1,1,264,0,0.482360," ","integrate((e*x+d)^4*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{12 \, a c^{5} e^{4} x^{5} + 3 \, {\left(20 \, a c^{5} d e^{3} - b c^{4} e^{4}\right)} x^{4} + 20 \, {\left(6 \, a c^{5} d^{2} e^{2} - b c^{4} d e^{3}\right)} x^{3} + 6 \, {\left(20 \, a c^{5} d^{3} e - 10 \, b c^{4} d^{2} e^{2} + b c^{2} e^{4}\right)} x^{2} + 60 \, {\left(a c^{5} d^{4} - 2 \, b c^{4} d^{3} e + b c^{2} d e^{3}\right)} x + 12 \, {\left(b c^{5} e^{4} x^{5} + 5 \, b c^{5} d e^{3} x^{4} + 10 \, b c^{5} d^{2} e^{2} x^{3} + 10 \, b c^{5} d^{3} e x^{2} + 5 \, b c^{5} d^{4} x + 10 \, b c^{3} d^{3} e - 5 \, b c d e^{3}\right)} \arctan\left(c x\right) - 6 \, {\left(5 \, b c^{4} d^{4} - 10 \, b c^{2} d^{2} e^{2} + b e^{4}\right)} \log\left(c^{2} x^{2} + 1\right)}{60 \, c^{5}}"," ",0,"1/60*(12*a*c^5*e^4*x^5 + 3*(20*a*c^5*d*e^3 - b*c^4*e^4)*x^4 + 20*(6*a*c^5*d^2*e^2 - b*c^4*d*e^3)*x^3 + 6*(20*a*c^5*d^3*e - 10*b*c^4*d^2*e^2 + b*c^2*e^4)*x^2 + 60*(a*c^5*d^4 - 2*b*c^4*d^3*e + b*c^2*d*e^3)*x + 12*(b*c^5*e^4*x^5 + 5*b*c^5*d*e^3*x^4 + 10*b*c^5*d^2*e^2*x^3 + 10*b*c^5*d^3*e*x^2 + 5*b*c^5*d^4*x + 10*b*c^3*d^3*e - 5*b*c*d*e^3)*arctan(c*x) - 6*(5*b*c^4*d^4 - 10*b*c^2*d^2*e^2 + b*e^4)*log(c^2*x^2 + 1))/c^5","A",0
2,1,196,0,0.919584," ","integrate((e*x+d)^3*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{3 \, a c^{4} e^{3} x^{4} + {\left(12 \, a c^{4} d e^{2} - b c^{3} e^{3}\right)} x^{3} + 6 \, {\left(3 \, a c^{4} d^{2} e - b c^{3} d e^{2}\right)} x^{2} + 3 \, {\left(4 \, a c^{4} d^{3} - 6 \, b c^{3} d^{2} e + b c e^{3}\right)} x + 3 \, {\left(b c^{4} e^{3} x^{4} + 4 \, b c^{4} d e^{2} x^{3} + 6 \, b c^{4} d^{2} e x^{2} + 4 \, b c^{4} d^{3} x + 6 \, b c^{2} d^{2} e - b e^{3}\right)} \arctan\left(c x\right) - 6 \, {\left(b c^{3} d^{3} - b c d e^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{12 \, c^{4}}"," ",0,"1/12*(3*a*c^4*e^3*x^4 + (12*a*c^4*d*e^2 - b*c^3*e^3)*x^3 + 6*(3*a*c^4*d^2*e - b*c^3*d*e^2)*x^2 + 3*(4*a*c^4*d^3 - 6*b*c^3*d^2*e + b*c*e^3)*x + 3*(b*c^4*e^3*x^4 + 4*b*c^4*d*e^2*x^3 + 6*b*c^4*d^2*e*x^2 + 4*b*c^4*d^3*x + 6*b*c^2*d^2*e - b*e^3)*arctan(c*x) - 6*(b*c^3*d^3 - b*c*d*e^2)*log(c^2*x^2 + 1))/c^4","A",0
3,1,133,0,3.000239," ","integrate((e*x+d)^2*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{2 \, a c^{3} e^{2} x^{3} + {\left(6 \, a c^{3} d e - b c^{2} e^{2}\right)} x^{2} + 6 \, {\left(a c^{3} d^{2} - b c^{2} d e\right)} x + 2 \, {\left(b c^{3} e^{2} x^{3} + 3 \, b c^{3} d e x^{2} + 3 \, b c^{3} d^{2} x + 3 \, b c d e\right)} \arctan\left(c x\right) - {\left(3 \, b c^{2} d^{2} - b e^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{6 \, c^{3}}"," ",0,"1/6*(2*a*c^3*e^2*x^3 + (6*a*c^3*d*e - b*c^2*e^2)*x^2 + 6*(a*c^3*d^2 - b*c^2*d*e)*x + 2*(b*c^3*e^2*x^3 + 3*b*c^3*d*e*x^2 + 3*b*c^3*d^2*x + 3*b*c*d*e)*arctan(c*x) - (3*b*c^2*d^2 - b*e^2)*log(c^2*x^2 + 1))/c^3","A",0
4,1,71,0,1.419296," ","integrate((e*x+d)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{a c^{2} e x^{2} - b c d \log\left(c^{2} x^{2} + 1\right) + {\left(2 \, a c^{2} d - b c e\right)} x + {\left(b c^{2} e x^{2} + 2 \, b c^{2} d x + b e\right)} \arctan\left(c x\right)}{2 \, c^{2}}"," ",0,"1/2*(a*c^2*e*x^2 - b*c*d*log(c^2*x^2 + 1) + (2*a*c^2*d - b*c*e)*x + (b*c^2*e*x^2 + 2*b*c^2*d*x + b*e)*arctan(c*x))/c^2","A",0
5,0,0,0,0.741698," ","integrate((a+b*arctan(c*x))/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e x + d}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e*x + d), x)","F",0
6,1,116,0,0.526979," ","integrate((a+b*arctan(c*x))/(e*x+d)^2,x, algorithm=""fricas"")","-\frac{2 \, a c^{2} d^{2} + 2 \, a e^{2} - 2 \, {\left(b c^{2} d e x - b e^{2}\right)} \arctan\left(c x\right) + {\left(b c e^{2} x + b c d e\right)} \log\left(c^{2} x^{2} + 1\right) - 2 \, {\left(b c e^{2} x + b c d e\right)} \log\left(e x + d\right)}{2 \, {\left(c^{2} d^{3} e + d e^{3} + {\left(c^{2} d^{2} e^{2} + e^{4}\right)} x\right)}}"," ",0,"-1/2*(2*a*c^2*d^2 + 2*a*e^2 - 2*(b*c^2*d*e*x - b*e^2)*arctan(c*x) + (b*c*e^2*x + b*c*d*e)*log(c^2*x^2 + 1) - 2*(b*c*e^2*x + b*c*d*e)*log(e*x + d))/(c^2*d^3*e + d*e^3 + (c^2*d^2*e^2 + e^4)*x)","A",0
