+3\,a\,b^2\,e^4-20\,a\,b\,c\,d\,e^3+20\,a\,c^2\,d^2\,e^2-3\,b^3\,d\,e^3+19\,b^2\,c\,d^2\,e^2-32\,b\,c^2\,d^3\,e+16\,c^3\,d^4\right)}{{\left(4\,a\,c-b^2\right)}^3}-\frac{\sqrt{2}\,\left(\frac{\sqrt{2}\,\left(8\,c^2\,e^3\,\left(c\,d^2-b\,d\,e+a\,e^2\right)-2\,\sqrt{2}\,c^2\,e^2\,\left(4\,a\,c-b^2\right)\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}\,\sqrt{\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-b^9\,e^3-2048\,a^3\,c^6\,d^3+32\,b^6\,c^3\,d^3-384\,a\,b^4\,c^4\,d^3+768\,a^4\,b\,c^4\,e^3-1536\,a^4\,c^5\,d\,e^2-48\,b^7\,c^2\,d^2\,e+1536\,a^2\,b^2\,c^5\,d^3+96\,a^2\,b^5\,c^2\,e^3-512\,a^3\,b^3\,c^3\,e^3+18\,b^8\,c\,d\,e^2+576\,a\,b^5\,c^3\,d^2\,e-192\,a\,b^6\,c^2\,d\,e^2+3072\,a^3\,b\,c^5\,d^2\,e-2304\,a^2\,b^3\,c^4\,d^2\,e+576\,a^2\,b^4\,c^3\,d\,e^2}{c\,{\left(4\,a\,c-b^2\right)}^6}}\right)\,\sqrt{\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-b^9\,e^3-2048\,a^3\,c^6\,d^3+32\,b^6\,c^3\,d^3-384\,a\,b^4\,c^4\,d^3+768\,a^4\,b\,c^4\,e^3-1536\,a^4\,c^5\,d\,e^2-48\,b^7\,c^2\,d^2\,e+1536\,a^2\,b^2\,c^5\,d^3+96\,a^2\,b^5\,c^2\,e^3-512\,a^3\,b^3\,c^3\,e^3+18\,b^8\,c\,d\,e^2+576\,a\,b^5\,c^3\,d^2\,e-192\,a\,b^6\,c^2\,d\,e^2+3072\,a^3\,b\,c^5\,d^2\,e-2304\,a^2\,b^3\,c^4\,d^2\,e+576\,a^2\,b^4\,c^3\,d\,e^2}{c\,{\left(4\,a\,c-b^2\right)}^6}}}{4}+\frac{2\,c\,e^2\,\sqrt{d+e\,x}\,\left(8\,a^2\,c^2\,e^4+2\,a\,b^2\,c\,e^4-24\,a\,b\,c^2\,d\,e^3+24\,a\,c^3\,d^2\,e^2+b^4\,e^4-10\,b^3\,c\,d\,e^3+42\,b^2\,c^2\,d^2\,e^2-64\,b\,c^3\,d^3\,e+32\,c^4\,d^4\right)}{{\left(4\,a\,c-b^2\right)}^2}\right)\,\sqrt{\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-b^9\,e^3-2048\,a^3\,c^6\,d^3+32\,b^6\,c^3\,d^3-384\,a\,b^4\,c^4\,d^3+768\,a^4\,b\,c^4\,e^3-1536\,a^4\,c^5\,d\,e^2-48\,b^7\,c^2\,d^2\,e+1536\,a^2\,b^2\,c^5\,d^3+96\,a^2\,b^5\,c^2\,e^3-512\,a^3\,b^3\,c^3\,e^3+18\,b^8\,c\,d\,e^2+576\,a\,b^5\,c^3\,d^2\,e-192\,a\,b^6\,c^2\,d\,e^2+3072\,a^3\,b\,c^5\,d^2\,e-2304\,a^2\,b^3\,c^4\,d^2\,e+576\,a^2\,b^4\,c^3\,d\,e^2}{c\,{\left(4\,a\,c-b^2\right)}^6}}}{4}\right)\,\sqrt{\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-b^9\,e^3-2048\,a^3\,c^6\,d^3+32\,b^6\,c^3\,d^3-384\,a\,b^4\,c^4\,d^3+768\,a^4\,b\,c^4\,e^3-1536\,a^4\,c^5\,d\,e^2-48\,b^7\,c^2\,d^2\,e+1536\,a^2\,b^2\,c^5\,d^3+96\,a^2\,b^5\,c^2\,e^3-512\,a^3\,b^3\,c^3\,e^3+18\,b^8\,c\,d\,e^2+576\,a\,b^5\,c^3\,d^2\,e-192\,a\,b^6\,c^2\,d\,e^2+3072\,a^3\,b\,c^5\,d^2\,e-2304\,a^2\,b^3\,c^4\,d^2\,e+576\,a^2\,b^4\,c^3\,d\,e^2}{8\,\left(4096\,a^6\,c^7-6144\,a^5\,b^2\,c^6+3840\,a^4\,b^4\,c^5-1280\,a^3\,b^6\,c^4+240\,a^2\,b^8\,c^3-24\,a\,b^{10}\,c^2+b^{12}\,c\right)}}-\frac{\frac{2\,\sqrt{d+e\,x}\,\left(c\,d^2\,e-b\,d\,e^2+a\,e^3\right)}{4\,a\,c-b^2}+\frac{e\,\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{3/2}}{4\,a\,c-b^2}}{\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)+c\,{\left(d+e\,x\right)}^2+a\,e^2+c\,d^2-b\,d\,e}-\ln\left(\frac{c\,e^3\,\left(b\,e-2\,c\,d\right)\,\left(4\,a^2\,c\,e^4+3\,a\,b^2\,e^4-20\,a\,b\,c\,d\,e^3+20\,a\,c^2\,d^2\,e^2-3\,b^3\,d\,e^3+19\,b^2\,c\,d^2\,e^2-32\,b\,c^2\,d^3\,e+16\,c^3\,d^4\right)}{{\left(4\,a\,c-b^2\right)}^3}-\left(\left(8\,c^2\,e^3\,\left(c\,d^2-b\,d\,e+a\,e^2\right)+8\,c^2\,e^2\,\left(4\,a\,c-b^2\right)\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}\,\sqrt{\frac{\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8}-\frac{b^9\,e^3}{8}-256\,a^3\,c^6\,d^3+4\,b^6\,c^3\,d^3-48\,a\,b^4\,c^4\,d^3+96\,a^4\,b\,c^4\,e^3-192\,a^4\,c^5\,d\,e^2-6\,b^7\,c^2\,d^2\,e+192\,a^2\,b^2\,c^5\,d^3+12\,a^2\,b^5\,c^2\,e^3-64\,a^3\,b^3\,c^3\,e^3+\frac{9\,b^8\,c\,d\,e^2}{4}+72\,a\,b^5\,c^3\,d^2\,e-24\,a\,b^6\,c^2\,d\,e^2+384\,a^3\,b\,c^5\,d^2\,e-288\,a^2\,b^3\,c^4\,d^2\,e+72\,a^2\,b^4\,c^3\,d\,e^2}{c\,{\left(4\,a\,c-b^2\right)}^6}}\right)\,\sqrt{\frac{\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8}-\frac{b^9\,e^3}{8}-256\,a^3\,c^6\,d^3+4\,b^6\,c^3\,d^3-48\,a\,b^4\,c^4\,d^3+96\,a^4\,b\,c^4\,e^3-192\,a^4\,c^5\,d\,e^2-6\,b^7\,c^2\,d^2\,e+192\,a^2\,b^2\,c^5\,d^3+12\,a^2\,b^5\,c^2\,e^3-64\,a^3\,b^3\,c^3\,e^3+\frac{9\,b^8\,c\,d\,e^2}{4}+72\,a\,b^5\,c^3\,d^2\,e-24\,a\,b^6\,c^2\,d\,e^2+384\,a^3\,b\,c^5\,d^2\,e-288\,a^2\,b^3\,c^4\,d^2\,e+72\,a^2\,b^4\,c^3\,d\,e^2}{c\,{\left(4\,a\,c-b^2\right)}^6}}-\frac{2\,c\,e^2\,\sqrt{d+e\,x}\,\left(8\,a^2\,c^2\,e^4+2\,a\,b^2\,c\,e^4-24\,a\,b\,c^2\,d\,e^3+24\,a\,c^3\,d^2\,e^2+b^4\,e^4-10\,b^3\,c\,d\,e^3+42\,b^2\,c^2\,d^2\,e^2-64\,b\,c^3\,d^3\,e+32\,c^4\,d^4\right)}{{\left(4\,a\,c-b^2\right)}^2}\right)\,\sqrt{\frac{\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8}-\frac{b^9\,e^3}{8}-256\,a^3\,c^6\,d^3+4\,b^6\,c^3\,d^3-48\,a\,b^4\,c^4\,d^3+96\,a^4\,b\,c^4\,e^3-192\,a^4\,c^5\,d\,e^2-6\,b^7\,c^2\,d^2\,e+192\,a^2\,b^2\,c^5\,d^3+12\,a^2\,b^5\,c^2\,e^3-64\,a^3\,b^3\,c^3\,e^3+\frac{9\,b^8\,c\,d\,e^2}{4}+72\,a\,b^5\,c^3\,d^2\,e-24\,a\,b^6\,c^2\,d\,e^2+384\,a^3\,b\,c^5\,d^2\,e-288\,a^2\,b^3\,c^4\,d^2\,e+72\,a^2\,b^4\,c^3\,d\,e^2}{c\,{\left(4\,a\,c-b^2\right)}^6}}\right)\,\sqrt{\frac{\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8}-\frac{b^9\,e^3}{8}-256\,a^3\,c^6\,d^3+4\,b^6\,c^3\,d^3-48\,a\,b^4\,c^4\,d^3+96\,a^4\,b\,c^4\,e^3-192\,a^4\,c^5\,d\,e^2-6\,b^7\,c^2\,d^2\,e+192\,a^2\,b^2\,c^5\,d^3+12\,a^2\,b^5\,c^2\,e^3-64\,a^3\,b^3\,c^3\,e^3+\frac{9\,b^8\,c\,d\,e^2}{4}+72\,a\,b^5\,c^3\,d^2\,e-24\,a\,b^6\,c^2\,d\,e^2+384\,a^3\,b\,c^5\,d^2\,e-288\,a^2\,b^3\,c^4\,d^2\,e+72\,a^2\,b^4\,c^3\,d\,e^2}{4096\,a^6\,c^7-6144\,a^5\,b^2\,c^6+3840\,a^4\,b^4\,c^5-1280\,a^3\,b^6\,c^4+240\,a^2\,b^8\,c^3-24\,a\,b^{10}\,c^2+b^{12}\,c}}-\ln\left(\frac{c\,e^3\,\left(b\,e-2\,c\,d\right)\,\left(4\,a^2\,c\,e^4+3\,a\,b^2\,e^4-20\,a\,b\,c\,d\,e^3+20\,a\,c^2\,d^2\,e^2-3\,b^3\,d\,e^3+19\,b^2\,c\,d^2\,e^2-32\,b\,c^2\,d^3\,e+16\,c^3\,d^4\right)}{{\left(4\,a\,c-b^2\right)}^3}-\left(\left(8\,c^2\,e^3\,\left(c\,d^2-b\,d\,e+a\,e^2\right)+8\,c^2\,e^2\,\left(4\,a\,c-b^2\right)\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}\,\sqrt{-\frac{\frac{b^9\,e^3}{8}+\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8}+256\,a^3\,c^6\,d^3-4\,b^6\,c^3\,d^3+48\,a\,b^4\,c^4\,d^3-96\,a^4\,b\,c^4\,e^3+192\,a^4\,c^5\,d\,e^2+6\,b^7\,c^2\,d^2\,e-192\,a^2\,b^2\,c^5\,d^3-12\,a^2\,b^5\,c^2\,e^3+64\,a^3\,b^3\,c^3\,e^3-\frac{9\,b^8\,c\,d\,e^2}{4}-72\,a\,b^5\,c^3\,d^2\,e+24\,a\,b^6\,c^2\,d\,e^2-384\,a^3\,b\,c^5\,d^2\,e+288\,a^2\,b^3\,c^4\,d^2\,e-72\,a^2\,b^4\,c^3\,d\,e^2}{c\,{\left(4\,a\,c-b^2\right)}^6}}\right)\,\sqrt{-\frac{\frac{b^9\,e^3}{8}+\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8}+256\,a^3\,c^6\,d^3-4\,b^6\,c^3\,d^3+48\,a\,b^4\,c^4\,d^3-96\,a^4\,b\,c^4\,e^3+192\,a^4\,c^5\,d\,e^2+6\,b^7\,c^2\,d^2\,e-192\,a^2\,b^2\,c^5\,d^3-12\,a^2\,b^5\,c^2\,e^3+64\,a^3\,b^3\,c^3\,e^3-\frac{9\,b^8\,c\,d\,e^2}{4}-72\,a\,b^5\,c^3\,d^2\,e+24\,a\,b^6\,c^2\,d\,e^2-384\,a^3\,b\,c^5\,d^2\,e+288\,a^2\,b^3\,c^4\,d^2\,e-72\,a^2\,b^4\,c^3\,d\,e^2}{c\,{\left(4\,a\,c-b^2\right)}^6}}-\frac{2\,c\,e^2\,\sqrt{d+e\,x}\,\left(8\,a^2\,c^2\,e^4+2\,a\,b^2\,c\,e^4-24\,a\,b\,c^2\,d\,e^3+24\,a\,c^3\,d^2\,e^2+b^4\,e^4-10\,b^3\,c\,d\,e^3+42\,b^2\,c^2\,d^2\,e^2-64\,b\,c^3\,d^3\,e+32\,c^4\,d^4\right)}{{\left(4\,a\,c-b^2\right)}^2}\right)\,\sqrt{-\frac{\frac{b^9\,e^3}{8}+\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8}+256\,a^3\,c^6\,d^3-4\,b^6\,c^3\,d^3+48\,a\,b^4\,c^4\,d^3-96\,a^4\,b\,c^4\,e^3+192\,a^4\,c^5\,d\,e^2+6\,b^7\,c^2\,d^2\,e-192\,a^2\,b^2\,c^5\,d^3-12\,a^2\,b^5\,c^2\,e^3+64\,a^3\,b^3\,c^3\,e^3-\frac{9\,b^8\,c\,d\,e^2}{4}-72\,a\,b^5\,c^3\,d^2\,e+24\,a\,b^6\,c^2\,d\,e^2-384\,a^3\,b\,c^5\,d^2\,e+288\,a^2\,b^3\,c^4\,d^2\,e-72\,a^2\,b^4\,c^3\,d\,e^2}{c\,{\left(4\,a\,c-b^2\right)}^6}}\right)\,\sqrt{-\frac{\frac{b^9\,e^3}{8}+\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8}+256\,a^3\,c^6\,d^3-4\,b^6\,c^3\,d^3+48\,a\,b^4\,c^4\,d^3-96\,a^4\,b\,c^4\,e^3+192\,a^4\,c^5\,d\,e^2+6\,b^7\,c^2\,d^2\,e-192\,a^2\,b^2\,c^5\,d^3-12\,a^2\,b^5\,c^2\,e^3+64\,a^3\,b^3\,c^3\,e^3-\frac{9\,b^8\,c\,d\,e^2}{4}-72\,a\,b^5\,c^3\,d^2\,e+24\,a\,b^6\,c^2\,d\,e^2-384\,a^3\,b\,c^5\,d^2\,e+288\,a^2\,b^3\,c^4\,d^2\,e-72\,a^2\,b^4\,c^3\,d\,e^2}{4096\,a^6\,c^7-6144\,a^5\,b^2\,c^6+3840\,a^4\,b^4\,c^5-1280\,a^3\,b^6\,c^4+240\,a^2\,b^8\,c^3-24\,a\,b^{10}\,c^2+b^{12}\,c}}","Not used",1,"log((c*e^3*(b*e - 2*c*d)*(16*c^3*d^4 + 3*a*b^2*e^4 + 4*a^2*c*e^4 - 3*b^3*d*e^3 + 20*a*c^2*d^2*e^2 + 19*b^2*c*d^2*e^2 - 32*b*c^2*d^3*e - 20*a*b*c*d*e^3))/(4*a*c - b^2)^3 - (2^(1/2)*((2^(1/2)*(8*c^2*e^3*(a*e^2 + c*d^2 - b*d*e) - 2*2^(1/2)*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(-(b^9*e^3 + e^3*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^6*d^3 - 32*b^6*c^3*d^3 + 384*a*b^4*c^4*d^3 - 768*a^4*b*c^4*e^3 + 1536*a^4*c^5*d*e^2 + 48*b^7*c^2*d^2*e - 1536*a^2*b^2*c^5*d^3 - 96*a^2*b^5*c^2*e^3 + 512*a^3*b^3*c^3*e^3 - 18*b^8*c*d*e^2 - 576*a*b^5*c^3*d^2*e + 192*a*b^6*c^2*d*e^2 - 3072*a^3*b*c^5*d^2*e + 2304*a^2*b^3*c^4*d^2*e - 576*a^2*b^4*c^3*d*e^2)/(c*(4*a*c - b^2)^6))^(1/2))*(-(b^9*e^3 + e^3*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^6*d^3 - 32*b^6*c^3*d^3 + 384*a*b^4*c^4*d^3 - 768*a^4*b*c^4*e^3 + 1536*a^4*c^5*d*e^2 + 48*b^7*c^2*d^2*e - 1536*a^2*b^2*c^5*d^3 - 96*a^2*b^5*c^2*e^3 + 512*a^3*b^3*c^3*e^3 - 18*b^8*c*d*e^2 - 576*a*b^5*c^3*d^2*e + 192*a*b^6*c^2*d*e^2 - 3072*a^3*b*c^5*d^2*e + 2304*a^2*b^3*c^4*d^2*e - 576*a^2*b^4*c^3*d*e^2)/(c*(4*a*c - b^2)^6))^(1/2))/4 + (2*c*e^2*(d + e*x)^(1/2)*(b^4*e^4 + 32*c^4*d^4 + 8*a^2*c^2*e^4 + 24*a*c^3*d^2*e^2 + 42*b^2*c^2*d^2*e^2 + 2*a*b^2*c*e^4 - 64*b*c^3*d^3*e - 10*b^3*c*d*e^3 - 24*a*b*c^2*d*e^3))/(4*a*c - b^2)^2)*(-(b^9*e^3 + e^3*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^6*d^3 - 32*b^6*c^3*d^3 + 384*a*b^4*c^4*d^3 - 768*a^4*b*c^4*e^3 + 1536*a^4*c^5*d*e^2 + 48*b^7*c^2*d^2*e - 1536*a^2*b^2*c^5*d^3 - 96*a^2*b^5*c^2*e^3 + 512*a^3*b^3*c^3*e^3 - 18*b^8*c*d*e^2 - 576*a*b^5*c^3*d^2*e + 192*a*b^6*c^2*d*e^2 - 3072*a^3*b*c^5*d^2*e + 2304*a^2*b^3*c^4*d^2*e - 576*a^2*b^4*c^3*d*e^2)/(c*(4*a*c - b^2)^6))^(1/2))/4)*(-(b^9*e^3 + e^3*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^6*d^3 - 32*b^6*c^3*d^3 + 384*a*b^4*c^4*d^3 - 768*a^4*b*c^4*e^3 + 1536*a^4*c^5*d*e^2 + 48*b^7*c^2*d^2*e - 1536*a^2*b^2*c^5*d^3 - 96*a^2*b^5*c^2*e^3 + 512*a^3*b^3*c^3*e^3 - 18*b^8*c*d*e^2 - 576*a*b^5*c^3*d^2*e + 192*a*b^6*c^2*d*e^2 - 3072*a^3*b*c^5*d^2*e + 2304*a^2*b^3*c^4*d^2*e - 576*a^2*b^4*c^3*d*e^2)/(8*(b^12*c + 4096*a^6*c^7 - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6)))^(1/2) + log((c*e^3*(b*e - 2*c*d)*(16*c^3*d^4 + 3*a*b^2*e^4 + 4*a^2*c*e^4 - 3*b^3*d*e^3 + 20*a*c^2*d^2*e^2 + 19*b^2*c*d^2*e^2 - 32*b*c^2*d^3*e - 20*a*b*c*d*e^3))/(4*a*c - b^2)^3 - (2^(1/2)*((2^(1/2)*(8*c^2*e^3*(a*e^2 + c*d^2 - b*d*e) - 2*2^(1/2)*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*((e^3*(-(4*a*c - b^2)^9)^(1/2) - b^9*e^3 - 2048*a^3*c^6*d^3 + 32*b^6*c^3*d^3 - 384*a*b^4*c^4*d^3 + 768*a^4*b*c^4*e^3 - 1536*a^4*c^5*d*e^2 - 48*b^7*c^2*d^2*e + 1536*a^2*b^2*c^5*d^3 + 96*a^2*b^5*c^2*e^3 - 512*a^3*b^3*c^3*e^3 + 18*b^8*c*d*e^2 + 576*a*b^5*c^3*d^2*e - 192*a*b^6*c^2*d*e^2 + 3072*a^3*b*c^5*d^2*e - 2304*a^2*b^3*c^4*d^2*e + 576*a^2*b^4*c^3*d*e^2)/(c*(4*a*c - b^2)^6))^(1/2))*((e^3*(-(4*a*c - b^2)^9)^(1/2) - b^9*e^3 - 2048*a^3*c^6*d^3 + 32*b^6*c^3*d^3 - 384*a*b^4*c^4*d^3 + 768*a^4*b*c^4*e^3 - 1536*a^4*c^5*d*e^2 - 48*b^7*c^2*d^2*e + 1536*a^2*b^2*c^5*d^3 + 96*a^2*b^5*c^2*e^3 - 512*a^3*b^3*c^3*e^3 + 18*b^8*c*d*e^2 + 576*a*b^5*c^3*d^2*e - 192*a*b^6*c^2*d*e^2 + 3072*a^3*b*c^5*d^2*e - 2304*a^2*b^3*c^4*d^2*e + 576*a^2*b^4*c^3*d*e^2)/(c*(4*a*c - b^2)^6))^(1/2))/4 + (2*c*e^2*(d + e*x)^(1/2)*(b^4*e^4 + 32*c^4*d^4 + 8*a^2*c^2*e^4 + 24*a*c^3*d^2*e^2 + 42*b^2*c^2*d^2*e^2 + 2*a*b^2*c*e^4 - 64*b*c^3*d^3*e - 10*b^3*c*d*e^3 - 24*a*b*c^2*d*e^3))/(4*a*c - b^2)^2)*((e^3*(-(4*a*c - b^2)^9)^(1/2) - b^9*e^3 - 2048*a^3*c^6*d^3 + 32*b^6*c^3*d^3 - 384*a*b^4*c^4*d^3 + 768*a^4*b*c^4*e^3 - 1536*a^4*c^5*d*e^2 - 48*b^7*c^2*d^2*e + 1536*a^2*b^2*c^5*d^3 + 96*a^2*b^5*c^2*e^3 - 512*a^3*b^3*c^3*e^3 + 18*b^8*c*d*e^2 + 576*a*b^5*c^3*d^2*e - 192*a*b^6*c^2*d*e^2 + 3072*a^3*b*c^5*d^2*e - 2304*a^2*b^3*c^4*d^2*e + 576*a^2*b^4*c^3*d*e^2)/(c*(4*a*c - b^2)^6))^(1/2))/4)*((e^3*(-(4*a*c - b^2)^9)^(1/2) - b^9*e^3 - 2048*a^3*c^6*d^3 + 32*b^6*c^3*d^3 - 384*a*b^4*c^4*d^3 + 768*a^4*b*c^4*e^3 - 1536*a^4*c^5*d*e^2 - 48*b^7*c^2*d^2*e + 1536*a^2*b^2*c^5*d^3 + 96*a^2*b^5*c^2*e^3 - 512*a^3*b^3*c^3*e^3 + 18*b^8*c*d*e^2 + 576*a*b^5*c^3*d^2*e - 192*a*b^6*c^2*d*e^2 + 3072*a^3*b*c^5*d^2*e - 2304*a^2*b^3*c^4*d^2*e + 576*a^2*b^4*c^3*d*e^2)/(8*(b^12*c + 4096*a^6*c^7 - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6)))^(1/2) - ((2*(d + e*x)^(1/2)*(a*e^3 - b*d*e^2 + c*d^2*e))/(4*a*c - b^2) + (e*(b*e - 2*c*d)*(d + e*x)^(3/2))/(4*a*c - b^2))/((b*e - 2*c*d)*(d + e*x) + c*(d + e*x)^2 + a*e^2 + c*d^2 - b*d*e) - log((c*e^3*(b*e - 2*c*d)*(16*c^3*d^4 + 3*a*b^2*e^4 + 4*a^2*c*e^4 - 3*b^3*d*e^3 + 20*a*c^2*d^2*e^2 + 19*b^2*c*d^2*e^2 - 32*b*c^2*d^3*e - 20*a*b*c*d*e^3))/(4*a*c - b^2)^3 - ((8*c^2*e^3*(a*e^2 + c*d^2 - b*d*e) + 8*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(((e^3*(-(4*a*c - b^2)^9)^(1/2))/8 - (b^9*e^3)/8 - 256*a^3*c^6*d^3 + 4*b^6*c^3*d^3 - 48*a*b^4*c^4*d^3 + 96*a^4*b*c^4*e^3 - 192*a^4*c^5*d*e^2 - 6*b^7*c^2*d^2*e + 192*a^2*b^2*c^5*d^3 + 12*a^2*b^5*c^2*e^3 - 64*a^3*b^3*c^3*e^3 + (9*b^8*c*d*e^2)/4 + 72*a*b^5*c^3*d^2*e - 24*a*b^6*c^2*d*e^2 + 384*a^3*b*c^5*d^2*e - 288*a^2*b^3*c^4*d^2*e + 72*a^2*b^4*c^3*d*e^2)/(c*(4*a*c - b^2)^6))^(1/2))*(((e^3*(-(4*a*c - b^2)^9)^(1/2))/8 - (b^9*e^3)/8 - 256*a^3*c^6*d^3 + 4*b^6*c^3*d^3 - 48*a*b^4*c^4*d^3 + 96*a^4*b*c^4*e^3 - 192*a^4*c^5*d*e^2 - 6*b^7*c^2*d^2*e + 192*a^2*b^2*c^5*d^3 + 12*a^2*b^5*c^2*e^3 - 64*a^3*b^3*c^3*e^3 + (9*b^8*c*d*e^2)/4 + 72*a*b^5*c^3*d^2*e - 24*a*b^6*c^2*d*e^2 + 384*a^3*b*c^5*d^2*e - 288*a^2*b^3*c^4*d^2*e + 72*a^2*b^4*c^3*d*e^2)/(c*(4*a*c - b^2)^6))^(1/2) - (2*c*e^2*(d + e*x)^(1/2)*(b^4*e^4 + 32*c^4*d^4 + 8*a^2*c^2*e^4 + 24*a*c^3*d^2*e^2 + 42*b^2*c^2*d^2*e^2 + 2*a*b^2*c*e^4 - 64*b*c^3*d^3*e - 10*b^3*c*d*e^3 - 24*a*b*c^2*d*e^3))/(4*a*c - b^2)^2)*(((e^3*(-(4*a*c - b^2)^9)^(1/2))/8 - (b^9*e^3)/8 - 256*a^3*c^6*d^3 + 4*b^6*c^3*d^3 - 48*a*b^4*c^4*d^3 + 96*a^4*b*c^4*e^3 - 192*a^4*c^5*d*e^2 - 6*b^7*c^2*d^2*e + 192*a^2*b^2*c^5*d^3 + 12*a^2*b^5*c^2*e^3 - 64*a^3*b^3*c^3*e^3 + (9*b^8*c*d*e^2)/4 + 72*a*b^5*c^3*d^2*e - 24*a*b^6*c^2*d*e^2 + 384*a^3*b*c^5*d^2*e - 288*a^2*b^3*c^4*d^2*e + 72*a^2*b^4*c^3*d*e^2)/(c*(4*a*c - b^2)^6))^(1/2))*(((e^3*(-(4*a*c - b^2)^9)^(1/2))/8 - (b^9*e^3)/8 - 256*a^3*c^6*d^3 + 4*b^6*c^3*d^3 - 48*a*b^4*c^4*d^3 + 96*a^4*b*c^4*e^3 - 192*a^4*c^5*d*e^2 - 6*b^7*c^2*d^2*e + 192*a^2*b^2*c^5*d^3 + 12*a^2*b^5*c^2*e^3 - 64*a^3*b^3*c^3*e^3 + (9*b^8*c*d*e^2)/4 + 72*a*b^5*c^3*d^2*e - 24*a*b^6*c^2*d*e^2 + 384*a^3*b*c^5*d^2*e - 288*a^2*b^3*c^4*d^2*e + 72*a^2*b^4*c^3*d*e^2)/(b^12*c + 4096*a^6*c^7 - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6))^(1/2) - log((c*e^3*(b*e - 2*c*d)*(16*c^3*d^4 + 3*a*b^2*e^4 + 4*a^2*c*e^4 - 3*b^3*d*e^3 + 20*a*c^2*d^2*e^2 + 19*b^2*c*d^2*e^2 - 32*b*c^2*d^3*e - 20*a*b*c*d*e^3))/(4*a*c - b^2)^3 - ((8*c^2*e^3*(a*e^2 + c*d^2 - b*d*e) + 8*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(-((b^9*e^3)/8 + (e^3*(-(4*a*c - b^2)^9)^(1/2))/8 + 256*a^3*c^6*d^3 - 4*b^6*c^3*d^3 + 48*a*b^4*c^4*d^3 - 96*a^4*b*c^4*e^3 + 192*a^4*c^5*d*e^2 + 6*b^7*c^2*d^2*e - 192*a^2*b^2*c^5*d^3 - 12*a^2*b^5*c^2*e^3 + 64*a^3*b^3*c^3*e^3 - (9*b^8*c*d*e^2)/4 - 72*a*b^5*c^3*d^2*e + 24*a*b^6*c^2*d*e^2 - 384*a^3*b*c^5*d^2*e + 288*a^2*b^3*c^4*d^2*e - 72*a^2*b^4*c^3*d*e^2)/(c*(4*a*c - b^2)^6))^(1/2))*(-((b^9*e^3)/8 + (e^3*(-(4*a*c - b^2)^9)^(1/2))/8 + 256*a^3*c^6*d^3 - 4*b^6*c^3*d^3 + 48*a*b^4*c^4*d^3 - 96*a^4*b*c^4*e^3 + 192*a^4*c^5*d*e^2 + 6*b^7*c^2*d^2*e - 192*a^2*b^2*c^5*d^3 - 12*a^2*b^5*c^2*e^3 + 64*a^3*b^3*c^3*e^3 - (9*b^8*c*d*e^2)/4 - 72*a*b^5*c^3*d^2*e + 24*a*b^6*c^2*d*e^2 - 384*a^3*b*c^5*d^2*e + 288*a^2*b^3*c^4*d^2*e - 72*a^2*b^4*c^3*d*e^2)/(c*(4*a*c - b^2)^6))^(1/2) - (2*c*e^2*(d + e*x)^(1/2)*(b^4*e^4 + 32*c^4*d^4 + 8*a^2*c^2*e^4 + 24*a*c^3*d^2*e^2 + 42*b^2*c^2*d^2*e^2 + 2*a*b^2*c*e^4 - 64*b*c^3*d^3*e - 10*b^3*c*d*e^3 - 24*a*b*c^2*d*e^3))/(4*a*c - b^2)^2)*(-((b^9*e^3)/8 + (e^3*(-(4*a*c - b^2)^9)^(1/2))/8 + 256*a^3*c^6*d^3 - 4*b^6*c^3*d^3 + 48*a*b^4*c^4*d^3 - 96*a^4*b*c^4*e^3 + 192*a^4*c^5*d*e^2 + 6*b^7*c^2*d^2*e - 192*a^2*b^2*c^5*d^3 - 12*a^2*b^5*c^2*e^3 + 64*a^3*b^3*c^3*e^3 - (9*b^8*c*d*e^2)/4 - 72*a*b^5*c^3*d^2*e + 24*a*b^6*c^2*d*e^2 - 384*a^3*b*c^5*d^2*e + 288*a^2*b^3*c^4*d^2*e - 72*a^2*b^4*c^3*d*e^2)/(c*(4*a*c - b^2)^6))^(1/2))*(-((b^9*e^3)/8 + (e^3*(-(4*a*c - b^2)^9)^(1/2))/8 + 256*a^3*c^6*d^3 - 4*b^6*c^3*d^3 + 48*a*b^4*c^4*d^3 - 96*a^4*b*c^4*e^3 + 192*a^4*c^5*d*e^2 + 6*b^7*c^2*d^2*e - 192*a^2*b^2*c^5*d^3 - 12*a^2*b^5*c^2*e^3 + 64*a^3*b^3*c^3*e^3 - (9*b^8*c*d*e^2)/4 - 72*a*b^5*c^3*d^2*e + 24*a*b^6*c^2*d*e^2 - 384*a^3*b*c^5*d^2*e + 288*a^2*b^3*c^4*d^2*e - 72*a^2*b^4*c^3*d*e^2)/(b^12*c + 4096*a^6*c^7 - 24*a*b^10*c^2 + 240*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 3840*a^4*b^4*c^5 - 6144*a^5*b^2*c^6))^(1/2)","B"
2298,1,5740,287,7.610372,"\text{Not used}","int((d + e*x)^(1/2)/(a + b*x + c*x^2)^2,x)","\frac{\frac{2\,c\,e\,{\left(d+e\,x\right)}^{3/2}}{4\,a\,c-b^2}+\frac{e\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}}{4\,a\,c-b^2}}{\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)+c\,{\left(d+e\,x\right)}^2+a\,e^2+c\,d^2-b\,d\,e}-\ln\left(\left(\left(4\,c^2\,e^3\,\left(b\,e-2\,c\,d\right)-8\,c^2\,e^2\,\left(4\,a\,c-b^2\right)\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}\,\sqrt{\frac{\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8}-\frac{b^9\,e^3}{8}-256\,a^3\,c^6\,d^3+4\,b^6\,c^3\,d^3-48\,a\,b^4\,c^4\,d^3+96\,a^4\,b\,c^4\,e^3-192\,a^4\,c^5\,d\,e^2-6\,b^7\,c^2\,d^2\,e+192\,a^2\,b^2\,c^5\,d^3+12\,a^2\,b^5\,c^2\,e^3-64\,a^3\,b^3\,c^3\,e^3+\frac{9\,b^8\,c\,d\,e^2}{4}+72\,a\,b^5\,c^3\,d^2\,e-24\,a\,b^6\,c^2\,d\,e^2+384\,a^3\,b\,c^5\,d^2\,e-288\,a^2\,b^3\,c^4\,d^2\,e+72\,a^2\,b^4\,c^3\,d\,e^2}{{\left(4\,a\,c-b^2\right)}^6\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}\right)\,\sqrt{\frac{\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8}-\frac{b^9\,e^3}{8}-256\,a^3\,c^6\,d^3+4\,b^6\,c^3\,d^3-48\,a\,b^4\,c^4\,d^3+96\,a^4\,b\,c^4\,e^3-192\,a^4\,c^5\,d\,e^2-6\,b^7\,c^2\,d^2\,e+192\,a^2\,b^2\,c^5\,d^3+12\,a^2\,b^5\,c^2\,e^3-64\,a^3\,b^3\,c^3\,e^3+\frac{9\,b^8\,c\,d\,e^2}{4}+72\,a\,b^5\,c^3\,d^2\,e-24\,a\,b^6\,c^2\,d\,e^2+384\,a^3\,b\,c^5\,d^2\,e-288\,a^2\,b^3\,c^4\,d^2\,e+72\,a^2\,b^4\,c^3\,d\,e^2}{{\left(4\,a\,c-b^2\right)}^6\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}+\frac{4\,c^3\,e^2\,\sqrt{d+e\,x}\,\left(5\,b^2\,e^2-16\,b\,c\,d\,e+16\,c^2\,d^2-4\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^2}\right)\,\sqrt{\frac{\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8}-\frac{b^9\,e^3}{8}-256\,a^3\,c^6\,d^3+4\,b^6\,c^3\,d^3-48\,a\,b^4\,c^4\,d^3+96\,a^4\,b\,c^4\,e^3-192\,a^4\,c^5\,d\,e^2-6\,b^7\,c^2\,d^2\,e+192\,a^2\,b^2\,c^5\,d^3+12\,a^2\,b^5\,c^2\,e^3-64\,a^3\,b^3\,c^3\,e^3+\frac{9\,b^8\,c\,d\,e^2}{4}+72\,a\,b^5\,c^3\,d^2\,e-24\,a\,b^6\,c^2\,d\,e^2+384\,a^3\,b\,c^5\,d^2\,e-288\,a^2\,b^3\,c^4\,d^2\,e+72\,a^2\,b^4\,c^3\,d\,e^2}{{\left(4\,a\,c-b^2\right)}^6\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}-\frac{2\,c^3\,e^3\,\left(3\,b^2\,e^2-16\,b\,c\,d\,e+16\,c^2\,d^2+4\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^3}\right)\,\sqrt{\frac{\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8}-\frac{b^9\,e^3}{8}-256\,a^3\,c^6\,d^3+4\,b^6\,c^3\,d^3-48\,a\,b^4\,c^4\,d^3+96\,a^4\,b\,c^4\,e^3-192\,a^4\,c^5\,d\,e^2-6\,b^7\,c^2\,d^2\,e+192\,a^2\,b^2\,c^5\,d^3+12\,a^2\,b^5\,c^2\,e^3-64\,a^3\,b^3\,c^3\,e^3+\frac{9\,b^8\,c\,d\,e^2}{4}+72\,a\,b^5\,c^3\,d^2\,e-24\,a\,b^6\,c^2\,d\,e^2+384\,a^3\,b\,c^5\,d^2\,e-288\,a^2\,b^3\,c^4\,d^2\,e+72\,a^2\,b^4\,c^3\,d\,e^2}{4096\,a^7\,c^6\,e^2-6144\,a^6\,b^2\,c^5\,e^2-4096\,a^6\,b\,c^6\,d\,e+4096\,a^6\,c^7\,d^2+3840\,a^5\,b^4\,c^4\,e^2+6144\,a^5\,b^3\,c^5\,d\,e-6144\,a^5\,b^2\,c^6\,d^2-1280\,a^4\,b^6\,c^3\,e^2-3840\,a^4\,b^5\,c^4\,d\,e+3840\,a^4\,b^4\,c^5\,d^2+240\,a^3\,b^8\,c^2\,e^2+1280\,a^3\,b^7\,c^3\,d\,e-1280\,a^3\,b^6\,c^4\,d^2-24\,a^2\,b^{10}\,c\,e^2-240\,a^2\,b^9\,c^2\,d\,e+240\,a^2\,b^8\,c^3\,d^2+a\,b^{12}\,e^2+24\,a\,b^{11}\,c\,d\,e-24\,a\,b^{10}\,c^2\,d^2-b^{13}\,d\,e+b^{12}\,c\,d^2}}-\ln\left(\left(\left(4\,c^2\,e^3\,\left(b\,e-2\,c\,d\right)-8\,c^2\,e^2\,\left(4\,a\,c-b^2\right)\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}\,\sqrt{-\frac{\frac{b^9\,e^3}{8}+\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8}+256\,a^3\,c^6\,d^3-4\,b^6\,c^3\,d^3+48\,a\,b^4\,c^4\,d^3-96\,a^4\,b\,c^4\,e^3+192\,a^4\,c^5\,d\,e^2+6\,b^7\,c^2\,d^2\,e-192\,a^2\,b^2\,c^5\,d^3-12\,a^2\,b^5\,c^2\,e^3+64\,a^3\,b^3\,c^3\,e^3-\frac{9\,b^8\,c\,d\,e^2}{4}-72\,a\,b^5\,c^3\,d^2\,e+24\,a\,b^6\,c^2\,d\,e^2-384\,a^3\,b\,c^5\,d^2\,e+288\,a^2\,b^3\,c^4\,d^2\,e-72\,a^2\,b^4\,c^3\,d\,e^2}{{\left(4\,a\,c-b^2\right)}^6\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}\right)\,\sqrt{-\frac{\frac{b^9\,e^3}{8}+\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8}+256\,a^3\,c^6\,d^3-4\,b^6\,c^3\,d^3+48\,a\,b^4\,c^4\,d^3-96\,a^4\,b\,c^4\,e^3+192\,a^4\,c^5\,d\,e^2+6\,b^7\,c^2\,d^2\,e-192\,a^2\,b^2\,c^5\,d^3-12\,a^2\,b^5\,c^2\,e^3+64\,a^3\,b^3\,c^3\,e^3-\frac{9\,b^8\,c\,d\,e^2}{4}-72\,a\,b^5\,c^3\,d^2\,e+24\,a\,b^6\,c^2\,d\,e^2-384\,a^3\,b\,c^5\,d^2\,e+288\,a^2\,b^3\,c^4\,d^2\,e-72\,a^2\,b^4\,c^3\,d\,e^2}{{\left(4\,a\,c-b^2\right)}^6\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}+\frac{4\,c^3\,e^2\,\sqrt{d+e\,x}\,\left(5\,b^2\,e^2-16\,b\,c\,d\,e+16\,c^2\,d^2-4\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^2}\right)\,\sqrt{-\frac{\frac{b^9\,e^3}{8}+\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8}+256\,a^3\,c^6\,d^3-4\,b^6\,c^3\,d^3+48\,a\,b^4\,c^4\,d^3-96\,a^4\,b\,c^4\,e^3+192\,a^4\,c^5\,d\,e^2+6\,b^7\,c^2\,d^2\,e-192\,a^2\,b^2\,c^5\,d^3-12\,a^2\,b^5\,c^2\,e^3+64\,a^3\,b^3\,c^3\,e^3-\frac{9\,b^8\,c\,d\,e^2}{4}-72\,a\,b^5\,c^3\,d^2\,e+24\,a\,b^6\,c^2\,d\,e^2-384\,a^3\,b\,c^5\,d^2\,e+288\,a^2\,b^3\,c^4\,d^2\,e-72\,a^2\,b^4\,c^3\,d\,e^2}{{\left(4\,a\,c-b^2\right)}^6\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}-\frac{2\,c^3\,e^3\,\left(3\,b^2\,e^2-16\,b\,c\,d\,e+16\,c^2\,d^2+4\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^3}\right)\,\sqrt{-\frac{\frac{b^9\,e^3}{8}+\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8}+256\,a^3\,c^6\,d^3-4\,b^6\,c^3\,d^3+48\,a\,b^4\,c^4\,d^3-96\,a^4\,b\,c^4\,e^3+192\,a^4\,c^5\,d\,e^2+6\,b^7\,c^2\,d^2\,e-192\,a^2\,b^2\,c^5\,d^3-12\,a^2\,b^5\,c^2\,e^3+64\,a^3\,b^3\,c^3\,e^3-\frac{9\,b^8\,c\,d\,e^2}{4}-72\,a\,b^5\,c^3\,d^2\,e+24\,a\,b^6\,c^2\,d\,e^2-384\,a^3\,b\,c^5\,d^2\,e+288\,a^2\,b^3\,c^4\,d^2\,e-72\,a^2\,b^4\,c^3\,d\,e^2}{4096\,a^7\,c^6\,e^2-6144\,a^6\,b^2\,c^5\,e^2-4096\,a^6\,b\,c^6\,d\,e+4096\,a^6\,c^7\,d^2+3840\,a^5\,b^4\,c^4\,e^2+6144\,a^5\,b^3\,c^5\,d\,e-6144\,a^5\,b^2\,c^6\,d^2-1280\,a^4\,b^6\,c^3\,e^2-3840\,a^4\,b^5\,c^4\,d\,e+3840\,a^4\,b^4\,c^5\,d^2+240\,a^3\,b^8\,c^2\,e^2+1280\,a^3\,b^7\,c^3\,d\,e-1280\,a^3\,b^6\,c^4\,d^2-24\,a^2\,b^{10}\,c\,e^2-240\,a^2\,b^9\,c^2\,d\,e+240\,a^2\,b^8\,c^3\,d^2+a\,b^{12}\,e^2+24\,a\,b^{11}\,c\,d\,e-24\,a\,b^{10}\,c^2\,d^2-b^{13}\,d\,e+b^{12}\,c\,d^2}}+\ln\left(\frac{\sqrt{2}\,\left(\frac{\sqrt{2}\,\left(4\,c^2\,e^3\,\left(b\,e-2\,c\,d\right)+2\,\sqrt{2}\,c^2\,e^2\,\left(4\,a\,c-b^2\right)\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^9\,e^3+e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+2048\,a^3\,c^6\,d^3-32\,b^6\,c^3\,d^3+384\,a\,b^4\,c^4\,d^3-768\,a^4\,b\,c^4\,e^3+1536\,a^4\,c^5\,d\,e^2+48\,b^7\,c^2\,d^2\,e-1536\,a^2\,b^2\,c^5\,d^3-96\,a^2\,b^5\,c^2\,e^3+512\,a^3\,b^3\,c^3\,e^3-18\,b^8\,c\,d\,e^2-576\,a\,b^5\,c^3\,d^2\,e+192\,a\,b^6\,c^2\,d\,e^2-3072\,a^3\,b\,c^5\,d^2\,e+2304\,a^2\,b^3\,c^4\,d^2\,e-576\,a^2\,b^4\,c^3\,d\,e^2}{{\left(4\,a\,c-b^2\right)}^6\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}\right)\,\sqrt{-\frac{b^9\,e^3+e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+2048\,a^3\,c^6\,d^3-32\,b^6\,c^3\,d^3+384\,a\,b^4\,c^4\,d^3-768\,a^4\,b\,c^4\,e^3+1536\,a^4\,c^5\,d\,e^2+48\,b^7\,c^2\,d^2\,e-1536\,a^2\,b^2\,c^5\,d^3-96\,a^2\,b^5\,c^2\,e^3+512\,a^3\,b^3\,c^3\,e^3-18\,b^8\,c\,d\,e^2-576\,a\,b^5\,c^3\,d^2\,e+192\,a\,b^6\,c^2\,d\,e^2-3072\,a^3\,b\,c^5\,d^2\,e+2304\,a^2\,b^3\,c^4\,d^2\,e-576\,a^2\,b^4\,c^3\,d\,e^2}{{\left(4\,a\,c-b^2\right)}^6\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}}{4}-\frac{4\,c^3\,e^2\,\sqrt{d+e\,x}\,\left(5\,b^2\,e^2-16\,b\,c\,d\,e+16\,c^2\,d^2-4\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^2}\right)\,\sqrt{-\frac{b^9\,e^3+e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+2048\,a^3\,c^6\,d^3-32\,b^6\,c^3\,d^3+384\,a\,b^4\,c^4\,d^3-768\,a^4\,b\,c^4\,e^3+1536\,a^4\,c^5\,d\,e^2+48\,b^7\,c^2\,d^2\,e-1536\,a^2\,b^2\,c^5\,d^3-96\,a^2\,b^5\,c^2\,e^3+512\,a^3\,b^3\,c^3\,e^3-18\,b^8\,c\,d\,e^2-576\,a\,b^5\,c^3\,d^2\,e+192\,a\,b^6\,c^2\,d\,e^2-3072\,a^3\,b\,c^5\,d^2\,e+2304\,a^2\,b^3\,c^4\,d^2\,e-576\,a^2\,b^4\,c^3\,d\,e^2}{{\left(4\,a\,c-b^2\right)}^6\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}}{4}-\frac{2\,c^3\,e^3\,\left(3\,b^2\,e^2-16\,b\,c\,d\,e+16\,c^2\,d^2+4\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^3}\right)\,\sqrt{-\frac{b^9\,e^3+e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+2048\,a^3\,c^6\,d^3-32\,b^6\,c^3\,d^3+384\,a\,b^4\,c^4\,d^3-768\,a^4\,b\,c^4\,e^3+1536\,a^4\,c^5\,d\,e^2+48\,b^7\,c^2\,d^2\,e-1536\,a^2\,b^2\,c^5\,d^3-96\,a^2\,b^5\,c^2\,e^3+512\,a^3\,b^3\,c^3\,e^3-18\,b^8\,c\,d\,e^2-576\,a\,b^5\,c^3\,d^2\,e+192\,a\,b^6\,c^2\,d\,e^2-3072\,a^3\,b\,c^5\,d^2\,e+2304\,a^2\,b^3\,c^4\,d^2\,e-576\,a^2\,b^4\,c^3\,d\,e^2}{8\,\left(4096\,a^7\,c^6\,e^2-6144\,a^6\,b^2\,c^5\,e^2-4096\,a^6\,b\,c^6\,d\,e+4096\,a^6\,c^7\,d^2+3840\,a^5\,b^4\,c^4\,e^2+6144\,a^5\,b^3\,c^5\,d\,e-6144\,a^5\,b^2\,c^6\,d^2-1280\,a^4\,b^6\,c^3\,e^2-3840\,a^4\,b^5\,c^4\,d\,e+3840\,a^4\,b^4\,c^5\,d^2+240\,a^3\,b^8\,c^2\,e^2+1280\,a^3\,b^7\,c^3\,d\,e-1280\,a^3\,b^6\,c^4\,d^2-24\,a^2\,b^{10}\,c\,e^2-240\,a^2\,b^9\,c^2\,d\,e+240\,a^2\,b^8\,c^3\,d^2+a\,b^{12}\,e^2+24\,a\,b^{11}\,c\,d\,e-24\,a\,b^{10}\,c^2\,d^2-b^{13}\,d\,e+b^{12}\,c\,d^2\right)}}+\ln\left(\frac{\sqrt{2}\,\left(\frac{\sqrt{2}\,\left(4\,c^2\,e^3\,\left(b\,e-2\,c\,d\right)+2\,\sqrt{2}\,c^2\,e^2\,\left(4\,a\,c-b^2\right)\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}\,\sqrt{\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-b^9\,e^3-2048\,a^3\,c^6\,d^3+32\,b^6\,c^3\,d^3-384\,a\,b^4\,c^4\,d^3+768\,a^4\,b\,c^4\,e^3-1536\,a^4\,c^5\,d\,e^2-48\,b^7\,c^2\,d^2\,e+1536\,a^2\,b^2\,c^5\,d^3+96\,a^2\,b^5\,c^2\,e^3-512\,a^3\,b^3\,c^3\,e^3+18\,b^8\,c\,d\,e^2+576\,a\,b^5\,c^3\,d^2\,e-192\,a\,b^6\,c^2\,d\,e^2+3072\,a^3\,b\,c^5\,d^2\,e-2304\,a^2\,b^3\,c^4\,d^2\,e+576\,a^2\,b^4\,c^3\,d\,e^2}{{\left(4\,a\,c-b^2\right)}^6\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}\right)\,\sqrt{\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-b^9\,e^3-2048\,a^3\,c^6\,d^3+32\,b^6\,c^3\,d^3-384\,a\,b^4\,c^4\,d^3+768\,a^4\,b\,c^4\,e^3-1536\,a^4\,c^5\,d\,e^2-48\,b^7\,c^2\,d^2\,e+1536\,a^2\,b^2\,c^5\,d^3+96\,a^2\,b^5\,c^2\,e^3-512\,a^3\,b^3\,c^3\,e^3+18\,b^8\,c\,d\,e^2+576\,a\,b^5\,c^3\,d^2\,e-192\,a\,b^6\,c^2\,d\,e^2+3072\,a^3\,b\,c^5\,d^2\,e-2304\,a^2\,b^3\,c^4\,d^2\,e+576\,a^2\,b^4\,c^3\,d\,e^2}{{\left(4\,a\,c-b^2\right)}^6\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}}{4}-\frac{4\,c^3\,e^2\,\sqrt{d+e\,x}\,\left(5\,b^2\,e^2-16\,b\,c\,d\,e+16\,c^2\,d^2-4\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^2}\right)\,\sqrt{\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-b^9\,e^3-2048\,a^3\,c^6\,d^3+32\,b^6\,c^3\,d^3-384\,a\,b^4\,c^4\,d^3+768\,a^4\,b\,c^4\,e^3-1536\,a^4\,c^5\,d\,e^2-48\,b^7\,c^2\,d^2\,e+1536\,a^2\,b^2\,c^5\,d^3+96\,a^2\,b^5\,c^2\,e^3-512\,a^3\,b^3\,c^3\,e^3+18\,b^8\,c\,d\,e^2+576\,a\,b^5\,c^3\,d^2\,e-192\,a\,b^6\,c^2\,d\,e^2+3072\,a^3\,b\,c^5\,d^2\,e-2304\,a^2\,b^3\,c^4\,d^2\,e+576\,a^2\,b^4\,c^3\,d\,e^2}{{\left(4\,a\,c-b^2\right)}^6\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}}{4}-\frac{2\,c^3\,e^3\,\left(3\,b^2\,e^2-16\,b\,c\,d\,e+16\,c^2\,d^2+4\,a\,c\,e^2\right)}{{\left(4\,a\,c-b^2\right)}^3}\right)\,\sqrt{\frac{e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-b^9\,e^3-2048\,a^3\,c^6\,d^3+32\,b^6\,c^3\,d^3-384\,a\,b^4\,c^4\,d^3+768\,a^4\,b\,c^4\,e^3-1536\,a^4\,c^5\,d\,e^2-48\,b^7\,c^2\,d^2\,e+1536\,a^2\,b^2\,c^5\,d^3+96\,a^2\,b^5\,c^2\,e^3-512\,a^3\,b^3\,c^3\,e^3+18\,b^8\,c\,d\,e^2+576\,a\,b^5\,c^3\,d^2\,e-192\,a\,b^6\,c^2\,d\,e^2+3072\,a^3\,b\,c^5\,d^2\,e-2304\,a^2\,b^3\,c^4\,d^2\,e+576\,a^2\,b^4\,c^3\,d\,e^2}{8\,\left(4096\,a^7\,c^6\,e^2-6144\,a^6\,b^2\,c^5\,e^2-4096\,a^6\,b\,c^6\,d\,e+4096\,a^6\,c^7\,d^2+3840\,a^5\,b^4\,c^4\,e^2+6144\,a^5\,b^3\,c^5\,d\,e-6144\,a^5\,b^2\,c^6\,d^2-1280\,a^4\,b^6\,c^3\,e^2-3840\,a^4\,b^5\,c^4\,d\,e+3840\,a^4\,b^4\,c^5\,d^2+240\,a^3\,b^8\,c^2\,e^2+1280\,a^3\,b^7\,c^3\,d\,e-1280\,a^3\,b^6\,c^4\,d^2-24\,a^2\,b^{10}\,c\,e^2-240\,a^2\,b^9\,c^2\,d\,e+240\,a^2\,b^8\,c^3\,d^2+a\,b^{12}\,e^2+24\,a\,b^{11}\,c\,d\,e-24\,a\,b^{10}\,c^2\,d^2-b^{13}\,d\,e+b^{12}\,c\,d^2\right)}}","Not used",1,"((2*c*e*(d + e*x)^(3/2))/(4*a*c - b^2) + (e*(b*e - 2*c*d)*(d + e*x)^(1/2))/(4*a*c - b^2))/((b*e - 2*c*d)*(d + e*x) + c*(d + e*x)^2 + a*e^2 + c*d^2 - b*d*e) - log(((4*c^2*e^3*(b*e - 2*c*d) - 8*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(((e^3*(-(4*a*c - b^2)^9)^(1/2))/8 - (b^9*e^3)/8 - 256*a^3*c^6*d^3 + 4*b^6*c^3*d^3 - 48*a*b^4*c^4*d^3 + 96*a^4*b*c^4*e^3 - 192*a^4*c^5*d*e^2 - 6*b^7*c^2*d^2*e + 192*a^2*b^2*c^5*d^3 + 12*a^2*b^5*c^2*e^3 - 64*a^3*b^3*c^3*e^3 + (9*b^8*c*d*e^2)/4 + 72*a*b^5*c^3*d^2*e - 24*a*b^6*c^2*d*e^2 + 384*a^3*b*c^5*d^2*e - 288*a^2*b^3*c^4*d^2*e + 72*a^2*b^4*c^3*d*e^2)/((4*a*c - b^2)^6*(a*e^2 + c*d^2 - b*d*e)))^(1/2))*(((e^3*(-(4*a*c - b^2)^9)^(1/2))/8 - (b^9*e^3)/8 - 256*a^3*c^6*d^3 + 4*b^6*c^3*d^3 - 48*a*b^4*c^4*d^3 + 96*a^4*b*c^4*e^3 - 192*a^4*c^5*d*e^2 - 6*b^7*c^2*d^2*e + 192*a^2*b^2*c^5*d^3 + 12*a^2*b^5*c^2*e^3 - 64*a^3*b^3*c^3*e^3 + (9*b^8*c*d*e^2)/4 + 72*a*b^5*c^3*d^2*e - 24*a*b^6*c^2*d*e^2 + 384*a^3*b*c^5*d^2*e - 288*a^2*b^3*c^4*d^2*e + 72*a^2*b^4*c^3*d*e^2)/((4*a*c - b^2)^6*(a*e^2 + c*d^2 - b*d*e)))^(1/2) + (4*c^3*e^2*(d + e*x)^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 - 4*a*c*e^2 - 16*b*c*d*e))/(4*a*c - b^2)^2)*(((e^3*(-(4*a*c - b^2)^9)^(1/2))/8 - (b^9*e^3)/8 - 256*a^3*c^6*d^3 + 4*b^6*c^3*d^3 - 48*a*b^4*c^4*d^3 + 96*a^4*b*c^4*e^3 - 192*a^4*c^5*d*e^2 - 6*b^7*c^2*d^2*e + 192*a^2*b^2*c^5*d^3 + 12*a^2*b^5*c^2*e^3 - 64*a^3*b^3*c^3*e^3 + (9*b^8*c*d*e^2)/4 + 72*a*b^5*c^3*d^2*e - 24*a*b^6*c^2*d*e^2 + 384*a^3*b*c^5*d^2*e - 288*a^2*b^3*c^4*d^2*e + 72*a^2*b^4*c^3*d*e^2)/((4*a*c - b^2)^6*(a*e^2 + c*d^2 - b*d*e)))^(1/2) - (2*c^3*e^3*(3*b^2*e^2 + 16*c^2*d^2 + 4*a*c*e^2 - 16*b*c*d*e))/(4*a*c - b^2)^3)*(((e^3*(-(4*a*c - b^2)^9)^(1/2))/8 - (b^9*e^3)/8 - 256*a^3*c^6*d^3 + 4*b^6*c^3*d^3 - 48*a*b^4*c^4*d^3 + 96*a^4*b*c^4*e^3 - 192*a^4*c^5*d*e^2 - 6*b^7*c^2*d^2*e + 192*a^2*b^2*c^5*d^3 + 12*a^2*b^5*c^2*e^3 - 64*a^3*b^3*c^3*e^3 + (9*b^8*c*d*e^2)/4 + 72*a*b^5*c^3*d^2*e - 24*a*b^6*c^2*d*e^2 + 384*a^3*b*c^5*d^2*e - 288*a^2*b^3*c^4*d^2*e + 72*a^2*b^4*c^3*d*e^2)/(a*b^12*e^2 + b^12*c*d^2 + 4096*a^6*c^7*d^2 + 4096*a^7*c^6*e^2 - b^13*d*e - 24*a*b^10*c^2*d^2 - 24*a^2*b^10*c*e^2 + 240*a^2*b^8*c^3*d^2 - 1280*a^3*b^6*c^4*d^2 + 3840*a^4*b^4*c^5*d^2 - 6144*a^5*b^2*c^6*d^2 + 240*a^3*b^8*c^2*e^2 - 1280*a^4*b^6*c^3*e^2 + 3840*a^5*b^4*c^4*e^2 - 6144*a^6*b^2*c^5*e^2 - 4096*a^6*b*c^6*d*e - 240*a^2*b^9*c^2*d*e + 1280*a^3*b^7*c^3*d*e - 3840*a^4*b^5*c^4*d*e + 6144*a^5*b^3*c^5*d*e + 24*a*b^11*c*d*e))^(1/2) - log(((4*c^2*e^3*(b*e - 2*c*d) - 8*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(-((b^9*e^3)/8 + (e^3*(-(4*a*c - b^2)^9)^(1/2))/8 + 256*a^3*c^6*d^3 - 4*b^6*c^3*d^3 + 48*a*b^4*c^4*d^3 - 96*a^4*b*c^4*e^3 + 192*a^4*c^5*d*e^2 + 6*b^7*c^2*d^2*e - 192*a^2*b^2*c^5*d^3 - 12*a^2*b^5*c^2*e^3 + 64*a^3*b^3*c^3*e^3 - (9*b^8*c*d*e^2)/4 - 72*a*b^5*c^3*d^2*e + 24*a*b^6*c^2*d*e^2 - 384*a^3*b*c^5*d^2*e + 288*a^2*b^3*c^4*d^2*e - 72*a^2*b^4*c^3*d*e^2)/((4*a*c - b^2)^6*(a*e^2 + c*d^2 - b*d*e)))^(1/2))*(-((b^9*e^3)/8 + (e^3*(-(4*a*c - b^2)^9)^(1/2))/8 + 256*a^3*c^6*d^3 - 4*b^6*c^3*d^3 + 48*a*b^4*c^4*d^3 - 96*a^4*b*c^4*e^3 + 192*a^4*c^5*d*e^2 + 6*b^7*c^2*d^2*e - 192*a^2*b^2*c^5*d^3 - 12*a^2*b^5*c^2*e^3 + 64*a^3*b^3*c^3*e^3 - (9*b^8*c*d*e^2)/4 - 72*a*b^5*c^3*d^2*e + 24*a*b^6*c^2*d*e^2 - 384*a^3*b*c^5*d^2*e + 288*a^2*b^3*c^4*d^2*e - 72*a^2*b^4*c^3*d*e^2)/((4*a*c - b^2)^6*(a*e^2 + c*d^2 - b*d*e)))^(1/2) + (4*c^3*e^2*(d + e*x)^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 - 4*a*c*e^2 - 16*b*c*d*e))/(4*a*c - b^2)^2)*(-((b^9*e^3)/8 + (e^3*(-(4*a*c - b^2)^9)^(1/2))/8 + 256*a^3*c^6*d^3 - 4*b^6*c^3*d^3 + 48*a*b^4*c^4*d^3 - 96*a^4*b*c^4*e^3 + 192*a^4*c^5*d*e^2 + 6*b^7*c^2*d^2*e - 192*a^2*b^2*c^5*d^3 - 12*a^2*b^5*c^2*e^3 + 64*a^3*b^3*c^3*e^3 - (9*b^8*c*d*e^2)/4 - 72*a*b^5*c^3*d^2*e + 24*a*b^6*c^2*d*e^2 - 384*a^3*b*c^5*d^2*e + 288*a^2*b^3*c^4*d^2*e - 72*a^2*b^4*c^3*d*e^2)/((4*a*c - b^2)^6*(a*e^2 + c*d^2 - b*d*e)))^(1/2) - (2*c^3*e^3*(3*b^2*e^2 + 16*c^2*d^2 + 4*a*c*e^2 - 16*b*c*d*e))/(4*a*c - b^2)^3)*(-((b^9*e^3)/8 + (e^3*(-(4*a*c - b^2)^9)^(1/2))/8 + 256*a^3*c^6*d^3 - 4*b^6*c^3*d^3 + 48*a*b^4*c^4*d^3 - 96*a^4*b*c^4*e^3 + 192*a^4*c^5*d*e^2 + 6*b^7*c^2*d^2*e - 192*a^2*b^2*c^5*d^3 - 12*a^2*b^5*c^2*e^3 + 64*a^3*b^3*c^3*e^3 - (9*b^8*c*d*e^2)/4 - 72*a*b^5*c^3*d^2*e + 24*a*b^6*c^2*d*e^2 - 384*a^3*b*c^5*d^2*e + 288*a^2*b^3*c^4*d^2*e - 72*a^2*b^4*c^3*d*e^2)/(a*b^12*e^2 + b^12*c*d^2 + 4096*a^6*c^7*d^2 + 4096*a^7*c^6*e^2 - b^13*d*e - 24*a*b^10*c^2*d^2 - 24*a^2*b^10*c*e^2 + 240*a^2*b^8*c^3*d^2 - 1280*a^3*b^6*c^4*d^2 + 3840*a^4*b^4*c^5*d^2 - 6144*a^5*b^2*c^6*d^2 + 240*a^3*b^8*c^2*e^2 - 1280*a^4*b^6*c^3*e^2 + 3840*a^5*b^4*c^4*e^2 - 6144*a^6*b^2*c^5*e^2 - 4096*a^6*b*c^6*d*e - 240*a^2*b^9*c^2*d*e + 1280*a^3*b^7*c^3*d*e - 3840*a^4*b^5*c^4*d*e + 6144*a^5*b^3*c^5*d*e + 24*a*b^11*c*d*e))^(1/2) + log((2^(1/2)*((2^(1/2)*(4*c^2*e^3*(b*e - 2*c*d) + 2*2^(1/2)*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(-(b^9*e^3 + e^3*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^6*d^3 - 32*b^6*c^3*d^3 + 384*a*b^4*c^4*d^3 - 768*a^4*b*c^4*e^3 + 1536*a^4*c^5*d*e^2 + 48*b^7*c^2*d^2*e - 1536*a^2*b^2*c^5*d^3 - 96*a^2*b^5*c^2*e^3 + 512*a^3*b^3*c^3*e^3 - 18*b^8*c*d*e^2 - 576*a*b^5*c^3*d^2*e + 192*a*b^6*c^2*d*e^2 - 3072*a^3*b*c^5*d^2*e + 2304*a^2*b^3*c^4*d^2*e - 576*a^2*b^4*c^3*d*e^2)/((4*a*c - b^2)^6*(a*e^2 + c*d^2 - b*d*e)))^(1/2))*(-(b^9*e^3 + e^3*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^6*d^3 - 32*b^6*c^3*d^3 + 384*a*b^4*c^4*d^3 - 768*a^4*b*c^4*e^3 + 1536*a^4*c^5*d*e^2 + 48*b^7*c^2*d^2*e - 1536*a^2*b^2*c^5*d^3 - 96*a^2*b^5*c^2*e^3 + 512*a^3*b^3*c^3*e^3 - 18*b^8*c*d*e^2 - 576*a*b^5*c^3*d^2*e + 192*a*b^6*c^2*d*e^2 - 3072*a^3*b*c^5*d^2*e + 2304*a^2*b^3*c^4*d^2*e - 576*a^2*b^4*c^3*d*e^2)/((4*a*c - b^2)^6*(a*e^2 + c*d^2 - b*d*e)))^(1/2))/4 - (4*c^3*e^2*(d + e*x)^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 - 4*a*c*e^2 - 16*b*c*d*e))/(4*a*c - b^2)^2)*(-(b^9*e^3 + e^3*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^6*d^3 - 32*b^6*c^3*d^3 + 384*a*b^4*c^4*d^3 - 768*a^4*b*c^4*e^3 + 1536*a^4*c^5*d*e^2 + 48*b^7*c^2*d^2*e - 1536*a^2*b^2*c^5*d^3 - 96*a^2*b^5*c^2*e^3 + 512*a^3*b^3*c^3*e^3 - 18*b^8*c*d*e^2 - 576*a*b^5*c^3*d^2*e + 192*a*b^6*c^2*d*e^2 - 3072*a^3*b*c^5*d^2*e + 2304*a^2*b^3*c^4*d^2*e - 576*a^2*b^4*c^3*d*e^2)/((4*a*c - b^2)^6*(a*e^2 + c*d^2 - b*d*e)))^(1/2))/4 - (2*c^3*e^3*(3*b^2*e^2 + 16*c^2*d^2 + 4*a*c*e^2 - 16*b*c*d*e))/(4*a*c - b^2)^3)*(-(b^9*e^3 + e^3*(-(4*a*c - b^2)^9)^(1/2) + 2048*a^3*c^6*d^3 - 32*b^6*c^3*d^3 + 384*a*b^4*c^4*d^3 - 768*a^4*b*c^4*e^3 + 1536*a^4*c^5*d*e^2 + 48*b^7*c^2*d^2*e - 1536*a^2*b^2*c^5*d^3 - 96*a^2*b^5*c^2*e^3 + 512*a^3*b^3*c^3*e^3 - 18*b^8*c*d*e^2 - 576*a*b^5*c^3*d^2*e + 192*a*b^6*c^2*d*e^2 - 3072*a^3*b*c^5*d^2*e + 2304*a^2*b^3*c^4*d^2*e - 576*a^2*b^4*c^3*d*e^2)/(8*(a*b^12*e^2 + b^12*c*d^2 + 4096*a^6*c^7*d^2 + 4096*a^7*c^6*e^2 - b^13*d*e - 24*a*b^10*c^2*d^2 - 24*a^2*b^10*c*e^2 + 240*a^2*b^8*c^3*d^2 - 1280*a^3*b^6*c^4*d^2 + 3840*a^4*b^4*c^5*d^2 - 6144*a^5*b^2*c^6*d^2 + 240*a^3*b^8*c^2*e^2 - 1280*a^4*b^6*c^3*e^2 + 3840*a^5*b^4*c^4*e^2 - 6144*a^6*b^2*c^5*e^2 - 4096*a^6*b*c^6*d*e - 240*a^2*b^9*c^2*d*e + 1280*a^3*b^7*c^3*d*e - 3840*a^4*b^5*c^4*d*e + 6144*a^5*b^3*c^5*d*e + 24*a*b^11*c*d*e)))^(1/2) + log((2^(1/2)*((2^(1/2)*(4*c^2*e^3*(b*e - 2*c*d) + 2*2^(1/2)*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*((e^3*(-(4*a*c - b^2)^9)^(1/2) - b^9*e^3 - 2048*a^3*c^6*d^3 + 32*b^6*c^3*d^3 - 384*a*b^4*c^4*d^3 + 768*a^4*b*c^4*e^3 - 1536*a^4*c^5*d*e^2 - 48*b^7*c^2*d^2*e + 1536*a^2*b^2*c^5*d^3 + 96*a^2*b^5*c^2*e^3 - 512*a^3*b^3*c^3*e^3 + 18*b^8*c*d*e^2 + 576*a*b^5*c^3*d^2*e - 192*a*b^6*c^2*d*e^2 + 3072*a^3*b*c^5*d^2*e - 2304*a^2*b^3*c^4*d^2*e + 576*a^2*b^4*c^3*d*e^2)/((4*a*c - b^2)^6*(a*e^2 + c*d^2 - b*d*e)))^(1/2))*((e^3*(-(4*a*c - b^2)^9)^(1/2) - b^9*e^3 - 2048*a^3*c^6*d^3 + 32*b^6*c^3*d^3 - 384*a*b^4*c^4*d^3 + 768*a^4*b*c^4*e^3 - 1536*a^4*c^5*d*e^2 - 48*b^7*c^2*d^2*e + 1536*a^2*b^2*c^5*d^3 + 96*a^2*b^5*c^2*e^3 - 512*a^3*b^3*c^3*e^3 + 18*b^8*c*d*e^2 + 576*a*b^5*c^3*d^2*e - 192*a*b^6*c^2*d*e^2 + 3072*a^3*b*c^5*d^2*e - 2304*a^2*b^3*c^4*d^2*e + 576*a^2*b^4*c^3*d*e^2)/((4*a*c - b^2)^6*(a*e^2 + c*d^2 - b*d*e)))^(1/2))/4 - (4*c^3*e^2*(d + e*x)^(1/2)*(5*b^2*e^2 + 16*c^2*d^2 - 4*a*c*e^2 - 16*b*c*d*e))/(4*a*c - b^2)^2)*((e^3*(-(4*a*c - b^2)^9)^(1/2) - b^9*e^3 - 2048*a^3*c^6*d^3 + 32*b^6*c^3*d^3 - 384*a*b^4*c^4*d^3 + 768*a^4*b*c^4*e^3 - 1536*a^4*c^5*d*e^2 - 48*b^7*c^2*d^2*e + 1536*a^2*b^2*c^5*d^3 + 96*a^2*b^5*c^2*e^3 - 512*a^3*b^3*c^3*e^3 + 18*b^8*c*d*e^2 + 576*a*b^5*c^3*d^2*e - 192*a*b^6*c^2*d*e^2 + 3072*a^3*b*c^5*d^2*e - 2304*a^2*b^3*c^4*d^2*e + 576*a^2*b^4*c^3*d*e^2)/((4*a*c - b^2)^6*(a*e^2 + c*d^2 - b*d*e)))^(1/2))/4 - (2*c^3*e^3*(3*b^2*e^2 + 16*c^2*d^2 + 4*a*c*e^2 - 16*b*c*d*e))/(4*a*c - b^2)^3)*((e^3*(-(4*a*c - b^2)^9)^(1/2) - b^9*e^3 - 2048*a^3*c^6*d^3 + 32*b^6*c^3*d^3 - 384*a*b^4*c^4*d^3 + 768*a^4*b*c^4*e^3 - 1536*a^4*c^5*d*e^2 - 48*b^7*c^2*d^2*e + 1536*a^2*b^2*c^5*d^3 + 96*a^2*b^5*c^2*e^3 - 512*a^3*b^3*c^3*e^3 + 18*b^8*c*d*e^2 + 576*a*b^5*c^3*d^2*e - 192*a*b^6*c^2*d*e^2 + 3072*a^3*b*c^5*d^2*e - 2304*a^2*b^3*c^4*d^2*e + 576*a^2*b^4*c^3*d*e^2)/(8*(a*b^12*e^2 + b^12*c*d^2 + 4096*a^6*c^7*d^2 + 4096*a^7*c^6*e^2 - b^13*d*e - 24*a*b^10*c^2*d^2 - 24*a^2*b^10*c*e^2 + 240*a^2*b^8*c^3*d^2 - 1280*a^3*b^6*c^4*d^2 + 3840*a^4*b^4*c^5*d^2 - 6144*a^5*b^2*c^6*d^2 + 240*a^3*b^8*c^2*e^2 - 1280*a^4*b^6*c^3*e^2 + 3840*a^5*b^4*c^4*e^2 - 6144*a^6*b^2*c^5*e^2 - 4096*a^6*b*c^6*d*e - 240*a^2*b^9*c^2*d*e + 1280*a^3*b^7*c^3*d*e - 3840*a^4*b^5*c^4*d*e + 6144*a^5*b^3*c^5*d*e + 24*a*b^11*c*d*e)))^(1/2)","B"
2299,1,45676,428,7.888572,"\text{Not used}","int(1/((d + e*x)^(1/2)*(a + b*x + c*x^2)^2),x)","-\frac{\frac{\sqrt{d+e\,x}\,\left(b^2\,e^3-2\,b\,c\,d\,e^2+2\,c^2\,d^2\,e-2\,a\,c\,e^3\right)}{\left(4\,a\,c-b^2\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}+\frac{c\,\left(b\,e^2-2\,c\,d\,e\right)\,{\left(d+e\,x\right)}^{3/2}}{\left(4\,a\,c-b^2\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}{\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)+c\,{\left(d+e\,x\right)}^2+a\,e^2+c\,d^2-b\,d\,e}-\mathrm{atan}\left(\frac{\left(\left(\frac{1536\,a^5\,c^6\,e^7-1408\,a^4\,b^2\,c^5\,e^7-2048\,a^4\,b\,c^6\,d\,e^6+2048\,a^4\,c^7\,d^2\,e^5+480\,a^3\,b^4\,c^4\,e^7+1792\,a^3\,b^3\,c^5\,d\,e^6-1280\,a^3\,b^2\,c^6\,d^2\,e^5-1024\,a^3\,b\,c^7\,d^3\,e^4+512\,a^3\,c^8\,d^4\,e^3-72\,a^2\,b^6\,c^3\,e^7-576\,a^2\,b^5\,c^4\,d\,e^6+192\,a^2\,b^4\,c^5\,d^2\,e^5+768\,a^2\,b^3\,c^6\,d^3\,e^4-384\,a^2\,b^2\,c^7\,d^4\,e^3+4\,a\,b^8\,c^2\,e^7+80\,a\,b^7\,c^3\,d\,e^6+16\,a\,b^6\,c^4\,d^2\,e^5-192\,a\,b^5\,c^5\,d^3\,e^4+96\,a\,b^4\,c^6\,d^4\,e^3-4\,b^9\,c^2\,d\,e^6-4\,b^8\,c^3\,d^2\,e^5+16\,b^7\,c^4\,d^3\,e^4-8\,b^6\,c^5\,d^4\,e^3}{-64\,a^5\,c^3\,e^4+48\,a^4\,b^2\,c^2\,e^4+128\,a^4\,b\,c^3\,d\,e^3-128\,a^4\,c^4\,d^2\,e^2-12\,a^3\,b^4\,c\,e^4-96\,a^3\,b^3\,c^2\,d\,e^3+32\,a^3\,b^2\,c^3\,d^2\,e^2+128\,a^3\,b\,c^4\,d^3\,e-64\,a^3\,c^5\,d^4+a^2\,b^6\,e^4+24\,a^2\,b^5\,c\,d\,e^3+24\,a^2\,b^4\,c^2\,d^2\,e^2-96\,a^2\,b^3\,c^3\,d^3\,e+48\,a^2\,b^2\,c^4\,d^4-2\,a\,b^7\,d\,e^3-10\,a\,b^6\,c\,d^2\,e^2+24\,a\,b^5\,c^2\,d^3\,e-12\,a\,b^4\,c^3\,d^4+b^8\,d^2\,e^2-2\,b^7\,c\,d^3\,e+b^6\,c^2\,d^4}-\frac{2\,\sqrt{d+e\,x}\,\sqrt{-\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5+b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3-5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5-9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4+5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(-4096\,a^9\,c^6\,e^6+6144\,a^8\,b^2\,c^5\,e^6+12288\,a^8\,b\,c^6\,d\,e^5-12288\,a^8\,c^7\,d^2\,e^4-3840\,a^7\,b^4\,c^4\,e^6-18432\,a^7\,b^3\,c^5\,d\,e^5+6144\,a^7\,b^2\,c^6\,d^2\,e^4+24576\,a^7\,b\,c^7\,d^3\,e^3-12288\,a^7\,c^8\,d^4\,e^2+1280\,a^6\,b^6\,c^3\,e^6+11520\,a^6\,b^5\,c^4\,d\,e^5+6912\,a^6\,b^4\,c^5\,d^2\,e^4-32768\,a^6\,b^3\,c^6\,d^3\,e^3+6144\,a^6\,b^2\,c^7\,d^4\,e^2+12288\,a^6\,b\,c^8\,d^5\,e-4096\,a^6\,c^9\,d^6-240\,a^5\,b^8\,c^2\,e^6-3840\,a^5\,b^7\,c^3\,d\,e^5-7680\,a^5\,b^6\,c^4\,d^2\,e^4+16896\,a^5\,b^5\,c^5\,d^3\,e^3+6912\,a^5\,b^4\,c^6\,d^4\,e^2-18432\,a^5\,b^3\,c^7\,d^5\,e+6144\,a^5\,b^2\,c^8\,d^6+24\,a^4\,b^{10}\,c\,e^6+720\,a^4\,b^9\,c^2\,d\,e^5+3120\,a^4\,b^8\,c^3\,d^2\,e^4-3840\,a^4\,b^7\,c^4\,d^3\,e^3-7680\,a^4\,b^6\,c^5\,d^4\,e^2+11520\,a^4\,b^5\,c^6\,d^5\,e-3840\,a^4\,b^4\,c^7\,d^6-a^3\,b^{12}\,e^6-72\,a^3\,b^{11}\,c\,d\,e^5-648\,a^3\,b^{10}\,c^2\,d^2\,e^4+160\,a^3\,b^9\,c^3\,d^3\,e^3+3120\,a^3\,b^8\,c^4\,d^4\,e^2-3840\,a^3\,b^7\,c^5\,d^5\,e+1280\,a^3\,b^6\,c^6\,d^6+3\,a^2\,b^{13}\,d\,e^5+69\,a^2\,b^{12}\,c\,d^2\,e^4+96\,a^2\,b^{11}\,c^2\,d^3\,e^3-648\,a^2\,b^{10}\,c^3\,d^4\,e^2+720\,a^2\,b^9\,c^4\,d^5\,e-240\,a^2\,b^8\,c^5\,d^6-3\,a\,b^{14}\,d^2\,e^4-18\,a\,b^{13}\,c\,d^3\,e^3+69\,a\,b^{12}\,c^2\,d^4\,e^2-72\,a\,b^{11}\,c^3\,d^5\,e+24\,a\,b^{10}\,c^4\,d^6+b^{15}\,d^3\,e^3-3\,b^{14}\,c\,d^4\,e^2+3\,b^{13}\,c^2\,d^5\,e-b^{12}\,c^3\,d^6\right)}}\,\left(-256\,a^5\,b\,c^5\,e^7+512\,a^5\,c^6\,d\,e^6+192\,a^4\,b^3\,c^4\,e^7+128\,a^4\,b^2\,c^5\,d\,e^6-1536\,a^4\,b\,c^6\,d^2\,e^5+1024\,a^4\,c^7\,d^3\,e^4-48\,a^3\,b^5\,c^3\,e^7-288\,a^3\,b^4\,c^4\,d\,e^6+896\,a^3\,b^3\,c^5\,d^2\,e^5+256\,a^3\,b^2\,c^6\,d^3\,e^4-1280\,a^3\,b\,c^7\,d^4\,e^3+512\,a^3\,c^8\,d^5\,e^2+4\,a^2\,b^7\,c^2\,e^7+88\,a^2\,b^6\,c^3\,d\,e^6-96\,a^2\,b^5\,c^4\,d^2\,e^5-576\,a^2\,b^4\,c^5\,d^3\,e^4+960\,a^2\,b^3\,c^6\,d^4\,e^3-384\,a^2\,b^2\,c^7\,d^5\,e^2-8\,a\,b^8\,c^2\,d\,e^6-24\,a\,b^7\,c^3\,d^2\,e^5+176\,a\,b^6\,c^4\,d^3\,e^4-240\,a\,b^5\,c^5\,d^4\,e^3+96\,a\,b^4\,c^6\,d^5\,e^2+4\,b^9\,c^2\,d^2\,e^5-16\,b^8\,c^3\,d^3\,e^4+20\,b^7\,c^4\,d^4\,e^3-8\,b^6\,c^5\,d^5\,e^2\right)}{16\,a^4\,c^2\,e^4-8\,a^3\,b^2\,c\,e^4-32\,a^3\,b\,c^2\,d\,e^3+32\,a^3\,c^3\,d^2\,e^2+a^2\,b^4\,e^4+16\,a^2\,b^3\,c\,d\,e^3-32\,a^2\,b\,c^3\,d^3\,e+16\,a^2\,c^4\,d^4-2\,a\,b^5\,d\,e^3-6\,a\,b^4\,c\,d^2\,e^2+16\,a\,b^3\,c^2\,d^3\,e-8\,a\,b^2\,c^3\,d^4+b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4}\right)\,\sqrt{-\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5+b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3-5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5-9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4+5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(-4096\,a^9\,c^6\,e^6+6144\,a^8\,b^2\,c^5\,e^6+12288\,a^8\,b\,c^6\,d\,e^5-12288\,a^8\,c^7\,d^2\,e^4-3840\,a^7\,b^4\,c^4\,e^6-18432\,a^7\,b^3\,c^5\,d\,e^5+6144\,a^7\,b^2\,c^6\,d^2\,e^4+24576\,a^7\,b\,c^7\,d^3\,e^3-12288\,a^7\,c^8\,d^4\,e^2+1280\,a^6\,b^6\,c^3\,e^6+11520\,a^6\,b^5\,c^4\,d\,e^5+6912\,a^6\,b^4\,c^5\,d^2\,e^4-32768\,a^6\,b^3\,c^6\,d^3\,e^3+6144\,a^6\,b^2\,c^7\,d^4\,e^2+12288\,a^6\,b\,c^8\,d^5\,e-4096\,a^6\,c^9\,d^6-240\,a^5\,b^8\,c^2\,e^6-3840\,a^5\,b^7\,c^3\,d\,e^5-7680\,a^5\,b^6\,c^4\,d^2\,e^4+16896\,a^5\,b^5\,c^5\,d^3\,e^3+6912\,a^5\,b^4\,c^6\,d^4\,e^2-18432\,a^5\,b^3\,c^7\,d^5\,e+6144\,a^5\,b^2\,c^8\,d^6+24\,a^4\,b^{10}\,c\,e^6+720\,a^4\,b^9\,c^2\,d\,e^5+3120\,a^4\,b^8\,c^3\,d^2\,e^4-3840\,a^4\,b^7\,c^4\,d^3\,e^3-7680\,a^4\,b^6\,c^5\,d^4\,e^2+11520\,a^4\,b^5\,c^6\,d^5\,e-3840\,a^4\,b^4\,c^7\,d^6-a^3\,b^{12}\,e^6-72\,a^3\,b^{11}\,c\,d\,e^5-648\,a^3\,b^{10}\,c^2\,d^2\,e^4+160\,a^3\,b^9\,c^3\,d^3\,e^3+3120\,a^3\,b^8\,c^4\,d^4\,e^2-3840\,a^3\,b^7\,c^5\,d^5\,e+1280\,a^3\,b^6\,c^6\,d^6+3\,a^2\,b^{13}\,d\,e^5+69\,a^2\,b^{12}\,c\,d^2\,e^4+96\,a^2\,b^{11}\,c^2\,d^3\,e^3-648\,a^2\,b^{10}\,c^3\,d^4\,e^2+720\,a^2\,b^9\,c^4\,d^5\,e-240\,a^2\,b^8\,c^5\,d^6-3\,a\,b^{14}\,d^2\,e^4-18\,a\,b^{13}\,c\,d^3\,e^3+69\,a\,b^{12}\,c^2\,d^4\,e^2-72\,a\,b^{11}\,c^3\,d^5\,e+24\,a\,b^{10}\,c^4\,d^6+b^{15}\,d^3\,e^3-3\,b^{14}\,c\,d^4\,e^2+3\,b^{13}\,c^2\,d^5\,e-b^{12}\,c^3\,d^6\right)}}-\frac{2\,\sqrt{d+e\,x}\,\left(72\,a^2\,c^5\,e^6-14\,a\,b^2\,c^4\,e^6-88\,a\,b\,c^5\,d\,e^5+88\,a\,c^6\,d^2\,e^4+b^4\,c^3\,e^6+6\,b^3\,c^4\,d\,e^5+26\,b^2\,c^5\,d^2\,e^4-64\,b\,c^6\,d^3\,e^3+32\,c^7\,d^4\,e^2\right)}{16\,a^4\,c^2\,e^4-8\,a^3\,b^2\,c\,e^4-32\,a^3\,b\,c^2\,d\,e^3+32\,a^3\,c^3\,d^2\,e^2+a^2\,b^4\,e^4+16\,a^2\,b^3\,c\,d\,e^3-32\,a^2\,b\,c^3\,d^3\,e+16\,a^2\,c^4\,d^4-2\,a\,b^5\,d\,e^3-6\,a\,b^4\,c\,d^2\,e^2+16\,a\,b^3\,c^2\,d^3\,e-8\,a\,b^2\,c^3\,d^4+b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4}\right)\,\sqrt{-\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5+b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3-5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5-9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4+5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(-4096\,a^9\,c^6\,e^6+6144\,a^8\,b^2\,c^5\,e^6+12288\,a^8\,b\,c^6\,d\,e^5-12288\,a^8\,c^7\,d^2\,e^4-3840\,a^7\,b^4\,c^4\,e^6-18432\,a^7\,b^3\,c^5\,d\,e^5+6144\,a^7\,b^2\,c^6\,d^2\,e^4+24576\,a^7\,b\,c^7\,d^3\,e^3-12288\,a^7\,c^8\,d^4\,e^2+1280\,a^6\,b^6\,c^3\,e^6+11520\,a^6\,b^5\,c^4\,d\,e^5+6912\,a^6\,b^4\,c^5\,d^2\,e^4-32768\,a^6\,b^3\,c^6\,d^3\,e^3+6144\,a^6\,b^2\,c^7\,d^4\,e^2+12288\,a^6\,b\,c^8\,d^5\,e-4096\,a^6\,c^9\,d^6-240\,a^5\,b^8\,c^2\,e^6-3840\,a^5\,b^7\,c^3\,d\,e^5-7680\,a^5\,b^6\,c^4\,d^2\,e^4+16896\,a^5\,b^5\,c^5\,d^3\,e^3+6912\,a^5\,b^4\,c^6\,d^4\,e^2-18432\,a^5\,b^3\,c^7\,d^5\,e+6144\,a^5\,b^2\,c^8\,d^6+24\,a^4\,b^{10}\,c\,e^6+720\,a^4\,b^9\,c^2\,d\,e^5+3120\,a^4\,b^8\,c^3\,d^2\,e^4-3840\,a^4\,b^7\,c^4\,d^3\,e^3-7680\,a^4\,b^6\,c^5\,d^4\,e^2+11520\,a^4\,b^5\,c^6\,d^5\,e-3840\,a^4\,b^4\,c^7\,d^6-a^3\,b^{12}\,e^6-72\,a^3\,b^{11}\,c\,d\,e^5-648\,a^3\,b^{10}\,c^2\,d^2\,e^4+160\,a^3\,b^9\,c^3\,d^3\,e^3+3120\,a^3\,b^8\,c^4\,d^4\,e^2-3840\,a^3\,b^7\,c^5\,d^5\,e+1280\,a^3\,b^6\,c^6\,d^6+3\,a^2\,b^{13}\,d\,e^5+69\,a^2\,b^{12}\,c\,d^2\,e^4+96\,a^2\,b^{11}\,c^2\,d^3\,e^3-648\,a^2\,b^{10}\,c^3\,d^4\,e^2+720\,a^2\,b^9\,c^4\,d^5\,e-240\,a^2\,b^8\,c^5\,d^6-3\,a\,b^{14}\,d^2\,e^4-18\,a\,b^{13}\,c\,d^3\,e^3+69\,a\,b^{12}\,c^2\,d^4\,e^2-72\,a\,b^{11}\,c^3\,d^5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2\,b^{12}\,c\,d^2\,e^4+96\,a^2\,b^{11}\,c^2\,d^3\,e^3-648\,a^2\,b^{10}\,c^3\,d^4\,e^2+720\,a^2\,b^9\,c^4\,d^5\,e-240\,a^2\,b^8\,c^5\,d^6-3\,a\,b^{14}\,d^2\,e^4-18\,a\,b^{13}\,c\,d^3\,e^3+69\,a\,b^{12}\,c^2\,d^4\,e^2-72\,a\,b^{11}\,c^3\,d^5\,e+24\,a\,b^{10}\,c^4\,d^6+b^{15}\,d^3\,e^3-3\,b^{14}\,c\,d^4\,e^2+3\,b^{13}\,c^2\,d^5\,e-b^{12}\,c^3\,d^6\right)}}\,\left(-256\,a^5\,b\,c^5\,e^7+512\,a^5\,c^6\,d\,e^6+192\,a^4\,b^3\,c^4\,e^7+128\,a^4\,b^2\,c^5\,d\,e^6-1536\,a^4\,b\,c^6\,d^2\,e^5+1024\,a^4\,c^7\,d^3\,e^4-48\,a^3\,b^5\,c^3\,e^7-288\,a^3\,b^4\,c^4\,d\,e^6+896\,a^3\,b^3\,c^5\,d^2\,e^5+256\,a^3\,b^2\,c^6\,d^3\,e^4-1280\,a^3\,b\,c^7\,d^4\,e^3+512\,a^3\,c^8\,d^5\,e^2+4\,a^2\,b^7\,c^2\,e^7+88\,a^2\,b^6\,c^3\,d\,e^6-96\,a^2\,b^5\,c^4\,d^2\,e^5-576\,a^2\,b^4\,c^5\,d^3\,e^4+960\,a^2\,b^3\,c^6\,d^4\,e^3-384\,a^2\,b^2\,c^7\,d^5\,e^2-8\,a\,b^8\,c^2\,d\,e^6-24\,a\,b^7\,c^3\,d^2\,e^5+176\,a\,b^6\,c^4\,d^3\,e^4-240\,a\,b^5\,c^5\,d^4\,e^3+96\,a\,b^4\,c^6\,d^5\,e^2+4\,b^9\,c^2\,d^2\,e^5-16\,b^8\,c^3\,d^3\,e^4+20\,b^7\,c^4\,d^4\,e^3-8\,b^6\,c^5\,d^5\,e^2\right)}{16\,a^4\,c^2\,e^4-8\,a^3\,b^2\,c\,e^4-32\,a^3\,b\,c^2\,d\,e^3+32\,a^3\,c^3\,d^2\,e^2+a^2\,b^4\,e^4+16\,a^2\,b^3\,c\,d\,e^3-32\,a^2\,b\,c^3\,d^3\,e+16\,a^2\,c^4\,d^4-2\,a\,b^5\,d\,e^3-6\,a\,b^4\,c\,d^2\,e^2+16\,a\,b^3\,c^2\,d^3\,e-8\,a\,b^2\,c^3\,d^4+b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4}\right)\,\sqrt{-\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5-b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3+5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5+9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4-5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(-4096\,a^9\,c^6\,e^6+6144\,a^8\,b^2\,c^5\,e^6+12288\,a^8\,b\,c^6\,d\,e^5-12288\,a^8\,c^7\,d^2\,e^4-3840\,a^7\,b^4\,c^4\,e^6-18432\,a^7\,b^3\,c^5\,d\,e^5+6144\,a^7\,b^2\,c^6\,d^2\,e^4+24576\,a^7\,b\,c^7\,d^3\,e^3-12288\,a^7\,c^8\,d^4\,e^2+1280\,a^6\,b^6\,c^3\,e^6+11520\,a^6\,b^5\,c^4\,d\,e^5+6912\,a^6\,b^4\,c^5\,d^2\,e^4-32768\,a^6\,b^3\,c^6\,d^3\,e^3+6144\,a^6\,b^2\,c^7\,d^4\,e^2+12288\,a^6\,b\,c^8\,d^5\,e-4096\,a^6\,c^9\,d^6-240\,a^5\,b^8\,c^2\,e^6-3840\,a^5\,b^7\,c^3\,d\,e^5-7680\,a^5\,b^6\,c^4\,d^2\,e^4+16896\,a^5\,b^5\,c^5\,d^3\,e^3+6912\,a^5\,b^4\,c^6\,d^4\,e^2-18432\,a^5\,b^3\,c^7\,d^5\,e+6144\,a^5\,b^2\,c^8\,d^6+24\,a^4\,b^{10}\,c\,e^6+720\,a^4\,b^9\,c^2\,d\,e^5+3120\,a^4\,b^8\,c^3\,d^2\,e^4-3840\,a^4\,b^7\,c^4\,d^3\,e^3-7680\,a^4\,b^6\,c^5\,d^4\,e^2+11520\,a^4\,b^5\,c^6\,d^5\,e-3840\,a^4\,b^4\,c^7\,d^6-a^3\,b^{12}\,e^6-72\,a^3\,b^{11}\,c\,d\,e^5-648\,a^3\,b^{10}\,c^2\,d^2\,e^4+160\,a^3\,b^9\,c^3\,d^3\,e^3+3120\,a^3\,b^8\,c^4\,d^4\,e^2-3840\,a^3\,b^7\,c^5\,d^5\,e+1280\,a^3\,b^6\,c^6\,d^6+3\,a^2\,b^{13}\,d\,e^5+69\,a^2\,b^{12}\,c\,d^2\,e^4+96\,a^2\,b^{11}\,c^2\,d^3\,e^3-648\,a^2\,b^{10}\,c^3\,d^4\,e^2+720\,a^2\,b^9\,c^4\,d^5\,e-240\,a^2\,b^8\,c^5\,d^6-3\,a\,b^{14}\,d^2\,e^4-18\,a\,b^{13}\,c\,d^3\,e^3+69\,a\,b^{12}\,c^2\,d^4\,e^2-72\,a\,b^{11}\,c^3\,d^5\,e+24\,a\,b^{10}\,c^4\,d^6+b^{15}\,d^3\,e^3-3\,b^{14}\,c\,d^4\,e^2+3\,b^{13}\,c^2\,d^5\,e-b^{12}\,c^3\,d^6\right)}}+\frac{2\,\sqrt{d+e\,x}\,\left(72\,a^2\,c^5\,e^6-14\,a\,b^2\,c^4\,e^6-88\,a\,b\,c^5\,d\,e^5+88\,a\,c^6\,d^2\,e^4+b^4\,c^3\,e^6+6\,b^3\,c^4\,d\,e^5+26\,b^2\,c^5\,d^2\,e^4-64\,b\,c^6\,d^3\,e^3+32\,c^7\,d^4\,e^2\right)}{16\,a^4\,c^2\,e^4-8\,a^3\,b^2\,c\,e^4-32\,a^3\,b\,c^2\,d\,e^3+32\,a^3\,c^3\,d^2\,e^2+a^2\,b^4\,e^4+16\,a^2\,b^3\,c\,d\,e^3-32\,a^2\,b\,c^3\,d^3\,e+16\,a^2\,c^4\,d^4-2\,a\,b^5\,d\,e^3-6\,a\,b^4\,c\,d^2\,e^2+16\,a\,b^3\,c^2\,d^3\,e-8\,a\,b^2\,c^3\,d^4+b^6\,d^2\,e^2-2\,b^5\,c\,d^3\,e+b^4\,c^2\,d^4}\right)\,\sqrt{-\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5-b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3+5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5+9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4-5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(-4096\,a^9\,c^6\,e^6+6144\,a^8\,b^2\,c^5\,e^6+12288\,a^8\,b\,c^6\,d\,e^5-12288\,a^8\,c^7\,d^2\,e^4-3840\,a^7\,b^4\,c^4\,e^6-18432\,a^7\,b^3\,c^5\,d\,e^5+6144\,a^7\,b^2\,c^6\,d^2\,e^4+24576\,a^7\,b\,c^7\,d^3\,e^3-12288\,a^7\,c^8\,d^4\,e^2+1280\,a^6\,b^6\,c^3\,e^6+11520\,a^6\,b^5\,c^4\,d\,e^5+6912\,a^6\,b^4\,c^5\,d^2\,e^4-32768\,a^6\,b^3\,c^6\,d^3\,e^3+6144\,a^6\,b^2\,c^7\,d^4\,e^2+12288\,a^6\,b\,c^8\,d^5\,e-4096\,a^6\,c^9\,d^6-240\,a^5\,b^8\,c^2\,e^6-3840\,a^5\,b^7\,c^3\,d\,e^5-7680\,a^5\,b^6\,c^4\,d^2\,e^4+16896\,a^5\,b^5\,c^5\,d^3\,e^3+6912\,a^5\,b^4\,c^6\,d^4\,e^2-18432\,a^5\,b^3\,c^7\,d^5\,e+6144\,a^5\,b^2\,c^8\,d^6+24\,a^4\,b^{10}\,c\,e^6+720\,a^4\,b^9\,c^2\,d\,e^5+3120\,a^4\,b^8\,c^3\,d^2\,e^4-3840\,a^4\,b^7\,c^4\,d^3\,e^3-7680\,a^4\,b^6\,c^5\,d^4\,e^2+11520\,a^4\,b^5\,c^6\,d^5\,e-3840\,a^4\,b^4\,c^7\,d^6-a^3\,b^{12}\,e^6-72\,a^3\,b^{11}\,c\,d\,e^5-648\,a^3\,b^{10}\,c^2\,d^2\,e^4+160\,a^3\,b^9\,c^3\,d^3\,e^3+3120\,a^3\,b^8\,c^4\,d^4\,e^2-3840\,a^3\,b^7\,c^5\,d^5\,e+1280\,a^3\,b^6\,c^6\,d^6+3\,a^2\,b^{13}\,d\,e^5+69\,a^2\,b^{12}\,c\,d^2\,e^4+96\,a^2\,b^{11}\,c^2\,d^3\,e^3-648\,a^2\,b^{10}\,c^3\,d^4\,e^2+720\,a^2\,b^9\,c^4\,d^5\,e-240\,a^2\,b^8\,c^5\,d^6-3\,a\,b^{14}\,d^2\,e^4-18\,a\,b^{13}\,c\,d^3\,e^3+69\,a\,b^{12}\,c^2\,d^4\,e^2-72\,a\,b^{11}\,c^3\,d^5\,e+24\,a\,b^{10}\,c^4\,d^6+b^{15}\,d^3\,e^3-3\,b^{14}\,c\,d^4\,e^2+3\,b^{13}\,c^2\,d^5\,e-b^{12}\,c^3\,d^6\right)}}}\right)\,\sqrt{-\frac{32\,b^6\,c^5\,d^5-2048\,a^3\,c^8\,d^5-b^{11}\,e^5-b^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-384\,a\,b^4\,c^6\,d^5+3840\,a^5\,b\,c^5\,e^5-7680\,a^5\,c^6\,d\,e^4-80\,b^7\,c^4\,d^4\,e+1536\,a^2\,b^2\,c^7\,d^5-288\,a^2\,b^7\,c^2\,e^5+1504\,a^3\,b^5\,c^3\,e^5-3840\,a^4\,b^3\,c^4\,e^5-7680\,a^4\,c^7\,d^3\,e^2+50\,b^8\,c^3\,d^3\,e^2+5\,b^9\,c^2\,d^2\,e^3+5\,c^2\,d^2\,e^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+27\,a\,b^9\,c\,e^5+9\,a\,c\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-5\,b^{10}\,c\,d\,e^4-5\,b\,c\,d\,e^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+960\,a^2\,b^4\,c^5\,d^3\,e^2+2400\,a^2\,b^5\,c^4\,d^2\,e^3+2560\,a^3\,b^2\,c^6\,d^3\,e^2-8960\,a^3\,b^3\,c^5\,d^2\,e^3+960\,a\,b^5\,c^5\,d^4\,e+90\,a\,b^8\,c^2\,d\,e^4+5120\,a^3\,b\,c^7\,d^4\,e-480\,a\,b^6\,c^4\,d^3\,e^2-240\,a\,b^7\,c^3\,d^2\,e^3-3840\,a^2\,b^3\,c^6\,d^4\,e-480\,a^2\,b^6\,c^3\,d\,e^4+320\,a^3\,b^4\,c^4\,d\,e^4+11520\,a^4\,b\,c^6\,d^2\,e^3+3840\,a^4\,b^2\,c^5\,d\,e^4}{8\,\left(-4096\,a^9\,c^6\,e^6+6144\,a^8\,b^2\,c^5\,e^6+12288\,a^8\,b\,c^6\,d\,e^5-12288\,a^8\,c^7\,d^2\,e^4-3840\,a^7\,b^4\,c^4\,e^6-18432\,a^7\,b^3\,c^5\,d\,e^5+6144\,a^7\,b^2\,c^6\,d^2\,e^4+24576\,a^7\,b\,c^7\,d^3\,e^3-12288\,a^7\,c^8\,d^4\,e^2+1280\,a^6\,b^6\,c^3\,e^6+11520\,a^6\,b^5\,c^4\,d\,e^5+6912\,a^6\,b^4\,c^5\,d^2\,e^4-32768\,a^6\,b^3\,c^6\,d^3\,e^3+6144\,a^6\,b^2\,c^7\,d^4\,e^2+12288\,a^6\,b\,c^8\,d^5\,e-4096\,a^6\,c^9\,d^6-240\,a^5\,b^8\,c^2\,e^6-3840\,a^5\,b^7\,c^3\,d\,e^5-7680\,a^5\,b^6\,c^4\,d^2\,e^4+16896\,a^5\,b^5\,c^5\,d^3\,e^3+6912\,a^5\,b^4\,c^6\,d^4\,e^2-18432\,a^5\,b^3\,c^7\,d^5\,e+6144\,a^5\,b^2\,c^8\,d^6+24\,a^4\,b^{10}\,c\,e^6+720\,a^4\,b^9\,c^2\,d\,e^5+3120\,a^4\,b^8\,c^3\,d^2\,e^4-3840\,a^4\,b^7\,c^4\,d^3\,e^3-7680\,a^4\,b^6\,c^5\,d^4\,e^2+11520\,a^4\,b^5\,c^6\,d^5\,e-3840\,a^4\,b^4\,c^7\,d^6-a^3\,b^{12}\,e^6-72\,a^3\,b^{11}\,c\,d\,e^5-648\,a^3\,b^{10}\,c^2\,d^2\,e^4+160\,a^3\,b^9\,c^3\,d^3\,e^3+3120\,a^3\,b^8\,c^4\,d^4\,e^2-3840\,a^3\,b^7\,c^5\,d^5\,e+1280\,a^3\,b^6\,c^6\,d^6+3\,a^2\,b^{13}\,d\,e^5+69\,a^2\,b^{12}\,c\,d^2\,e^4+96\,a^2\,b^{11}\,c^2\,d^3\,e^3-648\,a^2\,b^{10}\,c^3\,d^4\,e^2+720\,a^2\,b^9\,c^4\,d^5\,e-240\,a^2\,b^8\,c^5\,d^6-3\,a\,b^{14}\,d^2\,e^4-18\,a\,b^{13}\,c\,d^3\,e^3+69\,a\,b^{12}\,c^2\,d^4\,e^2-72\,a\,b^{11}\,c^3\,d^5\,e+24\,a\,b^{10}\,c^4\,d^6+b^{15}\,d^3\,e^3-3\,b^{14}\,c\,d^4\,e^2+3\,b^{13}\,c^2\,d^5\,e-b^{12}\,c^3\,d^6\right)}}\,2{}\mathrm{i}","Not used",1,"- (((d + e*x)^(1/2)*(b^2*e^3 + 2*c^2*d^2*e - 2*a*c*e^3 - 2*b*c*d*e^2))/((4*a*c - b^2)*(a*e^2 + c*d^2 - b*d*e)) + (c*(b*e^2 - 2*c*d*e)*(d + e*x)^(3/2))/((4*a*c - b^2)*(a*e^2 + c*d^2 - b*d*e)))/((b*e - 2*c*d)*(d + e*x) + c*(d + e*x)^2 + a*e^2 + c*d^2 - b*d*e) - atan(((((1536*a^5*c^6*e^7 + 4*a*b^8*c^2*e^7 - 4*b^9*c^2*d*e^6 - 72*a^2*b^6*c^3*e^7 + 480*a^3*b^4*c^4*e^7 - 1408*a^4*b^2*c^5*e^7 + 512*a^3*c^8*d^4*e^3 + 2048*a^4*c^7*d^2*e^5 - 8*b^6*c^5*d^4*e^3 + 16*b^7*c^4*d^3*e^4 - 4*b^8*c^3*d^2*e^5 - 384*a^2*b^2*c^7*d^4*e^3 + 768*a^2*b^3*c^6*d^3*e^4 + 192*a^2*b^4*c^5*d^2*e^5 - 1280*a^3*b^2*c^6*d^2*e^5 + 80*a*b^7*c^3*d*e^6 - 2048*a^4*b*c^6*d*e^6 + 96*a*b^4*c^6*d^4*e^3 - 192*a*b^5*c^5*d^3*e^4 + 16*a*b^6*c^4*d^2*e^5 - 576*a^2*b^5*c^4*d*e^6 - 1024*a^3*b*c^7*d^3*e^4 + 1792*a^3*b^3*c^5*d*e^6)/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) - (2*(d + e*x)^(1/2)*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*(512*a^5*c^6*d*e^6 - 256*a^5*b*c^5*e^7 + 4*a^2*b^7*c^2*e^7 - 48*a^3*b^5*c^3*e^7 + 192*a^4*b^3*c^4*e^7 + 512*a^3*c^8*d^5*e^2 + 1024*a^4*c^7*d^3*e^4 - 8*b^6*c^5*d^5*e^2 + 20*b^7*c^4*d^4*e^3 - 16*b^8*c^3*d^3*e^4 + 4*b^9*c^2*d^2*e^5 - 384*a^2*b^2*c^7*d^5*e^2 + 960*a^2*b^3*c^6*d^4*e^3 - 576*a^2*b^4*c^5*d^3*e^4 - 96*a^2*b^5*c^4*d^2*e^5 + 256*a^3*b^2*c^6*d^3*e^4 + 896*a^3*b^3*c^5*d^2*e^5 - 8*a*b^8*c^2*d*e^6 + 96*a*b^4*c^6*d^5*e^2 - 240*a*b^5*c^5*d^4*e^3 + 176*a*b^6*c^4*d^3*e^4 - 24*a*b^7*c^3*d^2*e^5 + 88*a^2*b^6*c^3*d*e^6 - 1280*a^3*b*c^7*d^4*e^3 - 288*a^3*b^4*c^4*d*e^6 - 1536*a^4*b*c^6*d^2*e^5 + 128*a^4*b^2*c^5*d*e^6))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2) - (2*(d + e*x)^(1/2)*(72*a^2*c^5*e^6 + b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 14*a*b^2*c^4*e^6 + 88*a*c^6*d^2*e^4 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4 - 88*a*b*c^5*d*e^5))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*1i - (((1536*a^5*c^6*e^7 + 4*a*b^8*c^2*e^7 - 4*b^9*c^2*d*e^6 - 72*a^2*b^6*c^3*e^7 + 480*a^3*b^4*c^4*e^7 - 1408*a^4*b^2*c^5*e^7 + 512*a^3*c^8*d^4*e^3 + 2048*a^4*c^7*d^2*e^5 - 8*b^6*c^5*d^4*e^3 + 16*b^7*c^4*d^3*e^4 - 4*b^8*c^3*d^2*e^5 - 384*a^2*b^2*c^7*d^4*e^3 + 768*a^2*b^3*c^6*d^3*e^4 + 192*a^2*b^4*c^5*d^2*e^5 - 1280*a^3*b^2*c^6*d^2*e^5 + 80*a*b^7*c^3*d*e^6 - 2048*a^4*b*c^6*d*e^6 + 96*a*b^4*c^6*d^4*e^3 - 192*a*b^5*c^5*d^3*e^4 + 16*a*b^6*c^4*d^2*e^5 - 576*a^2*b^5*c^4*d*e^6 - 1024*a^3*b*c^7*d^3*e^4 + 1792*a^3*b^3*c^5*d*e^6)/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) + (2*(d + e*x)^(1/2)*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*(512*a^5*c^6*d*e^6 - 256*a^5*b*c^5*e^7 + 4*a^2*b^7*c^2*e^7 - 48*a^3*b^5*c^3*e^7 + 192*a^4*b^3*c^4*e^7 + 512*a^3*c^8*d^5*e^2 + 1024*a^4*c^7*d^3*e^4 - 8*b^6*c^5*d^5*e^2 + 20*b^7*c^4*d^4*e^3 - 16*b^8*c^3*d^3*e^4 + 4*b^9*c^2*d^2*e^5 - 384*a^2*b^2*c^7*d^5*e^2 + 960*a^2*b^3*c^6*d^4*e^3 - 576*a^2*b^4*c^5*d^3*e^4 - 96*a^2*b^5*c^4*d^2*e^5 + 256*a^3*b^2*c^6*d^3*e^4 + 896*a^3*b^3*c^5*d^2*e^5 - 8*a*b^8*c^2*d*e^6 + 96*a*b^4*c^6*d^5*e^2 - 240*a*b^5*c^5*d^4*e^3 + 176*a*b^6*c^4*d^3*e^4 - 24*a*b^7*c^3*d^2*e^5 + 88*a^2*b^6*c^3*d*e^6 - 1280*a^3*b*c^7*d^4*e^3 - 288*a^3*b^4*c^4*d*e^6 - 1536*a^4*b*c^6*d^2*e^5 + 128*a^4*b^2*c^5*d*e^6))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2) + (2*(d + e*x)^(1/2)*(72*a^2*c^5*e^6 + b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 14*a*b^2*c^4*e^6 + 88*a*c^6*d^2*e^4 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4 - 88*a*b*c^5*d*e^5))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*1i)/((2*(5*b^3*c^4*e^6 + 32*c^7*d^3*e^3 - 48*b*c^6*d^2*e^4 + 6*b^2*c^5*d*e^5 - 36*a*b*c^5*e^6 + 72*a*c^6*d*e^5))/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) + (((1536*a^5*c^6*e^7 + 4*a*b^8*c^2*e^7 - 4*b^9*c^2*d*e^6 - 72*a^2*b^6*c^3*e^7 + 480*a^3*b^4*c^4*e^7 - 1408*a^4*b^2*c^5*e^7 + 512*a^3*c^8*d^4*e^3 + 2048*a^4*c^7*d^2*e^5 - 8*b^6*c^5*d^4*e^3 + 16*b^7*c^4*d^3*e^4 - 4*b^8*c^3*d^2*e^5 - 384*a^2*b^2*c^7*d^4*e^3 + 768*a^2*b^3*c^6*d^3*e^4 + 192*a^2*b^4*c^5*d^2*e^5 - 1280*a^3*b^2*c^6*d^2*e^5 + 80*a*b^7*c^3*d*e^6 - 2048*a^4*b*c^6*d*e^6 + 96*a*b^4*c^6*d^4*e^3 - 192*a*b^5*c^5*d^3*e^4 + 16*a*b^6*c^4*d^2*e^5 - 576*a^2*b^5*c^4*d*e^6 - 1024*a^3*b*c^7*d^3*e^4 + 1792*a^3*b^3*c^5*d*e^6)/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) - (2*(d + e*x)^(1/2)*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*(512*a^5*c^6*d*e^6 - 256*a^5*b*c^5*e^7 + 4*a^2*b^7*c^2*e^7 - 48*a^3*b^5*c^3*e^7 + 192*a^4*b^3*c^4*e^7 + 512*a^3*c^8*d^5*e^2 + 1024*a^4*c^7*d^3*e^4 - 8*b^6*c^5*d^5*e^2 + 20*b^7*c^4*d^4*e^3 - 16*b^8*c^3*d^3*e^4 + 4*b^9*c^2*d^2*e^5 - 384*a^2*b^2*c^7*d^5*e^2 + 960*a^2*b^3*c^6*d^4*e^3 - 576*a^2*b^4*c^5*d^3*e^4 - 96*a^2*b^5*c^4*d^2*e^5 + 256*a^3*b^2*c^6*d^3*e^4 + 896*a^3*b^3*c^5*d^2*e^5 - 8*a*b^8*c^2*d*e^6 + 96*a*b^4*c^6*d^5*e^2 - 240*a*b^5*c^5*d^4*e^3 + 176*a*b^6*c^4*d^3*e^4 - 24*a*b^7*c^3*d^2*e^5 + 88*a^2*b^6*c^3*d*e^6 - 1280*a^3*b*c^7*d^4*e^3 - 288*a^3*b^4*c^4*d*e^6 - 1536*a^4*b*c^6*d^2*e^5 + 128*a^4*b^2*c^5*d*e^6))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2) - (2*(d + e*x)^(1/2)*(72*a^2*c^5*e^6 + b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 14*a*b^2*c^4*e^6 + 88*a*c^6*d^2*e^4 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4 - 88*a*b*c^5*d*e^5))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2) + (((1536*a^5*c^6*e^7 + 4*a*b^8*c^2*e^7 - 4*b^9*c^2*d*e^6 - 72*a^2*b^6*c^3*e^7 + 480*a^3*b^4*c^4*e^7 - 1408*a^4*b^2*c^5*e^7 + 512*a^3*c^8*d^4*e^3 + 2048*a^4*c^7*d^2*e^5 - 8*b^6*c^5*d^4*e^3 + 16*b^7*c^4*d^3*e^4 - 4*b^8*c^3*d^2*e^5 - 384*a^2*b^2*c^7*d^4*e^3 + 768*a^2*b^3*c^6*d^3*e^4 + 192*a^2*b^4*c^5*d^2*e^5 - 1280*a^3*b^2*c^6*d^2*e^5 + 80*a*b^7*c^3*d*e^6 - 2048*a^4*b*c^6*d*e^6 + 96*a*b^4*c^6*d^4*e^3 - 192*a*b^5*c^5*d^3*e^4 + 16*a*b^6*c^4*d^2*e^5 - 576*a^2*b^5*c^4*d*e^6 - 1024*a^3*b*c^7*d^3*e^4 + 1792*a^3*b^3*c^5*d*e^6)/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) + (2*(d + e*x)^(1/2)*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*(512*a^5*c^6*d*e^6 - 256*a^5*b*c^5*e^7 + 4*a^2*b^7*c^2*e^7 - 48*a^3*b^5*c^3*e^7 + 192*a^4*b^3*c^4*e^7 + 512*a^3*c^8*d^5*e^2 + 1024*a^4*c^7*d^3*e^4 - 8*b^6*c^5*d^5*e^2 + 20*b^7*c^4*d^4*e^3 - 16*b^8*c^3*d^3*e^4 + 4*b^9*c^2*d^2*e^5 - 384*a^2*b^2*c^7*d^5*e^2 + 960*a^2*b^3*c^6*d^4*e^3 - 576*a^2*b^4*c^5*d^3*e^4 - 96*a^2*b^5*c^4*d^2*e^5 + 256*a^3*b^2*c^6*d^3*e^4 + 896*a^3*b^3*c^5*d^2*e^5 - 8*a*b^8*c^2*d*e^6 + 96*a*b^4*c^6*d^5*e^2 - 240*a*b^5*c^5*d^4*e^3 + 176*a*b^6*c^4*d^3*e^4 - 24*a*b^7*c^3*d^2*e^5 + 88*a^2*b^6*c^3*d*e^6 - 1280*a^3*b*c^7*d^4*e^3 - 288*a^3*b^4*c^4*d*e^6 - 1536*a^4*b*c^6*d^2*e^5 + 128*a^4*b^2*c^5*d*e^6))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2) + (2*(d + e*x)^(1/2)*(72*a^2*c^5*e^6 + b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 14*a*b^2*c^4*e^6 + 88*a*c^6*d^2*e^4 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4 - 88*a*b*c^5*d*e^5))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 + b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 - 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 - 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 + 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*2i - atan(((((1536*a^5*c^6*e^7 + 4*a*b^8*c^2*e^7 - 4*b^9*c^2*d*e^6 - 72*a^2*b^6*c^3*e^7 + 480*a^3*b^4*c^4*e^7 - 1408*a^4*b^2*c^5*e^7 + 512*a^3*c^8*d^4*e^3 + 2048*a^4*c^7*d^2*e^5 - 8*b^6*c^5*d^4*e^3 + 16*b^7*c^4*d^3*e^4 - 4*b^8*c^3*d^2*e^5 - 384*a^2*b^2*c^7*d^4*e^3 + 768*a^2*b^3*c^6*d^3*e^4 + 192*a^2*b^4*c^5*d^2*e^5 - 1280*a^3*b^2*c^6*d^2*e^5 + 80*a*b^7*c^3*d*e^6 - 2048*a^4*b*c^6*d*e^6 + 96*a*b^4*c^6*d^4*e^3 - 192*a*b^5*c^5*d^3*e^4 + 16*a*b^6*c^4*d^2*e^5 - 576*a^2*b^5*c^4*d*e^6 - 1024*a^3*b*c^7*d^3*e^4 + 1792*a^3*b^3*c^5*d*e^6)/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) - (2*(d + e*x)^(1/2)*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*(512*a^5*c^6*d*e^6 - 256*a^5*b*c^5*e^7 + 4*a^2*b^7*c^2*e^7 - 48*a^3*b^5*c^3*e^7 + 192*a^4*b^3*c^4*e^7 + 512*a^3*c^8*d^5*e^2 + 1024*a^4*c^7*d^3*e^4 - 8*b^6*c^5*d^5*e^2 + 20*b^7*c^4*d^4*e^3 - 16*b^8*c^3*d^3*e^4 + 4*b^9*c^2*d^2*e^5 - 384*a^2*b^2*c^7*d^5*e^2 + 960*a^2*b^3*c^6*d^4*e^3 - 576*a^2*b^4*c^5*d^3*e^4 - 96*a^2*b^5*c^4*d^2*e^5 + 256*a^3*b^2*c^6*d^3*e^4 + 896*a^3*b^3*c^5*d^2*e^5 - 8*a*b^8*c^2*d*e^6 + 96*a*b^4*c^6*d^5*e^2 - 240*a*b^5*c^5*d^4*e^3 + 176*a*b^6*c^4*d^3*e^4 - 24*a*b^7*c^3*d^2*e^5 + 88*a^2*b^6*c^3*d*e^6 - 1280*a^3*b*c^7*d^4*e^3 - 288*a^3*b^4*c^4*d*e^6 - 1536*a^4*b*c^6*d^2*e^5 + 128*a^4*b^2*c^5*d*e^6))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2) - (2*(d + e*x)^(1/2)*(72*a^2*c^5*e^6 + b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 14*a*b^2*c^4*e^6 + 88*a*c^6*d^2*e^4 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4 - 88*a*b*c^5*d*e^5))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*1i - (((1536*a^5*c^6*e^7 + 4*a*b^8*c^2*e^7 - 4*b^9*c^2*d*e^6 - 72*a^2*b^6*c^3*e^7 + 480*a^3*b^4*c^4*e^7 - 1408*a^4*b^2*c^5*e^7 + 512*a^3*c^8*d^4*e^3 + 2048*a^4*c^7*d^2*e^5 - 8*b^6*c^5*d^4*e^3 + 16*b^7*c^4*d^3*e^4 - 4*b^8*c^3*d^2*e^5 - 384*a^2*b^2*c^7*d^4*e^3 + 768*a^2*b^3*c^6*d^3*e^4 + 192*a^2*b^4*c^5*d^2*e^5 - 1280*a^3*b^2*c^6*d^2*e^5 + 80*a*b^7*c^3*d*e^6 - 2048*a^4*b*c^6*d*e^6 + 96*a*b^4*c^6*d^4*e^3 - 192*a*b^5*c^5*d^3*e^4 + 16*a*b^6*c^4*d^2*e^5 - 576*a^2*b^5*c^4*d*e^6 - 1024*a^3*b*c^7*d^3*e^4 + 1792*a^3*b^3*c^5*d*e^6)/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) + (2*(d + e*x)^(1/2)*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*(512*a^5*c^6*d*e^6 - 256*a^5*b*c^5*e^7 + 4*a^2*b^7*c^2*e^7 - 48*a^3*b^5*c^3*e^7 + 192*a^4*b^3*c^4*e^7 + 512*a^3*c^8*d^5*e^2 + 1024*a^4*c^7*d^3*e^4 - 8*b^6*c^5*d^5*e^2 + 20*b^7*c^4*d^4*e^3 - 16*b^8*c^3*d^3*e^4 + 4*b^9*c^2*d^2*e^5 - 384*a^2*b^2*c^7*d^5*e^2 + 960*a^2*b^3*c^6*d^4*e^3 - 576*a^2*b^4*c^5*d^3*e^4 - 96*a^2*b^5*c^4*d^2*e^5 + 256*a^3*b^2*c^6*d^3*e^4 + 896*a^3*b^3*c^5*d^2*e^5 - 8*a*b^8*c^2*d*e^6 + 96*a*b^4*c^6*d^5*e^2 - 240*a*b^5*c^5*d^4*e^3 + 176*a*b^6*c^4*d^3*e^4 - 24*a*b^7*c^3*d^2*e^5 + 88*a^2*b^6*c^3*d*e^6 - 1280*a^3*b*c^7*d^4*e^3 - 288*a^3*b^4*c^4*d*e^6 - 1536*a^4*b*c^6*d^2*e^5 + 128*a^4*b^2*c^5*d*e^6))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2) + (2*(d + e*x)^(1/2)*(72*a^2*c^5*e^6 + b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 14*a*b^2*c^4*e^6 + 88*a*c^6*d^2*e^4 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4 - 88*a*b*c^5*d*e^5))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*1i)/((2*(5*b^3*c^4*e^6 + 32*c^7*d^3*e^3 - 48*b*c^6*d^2*e^4 + 6*b^2*c^5*d*e^5 - 36*a*b*c^5*e^6 + 72*a*c^6*d*e^5))/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) + (((1536*a^5*c^6*e^7 + 4*a*b^8*c^2*e^7 - 4*b^9*c^2*d*e^6 - 72*a^2*b^6*c^3*e^7 + 480*a^3*b^4*c^4*e^7 - 1408*a^4*b^2*c^5*e^7 + 512*a^3*c^8*d^4*e^3 + 2048*a^4*c^7*d^2*e^5 - 8*b^6*c^5*d^4*e^3 + 16*b^7*c^4*d^3*e^4 - 4*b^8*c^3*d^2*e^5 - 384*a^2*b^2*c^7*d^4*e^3 + 768*a^2*b^3*c^6*d^3*e^4 + 192*a^2*b^4*c^5*d^2*e^5 - 1280*a^3*b^2*c^6*d^2*e^5 + 80*a*b^7*c^3*d*e^6 - 2048*a^4*b*c^6*d*e^6 + 96*a*b^4*c^6*d^4*e^3 - 192*a*b^5*c^5*d^3*e^4 + 16*a*b^6*c^4*d^2*e^5 - 576*a^2*b^5*c^4*d*e^6 - 1024*a^3*b*c^7*d^3*e^4 + 1792*a^3*b^3*c^5*d*e^6)/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) - (2*(d + e*x)^(1/2)*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*(512*a^5*c^6*d*e^6 - 256*a^5*b*c^5*e^7 + 4*a^2*b^7*c^2*e^7 - 48*a^3*b^5*c^3*e^7 + 192*a^4*b^3*c^4*e^7 + 512*a^3*c^8*d^5*e^2 + 1024*a^4*c^7*d^3*e^4 - 8*b^6*c^5*d^5*e^2 + 20*b^7*c^4*d^4*e^3 - 16*b^8*c^3*d^3*e^4 + 4*b^9*c^2*d^2*e^5 - 384*a^2*b^2*c^7*d^5*e^2 + 960*a^2*b^3*c^6*d^4*e^3 - 576*a^2*b^4*c^5*d^3*e^4 - 96*a^2*b^5*c^4*d^2*e^5 + 256*a^3*b^2*c^6*d^3*e^4 + 896*a^3*b^3*c^5*d^2*e^5 - 8*a*b^8*c^2*d*e^6 + 96*a*b^4*c^6*d^5*e^2 - 240*a*b^5*c^5*d^4*e^3 + 176*a*b^6*c^4*d^3*e^4 - 24*a*b^7*c^3*d^2*e^5 + 88*a^2*b^6*c^3*d*e^6 - 1280*a^3*b*c^7*d^4*e^3 - 288*a^3*b^4*c^4*d*e^6 - 1536*a^4*b*c^6*d^2*e^5 + 128*a^4*b^2*c^5*d*e^6))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2) - (2*(d + e*x)^(1/2)*(72*a^2*c^5*e^6 + b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 14*a*b^2*c^4*e^6 + 88*a*c^6*d^2*e^4 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4 - 88*a*b*c^5*d*e^5))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2) + (((1536*a^5*c^6*e^7 + 4*a*b^8*c^2*e^7 - 4*b^9*c^2*d*e^6 - 72*a^2*b^6*c^3*e^7 + 480*a^3*b^4*c^4*e^7 - 1408*a^4*b^2*c^5*e^7 + 512*a^3*c^8*d^4*e^3 + 2048*a^4*c^7*d^2*e^5 - 8*b^6*c^5*d^4*e^3 + 16*b^7*c^4*d^3*e^4 - 4*b^8*c^3*d^2*e^5 - 384*a^2*b^2*c^7*d^4*e^3 + 768*a^2*b^3*c^6*d^3*e^4 + 192*a^2*b^4*c^5*d^2*e^5 - 1280*a^3*b^2*c^6*d^2*e^5 + 80*a*b^7*c^3*d*e^6 - 2048*a^4*b*c^6*d*e^6 + 96*a*b^4*c^6*d^4*e^3 - 192*a*b^5*c^5*d^3*e^4 + 16*a*b^6*c^4*d^2*e^5 - 576*a^2*b^5*c^4*d*e^6 - 1024*a^3*b*c^7*d^3*e^4 + 1792*a^3*b^3*c^5*d*e^6)/(a^2*b^6*e^4 - 64*a^3*c^5*d^4 - 64*a^5*c^3*e^4 + b^6*c^2*d^4 + b^8*d^2*e^2 - 12*a*b^4*c^3*d^4 - 12*a^3*b^4*c*e^4 + 48*a^2*b^2*c^4*d^4 + 48*a^4*b^2*c^2*e^4 - 128*a^4*c^4*d^2*e^2 - 2*a*b^7*d*e^3 - 2*b^7*c*d^3*e + 24*a^2*b^4*c^2*d^2*e^2 + 32*a^3*b^2*c^3*d^2*e^2 + 24*a*b^5*c^2*d^3*e - 10*a*b^6*c*d^2*e^2 + 24*a^2*b^5*c*d*e^3 + 128*a^3*b*c^4*d^3*e + 128*a^4*b*c^3*d*e^3 - 96*a^2*b^3*c^3*d^3*e - 96*a^3*b^3*c^2*d*e^3) + (2*(d + e*x)^(1/2)*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*(512*a^5*c^6*d*e^6 - 256*a^5*b*c^5*e^7 + 4*a^2*b^7*c^2*e^7 - 48*a^3*b^5*c^3*e^7 + 192*a^4*b^3*c^4*e^7 + 512*a^3*c^8*d^5*e^2 + 1024*a^4*c^7*d^3*e^4 - 8*b^6*c^5*d^5*e^2 + 20*b^7*c^4*d^4*e^3 - 16*b^8*c^3*d^3*e^4 + 4*b^9*c^2*d^2*e^5 - 384*a^2*b^2*c^7*d^5*e^2 + 960*a^2*b^3*c^6*d^4*e^3 - 576*a^2*b^4*c^5*d^3*e^4 - 96*a^2*b^5*c^4*d^2*e^5 + 256*a^3*b^2*c^6*d^3*e^4 + 896*a^3*b^3*c^5*d^2*e^5 - 8*a*b^8*c^2*d*e^6 + 96*a*b^4*c^6*d^5*e^2 - 240*a*b^5*c^5*d^4*e^3 + 176*a*b^6*c^4*d^3*e^4 - 24*a*b^7*c^3*d^2*e^5 + 88*a^2*b^6*c^3*d*e^6 - 1280*a^3*b*c^7*d^4*e^3 - 288*a^3*b^4*c^4*d*e^6 - 1536*a^4*b*c^6*d^2*e^5 + 128*a^4*b^2*c^5*d*e^6))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2) + (2*(d + e*x)^(1/2)*(72*a^2*c^5*e^6 + b^4*c^3*e^6 + 32*c^7*d^4*e^2 - 14*a*b^2*c^4*e^6 + 88*a*c^6*d^2*e^4 - 64*b*c^6*d^3*e^3 + 6*b^3*c^4*d*e^5 + 26*b^2*c^5*d^2*e^4 - 88*a*b*c^5*d*e^5))/(a^2*b^4*e^4 + 16*a^2*c^4*d^4 + 16*a^4*c^2*e^4 + b^4*c^2*d^4 + b^6*d^2*e^2 - 8*a*b^2*c^3*d^4 - 8*a^3*b^2*c*e^4 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 6*a*b^4*c*d^2*e^2 - 32*a^2*b*c^3*d^3*e + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)))*(-(32*b^6*c^5*d^5 - 2048*a^3*c^8*d^5 - b^11*e^5 - b^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^6*d^5 + 3840*a^5*b*c^5*e^5 - 7680*a^5*c^6*d*e^4 - 80*b^7*c^4*d^4*e + 1536*a^2*b^2*c^7*d^5 - 288*a^2*b^7*c^2*e^5 + 1504*a^3*b^5*c^3*e^5 - 3840*a^4*b^3*c^4*e^5 - 7680*a^4*c^7*d^3*e^2 + 50*b^8*c^3*d^3*e^2 + 5*b^9*c^2*d^2*e^3 + 5*c^2*d^2*e^3*(-(4*a*c - b^2)^9)^(1/2) + 27*a*b^9*c*e^5 + 9*a*c*e^5*(-(4*a*c - b^2)^9)^(1/2) - 5*b^10*c*d*e^4 - 5*b*c*d*e^4*(-(4*a*c - b^2)^9)^(1/2) + 960*a^2*b^4*c^5*d^3*e^2 + 2400*a^2*b^5*c^4*d^2*e^3 + 2560*a^3*b^2*c^6*d^3*e^2 - 8960*a^3*b^3*c^5*d^2*e^3 + 960*a*b^5*c^5*d^4*e + 90*a*b^8*c^2*d*e^4 + 5120*a^3*b*c^7*d^4*e - 480*a*b^6*c^4*d^3*e^2 - 240*a*b^7*c^3*d^2*e^3 - 3840*a^2*b^3*c^6*d^4*e - 480*a^2*b^6*c^3*d*e^4 + 320*a^3*b^4*c^4*d*e^4 + 11520*a^4*b*c^6*d^2*e^3 + 3840*a^4*b^2*c^5*d*e^4)/(8*(b^15*d^3*e^3 - 4096*a^6*c^9*d^6 - 4096*a^9*c^6*e^6 - b^12*c^3*d^6 - a^3*b^12*e^6 + 24*a*b^10*c^4*d^6 + 24*a^4*b^10*c*e^6 - 3*a*b^14*d^2*e^4 + 3*a^2*b^13*d*e^5 + 3*b^13*c^2*d^5*e - 3*b^14*c*d^4*e^2 - 240*a^2*b^8*c^5*d^6 + 1280*a^3*b^6*c^6*d^6 - 3840*a^4*b^4*c^7*d^6 + 6144*a^5*b^2*c^8*d^6 - 240*a^5*b^8*c^2*e^6 + 1280*a^6*b^6*c^3*e^6 - 3840*a^7*b^4*c^4*e^6 + 6144*a^8*b^2*c^5*e^6 - 12288*a^7*c^8*d^4*e^2 - 12288*a^8*c^7*d^2*e^4 - 648*a^2*b^10*c^3*d^4*e^2 + 96*a^2*b^11*c^2*d^3*e^3 + 3120*a^3*b^8*c^4*d^4*e^2 + 160*a^3*b^9*c^3*d^3*e^3 - 648*a^3*b^10*c^2*d^2*e^4 - 7680*a^4*b^6*c^5*d^4*e^2 - 3840*a^4*b^7*c^4*d^3*e^3 + 3120*a^4*b^8*c^3*d^2*e^4 + 6912*a^5*b^4*c^6*d^4*e^2 + 16896*a^5*b^5*c^5*d^3*e^3 - 7680*a^5*b^6*c^4*d^2*e^4 + 6144*a^6*b^2*c^7*d^4*e^2 - 32768*a^6*b^3*c^6*d^3*e^3 + 6912*a^6*b^4*c^5*d^2*e^4 + 6144*a^7*b^2*c^6*d^2*e^4 - 72*a*b^11*c^3*d^5*e - 18*a*b^13*c*d^3*e^3 - 72*a^3*b^11*c*d*e^5 + 12288*a^6*b*c^8*d^5*e + 12288*a^8*b*c^6*d*e^5 + 69*a*b^12*c^2*d^4*e^2 + 720*a^2*b^9*c^4*d^5*e + 69*a^2*b^12*c*d^2*e^4 - 3840*a^3*b^7*c^5*d^5*e + 11520*a^4*b^5*c^6*d^5*e + 720*a^4*b^9*c^2*d*e^5 - 18432*a^5*b^3*c^7*d^5*e - 3840*a^5*b^7*c^3*d*e^5 + 11520*a^6*b^5*c^4*d*e^5 + 24576*a^7*b*c^7*d^3*e^3 - 18432*a^7*b^3*c^5*d*e^5)))^(1/2)*2i","B"
