1,1,252,0,0.412213," ","integrate((e*x+d)^4*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e^{4} x^{5} + a d e^{3} x^{4} + 2 \, a d^{2} e^{2} x^{3} + 2 \, a d^{3} e x^{2} + 2 \, {\left(x^{2} \arctan\left(c x\right) - c {\left(\frac{x}{c^{2}} - \frac{\arctan\left(c x\right)}{c^{3}}\right)}\right)} b d^{3} e + {\left(2 \, x^{3} \arctan\left(c x\right) - c {\left(\frac{x^{2}}{c^{2}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4}}\right)}\right)} b d^{2} e^{2} + \frac{1}{3} \, {\left(3 \, x^{4} \arctan\left(c x\right) - c {\left(\frac{c^{2} x^{3} - 3 \, x}{c^{4}} + \frac{3 \, \arctan\left(c x\right)}{c^{5}}\right)}\right)} b d e^{3} + \frac{1}{20} \, {\left(4 \, x^{5} \arctan\left(c x\right) - c {\left(\frac{c^{2} x^{4} - 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} + 1\right)}{c^{6}}\right)}\right)} b e^{4} + a d^{4} x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d^{4}}{2 \, c}"," ",0,"1/5*a*e^4*x^5 + a*d*e^3*x^4 + 2*a*d^2*e^2*x^3 + 2*a*d^3*e*x^2 + 2*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*d^3*e + (2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*d^2*e^2 + 1/3*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*d*e^3 + 1/20*(4*x^5*arctan(c*x) - c*((c^2*x^4 - 2*x^2)/c^4 + 2*log(c^2*x^2 + 1)/c^6))*b*e^4 + a*d^4*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d^4/c","A",0
2,1,186,0,0.410679," ","integrate((e*x+d)^3*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a e^{3} x^{4} + a d e^{2} x^{3} + \frac{3}{2} \, a d^{2} e x^{2} + \frac{3}{2} \, {\left(x^{2} \arctan\left(c x\right) - c {\left(\frac{x}{c^{2}} - \frac{\arctan\left(c x\right)}{c^{3}}\right)}\right)} b d^{2} e + \frac{1}{2} \, {\left(2 \, x^{3} \arctan\left(c x\right) - c {\left(\frac{x^{2}}{c^{2}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4}}\right)}\right)} b d e^{2} + \frac{1}{12} \, {\left(3 \, x^{4} \arctan\left(c x\right) - c {\left(\frac{c^{2} x^{3} - 3 \, x}{c^{4}} + \frac{3 \, \arctan\left(c x\right)}{c^{5}}\right)}\right)} b e^{3} + a d^{3} x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d^{3}}{2 \, c}"," ",0,"1/4*a*e^3*x^4 + a*d*e^2*x^3 + 3/2*a*d^2*e*x^2 + 3/2*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*d^2*e + 1/2*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*d*e^2 + 1/12*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*e^3 + a*d^3*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d^3/c","A",0
3,1,126,0,0.410859," ","integrate((e*x+d)^2*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a e^{2} x^{3} + a d e x^{2} + {\left(x^{2} \arctan\left(c x\right) - c {\left(\frac{x}{c^{2}} - \frac{\arctan\left(c x\right)}{c^{3}}\right)}\right)} b d e + \frac{1}{6} \, {\left(2 \, x^{3} \arctan\left(c x\right) - c {\left(\frac{x^{2}}{c^{2}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4}}\right)}\right)} b e^{2} + a d^{2} x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d^{2}}{2 \, c}"," ",0,"1/3*a*e^2*x^3 + a*d*e*x^2 + (x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*d*e + 1/6*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*e^2 + a*d^2*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d^2/c","A",0
4,1,71,0,0.468147," ","integrate((e*x+d)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{2} \, a e x^{2} + \frac{1}{2} \, {\left(x^{2} \arctan\left(c x\right) - c {\left(\frac{x}{c^{2}} - \frac{\arctan\left(c x\right)}{c^{3}}\right)}\right)} b e + a d x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d}{2 \, c}"," ",0,"1/2*a*e*x^2 + 1/2*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*e + a*d*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d/c","A",0
5,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/(e*x+d),x, algorithm=""maxima"")","2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e x + d\right)}}\,{d x} + \frac{a \log\left(e x + d\right)}{e}"," ",0,"2*b*integrate(1/2*arctan(c*x)/(e*x + d), x) + a*log(e*x + d)/e","F",0
6,1,107,0,0.420661," ","integrate((a+b*arctan(c*x))/(e*x+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left({\left(\frac{2 \, c d \arctan\left(c x\right)}{c^{2} d^{2} e + e^{3}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{2} d^{2} + e^{2}} + \frac{2 \, \log\left(e x + d\right)}{c^{2} d^{2} + e^{2}}\right)} c - \frac{2 \, \arctan\left(c x\right)}{e^{2} x + d e}\right)} b - \frac{a}{e^{2} x + d e}"," ",0,"1/2*((2*c*d*arctan(c*x)/(c^2*d^2*e + e^3) - log(c^2*x^2 + 1)/(c^2*d^2 + e^2) + 2*log(e*x + d)/(c^2*d^2 + e^2))*c - 2*arctan(c*x)/(e^2*x + d*e))*b - a/(e^2*x + d*e)","A",0
7,1,214,0,0.416975," ","integrate((a+b*arctan(c*x))/(e*x+d)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left({\left(\frac{c^{2} d \log\left(c^{2} x^{2} + 1\right)}{c^{4} d^{4} + 2 \, c^{2} d^{2} e^{2} + e^{4}} - \frac{2 \, c^{2} d \log\left(e x + d\right)}{c^{4} d^{4} + 2 \, c^{2} d^{2} e^{2} + e^{4}} - \frac{{\left(c^{4} d^{2} - c^{2} e^{2}\right)} \arctan\left(c x\right)}{{\left(c^{4} d^{4} e + 2 \, c^{2} d^{2} e^{3} + e^{5}\right)} c} + \frac{1}{c^{2} d^{3} + d e^{2} + {\left(c^{2} d^{2} e + e^{3}\right)} x}\right)} c + \frac{\arctan\left(c x\right)}{e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e}\right)} b - \frac{a}{2 \, {\left(e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e\right)}}"," ",0,"-1/2*((c^2*d*log(c^2*x^2 + 1)/(c^4*d^4 + 2*c^2*d^2*e^2 + e^4) - 2*c^2*d*log(e*x + d)/(c^4*d^4 + 2*c^2*d^2*e^2 + e^4) - (c^4*d^2 - c^2*e^2)*arctan(c*x)/((c^4*d^4*e + 2*c^2*d^2*e^3 + e^5)*c) + 1/(c^2*d^3 + d*e^2 + (c^2*d^2*e + e^3)*x))*c + arctan(c*x)/(e^3*x^2 + 2*d*e^2*x + d^2*e))*b - 1/2*a/(e^3*x^2 + 2*d*e^2*x + d^2*e)","A",0
8,1,374,0,0.434736," ","integrate((a+b*arctan(c*x))/(e*x+d)^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(c {\left(\frac{{\left(3 \, c^{4} d^{2} - c^{2} e^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{c^{6} d^{6} + 3 \, c^{4} d^{4} e^{2} + 3 \, c^{2} d^{2} e^{4} + e^{6}} - \frac{2 \, {\left(3 \, c^{4} d^{2} - c^{2} e^{2}\right)} \log\left(e x + d\right)}{c^{6} d^{6} + 3 \, c^{4} d^{4} e^{2} + 3 \, c^{2} d^{2} e^{4} + e^{6}} + \frac{4 \, c^{2} d e x + 5 \, c^{2} d^{2} + e^{2}}{c^{4} d^{6} + 2 \, c^{2} d^{4} e^{2} + d^{2} e^{4} + {\left(c^{4} d^{4} e^{2} + 2 \, c^{2} d^{2} e^{4} + e^{6}\right)} x^{2} + 2 \, {\left(c^{4} d^{5} e + 2 \, c^{2} d^{3} e^{3} + d e^{5}\right)} x} - \frac{2 \, {\left(c^{6} d^{3} - 3 \, c^{4} d e^{2}\right)} \arctan\left(c x\right)}{{\left(c^{6} d^{6} e + 3 \, c^{4} d^{4} e^{3} + 3 \, c^{2} d^{2} e^{5} + e^{7}\right)} c}\right)} + \frac{2 \, \arctan\left(c x\right)}{e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e}\right)} b - \frac{a}{3 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}}"," ",0,"-1/6*(c*((3*c^4*d^2 - c^2*e^2)*log(c^2*x^2 + 1)/(c^6*d^6 + 3*c^4*d^4*e^2 + 3*c^2*d^2*e^4 + e^6) - 2*(3*c^4*d^2 - c^2*e^2)*log(e*x + d)/(c^6*d^6 + 3*c^4*d^4*e^2 + 3*c^2*d^2*e^4 + e^6) + (4*c^2*d*e*x + 5*c^2*d^2 + e^2)/(c^4*d^6 + 2*c^2*d^4*e^2 + d^2*e^4 + (c^4*d^4*e^2 + 2*c^2*d^2*e^4 + e^6)*x^2 + 2*(c^4*d^5*e + 2*c^2*d^3*e^3 + d*e^5)*x) - 2*(c^6*d^3 - 3*c^4*d*e^2)*arctan(c*x)/((c^6*d^6*e + 3*c^4*d^4*e^3 + 3*c^2*d^2*e^5 + e^7)*c)) + 2*arctan(c*x)/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e))*b - 1/3*a/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e)","A",0