7,1,313,0,0.690075," ","integrate((a+b*arctan(c*x))/(e*x+d)^3,x, algorithm=""fricas"")","-\frac{a c^{4} d^{4} + b c^{3} d^{3} e + 2 \, a c^{2} d^{2} e^{2} + b c d e^{3} + a e^{4} + {\left(b c^{3} d^{2} e^{2} + b c e^{4}\right)} x + {\left(3 \, b c^{2} d^{2} e^{2} + b e^{4} - {\left(b c^{4} d^{2} e^{2} - b c^{2} e^{4}\right)} x^{2} - 2 \, {\left(b c^{4} d^{3} e - b c^{2} d e^{3}\right)} x\right)} \arctan\left(c x\right) + {\left(b c^{3} d e^{3} x^{2} + 2 \, b c^{3} d^{2} e^{2} x + b c^{3} d^{3} e\right)} \log\left(c^{2} x^{2} + 1\right) - 2 \, {\left(b c^{3} d e^{3} x^{2} + 2 \, b c^{3} d^{2} e^{2} x + b c^{3} d^{3} e\right)} \log\left(e x + d\right)}{2 \, {\left(c^{4} d^{6} e + 2 \, c^{2} d^{4} e^{3} + d^{2} e^{5} + {\left(c^{4} d^{4} e^{3} + 2 \, c^{2} d^{2} e^{5} + e^{7}\right)} x^{2} + 2 \, {\left(c^{4} d^{5} e^{2} + 2 \, c^{2} d^{3} e^{4} + d e^{6}\right)} x\right)}}"," ",0,"-1/2*(a*c^4*d^4 + b*c^3*d^3*e + 2*a*c^2*d^2*e^2 + b*c*d*e^3 + a*e^4 + (b*c^3*d^2*e^2 + b*c*e^4)*x + (3*b*c^2*d^2*e^2 + b*e^4 - (b*c^4*d^2*e^2 - b*c^2*e^4)*x^2 - 2*(b*c^4*d^3*e - b*c^2*d*e^3)*x)*arctan(c*x) + (b*c^3*d*e^3*x^2 + 2*b*c^3*d^2*e^2*x + b*c^3*d^3*e)*log(c^2*x^2 + 1) - 2*(b*c^3*d*e^3*x^2 + 2*b*c^3*d^2*e^2*x + b*c^3*d^3*e)*log(e*x + d))/(c^4*d^6*e + 2*c^2*d^4*e^3 + d^2*e^5 + (c^4*d^4*e^3 + 2*c^2*d^2*e^5 + e^7)*x^2 + 2*(c^4*d^5*e^2 + 2*c^2*d^3*e^4 + d*e^6)*x)","B",0
8,1,642,0,1.868134," ","integrate((a+b*arctan(c*x))/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{2 \, a c^{6} d^{6} + 5 \, b c^{5} d^{5} e + 6 \, a c^{4} d^{4} e^{2} + 6 \, b c^{3} d^{3} e^{3} + 6 \, a c^{2} d^{2} e^{4} + b c d e^{5} + 2 \, a e^{6} + 4 \, {\left(b c^{5} d^{3} e^{3} + b c^{3} d e^{5}\right)} x^{2} + {\left(9 \, b c^{5} d^{4} e^{2} + 10 \, b c^{3} d^{2} e^{4} + b c e^{6}\right)} x + 2 \, {\left(6 \, b c^{4} d^{4} e^{2} + 3 \, b c^{2} d^{2} e^{4} + b e^{6} - {\left(b c^{6} d^{3} e^{3} - 3 \, b c^{4} d e^{5}\right)} x^{3} - 3 \, {\left(b c^{6} d^{4} e^{2} - 3 \, b c^{4} d^{2} e^{4}\right)} x^{2} - 3 \, {\left(b c^{6} d^{5} e - 3 \, b c^{4} d^{3} e^{3}\right)} x\right)} \arctan\left(c x\right) + {\left(3 \, b c^{5} d^{5} e - b c^{3} d^{3} e^{3} + {\left(3 \, b c^{5} d^{2} e^{4} - b c^{3} e^{6}\right)} x^{3} + 3 \, {\left(3 \, b c^{5} d^{3} e^{3} - b c^{3} d e^{5}\right)} x^{2} + 3 \, {\left(3 \, b c^{5} d^{4} e^{2} - b c^{3} d^{2} e^{4}\right)} x\right)} \log\left(c^{2} x^{2} + 1\right) - 2 \, {\left(3 \, b c^{5} d^{5} e - b c^{3} d^{3} e^{3} + {\left(3 \, b c^{5} d^{2} e^{4} - b c^{3} e^{6}\right)} x^{3} + 3 \, {\left(3 \, b c^{5} d^{3} e^{3} - b c^{3} d e^{5}\right)} x^{2} + 3 \, {\left(3 \, b c^{5} d^{4} e^{2} - b c^{3} d^{2} e^{4}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(c^{6} d^{9} e + 3 \, c^{4} d^{7} e^{3} + 3 \, c^{2} d^{5} e^{5} + d^{3} e^{7} + {\left(c^{6} d^{6} e^{4} + 3 \, c^{4} d^{4} e^{6} + 3 \, c^{2} d^{2} e^{8} + e^{10}\right)} x^{3} + 3 \, {\left(c^{6} d^{7} e^{3} + 3 \, c^{4} d^{5} e^{5} + 3 \, c^{2} d^{3} e^{7} + d e^{9}\right)} x^{2} + 3 \, {\left(c^{6} d^{8} e^{2} + 3 \, c^{4} d^{6} e^{4} + 3 \, c^{2} d^{4} e^{6} + d^{2} e^{8}\right)} x\right)}}"," ",0,"-1/6*(2*a*c^6*d^6 + 5*b*c^5*d^5*e + 6*a*c^4*d^4*e^2 + 6*b*c^3*d^3*e^3 + 6*a*c^2*d^2*e^4 + b*c*d*e^5 + 2*a*e^6 + 4*(b*c^5*d^3*e^3 + b*c^3*d*e^5)*x^2 + (9*b*c^5*d^4*e^2 + 10*b*c^3*d^2*e^4 + b*c*e^6)*x + 2*(6*b*c^4*d^4*e^2 + 3*b*c^2*d^2*e^4 + b*e^6 - (b*c^6*d^3*e^3 - 3*b*c^4*d*e^5)*x^3 - 3*(b*c^6*d^4*e^2 - 3*b*c^4*d^2*e^4)*x^2 - 3*(b*c^6*d^5*e - 3*b*c^4*d^3*e^3)*x)*arctan(c*x) + (3*b*c^5*d^5*e - b*c^3*d^3*e^3 + (3*b*c^5*d^2*e^4 - b*c^3*e^6)*x^3 + 3*(3*b*c^5*d^3*e^3 - b*c^3*d*e^5)*x^2 + 3*(3*b*c^5*d^4*e^2 - b*c^3*d^2*e^4)*x)*log(c^2*x^2 + 1) - 2*(3*b*c^5*d^5*e - b*c^3*d^3*e^3 + (3*b*c^5*d^2*e^4 - b*c^3*e^6)*x^3 + 3*(3*b*c^5*d^3*e^3 - b*c^3*d*e^5)*x^2 + 3*(3*b*c^5*d^4*e^2 - b*c^3*d^2*e^4)*x)*log(e*x + d))/(c^6*d^9*e + 3*c^4*d^7*e^3 + 3*c^2*d^5*e^5 + d^3*e^7 + (c^6*d^6*e^4 + 3*c^4*d^4*e^6 + 3*c^2*d^2*e^8 + e^10)*x^3 + 3*(c^6*d^7*e^3 + 3*c^4*d^5*e^5 + 3*c^2*d^3*e^7 + d*e^9)*x^2 + 3*(c^6*d^8*e^2 + 3*c^4*d^6*e^4 + 3*c^2*d^4*e^6 + d^2*e^8)*x)","B",0
9,0,0,0,0.538052," ","integrate((e*x+d)^3*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} e^{3} x^{3} + 3 \, a^{2} d e^{2} x^{2} + 3 \, a^{2} d^{2} e x + a^{2} d^{3} + {\left(b^{2} e^{3} x^{3} + 3 \, b^{2} d e^{2} x^{2} + 3 \, b^{2} d^{2} e x + b^{2} d^{3}\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(a b e^{3} x^{3} + 3 \, a b d e^{2} x^{2} + 3 \, a b d^{2} e x + a b d^{3}\right)} \arctan\left(c x\right), x\right)"," ",0,"integral(a^2*e^3*x^3 + 3*a^2*d*e^2*x^2 + 3*a^2*d^2*e*x + a^2*d^3 + (b^2*e^3*x^3 + 3*b^2*d*e^2*x^2 + 3*b^2*d^2*e*x + b^2*d^3)*arctan(c*x)^2 + 2*(a*b*e^3*x^3 + 3*a*b*d*e^2*x^2 + 3*a*b*d^2*e*x + a*b*d^3)*arctan(c*x), x)","F",0
10,0,0,0,0.955727," ","integrate((e*x+d)^2*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} e^{2} x^{2} + 2 \, a^{2} d e x + a^{2} d^{2} + {\left(b^{2} e^{2} x^{2} + 2 \, b^{2} d e x + b^{2} d^{2}\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(a b e^{2} x^{2} + 2 \, a b d e x + a b d^{2}\right)} \arctan\left(c x\right), x\right)"," ",0,"integral(a^2*e^2*x^2 + 2*a^2*d*e*x + a^2*d^2 + (b^2*e^2*x^2 + 2*b^2*d*e*x + b^2*d^2)*arctan(c*x)^2 + 2*(a*b*e^2*x^2 + 2*a*b*d*e*x + a*b*d^2)*arctan(c*x), x)","F",0