2300,1,126405,604,19.158567,"\text{Not used}","int(1/((d + e*x)^(3/2)*(a + b*x + c*x^2)^2),x)","\frac{\frac{e\,{\left(d+e\,x\right)}^2\,\left(3\,b^2\,c\,e^2-2\,b\,c^2\,d\,e+2\,c^3\,d^2-10\,a\,c^2\,e^2\right)}{\left(4\,a\,c-b^2\right)\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}-\frac{2\,e^3}{c\,d^2-b\,d\,e+a\,e^2}+\frac{e\,\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)\,\left(3\,b^2\,e^2-b\,c\,d\,e+c^2\,d^2-11\,a\,c\,e^2\right)}{\left(4\,a\,c-b^2\right)\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}}{c\,{\left(d+e\,x\right)}^{5/2}+\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{3/2}+\sqrt{d+e\,x}\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}-\mathrm{atan}\left(\frac{\left(\sqrt{d+e\,x}\,\left(25600\,a^{12}\,c^9\,e^{20}-57344\,a^{11}\,b^2\,c^8\,e^{20}-77824\,a^{11}\,b\,c^9\,d\,e^{19}+77824\,a^{11}\,c^{10}\,d^2\,e^{18}+45696\,a^{10}\,b^4\,c^7\,e^{20}+265216\,a^{10}\,b^3\,c^8\,d\,e^{19}-367616\,a^{10}\,b^2\,c^9\,d^2\,e^{18}+204800\,a^{10}\,b\,c^{10}\,d^3\,e^{17}-102400\,a^{10}\,c^{11}\,d^4\,e^{16}-17920\,a^9\,b^6\,c^6\,e^{20}-241920\,a^9\,b^5\,c^7\,d\,e^{19}-116480\,a^9\,b^4\,c^8\,d^2\,e^{18}+1536000\,a^9\,b^3\,c^9\,d^3\,e^{17}-2816000\,a^9\,b^2\,c^{10}\,d^4\,e^{16}+2457600\,a^9\,b\,c^{11}\,d^5\,e^{15}-819200\,a^9\,c^{12}\,d^6\,e^{14}+3764\,a^8\,b^8\,c^5\,e^{20}+101056\,a^8\,b^7\,c^6\,d\,e^{19}+381248\,a^8\,b^6\,c^7\,d^2\,e^{18}-1175552\,a^8\,b^5\,c^8\,d^3\,e^{17}-517120\,a^8\,b^4\,c^9\,d^4\,e^{16}+5896192\,a^8\,b^3\,c^{10}\,d^5\,e^{15}-9582592\,a^8\,b^2\,c^{11}\,d^6\,e^{14}+6529024\,a^8\,b\,c^{12}\,d^7\,e^{13}-1632256\,a^8\,c^{13}\,d^8\,e^{12}-408\,a^7\,b^{10}\,c^4\,e^{20}-21952\,a^7\,b^9\,c^5\,d\,e^{19}-206656\,a^7\,b^8\,c^6\,d^2\,e^{18}+85504\,a^7\,b^7\,c^7\,d^3\,e^{17}+2051840\,a^7\,b^6\,c^8\,d^4\,e^{16}-4097024\,a^7\,b^5\,c^9\,d^5\,e^{15}-1033216\,a^7\,b^4\,c^{10}\,d^6\,e^{14}+12132352\,a^7\,b^3\,c^{11}\,d^7\,e^{13}-15628288\,a^7\,b^2\,c^{12}\,d^8\,e^{12}+8396800\,a^7\,b\,c^{13}\,d^9\,e^{11}-1679360\,a^7\,c^{14}\,d^{10}\,e^{10}+18\,a^6\,b^{12}\,c^3\,e^{20}+2424\,a^6\,b^{11}\,c^4\,d\,e^{19}+50168\,a^6\,b^{10}\,c^5\,d^2\,e^{18}+147744\,a^6\,b^9\,c^6\,d^3\,e^{17}-814480\,a^6\,b^8\,c^7\,d^4\,e^{16}-266240\,a^6\,b^7\,c^8\,d^5\,e^{15}+5401088\,a^6\,b^6\,c^9\,d^6\,e^{14}-8225792\,a^6\,b^5\,c^{10}\,d^7\,e^{13}-333568\,a^6\,b^4\,c^{11}\,d^8\,e^{12}+12451840\,a^6\,b^3\,c^{12}\,d^9\,e^{11}-13348864\,a^6\,b^2\,c^{13}\,d^{10}\,e^{10}+5922816\,a^6\,b\,c^{14}\,d^{11}\,e^9-987136\,a^6\,c^{15}\,d^{12}\,e^8-108\,a^5\,b^{13}\,c^3\,d\,e^{19}-5868\,a^5\,b^{12}\,c^4\,d^2\,e^{18}-53392\,a^5\,b^{11}\,c^5\,d^3\,e^{17}+72040\,a^5\,b^{10}\,c^6\,d^4\,e^{16}+689216\,a^5\,b^9\,c^7\,d^5\,e^{15}-1801408\,a^5\,b^8\,c^8\,d^6\,e^{14}-512000\,a^5\,b^7\,c^9\,d^7\,e^{13}+7065344\,a^5\,b^6\,c^{10}\,d^8\,e^{12}-9198080\,a^5\,b^5\,c^{11}\,d^9\,e^{11}+1726976\,a^5\,b^4\,c^{12}\,d^{10}\,e^{10}+6025216\,a^5\,b^3\,c^{13}\,d^{11}\,e^9-5974016\,a^5\,b^2\,c^{14}\,d^{12}\,e^8+2293760\,a^5\,b\,c^{15}\,d^{13}\,e^7-327680\,a^5\,c^{16}\,d^{14}\,e^6+270\,a^4\,b^{14}\,c^3\,d^2\,e^{18}+7260\,a^4\,b^{13}\,c^4\,d^3\,e^{17}+19550\,a^4\,b^{12}\,c^5\,d^4\,e^{16}-165880\,a^4\,b^{11}\,c^6\,d^5\,e^{15}+33880\,a^4\,b^{10}\,c^7\,d^6\,e^{14}+1189920\,a^4\,b^9\,c^8\,d^7\,e^{13}-2357320\,a^4\,b^8\,c^9\,d^8\,e^{12}+265600\,a^4\,b^7\,c^{10}\,d^9\,e^{11}+4227200\,a^4\,b^6\,c^{11}\,d^{10}\,e^{10}-5396480\,a^4\,b^5\,c^{12}\,d^{11}\,e^9+1986560\,a^4\,b^4\,c^{13}\,d^{12}\,e^8+1075200\,a^4\,b^3\,c^{14}\,d^{13}\,e^7-1280000\,a^4\,b^2\,c^{15}\,d^{14}\,e^6+450560\,a^4\,b\,c^{16}\,d^{15}\,e^5-56320\,a^4\,c^{17}\,d^{16}\,e^4-360\,a^3\,b^{15}\,c^3\,d^3\,e^{17}-4560\,a^3\,b^{14}\,c^4\,d^4\,e^{16}+9896\,a^3\,b^{13}\,c^5\,d^5\,e^{15}+67704\,a^3\,b^{12}\,c^6\,d^6\,e^{14}-251488\,a^3\,b^{11}\,c^7\,d^7\,e^{13}+96632\,a^3\,b^{10}\,c^8\,d^8\,e^{12}+832960\,a^3\,b^9\,c^9\,d^9\,e^{11}-1605568\,a^3\,b^8\,c^{10}\,d^{10}\,e^{10}+798208\,a^3\,b^7\,c^{11}\,d^{11}\,e^9+867584\,a^3\,b^6\,c^{12}\,d^{12}\,e^8-1412096\,a^3\,b^5\,c^{13}\,d^{13}\,e^7+701440\,a^3\,b^4\,c^{14}\,d^{14}\,e^6-32768\,a^3\,b^3\,c^{15}\,d^{15}\,e^5-100352\,a^3\,b^2\,c^{16}\,d^{16}\,e^4+36864\,a^3\,b\,c^{17}\,d^{17}\,e^3-4096\,a^3\,c^{18}\,d^{18}\,e^2+270\,a^2\,b^{16}\,c^3\,d^4\,e^{16}+1008\,a^2\,b^{15}\,c^4\,d^5\,e^{15}-9988\,a^2\,b^{14}\,c^5\,d^6\,e^{14}+10936\,a^2\,b^{13}\,c^6\,d^7\,e^{13}+58766\,a^2\,b^{12}\,c^7\,d^8\,e^{12}-188920\,a^2\,b^{11}\,c^8\,d^9\,e^{11}+165736\,a^2\,b^{10}\,c^9\,d^{10}\,e^{10}+136544\,a^2\,b^9\,c^{10}\,d^{11}\,e^9-404368\,a^2\,b^8\,c^{11}\,d^{12}\,e^8+297472\,a^2\,b^7\,c^{12}\,d^{13}\,e^7+5120\,a^2\,b^6\,c^{13}\,d^{14}\,e^6-144384\,a^2\,b^5\,c^{14}\,d^{15}\,e^5+96384\,a^2\,b^4\,c^{15}\,d^{16}\,e^4-27648\,a^2\,b^3\,c^{16}\,d^{17}\,e^3+3072\,a^2\,b^2\,c^{17}\,d^{18}\,e^2-108\,a\,b^{17}\,c^3\,d^5\,e^{15}+276\,a\,b^{16}\,c^4\,d^6\,e^{14}+1592\,a\,b^{15}\,c^5\,d^7\,e^{13}-8704\,a\,b^{14}\,c^6\,d^8\,e^{12}+14020\,a\,b^{13}\,c^7\,d^9\,e^{11}+1332\,a\,b^{12}\,c^8\,d^{10}\,e^{10}-33040\,a\,b^{11}\,c^9\,d^{11}\,e^9+37816\,a\,b^{10}\,c^{10}\,d^{12}\,e^8+4032\,a\,b^9\,c^{11}\,d^{13}\,e^7-47680\,a\,b^8\,c^{12}\,d^{14}\,e^6+50176\,a\,b^7\,c^{13}\,d^{15}\,e^5-25856\,a\,b^6\,c^{14}\,d^{16}\,e^4+6912\,a\,b^5\,c^{15}\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used",1,"((e*(d + e*x)^2*(2*c^3*d^2 - 10*a*c^2*e^2 + 3*b^2*c*e^2 - 2*b*c^2*d*e))/((4*a*c - b^2)*(a*e^2 + c*d^2 - b*d*e)^2) - (2*e^3)/(a*e^2 + c*d^2 - b*d*e) + (e*(b*e - 2*c*d)*(d + e*x)*(3*b^2*e^2 + c^2*d^2 - 11*a*c*e^2 - b*c*d*e))/((4*a*c - b^2)*(a*e^2 + c*d^2 - b*d*e)^2))/(c*(d + e*x)^(5/2) + (b*e - 2*c*d)*(d + e*x)^(3/2) + (d + e*x)^(1/2)*(a*e^2 + c*d^2 - b*d*e)) - atan((((d + e*x)^(1/2)*(25600*a^12*c^9*e^20 + 18*a^6*b^12*c^3*e^20 - 408*a^7*b^10*c^4*e^20 + 3764*a^8*b^8*c^5*e^20 - 17920*a^9*b^6*c^6*e^20 + 45696*a^10*b^4*c^7*e^20 - 57344*a^11*b^2*c^8*e^20 - 4096*a^3*c^18*d^18*e^2 - 56320*a^4*c^17*d^16*e^4 - 327680*a^5*c^16*d^14*e^6 - 987136*a^6*c^15*d^12*e^8 - 1679360*a^7*c^14*d^10*e^10 - 1632256*a^8*c^13*d^8*e^12 - 819200*a^9*c^12*d^6*e^14 - 102400*a^10*c^11*d^4*e^16 + 77824*a^11*c^10*d^2*e^18 + 64*b^6*c^15*d^18*e^2 - 576*b^7*c^14*d^17*e^3 + 2228*b^8*c^13*d^16*e^4 - 4768*b^9*c^12*d^15*e^5 + 5960*b^10*c^11*d^14*e^6 - 3976*b^11*c^10*d^13*e^7 + 578*b^12*c^9*d^12*e^8 + 1004*b^13*c^8*d^11*e^9 - 442*b^14*c^7*d^10*e^10 - 320*b^15*c^6*d^9*e^11 + 362*b^16*c^5*d^8*e^12 - 132*b^17*c^4*d^7*e^13 + 18*b^18*c^3*d^6*e^14 + 3072*a^2*b^2*c^17*d^18*e^2 - 27648*a^2*b^3*c^16*d^17*e^3 + 96384*a^2*b^4*c^15*d^16*e^4 - 144384*a^2*b^5*c^14*d^15*e^5 + 5120*a^2*b^6*c^13*d^14*e^6 + 297472*a^2*b^7*c^12*d^13*e^7 - 404368*a^2*b^8*c^11*d^12*e^8 + 136544*a^2*b^9*c^10*d^11*e^9 + 165736*a^2*b^10*c^9*d^10*e^10 - 188920*a^2*b^11*c^8*d^9*e^11 + 58766*a^2*b^12*c^7*d^8*e^12 + 10936*a^2*b^13*c^6*d^7*e^13 - 9988*a^2*b^14*c^5*d^6*e^14 + 1008*a^2*b^15*c^4*d^5*e^15 + 270*a^2*b^16*c^3*d^4*e^16 - 100352*a^3*b^2*c^16*d^16*e^4 - 32768*a^3*b^3*c^15*d^15*e^5 + 701440*a^3*b^4*c^14*d^14*e^6 - 1412096*a^3*b^5*c^13*d^13*e^7 + 867584*a^3*b^6*c^12*d^12*e^8 + 798208*a^3*b^7*c^11*d^11*e^9 - 1605568*a^3*b^8*c^10*d^10*e^10 + 832960*a^3*b^9*c^9*d^9*e^11 + 96632*a^3*b^10*c^8*d^8*e^12 - 251488*a^3*b^11*c^7*d^7*e^13 + 67704*a^3*b^12*c^6*d^6*e^14 + 9896*a^3*b^13*c^5*d^5*e^15 - 4560*a^3*b^14*c^4*d^4*e^16 - 360*a^3*b^15*c^3*d^3*e^17 - 1280000*a^4*b^2*c^15*d^14*e^6 + 1075200*a^4*b^3*c^14*d^13*e^7 + 1986560*a^4*b^4*c^13*d^12*e^8 - 5396480*a^4*b^5*c^12*d^11*e^9 + 4227200*a^4*b^6*c^11*d^10*e^10 + 265600*a^4*b^7*c^10*d^9*e^11 - 2357320*a^4*b^8*c^9*d^8*e^12 + 1189920*a^4*b^9*c^8*d^7*e^13 + 33880*a^4*b^10*c^7*d^6*e^14 - 165880*a^4*b^11*c^6*d^5*e^15 + 19550*a^4*b^12*c^5*d^4*e^16 + 7260*a^4*b^13*c^4*d^3*e^17 + 270*a^4*b^14*c^3*d^2*e^18 - 5974016*a^5*b^2*c^14*d^12*e^8 + 6025216*a^5*b^3*c^13*d^11*e^9 + 1726976*a^5*b^4*c^12*d^10*e^10 - 9198080*a^5*b^5*c^11*d^9*e^11 + 7065344*a^5*b^6*c^10*d^8*e^12 - 512000*a^5*b^7*c^9*d^7*e^13 - 1801408*a^5*b^8*c^8*d^6*e^14 + 689216*a^5*b^9*c^7*d^5*e^15 + 72040*a^5*b^10*c^6*d^4*e^16 - 53392*a^5*b^11*c^5*d^3*e^17 - 5868*a^5*b^12*c^4*d^2*e^18 - 13348864*a^6*b^2*c^13*d^10*e^10 + 12451840*a^6*b^3*c^12*d^9*e^11 - 333568*a^6*b^4*c^11*d^8*e^12 - 8225792*a^6*b^5*c^10*d^7*e^13 + 5401088*a^6*b^6*c^9*d^6*e^14 - 266240*a^6*b^7*c^8*d^5*e^15 - 814480*a^6*b^8*c^7*d^4*e^16 + 147744*a^6*b^9*c^6*d^3*e^17 + 50168*a^6*b^10*c^5*d^2*e^18 - 15628288*a^7*b^2*c^12*d^8*e^12 + 12132352*a^7*b^3*c^11*d^7*e^13 - 1033216*a^7*b^4*c^10*d^6*e^14 - 4097024*a^7*b^5*c^9*d^5*e^15 + 2051840*a^7*b^6*c^8*d^4*e^16 + 85504*a^7*b^7*c^7*d^3*e^17 - 206656*a^7*b^8*c^6*d^2*e^18 - 9582592*a^8*b^2*c^11*d^6*e^14 + 5896192*a^8*b^3*c^10*d^5*e^15 - 517120*a^8*b^4*c^9*d^4*e^16 - 1175552*a^8*b^5*c^8*d^3*e^17 + 381248*a^8*b^6*c^7*d^2*e^18 - 2816000*a^9*b^2*c^10*d^4*e^16 + 1536000*a^9*b^3*c^9*d^3*e^17 - 116480*a^9*b^4*c^8*d^2*e^18 - 367616*a^10*b^2*c^9*d^2*e^18 - 77824*a^11*b*c^9*d*e^19 - 768*a*b^4*c^16*d^18*e^2 + 6912*a*b^5*c^15*d^17*e^3 - 25856*a*b^6*c^14*d^16*e^4 + 50176*a*b^7*c^13*d^15*e^5 - 47680*a*b^8*c^12*d^14*e^6 + 4032*a*b^9*c^11*d^13*e^7 + 37816*a*b^10*c^10*d^12*e^8 - 33040*a*b^11*c^9*d^11*e^9 + 1332*a*b^12*c^8*d^10*e^10 + 14020*a*b^13*c^7*d^9*e^11 - 8704*a*b^14*c^6*d^8*e^12 + 1592*a*b^15*c^5*d^7*e^13 + 276*a*b^16*c^4*d^6*e^14 - 108*a*b^17*c^3*d^5*e^15 + 36864*a^3*b*c^17*d^17*e^3 + 450560*a^4*b*c^16*d^15*e^5 + 2293760*a^5*b*c^15*d^13*e^7 - 108*a^5*b^13*c^3*d*e^19 + 5922816*a^6*b*c^14*d^11*e^9 + 2424*a^6*b^11*c^4*d*e^19 + 8396800*a^7*b*c^13*d^9*e^11 - 21952*a^7*b^9*c^5*d*e^19 + 6529024*a^8*b*c^12*d^7*e^13 + 101056*a^8*b^7*c^6*d*e^19 + 2457600*a^9*b*c^11*d^5*e^15 - 241920*a^9*b^5*c^7*d*e^19 + 204800*a^10*b*c^10*d^3*e^17 + 265216*a^10*b^3*c^8*d*e^19) - ((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*((d + e*x)^(1/2)*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 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5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*1i + ((d + e*x)^(1/2)*(25600*a^12*c^9*e^20 + 18*a^6*b^12*c^3*e^20 - 408*a^7*b^10*c^4*e^20 + 3764*a^8*b^8*c^5*e^20 - 17920*a^9*b^6*c^6*e^20 + 45696*a^10*b^4*c^7*e^20 - 57344*a^11*b^2*c^8*e^20 - 4096*a^3*c^18*d^18*e^2 - 56320*a^4*c^17*d^16*e^4 - 327680*a^5*c^16*d^14*e^6 - 987136*a^6*c^15*d^12*e^8 - 1679360*a^7*c^14*d^10*e^10 - 1632256*a^8*c^13*d^8*e^12 - 819200*a^9*c^12*d^6*e^14 - 102400*a^10*c^11*d^4*e^16 + 77824*a^11*c^10*d^2*e^18 + 64*b^6*c^15*d^18*e^2 - 576*b^7*c^14*d^17*e^3 + 2228*b^8*c^13*d^16*e^4 - 4768*b^9*c^12*d^15*e^5 + 5960*b^10*c^11*d^14*e^6 - 3976*b^11*c^10*d^13*e^7 + 578*b^12*c^9*d^12*e^8 + 1004*b^13*c^8*d^11*e^9 - 442*b^14*c^7*d^10*e^10 - 320*b^15*c^6*d^9*e^11 + 362*b^16*c^5*d^8*e^12 - 132*b^17*c^4*d^7*e^13 + 18*b^18*c^3*d^6*e^14 + 3072*a^2*b^2*c^17*d^18*e^2 - 27648*a^2*b^3*c^16*d^17*e^3 + 96384*a^2*b^4*c^15*d^16*e^4 - 144384*a^2*b^5*c^14*d^15*e^5 + 5120*a^2*b^6*c^13*d^14*e^6 + 297472*a^2*b^7*c^12*d^13*e^7 - 404368*a^2*b^8*c^11*d^12*e^8 + 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19550*a^4*b^12*c^5*d^4*e^16 + 7260*a^4*b^13*c^4*d^3*e^17 + 270*a^4*b^14*c^3*d^2*e^18 - 5974016*a^5*b^2*c^14*d^12*e^8 + 6025216*a^5*b^3*c^13*d^11*e^9 + 1726976*a^5*b^4*c^12*d^10*e^10 - 9198080*a^5*b^5*c^11*d^9*e^11 + 7065344*a^5*b^6*c^10*d^8*e^12 - 512000*a^5*b^7*c^9*d^7*e^13 - 1801408*a^5*b^8*c^8*d^6*e^14 + 689216*a^5*b^9*c^7*d^5*e^15 + 72040*a^5*b^10*c^6*d^4*e^16 - 53392*a^5*b^11*c^5*d^3*e^17 - 5868*a^5*b^12*c^4*d^2*e^18 - 13348864*a^6*b^2*c^13*d^10*e^10 + 12451840*a^6*b^3*c^12*d^9*e^11 - 333568*a^6*b^4*c^11*d^8*e^12 - 8225792*a^6*b^5*c^10*d^7*e^13 + 5401088*a^6*b^6*c^9*d^6*e^14 - 266240*a^6*b^7*c^8*d^5*e^15 - 814480*a^6*b^8*c^7*d^4*e^16 + 147744*a^6*b^9*c^6*d^3*e^17 + 50168*a^6*b^10*c^5*d^2*e^18 - 15628288*a^7*b^2*c^12*d^8*e^12 + 12132352*a^7*b^3*c^11*d^7*e^13 - 1033216*a^7*b^4*c^10*d^6*e^14 - 4097024*a^7*b^5*c^9*d^5*e^15 + 2051840*a^7*b^6*c^8*d^4*e^16 + 85504*a^7*b^7*c^7*d^3*e^17 - 206656*a^7*b^8*c^6*d^2*e^18 - 9582592*a^8*b^2*c^11*d^6*e^14 + 5896192*a^8*b^3*c^10*d^5*e^15 - 517120*a^8*b^4*c^9*d^4*e^16 - 1175552*a^8*b^5*c^8*d^3*e^17 + 381248*a^8*b^6*c^7*d^2*e^18 - 2816000*a^9*b^2*c^10*d^4*e^16 + 1536000*a^9*b^3*c^9*d^3*e^17 - 116480*a^9*b^4*c^8*d^2*e^18 - 367616*a^10*b^2*c^9*d^2*e^18 - 77824*a^11*b*c^9*d*e^19 - 768*a*b^4*c^16*d^18*e^2 + 6912*a*b^5*c^15*d^17*e^3 - 25856*a*b^6*c^14*d^16*e^4 + 50176*a*b^7*c^13*d^15*e^5 - 47680*a*b^8*c^12*d^14*e^6 + 4032*a*b^9*c^11*d^13*e^7 + 37816*a*b^10*c^10*d^12*e^8 - 33040*a*b^11*c^9*d^11*e^9 + 1332*a*b^12*c^8*d^10*e^10 + 14020*a*b^13*c^7*d^9*e^11 - 8704*a*b^14*c^6*d^8*e^12 + 1592*a*b^15*c^5*d^7*e^13 + 276*a*b^16*c^4*d^6*e^14 - 108*a*b^17*c^3*d^5*e^15 + 36864*a^3*b*c^17*d^17*e^3 + 450560*a^4*b*c^16*d^15*e^5 + 2293760*a^5*b*c^15*d^13*e^7 - 108*a^5*b^13*c^3*d*e^19 + 5922816*a^6*b*c^14*d^11*e^9 + 2424*a^6*b^11*c^4*d*e^19 + 8396800*a^7*b*c^13*d^9*e^11 - 21952*a^7*b^9*c^5*d*e^19 + 6529024*a^8*b*c^12*d^7*e^13 + 101056*a^8*b^7*c^6*d*e^19 + 2457600*a^9*b*c^11*d^5*e^15 - 241920*a^9*b^5*c^7*d*e^19 + 204800*a^10*b*c^10*d^3*e^17 + 265216*a^10*b^3*c^8*d*e^19) - ((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*((d + e*x)^(1/2)*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 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b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 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235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*((d + e*x)^(1/2)*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*(65536*a^16*c^9*d*e^22 - 32768*a^16*b*c^8*e^23 - 8*a^10*b^13*c^2*e^23 + 192*a^11*b^11*c^3*e^23 - 1920*a^12*b^9*c^4*e^23 + 10240*a^13*b^7*c^5*e^23 - 30720*a^14*b^5*c^6*e^23 + 49152*a^15*b^3*c^7*e^23 + 65536*a^6*c^19*d^21*e^2 + 655360*a^7*c^18*d^19*e^4 + 2949120*a^8*c^17*d^17*e^6 + 7864320*a^9*c^16*d^15*e^8 + 13762560*a^10*c^15*d^13*e^10 + 16515072*a^11*c^14*d^11*e^12 + 13762560*a^12*c^13*d^9*e^14 + 7864320*a^13*c^12*d^7*e^16 + 2949120*a^14*c^11*d^5*e^18 + 655360*a^15*c^10*d^3*e^20 + 16*b^12*c^13*d^21*e^2 - 168*b^13*c^12*d^20*e^3 + 800*b^14*c^11*d^19*e^4 - 2280*b^15*c^10*d^18*e^5 + 4320*b^16*c^9*d^17*e^6 - 5712*b^17*c^8*d^16*e^7 + 5376*b^18*c^7*d^15*e^8 - 3600*b^19*c^6*d^14*e^9 + 1680*b^20*c^5*d^13*e^10 - 520*b^21*c^4*d^12*e^11 + 96*b^22*c^3*d^11*e^12 - 8*b^23*c^2*d^10*e^13 + 3840*a^2*b^8*c^15*d^21*e^2 - 40320*a^2*b^9*c^14*d^20*e^3 + 188160*a^2*b^10*c^13*d^19*e^4 - 510720*a^2*b^11*c^12*d^18*e^5 + 882000*a^2*b^12*c^11*d^17*e^6 - 985320*a^2*b^13*c^10*d^16*e^7 + 668160*a^2*b^14*c^9*d^15*e^8 - 188640*a^2*b^15*c^8*d^14*e^9 - 90720*a^2*b^16*c^7*d^13*e^10 + 109200*a^2*b^17*c^6*d^12*e^11 - 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14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2) - ((d + e*x)^(1/2)*(25600*a^12*c^9*e^20 + 18*a^6*b^12*c^3*e^20 - 408*a^7*b^10*c^4*e^20 + 3764*a^8*b^8*c^5*e^20 - 17920*a^9*b^6*c^6*e^20 + 45696*a^10*b^4*c^7*e^20 - 57344*a^11*b^2*c^8*e^20 - 4096*a^3*c^18*d^18*e^2 - 56320*a^4*c^17*d^16*e^4 - 327680*a^5*c^16*d^14*e^6 - 987136*a^6*c^15*d^12*e^8 - 1679360*a^7*c^14*d^10*e^10 - 1632256*a^8*c^13*d^8*e^12 - 819200*a^9*c^12*d^6*e^14 - 102400*a^10*c^11*d^4*e^16 + 77824*a^11*c^10*d^2*e^18 + 64*b^6*c^15*d^18*e^2 - 576*b^7*c^14*d^17*e^3 + 2228*b^8*c^13*d^16*e^4 - 4768*b^9*c^12*d^15*e^5 + 5960*b^10*c^11*d^14*e^6 - 3976*b^11*c^10*d^13*e^7 + 578*b^12*c^9*d^12*e^8 + 1004*b^13*c^8*d^11*e^9 - 442*b^14*c^7*d^10*e^10 - 320*b^15*c^6*d^9*e^11 + 362*b^16*c^5*d^8*e^12 - 132*b^17*c^4*d^7*e^13 + 18*b^18*c^3*d^6*e^14 + 3072*a^2*b^2*c^17*d^18*e^2 - 27648*a^2*b^3*c^16*d^17*e^3 + 96384*a^2*b^4*c^15*d^16*e^4 - 144384*a^2*b^5*c^14*d^15*e^5 + 5120*a^2*b^6*c^13*d^14*e^6 + 297472*a^2*b^7*c^12*d^13*e^7 - 404368*a^2*b^8*c^11*d^12*e^8 + 136544*a^2*b^9*c^10*d^11*e^9 + 165736*a^2*b^10*c^9*d^10*e^10 - 188920*a^2*b^11*c^8*d^9*e^11 + 58766*a^2*b^12*c^7*d^8*e^12 + 10936*a^2*b^13*c^6*d^7*e^13 - 9988*a^2*b^14*c^5*d^6*e^14 + 1008*a^2*b^15*c^4*d^5*e^15 + 270*a^2*b^16*c^3*d^4*e^16 - 100352*a^3*b^2*c^16*d^16*e^4 - 32768*a^3*b^3*c^15*d^15*e^5 + 701440*a^3*b^4*c^14*d^14*e^6 - 1412096*a^3*b^5*c^13*d^13*e^7 + 867584*a^3*b^6*c^12*d^12*e^8 + 798208*a^3*b^7*c^11*d^11*e^9 - 1605568*a^3*b^8*c^10*d^10*e^10 + 832960*a^3*b^9*c^9*d^9*e^11 + 96632*a^3*b^10*c^8*d^8*e^12 - 251488*a^3*b^11*c^7*d^7*e^13 + 67704*a^3*b^12*c^6*d^6*e^14 + 9896*a^3*b^13*c^5*d^5*e^15 - 4560*a^3*b^14*c^4*d^4*e^16 - 360*a^3*b^15*c^3*d^3*e^17 - 1280000*a^4*b^2*c^15*d^14*e^6 + 1075200*a^4*b^3*c^14*d^13*e^7 + 1986560*a^4*b^4*c^13*d^12*e^8 - 5396480*a^4*b^5*c^12*d^11*e^9 + 4227200*a^4*b^6*c^11*d^10*e^10 + 265600*a^4*b^7*c^10*d^9*e^11 - 2357320*a^4*b^8*c^9*d^8*e^12 + 1189920*a^4*b^9*c^8*d^7*e^13 + 33880*a^4*b^10*c^7*d^6*e^14 - 165880*a^4*b^11*c^6*d^5*e^15 + 19550*a^4*b^12*c^5*d^4*e^16 + 7260*a^4*b^13*c^4*d^3*e^17 + 270*a^4*b^14*c^3*d^2*e^18 - 5974016*a^5*b^2*c^14*d^12*e^8 + 6025216*a^5*b^3*c^13*d^11*e^9 + 1726976*a^5*b^4*c^12*d^10*e^10 - 9198080*a^5*b^5*c^11*d^9*e^11 + 7065344*a^5*b^6*c^10*d^8*e^12 - 512000*a^5*b^7*c^9*d^7*e^13 - 1801408*a^5*b^8*c^8*d^6*e^14 + 689216*a^5*b^9*c^7*d^5*e^15 + 72040*a^5*b^10*c^6*d^4*e^16 - 53392*a^5*b^11*c^5*d^3*e^17 - 5868*a^5*b^12*c^4*d^2*e^18 - 13348864*a^6*b^2*c^13*d^10*e^10 + 12451840*a^6*b^3*c^12*d^9*e^11 - 333568*a^6*b^4*c^11*d^8*e^12 - 8225792*a^6*b^5*c^10*d^7*e^13 + 5401088*a^6*b^6*c^9*d^6*e^14 - 266240*a^6*b^7*c^8*d^5*e^15 - 814480*a^6*b^8*c^7*d^4*e^16 + 147744*a^6*b^9*c^6*d^3*e^17 + 50168*a^6*b^10*c^5*d^2*e^18 - 15628288*a^7*b^2*c^12*d^8*e^12 + 12132352*a^7*b^3*c^11*d^7*e^13 - 1033216*a^7*b^4*c^10*d^6*e^14 - 4097024*a^7*b^5*c^9*d^5*e^15 + 2051840*a^7*b^6*c^8*d^4*e^16 + 85504*a^7*b^7*c^7*d^3*e^17 - 206656*a^7*b^8*c^6*d^2*e^18 - 9582592*a^8*b^2*c^11*d^6*e^14 + 5896192*a^8*b^3*c^10*d^5*e^15 - 517120*a^8*b^4*c^9*d^4*e^16 - 1175552*a^8*b^5*c^8*d^3*e^17 + 381248*a^8*b^6*c^7*d^2*e^18 - 2816000*a^9*b^2*c^10*d^4*e^16 + 1536000*a^9*b^3*c^9*d^3*e^17 - 116480*a^9*b^4*c^8*d^2*e^18 - 367616*a^10*b^2*c^9*d^2*e^18 - 77824*a^11*b*c^9*d*e^19 - 768*a*b^4*c^16*d^18*e^2 + 6912*a*b^5*c^15*d^17*e^3 - 25856*a*b^6*c^14*d^16*e^4 + 50176*a*b^7*c^13*d^15*e^5 - 47680*a*b^8*c^12*d^14*e^6 + 4032*a*b^9*c^11*d^13*e^7 + 37816*a*b^10*c^10*d^12*e^8 - 33040*a*b^11*c^9*d^11*e^9 + 1332*a*b^12*c^8*d^10*e^10 + 14020*a*b^13*c^7*d^9*e^11 - 8704*a*b^14*c^6*d^8*e^12 + 1592*a*b^15*c^5*d^7*e^13 + 276*a*b^16*c^4*d^6*e^14 - 108*a*b^17*c^3*d^5*e^15 + 36864*a^3*b*c^17*d^17*e^3 + 450560*a^4*b*c^16*d^15*e^5 + 2293760*a^5*b*c^15*d^13*e^7 - 108*a^5*b^13*c^3*d*e^19 + 5922816*a^6*b*c^14*d^11*e^9 + 2424*a^6*b^11*c^4*d*e^19 + 8396800*a^7*b*c^13*d^9*e^11 - 21952*a^7*b^9*c^5*d*e^19 + 6529024*a^8*b*c^12*d^7*e^13 + 101056*a^8*b^7*c^6*d*e^19 + 2457600*a^9*b*c^11*d^5*e^15 - 241920*a^9*b^5*c^7*d*e^19 + 204800*a^10*b*c^10*d^3*e^17 + 265216*a^10*b^3*c^8*d*e^19) - ((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*((d + e*x)^(1/2)*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*(65536*a^16*c^9*d*e^22 - 32768*a^16*b*c^8*e^23 - 8*a^10*b^13*c^2*e^23 + 192*a^11*b^11*c^3*e^23 - 1920*a^12*b^9*c^4*e^23 + 10240*a^13*b^7*c^5*e^23 - 30720*a^14*b^5*c^6*e^23 + 49152*a^15*b^3*c^7*e^23 + 65536*a^6*c^19*d^21*e^2 + 655360*a^7*c^18*d^19*e^4 + 2949120*a^8*c^17*d^17*e^6 + 7864320*a^9*c^16*d^15*e^8 + 13762560*a^10*c^15*d^13*e^10 + 16515072*a^11*c^14*d^11*e^12 + 13762560*a^12*c^13*d^9*e^14 + 7864320*a^13*c^12*d^7*e^16 + 2949120*a^14*c^11*d^5*e^18 + 655360*a^15*c^10*d^3*e^20 + 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23176*a^9*b^10*c^4*d*e^21 + 35610624*a^10*b*c^12*d^8*e^14 + 122720*a^10*b^8*c^5*d*e^21 + 21676032*a^11*b*c^11*d^6*e^16 - 359680*a^11*b^6*c^6*d*e^21 + 7618560*a^12*b*c^10*d^4*e^18 + 538624*a^12*b^4*c^7*d*e^21 + 1290240*a^13*b*c^9*d^2*e^20 - 272384*a^13*b^2*c^8*d*e^21))*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2) + 32000*a^10*c^9*e^19 + 126*a^6*b^8*c^5*e^19 - 2028*a^7*b^6*c^6*e^19 + 12176*a^8*b^4*c^7*e^19 - 32320*a^9*b^2*c^8*e^19 - 1024*a^2*c^17*d^16*e^3 - 7424*a^3*c^16*d^14*e^5 + 8960*a^4*c^15*d^12*e^7 + 152320*a^5*c^14*d^10*e^9 + 439040*a^6*c^13*d^8*e^11 + 614656*a^7*c^12*d^6*e^13 + 471296*a^8*c^11*d^4*e^15 + 190720*a^9*c^10*d^2*e^17 - 64*b^4*c^15*d^16*e^3 + 512*b^5*c^14*d^15*e^4 - 1804*b^6*c^13*d^14*e^5 + 3668*b^7*c^12*d^13*e^6 - 4606*b^8*c^11*d^12*e^7 + 3248*b^9*c^10*d^11*e^8 - 322*b^10*c^9*d^10*e^9 - 1756*b^11*c^8*d^9*e^10 + 1742*b^12*c^7*d^8*e^11 - 744*b^13*c^6*d^7*e^12 + 126*b^14*c^5*d^6*e^13 - 25152*a^2*b^2*c^15*d^14*e^5 + 32704*a^2*b^3*c^14*d^13*e^6 + 13552*a^2*b^4*c^13*d^12*e^7 - 133728*a^2*b^5*c^12*d^11*e^8 + 251860*a^2*b^6*c^11*d^10*e^9 - 230228*a^2*b^7*c^10*d^9*e^10 + 71706*a^2*b^8*c^9*d^8*e^11 + 44528*a^2*b^9*c^8*d^7*e^12 - 39088*a^2*b^10*c^7*d^6*e^13 + 4788*a^2*b^11*c^6*d^5*e^14 + 1890*a^2*b^12*c^5*d^4*e^15 - 177856*a^3*b^2*c^14*d^12*e^7 + 391552*a^3*b^3*c^13*d^11*e^8 - 517104*a^3*b^4*c^12*d^10*e^9 + 234864*a^3*b^5*c^11*d^9*e^10 + 308252*a^3*b^6*c^10*d^8*e^11 - 458384*a^3*b^7*c^9*d^7*e^12 + 156688*a^3*b^8*c^8*d^6*e^13 + 43064*a^3*b^9*c^7*d^5*e^14 - 23100*a^3*b^10*c^6*d^4*e^15 - 2520*a^3*b^11*c^5*d^3*e^16 - 42560*a^4*b^2*c^13*d^10*e^9 + 705600*a^4*b^3*c^12*d^9*e^10 - 1453200*a^4*b^4*c^11*d^8*e^11 + 987840*a^4*b^5*c^10*d^7*e^12 + 175420*a^4*b^6*c^9*d^6*e^13 - 428820*a^4*b^7*c^8*d^5*e^14 + 61670*a^4*b^8*c^7*d^4*e^15 + 36960*a^4*b^9*c^6*d^3*e^16 + 1890*a^4*b^10*c^5*d^2*e^17 + 1055040*a^5*b^2*c^12*d^8*e^11 + 349440*a^5*b^3*c^11*d^7*e^12 - 1803984*a^5*b^4*c^10*d^6*e^13 + 990192*a^5*b^5*c^9*d^5*e^14 + 231476*a^5*b^6*c^8*d^4*e^15 - 182392*a^5*b^7*c^7*d^3*e^16 - 29736*a^5*b^8*c^6*d^2*e^17 + 1997632*a^6*b^2*c^11*d^6*e^13 + 153664*a^6*b^3*c^10*d^5*e^14 - 1288112*a^6*b^4*c^9*d^4*e^15 + 271264*a^6*b^5*c^8*d^3*e^16 + 170492*a^6*b^6*c^7*d^2*e^17 + 1362368*a^7*b^2*c^10*d^4*e^15 + 348544*a^7*b^3*c^9*d^3*e^16 - 408528*a^7*b^4*c^8*d^2*e^17 + 277824*a^8*b^2*c^9*d^2*e^17 - 190720*a^9*b*c^9*d*e^18 + 512*a*b^2*c^16*d^16*e^3 - 4096*a*b^3*c^15*d^15*e^4 + 13968*a*b^4*c^14*d^14*e^5 - 26096*a*b^5*c^13*d^13*e^6 + 26012*a*b^6*c^12*d^12*e^7 - 3192*a*b^7*c^11*d^11*e^8 - 29288*a*b^8*c^10*d^10*e^9 + 41852*a*b^9*c^9*d^9*e^10 - 26004*a*b^10*c^8*d^8*e^11 + 5408*a*b^11*c^7*d^7*e^12 + 1680*a*b^12*c^6*d^6*e^13 - 756*a*b^13*c^5*d^5*e^14 + 8192*a^2*b*c^16*d^15*e^4 + 51968*a^3*b*c^15*d^13*e^6 - 53760*a^4*b*c^14*d^11*e^8 - 761600*a^5*b*c^13*d^9*e^10 - 756*a^5*b^9*c^5*d*e^18 - 1756160*a^6*b*c^12*d^7*e^12 + 12180*a^6*b^7*c^6*d*e^18 - 1843968*a^7*b*c^11*d^5*e^14 - 73072*a^7*b^5*c^7*d*e^18 - 942592*a^8*b*c^10*d^3*e^16 + 193472*a^8*b^3*c^8*d*e^18))*((32*b^6*c^7*d^7 - 2048*a^3*c^10*d^7 - 9*b^13*e^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) - 384*a*b^4*c^8*d^7 - 26880*a^6*b*c^6*e^7 + 53760*a^6*c^7*d*e^6 - 112*b^7*c^6*d^6*e + 1536*a^2*b^2*c^9*d^7 - 2077*a^2*b^9*c^2*e^7 + 10656*a^3*b^7*c^3*e^7 - 30240*a^4*b^5*c^4*e^7 + 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) - 17920*a^4*c^9*d^5*e^2 - 35840*a^5*c^8*d^3*e^4 + 98*b^8*c^5*d^5*e^2 + 35*b^9*c^4*d^4*e^3 - 70*b^10*c^3*d^3*e^4 + 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) + 213*a*b^11*c*e^7 + 21*b^12*c*d*e^6 + 1344*a^2*b^4*c^7*d^5*e^2 + 10080*a^2*b^5*c^6*d^4*e^3 - 7840*a^2*b^6*c^5*d^3*e^4 - 1008*a^2*b^7*c^4*d^2*e^5 + 7168*a^3*b^2*c^8*d^5*e^2 - 35840*a^3*b^3*c^7*d^4*e^3 + 17920*a^3*b^4*c^6*d^3*e^4 + 12544*a^3*b^5*c^5*d^2*e^5 - 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) + 1344*a*b^5*c^7*d^6*e - 532*a*b^10*c^2*d*e^6 + 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) - 896*a*b^6*c^6*d^5*e^2 - 1120*a*b^7*c^5*d^4*e^3 + 1260*a*b^8*c^4*d^3*e^4 - 98*a*b^9*c^3*d^2*e^5 - 5376*a^2*b^3*c^8*d^6*e + 5418*a^2*b^8*c^3*d*e^6 - 28224*a^3*b^6*c^4*d*e^6 + 44800*a^4*b*c^8*d^4*e^3 + 78400*a^4*b^4*c^5*d*e^6 + 53760*a^5*b*c^7*d^2*e^5 - 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*2i - atan((((d + e*x)^(1/2)*(25600*a^12*c^9*e^20 + 18*a^6*b^12*c^3*e^20 - 408*a^7*b^10*c^4*e^20 + 3764*a^8*b^8*c^5*e^20 - 17920*a^9*b^6*c^6*e^20 + 45696*a^10*b^4*c^7*e^20 - 57344*a^11*b^2*c^8*e^20 - 4096*a^3*c^18*d^18*e^2 - 56320*a^4*c^17*d^16*e^4 - 327680*a^5*c^16*d^14*e^6 - 987136*a^6*c^15*d^12*e^8 - 1679360*a^7*c^14*d^10*e^10 - 1632256*a^8*c^13*d^8*e^12 - 819200*a^9*c^12*d^6*e^14 - 102400*a^10*c^11*d^4*e^16 + 77824*a^11*c^10*d^2*e^18 + 64*b^6*c^15*d^18*e^2 - 576*b^7*c^14*d^17*e^3 + 2228*b^8*c^13*d^16*e^4 - 4768*b^9*c^12*d^15*e^5 + 5960*b^10*c^11*d^14*e^6 - 3976*b^11*c^10*d^13*e^7 + 578*b^12*c^9*d^12*e^8 + 1004*b^13*c^8*d^11*e^9 - 442*b^14*c^7*d^10*e^10 - 320*b^15*c^6*d^9*e^11 + 362*b^16*c^5*d^8*e^12 - 132*b^17*c^4*d^7*e^13 + 18*b^18*c^3*d^6*e^14 + 3072*a^2*b^2*c^17*d^18*e^2 - 27648*a^2*b^3*c^16*d^17*e^3 + 96384*a^2*b^4*c^15*d^16*e^4 - 144384*a^2*b^5*c^14*d^15*e^5 + 5120*a^2*b^6*c^13*d^14*e^6 + 297472*a^2*b^7*c^12*d^13*e^7 - 404368*a^2*b^8*c^11*d^12*e^8 + 136544*a^2*b^9*c^10*d^11*e^9 + 165736*a^2*b^10*c^9*d^10*e^10 - 188920*a^2*b^11*c^8*d^9*e^11 + 58766*a^2*b^12*c^7*d^8*e^12 + 10936*a^2*b^13*c^6*d^7*e^13 - 9988*a^2*b^14*c^5*d^6*e^14 + 1008*a^2*b^15*c^4*d^5*e^15 + 270*a^2*b^16*c^3*d^4*e^16 - 100352*a^3*b^2*c^16*d^16*e^4 - 32768*a^3*b^3*c^15*d^15*e^5 + 701440*a^3*b^4*c^14*d^14*e^6 - 1412096*a^3*b^5*c^13*d^13*e^7 + 867584*a^3*b^6*c^12*d^12*e^8 + 798208*a^3*b^7*c^11*d^11*e^9 - 1605568*a^3*b^8*c^10*d^10*e^10 + 832960*a^3*b^9*c^9*d^9*e^11 + 96632*a^3*b^10*c^8*d^8*e^12 - 251488*a^3*b^11*c^7*d^7*e^13 + 67704*a^3*b^12*c^6*d^6*e^14 + 9896*a^3*b^13*c^5*d^5*e^15 - 4560*a^3*b^14*c^4*d^4*e^16 - 360*a^3*b^15*c^3*d^3*e^17 - 1280000*a^4*b^2*c^15*d^14*e^6 + 1075200*a^4*b^3*c^14*d^13*e^7 + 1986560*a^4*b^4*c^13*d^12*e^8 - 5396480*a^4*b^5*c^12*d^11*e^9 + 4227200*a^4*b^6*c^11*d^10*e^10 + 265600*a^4*b^7*c^10*d^9*e^11 - 2357320*a^4*b^8*c^9*d^8*e^12 + 1189920*a^4*b^9*c^8*d^7*e^13 + 33880*a^4*b^10*c^7*d^6*e^14 - 165880*a^4*b^11*c^6*d^5*e^15 + 19550*a^4*b^12*c^5*d^4*e^16 + 7260*a^4*b^13*c^4*d^3*e^17 + 270*a^4*b^14*c^3*d^2*e^18 - 5974016*a^5*b^2*c^14*d^12*e^8 + 6025216*a^5*b^3*c^13*d^11*e^9 + 1726976*a^5*b^4*c^12*d^10*e^10 - 9198080*a^5*b^5*c^11*d^9*e^11 + 7065344*a^5*b^6*c^10*d^8*e^12 - 512000*a^5*b^7*c^9*d^7*e^13 - 1801408*a^5*b^8*c^8*d^6*e^14 + 689216*a^5*b^9*c^7*d^5*e^15 + 72040*a^5*b^10*c^6*d^4*e^16 - 53392*a^5*b^11*c^5*d^3*e^17 - 5868*a^5*b^12*c^4*d^2*e^18 - 13348864*a^6*b^2*c^13*d^10*e^10 + 12451840*a^6*b^3*c^12*d^9*e^11 - 333568*a^6*b^4*c^11*d^8*e^12 - 8225792*a^6*b^5*c^10*d^7*e^13 + 5401088*a^6*b^6*c^9*d^6*e^14 - 266240*a^6*b^7*c^8*d^5*e^15 - 814480*a^6*b^8*c^7*d^4*e^16 + 147744*a^6*b^9*c^6*d^3*e^17 + 50168*a^6*b^10*c^5*d^2*e^18 - 15628288*a^7*b^2*c^12*d^8*e^12 + 12132352*a^7*b^3*c^11*d^7*e^13 - 1033216*a^7*b^4*c^10*d^6*e^14 - 4097024*a^7*b^5*c^9*d^5*e^15 + 2051840*a^7*b^6*c^8*d^4*e^16 + 85504*a^7*b^7*c^7*d^3*e^17 - 206656*a^7*b^8*c^6*d^2*e^18 - 9582592*a^8*b^2*c^11*d^6*e^14 + 5896192*a^8*b^3*c^10*d^5*e^15 - 517120*a^8*b^4*c^9*d^4*e^16 - 1175552*a^8*b^5*c^8*d^3*e^17 + 381248*a^8*b^6*c^7*d^2*e^18 - 2816000*a^9*b^2*c^10*d^4*e^16 + 1536000*a^9*b^3*c^9*d^3*e^17 - 116480*a^9*b^4*c^8*d^2*e^18 - 367616*a^10*b^2*c^9*d^2*e^18 - 77824*a^11*b*c^9*d*e^19 - 768*a*b^4*c^16*d^18*e^2 + 6912*a*b^5*c^15*d^17*e^3 - 25856*a*b^6*c^14*d^16*e^4 + 50176*a*b^7*c^13*d^15*e^5 - 47680*a*b^8*c^12*d^14*e^6 + 4032*a*b^9*c^11*d^13*e^7 + 37816*a*b^10*c^10*d^12*e^8 - 33040*a*b^11*c^9*d^11*e^9 + 1332*a*b^12*c^8*d^10*e^10 + 14020*a*b^13*c^7*d^9*e^11 - 8704*a*b^14*c^6*d^8*e^12 + 1592*a*b^15*c^5*d^7*e^13 + 276*a*b^16*c^4*d^6*e^14 - 108*a*b^17*c^3*d^5*e^15 + 36864*a^3*b*c^17*d^17*e^3 + 450560*a^4*b*c^16*d^15*e^5 + 2293760*a^5*b*c^15*d^13*e^7 - 108*a^5*b^13*c^3*d*e^19 + 5922816*a^6*b*c^14*d^11*e^9 + 2424*a^6*b^11*c^4*d*e^19 + 8396800*a^7*b*c^13*d^9*e^11 - 21952*a^7*b^9*c^5*d*e^19 + 6529024*a^8*b*c^12*d^7*e^13 + 101056*a^8*b^7*c^6*d*e^19 + 2457600*a^9*b*c^11*d^5*e^15 - 241920*a^9*b^5*c^7*d*e^19 + 204800*a^10*b*c^10*d^3*e^17 + 265216*a^10*b^3*c^8*d*e^19) - (-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*((d + e*x)^(1/2)*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*(65536*a^16*c^9*d*e^22 - 32768*a^16*b*c^8*e^23 - 8*a^10*b^13*c^2*e^23 + 192*a^11*b^11*c^3*e^23 - 1920*a^12*b^9*c^4*e^23 + 10240*a^13*b^7*c^5*e^23 - 30720*a^14*b^5*c^6*e^23 + 49152*a^15*b^3*c^7*e^23 + 65536*a^6*c^19*d^21*e^2 + 655360*a^7*c^18*d^19*e^4 + 2949120*a^8*c^17*d^17*e^6 + 7864320*a^9*c^16*d^15*e^8 + 13762560*a^10*c^15*d^13*e^10 + 16515072*a^11*c^14*d^11*e^12 + 13762560*a^12*c^13*d^9*e^14 + 7864320*a^13*c^12*d^7*e^16 + 2949120*a^14*c^11*d^5*e^18 + 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23176*a^9*b^10*c^4*d*e^21 - 35610624*a^10*b*c^12*d^8*e^14 - 122720*a^10*b^8*c^5*d*e^21 - 21676032*a^11*b*c^11*d^6*e^16 + 359680*a^11*b^6*c^6*d*e^21 - 7618560*a^12*b*c^10*d^4*e^18 - 538624*a^12*b^4*c^7*d*e^21 - 1290240*a^13*b*c^9*d^2*e^20 + 272384*a^13*b^2*c^8*d*e^21))*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*1i + ((d + e*x)^(1/2)*(25600*a^12*c^9*e^20 + 18*a^6*b^12*c^3*e^20 - 408*a^7*b^10*c^4*e^20 + 3764*a^8*b^8*c^5*e^20 - 17920*a^9*b^6*c^6*e^20 + 45696*a^10*b^4*c^7*e^20 - 57344*a^11*b^2*c^8*e^20 - 4096*a^3*c^18*d^18*e^2 - 56320*a^4*c^17*d^16*e^4 - 327680*a^5*c^16*d^14*e^6 - 987136*a^6*c^15*d^12*e^8 - 1679360*a^7*c^14*d^10*e^10 - 1632256*a^8*c^13*d^8*e^12 - 819200*a^9*c^12*d^6*e^14 - 102400*a^10*c^11*d^4*e^16 + 77824*a^11*c^10*d^2*e^18 + 64*b^6*c^15*d^18*e^2 - 576*b^7*c^14*d^17*e^3 + 2228*b^8*c^13*d^16*e^4 - 4768*b^9*c^12*d^15*e^5 + 5960*b^10*c^11*d^14*e^6 - 3976*b^11*c^10*d^13*e^7 + 578*b^12*c^9*d^12*e^8 + 1004*b^13*c^8*d^11*e^9 - 442*b^14*c^7*d^10*e^10 - 320*b^15*c^6*d^9*e^11 + 362*b^16*c^5*d^8*e^12 - 132*b^17*c^4*d^7*e^13 + 18*b^18*c^3*d^6*e^14 + 3072*a^2*b^2*c^17*d^18*e^2 - 27648*a^2*b^3*c^16*d^17*e^3 + 96384*a^2*b^4*c^15*d^16*e^4 - 144384*a^2*b^5*c^14*d^15*e^5 + 5120*a^2*b^6*c^13*d^14*e^6 + 297472*a^2*b^7*c^12*d^13*e^7 - 404368*a^2*b^8*c^11*d^12*e^8 + 136544*a^2*b^9*c^10*d^11*e^9 + 165736*a^2*b^10*c^9*d^10*e^10 - 188920*a^2*b^11*c^8*d^9*e^11 + 58766*a^2*b^12*c^7*d^8*e^12 + 10936*a^2*b^13*c^6*d^7*e^13 - 9988*a^2*b^14*c^5*d^6*e^14 + 1008*a^2*b^15*c^4*d^5*e^15 + 270*a^2*b^16*c^3*d^4*e^16 - 100352*a^3*b^2*c^16*d^16*e^4 - 32768*a^3*b^3*c^15*d^15*e^5 + 701440*a^3*b^4*c^14*d^14*e^6 - 1412096*a^3*b^5*c^13*d^13*e^7 + 867584*a^3*b^6*c^12*d^12*e^8 + 798208*a^3*b^7*c^11*d^11*e^9 - 1605568*a^3*b^8*c^10*d^10*e^10 + 832960*a^3*b^9*c^9*d^9*e^11 + 96632*a^3*b^10*c^8*d^8*e^12 - 251488*a^3*b^11*c^7*d^7*e^13 + 67704*a^3*b^12*c^6*d^6*e^14 + 9896*a^3*b^13*c^5*d^5*e^15 - 4560*a^3*b^14*c^4*d^4*e^16 - 360*a^3*b^15*c^3*d^3*e^17 - 1280000*a^4*b^2*c^15*d^14*e^6 + 1075200*a^4*b^3*c^14*d^13*e^7 + 1986560*a^4*b^4*c^13*d^12*e^8 - 5396480*a^4*b^5*c^12*d^11*e^9 + 4227200*a^4*b^6*c^11*d^10*e^10 + 265600*a^4*b^7*c^10*d^9*e^11 - 2357320*a^4*b^8*c^9*d^8*e^12 + 1189920*a^4*b^9*c^8*d^7*e^13 + 33880*a^4*b^10*c^7*d^6*e^14 - 165880*a^4*b^11*c^6*d^5*e^15 + 19550*a^4*b^12*c^5*d^4*e^16 + 7260*a^4*b^13*c^4*d^3*e^17 + 270*a^4*b^14*c^3*d^2*e^18 - 5974016*a^5*b^2*c^14*d^12*e^8 + 6025216*a^5*b^3*c^13*d^11*e^9 + 1726976*a^5*b^4*c^12*d^10*e^10 - 9198080*a^5*b^5*c^11*d^9*e^11 + 7065344*a^5*b^6*c^10*d^8*e^12 - 512000*a^5*b^7*c^9*d^7*e^13 - 1801408*a^5*b^8*c^8*d^6*e^14 + 689216*a^5*b^9*c^7*d^5*e^15 + 72040*a^5*b^10*c^6*d^4*e^16 - 53392*a^5*b^11*c^5*d^3*e^17 - 5868*a^5*b^12*c^4*d^2*e^18 - 13348864*a^6*b^2*c^13*d^10*e^10 + 12451840*a^6*b^3*c^12*d^9*e^11 - 333568*a^6*b^4*c^11*d^8*e^12 - 8225792*a^6*b^5*c^10*d^7*e^13 + 5401088*a^6*b^6*c^9*d^6*e^14 - 266240*a^6*b^7*c^8*d^5*e^15 - 814480*a^6*b^8*c^7*d^4*e^16 + 147744*a^6*b^9*c^6*d^3*e^17 + 50168*a^6*b^10*c^5*d^2*e^18 - 15628288*a^7*b^2*c^12*d^8*e^12 + 12132352*a^7*b^3*c^11*d^7*e^13 - 1033216*a^7*b^4*c^10*d^6*e^14 - 4097024*a^7*b^5*c^9*d^5*e^15 + 2051840*a^7*b^6*c^8*d^4*e^16 + 85504*a^7*b^7*c^7*d^3*e^17 - 206656*a^7*b^8*c^6*d^2*e^18 - 9582592*a^8*b^2*c^11*d^6*e^14 + 5896192*a^8*b^3*c^10*d^5*e^15 - 517120*a^8*b^4*c^9*d^4*e^16 - 1175552*a^8*b^5*c^8*d^3*e^17 + 381248*a^8*b^6*c^7*d^2*e^18 - 2816000*a^9*b^2*c^10*d^4*e^16 + 1536000*a^9*b^3*c^9*d^3*e^17 - 116480*a^9*b^4*c^8*d^2*e^18 - 367616*a^10*b^2*c^9*d^2*e^18 - 77824*a^11*b*c^9*d*e^19 - 768*a*b^4*c^16*d^18*e^2 + 6912*a*b^5*c^15*d^17*e^3 - 25856*a*b^6*c^14*d^16*e^4 + 50176*a*b^7*c^13*d^15*e^5 - 47680*a*b^8*c^12*d^14*e^6 + 4032*a*b^9*c^11*d^13*e^7 + 37816*a*b^10*c^10*d^12*e^8 - 33040*a*b^11*c^9*d^11*e^9 + 1332*a*b^12*c^8*d^10*e^10 + 14020*a*b^13*c^7*d^9*e^11 - 8704*a*b^14*c^6*d^8*e^12 + 1592*a*b^15*c^5*d^7*e^13 + 276*a*b^16*c^4*d^6*e^14 - 108*a*b^17*c^3*d^5*e^15 + 36864*a^3*b*c^17*d^17*e^3 + 450560*a^4*b*c^16*d^15*e^5 + 2293760*a^5*b*c^15*d^13*e^7 - 108*a^5*b^13*c^3*d*e^19 + 5922816*a^6*b*c^14*d^11*e^9 + 2424*a^6*b^11*c^4*d*e^19 + 8396800*a^7*b*c^13*d^9*e^11 - 21952*a^7*b^9*c^5*d*e^19 + 6529024*a^8*b*c^12*d^7*e^13 + 101056*a^8*b^7*c^6*d*e^19 + 2457600*a^9*b*c^11*d^5*e^15 - 241920*a^9*b^5*c^7*d*e^19 + 204800*a^10*b*c^10*d^3*e^17 + 265216*a^10*b^3*c^8*d*e^19) - (-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*((d + e*x)^(1/2)*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 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112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 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8704*a*b^14*c^6*d^8*e^12 + 1592*a*b^15*c^5*d^7*e^13 + 276*a*b^16*c^4*d^6*e^14 - 108*a*b^17*c^3*d^5*e^15 + 36864*a^3*b*c^17*d^17*e^3 + 450560*a^4*b*c^16*d^15*e^5 + 2293760*a^5*b*c^15*d^13*e^7 - 108*a^5*b^13*c^3*d*e^19 + 5922816*a^6*b*c^14*d^11*e^9 + 2424*a^6*b^11*c^4*d*e^19 + 8396800*a^7*b*c^13*d^9*e^11 - 21952*a^7*b^9*c^5*d*e^19 + 6529024*a^8*b*c^12*d^7*e^13 + 101056*a^8*b^7*c^6*d*e^19 + 2457600*a^9*b*c^11*d^5*e^15 - 241920*a^9*b^5*c^7*d*e^19 + 204800*a^10*b*c^10*d^3*e^17 + 265216*a^10*b^3*c^8*d*e^19) - (-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*((d + e*x)^(1/2)*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 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76500*a^8*b^11*c^4*d^2*e^20 + 70103040*a^9*b^2*c^12*d^9*e^13 - 45803520*a^9*b^3*c^11*d^8*e^14 - 21934080*a^9*b^4*c^10*d^7*e^15 + 38836224*a^9*b^5*c^9*d^6*e^16 - 7314432*a^9*b^6*c^8*d^5*e^17 - 5905920*a^9*b^7*c^7*d^4*e^18 + 1030560*a^9*b^8*c^6*d^3*e^19 + 381840*a^9*b^9*c^5*d^2*e^20 + 54190080*a^10*b^2*c^11*d^7*e^15 - 23482368*a^10*b^3*c^10*d^6*e^16 - 14524416*a^10*b^4*c^9*d^5*e^17 + 11925504*a^10*b^5*c^8*d^4*e^18 + 713472*a^10*b^6*c^7*d^3*e^19 - 996480*a^10*b^7*c^6*d^2*e^20 + 23371776*a^11*b^2*c^10*d^5*e^17 - 4239360*a^11*b^3*c^9*d^4*e^18 - 5114880*a^11*b^4*c^8*d^3*e^19 + 1073664*a^11*b^5*c^7*d^2*e^20 + 4823040*a^12*b^2*c^9*d^3*e^19 + 384000*a^12*b^3*c^8*d^2*e^20 + 160*a*b^8*c^14*d^19*e^3 - 1520*a*b^9*c^13*d^18*e^4 + 5832*a*b^10*c^12*d^17*e^5 - 10812*a*b^11*c^11*d^16*e^6 + 6336*a*b^12*c^10*d^15*e^7 + 13680*a*b^13*c^9*d^14*e^8 - 35280*a*b^14*c^8*d^13*e^9 + 37752*a*b^15*c^7*d^12*e^10 - 21888*a*b^16*c^6*d^11*e^11 + 5984*a*b^17*c^5*d^10*e^12 + 200*a*b^18*c^4*d^9*e^13 - 540*a*b^19*c^3*d^8*e^14 + 96*a*b^20*c^2*d^7*e^15 - 77824*a^5*b*c^17*d^18*e^4 - 1462272*a^6*b*c^16*d^16*e^6 - 8110080*a^7*b*c^15*d^14*e^8 + 96*a^7*b^14*c^2*d*e^21 - 22364160*a^8*b*c^14*d^12*e^10 - 2316*a^8*b^12*c^3*d*e^21 - 35954688*a^9*b*c^13*d^10*e^12 + 23176*a^9*b^10*c^4*d*e^21 - 35610624*a^10*b*c^12*d^8*e^14 - 122720*a^10*b^8*c^5*d*e^21 - 21676032*a^11*b*c^11*d^6*e^16 + 359680*a^11*b^6*c^6*d*e^21 - 7618560*a^12*b*c^10*d^4*e^18 - 538624*a^12*b^4*c^7*d*e^21 - 1290240*a^13*b*c^9*d^2*e^20 + 272384*a^13*b^2*c^8*d*e^21))*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2) - ((d + e*x)^(1/2)*(25600*a^12*c^9*e^20 + 18*a^6*b^12*c^3*e^20 - 408*a^7*b^10*c^4*e^20 + 3764*a^8*b^8*c^5*e^20 - 17920*a^9*b^6*c^6*e^20 + 45696*a^10*b^4*c^7*e^20 - 57344*a^11*b^2*c^8*e^20 - 4096*a^3*c^18*d^18*e^2 - 56320*a^4*c^17*d^16*e^4 - 327680*a^5*c^16*d^14*e^6 - 987136*a^6*c^15*d^12*e^8 - 1679360*a^7*c^14*d^10*e^10 - 1632256*a^8*c^13*d^8*e^12 - 819200*a^9*c^12*d^6*e^14 - 102400*a^10*c^11*d^4*e^16 + 77824*a^11*c^10*d^2*e^18 + 64*b^6*c^15*d^18*e^2 - 576*b^7*c^14*d^17*e^3 + 2228*b^8*c^13*d^16*e^4 - 4768*b^9*c^12*d^15*e^5 + 5960*b^10*c^11*d^14*e^6 - 3976*b^11*c^10*d^13*e^7 + 578*b^12*c^9*d^12*e^8 + 1004*b^13*c^8*d^11*e^9 - 442*b^14*c^7*d^10*e^10 - 320*b^15*c^6*d^9*e^11 + 362*b^16*c^5*d^8*e^12 - 132*b^17*c^4*d^7*e^13 + 18*b^18*c^3*d^6*e^14 + 3072*a^2*b^2*c^17*d^18*e^2 - 27648*a^2*b^3*c^16*d^17*e^3 + 96384*a^2*b^4*c^15*d^16*e^4 - 144384*a^2*b^5*c^14*d^15*e^5 + 5120*a^2*b^6*c^13*d^14*e^6 + 297472*a^2*b^7*c^12*d^13*e^7 - 404368*a^2*b^8*c^11*d^12*e^8 + 136544*a^2*b^9*c^10*d^11*e^9 + 165736*a^2*b^10*c^9*d^10*e^10 - 188920*a^2*b^11*c^8*d^9*e^11 + 58766*a^2*b^12*c^7*d^8*e^12 + 10936*a^2*b^13*c^6*d^7*e^13 - 9988*a^2*b^14*c^5*d^6*e^14 + 1008*a^2*b^15*c^4*d^5*e^15 + 270*a^2*b^16*c^3*d^4*e^16 - 100352*a^3*b^2*c^16*d^16*e^4 - 32768*a^3*b^3*c^15*d^15*e^5 + 701440*a^3*b^4*c^14*d^14*e^6 - 1412096*a^3*b^5*c^13*d^13*e^7 + 867584*a^3*b^6*c^12*d^12*e^8 + 798208*a^3*b^7*c^11*d^11*e^9 - 1605568*a^3*b^8*c^10*d^10*e^10 + 832960*a^3*b^9*c^9*d^9*e^11 + 96632*a^3*b^10*c^8*d^8*e^12 - 251488*a^3*b^11*c^7*d^7*e^13 + 67704*a^3*b^12*c^6*d^6*e^14 + 9896*a^3*b^13*c^5*d^5*e^15 - 4560*a^3*b^14*c^4*d^4*e^16 - 360*a^3*b^15*c^3*d^3*e^17 - 1280000*a^4*b^2*c^15*d^14*e^6 + 1075200*a^4*b^3*c^14*d^13*e^7 + 1986560*a^4*b^4*c^13*d^12*e^8 - 5396480*a^4*b^5*c^12*d^11*e^9 + 4227200*a^4*b^6*c^11*d^10*e^10 + 265600*a^4*b^7*c^10*d^9*e^11 - 2357320*a^4*b^8*c^9*d^8*e^12 + 1189920*a^4*b^9*c^8*d^7*e^13 + 33880*a^4*b^10*c^7*d^6*e^14 - 165880*a^4*b^11*c^6*d^5*e^15 + 19550*a^4*b^12*c^5*d^4*e^16 + 7260*a^4*b^13*c^4*d^3*e^17 + 270*a^4*b^14*c^3*d^2*e^18 - 5974016*a^5*b^2*c^14*d^12*e^8 + 6025216*a^5*b^3*c^13*d^11*e^9 + 1726976*a^5*b^4*c^12*d^10*e^10 - 9198080*a^5*b^5*c^11*d^9*e^11 + 7065344*a^5*b^6*c^10*d^8*e^12 - 512000*a^5*b^7*c^9*d^7*e^13 - 1801408*a^5*b^8*c^8*d^6*e^14 + 689216*a^5*b^9*c^7*d^5*e^15 + 72040*a^5*b^10*c^6*d^4*e^16 - 53392*a^5*b^11*c^5*d^3*e^17 - 5868*a^5*b^12*c^4*d^2*e^18 - 13348864*a^6*b^2*c^13*d^10*e^10 + 12451840*a^6*b^3*c^12*d^9*e^11 - 333568*a^6*b^4*c^11*d^8*e^12 - 8225792*a^6*b^5*c^10*d^7*e^13 + 5401088*a^6*b^6*c^9*d^6*e^14 - 266240*a^6*b^7*c^8*d^5*e^15 - 814480*a^6*b^8*c^7*d^4*e^16 + 147744*a^6*b^9*c^6*d^3*e^17 + 50168*a^6*b^10*c^5*d^2*e^18 - 15628288*a^7*b^2*c^12*d^8*e^12 + 12132352*a^7*b^3*c^11*d^7*e^13 - 1033216*a^7*b^4*c^10*d^6*e^14 - 4097024*a^7*b^5*c^9*d^5*e^15 + 2051840*a^7*b^6*c^8*d^4*e^16 + 85504*a^7*b^7*c^7*d^3*e^17 - 206656*a^7*b^8*c^6*d^2*e^18 - 9582592*a^8*b^2*c^11*d^6*e^14 + 5896192*a^8*b^3*c^10*d^5*e^15 - 517120*a^8*b^4*c^9*d^4*e^16 - 1175552*a^8*b^5*c^8*d^3*e^17 + 381248*a^8*b^6*c^7*d^2*e^18 - 2816000*a^9*b^2*c^10*d^4*e^16 + 1536000*a^9*b^3*c^9*d^3*e^17 - 116480*a^9*b^4*c^8*d^2*e^18 - 367616*a^10*b^2*c^9*d^2*e^18 - 77824*a^11*b*c^9*d*e^19 - 768*a*b^4*c^16*d^18*e^2 + 6912*a*b^5*c^15*d^17*e^3 - 25856*a*b^6*c^14*d^16*e^4 + 50176*a*b^7*c^13*d^15*e^5 - 47680*a*b^8*c^12*d^14*e^6 + 4032*a*b^9*c^11*d^13*e^7 + 37816*a*b^10*c^10*d^12*e^8 - 33040*a*b^11*c^9*d^11*e^9 + 1332*a*b^12*c^8*d^10*e^10 + 14020*a*b^13*c^7*d^9*e^11 - 8704*a*b^14*c^6*d^8*e^12 + 1592*a*b^15*c^5*d^7*e^13 + 276*a*b^16*c^4*d^6*e^14 - 108*a*b^17*c^3*d^5*e^15 + 36864*a^3*b*c^17*d^17*e^3 + 450560*a^4*b*c^16*d^15*e^5 + 2293760*a^5*b*c^15*d^13*e^7 - 108*a^5*b^13*c^3*d*e^19 + 5922816*a^6*b*c^14*d^11*e^9 + 2424*a^6*b^11*c^4*d*e^19 + 8396800*a^7*b*c^13*d^9*e^11 - 21952*a^7*b^9*c^5*d*e^19 + 6529024*a^8*b*c^12*d^7*e^13 + 101056*a^8*b^7*c^6*d*e^19 + 2457600*a^9*b*c^11*d^5*e^15 - 241920*a^9*b^5*c^7*d*e^19 + 204800*a^10*b*c^10*d^3*e^17 + 265216*a^10*b^3*c^8*d*e^19) - (-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*((d + e*x)^(1/2)*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*(65536*a^16*c^9*d*e^22 - 32768*a^16*b*c^8*e^23 - 8*a^10*b^13*c^2*e^23 + 192*a^11*b^11*c^3*e^23 - 1920*a^12*b^9*c^4*e^23 + 10240*a^13*b^7*c^5*e^23 - 30720*a^14*b^5*c^6*e^23 + 49152*a^15*b^3*c^7*e^23 + 65536*a^6*c^19*d^21*e^2 + 655360*a^7*c^18*d^19*e^4 + 2949120*a^8*c^17*d^17*e^6 + 7864320*a^9*c^16*d^15*e^8 + 13762560*a^10*c^15*d^13*e^10 + 16515072*a^11*c^14*d^11*e^12 + 13762560*a^12*c^13*d^9*e^14 + 7864320*a^13*c^12*d^7*e^16 + 2949120*a^14*c^11*d^5*e^18 + 655360*a^15*c^10*d^3*e^20 + 16*b^12*c^13*d^21*e^2 - 168*b^13*c^12*d^20*e^3 + 800*b^14*c^11*d^19*e^4 - 2280*b^15*c^10*d^18*e^5 + 4320*b^16*c^9*d^17*e^6 - 5712*b^17*c^8*d^16*e^7 + 5376*b^18*c^7*d^15*e^8 - 3600*b^19*c^6*d^14*e^9 + 1680*b^20*c^5*d^13*e^10 - 520*b^21*c^4*d^12*e^11 + 96*b^22*c^3*d^11*e^12 - 8*b^23*c^2*d^10*e^13 + 3840*a^2*b^8*c^15*d^21*e^2 - 40320*a^2*b^9*c^14*d^20*e^3 + 188160*a^2*b^10*c^13*d^19*e^4 - 510720*a^2*b^11*c^12*d^18*e^5 + 882000*a^2*b^12*c^11*d^17*e^6 - 985320*a^2*b^13*c^10*d^16*e^7 + 668160*a^2*b^14*c^9*d^15*e^8 - 188640*a^2*b^15*c^8*d^14*e^9 - 90720*a^2*b^16*c^7*d^13*e^10 + 109200*a^2*b^17*c^6*d^12*e^11 - 40320*a^2*b^18*c^5*d^11*e^12 + 3360*a^2*b^19*c^4*d^10*e^13 + 1680*a^2*b^20*c^3*d^9*e^14 - 360*a^2*b^21*c^2*d^8*e^15 - 20480*a^3*b^6*c^16*d^21*e^2 + 215040*a^3*b^7*c^15*d^20*e^3 - 985600*a^3*b^8*c^14*d^19*e^4 + 2553600*a^3*b^9*c^13*d^18*e^5 - 3991680*a^3*b^10*c^12*d^17*e^6 + 3541440*a^3*b^11*c^11*d^16*e^7 - 981120*a^3*b^12*c^10*d^15*e^8 - 1454400*a^3*b^13*c^9*d^14*e^9 + 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17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2) + 32000*a^10*c^9*e^19 + 126*a^6*b^8*c^5*e^19 - 2028*a^7*b^6*c^6*e^19 + 12176*a^8*b^4*c^7*e^19 - 32320*a^9*b^2*c^8*e^19 - 1024*a^2*c^17*d^16*e^3 - 7424*a^3*c^16*d^14*e^5 + 8960*a^4*c^15*d^12*e^7 + 152320*a^5*c^14*d^10*e^9 + 439040*a^6*c^13*d^8*e^11 + 614656*a^7*c^12*d^6*e^13 + 471296*a^8*c^11*d^4*e^15 + 190720*a^9*c^10*d^2*e^17 - 64*b^4*c^15*d^16*e^3 + 512*b^5*c^14*d^15*e^4 - 1804*b^6*c^13*d^14*e^5 + 3668*b^7*c^12*d^13*e^6 - 4606*b^8*c^11*d^12*e^7 + 3248*b^9*c^10*d^11*e^8 - 322*b^10*c^9*d^10*e^9 - 1756*b^11*c^8*d^9*e^10 + 1742*b^12*c^7*d^8*e^11 - 744*b^13*c^6*d^7*e^12 + 126*b^14*c^5*d^6*e^13 - 25152*a^2*b^2*c^15*d^14*e^5 + 32704*a^2*b^3*c^14*d^13*e^6 + 13552*a^2*b^4*c^13*d^12*e^7 - 133728*a^2*b^5*c^12*d^11*e^8 + 251860*a^2*b^6*c^11*d^10*e^9 - 230228*a^2*b^7*c^10*d^9*e^10 + 71706*a^2*b^8*c^9*d^8*e^11 + 44528*a^2*b^9*c^8*d^7*e^12 - 39088*a^2*b^10*c^7*d^6*e^13 + 4788*a^2*b^11*c^6*d^5*e^14 + 1890*a^2*b^12*c^5*d^4*e^15 - 177856*a^3*b^2*c^14*d^12*e^7 + 391552*a^3*b^3*c^13*d^11*e^8 - 517104*a^3*b^4*c^12*d^10*e^9 + 234864*a^3*b^5*c^11*d^9*e^10 + 308252*a^3*b^6*c^10*d^8*e^11 - 458384*a^3*b^7*c^9*d^7*e^12 + 156688*a^3*b^8*c^8*d^6*e^13 + 43064*a^3*b^9*c^7*d^5*e^14 - 23100*a^3*b^10*c^6*d^4*e^15 - 2520*a^3*b^11*c^5*d^3*e^16 - 42560*a^4*b^2*c^13*d^10*e^9 + 705600*a^4*b^3*c^12*d^9*e^10 - 1453200*a^4*b^4*c^11*d^8*e^11 + 987840*a^4*b^5*c^10*d^7*e^12 + 175420*a^4*b^6*c^9*d^6*e^13 - 428820*a^4*b^7*c^8*d^5*e^14 + 61670*a^4*b^8*c^7*d^4*e^15 + 36960*a^4*b^9*c^6*d^3*e^16 + 1890*a^4*b^10*c^5*d^2*e^17 + 1055040*a^5*b^2*c^12*d^8*e^11 + 349440*a^5*b^3*c^11*d^7*e^12 - 1803984*a^5*b^4*c^10*d^6*e^13 + 990192*a^5*b^5*c^9*d^5*e^14 + 231476*a^5*b^6*c^8*d^4*e^15 - 182392*a^5*b^7*c^7*d^3*e^16 - 29736*a^5*b^8*c^6*d^2*e^17 + 1997632*a^6*b^2*c^11*d^6*e^13 + 153664*a^6*b^3*c^10*d^5*e^14 - 1288112*a^6*b^4*c^9*d^4*e^15 + 271264*a^6*b^5*c^8*d^3*e^16 + 170492*a^6*b^6*c^7*d^2*e^17 + 1362368*a^7*b^2*c^10*d^4*e^15 + 348544*a^7*b^3*c^9*d^3*e^16 - 408528*a^7*b^4*c^8*d^2*e^17 + 277824*a^8*b^2*c^9*d^2*e^17 - 190720*a^9*b*c^9*d*e^18 + 512*a*b^2*c^16*d^16*e^3 - 4096*a*b^3*c^15*d^15*e^4 + 13968*a*b^4*c^14*d^14*e^5 - 26096*a*b^5*c^13*d^13*e^6 + 26012*a*b^6*c^12*d^12*e^7 - 3192*a*b^7*c^11*d^11*e^8 - 29288*a*b^8*c^10*d^10*e^9 + 41852*a*b^9*c^9*d^9*e^10 - 26004*a*b^10*c^8*d^8*e^11 + 5408*a*b^11*c^7*d^7*e^12 + 1680*a*b^12*c^6*d^6*e^13 - 756*a*b^13*c^5*d^5*e^14 + 8192*a^2*b*c^16*d^15*e^4 + 51968*a^3*b*c^15*d^13*e^6 - 53760*a^4*b*c^14*d^11*e^8 - 761600*a^5*b*c^13*d^9*e^10 - 756*a^5*b^9*c^5*d*e^18 - 1756160*a^6*b*c^12*d^7*e^12 + 12180*a^6*b^7*c^6*d*e^18 - 1843968*a^7*b*c^11*d^5*e^14 - 73072*a^7*b^5*c^7*d*e^18 - 942592*a^8*b*c^10*d^3*e^16 + 193472*a^8*b^3*c^8*d*e^18))*(-(9*b^13*e^7 + 2048*a^3*c^10*d^7 - 32*b^6*c^7*d^7 - 9*b^4*e^7*(-(4*a*c - b^2)^9)^(1/2) + 384*a*b^4*c^8*d^7 + 26880*a^6*b*c^6*e^7 - 53760*a^6*c^7*d*e^6 + 112*b^7*c^6*d^6*e - 1536*a^2*b^2*c^9*d^7 + 2077*a^2*b^9*c^2*e^7 - 10656*a^3*b^7*c^3*e^7 + 30240*a^4*b^5*c^4*e^7 - 44800*a^5*b^3*c^5*e^7 - 25*a^2*c^2*e^7*(-(4*a*c - b^2)^9)^(1/2) + 17920*a^4*c^9*d^5*e^2 + 35840*a^5*c^8*d^3*e^4 - 98*b^8*c^5*d^5*e^2 - 35*b^9*c^4*d^4*e^3 + 70*b^10*c^3*d^3*e^4 - 14*b^11*c^2*d^2*e^5 + 35*c^4*d^4*e^3*(-(4*a*c - b^2)^9)^(1/2) - 213*a*b^11*c*e^7 - 21*b^12*c*d*e^6 - 1344*a^2*b^4*c^7*d^5*e^2 - 10080*a^2*b^5*c^6*d^4*e^3 + 7840*a^2*b^6*c^5*d^3*e^4 + 1008*a^2*b^7*c^4*d^2*e^5 - 7168*a^3*b^2*c^8*d^5*e^2 + 35840*a^3*b^3*c^7*d^4*e^3 - 17920*a^3*b^4*c^6*d^3*e^4 - 12544*a^3*b^5*c^5*d^2*e^5 + 44800*a^4*b^3*c^6*d^2*e^5 + 14*b^2*c^2*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) + 51*a*b^2*c*e^7*(-(4*a*c - b^2)^9)^(1/2) - 1344*a*b^5*c^7*d^6*e + 532*a*b^10*c^2*d*e^6 - 7168*a^3*b*c^9*d^6*e + 21*b^3*c*d*e^6*(-(4*a*c - b^2)^9)^(1/2) + 896*a*b^6*c^6*d^5*e^2 + 1120*a*b^7*c^5*d^4*e^3 - 1260*a*b^8*c^4*d^3*e^4 + 98*a*b^9*c^3*d^2*e^5 + 5376*a^2*b^3*c^8*d^6*e - 5418*a^2*b^8*c^3*d*e^6 + 28224*a^3*b^6*c^4*d*e^6 - 44800*a^4*b*c^8*d^4*e^3 - 78400*a^4*b^4*c^5*d*e^6 - 53760*a^5*b*c^7*d^2*e^5 + 107520*a^5*b^2*c^6*d*e^6 + 154*a*c^3*d^2*e^5*(-(4*a*c - b^2)^9)^(1/2) - 70*b*c^3*d^3*e^4*(-(4*a*c - b^2)^9)^(1/2) - 154*a*b*c^2*d*e^6*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^5*b^12*e^10 + 4096*a^6*c^11*d^10 + 4096*a^11*c^6*e^10 + b^12*c^5*d^10 - b^17*d^5*e^5 - 24*a*b^10*c^6*d^10 - 24*a^6*b^10*c*e^10 + 5*a*b^16*d^4*e^6 - 5*a^4*b^13*d*e^9 - 5*b^13*c^4*d^9*e + 5*b^16*c*d^6*e^4 + 240*a^2*b^8*c^7*d^10 - 1280*a^3*b^6*c^8*d^10 + 3840*a^4*b^4*c^9*d^10 - 6144*a^5*b^2*c^10*d^10 + 240*a^7*b^8*c^2*e^10 - 1280*a^8*b^6*c^3*e^10 + 3840*a^9*b^4*c^4*e^10 - 6144*a^10*b^2*c^5*e^10 - 10*a^2*b^15*d^3*e^7 + 10*a^3*b^14*d^2*e^8 + 20480*a^7*c^10*d^8*e^2 + 40960*a^8*c^9*d^6*e^4 + 40960*a^9*c^8*d^4*e^6 + 20480*a^10*c^7*d^2*e^8 + 10*b^14*c^3*d^8*e^2 - 10*b^15*c^2*d^7*e^3 + 2280*a^2*b^10*c^5*d^8*e^2 - 1920*a^2*b^11*c^4*d^7*e^3 + 490*a^2*b^12*c^3*d^6*e^4 + 210*a^2*b^13*c^2*d^5*e^5 - 11600*a^3*b^8*c^6*d^8*e^2 + 8000*a^3*b^9*c^5*d^7*e^3 + 560*a^3*b^10*c^4*d^6*e^4 - 2800*a^3*b^11*c^3*d^5*e^5 + 490*a^3*b^12*c^2*d^4*e^6 + 32000*a^4*b^6*c^7*d^8*e^2 - 12800*a^4*b^7*c^6*d^7*e^3 - 16800*a^4*b^8*c^5*d^6*e^4 + 14560*a^4*b^9*c^4*d^5*e^5 + 560*a^4*b^10*c^3*d^4*e^6 - 1920*a^4*b^11*c^2*d^3*e^7 - 42240*a^5*b^4*c^8*d^8*e^2 - 15360*a^5*b^5*c^7*d^7*e^3 + 71680*a^5*b^6*c^6*d^6*e^4 - 32256*a^5*b^7*c^5*d^5*e^5 - 16800*a^5*b^8*c^4*d^4*e^6 + 8000*a^5*b^9*c^3*d^3*e^7 + 2280*a^5*b^10*c^2*d^2*e^8 + 10240*a^6*b^2*c^9*d^8*e^2 + 81920*a^6*b^3*c^8*d^7*e^3 - 125440*a^6*b^4*c^7*d^6*e^4 + 3584*a^6*b^5*c^6*d^5*e^5 + 71680*a^6*b^6*c^5*d^4*e^6 - 12800*a^6*b^7*c^4*d^3*e^7 - 11600*a^6*b^8*c^3*d^2*e^8 + 61440*a^7*b^2*c^8*d^6*e^4 + 102400*a^7*b^3*c^7*d^5*e^5 - 125440*a^7*b^4*c^6*d^4*e^6 - 15360*a^7*b^5*c^5*d^3*e^7 + 32000*a^7*b^6*c^4*d^2*e^8 + 61440*a^8*b^2*c^7*d^4*e^6 + 81920*a^8*b^3*c^6*d^3*e^7 - 42240*a^8*b^4*c^5*d^2*e^8 + 10240*a^9*b^2*c^6*d^2*e^8 + 120*a*b^11*c^5*d^9*e + 4*a*b^15*c*d^5*e^5 + 120*a^5*b^11*c*d*e^9 - 20480*a^6*b*c^10*d^9*e - 20480*a^10*b*c^6*d*e^9 - 235*a*b^12*c^4*d^8*e^2 + 220*a*b^13*c^3*d^7*e^3 - 90*a*b^14*c^2*d^6*e^4 - 1200*a^2*b^9*c^6*d^9*e - 90*a^2*b^14*c*d^4*e^6 + 6400*a^3*b^7*c^7*d^9*e + 220*a^3*b^13*c*d^3*e^7 - 19200*a^4*b^5*c^8*d^9*e - 235*a^4*b^12*c*d^2*e^8 + 30720*a^5*b^3*c^9*d^9*e - 1200*a^6*b^9*c^2*d*e^9 - 81920*a^7*b*c^9*d^7*e^3 + 6400*a^7*b^7*c^3*d*e^9 - 122880*a^8*b*c^8*d^5*e^5 - 19200*a^8*b^5*c^4*d*e^9 - 81920*a^9*b*c^7*d^3*e^7 + 30720*a^9*b^3*c^5*d*e^9)))^(1/2)*2i","B"
2301,1,8768,360,4.044006,"\text{Not used}","int(1/(x^(5/2)*(a + b*x + c*x^2)^2),x)","-\frac{\frac{2}{3\,a}-\frac{10\,b\,x}{3\,a^2}+\frac{x^2\,\left(14\,a^2\,c^2-62\,a\,b^2\,c+15\,b^4\right)}{3\,a^3\,\left(4\,a\,c-b^2\right)}+\frac{c\,x^3\,\left(5\,b^3-19\,a\,b\,c\right)}{a^3\,\left(4\,a\,c-b^2\right)}}{a\,x^{3/2}+b\,x^{5/2}+c\,x^{7/2}}+\mathrm{atan}\left(\frac{\left(\sqrt{-\frac{25\,b^{15}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6+49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c-246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,\left(\sqrt{x}\,\sqrt{-\frac{25\,b^{15}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6+49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c-246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,\left(32768\,a^{21}\,b\,c^8-49152\,a^{20}\,b^3\,c^7+30720\,a^{19}\,b^5\,c^6-10240\,a^{18}\,b^7\,c^5+1920\,a^{17}\,b^9\,c^4-192\,a^{16}\,b^{11}\,c^3+8\,a^{15}\,b^{13}\,c^2\right)-57344\,a^{19}\,c^9+20\,a^{12}\,b^{14}\,c^2-496\,a^{13}\,b^{12}\,c^3+5176\,a^{14}\,b^{10}\,c^4-29280\,a^{15}\,b^8\,c^5+96000\,a^{16}\,b^6\,c^6-179200\,a^{17}\,b^4\,c^7+169984\,a^{18}\,b^2\,c^8\right)-\sqrt{x}\,\left(50176\,a^{16}\,c^{10}-233984\,a^{15}\,b^2\,c^9+300160\,a^{14}\,b^4\,c^8-182336\,a^{13}\,b^6\,c^7+61012\,a^{12}\,b^8\,c^6-11602\,a^{11}\,b^{10}\,c^5+1180\,a^{10}\,b^{12}\,c^4-50\,a^9\,b^{14}\,c^3\right)\right)\,\sqrt{-\frac{25\,b^{15}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6+49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c-246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,1{}\mathrm{i}+\left(\sqrt{-\frac{25\,b^{15}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6+49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c-246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,\left(57344\,a^{19}\,c^9+\sqrt{x}\,\sqrt{-\frac{25\,b^{15}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6+49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c-246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,\left(32768\,a^{21}\,b\,c^8-49152\,a^{20}\,b^3\,c^7+30720\,a^{19}\,b^5\,c^6-10240\,a^{18}\,b^7\,c^5+1920\,a^{17}\,b^9\,c^4-192\,a^{16}\,b^{11}\,c^3+8\,a^{15}\,b^{13}\,c^2\right)-20\,a^{12}\,b^{14}\,c^2+496\,a^{13}\,b^{12}\,c^3-5176\,a^{14}\,b^{10}\,c^4+29280\,a^{15}\,b^8\,c^5-96000\,a^{16}\,b^6\,c^6+179200\,a^{17}\,b^4\,c^7-169984\,a^{18}\,b^2\,c^8\right)-\sqrt{x}\,\left(50176\,a^{16}\,c^{10}-233984\,a^{15}\,b^2\,c^9+300160\,a^{14}\,b^4\,c^8-182336\,a^{13}\,b^6\,c^7+61012\,a^{12}\,b^8\,c^6-11602\,a^{11}\,b^{10}\,c^5+1180\,a^{10}\,b^{12}\,c^4-50\,a^9\,b^{14}\,c^3\right)\right)\,\sqrt{-\frac{25\,b^{15}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6+49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c-246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,1{}\mathrm{i}}{\left(\sqrt{-\frac{25\,b^{15}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6+49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c-246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,\left(\sqrt{x}\,\sqrt{-\frac{25\,b^{15}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6+49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c-246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,\left(32768\,a^{21}\,b\,c^8-49152\,a^{20}\,b^3\,c^7+30720\,a^{19}\,b^5\,c^6-10240\,a^{18}\,b^7\,c^5+1920\,a^{17}\,b^9\,c^4-192\,a^{16}\,b^{11}\,c^3+8\,a^{15}\,b^{13}\,c^2\right)-57344\,a^{19}\,c^9+20\,a^{12}\,b^{14}\,c^2-496\,a^{13}\,b^{12}\,c^3+5176\,a^{14}\,b^{10}\,c^4-29280\,a^{15}\,b^8\,c^5+96000\,a^{16}\,b^6\,c^6-179200\,a^{17}\,b^4\,c^7+169984\,a^{18}\,b^2\,c^8\right)-\sqrt{x}\,\left(50176\,a^{16}\,c^{10}-233984\,a^{15}\,b^2\,c^9+300160\,a^{14}\,b^4\,c^8-182336\,a^{13}\,b^6\,c^7+61012\,a^{12}\,b^8\,c^6-11602\,a^{11}\,b^{10}\,c^5+1180\,a^{10}\,b^{12}\,c^4-50\,a^9\,b^{14}\,c^3\right)\right)\,\sqrt{-\frac{25\,b^{15}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6+49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c-246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}-\left(\sqrt{-\frac{25\,b^{15}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6+49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c-246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,\left(57344\,a^{19}\,c^9+\sqrt{x}\,\sqrt{-\frac{25\,b^{15}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6+49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c-246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,\left(32768\,a^{21}\,b\,c^8-49152\,a^{20}\,b^3\,c^7+30720\,a^{19}\,b^5\,c^6-10240\,a^{18}\,b^7\,c^5+1920\,a^{17}\,b^9\,c^4-192\,a^{16}\,b^{11}\,c^3+8\,a^{15}\,b^{13}\,c^2\right)-20\,a^{12}\,b^{14}\,c^2+496\,a^{13}\,b^{12}\,c^3-5176\,a^{14}\,b^{10}\,c^4+29280\,a^{15}\,b^8\,c^5-96000\,a^{16}\,b^6\,c^6+179200\,a^{17}\,b^4\,c^7-169984\,a^{18}\,b^2\,c^8\right)-\sqrt{x}\,\left(50176\,a^{16}\,c^{10}-233984\,a^{15}\,b^2\,c^9+300160\,a^{14}\,b^4\,c^8-182336\,a^{13}\,b^6\,c^7+61012\,a^{12}\,b^8\,c^6-11602\,a^{11}\,b^{10}\,c^5+1180\,a^{10}\,b^{12}\,c^4-50\,a^9\,b^{14}\,c^3\right)\right)\,\sqrt{-\frac{25\,b^{15}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6+49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c-246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}+119168\,a^{13}\,b\,c^{10}+450\,a^9\,b^9\,c^6-7270\,a^{10}\,b^7\,c^7+44008\,a^{11}\,b^5\,c^8-118304\,a^{12}\,b^3\,c^9}\right)\,\sqrt{-\frac{25\,b^{15}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6+49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c-246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}+165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\sqrt{-\frac{25\,b^{15}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6-49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c+246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,\left(\sqrt{x}\,\sqrt{-\frac{25\,b^{15}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6-49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c+246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,\left(32768\,a^{21}\,b\,c^8-49152\,a^{20}\,b^3\,c^7+30720\,a^{19}\,b^5\,c^6-10240\,a^{18}\,b^7\,c^5+1920\,a^{17}\,b^9\,c^4-192\,a^{16}\,b^{11}\,c^3+8\,a^{15}\,b^{13}\,c^2\right)-57344\,a^{19}\,c^9+20\,a^{12}\,b^{14}\,c^2-496\,a^{13}\,b^{12}\,c^3+5176\,a^{14}\,b^{10}\,c^4-29280\,a^{15}\,b^8\,c^5+96000\,a^{16}\,b^6\,c^6-179200\,a^{17}\,b^4\,c^7+169984\,a^{18}\,b^2\,c^8\right)-\sqrt{x}\,\left(50176\,a^{16}\,c^{10}-233984\,a^{15}\,b^2\,c^9+300160\,a^{14}\,b^4\,c^8-182336\,a^{13}\,b^6\,c^7+61012\,a^{12}\,b^8\,c^6-11602\,a^{11}\,b^{10}\,c^5+1180\,a^{10}\,b^{12}\,c^4-50\,a^9\,b^{14}\,c^3\right)\right)\,\sqrt{-\frac{25\,b^{15}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6-49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c+246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,1{}\mathrm{i}+\left(\sqrt{-\frac{25\,b^{15}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6-49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c+246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,\left(57344\,a^{19}\,c^9+\sqrt{x}\,\sqrt{-\frac{25\,b^{15}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6-49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c+246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,\left(32768\,a^{21}\,b\,c^8-49152\,a^{20}\,b^3\,c^7+30720\,a^{19}\,b^5\,c^6-10240\,a^{18}\,b^7\,c^5+1920\,a^{17}\,b^9\,c^4-192\,a^{16}\,b^{11}\,c^3+8\,a^{15}\,b^{13}\,c^2\right)-20\,a^{12}\,b^{14}\,c^2+496\,a^{13}\,b^{12}\,c^3-5176\,a^{14}\,b^{10}\,c^4+29280\,a^{15}\,b^8\,c^5-96000\,a^{16}\,b^6\,c^6+179200\,a^{17}\,b^4\,c^7-169984\,a^{18}\,b^2\,c^8\right)-\sqrt{x}\,\left(50176\,a^{16}\,c^{10}-233984\,a^{15}\,b^2\,c^9+300160\,a^{14}\,b^4\,c^8-182336\,a^{13}\,b^6\,c^7+61012\,a^{12}\,b^8\,c^6-11602\,a^{11}\,b^{10}\,c^5+1180\,a^{10}\,b^{12}\,c^4-50\,a^9\,b^{14}\,c^3\right)\right)\,\sqrt{-\frac{25\,b^{15}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6-49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c+246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,1{}\mathrm{i}}{\left(\sqrt{-\frac{25\,b^{15}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6-49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c+246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,\left(\sqrt{x}\,\sqrt{-\frac{25\,b^{15}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6-49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c+246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,\left(32768\,a^{21}\,b\,c^8-49152\,a^{20}\,b^3\,c^7+30720\,a^{19}\,b^5\,c^6-10240\,a^{18}\,b^7\,c^5+1920\,a^{17}\,b^9\,c^4-192\,a^{16}\,b^{11}\,c^3+8\,a^{15}\,b^{13}\,c^2\right)-57344\,a^{19}\,c^9+20\,a^{12}\,b^{14}\,c^2-496\,a^{13}\,b^{12}\,c^3+5176\,a^{14}\,b^{10}\,c^4-29280\,a^{15}\,b^8\,c^5+96000\,a^{16}\,b^6\,c^6-179200\,a^{17}\,b^4\,c^7+169984\,a^{18}\,b^2\,c^8\right)-\sqrt{x}\,\left(50176\,a^{16}\,c^{10}-233984\,a^{15}\,b^2\,c^9+300160\,a^{14}\,b^4\,c^8-182336\,a^{13}\,b^6\,c^7+61012\,a^{12}\,b^8\,c^6-11602\,a^{11}\,b^{10}\,c^5+1180\,a^{10}\,b^{12}\,c^4-50\,a^9\,b^{14}\,c^3\right)\right)\,\sqrt{-\frac{25\,b^{15}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6-49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c+246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}-\left(\sqrt{-\frac{25\,b^{15}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6-49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c+246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,\left(57344\,a^{19}\,c^9+\sqrt{x}\,\sqrt{-\frac{25\,b^{15}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6-49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c+246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,\left(32768\,a^{21}\,b\,c^8-49152\,a^{20}\,b^3\,c^7+30720\,a^{19}\,b^5\,c^6-10240\,a^{18}\,b^7\,c^5+1920\,a^{17}\,b^9\,c^4-192\,a^{16}\,b^{11}\,c^3+8\,a^{15}\,b^{13}\,c^2\right)-20\,a^{12}\,b^{14}\,c^2+496\,a^{13}\,b^{12}\,c^3-5176\,a^{14}\,b^{10}\,c^4+29280\,a^{15}\,b^8\,c^5-96000\,a^{16}\,b^6\,c^6+179200\,a^{17}\,b^4\,c^7-169984\,a^{18}\,b^2\,c^8\right)-\sqrt{x}\,\left(50176\,a^{16}\,c^{10}-233984\,a^{15}\,b^2\,c^9+300160\,a^{14}\,b^4\,c^8-182336\,a^{13}\,b^6\,c^7+61012\,a^{12}\,b^8\,c^6-11602\,a^{11}\,b^{10}\,c^5+1180\,a^{10}\,b^{12}\,c^4-50\,a^9\,b^{14}\,c^3\right)\right)\,\sqrt{-\frac{25\,b^{15}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6-49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c+246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}+119168\,a^{13}\,b\,c^{10}+450\,a^9\,b^9\,c^6-7270\,a^{10}\,b^7\,c^7+44008\,a^{11}\,b^5\,c^8-118304\,a^{12}\,b^3\,c^9}\right)\,\sqrt{-\frac{25\,b^{15}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-80640\,a^7\,b\,c^7+6366\,a^2\,b^{11}\,c^2-35767\,a^3\,b^9\,c^3+116928\,a^4\,b^7\,c^4-219744\,a^5\,b^5\,c^5+215040\,a^6\,b^3\,c^6-49\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-615\,a\,b^{13}\,c+246\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}-165\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^9}}{8\,\left(4096\,a^{13}\,c^6-6144\,a^{12}\,b^2\,c^5+3840\,a^{11}\,b^4\,c^4-1280\,a^{10}\,b^6\,c^3+240\,a^9\,b^8\,c^2-24\,a^8\,b^{10}\,c+a^7\,b^{12}\right)}}\,2{}\mathrm{i}","Not used",1,"atan((((-(25*b^15 - 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 + 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c - 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) + 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(x^(1/2)*(-(25*b^15 - 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 + 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c - 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) + 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(32768*a^21*b*c^8 + 8*a^15*b^13*c^2 - 192*a^16*b^11*c^3 + 1920*a^17*b^9*c^4 - 10240*a^18*b^7*c^5 + 30720*a^19*b^5*c^6 - 49152*a^20*b^3*c^7) - 57344*a^19*c^9 + 20*a^12*b^14*c^2 - 496*a^13*b^12*c^3 + 5176*a^14*b^10*c^4 - 29280*a^15*b^8*c^5 + 96000*a^16*b^6*c^6 - 179200*a^17*b^4*c^7 + 169984*a^18*b^2*c^8) - x^(1/2)*(50176*a^16*c^10 - 50*a^9*b^14*c^3 + 1180*a^10*b^12*c^4 - 11602*a^11*b^10*c^5 + 61012*a^12*b^8*c^6 - 182336*a^13*b^6*c^7 + 300160*a^14*b^4*c^8 - 233984*a^15*b^2*c^9))*(-(25*b^15 - 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 + 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c - 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) + 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*1i + ((-(25*b^15 - 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 + 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c - 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) + 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(57344*a^19*c^9 + x^(1/2)*(-(25*b^15 - 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 + 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c - 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) + 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(32768*a^21*b*c^8 + 8*a^15*b^13*c^2 - 192*a^16*b^11*c^3 + 1920*a^17*b^9*c^4 - 10240*a^18*b^7*c^5 + 30720*a^19*b^5*c^6 - 49152*a^20*b^3*c^7) - 20*a^12*b^14*c^2 + 496*a^13*b^12*c^3 - 5176*a^14*b^10*c^4 + 29280*a^15*b^8*c^5 - 96000*a^16*b^6*c^6 + 179200*a^17*b^4*c^7 - 169984*a^18*b^2*c^8) - x^(1/2)*(50176*a^16*c^10 - 50*a^9*b^14*c^3 + 1180*a^10*b^12*c^4 - 11602*a^11*b^10*c^5 + 61012*a^12*b^8*c^6 - 182336*a^13*b^6*c^7 + 300160*a^14*b^4*c^8 - 233984*a^15*b^2*c^9))*(-(25*b^15 - 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 + 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c - 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) + 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*1i)/(((-(25*b^15 - 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 + 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c - 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) + 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(x^(1/2)*(-(25*b^15 - 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 + 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c - 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) + 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(32768*a^21*b*c^8 + 8*a^15*b^13*c^2 - 192*a^16*b^11*c^3 + 1920*a^17*b^9*c^4 - 10240*a^18*b^7*c^5 + 30720*a^19*b^5*c^6 - 49152*a^20*b^3*c^7) - 57344*a^19*c^9 + 20*a^12*b^14*c^2 - 496*a^13*b^12*c^3 + 5176*a^14*b^10*c^4 - 29280*a^15*b^8*c^5 + 96000*a^16*b^6*c^6 - 179200*a^17*b^4*c^7 + 169984*a^18*b^2*c^8) - x^(1/2)*(50176*a^16*c^10 - 50*a^9*b^14*c^3 + 1180*a^10*b^12*c^4 - 11602*a^11*b^10*c^5 + 61012*a^12*b^8*c^6 - 182336*a^13*b^6*c^7 + 300160*a^14*b^4*c^8 - 233984*a^15*b^2*c^9))*(-(25*b^15 - 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 + 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c - 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) + 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2) - ((-(25*b^15 - 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 + 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c - 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) + 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(57344*a^19*c^9 + x^(1/2)*(-(25*b^15 - 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 + 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c - 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) + 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(32768*a^21*b*c^8 + 8*a^15*b^13*c^2 - 192*a^16*b^11*c^3 + 1920*a^17*b^9*c^4 - 10240*a^18*b^7*c^5 + 30720*a^19*b^5*c^6 - 49152*a^20*b^3*c^7) - 20*a^12*b^14*c^2 + 496*a^13*b^12*c^3 - 5176*a^14*b^10*c^4 + 29280*a^15*b^8*c^5 - 96000*a^16*b^6*c^6 + 179200*a^17*b^4*c^7 - 169984*a^18*b^2*c^8) - x^(1/2)*(50176*a^16*c^10 - 50*a^9*b^14*c^3 + 1180*a^10*b^12*c^4 - 11602*a^11*b^10*c^5 + 61012*a^12*b^8*c^6 - 182336*a^13*b^6*c^7 + 300160*a^14*b^4*c^8 - 233984*a^15*b^2*c^9))*(-(25*b^15 - 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 + 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c - 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) + 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2) + 119168*a^13*b*c^10 + 450*a^9*b^9*c^6 - 7270*a^10*b^7*c^7 + 44008*a^11*b^5*c^8 - 118304*a^12*b^3*c^9))*(-(25*b^15 - 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 + 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c - 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) + 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*2i - (2/(3*a) - (10*b*x)/(3*a^2) + (x^2*(15*b^4 + 14*a^2*c^2 - 62*a*b^2*c))/(3*a^3*(4*a*c - b^2)) + (c*x^3*(5*b^3 - 19*a*b*c))/(a^3*(4*a*c - b^2)))/(a*x^(3/2) + b*x^(5/2) + c*x^(7/2)) + atan((((-(25*b^15 + 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 - 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c + 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(x^(1/2)*(-(25*b^15 + 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 - 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c + 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(32768*a^21*b*c^8 + 8*a^15*b^13*c^2 - 192*a^16*b^11*c^3 + 1920*a^17*b^9*c^4 - 10240*a^18*b^7*c^5 + 30720*a^19*b^5*c^6 - 49152*a^20*b^3*c^7) - 57344*a^19*c^9 + 20*a^12*b^14*c^2 - 496*a^13*b^12*c^3 + 5176*a^14*b^10*c^4 - 29280*a^15*b^8*c^5 + 96000*a^16*b^6*c^6 - 179200*a^17*b^4*c^7 + 169984*a^18*b^2*c^8) - x^(1/2)*(50176*a^16*c^10 - 50*a^9*b^14*c^3 + 1180*a^10*b^12*c^4 - 11602*a^11*b^10*c^5 + 61012*a^12*b^8*c^6 - 182336*a^13*b^6*c^7 + 300160*a^14*b^4*c^8 - 233984*a^15*b^2*c^9))*(-(25*b^15 + 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 - 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c + 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*1i + ((-(25*b^15 + 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 - 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c + 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(57344*a^19*c^9 + x^(1/2)*(-(25*b^15 + 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 - 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c + 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(32768*a^21*b*c^8 + 8*a^15*b^13*c^2 - 192*a^16*b^11*c^3 + 1920*a^17*b^9*c^4 - 10240*a^18*b^7*c^5 + 30720*a^19*b^5*c^6 - 49152*a^20*b^3*c^7) - 20*a^12*b^14*c^2 + 496*a^13*b^12*c^3 - 5176*a^14*b^10*c^4 + 29280*a^15*b^8*c^5 - 96000*a^16*b^6*c^6 + 179200*a^17*b^4*c^7 - 169984*a^18*b^2*c^8) - x^(1/2)*(50176*a^16*c^10 - 50*a^9*b^14*c^3 + 1180*a^10*b^12*c^4 - 11602*a^11*b^10*c^5 + 61012*a^12*b^8*c^6 - 182336*a^13*b^6*c^7 + 300160*a^14*b^4*c^8 - 233984*a^15*b^2*c^9))*(-(25*b^15 + 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 - 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c + 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*1i)/(((-(25*b^15 + 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 - 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c + 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(x^(1/2)*(-(25*b^15 + 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 - 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c + 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(32768*a^21*b*c^8 + 8*a^15*b^13*c^2 - 192*a^16*b^11*c^3 + 1920*a^17*b^9*c^4 - 10240*a^18*b^7*c^5 + 30720*a^19*b^5*c^6 - 49152*a^20*b^3*c^7) - 57344*a^19*c^9 + 20*a^12*b^14*c^2 - 496*a^13*b^12*c^3 + 5176*a^14*b^10*c^4 - 29280*a^15*b^8*c^5 + 96000*a^16*b^6*c^6 - 179200*a^17*b^4*c^7 + 169984*a^18*b^2*c^8) - x^(1/2)*(50176*a^16*c^10 - 50*a^9*b^14*c^3 + 1180*a^10*b^12*c^4 - 11602*a^11*b^10*c^5 + 61012*a^12*b^8*c^6 - 182336*a^13*b^6*c^7 + 300160*a^14*b^4*c^8 - 233984*a^15*b^2*c^9))*(-(25*b^15 + 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 - 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c + 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2) - ((-(25*b^15 + 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 - 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c + 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(57344*a^19*c^9 + x^(1/2)*(-(25*b^15 + 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 - 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c + 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*(32768*a^21*b*c^8 + 8*a^15*b^13*c^2 - 192*a^16*b^11*c^3 + 1920*a^17*b^9*c^4 - 10240*a^18*b^7*c^5 + 30720*a^19*b^5*c^6 - 49152*a^20*b^3*c^7) - 20*a^12*b^14*c^2 + 496*a^13*b^12*c^3 - 5176*a^14*b^10*c^4 + 29280*a^15*b^8*c^5 - 96000*a^16*b^6*c^6 + 179200*a^17*b^4*c^7 - 169984*a^18*b^2*c^8) - x^(1/2)*(50176*a^16*c^10 - 50*a^9*b^14*c^3 + 1180*a^10*b^12*c^4 - 11602*a^11*b^10*c^5 + 61012*a^12*b^8*c^6 - 182336*a^13*b^6*c^7 + 300160*a^14*b^4*c^8 - 233984*a^15*b^2*c^9))*(-(25*b^15 + 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 - 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c + 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2) + 119168*a^13*b*c^10 + 450*a^9*b^9*c^6 - 7270*a^10*b^7*c^7 + 44008*a^11*b^5*c^8 - 118304*a^12*b^3*c^9))*(-(25*b^15 + 25*b^6*(-(4*a*c - b^2)^9)^(1/2) - 80640*a^7*b*c^7 + 6366*a^2*b^11*c^2 - 35767*a^3*b^9*c^3 + 116928*a^4*b^7*c^4 - 219744*a^5*b^5*c^5 + 215040*a^6*b^3*c^6 - 49*a^3*c^3*(-(4*a*c - b^2)^9)^(1/2) - 615*a*b^13*c + 246*a^2*b^2*c^2*(-(4*a*c - b^2)^9)^(1/2) - 165*a*b^4*c*(-(4*a*c - b^2)^9)^(1/2))/(8*(a^7*b^12 + 4096*a^13*c^6 - 24*a^8*b^10*c + 240*a^9*b^8*c^2 - 1280*a^10*b^6*c^3 + 3840*a^11*b^4*c^4 - 6144*a^12*b^2*c^5)))^(1/2)*2i","B"
