1,1,273,184,1.048924,"\text{Not used}","int((a + b*atan(c*x))*(d + e*x)^4,x)","\frac{a\,e^4\,x^5}{5}+a\,d^4\,x-\frac{b\,d^4\,\ln\left(c^2\,x^2+1\right)}{2\,c}-\frac{b\,e^4\,\ln\left(c^2\,x^2+1\right)}{10\,c^5}+2\,a\,d^2\,e^2\,x^3-\frac{b\,e^4\,x^4}{20\,c}+\frac{b\,e^4\,x^2}{10\,c^3}+b\,d^4\,x\,\mathrm{atan}\left(c\,x\right)+2\,a\,d^3\,e\,x^2+a\,d\,e^3\,x^4+\frac{b\,e^4\,x^5\,\mathrm{atan}\left(c\,x\right)}{5}-\frac{2\,b\,d^3\,e\,x}{c}+\frac{b\,d\,e^3\,x}{c^3}+\frac{2\,b\,d^3\,e\,\mathrm{atan}\left(c\,x\right)}{c^2}-\frac{b\,d\,e^3\,\mathrm{atan}\left(c\,x\right)}{c^4}+2\,b\,d^3\,e\,x^2\,\mathrm{atan}\left(c\,x\right)+b\,d\,e^3\,x^4\,\mathrm{atan}\left(c\,x\right)-\frac{b\,d\,e^3\,x^3}{3\,c}+2\,b\,d^2\,e^2\,x^3\,\mathrm{atan}\left(c\,x\right)+\frac{b\,d^2\,e^2\,\ln\left(c^2\,x^2+1\right)}{c^3}-\frac{b\,d^2\,e^2\,x^2}{c}","Not used",1,"(a*e^4*x^5)/5 + a*d^4*x - (b*d^4*log(c^2*x^2 + 1))/(2*c) - (b*e^4*log(c^2*x^2 + 1))/(10*c^5) + 2*a*d^2*e^2*x^3 - (b*e^4*x^4)/(20*c) + (b*e^4*x^2)/(10*c^3) + b*d^4*x*atan(c*x) + 2*a*d^3*e*x^2 + a*d*e^3*x^4 + (b*e^4*x^5*atan(c*x))/5 - (2*b*d^3*e*x)/c + (b*d*e^3*x)/c^3 + (2*b*d^3*e*atan(c*x))/c^2 - (b*d*e^3*atan(c*x))/c^4 + 2*b*d^3*e*x^2*atan(c*x) + b*d*e^3*x^4*atan(c*x) - (b*d*e^3*x^3)/(3*c) + 2*b*d^2*e^2*x^3*atan(c*x) + (b*d^2*e^2*log(c^2*x^2 + 1))/c^3 - (b*d^2*e^2*x^2)/c","B"
2,1,197,144,0.802378,"\text{Not used}","int((a + b*atan(c*x))*(d + e*x)^3,x)","\frac{a\,e^3\,x^4}{4}+a\,d^3\,x-\frac{b\,d^3\,\ln\left(c^2\,x^2+1\right)}{2\,c}-\frac{b\,e^3\,x^3}{12\,c}+b\,d^3\,x\,\mathrm{atan}\left(c\,x\right)+\frac{3\,a\,d^2\,e\,x^2}{2}+a\,d\,e^2\,x^3+\frac{b\,e^3\,x}{4\,c^3}-\frac{b\,e^3\,\mathrm{atan}\left(c\,x\right)}{4\,c^4}+\frac{b\,e^3\,x^4\,\mathrm{atan}\left(c\,x\right)}{4}-\frac{3\,b\,d^2\,e\,x}{2\,c}+\frac{3\,b\,d^2\,e\,\mathrm{atan}\left(c\,x\right)}{2\,c^2}+\frac{3\,b\,d^2\,e\,x^2\,\mathrm{atan}\left(c\,x\right)}{2}+b\,d\,e^2\,x^3\,\mathrm{atan}\left(c\,x\right)+\frac{b\,d\,e^2\,\ln\left(c^2\,x^2+1\right)}{2\,c^3}-\frac{b\,d\,e^2\,x^2}{2\,c}","Not used",1,"(a*e^3*x^4)/4 + a*d^3*x - (b*d^3*log(c^2*x^2 + 1))/(2*c) - (b*e^3*x^3)/(12*c) + b*d^3*x*atan(c*x) + (3*a*d^2*e*x^2)/2 + a*d*e^2*x^3 + (b*e^3*x)/(4*c^3) - (b*e^3*atan(c*x))/(4*c^4) + (b*e^3*x^4*atan(c*x))/4 - (3*b*d^2*e*x)/(2*c) + (3*b*d^2*e*atan(c*x))/(2*c^2) + (3*b*d^2*e*x^2*atan(c*x))/2 + b*d*e^2*x^3*atan(c*x) + (b*d*e^2*log(c^2*x^2 + 1))/(2*c^3) - (b*d*e^2*x^2)/(2*c)","B"
3,1,127,103,0.352650,"\text{Not used}","int((a + b*atan(c*x))*(d + e*x)^2,x)","\frac{a\,e^2\,x^3}{3}+a\,d^2\,x-\frac{b\,d^2\,\ln\left(c^2\,x^2+1\right)}{2\,c}+\frac{b\,e^2\,\ln\left(c^2\,x^2+1\right)}{6\,c^3}-\frac{b\,e^2\,x^2}{6\,c}+a\,d\,e\,x^2+b\,d^2\,x\,\mathrm{atan}\left(c\,x\right)+\frac{b\,e^2\,x^3\,\mathrm{atan}\left(c\,x\right)}{3}-\frac{b\,d\,e\,x}{c}+\frac{b\,d\,e\,\mathrm{atan}\left(c\,x\right)}{c^2}+b\,d\,e\,x^2\,\mathrm{atan}\left(c\,x\right)","Not used",1,"(a*e^2*x^3)/3 + a*d^2*x - (b*d^2*log(c^2*x^2 + 1))/(2*c) + (b*e^2*log(c^2*x^2 + 1))/(6*c^3) - (b*e^2*x^2)/(6*c) + a*d*e*x^2 + b*d^2*x*atan(c*x) + (b*e^2*x^3*atan(c*x))/3 - (b*d*e*x)/c + (b*d*e*atan(c*x))/c^2 + b*d*e*x^2*atan(c*x)","B"
4,1,67,76,0.409847,"\text{Not used}","int((a + b*atan(c*x))*(d + e*x),x)","a\,d\,x+\frac{a\,e\,x^2}{2}+b\,d\,x\,\mathrm{atan}\left(c\,x\right)-\frac{b\,e\,x}{2\,c}+\frac{b\,e\,\mathrm{atan}\left(c\,x\right)}{2\,c^2}+\frac{b\,e\,x^2\,\mathrm{atan}\left(c\,x\right)}{2}-\frac{b\,d\,\ln\left(c^2\,x^2+1\right)}{2\,c}","Not used",1,"a*d*x + (a*e*x^2)/2 + b*d*x*atan(c*x) - (b*e*x)/(2*c) + (b*e*atan(c*x))/(2*c^2) + (b*e*x^2*atan(c*x))/2 - (b*d*log(c^2*x^2 + 1))/(2*c)","B"
