1,1,88,94,4.774793,"\text{Not used}","int((a + b*x^2)*(c + d*x^2)^4,x)","x^3\,\left(\frac{b\,c^4}{3}+\frac{4\,a\,d\,c^3}{3}\right)+x^9\,\left(\frac{a\,d^4}{9}+\frac{4\,b\,c\,d^3}{9}\right)+\frac{b\,d^4\,x^{11}}{11}+a\,c^4\,x+\frac{2\,c^2\,d\,x^5\,\left(3\,a\,d+2\,b\,c\right)}{5}+\frac{2\,c\,d^2\,x^7\,\left(2\,a\,d+3\,b\,c\right)}{7}","Not used",1,"x^3*((b*c^4)/3 + (4*a*c^3*d)/3) + x^9*((a*d^4)/9 + (4*b*c*d^3)/9) + (b*d^4*x^11)/11 + a*c^4*x + (2*c^2*d*x^5*(3*a*d + 2*b*c))/5 + (2*c*d^2*x^7*(2*a*d + 3*b*c))/7","B"
2,1,65,70,4.753199,"\text{Not used}","int((a + b*x^2)*(c + d*x^2)^3,x)","x^3\,\left(\frac{b\,c^3}{3}+a\,d\,c^2\right)+x^7\,\left(\frac{a\,d^3}{7}+\frac{3\,b\,c\,d^2}{7}\right)+\frac{b\,d^3\,x^9}{9}+a\,c^3\,x+\frac{3\,c\,d\,x^5\,\left(a\,d+b\,c\right)}{5}","Not used",1,"x^3*((b*c^3)/3 + a*c^2*d) + x^7*((a*d^3)/7 + (3*b*c*d^2)/7) + (b*d^3*x^9)/9 + a*c^3*x + (3*c*d*x^5*(a*d + b*c))/5","B"
3,1,48,50,0.046989,"\text{Not used}","int((a + b*x^2)*(c + d*x^2)^2,x)","x^3\,\left(\frac{b\,c^2}{3}+\frac{2\,a\,d\,c}{3}\right)+x^5\,\left(\frac{a\,d^2}{5}+\frac{2\,b\,c\,d}{5}\right)+\frac{b\,d^2\,x^7}{7}+a\,c^2\,x","Not used",1,"x^3*((b*c^2)/3 + (2*a*c*d)/3) + x^5*((a*d^2)/5 + (2*b*c*d)/5) + (b*d^2*x^7)/7 + a*c^2*x","B"
4,1,25,28,0.035829,"\text{Not used}","int((a + b*x^2)*(c + d*x^2),x)","\frac{b\,d\,x^5}{5}+\left(\frac{a\,d}{3}+\frac{b\,c}{3}\right)\,x^3+a\,c\,x","Not used",1,"x^3*((a*d)/3 + (b*c)/3) + a*c*x + (b*d*x^5)/5","B"
5,1,31,40,0.059703,"\text{Not used}","int((a + b*x^2)/(c + d*x^2),x)","\frac{b\,x}{d}+\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x}{\sqrt{c}}\right)\,\left(a\,d-b\,c\right)}{\sqrt{c}\,d^{3/2}}","Not used",1,"(b*x)/d + (atan((d^(1/2)*x)/c^(1/2))*(a*d - b*c))/(c^(1/2)*d^(3/2))","B"
6,1,51,63,5.006313,"\text{Not used}","int((a + b*x^2)/(c + d*x^2)^2,x)","\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x}{\sqrt{c}}\right)\,\left(a\,d+b\,c\right)}{2\,c^{3/2}\,d^{3/2}}+\frac{x\,\left(a\,d-b\,c\right)}{2\,c\,d\,\left(d\,x^2+c\right)}","Not used",1,"(atan((d^(1/2)*x)/c^(1/2))*(a*d + b*c))/(2*c^(3/2)*d^(3/2)) + (x*(a*d - b*c))/(2*c*d*(c + d*x^2))","B"
7,1,82,92,5.060872,"\text{Not used}","int((a + b*x^2)/(c + d*x^2)^3,x)","\frac{\frac{x^3\,\left(3\,a\,d+b\,c\right)}{8\,c^2}+\frac{x\,\left(5\,a\,d-b\,c\right)}{8\,c\,d}}{c^2+2\,c\,d\,x^2+d^2\,x^4}+\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x}{\sqrt{c}}\right)\,\left(3\,a\,d+b\,c\right)}{8\,c^{5/2}\,d^{3/2}}","Not used",1,"((x^3*(3*a*d + b*c))/(8*c^2) + (x*(5*a*d - b*c))/(8*c*d))/(c^2 + d^2*x^4 + 2*c*d*x^2) + (atan((d^(1/2)*x)/c^(1/2))*(3*a*d + b*c))/(8*c^(5/2)*d^(3/2))","B"
8,1,116,122,4.945125,"\text{Not used}","int((a + b*x^2)^2*(c + d*x^2)^3,x)","x^5\,\left(\frac{3\,a^2\,c\,d^2}{5}+\frac{6\,a\,b\,c^2\,d}{5}+\frac{b^2\,c^3}{5}\right)+x^7\,\left(\frac{a^2\,d^3}{7}+\frac{6\,a\,b\,c\,d^2}{7}+\frac{3\,b^2\,c^2\,d}{7}\right)+a^2\,c^3\,x+\frac{b^2\,d^3\,x^{11}}{11}+\frac{a\,c^2\,x^3\,\left(3\,a\,d+2\,b\,c\right)}{3}+\frac{b\,d^2\,x^9\,\left(2\,a\,d+3\,b\,c\right)}{9}","Not used",1,"x^5*((b^2*c^3)/5 + (3*a^2*c*d^2)/5 + (6*a*b*c^2*d)/5) + x^7*((a^2*d^3)/7 + (3*b^2*c^2*d)/7 + (6*a*b*c*d^2)/7) + a^2*c^3*x + (b^2*d^3*x^11)/11 + (a*c^2*x^3*(3*a*d + 2*b*c))/3 + (b*d^2*x^9*(2*a*d + 3*b*c))/9","B"
9,1,75,82,0.046623,"\text{Not used}","int((a + b*x^2)^2*(c + d*x^2)^2,x)","x^5\,\left(\frac{a^2\,d^2}{5}+\frac{4\,a\,b\,c\,d}{5}+\frac{b^2\,c^2}{5}\right)+a^2\,c^2\,x+\frac{b^2\,d^2\,x^9}{9}+\frac{2\,a\,c\,x^3\,\left(a\,d+b\,c\right)}{3}+\frac{2\,b\,d\,x^7\,\left(a\,d+b\,c\right)}{7}","Not used",1,"x^5*((a^2*d^2)/5 + (b^2*c^2)/5 + (4*a*b*c*d)/5) + a^2*c^2*x + (b^2*d^2*x^9)/9 + (2*a*c*x^3*(a*d + b*c))/3 + (2*b*d*x^7*(a*d + b*c))/7","B"
10,1,48,50,0.045548,"\text{Not used}","int((a + b*x^2)^2*(c + d*x^2),x)","x^3\,\left(\frac{d\,a^2}{3}+\frac{2\,b\,c\,a}{3}\right)+x^5\,\left(\frac{c\,b^2}{5}+\frac{2\,a\,d\,b}{5}\right)+\frac{b^2\,d\,x^7}{7}+a^2\,c\,x","Not used",1,"x^3*((a^2*d)/3 + (2*a*b*c)/3) + x^5*((b^2*c)/5 + (2*a*b*d)/5) + (b^2*d*x^7)/7 + a^2*c*x","B"
11,1,90,63,0.087854,"\text{Not used}","int((a + b*x^2)^2/(c + d*x^2),x)","\frac{b^2\,x^3}{3\,d}-x\,\left(\frac{b^2\,c}{d^2}-\frac{2\,a\,b}{d}\right)+\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x\,{\left(a\,d-b\,c\right)}^2}{\sqrt{c}\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,{\left(a\,d-b\,c\right)}^2}{\sqrt{c}\,d^{5/2}}","Not used",1,"(b^2*x^3)/(3*d) - x*((b^2*c)/d^2 - (2*a*b)/d) + (atan((d^(1/2)*x*(a*d - b*c)^2)/(c^(1/2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))*(a*d - b*c)^2)/(c^(1/2)*d^(5/2))","B"
12,1,124,82,5.020763,"\text{Not used}","int((a + b*x^2)^2/(c + d*x^2)^2,x)","\frac{b^2\,x}{d^2}+\frac{x\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{2\,c\,\left(d^3\,x^2+c\,d^2\right)}+\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x\,\left(a\,d-b\,c\right)\,\left(a\,d+3\,b\,c\right)}{\sqrt{c}\,\left(a^2\,d^2+2\,a\,b\,c\,d-3\,b^2\,c^2\right)}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d+3\,b\,c\right)}{2\,c^{3/2}\,d^{5/2}}","Not used",1,"(b^2*x)/d^2 + (x*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*c*(c*d^2 + d^3*x^2)) + (atan((d^(1/2)*x*(a*d - b*c)*(a*d + 3*b*c))/(c^(1/2)*(a^2*d^2 - 3*b^2*c^2 + 2*a*b*c*d)))*(a*d - b*c)*(a*d + 3*b*c))/(2*c^(3/2)*d^(5/2))","B"
13,1,130,116,5.030433,"\text{Not used}","int((a + b*x^2)^2/(c + d*x^2)^3,x)","\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x}{\sqrt{c}}\right)\,\left(3\,a^2\,d^2+2\,a\,b\,c\,d+3\,b^2\,c^2\right)}{8\,c^{5/2}\,d^{5/2}}-\frac{\frac{x\,\left(-5\,a^2\,d^2+2\,a\,b\,c\,d+3\,b^2\,c^2\right)}{8\,c\,d^2}-\frac{x^3\,\left(3\,a^2\,d^2+2\,a\,b\,c\,d-5\,b^2\,c^2\right)}{8\,c^2\,d}}{c^2+2\,c\,d\,x^2+d^2\,x^4}","Not used",1,"(atan((d^(1/2)*x)/c^(1/2))*(3*a^2*d^2 + 3*b^2*c^2 + 2*a*b*c*d))/(8*c^(5/2)*d^(5/2)) - ((x*(3*b^2*c^2 - 5*a^2*d^2 + 2*a*b*c*d))/(8*c*d^2) - (x^3*(3*a^2*d^2 - 5*b^2*c^2 + 2*a*b*c*d))/(8*c^2*d))/(c^2 + d^2*x^4 + 2*c*d*x^2)","B"
14,1,152,154,4.904838,"\text{Not used}","int((a + b*x^2)^3*(c + d*x^2)^3,x)","x^7\,\left(\frac{a^3\,d^3}{7}+\frac{9\,a^2\,b\,c\,d^2}{7}+\frac{9\,a\,b^2\,c^2\,d}{7}+\frac{b^3\,c^3}{7}\right)+a^3\,c^3\,x+\frac{b^3\,d^3\,x^{13}}{13}+\frac{3\,a\,c\,x^5\,\left(a^2\,d^2+3\,a\,b\,c\,d+b^2\,c^2\right)}{5}+\frac{b\,d\,x^9\,\left(a^2\,d^2+3\,a\,b\,c\,d+b^2\,c^2\right)}{3}+a^2\,c^2\,x^3\,\left(a\,d+b\,c\right)+\frac{3\,b^2\,d^2\,x^{11}\,\left(a\,d+b\,c\right)}{11}","Not used",1,"x^7*((a^3*d^3)/7 + (b^3*c^3)/7 + (9*a*b^2*c^2*d)/7 + (9*a^2*b*c*d^2)/7) + a^3*c^3*x + (b^3*d^3*x^13)/13 + (3*a*c*x^5*(a^2*d^2 + b^2*c^2 + 3*a*b*c*d))/5 + (b*d*x^9*(a^2*d^2 + b^2*c^2 + 3*a*b*c*d))/3 + a^2*c^2*x^3*(a*d + b*c) + (3*b^2*d^2*x^11*(a*d + b*c))/11","B"
15,1,116,122,4.874897,"\text{Not used}","int((a + b*x^2)^3*(c + d*x^2)^2,x)","x^5\,\left(\frac{a^3\,d^2}{5}+\frac{6\,a^2\,b\,c\,d}{5}+\frac{3\,a\,b^2\,c^2}{5}\right)+x^7\,\left(\frac{3\,a^2\,b\,d^2}{7}+\frac{6\,a\,b^2\,c\,d}{7}+\frac{b^3\,c^2}{7}\right)+a^3\,c^2\,x+\frac{b^3\,d^2\,x^{11}}{11}+\frac{a^2\,c\,x^3\,\left(2\,a\,d+3\,b\,c\right)}{3}+\frac{b^2\,d\,x^9\,\left(3\,a\,d+2\,b\,c\right)}{9}","Not used",1,"x^5*((a^3*d^2)/5 + (3*a*b^2*c^2)/5 + (6*a^2*b*c*d)/5) + x^7*((b^3*c^2)/7 + (3*a^2*b*d^2)/7 + (6*a*b^2*c*d)/7) + a^3*c^2*x + (b^3*d^2*x^11)/11 + (a^2*c*x^3*(2*a*d + 3*b*c))/3 + (b^2*d*x^9*(3*a*d + 2*b*c))/9","B"
16,1,65,70,0.033554,"\text{Not used}","int((a + b*x^2)^3*(c + d*x^2),x)","x^7\,\left(\frac{c\,b^3}{7}+\frac{3\,a\,d\,b^2}{7}\right)+x^3\,\left(\frac{d\,a^3}{3}+b\,c\,a^2\right)+\frac{b^3\,d\,x^9}{9}+a^3\,c\,x+\frac{3\,a\,b\,x^5\,\left(a\,d+b\,c\right)}{5}","Not used",1,"x^7*((b^3*c)/7 + (3*a*b^2*d)/7) + x^3*((a^3*d)/3 + a^2*b*c) + (b^3*d*x^9)/9 + a^3*c*x + (3*a*b*x^5*(a*d + b*c))/5","B"
17,1,145,98,4.869544,"\text{Not used}","int((a + b*x^2)^3/(c + d*x^2),x)","x^3\,\left(\frac{a\,b^2}{d}-\frac{b^3\,c}{3\,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{b^3\,x^5}{5\,d}+\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x\,{\left(a\,d-b\,c\right)}^3}{\sqrt{c}\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}\right)\,{\left(a\,d-b\,c\right)}^3}{\sqrt{c}\,d^{7/2}}","Not used",1,"x^3*((a*b^2)/d - (b^3*c)/(3*d^2)) + x*((3*a^2*b)/d - (c*((3*a*b^2)/d - (b^3*c)/d^2))/d) + (b^3*x^5)/(5*d) + (atan((d^(1/2)*x*(a*d - b*c)^3)/(c^(1/2)*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)))*(a*d - b*c)^3)/(c^(1/2)*d^(7/2))","B"
18,1,181,107,0.099775,"\text{Not used}","int((a + b*x^2)^3/(c + d*x^2)^2,x)","x\,\left(\frac{3\,a\,b^2}{d^2}-\frac{2\,b^3\,c}{d^3}\right)+\frac{b^3\,x^3}{3\,d^2}+\frac{x\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{2\,c\,\left(d^4\,x^2+c\,d^3\right)}+\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+5\,b\,c\right)}{\sqrt{c}\,\left(a^3\,d^3+3\,a^2\,b\,c\,d^2-9\,a\,b^2\,c^2\,d+5\,b^3\,c^3\right)}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+5\,b\,c\right)}{2\,c^{3/2}\,d^{7/2}}","Not used",1,"x*((3*a*b^2)/d^2 - (2*b^3*c)/d^3) + (b^3*x^3)/(3*d^2) + (x*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(2*c*(c*d^3 + d^4*x^2)) + (atan((d^(1/2)*x*(a*d - b*c)^2*(a*d + 5*b*c))/(c^(1/2)*(a^3*d^3 + 5*b^3*c^3 - 9*a*b^2*c^2*d + 3*a^2*b*c*d^2)))*(a*d - b*c)^2*(a*d + 5*b*c))/(2*c^(3/2)*d^(7/2))","B"
19,1,240,130,4.955643,"\text{Not used}","int((a + b*x^2)^3/(c + d*x^2)^3,x)","\frac{\frac{x\,\left(5\,a^3\,d^3-3\,a^2\,b\,c\,d^2-9\,a\,b^2\,c^2\,d+7\,b^3\,c^3\right)}{8\,c}+\frac{3\,x^3\,\left(a^3\,d^4+a^2\,b\,c\,d^3-5\,a\,b^2\,c^2\,d^2+3\,b^3\,c^3\,d\right)}{8\,c^2}}{c^2\,d^3+2\,c\,d^4\,x^2+d^5\,x^4}+\frac{b^3\,x}{d^3}+\frac{3\,\mathrm{atan}\left(\frac{\sqrt{d}\,x\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2+2\,a\,b\,c\,d+5\,b^2\,c^2\right)}{\sqrt{c}\,\left(a^3\,d^3+a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-5\,b^3\,c^3\right)}\right)\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2+2\,a\,b\,c\,d+5\,b^2\,c^2\right)}{8\,c^{5/2}\,d^{7/2}}","Not used",1,"((x*(5*a^3*d^3 + 7*b^3*c^3 - 9*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(8*c) + (3*x^3*(a^3*d^4 + 3*b^3*c^3*d - 5*a*b^2*c^2*d^2 + a^2*b*c*d^3))/(8*c^2))/(c^2*d^3 + d^5*x^4 + 2*c*d^4*x^2) + (b^3*x)/d^3 + (3*atan((d^(1/2)*x*(a*d - b*c)*(a^2*d^2 + 5*b^2*c^2 + 2*a*b*c*d))/(c^(1/2)*(a^3*d^3 - 5*b^3*c^3 + 3*a*b^2*c^2*d + a^2*b*c*d^2)))*(a*d - b*c)*(a^2*d^2 + 5*b^2*c^2 + 2*a*b*c*d))/(8*c^(5/2)*d^(7/2))","B"
20,1,216,142,4.861077,"\text{Not used}","int((c + d*x^2)^4/(a + b*x^2),x)","x\,\left(\frac{4\,c^3\,d}{b}-\frac{a\,\left(\frac{a\,\left(\frac{a\,d^4}{b^2}-\frac{4\,c\,d^3}{b}\right)}{b}+\frac{6\,c^2\,d^2}{b}\right)}{b}\right)-x^5\,\left(\frac{a\,d^4}{5\,b^2}-\frac{4\,c\,d^3}{5\,b}\right)+x^3\,\left(\frac{a\,\left(\frac{a\,d^4}{b^2}-\frac{4\,c\,d^3}{b}\right)}{3\,b}+\frac{2\,c^2\,d^2}{b}\right)+\frac{d^4\,x^7}{7\,b}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^4}{\sqrt{a}\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}\right)\,{\left(a\,d-b\,c\right)}^4}{\sqrt{a}\,b^{9/2}}","Not used",1,"x*((4*c^3*d)/b - (a*((a*((a*d^4)/b^2 - (4*c*d^3)/b))/b + (6*c^2*d^2)/b))/b) - x^5*((a*d^4)/(5*b^2) - (4*c*d^3)/(5*b)) + x^3*((a*((a*d^4)/b^2 - (4*c*d^3)/b))/(3*b) + (2*c^2*d^2)/b) + (d^4*x^7)/(7*b) + (atan((b^(1/2)*x*(a*d - b*c)^4)/(a^(1/2)*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3)))*(a*d - b*c)^4)/(a^(1/2)*b^(9/2))","B"
21,1,146,98,0.075925,"\text{Not used}","int((c + d*x^2)^3/(a + b*x^2),x)","x\,\left(\frac{3\,c^2\,d}{b}+\frac{a\,\left(\frac{a\,d^3}{b^2}-\frac{3\,c\,d^2}{b}\right)}{b}\right)-x^3\,\left(\frac{a\,d^3}{3\,b^2}-\frac{c\,d^2}{b}\right)+\frac{d^3\,x^5}{5\,b}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^3}{\sqrt{a}\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}\right)\,{\left(a\,d-b\,c\right)}^3}{\sqrt{a}\,b^{7/2}}","Not used",1,"x*((3*c^2*d)/b + (a*((a*d^3)/b^2 - (3*c*d^2)/b))/b) - x^3*((a*d^3)/(3*b^2) - (c*d^2)/b) + (d^3*x^5)/(5*b) - (atan((b^(1/2)*x*(a*d - b*c)^3)/(a^(1/2)*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)))*(a*d - b*c)^3)/(a^(1/2)*b^(7/2))","B"
22,1,90,63,4.902140,"\text{Not used}","int((c + d*x^2)^2/(a + b*x^2),x)","\frac{d^2\,x^3}{3\,b}-x\,\left(\frac{a\,d^2}{b^2}-\frac{2\,c\,d}{b}\right)+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^2}{\sqrt{a}\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,{\left(a\,d-b\,c\right)}^2}{\sqrt{a}\,b^{5/2}}","Not used",1,"(d^2*x^3)/(3*b) - x*((a*d^2)/b^2 - (2*c*d)/b) + (atan((b^(1/2)*x*(a*d - b*c)^2)/(a^(1/2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))*(a*d - b*c)^2)/(a^(1/2)*b^(5/2))","B"
23,1,32,39,0.055493,"\text{Not used}","int((c + d*x^2)/(a + b*x^2),x)","\frac{d\,x}{b}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(a\,d-b\,c\right)}{\sqrt{a}\,b^{3/2}}","Not used",1,"(d*x)/b - (atan((b^(1/2)*x)/a^(1/2))*(a*d - b*c))/(a^(1/2)*b^(3/2))","B"
24,1,135,70,0.319994,"\text{Not used}","int(1/((a + b*x^2)*(c + d*x^2)),x)","\frac{\ln\left(b\,x-\sqrt{-a\,b}\right)\,\sqrt{-a\,b}}{2\,a^2\,d-2\,a\,b\,c}-\frac{\ln\left(d\,x+\sqrt{-c\,d}\right)\,\sqrt{-c\,d}}{2\,\left(b\,c^2-a\,c\,d\right)}-\frac{\ln\left(b\,x+\sqrt{-a\,b}\right)\,\sqrt{-a\,b}}{2\,\left(a^2\,d-a\,b\,c\right)}+\frac{\ln\left(d\,x-\sqrt{-c\,d}\right)\,\sqrt{-c\,d}}{2\,b\,c^2-2\,a\,c\,d}","Not used",1,"(log(b*x - (-a*b)^(1/2))*(-a*b)^(1/2))/(2*a^2*d - 2*a*b*c) - (log(d*x + (-c*d)^(1/2))*(-c*d)^(1/2))/(2*(b*c^2 - a*c*d)) - (log(b*x + (-a*b)^(1/2))*(-a*b)^(1/2))/(2*(a^2*d - a*b*c)) + (log(d*x - (-c*d)^(1/2))*(-c*d)^(1/2))/(2*b*c^2 - 2*a*c*d)","B"
25,1,3637,109,5.687685,"\text{Not used}","int(1/((a + b*x^2)*(c + d*x^2)^2),x)","\frac{d\,x}{2\,c\,\left(d\,x^2+c\right)\,\left(a\,d-b\,c\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a\,b^3}\,\left(\frac{\left(\frac{-2\,a^5\,b^2\,c\,d^7+12\,a^4\,b^3\,c^2\,d^6-28\,a^3\,b^4\,c^3\,d^5+32\,a^2\,b^5\,c^4\,d^4-18\,a\,b^6\,c^5\,d^3+4\,b^7\,c^6\,d^2}{2\,\left(-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5\right)}-\frac{x\,\sqrt{-a\,b^3}\,\left(16\,a^5\,b^2\,c^2\,d^7-48\,a^4\,b^3\,c^3\,d^6+32\,a^3\,b^4\,c^4\,d^5+32\,a^2\,b^5\,c^5\,d^4-48\,a\,b^6\,c^6\,d^3+16\,b^7\,c^7\,d^2\right)}{8\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}\right)\,\sqrt{-a\,b^3}}{2\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}-\frac{x\,\left(a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+13\,b^5\,c^2\,d^3\right)}{4\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}\right)\,1{}\mathrm{i}}{a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2}-\frac{\sqrt{-a\,b^3}\,\left(\frac{\left(\frac{-2\,a^5\,b^2\,c\,d^7+12\,a^4\,b^3\,c^2\,d^6-28\,a^3\,b^4\,c^3\,d^5+32\,a^2\,b^5\,c^4\,d^4-18\,a\,b^6\,c^5\,d^3+4\,b^7\,c^6\,d^2}{2\,\left(-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5\right)}+\frac{x\,\sqrt{-a\,b^3}\,\left(16\,a^5\,b^2\,c^2\,d^7-48\,a^4\,b^3\,c^3\,d^6+32\,a^3\,b^4\,c^4\,d^5+32\,a^2\,b^5\,c^5\,d^4-48\,a\,b^6\,c^6\,d^3+16\,b^7\,c^7\,d^2\right)}{8\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}\right)\,\sqrt{-a\,b^3}}{2\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}+\frac{x\,\left(a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+13\,b^5\,c^2\,d^3\right)}{4\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}\right)\,1{}\mathrm{i}}{a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2}}{\frac{\sqrt{-a\,b^3}\,\left(\frac{\left(\frac{-2\,a^5\,b^2\,c\,d^7+12\,a^4\,b^3\,c^2\,d^6-28\,a^3\,b^4\,c^3\,d^5+32\,a^2\,b^5\,c^4\,d^4-18\,a\,b^6\,c^5\,d^3+4\,b^7\,c^6\,d^2}{2\,\left(-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5\right)}-\frac{x\,\sqrt{-a\,b^3}\,\left(16\,a^5\,b^2\,c^2\,d^7-48\,a^4\,b^3\,c^3\,d^6+32\,a^3\,b^4\,c^4\,d^5+32\,a^2\,b^5\,c^5\,d^4-48\,a\,b^6\,c^6\,d^3+16\,b^7\,c^7\,d^2\right)}{8\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}\right)\,\sqrt{-a\,b^3}}{2\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}-\frac{x\,\left(a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+13\,b^5\,c^2\,d^3\right)}{4\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}\right)}{a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2}-\frac{\frac{a\,b^4\,d^4}{2}-\frac{3\,b^5\,c\,d^3}{2}}{-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5}+\frac{\sqrt{-a\,b^3}\,\left(\frac{\left(\frac{-2\,a^5\,b^2\,c\,d^7+12\,a^4\,b^3\,c^2\,d^6-28\,a^3\,b^4\,c^3\,d^5+32\,a^2\,b^5\,c^4\,d^4-18\,a\,b^6\,c^5\,d^3+4\,b^7\,c^6\,d^2}{2\,\left(-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5\right)}+\frac{x\,\sqrt{-a\,b^3}\,\left(16\,a^5\,b^2\,c^2\,d^7-48\,a^4\,b^3\,c^3\,d^6+32\,a^3\,b^4\,c^4\,d^5+32\,a^2\,b^5\,c^5\,d^4-48\,a\,b^6\,c^6\,d^3+16\,b^7\,c^7\,d^2\right)}{8\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}\right)\,\sqrt{-a\,b^3}}{2\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}+\frac{x\,\left(a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+13\,b^5\,c^2\,d^3\right)}{4\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}\right)}{a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2}}\right)\,\sqrt{-a\,b^3}\,1{}\mathrm{i}}{a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,\left(\frac{x\,\left(a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+13\,b^5\,c^2\,d^3\right)}{2\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}-\frac{\left(\frac{-2\,a^5\,b^2\,c\,d^7+12\,a^4\,b^3\,c^2\,d^6-28\,a^3\,b^4\,c^3\,d^5+32\,a^2\,b^5\,c^4\,d^4-18\,a\,b^6\,c^5\,d^3+4\,b^7\,c^6\,d^2}{-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5}-\frac{x\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,\left(16\,a^5\,b^2\,c^2\,d^7-48\,a^4\,b^3\,c^3\,d^6+32\,a^3\,b^4\,c^4\,d^5+32\,a^2\,b^5\,c^5\,d^4-48\,a\,b^6\,c^6\,d^3+16\,b^7\,c^7\,d^2\right)}{8\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}\right)\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)}{4\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}+\frac{\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,\left(\frac{x\,\left(a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+13\,b^5\,c^2\,d^3\right)}{2\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}+\frac{\left(\frac{-2\,a^5\,b^2\,c\,d^7+12\,a^4\,b^3\,c^2\,d^6-28\,a^3\,b^4\,c^3\,d^5+32\,a^2\,b^5\,c^4\,d^4-18\,a\,b^6\,c^5\,d^3+4\,b^7\,c^6\,d^2}{-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5}+\frac{x\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,\left(16\,a^5\,b^2\,c^2\,d^7-48\,a^4\,b^3\,c^3\,d^6+32\,a^3\,b^4\,c^4\,d^5+32\,a^2\,b^5\,c^5\,d^4-48\,a\,b^6\,c^6\,d^3+16\,b^7\,c^7\,d^2\right)}{8\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}\right)\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)}{4\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}}{\frac{\frac{a\,b^4\,d^4}{2}-\frac{3\,b^5\,c\,d^3}{2}}{-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5}+\frac{\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,\left(\frac{x\,\left(a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+13\,b^5\,c^2\,d^3\right)}{2\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}-\frac{\left(\frac{-2\,a^5\,b^2\,c\,d^7+12\,a^4\,b^3\,c^2\,d^6-28\,a^3\,b^4\,c^3\,d^5+32\,a^2\,b^5\,c^4\,d^4-18\,a\,b^6\,c^5\,d^3+4\,b^7\,c^6\,d^2}{-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5}-\frac{x\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,\left(16\,a^5\,b^2\,c^2\,d^7-48\,a^4\,b^3\,c^3\,d^6+32\,a^3\,b^4\,c^4\,d^5+32\,a^2\,b^5\,c^5\,d^4-48\,a\,b^6\,c^6\,d^3+16\,b^7\,c^7\,d^2\right)}{8\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}\right)\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)}{4\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}\right)}{4\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}-\frac{\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,\left(\frac{x\,\left(a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+13\,b^5\,c^2\,d^3\right)}{2\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}+\frac{\left(\frac{-2\,a^5\,b^2\,c\,d^7+12\,a^4\,b^3\,c^2\,d^6-28\,a^3\,b^4\,c^3\,d^5+32\,a^2\,b^5\,c^4\,d^4-18\,a\,b^6\,c^5\,d^3+4\,b^7\,c^6\,d^2}{-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5}+\frac{x\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,\left(16\,a^5\,b^2\,c^2\,d^7-48\,a^4\,b^3\,c^3\,d^6+32\,a^3\,b^4\,c^4\,d^5+32\,a^2\,b^5\,c^5\,d^4-48\,a\,b^6\,c^6\,d^3+16\,b^7\,c^7\,d^2\right)}{8\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}\right)\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)}{4\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}\right)}{4\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}}\right)\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}","Not used",1,"(d*x)/(2*c*(c + d*x^2)*(a*d - b*c)) - (atan((((-c^3*d)^(1/2)*(a*d - 3*b*c)*((x*(a^2*b^3*d^5 + 13*b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(2*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)) - (((4*b^7*c^6*d^2 - 18*a*b^6*c^5*d^3 - 2*a^5*b^2*c*d^7 + 32*a^2*b^5*c^4*d^4 - 28*a^3*b^4*c^3*d^5 + 12*a^4*b^3*c^2*d^6)/(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d) - (x*(-c^3*d)^(1/2)*(a*d - 3*b*c)*(16*b^7*c^7*d^2 - 48*a*b^6*c^6*d^3 + 32*a^2*b^5*c^5*d^4 + 32*a^3*b^4*c^4*d^5 - 48*a^4*b^3*c^3*d^6 + 16*a^5*b^2*c^2*d^7))/(8*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)))*(-c^3*d)^(1/2)*(a*d - 3*b*c))/(4*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)))*1i)/(4*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)) + ((-c^3*d)^(1/2)*(a*d - 3*b*c)*((x*(a^2*b^3*d^5 + 13*b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(2*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)) + (((4*b^7*c^6*d^2 - 18*a*b^6*c^5*d^3 - 2*a^5*b^2*c*d^7 + 32*a^2*b^5*c^4*d^4 - 28*a^3*b^4*c^3*d^5 + 12*a^4*b^3*c^2*d^6)/(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d) + (x*(-c^3*d)^(1/2)*(a*d - 3*b*c)*(16*b^7*c^7*d^2 - 48*a*b^6*c^6*d^3 + 32*a^2*b^5*c^5*d^4 + 32*a^3*b^4*c^4*d^5 - 48*a^4*b^3*c^3*d^6 + 16*a^5*b^2*c^2*d^7))/(8*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)))*(-c^3*d)^(1/2)*(a*d - 3*b*c))/(4*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)))*1i)/(4*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)))/(((a*b^4*d^4)/2 - (3*b^5*c*d^3)/2)/(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d) + ((-c^3*d)^(1/2)*(a*d - 3*b*c)*((x*(a^2*b^3*d^5 + 13*b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(2*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)) - (((4*b^7*c^6*d^2 - 18*a*b^6*c^5*d^3 - 2*a^5*b^2*c*d^7 + 32*a^2*b^5*c^4*d^4 - 28*a^3*b^4*c^3*d^5 + 12*a^4*b^3*c^2*d^6)/(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d) - (x*(-c^3*d)^(1/2)*(a*d - 3*b*c)*(16*b^7*c^7*d^2 - 48*a*b^6*c^6*d^3 + 32*a^2*b^5*c^5*d^4 + 32*a^3*b^4*c^4*d^5 - 48*a^4*b^3*c^3*d^6 + 16*a^5*b^2*c^2*d^7))/(8*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)))*(-c^3*d)^(1/2)*(a*d - 3*b*c))/(4*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d))))/(4*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)) - ((-c^3*d)^(1/2)*(a*d - 3*b*c)*((x*(a^2*b^3*d^5 + 13*b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(2*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)) + (((4*b^7*c^6*d^2 - 18*a*b^6*c^5*d^3 - 2*a^5*b^2*c*d^7 + 32*a^2*b^5*c^4*d^4 - 28*a^3*b^4*c^3*d^5 + 12*a^4*b^3*c^2*d^6)/(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d) + (x*(-c^3*d)^(1/2)*(a*d - 3*b*c)*(16*b^7*c^7*d^2 - 48*a*b^6*c^6*d^3 + 32*a^2*b^5*c^5*d^4 + 32*a^3*b^4*c^4*d^5 - 48*a^4*b^3*c^3*d^6 + 16*a^5*b^2*c^2*d^7))/(8*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)))*(-c^3*d)^(1/2)*(a*d - 3*b*c))/(4*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d))))/(4*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d))))*(-c^3*d)^(1/2)*(a*d - 3*b*c)*1i)/(2*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)) - (atan((((-a*b^3)^(1/2)*((((4*b^7*c^6*d^2 - 18*a*b^6*c^5*d^3 - 2*a^5*b^2*c*d^7 + 32*a^2*b^5*c^4*d^4 - 28*a^3*b^4*c^3*d^5 + 12*a^4*b^3*c^2*d^6)/(2*(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d)) - (x*(-a*b^3)^(1/2)*(16*b^7*c^7*d^2 - 48*a*b^6*c^6*d^3 + 32*a^2*b^5*c^5*d^4 + 32*a^3*b^4*c^4*d^5 - 48*a^4*b^3*c^3*d^6 + 16*a^5*b^2*c^2*d^7))/(8*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)))*(-a*b^3)^(1/2))/(2*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)) - (x*(a^2*b^3*d^5 + 13*b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(4*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)))*1i)/(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d) - ((-a*b^3)^(1/2)*((((4*b^7*c^6*d^2 - 18*a*b^6*c^5*d^3 - 2*a^5*b^2*c*d^7 + 32*a^2*b^5*c^4*d^4 - 28*a^3*b^4*c^3*d^5 + 12*a^4*b^3*c^2*d^6)/(2*(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d)) + (x*(-a*b^3)^(1/2)*(16*b^7*c^7*d^2 - 48*a*b^6*c^6*d^3 + 32*a^2*b^5*c^5*d^4 + 32*a^3*b^4*c^4*d^5 - 48*a^4*b^3*c^3*d^6 + 16*a^5*b^2*c^2*d^7))/(8*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)))*(-a*b^3)^(1/2))/(2*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)) + (x*(a^2*b^3*d^5 + 13*b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(4*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)))*1i)/(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d))/(((-a*b^3)^(1/2)*((((4*b^7*c^6*d^2 - 18*a*b^6*c^5*d^3 - 2*a^5*b^2*c*d^7 + 32*a^2*b^5*c^4*d^4 - 28*a^3*b^4*c^3*d^5 + 12*a^4*b^3*c^2*d^6)/(2*(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d)) - (x*(-a*b^3)^(1/2)*(16*b^7*c^7*d^2 - 48*a*b^6*c^6*d^3 + 32*a^2*b^5*c^5*d^4 + 32*a^3*b^4*c^4*d^5 - 48*a^4*b^3*c^3*d^6 + 16*a^5*b^2*c^2*d^7))/(8*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)))*(-a*b^3)^(1/2))/(2*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)) - (x*(a^2*b^3*d^5 + 13*b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(4*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d))))/(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d) - ((a*b^4*d^4)/2 - (3*b^5*c*d^3)/2)/(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d) + ((-a*b^3)^(1/2)*((((4*b^7*c^6*d^2 - 18*a*b^6*c^5*d^3 - 2*a^5*b^2*c*d^7 + 32*a^2*b^5*c^4*d^4 - 28*a^3*b^4*c^3*d^5 + 12*a^4*b^3*c^2*d^6)/(2*(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d)) + (x*(-a*b^3)^(1/2)*(16*b^7*c^7*d^2 - 48*a*b^6*c^6*d^3 + 32*a^2*b^5*c^5*d^4 + 32*a^3*b^4*c^4*d^5 - 48*a^4*b^3*c^3*d^6 + 16*a^5*b^2*c^2*d^7))/(8*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)))*(-a*b^3)^(1/2))/(2*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)) + (x*(a^2*b^3*d^5 + 13*b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(4*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d))))/(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)))*(-a*b^3)^(1/2)*1i)/(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)","B"
26,1,6033,160,6.868847,"\text{Not used}","int(1/((a + b*x^2)*(c + d*x^2)^3),x)","\frac{\frac{x^3\,\left(3\,a\,d^3-7\,b\,c\,d^2\right)}{8\,c^2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{x\,\left(5\,a\,d^2-9\,b\,c\,d\right)}{8\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{c^2+2\,c\,d\,x^2+d^2\,x^4}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a\,b^5}\,\left(\frac{x\,\left(9\,a^4\,b^3\,d^7-60\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-300\,a\,b^6\,c^3\,d^4+289\,b^7\,c^4\,d^3\right)}{32\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}-\frac{\sqrt{-a\,b^5}\,\left(\frac{96\,a^8\,b^2\,c^2\,d^{10}-800\,a^7\,b^3\,c^3\,d^9+3040\,a^6\,b^4\,c^4\,d^8-6816\,a^5\,b^5\,c^5\,d^7+9760\,a^4\,b^6\,c^6\,d^6-9056\,a^3\,b^7\,c^7\,d^5+5280\,a^2\,b^8\,c^8\,d^4-1760\,a\,b^9\,c^9\,d^3+256\,b^{10}\,c^{10}\,d^2}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}-\frac{x\,\sqrt{-a\,b^5}\,\left(256\,a^7\,b^2\,c^4\,d^9-1280\,a^6\,b^3\,c^5\,d^8+2304\,a^5\,b^4\,c^6\,d^7-1280\,a^4\,b^5\,c^7\,d^6-1280\,a^3\,b^6\,c^8\,d^5+2304\,a^2\,b^7\,c^9\,d^4-1280\,a\,b^8\,c^{10}\,d^3+256\,b^9\,c^{11}\,d^2\right)}{64\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}\right)}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}\right)\,1{}\mathrm{i}}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}+\frac{\sqrt{-a\,b^5}\,\left(\frac{x\,\left(9\,a^4\,b^3\,d^7-60\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-300\,a\,b^6\,c^3\,d^4+289\,b^7\,c^4\,d^3\right)}{32\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}+\frac{\sqrt{-a\,b^5}\,\left(\frac{96\,a^8\,b^2\,c^2\,d^{10}-800\,a^7\,b^3\,c^3\,d^9+3040\,a^6\,b^4\,c^4\,d^8-6816\,a^5\,b^5\,c^5\,d^7+9760\,a^4\,b^6\,c^6\,d^6-9056\,a^3\,b^7\,c^7\,d^5+5280\,a^2\,b^8\,c^8\,d^4-1760\,a\,b^9\,c^9\,d^3+256\,b^{10}\,c^{10}\,d^2}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}+\frac{x\,\sqrt{-a\,b^5}\,\left(256\,a^7\,b^2\,c^4\,d^9-1280\,a^6\,b^3\,c^5\,d^8+2304\,a^5\,b^4\,c^6\,d^7-1280\,a^4\,b^5\,c^7\,d^6-1280\,a^3\,b^6\,c^8\,d^5+2304\,a^2\,b^7\,c^9\,d^4-1280\,a\,b^8\,c^{10}\,d^3+256\,b^9\,c^{11}\,d^2\right)}{64\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}\right)}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}\right)\,1{}\mathrm{i}}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}}{\frac{9\,a^3\,b^5\,d^6-51\,a^2\,b^6\,c\,d^5+115\,a\,b^7\,c^2\,d^4-105\,b^8\,c^3\,d^3}{32\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}+\frac{\sqrt{-a\,b^5}\,\left(\frac{x\,\left(9\,a^4\,b^3\,d^7-60\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-300\,a\,b^6\,c^3\,d^4+289\,b^7\,c^4\,d^3\right)}{32\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}-\frac{\sqrt{-a\,b^5}\,\left(\frac{96\,a^8\,b^2\,c^2\,d^{10}-800\,a^7\,b^3\,c^3\,d^9+3040\,a^6\,b^4\,c^4\,d^8-6816\,a^5\,b^5\,c^5\,d^7+9760\,a^4\,b^6\,c^6\,d^6-9056\,a^3\,b^7\,c^7\,d^5+5280\,a^2\,b^8\,c^8\,d^4-1760\,a\,b^9\,c^9\,d^3+256\,b^{10}\,c^{10}\,d^2}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}-\frac{x\,\sqrt{-a\,b^5}\,\left(256\,a^7\,b^2\,c^4\,d^9-1280\,a^6\,b^3\,c^5\,d^8+2304\,a^5\,b^4\,c^6\,d^7-1280\,a^4\,b^5\,c^7\,d^6-1280\,a^3\,b^6\,c^8\,d^5+2304\,a^2\,b^7\,c^9\,d^4-1280\,a\,b^8\,c^{10}\,d^3+256\,b^9\,c^{11}\,d^2\right)}{64\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}\right)}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}\right)}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}-\frac{\sqrt{-a\,b^5}\,\left(\frac{x\,\left(9\,a^4\,b^3\,d^7-60\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-300\,a\,b^6\,c^3\,d^4+289\,b^7\,c^4\,d^3\right)}{32\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}+\frac{\sqrt{-a\,b^5}\,\left(\frac{96\,a^8\,b^2\,c^2\,d^{10}-800\,a^7\,b^3\,c^3\,d^9+3040\,a^6\,b^4\,c^4\,d^8-6816\,a^5\,b^5\,c^5\,d^7+9760\,a^4\,b^6\,c^6\,d^6-9056\,a^3\,b^7\,c^7\,d^5+5280\,a^2\,b^8\,c^8\,d^4-1760\,a\,b^9\,c^9\,d^3+256\,b^{10}\,c^{10}\,d^2}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}+\frac{x\,\sqrt{-a\,b^5}\,\left(256\,a^7\,b^2\,c^4\,d^9-1280\,a^6\,b^3\,c^5\,d^8+2304\,a^5\,b^4\,c^6\,d^7-1280\,a^4\,b^5\,c^7\,d^6-1280\,a^3\,b^6\,c^8\,d^5+2304\,a^2\,b^7\,c^9\,d^4-1280\,a\,b^8\,c^{10}\,d^3+256\,b^9\,c^{11}\,d^2\right)}{64\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}\right)}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}\right)}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}}\right)\,\sqrt{-a\,b^5}\,1{}\mathrm{i}}{a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(9\,a^4\,b^3\,d^7-60\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-300\,a\,b^6\,c^3\,d^4+289\,b^7\,c^4\,d^3\right)}{32\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}-\frac{\left(\frac{96\,a^8\,b^2\,c^2\,d^{10}-800\,a^7\,b^3\,c^3\,d^9+3040\,a^6\,b^4\,c^4\,d^8-6816\,a^5\,b^5\,c^5\,d^7+9760\,a^4\,b^6\,c^6\,d^6-9056\,a^3\,b^7\,c^7\,d^5+5280\,a^2\,b^8\,c^8\,d^4-1760\,a\,b^9\,c^9\,d^3+256\,b^{10}\,c^{10}\,d^2}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}-\frac{x\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,\left(256\,a^7\,b^2\,c^4\,d^9-1280\,a^6\,b^3\,c^5\,d^8+2304\,a^5\,b^4\,c^6\,d^7-1280\,a^4\,b^5\,c^7\,d^6-1280\,a^3\,b^6\,c^8\,d^5+2304\,a^2\,b^7\,c^9\,d^4-1280\,a\,b^8\,c^{10}\,d^3+256\,b^9\,c^{11}\,d^2\right)}{512\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}+\frac{\left(\frac{x\,\left(9\,a^4\,b^3\,d^7-60\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-300\,a\,b^6\,c^3\,d^4+289\,b^7\,c^4\,d^3\right)}{32\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}+\frac{\left(\frac{96\,a^8\,b^2\,c^2\,d^{10}-800\,a^7\,b^3\,c^3\,d^9+3040\,a^6\,b^4\,c^4\,d^8-6816\,a^5\,b^5\,c^5\,d^7+9760\,a^4\,b^6\,c^6\,d^6-9056\,a^3\,b^7\,c^7\,d^5+5280\,a^2\,b^8\,c^8\,d^4-1760\,a\,b^9\,c^9\,d^3+256\,b^{10}\,c^{10}\,d^2}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}+\frac{x\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,\left(256\,a^7\,b^2\,c^4\,d^9-1280\,a^6\,b^3\,c^5\,d^8+2304\,a^5\,b^4\,c^6\,d^7-1280\,a^4\,b^5\,c^7\,d^6-1280\,a^3\,b^6\,c^8\,d^5+2304\,a^2\,b^7\,c^9\,d^4-1280\,a\,b^8\,c^{10}\,d^3+256\,b^9\,c^{11}\,d^2\right)}{512\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}}{\frac{9\,a^3\,b^5\,d^6-51\,a^2\,b^6\,c\,d^5+115\,a\,b^7\,c^2\,d^4-105\,b^8\,c^3\,d^3}{32\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}+\frac{\left(\frac{x\,\left(9\,a^4\,b^3\,d^7-60\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-300\,a\,b^6\,c^3\,d^4+289\,b^7\,c^4\,d^3\right)}{32\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}-\frac{\left(\frac{96\,a^8\,b^2\,c^2\,d^{10}-800\,a^7\,b^3\,c^3\,d^9+3040\,a^6\,b^4\,c^4\,d^8-6816\,a^5\,b^5\,c^5\,d^7+9760\,a^4\,b^6\,c^6\,d^6-9056\,a^3\,b^7\,c^7\,d^5+5280\,a^2\,b^8\,c^8\,d^4-1760\,a\,b^9\,c^9\,d^3+256\,b^{10}\,c^{10}\,d^2}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}-\frac{x\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,\left(256\,a^7\,b^2\,c^4\,d^9-1280\,a^6\,b^3\,c^5\,d^8+2304\,a^5\,b^4\,c^6\,d^7-1280\,a^4\,b^5\,c^7\,d^6-1280\,a^3\,b^6\,c^8\,d^5+2304\,a^2\,b^7\,c^9\,d^4-1280\,a\,b^8\,c^{10}\,d^3+256\,b^9\,c^{11}\,d^2\right)}{512\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}-\frac{\left(\frac{x\,\left(9\,a^4\,b^3\,d^7-60\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-300\,a\,b^6\,c^3\,d^4+289\,b^7\,c^4\,d^3\right)}{32\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}+\frac{\left(\frac{96\,a^8\,b^2\,c^2\,d^{10}-800\,a^7\,b^3\,c^3\,d^9+3040\,a^6\,b^4\,c^4\,d^8-6816\,a^5\,b^5\,c^5\,d^7+9760\,a^4\,b^6\,c^6\,d^6-9056\,a^3\,b^7\,c^7\,d^5+5280\,a^2\,b^8\,c^8\,d^4-1760\,a\,b^9\,c^9\,d^3+256\,b^{10}\,c^{10}\,d^2}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}+\frac{x\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,\left(256\,a^7\,b^2\,c^4\,d^9-1280\,a^6\,b^3\,c^5\,d^8+2304\,a^5\,b^4\,c^6\,d^7-1280\,a^4\,b^5\,c^7\,d^6-1280\,a^3\,b^6\,c^8\,d^5+2304\,a^2\,b^7\,c^9\,d^4-1280\,a\,b^8\,c^{10}\,d^3+256\,b^9\,c^{11}\,d^2\right)}{512\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,1{}\mathrm{i}}{8\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}","Not