2302,1,20000,751,25.582704,"\text{Not used}","int((d + e*x)^(7/2)/(a + b*x + c*x^2)^3,x)","\ln\left(\frac{e^3\,\left(b\,e-2\,c\,d\right)\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2\,\left(6400\,a^3\,c^3\,e^6+9456\,a^2\,b^2\,c^2\,e^6-57024\,a^2\,b\,c^3\,d\,e^5+57024\,a^2\,c^4\,d^2\,e^4-1176\,a\,b^4\,c\,e^6-9504\,a\,b^3\,c^2\,d\,e^5+85536\,a\,b^2\,c^3\,d^2\,e^4-152064\,a\,b\,c^4\,d^3\,e^3+76032\,a\,c^5\,d^4\,e^2+35\,b^6\,e^6+756\,b^5\,c\,d\,e^5+972\,b^4\,c^2\,d^2\,e^4-31104\,b^3\,c^3\,d^3\,e^3+84672\,b^2\,c^4\,d^4\,e^2-82944\,b\,c^5\,d^5\,e+27648\,c^6\,d^6\right)}{64\,c\,{\left(4\,a\,c-b^2\right)}^6}-\frac{\sqrt{2}\,\left(\frac{\sqrt{2}\,\left(\frac{c\,e^3\,\left(20\,a^2\,c\,e^4+a\,b^2\,e^4-44\,a\,b\,c\,d\,e^3+44\,a\,c^2\,d^2\,e^2-b^3\,d\,e^3+25\,b^2\,c\,d^2\,e^2-48\,b\,c^2\,d^3\,e+24\,c^3\,d^4\right)}{4\,a\,c-b^2}-\frac{\sqrt{2}\,c^2\,e^2\,\left(4\,a\,c-b^2\right)\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^{17}\,e^7+4718592\,a^5\,c^{12}\,d^7-4608\,b^{10}\,c^7\,d^7+b^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+92160\,a\,b^8\,c^8\,d^7-1720320\,a^8\,b\,c^8\,e^7+3440640\,a^8\,c^9\,d\,e^6+16128\,b^{11}\,c^6\,d^6\,e-737280\,a^2\,b^6\,c^9\,d^7+2949120\,a^3\,b^4\,c^{10}\,d^7-5898240\,a^4\,b^2\,c^{11}\,d^7+1140\,a^2\,b^{13}\,c^2\,e^7-10160\,a^3\,b^{11}\,c^3\,e^7+34880\,a^4\,b^9\,c^4\,e^7+43776\,a^5\,b^7\,c^5\,e^7-680960\,a^6\,b^5\,c^6\,e^7+1863680\,a^7\,b^3\,c^7\,e^7+13762560\,a^6\,c^{11}\,d^5\,e^2+12615680\,a^7\,c^{10}\,d^3\,e^4-20832\,b^{12}\,c^5\,d^5\,e^2+11760\,b^{13}\,c^4\,d^4\,e^3-2450\,b^{14}\,c^3\,d^3\,e^4-21\,b^{15}\,c^2\,d^2\,e^5-21\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-55\,a\,b^{15}\,c\,e^7-25\,a\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+21\,b^{16}\,c\,d\,e^6+21\,b\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-3064320\,a^2\,b^8\,c^7\,d^5\,e^2+1209600\,a^2\,b^9\,c^6\,d^4\,e^3+144480\,a^2\,b^{10}\,c^5\,d^3\,e^4-136080\,a^2\,b^{11}\,c^4\,d^2\,e^5+11182080\,a^3\,b^6\,c^8\,d^5\,e^2-2150400\,a^3\,b^7\,c^7\,d^4\,e^3-2576000\,a^3\,b^8\,c^6\,d^3\,e^4+853440\,a^3\,b^9\,c^5\,d^2\,e^5-18063360\,a^4\,b^4\,c^9\,d^5\,e^2-6451200\,a^4\,b^5\,c^8\,d^4\,e^3+12454400\,a^4\,b^6\,c^7\,d^3\,e^4-1908480\,a^4\,b^7\,c^6\,d^2\,e^5+4128768\,a^5\,b^2\,c^{10}\,d^5\,e^2+30965760\,a^5\,b^3\,c^9\,d^4\,e^3-24729600\,a^5\,b^4\,c^8\,d^3\,e^4-2128896\,a^5\,b^5\,c^7\,d^2\,e^5+12328960\,a^6\,b^2\,c^9\,d^3\,e^4+15912960\,a^6\,b^3\,c^8\,d^2\,e^5-322560\,a\,b^9\,c^7\,d^6\,e-630\,a\,b^{14}\,c^2\,d\,e^6-16515072\,a^5\,b\,c^{11}\,d^6\,e+403200\,a\,b^{10}\,c^6\,d^5\,e^2-201600\,a\,b^{11}\,c^5\,d^4\,e^3+21560\,a\,b^{12}\,c^4\,d^3\,e^4+7980\,a\,b^{13}\,c^3\,d^2\,e^5+2580480\,a^2\,b^7\,c^8\,d^6\,e+840\,a^2\,b^{12}\,c^3\,d\,e^6-10321920\,a^3\,b^5\,c^9\,d^6\,e+84000\,a^3\,b^{10}\,c^4\,d\,e^6+20643840\,a^4\,b^3\,c^{10}\,d^6\,e-846720\,a^4\,b^8\,c^5\,d\,e^6+3472896\,a^5\,b^6\,c^6\,d\,e^6-34406400\,a^6\,b\,c^{10}\,d^4\,e^3-6236160\,a^6\,b^4\,c^7\,d\,e^6-18923520\,a^7\,b\,c^9\,d^2\,e^5+2580480\,a^7\,b^2\,c^8\,d\,e^6}{c^3\,{\left(4\,a\,c-b^2\right)}^{10}}}}{2}\right)\,\sqrt{-\frac{b^{17}\,e^7+4718592\,a^5\,c^{12}\,d^7-4608\,b^{10}\,c^7\,d^7+b^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+92160\,a\,b^8\,c^8\,d^7-1720320\,a^8\,b\,c^8\,e^7+3440640\,a^8\,c^9\,d\,e^6+16128\,b^{11}\,c^6\,d^6\,e-737280\,a^2\,b^6\,c^9\,d^7+2949120\,a^3\,b^4\,c^{10}\,d^7-5898240\,a^4\,b^2\,c^{11}\,d^7+1140\,a^2\,b^{13}\,c^2\,e^7-10160\,a^3\,b^{11}\,c^3\,e^7+34880\,a^4\,b^9\,c^4\,e^7+43776\,a^5\,b^7\,c^5\,e^7-680960\,a^6\,b^5\,c^6\,e^7+1863680\,a^7\,b^3\,c^7\,e^7+13762560\,a^6\,c^{11}\,d^5\,e^2+12615680\,a^7\,c^{10}\,d^3\,e^4-20832\,b^{12}\,c^5\,d^5\,e^2+11760\,b^{13}\,c^4\,d^4\,e^3-2450\,b^{14}\,c^3\,d^3\,e^4-21\,b^{15}\,c^2\,d^2\,e^5-21\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-55\,a\,b^{15}\,c\,e^7-25\,a\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+21\,b^{16}\,c\,d\,e^6+21\,b\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-3064320\,a^2\,b^8\,c^7\,d^5\,e^2+1209600\,a^2\,b^9\,c^6\,d^4\,e^3+144480\,a^2\,b^{10}\,c^5\,d^3\,e^4-136080\,a^2\,b^{11}\,c^4\,d^2\,e^5+11182080\,a^3\,b^6\,c^8\,d^5\,e^2-2150400\,a^3\,b^7\,c^7\,d^4\,e^3-2576000\,a^3\,b^8\,c^6\,d^3\,e^4+853440\,a^3\,b^9\,c^5\,d^2\,e^5-18063360\,a^4\,b^4\,c^9\,d^5\,e^2-6451200\,a^4\,b^5\,c^8\,d^4\,e^3+12454400\,a^4\,b^6\,c^7\,d^3\,e^4-1908480\,a^4\,b^7\,c^6\,d^2\,e^5+4128768\,a^5\,b^2\,c^{10}\,d^5\,e^2+30965760\,a^5\,b^3\,c^9\,d^4\,e^3-24729600\,a^5\,b^4\,c^8\,d^3\,e^4-2128896\,a^5\,b^5\,c^7\,d^2\,e^5+12328960\,a^6\,b^2\,c^9\,d^3\,e^4+15912960\,a^6\,b^3\,c^8\,d^2\,e^5-322560\,a\,b^9\,c^7\,d^6\,e-630\,a\,b^{14}\,c^2\,d\,e^6-16515072\,a^5\,b\,c^{11}\,d^6\,e+403200\,a\,b^{10}\,c^6\,d^5\,e^2-201600\,a\,b^{11}\,c^5\,d^4\,e^3+21560\,a\,b^{12}\,c^4\,d^3\,e^4+7980\,a\,b^{13}\,c^3\,d^2\,e^5+2580480\,a^2\,b^7\,c^8\,d^6\,e+840\,a^2\,b^{12}\,c^3\,d\,e^6-10321920\,a^3\,b^5\,c^9\,d^6\,e+84000\,a^3\,b^{10}\,c^4\,d\,e^6+20643840\,a^4\,b^3\,c^{10}\,d^6\,e-846720\,a^4\,b^8\,c^5\,d\,e^6+3472896\,a^5\,b^6\,c^6\,d\,e^6-34406400\,a^6\,b\,c^{10}\,d^4\,e^3-6236160\,a^6\,b^4\,c^7\,d\,e^6-18923520\,a^7\,b\,c^9\,d^2\,e^5+2580480\,a^7\,b^2\,c^8\,d\,e^6}{c^3\,{\left(4\,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,e^4+15912960\,a^6\,b^3\,c^8\,d^2\,e^5-322560\,a\,b^9\,c^7\,d^6\,e-630\,a\,b^{14}\,c^2\,d\,e^6-16515072\,a^5\,b\,c^{11}\,d^6\,e+403200\,a\,b^{10}\,c^6\,d^5\,e^2-201600\,a\,b^{11}\,c^5\,d^4\,e^3+21560\,a\,b^{12}\,c^4\,d^3\,e^4+7980\,a\,b^{13}\,c^3\,d^2\,e^5+2580480\,a^2\,b^7\,c^8\,d^6\,e+840\,a^2\,b^{12}\,c^3\,d\,e^6-10321920\,a^3\,b^5\,c^9\,d^6\,e+84000\,a^3\,b^{10}\,c^4\,d\,e^6+20643840\,a^4\,b^3\,c^{10}\,d^6\,e-846720\,a^4\,b^8\,c^5\,d\,e^6+3472896\,a^5\,b^6\,c^6\,d\,e^6-34406400\,a^6\,b\,c^{10}\,d^4\,e^3-6236160\,a^6\,b^4\,c^7\,d\,e^6-18923520\,a^7\,b\,c^9\,d^2\,e^5+2580480\,a^7\,b^2\,c^8\,d\,e^6}{c^3\,{\left(4\,a\,c-b^2\right)}^{10}}}}{16}\right)\,\sqrt{-\frac{b^{17}\,e^7+4718592\,a^5\,c^{12}\,d^7-4608\,b^{10}\,c^7\,d^7-b^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+92160\,a\,b^8\,c^8\,d^7-1720320\,a^8\,b\,c^8\,e^7+3440640\,a^8\,c^9\,d\,e^6+16128\,b^{11}\,c^6\,d^6\,e-737280\,a^2\,b^6\,c^9\,d^7+2949120\,a^3\,b^4\,c^{10}\,d^7-5898240\,a^4\,b^2\,c^{11}\,d^7+1140\,a^2\,b^{13}\,c^2\,e^7-10160\,a^3\,b^{11}\,c^3\,e^7+34880\,a^4\,b^9\,c^4\,e^7+43776\,a^5\,b^7\,c^5\,e^7-680960\,a^6\,b^5\,c^6\,e^7+1863680\,a^7\,b^3\,c^7\,e^7+13762560\,a^6\,c^{11}\,d^5\,e^2+12615680\,a^7\,c^{10}\,d^3\,e^4-20832\,b^{12}\,c^5\,d^5\,e^2+11760\,b^{13}\,c^4\,d^4\,e^3-2450\,b^{14}\,c^3\,d^3\,e^4-21\,b^{15}\,c^2\,d^2\,e^5+21\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-55\,a\,b^{15}\,c\,e^7+25\,a\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+21\,b^{16}\,c\,d\,e^6-21\,b\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-3064320\,a^2\,b^8\,c^7\,d^5\,e^2+1209600\,a^2\,b^9\,c^6\,d^4\,e^3+144480\,a^2\,b^{10}\,c^5\,d^3\,e^4-136080\,a^2\,b^{11}\,c^4\,d^2\,e^5+11182080\,a^3\,b^6\,c^8\,d^5\,e^2-2150400\,a^3\,b^7\,c^7\,d^4\,e^3-2576000\,a^3\,b^8\,c^6\,d^3\,e^4+853440\,a^3\,b^9\,c^5\,d^2\,e^5-18063360\,a^4\,b^4\,c^9\,d^5\,e^2-6451200\,a^4\,b^5\,c^8\,d^4\,e^3+12454400\,a^4\,b^6\,c^7\,d^3\,e^4-1908480\,a^4\,b^7\,c^6\,d^2\,e^5+4128768\,a^5\,b^2\,c^{10}\,d^5\,e^2+30965760\,a^5\,b^3\,c^9\,d^4\,e^3-24729600\,a^5\,b^4\,c^8\,d^3\,e^4-2128896\,a^5\,b^5\,c^7\,d^2\,e^5+12328960\,a^6\,b^2\,c^9\,d^3\,e^4+15912960\,a^6\,b^3\,c^8\,d^2\,e^5-322560\,a\,b^9\,c^7\,d^6\,e-630\,a\,b^{14}\,c^2\,d\,e^6-16515072\,a^5\,b\,c^{11}\,d^6\,e+403200\,a\,b^{10}\,c^6\,d^5\,e^2-201600\,a\,b^{11}\,c^5\,d^4\,e^3+21560\,a\,b^{12}\,c^4\,d^3\,e^4+7980\,a\,b^{13}\,c^3\,d^2\,e^5+2580480\,a^2\,b^7\,c^8\,d^6\,e+840\,a^2\,b^{12}\,c^3\,d\,e^6-10321920\,a^3\,b^5\,c^9\,d^6\,e+84000\,a^3\,b^{10}\,c^4\,d\,e^6+20643840\,a^4\,b^3\,c^{10}\,d^6\,e-846720\,a^4\,b^8\,c^5\,d\,e^6+3472896\,a^5\,b^6\,c^6\,d\,e^6-34406400\,a^6\,b\,c^{10}\,d^4\,e^3-6236160\,a^6\,b^4\,c^7\,d\,e^6-18923520\,a^7\,b\,c^9\,d^2\,e^5+2580480\,a^7\,b^2\,c^8\,d\,e^6}{128\,\left(1048576\,a^{10}\,c^{13}-2621440\,a^9\,b^2\,c^{12}+2949120\,a^8\,b^4\,c^{11}-1966080\,a^7\,b^6\,c^{10}+860160\,a^6\,b^8\,c^9-258048\,a^5\,b^{10}\,c^8+53760\,a^4\,b^{12}\,c^7-7680\,a^3\,b^{14}\,c^6+720\,a^2\,b^{16}\,c^5-40\,a\,b^{18}\,c^4+b^{20}\,c^3\right)}}","Not used",1,"log((e^3*(b*e - 2*c*d)*(a*e^2 + c*d^2 - b*d*e)^2*(35*b^6*e^6 + 27648*c^6*d^6 + 6400*a^3*c^3*e^6 + 76032*a*c^5*d^4*e^2 + 9456*a^2*b^2*c^2*e^6 + 57024*a^2*c^4*d^2*e^4 + 84672*b^2*c^4*d^4*e^2 - 31104*b^3*c^3*d^3*e^3 + 972*b^4*c^2*d^2*e^4 - 1176*a*b^4*c*e^6 - 82944*b*c^5*d^5*e + 756*b^5*c*d*e^5 - 152064*a*b*c^4*d^3*e^3 - 9504*a*b^3*c^2*d*e^5 - 57024*a^2*b*c^3*d*e^5 + 85536*a*b^2*c^3*d^2*e^4))/(64*c*(4*a*c - b^2)^6) - (2^(1/2)*((2^(1/2)*((c*e^3*(24*c^3*d^4 + a*b^2*e^4 + 20*a^2*c*e^4 - b^3*d*e^3 + 44*a*c^2*d^2*e^2 + 25*b^2*c*d^2*e^2 - 48*b*c^2*d^3*e - 44*a*b*c*d*e^3))/(4*a*c - b^2) - (2^(1/2)*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(-(b^17*e^7 + 4718592*a^5*c^12*d^7 - 4608*b^10*c^7*d^7 + b^2*e^7*(-(4*a*c - b^2)^15)^(1/2) + 92160*a*b^8*c^8*d^7 - 1720320*a^8*b*c^8*e^7 + 3440640*a^8*c^9*d*e^6 + 16128*b^11*c^6*d^6*e - 737280*a^2*b^6*c^9*d^7 + 2949120*a^3*b^4*c^10*d^7 - 5898240*a^4*b^2*c^11*d^7 + 1140*a^2*b^13*c^2*e^7 - 10160*a^3*b^11*c^3*e^7 + 34880*a^4*b^9*c^4*e^7 + 43776*a^5*b^7*c^5*e^7 - 680960*a^6*b^5*c^6*e^7 + 1863680*a^7*b^3*c^7*e^7 + 13762560*a^6*c^11*d^5*e^2 + 12615680*a^7*c^10*d^3*e^4 - 20832*b^12*c^5*d^5*e^2 + 11760*b^13*c^4*d^4*e^3 - 2450*b^14*c^3*d^3*e^4 - 21*b^15*c^2*d^2*e^5 - 21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2) - 55*a*b^15*c*e^7 - 25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2) + 21*b^16*c*d*e^6 + 21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2) - 3064320*a^2*b^8*c^7*d^5*e^2 + 1209600*a^2*b^9*c^6*d^4*e^3 + 144480*a^2*b^10*c^5*d^3*e^4 - 136080*a^2*b^11*c^4*d^2*e^5 + 11182080*a^3*b^6*c^8*d^5*e^2 - 2150400*a^3*b^7*c^7*d^4*e^3 - 2576000*a^3*b^8*c^6*d^3*e^4 + 853440*a^3*b^9*c^5*d^2*e^5 - 18063360*a^4*b^4*c^9*d^5*e^2 - 6451200*a^4*b^5*c^8*d^4*e^3 + 12454400*a^4*b^6*c^7*d^3*e^4 - 1908480*a^4*b^7*c^6*d^2*e^5 + 4128768*a^5*b^2*c^10*d^5*e^2 + 30965760*a^5*b^3*c^9*d^4*e^3 - 24729600*a^5*b^4*c^8*d^3*e^4 - 2128896*a^5*b^5*c^7*d^2*e^5 + 12328960*a^6*b^2*c^9*d^3*e^4 + 15912960*a^6*b^3*c^8*d^2*e^5 - 322560*a*b^9*c^7*d^6*e - 630*a*b^14*c^2*d*e^6 - 16515072*a^5*b*c^11*d^6*e + 403200*a*b^10*c^6*d^5*e^2 - 201600*a*b^11*c^5*d^4*e^3 + 21560*a*b^12*c^4*d^3*e^4 + 7980*a*b^13*c^3*d^2*e^5 + 2580480*a^2*b^7*c^8*d^6*e + 840*a^2*b^12*c^3*d*e^6 - 10321920*a^3*b^5*c^9*d^6*e + 84000*a^3*b^10*c^4*d*e^6 + 20643840*a^4*b^3*c^10*d^6*e - 846720*a^4*b^8*c^5*d*e^6 + 3472896*a^5*b^6*c^6*d*e^6 - 34406400*a^6*b*c^10*d^4*e^3 - 6236160*a^6*b^4*c^7*d*e^6 - 18923520*a^7*b*c^9*d^2*e^5 + 2580480*a^7*b^2*c^8*d*e^6)/(c^3*(4*a*c - b^2)^10))^(1/2))/2)*(-(b^17*e^7 + 4718592*a^5*c^12*d^7 - 4608*b^10*c^7*d^7 + b^2*e^7*(-(4*a*c - b^2)^15)^(1/2) + 92160*a*b^8*c^8*d^7 - 1720320*a^8*b*c^8*e^7 + 3440640*a^8*c^9*d*e^6 + 16128*b^11*c^6*d^6*e - 737280*a^2*b^6*c^9*d^7 + 2949120*a^3*b^4*c^10*d^7 - 5898240*a^4*b^2*c^11*d^7 + 1140*a^2*b^13*c^2*e^7 - 10160*a^3*b^11*c^3*e^7 + 34880*a^4*b^9*c^4*e^7 + 43776*a^5*b^7*c^5*e^7 - 680960*a^6*b^5*c^6*e^7 + 1863680*a^7*b^3*c^7*e^7 + 13762560*a^6*c^11*d^5*e^2 + 12615680*a^7*c^10*d^3*e^4 - 20832*b^12*c^5*d^5*e^2 + 11760*b^13*c^4*d^4*e^3 - 2450*b^14*c^3*d^3*e^4 - 21*b^15*c^2*d^2*e^5 - 21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2) - 55*a*b^15*c*e^7 - 25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2) + 21*b^16*c*d*e^6 + 21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2) - 3064320*a^2*b^8*c^7*d^5*e^2 + 1209600*a^2*b^9*c^6*d^4*e^3 + 144480*a^2*b^10*c^5*d^3*e^4 - 136080*a^2*b^11*c^4*d^2*e^5 + 11182080*a^3*b^6*c^8*d^5*e^2 - 2150400*a^3*b^7*c^7*d^4*e^3 - 2576000*a^3*b^8*c^6*d^3*e^4 + 853440*a^3*b^9*c^5*d^2*e^5 - 18063360*a^4*b^4*c^9*d^5*e^2 - 6451200*a^4*b^5*c^8*d^4*e^3 + 12454400*a^4*b^6*c^7*d^3*e^4 - 1908480*a^4*b^7*c^6*d^2*e^5 + 4128768*a^5*b^2*c^10*d^5*e^2 + 30965760*a^5*b^3*c^9*d^4*e^3 - 24729600*a^5*b^4*c^8*d^3*e^4 - 2128896*a^5*b^5*c^7*d^2*e^5 + 12328960*a^6*b^2*c^9*d^3*e^4 + 15912960*a^6*b^3*c^8*d^2*e^5 - 322560*a*b^9*c^7*d^6*e - 630*a*b^14*c^2*d*e^6 - 16515072*a^5*b*c^11*d^6*e + 403200*a*b^10*c^6*d^5*e^2 - 201600*a*b^11*c^5*d^4*e^3 + 21560*a*b^12*c^4*d^3*e^4 + 7980*a*b^13*c^3*d^2*e^5 + 2580480*a^2*b^7*c^8*d^6*e + 840*a^2*b^12*c^3*d*e^6 - 10321920*a^3*b^5*c^9*d^6*e + 84000*a^3*b^10*c^4*d*e^6 + 20643840*a^4*b^3*c^10*d^6*e - 846720*a^4*b^8*c^5*d*e^6 + 3472896*a^5*b^6*c^6*d*e^6 - 34406400*a^6*b*c^10*d^4*e^3 - 6236160*a^6*b^4*c^7*d*e^6 - 18923520*a^7*b*c^9*d^2*e^5 + 2580480*a^7*b^2*c^8*d*e^6)/(c^3*(4*a*c - b^2)^10))^(1/2))/16 + ((d + e*x)^(1/2)*(b^8*e^10 + 800*a^4*c^4*e^10 + 4608*c^8*d^8*e^2 + 13440*a*c^7*d^6*e^4 - 18432*b*c^7*d^7*e^3 + 314*a^2*b^4*c^2*e^10 + 208*a^3*b^2*c^3*e^10 + 12320*a^2*c^6*d^4*e^6 + 4032*a^3*c^5*d^2*e^8 + 28896*b^2*c^6*d^6*e^4 - 22176*b^3*c^5*d^5*e^5 + 8330*b^4*c^4*d^4*e^6 - 1204*b^5*c^3*d^3*e^7 - 42*b^6*c^2*d^2*e^8 - 36*a*b^6*c*e^10 + 20*b^7*c*d*e^9 + 15456*a^2*b^2*c^4*d^2*e^8 - 40320*a*b*c^6*d^5*e^5 - 196*a*b^5*c^2*d*e^9 - 4032*a^3*b*c^4*d*e^9 + 44240*a*b^2*c^5*d^4*e^6 - 21280*a*b^3*c^4*d^3*e^7 + 4116*a*b^4*c^3*d^2*e^8 - 24640*a^2*b*c^5*d^3*e^7 - 3136*a^2*b^3*c^3*d*e^9))/(8*c*(4*a*c - b^2)^4))*(-(b^17*e^7 + 4718592*a^5*c^12*d^7 - 4608*b^10*c^7*d^7 + b^2*e^7*(-(4*a*c - b^2)^15)^(1/2) + 92160*a*b^8*c^8*d^7 - 1720320*a^8*b*c^8*e^7 + 3440640*a^8*c^9*d*e^6 + 16128*b^11*c^6*d^6*e - 737280*a^2*b^6*c^9*d^7 + 2949120*a^3*b^4*c^10*d^7 - 5898240*a^4*b^2*c^11*d^7 + 1140*a^2*b^13*c^2*e^7 - 10160*a^3*b^11*c^3*e^7 + 34880*a^4*b^9*c^4*e^7 + 43776*a^5*b^7*c^5*e^7 - 680960*a^6*b^5*c^6*e^7 + 1863680*a^7*b^3*c^7*e^7 + 13762560*a^6*c^11*d^5*e^2 + 12615680*a^7*c^10*d^3*e^4 - 20832*b^12*c^5*d^5*e^2 + 11760*b^13*c^4*d^4*e^3 - 2450*b^14*c^3*d^3*e^4 - 21*b^15*c^2*d^2*e^5 - 21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2) - 55*a*b^15*c*e^7 - 25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2) + 21*b^16*c*d*e^6 + 21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2) - 3064320*a^2*b^8*c^7*d^5*e^2 + 1209600*a^2*b^9*c^6*d^4*e^3 + 144480*a^2*b^10*c^5*d^3*e^4 - 136080*a^2*b^11*c^4*d^2*e^5 + 11182080*a^3*b^6*c^8*d^5*e^2 - 2150400*a^3*b^7*c^7*d^4*e^3 - 2576000*a^3*b^8*c^6*d^3*e^4 + 853440*a^3*b^9*c^5*d^2*e^5 - 18063360*a^4*b^4*c^9*d^5*e^2 - 6451200*a^4*b^5*c^8*d^4*e^3 + 12454400*a^4*b^6*c^7*d^3*e^4 - 1908480*a^4*b^7*c^6*d^2*e^5 + 4128768*a^5*b^2*c^10*d^5*e^2 + 30965760*a^5*b^3*c^9*d^4*e^3 - 24729600*a^5*b^4*c^8*d^3*e^4 - 2128896*a^5*b^5*c^7*d^2*e^5 + 12328960*a^6*b^2*c^9*d^3*e^4 + 15912960*a^6*b^3*c^8*d^2*e^5 - 322560*a*b^9*c^7*d^6*e - 630*a*b^14*c^2*d*e^6 - 16515072*a^5*b*c^11*d^6*e + 403200*a*b^10*c^6*d^5*e^2 - 201600*a*b^11*c^5*d^4*e^3 + 21560*a*b^12*c^4*d^3*e^4 + 7980*a*b^13*c^3*d^2*e^5 + 2580480*a^2*b^7*c^8*d^6*e + 840*a^2*b^12*c^3*d*e^6 - 10321920*a^3*b^5*c^9*d^6*e + 84000*a^3*b^10*c^4*d*e^6 + 20643840*a^4*b^3*c^10*d^6*e - 846720*a^4*b^8*c^5*d*e^6 + 3472896*a^5*b^6*c^6*d*e^6 - 34406400*a^6*b*c^10*d^4*e^3 - 6236160*a^6*b^4*c^7*d*e^6 - 18923520*a^7*b*c^9*d^2*e^5 + 2580480*a^7*b^2*c^8*d*e^6)/(c^3*(4*a*c - b^2)^10))^(1/2))/16)*(-(b^17*e^7 + 4718592*a^5*c^12*d^7 - 4608*b^10*c^7*d^7 + b^2*e^7*(-(4*a*c - b^2)^15)^(1/2) + 92160*a*b^8*c^8*d^7 - 1720320*a^8*b*c^8*e^7 + 3440640*a^8*c^9*d*e^6 + 16128*b^11*c^6*d^6*e - 737280*a^2*b^6*c^9*d^7 + 2949120*a^3*b^4*c^10*d^7 - 5898240*a^4*b^2*c^11*d^7 + 1140*a^2*b^13*c^2*e^7 - 10160*a^3*b^11*c^3*e^7 + 34880*a^4*b^9*c^4*e^7 + 43776*a^5*b^7*c^5*e^7 - 680960*a^6*b^5*c^6*e^7 + 1863680*a^7*b^3*c^7*e^7 + 13762560*a^6*c^11*d^5*e^2 + 12615680*a^7*c^10*d^3*e^4 - 20832*b^12*c^5*d^5*e^2 + 11760*b^13*c^4*d^4*e^3 - 2450*b^14*c^3*d^3*e^4 - 21*b^15*c^2*d^2*e^5 - 21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2) - 55*a*b^15*c*e^7 - 25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2) + 21*b^16*c*d*e^6 + 21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2) - 3064320*a^2*b^8*c^7*d^5*e^2 + 1209600*a^2*b^9*c^6*d^4*e^3 + 144480*a^2*b^10*c^5*d^3*e^4 - 136080*a^2*b^11*c^4*d^2*e^5 + 11182080*a^3*b^6*c^8*d^5*e^2 - 2150400*a^3*b^7*c^7*d^4*e^3 - 2576000*a^3*b^8*c^6*d^3*e^4 + 853440*a^3*b^9*c^5*d^2*e^5 - 18063360*a^4*b^4*c^9*d^5*e^2 - 6451200*a^4*b^5*c^8*d^4*e^3 + 12454400*a^4*b^6*c^7*d^3*e^4 - 1908480*a^4*b^7*c^6*d^2*e^5 + 4128768*a^5*b^2*c^10*d^5*e^2 + 30965760*a^5*b^3*c^9*d^4*e^3 - 24729600*a^5*b^4*c^8*d^3*e^4 - 2128896*a^5*b^5*c^7*d^2*e^5 + 12328960*a^6*b^2*c^9*d^3*e^4 + 15912960*a^6*b^3*c^8*d^2*e^5 - 322560*a*b^9*c^7*d^6*e - 630*a*b^14*c^2*d*e^6 - 16515072*a^5*b*c^11*d^6*e + 403200*a*b^10*c^6*d^5*e^2 - 201600*a*b^11*c^5*d^4*e^3 + 21560*a*b^12*c^4*d^3*e^4 + 7980*a*b^13*c^3*d^2*e^5 + 2580480*a^2*b^7*c^8*d^6*e + 840*a^2*b^12*c^3*d*e^6 - 10321920*a^3*b^5*c^9*d^6*e + 84000*a^3*b^10*c^4*d*e^6 + 20643840*a^4*b^3*c^10*d^6*e - 846720*a^4*b^8*c^5*d*e^6 + 3472896*a^5*b^6*c^6*d*e^6 - 34406400*a^6*b*c^10*d^4*e^3 - 6236160*a^6*b^4*c^7*d*e^6 - 18923520*a^7*b*c^9*d^2*e^5 + 2580480*a^7*b^2*c^8*d*e^6)/(128*(1048576*a^10*c^13 + b^20*c^3 - 40*a*b^18*c^4 + 720*a^2*b^16*c^5 - 7680*a^3*b^14*c^6 + 53760*a^4*b^12*c^7 - 258048*a^5*b^10*c^8 + 860160*a^6*b^8*c^9 - 1966080*a^7*b^6*c^10 + 2949120*a^8*b^4*c^11 - 2621440*a^9*b^2*c^12)))^(1/2) - log((e^3*(b*e - 2*c*d)*(a*e^2 + c*d^2 - b*d*e)^2*(35*b^6*e^6 + 27648*c^6*d^6 + 6400*a^3*c^3*e^6 + 76032*a*c^5*d^4*e^2 + 9456*a^2*b^2*c^2*e^6 + 57024*a^2*c^4*d^2*e^4 + 84672*b^2*c^4*d^4*e^2 - 31104*b^3*c^3*d^3*e^3 + 972*b^4*c^2*d^2*e^4 - 1176*a*b^4*c*e^6 - 82944*b*c^5*d^5*e + 756*b^5*c*d*e^5 - 152064*a*b*c^4*d^3*e^3 - 9504*a*b^3*c^2*d*e^5 - 57024*a^2*b*c^3*d*e^5 + 85536*a*b^2*c^3*d^2*e^4))/(64*c*(4*a*c - b^2)^6) - (((c*e^3*(24*c^3*d^4 + a*b^2*e^4 + 20*a^2*c*e^4 - b^3*d*e^3 + 44*a*c^2*d^2*e^2 + 25*b^2*c*d^2*e^2 - 48*b*c^2*d^3*e - 44*a*b*c*d*e^3))/(4*a*c - b^2) + 8*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(-((b^17*e^7)/128 + 36864*a^5*c^12*d^7 - 36*b^10*c^7*d^7 + (b^2*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + 720*a*b^8*c^8*d^7 - 13440*a^8*b*c^8*e^7 + 26880*a^8*c^9*d*e^6 + 126*b^11*c^6*d^6*e - 5760*a^2*b^6*c^9*d^7 + 23040*a^3*b^4*c^10*d^7 - 46080*a^4*b^2*c^11*d^7 + (285*a^2*b^13*c^2*e^7)/32 - (635*a^3*b^11*c^3*e^7)/8 + (545*a^4*b^9*c^4*e^7)/2 + 342*a^5*b^7*c^5*e^7 - 5320*a^6*b^5*c^6*e^7 + 14560*a^7*b^3*c^7*e^7 + 107520*a^6*c^11*d^5*e^2 + 98560*a^7*c^10*d^3*e^4 - (651*b^12*c^5*d^5*e^2)/4 + (735*b^13*c^4*d^4*e^3)/8 - (1225*b^14*c^3*d^3*e^4)/64 - (21*b^15*c^2*d^2*e^5)/128 - (21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (55*a*b^15*c*e^7)/128 - (25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + (21*b^16*c*d*e^6)/128 + (21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2))/128 - 23940*a^2*b^8*c^7*d^5*e^2 + 9450*a^2*b^9*c^6*d^4*e^3 + (4515*a^2*b^10*c^5*d^3*e^4)/4 - (8505*a^2*b^11*c^4*d^2*e^5)/8 + 87360*a^3*b^6*c^8*d^5*e^2 - 16800*a^3*b^7*c^7*d^4*e^3 - 20125*a^3*b^8*c^6*d^3*e^4 + (13335*a^3*b^9*c^5*d^2*e^5)/2 - 141120*a^4*b^4*c^9*d^5*e^2 - 50400*a^4*b^5*c^8*d^4*e^3 + 97300*a^4*b^6*c^7*d^3*e^4 - 14910*a^4*b^7*c^6*d^2*e^5 + 32256*a^5*b^2*c^10*d^5*e^2 + 241920*a^5*b^3*c^9*d^4*e^3 - 193200*a^5*b^4*c^8*d^3*e^4 - 16632*a^5*b^5*c^7*d^2*e^5 + 96320*a^6*b^2*c^9*d^3*e^4 + 124320*a^6*b^3*c^8*d^2*e^5 - 2520*a*b^9*c^7*d^6*e - (315*a*b^14*c^2*d*e^6)/64 - 129024*a^5*b*c^11*d^6*e + 3150*a*b^10*c^6*d^5*e^2 - 1575*a*b^11*c^5*d^4*e^3 + (2695*a*b^12*c^4*d^3*e^4)/16 + (1995*a*b^13*c^3*d^2*e^5)/32 + 20160*a^2*b^7*c^8*d^6*e + (105*a^2*b^12*c^3*d*e^6)/16 - 80640*a^3*b^5*c^9*d^6*e + (2625*a^3*b^10*c^4*d*e^6)/4 + 161280*a^4*b^3*c^10*d^6*e - 6615*a^4*b^8*c^5*d*e^6 + 27132*a^5*b^6*c^6*d*e^6 - 268800*a^6*b*c^10*d^4*e^3 - 48720*a^6*b^4*c^7*d*e^6 - 147840*a^7*b*c^9*d^2*e^5 + 20160*a^7*b^2*c^8*d*e^6)/(c^3*(4*a*c - b^2)^10))^(1/2))*(-((b^17*e^7)/128 + 36864*a^5*c^12*d^7 - 36*b^10*c^7*d^7 + (b^2*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + 720*a*b^8*c^8*d^7 - 13440*a^8*b*c^8*e^7 + 26880*a^8*c^9*d*e^6 + 126*b^11*c^6*d^6*e - 5760*a^2*b^6*c^9*d^7 + 23040*a^3*b^4*c^10*d^7 - 46080*a^4*b^2*c^11*d^7 + (285*a^2*b^13*c^2*e^7)/32 - (635*a^3*b^11*c^3*e^7)/8 + (545*a^4*b^9*c^4*e^7)/2 + 342*a^5*b^7*c^5*e^7 - 5320*a^6*b^5*c^6*e^7 + 14560*a^7*b^3*c^7*e^7 + 107520*a^6*c^11*d^5*e^2 + 98560*a^7*c^10*d^3*e^4 - (651*b^12*c^5*d^5*e^2)/4 + (735*b^13*c^4*d^4*e^3)/8 - (1225*b^14*c^3*d^3*e^4)/64 - (21*b^15*c^2*d^2*e^5)/128 - (21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (55*a*b^15*c*e^7)/128 - (25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + (21*b^16*c*d*e^6)/128 + (21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2))/128 - 23940*a^2*b^8*c^7*d^5*e^2 + 9450*a^2*b^9*c^6*d^4*e^3 + (4515*a^2*b^10*c^5*d^3*e^4)/4 - (8505*a^2*b^11*c^4*d^2*e^5)/8 + 87360*a^3*b^6*c^8*d^5*e^2 - 16800*a^3*b^7*c^7*d^4*e^3 - 20125*a^3*b^8*c^6*d^3*e^4 + (13335*a^3*b^9*c^5*d^2*e^5)/2 - 141120*a^4*b^4*c^9*d^5*e^2 - 50400*a^4*b^5*c^8*d^4*e^3 + 97300*a^4*b^6*c^7*d^3*e^4 - 14910*a^4*b^7*c^6*d^2*e^5 + 32256*a^5*b^2*c^10*d^5*e^2 + 241920*a^5*b^3*c^9*d^4*e^3 - 193200*a^5*b^4*c^8*d^3*e^4 - 16632*a^5*b^5*c^7*d^2*e^5 + 96320*a^6*b^2*c^9*d^3*e^4 + 124320*a^6*b^3*c^8*d^2*e^5 - 2520*a*b^9*c^7*d^6*e - (315*a*b^14*c^2*d*e^6)/64 - 129024*a^5*b*c^11*d^6*e + 3150*a*b^10*c^6*d^5*e^2 - 1575*a*b^11*c^5*d^4*e^3 + (2695*a*b^12*c^4*d^3*e^4)/16 + (1995*a*b^13*c^3*d^2*e^5)/32 + 20160*a^2*b^7*c^8*d^6*e + (105*a^2*b^12*c^3*d*e^6)/16 - 80640*a^3*b^5*c^9*d^6*e + (2625*a^3*b^10*c^4*d*e^6)/4 + 161280*a^4*b^3*c^10*d^6*e - 6615*a^4*b^8*c^5*d*e^6 + 27132*a^5*b^6*c^6*d*e^6 - 268800*a^6*b*c^10*d^4*e^3 - 48720*a^6*b^4*c^7*d*e^6 - 147840*a^7*b*c^9*d^2*e^5 + 20160*a^7*b^2*c^8*d*e^6)/(c^3*(4*a*c - b^2)^10))^(1/2) - ((d + e*x)^(1/2)*(b^8*e^10 + 800*a^4*c^4*e^10 + 4608*c^8*d^8*e^2 + 13440*a*c^7*d^6*e^4 - 18432*b*c^7*d^7*e^3 + 314*a^2*b^4*c^2*e^10 + 208*a^3*b^2*c^3*e^10 + 12320*a^2*c^6*d^4*e^6 + 4032*a^3*c^5*d^2*e^8 + 28896*b^2*c^6*d^6*e^4 - 22176*b^3*c^5*d^5*e^5 + 8330*b^4*c^4*d^4*e^6 - 1204*b^5*c^3*d^3*e^7 - 42*b^6*c^2*d^2*e^8 - 36*a*b^6*c*e^10 + 20*b^7*c*d*e^9 + 15456*a^2*b^2*c^4*d^2*e^8 - 40320*a*b*c^6*d^5*e^5 - 196*a*b^5*c^2*d*e^9 - 4032*a^3*b*c^4*d*e^9 + 44240*a*b^2*c^5*d^4*e^6 - 21280*a*b^3*c^4*d^3*e^7 + 4116*a*b^4*c^3*d^2*e^8 - 24640*a^2*b*c^5*d^3*e^7 - 3136*a^2*b^3*c^3*d*e^9))/(8*c*(4*a*c - b^2)^4))*(-((b^17*e^7)/128 + 36864*a^5*c^12*d^7 - 36*b^10*c^7*d^7 + (b^2*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + 720*a*b^8*c^8*d^7 - 13440*a^8*b*c^8*e^7 + 26880*a^8*c^9*d*e^6 + 126*b^11*c^6*d^6*e - 5760*a^2*b^6*c^9*d^7 + 23040*a^3*b^4*c^10*d^7 - 46080*a^4*b^2*c^11*d^7 + (285*a^2*b^13*c^2*e^7)/32 - (635*a^3*b^11*c^3*e^7)/8 + (545*a^4*b^9*c^4*e^7)/2 + 342*a^5*b^7*c^5*e^7 - 5320*a^6*b^5*c^6*e^7 + 14560*a^7*b^3*c^7*e^7 + 107520*a^6*c^11*d^5*e^2 + 98560*a^7*c^10*d^3*e^4 - (651*b^12*c^5*d^5*e^2)/4 + (735*b^13*c^4*d^4*e^3)/8 - (1225*b^14*c^3*d^3*e^4)/64 - (21*b^15*c^2*d^2*e^5)/128 - (21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (55*a*b^15*c*e^7)/128 - (25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + (21*b^16*c*d*e^6)/128 + (21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2))/128 - 23940*a^2*b^8*c^7*d^5*e^2 + 9450*a^2*b^9*c^6*d^4*e^3 + (4515*a^2*b^10*c^5*d^3*e^4)/4 - (8505*a^2*b^11*c^4*d^2*e^5)/8 + 87360*a^3*b^6*c^8*d^5*e^2 - 16800*a^3*b^7*c^7*d^4*e^3 - 20125*a^3*b^8*c^6*d^3*e^4 + (13335*a^3*b^9*c^5*d^2*e^5)/2 - 141120*a^4*b^4*c^9*d^5*e^2 - 50400*a^4*b^5*c^8*d^4*e^3 + 97300*a^4*b^6*c^7*d^3*e^4 - 14910*a^4*b^7*c^6*d^2*e^5 + 32256*a^5*b^2*c^10*d^5*e^2 + 241920*a^5*b^3*c^9*d^4*e^3 - 193200*a^5*b^4*c^8*d^3*e^4 - 16632*a^5*b^5*c^7*d^2*e^5 + 96320*a^6*b^2*c^9*d^3*e^4 + 124320*a^6*b^3*c^8*d^2*e^5 - 2520*a*b^9*c^7*d^6*e - (315*a*b^14*c^2*d*e^6)/64 - 129024*a^5*b*c^11*d^6*e + 3150*a*b^10*c^6*d^5*e^2 - 1575*a*b^11*c^5*d^4*e^3 + (2695*a*b^12*c^4*d^3*e^4)/16 + (1995*a*b^13*c^3*d^2*e^5)/32 + 20160*a^2*b^7*c^8*d^6*e + (105*a^2*b^12*c^3*d*e^6)/16 - 80640*a^3*b^5*c^9*d^6*e + (2625*a^3*b^10*c^4*d*e^6)/4 + 161280*a^4*b^3*c^10*d^6*e - 6615*a^4*b^8*c^5*d*e^6 + 27132*a^5*b^6*c^6*d*e^6 - 268800*a^6*b*c^10*d^4*e^3 - 48720*a^6*b^4*c^7*d*e^6 - 147840*a^7*b*c^9*d^2*e^5 + 20160*a^7*b^2*c^8*d*e^6)/(c^3*(4*a*c - b^2)^10))^(1/2))*(-((b^17*e^7)/128 + 36864*a^5*c^12*d^7 - 36*b^10*c^7*d^7 + (b^2*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + 720*a*b^8*c^8*d^7 - 13440*a^8*b*c^8*e^7 + 26880*a^8*c^9*d*e^6 + 126*b^11*c^6*d^6*e - 5760*a^2*b^6*c^9*d^7 + 23040*a^3*b^4*c^10*d^7 - 46080*a^4*b^2*c^11*d^7 + (285*a^2*b^13*c^2*e^7)/32 - (635*a^3*b^11*c^3*e^7)/8 + (545*a^4*b^9*c^4*e^7)/2 + 342*a^5*b^7*c^5*e^7 - 5320*a^6*b^5*c^6*e^7 + 14560*a^7*b^3*c^7*e^7 + 107520*a^6*c^11*d^5*e^2 + 98560*a^7*c^10*d^3*e^4 - (651*b^12*c^5*d^5*e^2)/4 + (735*b^13*c^4*d^4*e^3)/8 - (1225*b^14*c^3*d^3*e^4)/64 - (21*b^15*c^2*d^2*e^5)/128 - (21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (55*a*b^15*c*e^7)/128 - (25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + (21*b^16*c*d*e^6)/128 + (21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2))/128 - 23940*a^2*b^8*c^7*d^5*e^2 + 9450*a^2*b^9*c^6*d^4*e^3 + (4515*a^2*b^10*c^5*d^3*e^4)/4 - (8505*a^2*b^11*c^4*d^2*e^5)/8 + 87360*a^3*b^6*c^8*d^5*e^2 - 16800*a^3*b^7*c^7*d^4*e^3 - 20125*a^3*b^8*c^6*d^3*e^4 + (13335*a^3*b^9*c^5*d^2*e^5)/2 - 141120*a^4*b^4*c^9*d^5*e^2 - 50400*a^4*b^5*c^8*d^4*e^3 + 97300*a^4*b^6*c^7*d^3*e^4 - 14910*a^4*b^7*c^6*d^2*e^5 + 32256*a^5*b^2*c^10*d^5*e^2 + 241920*a^5*b^3*c^9*d^4*e^3 - 193200*a^5*b^4*c^8*d^3*e^4 - 16632*a^5*b^5*c^7*d^2*e^5 + 96320*a^6*b^2*c^9*d^3*e^4 + 124320*a^6*b^3*c^8*d^2*e^5 - 2520*a*b^9*c^7*d^6*e - (315*a*b^14*c^2*d*e^6)/64 - 129024*a^5*b*c^11*d^6*e + 3150*a*b^10*c^6*d^5*e^2 - 1575*a*b^11*c^5*d^4*e^3 + (2695*a*b^12*c^4*d^3*e^4)/16 + (1995*a*b^13*c^3*d^2*e^5)/32 + 20160*a^2*b^7*c^8*d^6*e + (105*a^2*b^12*c^3*d*e^6)/16 - 80640*a^3*b^5*c^9*d^6*e + (2625*a^3*b^10*c^4*d*e^6)/4 + 161280*a^4*b^3*c^10*d^6*e - 6615*a^4*b^8*c^5*d*e^6 + 27132*a^5*b^6*c^6*d*e^6 - 268800*a^6*b*c^10*d^4*e^3 - 48720*a^6*b^4*c^7*d*e^6 - 147840*a^7*b*c^9*d^2*e^5 + 20160*a^7*b^2*c^8*d*e^6)/(1048576*a^10*c^13 + b^20*c^3 - 40*a*b^18*c^4 + 720*a^2*b^16*c^5 - 7680*a^3*b^14*c^6 + 53760*a^4*b^12*c^7 - 258048*a^5*b^10*c^8 + 860160*a^6*b^8*c^9 - 1966080*a^7*b^6*c^10 + 2949120*a^8*b^4*c^11 - 2621440*a^9*b^2*c^12))^(1/2) - (((d + e*x)^(1/2)*(20*a^3*c*e^7 + 24*c^4*d^6*e + a^2*b^2*e^7 + b^4*d^2*e^5 + 68*a*c^3*d^4*e^3 - 72*b*c^3*d^5*e^2 - 26*b^3*c*d^3*e^4 + 64*a^2*c^2*d^2*e^5 + 73*b^2*c^2*d^4*e^3 - 2*a*b^3*d*e^6 - 64*a^2*b*c*d*e^6 - 136*a*b*c^2*d^3*e^4 + 70*a*b^2*c*d^2*e^5))/(4*c*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) - ((d + e*x)^(3/2)*(b^4*d*e^5 - a*b^3*e^6 + 36*c^4*d^5*e + 64*a*c^3*d^3*e^3 + 28*a^2*c^2*d*e^5 - 90*b*c^3*d^4*e^2 - 21*b^3*c*d^2*e^4 + 74*b^2*c^2*d^3*e^3 - 14*a^2*b*c*e^6 + 34*a*b^2*c*d*e^5 - 96*a*b*c^2*d^2*e^4))/(2*c*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) - (e*(d + e*x)^(7/2)*(b^3*e^3 + 24*c^3*d^3 - 16*a*b*c*e^3 + 32*a*c^2*d*e^2 - 36*b*c^2*d^2*e + 10*b^2*c*d*e^2))/(4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (e*(d + e*x)^(5/2)*(b^4*e^4 + 72*c^4*d^4 + 36*a^2*c^2*e^4 + 92*a*c^3*d^2*e^2 + 85*b^2*c^2*d^2*e^2 + 5*a*b^2*c*e^4 - 144*b*c^3*d^3*e - 13*b^3*c*d*e^3 - 92*a*b*c^2*d*e^3))/(4*c*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))/(c^2*(d + e*x)^4 - (d + e*x)*(4*c^2*d^3 + 2*b^2*d*e^2 - 2*a*b*e^3 + 4*a*c*d*e^2 - 6*b*c*d^2*e) - (4*c^2*d - 2*b*c*e)*(d + e*x)^3 + (d + e*x)^2*(b^2*e^2 + 6*c^2*d^2 + 2*a*c*e^2 - 6*b*c*d*e) + a^2*e^4 + c^2*d^4 + b^2*d^2*e^2 - 2*a*b*d*e^3 - 2*b*c*d^3*e + 2*a*c*d^2*e^2) - log((e^3*(b*e - 2*c*d)*(a*e^2 + c*d^2 - b*d*e)^2*(35*b^6*e^6 + 27648*c^6*d^6 + 6400*a^3*c^3*e^6 + 76032*a*c^5*d^4*e^2 + 9456*a^2*b^2*c^2*e^6 + 57024*a^2*c^4*d^2*e^4 + 84672*b^2*c^4*d^4*e^2 - 31104*b^3*c^3*d^3*e^3 + 972*b^4*c^2*d^2*e^4 - 1176*a*b^4*c*e^6 - 82944*b*c^5*d^5*e + 756*b^5*c*d*e^5 - 152064*a*b*c^4*d^3*e^3 - 9504*a*b^3*c^2*d*e^5 - 57024*a^2*b*c^3*d*e^5 + 85536*a*b^2*c^3*d^2*e^4))/(64*c*(4*a*c - b^2)^6) - (((c*e^3*(24*c^3*d^4 + a*b^2*e^4 + 20*a^2*c*e^4 - b^3*d*e^3 + 44*a*c^2*d^2*e^2 + 25*b^2*c*d^2*e^2 - 48*b*c^2*d^3*e - 44*a*b*c*d*e^3))/(4*a*c - b^2) + 8*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(-((b^17*e^7)/128 + 36864*a^5*c^12*d^7 - 36*b^10*c^7*d^7 - (b^2*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + 720*a*b^8*c^8*d^7 - 13440*a^8*b*c^8*e^7 + 26880*a^8*c^9*d*e^6 + 126*b^11*c^6*d^6*e - 5760*a^2*b^6*c^9*d^7 + 23040*a^3*b^4*c^10*d^7 - 46080*a^4*b^2*c^11*d^7 + (285*a^2*b^13*c^2*e^7)/32 - (635*a^3*b^11*c^3*e^7)/8 + (545*a^4*b^9*c^4*e^7)/2 + 342*a^5*b^7*c^5*e^7 - 5320*a^6*b^5*c^6*e^7 + 14560*a^7*b^3*c^7*e^7 + 107520*a^6*c^11*d^5*e^2 + 98560*a^7*c^10*d^3*e^4 - (651*b^12*c^5*d^5*e^2)/4 + (735*b^13*c^4*d^4*e^3)/8 - (1225*b^14*c^3*d^3*e^4)/64 - (21*b^15*c^2*d^2*e^5)/128 + (21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (55*a*b^15*c*e^7)/128 + (25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + (21*b^16*c*d*e^6)/128 - (21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2))/128 - 23940*a^2*b^8*c^7*d^5*e^2 + 9450*a^2*b^9*c^6*d^4*e^3 + (4515*a^2*b^10*c^5*d^3*e^4)/4 - (8505*a^2*b^11*c^4*d^2*e^5)/8 + 87360*a^3*b^6*c^8*d^5*e^2 - 16800*a^3*b^7*c^7*d^4*e^3 - 20125*a^3*b^8*c^6*d^3*e^4 + (13335*a^3*b^9*c^5*d^2*e^5)/2 - 141120*a^4*b^4*c^9*d^5*e^2 - 50400*a^4*b^5*c^8*d^4*e^3 + 97300*a^4*b^6*c^7*d^3*e^4 - 14910*a^4*b^7*c^6*d^2*e^5 + 32256*a^5*b^2*c^10*d^5*e^2 + 241920*a^5*b^3*c^9*d^4*e^3 - 193200*a^5*b^4*c^8*d^3*e^4 - 16632*a^5*b^5*c^7*d^2*e^5 + 96320*a^6*b^2*c^9*d^3*e^4 + 124320*a^6*b^3*c^8*d^2*e^5 - 2520*a*b^9*c^7*d^6*e - (315*a*b^14*c^2*d*e^6)/64 - 129024*a^5*b*c^11*d^6*e + 3150*a*b^10*c^6*d^5*e^2 - 1575*a*b^11*c^5*d^4*e^3 + (2695*a*b^12*c^4*d^3*e^4)/16 + (1995*a*b^13*c^3*d^2*e^5)/32 + 20160*a^2*b^7*c^8*d^6*e + (105*a^2*b^12*c^3*d*e^6)/16 - 80640*a^3*b^5*c^9*d^6*e + (2625*a^3*b^10*c^4*d*e^6)/4 + 161280*a^4*b^3*c^10*d^6*e - 6615*a^4*b^8*c^5*d*e^6 + 27132*a^5*b^6*c^6*d*e^6 - 268800*a^6*b*c^10*d^4*e^3 - 48720*a^6*b^4*c^7*d*e^6 - 147840*a^7*b*c^9*d^2*e^5 + 20160*a^7*b^2*c^8*d*e^6)/(c^3*(4*a*c - b^2)^10))^(1/2))*(-((b^17*e^7)/128 + 36864*a^5*c^12*d^7 - 36*b^10*c^7*d^7 - (b^2*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + 720*a*b^8*c^8*d^7 - 13440*a^8*b*c^8*e^7 + 26880*a^8*c^9*d*e^6 + 126*b^11*c^6*d^6*e - 5760*a^2*b^6*c^9*d^7 + 23040*a^3*b^4*c^10*d^7 - 46080*a^4*b^2*c^11*d^7 + (285*a^2*b^13*c^2*e^7)/32 - (635*a^3*b^11*c^3*e^7)/8 + (545*a^4*b^9*c^4*e^7)/2 + 342*a^5*b^7*c^5*e^7 - 5320*a^6*b^5*c^6*e^7 + 14560*a^7*b^3*c^7*e^7 + 107520*a^6*c^11*d^5*e^2 + 98560*a^7*c^10*d^3*e^4 - (651*b^12*c^5*d^5*e^2)/4 + (735*b^13*c^4*d^4*e^3)/8 - (1225*b^14*c^3*d^3*e^4)/64 - (21*b^15*c^2*d^2*e^5)/128 + (21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (55*a*b^15*c*e^7)/128 + (25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + (21*b^16*c*d*e^6)/128 - (21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2))/128 - 23940*a^2*b^8*c^7*d^5*e^2 + 9450*a^2*b^9*c^6*d^4*e^3 + (4515*a^2*b^10*c^5*d^3*e^4)/4 - (8505*a^2*b^11*c^4*d^2*e^5)/8 + 87360*a^3*b^6*c^8*d^5*e^2 - 16800*a^3*b^7*c^7*d^4*e^3 - 20125*a^3*b^8*c^6*d^3*e^4 + (13335*a^3*b^9*c^5*d^2*e^5)/2 - 141120*a^4*b^4*c^9*d^5*e^2 - 50400*a^4*b^5*c^8*d^4*e^3 + 97300*a^4*b^6*c^7*d^3*e^4 - 14910*a^4*b^7*c^6*d^2*e^5 + 32256*a^5*b^2*c^10*d^5*e^2 + 241920*a^5*b^3*c^9*d^4*e^3 - 193200*a^5*b^4*c^8*d^3*e^4 - 16632*a^5*b^5*c^7*d^2*e^5 + 96320*a^6*b^2*c^9*d^3*e^4 + 124320*a^6*b^3*c^8*d^2*e^5 - 2520*a*b^9*c^7*d^6*e - (315*a*b^14*c^2*d*e^6)/64 - 129024*a^5*b*c^11*d^6*e + 3150*a*b^10*c^6*d^5*e^2 - 1575*a*b^11*c^5*d^4*e^3 + (2695*a*b^12*c^4*d^3*e^4)/16 + (1995*a*b^13*c^3*d^2*e^5)/32 + 20160*a^2*b^7*c^8*d^6*e + (105*a^2*b^12*c^3*d*e^6)/16 - 80640*a^3*b^5*c^9*d^6*e + (2625*a^3*b^10*c^4*d*e^6)/4 + 161280*a^4*b^3*c^10*d^6*e - 6615*a^4*b^8*c^5*d*e^6 + 27132*a^5*b^6*c^6*d*e^6 - 268800*a^6*b*c^10*d^4*e^3 - 48720*a^6*b^4*c^7*d*e^6 - 147840*a^7*b*c^9*d^2*e^5 + 20160*a^7*b^2*c^8*d*e^6)/(c^3*(4*a*c - b^2)^10))^(1/2) - ((d + e*x)^(1/2)*(b^8*e^10 + 800*a^4*c^4*e^10 + 4608*c^8*d^8*e^2 + 13440*a*c^7*d^6*e^4 - 18432*b*c^7*d^7*e^3 + 314*a^2*b^4*c^2*e^10 + 208*a^3*b^2*c^3*e^10 + 12320*a^2*c^6*d^4*e^6 + 4032*a^3*c^5*d^2*e^8 + 28896*b^2*c^6*d^6*e^4 - 22176*b^3*c^5*d^5*e^5 + 8330*b^4*c^4*d^4*e^6 - 1204*b^5*c^3*d^3*e^7 - 42*b^6*c^2*d^2*e^8 - 36*a*b^6*c*e^10 + 20*b^7*c*d*e^9 + 15456*a^2*b^2*c^4*d^2*e^8 - 40320*a*b*c^6*d^5*e^5 - 196*a*b^5*c^2*d*e^9 - 4032*a^3*b*c^4*d*e^9 + 44240*a*b^2*c^5*d^4*e^6 - 21280*a*b^3*c^4*d^3*e^7 + 4116*a*b^4*c^3*d^2*e^8 - 24640*a^2*b*c^5*d^3*e^7 - 3136*a^2*b^3*c^3*d*e^9))/(8*c*(4*a*c - b^2)^4))*(-((b^17*e^7)/128 + 36864*a^5*c^12*d^7 - 36*b^10*c^7*d^7 - (b^2*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + 720*a*b^8*c^8*d^7 - 13440*a^8*b*c^8*e^7 + 26880*a^8*c^9*d*e^6 + 126*b^11*c^6*d^6*e - 5760*a^2*b^6*c^9*d^7 + 23040*a^3*b^4*c^10*d^7 - 46080*a^4*b^2*c^11*d^7 + (285*a^2*b^13*c^2*e^7)/32 - (635*a^3*b^11*c^3*e^7)/8 + (545*a^4*b^9*c^4*e^7)/2 + 342*a^5*b^7*c^5*e^7 - 5320*a^6*b^5*c^6*e^7 + 14560*a^7*b^3*c^7*e^7 + 107520*a^6*c^11*d^5*e^2 + 98560*a^7*c^10*d^3*e^4 - (651*b^12*c^5*d^5*e^2)/4 + (735*b^13*c^4*d^4*e^3)/8 - (1225*b^14*c^3*d^3*e^4)/64 - (21*b^15*c^2*d^2*e^5)/128 + (21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (55*a*b^15*c*e^7)/128 + (25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + (21*b^16*c*d*e^6)/128 - (21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2))/128 - 23940*a^2*b^8*c^7*d^5*e^2 + 9450*a^2*b^9*c^6*d^4*e^3 + (4515*a^2*b^10*c^5*d^3*e^4)/4 - (8505*a^2*b^11*c^4*d^2*e^5)/8 + 87360*a^3*b^6*c^8*d^5*e^2 - 16800*a^3*b^7*c^7*d^4*e^3 - 20125*a^3*b^8*c^6*d^3*e^4 + (13335*a^3*b^9*c^5*d^2*e^5)/2 - 141120*a^4*b^4*c^9*d^5*e^2 - 50400*a^4*b^5*c^8*d^4*e^3 + 97300*a^4*b^6*c^7*d^3*e^4 - 14910*a^4*b^7*c^6*d^2*e^5 + 32256*a^5*b^2*c^10*d^5*e^2 + 241920*a^5*b^3*c^9*d^4*e^3 - 193200*a^5*b^4*c^8*d^3*e^4 - 16632*a^5*b^5*c^7*d^2*e^5 + 96320*a^6*b^2*c^9*d^3*e^4 + 124320*a^6*b^3*c^8*d^2*e^5 - 2520*a*b^9*c^7*d^6*e - (315*a*b^14*c^2*d*e^6)/64 - 129024*a^5*b*c^11*d^6*e + 3150*a*b^10*c^6*d^5*e^2 - 1575*a*b^11*c^5*d^4*e^3 + (2695*a*b^12*c^4*d^3*e^4)/16 + (1995*a*b^13*c^3*d^2*e^5)/32 + 20160*a^2*b^7*c^8*d^6*e + (105*a^2*b^12*c^3*d*e^6)/16 - 80640*a^3*b^5*c^9*d^6*e + (2625*a^3*b^10*c^4*d*e^6)/4 + 161280*a^4*b^3*c^10*d^6*e - 6615*a^4*b^8*c^5*d*e^6 + 27132*a^5*b^6*c^6*d*e^6 - 268800*a^6*b*c^10*d^4*e^3 - 48720*a^6*b^4*c^7*d*e^6 - 147840*a^7*b*c^9*d^2*e^5 + 20160*a^7*b^2*c^8*d*e^6)/(c^3*(4*a*c - b^2)^10))^(1/2))*(-((b^17*e^7)/128 + 36864*a^5*c^12*d^7 - 36*b^10*c^7*d^7 - (b^2*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + 720*a*b^8*c^8*d^7 - 13440*a^8*b*c^8*e^7 + 26880*a^8*c^9*d*e^6 + 126*b^11*c^6*d^6*e - 5760*a^2*b^6*c^9*d^7 + 23040*a^3*b^4*c^10*d^7 - 46080*a^4*b^2*c^11*d^7 + (285*a^2*b^13*c^2*e^7)/32 - (635*a^3*b^11*c^3*e^7)/8 + (545*a^4*b^9*c^4*e^7)/2 + 342*a^5*b^7*c^5*e^7 - 5320*a^6*b^5*c^6*e^7 + 14560*a^7*b^3*c^7*e^7 + 107520*a^6*c^11*d^5*e^2 + 98560*a^7*c^10*d^3*e^4 - (651*b^12*c^5*d^5*e^2)/4 + (735*b^13*c^4*d^4*e^3)/8 - (1225*b^14*c^3*d^3*e^4)/64 - (21*b^15*c^2*d^2*e^5)/128 + (21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (55*a*b^15*c*e^7)/128 + (25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + (21*b^16*c*d*e^6)/128 - (21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2))/128 - 23940*a^2*b^8*c^7*d^5*e^2 + 9450*a^2*b^9*c^6*d^4*e^3 + (4515*a^2*b^10*c^5*d^3*e^4)/4 - (8505*a^2*b^11*c^4*d^2*e^5)/8 + 87360*a^3*b^6*c^8*d^5*e^2 - 16800*a^3*b^7*c^7*d^4*e^3 - 20125*a^3*b^8*c^6*d^3*e^4 + (13335*a^3*b^9*c^5*d^2*e^5)/2 - 141120*a^4*b^4*c^9*d^5*e^2 - 50400*a^4*b^5*c^8*d^4*e^3 + 97300*a^4*b^6*c^7*d^3*e^4 - 14910*a^4*b^7*c^6*d^2*e^5 + 32256*a^5*b^2*c^10*d^5*e^2 + 241920*a^5*b^3*c^9*d^4*e^3 - 193200*a^5*b^4*c^8*d^3*e^4 - 16632*a^5*b^5*c^7*d^2*e^5 + 96320*a^6*b^2*c^9*d^3*e^4 + 124320*a^6*b^3*c^8*d^2*e^5 - 2520*a*b^9*c^7*d^6*e - (315*a*b^14*c^2*d*e^6)/64 - 129024*a^5*b*c^11*d^6*e + 3150*a*b^10*c^6*d^5*e^2 - 1575*a*b^11*c^5*d^4*e^3 + (2695*a*b^12*c^4*d^3*e^4)/16 + (1995*a*b^13*c^3*d^2*e^5)/32 + 20160*a^2*b^7*c^8*d^6*e + (105*a^2*b^12*c^3*d*e^6)/16 - 80640*a^3*b^5*c^9*d^6*e + (2625*a^3*b^10*c^4*d*e^6)/4 + 161280*a^4*b^3*c^10*d^6*e - 6615*a^4*b^8*c^5*d*e^6 + 27132*a^5*b^6*c^6*d*e^6 - 268800*a^6*b*c^10*d^4*e^3 - 48720*a^6*b^4*c^7*d*e^6 - 147840*a^7*b*c^9*d^2*e^5 + 20160*a^7*b^2*c^8*d*e^6)/(1048576*a^10*c^13 + b^20*c^3 - 40*a*b^18*c^4 + 720*a^2*b^16*c^5 - 7680*a^3*b^14*c^6 + 53760*a^4*b^12*c^7 - 258048*a^5*b^10*c^8 + 860160*a^6*b^8*c^9 - 1966080*a^7*b^6*c^10 + 2949120*a^8*b^4*c^11 - 2621440*a^9*b^2*c^12))^(1/2) + log((e^3*(b*e - 2*c*d)*(a*e^2 + c*d^2 - b*d*e)^2*(35*b^6*e^6 + 27648*c^6*d^6 + 6400*a^3*c^3*e^6 + 76032*a*c^5*d^4*e^2 + 9456*a^2*b^2*c^2*e^6 + 57024*a^2*c^4*d^2*e^4 + 84672*b^2*c^4*d^4*e^2 - 31104*b^3*c^3*d^3*e^3 + 972*b^4*c^2*d^2*e^4 - 1176*a*b^4*c*e^6 - 82944*b*c^5*d^5*e + 756*b^5*c*d*e^5 - 152064*a*b*c^4*d^3*e^3 - 9504*a*b^3*c^2*d*e^5 - 57024*a^2*b*c^3*d*e^5 + 85536*a*b^2*c^3*d^2*e^4))/(64*c*(4*a*c - b^2)^6) - (2^(1/2)*((2^(1/2)*((c*e^3*(24*c^3*d^4 + a*b^2*e^4 + 20*a^2*c*e^4 - b^3*d*e^3 + 44*a*c^2*d^2*e^2 + 25*b^2*c*d^2*e^2 - 48*b*c^2*d^3*e - 44*a*b*c*d*e^3))/(4*a*c - b^2) - (2^(1/2)*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(-(b^17*e^7 + 4718592*a^5*c^12*d^7 - 4608*b^10*c^7*d^7 - b^2*e^7*(-(4*a*c - b^2)^15)^(1/2) + 92160*a*b^8*c^8*d^7 - 1720320*a^8*b*c^8*e^7 + 3440640*a^8*c^9*d*e^6 + 16128*b^11*c^6*d^6*e - 737280*a^2*b^6*c^9*d^7 + 2949120*a^3*b^4*c^10*d^7 - 5898240*a^4*b^2*c^11*d^7 + 1140*a^2*b^13*c^2*e^7 - 10160*a^3*b^11*c^3*e^7 + 34880*a^4*b^9*c^4*e^7 + 43776*a^5*b^7*c^5*e^7 - 680960*a^6*b^5*c^6*e^7 + 1863680*a^7*b^3*c^7*e^7 + 13762560*a^6*c^11*d^5*e^2 + 12615680*a^7*c^10*d^3*e^4 - 20832*b^12*c^5*d^5*e^2 + 11760*b^13*c^4*d^4*e^3 - 2450*b^14*c^3*d^3*e^4 - 21*b^15*c^2*d^2*e^5 + 21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2) - 55*a*b^15*c*e^7 + 25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2) + 21*b^16*c*d*e^6 - 21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2) - 3064320*a^2*b^8*c^7*d^5*e^2 + 1209600*a^2*b^9*c^6*d^4*e^3 + 144480*a^2*b^10*c^5*d^3*e^4 - 136080*a^2*b^11*c^4*d^2*e^5 + 11182080*a^3*b^6*c^8*d^5*e^2 - 2150400*a^3*b^7*c^7*d^4*e^3 - 2576000*a^3*b^8*c^6*d^3*e^4 + 853440*a^3*b^9*c^5*d^2*e^5 - 18063360*a^4*b^4*c^9*d^5*e^2 - 6451200*a^4*b^5*c^8*d^4*e^3 + 12454400*a^4*b^6*c^7*d^3*e^4 - 1908480*a^4*b^7*c^6*d^2*e^5 + 4128768*a^5*b^2*c^10*d^5*e^2 + 30965760*a^5*b^3*c^9*d^4*e^3 - 24729600*a^5*b^4*c^8*d^3*e^4 - 2128896*a^5*b^5*c^7*d^2*e^5 + 12328960*a^6*b^2*c^9*d^3*e^4 + 15912960*a^6*b^3*c^8*d^2*e^5 - 322560*a*b^9*c^7*d^6*e - 630*a*b^14*c^2*d*e^6 - 16515072*a^5*b*c^11*d^6*e + 403200*a*b^10*c^6*d^5*e^2 - 201600*a*b^11*c^5*d^4*e^3 + 21560*a*b^12*c^4*d^3*e^4 + 7980*a*b^13*c^3*d^2*e^5 + 2580480*a^2*b^7*c^8*d^6*e + 840*a^2*b^12*c^3*d*e^6 - 10321920*a^3*b^5*c^9*d^6*e + 84000*a^3*b^10*c^4*d*e^6 + 20643840*a^4*b^3*c^10*d^6*e - 846720*a^4*b^8*c^5*d*e^6 + 3472896*a^5*b^6*c^6*d*e^6 - 34406400*a^6*b*c^10*d^4*e^3 - 6236160*a^6*b^4*c^7*d*e^6 - 18923520*a^7*b*c^9*d^2*e^5 + 2580480*a^7*b^2*c^8*d*e^6)/(c^3*(4*a*c - b^2)^10))^(1/2))/2)*(-(b^17*e^7 + 4718592*a^5*c^12*d^7 - 4608*b^10*c^7*d^7 - b^2*e^7*(-(4*a*c - b^2)^15)^(1/2) + 92160*a*b^8*c^8*d^7 - 1720320*a^8*b*c^8*e^7 + 3440640*a^8*c^9*d*e^6 + 16128*b^11*c^6*d^6*e - 737280*a^2*b^6*c^9*d^7 + 2949120*a^3*b^4*c^10*d^7 - 5898240*a^4*b^2*c^11*d^7 + 1140*a^2*b^13*c^2*e^7 - 10160*a^3*b^11*c^3*e^7 + 34880*a^4*b^9*c^4*e^7 + 43776*a^5*b^7*c^5*e^7 - 680960*a^6*b^5*c^6*e^7 + 1863680*a^7*b^3*c^7*e^7 + 13762560*a^6*c^11*d^5*e^2 + 12615680*a^7*c^10*d^3*e^4 - 20832*b^12*c^5*d^5*e^2 + 11760*b^13*c^4*d^4*e^3 - 2450*b^14*c^3*d^3*e^4 - 21*b^15*c^2*d^2*e^5 + 21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2) - 55*a*b^15*c*e^7 + 25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2) + 21*b^16*c*d*e^6 - 21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2) - 3064320*a^2*b^8*c^7*d^5*e^2 + 1209600*a^2*b^9*c^6*d^4*e^3 + 144480*a^2*b^10*c^5*d^3*e^4 - 136080*a^2*b^11*c^4*d^2*e^5 + 11182080*a^3*b^6*c^8*d^5*e^2 - 2150400*a^3*b^7*c^7*d^4*e^3 - 2576000*a^3*b^8*c^6*d^3*e^4 + 853440*a^3*b^9*c^5*d^2*e^5 - 18063360*a^4*b^4*c^9*d^5*e^2 - 6451200*a^4*b^5*c^8*d^4*e^3 + 12454400*a^4*b^6*c^7*d^3*e^4 - 1908480*a^4*b^7*c^6*d^2*e^5 + 4128768*a^5*b^2*c^10*d^5*e^2 + 30965760*a^5*b^3*c^9*d^4*e^3 - 24729600*a^5*b^4*c^8*d^3*e^4 - 2128896*a^5*b^5*c^7*d^2*e^5 + 12328960*a^6*b^2*c^9*d^3*e^4 + 15912960*a^6*b^3*c^8*d^2*e^5 - 322560*a*b^9*c^7*d^6*e - 630*a*b^14*c^2*d*e^6 - 16515072*a^5*b*c^11*d^6*e + 403200*a*b^10*c^6*d^5*e^2 - 201600*a*b^11*c^5*d^4*e^3 + 21560*a*b^12*c^4*d^3*e^4 + 7980*a*b^13*c^3*d^2*e^5 + 2580480*a^2*b^7*c^8*d^6*e + 840*a^2*b^12*c^3*d*e^6 - 10321920*a^3*b^5*c^9*d^6*e + 84000*a^3*b^10*c^4*d*e^6 + 20643840*a^4*b^3*c^10*d^6*e - 846720*a^4*b^8*c^5*d*e^6 + 3472896*a^5*b^6*c^6*d*e^6 - 34406400*a^6*b*c^10*d^4*e^3 - 6236160*a^6*b^4*c^7*d*e^6 - 18923520*a^7*b*c^9*d^2*e^5 + 2580480*a^7*b^2*c^8*d*e^6)/(c^3*(4*a*c - b^2)^10))^(1/2))/16 + ((d + e*x)^(1/2)*(b^8*e^10 + 800*a^4*c^4*e^10 + 4608*c^8*d^8*e^2 + 13440*a*c^7*d^6*e^4 - 18432*b*c^7*d^7*e^3 + 314*a^2*b^4*c^2*e^10 + 208*a^3*b^2*c^3*e^10 + 12320*a^2*c^6*d^4*e^6 + 4032*a^3*c^5*d^2*e^8 + 28896*b^2*c^6*d^6*e^4 - 22176*b^3*c^5*d^5*e^5 + 8330*b^4*c^4*d^4*e^6 - 1204*b^5*c^3*d^3*e^7 - 42*b^6*c^2*d^2*e^8 - 36*a*b^6*c*e^10 + 20*b^7*c*d*e^9 + 15456*a^2*b^2*c^4*d^2*e^8 - 40320*a*b*c^6*d^5*e^5 - 196*a*b^5*c^2*d*e^9 - 4032*a^3*b*c^4*d*e^9 + 44240*a*b^2*c^5*d^4*e^6 - 21280*a*b^3*c^4*d^3*e^7 + 4116*a*b^4*c^3*d^2*e^8 - 24640*a^2*b*c^5*d^3*e^7 - 3136*a^2*b^3*c^3*d*e^9))/(8*c*(4*a*c - b^2)^4))*(-(b^17*e^7 + 4718592*a^5*c^12*d^7 - 4608*b^10*c^7*d^7 - b^2*e^7*(-(4*a*c - b^2)^15)^(1/2) + 92160*a*b^8*c^8*d^7 - 1720320*a^8*b*c^8*e^7 + 3440640*a^8*c^9*d*e^6 + 16128*b^11*c^6*d^6*e - 737280*a^2*b^6*c^9*d^7 + 2949120*a^3*b^4*c^10*d^7 - 5898240*a^4*b^2*c^11*d^7 + 1140*a^2*b^13*c^2*e^7 - 10160*a^3*b^11*c^3*e^7 + 34880*a^4*b^9*c^4*e^7 + 43776*a^5*b^7*c^5*e^7 - 680960*a^6*b^5*c^6*e^7 + 1863680*a^7*b^3*c^7*e^7 + 13762560*a^6*c^11*d^5*e^2 + 12615680*a^7*c^10*d^3*e^4 - 20832*b^12*c^5*d^5*e^2 + 11760*b^13*c^4*d^4*e^3 - 2450*b^14*c^3*d^3*e^4 - 21*b^15*c^2*d^2*e^5 + 21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2) - 55*a*b^15*c*e^7 + 25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2) + 21*b^16*c*d*e^6 - 21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2) - 3064320*a^2*b^8*c^7*d^5*e^2 + 1209600*a^2*b^9*c^6*d^4*e^3 + 144480*a^2*b^10*c^5*d^3*e^4 - 136080*a^2*b^11*c^4*d^2*e^5 + 11182080*a^3*b^6*c^8*d^5*e^2 - 2150400*a^3*b^7*c^7*d^4*e^3 - 2576000*a^3*b^8*c^6*d^3*e^4 + 853440*a^3*b^9*c^5*d^2*e^5 - 18063360*a^4*b^4*c^9*d^5*e^2 - 6451200*a^4*b^5*c^8*d^4*e^3 + 12454400*a^4*b^6*c^7*d^3*e^4 - 1908480*a^4*b^7*c^6*d^2*e^5 + 4128768*a^5*b^2*c^10*d^5*e^2 + 30965760*a^5*b^3*c^9*d^4*e^3 - 24729600*a^5*b^4*c^8*d^3*e^4 - 2128896*a^5*b^5*c^7*d^2*e^5 + 12328960*a^6*b^2*c^9*d^3*e^4 + 15912960*a^6*b^3*c^8*d^2*e^5 - 322560*a*b^9*c^7*d^6*e - 630*a*b^14*c^2*d*e^6 - 16515072*a^5*b*c^11*d^6*e + 403200*a*b^10*c^6*d^5*e^2 - 201600*a*b^11*c^5*d^4*e^3 + 21560*a*b^12*c^4*d^3*e^4 + 7980*a*b^13*c^3*d^2*e^5 + 2580480*a^2*b^7*c^8*d^6*e + 840*a^2*b^12*c^3*d*e^6 - 10321920*a^3*b^5*c^9*d^6*e + 84000*a^3*b^10*c^4*d*e^6 + 20643840*a^4*b^3*c^10*d^6*e - 846720*a^4*b^8*c^5*d*e^6 + 3472896*a^5*b^6*c^6*d*e^6 - 34406400*a^6*b*c^10*d^4*e^3 - 6236160*a^6*b^4*c^7*d*e^6 - 18923520*a^7*b*c^9*d^2*e^5 + 2580480*a^7*b^2*c^8*d*e^6)/(c^3*(4*a*c - b^2)^10))^(1/2))/16)*(-(b^17*e^7 + 4718592*a^5*c^12*d^7 - 4608*b^10*c^7*d^7 - b^2*e^7*(-(4*a*c - b^2)^15)^(1/2) + 92160*a*b^8*c^8*d^7 - 1720320*a^8*b*c^8*e^7 + 3440640*a^8*c^9*d*e^6 + 16128*b^11*c^6*d^6*e - 737280*a^2*b^6*c^9*d^7 + 2949120*a^3*b^4*c^10*d^7 - 5898240*a^4*b^2*c^11*d^7 + 1140*a^2*b^13*c^2*e^7 - 10160*a^3*b^11*c^3*e^7 + 34880*a^4*b^9*c^4*e^7 + 43776*a^5*b^7*c^5*e^7 - 680960*a^6*b^5*c^6*e^7 + 1863680*a^7*b^3*c^7*e^7 + 13762560*a^6*c^11*d^5*e^2 + 12615680*a^7*c^10*d^3*e^4 - 20832*b^12*c^5*d^5*e^2 + 11760*b^13*c^4*d^4*e^3 - 2450*b^14*c^3*d^3*e^4 - 21*b^15*c^2*d^2*e^5 + 21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2) - 55*a*b^15*c*e^7 + 25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2) + 21*b^16*c*d*e^6 - 21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2) - 3064320*a^2*b^8*c^7*d^5*e^2 + 1209600*a^2*b^9*c^6*d^4*e^3 + 144480*a^2*b^10*c^5*d^3*e^4 - 136080*a^2*b^11*c^4*d^2*e^5 + 11182080*a^3*b^6*c^8*d^5*e^2 - 2150400*a^3*b^7*c^7*d^4*e^3 - 2576000*a^3*b^8*c^6*d^3*e^4 + 853440*a^3*b^9*c^5*d^2*e^5 - 18063360*a^4*b^4*c^9*d^5*e^2 - 6451200*a^4*b^5*c^8*d^4*e^3 + 12454400*a^4*b^6*c^7*d^3*e^4 - 1908480*a^4*b^7*c^6*d^2*e^5 + 4128768*a^5*b^2*c^10*d^5*e^2 + 30965760*a^5*b^3*c^9*d^4*e^3 - 24729600*a^5*b^4*c^8*d^3*e^4 - 2128896*a^5*b^5*c^7*d^2*e^5 + 12328960*a^6*b^2*c^9*d^3*e^4 + 15912960*a^6*b^3*c^8*d^2*e^5 - 322560*a*b^9*c^7*d^6*e - 630*a*b^14*c^2*d*e^6 - 16515072*a^5*b*c^11*d^6*e + 403200*a*b^10*c^6*d^5*e^2 - 201600*a*b^11*c^5*d^4*e^3 + 21560*a*b^12*c^4*d^3*e^4 + 7980*a*b^13*c^3*d^2*e^5 + 2580480*a^2*b^7*c^8*d^6*e + 840*a^2*b^12*c^3*d*e^6 - 10321920*a^3*b^5*c^9*d^6*e + 84000*a^3*b^10*c^4*d*e^6 + 20643840*a^4*b^3*c^10*d^6*e - 846720*a^4*b^8*c^5*d*e^6 + 3472896*a^5*b^6*c^6*d*e^6 - 34406400*a^6*b*c^10*d^4*e^3 - 6236160*a^6*b^4*c^7*d*e^6 - 18923520*a^7*b*c^9*d^2*e^5 + 2580480*a^7*b^2*c^8*d*e^6)/(128*(1048576*a^10*c^13 + b^20*c^3 - 40*a*b^18*c^4 + 720*a^2*b^16*c^5 - 7680*a^3*b^14*c^6 + 53760*a^4*b^12*c^7 - 258048*a^5*b^10*c^8 + 860160*a^6*b^8*c^9 - 1966080*a^7*b^6*c^10 + 2949120*a^8*b^4*c^11 - 2621440*a^9*b^2*c^12)))^(1/2)","B"
2303,1,13637,577,18.154708,"\text{Not used}","int((d + e*x)^(5/2)/(a + b*x + c*x^2)^3,x)","\ln\left(\frac{3\,\sqrt{2}\,\left(\frac{3\,\sqrt{2}\,\left(\frac{12\,c^2\,e^3\,\left(b\,e-2\,c\,d\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}{4\,a\,c-b^2}+\frac{3\,\sqrt{2}\,c^2\,e^2\,\left(4\,a\,c-b^2\right)\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^{15}\,e^5+e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+524288\,a^5\,c^{10}\,d^5-512\,b^{10}\,c^5\,d^5+10240\,a\,b^8\,c^6\,d^5-81920\,a^7\,b\,c^7\,e^5+163840\,a^7\,c^8\,d\,e^4+1280\,b^{11}\,c^4\,d^4\,e-81920\,a^2\,b^6\,c^7\,d^5+327680\,a^3\,b^4\,c^8\,d^5-655360\,a^4\,b^2\,c^9\,d^5-560\,a^2\,b^{11}\,c^2\,e^5+4160\,a^3\,b^9\,c^3\,e^5-11520\,a^4\,b^7\,c^4\,e^5-1024\,a^5\,b^5\,c^5\,e^5+61440\,a^6\,b^3\,c^6\,e^5+655360\,a^6\,c^9\,d^3\,e^2-1120\,b^{12}\,c^3\,d^3\,e^2+400\,b^{13}\,c^2\,d^2\,e^3+20\,a\,b^{13}\,c\,e^5-50\,b^{14}\,c\,d\,e^4-166400\,a^2\,b^8\,c^5\,d^3\,e^2+44800\,a^2\,b^9\,c^4\,d^2\,e^3+614400\,a^3\,b^6\,c^6\,d^3\,e^2-102400\,a^3\,b^7\,c^5\,d^2\,e^3-1024000\,a^4\,b^4\,c^7\,d^3\,e^2-102400\,a^4\,b^5\,c^6\,d^2\,e^3+327680\,a^5\,b^2\,c^8\,d^3\,e^2+819200\,a^5\,b^3\,c^7\,d^2\,e^3-25600\,a\,b^9\,c^5\,d^4\,e+600\,a\,b^{12}\,c^2\,d\,e^4-1310720\,a^5\,b\,c^9\,d^4\,e+21760\,a\,b^{10}\,c^4\,d^3\,e^2-7040\,a\,b^{11}\,c^3\,d^2\,e^3+204800\,a^2\,b^7\,c^6\,d^4\,e-160\,a^2\,b^{10}\,c^3\,d\,e^4-819200\,a^3\,b^5\,c^7\,d^4\,e-28800\,a^3\,b^8\,c^4\,d\,e^4+1638400\,a^4\,b^3\,c^8\,d^4\,e+166400\,a^4\,b^6\,c^5\,d\,e^4-358400\,a^5\,b^4\,c^6\,d\,e^4-983040\,a^6\,b\,c^8\,d^2\,e^3+204800\,a^6\,b^2\,c^7\,d\,e^4}{c\,{\left(4\,a\,c-b^2\right)}^{10}}}}{2}\right)\,\sqrt{-\frac{b^{15}\,e^5+e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+524288\,a^5\,c^{10}\,d^5-512\,b^{10}\,c^5\,d^5+10240\,a\,b^8\,c^6\,d^5-81920\,a^7\,b\,c^7\,e^5+163840\,a^7\,c^8\,d\,e^4+1280\,b^{11}\,c^4\,d^4\,e-81920\,a^2\,b^6\,c^7\,d^5+327680\,a^3\,b^4\,c^8\,d^5-655360\,a^4\,b^2\,c^9\,d^5-560\,a^2\,b^{11}\,c^2\,e^5+4160\,a^3\,b^9\,c^3\,e^5-11520\,a^4\,b^7\,c^4\,e^5-1024\,a^5\,b^5\,c^5\,e^5+61440\,a^6\,b^3\,c^6\,e^5+655360\,a^6\,c^9\,d^3\,e^2-1120\,b^{12}\,c^3\,d^3\,e^2+400\,b^{13}\,c^2\,d^2\,e^3+20\,a\,b^{13}\,c\,e^5-50\,b^{14}\,c\,d\,e^4-166400\,a^2\,b^8\,c^5\,d^3\,e^2+44800\,a^2\,b^9\,c^4\,d^2\,e^3+614400\,a^3\,b^6\,c^6\,d^3\,e^2-102400\,a^3\,b^7\,c^5\,d^2\,e^3-1024000\,a^4\,b^4\,c^7\,d^3\,e^2-102400\,a^4\,b^5\,c^6\,d^2\,e^3+327680\,a^5\,b^2\,c^8\,d^3\,e^2+819200\,a^5\,b^3\,c^7\,d^2\,e^3-25600\,a\,b^9\,c^5\,d^4\,e+600\,a\,b^{12}\,c^2\,d\,e^4-1310720\,a^5\,b\,c^9\,d^4\,e+21760\,a\,b^{10}\,c^4\,d^3\,e^2-7040\,a\,b^{11}\,c^3\,d^2\,e^3+204800\,a^2\,b^7\,c^6\,d^4\,e-160\,a^2\,b^{10}\,c^3\,d\,e^4-819200\,a^3\,b^5\,c^7\,d^4\,e-28800\,a^3\,b^8\,c^4\,d\,e^4+1638400\,a^4\,b^3\,c^8\,d^4\,e+166400\,a^4\,b^6\,c^5\,d\,e^4-358400\,a^5\,b^4\,c^6\,d\,e^4-983040\,a^6\,b\,c^8\,d^2\,e^3+204800\,a^6\,b^2\,c^7\,d\,e^4}{c\,{\left(4\,a\,c-b^2\right)}^{10}}}}{16}-\frac{9\,c\,e^2\,\sqrt{d+e\,x}\,\left(-32\,a^3\,c^3\,e^6+64\,a^2\,b^2\,c^2\,e^6-160\,a^2\,b\,c^3\,d\,e^5+160\,a^2\,c^4\,d^2\,e^4+14\,a\,b^4\,c\,e^6-240\,a\,b^3\,c^2\,d\,e^5+880\,a\,b^2\,c^3\,d^2\,e^4-1280\,a\,b\,c^4\,d^3\,e^3+640\,a\,c^5\,d^4\,e^2+b^6\,e^6-26\,b^5\,c\,d\,e^5+250\,b^4\,c^2\,d^2\,e^4-960\,b^3\,c^3\,d^3\,e^3+1760\,b^2\,c^4\,d^4\,e^2-1536\,b\,c^5\,d^5\,e+512\,c^6\,d^6\right)}{8\,{\left(4\,a\,c-b^2\right)}^4}\right)\,\sqrt{-\frac{b^{15}\,e^5+e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+524288\,a^5\,c^{10}\,d^5-512\,b^{10}\,c^5\,d^5+10240\,a\,b^8\,c^6\,d^5-81920\,a^7\,b\,c^7\,e^5+163840\,a^7\,c^8\,d\,e^4+1280\,b^{11}\,c^4\,d^4\,e-81920\,a^2\,b^6\,c^7\,d^5+327680\,a^3\,b^4\,c^8\,d^5-655360\,a^4\,b^2\,c^9\,d^5-560\,a^2\,b^{11}\,c^2\,e^5+4160\,a^3\,b^9\,c^3\,e^5-11520\,a^4\,b^7\,c^4\,e^5-1024\,a^5\,b^5\,c^5\,e^5+61440\,a^6\,b^3\,c^6\,e^5+655360\,a^6\,c^9\,d^3\,e^2-1120\,b^{12}\,c^3\,d^3\,e^2+400\,b^{13}\,c^2\,d^2\,e^3+20\,a\,b^{13}\,c\,e^5-50\,b^{14}\,c\,d\,e^4-166400\,a^2\,b^8\,c^5\,d^3\,e^2+44800\,a^2\,b^9\,c^4\,d^2\,e^3+614400\,a^3\,b^6\,c^6\,d^3\,e^2-102400\,a^3\,b^7\,c^5\,d^2\,e^3-1024000\,a^4\,b^4\,c^7\,d^3\,e^2-102400\,a^4\,b^5\,c^6\,d^2\,e^3+327680\,a^5\,b^2\,c^8\,d^3\,e^2+819200\,a^5\,b^3\,c^7\,d^2\,e^3-25600\,a\,b^9\,c^5\,d^4\,e+600\,a\,b^{12}\,c^2\,d\,e^4-1310720\,a^5\,b\,c^9\,d^4\,e+21760\,a\,b^{10}\,c^4\,d^3\,e^2-7040\,a\,b^{11}\,c^3\,d^2\,e^3+204800\,a^2\,b^7\,c^6\,d^4\,e-160\,a^2\,b^{10}\,c^3\,d\,e^4-819200\,a^3\,b^5\,c^7\,d^4\,e-28800\,a^3\,b^8\,c^4\,d\,e^4+1638400\,a^4\,b^3\,c^8\,d^4\,e+166400\,a^4\,b^6\,c^5\,d\,e^4-358400\,a^5\,b^4\,c^6\,d\,e^4-983040\,a^6\,b\,c^8\,d^2\,e^3+204800\,a^6\,b^2\,c^7\,d\,e^4}{c\,{\left(4\,a\,c-b^2\right)}^{10}}}}{16}-\frac{3\,\left(576\,a^4\,c^4\,e^{11}+1584\,a^3\,b^2\,c^3\,e^{11}-8640\,a^3\,b\,c^4\,d\,e^{10}+8640\,a^3\,c^5\,d^2\,e^9+540\,a^2\,b^4\,c^2\,e^{11}-9072\,a^2\,b^3\,c^3\,d\,e^{10}+40176\,a^2\,b^2\,c^4\,d^2\,e^9-62208\,a^2\,b\,c^5\,d^3\,e^8+31104\,a^2\,c^6\,d^4\,e^7+45\,a\,b^6\,c\,e^{11}-1620\,a\,b^5\,c^2\,d\,e^{10}+17172\,a\,b^4\,c^3\,d^2\,e^9-72576\,a\,b^3\,c^4\,d^3\,e^8+139968\,a\,b^2\,c^5\,d^4\,e^7-124416\,a\,b\,c^6\,d^5\,e^6+41472\,a\,c^7\,d^6\,e^5-45\,b^7\,c\,d\,e^{10}+1125\,b^6\,c^2\,d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\,e^{11}-8640\,a^3\,b\,c^4\,d\,e^{10}+8640\,a^3\,c^5\,d^2\,e^9+540\,a^2\,b^4\,c^2\,e^{11}-9072\,a^2\,b^3\,c^3\,d\,e^{10}+40176\,a^2\,b^2\,c^4\,d^2\,e^9-62208\,a^2\,b\,c^5\,d^3\,e^8+31104\,a^2\,c^6\,d^4\,e^7+45\,a\,b^6\,c\,e^{11}-1620\,a\,b^5\,c^2\,d\,e^{10}+17172\,a\,b^4\,c^3\,d^2\,e^9-72576\,a\,b^3\,c^4\,d^3\,e^8+139968\,a\,b^2\,c^5\,d^4\,e^7-124416\,a\,b\,c^6\,d^5\,e^6+41472\,a\,c^7\,d^6\,e^5-45\,b^7\,c\,d\,e^{10}+1125\,b^6\,c^2\,d^2\,e^9-10224\,b^5\,c^3\,d^3\,e^8+43704\,b^4\,c^4\,d^4\,e^7-97920\,b^3\,c^5\,d^5\,e^6+118656\,b^2\,c^6\,d^6\,e^5-73728\,b\,c^7\,d^7\,e^4+18432\,c^8\,d^8\,e^3\right)}{64\,{\left(4\,a\,c-b^2\right)}^6}\right)\,\sqrt{\frac{9\,\left(e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-b^{15}\,e^5-524288\,a^5\,c^{10}\,d^5+512\,b^{10}\,c^5\,d^5-10240\,a\,b^8\,c^6\,d^5+81920\,a^7\,b\,c^7\,e^5-163840\,a^7\,c^8\,d\,e^4-1280\,b^{11}\,c^4\,d^4\,e+81920\,a^2\,b^6\,c^7\,d^5-327680\,a^3\,b^4\,c^8\,d^5+655360\,a^4\,b^2\,c^9\,d^5+560\,a^2\,b^{11}\,c^2\,e^5-4160\,a^3\,b^9\,c^3\,e^5+11520\,a^4\,b^7\,c^4\,e^5+1024\,a^5\,b^5\,c^5\,e^5-61440\,a^6\,b^3\,c^6\,e^5-655360\,a^6\,c^9\,d^3\,e^2+1120\,b^{12}\,c^3\,d^3\,e^2-400\,b^{13}\,c^2\,d^2\,e^3-20\,a\,b^{13}\,c\,e^5+50\,b^{14}\,c\,d\,e^4+166400\,a^2\,b^8\,c^5\,d^3\,e^2-44800\,a^2\,b^9\,c^4\,d^2\,e^3-614400\,a^3\,b^6\,c^6\,d^3\,e^2+102400\,a^3\,b^7\,c^5\,d^2\,e^3+1024000\,a^4\,b^4\,c^7\,d^3\,e^2+102400\,a^4\,b^5\,c^6\,d^2\,e^3-327680\,a^5\,b^2\,c^8\,d^3\,e^2-819200\,a^5\,b^3\,c^7\,d^2\,e^3+25600\,a\,b^9\,c^5\,d^4\,e-600\,a\,b^{12}\,c^2\,d\,e^4+1310720\,a^5\,b\,c^9\,d^4\,e-21760\,a\,b^{10}\,c^4\,d^3\,e^2+7040\,a\,b^{11}\,c^3\,d^2\,e^3-204800\,a^2\,b^7\,c^6\,d^4\,e+160\,a^2\,b^{10}\,c^3\,d\,e^4+819200\,a^3\,b^5\,c^7\,d^4\,e+28800\,a^3\,b^8\,c^4\,d\,e^4-1638400\,a^4\,b^3\,c^8\,d^4\,e-166400\,a^4\,b^6\,c^5\,d\,e^4+358400\,a^5\,b^4\,c^6\,d\,e^4+983040\,a^6\,b\,c^8\,d^2\,e^3-204800\,a^6\,b^2\,c^7\,d\,e^4\right)}{128\,\left(1048576\,a^{10}\,c^{11}-2621440\,a^9\,b^2\,c^{10}+2949120\,a^8\,b^4\,c^9-1966080\,a^7\,b^6\,c^8+860160\,a^6\,b^8\,c^7-258048\,a^5\,b^{10}\,c^6+53760\,a^4\,b^{12}\,c^5-7680\,a^3\,b^{14}\,c^4+720\,a^2\,b^{16}\,c^3-40\,a\,b^{18}\,c^2+b^{20}\,c\right)}}+\frac{\frac{{\left(d+e\,x\right)}^{3/2}\,\left(-4\,a^2\,c\,e^5+19\,a\,b^2\,e^5-68\,a\,b\,c\,d\,e^4+68\,a\,c^2\,d^2\,e^3-19\,b^3\,d\,e^4+91\,b^2\,c\,d^2\,e^3-144\,b\,c^2\,d^3\,e^2+72\,c^3\,d^4\,e\right)}{4\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}-\frac{3\,\sqrt{d+e\,x}\,\left(-a^2\,b\,e^6+2\,a^2\,c\,d\,e^5+2\,a\,b^2\,d\,e^5-6\,a\,b\,c\,d^2\,e^4+4\,a\,c^2\,d^3\,e^3-b^3\,d^2\,e^4+4\,b^2\,c\,d^3\,e^3-5\,b\,c^2\,d^4\,e^2+2\,c^3\,d^5\,e\right)}{16\,a^2\,c^2-8\,a\,b^2\,c+b^4}+\frac{\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{5/2}\,\left(5\,b^2\,e^3-36\,b\,c\,d\,e^2+36\,c^2\,d^2\,e+16\,a\,c\,e^3\right)}{4\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{3\,c\,e\,{\left(d+e\,x\right)}^{7/2}\,\left(b^2\,e^2-8\,b\,c\,d\,e+8\,c^2\,d^2+4\,a\,c\,e^2\right)}{4\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}}{c^2\,{\left(d+e\,x\right)}^4-\left(d+e\,x\right)\,\left(2\,b^2\,d\,e^2-6\,b\,c\,d^2\,e-2\,a\,b\,e^3+4\,c^2\,d^3+4\,a\,c\,d\,e^2\right)-\left(4\,c^2\,d-2\,b\,c\,e\right)\,{\left(d+e\,x\right)}^3+{\left(d+e\,x\right)}^2\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2+2\,a\,c\,e^2\right)+a^2\,e^4+c^2\,d^4+b^2\,d^2\,e^2-2\,a\,b\,d\,e^3-2\,b\,c\,d^3\,e+2\,a\,c\,d^2\,e^2}","Not used",1,"log((3*2^(1/2)*((3*2^(1/2)*((12*c^2*e^3*(b*e - 2*c*d)*(a*e^2 + c*d^2 - b*d*e))/(4*a*c - b^2) + (3*2^(1/2)*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(-(b^15*e^5 + e^5*(-(4*a*c - b^2)^15)^(1/2) + 524288*a^5*c^10*d^5 - 512*b^10*c^5*d^5 + 10240*a*b^8*c^6*d^5 - 81920*a^7*b*c^7*e^5 + 163840*a^7*c^8*d*e^4 + 1280*b^11*c^4*d^4*e - 81920*a^2*b^6*c^7*d^5 + 327680*a^3*b^4*c^8*d^5 - 655360*a^4*b^2*c^9*d^5 - 560*a^2*b^11*c^2*e^5 + 4160*a^3*b^9*c^3*e^5 - 11520*a^4*b^7*c^4*e^5 - 1024*a^5*b^5*c^5*e^5 + 61440*a^6*b^3*c^6*e^5 + 655360*a^6*c^9*d^3*e^2 - 1120*b^12*c^3*d^3*e^2 + 400*b^13*c^2*d^2*e^3 + 20*a*b^13*c*e^5 - 50*b^14*c*d*e^4 - 166400*a^2*b^8*c^5*d^3*e^2 + 44800*a^2*b^9*c^4*d^2*e^3 + 614400*a^3*b^6*c^6*d^3*e^2 - 102400*a^3*b^7*c^5*d^2*e^3 - 1024000*a^4*b^4*c^7*d^3*e^2 - 102400*a^4*b^5*c^6*d^2*e^3 + 327680*a^5*b^2*c^8*d^3*e^2 + 819200*a^5*b^3*c^7*d^2*e^3 - 25600*a*b^9*c^5*d^4*e + 600*a*b^12*c^2*d*e^4 - 1310720*a^5*b*c^9*d^4*e + 21760*a*b^10*c^4*d^3*e^2 - 7040*a*b^11*c^3*d^2*e^3 + 204800*a^2*b^7*c^6*d^4*e - 160*a^2*b^10*c^3*d*e^4 - 819200*a^3*b^5*c^7*d^4*e - 28800*a^3*b^8*c^4*d*e^4 + 1638400*a^4*b^3*c^8*d^4*e + 166400*a^4*b^6*c^5*d*e^4 - 358400*a^5*b^4*c^6*d*e^4 - 983040*a^6*b*c^8*d^2*e^3 + 204800*a^6*b^2*c^7*d*e^4)/(c*(4*a*c - b^2)^10))^(1/2))/2)*(-(b^15*e^5 + e^5*(-(4*a*c - b^2)^15)^(1/2) + 524288*a^5*c^10*d^5 - 512*b^10*c^5*d^5 + 10240*a*b^8*c^6*d^5 - 81920*a^7*b*c^7*e^5 + 163840*a^7*c^8*d*e^4 + 1280*b^11*c^4*d^4*e - 81920*a^2*b^6*c^7*d^5 + 327680*a^3*b^4*c^8*d^5 - 655360*a^4*b^2*c^9*d^5 - 560*a^2*b^11*c^2*e^5 + 4160*a^3*b^9*c^3*e^5 - 11520*a^4*b^7*c^4*e^5 - 1024*a^5*b^5*c^5*e^5 + 61440*a^6*b^3*c^6*e^5 + 655360*a^6*c^9*d^3*e^2 - 1120*b^12*c^3*d^3*e^2 + 400*b^13*c^2*d^2*e^3 + 20*a*b^13*c*e^5 - 50*b^14*c*d*e^4 - 166400*a^2*b^8*c^5*d^3*e^2 + 44800*a^2*b^9*c^4*d^2*e^3 + 614400*a^3*b^6*c^6*d^3*e^2 - 102400*a^3*b^7*c^5*d^2*e^3 - 1024000*a^4*b^4*c^7*d^3*e^2 - 102400*a^4*b^5*c^6*d^2*e^3 + 327680*a^5*b^2*c^8*d^3*e^2 + 819200*a^5*b^3*c^7*d^2*e^3 - 25600*a*b^9*c^5*d^4*e + 600*a*b^12*c^2*d*e^4 - 1310720*a^5*b*c^9*d^4*e + 21760*a*b^10*c^4*d^3*e^2 - 7040*a*b^11*c^3*d^2*e^3 + 204800*a^2*b^7*c^6*d^4*e - 160*a^2*b^10*c^3*d*e^4 - 819200*a^3*b^5*c^7*d^4*e - 28800*a^3*b^8*c^4*d*e^4 + 1638400*a^4*b^3*c^8*d^4*e + 166400*a^4*b^6*c^5*d*e^4 - 358400*a^5*b^4*c^6*d*e^4 - 983040*a^6*b*c^8*d^2*e^3 + 204800*a^6*b^2*c^7*d*e^4)/(c*(4*a*c - b^2)^10))^(1/2))/16 - (9*c*e^2*(d + e*x)^(1/2)*(b^6*e^6 + 512*c^6*d^6 - 32*a^3*c^3*e^6 + 640*a*c^5*d^4*e^2 + 64*a^2*b^2*c^2*e^6 + 160*a^2*c^4*d^2*e^4 + 1760*b^2*c^4*d^4*e^2 - 960*b^3*c^3*d^3*e^3 + 250*b^4*c^2*d^2*e^4 + 14*a*b^4*c*e^6 - 1536*b*c^5*d^5*e - 26*b^5*c*d*e^5 - 1280*a*b*c^4*d^3*e^3 - 240*a*b^3*c^2*d*e^5 - 160*a^2*b*c^3*d*e^5 + 880*a*b^2*c^3*d^2*e^4))/(8*(4*a*c - b^2)^4))*(-(b^15*e^5 + e^5*(-(4*a*c - b^2)^15)^(1/2) + 524288*a^5*c^10*d^5 - 512*b^10*c^5*d^5 + 10240*a*b^8*c^6*d^5 - 81920*a^7*b*c^7*e^5 + 163840*a^7*c^8*d*e^4 + 1280*b^11*c^4*d^4*e - 81920*a^2*b^6*c^7*d^5 + 327680*a^3*b^4*c^8*d^5 - 655360*a^4*b^2*c^9*d^5 - 560*a^2*b^11*c^2*e^5 + 4160*a^3*b^9*c^3*e^5 - 11520*a^4*b^7*c^4*e^5 - 1024*a^5*b^5*c^5*e^5 + 61440*a^6*b^3*c^6*e^5 + 655360*a^6*c^9*d^3*e^2 - 1120*b^12*c^3*d^3*e^2 + 400*b^13*c^2*d^2*e^3 + 20*a*b^13*c*e^5 - 50*b^14*c*d*e^4 - 166400*a^2*b^8*c^5*d^3*e^2 + 44800*a^2*b^9*c^4*d^2*e^3 + 614400*a^3*b^6*c^6*d^3*e^2 - 102400*a^3*b^7*c^5*d^2*e^3 - 1024000*a^4*b^4*c^7*d^3*e^2 - 102400*a^4*b^5*c^6*d^2*e^3 + 327680*a^5*b^2*c^8*d^3*e^2 + 819200*a^5*b^3*c^7*d^2*e^3 - 25600*a*b^9*c^5*d^4*e + 600*a*b^12*c^2*d*e^4 - 1310720*a^5*b*c^9*d^4*e + 21760*a*b^10*c^4*d^3*e^2 - 7040*a*b^11*c^3*d^2*e^3 + 204800*a^2*b^7*c^6*d^4*e - 160*a^2*b^10*c^3*d*e^4 - 819200*a^3*b^5*c^7*d^4*e - 28800*a^3*b^8*c^4*d*e^4 + 1638400*a^4*b^3*c^8*d^4*e + 166400*a^4*b^6*c^5*d*e^4 - 358400*a^5*b^4*c^6*d*e^4 - 983040*a^6*b*c^8*d^2*e^3 + 204800*a^6*b^2*c^7*d*e^4)/(c*(4*a*c - b^2)^10))^(1/2))/16 - (3*(576*a^4*c^4*e^11 + 18432*c^8*d^8*e^3 + 41472*a*c^7*d^6*e^5 - 73728*b*c^7*d^7*e^4 + 540*a^2*b^4*c^2*e^11 + 1584*a^3*b^2*c^3*e^11 + 31104*a^2*c^6*d^4*e^7 + 8640*a^3*c^5*d^2*e^9 + 118656*b^2*c^6*d^6*e^5 - 97920*b^3*c^5*d^5*e^6 + 43704*b^4*c^4*d^4*e^7 - 10224*b^5*c^3*d^3*e^8 + 1125*b^6*c^2*d^2*e^9 + 45*a*b^6*c*e^11 - 45*b^7*c*d*e^10 + 40176*a^2*b^2*c^4*d^2*e^9 - 124416*a*b*c^6*d^5*e^6 - 1620*a*b^5*c^2*d*e^10 - 8640*a^3*b*c^4*d*e^10 + 139968*a*b^2*c^5*d^4*e^7 - 72576*a*b^3*c^4*d^3*e^8 + 17172*a*b^4*c^3*d^2*e^9 - 62208*a^2*b*c^5*d^3*e^8 - 9072*a^2*b^3*c^3*d*e^10))/(64*(4*a*c - b^2)^6))*(-(9*(b^15*e^5 + e^5*(-(4*a*c - b^2)^15)^(1/2) + 524288*a^5*c^10*d^5 - 512*b^10*c^5*d^5 + 10240*a*b^8*c^6*d^5 - 81920*a^7*b*c^7*e^5 + 163840*a^7*c^8*d*e^4 + 1280*b^11*c^4*d^4*e - 81920*a^2*b^6*c^7*d^5 + 327680*a^3*b^4*c^8*d^5 - 655360*a^4*b^2*c^9*d^5 - 560*a^2*b^11*c^2*e^5 + 4160*a^3*b^9*c^3*e^5 - 11520*a^4*b^7*c^4*e^5 - 1024*a^5*b^5*c^5*e^5 + 61440*a^6*b^3*c^6*e^5 + 655360*a^6*c^9*d^3*e^2 - 1120*b^12*c^3*d^3*e^2 + 400*b^13*c^2*d^2*e^3 + 20*a*b^13*c*e^5 - 50*b^14*c*d*e^4 - 166400*a^2*b^8*c^5*d^3*e^2 + 44800*a^2*b^9*c^4*d^2*e^3 + 614400*a^3*b^6*c^6*d^3*e^2 - 102400*a^3*b^7*c^5*d^2*e^3 - 1024000*a^4*b^4*c^7*d^3*e^2 - 102400*a^4*b^5*c^6*d^2*e^3 + 327680*a^5*b^2*c^8*d^3*e^2 + 819200*a^5*b^3*c^7*d^2*e^3 - 25600*a*b^9*c^5*d^4*e + 600*a*b^12*c^2*d*e^4 - 1310720*a^5*b*c^9*d^4*e + 21760*a*b^10*c^4*d^3*e^2 - 7040*a*b^11*c^3*d^2*e^3 + 204800*a^2*b^7*c^6*d^4*e - 160*a^2*b^10*c^3*d*e^4 - 819200*a^3*b^5*c^7*d^4*e - 28800*a^3*b^8*c^4*d*e^4 + 1638400*a^4*b^3*c^8*d^4*e + 166400*a^4*b^6*c^5*d*e^4 - 358400*a^5*b^4*c^6*d*e^4 - 983040*a^6*b*c^8*d^2*e^3 + 204800*a^6*b^2*c^7*d*e^4))/(128*(b^20*c + 1048576*a^10*c^11 - 40*a*b^18*c^2 + 720*a^2*b^16*c^3 - 7680*a^3*b^14*c^4 + 53760*a^4*b^12*c^5 - 258048*a^5*b^10*c^6 + 860160*a^6*b^8*c^7 - 1966080*a^7*b^6*c^8 + 2949120*a^8*b^4*c^9 - 2621440*a^9*b^2*c^10)))^(1/2) - log((((12*c^2*e^3*(b*e - 2*c*d)*(a*e^2 + c*d^2 - b*d*e))/(4*a*c - b^2) - 8*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(-((9*b^15*e^5)/128 + (9*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 + 36864*a^5*c^10*d^5 - 36*b^10*c^5*d^5 + 720*a*b^8*c^6*d^5 - 5760*a^7*b*c^7*e^5 + 11520*a^7*c^8*d*e^4 + 90*b^11*c^4*d^4*e - 5760*a^2*b^6*c^7*d^5 + 23040*a^3*b^4*c^8*d^5 - 46080*a^4*b^2*c^9*d^5 - (315*a^2*b^11*c^2*e^5)/8 + (585*a^3*b^9*c^3*e^5)/2 - 810*a^4*b^7*c^4*e^5 - 72*a^5*b^5*c^5*e^5 + 4320*a^6*b^3*c^6*e^5 + 46080*a^6*c^9*d^3*e^2 - (315*b^12*c^3*d^3*e^2)/4 + (225*b^13*c^2*d^2*e^3)/8 + (45*a*b^13*c*e^5)/32 - (225*b^14*c*d*e^4)/64 - 11700*a^2*b^8*c^5*d^3*e^2 + 3150*a^2*b^9*c^4*d^2*e^3 + 43200*a^3*b^6*c^6*d^3*e^2 - 7200*a^3*b^7*c^5*d^2*e^3 - 72000*a^4*b^4*c^7*d^3*e^2 - 7200*a^4*b^5*c^6*d^2*e^3 + 23040*a^5*b^2*c^8*d^3*e^2 + 57600*a^5*b^3*c^7*d^2*e^3 - 1800*a*b^9*c^5*d^4*e + (675*a*b^12*c^2*d*e^4)/16 - 92160*a^5*b*c^9*d^4*e + 1530*a*b^10*c^4*d^3*e^2 - 495*a*b^11*c^3*d^2*e^3 + 14400*a^2*b^7*c^6*d^4*e - (45*a^2*b^10*c^3*d*e^4)/4 - 57600*a^3*b^5*c^7*d^4*e - 2025*a^3*b^8*c^4*d*e^4 + 115200*a^4*b^3*c^8*d^4*e + 11700*a^4*b^6*c^5*d*e^4 - 25200*a^5*b^4*c^6*d*e^4 - 69120*a^6*b*c^8*d^2*e^3 + 14400*a^6*b^2*c^7*d*e^4)/(c*(4*a*c - b^2)^10))^(1/2))*(-((9*b^15*e^5)/128 + (9*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 + 36864*a^5*c^10*d^5 - 36*b^10*c^5*d^5 + 720*a*b^8*c^6*d^5 - 5760*a^7*b*c^7*e^5 + 11520*a^7*c^8*d*e^4 + 90*b^11*c^4*d^4*e - 5760*a^2*b^6*c^7*d^5 + 23040*a^3*b^4*c^8*d^5 - 46080*a^4*b^2*c^9*d^5 - (315*a^2*b^11*c^2*e^5)/8 + (585*a^3*b^9*c^3*e^5)/2 - 810*a^4*b^7*c^4*e^5 - 72*a^5*b^5*c^5*e^5 + 4320*a^6*b^3*c^6*e^5 + 46080*a^6*c^9*d^3*e^2 - (315*b^12*c^3*d^3*e^2)/4 + (225*b^13*c^2*d^2*e^3)/8 + (45*a*b^13*c*e^5)/32 - (225*b^14*c*d*e^4)/64 - 11700*a^2*b^8*c^5*d^3*e^2 + 3150*a^2*b^9*c^4*d^2*e^3 + 43200*a^3*b^6*c^6*d^3*e^2 - 7200*a^3*b^7*c^5*d^2*e^3 - 72000*a^4*b^4*c^7*d^3*e^2 - 7200*a^4*b^5*c^6*d^2*e^3 + 23040*a^5*b^2*c^8*d^3*e^2 + 57600*a^5*b^3*c^7*d^2*e^3 - 1800*a*b^9*c^5*d^4*e + (675*a*b^12*c^2*d*e^4)/16 - 92160*a^5*b*c^9*d^4*e + 1530*a*b^10*c^4*d^3*e^2 - 495*a*b^11*c^3*d^2*e^3 + 14400*a^2*b^7*c^6*d^4*e - (45*a^2*b^10*c^3*d*e^4)/4 - 57600*a^3*b^5*c^7*d^4*e - 2025*a^3*b^8*c^4*d*e^4 + 115200*a^4*b^3*c^8*d^4*e + 11700*a^4*b^6*c^5*d*e^4 - 25200*a^5*b^4*c^6*d*e^4 - 69120*a^6*b*c^8*d^2*e^3 + 14400*a^6*b^2*c^7*d*e^4)/(c*(4*a*c - b^2)^10))^(1/2) + (9*c*e^2*(d + e*x)^(1/2)*(b^6*e^6 + 512*c^6*d^6 - 32*a^3*c^3*e^6 + 640*a*c^5*d^4*e^2 + 64*a^2*b^2*c^2*e^6 + 160*a^2*c^4*d^2*e^4 + 1760*b^2*c^4*d^4*e^2 - 960*b^3*c^3*d^3*e^3 + 250*b^4*c^2*d^2*e^4 + 14*a*b^4*c*e^6 - 1536*b*c^5*d^5*e - 26*b^5*c*d*e^5 - 1280*a*b*c^4*d^3*e^3 - 240*a*b^3*c^2*d*e^5 - 160*a^2*b*c^3*d*e^5 + 880*a*b^2*c^3*d^2*e^4))/(8*(4*a*c - b^2)^4))*(-((9*b^15*e^5)/128 + (9*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 + 36864*a^5*c^10*d^5 - 36*b^10*c^5*d^5 + 720*a*b^8*c^6*d^5 - 5760*a^7*b*c^7*e^5 + 11520*a^7*c^8*d*e^4 + 90*b^11*c^4*d^4*e - 5760*a^2*b^6*c^7*d^5 + 23040*a^3*b^4*c^8*d^5 - 46080*a^4*b^2*c^9*d^5 - (315*a^2*b^11*c^2*e^5)/8 + (585*a^3*b^9*c^3*e^5)/2 - 810*a^4*b^7*c^4*e^5 - 72*a^5*b^5*c^5*e^5 + 4320*a^6*b^3*c^6*e^5 + 46080*a^6*c^9*d^3*e^2 - (315*b^12*c^3*d^3*e^2)/4 + (225*b^13*c^2*d^2*e^3)/8 + (45*a*b^13*c*e^5)/32 - (225*b^14*c*d*e^4)/64 - 11700*a^2*b^8*c^5*d^3*e^2 + 3150*a^2*b^9*c^4*d^2*e^3 + 43200*a^3*b^6*c^6*d^3*e^2 - 7200*a^3*b^7*c^5*d^2*e^3 - 72000*a^4*b^4*c^7*d^3*e^2 - 7200*a^4*b^5*c^6*d^2*e^3 + 23040*a^5*b^2*c^8*d^3*e^2 + 57600*a^5*b^3*c^7*d^2*e^3 - 1800*a*b^9*c^5*d^4*e + (675*a*b^12*c^2*d*e^4)/16 - 92160*a^5*b*c^9*d^4*e + 1530*a*b^10*c^4*d^3*e^2 - 495*a*b^11*c^3*d^2*e^3 + 14400*a^2*b^7*c^6*d^4*e - (45*a^2*b^10*c^3*d*e^4)/4 - 57600*a^3*b^5*c^7*d^4*e - 2025*a^3*b^8*c^4*d*e^4 + 115200*a^4*b^3*c^8*d^4*e + 11700*a^4*b^6*c^5*d*e^4 - 25200*a^5*b^4*c^6*d*e^4 - 69120*a^6*b*c^8*d^2*e^3 + 14400*a^6*b^2*c^7*d*e^4)/(c*(4*a*c - b^2)^10))^(1/2) - (3*(576*a^4*c^4*e^11 + 18432*c^8*d^8*e^3 + 41472*a*c^7*d^6*e^5 - 73728*b*c^7*d^7*e^4 + 540*a^2*b^4*c^2*e^11 + 1584*a^3*b^2*c^3*e^11 + 31104*a^2*c^6*d^4*e^7 + 8640*a^3*c^5*d^2*e^9 + 118656*b^2*c^6*d^6*e^5 - 97920*b^3*c^5*d^5*e^6 + 43704*b^4*c^4*d^4*e^7 - 10224*b^5*c^3*d^3*e^8 + 1125*b^6*c^2*d^2*e^9 + 45*a*b^6*c*e^11 - 45*b^7*c*d*e^10 + 40176*a^2*b^2*c^4*d^2*e^9 - 124416*a*b*c^6*d^5*e^6 - 1620*a*b^5*c^2*d*e^10 - 8640*a^3*b*c^4*d*e^10 + 139968*a*b^2*c^5*d^4*e^7 - 72576*a*b^3*c^4*d^3*e^8 + 17172*a*b^4*c^3*d^2*e^9 - 62208*a^2*b*c^5*d^3*e^8 - 9072*a^2*b^3*c^3*d*e^10))/(64*(4*a*c - b^2)^6))*(-((9*b^15*e^5)/128 + (9*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 + 36864*a^5*c^10*d^5 - 36*b^10*c^5*d^5 + 720*a*b^8*c^6*d^5 - 5760*a^7*b*c^7*e^5 + 11520*a^7*c^8*d*e^4 + 90*b^11*c^4*d^4*e - 5760*a^2*b^6*c^7*d^5 + 23040*a^3*b^4*c^8*d^5 - 46080*a^4*b^2*c^9*d^5 - (315*a^2*b^11*c^2*e^5)/8 + (585*a^3*b^9*c^3*e^5)/2 - 810*a^4*b^7*c^4*e^5 - 72*a^5*b^5*c^5*e^5 + 4320*a^6*b^3*c^6*e^5 + 46080*a^6*c^9*d^3*e^2 - (315*b^12*c^3*d^3*e^2)/4 + (225*b^13*c^2*d^2*e^3)/8 + (45*a*b^13*c*e^5)/32 - (225*b^14*c*d*e^4)/64 - 11700*a^2*b^8*c^5*d^3*e^2 + 3150*a^2*b^9*c^4*d^2*e^3 + 43200*a^3*b^6*c^6*d^3*e^2 - 7200*a^3*b^7*c^5*d^2*e^3 - 72000*a^4*b^4*c^7*d^3*e^2 - 7200*a^4*b^5*c^6*d^2*e^3 + 23040*a^5*b^2*c^8*d^3*e^2 + 57600*a^5*b^3*c^7*d^2*e^3 - 1800*a*b^9*c^5*d^4*e + (675*a*b^12*c^2*d*e^4)/16 - 92160*a^5*b*c^9*d^4*e + 1530*a*b^10*c^4*d^3*e^2 - 495*a*b^11*c^3*d^2*e^3 + 14400*a^2*b^7*c^6*d^4*e - (45*a^2*b^10*c^3*d*e^4)/4 - 57600*a^3*b^5*c^7*d^4*e - 2025*a^3*b^8*c^4*d*e^4 + 115200*a^4*b^3*c^8*d^4*e + 11700*a^4*b^6*c^5*d*e^4 - 25200*a^5*b^4*c^6*d*e^4 - 69120*a^6*b*c^8*d^2*e^3 + 14400*a^6*b^2*c^7*d*e^4)/(b^20*c + 1048576*a^10*c^11 - 40*a*b^18*c^2 + 720*a^2*b^16*c^3 - 7680*a^3*b^14*c^4 + 53760*a^4*b^12*c^5 - 258048*a^5*b^10*c^6 + 860160*a^6*b^8*c^7 - 1966080*a^7*b^6*c^8 + 2949120*a^8*b^4*c^9 - 2621440*a^9*b^2*c^10))^(1/2) - log((((12*c^2*e^3*(b*e - 2*c*d)*(a*e^2 + c*d^2 - b*d*e))/(4*a*c - b^2) - 8*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(((9*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (9*b^15*e^5)/128 - 36864*a^5*c^10*d^5 + 36*b^10*c^5*d^5 - 720*a*b^8*c^6*d^5 + 5760*a^7*b*c^7*e^5 - 11520*a^7*c^8*d*e^4 - 90*b^11*c^4*d^4*e + 5760*a^2*b^6*c^7*d^5 - 23040*a^3*b^4*c^8*d^5 + 46080*a^4*b^2*c^9*d^5 + (315*a^2*b^11*c^2*e^5)/8 - (585*a^3*b^9*c^3*e^5)/2 + 810*a^4*b^7*c^4*e^5 + 72*a^5*b^5*c^5*e^5 - 4320*a^6*b^3*c^6*e^5 - 46080*a^6*c^9*d^3*e^2 + (315*b^12*c^3*d^3*e^2)/4 - (225*b^13*c^2*d^2*e^3)/8 - (45*a*b^13*c*e^5)/32 + (225*b^14*c*d*e^4)/64 + 11700*a^2*b^8*c^5*d^3*e^2 - 3150*a^2*b^9*c^4*d^2*e^3 - 43200*a^3*b^6*c^6*d^3*e^2 + 7200*a^3*b^7*c^5*d^2*e^3 + 72000*a^4*b^4*c^7*d^3*e^2 + 7200*a^4*b^5*c^6*d^2*e^3 - 23040*a^5*b^2*c^8*d^3*e^2 - 57600*a^5*b^3*c^7*d^2*e^3 + 1800*a*b^9*c^5*d^4*e - (675*a*b^12*c^2*d*e^4)/16 + 92160*a^5*b*c^9*d^4*e - 1530*a*b^10*c^4*d^3*e^2 + 495*a*b^11*c^3*d^2*e^3 - 14400*a^2*b^7*c^6*d^4*e + (45*a^2*b^10*c^3*d*e^4)/4 + 57600*a^3*b^5*c^7*d^4*e + 2025*a^3*b^8*c^4*d*e^4 - 115200*a^4*b^3*c^8*d^4*e - 11700*a^4*b^6*c^5*d*e^4 + 25200*a^5*b^4*c^6*d*e^4 + 69120*a^6*b*c^8*d^2*e^3 - 14400*a^6*b^2*c^7*d*e^4)/(c*(4*a*c - b^2)^10))^(1/2))*(((9*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (9*b^15*e^5)/128 - 36864*a^5*c^10*d^5 + 36*b^10*c^5*d^5 - 720*a*b^8*c^6*d^5 + 5760*a^7*b*c^7*e^5 - 11520*a^7*c^8*d*e^4 - 90*b^11*c^4*d^4*e + 5760*a^2*b^6*c^7*d^5 - 23040*a^3*b^4*c^8*d^5 + 46080*a^4*b^2*c^9*d^5 + (315*a^2*b^11*c^2*e^5)/8 - (585*a^3*b^9*c^3*e^5)/2 + 810*a^4*b^7*c^4*e^5 + 72*a^5*b^5*c^5*e^5 - 4320*a^6*b^3*c^6*e^5 - 46080*a^6*c^9*d^3*e^2 + (315*b^12*c^3*d^3*e^2)/4 - (225*b^13*c^2*d^2*e^3)/8 - (45*a*b^13*c*e^5)/32 + (225*b^14*c*d*e^4)/64 + 11700*a^2*b^8*c^5*d^3*e^2 - 3150*a^2*b^9*c^4*d^2*e^3 - 43200*a^3*b^6*c^6*d^3*e^2 + 7200*a^3*b^7*c^5*d^2*e^3 + 72000*a^4*b^4*c^7*d^3*e^2 + 7200*a^4*b^5*c^6*d^2*e^3 - 23040*a^5*b^2*c^8*d^3*e^2 - 57600*a^5*b^3*c^7*d^2*e^3 + 1800*a*b^9*c^5*d^4*e - (675*a*b^12*c^2*d*e^4)/16 + 92160*a^5*b*c^9*d^4*e - 1530*a*b^10*c^4*d^3*e^2 + 495*a*b^11*c^3*d^2*e^3 - 14400*a^2*b^7*c^6*d^4*e + (45*a^2*b^10*c^3*d*e^4)/4 + 57600*a^3*b^5*c^7*d^4*e + 2025*a^3*b^8*c^4*d*e^4 - 115200*a^4*b^3*c^8*d^4*e - 11700*a^4*b^6*c^5*d*e^4 + 25200*a^5*b^4*c^6*d*e^4 + 69120*a^6*b*c^8*d^2*e^3 - 14400*a^6*b^2*c^7*d*e^4)/(c*(4*a*c - b^2)^10))^(1/2) + (9*c*e^2*(d + e*x)^(1/2)*(b^6*e^6 + 512*c^6*d^6 - 32*a^3*c^3*e^6 + 640*a*c^5*d^4*e^2 + 64*a^2*b^2*c^2*e^6 + 160*a^2*c^4*d^2*e^4 + 1760*b^2*c^4*d^4*e^2 - 960*b^3*c^3*d^3*e^3 + 250*b^4*c^2*d^2*e^4 + 14*a*b^4*c*e^6 - 1536*b*c^5*d^5*e - 26*b^5*c*d*e^5 - 1280*a*b*c^4*d^3*e^3 - 240*a*b^3*c^2*d*e^5 - 160*a^2*b*c^3*d*e^5 + 880*a*b^2*c^3*d^2*e^4))/(8*(4*a*c - b^2)^4))*(((9*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (9*b^15*e^5)/128 - 36864*a^5*c^10*d^5 + 36*b^10*c^5*d^5 - 720*a*b^8*c^6*d^5 + 5760*a^7*b*c^7*e^5 - 11520*a^7*c^8*d*e^4 - 90*b^11*c^4*d^4*e + 5760*a^2*b^6*c^7*d^5 - 23040*a^3*b^4*c^8*d^5 + 46080*a^4*b^2*c^9*d^5 + (315*a^2*b^11*c^2*e^5)/8 - (585*a^3*b^9*c^3*e^5)/2 + 810*a^4*b^7*c^4*e^5 + 72*a^5*b^5*c^5*e^5 - 4320*a^6*b^3*c^6*e^5 - 46080*a^6*c^9*d^3*e^2 + (315*b^12*c^3*d^3*e^2)/4 - (225*b^13*c^2*d^2*e^3)/8 - (45*a*b^13*c*e^5)/32 + (225*b^14*c*d*e^4)/64 + 11700*a^2*b^8*c^5*d^3*e^2 - 3150*a^2*b^9*c^4*d^2*e^3 - 43200*a^3*b^6*c^6*d^3*e^2 + 7200*a^3*b^7*c^5*d^2*e^3 + 72000*a^4*b^4*c^7*d^3*e^2 + 7200*a^4*b^5*c^6*d^2*e^3 - 23040*a^5*b^2*c^8*d^3*e^2 - 57600*a^5*b^3*c^7*d^2*e^3 + 1800*a*b^9*c^5*d^4*e - (675*a*b^12*c^2*d*e^4)/16 + 92160*a^5*b*c^9*d^4*e - 1530*a*b^10*c^4*d^3*e^2 + 495*a*b^11*c^3*d^2*e^3 - 14400*a^2*b^7*c^6*d^4*e + (45*a^2*b^10*c^3*d*e^4)/4 + 57600*a^3*b^5*c^7*d^4*e + 2025*a^3*b^8*c^4*d*e^4 - 115200*a^4*b^3*c^8*d^4*e - 11700*a^4*b^6*c^5*d*e^4 + 25200*a^5*b^4*c^6*d*e^4 + 69120*a^6*b*c^8*d^2*e^3 - 14400*a^6*b^2*c^7*d*e^4)/(c*(4*a*c - b^2)^10))^(1/2) - (3*(576*a^4*c^4*e^11 + 18432*c^8*d^8*e^3 + 41472*a*c^7*d^6*e^5 - 73728*b*c^7*d^7*e^4 + 540*a^2*b^4*c^2*e^11 + 1584*a^3*b^2*c^3*e^11 + 31104*a^2*c^6*d^4*e^7 + 8640*a^3*c^5*d^2*e^9 + 118656*b^2*c^6*d^6*e^5 - 97920*b^3*c^5*d^5*e^6 + 43704*b^4*c^4*d^4*e^7 - 10224*b^5*c^3*d^3*e^8 + 1125*b^6*c^2*d^2*e^9 + 45*a*b^6*c*e^11 - 45*b^7*c*d*e^10 + 40176*a^2*b^2*c^4*d^2*e^9 - 124416*a*b*c^6*d^5*e^6 - 1620*a*b^5*c^2*d*e^10 - 8640*a^3*b*c^4*d*e^10 + 139968*a*b^2*c^5*d^4*e^7 - 72576*a*b^3*c^4*d^3*e^8 + 17172*a*b^4*c^3*d^2*e^9 - 62208*a^2*b*c^5*d^3*e^8 - 9072*a^2*b^3*c^3*d*e^10))/(64*(4*a*c - b^2)^6))*(((9*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (9*b^15*e^5)/128 - 36864*a^5*c^10*d^5 + 36*b^10*c^5*d^5 - 720*a*b^8*c^6*d^5 + 5760*a^7*b*c^7*e^5 - 11520*a^7*c^8*d*e^4 - 90*b^11*c^4*d^4*e + 5760*a^2*b^6*c^7*d^5 - 23040*a^3*b^4*c^8*d^5 + 46080*a^4*b^2*c^9*d^5 + (315*a^2*b^11*c^2*e^5)/8 - (585*a^3*b^9*c^3*e^5)/2 + 810*a^4*b^7*c^4*e^5 + 72*a^5*b^5*c^5*e^5 - 4320*a^6*b^3*c^6*e^5 - 46080*a^6*c^9*d^3*e^2 + (315*b^12*c^3*d^3*e^2)/4 - (225*b^13*c^2*d^2*e^3)/8 - (45*a*b^13*c*e^5)/32 + (225*b^14*c*d*e^4)/64 + 11700*a^2*b^8*c^5*d^3*e^2 - 3150*a^2*b^9*c^4*d^2*e^3 - 43200*a^3*b^6*c^6*d^3*e^2 + 7200*a^3*b^7*c^5*d^2*e^3 + 72000*a^4*b^4*c^7*d^3*e^2 + 7200*a^4*b^5*c^6*d^2*e^3 - 23040*a^5*b^2*c^8*d^3*e^2 - 57600*a^5*b^3*c^7*d^2*e^3 + 1800*a*b^9*c^5*d^4*e - (675*a*b^12*c^2*d*e^4)/16 + 92160*a^5*b*c^9*d^4*e - 1530*a*b^10*c^4*d^3*e^2 + 495*a*b^11*c^3*d^2*e^3 - 14400*a^2*b^7*c^6*d^4*e + (45*a^2*b^10*c^3*d*e^4)/4 + 57600*a^3*b^5*c^7*d^4*e + 2025*a^3*b^8*c^4*d*e^4 - 115200*a^4*b^3*c^8*d^4*e - 11700*a^4*b^6*c^5*d*e^4 + 25200*a^5*b^4*c^6*d*e^4 + 69120*a^6*b*c^8*d^2*e^3 - 14400*a^6*b^2*c^7*d*e^4)/(b^20*c + 1048576*a^10*c^11 - 40*a*b^18*c^2 + 720*a^2*b^16*c^3 - 7680*a^3*b^14*c^4 + 53760*a^4*b^12*c^5 - 258048*a^5*b^10*c^6 + 860160*a^6*b^8*c^7 - 1966080*a^7*b^6*c^8 + 2949120*a^8*b^4*c^9 - 2621440*a^9*b^2*c^10))^(1/2) + log((3*2^(1/2)*((3*2^(1/2)*((12*c^2*e^3*(b*e - 2*c*d)*(a*e^2 + c*d^2 - b*d*e))/(4*a*c - b^2) + (3*2^(1/2)*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*((e^5*(-(4*a*c - b^2)^15)^(1/2) - b^15*e^5 - 524288*a^5*c^10*d^5 + 512*b^10*c^5*d^5 - 10240*a*b^8*c^6*d^5 + 81920*a^7*b*c^7*e^5 - 163840*a^7*c^8*d*e^4 - 1280*b^11*c^4*d^4*e + 81920*a^2*b^6*c^7*d^5 - 327680*a^3*b^4*c^8*d^5 + 655360*a^4*b^2*c^9*d^5 + 560*a^2*b^11*c^2*e^5 - 4160*a^3*b^9*c^3*e^5 + 11520*a^4*b^7*c^4*e^5 + 1024*a^5*b^5*c^5*e^5 - 61440*a^6*b^3*c^6*e^5 - 655360*a^6*c^9*d^3*e^2 + 1120*b^12*c^3*d^3*e^2 - 400*b^13*c^2*d^2*e^3 - 20*a*b^13*c*e^5 + 50*b^14*c*d*e^4 + 166400*a^2*b^8*c^5*d^3*e^2 - 44800*a^2*b^9*c^4*d^2*e^3 - 614400*a^3*b^6*c^6*d^3*e^2 + 102400*a^3*b^7*c^5*d^2*e^3 + 1024000*a^4*b^4*c^7*d^3*e^2 + 102400*a^4*b^5*c^6*d^2*e^3 - 327680*a^5*b^2*c^8*d^3*e^2 - 819200*a^5*b^3*c^7*d^2*e^3 + 25600*a*b^9*c^5*d^4*e - 600*a*b^12*c^2*d*e^4 + 1310720*a^5*b*c^9*d^4*e - 21760*a*b^10*c^4*d^3*e^2 + 7040*a*b^11*c^3*d^2*e^3 - 204800*a^2*b^7*c^6*d^4*e + 160*a^2*b^10*c^3*d*e^4 + 819200*a^3*b^5*c^7*d^4*e + 28800*a^3*b^8*c^4*d*e^4 - 1638400*a^4*b^3*c^8*d^4*e - 166400*a^4*b^6*c^5*d*e^4 + 358400*a^5*b^4*c^6*d*e^4 + 983040*a^6*b*c^8*d^2*e^3 - 204800*a^6*b^2*c^7*d*e^4)/(c*(4*a*c - b^2)^10))^(1/2))/2)*((e^5*(-(4*a*c - b^2)^15)^(1/2) - b^15*e^5 - 524288*a^5*c^10*d^5 + 512*b^10*c^5*d^5 - 10240*a*b^8*c^6*d^5 + 81920*a^7*b*c^7*e^5 - 163840*a^7*c^8*d*e^4 - 1280*b^11*c^4*d^4*e + 81920*a^2*b^6*c^7*d^5 - 327680*a^3*b^4*c^8*d^5 + 655360*a^4*b^2*c^9*d^5 + 560*a^2*b^11*c^2*e^5 - 4160*a^3*b^9*c^3*e^5 + 11520*a^4*b^7*c^4*e^5 + 1024*a^5*b^5*c^5*e^5 - 61440*a^6*b^3*c^6*e^5 - 655360*a^6*c^9*d^3*e^2 + 1120*b^12*c^3*d^3*e^2 - 400*b^13*c^2*d^2*e^3 - 20*a*b^13*c*e^5 + 50*b^14*c*d*e^4 + 166400*a^2*b^8*c^5*d^3*e^2 - 44800*a^2*b^9*c^4*d^2*e^3 - 614400*a^3*b^6*c^6*d^3*e^2 + 102400*a^3*b^7*c^5*d^2*e^3 + 1024000*a^4*b^4*c^7*d^3*e^2 + 102400*a^4*b^5*c^6*d^2*e^3 - 327680*a^5*b^2*c^8*d^3*e^2 - 819200*a^5*b^3*c^7*d^2*e^3 + 25600*a*b^9*c^5*d^4*e - 600*a*b^12*c^2*d*e^4 + 1310720*a^5*b*c^9*d^4*e - 21760*a*b^10*c^4*d^3*e^2 + 7040*a*b^11*c^3*d^2*e^3 - 204800*a^2*b^7*c^6*d^4*e + 160*a^2*b^10*c^3*d*e^4 + 819200*a^3*b^5*c^7*d^4*e + 28800*a^3*b^8*c^4*d*e^4 - 1638400*a^4*b^3*c^8*d^4*e - 166400*a^4*b^6*c^5*d*e^4 + 358400*a^5*b^4*c^6*d*e^4 + 983040*a^6*b*c^8*d^2*e^3 - 204800*a^6*b^2*c^7*d*e^4)/(c*(4*a*c - b^2)^10))^(1/2))/16 - (9*c*e^2*(d + e*x)^(1/2)*(b^6*e^6 + 512*c^6*d^6 - 32*a^3*c^3*e^6 + 640*a*c^5*d^4*e^2 + 64*a^2*b^2*c^2*e^6 + 160*a^2*c^4*d^2*e^4 + 1760*b^2*c^4*d^4*e^2 - 960*b^3*c^3*d^3*e^3 + 250*b^4*c^2*d^2*e^4 + 14*a*b^4*c*e^6 - 1536*b*c^5*d^5*e - 26*b^5*c*d*e^5 - 1280*a*b*c^4*d^3*e^3 - 240*a*b^3*c^2*d*e^5 - 160*a^2*b*c^3*d*e^5 + 880*a*b^2*c^3*d^2*e^4))/(8*(4*a*c - b^2)^4))*((e^5*(-(4*a*c - b^2)^15)^(1/2) - b^15*e^5 - 524288*a^5*c^10*d^5 + 512*b^10*c^5*d^5 - 10240*a*b^8*c^6*d^5 + 81920*a^7*b*c^7*e^5 - 163840*a^7*c^8*d*e^4 - 1280*b^11*c^4*d^4*e + 81920*a^2*b^6*c^7*d^5 - 327680*a^3*b^4*c^8*d^5 + 655360*a^4*b^2*c^9*d^5 + 560*a^2*b^11*c^2*e^5 - 4160*a^3*b^9*c^3*e^5 + 11520*a^4*b^7*c^4*e^5 + 1024*a^5*b^5*c^5*e^5 - 61440*a^6*b^3*c^6*e^5 - 655360*a^6*c^9*d^3*e^2 + 1120*b^12*c^3*d^3*e^2 - 400*b^13*c^2*d^2*e^3 - 20*a*b^13*c*e^5 + 50*b^14*c*d*e^4 + 166400*a^2*b^8*c^5*d^3*e^2 - 44800*a^2*b^9*c^4*d^2*e^3 - 614400*a^3*b^6*c^6*d^3*e^2 + 102400*a^3*b^7*c^5*d^2*e^3 + 1024000*a^4*b^4*c^7*d^3*e^2 + 102400*a^4*b^5*c^6*d^2*e^3 - 327680*a^5*b^2*c^8*d^3*e^2 - 819200*a^5*b^3*c^7*d^2*e^3 + 25600*a*b^9*c^5*d^4*e - 600*a*b^12*c^2*d*e^4 + 1310720*a^5*b*c^9*d^4*e - 21760*a*b^10*c^4*d^3*e^2 + 7040*a*b^11*c^3*d^2*e^3 - 204800*a^2*b^7*c^6*d^4*e + 160*a^2*b^10*c^3*d*e^4 + 819200*a^3*b^5*c^7*d^4*e + 28800*a^3*b^8*c^4*d*e^4 - 1638400*a^4*b^3*c^8*d^4*e - 166400*a^4*b^6*c^5*d*e^4 + 358400*a^5*b^4*c^6*d*e^4 + 983040*a^6*b*c^8*d^2*e^3 - 204800*a^6*b^2*c^7*d*e^4)/(c*(4*a*c - b^2)^10))^(1/2))/16 - (3*(576*a^4*c^4*e^11 + 18432*c^8*d^8*e^3 + 41472*a*c^7*d^6*e^5 - 73728*b*c^7*d^7*e^4 + 540*a^2*b^4*c^2*e^11 + 1584*a^3*b^2*c^3*e^11 + 31104*a^2*c^6*d^4*e^7 + 8640*a^3*c^5*d^2*e^9 + 118656*b^2*c^6*d^6*e^5 - 97920*b^3*c^5*d^5*e^6 + 43704*b^4*c^4*d^4*e^7 - 10224*b^5*c^3*d^3*e^8 + 1125*b^6*c^2*d^2*e^9 + 45*a*b^6*c*e^11 - 45*b^7*c*d*e^10 + 40176*a^2*b^2*c^4*d^2*e^9 - 124416*a*b*c^6*d^5*e^6 - 1620*a*b^5*c^2*d*e^10 - 8640*a^3*b*c^4*d*e^10 + 139968*a*b^2*c^5*d^4*e^7 - 72576*a*b^3*c^4*d^3*e^8 + 17172*a*b^4*c^3*d^2*e^9 - 62208*a^2*b*c^5*d^3*e^8 - 9072*a^2*b^3*c^3*d*e^10))/(64*(4*a*c - b^2)^6))*((9*(e^5*(-(4*a*c - b^2)^15)^(1/2) - b^15*e^5 - 524288*a^5*c^10*d^5 + 512*b^10*c^5*d^5 - 10240*a*b^8*c^6*d^5 + 81920*a^7*b*c^7*e^5 - 163840*a^7*c^8*d*e^4 - 1280*b^11*c^4*d^4*e + 81920*a^2*b^6*c^7*d^5 - 327680*a^3*b^4*c^8*d^5 + 655360*a^4*b^2*c^9*d^5 + 560*a^2*b^11*c^2*e^5 - 4160*a^3*b^9*c^3*e^5 + 11520*a^4*b^7*c^4*e^5 + 1024*a^5*b^5*c^5*e^5 - 61440*a^6*b^3*c^6*e^5 - 655360*a^6*c^9*d^3*e^2 + 1120*b^12*c^3*d^3*e^2 - 400*b^13*c^2*d^2*e^3 - 20*a*b^13*c*e^5 + 50*b^14*c*d*e^4 + 166400*a^2*b^8*c^5*d^3*e^2 - 44800*a^2*b^9*c^4*d^2*e^3 - 614400*a^3*b^6*c^6*d^3*e^2 + 102400*a^3*b^7*c^5*d^2*e^3 + 1024000*a^4*b^4*c^7*d^3*e^2 + 102400*a^4*b^5*c^6*d^2*e^3 - 327680*a^5*b^2*c^8*d^3*e^2 - 819200*a^5*b^3*c^7*d^2*e^3 + 25600*a*b^9*c^5*d^4*e - 600*a*b^12*c^2*d*e^4 + 1310720*a^5*b*c^9*d^4*e - 21760*a*b^10*c^4*d^3*e^2 + 7040*a*b^11*c^3*d^2*e^3 - 204800*a^2*b^7*c^6*d^4*e + 160*a^2*b^10*c^3*d*e^4 + 819200*a^3*b^5*c^7*d^4*e + 28800*a^3*b^8*c^4*d*e^4 - 1638400*a^4*b^3*c^8*d^4*e - 166400*a^4*b^6*c^5*d*e^4 + 358400*a^5*b^4*c^6*d*e^4 + 983040*a^6*b*c^8*d^2*e^3 - 204800*a^6*b^2*c^7*d*e^4))/(128*(b^20*c + 1048576*a^10*c^11 - 40*a*b^18*c^2 + 720*a^2*b^16*c^3 - 7680*a^3*b^14*c^4 + 53760*a^4*b^12*c^5 - 258048*a^5*b^10*c^6 + 860160*a^6*b^8*c^7 - 1966080*a^7*b^6*c^8 + 2949120*a^8*b^4*c^9 - 2621440*a^9*b^2*c^10)))^(1/2) + (((d + e*x)^(3/2)*(19*a*b^2*e^5 - 4*a^2*c*e^5 - 19*b^3*d*e^4 + 72*c^3*d^4*e + 68*a*c^2*d^2*e^3 - 144*b*c^2*d^3*e^2 + 91*b^2*c*d^2*e^3 - 68*a*b*c*d*e^4))/(4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) - (3*(d + e*x)^(1/2)*(2*c^3*d^5*e - a^2*b*e^6 - b^3*d^2*e^4 + 4*a*c^2*d^3*e^3 - 5*b*c^2*d^4*e^2 + 4*b^2*c*d^3*e^3 + 2*a*b^2*d*e^5 + 2*a^2*c*d*e^5 - 6*a*b*c*d^2*e^4))/(b^4 + 16*a^2*c^2 - 8*a*b^2*c) + ((b*e - 2*c*d)*(d + e*x)^(5/2)*(5*b^2*e^3 + 36*c^2*d^2*e + 16*a*c*e^3 - 36*b*c*d*e^2))/(4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (3*c*e*(d + e*x)^(7/2)*(b^2*e^2 + 8*c^2*d^2 + 4*a*c*e^2 - 8*b*c*d*e))/(4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))/(c^2*(d + e*x)^4 - (d + e*x)*(4*c^2*d^3 + 2*b^2*d*e^2 - 2*a*b*e^3 + 4*a*c*d*e^2 - 6*b*c*d^2*e) - (4*c^2*d - 2*b*c*e)*(d + e*x)^3 + (d + e*x)^2*(b^2*e^2 + 6*c^2*d^2 + 2*a*c*e^2 - 6*b*c*d*e) + a^2*e^4 + c^2*d^4 + b^2*d^2*e^2 - 2*a*b*d*e^3 - 2*b*c*d^3*e + 2*a*c*d^2*e^2)","B"