5,0,-1,138,0.000000,"\text{Not used}","int((a + b*atan(c*x))/(d + e*x),x)","\int \frac{a+b\,\mathrm{atan}\left(c\,x\right)}{d+e\,x} \,d x","Not used",1,"int((a + b*atan(c*x))/(d + e*x), x)","F"
6,1,112,98,3.459892,"\text{Not used}","int((a + b*atan(c*x))/(d + e*x)^2,x)","\frac{d^2\,\left(b\,c\,\ln\left(d+e\,x\right)-\frac{b\,c\,\ln\left(c^2\,x^2+1\right)}{2}+a\,c^2\,x+b\,c^2\,x\,\mathrm{atan}\left(c\,x\right)\right)-d\,e\,\left(b\,\mathrm{atan}\left(c\,x\right)-b\,c\,x\,\ln\left(d+e\,x\right)+\frac{b\,c\,x\,\ln\left(c^2\,x^2+1\right)}{2}\right)+a\,e^2\,x}{d\,\left(c^2\,d^2+e^2\right)\,\left(d+e\,x\right)}","Not used",1,"(d^2*(b*c*log(d + e*x) - (b*c*log(c^2*x^2 + 1))/2 + a*c^2*x + b*c^2*x*atan(c*x)) - d*e*(b*atan(c*x) - b*c*x*log(d + e*x) + (b*c*x*log(c^2*x^2 + 1))/2) + a*e^2*x)/(d*(e^2 + c^2*d^2)*(d + e*x))","B"
7,1,591,146,4.428186,"\text{Not used}","int((a + b*atan(c*x))/(d + e*x)^3,x)","\frac{\frac{x\,\left(a\,c^2\,d^2+\frac{b\,c\,d\,e}{2}+a\,e^2\right)}{d\,\left(c^2\,d^2+e^2\right)}-\frac{b\,\mathrm{atan}\left(c\,x\right)}{2\,e}+\frac{x^2\,\left(\frac{a\,c^2\,d^2\,e}{2}+\frac{b\,c\,d\,e^2}{2}+\frac{a\,e^3}{2}\right)}{d^2\,\left(c^2\,d^2+e^2\right)}+\frac{x^4\,\left(\frac{a\,c^4\,d^2\,e}{2}+\frac{b\,c^3\,d\,e^2}{2}+\frac{a\,c^2\,e^3}{2}\right)}{d^2\,\left(c^2\,d^2+e^2\right)}+\frac{x^3\,\left(a\,c^4\,d^2+\frac{b\,c^3\,d\,e}{2}+a\,c^2\,e^2\right)}{d\,\left(c^2\,d^2+e^2\right)}-\frac{b\,c^2\,x^2\,\mathrm{atan}\left(c\,x\right)}{2\,e}}{c^2\,d^2\,x^2+2\,c^2\,d\,e\,x^3+c^2\,e^2\,x^4+d^2+2\,d\,e\,x+e^2\,x^2}+\frac{b\,c^3\,d\,\ln\left(d+e\,x\right)}{c^4\,d^4+2\,c^2\,d^2\,e^2+e^4}-\frac{b\,c^3\,d\,\ln\left(c^2\,x^2+1\right)}{2\,\left(c^4\,d^4+2\,c^2\,d^2\,e^2+e^4\right)}+\frac{\mathrm{atan}\left(\frac{c^2\,x}{\sqrt{c^2}}\right)\,{\left(c^2\right)}^{7/2}\,\left(c^4\,d^4+8\,c^2\,d^2\,e^2+2\,e^4\right)\,\left(3\,c^6\,d^4+26\,c^4\,d^2\,e^2+4\,c^2\,e^4\right)\,\left(27\,b\,c^{10}\,d^{10}+23\,b\,c^8\,d^8\,e^2-34\,b\,c^6\,d^6\,e^4-26\,b\,c^4\,d^4\,e^6+7\,b\,c^2\,d^2\,e^8+3\,b\,e^{10}\right)}{2\,c\,\left(81\,c^{26}\,d^{20}\,e+1662\,c^{24}\,d^{18}\,e^3+11515\,c^{22}\,d^{16}\,e^5+32306\,c^{20}\,d^{14}\,e^7+43705\,c^{18}\,d^{12}\,e^9+28142\,c^{16}\,d^{10}\,e^{11}+4857\,c^{14}\,d^8\,e^{13}-3650\,c^{12}\,d^6\,e^{15}-2054\,c^{10}\,d^4\,e^{17}-380\,c^8\,d^2\,e^{19}-24\,c^6\,e^{21}\right)}","Not used",1,"((x*(a*e^2 + a*c^2*d^2 + (b*c*d*e)/2))/(d*(e^2 + c^2*d^2)) - (b*atan(c*x))/(2*e) + (x^2*((a*e^3)/2 + (b*c*d*e^2)/2 + (a*c^2*d^2*e)/2))/(d^2*(e^2 + c^2*d^2)) + (x^4*((a*c^2*e^3)/2 + (a*c^4*d^2*e)/2 + (b*c^3*d*e^2)/2))/(d^2*(e^2 + c^2*d^2)) + (x^3*(a*c^4*d^2 + a*c^2*e^2 + (b*c^3*d*e)/2))/(d*(e^2 + c^2*d^2)) - (b*c^2*x^2*atan(c*x))/(2*e))/(d^2 + e^2*x^2 + 2*d*e*x + c^2*d^2*x^2 + c^2*e^2*x^4 + 2*c^2*d*e*x^3) + (b*c^3*d*log(d + e*x))/(e^4 + c^4*d^4 + 2*c^2*d^2*e^2) - (b*c^3*d*log(c^2*x^2 + 1))/(2*(e^4 + c^4*d^4 + 2*c^2*d^2*e^2)) + (atan((c^2*x)/(c^2)^(1/2))*(c^2)^(7/2)*(2*e^4 + c^4*d^4 + 8*c^2*d^2*e^2)*(3*c^6*d^4 + 4*c^2*e^4 + 26*c^4*d^2*e^2)*(3*b*e^10 + 27*b*c^10*d^10 + 7*b*c^2*d^2*e^8 - 26*b*c^4*d^4*e^6 - 34*b*c^6*d^6*e^4 + 23*b*c^8*d^8*e^2))/(2*c*(81*c^26*d^20*e - 24*c^6*e^21 - 380*c^8*d^2*e^19 - 2054*c^10*d^4*e^17 - 3650*c^12*d^6*e^15 + 4857*c^14*d^8*e^13 + 28142*c^16*d^10*e^11 + 43705*c^18*d^12*e^9 + 32306*c^20*d^14*e^7 + 11515*c^22*d^16*e^5 + 1662*c^24*d^18*e^3))","B"
8,0,-1,206,0.000000,"\text{Not used}","int((a + b*atan(c*x))/(d + e*x)^4,x)","\int \frac{a+b\,\mathrm{atan}\left(c\,x\right)}{{\left(d+e\,x\right)}^4} \,d x","Not used",1,"int((a + b*atan(c*x))/(d + e*x)^4, x)","F"