9,0,0,0,0.000000," ","integrate((e*x+d)^3*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} e^{3} x^{4} + a^{2} d e^{2} x^{3} + 12 \, b^{2} c^{2} e^{3} \int \frac{x^{5} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + b^{2} c^{2} e^{3} \int \frac{x^{5} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 36 \, b^{2} c^{2} d e^{2} \int \frac{x^{4} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + b^{2} c^{2} e^{3} \int \frac{x^{5} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{2} c^{2} d e^{2} \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 36 \, b^{2} c^{2} d^{2} e \int \frac{x^{3} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 4 \, b^{2} c^{2} d e^{2} \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{2} c^{2} d^{2} e \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{2} c^{2} d^{3} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 6 \, b^{2} c^{2} d^{2} e \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + b^{2} c^{2} d^{3} \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 4 \, b^{2} c^{2} d^{3} \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{3}{2} \, a^{2} d^{2} e x^{2} + \frac{b^{2} d^{3} \arctan\left(c x\right)^{3}}{4 \, c} - 2 \, b^{2} c e^{3} \int \frac{x^{4} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 8 \, b^{2} c d e^{2} \int \frac{x^{3} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 12 \, b^{2} c d^{2} e \int \frac{x^{2} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 8 \, b^{2} c d^{3} \int \frac{x \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, {\left(x^{2} \arctan\left(c x\right) - c {\left(\frac{x}{c^{2}} - \frac{\arctan\left(c x\right)}{c^{3}}\right)}\right)} a b d^{2} e + {\left(2 \, x^{3} \arctan\left(c x\right) - c {\left(\frac{x^{2}}{c^{2}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4}}\right)}\right)} a b d e^{2} + \frac{1}{6} \, {\left(3 \, x^{4} \arctan\left(c x\right) - c {\left(\frac{c^{2} x^{3} - 3 \, x}{c^{4}} + \frac{3 \, \arctan\left(c x\right)}{c^{5}}\right)}\right)} a b e^{3} + a^{2} d^{3} x + 12 \, b^{2} e^{3} \int \frac{x^{3} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + b^{2} e^{3} \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 36 \, b^{2} d e^{2} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{2} d e^{2} \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 36 \, b^{2} d^{2} e \int \frac{x \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{2} d^{2} e \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + b^{2} d^{3} \int \frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} a b d^{3}}{c} + \frac{1}{16} \, {\left(b^{2} e^{3} x^{4} + 4 \, b^{2} d e^{2} x^{3} + 6 \, b^{2} d^{2} e x^{2} + 4 \, b^{2} d^{3} x\right)} \arctan\left(c x\right)^{2} - \frac{1}{64} \, {\left(b^{2} e^{3} x^{4} + 4 \, b^{2} d e^{2} x^{3} + 6 \, b^{2} d^{2} e x^{2} + 4 \, b^{2} d^{3} x\right)} \log\left(c^{2} x^{2} + 1\right)^{2}"," ",0,"1/4*a^2*e^3*x^4 + a^2*d*e^2*x^3 + 12*b^2*c^2*e^3*integrate(1/16*x^5*arctan(c*x)^2/(c^2*x^2 + 1), x) + b^2*c^2*e^3*integrate(1/16*x^5*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 36*b^2*c^2*d*e^2*integrate(1/16*x^4*arctan(c*x)^2/(c^2*x^2 + 1), x) + b^2*c^2*e^3*integrate(1/16*x^5*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 3*b^2*c^2*d*e^2*integrate(1/16*x^4*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 36*b^2*c^2*d^2*e*integrate(1/16*x^3*arctan(c*x)^2/(c^2*x^2 + 1), x) + 4*b^2*c^2*d*e^2*integrate(1/16*x^4*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 3*b^2*c^2*d^2*e*integrate(1/16*x^3*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 12*b^2*c^2*d^3*integrate(1/16*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 6*b^2*c^2*d^2*e*integrate(1/16*x^3*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + b^2*c^2*d^3*integrate(1/16*x^2*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 4*b^2*c^2*d^3*integrate(1/16*x^2*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 3/2*a^2*d^2*e*x^2 + 1/4*b^2*d^3*arctan(c*x)^3/c - 2*b^2*c*e^3*integrate(1/16*x^4*arctan(c*x)/(c^2*x^2 + 1), x) - 8*b^2*c*d*e^2*integrate(1/16*x^3*arctan(c*x)/(c^2*x^2 + 1), x) - 12*b^2*c*d^2*e*integrate(1/16*x^2*arctan(c*x)/(c^2*x^2 + 1), x) - 8*b^2*c*d^3*integrate(1/16*x*arctan(c*x)/(c^2*x^2 + 1), x) + 3*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a*b*d^2*e + (2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a*b*d*e^2 + 1/6*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*a*b*e^3 + a^2*d^3*x + 12*b^2*e^3*integrate(1/16*x^3*arctan(c*x)^2/(c^2*x^2 + 1), x) + b^2*e^3*integrate(1/16*x^3*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 36*b^2*d*e^2*integrate(1/16*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 3*b^2*d*e^2*integrate(1/16*x^2*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 36*b^2*d^2*e*integrate(1/16*x*arctan(c*x)^2/(c^2*x^2 + 1), x) + 3*b^2*d^2*e*integrate(1/16*x*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + b^2*d^3*integrate(1/16*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + (2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*a*b*d^3/c + 1/16*(b^2*e^3*x^4 + 4*b^2*d*e^2*x^3 + 6*b^2*d^2*e*x^2 + 4*b^2*d^3*x)*arctan(c*x)^2 - 1/64*(b^2*e^3*x^4 + 4*b^2*d*e^2*x^3 + 6*b^2*d^2*e*x^2 + 4*b^2*d^3*x)*log(c^2*x^2 + 1)^2","F",0
10,0,0,0,0.000000," ","integrate((e*x+d)^2*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} e^{2} x^{3} + 36 \, b^{2} c^{2} e^{2} \int \frac{x^{4} \arctan\left(c x\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{2} c^{2} e^{2} \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 72 \, b^{2} c^{2} d e \int \frac{x^{3} \arctan\left(c x\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 4 \, b^{2} c^{2} e^{2} \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 6 \, b^{2} c^{2} d e \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 36 \, b^{2} c^{2} d^{2} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{2} c^{2} d e \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{2} c^{2} d^{2} \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{2} c^{2} d^{2} \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + a^{2} d e x^{2} + \frac{b^{2} d^{2} \arctan\left(c x\right)^{3}}{4 \, c} - 8 \, b^{2} c e^{2} \int \frac{x^{3} \arctan\left(c x\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 24 \, b^{2} c d e \int \frac{x^{2} \arctan\left(c x\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 24 \, b^{2} c d^{2} \int \frac{x \arctan\left(c x\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 2 \, {\left(x^{2} \arctan\left(c x\right) - c {\left(\frac{x}{c^{2}} - \frac{\arctan\left(c x\right)}{c^{3}}\right)}\right)} a b d e + \frac{1}{3} \, {\left(2 \, x^{3} \arctan\left(c x\right) - c {\left(\frac{x^{2}}{c^{2}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4}}\right)}\right)} a b e^{2} + a^{2} d^{2} x + 36 \, b^{2} e^{2} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{2} e^{2} \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 72 \, b^{2} d e \int \frac{x \arctan\left(c x\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 6 \, b^{2} d e \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{2} d^{2} \int \frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} a b d^{2}}{c} + \frac{1}{12} \, {\left(b^{2} e^{2} x^{3} + 3 \, b^{2} d e x^{2} + 3 \, b^{2} d^{2} x\right)} \arctan\left(c x\right)^{2} - \frac{1}{48} \, {\left(b^{2} e^{2} x^{3} + 3 \, b^{2} d e x^{2} + 3 \, b^{2} d^{2} x\right)} \log\left(c^{2} x^{2} + 1\right)^{2}"," ",0,"1/3*a^2*e^2*x^3 + 36*b^2*c^2*e^2*integrate(1/48*x^4*arctan(c*x)^2/(c^2*x^2 + 1), x) + 3*b^2*c^2*e^2*integrate(1/48*x^4*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 72*b^2*c^2*d*e*integrate(1/48*x^3*arctan(c*x)^2/(c^2*x^2 + 1), x) + 4*b^2*c^2*e^2*integrate(1/48*x^4*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 6*b^2*c^2*d*e*integrate(1/48*x^3*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 36*b^2*c^2*d^2*integrate(1/48*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 12*b^2*c^2*d*e*integrate(1/48*x^3*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 3*b^2*c^2*d^2*integrate(1/48*x^2*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 12*b^2*c^2*d^2*integrate(1/48*x^2*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + a^2*d*e*x^2 + 1/4*b^2*d^2*arctan(c*x)^3/c - 8*b^2*c*e^2*integrate(1/48*x^3*arctan(c*x)/(c^2*x^2 + 1), x) - 24*b^2*c*d*e*integrate(1/48*x^2*arctan(c*x)/(c^2*x^2 + 1), x) - 24*b^2*c*d^2*integrate(1/48*x*arctan(c*x)/(c^2*x^2 + 1), x) + 2*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a*b*d*e + 1/3*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a*b*e^2 + a^2*d^2*x + 36*b^2*e^2*integrate(1/48*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 3*b^2*e^2*integrate(1/48*x^2*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 72*b^2*d*e*integrate(1/48*x*arctan(c*x)^2/(c^2*x^2 + 1), x) + 6*b^2*d*e*integrate(1/48*x*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 3*b^2*d^2*integrate(1/48*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + (2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*a*b*d^2/c + 1/12*(b^2*e^2*x^3 + 3*b^2*d*e*x^2 + 3*b^2*d^2*x)*arctan(c*x)^2 - 1/48*(b^2*e^2*x^3 + 3*b^2*d*e*x^2 + 3*b^2*d^2*x)*log(c^2*x^2 + 1)^2","F",0
11,0,0,0,0.000000," ","integrate((e*x+d)*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","12 \, b^{2} c^{2} e \int \frac{x^{3} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + b^{2} c^{2} e \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{2} c^{2} d \int \frac{x^{2} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 2 \, b^{2} c^{2} e \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + b^{2} c^{2} d \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 4 \, b^{2} c^{2} d \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{1}{2} \, a^{2} e x^{2} + \frac{b^{2} d \arctan\left(c x\right)^{3}}{4 \, c} - 4 \, b^{2} c e \int \frac{x^{2} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 8 \, b^{2} c d \int \frac{x \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + {\left(x^{2} \arctan\left(c x\right) - c {\left(\frac{x}{c^{2}} - \frac{\arctan\left(c x\right)}{c^{3}}\right)}\right)} a b e + a^{2} d x + 12 \, b^{2} e \int \frac{x \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + b^{2} e \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + b^{2} d \int \frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} a b d}{c} + \frac{1}{8} \, {\left(b^{2} e x^{2} + 2 \, b^{2} d x\right)} \arctan\left(c x\right)^{2} - \frac{1}{32} \, {\left(b^{2} e x^{2} + 2 \, b^{2} d x\right)} \log\left(c^{2} x^{2} + 1\right)^{2}"," ",0,"12*b^2*c^2*e*integrate(1/16*x^3*arctan(c*x)^2/(c^2*x^2 + 1), x) + b^2*c^2*e*integrate(1/16*x^3*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 12*b^2*c^2*d*integrate(1/16*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 2*b^2*c^2*e*integrate(1/16*x^3*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + b^2*c^2*d*integrate(1/16*x^2*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 4*b^2*c^2*d*integrate(1/16*x^2*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 1/2*a^2*e*x^2 + 1/4*b^2*d*arctan(c*x)^3/c - 4*b^2*c*e*integrate(1/16*x^2*arctan(c*x)/(c^2*x^2 + 1), x) - 8*b^2*c*d*integrate(1/16*x*arctan(c*x)/(c^2*x^2 + 1), x) + (x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a*b*e + a^2*d*x + 12*b^2*e*integrate(1/16*x*arctan(c*x)^2/(c^2*x^2 + 1), x) + b^2*e*integrate(1/16*x*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + b^2*d*integrate(1/16*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + (2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*a*b*d/c + 1/8*(b^2*e*x^2 + 2*b^2*d*x)*arctan(c*x)^2 - 1/32*(b^2*e*x^2 + 2*b^2*d*x)*log(c^2*x^2 + 1)^2","F",0
12,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/(e*x+d),x, algorithm=""maxima"")","\frac{a^{2} \log\left(e x + d\right)}{e} + \int \frac{12 \, b^{2} \arctan\left(c x\right)^{2} + b^{2} \log\left(c^{2} x^{2} + 1\right)^{2} + 32 \, a b \arctan\left(c x\right)}{16 \, {\left(e x + d\right)}}\,{d x}"," ",0,"a^2*log(e*x + d)/e + integrate(1/16*(12*b^2*arctan(c*x)^2 + b^2*log(c^2*x^2 + 1)^2 + 32*a*b*arctan(c*x))/(e*x + d), x)","F",0
13,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/(e*x+d)^2,x, algorithm=""maxima"")","{\left({\left(\frac{2 \, c d \arctan\left(c x\right)}{c^{2} d^{2} e + e^{3}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{2} d^{2} + e^{2}} + \frac{2 \, \log\left(e x + d\right)}{c^{2} d^{2} + e^{2}}\right)} c - \frac{2 \, \arctan\left(c x\right)}{e^{2} x + d e}\right)} a b - \frac{\frac{1}{4} \, {\left(28 \, \arctan\left(c x\right)^{2} - 4 \, {\left(e^{2} x + d e\right)} \int \frac{36 \, {\left(c^{2} e x^{2} + e\right)} \arctan\left(c x\right)^{2} + 3 \, {\left(c^{2} e x^{2} + e\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 56 \, {\left(c e x + c d\right)} \arctan\left(c x\right) - 12 \, {\left(c^{2} e x^{2} + c^{2} d x\right)} \log\left(c^{2} x^{2} + 1\right)}{4 \, {\left(c^{2} e^{3} x^{4} + 2 \, c^{2} d e^{2} x^{3} + 2 \, d e^{2} x + d^{2} e + {\left(c^{2} d^{2} e + e^{3}\right)} x^{2}\right)}}\,{d x} - 3 \, \log\left(c^{2} x^{2} + 1\right)^{2}\right)} b^{2}}{16 \, {\left(e^{2} x + d e\right)}} - \frac{a^{2}}{e^{2} x + d e}"," ",0,"((2*c*d*arctan(c*x)/(c^2*d^2*e + e^3) - log(c^2*x^2 + 1)/(c^2*d^2 + e^2) + 2*log(e*x + d)/(c^2*d^2 + e^2))*c - 2*arctan(c*x)/(e^2*x + d*e))*a*b - 1/16*(4*arctan(c*x)^2 - 16*(e^2*x + d*e)*integrate(1/16*(12*(c^2*e*x^2 + e)*arctan(c*x)^2 + (c^2*e*x^2 + e)*log(c^2*x^2 + 1)^2 + 8*(c*e*x + c*d)*arctan(c*x) - 4*(c^2*e*x^2 + c^2*d*x)*log(c^2*x^2 + 1))/(c^2*e^3*x^4 + 2*c^2*d*e^2*x^3 + 2*d*e^2*x + d^2*e + (c^2*d^2*e + e^3)*x^2), x) - log(c^2*x^2 + 1)^2)*b^2/(e^2*x + d*e) - a^2/(e^2*x + d*e)","F",0