2304,1,13764,441,21.967458,"\text{Not used}","int((d + e*x)^(3/2)/(a + b*x + c*x^2)^3,x)","\ln\left(\frac{27\,c^3\,e^3\,\left(b\,e-2\,c\,d\right)\,\left(16\,a^2\,c^2\,e^4+40\,a\,b^2\,c\,e^4-192\,a\,b\,c^2\,d\,e^3+192\,a\,c^3\,d^2\,e^2+5\,b^4\,e^4-80\,b^3\,c\,d\,e^3+336\,b^2\,c^2\,d^2\,e^2-512\,b\,c^3\,d^3\,e+256\,c^4\,d^4\right)}{16\,{\left(4\,a\,c-b^2\right)}^6}-\frac{3\,\sqrt{2}\,\left(\frac{3\,\sqrt{2}\,\left(\frac{3\,c^2\,e^3\,\left(b^2\,e^2-8\,b\,c\,d\,e+8\,c^2\,d^2+4\,a\,c\,e^2\right)}{4\,a\,c-b^2}-\frac{3\,\sqrt{2}\,c^2\,e^2\,\left(4\,a\,c-b^2\right)\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^{15}\,e^5+e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+524288\,a^5\,c^{10}\,d^5-512\,b^{10}\,c^5\,d^5+10240\,a\,b^8\,c^6\,d^5-81920\,a^7\,b\,c^7\,e^5+163840\,a^7\,c^8\,d\,e^4+1280\,b^{11}\,c^4\,d^4\,e-81920\,a^2\,b^6\,c^7\,d^5+327680\,a^3\,b^4\,c^8\,d^5-655360\,a^4\,b^2\,c^9\,d^5-560\,a^2\,b^{11}\,c^2\,e^5+4160\,a^3\,b^9\,c^3\,e^5-11520\,a^4\,b^7\,c^4\,e^5-1024\,a^5\,b^5\,c^5\,e^5+61440\,a^6\,b^3\,c^6\,e^5+655360\,a^6\,c^9\,d^3\,e^2-1120\,b^{12}\,c^3\,d^3\,e^2+400\,b^{13}\,c^2\,d^2\,e^3+20\,a\,b^{13}\,c\,e^5-50\,b^{14}\,c\,d\,e^4-166400\,a^2\,b^8\,c^5\,d^3\,e^2+44800\,a^2\,b^9\,c^4\,d^2\,e^3+614400\,a^3\,b^6\,c^6\,d^3\,e^2-102400\,a^3\,b^7\,c^5\,d^2\,e^3-1024000\,a^4\,b^4\,c^7\,d^3\,e^2-102400\,a^4\,b^5\,c^6\,d^2\,e^3+327680\,a^5\,b^2\,c^8\,d^3\,e^2+819200\,a^5\,b^3\,c^7\,d^2\,e^3-25600\,a\,b^9\,c^5\,d^4\,e+600\,a\,b^{12}\,c^2\,d\,e^4-1310720\,a^5\,b\,c^9\,d^4\,e+21760\,a\,b^{10}\,c^4\,d^3\,e^2-7040\,a\,b^{11}\,c^3\,d^2\,e^3+204800\,a^2\,b^7\,c^6\,d^4\,e-160\,a^2\,b^{10}\,c^3\,d\,e^4-819200\,a^3\,b^5\,c^7\,d^4\,e-28800\,a^3\,b^8\,c^4\,d\,e^4+1638400\,a^4\,b^3\,c^8\,d^4\,e+166400\,a^4\,b^6\,c^5\,d\,e^4-358400\,a^5\,b^4\,c^6\,d\,e^4-983040\,a^6\,b\,c^8\,d^2\,e^3+204800\,a^6\,b^2\,c^7\,d\,e^4}{{\left(4\,a\,c-b^2\right)}^{10}\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}}{2}\right)\,\sqrt{-\frac{b^{15}\,e^5+e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+524288\,a^5\,c^{10}\,d^5-512\,b^{10}\,c^5\,d^5+10240\,a\,b^8\,c^6\,d^5-81920\,a^7\,b\,c^7\,e^5+163840\,a^7\,c^8\,d\,e^4+1280\,b^{11}\,c^4\,d^4\,e-81920\,a^2\,b^6\,c^7\,d^5+327680\,a^3\,b^4\,c^8\,d^5-655360\,a^4\,b^2\,c^9\,d^5-560\,a^2\,b^{11}\,c^2\,e^5+4160\,a^3\,b^9\,c^3\,e^5-11520\,a^4\,b^7\,c^4\,e^5-1024\,a^5\,b^5\,c^5\,e^5+61440\,a^6\,b^3\,c^6\,e^5+655360\,a^6\,c^9\,d^3\,e^2-1120\,b^{12}\,c^3\,d^3\,e^2+400\,b^{13}\,c^2\,d^2\,e^3+20\,a\,b^{13}\,c\,e^5-50\,b^{14}\,c\,d\,e^4-166400\,a^2\,b^8\,c^5\,d^3\,e^2+44800\,a^2\,b^9\,c^4\,d^2\,e^3+614400\,a^3\,b^6\,c^6\,d^3\,e^2-102400\,a^3\,b^7\,c^5\,d^2\,e^3-1024000\,a^4\,b^4\,c^7\,d^3\,e^2-102400\,a^4\,b^5\,c^6\,d^2\,e^3+327680\,a^5\,b^2\,c^8\,d^3\,e^2+819200\,a^5\,b^3\,c^7\,d^2\,e^3-25600\,a\,b^9\,c^5\,d^4\,e+600\,a\,b^{12}\,c^2\,d\,e^4-1310720\,a^5\,b\,c^9\,d^4\,e+21760\,a\,b^{10}\,c^4\,d^3\,e^2-7040\,a\,b^{11}\,c^3\,d^2\,e^3+204800\,a^2\,b^7\,c^6\,d^4\,e-160\,a^2\,b^{10}\,c^3\,d\,e^4-819200\,a^3\,b^5\,c^7\,d^4\,e-28800\,a^3\,b^8\,c^4\,d\,e^4+1638400\,a^4\,b^3\,c^8\,d^4\,e+166400\,a^4\,b^6\,c^5\,d\,e^4-358400\,a^5\,b^4\,c^6\,d\,e^4-983040\,a^6\,b\,c^8\,d^2\,e^3+204800\,a^6\,b^2\,c^7\,d\,e^4}{{\left(4\,a\,c-b^2\right)}^{10}\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}}{16}+\frac{9\,c^3\,e^2\,\sqrt{d+e\,x}\,\left(16\,a^2\,c^2\,e^4+8\,a\,b^2\,c\,e^4-64\,a\,b\,c^2\,d\,e^3+64\,a\,c^3\,d^2\,e^2+13\,b^4\,e^4-112\,b^3\,c\,d\,e^3+368\,b^2\,c^2\,d^2\,e^2-512\,b\,c^3\,d^3\,e+256\,c^4\,d^4\right)}{4\,{\left(4\,a\,c-b^2\right)}^4}\right)\,\sqrt{-\frac{b^{15}\,e^5+e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+524288\,a^5\,c^{10}\,d^5-512\,b^{10}\,c^5\,d^5+10240\,a\,b^8\,c^6\,d^5-81920\,a^7\,b\,c^7\,e^5+163840\,a^7\,c^8\,d\,e^4+1280\,b^{11}\,c^4\,d^4\,e-81920\,a^2\,b^6\,c^7\,d^5+327680\,a^3\,b^4\,c^8\,d^5-655360\,a^4\,b^2\,c^9\,d^5-560\,a^2\,b^{11}\,c^2\,e^5+4160\,a^3\,b^9\,c^3\,e^5-11520\,a^4\,b^7\,c^4\,e^5-1024\,a^5\,b^5\,c^5\,e^5+61440\,a^6\,b^3\,c^6\,e^5+655360\,a^6\,c^9\,d^3\,e^2-1120\,b^{12}\,c^3\,d^3\,e^2+400\,b^{13}\,c^2\,d^2\,e^3+20\,a\,b^{13}\,c\,e^5-50\,b^{14}\,c\,d\,e^4-166400\,a^2\,b^8\,c^5\,d^3\,e^2+44800\,a^2\,b^9\,c^4\,d^2\,e^3+614400\,a^3\,b^6\,c^6\,d^3\,e^2-102400\,a^3\,b^7\,c^5\,d^2\,e^3-1024000\,a^4\,b^4\,c^7\,d^3\,e^2-102400\,a^4\,b^5\,c^6\,d^2\,e^3+327680\,a^5\,b^2\,c^8\,d^3\,e^2+819200\,a^5\,b^3\,c^7\,d^2\,e^3-25600\,a\,b^9\,c^5\,d^4\,e+600\,a\,b^{12}\,c^2\,d\,e^4-1310720\,a^5\,b\,c^9\,d^4\,e+21760\,a\,b^{10}\,c^4\,d^3\,e^2-7040\,a\,b^{11}\,c^3\,d^2\,e^3+204800\,a^2\,b^7\,c^6\,d^4\,e-160\,a^2\,b^{10}\,c^3\,d\,e^4-819200\,a^3\,b^5\,c^7\,d^4\,e-28800\,a^3\,b^8\,c^4\,d\,e^4+1638400\,a^4\,b^3\,c^8\,d^4\,e+166400\,a^4\,b^6\,c^5\,d\,e^4-358400\,a^5\,b^4\,c^6\,d\,e^4-983040\,a^6\,b\,c^8\,d^2\,e^3+204800\,a^6\,b^2\,c^7\,d\,e^4}{{\left(4\,a\,c-b^2\right)}^{10}\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}}{16}\right)\,\sqrt{-\frac{9\,\left(b^{15}\,e^5+e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+524288\,a^5\,c^{10}\,d^5-512\,b^{10}\,c^5\,d^5+10240\,a\,b^8\,c^6\,d^5-81920\,a^7\,b\,c^7\,e^5+163840\,a^7\,c^8\,d\,e^4+1280\,b^{11}\,c^4\,d^4\,e-81920\,a^2\,b^6\,c^7\,d^5+327680\,a^3\,b^4\,c^8\,d^5-655360\,a^4\,b^2\,c^9\,d^5-560\,a^2\,b^{11}\,c^2\,e^5+4160\,a^3\,b^9\,c^3\,e^5-11520\,a^4\,b^7\,c^4\,e^5-1024\,a^5\,b^5\,c^5\,e^5+61440\,a^6\,b^3\,c^6\,e^5+655360\,a^6\,c^9\,d^3\,e^2-1120\,b^{12}\,c^3\,d^3\,e^2+400\,b^{13}\,c^2\,d^2\,e^3+20\,a\,b^{13}\,c\,e^5-50\,b^{14}\,c\,d\,e^4-166400\,a^2\,b^8\,c^5\,d^3\,e^2+44800\,a^2\,b^9\,c^4\,d^2\,e^3+614400\,a^3\,b^6\,c^6\,d^3\,e^2-102400\,a^3\,b^7\,c^5\,d^2\,e^3-1024000\,a^4\,b^4\,c^7\,d^3\,e^2-102400\,a^4\,b^5\,c^6\,d^2\,e^3+327680\,a^5\,b^2\,c^8\,d^3\,e^2+819200\,a^5\,b^3\,c^7\,d^2\,e^3-25600\,a\,b^9\,c^5\,d^4\,e+600\,a\,b^{12}\,c^2\,d\,e^4-1310720\,a^5\,b\,c^9\,d^4\,e+21760\,a\,b^{10}\,c^4\,d^3\,e^2-7040\,a\,b^{11}\,c^3\,d^2\,e^3+204800\,a^2\,b^7\,c^6\,d^4\,e-160\,a^2\,b^{10}\,c^3\,d\,e^4-819200\,a^3\,b^5\,c^7\,d^4\,e-28800\,a^3\,b^8\,c^4\,d\,e^4+1638400\,a^4\,b^3\,c^8\,d^4\,e+166400\,a^4\,b^6\,c^5\,d\,e^4-358400\,a^5\,b^4\,c^6\,d\,e^4-983040\,a^6\,b\,c^8\,d^2\,e^3+204800\,a^6\,b^2\,c^7\,d\,e^4\right)}{128\,\left(1048576\,a^{11}\,c^{10}\,e^2-2621440\,a^{10}\,b^2\,c^9\,e^2-1048576\,a^{10}\,b\,c^{10}\,d\,e+1048576\,a^{10}\,c^{11}\,d^2+2949120\,a^9\,b^4\,c^8\,e^2+2621440\,a^9\,b^3\,c^9\,d\,e-2621440\,a^9\,b^2\,c^{10}\,d^2-1966080\,a^8\,b^6\,c^7\,e^2-2949120\,a^8\,b^5\,c^8\,d\,e+2949120\,a^8\,b^4\,c^9\,d^2+860160\,a^7\,b^8\,c^6\,e^2+1966080\,a^7\,b^7\,c^7\,d\,e-1966080\,a^7\,b^6\,c^8\,d^2-258048\,a^6\,b^{10}\,c^5\,e^2-860160\,a^6\,b^9\,c^6\,d\,e+860160\,a^6\,b^8\,c^7\,d^2+53760\,a^5\,b^{12}\,c^4\,e^2+258048\,a^5\,b^{11}\,c^5\,d\,e-258048\,a^5\,b^{10}\,c^6\,d^2-7680\,a^4\,b^{14}\,c^3\,e^2-53760\,a^4\,b^{13}\,c^4\,d\,e+53760\,a^4\,b^{12}\,c^5\,d^2+720\,a^3\,b^{16}\,c^2\,e^2+7680\,a^3\,b^{15}\,c^3\,d\,e-7680\,a^3\,b^{14}\,c^4\,d^2-40\,a^2\,b^{18}\,c\,e^2-720\,a^2\,b^{17}\,c^2\,d\,e+720\,a^2\,b^{16}\,c^3\,d^2+a\,b^{20}\,e^2+40\,a\,b^{19}\,c\,d\,e-40\,a\,b^{18}\,c^2\,d^2-b^{21}\,d\,e+b^{20}\,c\,d^2\right)}}-\ln\left(\frac{27\,c^3\,e^3\,\left(b\,e-2\,c\,d\right)\,\left(16\,a^2\,c^2\,e^4+40\,a\,b^2\,c\,e^4-192\,a\,b\,c^2\,d\,e^3+192\,a\,c^3\,d^2\,e^2+5\,b^4\,e^4-80\,b^3\,c\,d\,e^3+336\,b^2\,c^2\,d^2\,e^2-512\,b\,c^3\,d^3\,e+256\,c^4\,d^4\right)}{16\,{\left(4\,a\,c-b^2\right)}^6}-\left(\left(\frac{3\,c^2\,e^3\,\left(b^2\,e^2-8\,b\,c\,d\,e+8\,c^2\,d^2+4\,a\,c\,e^2\right)}{4\,a\,c-b^2}+8\,c^2\,e^2\,\left(4\,a\,c-b^2\right)\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}\,\sqrt{-\frac{\frac{9\,b^{15}\,e^5}{128}+\frac{9\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}}{128}+36864\,a^5\,c^{10}\,d^5-36\,b^{10}\,c^5\,d^5+720\,a\,b^8\,c^6\,d^5-5760\,a^7\,b\,c^7\,e^5+11520\,a^7\,c^8\,d\,e^4+90\,b^{11}\,c^4\,d^4\,e-5760\,a^2\,b^6\,c^7\,d^5+23040\,a^3\,b^4\,c^8\,d^5-46080\,a^4\,b^2\,c^9\,d^5-\frac{315\,a^2\,b^{11}\,c^2\,e^5}{8}+\frac{585\,a^3\,b^9\,c^3\,e^5}{2}-810\,a^4\,b^7\,c^4\,e^5-72\,a^5\,b^5\,c^5\,e^5+4320\,a^6\,b^3\,c^6\,e^5+46080\,a^6\,c^9\,d^3\,e^2-\frac{315\,b^{12}\,c^3\,d^3\,e^2}{4}+\frac{225\,b^{13}\,c^2\,d^2\,e^3}{8}+\frac{45\,a\,b^{13}\,c\,e^5}{32}-\frac{225\,b^{14}\,c\,d\,e^4}{64}-11700\,a^2\,b^8\,c^5\,d^3\,e^2+3150\,a^2\,b^9\,c^4\,d^2\,e^3+43200\,a^3\,b^6\,c^6\,d^3\,e^2-7200\,a^3\,b^7\,c^5\,d^2\,e^3-72000\,a^4\,b^4\,c^7\,d^3\,e^2-7200\,a^4\,b^5\,c^6\,d^2\,e^3+23040\,a^5\,b^2\,c^8\,d^3\,e^2+57600\,a^5\,b^3\,c^7\,d^2\,e^3-1800\,a\,b^9\,c^5\,d^4\,e+\frac{675\,a\,b^{12}\,c^2\,d\,e^4}{16}-92160\,a^5\,b\,c^9\,d^4\,e+1530\,a\,b^{10}\,c^4\,d^3\,e^2-495\,a\,b^{11}\,c^3\,d^2\,e^3+14400\,a^2\,b^7\,c^6\,d^4\,e-\frac{45\,a^2\,b^{10}\,c^3\,d\,e^4}{4}-57600\,a^3\,b^5\,c^7\,d^4\,e-2025\,a^3\,b^8\,c^4\,d\,e^4+115200\,a^4\,b^3\,c^8\,d^4\,e+11700\,a^4\,b^6\,c^5\,d\,e^4-25200\,a^5\,b^4\,c^6\,d\,e^4-69120\,a^6\,b\,c^8\,d^2\,e^3+14400\,a^6\,b^2\,c^7\,d\,e^4}{{\left(4\,a\,c-b^2\right)}^{10}\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}\right)\,\sqrt{-\frac{\frac{9\,b^{15}\,e^5}{128}+\frac{9\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}}{128}+36864\,a^5\,c^{10}\,d^5-36\,b^{10}\,c^5\,d^5+720\,a\,b^8\,c^6\,d^5-5760\,a^7\,b\,c^7\,e^5+11520\,a^7\,c^8\,d\,e^4+90\,b^{11}\,c^4\,d^4\,e-5760\,a^2\,b^6\,c^7\,d^5+23040\,a^3\,b^4\,c^8\,d^5-46080\,a^4\,b^2\,c^9\,d^5-\frac{315\,a^2\,b^{11}\,c^2\,e^5}{8}+\frac{585\,a^3\,b^9\,c^3\,e^5}{2}-810\,a^4\,b^7\,c^4\,e^5-72\,a^5\,b^5\,c^5\,e^5+4320\,a^6\,b^3\,c^6\,e^5+46080\,a^6\,c^9\,d^3\,e^2-\frac{315\,b^{12}\,c^3\,d^3\,e^2}{4}+\frac{225\,b^{13}\,c^2\,d^2\,e^3}{8}+\frac{45\,a\,b^{13}\,c\,e^5}{32}-\frac{225\,b^{14}\,c\,d\,e^4}{64}-11700\,a^2\,b^8\,c^5\,d^3\,e^2+3150\,a^2\,b^9\,c^4\,d^2\,e^3+43200\,a^3\,b^6\,c^6\,d^3\,e^2-7200\,a^3\,b^7\,c^5\,d^2\,e^3-72000\,a^4\,b^4\,c^7\,d^3\,e^2-7200\,a^4\,b^5\,c^6\,d^2\,e^3+23040\,a^5\,b^2\,c^8\,d^3\,e^2+57600\,a^5\,b^3\,c^7\,d^2\,e^3-1800\,a\,b^9\,c^5\,d^4\,e+\frac{675\,a\,b^{12}\,c^2\,d\,e^4}{16}-92160\,a^5\,b\,c^9\,d^4\,e+1530\,a\,b^{10}\,c^4\,d^3\,e^2-495\,a\,b^{11}\,c^3\,d^2\,e^3+14400\,a^2\,b^7\,c^6\,d^4\,e-\frac{45\,a^2\,b^{10}\,c^3\,d\,e^4}{4}-57600\,a^3\,b^5\,c^7\,d^4\,e-2025\,a^3\,b^8\,c^4\,d\,e^4+115200\,a^4\,b^3\,c^8\,d^4\,e+11700\,a^4\,b^6\,c^5\,d\,e^4-25200\,a^5\,b^4\,c^6\,d\,e^4-69120\,a^6\,b\,c^8\,d^2\,e^3+14400\,a^6\,b^2\,c^7\,d\,e^4}{{\left(4\,a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,e^4}{{\left(4\,a\,c-b^2\right)}^{10}\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}}{16}+\frac{9\,c^3\,e^2\,\sqrt{d+e\,x}\,\left(16\,a^2\,c^2\,e^4+8\,a\,b^2\,c\,e^4-64\,a\,b\,c^2\,d\,e^3+64\,a\,c^3\,d^2\,e^2+13\,b^4\,e^4-112\,b^3\,c\,d\,e^3+368\,b^2\,c^2\,d^2\,e^2-512\,b\,c^3\,d^3\,e+256\,c^4\,d^4\right)}{4\,{\left(4\,a\,c-b^2\right)}^4}\right)\,\sqrt{\frac{e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-b^{15}\,e^5-524288\,a^5\,c^{10}\,d^5+512\,b^{10}\,c^5\,d^5-10240\,a\,b^8\,c^6\,d^5+81920\,a^7\,b\,c^7\,e^5-163840\,a^7\,c^8\,d\,e^4-1280\,b^{11}\,c^4\,d^4\,e+81920\,a^2\,b^6\,c^7\,d^5-327680\,a^3\,b^4\,c^8\,d^5+655360\,a^4\,b^2\,c^9\,d^5+560\,a^2\,b^{11}\,c^2\,e^5-4160\,a^3\,b^9\,c^3\,e^5+11520\,a^4\,b^7\,c^4\,e^5+1024\,a^5\,b^5\,c^5\,e^5-61440\,a^6\,b^3\,c^6\,e^5-655360\,a^6\,c^9\,d^3\,e^2+1120\,b^{12}\,c^3\,d^3\,e^2-400\,b^{13}\,c^2\,d^2\,e^3-20\,a\,b^{13}\,c\,e^5+50\,b^{14}\,c\,d\,e^4+166400\,a^2\,b^8\,c^5\,d^3\,e^2-44800\,a^2\,b^9\,c^4\,d^2\,e^3-614400\,a^3\,b^6\,c^6\,d^3\,e^2+102400\,a^3\,b^7\,c^5\,d^2\,e^3+1024000\,a^4\,b^4\,c^7\,d^3\,e^2+102400\,a^4\,b^5\,c^6\,d^2\,e^3-327680\,a^5\,b^2\,c^8\,d^3\,e^2-819200\,a^5\,b^3\,c^7\,d^2\,e^3+25600\,a\,b^9\,c^5\,d^4\,e-600\,a\,b^{12}\,c^2\,d\,e^4+1310720\,a^5\,b\,c^9\,d^4\,e-21760\,a\,b^{10}\,c^4\,d^3\,e^2+7040\,a\,b^{11}\,c^3\,d^2\,e^3-204800\,a^2\,b^7\,c^6\,d^4\,e+160\,a^2\,b^{10}\,c^3\,d\,e^4+819200\,a^3\,b^5\,c^7\,d^4\,e+28800\,a^3\,b^8\,c^4\,d\,e^4-1638400\,a^4\,b^3\,c^8\,d^4\,e-166400\,a^4\,b^6\,c^5\,d\,e^4+358400\,a^5\,b^4\,c^6\,d\,e^4+983040\,a^6\,b\,c^8\,d^2\,e^3-204800\,a^6\,b^2\,c^7\,d\,e^4}{{\left(4\,a\,c-b^2\right)}^{10}\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}}{16}\right)\,\sqrt{\frac{9\,\left(e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-b^{15}\,e^5-524288\,a^5\,c^{10}\,d^5+512\,b^{10}\,c^5\,d^5-10240\,a\,b^8\,c^6\,d^5+81920\,a^7\,b\,c^7\,e^5-163840\,a^7\,c^8\,d\,e^4-1280\,b^{11}\,c^4\,d^4\,e+81920\,a^2\,b^6\,c^7\,d^5-327680\,a^3\,b^4\,c^8\,d^5+655360\,a^4\,b^2\,c^9\,d^5+560\,a^2\,b^{11}\,c^2\,e^5-4160\,a^3\,b^9\,c^3\,e^5+11520\,a^4\,b^7\,c^4\,e^5+1024\,a^5\,b^5\,c^5\,e^5-61440\,a^6\,b^3\,c^6\,e^5-655360\,a^6\,c^9\,d^3\,e^2+1120\,b^{12}\,c^3\,d^3\,e^2-400\,b^{13}\,c^2\,d^2\,e^3-20\,a\,b^{13}\,c\,e^5+50\,b^{14}\,c\,d\,e^4+166400\,a^2\,b^8\,c^5\,d^3\,e^2-44800\,a^2\,b^9\,c^4\,d^2\,e^3-614400\,a^3\,b^6\,c^6\,d^3\,e^2+102400\,a^3\,b^7\,c^5\,d^2\,e^3+1024000\,a^4\,b^4\,c^7\,d^3\,e^2+102400\,a^4\,b^5\,c^6\,d^2\,e^3-327680\,a^5\,b^2\,c^8\,d^3\,e^2-819200\,a^5\,b^3\,c^7\,d^2\,e^3+25600\,a\,b^9\,c^5\,d^4\,e-600\,a\,b^{12}\,c^2\,d\,e^4+1310720\,a^5\,b\,c^9\,d^4\,e-21760\,a\,b^{10}\,c^4\,d^3\,e^2+7040\,a\,b^{11}\,c^3\,d^2\,e^3-204800\,a^2\,b^7\,c^6\,d^4\,e+160\,a^2\,b^{10}\,c^3\,d\,e^4+819200\,a^3\,b^5\,c^7\,d^4\,e+28800\,a^3\,b^8\,c^4\,d\,e^4-1638400\,a^4\,b^3\,c^8\,d^4\,e-166400\,a^4\,b^6\,c^5\,d\,e^4+358400\,a^5\,b^4\,c^6\,d\,e^4+983040\,a^6\,b\,c^8\,d^2\,e^3-204800\,a^6\,b^2\,c^7\,d\,e^4\right)}{128\,\left(1048576\,a^{11}\,c^{10}\,e^2-2621440\,a^{10}\,b^2\,c^9\,e^2-1048576\,a^{10}\,b\,c^{10}\,d\,e+1048576\,a^{10}\,c^{11}\,d^2+2949120\,a^9\,b^4\,c^8\,e^2+2621440\,a^9\,b^3\,c^9\,d\,e-2621440\,a^9\,b^2\,c^{10}\,d^2-1966080\,a^8\,b^6\,c^7\,e^2-2949120\,a^8\,b^5\,c^8\,d\,e+2949120\,a^8\,b^4\,c^9\,d^2+860160\,a^7\,b^8\,c^6\,e^2+1966080\,a^7\,b^7\,c^7\,d\,e-1966080\,a^7\,b^6\,c^8\,d^2-258048\,a^6\,b^{10}\,c^5\,e^2-860160\,a^6\,b^9\,c^6\,d\,e+860160\,a^6\,b^8\,c^7\,d^2+53760\,a^5\,b^{12}\,c^4\,e^2+258048\,a^5\,b^{11}\,c^5\,d\,e-258048\,a^5\,b^{10}\,c^6\,d^2-7680\,a^4\,b^{14}\,c^3\,e^2-53760\,a^4\,b^{13}\,c^4\,d\,e+53760\,a^4\,b^{12}\,c^5\,d^2+720\,a^3\,b^{16}\,c^2\,e^2+7680\,a^3\,b^{15}\,c^3\,d\,e-7680\,a^3\,b^{14}\,c^4\,d^2-40\,a^2\,b^{18}\,c\,e^2-720\,a^2\,b^{17}\,c^2\,d\,e+720\,a^2\,b^{16}\,c^3\,d^2+a\,b^{20}\,e^2+40\,a\,b^{19}\,c\,d\,e-40\,a\,b^{18}\,c^2\,d^2-b^{21}\,d\,e+b^{20}\,c\,d^2\right)}}","Not used",1,"log((27*c^3*e^3*(b*e - 2*c*d)*(5*b^4*e^4 + 256*c^4*d^4 + 16*a^2*c^2*e^4 + 192*a*c^3*d^2*e^2 + 336*b^2*c^2*d^2*e^2 + 40*a*b^2*c*e^4 - 512*b*c^3*d^3*e - 80*b^3*c*d*e^3 - 192*a*b*c^2*d*e^3))/(16*(4*a*c - b^2)^6) - (3*2^(1/2)*((3*2^(1/2)*((3*c^2*e^3*(b^2*e^2 + 8*c^2*d^2 + 4*a*c*e^2 - 8*b*c*d*e))/(4*a*c - b^2) - (3*2^(1/2)*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(-(b^15*e^5 + e^5*(-(4*a*c - b^2)^15)^(1/2) + 524288*a^5*c^10*d^5 - 512*b^10*c^5*d^5 + 10240*a*b^8*c^6*d^5 - 81920*a^7*b*c^7*e^5 + 163840*a^7*c^8*d*e^4 + 1280*b^11*c^4*d^4*e - 81920*a^2*b^6*c^7*d^5 + 327680*a^3*b^4*c^8*d^5 - 655360*a^4*b^2*c^9*d^5 - 560*a^2*b^11*c^2*e^5 + 4160*a^3*b^9*c^3*e^5 - 11520*a^4*b^7*c^4*e^5 - 1024*a^5*b^5*c^5*e^5 + 61440*a^6*b^3*c^6*e^5 + 655360*a^6*c^9*d^3*e^2 - 1120*b^12*c^3*d^3*e^2 + 400*b^13*c^2*d^2*e^3 + 20*a*b^13*c*e^5 - 50*b^14*c*d*e^4 - 166400*a^2*b^8*c^5*d^3*e^2 + 44800*a^2*b^9*c^4*d^2*e^3 + 614400*a^3*b^6*c^6*d^3*e^2 - 102400*a^3*b^7*c^5*d^2*e^3 - 1024000*a^4*b^4*c^7*d^3*e^2 - 102400*a^4*b^5*c^6*d^2*e^3 + 327680*a^5*b^2*c^8*d^3*e^2 + 819200*a^5*b^3*c^7*d^2*e^3 - 25600*a*b^9*c^5*d^4*e + 600*a*b^12*c^2*d*e^4 - 1310720*a^5*b*c^9*d^4*e + 21760*a*b^10*c^4*d^3*e^2 - 7040*a*b^11*c^3*d^2*e^3 + 204800*a^2*b^7*c^6*d^4*e - 160*a^2*b^10*c^3*d*e^4 - 819200*a^3*b^5*c^7*d^4*e - 28800*a^3*b^8*c^4*d*e^4 + 1638400*a^4*b^3*c^8*d^4*e + 166400*a^4*b^6*c^5*d*e^4 - 358400*a^5*b^4*c^6*d*e^4 - 983040*a^6*b*c^8*d^2*e^3 + 204800*a^6*b^2*c^7*d*e^4)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)))^(1/2))/2)*(-(b^15*e^5 + e^5*(-(4*a*c - b^2)^15)^(1/2) + 524288*a^5*c^10*d^5 - 512*b^10*c^5*d^5 + 10240*a*b^8*c^6*d^5 - 81920*a^7*b*c^7*e^5 + 163840*a^7*c^8*d*e^4 + 1280*b^11*c^4*d^4*e - 81920*a^2*b^6*c^7*d^5 + 327680*a^3*b^4*c^8*d^5 - 655360*a^4*b^2*c^9*d^5 - 560*a^2*b^11*c^2*e^5 + 4160*a^3*b^9*c^3*e^5 - 11520*a^4*b^7*c^4*e^5 - 1024*a^5*b^5*c^5*e^5 + 61440*a^6*b^3*c^6*e^5 + 655360*a^6*c^9*d^3*e^2 - 1120*b^12*c^3*d^3*e^2 + 400*b^13*c^2*d^2*e^3 + 20*a*b^13*c*e^5 - 50*b^14*c*d*e^4 - 166400*a^2*b^8*c^5*d^3*e^2 + 44800*a^2*b^9*c^4*d^2*e^3 + 614400*a^3*b^6*c^6*d^3*e^2 - 102400*a^3*b^7*c^5*d^2*e^3 - 1024000*a^4*b^4*c^7*d^3*e^2 - 102400*a^4*b^5*c^6*d^2*e^3 + 327680*a^5*b^2*c^8*d^3*e^2 + 819200*a^5*b^3*c^7*d^2*e^3 - 25600*a*b^9*c^5*d^4*e + 600*a*b^12*c^2*d*e^4 - 1310720*a^5*b*c^9*d^4*e + 21760*a*b^10*c^4*d^3*e^2 - 7040*a*b^11*c^3*d^2*e^3 + 204800*a^2*b^7*c^6*d^4*e - 160*a^2*b^10*c^3*d*e^4 - 819200*a^3*b^5*c^7*d^4*e - 28800*a^3*b^8*c^4*d*e^4 + 1638400*a^4*b^3*c^8*d^4*e + 166400*a^4*b^6*c^5*d*e^4 - 358400*a^5*b^4*c^6*d*e^4 - 983040*a^6*b*c^8*d^2*e^3 + 204800*a^6*b^2*c^7*d*e^4)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)))^(1/2))/16 + (9*c^3*e^2*(d + e*x)^(1/2)*(13*b^4*e^4 + 256*c^4*d^4 + 16*a^2*c^2*e^4 + 64*a*c^3*d^2*e^2 + 368*b^2*c^2*d^2*e^2 + 8*a*b^2*c*e^4 - 512*b*c^3*d^3*e - 112*b^3*c*d*e^3 - 64*a*b*c^2*d*e^3))/(4*(4*a*c - b^2)^4))*(-(b^15*e^5 + e^5*(-(4*a*c - b^2)^15)^(1/2) + 524288*a^5*c^10*d^5 - 512*b^10*c^5*d^5 + 10240*a*b^8*c^6*d^5 - 81920*a^7*b*c^7*e^5 + 163840*a^7*c^8*d*e^4 + 1280*b^11*c^4*d^4*e - 81920*a^2*b^6*c^7*d^5 + 327680*a^3*b^4*c^8*d^5 - 655360*a^4*b^2*c^9*d^5 - 560*a^2*b^11*c^2*e^5 + 4160*a^3*b^9*c^3*e^5 - 11520*a^4*b^7*c^4*e^5 - 1024*a^5*b^5*c^5*e^5 + 61440*a^6*b^3*c^6*e^5 + 655360*a^6*c^9*d^3*e^2 - 1120*b^12*c^3*d^3*e^2 + 400*b^13*c^2*d^2*e^3 + 20*a*b^13*c*e^5 - 50*b^14*c*d*e^4 - 166400*a^2*b^8*c^5*d^3*e^2 + 44800*a^2*b^9*c^4*d^2*e^3 + 614400*a^3*b^6*c^6*d^3*e^2 - 102400*a^3*b^7*c^5*d^2*e^3 - 1024000*a^4*b^4*c^7*d^3*e^2 - 102400*a^4*b^5*c^6*d^2*e^3 + 327680*a^5*b^2*c^8*d^3*e^2 + 819200*a^5*b^3*c^7*d^2*e^3 - 25600*a*b^9*c^5*d^4*e + 600*a*b^12*c^2*d*e^4 - 1310720*a^5*b*c^9*d^4*e + 21760*a*b^10*c^4*d^3*e^2 - 7040*a*b^11*c^3*d^2*e^3 + 204800*a^2*b^7*c^6*d^4*e - 160*a^2*b^10*c^3*d*e^4 - 819200*a^3*b^5*c^7*d^4*e - 28800*a^3*b^8*c^4*d*e^4 + 1638400*a^4*b^3*c^8*d^4*e + 166400*a^4*b^6*c^5*d*e^4 - 358400*a^5*b^4*c^6*d*e^4 - 983040*a^6*b*c^8*d^2*e^3 + 204800*a^6*b^2*c^7*d*e^4)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)))^(1/2))/16)*(-(9*(b^15*e^5 + e^5*(-(4*a*c - b^2)^15)^(1/2) + 524288*a^5*c^10*d^5 - 512*b^10*c^5*d^5 + 10240*a*b^8*c^6*d^5 - 81920*a^7*b*c^7*e^5 + 163840*a^7*c^8*d*e^4 + 1280*b^11*c^4*d^4*e - 81920*a^2*b^6*c^7*d^5 + 327680*a^3*b^4*c^8*d^5 - 655360*a^4*b^2*c^9*d^5 - 560*a^2*b^11*c^2*e^5 + 4160*a^3*b^9*c^3*e^5 - 11520*a^4*b^7*c^4*e^5 - 1024*a^5*b^5*c^5*e^5 + 61440*a^6*b^3*c^6*e^5 + 655360*a^6*c^9*d^3*e^2 - 1120*b^12*c^3*d^3*e^2 + 400*b^13*c^2*d^2*e^3 + 20*a*b^13*c*e^5 - 50*b^14*c*d*e^4 - 166400*a^2*b^8*c^5*d^3*e^2 + 44800*a^2*b^9*c^4*d^2*e^3 + 614400*a^3*b^6*c^6*d^3*e^2 - 102400*a^3*b^7*c^5*d^2*e^3 - 1024000*a^4*b^4*c^7*d^3*e^2 - 102400*a^4*b^5*c^6*d^2*e^3 + 327680*a^5*b^2*c^8*d^3*e^2 + 819200*a^5*b^3*c^7*d^2*e^3 - 25600*a*b^9*c^5*d^4*e + 600*a*b^12*c^2*d*e^4 - 1310720*a^5*b*c^9*d^4*e + 21760*a*b^10*c^4*d^3*e^2 - 7040*a*b^11*c^3*d^2*e^3 + 204800*a^2*b^7*c^6*d^4*e - 160*a^2*b^10*c^3*d*e^4 - 819200*a^3*b^5*c^7*d^4*e - 28800*a^3*b^8*c^4*d*e^4 + 1638400*a^4*b^3*c^8*d^4*e + 166400*a^4*b^6*c^5*d*e^4 - 358400*a^5*b^4*c^6*d*e^4 - 983040*a^6*b*c^8*d^2*e^3 + 204800*a^6*b^2*c^7*d*e^4))/(128*(a*b^20*e^2 + b^20*c*d^2 + 1048576*a^10*c^11*d^2 + 1048576*a^11*c^10*e^2 - b^21*d*e - 40*a*b^18*c^2*d^2 - 40*a^2*b^18*c*e^2 + 720*a^2*b^16*c^3*d^2 - 7680*a^3*b^14*c^4*d^2 + 53760*a^4*b^12*c^5*d^2 - 258048*a^5*b^10*c^6*d^2 + 860160*a^6*b^8*c^7*d^2 - 1966080*a^7*b^6*c^8*d^2 + 2949120*a^8*b^4*c^9*d^2 - 2621440*a^9*b^2*c^10*d^2 + 720*a^3*b^16*c^2*e^2 - 7680*a^4*b^14*c^3*e^2 + 53760*a^5*b^12*c^4*e^2 - 258048*a^6*b^10*c^5*e^2 + 860160*a^7*b^8*c^6*e^2 - 1966080*a^8*b^6*c^7*e^2 + 2949120*a^9*b^4*c^8*e^2 - 2621440*a^10*b^2*c^9*e^2 - 1048576*a^10*b*c^10*d*e - 720*a^2*b^17*c^2*d*e + 7680*a^3*b^15*c^3*d*e - 53760*a^4*b^13*c^4*d*e + 258048*a^5*b^11*c^5*d*e - 860160*a^6*b^9*c^6*d*e + 1966080*a^7*b^7*c^7*d*e - 2949120*a^8*b^5*c^8*d*e + 2621440*a^9*b^3*c^9*d*e + 40*a*b^19*c*d*e)))^(1/2) - log((27*c^3*e^3*(b*e - 2*c*d)*(5*b^4*e^4 + 256*c^4*d^4 + 16*a^2*c^2*e^4 + 192*a*c^3*d^2*e^2 + 336*b^2*c^2*d^2*e^2 + 40*a*b^2*c*e^4 - 512*b*c^3*d^3*e - 80*b^3*c*d*e^3 - 192*a*b*c^2*d*e^3))/(16*(4*a*c - b^2)^6) - (((3*c^2*e^3*(b^2*e^2 + 8*c^2*d^2 + 4*a*c*e^2 - 8*b*c*d*e))/(4*a*c - b^2) + 8*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(-((9*b^15*e^5)/128 + (9*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 + 36864*a^5*c^10*d^5 - 36*b^10*c^5*d^5 + 720*a*b^8*c^6*d^5 - 5760*a^7*b*c^7*e^5 + 11520*a^7*c^8*d*e^4 + 90*b^11*c^4*d^4*e - 5760*a^2*b^6*c^7*d^5 + 23040*a^3*b^4*c^8*d^5 - 46080*a^4*b^2*c^9*d^5 - (315*a^2*b^11*c^2*e^5)/8 + (585*a^3*b^9*c^3*e^5)/2 - 810*a^4*b^7*c^4*e^5 - 72*a^5*b^5*c^5*e^5 + 4320*a^6*b^3*c^6*e^5 + 46080*a^6*c^9*d^3*e^2 - (315*b^12*c^3*d^3*e^2)/4 + (225*b^13*c^2*d^2*e^3)/8 + (45*a*b^13*c*e^5)/32 - (225*b^14*c*d*e^4)/64 - 11700*a^2*b^8*c^5*d^3*e^2 + 3150*a^2*b^9*c^4*d^2*e^3 + 43200*a^3*b^6*c^6*d^3*e^2 - 7200*a^3*b^7*c^5*d^2*e^3 - 72000*a^4*b^4*c^7*d^3*e^2 - 7200*a^4*b^5*c^6*d^2*e^3 + 23040*a^5*b^2*c^8*d^3*e^2 + 57600*a^5*b^3*c^7*d^2*e^3 - 1800*a*b^9*c^5*d^4*e + (675*a*b^12*c^2*d*e^4)/16 - 92160*a^5*b*c^9*d^4*e + 1530*a*b^10*c^4*d^3*e^2 - 495*a*b^11*c^3*d^2*e^3 + 14400*a^2*b^7*c^6*d^4*e - (45*a^2*b^10*c^3*d*e^4)/4 - 57600*a^3*b^5*c^7*d^4*e - 2025*a^3*b^8*c^4*d*e^4 + 115200*a^4*b^3*c^8*d^4*e + 11700*a^4*b^6*c^5*d*e^4 - 25200*a^5*b^4*c^6*d*e^4 - 69120*a^6*b*c^8*d^2*e^3 + 14400*a^6*b^2*c^7*d*e^4)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)))^(1/2))*(-((9*b^15*e^5)/128 + (9*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 + 36864*a^5*c^10*d^5 - 36*b^10*c^5*d^5 + 720*a*b^8*c^6*d^5 - 5760*a^7*b*c^7*e^5 + 11520*a^7*c^8*d*e^4 + 90*b^11*c^4*d^4*e - 5760*a^2*b^6*c^7*d^5 + 23040*a^3*b^4*c^8*d^5 - 46080*a^4*b^2*c^9*d^5 - (315*a^2*b^11*c^2*e^5)/8 + (585*a^3*b^9*c^3*e^5)/2 - 810*a^4*b^7*c^4*e^5 - 72*a^5*b^5*c^5*e^5 + 4320*a^6*b^3*c^6*e^5 + 46080*a^6*c^9*d^3*e^2 - (315*b^12*c^3*d^3*e^2)/4 + (225*b^13*c^2*d^2*e^3)/8 + (45*a*b^13*c*e^5)/32 - (225*b^14*c*d*e^4)/64 - 11700*a^2*b^8*c^5*d^3*e^2 + 3150*a^2*b^9*c^4*d^2*e^3 + 43200*a^3*b^6*c^6*d^3*e^2 - 7200*a^3*b^7*c^5*d^2*e^3 - 72000*a^4*b^4*c^7*d^3*e^2 - 7200*a^4*b^5*c^6*d^2*e^3 + 23040*a^5*b^2*c^8*d^3*e^2 + 57600*a^5*b^3*c^7*d^2*e^3 - 1800*a*b^9*c^5*d^4*e + (675*a*b^12*c^2*d*e^4)/16 - 92160*a^5*b*c^9*d^4*e + 1530*a*b^10*c^4*d^3*e^2 - 495*a*b^11*c^3*d^2*e^3 + 14400*a^2*b^7*c^6*d^4*e - (45*a^2*b^10*c^3*d*e^4)/4 - 57600*a^3*b^5*c^7*d^4*e - 2025*a^3*b^8*c^4*d*e^4 + 115200*a^4*b^3*c^8*d^4*e + 11700*a^4*b^6*c^5*d*e^4 - 25200*a^5*b^4*c^6*d*e^4 - 69120*a^6*b*c^8*d^2*e^3 + 14400*a^6*b^2*c^7*d*e^4)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)))^(1/2) - (9*c^3*e^2*(d + e*x)^(1/2)*(13*b^4*e^4 + 256*c^4*d^4 + 16*a^2*c^2*e^4 + 64*a*c^3*d^2*e^2 + 368*b^2*c^2*d^2*e^2 + 8*a*b^2*c*e^4 - 512*b*c^3*d^3*e - 112*b^3*c*d*e^3 - 64*a*b*c^2*d*e^3))/(4*(4*a*c - b^2)^4))*(-((9*b^15*e^5)/128 + (9*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 + 36864*a^5*c^10*d^5 - 36*b^10*c^5*d^5 + 720*a*b^8*c^6*d^5 - 5760*a^7*b*c^7*e^5 + 11520*a^7*c^8*d*e^4 + 90*b^11*c^4*d^4*e - 5760*a^2*b^6*c^7*d^5 + 23040*a^3*b^4*c^8*d^5 - 46080*a^4*b^2*c^9*d^5 - (315*a^2*b^11*c^2*e^5)/8 + (585*a^3*b^9*c^3*e^5)/2 - 810*a^4*b^7*c^4*e^5 - 72*a^5*b^5*c^5*e^5 + 4320*a^6*b^3*c^6*e^5 + 46080*a^6*c^9*d^3*e^2 - (315*b^12*c^3*d^3*e^2)/4 + (225*b^13*c^2*d^2*e^3)/8 + (45*a*b^13*c*e^5)/32 - (225*b^14*c*d*e^4)/64 - 11700*a^2*b^8*c^5*d^3*e^2 + 3150*a^2*b^9*c^4*d^2*e^3 + 43200*a^3*b^6*c^6*d^3*e^2 - 7200*a^3*b^7*c^5*d^2*e^3 - 72000*a^4*b^4*c^7*d^3*e^2 - 7200*a^4*b^5*c^6*d^2*e^3 + 23040*a^5*b^2*c^8*d^3*e^2 + 57600*a^5*b^3*c^7*d^2*e^3 - 1800*a*b^9*c^5*d^4*e + (675*a*b^12*c^2*d*e^4)/16 - 92160*a^5*b*c^9*d^4*e + 1530*a*b^10*c^4*d^3*e^2 - 495*a*b^11*c^3*d^2*e^3 + 14400*a^2*b^7*c^6*d^4*e - (45*a^2*b^10*c^3*d*e^4)/4 - 57600*a^3*b^5*c^7*d^4*e - 2025*a^3*b^8*c^4*d*e^4 + 115200*a^4*b^3*c^8*d^4*e + 11700*a^4*b^6*c^5*d*e^4 - 25200*a^5*b^4*c^6*d*e^4 - 69120*a^6*b*c^8*d^2*e^3 + 14400*a^6*b^2*c^7*d*e^4)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)))^(1/2))*(-((9*b^15*e^5)/128 + (9*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 + 36864*a^5*c^10*d^5 - 36*b^10*c^5*d^5 + 720*a*b^8*c^6*d^5 - 5760*a^7*b*c^7*e^5 + 11520*a^7*c^8*d*e^4 + 90*b^11*c^4*d^4*e - 5760*a^2*b^6*c^7*d^5 + 23040*a^3*b^4*c^8*d^5 - 46080*a^4*b^2*c^9*d^5 - (315*a^2*b^11*c^2*e^5)/8 + (585*a^3*b^9*c^3*e^5)/2 - 810*a^4*b^7*c^4*e^5 - 72*a^5*b^5*c^5*e^5 + 4320*a^6*b^3*c^6*e^5 + 46080*a^6*c^9*d^3*e^2 - (315*b^12*c^3*d^3*e^2)/4 + (225*b^13*c^2*d^2*e^3)/8 + (45*a*b^13*c*e^5)/32 - (225*b^14*c*d*e^4)/64 - 11700*a^2*b^8*c^5*d^3*e^2 + 3150*a^2*b^9*c^4*d^2*e^3 + 43200*a^3*b^6*c^6*d^3*e^2 - 7200*a^3*b^7*c^5*d^2*e^3 - 72000*a^4*b^4*c^7*d^3*e^2 - 7200*a^4*b^5*c^6*d^2*e^3 + 23040*a^5*b^2*c^8*d^3*e^2 + 57600*a^5*b^3*c^7*d^2*e^3 - 1800*a*b^9*c^5*d^4*e + (675*a*b^12*c^2*d*e^4)/16 - 92160*a^5*b*c^9*d^4*e + 1530*a*b^10*c^4*d^3*e^2 - 495*a*b^11*c^3*d^2*e^3 + 14400*a^2*b^7*c^6*d^4*e - (45*a^2*b^10*c^3*d*e^4)/4 - 57600*a^3*b^5*c^7*d^4*e - 2025*a^3*b^8*c^4*d*e^4 + 115200*a^4*b^3*c^8*d^4*e + 11700*a^4*b^6*c^5*d*e^4 - 25200*a^5*b^4*c^6*d*e^4 - 69120*a^6*b*c^8*d^2*e^3 + 14400*a^6*b^2*c^7*d*e^4)/(a*b^20*e^2 + b^20*c*d^2 + 1048576*a^10*c^11*d^2 + 1048576*a^11*c^10*e^2 - b^21*d*e - 40*a*b^18*c^2*d^2 - 40*a^2*b^18*c*e^2 + 720*a^2*b^16*c^3*d^2 - 7680*a^3*b^14*c^4*d^2 + 53760*a^4*b^12*c^5*d^2 - 258048*a^5*b^10*c^6*d^2 + 860160*a^6*b^8*c^7*d^2 - 1966080*a^7*b^6*c^8*d^2 + 2949120*a^8*b^4*c^9*d^2 - 2621440*a^9*b^2*c^10*d^2 + 720*a^3*b^16*c^2*e^2 - 7680*a^4*b^14*c^3*e^2 + 53760*a^5*b^12*c^4*e^2 - 258048*a^6*b^10*c^5*e^2 + 860160*a^7*b^8*c^6*e^2 - 1966080*a^8*b^6*c^7*e^2 + 2949120*a^9*b^4*c^8*e^2 - 2621440*a^10*b^2*c^9*e^2 - 1048576*a^10*b*c^10*d*e - 720*a^2*b^17*c^2*d*e + 7680*a^3*b^15*c^3*d*e - 53760*a^4*b^13*c^4*d*e + 258048*a^5*b^11*c^5*d*e - 860160*a^6*b^9*c^6*d*e + 1966080*a^7*b^7*c^7*d*e - 2949120*a^8*b^5*c^8*d*e + 2621440*a^9*b^3*c^9*d*e + 40*a*b^19*c*d*e))^(1/2) - (((d + e*x)^(3/2)*(5*b^3*e^4 - 72*c^3*d^3*e + 108*b*c^2*d^2*e^2 + 16*a*b*c*e^4 - 32*a*c^2*d*e^3 - 46*b^2*c*d*e^3))/(4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (3*(d + e*x)^(1/2)*(a*b^2*e^5 + 4*a^2*c*e^5 - b^3*d*e^4 + 8*c^3*d^4*e + 12*a*c^2*d^2*e^3 - 16*b*c^2*d^3*e^2 + 9*b^2*c*d^2*e^3 - 12*a*b*c*d*e^4))/(4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (e*(d + e*x)^(5/2)*(72*c^3*d^2 - 4*a*c^2*e^2 + 19*b^2*c*e^2 - 72*b*c^2*d*e))/(4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) - (3*c*e*(2*c^2*d - b*c*e)*(d + e*x)^(7/2))/(b^4 + 16*a^2*c^2 - 8*a*b^2*c))/(c^2*(d + e*x)^4 - (d + e*x)*(4*c^2*d^3 + 2*b^2*d*e^2 - 2*a*b*e^3 + 4*a*c*d*e^2 - 6*b*c*d^2*e) - (4*c^2*d - 2*b*c*e)*(d + e*x)^3 + (d + e*x)^2*(b^2*e^2 + 6*c^2*d^2 + 2*a*c*e^2 - 6*b*c*d*e) + a^2*e^4 + c^2*d^4 + b^2*d^2*e^2 - 2*a*b*d*e^3 - 2*b*c*d^3*e + 2*a*c*d^2*e^2) - log((27*c^3*e^3*(b*e - 2*c*d)*(5*b^4*e^4 + 256*c^4*d^4 + 16*a^2*c^2*e^4 + 192*a*c^3*d^2*e^2 + 336*b^2*c^2*d^2*e^2 + 40*a*b^2*c*e^4 - 512*b*c^3*d^3*e - 80*b^3*c*d*e^3 - 192*a*b*c^2*d*e^3))/(16*(4*a*c - b^2)^6) - (((3*c^2*e^3*(b^2*e^2 + 8*c^2*d^2 + 4*a*c*e^2 - 8*b*c*d*e))/(4*a*c - b^2) + 8*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(((9*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (9*b^15*e^5)/128 - 36864*a^5*c^10*d^5 + 36*b^10*c^5*d^5 - 720*a*b^8*c^6*d^5 + 5760*a^7*b*c^7*e^5 - 11520*a^7*c^8*d*e^4 - 90*b^11*c^4*d^4*e + 5760*a^2*b^6*c^7*d^5 - 23040*a^3*b^4*c^8*d^5 + 46080*a^4*b^2*c^9*d^5 + (315*a^2*b^11*c^2*e^5)/8 - (585*a^3*b^9*c^3*e^5)/2 + 810*a^4*b^7*c^4*e^5 + 72*a^5*b^5*c^5*e^5 - 4320*a^6*b^3*c^6*e^5 - 46080*a^6*c^9*d^3*e^2 + (315*b^12*c^3*d^3*e^2)/4 - (225*b^13*c^2*d^2*e^3)/8 - (45*a*b^13*c*e^5)/32 + (225*b^14*c*d*e^4)/64 + 11700*a^2*b^8*c^5*d^3*e^2 - 3150*a^2*b^9*c^4*d^2*e^3 - 43200*a^3*b^6*c^6*d^3*e^2 + 7200*a^3*b^7*c^5*d^2*e^3 + 72000*a^4*b^4*c^7*d^3*e^2 + 7200*a^4*b^5*c^6*d^2*e^3 - 23040*a^5*b^2*c^8*d^3*e^2 - 57600*a^5*b^3*c^7*d^2*e^3 + 1800*a*b^9*c^5*d^4*e - (675*a*b^12*c^2*d*e^4)/16 + 92160*a^5*b*c^9*d^4*e - 1530*a*b^10*c^4*d^3*e^2 + 495*a*b^11*c^3*d^2*e^3 - 14400*a^2*b^7*c^6*d^4*e + (45*a^2*b^10*c^3*d*e^4)/4 + 57600*a^3*b^5*c^7*d^4*e + 2025*a^3*b^8*c^4*d*e^4 - 115200*a^4*b^3*c^8*d^4*e - 11700*a^4*b^6*c^5*d*e^4 + 25200*a^5*b^4*c^6*d*e^4 + 69120*a^6*b*c^8*d^2*e^3 - 14400*a^6*b^2*c^7*d*e^4)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)))^(1/2))*(((9*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (9*b^15*e^5)/128 - 36864*a^5*c^10*d^5 + 36*b^10*c^5*d^5 - 720*a*b^8*c^6*d^5 + 5760*a^7*b*c^7*e^5 - 11520*a^7*c^8*d*e^4 - 90*b^11*c^4*d^4*e + 5760*a^2*b^6*c^7*d^5 - 23040*a^3*b^4*c^8*d^5 + 46080*a^4*b^2*c^9*d^5 + (315*a^2*b^11*c^2*e^5)/8 - (585*a^3*b^9*c^3*e^5)/2 + 810*a^4*b^7*c^4*e^5 + 72*a^5*b^5*c^5*e^5 - 4320*a^6*b^3*c^6*e^5 - 46080*a^6*c^9*d^3*e^2 + (315*b^12*c^3*d^3*e^2)/4 - (225*b^13*c^2*d^2*e^3)/8 - (45*a*b^13*c*e^5)/32 + (225*b^14*c*d*e^4)/64 + 11700*a^2*b^8*c^5*d^3*e^2 - 3150*a^2*b^9*c^4*d^2*e^3 - 43200*a^3*b^6*c^6*d^3*e^2 + 7200*a^3*b^7*c^5*d^2*e^3 + 72000*a^4*b^4*c^7*d^3*e^2 + 7200*a^4*b^5*c^6*d^2*e^3 - 23040*a^5*b^2*c^8*d^3*e^2 - 57600*a^5*b^3*c^7*d^2*e^3 + 1800*a*b^9*c^5*d^4*e - (675*a*b^12*c^2*d*e^4)/16 + 92160*a^5*b*c^9*d^4*e - 1530*a*b^10*c^4*d^3*e^2 + 495*a*b^11*c^3*d^2*e^3 - 14400*a^2*b^7*c^6*d^4*e + (45*a^2*b^10*c^3*d*e^4)/4 + 57600*a^3*b^5*c^7*d^4*e + 2025*a^3*b^8*c^4*d*e^4 - 115200*a^4*b^3*c^8*d^4*e - 11700*a^4*b^6*c^5*d*e^4 + 25200*a^5*b^4*c^6*d*e^4 + 69120*a^6*b*c^8*d^2*e^3 - 14400*a^6*b^2*c^7*d*e^4)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)))^(1/2) - (9*c^3*e^2*(d + e*x)^(1/2)*(13*b^4*e^4 + 256*c^4*d^4 + 16*a^2*c^2*e^4 + 64*a*c^3*d^2*e^2 + 368*b^2*c^2*d^2*e^2 + 8*a*b^2*c*e^4 - 512*b*c^3*d^3*e - 112*b^3*c*d*e^3 - 64*a*b*c^2*d*e^3))/(4*(4*a*c - b^2)^4))*(((9*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (9*b^15*e^5)/128 - 36864*a^5*c^10*d^5 + 36*b^10*c^5*d^5 - 720*a*b^8*c^6*d^5 + 5760*a^7*b*c^7*e^5 - 11520*a^7*c^8*d*e^4 - 90*b^11*c^4*d^4*e + 5760*a^2*b^6*c^7*d^5 - 23040*a^3*b^4*c^8*d^5 + 46080*a^4*b^2*c^9*d^5 + (315*a^2*b^11*c^2*e^5)/8 - (585*a^3*b^9*c^3*e^5)/2 + 810*a^4*b^7*c^4*e^5 + 72*a^5*b^5*c^5*e^5 - 4320*a^6*b^3*c^6*e^5 - 46080*a^6*c^9*d^3*e^2 + (315*b^12*c^3*d^3*e^2)/4 - (225*b^13*c^2*d^2*e^3)/8 - (45*a*b^13*c*e^5)/32 + (225*b^14*c*d*e^4)/64 + 11700*a^2*b^8*c^5*d^3*e^2 - 3150*a^2*b^9*c^4*d^2*e^3 - 43200*a^3*b^6*c^6*d^3*e^2 + 7200*a^3*b^7*c^5*d^2*e^3 + 72000*a^4*b^4*c^7*d^3*e^2 + 7200*a^4*b^5*c^6*d^2*e^3 - 23040*a^5*b^2*c^8*d^3*e^2 - 57600*a^5*b^3*c^7*d^2*e^3 + 1800*a*b^9*c^5*d^4*e - (675*a*b^12*c^2*d*e^4)/16 + 92160*a^5*b*c^9*d^4*e - 1530*a*b^10*c^4*d^3*e^2 + 495*a*b^11*c^3*d^2*e^3 - 14400*a^2*b^7*c^6*d^4*e + (45*a^2*b^10*c^3*d*e^4)/4 + 57600*a^3*b^5*c^7*d^4*e + 2025*a^3*b^8*c^4*d*e^4 - 115200*a^4*b^3*c^8*d^4*e - 11700*a^4*b^6*c^5*d*e^4 + 25200*a^5*b^4*c^6*d*e^4 + 69120*a^6*b*c^8*d^2*e^3 - 14400*a^6*b^2*c^7*d*e^4)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)))^(1/2))*(((9*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (9*b^15*e^5)/128 - 36864*a^5*c^10*d^5 + 36*b^10*c^5*d^5 - 720*a*b^8*c^6*d^5 + 5760*a^7*b*c^7*e^5 - 11520*a^7*c^8*d*e^4 - 90*b^11*c^4*d^4*e + 5760*a^2*b^6*c^7*d^5 - 23040*a^3*b^4*c^8*d^5 + 46080*a^4*b^2*c^9*d^5 + (315*a^2*b^11*c^2*e^5)/8 - (585*a^3*b^9*c^3*e^5)/2 + 810*a^4*b^7*c^4*e^5 + 72*a^5*b^5*c^5*e^5 - 4320*a^6*b^3*c^6*e^5 - 46080*a^6*c^9*d^3*e^2 + (315*b^12*c^3*d^3*e^2)/4 - (225*b^13*c^2*d^2*e^3)/8 - (45*a*b^13*c*e^5)/32 + (225*b^14*c*d*e^4)/64 + 11700*a^2*b^8*c^5*d^3*e^2 - 3150*a^2*b^9*c^4*d^2*e^3 - 43200*a^3*b^6*c^6*d^3*e^2 + 7200*a^3*b^7*c^5*d^2*e^3 + 72000*a^4*b^4*c^7*d^3*e^2 + 7200*a^4*b^5*c^6*d^2*e^3 - 23040*a^5*b^2*c^8*d^3*e^2 - 57600*a^5*b^3*c^7*d^2*e^3 + 1800*a*b^9*c^5*d^4*e - (675*a*b^12*c^2*d*e^4)/16 + 92160*a^5*b*c^9*d^4*e - 1530*a*b^10*c^4*d^3*e^2 + 495*a*b^11*c^3*d^2*e^3 - 14400*a^2*b^7*c^6*d^4*e + (45*a^2*b^10*c^3*d*e^4)/4 + 57600*a^3*b^5*c^7*d^4*e + 2025*a^3*b^8*c^4*d*e^4 - 115200*a^4*b^3*c^8*d^4*e - 11700*a^4*b^6*c^5*d*e^4 + 25200*a^5*b^4*c^6*d*e^4 + 69120*a^6*b*c^8*d^2*e^3 - 14400*a^6*b^2*c^7*d*e^4)/(a*b^20*e^2 + b^20*c*d^2 + 1048576*a^10*c^11*d^2 + 1048576*a^11*c^10*e^2 - b^21*d*e - 40*a*b^18*c^2*d^2 - 40*a^2*b^18*c*e^2 + 720*a^2*b^16*c^3*d^2 - 7680*a^3*b^14*c^4*d^2 + 53760*a^4*b^12*c^5*d^2 - 258048*a^5*b^10*c^6*d^2 + 860160*a^6*b^8*c^7*d^2 - 1966080*a^7*b^6*c^8*d^2 + 2949120*a^8*b^4*c^9*d^2 - 2621440*a^9*b^2*c^10*d^2 + 720*a^3*b^16*c^2*e^2 - 7680*a^4*b^14*c^3*e^2 + 53760*a^5*b^12*c^4*e^2 - 258048*a^6*b^10*c^5*e^2 + 860160*a^7*b^8*c^6*e^2 - 1966080*a^8*b^6*c^7*e^2 + 2949120*a^9*b^4*c^8*e^2 - 2621440*a^10*b^2*c^9*e^2 - 1048576*a^10*b*c^10*d*e - 720*a^2*b^17*c^2*d*e + 7680*a^3*b^15*c^3*d*e - 53760*a^4*b^13*c^4*d*e + 258048*a^5*b^11*c^5*d*e - 860160*a^6*b^9*c^6*d*e + 1966080*a^7*b^7*c^7*d*e - 2949120*a^8*b^5*c^8*d*e + 2621440*a^9*b^3*c^9*d*e + 40*a*b^19*c*d*e))^(1/2) + log((27*c^3*e^3*(b*e - 2*c*d)*(5*b^4*e^4 + 256*c^4*d^4 + 16*a^2*c^2*e^4 + 192*a*c^3*d^2*e^2 + 336*b^2*c^2*d^2*e^2 + 40*a*b^2*c*e^4 - 512*b*c^3*d^3*e - 80*b^3*c*d*e^3 - 192*a*b*c^2*d*e^3))/(16*(4*a*c - b^2)^6) - (3*2^(1/2)*((3*2^(1/2)*((3*c^2*e^3*(b^2*e^2 + 8*c^2*d^2 + 4*a*c*e^2 - 8*b*c*d*e))/(4*a*c - b^2) - (3*2^(1/2)*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*((e^5*(-(4*a*c - b^2)^15)^(1/2) - b^15*e^5 - 524288*a^5*c^10*d^5 + 512*b^10*c^5*d^5 - 10240*a*b^8*c^6*d^5 + 81920*a^7*b*c^7*e^5 - 163840*a^7*c^8*d*e^4 - 1280*b^11*c^4*d^4*e + 81920*a^2*b^6*c^7*d^5 - 327680*a^3*b^4*c^8*d^5 + 655360*a^4*b^2*c^9*d^5 + 560*a^2*b^11*c^2*e^5 - 4160*a^3*b^9*c^3*e^5 + 11520*a^4*b^7*c^4*e^5 + 1024*a^5*b^5*c^5*e^5 - 61440*a^6*b^3*c^6*e^5 - 655360*a^6*c^9*d^3*e^2 + 1120*b^12*c^3*d^3*e^2 - 400*b^13*c^2*d^2*e^3 - 20*a*b^13*c*e^5 + 50*b^14*c*d*e^4 + 166400*a^2*b^8*c^5*d^3*e^2 - 44800*a^2*b^9*c^4*d^2*e^3 - 614400*a^3*b^6*c^6*d^3*e^2 + 102400*a^3*b^7*c^5*d^2*e^3 + 1024000*a^4*b^4*c^7*d^3*e^2 + 102400*a^4*b^5*c^6*d^2*e^3 - 327680*a^5*b^2*c^8*d^3*e^2 - 819200*a^5*b^3*c^7*d^2*e^3 + 25600*a*b^9*c^5*d^4*e - 600*a*b^12*c^2*d*e^4 + 1310720*a^5*b*c^9*d^4*e - 21760*a*b^10*c^4*d^3*e^2 + 7040*a*b^11*c^3*d^2*e^3 - 204800*a^2*b^7*c^6*d^4*e + 160*a^2*b^10*c^3*d*e^4 + 819200*a^3*b^5*c^7*d^4*e + 28800*a^3*b^8*c^4*d*e^4 - 1638400*a^4*b^3*c^8*d^4*e - 166400*a^4*b^6*c^5*d*e^4 + 358400*a^5*b^4*c^6*d*e^4 + 983040*a^6*b*c^8*d^2*e^3 - 204800*a^6*b^2*c^7*d*e^4)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)))^(1/2))/2)*((e^5*(-(4*a*c - b^2)^15)^(1/2) - b^15*e^5 - 524288*a^5*c^10*d^5 + 512*b^10*c^5*d^5 - 10240*a*b^8*c^6*d^5 + 81920*a^7*b*c^7*e^5 - 163840*a^7*c^8*d*e^4 - 1280*b^11*c^4*d^4*e + 81920*a^2*b^6*c^7*d^5 - 327680*a^3*b^4*c^8*d^5 + 655360*a^4*b^2*c^9*d^5 + 560*a^2*b^11*c^2*e^5 - 4160*a^3*b^9*c^3*e^5 + 11520*a^4*b^7*c^4*e^5 + 1024*a^5*b^5*c^5*e^5 - 61440*a^6*b^3*c^6*e^5 - 655360*a^6*c^9*d^3*e^2 + 1120*b^12*c^3*d^3*e^2 - 400*b^13*c^2*d^2*e^3 - 20*a*b^13*c*e^5 + 50*b^14*c*d*e^4 + 166400*a^2*b^8*c^5*d^3*e^2 - 44800*a^2*b^9*c^4*d^2*e^3 - 614400*a^3*b^6*c^6*d^3*e^2 + 102400*a^3*b^7*c^5*d^2*e^3 + 1024000*a^4*b^4*c^7*d^3*e^2 + 102400*a^4*b^5*c^6*d^2*e^3 - 327680*a^5*b^2*c^8*d^3*e^2 - 819200*a^5*b^3*c^7*d^2*e^3 + 25600*a*b^9*c^5*d^4*e - 600*a*b^12*c^2*d*e^4 + 1310720*a^5*b*c^9*d^4*e - 21760*a*b^10*c^4*d^3*e^2 + 7040*a*b^11*c^3*d^2*e^3 - 204800*a^2*b^7*c^6*d^4*e + 160*a^2*b^10*c^3*d*e^4 + 819200*a^3*b^5*c^7*d^4*e + 28800*a^3*b^8*c^4*d*e^4 - 1638400*a^4*b^3*c^8*d^4*e - 166400*a^4*b^6*c^5*d*e^4 + 358400*a^5*b^4*c^6*d*e^4 + 983040*a^6*b*c^8*d^2*e^3 - 204800*a^6*b^2*c^7*d*e^4)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)))^(1/2))/16 + (9*c^3*e^2*(d + e*x)^(1/2)*(13*b^4*e^4 + 256*c^4*d^4 + 16*a^2*c^2*e^4 + 64*a*c^3*d^2*e^2 + 368*b^2*c^2*d^2*e^2 + 8*a*b^2*c*e^4 - 512*b*c^3*d^3*e - 112*b^3*c*d*e^3 - 64*a*b*c^2*d*e^3))/(4*(4*a*c - b^2)^4))*((e^5*(-(4*a*c - b^2)^15)^(1/2) - b^15*e^5 - 524288*a^5*c^10*d^5 + 512*b^10*c^5*d^5 - 10240*a*b^8*c^6*d^5 + 81920*a^7*b*c^7*e^5 - 163840*a^7*c^8*d*e^4 - 1280*b^11*c^4*d^4*e + 81920*a^2*b^6*c^7*d^5 - 327680*a^3*b^4*c^8*d^5 + 655360*a^4*b^2*c^9*d^5 + 560*a^2*b^11*c^2*e^5 - 4160*a^3*b^9*c^3*e^5 + 11520*a^4*b^7*c^4*e^5 + 1024*a^5*b^5*c^5*e^5 - 61440*a^6*b^3*c^6*e^5 - 655360*a^6*c^9*d^3*e^2 + 1120*b^12*c^3*d^3*e^2 - 400*b^13*c^2*d^2*e^3 - 20*a*b^13*c*e^5 + 50*b^14*c*d*e^4 + 166400*a^2*b^8*c^5*d^3*e^2 - 44800*a^2*b^9*c^4*d^2*e^3 - 614400*a^3*b^6*c^6*d^3*e^2 + 102400*a^3*b^7*c^5*d^2*e^3 + 1024000*a^4*b^4*c^7*d^3*e^2 + 102400*a^4*b^5*c^6*d^2*e^3 - 327680*a^5*b^2*c^8*d^3*e^2 - 819200*a^5*b^3*c^7*d^2*e^3 + 25600*a*b^9*c^5*d^4*e - 600*a*b^12*c^2*d*e^4 + 1310720*a^5*b*c^9*d^4*e - 21760*a*b^10*c^4*d^3*e^2 + 7040*a*b^11*c^3*d^2*e^3 - 204800*a^2*b^7*c^6*d^4*e + 160*a^2*b^10*c^3*d*e^4 + 819200*a^3*b^5*c^7*d^4*e + 28800*a^3*b^8*c^4*d*e^4 - 1638400*a^4*b^3*c^8*d^4*e - 166400*a^4*b^6*c^5*d*e^4 + 358400*a^5*b^4*c^6*d*e^4 + 983040*a^6*b*c^8*d^2*e^3 - 204800*a^6*b^2*c^7*d*e^4)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)))^(1/2))/16)*((9*(e^5*(-(4*a*c - b^2)^15)^(1/2) - b^15*e^5 - 524288*a^5*c^10*d^5 + 512*b^10*c^5*d^5 - 10240*a*b^8*c^6*d^5 + 81920*a^7*b*c^7*e^5 - 163840*a^7*c^8*d*e^4 - 1280*b^11*c^4*d^4*e + 81920*a^2*b^6*c^7*d^5 - 327680*a^3*b^4*c^8*d^5 + 655360*a^4*b^2*c^9*d^5 + 560*a^2*b^11*c^2*e^5 - 4160*a^3*b^9*c^3*e^5 + 11520*a^4*b^7*c^4*e^5 + 1024*a^5*b^5*c^5*e^5 - 61440*a^6*b^3*c^6*e^5 - 655360*a^6*c^9*d^3*e^2 + 1120*b^12*c^3*d^3*e^2 - 400*b^13*c^2*d^2*e^3 - 20*a*b^13*c*e^5 + 50*b^14*c*d*e^4 + 166400*a^2*b^8*c^5*d^3*e^2 - 44800*a^2*b^9*c^4*d^2*e^3 - 614400*a^3*b^6*c^6*d^3*e^2 + 102400*a^3*b^7*c^5*d^2*e^3 + 1024000*a^4*b^4*c^7*d^3*e^2 + 102400*a^4*b^5*c^6*d^2*e^3 - 327680*a^5*b^2*c^8*d^3*e^2 - 819200*a^5*b^3*c^7*d^2*e^3 + 25600*a*b^9*c^5*d^4*e - 600*a*b^12*c^2*d*e^4 + 1310720*a^5*b*c^9*d^4*e - 21760*a*b^10*c^4*d^3*e^2 + 7040*a*b^11*c^3*d^2*e^3 - 204800*a^2*b^7*c^6*d^4*e + 160*a^2*b^10*c^3*d*e^4 + 819200*a^3*b^5*c^7*d^4*e + 28800*a^3*b^8*c^4*d*e^4 - 1638400*a^4*b^3*c^8*d^4*e - 166400*a^4*b^6*c^5*d*e^4 + 358400*a^5*b^4*c^6*d*e^4 + 983040*a^6*b*c^8*d^2*e^3 - 204800*a^6*b^2*c^7*d*e^4))/(128*(a*b^20*e^2 + b^20*c*d^2 + 1048576*a^10*c^11*d^2 + 1048576*a^11*c^10*e^2 - b^21*d*e - 40*a*b^18*c^2*d^2 - 40*a^2*b^18*c*e^2 + 720*a^2*b^16*c^3*d^2 - 7680*a^3*b^14*c^4*d^2 + 53760*a^4*b^12*c^5*d^2 - 258048*a^5*b^10*c^6*d^2 + 860160*a^6*b^8*c^7*d^2 - 1966080*a^7*b^6*c^8*d^2 + 2949120*a^8*b^4*c^9*d^2 - 2621440*a^9*b^2*c^10*d^2 + 720*a^3*b^16*c^2*e^2 - 7680*a^4*b^14*c^3*e^2 + 53760*a^5*b^12*c^4*e^2 - 258048*a^6*b^10*c^5*e^2 + 860160*a^7*b^8*c^6*e^2 - 1966080*a^8*b^6*c^7*e^2 + 2949120*a^9*b^4*c^8*e^2 - 2621440*a^10*b^2*c^9*e^2 - 1048576*a^10*b*c^10*d*e - 720*a^2*b^17*c^2*d*e + 7680*a^3*b^15*c^3*d*e - 53760*a^4*b^13*c^4*d*e + 258048*a^5*b^11*c^5*d*e - 860160*a^6*b^9*c^6*d*e + 1966080*a^7*b^7*c^7*d*e - 2949120*a^8*b^5*c^8*d*e + 2621440*a^9*b^3*c^9*d*e + 40*a*b^19*c*d*e)))^(1/2)","B"
2305,1,23750,634,69.776977,"\text{Not used}","int((d + e*x)^(1/2)/(a + b*x + c*x^2)^3,x)","\ln\left(-\frac{\sqrt{2}\,\left(\frac{\sqrt{2}\,\left(\frac{c^2\,e^3\,\left(b\,e-2\,c\,d\right)\,\left(b^2\,e^2+12\,b\,c\,d\,e-12\,c^2\,d^2-16\,a\,c\,e^2\right)}{\left(4\,a\,c-b^2\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}-\frac{\sqrt{2}\,c^2\,e^2\,\left(4\,a\,c-b^2\right)\,\left(b\,e-2\,c\,d\right)\,\sqrt{d+e\,x}\,\sqrt{-\frac{b^{17}\,e^7+4718592\,a^5\,c^{12}\,d^7-4608\,b^{10}\,c^7\,d^7+b^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+92160\,a\,b^8\,c^8\,d^7-1720320\,a^8\,b\,c^8\,e^7+3440640\,a^8\,c^9\,d\,e^6+16128\,b^{11}\,c^6\,d^6\,e-737280\,a^2\,b^6\,c^9\,d^7+2949120\,a^3\,b^4\,c^{10}\,d^7-5898240\,a^4\,b^2\,c^{11}\,d^7+1140\,a^2\,b^{13}\,c^2\,e^7-10160\,a^3\,b^{11}\,c^3\,e^7+34880\,a^4\,b^9\,c^4\,e^7+43776\,a^5\,b^7\,c^5\,e^7-680960\,a^6\,b^5\,c^6\,e^7+1863680\,a^7\,b^3\,c^7\,e^7+13762560\,a^6\,c^{11}\,d^5\,e^2+12615680\,a^7\,c^{10}\,d^3\,e^4-20832\,b^{12}\,c^5\,d^5\,e^2+11760\,b^{13}\,c^4\,d^4\,e^3-2450\,b^{14}\,c^3\,d^3\,e^4-21\,b^{15}\,c^2\,d^2\,e^5-21\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-55\,a\,b^{15}\,c\,e^7-25\,a\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+21\,b^{16}\,c\,d\,e^6+21\,b\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-3064320\,a^2\,b^8\,c^7\,d^5\,e^2+1209600\,a^2\,b^9\,c^6\,d^4\,e^3+144480\,a^2\,b^{10}\,c^5\,d^3\,e^4-136080\,a^2\,b^{11}\,c^4\,d^2\,e^5+11182080\,a^3\,b^6\,c^8\,d^5\,e^2-2150400\,a^3\,b^7\,c^7\,d^4\,e^3-2576000\,a^3\,b^8\,c^6\,d^3\,e^4+853440\,a^3\,b^9\,c^5\,d^2\,e^5-18063360\,a^4\,b^4\,c^9\,d^5\,e^2-6451200\,a^4\,b^5\,c^8\,d^4\,e^3+12454400\,a^4\,b^6\,c^7\,d^3\,e^4-1908480\,a^4\,b^7\,c^6\,d^2\,e^5+4128768\,a^5\,b^2\,c^{10}\,d^5\,e^2+30965760\,a^5\,b^3\,c^9\,d^4\,e^3-24729600\,a^5\,b^4\,c^8\,d^3\,e^4-2128896\,a^5\,b^5\,c^7\,d^2\,e^5+12328960\,a^6\,b^2\,c^9\,d^3\,e^4+15912960\,a^6\,b^3\,c^8\,d^2\,e^5-322560\,a\,b^9\,c^7\,d^6\,e-630\,a\,b^{14}\,c^2\,d\,e^6-16515072\,a^5\,b\,c^{11}\,d^6\,e+403200\,a\,b^{10}\,c^6\,d^5\,e^2-201600\,a\,b^{11}\,c^5\,d^4\,e^3+21560\,a\,b^{12}\,c^4\,d^3\,e^4+7980\,a\,b^{13}\,c^3\,d^2\,e^5+2580480\,a^2\,b^7\,c^8\,d^6\,e+840\,a^2\,b^{12}\,c^3\,d\,e^6-10321920\,a^3\,b^5\,c^9\,d^6\,e+84000\,a^3\,b^{10}\,c^4\,d\,e^6+20643840\,a^4\,b^3\,c^{10}\,d^6\,e-846720\,a^4\,b^8\,c^5\,d\,e^6+3472896\,a^5\,b^6\,c^6\,d\,e^6-34406400\,a^6\,b\,c^{10}\,d^4\,e^3-6236160\,a^6\,b^4\,c^7\,d\,e^6-18923520\,a^7\,b\,c^9\,d^2\,e^5+2580480\,a^7\,b^2\,c^8\,d\,e^6}{{\left(4\,a\,c-b^2\right)}^{10}\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^3}}}{2}\right)\,\sqrt{-\frac{b^{17}\,e^7+4718592\,a^5\,c^{12}\,d^7-4608\,b^{10}\,c^7\,d^7+b^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+92160\,a\,b^8\,c^8\,d^7-1720320\,a^8\,b\,c^8\,e^7+3440640\,a^8\,c^9\,d\,e^6+16128\,b^{11}\,c^6\,d^6\,e-737280\,a^2\,b^6\,c^9\,d^7+2949120\,a^3\,b^4\,c^{10}\,d^7-5898240\,a^4\,b^2\,c^{11}\,d^7+1140\,a^2\,b^{13}\,c^2\,e^7-10160\,a^3\,b^{11}\,c^3\,e^7+34880\,a^4\,b^9\,c^4\,e^7+43776\,a^5\,b^7\,c^5\,e^7-680960\,a^6\,b^5\,c^6\,e^7+1863680\,a^7\,b^3\,c^7\,e^7+13762560\,a^6\,c^{11}\,d^5\,e^2+12615680\,a^7\,c^{10}\,d^3\,e^4-20832\,b^{12}\,c^5\,d^5\,e^2+11760\,b^{13}\,c^4\,d^4\,e^3-2450\,b^{14}\,c^3\,d^3\,e^4-21\,b^{15}\,c^2\,d^2\,e^5-21\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-55\,a\,b^{15}\,c\,e^7-25\,a\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+21\,b^{16}\,c\,d\,e^6+21\,b\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-3064320\,a^2\,b^8\,c^7\,d^5\,e^2+1209600\,a^2\,b^9\,c^6\,d^4\,e^3+144480\,a^2\,b^{10}\,c^5\,d^3\,e^4-136080\,a^2\,b^{11}\,c^4\,d^2\,e^5+11182080\,a^3\,b^6\,c^8\,d^5\,e^2-2150400\,a^3\,b^7\,c^7\,d^4\,e^3-2576000\,a^3\,b^8\,c^6\,d^3\,e^4+853440\,a^3\,b^9\,c^5\,d^2\,e^5-18063360\,a^4\,b^4\,c^9\,d^5\,e^2-6451200\,a^4\,b^5\,c^8\,d^4\,e^3+12454400\,a^4\,b^6\,c^7\,d^3\,e^4-1908480\,a^4\,b^7\,c^6\,d^2\,e^5+4128768\,a^5\,b^2\,c^{10}\,d^5\,e^2+30965760\,a^5\,b^3\,c^9\,d^4\,e^3-24729600\,a^5\,b^4\,c^8\,d^3\,e^4-2128896\,a^5\,b^5\,c^7\,d^2\,e^5+12328960\,a^6\,b^2\,c^9\,d^3\,e^4+15912960\,a^6\,b^3\,c^8\,d^2\,e^5-322560\,a\,b^9\,c^7\,d^6\,e-630\,a\,b^{14}\,c^2\,d\,e^6-16515072\,a^5\,b\,c^{11}\,d^6\,e+403200\,a\,b^{10}\,c^6\,d^5\,e^2-201600\,a\,b^{11}\,c^5\,d^4\,e^3+21560\,a\,b^{12}\,c^4\,d^3\,e^4+7980\,a\,b^{13}\,c^3\,d^2\,e^5+2580480\,a^2\,b^7\,c^8\,d^6\,e+840\,a^2\,b^{12}\,c^3\,d\,e^6-10321920\,a^3\,b^5\,c^9\,d^6\,e+84000\,a^3\,b^{10}\,c^4\,d\,e^6+20643840\,a^4\,b^3\,c^{10}\,d^6\,e-846720\,a^4\,b^8\,c^5\,d\,e^6+3472896\,a^5\,b^6\,c^6\,d\,e^6-34406400\,a^6\,b\,c^{10}\,d^4\,e^3-6236160\,a^6\,b^4\,c^7\,d\,e^6-18923520\,a^7\,b\,c^9\,d^2\,e^5+2580480\,a^7\,b^2\,c^8\,d\,e^6}{{\left(4\,a\,c-b^2\right)}^{10}\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^3}}}{16}+\frac{c^3\,e^2\,\sqrt{d+e\,x}\,\left(-800\,a^3\,c^3\,e^6+1472\,a^2\,b^2\,c^2\,e^6-3488\,a^2\,b\,c^3\,d\,e^5+3488\,a^2\,c^4\,d^2\,e^4-34\,a\,b^4\,c\,e^6-2672\,a\,b^3\,c^2\,d\,e^5+11504\,a\,b^2\,c^3\,d^2\,e^4-17664\,a\,b\,c^4\,d^3\,e^3+8832\,a\,c^5\,d^4\,e^2+b^6\,e^6+22\,b^5\,c\,d\,e^5+1226\,b^4\,c^2\,d^2\,e^4-7104\,b^3\,c^3\,d^3\,e^3+15072\,b^2\,c^4\,d^4\,e^2-13824\,b\,c^5\,d^5\,e+4608\,c^6\,d^6\right)}{8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\,b^5\,c\,d\,e^5+9864\,b^4\,c^2\,d^2\,e^4-76032\,b^3\,c^3\,d^3\,e^3+176256\,b^2\,c^4\,d^4\,e^2-165888\,b\,c^5\,d^5\,e+55296\,c^6\,d^6\right)}{64\,{\left(4\,a\,c-b^2\right)}^6\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}\right)\,\sqrt{-\frac{\frac{b^{17}\,e^7}{128}+36864\,a^5\,c^{12}\,d^7-36\,b^{10}\,c^7\,d^7+\frac{b^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}}{128}+720\,a\,b^8\,c^8\,d^7-13440\,a^8\,b\,c^8\,e^7+26880\,a^8\,c^9\,d\,e^6+126\,b^{11}\,c^6\,d^6\,e-5760\,a^2\,b^6\,c^9\,d^7+23040\,a^3\,b^4\,c^{10}\,d^7-46080\,a^4\,b^2\,c^{11}\,d^7+\frac{285\,a^2\,b^{13}\,c^2\,e^7}{32}-\frac{635\,a^3\,b^{11}\,c^3\,e^7}{8}+\frac{545\,a^4\,b^9\,c^4\,e^7}{2}+342\,a^5\,b^7\,c^5\,e^7-5320\,a^6\,b^5\,c^6\,e^7+14560\,a^7\,b^3\,c^7\,e^7+107520\,a^6\,c^{11}\,d^5\,e^2+98560\,a^7\,c^{10}\,d^3\,e^4-\frac{651\,b^{12}\,c^5\,d^5\,e^2}{4}+\frac{735\,b^{13}\,c^4\,d^4\,e^3}{8}-\frac{1225\,b^{14}\,c^3\,d^3\,e^4}{64}-\frac{21\,b^{15}\,c^2\,d^2\,e^5}{128}-\frac{21\,c^2\,d^2\,e^5\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}}{128}-\frac{55\,a\,b^{15}\,c\,e^7}{128}-\frac{25\,a\,c\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}}{128}+\frac{21\,b^{16}\,c\,d\,e^6}{128}+\frac{21\,b\,c\,d\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}}{128}-23940\,a^2\,b^8\,c^7\,d^5\,e^2+9450\,a^2\,b^9\,c^6\,d^4\,e^3+\frac{4515\,a^2\,b^{10}\,c^5\,d^3\,e^4}{4}-\frac{8505\,a^2\,b^{11}\,c^4\,d^2\,e^5}{8}+87360\,a^3\,b^6\,c^8\,d^5\,e^2-16800\,a^3\,b^7\,c^7\,d^4\,e^3-20125\,a^3\,b^8\,c^6\,d^3\,e^4+\frac{13335\,a^3\,b^9\,c^5\,d^2\,e^5}{2}-141120\,a^4\,b^4\,c^9\,d^5\,e^2-50400\,a^4\,b^5\,c^8\,d^4\,e^3+97300\,a^4\,b^6\,c^7\,d^3\,e^4-14910\,a^4\,b^7\,c^6\,d^2\,e^5+32256\,a^5\,b^2\,c^{10}\,d^5\,e^2+241920\,a^5\,b^3\,c^9\,d^4\,e^3-193200\,a^5\,b^4\,c^8\,d^3\,e^4-16632\,a^5\,b^5\,c^7\,d^2\,e^5+96320\,a^6\,b^2\,c^9\,d^3\,e^4+124320\,a^6\,b^3\,c^8\,d^2\,e^5-2520\,a\,b^9\,c^7\,d^6\,e-\frac{315\,a\,b^{14}\,c^2\,d\,e^6}{64}-129024\,a^5\,b\,c^{11}\,d^6\,e+3150\,a\,b^{10}\,c^6\,d^5\,e^2-1575\,a\,b^{11}\,c^5\,d^4\,e^3+\frac{2695\,a\,b^{12}\,c^4\,d^3\,e^4}{16}+\frac{1995\,a\,b^{13}\,c^3\,d^2\,e^5}{32}+20160\,a^2\,b^7\,c^8\,d^6\,e+\frac{105\,a^2\,b^{12}\,c^3\,d\,e^6}{16}-80640\,a^3\,b^5\,c^9\,d^6\,e+\frac{2625\,a^3\,b^{10}\,c^4\,d\,e^6}{4}+161280\,a^4\,b^3\,c^{10}\,d^6\,e-6615\,a^4\,b^8\,c^5\,d\,e^6+27132\,a^5\,b^6\,c^6\,d\,e^6-268800\,a^6\,b\,c^{10}\,d^4\,e^3-48720\,a^6\,b^4\,c^7\,d\,e^6-147840\,a^7\,b\,c^9\,d^2\,e^5+20160\,a^7\,b^2\,c^8\,d\,e^6}{1048576\,a^{13}\,c^{10}\,e^6-2621440\,a^{12}\,b^2\,c^9\,e^6-3145728\,a^{12}\,b\,c^{10}\,d\,e^5+3145728\,a^{12}\,c^{11}\,d^2\,e^4+2949120\,a^{11}\,b^4\,c^8\,e^6+7864320\,a^{11}\,b^3\,c^9\,d\,e^5-4718592\,a^{11}\,b^2\,c^{10}\,d^2\,e^4-6291456\,a^{11}\,b\,c^{11}\,d^3\,e^3+3145728\,a^{11}\,c^{12}\,d^4\,e^2-1966080\,a^{10}\,b^6\,c^7\,e^6-8847360\,a^{10}\,b^5\,c^8\,d\,e^5+983040\,a^{10}\,b^4\,c^9\,d^2\,e^4+14680064\,a^{10}\,b^3\,c^{10}\,d^3\,e^3-4718592\,a^{10}\,b^2\,c^{11}\,d^4\,e^2-3145728\,a^{10}\,b\,c^{12}\,d^5\,e+1048576\,a^{10}\,c^{13}\,d^6+860160\,a^9\,b^8\,c^6\,e^6+5898240\,a^9\,b^7\,c^7\,d\,e^5+2949120\,a^9\,b^6\,c^8\,d^2\,e^4-15073280\,a^9\,b^5\,c^9\,d^3\,e^3+983040\,a^9\,b^4\,c^{10}\,d^4\,e^2+7864320\,a^9\,b^3\,c^{11}\,d^5\,e-2621440\,a^9\,b^2\,c^{12}\,d^6-258048\,a^8\,b^{10}\,c^5\,e^6-2580480\,a^8\,b^9\,c^6\,d\,e^5-3317760\,a^8\,b^8\,c^7\,d^2\,e^4+8847360\,a^8\,b^7\,c^8\,d^3\,e^3+2949120\,a^8\,b^6\,c^9\,d^4\,e^2-8847360\,a^8\,b^5\,c^{10}\,d^5\,e+2949120\,a^8\,b^4\,c^{11}\,d^6+53760\,a^7\,b^{12}\,c^4\,e^6+774144\,a^7\,b^{11}\,c^5\,d\,e^5+1806336\,a^7\,b^{10}\,c^6\,d^2\,e^4-3194880\,a^7\,b^9\,c^7\,d^3\,e^3-3317760\,a^7\,b^8\,c^8\,d^4\,e^2+5898240\,a^7\,b^7\,c^9\,d^5\,e-1966080\,a^7\,b^6\,c^{10}\,d^6-7680\,a^6\,b^{14}\,c^3\,e^6-161280\,a^6\,b^{13}\,c^4\,d\,e^5-612864\,a^6\,b^{12}\,c^5\,d^2\,e^4+688128\,a^6\,b^{11}\,c^6\,d^3\,e^3+1806336\,a^6\,b^{10}\,c^7\,d^4\,e^2-2580480\,a^6\,b^9\,c^8\,d^5\,e+860160\,a^6\,b^8\,c^9\,d^6+720\,a^5\,b^{16}\,c^2\,e^6+23040\,a^5\,b^{15}\,c^3\,d\,e^5+138240\,a^5\,b^{14}\,c^4\,d^2\,e^4-64512\,a^5\,b^{13}\,c^5\,d^3\,e^3-612864\,a^5\,b^{12}\,c^6\,d^4\,e^2+774144\,a^5\,b^{11}\,c^7\,d^5\,e-258048\,a^5\,b^{10}\,c^8\,d^6-40\,a^4\,b^{18}\,c\,e^6-2160\,a^4\,b^{17}\,c^2\,d\,e^5-20880\,a^4\,b^{16}\,c^3\,d^2\,e^4-7680\,a^4\,b^{15}\,c^4\,d^3\,e^3+138240\,a^4\,b^{14}\,c^5\,d^4\,e^2-161280\,a^4\,b^{13}\,c^6\,d^5\,e+53760\,a^4\,b^{12}\,c^7\,d^6+a^3\,b^{20}\,e^6+120\,a^3\,b^{19}\,c\,d\,e^5+2040\,a^3\,b^{18}\,c^2\,d^2\,e^4+3360\,a^3\,b^{17}\,c^3\,d^3\,e^3-20880\,a^3\,b^{16}\,c^4\,d^4\,e^2+23040\,a^3\,b^{15}\,c^5\,d^5\,e-7680\,a^3\,b^{14}\,c^6\,d^6-3\,a^2\,b^{21}\,d\,e^5-117\,a^2\,b^{20}\,c\,d^2\,e^4-480\,a^2\,b^{19}\,c^2\,d^3\,e^3+2040\,a^2\,b^{18}\,c^3\,d^4\,e^2-2160\,a^2\,b^{17}\,c^4\,d^5\,e+720\,a^2\,b^{16}\,c^5\,d^6+3\,a\,b^{22}\,d^2\,e^4+34\,a\,b^{21}\,c\,d^3\,e^3-117\,a\,b^{20}\,c^2\,d^4\,e^2+120\,a\,b^{19}\,c^3\,d^5\,e-40\,a\,b^{18}\,c^4\,d^6-b^{23}\,d^3\,e^3+3\,b^{22}\,c\,d^4\,e^2-3\,b^{21}\,c^2\,d^5\,e+b^{20}\,c^3\,d^6}}+\frac{\frac{{\left(d+e\,x\right)}^{3/2}\,\left(36\,a^2\,c^2\,e^5+5\,a\,b^2\,c\,e^5-92\,a\,b\,c^2\,d\,e^4+92\,a\,c^3\,d^2\,e^3+b^4\,e^5-13\,b^3\,c\,d\,e^4+85\,b^2\,c^2\,d^2\,e^3-144\,b\,c^3\,d^3\,e^2+72\,c^4\,d^4\,e\right)}{4\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}-\frac{\sqrt{d+e\,x}\,\left(b^3\,e^4+10\,b^2\,c\,d\,e^3-36\,b\,c^2\,d^2\,e^2-16\,a\,b\,c\,e^4+24\,c^3\,d^3\,e+32\,a\,c^2\,d\,e^3\right)}{4\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{\left(b\,e-2\,c\,d\right)\,{\left(d+e\,x\right)}^{5/2}\,\left(b^2\,c\,e^3-18\,b\,c^2\,d\,e^2+18\,c^3\,d^2\,e+14\,a\,c^2\,e^3\right)}{2\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}+\frac{c\,e\,{\left(d+e\,x\right)}^{7/2}\,\left(b^2\,c\,e^2-24\,b\,c^2\,d\,e+24\,c^3\,d^2+20\,a\,c^2\,e^2\right)}{4\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}}{c^2\,{\left(d+e\,x\right)}^4-\left(d+e\,x\right)\,\left(2\,b^2\,d\,e^2-6\,b\,c\,d^2\,e-2\,a\,b\,e^3+4\,c^2\,d^3+4\,a\,c\,d\,e^2\right)-\left(4\,c^2\,d-2\,b\,c\,e\right)\,{\left(d+e\,x\right)}^3+{\left(d+e\,x\right)}^2\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2+2\,a\,c\,e^2\right)+a^2\,e^4+c^2\,d^4+b^2\,d^2\,e^2-2\,a\,b\,d\,e^3-2\,b\,c\,d^3\,e+2\,a\,c\,d^2\,e^2}","Not used",1,"log(- (2^(1/2)*((2^(1/2)*((c^2*e^3*(b*e - 2*c*d)*(b^2*e^2 - 12*c^2*d^2 - 16*a*c*e^2 + 12*b*c*d*e))/((4*a*c - b^2)*(a*e^2 + c*d^2 - b*d*e)) - (2^(1/2)*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(-(b^17*e^7 + 4718592*a^5*c^12*d^7 - 4608*b^10*c^7*d^7 + b^2*e^7*(-(4*a*c - b^2)^15)^(1/2) + 92160*a*b^8*c^8*d^7 - 1720320*a^8*b*c^8*e^7 + 3440640*a^8*c^9*d*e^6 + 16128*b^11*c^6*d^6*e - 737280*a^2*b^6*c^9*d^7 + 2949120*a^3*b^4*c^10*d^7 - 5898240*a^4*b^2*c^11*d^7 + 1140*a^2*b^13*c^2*e^7 - 10160*a^3*b^11*c^3*e^7 + 34880*a^4*b^9*c^4*e^7 + 43776*a^5*b^7*c^5*e^7 - 680960*a^6*b^5*c^6*e^7 + 1863680*a^7*b^3*c^7*e^7 + 13762560*a^6*c^11*d^5*e^2 + 12615680*a^7*c^10*d^3*e^4 - 20832*b^12*c^5*d^5*e^2 + 11760*b^13*c^4*d^4*e^3 - 2450*b^14*c^3*d^3*e^4 - 21*b^15*c^2*d^2*e^5 - 21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2) - 55*a*b^15*c*e^7 - 25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2) + 21*b^16*c*d*e^6 + 21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2) - 3064320*a^2*b^8*c^7*d^5*e^2 + 1209600*a^2*b^9*c^6*d^4*e^3 + 144480*a^2*b^10*c^5*d^3*e^4 - 136080*a^2*b^11*c^4*d^2*e^5 + 11182080*a^3*b^6*c^8*d^5*e^2 - 2150400*a^3*b^7*c^7*d^4*e^3 - 2576000*a^3*b^8*c^6*d^3*e^4 + 853440*a^3*b^9*c^5*d^2*e^5 - 18063360*a^4*b^4*c^9*d^5*e^2 - 6451200*a^4*b^5*c^8*d^4*e^3 + 12454400*a^4*b^6*c^7*d^3*e^4 - 1908480*a^4*b^7*c^6*d^2*e^5 + 4128768*a^5*b^2*c^10*d^5*e^2 + 30965760*a^5*b^3*c^9*d^4*e^3 - 24729600*a^5*b^4*c^8*d^3*e^4 - 2128896*a^5*b^5*c^7*d^2*e^5 + 12328960*a^6*b^2*c^9*d^3*e^4 + 15912960*a^6*b^3*c^8*d^2*e^5 - 322560*a*b^9*c^7*d^6*e - 630*a*b^14*c^2*d*e^6 - 16515072*a^5*b*c^11*d^6*e + 403200*a*b^10*c^6*d^5*e^2 - 201600*a*b^11*c^5*d^4*e^3 + 21560*a*b^12*c^4*d^3*e^4 + 7980*a*b^13*c^3*d^2*e^5 + 2580480*a^2*b^7*c^8*d^6*e + 840*a^2*b^12*c^3*d*e^6 - 10321920*a^3*b^5*c^9*d^6*e + 84000*a^3*b^10*c^4*d*e^6 + 20643840*a^4*b^3*c^10*d^6*e - 846720*a^4*b^8*c^5*d*e^6 + 3472896*a^5*b^6*c^6*d*e^6 - 34406400*a^6*b*c^10*d^4*e^3 - 6236160*a^6*b^4*c^7*d*e^6 - 18923520*a^7*b*c^9*d^2*e^5 + 2580480*a^7*b^2*c^8*d*e^6)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)^3))^(1/2))/2)*(-(b^17*e^7 + 4718592*a^5*c^12*d^7 - 4608*b^10*c^7*d^7 + b^2*e^7*(-(4*a*c - b^2)^15)^(1/2) + 92160*a*b^8*c^8*d^7 - 1720320*a^8*b*c^8*e^7 + 3440640*a^8*c^9*d*e^6 + 16128*b^11*c^6*d^6*e - 737280*a^2*b^6*c^9*d^7 + 2949120*a^3*b^4*c^10*d^7 - 5898240*a^4*b^2*c^11*d^7 + 1140*a^2*b^13*c^2*e^7 - 10160*a^3*b^11*c^3*e^7 + 34880*a^4*b^9*c^4*e^7 + 43776*a^5*b^7*c^5*e^7 - 680960*a^6*b^5*c^6*e^7 + 1863680*a^7*b^3*c^7*e^7 + 13762560*a^6*c^11*d^5*e^2 + 12615680*a^7*c^10*d^3*e^4 - 20832*b^12*c^5*d^5*e^2 + 11760*b^13*c^4*d^4*e^3 - 2450*b^14*c^3*d^3*e^4 - 21*b^15*c^2*d^2*e^5 - 21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2) - 55*a*b^15*c*e^7 - 25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2) + 21*b^16*c*d*e^6 + 21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2) - 3064320*a^2*b^8*c^7*d^5*e^2 + 1209600*a^2*b^9*c^6*d^4*e^3 + 144480*a^2*b^10*c^5*d^3*e^4 - 136080*a^2*b^11*c^4*d^2*e^5 + 11182080*a^3*b^6*c^8*d^5*e^2 - 2150400*a^3*b^7*c^7*d^4*e^3 - 2576000*a^3*b^8*c^6*d^3*e^4 + 853440*a^3*b^9*c^5*d^2*e^5 - 18063360*a^4*b^4*c^9*d^5*e^2 - 6451200*a^4*b^5*c^8*d^4*e^3 + 12454400*a^4*b^6*c^7*d^3*e^4 - 1908480*a^4*b^7*c^6*d^2*e^5 + 4128768*a^5*b^2*c^10*d^5*e^2 + 30965760*a^5*b^3*c^9*d^4*e^3 - 24729600*a^5*b^4*c^8*d^3*e^4 - 2128896*a^5*b^5*c^7*d^2*e^5 + 12328960*a^6*b^2*c^9*d^3*e^4 + 15912960*a^6*b^3*c^8*d^2*e^5 - 322560*a*b^9*c^7*d^6*e - 630*a*b^14*c^2*d*e^6 - 16515072*a^5*b*c^11*d^6*e + 403200*a*b^10*c^6*d^5*e^2 - 201600*a*b^11*c^5*d^4*e^3 + 21560*a*b^12*c^4*d^3*e^4 + 7980*a*b^13*c^3*d^2*e^5 + 2580480*a^2*b^7*c^8*d^6*e + 840*a^2*b^12*c^3*d*e^6 - 10321920*a^3*b^5*c^9*d^6*e + 84000*a^3*b^10*c^4*d*e^6 + 20643840*a^4*b^3*c^10*d^6*e - 846720*a^4*b^8*c^5*d*e^6 + 3472896*a^5*b^6*c^6*d*e^6 - 34406400*a^6*b*c^10*d^4*e^3 - 6236160*a^6*b^4*c^7*d*e^6 - 18923520*a^7*b*c^9*d^2*e^5 + 2580480*a^7*b^2*c^8*d*e^6)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)^3))^(1/2))/16 + (c^3*e^2*(d + e*x)^(1/2)*(b^6*e^6 + 4608*c^6*d^6 - 800*a^3*c^3*e^6 + 8832*a*c^5*d^4*e^2 + 1472*a^2*b^2*c^2*e^6 + 3488*a^2*c^4*d^2*e^4 + 15072*b^2*c^4*d^4*e^2 - 7104*b^3*c^3*d^3*e^3 + 1226*b^4*c^2*d^2*e^4 - 34*a*b^4*c*e^6 - 13824*b*c^5*d^5*e + 22*b^5*c*d*e^5 - 17664*a*b*c^4*d^3*e^3 - 2672*a*b^3*c^2*d*e^5 - 3488*a^2*b*c^3*d*e^5 + 11504*a*b^2*c^3*d^2*e^4))/(8*(4*a*c - b^2)^4*(a*e^2 + c*d^2 - b*d*e)^2))*(-(b^17*e^7 + 4718592*a^5*c^12*d^7 - 4608*b^10*c^7*d^7 + b^2*e^7*(-(4*a*c - b^2)^15)^(1/2) + 92160*a*b^8*c^8*d^7 - 1720320*a^8*b*c^8*e^7 + 3440640*a^8*c^9*d*e^6 + 16128*b^11*c^6*d^6*e - 737280*a^2*b^6*c^9*d^7 + 2949120*a^3*b^4*c^10*d^7 - 5898240*a^4*b^2*c^11*d^7 + 1140*a^2*b^13*c^2*e^7 - 10160*a^3*b^11*c^3*e^7 + 34880*a^4*b^9*c^4*e^7 + 43776*a^5*b^7*c^5*e^7 - 680960*a^6*b^5*c^6*e^7 + 1863680*a^7*b^3*c^7*e^7 + 13762560*a^6*c^11*d^5*e^2 + 12615680*a^7*c^10*d^3*e^4 - 20832*b^12*c^5*d^5*e^2 + 11760*b^13*c^4*d^4*e^3 - 2450*b^14*c^3*d^3*e^4 - 21*b^15*c^2*d^2*e^5 - 21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2) - 55*a*b^15*c*e^7 - 25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2) + 21*b^16*c*d*e^6 + 21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2) - 3064320*a^2*b^8*c^7*d^5*e^2 + 1209600*a^2*b^9*c^6*d^4*e^3 + 144480*a^2*b^10*c^5*d^3*e^4 - 136080*a^2*b^11*c^4*d^2*e^5 + 11182080*a^3*b^6*c^8*d^5*e^2 - 2150400*a^3*b^7*c^7*d^4*e^3 - 2576000*a^3*b^8*c^6*d^3*e^4 + 853440*a^3*b^9*c^5*d^2*e^5 - 18063360*a^4*b^4*c^9*d^5*e^2 - 6451200*a^4*b^5*c^8*d^4*e^3 + 12454400*a^4*b^6*c^7*d^3*e^4 - 1908480*a^4*b^7*c^6*d^2*e^5 + 4128768*a^5*b^2*c^10*d^5*e^2 + 30965760*a^5*b^3*c^9*d^4*e^3 - 24729600*a^5*b^4*c^8*d^3*e^4 - 2128896*a^5*b^5*c^7*d^2*e^5 + 12328960*a^6*b^2*c^9*d^3*e^4 + 15912960*a^6*b^3*c^8*d^2*e^5 - 322560*a*b^9*c^7*d^6*e - 630*a*b^14*c^2*d*e^6 - 16515072*a^5*b*c^11*d^6*e + 403200*a*b^10*c^6*d^5*e^2 - 201600*a*b^11*c^5*d^4*e^3 + 21560*a*b^12*c^4*d^3*e^4 + 7980*a*b^13*c^3*d^2*e^5 + 2580480*a^2*b^7*c^8*d^6*e + 840*a^2*b^12*c^3*d*e^6 - 10321920*a^3*b^5*c^9*d^6*e + 84000*a^3*b^10*c^4*d*e^6 + 20643840*a^4*b^3*c^10*d^6*e - 846720*a^4*b^8*c^5*d*e^6 + 3472896*a^5*b^6*c^6*d*e^6 - 34406400*a^6*b*c^10*d^4*e^3 - 6236160*a^6*b^4*c^7*d*e^6 - 18923520*a^7*b*c^9*d^2*e^5 + 2580480*a^7*b^2*c^8*d*e^6)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)^3))^(1/2))/16 - (c^4*e^3*(55296*c^6*d^6 - 35*b^6*e^6 + 8000*a^3*c^3*e^6 + 124416*a*c^5*d^4*e^2 + 12720*a^2*b^2*c^2*e^6 + 74880*a^2*c^4*d^2*e^4 + 176256*b^2*c^4*d^4*e^2 - 76032*b^3*c^3*d^3*e^3 + 9864*b^4*c^2*d^2*e^4 - 84*a*b^4*c*e^6 - 165888*b*c^5*d^5*e + 504*b^5*c*d*e^5 - 248832*a*b*c^4*d^3*e^3 - 24768*a*b^3*c^2*d*e^5 - 74880*a^2*b*c^3*d*e^5 + 149184*a*b^2*c^3*d^2*e^4))/(64*(4*a*c - b^2)^6*(a*e^2 + c*d^2 - b*d*e)^2))*(-(b^17*e^7 + 4718592*a^5*c^12*d^7 - 4608*b^10*c^7*d^7 + b^2*e^7*(-(4*a*c - b^2)^15)^(1/2) + 92160*a*b^8*c^8*d^7 - 1720320*a^8*b*c^8*e^7 + 3440640*a^8*c^9*d*e^6 + 16128*b^11*c^6*d^6*e - 737280*a^2*b^6*c^9*d^7 + 2949120*a^3*b^4*c^10*d^7 - 5898240*a^4*b^2*c^11*d^7 + 1140*a^2*b^13*c^2*e^7 - 10160*a^3*b^11*c^3*e^7 + 34880*a^4*b^9*c^4*e^7 + 43776*a^5*b^7*c^5*e^7 - 680960*a^6*b^5*c^6*e^7 + 1863680*a^7*b^3*c^7*e^7 + 13762560*a^6*c^11*d^5*e^2 + 12615680*a^7*c^10*d^3*e^4 - 20832*b^12*c^5*d^5*e^2 + 11760*b^13*c^4*d^4*e^3 - 2450*b^14*c^3*d^3*e^4 - 21*b^15*c^2*d^2*e^5 - 21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2) - 55*a*b^15*c*e^7 - 25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2) + 21*b^16*c*d*e^6 + 21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2) - 3064320*a^2*b^8*c^7*d^5*e^2 + 1209600*a^2*b^9*c^6*d^4*e^3 + 144480*a^2*b^10*c^5*d^3*e^4 - 136080*a^2*b^11*c^4*d^2*e^5 + 11182080*a^3*b^6*c^8*d^5*e^2 - 2150400*a^3*b^7*c^7*d^4*e^3 - 2576000*a^3*b^8*c^6*d^3*e^4 + 853440*a^3*b^9*c^5*d^2*e^5 - 18063360*a^4*b^4*c^9*d^5*e^2 - 6451200*a^4*b^5*c^8*d^4*e^3 + 12454400*a^4*b^6*c^7*d^3*e^4 - 1908480*a^4*b^7*c^6*d^2*e^5 + 4128768*a^5*b^2*c^10*d^5*e^2 + 30965760*a^5*b^3*c^9*d^4*e^3 - 24729600*a^5*b^4*c^8*d^3*e^4 - 2128896*a^5*b^5*c^7*d^2*e^5 + 12328960*a^6*b^2*c^9*d^3*e^4 + 15912960*a^6*b^3*c^8*d^2*e^5 - 322560*a*b^9*c^7*d^6*e - 630*a*b^14*c^2*d*e^6 - 16515072*a^5*b*c^11*d^6*e + 403200*a*b^10*c^6*d^5*e^2 - 201600*a*b^11*c^5*d^4*e^3 + 21560*a*b^12*c^4*d^3*e^4 + 7980*a*b^13*c^3*d^2*e^5 + 2580480*a^2*b^7*c^8*d^6*e + 840*a^2*b^12*c^3*d*e^6 - 10321920*a^3*b^5*c^9*d^6*e + 84000*a^3*b^10*c^4*d*e^6 + 20643840*a^4*b^3*c^10*d^6*e - 846720*a^4*b^8*c^5*d*e^6 + 3472896*a^5*b^6*c^6*d*e^6 - 34406400*a^6*b*c^10*d^4*e^3 - 6236160*a^6*b^4*c^7*d*e^6 - 18923520*a^7*b*c^9*d^2*e^5 + 2580480*a^7*b^2*c^8*d*e^6)/(128*(a^3*b^20*e^6 + 1048576*a^10*c^13*d^6 + 1048576*a^13*c^10*e^6 + b^20*c^3*d^6 - b^23*d^3*e^3 - 40*a*b^18*c^4*d^6 - 40*a^4*b^18*c*e^6 + 3*a*b^22*d^2*e^4 - 3*a^2*b^21*d*e^5 - 3*b^21*c^2*d^5*e + 3*b^22*c*d^4*e^2 + 720*a^2*b^16*c^5*d^6 - 7680*a^3*b^14*c^6*d^6 + 53760*a^4*b^12*c^7*d^6 - 258048*a^5*b^10*c^8*d^6 + 860160*a^6*b^8*c^9*d^6 - 1966080*a^7*b^6*c^10*d^6 + 2949120*a^8*b^4*c^11*d^6 - 2621440*a^9*b^2*c^12*d^6 + 720*a^5*b^16*c^2*e^6 - 7680*a^6*b^14*c^3*e^6 + 53760*a^7*b^12*c^4*e^6 - 258048*a^8*b^10*c^5*e^6 + 860160*a^9*b^8*c^6*e^6 - 1966080*a^10*b^6*c^7*e^6 + 2949120*a^11*b^4*c^8*e^6 - 2621440*a^12*b^2*c^9*e^6 + 3145728*a^11*c^12*d^4*e^2 + 3145728*a^12*c^11*d^2*e^4 + 2040*a^2*b^18*c^3*d^4*e^2 - 480*a^2*b^19*c^2*d^3*e^3 - 20880*a^3*b^16*c^4*d^4*e^2 + 3360*a^3*b^17*c^3*d^3*e^3 + 2040*a^3*b^18*c^2*d^2*e^4 + 138240*a^4*b^14*c^5*d^4*e^2 - 7680*a^4*b^15*c^4*d^3*e^3 - 20880*a^4*b^16*c^3*d^2*e^4 - 612864*a^5*b^12*c^6*d^4*e^2 - 64512*a^5*b^13*c^5*d^3*e^3 + 138240*a^5*b^14*c^4*d^2*e^4 + 1806336*a^6*b^10*c^7*d^4*e^2 + 688128*a^6*b^11*c^6*d^3*e^3 - 612864*a^6*b^12*c^5*d^2*e^4 - 3317760*a^7*b^8*c^8*d^4*e^2 - 3194880*a^7*b^9*c^7*d^3*e^3 + 1806336*a^7*b^10*c^6*d^2*e^4 + 2949120*a^8*b^6*c^9*d^4*e^2 + 8847360*a^8*b^7*c^8*d^3*e^3 - 3317760*a^8*b^8*c^7*d^2*e^4 + 983040*a^9*b^4*c^10*d^4*e^2 - 15073280*a^9*b^5*c^9*d^3*e^3 + 2949120*a^9*b^6*c^8*d^2*e^4 - 4718592*a^10*b^2*c^11*d^4*e^2 + 14680064*a^10*b^3*c^10*d^3*e^3 + 983040*a^10*b^4*c^9*d^2*e^4 - 4718592*a^11*b^2*c^10*d^2*e^4 + 120*a*b^19*c^3*d^5*e + 34*a*b^21*c*d^3*e^3 + 120*a^3*b^19*c*d*e^5 - 3145728*a^10*b*c^12*d^5*e - 3145728*a^12*b*c^10*d*e^5 - 117*a*b^20*c^2*d^4*e^2 - 2160*a^2*b^17*c^4*d^5*e - 117*a^2*b^20*c*d^2*e^4 + 23040*a^3*b^15*c^5*d^5*e - 161280*a^4*b^13*c^6*d^5*e - 2160*a^4*b^17*c^2*d*e^5 + 774144*a^5*b^11*c^7*d^5*e + 23040*a^5*b^15*c^3*d*e^5 - 2580480*a^6*b^9*c^8*d^5*e - 161280*a^6*b^13*c^4*d*e^5 + 5898240*a^7*b^7*c^9*d^5*e + 774144*a^7*b^11*c^5*d*e^5 - 8847360*a^8*b^5*c^10*d^5*e - 2580480*a^8*b^9*c^6*d*e^5 + 7864320*a^9*b^3*c^11*d^5*e + 5898240*a^9*b^7*c^7*d*e^5 - 8847360*a^10*b^5*c^8*d*e^5 - 6291456*a^11*b*c^11*d^3*e^3 + 7864320*a^11*b^3*c^9*d*e^5)))^(1/2) + log(- (2^(1/2)*((2^(1/2)*((c^2*e^3*(b*e - 2*c*d)*(b^2*e^2 - 12*c^2*d^2 - 16*a*c*e^2 + 12*b*c*d*e))/((4*a*c - b^2)*(a*e^2 + c*d^2 - b*d*e)) - (2^(1/2)*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(-(b^17*e^7 + 4718592*a^5*c^12*d^7 - 4608*b^10*c^7*d^7 - b^2*e^7*(-(4*a*c - b^2)^15)^(1/2) + 92160*a*b^8*c^8*d^7 - 1720320*a^8*b*c^8*e^7 + 3440640*a^8*c^9*d*e^6 + 16128*b^11*c^6*d^6*e - 737280*a^2*b^6*c^9*d^7 + 2949120*a^3*b^4*c^10*d^7 - 5898240*a^4*b^2*c^11*d^7 + 1140*a^2*b^13*c^2*e^7 - 10160*a^3*b^11*c^3*e^7 + 34880*a^4*b^9*c^4*e^7 + 43776*a^5*b^7*c^5*e^7 - 680960*a^6*b^5*c^6*e^7 + 1863680*a^7*b^3*c^7*e^7 + 13762560*a^6*c^11*d^5*e^2 + 12615680*a^7*c^10*d^3*e^4 - 20832*b^12*c^5*d^5*e^2 + 11760*b^13*c^4*d^4*e^3 - 2450*b^14*c^3*d^3*e^4 - 21*b^15*c^2*d^2*e^5 + 21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2) - 55*a*b^15*c*e^7 + 25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2) + 21*b^16*c*d*e^6 - 21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2) - 3064320*a^2*b^8*c^7*d^5*e^2 + 1209600*a^2*b^9*c^6*d^4*e^3 + 144480*a^2*b^10*c^5*d^3*e^4 - 136080*a^2*b^11*c^4*d^2*e^5 + 11182080*a^3*b^6*c^8*d^5*e^2 - 2150400*a^3*b^7*c^7*d^4*e^3 - 2576000*a^3*b^8*c^6*d^3*e^4 + 853440*a^3*b^9*c^5*d^2*e^5 - 18063360*a^4*b^4*c^9*d^5*e^2 - 6451200*a^4*b^5*c^8*d^4*e^3 + 12454400*a^4*b^6*c^7*d^3*e^4 - 1908480*a^4*b^7*c^6*d^2*e^5 + 4128768*a^5*b^2*c^10*d^5*e^2 + 30965760*a^5*b^3*c^9*d^4*e^3 - 24729600*a^5*b^4*c^8*d^3*e^4 - 2128896*a^5*b^5*c^7*d^2*e^5 + 12328960*a^6*b^2*c^9*d^3*e^4 + 15912960*a^6*b^3*c^8*d^2*e^5 - 322560*a*b^9*c^7*d^6*e - 630*a*b^14*c^2*d*e^6 - 16515072*a^5*b*c^11*d^6*e + 403200*a*b^10*c^6*d^5*e^2 - 201600*a*b^11*c^5*d^4*e^3 + 21560*a*b^12*c^4*d^3*e^4 + 7980*a*b^13*c^3*d^2*e^5 + 2580480*a^2*b^7*c^8*d^6*e + 840*a^2*b^12*c^3*d*e^6 - 10321920*a^3*b^5*c^9*d^6*e + 84000*a^3*b^10*c^4*d*e^6 + 20643840*a^4*b^3*c^10*d^6*e - 846720*a^4*b^8*c^5*d*e^6 + 3472896*a^5*b^6*c^6*d*e^6 - 34406400*a^6*b*c^10*d^4*e^3 - 6236160*a^6*b^4*c^7*d*e^6 - 18923520*a^7*b*c^9*d^2*e^5 + 2580480*a^7*b^2*c^8*d*e^6)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)^3))^(1/2))/2)*(-(b^17*e^7 + 4718592*a^5*c^12*d^7 - 4608*b^10*c^7*d^7 - b^2*e^7*(-(4*a*c - b^2)^15)^(1/2) + 92160*a*b^8*c^8*d^7 - 1720320*a^8*b*c^8*e^7 + 3440640*a^8*c^9*d*e^6 + 16128*b^11*c^6*d^6*e - 737280*a^2*b^6*c^9*d^7 + 2949120*a^3*b^4*c^10*d^7 - 5898240*a^4*b^2*c^11*d^7 + 1140*a^2*b^13*c^2*e^7 - 10160*a^3*b^11*c^3*e^7 + 34880*a^4*b^9*c^4*e^7 + 43776*a^5*b^7*c^5*e^7 - 680960*a^6*b^5*c^6*e^7 + 1863680*a^7*b^3*c^7*e^7 + 13762560*a^6*c^11*d^5*e^2 + 12615680*a^7*c^10*d^3*e^4 - 20832*b^12*c^5*d^5*e^2 + 11760*b^13*c^4*d^4*e^3 - 2450*b^14*c^3*d^3*e^4 - 21*b^15*c^2*d^2*e^5 + 21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2) - 55*a*b^15*c*e^7 + 25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2) + 21*b^16*c*d*e^6 - 21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2) - 3064320*a^2*b^8*c^7*d^5*e^2 + 1209600*a^2*b^9*c^6*d^4*e^3 + 144480*a^2*b^10*c^5*d^3*e^4 - 136080*a^2*b^11*c^4*d^2*e^5 + 11182080*a^3*b^6*c^8*d^5*e^2 - 2150400*a^3*b^7*c^7*d^4*e^3 - 2576000*a^3*b^8*c^6*d^3*e^4 + 853440*a^3*b^9*c^5*d^2*e^5 - 18063360*a^4*b^4*c^9*d^5*e^2 - 6451200*a^4*b^5*c^8*d^4*e^3 + 12454400*a^4*b^6*c^7*d^3*e^4 - 1908480*a^4*b^7*c^6*d^2*e^5 + 4128768*a^5*b^2*c^10*d^5*e^2 + 30965760*a^5*b^3*c^9*d^4*e^3 - 24729600*a^5*b^4*c^8*d^3*e^4 - 2128896*a^5*b^5*c^7*d^2*e^5 + 12328960*a^6*b^2*c^9*d^3*e^4 + 15912960*a^6*b^3*c^8*d^2*e^5 - 322560*a*b^9*c^7*d^6*e - 630*a*b^14*c^2*d*e^6 - 16515072*a^5*b*c^11*d^6*e + 403200*a*b^10*c^6*d^5*e^2 - 201600*a*b^11*c^5*d^4*e^3 + 21560*a*b^12*c^4*d^3*e^4 + 7980*a*b^13*c^3*d^2*e^5 + 2580480*a^2*b^7*c^8*d^6*e + 840*a^2*b^12*c^3*d*e^6 - 10321920*a^3*b^5*c^9*d^6*e + 84000*a^3*b^10*c^4*d*e^6 + 20643840*a^4*b^3*c^10*d^6*e - 846720*a^4*b^8*c^5*d*e^6 + 3472896*a^5*b^6*c^6*d*e^6 - 34406400*a^6*b*c^10*d^4*e^3 - 6236160*a^6*b^4*c^7*d*e^6 - 18923520*a^7*b*c^9*d^2*e^5 + 2580480*a^7*b^2*c^8*d*e^6)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)^3))^(1/2))/16 + (c^3*e^2*(d + e*x)^(1/2)*(b^6*e^6 + 4608*c^6*d^6 - 800*a^3*c^3*e^6 + 8832*a*c^5*d^4*e^2 + 1472*a^2*b^2*c^2*e^6 + 3488*a^2*c^4*d^2*e^4 + 15072*b^2*c^4*d^4*e^2 - 7104*b^3*c^3*d^3*e^3 + 1226*b^4*c^2*d^2*e^4 - 34*a*b^4*c*e^6 - 13824*b*c^5*d^5*e + 22*b^5*c*d*e^5 - 17664*a*b*c^4*d^3*e^3 - 2672*a*b^3*c^2*d*e^5 - 3488*a^2*b*c^3*d*e^5 + 11504*a*b^2*c^3*d^2*e^4))/(8*(4*a*c - b^2)^4*(a*e^2 + c*d^2 - b*d*e)^2))*(-(b^17*e^7 + 4718592*a^5*c^12*d^7 - 4608*b^10*c^7*d^7 - b^2*e^7*(-(4*a*c - b^2)^15)^(1/2) + 92160*a*b^8*c^8*d^7 - 1720320*a^8*b*c^8*e^7 + 3440640*a^8*c^9*d*e^6 + 16128*b^11*c^6*d^6*e - 737280*a^2*b^6*c^9*d^7 + 2949120*a^3*b^4*c^10*d^7 - 5898240*a^4*b^2*c^11*d^7 + 1140*a^2*b^13*c^2*e^7 - 10160*a^3*b^11*c^3*e^7 + 34880*a^4*b^9*c^4*e^7 + 43776*a^5*b^7*c^5*e^7 - 680960*a^6*b^5*c^6*e^7 + 1863680*a^7*b^3*c^7*e^7 + 13762560*a^6*c^11*d^5*e^2 + 12615680*a^7*c^10*d^3*e^4 - 20832*b^12*c^5*d^5*e^2 + 11760*b^13*c^4*d^4*e^3 - 2450*b^14*c^3*d^3*e^4 - 21*b^15*c^2*d^2*e^5 + 21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2) - 55*a*b^15*c*e^7 + 25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2) + 21*b^16*c*d*e^6 - 21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2) - 3064320*a^2*b^8*c^7*d^5*e^2 + 1209600*a^2*b^9*c^6*d^4*e^3 + 144480*a^2*b^10*c^5*d^3*e^4 - 136080*a^2*b^11*c^4*d^2*e^5 + 11182080*a^3*b^6*c^8*d^5*e^2 - 2150400*a^3*b^7*c^7*d^4*e^3 - 2576000*a^3*b^8*c^6*d^3*e^4 + 853440*a^3*b^9*c^5*d^2*e^5 - 18063360*a^4*b^4*c^9*d^5*e^2 - 6451200*a^4*b^5*c^8*d^4*e^3 + 12454400*a^4*b^6*c^7*d^3*e^4 - 1908480*a^4*b^7*c^6*d^2*e^5 + 4128768*a^5*b^2*c^10*d^5*e^2 + 30965760*a^5*b^3*c^9*d^4*e^3 - 24729600*a^5*b^4*c^8*d^3*e^4 - 2128896*a^5*b^5*c^7*d^2*e^5 + 12328960*a^6*b^2*c^9*d^3*e^4 + 15912960*a^6*b^3*c^8*d^2*e^5 - 322560*a*b^9*c^7*d^6*e - 630*a*b^14*c^2*d*e^6 - 16515072*a^5*b*c^11*d^6*e + 403200*a*b^10*c^6*d^5*e^2 - 201600*a*b^11*c^5*d^4*e^3 + 21560*a*b^12*c^4*d^3*e^4 + 7980*a*b^13*c^3*d^2*e^5 + 2580480*a^2*b^7*c^8*d^6*e + 840*a^2*b^12*c^3*d*e^6 - 10321920*a^3*b^5*c^9*d^6*e + 84000*a^3*b^10*c^4*d*e^6 + 20643840*a^4*b^3*c^10*d^6*e - 846720*a^4*b^8*c^5*d*e^6 + 3472896*a^5*b^6*c^6*d*e^6 - 34406400*a^6*b*c^10*d^4*e^3 - 6236160*a^6*b^4*c^7*d*e^6 - 18923520*a^7*b*c^9*d^2*e^5 + 2580480*a^7*b^2*c^8*d*e^6)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)^3))^(1/2))/16 - (c^4*e^3*(55296*c^6*d^6 - 35*b^6*e^6 + 8000*a^3*c^3*e^6 + 124416*a*c^5*d^4*e^2 + 12720*a^2*b^2*c^2*e^6 + 74880*a^2*c^4*d^2*e^4 + 176256*b^2*c^4*d^4*e^2 - 76032*b^3*c^3*d^3*e^3 + 9864*b^4*c^2*d^2*e^4 - 84*a*b^4*c*e^6 - 165888*b*c^5*d^5*e + 504*b^5*c*d*e^5 - 248832*a*b*c^4*d^3*e^3 - 24768*a*b^3*c^2*d*e^5 - 74880*a^2*b*c^3*d*e^5 + 149184*a*b^2*c^3*d^2*e^4))/(64*(4*a*c - b^2)^6*(a*e^2 + c*d^2 - b*d*e)^2))*(-(b^17*e^7 + 4718592*a^5*c^12*d^7 - 4608*b^10*c^7*d^7 - b^2*e^7*(-(4*a*c - b^2)^15)^(1/2) + 92160*a*b^8*c^8*d^7 - 1720320*a^8*b*c^8*e^7 + 3440640*a^8*c^9*d*e^6 + 16128*b^11*c^6*d^6*e - 737280*a^2*b^6*c^9*d^7 + 2949120*a^3*b^4*c^10*d^7 - 5898240*a^4*b^2*c^11*d^7 + 1140*a^2*b^13*c^2*e^7 - 10160*a^3*b^11*c^3*e^7 + 34880*a^4*b^9*c^4*e^7 + 43776*a^5*b^7*c^5*e^7 - 680960*a^6*b^5*c^6*e^7 + 1863680*a^7*b^3*c^7*e^7 + 13762560*a^6*c^11*d^5*e^2 + 12615680*a^7*c^10*d^3*e^4 - 20832*b^12*c^5*d^5*e^2 + 11760*b^13*c^4*d^4*e^3 - 2450*b^14*c^3*d^3*e^4 - 21*b^15*c^2*d^2*e^5 + 21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2) - 55*a*b^15*c*e^7 + 25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2) + 21*b^16*c*d*e^6 - 21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2) - 3064320*a^2*b^8*c^7*d^5*e^2 + 1209600*a^2*b^9*c^6*d^4*e^3 + 144480*a^2*b^10*c^5*d^3*e^4 - 136080*a^2*b^11*c^4*d^2*e^5 + 11182080*a^3*b^6*c^8*d^5*e^2 - 2150400*a^3*b^7*c^7*d^4*e^3 - 2576000*a^3*b^8*c^6*d^3*e^4 + 853440*a^3*b^9*c^5*d^2*e^5 - 18063360*a^4*b^4*c^9*d^5*e^2 - 6451200*a^4*b^5*c^8*d^4*e^3 + 12454400*a^4*b^6*c^7*d^3*e^4 - 1908480*a^4*b^7*c^6*d^2*e^5 + 4128768*a^5*b^2*c^10*d^5*e^2 + 30965760*a^5*b^3*c^9*d^4*e^3 - 24729600*a^5*b^4*c^8*d^3*e^4 - 2128896*a^5*b^5*c^7*d^2*e^5 + 12328960*a^6*b^2*c^9*d^3*e^4 + 15912960*a^6*b^3*c^8*d^2*e^5 - 322560*a*b^9*c^7*d^6*e - 630*a*b^14*c^2*d*e^6 - 16515072*a^5*b*c^11*d^6*e + 403200*a*b^10*c^6*d^5*e^2 - 201600*a*b^11*c^5*d^4*e^3 + 21560*a*b^12*c^4*d^3*e^4 + 7980*a*b^13*c^3*d^2*e^5 + 2580480*a^2*b^7*c^8*d^6*e + 840*a^2*b^12*c^3*d*e^6 - 10321920*a^3*b^5*c^9*d^6*e + 84000*a^3*b^10*c^4*d*e^6 + 20643840*a^4*b^3*c^10*d^6*e - 846720*a^4*b^8*c^5*d*e^6 + 3472896*a^5*b^6*c^6*d*e^6 - 34406400*a^6*b*c^10*d^4*e^3 - 6236160*a^6*b^4*c^7*d*e^6 - 18923520*a^7*b*c^9*d^2*e^5 + 2580480*a^7*b^2*c^8*d*e^6)/(128*(a^3*b^20*e^6 + 1048576*a^10*c^13*d^6 + 1048576*a^13*c^10*e^6 + b^20*c^3*d^6 - b^23*d^3*e^3 - 40*a*b^18*c^4*d^6 - 40*a^4*b^18*c*e^6 + 3*a*b^22*d^2*e^4 - 3*a^2*b^21*d*e^5 - 3*b^21*c^2*d^5*e + 3*b^22*c*d^4*e^2 + 720*a^2*b^16*c^5*d^6 - 7680*a^3*b^14*c^6*d^6 + 53760*a^4*b^12*c^7*d^6 - 258048*a^5*b^10*c^8*d^6 + 860160*a^6*b^8*c^9*d^6 - 1966080*a^7*b^6*c^10*d^6 + 2949120*a^8*b^4*c^11*d^6 - 2621440*a^9*b^2*c^12*d^6 + 720*a^5*b^16*c^2*e^6 - 7680*a^6*b^14*c^3*e^6 + 53760*a^7*b^12*c^4*e^6 - 258048*a^8*b^10*c^5*e^6 + 860160*a^9*b^8*c^6*e^6 - 1966080*a^10*b^6*c^7*e^6 + 2949120*a^11*b^4*c^8*e^6 - 2621440*a^12*b^2*c^9*e^6 + 3145728*a^11*c^12*d^4*e^2 + 3145728*a^12*c^11*d^2*e^4 + 2040*a^2*b^18*c^3*d^4*e^2 - 480*a^2*b^19*c^2*d^3*e^3 - 20880*a^3*b^16*c^4*d^4*e^2 + 3360*a^3*b^17*c^3*d^3*e^3 + 2040*a^3*b^18*c^2*d^2*e^4 + 138240*a^4*b^14*c^5*d^4*e^2 - 7680*a^4*b^15*c^4*d^3*e^3 - 20880*a^4*b^16*c^3*d^2*e^4 - 612864*a^5*b^12*c^6*d^4*e^2 - 64512*a^5*b^13*c^5*d^3*e^3 + 138240*a^5*b^14*c^4*d^2*e^4 + 1806336*a^6*b^10*c^7*d^4*e^2 + 688128*a^6*b^11*c^6*d^3*e^3 - 612864*a^6*b^12*c^5*d^2*e^4 - 3317760*a^7*b^8*c^8*d^4*e^2 - 3194880*a^7*b^9*c^7*d^3*e^3 + 1806336*a^7*b^10*c^6*d^2*e^4 + 2949120*a^8*b^6*c^9*d^4*e^2 + 8847360*a^8*b^7*c^8*d^3*e^3 - 3317760*a^8*b^8*c^7*d^2*e^4 + 983040*a^9*b^4*c^10*d^4*e^2 - 15073280*a^9*b^5*c^9*d^3*e^3 + 2949120*a^9*b^6*c^8*d^2*e^4 - 4718592*a^10*b^2*c^11*d^4*e^2 + 14680064*a^10*b^3*c^10*d^3*e^3 + 983040*a^10*b^4*c^9*d^2*e^4 - 4718592*a^11*b^2*c^10*d^2*e^4 + 120*a*b^19*c^3*d^5*e + 34*a*b^21*c*d^3*e^3 + 120*a^3*b^19*c*d*e^5 - 3145728*a^10*b*c^12*d^5*e - 3145728*a^12*b*c^10*d*e^5 - 117*a*b^20*c^2*d^4*e^2 - 2160*a^2*b^17*c^4*d^5*e - 117*a^2*b^20*c*d^2*e^4 + 23040*a^3*b^15*c^5*d^5*e - 161280*a^4*b^13*c^6*d^5*e - 2160*a^4*b^17*c^2*d*e^5 + 774144*a^5*b^11*c^7*d^5*e + 23040*a^5*b^15*c^3*d*e^5 - 2580480*a^6*b^9*c^8*d^5*e - 161280*a^6*b^13*c^4*d*e^5 + 5898240*a^7*b^7*c^9*d^5*e + 774144*a^7*b^11*c^5*d*e^5 - 8847360*a^8*b^5*c^10*d^5*e - 2580480*a^8*b^9*c^6*d*e^5 + 7864320*a^9*b^3*c^11*d^5*e + 5898240*a^9*b^7*c^7*d*e^5 - 8847360*a^10*b^5*c^8*d*e^5 - 6291456*a^11*b*c^11*d^3*e^3 + 7864320*a^11*b^3*c^9*d*e^5)))^(1/2) - log(- (((c^2*e^3*(b*e - 2*c*d)*(b^2*e^2 - 12*c^2*d^2 - 16*a*c*e^2 + 12*b*c*d*e))/((4*a*c - b^2)*(a*e^2 + c*d^2 - b*d*e)) + 8*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(-((b^17*e^7)/128 + 36864*a^5*c^12*d^7 - 36*b^10*c^7*d^7 - (b^2*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + 720*a*b^8*c^8*d^7 - 13440*a^8*b*c^8*e^7 + 26880*a^8*c^9*d*e^6 + 126*b^11*c^6*d^6*e - 5760*a^2*b^6*c^9*d^7 + 23040*a^3*b^4*c^10*d^7 - 46080*a^4*b^2*c^11*d^7 + (285*a^2*b^13*c^2*e^7)/32 - (635*a^3*b^11*c^3*e^7)/8 + (545*a^4*b^9*c^4*e^7)/2 + 342*a^5*b^7*c^5*e^7 - 5320*a^6*b^5*c^6*e^7 + 14560*a^7*b^3*c^7*e^7 + 107520*a^6*c^11*d^5*e^2 + 98560*a^7*c^10*d^3*e^4 - (651*b^12*c^5*d^5*e^2)/4 + (735*b^13*c^4*d^4*e^3)/8 - (1225*b^14*c^3*d^3*e^4)/64 - (21*b^15*c^2*d^2*e^5)/128 + (21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (55*a*b^15*c*e^7)/128 + (25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + (21*b^16*c*d*e^6)/128 - (21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2))/128 - 23940*a^2*b^8*c^7*d^5*e^2 + 9450*a^2*b^9*c^6*d^4*e^3 + (4515*a^2*b^10*c^5*d^3*e^4)/4 - (8505*a^2*b^11*c^4*d^2*e^5)/8 + 87360*a^3*b^6*c^8*d^5*e^2 - 16800*a^3*b^7*c^7*d^4*e^3 - 20125*a^3*b^8*c^6*d^3*e^4 + (13335*a^3*b^9*c^5*d^2*e^5)/2 - 141120*a^4*b^4*c^9*d^5*e^2 - 50400*a^4*b^5*c^8*d^4*e^3 + 97300*a^4*b^6*c^7*d^3*e^4 - 14910*a^4*b^7*c^6*d^2*e^5 + 32256*a^5*b^2*c^10*d^5*e^2 + 241920*a^5*b^3*c^9*d^4*e^3 - 193200*a^5*b^4*c^8*d^3*e^4 - 16632*a^5*b^5*c^7*d^2*e^5 + 96320*a^6*b^2*c^9*d^3*e^4 + 124320*a^6*b^3*c^8*d^2*e^5 - 2520*a*b^9*c^7*d^6*e - (315*a*b^14*c^2*d*e^6)/64 - 129024*a^5*b*c^11*d^6*e + 3150*a*b^10*c^6*d^5*e^2 - 1575*a*b^11*c^5*d^4*e^3 + (2695*a*b^12*c^4*d^3*e^4)/16 + (1995*a*b^13*c^3*d^2*e^5)/32 + 20160*a^2*b^7*c^8*d^6*e + (105*a^2*b^12*c^3*d*e^6)/16 - 80640*a^3*b^5*c^9*d^6*e + (2625*a^3*b^10*c^4*d*e^6)/4 + 161280*a^4*b^3*c^10*d^6*e - 6615*a^4*b^8*c^5*d*e^6 + 27132*a^5*b^6*c^6*d*e^6 - 268800*a^6*b*c^10*d^4*e^3 - 48720*a^6*b^4*c^7*d*e^6 - 147840*a^7*b*c^9*d^2*e^5 + 20160*a^7*b^2*c^8*d*e^6)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)^3))^(1/2))*(-((b^17*e^7)/128 + 36864*a^5*c^12*d^7 - 36*b^10*c^7*d^7 - (b^2*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + 720*a*b^8*c^8*d^7 - 13440*a^8*b*c^8*e^7 + 26880*a^8*c^9*d*e^6 + 126*b^11*c^6*d^6*e - 5760*a^2*b^6*c^9*d^7 + 23040*a^3*b^4*c^10*d^7 - 46080*a^4*b^2*c^11*d^7 + (285*a^2*b^13*c^2*e^7)/32 - (635*a^3*b^11*c^3*e^7)/8 + (545*a^4*b^9*c^4*e^7)/2 + 342*a^5*b^7*c^5*e^7 - 5320*a^6*b^5*c^6*e^7 + 14560*a^7*b^3*c^7*e^7 + 107520*a^6*c^11*d^5*e^2 + 98560*a^7*c^10*d^3*e^4 - (651*b^12*c^5*d^5*e^2)/4 + (735*b^13*c^4*d^4*e^3)/8 - (1225*b^14*c^3*d^3*e^4)/64 - (21*b^15*c^2*d^2*e^5)/128 + (21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (55*a*b^15*c*e^7)/128 + (25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + (21*b^16*c*d*e^6)/128 - (21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2))/128 - 23940*a^2*b^8*c^7*d^5*e^2 + 9450*a^2*b^9*c^6*d^4*e^3 + (4515*a^2*b^10*c^5*d^3*e^4)/4 - (8505*a^2*b^11*c^4*d^2*e^5)/8 + 87360*a^3*b^6*c^8*d^5*e^2 - 16800*a^3*b^7*c^7*d^4*e^3 - 20125*a^3*b^8*c^6*d^3*e^4 + (13335*a^3*b^9*c^5*d^2*e^5)/2 - 141120*a^4*b^4*c^9*d^5*e^2 - 50400*a^4*b^5*c^8*d^4*e^3 + 97300*a^4*b^6*c^7*d^3*e^4 - 14910*a^4*b^7*c^6*d^2*e^5 + 32256*a^5*b^2*c^10*d^5*e^2 + 241920*a^5*b^3*c^9*d^4*e^3 - 193200*a^5*b^4*c^8*d^3*e^4 - 16632*a^5*b^5*c^7*d^2*e^5 + 96320*a^6*b^2*c^9*d^3*e^4 + 124320*a^6*b^3*c^8*d^2*e^5 - 2520*a*b^9*c^7*d^6*e - (315*a*b^14*c^2*d*e^6)/64 - 129024*a^5*b*c^11*d^6*e + 3150*a*b^10*c^6*d^5*e^2 - 1575*a*b^11*c^5*d^4*e^3 + (2695*a*b^12*c^4*d^3*e^4)/16 + (1995*a*b^13*c^3*d^2*e^5)/32 + 20160*a^2*b^7*c^8*d^6*e + (105*a^2*b^12*c^3*d*e^6)/16 - 80640*a^3*b^5*c^9*d^6*e + (2625*a^3*b^10*c^4*d*e^6)/4 + 161280*a^4*b^3*c^10*d^6*e - 6615*a^4*b^8*c^5*d*e^6 + 27132*a^5*b^6*c^6*d*e^6 - 268800*a^6*b*c^10*d^4*e^3 - 48720*a^6*b^4*c^7*d*e^6 - 147840*a^7*b*c^9*d^2*e^5 + 20160*a^7*b^2*c^8*d*e^6)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)^3))^(1/2) - (c^3*e^2*(d + e*x)^(1/2)*(b^6*e^6 + 4608*c^6*d^6 - 800*a^3*c^3*e^6 + 8832*a*c^5*d^4*e^2 + 1472*a^2*b^2*c^2*e^6 + 3488*a^2*c^4*d^2*e^4 + 15072*b^2*c^4*d^4*e^2 - 7104*b^3*c^3*d^3*e^3 + 1226*b^4*c^2*d^2*e^4 - 34*a*b^4*c*e^6 - 13824*b*c^5*d^5*e + 22*b^5*c*d*e^5 - 17664*a*b*c^4*d^3*e^3 - 2672*a*b^3*c^2*d*e^5 - 3488*a^2*b*c^3*d*e^5 + 11504*a*b^2*c^3*d^2*e^4))/(8*(4*a*c - b^2)^4*(a*e^2 + c*d^2 - b*d*e)^2))*(-((b^17*e^7)/128 + 36864*a^5*c^12*d^7 - 36*b^10*c^7*d^7 - (b^2*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + 720*a*b^8*c^8*d^7 - 13440*a^8*b*c^8*e^7 + 26880*a^8*c^9*d*e^6 + 126*b^11*c^6*d^6*e - 5760*a^2*b^6*c^9*d^7 + 23040*a^3*b^4*c^10*d^7 - 46080*a^4*b^2*c^11*d^7 + (285*a^2*b^13*c^2*e^7)/32 - (635*a^3*b^11*c^3*e^7)/8 + (545*a^4*b^9*c^4*e^7)/2 + 342*a^5*b^7*c^5*e^7 - 5320*a^6*b^5*c^6*e^7 + 14560*a^7*b^3*c^7*e^7 + 107520*a^6*c^11*d^5*e^2 + 98560*a^7*c^10*d^3*e^4 - (651*b^12*c^5*d^5*e^2)/4 + (735*b^13*c^4*d^4*e^3)/8 - (1225*b^14*c^3*d^3*e^4)/64 - (21*b^15*c^2*d^2*e^5)/128 + (21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (55*a*b^15*c*e^7)/128 + (25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + (21*b^16*c*d*e^6)/128 - (21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2))/128 - 23940*a^2*b^8*c^7*d^5*e^2 + 9450*a^2*b^9*c^6*d^4*e^3 + (4515*a^2*b^10*c^5*d^3*e^4)/4 - (8505*a^2*b^11*c^4*d^2*e^5)/8 + 87360*a^3*b^6*c^8*d^5*e^2 - 16800*a^3*b^7*c^7*d^4*e^3 - 20125*a^3*b^8*c^6*d^3*e^4 + (13335*a^3*b^9*c^5*d^2*e^5)/2 - 141120*a^4*b^4*c^9*d^5*e^2 - 50400*a^4*b^5*c^8*d^4*e^3 + 97300*a^4*b^6*c^7*d^3*e^4 - 14910*a^4*b^7*c^6*d^2*e^5 + 32256*a^5*b^2*c^10*d^5*e^2 + 241920*a^5*b^3*c^9*d^4*e^3 - 193200*a^5*b^4*c^8*d^3*e^4 - 16632*a^5*b^5*c^7*d^2*e^5 + 96320*a^6*b^2*c^9*d^3*e^4 + 124320*a^6*b^3*c^8*d^2*e^5 - 2520*a*b^9*c^7*d^6*e - (315*a*b^14*c^2*d*e^6)/64 - 129024*a^5*b*c^11*d^6*e + 3150*a*b^10*c^6*d^5*e^2 - 1575*a*b^11*c^5*d^4*e^3 + (2695*a*b^12*c^4*d^3*e^4)/16 + (1995*a*b^13*c^3*d^2*e^5)/32 + 20160*a^2*b^7*c^8*d^6*e + (105*a^2*b^12*c^3*d*e^6)/16 - 80640*a^3*b^5*c^9*d^6*e + (2625*a^3*b^10*c^4*d*e^6)/4 + 161280*a^4*b^3*c^10*d^6*e - 6615*a^4*b^8*c^5*d*e^6 + 27132*a^5*b^6*c^6*d*e^6 - 268800*a^6*b*c^10*d^4*e^3 - 48720*a^6*b^4*c^7*d*e^6 - 147840*a^7*b*c^9*d^2*e^5 + 20160*a^7*b^2*c^8*d*e^6)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)^3))^(1/2) - (c^4*e^3*(55296*c^6*d^6 - 35*b^6*e^6 + 8000*a^3*c^3*e^6 + 124416*a*c^5*d^4*e^2 + 12720*a^2*b^2*c^2*e^6 + 74880*a^2*c^4*d^2*e^4 + 176256*b^2*c^4*d^4*e^2 - 76032*b^3*c^3*d^3*e^3 + 9864*b^4*c^2*d^2*e^4 - 84*a*b^4*c*e^6 - 165888*b*c^5*d^5*e + 504*b^5*c*d*e^5 - 248832*a*b*c^4*d^3*e^3 - 24768*a*b^3*c^2*d*e^5 - 74880*a^2*b*c^3*d*e^5 + 149184*a*b^2*c^3*d^2*e^4))/(64*(4*a*c - b^2)^6*(a*e^2 + c*d^2 - b*d*e)^2))*(-((b^17*e^7)/128 + 36864*a^5*c^12*d^7 - 36*b^10*c^7*d^7 - (b^2*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + 720*a*b^8*c^8*d^7 - 13440*a^8*b*c^8*e^7 + 26880*a^8*c^9*d*e^6 + 126*b^11*c^6*d^6*e - 5760*a^2*b^6*c^9*d^7 + 23040*a^3*b^4*c^10*d^7 - 46080*a^4*b^2*c^11*d^7 + (285*a^2*b^13*c^2*e^7)/32 - (635*a^3*b^11*c^3*e^7)/8 + (545*a^4*b^9*c^4*e^7)/2 + 342*a^5*b^7*c^5*e^7 - 5320*a^6*b^5*c^6*e^7 + 14560*a^7*b^3*c^7*e^7 + 107520*a^6*c^11*d^5*e^2 + 98560*a^7*c^10*d^3*e^4 - (651*b^12*c^5*d^5*e^2)/4 + (735*b^13*c^4*d^4*e^3)/8 - (1225*b^14*c^3*d^3*e^4)/64 - (21*b^15*c^2*d^2*e^5)/128 + (21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (55*a*b^15*c*e^7)/128 + (25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + (21*b^16*c*d*e^6)/128 - (21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2))/128 - 23940*a^2*b^8*c^7*d^5*e^2 + 9450*a^2*b^9*c^6*d^4*e^3 + (4515*a^2*b^10*c^5*d^3*e^4)/4 - (8505*a^2*b^11*c^4*d^2*e^5)/8 + 87360*a^3*b^6*c^8*d^5*e^2 - 16800*a^3*b^7*c^7*d^4*e^3 - 20125*a^3*b^8*c^6*d^3*e^4 + (13335*a^3*b^9*c^5*d^2*e^5)/2 - 141120*a^4*b^4*c^9*d^5*e^2 - 50400*a^4*b^5*c^8*d^4*e^3 + 97300*a^4*b^6*c^7*d^3*e^4 - 14910*a^4*b^7*c^6*d^2*e^5 + 32256*a^5*b^2*c^10*d^5*e^2 + 241920*a^5*b^3*c^9*d^4*e^3 - 193200*a^5*b^4*c^8*d^3*e^4 - 16632*a^5*b^5*c^7*d^2*e^5 + 96320*a^6*b^2*c^9*d^3*e^4 + 124320*a^6*b^3*c^8*d^2*e^5 - 2520*a*b^9*c^7*d^6*e - (315*a*b^14*c^2*d*e^6)/64 - 129024*a^5*b*c^11*d^6*e + 3150*a*b^10*c^6*d^5*e^2 - 1575*a*b^11*c^5*d^4*e^3 + (2695*a*b^12*c^4*d^3*e^4)/16 + (1995*a*b^13*c^3*d^2*e^5)/32 + 20160*a^2*b^7*c^8*d^6*e + (105*a^2*b^12*c^3*d*e^6)/16 - 80640*a^3*b^5*c^9*d^6*e + (2625*a^3*b^10*c^4*d*e^6)/4 + 161280*a^4*b^3*c^10*d^6*e - 6615*a^4*b^8*c^5*d*e^6 + 27132*a^5*b^6*c^6*d*e^6 - 268800*a^6*b*c^10*d^4*e^3 - 48720*a^6*b^4*c^7*d*e^6 - 147840*a^7*b*c^9*d^2*e^5 + 20160*a^7*b^2*c^8*d*e^6)/(a^3*b^20*e^6 + 1048576*a^10*c^13*d^6 + 1048576*a^13*c^10*e^6 + b^20*c^3*d^6 - b^23*d^3*e^3 - 40*a*b^18*c^4*d^6 - 40*a^4*b^18*c*e^6 + 3*a*b^22*d^2*e^4 - 3*a^2*b^21*d*e^5 - 3*b^21*c^2*d^5*e + 3*b^22*c*d^4*e^2 + 720*a^2*b^16*c^5*d^6 - 7680*a^3*b^14*c^6*d^6 + 53760*a^4*b^12*c^7*d^6 - 258048*a^5*b^10*c^8*d^6 + 860160*a^6*b^8*c^9*d^6 - 1966080*a^7*b^6*c^10*d^6 + 2949120*a^8*b^4*c^11*d^6 - 2621440*a^9*b^2*c^12*d^6 + 720*a^5*b^16*c^2*e^6 - 7680*a^6*b^14*c^3*e^6 + 53760*a^7*b^12*c^4*e^6 - 258048*a^8*b^10*c^5*e^6 + 860160*a^9*b^8*c^6*e^6 - 1966080*a^10*b^6*c^7*e^6 + 2949120*a^11*b^4*c^8*e^6 - 2621440*a^12*b^2*c^9*e^6 + 3145728*a^11*c^12*d^4*e^2 + 3145728*a^12*c^11*d^2*e^4 + 2040*a^2*b^18*c^3*d^4*e^2 - 480*a^2*b^19*c^2*d^3*e^3 - 20880*a^3*b^16*c^4*d^4*e^2 + 3360*a^3*b^17*c^3*d^3*e^3 + 2040*a^3*b^18*c^2*d^2*e^4 + 138240*a^4*b^14*c^5*d^4*e^2 - 7680*a^4*b^15*c^4*d^3*e^3 - 20880*a^4*b^16*c^3*d^2*e^4 - 612864*a^5*b^12*c^6*d^4*e^2 - 64512*a^5*b^13*c^5*d^3*e^3 + 138240*a^5*b^14*c^4*d^2*e^4 + 1806336*a^6*b^10*c^7*d^4*e^2 + 688128*a^6*b^11*c^6*d^3*e^3 - 612864*a^6*b^12*c^5*d^2*e^4 - 3317760*a^7*b^8*c^8*d^4*e^2 - 3194880*a^7*b^9*c^7*d^3*e^3 + 1806336*a^7*b^10*c^6*d^2*e^4 + 2949120*a^8*b^6*c^9*d^4*e^2 + 8847360*a^8*b^7*c^8*d^3*e^3 - 3317760*a^8*b^8*c^7*d^2*e^4 + 983040*a^9*b^4*c^10*d^4*e^2 - 15073280*a^9*b^5*c^9*d^3*e^3 + 2949120*a^9*b^6*c^8*d^2*e^4 - 4718592*a^10*b^2*c^11*d^4*e^2 + 14680064*a^10*b^3*c^10*d^3*e^3 + 983040*a^10*b^4*c^9*d^2*e^4 - 4718592*a^11*b^2*c^10*d^2*e^4 + 