9,0,-1,376,0.000000,"\text{Not used}","int((a + b*atan(c*x))^2*(d + e*x)^3,x)","\int {\left(a+b\,\mathrm{atan}\left(c\,x\right)\right)}^2\,{\left(d+e\,x\right)}^3 \,d x","Not used",1,"int((a + b*atan(c*x))^2*(d + e*x)^3, x)","F"
10,0,-1,270,0.000000,"\text{Not used}","int((a + b*atan(c*x))^2*(d + e*x)^2,x)","\int {\left(a+b\,\mathrm{atan}\left(c\,x\right)\right)}^2\,{\left(d+e\,x\right)}^2 \,d x","Not used",1,"int((a + b*atan(c*x))^2*(d + e*x)^2, x)","F"
11,0,-1,171,0.000000,"\text{Not used}","int((a + b*atan(c*x))^2*(d + e*x),x)","\int {\left(a+b\,\mathrm{atan}\left(c\,x\right)\right)}^2\,\left(d+e\,x\right) \,d x","Not used",1,"int((a + b*atan(c*x))^2*(d + e*x), x)","F"
12,0,-1,223,0.000000,"\text{Not used}","int((a + b*atan(c*x))^2/(d + e*x),x)","\int \frac{{\left(a+b\,\mathrm{atan}\left(c\,x\right)\right)}^2}{d+e\,x} \,d x","Not used",1,"int((a + b*atan(c*x))^2/(d + e*x), x)","F"
13,0,-1,341,0.000000,"\text{Not used}","int((a + b*atan(c*x))^2/(d + e*x)^2,x)","\int \frac{{\left(a+b\,\mathrm{atan}\left(c\,x\right)\right)}^2}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a + b*atan(c*x))^2/(d + e*x)^2, x)","F"
14,0,-1,496,0.000000,"\text{Not used}","int((a + b*atan(c*x))^2/(d + e*x)^3,x)","\int \frac{{\left(a+b\,\mathrm{atan}\left(c\,x\right)\right)}^2}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((a + b*atan(c*x))^2/(d + e*x)^3, x)","F"
15,0,-1,652,0.000000,"\text{Not used}","int((a + b*atan(c*x))^3*(d + e*x)^3,x)","\int {\left(a+b\,\mathrm{atan}\left(c\,x\right)\right)}^3\,{\left(d+e\,x\right)}^3 \,d x","Not used",1,"int((a + b*atan(c*x))^3*(d + e*x)^3, x)","F"
16,0,-1,411,0.000000,"\text{Not used}","int((a + b*atan(c*x))^3*(d + e*x)^2,x)","\int {\left(a+b\,\mathrm{atan}\left(c\,x\right)\right)}^3\,{\left(d+e\,x\right)}^2 \,d x","Not used",1,"int((a + b*atan(c*x))^3*(d + e*x)^2, x)","F"
17,0,-1,264,0.000000,"\text{Not used}","int((a + b*atan(c*x))^3*(d + e*x),x)","\int {\left(a+b\,\mathrm{atan}\left(c\,x\right)\right)}^3\,\left(d+e\,x\right) \,d x","Not used",1,"int((a + b*atan(c*x))^3*(d + e*x), x)","F"
18,0,-1,320,0.000000,"\text{Not used}","int((a + b*atan(c*x))^3/(d + e*x),x)","\int \frac{{\left(a+b\,\mathrm{atan}\left(c\,x\right)\right)}^3}{d+e\,x} \,d x","Not used",1,"int((a + b*atan(c*x))^3/(d + e*x), x)","F"
19,0,-1,499,0.000000,"\text{Not used}","int((a + b*atan(c*x))^3/(d + e*x)^2,x)","\int \frac{{\left(a+b\,\mathrm{atan}\left(c\,x\right)\right)}^3}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a + b*atan(c*x))^3/(d + e*x)^2, x)","F"
20,0,-1,936,0.000000,"\text{Not used}","int((a + b*atan(c*x))^3/(d + e*x)^3,x)","\int \frac{{\left(a+b\,\mathrm{atan}\left(c\,x\right)\right)}^3}{{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((a + b*atan(c*x))^3/(d + e*x)^3, x)","F"
21,1,419,250,3.365833,"\text{Not used}","int((a + b*atan(c*x^2))*(d + e*x)^2,x)","\frac{a\,e^2\,x^3}{3}+a\,d^2\,x+\frac{b\,e^2\,x^3\,\mathrm{atan}\left(c\,x^2\right)}{3}+a\,d\,e\,x^2-\frac{3\,b\,d^2\,\ln\left(3\,c\,x\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}-1\right)\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}}{2}+\frac{3\,b\,d^2\,\ln\left(3\,c\,x\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}+1\right)\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}}{2}-\frac{b\,d^2\,\ln\left(3\,c\,x\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}+1{}\mathrm{i}\right)\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}\,3{}\mathrm{i}}{2}+\frac{b\,d^2\,\ln\left(1+c\,x\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