used",1,"((x^3*(3*a*d^3 - 7*b*c*d^2))/(8*c^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (x*(5*a*d^2 - 9*b*c*d))/(8*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(c^2 + d^2*x^4 + 2*c*d*x^2) - (atan((((-a*b^5)^(1/2)*((x*(9*a^4*b^3*d^7 + 289*b^7*c^4*d^3 - 300*a*b^6*c^3*d^4 - 60*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)) - ((-a*b^5)^(1/2)*((256*b^10*c^10*d^2 - 1760*a*b^9*c^9*d^3 + 5280*a^2*b^8*c^8*d^4 - 9056*a^3*b^7*c^7*d^5 + 9760*a^4*b^6*c^6*d^6 - 6816*a^5*b^5*c^5*d^7 + 3040*a^6*b^4*c^4*d^8 - 800*a^7*b^3*c^3*d^9 + 96*a^8*b^2*c^2*d^10)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)) - (x*(-a*b^5)^(1/2)*(256*b^9*c^11*d^2 - 1280*a*b^8*c^10*d^3 + 2304*a^2*b^7*c^9*d^4 - 1280*a^3*b^6*c^8*d^5 - 1280*a^4*b^5*c^7*d^6 + 2304*a^5*b^4*c^6*d^7 - 1280*a^6*b^3*c^5*d^8 + 256*a^7*b^2*c^4*d^9))/(64*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d))))/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)))*1i)/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)) + ((-a*b^5)^(1/2)*((x*(9*a^4*b^3*d^7 + 289*b^7*c^4*d^3 - 300*a*b^6*c^3*d^4 - 60*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)) + ((-a*b^5)^(1/2)*((256*b^10*c^10*d^2 - 1760*a*b^9*c^9*d^3 + 5280*a^2*b^8*c^8*d^4 - 9056*a^3*b^7*c^7*d^5 + 9760*a^4*b^6*c^6*d^6 - 6816*a^5*b^5*c^5*d^7 + 3040*a^6*b^4*c^4*d^8 - 800*a^7*b^3*c^3*d^9 + 96*a^8*b^2*c^2*d^10)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)) + (x*(-a*b^5)^(1/2)*(256*b^9*c^11*d^2 - 1280*a*b^8*c^10*d^3 + 2304*a^2*b^7*c^9*d^4 - 1280*a^3*b^6*c^8*d^5 - 1280*a^4*b^5*c^7*d^6 + 2304*a^5*b^4*c^6*d^7 - 1280*a^6*b^3*c^5*d^8 + 256*a^7*b^2*c^4*d^9))/(64*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d))))/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)))*1i)/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)))/((9*a^3*b^5*d^6 - 105*b^8*c^3*d^3 + 115*a*b^7*c^2*d^4 - 51*a^2*b^6*c*d^5)/(32*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)) + ((-a*b^5)^(1/2)*((x*(9*a^4*b^3*d^7 + 289*b^7*c^4*d^3 - 300*a*b^6*c^3*d^4 - 60*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)) - ((-a*b^5)^(1/2)*((256*b^10*c^10*d^2 - 1760*a*b^9*c^9*d^3 + 5280*a^2*b^8*c^8*d^4 - 9056*a^3*b^7*c^7*d^5 + 9760*a^4*b^6*c^6*d^6 - 6816*a^5*b^5*c^5*d^7 + 3040*a^6*b^4*c^4*d^8 - 800*a^7*b^3*c^3*d^9 + 96*a^8*b^2*c^2*d^10)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)) - (x*(-a*b^5)^(1/2)*(256*b^9*c^11*d^2 - 1280*a*b^8*c^10*d^3 + 2304*a^2*b^7*c^9*d^4 - 1280*a^3*b^6*c^8*d^5 - 1280*a^4*b^5*c^7*d^6 + 2304*a^5*b^4*c^6*d^7 - 1280*a^6*b^3*c^5*d^8 + 256*a^7*b^2*c^4*d^9))/(64*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d))))/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2))))/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)) - ((-a*b^5)^(1/2)*((x*(9*a^4*b^3*d^7 + 289*b^7*c^4*d^3 - 300*a*b^6*c^3*d^4 - 60*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)) + ((-a*b^5)^(1/2)*((256*b^10*c^10*d^2 - 1760*a*b^9*c^9*d^3 + 5280*a^2*b^8*c^8*d^4 - 9056*a^3*b^7*c^7*d^5 + 9760*a^4*b^6*c^6*d^6 - 6816*a^5*b^5*c^5*d^7 + 3040*a^6*b^4*c^4*d^8 - 800*a^7*b^3*c^3*d^9 + 96*a^8*b^2*c^2*d^10)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)) + (x*(-a*b^5)^(1/2)*(256*b^9*c^11*d^2 - 1280*a*b^8*c^10*d^3 + 2304*a^2*b^7*c^9*d^4 - 1280*a^3*b^6*c^8*d^5 - 1280*a^4*b^5*c^7*d^6 + 2304*a^5*b^4*c^6*d^7 - 1280*a^6*b^3*c^5*d^8 + 256*a^7*b^2*c^4*d^9))/(64*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d))))/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2))))/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2))))*(-a*b^5)^(1/2)*1i)/(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2) - (atan(((((x*(9*a^4*b^3*d^7 + 289*b^7*c^4*d^3 - 300*a*b^6*c^3*d^4 - 60*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)) - (((256*b^10*c^10*d^2 - 1760*a*b^9*c^9*d^3 + 5280*a^2*b^8*c^8*d^4 - 9056*a^3*b^7*c^7*d^5 + 9760*a^4*b^6*c^6*d^6 - 6816*a^5*b^5*c^5*d^7 + 3040*a^6*b^4*c^4*d^8 - 800*a^7*b^3*c^3*d^9 + 96*a^8*b^2*c^2*d^10)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)) - (x*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d)*(256*b^9*c^11*d^2 - 1280*a*b^8*c^10*d^3 + 2304*a^2*b^7*c^9*d^4 - 1280*a^3*b^6*c^8*d^5 - 1280*a^4*b^5*c^7*d^6 + 2304*a^5*b^4*c^6*d^7 - 1280*a^6*b^3*c^5*d^8 + 256*a^7*b^2*c^4*d^9))/(512*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d))/(16*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d)*1i)/(16*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)) + (((x*(9*a^4*b^3*d^7 + 289*b^7*c^4*d^3 - 300*a*b^6*c^3*d^4 - 60*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)) + (((256*b^10*c^10*d^2 - 1760*a*b^9*c^9*d^3 + 5280*a^2*b^8*c^8*d^4 - 9056*a^3*b^7*c^7*d^5 + 9760*a^4*b^6*c^6*d^6 - 6816*a^5*b^5*c^5*d^7 + 3040*a^6*b^4*c^4*d^8 - 800*a^7*b^3*c^3*d^9 + 96*a^8*b^2*c^2*d^10)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)) + (x*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d)*(256*b^9*c^11*d^2 - 1280*a*b^8*c^10*d^3 + 2304*a^2*b^7*c^9*d^4 - 1280*a^3*b^6*c^8*d^5 - 1280*a^4*b^5*c^7*d^6 + 2304*a^5*b^4*c^6*d^7 - 1280*a^6*b^3*c^5*d^8 + 256*a^7*b^2*c^4*d^9))/(512*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d))/(16*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d)*1i)/(16*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)))/((9*a^3*b^5*d^6 - 105*b^8*c^3*d^3 + 115*a*b^7*c^2*d^4 - 51*a^2*b^6*c*d^5)/(32*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)) + (((x*(9*a^4*b^3*d^7 + 289*b^7*c^4*d^3 - 300*a*b^6*c^3*d^4 - 60*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)) - (((256*b^10*c^10*d^2 - 1760*a*b^9*c^9*d^3 + 5280*a^2*b^8*c^8*d^4 - 9056*a^3*b^7*c^7*d^5 + 9760*a^4*b^6*c^6*d^6 - 6816*a^5*b^5*c^5*d^7 + 3040*a^6*b^4*c^4*d^8 - 800*a^7*b^3*c^3*d^9 + 96*a^8*b^2*c^2*d^10)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)) - (x*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d)*(256*b^9*c^11*d^2 - 1280*a*b^8*c^10*d^3 + 2304*a^2*b^7*c^9*d^4 - 1280*a^3*b^6*c^8*d^5 - 1280*a^4*b^5*c^7*d^6 + 2304*a^5*b^4*c^6*d^7 - 1280*a^6*b^3*c^5*d^8 + 256*a^7*b^2*c^4*d^9))/(512*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d))/(16*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d))/(16*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)) - (((x*(9*a^4*b^3*d^7 + 289*b^7*c^4*d^3 - 300*a*b^6*c^3*d^4 - 60*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)) + (((256*b^10*c^10*d^2 - 1760*a*b^9*c^9*d^3 + 5280*a^2*b^8*c^8*d^4 - 9056*a^3*b^7*c^7*d^5 + 9760*a^4*b^6*c^6*d^6 - 6816*a^5*b^5*c^5*d^7 + 3040*a^6*b^4*c^4*d^8 - 800*a^7*b^3*c^3*d^9 + 96*a^8*b^2*c^2*d^10)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)) + (x*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d)*(256*b^9*c^11*d^2 - 1280*a*b^8*c^10*d^3 + 2304*a^2*b^7*c^9*d^4 - 1280*a^3*b^6*c^8*d^5 - 1280*a^4*b^5*c^7*d^6 + 2304*a^5*b^4*c^6*d^7 - 1280*a^6*b^3*c^5*d^8 + 256*a^7*b^2*c^4*d^9))/(512*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d))/(16*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d))/(16*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d))))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d)*1i)/(8*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d))","B"
27,1,386,192,5.023761,"\text{Not used}","int((c + d*x^2)^5/(a + b*x^2)^2,x)","x\,\left(\frac{10\,c^3\,d^2}{b^2}-\frac{2\,a\,\left(\frac{2\,a\,\left(\frac{2\,a\,d^5}{b^3}-\frac{5\,c\,d^4}{b^2}\right)}{b}-\frac{a^2\,d^5}{b^4}+\frac{10\,c^2\,d^3}{b^2}\right)}{b}+\frac{a^2\,\left(\frac{2\,a\,d^5}{b^3}-\frac{5\,c\,d^4}{b^2}\right)}{b^2}\right)-x^5\,\left(\frac{2\,a\,d^5}{5\,b^3}-\frac{c\,d^4}{b^2}\right)+x^3\,\left(\frac{2\,a\,\left(\frac{2\,a\,d^5}{b^3}-\frac{5\,c\,d^4}{b^2}\right)}{3\,b}-\frac{a^2\,d^5}{3\,b^4}+\frac{10\,c^2\,d^3}{3\,b^2}\right)+\frac{d^5\,x^7}{7\,b^2}-\frac{x\,\left(a^5\,d^5-5\,a^4\,b\,c\,d^4+10\,a^3\,b^2\,c^2\,d^3-10\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d-b^5\,c^5\right)}{2\,a\,\left(b^6\,x^2+a\,b^5\right)}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^4\,\left(9\,a\,d+b\,c\right)}{\sqrt{a}\,\left(9\,a^5\,d^5-35\,a^4\,b\,c\,d^4+50\,a^3\,b^2\,c^2\,d^3-30\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d+b^5\,c^5\right)}\right)\,{\left(a\,d-b\,c\right)}^4\,\left(9\,a\,d+b\,c\right)}{2\,a^{3/2}\,b^{11/2}}","Not used",1,"x*((10*c^3*d^2)/b^2 - (2*a*((2*a*((2*a*d^5)/b^3 - (5*c*d^4)/b^2))/b - (a^2*d^5)/b^4 + (10*c^2*d^3)/b^2))/b + (a^2*((2*a*d^5)/b^3 - (5*c*d^4)/b^2))/b^2) - x^5*((2*a*d^5)/(5*b^3) - (c*d^4)/b^2) + x^3*((2*a*((2*a*d^5)/b^3 - (5*c*d^4)/b^2))/(3*b) - (a^2*d^5)/(3*b^4) + (10*c^2*d^3)/(3*b^2)) + (d^5*x^7)/(7*b^2) - (x*(a^5*d^5 - b^5*c^5 - 10*a^2*b^3*c^3*d^2 + 10*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 5*a^4*b*c*d^4))/(2*a*(a*b^5 + b^6*x^2)) + (atan((b^(1/2)*x*(a*d - b*c)^4*(9*a*d + b*c))/(a^(1/2)*(9*a^5*d^5 + b^5*c^5 - 30*a^2*b^3*c^3*d^2 + 50*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 35*a^4*b*c*d^4)))*(a*d - b*c)^4*(9*a*d + b*c))/(2*a^(3/2)*b^(11/2))","B"
28,1,261,142,5.053868,"\text{Not used}","int((c + d*x^2)^4/(a + b*x^2)^2,x)","x\,\left(\frac{2\,a\,\left(\frac{2\,a\,d^4}{b^3}-\frac{4\,c\,d^3}{b^2}\right)}{b}-\frac{a^2\,d^4}{b^4}+\frac{6\,c^2\,d^2}{b^2}\right)-x^3\,\left(\frac{2\,a\,d^4}{3\,b^3}-\frac{4\,c\,d^3}{3\,b^2}\right)+\frac{d^4\,x^5}{5\,b^2}+\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{2\,a\,\left(b^5\,x^2+a\,b^4\right)}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^3\,\left(7\,a\,d+b\,c\right)}{\sqrt{a}\,\left(-7\,a^4\,d^4+20\,a^3\,b\,c\,d^3-18\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}\right)\,{\left(a\,d-b\,c\right)}^3\,\left(7\,a\,d+b\,c\right)}{2\,a^{3/2}\,b^{9/2}}","Not used",1,"x*((2*a*((2*a*d^4)/b^3 - (4*c*d^3)/b^2))/b - (a^2*d^4)/b^4 + (6*c^2*d^2)/b^2) - x^3*((2*a*d^4)/(3*b^3) - (4*c*d^3)/(3*b^2)) + (d^4*x^5)/(5*b^2) + (x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/(2*a*(a*b^4 + b^5*x^2)) + (atan((b^(1/2)*x*(a*d - b*c)^3*(7*a*d + b*c))/(a^(1/2)*(b^4*c^4 - 7*a^4*d^4 - 18*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d + 20*a^3*b*c*d^3)))*(a*d - b*c)^3*(7*a*d + b*c))/(2*a^(3/2)*b^(9/2))","B"
29,1,182,106,0.102140,"\text{Not used}","int((c + d*x^2)^3/(a + b*x^2)^2,x)","\frac{d^3\,x^3}{3\,b^2}-x\,\left(\frac{2\,a\,d^3}{b^3}-\frac{3\,c\,d^2}{b^2}\right)-\frac{x\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{2\,a\,\left(b^4\,x^2+a\,b^3\right)}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+b\,c\right)}{\sqrt{a}\,\left(5\,a^3\,d^3-9\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d+b^3\,c^3\right)}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+b\,c\right)}{2\,a^{3/2}\,b^{7/2}}","Not used",1,"(d^3*x^3)/(3*b^2) - x*((2*a*d^3)/b^3 - (3*c*d^2)/b^2) - (x*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(2*a*(a*b^3 + b^4*x^2)) + (atan((b^(1/2)*x*(a*d - b*c)^2*(5*a*d + b*c))/(a^(1/2)*(5*a^3*d^3 + b^3*c^3 + 3*a*b^2*c^2*d - 9*a^2*b*c*d^2)))*(a*d - b*c)^2*(5*a*d + b*c))/(2*a^(3/2)*b^(7/2))","B"
30,1,124,82,5.062166,"\text{Not used}","int((c + d*x^2)^2/(a + b*x^2)^2,x)","\frac{d^2\,x}{b^2}+\frac{x\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{2\,a\,\left(b^3\,x^2+a\,b^2\right)}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+b\,c\right)}{\sqrt{a}\,\left(-3\,a^2\,d^2+2\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+b\,c\right)}{2\,a^{3/2}\,b^{5/2}}","Not used",1,"(d^2*x)/b^2 + (x*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*a*(a*b^2 + b^3*x^2)) + (atan((b^(1/2)*x*(a*d - b*c)*(3*a*d + b*c))/(a^(1/2)*(b^2*c^2 - 3*a^2*d^2 + 2*a*b*c*d)))*(a*d - b*c)*(3*a*d + b*c))/(2*a^(3/2)*b^(5/2))","B"
31,1,51,63,5.041652,"\text{Not used}","int((c + d*x^2)/(a + b*x^2)^2,x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(a\,d+b\,c\right)}{2\,a^{3/2}\,b^{3/2}}-\frac{x\,\left(a\,d-b\,c\right)}{2\,a\,b\,\left(b\,x^2+a\right)}","Not used",1,"(atan((b^(1/2)*x)/a^(1/2))*(a*d + b*c))/(2*a^(3/2)*b^(3/2)) - (x*(a*d - b*c))/(2*a*b*(a + b*x^2))","B"
32,1,3649,108,5.766254,"\text{Not used}","int(1/((a + b*x^2)^2*(c + d*x^2)),x)","-\frac{b\,x}{2\,a\,\left(b\,x^2+a\right)\,\left(a\,d-b\,c\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c\,d^3}\,\left(\frac{\left(\frac{4\,a^6\,b^2\,d^7-18\,a^5\,b^3\,c\,d^6+32\,a^4\,b^4\,c^2\,d^5-28\,a^3\,b^5\,c^3\,d^4+12\,a^2\,b^6\,c^4\,d^3-2\,a\,b^7\,c^5\,d^2}{2\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}-\frac{x\,\sqrt{-c\,d^3}\,\left(16\,a^7\,b^2\,d^7-48\,a^6\,b^3\,c\,d^6+32\,a^5\,b^4\,c^2\,d^5+32\,a^4\,b^5\,c^3\,d^4-48\,a^3\,b^6\,c^4\,d^3+16\,a^2\,b^7\,c^5\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}\right)\,\sqrt{-c\,d^3}}{2\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}-\frac{x\,\left(13\,a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+b^5\,c^2\,d^3\right)}{4\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}\right)\,1{}\mathrm{i}}{a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3}-\frac{\sqrt{-c\,d^3}\,\left(\frac{\left(\frac{4\,a^6\,b^2\,d^7-18\,a^5\,b^3\,c\,d^6+32\,a^4\,b^4\,c^2\,d^5-28\,a^3\,b^5\,c^3\,d^4+12\,a^2\,b^6\,c^4\,d^3-2\,a\,b^7\,c^5\,d^2}{2\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}+\frac{x\,\sqrt{-c\,d^3}\,\left(16\,a^7\,b^2\,d^7-48\,a^6\,b^3\,c\,d^6+32\,a^5\,b^4\,c^2\,d^5+32\,a^4\,b^5\,c^3\,d^4-48\,a^3\,b^6\,c^4\,d^3+16\,a^2\,b^7\,c^5\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}\right)\,\sqrt{-c\,d^3}}{2\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}+\frac{x\,\left(13\,a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+b^5\,c^2\,d^3\right)}{4\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}\right)\,1{}\mathrm{i}}{a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3}}{\frac{\frac{3\,a\,b^3\,d^5}{2}-\frac{b^4\,c\,d^4}{2}}{a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3}+\frac{\sqrt{-c\,d^3}\,\left(\frac{\left(\frac{4\,a^6\,b^2\,d^7-18\,a^5\,b^3\,c\,d^6+32\,a^4\,b^4\,c^2\,d^5-28\,a^3\,b^5\,c^3\,d^4+12\,a^2\,b^6\,c^4\,d^3-2\,a\,b^7\,c^5\,d^2}{2\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}-\frac{x\,\sqrt{-c\,d^3}\,\left(16\,a^7\,b^2\,d^7-48\,a^6\,b^3\,c\,d^6+32\,a^5\,b^4\,c^2\,d^5+32\,a^4\,b^5\,c^3\,d^4-48\,a^3\,b^6\,c^4\,d^3+16\,a^2\,b^7\,c^5\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}\right)\,\sqrt{-c\,d^3}}{2\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}-\frac{x\,\left(13\,a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+b^5\,c^2\,d^3\right)}{4\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}\right)}{a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3}+\frac{\sqrt{-c\,d^3}\,\left(\frac{\left(\frac{4\,a^6\,b^2\,d^7-18\,a^5\,b^3\,c\,d^6+32\,a^4\,b^4\,c^2\,d^5-28\,a^3\,b^5\,c^3\,d^4+12\,a^2\,b^6\,c^4\,d^3-2\,a\,b^7\,c^5\,d^2}{2\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}+\frac{x\,\sqrt{-c\,d^3}\,\left(16\,a^7\,b^2\,d^7-48\,a^6\,b^3\,c\,d^6+32\,a^5\,b^4\,c^2\,d^5+32\,a^4\,b^5\,c^3\,d^4-48\,a^3\,b^6\,c^4\,d^3+16\,a^2\,b^7\,c^5\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}\right)\,\sqrt{-c\,d^3}}{2\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}+\frac{x\,\left(13\,a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+b^5\,c^2\,d^3\right)}{4\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}\right)}{a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3}}\right)\,\sqrt{-c\,d^3}\,1{}\mathrm{i}}{a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,\left(\frac{x\,\left(13\,a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+b^5\,c^2\,d^3\right)}{2\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}-\frac{\left(\frac{4\,a^6\,b^2\,d^7-18\,a^5\,b^3\,c\,d^6+32\,a^4\,b^4\,c^2\,d^5-28\,a^3\,b^5\,c^3\,d^4+12\,a^2\,b^6\,c^4\,d^3-2\,a\,b^7\,c^5\,d^2}{a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3}-\frac{x\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,\left(16\,a^7\,b^2\,d^7-48\,a^6\,b^3\,c\,d^6+32\,a^5\,b^4\,c^2\,d^5+32\,a^4\,b^5\,c^3\,d^4-48\,a^3\,b^6\,c^4\,d^3+16\,a^2\,b^7\,c^5\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}\right)\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}+\frac{\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,\left(\frac{x\,\left(13\,a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+b^5\,c^2\,d^3\right)}{2\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}+\frac{\left(\frac{4\,a^6\,b^2\,d^7-18\,a^5\,b^3\,c\,d^6+32\,a^4\,b^4\,c^2\,d^5-28\,a^3\,b^5\,c^3\,d^4+12\,a^2\,b^6\,c^4\,d^3-2\,a\,b^7\,c^5\,d^2}{a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3}+\frac{x\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,\left(16\,a^7\,b^2\,d^7-48\,a^6\,b^3\,c\,d^6+32\,a^5\,b^4\,c^2\,d^5+32\,a^4\,b^5\,c^3\,d^4-48\,a^3\,b^6\,c^4\,d^3+16\,a^2\,b^7\,c^5\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}\right)\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}}{\frac{\frac{3\,a\,b^3\,d^5}{2}-\frac{b^4\,c\,d^4}{2}}{a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3}-\frac{\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,\left(\frac{x\,\left(13\,a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+b^5\,c^2\,d^3\right)}{2\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}-\frac{\left(\frac{4\,a^6\,b^2\,d^7-18\,a^5\,b^3\,c\,d^6+32\,a^4\,b^4\,c^2\,d^5-28\,a^3\,b^5\,c^3\,d^4+12\,a^2\,b^6\,c^4\,d^3-2\,a\,b^7\,c^5\,d^2}{a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3}-\frac{x\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,\left(16\,a^7\,b^2\,d^7-48\,a^6\,b^3\,c\,d^6+32\,a^5\,b^4\,c^2\,d^5+32\,a^4\,b^5\,c^3\,d^4-48\,a^3\,b^6\,c^4\,d^3+16\,a^2\,b^7\,c^5\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}\right)\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}\right)}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}+\frac{\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,\left(\frac{x\,\left(13\,a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+b^5\,c^2\,d^3\right)}{2\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}+\frac{\left(\frac{4\,a^6\,b^2\,d^7-18\,a^5\,b^3\,c\,d^6+32\,a^4\,b^4\,c^2\,d^5-28\,a^3\,b^5\,c^3\,d^4+12\,a^2\,b^6\,c^4\,d^3-2\,a\,b^7\,c^5\,d^2}{a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3}+\frac{x\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,\left(16\,a^7\,b^2\,d^7-48\,a^6\,b^3\,c\,d^6+32\,a^5\,b^4\,c^2\,d^5+32\,a^4\,b^5\,c^3\,d^4-48\,a^3\,b^6\,c^4\,d^3+16\,a^2\,b^7\,c^5\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}\right)\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}\right)}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}}\right)\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}","Not used",1,"(atan((((-a^3*b)^(1/2)*(3*a*d - b*c)*((x*(13*a^2*b^3*d^5 + b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(2*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) - (((4*a^6*b^2*d^7 - 2*a*b^7*c^5*d^2 - 18*a^5*b^3*c*d^6 + 12*a^2*b^6*c^4*d^3 - 28*a^3*b^5*c^3*d^4 + 32*a^4*b^4*c^2*d^5)/(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2) - (x*(-a^3*b)^(1/2)*(3*a*d - b*c)*(16*a^7*b^2*d^7 - 48*a^6*b^3*c*d^6 + 16*a^2*b^7*c^5*d^2 - 48*a^3*b^6*c^4*d^3 + 32*a^4*b^5*c^3*d^4 + 32*a^5*b^4*c^2*d^5))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)))*(-a^3*b)^(1/2)*(3*a*d - b*c))/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)))*1i)/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) + ((-a^3*b)^(1/2)*(3*a*d - b*c)*((x*(13*a^2*b^3*d^5 + b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(2*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) + (((4*a^6*b^2*d^7 - 2*a*b^7*c^5*d^2 - 18*a^5*b^3*c*d^6 + 12*a^2*b^6*c^4*d^3 - 28*a^3*b^5*c^3*d^4 + 32*a^4*b^4*c^2*d^5)/(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2) + (x*(-a^3*b)^(1/2)*(3*a*d - b*c)*(16*a^7*b^2*d^7 - 48*a^6*b^3*c*d^6 + 16*a^2*b^7*c^5*d^2 - 48*a^3*b^6*c^4*d^3 + 32*a^4*b^5*c^3*d^4 + 32*a^5*b^4*c^2*d^5))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)))*(-a^3*b)^(1/2)*(3*a*d - b*c))/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)))*1i)/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)))/(((3*a*b^3*d^5)/2 - (b^4*c*d^4)/2)/(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2) - ((-a^3*b)^(1/2)*(3*a*d - b*c)*((x*(13*a^2*b^3*d^5 + b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(2*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) - (((4*a^6*b^2*d^7 - 2*a*b^7*c^5*d^2 - 18*a^5*b^3*c*d^6 + 12*a^2*b^6*c^4*d^3 - 28*a^3*b^5*c^3*d^4 + 32*a^4*b^4*c^2*d^5)/(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2) - (x*(-a^3*b)^(1/2)*(3*a*d - b*c)*(16*a^7*b^2*d^7 - 48*a^6*b^3*c*d^6 + 16*a^2*b^7*c^5*d^2 - 48*a^3*b^6*c^4*d^3 + 32*a^4*b^5*c^3*d^4 + 32*a^5*b^4*c^2*d^5))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)))*(-a^3*b)^(1/2)*(3*a*d - b*c))/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d))))/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) + ((-a^3*b)^(1/2)*(3*a*d - b*c)*((x*(13*a^2*b^3*d^5 + b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(2*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) + (((4*a^6*b^2*d^7 - 2*a*b^7*c^5*d^2 - 18*a^5*b^3*c*d^6 + 12*a^2*b^6*c^4*d^3 - 28*a^3*b^5*c^3*d^4 + 32*a^4*b^4*c^2*d^5)/(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2) + (x*(-a^3*b)^(1/2)*(3*a*d - b*c)*(16*a^7*b^2*d^7 - 48*a^6*b^3*c*d^6 + 16*a^2*b^7*c^5*d^2 - 48*a^3*b^6*c^4*d^3 + 32*a^4*b^5*c^3*d^4 + 32*a^5*b^4*c^2*d^5))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)))*(-a^3*b)^(1/2)*(3*a*d - b*c))/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d))))/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d))))*(-a^3*b)^(1/2)*(3*a*d - b*c)*1i)/(2*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) - (atan((((-c*d^3)^(1/2)*((((4*a^6*b^2*d^7 - 2*a*b^7*c^5*d^2 - 18*a^5*b^3*c*d^6 + 12*a^2*b^6*c^4*d^3 - 28*a^3*b^5*c^3*d^4 + 32*a^4*b^4*c^2*d^5)/(2*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)) - (x*(-c*d^3)^(1/2)*(16*a^7*b^2*d^7 - 48*a^6*b^3*c*d^6 + 16*a^2*b^7*c^5*d^2 - 48*a^3*b^6*c^4*d^3 + 32*a^4*b^5*c^3*d^4 + 32*a^5*b^4*c^2*d^5))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)))*(-c*d^3)^(1/2))/(2*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)) - (x*(13*a^2*b^3*d^5 + b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(4*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))*1i)/(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d) - ((-c*d^3)^(1/2)*((((4*a^6*b^2*d^7 - 2*a*b^7*c^5*d^2 - 18*a^5*b^3*c*d^6 + 12*a^2*b^6*c^4*d^3 - 28*a^3*b^5*c^3*d^4 + 32*a^4*b^4*c^2*d^5)/(2*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)) + (x*(-c*d^3)^(1/2)*(16*a^7*b^2*d^7 - 48*a^6*b^3*c*d^6 + 16*a^2*b^7*c^5*d^2 - 48*a^3*b^6*c^4*d^3 + 32*a^4*b^5*c^3*d^4 + 32*a^5*b^4*c^2*d^5))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)))*(-c*d^3)^(1/2))/(2*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)) + (x*(13*a^2*b^3*d^5 + b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(4*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))*1i)/(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d))/(((3*a*b^3*d^5)/2 - (b^4*c*d^4)/2)/(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2) + ((-c*d^3)^(1/2)*((((4*a^6*b^2*d^7 - 2*a*b^7*c^5*d^2 - 18*a^5*b^3*c*d^6 + 12*a^2*b^6*c^4*d^3 - 28*a^3*b^5*c^3*d^4 + 32*a^4*b^4*c^2*d^5)/(2*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)) - (x*(-c*d^3)^(1/2)*(16*a^7*b^2*d^7 - 48*a^6*b^3*c*d^6 + 16*a^2*b^7*c^5*d^2 - 48*a^3*b^6*c^4*d^3 + 32*a^4*b^5*c^3*d^4 + 32*a^5*b^4*c^2*d^5))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)))*(-c*d^3)^(1/2))/(2*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)) - (x*(13*a^2*b^3*d^5 + b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(4*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d))))/(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d) + ((-c*d^3)^(1/2)*((((4*a^6*b^2*d^7 - 2*a*b^7*c^5*d^2 - 18*a^5*b^3*c*d^6 + 12*a^2*b^6*c^4*d^3 - 28*a^3*b^5*c^3*d^4 + 32*a^4*b^4*c^2*d^5)/(2*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)) + (x*(-c*d^3)^(1/2)*(16*a^7*b^2*d^7 - 48*a^6*b^3*c*d^6 + 16*a^2*b^7*c^5*d^2 - 48*a^3*b^6*c^4*d^3 + 32*a^4*b^5*c^3*d^4 + 32*a^5*b^4*c^2*d^5))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)))*(-c*d^3)^(1/2))/(2*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)) + (x*(13*a^2*b^3*d^5 + b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(4*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d))))/(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)))*(-c*d^3)^(1/2)*1i)/(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d) - (b*x)/(2*a*(a + b*x^2)*(a*d - b*c))","B"
33,1,6183,167,6.874575,"\text{Not used}","int(1/((a + b*x^2)^2*(c + d*x^2)^2),x)","\frac{\frac{x\,\left(a^2\,d^2+b^2\,c^2\right)}{2\,a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{b\,d\,x^3\,\left(a\,d+b\,c\right)}{2\,a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{b\,d\,x^4+\left(a\,d+b\,c\right)\,x^2+a\,c}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-10\,a^3\,b^4\,c\,d^6+50\,a^2\,b^5\,c^2\,d^5-10\,a\,b^6\,c^3\,d^4+b^7\,c^4\,d^3\right)}{2\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}-\frac{\left(\frac{2\,a^9\,b^2\,c\,d^{10}-20\,a^8\,b^3\,c^2\,d^9+80\,a^7\,b^4\,c^3\,d^8-172\,a^6\,b^5\,c^4\,d^7+220\,a^5\,b^6\,c^5\,d^6-172\,a^4\,b^7\,c^6\,d^5+80\,a^3\,b^8\,c^7\,d^4-20\,a^2\,b^9\,c^8\,d^3+2\,a\,b^{10}\,c^9\,d^2}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}-\frac{x\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}\,\left(16\,a^9\,b^2\,c^2\,d^9-80\,a^8\,b^3\,c^3\,d^8+144\,a^7\,b^4\,c^4\,d^7-80\,a^6\,b^5\,c^5\,d^6-80\,a^5\,b^6\,c^6\,d^5+144\,a^4\,b^7\,c^7\,d^4-80\,a^3\,b^8\,c^8\,d^3+16\,a^2\,b^9\,c^9\,d^2\right)}{8\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}\,1{}\mathrm{i}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}+\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-10\,a^3\,b^4\,c\,d^6+50\,a^2\,b^5\,c^2\,d^5-10\,a\,b^6\,c^3\,d^4+b^7\,c^4\,d^3\right)}{2\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}+\frac{\left(\frac{2\,a^9\,b^2\,c\,d^{10}-20\,a^8\,b^3\,c^2\,d^9+80\,a^7\,b^4\,c^3\,d^8-172\,a^6\,b^5\,c^4\,d^7+220\,a^5\,b^6\,c^5\,d^6-172\,a^4\,b^7\,c^6\,d^5+80\,a^3\,b^8\,c^7\,d^4-20\,a^2\,b^9\,c^8\,d^3+2\,a\,b^{10}\,c^9\,d^2}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}+\frac{x\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}\,\left(16\,a^9\,b^2\,c^2\,d^9-80\,a^8\,b^3\,c^3\,d^8+144\,a^7\,b^4\,c^4\,d^7-80\,a^6\,b^5\,c^5\,d^6-80\,a^5\,b^6\,c^6\,d^5+144\,a^4\,b^7\,c^7\,d^4-80\,a^3\,b^8\,c^8\,d^3+16\,a^2\,b^9\,c^9\,d^2\right)}{8\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}\,1{}\mathrm{i}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}}{\frac{\frac{5\,a^3\,b^4\,d^7}{4}-\frac{21\,a^2\,b^5\,c\,d^6}{4}-\frac{21\,a\,b^6\,c^2\,d^5}{4}+\frac{5\,b^7\,c^3\,d^4}{4}}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}-\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-10\,a^3\,b^4\,c\,d^6+50\,a^2\,b^5\,c^2\,d^5-10\,a\,b^6\,c^3\,d^4+b^7\,c^4\,d^3\right)}{2\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}-\frac{\left(\frac{2\,a^9\,b^2\,c\,d^{10}-20\,a^8\,b^3\,c^2\,d^9+80\,a^7\,b^4\,c^3\,d^8-172\,a^6\,b^5\,c^4\,d^7+220\,a^5\,b^6\,c^5\,d^6-172\,a^4\,b^7\,c^6\,d^5+80\,a^3\,b^8\,c^7\,d^4-20\,a^2\,b^9\,c^8\,d^3+2\,a\,b^{10}\,c^9\,d^2}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}-\frac{x\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}\,\left(16\,a^9\,b^2\,c^2\,d^9-80\,a^8\,b^3\,c^3\,d^8+144\,a^7\,b^4\,c^4\,d^7-80\,a^6\,b^5\,c^5\,d^6-80\,a^5\,b^6\,c^6\,d^5+144\,a^4\,b^7\,c^7\,d^4-80\,a^3\,b^8\,c^8\,d^3+16\,a^2\,b^9\,c^9\,d^2\right)}{8\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}+\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-10\,a^3\,b^4\,c\,d^6+50\,a^2\,b^5\,c^2\,d^5-10\,a\,b^6\,c^3\,d^4+b^7\,c^4\,d^3\right)}{2\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}+\frac{\left(\frac{2\,a^9\,b^2\,c\,d^{10}-20\,a^8\,b^3\,c^2\,d^9+80\,a^7\,b^4\,c^3\,d^8-172\,a^6\,b^5\,c^4\,d^7+220\,a^5\,b^6\,c^5\,d^6-172\,a^4\,b^7\,c^6\,d^5+80\,a^3\,b^8\,c^7\,d^4-20\,a^2\,b^9\,c^8\,d^3+2\,a\,b^{10}\,c^9\,d^2}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}+\frac{x\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}\,\left(16\,a^9\,b^2\,c^2\,d^9-80\,a^8\,b^3\,c^3\,d^8+144\,a^7\,b^4\,c^4\,d^7-80\,a^6\,b^5\,c^5\,d^6-80\,a^5\,b^6\,c^6\,d^5+144\,a^4\,b^7\,c^7\,d^4-80\,a^3\,b^8\,c^8\,d^3+16\,a^2\,b^9\,c^9\,d^2\right)}{8\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}\,1{}\mathrm{i}}{2\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-10\,a^3\,b^4\,c\,d^6+50\,a^2\,b^5\,c^2\,d^5-10\,a\,b^6\,c^3\,d^4+b^7\,c^4\,d^3\right)}{2\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}-\frac{\left(\frac{2\,a^9\,b^2\,c\,d^{10}-20\,a^8\,b^3\,c^2\,d^9+80\,a^7\,b^4\,c^3\,d^8-172\,a^6\,b^5\,c^4\,d^7+220\,a^5\,b^6\,c^5\,d^6-172\,a^4\,b^7\,c^6\,d^5+80\,a^3\,b^8\,c^7\,d^4-20\,a^2\,b^9\,c^8\,d^3+2\,a\,b^{10}\,c^9\,d^2}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}-\frac{x\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}\,\left(16\,a^9\,b^2\,c^2\,d^9-80\,a^8\,b^3\,c^3\,d^8+144\,a^7\,b^4\,c^4\,d^7-80\,a^6\,b^5\,c^5\,d^6-80\,a^5\,b^6\,c^6\,d^5+144\,a^4\,b^7\,c^7\,d^4-80\,a^3\,b^8\,c^8\,d^3+16\,a^2\,b^9\,c^9\,d^2\right)}{8\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}\right)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}}{4\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}\right)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}\,1{}\mathrm{i}}{4\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}+\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-10\,a^3\,b^4\,c\,d^6+50\,a^2\,b^5\,c^2\,d^5-10\,a\,b^6\,c^3\,d^4+b^7\,c^4\,d^3\right)}{2\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}+\frac{\left(\frac{2\,a^9\,b^2\,c\,d^{10}-20\,a^8\,b^3\,c^2\,d^9+80\,a^7\,b^4\,c^3\,d^8-172\,a^6\,b^5\,c^4\,d^7+220\,a^5\,b^6\,c^5\,d^6-172\,a^4\,b^7\,c^6\,d^5+80\,a^3\,b^8\,c^7\,d^4-20\,a^2\,b^9\,c^8\,d^3+2\,a\,b^{10}\,c^9\,d^2}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}+\frac{x\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}\,\left(16\,a^9\,b^2\,c^2\,d^9-80\,a^8\,b^3\,c^3\,d^8+144\,a^7\,b^4\,c^4\,d^7-80\,a^6\,b^5\,c^5\,d^6-80\,a^5\,b^6\,c^6\,d^5+144\,a^4\,b^7\,c^7\,d^4-80\,a^3\,b^8\,c^8\,d^3+16\,a^2\,b^9\,c^9\,d^2\right)}{8\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}\right)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}}{4\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}\right)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}\,1{}\mathrm{i}}{4\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}}{\frac{\frac{5\,a^3\,b^4\,d^7}{4}-\frac{21\,a^2\,b^5\,c\,d^6}{4}-\frac{21\,a\,b^6\,c^2\,d^5}{4}+\frac{5\,b^7\,c^3\,d^4}{4}}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}-\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-10\,a^3\,b^4\,c\,d^6+50\,a^2\,b^5\,c^2\,d^5-10\,a\,b^6\,c^3\,d^4+b^7\,c^4\,d^3\right)}{2\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}-\frac{\left(\frac{2\,a^9\,b^2\,c\,d^{10}-20\,a^8\,b^3\,c^2\,d^9+80\,a^7\,b^4\,c^3\,d^8-172\,a^6\,b^5\,c^4\,d^7+220\,a^5\,b^6\,c^5\,d^6-172\,a^4\,b^7\,c^6\,d^5+80\,a^3\,b^8\,c^7\,d^4-20\,a^2\,b^9\,c^8\,d^3+2\,a\,b^{10}\,c^9\,d^2}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}-\frac{x\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}\,\left(16\,a^9\,b^2\,c^2\,d^9-80\,a^8\,b^3\,c^3\,d^8+144\,a^7\,b^4\,c^4\,d^7-80\,a^6\,b^5\,c^5\,d^6-80\,a^5\,b^6\,c^6\,d^5+144\,a^4\,b^7\,c^7\,d^4-80\,a^3\,b^8\,c^8\,d^3+16\,a^2\,b^9\,c^9\,d^2\right)}{8\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}\right)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}}{4\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}\right)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}}{4\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}+\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-10\,a^3\,b^4\,c\,d^6+50\,a^2\,b^5\,c^2\,d^5-10\,a\,b^6\,c^3\,d^4+b^7\,c^4\,d^3\right)}{2\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}+\frac{\left(\frac{2\,a^9\,b^2\,c\,d^{10}-20\,a^8\,b^3\,c^2\,d^9+80\,a^7\,b^4\,c^3\,d^8-172\,a^6\,b^5\,c^4\,d^7+220\,a^5\,b^6\,c^5\,d^6-172\,a^4\,b^7\,c^6\,d^5+80\,a^3\,b^8\,c^7\,d^4-20\,a^2\,b^9\,c^8\,d^3+2\,a\,b^{10}\,c^9\,d^2}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}+\frac{x\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}\,\left(16\,a^9\,b^2\,c^2\,d^9-80\,a^8\,b^3\,c^3\,d^8+144\,a^7\,b^4\,c^4\,d^7-80\,a^6\,b^5\,c^5\,d^6-80\,a^5\,b^6\,c^6\,d^5+144\,a^4\,b^7\,c^7\,d^4-80\,a^3\,b^8\,c^8\,d^3+16\,a^2\,b^9\,c^9\,d^2\right)}{8\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}\right)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}}{4\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}\right)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}}{4\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}}\right)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}\,1{}\mathrm{i}}{2\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}","Not