120*a*b^19*c^3*d^5*e + 34*a*b^21*c*d^3*e^3 + 120*a^3*b^19*c*d*e^5 - 3145728*a^10*b*c^12*d^5*e - 3145728*a^12*b*c^10*d*e^5 - 117*a*b^20*c^2*d^4*e^2 - 2160*a^2*b^17*c^4*d^5*e - 117*a^2*b^20*c*d^2*e^4 + 23040*a^3*b^15*c^5*d^5*e - 161280*a^4*b^13*c^6*d^5*e - 2160*a^4*b^17*c^2*d*e^5 + 774144*a^5*b^11*c^7*d^5*e + 23040*a^5*b^15*c^3*d*e^5 - 2580480*a^6*b^9*c^8*d^5*e - 161280*a^6*b^13*c^4*d*e^5 + 5898240*a^7*b^7*c^9*d^5*e + 774144*a^7*b^11*c^5*d*e^5 - 8847360*a^8*b^5*c^10*d^5*e - 2580480*a^8*b^9*c^6*d*e^5 + 7864320*a^9*b^3*c^11*d^5*e + 5898240*a^9*b^7*c^7*d*e^5 - 8847360*a^10*b^5*c^8*d*e^5 - 6291456*a^11*b*c^11*d^3*e^3 + 7864320*a^11*b^3*c^9*d*e^5))^(1/2) - log(- (((c^2*e^3*(b*e - 2*c*d)*(b^2*e^2 - 12*c^2*d^2 - 16*a*c*e^2 + 12*b*c*d*e))/((4*a*c - b^2)*(a*e^2 + c*d^2 - b*d*e)) + 8*c^2*e^2*(4*a*c - b^2)*(b*e - 2*c*d)*(d + e*x)^(1/2)*(-((b^17*e^7)/128 + 36864*a^5*c^12*d^7 - 36*b^10*c^7*d^7 + (b^2*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + 720*a*b^8*c^8*d^7 - 13440*a^8*b*c^8*e^7 + 26880*a^8*c^9*d*e^6 + 126*b^11*c^6*d^6*e - 5760*a^2*b^6*c^9*d^7 + 23040*a^3*b^4*c^10*d^7 - 46080*a^4*b^2*c^11*d^7 + (285*a^2*b^13*c^2*e^7)/32 - (635*a^3*b^11*c^3*e^7)/8 + (545*a^4*b^9*c^4*e^7)/2 + 342*a^5*b^7*c^5*e^7 - 5320*a^6*b^5*c^6*e^7 + 14560*a^7*b^3*c^7*e^7 + 107520*a^6*c^11*d^5*e^2 + 98560*a^7*c^10*d^3*e^4 - (651*b^12*c^5*d^5*e^2)/4 + (735*b^13*c^4*d^4*e^3)/8 - (1225*b^14*c^3*d^3*e^4)/64 - (21*b^15*c^2*d^2*e^5)/128 - (21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (55*a*b^15*c*e^7)/128 - (25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + (21*b^16*c*d*e^6)/128 + (21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2))/128 - 23940*a^2*b^8*c^7*d^5*e^2 + 9450*a^2*b^9*c^6*d^4*e^3 + (4515*a^2*b^10*c^5*d^3*e^4)/4 - (8505*a^2*b^11*c^4*d^2*e^5)/8 + 87360*a^3*b^6*c^8*d^5*e^2 - 16800*a^3*b^7*c^7*d^4*e^3 - 20125*a^3*b^8*c^6*d^3*e^4 + (13335*a^3*b^9*c^5*d^2*e^5)/2 - 141120*a^4*b^4*c^9*d^5*e^2 - 50400*a^4*b^5*c^8*d^4*e^3 + 97300*a^4*b^6*c^7*d^3*e^4 - 14910*a^4*b^7*c^6*d^2*e^5 + 32256*a^5*b^2*c^10*d^5*e^2 + 241920*a^5*b^3*c^9*d^4*e^3 - 193200*a^5*b^4*c^8*d^3*e^4 - 16632*a^5*b^5*c^7*d^2*e^5 + 96320*a^6*b^2*c^9*d^3*e^4 + 124320*a^6*b^3*c^8*d^2*e^5 - 2520*a*b^9*c^7*d^6*e - (315*a*b^14*c^2*d*e^6)/64 - 129024*a^5*b*c^11*d^6*e + 3150*a*b^10*c^6*d^5*e^2 - 1575*a*b^11*c^5*d^4*e^3 + (2695*a*b^12*c^4*d^3*e^4)/16 + (1995*a*b^13*c^3*d^2*e^5)/32 + 20160*a^2*b^7*c^8*d^6*e + (105*a^2*b^12*c^3*d*e^6)/16 - 80640*a^3*b^5*c^9*d^6*e + (2625*a^3*b^10*c^4*d*e^6)/4 + 161280*a^4*b^3*c^10*d^6*e - 6615*a^4*b^8*c^5*d*e^6 + 27132*a^5*b^6*c^6*d*e^6 - 268800*a^6*b*c^10*d^4*e^3 - 48720*a^6*b^4*c^7*d*e^6 - 147840*a^7*b*c^9*d^2*e^5 + 20160*a^7*b^2*c^8*d*e^6)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)^3))^(1/2))*(-((b^17*e^7)/128 + 36864*a^5*c^12*d^7 - 36*b^10*c^7*d^7 + (b^2*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + 720*a*b^8*c^8*d^7 - 13440*a^8*b*c^8*e^7 + 26880*a^8*c^9*d*e^6 + 126*b^11*c^6*d^6*e - 5760*a^2*b^6*c^9*d^7 + 23040*a^3*b^4*c^10*d^7 - 46080*a^4*b^2*c^11*d^7 + (285*a^2*b^13*c^2*e^7)/32 - (635*a^3*b^11*c^3*e^7)/8 + (545*a^4*b^9*c^4*e^7)/2 + 342*a^5*b^7*c^5*e^7 - 5320*a^6*b^5*c^6*e^7 + 14560*a^7*b^3*c^7*e^7 + 107520*a^6*c^11*d^5*e^2 + 98560*a^7*c^10*d^3*e^4 - (651*b^12*c^5*d^5*e^2)/4 + (735*b^13*c^4*d^4*e^3)/8 - (1225*b^14*c^3*d^3*e^4)/64 - (21*b^15*c^2*d^2*e^5)/128 - (21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (55*a*b^15*c*e^7)/128 - (25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + (21*b^16*c*d*e^6)/128 + (21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2))/128 - 23940*a^2*b^8*c^7*d^5*e^2 + 9450*a^2*b^9*c^6*d^4*e^3 + (4515*a^2*b^10*c^5*d^3*e^4)/4 - (8505*a^2*b^11*c^4*d^2*e^5)/8 + 87360*a^3*b^6*c^8*d^5*e^2 - 16800*a^3*b^7*c^7*d^4*e^3 - 20125*a^3*b^8*c^6*d^3*e^4 + (13335*a^3*b^9*c^5*d^2*e^5)/2 - 141120*a^4*b^4*c^9*d^5*e^2 - 50400*a^4*b^5*c^8*d^4*e^3 + 97300*a^4*b^6*c^7*d^3*e^4 - 14910*a^4*b^7*c^6*d^2*e^5 + 32256*a^5*b^2*c^10*d^5*e^2 + 241920*a^5*b^3*c^9*d^4*e^3 - 193200*a^5*b^4*c^8*d^3*e^4 - 16632*a^5*b^5*c^7*d^2*e^5 + 96320*a^6*b^2*c^9*d^3*e^4 + 124320*a^6*b^3*c^8*d^2*e^5 - 2520*a*b^9*c^7*d^6*e - (315*a*b^14*c^2*d*e^6)/64 - 129024*a^5*b*c^11*d^6*e + 3150*a*b^10*c^6*d^5*e^2 - 1575*a*b^11*c^5*d^4*e^3 + (2695*a*b^12*c^4*d^3*e^4)/16 + (1995*a*b^13*c^3*d^2*e^5)/32 + 20160*a^2*b^7*c^8*d^6*e + (105*a^2*b^12*c^3*d*e^6)/16 - 80640*a^3*b^5*c^9*d^6*e + (2625*a^3*b^10*c^4*d*e^6)/4 + 161280*a^4*b^3*c^10*d^6*e - 6615*a^4*b^8*c^5*d*e^6 + 27132*a^5*b^6*c^6*d*e^6 - 268800*a^6*b*c^10*d^4*e^3 - 48720*a^6*b^4*c^7*d*e^6 - 147840*a^7*b*c^9*d^2*e^5 + 20160*a^7*b^2*c^8*d*e^6)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)^3))^(1/2) - (c^3*e^2*(d + e*x)^(1/2)*(b^6*e^6 + 4608*c^6*d^6 - 800*a^3*c^3*e^6 + 8832*a*c^5*d^4*e^2 + 1472*a^2*b^2*c^2*e^6 + 3488*a^2*c^4*d^2*e^4 + 15072*b^2*c^4*d^4*e^2 - 7104*b^3*c^3*d^3*e^3 + 1226*b^4*c^2*d^2*e^4 - 34*a*b^4*c*e^6 - 13824*b*c^5*d^5*e + 22*b^5*c*d*e^5 - 17664*a*b*c^4*d^3*e^3 - 2672*a*b^3*c^2*d*e^5 - 3488*a^2*b*c^3*d*e^5 + 11504*a*b^2*c^3*d^2*e^4))/(8*(4*a*c - b^2)^4*(a*e^2 + c*d^2 - b*d*e)^2))*(-((b^17*e^7)/128 + 36864*a^5*c^12*d^7 - 36*b^10*c^7*d^7 + (b^2*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + 720*a*b^8*c^8*d^7 - 13440*a^8*b*c^8*e^7 + 26880*a^8*c^9*d*e^6 + 126*b^11*c^6*d^6*e - 5760*a^2*b^6*c^9*d^7 + 23040*a^3*b^4*c^10*d^7 - 46080*a^4*b^2*c^11*d^7 + (285*a^2*b^13*c^2*e^7)/32 - (635*a^3*b^11*c^3*e^7)/8 + (545*a^4*b^9*c^4*e^7)/2 + 342*a^5*b^7*c^5*e^7 - 5320*a^6*b^5*c^6*e^7 + 14560*a^7*b^3*c^7*e^7 + 107520*a^6*c^11*d^5*e^2 + 98560*a^7*c^10*d^3*e^4 - (651*b^12*c^5*d^5*e^2)/4 + (735*b^13*c^4*d^4*e^3)/8 - (1225*b^14*c^3*d^3*e^4)/64 - (21*b^15*c^2*d^2*e^5)/128 - (21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (55*a*b^15*c*e^7)/128 - (25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + (21*b^16*c*d*e^6)/128 + (21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2))/128 - 23940*a^2*b^8*c^7*d^5*e^2 + 9450*a^2*b^9*c^6*d^4*e^3 + (4515*a^2*b^10*c^5*d^3*e^4)/4 - (8505*a^2*b^11*c^4*d^2*e^5)/8 + 87360*a^3*b^6*c^8*d^5*e^2 - 16800*a^3*b^7*c^7*d^4*e^3 - 20125*a^3*b^8*c^6*d^3*e^4 + (13335*a^3*b^9*c^5*d^2*e^5)/2 - 141120*a^4*b^4*c^9*d^5*e^2 - 50400*a^4*b^5*c^8*d^4*e^3 + 97300*a^4*b^6*c^7*d^3*e^4 - 14910*a^4*b^7*c^6*d^2*e^5 + 32256*a^5*b^2*c^10*d^5*e^2 + 241920*a^5*b^3*c^9*d^4*e^3 - 193200*a^5*b^4*c^8*d^3*e^4 - 16632*a^5*b^5*c^7*d^2*e^5 + 96320*a^6*b^2*c^9*d^3*e^4 + 124320*a^6*b^3*c^8*d^2*e^5 - 2520*a*b^9*c^7*d^6*e - (315*a*b^14*c^2*d*e^6)/64 - 129024*a^5*b*c^11*d^6*e + 3150*a*b^10*c^6*d^5*e^2 - 1575*a*b^11*c^5*d^4*e^3 + (2695*a*b^12*c^4*d^3*e^4)/16 + (1995*a*b^13*c^3*d^2*e^5)/32 + 20160*a^2*b^7*c^8*d^6*e + (105*a^2*b^12*c^3*d*e^6)/16 - 80640*a^3*b^5*c^9*d^6*e + (2625*a^3*b^10*c^4*d*e^6)/4 + 161280*a^4*b^3*c^10*d^6*e - 6615*a^4*b^8*c^5*d*e^6 + 27132*a^5*b^6*c^6*d*e^6 - 268800*a^6*b*c^10*d^4*e^3 - 48720*a^6*b^4*c^7*d*e^6 - 147840*a^7*b*c^9*d^2*e^5 + 20160*a^7*b^2*c^8*d*e^6)/((4*a*c - b^2)^10*(a*e^2 + c*d^2 - b*d*e)^3))^(1/2) - (c^4*e^3*(55296*c^6*d^6 - 35*b^6*e^6 + 8000*a^3*c^3*e^6 + 124416*a*c^5*d^4*e^2 + 12720*a^2*b^2*c^2*e^6 + 74880*a^2*c^4*d^2*e^4 + 176256*b^2*c^4*d^4*e^2 - 76032*b^3*c^3*d^3*e^3 + 9864*b^4*c^2*d^2*e^4 - 84*a*b^4*c*e^6 - 165888*b*c^5*d^5*e + 504*b^5*c*d*e^5 - 248832*a*b*c^4*d^3*e^3 - 24768*a*b^3*c^2*d*e^5 - 74880*a^2*b*c^3*d*e^5 + 149184*a*b^2*c^3*d^2*e^4))/(64*(4*a*c - b^2)^6*(a*e^2 + c*d^2 - b*d*e)^2))*(-((b^17*e^7)/128 + 36864*a^5*c^12*d^7 - 36*b^10*c^7*d^7 + (b^2*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + 720*a*b^8*c^8*d^7 - 13440*a^8*b*c^8*e^7 + 26880*a^8*c^9*d*e^6 + 126*b^11*c^6*d^6*e - 5760*a^2*b^6*c^9*d^7 + 23040*a^3*b^4*c^10*d^7 - 46080*a^4*b^2*c^11*d^7 + (285*a^2*b^13*c^2*e^7)/32 - (635*a^3*b^11*c^3*e^7)/8 + (545*a^4*b^9*c^4*e^7)/2 + 342*a^5*b^7*c^5*e^7 - 5320*a^6*b^5*c^6*e^7 + 14560*a^7*b^3*c^7*e^7 + 107520*a^6*c^11*d^5*e^2 + 98560*a^7*c^10*d^3*e^4 - (651*b^12*c^5*d^5*e^2)/4 + (735*b^13*c^4*d^4*e^3)/8 - (1225*b^14*c^3*d^3*e^4)/64 - (21*b^15*c^2*d^2*e^5)/128 - (21*c^2*d^2*e^5*(-(4*a*c - b^2)^15)^(1/2))/128 - (55*a*b^15*c*e^7)/128 - (25*a*c*e^7*(-(4*a*c - b^2)^15)^(1/2))/128 + (21*b^16*c*d*e^6)/128 + (21*b*c*d*e^6*(-(4*a*c - b^2)^15)^(1/2))/128 - 23940*a^2*b^8*c^7*d^5*e^2 + 9450*a^2*b^9*c^6*d^4*e^3 + (4515*a^2*b^10*c^5*d^3*e^4)/4 - (8505*a^2*b^11*c^4*d^2*e^5)/8 + 87360*a^3*b^6*c^8*d^5*e^2 - 16800*a^3*b^7*c^7*d^4*e^3 - 20125*a^3*b^8*c^6*d^3*e^4 + (13335*a^3*b^9*c^5*d^2*e^5)/2 - 141120*a^4*b^4*c^9*d^5*e^2 - 50400*a^4*b^5*c^8*d^4*e^3 + 97300*a^4*b^6*c^7*d^3*e^4 - 14910*a^4*b^7*c^6*d^2*e^5 + 32256*a^5*b^2*c^10*d^5*e^2 + 241920*a^5*b^3*c^9*d^4*e^3 - 193200*a^5*b^4*c^8*d^3*e^4 - 16632*a^5*b^5*c^7*d^2*e^5 + 96320*a^6*b^2*c^9*d^3*e^4 + 124320*a^6*b^3*c^8*d^2*e^5 - 2520*a*b^9*c^7*d^6*e - (315*a*b^14*c^2*d*e^6)/64 - 129024*a^5*b*c^11*d^6*e + 3150*a*b^10*c^6*d^5*e^2 - 1575*a*b^11*c^5*d^4*e^3 + (2695*a*b^12*c^4*d^3*e^4)/16 + (1995*a*b^13*c^3*d^2*e^5)/32 + 20160*a^2*b^7*c^8*d^6*e + (105*a^2*b^12*c^3*d*e^6)/16 - 80640*a^3*b^5*c^9*d^6*e + (2625*a^3*b^10*c^4*d*e^6)/4 + 161280*a^4*b^3*c^10*d^6*e - 6615*a^4*b^8*c^5*d*e^6 + 27132*a^5*b^6*c^6*d*e^6 - 268800*a^6*b*c^10*d^4*e^3 - 48720*a^6*b^4*c^7*d*e^6 - 147840*a^7*b*c^9*d^2*e^5 + 20160*a^7*b^2*c^8*d*e^6)/(a^3*b^20*e^6 + 1048576*a^10*c^13*d^6 + 1048576*a^13*c^10*e^6 + b^20*c^3*d^6 - b^23*d^3*e^3 - 40*a*b^18*c^4*d^6 - 40*a^4*b^18*c*e^6 + 3*a*b^22*d^2*e^4 - 3*a^2*b^21*d*e^5 - 3*b^21*c^2*d^5*e + 3*b^22*c*d^4*e^2 + 720*a^2*b^16*c^5*d^6 - 7680*a^3*b^14*c^6*d^6 + 53760*a^4*b^12*c^7*d^6 - 258048*a^5*b^10*c^8*d^6 + 860160*a^6*b^8*c^9*d^6 - 1966080*a^7*b^6*c^10*d^6 + 2949120*a^8*b^4*c^11*d^6 - 2621440*a^9*b^2*c^12*d^6 + 720*a^5*b^16*c^2*e^6 - 7680*a^6*b^14*c^3*e^6 + 53760*a^7*b^12*c^4*e^6 - 258048*a^8*b^10*c^5*e^6 + 860160*a^9*b^8*c^6*e^6 - 1966080*a^10*b^6*c^7*e^6 + 2949120*a^11*b^4*c^8*e^6 - 2621440*a^12*b^2*c^9*e^6 + 3145728*a^11*c^12*d^4*e^2 + 3145728*a^12*c^11*d^2*e^4 + 2040*a^2*b^18*c^3*d^4*e^2 - 480*a^2*b^19*c^2*d^3*e^3 - 20880*a^3*b^16*c^4*d^4*e^2 + 3360*a^3*b^17*c^3*d^3*e^3 + 2040*a^3*b^18*c^2*d^2*e^4 + 138240*a^4*b^14*c^5*d^4*e^2 - 7680*a^4*b^15*c^4*d^3*e^3 - 20880*a^4*b^16*c^3*d^2*e^4 - 612864*a^5*b^12*c^6*d^4*e^2 - 64512*a^5*b^13*c^5*d^3*e^3 + 138240*a^5*b^14*c^4*d^2*e^4 + 1806336*a^6*b^10*c^7*d^4*e^2 + 688128*a^6*b^11*c^6*d^3*e^3 - 612864*a^6*b^12*c^5*d^2*e^4 - 3317760*a^7*b^8*c^8*d^4*e^2 - 3194880*a^7*b^9*c^7*d^3*e^3 + 1806336*a^7*b^10*c^6*d^2*e^4 + 2949120*a^8*b^6*c^9*d^4*e^2 + 8847360*a^8*b^7*c^8*d^3*e^3 - 3317760*a^8*b^8*c^7*d^2*e^4 + 983040*a^9*b^4*c^10*d^4*e^2 - 15073280*a^9*b^5*c^9*d^3*e^3 + 2949120*a^9*b^6*c^8*d^2*e^4 - 4718592*a^10*b^2*c^11*d^4*e^2 + 14680064*a^10*b^3*c^10*d^3*e^3 + 983040*a^10*b^4*c^9*d^2*e^4 - 4718592*a^11*b^2*c^10*d^2*e^4 + 120*a*b^19*c^3*d^5*e + 34*a*b^21*c*d^3*e^3 + 120*a^3*b^19*c*d*e^5 - 3145728*a^10*b*c^12*d^5*e - 3145728*a^12*b*c^10*d*e^5 - 117*a*b^20*c^2*d^4*e^2 - 2160*a^2*b^17*c^4*d^5*e - 117*a^2*b^20*c*d^2*e^4 + 23040*a^3*b^15*c^5*d^5*e - 161280*a^4*b^13*c^6*d^5*e - 2160*a^4*b^17*c^2*d*e^5 + 774144*a^5*b^11*c^7*d^5*e + 23040*a^5*b^15*c^3*d*e^5 - 2580480*a^6*b^9*c^8*d^5*e - 161280*a^6*b^13*c^4*d*e^5 + 5898240*a^7*b^7*c^9*d^5*e + 774144*a^7*b^11*c^5*d*e^5 - 8847360*a^8*b^5*c^10*d^5*e - 2580480*a^8*b^9*c^6*d*e^5 + 7864320*a^9*b^3*c^11*d^5*e + 5898240*a^9*b^7*c^7*d*e^5 - 8847360*a^10*b^5*c^8*d*e^5 - 6291456*a^11*b*c^11*d^3*e^3 + 7864320*a^11*b^3*c^9*d*e^5))^(1/2) + (((d + e*x)^(3/2)*(b^4*e^5 + 72*c^4*d^4*e + 36*a^2*c^2*e^5 + 92*a*c^3*d^2*e^3 - 144*b*c^3*d^3*e^2 + 85*b^2*c^2*d^2*e^3 + 5*a*b^2*c*e^5 - 13*b^3*c*d*e^4 - 92*a*b*c^2*d*e^4))/(4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)*(a*e^2 + c*d^2 - b*d*e)) - ((d + e*x)^(1/2)*(b^3*e^4 + 24*c^3*d^3*e - 36*b*c^2*d^2*e^2 - 16*a*b*c*e^4 + 32*a*c^2*d*e^3 + 10*b^2*c*d*e^3))/(4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + ((b*e - 2*c*d)*(d + e*x)^(5/2)*(14*a*c^2*e^3 + b^2*c*e^3 + 18*c^3*d^2*e - 18*b*c^2*d*e^2))/(2*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)*(a*e^2 + c*d^2 - b*d*e)) + (c*e*(d + e*x)^(7/2)*(24*c^3*d^2 + 20*a*c^2*e^2 + b^2*c*e^2 - 24*b*c^2*d*e))/(4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)*(a*e^2 + c*d^2 - b*d*e)))/(c^2*(d + e*x)^4 - (d + e*x)*(4*c^2*d^3 + 2*b^2*d*e^2 - 2*a*b*e^3 + 4*a*c*d*e^2 - 6*b*c*d^2*e) - (4*c^2*d - 2*b*c*e)*(d + e*x)^3 + (d + e*x)^2*(b^2*e^2 + 6*c^2*d^2 + 2*a*c*e^2 - 6*b*c*d*e) + a^2*e^4 + c^2*d^4 + b^2*d^2*e^2 - 2*a*b*d*e^3 - 2*b*c*d^3*e + 2*a*c*d^2*e^2)","B"
2306,1,132771,835,18.167922,"\text{Not used}","int(1/((d + e*x)^(1/2)*(a + b*x + c*x^2)^3),x)","\frac{\frac{e\,{\left(d+e\,x\right)}^{5/2}\,\left(28\,a^2\,c^3\,e^4-49\,a\,b^2\,c^2\,e^4+140\,a\,b\,c^3\,d\,e^3-140\,a\,c^4\,d^2\,e^2+6\,b^4\,c\,e^4+b^3\,c^2\,d\,e^3-73\,b^2\,c^3\,d^2\,e^2+144\,b\,c^4\,d^3\,e-72\,c^5\,d^4\right)}{4\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}-\frac{\sqrt{d+e\,x}\,\left(-44\,a^2\,c^2\,e^5+37\,a\,b^2\,c\,e^5-60\,a\,b\,c^2\,d\,e^4+60\,a\,c^3\,d^2\,e^3-5\,b^4\,e^5+3\,b^3\,c\,d\,e^4+21\,b^2\,c^2\,d^2\,e^3-48\,b\,c^3\,d^3\,e^2+24\,c^4\,d^4\,e\right)}{4\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)\,\left(c\,d^2-b\,d\,e+a\,e^2\right)}+\frac{e\,{\left(d+e\,x\right)}^{3/2}\,\left(-4\,a^2\,b\,c^2\,e^5+8\,a^2\,c^3\,d\,e^4-20\,a\,b^3\,c\,e^5+128\,a\,b^2\,c^2\,d\,e^4-264\,a\,b\,c^3\,d^2\,e^3+176\,a\,c^4\,d^3\,e^2+3\,b^5\,e^5-10\,b^4\,c\,d\,e^4-24\,b^3\,c^2\,d^2\,e^3+136\,b^2\,c^3\,d^3\,e^2-180\,b\,c^4\,d^4\,e+72\,c^5\,d^5\right)}{4\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}+\frac{3\,c\,e\,{\left(d+e\,x\right)}^{7/2}\,\left(b^3\,c\,e^3+2\,b^2\,c^2\,d\,e^2-12\,b\,c^3\,d^2\,e-8\,a\,b\,c^2\,e^3+8\,c^4\,d^3+16\,a\,c^3\,d\,e^2\right)}{4\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)\,{\left(c\,d^2-b\,d\,e+a\,e^2\right)}^2}}{c^2\,{\left(d+e\,x\right)}^4-\left(d+e\,x\right)\,\left(2\,b^2\,d\,e^2-6\,b\,c\,d^2\,e-2\,a\,b\,e^3+4\,c^2\,d^3+4\,a\,c\,d\,e^2\right)-\left(4\,c^2\,d-2\,b\,c\,e\right)\,{\left(d+e\,x\right)}^3+{\left(d+e\,x\right)}^2\,\left(b^2\,e^2-6\,b\,c\,d\,e+6\,c^2\,d^2+2\,a\,c\,e^2\right)+a^2\,e^4+c^2\,d^4+b^2\,d^2\,e^2-2\,a\,b\,d\,e^3-2\,b\,c\,d^3\,e+2\,a\,c\,d^2\,e^2}+\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(1835008\,a^9\,c^9\,e^{11}-2883584\,a^8\,b^2\,c^8\,e^{11}-4980736\,a^8\,b\,c^9\,d\,e^{10}+4980736\,a^8\,c^{10}\,d^2\,e^9+1949696\,a^7\,b^4\,c^7\,e^{11}+7471104\,a^7\,b^3\,c^8\,d\,e^{10}-2490368\,a^7\,b^2\,c^9\,d^2\,e^9-9961472\,a^7\,b\,c^{10}\,d^3\,e^8+4980736\,a^7\,c^{11}\,d^4\,e^7-737280\,a^6\,b^6\,c^6\,e^{11}-4800512\,a^6\,b^5\,c^7\,d\,e^{10}-2146304\,a^6\,b^4\,c^8\,d^2\,e^9+11534336\,a^6\,b^3\,c^9\,d^3\,e^8+131072\,a^6\,b^2\,c^{10}\,d^4\,e^7-7077888\,a^6\,b\,c^{11}\,d^5\,e^6+2359296\,a^6\,c^{12}\,d^6\,e^5+168960\,a^5\,b^8\,c^5\,e^{11}+1720320\,a^5\,b^7\,c^6\,d\,e^{10}+2359296\,a^5\,b^6\,c^7\,d^2\,e^9-5144576\,a^5\,b^5\,c^8\,d^3\,e^8-4440064\,a^5\,b^4\,c^9\,d^4\,e^7+6946816\,a^5\,b^3\,c^{10}\,d^5\,e^6+131072\,a^5\,b^2\,c^{11}\,d^6\,e^5-2097152\,a^5\,b\,c^{12}\,d^7\,e^4+524288\,a^5\,c^{13}\,d^8\,e^3-23552\,a^4\,b^{10}\,c^4\,e^{11}-373760\,a^4\,b^9\,c^5\,d\,e^{10}-936960\,a^4\,b^8\,c^6\,d^2\,e^9+1064960\,a^4\,b^7\,c^7\,d^3\,e^8+2703360\,a^4\,b^6\,c^8\,d^4\,e^7-2048000\,a^4\,b^5\,c^9\,d^5\,e^6-2375680\,a^4\,b^4\,c^{10}\,d^6\,e^5+2621440\,a^4\,b^3\,c^{11}\,d^7\,e^4-655360\,a^4\,b^2\,c^{12}\,d^8\,e^3+1856\,a^3\,b^{12}\,c^3\,e^{11}+49664\,a^3\,b^{11}\,c^4\,d\,e^{10}+201216\,a^3\,b^{10}\,c^5\,d^2\,e^9-92160\,a^3\,b^9\,c^6\,d^3\,e^8-650240\,a^3\,b^8\,c^7\,d^4\,e^7-81920\,a^3\,b^7\,c^8\,d^5\,e^6+1556480\,a^3\,b^6\,c^9\,d^6\,e^5-1310720\,a^3\,b^5\,c^{10}\,d^7\,e^4+327680\,a^3\,b^4\,c^{11}\,d^8\,e^3-64\,a^2\,b^{14}\,c^2\,e^{11}-3776\,a^2\,b^{13}\,c^3\,d\,e^{10}-25408\,a^2\,b^{12}\,c^4\,d^2\,e^9+2048\,a^2\,b^{11}\,c^5\,d^3\,e^8+57856\,a^2\,b^{10}\,c^6\,d^4\,e^7+158720\,a^2\,b^9\,c^7\,d^5\,e^6-435200\,a^2\,b^8\,c^8\,d^6\,e^5+327680\,a^2\,b^7\,c^9\,d^7\,e^4-81920\,a^2\,b^6\,c^{10}\,d^8\,e^3+128\,a\,b^{15}\,c^2\,d\,e^{10}+1856\,a\,b^{14}\,c^3\,d^2\,e^9-384\,a\,b^{13}\,c^4\,d^3\,e^8+1472\,a\,b^{12}\,c^5\,d^4\,e^7-30208\,a\,b^{11}\,c^6\,d^5\,e^6+57856\,a\,b^{10}\,c^7\,d^6\,e^5-40960\,a\,b^9\,c^8\,d^7\,e^4+10240\,a\,b^8\,c^9\,d^8\,e^3-64\,b^{16}\,c^2\,d^2\,e^9+64\,b^{15}\,c^3\,d^3\,e^8-384\,b^{14}\,c^4\,d^4\,e^7+1856\,b^{13}\,c^5\,d^5\,e^6-3008\,b^{12}\,c^6\,d^6\,e^5+2048\,b^{11}\,c^7\,d^7\,e^4-512\,b^{10}\,c^8\,d^8\,e^3\right)}{64\,\left(4096\,a^{10}\,c^6\,e^8-6144\,a^9\,b^2\,c^5\,e^8-16384\,a^9\,b\,c^6\,d\,e^7+16384\,a^9\,c^7\,d^2\,e^6+3840\,a^8\,b^4\,c^4\,e^8+24576\,a^8\,b^3\,c^5\,d\,e^7-49152\,a^8\,b\,c^7\,d^3\,e^5+24576\,a^8\,c^8\,d^4\,e^4-1280\,a^7\,b^6\,c^3\,e^8-15360\,a^7\,b^5\,c^4\,d\,e^7-21504\,a^7\,b^4\,c^5\,d^2\,e^6+57344\,a^7\,b^3\,c^6\,d^3\,e^5+12288\,a^7\,b^2\,c^7\,d^4\,e^4-49152\,a^7\,b\,c^8\,d^5\,e^3+16384\,a^7\,c^9\,d^6\,e^2+240\,a^6\,b^8\,c^2\,e^8+5120\,a^6\,b^7\,c^3\,d\,e^7+17920\,a^6\,b^6\,c^4\,d^2\,e^6-21504\,a^6\,b^5\,c^5\,d^3\,e^5-46592\,a^6\,b^4\,c^6\,d^4\,e^4+57344\,a^6\,b^3\,c^7\,d^5\,e^3-16384\,a^6\,b\,c^9\,d^7\,e+4096\,a^6\,c^{10}\,d^8-24\,a^5\,b^{10}\,c\,e^8-960\,a^5\,b^9\,c^2\,d\,e^7-6720\,a^5\,b^8\,c^3\,d^2\,e^6+32256\,a^5\,b^6\,c^5\,d^4\,e^4-21504\,a^5\,b^5\,c^6\,d^5\,e^3-21504\,a^5\,b^4\,c^7\,d^6\,e^2+24576\,a^5\,b^3\,c^8\,d^7\,e-6144\,a^5\,b^2\,c^9\,d^8+a^4\,b^{12}\,e^8+96\,a^4\,b^{11}\,c\,d\,e^7+1344\,a^4\,b^{10}\,c^2\,d^2\,e^6+2240\,a^4\,b^9\,c^3\,d^3\,e^5-10080\,a^4\,b^8\,c^4\,d^4\,e^4+17920\,a^4\,b^6\,c^6\,d^6\,e^2-15360\,a^4\,b^5\,c^7\,d^7\,e+3840\,a^4\,b^4\,c^8\,d^8-4\,a^3\,b^{13}\,d\,e^7-140\,a^3\,b^{12}\,c\,d^2\,e^6-672\,a^3\,b^{11}\,c^2\,d^3\,e^5+1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\,c^6\,d^5\,e^4-3780\,a\,b^{13}\,c^5\,d^4\,e^5-1260\,a\,b^{14}\,c^4\,d^3\,e^6+486\,a\,b^{15}\,c^3\,d^2\,e^7-368640\,a^2\,b^7\,c^{10}\,d^8\,e-2790\,a^2\,b^{14}\,c^3\,d\,e^8+1474560\,a^3\,b^5\,c^{11}\,d^8\,e+29640\,a^3\,b^{12}\,c^4\,d\,e^8-2949120\,a^4\,b^3\,c^{12}\,d^8\,e-188640\,a^4\,b^{10}\,c^5\,d\,e^8+715392\,a^5\,b^8\,c^6\,d\,e^8+9633792\,a^6\,b\,c^{12}\,d^6\,e^3-1430016\,a^6\,b^6\,c^7\,d\,e^8+15482880\,a^7\,b\,c^{11}\,d^4\,e^5+645120\,a^7\,b^4\,c^8\,d\,e^8+10321920\,a^8\,b\,c^{10}\,d^2\,e^7+2580480\,a^8\,b^2\,c^9\,d\,e^8+54\,a\,c^3\,d^2\,e^7\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-42\,b\,c^3\,d^3\,e^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-54\,a\,b\,c^2\,d\,e^8\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{15}\,c^{10}\,e^{10}-2621440\,a^{14}\,b^2\,c^9\,e^{10}-5242880\,a^{14}\,b\,c^{10}\,d\,e^9+5242880\,a^{14}\,c^{11}\,d^2\,e^8+2949120\,a^{13}\,b^4\,c^8\,e^{10}+13107200\,a^{13}\,b^3\,c^9\,d\,e^9-2621440\,a^{13}\,b^2\,c^{10}\,d^2\,e^8-20971520\,a^{13}\,b\,c^{11}\,d^3\,e^7+10485760\,a^{13}\,c^{12}\,d^4\,e^6-1966080\,a^{12}\,b^6\,c^7\,e^{10}-14745600\,a^{12}\,b^5\,c^8\,d\,e^9-11468800\,a^{12}\,b^4\,c^9\,d^2\,e^8+41943040\,a^{12}\,b^3\,c^{10}\,d^3\,e^7+5242880\,a^{12}\,b^2\,c^{11}\,d^4\,e^6-31457280\,a^{12}\,b\,c^{12}\,d^5\,e^5+10485760\,a^{12}\,c^{13}\,d^6\,e^4+860160\,a^{11}\,b^8\,c^6\,e^{10}+9830400\,a^{11}\,b^7\,c^7\,d\,e^9+19660800\,a^{11}\,b^6\,c^8\,d^2\,e^8-32768000\,a^{11}\,b^5\,c^9\,d^3\,e^7-43909120\,a^{11}\,b^4\,c^{10}\,d^4\,e^6+57671680\,a^{11}\,b^3\,c^{11}\,d^5\,e^5+5242880\,a^{11}\,b^2\,c^{12}\,d^6\,e^4-20971520\,a^{11}\,b\,c^{13}\,d^7\,e^3+5242880\,a^{11}\,c^{14}\,d^8\,e^2-258048\,a^{10}\,b^{10}\,c^5\,e^{10}-4300800\,a^{10}\,b^9\,c^6\,d\,e^9-15360000\,a^{10}\,b^8\,c^7\,d^2\,e^8+9830400\,a^{10}\,b^7\,c^8\,d^3\,e^7+55705600\,a^{10}\,b^6\,c^9\,d^4\,e^6-37093376\,a^{10}\,b^5\,c^{10}\,d^5\,e^5-43909120\,a^{10}\,b^4\,c^{11}\,d^6\,e^4+41943040\,a^{10}\,b^3\,c^{12}\,d^7\,e^3-2621440\,a^{10}\,b^2\,c^{13}\,d^8\,e^2-5242880\,a^{10}\,b\,c^{14}\,d^9\,e+1048576\,a^{10}\,c^{15}\,d^{10}+53760\,a^9\,b^{12}\,c^4\,e^{10}+1290240\,a^9\,b^{11}\,c^5\,d\,e^9+7311360\,a^9\,b^{10}\,c^6\,d^2\,e^8+2457600\,a^9\,b^9\,c^7\,d^3\,e^7-35635200\,a^9\,b^8\,c^8\,d^4\,e^6+2621440\,a^9\,b^7\,c^9\,d^5\,e^5+55705600\,a^9\,b^6\,c^{10}\,d^6\,e^4-32768000\,a^9\,b^5\,c^{11}\,d^7\,e^3-11468800\,a^9\,b^4\,c^{12}\,d^8\,e^2+13107200\,a^9\,b^3\,c^{13}\,d^9\,e-2621440\,a^9\,b^2\,c^{14}\,d^{10}-7680\,a^8\,b^{14}\,c^3\,e^{10}-268800\,a^8\,b^{13}\,c^4\,d\,e^9-2311680\,a^8\,b^{12}\,c^5\,d^2\,e^8-3440640\,a^8\,b^{11}\,c^6\,d^3\,e^7+13393920\,a^8\,b^{10}\,c^7\,d^4\,e^6+10567680\,a^8\,b^9\,c^8\,d^5\,e^5-35635200\,a^8\,b^8\,c^9\,d^6\,e^4+9830400\,a^8\,b^7\,c^{10}\,d^7\,e^3+19660800\,a^8\,b^6\,c^{11}\,d^8\,e^2-14745600\,a^8\,b^5\,c^{12}\,d^9\,e+2949120\,a^8\,b^4\,c^{13}\,d^{10}+720\,a^7\,b^{16}\,c^2\,e^{10}+38400\,a^7\,b^{15}\,c^3\,d\,e^9+499200\,a^7\,b^{14}\,c^4\,d^2\,e^8+1505280\,a^7\,b^{13}\,c^5\,d^3\,e^7-2903040\,a^7\,b^{12}\,c^6\,d^4\,e^6-7495680\,a^7\,b^{11}\,c^7\,d^5\,e^5+13393920\,a^7\,b^{10}\,c^8\,d^6\,e^4+2457600\,a^7\,b^9\,c^9\,d^7\,e^3-15360000\,a^7\,b^8\,c^{10}\,d^8\,e^2+9830400\,a^7\,b^7\,c^{11}\,d^9\,e-1966080\,a^7\,b^6\,c^{12}\,d^{10}-40\,a^6\,b^{18}\,c\,e^{10}-3600\,a^6\,b^{17}\,c^2\,d\,e^9-73200\,a^6\,b^{16}\,c^3\,d^2\,e^8-384000\,a^6\,b^{15}\,c^4\,d^3\,e^7+245760\,a^6\,b^{14}\,c^5\,d^4\,e^6+2688000\,a^6\,b^{13}\,c^6\,d^5\,e^5-2903040\,a^6\,b^{12}\,c^7\,d^6\,e^4-3440640\,a^6\,b^{11}\,c^8\,d^7\,e^3+7311360\,a^6\,b^{10}\,c^9\,d^8\,e^2-4300800\,a^6\,b^9\,c^{10}\,d^9\,e+860160\,a^6\,b^8\,c^{11}\,d^{10}+a^5\,b^{20}\,e^{10}+200\,a^5\,b^{19}\,c\,d\,e^9+7000\,a^5\,b^{18}\,c^2\,d^2\,e^8+62400\,a^5\,b^{17}\,c^3\,d^3\,e^7+45600\,a^5\,b^{16}\,c^4\,d^4\,e^6-586752\,a^5\,b^{15}\,c^5\,d^5\,e^5+245760\,a^5\,b^{14}\,c^6\,d^6\,e^4+1505280\,a^5\,b^{13}\,c^7\,d^7\,e^3-2311680\,a^5\,b^{12}\,c^8\,d^8\,e^2+1290240\,a^5\,b^{11}\,c^9\,d^9\,e-258048\,a^5\,b^{10}\,c^{10}\,d^{10}-5\,a^4\,b^{21}\,d\,e^9-395\,a^4\,b^{20}\,c\,d^2\,e^8-6400\,a^4\,b^{19}\,c^2\,d^3\,e^7-17200\,a^4\,b^{18}\,c^3\,d^4\,e^6+78240\,a^4\,b^{17}\,c^4\,d^5\,e^5+45600\,a^4\,b^{16}\,c^5\,d^6\,e^4-384000\,a^4\,b^{15}\,c^6\,d^7\,e^3+499200\,a^4\,b^{14}\,c^7\,d^8\,e^2-268800\,a^4\,b^{13}\,c^8\,d^9\,e+53760\,a^4\,b^{12}\,c^9\,d^{10}+10\,a^3\,b^{22}\,d^2\,e^8+380\,a^3\,b^{21}\,c\,d^3\,e^7+2410\,a^3\,b^{20}\,c^2\,d^4\,e^6-5520\,a^3\,b^{19}\,c^3\,d^5\,e^5-17200\,a^3\,b^{18}\,c^4\,d^6\,e^4+62400\,a^3\,b^{17}\,c^5\,d^7\,e^3-73200\,a^3\,b^{16}\,c^6\,d^8\,e^2+38400\,a^3\,b^{15}\,c^7\,d^9\,e-7680\,a^3\,b^{14}\,c^8\,d^{10}-10\,a^2\,b^{23}\,d^3\,e^7-170\,a^2\,b^{22}\,c\,d^4\,e^6+50\,a^2\,b^{21}\,c^2\,d^5\,e^5+2410\,a^2\,b^{20}\,c^3\,d^6\,e^4-6400\,a^2\,b^{19}\,c^4\,d^7\,e^3+7000\,a^2\,b^{18}\,c^5\,d^8\,e^2-3600\,a^2\,b^{17}\,c^6\,d^9\,e+720\,a^2\,b^{16}\,c^7\,d^{10}+5\,a\,b^{24}\,d^4\,e^6+20\,a\,b^{23}\,c\,d^5\,e^5-170\,a\,b^{22}\,c^2\,d^6\,e^4+380\,a\,b^{21}\,c^3\,d^7\,e^3-395\,a\,b^{20}\,c^4\,d^8\,e^2+200\,a\,b^{19}\,c^5\,d^9\,e-40\,a\,b^{18}\,c^6\,d^{10}-b^{25}\,d^5\,e^5+5\,b^{24}\,c\,d^6\,e^4-10\,b^{23}\,c^2\,d^7\,e^3+10\,b^{22}\,c^3\,d^8\,e^2-5\,b^{21}\,c^4\,d^9\,e+b^{20}\,c^5\,d^{10}\right)}}\,2{}\mathrm{i}","Not used",1,"((e*(d + e*x)^(5/2)*(6*b^4*c*e^4 - 72*c^5*d^4 + 28*a^2*c^3*e^4 - 49*a*b^2*c^2*e^4 - 140*a*c^4*d^2*e^2 + b^3*c^2*d*e^3 - 73*b^2*c^3*d^2*e^2 + 144*b*c^4*d^3*e + 140*a*b*c^3*d*e^3))/(4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)*(a*e^2 + c*d^2 - b*d*e)^2) - ((d + e*x)^(1/2)*(24*c^4*d^4*e - 5*b^4*e^5 - 44*a^2*c^2*e^5 + 60*a*c^3*d^2*e^3 - 48*b*c^3*d^3*e^2 + 21*b^2*c^2*d^2*e^3 + 37*a*b^2*c*e^5 + 3*b^3*c*d*e^4 - 60*a*b*c^2*d*e^4))/(4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)*(a*e^2 + c*d^2 - b*d*e)) + (e*(d + e*x)^(3/2)*(3*b^5*e^5 + 72*c^5*d^5 - 4*a^2*b*c^2*e^5 + 176*a*c^4*d^3*e^2 + 8*a^2*c^3*d*e^4 + 136*b^2*c^3*d^3*e^2 - 24*b^3*c^2*d^2*e^3 - 20*a*b^3*c*e^5 - 180*b*c^4*d^4*e - 10*b^4*c*d*e^4 - 264*a*b*c^3*d^2*e^3 + 128*a*b^2*c^2*d*e^4))/(4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)*(a*e^2 + c*d^2 - b*d*e)^2) + (3*c*e*(d + e*x)^(7/2)*(8*c^4*d^3 + b^3*c*e^3 + 2*b^2*c^2*d*e^2 - 8*a*b*c^2*e^3 + 16*a*c^3*d*e^2 - 12*b*c^3*d^2*e))/(4*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)*(a*e^2 + c*d^2 - b*d*e)^2))/(c^2*(d + e*x)^4 - (d + e*x)*(4*c^2*d^3 + 2*b^2*d*e^2 - 2*a*b*e^3 + 4*a*c*d*e^2 - 6*b*c*d^2*e) - (4*c^2*d - 2*b*c*e)*(d + e*x)^3 + (d + e*x)^2*(b^2*e^2 + 6*c^2*d^2 + 2*a*c*e^2 - 6*b*c*d*e) + a^2*e^4 + c^2*d^4 + b^2*d^2*e^2 - 2*a*b*d*e^3 - 2*b*c*d^3*e + 2*a*c*d^2*e^2) + atan(((((3*(1835008*a^9*c^9*e^11 - 64*a^2*b^14*c^2*e^11 + 1856*a^3*b^12*c^3*e^11 - 23552*a^4*b^10*c^4*e^11 + 168960*a^5*b^8*c^5*e^11 - 737280*a^6*b^6*c^6*e^11 + 1949696*a^7*b^4*c^7*e^11 - 2883584*a^8*b^2*c^8*e^11 + 524288*a^5*c^13*d^8*e^3 + 2359296*a^6*c^12*d^6*e^5 + 4980736*a^7*c^11*d^4*e^7 + 4980736*a^8*c^10*d^2*e^9 - 512*b^10*c^8*d^8*e^3 + 2048*b^11*c^7*d^7*e^4 - 3008*b^12*c^6*d^6*e^5 + 1856*b^13*c^5*d^5*e^6 - 384*b^14*c^4*d^4*e^7 + 64*b^15*c^3*d^3*e^8 - 64*b^16*c^2*d^2*e^9 - 81920*a^2*b^6*c^10*d^8*e^3 + 327680*a^2*b^7*c^9*d^7*e^4 - 435200*a^2*b^8*c^8*d^6*e^5 + 158720*a^2*b^9*c^7*d^5*e^6 + 57856*a^2*b^10*c^6*d^4*e^7 + 2048*a^2*b^11*c^5*d^3*e^8 - 25408*a^2*b^12*c^4*d^2*e^9 + 327680*a^3*b^4*c^11*d^8*e^3 - 1310720*a^3*b^5*c^10*d^7*e^4 + 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16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 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245760*a^5*b^14*c^6*d^6*e^4 - 586752*a^5*b^15*c^5*d^5*e^5 + 45600*a^5*b^16*c^4*d^4*e^6 + 62400*a^5*b^17*c^3*d^3*e^7 + 7000*a^5*b^18*c^2*d^2*e^8 + 7311360*a^6*b^10*c^9*d^8*e^2 - 3440640*a^6*b^11*c^8*d^7*e^3 - 2903040*a^6*b^12*c^7*d^6*e^4 + 2688000*a^6*b^13*c^6*d^5*e^5 + 245760*a^6*b^14*c^5*d^4*e^6 - 384000*a^6*b^15*c^4*d^3*e^7 - 73200*a^6*b^16*c^3*d^2*e^8 - 15360000*a^7*b^8*c^10*d^8*e^2 + 2457600*a^7*b^9*c^9*d^7*e^3 + 13393920*a^7*b^10*c^8*d^6*e^4 - 7495680*a^7*b^11*c^7*d^5*e^5 - 2903040*a^7*b^12*c^6*d^4*e^6 + 1505280*a^7*b^13*c^5*d^3*e^7 + 499200*a^7*b^14*c^4*d^2*e^8 + 19660800*a^8*b^6*c^11*d^8*e^2 + 9830400*a^8*b^7*c^10*d^7*e^3 - 35635200*a^8*b^8*c^9*d^6*e^4 + 10567680*a^8*b^9*c^8*d^5*e^5 + 13393920*a^8*b^10*c^7*d^4*e^6 - 3440640*a^8*b^11*c^6*d^3*e^7 - 2311680*a^8*b^12*c^5*d^2*e^8 - 11468800*a^9*b^4*c^12*d^8*e^2 - 32768000*a^9*b^5*c^11*d^7*e^3 + 55705600*a^9*b^6*c^10*d^6*e^4 + 2621440*a^9*b^7*c^9*d^5*e^5 - 35635200*a^9*b^8*c^8*d^4*e^6 + 2457600*a^9*b^9*c^7*d^3*e^7 + 7311360*a^9*b^10*c^6*d^2*e^8 - 2621440*a^10*b^2*c^13*d^8*e^2 + 41943040*a^10*b^3*c^12*d^7*e^3 - 43909120*a^10*b^4*c^11*d^6*e^4 - 37093376*a^10*b^5*c^10*d^5*e^5 + 55705600*a^10*b^6*c^9*d^4*e^6 + 9830400*a^10*b^7*c^8*d^3*e^7 - 15360000*a^10*b^8*c^7*d^2*e^8 + 5242880*a^11*b^2*c^12*d^6*e^4 + 57671680*a^11*b^3*c^11*d^5*e^5 - 43909120*a^11*b^4*c^10*d^4*e^6 - 32768000*a^11*b^5*c^9*d^3*e^7 + 19660800*a^11*b^6*c^8*d^2*e^8 + 5242880*a^12*b^2*c^11*d^4*e^6 + 41943040*a^12*b^3*c^10*d^3*e^7 - 11468800*a^12*b^4*c^9*d^2*e^8 - 2621440*a^13*b^2*c^10*d^2*e^8 + 200*a*b^19*c^5*d^9*e + 20*a*b^23*c*d^5*e^5 + 200*a^5*b^19*c*d*e^9 - 5242880*a^10*b*c^14*d^9*e - 5242880*a^14*b*c^10*d*e^9 - 395*a*b^20*c^4*d^8*e^2 + 380*a*b^21*c^3*d^7*e^3 - 170*a*b^22*c^2*d^6*e^4 - 3600*a^2*b^17*c^6*d^9*e - 170*a^2*b^22*c*d^4*e^6 + 38400*a^3*b^15*c^7*d^9*e + 380*a^3*b^21*c*d^3*e^7 - 268800*a^4*b^13*c^8*d^9*e - 395*a^4*b^20*c*d^2*e^8 + 1290240*a^5*b^11*c^9*d^9*e - 4300800*a^6*b^9*c^10*d^9*e - 3600*a^6*b^17*c^2*d*e^9 + 9830400*a^7*b^7*c^11*d^9*e + 38400*a^7*b^15*c^3*d*e^9 - 14745600*a^8*b^5*c^12*d^9*e - 268800*a^8*b^13*c^4*d*e^9 + 13107200*a^9*b^3*c^13*d^9*e + 1290240*a^9*b^11*c^5*d*e^9 - 4300800*a^10*b^9*c^6*d*e^9 - 20971520*a^11*b*c^13*d^7*e^3 + 9830400*a^11*b^7*c^7*d*e^9 - 31457280*a^12*b*c^12*d^5*e^5 - 14745600*a^12*b^5*c^8*d*e^9 - 20971520*a^13*b*c^11*d^3*e^7 + 13107200*a^13*b^3*c^9*d*e^9)))^(1/2) - ((d + e*x)^(1/2)*(14112*a^4*c^7*e^10 + 9*b^8*c^3*e^10 + 4608*c^11*d^8*e^2 - 180*a*b^6*c^4*e^10 + 19584*a*c^10*d^6*e^4 - 18432*b*c^10*d^7*e^3 + 36*b^7*c^4*d*e^9 + 1530*a^2*b^4*c^5*e^10 - 6192*a^3*b^2*c^6*e^10 + 34848*a^2*c^9*d^4*e^6 + 31680*a^3*c^8*d^2*e^8 + 27360*b^2*c^9*d^6*e^4 - 17568*b^3*c^8*d^5*e^5 + 3978*b^4*c^7*d^4*e^6 - 180*b^5*c^6*d^3*e^7 + 198*b^6*c^5*d^2*e^8 + 28512*a^2*b^2*c^7*d^2*e^8 - 58752*a*b*c^9*d^5*e^5 - 900*a*b^5*c^5*d*e^9 - 31680*a^3*b*c^7*d*e^9 + 56016*a*b^2*c^8*d^4*e^6 - 14112*a*b^3*c^7*d^3*e^7 - 1836*a*b^4*c^6*d^2*e^8 - 69696*a^2*b*c^8*d^3*e^7 + 6336*a^2*b^3*c^6*d*e^9))/(8*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)))*(-(9*(b^19*e^9 + 524288*a^5*c^14*d^9 - 512*b^10*c^9*d^9 + b^4*e^9*(-(4*a*c - b^2)^15)^(1/2) + 10240*a*b^8*c^10*d^9 - 1720320*a^9*b*c^9*e^9 + 3440640*a^9*c^10*d*e^8 + 2304*b^11*c^8*d^8*e - 81920*a^2*b^6*c^11*d^9 + 327680*a^3*b^4*c^12*d^9 - 655360*a^4*b^2*c^13*d^9 + 769*a^2*b^15*c^2*e^9 - 8620*a^3*b^13*c^3*e^9 + 63440*a^4*b^11*c^4*e^9 - 316864*a^5*b^9*c^5*e^9 + 1069824*a^6*b^7*c^6*e^9 - 2343936*a^7*b^5*c^7*e^9 + 3010560*a^8*b^3*c^8*e^9 + 49*a^2*c^2*e^9*(-(4*a*c - b^2)^15)^(1/2) + 2752512*a^6*c^13*d^7*e^2 + 6193152*a^7*c^12*d^5*e^4 + 6881280*a^8*c^11*d^3*e^6 - 3936*b^12*c^7*d^7*e^2 + 3024*b^13*c^6*d^6*e^3 - 882*b^14*c^5*d^5*e^4 + 21*b^15*c^4*d^4*e^5 - 42*b^16*c^3*d^3*e^6 + 18*b^17*c^2*d^2*e^7 + 21*c^4*d^4*e^5*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c*e^9 + 3*b^18*c*d*e^8 - 576000*a^2*b^8*c^9*d^7*e^2 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245760*a^7*b^4*c^6*d*e^10 - 786432*a^8*b*c^8*d^2*e^9 + 98304*a^8*b^2*c^7*d*e^10))/(8*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 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b^2)^15)^(1/2) - 41*a*b^17*c*e^9 + 3*b^18*c*d*e^8 - 576000*a^2*b^8*c^9*d^7*e^2 + 295680*a^2*b^9*c^8*d^6*e^3 + 74592*a^2*b^10*c^7*d^5*e^4 - 65520*a^2*b^11*c^6*d^4*e^5 - 25200*a^2*b^12*c^5*d^3*e^6 + 5400*a^2*b^13*c^4*d^2*e^7 + 2088960*a^3*b^6*c^10*d^7*e^2 - 430080*a^3*b^7*c^9*d^6*e^3 - 1088640*a^3*b^8*c^8*d^5*e^4 + 356160*a^3*b^9*c^7*d^4*e^5 + 288960*a^3*b^10*c^6*d^3*e^6 - 21600*a^3*b^11*c^5*d^2*e^7 - 3317760*a^4*b^4*c^11*d^7*e^2 - 2150400*a^4*b^5*c^10*d^6*e^3 + 4999680*a^4*b^6*c^9*d^5*e^4 - 241920*a^4*b^7*c^8*d^4*e^5 - 1800960*a^4*b^8*c^7*d^3*e^6 - 97920*a^4*b^9*c^6*d^2*e^7 + 589824*a^5*b^2*c^12*d^7*e^2 + 8945664*a^5*b^3*c^11*d^6*e^3 - 9418752*a^5*b^4*c^10*d^5*e^4 - 4322304*a^5*b^5*c^9*d^4*e^5 + 5956608*a^5*b^6*c^8*d^3*e^6 + 1433088*a^5*b^7*c^7*d^2*e^7 + 3612672*a^6*b^2*c^11*d^5*e^4 + 15052800*a^6*b^3*c^10*d^4*e^5 - 9031680*a^6*b^4*c^9*d^3*e^6 - 6322176*a^6*b^5*c^8*d^2*e^7 + 1720320*a^7*b^2*c^10*d^3*e^6 + 12902400*a^7*b^3*c^9*d^2*e^7 + 18*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^15)^(1/2) - 11*a*b^2*c*e^9*(-(4*a*c - b^2)^15)^(1/2) - 46080*a*b^9*c^9*d^8*e - 144*a*b^16*c^2*d*e^8 - 2359296*a^5*b*c^13*d^8*e + 3*b^3*c*d*e^8*(-(4*a*c - b^2)^15)^(1/2) + 76032*a*b^10*c^8*d^7*e^2 - 51072*a*b^11*c^7*d^6*e^3 + 6552*a*b^12*c^6*d^5*e^4 + 3780*a*b^13*c^5*d^4*e^5 + 1260*a*b^14*c^4*d^3*e^6 - 486*a*b^15*c^3*d^2*e^7 + 368640*a^2*b^7*c^10*d^8*e + 2790*a^2*b^14*c^3*d*e^8 - 1474560*a^3*b^5*c^11*d^8*e - 29640*a^3*b^12*c^4*d*e^8 + 2949120*a^4*b^3*c^12*d^8*e + 188640*a^4*b^10*c^5*d*e^8 - 715392*a^5*b^8*c^6*d*e^8 - 9633792*a^6*b*c^12*d^6*e^3 + 1430016*a^6*b^6*c^7*d*e^8 - 15482880*a^7*b*c^11*d^4*e^5 - 645120*a^7*b^4*c^8*d*e^8 - 10321920*a^8*b*c^10*d^2*e^7 - 2580480*a^8*b^2*c^9*d*e^8 + 54*a*c^3*d^2*e^7*(-(4*a*c - b^2)^15)^(1/2) - 42*b*c^3*d^3*e^6*(-(4*a*c - b^2)^15)^(1/2) - 54*a*b*c^2*d*e^8*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^5*b^20*e^10 + 1048576*a^10*c^15*d^10 + 1048576*a^15*c^10*e^10 + b^20*c^5*d^10 - b^25*d^5*e^5 - 40*a*b^18*c^6*d^10 - 40*a^6*b^18*c*e^10 + 5*a*b^24*d^4*e^6 - 5*a^4*b^21*d*e^9 - 5*b^21*c^4*d^9*e + 5*b^24*c*d^6*e^4 + 720*a^2*b^16*c^7*d^10 - 7680*a^3*b^14*c^8*d^10 + 53760*a^4*b^12*c^9*d^10 - 258048*a^5*b^10*c^10*d^10 + 860160*a^6*b^8*c^11*d^10 - 1966080*a^7*b^6*c^12*d^10 + 2949120*a^8*b^4*c^13*d^10 - 2621440*a^9*b^2*c^14*d^10 + 720*a^7*b^16*c^2*e^10 - 7680*a^8*b^14*c^3*e^10 + 53760*a^9*b^12*c^4*e^10 - 258048*a^10*b^10*c^5*e^10 + 860160*a^11*b^8*c^6*e^10 - 1966080*a^12*b^6*c^7*e^10 + 2949120*a^13*b^4*c^8*e^10 - 2621440*a^14*b^2*c^9*e^10 - 10*a^2*b^23*d^3*e^7 + 10*a^3*b^22*d^2*e^8 + 5242880*a^11*c^14*d^8*e^2 + 10485760*a^12*c^13*d^6*e^4 + 10485760*a^13*c^12*d^4*e^6 + 5242880*a^14*c^11*d^2*e^8 + 10*b^22*c^3*d^8*e^2 - 10*b^23*c^2*d^7*e^3 + 7000*a^2*b^18*c^5*d^8*e^2 - 6400*a^2*b^19*c^4*d^7*e^3 + 2410*a^2*b^20*c^3*d^6*e^4 + 50*a^2*b^21*c^2*d^5*e^5 - 73200*a^3*b^16*c^6*d^8*e^2 + 62400*a^3*b^17*c^5*d^7*e^3 - 17200*a^3*b^18*c^4*d^6*e^4 - 5520*a^3*b^19*c^3*d^5*e^5 + 2410*a^3*b^20*c^2*d^4*e^6 + 499200*a^4*b^14*c^7*d^8*e^2 - 384000*a^4*b^15*c^6*d^7*e^3 + 45600*a^4*b^16*c^5*d^6*e^4 + 78240*a^4*b^17*c^4*d^5*e^5 - 17200*a^4*b^18*c^3*d^4*e^6 - 6400*a^4*b^19*c^2*d^3*e^7 - 2311680*a^5*b^12*c^8*d^8*e^2 + 1505280*a^5*b^13*c^7*d^7*e^3 + 245760*a^5*b^14*c^6*d^6*e^4 - 586752*a^5*b^15*c^5*d^5*e^5 + 45600*a^5*b^16*c^4*d^4*e^6 + 62400*a^5*b^17*c^3*d^3*e^7 + 7000*a^5*b^18*c^2*d^2*e^8 + 7311360*a^6*b^10*c^9*d^8*e^2 - 3440640*a^6*b^11*c^8*d^7*e^3 - 2903040*a^6*b^12*c^7*d^6*e^4 + 2688000*a^6*b^13*c^6*d^5*e^5 + 245760*a^6*b^14*c^5*d^4*e^6 - 384000*a^6*b^15*c^4*d^3*e^7 - 73200*a^6*b^16*c^3*d^2*e^8 - 15360000*a^7*b^8*c^10*d^8*e^2 + 2457600*a^7*b^9*c^9*d^7*e^3 + 13393920*a^7*b^10*c^8*d^6*e^4 - 7495680*a^7*b^11*c^7*d^5*e^5 - 2903040*a^7*b^12*c^6*d^4*e^6 + 1505280*a^7*b^13*c^5*d^3*e^7 + 499200*a^7*b^14*c^4*d^2*e^8 + 19660800*a^8*b^6*c^11*d^8*e^2 + 9830400*a^8*b^7*c^10*d^7*e^3 - 35635200*a^8*b^8*c^9*d^6*e^4 + 10567680*a^8*b^9*c^8*d^5*e^5 + 13393920*a^8*b^10*c^7*d^4*e^6 - 3440640*a^8*b^11*c^6*d^3*e^7 - 2311680*a^8*b^12*c^5*d^2*e^8 - 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38400*a^3*b^15*c^7*d^9*e + 380*a^3*b^21*c*d^3*e^7 - 268800*a^4*b^13*c^8*d^9*e - 395*a^4*b^20*c*d^2*e^8 + 1290240*a^5*b^11*c^9*d^9*e - 4300800*a^6*b^9*c^10*d^9*e - 3600*a^6*b^17*c^2*d*e^9 + 9830400*a^7*b^7*c^11*d^9*e + 38400*a^7*b^15*c^3*d*e^9 - 14745600*a^8*b^5*c^12*d^9*e - 268800*a^8*b^13*c^4*d*e^9 + 13107200*a^9*b^3*c^13*d^9*e + 1290240*a^9*b^11*c^5*d*e^9 - 4300800*a^10*b^9*c^6*d*e^9 - 20971520*a^11*b*c^13*d^7*e^3 + 9830400*a^11*b^7*c^7*d*e^9 - 31457280*a^12*b*c^12*d^5*e^5 - 14745600*a^12*b^5*c^8*d*e^9 - 20971520*a^13*b*c^11*d^3*e^7 + 13107200*a^13*b^3*c^9*d*e^9)))^(1/2) + ((d + e*x)^(1/2)*(14112*a^4*c^7*e^10 + 9*b^8*c^3*e^10 + 4608*c^11*d^8*e^2 - 180*a*b^6*c^4*e^10 + 19584*a*c^10*d^6*e^4 - 18432*b*c^10*d^7*e^3 + 36*b^7*c^4*d*e^9 + 1530*a^2*b^4*c^5*e^10 - 6192*a^3*b^2*c^6*e^10 + 34848*a^2*c^9*d^4*e^6 + 31680*a^3*c^8*d^2*e^8 + 27360*b^2*c^9*d^6*e^4 - 17568*b^3*c^8*d^5*e^5 + 3978*b^4*c^7*d^4*e^6 - 180*b^5*c^6*d^3*e^7 + 198*b^6*c^5*d^2*e^8 + 28512*a^2*b^2*c^7*d^2*e^8 - 58752*a*b*c^9*d^5*e^5 - 900*a*b^5*c^5*d*e^9 - 31680*a^3*b*c^7*d*e^9 + 56016*a*b^2*c^8*d^4*e^6 - 14112*a*b^3*c^7*d^3*e^7 - 1836*a*b^4*c^6*d^2*e^8 - 69696*a^2*b*c^8*d^3*e^7 + 6336*a^2*b^3*c^6*d*e^9))/(8*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)))*(-(9*(b^19*e^9 + 524288*a^5*c^14*d^9 - 512*b^10*c^9*d^9 + b^4*e^9*(-(4*a*c - b^2)^15)^(1/2) + 10240*a*b^8*c^10*d^9 - 1720320*a^9*b*c^9*e^9 + 3440640*a^9*c^10*d*e^8 + 2304*b^11*c^8*d^8*e - 81920*a^2*b^6*c^11*d^9 + 327680*a^3*b^4*c^12*d^9 - 655360*a^4*b^2*c^13*d^9 + 769*a^2*b^15*c^2*e^9 - 8620*a^3*b^13*c^3*e^9 + 63440*a^4*b^11*c^4*e^9 - 316864*a^5*b^9*c^5*e^9 + 1069824*a^6*b^7*c^6*e^9 - 2343936*a^7*b^5*c^7*e^9 + 3010560*a^8*b^3*c^8*e^9 + 49*a^2*c^2*e^9*(-(4*a*c - b^2)^15)^(1/2) + 2752512*a^6*c^13*d^7*e^2 + 6193152*a^7*c^12*d^5*e^4 + 6881280*a^8*c^11*d^3*e^6 - 3936*b^12*c^7*d^7*e^2 + 3024*b^13*c^6*d^6*e^3 - 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3840*a^8*b^4*c^4*e^8 - 6144*a^9*b^2*c^5*e^8 + 6*a^2*b^14*d^2*e^6 + 16384*a^7*c^9*d^6*e^2 + 24576*a^8*c^8*d^4*e^4 + 16384*a^9*c^7*d^2*e^6 + 6*b^14*c^2*d^6*e^2 + 1344*a^2*b^10*c^4*d^6*e^2 - 672*a^2*b^11*c^3*d^5*e^3 - 42*a^2*b^12*c^2*d^4*e^4 - 6720*a^3*b^8*c^5*d^6*e^2 + 2240*a^3*b^9*c^4*d^5*e^3 + 1456*a^3*b^10*c^3*d^4*e^4 - 672*a^3*b^11*c^2*d^3*e^5 + 17920*a^4*b^6*c^6*d^6*e^2 - 10080*a^4*b^8*c^4*d^4*e^4 + 2240*a^4*b^9*c^3*d^3*e^5 + 1344*a^4*b^10*c^2*d^2*e^6 - 21504*a^5*b^4*c^7*d^6*e^2 - 21504*a^5*b^5*c^6*d^5*e^3 + 32256*a^5*b^6*c^5*d^4*e^4 - 6720*a^5*b^8*c^3*d^2*e^6 + 57344*a^6*b^3*c^7*d^5*e^3 - 46592*a^6*b^4*c^6*d^4*e^4 - 21504*a^6*b^5*c^5*d^3*e^5 + 17920*a^6*b^6*c^4*d^2*e^6 + 12288*a^7*b^2*c^7*d^4*e^4 + 57344*a^7*b^3*c^6*d^3*e^5 - 21504*a^7*b^4*c^5*d^2*e^6 + 96*a*b^11*c^4*d^7*e - 12*a*b^14*c*d^4*e^4 + 96*a^4*b^11*c*d*e^7 - 16384*a^6*b*c^9*d^7*e - 16384*a^9*b*c^6*d*e^7 - 140*a*b^12*c^3*d^6*e^2 + 84*a*b^13*c^2*d^5*e^3 - 960*a^2*b^9*c^5*d^7*e + 84*a^2*b^13*c*d^3*e^5 + 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11*a*b^2*c*e^9*(-(4*a*c - b^2)^15)^(1/2) - 46080*a*b^9*c^9*d^8*e - 144*a*b^16*c^2*d*e^8 - 2359296*a^5*b*c^13*d^8*e + 3*b^3*c*d*e^8*(-(4*a*c - b^2)^15)^(1/2) + 76032*a*b^10*c^8*d^7*e^2 - 51072*a*b^11*c^7*d^6*e^3 + 6552*a*b^12*c^6*d^5*e^4 + 3780*a*b^13*c^5*d^4*e^5 + 1260*a*b^14*c^4*d^3*e^6 - 486*a*b^15*c^3*d^2*e^7 + 368640*a^2*b^7*c^10*d^8*e + 2790*a^2*b^14*c^3*d*e^8 - 1474560*a^3*b^5*c^11*d^8*e - 29640*a^3*b^12*c^4*d*e^8 + 2949120*a^4*b^3*c^12*d^8*e + 188640*a^4*b^10*c^5*d*e^8 - 715392*a^5*b^8*c^6*d*e^8 - 9633792*a^6*b*c^12*d^6*e^3 + 1430016*a^6*b^6*c^7*d*e^8 - 15482880*a^7*b*c^11*d^4*e^5 - 645120*a^7*b^4*c^8*d*e^8 - 10321920*a^8*b*c^10*d^2*e^7 - 2580480*a^8*b^2*c^9*d*e^8 + 54*a*c^3*d^2*e^7*(-(4*a*c - b^2)^15)^(1/2) - 42*b*c^3*d^3*e^6*(-(4*a*c - b^2)^15)^(1/2) - 54*a*b*c^2*d*e^8*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^5*b^20*e^10 + 1048576*a^10*c^15*d^10 + 1048576*a^15*c^10*e^10 + b^20*c^5*d^10 - b^25*d^5*e^5 - 40*a*b^18*c^6*d^10 - 40*a^6*b^18*c*e^10 + 5*a*b^24*d^4*e^6 - 5*a^4*b^21*d*e^9 - 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20480*a^2*b^6*c^9*d^9*e^2 + 92160*a^2*b^7*c^8*d^8*e^3 - 153600*a^2*b^8*c^7*d^7*e^4 + 107520*a^2*b^9*c^6*d^6*e^5 - 16128*a^2*b^10*c^5*d^5*e^6 - 13440*a^2*b^11*c^4*d^4*e^7 + 3584*a^2*b^12*c^3*d^3*e^8 + 384*a^2*b^13*c^2*d^2*e^9 + 81920*a^3*b^4*c^10*d^9*e^2 - 368640*a^3*b^5*c^9*d^8*e^3 + 573440*a^3*b^6*c^8*d^7*e^4 - 286720*a^3*b^7*c^7*d^6*e^5 - 107520*a^3*b^8*c^6*d^5*e^6 + 125440*a^3*b^9*c^5*d^4*e^7 - 10752*a^3*b^10*c^4*d^3*e^8 - 6912*a^3*b^11*c^3*d^2*e^9 - 163840*a^4*b^2*c^11*d^9*e^2 + 737280*a^4*b^3*c^10*d^8*e^3 - 983040*a^4*b^4*c^9*d^7*e^4 + 860160*a^4*b^6*c^7*d^5*e^6 - 430080*a^4*b^7*c^6*d^4*e^7 - 71680*a^4*b^8*c^5*d^3*e^8 + 46080*a^4*b^9*c^4*d^2*e^9 + 393216*a^5*b^2*c^10*d^7*e^4 + 1376256*a^5*b^3*c^9*d^6*e^5 - 2064384*a^5*b^4*c^8*d^5*e^6 + 344064*a^5*b^5*c^7*d^4*e^7 + 573440*a^5*b^6*c^6*d^3*e^8 - 122880*a^5*b^7*c^5*d^2*e^9 + 1376256*a^6*b^2*c^9*d^5*e^6 + 1146880*a^6*b^3*c^8*d^4*e^7 - 1376256*a^6*b^4*c^7*d^3*e^8 + 917504*a^7*b^2*c^8*d^3*e^8 + 589824*a^7*b^3*c^7*d^2*e^9 + 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192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)))*(-(9*(b^19*e^9 + 524288*a^5*c^14*d^9 - 512*b^10*c^9*d^9 + b^4*e^9*(-(4*a*c - b^2)^15)^(1/2) + 10240*a*b^8*c^10*d^9 - 1720320*a^9*b*c^9*e^9 + 3440640*a^9*c^10*d*e^8 + 2304*b^11*c^8*d^8*e - 81920*a^2*b^6*c^11*d^9 + 327680*a^3*b^4*c^12*d^9 - 655360*a^4*b^2*c^13*d^9 + 769*a^2*b^15*c^2*e^9 - 8620*a^3*b^13*c^3*e^9 + 63440*a^4*b^11*c^4*e^9 - 316864*a^5*b^9*c^5*e^9 + 1069824*a^6*b^7*c^6*e^9 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7495680*a^7*b^11*c^7*d^5*e^5 - 2903040*a^7*b^12*c^6*d^4*e^6 + 1505280*a^7*b^13*c^5*d^3*e^7 + 499200*a^7*b^14*c^4*d^2*e^8 + 19660800*a^8*b^6*c^11*d^8*e^2 + 9830400*a^8*b^7*c^10*d^7*e^3 - 35635200*a^8*b^8*c^9*d^6*e^4 + 10567680*a^8*b^9*c^8*d^5*e^5 + 13393920*a^8*b^10*c^7*d^4*e^6 - 3440640*a^8*b^11*c^6*d^3*e^7 - 2311680*a^8*b^12*c^5*d^2*e^8 - 11468800*a^9*b^4*c^12*d^8*e^2 - 32768000*a^9*b^5*c^11*d^7*e^3 + 55705600*a^9*b^6*c^10*d^6*e^4 + 2621440*a^9*b^7*c^9*d^5*e^5 - 35635200*a^9*b^8*c^8*d^4*e^6 + 2457600*a^9*b^9*c^7*d^3*e^7 + 7311360*a^9*b^10*c^6*d^2*e^8 - 2621440*a^10*b^2*c^13*d^8*e^2 + 41943040*a^10*b^3*c^12*d^7*e^3 - 43909120*a^10*b^4*c^11*d^6*e^4 - 37093376*a^10*b^5*c^10*d^5*e^5 + 55705600*a^10*b^6*c^9*d^4*e^6 + 9830400*a^10*b^7*c^8*d^3*e^7 - 15360000*a^10*b^8*c^7*d^2*e^8 + 5242880*a^11*b^2*c^12*d^6*e^4 + 57671680*a^11*b^3*c^11*d^5*e^5 - 43909120*a^11*b^4*c^10*d^4*e^6 - 32768000*a^11*b^5*c^9*d^3*e^7 + 19660800*a^11*b^6*c^8*d^2*e^8 + 5242880*a^12*b^2*c^11*d^4*e^6 + 41943040*a^12*b^3*c^10*d^3*e^7 - 11468800*a^12*b^4*c^9*d^2*e^8 - 2621440*a^13*b^2*c^10*d^2*e^8 + 200*a*b^19*c^5*d^9*e + 20*a*b^23*c*d^5*e^5 + 200*a^5*b^19*c*d*e^9 - 5242880*a^10*b*c^14*d^9*e - 5242880*a^14*b*c^10*d*e^9 - 395*a*b^20*c^4*d^8*e^2 + 380*a*b^21*c^3*d^7*e^3 - 170*a*b^22*c^2*d^6*e^4 - 3600*a^2*b^17*c^6*d^9*e - 170*a^2*b^22*c*d^4*e^6 + 38400*a^3*b^15*c^7*d^9*e + 380*a^3*b^21*c*d^3*e^7 - 268800*a^4*b^13*c^8*d^9*e - 395*a^4*b^20*c*d^2*e^8 + 1290240*a^5*b^11*c^9*d^9*e - 4300800*a^6*b^9*c^10*d^9*e - 3600*a^6*b^17*c^2*d*e^9 + 9830400*a^7*b^7*c^11*d^9*e + 38400*a^7*b^15*c^3*d*e^9 - 14745600*a^8*b^5*c^12*d^9*e - 268800*a^8*b^13*c^4*d*e^9 + 13107200*a^9*b^3*c^13*d^9*e + 1290240*a^9*b^11*c^5*d*e^9 - 4300800*a^10*b^9*c^6*d*e^9 - 20971520*a^11*b*c^13*d^7*e^3 + 9830400*a^11*b^7*c^7*d*e^9 - 31457280*a^12*b*c^12*d^5*e^5 - 14745600*a^12*b^5*c^8*d*e^9 - 20971520*a^13*b*c^11*d^3*e^7 + 13107200*a^13*b^3*c^9*d*e^9)))^(1/2) - ((d + e*x)^(1/2)*(14112*a^4*c^7*e^10 + 9*b^8*c^3*e^10 + 4608*c^11*d^8*e^2 - 180*a*b^6*c^4*e^10 + 19584*a*c^10*d^6*e^4 - 18432*b*c^10*d^7*e^3 + 36*b^7*c^4*d*e^9 + 1530*a^2*b^4*c^5*e^10 - 6192*a^3*b^2*c^6*e^10 + 34848*a^2*c^9*d^4*e^6 + 31680*a^3*c^8*d^2*e^8 + 27360*b^2*c^9*d^6*e^4 - 17568*b^3*c^8*d^5*e^5 + 3978*b^4*c^7*d^4*e^6 - 180*b^5*c^6*d^3*e^7 + 198*b^6*c^5*d^2*e^8 + 28512*a^2*b^2*c^7*d^2*e^8 - 58752*a*b*c^9*d^5*e^5 - 900*a*b^5*c^5*d*e^9 - 31680*a^3*b*c^7*d*e^9 + 56016*a*b^2*c^8*d^4*e^6 - 14112*a*b^3*c^7*d^3*e^7 - 1836*a*b^4*c^6*d^2*e^8 - 69696*a^2*b*c^8*d^3*e^7 + 6336*a^2*b^3*c^6*d*e^9))/(8*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)))*(-(9*(b^19*e^9 + 524288*a^5*c^14*d^9 - 512*b^10*c^9*d^9 + b^4*e^9*(-(4*a*c - b^2)^15)^(1/2) + 10240*a*b^8*c^10*d^9 - 1720320*a^9*b*c^9*e^9 + 3440640*a^9*c^10*d*e^8 + 2304*b^11*c^8*d^8*e - 81920*a^2*b^6*c^11*d^9 + 327680*a^3*b^4*c^12*d^9 - 655360*a^4*b^2*c^13*d^9 + 769*a^2*b^15*c^2*e^9 - 8620*a^3*b^13*c^3*e^9 + 63440*a^4*b^11*c^4*e^9 - 316864*a^5*b^9*c^5*e^9 + 1069824*a^6*b^7*c^6*e^9 - 2343936*a^7*b^5*c^7*e^9 + 3010560*a^8*b^3*c^8*e^9 + 49*a^2*c^2*e^9*(-(4*a*c - b^2)^15)^(1/2) + 2752512*a^6*c^13*d^7*e^2 + 6193152*a^7*c^12*d^5*e^4 + 6881280*a^8*c^11*d^3*e^6 - 3936*b^12*c^7*d^7*e^2 + 3024*b^13*c^6*d^6*e^3 - 882*b^14*c^5*d^5*e^4 + 21*b^15*c^4*d^4*e^5 - 42*b^16*c^3*d^3*e^6 + 18*b^17*c^2*d^2*e^7 + 21*c^4*d^4*e^5*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c*e^9 + 3*b^18*c*d*e^8 - 576000*a^2*b^8*c^9*d^7*e^2 + 295680*a^2*b^9*c^8*d^6*e^3 + 74592*a^2*b^10*c^7*d^5*e^4 - 65520*a^2*b^11*c^6*d^4*e^5 - 25200*a^2*b^12*c^5*d^3*e^6 + 5400*a^2*b^13*c^4*d^2*e^7 + 2088960*a^3*b^6*c^10*d^7*e^2 - 430080*a^3*b^7*c^9*d^6*e^3 - 1088640*a^3*b^8*c^8*d^5*e^4 + 356160*a^3*b^9*c^7*d^4*e^5 + 288960*a^3*b^10*c^6*d^3*e^6 - 21600*a^3*b^11*c^5*d^2*e^7 - 3317760*a^4*b^4*c^11*d^7*e^2 - 2150400*a^4*b^5*c^10*d^6*e^3 + 4999680*a^4*b^6*c^9*d^5*e^4 - 241920*a^4*b^7*c^8*d^4*e^5 - 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96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)))*(-(9*(b^19*e^9 + 524288*a^5*c^14*d^9 - 512*b^10*c^9*d^9 + b^4*e^9*(-(4*a*c - b^2)^15)^(1/2) + 10240*a*b^8*c^10*d^9 - 1720320*a^9*b*c^9*e^9 + 3440640*a^9*c^10*d*e^8 + 2304*b^11*c^8*d^8*e - 81920*a^2*b^6*c^11*d^9 + 327680*a^3*b^4*c^12*d^9 - 655360*a^4*b^2*c^13*d^9 + 769*a^2*b^15*c^2*e^9 - 8620*a^3*b^13*c^3*e^9 + 63440*a^4*b^11*c^4*e^9 - 316864*a^5*b^9*c^5*e^9 + 1069824*a^6*b^7*c^6*e^9 - 2343936*a^7*b^5*c^7*e^9 + 3010560*a^8*b^3*c^8*e^9 + 49*a^2*c^2*e^9*(-(4*a*c - b^2)^15)^(1/2) + 2752512*a^6*c^13*d^7*e^2 + 6193152*a^7*c^12*d^5*e^4 + 6881280*a^8*c^11*d^3*e^6 - 3936*b^12*c^7*d^7*e^2 + 3024*b^13*c^6*d^6*e^3 - 882*b^14*c^5*d^5*e^4 + 21*b^15*c^4*d^4*e^5 - 42*b^16*c^3*d^3*e^6 + 18*b^17*c^2*d^2*e^7 + 21*c^4*d^4*e^5*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c*e^9 + 3*b^18*c*d*e^8 - 576000*a^2*b^8*c^9*d^7*e^2 + 295680*a^2*b^9*c^8*d^6*e^3 + 74592*a^2*b^10*c^7*d^5*e^4 - 65520*a^2*b^11*c^6*d^4*e^5 - 25200*a^2*b^12*c^5*d^3*e^6 + 5400*a^2*b^13*c^4*d^2*e^7 + 2088960*a^3*b^6*c^10*d^7*e^2 - 430080*a^3*b^7*c^9*d^6*e^3 - 1088640*a^3*b^8*c^8*d^5*e^4 + 356160*a^3*b^9*c^7*d^4*e^5 + 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2790*a^2*b^14*c^3*d*e^8 - 1474560*a^3*b^5*c^11*d^8*e - 29640*a^3*b^12*c^4*d*e^8 + 2949120*a^4*b^3*c^12*d^8*e + 188640*a^4*b^10*c^5*d*e^8 - 715392*a^5*b^8*c^6*d*e^8 - 9633792*a^6*b*c^12*d^6*e^3 + 1430016*a^6*b^6*c^7*d*e^8 - 15482880*a^7*b*c^11*d^4*e^5 - 645120*a^7*b^4*c^8*d*e^8 - 10321920*a^8*b*c^10*d^2*e^7 - 2580480*a^8*b^2*c^9*d*e^8 + 54*a*c^3*d^2*e^7*(-(4*a*c - b^2)^15)^(1/2) - 42*b*c^3*d^3*e^6*(-(4*a*c - b^2)^15)^(1/2) - 54*a*b*c^2*d*e^8*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^5*b^20*e^10 + 1048576*a^10*c^15*d^10 + 1048576*a^15*c^10*e^10 + b^20*c^5*d^10 - b^25*d^5*e^5 - 40*a*b^18*c^6*d^10 - 40*a^6*b^18*c*e^10 + 5*a*b^24*d^4*e^6 - 5*a^4*b^21*d*e^9 - 5*b^21*c^4*d^9*e + 5*b^24*c*d^6*e^4 + 720*a^2*b^16*c^7*d^10 - 7680*a^3*b^14*c^8*d^10 + 53760*a^4*b^12*c^9*d^10 - 258048*a^5*b^10*c^10*d^10 + 860160*a^6*b^8*c^11*d^10 - 1966080*a^7*b^6*c^12*d^10 + 2949120*a^8*b^4*c^13*d^10 - 2621440*a^9*b^2*c^14*d^10 + 720*a^7*b^16*c^2*e^10 - 7680*a^8*b^14*c^3*e^10 + 53760*a^9*b^12*c^4*e^10 - 258048*a^10*b^10*c^5*e^10 + 860160*a^11*b^8*c^6*e^10 - 1966080*a^12*b^6*c^7*e^10 + 2949120*a^13*b^4*c^8*e^10 - 2621440*a^14*b^2*c^9*e^10 - 10*a^2*b^23*d^3*e^7 + 10*a^3*b^22*d^2*e^8 + 5242880*a^11*c^14*d^8*e^2 + 10485760*a^12*c^13*d^6*e^4 + 10485760*a^13*c^12*d^4*e^6 + 5242880*a^14*c^11*d^2*e^8 + 10*b^22*c^3*d^8*e^2 - 10*b^23*c^2*d^7*e^3 + 7000*a^2*b^18*c^5*d^8*e^2 - 6400*a^2*b^19*c^4*d^7*e^3 + 2410*a^2*b^20*c^3*d^6*e^4 + 50*a^2*b^21*c^2*d^5*e^5 - 73200*a^3*b^16*c^6*d^8*e^2 + 62400*a^3*b^17*c^5*d^7*e^3 - 17200*a^3*b^18*c^4*d^6*e^4 - 5520*a^3*b^19*c^3*d^5*e^5 + 2410*a^3*b^20*c^2*d^4*e^6 + 499200*a^4*b^14*c^7*d^8*e^2 - 384000*a^4*b^15*c^6*d^7*e^3 + 45600*a^4*b^16*c^5*d^6*e^4 + 78240*a^4*b^17*c^4*d^5*e^5 - 17200*a^4*b^18*c^3*d^4*e^6 - 6400*a^4*b^19*c^2*d^3*e^7 - 2311680*a^5*b^12*c^8*d^8*e^2 + 1505280*a^5*b^13*c^7*d^7*e^3 + 245760*a^5*b^14*c^6*d^6*e^4 - 586752*a^5*b^15*c^5*d^5*e^5 + 45600*a^5*b^16*c^4*d^4*e^6 + 62400*a^5*b^17*c^3*d^3*e^7 + 7000*a^5*b^18*c^2*d^2*e^8 + 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55705600*a^10*b^6*c^9*d^4*e^6 + 9830400*a^10*b^7*c^8*d^3*e^7 - 15360000*a^10*b^8*c^7*d^2*e^8 + 5242880*a^11*b^2*c^12*d^6*e^4 + 57671680*a^11*b^3*c^11*d^5*e^5 - 43909120*a^11*b^4*c^10*d^4*e^6 - 32768000*a^11*b^5*c^9*d^3*e^7 + 19660800*a^11*b^6*c^8*d^2*e^8 + 5242880*a^12*b^2*c^11*d^4*e^6 + 41943040*a^12*b^3*c^10*d^3*e^7 - 11468800*a^12*b^4*c^9*d^2*e^8 - 2621440*a^13*b^2*c^10*d^2*e^8 + 200*a*b^19*c^5*d^9*e + 20*a*b^23*c*d^5*e^5 + 200*a^5*b^19*c*d*e^9 - 5242880*a^10*b*c^14*d^9*e - 5242880*a^14*b*c^10*d*e^9 - 395*a*b^20*c^4*d^8*e^2 + 380*a*b^21*c^3*d^7*e^3 - 170*a*b^22*c^2*d^6*e^4 - 3600*a^2*b^17*c^6*d^9*e - 170*a^2*b^22*c*d^4*e^6 + 38400*a^3*b^15*c^7*d^9*e + 380*a^3*b^21*c*d^3*e^7 - 268800*a^4*b^13*c^8*d^9*e - 395*a^4*b^20*c*d^2*e^8 + 1290240*a^5*b^11*c^9*d^9*e - 4300800*a^6*b^9*c^10*d^9*e - 3600*a^6*b^17*c^2*d*e^9 + 9830400*a^7*b^7*c^11*d^9*e + 38400*a^7*b^15*c^3*d*e^9 - 14745600*a^8*b^5*c^12*d^9*e - 268800*a^8*b^13*c^4*d*e^9 + 13107200*a^9*b^3*c^13*d^9*e + 1290240*a^9*b^11*c^5*d*e^9 - 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4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)))*(-(9*(b^19*e^9 + 524288*a^5*c^14*d^9 - 512*b^10*c^9*d^9 + b^4*e^9*(-(4*a*c - b^2)^15)^(1/2) + 10240*a*b^8*c^10*d^9 - 1720320*a^9*b*c^9*e^9 + 3440640*a^9*c^10*d*e^8 + 2304*b^11*c^8*d^8*e - 81920*a^2*b^6*c^11*d^9 + 327680*a^3*b^4*c^12*d^9 - 655360*a^4*b^2*c^13*d^9 + 769*a^2*b^15*c^2*e^9 - 8620*a^3*b^13*c^3*e^9 + 63440*a^4*b^11*c^4*e^9 - 316864*a^5*b^9*c^5*e^9 + 1069824*a^6*b^7*c^6*e^9 - 2343936*a^7*b^5*c^7*e^9 + 3010560*a^8*b^3*c^8*e^9 + 49*a^2*c^2*e^9*(-(4*a*c - b^2)^15)^(1/2) + 2752512*a^6*c^13*d^7*e^2 + 6193152*a^7*c^12*d^5*e^4 + 6881280*a^8*c^11*d^3*e^6 - 3936*b^12*c^7*d^7*e^2 + 3024*b^13*c^6*d^6*e^3 - 882*b^14*c^5*d^5*e^4 + 21*b^15*c^4*d^4*e^5 - 42*b^16*c^3*d^3*e^6 + 18*b^17*c^2*d^2*e^7 + 21*c^4*d^4*e^5*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c*e^9 + 3*b^18*c*d*e^8 - 576000*a^2*b^8*c^9*d^7*e^2 + 295680*a^2*b^9*c^8*d^6*e^3 + 74592*a^2*b^10*c^7*d^5*e^4 - 65520*a^2*b^11*c^6*d^4*e^5 - 25200*a^2*b^12*c^5*d^3*e^6 + 5400*a^2*b^13*c^4*d^2*e^7 + 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6552*a*b^12*c^6*d^5*e^4 + 3780*a*b^13*c^5*d^4*e^5 + 1260*a*b^14*c^4*d^3*e^6 - 486*a*b^15*c^3*d^2*e^7 + 368640*a^2*b^7*c^10*d^8*e + 2790*a^2*b^14*c^3*d*e^8 - 1474560*a^3*b^5*c^11*d^8*e - 29640*a^3*b^12*c^4*d*e^8 + 2949120*a^4*b^3*c^12*d^8*e + 188640*a^4*b^10*c^5*d*e^8 - 715392*a^5*b^8*c^6*d*e^8 - 9633792*a^6*b*c^12*d^6*e^3 + 1430016*a^6*b^6*c^7*d*e^8 - 15482880*a^7*b*c^11*d^4*e^5 - 645120*a^7*b^4*c^8*d*e^8 - 10321920*a^8*b*c^10*d^2*e^7 - 2580480*a^8*b^2*c^9*d*e^8 + 54*a*c^3*d^2*e^7*(-(4*a*c - b^2)^15)^(1/2) - 42*b*c^3*d^3*e^6*(-(4*a*c - b^2)^15)^(1/2) - 54*a*b*c^2*d*e^8*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^5*b^20*e^10 + 1048576*a^10*c^15*d^10 + 1048576*a^15*c^10*e^10 + b^20*c^5*d^10 - b^25*d^5*e^5 - 40*a*b^18*c^6*d^10 - 40*a^6*b^18*c*e^10 + 5*a*b^24*d^4*e^6 - 5*a^4*b^21*d*e^9 - 5*b^21*c^4*d^9*e + 5*b^24*c*d^6*e^4 + 720*a^2*b^16*c^7*d^10 - 7680*a^3*b^14*c^8*d^10 + 53760*a^4*b^12*c^9*d^10 - 258048*a^5*b^10*c^10*d^10 + 860160*a^6*b^8*c^11*d^10 - 1966080*a^7*b^6*c^12*d^10 + 2949120*a^8*b^4*c^13*d^10 - 2621440*a^9*b^2*c^14*d^10 + 720*a^7*b^16*c^2*e^10 - 7680*a^8*b^14*c^3*e^10 + 53760*a^9*b^12*c^4*e^10 - 258048*a^10*b^10*c^5*e^10 + 860160*a^11*b^8*c^6*e^10 - 1966080*a^12*b^6*c^7*e^10 + 2949120*a^13*b^4*c^8*e^10 - 2621440*a^14*b^2*c^9*e^10 - 10*a^2*b^23*d^3*e^7 + 10*a^3*b^22*d^2*e^8 + 5242880*a^11*c^14*d^8*e^2 + 10485760*a^12*c^13*d^6*e^4 + 10485760*a^13*c^12*d^4*e^6 + 5242880*a^14*c^11*d^2*e^8 + 10*b^22*c^3*d^8*e^2 - 10*b^23*c^2*d^7*e^3 + 7000*a^2*b^18*c^5*d^8*e^2 - 6400*a^2*b^19*c^4*d^7*e^3 + 2410*a^2*b^20*c^3*d^6*e^4 + 50*a^2*b^21*c^2*d^5*e^5 - 73200*a^3*b^16*c^6*d^8*e^2 + 62400*a^3*b^17*c^5*d^7*e^3 - 17200*a^3*b^18*c^4*d^6*e^4 - 5520*a^3*b^19*c^3*d^5*e^5 + 2410*a^3*b^20*c^2*d^4*e^6 + 499200*a^4*b^14*c^7*d^8*e^2 - 384000*a^4*b^15*c^6*d^7*e^3 + 45600*a^4*b^16*c^5*d^6*e^4 + 78240*a^4*b^17*c^4*d^5*e^5 - 17200*a^4*b^18*c^3*d^4*e^6 - 6400*a^4*b^19*c^2*d^3*e^7 - 2311680*a^5*b^12*c^8*d^8*e^2 + 1505280*a^5*b^13*c^7*d^7*e^3 + 245760*a^5*b^14*c^6*d^6*e^4 - 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2621440*a^10*b^2*c^13*d^8*e^2 + 41943040*a^10*b^3*c^12*d^7*e^3 - 43909120*a^10*b^4*c^11*d^6*e^4 - 37093376*a^10*b^5*c^10*d^5*e^5 + 55705600*a^10*b^6*c^9*d^4*e^6 + 9830400*a^10*b^7*c^8*d^3*e^7 - 15360000*a^10*b^8*c^7*d^2*e^8 + 5242880*a^11*b^2*c^12*d^6*e^4 + 57671680*a^11*b^3*c^11*d^5*e^5 - 43909120*a^11*b^4*c^10*d^4*e^6 - 32768000*a^11*b^5*c^9*d^3*e^7 + 19660800*a^11*b^6*c^8*d^2*e^8 + 5242880*a^12*b^2*c^11*d^4*e^6 + 41943040*a^12*b^3*c^10*d^3*e^7 - 11468800*a^12*b^4*c^9*d^2*e^8 - 2621440*a^13*b^2*c^10*d^2*e^8 + 200*a*b^19*c^5*d^9*e + 20*a*b^23*c*d^5*e^5 + 200*a^5*b^19*c*d*e^9 - 5242880*a^10*b*c^14*d^9*e - 5242880*a^14*b*c^10*d*e^9 - 395*a*b^20*c^4*d^8*e^2 + 380*a*b^21*c^3*d^7*e^3 - 170*a*b^22*c^2*d^6*e^4 - 3600*a^2*b^17*c^6*d^9*e - 170*a^2*b^22*c*d^4*e^6 + 38400*a^3*b^15*c^7*d^9*e + 380*a^3*b^21*c*d^3*e^7 - 268800*a^4*b^13*c^8*d^9*e - 395*a^4*b^20*c*d^2*e^8 + 1290240*a^5*b^11*c^9*d^9*e - 4300800*a^6*b^9*c^10*d^9*e - 3600*a^6*b^17*c^2*d*e^9 + 9830400*a^7*b^7*c^11*d^9*e + 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2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)))*((9*(512*b^10*c^9*d^9 - 524288*a^5*c^14*d^9 - b^19*e^9 + b^4*e^9*(-(4*a*c - b^2)^15)^(1/2) - 10240*a*b^8*c^10*d^9 + 1720320*a^9*b*c^9*e^9 - 3440640*a^9*c^10*d*e^8 - 2304*b^11*c^8*d^8*e + 81920*a^2*b^6*c^11*d^9 - 327680*a^3*b^4*c^12*d^9 + 655360*a^4*b^2*c^13*d^9 - 769*a^2*b^15*c^2*e^9 + 8620*a^3*b^13*c^3*e^9 - 63440*a^4*b^11*c^4*e^9 + 316864*a^5*b^9*c^5*e^9 - 1069824*a^6*b^7*c^6*e^9 + 2343936*a^7*b^5*c^7*e^9 - 3010560*a^8*b^3*c^8*e^9 + 49*a^2*c^2*e^9*(-(4*a*c - 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57671680*a^11*b^3*c^11*d^5*e^5 - 43909120*a^11*b^4*c^10*d^4*e^6 - 32768000*a^11*b^5*c^9*d^3*e^7 + 19660800*a^11*b^6*c^8*d^2*e^8 + 5242880*a^12*b^2*c^11*d^4*e^6 + 41943040*a^12*b^3*c^10*d^3*e^7 - 11468800*a^12*b^4*c^9*d^2*e^8 - 2621440*a^13*b^2*c^10*d^2*e^8 + 200*a*b^19*c^5*d^9*e + 20*a*b^23*c*d^5*e^5 + 200*a^5*b^19*c*d*e^9 - 5242880*a^10*b*c^14*d^9*e - 5242880*a^14*b*c^10*d*e^9 - 395*a*b^20*c^4*d^8*e^2 + 380*a*b^21*c^3*d^7*e^3 - 170*a*b^22*c^2*d^6*e^4 - 3600*a^2*b^17*c^6*d^9*e - 170*a^2*b^22*c*d^4*e^6 + 38400*a^3*b^15*c^7*d^9*e + 380*a^3*b^21*c*d^3*e^7 - 268800*a^4*b^13*c^8*d^9*e - 395*a^4*b^20*c*d^2*e^8 + 1290240*a^5*b^11*c^9*d^9*e - 4300800*a^6*b^9*c^10*d^9*e - 3600*a^6*b^17*c^2*d*e^9 + 9830400*a^7*b^7*c^11*d^9*e + 38400*a^7*b^15*c^3*d*e^9 - 14745600*a^8*b^5*c^12*d^9*e - 268800*a^8*b^13*c^4*d*e^9 + 13107200*a^9*b^3*c^13*d^9*e + 1290240*a^9*b^11*c^5*d*e^9 - 4300800*a^10*b^9*c^6*d*e^9 - 20971520*a^11*b*c^13*d^7*e^3 + 9830400*a^11*b^7*c^7*d*e^9 - 31457280*a^12*b*c^12*d^5*e^5 - 14745600*a^12*b^5*c^8*d*e^9 - 20971520*a^13*b*c^11*d^3*e^7 + 13107200*a^13*b^3*c^9*d*e^9)))^(1/2) + ((d + e*x)^(1/2)*(14112*a^4*c^7*e^10 + 9*b^8*c^3*e^10 + 4608*c^11*d^8*e^2 - 180*a*b^6*c^4*e^10 + 19584*a*c^10*d^6*e^4 - 18432*b*c^10*d^7*e^3 + 36*b^7*c^4*d*e^9 + 1530*a^2*b^4*c^5*e^10 - 6192*a^3*b^2*c^6*e^10 + 34848*a^2*c^9*d^4*e^6 + 31680*a^3*c^8*d^2*e^8 + 27360*b^2*c^9*d^6*e^4 - 17568*b^3*c^8*d^5*e^5 + 3978*b^4*c^7*d^4*e^6 - 180*b^5*c^6*d^3*e^7 + 198*b^6*c^5*d^2*e^8 + 28512*a^2*b^2*c^7*d^2*e^8 - 58752*a*b*c^9*d^5*e^5 - 900*a*b^5*c^5*d*e^9 - 31680*a^3*b*c^7*d*e^9 + 56016*a*b^2*c^8*d^4*e^6 - 14112*a*b^3*c^7*d^3*e^7 - 1836*a*b^4*c^6*d^2*e^8 - 69696*a^2*b*c^8*d^3*e^7 + 6336*a^2*b^3*c^6*d*e^9))/(8*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)))*((9*(512*b^10*c^9*d^9 - 524288*a^5*c^14*d^9 - b^19*e^9 + b^4*e^9*(-(4*a*c - b^2)^15)^(1/2) - 10240*a*b^8*c^10*d^9 + 1720320*a^9*b*c^9*e^9 - 3440640*a^9*c^10*d*e^8 - 2304*b^11*c^8*d^8*e + 81920*a^2*b^6*c^11*d^9 - 327680*a^3*b^4*c^12*d^9 + 655360*a^4*b^2*c^13*d^9 - 769*a^2*b^15*c^2*e^9 + 8620*a^3*b^13*c^3*e^9 - 63440*a^4*b^11*c^4*e^9 + 316864*a^5*b^9*c^5*e^9 - 1069824*a^6*b^7*c^6*e^9 + 2343936*a^7*b^5*c^7*e^9 - 3010560*a^8*b^3*c^8*e^9 + 49*a^2*c^2*e^9*(-(4*a*c - b^2)^15)^(1/2) - 2752512*a^6*c^13*d^7*e^2 - 6193152*a^7*c^12*d^5*e^4 - 6881280*a^8*c^11*d^3*e^6 + 3936*b^12*c^7*d^7*e^2 - 3024*b^13*c^6*d^6*e^3 + 882*b^14*c^5*d^5*e^4 - 21*b^15*c^4*d^4*e^5 + 42*b^16*c^3*d^3*e^6 - 18*b^17*c^2*d^2*e^7 + 21*c^4*d^4*e^5*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c*e^9 - 3*b^18*c*d*e^8 + 576000*a^2*b^8*c^9*d^7*e^2 - 295680*a^2*b^9*c^8*d^6*e^3 - 74592*a^2*b^10*c^7*d^5*e^4 + 65520*a^2*b^11*c^6*d^4*e^5 + 25200*a^2*b^12*c^5*d^3*e^6 - 5400*a^2*b^13*c^4*d^2*e^7 - 2088960*a^3*b^6*c^10*d^7*e^2 + 430080*a^3*b^7*c^9*d^6*e^3 + 1088640*a^3*b^8*c^8*d^5*e^4 - 356160*a^3*b^9*c^7*d^4*e^5 - 288960*a^3*b^10*c^6*d^3*e^6 + 21600*a^3*b^11*c^5*d^2*e^7 + 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9830400*a^7*b^7*c^11*d^9*e + 38400*a^7*b^15*c^3*d*e^9 - 14745600*a^8*b^5*c^12*d^9*e - 268800*a^8*b^13*c^4*d*e^9 + 13107200*a^9*b^3*c^13*d^9*e + 1290240*a^9*b^11*c^5*d*e^9 - 4300800*a^10*b^9*c^6*d*e^9 - 20971520*a^11*b*c^13*d^7*e^3 + 9830400*a^11*b^7*c^7*d*e^9 - 31457280*a^12*b*c^12*d^5*e^5 - 14745600*a^12*b^5*c^8*d*e^9 - 20971520*a^13*b*c^11*d^3*e^7 + 13107200*a^13*b^3*c^9*d*e^9)))^(1/2) - ((d + e*x)^(1/2)*(14112*a^4*c^7*e^10 + 9*b^8*c^3*e^10 + 4608*c^11*d^8*e^2 - 180*a*b^6*c^4*e^10 + 19584*a*c^10*d^6*e^4 - 18432*b*c^10*d^7*e^3 + 36*b^7*c^4*d*e^9 + 1530*a^2*b^4*c^5*e^10 - 6192*a^3*b^2*c^6*e^10 + 34848*a^2*c^9*d^4*e^6 + 31680*a^3*c^8*d^2*e^8 + 27360*b^2*c^9*d^6*e^4 - 17568*b^3*c^8*d^5*e^5 + 3978*b^4*c^7*d^4*e^6 - 180*b^5*c^6*d^3*e^7 + 198*b^6*c^5*d^2*e^8 + 28512*a^2*b^2*c^7*d^2*e^8 - 58752*a*b*c^9*d^5*e^5 - 900*a*b^5*c^5*d*e^9 - 31680*a^3*b*c^7*d*e^9 + 56016*a*b^2*c^8*d^4*e^6 - 14112*a*b^3*c^7*d^3*e^7 - 1836*a*b^4*c^6*d^2*e^8 - 69696*a^2*b*c^8*d^3*e^7 + 6336*a^2*b^3*c^6*d*e^9))/(8*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)))*((9*(512*b^10*c^9*d^9 - 524288*a^5*c^14*d^9 - b^19*e^9 + b^4*e^9*(-(4*a*c - b^2)^15)^(1/2) - 10240*a*b^8*c^10*d^9 + 1720320*a^9*b*c^9*e^9 - 3440640*a^9*c^10*d*e^8 - 2304*b^11*c^8*d^8*e + 81920*a^2*b^6*c^11*d^9 - 327680*a^3*b^4*c^12*d^9 + 655360*a^4*b^2*c^13*d^9 - 769*a^2*b^15*c^2*e^9 + 8620*a^3*b^13*c^3*e^9 - 63440*a^4*b^11*c^4*e^9 + 316864*a^5*b^9*c^5*e^9 - 1069824*a^6*b^7*c^6*e^9 + 2343936*a^7*b^5*c^7*e^9 - 3010560*a^8*b^3*c^8*e^9 + 49*a^2*c^2*e^9*(-(4*a*c - b^2)^15)^(1/2) - 2752512*a^6*c^13*d^7*e^2 - 6193152*a^7*c^12*d^5*e^4 - 6881280*a^8*c^11*d^3*e^6 + 3936*b^12*c^7*d^7*e^2 - 3024*b^13*c^6*d^6*e^3 + 882*b^14*c^5*d^5*e^4 - 21*b^15*c^4*d^4*e^5 + 42*b^16*c^3*d^3*e^6 - 18*b^17*c^2*d^2*e^7 + 21*c^4*d^4*e^5*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c*e^9 - 3*b^18*c*d*e^8 + 576000*a^2*b^8*c^9*d^7*e^2 - 295680*a^2*b^9*c^8*d^6*e^3 - 74592*a^2*b^10*c^7*d^5*e^4 + 65520*a^2*b^11*c^6*d^4*e^5 + 25200*a^2*b^12*c^5*d^3*e^6 - 5400*a^2*b^13*c^4*d^2*e^7 - 2088960*a^3*b^6*c^10*d^7*e^2 + 430080*a^3*b^7*c^9*d^6*e^3 + 1088640*a^3*b^8*c^8*d^5*e^4 - 356160*a^3*b^9*c^7*d^4*e^5 - 288960*a^3*b^10*c^6*d^3*e^6 + 21600*a^3*b^11*c^5*d^2*e^7 + 3317760*a^4*b^4*c^11*d^7*e^2 + 2150400*a^4*b^5*c^10*d^6*e^3 - 4999680*a^4*b^6*c^9*d^5*e^4 + 241920*a^4*b^7*c^8*d^4*e^5 + 1800960*a^4*b^8*c^7*d^3*e^6 + 97920*a^4*b^9*c^6*d^2*e^7 - 589824*a^5*b^2*c^12*d^7*e^2 - 8945664*a^5*b^3*c^11*d^6*e^3 + 9418752*a^5*b^4*c^10*d^5*e^4 + 4322304*a^5*b^5*c^9*d^4*e^5 - 5956608*a^5*b^6*c^8*d^3*e^6 - 1433088*a^5*b^7*c^7*d^2*e^7 - 3612672*a^6*b^2*c^11*d^5*e^4 - 15052800*a^6*b^3*c^10*d^4*e^5 + 9031680*a^6*b^4*c^9*d^3*e^6 + 6322176*a^6*b^5*c^8*d^2*e^7 - 1720320*a^7*b^2*c^10*d^3*e^6 - 12902400*a^7*b^3*c^9*d^2*e^7 + 18*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^15)^(1/2) - 11*a*b^2*c*e^9*(-(4*a*c - b^2)^15)^(1/2) + 46080*a*b^9*c^9*d^8*e + 144*a*b^16*c^2*d*e^8 + 2359296*a^5*b*c^13*d^8*e + 3*b^3*c*d*e^8*(-(4*a*c - b^2)^15)^(1/2) - 76032*a*b^10*c^8*d^7*e^2 + 51072*a*b^11*c^7*d^6*e^3 - 6552*a*b^12*c^6*d^5*e^4 - 3780*a*b^13*c^5*d^4*e^5 - 1260*a*b^14*c^4*d^3*e^6 + 486*a*b^15*c^3*d^2*e^7 - 368640*a^2*b^7*c^10*d^8*e - 2790*a^2*b^14*c^3*d*e^8 + 1474560*a^3*b^5*c^11*d^8*e + 29640*a^3*b^12*c^4*d*e^8 - 2949120*a^4*b^3*c^12*d^8*e - 188640*a^4*b^10*c^5*d*e^8 + 715392*a^5*b^8*c^6*d*e^8 + 9633792*a^6*b*c^12*d^6*e^3 - 1430016*a^6*b^6*c^7*d*e^8 + 15482880*a^7*b*c^11*d^4*e^5 + 645120*a^7*b^4*c^8*d*e^8 + 10321920*a^8*b*c^10*d^2*e^7 + 2580480*a^8*b^2*c^9*d*e^8 + 54*a*c^3*d^2*e^7*(-(4*a*c - b^2)^15)^(1/2) - 42*b*c^3*d^3*e^6*(-(4*a*c - b^2)^15)^(1/2) - 54*a*b*c^2*d*e^8*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^5*b^20*e^10 + 1048576*a^10*c^15*d^10 + 1048576*a^15*c^10*e^10 + b^20*c^5*d^10 - b^25*d^5*e^5 - 40*a*b^18*c^6*d^10 - 40*a^6*b^18*c*e^10 + 5*a*b^24*d^4*e^6 - 5*a^4*b^21*d*e^9 - 5*b^21*c^4*d^9*e + 5*b^24*c*d^6*e^4 + 720*a^2*b^16*c^7*d^10 - 7680*a^3*b^14*c^8*d^10 + 53760*a^4*b^12*c^9*d^10 - 258048*a^5*b^10*c^10*d^10 + 860160*a^6*b^8*c^11*d^10 - 1966080*a^7*b^6*c^12*d^10 + 2949120*a^8*b^4*c^13*d^10 - 2621440*a^9*b^2*c^14*d^10 + 720*a^7*b^16*c^2*e^10 - 7680*a^8*b^14*c^3*e^10 + 53760*a^9*b^12*c^4*e^10 - 258048*a^10*b^10*c^5*e^10 + 860160*a^11*b^8*c^6*e^10 - 1966080*a^12*b^6*c^7*e^10 + 2949120*a^13*b^4*c^8*e^10 - 2621440*a^14*b^2*c^9*e^10 - 10*a^2*b^23*d^3*e^7 + 10*a^3*b^22*d^2*e^8 + 5242880*a^11*c^14*d^8*e^2 + 10485760*a^12*c^13*d^6*e^4 + 10485760*a^13*c^12*d^4*e^6 + 5242880*a^14*c^11*d^2*e^8 + 10*b^22*c^3*d^8*e^2 - 10*b^23*c^2*d^7*e^3 + 7000*a^2*b^18*c^5*d^8*e^2 - 6400*a^2*b^19*c^4*d^7*e^3 + 2410*a^2*b^20*c^3*d^6*e^4 + 50*a^2*b^21*c^2*d^5*e^5 - 73200*a^3*b^16*c^6*d^8*e^2 + 62400*a^3*b^17*c^5*d^7*e^3 - 17200*a^3*b^18*c^4*d^6*e^4 - 5520*a^3*b^19*c^3*d^5*e^5 + 2410*a^3*b^20*c^2*d^4*e^6 + 499200*a^4*b^14*c^7*d^8*e^2 - 384000*a^4*b^15*c^6*d^7*e^3 + 45600*a^4*b^16*c^5*d^6*e^4 + 78240*a^4*b^17*c^4*d^5*e^5 - 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14745600*a^8*b^5*c^12*d^9*e - 268800*a^8*b^13*c^4*d*e^9 + 13107200*a^9*b^3*c^13*d^9*e + 1290240*a^9*b^11*c^5*d*e^9 - 4300800*a^10*b^9*c^6*d*e^9 - 20971520*a^11*b*c^13*d^7*e^3 + 9830400*a^11*b^7*c^7*d*e^9 - 31457280*a^12*b*c^12*d^5*e^5 - 14745600*a^12*b^5*c^8*d*e^9 - 20971520*a^13*b*c^11*d^3*e^7 + 13107200*a^13*b^3*c^9*d*e^9)))^(1/2)*(131072*a^9*c^8*d*e^10 - 65536*a^9*b*c^7*e^11 + 64*a^4*b^11*c^2*e^11 - 1280*a^5*b^9*c^3*e^11 + 10240*a^6*b^7*c^4*e^11 - 40960*a^7*b^5*c^5*e^11 + 81920*a^8*b^3*c^6*e^11 + 131072*a^5*c^12*d^9*e^2 + 524288*a^6*c^11*d^7*e^4 + 786432*a^7*c^10*d^5*e^6 + 524288*a^8*c^9*d^3*e^8 - 128*b^10*c^7*d^9*e^2 + 576*b^11*c^6*d^8*e^3 - 1024*b^12*c^5*d^7*e^4 + 896*b^13*c^4*d^6*e^5 - 384*b^14*c^3*d^5*e^6 + 64*b^15*c^2*d^4*e^7 - 20480*a^2*b^6*c^9*d^9*e^2 + 92160*a^2*b^7*c^8*d^8*e^3 - 153600*a^2*b^8*c^7*d^7*e^4 + 107520*a^2*b^9*c^6*d^6*e^5 - 16128*a^2*b^10*c^5*d^5*e^6 - 13440*a^2*b^11*c^4*d^4*e^7 + 3584*a^2*b^12*c^3*d^3*e^8 + 384*a^2*b^13*c^2*d^2*e^9 + 81920*a^3*b^4*c^10*d^9*e^2 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1835008*a^6*b*c^10*d^6*e^5 + 143360*a^6*b^6*c^5*d*e^10 - 1966080*a^7*b*c^9*d^4*e^7 - 245760*a^7*b^4*c^6*d*e^10 - 786432*a^8*b*c^8*d^2*e^9 + 98304*a^8*b^2*c^7*d*e^10))/(8*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 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12902400*a^7*b^3*c^9*d^2*e^7 + 18*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^15)^(1/2) - 11*a*b^2*c*e^9*(-(4*a*c - b^2)^15)^(1/2) + 46080*a*b^9*c^9*d^8*e + 144*a*b^16*c^2*d*e^8 + 2359296*a^5*b*c^13*d^8*e + 3*b^3*c*d*e^8*(-(4*a*c - b^2)^15)^(1/2) - 76032*a*b^10*c^8*d^7*e^2 + 51072*a*b^11*c^7*d^6*e^3 - 6552*a*b^12*c^6*d^5*e^4 - 3780*a*b^13*c^5*d^4*e^5 - 1260*a*b^14*c^4*d^3*e^6 + 486*a*b^15*c^3*d^2*e^7 - 368640*a^2*b^7*c^10*d^8*e - 2790*a^2*b^14*c^3*d*e^8 + 1474560*a^3*b^5*c^11*d^8*e + 29640*a^3*b^12*c^4*d*e^8 - 2949120*a^4*b^3*c^12*d^8*e - 188640*a^4*b^10*c^5*d*e^8 + 715392*a^5*b^8*c^6*d*e^8 + 9633792*a^6*b*c^12*d^6*e^3 - 1430016*a^6*b^6*c^7*d*e^8 + 15482880*a^7*b*c^11*d^4*e^5 + 645120*a^7*b^4*c^8*d*e^8 + 10321920*a^8*b*c^10*d^2*e^7 + 2580480*a^8*b^2*c^9*d*e^8 + 54*a*c^3*d^2*e^7*(-(4*a*c - b^2)^15)^(1/2) - 42*b*c^3*d^3*e^6*(-(4*a*c - b^2)^15)^(1/2) - 54*a*b*c^2*d*e^8*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^5*b^20*e^10 + 1048576*a^10*c^15*d^10 + 1048576*a^15*c^10*e^10 + b^20*c^5*d^10 - b^25*d^5*e^5 - 40*a*b^18*c^6*d^10 - 40*a^6*b^18*c*e^10 + 5*a*b^24*d^4*e^6 - 5*a^4*b^21*d*e^9 - 5*b^21*c^4*d^9*e + 5*b^24*c*d^6*e^4 + 720*a^2*b^16*c^7*d^10 - 7680*a^3*b^14*c^8*d^10 + 53760*a^4*b^12*c^9*d^10 - 258048*a^5*b^10*c^10*d^10 + 860160*a^6*b^8*c^11*d^10 - 1966080*a^7*b^6*c^12*d^10 + 2949120*a^8*b^4*c^13*d^10 - 2621440*a^9*b^2*c^14*d^10 + 720*a^7*b^16*c^2*e^10 - 7680*a^8*b^14*c^3*e^10 + 53760*a^9*b^12*c^4*e^10 - 258048*a^10*b^10*c^5*e^10 + 860160*a^11*b^8*c^6*e^10 - 1966080*a^12*b^6*c^7*e^10 + 2949120*a^13*b^4*c^8*e^10 - 2621440*a^14*b^2*c^9*e^10 - 10*a^2*b^23*d^3*e^7 + 10*a^3*b^22*d^2*e^8 + 5242880*a^11*c^14*d^8*e^2 + 10485760*a^12*c^13*d^6*e^4 + 10485760*a^13*c^12*d^4*e^6 + 5242880*a^14*c^11*d^2*e^8 + 10*b^22*c^3*d^8*e^2 - 10*b^23*c^2*d^7*e^3 + 7000*a^2*b^18*c^5*d^8*e^2 - 6400*a^2*b^19*c^4*d^7*e^3 + 2410*a^2*b^20*c^3*d^6*e^4 + 50*a^2*b^21*c^2*d^5*e^5 - 73200*a^3*b^16*c^6*d^8*e^2 + 62400*a^3*b^17*c^5*d^7*e^3 - 17200*a^3*b^18*c^4*d^6*e^4 - 5520*a^3*b^19*c^3*d^5*e^5 + 2410*a^3*b^20*c^2*d^4*e^6 + 499200*a^4*b^14*c^7*d^8*e^2 - 384000*a^4*b^15*c^6*d^7*e^3 + 45600*a^4*b^16*c^5*d^6*e^4 + 78240*a^4*b^17*c^4*d^5*e^5 - 17200*a^4*b^18*c^3*d^4*e^6 - 6400*a^4*b^19*c^2*d^3*e^7 - 2311680*a^5*b^12*c^8*d^8*e^2 + 1505280*a^5*b^13*c^7*d^7*e^3 + 245760*a^5*b^14*c^6*d^6*e^4 - 586752*a^5*b^15*c^5*d^5*e^5 + 45600*a^5*b^16*c^4*d^4*e^6 + 62400*a^5*b^17*c^3*d^3*e^7 + 7000*a^5*b^18*c^2*d^2*e^8 + 7311360*a^6*b^10*c^9*d^8*e^2 - 3440640*a^6*b^11*c^8*d^7*e^3 - 2903040*a^6*b^12*c^7*d^6*e^4 + 2688000*a^6*b^13*c^6*d^5*e^5 + 245760*a^6*b^14*c^5*d^4*e^6 - 384000*a^6*b^15*c^4*d^3*e^7 - 73200*a^6*b^16*c^3*d^2*e^8 - 15360000*a^7*b^8*c^10*d^8*e^2 + 2457600*a^7*b^9*c^9*d^7*e^3 + 13393920*a^7*b^10*c^8*d^6*e^4 - 7495680*a^7*b^11*c^7*d^5*e^5 - 2903040*a^7*b^12*c^6*d^4*e^6 + 1505280*a^7*b^13*c^5*d^3*e^7 + 499200*a^7*b^14*c^4*d^2*e^8 + 19660800*a^8*b^6*c^11*d^8*e^2 + 9830400*a^8*b^7*c^10*d^7*e^3 - 35635200*a^8*b^8*c^9*d^6*e^4 + 10567680*a^8*b^9*c^8*d^5*e^5 + 13393920*a^8*b^10*c^7*d^4*e^6 - 3440640*a^8*b^11*c^6*d^3*e^7 - 2311680*a^8*b^12*c^5*d^2*e^8 - 11468800*a^9*b^4*c^12*d^8*e^2 - 32768000*a^9*b^5*c^11*d^7*e^3 + 55705600*a^9*b^6*c^10*d^6*e^4 + 2621440*a^9*b^7*c^9*d^5*e^5 - 35635200*a^9*b^8*c^8*d^4*e^6 + 2457600*a^9*b^9*c^7*d^3*e^7 + 7311360*a^9*b^10*c^6*d^2*e^8 - 2621440*a^10*b^2*c^13*d^8*e^2 + 41943040*a^10*b^3*c^12*d^7*e^3 - 43909120*a^10*b^4*c^11*d^6*e^4 - 37093376*a^10*b^5*c^10*d^5*e^5 + 55705600*a^10*b^6*c^9*d^4*e^6 + 9830400*a^10*b^7*c^8*d^3*e^7 - 15360000*a^10*b^8*c^7*d^2*e^8 + 5242880*a^11*b^2*c^12*d^6*e^4 + 57671680*a^11*b^3*c^11*d^5*e^5 - 43909120*a^11*b^4*c^10*d^4*e^6 - 32768000*a^11*b^5*c^9*d^3*e^7 + 19660800*a^11*b^6*c^8*d^2*e^8 + 5242880*a^12*b^2*c^11*d^4*e^6 + 41943040*a^12*b^3*c^10*d^3*e^7 - 11468800*a^12*b^4*c^9*d^2*e^8 - 2621440*a^13*b^2*c^10*d^2*e^8 + 200*a*b^19*c^5*d^9*e + 20*a*b^23*c*d^5*e^5 + 200*a^5*b^19*c*d*e^9 - 5242880*a^10*b*c^14*d^9*e - 5242880*a^14*b*c^10*d*e^9 - 395*a*b^20*c^4*d^8*e^2 + 380*a*b^21*c^3*d^7*e^3 - 170*a*b^22*c^2*d^6*e^4 - 3600*a^2*b^17*c^6*d^9*e - 170*a^2*b^22*c*d^4*e^6 + 38400*a^3*b^15*c^7*d^9*e + 380*a^3*b^21*c*d^3*e^7 - 268800*a^4*b^13*c^8*d^9*e - 395*a^4*b^20*c*d^2*e^8 + 1290240*a^5*b^11*c^9*d^9*e - 4300800*a^6*b^9*c^10*d^9*e - 3600*a^6*b^17*c^2*d*e^9 + 9830400*a^7*b^7*c^11*d^9*e + 38400*a^7*b^15*c^3*d*e^9 - 14745600*a^8*b^5*c^12*d^9*e - 268800*a^8*b^13*c^4*d*e^9 + 13107200*a^9*b^3*c^13*d^9*e + 1290240*a^9*b^11*c^5*d*e^9 - 4300800*a^10*b^9*c^6*d*e^9 - 20971520*a^11*b*c^13*d^7*e^3 + 9830400*a^11*b^7*c^7*d*e^9 - 31457280*a^12*b*c^12*d^5*e^5 - 14745600*a^12*b^5*c^8*d*e^9 - 20971520*a^13*b*c^11*d^3*e^7 + 13107200*a^13*b^3*c^9*d*e^9)))^(1/2) + ((d + e*x)^(1/2)*(14112*a^4*c^7*e^10 + 9*b^8*c^3*e^10 + 4608*c^11*d^8*e^2 - 180*a*b^6*c^4*e^10 + 19584*a*c^10*d^6*e^4 - 18432*b*c^10*d^7*e^3 + 36*b^7*c^4*d*e^9 + 1530*a^2*b^4*c^5*e^10 - 6192*a^3*b^2*c^6*e^10 + 34848*a^2*c^9*d^4*e^6 + 31680*a^3*c^8*d^2*e^8 + 27360*b^2*c^9*d^6*e^4 - 17568*b^3*c^8*d^5*e^5 + 3978*b^4*c^7*d^4*e^6 - 180*b^5*c^6*d^3*e^7 + 198*b^6*c^5*d^2*e^8 + 28512*a^2*b^2*c^7*d^2*e^8 - 58752*a*b*c^9*d^5*e^5 - 900*a*b^5*c^5*d*e^9 - 31680*a^3*b*c^7*d*e^9 + 56016*a*b^2*c^8*d^4*e^6 - 14112*a*b^3*c^7*d^3*e^7 - 1836*a*b^4*c^6*d^2*e^8 - 69696*a^2*b*c^8*d^3*e^7 + 6336*a^2*b^3*c^6*d*e^9))/(8*(a^4*b^8*e^8 + 256*a^4*c^8*d^8 + 256*a^8*c^4*e^8 + b^8*c^4*d^8 + b^12*d^4*e^4 - 16*a*b^6*c^5*d^8 - 16*a^5*b^6*c*e^8 - 4*a*b^11*d^3*e^5 - 4*a^3*b^9*d*e^7 - 4*b^9*c^3*d^7*e - 4*b^11*c*d^5*e^3 + 96*a^2*b^4*c^6*d^8 - 256*a^3*b^2*c^7*d^8 + 96*a^6*b^4*c^2*e^8 - 256*a^7*b^2*c^3*e^8 + 6*a^2*b^10*d^2*e^6 + 1024*a^5*c^7*d^6*e^2 + 1536*a^6*c^6*d^4*e^4 + 1024*a^7*c^5*d^2*e^6 + 6*b^10*c^2*d^6*e^2 + 512*a^2*b^6*c^4*d^6*e^2 - 192*a^2*b^7*c^3*d^5*e^3 - 90*a^2*b^8*c^2*d^4*e^4 - 1152*a^3*b^4*c^5*d^6*e^2 - 128*a^3*b^5*c^4*d^5*e^3 + 800*a^3*b^6*c^3*d^4*e^4 - 192*a^3*b^7*c^2*d^3*e^5 + 512*a^4*b^2*c^6*d^6*e^2 + 2048*a^4*b^3*c^5*d^5*e^3 - 2240*a^4*b^4*c^4*d^4*e^4 - 128*a^4*b^5*c^3*d^3*e^5 + 512*a^4*b^6*c^2*d^2*e^6 + 1536*a^5*b^2*c^5*d^4*e^4 + 2048*a^5*b^3*c^4*d^3*e^5 - 1152*a^5*b^4*c^3*d^2*e^6 + 512*a^6*b^2*c^4*d^2*e^6 + 64*a*b^7*c^4*d^7*e - 4*a*b^10*c*d^4*e^4 - 1024*a^4*b*c^7*d^7*e + 64*a^4*b^7*c*d*e^7 - 1024*a^7*b*c^4*d*e^7 - 92*a*b^8*c^3*d^6*e^2 + 52*a*b^9*c^2*d^5*e^3 - 384*a^2*b^5*c^5*d^7*e + 52*a^2*b^9*c*d^3*e^5 + 1024*a^3*b^3*c^6*d^7*e - 92*a^3*b^8*c*d^2*e^6 - 3072*a^5*b*c^6*d^5*e^3 - 384*a^5*b^5*c^2*d*e^7 - 3072*a^6*b*c^5*d^3*e^5 + 1024*a^6*b^3*c^3*d*e^7)))*((9*(512*b^10*c^9*d^9 - 524288*a^5*c^14*d^9 - b^19*e^9 + b^4*e^9*(-(4*a*c - b^2)^15)^(1/2) - 10240*a*b^8*c^10*d^9 + 1720320*a^9*b*c^9*e^9 - 3440640*a^9*c^10*d*e^8 - 2304*b^11*c^8*d^8*e + 81920*a^2*b^6*c^11*d^9 - 327680*a^3*b^4*c^12*d^9 + 655360*a^4*b^2*c^13*d^9 - 769*a^2*b^15*c^2*e^9 + 8620*a^3*b^13*c^3*e^9 - 63440*a^4*b^11*c^4*e^9 + 316864*a^5*b^9*c^5*e^9 - 1069824*a^6*b^7*c^6*e^9 + 2343936*a^7*b^5*c^7*e^9 - 3010560*a^8*b^3*c^8*e^9 + 49*a^2*c^2*e^9*(-(4*a*c - b^2)^15)^(1/2) - 2752512*a^6*c^13*d^7*e^2 - 6193152*a^7*c^12*d^5*e^4 - 6881280*a^8*c^11*d^3*e^6 + 3936*b^12*c^7*d^7*e^2 - 3024*b^13*c^6*d^6*e^3 + 882*b^14*c^5*d^5*e^4 - 21*b^15*c^4*d^4*e^5 + 42*b^16*c^3*d^3*e^6 - 18*b^17*c^2*d^2*e^7 + 21*c^4*d^4*e^5*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c*e^9 - 3*b^18*c*d*e^8 + 576000*a^2*b^8*c^9*d^7*e^2 - 295680*a^2*b^9*c^8*d^6*e^3 - 74592*a^2*b^10*c^7*d^5*e^4 + 65520*a^2*b^11*c^6*d^4*e^5 + 25200*a^2*b^12*c^5*d^3*e^6 - 5400*a^2*b^13*c^4*d^2*e^7 - 2088960*a^3*b^6*c^10*d^7*e^2 + 430080*a^3*b^7*c^9*d^6*e^3 + 1088640*a^3*b^8*c^8*d^5*e^4 - 356160*a^3*b^9*c^7*d^4*e^5 - 288960*a^3*b^10*c^6*d^3*e^6 + 21600*a^3*b^11*c^5*d^2*e^7 + 3317760*a^4*b^4*c^11*d^7*e^2 + 2150400*a^4*b^5*c^10*d^6*e^3 - 4999680*a^4*b^6*c^9*d^5*e^4 + 241920*a^4*b^7*c^8*d^4*e^5 + 1800960*a^4*b^8*c^7*d^3*e^6 + 97920*a^4*b^9*c^6*d^2*e^7 - 589824*a^5*b^2*c^12*d^7*e^2 - 8945664*a^5*b^3*c^11*d^6*e^3 + 9418752*a^5*b^4*c^10*d^5*e^4 + 4322304*a^5*b^5*c^9*d^4*e^5 - 5956608*a^5*b^6*c^8*d^3*e^6 - 1433088*a^5*b^7*c^7*d^2*e^7 - 3612672*a^6*b^2*c^11*d^5*e^4 - 15052800*a^6*b^3*c^10*d^4*e^5 + 9031680*a^6*b^4*c^9*d^3*e^6 + 6322176*a^6*b^5*c^8*d^2*e^7 - 1720320*a^7*b^2*c^10*d^3*e^6 - 12902400*a^7*b^3*c^9*d^2*e^7 + 18*b^2*c^2*d^2*e^7*(-(4*a*c - b^2)^15)^(1/2) - 11*a*b^2*c*e^9*(-(4*a*c - b^2)^15)^(1/2) + 46080*a*b^9*c^9*d^8*e + 144*a*b^16*c^2*d*e^8 + 2359296*a^5*b*c^13*d^8*e + 3*b^3*c*d*e^8*(-(4*a*c - b^2)^15)^(1/2) - 76032*a*b^10*c^8*d^7*e^2 + 51072*a*b^11*c^7*d^6*e^3 - 6552*a*b^12*c^6*d^5*e^4 - 3780*a*b^13*c^5*d^4*e^5 - 1260*a*b^14*c^4*d^3*e^6 + 486*a*b^15*c^3*d^2*e^7 - 368640*a^2*b^7*c^10*d^8*e - 2790*a^2*b^14*c^3*d*e^8 + 1474560*a^3*b^5*c^11*d^8*e + 29640*a^3*b^12*c^4*d*e^8 - 2949120*a^4*b^3*c^12*d^8*e - 188640*a^4*b^10*c^5*d*e^8 + 715392*a^5*b^8*c^6*d*e^8 + 9633792*a^6*b*c^12*d^6*e^3 - 1430016*a^6*b^6*c^7*d*e^8 + 15482880*a^7*b*c^11*d^4*e^5 + 645120*a^7*b^4*c^8*d*e^8 + 10321920*a^8*b*c^10*d^2*e^7 + 2580480*a^8*b^2*c^9*d*e^8 + 54*a*c^3*d^2*e^7*(-(4*a*c - b^2)^15)^(1/2) - 42*b*c^3*d^3*e^6*(-(4*a*c - b^2)^15)^(1/2) - 54*a*b*c^2*d*e^8*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^5*b^20*e^10 + 1048576*a^10*c^15*d^10 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13393920*a^8*b^10*c^7*d^4*e^6 - 3440640*a^8*b^11*c^6*d^3*e^7 - 2311680*a^8*b^12*c^5*d^2*e^8 - 11468800*a^9*b^4*c^12*d^8*e^2 - 32768000*a^9*b^5*c^11*d^7*e^3 + 55705600*a^9*b^6*c^10*d^6*e^4 + 2621440*a^9*b^7*c^9*d^5*e^5 - 35635200*a^9*b^8*c^8*d^4*e^6 + 2457600*a^9*b^9*c^7*d^3*e^7 + 7311360*a^9*b^10*c^6*d^2*e^8 - 2621440*a^10*b^2*c^13*d^8*e^2 + 41943040*a^10*b^3*c^12*d^7*e^3 - 43909120*a^10*b^4*c^11*d^6*e^4 - 37093376*a^10*b^5*c^10*d^5*e^5 + 55705600*a^10*b^6*c^9*d^4*e^6 + 9830400*a^10*b^7*c^8*d^3*e^7 - 15360000*a^10*b^8*c^7*d^2*e^8 + 5242880*a^11*b^2*c^12*d^6*e^4 + 57671680*a^11*b^3*c^11*d^5*e^5 - 43909120*a^11*b^4*c^10*d^4*e^6 - 32768000*a^11*b^5*c^9*d^3*e^7 + 19660800*a^11*b^6*c^8*d^2*e^8 + 5242880*a^12*b^2*c^11*d^4*e^6 + 41943040*a^12*b^3*c^10*d^3*e^7 - 11468800*a^12*b^4*c^9*d^2*e^8 - 2621440*a^13*b^2*c^10*d^2*e^8 + 200*a*b^19*c^5*d^9*e + 20*a*b^23*c*d^5*e^5 + 200*a^5*b^19*c*d*e^9 - 5242880*a^10*b*c^14*d^9*e - 5242880*a^14*b*c^10*d*e^9 - 395*a*b^20*c^4*d^8*e^2 + 380*a*b^21*c^3*d^7*e^3 - 170*a*b^22*c^2*d^6*e^4 - 3600*a^2*b^17*c^6*d^9*e - 170*a^2*b^22*c*d^4*e^6 + 38400*a^3*b^15*c^7*d^9*e + 380*a^3*b^21*c*d^3*e^7 - 268800*a^4*b^13*c^8*d^9*e - 395*a^4*b^20*c*d^2*e^8 + 1290240*a^5*b^11*c^9*d^9*e - 4300800*a^6*b^9*c^10*d^9*e - 3600*a^6*b^17*c^2*d*e^9 + 9830400*a^7*b^7*c^11*d^9*e + 38400*a^7*b^15*c^3*d*e^9 - 14745600*a^8*b^5*c^12*d^9*e - 268800*a^8*b^13*c^4*d*e^9 + 13107200*a^9*b^3*c^13*d^9*e + 1290240*a^9*b^11*c^5*d*e^9 - 4300800*a^10*b^9*c^6*d*e^9 - 20971520*a^11*b*c^13*d^7*e^3 + 9830400*a^11*b^7*c^7*d*e^9 - 31457280*a^12*b*c^12*d^5*e^5 - 14745600*a^12*b^5*c^8*d*e^9 - 20971520*a^13*b*c^11*d^3*e^7 + 13107200*a^13*b^3*c^9*d*e^9)))^(1/2)))*((9*(512*b^10*c^9*d^9 - 524288*a^5*c^14*d^9 - b^19*e^9 + b^4*e^9*(-(4*a*c - b^2)^15)^(1/2) - 10240*a*b^8*c^10*d^9 + 1720320*a^9*b*c^9*e^9 - 3440640*a^9*c^10*d*e^8 - 2304*b^11*c^8*d^8*e + 81920*a^2*b^6*c^11*d^9 - 327680*a^3*b^4*c^12*d^9 + 655360*a^4*b^2*c^13*d^9 - 769*a^2*b^15*c^2*e^9 + 8620*a^3*b^13*c^3*e^9 - 63440*a^4*b^11*c^4*e^9 + 316864*a^5*b^9*c^5*e^9 - 1069824*a^6*b^7*c^6*e^9 + 2343936*a^7*b^5*c^7*e^9 - 3010560*a^8*b^3*c^8*e^9 + 49*a^2*c^2*e^9*(-(4*a*c - b^2)^15)^(1/2) - 2752512*a^6*c^13*d^7*e^2 - 6193152*a^7*c^12*d^5*e^4 - 6881280*a^8*c^11*d^3*e^6 + 3936*b^12*c^7*d^7*e^2 - 3024*b^13*c^6*d^6*e^3 + 882*b^14*c^5*d^5*e^4 - 21*b^15*c^4*d^4*e^5 + 42*b^16*c^3*d^3*e^6 - 18*b^17*c^2*d^2*e^7 + 21*c^4*d^4*e^5*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c*e^9 - 3*b^18*c*d*e^8 + 576000*a^2*b^8*c^9*d^7*e^2 - 295680*a^2*b^9*c^8*d^6*e^3 - 74592*a^2*b^10*c^7*d^5*e^4 + 65520*a^2*b^11*c^6*d^4*e^5 + 25200*a^2*b^12*c^5*d^3*e^6 - 5400*a^2*b^13*c^4*d^2*e^7 - 2088960*a^3*b^6*c^10*d^7*e^2 + 430080*a^3*b^7*c^9*d^6*e^3 + 1088640*a^3*b^8*c^8*d^5*e^4 - 356160*a^3*b^9*c^7*d^4*e^5 - 288960*a^3*b^10*c^6*d^3*e^6 + 21600*a^3*b^11*c^5*d^2*e^7 + 3317760*a^4*b^4*c^11*d^7*e^2 + 2150400*a^4*b^5*c^10*d^6*e^3 - 4999680*a^4*b^6*c^9*d^5*e^4 + 241920*a^4*b^7*c^8*d^4*e^5 + 1800960*a^4*b^8*c^7*d^3*e^6 + 97920*a^4*b^9*c^6*d^2*e^7 - 589824*a^5*b^2*c^12*d^7*e^2 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645120*a^7*b^4*c^8*d*e^8 + 10321920*a^8*b*c^10*d^2*e^7 + 2580480*a^8*b^2*c^9*d*e^8 + 54*a*c^3*d^2*e^7*(-(4*a*c - b^2)^15)^(1/2) - 42*b*c^3*d^3*e^6*(-(4*a*c - b^2)^15)^(1/2) - 54*a*b*c^2*d*e^8*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^5*b^20*e^10 + 1048576*a^10*c^15*d^10 + 1048576*a^15*c^10*e^10 + b^20*c^5*d^10 - b^25*d^5*e^5 - 40*a*b^18*c^6*d^10 - 40*a^6*b^18*c*e^10 + 5*a*b^24*d^4*e^6 - 5*a^4*b^21*d*e^9 - 5*b^21*c^4*d^9*e + 5*b^24*c*d^6*e^4 + 720*a^2*b^16*c^7*d^10 - 7680*a^3*b^14*c^8*d^10 + 53760*a^4*b^12*c^9*d^10 - 258048*a^5*b^10*c^10*d^10 + 860160*a^6*b^8*c^11*d^10 - 1966080*a^7*b^6*c^12*d^10 + 2949120*a^8*b^4*c^13*d^10 - 2621440*a^9*b^2*c^14*d^10 + 720*a^7*b^16*c^2*e^10 - 7680*a^8*b^14*c^3*e^10 + 53760*a^9*b^12*c^4*e^10 - 258048*a^10*b^10*c^5*e^10 + 860160*a^11*b^8*c^6*e^10 - 1966080*a^12*b^6*c^7*e^10 + 2949120*a^13*b^4*c^8*e^10 - 2621440*a^14*b^2*c^9*e^10 - 10*a^2*b^23*d^3*e^7 + 10*a^3*b^22*d^2*e^8 + 5242880*a^11*c^14*d^8*e^2 + 10485760*a^12*c^13*d^6*e^4 + 10485760*a^13*c^12*d^4*e^6 + 5242880*a^14*c^11*d^2*e^8 + 10*b^22*c^3*d^8*e^2 - 10*b^23*c^2*d^7*e^3 + 7000*a^2*b^18*c^5*d^8*e^2 - 6400*a^2*b^19*c^4*d^7*e^3 + 2410*a^2*b^20*c^3*d^6*e^4 + 50*a^2*b^21*c^2*d^5*e^5 - 73200*a^3*b^16*c^6*d^8*e^2 + 62400*a^3*b^17*c^5*d^7*e^3 - 17200*a^3*b^18*c^4*d^6*e^4 - 5520*a^3*b^19*c^3*d^5*e^5 + 2410*a^3*b^20*c^2*d^4*e^6 + 499200*a^4*b^14*c^7*d^8*e^2 - 384000*a^4*b^15*c^6*d^7*e^3 + 45600*a^4*b^16*c^5*d^6*e^4 + 78240*a^4*b^17*c^4*d^5*e^5 - 17200*a^4*b^18*c^3*d^4*e^6 - 6400*a^4*b^19*c^2*d^3*e^7 - 2311680*a^5*b^12*c^8*d^8*e^2 + 1505280*a^5*b^13*c^7*d^7*e^3 + 245760*a^5*b^14*c^6*d^6*e^4 - 586752*a^5*b^15*c^5*d^5*e^5 + 45600*a^5*b^16*c^4*d^4*e^6 + 62400*a^5*b^17*c^3*d^3*e^7 + 7000*a^5*b^18*c^2*d^2*e^8 + 7311360*a^6*b^10*c^9*d^8*e^2 - 3440640*a^6*b^11*c^8*d^7*e^3 - 2903040*a^6*b^12*c^7*d^6*e^4 + 2688000*a^6*b^13*c^6*d^5*e^5 + 245760*a^6*b^14*c^5*d^4*e^6 - 384000*a^6*b^15*c^4*d^3*e^7 - 73200*a^6*b^16*c^3*d^2*e^8 - 15360000*a^7*b^8*c^10*d^8*e^2 + 2457600*a^7*b^9*c^9*d^7*e^3 + 13393920*a^7*b^10*c^8*d^6*e^4 - 7495680*a^7*b^11*c^7*d^5*e^5 - 2903040*a^7*b^12*c^6*d^4*e^6 + 1505280*a^7*b^13*c^5*d^3*e^7 + 499200*a^7*b^14*c^4*d^2*e^8 + 19660800*a^8*b^6*c^11*d^8*e^2 + 9830400*a^8*b^7*c^10*d^7*e^3 - 35635200*a^8*b^8*c^9*d^6*e^4 + 10567680*a^8*b^9*c^8*d^5*e^5 + 13393920*a^8*b^10*c^7*d^4*e^6 - 3440640*a^8*b^11*c^6*d^3*e^7 - 2311680*a^8*b^12*c^5*d^2*e^8 - 11468800*a^9*b^4*c^12*d^8*e^2 - 32768000*a^9*b^5*c^11*d^7*e^3 + 55705600*a^9*b^6*c^10*d^6*e^4 + 2621440*a^9*b^7*c^9*d^5*e^5 - 35635200*a^9*b^8*c^8*d^4*e^6 + 2457600*a^9*b^9*c^7*d^3*e^7 + 7311360*a^9*b^10*c^6*d^2*e^8 - 2621440*a^10*b^2*c^13*d^8*e^2 + 41943040*a^10*b^3*c^12*d^7*e^3 - 43909120*a^10*b^4*c^11*d^6*e^4 - 37093376*a^10*b^5*c^10*d^5*e^5 + 55705600*a^10*b^6*c^9*d^4*e^6 + 9830400*a^10*b^7*c^8*d^3*e^7 - 15360000*a^10*b^8*c^7*d^2*e^8 + 5242880*a^11*b^2*c^12*d^6*e^4 + 57671680*a^11*b^3*c^11*d^5*e^5 - 43909120*a^11*b^4*c^10*d^4*e^6 - 32768000*a^11*b^5*c^9*d^3*e^7 + 19660800*a^11*b^6*c^8*d^2*e^8 + 5242880*a^12*b^2*c^11*d^4*e^6 + 41943040*a^12*b^3*c^10*d^3*e^7 - 11468800*a^12*b^4*c^9*d^2*e^8 - 2621440*a^13*b^2*c^10*d^2*e^8 + 200*a*b^19*c^5*d^9*e + 20*a*b^23*c*d^5*e^5 + 200*a^5*b^19*c*d*e^9 - 5242880*a^10*b*c^14*d^9*e - 5242880*a^14*b*c^10*d*e^9 - 395*a*b^20*c^4*d^8*e^2 + 380*a*b^21*c^3*d^7*e^3 - 170*a*b^22*c^2*d^6*e^4 - 3600*a^2*b^17*c^6*d^9*e - 170*a^2*b^22*c*d^4*e^6 + 38400*a^3*b^15*c^7*d^9*e + 380*a^3*b^21*c*d^3*e^7 - 268800*a^4*b^13*c^8*d^9*e - 395*a^4*b^20*c*d^2*e^8 + 1290240*a^5*b^11*c^9*d^9*e - 4300800*a^6*b^9*c^10*d^9*e - 3600*a^6*b^17*c^2*d*e^9 + 9830400*a^7*b^7*c^11*d^9*e + 38400*a^7*b^15*c^3*d*e^9 - 14745600*a^8*b^5*c^12*d^9*e - 268800*a^8*b^13*c^4*d*e^9 + 13107200*a^9*b^3*c^13*d^9*e + 1290240*a^9*b^11*c^5*d*e^9 - 4300800*a^10*b^9*c^6*d*e^9 - 20971520*a^11*b*c^13*d^7*e^3 + 9830400*a^11*b^7*c^7*d*e^9 - 31457280*a^12*b*c^12*d^5*e^5 - 14745600*a^12*b^5*c^8*d*e^9 - 20971520*a^13*b*c^11*d^3*e^7 + 13107200*a^13*b^3*c^9*d*e^9)))^(1/2)*2i","B"