}\,3{}\mathrm{i}\right)\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}\,3{}\mathrm{i}}{2}-\frac{2\,b\,e^2\,x}{3\,c}+b\,d^2\,x\,\mathrm{atan}\left(c\,x^2\right)+\frac{b\,e^2\,\ln\left(3\,c\,x\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}-1\right)\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}\,1{}\mathrm{i}}{2\,c}-\frac{b\,e^2\,\ln\left(3\,c\,x\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}+1\right)\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}\,1{}\mathrm{i}}{2\,c}+\frac{b\,e^2\,\ln\left(3\,c\,x\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}+1{}\mathrm{i}\right)\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}}{2\,c}-\frac{b\,e^2\,\ln\left(1+c\,x\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}\,3{}\mathrm{i}\right)\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}}{2\,c}+b\,d\,e\,x^2\,\mathrm{atan}\left(c\,x^2\right)-\frac{b\,d\,e\,\ln\left(3\,c\,x\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}-1\right)}{2\,c}-\frac{b\,d\,e\,\ln\left(3\,c\,x\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}+1\right)}{2\,c}-\frac{b\,d\,e\,\ln\left(3\,c\,x\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}+1{}\mathrm{i}\right)}{2\,c}-\frac{b\,d\,e\,\ln\left(1+c\,x\,\sqrt{\frac{1{}\mathrm{i}}{9\,c}}\,3{}\mathrm{i}\right)}{2\,c}","Not used",1,"(a*e^2*x^3)/3 + a*d^2*x + (b*e^2*x^3*atan(c*x^2))/3 + a*d*e*x^2 - (3*b*d^2*log(3*c*x*(1i/(9*c))^(1/2) - 1)*(1i/(9*c))^(1/2))/2 + (3*b*d^2*log(3*c*x*(1i/(9*c))^(1/2) + 1)*(1i/(9*c))^(1/2))/2 - (b*d^2*log(3*c*x*(1i/(9*c))^(1/2) + 1i)*(1i/(9*c))^(1/2)*3i)/2 + (b*d^2*log(c*x*(1i/(9*c))^(1/2)*3i + 1)*(1i/(9*c))^(1/2)*3i)/2 - (2*b*e^2*x)/(3*c) + b*d^2*x*atan(c*x^2) + (b*e^2*log(3*c*x*(1i/(9*c))^(1/2) - 1)*(1i/(9*c))^(1/2)*1i)/(2*c) - (b*e^2*log(3*c*x*(1i/(9*c))^(1/2) + 1)*(1i/(9*c))^(1/2)*1i)/(2*c) + (b*e^2*log(3*c*x*(1i/(9*c))^(1/2) + 1i)*(1i/(9*c))^(1/2))/(2*c) - (b*e^2*log(c*x*(1i/(9*c))^(1/2)*3i + 1)*(1i/(9*c))^(1/2))/(2*c) + b*d*e*x^2*atan(c*x^2) - (b*d*e*log(3*c*x*(1i/(9*c))^(1/2) - 1))/(2*c) - (b*d*e*log(3*c*x*(1i/(9*c))^(1/2) + 1))/(2*c) - (b*d*e*log(3*c*x*(1i/(9*c))^(1/2) + 1i))/(2*c) - (b*d*e*log(c*x*(1i/(9*c))^(1/2)*3i + 1))/(2*c)","B"
22,1,203,192,2.533620,"\text{Not used}","int((a + b*atan(c*x^2))*(d + e*x),x)","a\,d\,x+\frac{a\,e\,x^2}{2}+b\,d\,x\,\mathrm{atan}\left(c\,x^2\right)-\frac{b\,e\,\ln\left(x\,\sqrt{-c\,1{}\mathrm{i}}-1\right)}{4\,c}-\frac{b\,e\,\ln\left(x\,\sqrt{-c\,1{}\mathrm{i}}+1\right)}{4\,c}-\frac{b\,e\,\ln\left(x\,\sqrt{c\,1{}\mathrm{i}}-1\right)}{4\,c}-\frac{b\,e\,\ln\left(x\,\sqrt{c\,1{}\mathrm{i}}+1\right)}{4\,c}+\frac{b\,e\,x^2\,\mathrm{atan}\left(c\,x^2\right)}{2}-\frac{b\,d\,\ln\left(x\,\sqrt{-c\,1{}\mathrm{i}}-1\right)\,\sqrt{-c\,1{}\mathrm{i}}}{2\,c}+\frac{b\,d\,\ln\left(x\,\sqrt{-c\,1{}\mathrm{i}}+1\right)\,\sqrt{-c\,1{}\mathrm{i}}}{2\,c}-\frac{b\,d\,\ln\left(x\,\sqrt{c\,1{}\mathrm{i}}-1\right)\,\sqrt{c\,1{}\mathrm{i}}}{2\,c}+\frac{b\,d\,\ln\left(x\,\sqrt{c\,1{}\mathrm{i}}+1\right)\,\sqrt{c\,1{}\mathrm{i}}}{2\,c}","Not used",1,"a*d*x + (a*e*x^2)/2 + b*d*x*atan(c*x^2) - (b*e*log(x*(-c*1i)^(1/2) - 1))/(4*c) - (b*e*log(x*(-c*1i)^(1/2) + 1))/(4*c) - (b*e*log(x*(c*1i)^(1/2) - 1))/(4*c) - (b*e*log(x*(c*1i)^(1/2) + 1))/(4*c) + (b*e*x^2*atan(c*x^2))/2 - (b*d*log(x*(-c*1i)^(1/2) - 1)*(-c*1i)^(1/2))/(2*c) + (b*d*log(x*(-c*1i)^(1/2) + 1)*(-c*1i)^(1/2))/(2*c) - (b*d*log(x*(c*1i)^(1/2) - 1)*(c*1i)^(1/2))/(2*c) + (b*d*log(x*(c*1i)^(1/2) + 1)*(c*1i)^(1/2))/(2*c)","B"