14,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/(e*x+d)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,0,0,0,0.000000," ","integrate((e*x+d)^3*(a+b*arctan(c*x))^3,x, algorithm=""maxima"")","\frac{1}{4} \, a^{3} e^{3} x^{4} + a^{3} d e^{2} x^{3} + \frac{7 \, b^{3} d^{3} \arctan\left(c x\right)^{4}}{32 \, c} + 112 \, b^{3} c^{2} e^{3} \int \frac{x^{5} \arctan\left(c x\right)^{3}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c^{2} e^{3} \int \frac{x^{5} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 384 \, a b^{2} c^{2} e^{3} \int \frac{x^{5} \arctan\left(c x\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 336 \, b^{3} c^{2} d e^{2} \int \frac{x^{4} \arctan\left(c x\right)^{3}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c^{2} e^{3} \int \frac{x^{5} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 36 \, b^{3} c^{2} d e^{2} \int \frac{x^{4} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 1152 \, a b^{2} c^{2} d e^{2} \int \frac{x^{4} \arctan\left(c x\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 336 \, b^{3} c^{2} d^{2} e \int \frac{x^{3} \arctan\left(c x\right)^{3}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 48 \, b^{3} c^{2} d e^{2} \int \frac{x^{4} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 36 \, b^{3} c^{2} d^{2} e \int \frac{x^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 1152 \, a b^{2} c^{2} d^{2} e \int \frac{x^{3} \arctan\left(c x\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 112 \, b^{3} c^{2} d^{3} \int \frac{x^{2} \arctan\left(c x\right)^{3}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 72 \, b^{3} c^{2} d^{2} e \int \frac{x^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c^{2} d^{3} \int \frac{x^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 384 \, a b^{2} c^{2} d^{3} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 48 \, b^{3} c^{2} d^{3} \int \frac{x^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{3}{2} \, a^{3} d^{2} e x^{2} + \frac{a b^{2} d^{3} \arctan\left(c x\right)^{3}}{c} - 12 \, b^{3} c e^{3} \int \frac{x^{4} \arctan\left(c x\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c e^{3} \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 48 \, b^{3} c d e^{2} \int \frac{x^{3} \arctan\left(c x\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c d e^{2} \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 72 \, b^{3} c d^{2} e \int \frac{x^{2} \arctan\left(c x\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 18 \, b^{3} c d^{2} e \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 48 \, b^{3} c d^{3} \int \frac{x \arctan\left(c x\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c d^{3} \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{9}{2} \, {\left(x^{2} \arctan\left(c x\right) - c {\left(\frac{x}{c^{2}} - \frac{\arctan\left(c x\right)}{c^{3}}\right)}\right)} a^{2} b d^{2} e + \frac{3}{2} \, {\left(2 \, x^{3} \arctan\left(c x\right) - c {\left(\frac{x^{2}}{c^{2}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4}}\right)}\right)} a^{2} b d e^{2} + \frac{1}{4} \, {\left(3 \, x^{4} \arctan\left(c x\right) - c {\left(\frac{c^{2} x^{3} - 3 \, x}{c^{4}} + \frac{3 \, \arctan\left(c x\right)}{c^{5}}\right)}\right)} a^{2} b e^{3} + a^{3} d^{3} x + 112 \, b^{3} e^{3} \int \frac{x^{3} \arctan\left(c x\right)^{3}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{3} e^{3} \int \frac{x^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 384 \, a b^{2} e^{3} \int \frac{x^{3} \arctan\left(c x\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 336 \, b^{3} d e^{2} \int \frac{x^{2} \arctan\left(c x\right)^{3}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 36 \, b^{3} d e^{2} \int \frac{x^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 1152 \, a b^{2} d e^{2} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 336 \, b^{3} d^{2} e \int \frac{x \arctan\left(c x\right)^{3}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 36 \, b^{3} d^{2} e \int \frac{x \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 1152 \, a b^{2} d^{2} e \int \frac{x \arctan\left(c x\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{3} d^{3} \int \frac{\arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{3 \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} a^{2} b d^{3}}{2 \, c} + \frac{1}{32} \, {\left(b^{3} e^{3} x^{4} + 4 \, b^{3} d e^{2} x^{3} + 6 \, b^{3} d^{2} e x^{2} + 4 \, b^{3} d^{3} x\right)} \arctan\left(c x\right)^{3} - \frac{3}{128} \, {\left(b^{3} e^{3} x^{4} + 4 \, b^{3} d e^{2} x^{3} + 6 \, b^{3} d^{2} e x^{2} + 4 \, b^{3} d^{3} x\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}"," ",0,"1/4*a^3*e^3*x^4 + a^3*d*e^2*x^3 + 7/32*b^3*d^3*arctan(c*x)^4/c + 112*b^3*c^2*e^3*integrate(1/128*x^5*arctan(c*x)^3/(c^2*x^2 + 1), x) + 12*b^3*c^2*e^3*integrate(1/128*x^5*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 384*a*b^2*c^2*e^3*integrate(1/128*x^5*arctan(c*x)^2/(c^2*x^2 + 1), x) + 336*b^3*c^2*d*e^2*integrate(1/128*x^4*arctan(c*x)^3/(c^2*x^2 + 1), x) + 12*b^3*c^2*e^3*integrate(1/128*x^5*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 36*b^3*c^2*d*e^2*integrate(1/128*x^4*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 1152*a*b^2*c^2*d*e^2*integrate(1/128*x^4*arctan(c*x)^2/(c^2*x^2 + 1), x) + 336*b^3*c^2*d^2*e*integrate(1/128*x^3*arctan(c*x)^3/(c^2*x^2 + 1), x) + 48*b^3*c^2*d*e^2*integrate(1/128*x^4*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 36*b^3*c^2*d^2*e*integrate(1/128*x^3*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 1152*a*b^2*c^2*d^2*e*integrate(1/128*x^3*arctan(c*x)^2/(c^2*x^2 + 1), x) + 112*b^3*c^2*d^3*integrate(1/128*x^2*arctan(c*x)^3/(c^2*x^2 + 1), x) + 72*b^3*c^2*d^2*e*integrate(1/128*x^3*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 12*b^3*c^2*d^3*integrate(1/128*x^2*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 384*a*b^2*c^2*d^3*integrate(1/128*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 48*b^3*c^2*d^3*integrate(1/128*x^2*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 3/2*a^3*d^2*e*x^2 + a*b^2*d^3*arctan(c*x)^3/c - 12*b^3*c*e^3*integrate(1/128*x^4*arctan(c*x)^2/(c^2*x^2 + 1), x) + 3*b^3*c*e^3*integrate(1/128*x^4*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) - 48*b^3*c*d*e^2*integrate(1/128*x^3*arctan(c*x)^2/(c^2*x^2 + 1), x) + 12*b^3*c*d*e^2*integrate(1/128*x^3*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) - 72*b^3*c*d^2*e*integrate(1/128*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 18*b^3*c*d^2*e*integrate(1/128*x^2*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) - 48*b^3*c*d^3*integrate(1/128*x*arctan(c*x)^2/(c^2*x^2 + 1), x) + 12*b^3*c*d^3*integrate(1/128*x*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 9/2*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a^2*b*d^2*e + 3/2*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a^2*b*d*e^2 + 1/4*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*a^2*b*e^3 + a^3*d^3*x + 112*b^3*e^3*integrate(1/128*x^3*arctan(c*x)^3/(c^2*x^2 + 1), x) + 12*b^3*e^3*integrate(1/128*x^3*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 384*a*b^2*e^3*integrate(1/128*x^3*arctan(c*x)^2/(c^2*x^2 + 1), x) + 336*b^3*d*e^2*integrate(1/128*x^2*arctan(c*x)^3/(c^2*x^2 + 1), x) + 36*b^3*d*e^2*integrate(1/128*x^2*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 1152*a*b^2*d*e^2*integrate(1/128*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 336*b^3*d^2*e*integrate(1/128*x*arctan(c*x)^3/(c^2*x^2 + 1), x) + 36*b^3*d^2*e*integrate(1/128*x*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 1152*a*b^2*d^2*e*integrate(1/128*x*arctan(c*x)^2/(c^2*x^2 + 1), x) + 12*b^3*d^3*integrate(1/128*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 3/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*a^2*b*d^3/c + 1/32*(b^3*e^3*x^4 + 4*b^3*d*e^2*x^3 + 6*b^3*d^2*e*x^2 + 4*b^3*d^3*x)*arctan(c*x)^3 - 3/128*(b^3*e^3*x^4 + 4*b^3*d*e^2*x^3 + 6*b^3*d^2*e*x^2 + 4*b^3*d^3*x)*arctan(c*x)*log(c^2*x^2 + 1)^2","F",0