2307,1,711,629,1.817592,"\text{Not used}","int((d + e*x)^(1/2)/(a + b*x*1i + c*x^2),x)","-2\,\mathrm{atanh}\left(\frac{\left(8\,c^2\,\sqrt{d+e\,x}\,\left(b^2\,e^4+b\,c\,d\,e^3\,2{}\mathrm{i}-2\,c^2\,d^2\,e^2+2\,a\,c\,e^4\right)-\frac{4\,c^2\,\sqrt{d+e\,x}\,\left(b^3\,c\,e^3\,1{}\mathrm{i}-2\,d\,b^2\,c^2\,e^2+4{}\mathrm{i}\,a\,b\,c^2\,e^3-8\,a\,d\,c^3\,e^2\right)\,\left(e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}-b^3\,e\,1{}\mathrm{i}+8\,a\,c^2\,d+2\,b^2\,c\,d-a\,b\,c\,e\,4{}\mathrm{i}\right)}{16\,a^2\,c^3+8\,a\,b^2\,c^2+b^4\,c}\right)\,\sqrt{-\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}-b^3\,e\,1{}\mathrm{i}+8\,a\,c^2\,d+2\,b^2\,c\,d-a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^2\,c^3+8\,a\,b^2\,c^2+b^4\,c\right)}}}{8\,c^2\,\left(c\,d^2\,e^3-1{}\mathrm{i}\,b\,d\,e^4+a\,e^5\right)}\right)\,\sqrt{-\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}-b^3\,e\,1{}\mathrm{i}+8\,a\,c^2\,d+2\,b^2\,c\,d-a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^2\,c^3+8\,a\,b^2\,c^2+b^4\,c\right)}}-2\,\mathrm{atanh}\left(\frac{\left(8\,c^2\,\sqrt{d+e\,x}\,\left(b^2\,e^4+b\,c\,d\,e^3\,2{}\mathrm{i}-2\,c^2\,d^2\,e^2+2\,a\,c\,e^4\right)+\frac{4\,c^2\,\sqrt{d+e\,x}\,\left(b^3\,c\,e^3\,1{}\mathrm{i}-2\,d\,b^2\,c^2\,e^2+4{}\mathrm{i}\,a\,b\,c^2\,e^3-8\,a\,d\,c^3\,e^2\right)\,\left(e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}+b^3\,e\,1{}\mathrm{i}-8\,a\,c^2\,d-2\,b^2\,c\,d+a\,b\,c\,e\,4{}\mathrm{i}\right)}{16\,a^2\,c^3+8\,a\,b^2\,c^2+b^4\,c}\right)\,\sqrt{\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}+b^3\,e\,1{}\mathrm{i}-8\,a\,c^2\,d-2\,b^2\,c\,d+a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^2\,c^3+8\,a\,b^2\,c^2+b^4\,c\right)}}}{8\,c^2\,\left(c\,d^2\,e^3-1{}\mathrm{i}\,b\,d\,e^4+a\,e^5\right)}\right)\,\sqrt{\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}+b^3\,e\,1{}\mathrm{i}-8\,a\,c^2\,d-2\,b^2\,c\,d+a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^2\,c^3+8\,a\,b^2\,c^2+b^4\,c\right)}}","Not used",1,"- 2*atanh(((8*c^2*(d + e*x)^(1/2)*(b^2*e^4 - 2*c^2*d^2*e^2 + 2*a*c*e^4 + b*c*d*e^3*2i) - (4*c^2*(d + e*x)^(1/2)*(b^3*c*e^3*1i - 2*b^2*c^2*d*e^2 + a*b*c^2*e^3*4i - 8*a*c^3*d*e^2)*(e*(-(4*a*c + b^2)^3)^(1/2) - b^3*e*1i + 8*a*c^2*d + 2*b^2*c*d - a*b*c*e*4i))/(b^4*c + 16*a^2*c^3 + 8*a*b^2*c^2))*(-(e*(-(4*a*c + b^2)^3)^(1/2) - b^3*e*1i + 8*a*c^2*d + 2*b^2*c*d - a*b*c*e*4i)/(2*(b^4*c + 16*a^2*c^3 + 8*a*b^2*c^2)))^(1/2))/(8*c^2*(a*e^5 + c*d^2*e^3 - b*d*e^4*1i)))*(-(e*(-(4*a*c + b^2)^3)^(1/2) - b^3*e*1i + 8*a*c^2*d + 2*b^2*c*d - a*b*c*e*4i)/(2*(b^4*c + 16*a^2*c^3 + 8*a*b^2*c^2)))^(1/2) - 2*atanh(((8*c^2*(d + e*x)^(1/2)*(b^2*e^4 - 2*c^2*d^2*e^2 + 2*a*c*e^4 + b*c*d*e^3*2i) + (4*c^2*(d + e*x)^(1/2)*(b^3*c*e^3*1i - 2*b^2*c^2*d*e^2 + a*b*c^2*e^3*4i - 8*a*c^3*d*e^2)*(e*(-(4*a*c + b^2)^3)^(1/2) + b^3*e*1i - 8*a*c^2*d - 2*b^2*c*d + a*b*c*e*4i))/(b^4*c + 16*a^2*c^3 + 8*a*b^2*c^2))*((e*(-(4*a*c + b^2)^3)^(1/2) + b^3*e*1i - 8*a*c^2*d - 2*b^2*c*d + a*b*c*e*4i)/(2*(b^4*c + 16*a^2*c^3 + 8*a*b^2*c^2)))^(1/2))/(8*c^2*(a*e^5 + c*d^2*e^3 - b*d*e^4*1i)))*((e*(-(4*a*c + b^2)^3)^(1/2) + b^3*e*1i - 8*a*c^2*d - 2*b^2*c*d + a*b*c*e*4i)/(2*(b^4*c + 16*a^2*c^3 + 8*a*b^2*c^2)))^(1/2)","B"
2308,1,4530,705,2.911794,"\text{Not used}","int(1/((d + e*x)^(1/2)*(a + b*x*1i + c*x^2)),x)","-\mathrm{atan}\left(\frac{\left(\left(8\,c^2\,\left(b^2\,e^3+4\,a\,c\,e^3\right)-8\,c^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}-b^3\,e\,1{}\mathrm{i}+8\,a\,c^2\,d+2\,b^2\,c\,d-a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}\,\left(b^3\,e^3\,1{}\mathrm{i}-2\,d\,b^2\,c\,e^2+4{}\mathrm{i}\,a\,b\,c\,e^3-8\,a\,d\,c^2\,e^2\right)\right)\,\sqrt{-\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}-b^3\,e\,1{}\mathrm{i}+8\,a\,c^2\,d+2\,b^2\,c\,d-a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}+16\,c^3\,e^2\,\sqrt{d+e\,x}\right)\,\sqrt{-\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}-b^3\,e\,1{}\mathrm{i}+8\,a\,c^2\,d+2\,b^2\,c\,d-a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(8\,c^2\,\left(b^2\,e^3+4\,a\,c\,e^3\right)+8\,c^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}-b^3\,e\,1{}\mathrm{i}+8\,a\,c^2\,d+2\,b^2\,c\,d-a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}\,\left(b^3\,e^3\,1{}\mathrm{i}-2\,d\,b^2\,c\,e^2+4{}\mathrm{i}\,a\,b\,c\,e^3-8\,a\,d\,c^2\,e^2\right)\right)\,\sqrt{-\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}-b^3\,e\,1{}\mathrm{i}+8\,a\,c^2\,d+2\,b^2\,c\,d-a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}-16\,c^3\,e^2\,\sqrt{d+e\,x}\right)\,\sqrt{-\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}-b^3\,e\,1{}\mathrm{i}+8\,a\,c^2\,d+2\,b^2\,c\,d-a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}\,1{}\mathrm{i}}{\left(\left(8\,c^2\,\left(b^2\,e^3+4\,a\,c\,e^3\right)-8\,c^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}-b^3\,e\,1{}\mathrm{i}+8\,a\,c^2\,d+2\,b^2\,c\,d-a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}\,\left(b^3\,e^3\,1{}\mathrm{i}-2\,d\,b^2\,c\,e^2+4{}\mathrm{i}\,a\,b\,c\,e^3-8\,a\,d\,c^2\,e^2\right)\right)\,\sqrt{-\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}-b^3\,e\,1{}\mathrm{i}+8\,a\,c^2\,d+2\,b^2\,c\,d-a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}+16\,c^3\,e^2\,\sqrt{d+e\,x}\right)\,\sqrt{-\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}-b^3\,e\,1{}\mathrm{i}+8\,a\,c^2\,d+2\,b^2\,c\,d-a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}+\left(\left(8\,c^2\,\left(b^2\,e^3+4\,a\,c\,e^3\right)+8\,c^2\,\sqrt{d+e\,x}\,\sqrt{-\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}-b^3\,e\,1{}\mathrm{i}+8\,a\,c^2\,d+2\,b^2\,c\,d-a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}\,\left(b^3\,e^3\,1{}\mathrm{i}-2\,d\,b^2\,c\,e^2+4{}\mathrm{i}\,a\,b\,c\,e^3-8\,a\,d\,c^2\,e^2\right)\right)\,\sqrt{-\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}-b^3\,e\,1{}\mathrm{i}+8\,a\,c^2\,d+2\,b^2\,c\,d-a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}-16\,c^3\,e^2\,\sqrt{d+e\,x}\right)\,\sqrt{-\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}-b^3\,e\,1{}\mathrm{i}+8\,a\,c^2\,d+2\,b^2\,c\,d-a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}}\right)\,\sqrt{-\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}-b^3\,e\,1{}\mathrm{i}+8\,a\,c^2\,d+2\,b^2\,c\,d-a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(8\,c^2\,\left(b^2\,e^3+4\,a\,c\,e^3\right)-8\,c^2\,\sqrt{d+e\,x}\,\sqrt{\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}+b^3\,e\,1{}\mathrm{i}-8\,a\,c^2\,d-2\,b^2\,c\,d+a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}\,\left(b^3\,e^3\,1{}\mathrm{i}-2\,d\,b^2\,c\,e^2+4{}\mathrm{i}\,a\,b\,c\,e^3-8\,a\,d\,c^2\,e^2\right)\right)\,\sqrt{\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}+b^3\,e\,1{}\mathrm{i}-8\,a\,c^2\,d-2\,b^2\,c\,d+a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}+16\,c^3\,e^2\,\sqrt{d+e\,x}\right)\,\sqrt{\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}+b^3\,e\,1{}\mathrm{i}-8\,a\,c^2\,d-2\,b^2\,c\,d+a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(8\,c^2\,\left(b^2\,e^3+4\,a\,c\,e^3\right)+8\,c^2\,\sqrt{d+e\,x}\,\sqrt{\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}+b^3\,e\,1{}\mathrm{i}-8\,a\,c^2\,d-2\,b^2\,c\,d+a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}\,\left(b^3\,e^3\,1{}\mathrm{i}-2\,d\,b^2\,c\,e^2+4{}\mathrm{i}\,a\,b\,c\,e^3-8\,a\,d\,c^2\,e^2\right)\right)\,\sqrt{\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}+b^3\,e\,1{}\mathrm{i}-8\,a\,c^2\,d-2\,b^2\,c\,d+a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}-16\,c^3\,e^2\,\sqrt{d+e\,x}\right)\,\sqrt{\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}+b^3\,e\,1{}\mathrm{i}-8\,a\,c^2\,d-2\,b^2\,c\,d+a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}\,1{}\mathrm{i}}{\left(\left(8\,c^2\,\left(b^2\,e^3+4\,a\,c\,e^3\right)-8\,c^2\,\sqrt{d+e\,x}\,\sqrt{\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}+b^3\,e\,1{}\mathrm{i}-8\,a\,c^2\,d-2\,b^2\,c\,d+a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}\,\left(b^3\,e^3\,1{}\mathrm{i}-2\,d\,b^2\,c\,e^2+4{}\mathrm{i}\,a\,b\,c\,e^3-8\,a\,d\,c^2\,e^2\right)\right)\,\sqrt{\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}+b^3\,e\,1{}\mathrm{i}-8\,a\,c^2\,d-2\,b^2\,c\,d+a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}+16\,c^3\,e^2\,\sqrt{d+e\,x}\right)\,\sqrt{\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}+b^3\,e\,1{}\mathrm{i}-8\,a\,c^2\,d-2\,b^2\,c\,d+a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}+\left(\left(8\,c^2\,\left(b^2\,e^3+4\,a\,c\,e^3\right)+8\,c^2\,\sqrt{d+e\,x}\,\sqrt{\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}+b^3\,e\,1{}\mathrm{i}-8\,a\,c^2\,d-2\,b^2\,c\,d+a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}\,\left(b^3\,e^3\,1{}\mathrm{i}-2\,d\,b^2\,c\,e^2+4{}\mathrm{i}\,a\,b\,c\,e^3-8\,a\,d\,c^2\,e^2\right)\right)\,\sqrt{\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}+b^3\,e\,1{}\mathrm{i}-8\,a\,c^2\,d-2\,b^2\,c\,d+a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}-16\,c^3\,e^2\,\sqrt{d+e\,x}\right)\,\sqrt{\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}+b^3\,e\,1{}\mathrm{i}-8\,a\,c^2\,d-2\,b^2\,c\,d+a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}}\right)\,\sqrt{\frac{e\,\sqrt{-{\left(b^2+4\,a\,c\right)}^3}+b^3\,e\,1{}\mathrm{i}-8\,a\,c^2\,d-2\,b^2\,c\,d+a\,b\,c\,e\,4{}\mathrm{i}}{2\,\left(16\,a^3\,c^2\,e^2+8\,a^2\,b^2\,c\,e^2-a^2\,b\,c^2\,d\,e\,16{}\mathrm{i}+16\,a^2\,c^3\,d^2+a\,b^4\,e^2-a\,b^3\,c\,d\,e\,8{}\mathrm{i}+8\,a\,b^2\,c^2\,d^2-b^5\,d\,e\,1{}\mathrm{i}+b^4\,c\,d^2\right)}}\,2{}\mathrm{i}","Not used",1,"- atan((((8*c^2*(b^2*e^3 + 4*a*c*e^3) - 8*c^2*(d + e*x)^(1/2)*(-(e*(-(4*a*c + b^2)^3)^(1/2) - b^3*e*1i + 8*a*c^2*d + 2*b^2*c*d - a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2)*(b^3*e^3*1i + a*b*c*e^3*4i - 8*a*c^2*d*e^2 - 2*b^2*c*d*e^2))*(-(e*(-(4*a*c + b^2)^3)^(1/2) - b^3*e*1i + 8*a*c^2*d + 2*b^2*c*d - a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2) + 16*c^3*e^2*(d + e*x)^(1/2))*(-(e*(-(4*a*c + b^2)^3)^(1/2) - b^3*e*1i + 8*a*c^2*d + 2*b^2*c*d - a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2)*1i - ((8*c^2*(b^2*e^3 + 4*a*c*e^3) + 8*c^2*(d + e*x)^(1/2)*(-(e*(-(4*a*c + b^2)^3)^(1/2) - b^3*e*1i + 8*a*c^2*d + 2*b^2*c*d - a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2)*(b^3*e^3*1i + a*b*c*e^3*4i - 8*a*c^2*d*e^2 - 2*b^2*c*d*e^2))*(-(e*(-(4*a*c + b^2)^3)^(1/2) - b^3*e*1i + 8*a*c^2*d + 2*b^2*c*d - a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2) - 16*c^3*e^2*(d + e*x)^(1/2))*(-(e*(-(4*a*c + b^2)^3)^(1/2) - b^3*e*1i + 8*a*c^2*d + 2*b^2*c*d - a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2)*1i)/(((8*c^2*(b^2*e^3 + 4*a*c*e^3) - 8*c^2*(d + e*x)^(1/2)*(-(e*(-(4*a*c + b^2)^3)^(1/2) - b^3*e*1i + 8*a*c^2*d + 2*b^2*c*d - a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2)*(b^3*e^3*1i + a*b*c*e^3*4i - 8*a*c^2*d*e^2 - 2*b^2*c*d*e^2))*(-(e*(-(4*a*c + b^2)^3)^(1/2) - b^3*e*1i + 8*a*c^2*d + 2*b^2*c*d - a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2) + 16*c^3*e^2*(d + e*x)^(1/2))*(-(e*(-(4*a*c + b^2)^3)^(1/2) - b^3*e*1i + 8*a*c^2*d + 2*b^2*c*d - a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2) + ((8*c^2*(b^2*e^3 + 4*a*c*e^3) + 8*c^2*(d + e*x)^(1/2)*(-(e*(-(4*a*c + b^2)^3)^(1/2) - b^3*e*1i + 8*a*c^2*d + 2*b^2*c*d - a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2)*(b^3*e^3*1i + a*b*c*e^3*4i - 8*a*c^2*d*e^2 - 2*b^2*c*d*e^2))*(-(e*(-(4*a*c + b^2)^3)^(1/2) - b^3*e*1i + 8*a*c^2*d + 2*b^2*c*d - a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2) - 16*c^3*e^2*(d + e*x)^(1/2))*(-(e*(-(4*a*c + b^2)^3)^(1/2) - b^3*e*1i + 8*a*c^2*d + 2*b^2*c*d - a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2)))*(-(e*(-(4*a*c + b^2)^3)^(1/2) - b^3*e*1i + 8*a*c^2*d + 2*b^2*c*d - a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2)*2i - atan((((8*c^2*(b^2*e^3 + 4*a*c*e^3) - 8*c^2*(d + e*x)^(1/2)*((e*(-(4*a*c + b^2)^3)^(1/2) + b^3*e*1i - 8*a*c^2*d - 2*b^2*c*d + a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2)*(b^3*e^3*1i + a*b*c*e^3*4i - 8*a*c^2*d*e^2 - 2*b^2*c*d*e^2))*((e*(-(4*a*c + b^2)^3)^(1/2) + b^3*e*1i - 8*a*c^2*d - 2*b^2*c*d + a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2) + 16*c^3*e^2*(d + e*x)^(1/2))*((e*(-(4*a*c + b^2)^3)^(1/2) + b^3*e*1i - 8*a*c^2*d - 2*b^2*c*d + a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2)*1i - ((8*c^2*(b^2*e^3 + 4*a*c*e^3) + 8*c^2*(d + e*x)^(1/2)*((e*(-(4*a*c + b^2)^3)^(1/2) + b^3*e*1i - 8*a*c^2*d - 2*b^2*c*d + a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2)*(b^3*e^3*1i + a*b*c*e^3*4i - 8*a*c^2*d*e^2 - 2*b^2*c*d*e^2))*((e*(-(4*a*c + b^2)^3)^(1/2) + b^3*e*1i - 8*a*c^2*d - 2*b^2*c*d + a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2) - 16*c^3*e^2*(d + e*x)^(1/2))*((e*(-(4*a*c + b^2)^3)^(1/2) + b^3*e*1i - 8*a*c^2*d - 2*b^2*c*d + a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2)*1i)/(((8*c^2*(b^2*e^3 + 4*a*c*e^3) - 8*c^2*(d + e*x)^(1/2)*((e*(-(4*a*c + b^2)^3)^(1/2) + b^3*e*1i - 8*a*c^2*d - 2*b^2*c*d + a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2)*(b^3*e^3*1i + a*b*c*e^3*4i - 8*a*c^2*d*e^2 - 2*b^2*c*d*e^2))*((e*(-(4*a*c + b^2)^3)^(1/2) + b^3*e*1i - 8*a*c^2*d - 2*b^2*c*d + a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2) + 16*c^3*e^2*(d + e*x)^(1/2))*((e*(-(4*a*c + b^2)^3)^(1/2) + b^3*e*1i - 8*a*c^2*d - 2*b^2*c*d + a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2) + ((8*c^2*(b^2*e^3 + 4*a*c*e^3) + 8*c^2*(d + e*x)^(1/2)*((e*(-(4*a*c + b^2)^3)^(1/2) + b^3*e*1i - 8*a*c^2*d - 2*b^2*c*d + a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2)*(b^3*e^3*1i + a*b*c*e^3*4i - 8*a*c^2*d*e^2 - 2*b^2*c*d*e^2))*((e*(-(4*a*c + b^2)^3)^(1/2) + b^3*e*1i - 8*a*c^2*d - 2*b^2*c*d + a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2) - 16*c^3*e^2*(d + e*x)^(1/2))*((e*(-(4*a*c + b^2)^3)^(1/2) + b^3*e*1i - 8*a*c^2*d - 2*b^2*c*d + a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2)))*((e*(-(4*a*c + b^2)^3)^(1/2) + b^3*e*1i - 8*a*c^2*d - 2*b^2*c*d + a*b*c*e*4i)/(2*(a*b^4*e^2 + b^4*c*d^2 + 16*a^2*c^3*d^2 + 16*a^3*c^2*e^2 - b^5*d*e*1i + 8*a*b^2*c^2*d^2 + 8*a^2*b^2*c*e^2 - a^2*b*c^2*d*e*16i - a*b^3*c*d*e*8i)))^(1/2)*2i","B"
2309,1,200,279,1.044356,"\text{Not used}","int((2*x + 1)^(7/2)/(3*x + 5*x^2 + 2),x)","\frac{16\,{\left(2\,x+1\right)}^{3/2}}{75}-\frac{76\,\sqrt{2\,x+1}}{125}+\frac{4\,{\left(2\,x+1\right)}^{5/2}}{25}+\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{168698+\sqrt{31}\,34021{}\mathrm{i}}\,\sqrt{2\,x+1}\,4354688{}\mathrm{i}}{6103515625\,\left(-\frac{5425941248}{1220703125}+\frac{\sqrt{31}\,579173504{}\mathrm{i}}{1220703125}\right)}+\frac{8709376\,\sqrt{31}\,\sqrt{155}\,\sqrt{168698+\sqrt{31}\,34021{}\mathrm{i}}\,\sqrt{2\,x+1}}{189208984375\,\left(-\frac{5425941248}{1220703125}+\frac{\sqrt{31}\,579173504{}\mathrm{i}}{1220703125}\right)}\right)\,\sqrt{168698+\sqrt{31}\,34021{}\mathrm{i}}\,2{}\mathrm{i}}{19375}-\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{168698-\sqrt{31}\,34021{}\mathrm{i}}\,\sqrt{2\,x+1}\,4354688{}\mathrm{i}}{6103515625\,\left(\frac{5425941248}{1220703125}+\frac{\sqrt{31}\,579173504{}\mathrm{i}}{1220703125}\right)}-\frac{8709376\,\sqrt{31}\,\sqrt{155}\,\sqrt{168698-\sqrt{31}\,34021{}\mathrm{i}}\,\sqrt{2\,x+1}}{189208984375\,\left(\frac{5425941248}{1220703125}+\frac{\sqrt{31}\,579173504{}\mathrm{i}}{1220703125}\right)}\right)\,\sqrt{168698-\sqrt{31}\,34021{}\mathrm{i}}\,2{}\mathrm{i}}{19375}","Not used",1,"(16*(2*x + 1)^(3/2))/75 - (76*(2*x + 1)^(1/2))/125 + (4*(2*x + 1)^(5/2))/25 + (155^(1/2)*atan((155^(1/2)*(31^(1/2)*34021i + 168698)^(1/2)*(2*x + 1)^(1/2)*4354688i)/(6103515625*((31^(1/2)*579173504i)/1220703125 - 5425941248/1220703125)) + (8709376*31^(1/2)*155^(1/2)*(31^(1/2)*34021i + 168698)^(1/2)*(2*x + 1)^(1/2))/(189208984375*((31^(1/2)*579173504i)/1220703125 - 5425941248/1220703125)))*(31^(1/2)*34021i + 168698)^(1/2)*2i)/19375 - (155^(1/2)*atan((155^(1/2)*(168698 - 31^(1/2)*34021i)^(1/2)*(2*x + 1)^(1/2)*4354688i)/(6103515625*((31^(1/2)*579173504i)/1220703125 + 5425941248/1220703125)) - (8709376*31^(1/2)*155^(1/2)*(168698 - 31^(1/2)*34021i)^(1/2)*(2*x + 1)^(1/2))/(189208984375*((31^(1/2)*579173504i)/1220703125 + 5425941248/1220703125)))*(168698 - 31^(1/2)*34021i)^(1/2)*2i)/19375","B"
2310,1,191,266,0.138784,"\text{Not used}","int((2*x + 1)^(5/2)/(3*x + 5*x^2 + 2),x)","\frac{16\,\sqrt{2\,x+1}}{25}+\frac{4\,{\left(2\,x+1\right)}^{3/2}}{15}-\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{-7162-\sqrt{31}\,199{}\mathrm{i}}\,\sqrt{2\,x+1}\,25472{}\mathrm{i}}{48828125\,\left(\frac{4814208}{9765625}+\frac{\sqrt{31}\,713216{}\mathrm{i}}{9765625}\right)}+\frac{50944\,\sqrt{31}\,\sqrt{155}\,\sqrt{-7162-\sqrt{31}\,199{}\mathrm{i}}\,\sqrt{2\,x+1}}{1513671875\,\left(\frac{4814208}{9765625}+\frac{\sqrt{31}\,713216{}\mathrm{i}}{9765625}\right)}\right)\,\sqrt{-7162-\sqrt{31}\,199{}\mathrm{i}}\,2{}\mathrm{i}}{3875}+\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{-7162+\sqrt{31}\,199{}\mathrm{i}}\,\sqrt{2\,x+1}\,25472{}\mathrm{i}}{48828125\,\left(-\frac{4814208}{9765625}+\frac{\sqrt{31}\,713216{}\mathrm{i}}{9765625}\right)}-\frac{50944\,\sqrt{31}\,\sqrt{155}\,\sqrt{-7162+\sqrt{31}\,199{}\mathrm{i}}\,\sqrt{2\,x+1}}{1513671875\,\left(-\frac{4814208}{9765625}+\frac{\sqrt{31}\,713216{}\mathrm{i}}{9765625}\right)}\right)\,\sqrt{-7162+\sqrt{31}\,199{}\mathrm{i}}\,2{}\mathrm{i}}{3875}","Not used",1,"(16*(2*x + 1)^(1/2))/25 + (4*(2*x + 1)^(3/2))/15 - (155^(1/2)*atan((155^(1/2)*(- 31^(1/2)*199i - 7162)^(1/2)*(2*x + 1)^(1/2)*25472i)/(48828125*((31^(1/2)*713216i)/9765625 + 4814208/9765625)) + (50944*31^(1/2)*155^(1/2)*(- 31^(1/2)*199i - 7162)^(1/2)*(2*x + 1)^(1/2))/(1513671875*((31^(1/2)*713216i)/9765625 + 4814208/9765625)))*(- 31^(1/2)*199i - 7162)^(1/2)*2i)/3875 + (155^(1/2)*atan((155^(1/2)*(31^(1/2)*199i - 7162)^(1/2)*(2*x + 1)^(1/2)*25472i)/(48828125*((31^(1/2)*713216i)/9765625 - 4814208/9765625)) - (50944*31^(1/2)*155^(1/2)*(31^(1/2)*199i - 7162)^(1/2)*(2*x + 1)^(1/2))/(1513671875*((31^(1/2)*713216i)/9765625 - 4814208/9765625)))*(31^(1/2)*199i - 7162)^(1/2)*2i)/3875","B"
2311,1,182,253,1.043739,"\text{Not used}","int((2*x + 1)^(3/2)/(3*x + 5*x^2 + 2),x)","\frac{4\,\sqrt{2\,x+1}}{5}-\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{178-\sqrt{31}\,19{}\mathrm{i}}\,\sqrt{2\,x+1}\,2432{}\mathrm{i}}{390625\,\left(-\frac{34048}{78125}+\frac{\sqrt{31}\,17024{}\mathrm{i}}{78125}\right)}+\frac{4864\,\sqrt{31}\,\sqrt{155}\,\sqrt{178-\sqrt{31}\,19{}\mathrm{i}}\,\sqrt{2\,x+1}}{12109375\,\left(-\frac{34048}{78125}+\frac{\sqrt{31}\,17024{}\mathrm{i}}{78125}\right)}\right)\,\sqrt{178-\sqrt{31}\,19{}\mathrm{i}}\,2{}\mathrm{i}}{775}+\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{178+\sqrt{31}\,19{}\mathrm{i}}\,\sqrt{2\,x+1}\,2432{}\mathrm{i}}{390625\,\left(\frac{34048}{78125}+\frac{\sqrt{31}\,17024{}\mathrm{i}}{78125}\right)}-\frac{4864\,\sqrt{31}\,\sqrt{155}\,\sqrt{178+\sqrt{31}\,19{}\mathrm{i}}\,\sqrt{2\,x+1}}{12109375\,\left(\frac{34048}{78125}+\frac{\sqrt{31}\,17024{}\mathrm{i}}{78125}\right)}\right)\,\sqrt{178+\sqrt{31}\,19{}\mathrm{i}}\,2{}\mathrm{i}}{775}","Not used",1,"(4*(2*x + 1)^(1/2))/5 - (155^(1/2)*atan((155^(1/2)*(178 - 31^(1/2)*19i)^(1/2)*(2*x + 1)^(1/2)*2432i)/(390625*((31^(1/2)*17024i)/78125 - 34048/78125)) + (4864*31^(1/2)*155^(1/2)*(178 - 31^(1/2)*19i)^(1/2)*(2*x + 1)^(1/2))/(12109375*((31^(1/2)*17024i)/78125 - 34048/78125)))*(178 - 31^(1/2)*19i)^(1/2)*2i)/775 + (155^(1/2)*atan((155^(1/2)*(31^(1/2)*19i + 178)^(1/2)*(2*x + 1)^(1/2)*2432i)/(390625*((31^(1/2)*17024i)/78125 + 34048/78125)) - (4864*31^(1/2)*155^(1/2)*(31^(1/2)*19i + 178)^(1/2)*(2*x + 1)^(1/2))/(12109375*((31^(1/2)*17024i)/78125 + 34048/78125)))*(31^(1/2)*19i + 178)^(1/2)*2i)/775","B"
2312,1,116,222,0.130190,"\text{Not used}","int((2*x + 1)^(1/2)/(3*x + 5*x^2 + 2),x)","-\frac{2\,\sqrt{155}\,\mathrm{atanh}\left(\sqrt{155}\,\sqrt{-2-\sqrt{31}\,1{}\mathrm{i}}\,\left(\frac{2\,\left(\frac{2}{155}+\frac{\sqrt{31}\,1{}\mathrm{i}}{155}\right)\,\sqrt{2\,x+1}}{7}+\frac{27\,\sqrt{2\,x+1}}{1085}\right)\right)\,\sqrt{-2-\sqrt{31}\,1{}\mathrm{i}}}{155}-\frac{2\,\sqrt{155}\,\mathrm{atanh}\left(-\sqrt{155}\,\sqrt{-2+\sqrt{31}\,1{}\mathrm{i}}\,\left(\frac{2\,\left(-\frac{2}{155}+\frac{\sqrt{31}\,1{}\mathrm{i}}{155}\right)\,\sqrt{2\,x+1}}{7}-\frac{27\,\sqrt{2\,x+1}}{1085}\right)\right)\,\sqrt{-2+\sqrt{31}\,1{}\mathrm{i}}}{155}","Not used",1,"- (2*155^(1/2)*atanh(155^(1/2)*(- 31^(1/2)*1i - 2)^(1/2)*((2*((31^(1/2)*1i)/155 + 2/155)*(2*x + 1)^(1/2))/7 + (27*(2*x + 1)^(1/2))/1085))*(- 31^(1/2)*1i - 2)^(1/2))/155 - (2*155^(1/2)*atanh(-155^(1/2)*(31^(1/2)*1i - 2)^(1/2)*((2*((31^(1/2)*1i)/155 - 2/155)*(2*x + 1)^(1/2))/7 - (27*(2*x + 1)^(1/2))/1085))*(31^(1/2)*1i - 2)^(1/2))/155","B"
2313,1,167,218,1.018854,"\text{Not used}","int(1/((2*x + 1)^(1/2)*(3*x + 5*x^2 + 2)),x)","\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{256\,\sqrt{7}\,\sqrt{-2-\sqrt{31}\,1{}\mathrm{i}}\,\sqrt{2\,x+1}}{6125\,\left(\frac{256}{875}+\frac{\sqrt{31}\,128{}\mathrm{i}}{875}\right)}+\frac{\sqrt{217}\,\sqrt{-2-\sqrt{31}\,1{}\mathrm{i}}\,\sqrt{2\,x+1}\,128{}\mathrm{i}}{6125\,\left(\frac{256}{875}+\frac{\sqrt{31}\,128{}\mathrm{i}}{875}\right)}\right)\,\sqrt{-2-\sqrt{31}\,1{}\mathrm{i}}\,2{}\mathrm{i}}{217}+\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{256\,\sqrt{7}\,\sqrt{-2+\sqrt{31}\,1{}\mathrm{i}}\,\sqrt{2\,x+1}}{6125\,\left(-\frac{256}{875}+\frac{\sqrt{31}\,128{}\mathrm{i}}{875}\right)}-\frac{\sqrt{217}\,\sqrt{-2+\sqrt{31}\,1{}\mathrm{i}}\,\sqrt{2\,x+1}\,128{}\mathrm{i}}{6125\,\left(-\frac{256}{875}+\frac{\sqrt{31}\,128{}\mathrm{i}}{875}\right)}\right)\,\sqrt{-2+\sqrt{31}\,1{}\mathrm{i}}\,2{}\mathrm{i}}{217}","Not used",1,"(217^(1/2)*atan((256*7^(1/2)*(- 31^(1/2)*1i - 2)^(1/2)*(2*x + 1)^(1/2))/(6125*((31^(1/2)*128i)/875 + 256/875)) + (217^(1/2)*(- 31^(1/2)*1i - 2)^(1/2)*(2*x + 1)^(1/2)*128i)/(6125*((31^(1/2)*128i)/875 + 256/875)))*(- 31^(1/2)*1i - 2)^(1/2)*2i)/217 + (217^(1/2)*atan((256*7^(1/2)*(31^(1/2)*1i - 2)^(1/2)*(2*x + 1)^(1/2))/(6125*((31^(1/2)*128i)/875 - 256/875)) - (217^(1/2)*(31^(1/2)*1i - 2)^(1/2)*(2*x + 1)^(1/2)*128i)/(6125*((31^(1/2)*128i)/875 - 256/875)))*(31^(1/2)*1i - 2)^(1/2)*2i)/217","B"
2314,1,182,253,0.136634,"\text{Not used}","int(1/((2*x + 1)^(3/2)*(3*x + 5*x^2 + 2)),x)","-\frac{4}{7\,\sqrt{2\,x+1}}-\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{178-\sqrt{31}\,19{}\mathrm{i}}\,\sqrt{2\,x+1}\,2432{}\mathrm{i}}{2100875\,\left(\frac{65664}{300125}+\frac{\sqrt{31}\,9728{}\mathrm{i}}{300125}\right)}-\frac{4864\,\sqrt{31}\,\sqrt{217}\,\sqrt{178-\sqrt{31}\,19{}\mathrm{i}}\,\sqrt{2\,x+1}}{65127125\,\left(\frac{65664}{300125}+\frac{\sqrt{31}\,9728{}\mathrm{i}}{300125}\right)}\right)\,\sqrt{178-\sqrt{31}\,19{}\mathrm{i}}\,2{}\mathrm{i}}{1519}+\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{178+\sqrt{31}\,19{}\mathrm{i}}\,\sqrt{2\,x+1}\,2432{}\mathrm{i}}{2100875\,\left(-\frac{65664}{300125}+\frac{\sqrt{31}\,9728{}\mathrm{i}}{300125}\right)}+\frac{4864\,\sqrt{31}\,\sqrt{217}\,\sqrt{178+\sqrt{31}\,19{}\mathrm{i}}\,\sqrt{2\,x+1}}{65127125\,\left(-\frac{65664}{300125}+\frac{\sqrt{31}\,9728{}\mathrm{i}}{300125}\right)}\right)\,\sqrt{178+\sqrt{31}\,19{}\mathrm{i}}\,2{}\mathrm{i}}{1519}","Not used",1,"(217^(1/2)*atan((217^(1/2)*(31^(1/2)*19i + 178)^(1/2)*(2*x + 1)^(1/2)*2432i)/(2100875*((31^(1/2)*9728i)/300125 - 65664/300125)) + (4864*31^(1/2)*217^(1/2)*(31^(1/2)*19i + 178)^(1/2)*(2*x + 1)^(1/2))/(65127125*((31^(1/2)*9728i)/300125 - 65664/300125)))*(31^(1/2)*19i + 178)^(1/2)*2i)/1519 - (217^(1/2)*atan((217^(1/2)*(178 - 31^(1/2)*19i)^(1/2)*(2*x + 1)^(1/2)*2432i)/(2100875*((31^(1/2)*9728i)/300125 + 65664/300125)) - (4864*31^(1/2)*217^(1/2)*(178 - 31^(1/2)*19i)^(1/2)*(2*x + 1)^(1/2))/(65127125*((31^(1/2)*9728i)/300125 + 65664/300125)))*(178 - 31^(1/2)*19i)^(1/2)*2i)/1519 - 4/(7*(2*x + 1)^(1/2))","B"
2315,1,187,266,0.147967,"\text{Not used}","int(1/((2*x + 1)^(5/2)*(3*x + 5*x^2 + 2)),x)","-\frac{\frac{32\,x}{49}+\frac{76}{147}}{{\left(2\,x+1\right)}^{3/2}}+\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{-7162-\sqrt{31}\,199{}\mathrm{i}}\,\sqrt{2\,x+1}\,25472{}\mathrm{i}}{720600125\,\left(-\frac{4534016}{102942875}+\frac{\sqrt{31}\,483968{}\mathrm{i}}{102942875}\right)}-\frac{50944\,\sqrt{31}\,\sqrt{217}\,\sqrt{-7162-\sqrt{31}\,199{}\mathrm{i}}\,\sqrt{2\,x+1}}{22338603875\,\left(-\frac{4534016}{102942875}+\frac{\sqrt{31}\,483968{}\mathrm{i}}{102942875}\right)}\right)\,\sqrt{-7162-\sqrt{31}\,199{}\mathrm{i}}\,2{}\mathrm{i}}{10633}-\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{-7162+\sqrt{31}\,199{}\mathrm{i}}\,\sqrt{2\,x+1}\,25472{}\mathrm{i}}{720600125\,\left(\frac{4534016}{102942875}+\frac{\sqrt{31}\,483968{}\mathrm{i}}{102942875}\right)}+\frac{50944\,\sqrt{31}\,\sqrt{217}\,\sqrt{-7162+\sqrt{31}\,199{}\mathrm{i}}\,\sqrt{2\,x+1}}{22338603875\,\left(\frac{4534016}{102942875}+\frac{\sqrt{31}\,483968{}\mathrm{i}}{102942875}\right)}\right)\,\sqrt{-7162+\sqrt{31}\,199{}\mathrm{i}}\,2{}\mathrm{i}}{10633}","Not used",1,"(217^(1/2)*atan((217^(1/2)*(- 31^(1/2)*199i - 7162)^(1/2)*(2*x + 1)^(1/2)*25472i)/(720600125*((31^(1/2)*483968i)/102942875 - 4534016/102942875)) - (50944*31^(1/2)*217^(1/2)*(- 31^(1/2)*199i - 7162)^(1/2)*(2*x + 1)^(1/2))/(22338603875*((31^(1/2)*483968i)/102942875 - 4534016/102942875)))*(- 31^(1/2)*199i - 7162)^(1/2)*2i)/10633 - ((32*x)/49 + 76/147)/(2*x + 1)^(3/2) - (217^(1/2)*atan((217^(1/2)*(31^(1/2)*199i - 7162)^(1/2)*(2*x + 1)^(1/2)*25472i)/(720600125*((31^(1/2)*483968i)/102942875 + 4534016/102942875)) + (50944*31^(1/2)*217^(1/2)*(31^(1/2)*199i - 7162)^(1/2)*(2*x + 1)^(1/2))/(22338603875*((31^(1/2)*483968i)/102942875 + 4534016/102942875)))*(31^(1/2)*199i - 7162)^(1/2)*2i)/10633","B"
2316,1,216,296,0.148451,"\text{Not used}","int((2*x + 1)^(7/2)/(3*x + 5*x^2 + 2)^2,x)","\frac{16\,\sqrt{2\,x+1}}{25}+\frac{\frac{756\,\sqrt{2\,x+1}}{3875}-\frac{712\,{\left(2\,x+1\right)}^{3/2}}{3875}}{{\left(2\,x+1\right)}^2-\frac{8\,x}{5}+\frac{3}{5}}-\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{5682718-\sqrt{31}\,135439{}\mathrm{i}}\,\sqrt{2\,x+1}\,559232{}\mathrm{i}}{46923828125\,\left(-\frac{2004287488}{9384765625}+\frac{\sqrt{31}\,591108224{}\mathrm{i}}{9384765625}\right)}+\frac{1118464\,\sqrt{31}\,\sqrt{155}\,\sqrt{5682718-\sqrt{31}\,135439{}\mathrm{i}}\,\sqrt{2\,x+1}}{1454638671875\,\left(-\frac{2004287488}{9384765625}+\frac{\sqrt{31}\,591108224{}\mathrm{i}}{9384765625}\right)}\right)\,\sqrt{5682718-\sqrt{31}\,135439{}\mathrm{i}}\,2{}\mathrm{i}}{120125}+\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{5682718+\sqrt{31}\,135439{}\mathrm{i}}\,\sqrt{2\,x+1}\,559232{}\mathrm{i}}{46923828125\,\left(\frac{2004287488}{9384765625}+\frac{\sqrt{31}\,591108224{}\mathrm{i}}{9384765625}\right)}-\frac{1118464\,\sqrt{31}\,\sqrt{155}\,\sqrt{5682718+\sqrt{31}\,135439{}\mathrm{i}}\,\sqrt{2\,x+1}}{1454638671875\,\left(\frac{2004287488}{9384765625}+\frac{\sqrt{31}\,591108224{}\mathrm{i}}{9384765625}\right)}\right)\,\sqrt{5682718+\sqrt{31}\,135439{}\mathrm{i}}\,2{}\mathrm{i}}{120125}","Not used",1,"(16*(2*x + 1)^(1/2))/25 + ((756*(2*x + 1)^(1/2))/3875 - (712*(2*x + 1)^(3/2))/3875)/((2*x + 1)^2 - (8*x)/5 + 3/5) - (155^(1/2)*atan((155^(1/2)*(5682718 - 31^(1/2)*135439i)^(1/2)*(2*x + 1)^(1/2)*559232i)/(46923828125*((31^(1/2)*591108224i)/9384765625 - 2004287488/9384765625)) + (1118464*31^(1/2)*155^(1/2)*(5682718 - 31^(1/2)*135439i)^(1/2)*(2*x + 1)^(1/2))/(1454638671875*((31^(1/2)*591108224i)/9384765625 - 2004287488/9384765625)))*(5682718 - 31^(1/2)*135439i)^(1/2)*2i)/120125 + (155^(1/2)*atan((155^(1/2)*(31^(1/2)*135439i + 5682718)^(1/2)*(2*x + 1)^(1/2)*559232i)/(46923828125*((31^(1/2)*591108224i)/9384765625 + 2004287488/9384765625)) - (1118464*31^(1/2)*155^(1/2)*(31^(1/2)*135439i + 5682718)^(1/2)*(2*x + 1)^(1/2))/(1454638671875*((31^(1/2)*591108224i)/9384765625 + 2004287488/9384765625)))*(31^(1/2)*135439i + 5682718)^(1/2)*2i)/120125","B"
2317,1,208,283,0.157988,"\text{Not used}","int((2*x + 1)^(5/2)/(3*x + 5*x^2 + 2)^2,x)","-\frac{\frac{56\,\sqrt{2\,x+1}}{775}+\frac{108\,{\left(2\,x+1\right)}^{3/2}}{775}}{{\left(2\,x+1\right)}^2-\frac{8\,x}{5}+\frac{3}{5}}-\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{-32678-\sqrt{31}\,9269{}\mathrm{i}}\,\sqrt{2\,x+1}\,38272{}\mathrm{i}}{375390625\,\left(-\frac{27058304}{75078125}+\frac{\sqrt{31}\,535808{}\mathrm{i}}{75078125}\right)}-\frac{76544\,\sqrt{31}\,\sqrt{155}\,\sqrt{-32678-\sqrt{31}\,9269{}\mathrm{i}}\,\sqrt{2\,x+1}}{11637109375\,\left(-\frac{27058304}{75078125}+\frac{\sqrt{31}\,535808{}\mathrm{i}}{75078125}\right)}\right)\,\sqrt{-32678-\sqrt{31}\,9269{}\mathrm{i}}\,2{}\mathrm{i}}{24025}+\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{-32678+\sqrt{31}\,9269{}\mathrm{i}}\,\sqrt{2\,x+1}\,38272{}\mathrm{i}}{375390625\,\left(\frac{27058304}{75078125}+\frac{\sqrt{31}\,535808{}\mathrm{i}}{75078125}\right)}+\frac{76544\,\sqrt{31}\,\sqrt{155}\,\sqrt{-32678+\sqrt{31}\,9269{}\mathrm{i}}\,\sqrt{2\,x+1}}{11637109375\,\left(\frac{27058304}{75078125}+\frac{\sqrt{31}\,535808{}\mathrm{i}}{75078125}\right)}\right)\,\sqrt{-32678+\sqrt{31}\,9269{}\mathrm{i}}\,2{}\mathrm{i}}{24025}","Not used",1,"(155^(1/2)*atan((155^(1/2)*(31^(1/2)*9269i - 32678)^(1/2)*(2*x + 1)^(1/2)*38272i)/(375390625*((31^(1/2)*535808i)/75078125 + 27058304/75078125)) + (76544*31^(1/2)*155^(1/2)*(31^(1/2)*9269i - 32678)^(1/2)*(2*x + 1)^(1/2))/(11637109375*((31^(1/2)*535808i)/75078125 + 27058304/75078125)))*(31^(1/2)*9269i - 32678)^(1/2)*2i)/24025 - (155^(1/2)*atan((155^(1/2)*(- 31^(1/2)*9269i - 32678)^(1/2)*(2*x + 1)^(1/2)*38272i)/(375390625*((31^(1/2)*535808i)/75078125 - 27058304/75078125)) - (76544*31^(1/2)*155^(1/2)*(- 31^(1/2)*9269i - 32678)^(1/2)*(2*x + 1)^(1/2))/(11637109375*((31^(1/2)*535808i)/75078125 - 27058304/75078125)))*(- 31^(1/2)*9269i - 32678)^(1/2)*2i)/24025 - ((56*(2*x + 1)^(1/2))/775 + (108*(2*x + 1)^(3/2))/775)/((2*x + 1)^2 - (8*x)/5 + 3/5)","B"
2318,1,208,270,1.039748,"\text{Not used}","int((2*x + 1)^(3/2)/(3*x + 5*x^2 + 2)^2,x)","-\frac{\frac{28\,\sqrt{2\,x+1}}{155}-\frac{8\,{\left(2\,x+1\right)}^{3/2}}{155}}{{\left(2\,x+1\right)}^2-\frac{8\,x}{5}+\frac{3}{5}}+\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{-218-\sqrt{31}\,31{}\mathrm{i}}\,\sqrt{2\,x+1}\,128{}\mathrm{i}}{3003125\,\left(\frac{3584}{600625}+\frac{\sqrt{31}\,896{}\mathrm{i}}{600625}\right)}+\frac{256\,\sqrt{31}\,\sqrt{155}\,\sqrt{-218-\sqrt{31}\,31{}\mathrm{i}}\,\sqrt{2\,x+1}}{93096875\,\left(\frac{3584}{600625}+\frac{\sqrt{31}\,896{}\mathrm{i}}{600625}\right)}\right)\,\sqrt{-218-\sqrt{31}\,31{}\mathrm{i}}\,2{}\mathrm{i}}{4805}-\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{-218+\sqrt{31}\,31{}\mathrm{i}}\,\sqrt{2\,x+1}\,128{}\mathrm{i}}{3003125\,\left(-\frac{3584}{600625}+\frac{\sqrt{31}\,896{}\mathrm{i}}{600625}\right)}-\frac{256\,\sqrt{31}\,\sqrt{155}\,\sqrt{-218+\sqrt{31}\,31{}\mathrm{i}}\,\sqrt{2\,x+1}}{93096875\,\left(-\frac{3584}{600625}+\frac{\sqrt{31}\,896{}\mathrm{i}}{600625}\right)}\right)\,\sqrt{-218+\sqrt{31}\,31{}\mathrm{i}}\,2{}\mathrm{i}}{4805}","Not used",1,"(155^(1/2)*atan((155^(1/2)*(- 31^(1/2)*31i - 218)^(1/2)*(2*x + 1)^(1/2)*128i)/(3003125*((31^(1/2)*896i)/600625 + 3584/600625)) + (256*31^(1/2)*155^(1/2)*(- 31^(1/2)*31i - 218)^(1/2)*(2*x + 1)^(1/2))/(93096875*((31^(1/2)*896i)/600625 + 3584/600625)))*(- 31^(1/2)*31i - 218)^(1/2)*2i)/4805 - ((28*(2*x + 1)^(1/2))/155 - (8*(2*x + 1)^(3/2))/155)/((2*x + 1)^2 - (8*x)/5 + 3/5) - (155^(1/2)*atan((155^(1/2)*(31^(1/2)*31i - 218)^(1/2)*(2*x + 1)^(1/2)*128i)/(3003125*((31^(1/2)*896i)/600625 - 3584/600625)) - (256*31^(1/2)*155^(1/2)*(31^(1/2)*31i - 218)^(1/2)*(2*x + 1)^(1/2))/(93096875*((31^(1/2)*896i)/600625 - 3584/600625)))*(31^(1/2)*31i - 218)^(1/2)*2i)/4805","B"
2319,1,208,270,1.031656,"\text{Not used}","int((2*x + 1)^(1/2)/(3*x + 5*x^2 + 2)^2,x)","-\frac{\frac{8\,\sqrt{2\,x+1}}{155}-\frac{4\,{\left(2\,x+1\right)}^{3/2}}{31}}{{\left(2\,x+1\right)}^2-\frac{8\,x}{5}+\frac{3}{5}}-\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{-218-\sqrt{31}\,31{}\mathrm{i}}\,\sqrt{2\,x+1}\,128{}\mathrm{i}}{5886125\,\left(-\frac{4992}{840875}+\frac{\sqrt{31}\,256{}\mathrm{i}}{840875}\right)}-\frac{256\,\sqrt{31}\,\sqrt{217}\,\sqrt{-218-\sqrt{31}\,31{}\mathrm{i}}\,\sqrt{2\,x+1}}{182469875\,\left(-\frac{4992}{840875}+\frac{\sqrt{31}\,256{}\mathrm{i}}{840875}\right)}\right)\,\sqrt{-218-\sqrt{31}\,31{}\mathrm{i}}\,2{}\mathrm{i}}{6727}+\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{-218+\sqrt{31}\,31{}\mathrm{i}}\,\sqrt{2\,x+1}\,128{}\mathrm{i}}{5886125\,\left(\frac{4992}{840875}+\frac{\sqrt{31}\,256{}\mathrm{i}}{840875}\right)}+\frac{256\,\sqrt{31}\,\sqrt{217}\,\sqrt{-218+\sqrt{31}\,31{}\mathrm{i}}\,\sqrt{2\,x+1}}{182469875\,\left(\frac{4992}{840875}+\frac{\sqrt{31}\,256{}\mathrm{i}}{840875}\right)}\right)\,\sqrt{-218+\sqrt{31}\,31{}\mathrm{i}}\,2{}\mathrm{i}}{6727}","Not used",1,"(217^(1/2)*atan((217^(1/2)*(31^(1/2)*31i - 218)^(1/2)*(2*x + 1)^(1/2)*128i)/(5886125*((31^(1/2)*256i)/840875 + 4992/840875)) + (256*31^(1/2)*217^(1/2)*(31^(1/2)*31i - 218)^(1/2)*(2*x + 1)^(1/2))/(182469875*((31^(1/2)*256i)/840875 + 4992/840875)))*(31^(1/2)*31i - 218)^(1/2)*2i)/6727 - (217^(1/2)*atan((217^(1/2)*(- 31^(1/2)*31i - 218)^(1/2)*(2*x + 1)^(1/2)*128i)/(5886125*((31^(1/2)*256i)/840875 - 4992/840875)) - (256*31^(1/2)*217^(1/2)*(- 31^(1/2)*31i - 218)^(1/2)*(2*x + 1)^(1/2))/(182469875*((31^(1/2)*256i)/840875 - 4992/840875)))*(- 31^(1/2)*31i - 218)^(1/2)*2i)/6727 - ((8*(2*x + 1)^(1/2))/155 - (4*(2*x + 1)^(3/2))/31)/((2*x + 1)^2 - (8*x)/5 + 3/5)","B"
2320,1,207,270,1.025959,"\text{Not used}","int(1/((2*x + 1)^(1/2)*(3*x + 5*x^2 + 2)^2),x)","\frac{\frac{108\,\sqrt{2\,x+1}}{1085}+\frac{8\,{\left(2\,x+1\right)}^{3/2}}{217}}{{\left(2\,x+1\right)}^2-\frac{8\,x}{5}+\frac{3}{5}}+\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{-32678-\sqrt{31}\,9269{}\mathrm{i}}\,\sqrt{2\,x+1}\,38272{}\mathrm{i}}{2018940875\,\left(\frac{10103808}{288420125}+\frac{\sqrt{31}\,3712384{}\mathrm{i}}{288420125}\right)}+\frac{76544\,\sqrt{31}\,\sqrt{217}\,\sqrt{-32678-\sqrt{31}\,9269{}\mathrm{i}}\,\sqrt{2\,x+1}}{62587167125\,\left(\frac{10103808}{288420125}+\frac{\sqrt{31}\,3712384{}\mathrm{i}}{288420125}\right)}\right)\,\sqrt{-32678-\sqrt{31}\,9269{}\mathrm{i}}\,2{}\mathrm{i}}{47089}-\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{-32678+\sqrt{31}\,9269{}\mathrm{i}}\,\sqrt{2\,x+1}\,38272{}\mathrm{i}}{2018940875\,\left(-\frac{10103808}{288420125}+\frac{\sqrt{31}\,3712384{}\mathrm{i}}{288420125}\right)}-\frac{76544\,\sqrt{31}\,\sqrt{217}\,\sqrt{-32678+\sqrt{31}\,9269{}\mathrm{i}}\,\sqrt{2\,x+1}}{62587167125\,\left(-\frac{10103808}{288420125}+\frac{\sqrt{31}\,3712384{}\mathrm{i}}{288420125}\right)}\right)\,\sqrt{-32678+\sqrt{31}\,9269{}\mathrm{i}}\,2{}\mathrm{i}}{47089}","Not used",1,"((108*(2*x + 1)^(1/2))/1085 + (8*(2*x + 1)^(3/2))/217)/((2*x + 1)^2 - (8*x)/5 + 3/5) + (217^(1/2)*atan((217^(1/2)*(- 31^(1/2)*9269i - 32678)^(1/2)*(2*x + 1)^(1/2)*38272i)/(2018940875*((31^(1/2)*3712384i)/288420125 + 10103808/288420125)) + (76544*31^(1/2)*217^(1/2)*(- 31^(1/2)*9269i - 32678)^(1/2)*(2*x + 1)^(1/2))/(62587167125*((31^(1/2)*3712384i)/288420125 + 10103808/288420125)))*(- 31^(1/2)*9269i - 32678)^(1/2)*2i)/47089 - (217^(1/2)*atan((217^(1/2)*(31^(1/2)*9269i - 32678)^(1/2)*(2*x + 1)^(1/2)*38272i)/(2018940875*((31^(1/2)*3712384i)/288420125 - 10103808/288420125)) - (76544*31^(1/2)*217^(1/2)*(31^(1/2)*9269i - 32678)^(1/2)*(2*x + 1)^(1/2))/(62587167125*((31^(1/2)*3712384i)/288420125 - 10103808/288420125)))*(31^(1/2)*9269i - 32678)^(1/2)*2i)/47089","B"
2321,1,217,283,1.038239,"\text{Not used}","int(1/((2*x + 1)^(3/2)*(3*x + 5*x^2 + 2)^2),x)","-\frac{\frac{604\,{\left(2\,x+1\right)}^2}{1519}-\frac{5392\,x}{7595}+\frac{776}{7595}}{\frac{7\,\sqrt{2\,x+1}}{5}-\frac{4\,{\left(2\,x+1\right)}^{3/2}}{5}+{\left(2\,x+1\right)}^{5/2}}-\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{5682718-\sqrt{31}\,135439{}\mathrm{i}}\,\sqrt{2\,x+1}\,559232{}\mathrm{i}}{692496720125\,\left(\frac{2045111424}{98928102875}+\frac{\sqrt{31}\,455214848{}\mathrm{i}}{98928102875}\right)}-\frac{1118464\,\sqrt{31}\,\sqrt{217}\,\sqrt{5682718-\sqrt{31}\,135439{}\mathrm{i}}\,\sqrt{2\,x+1}}{21467398323875\,\left(\frac{2045111424}{98928102875}+\frac{\sqrt{31}\,455214848{}\mathrm{i}}{98928102875}\right)}\right)\,\sqrt{5682718-\sqrt{31}\,135439{}\mathrm{i}}\,2{}\mathrm{i}}{329623}+\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{5682718+\sqrt{31}\,135439{}\mathrm{i}}\,\sqrt{2\,x+1}\,559232{}\mathrm{i}}{692496720125\,\left(-\frac{2045111424}{98928102875}+\frac{\sqrt{31}\,455214848{}\mathrm{i}}{98928102875}\right)}+\frac{1118464\,\sqrt{31}\,\sqrt{217}\,\sqrt{5682718+\sqrt{31}\,135439{}\mathrm{i}}\,\sqrt{2\,x+1}}{21467398323875\,\left(-\frac{2045111424}{98928102875}+\frac{\sqrt{31}\,455214848{}\mathrm{i}}{98928102875}\right)}\right)\,\sqrt{5682718+\sqrt{31}\,135439{}\mathrm{i}}\,2{}\mathrm{i}}{329623}","Not used",1,"(217^(1/2)*atan((217^(1/2)*(31^(1/2)*135439i + 5682718)^(1/2)*(2*x + 1)^(1/2)*559232i)/(692496720125*((31^(1/2)*455214848i)/98928102875 - 2045111424/98928102875)) + (1118464*31^(1/2)*217^(1/2)*(31^(1/2)*135439i + 5682718)^(1/2)*(2*x + 1)^(1/2))/(21467398323875*((31^(1/2)*455214848i)/98928102875 - 2045111424/98928102875)))*(31^(1/2)*135439i + 5682718)^(1/2)*2i)/329623 - (217^(1/2)*atan((217^(1/2)*(5682718 - 31^(1/2)*135439i)^(1/2)*(2*x + 1)^(1/2)*559232i)/(692496720125*((31^(1/2)*455214848i)/98928102875 + 2045111424/98928102875)) - (1118464*31^(1/2)*217^(1/2)*(5682718 - 31^(1/2)*135439i)^(1/2)*(2*x + 1)^(1/2))/(21467398323875*((31^(1/2)*455214848i)/98928102875 + 2045111424/98928102875)))*(5682718 - 31^(1/2)*135439i)^(1/2)*2i)/329623 - ((604*(2*x + 1)^2)/1519 - (5392*x)/7595 + 776/7595)/((7*(2*x + 1)^(1/2))/5 - (4*(2*x + 1)^(3/2))/5 + (2*x + 1)^(5/2))","B"
2322,1,226,296,0.170053,"\text{Not used}","int(1/((2*x + 1)^(5/2)*(3*x + 5*x^2 + 2)^2),x)","-\frac{\frac{128\,x}{147}-\frac{5492\,{\left(2\,x+1\right)}^2}{31899}+\frac{4680\,{\left(2\,x+1\right)}^3}{10633}+\frac{144}{245}}{\frac{7\,{\left(2\,x+1\right)}^{3/2}}{5}-\frac{4\,{\left(2\,x+1\right)}^{5/2}}{5}+{\left(2\,x+1\right)}^{7/2}}+\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{-12504542-\sqrt{31}\,1667459{}\mathrm{i}}\,\sqrt{2\,x+1}\,6884992{}\mathrm{i}}{1900211000023\,\left(-\frac{63259306496}{271458714289}+\frac{\sqrt{31}\,3435611008{}\mathrm{i}}{271458714289}\right)}-\frac{13769984\,\sqrt{31}\,\sqrt{217}\,\sqrt{-12504542-\sqrt{31}\,1667459{}\mathrm{i}}\,\sqrt{2\,x+1}}{58906541000713\,\left(-\frac{63259306496}{271458714289}+\frac{\sqrt{31}\,3435611008{}\mathrm{i}}{271458714289}\right)}\right)\,\sqrt{-12504542-\sqrt{31}\,1667459{}\mathrm{i}}\,10{}\mathrm{i}}{2307361}-\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{-12504542+\sqrt{31}\,1667459{}\mathrm{i}}\,\sqrt{2\,x+1}\,6884992{}\mathrm{i}}{1900211000023\,\left(\frac{63259306496}{271458714289}+\frac{\sqrt{31}\,3435611008{}\mathrm{i}}{271458714289}\right)}+\frac{13769984\,\sqrt{31}\,\sqrt{217}\,\sqrt{-12504542+\sqrt{31}\,1667459{}\mathrm{i}}\,\sqrt{2\,x+1}}{58906541000713\,\left(\frac{63259306496}{271458714289}+\frac{\sqrt{31}\,3435611008{}\mathrm{i}}{271458714289}\right)}\right)\,\sqrt{-12504542+\sqrt{31}\,1667459{}\mathrm{i}}\,10{}\mathrm{i}}{2307361}","Not used",1,"(217^(1/2)*atan((217^(1/2)*(- 31^(1/2)*1667459i - 12504542)^(1/2)*(2*x + 1)^(1/2)*6884992i)/(1900211000023*((31^(1/2)*3435611008i)/271458714289 - 63259306496/271458714289)) - (13769984*31^(1/2)*217^(1/2)*(- 31^(1/2)*1667459i - 12504542)^(1/2)*(2*x + 1)^(1/2))/(58906541000713*((31^(1/2)*3435611008i)/271458714289 - 63259306496/271458714289)))*(- 31^(1/2)*1667459i - 12504542)^(1/2)*10i)/2307361 - ((128*x)/147 - (5492*(2*x + 1)^2)/31899 + (4680*(2*x + 1)^3)/10633 + 144/245)/((7*(2*x + 1)^(3/2))/5 - (4*(2*x + 1)^(5/2))/5 + (2*x + 1)^(7/2)) - (217^(1/2)*atan((217^(1/2)*(31^(1/2)*1667459i - 12504542)^(1/2)*(2*x + 1)^(1/2)*6884992i)/(1900211000023*((31^(1/2)*3435611008i)/271458714289 + 63259306496/271458714289)) + (13769984*31^(1/2)*217^(1/2)*(31^(1/2)*1667459i - 12504542)^(1/2)*(2*x + 1)^(1/2))/(58906541000713*((31^(1/2)*3435611008i)/271458714289 + 63259306496/271458714289)))*(31^(1/2)*1667459i - 12504542)^(1/2)*10i)/2307361","B"
2323,1,245,313,1.066817,"\text{Not used}","int((2*x + 1)^(9/2)/(3*x + 5*x^2 + 2)^3,x)","\frac{\frac{77616\,\sqrt{2\,x+1}}{600625}+\frac{29386\,{\left(2\,x+1\right)}^{3/2}}{600625}+\frac{30664\,{\left(2\,x+1\right)}^{5/2}}{600625}+\frac{3446\,{\left(2\,x+1\right)}^{7/2}}{24025}}{\frac{112\,x}{25}-\frac{86\,{\left(2\,x+1\right)}^2}{25}+\frac{8\,{\left(2\,x+1\right)}^3}{5}-{\left(2\,x+1\right)}^4+\frac{7}{25}}-\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{-250141922-\sqrt{31}\,52010281{}\mathrm{i}}\,\sqrt{2\,x+1}\,23380272{}\mathrm{i}}{45093798828125\,\left(-\frac{1294074674928}{9018759765625}+\frac{\sqrt{31}\,43206742656{}\mathrm{i}}{9018759765625}\right)}-\frac{46760544\,\sqrt{31}\,\sqrt{155}\,\sqrt{-250141922-\sqrt{31}\,52010281{}\mathrm{i}}\,\sqrt{2\,x+1}}{1397907763671875\,\left(-\frac{1294074674928}{9018759765625}+\frac{\sqrt{31}\,43206742656{}\mathrm{i}}{9018759765625}\right)}\right)\,\sqrt{-250141922-\sqrt{31}\,52010281{}\mathrm{i}}\,3{}\mathrm{i}}{3723875}+\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{-250141922+\sqrt{31}\,52010281{}\mathrm{i}}\,\sqrt{2\,x+1}\,23380272{}\mathrm{i}}{45093798828125\,\left(\frac{1294074674928}{9018759765625}+\frac{\sqrt{31}\,43206742656{}\mathrm{i}}{9018759765625}\right)}+\frac{46760544\,\sqrt{31}\,\sqrt{155}\,\sqrt{-250141922+\sqrt{31}\,52010281{}\mathrm{i}}\,\sqrt{2\,x+1}}{1397907763671875\,\left(\frac{1294074674928}{9018759765625}+\frac{\sqrt{31}\,43206742656{}\mathrm{i}}{9018759765625}\right)}\right)\,\sqrt{-250141922+\sqrt{31}\,52010281{}\mathrm{i}}\,3{}\mathrm{i}}{3723875}","Not used",1,"((77616*(2*x + 1)^(1/2))/600625 + (29386*(2*x + 1)^(3/2))/600625 + (30664*(2*x + 1)^(5/2))/600625 + (3446*(2*x + 1)^(7/2))/24025)/((112*x)/25 - (86*(2*x + 1)^2)/25 + (8*(2*x + 1)^3)/5 - (2*x + 1)^4 + 7/25) - (155^(1/2)*atan((155^(1/2)*(- 31^(1/2)*52010281i - 250141922)^(1/2)*(2*x + 1)^(1/2)*23380272i)/(45093798828125*((31^(1/2)*43206742656i)/9018759765625 - 1294074674928/9018759765625)) - (46760544*31^(1/2)*155^(1/2)*(- 31^(1/2)*52010281i - 250141922)^(1/2)*(2*x + 1)^(1/2))/(1397907763671875*((31^(1/2)*43206742656i)/9018759765625 - 1294074674928/9018759765625)))*(- 31^(1/2)*52010281i - 250141922)^(1/2)*3i)/3723875 + (155^(1/2)*atan((155^(1/2)*(31^(1/2)*52010281i - 250141922)^(1/2)*(2*x + 1)^(1/2)*23380272i)/(45093798828125*((31^(1/2)*43206742656i)/9018759765625 + 1294074674928/9018759765625)) + (46760544*31^(1/2)*155^(1/2)*(31^(1/2)*52010281i - 250141922)^(1/2)*(2*x + 1)^(1/2))/(1397907763671875*((31^(1/2)*43206742656i)/9018759765625 + 1294074674928/9018759765625)))*(31^(1/2)*52010281i - 250141922)^(1/2)*3i)/3723875","B"
2324,1,245,300,1.064691,"\text{Not used}","int((2*x + 1)^(7/2)/(3*x + 5*x^2 + 2)^3,x)","\frac{\frac{17542\,\sqrt{2\,x+1}}{120125}-\frac{14168\,{\left(2\,x+1\right)}^{3/2}}{120125}+\frac{23578\,{\left(2\,x+1\right)}^{5/2}}{120125}-\frac{1088\,{\left(2\,x+1\right)}^{7/2}}{24025}}{\frac{112\,x}{25}-\frac{86\,{\left(2\,x+1\right)}^2}{25}+\frac{8\,{\left(2\,x+1\right)}^3}{5}-{\left(2\,x+1\right)}^4+\frac{7}{25}}+\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{-9651062-\sqrt{31}\,825499{}\mathrm{i}}\,\sqrt{2\,x+1}\,13744{}\mathrm{i}}{360750390625\,\left(\frac{86779616}{72150078125}+\frac{\sqrt{31}\,17221232{}\mathrm{i}}{72150078125}\right)}+\frac{27488\,\sqrt{31}\,\sqrt{155}\,\sqrt{-9651062-\sqrt{31}\,825499{}\mathrm{i}}\,\sqrt{2\,x+1}}{11183262109375\,\left(\frac{86779616}{72150078125}+\frac{\sqrt{31}\,17221232{}\mathrm{i}}{72150078125}\right)}\right)\,\sqrt{-9651062-\sqrt{31}\,825499{}\mathrm{i}}\,1{}\mathrm{i}}{744775}-\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{-9651062+\sqrt{31}\,825499{}\mathrm{i}}\,\sqrt{2\,x+1}\,13744{}\mathrm{i}}{360750390625\,\left(-\frac{86779616}{72150078125}+\frac{\sqrt{31}\,17221232{}\mathrm{i}}{72150078125}\right)}-\frac{27488\,\sqrt{31}\,\sqrt{155}\,\sqrt{-9651062+\sqrt{31}\,825499{}\mathrm{i}}\,\sqrt{2\,x+1}}{11183262109375\,\left(-\frac{86779616}{72150078125}+\frac{\sqrt{31}\,17221232{}\mathrm{i}}{72150078125}\right)}\right)\,\sqrt{-9651062+\sqrt{31}\,825499{}\mathrm{i}}\,1{}\mathrm{i}}{744775}","Not used",1,"((17542*(2*x + 1)^(1/2))/120125 - (14168*(2*x + 1)^(3/2))/120125 + (23578*(2*x + 1)^(5/2))/120125 - (1088*(2*x + 1)^(7/2))/24025)/((112*x)/25 - (86*(2*x + 1)^2)/25 + (8*(2*x + 1)^3)/5 - (2*x + 1)^4 + 7/25) + (155^(1/2)*atan((155^(1/2)*(- 31^(1/2)*825499i - 9651062)^(1/2)*(2*x + 1)^(1/2)*13744i)/(360750390625*((31^(1/2)*17221232i)/72150078125 + 86779616/72150078125)) + (27488*31^(1/2)*155^(1/2)*(- 31^(1/2)*825499i - 9651062)^(1/2)*(2*x + 1)^(1/2))/(11183262109375*((31^(1/2)*17221232i)/72150078125 + 86779616/72150078125)))*(- 31^(1/2)*825499i - 9651062)^(1/2)*1i)/744775 - (155^(1/2)*atan((155^(1/2)*(31^(1/2)*825499i - 9651062)^(1/2)*(2*x + 1)^(1/2)*13744i)/(360750390625*((31^(1/2)*17221232i)/72150078125 - 86779616/72150078125)) - (27488*31^(1/2)*155^(1/2)*(31^(1/2)*825499i - 9651062)^(1/2)*(2*x + 1)^(1/2))/(11183262109375*((31^(1/2)*17221232i)/72150078125 - 86779616/72150078125)))*(31^(1/2)*825499i - 9651062)^(1/2)*1i)/744775","B"
2325,1,245,300,1.049531,"\text{Not used}","int((2*x + 1)^(5/2)/(3*x + 5*x^2 + 2)^3,x)","\frac{\frac{1176\,\sqrt{2\,x+1}}{24025}-\frac{574\,{\left(2\,x+1\right)}^{3/2}}{24025}+\frac{256\,{\left(2\,x+1\right)}^{5/2}}{4805}-\frac{234\,{\left(2\,x+1\right)}^{7/2}}{4805}}{\frac{112\,x}{25}-\frac{86\,{\left(2\,x+1\right)}^2}{25}+\frac{8\,{\left(2\,x+1\right)}^3}{5}-{\left(2\,x+1\right)}^4+\frac{7}{25}}-\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{-15082-\sqrt{31}\,961{}\mathrm{i}}\,\sqrt{2\,x+1}\,432{}\mathrm{i}}{2886003125\,\left(-\frac{142128}{577200625}+\frac{\sqrt{31}\,12096{}\mathrm{i}}{577200625}\right)}-\frac{864\,\sqrt{31}\,\sqrt{155}\,\sqrt{-15082-\sqrt{31}\,961{}\mathrm{i}}\,\sqrt{2\,x+1}}{89466096875\,\left(-\frac{142128}{577200625}+\frac{\sqrt{31}\,12096{}\mathrm{i}}{577200625}\right)}\right)\,\sqrt{-15082-\sqrt{31}\,961{}\mathrm{i}}\,3{}\mathrm{i}}{148955}+\frac{\sqrt{155}\,\mathrm{atan}\left(\frac{\sqrt{155}\,\sqrt{-15082+\sqrt{31}\,961{}\mathrm{i}}\,\sqrt{2\,x+1}\,432{}\mathrm{i}}{2886003125\,\left(\frac{142128}{577200625}+\frac{\sqrt{31}\,12096{}\mathrm{i}}{577200625}\right)}+\frac{864\,\sqrt{31}\,\sqrt{155}\,\sqrt{-15082+\sqrt{31}\,961{}\mathrm{i}}\,\sqrt{2\,x+1}}{89466096875\,\left(\frac{142128}{577200625}+\frac{\sqrt{31}\,12096{}\mathrm{i}}{577200625}\right)}\right)\,\sqrt{-15082+\sqrt{31}\,961{}\mathrm{i}}\,3{}\mathrm{i}}{148955}","Not used",1,"((1176*(2*x + 1)^(1/2))/24025 - (574*(2*x + 1)^(3/2))/24025 + (256*(2*x + 1)^(5/2))/4805 - (234*(2*x + 1)^(7/2))/4805)/((112*x)/25 - (86*(2*x + 1)^2)/25 + (8*(2*x + 1)^3)/5 - (2*x + 1)^4 + 7/25) - (155^(1/2)*atan((155^(1/2)*(- 31^(1/2)*961i - 15082)^(1/2)*(2*x + 1)^(1/2)*432i)/(2886003125*((31^(1/2)*12096i)/577200625 - 142128/577200625)) - (864*31^(1/2)*155^(1/2)*(- 31^(1/2)*961i - 15082)^(1/2)*(2*x + 1)^(1/2))/(89466096875*((31^(1/2)*12096i)/577200625 - 142128/577200625)))*(- 31^(1/2)*961i - 15082)^(1/2)*3i)/148955 + (155^(1/2)*atan((155^(1/2)*(31^(1/2)*961i - 15082)^(1/2)*(2*x + 1)^(1/2)*432i)/(2886003125*((31^(1/2)*12096i)/577200625 + 142128/577200625)) + (864*31^(1/2)*155^(1/2)*(31^(1/2)*961i - 15082)^(1/2)*(2*x + 1)^(1/2))/(89466096875*((31^(1/2)*12096i)/577200625 + 142128/577200625)))*(31^(1/2)*961i - 15082)^(1/2)*3i)/148955","B"
2326,1,245,300,1.042176,"\text{Not used}","int((2*x + 1)^(3/2)/(3*x + 5*x^2 + 2)^3,x)","\frac{\frac{1638\,\sqrt{2\,x+1}}{24025}-\frac{256\,{\left(2\,x+1\right)}^{3/2}}{4805}+\frac{82\,{\left(2\,x+1\right)}^{5/2}}{4805}-\frac{24\,{\left(2\,x+1\right)}^{7/2}}{961}}{\frac{112\,x}{25}-\frac{86\,{\left(2\,x+1\right)}^2}{25}+\frac{8\,{\left(2\,x+1\right)}^3}{5}-{\left(2\,x+1\right)}^4+\frac{7}{25}}+\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{-15082-\sqrt{31}\,961{}\mathrm{i}}\,\sqrt{2\,x+1}\,432{}\mathrm{i}}{5656566125\,\left(\frac{94176}{808080875}+\frac{\sqrt{31}\,16848{}\mathrm{i}}{808080875}\right)}+\frac{864\,\sqrt{31}\,\sqrt{217}\,\sqrt{-15082-\sqrt{31}\,961{}\mathrm{i}}\,\sqrt{2\,x+1}}{175353549875\,\left(\frac{94176}{808080875}+\frac{\sqrt{31}\,16848{}\mathrm{i}}{808080875}\right)}\right)\,\sqrt{-15082-\sqrt{31}\,961{}\mathrm{i}}\,3{}\mathrm{i}}{208537}-\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{-15082+\sqrt{31}\,961{}\mathrm{i}}\,\sqrt{2\,x+1}\,432{}\mathrm{i}}{5656566125\,\left(-\frac{94176}{808080875}+\frac{\sqrt{31}\,16848{}\mathrm{i}}{808080875}\right)}-\frac{864\,\sqrt{31}\,\sqrt{217}\,\sqrt{-15082+\sqrt{31}\,961{}\mathrm{i}}\,\sqrt{2\,x+1}}{175353549875\,\left(-\frac{94176}{808080875}+\frac{\sqrt{31}\,16848{}\mathrm{i}}{808080875}\right)}\right)\,\sqrt{-15082+\sqrt{31}\,961{}\mathrm{i}}\,3{}\mathrm{i}}{208537}","Not used",1,"((1638*(2*x + 1)^(1/2))/24025 - (256*(2*x + 1)^(3/2))/4805 + (82*(2*x + 1)^(5/2))/4805 - (24*(2*x + 1)^(7/2))/961)/((112*x)/25 - (86*(2*x + 1)^2)/25 + (8*(2*x + 1)^3)/5 - (2*x + 1)^4 + 7/25) + (217^(1/2)*atan((217^(1/2)*(- 31^(1/2)*961i - 15082)^(1/2)*(2*x + 1)^(1/2)*432i)/(5656566125*((31^(1/2)*16848i)/808080875 + 94176/808080875)) + (864*31^(1/2)*217^(1/2)*(- 31^(1/2)*961i - 15082)^(1/2)*(2*x + 1)^(1/2))/(175353549875*((31^(1/2)*16848i)/808080875 + 94176/808080875)))*(- 31^(1/2)*961i - 15082)^(1/2)*3i)/208537 - (217^(1/2)*atan((217^(1/2)*(31^(1/2)*961i - 15082)^(1/2)*(2*x + 1)^(1/2)*432i)/(5656566125*((31^(1/2)*16848i)/808080875 - 94176/808080875)) - (864*31^(1/2)*217^(1/2)*(31^(1/2)*961i - 15082)^(1/2)*(2*x + 1)^(1/2))/(175353549875*((31^(1/2)*16848i)/808080875 - 94176/808080875)))*(31^(1/2)*961i - 15082)^(1/2)*3i)/208537","B"
2327,1,245,300,1.057188,"\text{Not used}","int((2*x + 1)^(1/2)/(3*x + 5*x^2 + 2)^3,x)","\frac{\frac{1088\,\sqrt{2\,x+1}}{24025}-\frac{23578\,{\left(2\,x+1\right)}^{3/2}}{168175}+\frac{2024\,{\left(2\,x+1\right)}^{5/2}}{33635}-\frac{358\,{\left(2\,x+1\right)}^{7/2}}{6727}}{\frac{112\,x}{25}-\frac{86\,{\left(2\,x+1\right)}^2}{25}+\frac{8\,{\left(2\,x+1\right)}^3}{5}-{\left(2\,x+1\right)}^4+\frac{7}{25}}-\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{-9651062-\sqrt{31}\,825499{}\mathrm{i}}\,\sqrt{2\,x+1}\,13744{}\mathrm{i}}{1940202180875\,\left(-\frac{101059632}{277171740125}+\frac{\sqrt{31}\,7476736{}\mathrm{i}}{277171740125}\right)}-\frac{27488\,\sqrt{31}\,\sqrt{217}\,\sqrt{-9651062-\sqrt{31}\,825499{}\mathrm{i}}\,\sqrt{2\,x+1}}{60146267607125\,\left(-\frac{101059632}{277171740125}+\frac{\sqrt{31}\,7476736{}\mathrm{i}}{277171740125}\right)}\right)\,\sqrt{-9651062-\sqrt{31}\,825499{}\mathrm{i}}\,1{}\mathrm{i}}{1459759}+\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{-9651062+\sqrt{31}\,825499{}\mathrm{i}}\,\sqrt{2\,x+1}\,13744{}\mathrm{i}}{1940202180875\,\left(\frac{101059632}{277171740125}+\frac{\sqrt{31}\,7476736{}\mathrm{i}}{277171740125}\right)}+\frac{27488\,\sqrt{31}\,\sqrt{217}\,\sqrt{-9651062+\sqrt{31}\,825499{}\mathrm{i}}\,\sqrt{2\,x+1}}{60146267607125\,\left(\frac{101059632}{277171740125}+\frac{\sqrt{31}\,7476736{}\mathrm{i}}{277171740125}\right)}\right)\,\sqrt{-9651062+\sqrt{31}\,825499{}\mathrm{i}}\,1{}\mathrm{i}}{1459759}","Not used",1,"((1088*(2*x + 1)^(1/2))/24025 - (23578*(2*x + 1)^(3/2))/168175 + (2024*(2*x + 1)^(5/2))/33635 - (358*(2*x + 1)^(7/2))/6727)/((112*x)/25 - (86*(2*x + 1)^2)/25 + (8*(2*x + 1)^3)/5 - (2*x + 1)^4 + 7/25) - (217^(1/2)*atan((217^(1/2)*(- 31^(1/2)*825499i - 9651062)^(1/2)*(2*x + 1)^(1/2)*13744i)/(1940202180875*((31^(1/2)*7476736i)/277171740125 - 101059632/277171740125)) - (27488*31^(1/2)*217^(1/2)*(- 31^(1/2)*825499i - 9651062)^(1/2)*(2*x + 1)^(1/2))/(60146267607125*((31^(1/2)*7476736i)/277171740125 - 101059632/277171740125)))*(- 31^(1/2)*825499i - 9651062)^(1/2)*1i)/1459759 + (217^(1/2)*atan((217^(1/2)*(31^(1/2)*825499i - 9651062)^(1/2)*(2*x + 1)^(1/2)*13744i)/(1940202180875*((31^(1/2)*7476736i)/277171740125 + 101059632/277171740125)) + (27488*31^(1/2)*217^(1/2)*(31^(1/2)*825499i - 9651062)^(1/2)*(2*x + 1)^(1/2))/(60146267607125*((31^(1/2)*7476736i)/277171740125 + 101059632/277171740125)))*(31^(1/2)*825499i - 9651062)^(1/2)*1i)/1459759","B"
2328,1,246,314,0.150193,"\text{Not used}","int(1/((2*x + 1)^(1/2)*(3*x + 5*x^2 + 2)^3),x)","-\frac{\frac{3446\,\sqrt{2\,x+1}}{33635}+\frac{30664\,{\left(2\,x+1\right)}^{3/2}}{1177225}+\frac{4198\,{\left(2\,x+1\right)}^{5/2}}{235445}+\frac{1584\,{\left(2\,x+1\right)}^{7/2}}{47089}}{\frac{112\,x}{25}-\frac{86\,{\left(2\,x+1\right)}^2}{25}+\frac{8\,{\left(2\,x+1\right)}^3}{5}-{\left(2\,x+1\right)}^4+\frac{7}{25}}+\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{-250141922-\sqrt{31}\,52010281{}\mathrm{i}}\,\sqrt{2\,x+1}\,23380272{}\mathrm{i}}{665489348040125\,\left(\frac{561079767456}{95069906862875}+\frac{\sqrt{31}\,172523027088{}\mathrm{i}}{95069906862875}\right)}+\frac{46760544\,\sqrt{31}\,\sqrt{217}\,\sqrt{-250141922-\sqrt{31}\,52010281{}\mathrm{i}}\,\sqrt{2\,x+1}}{20630169789243875\,\left(\frac{561079767456}{95069906862875}+\frac{\sqrt{31}\,172523027088{}\mathrm{i}}{95069906862875}\right)}\right)\,\sqrt{-250141922-\sqrt{31}\,52010281{}\mathrm{i}}\,3{}\mathrm{i}}{10218313}-\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{-250141922+\sqrt{31}\,52010281{}\mathrm{i}}\,\sqrt{2\,x+1}\,23380272{}\mathrm{i}}{665489348040125\,\left(-\frac{561079767456}{95069906862875}+\frac{\sqrt{31}\,172523027088{}\mathrm{i}}{95069906862875}\right)}-\frac{46760544\,\sqrt{31}\,\sqrt{217}\,\sqrt{-250141922+\sqrt{31}\,52010281{}\mathrm{i}}\,\sqrt{2\,x+1}}{20630169789243875\,\left(-\frac{561079767456}{95069906862875}+\frac{\sqrt{31}\,172523027088{}\mathrm{i}}{95069906862875}\right)}\right)\,\sqrt{-250141922+\sqrt{31}\,52010281{}\mathrm{i}}\,3{}\mathrm{i}}{10218313}","Not used",1,"(217^(1/2)*atan((217^(1/2)*(- 31^(1/2)*52010281i - 250141922)^(1/2)*(2*x + 1)^(1/2)*23380272i)/(665489348040125*((31^(1/2)*172523027088i)/95069906862875 + 561079767456/95069906862875)) + (46760544*31^(1/2)*217^(1/2)*(- 31^(1/2)*52010281i - 250141922)^(1/2)*(2*x + 1)^(1/2))/(20630169789243875*((31^(1/2)*172523027088i)/95069906862875 + 561079767456/95069906862875)))*(- 31^(1/2)*52010281i - 250141922)^(1/2)*3i)/10218313 - ((3446*(2*x + 1)^(1/2))/33635 + (30664*(2*x + 1)^(3/2))/1177225 + (4198*(2*x + 1)^(5/2))/235445 + (1584*(2*x + 1)^(7/2))/47089)/((112*x)/25 - (86*(2*x + 1)^2)/25 + (8*(2*x + 1)^3)/5 - (2*x + 1)^4 + 7/25) - (217^(1/2)*atan((217^(1/2)*(31^(1/2)*52010281i - 250141922)^(1/2)*(2*x + 1)^(1/2)*23380272i)/(665489348040125*((31^(1/2)*172523027088i)/95069906862875 - 561079767456/95069906862875)) - (46760544*31^(1/2)*217^(1/2)*(31^(1/2)*52010281i - 250141922)^(1/2)*(2*x + 1)^(1/2))/(20630169789243875*((31^(1/2)*172523027088i)/95069906862875 - 561079767456/95069906862875)))*(31^(1/2)*52010281i - 250141922)^(1/2)*3i)/10218313","B"
2329,1,252,313,0.177441,"\text{Not used}","int(1/((2*x + 1)^(3/2)*(3*x + 5*x^2 + 2)^3),x)","\frac{\frac{274928\,x}{235445}-\frac{1362758\,{\left(2\,x+1\right)}^2}{1648115}+\frac{144304\,{\left(2\,x+1\right)}^3}{329623}-\frac{81090\,{\left(2\,x+1\right)}^4}{329623}+\frac{256792}{1177225}}{\frac{49\,\sqrt{2\,x+1}}{25}-\frac{56\,{\left(2\,x+1\right)}^{3/2}}{25}+\frac{86\,{\left(2\,x+1\right)}^{5/2}}{25}-\frac{8\,{\left(2\,x+1\right)}^{7/2}}{5}+{\left(2\,x+1\right)}^{9/2}}+\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{2\,x+1}\,\sqrt{2257111762-\sqrt{31}\,71603149{}\mathrm{i}}\,32187888{}\mathrm{i}}{1826102771022103\,\left(-\frac{1880448604848}{260871824431729}+\frac{\sqrt{31}\,582343269696{}\mathrm{i}}{260871824431729}\right)}+\frac{64375776\,\sqrt{31}\,\sqrt{217}\,\sqrt{2\,x+1}\,\sqrt{2257111762-\sqrt{31}\,71603149{}\mathrm{i}}}{56609185901685193\,\left(-\frac{1880448604848}{260871824431729}+\frac{\sqrt{31}\,582343269696{}\mathrm{i}}{260871824431729}\right)}\right)\,\sqrt{2257111762-\sqrt{31}\,71603149{}\mathrm{i}}\,15{}\mathrm{i}}{71528191}-\frac{\sqrt{217}\,\mathrm{atan}\left(\frac{\sqrt{217}\,\sqrt{2\,x+1}\,\sqrt{2257111762+\sqrt{31}\,71603149{}\mathrm{i}}\,32187888{}\mathrm{i}}{1826102771022103\,\left(\frac{1880448604848}{260871824431729}+\frac{\sqrt{31}\,582343269696{}\mathrm{i}}{260871824431729}\right)}-\frac{64375776\,\sqrt{31}\,\sqrt{217}\,\sqrt{2\,x+1}\,\sqrt{2257111762+\sqrt{31}\,71603149{}\mathrm{i}}}{56609185901685193\,\left(\frac{1880448604848}{260871824431729}+\frac{\sqrt{31}\,582343269696{}\mathrm{i}}{260871824431729}\right)}\right)\,\sqrt{2257111762+\sqrt{31}\,71603149{}\mathrm{i}}\,15{}\mathrm{i}}{71528191}","Not used",1,"((274928*x)/235445 - (1362758*(2*x + 1)^2)/1648115 + (144304*(2*x + 1)^3)/329623 - (81090*(2*x + 1)^4)/329623 + 256792/1177225)/((49*(2*x + 1)^(1/2))/25 - (56*(2*x + 1)^(3/2))/25 + (86*(2*x + 1)^(5/2))/25 - (8*(2*x + 1)^(7/2))/5 + (2*x + 1)^(9/2)) + (217^(1/2)*atan((217^(1/2)*(2*x + 1)^(1/2)*(2257111762 - 31^(1/2)*71603149i)^(1/2)*32187888i)/(1826102771022103*((31^(1/2)*582343269696i)/260871824431729 - 1880448604848/260871824431729)) + (64375776*31^(1/2)*217^(1/2)*(2*x + 1)^(1/2)*(2257111762 - 31^(1/2)*71603149i)^(1/2))/(56609185901685193*((31^(1/2)*582343269696i)/260871824431729 - 1880448604848/260871824431729)))*(2257111762 - 31^(1/2)*71603149i)^(1/2)*15i)/71528191 - (217^(1/2)*atan((217^(1/2)*(2*x + 1)^(1/2)*(31^(1/2)*71603149i + 2257111762)^(1/2)*32187888i)/(1826102771022103*((31^(1/2)*582343269696i)/260871824431729 + 1880448604848/260871824431729)) - (64375776*31^(1/2)*217^(1/2)*(2*x + 1)^(1/2)*(31^(1/2)*71603149i + 2257111762)^(1/2))/(56609185901685193*((31^(1/2)*582343269696i)/260871824431729 + 1880448604848/260871824431729)))*(31^(1/2)*71603149i + 2257111762)^(1/2)*15i)/71528191","B"
2330,1,10944,389,5.877713,"\text{Not used}","int(x^(9/2)/(a + b*x + c*x^2)^3,x)","-\frac{\frac{x^{3/2}\,\left(28\,a^3\,c^2-49\,a^2\,b^2\,c+6\,a\,b^4\right)}{4\,c^2\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{x^{7/2}\,\left(44\,a^2\,c^2-37\,a\,b^2\,c+5\,b^4\right)}{4\,c\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}-\frac{b\,x^{5/2}\,\left(4\,a^2\,c^2+20\,a\,b^2\,c-3\,b^4\right)}{4\,c^2\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}-\frac{3\,a^2\,b\,\sqrt{x}\,\left(8\,a\,c-b^2\right)}{4\,c^2\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}}{x^2\,\left(b^2+2\,a\,c\right)+a^2+c^2\,x^4+2\,a\,b\,x+2\,b\,c\,x^3}-\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(524288\,a^7\,b\,c^9-720896\,a^6\,b^3\,c^8+409600\,a^5\,b^5\,c^7-122880\,a^4\,b^7\,c^6+20480\,a^3\,b^9\,c^5-1792\,a^2\,b^{11}\,c^4+64\,a\,b^{13}\,c^3\right)}{64\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}-\frac{\sqrt{x}\,\sqrt{\frac{9\,\left(b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-b^{19}+1720320\,a^9\,b\,c^9-769\,a^2\,b^{15}\,c^2+8620\,a^3\,b^{13}\,c^3-63440\,a^4\,b^{11}\,c^4+316864\,a^5\,b^9\,c^5-1069824\,a^6\,b^7\,c^6+2343936\,a^7\,b^5\,c^7-3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}\,\left(-65536\,a^5\,b\,c^{10}+81920\,a^4\,b^3\,c^9-40960\,a^3\,b^5\,c^8+10240\,a^2\,b^7\,c^7-1280\,a\,b^9\,c^6+64\,b^{11}\,c^5\right)}{8\,\left(256\,a^4\,c^7-256\,a^3\,b^2\,c^6+96\,a^2\,b^4\,c^5-16\,a\,b^6\,c^4+b^8\,c^3\right)}\right)\,\sqrt{\frac{9\,\left(b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-b^{19}+1720320\,a^9\,b\,c^9-769\,a^2\,b^{15}\,c^2+8620\,a^3\,b^{13}\,c^3-63440\,a^4\,b^{11}\,c^4+316864\,a^5\,b^9\,c^5-1069824\,a^6\,b^7\,c^6+2343936\,a^7\,b^5\,c^7-3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}-\frac{\sqrt{x}\,\left(-14112\,a^5\,c^5+21312\,a^4\,b^2\,c^4-9090\,a^3\,b^4\,c^3+1881\,a^2\,b^6\,c^2-198\,a\,b^8\,c+9\,b^{10}\right)}{8\,\left(256\,a^4\,c^7-256\,a^3\,b^2\,c^6+96\,a^2\,b^4\,c^5-16\,a\,b^6\,c^4+b^8\,c^3\right)}\right)\,\sqrt{\frac{9\,\left(b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-b^{19}+1720320\,a^9\,b\,c^9-769\,a^2\,b^{15}\,c^2+8620\,a^3\,b^{13}\,c^3-63440\,a^4\,b^{11}\,c^4+316864\,a^5\,b^9\,c^5-1069824\,a^6\,b^7\,c^6+2343936\,a^7\,b^5\,c^7-3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3\,\left(524288\,a^7\,b\,c^9-720896\,a^6\,b^3\,c^8+409600\,a^5\,b^5\,c^7-122880\,a^4\,b^7\,c^6+20480\,a^3\,b^9\,c^5-1792\,a^2\,b^{11}\,c^4+64\,a\,b^{13}\,c^3\right)}{64\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}+\frac{\sqrt{x}\,\sqrt{\frac{9\,\left(b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-b^{19}+1720320\,a^9\,b\,c^9-769\,a^2\,b^{15}\,c^2+8620\,a^3\,b^{13}\,c^3-63440\,a^4\,b^{11}\,c^4+316864\,a^5\,b^9\,c^5-1069824\,a^6\,b^7\,c^6+2343936\,a^7\,b^5\,c^7-3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}\,\left(-65536\,a^5\,b\,c^{10}+81920\,a^4\,b^3\,c^9-40960\,a^3\,b^5\,c^8+10240\,a^2\,b^7\,c^7-1280\,a\,b^9\,c^6+64\,b^{11}\,c^5\right)}{8\,\left(256\,a^4\,c^7-256\,a^3\,b^2\,c^6+96\,a^2\,b^4\,c^5-16\,a\,b^6\,c^4+b^8\,c^3\right)}\right)\,\sqrt{\frac{9\,\left(b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-b^{19}+1720320\,a^9\,b\,c^9-769\,a^2\,b^{15}\,c^2+8620\,a^3\,b^{13}\,c^3-63440\,a^4\,b^{11}\,c^4+316864\,a^5\,b^9\,c^5-1069824\,a^6\,b^7\,c^6+2343936\,a^7\,b^5\,c^7-3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}+\frac{\sqrt{x}\,\left(-14112\,a^5\,c^5+21312\,a^4\,b^2\,c^4-9090\,a^3\,b^4\,c^3+1881\,a^2\,b^6\,c^2-198\,a\,b^8\,c+9\,b^{10}\right)}{8\,\left(256\,a^4\,c^7-256\,a^3\,b^2\,c^6+96\,a^2\,b^4\,c^5-16\,a\,b^6\,c^4+b^8\,c^3\right)}\right)\,\sqrt{\frac{9\,\left(b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-b^{19}+1720320\,a^9\,b\,c^9-769\,a^2\,b^{15}\,c^2+8620\,a^3\,b^{13}\,c^3-63440\,a^4\,b^{11}\,c^4+316864\,a^5\,b^9\,c^5-1069824\,a^6\,b^7\,c^6+2343936\,a^7\,b^5\,c^7-3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{3\,\left(524288\,a^7\,b\,c^9-720896\,a^6\,b^3\,c^8+409600\,a^5\,b^5\,c^7-122880\,a^4\,b^7\,c^6+20480\,a^3\,b^9\,c^5-1792\,a^2\,b^{11}\,c^4+64\,a\,b^{13}\,c^3\right)}{64\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}-\frac{\sqrt{x}\,\sqrt{\frac{9\,\left(b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-b^{19}+1720320\,a^9\,b\,c^9-769\,a^2\,b^{15}\,c^2+8620\,a^3\,b^{13}\,c^3-63440\,a^4\,b^{11}\,c^4+316864\,a^5\,b^9\,c^5-1069824\,a^6\,b^7\,c^6+2343936\,a^7\,b^5\,c^7-3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}\,\left(-65536\,a^5\,b\,c^{10}+81920\,a^4\,b^3\,c^9-40960\,a^3\,b^5\,c^8+10240\,a^2\,b^7\,c^7-1280\,a\,b^9\,c^6+64\,b^{11}\,c^5\right)}{8\,\left(256\,a^4\,c^7-256\,a^3\,b^2\,c^6+96\,a^2\,b^4\,c^5-16\,a\,b^6\,c^4+b^8\,c^3\right)}\right)\,\sqrt{\frac{9\,\left(b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-b^{19}+1720320\,a^9\,b\,c^9-769\,a^2\,b^{15}\,c^2+8620\,a^3\,b^{13}\,c^3-63440\,a^4\,b^{11}\,c^4+316864\,a^5\,b^9\,c^5-1069824\,a^6\,b^7\,c^6+2343936\,a^7\,b^5\,c^7-3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}-\frac{\sqrt{x}\,\left(-14112\,a^5\,c^5+21312\,a^4\,b^2\,c^4-9090\,a^3\,b^4\,c^3+1881\,a^2\,b^6\,c^2-198\,a\,b^8\,c+9\,b^{10}\right)}{8\,\left(256\,a^4\,c^7-256\,a^3\,b^2\,c^6+96\,a^2\,b^4\,c^5-16\,a\,b^6\,c^4+b^8\,c^3\right)}\right)\,\sqrt{\frac{9\,\left(b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-b^{19}+1720320\,a^9\,b\,c^9-769\,a^2\,b^{15}\,c^2+8620\,a^3\,b^{13}\,c^3-63440\,a^4\,b^{11}\,c^4+316864\,a^5\,b^9\,c^5-1069824\,a^6\,b^7\,c^6+2343936\,a^7\,b^5\,c^7-3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}-\frac{3\,\left(197568\,a^7\,c^4-117936\,a^6\,b^2\,c^3+29844\,a^5\,b^4\,c^2-3645\,a^4\,b^6\,c+189\,a^3\,b^8\right)}{32\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}+\left(\left(\frac{3\,\left(524288\,a^7\,b\,c^9-720896\,a^6\,b^3\,c^8+409600\,a^5\,b^5\,c^7-122880\,a^4\,b^7\,c^6+20480\,a^3\,b^9\,c^5-1792\,a^2\,b^{11}\,c^4+64\,a\,b^{13}\,c^3\right)}{64\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}+\frac{\sqrt{x}\,\sqrt{\frac{9\,\left(b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-b^{19}+1720320\,a^9\,b\,c^9-769\,a^2\,b^{15}\,c^2+8620\,a^3\,b^{13}\,c^3-63440\,a^4\,b^{11}\,c^4+316864\,a^5\,b^9\,c^5-1069824\,a^6\,b^7\,c^6+2343936\,a^7\,b^5\,c^7-3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}\,\left(-65536\,a^5\,b\,c^{10}+81920\,a^4\,b^3\,c^9-40960\,a^3\,b^5\,c^8+10240\,a^2\,b^7\,c^7-1280\,a\,b^9\,c^6+64\,b^{11}\,c^5\right)}{8\,\left(256\,a^4\,c^7-256\,a^3\,b^2\,c^6+96\,a^2\,b^4\,c^5-16\,a\,b^6\,c^4+b^8\,c^3\right)}\right)\,\sqrt{\frac{9\,\left(b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-b^{19}+1720320\,a^9\,b\,c^9-769\,a^2\,b^{15}\,c^2+8620\,a^3\,b^{13}\,c^3-63440\,a^4\,b^{11}\,c^4+316864\,a^5\,b^9\,c^5-1069824\,a^6\,b^7\,c^6+2343936\,a^7\,b^5\,c^7-3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}+\frac{\sqrt{x}\,\left(-14112\,a^5\,c^5+21312\,a^4\,b^2\,c^4-9090\,a^3\,b^4\,c^3+1881\,a^2\,b^6\,c^2-198\,a\,b^8\,c+9\,b^{10}\right)}{8\,\left(256\,a^4\,c^7-256\,a^3\,b^2\,c^6+96\,a^2\,b^4\,c^5-16\,a\,b^6\,c^4+b^8\,c^3\right)}\right)\,\sqrt{\frac{9\,\left(b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-b^{19}+1720320\,a^9\,b\,c^9-769\,a^2\,b^{15}\,c^2+8620\,a^3\,b^{13}\,c^3-63440\,a^4\,b^{11}\,c^4+316864\,a^5\,b^9\,c^5-1069824\,a^6\,b^7\,c^6+2343936\,a^7\,b^5\,c^7-3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}}\right)\,\sqrt{\frac{9\,\left(b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-b^{19}+1720320\,a^9\,b\,c^9-769\,a^2\,b^{15}\,c^2+8620\,a^3\,b^{13}\,c^3-63440\,a^4\,b^{11}\,c^4+316864\,a^5\,b^9\,c^5-1069824\,a^6\,b^7\,c^6+2343936\,a^7\,b^5\,c^7-3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(\frac{3\,\left(524288\,a^7\,b\,c^9-720896\,a^6\,b^3\,c^8+409600\,a^5\,b^5\,c^7-122880\,a^4\,b^7\,c^6+20480\,a^3\,b^9\,c^5-1792\,a^2\,b^{11}\,c^4+64\,a\,b^{13}\,c^3\right)}{64\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}-\frac{\sqrt{x}\,\sqrt{-\frac{9\,\left(b^{19}+b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-1720320\,a^9\,b\,c^9+769\,a^2\,b^{15}\,c^2-8620\,a^3\,b^{13}\,c^3+63440\,a^4\,b^{11}\,c^4-316864\,a^5\,b^9\,c^5+1069824\,a^6\,b^7\,c^6-2343936\,a^7\,b^5\,c^7+3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}\,\left(-65536\,a^5\,b\,c^{10}+81920\,a^4\,b^3\,c^9-40960\,a^3\,b^5\,c^8+10240\,a^2\,b^7\,c^7-1280\,a\,b^9\,c^6+64\,b^{11}\,c^5\right)}{8\,\left(256\,a^4\,c^7-256\,a^3\,b^2\,c^6+96\,a^2\,b^4\,c^5-16\,a\,b^6\,c^4+b^8\,c^3\right)}\right)\,\sqrt{-\frac{9\,\left(b^{19}+b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-1720320\,a^9\,b\,c^9+769\,a^2\,b^{15}\,c^2-8620\,a^3\,b^{13}\,c^3+63440\,a^4\,b^{11}\,c^4-316864\,a^5\,b^9\,c^5+1069824\,a^6\,b^7\,c^6-2343936\,a^7\,b^5\,c^7+3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}-\frac{\sqrt{x}\,\left(-14112\,a^5\,c^5+21312\,a^4\,b^2\,c^4-9090\,a^3\,b^4\,c^3+1881\,a^2\,b^6\,c^2-198\,a\,b^8\,c+9\,b^{10}\right)}{8\,\left(256\,a^4\,c^7-256\,a^3\,b^2\,c^6+96\,a^2\,b^4\,c^5-16\,a\,b^6\,c^4+b^8\,c^3\right)}\right)\,\sqrt{-\frac{9\,\left(b^{19}+b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-1720320\,a^9\,b\,c^9+769\,a^2\,b^{15}\,c^2-8620\,a^3\,b^{13}\,c^3+63440\,a^4\,b^{11}\,c^4-316864\,a^5\,b^9\,c^5+1069824\,a^6\,b^7\,c^6-2343936\,a^7\,b^5\,c^7+3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}\,1{}\mathrm{i}-\left(\left(\frac{3\,\left(524288\,a^7\,b\,c^9-720896\,a^6\,b^3\,c^8+409600\,a^5\,b^5\,c^7-122880\,a^4\,b^7\,c^6+20480\,a^3\,b^9\,c^5-1792\,a^2\,b^{11}\,c^4+64\,a\,b^{13}\,c^3\right)}{64\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}+\frac{\sqrt{x}\,\sqrt{-\frac{9\,\left(b^{19}+b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-1720320\,a^9\,b\,c^9+769\,a^2\,b^{15}\,c^2-8620\,a^3\,b^{13}\,c^3+63440\,a^4\,b^{11}\,c^4-316864\,a^5\,b^9\,c^5+1069824\,a^6\,b^7\,c^6-2343936\,a^7\,b^5\,c^7+3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}\,\left(-65536\,a^5\,b\,c^{10}+81920\,a^4\,b^3\,c^9-40960\,a^3\,b^5\,c^8+10240\,a^2\,b^7\,c^7-1280\,a\,b^9\,c^6+64\,b^{11}\,c^5\right)}{8\,\left(256\,a^4\,c^7-256\,a^3\,b^2\,c^6+96\,a^2\,b^4\,c^5-16\,a\,b^6\,c^4+b^8\,c^3\right)}\right)\,\sqrt{-\frac{9\,\left(b^{19}+b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-1720320\,a^9\,b\,c^9+769\,a^2\,b^{15}\,c^2-8620\,a^3\,b^{13}\,c^3+63440\,a^4\,b^{11}\,c^4-316864\,a^5\,b^9\,c^5+1069824\,a^6\,b^7\,c^6-2343936\,a^7\,b^5\,c^7+3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}+\frac{\sqrt{x}\,\left(-14112\,a^5\,c^5+21312\,a^4\,b^2\,c^4-9090\,a^3\,b^4\,c^3+1881\,a^2\,b^6\,c^2-198\,a\,b^8\,c+9\,b^{10}\right)}{8\,\left(256\,a^4\,c^7-256\,a^3\,b^2\,c^6+96\,a^2\,b^4\,c^5-16\,a\,b^6\,c^4+b^8\,c^3\right)}\right)\,\sqrt{-\frac{9\,\left(b^{19}+b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-1720320\,a^9\,b\,c^9+769\,a^2\,b^{15}\,c^2-8620\,a^3\,b^{13}\,c^3+63440\,a^4\,b^{11}\,c^4-316864\,a^5\,b^9\,c^5+1069824\,a^6\,b^7\,c^6-2343936\,a^7\,b^5\,c^7+3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{3\,\left(524288\,a^7\,b\,c^9-720896\,a^6\,b^3\,c^8+409600\,a^5\,b^5\,c^7-122880\,a^4\,b^7\,c^6+20480\,a^3\,b^9\,c^5-1792\,a^2\,b^{11}\,c^4+64\,a\,b^{13}\,c^3\right)}{64\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}-\frac{\sqrt{x}\,\sqrt{-\frac{9\,\left(b^{19}+b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-1720320\,a^9\,b\,c^9+769\,a^2\,b^{15}\,c^2-8620\,a^3\,b^{13}\,c^3+63440\,a^4\,b^{11}\,c^4-316864\,a^5\,b^9\,c^5+1069824\,a^6\,b^7\,c^6-2343936\,a^7\,b^5\,c^7+3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}\,\left(-65536\,a^5\,b\,c^{10}+81920\,a^4\,b^3\,c^9-40960\,a^3\,b^5\,c^8+10240\,a^2\,b^7\,c^7-1280\,a\,b^9\,c^6+64\,b^{11}\,c^5\right)}{8\,\left(256\,a^4\,c^7-256\,a^3\,b^2\,c^6+96\,a^2\,b^4\,c^5-16\,a\,b^6\,c^4+b^8\,c^3\right)}\right)\,\sqrt{-\frac{9\,\left(b^{19}+b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-1720320\,a^9\,b\,c^9+769\,a^2\,b^{15}\,c^2-8620\,a^3\,b^{13}\,c^3+63440\,a^4\,b^{11}\,c^4-316864\,a^5\,b^9\,c^5+1069824\,a^6\,b^7\,c^6-2343936\,a^7\,b^5\,c^7+3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}-\frac{\sqrt{x}\,\left(-14112\,a^5\,c^5+21312\,a^4\,b^2\,c^4-9090\,a^3\,b^4\,c^3+1881\,a^2\,b^6\,c^2-198\,a\,b^8\,c+9\,b^{10}\right)}{8\,\left(256\,a^4\,c^7-256\,a^3\,b^2\,c^6+96\,a^2\,b^4\,c^5-16\,a\,b^6\,c^4+b^8\,c^3\right)}\right)\,\sqrt{-\frac{9\,\left(b^{19}+b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-1720320\,a^9\,b\,c^9+769\,a^2\,b^{15}\,c^2-8620\,a^3\,b^{13}\,c^3+63440\,a^4\,b^{11}\,c^4-316864\,a^5\,b^9\,c^5+1069824\,a^6\,b^7\,c^6-2343936\,a^7\,b^5\,c^7+3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}-\frac{3\,\left(197568\,a^7\,c^4-117936\,a^6\,b^2\,c^3+29844\,a^5\,b^4\,c^2-3645\,a^4\,b^6\,c+189\,a^3\,b^8\right)}{32\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}+\left(\left(\frac{3\,\left(524288\,a^7\,b\,c^9-720896\,a^6\,b^3\,c^8+409600\,a^5\,b^5\,c^7-122880\,a^4\,b^7\,c^6+20480\,a^3\,b^9\,c^5-1792\,a^2\,b^{11}\,c^4+64\,a\,b^{13}\,c^3\right)}{64\,\left(4096\,a^6\,c^9-6144\,a^5\,b^2\,c^8+3840\,a^4\,b^4\,c^7-1280\,a^3\,b^6\,c^6+240\,a^2\,b^8\,c^5-24\,a\,b^{10}\,c^4+b^{12}\,c^3\right)}+\frac{\sqrt{x}\,\sqrt{-\frac{9\,\left(b^{19}+b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-1720320\,a^9\,b\,c^9+769\,a^2\,b^{15}\,c^2-8620\,a^3\,b^{13}\,c^3+63440\,a^4\,b^{11}\,c^4-316864\,a^5\,b^9\,c^5+1069824\,a^6\,b^7\,c^6-2343936\,a^7\,b^5\,c^7+3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}\,\left(-65536\,a^5\,b\,c^{10}+81920\,a^4\,b^3\,c^9-40960\,a^3\,b^5\,c^8+10240\,a^2\,b^7\,c^7-1280\,a\,b^9\,c^6+64\,b^{11}\,c^5\right)}{8\,\left(256\,a^4\,c^7-256\,a^3\,b^2\,c^6+96\,a^2\,b^4\,c^5-16\,a\,b^6\,c^4+b^8\,c^3\right)}\right)\,\sqrt{-\frac{9\,\left(b^{19}+b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-1720320\,a^9\,b\,c^9+769\,a^2\,b^{15}\,c^2-8620\,a^3\,b^{13}\,c^3+63440\,a^4\,b^{11}\,c^4-316864\,a^5\,b^9\,c^5+1069824\,a^6\,b^7\,c^6-2343936\,a^7\,b^5\,c^7+3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}+\frac{\sqrt{x}\,\left(-14112\,a^5\,c^5+21312\,a^4\,b^2\,c^4-9090\,a^3\,b^4\,c^3+1881\,a^2\,b^6\,c^2-198\,a\,b^8\,c+9\,b^{10}\right)}{8\,\left(256\,a^4\,c^7-256\,a^3\,b^2\,c^6+96\,a^2\,b^4\,c^5-16\,a\,b^6\,c^4+b^8\,c^3\right)}\right)\,\sqrt{-\frac{9\,\left(b^{19}+b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-1720320\,a^9\,b\,c^9+769\,a^2\,b^{15}\,c^2-8620\,a^3\,b^{13}\,c^3+63440\,a^4\,b^{11}\,c^4-316864\,a^5\,b^9\,c^5+1069824\,a^6\,b^7\,c^6-2343936\,a^7\,b^5\,c^7+3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}}\right)\,\sqrt{-\frac{9\,\left(b^{19}+b^4\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-1720320\,a^9\,b\,c^9+769\,a^2\,b^{15}\,c^2-8620\,a^3\,b^{13}\,c^3+63440\,a^4\,b^{11}\,c^4-316864\,a^5\,b^9\,c^5+1069824\,a^6\,b^7\,c^6-2343936\,a^7\,b^5\,c^7+3010560\,a^8\,b^3\,c^8+49\,a^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-41\,a\,b^{17}\,c-11\,a\,b^2\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{10}\,c^{15}-2621440\,a^9\,b^2\,c^{14}+2949120\,a^8\,b^4\,c^{13}-1966080\,a^7\,b^6\,c^{12}+860160\,a^6\,b^8\,c^{11}-258048\,a^5\,b^{10}\,c^{10}+53760\,a^4\,b^{12}\,c^9-7680\,a^3\,b^{14}\,c^8+720\,a^2\,b^{16}\,c^7-40\,a\,b^{18}\,c^6+b^{20}\,c^5\right)}}\,2{}\mathrm{i}","Not