11,0,0,0,1.352047," ","integrate((e*x+d)*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} e x + a^{2} d + {\left(b^{2} e x + b^{2} d\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(a b e x + a b d\right)} \arctan\left(c x\right), x\right)"," ",0,"integral(a^2*e*x + a^2*d + (b^2*e*x + b^2*d)*arctan(c*x)^2 + 2*(a*b*e*x + a*b*d)*arctan(c*x), x)","F",0
12,0,0,0,0.661418," ","integrate((a+b*arctan(c*x))^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{e x + d}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/(e*x + d), x)","F",0
13,0,0,0,1.097351," ","integrate((a+b*arctan(c*x))^2/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
14,0,0,0,1.294928," ","integrate((a+b*arctan(c*x))^2/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
15,0,0,0,0.639296," ","integrate((e*x+d)^3*(a+b*arctan(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(a^{3} e^{3} x^{3} + 3 \, a^{3} d e^{2} x^{2} + 3 \, a^{3} d^{2} e x + a^{3} d^{3} + {\left(b^{3} e^{3} x^{3} + 3 \, b^{3} d e^{2} x^{2} + 3 \, b^{3} d^{2} e x + b^{3} d^{3}\right)} \arctan\left(c x\right)^{3} + 3 \, {\left(a b^{2} e^{3} x^{3} + 3 \, a b^{2} d e^{2} x^{2} + 3 \, a b^{2} d^{2} e x + a b^{2} d^{3}\right)} \arctan\left(c x\right)^{2} + 3 \, {\left(a^{2} b e^{3} x^{3} + 3 \, a^{2} b d e^{2} x^{2} + 3 \, a^{2} b d^{2} e x + a^{2} b d^{3}\right)} \arctan\left(c x\right), x\right)"," ",0,"integral(a^3*e^3*x^3 + 3*a^3*d*e^2*x^2 + 3*a^3*d^2*e*x + a^3*d^3 + (b^3*e^3*x^3 + 3*b^3*d*e^2*x^2 + 3*b^3*d^2*e*x + b^3*d^3)*arctan(c*x)^3 + 3*(a*b^2*e^3*x^3 + 3*a*b^2*d*e^2*x^2 + 3*a*b^2*d^2*e*x + a*b^2*d^3)*arctan(c*x)^2 + 3*(a^2*b*e^3*x^3 + 3*a^2*b*d*e^2*x^2 + 3*a^2*b*d^2*e*x + a^2*b*d^3)*arctan(c*x), x)","F",0
16,0,0,0,0.596848," ","integrate((e*x+d)^2*(a+b*arctan(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(a^{3} e^{2} x^{2} + 2 \, a^{3} d e x + a^{3} d^{2} + {\left(b^{3} e^{2} x^{2} + 2 \, b^{3} d e x + b^{3} d^{2}\right)} \arctan\left(c x\right)^{3} + 3 \, {\left(a b^{2} e^{2} x^{2} + 2 \, a b^{2} d e x + a b^{2} d^{2}\right)} \arctan\left(c x\right)^{2} + 3 \, {\left(a^{2} b e^{2} x^{2} + 2 \, a^{2} b d e x + a^{2} b d^{2}\right)} \arctan\left(c x\right), x\right)"," ",0,"integral(a^3*e^2*x^2 + 2*a^3*d*e*x + a^3*d^2 + (b^3*e^2*x^2 + 2*b^3*d*e*x + b^3*d^2)*arctan(c*x)^3 + 3*(a*b^2*e^2*x^2 + 2*a*b^2*d*e*x + a*b^2*d^2)*arctan(c*x)^2 + 3*(a^2*b*e^2*x^2 + 2*a^2*b*d*e*x + a^2*b*d^2)*arctan(c*x), x)","F",0
17,0,0,0,0.412031," ","integrate((e*x+d)*(a+b*arctan(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(a^{3} e x + a^{3} d + {\left(b^{3} e x + b^{3} d\right)} \arctan\left(c x\right)^{3} + 3 \, {\left(a b^{2} e x + a b^{2} d\right)} \arctan\left(c x\right)^{2} + 3 \, {\left(a^{2} b e x + a^{2} b d\right)} \arctan\left(c x\right), x\right)"," ",0,"integral(a^3*e*x + a^3*d + (b^3*e*x + b^3*d)*arctan(c*x)^3 + 3*(a*b^2*e*x + a*b^2*d)*arctan(c*x)^2 + 3*(a^2*b*e*x + a^2*b*d)*arctan(c*x), x)","F",0
18,0,0,0,0.409260," ","integrate((a+b*arctan(c*x))^3/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(c x\right)^{3} + 3 \, a b^{2} \arctan\left(c x\right)^{2} + 3 \, a^{2} b \arctan\left(c x\right) + a^{3}}{e x + d}, x\right)"," ",0,"integral((b^3*arctan(c*x)^3 + 3*a*b^2*arctan(c*x)^2 + 3*a^2*b*arctan(c*x) + a^3)/(e*x + d), x)","F",0
19,0,0,0,0.425466," ","integrate((a+b*arctan(c*x))^3/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(c x\right)^{3} + 3 \, a b^{2} \arctan\left(c x\right)^{2} + 3 \, a^{2} b \arctan\left(c x\right) + a^{3}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((b^3*arctan(c*x)^3 + 3*a*b^2*arctan(c*x)^2 + 3*a^2*b*arctan(c*x) + a^3)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
20,0,0,0,0.475127," ","integrate((a+b*arctan(c*x))^3/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(c x\right)^{3} + 3 \, a b^{2} \arctan\left(c x\right)^{2} + 3 \, a^{2} b \arctan\left(c x\right) + a^{3}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((b^3*arctan(c*x)^3 + 3*a*b^2*arctan(c*x)^2 + 3*a^2*b*arctan(c*x) + a^3)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