16,0,0,0,0.000000," ","integrate((e*x+d)^2*(a+b*arctan(c*x))^3,x, algorithm=""maxima"")","\frac{1}{3} \, a^{3} e^{2} x^{3} + \frac{7 \, b^{3} d^{2} \arctan\left(c x\right)^{4}}{32 \, c} + 28 \, b^{3} c^{2} e^{2} \int \frac{x^{4} \arctan\left(c x\right)^{3}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c^{2} e^{2} \int \frac{x^{4} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 96 \, a b^{2} c^{2} e^{2} \int \frac{x^{4} \arctan\left(c x\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 56 \, b^{3} c^{2} d e \int \frac{x^{3} \arctan\left(c x\right)^{3}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 4 \, b^{3} c^{2} e^{2} \int \frac{x^{4} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 6 \, b^{3} c^{2} d e \int \frac{x^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} c^{2} d e \int \frac{x^{3} \arctan\left(c x\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 28 \, b^{3} c^{2} d^{2} \int \frac{x^{2} \arctan\left(c x\right)^{3}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c^{2} d e \int \frac{x^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c^{2} d^{2} \int \frac{x^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 96 \, a b^{2} c^{2} d^{2} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c^{2} d^{2} \int \frac{x^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + a^{3} d e x^{2} + \frac{a b^{2} d^{2} \arctan\left(c x\right)^{3}}{c} - 4 \, b^{3} c e^{2} \int \frac{x^{3} \arctan\left(c x\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + b^{3} c e^{2} \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 12 \, b^{3} c d e \int \frac{x^{2} \arctan\left(c x\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c d e \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 12 \, b^{3} c d^{2} \int \frac{x \arctan\left(c x\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c d^{2} \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, {\left(x^{2} \arctan\left(c x\right) - c {\left(\frac{x}{c^{2}} - \frac{\arctan\left(c x\right)}{c^{3}}\right)}\right)} a^{2} b d e + \frac{1}{2} \, {\left(2 \, x^{3} \arctan\left(c x\right) - c {\left(\frac{x^{2}}{c^{2}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4}}\right)}\right)} a^{2} b e^{2} + a^{3} d^{2} x + 28 \, b^{3} e^{2} \int \frac{x^{2} \arctan\left(c x\right)^{3}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{3} e^{2} \int \frac{x^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 96 \, a b^{2} e^{2} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 56 \, b^{3} d e \int \frac{x \arctan\left(c x\right)^{3}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 6 \, b^{3} d e \int \frac{x \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} d e \int \frac{x \arctan\left(c x\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{3} d^{2} \int \frac{\arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{3 \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} a^{2} b d^{2}}{2 \, c} + \frac{1}{24} \, {\left(b^{3} e^{2} x^{3} + 3 \, b^{3} d e x^{2} + 3 \, b^{3} d^{2} x\right)} \arctan\left(c x\right)^{3} - \frac{1}{32} \, {\left(b^{3} e^{2} x^{3} + 3 \, b^{3} d e x^{2} + 3 \, b^{3} d^{2} x\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}"," ",0,"1/3*a^3*e^2*x^3 + 7/32*b^3*d^2*arctan(c*x)^4/c + 28*b^3*c^2*e^2*integrate(1/32*x^4*arctan(c*x)^3/(c^2*x^2 + 1), x) + 3*b^3*c^2*e^2*integrate(1/32*x^4*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 96*a*b^2*c^2*e^2*integrate(1/32*x^4*arctan(c*x)^2/(c^2*x^2 + 1), x) + 56*b^3*c^2*d*e*integrate(1/32*x^3*arctan(c*x)^3/(c^2*x^2 + 1), x) + 4*b^3*c^2*e^2*integrate(1/32*x^4*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 6*b^3*c^2*d*e*integrate(1/32*x^3*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 192*a*b^2*c^2*d*e*integrate(1/32*x^3*arctan(c*x)^2/(c^2*x^2 + 1), x) + 28*b^3*c^2*d^2*integrate(1/32*x^2*arctan(c*x)^3/(c^2*x^2 + 1), x) + 12*b^3*c^2*d*e*integrate(1/32*x^3*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 3*b^3*c^2*d^2*integrate(1/32*x^2*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 96*a*b^2*c^2*d^2*integrate(1/32*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 12*b^3*c^2*d^2*integrate(1/32*x^2*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + a^3*d*e*x^2 + a*b^2*d^2*arctan(c*x)^3/c - 4*b^3*c*e^2*integrate(1/32*x^3*arctan(c*x)^2/(c^2*x^2 + 1), x) + b^3*c*e^2*integrate(1/32*x^3*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) - 12*b^3*c*d*e*integrate(1/32*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 3*b^3*c*d*e*integrate(1/32*x^2*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) - 12*b^3*c*d^2*integrate(1/32*x*arctan(c*x)^2/(c^2*x^2 + 1), x) + 3*b^3*c*d^2*integrate(1/32*x*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 3*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a^2*b*d*e + 1/2*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a^2*b*e^2 + a^3*d^2*x + 28*b^3*e^2*integrate(1/32*x^2*arctan(c*x)^3/(c^2*x^2 + 1), x) + 3*b^3*e^2*integrate(1/32*x^2*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 96*a*b^2*e^2*integrate(1/32*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 56*b^3*d*e*integrate(1/32*x*arctan(c*x)^3/(c^2*x^2 + 1), x) + 6*b^3*d*e*integrate(1/32*x*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 192*a*b^2*d*e*integrate(1/32*x*arctan(c*x)^2/(c^2*x^2 + 1), x) + 3*b^3*d^2*integrate(1/32*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 3/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*a^2*b*d^2/c + 1/24*(b^3*e^2*x^3 + 3*b^3*d*e*x^2 + 3*b^3*d^2*x)*arctan(c*x)^3 - 1/32*(b^3*e^2*x^3 + 3*b^3*d*e*x^2 + 3*b^3*d^2*x)*arctan(c*x)*log(c^2*x^2 + 1)^2","F",0