used",1,"- ((x^(3/2)*(6*a*b^4 + 28*a^3*c^2 - 49*a^2*b^2*c))/(4*c^2*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (x^(7/2)*(5*b^4 + 44*a^2*c^2 - 37*a*b^2*c))/(4*c*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) - (b*x^(5/2)*(4*a^2*c^2 - 3*b^4 + 20*a*b^2*c))/(4*c^2*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) - (3*a^2*b*x^(1/2)*(8*a*c - b^2))/(4*c^2*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))/(x^2*(2*a*c + b^2) + a^2 + c^2*x^4 + 2*a*b*x + 2*b*c*x^3) - atan(((((3*(64*a*b^13*c^3 + 524288*a^7*b*c^9 - 1792*a^2*b^11*c^4 + 20480*a^3*b^9*c^5 - 122880*a^4*b^7*c^6 + 409600*a^5*b^5*c^7 - 720896*a^6*b^3*c^8))/(64*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)) - (x^(1/2)*((9*(b^4*(-(4*a*c - b^2)^15)^(1/2) - b^19 + 1720320*a^9*b*c^9 - 769*a^2*b^15*c^2 + 8620*a^3*b^13*c^3 - 63440*a^4*b^11*c^4 + 316864*a^5*b^9*c^5 - 1069824*a^6*b^7*c^6 + 2343936*a^7*b^5*c^7 - 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2)*(64*b^11*c^5 - 1280*a*b^9*c^6 - 65536*a^5*b*c^10 + 10240*a^2*b^7*c^7 - 40960*a^3*b^5*c^8 + 81920*a^4*b^3*c^9))/(8*(256*a^4*c^7 + b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6)))*((9*(b^4*(-(4*a*c - b^2)^15)^(1/2) - b^19 + 1720320*a^9*b*c^9 - 769*a^2*b^15*c^2 + 8620*a^3*b^13*c^3 - 63440*a^4*b^11*c^4 + 316864*a^5*b^9*c^5 - 1069824*a^6*b^7*c^6 + 2343936*a^7*b^5*c^7 - 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2) - (x^(1/2)*(9*b^10 - 14112*a^5*c^5 + 1881*a^2*b^6*c^2 - 9090*a^3*b^4*c^3 + 21312*a^4*b^2*c^4 - 198*a*b^8*c))/(8*(256*a^4*c^7 + b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6)))*((9*(b^4*(-(4*a*c - b^2)^15)^(1/2) - b^19 + 1720320*a^9*b*c^9 - 769*a^2*b^15*c^2 + 8620*a^3*b^13*c^3 - 63440*a^4*b^11*c^4 + 316864*a^5*b^9*c^5 - 1069824*a^6*b^7*c^6 + 2343936*a^7*b^5*c^7 - 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2)*1i - (((3*(64*a*b^13*c^3 + 524288*a^7*b*c^9 - 1792*a^2*b^11*c^4 + 20480*a^3*b^9*c^5 - 122880*a^4*b^7*c^6 + 409600*a^5*b^5*c^7 - 720896*a^6*b^3*c^8))/(64*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)) + (x^(1/2)*((9*(b^4*(-(4*a*c - b^2)^15)^(1/2) - b^19 + 1720320*a^9*b*c^9 - 769*a^2*b^15*c^2 + 8620*a^3*b^13*c^3 - 63440*a^4*b^11*c^4 + 316864*a^5*b^9*c^5 - 1069824*a^6*b^7*c^6 + 2343936*a^7*b^5*c^7 - 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2)*(64*b^11*c^5 - 1280*a*b^9*c^6 - 65536*a^5*b*c^10 + 10240*a^2*b^7*c^7 - 40960*a^3*b^5*c^8 + 81920*a^4*b^3*c^9))/(8*(256*a^4*c^7 + b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6)))*((9*(b^4*(-(4*a*c - b^2)^15)^(1/2) - b^19 + 1720320*a^9*b*c^9 - 769*a^2*b^15*c^2 + 8620*a^3*b^13*c^3 - 63440*a^4*b^11*c^4 + 316864*a^5*b^9*c^5 - 1069824*a^6*b^7*c^6 + 2343936*a^7*b^5*c^7 - 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2) + (x^(1/2)*(9*b^10 - 14112*a^5*c^5 + 1881*a^2*b^6*c^2 - 9090*a^3*b^4*c^3 + 21312*a^4*b^2*c^4 - 198*a*b^8*c))/(8*(256*a^4*c^7 + b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6)))*((9*(b^4*(-(4*a*c - b^2)^15)^(1/2) - b^19 + 1720320*a^9*b*c^9 - 769*a^2*b^15*c^2 + 8620*a^3*b^13*c^3 - 63440*a^4*b^11*c^4 + 316864*a^5*b^9*c^5 - 1069824*a^6*b^7*c^6 + 2343936*a^7*b^5*c^7 - 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2)*1i)/((((3*(64*a*b^13*c^3 + 524288*a^7*b*c^9 - 1792*a^2*b^11*c^4 + 20480*a^3*b^9*c^5 - 122880*a^4*b^7*c^6 + 409600*a^5*b^5*c^7 - 720896*a^6*b^3*c^8))/(64*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)) - (x^(1/2)*((9*(b^4*(-(4*a*c - b^2)^15)^(1/2) - b^19 + 1720320*a^9*b*c^9 - 769*a^2*b^15*c^2 + 8620*a^3*b^13*c^3 - 63440*a^4*b^11*c^4 + 316864*a^5*b^9*c^5 - 1069824*a^6*b^7*c^6 + 2343936*a^7*b^5*c^7 - 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2)*(64*b^11*c^5 - 1280*a*b^9*c^6 - 65536*a^5*b*c^10 + 10240*a^2*b^7*c^7 - 40960*a^3*b^5*c^8 + 81920*a^4*b^3*c^9))/(8*(256*a^4*c^7 + b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6)))*((9*(b^4*(-(4*a*c - b^2)^15)^(1/2) - b^19 + 1720320*a^9*b*c^9 - 769*a^2*b^15*c^2 + 8620*a^3*b^13*c^3 - 63440*a^4*b^11*c^4 + 316864*a^5*b^9*c^5 - 1069824*a^6*b^7*c^6 + 2343936*a^7*b^5*c^7 - 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2) - (x^(1/2)*(9*b^10 - 14112*a^5*c^5 + 1881*a^2*b^6*c^2 - 9090*a^3*b^4*c^3 + 21312*a^4*b^2*c^4 - 198*a*b^8*c))/(8*(256*a^4*c^7 + b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6)))*((9*(b^4*(-(4*a*c - b^2)^15)^(1/2) - b^19 + 1720320*a^9*b*c^9 - 769*a^2*b^15*c^2 + 8620*a^3*b^13*c^3 - 63440*a^4*b^11*c^4 + 316864*a^5*b^9*c^5 - 1069824*a^6*b^7*c^6 + 2343936*a^7*b^5*c^7 - 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2) - (3*(189*a^3*b^8 + 197568*a^7*c^4 - 3645*a^4*b^6*c + 29844*a^5*b^4*c^2 - 117936*a^6*b^2*c^3))/(32*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)) + (((3*(64*a*b^13*c^3 + 524288*a^7*b*c^9 - 1792*a^2*b^11*c^4 + 20480*a^3*b^9*c^5 - 122880*a^4*b^7*c^6 + 409600*a^5*b^5*c^7 - 720896*a^6*b^3*c^8))/(64*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)) + (x^(1/2)*((9*(b^4*(-(4*a*c - b^2)^15)^(1/2) - b^19 + 1720320*a^9*b*c^9 - 769*a^2*b^15*c^2 + 8620*a^3*b^13*c^3 - 63440*a^4*b^11*c^4 + 316864*a^5*b^9*c^5 - 1069824*a^6*b^7*c^6 + 2343936*a^7*b^5*c^7 - 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2)*(64*b^11*c^5 - 1280*a*b^9*c^6 - 65536*a^5*b*c^10 + 10240*a^2*b^7*c^7 - 40960*a^3*b^5*c^8 + 81920*a^4*b^3*c^9))/(8*(256*a^4*c^7 + b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6)))*((9*(b^4*(-(4*a*c - b^2)^15)^(1/2) - b^19 + 1720320*a^9*b*c^9 - 769*a^2*b^15*c^2 + 8620*a^3*b^13*c^3 - 63440*a^4*b^11*c^4 + 316864*a^5*b^9*c^5 - 1069824*a^6*b^7*c^6 + 2343936*a^7*b^5*c^7 - 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2) + (x^(1/2)*(9*b^10 - 14112*a^5*c^5 + 1881*a^2*b^6*c^2 - 9090*a^3*b^4*c^3 + 21312*a^4*b^2*c^4 - 198*a*b^8*c))/(8*(256*a^4*c^7 + b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6)))*((9*(b^4*(-(4*a*c - b^2)^15)^(1/2) - b^19 + 1720320*a^9*b*c^9 - 769*a^2*b^15*c^2 + 8620*a^3*b^13*c^3 - 63440*a^4*b^11*c^4 + 316864*a^5*b^9*c^5 - 1069824*a^6*b^7*c^6 + 2343936*a^7*b^5*c^7 - 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2)))*((9*(b^4*(-(4*a*c - b^2)^15)^(1/2) - b^19 + 1720320*a^9*b*c^9 - 769*a^2*b^15*c^2 + 8620*a^3*b^13*c^3 - 63440*a^4*b^11*c^4 + 316864*a^5*b^9*c^5 - 1069824*a^6*b^7*c^6 + 2343936*a^7*b^5*c^7 - 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2)*2i - atan(((((3*(64*a*b^13*c^3 + 524288*a^7*b*c^9 - 1792*a^2*b^11*c^4 + 20480*a^3*b^9*c^5 - 122880*a^4*b^7*c^6 + 409600*a^5*b^5*c^7 - 720896*a^6*b^3*c^8))/(64*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)) - (x^(1/2)*(-(9*(b^19 + b^4*(-(4*a*c - b^2)^15)^(1/2) - 1720320*a^9*b*c^9 + 769*a^2*b^15*c^2 - 8620*a^3*b^13*c^3 + 63440*a^4*b^11*c^4 - 316864*a^5*b^9*c^5 + 1069824*a^6*b^7*c^6 - 2343936*a^7*b^5*c^7 + 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2)*(64*b^11*c^5 - 1280*a*b^9*c^6 - 65536*a^5*b*c^10 + 10240*a^2*b^7*c^7 - 40960*a^3*b^5*c^8 + 81920*a^4*b^3*c^9))/(8*(256*a^4*c^7 + b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6)))*(-(9*(b^19 + b^4*(-(4*a*c - b^2)^15)^(1/2) - 1720320*a^9*b*c^9 + 769*a^2*b^15*c^2 - 8620*a^3*b^13*c^3 + 63440*a^4*b^11*c^4 - 316864*a^5*b^9*c^5 + 1069824*a^6*b^7*c^6 - 2343936*a^7*b^5*c^7 + 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2) - (x^(1/2)*(9*b^10 - 14112*a^5*c^5 + 1881*a^2*b^6*c^2 - 9090*a^3*b^4*c^3 + 21312*a^4*b^2*c^4 - 198*a*b^8*c))/(8*(256*a^4*c^7 + b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6)))*(-(9*(b^19 + b^4*(-(4*a*c - b^2)^15)^(1/2) - 1720320*a^9*b*c^9 + 769*a^2*b^15*c^2 - 8620*a^3*b^13*c^3 + 63440*a^4*b^11*c^4 - 316864*a^5*b^9*c^5 + 1069824*a^6*b^7*c^6 - 2343936*a^7*b^5*c^7 + 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2)*1i - (((3*(64*a*b^13*c^3 + 524288*a^7*b*c^9 - 1792*a^2*b^11*c^4 + 20480*a^3*b^9*c^5 - 122880*a^4*b^7*c^6 + 409600*a^5*b^5*c^7 - 720896*a^6*b^3*c^8))/(64*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)) + (x^(1/2)*(-(9*(b^19 + b^4*(-(4*a*c - b^2)^15)^(1/2) - 1720320*a^9*b*c^9 + 769*a^2*b^15*c^2 - 8620*a^3*b^13*c^3 + 63440*a^4*b^11*c^4 - 316864*a^5*b^9*c^5 + 1069824*a^6*b^7*c^6 - 2343936*a^7*b^5*c^7 + 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2)*(64*b^11*c^5 - 1280*a*b^9*c^6 - 65536*a^5*b*c^10 + 10240*a^2*b^7*c^7 - 40960*a^3*b^5*c^8 + 81920*a^4*b^3*c^9))/(8*(256*a^4*c^7 + b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6)))*(-(9*(b^19 + b^4*(-(4*a*c - b^2)^15)^(1/2) - 1720320*a^9*b*c^9 + 769*a^2*b^15*c^2 - 8620*a^3*b^13*c^3 + 63440*a^4*b^11*c^4 - 316864*a^5*b^9*c^5 + 1069824*a^6*b^7*c^6 - 2343936*a^7*b^5*c^7 + 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2) + (x^(1/2)*(9*b^10 - 14112*a^5*c^5 + 1881*a^2*b^6*c^2 - 9090*a^3*b^4*c^3 + 21312*a^4*b^2*c^4 - 198*a*b^8*c))/(8*(256*a^4*c^7 + b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6)))*(-(9*(b^19 + b^4*(-(4*a*c - b^2)^15)^(1/2) - 1720320*a^9*b*c^9 + 769*a^2*b^15*c^2 - 8620*a^3*b^13*c^3 + 63440*a^4*b^11*c^4 - 316864*a^5*b^9*c^5 + 1069824*a^6*b^7*c^6 - 2343936*a^7*b^5*c^7 + 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2)*1i)/((((3*(64*a*b^13*c^3 + 524288*a^7*b*c^9 - 1792*a^2*b^11*c^4 + 20480*a^3*b^9*c^5 - 122880*a^4*b^7*c^6 + 409600*a^5*b^5*c^7 - 720896*a^6*b^3*c^8))/(64*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)) - (x^(1/2)*(-(9*(b^19 + b^4*(-(4*a*c - b^2)^15)^(1/2) - 1720320*a^9*b*c^9 + 769*a^2*b^15*c^2 - 8620*a^3*b^13*c^3 + 63440*a^4*b^11*c^4 - 316864*a^5*b^9*c^5 + 1069824*a^6*b^7*c^6 - 2343936*a^7*b^5*c^7 + 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2)*(64*b^11*c^5 - 1280*a*b^9*c^6 - 65536*a^5*b*c^10 + 10240*a^2*b^7*c^7 - 40960*a^3*b^5*c^8 + 81920*a^4*b^3*c^9))/(8*(256*a^4*c^7 + b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6)))*(-(9*(b^19 + b^4*(-(4*a*c - b^2)^15)^(1/2) - 1720320*a^9*b*c^9 + 769*a^2*b^15*c^2 - 8620*a^3*b^13*c^3 + 63440*a^4*b^11*c^4 - 316864*a^5*b^9*c^5 + 1069824*a^6*b^7*c^6 - 2343936*a^7*b^5*c^7 + 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2) - (x^(1/2)*(9*b^10 - 14112*a^5*c^5 + 1881*a^2*b^6*c^2 - 9090*a^3*b^4*c^3 + 21312*a^4*b^2*c^4 - 198*a*b^8*c))/(8*(256*a^4*c^7 + b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6)))*(-(9*(b^19 + b^4*(-(4*a*c - b^2)^15)^(1/2) - 1720320*a^9*b*c^9 + 769*a^2*b^15*c^2 - 8620*a^3*b^13*c^3 + 63440*a^4*b^11*c^4 - 316864*a^5*b^9*c^5 + 1069824*a^6*b^7*c^6 - 2343936*a^7*b^5*c^7 + 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2) - (3*(189*a^3*b^8 + 197568*a^7*c^4 - 3645*a^4*b^6*c + 29844*a^5*b^4*c^2 - 117936*a^6*b^2*c^3))/(32*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)) + (((3*(64*a*b^13*c^3 + 524288*a^7*b*c^9 - 1792*a^2*b^11*c^4 + 20480*a^3*b^9*c^5 - 122880*a^4*b^7*c^6 + 409600*a^5*b^5*c^7 - 720896*a^6*b^3*c^8))/(64*(4096*a^6*c^9 + b^12*c^3 - 24*a*b^10*c^4 + 240*a^2*b^8*c^5 - 1280*a^3*b^6*c^6 + 3840*a^4*b^4*c^7 - 6144*a^5*b^2*c^8)) + (x^(1/2)*(-(9*(b^19 + b^4*(-(4*a*c - b^2)^15)^(1/2) - 1720320*a^9*b*c^9 + 769*a^2*b^15*c^2 - 8620*a^3*b^13*c^3 + 63440*a^4*b^11*c^4 - 316864*a^5*b^9*c^5 + 1069824*a^6*b^7*c^6 - 2343936*a^7*b^5*c^7 + 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2)*(64*b^11*c^5 - 1280*a*b^9*c^6 - 65536*a^5*b*c^10 + 10240*a^2*b^7*c^7 - 40960*a^3*b^5*c^8 + 81920*a^4*b^3*c^9))/(8*(256*a^4*c^7 + b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6)))*(-(9*(b^19 + b^4*(-(4*a*c - b^2)^15)^(1/2) - 1720320*a^9*b*c^9 + 769*a^2*b^15*c^2 - 8620*a^3*b^13*c^3 + 63440*a^4*b^11*c^4 - 316864*a^5*b^9*c^5 + 1069824*a^6*b^7*c^6 - 2343936*a^7*b^5*c^7 + 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2) + (x^(1/2)*(9*b^10 - 14112*a^5*c^5 + 1881*a^2*b^6*c^2 - 9090*a^3*b^4*c^3 + 21312*a^4*b^2*c^4 - 198*a*b^8*c))/(8*(256*a^4*c^7 + b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6)))*(-(9*(b^19 + b^4*(-(4*a*c - b^2)^15)^(1/2) - 1720320*a^9*b*c^9 + 769*a^2*b^15*c^2 - 8620*a^3*b^13*c^3 + 63440*a^4*b^11*c^4 - 316864*a^5*b^9*c^5 + 1069824*a^6*b^7*c^6 - 2343936*a^7*b^5*c^7 + 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2)))*(-(9*(b^19 + b^4*(-(4*a*c - b^2)^15)^(1/2) - 1720320*a^9*b*c^9 + 769*a^2*b^15*c^2 - 8620*a^3*b^13*c^3 + 63440*a^4*b^11*c^4 - 316864*a^5*b^9*c^5 + 1069824*a^6*b^7*c^6 - 2343936*a^7*b^5*c^7 + 3010560*a^8*b^3*c^8 + 49*a^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 41*a*b^17*c - 11*a*b^2*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(1048576*a^10*c^15 + b^20*c^5 - 40*a*b^18*c^6 + 720*a^2*b^16*c^7 - 7680*a^3*b^14*c^8 + 53760*a^4*b^12*c^9 - 258048*a^5*b^10*c^10 + 860160*a^6*b^8*c^11 - 1966080*a^7*b^6*c^12 + 2949120*a^8*b^4*c^13 - 2621440*a^9*b^2*c^14)))^(1/2)*2i","B"
2331,1,12164,458,6.483615,"\text{Not used}","int(1/(x^(3/2)*(a + b*x + c*x^2)^3),x)","-\frac{\frac{2}{a}+\frac{x^2\,\left(324\,a^3\,c^3+25\,a^2\,b^2\,c^2-91\,a\,b^4\,c+15\,b^6\right)}{4\,a^3\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{b\,x\,\left(364\,a^2\,c^2-194\,a\,b^2\,c+25\,b^4\right)}{4\,a^2\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{b\,x^3\,\left(392\,a^2\,c^3-227\,a\,b^2\,c^2+30\,b^4\,c\right)}{4\,a^3\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}+\frac{3\,c\,x^4\,\left(60\,a^2\,c^3-37\,a\,b^2\,c^2+5\,b^4\,c\right)}{4\,a^3\,\left(16\,a^2\,c^2-8\,a\,b^2\,c+b^4\right)}}{x^{5/2}\,\left(b^2+2\,a\,c\right)+a^2\,\sqrt{x}+c^2\,x^{9/2}+2\,a\,b\,x^{3/2}+2\,b\,c\,x^{7/2}}-\mathrm{atan}\left(\frac{\left(\sqrt{-\frac{9\,\left(25\,b^{21}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9+225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c-694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,\left(\sqrt{x}\,\sqrt{-\frac{9\,\left(25\,b^{21}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9+225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c-694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,\left(34359738368\,a^{26}\,b\,c^{13}-94489280512\,a^{25}\,b^3\,c^{12}+118111600640\,a^{24}\,b^5\,c^{11}-88583700480\,a^{23}\,b^7\,c^{10}+44291850240\,a^{22}\,b^9\,c^9-15502147584\,a^{21}\,b^{11}\,c^8+3875536896\,a^{20}\,b^{13}\,c^7-692060160\,a^{19}\,b^{15}\,c^6+86507520\,a^{18}\,b^{17}\,c^5-7208960\,a^{17}\,b^{19}\,c^4+360448\,a^{16}\,b^{21}\,c^3-8192\,a^{15}\,b^{23}\,c^2\right)-74088185856\,a^{23}\,b\,c^{13}+15360\,a^{12}\,b^{23}\,c^2-681984\,a^{13}\,b^{21}\,c^3+13774848\,a^{14}\,b^{19}\,c^4-167067648\,a^{15}\,b^{17}\,c^5+1351876608\,a^{16}\,b^{15}\,c^6-7662993408\,a^{17}\,b^{13}\,c^7+31048335360\,a^{18}\,b^{11}\,c^8-89917489152\,a^{19}\,b^9\,c^9+182401892352\,a^{20}\,b^7\,c^{10}-246826401792\,a^{21}\,b^5\,c^{11}+200521285632\,a^{22}\,b^3\,c^{12}\right)+\sqrt{x}\,\left(33973862400\,a^{20}\,c^{14}-137631891456\,a^{19}\,b^2\,c^{13}+218414186496\,a^{18}\,b^4\,c^{12}-192980975616\,a^{17}\,b^6\,c^{11}+108726976512\,a^{16}\,b^8\,c^{10}-41653370880\,a^{15}\,b^{10}\,c^9+11171856384\,a^{14}\,b^{12}\,c^8-2109763584\,a^{13}\,b^{14}\,c^7+275975424\,a^{12}\,b^{16}\,c^6-23879808\,a^{11}\,b^{18}\,c^5+1232640\,a^{10}\,b^{20}\,c^4-28800\,a^9\,b^{22}\,c^3\right)\right)\,\sqrt{-\frac{9\,\left(25\,b^{21}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9+225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c-694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,1{}\mathrm{i}+\left(\sqrt{-\frac{9\,\left(25\,b^{21}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9+225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c-694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,\left(\sqrt{x}\,\sqrt{-\frac{9\,\left(25\,b^{21}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9+225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c-694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,\left(34359738368\,a^{26}\,b\,c^{13}-94489280512\,a^{25}\,b^3\,c^{12}+118111600640\,a^{24}\,b^5\,c^{11}-88583700480\,a^{23}\,b^7\,c^{10}+44291850240\,a^{22}\,b^9\,c^9-15502147584\,a^{21}\,b^{11}\,c^8+3875536896\,a^{20}\,b^{13}\,c^7-692060160\,a^{19}\,b^{15}\,c^6+86507520\,a^{18}\,b^{17}\,c^5-7208960\,a^{17}\,b^{19}\,c^4+360448\,a^{16}\,b^{21}\,c^3-8192\,a^{15}\,b^{23}\,c^2\right)+74088185856\,a^{23}\,b\,c^{13}-15360\,a^{12}\,b^{23}\,c^2+681984\,a^{13}\,b^{21}\,c^3-13774848\,a^{14}\,b^{19}\,c^4+167067648\,a^{15}\,b^{17}\,c^5-1351876608\,a^{16}\,b^{15}\,c^6+7662993408\,a^{17}\,b^{13}\,c^7-31048335360\,a^{18}\,b^{11}\,c^8+89917489152\,a^{19}\,b^9\,c^9-182401892352\,a^{20}\,b^7\,c^{10}+246826401792\,a^{21}\,b^5\,c^{11}-200521285632\,a^{22}\,b^3\,c^{12}\right)+\sqrt{x}\,\left(33973862400\,a^{20}\,c^{14}-137631891456\,a^{19}\,b^2\,c^{13}+218414186496\,a^{18}\,b^4\,c^{12}-192980975616\,a^{17}\,b^6\,c^{11}+108726976512\,a^{16}\,b^8\,c^{10}-41653370880\,a^{15}\,b^{10}\,c^9+11171856384\,a^{14}\,b^{12}\,c^8-2109763584\,a^{13}\,b^{14}\,c^7+275975424\,a^{12}\,b^{16}\,c^6-23879808\,a^{11}\,b^{18}\,c^5+1232640\,a^{10}\,b^{20}\,c^4-28800\,a^9\,b^{22}\,c^3\right)\right)\,\sqrt{-\frac{9\,\left(25\,b^{21}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9+225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c-694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,1{}\mathrm{i}}{\left(\sqrt{-\frac{9\,\left(25\,b^{21}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9+225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c-694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,\left(\sqrt{x}\,\sqrt{-\frac{9\,\left(25\,b^{21}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9+225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c-694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,\left(34359738368\,a^{26}\,b\,c^{13}-94489280512\,a^{25}\,b^3\,c^{12}+118111600640\,a^{24}\,b^5\,c^{11}-88583700480\,a^{23}\,b^7\,c^{10}+44291850240\,a^{22}\,b^9\,c^9-15502147584\,a^{21}\,b^{11}\,c^8+3875536896\,a^{20}\,b^{13}\,c^7-692060160\,a^{19}\,b^{15}\,c^6+86507520\,a^{18}\,b^{17}\,c^5-7208960\,a^{17}\,b^{19}\,c^4+360448\,a^{16}\,b^{21}\,c^3-8192\,a^{15}\,b^{23}\,c^2\right)+74088185856\,a^{23}\,b\,c^{13}-15360\,a^{12}\,b^{23}\,c^2+681984\,a^{13}\,b^{21}\,c^3-13774848\,a^{14}\,b^{19}\,c^4+167067648\,a^{15}\,b^{17}\,c^5-1351876608\,a^{16}\,b^{15}\,c^6+7662993408\,a^{17}\,b^{13}\,c^7-31048335360\,a^{18}\,b^{11}\,c^8+89917489152\,a^{19}\,b^9\,c^9-182401892352\,a^{20}\,b^7\,c^{10}+246826401792\,a^{21}\,b^5\,c^{11}-200521285632\,a^{22}\,b^3\,c^{12}\right)+\sqrt{x}\,\left(33973862400\,a^{20}\,c^{14}-137631891456\,a^{19}\,b^2\,c^{13}+218414186496\,a^{18}\,b^4\,c^{12}-192980975616\,a^{17}\,b^6\,c^{11}+108726976512\,a^{16}\,b^8\,c^{10}-41653370880\,a^{15}\,b^{10}\,c^9+11171856384\,a^{14}\,b^{12}\,c^8-2109763584\,a^{13}\,b^{14}\,c^7+275975424\,a^{12}\,b^{16}\,c^6-23879808\,a^{11}\,b^{18}\,c^5+1232640\,a^{10}\,b^{20}\,c^4-28800\,a^9\,b^{22}\,c^3\right)\right)\,\sqrt{-\frac{9\,\left(25\,b^{21}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9+225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c-694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}-\left(\sqrt{-\frac{9\,\left(25\,b^{21}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9+225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c-694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,\left(\sqrt{x}\,\sqrt{-\frac{9\,\left(25\,b^{21}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9+225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c-694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,\left(34359738368\,a^{26}\,b\,c^{13}-94489280512\,a^{25}\,b^3\,c^{12}+118111600640\,a^{24}\,b^5\,c^{11}-88583700480\,a^{23}\,b^7\,c^{10}+44291850240\,a^{22}\,b^9\,c^9-15502147584\,a^{21}\,b^{11}\,c^8+3875536896\,a^{20}\,b^{13}\,c^7-692060160\,a^{19}\,b^{15}\,c^6+86507520\,a^{18}\,b^{17}\,c^5-7208960\,a^{17}\,b^{19}\,c^4+360448\,a^{16}\,b^{21}\,c^3-8192\,a^{15}\,b^{23}\,c^2\right)-74088185856\,a^{23}\,b\,c^{13}+15360\,a^{12}\,b^{23}\,c^2-681984\,a^{13}\,b^{21}\,c^3+13774848\,a^{14}\,b^{19}\,c^4-167067648\,a^{15}\,b^{17}\,c^5+1351876608\,a^{16}\,b^{15}\,c^6-7662993408\,a^{17}\,b^{13}\,c^7+31048335360\,a^{18}\,b^{11}\,c^8-89917489152\,a^{19}\,b^9\,c^9+182401892352\,a^{20}\,b^7\,c^{10}-246826401792\,a^{21}\,b^5\,c^{11}+200521285632\,a^{22}\,b^3\,c^{12}\right)+\sqrt{x}\,\left(33973862400\,a^{20}\,c^{14}-137631891456\,a^{19}\,b^2\,c^{13}+218414186496\,a^{18}\,b^4\,c^{12}-192980975616\,a^{17}\,b^6\,c^{11}+108726976512\,a^{16}\,b^8\,c^{10}-41653370880\,a^{15}\,b^{10}\,c^9+11171856384\,a^{14}\,b^{12}\,c^8-2109763584\,a^{13}\,b^{14}\,c^7+275975424\,a^{12}\,b^{16}\,c^6-23879808\,a^{11}\,b^{18}\,c^5+1232640\,a^{10}\,b^{20}\,c^4-28800\,a^9\,b^{22}\,c^3\right)\right)\,\sqrt{-\frac{9\,\left(25\,b^{21}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9+225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c-694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}+47775744000\,a^{17}\,c^{14}+712800\,a^9\,b^{16}\,c^6-23142240\,a^{10}\,b^{14}\,c^7+328157568\,a^{11}\,b^{12}\,c^8-2652784128\,a^{12}\,b^{10}\,c^9+13361338368\,a^{13}\,b^8\,c^{10}-42897973248\,a^{14}\,b^6\,c^{11}+85645099008\,a^{15}\,b^4\,c^{12}-97090928640\,a^{16}\,b^2\,c^{13}}\right)\,\sqrt{-\frac{9\,\left(25\,b^{21}-25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9+225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c-694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\sqrt{-\frac{9\,\left(25\,b^{21}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9-225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c+694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,\left(\sqrt{x}\,\sqrt{-\frac{9\,\left(25\,b^{21}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9-225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c+694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,\left(34359738368\,a^{26}\,b\,c^{13}-94489280512\,a^{25}\,b^3\,c^{12}+118111600640\,a^{24}\,b^5\,c^{11}-88583700480\,a^{23}\,b^7\,c^{10}+44291850240\,a^{22}\,b^9\,c^9-15502147584\,a^{21}\,b^{11}\,c^8+3875536896\,a^{20}\,b^{13}\,c^7-692060160\,a^{19}\,b^{15}\,c^6+86507520\,a^{18}\,b^{17}\,c^5-7208960\,a^{17}\,b^{19}\,c^4+360448\,a^{16}\,b^{21}\,c^3-8192\,a^{15}\,b^{23}\,c^2\right)-74088185856\,a^{23}\,b\,c^{13}+15360\,a^{12}\,b^{23}\,c^2-681984\,a^{13}\,b^{21}\,c^3+13774848\,a^{14}\,b^{19}\,c^4-167067648\,a^{15}\,b^{17}\,c^5+1351876608\,a^{16}\,b^{15}\,c^6-7662993408\,a^{17}\,b^{13}\,c^7+31048335360\,a^{18}\,b^{11}\,c^8-89917489152\,a^{19}\,b^9\,c^9+182401892352\,a^{20}\,b^7\,c^{10}-246826401792\,a^{21}\,b^5\,c^{11}+200521285632\,a^{22}\,b^3\,c^{12}\right)+\sqrt{x}\,\left(33973862400\,a^{20}\,c^{14}-137631891456\,a^{19}\,b^2\,c^{13}+218414186496\,a^{18}\,b^4\,c^{12}-192980975616\,a^{17}\,b^6\,c^{11}+108726976512\,a^{16}\,b^8\,c^{10}-41653370880\,a^{15}\,b^{10}\,c^9+11171856384\,a^{14}\,b^{12}\,c^8-2109763584\,a^{13}\,b^{14}\,c^7+275975424\,a^{12}\,b^{16}\,c^6-23879808\,a^{11}\,b^{18}\,c^5+1232640\,a^{10}\,b^{20}\,c^4-28800\,a^9\,b^{22}\,c^3\right)\right)\,\sqrt{-\frac{9\,\left(25\,b^{21}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9-225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c+694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,1{}\mathrm{i}+\left(\sqrt{-\frac{9\,\left(25\,b^{21}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9-225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c+694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,\left(\sqrt{x}\,\sqrt{-\frac{9\,\left(25\,b^{21}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9-225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c+694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,\left(34359738368\,a^{26}\,b\,c^{13}-94489280512\,a^{25}\,b^3\,c^{12}+118111600640\,a^{24}\,b^5\,c^{11}-88583700480\,a^{23}\,b^7\,c^{10}+44291850240\,a^{22}\,b^9\,c^9-15502147584\,a^{21}\,b^{11}\,c^8+3875536896\,a^{20}\,b^{13}\,c^7-692060160\,a^{19}\,b^{15}\,c^6+86507520\,a^{18}\,b^{17}\,c^5-7208960\,a^{17}\,b^{19}\,c^4+360448\,a^{16}\,b^{21}\,c^3-8192\,a^{15}\,b^{23}\,c^2\right)+74088185856\,a^{23}\,b\,c^{13}-15360\,a^{12}\,b^{23}\,c^2+681984\,a^{13}\,b^{21}\,c^3-13774848\,a^{14}\,b^{19}\,c^4+167067648\,a^{15}\,b^{17}\,c^5-1351876608\,a^{16}\,b^{15}\,c^6+7662993408\,a^{17}\,b^{13}\,c^7-31048335360\,a^{18}\,b^{11}\,c^8+89917489152\,a^{19}\,b^9\,c^9-182401892352\,a^{20}\,b^7\,c^{10}+246826401792\,a^{21}\,b^5\,c^{11}-200521285632\,a^{22}\,b^3\,c^{12}\right)+\sqrt{x}\,\left(33973862400\,a^{20}\,c^{14}-137631891456\,a^{19}\,b^2\,c^{13}+218414186496\,a^{18}\,b^4\,c^{12}-192980975616\,a^{17}\,b^6\,c^{11}+108726976512\,a^{16}\,b^8\,c^{10}-41653370880\,a^{15}\,b^{10}\,c^9+11171856384\,a^{14}\,b^{12}\,c^8-2109763584\,a^{13}\,b^{14}\,c^7+275975424\,a^{12}\,b^{16}\,c^6-23879808\,a^{11}\,b^{18}\,c^5+1232640\,a^{10}\,b^{20}\,c^4-28800\,a^9\,b^{22}\,c^3\right)\right)\,\sqrt{-\frac{9\,\left(25\,b^{21}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9-225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c+694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,1{}\mathrm{i}}{\left(\sqrt{-\frac{9\,\left(25\,b^{21}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9-225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c+694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,\left(\sqrt{x}\,\sqrt{-\frac{9\,\left(25\,b^{21}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9-225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c+694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,\left(34359738368\,a^{26}\,b\,c^{13}-94489280512\,a^{25}\,b^3\,c^{12}+118111600640\,a^{24}\,b^5\,c^{11}-88583700480\,a^{23}\,b^7\,c^{10}+44291850240\,a^{22}\,b^9\,c^9-15502147584\,a^{21}\,b^{11}\,c^8+3875536896\,a^{20}\,b^{13}\,c^7-692060160\,a^{19}\,b^{15}\,c^6+86507520\,a^{18}\,b^{17}\,c^5-7208960\,a^{17}\,b^{19}\,c^4+360448\,a^{16}\,b^{21}\,c^3-8192\,a^{15}\,b^{23}\,c^2\right)+74088185856\,a^{23}\,b\,c^{13}-15360\,a^{12}\,b^{23}\,c^2+681984\,a^{13}\,b^{21}\,c^3-13774848\,a^{14}\,b^{19}\,c^4+167067648\,a^{15}\,b^{17}\,c^5-1351876608\,a^{16}\,b^{15}\,c^6+7662993408\,a^{17}\,b^{13}\,c^7-31048335360\,a^{18}\,b^{11}\,c^8+89917489152\,a^{19}\,b^9\,c^9-182401892352\,a^{20}\,b^7\,c^{10}+246826401792\,a^{21}\,b^5\,c^{11}-200521285632\,a^{22}\,b^3\,c^{12}\right)+\sqrt{x}\,\left(33973862400\,a^{20}\,c^{14}-137631891456\,a^{19}\,b^2\,c^{13}+218414186496\,a^{18}\,b^4\,c^{12}-192980975616\,a^{17}\,b^6\,c^{11}+108726976512\,a^{16}\,b^8\,c^{10}-41653370880\,a^{15}\,b^{10}\,c^9+11171856384\,a^{14}\,b^{12}\,c^8-2109763584\,a^{13}\,b^{14}\,c^7+275975424\,a^{12}\,b^{16}\,c^6-23879808\,a^{11}\,b^{18}\,c^5+1232640\,a^{10}\,b^{20}\,c^4-28800\,a^9\,b^{22}\,c^3\right)\right)\,\sqrt{-\frac{9\,\left(25\,b^{21}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9-225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c+694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}-\left(\sqrt{-\frac{9\,\left(25\,b^{21}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9-225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c+694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,\left(\sqrt{x}\,\sqrt{-\frac{9\,\left(25\,b^{21}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9-225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c+694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,\left(34359738368\,a^{26}\,b\,c^{13}-94489280512\,a^{25}\,b^3\,c^{12}+118111600640\,a^{24}\,b^5\,c^{11}-88583700480\,a^{23}\,b^7\,c^{10}+44291850240\,a^{22}\,b^9\,c^9-15502147584\,a^{21}\,b^{11}\,c^8+3875536896\,a^{20}\,b^{13}\,c^7-692060160\,a^{19}\,b^{15}\,c^6+86507520\,a^{18}\,b^{17}\,c^5-7208960\,a^{17}\,b^{19}\,c^4+360448\,a^{16}\,b^{21}\,c^3-8192\,a^{15}\,b^{23}\,c^2\right)-74088185856\,a^{23}\,b\,c^{13}+15360\,a^{12}\,b^{23}\,c^2-681984\,a^{13}\,b^{21}\,c^3+13774848\,a^{14}\,b^{19}\,c^4-167067648\,a^{15}\,b^{17}\,c^5+1351876608\,a^{16}\,b^{15}\,c^6-7662993408\,a^{17}\,b^{13}\,c^7+31048335360\,a^{18}\,b^{11}\,c^8-89917489152\,a^{19}\,b^9\,c^9+182401892352\,a^{20}\,b^7\,c^{10}-246826401792\,a^{21}\,b^5\,c^{11}+200521285632\,a^{22}\,b^3\,c^{12}\right)+\sqrt{x}\,\left(33973862400\,a^{20}\,c^{14}-137631891456\,a^{19}\,b^2\,c^{13}+218414186496\,a^{18}\,b^4\,c^{12}-192980975616\,a^{17}\,b^6\,c^{11}+108726976512\,a^{16}\,b^8\,c^{10}-41653370880\,a^{15}\,b^{10}\,c^9+11171856384\,a^{14}\,b^{12}\,c^8-2109763584\,a^{13}\,b^{14}\,c^7+275975424\,a^{12}\,b^{16}\,c^6-23879808\,a^{11}\,b^{18}\,c^5+1232640\,a^{10}\,b^{20}\,c^4-28800\,a^9\,b^{22}\,c^3\right)\right)\,\sqrt{-\frac{9\,\left(25\,b^{21}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9-225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c+694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}+47775744000\,a^{17}\,c^{14}+712800\,a^9\,b^{16}\,c^6-23142240\,a^{10}\,b^{14}\,c^7+328157568\,a^{11}\,b^{12}\,c^8-2652784128\,a^{12}\,b^{10}\,c^9+13361338368\,a^{13}\,b^8\,c^{10}-42897973248\,a^{14}\,b^6\,c^{11}+85645099008\,a^{15}\,b^4\,c^{12}-97090928640\,a^{16}\,b^2\,c^{13}}\right)\,\sqrt{-\frac{9\,\left(25\,b^{21}+25\,b^6\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}+18923520\,a^{10}\,b\,c^{10}+17794\,a^2\,b^{17}\,c^2-188095\,a^3\,b^{15}\,c^3+1299860\,a^4\,b^{13}\,c^4-6126640\,a^5\,b^{11}\,c^5+19905600\,a^6\,b^9\,c^6-43904256\,a^7\,b^7\,c^7+62684160\,a^8\,b^5\,c^8-52039680\,a^9\,b^3\,c^9-225\,a^3\,c^3\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-995\,a\,b^{19}\,c+694\,a^2\,b^2\,c^2\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}-245\,a\,b^4\,c\,\sqrt{-{\left(4\,a\,c-b^2\right)}^{15}}\right)}{128\,\left(1048576\,a^{17}\,c^{10}-2621440\,a^{16}\,b^2\,c^9+2949120\,a^{15}\,b^4\,c^8-1966080\,a^{14}\,b^6\,c^7+860160\,a^{13}\,b^8\,c^6-258048\,a^{12}\,b^{10}\,c^5+53760\,a^{11}\,b^{12}\,c^4-7680\,a^{10}\,b^{14}\,c^3+720\,a^9\,b^{16}\,c^2-40\,a^8\,b^{18}\,c+a^7\,b^{20}\right)}}\,2{}\mathrm{i}","Not used",1,"- (2/a + (x^2*(15*b^6 + 324*a^3*c^3 + 25*a^2*b^2*c^2 - 91*a*b^4*c))/(4*a^3*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (b*x*(25*b^4 + 364*a^2*c^2 - 194*a*b^2*c))/(4*a^2*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (b*x^3*(30*b^4*c + 392*a^2*c^3 - 227*a*b^2*c^2))/(4*a^3*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)) + (3*c*x^4*(5*b^4*c + 60*a^2*c^3 - 37*a*b^2*c^2))/(4*a^3*(b^4 + 16*a^2*c^2 - 8*a*b^2*c)))/(x^(5/2)*(2*a*c + b^2) + a^2*x^(1/2) + c^2*x^(9/2) + 2*a*b*x^(3/2) + 2*b*c*x^(7/2)) - atan((((-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*(x^(1/2)*(-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*(34359738368*a^26*b*c^13 - 8192*a^15*b^23*c^2 + 360448*a^16*b^21*c^3 - 7208960*a^17*b^19*c^4 + 86507520*a^18*b^17*c^5 - 692060160*a^19*b^15*c^6 + 3875536896*a^20*b^13*c^7 - 15502147584*a^21*b^11*c^8 + 44291850240*a^22*b^9*c^9 - 88583700480*a^23*b^7*c^10 + 118111600640*a^24*b^5*c^11 - 94489280512*a^25*b^3*c^12) - 74088185856*a^23*b*c^13 + 15360*a^12*b^23*c^2 - 681984*a^13*b^21*c^3 + 13774848*a^14*b^19*c^4 - 167067648*a^15*b^17*c^5 + 1351876608*a^16*b^15*c^6 - 7662993408*a^17*b^13*c^7 + 31048335360*a^18*b^11*c^8 - 89917489152*a^19*b^9*c^9 + 182401892352*a^20*b^7*c^10 - 246826401792*a^21*b^5*c^11 + 200521285632*a^22*b^3*c^12) + x^(1/2)*(33973862400*a^20*c^14 - 28800*a^9*b^22*c^3 + 1232640*a^10*b^20*c^4 - 23879808*a^11*b^18*c^5 + 275975424*a^12*b^16*c^6 - 2109763584*a^13*b^14*c^7 + 11171856384*a^14*b^12*c^8 - 41653370880*a^15*b^10*c^9 + 108726976512*a^16*b^8*c^10 - 192980975616*a^17*b^6*c^11 + 218414186496*a^18*b^4*c^12 - 137631891456*a^19*b^2*c^13))*(-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*1i + ((-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*(x^(1/2)*(-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*(34359738368*a^26*b*c^13 - 8192*a^15*b^23*c^2 + 360448*a^16*b^21*c^3 - 7208960*a^17*b^19*c^4 + 86507520*a^18*b^17*c^5 - 692060160*a^19*b^15*c^6 + 3875536896*a^20*b^13*c^7 - 15502147584*a^21*b^11*c^8 + 44291850240*a^22*b^9*c^9 - 88583700480*a^23*b^7*c^10 + 118111600640*a^24*b^5*c^11 - 94489280512*a^25*b^3*c^12) + 74088185856*a^23*b*c^13 - 15360*a^12*b^23*c^2 + 681984*a^13*b^21*c^3 - 13774848*a^14*b^19*c^4 + 167067648*a^15*b^17*c^5 - 1351876608*a^16*b^15*c^6 + 7662993408*a^17*b^13*c^7 - 31048335360*a^18*b^11*c^8 + 89917489152*a^19*b^9*c^9 - 182401892352*a^20*b^7*c^10 + 246826401792*a^21*b^5*c^11 - 200521285632*a^22*b^3*c^12) + x^(1/2)*(33973862400*a^20*c^14 - 28800*a^9*b^22*c^3 + 1232640*a^10*b^20*c^4 - 23879808*a^11*b^18*c^5 + 275975424*a^12*b^16*c^6 - 2109763584*a^13*b^14*c^7 + 11171856384*a^14*b^12*c^8 - 41653370880*a^15*b^10*c^9 + 108726976512*a^16*b^8*c^10 - 192980975616*a^17*b^6*c^11 + 218414186496*a^18*b^4*c^12 - 137631891456*a^19*b^2*c^13))*(-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*1i)/(((-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*(x^(1/2)*(-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*(34359738368*a^26*b*c^13 - 8192*a^15*b^23*c^2 + 360448*a^16*b^21*c^3 - 7208960*a^17*b^19*c^4 + 86507520*a^18*b^17*c^5 - 692060160*a^19*b^15*c^6 + 3875536896*a^20*b^13*c^7 - 15502147584*a^21*b^11*c^8 + 44291850240*a^22*b^9*c^9 - 88583700480*a^23*b^7*c^10 + 118111600640*a^24*b^5*c^11 - 94489280512*a^25*b^3*c^12) + 74088185856*a^23*b*c^13 - 15360*a^12*b^23*c^2 + 681984*a^13*b^21*c^3 - 13774848*a^14*b^19*c^4 + 167067648*a^15*b^17*c^5 - 1351876608*a^16*b^15*c^6 + 7662993408*a^17*b^13*c^7 - 31048335360*a^18*b^11*c^8 + 89917489152*a^19*b^9*c^9 - 182401892352*a^20*b^7*c^10 + 246826401792*a^21*b^5*c^11 - 200521285632*a^22*b^3*c^12) + x^(1/2)*(33973862400*a^20*c^14 - 28800*a^9*b^22*c^3 + 1232640*a^10*b^20*c^4 - 23879808*a^11*b^18*c^5 + 275975424*a^12*b^16*c^6 - 2109763584*a^13*b^14*c^7 + 11171856384*a^14*b^12*c^8 - 41653370880*a^15*b^10*c^9 + 108726976512*a^16*b^8*c^10 - 192980975616*a^17*b^6*c^11 + 218414186496*a^18*b^4*c^12 - 137631891456*a^19*b^2*c^13))*(-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2) - ((-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*(x^(1/2)*(-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*(34359738368*a^26*b*c^13 - 8192*a^15*b^23*c^2 + 360448*a^16*b^21*c^3 - 7208960*a^17*b^19*c^4 + 86507520*a^18*b^17*c^5 - 692060160*a^19*b^15*c^6 + 3875536896*a^20*b^13*c^7 - 15502147584*a^21*b^11*c^8 + 44291850240*a^22*b^9*c^9 - 88583700480*a^23*b^7*c^10 + 118111600640*a^24*b^5*c^11 - 94489280512*a^25*b^3*c^12) - 74088185856*a^23*b*c^13 + 15360*a^12*b^23*c^2 - 681984*a^13*b^21*c^3 + 13774848*a^14*b^19*c^4 - 167067648*a^15*b^17*c^5 + 1351876608*a^16*b^15*c^6 - 7662993408*a^17*b^13*c^7 + 31048335360*a^18*b^11*c^8 - 89917489152*a^19*b^9*c^9 + 182401892352*a^20*b^7*c^10 - 246826401792*a^21*b^5*c^11 + 200521285632*a^22*b^3*c^12) + x^(1/2)*(33973862400*a^20*c^14 - 28800*a^9*b^22*c^3 + 1232640*a^10*b^20*c^4 - 23879808*a^11*b^18*c^5 + 275975424*a^12*b^16*c^6 - 2109763584*a^13*b^14*c^7 + 11171856384*a^14*b^12*c^8 - 41653370880*a^15*b^10*c^9 + 108726976512*a^16*b^8*c^10 - 192980975616*a^17*b^6*c^11 + 218414186496*a^18*b^4*c^12 - 137631891456*a^19*b^2*c^13))*(-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2) + 47775744000*a^17*c^14 + 712800*a^9*b^16*c^6 - 23142240*a^10*b^14*c^7 + 328157568*a^11*b^12*c^8 - 2652784128*a^12*b^10*c^9 + 13361338368*a^13*b^8*c^10 - 42897973248*a^14*b^6*c^11 + 85645099008*a^15*b^4*c^12 - 97090928640*a^16*b^2*c^13))*(-(9*(25*b^21 - 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 + 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c - 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) + 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*2i - atan((((-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*(x^(1/2)*(-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*(34359738368*a^26*b*c^13 - 8192*a^15*b^23*c^2 + 360448*a^16*b^21*c^3 - 7208960*a^17*b^19*c^4 + 86507520*a^18*b^17*c^5 - 692060160*a^19*b^15*c^6 + 3875536896*a^20*b^13*c^7 - 15502147584*a^21*b^11*c^8 + 44291850240*a^22*b^9*c^9 - 88583700480*a^23*b^7*c^10 + 118111600640*a^24*b^5*c^11 - 94489280512*a^25*b^3*c^12) - 74088185856*a^23*b*c^13 + 15360*a^12*b^23*c^2 - 681984*a^13*b^21*c^3 + 13774848*a^14*b^19*c^4 - 167067648*a^15*b^17*c^5 + 1351876608*a^16*b^15*c^6 - 7662993408*a^17*b^13*c^7 + 31048335360*a^18*b^11*c^8 - 89917489152*a^19*b^9*c^9 + 182401892352*a^20*b^7*c^10 - 246826401792*a^21*b^5*c^11 + 200521285632*a^22*b^3*c^12) + x^(1/2)*(33973862400*a^20*c^14 - 28800*a^9*b^22*c^3 + 1232640*a^10*b^20*c^4 - 23879808*a^11*b^18*c^5 + 275975424*a^12*b^16*c^6 - 2109763584*a^13*b^14*c^7 + 11171856384*a^14*b^12*c^8 - 41653370880*a^15*b^10*c^9 + 108726976512*a^16*b^8*c^10 - 192980975616*a^17*b^6*c^11 + 218414186496*a^18*b^4*c^12 - 137631891456*a^19*b^2*c^13))*(-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*1i + ((-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*(x^(1/2)*(-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*(34359738368*a^26*b*c^13 - 8192*a^15*b^23*c^2 + 360448*a^16*b^21*c^3 - 7208960*a^17*b^19*c^4 + 86507520*a^18*b^17*c^5 - 692060160*a^19*b^15*c^6 + 3875536896*a^20*b^13*c^7 - 15502147584*a^21*b^11*c^8 + 44291850240*a^22*b^9*c^9 - 88583700480*a^23*b^7*c^10 + 118111600640*a^24*b^5*c^11 - 94489280512*a^25*b^3*c^12) + 74088185856*a^23*b*c^13 - 15360*a^12*b^23*c^2 + 681984*a^13*b^21*c^3 - 13774848*a^14*b^19*c^4 + 167067648*a^15*b^17*c^5 - 1351876608*a^16*b^15*c^6 + 7662993408*a^17*b^13*c^7 - 31048335360*a^18*b^11*c^8 + 89917489152*a^19*b^9*c^9 - 182401892352*a^20*b^7*c^10 + 246826401792*a^21*b^5*c^11 - 200521285632*a^22*b^3*c^12) + x^(1/2)*(33973862400*a^20*c^14 - 28800*a^9*b^22*c^3 + 1232640*a^10*b^20*c^4 - 23879808*a^11*b^18*c^5 + 275975424*a^12*b^16*c^6 - 2109763584*a^13*b^14*c^7 + 11171856384*a^14*b^12*c^8 - 41653370880*a^15*b^10*c^9 + 108726976512*a^16*b^8*c^10 - 192980975616*a^17*b^6*c^11 + 218414186496*a^18*b^4*c^12 - 137631891456*a^19*b^2*c^13))*(-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*1i)/(((-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*(x^(1/2)*(-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*(34359738368*a^26*b*c^13 - 8192*a^15*b^23*c^2 + 360448*a^16*b^21*c^3 - 7208960*a^17*b^19*c^4 + 86507520*a^18*b^17*c^5 - 692060160*a^19*b^15*c^6 + 3875536896*a^20*b^13*c^7 - 15502147584*a^21*b^11*c^8 + 44291850240*a^22*b^9*c^9 - 88583700480*a^23*b^7*c^10 + 118111600640*a^24*b^5*c^11 - 94489280512*a^25*b^3*c^12) + 74088185856*a^23*b*c^13 - 15360*a^12*b^23*c^2 + 681984*a^13*b^21*c^3 - 13774848*a^14*b^19*c^4 + 167067648*a^15*b^17*c^5 - 1351876608*a^16*b^15*c^6 + 7662993408*a^17*b^13*c^7 - 31048335360*a^18*b^11*c^8 + 89917489152*a^19*b^9*c^9 - 182401892352*a^20*b^7*c^10 + 246826401792*a^21*b^5*c^11 - 200521285632*a^22*b^3*c^12) + x^(1/2)*(33973862400*a^20*c^14 - 28800*a^9*b^22*c^3 + 1232640*a^10*b^20*c^4 - 23879808*a^11*b^18*c^5 + 275975424*a^12*b^16*c^6 - 2109763584*a^13*b^14*c^7 + 11171856384*a^14*b^12*c^8 - 41653370880*a^15*b^10*c^9 + 108726976512*a^16*b^8*c^10 - 192980975616*a^17*b^6*c^11 + 218414186496*a^18*b^4*c^12 - 137631891456*a^19*b^2*c^13))*(-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2) - ((-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*(x^(1/2)*(-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*(34359738368*a^26*b*c^13 - 8192*a^15*b^23*c^2 + 360448*a^16*b^21*c^3 - 7208960*a^17*b^19*c^4 + 86507520*a^18*b^17*c^5 - 692060160*a^19*b^15*c^6 + 3875536896*a^20*b^13*c^7 - 15502147584*a^21*b^11*c^8 + 44291850240*a^22*b^9*c^9 - 88583700480*a^23*b^7*c^10 + 118111600640*a^24*b^5*c^11 - 94489280512*a^25*b^3*c^12) - 74088185856*a^23*b*c^13 + 15360*a^12*b^23*c^2 - 681984*a^13*b^21*c^3 + 13774848*a^14*b^19*c^4 - 167067648*a^15*b^17*c^5 + 1351876608*a^16*b^15*c^6 - 7662993408*a^17*b^13*c^7 + 31048335360*a^18*b^11*c^8 - 89917489152*a^19*b^9*c^9 + 182401892352*a^20*b^7*c^10 - 246826401792*a^21*b^5*c^11 + 200521285632*a^22*b^3*c^12) + x^(1/2)*(33973862400*a^20*c^14 - 28800*a^9*b^22*c^3 + 1232640*a^10*b^20*c^4 - 23879808*a^11*b^18*c^5 + 275975424*a^12*b^16*c^6 - 2109763584*a^13*b^14*c^7 + 11171856384*a^14*b^12*c^8 - 41653370880*a^15*b^10*c^9 + 108726976512*a^16*b^8*c^10 - 192980975616*a^17*b^6*c^11 + 218414186496*a^18*b^4*c^12 - 137631891456*a^19*b^2*c^13))*(-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2) + 47775744000*a^17*c^14 + 712800*a^9*b^16*c^6 - 23142240*a^10*b^14*c^7 + 328157568*a^11*b^12*c^8 - 2652784128*a^12*b^10*c^9 + 13361338368*a^13*b^8*c^10 - 42897973248*a^14*b^6*c^11 + 85645099008*a^15*b^4*c^12 - 97090928640*a^16*b^2*c^13))*(-(9*(25*b^21 + 25*b^6*(-(4*a*c - b^2)^15)^(1/2) + 18923520*a^10*b*c^10 + 17794*a^2*b^17*c^2 - 188095*a^3*b^15*c^3 + 1299860*a^4*b^13*c^4 - 6126640*a^5*b^11*c^5 + 19905600*a^6*b^9*c^6 - 43904256*a^7*b^7*c^7 + 62684160*a^8*b^5*c^8 - 52039680*a^9*b^3*c^9 - 225*a^3*c^3*(-(4*a*c - b^2)^15)^(1/2) - 995*a*b^19*c + 694*a^2*b^2*c^2*(-(4*a*c - b^2)^15)^(1/2) - 245*a*b^4*c*(-(4*a*c - b^2)^15)^(1/2)))/(128*(a^7*b^20 + 1048576*a^17*c^10 - 40*a^8*b^18*c + 720*a^9*b^16*c^2 - 7680*a^10*b^14*c^3 + 53760*a^11*b^12*c^4 - 258048*a^12*b^10*c^5 + 860160*a^13*b^8*c^6 - 1966080*a^14*b^6*c^7 + 2949120*a^15*b^4*c^8 - 2621440*a^16*b^2*c^9)))^(1/2)*2i","B"
2332,1,15,28,0.033570,"\text{Not used}","int((x^2 - x + 3)/x^(1/3),x)","\frac{3\,x^{2/3}\,\left(5\,x^2-8\,x+60\right)}{40}","Not used",1,"(3*x^(2/3)*(5*x^2 - 8*x + 60))/40","B"
2333,1,632,248,2.248693,"\text{Not used}","int((d + e*x)^3*(a + b*x + c*x^2)^(1/2),x)","d^3\,\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}+\frac{7\,b\,e^3\,\left(\frac{5\,b\,\left(\frac{\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x+a}\right)\,\left(b^3-4\,a\,b\,c\right)}{16\,c^{5/2}}+\frac{\left(-3\,b^2+2\,c\,x\,b+8\,c\,\left(c\,x^2+a\right)\right)\,\sqrt{c\,x^2+b\,x+a}}{24\,c^2}\right)}{8\,c}-\frac{x\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{4\,c}+\frac{a\,\left(\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}+\frac{\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}\right)}{4\,c}\right)}{10\,c}+\frac{e^3\,x^2\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{5\,c}+\frac{d^3\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}-\frac{2\,a\,e^3\,\left(\frac{\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x+a}\right)\,\left(b^3-4\,a\,b\,c\right)}{16\,c^{5/2}}+\frac{\left(-3\,b^2+2\,c\,x\,b+8\,c\,\left(c\,x^2+a\right)\right)\,\sqrt{c\,x^2+b\,x+a}}{24\,c^2}\right)}{5\,c}-\frac{3\,a\,d\,e^2\,\left(\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}+\frac{\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}\right)}{4\,c}+\frac{3\,d^2\,e\,\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x+a}\right)\,\left(b^3-4\,a\,b\,c\right)}{16\,c^{5/2}}-\frac{15\,b\,d\,e^2\,\left(\frac{\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x+a}\right)\,\left(b^3-4\,a\,b\,c\right)}{16\,c^{5/2}}+\frac{\left(-3\,b^2+2\,c\,x\,b+8\,c\,\left(c\,x^2+a\right)\right)\,\sqrt{c\,x^2+b\,x+a}}{24\,c^2}\right)}{8\,c}+\frac{d^2\,e\,\left(-3\,b^2+2\,c\,x\,b+8\,c\,\left(c\,x^2+a\right)\right)\,\sqrt{c\,x^2+b\,x+a}}{8\,c^2}+\frac{3\,d\,e^2\,x\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{4\,c}","Not used",1,"d^3*(x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) + (7*b*e^3*((5*b*((log((b + 2*c*x)/c^(1/2) + 2*(a + b*x + c*x^2)^(1/2))*(b^3 - 4*a*b*c))/(16*c^(5/2)) + ((8*c*(a + c*x^2) - 3*b^2 + 2*b*c*x)*(a + b*x + c*x^2)^(1/2))/(24*c^2)))/(8*c) - (x*(a + b*x + c*x^2)^(3/2))/(4*c) + (a*((x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) + (log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2))))/(4*c)))/(10*c) + (e^3*x^2*(a + b*x + c*x^2)^(3/2))/(5*c) + (d^3*log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2)) - (2*a*e^3*((log((b + 2*c*x)/c^(1/2) + 2*(a + b*x + c*x^2)^(1/2))*(b^3 - 4*a*b*c))/(16*c^(5/2)) + ((8*c*(a + c*x^2) - 3*b^2 + 2*b*c*x)*(a + b*x + c*x^2)^(1/2))/(24*c^2)))/(5*c) - (3*a*d*e^2*((x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) + (log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2))))/(4*c) + (3*d^2*e*log((b + 2*c*x)/c^(1/2) + 2*(a + b*x + c*x^2)^(1/2))*(b^3 - 4*a*b*c))/(16*c^(5/2)) - (15*b*d*e^2*((log((b + 2*c*x)/c^(1/2) + 2*(a + b*x + c*x^2)^(1/2))*(b^3 - 4*a*b*c))/(16*c^(5/2)) + ((8*c*(a + c*x^2) - 3*b^2 + 2*b*c*x)*(a + b*x + c*x^2)^(1/2))/(24*c^2)))/(8*c) + (d^2*e*(8*c*(a + c*x^2) - 3*b^2 + 2*b*c*x)*(a + b*x + c*x^2)^(1/2))/(8*c^2) + (3*d*e^2*x*(a + b*x + c*x^2)^(3/2))/(4*c)","B"
2334,1,332,191,1.565848,"\text{Not used}","int((d + e*x)^2*(a + b*x + c*x^2)^(1/2),x)","d^2\,\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}+\frac{e^2\,x\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{4\,c}-\frac{a\,e^2\,\left(\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}+\frac{\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}\right)}{4\,c}+\frac{d^2\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}-\frac{5\,b\,e^2\,\left(\frac{\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x+a}\right)\,\left(b^3-4\,a\,b\,c\right)}{16\,c^{5/2}}+\frac{\left(-3\,b^2+2\,c\,x\,b+8\,c\,\left(c\,x^2+a\right)\right)\,\sqrt{c\,x^2+b\,x+a}}{24\,c^2}\right)}{8\,c}+\frac{d\,e\,\left(-3\,b^2+2\,c\,x\,b+8\,c\,\left(c\,x^2+a\right)\right)\,\sqrt{c\,x^2+b\,x+a}}{12\,c^2}+\frac{d\,e\,\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x+a}\right)\,\left(b^3-4\,a\,b\,c\right)}{8\,c^{5/2}}","Not used",1,"d^2*(x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) + (e^2*x*(a + b*x + c*x^2)^(3/2))/(4*c) - (a*e^2*((x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) + (log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2))))/(4*c) + (d^2*log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2)) - (5*b*e^2*((log((b + 2*c*x)/c^(1/2) + 2*(a + b*x + c*x^2)^(1/2))*(b^3 - 4*a*b*c))/(16*c^(5/2)) + ((8*c*(a + c*x^2) - 3*b^2 + 2*b*c*x)*(a + b*x + c*x^2)^(1/2))/(24*c^2)))/(8*c) + (d*e*(8*c*(a + c*x^2) - 3*b^2 + 2*b*c*x)*(a + b*x + c*x^2)^(1/2))/(12*c^2) + (d*e*log((b + 2*c*x)/c^(1/2) + 2*(a + b*x + c*x^2)^(1/2))*(b^3 - 4*a*b*c))/(8*c^(5/2))","B"
2335,1,145,115,1.206276,"\text{Not used}","int((d + e*x)*(a + b*x + c*x^2)^(1/2),x)","d\,\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}+\frac{d\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}+\frac{e\,\ln\left(\frac{b+2\,c\,x}{\sqrt{c}}+2\,\sqrt{c\,x^2+b\,x+a}\right)\,\left(b^3-4\,a\,b\,c\right)}{16\,c^{5/2}}+\frac{e\,\left(-3\,b^2+2\,c\,x\,b+8\,c\,\left(c\,x^2+a\right)\right)\,\sqrt{c\,x^2+b\,x+a}}{24\,c^2}","Not used",1,"d*(x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) + (d*log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2)) + (e*log((b + 2*c*x)/c^(1/2) + 2*(a + b*x + c*x^2)^(1/2))*(b^3 - 4*a*b*c))/(16*c^(5/2)) + (e*(8*c*(a + c*x^2) - 3*b^2 + 2*b*c*x)*(a + b*x + c*x^2)^(1/2))/(24*c^2)","B"
2336,1,63,75,1.020907,"\text{Not used}","int((a + b*x + c*x^2)^(1/2),x)","\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}+\frac{\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}","Not used",1,"(x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) + (log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2))","B"
2337,0,-1,152,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(d + e*x),x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{d+e\,x} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(d + e*x), x)","F"
2338,0,-1,160,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(d + e*x)^2,x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(d + e*x)^2, x)","F"
2339,0,-1,153,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(d + e*x)^3,x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(d + e*x)^3, x)","F"
2340,0,-1,215,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(d + e*x)^4,x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(d + e*x)^4, x)","F"
2341,0,-1,308,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(d + e*x)^5,x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(d+e\,x\right)}^5} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(d + e*x)^5, x)","F"
2342,0,-1,402,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(d + e*x)^6,x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(d+e\,x\right)}^6} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(d + e*x)^6, x)","F"
2343,0,-1,321,0.000000,"\text{Not used}","int((d + e*x)^3*(a + b*x + c*x^2)^(3/2),x)","\int {\left(d+e\,x\right)}^3\,{\left(c\,x^2+b\,x+a\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^3*(a + b*x + c*x^2)^(3/2), x)","F"
2344,0,-1,257,0.000000,"\text{Not used}","int((d + e*x)^2*(a + b*x + c*x^2)^(3/2),x)","\int {\left(d+e\,x\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^2*(a + b*x + c*x^2)^(3/2), x)","F"
2345,1,305,161,1.508708,"\text{Not used}","int((d + e*x)*(a + b*x + c*x^2)^(3/2),x)","\frac{e\,{\left(c\,x^2+b\,x+a\right)}^{5/2}}{5\,c}+\frac{d\,\left(\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}+\frac{\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}\right)\,\left(3\,a\,c-\frac{3\,b^2}{4}\right)}{4\,c}-\frac{b\,e\,\left(\frac{3\,a\,\left(\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(\frac{a}{2\,\sqrt{c}}-\frac{b^2}{8\,c^{3/2}}\right)+\frac{\left(b+2\,c\,x\right)\,\sqrt{c\,x^2+b\,x+a}}{4\,c}\right)}{4}+\frac{x\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{4}+\frac{b\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{8\,c}-\frac{3\,b^2\,\left(\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(\frac{a}{2\,\sqrt{c}}-\frac{b^2}{8\,c^{3/2}}\right)+\frac{\left(b+2\,c\,x\right)\,\sqrt{c\,x^2+b\,x+a}}{4\,c}\right)}{16\,c}\right)}{2\,c}+\frac{d\,\left(\frac{b}{2}+c\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{4\,c}","Not used",1,"(e*(a + b*x + c*x^2)^(5/2))/(5*c) + (d*((x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) + (log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2)))*(3*a*c - (3*b^2)/4))/(4*c) - (b*e*((3*a*(log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a/(2*c^(1/2)) - b^2/(8*c^(3/2))) + ((b + 2*c*x)*(a + b*x + c*x^2)^(1/2))/(4*c)))/4 + (x*(a + b*x + c*x^2)^(3/2))/4 + (b*(a + b*x + c*x^2)^(3/2))/(8*c) - (3*b^2*(log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a/(2*c^(1/2)) - b^2/(8*c^(3/2))) + ((b + 2*c*x)*(a + b*x + c*x^2)^(1/2))/(4*c)))/(16*c)))/(2*c) + (d*(b/2 + c*x)*(a + b*x + c*x^2)^(3/2))/(4*c)","B"
2346,1,103,112,0.173875,"\text{Not used}","int((a + b*x + c*x^2)^(3/2),x)","\frac{\left(\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}+\frac{\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}\right)\,\left(3\,a\,c-\frac{3\,b^2}{4}\right)}{4\,c}+\frac{\left(\frac{b}{2}+c\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{4\,c}","Not used",1,"(((x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) + (log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2)))*(3*a*c - (3*b^2)/4))/(4*c) + ((b/2 + c*x)*(a + b*x + c*x^2)^(3/2))/(4*c)","B"
2347,0,-1,252,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(d + e*x),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{d+e\,x} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(d + e*x), x)","F"
2348,0,-1,227,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(d + e*x)^2,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(d + e*x)^2, x)","F"
2349,0,-1,236,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(d + e*x)^3,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(d + e*x)^3, x)","F"
2350,0,-1,307,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(d + e*x)^4,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(d + e*x)^4, x)","F"
2351,0,-1,225,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(d + e*x)^5,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(d+e\,x\right)}^5} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(d + e*x)^5, x)","F"
2352,0,-1,296,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(d + e*x)^6,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(d+e\,x\right)}^6} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(d + e*x)^6, x)","F"
2353,0,-1,409,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(d + e*x)^7,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(d+e\,x\right)}^7} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(d + e*x)^7, x)","F"
2354,0,-1,510,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(d + e*x)^8,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(d+e\,x\right)}^8} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(d + e*x)^8, x)","F"
2355,0,-1,400,0.000000,"\text{Not used}","int((d + e*x)^3*(a + b*x + c*x^2)^(5/2),x)","\int {\left(d+e\,x\right)}^3\,{\left(c\,x^2+b\,x+a\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)^3*(a + b*x + c*x^2)^(5/2), x)","F"
2356,0,-1,323,0.000000,"\text{Not used}","int((d + e*x)^2*(a + b*x + c*x^2)^(5/2),x)","\int {\left(d+e\,x\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)^2*(a + b*x + c*x^2)^(5/2), x)","F"
2357,0,-1,207,0.000000,"\text{Not used}","int((d + e*x)*(a + b*x + c*x^2)^(5/2),x)","\int \left(d+e\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)*(a + b*x + c*x^2)^(5/2), x)","F"
2358,1,143,149,1.171306,"\text{Not used}","int((a + b*x + c*x^2)^(5/2),x)","\frac{\left(\frac{b}{2}+c\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{5/2}}{6\,c}+\frac{\left(\frac{\left(\left(\frac{x}{2}+\frac{b}{4\,c}\right)\,\sqrt{c\,x^2+b\,x+a}+\frac{\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)\,\left(a\,c-\frac{b^2}{4}\right)}{2\,c^{3/2}}\right)\,\left(3\,a\,c-\frac{3\,b^2}{4}\right)}{4\,c}+\frac{\left(\frac{b}{2}+c\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}{4\,c}\right)\,\left(5\,a\,c-\frac{5\,b^2}{4}\right)}{6\,c}","Not used",1,"((b/2 + c*x)*(a + b*x + c*x^2)^(5/2))/(6*c) + (((((x/2 + b/(4*c))*(a + b*x + c*x^2)^(1/2) + (log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))*(a*c - b^2/4))/(2*c^(3/2)))*(3*a*c - (3*b^2)/4))/(4*c) + ((b/2 + c*x)*(a + b*x + c*x^2)^(3/2))/(4*c))*(5*a*c - (5*b^2)/4))/(6*c)","B"
2359,0,-1,459,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(d + e*x),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{d+e\,x} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(d + e*x), x)","F"
2360,0,-1,388,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(d + e*x)^2,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(d + e*x)^2, x)","F"
2361,0,-1,331,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(d + e*x)^3,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(d + e*x)^3, x)","F"
2362,0,-1,337,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(d + e*x)^4,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(d + e*x)^4, x)","F"
2363,0,-1,492,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(d + e*x)^5,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(d+e\,x\right)}^5} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(d + e*x)^5, x)","F"
2364,1,77,88,0.212953,"\text{Not used}","int((5*x^2 - 3*x - 2)^(1/2)/x,x)","\sqrt{5\,x^2-3\,x-2}-\frac{3\,\sqrt{5}\,\ln\left(\sqrt{5\,x^2-3\,x-2}+\frac{\sqrt{5}\,\left(5\,x-\frac{3}{2}\right)}{5}\right)}{10}-\sqrt{2}\,\ln\left(-\frac{2}{x}-\frac{3}{2}+\frac{\sqrt{2}\,\sqrt{5\,x^2-3\,x-2}\,1{}\mathrm{i}}{x}\right)\,1{}\mathrm{i}","Not used",1,"(5*x^2 - 3*x - 2)^(1/2) - (3*5^(1/2)*log((5*x^2 - 3*x - 2)^(1/2) + (5^(1/2)*(5*x - 3/2))/5))/10 - 2^(1/2)*log((2^(1/2)*(5*x^2 - 3*x - 2)^(1/2)*1i)/x - 2/x - 3/2)*1i","B"
2365,1,73,68,1.062317,"\text{Not used}","int((2 - x^2 - x)^(1/2)/x^2,x)","\frac{\sqrt{2}\,\ln\left(\frac{2}{x}+\frac{\sqrt{2}\,\sqrt{-x^2-x+2}}{x}-\frac{1}{2}\right)}{4}-\frac{\sqrt{-x^2-x+2}}{x}+\ln\left(x\,1{}\mathrm{i}+\sqrt{-x^2-x+2}+\frac{1}{2}{}\mathrm{i}\right)\,1{}\mathrm{i}","Not used",1,"log(x*1i + (2 - x^2 - x)^(1/2) + 1i/2)*1i - (2 - x^2 - x)^(1/2)/x + (2^(1/2)*log(2/x + (2^(1/2)*(2 - x^2 - x)^(1/2))/x - 1/2))/4","B"
2366,1,22,38,1.063175,"\text{Not used}","int((x + 1)^3*(2*x + x^2 + 2)^(1/2),x)","\frac{{\left(x^2+2\,x+2\right)}^{3/2}\,\left(3\,x^2+6\,x+1\right)}{15}","Not used",1,"((2*x + x^2 + 2)^(3/2)*(6*x + 3*x^2 + 1))/15","B"
2367,1,84,54,1.236453,"\text{Not used}","int((3*x - 2)*(12*x + 9*x^2 + 8)^(1/2),x)","\frac{\sqrt{9\,x^2+12\,x+8}\,\left(648\,x^2+216\,x+144\right)}{648}-\frac{4\,\ln\left(x+\frac{\sqrt{9\,x^2+12\,x+8}}{3}+\frac{2}{3}\right)}{3}-2\,\left(\frac{x}{2}+\frac{1}{3}\right)\,\sqrt{9\,x^2+12\,x+8}-\frac{4\,\ln\left(3\,x+\sqrt{9\,x^2+12\,x+8}+2\right)}{3}","Not used",1,"((12*x + 9*x^2 + 8)^(1/2)*(216*x + 648*x^2 + 144))/648 - (4*log(x + (12*x + 9*x^2 + 8)^(1/2)/3 + 2/3))/3 - 2*(x/2 + 1/3)*(12*x + 9*x^2 + 8)^(1/2) - (4*log(3*x + (12*x + 9*x^2 + 8)^(1/2) + 2))/3","B"
2368,1,74,56,0.205323,"\text{Not used}","int(-(2*x - 7)*(16*x - 4*x^2 + 9)^(1/2),x)","\frac{175\,\mathrm{asin}\left(\frac{2\,x}{5}-\frac{4}{5}\right)}{4}+7\,\left(\frac{x}{2}-1\right)\,\sqrt{-4\,x^2+16\,x+9}+\frac{\sqrt{-4\,x^2+16\,x+9}\,\left(-128\,x^2+128\,x+1056\right)}{192}+\ln\left(x-2-\frac{\sqrt{-4\,x^2+16\,x+9}\,1{}\mathrm{i}}{2}\right)\,25{}\mathrm{i}","Not used",1,"log(x - ((16*x - 4*x^2 + 9)^(1/2)*1i)/2 - 2)*25i + (175*asin((2*x)/5 - 4/5))/4 + 7*(x/2 - 1)*(16*x - 4*x^2 + 9)^(1/2) + ((16*x - 4*x^2 + 9)^(1/2)*(128*x - 128*x^2 + 1056))/192","B"
2369,0,-1,61,0.000000,"\text{Not used}","int((x^2 - x - 1)^(1/2)/(x + 1),x)","\int \frac{\sqrt{x^2-x-1}}{x+1} \,d x","Not used",1,"int((x^2 - x - 1)^(1/2)/(x + 1), x)","F"
2370,0,-1,65,0.000000,"\text{Not used}","int(-(x^2 - x - 1)^(1/2)/(x - 1),x)","-\int \frac{\sqrt{x^2-x-1}}{x-1} \,d x","Not used",1,"-int((x^2 - x - 1)^(1/2)/(x - 1), x)","F"
2371,0,-1,261,0.000000,"\text{Not used}","int(x^6/(a + b*x + c*x^2)^(1/2),x)","\int \frac{x^6}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(x^6/(a + b*x + c*x^2)^(1/2), x)","F"
2372,0,-1,202,0.000000,"\text{Not used}","int(x^5/(a + b*x + c*x^2)^(1/2),x)","\int \frac{x^5}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(x^5/(a + b*x + c*x^2)^(1/2), x)","F"
2373,0,-1,296,0.000000,"\text{Not used}","int((d + e*x)^4/(a + b*x + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int((d + e*x)^4/(a + b*x + c*x^2)^(1/2), x)","F"
2374,0,-1,174,0.000000,"\text{Not used}","int((d + e*x)^3/(a + b*x + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^3}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int((d + e*x)^3/(a + b*x + c*x^2)^(1/2), x)","F"
2375,0,-1,127,0.000000,"\text{Not used}","int((d + e*x)^2/(a + b*x + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^2}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int((d + e*x)^2/(a + b*x + c*x^2)^(1/2), x)","F"
2376,1,80,68,1.320803,"\text{Not used}","int((d + e*x)/(a + b*x + c*x^2)^(1/2),x)","\frac{e\,\sqrt{c\,x^2+b\,x+a}}{c}+\frac{d\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)}{\sqrt{c}}-\frac{b\,e\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)}{2\,c^{3/2}}","Not used",1,"(e*(a + b*x + c*x^2)^(1/2))/c + (d*log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2)))/c^(1/2) - (b*e*log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2)))/(2*c^(3/2))","B"
2377,1,29,36,1.089635,"\text{Not used}","int(1/(a + b*x + c*x^2)^(1/2),x)","\frac{\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)}{\sqrt{c}}","Not used",1,"log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2))/c^(1/2)","B"
2378,0,-1,79,0.000000,"\text{Not used}","int(1/((d + e*x)*(a + b*x + c*x^2)^(1/2)),x)","\int \frac{1}{\left(d+e\,x\right)\,\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(1/((d + e*x)*(a + b*x + c*x^2)^(1/2)), x)","F"
2379,0,-1,134,0.000000,"\text{Not used}","int(1/((d + e*x)^2*(a + b*x + c*x^2)^(1/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^2\,\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(1/((d + e*x)^2*(a + b*x + c*x^2)^(1/2)), x)","F"
2380,0,-1,209,0.000000,"\text{Not used}","int(1/((d + e*x)^3*(a + b*x + c*x^2)^(1/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^3\,\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(1/((d + e*x)^3*(a + b*x + c*x^2)^(1/2)), x)","F"
2381,0,-1,293,0.000000,"\text{Not used}","int(1/((d + e*x)^4*(a + b*x + c*x^2)^(1/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^4\,\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(1/((d + e*x)^4*(a + b*x + c*x^2)^(1/2)), x)","F"
2382,0,-1,286,0.000000,"\text{Not used}","int((d + e*x)^4/(a + b*x + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^4/(a + b*x + c*x^2)^(3/2), x)","F"
2383,0,-1,177,0.000000,"\text{Not used}","int((d + e*x)^3/(a + b*x + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^3}{{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^3/(a + b*x + c*x^2)^(3/2), x)","F"
2384,1,150,129,1.471313,"\text{Not used}","int((d + e*x)^2/(a + b*x + c*x^2)^(3/2),x)","\frac{e^2\,\ln\left(\frac{\frac{b}{2}+c\,x}{\sqrt{c}}+\sqrt{c\,x^2+b\,x+a}\right)}{c^{3/2}}+\frac{d^2\,\left(\frac{b}{2}+c\,x\right)}{\left(a\,c-\frac{b^2}{4}\right)\,\sqrt{c\,x^2+b\,x+a}}-\frac{2\,d\,e\,\left(4\,a+2\,b\,x\right)}{\left(4\,a\,c-b^2\right)\,\sqrt{c\,x^2+b\,x+a}}+\frac{e^2\,\left(\frac{a\,b}{2}-x\,\left(a\,c-\frac{b^2}{2}\right)\right)}{c\,\left(a\,c-\frac{b^2}{4}\right)\,\sqrt{c\,x^2+b\,x+a}}","Not used",1,"(e^2*log((b/2 + c*x)/c^(1/2) + (a + b*x + c*x^2)^(1/2)))/c^(3/2) + (d^2*(b/2 + c*x))/((a*c - b^2/4)*(a + b*x + c*x^2)^(1/2)) - (2*d*e*(4*a + 2*b*x))/((4*a*c - b^2)*(a + b*x + c*x^2)^(1/2)) + (e^2*((a*b)/2 - x*(a*c - b^2/2)))/(c*(a*c - b^2/4)*(a + b*x + c*x^2)^(1/2))","B"
2385,1,45,45,1.167551,"\text{Not used}","int((d + e*x)/(a + b*x + c*x^2)^(3/2),x)","-\frac{4\,a\,e-2\,b\,d+2\,b\,e\,x-4\,c\,d\,x}{\left(4\,a\,c-b^2\right)\,\sqrt{c\,x^2+b\,x+a}}","Not used",1,"-(4*a*e - 2*b*d + 2*b*e*x - 4*c*d*x)/((4*a*c - b^2)*(a + b*x + c*x^2)^(1/2))","B"
2386,1,31,32,1.012968,"\text{Not used}","int(1/(a + b*x + c*x^2)^(3/2),x)","\frac{\frac{b}{2}+c\,x}{\left(a\,c-\frac{b^2}{4}\right)\,\sqrt{c\,x^2+b\,x+a}}","Not used",1,"(b/2 + c*x)/((a*c - b^2/4)*(a + b*x + c*x^2)^(1/2))","B"
2387,0,-1,155,0.000000,"\text{Not used}","int(1/((d + e*x)*(a + b*x + c*x^2)^(3/2)),x)","\int \frac{1}{\left(d+e\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)*(a + b*x + c*x^2)^(3/2)), x)","F"
2388,0,-1,255,0.000000,"\text{Not used}","int(1/((d + e*x)^2*(a + b*x + c*x^2)^(3/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)^2*(a + b*x + c*x^2)^(3/2)), x)","F"
2389,0,-1,371,0.000000,"\text{Not used}","int(1/((d + e*x)^3*(a + b*x + c*x^2)^(3/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^3\,{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)^3*(a + b*x + c*x^2)^(3/2)), x)","F"
2390,0,-1,519,0.000000,"\text{Not used}","int(1/((d + e*x)^4*(a + b*x + c*x^2)^(3/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^4\,{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)^4*(a + b*x + c*x^2)^(3/2)), x)","F"
2391,0,-1,389,0.000000,"\text{Not used}","int((d + e*x)^5/(a + b*x + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^5}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^5/(a + b*x + c*x^2)^(5/2), x)","F"
2392,0,-1,295,0.000000,"\text{Not used}","int((d + e*x)^4/(a + b*x + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^4}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^4/(a + b*x + c*x^2)^(5/2), x)","F"
2393,1,528,118,1.621466,"\text{Not used}","int((d + e*x)^3/(a + b*x + c*x^2)^(5/2),x)","\frac{2\,a\,b^4\,e^3+2\,b^5\,e^3\,x-2\,b^4\,e^3\,\left(c\,x^2+b\,x+a\right)+16\,a^3\,c^2\,e^3-2\,b^3\,c^2\,d^3-12\,a^2\,b^2\,c\,e^3-48\,a^2\,c^3\,d^2\,e-4\,b^2\,c^3\,d^3\,x-48\,a^2\,c^2\,e^3\,\left(c\,x^2+b\,x+a\right)+8\,a\,b\,c^3\,d^3+16\,a\,c^4\,d^3\,x+16\,b\,c^3\,d^3\,\left(c\,x^2+b\,x+a\right)+32\,c^4\,d^3\,x\,\left(c\,x^2+b\,x+a\right)-6\,a\,b^3\,c\,d\,e^2-14\,a\,b^3\,c\,e^3\,x-6\,b^4\,c\,d\,e^2\,x+12\,a\,b^2\,c\,e^3\,\left(c\,x^2+b\,x+a\right)+6\,b^3\,c\,d\,e^2\,\left(c\,x^2+b\,x+a\right)+2\,b^3\,c\,e^3\,x\,\left(c\,x^2+b\,x+a\right)+12\,a\,b^2\,c^2\,d^2\,e+24\,a^2\,b\,c^2\,d\,e^2+24\,a^2\,b\,c^2\,e^3\,x-48\,a^2\,c^3\,d\,e^2\,x+6\,b^3\,c^2\,d^2\,e\,x-24\,b^2\,c^2\,d^2\,e\,\left(c\,x^2+b\,x+a\right)+12\,b^2\,c^2\,d\,e^2\,x\,\left(c\,x^2+b\,x+a\right)-24\,a\,b\,c^3\,d^2\,e\,x+24\,a\,b\,c^2\,d\,e^2\,\left(c\,x^2+b\,x+a\right)-24\,a\,b\,c^2\,e^3\,x\,\left(c\,x^2+b\,x+a\right)+48\,a\,c^3\,d\,e^2\,x\,\left(c\,x^2+b\,x+a\right)-48\,b\,c^3\,d^2\,e\,x\,\left(c\,x^2+b\,x+a\right)+36\,a\,b^2\,c^2\,d\,e^2\,x}{\left(48\,a^2\,c^4-24\,a\,b^2\,c^3+3\,b^4\,c^2\right)\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}","Not used",1,"(2*a*b^4*e^3 + 2*b^5*e^3*x - 2*b^4*e^3*(a + b*x + c*x^2) + 16*a^3*c^2*e^3 - 2*b^3*c^2*d^3 - 12*a^2*b^2*c*e^3 - 48*a^2*c^3*d^2*e - 4*b^2*c^3*d^3*x - 48*a^2*c^2*e^3*(a + b*x + c*x^2) + 8*a*b*c^3*d^3 + 16*a*c^4*d^3*x + 16*b*c^3*d^3*(a + b*x + c*x^2) + 32*c^4*d^3*x*(a + b*x + c*x^2) - 6*a*b^3*c*d*e^2 - 14*a*b^3*c*e^3*x - 6*b^4*c*d*e^2*x + 12*a*b^2*c*e^3*(a + b*x + c*x^2) + 6*b^3*c*d*e^2*(a + b*x + c*x^2) + 2*b^3*c*e^3*x*(a + b*x + c*x^2) + 12*a*b^2*c^2*d^2*e + 24*a^2*b*c^2*d*e^2 + 24*a^2*b*c^2*e^3*x - 48*a^2*c^3*d*e^2*x + 6*b^3*c^2*d^2*e*x - 24*b^2*c^2*d^2*e*(a + b*x + c*x^2) + 12*b^2*c^2*d*e^2*x*(a + b*x + c*x^2) - 24*a*b*c^3*d^2*e*x + 24*a*b*c^2*d*e^2*(a + b*x + c*x^2) - 24*a*b*c^2*e^3*x*(a + b*x + c*x^2) + 48*a*c^3*d*e^2*x*(a + b*x + c*x^2) - 48*b*c^3*d^2*e*x*(a + b*x + c*x^2) + 36*a*b^2*c^2*d*e^2*x)/((48*a^2*c^4 + 3*b^4*c^2 - 24*a*b^2*c^3)*(a + b*x + c*x^2)^(3/2))","B"
2394,1,321,98,1.421853,"\text{Not used}","int((d + e*x)^2/(a + b*x + c*x^2)^(5/2),x)","\frac{2\,b^3\,e^2\,\left(c\,x^2+b\,x+a\right)-2\,b^3\,c\,d^2-2\,b^4\,e^2\,x-2\,a\,b^3\,e^2-16\,a^2\,c^2\,e^2\,x-4\,b^2\,c^2\,d^2\,x+8\,a\,b\,c^2\,d^2+8\,a^2\,b\,c\,e^2-32\,a^2\,c^2\,d\,e+16\,a\,c^3\,d^2\,x+16\,b\,c^2\,d^2\,\left(c\,x^2+b\,x+a\right)+32\,c^3\,d^2\,x\,\left(c\,x^2+b\,x+a\right)+12\,a\,b^2\,c\,e^2\,x+16\,a\,c^2\,e^2\,x\,\left(c\,x^2+b\,x+a\right)+4\,b^2\,c\,e^2\,x\,\left(c\,x^2+b\,x+a\right)+8\,a\,b^2\,c\,d\,e+4\,b^3\,c\,d\,e\,x+8\,a\,b\,c\,e^2\,\left(c\,x^2+b\,x+a\right)-16\,b^2\,c\,d\,e\,\left(c\,x^2+b\,x+a\right)-16\,a\,b\,c^2\,d\,e\,x-32\,b\,c^2\,d\,e\,x\,\left(c\,x^2+b\,x+a\right)}{\left(48\,a^2\,c^3-24\,a\,b^2\,c^2+3\,b^4\,c\right)\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}","Not used",1,"(2*b^3*e^2*(a + b*x + c*x^2) - 2*b^3*c*d^2 - 2*b^4*e^2*x - 2*a*b^3*e^2 - 16*a^2*c^2*e^2*x - 4*b^2*c^2*d^2*x + 8*a*b*c^2*d^2 + 8*a^2*b*c*e^2 - 32*a^2*c^2*d*e + 16*a*c^3*d^2*x + 16*b*c^2*d^2*(a + b*x + c*x^2) + 32*c^3*d^2*x*(a + b*x + c*x^2) + 12*a*b^2*c*e^2*x + 16*a*c^2*e^2*x*(a + b*x + c*x^2) + 4*b^2*c*e^2*x*(a + b*x + c*x^2) + 8*a*b^2*c*d*e + 4*b^3*c*d*e*x + 8*a*b*c*e^2*(a + b*x + c*x^2) - 16*b^2*c*d*e*(a + b*x + c*x^2) - 16*a*b*c^2*d*e*x - 32*b*c^2*d*e*x*(a + b*x + c*x^2))/((3*b^4*c + 48*a^2*c^3 - 24*a*b^2*c^2)*(a + b*x + c*x^2)^(3/2))","B"
2395,1,121,91,1.303914,"\text{Not used}","int((d + e*x)/(a + b*x + c*x^2)^(5/2),x)","-\frac{2\,\left(8\,e\,a^2\,c+2\,e\,a\,b^2+12\,e\,a\,b\,c\,x-12\,d\,a\,b\,c-24\,d\,a\,c^2\,x+3\,e\,b^3\,x+d\,b^3+12\,e\,b^2\,c\,x^2-6\,d\,b^2\,c\,x+8\,e\,b\,c^2\,x^3-24\,d\,b\,c^2\,x^2-16\,d\,c^3\,x^3\right)}{3\,{\left(4\,a\,c-b^2\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}","Not used",1,"-(2*(b^3*d - 16*c^3*d*x^3 + 2*a*b^2*e + 8*a^2*c*e + 3*b^3*e*x - 24*a*c^2*d*x - 6*b^2*c*d*x - 24*b*c^2*d*x^2 + 12*b^2*c*e*x^2 + 8*b*c^2*e*x^3 - 12*a*b*c*d + 12*a*b*c*e*x))/(3*(4*a*c - b^2)^2*(a + b*x + c*x^2)^(3/2))","B"
2396,1,57,70,1.041676,"\text{Not used}","int(1/(a + b*x + c*x^2)^(5/2),x)","\frac{\left(2\,b+4\,c\,x\right)\,\left(-b^2+8\,b\,c\,x+8\,c^2\,x^2+12\,a\,c\right)}{3\,{\left(4\,a\,c-b^2\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^{3/2}}","Not used",1,"((2*b + 4*c*x)*(12*a*c - b^2 + 8*c^2*x^2 + 8*b*c*x))/(3*(4*a*c - b^2)^2*(a + b*x + c*x^2)^(3/2))","B"
2397,0,-1,310,0.000000,"\text{Not used}","int(1/((d + e*x)*(a + b*x + c*x^2)^(5/2)),x)","\int \frac{1}{\left(d+e\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int(1/((d + e*x)*(a + b*x + c*x^2)^(5/2)), x)","F"
2398,0,-1,473,0.000000,"\text{Not used}","int(1/((d + e*x)^2*(a + b*x + c*x^2)^(5/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int(1/((d + e*x)^2*(a + b*x + c*x^2)^(5/2)), x)","F"
2399,0,-1,621,0.000000,"\text{Not used}","int(1/((d + e*x)^3*(a + b*x + c*x^2)^(5/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^3\,{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int(1/((d + e*x)^3*(a + b*x + c*x^2)^(5/2)), x)","F"
2400,1,46,29,1.196797,"\text{Not used}","int((x + 3)/(5 - x^2 - 4*x)^(1/2),x)","3\,\mathrm{asin}\left(\frac{x}{3}+\frac{2}{3}\right)-\sqrt{-x^2-4\,x+5}+\ln\left(x\,1{}\mathrm{i}+\sqrt{-x^2-4\,x+5}+2{}\mathrm{i}\right)\,2{}\mathrm{i}","Not used",1,"log(x*1i + (5 - x^2 - 4*x)^(1/2) + 2i)*2i + 3*asin(x/3 + 2/3) - (5 - x^2 - 4*x)^(1/2)","B"
2401,1,46,25,1.296814,"\text{Not used}","int(-(2*x - 5/2)/(3*x - x^2 - 2)^(1/2),x)","\frac{5\,\mathrm{asin}\left(2\,x-3\right)}{2}+2\,\sqrt{-x^2+3\,x-2}+\ln\left(x\,1{}\mathrm{i}+\sqrt{-x^2+3\,x-2}-\frac{3}{2}{}\mathrm{i}\right)\,3{}\mathrm{i}","Not used",1,"log(x*1i + (3*x - x^2 - 2)^(1/2) - 3i/2)*3i + (5*asin(2*x - 3))/2 + 2*(3*x - x^2 - 2)^(1/2)","B"
2402,1,27,23,1.298142,"\text{Not used}","int((2*x + 3)/(2*x + x^2 + 5)^(1/2),x)","\ln\left(x+\sqrt{x^2+2\,x+5}+1\right)+2\,\sqrt{x^2+2\,x+5}","Not used",1,"log(x + (2*x + x^2 + 5)^(1/2) + 1) + 2*(2*x + x^2 + 5)^(1/2)","B"
2403,1,25,34,1.518887,"\text{Not used}","int((x - 1)/(x^2 - 4*x + 3)^(1/2),x)","\ln\left(x+\sqrt{x^2-4\,x+3}-2\right)+\sqrt{x^2-4\,x+3}","Not used",1,"log(x + (x^2 - 4*x + 3)^(1/2) - 2) + (x^2 - 4*x + 3)^(1/2)","B"
2404,0,-1,19,0.000000,"\text{Not used}","int(-1/((x - 1)*(2*x + x^2 - 4)^(1/2)),x)","-\int \frac{1}{\left(x-1\right)\,\sqrt{x^2+2\,x-4}} \,d x","Not used",1,"-int(1/((x - 1)*(2*x + x^2 - 4)^(1/2)), x)","F"
2405,0,-1,13,0.000000,"\text{Not used}","int(1/((x - 2)*(x^2 - 4*x + 3)^(1/2)),x)","\int \frac{1}{\left(x-2\right)\,\sqrt{x^2-4\,x+3}} \,d x","Not used",1,"int(1/((x - 2)*(x^2 - 4*x + 3)^(1/2)), x)","F"
2406,1,17,17,0.085954,"\text{Not used}","int((x + 1)/(3*x + x^2 + 2)^(3/2),x)","\frac{2\,\sqrt{x^2+3\,x+2}}{x+2}","Not used",1,"(2*(3*x + x^2 + 2)^(1/2))/(x + 2)","B"
2407,0,-1,96,0.000000,"\text{Not used}","int(2/((d + e*x)*(4*b*x + 4*c*x^2 + b^2/c)^(1/2)),x)","\int \frac{2}{\left(d+e\,x\right)\,\sqrt{4\,b\,x+4\,c\,x^2+\frac{b^2}{c}}} \,d x","Not used",1,"int(2/((d + e*x)*(4*b*x + 4*c*x^2 + b^2/c)^(1/2)), x)","F"
2408,0,-1,56,0.000000,"\text{Not used}","int(1/((e*x + (b*e)/(2*c))*(a + b*x + c*x^2)^(1/2)),x)","\int \frac{1}{\left(e\,x+\frac{b\,e}{2\,c}\right)\,\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(1/((e*x + (b*e)/(2*c))*(a + b*x + c*x^2)^(1/2)), x)","F"
2409,1,47,48,1.183935,"\text{Not used}","int(1/((d + e*x)*(b*x - (c*d^2 - b*d*e)/e^2 + c*x^2)^(1/2)),x)","-\frac{2\,e\,\sqrt{b\,x-\frac{c\,d^2-b\,d\,e}{e^2}+c\,x^2}}{\left(b\,e-2\,c\,d\right)\,\left(d+e\,x\right)}","Not used",1,"-(2*e*(b*x - (c*d^2 - b*d*e)/e^2 + c*x^2)^(1/2))/((b*e - 2*c*d)*(d + e*x))","B"
2410,1,25,27,1.119634,"\text{Not used}","int(2/((e*x + (b*e)/(2*c))*(4*b*x + 4*c*x^2 + b^2/c)^(1/2)),x)","-\frac{2}{e\,\sqrt{4\,b\,x+4\,c\,x^2+\frac{b^2}{c}}}","Not used",1,"-2/(e*(4*b*x + 4*c*x^2 + b^2/c)^(1/2))","B"
2411,1,44,40,0.106130,"\text{Not used}","int(x/(4*x + 3*x^2 + 2)^(1/2),x)","\frac{\sqrt{3\,x^2+4\,x+2}}{3}-\frac{2\,\sqrt{3}\,\ln\left(\sqrt{3\,x^2+4\,x+2}+\frac{\sqrt{3}\,\left(3\,x+2\right)}{3}\right)}{9}","Not used",1,"(4*x + 3*x^2 + 2)^(1/2)/3 - (2*3^(1/2)*log((4*x + 3*x^2 + 2)^(1/2) + (3^(1/2)*(3*x + 2))/3))/9","B"
2412,1,46,40,1.146481,"\text{Not used}","int(x/(4*x - 3*x^2 + 2)^(1/2),x)","-\frac{\sqrt{-3\,x^2+4\,x+2}}{3}-\frac{\sqrt{3}\,\ln\left(\sqrt{-3\,x^2+4\,x+2}+\frac{\sqrt{3}\,\left(3\,x-2\right)\,1{}\mathrm{i}}{3}\right)\,2{}\mathrm{i}}{9}","Not used",1,"- (3^(1/2)*log((4*x - 3*x^2 + 2)^(1/2) + (3^(1/2)*(3*x - 2)*1i)/3)*2i)/9 - (4*x - 3*x^2 + 2)^(1/2)/3","B"
2413,1,44,57,1.087697,"\text{Not used}","int(x/(5*x + 3*x^2 + 2)^(1/2),x)","\frac{\sqrt{3\,x^2+5\,x+2}}{3}-\frac{5\,\sqrt{3}\,\ln\left(\sqrt{3\,x^2+5\,x+2}+\frac{\sqrt{3}\,\left(3\,x+\frac{5}{2}\right)}{3}\right)}{18}","Not used",1,"(5*x + 3*x^2 + 2)^(1/2)/3 - (5*3^(1/2)*log((5*x + 3*x^2 + 2)^(1/2) + (3^(1/2)*(3*x + 5/2))/3))/18","B"
2414,1,46,38,1.136755,"\text{Not used}","int(x/(5*x - 3*x^2 + 2)^(1/2),x)","-\frac{\sqrt{-3\,x^2+5\,x+2}}{3}-\frac{\sqrt{3}\,\ln\left(\sqrt{-3\,x^2+5\,x+2}+\frac{\sqrt{3}\,\left(3\,x-\frac{5}{2}\right)\,1{}\mathrm{i}}{3}\right)\,5{}\mathrm{i}}{18}","Not used",1,"- (3^(1/2)*log((5*x - 3*x^2 + 2)^(1/2) + (3^(1/2)*(3*x - 5/2)*1i)/3)*5i)/18 - (5*x - 3*x^2 + 2)^(1/2)/3","B"
2415,1,44,54,0.110034,"\text{Not used}","int(x/(4*x + 3*x^2 - 2)^(1/2),x)","\frac{\sqrt{3\,x^2+4\,x-2}}{3}-\frac{2\,\sqrt{3}\,\ln\left(\sqrt{3\,x^2+4\,x-2}+\frac{\sqrt{3}\,\left(3\,x+2\right)}{3}\right)}{9}","Not used",1,"(4*x + 3*x^2 - 2)^(1/2)/3 - (2*3^(1/2)*log((4*x + 3*x^2 - 2)^(1/2) + (3^(1/2)*(3*x + 2))/3))/9","B"
2416,1,46,54,1.102218,"\text{Not used}","int(x/(4*x - 3*x^2 - 2)^(1/2),x)","-\frac{\sqrt{-3\,x^2+4\,x-2}}{3}-\frac{\sqrt{3}\,\ln\left(\sqrt{-3\,x^2+4\,x-2}+\frac{\sqrt{3}\,\left(3\,x-2\right)\,1{}\mathrm{i}}{3}\right)\,2{}\mathrm{i}}{9}","Not used",1,"- (3^(1/2)*log((4*x - 3*x^2 - 2)^(1/2) + (3^(1/2)*(3*x - 2)*1i)/3)*2i)/9 - (4*x - 3*x^2 - 2)^(1/2)/3","B"
2417,1,44,57,0.107373,"\text{Not used}","int(x/(5*x + 3*x^2 - 2)^(1/2),x)","\frac{\sqrt{3\,x^2+5\,x-2}}{3}-\frac{5\,\sqrt{3}\,\ln\left(\sqrt{3\,x^2+5\,x-2}+\frac{\sqrt{3}\,\left(3\,x+\frac{5}{2}\right)}{3}\right)}{18}","Not used",1,"(5*x + 3*x^2 - 2)^(1/2)/3 - (5*3^(1/2)*log((5*x + 3*x^2 - 2)^(1/2) + (3^(1/2)*(3*x + 5/2))/3))/18","B"
2418,1,46,34,1.142313,"\text{Not used}","int(x/(5*x - 3*x^2 - 2)^(1/2),x)","-\frac{\sqrt{-3\,x^2+5\,x-2}}{3}-\frac{\sqrt{3}\,\ln\left(\sqrt{-3\,x^2+5\,x-2}+\frac{\sqrt{3}\,\left(3\,x-\frac{5}{2}\right)\,1{}\mathrm{i}}{3}\right)\,5{}\mathrm{i}}{18}","Not used",1,"- (3^(1/2)*log((5*x - 3*x^2 - 2)^(1/2) + (3^(1/2)*(3*x - 5/2)*1i)/3)*5i)/18 - (5*x - 3*x^2 - 2)^(1/2)/3","B"
2419,1,23,27,1.315414,"\text{Not used}","int(1/(x*((3*x + 2)^2)^(1/2)),x)","-\frac{\ln\left(\frac{6\,x+2\,\sqrt{{\left(3\,x+2\right)}^2}+4}{x}\right)}{2}","Not used",1,"-log((6*x + 2*((3*x + 2)^2)^(1/2) + 4)/x)/2","B"
2420,1,23,27,1.225707,"\text{Not used}","int(1/(x*((3*x - 2)^2)^(1/2)),x)","-\frac{\ln\left(\frac{2\,\sqrt{{\left(3\,x-2\right)}^2}-6\,x+4}{x}\right)}{2}","Not used",1,"-log((2*((3*x - 2)^2)^(1/2) - 6*x + 4)/x)/2","B"
2421,1,27,27,1.273080,"\text{Not used}","int(1/(x*(-(3*x - 2)^2)^(1/2)),x)","\frac{\ln\left(\frac{6\,x-4+\sqrt{-{\left(3\,x-2\right)}^2}\,2{}\mathrm{i}}{x}\right)\,1{}\mathrm{i}}{2}","Not used",1,"(log((6*x + (-(3*x - 2)^2)^(1/2)*2i - 4)/x)*1i)/2","B"
2422,1,27,27,1.243184,"\text{Not used}","int(1/(x*(-(3*x + 2)^2)^(1/2)),x)","\frac{\ln\left(\frac{6\,x+4-\sqrt{-{\left(3\,x+2\right)}^2}\,2{}\mathrm{i}}{x}\right)\,1{}\mathrm{i}}{2}","Not used",1,"(log((6*x - (-(3*x + 2)^2)^(1/2)*2i + 4)/x)*1i)/2","B"