used",1,"((x*(a^2*d^2 + b^2*c^2))/(2*a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*d*x^3*(a*d + b*c))/(2*a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(a*c + x^2*(a*d + b*c) + b*d*x^4) + (atan(((((x*(a^4*b^3*d^7 + b^7*c^4*d^3 - 10*a*b^6*c^3*d^4 - 10*a^3*b^4*c*d^6 + 50*a^2*b^5*c^2*d^5))/(2*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)) - (((2*a*b^10*c^9*d^2 + 2*a^9*b^2*c*d^10 - 20*a^2*b^9*c^8*d^3 + 80*a^3*b^8*c^7*d^4 - 172*a^4*b^7*c^6*d^5 + 220*a^5*b^6*c^5*d^6 - 172*a^6*b^5*c^4*d^7 + 80*a^7*b^4*c^3*d^8 - 20*a^8*b^3*c^2*d^9)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) - (x*(5*a*d - b*c)*(-a^3*b^3)^(1/2)*(16*a^2*b^9*c^9*d^2 - 80*a^3*b^8*c^8*d^3 + 144*a^4*b^7*c^7*d^4 - 80*a^5*b^6*c^6*d^5 - 80*a^6*b^5*c^5*d^6 + 144*a^7*b^4*c^4*d^7 - 80*a^8*b^3*c^3*d^8 + 16*a^9*b^2*c^2*d^9))/(8*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)))*(5*a*d - b*c)*(-a^3*b^3)^(1/2))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)))*(5*a*d - b*c)*(-a^3*b^3)^(1/2)*1i)/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)) + (((x*(a^4*b^3*d^7 + b^7*c^4*d^3 - 10*a*b^6*c^3*d^4 - 10*a^3*b^4*c*d^6 + 50*a^2*b^5*c^2*d^5))/(2*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)) + (((2*a*b^10*c^9*d^2 + 2*a^9*b^2*c*d^10 - 20*a^2*b^9*c^8*d^3 + 80*a^3*b^8*c^7*d^4 - 172*a^4*b^7*c^6*d^5 + 220*a^5*b^6*c^5*d^6 - 172*a^6*b^5*c^4*d^7 + 80*a^7*b^4*c^3*d^8 - 20*a^8*b^3*c^2*d^9)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) + (x*(5*a*d - b*c)*(-a^3*b^3)^(1/2)*(16*a^2*b^9*c^9*d^2 - 80*a^3*b^8*c^8*d^3 + 144*a^4*b^7*c^7*d^4 - 80*a^5*b^6*c^6*d^5 - 80*a^6*b^5*c^5*d^6 + 144*a^7*b^4*c^4*d^7 - 80*a^8*b^3*c^3*d^8 + 16*a^9*b^2*c^2*d^9))/(8*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)))*(5*a*d - b*c)*(-a^3*b^3)^(1/2))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)))*(5*a*d - b*c)*(-a^3*b^3)^(1/2)*1i)/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)))/(((5*a^3*b^4*d^7)/4 + (5*b^7*c^3*d^4)/4 - (21*a*b^6*c^2*d^5)/4 - (21*a^2*b^5*c*d^6)/4)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) - (((x*(a^4*b^3*d^7 + b^7*c^4*d^3 - 10*a*b^6*c^3*d^4 - 10*a^3*b^4*c*d^6 + 50*a^2*b^5*c^2*d^5))/(2*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)) - (((2*a*b^10*c^9*d^2 + 2*a^9*b^2*c*d^10 - 20*a^2*b^9*c^8*d^3 + 80*a^3*b^8*c^7*d^4 - 172*a^4*b^7*c^6*d^5 + 220*a^5*b^6*c^5*d^6 - 172*a^6*b^5*c^4*d^7 + 80*a^7*b^4*c^3*d^8 - 20*a^8*b^3*c^2*d^9)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) - (x*(5*a*d - b*c)*(-a^3*b^3)^(1/2)*(16*a^2*b^9*c^9*d^2 - 80*a^3*b^8*c^8*d^3 + 144*a^4*b^7*c^7*d^4 - 80*a^5*b^6*c^6*d^5 - 80*a^6*b^5*c^5*d^6 + 144*a^7*b^4*c^4*d^7 - 80*a^8*b^3*c^3*d^8 + 16*a^9*b^2*c^2*d^9))/(8*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)))*(5*a*d - b*c)*(-a^3*b^3)^(1/2))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)))*(5*a*d - b*c)*(-a^3*b^3)^(1/2))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)) + (((x*(a^4*b^3*d^7 + b^7*c^4*d^3 - 10*a*b^6*c^3*d^4 - 10*a^3*b^4*c*d^6 + 50*a^2*b^5*c^2*d^5))/(2*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)) + (((2*a*b^10*c^9*d^2 + 2*a^9*b^2*c*d^10 - 20*a^2*b^9*c^8*d^3 + 80*a^3*b^8*c^7*d^4 - 172*a^4*b^7*c^6*d^5 + 220*a^5*b^6*c^5*d^6 - 172*a^6*b^5*c^4*d^7 + 80*a^7*b^4*c^3*d^8 - 20*a^8*b^3*c^2*d^9)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) + (x*(5*a*d - b*c)*(-a^3*b^3)^(1/2)*(16*a^2*b^9*c^9*d^2 - 80*a^3*b^8*c^8*d^3 + 144*a^4*b^7*c^7*d^4 - 80*a^5*b^6*c^6*d^5 - 80*a^6*b^5*c^5*d^6 + 144*a^7*b^4*c^4*d^7 - 80*a^8*b^3*c^3*d^8 + 16*a^9*b^2*c^2*d^9))/(8*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)))*(5*a*d - b*c)*(-a^3*b^3)^(1/2))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)))*(5*a*d - b*c)*(-a^3*b^3)^(1/2))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2))))*(5*a*d - b*c)*(-a^3*b^3)^(1/2)*1i)/(2*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)) + (atan(((((x*(a^4*b^3*d^7 + b^7*c^4*d^3 - 10*a*b^6*c^3*d^4 - 10*a^3*b^4*c*d^6 + 50*a^2*b^5*c^2*d^5))/(2*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)) - (((2*a*b^10*c^9*d^2 + 2*a^9*b^2*c*d^10 - 20*a^2*b^9*c^8*d^3 + 80*a^3*b^8*c^7*d^4 - 172*a^4*b^7*c^6*d^5 + 220*a^5*b^6*c^5*d^6 - 172*a^6*b^5*c^4*d^7 + 80*a^7*b^4*c^3*d^8 - 20*a^8*b^3*c^2*d^9)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) - (x*(a*d - 5*b*c)*(-c^3*d^3)^(1/2)*(16*a^2*b^9*c^9*d^2 - 80*a^3*b^8*c^8*d^3 + 144*a^4*b^7*c^7*d^4 - 80*a^5*b^6*c^6*d^5 - 80*a^6*b^5*c^5*d^6 + 144*a^7*b^4*c^4*d^7 - 80*a^8*b^3*c^3*d^8 + 16*a^9*b^2*c^2*d^9))/(8*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2))/(4*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2)*1i)/(4*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)) + (((x*(a^4*b^3*d^7 + b^7*c^4*d^3 - 10*a*b^6*c^3*d^4 - 10*a^3*b^4*c*d^6 + 50*a^2*b^5*c^2*d^5))/(2*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)) + (((2*a*b^10*c^9*d^2 + 2*a^9*b^2*c*d^10 - 20*a^2*b^9*c^8*d^3 + 80*a^3*b^8*c^7*d^4 - 172*a^4*b^7*c^6*d^5 + 220*a^5*b^6*c^5*d^6 - 172*a^6*b^5*c^4*d^7 + 80*a^7*b^4*c^3*d^8 - 20*a^8*b^3*c^2*d^9)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) + (x*(a*d - 5*b*c)*(-c^3*d^3)^(1/2)*(16*a^2*b^9*c^9*d^2 - 80*a^3*b^8*c^8*d^3 + 144*a^4*b^7*c^7*d^4 - 80*a^5*b^6*c^6*d^5 - 80*a^6*b^5*c^5*d^6 + 144*a^7*b^4*c^4*d^7 - 80*a^8*b^3*c^3*d^8 + 16*a^9*b^2*c^2*d^9))/(8*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2))/(4*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2)*1i)/(4*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)))/(((5*a^3*b^4*d^7)/4 + (5*b^7*c^3*d^4)/4 - (21*a*b^6*c^2*d^5)/4 - (21*a^2*b^5*c*d^6)/4)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) - (((x*(a^4*b^3*d^7 + b^7*c^4*d^3 - 10*a*b^6*c^3*d^4 - 10*a^3*b^4*c*d^6 + 50*a^2*b^5*c^2*d^5))/(2*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)) - (((2*a*b^10*c^9*d^2 + 2*a^9*b^2*c*d^10 - 20*a^2*b^9*c^8*d^3 + 80*a^3*b^8*c^7*d^4 - 172*a^4*b^7*c^6*d^5 + 220*a^5*b^6*c^5*d^6 - 172*a^6*b^5*c^4*d^7 + 80*a^7*b^4*c^3*d^8 - 20*a^8*b^3*c^2*d^9)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) - (x*(a*d - 5*b*c)*(-c^3*d^3)^(1/2)*(16*a^2*b^9*c^9*d^2 - 80*a^3*b^8*c^8*d^3 + 144*a^4*b^7*c^7*d^4 - 80*a^5*b^6*c^6*d^5 - 80*a^6*b^5*c^5*d^6 + 144*a^7*b^4*c^4*d^7 - 80*a^8*b^3*c^3*d^8 + 16*a^9*b^2*c^2*d^9))/(8*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2))/(4*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2))/(4*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)) + (((x*(a^4*b^3*d^7 + b^7*c^4*d^3 - 10*a*b^6*c^3*d^4 - 10*a^3*b^4*c*d^6 + 50*a^2*b^5*c^2*d^5))/(2*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)) + (((2*a*b^10*c^9*d^2 + 2*a^9*b^2*c*d^10 - 20*a^2*b^9*c^8*d^3 + 80*a^3*b^8*c^7*d^4 - 172*a^4*b^7*c^6*d^5 + 220*a^5*b^6*c^5*d^6 - 172*a^6*b^5*c^4*d^7 + 80*a^7*b^4*c^3*d^8 - 20*a^8*b^3*c^2*d^9)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) + (x*(a*d - 5*b*c)*(-c^3*d^3)^(1/2)*(16*a^2*b^9*c^9*d^2 - 80*a^3*b^8*c^8*d^3 + 144*a^4*b^7*c^7*d^4 - 80*a^5*b^6*c^6*d^5 - 80*a^6*b^5*c^5*d^6 + 144*a^7*b^4*c^4*d^7 - 80*a^8*b^3*c^3*d^8 + 16*a^9*b^2*c^2*d^9))/(8*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2))/(4*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2))/(4*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d))))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2)*1i)/(2*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d))","B"
34,1,8649,230,7.793021,"\text{Not used}","int(1/((a + b*x^2)^2*(c + d*x^2)^3),x)","-\frac{\frac{x^5\,\left(-3\,a^2\,b\,d^4+11\,a\,b^2\,c\,d^3+4\,b^3\,c^2\,d^2\right)}{8\,a\,c^2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{x\,\left(-5\,a^3\,d^3+13\,a^2\,b\,c\,d^2+4\,b^3\,c^3\right)}{8\,a\,c\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{d\,x^3\,\left(-3\,a^3\,d^3+6\,a^2\,b\,c\,d^2+13\,a\,b^2\,c^2\,d+8\,b^3\,c^3\right)}{8\,a\,c^2\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{a\,c^2+x^2\,\left(b\,c^2+2\,a\,d\,c\right)+x^4\,\left(a\,d^2+2\,b\,c\,d\right)+b\,d^2\,x^6}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(9\,a^6\,b^3\,d^9-84\,a^5\,b^4\,c\,d^8+406\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+2009\,a^2\,b^7\,c^4\,d^5-224\,a\,b^8\,c^5\,d^4+16\,b^9\,c^6\,d^3\right)}{32\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}-\frac{\left(\frac{-\frac{3\,a^{12}\,b^2\,c^2\,d^{13}}{2}+\frac{35\,a^{11}\,b^3\,c^3\,d^{12}}{2}-98\,a^{10}\,b^4\,c^4\,d^{11}+336\,a^9\,b^5\,c^5\,d^{10}-765\,a^8\,b^6\,c^6\,d^9+1197\,a^7\,b^7\,c^7\,d^8-1302\,a^6\,b^8\,c^8\,d^7+978\,a^5\,b^9\,c^9\,d^6-\frac{987\,a^4\,b^{10}\,c^{10}\,d^5}{2}+\frac{315\,a^3\,b^{11}\,c^{11}\,d^4}{2}-28\,a^2\,b^{12}\,c^{12}\,d^3+2\,a\,b^{13}\,c^{13}\,d^2}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}-\frac{x\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)\,\left(256\,a^{11}\,b^2\,c^4\,d^{11}-1792\,a^{10}\,b^3\,c^5\,d^{10}+5120\,a^9\,b^4\,c^6\,d^9-7168\,a^8\,b^5\,c^7\,d^8+3584\,a^7\,b^6\,c^8\,d^7+3584\,a^6\,b^7\,c^9\,d^6-7168\,a^5\,b^8\,c^{10}\,d^5+5120\,a^4\,b^9\,c^{11}\,d^4-1792\,a^3\,b^{10}\,c^{12}\,d^3+256\,a^2\,b^{11}\,c^{13}\,d^2\right)}{512\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)}{16\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}+\frac{\left(\frac{x\,\left(9\,a^6\,b^3\,d^9-84\,a^5\,b^4\,c\,d^8+406\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+2009\,a^2\,b^7\,c^4\,d^5-224\,a\,b^8\,c^5\,d^4+16\,b^9\,c^6\,d^3\right)}{32\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}+\frac{\left(\frac{-\frac{3\,a^{12}\,b^2\,c^2\,d^{13}}{2}+\frac{35\,a^{11}\,b^3\,c^3\,d^{12}}{2}-98\,a^{10}\,b^4\,c^4\,d^{11}+336\,a^9\,b^5\,c^5\,d^{10}-765\,a^8\,b^6\,c^6\,d^9+1197\,a^7\,b^7\,c^7\,d^8-1302\,a^6\,b^8\,c^8\,d^7+978\,a^5\,b^9\,c^9\,d^6-\frac{987\,a^4\,b^{10}\,c^{10}\,d^5}{2}+\frac{315\,a^3\,b^{11}\,c^{11}\,d^4}{2}-28\,a^2\,b^{12}\,c^{12}\,d^3+2\,a\,b^{13}\,c^{13}\,d^2}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}+\frac{x\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)\,\left(256\,a^{11}\,b^2\,c^4\,d^{11}-1792\,a^{10}\,b^3\,c^5\,d^{10}+5120\,a^9\,b^4\,c^6\,d^9-7168\,a^8\,b^5\,c^7\,d^8+3584\,a^7\,b^6\,c^8\,d^7+3584\,a^6\,b^7\,c^9\,d^6-7168\,a^5\,b^8\,c^{10}\,d^5+5120\,a^4\,b^9\,c^{11}\,d^4-1792\,a^3\,b^{10}\,c^{12}\,d^3+256\,a^2\,b^{11}\,c^{13}\,d^2\right)}{512\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)}{16\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}}{\frac{\frac{63\,a^5\,b^5\,d^9}{64}-\frac{267\,a^4\,b^6\,c\,d^8}{32}+\frac{451\,a^3\,b^7\,c^2\,d^7}{16}-\frac{1275\,a^2\,b^8\,c^3\,d^6}{32}-\frac{651\,a\,b^9\,c^4\,d^5}{64}+\frac{35\,b^{10}\,c^5\,d^4}{16}}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}-\frac{\left(\frac{x\,\left(9\,a^6\,b^3\,d^9-84\,a^5\,b^4\,c\,d^8+406\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+2009\,a^2\,b^7\,c^4\,d^5-224\,a\,b^8\,c^5\,d^4+16\,b^9\,c^6\,d^3\right)}{32\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}-\frac{\left(\frac{-\frac{3\,a^{12}\,b^2\,c^2\,d^{13}}{2}+\frac{35\,a^{11}\,b^3\,c^3\,d^{12}}{2}-98\,a^{10}\,b^4\,c^4\,d^{11}+336\,a^9\,b^5\,c^5\,d^{10}-765\,a^8\,b^6\,c^6\,d^9+1197\,a^7\,b^7\,c^7\,d^8-1302\,a^6\,b^8\,c^8\,d^7+978\,a^5\,b^9\,c^9\,d^6-\frac{987\,a^4\,b^{10}\,c^{10}\,d^5}{2}+\frac{315\,a^3\,b^{11}\,c^{11}\,d^4}{2}-28\,a^2\,b^{12}\,c^{12}\,d^3+2\,a\,b^{13}\,c^{13}\,d^2}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}-\frac{x\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)\,\left(256\,a^{11}\,b^2\,c^4\,d^{11}-1792\,a^{10}\,b^3\,c^5\,d^{10}+5120\,a^9\,b^4\,c^6\,d^9-7168\,a^8\,b^5\,c^7\,d^8+3584\,a^7\,b^6\,c^8\,d^7+3584\,a^6\,b^7\,c^9\,d^6-7168\,a^5\,b^8\,c^{10}\,d^5+5120\,a^4\,b^9\,c^{11}\,d^4-1792\,a^3\,b^{10}\,c^{12}\,d^3+256\,a^2\,b^{11}\,c^{13}\,d^2\right)}{512\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)}{16\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)}{16\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}+\frac{\left(\frac{x\,\left(9\,a^6\,b^3\,d^9-84\,a^5\,b^4\,c\,d^8+406\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+2009\,a^2\,b^7\,c^4\,d^5-224\,a\,b^8\,c^5\,d^4+16\,b^9\,c^6\,d^3\right)}{32\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}+\frac{\left(\frac{-\frac{3\,a^{12}\,b^2\,c^2\,d^{13}}{2}+\frac{35\,a^{11}\,b^3\,c^3\,d^{12}}{2}-98\,a^{10}\,b^4\,c^4\,d^{11}+336\,a^9\,b^5\,c^5\,d^{10}-765\,a^8\,b^6\,c^6\,d^9+1197\,a^7\,b^7\,c^7\,d^8-1302\,a^6\,b^8\,c^8\,d^7+978\,a^5\,b^9\,c^9\,d^6-\frac{987\,a^4\,b^{10}\,c^{10}\,d^5}{2}+\frac{315\,a^3\,b^{11}\,c^{11}\,d^4}{2}-28\,a^2\,b^{12}\,c^{12}\,d^3+2\,a\,b^{13}\,c^{13}\,d^2}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}+\frac{x\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)\,\left(256\,a^{11}\,b^2\,c^4\,d^{11}-1792\,a^{10}\,b^3\,c^5\,d^{10}+5120\,a^9\,b^4\,c^6\,d^9-7168\,a^8\,b^5\,c^7\,d^8+3584\,a^7\,b^6\,c^8\,d^7+3584\,a^6\,b^7\,c^9\,d^6-7168\,a^5\,b^8\,c^{10}\,d^5+5120\,a^4\,b^9\,c^{11}\,d^4-1792\,a^3\,b^{10}\,c^{12}\,d^3+256\,a^2\,b^{11}\,c^{13}\,d^2\right)}{512\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)}{16\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)}{16\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)\,1{}\mathrm{i}}{8\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(9\,a^6\,b^3\,d^9-84\,a^5\,b^4\,c\,d^8+406\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+2009\,a^2\,b^7\,c^4\,d^5-224\,a\,b^8\,c^5\,d^4+16\,b^9\,c^6\,d^3\right)}{32\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}-\frac{\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,\left(\frac{-\frac{3\,a^{12}\,b^2\,c^2\,d^{13}}{2}+\frac{35\,a^{11}\,b^3\,c^3\,d^{12}}{2}-98\,a^{10}\,b^4\,c^4\,d^{11}+336\,a^9\,b^5\,c^5\,d^{10}-765\,a^8\,b^6\,c^6\,d^9+1197\,a^7\,b^7\,c^7\,d^8-1302\,a^6\,b^8\,c^8\,d^7+978\,a^5\,b^9\,c^9\,d^6-\frac{987\,a^4\,b^{10}\,c^{10}\,d^5}{2}+\frac{315\,a^3\,b^{11}\,c^{11}\,d^4}{2}-28\,a^2\,b^{12}\,c^{12}\,d^3+2\,a\,b^{13}\,c^{13}\,d^2}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}-\frac{x\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,\left(256\,a^{11}\,b^2\,c^4\,d^{11}-1792\,a^{10}\,b^3\,c^5\,d^{10}+5120\,a^9\,b^4\,c^6\,d^9-7168\,a^8\,b^5\,c^7\,d^8+3584\,a^7\,b^6\,c^8\,d^7+3584\,a^6\,b^7\,c^9\,d^6-7168\,a^5\,b^8\,c^{10}\,d^5+5120\,a^4\,b^9\,c^{11}\,d^4-1792\,a^3\,b^{10}\,c^{12}\,d^3+256\,a^2\,b^{11}\,c^{13}\,d^2\right)}{128\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}\right)}{4\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}\right)\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,1{}\mathrm{i}}{4\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}+\frac{\left(\frac{x\,\left(9\,a^6\,b^3\,d^9-84\,a^5\,b^4\,c\,d^8+406\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+2009\,a^2\,b^7\,c^4\,d^5-224\,a\,b^8\,c^5\,d^4+16\,b^9\,c^6\,d^3\right)}{32\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}+\frac{\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,\left(\frac{-\frac{3\,a^{12}\,b^2\,c^2\,d^{13}}{2}+\frac{35\,a^{11}\,b^3\,c^3\,d^{12}}{2}-98\,a^{10}\,b^4\,c^4\,d^{11}+336\,a^9\,b^5\,c^5\,d^{10}-765\,a^8\,b^6\,c^6\,d^9+1197\,a^7\,b^7\,c^7\,d^8-1302\,a^6\,b^8\,c^8\,d^7+978\,a^5\,b^9\,c^9\,d^6-\frac{987\,a^4\,b^{10}\,c^{10}\,d^5}{2}+\frac{315\,a^3\,b^{11}\,c^{11}\,d^4}{2}-28\,a^2\,b^{12}\,c^{12}\,d^3+2\,a\,b^{13}\,c^{13}\,d^2}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}+\frac{x\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,\left(256\,a^{11}\,b^2\,c^4\,d^{11}-1792\,a^{10}\,b^3\,c^5\,d^{10}+5120\,a^9\,b^4\,c^6\,d^9-7168\,a^8\,b^5\,c^7\,d^8+3584\,a^7\,b^6\,c^8\,d^7+3584\,a^6\,b^7\,c^9\,d^6-7168\,a^5\,b^8\,c^{10}\,d^5+5120\,a^4\,b^9\,c^{11}\,d^4-1792\,a^3\,b^{10}\,c^{12}\,d^3+256\,a^2\,b^{11}\,c^{13}\,d^2\right)}{128\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}\right)}{4\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}\right)\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,1{}\mathrm{i}}{4\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}}{\frac{\frac{63\,a^5\,b^5\,d^9}{64}-\frac{267\,a^4\,b^6\,c\,d^8}{32}+\frac{451\,a^3\,b^7\,c^2\,d^7}{16}-\frac{1275\,a^2\,b^8\,c^3\,d^6}{32}-\frac{651\,a\,b^9\,c^4\,d^5}{64}+\frac{35\,b^{10}\,c^5\,d^4}{16}}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}-\frac{\left(\frac{x\,\left(9\,a^6\,b^3\,d^9-84\,a^5\,b^4\,c\,d^8+406\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+2009\,a^2\,b^7\,c^4\,d^5-224\,a\,b^8\,c^5\,d^4+16\,b^9\,c^6\,d^3\right)}{32\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}-\frac{\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,\left(\frac{-\frac{3\,a^{12}\,b^2\,c^2\,d^{13}}{2}+\frac{35\,a^{11}\,b^3\,c^3\,d^{12}}{2}-98\,a^{10}\,b^4\,c^4\,d^{11}+336\,a^9\,b^5\,c^5\,d^{10}-765\,a^8\,b^6\,c^6\,d^9+1197\,a^7\,b^7\,c^7\,d^8-1302\,a^6\,b^8\,c^8\,d^7+978\,a^5\,b^9\,c^9\,d^6-\frac{987\,a^4\,b^{10}\,c^{10}\,d^5}{2}+\frac{315\,a^3\,b^{11}\,c^{11}\,d^4}{2}-28\,a^2\,b^{12}\,c^{12}\,d^3+2\,a\,b^{13}\,c^{13}\,d^2}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}-\frac{x\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,\left(256\,a^{11}\,b^2\,c^4\,d^{11}-1792\,a^{10}\,b^3\,c^5\,d^{10}+5120\,a^9\,b^4\,c^6\,d^9-7168\,a^8\,b^5\,c^7\,d^8+3584\,a^7\,b^6\,c^8\,d^7+3584\,a^6\,b^7\,c^9\,d^6-7168\,a^5\,b^8\,c^{10}\,d^5+5120\,a^4\,b^9\,c^{11}\,d^4-1792\,a^3\,b^{10}\,c^{12}\,d^3+256\,a^2\,b^{11}\,c^{13}\,d^2\right)}{128\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}\right)}{4\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}\right)\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}}{4\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}+\frac{\left(\frac{x\,\left(9\,a^6\,b^3\,d^9-84\,a^5\,b^4\,c\,d^8+406\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+2009\,a^2\,b^7\,c^4\,d^5-224\,a\,b^8\,c^5\,d^4+16\,b^9\,c^6\,d^3\right)}{32\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}+\frac{\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,\left(\frac{-\frac{3\,a^{12}\,b^2\,c^2\,d^{13}}{2}+\frac{35\,a^{11}\,b^3\,c^3\,d^{12}}{2}-98\,a^{10}\,b^4\,c^4\,d^{11}+336\,a^9\,b^5\,c^5\,d^{10}-765\,a^8\,b^6\,c^6\,d^9+1197\,a^7\,b^7\,c^7\,d^8-1302\,a^6\,b^8\,c^8\,d^7+978\,a^5\,b^9\,c^9\,d^6-\frac{987\,a^4\,b^{10}\,c^{10}\,d^5}{2}+\frac{315\,a^3\,b^{11}\,c^{11}\,d^4}{2}-28\,a^2\,b^{12}\,c^{12}\,d^3+2\,a\,b^{13}\,c^{13}\,d^2}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}+\frac{x\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,\left(256\,a^{11}\,b^2\,c^4\,d^{11}-1792\,a^{10}\,b^3\,c^5\,d^{10}+5120\,a^9\,b^4\,c^6\,d^9-7168\,a^8\,b^5\,c^7\,d^8+3584\,a^7\,b^6\,c^8\,d^7+3584\,a^6\,b^7\,c^9\,d^6-7168\,a^5\,b^8\,c^{10}\,d^5+5120\,a^4\,b^9\,c^{11}\,d^4-1792\,a^3\,b^{10}\,c^{12}\,d^3+256\,a^2\,b^{11}\,c^{13}\,d^2\right)}{128\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}\right)}{4\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}\right)\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}}{4\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}}\right)\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,1{}\mathrm{i}}{2\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}","Not used",1,"(atan(((((x*(9*a^6*b^3*d^9 + 16*b^9*c^6*d^3 - 224*a*b^8*c^5*d^4 - 84*a^5*b^4*c*d^8 + 2009*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 406*a^4*b^5*c^2*d^7))/(32*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)) - (((2*a*b^13*c^13*d^2 - 28*a^2*b^12*c^12*d^3 + (315*a^3*b^11*c^11*d^4)/2 - (987*a^4*b^10*c^10*d^5)/2 + 978*a^5*b^9*c^9*d^6 - 1302*a^6*b^8*c^8*d^7 + 1197*a^7*b^7*c^7*d^8 - 765*a^8*b^6*c^6*d^9 + 336*a^9*b^5*c^5*d^10 - 98*a^10*b^4*c^4*d^11 + (35*a^11*b^3*c^3*d^12)/2 - (3*a^12*b^2*c^2*d^13)/2)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) - (x*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d)*(256*a^2*b^11*c^13*d^2 - 1792*a^3*b^10*c^12*d^3 + 5120*a^4*b^9*c^11*d^4 - 7168*a^5*b^8*c^10*d^5 + 3584*a^6*b^7*c^9*d^6 + 3584*a^7*b^6*c^8*d^7 - 7168*a^8*b^5*c^7*d^8 + 5120*a^9*b^4*c^6*d^9 - 1792*a^10*b^3*c^5*d^10 + 256*a^11*b^2*c^4*d^11))/(512*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d))/(16*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d)*1i)/(16*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)) + (((x*(9*a^6*b^3*d^9 + 16*b^9*c^6*d^3 - 224*a*b^8*c^5*d^4 - 84*a^5*b^4*c*d^8 + 2009*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 406*a^4*b^5*c^2*d^7))/(32*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)) + (((2*a*b^13*c^13*d^2 - 28*a^2*b^12*c^12*d^3 + (315*a^3*b^11*c^11*d^4)/2 - (987*a^4*b^10*c^10*d^5)/2 + 978*a^5*b^9*c^9*d^6 - 1302*a^6*b^8*c^8*d^7 + 1197*a^7*b^7*c^7*d^8 - 765*a^8*b^6*c^6*d^9 + 336*a^9*b^5*c^5*d^10 - 98*a^10*b^4*c^4*d^11 + (35*a^11*b^3*c^3*d^12)/2 - (3*a^12*b^2*c^2*d^13)/2)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) + (x*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d)*(256*a^2*b^11*c^13*d^2 - 1792*a^3*b^10*c^12*d^3 + 5120*a^4*b^9*c^11*d^4 - 7168*a^5*b^8*c^10*d^5 + 3584*a^6*b^7*c^9*d^6 + 3584*a^7*b^6*c^8*d^7 - 7168*a^8*b^5*c^7*d^8 + 5120*a^9*b^4*c^6*d^9 - 1792*a^10*b^3*c^5*d^10 + 256*a^11*b^2*c^4*d^11))/(512*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d))/(16*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d)*1i)/(16*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)))/(((63*a^5*b^5*d^9)/64 + (35*b^10*c^5*d^4)/16 - (651*a*b^9*c^4*d^5)/64 - (267*a^4*b^6*c*d^8)/32 - (1275*a^2*b^8*c^3*d^6)/32 + (451*a^3*b^7*c^2*d^7)/16)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) - (((x*(9*a^6*b^3*d^9 + 16*b^9*c^6*d^3 - 224*a*b^8*c^5*d^4 - 84*a^5*b^4*c*d^8 + 2009*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 406*a^4*b^5*c^2*d^7))/(32*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)) - (((2*a*b^13*c^13*d^2 - 28*a^2*b^12*c^12*d^3 + (315*a^3*b^11*c^11*d^4)/2 - (987*a^4*b^10*c^10*d^5)/2 + 978*a^5*b^9*c^9*d^6 - 1302*a^6*b^8*c^8*d^7 + 1197*a^7*b^7*c^7*d^8 - 765*a^8*b^6*c^6*d^9 + 336*a^9*b^5*c^5*d^10 - 98*a^10*b^4*c^4*d^11 + (35*a^11*b^3*c^3*d^12)/2 - (3*a^12*b^2*c^2*d^13)/2)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) - (x*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d)*(256*a^2*b^11*c^13*d^2 - 1792*a^3*b^10*c^12*d^3 + 5120*a^4*b^9*c^11*d^4 - 7168*a^5*b^8*c^10*d^5 + 3584*a^6*b^7*c^9*d^6 + 3584*a^7*b^6*c^8*d^7 - 7168*a^8*b^5*c^7*d^8 + 5120*a^9*b^4*c^6*d^9 - 1792*a^10*b^3*c^5*d^10 + 256*a^11*b^2*c^4*d^11))/(512*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d))/(16*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d))/(16*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)) + (((x*(9*a^6*b^3*d^9 + 16*b^9*c^6*d^3 - 224*a*b^8*c^5*d^4 - 84*a^5*b^4*c*d^8 + 2009*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 406*a^4*b^5*c^2*d^7))/(32*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)) + (((2*a*b^13*c^13*d^2 - 28*a^2*b^12*c^12*d^3 + (315*a^3*b^11*c^11*d^4)/2 - (987*a^4*b^10*c^10*d^5)/2 + 978*a^5*b^9*c^9*d^6 - 1302*a^6*b^8*c^8*d^7 + 1197*a^7*b^7*c^7*d^8 - 765*a^8*b^6*c^6*d^9 + 336*a^9*b^5*c^5*d^10 - 98*a^10*b^4*c^4*d^11 + (35*a^11*b^3*c^3*d^12)/2 - (3*a^12*b^2*c^2*d^13)/2)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) + (x*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d)*(256*a^2*b^11*c^13*d^2 - 1792*a^3*b^10*c^12*d^3 + 5120*a^4*b^9*c^11*d^4 - 7168*a^5*b^8*c^10*d^5 + 3584*a^6*b^7*c^9*d^6 + 3584*a^7*b^6*c^8*d^7 - 7168*a^8*b^5*c^7*d^8 + 5120*a^9*b^4*c^6*d^9 - 1792*a^10*b^3*c^5*d^10 + 256*a^11*b^2*c^4*d^11))/(512*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d))/(16*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d))/(16*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d))))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d)*1i)/(8*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)) - ((x^5*(4*b^3*c^2*d^2 - 3*a^2*b*d^4 + 11*a*b^2*c*d^3))/(8*a*c^2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x*(4*b^3*c^3 - 5*a^3*d^3 + 13*a^2*b*c*d^2))/(8*a*c*(a*d - b*c)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (d*x^3*(8*b^3*c^3 - 3*a^3*d^3 + 13*a*b^2*c^2*d + 6*a^2*b*c*d^2))/(8*a*c^2*(a*d - b*c)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(a*c^2 + x^2*(b*c^2 + 2*a*c*d) + x^4*(a*d^2 + 2*b*c*d) + b*d^2*x^6) + (atan(((((x*(9*a^6*b^3*d^9 + 16*b^9*c^6*d^3 - 224*a*b^8*c^5*d^4 - 84*a^5*b^4*c*d^8 + 2009*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 406*a^4*b^5*c^2*d^7))/(32*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)) - ((7*a*d - b*c)*(-a^3*b^5)^(1/2)*((2*a*b^13*c^13*d^2 - 28*a^2*b^12*c^12*d^3 + (315*a^3*b^11*c^11*d^4)/2 - (987*a^4*b^10*c^10*d^5)/2 + 978*a^5*b^9*c^9*d^6 - 1302*a^6*b^8*c^8*d^7 + 1197*a^7*b^7*c^7*d^8 - 765*a^8*b^6*c^6*d^9 + 336*a^9*b^5*c^5*d^10 - 98*a^10*b^4*c^4*d^11 + (35*a^11*b^3*c^3*d^12)/2 - (3*a^12*b^2*c^2*d^13)/2)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) - (x*(7*a*d - b*c)*(-a^3*b^5)^(1/2)*(256*a^2*b^11*c^13*d^2 - 1792*a^3*b^10*c^12*d^3 + 5120*a^4*b^9*c^11*d^4 - 7168*a^5*b^8*c^10*d^5 + 3584*a^6*b^7*c^9*d^6 + 3584*a^7*b^6*c^8*d^7 - 7168*a^8*b^5*c^7*d^8 + 5120*a^9*b^4*c^6*d^9 - 1792*a^10*b^3*c^5*d^10 + 256*a^11*b^2*c^4*d^11))/(128*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4))))/(4*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)))*(7*a*d - b*c)*(-a^3*b^5)^(1/2)*1i)/(4*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)) + (((x*(9*a^6*b^3*d^9 + 16*b^9*c^6*d^3 - 224*a*b^8*c^5*d^4 - 84*a^5*b^4*c*d^8 + 2009*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 406*a^4*b^5*c^2*d^7))/(32*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)) + ((7*a*d - b*c)*(-a^3*b^5)^(1/2)*((2*a*b^13*c^13*d^2 - 28*a^2*b^12*c^12*d^3 + (315*a^3*b^11*c^11*d^4)/2 - (987*a^4*b^10*c^10*d^5)/2 + 978*a^5*b^9*c^9*d^6 - 1302*a^6*b^8*c^8*d^7 + 1197*a^7*b^7*c^7*d^8 - 765*a^8*b^6*c^6*d^9 + 336*a^9*b^5*c^5*d^10 - 98*a^10*b^4*c^4*d^11 + (35*a^11*b^3*c^3*d^12)/2 - (3*a^12*b^2*c^2*d^13)/2)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) + (x*(7*a*d - b*c)*(-a^3*b^5)^(1/2)*(256*a^2*b^11*c^13*d^2 - 1792*a^3*b^10*c^12*d^3 + 5120*a^4*b^9*c^11*d^4 - 7168*a^5*b^8*c^10*d^5 + 3584*a^6*b^7*c^9*d^6 + 3584*a^7*b^6*c^8*d^7 - 7168*a^8*b^5*c^7*d^8 + 5120*a^9*b^4*c^6*d^9 - 1792*a^10*b^3*c^5*d^10 + 256*a^11*b^2*c^4*d^11))/(128*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4))))/(4*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)))*(7*a*d - b*c)*(-a^3*b^5)^(1/2)*1i)/(4*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)))/(((63*a^5*b^5*d^9)/64 + (35*b^10*c^5*d^4)/16 - (651*a*b^9*c^4*d^5)/64 - (267*a^4*b^6*c*d^8)/32 - (1275*a^2*b^8*c^3*d^6)/32 + (451*a^3*b^7*c^2*d^7)/16)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) - (((x*(9*a^6*b^3*d^9 + 16*b^9*c^6*d^3 - 224*a*b^8*c^5*d^4 - 84*a^5*b^4*c*d^8 + 2009*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 406*a^4*b^5*c^2*d^7))/(32*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)) - ((7*a*d - b*c)*(-a^3*b^5)^(1/2)*((2*a*b^13*c^13*d^2 - 28*a^2*b^12*c^12*d^3 + (315*a^3*b^11*c^11*d^4)/2 - (987*a^4*b^10*c^10*d^5)/2 + 978*a^5*b^9*c^9*d^6 - 1302*a^6*b^8*c^8*d^7 + 1197*a^7*b^7*c^7*d^8 - 765*a^8*b^6*c^6*d^9 + 336*a^9*b^5*c^5*d^10 - 98*a^10*b^4*c^4*d^11 + (35*a^11*b^3*c^3*d^12)/2 - (3*a^12*b^2*c^2*d^13)/2)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) - (x*(7*a*d - b*c)*(-a^3*b^5)^(1/2)*(256*a^2*b^11*c^13*d^2 - 1792*a^3*b^10*c^12*d^3 + 5120*a^4*b^9*c^11*d^4 - 7168*a^5*b^8*c^10*d^5 + 3584*a^6*b^7*c^9*d^6 + 3584*a^7*b^6*c^8*d^7 - 7168*a^8*b^5*c^7*d^8 + 5120*a^9*b^4*c^6*d^9 - 1792*a^10*b^3*c^5*d^10 + 256*a^11*b^2*c^4*d^11))/(128*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4))))/(4*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)))*(7*a*d - b*c)*(-a^3*b^5)^(1/2))/(4*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)) + (((x*(9*a^6*b^3*d^9 + 16*b^9*c^6*d^3 - 224*a*b^8*c^5*d^4 - 84*a^5*b^4*c*d^8 + 2009*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 406*a^4*b^5*c^2*d^7))/(32*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)) + ((7*a*d - b*c)*(-a^3*b^5)^(1/2)*((2*a*b^13*c^13*d^2 - 28*a^2*b^12*c^12*d^3 + (315*a^3*b^11*c^11*d^4)/2 - (987*a^4*b^10*c^10*d^5)/2 + 978*a^5*b^9*c^9*d^6 - 1302*a^6*b^8*c^8*d^7 + 1197*a^7*b^7*c^7*d^8 - 765*a^8*b^6*c^6*d^9 + 336*a^9*b^5*c^5*d^10 - 98*a^10*b^4*c^4*d^11 + (35*a^11*b^3*c^3*d^12)/2 - (3*a^12*b^2*c^2*d^13)/2)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) + (x*(7*a*d - b*c)*(-a^3*b^5)^(1/2)*(256*a^2*b^11*c^13*d^2 - 1792*a^3*b^10*c^12*d^3 + 5120*a^4*b^9*c^11*d^4 - 7168*a^5*b^8*c^10*d^5 + 3584*a^6*b^7*c^9*d^6 + 3584*a^7*b^6*c^8*d^7 - 7168*a^8*b^5*c^7*d^8 + 5120*a^9*b^4*c^6*d^9 - 1792*a^10*b^3*c^5*d^10 + 256*a^11*b^2*c^4*d^11))/(128*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4))))/(4*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)))*(7*a*d - b*c)*(-a^3*b^5)^(1/2))/(4*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3))))*(7*a*d - b*c)*(-a^3*b^5)^(1/2)*1i)/(2*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3))","B"
35,1,409,196,5.023251,"\text{Not used}","int((c + d*x^2)^5/(a + b*x^2)^3,x)","\frac{\frac{5\,x\,\left(3\,a^5\,d^5-11\,a^4\,b\,c\,d^4+14\,a^3\,b^2\,c^2\,d^3-6\,a^2\,b^3\,c^3\,d^2-a\,b^4\,c^4\,d+b^5\,c^5\right)}{8\,a}+\frac{x^3\,\left(17\,a^5\,b\,d^5-65\,a^4\,b^2\,c\,d^4+90\,a^3\,b^3\,c^2\,d^3-50\,a^2\,b^4\,c^3\,d^2+5\,a\,b^5\,c^4\,d+3\,b^6\,c^5\right)}{8\,a^2}}{a^2\,b^5+2\,a\,b^6\,x^2+b^7\,x^4}-x^3\,\left(\frac{a\,d^5}{b^4}-\frac{5\,c\,d^4}{3\,b^3}\right)+x\,\left(\frac{3\,a\,\left(\frac{3\,a\,d^5}{b^4}-\frac{5\,c\,d^4}{b^3}\right)}{b}-\frac{3\,a^2\,d^5}{b^5}+\frac{10\,c^2\,d^3}{b^3}\right)+\frac{d^5\,x^5}{5\,b^3}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^3\,\left(63\,a^2\,d^2+14\,a\,b\,c\,d+3\,b^2\,c^2\right)}{\sqrt{a}\,\left(-63\,a^5\,d^5+175\,a^4\,b\,c\,d^4-150\,a^3\,b^2\,c^2\,d^3+30\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d+3\,b^5\,c^5\right)}\right)\,{\left(a\,d-b\,c\right)}^3\,\left(63\,a^2\,d^2+14\,a\,b\,c\,d+3\,b^2\,c^2\right)}{8\,a^{5/2}\,b^{11/2}}","Not used",1,"((5*x*(3*a^5*d^5 + b^5*c^5 - 6*a^2*b^3*c^3*d^2 + 14*a^3*b^2*c^2*d^3 - a*b^4*c^4*d - 11*a^4*b*c*d^4))/(8*a) + (x^3*(3*b^6*c^5 + 17*a^5*b*d^5 - 65*a^4*b^2*c*d^4 - 50*a^2*b^4*c^3*d^2 + 90*a^3*b^3*c^2*d^3 + 5*a*b^5*c^4*d))/(8*a^2))/(a^2*b^5 + b^7*x^4 + 2*a*b^6*x^2) - x^3*((a*d^5)/b^4 - (5*c*d^4)/(3*b^3)) + x*((3*a*((3*a*d^5)/b^4 - (5*c*d^4)/b^3))/b - (3*a^2*d^5)/b^5 + (10*c^2*d^3)/b^3) + (d^5*x^5)/(5*b^3) + (atan((b^(1/2)*x*(a*d - b*c)^3*(63*a^2*d^2 + 3*b^2*c^2 + 14*a*b*c*d))/(a^(1/2)*(3*b^5*c^5 - 63*a^5*d^5 + 30*a^2*b^3*c^3*d^2 - 150*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d + 175*a^4*b*c*d^4)))*(a*d - b*c)^3*(63*a^2*d^2 + 3*b^2*c^2 + 14*a*b*c*d))/(8*a^(5/2)*b^(11/2))","B"