17,0,0,0,0.000000," ","integrate((e*x+d)*(a+b*arctan(c*x))^3,x, algorithm=""maxima"")","\frac{7 \, b^{3} d \arctan\left(c x\right)^{4}}{32 \, c} + 56 \, b^{3} c^{2} e \int \frac{x^{3} \arctan\left(c x\right)^{3}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 6 \, b^{3} c^{2} e \int \frac{x^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} c^{2} e \int \frac{x^{3} \arctan\left(c x\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 56 \, b^{3} c^{2} d \int \frac{x^{2} \arctan\left(c x\right)^{3}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c^{2} e \int \frac{x^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 6 \, b^{3} c^{2} d \int \frac{x^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} c^{2} d \int \frac{x^{2} \arctan\left(c x\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 24 \, b^{3} c^{2} d \int \frac{x^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{1}{2} \, a^{3} e x^{2} + \frac{a b^{2} d \arctan\left(c x\right)^{3}}{c} - 12 \, b^{3} c e \int \frac{x^{2} \arctan\left(c x\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c e \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 24 \, b^{3} c d \int \frac{x \arctan\left(c x\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 6 \, b^{3} c d \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{3}{2} \, {\left(x^{2} \arctan\left(c x\right) - c {\left(\frac{x}{c^{2}} - \frac{\arctan\left(c x\right)}{c^{3}}\right)}\right)} a^{2} b e + a^{3} d x + 56 \, b^{3} e \int \frac{x \arctan\left(c x\right)^{3}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 6 \, b^{3} e \int \frac{x \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} e \int \frac{x \arctan\left(c x\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 6 \, b^{3} d \int \frac{\arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{3 \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} a^{2} b d}{2 \, c} + \frac{1}{16} \, {\left(b^{3} e x^{2} + 2 \, b^{3} d x\right)} \arctan\left(c x\right)^{3} - \frac{3}{64} \, {\left(b^{3} e x^{2} + 2 \, b^{3} d x\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}"," ",0,"7/32*b^3*d*arctan(c*x)^4/c + 56*b^3*c^2*e*integrate(1/64*x^3*arctan(c*x)^3/(c^2*x^2 + 1), x) + 6*b^3*c^2*e*integrate(1/64*x^3*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 192*a*b^2*c^2*e*integrate(1/64*x^3*arctan(c*x)^2/(c^2*x^2 + 1), x) + 56*b^3*c^2*d*integrate(1/64*x^2*arctan(c*x)^3/(c^2*x^2 + 1), x) + 12*b^3*c^2*e*integrate(1/64*x^3*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 6*b^3*c^2*d*integrate(1/64*x^2*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 192*a*b^2*c^2*d*integrate(1/64*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 24*b^3*c^2*d*integrate(1/64*x^2*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 1/2*a^3*e*x^2 + a*b^2*d*arctan(c*x)^3/c - 12*b^3*c*e*integrate(1/64*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 3*b^3*c*e*integrate(1/64*x^2*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) - 24*b^3*c*d*integrate(1/64*x*arctan(c*x)^2/(c^2*x^2 + 1), x) + 6*b^3*c*d*integrate(1/64*x*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 3/2*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a^2*b*e + a^3*d*x + 56*b^3*e*integrate(1/64*x*arctan(c*x)^3/(c^2*x^2 + 1), x) + 6*b^3*e*integrate(1/64*x*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 192*a*b^2*e*integrate(1/64*x*arctan(c*x)^2/(c^2*x^2 + 1), x) + 6*b^3*d*integrate(1/64*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 3/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*a^2*b*d/c + 1/16*(b^3*e*x^2 + 2*b^3*d*x)*arctan(c*x)^3 - 3/64*(b^3*e*x^2 + 2*b^3*d*x)*arctan(c*x)*log(c^2*x^2 + 1)^2","F",0
18,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^3/(e*x+d),x, algorithm=""maxima"")","\frac{a^{3} \log\left(e x + d\right)}{e} + \int \frac{28 \, b^{3} \arctan\left(c x\right)^{3} + 3 \, b^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2} + 96 \, a b^{2} \arctan\left(c x\right)^{2} + 96 \, a^{2} b \arctan\left(c x\right)}{32 \, {\left(e x + d\right)}}\,{d x}"," ",0,"a^3*log(e*x + d)/e + integrate(1/32*(28*b^3*arctan(c*x)^3 + 3*b^3*arctan(c*x)*log(c^2*x^2 + 1)^2 + 96*a*b^2*arctan(c*x)^2 + 96*a^2*b*arctan(c*x))/(e*x + d), x)","F",0
19,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^3/(e*x+d)^2,x, algorithm=""maxima"")","\frac{3}{2} \, {\left({\left(\frac{2 \, c d \arctan\left(c x\right)}{c^{2} d^{2} e + e^{3}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{2} d^{2} + e^{2}} + \frac{2 \, \log\left(e x + d\right)}{c^{2} d^{2} + e^{2}}\right)} c - \frac{2 \, \arctan\left(c x\right)}{e^{2} x + d e}\right)} a^{2} b - \frac{a^{3}}{e^{2} x + d e} - \frac{\frac{15}{2} \, b^{3} \arctan\left(c x\right)^{3} - \frac{21}{8} \, b^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2} - {\left(e^{2} x + d e\right)} \int \frac{196 \, {\left(b^{3} c^{2} e x^{2} + b^{3} e\right)} \arctan\left(c x\right)^{3} + 12 \, {\left(64 \, a b^{2} c^{2} e x^{2} + 15 \, b^{3} c e x + 15 \, b^{3} c d + 64 \, a b^{2} e\right)} \arctan\left(c x\right)^{2} - 84 \, {\left(b^{3} c^{2} e x^{2} + b^{3} c^{2} d x\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) - 21 \, {\left(b^{3} c e x + b^{3} c d - {\left(b^{3} c^{2} e x^{2} + b^{3} e\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{8 \, {\left(c^{2} e^{3} x^{4} + 2 \, c^{2} d e^{2} x^{3} + 2 \, d e^{2} x + d^{2} e + {\left(c^{2} d^{2} e + e^{3}\right)} x^{2}\right)}}\,{d x}}{32 \, {\left(e^{2} x + d e\right)}}"," ",0,"3/2*((2*c*d*arctan(c*x)/(c^2*d^2*e + e^3) - log(c^2*x^2 + 1)/(c^2*d^2 + e^2) + 2*log(e*x + d)/(c^2*d^2 + e^2))*c - 2*arctan(c*x)/(e^2*x + d*e))*a^2*b - a^3/(e^2*x + d*e) - 1/32*(4*b^3*arctan(c*x)^3 - 3*b^3*arctan(c*x)*log(c^2*x^2 + 1)^2 - 32*(e^2*x + d*e)*integrate(1/32*(28*(b^3*c^2*e*x^2 + b^3*e)*arctan(c*x)^3 + 12*(8*a*b^2*c^2*e*x^2 + b^3*c*e*x + b^3*c*d + 8*a*b^2*e)*arctan(c*x)^2 - 12*(b^3*c^2*e*x^2 + b^3*c^2*d*x)*arctan(c*x)*log(c^2*x^2 + 1) - 3*(b^3*c*e*x + b^3*c*d - (b^3*c^2*e*x^2 + b^3*e)*arctan(c*x))*log(c^2*x^2 + 1)^2)/(c^2*e^3*x^4 + 2*c^2*d*e^2*x^3 + 2*d*e^2*x + d^2*e + (c^2*d^2*e + e^3)*x^2), x))/(e^2*x + d*e)","F",0
20,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^3/(e*x+d)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
21,1,323,0,0.417609," ","integrate((e*x+d)^2*(a+b*arctan(c*x^2)),x, algorithm=""maxima"")","\frac{1}{3} \, a e^{2} x^{3} + a d e x^{2} - \frac{1}{4} \, {\left(c {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x + \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x - \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(c x^{2} + \sqrt{2} \sqrt{c} x + 1\right)}{c^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(c x^{2} - \sqrt{2} \sqrt{c} x + 1\right)}{c^{\frac{3}{2}}}\right)} - 4 \, x \arctan\left(c x^{2}\right)\right)} b d^{2} + \frac{1}{12} \, {\left(4 \, x^{3} \arctan\left(c x^{2}\right) - c {\left(\frac{8 \, x}{c^{2}} - \frac{\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x + \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x - \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} + \frac{\sqrt{2} \log\left(c x^{2} + \sqrt{2} \sqrt{c} x + 1\right)}{\sqrt{c}} - \frac{\sqrt{2} \log\left(c x^{2} - \sqrt{2} \sqrt{c} x + 1\right)}{\sqrt{c}}}{c^{2}}\right)}\right)} b e^{2} + a d^{2} x + \frac{{\left(2 \, c x^{2} \arctan\left(c x^{2}\right) - \log\left(c^{2} x^{4} + 1\right)\right)} b d e}{2 \, c}"," ",0,"1/3*a*e^2*x^3 + a*d*e*x^2 - 1/4*(c*(2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x + sqrt(2)*sqrt(c))/sqrt(c))/c^(3/2) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x - sqrt(2)*sqrt(c))/sqrt(c))/c^(3/2) - sqrt(2)*log(c*x^2 + sqrt(2)*sqrt(c)*x + 1)/c^(3/2) + sqrt(2)*log(c*x^2 - sqrt(2)*sqrt(c)*x + 1)/c^(3/2)) - 4*x*arctan(c*x^2))*b*d^2 + 1/12*(4*x^3*arctan(c*x^2) - c*(8*x/c^2 - (2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x + sqrt(2)*sqrt(c))/sqrt(c))/sqrt(c) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x - sqrt(2)*sqrt(c))/sqrt(c))/sqrt(c) + sqrt(2)*log(c*x^2 + sqrt(2)*sqrt(c)*x + 1)/sqrt(c) - sqrt(2)*log(c*x^2 - sqrt(2)*sqrt(c)*x + 1)/sqrt(c))/c^2))*b*e^2 + a*d^2*x + 1/2*(2*c*x^2*arctan(c*x^2) - log(c^2*x^4 + 1))*b*d*e/c","A",0