21,1,4861,0,0.652505," ","integrate((e*x+d)^2*(a+b*arctan(c*x^2)),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} c^{7} \sqrt{\frac{81 \, b^{2} c^{4} d^{8} + 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8} - 6 \, c^{4} d^{2} e^{2} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}}{81 \, b^{2} c^{4} d^{8} - 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8}}} \left(\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}\right)^{\frac{3}{4}} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} - 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}} \arctan\left(\frac{\sqrt{2} {\left(c^{11} e^{2} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} - 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}} + 3 \, {\left(9 \, b^{2} c^{11} d^{6} + b^{2} c^{9} d^{2} e^{4}\right)} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} - 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}\right)} \sqrt{{\left(6561 \, b^{6} c^{8} d^{16} - 162 \, b^{6} c^{4} d^{8} e^{8} + b^{6} e^{16}\right)} x^{2} + \sqrt{2} {\left(3 \, {\left(81 \, b^{3} c^{9} d^{10} - 18 \, b^{3} c^{7} d^{6} e^{4} + b^{3} c^{5} d^{2} e^{8}\right)} x \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}} + {\left(729 \, b^{5} c^{7} d^{12} e^{2} - 81 \, b^{5} c^{5} d^{8} e^{6} - 9 \, b^{5} c^{3} d^{4} e^{10} + b^{5} c e^{14}\right)} x\right)} \sqrt{\frac{81 \, b^{2} c^{4} d^{8} + 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8} - 6 \, c^{4} d^{2} e^{2} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}}{81 \, b^{2} c^{4} d^{8} - 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8}}} \left(\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}\right)^{\frac{1}{4}} + {\left(729 \, b^{4} c^{8} d^{12} - 81 \, b^{4} c^{6} d^{8} e^{4} - 9 \, b^{4} c^{4} d^{4} e^{8} + b^{4} c^{2} e^{12}\right)} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}} \sqrt{\frac{81 \, b^{2} c^{4} d^{8} + 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8} - 6 \, c^{4} d^{2} e^{2} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}}{81 \, b^{2} c^{4} d^{8} - 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8}}} \left(\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(81 \, b^{3} c^{15} d^{8} e^{2} - b^{3} c^{11} e^{10}\right)} x \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} - 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}} + 3 \, {\left(729 \, b^{5} c^{15} d^{14} + 81 \, b^{5} c^{13} d^{10} e^{4} - 9 \, b^{5} c^{11} d^{6} e^{8} - b^{5} c^{9} d^{2} e^{12}\right)} x \sqrt{\frac{81 \, b^{4} c^{4} d^{8} - 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}\right)} \sqrt{\frac{81 \, b^{2} c^{4} d^{8} + 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8} - 6 \, c^{4} d^{2} e^{2} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}}{81 \, b^{2} c^{4} d^{8} - 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8}}} \left(\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}\right)^{\frac{3}{4}} + {\left(6561 \, b^{6} c^{14} d^{16} + 1458 \, b^{6} c^{12} d^{12} e^{4} - 18 \, b^{6} c^{8} d^{4} e^{12} - b^{6} c^{6} e^{16}\right)} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} - 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}}{531441 \, b^{10} c^{12} d^{24} + 118098 \, b^{10} c^{10} d^{20} e^{4} - 6561 \, b^{10} c^{8} d^{16} e^{8} - 2916 \, b^{10} c^{6} d^{12} e^{12} - 81 \, b^{10} c^{4} d^{8} e^{16} + 18 \, b^{10} c^{2} d^{4} e^{20} + b^{10} e^{24}}\right) + 4 \, \sqrt{2} c^{7} \sqrt{\frac{81 \, b^{2} c^{4} d^{8} + 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8} - 6 \, c^{4} d^{2} e^{2} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}}{81 \, b^{2} c^{4} d^{8} - 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8}}} \left(\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}\right)^{\frac{3}{4}} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} - 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}} \arctan\left(\frac{\sqrt{2} {\left(c^{11} e^{2} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} - 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}} + 3 \, {\left(9 \, b^{2} c^{11} d^{6} + b^{2} c^{9} d^{2} e^{4}\right)} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} - 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}\right)} \sqrt{{\left(6561 \, b^{6} c^{8} d^{16} - 162 \, b^{6} c^{4} d^{8} e^{8} + b^{6} e^{16}\right)} x^{2} - \sqrt{2} {\left(3 \, {\left(81 \, b^{3} c^{9} d^{10} - 18 \, b^{3} c^{7} d^{6} e^{4} + b^{3} c^{5} d^{2} e^{8}\right)} x \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}} + {\left(729 \, b^{5} c^{7} d^{12} e^{2} - 81 \, b^{5} c^{5} d^{8} e^{6} - 9 \, b^{5} c^{3} d^{4} e^{10} + b^{5} c e^{14}\right)} x\right)} \sqrt{\frac{81 \, b^{2} c^{4} d^{8} + 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8} - 6 \, c^{4} d^{2} e^{2} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}}{81 \, b^{2} c^{4} d^{8} - 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8}}} \left(\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}\right)^{\frac{1}{4}} + {\left(729 \, b^{4} c^{8} d^{12} - 81 \, b^{4} c^{6} d^{8} e^{4} - 9 \, b^{4} c^{4} d^{4} e^{8} + b^{4} c^{2} e^{12}\right)} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}} \sqrt{\frac{81 \, b^{2} c^{4} d^{8} + 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8} - 6 \, c^{4} d^{2} e^{2} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}}{81 \, b^{2} c^{4} d^{8} - 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8}}} \left(\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}\right)^{\frac{3}{4}} + \sqrt{2} {\left({\left(81 \, b^{3} c^{15} d^{8} e^{2} - b^{3} c^{11} e^{10}\right)} x \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} - 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}} + 3 \, {\left(729 \, b^{5} c^{15} d^{14} + 81 \, b^{5} c^{13} d^{10} e^{4} - 9 \, b^{5} c^{11} d^{6} e^{8} - b^{5} c^{9} d^{2} e^{12}\right)} x \sqrt{\frac{81 \, b^{4} c^{4} d^{8} - 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}\right)} \sqrt{\frac{81 \, b^{2} c^{4} d^{8} + 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8} - 6 \, c^{4} d^{2} e^{2} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}}{81 \, b^{2} c^{4} d^{8} - 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8}}} \left(\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}\right)^{\frac{3}{4}} - {\left(6561 \, b^{6} c^{14} d^{16} + 1458 \, b^{6} c^{12} d^{12} e^{4} - 18 \, b^{6} c^{8} d^{4} e^{12} - b^{6} c^{6} e^{16}\right)} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} - 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}}{531441 \, b^{10} c^{12} d^{24} + 118098 \, b^{10} c^{10} d^{20} e^{4} - 6561 \, b^{10} c^{8} d^{16} e^{8} - 2916 \, b^{10} c^{6} d^{12} e^{12} - 81 \, b^{10} c^{4} d^{8} e^{16} + 18 \, b^{10} c^{2} d^{4} e^{20} + b^{10} e^{24}}\right) - 4 \, {\left(81 \, a b^{4} c^{5} d^{8} e^{2} + 18 \, a b^{4} c^{3} d^{4} e^{6} + a b^{4} c e^{10}\right)} x^{3} - 12 \, {\left(81 \, a b^{4} c^{5} d^{9} e + 18 \, a b^{4} c^{3} d^{5} e^{5} + a b^{4} c d e^{9}\right)} x^{2} - 4 \, {\left(243 \, a b^{4} c^{5} d^{10} - 162 \, b^{5} c^{4} d^{8} e^{2} + 54 \, a b^{4} c^{3} d^{6} e^{4} - 36 \, b^{5} c^{2} d^{4} e^{6} + 3 \, a b^{4} c d^{2} e^{8} - 2 \, b^{5} e^{10}\right)} x - 4 \, {\left({\left(81 \, b^{5} c^{5} d^{8} e^{2} + 18 \, b^{5} c^{3} d^{4} e^{6} + b^{5} c e^{10}\right)} x^{3} + 3 \, {\left(81 \, b^{5} c^{5} d^{9} e + 18 \, b^{5} c^{3} d^{5} e^{5} + b^{5} c d e^{9}\right)} x^{2} + 3 \, {\left(81 \, b^{5} c^{5} d^{10} + 18 \, b^{5} c^{3} d^{6} e^{4} + b^{5} c d^{2} e^{8}\right)} x\right)} \arctan\left(c x^{2}\right) + {\left(486 \, b^{5} c^{4} d^{9} e + 108 \, b^{5} c^{2} d^{5} e^{5} + 6 \, b^{5} d e^{9} - \sqrt{2} {\left(81 \, b^{4} c^{5} d^{8} + 18 \, b^{4} c^{3} d^{4} e^{4} + b^{4} c e^{8} + 6 \, b^{2} c^{5} d^{2} e^{2} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}\right)} \sqrt{\frac{81 \, b^{2} c^{4} d^{8} + 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8} - 6 \, c^{4} d^{2} e^{2} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}}{81 \, b^{2} c^{4} d^{8} - 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8}}} \left(\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}\right)^{\frac{1}{4}}\right)} \log\left({\left(6561 \, b^{6} c^{8} d^{16} - 162 \, b^{6} c^{4} d^{8} e^{8} + b^{6} e^{16}\right)} x^{2} + \sqrt{2} {\left(3 \, {\left(81 \, b^{3} c^{9} d^{10} - 18 \, b^{3} c^{7} d^{6} e^{4} + b^{3} c^{5} d^{2} e^{8}\right)} x \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}} + {\left(729 \, b^{5} c^{7} d^{12} e^{2} - 81 \, b^{5} c^{5} d^{8} e^{6} - 9 \, b^{5} c^{3} d^{4} e^{10} + b^{5} c e^{14}\right)} x\right)} \sqrt{\frac{81 \, b^{2} c^{4} d^{8} + 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8} - 6 \, c^{4} d^{2} e^{2} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}}{81 \, b^{2} c^{4} d^{8} - 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8}}} \left(\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}\right)^{\frac{1}{4}} + {\left(729 \, b^{4} c^{8} d^{12} - 81 \, b^{4} c^{6} d^{8} e^{4} - 9 \, b^{4} c^{4} d^{4} e^{8} + b^{4} c^{2} e^{12}\right)} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}\right) + {\left(486 \, b^{5} c^{4} d^{9} e + 108 \, b^{5} c^{2} d^{5} e^{5} + 6 \, b^{5} d e^{9} + \sqrt{2} {\left(81 \, b^{4} c^{5} d^{8} + 18 \, b^{4} c^{3} d^{4} e^{4} + b^{4} c