36,1,318,160,0.135269,"\text{Not used}","int((c + d*x^2)^4/(a + b*x^2)^3,x)","\frac{d^4\,x^3}{3\,b^3}-x\,\left(\frac{3\,a\,d^4}{b^4}-\frac{4\,c\,d^3}{b^3}\right)-\frac{\frac{x\,\left(11\,a^4\,d^4-28\,a^3\,b\,c\,d^3+18\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d-5\,b^4\,c^4\right)}{8\,a}-\frac{x^3\,\left(-13\,a^4\,b\,d^4+36\,a^3\,b^2\,c\,d^3-30\,a^2\,b^3\,c^2\,d^2+4\,a\,b^4\,c^3\,d+3\,b^5\,c^4\right)}{8\,a^2}}{a^2\,b^4+2\,a\,b^5\,x^2+b^6\,x^4}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^2\,\left(35\,a^2\,d^2+10\,a\,b\,c\,d+3\,b^2\,c^2\right)}{\sqrt{a}\,\left(35\,a^4\,d^4-60\,a^3\,b\,c\,d^3+18\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d+3\,b^4\,c^4\right)}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(35\,a^2\,d^2+10\,a\,b\,c\,d+3\,b^2\,c^2\right)}{8\,a^{5/2}\,b^{9/2}}","Not used",1,"(d^4*x^3)/(3*b^3) - x*((3*a*d^4)/b^4 - (4*c*d^3)/b^3) - ((x*(11*a^4*d^4 - 5*b^4*c^4 + 18*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d - 28*a^3*b*c*d^3))/(8*a) - (x^3*(3*b^5*c^4 - 13*a^4*b*d^4 + 36*a^3*b^2*c*d^3 - 30*a^2*b^3*c^2*d^2 + 4*a*b^4*c^3*d))/(8*a^2))/(a^2*b^4 + b^6*x^4 + 2*a*b^5*x^2) + (atan((b^(1/2)*x*(a*d - b*c)^2*(35*a^2*d^2 + 3*b^2*c^2 + 10*a*b*c*d))/(a^(1/2)*(35*a^4*d^4 + 3*b^4*c^4 + 18*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d - 60*a^3*b*c*d^3)))*(a*d - b*c)^2*(35*a^2*d^2 + 3*b^2*c^2 + 10*a*b*c*d))/(8*a^(5/2)*b^(9/2))","B"
37,1,240,130,5.051720,"\text{Not used}","int((c + d*x^2)^3/(a + b*x^2)^3,x)","\frac{\frac{x\,\left(7\,a^3\,d^3-9\,a^2\,b\,c\,d^2-3\,a\,b^2\,c^2\,d+5\,b^3\,c^3\right)}{8\,a}+\frac{3\,x^3\,\left(3\,a^3\,b\,d^3-5\,a^2\,b^2\,c\,d^2+a\,b^3\,c^2\,d+b^4\,c^3\right)}{8\,a^2}}{a^2\,b^3+2\,a\,b^4\,x^2+b^5\,x^4}+\frac{d^3\,x}{b^3}+\frac{3\,\mathrm{atan}\left(\frac{\sqrt{b}\,x\,\left(a\,d-b\,c\right)\,\left(5\,a^2\,d^2+2\,a\,b\,c\,d+b^2\,c^2\right)}{\sqrt{a}\,\left(-5\,a^3\,d^3+3\,a^2\,b\,c\,d^2+a\,b^2\,c^2\,d+b^3\,c^3\right)}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a^2\,d^2+2\,a\,b\,c\,d+b^2\,c^2\right)}{8\,a^{5/2}\,b^{7/2}}","Not used",1,"((x*(7*a^3*d^3 + 5*b^3*c^3 - 3*a*b^2*c^2*d - 9*a^2*b*c*d^2))/(8*a) + (3*x^3*(b^4*c^3 + 3*a^3*b*d^3 - 5*a^2*b^2*c*d^2 + a*b^3*c^2*d))/(8*a^2))/(a^2*b^3 + b^5*x^4 + 2*a*b^4*x^2) + (d^3*x)/b^3 + (3*atan((b^(1/2)*x*(a*d - b*c)*(5*a^2*d^2 + b^2*c^2 + 2*a*b*c*d))/(a^(1/2)*(b^3*c^3 - 5*a^3*d^3 + a*b^2*c^2*d + 3*a^2*b*c*d^2)))*(a*d - b*c)*(5*a^2*d^2 + b^2*c^2 + 2*a*b*c*d))/(8*a^(5/2)*b^(7/2))","B"
38,1,130,116,5.023407,"\text{Not used}","int((c + d*x^2)^2/(a + b*x^2)^3,x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(3\,a^2\,d^2+2\,a\,b\,c\,d+3\,b^2\,c^2\right)}{8\,a^{5/2}\,b^{5/2}}-\frac{\frac{x\,\left(3\,a^2\,d^2+2\,a\,b\,c\,d-5\,b^2\,c^2\right)}{8\,a\,b^2}-\frac{x^3\,\left(-5\,a^2\,d^2+2\,a\,b\,c\,d+3\,b^2\,c^2\right)}{8\,a^2\,b}}{a^2+2\,a\,b\,x^2+b^2\,x^4}","Not used",1,"(atan((b^(1/2)*x)/a^(1/2))*(3*a^2*d^2 + 3*b^2*c^2 + 2*a*b*c*d))/(8*a^(5/2)*b^(5/2)) - ((x*(3*a^2*d^2 - 5*b^2*c^2 + 2*a*b*c*d))/(8*a*b^2) - (x^3*(3*b^2*c^2 - 5*a^2*d^2 + 2*a*b*c*d))/(8*a^2*b))/(a^2 + b^2*x^4 + 2*a*b*x^2)","B"
39,1,81,92,5.015524,"\text{Not used}","int((c + d*x^2)/(a + b*x^2)^3,x)","\frac{\frac{x^3\,\left(a\,d+3\,b\,c\right)}{8\,a^2}-\frac{x\,\left(a\,d-5\,b\,c\right)}{8\,a\,b}}{a^2+2\,a\,b\,x^2+b^2\,x^4}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(a\,d+3\,b\,c\right)}{8\,a^{5/2}\,b^{3/2}}","Not used",1,"((x^3*(a*d + 3*b*c))/(8*a^2) - (x*(a*d - 5*b*c))/(8*a*b))/(a^2 + b^2*x^4 + 2*a*b*x^2) + (atan((b^(1/2)*x)/a^(1/2))*(a*d + 3*b*c))/(8*a^(5/2)*b^(3/2))","B"
40,1,6033,161,6.891989,"\text{Not used}","int(1/((a + b*x^2)^3*(c + d*x^2)),x)","\frac{\frac{x^3\,\left(3\,b^3\,c-7\,a\,b^2\,d\right)}{8\,a^2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{x\,\left(5\,b^2\,c-9\,a\,b\,d\right)}{8\,a\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{a^2+2\,a\,b\,x^2+b^2\,x^4}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(289\,a^4\,b^3\,d^7-300\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-60\,a\,b^6\,c^3\,d^4+9\,b^7\,c^4\,d^3\right)}{32\,\left(a^8\,d^4-4\,a^7\,b\,c\,d^3+6\,a^6\,b^2\,c^2\,d^2-4\,a^5\,b^3\,c^3\,d+a^4\,b^4\,c^4\right)}-\frac{\sqrt{-c\,d^5}\,\left(\frac{256\,a^{10}\,b^2\,d^{10}-1760\,a^9\,b^3\,c\,d^9+5280\,a^8\,b^4\,c^2\,d^8-9056\,a^7\,b^5\,c^3\,d^7+9760\,a^6\,b^6\,c^4\,d^6-6816\,a^5\,b^7\,c^5\,d^5+3040\,a^4\,b^8\,c^6\,d^4-800\,a^3\,b^9\,c^7\,d^3+96\,a^2\,b^{10}\,c^8\,d^2}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}-\frac{x\,\sqrt{-c\,d^5}\,\left(256\,a^{11}\,b^2\,d^9-1280\,a^{10}\,b^3\,c\,d^8+2304\,a^9\,b^4\,c^2\,d^7-1280\,a^8\,b^5\,c^3\,d^6-1280\,a^7\,b^6\,c^4\,d^5+2304\,a^6\,b^7\,c^5\,d^4-1280\,a^5\,b^8\,c^6\,d^3+256\,a^4\,b^9\,c^7\,d^2\right)}{64\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)\,\left(a^8\,d^4-4\,a^7\,b\,c\,d^3+6\,a^6\,b^2\,c^2\,d^2-4\,a^5\,b^3\,c^3\,d+a^4\,b^4\,c^4\right)}\right)}{2\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}\right)\,\sqrt{-c\,d^5}\,1{}\mathrm{i}}{2\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}+\frac{\left(\frac{x\,\left(289\,a^4\,b^3\,d^7-300\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-60\,a\,b^6\,c^3\,d^4+9\,b^7\,c^4\,d^3\right)}{32\,\left(a^8\,d^4-4\,a^7\,b\,c\,d^3+6\,a^6\,b^2\,c^2\,d^2-4\,a^5\,b^3\,c^3\,d+a^4\,b^4\,c^4\right)}+\frac{\sqrt{-c\,d^5}\,\left(\frac{256\,a^{10}\,b^2\,d^{10}-1760\,a^9\,b^3\,c\,d^9+5280\,a^8\,b^4\,c^2\,d^8-9056\,a^7\,b^5\,c^3\,d^7+9760\,a^6\,b^6\,c^4\,d^6-6816\,a^5\,b^7\,c^5\,d^5+3040\,a^4\,b^8\,c^6\,d^4-800\,a^3\,b^9\,c^7\,d^3+96\,a^2\,b^{10}\,c^8\,d^2}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}+\frac{x\,\sqrt{-c\,d^5}\,\left(256\,a^{11}\,b^2\,d^9-1280\,a^{10}\,b^3\,c\,d^8+2304\,a^9\,b^4\,c^2\,d^7-1280\,a^8\,b^5\,c^3\,d^6-1280\,a^7\,b^6\,c^4\,d^5+2304\,a^6\,b^7\,c^5\,d^4-1280\,a^5\,b^8\,c^6\,d^3+256\,a^4\,b^9\,c^7\,d^2\right)}{64\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)\,\left(a^8\,d^4-4\,a^7\,b\,c\,d^3+6\,a^6\,b^2\,c^2\,d^2-4\,a^5\,b^3\,c^3\,d+a^4\,b^4\,c^4\right)}\right)}{2\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}\right)\,\sqrt{-c\,d^5}\,1{}\mathrm{i}}{2\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}}{\frac{105\,a^3\,b^3\,d^8-115\,a^2\,b^4\,c\,d^7+51\,a\,b^5\,c^2\,d^6-9\,b^6\,c^3\,d^5}{32\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}-\frac{\left(\frac{x\,\left(289\,a^4\,b^3\,d^7-300\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-60\,a\,b^6\,c^3\,d^4+9\,b^7\,c^4\,d^3\right)}{32\,\left(a^8\,d^4-4\,a^7\,b\,c\,d^3+6\,a^6\,b^2\,c^2\,d^2-4\,a^5\,b^3\,c^3\,d+a^4\,b^4\,c^4\right)}-\frac{\sqrt{-c\,d^5}\,\left(\frac{256\,a^{10}\,b^2\,d^{10}-1760\,a^9\,b^3\,c\,d^9+5280\,a^8\,b^4\,c^2\,d^8-9056\,a^7\,b^5\,c^3\,d^7+9760\,a^6\,b^6\,c^4\,d^6-6816\,a^5\,b^7\,c^5\,d^5+3040\,a^4\,b^8\,c^6\,d^4-800\,a^3\,b^9\,c^7\,d^3+96\,a^2\,b^{10}\,c^8\,d^2}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}-\frac{x\,\sqrt{-c\,d^5}\,\left(256\,a^{11}\,b^2\,d^9-1280\,a^{10}\,b^3\,c\,d^8+2304\,a^9\,b^4\,c^2\,d^7-1280\,a^8\,b^5\,c^3\,d^6-1280\,a^7\,b^6\,c^4\,d^5+2304\,a^6\,b^7\,c^5\,d^4-1280\,a^5\,b^8\,c^6\,d^3+256\,a^4\,b^9\,c^7\,d^2\right)}{64\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)\,\left(a^8\,d^4-4\,a^7\,b\,c\,d^3+6\,a^6\,b^2\,c^2\,d^2-4\,a^5\,b^3\,c^3\,d+a^4\,b^4\,c^4\right)}\right)}{2\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}\right)\,\sqrt{-c\,d^5}}{2\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}+\frac{\left(\frac{x\,\left(289\,a^4\,b^3\,d^7-300\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-60\,a\,b^6\,c^3\,d^4+9\,b^7\,c^4\,d^3\right)}{32\,\left(a^8\,d^4-4\,a^7\,b\,c\,d^3+6\,a^6\,b^2\,c^2\,d^2-4\,a^5\,b^3\,c^3\,d+a^4\,b^4\,c^4\right)}+\frac{\sqrt{-c\,d^5}\,\left(\frac{256\,a^{10}\,b^2\,d^{10}-1760\,a^9\,b^3\,c\,d^9+5280\,a^8\,b^4\,c^2\,d^8-9056\,a^7\,b^5\,c^3\,d^7+9760\,a^6\,b^6\,c^4\,d^6-6816\,a^5\,b^7\,c^5\,d^5+3040\,a^4\,b^8\,c^6\,d^4-800\,a^3\,b^9\,c^7\,d^3+96\,a^2\,b^{10}\,c^8\,d^2}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}+\frac{x\,\sqrt{-c\,d^5}\,\left(256\,a^{11}\,b^2\,d^9-1280\,a^{10}\,b^3\,c\,d^8+2304\,a^9\,b^4\,c^2\,d^7-1280\,a^8\,b^5\,c^3\,d^6-1280\,a^7\,b^6\,c^4\,d^5+2304\,a^6\,b^7\,c^5\,d^4-1280\,a^5\,b^8\,c^6\,d^3+256\,a^4\,b^9\,c^7\,d^2\right)}{64\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)\,\left(a^8\,d^4-4\,a^7\,b\,c\,d^3+6\,a^6\,b^2\,c^2\,d^2-4\,a^5\,b^3\,c^3\,d+a^4\,b^4\,c^4\right)}\right)}{2\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}\right)\,\sqrt{-c\,d^5}}{2\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}}\right)\,\sqrt{-c\,d^5}\,1{}\mathrm{i}}{-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(289\,a^4\,b^3\,d^7-300\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-60\,a\,b^6\,c^3\,d^4+9\,b^7\,c^4\,d^3\right)}{32\,\left(a^8\,d^4-4\,a^7\,b\,c\,d^3+6\,a^6\,b^2\,c^2\,d^2-4\,a^5\,b^3\,c^3\,d+a^4\,b^4\,c^4\right)}-\frac{\left(\frac{256\,a^{10}\,b^2\,d^{10}-1760\,a^9\,b^3\,c\,d^9+5280\,a^8\,b^4\,c^2\,d^8-9056\,a^7\,b^5\,c^3\,d^7+9760\,a^6\,b^6\,c^4\,d^6-6816\,a^5\,b^7\,c^5\,d^5+3040\,a^4\,b^8\,c^6\,d^4-800\,a^3\,b^9\,c^7\,d^3+96\,a^2\,b^{10}\,c^8\,d^2}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}-\frac{x\,\sqrt{-a^5\,b}\,\left(15\,a^2\,d^2-10\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(256\,a^{11}\,b^2\,d^9-1280\,a^{10}\,b^3\,c\,d^8+2304\,a^9\,b^4\,c^2\,d^7-1280\,a^8\,b^5\,c^3\,d^6-1280\,a^7\,b^6\,c^4\,d^5+2304\,a^6\,b^7\,c^5\,d^4-1280\,a^5\,b^8\,c^6\,d^3+256\,a^4\,b^9\,c^7\,d^2\right)}{512\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)\,\left(a^8\,d^4-4\,a^7\,b\,c\,d^3+6\,a^6\,b^2\,c^2\,d^2-4\,a^5\,b^3\,c^3\,d+a^4\,b^4\,c^4\right)}\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2\,d^2-10\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2\,d^2-10\,a\,b\,c\,d+3\,b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}+\frac{\left(\frac{x\,\left(289\,a^4\,b^3\,d^7-300\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-60\,a\,b^6\,c^3\,d^4+9\,b^7\,c^4\,d^3\right)}{32\,\left(a^8\,d^4-4\,a^7\,b\,c\,d^3+6\,a^6\,b^2\,c^2\,d^2-4\,a^5\,b^3\,c^3\,d+a^4\,b^4\,c^4\right)}+\frac{\left(\frac{256\,a^{10}\,b^2\,d^{10}-1760\,a^9\,b^3\,c\,d^9+5280\,a^8\,b^4\,c^2\,d^8-9056\,a^7\,b^5\,c^3\,d^7+9760\,a^6\,b^6\,c^4\,d^6-6816\,a^5\,b^7\,c^5\,d^5+3040\,a^4\,b^8\,c^6\,d^4-800\,a^3\,b^9\,c^7\,d^3+96\,a^2\,b^{10}\,c^8\,d^2}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}+\frac{x\,\sqrt{-a^5\,b}\,\left(15\,a^2\,d^2-10\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(256\,a^{11}\,b^2\,d^9-1280\,a^{10}\,b^3\,c\,d^8+2304\,a^9\,b^4\,c^2\,d^7-1280\,a^8\,b^5\,c^3\,d^6-1280\,a^7\,b^6\,c^4\,d^5+2304\,a^6\,b^7\,c^5\,d^4-1280\,a^5\,b^8\,c^6\,d^3+256\,a^4\,b^9\,c^7\,d^2\right)}{512\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)\,\left(a^8\,d^4-4\,a^7\,b\,c\,d^3+6\,a^6\,b^2\,c^2\,d^2-4\,a^5\,b^3\,c^3\,d+a^4\,b^4\,c^4\right)}\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2\,d^2-10\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2\,d^2-10\,a\,b\,c\,d+3\,b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}}{\frac{105\,a^3\,b^3\,d^8-115\,a^2\,b^4\,c\,d^7+51\,a\,b^5\,c^2\,d^6-9\,b^6\,c^3\,d^5}{32\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}-\frac{\left(\frac{x\,\left(289\,a^4\,b^3\,d^7-300\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-60\,a\,b^6\,c^3\,d^4+9\,b^7\,c^4\,d^3\right)}{32\,\left(a^8\,d^4-4\,a^7\,b\,c\,d^3+6\,a^6\,b^2\,c^2\,d^2-4\,a^5\,b^3\,c^3\,d+a^4\,b^4\,c^4\right)}-\frac{\left(\frac{256\,a^{10}\,b^2\,d^{10}-1760\,a^9\,b^3\,c\,d^9+5280\,a^8\,b^4\,c^2\,d^8-9056\,a^7\,b^5\,c^3\,d^7+9760\,a^6\,b^6\,c^4\,d^6-6816\,a^5\,b^7\,c^5\,d^5+3040\,a^4\,b^8\,c^6\,d^4-800\,a^3\,b^9\,c^7\,d^3+96\,a^2\,b^{10}\,c^8\,d^2}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}-\frac{x\,\sqrt{-a^5\,b}\,\left(15\,a^2\,d^2-10\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(256\,a^{11}\,b^2\,d^9-1280\,a^{10}\,b^3\,c\,d^8+2304\,a^9\,b^4\,c^2\,d^7-1280\,a^8\,b^5\,c^3\,d^6-1280\,a^7\,b^6\,c^4\,d^5+2304\,a^6\,b^7\,c^5\,d^4-1280\,a^5\,b^8\,c^6\,d^3+256\,a^4\,b^9\,c^7\,d^2\right)}{512\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)\,\left(a^8\,d^4-4\,a^7\,b\,c\,d^3+6\,a^6\,b^2\,c^2\,d^2-4\,a^5\,b^3\,c^3\,d+a^4\,b^4\,c^4\right)}\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2\,d^2-10\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2\,d^2-10\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}+\frac{\left(\frac{x\,\left(289\,a^4\,b^3\,d^7-300\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-60\,a\,b^6\,c^3\,d^4+9\,b^7\,c^4\,d^3\right)}{32\,\left(a^8\,d^4-4\,a^7\,b\,c\,d^3+6\,a^6\,b^2\,c^2\,d^2-4\,a^5\,b^3\,c^3\,d+a^4\,b^4\,c^4\right)}+\frac{\left(\frac{256\,a^{10}\,b^2\,d^{10}-1760\,a^9\,b^3\,c\,d^9+5280\,a^8\,b^4\,c^2\,d^8-9056\,a^7\,b^5\,c^3\,d^7+9760\,a^6\,b^6\,c^4\,d^6-6816\,a^5\,b^7\,c^5\,d^5+3040\,a^4\,b^8\,c^6\,d^4-800\,a^3\,b^9\,c^7\,d^3+96\,a^2\,b^{10}\,c^8\,d^2}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}+\frac{x\,\sqrt{-a^5\,b}\,\left(15\,a^2\,d^2-10\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(256\,a^{11}\,b^2\,d^9-1280\,a^{10}\,b^3\,c\,d^8+2304\,a^9\,b^4\,c^2\,d^7-1280\,a^8\,b^5\,c^3\,d^6-1280\,a^7\,b^6\,c^4\,d^5+2304\,a^6\,b^7\,c^5\,d^4-1280\,a^5\,b^8\,c^6\,d^3+256\,a^4\,b^9\,c^7\,d^2\right)}{512\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)\,\left(a^8\,d^4-4\,a^7\,b\,c\,d^3+6\,a^6\,b^2\,c^2\,d^2-4\,a^5\,b^3\,c^3\,d+a^4\,b^4\,c^4\right)}\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2\,d^2-10\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2\,d^2-10\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}}\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2\,d^2-10\,a\,b\,c\,d+3\,b^2\,c^2\right)\,1{}\mathrm{i}}{8\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}","Not used",1,"((x^3*(3*b^3*c - 7*a*b^2*d))/(8*a^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (x*(5*b^2*c - 9*a*b*d))/(8*a*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(a^2 + b^2*x^4 + 2*a*b*x^2) + (atan(((((x*(289*a^4*b^3*d^7 + 9*b^7*c^4*d^3 - 60*a*b^6*c^3*d^4 - 300*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(a^8*d^4 + a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3)) - ((-c*d^5)^(1/2)*((256*a^10*b^2*d^10 - 1760*a^9*b^3*c*d^9 + 96*a^2*b^10*c^8*d^2 - 800*a^3*b^9*c^7*d^3 + 3040*a^4*b^8*c^6*d^4 - 6816*a^5*b^7*c^5*d^5 + 9760*a^6*b^6*c^4*d^6 - 9056*a^7*b^5*c^3*d^7 + 5280*a^8*b^4*c^2*d^8)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)) - (x*(-c*d^5)^(1/2)*(256*a^11*b^2*d^9 - 1280*a^10*b^3*c*d^8 + 256*a^4*b^9*c^7*d^2 - 1280*a^5*b^8*c^6*d^3 + 2304*a^6*b^7*c^5*d^4 - 1280*a^7*b^6*c^4*d^5 - 1280*a^8*b^5*c^3*d^6 + 2304*a^9*b^4*c^2*d^7))/(64*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)*(a^8*d^4 + a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3))))/(2*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)))*(-c*d^5)^(1/2)*1i)/(2*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)) + (((x*(289*a^4*b^3*d^7 + 9*b^7*c^4*d^3 - 60*a*b^6*c^3*d^4 - 300*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(a^8*d^4 + a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3)) + ((-c*d^5)^(1/2)*((256*a^10*b^2*d^10 - 1760*a^9*b^3*c*d^9 + 96*a^2*b^10*c^8*d^2 - 800*a^3*b^9*c^7*d^3 + 3040*a^4*b^8*c^6*d^4 - 6816*a^5*b^7*c^5*d^5 + 9760*a^6*b^6*c^4*d^6 - 9056*a^7*b^5*c^3*d^7 + 5280*a^8*b^4*c^2*d^8)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)) + (x*(-c*d^5)^(1/2)*(256*a^11*b^2*d^9 - 1280*a^10*b^3*c*d^8 + 256*a^4*b^9*c^7*d^2 - 1280*a^5*b^8*c^6*d^3 + 2304*a^6*b^7*c^5*d^4 - 1280*a^7*b^6*c^4*d^5 - 1280*a^8*b^5*c^3*d^6 + 2304*a^9*b^4*c^2*d^7))/(64*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)*(a^8*d^4 + a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3))))/(2*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)))*(-c*d^5)^(1/2)*1i)/(2*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)))/((105*a^3*b^3*d^8 - 9*b^6*c^3*d^5 + 51*a*b^5*c^2*d^6 - 115*a^2*b^4*c*d^7)/(32*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)) - (((x*(289*a^4*b^3*d^7 + 9*b^7*c^4*d^3 - 60*a*b^6*c^3*d^4 - 300*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(a^8*d^4 + a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3)) - ((-c*d^5)^(1/2)*((256*a^10*b^2*d^10 - 1760*a^9*b^3*c*d^9 + 96*a^2*b^10*c^8*d^2 - 800*a^3*b^9*c^7*d^3 + 3040*a^4*b^8*c^6*d^4 - 6816*a^5*b^7*c^5*d^5 + 9760*a^6*b^6*c^4*d^6 - 9056*a^7*b^5*c^3*d^7 + 5280*a^8*b^4*c^2*d^8)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)) - (x*(-c*d^5)^(1/2)*(256*a^11*b^2*d^9 - 1280*a^10*b^3*c*d^8 + 256*a^4*b^9*c^7*d^2 - 1280*a^5*b^8*c^6*d^3 + 2304*a^6*b^7*c^5*d^4 - 1280*a^7*b^6*c^4*d^5 - 1280*a^8*b^5*c^3*d^6 + 2304*a^9*b^4*c^2*d^7))/(64*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)*(a^8*d^4 + a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3))))/(2*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)))*(-c*d^5)^(1/2))/(2*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)) + (((x*(289*a^4*b^3*d^7 + 9*b^7*c^4*d^3 - 60*a*b^6*c^3*d^4 - 300*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(a^8*d^4 + a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3)) + ((-c*d^5)^(1/2)*((256*a^10*b^2*d^10 - 1760*a^9*b^3*c*d^9 + 96*a^2*b^10*c^8*d^2 - 800*a^3*b^9*c^7*d^3 + 3040*a^4*b^8*c^6*d^4 - 6816*a^5*b^7*c^5*d^5 + 9760*a^6*b^6*c^4*d^6 - 9056*a^7*b^5*c^3*d^7 + 5280*a^8*b^4*c^2*d^8)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)) + (x*(-c*d^5)^(1/2)*(256*a^11*b^2*d^9 - 1280*a^10*b^3*c*d^8 + 256*a^4*b^9*c^7*d^2 - 1280*a^5*b^8*c^6*d^3 + 2304*a^6*b^7*c^5*d^4 - 1280*a^7*b^6*c^4*d^5 - 1280*a^8*b^5*c^3*d^6 + 2304*a^9*b^4*c^2*d^7))/(64*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)*(a^8*d^4 + a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3))))/(2*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)))*(-c*d^5)^(1/2))/(2*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d))))*(-c*d^5)^(1/2)*1i)/(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d) + (atan(((((x*(289*a^4*b^3*d^7 + 9*b^7*c^4*d^3 - 60*a*b^6*c^3*d^4 - 300*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(a^8*d^4 + a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3)) - (((256*a^10*b^2*d^10 - 1760*a^9*b^3*c*d^9 + 96*a^2*b^10*c^8*d^2 - 800*a^3*b^9*c^7*d^3 + 3040*a^4*b^8*c^6*d^4 - 6816*a^5*b^7*c^5*d^5 + 9760*a^6*b^6*c^4*d^6 - 9056*a^7*b^5*c^3*d^7 + 5280*a^8*b^4*c^2*d^8)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)) - (x*(-a^5*b)^(1/2)*(15*a^2*d^2 + 3*b^2*c^2 - 10*a*b*c*d)*(256*a^11*b^2*d^9 - 1280*a^10*b^3*c*d^8 + 256*a^4*b^9*c^7*d^2 - 1280*a^5*b^8*c^6*d^3 + 2304*a^6*b^7*c^5*d^4 - 1280*a^7*b^6*c^4*d^5 - 1280*a^8*b^5*c^3*d^6 + 2304*a^9*b^4*c^2*d^7))/(512*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)*(a^8*d^4 + a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3)))*(-a^5*b)^(1/2)*(15*a^2*d^2 + 3*b^2*c^2 - 10*a*b*c*d))/(16*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)))*(-a^5*b)^(1/2)*(15*a^2*d^2 + 3*b^2*c^2 - 10*a*b*c*d)*1i)/(16*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)) + (((x*(289*a^4*b^3*d^7 + 9*b^7*c^4*d^3 - 60*a*b^6*c^3*d^4 - 300*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(a^8*d^4 + a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3)) + (((256*a^10*b^2*d^10 - 1760*a^9*b^3*c*d^9 + 96*a^2*b^10*c^8*d^2 - 800*a^3*b^9*c^7*d^3 + 3040*a^4*b^8*c^6*d^4 - 6816*a^5*b^7*c^5*d^5 + 9760*a^6*b^6*c^4*d^6 - 9056*a^7*b^5*c^3*d^7 + 5280*a^8*b^4*c^2*d^8)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)) + (x*(-a^5*b)^(1/2)*(15*a^2*d^2 + 3*b^2*c^2 - 10*a*b*c*d)*(256*a^11*b^2*d^9 - 1280*a^10*b^3*c*d^8 + 256*a^4*b^9*c^7*d^2 - 1280*a^5*b^8*c^6*d^3 + 2304*a^6*b^7*c^5*d^4 - 1280*a^7*b^6*c^4*d^5 - 1280*a^8*b^5*c^3*d^6 + 2304*a^9*b^4*c^2*d^7))/(512*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)*(a^8*d^4 + a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3)))*(-a^5*b)^(1/2)*(15*a^2*d^2 + 3*b^2*c^2 - 10*a*b*c*d))/(16*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)))*(-a^5*b)^(1/2)*(15*a^2*d^2 + 3*b^2*c^2 - 10*a*b*c*d)*1i)/(16*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)))/((105*a^3*b^3*d^8 - 9*b^6*c^3*d^5 + 51*a*b^5*c^2*d^6 - 115*a^2*b^4*c*d^7)/(32*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)) - (((x*(289*a^4*b^3*d^7 + 9*b^7*c^4*d^3 - 60*a*b^6*c^3*d^4 - 300*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(a^8*d^4 + a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3)) - (((256*a^10*b^2*d^10 - 1760*a^9*b^3*c*d^9 + 96*a^2*b^10*c^8*d^2 - 800*a^3*b^9*c^7*d^3 + 3040*a^4*b^8*c^6*d^4 - 6816*a^5*b^7*c^5*d^5 + 9760*a^6*b^6*c^4*d^6 - 9056*a^7*b^5*c^3*d^7 + 5280*a^8*b^4*c^2*d^8)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)) - (x*(-a^5*b)^(1/2)*(15*a^2*d^2 + 3*b^2*c^2 - 10*a*b*c*d)*(256*a^11*b^2*d^9 - 1280*a^10*b^3*c*d^8 + 256*a^4*b^9*c^7*d^2 - 1280*a^5*b^8*c^6*d^3 + 2304*a^6*b^7*c^5*d^4 - 1280*a^7*b^6*c^4*d^5 - 1280*a^8*b^5*c^3*d^6 + 2304*a^9*b^4*c^2*d^7))/(512*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)*(a^8*d^4 + a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3)))*(-a^5*b)^(1/2)*(15*a^2*d^2 + 3*b^2*c^2 - 10*a*b*c*d))/(16*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)))*(-a^5*b)^(1/2)*(15*a^2*d^2 + 3*b^2*c^2 - 10*a*b*c*d))/(16*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)) + (((x*(289*a^4*b^3*d^7 + 9*b^7*c^4*d^3 - 60*a*b^6*c^3*d^4 - 300*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(a^8*d^4 + a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3)) + (((256*a^10*b^2*d^10 - 1760*a^9*b^3*c*d^9 + 96*a^2*b^10*c^8*d^2 - 800*a^3*b^9*c^7*d^3 + 3040*a^4*b^8*c^6*d^4 - 6816*a^5*b^7*c^5*d^5 + 9760*a^6*b^6*c^4*d^6 - 9056*a^7*b^5*c^3*d^7 + 5280*a^8*b^4*c^2*d^8)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)) + (x*(-a^5*b)^(1/2)*(15*a^2*d^2 + 3*b^2*c^2 - 10*a*b*c*d)*(256*a^11*b^2*d^9 - 1280*a^10*b^3*c*d^8 + 256*a^4*b^9*c^7*d^2 - 1280*a^5*b^8*c^6*d^3 + 2304*a^6*b^7*c^5*d^4 - 1280*a^7*b^6*c^4*d^5 - 1280*a^8*b^5*c^3*d^6 + 2304*a^9*b^4*c^2*d^7))/(512*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)*(a^8*d^4 + a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3)))*(-a^5*b)^(1/2)*(15*a^2*d^2 + 3*b^2*c^2 - 10*a*b*c*d))/(16*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)))*(-a^5*b)^(1/2)*(15*a^2*d^2 + 3*b^2*c^2 - 10*a*b*c*d))/(16*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2))))*(-a^5*b)^(1/2)*(15*a^2*d^2 + 3*b^2*c^2 - 10*a*b*c*d)*1i)/(8*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2))","B"
41,1,8635,236,7.854714,"\text{Not used}","int(1/((a + b*x^2)^3*(c + d*x^2)^2),x)","\frac{\frac{x^5\,\left(4\,a^2\,b^2\,d^3+11\,a\,b^3\,c\,d^2-3\,b^4\,c^2\,d\right)}{8\,a^2\,c\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{x\,\left(4\,a^3\,d^3+13\,a\,b^2\,c^2\,d-5\,b^3\,c^3\right)}{8\,a\,c\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{b\,x^3\,\left(8\,a^3\,d^3+13\,a^2\,b\,c\,d^2+6\,a\,b^2\,c^2\,d-3\,b^3\,c^3\right)}{8\,a^2\,c\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{a^2\,c+x^2\,\left(d\,a^2+2\,b\,c\,a\right)+x^4\,\left(c\,b^2+2\,a\,d\,b\right)+b^2\,d\,x^6}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(16\,a^6\,b^3\,d^9-224\,a^5\,b^4\,c\,d^8+2009\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+406\,a^2\,b^7\,c^4\,d^5-84\,a\,b^8\,c^5\,d^4+9\,b^9\,c^6\,d^3\right)}{32\,\left(a^{10}\,c^2\,d^6-6\,a^9\,b\,c^3\,d^5+15\,a^8\,b^2\,c^4\,d^4-20\,a^7\,b^3\,c^5\,d^3+15\,a^6\,b^4\,c^6\,d^2-6\,a^5\,b^5\,c^7\,d+a^4\,b^6\,c^8\right)}-\frac{\left(\frac{2\,a^{13}\,b^2\,c\,d^{13}-28\,a^{12}\,b^3\,c^2\,d^{12}+\frac{315\,a^{11}\,b^4\,c^3\,d^{11}}{2}-\frac{987\,a^{10}\,b^5\,c^4\,d^{10}}{2}+978\,a^9\,b^6\,c^5\,d^9-1302\,a^8\,b^7\,c^6\,d^8+1197\,a^7\,b^8\,c^7\,d^7-765\,a^6\,b^9\,c^8\,d^6+336\,a^5\,b^{10}\,c^9\,d^5-98\,a^4\,b^{11}\,c^{10}\,d^4+\frac{35\,a^3\,b^{12}\,c^{11}\,d^3}{2}-\frac{3\,a^2\,b^{13}\,c^{12}\,d^2}{2}}{-a^{13}\,c^2\,d^9+9\,a^{12}\,b\,c^3\,d^8-36\,a^{11}\,b^2\,c^4\,d^7+84\,a^{10}\,b^3\,c^5\,d^6-126\,a^9\,b^4\,c^6\,d^5+126\,a^8\,b^5\,c^7\,d^4-84\,a^7\,b^6\,c^8\,d^3+36\,a^6\,b^7\,c^9\,d^2-9\,a^5\,b^8\,c^{10}\,d+a^4\,b^9\,c^{11}}-\frac{x\,\sqrt{-a^5\,b^3}\,\left(35\,a^2\,d^2-14\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(256\,a^{13}\,b^2\,c^2\,d^{11}-1792\,a^{12}\,b^3\,c^3\,d^{10}+5120\,a^{11}\,b^4\,c^4\,d^9-7168\,a^{10}\,b^5\,c^5\,d^8+3584\,a^9\,b^6\,c^6\,d^7+3584\,a^8\,b^7\,c^7\,d^6-7168\,a^7\,b^8\,c^8\,d^5+5120\,a^6\,b^9\,c^9\,d^4-1792\,a^5\,b^{10}\,c^{10}\,d^3+256\,a^4\,b^{11}\,c^{11}\,d^2\right)}{512\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)\,\left(a^{10}\,c^2\,d^6-6\,a^9\,b\,c^3\,d^5+15\,a^8\,b^2\,c^4\,d^4-20\,a^7\,b^3\,c^5\,d^3+15\,a^6\,b^4\,c^6\,d^2-6\,a^5\,b^5\,c^7\,d+a^4\,b^6\,c^8\right)}\right)\,\sqrt{-a^5\,b^3}\,\left(35\,a^2\,d^2-14\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}\right)\,\sqrt{-a^5\,b^3}\,\left(35\,a^2\,d^2-14\,a\,b\,c\,d+3\,b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}+\frac{\left(\frac{x\,\left(16\,a^6\,b^3\,d^9-224\,a^5\,b^4\,c\,d^8+2009\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+406\,a^2\,b^7\,c^4\,d^5-84\,a\,b^8\,c^5\,d^4+9\,b^9\,c^6\,d^3\right)}{32\,\left(a^{10}\,c^2\,d^6-6\,a^9\,b\,c^3\,d^5+15\,a^8\,b^2\,c^4\,d^4-20\,a^7\,b^3\,c^5\,d^3+15\,a^6\,b^4\,c^6\,d^2-6\,a^5\,b^5\,c^7\,d+a^4\,b^6\,c^8\right)}+\frac{\left(\frac{2\,a^{13}\,b^2\,c\,d^{13}-28\,a^{12}\,b^3\,c^2\,d^{12}+\frac{315\,a^{11}\,b^4\,c^3\,d^{11}}{2}-\frac{987\,a^{10}\,b^5\,c^4\,d^{10}}{2}+978\,a^9\,b^6\,c^5\,d^9-1302\,a^8\,b^7\,c^6\,d^8+1197\,a^7\,b^8\,c^7\,d^7-765\,a^6\,b^9\,c^8\,d^6+336\,a^5\,b^{10}\,c^9\,d^5-98\,a^4\,b^{11}\,c^{10}\,d^4+\frac{35\,a^3\,b^{12}\,c^{11}\,d^3}{2}-\frac{3\,a^2\,b^{13}\,c^{12}\,d^2}{2}}{-a^{13}\,c^2\,d^9+9\,a^{12}\,b\,c^3\,d^8-36\,a^{11}\,b^2\,c^4\,d^7+84\,a^{10}\,b^3\,c^5\,d^6-126\,a^9\,b^4\,c^6\,d^5+126\,a^8\,b^5\,c^7\,d^4-84\,a^7\,b^6\,c^8\,d^3+36\,a^6\,b^7\,c^9\,d^2-9\,a^5\,b^8\,c^{10}\,d+a^4\,b^9\,c^{11}}+\frac{x\,\sqrt{-a^5\,b^3}\,\left(35\,a^2\,d^2-14\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(256\,a^{13}\,b^2\,c^2\,d^{11}-1792\,a^{12}\,b^3\,c^3\,d^{10}+5120\,a^{11}\,b^4\,c^4\,d^9-7168\,a^{10}\,b^5\,c^5\,d^8+3584\,a^9\,b^6\,c^6\,d^7+3584\,a^8\,b^7\,c^7\,d^6-7168\,a^7\,b^8\,c^8\,d^5+5120\,a^6\,b^9\,c^9\,d^4-1792\,a^5\,b^{10}\,c^{10}\,d^3+256\,a^4\,b^{11}\,c^{11}\,d^2\right)}{512\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)\,\left(a^{10}\,c^2\,d^6-6\,a^9\,b\,c^3\,d^5+15\,a^8\,b^2\,c^4\,d^4-20\,a^7\,b^3\,c^5\,d^3+15\,a^6\,b^4\,c^6\,d^2-6\,a^5\,b^5\,c^7\,d+a^4\,b^6\,c^8\right)}\right)\,\sqrt{-a^5\,b^3}\,\left(35\,a^2\,d^2-14\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}\right)\,\sqrt{-a^5\,b^3}\,\left(35\,a^2\,d^2-14\,a\,b\,c\,d+3\,b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}}{\frac{\frac{35\,a^5\,b^4\,d^{10}}{16}-\frac{651\,a^4\,b^5\,c\,d^9}{64}-\frac{1275\,a^3\,b^6\,c^2\,d^8}{32}+\frac{451\,a^2\,b^7\,c^3\,d^7}{16}-\frac{267\,a\,b^8\,c^4\,d^6}{32}+\frac{63\,b^9\,c^5\,d^5}{64}}{-a^{13}\,c^2\,d^9+9\,a^{12}\,b\,c^3\,d^8-36\,a^{11}\,b^2\,c^4\,d^7+84\,a^{10}\,b^3\,c^5\,d^6-126\,a^9\,b^4\,c^6\,d^5+126\,a^8\,b^5\,c^7\,d^4-84\,a^7\,b^6\,c^8\,d^3+36\,a^6\,b^7\,c^9\,d^2-9\,a^5\,b^8\,c^{10}\,d+a^4\,b^9\,c^{11}}-\frac{\left(\frac{x\,\left(16\,a^6\,b^3\,d^9-224\,a^5\,b^4\,c\,d^8+2009\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+406\,a^2\,b^7\,c^4\,d^5-84\,a\,b^8\,c^5\,d^4+9\,b^9\,c^6\,d^3\right)}{32\,\left(a^{10}\,c^2\,d^6-6\,a^9\,b\,c^3\,d^5+15\,a^8\,b^2\,c^4\,d^4-20\,a^7\,b^3\,c^5\,d^3+15\,a^6\,b^4\,c^6\,d^2-6\,a^5\,b^5\,c^7\,d+a^4\,b^6\,c^8\right)}-\frac{\left(\frac{2\,a^{13}\,b^2\,c\,d^{13}-28\,a^{12}\,b^3\,c^2\,d^{12}+\frac{315\,a^{11}\,b^4\,c^3\,d^{11}}{2}-\frac{987\,a^{10}\,b^5\,c^4\,d^{10}}{2}+978\,a^9\,b^6\,c^5\,d^9-1302\,a^8\,b^7\,c^6\,d^8+1197\,a^7\,b^8\,c^7\,d^7-765\,a^6\,b^9\,c^8\,d^6+336\,a^5\,b^{10}\,c^9\,d^5-98\,a^4\,b^{11}\,c^{10}\,d^4+\frac{35\,a^3\,b^{12}\,c^{11}\,d^3}{2}-\frac{3\,a^2\,b^{13}\,c^{12}\,d^2}{2}}{-a^{13}\,c^2\,d^9+9\,a^{12}\,b\,c^3\,d^8-36\,a^{11}\,b^2\,c^4\,d^7+84\,a^{10}\,b^3\,c^5\,d^6-126\,a^9\,b^4\,c^6\,d^5+126\,a^8\,b^5\,c^7\,d^4-84\,a^7\,b^6\,c^8\,d^3+36\,a^6\,b^7\,c^9\,d^2-9\,a^5\,b^8\,c^{10}\,d+a^4\,b^9\,c^{11}}-\frac{x\,\sqrt{-a^5\,b^3}\,\left(35\,a^2\,d^2-14\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(256\,a^{13}\,b^2\,c^2\,d^{11}-1792\,a^{12}\,b^3\,c^3\,d^{10}+5120\,a^{11}\,b^4\,c^4\,d^9-7168\,a^{10}\,b^5\,c^5\,d^8+3584\,a^9\,b^6\,c^6\,d^7+3584\,a^8\,b^7\,c^7\,d^6-7168\,a^7\,b^8\,c^8\,d^5+5120\,a^6\,b^9\,c^9\,d^4-1792\,a^5\,b^{10}\,c^{10}\,d^3+256\,a^4\,b^{11}\,c^{11}\,d^2\right)}{512\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)\,\left(a^{10}\,c^2\,d^6-6\,a^9\,b\,c^3\,d^5+15\,a^8\,b^2\,c^4\,d^4-20\,a^7\,b^3\,c^5\,d^3+15\,a^6\,b^4\,c^6\,d^2-6\,a^5\,b^5\,c^7\,d+a^4\,b^6\,c^8\right)}\right)\,\sqrt{-a^5\,b^3}\,\left(35\,a^2\,d^2-14\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}\right)\,\sqrt{-a^5\,b^3}\,\left(35\,a^2\,d^2-14\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}+\frac{\left(\frac{x\,\left(16\,a^6\,b^3\,d^9-224\,a^5\,b^4\,c\,d^8+2009\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+406\,a^2\,b^7\,c^4\,d^5-84\,a\,b^8\,c^5\,d^4+9\,b^9\,c^6\,d^3\right)}{32\,\left(a^{10}\,c^2\,d^6-6\,a^9\,b\,c^3\,d^5+15\,a^8\,b^2\,c^4\,d^4-20\,a^7\,b^3\,c^5\,d^3+15\,a^6\,b^4\,c^6\,d^2-6\,a^5\,b^5\,c^7\,d+a^4\,b^6\,c^8\right)}+\frac{\left(\frac{2\,a^{13}\,b^2\,c\,d^{13}-28\,a^{12}\,b^3\,c^2\,d^{12}+\frac{315\,a^{11}\,b^4\,c^3\,d^{11}}{2}-\frac{987\,a^{10}\,b^5\,c^4\,d^{10}}{2}+978\,a^9\,b^6\,c^5\,d^9-1302\,a^8\,b^7\,c^6\,d^8+1197\,a^7\,b^8\,c^7\,d^7-765\,a^6\,b^9\,c^8\,d^6+336\,a^5\,b^{10}\,c^9\,d^5-98\,a^4\,b^{11}\,c^{10}\,d^4+\frac{35\,a^3\,b^{12}\,c^{11}\,d^3}{2}-\frac{3\,a^2\,b^{13}\,c^{12}\,d^2}{2}}{-a^{13}\,c^2\,d^9+9\,a^{12}\,b\,c^3\,d^8-36\,a^{11}\,b^2\,c^4\,d^7+84\,a^{10}\,b^3\,c^5\,d^6-126\,a^9\,b^4\,c^6\,d^5+126\,a^8\,b^5\,c^7\,d^4-84\,a^7\,b^6\,c^8\,d^3+36\,a^6\,b^7\,c^9\,d^2-9\,a^5\,b^8\,c^{10}\,d+a^4\,b^9\,c^{11}}+\frac{x\,\sqrt{-a^5\,b^3}\,\left(35\,a^2\,d^2-14\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(256\,a^{13}\,b^2\,c^2\,d^{11}-1792\,a^{12}\,b^3\,c^3\,d^{10}+5120\,a^{11}\,b^4\,c^4\,d^9-7168\,a^{10}\,b^5\,c^5\,d^8+3584\,a^9\,b^6\,c^6\,d^7+3584\,a^8\,b^7\,c^7\,d^6-7168\,a^7\,b^8\,c^8\,d^5+5120\,a^6\,b^9\,c^9\,d^4-1792\,a^5\,b^{10}\,c^{10}\,d^3+256\,a^4\,b^{11}\,c^{11}\,d^2\right)}{512\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)\,\left(a^{10}\,c^2\,d^6-6\,a^9\,b\,c^3\,d^5+15\,a^8\,b^2\,c^4\,d^4-20\,a^7\,b^3\,c^5\,d^3+15\,a^6\,b^4\,c^6\,d^2-6\,a^5\,b^5\,c^7\,d+a^4\,b^6\,c^8\right)}\right)\,\sqrt{-a^5\,b^3}\,\left(35\,a^2\,d^2-14\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}\right)\,\sqrt{-a^5\,b^3}\,\left(35\,a^2\,d^2-14\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}}\right)\,\sqrt{-a^5\,b^3}\,\left(35\,a^2\,d^2-14\,a\,b\,c\,d+3\,b^2\,c^2\right)\,1{}\mathrm{i}}{8\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(16\,a^6\,b^3\,d^9-224\,a^5\,b^4\,c\,d^8+2009\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+406\,a^2\,b^7\,c^4\,d^5-84\,a\,b^8\,c^5\,d^4+9\,b^9\,c^6\,d^3\right)}{32\,\left(a^{10}\,c^2\,d^6-6\,a^9\,b\,c^3\,d^5+15\,a^8\,b^2\,c^4\,d^4-20\,a^7\,b^3\,c^5\,d^3+15\,a^6\,b^4\,c^6\,d^2-6\,a^5\,b^5\,c^7\,d+a^4\,b^6\,c^8\right)}-\frac{\left(a\,d-7\,b\,c\right)\,\sqrt{-c^3\,d^5}\,\left(\frac{2\,a^{13}\,b^2\,c\,d^{13}-28\,a^{12}\,b^3\,c^2\,d^{12}+\frac{315\,a^{11}\,b^4\,c^3\,d^{11}}{2}-\frac{987\,a^{10}\,b^5\,c^4\,d^{10}}{2}+978\,a^9\,b^6\,c^5\,d^9-1302\,a^8\,b^7\,c^6\,d^8+1197\,a^7\,b^8\,c^7\,d^7-765\,a^6\,b^9\,c^8\,d^6+336\,a^5\,b^{10}\,c^9\,d^5-98\,a^4\,b^{11}\,c^{10}