22,1,168,0,0.411683," ","integrate((e*x+d)*(a+b*arctan(c*x^2)),x, algorithm=""maxima"")","\frac{1}{2} \, a e x^{2} - \frac{1}{4} \, {\left(c {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x + \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x - \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(c x^{2} + \sqrt{2} \sqrt{c} x + 1\right)}{c^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(c x^{2} - \sqrt{2} \sqrt{c} x + 1\right)}{c^{\frac{3}{2}}}\right)} - 4 \, x \arctan\left(c x^{2}\right)\right)} b d + a d x + \frac{{\left(2 \, c x^{2} \arctan\left(c x^{2}\right) - \log\left(c^{2} x^{4} + 1\right)\right)} b e}{4 \, c}"," ",0,"1/2*a*e*x^2 - 1/4*(c*(2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x + sqrt(2)*sqrt(c))/sqrt(c))/c^(3/2) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x - sqrt(2)*sqrt(c))/sqrt(c))/c^(3/2) - sqrt(2)*log(c*x^2 + sqrt(2)*sqrt(c)*x + 1)/c^(3/2) + sqrt(2)*log(c*x^2 - sqrt(2)*sqrt(c)*x + 1)/c^(3/2)) - 4*x*arctan(c*x^2))*b*d + a*d*x + 1/4*(2*c*x^2*arctan(c*x^2) - log(c^2*x^4 + 1))*b*e/c","A",0
23,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^2))/(e*x+d),x, algorithm=""maxima"")","2 \, b \int \frac{\arctan\left(c x^{2}\right)}{2 \, {\left(e x + d\right)}}\,{d x} + \frac{a \log\left(e x + d\right)}{e}"," ",0,"2*b*integrate(1/2*arctan(c*x^2)/(e*x + d), x) + a*log(e*x + d)/e","F",0
24,1,287,0,0.544931," ","integrate((a+b*arctan(c*x^2))/(e*x+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left({\left(\frac{8 \, d e \log\left(e x + d\right)}{c^{2} d^{4} + e^{4}} - \frac{\frac{\sqrt{2} {\left(c d^{2} e + \sqrt{2} \sqrt{c} d e^{2} + e^{3}\right)} \log\left(c x^{2} + \sqrt{2} \sqrt{c} x + 1\right)}{\sqrt{c}} - \frac{\sqrt{2} {\left(c d^{2} e - \sqrt{2} \sqrt{c} d e^{2} + e^{3}\right)} \log\left(c x^{2} - \sqrt{2} \sqrt{c} x + 1\right)}{\sqrt{c}} - \frac{2 \, {\left(2 \, c^{2} d^{3} + \sqrt{2} c^{\frac{3}{2}} d^{2} e - \sqrt{2} \sqrt{c} e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x + \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c} + \frac{2 \, {\left(2 \, c^{2} d^{3} - \sqrt{2} c^{\frac{3}{2}} d^{2} e + \sqrt{2} \sqrt{c} e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x - \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c}}{c^{2} d^{4} e + e^{5}}\right)} c + \frac{4 \, \arctan\left(c x^{2}\right)}{e^{2} x + d e}\right)} b - \frac{a}{e^{2} x + d e}"," ",0,"-1/4*((8*d*e*log(e*x + d)/(c^2*d^4 + e^4) - (sqrt(2)*(c*d^2*e + sqrt(2)*sqrt(c)*d*e^2 + e^3)*log(c*x^2 + sqrt(2)*sqrt(c)*x + 1)/sqrt(c) - sqrt(2)*(c*d^2*e - sqrt(2)*sqrt(c)*d*e^2 + e^3)*log(c*x^2 - sqrt(2)*sqrt(c)*x + 1)/sqrt(c) - 2*(2*c^2*d^3 + sqrt(2)*c^(3/2)*d^2*e - sqrt(2)*sqrt(c)*e^3)*arctan(1/2*sqrt(2)*(2*c*x + sqrt(2)*sqrt(c))/sqrt(c))/c + 2*(2*c^2*d^3 - sqrt(2)*c^(3/2)*d^2*e + sqrt(2)*sqrt(c)*e^3)*arctan(1/2*sqrt(2)*(2*c*x - sqrt(2)*sqrt(c))/sqrt(c))/c)/(c^2*d^4*e + e^5))*c + 4*arctan(c*x^2)/(e^2*x + d*e))*b - a/(e^2*x + d*e)","A",0
25,0,0,0,0.000000," ","integrate((e*x+d)*(a+b*arctan(c*x^2))^2,x, algorithm=""maxima"")","12 \, b^{2} c^{2} e \int \frac{x^{5} \arctan\left(c x^{2}\right)^{2}}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + b^{2} c^{2} e \int \frac{x^{5} \log\left(c^{2} x^{4} + 1\right)^{2}}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + 12 \, b^{2} c^{2} d \int \frac{x^{4} \arctan\left(c x^{2}\right)^{2}}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + 4 \, b^{2} c^{2} e \int \frac{x^{5} \log\left(c^{2} x^{4} + 1\right)}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + b^{2} c^{2} d \int \frac{x^{4} \log\left(c^{2} x^{4} + 1\right)^{2}}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + 8 \, b^{2} c^{2} d \int \frac{x^{4} \log\left(c^{2} x^{4} + 1\right)}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + \frac{1}{2} \, a^{2} e x^{2} + \frac{b^{2} e \arctan\left(c x^{2}\right)^{3}}{8 \, c} - 8 \, b^{2} c e \int \frac{x^{3} \arctan\left(c x^{2}\right)}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} - 16 \, b^{2} c d \int \frac{x^{2} \arctan\left(c x^{2}\right)}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} - \frac{1}{2} \, {\left(c {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x + \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x - \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(c x^{2} + \sqrt{2} \sqrt{c} x + 1\right)}{c^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(c x^{2} - \sqrt{2} \sqrt{c} x + 1\right)}{c^{\frac{3}{2}}}\right)} - 4 \, x \arctan\left(c x^{2}\right)\right)} a b d + a^{2} d x + b^{2} e \int \frac{x \log\left(c^{2} x^{4} + 1\right)^{2}}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + 12 \, b^{2} d \int \frac{\arctan\left(c x^{2}\right)^{2}}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + b^{2} d \int \frac{\log\left(c^{2} x^{4} + 1\right)^{2}}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + \frac{{\left(2 \, c x^{2} \arctan\left(c x^{2}\right) - \log\left(c^{2} x^{4} + 1\right)\right)} a b e}{2 \, c} + \frac{1}{8} \, {\left(b^{2} e x^{2} + 2 \, b^{2} d x\right)} \arctan\left(c x^{2}\right)^{2} - \frac{1}{32} \, {\left(b^{2} e x^{2} + 2 \, b^{2} d x\right)} \log\left(c^{2} x^{4} + 1\right)^{2}"," ",0,"12*b^2*c^2*e*integrate(1/16*x^5*arctan(c*x^2)^2/(c^2*x^4 + 1), x) + b^2*c^2*e*integrate(1/16*x^5*log(c^2*x^4 + 1)^2/(c^2*x^4 + 1), x) + 12*b^2*c^2*d*integrate(1/16*x^4*arctan(c*x^2)^2/(c^2*x^4 + 1), x) + 4*b^2*c^2*e*integrate(1/16*x^5*log(c^2*x^4 + 1)/(c^2*x^4 + 1), x) + b^2*c^2*d*integrate(1/16*x^4*log(c^2*x^4 + 1)^2/(c^2*x^4 + 1), x) + 8*b^2*c^2*d*integrate(1/16*x^4*log(c^2*x^4 + 1)/(c^2*x^4 + 1), x) + 1/2*a^2*e*x^2 + 1/8*b^2*e*arctan(c*x^2)^3/c - 8*b^2*c*e*integrate(1/16*x^3*arctan(c*x^2)/(c^2*x^4 + 1), x) - 16*b^2*c*d*integrate(1/16*x^2*arctan(c*x^2)/(c^2*x^4 + 1), x) - 1/2*(c*(2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x + sqrt(2)*sqrt(c))/sqrt(c))/c^(3/2) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x - sqrt(2)*sqrt(c))/sqrt(c))/c^(3/2) - sqrt(2)*log(c*x^2 + sqrt(2)*sqrt(c)*x + 1)/c^(3/2) + sqrt(2)*log(c*x^2 - sqrt(2)*sqrt(c)*x + 1)/c^(3/2)) - 4*x*arctan(c*x^2))*a*b*d + a^2*d*x + b^2*e*integrate(1/16*x*log(c^2*x^4 + 1)^2/(c^2*x^4 + 1), x) + 12*b^2*d*integrate(1/16*arctan(c*x^2)^2/(c^2*x^4 + 1), x) + b^2*d*integrate(1/16*log(c^2*x^4 + 1)^2/(c^2*x^4 + 1), x) + 1/2*(2*c*x^2*arctan(c*x^2) - log(c^2*x^4 + 1))*a*b*e/c + 1/8*(b^2*e*x^2 + 2*b^2*d*x)*arctan(c*x^2)^2 - 1/32*(b^2*e*x^2 + 2*b^2*d*x)*log(c^2*x^4 + 1)^2","F",0