e^{8} + 6 \, b^{2} c^{5} d^{2} e^{2} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}\right)} \sqrt{\frac{81 \, b^{2} c^{4} d^{8} + 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8} - 6 \, c^{4} d^{2} e^{2} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}}{81 \, b^{2} c^{4} d^{8} - 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8}}} \left(\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}\right)^{\frac{1}{4}}\right)} \log\left({\left(6561 \, b^{6} c^{8} d^{16} - 162 \, b^{6} c^{4} d^{8} e^{8} + b^{6} e^{16}\right)} x^{2} - \sqrt{2} {\left(3 \, {\left(81 \, b^{3} c^{9} d^{10} - 18 \, b^{3} c^{7} d^{6} e^{4} + b^{3} c^{5} d^{2} e^{8}\right)} x \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}} + {\left(729 \, b^{5} c^{7} d^{12} e^{2} - 81 \, b^{5} c^{5} d^{8} e^{6} - 9 \, b^{5} c^{3} d^{4} e^{10} + b^{5} c e^{14}\right)} x\right)} \sqrt{\frac{81 \, b^{2} c^{4} d^{8} + 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8} - 6 \, c^{4} d^{2} e^{2} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}}{81 \, b^{2} c^{4} d^{8} - 18 \, b^{2} c^{2} d^{4} e^{4} + b^{2} e^{8}}} \left(\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}\right)^{\frac{1}{4}} + {\left(729 \, b^{4} c^{8} d^{12} - 81 \, b^{4} c^{6} d^{8} e^{4} - 9 \, b^{4} c^{4} d^{4} e^{8} + b^{4} c^{2} e^{12}\right)} \sqrt{\frac{81 \, b^{4} c^{4} d^{8} + 18 \, b^{4} c^{2} d^{4} e^{4} + b^{4} e^{8}}{c^{6}}}\right)}{12 \, {\left(81 \, b^{4} c^{5} d^{8} + 18 \, b^{4} c^{3} d^{4} e^{4} + b^{4} c e^{8}\right)}}"," ",0,"-1/12*(4*sqrt(2)*c^7*sqrt((81*b^2*c^4*d^8 + 18*b^2*c^2*d^4*e^4 + b^2*e^8 - 6*c^4*d^2*e^2*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))/(81*b^2*c^4*d^8 - 18*b^2*c^2*d^4*e^4 + b^2*e^8))*((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)^(3/4)*sqrt((81*b^4*c^4*d^8 - 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)*arctan((sqrt(2)*(c^11*e^2*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)*sqrt((81*b^4*c^4*d^8 - 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6) + 3*(9*b^2*c^11*d^6 + b^2*c^9*d^2*e^4)*sqrt((81*b^4*c^4*d^8 - 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))*sqrt((6561*b^6*c^8*d^16 - 162*b^6*c^4*d^8*e^8 + b^6*e^16)*x^2 + sqrt(2)*(3*(81*b^3*c^9*d^10 - 18*b^3*c^7*d^6*e^4 + b^3*c^5*d^2*e^8)*x*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6) + (729*b^5*c^7*d^12*e^2 - 81*b^5*c^5*d^8*e^6 - 9*b^5*c^3*d^4*e^10 + b^5*c*e^14)*x)*sqrt((81*b^2*c^4*d^8 + 18*b^2*c^2*d^4*e^4 + b^2*e^8 - 6*c^4*d^2*e^2*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))/(81*b^2*c^4*d^8 - 18*b^2*c^2*d^4*e^4 + b^2*e^8))*((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)^(1/4) + (729*b^4*c^8*d^12 - 81*b^4*c^6*d^8*e^4 - 9*b^4*c^4*d^4*e^8 + b^4*c^2*e^12)*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))*sqrt((81*b^2*c^4*d^8 + 18*b^2*c^2*d^4*e^4 + b^2*e^8 - 6*c^4*d^2*e^2*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))/(81*b^2*c^4*d^8 - 18*b^2*c^2*d^4*e^4 + b^2*e^8))*((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)^(3/4) + sqrt(2)*((81*b^3*c^15*d^8*e^2 - b^3*c^11*e^10)*x*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)*sqrt((81*b^4*c^4*d^8 - 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6) + 3*(729*b^5*c^15*d^14 + 81*b^5*c^13*d^10*e^4 - 9*b^5*c^11*d^6*e^8 - b^5*c^9*d^2*e^12)*x*sqrt((81*b^4*c^4*d^8 - 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))*sqrt((81*b^2*c^4*d^8 + 18*b^2*c^2*d^4*e^4 + b^2*e^8 - 6*c^4*d^2*e^2*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))/(81*b^2*c^4*d^8 - 18*b^2*c^2*d^4*e^4 + b^2*e^8))*((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)^(3/4) + (6561*b^6*c^14*d^16 + 1458*b^6*c^12*d^12*e^4 - 18*b^6*c^8*d^4*e^12 - b^6*c^6*e^16)*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)*sqrt((81*b^4*c^4*d^8 - 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))/(531441*b^10*c^12*d^24 + 118098*b^10*c^10*d^20*e^4 - 6561*b^10*c^8*d^16*e^8 - 2916*b^10*c^6*d^12*e^12 - 81*b^10*c^4*d^8*e^16 + 18*b^10*c^2*d^4*e^20 + b^10*e^24)) + 4*sqrt(2)*c^7*sqrt((81*b^2*c^4*d^8 + 18*b^2*c^2*d^4*e^4 + b^2*e^8 - 6*c^4*d^2*e^2*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))/(81*b^2*c^4*d^8 - 18*b^2*c^2*d^4*e^4 + b^2*e^8))*((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)^(3/4)*sqrt((81*b^4*c^4*d^8 - 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)*arctan((sqrt(2)*(c^11*e^2*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)*sqrt((81*b^4*c^4*d^8 - 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6) + 3*(9*b^2*c^11*d^6 + b^2*c^9*d^2*e^4)*sqrt((81*b^4*c^4*d^8 - 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))*sqrt((6561*b^6*c^8*d^16 - 162*b^6*c^4*d^8*e^8 + b^6*e^16)*x^2 - sqrt(2)*(3*(81*b^3*c^9*d^10 - 18*b^3*c^7*d^6*e^4 + b^3*c^5*d^2*e^8)*x*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6) + (729*b^5*c^7*d^12*e^2 - 81*b^5*c^5*d^8*e^6 - 9*b^5*c^3*d^4*e^10 + b^5*c*e^14)*x)*sqrt((81*b^2*c^4*d^8 + 18*b^2*c^2*d^4*e^4 + b^2*e^8 - 6*c^4*d^2*e^2*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))/(81*b^2*c^4*d^8 - 18*b^2*c^2*d^4*e^4 + b^2*e^8))*((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)^(1/4) + (729*b^4*c^8*d^12 - 81*b^4*c^6*d^8*e^4 - 9*b^4*c^4*d^4*e^8 + b^4*c^2*e^12)*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))*sqrt((81*b^2*c^4*d^8 + 18*b^2*c^2*d^4*e^4 + b^2*e^8 - 6*c^4*d^2*e^2*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))/(81*b^2*c^4*d^8 - 18*b^2*c^2*d^4*e^4 + b^2*e^8))*((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)^(3/4) + sqrt(2)*((81*b^3*c^15*d^8*e^2 - b^3*c^11*e^10)*x*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)*sqrt((81*b^4*c^4*d^8 - 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6) + 3*(729*b^5*c^15*d^14 + 81*b^5*c^13*d^10*e^4 - 9*b^5*c^11*d^6*e^8 - b^5*c^9*d^2*e^12)*x*sqrt((81*b^4*c^4*d^8 - 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))*sqrt((81*b^2*c^4*d^8 + 18*b^2*c^2*d^4*e^4 + b^2*e^8 - 6*c^4*d^2*e^2*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))/(81*b^2*c^4*d^8 - 18*b^2*c^2*d^4*e^4 + b^2*e^8))*((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)^(3/4) - (6561*b^6*c^14*d^16 + 1458*b^6*c^12*d^12*e^4 - 18*b^6*c^8*d^4*e^12 - b^6*c^6*e^16)*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)*sqrt((81*b^4*c^4*d^8 - 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))/(531441*b^10*c^12*d^24 + 118098*b^10*c^10*d^20*e^4 - 6561*b^10*c^8*d^16*e^8 - 2916*b^10*c^6*d^12*e^12 - 81*b^10*c^4*d^8*e^16 + 18*b^10*c^2*d^4*e^20 + b^10*e^24)) - 4*(81*a*b^4*c^5*d^8*e^2 + 18*a*b^4*c^3*d^4*e^6 + a*b^4*c*e^10)*x^3 - 12*(81*a*b^4*c^5*d^9*e + 18*a*b^4*c^3*d^5*e^5 + a*b^4*c*d*e^9)*x^2 - 4*(243*a*b^4*c^5*d^10 - 162*b^5*c^4*d^8*e^2 + 54*a*b^4*c^3*d^6*e^4 - 36*b^5*c^2*d^4*e^6 + 3*a*b^4*c*d^2*e^8 - 2*b^5*e^10)*x - 4*((81*b^5*c^5*d^8*e^2 + 18*b^5*c^3*d^4*e^6 + b^5*c*e^10)*x^3 + 3*(81*b^5*c^5*d^9*e + 18*b^5*c^3*d^5*e^5 + b^5*c*d*e^9)*x^2 + 3*(81*b^5*c^5*d^10 + 18*b^5*c^3*d^6*e^4 + b^5*c*d^2*e^8)*x)*arctan(c*x^2) + (486*b^5*c^4*d^9*e + 108*b^5*c^2*d^5*e^5 + 6*b^5*d*e^9 - sqrt(2)*(81*b^4*c^5*d^8 + 18*b^4*c^3*d^4*e^4 + b^4*c*e^8 + 6*b^2*c^5*d^2*e^2*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))*sqrt((81*b^2*c^4*d^8 + 18*b^2*c^2*d^4*e^4 + b^2*e^8 - 6*c^4*d^2*e^2*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))/(81*b^2*c^4*d^8 - 18*b^2*c^2*d^4*e^4 + b^2*e^8))*((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)^(1/4))*log((6561*b^6*c^8*d^16 - 162*b^6*c^4*d^8*e^8 + b^6*e^16)*x^2 + sqrt(2)*(3*(81*b^3*c^9*d^10 - 18*b^3*c^7*d^6*e^4 + b^3*c^5*d^2*e^8)*x*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6) + (729*b^5*c^7*d^12*e^2 - 81*b^5*c^5*d^8*e^6 - 9*b^5*c^3*d^4*e^10 + b^5*c*e^14)*x)*sqrt((81*b^2*c^4*d^8 + 18*b^2*c^2*d^4*e^4 + b^2*e^8 - 6*c^4*d^2*e^2*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))/(81*b^2*c^4*d^8 - 18*b^2*c^2*d^4*e^4 + b^2*e^8))*((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)^(1/4) + (729*b^4*c^8*d^12 - 81*b^4*c^6*d^8*e^4 - 9*b^4*c^4*d^4*e^8 + b^4*c^2*e^12)*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)) + (486*b^5*c^4*d^9*e + 108*b^5*c^2*d^5*e^5 + 6*b^5*d*e^9 + sqrt(2)*(81*b^4*c^5*d^8 + 18*b^4*c^3*d^4*e^4 + b^4*c*e^8 + 6*b^2*c^5*d^2*e^2*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))*sqrt((81*b^2*c^4*d^8 + 18*b^2*c^2*d^4*e^4 + b^2*e^8 - 6*c^4*d^2*e^2*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))/(81*b^2*c^4*d^8 - 18*b^2*c^2*d^4*e^4 + b^2*e^8))*((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)^(1/4))*log((6561*b^6*c^8*d^16 - 162*b^6*c^4*d^8*e^8 + b^6*e^16)*x^2 - sqrt(2)*(3*(81*b^3*c^9*d^10 - 18*b^3*c^7*d^6*e^4 + b^3*c^5*d^2*e^8)*x*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6) + (729*b^5*c^7*d^12*e^2 - 81*b^5*c^5*d^8*e^6 - 9*b^5*c^3*d^4*e^10 + b^5*c*e^14)*x)*sqrt((81*b^2*c^4*d^8 + 18*b^2*c^2*d^4*e^4 + b^2*e^8 - 6*c^4*d^2*e^2*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6))/(81*b^2*c^4*d^8 - 18*b^2*c^2*d^4*e^4 + b^2*e^8))*((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)^(1/4) + (729*b^4*c^8*d^12 - 81*b^4*c^6*d^8*e^4 - 9*b^4*c^4*d^4*e^8 + b^4*c^2*e^12)*sqrt((81*b^4*c^4*d^8 + 18*b^4*c^2*d^4*e^4 + b^4*e^8)/c^6)))/(81*b^4*c^5*d^8 + 18*b^4*c^3*d^4*e^4 + b^4*c*e^8)","B",0