\,d^4+\frac{35\,a^3\,b^{12}\,c^{11}\,d^3}{2}-\frac{3\,a^2\,b^{13}\,c^{12}\,d^2}{2}}{-a^{13}\,c^2\,d^9+9\,a^{12}\,b\,c^3\,d^8-36\,a^{11}\,b^2\,c^4\,d^7+84\,a^{10}\,b^3\,c^5\,d^6-126\,a^9\,b^4\,c^6\,d^5+126\,a^8\,b^5\,c^7\,d^4-84\,a^7\,b^6\,c^8\,d^3+36\,a^6\,b^7\,c^9\,d^2-9\,a^5\,b^8\,c^{10}\,d+a^4\,b^9\,c^{11}}-\frac{x\,\left(a\,d-7\,b\,c\right)\,\sqrt{-c^3\,d^5}\,\left(256\,a^{13}\,b^2\,c^2\,d^{11}-1792\,a^{12}\,b^3\,c^3\,d^{10}+5120\,a^{11}\,b^4\,c^4\,d^9-7168\,a^{10}\,b^5\,c^5\,d^8+3584\,a^9\,b^6\,c^6\,d^7+3584\,a^8\,b^7\,c^7\,d^6-7168\,a^7\,b^8\,c^8\,d^5+5120\,a^6\,b^9\,c^9\,d^4-1792\,a^5\,b^{10}\,c^{10}\,d^3+256\,a^4\,b^{11}\,c^{11}\,d^2\right)}{128\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)\,\left(a^{10}\,c^2\,d^6-6\,a^9\,b\,c^3\,d^5+15\,a^8\,b^2\,c^4\,d^4-20\,a^7\,b^3\,c^5\,d^3+15\,a^6\,b^4\,c^6\,d^2-6\,a^5\,b^5\,c^7\,d+a^4\,b^6\,c^8\right)}\right)}{4\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}\right)\,\left(a\,d-7\,b\,c\right)\,\sqrt{-c^3\,d^5}\,1{}\mathrm{i}}{4\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}+\frac{\left(\frac{x\,\left(16\,a^6\,b^3\,d^9-224\,a^5\,b^4\,c\,d^8+2009\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+406\,a^2\,b^7\,c^4\,d^5-84\,a\,b^8\,c^5\,d^4+9\,b^9\,c^6\,d^3\right)}{32\,\left(a^{10}\,c^2\,d^6-6\,a^9\,b\,c^3\,d^5+15\,a^8\,b^2\,c^4\,d^4-20\,a^7\,b^3\,c^5\,d^3+15\,a^6\,b^4\,c^6\,d^2-6\,a^5\,b^5\,c^7\,d+a^4\,b^6\,c^8\right)}+\frac{\left(a\,d-7\,b\,c\right)\,\sqrt{-c^3\,d^5}\,\left(\frac{2\,a^{13}\,b^2\,c\,d^{13}-28\,a^{12}\,b^3\,c^2\,d^{12}+\frac{315\,a^{11}\,b^4\,c^3\,d^{11}}{2}-\frac{987\,a^{10}\,b^5\,c^4\,d^{10}}{2}+978\,a^9\,b^6\,c^5\,d^9-1302\,a^8\,b^7\,c^6\,d^8+1197\,a^7\,b^8\,c^7\,d^7-765\,a^6\,b^9\,c^8\,d^6+336\,a^5\,b^{10}\,c^9\,d^5-98\,a^4\,b^{11}\,c^{10}\,d^4+\frac{35\,a^3\,b^{12}\,c^{11}\,d^3}{2}-\frac{3\,a^2\,b^{13}\,c^{12}\,d^2}{2}}{-a^{13}\,c^2\,d^9+9\,a^{12}\,b\,c^3\,d^8-36\,a^{11}\,b^2\,c^4\,d^7+84\,a^{10}\,b^3\,c^5\,d^6-126\,a^9\,b^4\,c^6\,d^5+126\,a^8\,b^5\,c^7\,d^4-84\,a^7\,b^6\,c^8\,d^3+36\,a^6\,b^7\,c^9\,d^2-9\,a^5\,b^8\,c^{10}\,d+a^4\,b^9\,c^{11}}+\frac{x\,\left(a\,d-7\,b\,c\right)\,\sqrt{-c^3\,d^5}\,\left(256\,a^{13}\,b^2\,c^2\,d^{11}-1792\,a^{12}\,b^3\,c^3\,d^{10}+5120\,a^{11}\,b^4\,c^4\,d^9-7168\,a^{10}\,b^5\,c^5\,d^8+3584\,a^9\,b^6\,c^6\,d^7+3584\,a^8\,b^7\,c^7\,d^6-7168\,a^7\,b^8\,c^8\,d^5+5120\,a^6\,b^9\,c^9\,d^4-1792\,a^5\,b^{10}\,c^{10}\,d^3+256\,a^4\,b^{11}\,c^{11}\,d^2\right)}{128\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)\,\left(a^{10}\,c^2\,d^6-6\,a^9\,b\,c^3\,d^5+15\,a^8\,b^2\,c^4\,d^4-20\,a^7\,b^3\,c^5\,d^3+15\,a^6\,b^4\,c^6\,d^2-6\,a^5\,b^5\,c^7\,d+a^4\,b^6\,c^8\right)}\right)}{4\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}\right)\,\left(a\,d-7\,b\,c\right)\,\sqrt{-c^3\,d^5}\,1{}\mathrm{i}}{4\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}}{\frac{\frac{35\,a^5\,b^4\,d^{10}}{16}-\frac{651\,a^4\,b^5\,c\,d^9}{64}-\frac{1275\,a^3\,b^6\,c^2\,d^8}{32}+\frac{451\,a^2\,b^7\,c^3\,d^7}{16}-\frac{267\,a\,b^8\,c^4\,d^6}{32}+\frac{63\,b^9\,c^5\,d^5}{64}}{-a^{13}\,c^2\,d^9+9\,a^{12}\,b\,c^3\,d^8-36\,a^{11}\,b^2\,c^4\,d^7+84\,a^{10}\,b^3\,c^5\,d^6-126\,a^9\,b^4\,c^6\,d^5+126\,a^8\,b^5\,c^7\,d^4-84\,a^7\,b^6\,c^8\,d^3+36\,a^6\,b^7\,c^9\,d^2-9\,a^5\,b^8\,c^{10}\,d+a^4\,b^9\,c^{11}}-\frac{\left(\frac{x\,\left(16\,a^6\,b^3\,d^9-224\,a^5\,b^4\,c\,d^8+2009\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+406\,a^2\,b^7\,c^4\,d^5-84\,a\,b^8\,c^5\,d^4+9\,b^9\,c^6\,d^3\right)}{32\,\left(a^{10}\,c^2\,d^6-6\,a^9\,b\,c^3\,d^5+15\,a^8\,b^2\,c^4\,d^4-20\,a^7\,b^3\,c^5\,d^3+15\,a^6\,b^4\,c^6\,d^2-6\,a^5\,b^5\,c^7\,d+a^4\,b^6\,c^8\right)}-\frac{\left(a\,d-7\,b\,c\right)\,\sqrt{-c^3\,d^5}\,\left(\frac{2\,a^{13}\,b^2\,c\,d^{13}-28\,a^{12}\,b^3\,c^2\,d^{12}+\frac{315\,a^{11}\,b^4\,c^3\,d^{11}}{2}-\frac{987\,a^{10}\,b^5\,c^4\,d^{10}}{2}+978\,a^9\,b^6\,c^5\,d^9-1302\,a^8\,b^7\,c^6\,d^8+1197\,a^7\,b^8\,c^7\,d^7-765\,a^6\,b^9\,c^8\,d^6+336\,a^5\,b^{10}\,c^9\,d^5-98\,a^4\,b^{11}\,c^{10}\,d^4+\frac{35\,a^3\,b^{12}\,c^{11}\,d^3}{2}-\frac{3\,a^2\,b^{13}\,c^{12}\,d^2}{2}}{-a^{13}\,c^2\,d^9+9\,a^{12}\,b\,c^3\,d^8-36\,a^{11}\,b^2\,c^4\,d^7+84\,a^{10}\,b^3\,c^5\,d^6-126\,a^9\,b^4\,c^6\,d^5+126\,a^8\,b^5\,c^7\,d^4-84\,a^7\,b^6\,c^8\,d^3+36\,a^6\,b^7\,c^9\,d^2-9\,a^5\,b^8\,c^{10}\,d+a^4\,b^9\,c^{11}}-\frac{x\,\left(a\,d-7\,b\,c\right)\,\sqrt{-c^3\,d^5}\,\left(256\,a^{13}\,b^2\,c^2\,d^{11}-1792\,a^{12}\,b^3\,c^3\,d^{10}+5120\,a^{11}\,b^4\,c^4\,d^9-7168\,a^{10}\,b^5\,c^5\,d^8+3584\,a^9\,b^6\,c^6\,d^7+3584\,a^8\,b^7\,c^7\,d^6-7168\,a^7\,b^8\,c^8\,d^5+5120\,a^6\,b^9\,c^9\,d^4-1792\,a^5\,b^{10}\,c^{10}\,d^3+256\,a^4\,b^{11}\,c^{11}\,d^2\right)}{128\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)\,\left(a^{10}\,c^2\,d^6-6\,a^9\,b\,c^3\,d^5+15\,a^8\,b^2\,c^4\,d^4-20\,a^7\,b^3\,c^5\,d^3+15\,a^6\,b^4\,c^6\,d^2-6\,a^5\,b^5\,c^7\,d+a^4\,b^6\,c^8\right)}\right)}{4\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}\right)\,\left(a\,d-7\,b\,c\right)\,\sqrt{-c^3\,d^5}}{4\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}+\frac{\left(\frac{x\,\left(16\,a^6\,b^3\,d^9-224\,a^5\,b^4\,c\,d^8+2009\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+406\,a^2\,b^7\,c^4\,d^5-84\,a\,b^8\,c^5\,d^4+9\,b^9\,c^6\,d^3\right)}{32\,\left(a^{10}\,c^2\,d^6-6\,a^9\,b\,c^3\,d^5+15\,a^8\,b^2\,c^4\,d^4-20\,a^7\,b^3\,c^5\,d^3+15\,a^6\,b^4\,c^6\,d^2-6\,a^5\,b^5\,c^7\,d+a^4\,b^6\,c^8\right)}+\frac{\left(a\,d-7\,b\,c\right)\,\sqrt{-c^3\,d^5}\,\left(\frac{2\,a^{13}\,b^2\,c\,d^{13}-28\,a^{12}\,b^3\,c^2\,d^{12}+\frac{315\,a^{11}\,b^4\,c^3\,d^{11}}{2}-\frac{987\,a^{10}\,b^5\,c^4\,d^{10}}{2}+978\,a^9\,b^6\,c^5\,d^9-1302\,a^8\,b^7\,c^6\,d^8+1197\,a^7\,b^8\,c^7\,d^7-765\,a^6\,b^9\,c^8\,d^6+336\,a^5\,b^{10}\,c^9\,d^5-98\,a^4\,b^{11}\,c^{10}\,d^4+\frac{35\,a^3\,b^{12}\,c^{11}\,d^3}{2}-\frac{3\,a^2\,b^{13}\,c^{12}\,d^2}{2}}{-a^{13}\,c^2\,d^9+9\,a^{12}\,b\,c^3\,d^8-36\,a^{11}\,b^2\,c^4\,d^7+84\,a^{10}\,b^3\,c^5\,d^6-126\,a^9\,b^4\,c^6\,d^5+126\,a^8\,b^5\,c^7\,d^4-84\,a^7\,b^6\,c^8\,d^3+36\,a^6\,b^7\,c^9\,d^2-9\,a^5\,b^8\,c^{10}\,d+a^4\,b^9\,c^{11}}+\frac{x\,\left(a\,d-7\,b\,c\right)\,\sqrt{-c^3\,d^5}\,\left(256\,a^{13}\,b^2\,c^2\,d^{11}-1792\,a^{12}\,b^3\,c^3\,d^{10}+5120\,a^{11}\,b^4\,c^4\,d^9-7168\,a^{10}\,b^5\,c^5\,d^8+3584\,a^9\,b^6\,c^6\,d^7+3584\,a^8\,b^7\,c^7\,d^6-7168\,a^7\,b^8\,c^8\,d^5+5120\,a^6\,b^9\,c^9\,d^4-1792\,a^5\,b^{10}\,c^{10}\,d^3+256\,a^4\,b^{11}\,c^{11}\,d^2\right)}{128\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)\,\left(a^{10}\,c^2\,d^6-6\,a^9\,b\,c^3\,d^5+15\,a^8\,b^2\,c^4\,d^4-20\,a^7\,b^3\,c^5\,d^3+15\,a^6\,b^4\,c^6\,d^2-6\,a^5\,b^5\,c^7\,d+a^4\,b^6\,c^8\right)}\right)}{4\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}\right)\,\left(a\,d-7\,b\,c\right)\,\sqrt{-c^3\,d^5}}{4\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}}\right)\,\left(a\,d-7\,b\,c\right)\,\sqrt{-c^3\,d^5}\,1{}\mathrm{i}}{2\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}","Not used",1,"((x^5*(4*a^2*b^2*d^3 - 3*b^4*c^2*d + 11*a*b^3*c*d^2))/(8*a^2*c*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x*(4*a^3*d^3 - 5*b^3*c^3 + 13*a*b^2*c^2*d))/(8*a*c*(a*d - b*c)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*x^3*(8*a^3*d^3 - 3*b^3*c^3 + 6*a*b^2*c^2*d + 13*a^2*b*c*d^2))/(8*a^2*c*(a*d - b*c)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(a^2*c + x^2*(a^2*d + 2*a*b*c) + x^4*(b^2*c + 2*a*b*d) + b^2*d*x^6) - (atan(((((x*(16*a^6*b^3*d^9 + 9*b^9*c^6*d^3 - 84*a*b^8*c^5*d^4 - 224*a^5*b^4*c*d^8 + 406*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 2009*a^4*b^5*c^2*d^7))/(32*(a^4*b^6*c^8 + a^10*c^2*d^6 - 6*a^5*b^5*c^7*d - 6*a^9*b*c^3*d^5 + 15*a^6*b^4*c^6*d^2 - 20*a^7*b^3*c^5*d^3 + 15*a^8*b^2*c^4*d^4)) - (((2*a^13*b^2*c*d^13 - (3*a^2*b^13*c^12*d^2)/2 + (35*a^3*b^12*c^11*d^3)/2 - 98*a^4*b^11*c^10*d^4 + 336*a^5*b^10*c^9*d^5 - 765*a^6*b^9*c^8*d^6 + 1197*a^7*b^8*c^7*d^7 - 1302*a^8*b^7*c^6*d^8 + 978*a^9*b^6*c^5*d^9 - (987*a^10*b^5*c^4*d^10)/2 + (315*a^11*b^4*c^3*d^11)/2 - 28*a^12*b^3*c^2*d^12)/(a^4*b^9*c^11 - a^13*c^2*d^9 - 9*a^5*b^8*c^10*d + 9*a^12*b*c^3*d^8 + 36*a^6*b^7*c^9*d^2 - 84*a^7*b^6*c^8*d^3 + 126*a^8*b^5*c^7*d^4 - 126*a^9*b^4*c^6*d^5 + 84*a^10*b^3*c^5*d^6 - 36*a^11*b^2*c^4*d^7) - (x*(-a^5*b^3)^(1/2)*(35*a^2*d^2 + 3*b^2*c^2 - 14*a*b*c*d)*(256*a^4*b^11*c^11*d^2 - 1792*a^5*b^10*c^10*d^3 + 5120*a^6*b^9*c^9*d^4 - 7168*a^7*b^8*c^8*d^5 + 3584*a^8*b^7*c^7*d^6 + 3584*a^9*b^6*c^6*d^7 - 7168*a^10*b^5*c^5*d^8 + 5120*a^11*b^4*c^4*d^9 - 1792*a^12*b^3*c^3*d^10 + 256*a^13*b^2*c^2*d^11))/(512*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)*(a^4*b^6*c^8 + a^10*c^2*d^6 - 6*a^5*b^5*c^7*d - 6*a^9*b*c^3*d^5 + 15*a^6*b^4*c^6*d^2 - 20*a^7*b^3*c^5*d^3 + 15*a^8*b^2*c^4*d^4)))*(-a^5*b^3)^(1/2)*(35*a^2*d^2 + 3*b^2*c^2 - 14*a*b*c*d))/(16*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)))*(-a^5*b^3)^(1/2)*(35*a^2*d^2 + 3*b^2*c^2 - 14*a*b*c*d)*1i)/(16*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)) + (((x*(16*a^6*b^3*d^9 + 9*b^9*c^6*d^3 - 84*a*b^8*c^5*d^4 - 224*a^5*b^4*c*d^8 + 406*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 2009*a^4*b^5*c^2*d^7))/(32*(a^4*b^6*c^8 + a^10*c^2*d^6 - 6*a^5*b^5*c^7*d - 6*a^9*b*c^3*d^5 + 15*a^6*b^4*c^6*d^2 - 20*a^7*b^3*c^5*d^3 + 15*a^8*b^2*c^4*d^4)) + (((2*a^13*b^2*c*d^13 - (3*a^2*b^13*c^12*d^2)/2 + (35*a^3*b^12*c^11*d^3)/2 - 98*a^4*b^11*c^10*d^4 + 336*a^5*b^10*c^9*d^5 - 765*a^6*b^9*c^8*d^6 + 1197*a^7*b^8*c^7*d^7 - 1302*a^8*b^7*c^6*d^8 + 978*a^9*b^6*c^5*d^9 - (987*a^10*b^5*c^4*d^10)/2 + (315*a^11*b^4*c^3*d^11)/2 - 28*a^12*b^3*c^2*d^12)/(a^4*b^9*c^11 - a^13*c^2*d^9 - 9*a^5*b^8*c^10*d + 9*a^12*b*c^3*d^8 + 36*a^6*b^7*c^9*d^2 - 84*a^7*b^6*c^8*d^3 + 126*a^8*b^5*c^7*d^4 - 126*a^9*b^4*c^6*d^5 + 84*a^10*b^3*c^5*d^6 - 36*a^11*b^2*c^4*d^7) + (x*(-a^5*b^3)^(1/2)*(35*a^2*d^2 + 3*b^2*c^2 - 14*a*b*c*d)*(256*a^4*b^11*c^11*d^2 - 1792*a^5*b^10*c^10*d^3 + 5120*a^6*b^9*c^9*d^4 - 7168*a^7*b^8*c^8*d^5 + 3584*a^8*b^7*c^7*d^6 + 3584*a^9*b^6*c^6*d^7 - 7168*a^10*b^5*c^5*d^8 + 5120*a^11*b^4*c^4*d^9 - 1792*a^12*b^3*c^3*d^10 + 256*a^13*b^2*c^2*d^11))/(512*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)*(a^4*b^6*c^8 + a^10*c^2*d^6 - 6*a^5*b^5*c^7*d - 6*a^9*b*c^3*d^5 + 15*a^6*b^4*c^6*d^2 - 20*a^7*b^3*c^5*d^3 + 15*a^8*b^2*c^4*d^4)))*(-a^5*b^3)^(1/2)*(35*a^2*d^2 + 3*b^2*c^2 - 14*a*b*c*d))/(16*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)))*(-a^5*b^3)^(1/2)*(35*a^2*d^2 + 3*b^2*c^2 - 14*a*b*c*d)*1i)/(16*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)))/(((35*a^5*b^4*d^10)/16 + (63*b^9*c^5*d^5)/64 - (267*a*b^8*c^4*d^6)/32 - (651*a^4*b^5*c*d^9)/64 + (451*a^2*b^7*c^3*d^7)/16 - (1275*a^3*b^6*c^2*d^8)/32)/(a^4*b^9*c^11 - a^13*c^2*d^9 - 9*a^5*b^8*c^10*d + 9*a^12*b*c^3*d^8 + 36*a^6*b^7*c^9*d^2 - 84*a^7*b^6*c^8*d^3 + 126*a^8*b^5*c^7*d^4 - 126*a^9*b^4*c^6*d^5 + 84*a^10*b^3*c^5*d^6 - 36*a^11*b^2*c^4*d^7) - (((x*(16*a^6*b^3*d^9 + 9*b^9*c^6*d^3 - 84*a*b^8*c^5*d^4 - 224*a^5*b^4*c*d^8 + 406*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 2009*a^4*b^5*c^2*d^7))/(32*(a^4*b^6*c^8 + a^10*c^2*d^6 - 6*a^5*b^5*c^7*d - 6*a^9*b*c^3*d^5 + 15*a^6*b^4*c^6*d^2 - 20*a^7*b^3*c^5*d^3 + 15*a^8*b^2*c^4*d^4)) - (((2*a^13*b^2*c*d^13 - (3*a^2*b^13*c^12*d^2)/2 + (35*a^3*b^12*c^11*d^3)/2 - 98*a^4*b^11*c^10*d^4 + 336*a^5*b^10*c^9*d^5 - 765*a^6*b^9*c^8*d^6 + 1197*a^7*b^8*c^7*d^7 - 1302*a^8*b^7*c^6*d^8 + 978*a^9*b^6*c^5*d^9 - (987*a^10*b^5*c^4*d^10)/2 + (315*a^11*b^4*c^3*d^11)/2 - 28*a^12*b^3*c^2*d^12)/(a^4*b^9*c^11 - a^13*c^2*d^9 - 9*a^5*b^8*c^10*d + 9*a^12*b*c^3*d^8 + 36*a^6*b^7*c^9*d^2 - 84*a^7*b^6*c^8*d^3 + 126*a^8*b^5*c^7*d^4 - 126*a^9*b^4*c^6*d^5 + 84*a^10*b^3*c^5*d^6 - 36*a^11*b^2*c^4*d^7) - (x*(-a^5*b^3)^(1/2)*(35*a^2*d^2 + 3*b^2*c^2 - 14*a*b*c*d)*(256*a^4*b^11*c^11*d^2 - 1792*a^5*b^10*c^10*d^3 + 5120*a^6*b^9*c^9*d^4 - 7168*a^7*b^8*c^8*d^5 + 3584*a^8*b^7*c^7*d^6 + 3584*a^9*b^6*c^6*d^7 - 7168*a^10*b^5*c^5*d^8 + 5120*a^11*b^4*c^4*d^9 - 1792*a^12*b^3*c^3*d^10 + 256*a^13*b^2*c^2*d^11))/(512*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)*(a^4*b^6*c^8 + a^10*c^2*d^6 - 6*a^5*b^5*c^7*d - 6*a^9*b*c^3*d^5 + 15*a^6*b^4*c^6*d^2 - 20*a^7*b^3*c^5*d^3 + 15*a^8*b^2*c^4*d^4)))*(-a^5*b^3)^(1/2)*(35*a^2*d^2 + 3*b^2*c^2 - 14*a*b*c*d))/(16*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)))*(-a^5*b^3)^(1/2)*(35*a^2*d^2 + 3*b^2*c^2 - 14*a*b*c*d))/(16*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)) + (((x*(16*a^6*b^3*d^9 + 9*b^9*c^6*d^3 - 84*a*b^8*c^5*d^4 - 224*a^5*b^4*c*d^8 + 406*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 2009*a^4*b^5*c^2*d^7))/(32*(a^4*b^6*c^8 + a^10*c^2*d^6 - 6*a^5*b^5*c^7*d - 6*a^9*b*c^3*d^5 + 15*a^6*b^4*c^6*d^2 - 20*a^7*b^3*c^5*d^3 + 15*a^8*b^2*c^4*d^4)) + (((2*a^13*b^2*c*d^13 - (3*a^2*b^13*c^12*d^2)/2 + (35*a^3*b^12*c^11*d^3)/2 - 98*a^4*b^11*c^10*d^4 + 336*a^5*b^10*c^9*d^5 - 765*a^6*b^9*c^8*d^6 + 1197*a^7*b^8*c^7*d^7 - 1302*a^8*b^7*c^6*d^8 + 978*a^9*b^6*c^5*d^9 - (987*a^10*b^5*c^4*d^10)/2 + (315*a^11*b^4*c^3*d^11)/2 - 28*a^12*b^3*c^2*d^12)/(a^4*b^9*c^11 - a^13*c^2*d^9 - 9*a^5*b^8*c^10*d + 9*a^12*b*c^3*d^8 + 36*a^6*b^7*c^9*d^2 - 84*a^7*b^6*c^8*d^3 + 126*a^8*b^5*c^7*d^4 - 126*a^9*b^4*c^6*d^5 + 84*a^10*b^3*c^5*d^6 - 36*a^11*b^2*c^4*d^7) + (x*(-a^5*b^3)^(1/2)*(35*a^2*d^2 + 3*b^2*c^2 - 14*a*b*c*d)*(256*a^4*b^11*c^11*d^2 - 1792*a^5*b^10*c^10*d^3 + 5120*a^6*b^9*c^9*d^4 - 7168*a^7*b^8*c^8*d^5 + 3584*a^8*b^7*c^7*d^6 + 3584*a^9*b^6*c^6*d^7 - 7168*a^10*b^5*c^5*d^8 + 5120*a^11*b^4*c^4*d^9 - 1792*a^12*b^3*c^3*d^10 + 256*a^13*b^2*c^2*d^11))/(512*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)*(a^4*b^6*c^8 + a^10*c^2*d^6 - 6*a^5*b^5*c^7*d - 6*a^9*b*c^3*d^5 + 15*a^6*b^4*c^6*d^2 - 20*a^7*b^3*c^5*d^3 + 15*a^8*b^2*c^4*d^4)))*(-a^5*b^3)^(1/2)*(35*a^2*d^2 + 3*b^2*c^2 - 14*a*b*c*d))/(16*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)))*(-a^5*b^3)^(1/2)*(35*a^2*d^2 + 3*b^2*c^2 - 14*a*b*c*d))/(16*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3))))*(-a^5*b^3)^(1/2)*(35*a^2*d^2 + 3*b^2*c^2 - 14*a*b*c*d)*1i)/(8*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)) - (atan(((((x*(16*a^6*b^3*d^9 + 9*b^9*c^6*d^3 - 84*a*b^8*c^5*d^4 - 224*a^5*b^4*c*d^8 + 406*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 2009*a^4*b^5*c^2*d^7))/(32*(a^4*b^6*c^8 + a^10*c^2*d^6 - 6*a^5*b^5*c^7*d - 6*a^9*b*c^3*d^5 + 15*a^6*b^4*c^6*d^2 - 20*a^7*b^3*c^5*d^3 + 15*a^8*b^2*c^4*d^4)) - ((a*d - 7*b*c)*(-c^3*d^5)^(1/2)*((2*a^13*b^2*c*d^13 - (3*a^2*b^13*c^12*d^2)/2 + (35*a^3*b^12*c^11*d^3)/2 - 98*a^4*b^11*c^10*d^4 + 336*a^5*b^10*c^9*d^5 - 765*a^6*b^9*c^8*d^6 + 1197*a^7*b^8*c^7*d^7 - 1302*a^8*b^7*c^6*d^8 + 978*a^9*b^6*c^5*d^9 - (987*a^10*b^5*c^4*d^10)/2 + (315*a^11*b^4*c^3*d^11)/2 - 28*a^12*b^3*c^2*d^12)/(a^4*b^9*c^11 - a^13*c^2*d^9 - 9*a^5*b^8*c^10*d + 9*a^12*b*c^3*d^8 + 36*a^6*b^7*c^9*d^2 - 84*a^7*b^6*c^8*d^3 + 126*a^8*b^5*c^7*d^4 - 126*a^9*b^4*c^6*d^5 + 84*a^10*b^3*c^5*d^6 - 36*a^11*b^2*c^4*d^7) - (x*(a*d - 7*b*c)*(-c^3*d^5)^(1/2)*(256*a^4*b^11*c^11*d^2 - 1792*a^5*b^10*c^10*d^3 + 5120*a^6*b^9*c^9*d^4 - 7168*a^7*b^8*c^8*d^5 + 3584*a^8*b^7*c^7*d^6 + 3584*a^9*b^6*c^6*d^7 - 7168*a^10*b^5*c^5*d^8 + 5120*a^11*b^4*c^4*d^9 - 1792*a^12*b^3*c^3*d^10 + 256*a^13*b^2*c^2*d^11))/(128*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)*(a^4*b^6*c^8 + a^10*c^2*d^6 - 6*a^5*b^5*c^7*d - 6*a^9*b*c^3*d^5 + 15*a^6*b^4*c^6*d^2 - 20*a^7*b^3*c^5*d^3 + 15*a^8*b^2*c^4*d^4))))/(4*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)))*(a*d - 7*b*c)*(-c^3*d^5)^(1/2)*1i)/(4*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)) + (((x*(16*a^6*b^3*d^9 + 9*b^9*c^6*d^3 - 84*a*b^8*c^5*d^4 - 224*a^5*b^4*c*d^8 + 406*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 2009*a^4*b^5*c^2*d^7))/(32*(a^4*b^6*c^8 + a^10*c^2*d^6 - 6*a^5*b^5*c^7*d - 6*a^9*b*c^3*d^5 + 15*a^6*b^4*c^6*d^2 - 20*a^7*b^3*c^5*d^3 + 15*a^8*b^2*c^4*d^4)) + ((a*d - 7*b*c)*(-c^3*d^5)^(1/2)*((2*a^13*b^2*c*d^13 - (3*a^2*b^13*c^12*d^2)/2 + (35*a^3*b^12*c^11*d^3)/2 - 98*a^4*b^11*c^10*d^4 + 336*a^5*b^10*c^9*d^5 - 765*a^6*b^9*c^8*d^6 + 1197*a^7*b^8*c^7*d^7 - 1302*a^8*b^7*c^6*d^8 + 978*a^9*b^6*c^5*d^9 - (987*a^10*b^5*c^4*d^10)/2 + (315*a^11*b^4*c^3*d^11)/2 - 28*a^12*b^3*c^2*d^12)/(a^4*b^9*c^11 - a^13*c^2*d^9 - 9*a^5*b^8*c^10*d + 9*a^12*b*c^3*d^8 + 36*a^6*b^7*c^9*d^2 - 84*a^7*b^6*c^8*d^3 + 126*a^8*b^5*c^7*d^4 - 126*a^9*b^4*c^6*d^5 + 84*a^10*b^3*c^5*d^6 - 36*a^11*b^2*c^4*d^7) + (x*(a*d - 7*b*c)*(-c^3*d^5)^(1/2)*(256*a^4*b^11*c^11*d^2 - 1792*a^5*b^10*c^10*d^3 + 5120*a^6*b^9*c^9*d^4 - 7168*a^7*b^8*c^8*d^5 + 3584*a^8*b^7*c^7*d^6 + 3584*a^9*b^6*c^6*d^7 - 7168*a^10*b^5*c^5*d^8 + 5120*a^11*b^4*c^4*d^9 - 1792*a^12*b^3*c^3*d^10 + 256*a^13*b^2*c^2*d^11))/(128*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)*(a^4*b^6*c^8 + a^10*c^2*d^6 - 6*a^5*b^5*c^7*d - 6*a^9*b*c^3*d^5 + 15*a^6*b^4*c^6*d^2 - 20*a^7*b^3*c^5*d^3 + 15*a^8*b^2*c^4*d^4))))/(4*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)))*(a*d - 7*b*c)*(-c^3*d^5)^(1/2)*1i)/(4*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)))/(((35*a^5*b^4*d^10)/16 + (63*b^9*c^5*d^5)/64 - (267*a*b^8*c^4*d^6)/32 - (651*a^4*b^5*c*d^9)/64 + (451*a^2*b^7*c^3*d^7)/16 - (1275*a^3*b^6*c^2*d^8)/32)/(a^4*b^9*c^11 - a^13*c^2*d^9 - 9*a^5*b^8*c^10*d + 9*a^12*b*c^3*d^8 + 36*a^6*b^7*c^9*d^2 - 84*a^7*b^6*c^8*d^3 + 126*a^8*b^5*c^7*d^4 - 126*a^9*b^4*c^6*d^5 + 84*a^10*b^3*c^5*d^6 - 36*a^11*b^2*c^4*d^7) - (((x*(16*a^6*b^3*d^9 + 9*b^9*c^6*d^3 - 84*a*b^8*c^5*d^4 - 224*a^5*b^4*c*d^8 + 406*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 2009*a^4*b^5*c^2*d^7))/(32*(a^4*b^6*c^8 + a^10*c^2*d^6 - 6*a^5*b^5*c^7*d - 6*a^9*b*c^3*d^5 + 15*a^6*b^4*c^6*d^2 - 20*a^7*b^3*c^5*d^3 + 15*a^8*b^2*c^4*d^4)) - ((a*d - 7*b*c)*(-c^3*d^5)^(1/2)*((2*a^13*b^2*c*d^13 - (3*a^2*b^13*c^12*d^2)/2 + (35*a^3*b^12*c^11*d^3)/2 - 98*a^4*b^11*c^10*d^4 + 336*a^5*b^10*c^9*d^5 - 765*a^6*b^9*c^8*d^6 + 1197*a^7*b^8*c^7*d^7 - 1302*a^8*b^7*c^6*d^8 + 978*a^9*b^6*c^5*d^9 - (987*a^10*b^5*c^4*d^10)/2 + (315*a^11*b^4*c^3*d^11)/2 - 28*a^12*b^3*c^2*d^12)/(a^4*b^9*c^11 - a^13*c^2*d^9 - 9*a^5*b^8*c^10*d + 9*a^12*b*c^3*d^8 + 36*a^6*b^7*c^9*d^2 - 84*a^7*b^6*c^8*d^3 + 126*a^8*b^5*c^7*d^4 - 126*a^9*b^4*c^6*d^5 + 84*a^10*b^3*c^5*d^6 - 36*a^11*b^2*c^4*d^7) - (x*(a*d - 7*b*c)*(-c^3*d^5)^(1/2)*(256*a^4*b^11*c^11*d^2 - 1792*a^5*b^10*c^10*d^3 + 5120*a^6*b^9*c^9*d^4 - 7168*a^7*b^8*c^8*d^5 + 3584*a^8*b^7*c^7*d^6 + 3584*a^9*b^6*c^6*d^7 - 7168*a^10*b^5*c^5*d^8 + 5120*a^11*b^4*c^4*d^9 - 1792*a^12*b^3*c^3*d^10 + 256*a^13*b^2*c^2*d^11))/(128*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)*(a^4*b^6*c^8 + a^10*c^2*d^6 - 6*a^5*b^5*c^7*d - 6*a^9*b*c^3*d^5 + 15*a^6*b^4*c^6*d^2 - 20*a^7*b^3*c^5*d^3 + 15*a^8*b^2*c^4*d^4))))/(4*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)))*(a*d - 7*b*c)*(-c^3*d^5)^(1/2))/(4*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)) + (((x*(16*a^6*b^3*d^9 + 9*b^9*c^6*d^3 - 84*a*b^8*c^5*d^4 - 224*a^5*b^4*c*d^8 + 406*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 2009*a^4*b^5*c^2*d^7))/(32*(a^4*b^6*c^8 + a^10*c^2*d^6 - 6*a^5*b^5*c^7*d - 6*a^9*b*c^3*d^5 + 15*a^6*b^4*c^6*d^2 - 20*a^7*b^3*c^5*d^3 + 15*a^8*b^2*c^4*d^4)) + ((a*d - 7*b*c)*(-c^3*d^5)^(1/2)*((2*a^13*b^2*c*d^13 - (3*a^2*b^13*c^12*d^2)/2 + (35*a^3*b^12*c^11*d^3)/2 - 98*a^4*b^11*c^10*d^4 + 336*a^5*b^10*c^9*d^5 - 765*a^6*b^9*c^8*d^6 + 1197*a^7*b^8*c^7*d^7 - 1302*a^8*b^7*c^6*d^8 + 978*a^9*b^6*c^5*d^9 - (987*a^10*b^5*c^4*d^10)/2 + (315*a^11*b^4*c^3*d^11)/2 - 28*a^12*b^3*c^2*d^12)/(a^4*b^9*c^11 - a^13*c^2*d^9 - 9*a^5*b^8*c^10*d + 9*a^12*b*c^3*d^8 + 36*a^6*b^7*c^9*d^2 - 84*a^7*b^6*c^8*d^3 + 126*a^8*b^5*c^7*d^4 - 126*a^9*b^4*c^6*d^5 + 84*a^10*b^3*c^5*d^6 - 36*a^11*b^2*c^4*d^7) + (x*(a*d - 7*b*c)*(-c^3*d^5)^(1/2)*(256*a^4*b^11*c^11*d^2 - 1792*a^5*b^10*c^10*d^3 + 5120*a^6*b^9*c^9*d^4 - 7168*a^7*b^8*c^8*d^5 + 3584*a^8*b^7*c^7*d^6 + 3584*a^9*b^6*c^6*d^7 - 7168*a^10*b^5*c^5*d^8 + 5120*a^11*b^4*c^4*d^9 - 1792*a^12*b^3*c^3*d^10 + 256*a^13*b^2*c^2*d^11))/(128*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)*(a^4*b^6*c^8 + a^10*c^2*d^6 - 6*a^5*b^5*c^7*d - 6*a^9*b*c^3*d^5 + 15*a^6*b^4*c^6*d^2 - 20*a^7*b^3*c^5*d^3 + 15*a^8*b^2*c^4*d^4))))/(4*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)))*(a*d - 7*b*c)*(-c^3*d^5)^(1/2))/(4*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d))))*(a*d - 7*b*c)*(-c^3*d^5)^(1/2)*1i)/(2*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d))","B"
42,1,11150,315,8.554847,"\text{Not used}","int(1/((a + b*x^2)^3*(c + d*x^2)^3),x)","\frac{\frac{x\,\left(5\,a^4\,d^4-17\,a^3\,b\,c\,d^3-17\,a\,b^3\,c^3\,d+5\,b^4\,c^4\right)}{8\,a\,c\,\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{x^3\,\left(-3\,a^5\,d^5+5\,a^4\,b\,c\,d^4+34\,a^3\,b^2\,c^2\,d^3+34\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d-3\,b^5\,c^5\right)}{8\,a^2\,c^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{x^5\,\left(-6\,a^4\,b\,d^5+25\,a^3\,b^2\,c\,d^4+34\,a^2\,b^3\,c^2\,d^3+25\,a\,b^4\,c^3\,d^2-6\,b^5\,c^4\,d\right)}{8\,a^2\,c^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{3\,b\,d\,x^7\,\left(a^3\,b\,d^4-5\,a^2\,b^2\,c\,d^3-5\,a\,b^3\,c^2\,d^2+b^4\,c^3\,d\right)}{8\,a^2\,c^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)}}{x^4\,\left(a^2\,d^2+4\,a\,b\,c\,d+b^2\,c^2\right)+x^2\,\left(2\,d\,a^2\,c+2\,b\,a\,c^2\right)+x^6\,\left(2\,c\,b^2\,d+2\,a\,b\,d^2\right)+a^2\,c^2+b^2\,d^2\,x^8}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(9\,a^8\,b^3\,d^{11}-108\,a^7\,b^4\,c\,d^{10}+702\,a^6\,b^5\,c^2\,d^9-2268\,a^5\,b^6\,c^3\,d^8+7938\,a^4\,b^7\,c^4\,d^7-2268\,a^3\,b^8\,c^5\,d^6+702\,a^2\,b^9\,c^6\,d^5-108\,a\,b^{10}\,c^7\,d^4+9\,b^{11}\,c^8\,d^3\right)}{32\,\left(a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}\right)}-\frac{3\,\left(\frac{\frac{3\,a^{16}\,b^2\,c^2\,d^{16}}{2}-\frac{45\,a^{15}\,b^3\,c^3\,d^{15}}{2}+\frac{333\,a^{14}\,b^4\,c^4\,d^{14}}{2}-765\,a^{13}\,b^5\,c^5\,d^{13}+\frac{4743\,a^{12}\,b^6\,c^6\,d^{12}}{2}-\frac{10371\,a^{11}\,b^7\,c^7\,d^{11}}{2}+\frac{16425\,a^{10}\,b^8\,c^8\,d^{10}}{2}-9558\,a^9\,b^9\,c^9\,d^9+\frac{16425\,a^8\,b^{10}\,c^{10}\,d^8}{2}-\frac{10371\,a^7\,b^{11}\,c^{11}\,d^7}{2}+\frac{4743\,a^6\,b^{12}\,c^{12}\,d^6}{2}-765\,a^5\,b^{13}\,c^{13}\,d^5+\frac{333\,a^4\,b^{14}\,c^{14}\,d^4}{2}-\frac{45\,a^3\,b^{15}\,c^{15}\,d^3}{2}+\frac{3\,a^2\,b^{16}\,c^{16}\,d^2}{2}}{a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}}-\frac{3\,x\,\sqrt{-a^5\,b^5}\,\left(21\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)\,\left(256\,a^{15}\,b^2\,c^4\,d^{13}-2304\,a^{14}\,b^3\,c^5\,d^{12}+8960\,a^{13}\,b^4\,c^6\,d^{11}-19200\,a^{12}\,b^5\,c^7\,d^{10}+23040\,a^{11}\,b^6\,c^8\,d^9-10752\,a^{10}\,b^7\,c^9\,d^8-10752\,a^9\,b^8\,c^{10}\,d^7+23040\,a^8\,b^9\,c^{11}\,d^6-19200\,a^7\,b^{10}\,c^{12}\,d^5+8960\,a^6\,b^{11}\,c^{13}\,d^4-2304\,a^5\,b^{12}\,c^{14}\,d^3+256\,a^4\,b^{13}\,c^{15}\,d^2\right)}{512\,\left(a^{10}\,d^5-5\,a^9\,b\,c\,d^4+10\,a^8\,b^2\,c^2\,d^3-10\,a^7\,b^3\,c^3\,d^2+5\,a^6\,b^4\,c^4\,d-a^5\,b^5\,c^5\right)\,\left(a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}\right)}\right)\,\sqrt{-a^5\,b^5}\,\left(21\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)}{16\,\left(a^{10}\,d^5-5\,a^9\,b\,c\,d^4+10\,a^8\,b^2\,c^2\,d^3-10\,a^7\,b^3\,c^3\,d^2+5\,a^6\,b^4\,c^4\,d-a^5\,b^5\,c^5\right)}\right)\,\sqrt{-a^5\,b^5}\,\left(21\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)\,3{}\mathrm{i}}{16\,\left(a^{10}\,d^5-5\,a^9\,b\,c\,d^4+10\,a^8\,b^2\,c^2\,d^3-10\,a^7\,b^3\,c^3\,d^2+5\,a^6\,b^4\,c^4\,d-a^5\,b^5\,c^5\right)}+\frac{\left(\frac{x\,\left(9\,a^8\,b^3\,d^{11}-108\,a^7\,b^4\,c\,d^{10}+702\,a^6\,b^5\,c^2\,d^9-2268\,a^5\,b^6\,c^3\,d^8+7938\,a^4\,b^7\,c^4\,d^7-2268\,a^3\,b^8\,c^5\,d^6+702\,a^2\,b^9\,c^6\,d^5-108\,a\,b^{10}\,c^7\,d^4+9\,b^{11}\,c^8\,d^3\right)}{32\,\left(a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}\right)}+\frac{3\,\left(\frac{\frac{3\,a^{16}\,b^2\,c^2\,d^{16}}{2}-\frac{45\,a^{15}\,b^3\,c^3\,d^{15}}{2}+\frac{333\,a^{14}\,b^4\,c^4\,d^{14}}{2}-765\,a^{13}\,b^5\,c^5\,d^{13}+\frac{4743\,a^{12}\,b^6\,c^6\,d^{12}}{2}-\frac{10371\,a^{11}\,b^7\,c^7\,d^{11}}{2}+\frac{16425\,a^{10}\,b^8\,c^8\,d^{10}}{2}-9558\,a^9\,b^9\,c^9\,d^9+\frac{16425\,a^8\,b^{10}\,c^{10}\,d^8}{2}-\frac{10371\,a^7\,b^{11}\,c^{11}\,d^7}{2}+\frac{4743\,a^6\,b^{12}\,c^{12}\,d^6}{2}-765\,a^5\,b^{13}\,c^{13}\,d^5+\frac{333\,a^4\,b^{14}\,c^{14}\,d^4}{2}-\frac{45\,a^3\,b^{15}\,c^{15}\,d^3}{2}+\frac{3\,a^2\,b^{16}\,c^{16}\,d^2}{2}}{a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}}+\frac{3\,x\,\sqrt{-a^5\,b^5}\,\left(21\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)\,\left(256\,a^{15}\,b^2\,c^4\,d^{13}-2304\,a^{14}\,b^3\,c^5\,d^{12}+8960\,a^{13}\,b^4\,c^6\,d^{11}-19200\,a^{12}\,b^5\,c^7\,d^{10}+23040\,a^{11}\,b^6\,c^8\,d^9-10752\,a^{10}\,b^7\,c^9\,d^8-10752\,a^9\,b^8\,c^{10}\,d^7+23040\,a^8\,b^9\,c^{11}\,d^6-19200\,a^7\,b^{10}\,c^{12}\,d^5+8960\,a^6\,b^{11}\,c^{13}\,d^4-2304\,a^5\,b^{12}\,c^{14}\,d^3+256\,a^4\,b^{13}\,c^{15}\,d^2\right)}{512\,\left(a^{10}\,d^5-5\,a^9\,b\,c\,d^4+10\,a^8\,b^2\,c^2\,d^3-10\,a^7\,b^3\,c^3\,d^2+5\,a^6\,b^4\,c^4\,d-a^5\,b^5\,c^5\right)\,\left(a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}\right)}\right)\,\sqrt{-a^5\,b^5}\,\left(21\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)}{16\,\left(a^{10}\,d^5-5\,a^9\,b\,c\,d^4+10\,a^8\,b^2\,c^2\,d^3-10\,a^7\,b^3\,c^3\,d^2+5\,a^6\,b^4\,c^4\,d-a^5\,b^5\,c^5\right)}\right)\,\sqrt{-a^5\,b^5}\,\left(21\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)\,3{}\mathrm{i}}{16\,\left(a^{10}\,d^5-5\,a^9\,b\,c\,d^4+10\,a^8\,b^2\,c^2\,d^3-10\,a^7\,b^3\,c^3\,d^2+5\,a^6\,b^4\,c^4\,d-a^5\,b^5\,c^5\right)}}{\frac{\frac{567\,a^7\,b^5\,d^{12}}{256}-\frac{6399\,a^6\,b^6\,c\,d^{11}}{256}+\frac{27891\,a^5\,b^7\,c^2\,d^{10}}{256}-\frac{49707\,a^4\,b^8\,c^3\,d^9}{256}-\frac{49707\,a^3\,b^9\,c^4\,d^8}{256}+\frac{27891\,a^2\,b^{10}\,c^5\,d^7}{256}-\frac{6399\,a\,b^{11}\,c^6\,d^6}{256}+\frac{567\,b^{12}\,c^7\,d^5}{256}}{a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}}+\frac{3\,\left(\frac{x\,\left(9\,a^8\,b^3\,d^{11}-108\,a^7\,b^4\,c\,d^{10}+702\,a^6\,b^5\,c^2\,d^9-2268\,a^5\,b^6\,c^3\,d^8+7938\,a^4\,b^7\,c^4\,d^7-2268\,a^3\,b^8\,c^5\,d^6+702\,a^2\,b^9\,c^6\,d^5-108\,a\,b^{10}\,c^7\,d^4+9\,b^{11}\,c^8\,d^3\right)}{32\,\left(a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}\right)}-\frac{3\,\left(\frac{\frac{3\,a^{16}\,b^2\,c^2\,d^{16}}{2}-\frac{45\,a^{15}\,b^3\,c^3\,d^{15}}{2}+\frac{333\,a^{14}\,b^4\,c^4\,d^{14}}{2}-765\,a^{13}\,b^5\,c^5\,d^{13}+\frac{4743\,a^{12}\,b^6\,c^6\,d^{12}}{2}-\frac{10371\,a^{11}\,b^7\,c^7\,d^{11}}{2}+\frac{16425\,a^{10}\,b^8\,c^8\,d^{10}}{2}-9558\,a^9\,b^9\,c^9\,d^9+\frac{16425\,a^8\,b^{10}\,c^{10}\,d^8}{2}-\frac{10371\,a^7\,b^{11}\,c^{11}\,d^7}{2}+\frac{4743\,a^6\,b^{12}\,c^{12}\,d^6}{2}-765\,a^5\,b^{13}\,c^{13}\,d^5+\frac{333\,a^4\,b^{14}\,c^{14}\,d^4}{2}-\frac{45\,a^3\,b^{15}\,c^{15}\,d^3}{2}+\frac{3\,a^2\,b^{16}\,c^{16}\,d^2}{2}}{a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}}-\frac{3\,x\,\sqrt{-a^5\,b^5}\,\left(21\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)\,\left(256\,a^{15}\,b^2\,c^4\,d^{13}-2304\,a^{14}\,b^3\,c^5\,d^{12}+8960\,a^{13}\,b^4\,c^6\,d^{11}-19200\,a^{12}\,b^5\,c^7\,d^{10}+23040\,a^{11}\,b^6\,c^8\,d^9-10752\,a^{10}\,b^7\,c^9\,d^8-10752\,a^9\,b^8\,c^{10}\,d^7+23040\,a^8\,b^9\,c^{11}\,d^6-19200\,a^7\,b^{10}\,c^{12}\,d^5+8960\,a^6\,b^{11}\,c^{13}\,d^4-2304\,a^5\,b^{12}\,c^{14}\,d^3+256\,a^4\,b^{13}\,c^{15}\,d^2\right)}{512\,\left(a^{10}\,d^5-5\,a^9\,b\,c\,d^4+10\,a^8\,b^2\,c^2\,d^3-10\,a^7\,b^3\,c^3\,d^2+5\,a^6\,b^4\,c^4\,d-a^5\,b^5\,c^5\right)\,\left(a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}\right)}\right)\,\sqrt{-a^5\,b^5}\,\left(21\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)}{16\,\left(a^{10}\,d^5-5\,a^9\,b\,c\,d^4+10\,a^8\,b^2\,c^2\,d^3-10\,a^7\,b^3\,c^3\,d^2+5\,a^6\,b^4\,c^4\,d-a^5\,b^5\,c^5\right)}\right)\,\sqrt{-a^5\,b^5}\,\left(21\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)}{16\,\left(a^{10}\,d^5-5\,a^9\,b\,c\,d^4+10\,a^8\,b^2\,c^2\,d^3-10\,a^7\,b^3\,c^3\,d^2+5\,a^6\,b^4\,c^4\,d-a^5\,b^5\,c^5\right)}-\frac{3\,\left(\frac{x\,\left(9\,a^8\,b^3\,d^{11}-108\,a^7\,b^4\,c\,d^{10}+702\,a^6\,b^5\,c^2\,d^9-2268\,a^5\,b^6\,c^3\,d^8+7938\,a^4\,b^7\,c^4\,d^7-2268\,a^3\,b^8\,c^5\,d^6+702\,a^2\,b^9\,c^6\,d^5-108\,a\,b^{10}\,c^7\,d^4+9\,b^{11}\,c^8\,d^3\right)}{32\,\left(a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}\right)}+\frac{3\,\left(\frac{\frac{3\,a^{16}\,b^2\,c^2\,d^{16}}{2}-\frac{45\,a^{15}\,b^3\,c^3\,d^{15}}{2}+\frac{333\,a^{14}\,b^4\,c^4\,d^{14}}{2}-765\,a^{13}\,b^5\,c^5\,d^{13}+\frac{4743\,a^{12}\,b^6\,c^6\,d^{12}}{2}-\frac{10371\,a^{11}\,b^7\,c^7\,d^{11}}{2}+\frac{16425\,a^{10}\,b^8\,c^8\,d^{10}}{2}-9558\,a^9\,b^9\,c^9\,d^9+\frac{16425\,a^8\,b^{10}\,c^{10}\,d^8}{2}-\frac{10371\,a^7\,b^{11}\,c^{11}\,d^7}{2}+\frac{4743\,a^6\,b^{12}\,c^{12}\,d^6}{2}-765\,a^5\,b^{13}\,c^{13}\,d^5+\frac{333\,a^4\,b^{14}\,c^{14}\,d^4}{2}-\frac{45\,a^3\,b^{15}\,c^{15}\,d^3}{2}+\frac{3\,a^2\,b^{16}\,c^{16}\,d^2}{2}}{a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}}+\frac{3\,x\,\sqrt{-a^5\,b^5}\,\left(21\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)\,\left(256\,a^{15}\,b^2\,c^4\,d^{13}-2304\,a^{14}\,b^3\,c^5\,d^{12}+8960\,a^{13}\,b^4\,c^6\,d^{11}-19200\,a^{12}\,b^5\,c^7\,d^{10}+23040\,a^{11}\,b^6\,c^8\,d^9-10752\,a^{10}\,b^7\,c^9\,d^8-10752\,a^9\,b^8\,c^{10}\,d^7+23040\,a^8\,b^9\,c^{11}\,d^6-19200\,a^7\,b^{10}\,c^{12}\,d^5+8960\,a^6\,b^{11}\,c^{13}\,d^4-2304\,a^5\,b^{12}\,c^{14}\,d^3+256\,a^4\,b^{13}\,c^{15}\,d^2\right)}{512\,\left(a^{10}\,d^5-5\,a^9\,b\,c\,d^4+10\,a^8\,b^2\,c^2\,d^3-10\,a^7\,b^3\,c^3\,d^2+5\,a^6\,b^4\,c^4\,d-a^5\,b^5\,c^5\right)\,\left(a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}\right)}\right)\,\sqrt{-a^5\,b^5}\,\left(21\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)}{16\,\left(a^{10}\,d^5-5\,a^9\,b\,c\,d^4+10\,a^8\,b^2\,c^2\,d^3-10\,a^7\,b^3\,c^3\,d^2+5\,a^6\,b^4\,c^4\,d-a^5\,b^5\,c^5\right)}\right)\,\sqrt{-a^5\,b^5}\,\left(21\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)}{16\,\left(a^{10}\,d^5-5\,a^9\,b\,c\,d^4+10\,a^8\,b^2\,c^2\,d^3-10\,a^7\,b^3\,c^3\,d^2+5\,a^6\,b^4\,c^4\,d-a^5\,b^5\,c^5\right)}}\right)\,\sqrt{-a^5\,b^5}\,\left(21\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)\,3{}\mathrm{i}}{8\,\left(a^{10}\,d^5-5\,a^9\,b\,c\,d^4+10\,a^8\,b^2\,c^2\,d^3-10\,a^7\,b^3\,c^3\,d^2+5\,a^6\,b^4\,c^4\,d-a^5\,b^5\,c^5\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(9\,a^8\,b^3\,d^{11}-108\,a^7\,b^4\,c\,d^{10}+702\,a^6\,b^5\,c^2\,d^9-2268\,a^5\,b^6\,c^3\,d^8+7938\,a^4\,b^7\,c^4\,d^7-2268\,a^3\,b^8\,c^5\,d^6+702\,a^2\,b^9\,c^6\,d^5-108\,a\,b^{10}\,c^7\,d^4+9\,b^{11}\,c^8\,d^3\right)}{32\,\left(a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}\right)}-\frac{3\,\left(\frac{\frac{3\,a^{16}\,b^2\,c^2\,d^{16}}{2}-\frac{45\,a^{15}\,b^3\,c^3\,d^{15}}{2}+\frac{333\,a^{14}\,b^4\,c^4\,d^{14}}{2}-765\,a^{13}\,b^5\,c^5\,d^{13}+\frac{4743\,a^{12}\,b^6\,c^6\,d^{12}}{2}-\frac{10371\,a^{11}\,b^7\,c^7\,d^{11}}{2}+\frac{16425\,a^{10}\,b^8\,c^8\,d^{10}}{2}-9558\,a^9\,b^9\,c^9\,d^9+\frac{16425\,a^8\,b^{10}\,c^{10}\,d^8}{2}-\frac{10371\,a^7\,b^{11}\,c^{11}\,d^7}{2}+\frac{4743\,a^6\,b^{12}\,c^{12}\,d^6}{2}-765\,a^5\,b^{13}\,c^{13}\,d^5+\frac{333\,a^4\,b^{14}\,c^{14}\,d^4}{2}-\frac{45\,a^3\,b^{15}\,c^{15}\,d^3}{2}+\frac{3\,a^2\,b^{16}\,c^{16}\,d^2}{2}}{a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}}-\frac{3\,x\,\sqrt{-c^5\,d^5}\,\left(a^2\,d^2-6\,a\,b\,c\,d+21\,b^2\,c^2\right)\,\left(256\,a^{15}\,b^2\,c^4\,d^{13}-2304\,a^{14}\,b^3\,c^5\,d^{12}+8960\,a^{13}\,b^4\,c^6\,d^{11}-19200\,a^{12}\,b^5\,c^7\,d^{10}+23040\,a^{11}\,b^6\,c^8\,d^9-10752\,a^{10}\,b^7\,c^9\,d^8-10752\,a^9\,b^8\,c^{10}\,d^7+23040\,a^8\,b^9\,c^{11}\,d^6-19200\,a^7\,b^{10}\,c^{12}\,d^5+8960\,a^6\,b^{11}\,c^{13}\,d^4-2304\,a^5\,b^{12}\,c^{14}\,d^3+256\,a^4\,b^{13}\,c^{15}\,d^2\right)}{512\,\left(-a^5\,c^5\,d^5+5\,a^4\,b\,c^6\,d^4-10\,a^3\,b^2\,c^7\,d^3+10\,a^2\,b^3\,c^8\,d^2-5\,a\,b^4\,c^9\,d+b^5\,c^{10}\right)\,\left(a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}\right)}\right)\,\sqrt{-c^5\,d^5}\,\left(a^2\,d^2-6\,a\,b\,c\,d+21\,b^2\,c^2\right)}{16\,\left(-a^5\,c^5\,d^5+5\,a^4\,b\,c^6\,d^4-10\,a^3\,b^2\,c^7\,d^3+10\,a^2\,b^3\,c^8\,d^2-5\,a\,b^4\,c^9\,d+b^5\,c^{10}\right)}\right)\,\sqrt{-c^5\,d^5}\,\left(a^2\,d^2-6\,a\,b\,c\,d+21\,b^2\,c^2\right)\,3{}\mathrm{i}}{16\,\left(-a^5\,c^5\,d^5+5\,a^4\,b\,c^6\,d^4-10\,a^3\,b^2\,c^7\,d^3+10\,a^2\,b^3\,c^8\,d^2-5\,a\,b^4\,c^9\,d+b^5\,c^{10}\right)}+\