26,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^2))^2/(e*x+d),x, algorithm=""maxima"")","\frac{a^{2} \log\left(e x + d\right)}{e} + \int \frac{b^{2} \arctan\left(c x^{2}\right)^{2} + 2 \, a b \arctan\left(c x^{2}\right)}{e x + d}\,{d x}"," ",0,"a^2*log(e*x + d)/e + integrate((b^2*arctan(c*x^2)^2 + 2*a*b*arctan(c*x^2))/(e*x + d), x)","F",0
27,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x^2))^2/(e*x+d)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
28,1,280,0,0.411084," ","integrate((e*x+d)^2*(a+b*arctan(c*x^3)),x, algorithm=""maxima"")","\frac{1}{3} \, a e^{2} x^{3} + a d e x^{2} - \frac{1}{4} \, {\left(c {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{4}{3}} x^{2} - c^{\frac{2}{3}}\right)}}{3 \, c^{\frac{2}{3}}}\right)}{c^{\frac{4}{3}}} + \frac{\log\left(c^{\frac{4}{3}} x^{4} - c^{\frac{2}{3}} x^{2} + 1\right)}{c^{\frac{4}{3}}} - \frac{2 \, \log\left(\frac{c^{\frac{2}{3}} x^{2} + 1}{c^{\frac{2}{3}}}\right)}{c^{\frac{4}{3}}}\right)} - 4 \, x \arctan\left(c x^{3}\right)\right)} b d^{2} + \frac{1}{4} \, {\left(4 \, x^{2} \arctan\left(c x^{3}\right) + c {\left(\frac{\sqrt{3} \log\left(c^{\frac{2}{3}} x^{2} + \sqrt{3} c^{\frac{1}{3}} x + 1\right)}{c^{\frac{5}{3}}} - \frac{\sqrt{3} \log\left(c^{\frac{2}{3}} x^{2} - \sqrt{3} c^{\frac{1}{3}} x + 1\right)}{c^{\frac{5}{3}}} - \frac{4 \, \arctan\left(c^{\frac{1}{3}} x\right)}{c^{\frac{5}{3}}} - \frac{2 \, \arctan\left(\frac{2 \, c^{\frac{2}{3}} x + \sqrt{3} c^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} - \frac{2 \, \arctan\left(\frac{2 \, c^{\frac{2}{3}} x - \sqrt{3} c^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}}\right)}\right)} b d e + a d^{2} x + \frac{{\left(2 \, c x^{3} \arctan\left(c x^{3}\right) - \log\left(c^{2} x^{6} + 1\right)\right)} b e^{2}}{6 \, c}"," ",0,"1/3*a*e^2*x^3 + a*d*e*x^2 - 1/4*(c*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(4/3)*x^2 - c^(2/3))/c^(2/3))/c^(4/3) + log(c^(4/3)*x^4 - c^(2/3)*x^2 + 1)/c^(4/3) - 2*log((c^(2/3)*x^2 + 1)/c^(2/3))/c^(4/3)) - 4*x*arctan(c*x^3))*b*d^2 + 1/4*(4*x^2*arctan(c*x^3) + c*(sqrt(3)*log(c^(2/3)*x^2 + sqrt(3)*c^(1/3)*x + 1)/c^(5/3) - sqrt(3)*log(c^(2/3)*x^2 - sqrt(3)*c^(1/3)*x + 1)/c^(5/3) - 4*arctan(c^(1/3)*x)/c^(5/3) - 2*arctan((2*c^(2/3)*x + sqrt(3)*c^(1/3))/c^(1/3))/c^(5/3) - 2*arctan((2*c^(2/3)*x - sqrt(3)*c^(1/3))/c^(1/3))/c^(5/3)))*b*d*e + a*d^2*x + 1/6*(2*c*x^3*arctan(c*x^3) - log(c^2*x^6 + 1))*b*e^2/c","A",0
29,1,232,0,0.412417," ","integrate((e*x+d)*(a+b*arctan(c*x^3)),x, algorithm=""maxima"")","\frac{1}{2} \, a e x^{2} - \frac{1}{4} \, {\left(c {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{4}{3}} x^{2} - c^{\frac{2}{3}}\right)}}{3 \, c^{\frac{2}{3}}}\right)}{c^{\frac{4}{3}}} + \frac{\log\left(c^{\frac{4}{3}} x^{4} - c^{\frac{2}{3}} x^{2} + 1\right)}{c^{\frac{4}{3}}} - \frac{2 \, \log\left(\frac{c^{\frac{2}{3}} x^{2} + 1}{c^{\frac{2}{3}}}\right)}{c^{\frac{4}{3}}}\right)} - 4 \, x \arctan\left(c x^{3}\right)\right)} b d + \frac{1}{8} \, {\left(4 \, x^{2} \arctan\left(c x^{3}\right) + c {\left(\frac{\sqrt{3} \log\left(c^{\frac{2}{3}} x^{2} + \sqrt{3} c^{\frac{1}{3}} x + 1\right)}{c^{\frac{5}{3}}} - \frac{\sqrt{3} \log\left(c^{\frac{2}{3}} x^{2} - \sqrt{3} c^{\frac{1}{3}} x + 1\right)}{c^{\frac{5}{3}}} - \frac{4 \, \arctan\left(c^{\frac{1}{3}} x\right)}{c^{\frac{5}{3}}} - \frac{2 \, \arctan\left(\frac{2 \, c^{\frac{2}{3}} x + \sqrt{3} c^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} - \frac{2 \, \arctan\left(\frac{2 \, c^{\frac{2}{3}} x - \sqrt{3} c^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}}\right)}\right)} b e + a d x"," ",0,"1/2*a*e*x^2 - 1/4*(c*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(4/3)*x^2 - c^(2/3))/c^(2/3))/c^(4/3) + log(c^(4/3)*x^4 - c^(2/3)*x^2 + 1)/c^(4/3) - 2*log((c^(2/3)*x^2 + 1)/c^(2/3))/c^(4/3)) - 4*x*arctan(c*x^3))*b*d + 1/8*(4*x^2*arctan(c*x^3) + c*(sqrt(3)*log(c^(2/3)*x^2 + sqrt(3)*c^(1/3)*x + 1)/c^(5/3) - sqrt(3)*log(c^(2/3)*x^2 - sqrt(3)*c^(1/3)*x + 1)/c^(5/3) - 4*arctan(c^(1/3)*x)/c^(5/3) - 2*arctan((2*c^(2/3)*x + sqrt(3)*c^(1/3))/c^(1/3))/c^(5/3) - 2*arctan((2*c^(2/3)*x - sqrt(3)*c^(1/3))/c^(1/3))/c^(5/3)))*b*e + a*d*x","A",0
30,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^3))/(e*x+d),x, algorithm=""maxima"")","2 \, b \int \frac{\arctan\left(c x^{3}\right)}{2 \, {\left(e x + d\right)}}\,{d x} + \frac{a \log\left(e x + d\right)}{e}"," ",0,"2*b*integrate(1/2*arctan(c*x^3)/(e*x + d), x) + a*log(e*x + d)/e","F",0
31,1,464,0,0.411048," ","integrate((a+b*arctan(c*x^3))/(e*x+d)^2,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(\frac{12 \, d^{2} e^{2} \log\left(e x + d\right)}{c^{2} d^{6} + e^{6}} - \frac{\frac{4 \, {\left(c^{\frac{8}{3}} d^{5} - c^{2} d^{3} e^{2} + c^{\frac{4}{3}} d e^{4}\right)} \arctan\left(c^{\frac{1}{3}} x\right)}{c^{\frac{5}{3}}} - \frac{2 \, {\left(\sqrt{3} c^{\frac{8}{3}} d^{4} e + 2 \, c^{3} d^{5} + c^{\frac{7}{3}} d^{3} e^{2} - \sqrt{3} c^{\frac{4}{3}} e^{5} - c^{\frac{5}{3}} d e^{4}\right)} \arctan\left(\frac{2 \, c^{\frac{2}{3}} x + \sqrt{3} c^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{2}} + \frac{2 \, {\left(\sqrt{3} c^{\frac{8}{3}} d^{4} e - 2 \, c^{3} d^{5} - c^{\frac{7}{3}} d^{3} e^{2} - \sqrt{3} c^{\frac{4}{3}} e^{5} + c^{\frac{5}{3}} d e^{4}\right)} \arctan\left(\frac{2 \, c^{\frac{2}{3}} x - \sqrt{3} c^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{2}} + \frac{{\left(\sqrt{3} c^{\frac{7}{3}} d^{3} e^{2} + c^{\frac{8}{3}} d^{4} e + \sqrt{3} c^{\frac{5}{3}} d e^{4} + 2 \, c^{2} d^{2} e^{3} + c^{\frac{4}{3}} e^{5}\right)} \log\left(c^{\frac{2}{3}} x^{2} + \sqrt{3} c^{\frac{1}{3}} x + 1\right)}{c^{2}} - \frac{{\left(\sqrt{3} c^{\frac{7}{3}} d^{3} e^{2} - c^{\frac{8}{3}} d^{4} e + \sqrt{3} c^{\frac{5}{3}} d e^{4} - 2 \, c^{2} d^{2} e^{3} - c^{\frac{4}{3}} e^{5}\right)} \log\left(c^{\frac{2}{3}} x^{2} - \sqrt{3} c^{\frac{1}{3}} x + 1\right)}{c^{2}} - \frac{2 \, {\left(c^{\frac{8}{3}} d^{4} e - c^{2} d^{2} e^{3} + c^{\frac{4}{3}} e^{5}\right)} \log\left(c^{\frac{2}{3}} x^{2} + 1\right)}{c^{2}}}{c^{2} d^{6} e + e^{7}}\right)} c - \frac{4 \, \arctan\left(c x^{3}\right)}{e^{2} x + d e}\right)} b - \frac{a}{e^{2} x + d e}"," ",0,"1/4*((12*d^2*e^2*log(e*x + d)/(c^2*d^6 + e^6) - (4*(c^(8/3)*d^5 - c^2*d^3*e^2 + c^(4/3)*d*e^4)*arctan(c^(1/3)*x)/c^(5/3) - 2*(sqrt(3)*c^(8/3)*d^4*e + 2*c^3*d^5 + c^(7/3)*d^3*e^2 - sqrt(3)*c^(4/3)*e^5 - c^(5/3)*d*e^4)*arctan((2*c^(2/3)*x + sqrt(3)*c^(1/3))/c^(1/3))/c^2 + 2*(sqrt(3)*c^(8/3)*d^4*e - 2*c^3*d^5 - c^(7/3)*d^3*e^2 - sqrt(3)*c^(4/3)*e^5 + c^(5/3)*d*e^4)*arctan((2*c^(2/3)*x - sqrt(3)*c^(1/3))/c^(1/3))/c^2 + (sqrt(3)*c^(7/3)*d^3*e^2 + c^(8/3)*d^4*e + sqrt(3)*c^(5/3)*d*e^4 + 2*c^2*d^2*e^3 + c^(4/3)*e^5)*log(c^(2/3)*x^2 + sqrt(3)*c^(1/3)*x + 1)/c^2 - (sqrt(3)*c^(7/3)*d^3*e^2 - c^(8/3)*d^4*e + sqrt(3)*c^(5/3)*d*e^4 - 2*c^2*d^2*e^3 - c^(4/3)*e^5)*log(c^(2/3)*x^2 - sqrt(3)*c^(1/3)*x + 1)/c^2 - 2*(c^(8/3)*d^4*e - c^2*d^2*e^3 + c^(4/3)*e^5)*log(c^(2/3)*x^2 + 1)/c^2)/(c^2*d^6*e + e^7))*c - 4*arctan(c*x^3)/(e^2*x + d*e))*b - a/(e^2*x + d*e)","A",0