23,0,-1,501,0.000000,"\text{Not used}","int((a + b*atan(c*x^2))/(d + e*x),x)","\int \frac{a+b\,\mathrm{atan}\left(c\,x^2\right)}{d+e\,x} \,d x","Not used",1,"int((a + b*atan(c*x^2))/(d + e*x), x)","F"
24,1,883,328,0.660887,"\text{Not used}","int((a + b*atan(c*x^2))/(d + e*x)^2,x)","\left(\sum _{k=1}^4\ln\left(\frac{{\mathrm{root}\left(16\,c^2\,d^4\,e^4\,z^4+16\,e^8\,z^4-32\,b\,c\,d\,e^5\,z^3+8\,b^2\,c^2\,d^2\,e^2\,z^2+b^4\,c^2,z,k\right)}^4\,c^8\,e^9\,x\,320-{\mathrm{root}\left(16\,c^2\,d^4\,e^4\,z^4+16\,e^8\,z^4-32\,b\,c\,d\,e^5\,z^3+8\,b^2\,c^2\,d^2\,e^2\,z^2+b^4\,c^2,z,k\right)}^4\,c^{10}\,d^5\,e^4\,128+16\,b^4\,c^{10}\,e\,x-\mathrm{root}\left(16\,c^2\,d^4\,e^4\,z^4+16\,e^8\,z^4-32\,b\,c\,d\,e^5\,z^3+8\,b^2\,c^2\,d^2\,e^2\,z^2+b^4\,c^2,z,k\right)\,b^3\,c^9\,e^3\,8+{\mathrm{root}\left(16\,c^2\,d^4\,e^4\,z^4+16\,e^8\,z^4-32\,b\,c\,d\,e^5\,z^3+8\,b^2\,c^2\,d^2\,e^2\,z^2+b^4\,c^2,z,k\right)}^4\,c^8\,d\,e^8\,384+\mathrm{root}\left(16\,c^2\,d^4\,e^4\,z^4+16\,e^8\,z^4-32\,b\,c\,d\,e^5\,z^3+8\,b^2\,c^2\,d^2\,e^2\,z^2+b^4\,c^2,z,k\right)\,b^3\,c^{11}\,d^3\,x\,8-{\mathrm{root}\left(16\,c^2\,d^4\,e^4\,z^4+16\,e^8\,z^4-32\,b\,c\,d\,e^5\,z^3+8\,b^2\,c^2\,d^2\,e^2\,z^2+b^4\,c^2,z,k\right)}^3\,b\,c^9\,d^2\,e^5\,320-{\mathrm{root}\left(16\,c^2\,d^4\,e^4\,z^4+16\,e^8\,z^4-32\,b\,c\,d\,e^5\,z^3+8\,b^2\,c^2\,d^2\,e^2\,z^2+b^4\,c^2,z,k\right)}^4\,c^{10}\,d^4\,e^5\,x\,192+{\mathrm{root}\left(16\,c^2\,d^4\,e^4\,z^4+16\,e^8\,z^4-32\,b\,c\,d\,e^5\,z^3+8\,b^2\,c^2\,d^2\,e^2\,z^2+b^4\,c^2,z,k\right)}^3\,b\,c^{11}\,d^5\,e^2\,x\,32+{\mathrm{root}\left(16\,c^2\,d^4\,e^4\,z^4+16\,e^8\,z^4-32\,b\,c\,d\,e^5\,z^3+8\,b^2\,c^2\,d^2\,e^2\,z^2+b^4\,c^2,z,k\right)}^2\,b^2\,c^{10}\,d^2\,e^3\,x\,64-{\mathrm{root}\left(16\,c^2\,d^4\,e^4\,z^4+16\,e^8\,z^4-32\,b\,c\,d\,e^5\,z^3+8\,b^2\,c^2\,d^2\,e^2\,z^2+b^4\,c^2,z,k\right)}^3\,b\,c^9\,d\,e^6\,x\,416}{e^2}\right)\,\mathrm{root}\left(16\,c^2\,d^4\,e^4\,z^4+16\,e^8\,z^4-32\,b\,c\,d\,e^5\,z^3+8\,b^2\,c^2\,d^2\,e^2\,z^2+b^4\,c^2,z,k\right)\right)-\frac{a}{x\,e^2+d\,e}-\frac{b\,\mathrm{atan}\left(c\,x^2\right)}{x\,e^2+d\,e}-\frac{2\,b\,c\,d\,e\,\ln\left(d+e\,x\right)}{c^2\,d^4+e^4}","Not used",1,"symsum(log((320*root(16*c^2*d^4*e^4*z^4 + 16*e^8*z^4 - 32*b*c*d*e^5*z^3 + 8*b^2*c^2*d^2*e^2*z^2 + b^4*c^2, z, k)^4*c^8*e^9*x - 128*root(16*c^2*d^4*e^4*z^4 + 16*e^8*z^4 - 32*b*c*d*e^5*z^3 + 8*b^2*c^2*d^2*e^2*z^2 + b^4*c^2, z, k)^4*c^10*d^5*e^4 + 16*b^4*c^10*e*x - 8*root(16*c^2*d^4*e^4*z^4 + 16*e^8*z^4 - 32*b*c*d*e^5*z^3 + 8*b^2*c^2*d^2*e^2*z^2 + b^4*c^2, z, k)*b^3*c^9*e^3 + 384*root(16*c^2*d^4*e^4*z^4 + 16*e^8*z^4 - 32*b*c*d*e^5*z^3 + 8*b^2*c^2*d^2*e^2*z^2 + b^4*c^2, z, k)^4*c^8*d*e^8 + 8*root(16*c^2*d^4*e^4*z^4 + 16*e^8*z^4 - 32*b*c*d*e^5*z^3 + 8*b^2*c^2*d^2*e^2*z^2 + b^4*c^2, z, k)*b^3*c^11*d^3*x - 320*root(16*c^2*d^4*e^4*z^4 + 16*e^8*z^4 - 32*b*c*d*e^5*z^3 + 8*b^2*c^2*d^2*e^2*z^2 + b^4*c^2, z, k)^3*b*c^9*d^2*e^5 - 192*root(16*c^2*d^4*e^4*z^4 + 16*e^8*z^4 - 32*b*c*d*e^5*z^3 + 8*b^2*c^2*d^2*e^2*z^2 + b^4*c^2, z, k)^4*c^10*d^4*e^5*x + 32*root(16*c^2*d^4*e^4*z^4 + 16*e^8*z^4 - 32*b*c*d*e^5*z^3 + 8*b^2*c^2*d^2*e^2*z^2 + b^4*c^2, z, k)^3*b*c^11*d^5*e^2*x + 64*root(16*c^2*d^4*e^4*z^4 + 16*e^8*z^4 - 32*b*c*d*e^5*z^3 + 8*b^2*c^2*d^2*e^2*z^2 + b^4*c^2, z, k)^2*b^2*c^10*d^2*e^3*x - 416*root(16*c^2*d^4*e^4*z^4 + 16*e^8*z^4 - 32*b*c*d*e^5*z^3 + 8*b^2*c^2*d^2*e^2*z^2 + b^4*c^2, z, k)^3*b*c^9*d*e^6*x)/e^2)*root(16*c^2*d^4*e^4*z^4 + 16*e^8*z^4 - 32*b*c*d*e^5*z^3 + 8*b^2*c^2*d^2*e^2*z^2 + b^4*c^2, z, k), k, 1, 4) - a/(d*e + e^2*x) - (b*atan(c*x^2))/(d*e + e^2*x) - (2*b*c*d*e*log(d + e*x))/(e^4 + c^2*d^4)","B"