frac{\left(\frac{x\,\left(9\,a^8\,b^3\,d^{11}-108\,a^7\,b^4\,c\,d^{10}+702\,a^6\,b^5\,c^2\,d^9-2268\,a^5\,b^6\,c^3\,d^8+7938\,a^4\,b^7\,c^4\,d^7-2268\,a^3\,b^8\,c^5\,d^6+702\,a^2\,b^9\,c^6\,d^5-108\,a\,b^{10}\,c^7\,d^4+9\,b^{11}\,c^8\,d^3\right)}{32\,\left(a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}\right)}+\frac{3\,\left(\frac{\frac{3\,a^{16}\,b^2\,c^2\,d^{16}}{2}-\frac{45\,a^{15}\,b^3\,c^3\,d^{15}}{2}+\frac{333\,a^{14}\,b^4\,c^4\,d^{14}}{2}-765\,a^{13}\,b^5\,c^5\,d^{13}+\frac{4743\,a^{12}\,b^6\,c^6\,d^{12}}{2}-\frac{10371\,a^{11}\,b^7\,c^7\,d^{11}}{2}+\frac{16425\,a^{10}\,b^8\,c^8\,d^{10}}{2}-9558\,a^9\,b^9\,c^9\,d^9+\frac{16425\,a^8\,b^{10}\,c^{10}\,d^8}{2}-\frac{10371\,a^7\,b^{11}\,c^{11}\,d^7}{2}+\frac{4743\,a^6\,b^{12}\,c^{12}\,d^6}{2}-765\,a^5\,b^{13}\,c^{13}\,d^5+\frac{333\,a^4\,b^{14}\,c^{14}\,d^4}{2}-\frac{45\,a^3\,b^{15}\,c^{15}\,d^3}{2}+\frac{3\,a^2\,b^{16}\,c^{16}\,d^2}{2}}{a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}}+\frac{3\,x\,\sqrt{-c^5\,d^5}\,\left(a^2\,d^2-6\,a\,b\,c\,d+21\,b^2\,c^2\right)\,\left(256\,a^{15}\,b^2\,c^4\,d^{13}-2304\,a^{14}\,b^3\,c^5\,d^{12}+8960\,a^{13}\,b^4\,c^6\,d^{11}-19200\,a^{12}\,b^5\,c^7\,d^{10}+23040\,a^{11}\,b^6\,c^8\,d^9-10752\,a^{10}\,b^7\,c^9\,d^8-10752\,a^9\,b^8\,c^{10}\,d^7+23040\,a^8\,b^9\,c^{11}\,d^6-19200\,a^7\,b^{10}\,c^{12}\,d^5+8960\,a^6\,b^{11}\,c^{13}\,d^4-2304\,a^5\,b^{12}\,c^{14}\,d^3+256\,a^4\,b^{13}\,c^{15}\,d^2\right)}{512\,\left(-a^5\,c^5\,d^5+5\,a^4\,b\,c^6\,d^4-10\,a^3\,b^2\,c^7\,d^3+10\,a^2\,b^3\,c^8\,d^2-5\,a\,b^4\,c^9\,d+b^5\,c^{10}\right)\,\left(a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}\right)}\right)\,\sqrt{-c^5\,d^5}\,\left(a^2\,d^2-6\,a\,b\,c\,d+21\,b^2\,c^2\right)}{16\,\left(-a^5\,c^5\,d^5+5\,a^4\,b\,c^6\,d^4-10\,a^3\,b^2\,c^7\,d^3+10\,a^2\,b^3\,c^8\,d^2-5\,a\,b^4\,c^9\,d+b^5\,c^{10}\right)}\right)\,\sqrt{-c^5\,d^5}\,\left(a^2\,d^2-6\,a\,b\,c\,d+21\,b^2\,c^2\right)\,3{}\mathrm{i}}{16\,\left(-a^5\,c^5\,d^5+5\,a^4\,b\,c^6\,d^4-10\,a^3\,b^2\,c^7\,d^3+10\,a^2\,b^3\,c^8\,d^2-5\,a\,b^4\,c^9\,d+b^5\,c^{10}\right)}}{\frac{\frac{567\,a^7\,b^5\,d^{12}}{256}-\frac{6399\,a^6\,b^6\,c\,d^{11}}{256}+\frac{27891\,a^5\,b^7\,c^2\,d^{10}}{256}-\frac{49707\,a^4\,b^8\,c^3\,d^9}{256}-\frac{49707\,a^3\,b^9\,c^4\,d^8}{256}+\frac{27891\,a^2\,b^{10}\,c^5\,d^7}{256}-\frac{6399\,a\,b^{11}\,c^6\,d^6}{256}+\frac{567\,b^{12}\,c^7\,d^5}{256}}{a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}}+\frac{3\,\left(\frac{x\,\left(9\,a^8\,b^3\,d^{11}-108\,a^7\,b^4\,c\,d^{10}+702\,a^6\,b^5\,c^2\,d^9-2268\,a^5\,b^6\,c^3\,d^8+7938\,a^4\,b^7\,c^4\,d^7-2268\,a^3\,b^8\,c^5\,d^6+702\,a^2\,b^9\,c^6\,d^5-108\,a\,b^{10}\,c^7\,d^4+9\,b^{11}\,c^8\,d^3\right)}{32\,\left(a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}\right)}-\frac{3\,\left(\frac{\frac{3\,a^{16}\,b^2\,c^2\,d^{16}}{2}-\frac{45\,a^{15}\,b^3\,c^3\,d^{15}}{2}+\frac{333\,a^{14}\,b^4\,c^4\,d^{14}}{2}-765\,a^{13}\,b^5\,c^5\,d^{13}+\frac{4743\,a^{12}\,b^6\,c^6\,d^{12}}{2}-\frac{10371\,a^{11}\,b^7\,c^7\,d^{11}}{2}+\frac{16425\,a^{10}\,b^8\,c^8\,d^{10}}{2}-9558\,a^9\,b^9\,c^9\,d^9+\frac{16425\,a^8\,b^{10}\,c^{10}\,d^8}{2}-\frac{10371\,a^7\,b^{11}\,c^{11}\,d^7}{2}+\frac{4743\,a^6\,b^{12}\,c^{12}\,d^6}{2}-765\,a^5\,b^{13}\,c^{13}\,d^5+\frac{333\,a^4\,b^{14}\,c^{14}\,d^4}{2}-\frac{45\,a^3\,b^{15}\,c^{15}\,d^3}{2}+\frac{3\,a^2\,b^{16}\,c^{16}\,d^2}{2}}{a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}}-\frac{3\,x\,\sqrt{-c^5\,d^5}\,\left(a^2\,d^2-6\,a\,b\,c\,d+21\,b^2\,c^2\right)\,\left(256\,a^{15}\,b^2\,c^4\,d^{13}-2304\,a^{14}\,b^3\,c^5\,d^{12}+8960\,a^{13}\,b^4\,c^6\,d^{11}-19200\,a^{12}\,b^5\,c^7\,d^{10}+23040\,a^{11}\,b^6\,c^8\,d^9-10752\,a^{10}\,b^7\,c^9\,d^8-10752\,a^9\,b^8\,c^{10}\,d^7+23040\,a^8\,b^9\,c^{11}\,d^6-19200\,a^7\,b^{10}\,c^{12}\,d^5+8960\,a^6\,b^{11}\,c^{13}\,d^4-2304\,a^5\,b^{12}\,c^{14}\,d^3+256\,a^4\,b^{13}\,c^{15}\,d^2\right)}{512\,\left(-a^5\,c^5\,d^5+5\,a^4\,b\,c^6\,d^4-10\,a^3\,b^2\,c^7\,d^3+10\,a^2\,b^3\,c^8\,d^2-5\,a\,b^4\,c^9\,d+b^5\,c^{10}\right)\,\left(a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}\right)}\right)\,\sqrt{-c^5\,d^5}\,\left(a^2\,d^2-6\,a\,b\,c\,d+21\,b^2\,c^2\right)}{16\,\left(-a^5\,c^5\,d^5+5\,a^4\,b\,c^6\,d^4-10\,a^3\,b^2\,c^7\,d^3+10\,a^2\,b^3\,c^8\,d^2-5\,a\,b^4\,c^9\,d+b^5\,c^{10}\right)}\right)\,\sqrt{-c^5\,d^5}\,\left(a^2\,d^2-6\,a\,b\,c\,d+21\,b^2\,c^2\right)}{16\,\left(-a^5\,c^5\,d^5+5\,a^4\,b\,c^6\,d^4-10\,a^3\,b^2\,c^7\,d^3+10\,a^2\,b^3\,c^8\,d^2-5\,a\,b^4\,c^9\,d+b^5\,c^{10}\right)}-\frac{3\,\left(\frac{x\,\left(9\,a^8\,b^3\,d^{11}-108\,a^7\,b^4\,c\,d^{10}+702\,a^6\,b^5\,c^2\,d^9-2268\,a^5\,b^6\,c^3\,d^8+7938\,a^4\,b^7\,c^4\,d^7-2268\,a^3\,b^8\,c^5\,d^6+702\,a^2\,b^9\,c^6\,d^5-108\,a\,b^{10}\,c^7\,d^4+9\,b^{11}\,c^8\,d^3\right)}{32\,\left(a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}\right)}+\frac{3\,\left(\frac{\frac{3\,a^{16}\,b^2\,c^2\,d^{16}}{2}-\frac{45\,a^{15}\,b^3\,c^3\,d^{15}}{2}+\frac{333\,a^{14}\,b^4\,c^4\,d^{14}}{2}-765\,a^{13}\,b^5\,c^5\,d^{13}+\frac{4743\,a^{12}\,b^6\,c^6\,d^{12}}{2}-\frac{10371\,a^{11}\,b^7\,c^7\,d^{11}}{2}+\frac{16425\,a^{10}\,b^8\,c^8\,d^{10}}{2}-9558\,a^9\,b^9\,c^9\,d^9+\frac{16425\,a^8\,b^{10}\,c^{10}\,d^8}{2}-\frac{10371\,a^7\,b^{11}\,c^{11}\,d^7}{2}+\frac{4743\,a^6\,b^{12}\,c^{12}\,d^6}{2}-765\,a^5\,b^{13}\,c^{13}\,d^5+\frac{333\,a^4\,b^{14}\,c^{14}\,d^4}{2}-\frac{45\,a^3\,b^{15}\,c^{15}\,d^3}{2}+\frac{3\,a^2\,b^{16}\,c^{16}\,d^2}{2}}{a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}}+\frac{3\,x\,\sqrt{-c^5\,d^5}\,\left(a^2\,d^2-6\,a\,b\,c\,d+21\,b^2\,c^2\right)\,\left(256\,a^{15}\,b^2\,c^4\,d^{13}-2304\,a^{14}\,b^3\,c^5\,d^{12}+8960\,a^{13}\,b^4\,c^6\,d^{11}-19200\,a^{12}\,b^5\,c^7\,d^{10}+23040\,a^{11}\,b^6\,c^8\,d^9-10752\,a^{10}\,b^7\,c^9\,d^8-10752\,a^9\,b^8\,c^{10}\,d^7+23040\,a^8\,b^9\,c^{11}\,d^6-19200\,a^7\,b^{10}\,c^{12}\,d^5+8960\,a^6\,b^{11}\,c^{13}\,d^4-2304\,a^5\,b^{12}\,c^{14}\,d^3+256\,a^4\,b^{13}\,c^{15}\,d^2\right)}{512\,\left(-a^5\,c^5\,d^5+5\,a^4\,b\,c^6\,d^4-10\,a^3\,b^2\,c^7\,d^3+10\,a^2\,b^3\,c^8\,d^2-5\,a\,b^4\,c^9\,d+b^5\,c^{10}\right)\,\left(a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}\right)}\right)\,\sqrt{-c^5\,d^5}\,\left(a^2\,d^2-6\,a\,b\,c\,d+21\,b^2\,c^2\right)}{16\,\left(-a^5\,c^5\,d^5+5\,a^4\,b\,c^6\,d^4-10\,a^3\,b^2\,c^7\,d^3+10\,a^2\,b^3\,c^8\,d^2-5\,a\,b^4\,c^9\,d+b^5\,c^{10}\right)}\right)\,\sqrt{-c^5\,d^5}\,\left(a^2\,d^2-6\,a\,b\,c\,d+21\,b^2\,c^2\right)}{16\,\left(-a^5\,c^5\,d^5+5\,a^4\,b\,c^6\,d^4-10\,a^3\,b^2\,c^7\,d^3+10\,a^2\,b^3\,c^8\,d^2-5\,a\,b^4\,c^9\,d+b^5\,c^{10}\right)}}\right)\,\sqrt{-c^5\,d^5}\,\left(a^2\,d^2-6\,a\,b\,c\,d+21\,b^2\,c^2\right)\,3{}\mathrm{i}}{8\,\left(-a^5\,c^5\,d^5+5\,a^4\,b\,c^6\,d^4-10\,a^3\,b^2\,c^7\,d^3+10\,a^2\,b^3\,c^8\,d^2-5\,a\,b^4\,c^9\,d+b^5\,c^{10}\right)}","Not used",1,"((x*(5*a^4*d^4 + 5*b^4*c^4 - 17*a*b^3*c^3*d - 17*a^3*b*c*d^3))/(8*a*c*(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^3*(34*a^2*b^3*c^3*d^2 - 3*b^5*c^5 - 3*a^5*d^5 + 34*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d + 5*a^4*b*c*d^4))/(8*a^2*c^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)) - (x^5*(25*a*b^4*c^3*d^2 - 6*b^5*c^4*d - 6*a^4*b*d^5 + 25*a^3*b^2*c*d^4 + 34*a^2*b^3*c^2*d^3))/(8*a^2*c^2*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3)) + (3*b*d*x^7*(a^3*b*d^4 + b^4*c^3*d - 5*a*b^3*c^2*d^2 - 5*a^2*b^2*c*d^3))/(8*a^2*c^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)))/(x^4*(a^2*d^2 + b^2*c^2 + 4*a*b*c*d) + x^2*(2*a*b*c^2 + 2*a^2*c*d) + x^6*(2*a*b*d^2 + 2*b^2*c*d) + a^2*c^2 + b^2*d^2*x^8) - (atan(((((x*(9*a^8*b^3*d^11 + 9*b^11*c^8*d^3 - 108*a*b^10*c^7*d^4 - 108*a^7*b^4*c*d^10 + 702*a^2*b^9*c^6*d^5 - 2268*a^3*b^8*c^5*d^6 + 7938*a^4*b^7*c^4*d^7 - 2268*a^5*b^6*c^3*d^8 + 702*a^6*b^5*c^2*d^9))/(32*(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)) - (3*(((3*a^2*b^16*c^16*d^2)/2 - (45*a^3*b^15*c^15*d^3)/2 + (333*a^4*b^14*c^14*d^4)/2 - 765*a^5*b^13*c^13*d^5 + (4743*a^6*b^12*c^12*d^6)/2 - (10371*a^7*b^11*c^11*d^7)/2 + (16425*a^8*b^10*c^10*d^8)/2 - 9558*a^9*b^9*c^9*d^9 + (16425*a^10*b^8*c^8*d^10)/2 - (10371*a^11*b^7*c^7*d^11)/2 + (4743*a^12*b^6*c^6*d^12)/2 - 765*a^13*b^5*c^5*d^13 + (333*a^14*b^4*c^4*d^14)/2 - (45*a^15*b^3*c^3*d^15)/2 + (3*a^16*b^2*c^2*d^16)/2)/(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10) - (3*x*(-a^5*b^5)^(1/2)*(21*a^2*d^2 + b^2*c^2 - 6*a*b*c*d)*(256*a^4*b^13*c^15*d^2 - 2304*a^5*b^12*c^14*d^3 + 8960*a^6*b^11*c^13*d^4 - 19200*a^7*b^10*c^12*d^5 + 23040*a^8*b^9*c^11*d^6 - 10752*a^9*b^8*c^10*d^7 - 10752*a^10*b^7*c^9*d^8 + 23040*a^11*b^6*c^8*d^9 - 19200*a^12*b^5*c^7*d^10 + 8960*a^13*b^4*c^6*d^11 - 2304*a^14*b^3*c^5*d^12 + 256*a^15*b^2*c^4*d^13))/(512*(a^10*d^5 - a^5*b^5*c^5 + 5*a^6*b^4*c^4*d - 10*a^7*b^3*c^3*d^2 + 10*a^8*b^2*c^2*d^3 - 5*a^9*b*c*d^4)*(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)))*(-a^5*b^5)^(1/2)*(21*a^2*d^2 + b^2*c^2 - 6*a*b*c*d))/(16*(a^10*d^5 - a^5*b^5*c^5 + 5*a^6*b^4*c^4*d - 10*a^7*b^3*c^3*d^2 + 10*a^8*b^2*c^2*d^3 - 5*a^9*b*c*d^4)))*(-a^5*b^5)^(1/2)*(21*a^2*d^2 + b^2*c^2 - 6*a*b*c*d)*3i)/(16*(a^10*d^5 - a^5*b^5*c^5 + 5*a^6*b^4*c^4*d - 10*a^7*b^3*c^3*d^2 + 10*a^8*b^2*c^2*d^3 - 5*a^9*b*c*d^4)) + (((x*(9*a^8*b^3*d^11 + 9*b^11*c^8*d^3 - 108*a*b^10*c^7*d^4 - 108*a^7*b^4*c*d^10 + 702*a^2*b^9*c^6*d^5 - 2268*a^3*b^8*c^5*d^6 + 7938*a^4*b^7*c^4*d^7 - 2268*a^5*b^6*c^3*d^8 + 702*a^6*b^5*c^2*d^9))/(32*(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)) + (3*(((3*a^2*b^16*c^16*d^2)/2 - (45*a^3*b^15*c^15*d^3)/2 + (333*a^4*b^14*c^14*d^4)/2 - 765*a^5*b^13*c^13*d^5 + (4743*a^6*b^12*c^12*d^6)/2 - (10371*a^7*b^11*c^11*d^7)/2 + (16425*a^8*b^10*c^10*d^8)/2 - 9558*a^9*b^9*c^9*d^9 + (16425*a^10*b^8*c^8*d^10)/2 - (10371*a^11*b^7*c^7*d^11)/2 + (4743*a^12*b^6*c^6*d^12)/2 - 765*a^13*b^5*c^5*d^13 + (333*a^14*b^4*c^4*d^14)/2 - (45*a^15*b^3*c^3*d^15)/2 + (3*a^16*b^2*c^2*d^16)/2)/(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10) + (3*x*(-a^5*b^5)^(1/2)*(21*a^2*d^2 + b^2*c^2 - 6*a*b*c*d)*(256*a^4*b^13*c^15*d^2 - 2304*a^5*b^12*c^14*d^3 + 8960*a^6*b^11*c^13*d^4 - 19200*a^7*b^10*c^12*d^5 + 23040*a^8*b^9*c^11*d^6 - 10752*a^9*b^8*c^10*d^7 - 10752*a^10*b^7*c^9*d^8 + 23040*a^11*b^6*c^8*d^9 - 19200*a^12*b^5*c^7*d^10 + 8960*a^13*b^4*c^6*d^11 - 2304*a^14*b^3*c^5*d^12 + 256*a^15*b^2*c^4*d^13))/(512*(a^10*d^5 - a^5*b^5*c^5 + 5*a^6*b^4*c^4*d - 10*a^7*b^3*c^3*d^2 + 10*a^8*b^2*c^2*d^3 - 5*a^9*b*c*d^4)*(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)))*(-a^5*b^5)^(1/2)*(21*a^2*d^2 + b^2*c^2 - 6*a*b*c*d))/(16*(a^10*d^5 - a^5*b^5*c^5 + 5*a^6*b^4*c^4*d - 10*a^7*b^3*c^3*d^2 + 10*a^8*b^2*c^2*d^3 - 5*a^9*b*c*d^4)))*(-a^5*b^5)^(1/2)*(21*a^2*d^2 + b^2*c^2 - 6*a*b*c*d)*3i)/(16*(a^10*d^5 - a^5*b^5*c^5 + 5*a^6*b^4*c^4*d - 10*a^7*b^3*c^3*d^2 + 10*a^8*b^2*c^2*d^3 - 5*a^9*b*c*d^4)))/(((567*a^7*b^5*d^12)/256 + (567*b^12*c^7*d^5)/256 - (6399*a*b^11*c^6*d^6)/256 - (6399*a^6*b^6*c*d^11)/256 + (27891*a^2*b^10*c^5*d^7)/256 - (49707*a^3*b^9*c^4*d^8)/256 - (49707*a^4*b^8*c^3*d^9)/256 + (27891*a^5*b^7*c^2*d^10)/256)/(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10) + (3*((x*(9*a^8*b^3*d^11 + 9*b^11*c^8*d^3 - 108*a*b^10*c^7*d^4 - 108*a^7*b^4*c*d^10 + 702*a^2*b^9*c^6*d^5 - 2268*a^3*b^8*c^5*d^6 + 7938*a^4*b^7*c^4*d^7 - 2268*a^5*b^6*c^3*d^8 + 702*a^6*b^5*c^2*d^9))/(32*(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)) - (3*(((3*a^2*b^16*c^16*d^2)/2 - (45*a^3*b^15*c^15*d^3)/2 + (333*a^4*b^14*c^14*d^4)/2 - 765*a^5*b^13*c^13*d^5 + (4743*a^6*b^12*c^12*d^6)/2 - (10371*a^7*b^11*c^11*d^7)/2 + (16425*a^8*b^10*c^10*d^8)/2 - 9558*a^9*b^9*c^9*d^9 + (16425*a^10*b^8*c^8*d^10)/2 - (10371*a^11*b^7*c^7*d^11)/2 + (4743*a^12*b^6*c^6*d^12)/2 - 765*a^13*b^5*c^5*d^13 + (333*a^14*b^4*c^4*d^14)/2 - (45*a^15*b^3*c^3*d^15)/2 + (3*a^16*b^2*c^2*d^16)/2)/(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10) - (3*x*(-a^5*b^5)^(1/2)*(21*a^2*d^2 + b^2*c^2 - 6*a*b*c*d)*(256*a^4*b^13*c^15*d^2 - 2304*a^5*b^12*c^14*d^3 + 8960*a^6*b^11*c^13*d^4 - 19200*a^7*b^10*c^12*d^5 + 23040*a^8*b^9*c^11*d^6 - 10752*a^9*b^8*c^10*d^7 - 10752*a^10*b^7*c^9*d^8 + 23040*a^11*b^6*c^8*d^9 - 19200*a^12*b^5*c^7*d^10 + 8960*a^13*b^4*c^6*d^11 - 2304*a^14*b^3*c^5*d^12 + 256*a^15*b^2*c^4*d^13))/(512*(a^10*d^5 - a^5*b^5*c^5 + 5*a^6*b^4*c^4*d - 10*a^7*b^3*c^3*d^2 + 10*a^8*b^2*c^2*d^3 - 5*a^9*b*c*d^4)*(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)))*(-a^5*b^5)^(1/2)*(21*a^2*d^2 + b^2*c^2 - 6*a*b*c*d))/(16*(a^10*d^5 - a^5*b^5*c^5 + 5*a^6*b^4*c^4*d - 10*a^7*b^3*c^3*d^2 + 10*a^8*b^2*c^2*d^3 - 5*a^9*b*c*d^4)))*(-a^5*b^5)^(1/2)*(21*a^2*d^2 + b^2*c^2 - 6*a*b*c*d))/(16*(a^10*d^5 - a^5*b^5*c^5 + 5*a^6*b^4*c^4*d - 10*a^7*b^3*c^3*d^2 + 10*a^8*b^2*c^2*d^3 - 5*a^9*b*c*d^4)) - (3*((x*(9*a^8*b^3*d^11 + 9*b^11*c^8*d^3 - 108*a*b^10*c^7*d^4 - 108*a^7*b^4*c*d^10 + 702*a^2*b^9*c^6*d^5 - 2268*a^3*b^8*c^5*d^6 + 7938*a^4*b^7*c^4*d^7 - 2268*a^5*b^6*c^3*d^8 + 702*a^6*b^5*c^2*d^9))/(32*(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)) + (3*(((3*a^2*b^16*c^16*d^2)/2 - (45*a^3*b^15*c^15*d^3)/2 + (333*a^4*b^14*c^14*d^4)/2 - 765*a^5*b^13*c^13*d^5 + (4743*a^6*b^12*c^12*d^6)/2 - (10371*a^7*b^11*c^11*d^7)/2 + (16425*a^8*b^10*c^10*d^8)/2 - 9558*a^9*b^9*c^9*d^9 + (16425*a^10*b^8*c^8*d^10)/2 - (10371*a^11*b^7*c^7*d^11)/2 + (4743*a^12*b^6*c^6*d^12)/2 - 765*a^13*b^5*c^5*d^13 + (333*a^14*b^4*c^4*d^14)/2 - (45*a^15*b^3*c^3*d^15)/2 + (3*a^16*b^2*c^2*d^16)/2)/(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10) + (3*x*(-a^5*b^5)^(1/2)*(21*a^2*d^2 + b^2*c^2 - 6*a*b*c*d)*(256*a^4*b^13*c^15*d^2 - 2304*a^5*b^12*c^14*d^3 + 8960*a^6*b^11*c^13*d^4 - 19200*a^7*b^10*c^12*d^5 + 23040*a^8*b^9*c^11*d^6 - 10752*a^9*b^8*c^10*d^7 - 10752*a^10*b^7*c^9*d^8 + 23040*a^11*b^6*c^8*d^9 - 19200*a^12*b^5*c^7*d^10 + 8960*a^13*b^4*c^6*d^11 - 2304*a^14*b^3*c^5*d^12 + 256*a^15*b^2*c^4*d^13))/(512*(a^10*d^5 - a^5*b^5*c^5 + 5*a^6*b^4*c^4*d - 10*a^7*b^3*c^3*d^2 + 10*a^8*b^2*c^2*d^3 - 5*a^9*b*c*d^4)*(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)))*(-a^5*b^5)^(1/2)*(21*a^2*d^2 + b^2*c^2 - 6*a*b*c*d))/(16*(a^10*d^5 - a^5*b^5*c^5 + 5*a^6*b^4*c^4*d - 10*a^7*b^3*c^3*d^2 + 10*a^8*b^2*c^2*d^3 - 5*a^9*b*c*d^4)))*(-a^5*b^5)^(1/2)*(21*a^2*d^2 + b^2*c^2 - 6*a*b*c*d))/(16*(a^10*d^5 - a^5*b^5*c^5 + 5*a^6*b^4*c^4*d - 10*a^7*b^3*c^3*d^2 + 10*a^8*b^2*c^2*d^3 - 5*a^9*b*c*d^4))))*(-a^5*b^5)^(1/2)*(21*a^2*d^2 + b^2*c^2 - 6*a*b*c*d)*3i)/(8*(a^10*d^5 - a^5*b^5*c^5 + 5*a^6*b^4*c^4*d - 10*a^7*b^3*c^3*d^2 + 10*a^8*b^2*c^2*d^3 - 5*a^9*b*c*d^4)) - (atan(((((x*(9*a^8*b^3*d^11 + 9*b^11*c^8*d^3 - 108*a*b^10*c^7*d^4 - 108*a^7*b^4*c*d^10 + 702*a^2*b^9*c^6*d^5 - 2268*a^3*b^8*c^5*d^6 + 7938*a^4*b^7*c^4*d^7 - 2268*a^5*b^6*c^3*d^8 + 702*a^6*b^5*c^2*d^9))/(32*(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)) - (3*(((3*a^2*b^16*c^16*d^2)/2 - (45*a^3*b^15*c^15*d^3)/2 + (333*a^4*b^14*c^14*d^4)/2 - 765*a^5*b^13*c^13*d^5 + (4743*a^6*b^12*c^12*d^6)/2 - (10371*a^7*b^11*c^11*d^7)/2 + (16425*a^8*b^10*c^10*d^8)/2 - 9558*a^9*b^9*c^9*d^9 + (16425*a^10*b^8*c^8*d^10)/2 - (10371*a^11*b^7*c^7*d^11)/2 + (4743*a^12*b^6*c^6*d^12)/2 - 765*a^13*b^5*c^5*d^13 + (333*a^14*b^4*c^4*d^14)/2 - (45*a^15*b^3*c^3*d^15)/2 + (3*a^16*b^2*c^2*d^16)/2)/(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10) - (3*x*(-c^5*d^5)^(1/2)*(a^2*d^2 + 21*b^2*c^2 - 6*a*b*c*d)*(256*a^4*b^13*c^15*d^2 - 2304*a^5*b^12*c^14*d^3 + 8960*a^6*b^11*c^13*d^4 - 19200*a^7*b^10*c^12*d^5 + 23040*a^8*b^9*c^11*d^6 - 10752*a^9*b^8*c^10*d^7 - 10752*a^10*b^7*c^9*d^8 + 23040*a^11*b^6*c^8*d^9 - 19200*a^12*b^5*c^7*d^10 + 8960*a^13*b^4*c^6*d^11 - 2304*a^14*b^3*c^5*d^12 + 256*a^15*b^2*c^4*d^13))/(512*(b^5*c^10 - a^5*c^5*d^5 + 5*a^4*b*c^6*d^4 + 10*a^2*b^3*c^8*d^2 - 10*a^3*b^2*c^7*d^3 - 5*a*b^4*c^9*d)*(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)))*(-c^5*d^5)^(1/2)*(a^2*d^2 + 21*b^2*c^2 - 6*a*b*c*d))/(16*(b^5*c^10 - a^5*c^5*d^5 + 5*a^4*b*c^6*d^4 + 10*a^2*b^3*c^8*d^2 - 10*a^3*b^2*c^7*d^3 - 5*a*b^4*c^9*d)))*(-c^5*d^5)^(1/2)*(a^2*d^2 + 21*b^2*c^2 - 6*a*b*c*d)*3i)/(16*(b^5*c^10 - a^5*c^5*d^5 + 5*a^4*b*c^6*d^4 + 10*a^2*b^3*c^8*d^2 - 10*a^3*b^2*c^7*d^3 - 5*a*b^4*c^9*d)) + (((x*(9*a^8*b^3*d^11 + 9*b^11*c^8*d^3 - 108*a*b^10*c^7*d^4 - 108*a^7*b^4*c*d^10 + 702*a^2*b^9*c^6*d^5 - 2268*a^3*b^8*c^5*d^6 + 7938*a^4*b^7*c^4*d^7 - 2268*a^5*b^6*c^3*d^8 + 702*a^6*b^5*c^2*d^9))/(32*(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)) + (3*(((3*a^2*b^16*c^16*d^2)/2 - (45*a^3*b^15*c^15*d^3)/2 + (333*a^4*b^14*c^14*d^4)/2 - 765*a^5*b^13*c^13*d^5 + (4743*a^6*b^12*c^12*d^6)/2 - (10371*a^7*b^11*c^11*d^7)/2 + (16425*a^8*b^10*c^10*d^8)/2 - 9558*a^9*b^9*c^9*d^9 + (16425*a^10*b^8*c^8*d^10)/2 - (10371*a^11*b^7*c^7*d^11)/2 + (4743*a^12*b^6*c^6*d^12)/2 - 765*a^13*b^5*c^5*d^13 + (333*a^14*b^4*c^4*d^14)/2 - (45*a^15*b^3*c^3*d^15)/2 + (3*a^16*b^2*c^2*d^16)/2)/(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10) + (3*x*(-c^5*d^5)^(1/2)*(a^2*d^2 + 21*b^2*c^2 - 6*a*b*c*d)*(256*a^4*b^13*c^15*d^2 - 2304*a^5*b^12*c^14*d^3 + 8960*a^6*b^11*c^13*d^4 - 19200*a^7*b^10*c^12*d^5 + 23040*a^8*b^9*c^11*d^6 - 10752*a^9*b^8*c^10*d^7 - 10752*a^10*b^7*c^9*d^8 + 23040*a^11*b^6*c^8*d^9 - 19200*a^12*b^5*c^7*d^10 + 8960*a^13*b^4*c^6*d^11 - 2304*a^14*b^3*c^5*d^12 + 256*a^15*b^2*c^4*d^13))/(512*(b^5*c^10 - a^5*c^5*d^5 + 5*a^4*b*c^6*d^4 + 10*a^2*b^3*c^8*d^2 - 10*a^3*b^2*c^7*d^3 - 5*a*b^4*c^9*d)*(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)))*(-c^5*d^5)^(1/2)*(a^2*d^2 + 21*b^2*c^2 - 6*a*b*c*d))/(16*(b^5*c^10 - a^5*c^5*d^5 + 5*a^4*b*c^6*d^4 + 10*a^2*b^3*c^8*d^2 - 10*a^3*b^2*c^7*d^3 - 5*a*b^4*c^9*d)))*(-c^5*d^5)^(1/2)*(a^2*d^2 + 21*b^2*c^2 - 6*a*b*c*d)*3i)/(16*(b^5*c^10 - a^5*c^5*d^5 + 5*a^4*b*c^6*d^4 + 10*a^2*b^3*c^8*d^2 - 10*a^3*b^2*c^7*d^3 - 5*a*b^4*c^9*d)))/(((567*a^7*b^5*d^12)/256 + (567*b^12*c^7*d^5)/256 - (6399*a*b^11*c^6*d^6)/256 - (6399*a^6*b^6*c*d^11)/256 + (27891*a^2*b^10*c^5*d^7)/256 - (49707*a^3*b^9*c^4*d^8)/256 - (49707*a^4*b^8*c^3*d^9)/256 + (27891*a^5*b^7*c^2*d^10)/256)/(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10) + (3*((x*(9*a^8*b^3*d^11 + 9*b^11*c^8*d^3 - 108*a*b^10*c^7*d^4 - 108*a^7*b^4*c*d^10 + 702*a^2*b^9*c^6*d^5 - 2268*a^3*b^8*c^5*d^6 + 7938*a^4*b^7*c^4*d^7 - 2268*a^5*b^6*c^3*d^8 + 702*a^6*b^5*c^2*d^9))/(32*(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)) - (3*(((3*a^2*b^16*c^16*d^2)/2 - (45*a^3*b^15*c^15*d^3)/2 + (333*a^4*b^14*c^14*d^4)/2 - 765*a^5*b^13*c^13*d^5 + (4743*a^6*b^12*c^12*d^6)/2 - (10371*a^7*b^11*c^11*d^7)/2 + (16425*a^8*b^10*c^10*d^8)/2 - 9558*a^9*b^9*c^9*d^9 + (16425*a^10*b^8*c^8*d^10)/2 - (10371*a^11*b^7*c^7*d^11)/2 + (4743*a^12*b^6*c^6*d^12)/2 - 765*a^13*b^5*c^5*d^13 + (333*a^14*b^4*c^4*d^14)/2 - (45*a^15*b^3*c^3*d^15)/2 + (3*a^16*b^2*c^2*d^16)/2)/(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10) - (3*x*(-c^5*d^5)^(1/2)*(a^2*d^2 + 21*b^2*c^2 - 6*a*b*c*d)*(256*a^4*b^13*c^15*d^2 - 2304*a^5*b^12*c^14*d^3 + 8960*a^6*b^11*c^13*d^4 - 19200*a^7*b^10*c^12*d^5 + 23040*a^8*b^9*c^11*d^6 - 10752*a^9*b^8*c^10*d^7 - 10752*a^10*b^7*c^9*d^8 + 23040*a^11*b^6*c^8*d^9 - 19200*a^12*b^5*c^7*d^10 + 8960*a^13*b^4*c^6*d^11 - 2304*a^14*b^3*c^5*d^12 + 256*a^15*b^2*c^4*d^13))/(512*(b^5*c^10 - a^5*c^5*d^5 + 5*a^4*b*c^6*d^4 + 10*a^2*b^3*c^8*d^2 - 10*a^3*b^2*c^7*d^3 - 5*a*b^4*c^9*d)*(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)))*(-c^5*d^5)^(1/2)*(a^2*d^2 + 21*b^2*c^2 - 6*a*b*c*d))/(16*(b^5*c^10 - a^5*c^5*d^5 + 5*a^4*b*c^6*d^4 + 10*a^2*b^3*c^8*d^2 - 10*a^3*b^2*c^7*d^3 - 5*a*b^4*c^9*d)))*(-c^5*d^5)^(1/2)*(a^2*d^2 + 21*b^2*c^2 - 6*a*b*c*d))/(16*(b^5*c^10 - a^5*c^5*d^5 + 5*a^4*b*c^6*d^4 + 10*a^2*b^3*c^8*d^2 - 10*a^3*b^2*c^7*d^3 - 5*a*b^4*c^9*d)) - (3*((x*(9*a^8*b^3*d^11 + 9*b^11*c^8*d^3 - 108*a*b^10*c^7*d^4 - 108*a^7*b^4*c*d^10 + 702*a^2*b^9*c^6*d^5 - 2268*a^3*b^8*c^5*d^6 + 7938*a^4*b^7*c^4*d^7 - 2268*a^5*b^6*c^3*d^8 + 702*a^6*b^5*c^2*d^9))/(32*(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)) + (3*(((3*a^2*b^16*c^16*d^2)/2 - (45*a^3*b^15*c^15*d^3)/2 + (333*a^4*b^14*c^14*d^4)/2 - 765*a^5*b^13*c^13*d^5 + (4743*a^6*b^12*c^12*d^6)/2 - (10371*a^7*b^11*c^11*d^7)/2 + (16425*a^8*b^10*c^10*d^8)/2 - 9558*a^9*b^9*c^9*d^9 + (16425*a^10*b^8*c^8*d^10)/2 - (10371*a^11*b^7*c^7*d^11)/2 + (4743*a^12*b^6*c^6*d^12)/2 - 765*a^13*b^5*c^5*d^13 + (333*a^14*b^4*c^4*d^14)/2 - (45*a^15*b^3*c^3*d^15)/2 + (3*a^16*b^2*c^2*d^16)/2)/(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10) + (3*x*(-c^5*d^5)^(1/2)*(a^2*d^2 + 21*b^2*c^2 - 6*a*b*c*d)*(256*a^4*b^13*c^15*d^2 - 2304*a^5*b^12*c^14*d^3 + 8960*a^6*b^11*c^13*d^4 - 19200*a^7*b^10*c^12*d^5 + 23040*a^8*b^9*c^11*d^6 - 10752*a^9*b^8*c^10*d^7 - 10752*a^10*b^7*c^9*d^8 + 23040*a^11*b^6*c^8*d^9 - 19200*a^12*b^5*c^7*d^10 + 8960*a^13*b^4*c^6*d^11 - 2304*a^14*b^3*c^5*d^12 + 256*a^15*b^2*c^4*d^13))/(512*(b^5*c^10 - a^5*c^5*d^5 + 5*a^4*b*c^6*d^4 + 10*a^2*b^3*c^8*d^2 - 10*a^3*b^2*c^7*d^3 - 5*a*b^4*c^9*d)*(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)))*(-c^5*d^5)^(1/2)*(a^2*d^2 + 21*b^2*c^2 - 6*a*b*c*d))/(16*(b^5*c^10 - a^5*c^5*d^5 + 5*a^4*b*c^6*d^4 + 10*a^2*b^3*c^8*d^2 - 10*a^3*b^2*c^7*d^3 - 5*a*b^4*c^9*d)))*(-c^5*d^5)^(1/2)*(a^2*d^2 + 21*b^2*c^2 - 6*a*b*c*d))/(16*(b^5*c^10 - a^5*c^5*d^5 + 5*a^4*b*c^6*d^4 + 10*a^2*b^3*c^8*d^2 - 10*a^3*b^2*c^7*d^3 - 5*a*b^4*c^9*d))))*(-c^5*d^5)^(1/2)*(a^2*d^2 + 21*b^2*c^2 - 6*a*b*c*d)*3i)/(8*(b^5*c^10 - a^5*c^5*d^5 + 5*a^4*b*c^6*d^4 + 10*a^2*b^3*c^8*d^2 - 10*a^3*b^2*c^7*d^3 - 5*a*b^4*c^9*d))","B"
43,1,31,34,4.995429,"\text{Not used}","int((x^2 - 1)^3/(x^2 + 1)^4,x)","\frac{4\,x}{3\,{\left(x^2+1\right)}^2}-\frac{x}{x^2+1}-\frac{4\,x}{3\,{\left(x^2+1\right)}^3}","Not used",1,"(4*x)/(3*(x^2 + 1)^2) - x/(x^2 + 1) - (4*x)/(3*(x^2 + 1)^3)","B"
44,1,47,47,0.042015,"\text{Not used}","int((x^2 - 1)^4/(x^2 + 1)^5,x)","\frac{3\,\mathrm{atan}\left(x\right)}{8}+\frac{-\frac{5\,x^7}{8}+\frac{3\,x^5}{8}-\frac{3\,x^3}{8}+\frac{5\,x}{8}}{x^8+4\,x^6+6\,x^4+4\,x^2+1}","Not used",1,"(3*atan(x))/8 + ((5*x)/8 - (3*x^3)/8 + (3*x^5)/8 - (5*x^7)/8)/(4*x^2 + 6*x^4 + 4*x^6 + x^8 + 1)","B"
45,0,-1,231,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)*(c + d*x^2)^3,x)","\int \sqrt{b\,x^2+a}\,{\left(d\,x^2+c\right)}^3 \,d x","Not used",1,"int((a + b*x^2)^(1/2)*(c + d*x^2)^3, x)","F"
46,0,-1,149,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)*(c + d*x^2)^2,x)","\int \sqrt{b\,x^2+a}\,{\left(d\,x^2+c\right)}^2 \,d x","Not used",1,"int((a + b*x^2)^(1/2)*(c + d*x^2)^2, x)","F"
47,0,-1,87,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)*(c + d*x^2),x)","\int \sqrt{b\,x^2+a}\,\left(d\,x^2+c\right) \,d x","Not used",1,"int((a + b*x^2)^(1/2)*(c + d*x^2), x)","F"
48,1,35,46,4.712041,"\text{Not used}","int((a + b*x^2)^(1/2),x)","\frac{x\,\sqrt{b\,x^2+a}}{2}+\frac{a\,\ln\left(\sqrt{b}\,x+\sqrt{b\,x^2+a}\right)}{2\,\sqrt{b}}","Not used",1,"(x*(a + b*x^2)^(1/2))/2 + (a*log(b^(1/2)*x + (a + b*x^2)^(1/2)))/(2*b^(1/2))","B"
49,0,-1,82,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)/(c + d*x^2),x)","\left\{\begin{array}{cl} \frac{\sqrt{-b}\,\mathrm{asin}\left(x\,\sqrt{-\frac{b}{a}}\right)}{c} & \text{\ if\ \ }\left(\left(a+b\,c=0\wedge d=-1\right)\vee a\,d=b\,c\right)\wedge b<0\\ \frac{\sqrt{b}\,\ln\left(2\,\sqrt{b}\,x+2\,\sqrt{b\,x^2+a}\right)}{d}+\frac{\mathrm{atan}\left(\frac{x\,\sqrt{a\,d-b\,c}}{\sqrt{c}\,\sqrt{b\,x^2+a}}\right)\,\sqrt{a\,d-b\,c}}{\sqrt{c}\,d} & \text{\ if\ \ }a\neq 0\wedge \left(\left(\left(a+b\,c\neq 0\vee d\neq -1\right)\wedge a\,d\neq b\,c\right)\vee \neg b<0\right)\\ \int \frac{\sqrt{b\,x^2+a}}{d\,x^2+c} \,d x & \text{\ if\ \ }\left(\left(\left(\left(a+b\,c=0\wedge d=-1\right)\vee a\,d=b\,c\right)\wedge b<0\right)\vee a=0\right)\wedge \left(\left(\left(a+b\,c\neq 0\vee d\neq -1\right)\wedge a\,d\neq b\,c\right)\vee \neg b<0\right) \end{array}\right.","Not used",1,"piecewise((a + b*c == 0 & d == -1 | a*d == b*c) & b < 0, ((-b)^(1/2)*asin(x*(-b/a)^(1/2)))/c, a ~= 0 & ((a + b*c ~= 0 | d ~= -1) & a*d ~= b*c | ~b < 0), (b^(1/2)*log(2*b^(1/2)*x + 2*(a + b*x^2)^(1/2)))/d + (atan((x*(a*d - b*c)^(1/2))/(c^(1/2)*(a + b*x^2)^(1/2)))*(a*d - b*c)^(1/2))/(c^(1/2)*d), ((a + b*c == 0 & d == -1 | a*d == b*c) & b < 0 | a == 0) & ((a + b*c ~= 0 | d ~= -1) & a*d ~= b*c | ~b < 0), int((a + b*x^2)^(1/2)/(c + d*x^2), x))","F"
50,0,-1,82,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)/(c + d*x^2)^2,x)","\int \frac{\sqrt{b\,x^2+a}}{{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int((a + b*x^2)^(1/2)/(c + d*x^2)^2, x)","F"
51,0,-1,149,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)/(c + d*x^2)^3,x)","\int \frac{\sqrt{b\,x^2+a}}{{\left(d\,x^2+c\right)}^3} \,d x","Not used",1,"int((a + b*x^2)^(1/2)/(c + d*x^2)^3, x)","F"
52,0,-1,208,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)/(c + d*x^2)^4,x)","\int \frac{\sqrt{b\,x^2+a}}{{\left(d\,x^2+c\right)}^4} \,d x","Not used",1,"int((a + b*x^2)^(1/2)/(c + d*x^2)^4, x)","F"
53,0,-1,272,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)*(c + d*x^2)^3,x)","\int {\left(b\,x^2+a\right)}^{3/2}\,{\left(d\,x^2+c\right)}^3 \,d x","Not used",1,"int((a + b*x^2)^(3/2)*(c + d*x^2)^3, x)","F"
54,0,-1,196,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)*(c + d*x^2)^2,x)","\int {\left(b\,x^2+a\right)}^{3/2}\,{\left(d\,x^2+c\right)}^2 \,d x","Not used",1,"int((a + b*x^2)^(3/2)*(c + d*x^2)^2, x)","F"
55,0,-1,118,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)*(c + d*x^2),x)","\int {\left(b\,x^2+a\right)}^{3/2}\,\left(d\,x^2+c\right) \,d x","Not used",1,"int((a + b*x^2)^(3/2)*(c + d*x^2), x)","F"
56,1,37,65,4.709198,"\text{Not used}","int((a + b*x^2)^(3/2),x)","\frac{x\,{\left(b\,x^2+a\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{2},\frac{1}{2};\ \frac{3}{2};\ -\frac{b\,x^2}{a}\right)}{{\left(\frac{b\,x^2}{a}+1\right)}^{3/2}}","Not used",1,"(x*(a + b*x^2)^(3/2)*hypergeom([-3/2, 1/2], 3/2, -(b*x^2)/a))/((b*x^2)/a + 1)^(3/2)","B"
57,0,-1,113,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)/(c + d*x^2),x)","\int \frac{{\left(b\,x^2+a\right)}^{3/2}}{d\,x^2+c} \,d x","Not used",1,"int((a + b*x^2)^(3/2)/(c + d*x^2), x)","F"
58,0,-1,131,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)/(c + d*x^2)^2,x)","\int \frac{{\left(b\,x^2+a\right)}^{3/2}}{{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int((a + b*x^2)^(3/2)/(c + d*x^2)^2, x)","F"
59,0,-1,113,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)/(c + d*x^2)^3,x)","\int \frac{{\left(b\,x^2+a\right)}^{3/2}}{{\left(d\,x^2+c\right)}^3} \,d x","Not used",1,"int((a + b*x^2)^(3/2)/(c + d*x^2)^3, x)","F"
60,0,-1,199,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)/(c + d*x^2)^4,x)","\int \frac{{\left(b\,x^2+a\right)}^{3/2}}{{\left(d\,x^2+c\right)}^4} \,d x","Not used",1,"int((a + b*x^2)^(3/2)/(c + d*x^2)^4, x)","F"
61,0,-1,300,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)/(c + d*x^2)^5,x)","\int \frac{{\left(b\,x^2+a\right)}^{3/2}}{{\left(d\,x^2+c\right)}^5} \,d x","Not used",1,"int((a + b*x^2)^(3/2)/(c + d*x^2)^5, x)","F"
62,0,-1,349,0.000000,"\text{Not used}","int((a + b*x^2)^(5/2)*(c + d*x^2)^3,x)","\int {\left(b\,x^2+a\right)}^{5/2}\,{\left(d\,x^2+c\right)}^3 \,d x","Not used",1,"int((a + b*x^2)^(5/2)*(c + d*x^2)^3, x)","F"
63,0,-1,241,0.000000,"\text{Not used}","int((a + b*x^2)^(5/2)*(c + d*x^2)^2,x)","\int {\left(b\,x^2+a\right)}^{5/2}\,{\left(d\,x^2+c\right)}^2 \,d x","Not used",1,"int((a + b*x^2)^(5/2)*(c + d*x^2)^2, x)","F"
64,0,-1,149,0.000000,"\text{Not used}","int((a + b*x^2)^(5/2)*(c + d*x^2),x)","\int {\left(b\,x^2+a\right)}^{5/2}\,\left(d\,x^2+c\right) \,d x","Not used",1,"int((a + b*x^2)^(5/2)*(c + d*x^2), x)","F"
65,1,37,84,4.693023,"\text{Not used}","int((a + b*x^2)^(5/2),x)","\frac{x\,{\left(b\,x^2+a\right)}^{5/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{2},\frac{1}{2};\ \frac{3}{2};\ -\frac{b\,x^2}{a}\right)}{{\left(\frac{b\,x^2}{a}+1\right)}^{5/2}}","Not used",1,"(x*(a + b*x^2)^(5/2)*hypergeom([-5/2, 1/2], 3/2, -(b*x^2)/a))/((b*x^2)/a + 1)^(5/2)","B"
66,0,-1,157,0.000000,"\text{Not used}","int((a + b*x^2)^(5/2)/(c + d*x^2),x)","\int \frac{{\left(b\,x^2+a\right)}^{5/2}}{d\,x^2+c} \,d x","Not used",1,"int((a + b*x^2)^(5/2)/(c + d*x^2), x)","F"
67,0,-1,175,0.000000,"\text{Not used}","int((a + b*x^2)^(5/2)/(c + d*x^2)^2,x)","\int \frac{{\left(b\,x^2+a\right)}^{5/2}}{{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int((a + b*x^2)^(5/2)/(c + d*x^2)^2, x)","F"
68,0,-1,194,0.000000,"\text{Not used}","int((a + b*x^2)^(5/2)/(c + d*x^2)^3,x)","\int \frac{{\left(b\,x^2+a\right)}^{5/2}}{{\left(d\,x^2+c\right)}^3} \,d x","Not used",1,"int((a + b*x^2)^(5/2)/(c + d*x^2)^3, x)","F"
69,0,-1,144,0.000000,"\text{Not used}","int((a + b*x^2)^(5/2)/(c + d*x^2)^4,x)","\int \frac{{\left(b\,x^2+a\right)}^{5/2}}{{\left(d\,x^2+c\right)}^4} \,d x","Not used",1,"int((a + b*x^2)^(5/2)/(c + d*x^2)^4, x)","F"
70,0,-1,249,0.000000,"\text{Not used}","int((a + b*x^2)^(5/2)/(c + d*x^2)^5,x)","\int \frac{{\left(b\,x^2+a\right)}^{5/2}}{{\left(d\,x^2+c\right)}^5} \,d x","Not used",1,"int((a + b*x^2)^(5/2)/(c + d*x^2)^5, x)","F"
71,1,83,30,0.394220,"\text{Not used}","int((1 - x^2)^(1/2)/(x^2 + 1),x)","-\mathrm{asin}\left(x\right)+\frac{\sqrt{2}\,\ln\left(\frac{\frac{\sqrt{2}\,\left(-1+x\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}-\sqrt{1-x^2}\,1{}\mathrm{i}}{x-\mathrm{i}}\right)\,1{}\mathrm{i}}{2}-\frac{\sqrt{2}\,\ln\left(\frac{\frac{\sqrt{2}\,\left(1+x\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}+\sqrt{1-x^2}\,1{}\mathrm{i}}{x+1{}\mathrm{i}}\right)\,1{}\mathrm{i}}{2}","Not used",1,"(2^(1/2)*log(((2^(1/2)*(x*1i - 1)*1i)/2 - (1 - x^2)^(1/2)*1i)/(x - 1i))*1i)/2 - asin(x) - (2^(1/2)*log(((2^(1/2)*(x*1i + 1)*1i)/2 + (1 - x^2)^(1/2)*1i)/(x + 1i))*1i)/2","B"
72,1,59,27,0.166756,"\text{Not used}","int((x^2 + 1)^(1/2)/(x^2 - 1),x)","\mathrm{asinh}\left(x\right)+\frac{\sqrt{2}\,\left(\ln\left(x-1\right)-\ln\left(x+\sqrt{2}\,\sqrt{x^2+1}+1\right)\right)}{2}-\frac{\sqrt{2}\,\left(\ln\left(x+1\right)-\ln\left(\sqrt{2}\,\sqrt{x^2+1}-x+1\right)\right)}{2}","Not used",1,"asinh(x) + (2^(1/2)*(log(x - 1) - log(x + 2^(1/2)*(x^2 + 1)^(1/2) + 1)))/2 - (2^(1/2)*(log(x + 1) - log(2^(1/2)*(x^2 + 1)^(1/2) - x + 1)))/2","B"
73,1,85,25,5.347240,"\text{Not used}","int((1 - x^2)^(1/2)/(2*x^2 - 1),x)","-\frac{\ln\left(\frac{\sqrt{2}\,\left(\frac{\sqrt{2}\,x}{2}-1\right)\,1{}\mathrm{i}-\sqrt{1-x^2}\,1{}\mathrm{i}}{x-\frac{\sqrt{2}}{2}}\right)}{4}+\frac{\ln\left(\frac{\sqrt{2}\,\left(\frac{\sqrt{2}\,x}{2}+1\right)\,1{}\mathrm{i}+\sqrt{1-x^2}\,1{}\mathrm{i}}{x+\frac{\sqrt{2}}{2}}\right)}{4}-\frac{\mathrm{asin}\left(x\right)}{2}","Not used",1,"log((2^(1/2)*((2^(1/2)*x)/2 + 1)*1i + (1 - x^2)^(1/2)*1i)/(x + 2^(1/2)/2))/4 - log((2^(1/2)*((2^(1/2)*x)/2 - 1)*1i - (1 - x^2)^(1/2)*1i)/(x - 2^(1/2)/2))/4 - asin(x)/2","B"
74,0,-1,169,0.000000,"\text{Not used}","int((c + d*x^2)^3/(a + b*x^2)^(1/2),x)","\int \frac{{\left(d\,x^2+c\right)}^3}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((c + d*x^2)^3/(a + b*x^2)^(1/2), x)","F"
75,0,-1,108,0.000000,"\text{Not used}","int((c + d*x^2)^2/(a + b*x^2)^(1/2),x)","\int \frac{{\left(d\,x^2+c\right)}^2}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((c + d*x^2)^2/(a + b*x^2)^(1/2), x)","F"
76,1,86,58,5.514661,"\text{Not used}","int((c + d*x^2)/(a + b*x^2)^(1/2),x)","\left\{\begin{array}{cl} \frac{d\,x^3+3\,c\,x}{3\,\sqrt{a}} & \text{\ if\ \ }b=0\\ \frac{c\,\ln\left(\sqrt{b}\,x+\sqrt{b\,x^2+a}\right)}{\sqrt{b}}-\frac{a\,d\,\ln\left(2\,\sqrt{b}\,x+2\,\sqrt{b\,x^2+a}\right)}{2\,b^{3/2}}+\frac{d\,x\,\sqrt{b\,x^2+a}}{2\,b} & \text{\ if\ \ }b\neq 0 \end{array}\right.","Not used",1,"piecewise(b == 0, (3*c*x + d*x^3)/(3*a^(1/2)), b ~= 0, (c*log(b^(1/2)*x + (a + b*x^2)^(1/2)))/b^(1/2) - (a*d*log(2*b^(1/2)*x + 2*(a + b*x^2)^(1/2)))/(2*b^(3/2)) + (d*x*(a + b*x^2)^(1/2))/(2*b))","B"
77,1,20,25,0.121178,"\text{Not used}","int(1/(a + b*x^2)^(1/2),x)","\frac{\ln\left(\sqrt{b}\,x+\sqrt{b\,x^2+a}\right)}{\sqrt{b}}","Not used",1,"log(b^(1/2)*x + (a + b*x^2)^(1/2))/b^(1/2)","B"
78,0,-1,49,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(1/2)*(c + d*x^2)),x)","\left\{\begin{array}{cl} \frac{\mathrm{atan}\left(\frac{x\,\sqrt{a\,d-b\,c}}{\sqrt{c}\,\sqrt{b\,x^2+a}}\right)}{\sqrt{c\,\left(a\,d-b\,c\right)}} & \text{\ if\ \ }0<a\,d-b\,c\\ \frac{\ln\left(\frac{\sqrt{c\,\left(b\,x^2+a\right)}+x\,\sqrt{b\,c-a\,d}}{\sqrt{c\,\left(b\,x^2+a\right)}-x\,\sqrt{b\,c-a\,d}}\right)}{2\,\sqrt{-c\,\left(a\,d-b\,c\right)}} & \text{\ if\ \ }a\,d-b\,c<0\\ \int \frac{1}{\sqrt{b\,x^2+a}\,\left(d\,x^2+c\right)} \,d x & \text{\ if\ \ }a\,d-b\,c\notin \mathbb{R}\vee a\,d=b\,c \end{array}\right.","Not used",1,"piecewise(0 < a*d - b*c, atan((x*(a*d - b*c)^(1/2))/(c^(1/2)*(a + b*x^2)^(1/2)))/(c*(a*d - b*c))^(1/2), a*d - b*c < 0, log(((c*(a + b*x^2))^(1/2) + x*(- a*d + b*c)^(1/2))/((c*(a + b*x^2))^(1/2) - x*(- a*d + b*c)^(1/2)))/(2*(-c*(a*d - b*c))^(1/2)), ~in(a*d - b*c, 'real') | a*d == b*c, int(1/((a + b*x^2)^(1/2)*(c + d*x^2)), x))","F"