2423,1,46,68,1.178371,"\text{Not used}","int(1/(x*((a + b*x)^2)^(1/2)),x)","-\frac{\ln\left(a\,b+\frac{a^2}{x}+\frac{\sqrt{a^2}\,\sqrt{a^2+2\,a\,b\,x+b^2\,x^2}}{x}\right)}{\sqrt{a^2}}","Not used",1,"-log(a*b + a^2/x + ((a^2)^(1/2)*(a^2 + b^2*x^2 + 2*a*b*x)^(1/2))/x)/(a^2)^(1/2)","B"
2424,1,47,71,1.172474,"\text{Not used}","int(1/(x*((a - b*x)^2)^(1/2)),x)","-\frac{\ln\left(\frac{a^2}{x}-a\,b+\frac{\sqrt{a^2}\,\sqrt{a^2-2\,a\,b\,x+b^2\,x^2}}{x}\right)}{\sqrt{a^2}}","Not used",1,"-log(a^2/x - a*b + ((a^2)^(1/2)*(a^2 + b^2*x^2 - 2*a*b*x)^(1/2))/x)/(a^2)^(1/2)","B"
2425,1,54,77,1.180169,"\text{Not used}","int(1/(x*(-(a - b*x)^2)^(1/2)),x)","-\frac{\ln\left(a\,b-\frac{a^2}{x}+\frac{\sqrt{-a^2}\,\sqrt{-a^2+2\,a\,b\,x-b^2\,x^2}}{x}\right)}{\sqrt{-a^2}}","Not used",1,"-log(a*b - a^2/x + ((-a^2)^(1/2)*(2*a*b*x - b^2*x^2 - a^2)^(1/2))/x)/(-a^2)^(1/2)","B"
2426,1,55,74,1.165270,"\text{Not used}","int(1/(x*(-(a + b*x)^2)^(1/2)),x)","-\frac{\ln\left(\frac{\sqrt{-a^2}\,\sqrt{-a^2-2\,a\,b\,x-b^2\,x^2}}{x}-\frac{a^2}{x}-a\,b\right)}{\sqrt{-a^2}}","Not used",1,"-log(((-a^2)^(1/2)*(- a^2 - b^2*x^2 - 2*a*b*x)^(1/2))/x - a^2/x - a*b)/(-a^2)^(1/2)","B"
2427,1,47,52,0.073371,"\text{Not used}","int(x*(3 - x^2 - 2*x)^(1/2),x)","\frac{\sqrt{-x^2-2\,x+3}\,\left(8\,x^2+4\,x-36\right)}{24}+\ln\left(x+1-\sqrt{-x^2-2\,x+3}\,1{}\mathrm{i}\right)\,2{}\mathrm{i}","Not used",1,"log(x - (3 - x^2 - 2*x)^(1/2)*1i + 1)*2i + ((3 - x^2 - 2*x)^(1/2)*(4*x + 8*x^2 - 36))/24","B"
2428,1,47,56,0.075490,"\text{Not used}","int(x*(2*x - x^2 + 8)^(1/2),x)","-\frac{\sqrt{-x^2+2\,x+8}\,\left(-8\,x^2+4\,x+76\right)}{24}-\frac{\ln\left(x-1-\sqrt{-x^2+2\,x+8}\,1{}\mathrm{i}\right)\,9{}\mathrm{i}}{2}","Not used",1,"- (log(x - (2*x - x^2 + 8)^(1/2)*1i - 1)*9i)/2 - ((2*x - x^2 + 8)^(1/2)*(4*x - 8*x^2 + 76))/24","B"
2429,1,39,50,0.082763,"\text{Not used}","int(x*(2*x + x^2 + 4)^(1/2),x)","\frac{\sqrt{x^2+2\,x+4}\,\left(8\,x^2+4\,x+20\right)}{24}-\frac{3\,\ln\left(x+\sqrt{x^2+2\,x+4}+1\right)}{2}","Not used",1,"((2*x + x^2 + 4)^(1/2)*(4*x + 8*x^2 + 20))/24 - (3*log(x + (2*x + x^2 + 4)^(1/2) + 1))/2","B"
2430,1,27,31,1.160348,"\text{Not used}","int(1/(x*(4*x + 3*x^2 + 2)^(1/2)),x)","-\frac{\sqrt{2}\,\ln\left(\frac{2\,x+\sqrt{6\,x^2+8\,x+4}+2}{x}\right)}{2}","Not used",1,"-(2^(1/2)*log((2*x + (8*x + 6*x^2 + 4)^(1/2) + 2)/x))/2","B"
2431,1,27,31,1.196263,"\text{Not used}","int(1/(x*(4*x - 3*x^2 + 2)^(1/2)),x)","-\frac{\sqrt{2}\,\ln\left(\frac{2\,x+\sqrt{-6\,x^2+8\,x+4}+2}{x}\right)}{2}","Not used",1,"-(2^(1/2)*log((2*x + (8*x - 6*x^2 + 4)^(1/2) + 2)/x))/2","B"
2432,1,29,36,1.371130,"\text{Not used}","int(1/(x*(5*x + 3*x^2 + 2)^(1/2)),x)","-\frac{\sqrt{2}\,\ln\left(\frac{5\,x+2\,\sqrt{6\,x^2+10\,x+4}+4}{x}\right)}{2}","Not used",1,"-(2^(1/2)*log((5*x + 2*(10*x + 6*x^2 + 4)^(1/2) + 4)/x))/2","B"
2433,1,29,36,0.296322,"\text{Not used}","int(1/(x*(5*x - 3*x^2 + 2)^(1/2)),x)","-\frac{\sqrt{2}\,\ln\left(\frac{5\,x+2\,\sqrt{-6\,x^2+10\,x+4}+4}{x}\right)}{2}","Not used",1,"-(2^(1/2)*log((5*x + 2*(10*x - 6*x^2 + 4)^(1/2) + 4)/x))/2","B"
2434,1,34,33,0.367598,"\text{Not used}","int(1/(x*(4*x + 3*x^2 - 2)^(1/2)),x)","\frac{\sqrt{2}\,\ln\left(\frac{2\,x-2+\sqrt{2}\,\sqrt{3\,x^2+4\,x-2}\,1{}\mathrm{i}}{x}\right)\,1{}\mathrm{i}}{2}","Not used",1,"(2^(1/2)*log((2*x + 2^(1/2)*(4*x + 3*x^2 - 2)^(1/2)*1i - 2)/x)*1i)/2","B"
2435,1,34,33,1.263335,"\text{Not used}","int(1/(x*(4*x - 3*x^2 - 2)^(1/2)),x)","\frac{\sqrt{2}\,\ln\left(\frac{2\,x-2+\sqrt{2}\,\sqrt{-3\,x^2+4\,x-2}\,1{}\mathrm{i}}{x}\right)\,1{}\mathrm{i}}{2}","Not used",1,"(2^(1/2)*log((2*x + 2^(1/2)*(4*x - 3*x^2 - 2)^(1/2)*1i - 2)/x)*1i)/2","B"
2436,1,34,36,0.349058,"\text{Not used}","int(1/(x*(5*x + 3*x^2 - 2)^(1/2)),x)","\frac{\sqrt{2}\,\ln\left(\frac{5\,x-4+\sqrt{2}\,\sqrt{3\,x^2+5\,x-2}\,2{}\mathrm{i}}{x}\right)\,1{}\mathrm{i}}{2}","Not used",1,"(2^(1/2)*log((5*x + 2^(1/2)*(5*x + 3*x^2 - 2)^(1/2)*2i - 4)/x)*1i)/2","B"
2437,1,34,36,1.325913,"\text{Not used}","int(1/(x*(5*x - 3*x^2 - 2)^(1/2)),x)","\frac{\sqrt{2}\,\ln\left(\frac{5\,x-4+\sqrt{2}\,\sqrt{-3\,x^2+5\,x-2}\,2{}\mathrm{i}}{x}\right)\,1{}\mathrm{i}}{2}","Not used",1,"(2^(1/2)*log((5*x + 2^(1/2)*(5*x - 3*x^2 - 2)^(1/2)*2i - 4)/x)*1i)/2","B"
2438,0,-1,57,0.000000,"\text{Not used}","int(1/(x^3*(x + x^2 + 1)^(1/2)),x)","\int \frac{1}{x^3\,\sqrt{x^2+x+1}} \,d x","Not used",1,"int(1/(x^3*(x + x^2 + 1)^(1/2)), x)","F"
2439,1,27,23,1.091100,"\text{Not used}","int(1/x - 1/(x*(b*x + c*x^2 + 1)^(1/2)),x)","\ln\left(\frac{b}{2}+\frac{\sqrt{c\,x^2+b\,x+1}}{x}+\frac{1}{x}\right)+\ln\left(x\right)","Not used",1,"log(b/2 + (b*x + c*x^2 + 1)^(1/2)/x + 1/x) + log(x)","B"
2440,0,-1,504,0.000000,"\text{Not used}","int((d*x)^(5/2)*(a + b*x + c*x^2)^(1/2),x)","\int {\left(d\,x\right)}^{5/2}\,\sqrt{c\,x^2+b\,x+a} \,d x","Not used",1,"int((d*x)^(5/2)*(a + b*x + c*x^2)^(1/2), x)","F"
2441,0,-1,581,0.000000,"\text{Not used}","int((d + e*x)^(3/2)*(a + b*x + c*x^2)^(1/2),x)","\int {\left(d+e\,x\right)}^{3/2}\,\sqrt{c\,x^2+b\,x+a} \,d x","Not used",1,"int((d + e*x)^(3/2)*(a + b*x + c*x^2)^(1/2), x)","F"
2442,0,-1,513,0.000000,"\text{Not used}","int((d + e*x)^(1/2)*(a + b*x + c*x^2)^(1/2),x)","\int \sqrt{d+e\,x}\,\sqrt{c\,x^2+b\,x+a} \,d x","Not used",1,"int((d + e*x)^(1/2)*(a + b*x + c*x^2)^(1/2), x)","F"
2443,0,-1,444,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(d + e*x)^(1/2),x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{\sqrt{d+e\,x}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(d + e*x)^(1/2), x)","F"
2444,0,-1,419,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(d + e*x)^(3/2),x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(d + e*x)^(3/2), x)","F"
2445,0,-1,497,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(d + e*x)^(5/2),x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(d + e*x)^(5/2), x)","F"
2446,0,-1,617,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/2)/(d + e*x)^(7/2),x)","\int \frac{\sqrt{c\,x^2+b\,x+a}}{{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/2)/(d + e*x)^(7/2), x)","F"
2447,0,-1,816,0.000000,"\text{Not used}","int((d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2),x)","\int {\left(d+e\,x\right)}^{3/2}\,{\left(c\,x^2+b\,x+a\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2), x)","F"
2448,0,-1,712,0.000000,"\text{Not used}","int((d + e*x)^(1/2)*(a + b*x + c*x^2)^(3/2),x)","\int \sqrt{d+e\,x}\,{\left(c\,x^2+b\,x+a\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^(1/2)*(a + b*x + c*x^2)^(3/2), x)","F"
2449,0,-1,579,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(d + e*x)^(1/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{\sqrt{d+e\,x}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(d + e*x)^(1/2), x)","F"
2450,0,-1,515,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(d + e*x)^(3/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(d + e*x)^(3/2), x)","F"
2451,0,-1,499,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(d + e*x)^(5/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(d + e*x)^(5/2), x)","F"
2452,0,-1,578,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(d + e*x)^(7/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(d + e*x)^(7/2), x)","F"
2453,0,-1,721,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/2)/(d + e*x)^(9/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/2}}{{\left(d+e\,x\right)}^{9/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/2)/(d + e*x)^(9/2), x)","F"
2454,0,-1,616,0.000000,"\text{Not used}","int((d*x)^(1/2)*(a + b*x + c*x^2)^(5/2),x)","\int \sqrt{d\,x}\,{\left(c\,x^2+b\,x+a\right)}^{5/2} \,d x","Not used",1,"int((d*x)^(1/2)*(a + b*x + c*x^2)^(5/2), x)","F"
2455,0,-1,847,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(d + e*x)^(1/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{\sqrt{d+e\,x}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(d + e*x)^(1/2), x)","F"
2456,0,-1,716,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(d + e*x)^(3/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(d + e*x)^(3/2), x)","F"
2457,0,-1,622,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(d + e*x)^(5/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(d+e\,x\right)}^{5/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(d + e*x)^(5/2), x)","F"
2458,0,-1,603,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(d + e*x)^(7/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(d+e\,x\right)}^{7/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(d + e*x)^(7/2), x)","F"
2459,0,-1,731,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(d + e*x)^(9/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(d+e\,x\right)}^{9/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(d + e*x)^(9/2), x)","F"
2460,0,-1,923,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/2)/(d + e*x)^(11/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/2}}{{\left(d+e\,x\right)}^{11/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/2)/(d + e*x)^(11/2), x)","F"
2461,0,-1,600,0.000000,"\text{Not used}","int((d + e*x)^(7/2)/(a + b*x + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^{7/2}}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int((d + e*x)^(7/2)/(a + b*x + c*x^2)^(1/2), x)","F"
2462,0,-1,509,0.000000,"\text{Not used}","int((d + e*x)^(5/2)/(a + b*x + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^{5/2}}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int((d + e*x)^(5/2)/(a + b*x + c*x^2)^(1/2), x)","F"
2463,0,-1,439,0.000000,"\text{Not used}","int((d + e*x)^(3/2)/(a + b*x + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^{3/2}}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int((d + e*x)^(3/2)/(a + b*x + c*x^2)^(1/2), x)","F"
2464,0,-1,188,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/(a + b*x + c*x^2)^(1/2),x)","\int \frac{\sqrt{d+e\,x}}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int((d + e*x)^(1/2)/(a + b*x + c*x^2)^(1/2), x)","F"
2465,0,-1,189,0.000000,"\text{Not used}","int(1/((d + e*x)^(1/2)*(a + b*x + c*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{d+e\,x}\,\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(1/((d + e*x)^(1/2)*(a + b*x + c*x^2)^(1/2)), x)","F"
2466,0,-1,248,0.000000,"\text{Not used}","int(1/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(1/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{3/2}\,\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(1/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(1/2)), x)","F"
2467,0,-1,523,0.000000,"\text{Not used}","int(1/((d + e*x)^(5/2)*(a + b*x + c*x^2)^(1/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{5/2}\,\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(1/((d + e*x)^(5/2)*(a + b*x + c*x^2)^(1/2)), x)","F"
2468,0,-1,629,0.000000,"\text{Not used}","int(1/((d + e*x)^(7/2)*(a + b*x + c*x^2)^(1/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{7/2}\,\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int(1/((d + e*x)^(7/2)*(a + b*x + c*x^2)^(1/2)), x)","F"
2469,0,-1,641,0.000000,"\text{Not used}","int((d + e*x)^(7/2)/(a + b*x + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^{7/2}}{{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(7/2)/(a + b*x + c*x^2)^(3/2), x)","F"
2470,0,-1,533,0.000000,"\text{Not used}","int((d + e*x)^(5/2)/(a + b*x + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^{5/2}}{{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(5/2)/(a + b*x + c*x^2)^(3/2), x)","F"
2471,0,-1,457,0.000000,"\text{Not used}","int((d + e*x)^(3/2)/(a + b*x + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^{3/2}}{{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(3/2)/(a + b*x + c*x^2)^(3/2), x)","F"
2472,0,-1,426,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/(a + b*x + c*x^2)^(3/2),x)","\int \frac{\sqrt{d+e\,x}}{{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^(1/2)/(a + b*x + c*x^2)^(3/2), x)","F"
2473,0,-1,480,0.000000,"\text{Not used}","int(1/((d + e*x)^(1/2)*(a + b*x + c*x^2)^(3/2)),x)","\int \frac{1}{\sqrt{d+e\,x}\,{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)^(1/2)*(a + b*x + c*x^2)^(3/2)), x)","F"
2474,0,-1,607,0.000000,"\text{Not used}","int(1/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{3/2}\,{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2)), x)","F"
2475,0,-1,744,0.000000,"\text{Not used}","int(1/((d + e*x)^(5/2)*(a + b*x + c*x^2)^(3/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{5/2}\,{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int(1/((d + e*x)^(5/2)*(a + b*x + c*x^2)^(3/2)), x)","F"
2476,0,-1,659,0.000000,"\text{Not used}","int((d + e*x)^(7/2)/(a + b*x + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{7/2}}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(7/2)/(a + b*x + c*x^2)^(5/2), x)","F"
2477,0,-1,590,0.000000,"\text{Not used}","int((d + e*x)^(5/2)/(a + b*x + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{5/2}}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(5/2)/(a + b*x + c*x^2)^(5/2), x)","F"
2478,0,-1,542,0.000000,"\text{Not used}","int((d + e*x)^(3/2)/(a + b*x + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^{3/2}}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(3/2)/(a + b*x + c*x^2)^(5/2), x)","F"
2479,0,-1,605,0.000000,"\text{Not used}","int((d + e*x)^(1/2)/(a + b*x + c*x^2)^(5/2),x)","\int \frac{\sqrt{d+e\,x}}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^(1/2)/(a + b*x + c*x^2)^(5/2), x)","F"
2480,0,-1,725,0.000000,"\text{Not used}","int(1/((d + e*x)^(1/2)*(a + b*x + c*x^2)^(5/2)),x)","\int \frac{1}{\sqrt{d+e\,x}\,{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int(1/((d + e*x)^(1/2)*(a + b*x + c*x^2)^(5/2)), x)","F"
2481,0,-1,918,0.000000,"\text{Not used}","int(1/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(5/2)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{3/2}\,{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int(1/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(5/2)), x)","F"
2482,0,-1,30,0.000000,"\text{Not used}","int((5*x + 3)^(1/2)/(5*x - 12*x^2 + 2)^(1/2),x)","\int \frac{\sqrt{5\,x+3}}{\sqrt{-12\,x^2+5\,x+2}} \,d x","Not used",1,"int((5*x + 3)^(1/2)/(5*x - 12*x^2 + 2)^(1/2), x)","F"
2483,0,-1,638,0.000000,"\text{Not used}","int((d + e*x)^2*(a + b*x + c*x^2)^(4/3),x)","\int {\left(d+e\,x\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^{4/3} \,d x","Not used",1,"int((d + e*x)^2*(a + b*x + c*x^2)^(4/3), x)","F"
2484,0,-1,539,0.000000,"\text{Not used}","int((d + e*x)*(a + b*x + c*x^2)^(4/3),x)","\int \left(d+e\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{4/3} \,d x","Not used",1,"int((d + e*x)*(a + b*x + c*x^2)^(4/3), x)","F"
2485,0,-1,490,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(4/3),x)","\int {\left(c\,x^2+b\,x+a\right)}^{4/3} \,d x","Not used",1,"int((a + b*x + c*x^2)^(4/3), x)","F"
2486,0,-1,180,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(4/3)/(d + e*x),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{4/3}}{d+e\,x} \,d x","Not used",1,"int((a + b*x + c*x^2)^(4/3)/(d + e*x), x)","F"
2487,0,-1,189,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(4/3)/(d + e*x)^2,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{4/3}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a + b*x + c*x^2)^(4/3)/(d + e*x)^2, x)","F"
2488,0,-1,187,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(4/3)/(d + e*x)^3,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{4/3}}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((a + b*x + c*x^2)^(4/3)/(d + e*x)^3, x)","F"
2489,0,-1,1224,0.000000,"\text{Not used}","int((d + e*x)^3/(a + b*x + c*x^2)^(7/3),x)","\int \frac{{\left(d+e\,x\right)}^3}{{\left(c\,x^2+b\,x+a\right)}^{7/3}} \,d x","Not used",1,"int((d + e*x)^3/(a + b*x + c*x^2)^(7/3), x)","F"
2490,0,-1,1153,0.000000,"\text{Not used}","int((d + e*x)^2/(a + b*x + c*x^2)^(7/3),x)","\int \frac{{\left(d+e\,x\right)}^2}{{\left(c\,x^2+b\,x+a\right)}^{7/3}} \,d x","Not used",1,"int((d + e*x)^2/(a + b*x + c*x^2)^(7/3), x)","F"
2491,0,-1,1043,0.000000,"\text{Not used}","int((d + e*x)/(a + b*x + c*x^2)^(7/3),x)","\int \frac{d+e\,x}{{\left(c\,x^2+b\,x+a\right)}^{7/3}} \,d x","Not used",1,"int((d + e*x)/(a + b*x + c*x^2)^(7/3), x)","F"
2492,0,-1,993,0.000000,"\text{Not used}","int(1/(a + b*x + c*x^2)^(7/3),x)","\int \frac{1}{{\left(c\,x^2+b\,x+a\right)}^{7/3}} \,d x","Not used",1,"int(1/(a + b*x + c*x^2)^(7/3), x)","F"
2493,0,-1,182,0.000000,"\text{Not used}","int(1/((d + e*x)*(a + b*x + c*x^2)^(7/3)),x)","\int \frac{1}{\left(d+e\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{7/3}} \,d x","Not used",1,"int(1/((d + e*x)*(a + b*x + c*x^2)^(7/3)), x)","F"
2494,0,-1,189,0.000000,"\text{Not used}","int(1/((d + e*x)^2*(a + b*x + c*x^2)^(7/3)),x)","\int \frac{1}{{\left(d+e\,x\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^{7/3}} \,d x","Not used",1,"int(1/((d + e*x)^2*(a + b*x + c*x^2)^(7/3)), x)","F"
2495,0,-1,189,0.000000,"\text{Not used}","int(1/((d + e*x)^3*(a + b*x + c*x^2)^(7/3)),x)","\int \frac{1}{{\left(d+e\,x\right)}^3\,{\left(c\,x^2+b\,x+a\right)}^{7/3}} \,d x","Not used",1,"int(1/((d + e*x)^3*(a + b*x + c*x^2)^(7/3)), x)","F"
2496,0,-1,242,0.000000,"\text{Not used}","int(1/((d + e*x)*(b^2*e^2 + c^2*d^2 + 3*c^2*e^2*x^2 + 3*b*c*e^2*x - b*c*d*e)^(1/3)),x)","\int \frac{1}{\left(d+e\,x\right)\,{\left(b^2\,e^2-b\,c\,d\,e+3\,b\,c\,e^2\,x+c^2\,d^2+3\,c^2\,e^2\,x^2\right)}^{1/3}} \,d x","Not used",1,"int(1/((d + e*x)*(b^2*e^2 + c^2*d^2 + 3*c^2*e^2*x^2 + 3*b*c*e^2*x - b*c*d*e)^(1/3)), x)","F"
2497,0,-1,635,0.000000,"\text{Not used}","int((3*x + 2)^3/(27*x^2 - 54*x + 52)^(1/3),x)","\int \frac{{\left(3\,x+2\right)}^3}{{\left(27\,x^2-54\,x+52\right)}^{1/3}} \,d x","Not used",1,"int((3*x + 2)^3/(27*x^2 - 54*x + 52)^(1/3), x)","F"
2498,0,-1,628,0.000000,"\text{Not used}","int((3*x + 2)^2/(27*x^2 - 54*x + 52)^(1/3),x)","\int \frac{{\left(3\,x+2\right)}^2}{{\left(27\,x^2-54\,x+52\right)}^{1/3}} \,d x","Not used",1,"int((3*x + 2)^2/(27*x^2 - 54*x + 52)^(1/3), x)","F"
2499,0,-1,603,0.000000,"\text{Not used}","int((3*x + 2)/(27*x^2 - 54*x + 52)^(1/3),x)","\int \frac{3\,x+2}{{\left(27\,x^2-54\,x+52\right)}^{1/3}} \,d x","Not used",1,"int((3*x + 2)/(27*x^2 - 54*x + 52)^(1/3), x)","F"
2500,0,-1,108,0.000000,"\text{Not used}","int(1/((3*x + 2)*(27*x^2 - 54*x + 52)^(1/3)),x)","\int \frac{1}{\left(3\,x+2\right)\,{\left(27\,x^2-54\,x+52\right)}^{1/3}} \,d x","Not used",1,"int(1/((3*x + 2)*(27*x^2 - 54*x + 52)^(1/3)), x)","F"
2501,0,-1,719,0.000000,"\text{Not used}","int(1/((3*x + 2)^2*(27*x^2 - 54*x + 52)^(1/3)),x)","\int \frac{1}{{\left(3\,x+2\right)}^2\,{\left(27\,x^2-54\,x+52\right)}^{1/3}} \,d x","Not used",1,"int(1/((3*x + 2)^2*(27*x^2 - 54*x + 52)^(1/3)), x)","F"
2502,0,-1,744,0.000000,"\text{Not used}","int(1/((3*x + 2)^3*(27*x^2 - 54*x + 52)^(1/3)),x)","\int \frac{1}{{\left(3\,x+2\right)}^3\,{\left(27\,x^2-54\,x+52\right)}^{1/3}} \,d x","Not used",1,"int(1/((3*x + 2)^3*(27*x^2 - 54*x + 52)^(1/3)), x)","F"
2503,0,-1,589,0.000000,"\text{Not used}","int((3*x + 2)^3/(54*x + 27*x^2 + 28)^(1/3),x)","\int \frac{{\left(3\,x+2\right)}^3}{{\left(27\,x^2+54\,x+28\right)}^{1/3}} \,d x","Not used",1,"int((3*x + 2)^3/(54*x + 27*x^2 + 28)^(1/3), x)","F"
2504,0,-1,585,0.000000,"\text{Not used}","int((3*x + 2)^2/(54*x + 27*x^2 + 28)^(1/3),x)","\int \frac{{\left(3\,x+2\right)}^2}{{\left(27\,x^2+54\,x+28\right)}^{1/3}} \,d x","Not used",1,"int((3*x + 2)^2/(54*x + 27*x^2 + 28)^(1/3), x)","F"
2505,0,-1,560,0.000000,"\text{Not used}","int((3*x + 2)/(54*x + 27*x^2 + 28)^(1/3),x)","\int \frac{3\,x+2}{{\left(27\,x^2+54\,x+28\right)}^{1/3}} \,d x","Not used",1,"int((3*x + 2)/(54*x + 27*x^2 + 28)^(1/3), x)","F"
2506,0,-1,103,0.000000,"\text{Not used}","int(1/((3*x + 2)*(54*x + 27*x^2 + 28)^(1/3)),x)","\int \frac{1}{\left(3\,x+2\right)\,{\left(27\,x^2+54\,x+28\right)}^{1/3}} \,d x","Not used",1,"int(1/((3*x + 2)*(54*x + 27*x^2 + 28)^(1/3)), x)","F"
2507,0,-1,671,0.000000,"\text{Not used}","int(1/((3*x + 2)^2*(54*x + 27*x^2 + 28)^(1/3)),x)","\int \frac{1}{{\left(3\,x+2\right)}^2\,{\left(27\,x^2+54\,x+28\right)}^{1/3}} \,d x","Not used",1,"int(1/((3*x + 2)^2*(54*x + 27*x^2 + 28)^(1/3)), x)","F"
2508,0,-1,696,0.000000,"\text{Not used}","int(1/((3*x + 2)^3*(54*x + 27*x^2 + 28)^(1/3)),x)","\int \frac{1}{{\left(3\,x+2\right)}^3\,{\left(27\,x^2+54\,x+28\right)}^{1/3}} \,d x","Not used",1,"int(1/((3*x + 2)^3*(54*x + 27*x^2 + 28)^(1/3)), x)","F"
2509,0,-1,564,0.000000,"\text{Not used}","int(1/((d + e*x)*(2*b^2*e^2 - c^2*d^2 + 9*c^2*e^2*x^2 + 9*b*c*e^2*x + b*c*d*e)^(1/3)),x)","\int \frac{1}{\left(d+e\,x\right)\,{\left(2\,b^2\,e^2+b\,c\,d\,e+9\,b\,c\,e^2\,x-c^2\,d^2+9\,c^2\,e^2\,x^2\right)}^{1/3}} \,d x","Not used",1,"int(1/((d + e*x)*(2*b^2*e^2 - c^2*d^2 + 9*c^2*e^2*x^2 + 9*b*c*e^2*x + b*c*d*e)^(1/3)), x)","F"
2510,0,-1,374,0.000000,"\text{Not used}","int((d + e*x)^3*(a + b*x + c*x^2)^(1/4),x)","\int {\left(d+e\,x\right)}^3\,{\left(c\,x^2+b\,x+a\right)}^{1/4} \,d x","Not used",1,"int((d + e*x)^3*(a + b*x + c*x^2)^(1/4), x)","F"
2511,0,-1,319,0.000000,"\text{Not used}","int((d + e*x)^2*(a + b*x + c*x^2)^(1/4),x)","\int {\left(d+e\,x\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^{1/4} \,d x","Not used",1,"int((d + e*x)^2*(a + b*x + c*x^2)^(1/4), x)","F"
2512,0,-1,241,0.000000,"\text{Not used}","int((d + e*x)*(a + b*x + c*x^2)^(1/4),x)","\int \left(d+e\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{1/4} \,d x","Not used",1,"int((d + e*x)*(a + b*x + c*x^2)^(1/4), x)","F"
2513,0,-1,201,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/4),x)","\int {\left(c\,x^2+b\,x+a\right)}^{1/4} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/4), x)","F"
2514,0,-1,881,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/4)/(d + e*x),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{1/4}}{d+e\,x} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/4)/(d + e*x), x)","F"
2515,0,-1,944,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(1/4)/(d + e*x)^2,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{1/4}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a + b*x + c*x^2)^(1/4)/(d + e*x)^2, x)","F"
2516,0,-1,703,0.000000,"\text{Not used}","int((d + e*x)^3*(a + b*x + c*x^2)^(3/4),x)","\int {\left(d+e\,x\right)}^3\,{\left(c\,x^2+b\,x+a\right)}^{3/4} \,d x","Not used",1,"int((d + e*x)^3*(a + b*x + c*x^2)^(3/4), x)","F"
2517,0,-1,630,0.000000,"\text{Not used}","int((d + e*x)^2*(a + b*x + c*x^2)^(3/4),x)","\int {\left(d+e\,x\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^{3/4} \,d x","Not used",1,"int((d + e*x)^2*(a + b*x + c*x^2)^(3/4), x)","F"
2518,0,-1,510,0.000000,"\text{Not used}","int((d + e*x)*(a + b*x + c*x^2)^(3/4),x)","\int \left(d+e\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{3/4} \,d x","Not used",1,"int((d + e*x)*(a + b*x + c*x^2)^(3/4), x)","F"
2519,0,-1,452,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/4),x)","\int {\left(c\,x^2+b\,x+a\right)}^{3/4} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/4), x)","F"
2520,0,-1,1209,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/4)/(d + e*x),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/4}}{d+e\,x} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/4)/(d + e*x), x)","F"
2521,0,-1,1220,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(3/4)/(d + e*x)^2,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{3/4}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a + b*x + c*x^2)^(3/4)/(d + e*x)^2, x)","F"
2522,0,-1,448,0.000000,"\text{Not used}","int((d + e*x)^3*(a + b*x + c*x^2)^(5/4),x)","\int {\left(d+e\,x\right)}^3\,{\left(c\,x^2+b\,x+a\right)}^{5/4} \,d x","Not used",1,"int((d + e*x)^3*(a + b*x + c*x^2)^(5/4), x)","F"
2523,0,-1,384,0.000000,"\text{Not used}","int((d + e*x)^2*(a + b*x + c*x^2)^(5/4),x)","\int {\left(d+e\,x\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^{5/4} \,d x","Not used",1,"int((d + e*x)^2*(a + b*x + c*x^2)^(5/4), x)","F"
2524,0,-1,285,0.000000,"\text{Not used}","int((d + e*x)*(a + b*x + c*x^2)^(5/4),x)","\int \left(d+e\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{5/4} \,d x","Not used",1,"int((d + e*x)*(a + b*x + c*x^2)^(5/4), x)","F"
2525,0,-1,236,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/4),x)","\int {\left(c\,x^2+b\,x+a\right)}^{5/4} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/4), x)","F"
2526,0,-1,1014,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/4)/(d + e*x),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/4}}{d+e\,x} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/4)/(d + e*x), x)","F"
2527,0,-1,975,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^(5/4)/(d + e*x)^2,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^{5/4}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a + b*x + c*x^2)^(5/4)/(d + e*x)^2, x)","F"
2528,0,-1,637,0.000000,"\text{Not used}","int((d + e*x)^3/(a + b*x + c*x^2)^(1/4),x)","\int \frac{{\left(d+e\,x\right)}^3}{{\left(c\,x^2+b\,x+a\right)}^{1/4}} \,d x","Not used",1,"int((d + e*x)^3/(a + b*x + c*x^2)^(1/4), x)","F"
2529,0,-1,573,0.000000,"\text{Not used}","int((d + e*x)^2/(a + b*x + c*x^2)^(1/4),x)","\int \frac{{\left(d+e\,x\right)}^2}{{\left(c\,x^2+b\,x+a\right)}^{1/4}} \,d x","Not used",1,"int((d + e*x)^2/(a + b*x + c*x^2)^(1/4), x)","F"
2530,0,-1,469,0.000000,"\text{Not used}","int((d + e*x)/(a + b*x + c*x^2)^(1/4),x)","\int \frac{d+e\,x}{{\left(c\,x^2+b\,x+a\right)}^{1/4}} \,d x","Not used",1,"int((d + e*x)/(a + b*x + c*x^2)^(1/4), x)","F"
2531,0,-1,418,0.000000,"\text{Not used}","int(1/(a + b*x + c*x^2)^(1/4),x)","\int \frac{1}{{\left(c\,x^2+b\,x+a\right)}^{1/4}} \,d x","Not used",1,"int(1/(a + b*x + c*x^2)^(1/4), x)","F"
2532,0,-1,733,0.000000,"\text{Not used}","int(1/((d + e*x)*(a + b*x + c*x^2)^(1/4)),x)","\int \frac{1}{\left(d+e\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{1/4}} \,d x","Not used",1,"int(1/((d + e*x)*(a + b*x + c*x^2)^(1/4)), x)","F"
2533,0,-1,1280,0.000000,"\text{Not used}","int(1/((d + e*x)^2*(a + b*x + c*x^2)^(1/4)),x)","\int \frac{1}{{\left(d+e\,x\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^{1/4}} \,d x","Not used",1,"int(1/((d + e*x)^2*(a + b*x + c*x^2)^(1/4)), x)","F"
2534,0,-1,1465,0.000000,"\text{Not used}","int(1/((d + e*x)^3*(a + b*x + c*x^2)^(1/4)),x)","\int \frac{1}{{\left(d+e\,x\right)}^3\,{\left(c\,x^2+b\,x+a\right)}^{1/4}} \,d x","Not used",1,"int(1/((d + e*x)^3*(a + b*x + c*x^2)^(1/4)), x)","F"
2535,0,-1,307,0.000000,"\text{Not used}","int((d + e*x)^3/(a + b*x + c*x^2)^(3/4),x)","\int \frac{{\left(d+e\,x\right)}^3}{{\left(c\,x^2+b\,x+a\right)}^{3/4}} \,d x","Not used",1,"int((d + e*x)^3/(a + b*x + c*x^2)^(3/4), x)","F"
2536,0,-1,262,0.000000,"\text{Not used}","int((d + e*x)^2/(a + b*x + c*x^2)^(3/4),x)","\int \frac{{\left(d+e\,x\right)}^2}{{\left(c\,x^2+b\,x+a\right)}^{3/4}} \,d x","Not used",1,"int((d + e*x)^2/(a + b*x + c*x^2)^(3/4), x)","F"
2537,0,-1,200,0.000000,"\text{Not used}","int((d + e*x)/(a + b*x + c*x^2)^(3/4),x)","\int \frac{d+e\,x}{{\left(c\,x^2+b\,x+a\right)}^{3/4}} \,d x","Not used",1,"int((d + e*x)/(a + b*x + c*x^2)^(3/4), x)","F"
2538,0,-1,170,0.000000,"\text{Not used}","int(1/(a + b*x + c*x^2)^(3/4),x)","\int \frac{1}{{\left(c\,x^2+b\,x+a\right)}^{3/4}} \,d x","Not used",1,"int(1/(a + b*x + c*x^2)^(3/4), x)","F"
2539,0,-1,709,0.000000,"\text{Not used}","int(1/((d + e*x)*(a + b*x + c*x^2)^(3/4)),x)","\int \frac{1}{\left(d+e\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{3/4}} \,d x","Not used",1,"int(1/((d + e*x)*(a + b*x + c*x^2)^(3/4)), x)","F"
2540,0,-1,970,0.000000,"\text{Not used}","int(1/((d + e*x)^2*(a + b*x + c*x^2)^(3/4)),x)","\int \frac{1}{{\left(d+e\,x\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^{3/4}} \,d x","Not used",1,"int(1/((d + e*x)^2*(a + b*x + c*x^2)^(3/4)), x)","F"
2541,0,-1,1134,0.000000,"\text{Not used}","int(1/((d + e*x)^3*(a + b*x + c*x^2)^(3/4)),x)","\int \frac{1}{{\left(d+e\,x\right)}^3\,{\left(c\,x^2+b\,x+a\right)}^{3/4}} \,d x","Not used",1,"int(1/((d + e*x)^3*(a + b*x + c*x^2)^(3/4)), x)","F"
2542,0,-1,662,0.000000,"\text{Not used}","int((d + e*x)^3/(a + b*x + c*x^2)^(5/4),x)","\int \frac{{\left(d+e\,x\right)}^3}{{\left(c\,x^2+b\,x+a\right)}^{5/4}} \,d x","Not used",1,"int((d + e*x)^3/(a + b*x + c*x^2)^(5/4), x)","F"
2543,0,-1,594,0.000000,"\text{Not used}","int((d + e*x)^2/(a + b*x + c*x^2)^(5/4),x)","\int \frac{{\left(d+e\,x\right)}^2}{{\left(c\,x^2+b\,x+a\right)}^{5/4}} \,d x","Not used",1,"int((d + e*x)^2/(a + b*x + c*x^2)^(5/4), x)","F"
2544,0,-1,490,0.000000,"\text{Not used}","int((d + e*x)/(a + b*x + c*x^2)^(5/4),x)","\int \frac{d+e\,x}{{\left(c\,x^2+b\,x+a\right)}^{5/4}} \,d x","Not used",1,"int((d + e*x)/(a + b*x + c*x^2)^(5/4), x)","F"
2545,0,-1,451,0.000000,"\text{Not used}","int(1/(a + b*x + c*x^2)^(5/4),x)","\int \frac{1}{{\left(c\,x^2+b\,x+a\right)}^{5/4}} \,d x","Not used",1,"int(1/(a + b*x + c*x^2)^(5/4), x)","F"
2546,0,-1,1299,0.000000,"\text{Not used}","int(1/((d + e*x)*(a + b*x + c*x^2)^(5/4)),x)","\int \frac{1}{\left(d+e\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^{5/4}} \,d x","Not used",1,"int(1/((d + e*x)*(a + b*x + c*x^2)^(5/4)), x)","F"
2547,0,-1,1485,0.000000,"\text{Not used}","int(1/((d + e*x)^2*(a + b*x + c*x^2)^(5/4)),x)","\int \frac{1}{{\left(d+e\,x\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^{5/4}} \,d x","Not used",1,"int(1/((d + e*x)^2*(a + b*x + c*x^2)^(5/4)), x)","F"
2548,0,-1,239,0.000000,"\text{Not used}","int(1/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(1/4)),x)","\int \frac{1}{{\left(d+e\,x\right)}^{3/2}\,{\left(c\,x^2+b\,x+a\right)}^{1/4}} \,d x","Not used",1,"int(1/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(1/4)), x)","F"
2549,1,5907,485,4.442996,"\text{Not used}","int((d + e*x)^m*(a + b*x + c*x^2)^4,x)","\frac{{\left(d+e\,x\right)}^m\,\left(a^4\,d\,e^8\,m^8+44\,a^4\,d\,e^8\,m^7+826\,a^4\,d\,e^8\,m^6+8624\,a^4\,d\,e^8\,m^5+54649\,a^4\,d\,e^8\,m^4+214676\,a^4\,d\,e^8\,m^3+509004\,a^4\,d\,e^8\,m^2+663696\,a^4\,d\,e^8\,m+362880\,a^4\,d\,e^8-4\,a^3\,b\,d^2\,e^7\,m^7-168\,a^3\,b\,d^2\,e^7\,m^6-2968\,a^3\,b\,d^2\,e^7\,m^5-28560\,a^3\,b\,d^2\,e^7\,m^4-161476\,a^3\,b\,d^2\,e^7\,m^3-535752\,a^3\,b\,d^2\,e^7\,m^2-964512\,a^3\,b\,d^2\,e^7\,m-725760\,a^3\,b\,d^2\,e^7+8\,a^3\,c\,d^3\,e^6\,m^6+312\,a^3\,c\,d^3\,e^6\,m^5+5000\,a^3\,c\,d^3\,e^6\,m^4+42120\,a^3\,c\,d^3\,e^6\,m^3+196592\,a^3\,c\,d^3\,e^6\,m^2+481728\,a^3\,c\,d^3\,e^6\,m+483840\,a^3\,c\,d^3\,e^6+12\,a^2\,b^2\,d^3\,e^6\,m^6+468\,a^2\,b^2\,d^3\,e^6\,m^5+7500\,a^2\,b^2\,d^3\,e^6\,m^4+63180\,a^2\,b^2\,d^3\,e^6\,m^3+294888\,a^2\,b^2\,d^3\,e^6\,m^2+722592\,a^2\,b^2\,d^3\,e^6\,m+725760\,a^2\,b^2\,d^3\,e^6-72\,a^2\,b\,c\,d^4\,e^5\,m^5-2520\,a^2\,b\,c\,d^4\,e^5\,m^4-34920\,a^2\,b\,c\,d^4\,e^5\,m^3-239400\,a^2\,b\,c\,d^4\,e^5\,m^2-811728\,a^2\,b\,c\,d^4\,e^5\,m-1088640\,a^2\,b\,c\,d^4\,e^5+144\,a^2\,c^2\,d^5\,e^4\,m^4+4320\,a^2\,c^2\,d^5\,e^4\,m^3+48240\,a^2\,c^2\,d^5\,e^4\,m^2+237600\,a^2\,c^2\,d^5\,e^4\,m+435456\,a^2\,c^2\,d^5\,e^4-24\,a\,b^3\,d^4\,e^5\,m^5-840\,a\,b^3\,d^4\,e^5\,m^4-11640\,a\,b^3\,d^4\,e^5\,m^3-79800\,a\,b^3\,d^4\,e^5\,m^2-270576\,a\,b^3\,d^4\,e^5\,m-362880\,a\,b^3\,d^4\,e^5+288\,a\,b^2\,c\,d^5\,e^4\,m^4+8640\,a\,b^2\,c\,d^5\,e^4\,m^3+96480\,a\,b^2\,c\,d^5\,e^4\,m^2+475200\,a\,b^2\,c\,d^5\,e^4\,m+870912\,a\,b^2\,c\,d^5\,e^4-1440\,a\,b\,c^2\,d^6\,e^3\,m^3-34560\,a\,b\,c^2\,d^6\,e^3\,m^2-275040\,a\,b\,c^2\,d^6\,e^3\,m-725760\,a\,b\,c^2\,d^6\,e^3+2880\,a\,c^3\,d^7\,e^2\,m^2+48960\,a\,c^3\,d^7\,e^2\,m+207360\,a\,c^3\,d^7\,e^2+24\,b^4\,d^5\,e^4\,m^4+720\,b^4\,d^5\,e^4\,m^3+8040\,b^4\,d^5\,e^4\,m^2+39600\,b^4\,d^5\,e^4\,m+72576\,b^4\,d^5\,e^4-480\,b^3\,c\,d^6\,e^3\,m^3-11520\,b^3\,c\,d^6\,e^3\,m^2-91680\,b^3\,c\,d^6\,e^3\,m-241920\,b^3\,c\,d^6\,e^3+4320\,b^2\,c^2\,d^7\,e^2\,m^2+73440\,b^2\,c^2\,d^7\,e^2\,m+311040\,b^2\,c^2\,d^7\,e^2-20160\,b\,c^3\,d^8\,e\,m-181440\,b\,c^3\,d^8\,e+40320\,c^4\,d^9\right)}{e^9\,\left(m^9+45\,m^8+870\,m^7+9450\,m^6+63273\,m^5+269325\,m^4+723680\,m^3+1172700\,m^2+1026576\,m+362880\right)}+\frac{x\,{\left(d+e\,x\right)}^m\,\left(a^4\,e^9\,m^8+44\,a^4\,e^9\,m^7+826\,a^4\,e^9\,m^6+8624\,a^4\,e^9\,m^5+54649\,a^4\,e^9\,m^4+214676\,a^4\,e^9\,m^3+509004\,a^4\,e^9\,m^2+663696\,a^4\,e^9\,m+362880\,a^4\,e^9+4\,a^3\,b\,d\,e^8\,m^8+168\,a^3\,b\,d\,e^8\,m^7+2968\,a^3\,b\,d\,e^8\,m^6+28560\,a^3\,b\,d\,e^8\,m^5+161476\,a^3\,b\,d\,e^8\,m^4+535752\,a^3\,b\,d\,e^8\,m^3+964512\,a^3\,b\,d\,e^8\,m^2+725760\,a^3\,b\,d\,e^8\,m-8\,a^3\,c\,d^2\,e^7\,m^7-312\,a^3\,c\,d^2\,e^7\,m^6-5000\,a^3\,c\,d^2\,e^7\,m^5-42120\,a^3\,c\,d^2\,e^7\,m^4-196592\,a^3\,c\,d^2\,e^7\,m^3-481728\,a^3\,c\,d^2\,e^7\,m^2-483840\,a^3\,c\,d^2\,e^7\,m-12\,a^2\,b^2\,d^2\,e^7\,m^7-468\,a^2\,b^2\,d^2\,e^7\,m^6-7500\,a^2\,b^2\,d^2\,e^7\,m^5-63180\,a^2\,b^2\,d^2\,e^7\,m^4-294888\,a^2\,b^2\,d^2\,e^7\,m^3-722592\,a^2\,b^2\,d^2\,e^7\,m^2-725760\,a^2\,b^2\,d^2\,e^7\,m+72\,a^2\,b\,c\,d^3\,e^6\,m^6+2520\,a^2\,b\,c\,d^3\,e^6\,m^5+34920\,a^2\,b\,c\,d^3\,e^6\,m^4+239400\,a^2\,b\,c\,d^3\,e^6\,m^3+811728\,a^2\,b\,c\,d^3\,e^6\,m^2+1088640\,a^2\,b\,c\,d^3\,e^6\,m-144\,a^2\,c^2\,d^4\,e^5\,m^5-4320\,a^2\,c^2\,d^4\,e^5\,m^4-48240\,a^2\,c^2\,d^4\,e^5\,m^3-237600\,a^2\,c^2\,d^4\,e^5\,m^2-435456\,a^2\,c^2\,d^4\,e^5\,m+24\,a\,b^3\,d^3\,e^6\,m^6+840\,a\,b^3\,d^3\,e^6\,m^5+11640\,a\,b^3\,d^3\,e^6\,m^4+79800\,a\,b^3\,d^3\,e^6\,m^3+270576\,a\,b^3\,d^3\,e^6\,m^2+362880\,a\,b^3\,d^3\,e^6\,m-288\,a\,b^2\,c\,d^4\,e^5\,m^5-8640\,a\,b^2\,c\,d^4\,e^5\,m^4-96480\,a\,b^2\,c\,d^4\,e^5\,m^3-475200\,a\,b^2\,c\,d^4\,e^5\,m^2-870912\,a\,b^2\,c\,d^4\,e^5\,m+1440\,a\,b\,c^2\,d^5\,e^4\,m^4+34560\,a\,b\,c^2\,d^5\,e^4\,m^3+275040\,a\,b\,c^2\,d^5\,e^4\,m^2+725760\,a\,b\,c^2\,d^5\,e^4\,m-2880\,a\,c^3\,d^6\,e^3\,m^3-48960\,a\,c^3\,d^6\,e^3\,m^2-207360\,a\,c^3\,d^6\,e^3\,m-24\,b^4\,d^4\,e^5\,m^5-720\,b^4\,d^4\,e^5\,m^4-8040\,b^4\,d^4\,e^5\,m^3-39600\,b^4\,d^4\,e^5\,m^2-72576\,b^4\,d^4\,e^5\,m+480\,b^3\,c\,d^5\,e^4\,m^4+11520\,b^3\,c\,d^5\,e^4\,m^3+91680\,b^3\,c\,d^5\,e^4\,m^2+241920\,b^3\,c\,d^5\,e^4\,m-4320\,b^2\,c^2\,d^6\,e^3\,m^3-73440\,b^2\,c^2\,d^6\,e^3\,m^2-311040\,b^2\,c^2\,d^6\,e^3\,m+20160\,b\,c^3\,d^7\,e^2\,m^2+181440\,b\,c^3\,d^7\,e^2\,m-40320\,c^4\,d^8\,e\,m\right)}{e^9\,\left(m^9+45\,m^8+870\,m^7+9450\,m^6+63273\,m^5+269325\,m^4+723680\,m^3+1172700\,m^2+1026576\,m+362880\right)}+\frac{c^4\,x^9\,{\left(d+e\,x\right)}^m\,\left(m^8+36\,m^7+546\,m^6+4536\,m^5+22449\,m^4+67284\,m^3+118124\,m^2+109584\,m+40320\right)}{m^9+45\,m^8+870\,m^7+9450\,m^6+63273\,m^5+269325\,m^4+723680\,m^3+1172700\,m^2+1026576\,m+362880}+\frac{2\,x^2\,\left(m+1\right)\,{\left(d+e\,x\right)}^m\,\left(2\,a^3\,b\,e^7\,m^7+84\,a^3\,b\,e^7\,m^6+1484\,a^3\,b\,e^7\,m^5+14280\,a^3\,b\,e^7\,m^4+80738\,a^3\,b\,e^7\,m^3+267876\,a^3\,b\,e^7\,m^2+482256\,a^3\,b\,e^7\,m+362880\,a^3\,b\,e^7+2\,a^3\,c\,d\,e^6\,m^7+78\,a^3\,c\,d\,e^6\,m^6+1250\,a^3\,c\,d\,e^6\,m^5+10530\,a^3\,c\,d\,e^6\,m^4+49148\,a^3\,c\,d\,e^6\,m^3+120432\,a^3\,c\,d\,e^6\,m^2+120960\,a^3\,c\,d\,e^6\,m+3\,a^2\,b^2\,d\,e^6\,m^7+117\,a^2\,b^2\,d\,e^6\,m^6+1875\,a^2\,b^2\,d\,e^6\,m^5+15795\,a^2\,b^2\,d\,e^6\,m^4+73722\,a^2\,b^2\,d\,e^6\,m^3+180648\,a^2\,b^2\,d\,e^6\,m^2+181440\,a^2\,b^2\,d\,e^6\,m-18\,a^2\,b\,c\,d^2\,e^5\,m^6-630\,a^2\,b\,c\,d^2\,e^5\,m^5-8730\,a^2\,b\,c\,d^2\,e^5\,m^4-59850\,a^2\,b\,c\,d^2\,e^5\,m^3-202932\,a^2\,b\,c\,d^2\,e^5\,m^2-272160\,a^2\,b\,c\,d^2\,e^5\,m+36\,a^2\,c^2\,d^3\,e^4\,m^5+1080\,a^2\,c^2\,d^3\,e^4\,m^4+12060\,a^2\,c^2\,d^3\,e^4\,m^3+59400\,a^2\,c^2\,d^3\,e^4\,m^2+108864\,a^2\,c^2\,d^3\,e^4\,m-6\,a\,b^3\,d^2\,e^5\,m^6-210\,a\,b^3\,d^2\,e^5\,m^5-2910\,a\,b^3\,d^2\,e^5\,m^4-19950\,a\,b^3\,d^2\,e^5\,m^3-67644\,a\,b^3\,d^2\,e^5\,m^2-90720\,a\,b^3\,d^2\,e^5\,m+72\,a\,b^2\,c\,d^3\,e^4\,m^5+2160\,a\,b^2\,c\,d^3\,e^4\,m^4+24120\,a\,b^2\,c\,d^3\,e^4\,m^3+118800\,a\,b^2\,c\,d^3\,e^4\,m^2+217728\,a\,b^2\,c\,d^3\,e^4\,m-360\,a\,b\,c^2\,d^4\,e^3\,m^4-8640\,a\,b\,c^2\,d^4\,e^3\,m^3-68760\,a\,b\,c^2\,d^4\,e^3\,m^2-181440\,a\,b\,c^2\,d^4\,e^3\,m+720\,a\,c^3\,d^5\,e^2\,m^3+12240\,a\,c^3\,d^5\,e^2\,m^2+51840\,a\,c^3\,d^5\,e^2\,m+6\,b^4\,d^3\,e^4\,m^5+180\,b^4\,d^3\,e^4\,m^4+2010\,b^4\,d^3\,e^4\,m^3+9900\,b^4\,d^3\,e^4\,m^2+18144\,b^4\,d^3\,e^4\,m-120\,b^3\,c\,d^4\,e^3\,m^4-2880\,b^3\,c\,d^4\,e^3\,m^3-22920\,b^3\,c\,d^4\,e^3\,m^2-60480\,b^3\,c\,d^4\,e^3\,m+1080\,b^2\,c^2\,d^5\,e^2\,m^3+18360\,b^2\,c^2\,d^5\,e^2\,m^2+77760\,b^2\,c^2\,d^5\,e^2\,m-5040\,b\,c^3\,d^6\,e\,m^2-45360\,b\,c^3\,d^6\,e\,m+10080\,c^4\,d^7\,m\right)}{e^7\,\left(m^9+45\,m^8+870\,m^7+9450\,m^6+63273\,m^5+269325\,m^4+723680\,m^3+1172700\,m^2+1026576\,m+362880\right)}+\frac{x^4\,{\left(d+e\,x\right)}^m\,\left(m^3+6\,m^2+11\,m+6\right)\,\left(12\,a^2\,b\,c\,e^5\,m^5+420\,a^2\,b\,c\,e^5\,m^4+5820\,a^2\,b\,c\,e^5\,m^3+39900\,a^2\,b\,c\,e^5\,m^2+135288\,a^2\,b\,c\,e^5\,m+181440\,a^2\,b\,c\,e^5+6\,a^2\,c^2\,d\,e^4\,m^5+180\,a^2\,c^2\,d\,e^4\,m^4+2010\,a^2\,c^2\,d\,e^4\,m^3+9900\,a^2\,c^2\,d\,e^4\,m^2+18144\,a^2\,c^2\,d\,e^4\,m+4\,a\,b^3\,e^5\,m^5+140\,a\,b^3\,e^5\,m^4+1940\,a\,b^3\,e^5\,m^3+13300\,a\,b^3\,e^5\,m^2+45096\,a\,b^3\,e^5\,m+60480\,a\,b^3\,e^5+12\,a\,b^2\,c\,d\,e^4\,m^5+360\,a\,b^2\,c\,d\,e^4\,m^4+4020\,a\,b^2\,c\,d\,e^4\,m^3+19800\,a\,b^2\,c\,d\,e^4\,m^2+36288\,a\,b^2\,c\,d\,e^4\,m-60\,a\,b\,c^2\,d^2\,e^3\,m^4-1440\,a\,b\,c^2\,d^2\,e^3\,m^3-11460\,a\,b\,c^2\,d^2\,e^3\,m^2-30240\,a\,b\,c^2\,d^2\,e^3\,m+120\,a\,c^3\,d^3\,e^2\,m^3+2040\,a\,c^3\,d^3\,e^2\,m^2+8640\,a\,c^3\,d^3\,e^2\,m+b^4\,d\,e^4\,m^5+30\,b^4\,d\,e^4\,m^4+335\,b^4\,d\,e^4\,m^3+1650\,b^4\,d\,e^4\,m^2+3024\,b^4\,d\,e^4\,m-20\,b^3\,c\,d^2\,e^3\,m^4-480\,b^3\,c\,d^2\,e^3\,m^3-3820\,b^3\,c\,d^2\,e^3\,m^2-10080\,b^3\,c\,d^2\,e^3\,m+180\,b^2\,c^2\,d^3\,e^2\,m^3+3060\,b^2\,c^2\,d^3\,e^2\,m^2+12960\,b^2\,c^2\,d^3\,e^2\,m-840\,b\,c^3\,d^4\,e\,m^2-7560\,b\,c^3\,d^4\,e\,m+1680\,c^4\,d^5\,m\right)}{e^5\,\left(m^9+45\,m^8+870\,m^7+9450\,m^6+63273\,m^5+269325\,m^4+723680\,m^3+1172700\,m^2+1026576\,m+362880\right)}+\frac{2\,x^3\,{\left(d+e\,x\right)}^m\,\left(m^2+3\,m+2\right)\,\left(2\,a^3\,c\,e^6\,m^6+78\,a^3\,c\,e^6\,m^5+1250\,a^3\,c\,e^6\,m^4+10530\,a^3\,c\,e^6\,m^3+49148\,a^3\,c\,e^6\,m^2+120432\,a^3\,c\,e^6\,m+120960\,a^3\,c\,e^6+3\,a^2\,b^2\,e^6\,m^6+117\,a^2\,b^2\,e^6\,m^5+1875\,a^2\,b^2\,e^6\,m^4+15795\,a^2\,b^2\,e^6\,m^3+73722\,a^2\,b^2\,e^6\,m^2+180648\,a^2\,b^2\,e^6\,m+181440\,a^2\,b^2\,e^6+6\,a^2\,b\,c\,d\,e^5\,m^6+210\,a^2\,b\,c\,d\,e^5\,m^5+2910\,a^2\,b\,c\,d\,e^5\,m^4+19950\,a^2\,b\,c\,d\,e^5\,m^3+67644\,a^2\,b\,c\,d\,e^5\,m^2+90720\,a^2\,b\,c\,d\,e^5\,m-12\,a^2\,c^2\,d^2\,e^4\,m^5-360\,a^2\,c^2\,d^2\,e^4\,m^4-4020\,a^2\,c^2\,d^2\,e^4\,m^3-19800\,a^2\,c^2\,d^2\,e^4\,m^2-36288\,a^2\,c^2\,d^2\,e^4\,m+2\,a\,b^3\,d\,e^5\,m^6+70\,a\,b^3\,d\,e^5\,m^5+970\,a\,b^3\,d\,e^5\,m^4+6650\,a\,b^3\,d\,e^5\,m^3+22548\,a\,b^3\,d\,e^5\,m^2+30240\,a\,b^3\,d\,e^5\,m-24\,a\,b^2\,c\,d^2\,e^4\,m^5-720\,a\,b^2\,c\,d^2\,e^4\,m^4-8040\,a\,b^2\,c\,d^2\,e^4\,m^3-39600\,a\,b^2\,c\,d^2\,e^4\,m^2-72576\,a\,b^2\,c\,d^2\,e^4\,m+120\,a\,b\,c^2\,d^3\,e^3\,m^4+2880\,a\,b\,c^2\,d^3\,e^3\,m^3+22920\,a\,b\,c^2\,d^3\,e^3\,m^2+60480\,a\,b\,c^2\,d^3\,e^3\,m-240\,a\,c^3\,d^4\,e^2\,m^3-4080\,a\,c^3\,d^4\,e^2\,m^2-17280\,a\,c^3\,d^4\,e^2\,m-2\,b^4\,d^2\,e^4\,m^5-60\,b^4\,d^2\,e^4\,m^4-670\,b^4\,d^2\,e^4\,m^3-3300\,b^4\,d^2\,e^4\,m^2-6048\,b^4\,d^2\,e^4\,m+40\,b^3\,c\,d^3\,e^3\,m^4+960\,b^3\,c\,d^3\,e^3\,m^3+7640\,b^3\,c\,d^3\,e^3\,m^2+20160\,b^3\,c\,d^3\,e^3\,m-360\,b^2\,c^2\,d^4\,e^2\,m^3-6120\,b^2\,c^2\,d^4\,e^2\,m^2-25920\,b^2\,c^2\,d^4\,e^2\,m+1680\,b\,c^3\,d^5\,e\,m^2+15120\,b\,c^3\,d^5\,e\,m-3360\,c^4\,d^6\,m\right)}{e^6\,\left(m^9+45\,m^8+870\,m^7+9450\,m^6+63273\,m^5+269325\,m^4+723680\,m^3+1172700\,m^2+1026576\,m+362880\right)}+\frac{x^5\,{\left(d+e\,x\right)}^m\,\left(m^4+10\,m^3+35\,m^2+50\,m+24\right)\,\left(6\,a^2\,c^2\,e^4\,m^4+180\,a^2\,c^2\,e^4\,m^3+2010\,a^2\,c^2\,e^4\,m^2+9900\,a^2\,c^2\,e^4\,m+18144\,a^2\,c^2\,e^4+12\,a\,b^2\,c\,e^4\,m^4+360\,a\,b^2\,c\,e^4\,m^3+4020\,a\,b^2\,c\,e^4\,m^2+19800\,a\,b^2\,c\,e^4\,m+36288\,a\,b^2\,c\,e^4+12\,a\,b\,c^2\,d\,e^3\,m^4+288\,a\,b\,c^2\,d\,e^3\,m^3+2292\,a\,b\,c^2\,d\,e^3\,m^2+6048\,a\,b\,c^2\,d\,e^3\,m-24\,a\,c^3\,d^2\,e^2\,m^3-408\,a\,c^3\,d^2\,e^2\,m^2-1728\,a\,c^3\,d^2\,e^2\,m+b^4\,e^4\,m^4+30\,b^4\,e^4\,m^3+335\,b^4\,e^4\,m^2+1650\,b^4\,e^4\,m+3024\,b^4\,e^4+4\,b^3\,c\,d\,e^3\,m^4+96\,b^3\,c\,d\,e^3\,m^3+764\,b^3\,c\,d\,e^3\,m^2+2016\,b^3\,c\,d\,e^3\,m-36\,b^2\,c^2\,d^2\,e^2\,m^3-612\,b^2\,c^2\,d^2\,e^2\,m^2-2592\,b^2\,c^2\,d^2\,e^2\,m+168\,b\,c^3\,d^3\,e\,m^2+1512\,b\,c^3\,d^3\,e\,m-336\,c^4\,d^4\,m\right)}{e^4\,\left(m^9+45\,m^8+870\,m^7+9450\,m^6+63273\,m^5+269325\,m^4+723680\,m^3+1172700\,m^2+1026576\,m+362880\right)}+\frac{2\,c\,x^6\,{\left(d+e\,x\right)}^m\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)\,\left(2\,b^3\,e^3\,m^3+48\,b^3\,e^3\,m^2+382\,b^3\,e^3\,m+1008\,b^3\,e^3+3\,b^2\,c\,d\,e^2\,m^3+51\,b^2\,c\,d\,e^2\,m^2+216\,b^2\,c\,d\,e^2\,m-14\,b\,c^2\,d^2\,e\,m^2-126\,b\,c^2\,d^2\,e\,m+6\,a\,b\,c\,e^3\,m^3+144\,a\,b\,c\,e^3\,m^2+1146\,a\,b\,c\,e^3\,m+3024\,a\,b\,c\,e^3+28\,c^3\,d^3\,m+2\,a\,c^2\,d\,e^2\,m^3+34\,a\,c^2\,d\,e^2\,m^2+144\,a\,c^2\,d\,e^2\,m\right)}{e^3\,\left(m^9+45\,m^8+870\,m^7+9450\,m^6+63273\,m^5+269325\,m^4+723680\,m^3+1172700\,m^2+1026576\,m+362880\right)}+\frac{2\,c^2\,x^7\,{\left(d+e\,x\right)}^m\,\left(m^6+21\,m^5+175\,m^4+735\,m^3+1624\,m^2+1764\,m+720\right)\,\left(3\,b^2\,e^2\,m^2+51\,b^2\,e^2\,m+216\,b^2\,e^2+2\,b\,c\,d\,e\,m^2+18\,b\,c\,d\,e\,m-4\,c^2\,d^2\,m+2\,a\,c\,e^2\,m^2+34\,a\,c\,e^2\,m+144\,a\,c\,e^2\right)}{e^2\,\left(m^9+45\,m^8+870\,m^7+9450\,m^6+63273\,m^5+269325\,m^4+723680\,m^3+1172700\,m^2+1026576\,m+362880\right)}+\frac{c^3\,x^8\,{\left(d+e\,x\right)}^m\,\left(36\,b\,e+4\,b\,e\,m+c\,d\,m\right)\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}{e\,\left(m^9+45\,m^8+870\,m^7+9450\,m^6+63273\,m^5+269325\,m^4+723680\,m^3+1172700\,m^2+1026576\,m+362880\right)}","Not used",1,"((d + e*x)^m*(40320*c^4*d^9 + 362880*a^4*d*e^8 + 72576*b^4*d^5*e^4 - 362880*a*b^3*d^4*e^5 - 725760*a^3*b*d^2*e^7 + 207360*a*c^3*d^7*e^2 + 483840*a^3*c*d^3*e^6 - 241920*b^3*c*d^6*e^3 + 509004*a^4*d*e^8*m^2 + 214676*a^4*d*e^8*m^3 + 54649*a^4*d*e^8*m^4 + 8624*a^4*d*e^8*m^5 + 826*a^4*d*e^8*m^6 + 44*a^4*d*e^8*m^7 + a^4*d*e^8*m^8 + 39600*b^4*d^5*e^4*m + 725760*a^2*b^2*d^3*e^6 + 435456*a^2*c^2*d^5*e^4 + 311040*b^2*c^2*d^7*e^2 + 8040*b^4*d^5*e^4*m^2 + 720*b^4*d^5*e^4*m^3 + 24*b^4*d^5*e^4*m^4 - 181440*b*c^3*d^8*e + 663696*a^4*d*e^8*m - 20160*b*c^3*d^8*e*m + 294888*a^2*b^2*d^3*e^6*m^2 + 63180*a^2*b^2*d^3*e^6*m^3 + 7500*a^2*b^2*d^3*e^6*m^4 + 468*a^2*b^2*d^3*e^6*m^5 + 12*a^2*b^2*d^3*e^6*m^6 + 48240*a^2*c^2*d^5*e^4*m^2 + 4320*a^2*c^2*d^5*e^4*m^3 + 144*a^2*c^2*d^5*e^4*m^4 + 4320*b^2*c^2*d^7*e^2*m^2 - 725760*a*b*c^2*d^6*e^3 + 870912*a*b^2*c*d^5*e^4 - 1088640*a^2*b*c*d^4*e^5 - 270576*a*b^3*d^4*e^5*m - 964512*a^3*b*d^2*e^7*m + 48960*a*c^3*d^7*e^2*m + 481728*a^3*c*d^3*e^6*m - 91680*b^3*c*d^6*e^3*m + 722592*a^2*b^2*d^3*e^6*m - 79800*a*b^3*d^4*e^5*m^2 - 535752*a^3*b*d^2*e^7*m^2 - 11640*a*b^3*d^4*e^5*m^3 - 161476*a^3*b*d^2*e^7*m^3 - 840*a*b^3*d^4*e^5*m^4 - 28560*a^3*b*d^2*e^7*m^4 - 24*a*b^3*d^4*e^5*m^5 - 2968*a^3*b*d^2*e^7*m^5 - 168*a^3*b*d^2*e^7*m^6 - 4*a^3*b*d^2*e^7*m^7 + 237600*a^2*c^2*d^5*e^4*m + 2880*a*c^3*d^7*e^2*m^2 + 196592*a^3*c*d^3*e^6*m^2 + 42120*a^3*c*d^3*e^6*m^3 + 5000*a^3*c*d^3*e^6*m^4 + 312*a^3*c*d^3*e^6*m^5 + 8*a^3*c*d^3*e^6*m^6 + 73440*b^2*c^2*d^7*e^2*m - 11520*b^3*c*d^6*e^3*m^2 - 480*b^3*c*d^6*e^3*m^3 - 34560*a*b*c^2*d^6*e^3*m^2 + 96480*a*b^2*c*d^5*e^4*m^2 - 239400*a^2*b*c*d^4*e^5*m^2 - 1440*a*b*c^2*d^6*e^3*m^3 + 8640*a*b^2*c*d^5*e^4*m^3 - 34920*a^2*b*c*d^4*e^5*m^3 + 288*a*b^2*c*d^5*e^4*m^4 - 2520*a^2*b*c*d^4*e^5*m^4 - 72*a^2*b*c*d^4*e^5*m^5 - 275040*a*b*c^2*d^6*e^3*m + 475200*a*b^2*c*d^5*e^4*m - 811728*a^2*b*c*d^4*e^5*m))/(e^9*(1026576*m + 1172700*m^2 + 723680*m^3 + 269325*m^4 + 63273*m^5 + 9450*m^6 + 870*m^7 + 45*m^8 + m^9 + 362880)) + (x*(d + e*x)^m*(362880*a^4*e^9 + 663696*a^4*e^9*m + 509004*a^4*e^9*m^2 + 214676*a^4*e^9*m^3 + 54649*a^4*e^9*m^4 + 8624*a^4*e^9*m^5 + 826*a^4*e^9*m^6 + 44*a^4*e^9*m^7 + a^4*e^9*m^8 - 72576*b^4*d^4*e^5*m - 39600*b^4*d^4*e^5*m^2 - 8040*b^4*d^4*e^5*m^3 - 720*b^4*d^4*e^5*m^4 - 24*b^4*d^4*e^5*m^5 - 40320*c^4*d^8*e*m + 725760*a^3*b*d*e^8*m - 722592*a^2*b^2*d^2*e^7*m^2 - 294888*a^2*b^2*d^2*e^7*m^3 - 63180*a^2*b^2*d^2*e^7*m^4 - 7500*a^2*b^2*d^2*e^7*m^5 - 468*a^2*b^2*d^2*e^7*m^6 - 12*a^2*b^2*d^2*e^7*m^7 - 237600*a^2*c^2*d^4*e^5*m^2 - 48240*a^2*c^2*d^4*e^5*m^3 - 4320*a^2*c^2*d^4*e^5*m^4 - 144*a^2*c^2*d^4*e^5*m^5 - 73440*b^2*c^2*d^6*e^3*m^2 - 4320*b^2*c^2*d^6*e^3*m^3 + 362880*a*b^3*d^3*e^6*m + 964512*a^3*b*d*e^8*m^2 + 535752*a^3*b*d*e^8*m^3 + 161476*a^3*b*d*e^8*m^4 + 28560*a^3*b*d*e^8*m^5 + 2968*a^3*b*d*e^8*m^6 + 168*a^3*b*d*e^8*m^7 + 4*a^3*b*d*e^8*m^8 - 207360*a*c^3*d^6*e^3*m - 483840*a^3*c*d^2*e^7*m + 181440*b*c^3*d^7*e^2*m + 241920*b^3*c*d^5*e^4*m - 725760*a^2*b^2*d^2*e^7*m + 270576*a*b^3*d^3*e^6*m^2 + 79800*a*b^3*d^3*e^6*m^3 + 11640*a*b^3*d^3*e^6*m^4 + 840*a*b^3*d^3*e^6*m^5 + 24*a*b^3*d^3*e^6*m^6 - 435456*a^2*c^2*d^4*e^5*m - 48960*a*c^3*d^6*e^3*m^2 - 481728*a^3*c*d^2*e^7*m^2 - 2880*a*c^3*d^6*e^3*m^3 - 196592*a^3*c*d^2*e^7*m^3 - 42120*a^3*c*d^2*e^7*m^4 - 5000*a^3*c*d^2*e^7*m^5 - 312*a^3*c*d^2*e^7*m^6 - 8*a^3*c*d^2*e^7*m^7 - 311040*b^2*c^2*d^6*e^3*m + 20160*b*c^3*d^7*e^2*m^2 + 91680*b^3*c*d^5*e^4*m^2 + 11520*b^3*c*d^5*e^4*m^3 + 480*b^3*c*d^5*e^4*m^4 + 275040*a*b*c^2*d^5*e^4*m^2 - 475200*a*b^2*c*d^4*e^5*m^2 + 811728*a^2*b*c*d^3*e^6*m^2 + 34560*a*b*c^2*d^5*e^4*m^3 - 96480*a*b^2*c*d^4*e^5*m^3 + 239400*a^2*b*c*d^3*e^6*m^3 + 1440*a*b*c^2*d^5*e^4*m^4 - 8640*a*b^2*c*d^4*e^5*m^4 + 34920*a^2*b*c*d^3*e^6*m^4 - 288*a*b^2*c*d^4*e^5*m^5 + 2520*a^2*b*c*d^3*e^6*m^5 + 72*a^2*b*c*d^3*e^6*m^6 + 725760*a*b*c^2*d^5*e^4*m - 870912*a*b^2*c*d^4*e^5*m + 1088640*a^2*b*c*d^3*e^6*m))/(e^9*(1026576*m + 1172700*m^2 + 723680*m^3 + 269325*m^4 + 63273*m^5 + 9450*m^6 + 870*m^7 + 45*m^8 + m^9 + 362880)) + (c^4*x^9*(d + e*x)^m*(109584*m + 118124*m^2 + 67284*m^3 + 22449*m^4 + 4536*m^5 + 546*m^6 + 36*m^7 + m^8 + 40320))/(1026576*m + 1172700*m^2 + 723680*m^3 + 269325*m^4 + 63273*m^5 + 9450*m^6 + 870*m^7 + 45*m^8 + m^9 + 362880) + (2*x^2*(m + 1)*(d + e*x)^m*(362880*a^3*b*e^7 + 10080*c^4*d^7*m + 267876*a^3*b*e^7*m^2 + 80738*a^3*b*e^7*m^3 + 14280*a^3*b*e^7*m^4 + 1484*a^3*b*e^7*m^5 + 84*a^3*b*e^7*m^6 + 2*a^3*b*e^7*m^7 + 18144*b^4*d^3*e^4*m + 9900*b^4*d^3*e^4*m^2 + 2010*b^4*d^3*e^4*m^3 + 180*b^4*d^3*e^4*m^4 + 6*b^4*d^3*e^4*m^5 + 482256*a^3*b*e^7*m + 120960*a^3*c*d*e^6*m - 45360*b*c^3*d^6*e*m + 59400*a^2*c^2*d^3*e^4*m^2 + 12060*a^2*c^2*d^3*e^4*m^3 + 1080*a^2*c^2*d^3*e^4*m^4 + 36*a^2*c^2*d^3*e^4*m^5 + 18360*b^2*c^2*d^5*e^2*m^2 + 1080*b^2*c^2*d^5*e^2*m^3 - 90720*a*b^3*d^2*e^5*m + 181440*a^2*b^2*d*e^6*m + 51840*a*c^3*d^5*e^2*m + 120432*a^3*c*d*e^6*m^2 + 49148*a^3*c*d*e^6*m^3 + 10530*a^3*c*d*e^6*m^4 + 1250*a^3*c*d*e^6*m^5 + 78*a^3*c*d*e^6*m^6 + 2*a^3*c*d*e^6*m^7 - 60480*b^3*c*d^4*e^3*m - 5040*b*c^3*d^6*e*m^2 - 67644*a*b^3*d^2*e^5*m^2 + 180648*a^2*b^2*d*e^6*m^2 - 19950*a*b^3*d^2*e^5*m^3 + 73722*a^2*b^2*d*e^6*m^3 - 2910*a*b^3*d^2*e^5*m^4 + 15795*a^2*b^2*d*e^6*m^4 - 210*a*b^3*d^2*e^5*m^5 + 1875*a^2*b^2*d*e^6*m^5 - 6*a*b^3*d^2*e^5*m^6 + 117*a^2*b^2*d*e^6*m^6 + 3*a^2*b^2*d*e^6*m^7 + 108864*a^2*c^2*d^3*e^4*m + 12240*a*c^3*d^5*e^2*m^2 + 720*a*c^3*d^5*e^2*m^3 + 77760*b^2*c^2*d^5*e^2*m - 22920*b^3*c*d^4*e^3*m^2 - 2880*b^3*c*d^4*e^3*m^3 - 120*b^3*c*d^4*e^3*m^4 - 68760*a*b*c^2*d^4*e^3*m^2 + 118800*a*b^2*c*d^3*e^4*m^2 - 202932*a^2*b*c*d^2*e^5*m^2 - 8640*a*b*c^2*d^4*e^3*m^3 + 24120*a*b^2*c*d^3*e^4*m^3 - 59850*a^2*b*c*d^2*e^5*m^3 - 360*a*b*c^2*d^4*e^3*m^4 + 2160*a*b^2*c*d^3*e^4*m^4 - 8730*a^2*b*c*d^2*e^5*m^4 + 72*a*b^2*c*d^3*e^4*m^5 - 630*a^2*b*c*d^2*e^5*m^5 - 18*a^2*b*c*d^2*e^5*m^6 - 181440*a*b*c^2*d^4*e^3*m + 217728*a*b^2*c*d^3*e^4*m - 272160*a^2*b*c*d^2*e^5*m))/(e^7*(1026576*m + 1172700*m^2 + 723680*m^3 + 269325*m^4 + 63273*m^5 + 9450*m^6 + 870*m^7 + 45*m^8 + m^9 + 362880)) + (x^4*(d + e*x)^m*(11*m + 6*m^2 + m^3 + 6)*(60480*a*b^3*e^5 + 1680*c^4*d^5*m + 13300*a*b^3*e^5*m^2 + 1940*a*b^3*e^5*m^3 + 140*a*b^3*e^5*m^4 + 4*a*b^3*e^5*m^5 + 1650*b^4*d*e^4*m^2 + 335*b^4*d*e^4*m^3 + 30*b^4*d*e^4*m^4 + b^4*d*e^4*m^5 + 181440*a^2*b*c*e^5 + 45096*a*b^3*e^5*m + 3024*b^4*d*e^4*m + 135288*a^2*b*c*e^5*m - 7560*b*c^3*d^4*e*m + 3060*b^2*c^2*d^3*e^2*m^2 + 180*b^2*c^2*d^3*e^2*m^3 + 39900*a^2*b*c*e^5*m^2 + 5820*a^2*b*c*e^5*m^3 + 420*a^2*b*c*e^5*m^4 + 12*a^2*b*c*e^5*m^5 + 8640*a*c^3*d^3*e^2*m + 18144*a^2*c^2*d*e^4*m - 10080*b^3*c*d^2*e^3*m - 840*b*c^3*d^4*e*m^2 + 2040*a*c^3*d^3*e^2*m^2 + 9900*a^2*c^2*d*e^4*m^2 + 120*a*c^3*d^3*e^2*m^3 + 2010*a^2*c^2*d*e^4*m^3 + 180*a^2*c^2*d*e^4*m^4 + 6*a^2*c^2*d*e^4*m^5 + 12960*b^2*c^2*d^3*e^2*m - 3820*b^3*c*d^2*e^3*m^2 - 480*b^3*c*d^2*e^3*m^3 - 20*b^3*c*d^2*e^3*m^4 - 11460*a*b*c^2*d^2*e^3*m^2 - 1440*a*b*c^2*d^2*e^3*m^3 - 60*a*b*c^2*d^2*e^3*m^4 + 36288*a*b^2*c*d*e^4*m - 30240*a*b*c^2*d^2*e^3*m + 19800*a*b^2*c*d*e^4*m^2 + 4020*a*b^2*c*d*e^4*m^3 + 360*a*b^2*c*d*e^4*m^4 + 12*a*b^2*c*d*e^4*m^5))/(e^5*(1026576*m + 1172700*m^2 + 723680*m^3 + 269325*m^4 + 63273*m^5 + 9450*m^6 + 870*m^7 + 45*m^8 + m^9 + 362880)) + (2*x^3*(d + e*x)^m*(3*m + m^2 + 2)*(120960*a^3*c*e^6 - 3360*c^4*d^6*m + 181440*a^2*b^2*e^6 + 180648*a^2*b^2*e^6*m + 49148*a^3*c*e^6*m^2 + 10530*a^3*c*e^6*m^3 + 1250*a^3*c*e^6*m^4 + 78*a^3*c*e^6*m^5 + 2*a^3*c*e^6*m^6 - 6048*b^4*d^2*e^4*m + 73722*a^2*b^2*e^6*m^2 + 15795*a^2*b^2*e^6*m^3 + 1875*a^2*b^2*e^6*m^4 + 117*a^2*b^2*e^6*m^5 + 3*a^2*b^2*e^6*m^6 - 3300*b^4*d^2*e^4*m^2 - 670*b^4*d^2*e^4*m^3 - 60*b^4*d^2*e^4*m^4 - 2*b^4*d^2*e^4*m^5 + 120432*a^3*c*e^6*m + 30240*a*b^3*d*e^5*m + 15120*b*c^3*d^5*e*m - 19800*a^2*c^2*d^2*e^4*m^2 - 4020*a^2*c^2*d^2*e^4*m^3 - 360*a^2*c^2*d^2*e^4*m^4 - 12*a^2*c^2*d^2*e^4*m^5 - 6120*b^2*c^2*d^4*e^2*m^2 - 360*b^2*c^2*d^4*e^2*m^3 + 22548*a*b^3*d*e^5*m^2 + 6650*a*b^3*d*e^5*m^3 + 970*a*b^3*d*e^5*m^4 + 70*a*b^3*d*e^5*m^5 + 2*a*b^3*d*e^5*m^6 - 17280*a*c^3*d^4*e^2*m + 20160*b^3*c*d^3*e^3*m + 1680*b*c^3*d^5*e*m^2 - 36288*a^2*c^2*d^2*e^4*m - 4080*a*c^3*d^4*e^2*m^2 - 240*a*c^3*d^4*e^2*m^3 - 25920*b^2*c^2*d^4*e^2*m + 7640*b^3*c*d^3*e^3*m^2 + 960*b^3*c*d^3*e^3*m^3 + 40*b^3*c*d^3*e^3*m^4 + 22920*a*b*c^2*d^3*e^3*m^2 - 39600*a*b^2*c*d^2*e^4*m^2 + 2880*a*b*c^2*d^3*e^3*m^3 - 8040*a*b^2*c*d^2*e^4*m^3 + 120*a*b*c^2*d^3*e^3*m^4 - 720*a*b^2*c*d^2*e^4*m^4 - 24*a*b^2*c*d^2*e^4*m^5 + 90720*a^2*b*c*d*e^5*m + 60480*a*b*c^2*d^3*e^3*m - 72576*a*b^2*c*d^2*e^4*m + 67644*a^2*b*c*d*e^5*m^2 + 19950*a^2*b*c*d*e^5*m^3 + 2910*a^2*b*c*d*e^5*m^4 + 210*a^2*b*c*d*e^5*m^5 + 6*a^2*b*c*d*e^5*m^6))/(e^6*(1026576*m + 1172700*m^2 + 723680*m^3 + 269325*m^4 + 63273*m^5 + 9450*m^6 + 870*m^7 + 45*m^8 + m^9 + 362880)) + (x^5*(d + e*x)^m*(50*m + 35*m^2 + 10*m^3 + m^4 + 24)*(3024*b^4*e^4 + 1650*b^4*e^4*m - 336*c^4*d^4*m + 18144*a^2*c^2*e^4 + 335*b^4*e^4*m^2 + 30*b^4*e^4*m^3 + b^4*e^4*m^4 + 9900*a^2*c^2*e^4*m + 2010*a^2*c^2*e^4*m^2 + 180*a^2*c^2*e^4*m^3 + 6*a^2*c^2*e^4*m^4 + 36288*a*b^2*c*e^4 + 19800*a*b^2*c*e^4*m + 1512*b*c^3*d^3*e*m + 2016*b^3*c*d*e^3*m - 612*b^2*c^2*d^2*e^2*m^2 - 36*b^2*c^2*d^2*e^2*m^3 + 4020*a*b^2*c*e^4*m^2 + 360*a*b^2*c*e^4*m^3 + 12*a*b^2*c*e^4*m^4 - 1728*a*c^3*d^2*e^2*m + 168*b*c^3*d^3*e*m^2 + 764*b^3*c*d*e^3*m^2 + 96*b^3*c*d*e^3*m^3 + 4*b^3*c*d*e^3*m^4 - 408*a*c^3*d^2*e^2*m^2 - 24*a*c^3*d^2*e^2*m^3 - 2592*b^2*c^2*d^2*e^2*m + 6048*a*b*c^2*d*e^3*m + 2292*a*b*c^2*d*e^3*m^2 + 288*a*b*c^2*d*e^3*m^3 + 12*a*b*c^2*d*e^3*m^4))/(e^4*(1026576*m + 1172700*m^2 + 723680*m^3 + 269325*m^4 + 63273*m^5 + 9450*m^6 + 870*m^7 + 45*m^8 + m^9 + 362880)) + (2*c*x^6*(d + e*x)^m*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)*(1008*b^3*e^3 + 382*b^3*e^3*m + 28*c^3*d^3*m + 48*b^3*e^3*m^2 + 2*b^3*e^3*m^3 + 3024*a*b*c*e^3 + 144*a*b*c*e^3*m^2 + 6*a*b*c*e^3*m^3 + 144*a*c^2*d*e^2*m - 126*b*c^2*d^2*e*m + 216*b^2*c*d*e^2*m + 34*a*c^2*d*e^2*m^2 + 2*a*c^2*d*e^2*m^3 - 14*b*c^2*d^2*e*m^2 + 51*b^2*c*d*e^2*m^2 + 3*b^2*c*d*e^2*m^3 + 1146*a*b*c*e^3*m))/(e^3*(1026576*m + 1172700*m^2 + 723680*m^3 + 269325*m^4 + 63273*m^5 + 9450*m^6 + 870*m^7 + 45*m^8 + m^9 + 362880)) + (2*c^2*x^7*(d + e*x)^m*(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720)*(216*b^2*e^2 + 51*b^2*e^2*m - 4*c^2*d^2*m + 3*b^2*e^2*m^2 + 144*a*c*e^2 + 34*a*c*e^2*m + 2*a*c*e^2*m^2 + 18*b*c*d*e*m + 2*b*c*d*e*m^2))/(e^2*(1026576*m + 1172700*m^2 + 723680*m^3 + 269325*m^4 + 63273*m^5 + 9450*m^6 + 870*m^7 + 45*m^8 + m^9 + 362880)) + (c^3*x^8*(d + e*x)^m*(36*b*e + 4*b*e*m + c*d*m)*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040))/(e*(1026576*m + 1172700*m^2 + 723680*m^3 + 269325*m^4 + 63273*m^5 + 9450*m^6 + 870*m^7 + 45*m^8 + m^9 + 362880))","B"
2550,1,2542,305,2.392302,"\text{Not used}","int((d + e*x)^m*(a + b*x + c*x^2)^3,x)","\frac{{\left(d+e\,x\right)}^m\,\left(a^3\,d\,e^6\,m^6+27\,a^3\,d\,e^6\,m^5+295\,a^3\,d\,e^6\,m^4+1665\,a^3\,d\,e^6\,m^3+5104\,a^3\,d\,e^6\,m^2+8028\,a^3\,d\,e^6\,m+5040\,a^3\,d\,e^6-3\,a^2\,b\,d^2\,e^5\,m^5-75\,a^2\,b\,d^2\,e^5\,m^4-735\,a^2\,b\,d^2\,e^5\,m^3-3525\,a^2\,b\,d^2\,e^5\,m^2-8262\,a^2\,b\,d^2\,e^5\,m-7560\,a^2\,b\,d^2\,e^5+6\,a^2\,c\,d^3\,e^4\,m^4+132\,a^2\,c\,d^3\,e^4\,m^3+1074\,a^2\,c\,d^3\,e^4\,m^2+3828\,a^2\,c\,d^3\,e^4\,m+5040\,a^2\,c\,d^3\,e^4+6\,a\,b^2\,d^3\,e^4\,m^4+132\,a\,b^2\,d^3\,e^4\,m^3+1074\,a\,b^2\,d^3\,e^4\,m^2+3828\,a\,b^2\,d^3\,e^4\,m+5040\,a\,b^2\,d^3\,e^4-36\,a\,b\,c\,d^4\,e^3\,m^3-648\,a\,b\,c\,d^4\,e^3\,m^2-3852\,a\,b\,c\,d^4\,e^3\,m-7560\,a\,b\,c\,d^4\,e^3+72\,a\,c^2\,d^5\,e^2\,m^2+936\,a\,c^2\,d^5\,e^2\,m+3024\,a\,c^2\,d^5\,e^2-6\,b^3\,d^4\,e^3\,m^3-108\,b^3\,d^4\,e^3\,m^2-642\,b^3\,d^4\,e^3\,m-1260\,b^3\,d^4\,e^3+72\,b^2\,c\,d^5\,e^2\,m^2+936\,b^2\,c\,d^5\,e^2\,m+3024\,b^2\,c\,d^5\,e^2-360\,b\,c^2\,d^6\,e\,m-2520\,b\,c^2\,d^6\,e+720\,c^3\,d^7\right)}{e^7\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{x\,{\left(d+e\,x\right)}^m\,\left(a^3\,e^7\,m^6+27\,a^3\,e^7\,m^5+295\,a^3\,e^7\,m^4+1665\,a^3\,e^7\,m^3+5104\,a^3\,e^7\,m^2+8028\,a^3\,e^7\,m+5040\,a^3\,e^7+3\,a^2\,b\,d\,e^6\,m^6+75\,a^2\,b\,d\,e^6\,m^5+735\,a^2\,b\,d\,e^6\,m^4+3525\,a^2\,b\,d\,e^6\,m^3+8262\,a^2\,b\,d\,e^6\,m^2+7560\,a^2\,b\,d\,e^6\,m-6\,a^2\,c\,d^2\,e^5\,m^5-132\,a^2\,c\,d^2\,e^5\,m^4-1074\,a^2\,c\,d^2\,e^5\,m^3-3828\,a^2\,c\,d^2\,e^5\,m^2-5040\,a^2\,c\,d^2\,e^5\,m-6\,a\,b^2\,d^2\,e^5\,m^5-132\,a\,b^2\,d^2\,e^5\,m^4-1074\,a\,b^2\,d^2\,e^5\,m^3-3828\,a\,b^2\,d^2\,e^5\,m^2-5040\,a\,b^2\,d^2\,e^5\,m+36\,a\,b\,c\,d^3\,e^4\,m^4+648\,a\,b\,c\,d^3\,e^4\,m^3+3852\,a\,b\,c\,d^3\,e^4\,m^2+7560\,a\,b\,c\,d^3\,e^4\,m-72\,a\,c^2\,d^4\,e^3\,m^3-936\,a\,c^2\,d^4\,e^3\,m^2-3024\,a\,c^2\,d^4\,e^3\,m+6\,b^3\,d^3\,e^4\,m^4+108\,b^3\,d^3\,e^4\,m^3+642\,b^3\,d^3\,e^4\,m^2+1260\,b^3\,d^3\,e^4\,m-72\,b^2\,c\,d^4\,e^3\,m^3-936\,b^2\,c\,d^4\,e^3\,m^2-3024\,b^2\,c\,d^4\,e^3\,m+360\,b\,c^2\,d^5\,e^2\,m^2+2520\,b\,c^2\,d^5\,e^2\,m-720\,c^3\,d^6\,e\,m\right)}{e^7\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{c^3\,x^7\,{\left(d+e\,x\right)}^m\,\left(m^6+21\,m^5+175\,m^4+735\,m^3+1624\,m^2+1764\,m+720\right)}{m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040}+\frac{3\,x^2\,\left(m+1\right)\,{\left(d+e\,x\right)}^m\,\left(a^2\,b\,e^5\,m^5+25\,a^2\,b\,e^5\,m^4+245\,a^2\,b\,e^5\,m^3+1175\,a^2\,b\,e^5\,m^2+2754\,a^2\,b\,e^5\,m+2520\,a^2\,b\,e^5+a^2\,c\,d\,e^4\,m^5+22\,a^2\,c\,d\,e^4\,m^4+179\,a^2\,c\,d\,e^4\,m^3+638\,a^2\,c\,d\,e^4\,m^2+840\,a^2\,c\,d\,e^4\,m+a\,b^2\,d\,e^4\,m^5+22\,a\,b^2\,d\,e^4\,m^4+179\,a\,b^2\,d\,e^4\,m^3+638\,a\,b^2\,d\,e^4\,m^2+840\,a\,b^2\,d\,e^4\,m-6\,a\,b\,c\,d^2\,e^3\,m^4-108\,a\,b\,c\,d^2\,e^3\,m^3-642\,a\,b\,c\,d^2\,e^3\,m^2-1260\,a\,b\,c\,d^2\,e^3\,m+12\,a\,c^2\,d^3\,e^2\,m^3+156\,a\,c^2\,d^3\,e^2\,m^2+504\,a\,c^2\,d^3\,e^2\,m-b^3\,d^2\,e^3\,m^4-18\,b^3\,d^2\,e^3\,m^3-107\,b^3\,d^2\,e^3\,m^2-210\,b^3\,d^2\,e^3\,m+12\,b^2\,c\,d^3\,e^2\,m^3+156\,b^2\,c\,d^3\,e^2\,m^2+504\,b^2\,c\,d^3\,e^2\,m-60\,b\,c^2\,d^4\,e\,m^2-420\,b\,c^2\,d^4\,e\,m+120\,c^3\,d^5\,m\right)}{e^5\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{x^4\,{\left(d+e\,x\right)}^m\,\left(m^3+6\,m^2+11\,m+6\right)\,\left(b^3\,e^3\,m^3+18\,b^3\,e^3\,m^2+107\,b^3\,e^3\,m+210\,b^3\,e^3+3\,b^2\,c\,d\,e^2\,m^3+39\,b^2\,c\,d\,e^2\,m^2+126\,b^2\,c\,d\,e^2\,m-15\,b\,c^2\,d^2\,e\,m^2-105\,b\,c^2\,d^2\,e\,m+6\,a\,b\,c\,e^3\,m^3+108\,a\,b\,c\,e^3\,m^2+642\,a\,b\,c\,e^3\,m+1260\,a\,b\,c\,e^3+30\,c^3\,d^3\,m+3\,a\,c^2\,d\,e^2\,m^3+39\,a\,c^2\,d\,e^2\,m^2+126\,a\,c^2\,d\,e^2\,m\right)}{e^3\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{x^3\,{\left(d+e\,x\right)}^m\,\left(m^2+3\,m+2\right)\,\left(3\,a^2\,c\,e^4\,m^4+66\,a^2\,c\,e^4\,m^3+537\,a^2\,c\,e^4\,m^2+1914\,a^2\,c\,e^4\,m+2520\,a^2\,c\,e^4+3\,a\,b^2\,e^4\,m^4+66\,a\,b^2\,e^4\,m^3+537\,a\,b^2\,e^4\,m^2+1914\,a\,b^2\,e^4\,m+2520\,a\,b^2\,e^4+6\,a\,b\,c\,d\,e^3\,m^4+108\,a\,b\,c\,d\,e^3\,m^3+642\,a\,b\,c\,d\,e^3\,m^2+1260\,a\,b\,c\,d\,e^3\,m-12\,a\,c^2\,d^2\,e^2\,m^3-156\,a\,c^2\,d^2\,e^2\,m^2-504\,a\,c^2\,d^2\,e^2\,m+b^3\,d\,e^3\,m^4+18\,b^3\,d\,e^3\,m^3+107\,b^3\,d\,e^3\,m^2+210\,b^3\,d\,e^3\,m-12\,b^2\,c\,d^2\,e^2\,m^3-156\,b^2\,c\,d^2\,e^2\,m^2-504\,b^2\,c\,d^2\,e^2\,m+60\,b\,c^2\,d^3\,e\,m^2+420\,b\,c^2\,d^3\,e\,m-120\,c^3\,d^4\,m\right)}{e^4\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{3\,c\,x^5\,{\left(d+e\,x\right)}^m\,\left(m^4+10\,m^3+35\,m^2+50\,m+24\right)\,\left(b^2\,e^2\,m^2+13\,b^2\,e^2\,m+42\,b^2\,e^2+b\,c\,d\,e\,m^2+7\,b\,c\,d\,e\,m-2\,c^2\,d^2\,m+a\,c\,e^2\,m^2+13\,a\,c\,e^2\,m+42\,a\,c\,e^2\right)}{e^2\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}+\frac{c^2\,x^6\,{\left(d+e\,x\right)}^m\,\left(21\,b\,e+3\,b\,e\,m+c\,d\,m\right)\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}{e\,\left(m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right)}","Not used",1,"((d + e*x)^m*(720*c^3*d^7 + 5040*a^3*d*e^6 - 1260*b^3*d^4*e^3 + 5040*a*b^2*d^3*e^4 - 7560*a^2*b*d^2*e^5 + 3024*a*c^2*d^5*e^2 + 5040*a^2*c*d^3*e^4 + 3024*b^2*c*d^5*e^2 + 5104*a^3*d*e^6*m^2 + 1665*a^3*d*e^6*m^3 + 295*a^3*d*e^6*m^4 + 27*a^3*d*e^6*m^5 + a^3*d*e^6*m^6 - 642*b^3*d^4*e^3*m - 108*b^3*d^4*e^3*m^2 - 6*b^3*d^4*e^3*m^3 - 2520*b*c^2*d^6*e + 8028*a^3*d*e^6*m - 7560*a*b*c*d^4*e^3 - 360*b*c^2*d^6*e*m + 3828*a*b^2*d^3*e^4*m - 8262*a^2*b*d^2*e^5*m + 936*a*c^2*d^5*e^2*m + 3828*a^2*c*d^3*e^4*m + 936*b^2*c*d^5*e^2*m + 1074*a*b^2*d^3*e^4*m^2 - 3525*a^2*b*d^2*e^5*m^2 + 132*a*b^2*d^3*e^4*m^3 - 735*a^2*b*d^2*e^5*m^3 + 6*a*b^2*d^3*e^4*m^4 - 75*a^2*b*d^2*e^5*m^4 - 3*a^2*b*d^2*e^5*m^5 + 72*a*c^2*d^5*e^2*m^2 + 1074*a^2*c*d^3*e^4*m^2 + 132*a^2*c*d^3*e^4*m^3 + 6*a^2*c*d^3*e^4*m^4 + 72*b^2*c*d^5*e^2*m^2 - 3852*a*b*c*d^4*e^3*m - 648*a*b*c*d^4*e^3*m^2 - 36*a*b*c*d^4*e^3*m^3))/(e^7*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (x*(d + e*x)^m*(5040*a^3*e^7 + 8028*a^3*e^7*m + 5104*a^3*e^7*m^2 + 1665*a^3*e^7*m^3 + 295*a^3*e^7*m^4 + 27*a^3*e^7*m^5 + a^3*e^7*m^6 + 1260*b^3*d^3*e^4*m + 642*b^3*d^3*e^4*m^2 + 108*b^3*d^3*e^4*m^3 + 6*b^3*d^3*e^4*m^4 - 720*c^3*d^6*e*m + 7560*a^2*b*d*e^6*m - 5040*a*b^2*d^2*e^5*m + 8262*a^2*b*d*e^6*m^2 + 3525*a^2*b*d*e^6*m^3 + 735*a^2*b*d*e^6*m^4 + 75*a^2*b*d*e^6*m^5 + 3*a^2*b*d*e^6*m^6 - 3024*a*c^2*d^4*e^3*m - 5040*a^2*c*d^2*e^5*m + 2520*b*c^2*d^5*e^2*m - 3024*b^2*c*d^4*e^3*m - 3828*a*b^2*d^2*e^5*m^2 - 1074*a*b^2*d^2*e^5*m^3 - 132*a*b^2*d^2*e^5*m^4 - 6*a*b^2*d^2*e^5*m^5 - 936*a*c^2*d^4*e^3*m^2 - 3828*a^2*c*d^2*e^5*m^2 - 72*a*c^2*d^4*e^3*m^3 - 1074*a^2*c*d^2*e^5*m^3 - 132*a^2*c*d^2*e^5*m^4 - 6*a^2*c*d^2*e^5*m^5 + 360*b*c^2*d^5*e^2*m^2 - 936*b^2*c*d^4*e^3*m^2 - 72*b^2*c*d^4*e^3*m^3 + 7560*a*b*c*d^3*e^4*m + 3852*a*b*c*d^3*e^4*m^2 + 648*a*b*c*d^3*e^4*m^3 + 36*a*b*c*d^3*e^4*m^4))/(e^7*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (c^3*x^7*(d + e*x)^m*(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720))/(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040) + (3*x^2*(m + 1)*(d + e*x)^m*(2520*a^2*b*e^5 + 120*c^3*d^5*m + 1175*a^2*b*e^5*m^2 + 245*a^2*b*e^5*m^3 + 25*a^2*b*e^5*m^4 + a^2*b*e^5*m^5 - 210*b^3*d^2*e^3*m - 107*b^3*d^2*e^3*m^2 - 18*b^3*d^2*e^3*m^3 - b^3*d^2*e^3*m^4 + 2754*a^2*b*e^5*m + 840*a*b^2*d*e^4*m + 840*a^2*c*d*e^4*m - 420*b*c^2*d^4*e*m + 638*a*b^2*d*e^4*m^2 + 179*a*b^2*d*e^4*m^3 + 22*a*b^2*d*e^4*m^4 + a*b^2*d*e^4*m^5 + 504*a*c^2*d^3*e^2*m + 638*a^2*c*d*e^4*m^2 + 179*a^2*c*d*e^4*m^3 + 22*a^2*c*d*e^4*m^4 + a^2*c*d*e^4*m^5 + 504*b^2*c*d^3*e^2*m - 60*b*c^2*d^4*e*m^2 + 156*a*c^2*d^3*e^2*m^2 + 12*a*c^2*d^3*e^2*m^3 + 156*b^2*c*d^3*e^2*m^2 + 12*b^2*c*d^3*e^2*m^3 - 1260*a*b*c*d^2*e^3*m - 642*a*b*c*d^2*e^3*m^2 - 108*a*b*c*d^2*e^3*m^3 - 6*a*b*c*d^2*e^3*m^4))/(e^5*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (x^4*(d + e*x)^m*(11*m + 6*m^2 + m^3 + 6)*(210*b^3*e^3 + 107*b^3*e^3*m + 30*c^3*d^3*m + 18*b^3*e^3*m^2 + b^3*e^3*m^3 + 1260*a*b*c*e^3 + 108*a*b*c*e^3*m^2 + 6*a*b*c*e^3*m^3 + 126*a*c^2*d*e^2*m - 105*b*c^2*d^2*e*m + 126*b^2*c*d*e^2*m + 39*a*c^2*d*e^2*m^2 + 3*a*c^2*d*e^2*m^3 - 15*b*c^2*d^2*e*m^2 + 39*b^2*c*d*e^2*m^2 + 3*b^2*c*d*e^2*m^3 + 642*a*b*c*e^3*m))/(e^3*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (x^3*(d + e*x)^m*(3*m + m^2 + 2)*(2520*a*b^2*e^4 + 2520*a^2*c*e^4 - 120*c^3*d^4*m + 537*a*b^2*e^4*m^2 + 66*a*b^2*e^4*m^3 + 3*a*b^2*e^4*m^4 + 537*a^2*c*e^4*m^2 + 66*a^2*c*e^4*m^3 + 3*a^2*c*e^4*m^4 + 107*b^3*d*e^3*m^2 + 18*b^3*d*e^3*m^3 + b^3*d*e^3*m^4 + 1914*a*b^2*e^4*m + 1914*a^2*c*e^4*m + 210*b^3*d*e^3*m + 420*b*c^2*d^3*e*m - 504*a*c^2*d^2*e^2*m - 504*b^2*c*d^2*e^2*m + 60*b*c^2*d^3*e*m^2 - 156*a*c^2*d^2*e^2*m^2 - 12*a*c^2*d^2*e^2*m^3 - 156*b^2*c*d^2*e^2*m^2 - 12*b^2*c*d^2*e^2*m^3 + 1260*a*b*c*d*e^3*m + 642*a*b*c*d*e^3*m^2 + 108*a*b*c*d*e^3*m^3 + 6*a*b*c*d*e^3*m^4))/(e^4*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (3*c*x^5*(d + e*x)^m*(50*m + 35*m^2 + 10*m^3 + m^4 + 24)*(42*b^2*e^2 + 13*b^2*e^2*m - 2*c^2*d^2*m + b^2*e^2*m^2 + 42*a*c*e^2 + 13*a*c*e^2*m + a*c*e^2*m^2 + 7*b*c*d*e*m + b*c*d*e*m^2))/(e^2*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (c^2*x^6*(d + e*x)^m*(21*b*e + 3*b*e*m + c*d*m)*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120))/(e*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040))","B"
2551,1,895,178,1.554531,"\text{Not used}","int((d + e*x)^m*(a + b*x + c*x^2)^2,x)","\frac{{\left(d+e\,x\right)}^m\,\left(a^2\,d\,e^4\,m^4+14\,a^2\,d\,e^4\,m^3+71\,a^2\,d\,e^4\,m^2+154\,a^2\,d\,e^4\,m+120\,a^2\,d\,e^4-2\,a\,b\,d^2\,e^3\,m^3-24\,a\,b\,d^2\,e^3\,m^2-94\,a\,b\,d^2\,e^3\,m-120\,a\,b\,d^2\,e^3+4\,a\,c\,d^3\,e^2\,m^2+36\,a\,c\,d^3\,e^2\,m+80\,a\,c\,d^3\,e^2+2\,b^2\,d^3\,e^2\,m^2+18\,b^2\,d^3\,e^2\,m+40\,b^2\,d^3\,e^2-12\,b\,c\,d^4\,e\,m-60\,b\,c\,d^4\,e+24\,c^2\,d^5\right)}{e^5\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}+\frac{x\,{\left(d+e\,x\right)}^m\,\left(a^2\,e^5\,m^4+14\,a^2\,e^5\,m^3+71\,a^2\,e^5\,m^2+154\,a^2\,e^5\,m+120\,a^2\,e^5+2\,a\,b\,d\,e^4\,m^4+24\,a\,b\,d\,e^4\,m^3+94\,a\,b\,d\,e^4\,m^2+120\,a\,b\,d\,e^4\,m-4\,a\,c\,d^2\,e^3\,m^3-36\,a\,c\,d^2\,e^3\,m^2-80\,a\,c\,d^2\,e^3\,m-2\,b^2\,d^2\,e^3\,m^3-18\,b^2\,d^2\,e^3\,m^2-40\,b^2\,d^2\,e^3\,m+12\,b\,c\,d^3\,e^2\,m^2+60\,b\,c\,d^3\,e^2\,m-24\,c^2\,d^4\,e\,m\right)}{e^5\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}+\frac{c^2\,x^5\,{\left(d+e\,x\right)}^m\,\left(m^4+10\,m^3+35\,m^2+50\,m+24\right)}{m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120}+\frac{x^3\,{\left(d+e\,x\right)}^m\,\left(m^2+3\,m+2\right)\,\left(b^2\,e^2\,m^2+9\,b^2\,e^2\,m+20\,b^2\,e^2+2\,b\,c\,d\,e\,m^2+10\,b\,c\,d\,e\,m-4\,c^2\,d^2\,m+2\,a\,c\,e^2\,m^2+18\,a\,c\,e^2\,m+40\,a\,c\,e^2\right)}{e^2\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}+\frac{x^2\,\left(m+1\right)\,{\left(d+e\,x\right)}^m\,\left(b^2\,d\,e^2\,m^3+9\,b^2\,d\,e^2\,m^2+20\,b^2\,d\,e^2\,m-6\,b\,c\,d^2\,e\,m^2-30\,b\,c\,d^2\,e\,m+2\,a\,b\,e^3\,m^3+24\,a\,b\,e^3\,m^2+94\,a\,b\,e^3\,m+120\,a\,b\,e^3+12\,c^2\,d^3\,m+2\,a\,c\,d\,e^2\,m^3+18\,a\,c\,d\,e^2\,m^2+40\,a\,c\,d\,e^2\,m\right)}{e^3\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}+\frac{c\,x^4\,{\left(d+e\,x\right)}^m\,\left(10\,b\,e+2\,b\,e\,m+c\,d\,m\right)\,\left(m^3+6\,m^2+11\,m+6\right)}{e\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}","Not used",1,"((d + e*x)^m*(24*c^2*d^5 + 120*a^2*d*e^4 + 40*b^2*d^3*e^2 + 71*a^2*d*e^4*m^2 + 14*a^2*d*e^4*m^3 + a^2*d*e^4*m^4 + 18*b^2*d^3*e^2*m - 60*b*c*d^4*e + 2*b^2*d^3*e^2*m^2 - 120*a*b*d^2*e^3 + 80*a*c*d^3*e^2 + 154*a^2*d*e^4*m - 94*a*b*d^2*e^3*m + 36*a*c*d^3*e^2*m - 24*a*b*d^2*e^3*m^2 - 2*a*b*d^2*e^3*m^3 + 4*a*c*d^3*e^2*m^2 - 12*b*c*d^4*e*m))/(e^5*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)) + (x*(d + e*x)^m*(120*a^2*e^5 + 154*a^2*e^5*m + 71*a^2*e^5*m^2 + 14*a^2*e^5*m^3 + a^2*e^5*m^4 - 40*b^2*d^2*e^3*m - 18*b^2*d^2*e^3*m^2 - 2*b^2*d^2*e^3*m^3 - 24*c^2*d^4*e*m + 94*a*b*d*e^4*m^2 + 24*a*b*d*e^4*m^3 + 2*a*b*d*e^4*m^4 - 80*a*c*d^2*e^3*m + 60*b*c*d^3*e^2*m - 36*a*c*d^2*e^3*m^2 - 4*a*c*d^2*e^3*m^3 + 12*b*c*d^3*e^2*m^2 + 120*a*b*d*e^4*m))/(e^5*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)) + (c^2*x^5*(d + e*x)^m*(50*m + 35*m^2 + 10*m^3 + m^4 + 24))/(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120) + (x^3*(d + e*x)^m*(3*m + m^2 + 2)*(20*b^2*e^2 + 9*b^2*e^2*m - 4*c^2*d^2*m + b^2*e^2*m^2 + 40*a*c*e^2 + 18*a*c*e^2*m + 2*a*c*e^2*m^2 + 10*b*c*d*e*m + 2*b*c*d*e*m^2))/(e^2*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)) + (x^2*(m + 1)*(d + e*x)^m*(12*c^2*d^3*m + 120*a*b*e^3 + 9*b^2*d*e^2*m^2 + b^2*d*e^2*m^3 + 94*a*b*e^3*m + 24*a*b*e^3*m^2 + 2*a*b*e^3*m^3 + 20*b^2*d*e^2*m + 18*a*c*d*e^2*m^2 + 2*a*c*d*e^2*m^3 - 6*b*c*d^2*e*m^2 + 40*a*c*d*e^2*m - 30*b*c*d^2*e*m))/(e^3*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120)) + (c*x^4*(d + e*x)^m*(10*b*e + 2*b*e*m + c*d*m)*(11*m + 6*m^2 + m^3 + 6))/(e*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120))","B"
2552,1,201,82,1.182631,"\text{Not used}","int((d + e*x)^m*(a + b*x + c*x^2),x)","{\left(d+e\,x\right)}^m\,\left(\frac{c\,x^3\,\left(m^2+3\,m+2\right)}{m^3+6\,m^2+11\,m+6}+\frac{d\,\left(2\,c\,d^2-b\,d\,e\,m-3\,b\,d\,e+a\,e^2\,m^2+5\,a\,e^2\,m+6\,a\,e^2\right)}{e^3\,\left(m^3+6\,m^2+11\,m+6\right)}+\frac{x\,\left(-2\,c\,d^2\,e\,m+b\,d\,e^2\,m^2+3\,b\,d\,e^2\,m+a\,e^3\,m^2+5\,a\,e^3\,m+6\,a\,e^3\right)}{e^3\,\left(m^3+6\,m^2+11\,m+6\right)}+\frac{x^2\,\left(m+1\right)\,\left(3\,b\,e+b\,e\,m+c\,d\,m\right)}{e\,\left(m^3+6\,m^2+11\,m+6\right)}\right)","Not used",1,"(d + e*x)^m*((c*x^3*(3*m + m^2 + 2))/(11*m + 6*m^2 + m^3 + 6) + (d*(6*a*e^2 + 2*c*d^2 + a*e^2*m^2 - 3*b*d*e + 5*a*e^2*m - b*d*e*m))/(e^3*(11*m + 6*m^2 + m^3 + 6)) + (x*(6*a*e^3 + a*e^3*m^2 + 5*a*e^3*m + 3*b*d*e^2*m - 2*c*d^2*e*m + b*d*e^2*m^2))/(e^3*(11*m + 6*m^2 + m^3 + 6)) + (x^2*(m + 1)*(3*b*e + b*e*m + c*d*m))/(e*(11*m + 6*m^2 + m^3 + 6)))","B"
2553,0,-1,191,0.000000,"\text{Not used}","int((d + e*x)^m/(a + b*x + c*x^2),x)","\int \frac{{\left(d+e\,x\right)}^m}{c\,x^2+b\,x+a} \,d x","Not used",1,"int((d + e*x)^m/(a + b*x + c*x^2), x)","F"
2554,0,-1,425,0.000000,"\text{Not used}","int((d + e*x)^m/(a + b*x + c*x^2)^2,x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(c\,x^2+b\,x+a\right)}^2} \,d x","Not used",1,"int((d + e*x)^m/(a + b*x + c*x^2)^2, x)","F"
2555,0,-1,189,0.000000,"\text{Not used}","int((d + e*x)^m*(a + b*x + c*x^2)^(5/2),x)","\int {\left(d+e\,x\right)}^m\,{\left(c\,x^2+b\,x+a\right)}^{5/2} \,d x","Not used",1,"int((d + e*x)^m*(a + b*x + c*x^2)^(5/2), x)","F"
2556,0,-1,189,0.000000,"\text{Not used}","int((d + e*x)^m*(a + b*x + c*x^2)^(3/2),x)","\int {\left(d+e\,x\right)}^m\,{\left(c\,x^2+b\,x+a\right)}^{3/2} \,d x","Not used",1,"int((d + e*x)^m*(a + b*x + c*x^2)^(3/2), x)","F"
2557,0,-1,189,0.000000,"\text{Not used}","int((d + e*x)^m*(a + b*x + c*x^2)^(1/2),x)","\int {\left(d+e\,x\right)}^m\,\sqrt{c\,x^2+b\,x+a} \,d x","Not used",1,"int((d + e*x)^m*(a + b*x + c*x^2)^(1/2), x)","F"
2558,0,-1,189,0.000000,"\text{Not used}","int((d + e*x)^m/(a + b*x + c*x^2)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^m}{\sqrt{c\,x^2+b\,x+a}} \,d x","Not used",1,"int((d + e*x)^m/(a + b*x + c*x^2)^(1/2), x)","F"
2559,0,-1,189,0.000000,"\text{Not used}","int((d + e*x)^m/(a + b*x + c*x^2)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(c\,x^2+b\,x+a\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^m/(a + b*x + c*x^2)^(3/2), x)","F"
2560,0,-1,189,0.000000,"\text{Not used}","int((d + e*x)^m/(a + b*x + c*x^2)^(5/2),x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(c\,x^2+b\,x+a\right)}^{5/2}} \,d x","Not used",1,"int((d + e*x)^m/(a + b*x + c*x^2)^(5/2), x)","F"
2561,0,-1,137,0.000000,"\text{Not used}","int((d*x)^m*(a + b*x + c*x^2)^p,x)","\int {\left(d\,x\right)}^m\,{\left(c\,x^2+b\,x+a\right)}^p \,d x","Not used",1,"int((d*x)^m*(a + b*x + c*x^2)^p, x)","F"
2562,0,-1,187,0.000000,"\text{Not used}","int((d + e*x)^m*(a + b*x + c*x^2)^p,x)","\int {\left(d+e\,x\right)}^m\,{\left(c\,x^2+b\,x+a\right)}^p \,d x","Not used",1,"int((d + e*x)^m*(a + b*x + c*x^2)^p, x)","F"
2563,0,-1,327,0.000000,"\text{Not used}","int((d + e*x)^3*(a + b*x + c*x^2)^p,x)","\int {\left(d+e\,x\right)}^3\,{\left(c\,x^2+b\,x+a\right)}^p \,d x","Not used",1,"int((d + e*x)^3*(a + b*x + c*x^2)^p, x)","F"
2564,0,-1,248,0.000000,"\text{Not used}","int((d + e*x)^2*(a + b*x + c*x^2)^p,x)","\int {\left(d+e\,x\right)}^2\,{\left(c\,x^2+b\,x+a\right)}^p \,d x","Not used",1,"int((d + e*x)^2*(a + b*x + c*x^2)^p, x)","F"
2565,0,-1,160,0.000000,"\text{Not used}","int((d + e*x)*(a + b*x + c*x^2)^p,x)","\int \left(d+e\,x\right)\,{\left(c\,x^2+b\,x+a\right)}^p \,d x","Not used",1,"int((d + e*x)*(a + b*x + c*x^2)^p, x)","F"
2566,0,-1,122,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p,x)","\int {\left(c\,x^2+b\,x+a\right)}^p \,d x","Not used",1,"int((a + b*x + c*x^2)^p, x)","F"
2567,0,-1,184,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(d + e*x),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{d+e\,x} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(d + e*x), x)","F"
2568,0,-1,196,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(d + e*x)^2,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(d + e*x)^2, x)","F"
2569,0,-1,200,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(d + e*x)^3,x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(d + e*x)^3, x)","F"
2570,0,-1,185,0.000000,"\text{Not used}","int((d + e*x)^(3/2)*(a + b*x + c*x^2)^p,x)","\int {\left(d+e\,x\right)}^{3/2}\,{\left(c\,x^2+b\,x+a\right)}^p \,d x","Not used",1,"int((d + e*x)^(3/2)*(a + b*x + c*x^2)^p, x)","F"
2571,0,-1,185,0.000000,"\text{Not used}","int((d + e*x)^(1/2)*(a + b*x + c*x^2)^p,x)","\int \sqrt{d+e\,x}\,{\left(c\,x^2+b\,x+a\right)}^p \,d x","Not used",1,"int((d + e*x)^(1/2)*(a + b*x + c*x^2)^p, x)","F"
2572,0,-1,183,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(d + e*x)^(1/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{\sqrt{d+e\,x}} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(d + e*x)^(1/2), x)","F"
2573,0,-1,183,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(d + e*x)^(3/2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{{\left(d+e\,x\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(d + e*x)^(3/2), x)","F"
2574,0,-1,195,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(d + e*x)^(2*p),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{{\left(d+e\,x\right)}^{2\,p}} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(d + e*x)^(2*p), x)","F"
2575,0,-1,190,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(d + e*x)^(2*p + 1),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{{\left(d+e\,x\right)}^{2\,p+1}} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(d + e*x)^(2*p + 1), x)","F"
2576,0,-1,248,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(d + e*x)^(2*p + 2),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{{\left(d+e\,x\right)}^{2\,p+2}} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(d + e*x)^(2*p + 2), x)","F"
2577,0,-1,332,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(d + e*x)^(2*p + 3),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{{\left(d+e\,x\right)}^{2\,p+3}} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(d + e*x)^(2*p + 3), x)","F"
2578,0,-1,442,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(d + e*x)^(2*p + 4),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{{\left(d+e\,x\right)}^{2\,p+4}} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(d + e*x)^(2*p + 4), x)","F"
2579,0,-1,577,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(d + e*x)^(2*p + 5),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{{\left(d+e\,x\right)}^{2\,p+5}} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(d + e*x)^(2*p + 5), x)","F"
2580,0,-1,809,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^p/(d + e*x)^(2*p + 6),x)","\int \frac{{\left(c\,x^2+b\,x+a\right)}^p}{{\left(d+e\,x\right)}^{2\,p+6}} \,d x","Not used",1,"int((a + b*x + c*x^2)^p/(d + e*x)^(2*p + 6), x)","F"
2581,0,-1,440,0.000000,"\text{Not used}","int((d + e*x)^m/(a + b*x + c*x^2)^(m/2 + 2),x)","\int \frac{{\left(d+e\,x\right)}^m}{{\left(c\,x^2+b\,x+a\right)}^{\frac{m}{2}+2}} \,d x","Not used",1,"int((d + e*x)^m/(a + b*x + c*x^2)^(m/2 + 2), x)","F"
2582,0,-1,102,0.000000,"\text{Not used}","int(1/((x + 1)^(1/3)*(x^2 - x + 1)^(1/3)),x)","\int \frac{1}{{\left(x+1\right)}^{1/3}\,{\left(x^2-x+1\right)}^{1/3}} \,d x","Not used",1,"int(1/((x + 1)^(1/3)*(x^2 - x + 1)^(1/3)), x)","F"
2583,0,-1,45,0.000000,"\text{Not used}","int(1/((x + 1)^(2/3)*(x^2 - x + 1)^(2/3)),x)","\int \frac{1}{{\left(x+1\right)}^{2/3}\,{\left(x^2-x+1\right)}^{2/3}} \,d x","Not used",1,"int(1/((x + 1)^(2/3)*(x^2 - x + 1)^(2/3)), x)","F"
2584,0,-1,41,0.000000,"\text{Not used}","int((x + 1)^p*(x^2 - x + 1)^p,x)","\int {\left(x+1\right)}^p\,{\left(x^2-x+1\right)}^p \,d x","Not used",1,"int((x + 1)^p*(x^2 - x + 1)^p, x)","F"
2585,0,-1,109,0.000000,"\text{Not used}","int(1/((1 - x)^(1/3)*(x + x^2 + 1)^(1/3)),x)","\int \frac{1}{{\left(1-x\right)}^{1/3}\,{\left(x^2+x+1\right)}^{1/3}} \,d x","Not used",1,"int(1/((1 - x)^(1/3)*(x + x^2 + 1)^(1/3)), x)","F"
2586,0,-1,45,0.000000,"\text{Not used}","int(1/((1 - x)^(2/3)*(x + x^2 + 1)^(2/3)),x)","\int \frac{1}{{\left(1-x\right)}^{2/3}\,{\left(x^2+x+1\right)}^{2/3}} \,d x","Not used",1,"int(1/((1 - x)^(2/3)*(x + x^2 + 1)^(2/3)), x)","F"
2587,0,-1,41,0.000000,"\text{Not used}","int((1 - x)^p*(x + x^2 + 1)^p,x)","\int {\left(1-x\right)}^p\,{\left(x^2+x+1\right)}^p \,d x","Not used",1,"int((1 - x)^p*(x + x^2 + 1)^p, x)","F"
2588,0,-1,196,0.000000,"\text{Not used}","int(1/((b*e - c*e*x)^(1/3)*(b^2 + c^2*x^2 + b*c*x)^(1/3)),x)","\int \frac{1}{{\left(b\,e-c\,e\,x\right)}^{1/3}\,{\left(b^2+b\,c\,x+c^2\,x^2\right)}^{1/3}} \,d x","Not used",1,"int(1/((b*e - c*e*x)^(1/3)*(b^2 + c^2*x^2 + b*c*x)^(1/3)), x)","F"
2589,0,-1,71,0.000000,"\text{Not used}","int(1/((b*e - c*e*x)^(2/3)*(b^2 + c^2*x^2 + b*c*x)^(2/3)),x)","\int \frac{1}{{\left(b\,e-c\,e\,x\right)}^{2/3}\,{\left(b^2+b\,c\,x+c^2\,x^2\right)}^{2/3}} \,d x","Not used",1,"int(1/((b*e - c*e*x)^(2/3)*(b^2 + c^2*x^2 + b*c*x)^(2/3)), x)","F"
2590,0,-1,67,0.000000,"\text{Not used}","int((b*e - c*e*x)^p*(b^2 + c^2*x^2 + b*c*x)^p,x)","\int {\left(b\,e-c\,e\,x\right)}^p\,{\left(b^2+b\,c\,x+c^2\,x^2\right)}^p \,d x","Not used",1,"int((b*e - c*e*x)^p*(b^2 + c^2*x^2 + b*c*x)^p, x)","F"