25,0,-1,1325,0.000000,"\text{Not used}","int((a + b*atan(c*x^2))^2*(d + e*x),x)","\int {\left(a+b\,\mathrm{atan}\left(c\,x^2\right)\right)}^2\,\left(d+e\,x\right) \,d x","Not used",1,"int((a + b*atan(c*x^2))^2*(d + e*x), x)","F"
26,0,-1,23,0.000000,"\text{Not used}","int((a + b*atan(c*x^2))^2/(d + e*x),x)","\int \frac{{\left(a+b\,\mathrm{atan}\left(c\,x^2\right)\right)}^2}{d+e\,x} \,d x","Not used",0,"int((a + b*atan(c*x^2))^2/(d + e*x), x)","F"
27,0,-1,23,0.000000,"\text{Not used}","int((a + b*atan(c*x^2))^2/(d + e*x)^2,x)","\int \frac{{\left(a+b\,\mathrm{atan}\left(c\,x^2\right)\right)}^2}{{\left(d+e\,x\right)}^2} \,d x","Not used",0,"int((a + b*atan(c*x^2))^2/(d + e*x)^2, x)","F"
28,1,988,315,0.516692,"\text{Not used}","int((a + b*atan(c*x^3))*(d + e*x)^2,x)","\mathrm{atan}\left(c\,x^3\right)\,\left(b\,d^2\,x+b\,d\,e\,x^2+\frac{b\,e^2\,x^3}{3}\right)+\left(\sum _{k=1}^6\ln\left(x\,\left(6\,b^5\,c^7\,d^2\,e^8-162\,b^5\,c^9\,d^8\,e^2\right)+\mathrm{root}\left(46656\,a^6\,c^6+46656\,a^5\,b\,c^5\,e^2+19440\,a^4\,b^2\,c^4\,e^4+4320\,a^3\,b^3\,c^3\,e^6-11664\,a^3\,b^3\,c^5\,d^6+20412\,a^2\,b^4\,c^4\,d^6\,e^2+540\,a^2\,b^4\,c^2\,e^8-972\,a\,b^5\,c^3\,d^6\,e^4+36\,a\,b^5\,c\,e^{10}-54\,b^6\,c^2\,d^6\,e^6+729\,b^6\,c^4\,d^{12}+b^6\,e^{12},a,k\right)\,\left(x\,\left(486\,b^4\,c^{10}\,d^8+90\,b^4\,c^8\,d^2\,e^6\right)-\mathrm{root}\left(46656\,a^6\,c^6+46656\,a^5\,b\,c^5\,e^2+19440\,a^4\,b^2\,c^4\,e^4+4320\,a^3\,b^3\,c^3\,e^6-11664\,a^3\,b^3\,c^5\,d^6+20412\,a^2\,b^4\,c^4\,d^6\,e^2+540\,a^2\,b^4\,c^2\,e^8-972\,a\,b^5\,c^3\,d^6\,e^4+36\,a\,b^5\,c\,e^{10}-54\,b^6\,c^2\,d^6\,e^6+729\,b^6\,c^4\,d^{12}+b^6\,e^{12},a,k\right)\,\left(\mathrm{root}\left(46656\,a^6\,c^6+46656\,a^5\,b\,c^5\,e^2+19440\,a^4\,b^2\,c^4\,e^4+4320\,a^3\,b^3\,c^3\,e^6-11664\,a^3\,b^3\,c^5\,d^6+20412\,a^2\,b^4\,c^4\,d^6\,e^2+540\,a^2\,b^4\,c^2\,e^8-972\,a\,b^5\,c^3\,d^6\,e^4+36\,a\,b^5\,c\,e^{10}-54\,b^6\,c^2\,d^6\,e^6+729\,b^6\,c^4\,d^{12}+b^6\,e^{12},a,k\right)\,\left(3888\,b^2\,c^{10}\,d^3\,e+\mathrm{root}\left(46656\,a^6\,c^6+46656\,a^5\,b\,c^5\,e^2+19440\,a^4\,b^2\,c^4\,e^4+4320\,a^3\,b^3\,c^3\,e^6-11664\,a^3\,b^3\,c^5\,d^6+20412\,a^2\,b^4\,c^4\,d^6\,e^2+540\,a^2\,b^4\,c^2\,e^8-972\,a\,b^5\,c^3\,d^6\,e^4+36\,a\,b^5\,c\,e^{10}-54\,b^6\,c^2\,d^6\,e^6+729\,b^6\,c^4\,d^{12}+b^6\,e^{12},a,k\right)\,b\,c^{11}\,d^2\,x\,3888+648\,b^2\,c^{10}\,d^2\,e^2\,x\right)+972\,b^3\,c^9\,d^3\,e^3-324\,b^3\,c^9\,d^2\,e^4\,x\right)\right)-243\,b^5\,c^9\,d^9\,e+9\,b^5\,c^7\,d^3\,e^7\right)\,\mathrm{root}\left(46656\,a^6\,c^6+46656\,a^5\,b\,c^5\,e^2+19440\,a^4\,b^2\,c^4\,e^4+4320\,a^3\,b^3\,c^3\,e^6-11664\,a^3\,b^3\,c^5\,d^6+20412\,a^2\,b^4\,c^4\,d^6\,e^2+540\,a^2\,b^4\,c^2\,e^8-972\,a\,b^5\,c^3\,d^6\,e^4+36\,a\,b^5\,c\,e^{10}-54\,b^6\,c^2\,d^6\,e^6+729\,b^6\,c^4\,d^{12}+b^6\,e^{12},a,k\right)\right)+\frac{a\,e^2\,x^3}{3}+a\,d^2\,x+a\,d\,e\,x^2","Not used",1,"atan(c*x^3)*((b*e^2*x^3)/3 + b*d^2*x + b*d*e*x^2) + symsum(log(x*(6*b^5*c^7*d^2*e^8 - 162*b^5*c^9*d^8*e^2) + root(46656*a^6*c^6 + 46656*a^5*b*c^5*e^2 + 19440*a^4*b^2*c^4*e^4 + 4320*a^3*b^3*c^3*e^6 - 11664*a^3*b^3*c^5*d^6 + 20412*a^2*b^4*c^4*d^6*e^2 + 540*a^2*b^4*c^2*e^8 - 972*a*b^5*c^3*d^6*e^4 + 36*a*b^5*c*e^10 - 54*b^6*c^2*d^6*e^6 + 729*b^6*c^4*d^12 + b^6*e^12, a, k)*(x*(486*b^4*c^10*d^8 + 90*b^4*c^8*d^2*e^6) - root(46656*a^6*c^6 + 46656*a^5*b*c^5*e^2 + 19440*a^4*b^2*c^4*e^4 + 4320*a^3*b^3*c^3*e^6 - 11664*a^3*b^3*c^5*d^6 + 20412*a^2*b^4*c^4*d^6*e^2 + 540*a^2*b^4*c^2*e^8 - 972*a*b^5*c^3*d^6*e^4 + 36*a*b^5*c*e^10 - 54*b^6*c^2*d^6*e^6 + 729*b^6*c^4*d^12 + b^6*e^12, a, k)*(root(46656*a^6*c^6 + 46656*a^5*b*c^5*e^2 + 19440*a^4*b^2*c^4*e^4 + 