79,0,-1,101,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(1/2)*(c + d*x^2)^2),x)","\int \frac{1}{\sqrt{b\,x^2+a}\,{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^2)^(1/2)*(c + d*x^2)^2), x)","F"
80,0,-1,163,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(1/2)*(c + d*x^2)^3),x)","\int \frac{1}{\sqrt{b\,x^2+a}\,{\left(d\,x^2+c\right)}^3} \,d x","Not used",1,"int(1/((a + b*x^2)^(1/2)*(c + d*x^2)^3), x)","F"
81,0,-1,257,0.000000,"\text{Not used}","int((c + d*x^2)^4/(a + b*x^2)^(3/2),x)","\int \frac{{\left(d\,x^2+c\right)}^4}{{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((c + d*x^2)^4/(a + b*x^2)^(3/2), x)","F"
82,0,-1,169,0.000000,"\text{Not used}","int((c + d*x^2)^3/(a + b*x^2)^(3/2),x)","\int \frac{{\left(d\,x^2+c\right)}^3}{{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((c + d*x^2)^3/(a + b*x^2)^(3/2), x)","F"
83,0,-1,90,0.000000,"\text{Not used}","int((c + d*x^2)^2/(a + b*x^2)^(3/2),x)","\int \frac{{\left(d\,x^2+c\right)}^2}{{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((c + d*x^2)^2/(a + b*x^2)^(3/2), x)","F"
84,1,53,54,5.117241,"\text{Not used}","int((c + d*x^2)/(a + b*x^2)^(3/2),x)","\frac{d\,\ln\left(\sqrt{b}\,x+\sqrt{b\,x^2+a}\right)}{b^{3/2}}+\frac{c\,x}{a\,\sqrt{b\,x^2+a}}-\frac{d\,x}{b\,\sqrt{b\,x^2+a}}","Not used",1,"(d*log(b^(1/2)*x + (a + b*x^2)^(1/2)))/b^(3/2) + (c*x)/(a*(a + b*x^2)^(1/2)) - (d*x)/(b*(a + b*x^2)^(1/2))","B"
85,1,14,16,0.040069,"\text{Not used}","int(1/(a + b*x^2)^(3/2),x)","\frac{x}{a\,\sqrt{b\,x^2+a}}","Not used",1,"x/(a*(a + b*x^2)^(1/2))","B"
86,0,-1,79,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(3/2)*(c + d*x^2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{3/2}\,\left(d\,x^2+c\right)} \,d x","Not used",1,"int(1/((a + b*x^2)^(3/2)*(c + d*x^2)), x)","F"
87,0,-1,143,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(3/2)*(c + d*x^2)^2),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{3/2}\,{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^2)^(3/2)*(c + d*x^2)^2), x)","F"
88,0,-1,225,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(3/2)*(c + d*x^2)^3),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{3/2}\,{\left(d\,x^2+c\right)}^3} \,d x","Not used",1,"int(1/((a + b*x^2)^(3/2)*(c + d*x^2)^3), x)","F"
89,0,-1,255,0.000000,"\text{Not used}","int((c + d*x^2)^4/(a + b*x^2)^(5/2),x)","\int \frac{{\left(d\,x^2+c\right)}^4}{{\left(b\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((c + d*x^2)^4/(a + b*x^2)^(5/2), x)","F"
90,0,-1,172,0.000000,"\text{Not used}","int((c + d*x^2)^3/(a + b*x^2)^(5/2),x)","\int \frac{{\left(d\,x^2+c\right)}^3}{{\left(b\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((c + d*x^2)^3/(a + b*x^2)^(5/2), x)","F"
91,0,-1,105,0.000000,"\text{Not used}","int((c + d*x^2)^2/(a + b*x^2)^(5/2),x)","\int \frac{{\left(d\,x^2+c\right)}^2}{{\left(b\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((c + d*x^2)^2/(a + b*x^2)^(5/2), x)","F"
92,1,33,47,4.784834,"\text{Not used}","int((c + d*x^2)/(a + b*x^2)^(5/2),x)","\frac{3\,a\,c\,x+a\,d\,x^3+2\,b\,c\,x^3}{3\,a^2\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"(3*a*c*x + a*d*x^3 + 2*b*c*x^3)/(3*a^2*(a + b*x^2)^(3/2))","B"
93,1,28,39,4.753942,"\text{Not used}","int(1/(a + b*x^2)^(5/2),x)","\frac{2\,x\,\left(b\,x^2+a\right)+a\,x}{3\,a^2\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"(2*x*(a + b*x^2) + a*x)/(3*a^2*(a + b*x^2)^(3/2))","B"
94,0,-1,122,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(5/2)*(c + d*x^2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{5/2}\,\left(d\,x^2+c\right)} \,d x","Not used",1,"int(1/((a + b*x^2)^(5/2)*(c + d*x^2)), x)","F"
95,0,-1,202,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(5/2)*(c + d*x^2)^2),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{5/2}\,{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^2)^(5/2)*(c + d*x^2)^2), x)","F"
96,0,-1,313,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(5/2)*(c + d*x^2)^3),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{5/2}\,{\left(d\,x^2+c\right)}^3} \,d x","Not used",1,"int(1/((a + b*x^2)^(5/2)*(c + d*x^2)^3), x)","F"
97,1,326,224,5.151909,"\text{Not used}","int((a + b*x^2)^3/(c + d*x^2)^(11/2),x)","\frac{x\,\left(\frac{a^3}{9\,c}-\frac{c\,\left(\frac{c\,\left(\frac{b^3}{9\,d}-\frac{a\,b^2}{3\,c}\right)}{d}+\frac{a^2\,b}{3\,c}\right)}{d}\right)}{{\left(d\,x^2+c\right)}^{9/2}}-\frac{x\,\left(\frac{b^3}{5\,d^3}-\frac{16\,a^3\,d^3+6\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-4\,b^3\,c^3}{105\,c^3\,d^3}\right)}{{\left(d\,x^2+c\right)}^{5/2}}+\frac{x\,\left(\frac{c\,\left(\frac{b^3}{7\,d^2}-\frac{b^2\,\left(3\,a\,d-b\,c\right)}{7\,c\,d^2}\right)}{d}+\frac{8\,a^3\,d^3+3\,a^2\,b\,c\,d^2-3\,a\,b^2\,c^2\,d+b^3\,c^3}{63\,c^2\,d^3}\right)}{{\left(d\,x^2+c\right)}^{7/2}}+\frac{x\,\left(64\,a^3\,d^3+24\,a^2\,b\,c\,d^2+12\,a\,b^2\,c^2\,d+5\,b^3\,c^3\right)}{315\,c^4\,d^3\,{\left(d\,x^2+c\right)}^{3/2}}+\frac{x\,\left(128\,a^3\,d^3+48\,a^2\,b\,c\,d^2+24\,a\,b^2\,c^2\,d+10\,b^3\,c^3\right)}{315\,c^5\,d^3\,\sqrt{d\,x^2+c}}","Not used",1,"(x*(a^3/(9*c) - (c*((c*(b^3/(9*d) - (a*b^2)/(3*c)))/d + (a^2*b)/(3*c)))/d))/(c + d*x^2)^(9/2) - (x*(b^3/(5*d^3) - (16*a^3*d^3 - 4*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2)/(105*c^3*d^3)))/(c + d*x^2)^(5/2) + (x*((c*(b^3/(7*d^2) - (b^2*(3*a*d - b*c))/(7*c*d^2)))/d + (8*a^3*d^3 + b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2)/(63*c^2*d^3)))/(c + d*x^2)^(7/2) + (x*(64*a^3*d^3 + 5*b^3*c^3 + 12*a*b^2*c^2*d + 24*a^2*b*c*d^2))/(315*c^4*d^3*(c + d*x^2)^(3/2)) + (x*(128*a^3*d^3 + 10*b^3*c^3 + 24*a*b^2*c^2*d + 48*a^2*b*c*d^2))/(315*c^5*d^3*(c + d*x^2)^(1/2))","B"
98,1,176,174,4.986813,"\text{Not used}","int((a + b*x^2)^2/(c + d*x^2)^(9/2),x)","\frac{x\,\left(\frac{a^2}{7\,c}+\frac{c\,\left(\frac{b^2}{7\,d}-\frac{2\,a\,b}{7\,c}\right)}{d}\right)}{{\left(d\,x^2+c\right)}^{7/2}}-\frac{x\,\left(\frac{b^2}{5\,d^2}-\frac{6\,a^2\,d^2+2\,a\,b\,c\,d-b^2\,c^2}{35\,c^2\,d^2}\right)}{{\left(d\,x^2+c\right)}^{5/2}}+\frac{x\,\left(24\,a^2\,d^2+8\,a\,b\,c\,d+3\,b^2\,c^2\right)}{105\,c^3\,d^2\,{\left(d\,x^2+c\right)}^{3/2}}+\frac{x\,\left(48\,a^2\,d^2+16\,a\,b\,c\,d+6\,b^2\,c^2\right)}{105\,c^4\,d^2\,\sqrt{d\,x^2+c}}","Not used",1,"(x*(a^2/(7*c) + (c*(b^2/(7*d) - (2*a*b)/(7*c)))/d))/(c + d*x^2)^(7/2) - (x*(b^2/(5*d^2) - (6*a^2*d^2 - b^2*c^2 + 2*a*b*c*d)/(35*c^2*d^2)))/(c + d*x^2)^(5/2) + (x*(24*a^2*d^2 + 3*b^2*c^2 + 8*a*b*c*d))/(105*c^3*d^2*(c + d*x^2)^(3/2)) + (x*(48*a^2*d^2 + 6*b^2*c^2 + 16*a*b*c*d))/(105*c^4*d^2*(c + d*x^2)^(1/2))","B"
99,1,87,91,4.849342,"\text{Not used}","int((a + b*x^2)/(c + d*x^2)^(7/2),x)","\frac{8\,a\,d\,x\,{\left(d\,x^2+c\right)}^2-3\,b\,c^3\,x+2\,b\,c\,x\,{\left(d\,x^2+c\right)}^2+b\,c^2\,x\,\left(d\,x^2+c\right)+3\,a\,c^2\,d\,x+4\,a\,c\,d\,x\,\left(d\,x^2+c\right)}{15\,c^3\,d\,{\left(d\,x^2+c\right)}^{5/2}}","Not used",1,"(8*a*d*x*(c + d*x^2)^2 - 3*b*c^3*x + 2*b*c*x*(c + d*x^2)^2 + b*c^2*x*(c + d*x^2) + 3*a*c^2*d*x + 4*a*c*d*x*(c + d*x^2))/(15*c^3*d*(c + d*x^2)^(5/2))","B"
100,1,28,39,4.787109,"\text{Not used}","int(1/(c + d*x^2)^(5/2),x)","\frac{2\,x\,\left(d\,x^2+c\right)+c\,x}{3\,c^2\,{\left(d\,x^2+c\right)}^{3/2}}","Not used",1,"(2*x*(c + d*x^2) + c*x)/(3*c^2*(c + d*x^2)^(3/2))","B"
101,0,-1,79,0.000000,"\text{Not used}","int(1/((a + b*x^2)*(c + d*x^2)^(3/2)),x)","\int \frac{1}{\left(b\,x^2+a\right)\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + b*x^2)*(c + d*x^2)^(3/2)), x)","F"
102,0,-1,100,0.000000,"\text{Not used}","int(1/((a + b*x^2)^2*(c + d*x^2)^(1/2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/((a + b*x^2)^2*(c + d*x^2)^(1/2)), x)","F"
103,0,-1,149,0.000000,"\text{Not used}","int((c + d*x^2)^(1/2)/(a + b*x^2)^3,x)","\int \frac{\sqrt{d\,x^2+c}}{{\left(b\,x^2+a\right)}^3} \,d x","Not used",1,"int((c + d*x^2)^(1/2)/(a + b*x^2)^3, x)","F"
104,0,-1,199,0.000000,"\text{Not used}","int((c + d*x^2)^(3/2)/(a + b*x^2)^4,x)","\int \frac{{\left(d\,x^2+c\right)}^{3/2}}{{\left(b\,x^2+a\right)}^4} \,d x","Not used",1,"int((c + d*x^2)^(3/2)/(a + b*x^2)^4, x)","F"
105,1,18,20,4.771337,"\text{Not used}","int(1/((c + d*x^2)^(1/2)*(b*x^2 + (b*c)/d)),x)","\frac{d\,x}{b\,c\,\sqrt{d\,x^2+c}}","Not used",1,"(d*x)/(b*c*(c + d*x^2)^(1/2))","B"
106,1,79,25,0.368225,"\text{Not used}","int(1/((1 - x^2)^(1/2)*(x^2 + 1)),x)","\frac{\sqrt{2}\,\ln\left(\frac{\frac{\sqrt{2}\,\left(-1+x\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}-\sqrt{1-x^2}\,1{}\mathrm{i}}{x-\mathrm{i}}\right)\,1{}\mathrm{i}}{4}-\frac{\sqrt{2}\,\ln\left(\frac{\frac{\sqrt{2}\,\left(1+x\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}+\sqrt{1-x^2}\,1{}\mathrm{i}}{x+1{}\mathrm{i}}\right)\,1{}\mathrm{i}}{4}","Not used",1,"(2^(1/2)*log(((2^(1/2)*(x*1i - 1)*1i)/2 - (1 - x^2)^(1/2)*1i)/(x - 1i))*1i)/4 - (2^(1/2)*log(((2^(1/2)*(x*1i + 1)*1i)/2 + (1 - x^2)^(1/2)*1i)/(x + 1i))*1i)/4","B"
107,0,-1,49,0.000000,"\text{Not used}","int(1/((a + b*x^2)*(c + d*x^2)^(1/2)),x)","\left\{\begin{array}{cl} \frac{\mathrm{atan}\left(\frac{x\,\sqrt{b\,c-a\,d}}{\sqrt{a}\,\sqrt{d\,x^2+c}}\right)}{\sqrt{-a\,\left(a\,d-b\,c\right)}} & \text{\ if\ \ }0<b\,c-a\,d\\ \frac{\ln\left(\frac{\sqrt{a\,\left(d\,x^2+c\right)}+x\,\sqrt{a\,d-b\,c}}{\sqrt{a\,\left(d\,x^2+c\right)}-x\,\sqrt{a\,d-b\,c}}\right)}{2\,\sqrt{a\,\left(a\,d-b\,c\right)}} & \text{\ if\ \ }b\,c-a\,d<0\\ \int \frac{1}{\left(b\,x^2+a\right)\,\sqrt{d\,x^2+c}} \,d x & \text{\ if\ \ }b\,c-a\,d\notin \mathbb{R}\vee a\,d=b\,c \end{array}\right.","Not used",1,"piecewise(0 < - a*d + b*c, atan((x*(- a*d + b*c)^(1/2))/(a^(1/2)*(c + d*x^2)^(1/2)))/(-a*(a*d - b*c))^(1/2), - a*d + b*c < 0, log(((a*(c + d*x^2))^(1/2) + x*(a*d - b*c)^(1/2))/((a*(c + d*x^2))^(1/2) - x*(a*d - b*c)^(1/2)))/(2*(a*(a*d - b*c))^(1/2)), ~in(- a*d + b*c, 'real') | a*d == b*c, int(1/((a + b*x^2)*(c + d*x^2)^(1/2)), x))","F"
108,1,27,15,0.039265,"\text{Not used}","int((x^2 - 1)/(x^2 + 1)^(3/2),x)","\frac{\mathrm{asinh}\left(x\right)+x^2\,\mathrm{asinh}\left(x\right)-2\,x\,\sqrt{x^2+1}}{x^2+1}","Not used",1,"(asinh(x) + x^2*asinh(x) - 2*x*(x^2 + 1)^(1/2))/(x^2 + 1)","B"
109,0,-1,648,0.000000,"\text{Not used}","int((a - b*x^2)^(2/3)*(3*a + b*x^2)^3,x)","\int {\left(a-b\,x^2\right)}^{2/3}\,{\left(b\,x^2+3\,a\right)}^3 \,d x","Not used",1,"int((a - b*x^2)^(2/3)*(3*a + b*x^2)^3, x)","F"
110,0,-1,617,0.000000,"\text{Not used}","int((a - b*x^2)^(2/3)*(3*a + b*x^2)^2,x)","\int {\left(a-b\,x^2\right)}^{2/3}\,{\left(b\,x^2+3\,a\right)}^2 \,d x","Not used",1,"int((a - b*x^2)^(2/3)*(3*a + b*x^2)^2, x)","F"
111,0,-1,588,0.000000,"\text{Not used}","int((a - b*x^2)^(2/3)*(3*a + b*x^2),x)","\int {\left(a-b\,x^2\right)}^{2/3}\,\left(b\,x^2+3\,a\right) \,d x","Not used",1,"int((a - b*x^2)^(2/3)*(3*a + b*x^2), x)","F"
112,0,-1,740,0.000000,"\text{Not used}","int((a - b*x^2)^(2/3)/(3*a + b*x^2),x)","\int \frac{{\left(a-b\,x^2\right)}^{2/3}}{b\,x^2+3\,a} \,d x","Not used",1,"int((a - b*x^2)^(2/3)/(3*a + b*x^2), x)","F"
113,0,-1,584,0.000000,"\text{Not used}","int((a - b*x^2)^(2/3)/(3*a + b*x^2)^2,x)","\int \frac{{\left(a-b\,x^2\right)}^{2/3}}{{\left(b\,x^2+3\,a\right)}^2} \,d x","Not used",1,"int((a - b*x^2)^(2/3)/(3*a + b*x^2)^2, x)","F"
114,0,-1,818,0.000000,"\text{Not used}","int((a - b*x^2)^(2/3)/(3*a + b*x^2)^3,x)","\int \frac{{\left(a-b\,x^2\right)}^{2/3}}{{\left(b\,x^2+3\,a\right)}^3} \,d x","Not used",1,"int((a - b*x^2)^(2/3)/(3*a + b*x^2)^3, x)","F"
115,0,-1,849,0.000000,"\text{Not used}","int((a - b*x^2)^(2/3)/(3*a + b*x^2)^4,x)","\int \frac{{\left(a-b\,x^2\right)}^{2/3}}{{\left(b\,x^2+3\,a\right)}^4} \,d x","Not used",1,"int((a - b*x^2)^(2/3)/(3*a + b*x^2)^4, x)","F"
116,0,-1,668,0.000000,"\text{Not used}","int((a - b*x^2)^(5/3)*(3*a + b*x^2)^3,x)","\int {\left(a-b\,x^2\right)}^{5/3}\,{\left(b\,x^2+3\,a\right)}^3 \,d x","Not used",1,"int((a - b*x^2)^(5/3)*(3*a + b*x^2)^3, x)","F"
117,0,-1,637,0.000000,"\text{Not used}","int((a - b*x^2)^(5/3)*(3*a + b*x^2)^2,x)","\int {\left(a-b\,x^2\right)}^{5/3}\,{\left(b\,x^2+3\,a\right)}^2 \,d x","Not used",1,"int((a - b*x^2)^(5/3)*(3*a + b*x^2)^2, x)","F"
118,0,-1,608,0.000000,"\text{Not used}","int((a - b*x^2)^(5/3)*(3*a + b*x^2),x)","\int {\left(a-b\,x^2\right)}^{5/3}\,\left(b\,x^2+3\,a\right) \,d x","Not used",1,"int((a - b*x^2)^(5/3)*(3*a + b*x^2), x)","F"
119,0,-1,765,0.000000,"\text{Not used}","int((a - b*x^2)^(5/3)/(3*a + b*x^2),x)","\int \frac{{\left(a-b\,x^2\right)}^{5/3}}{b\,x^2+3\,a} \,d x","Not used",1,"int((a - b*x^2)^(5/3)/(3*a + b*x^2), x)","F"
120,0,-1,775,0.000000,"\text{Not used}","int((a - b*x^2)^(5/3)/(3*a + b*x^2)^2,x)","\int \frac{{\left(a-b\,x^2\right)}^{5/3}}{{\left(b\,x^2+3\,a\right)}^2} \,d x","Not used",1,"int((a - b*x^2)^(5/3)/(3*a + b*x^2)^2, x)","F"
121,0,-1,815,0.000000,"\text{Not used}","int((a - b*x^2)^(5/3)/(3*a + b*x^2)^3,x)","\int \frac{{\left(a-b\,x^2\right)}^{5/3}}{{\left(b\,x^2+3\,a\right)}^3} \,d x","Not used",1,"int((a - b*x^2)^(5/3)/(3*a + b*x^2)^3, x)","F"
122,0,-1,659,0.000000,"\text{Not used}","int((3*a + b*x^2)^4/(a - b*x^2)^(1/3),x)","\int \frac{{\left(b\,x^2+3\,a\right)}^4}{{\left(a-b\,x^2\right)}^{1/3}} \,d x","Not used",1,"int((3*a + b*x^2)^4/(a - b*x^2)^(1/3), x)","F"
123,0,-1,628,0.000000,"\text{Not used}","int((3*a + b*x^2)^3/(a - b*x^2)^(1/3),x)","\int \frac{{\left(b\,x^2+3\,a\right)}^3}{{\left(a-b\,x^2\right)}^{1/3}} \,d x","Not used",1,"int((3*a + b*x^2)^3/(a - b*x^2)^(1/3), x)","F"
124,0,-1,597,0.000000,"\text{Not used}","int((3*a + b*x^2)^2/(a - b*x^2)^(1/3),x)","\int \frac{{\left(b\,x^2+3\,a\right)}^2}{{\left(a-b\,x^2\right)}^{1/3}} \,d x","Not used",1,"int((3*a + b*x^2)^2/(a - b*x^2)^(1/3), x)","F"
125,0,-1,568,0.000000,"\text{Not used}","int((3*a + b*x^2)/(a - b*x^2)^(1/3),x)","\int \frac{b\,x^2+3\,a}{{\left(a-b\,x^2\right)}^{1/3}} \,d x","Not used",1,"int((3*a + b*x^2)/(a - b*x^2)^(1/3), x)","F"
126,0,-1,204,0.000000,"\text{Not used}","int(1/((a - b*x^2)^(1/3)*(3*a + b*x^2)),x)","\int \frac{1}{{\left(a-b\,x^2\right)}^{1/3}\,\left(b\,x^2+3\,a\right)} \,d x","Not used",1,"int(1/((a - b*x^2)^(1/3)*(3*a + b*x^2)), x)","F"
127,0,-1,787,0.000000,"\text{Not used}","int(1/((a - b*x^2)^(1/3)*(3*a + b*x^2)^2),x)","\int \frac{1}{{\left(a-b\,x^2\right)}^{1/3}\,{\left(b\,x^2+3\,a\right)}^2} \,d x","Not used",1,"int(1/((a - b*x^2)^(1/3)*(3*a + b*x^2)^2), x)","F"
128,0,-1,818,0.000000,"\text{Not used}","int(1/((a - b*x^2)^(1/3)*(3*a + b*x^2)^3),x)","\int \frac{1}{{\left(a-b\,x^2\right)}^{1/3}\,{\left(b\,x^2+3\,a\right)}^3} \,d x","Not used",1,"int(1/((a - b*x^2)^(1/3)*(3*a + b*x^2)^3), x)","F"
129,0,-1,623,0.000000,"\text{Not used}","int((3*a + b*x^2)^3/(a - b*x^2)^(4/3),x)","\int \frac{{\left(b\,x^2+3\,a\right)}^3}{{\left(a-b\,x^2\right)}^{4/3}} \,d x","Not used",1,"int((3*a + b*x^2)^3/(a - b*x^2)^(4/3), x)","F"
130,0,-1,592,0.000000,"\text{Not used}","int((3*a + b*x^2)^2/(a - b*x^2)^(4/3),x)","\int \frac{{\left(b\,x^2+3\,a\right)}^2}{{\left(a-b\,x^2\right)}^{4/3}} \,d x","Not used",1,"int((3*a + b*x^2)^2/(a - b*x^2)^(4/3), x)","F"
131,0,-1,561,0.000000,"\text{Not used}","int((3*a + b*x^2)/(a - b*x^2)^(4/3),x)","\int \frac{b\,x^2+3\,a}{{\left(a-b\,x^2\right)}^{4/3}} \,d x","Not used",1,"int((3*a + b*x^2)/(a - b*x^2)^(4/3), x)","F"
132,0,-1,776,0.000000,"\text{Not used}","int(1/((a - b*x^2)^(4/3)*(3*a + b*x^2)),x)","\int \frac{1}{{\left(a-b\,x^2\right)}^{4/3}\,\left(b\,x^2+3\,a\right)} \,d x","Not used",1,"int(1/((a - b*x^2)^(4/3)*(3*a + b*x^2)), x)","F"
133,0,-1,807,0.000000,"\text{Not used}","int(1/((a - b*x^2)^(4/3)*(3*a + b*x^2)^2),x)","\int \frac{1}{{\left(a-b\,x^2\right)}^{4/3}\,{\left(b\,x^2+3\,a\right)}^2} \,d x","Not used",1,"int(1/((a - b*x^2)^(4/3)*(3*a + b*x^2)^2), x)","F"
134,0,-1,849,0.000000,"\text{Not used}","int(1/((a - b*x^2)^(4/3)*(3*a + b*x^2)^3),x)","\int \frac{1}{{\left(a-b\,x^2\right)}^{4/3}\,{\left(b\,x^2+3\,a\right)}^3} \,d x","Not used",1,"int(1/((a - b*x^2)^(4/3)*(3*a + b*x^2)^3), x)","F"
135,0,-1,653,0.000000,"\text{Not used}","int((3*a + b*x^2)^4/(a - b*x^2)^(7/3),x)","\int \frac{{\left(b\,x^2+3\,a\right)}^4}{{\left(a-b\,x^2\right)}^{7/3}} \,d x","Not used",1,"int((3*a + b*x^2)^4/(a - b*x^2)^(7/3), x)","F"
136,0,-1,596,0.000000,"\text{Not used}","int((3*a + b*x^2)^3/(a - b*x^2)^(7/3),x)","\int \frac{{\left(b\,x^2+3\,a\right)}^3}{{\left(a-b\,x^2\right)}^{7/3}} \,d x","Not used",1,"int((3*a + b*x^2)^3/(a - b*x^2)^(7/3), x)","F"
137,1,27,44,4.784980,"\text{Not used}","int((3*a + b*x^2)^2/(a - b*x^2)^(7/3),x)","\frac{3\,x\,\left(a-b\,x^2\right)+6\,a\,x}{{\left(a-b\,x^2\right)}^{4/3}}","Not used",1,"(3*x*(a - b*x^2) + 6*a*x)/(a - b*x^2)^(4/3)","B"
138,0,-1,590,0.000000,"\text{Not used}","int((3*a + b*x^2)/(a - b*x^2)^(7/3),x)","\int \frac{b\,x^2+3\,a}{{\left(a-b\,x^2\right)}^{7/3}} \,d x","Not used",1,"int((3*a + b*x^2)/(a - b*x^2)^(7/3), x)","F"
139,0,-1,796,0.000000,"\text{Not used}","int(1/((a - b*x^2)^(7/3)*(3*a + b*x^2)),x)","\int \frac{1}{{\left(a-b\,x^2\right)}^{7/3}\,\left(b\,x^2+3\,a\right)} \,d x","Not used",1,"int(1/((a - b*x^2)^(7/3)*(3*a + b*x^2)), x)","F"
140,0,-1,827,0.000000,"\text{Not used}","int(1/((a - b*x^2)^(7/3)*(3*a + b*x^2)^2),x)","\int \frac{1}{{\left(a-b\,x^2\right)}^{7/3}\,{\left(b\,x^2+3\,a\right)}^2} \,d x","Not used",1,"int(1/((a - b*x^2)^(7/3)*(3*a + b*x^2)^2), x)","F"
141,0,-1,252,0.000000,"\text{Not used}","int(-1/((b*x^2 - a)^(1/3)*(3*a + b*x^2)),x)","-\int \frac{1}{{\left(b\,x^2-a\right)}^{1/3}\,\left(b\,x^2+3\,a\right)} \,d x","Not used",1,"-int(1/((b*x^2 - a)^(1/3)*(3*a + b*x^2)), x)","F"
142,0,-1,202,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(1/3)*(3*a - b*x^2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{1/3}\,\left(3\,a-b\,x^2\right)} \,d x","Not used",1,"int(1/((a + b*x^2)^(1/3)*(3*a - b*x^2)), x)","F"
143,0,-1,204,0.000000,"\text{Not used}","int(1/((c - d*x^2)*(c + 3*d*x^2)^(1/3)),x)","\int \frac{1}{\left(c-d\,x^2\right)\,{\left(3\,d\,x^2+c\right)}^{1/3}} \,d x","Not used",1,"int(1/((c - d*x^2)*(c + 3*d*x^2)^(1/3)), x)","F"
144,0,-1,204,0.000000,"\text{Not used}","int(1/((a - b*x^2)^(1/3)*(3*a + b*x^2)),x)","\int \frac{1}{{\left(a-b\,x^2\right)}^{1/3}\,\left(b\,x^2+3\,a\right)} \,d x","Not used",1,"int(1/((a - b*x^2)^(1/3)*(3*a + b*x^2)), x)","F"
145,0,-1,204,0.000000,"\text{Not used}","int(1/((c + d*x^2)*(c - 3*d*x^2)^(1/3)),x)","\int \frac{1}{\left(d\,x^2+c\right)\,{\left(c-3\,d\,x^2\right)}^{1/3}} \,d x","Not used",1,"int(1/((c + d*x^2)*(c - 3*d*x^2)^(1/3)), x)","F"
146,0,-1,113,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/3)*(x^2 + 3)),x)","\int \frac{1}{{\left(1-x^2\right)}^{1/3}\,\left(x^2+3\right)} \,d x","Not used",1,"int(1/((1 - x^2)^(1/3)*(x^2 + 3)), x)","F"
147,0,-1,109,0.000000,"\text{Not used}","int(-1/((x^2 + 1)^(1/3)*(x^2 - 3)),x)","-\int \frac{1}{{\left(x^2+1\right)}^{1/3}\,\left(x^2-3\right)} \,d x","Not used",1,"-int(1/((x^2 + 1)^(1/3)*(x^2 - 3)), x)","F"
148,0,-1,96,0.000000,"\text{Not used}","int(-(x - 3)/((1 - x^2)^(1/3)*(x^2 + 3)),x)","-\int \frac{x-3}{{\left(1-x^2\right)}^{1/3}\,\left(x^2+3\right)} \,d x","Not used",1,"-int((x - 3)/((1 - x^2)^(1/3)*(x^2 + 3)), x)","F"
149,0,-1,95,0.000000,"\text{Not used}","int((x + 3)/((1 - x^2)^(1/3)*(x^2 + 3)),x)","\int \frac{x+3}{{\left(1-x^2\right)}^{1/3}\,\left(x^2+3\right)} \,d x","Not used",1,"int((x + 3)/((1 - x^2)^(1/3)*(x^2 + 3)), x)","F"
150,0,-1,151,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(1/3)*(d*x^2 + (9*a*d)/b)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{1/3}\,\left(d\,x^2+\frac{9\,a\,d}{b}\right)} \,d x","Not used",1,"int(1/((a + b*x^2)^(1/3)*(d*x^2 + (9*a*d)/b)), x)","F"
151,0,-1,153,0.000000,"\text{Not used}","int(1/((a - b*x^2)^(1/3)*(d*x^2 - (9*a*d)/b)),x)","\int \frac{1}{{\left(a-b\,x^2\right)}^{1/3}\,\left(d\,x^2-\frac{9\,a\,d}{b}\right)} \,d x","Not used",1,"int(1/((a - b*x^2)^(1/3)*(d*x^2 - (9*a*d)/b)), x)","F"
152,0,-1,151,0.000000,"\text{Not used}","int(1/((b*x^2 - a)^(1/3)*(d*x^2 - (9*a*d)/b)),x)","\int \frac{1}{{\left(b\,x^2-a\right)}^{1/3}\,\left(d\,x^2-\frac{9\,a\,d}{b}\right)} \,d x","Not used",1,"int(1/((b*x^2 - a)^(1/3)*(d*x^2 - (9*a*d)/b)), x)","F"
153,0,-1,153,0.000000,"\text{Not used}","int(1/((- a - b*x^2)^(1/3)*(d*x^2 + (9*a*d)/b)),x)","\int \frac{1}{{\left(-b\,x^2-a\right)}^{1/3}\,\left(d\,x^2+\frac{9\,a\,d}{b}\right)} \,d x","Not used",1,"int(1/((- a - b*x^2)^(1/3)*(d*x^2 + (9*a*d)/b)), x)","F"
154,0,-1,151,0.000000,"\text{Not used}","int(1/(((18*d)/b + d*x^2)*(b*x^2 + 2)^(1/3)),x)","\int \frac{1}{\left(\frac{18\,d}{b}+d\,x^2\right)\,{\left(b\,x^2+2\right)}^{1/3}} \,d x","Not used",1,"int(1/(((18*d)/b + d*x^2)*(b*x^2 + 2)^(1/3)), x)","F"
155,0,-1,147,0.000000,"\text{Not used}","int(-1/(((18*d)/b - d*x^2)*(b*x^2 - 2)^(1/3)),x)","\int -\frac{1}{\left(\frac{18\,d}{b}-d\,x^2\right)\,{\left(b\,x^2-2\right)}^{1/3}} \,d x","Not used",1,"int(-1/(((18*d)/b - d*x^2)*(b*x^2 - 2)^(1/3)), x)","F"
156,0,-1,123,0.000000,"\text{Not used}","int(1/((3*x^2 + 2)^(1/3)*(6*d + d*x^2)),x)","\int \frac{1}{{\left(3\,x^2+2\right)}^{1/3}\,\left(d\,x^2+6\,d\right)} \,d x","Not used",1,"int(1/((3*x^2 + 2)^(1/3)*(6*d + d*x^2)), x)","F"
157,0,-1,123,0.000000,"\text{Not used}","int(-1/((2 - 3*x^2)^(1/3)*(6*d - d*x^2)),x)","-\int \frac{1}{{\left(2-3\,x^2\right)}^{1/3}\,\left(6\,d-d\,x^2\right)} \,d x","Not used",1,"-int(1/((2 - 3*x^2)^(1/3)*(6*d - d*x^2)), x)","F"
158,0,-1,119,0.000000,"\text{Not used}","int(-1/((3*x^2 - 2)^(1/3)*(6*d - d*x^2)),x)","-\int \frac{1}{{\left(3\,x^2-2\right)}^{1/3}\,\left(6\,d-d\,x^2\right)} \,d x","Not used",1,"-int(1/((3*x^2 - 2)^(1/3)*(6*d - d*x^2)), x)","F"
159,0,-1,119,0.000000,"\text{Not used}","int(1/((- 3*x^2 - 2)^(1/3)*(6*d + d*x^2)),x)","\int \frac{1}{{\left(-3\,x^2-2\right)}^{1/3}\,\left(d\,x^2+6\,d\right)} \,d x","Not used",1,"int(1/((- 3*x^2 - 2)^(1/3)*(6*d + d*x^2)), x)","F"
160,0,-1,70,0.000000,"\text{Not used}","int(1/((x^2 + 1)^(1/3)*(x^2 + 9)),x)","\int \frac{1}{{\left(x^2+1\right)}^{1/3}\,\left(x^2+9\right)} \,d x","Not used",1,"int(1/((x^2 + 1)^(1/3)*(x^2 + 9)), x)","F"
161,0,-1,104,0.000000,"\text{Not used}","int(1/((b*x^2 + 1)^(1/3)*(b*x^2 + 9)),x)","\int \frac{1}{{\left(b\,x^2+1\right)}^{1/3}\,\left(b\,x^2+9\right)} \,d x","Not used",1,"int(1/((b*x^2 + 1)^(1/3)*(b*x^2 + 9)), x)","F"
162,0,-1,74,0.000000,"\text{Not used}","int(-1/((1 - x^2)^(1/3)*(x^2 - 9)),x)","-\int \frac{1}{{\left(1-x^2\right)}^{1/3}\,\left(x^2-9\right)} \,d x","Not used",1,"-int(1/((1 - x^2)^(1/3)*(x^2 - 9)), x)","F"
163,0,-1,79,0.000000,"\text{Not used}","int((c^2*x^2 - 1)^(1/2)/(d - c^2*d*x^2)^(5/2),x)","\int \frac{\sqrt{c^2\,x^2-1}}{{\left(d-c^2\,d\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((c^2*x^2 - 1)^(1/2)/(d - c^2*d*x^2)^(5/2), x)","F"
164,0,-1,74,0.000000,"\text{Not used}","int(1/((d - c^2*d*x^2)^(1/2)*(c^2*x^2 - 1)^(3/2)),x)","\int \frac{1}{\sqrt{d-c^2\,d\,x^2}\,{\left(c^2\,x^2-1\right)}^{3/2}} \,d x","Not used",1,"int(1/((d - c^2*d*x^2)^(1/2)*(c^2*x^2 - 1)^(3/2)), x)","F"
165,0,-1,76,0.000000,"\text{Not used}","int(1/((d - c^2*d*x^2)^(3/2)*(c^2*x^2 - 1)^(1/2)),x)","\int \frac{1}{{\left(d-c^2\,d\,x^2\right)}^{3/2}\,\sqrt{c^2\,x^2-1}} \,d x","Not used",1,"int(1/((d - c^2*d*x^2)^(3/2)*(c^2*x^2 - 1)^(1/2)), x)","F"
166,0,-1,328,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)*(c + d*x^2)^(1/2),x)","\int {\left(b\,x^2+a\right)}^{3/2}\,\sqrt{d\,x^2+c} \,d x","Not used",1,"int((a + b*x^2)^(3/2)*(c + d*x^2)^(1/2), x)","F"
167,0,-1,249,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)*(c + d*x^2)^(1/2),x)","\int \sqrt{b\,x^2+a}\,\sqrt{d\,x^2+c} \,d x","Not used",1,"int((a + b*x^2)^(1/2)*(c + d*x^2)^(1/2), x)","F"
168,0,-1,204,0.000000,"\text{Not used}","int((c + d*x^2)^(1/2)/(a + b*x^2)^(1/2),x)","\int \frac{\sqrt{d\,x^2+c}}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((c + d*x^2)^(1/2)/(a + b*x^2)^(1/2), x)","F"
169,0,-1,84,0.000000,"\text{Not used}","int((c + d*x^2)^(1/2)/(a + b*x^2)^(3/2),x)","\int \frac{\sqrt{d\,x^2+c}}{{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((c + d*x^2)^(1/2)/(a + b*x^2)^(3/2), x)","F"
170,0,-1,237,0.000000,"\text{Not used}","int((c + d*x^2)^(1/2)/(a + b*x^2)^(5/2),x)","\int \frac{\sqrt{d\,x^2+c}}{{\left(b\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((c + d*x^2)^(1/2)/(a + b*x^2)^(5/2), x)","F"
171,0,-1,309,0.000000,"\text{Not used}","int((c + d*x^2)^(1/2)/(a + b*x^2)^(7/2),x)","\int \frac{\sqrt{d\,x^2+c}}{{\left(b\,x^2+a\right)}^{7/2}} \,d x","Not used",1,"int((c + d*x^2)^(1/2)/(a + b*x^2)^(7/2), x)","F"
172,0,-1,410,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)*(c + d*x^2)^(3/2),x)","\int {\left(b\,x^2+a\right)}^{3/2}\,{\left(d\,x^2+c\right)}^{3/2} \,d x","Not used",1,"int((a + b*x^2)^(3/2)*(c + d*x^2)^(3/2), x)","F"
173,0,-1,336,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)*(c + d*x^2)^(3/2),x)","\int \sqrt{b\,x^2+a}\,{\left(d\,x^2+c\right)}^{3/2} \,d x","Not used",1,"int((a + b*x^2)^(1/2)*(c + d*x^2)^(3/2), x)","F"
174,0,-1,273,0.000000,"\text{Not used}","int((c + d*x^2)^(3/2)/(a + b*x^2)^(1/2),x)","\int \frac{{\left(d\,x^2+c\right)}^{3/2}}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((c + d*x^2)^(3/2)/(a + b*x^2)^(1/2), x)","F"
175,0,-1,267,0.000000,"\text{Not used}","int((c + d*x^2)^(3/2)/(a + b*x^2)^(3/2),x)","\int \frac{{\left(d\,x^2+c\right)}^{3/2}}{{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((c + d*x^2)^(3/2)/(a + b*x^2)^(3/2), x)","F"
176,0,-1,229,0.000000,"\text{Not used}","int((c + d*x^2)^(3/2)/(a + b*x^2)^(5/2),x)","\int \frac{{\left(d\,x^2+c\right)}^{3/2}}{{\left(b\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((c + d*x^2)^(3/2)/(a + b*x^2)^(5/2), x)","F"
177,0,-1,315,0.000000,"\text{Not used}","int((c + d*x^2)^(3/2)/(a + b*x^2)^(7/2),x)","\int \frac{{\left(d\,x^2+c\right)}^{3/2}}{{\left(b\,x^2+a\right)}^{7/2}} \,d x","Not used",1,"int((c + d*x^2)^(3/2)/(a + b*x^2)^(7/2), x)","F"
178,0,-1,235,0.000000,"\text{Not used}","int((b*x^2 + 2)^(1/2)*(d*x^2 + 3)^(1/2),x)","\int \sqrt{b\,x^2+2}\,\sqrt{d\,x^2+3} \,d x","Not used",1,"int((b*x^2 + 2)^(1/2)*(d*x^2 + 3)^(1/2), x)","F"
179,0,-1,38,0.000000,"\text{Not used}","int((4*x^2 + 2)^(1/2)*(3 - 6*x^2)^(1/2),x)","\int \sqrt{4\,x^2+2}\,\sqrt{3-6\,x^2} \,d x","Not used",1,"int((4*x^2 + 2)^(1/2)*(3 - 6*x^2)^(1/2), x)","F"
180,0,-1,20,0.000000,"\text{Not used}","int((4*x^2 + 2)^(1/2)*(6*x^2 + 3)^(1/2),x)","\int \sqrt{4\,x^2+2}\,\sqrt{6\,x^2+3} \,d x","Not used",1,"int((4*x^2 + 2)^(1/2)*(6*x^2 + 3)^(1/2), x)","F"
181,0,-1,182,0.000000,"\text{Not used}","int((b*x^2 + 2)^(1/2)/(d*x^2 + 3)^(1/2),x)","\int \frac{\sqrt{b\,x^2+2}}{\sqrt{d\,x^2+3}} \,d x","Not used",1,"int((b*x^2 + 2)^(1/2)/(d*x^2 + 3)^(1/2), x)","F"
182,0,-1,91,0.000000,"\text{Not used}","int((4 - x^2)^(1/2)/(c + d*x^2)^(1/2),x)","\int \frac{\sqrt{4-x^2}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((4 - x^2)^(1/2)/(c + d*x^2)^(1/2), x)","F"
183,0,-1,150,0.000000,"\text{Not used}","int((x^2 + 4)^(1/2)/(c + d*x^2)^(1/2),x)","\int \frac{\sqrt{x^2+4}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((x^2 + 4)^(1/2)/(c + d*x^2)^(1/2), x)","F"
184,0,-1,20,0.000000,"\text{Not used}","int((1 - x^2)^(1/2)/(2 - 3*x^2)^(1/2),x)","\int \frac{\sqrt{1-x^2}}{\sqrt{2-3\,x^2}} \,d x","Not used",1,"int((1 - x^2)^(1/2)/(2 - 3*x^2)^(1/2), x)","F"
185,0,-1,21,0.000000,"\text{Not used}","int((4 - x^2)^(1/2)/(2 - 3*x^2)^(1/2),x)","\int \frac{\sqrt{4-x^2}}{\sqrt{2-3\,x^2}} \,d x","Not used",1,"int((4 - x^2)^(1/2)/(2 - 3*x^2)^(1/2), x)","F"
186,0,-1,20,0.000000,"\text{Not used}","int((1 - 4*x^2)^(1/2)/(2 - 3*x^2)^(1/2),x)","\int \frac{\sqrt{1-4\,x^2}}{\sqrt{2-3\,x^2}} \,d x","Not used",1,"int((1 - 4*x^2)^(1/2)/(2 - 3*x^2)^(1/2), x)","F"
187,0,-1,4,0.000000,"\text{Not used}","int((x^2 + 1)^(1/2)/(1 - x^2)^(1/2),x)","\int \frac{\sqrt{x^2+1}}{\sqrt{1-x^2}} \,d x","Not used",1,"int((x^2 + 1)^(1/2)/(1 - x^2)^(1/2), x)","F"
188,0,-1,20,0.000000,"\text{Not used}","int((x^2 + 1)^(1/2)/(2 - 3*x^2)^(1/2),x)","\int \frac{\sqrt{x^2+1}}{\sqrt{2-3\,x^2}} \,d x","Not used",1,"int((x^2 + 1)^(1/2)/(2 - 3*x^2)^(1/2), x)","F"
189,0,-1,21,0.000000,"\text{Not used}","int((x^2 + 4)^(1/2)/(2 - 3*x^2)^(1/2),x)","\int \frac{\sqrt{x^2+4}}{\sqrt{2-3\,x^2}} \,d x","Not used",1,"int((x^2 + 4)^(1/2)/(2 - 3*x^2)^(1/2), x)","F"
190,0,-1,20,0.000000,"\text{Not used}","int((4*x^2 + 1)^(1/2)/(2 - 3*x^2)^(1/2),x)","\int \frac{\sqrt{4\,x^2+1}}{\sqrt{2-3\,x^2}} \,d x","Not used",1,"int((4*x^2 + 1)^(1/2)/(2 - 3*x^2)^(1/2), x)","F"
191,0,-1,13,0.000000,"\text{Not used}","int((1 - x^2)^(1/2)/(x^2 + 1)^(1/2),x)","\int \frac{\sqrt{1-x^2}}{\sqrt{x^2+1}} \,d x","Not used",1,"int((1 - x^2)^(1/2)/(x^2 + 1)^(1/2), x)","F"
192,0,-1,31,0.000000,"\text{Not used}","int((1 - x^2)^(1/2)/(3*x^2 + 2)^(1/2),x)","\int \frac{\sqrt{1-x^2}}{\sqrt{3\,x^2+2}} \,d x","Not used",1,"int((1 - x^2)^(1/2)/(3*x^2 + 2)^(1/2), x)","F"
193,0,-1,35,0.000000,"\text{Not used}","int((4 - x^2)^(1/2)/(3*x^2 + 2)^(1/2),x)","\int \frac{\sqrt{4-x^2}}{\sqrt{3\,x^2+2}} \,d x","Not used",1,"int((4 - x^2)^(1/2)/(3*x^2 + 2)^(1/2), x)","F"
194,0,-1,35,0.000000,"\text{Not used}","int((1 - 4*x^2)^(1/2)/(3*x^2 + 2)^(1/2),x)","\int \frac{\sqrt{1-4\,x^2}}{\sqrt{3\,x^2+2}} \,d x","Not used",1,"int((1 - 4*x^2)^(1/2)/(3*x^2 + 2)^(1/2), x)","F"
195,0,-1,131,0.000000,"\text{Not used}","int((x^2 + 1)^(1/2)/(3*x^2 + 2)^(1/2),x)","\int \frac{\sqrt{x^2+1}}{\sqrt{3\,x^2+2}} \,d x","Not used",1,"int((x^2 + 1)^(1/2)/(3*x^2 + 2)^(1/2), x)","F"
196,0,-1,136,0.000000,"\text{Not used}","int((x^2 + 4)^(1/2)/(3*x^2 + 2)^(1/2),x)","\int \frac{\sqrt{x^2+4}}{\sqrt{3\,x^2+2}} \,d x","Not used",1,"int((x^2 + 4)^(1/2)/(3*x^2 + 2)^(1/2), x)","F"
197,0,-1,148,0.000000,"\text{Not used}","int((4*x^2 + 1)^(1/2)/(3*x^2 + 2)^(1/2),x)","\int \frac{\sqrt{4\,x^2+1}}{\sqrt{3\,x^2+2}} \,d x","Not used",1,"int((4*x^2 + 1)^(1/2)/(3*x^2 + 2)^(1/2), x)","F"
198,0,-1,40,0.000000,"\text{Not used}","int((1 - x^2)^(1/2)/(2*x^2 - 1)^(1/2),x)","\int \frac{\sqrt{1-x^2}}{\sqrt{2\,x^2-1}} \,d x","Not used",1,"int((1 - x^2)^(1/2)/(2*x^2 - 1)^(1/2), x)","F"
199,0,-1,423,0.000000,"\text{Not used}","int((a + b*x^2)^(7/2)/(c + d*x^2)^(1/2),x)","\int \frac{{\left(b\,x^2+a\right)}^{7/2}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(7/2)/(c + d*x^2)^(1/2), x)","F"
200,0,-1,344,0.000000,"\text{Not used}","int((a + b*x^2)^(5/2)/(c + d*x^2)^(1/2),x)","\int \frac{{\left(b\,x^2+a\right)}^{5/2}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(5/2)/(c + d*x^2)^(1/2), x)","F"
201,0,-1,260,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)/(c + d*x^2)^(1/2),x)","\int \frac{{\left(b\,x^2+a\right)}^{3/2}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(3/2)/(c + d*x^2)^(1/2), x)","F"
202,0,-1,194,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)/(c + d*x^2)^(1/2),x)","\int \frac{\sqrt{b\,x^2+a}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(1/2)/(c + d*x^2)^(1/2), x)","F"
203,0,-1,87,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{b\,x^2+a}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/((a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)), x)","F"
204,0,-1,273,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(3/2)*(c + d*x^2)^(1/2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{3/2}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/((a + b*x^2)^(3/2)*(c + d*x^2)^(1/2)), x)","F"
205,0,-1,255,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(5/2)*(c + d*x^2)^(1/2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{5/2}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/((a + b*x^2)^(5/2)*(c + d*x^2)^(1/2)), x)","F"
206,0,-1,334,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(7/2)*(c + d*x^2)^(1/2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{7/2}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/((a + b*x^2)^(7/2)*(c + d*x^2)^(1/2)), x)","F"
207,0,-1,445,0.000000,"\text{Not used}","int((a + b*x^2)^(7/2)/(c + d*x^2)^(3/2),x)","\int \frac{{\left(b\,x^2+a\right)}^{7/2}}{{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x^2)^(7/2)/(c + d*x^2)^(3/2), x)","F"