22,1,534,0,0.491567," ","integrate((e*x+d)*(a+b*arctan(c*x^2)),x, algorithm=""fricas"")","\frac{2 \, a b^{4} c d^{4} e x^{2} + 4 \, a b^{4} c d^{5} x + 4 \, \sqrt{2} \left(\frac{b^{4} d^{4}}{c^{2}}\right)^{\frac{1}{4}} b^{4} c d^{4} \arctan\left(-\frac{b^{8} d^{8} + \sqrt{2} \left(\frac{b^{4} d^{4}}{c^{2}}\right)^{\frac{5}{4}} b^{3} c^{3} d^{3} x - \sqrt{2} \sqrt{b^{6} d^{6} x^{2} + \sqrt{2} \left(\frac{b^{4} d^{4}}{c^{2}}\right)^{\frac{3}{4}} b^{3} c d^{3} x + \sqrt{\frac{b^{4} d^{4}}{c^{2}}} b^{4} d^{4}} \left(\frac{b^{4} d^{4}}{c^{2}}\right)^{\frac{5}{4}} c^{3}}{b^{8} d^{8}}\right) + 4 \, \sqrt{2} \left(\frac{b^{4} d^{4}}{c^{2}}\right)^{\frac{1}{4}} b^{4} c d^{4} \arctan\left(\frac{b^{8} d^{8} - \sqrt{2} \left(\frac{b^{4} d^{4}}{c^{2}}\right)^{\frac{5}{4}} b^{3} c^{3} d^{3} x + \sqrt{2} \sqrt{b^{6} d^{6} x^{2} - \sqrt{2} \left(\frac{b^{4} d^{4}}{c^{2}}\right)^{\frac{3}{4}} b^{3} c d^{3} x + \sqrt{\frac{b^{4} d^{4}}{c^{2}}} b^{4} d^{4}} \left(\frac{b^{4} d^{4}}{c^{2}}\right)^{\frac{5}{4}} c^{3}}{b^{8} d^{8}}\right) + 2 \, {\left(b^{5} c d^{4} e x^{2} + 2 \, b^{5} c d^{5} x\right)} \arctan\left(c x^{2}\right) - {\left(b^{5} d^{4} e - \sqrt{2} \left(\frac{b^{4} d^{4}}{c^{2}}\right)^{\frac{1}{4}} b^{4} c d^{4}\right)} \log\left(b^{6} d^{6} x^{2} + \sqrt{2} \left(\frac{b^{4} d^{4}}{c^{2}}\right)^{\frac{3}{4}} b^{3} c d^{3} x + \sqrt{\frac{b^{4} d^{4}}{c^{2}}} b^{4} d^{4}\right) - {\left(b^{5} d^{4} e + \sqrt{2} \left(\frac{b^{4} d^{4}}{c^{2}}\right)^{\frac{1}{4}} b^{4} c d^{4}\right)} \log\left(b^{6} d^{6} x^{2} - \sqrt{2} \left(\frac{b^{4} d^{4}}{c^{2}}\right)^{\frac{3}{4}} b^{3} c d^{3} x + \sqrt{\frac{b^{4} d^{4}}{c^{2}}} b^{4} d^{4}\right)}{4 \, b^{4} c d^{4}}"," ",0,"1/4*(2*a*b^4*c*d^4*e*x^2 + 4*a*b^4*c*d^5*x + 4*sqrt(2)*(b^4*d^4/c^2)^(1/4)*b^4*c*d^4*arctan(-(b^8*d^8 + sqrt(2)*(b^4*d^4/c^2)^(5/4)*b^3*c^3*d^3*x - sqrt(2)*sqrt(b^6*d^6*x^2 + sqrt(2)*(b^4*d^4/c^2)^(3/4)*b^3*c*d^3*x + sqrt(b^4*d^4/c^2)*b^4*d^4)*(b^4*d^4/c^2)^(5/4)*c^3)/(b^8*d^8)) + 4*sqrt(2)*(b^4*d^4/c^2)^(1/4)*b^4*c*d^4*arctan((b^8*d^8 - sqrt(2)*(b^4*d^4/c^2)^(5/4)*b^3*c^3*d^3*x + sqrt(2)*sqrt(b^6*d^6*x^2 - sqrt(2)*(b^4*d^4/c^2)^(3/4)*b^3*c*d^3*x + sqrt(b^4*d^4/c^2)*b^4*d^4)*(b^4*d^4/c^2)^(5/4)*c^3)/(b^8*d^8)) + 2*(b^5*c*d^4*e*x^2 + 2*b^5*c*d^5*x)*arctan(c*x^2) - (b^5*d^4*e - sqrt(2)*(b^4*d^4/c^2)^(1/4)*b^4*c*d^4)*log(b^6*d^6*x^2 + sqrt(2)*(b^4*d^4/c^2)^(3/4)*b^3*c*d^3*x + sqrt(b^4*d^4/c^2)*b^4*d^4) - (b^5*d^4*e + sqrt(2)*(b^4*d^4/c^2)^(1/4)*b^4*c*d^4)*log(b^6*d^6*x^2 - sqrt(2)*(b^4*d^4/c^2)^(3/4)*b^3*c*d^3*x + sqrt(b^4*d^4/c^2)*b^4*d^4))/(b^4*c*d^4)","B",0
23,0,0,0,0.405659," ","integrate((a+b*arctan(c*x^2))/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x^{2}\right) + a}{e x + d}, x\right)"," ",0,"integral((b*arctan(c*x^2) + a)/(e*x + d), x)","F",0
24,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x^2))/(e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,0,0,0,0.753045," ","integrate((e*x+d)*(a+b*arctan(c*x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} e x + a^{2} d + {\left(b^{2} e x + b^{2} d\right)} \arctan\left(c x^{2}\right)^{2} + 2 \, {\left(a b e x + a b d\right)} \arctan\left(c x^{2}\right), x\right)"," ",0,"integral(a^2*e*x + a^2*d + (b^2*e*x + b^2*d)*arctan(c*x^2)^2 + 2*(a*b*e*x + a*b*d)*arctan(c*x^2), x)","F",0
26,0,0,0,1.614682," ","integrate((a+b*arctan(c*x^2))^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x^{2}\right)^{2} + 2 \, a b \arctan\left(c x^{2}\right) + a^{2}}{e x + d}, x\right)"," ",0,"integral((b^2*arctan(c*x^2)^2 + 2*a*b*arctan(c*x^2) + a^2)/(e*x + d), x)","F",0
27,0,0,0,0.600247," ","integrate((a+b*arctan(c*x^2))^2/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x^{2}\right)^{2} + 2 \, a b \arctan\left(c x^{2}\right) + a^{2}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((b^2*arctan(c*x^2)^2 + 2*a*b*arctan(c*x^2) + a^2)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
28,-1,0,0,0.000000," ","integrate((e*x+d)^2*(a+b*arctan(c*x^3)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
29,-2,0,0,0.000000," ","integrate((e*x+d)*(a+b*arctan(c*x^3)),x, algorithm=""fricas"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> no explicit roots found","F(-2)",0
30,0,0,0,0.405452," ","integrate((a+b*arctan(c*x^3))/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x^{3}\right) + a}{e x + d}, x\right)"," ",0,"integral((b*arctan(c*x^3) + a)/(e*x + d), x)","F",0
31,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x^3))/(e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