4320*a^3*b^3*c^3*e^6 - 11664*a^3*b^3*c^5*d^6 + 20412*a^2*b^4*c^4*d^6*e^2 + 540*a^2*b^4*c^2*e^8 - 972*a*b^5*c^3*d^6*e^4 + 36*a*b^5*c*e^10 - 54*b^6*c^2*d^6*e^6 + 729*b^6*c^4*d^12 + b^6*e^12, a, k)*(3888*b^2*c^10*d^3*e + 3888*root(46656*a^6*c^6 + 46656*a^5*b*c^5*e^2 + 19440*a^4*b^2*c^4*e^4 + 4320*a^3*b^3*c^3*e^6 - 11664*a^3*b^3*c^5*d^6 + 20412*a^2*b^4*c^4*d^6*e^2 + 540*a^2*b^4*c^2*e^8 - 972*a*b^5*c^3*d^6*e^4 + 36*a*b^5*c*e^10 - 54*b^6*c^2*d^6*e^6 + 729*b^6*c^4*d^12 + b^6*e^12, a, k)*b*c^11*d^2*x + 648*b^2*c^10*d^2*e^2*x) + 972*b^3*c^9*d^3*e^3 - 324*b^3*c^9*d^2*e^4*x)) - 243*b^5*c^9*d^9*e + 9*b^5*c^7*d^3*e^7)*root(46656*a^6*c^6 + 46656*a^5*b*c^5*e^2 + 19440*a^4*b^2*c^4*e^4 + 4320*a^3*b^3*c^3*e^6 - 11664*a^3*b^3*c^5*d^6 + 20412*a^2*b^4*c^4*d^6*e^2 + 540*a^2*b^4*c^2*e^8 - 972*a*b^5*c^3*d^6*e^4 + 36*a*b^5*c*e^10 - 54*b^6*c^2*d^6*e^6 + 729*b^6*c^4*d^12 + b^6*e^12, a, k), k, 1, 6) + (a*e^2*x^3)/3 + a*d^2*x + a*d*e*x^2","B"
29,1,485,285,0.436167,"\text{Not used}","int((a + b*atan(c*x^3))*(d + e*x),x)","\mathrm{atan}\left(c\,x^3\right)\,\left(\frac{b\,e\,x^2}{2}+b\,d\,x\right)+\left(\sum _{k=1}^6\ln\left(-\mathrm{root}\left(4096\,a^6\,c^4-1024\,a^3\,b^3\,c^3\,d^3+576\,a^2\,b^4\,c^2\,d^2\,e^2-48\,a\,b^5\,c\,d\,e^4+64\,b^6\,c^2\,d^6+b^6\,e^6,a,k\right)\,\left(\mathrm{root}\left(4096\,a^6\,c^4-1024\,a^3\,b^3\,c^3\,d^3+576\,a^2\,b^4\,c^2\,d^2\,e^2-48\,a\,b^5\,c\,d\,e^4+64\,b^6\,c^2\,d^6+b^6\,e^6,a,k\right)\,\left(\mathrm{root}\left(4096\,a^6\,c^4-1024\,a^3\,b^3\,c^3\,d^3+576\,a^2\,b^4\,c^2\,d^2\,e^2-48\,a\,b^5\,c\,d\,e^4+64\,b^6\,c^2\,d^6+b^6\,e^6,a,k\right)\,\left(-486\,b^2\,c^{10}\,e^2\,x+1944\,b^2\,c^{10}\,d\,e+\mathrm{root}\left(4096\,a^6\,c^4-1024\,a^3\,b^3\,c^3\,d^3+576\,a^2\,b^4\,c^2\,d^2\,e^2-48\,a\,b^5\,c\,d\,e^4+64\,b^6\,c^2\,d^6+b^6\,e^6,a,k\right)\,b\,c^{11}\,d\,x\,3888\right)-\frac{243\,b^3\,c^9\,e^3}{2}\right)-486\,b^4\,c^{10}\,d^4\,x\right)-\frac{243\,b^5\,c^9\,d^4\,e}{2}-\frac{243\,b^5\,c^9\,d^3\,e^2\,x}{4}\right)\,\mathrm{root}\left(4096\,a^6\,c^4-1024\,a^3\,b^3\,c^3\,d^3+576\,a^2\,b^4\,c^2\,d^2\,e^2-48\,a\,b^5\,c\,d\,e^4+64\,b^6\,c^2\,d^6+b^6\,e^6,a,k\right)\right)+a\,d\,x+\frac{a\,e\,x^2}{2}","Not used",1,"atan(c*x^3)*(b*d*x + (b*e*x^2)/2) + symsum(log(- root(4096*a^6*c^4 - 1024*a^3*b^3*c^3*d^3 + 576*a^2*b^4*c^2*d^2*e^2 - 48*a*b^5*c*d*e^4 + 64*b^6*c^2*d^6 + b^6*e^6, a, k)*(root(4096*a^6*c^4 - 1024*a^3*b^3*c^3*d^3 + 576*a^2*b^4*c^2*d^2*e^2 - 48*a*b^5*c*d*e^4 + 64*b^6*c^2*d^6 + b^6*e^6, a, k)*(root(4096*a^6*c^4 - 1024*a^3*b^3*c^3*d^3 + 576*a^2*b^4*c^2*d^2*e^2 - 48*a*b^5*c*d*e^4 + 64*b^6*c^2*d^6 + b^6*e^6, a, k)*(1944*b^2*c^10*d*e - 486*b^2*c^10*e^2*x + 3888*root(4096*a^6*c^4 - 1024*a^3*b^3*c^3*d^3 + 576*a^2*b^4*c^2*d^2*e^2 - 48*a*b^5*c*d*e^4 + 64*b^6*c^2*d^6 + b^6*e^6, a, k)*b*c^11*d*x) - (243*b^3*c^9*e^3)/2) - 486*b^4*c^10*d^4*x) - (243*b^5*c^9*d^4*e)/2 - (243*b^5*c^9*d^3*e^2*x)/4)*root(4096*a^6*c^4 - 1024*a^3*b^3*c^3*d^3 + 576*a^2*b^4*c^2*d^2*e^2 - 48*a*b^5*c*d*e^4 + 64*b^6*c^2*d^6 + b^6*e^6, a, k), k, 1, 6) + a*d*x + (a*e*x^2)/2","B"
30,0,-1,739,0.000000,"\text{Not used}","int((a + b*atan(c*x^3))/(d + e*x),x)","\int \frac{a+b\,\mathrm{atan}\left(c\,x^3\right)}{d+e\,x} \,d x","Not used",1,"int((a + b*atan(c*x^3))/(d + e*x), x)","F"