208,0,-1,346,0.000000,"\text{Not used}","int((a + b*x^2)^(5/2)/(c + d*x^2)^(3/2),x)","\int \frac{{\left(b\,x^2+a\right)}^{5/2}}{{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x^2)^(5/2)/(c + d*x^2)^(3/2), x)","F"
209,0,-1,258,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)/(c + d*x^2)^(3/2),x)","\int \frac{{\left(b\,x^2+a\right)}^{3/2}}{{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x^2)^(3/2)/(c + d*x^2)^(3/2), x)","F"
210,0,-1,84,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)/(c + d*x^2)^(3/2),x)","\int \frac{\sqrt{b\,x^2+a}}{{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x^2)^(1/2)/(c + d*x^2)^(3/2), x)","F"
211,0,-1,194,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(1/2)*(c + d*x^2)^(3/2)),x)","\int \frac{1}{\sqrt{b\,x^2+a}\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + b*x^2)^(1/2)*(c + d*x^2)^(3/2)), x)","F"
212,0,-1,242,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(3/2)*(c + d*x^2)^(3/2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{3/2}\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + b*x^2)^(3/2)*(c + d*x^2)^(3/2)), x)","F"
213,0,-1,323,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(5/2)*(c + d*x^2)^(3/2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{5/2}\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + b*x^2)^(5/2)*(c + d*x^2)^(3/2)), x)","F"
214,0,-1,87,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{b\,x^2+a}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/((a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)), x)","F"
215,0,-1,87,0.000000,"\text{Not used}","int(1/((a - b*x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{a-b\,x^2}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/((a - b*x^2)^(1/2)*(c + d*x^2)^(1/2)), x)","F"
216,0,-1,87,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(1/2)*(c - d*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{b\,x^2+a}\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int(1/((a + b*x^2)^(1/2)*(c - d*x^2)^(1/2)), x)","F"
217,0,-1,88,0.000000,"\text{Not used}","int(1/((a - b*x^2)^(1/2)*(c - d*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{a-b\,x^2}\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int(1/((a - b*x^2)^(1/2)*(c - d*x^2)^(1/2)), x)","F"
218,0,-1,12,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/2)*(5*x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{1-x^2}\,\sqrt{5\,x^2+2}} \,d x","Not used",1,"int(1/((1 - x^2)^(1/2)*(5*x^2 + 2)^(1/2)), x)","F"
219,0,-1,10,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/2)*(4*x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{1-x^2}\,\sqrt{4\,x^2+2}} \,d x","Not used",1,"int(1/((1 - x^2)^(1/2)*(4*x^2 + 2)^(1/2)), x)","F"
220,0,-1,12,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/2)*(3*x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{1-x^2}\,\sqrt{3\,x^2+2}} \,d x","Not used",1,"int(1/((1 - x^2)^(1/2)*(3*x^2 + 2)^(1/2)), x)","F"
221,0,-1,10,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/2)*(2*x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{1-x^2}\,\sqrt{2\,x^2+2}} \,d x","Not used",1,"int(1/((1 - x^2)^(1/2)*(2*x^2 + 2)^(1/2)), x)","F"
222,0,-1,12,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/2)*(x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{1-x^2}\,\sqrt{x^2+2}} \,d x","Not used",1,"int(1/((1 - x^2)^(1/2)*(x^2 + 2)^(1/2)), x)","F"
223,0,-1,12,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/2)*(2 - x^2)^(1/2)),x)","\int \frac{1}{\sqrt{1-x^2}\,\sqrt{2-x^2}} \,d x","Not used",1,"int(1/((1 - x^2)^(1/2)*(2 - x^2)^(1/2)), x)","F"
224,0,-1,8,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/2)*(2 - 2*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{1-x^2}\,\sqrt{2-2\,x^2}} \,d x","Not used",1,"int(1/((1 - x^2)^(1/2)*(2 - 2*x^2)^(1/2)), x)","F"
225,0,-1,12,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/2)*(2 - 3*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{1-x^2}\,\sqrt{2-3\,x^2}} \,d x","Not used",1,"int(1/((1 - x^2)^(1/2)*(2 - 3*x^2)^(1/2)), x)","F"
226,0,-1,10,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/2)*(2 - 4*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{1-x^2}\,\sqrt{2-4\,x^2}} \,d x","Not used",1,"int(1/((1 - x^2)^(1/2)*(2 - 4*x^2)^(1/2)), x)","F"
227,0,-1,12,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/2)*(2 - 5*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{1-x^2}\,\sqrt{2-5\,x^2}} \,d x","Not used",1,"int(1/((1 - x^2)^(1/2)*(2 - 5*x^2)^(1/2)), x)","F"
228,0,-1,51,0.000000,"\text{Not used}","int(1/((x^2 + 1)^(1/2)*(5*x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2+1}\,\sqrt{5\,x^2+2}} \,d x","Not used",1,"int(1/((x^2 + 1)^(1/2)*(5*x^2 + 2)^(1/2)), x)","F"
229,0,-1,49,0.000000,"\text{Not used}","int(1/((x^2 + 1)^(1/2)*(4*x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2+1}\,\sqrt{4\,x^2+2}} \,d x","Not used",1,"int(1/((x^2 + 1)^(1/2)*(4*x^2 + 2)^(1/2)), x)","F"
230,0,-1,51,0.000000,"\text{Not used}","int(1/((x^2 + 1)^(1/2)*(3*x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2+1}\,\sqrt{3\,x^2+2}} \,d x","Not used",1,"int(1/((x^2 + 1)^(1/2)*(3*x^2 + 2)^(1/2)), x)","F"
231,0,-1,8,0.000000,"\text{Not used}","int(1/((x^2 + 1)^(1/2)*(2*x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2+1}\,\sqrt{2\,x^2+2}} \,d x","Not used",1,"int(1/((x^2 + 1)^(1/2)*(2*x^2 + 2)^(1/2)), x)","F"
232,0,-1,47,0.000000,"\text{Not used}","int(1/((x^2 + 1)^(1/2)*(x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2+1}\,\sqrt{x^2+2}} \,d x","Not used",1,"int(1/((x^2 + 1)^(1/2)*(x^2 + 2)^(1/2)), x)","F"
233,0,-1,10,0.000000,"\text{Not used}","int(1/((x^2 + 1)^(1/2)*(2 - x^2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2+1}\,\sqrt{2-x^2}} \,d x","Not used",1,"int(1/((x^2 + 1)^(1/2)*(2 - x^2)^(1/2)), x)","F"
234,0,-1,10,0.000000,"\text{Not used}","int(1/((x^2 + 1)^(1/2)*(2 - 2*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2+1}\,\sqrt{2-2\,x^2}} \,d x","Not used",1,"int(1/((x^2 + 1)^(1/2)*(2 - 2*x^2)^(1/2)), x)","F"
235,0,-1,20,0.000000,"\text{Not used}","int(1/((x^2 + 1)^(1/2)*(2 - 3*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2+1}\,\sqrt{2-3\,x^2}} \,d x","Not used",1,"int(1/((x^2 + 1)^(1/2)*(2 - 3*x^2)^(1/2)), x)","F"
236,0,-1,16,0.000000,"\text{Not used}","int(1/((x^2 + 1)^(1/2)*(2 - 4*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2+1}\,\sqrt{2-4\,x^2}} \,d x","Not used",1,"int(1/((x^2 + 1)^(1/2)*(2 - 4*x^2)^(1/2)), x)","F"
237,0,-1,20,0.000000,"\text{Not used}","int(1/((x^2 + 1)^(1/2)*(2 - 5*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2+1}\,\sqrt{2-5\,x^2}} \,d x","Not used",1,"int(1/((x^2 + 1)^(1/2)*(2 - 5*x^2)^(1/2)), x)","F"
238,0,-1,32,0.000000,"\text{Not used}","int(1/((x^2 - 1)^(1/2)*(5*x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2-1}\,\sqrt{5\,x^2+2}} \,d x","Not used",1,"int(1/((x^2 - 1)^(1/2)*(5*x^2 + 2)^(1/2)), x)","F"
239,0,-1,30,0.000000,"\text{Not used}","int(1/((x^2 - 1)^(1/2)*(4*x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2-1}\,\sqrt{4\,x^2+2}} \,d x","Not used",1,"int(1/((x^2 - 1)^(1/2)*(4*x^2 + 2)^(1/2)), x)","F"
240,0,-1,32,0.000000,"\text{Not used}","int(1/((x^2 - 1)^(1/2)*(3*x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2-1}\,\sqrt{3\,x^2+2}} \,d x","Not used",1,"int(1/((x^2 - 1)^(1/2)*(3*x^2 + 2)^(1/2)), x)","F"
241,0,-1,25,0.000000,"\text{Not used}","int(1/((x^2 - 1)^(1/2)*(2*x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2-1}\,\sqrt{2\,x^2+2}} \,d x","Not used",1,"int(1/((x^2 - 1)^(1/2)*(2*x^2 + 2)^(1/2)), x)","F"
242,0,-1,32,0.000000,"\text{Not used}","int(1/((x^2 - 1)^(1/2)*(x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2-1}\,\sqrt{x^2+2}} \,d x","Not used",1,"int(1/((x^2 - 1)^(1/2)*(x^2 + 2)^(1/2)), x)","F"
243,0,-1,12,0.000000,"\text{Not used}","int(1/((x^2 - 1)^(1/2)*(2 - x^2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2-1}\,\sqrt{2-x^2}} \,d x","Not used",1,"int(1/((x^2 - 1)^(1/2)*(2 - x^2)^(1/2)), x)","F"
244,0,-1,29,0.000000,"\text{Not used}","int(1/((x^2 - 1)^(1/2)*(2 - 2*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2-1}\,\sqrt{2-2\,x^2}} \,d x","Not used",1,"int(1/((x^2 - 1)^(1/2)*(2 - 2*x^2)^(1/2)), x)","F"
245,0,-1,32,0.000000,"\text{Not used}","int(1/((x^2 - 1)^(1/2)*(2 - 3*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2-1}\,\sqrt{2-3\,x^2}} \,d x","Not used",1,"int(1/((x^2 - 1)^(1/2)*(2 - 3*x^2)^(1/2)), x)","F"
246,0,-1,30,0.000000,"\text{Not used}","int(1/((x^2 - 1)^(1/2)*(2 - 4*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2-1}\,\sqrt{2-4\,x^2}} \,d x","Not used",1,"int(1/((x^2 - 1)^(1/2)*(2 - 4*x^2)^(1/2)), x)","F"
247,0,-1,32,0.000000,"\text{Not used}","int(1/((x^2 - 1)^(1/2)*(2 - 5*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2-1}\,\sqrt{2-5\,x^2}} \,d x","Not used",1,"int(1/((x^2 - 1)^(1/2)*(2 - 5*x^2)^(1/2)), x)","F"
248,0,-1,53,0.000000,"\text{Not used}","int(1/((- x^2 - 1)^(1/2)*(5*x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{-x^2-1}\,\sqrt{5\,x^2+2}} \,d x","Not used",1,"int(1/((- x^2 - 1)^(1/2)*(5*x^2 + 2)^(1/2)), x)","F"
249,0,-1,51,0.000000,"\text{Not used}","int(1/((- x^2 - 1)^(1/2)*(4*x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{-x^2-1}\,\sqrt{4\,x^2+2}} \,d x","Not used",1,"int(1/((- x^2 - 1)^(1/2)*(4*x^2 + 2)^(1/2)), x)","F"
250,0,-1,53,0.000000,"\text{Not used}","int(1/((- x^2 - 1)^(1/2)*(3*x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{-x^2-1}\,\sqrt{3\,x^2+2}} \,d x","Not used",1,"int(1/((- x^2 - 1)^(1/2)*(3*x^2 + 2)^(1/2)), x)","F"
251,0,-1,28,0.000000,"\text{Not used}","int(1/((- x^2 - 1)^(1/2)*(2*x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{-x^2-1}\,\sqrt{2\,x^2+2}} \,d x","Not used",1,"int(1/((- x^2 - 1)^(1/2)*(2*x^2 + 2)^(1/2)), x)","F"
252,0,-1,49,0.000000,"\text{Not used}","int(1/((- x^2 - 1)^(1/2)*(x^2 + 2)^(1/2)),x)","\int \frac{1}{\sqrt{-x^2-1}\,\sqrt{x^2+2}} \,d x","Not used",1,"int(1/((- x^2 - 1)^(1/2)*(x^2 + 2)^(1/2)), x)","F"
253,0,-1,31,0.000000,"\text{Not used}","int(1/((- x^2 - 1)^(1/2)*(2 - x^2)^(1/2)),x)","\int \frac{1}{\sqrt{-x^2-1}\,\sqrt{2-x^2}} \,d x","Not used",1,"int(1/((- x^2 - 1)^(1/2)*(2 - x^2)^(1/2)), x)","F"
254,0,-1,42,0.000000,"\text{Not used}","int(1/((- x^2 - 1)^(1/2)*(2 - 2*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{-x^2-1}\,\sqrt{2-2\,x^2}} \,d x","Not used",1,"int(1/((- x^2 - 1)^(1/2)*(2 - 2*x^2)^(1/2)), x)","F"
255,0,-1,40,0.000000,"\text{Not used}","int(1/((- x^2 - 1)^(1/2)*(2 - 3*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{-x^2-1}\,\sqrt{2-3\,x^2}} \,d x","Not used",1,"int(1/((- x^2 - 1)^(1/2)*(2 - 3*x^2)^(1/2)), x)","F"
256,0,-1,36,0.000000,"\text{Not used}","int(1/((- x^2 - 1)^(1/2)*(2 - 4*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{-x^2-1}\,\sqrt{2-4\,x^2}} \,d x","Not used",1,"int(1/((- x^2 - 1)^(1/2)*(2 - 4*x^2)^(1/2)), x)","F"
257,0,-1,40,0.000000,"\text{Not used}","int(1/((- x^2 - 1)^(1/2)*(2 - 5*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{-x^2-1}\,\sqrt{2-5\,x^2}} \,d x","Not used",1,"int(1/((- x^2 - 1)^(1/2)*(2 - 5*x^2)^(1/2)), x)","F"
258,0,-1,87,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)/(c - d*x^2)^(1/2),x)","\int \frac{\sqrt{b\,x^2+a}}{\sqrt{c-d\,x^2}} \,d x","Not used",1,"int((a + b*x^2)^(1/2)/(c - d*x^2)^(1/2), x)","F"
259,0,-1,90,0.000000,"\text{Not used}","int((- a - b*x^2)^(1/2)/(c - d*x^2)^(1/2),x)","\int \frac{\sqrt{-b\,x^2-a}}{\sqrt{c-d\,x^2}} \,d x","Not used",1,"int((- a - b*x^2)^(1/2)/(c - d*x^2)^(1/2), x)","F"
260,0,-1,88,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)/(d*x^2 - c)^(1/2),x)","\int \frac{\sqrt{b\,x^2+a}}{\sqrt{d\,x^2-c}} \,d x","Not used",1,"int((a + b*x^2)^(1/2)/(d*x^2 - c)^(1/2), x)","F"
261,0,-1,91,0.000000,"\text{Not used}","int((- a - b*x^2)^(1/2)/(d*x^2 - c)^(1/2),x)","\int \frac{\sqrt{-b\,x^2-a}}{\sqrt{d\,x^2-c}} \,d x","Not used",1,"int((- a - b*x^2)^(1/2)/(d*x^2 - c)^(1/2), x)","F"
262,0,-1,88,0.000000,"\text{Not used}","int((a - b*x^2)^(1/2)/(c - d*x^2)^(1/2),x)","\int \frac{\sqrt{a-b\,x^2}}{\sqrt{c-d\,x^2}} \,d x","Not used",1,"int((a - b*x^2)^(1/2)/(c - d*x^2)^(1/2), x)","F"
263,0,-1,89,0.000000,"\text{Not used}","int((b*x^2 - a)^(1/2)/(c - d*x^2)^(1/2),x)","\int \frac{\sqrt{b\,x^2-a}}{\sqrt{c-d\,x^2}} \,d x","Not used",1,"int((b*x^2 - a)^(1/2)/(c - d*x^2)^(1/2), x)","F"
264,0,-1,89,0.000000,"\text{Not used}","int((a - b*x^2)^(1/2)/(d*x^2 - c)^(1/2),x)","\int \frac{\sqrt{a-b\,x^2}}{\sqrt{d\,x^2-c}} \,d x","Not used",1,"int((a - b*x^2)^(1/2)/(d*x^2 - c)^(1/2), x)","F"
265,0,-1,90,0.000000,"\text{Not used}","int((b*x^2 - a)^(1/2)/(d*x^2 - c)^(1/2),x)","\int \frac{\sqrt{b\,x^2-a}}{\sqrt{d\,x^2-c}} \,d x","Not used",1,"int((b*x^2 - a)^(1/2)/(d*x^2 - c)^(1/2), x)","F"
266,0,-1,194,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)/(c + d*x^2)^(1/2),x)","\int \frac{\sqrt{b\,x^2+a}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(1/2)/(c + d*x^2)^(1/2), x)","F"
267,0,-1,203,0.000000,"\text{Not used}","int((- a - b*x^2)^(1/2)/(c + d*x^2)^(1/2),x)","\int \frac{\sqrt{-b\,x^2-a}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((- a - b*x^2)^(1/2)/(c + d*x^2)^(1/2), x)","F"
268,0,-1,203,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)/(- c - d*x^2)^(1/2),x)","\int \frac{\sqrt{b\,x^2+a}}{\sqrt{-d\,x^2-c}} \,d x","Not used",1,"int((a + b*x^2)^(1/2)/(- c - d*x^2)^(1/2), x)","F"
269,0,-1,212,0.000000,"\text{Not used}","int((- a - b*x^2)^(1/2)/(- c - d*x^2)^(1/2),x)","\int \frac{\sqrt{-b\,x^2-a}}{\sqrt{-d\,x^2-c}} \,d x","Not used",1,"int((- a - b*x^2)^(1/2)/(- c - d*x^2)^(1/2), x)","F"
270,0,-1,189,0.000000,"\text{Not used}","int((a - b*x^2)^(1/2)/(c + d*x^2)^(1/2),x)","\int \frac{\sqrt{a-b\,x^2}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a - b*x^2)^(1/2)/(c + d*x^2)^(1/2), x)","F"
271,0,-1,191,0.000000,"\text{Not used}","int((b*x^2 - a)^(1/2)/(c + d*x^2)^(1/2),x)","\int \frac{\sqrt{b\,x^2-a}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((b*x^2 - a)^(1/2)/(c + d*x^2)^(1/2), x)","F"
272,0,-1,194,0.000000,"\text{Not used}","int((a - b*x^2)^(1/2)/(- c - d*x^2)^(1/2),x)","\int \frac{\sqrt{a-b\,x^2}}{\sqrt{-d\,x^2-c}} \,d x","Not used",1,"int((a - b*x^2)^(1/2)/(- c - d*x^2)^(1/2), x)","F"
273,0,-1,198,0.000000,"\text{Not used}","int((b*x^2 - a)^(1/2)/(- c - d*x^2)^(1/2),x)","\int \frac{\sqrt{b\,x^2-a}}{\sqrt{-d\,x^2-c}} \,d x","Not used",1,"int((b*x^2 - a)^(1/2)/(- c - d*x^2)^(1/2), x)","F"
274,0,-1,87,0.000000,"\text{Not used}","int((c + d*x^2)^(1/2)/(a - b*x^2)^(1/2),x)","\int \frac{\sqrt{d\,x^2+c}}{\sqrt{a-b\,x^2}} \,d x","Not used",1,"int((c + d*x^2)^(1/2)/(a - b*x^2)^(1/2), x)","F"
275,0,-1,90,0.000000,"\text{Not used}","int((- c - d*x^2)^(1/2)/(a - b*x^2)^(1/2),x)","\int \frac{\sqrt{-d\,x^2-c}}{\sqrt{a-b\,x^2}} \,d x","Not used",1,"int((- c - d*x^2)^(1/2)/(a - b*x^2)^(1/2), x)","F"
276,0,-1,88,0.000000,"\text{Not used}","int((c + d*x^2)^(1/2)/(b*x^2 - a)^(1/2),x)","\int \frac{\sqrt{d\,x^2+c}}{\sqrt{b\,x^2-a}} \,d x","Not used",1,"int((c + d*x^2)^(1/2)/(b*x^2 - a)^(1/2), x)","F"
277,0,-1,91,0.000000,"\text{Not used}","int((- c - d*x^2)^(1/2)/(b*x^2 - a)^(1/2),x)","\int \frac{\sqrt{-d\,x^2-c}}{\sqrt{b\,x^2-a}} \,d x","Not used",1,"int((- c - d*x^2)^(1/2)/(b*x^2 - a)^(1/2), x)","F"
278,0,-1,88,0.000000,"\text{Not used}","int((c - d*x^2)^(1/2)/(a - b*x^2)^(1/2),x)","\int \frac{\sqrt{c-d\,x^2}}{\sqrt{a-b\,x^2}} \,d x","Not used",1,"int((c - d*x^2)^(1/2)/(a - b*x^2)^(1/2), x)","F"
279,0,-1,89,0.000000,"\text{Not used}","int((d*x^2 - c)^(1/2)/(a - b*x^2)^(1/2),x)","\int \frac{\sqrt{d\,x^2-c}}{\sqrt{a-b\,x^2}} \,d x","Not used",1,"int((d*x^2 - c)^(1/2)/(a - b*x^2)^(1/2), x)","F"
280,0,-1,89,0.000000,"\text{Not used}","int((c - d*x^2)^(1/2)/(b*x^2 - a)^(1/2),x)","\int \frac{\sqrt{c-d\,x^2}}{\sqrt{b\,x^2-a}} \,d x","Not used",1,"int((c - d*x^2)^(1/2)/(b*x^2 - a)^(1/2), x)","F"
281,0,-1,90,0.000000,"\text{Not used}","int((d*x^2 - c)^(1/2)/(b*x^2 - a)^(1/2),x)","\int \frac{\sqrt{d\,x^2-c}}{\sqrt{b\,x^2-a}} \,d x","Not used",1,"int((d*x^2 - c)^(1/2)/(b*x^2 - a)^(1/2), x)","F"
282,0,-1,204,0.000000,"\text{Not used}","int((c + d*x^2)^(1/2)/(a + b*x^2)^(1/2),x)","\int \frac{\sqrt{d\,x^2+c}}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((c + d*x^2)^(1/2)/(a + b*x^2)^(1/2), x)","F"
283,0,-1,214,0.000000,"\text{Not used}","int((- c - d*x^2)^(1/2)/(a + b*x^2)^(1/2),x)","\int \frac{\sqrt{-d\,x^2-c}}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((- c - d*x^2)^(1/2)/(a + b*x^2)^(1/2), x)","F"
284,0,-1,214,0.000000,"\text{Not used}","int((c + d*x^2)^(1/2)/(- a - b*x^2)^(1/2),x)","\int \frac{\sqrt{d\,x^2+c}}{\sqrt{-b\,x^2-a}} \,d x","Not used",1,"int((c + d*x^2)^(1/2)/(- a - b*x^2)^(1/2), x)","F"
285,0,-1,222,0.000000,"\text{Not used}","int((- c - d*x^2)^(1/2)/(- a - b*x^2)^(1/2),x)","\int \frac{\sqrt{-d\,x^2-c}}{\sqrt{-b\,x^2-a}} \,d x","Not used",1,"int((- c - d*x^2)^(1/2)/(- a - b*x^2)^(1/2), x)","F"
286,0,-1,189,0.000000,"\text{Not used}","int((c - d*x^2)^(1/2)/(a + b*x^2)^(1/2),x)","\int \frac{\sqrt{c-d\,x^2}}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((c - d*x^2)^(1/2)/(a + b*x^2)^(1/2), x)","F"
287,0,-1,191,0.000000,"\text{Not used}","int((d*x^2 - c)^(1/2)/(a + b*x^2)^(1/2),x)","\int \frac{\sqrt{d\,x^2-c}}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((d*x^2 - c)^(1/2)/(a + b*x^2)^(1/2), x)","F"
288,0,-1,194,0.000000,"\text{Not used}","int((c - d*x^2)^(1/2)/(- a - b*x^2)^(1/2),x)","\int \frac{\sqrt{c-d\,x^2}}{\sqrt{-b\,x^2-a}} \,d x","Not used",1,"int((c - d*x^2)^(1/2)/(- a - b*x^2)^(1/2), x)","F"
289,0,-1,198,0.000000,"\text{Not used}","int((d*x^2 - c)^(1/2)/(- a - b*x^2)^(1/2),x)","\int \frac{\sqrt{d\,x^2-c}}{\sqrt{-b\,x^2-a}} \,d x","Not used",1,"int((d*x^2 - c)^(1/2)/(- a - b*x^2)^(1/2), x)","F"
290,0,-1,78,0.000000,"\text{Not used}","int(1/((b*x^2 + 2)^(1/2)*(d*x^2 + 3)^(1/2)),x)","\int \frac{1}{\sqrt{b\,x^2+2}\,\sqrt{d\,x^2+3}} \,d x","Not used",1,"int(1/((b*x^2 + 2)^(1/2)*(d*x^2 + 3)^(1/2)), x)","F"
291,0,-1,39,0.000000,"\text{Not used}","int(1/((4 - x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{4-x^2}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/((4 - x^2)^(1/2)*(c + d*x^2)^(1/2)), x)","F"
292,0,-1,61,0.000000,"\text{Not used}","int(1/((x^2 + 4)^(1/2)*(c + d*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{x^2+4}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/((x^2 + 4)^(1/2)*(c + d*x^2)^(1/2)), x)","F"
293,0,-1,6,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/2)*(2*x^2 - 1)^(1/2)),x)","\int \frac{1}{\sqrt{1-x^2}\,\sqrt{2\,x^2-1}} \,d x","Not used",1,"int(1/((1 - x^2)^(1/2)*(2*x^2 - 1)^(1/2)), x)","F"
294,0,-1,23,0.000000,"\text{Not used}","int((1 - c^2*x^2)^(1/2)/(c^2*x^2 + 1)^(1/2),x)","\int \frac{\sqrt{1-c^2\,x^2}}{\sqrt{c^2\,x^2+1}} \,d x","Not used",1,"int((1 - c^2*x^2)^(1/2)/(c^2*x^2 + 1)^(1/2), x)","F"
295,0,-1,182,0.000000,"\text{Not used}","int((b*x^2 + 2)^(1/2)/(d*x^2 + 3)^(1/2),x)","\int \frac{\sqrt{b\,x^2+2}}{\sqrt{d\,x^2+3}} \,d x","Not used",1,"int((b*x^2 + 2)^(1/2)/(d*x^2 + 3)^(1/2), x)","F"
296,0,-1,19,0.000000,"\text{Not used}","int((3*x^2 - 1)^(1/2)/(2 - 3*x^2)^(1/2),x)","\int \frac{\sqrt{3\,x^2-1}}{\sqrt{2-3\,x^2}} \,d x","Not used",1,"int((3*x^2 - 1)^(1/2)/(2 - 3*x^2)^(1/2), x)","F"
297,0,-1,95,0.000000,"\text{Not used}","int(((2*c*x^2)/(b - (b^2 - 4*a*c)^(1/2)) + 1)^(1/2)/(1 - (2*c*x^2)/(b + (b^2 - 4*a*c)^(1/2)))^(1/2),x)","\int \frac{\sqrt{\frac{2\,c\,x^2}{b-\sqrt{b^2-4\,a\,c}}+1}}{\sqrt{1-\frac{2\,c\,x^2}{b+\sqrt{b^2-4\,a\,c}}}} \,d x","Not used",1,"int(((2*c*x^2)/(b - (b^2 - 4*a*c)^(1/2)) + 1)^(1/2)/(1 - (2*c*x^2)/(b + (b^2 - 4*a*c)^(1/2)))^(1/2), x)","F"
298,0,-1,94,0.000000,"\text{Not used}","int((1 - (2*c*x^2)/(b - (b^2 - 4*a*c)^(1/2)))^(1/2)/(1 - (2*c*x^2)/(b + (b^2 - 4*a*c)^(1/2)))^(1/2),x)","\int \frac{\sqrt{1-\frac{2\,c\,x^2}{b-\sqrt{b^2-4\,a\,c}}}}{\sqrt{1-\frac{2\,c\,x^2}{b+\sqrt{b^2-4\,a\,c}}}} \,d x","Not used",1,"int((1 - (2*c*x^2)/(b - (b^2 - 4*a*c)^(1/2)))^(1/2)/(1 - (2*c*x^2)/(b + (b^2 - 4*a*c)^(1/2)))^(1/2), x)","F"
299,0,-1,478,0.000000,"\text{Not used}","int(((2*c*x^2)/(b - (b^2 - 4*a*c)^(1/2)) + 1)^(1/2)/((2*c*x^2)/(b + (b^2 - 4*a*c)^(1/2)) + 1)^(1/2),x)","\int \frac{\sqrt{\frac{2\,c\,x^2}{b-\sqrt{b^2-4\,a\,c}}+1}}{\sqrt{\frac{2\,c\,x^2}{b+\sqrt{b^2-4\,a\,c}}+1}} \,d x","Not used",1,"int(((2*c*x^2)/(b - (b^2 - 4*a*c)^(1/2)) + 1)^(1/2)/((2*c*x^2)/(b + (b^2 - 4*a*c)^(1/2)) + 1)^(1/2), x)","F"
300,0,-1,215,0.000000,"\text{Not used}","int((1 - (2*c*x^2)/(b - (b^2 - 4*a*c)^(1/2)))^(1/2)/((2*c*x^2)/(b + (b^2 - 4*a*c)^(1/2)) + 1)^(1/2),x)","\int \frac{\sqrt{1-\frac{2\,c\,x^2}{b-\sqrt{b^2-4\,a\,c}}}}{\sqrt{\frac{2\,c\,x^2}{b+\sqrt{b^2-4\,a\,c}}+1}} \,d x","Not used",1,"int((1 - (2*c*x^2)/(b - (b^2 - 4*a*c)^(1/2)))^(1/2)/((2*c*x^2)/(b + (b^2 - 4*a*c)^(1/2)) + 1)^(1/2), x)","F"
301,0,-1,62,0.000000,"\text{Not used}","int((1 - 2*x^2)^m/(1 - x^2)^(1/2),x)","\int \frac{{\left(1-2\,x^2\right)}^m}{\sqrt{1-x^2}} \,d x","Not used",1,"int((1 - 2*x^2)^m/(1 - x^2)^(1/2), x)","F"
302,0,-1,46,0.000000,"\text{Not used}","int(1/((x^2 - 1)^(1/2)*(x^2 - 4*3^(1/2) + 7)^(1/2)),x)","\int \frac{1}{\sqrt{x^2-1}\,\sqrt{x^2-4\,\sqrt{3}+7}} \,d x","Not used",1,"int(1/((x^2 - 1)^(1/2)*(x^2 - 4*3^(1/2) + 7)^(1/2)), x)","F"
303,0,-1,47,0.000000,"\text{Not used}","int(1/((x^2*(3^(1/2) - 3) + 3)^(1/2)*(2*3^(1/2)*x^2 - 3*3^(1/2) + 3)^(1/2)),x)","\int \frac{1}{\sqrt{\left(\sqrt{3}-3\right)\,x^2+3}\,\sqrt{2\,\sqrt{3}\,x^2-3\,\sqrt{3}+3}} \,d x","Not used",1,"int(1/((x^2*(3^(1/2) - 3) + 3)^(1/2)*(2*3^(1/2)*x^2 - 3*3^(1/2) + 3)^(1/2)), x)","F"
304,0,-1,129,0.000000,"\text{Not used}","int(1/((3*x^2 + 2)^(1/4)*(3*x^2 + 4)),x)","\int \frac{1}{{\left(3\,x^2+2\right)}^{1/4}\,\left(3\,x^2+4\right)} \,d x","Not used",1,"int(1/((3*x^2 + 2)^(1/4)*(3*x^2 + 4)), x)","F"
305,0,-1,120,0.000000,"\text{Not used}","int(-1/((2 - 3*x^2)^(1/4)*(3*x^2 - 4)),x)","-\int \frac{1}{{\left(2-3\,x^2\right)}^{1/4}\,\left(3\,x^2-4\right)} \,d x","Not used",1,"-int(1/((2 - 3*x^2)^(1/4)*(3*x^2 - 4)), x)","F"
306,0,-1,129,0.000000,"\text{Not used}","int(1/((b*x^2 + 2)^(1/4)*(b*x^2 + 4)),x)","\int \frac{1}{{\left(b\,x^2+2\right)}^{1/4}\,\left(b\,x^2+4\right)} \,d x","Not used",1,"int(1/((b*x^2 + 2)^(1/4)*(b*x^2 + 4)), x)","F"
307,0,-1,124,0.000000,"\text{Not used}","int(-1/((2 - b*x^2)^(1/4)*(b*x^2 - 4)),x)","-\int \frac{1}{{\left(2-b\,x^2\right)}^{1/4}\,\left(b\,x^2-4\right)} \,d x","Not used",1,"-int(1/((2 - b*x^2)^(1/4)*(b*x^2 - 4)), x)","F"
308,0,-1,120,0.000000,"\text{Not used}","int(1/((2*a + 3*x^2)*(a + 3*x^2)^(1/4)),x)","\int \frac{1}{\left(3\,x^2+2\,a\right)\,{\left(3\,x^2+a\right)}^{1/4}} \,d x","Not used",1,"int(1/((2*a + 3*x^2)*(a + 3*x^2)^(1/4)), x)","F"
309,0,-1,120,0.000000,"\text{Not used}","int(1/((2*a - 3*x^2)*(a - 3*x^2)^(1/4)),x)","\int \frac{1}{\left(2\,a-3\,x^2\right)\,{\left(a-3\,x^2\right)}^{1/4}} \,d x","Not used",1,"int(1/((2*a - 3*x^2)*(a - 3*x^2)^(1/4)), x)","F"
310,0,-1,120,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(1/4)*(2*a + b*x^2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{1/4}\,\left(b\,x^2+2\,a\right)} \,d x","Not used",1,"int(1/((a + b*x^2)^(1/4)*(2*a + b*x^2)), x)","F"
311,0,-1,124,0.000000,"\text{Not used}","int(1/((a - b*x^2)^(1/4)*(2*a - b*x^2)),x)","\int \frac{1}{{\left(a-b\,x^2\right)}^{1/4}\,\left(2\,a-b\,x^2\right)} \,d x","Not used",1,"int(1/((a - b*x^2)^(1/4)*(2*a - b*x^2)), x)","F"
312,0,-1,61,0.000000,"\text{Not used}","int(1/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)),x)","\int \frac{1}{{\left(3\,x^2-1\right)}^{1/4}\,\left(3\,x^2-2\right)} \,d x","Not used",1,"int(1/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)), x)","F"
313,0,-1,61,0.000000,"\text{Not used}","int(-1/((- 3*x^2 - 1)^(1/4)*(3*x^2 + 2)),x)","-\int \frac{1}{{\left(-3\,x^2-1\right)}^{1/4}\,\left(3\,x^2+2\right)} \,d x","Not used",1,"-int(1/((- 3*x^2 - 1)^(1/4)*(3*x^2 + 2)), x)","F"
314,0,-1,77,0.000000,"\text{Not used}","int(1/((b*x^2 - 1)^(1/4)*(b*x^2 - 2)),x)","\int \frac{1}{{\left(b\,x^2-1\right)}^{1/4}\,\left(b\,x^2-2\right)} \,d x","Not used",1,"int(1/((b*x^2 - 1)^(1/4)*(b*x^2 - 2)), x)","F"
315,0,-1,79,0.000000,"\text{Not used}","int(-1/((- b*x^2 - 1)^(1/4)*(b*x^2 + 2)),x)","-\int \frac{1}{{\left(-b\,x^2-1\right)}^{1/4}\,\left(b\,x^2+2\right)} \,d x","Not used",1,"-int(1/((- b*x^2 - 1)^(1/4)*(b*x^2 + 2)), x)","F"
316,0,-1,85,0.000000,"\text{Not used}","int(-1/((2*a - 3*x^2)*(3*x^2 - a)^(1/4)),x)","-\int \frac{1}{\left(2\,a-3\,x^2\right)\,{\left(3\,x^2-a\right)}^{1/4}} \,d x","Not used",1,"-int(1/((2*a - 3*x^2)*(3*x^2 - a)^(1/4)), x)","F"
317,0,-1,85,0.000000,"\text{Not used}","int(-1/((2*a + 3*x^2)*(- a - 3*x^2)^(1/4)),x)","-\int \frac{1}{\left(3\,x^2+2\,a\right)\,{\left(-3\,x^2-a\right)}^{1/4}} \,d x","Not used",1,"-int(1/((2*a + 3*x^2)*(- a - 3*x^2)^(1/4)), x)","F"
318,0,-1,101,0.000000,"\text{Not used}","int(-1/((b*x^2 - a)^(1/4)*(2*a - b*x^2)),x)","-\int \frac{1}{{\left(b\,x^2-a\right)}^{1/4}\,\left(2\,a-b\,x^2\right)} \,d x","Not used",1,"-int(1/((b*x^2 - a)^(1/4)*(2*a - b*x^2)), x)","F"
319,0,-1,103,0.000000,"\text{Not used}","int(-1/((- a - b*x^2)^(1/4)*(2*a + b*x^2)),x)","-\int \frac{1}{{\left(-b\,x^2-a\right)}^{1/4}\,\left(b\,x^2+2\,a\right)} \,d x","Not used",1,"-int(1/((- a - b*x^2)^(1/4)*(2*a + b*x^2)), x)","F"
320,0,-1,53,0.000000,"\text{Not used}","int(-1/((x^2 - 1)^(1/4)*(x^2 - 2)),x)","-\int \frac{1}{{\left(x^2-1\right)}^{1/4}\,\left(x^2-2\right)} \,d x","Not used",1,"-int(1/((x^2 - 1)^(1/4)*(x^2 - 2)), x)","F"
321,0,-1,362,0.000000,"\text{Not used}","int((a + b*x^2)^(7/4)/(c + d*x^2),x)","\int \frac{{\left(b\,x^2+a\right)}^{7/4}}{d\,x^2+c} \,d x","Not used",1,"int((a + b*x^2)^(7/4)/(c + d*x^2), x)","F"
322,0,-1,302,0.000000,"\text{Not used}","int((a + b*x^2)^(5/4)/(c + d*x^2),x)","\int \frac{{\left(b\,x^2+a\right)}^{5/4}}{d\,x^2+c} \,d x","Not used",1,"int((a + b*x^2)^(5/4)/(c + d*x^2), x)","F"
323,0,-1,244,0.000000,"\text{Not used}","int((a + b*x^2)^(3/4)/(c + d*x^2),x)","\int \frac{{\left(b\,x^2+a\right)}^{3/4}}{d\,x^2+c} \,d x","Not used",1,"int((a + b*x^2)^(3/4)/(c + d*x^2), x)","F"
324,0,-1,199,0.000000,"\text{Not used}","int((a + b*x^2)^(1/4)/(c + d*x^2),x)","\int \frac{{\left(b\,x^2+a\right)}^{1/4}}{d\,x^2+c} \,d x","Not used",1,"int((a + b*x^2)^(1/4)/(c + d*x^2), x)","F"
325,0,-1,167,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(1/4)*(c + d*x^2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{1/4}\,\left(d\,x^2+c\right)} \,d x","Not used",1,"int(1/((a + b*x^2)^(1/4)*(c + d*x^2)), x)","F"
326,0,-1,152,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(3/4)*(c + d*x^2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{3/4}\,\left(d\,x^2+c\right)} \,d x","Not used",1,"int(1/((a + b*x^2)^(3/4)*(c + d*x^2)), x)","F"
327,0,-1,233,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(5/4)*(c + d*x^2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{5/4}\,\left(d\,x^2+c\right)} \,d x","Not used",1,"int(1/((a + b*x^2)^(5/4)*(c + d*x^2)), x)","F"
328,0,-1,254,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(7/4)*(c + d*x^2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{7/4}\,\left(d\,x^2+c\right)} \,d x","Not used",1,"int(1/((a + b*x^2)^(7/4)*(c + d*x^2)), x)","F"
329,0,-1,274,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(9/4)*(c + d*x^2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{9/4}\,\left(d\,x^2+c\right)} \,d x","Not used",1,"int(1/((a + b*x^2)^(9/4)*(c + d*x^2)), x)","F"
330,0,-1,304,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(11/4)*(c + d*x^2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{11/4}\,\left(d\,x^2+c\right)} \,d x","Not used",1,"int(1/((a + b*x^2)^(11/4)*(c + d*x^2)), x)","F"
331,0,-1,340,0.000000,"\text{Not used}","int((a + b*x^2)^(7/4)/(c + d*x^2)^2,x)","\int \frac{{\left(b\,x^2+a\right)}^{7/4}}{{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int((a + b*x^2)^(7/4)/(c + d*x^2)^2, x)","F"
332,0,-1,279,0.000000,"\text{Not used}","int((a + b*x^2)^(5/4)/(c + d*x^2)^2,x)","\int \frac{{\left(b\,x^2+a\right)}^{5/4}}{{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int((a + b*x^2)^(5/4)/(c + d*x^2)^2, x)","F"
333,0,-1,309,0.000000,"\text{Not used}","int((a + b*x^2)^(3/4)/(c + d*x^2)^2,x)","\int \frac{{\left(b\,x^2+a\right)}^{3/4}}{{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int((a + b*x^2)^(3/4)/(c + d*x^2)^2, x)","F"
334,0,-1,278,0.000000,"\text{Not used}","int((a + b*x^2)^(1/4)/(c + d*x^2)^2,x)","\int \frac{{\left(b\,x^2+a\right)}^{1/4}}{{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int((a + b*x^2)^(1/4)/(c + d*x^2)^2, x)","F"
335,0,-1,336,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(1/4)*(c + d*x^2)^2),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{1/4}\,{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^2)^(1/4)*(c + d*x^2)^2), x)","F"
336,0,-1,292,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(3/4)*(c + d*x^2)^2),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{3/4}\,{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^2)^(3/4)*(c + d*x^2)^2), x)","F"
337,0,-1,314,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(5/4)*(c + d*x^2)^2),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{5/4}\,{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^2)^(5/4)*(c + d*x^2)^2), x)","F"
338,0,-1,345,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(7/4)*(c + d*x^2)^2),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{7/4}\,{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^2)^(7/4)*(c + d*x^2)^2), x)","F"
339,0,-1,371,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(9/4)*(c + d*x^2)^2),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{9/4}\,{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^2)^(9/4)*(c + d*x^2)^2), x)","F"
340,0,-1,419,0.000000,"\text{Not used}","int(1/((a + b*x^2)^(11/4)*(c + d*x^2)^2),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^{11/4}\,{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^2)^(11/4)*(c + d*x^2)^2), x)","F"
341,0,-1,79,0.000000,"\text{Not used}","int((a + b*x^2)^p*(c + d*x^2)^q,x)","\int {\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q \,d x","Not used",1,"int((a + b*x^2)^p*(c + d*x^2)^q, x)","F"
342,0,-1,296,0.000000,"\text{Not used}","int((a + b*x^2)^p*(c + d*x^2)^3,x)","\int {\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^3 \,d x","Not used",1,"int((a + b*x^2)^p*(c + d*x^2)^3, x)","F"
343,0,-1,176,0.000000,"\text{Not used}","int((a + b*x^2)^p*(c + d*x^2)^2,x)","\int {\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^2 \,d x","Not used",1,"int((a + b*x^2)^p*(c + d*x^2)^2, x)","F"
344,0,-1,93,0.000000,"\text{Not used}","int((a + b*x^2)^p*(c + d*x^2),x)","\int {\left(b\,x^2+a\right)}^p\,\left(d\,x^2+c\right) \,d x","Not used",1,"int((a + b*x^2)^p*(c + d*x^2), x)","F"
345,1,41,44,5.567494,"\text{Not used}","int((a + b*x^2)^p,x)","\frac{x\,{\left(b\,x^2+a\right)}^p\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},-p;\ \frac{3}{2};\ -\frac{b\,x^2}{a}\right)}{{\left(\frac{b\,x^2}{a}+1\right)}^p}","Not used",1,"(x*(a + b*x^2)^p*hypergeom([1/2, -p], 3/2, -(b*x^2)/a))/((b*x^2)/a + 1)^p","B"
346,0,-1,57,0.000000,"\text{Not used}","int((a + b*x^2)^p/(c + d*x^2),x)","\int \frac{{\left(b\,x^2+a\right)}^p}{d\,x^2+c} \,d x","Not used",1,"int((a + b*x^2)^p/(c + d*x^2), x)","F"
347,0,-1,57,0.000000,"\text{Not used}","int((a + b*x^2)^p/(c + d*x^2)^2,x)","\int \frac{{\left(b\,x^2+a\right)}^p}{{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int((a + b*x^2)^p/(c + d*x^2)^2, x)","F"
348,0,-1,57,0.000000,"\text{Not used}","int((a + b*x^2)^p/(c + d*x^2)^3,x)","\int \frac{{\left(b\,x^2+a\right)}^p}{{\left(d\,x^2+c\right)}^3} \,d x","Not used",1,"int((a + b*x^2)^p/(c + d*x^2)^3, x)","F"
349,1,131,53,5.736462,"\text{Not used}","int((a + b*x^2)^((b*c)/(2*a*d - 2*b*c) - 1)/(c + d*x^2)^((a*d)/(2*a*d - 2*b*c) + 1),x)","\frac{x\,{\left(b\,x^2+a\right)}^{\frac{b\,c}{2\,a\,d-2\,b\,c}-1}+\frac{x^3\,{\left(b\,x^2+a\right)}^{\frac{b\,c}{2\,a\,d-2\,b\,c}-1}\,\left(a\,d+b\,c\right)}{a\,c}+\frac{b\,d\,x^5\,{\left(b\,x^2+a\right)}^{\frac{b\,c}{2\,a\,d-2\,b\,c}-1}}{a\,c}}{{\left(d\,x^2+c\right)}^{\frac{a\,d}{2\,a\,d-2\,b\,c}+1}}","Not used",1,"(x*(a + b*x^2)^((b*c)/(2*a*d - 2*b*c) - 1) + (x^3*(a + b*x^2)^((b*c)/(2*a*d - 2*b*c) - 1)*(a*d + b*c))/(a*c) + (b*d*x^5*(a + b*x^2)^((b*c)/(2*a*d - 2*b*c) - 1))/(a*c))/(c + d*x^2)^((a*d)/(2*a*d - 2*b*c) + 1)","B"