31,1,2105,906,0.775778,"\text{Not used}","int((a + b*atan(c*x^3))/(d + e*x)^2,x)","\left(\sum _{k=1}^6\ln\left(\frac{729\,b^6\,c^{14}\,d\,e^2+{\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)}^6\,c^{12}\,e^{15}\,x\,54432+729\,b^6\,c^{14}\,e^3\,x-{\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)}^6\,c^{14}\,d^7\,e^8\,31104-\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)\,b^5\,c^{15}\,d^5\,243+{\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)}^6\,c^{12}\,d\,e^{14}\,62208+{\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)}^2\,b^4\,c^{14}\,d^3\,e^4\,5832-{\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)}^3\,b^3\,c^{15}\,d^7\,e^2\,1944+{\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)}^4\,b^2\,c^{14}\,d^5\,e^6\,15552-{\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)}^3\,b^3\,c^{13}\,d\,e^8\,10692+{\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)}^5\,b\,c^{13}\,d^3\,e^{10}\,101088-{\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)}^5\,b\,c^{15}\,d^9\,e^4\,3888-{\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)}^3\,b^3\,c^{13}\,e^9\,x\,12636-{\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)}^6\,c^{14}\,d^6\,e^9\,x\,38880+{\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)}^5\,b\,c^{13}\,d^2\,e^{11}\,x\,116640-{\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)}^5\,b\,c^{15}\,d^8\,e^5\,x\,11664+{\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)}^2\,b^4\,c^{14}\,d^2\,e^5\,x\,11664-{\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)}^3\,b^3\,c^{15}\,d^6\,e^3\,x\,3888+{\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)}^4\,b^2\,c^{14}\,d^4\,e^7\,x\,38880-\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)\,b^5\,c^{15}\,d^4\,e\,x\,243}{e^4}\right)\,\mathrm{root}\left(64\,c^2\,d^6\,e^6\,z^6+64\,e^{12}\,z^6+192\,b\,c\,d^2\,e^8\,z^5+48\,b^2\,c^2\,d^4\,e^4\,z^4-16\,b^3\,c\,e^6\,z^3+12\,b^4\,c^2\,d^2\,e^2\,z^2+b^6\,c^2,z,k\right)\right)-\frac{a}{x\,e^2+d\,e}-\frac{b\,\mathrm{atan}\left(c\,x^3\right)}{x\,e^2+d\,e}+\frac{3\,b\,c\,d^2\,e^2\,\ln\left(d+e\,x\right)}{c^2\,d^6+e^6}","Not used",1,"symsum(log((729*b^6*c^14*d*e^2 + 54432*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)^6*c^12*e^15*x + 729*b^6*c^14*e^3*x - 31104*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)^6*c^14*d^7*e^8 - 243*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)*b^5*c^15*d^5 + 62208*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)^6*c^12*d*e^14 + 5832*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)^2*b^4*c^14*d^3*e^4 - 1944*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)^3*b^3*c^15*d^7*e^2 + 15552*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)^4*b^2*c^14*d^5*e^6 - 10692*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)^3*b^3*c^13*d*e^8 + 101088*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)^5*b*c^13*d^3*e^10 - 3888*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)^5*b*c^15*d^9*e^4 - 12636*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)^3*b^3*c^13*e^9*x - 38880*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)^6*c^14*d^6*e^9*x + 116640*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)^5*b*c^13*d^2*e^11*x - 11664*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)^5*b*c^15*d^8*e^5*x + 11664*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)^2*b^4*c^14*d^2*e^5*x - 3888*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)^3*b^3*c^15*d^6*e^3*x + 38880*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)^4*b^2*c^14*d^4*e^7*x - 243*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k)*b^5*c^15*d^4*e*x)/e^4)*root(64*c^2*d^6*e^6*z^6 + 64*e^12*z^6 + 192*b*c*d^2*e^8*z^5 + 48*b^2*c^2*d^4*e^4*z^4 - 16*b^3*c*e^6*z^3 + 12*b^4*c^2*d^2*e^2*z^2 + b^6*c^2, z, k), k, 1, 6) - a/(d*e + e^2*x) - (b*atan(c*x^3))/(d*e + e^2*x) + (3*b*c*d^2*e^2*log(d + e*x))/(e^6 + c^2*d^6)","B"