1,1,151,0,0.511470," ","integrate((d*e*x+c*e)^3*(a+b*arctan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a d^{4} e^{3} x^{4} + {\left(12 \, a c - b\right)} d^{3} e^{3} x^{3} + 3 \, {\left(6 \, a c^{2} - b c\right)} d^{2} e^{3} x^{2} + 3 \, {\left(4 \, a c^{3} - b c^{2} + b\right)} d e^{3} x + 3 \, {\left(b d^{4} e^{3} x^{4} + 4 \, b c d^{3} e^{3} x^{3} + 6 \, b c^{2} d^{2} e^{3} x^{2} + 4 \, b c^{3} d e^{3} x + {\left(b c^{4} - b\right)} e^{3}\right)} \arctan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*a*d^4*e^3*x^4 + (12*a*c - b)*d^3*e^3*x^3 + 3*(6*a*c^2 - b*c)*d^2*e^3*x^2 + 3*(4*a*c^3 - b*c^2 + b)*d*e^3*x + 3*(b*d^4*e^3*x^4 + 4*b*c*d^3*e^3*x^3 + 6*b*c^2*d^2*e^3*x^2 + 4*b*c^3*d*e^3*x + (b*c^4 - b)*e^3)*arctan(d*x + c))/d","B",0
2,1,129,0,0.655694," ","integrate((d*e*x+c*e)^2*(a+b*arctan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a d^{3} e^{2} x^{3} + {\left(6 \, a c - b\right)} d^{2} e^{2} x^{2} + 2 \, {\left(3 \, a c^{2} - b c\right)} d e^{2} x + b e^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) + 2 \, {\left(b d^{3} e^{2} x^{3} + 3 \, b c d^{2} e^{2} x^{2} + 3 \, b c^{2} d e^{2} x + b c^{3} e^{2}\right)} \arctan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*a*d^3*e^2*x^3 + (6*a*c - b)*d^2*e^2*x^2 + 2*(3*a*c^2 - b*c)*d*e^2*x + b*e^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*(b*d^3*e^2*x^3 + 3*b*c*d^2*e^2*x^2 + 3*b*c^2*d*e^2*x + b*c^3*e^2)*arctan(d*x + c))/d","B",0
3,1,60,0,0.576510," ","integrate((d*e*x+c*e)*(a+b*arctan(d*x+c)),x, algorithm=""fricas"")","\frac{a d^{2} e x^{2} + {\left(2 \, a c - b\right)} d e x + {\left(b d^{2} e x^{2} + 2 \, b c d e x + {\left(b c^{2} + b\right)} e\right)} \arctan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(a*d^2*e*x^2 + (2*a*c - b)*d*e*x + (b*d^2*e*x^2 + 2*b*c*d*e*x + (b*c^2 + b)*e)*arctan(d*x + c))/d","A",0
4,0,0,0,0.539280," ","integrate((a+b*arctan(d*x+c))/(d*e*x+c*e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(d x + c\right) + a}{d e x + c e}, x\right)"," ",0,"integral((b*arctan(d*x + c) + a)/(d*e*x + c*e), x)","F",0
5,1,75,0,0.511541," ","integrate((a+b*arctan(d*x+c))/(d*e*x+c*e)^2,x, algorithm=""fricas"")","-\frac{2 \, b \arctan\left(d x + c\right) + {\left(b d x + b c\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) - 2 \, {\left(b d x + b c\right)} \log\left(d x + c\right) + 2 \, a}{2 \, {\left(d^{2} e^{2} x + c d e^{2}\right)}}"," ",0,"-1/2*(2*b*arctan(d*x + c) + (b*d*x + b*c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1) - 2*(b*d*x + b*c)*log(d*x + c) + 2*a)/(d^2*e^2*x + c*d*e^2)","A",0
6,1,70,0,0.565265," ","integrate((a+b*arctan(d*x+c))/(d*e*x+c*e)^3,x, algorithm=""fricas"")","-\frac{b d x + b c + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + b\right)} \arctan\left(d x + c\right) + a}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}}"," ",0,"-1/2*(b*d*x + b*c + (b*d^2*x^2 + 2*b*c*d*x + b*c^2 + b)*arctan(d*x + c) + a)/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)","A",0
7,1,337,0,0.647255," ","integrate((d*e*x+c*e)^3*(a+b*arctan(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} d^{4} e^{3} x^{4} + 2 \, {\left(6 \, a^{2} c - a b\right)} d^{3} e^{3} x^{3} + {\left(18 \, a^{2} c^{2} - 6 \, a b c + b^{2}\right)} d^{2} e^{3} x^{2} + 2 \, {\left(6 \, a^{2} c^{3} - 3 \, a b c^{2} + b^{2} c + 3 \, a b\right)} d e^{3} x - 4 \, b^{2} e^{3} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) + 3 \, {\left(b^{2} d^{4} e^{3} x^{4} + 4 \, b^{2} c d^{3} e^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} e^{3} x^{2} + 4 \, b^{2} c^{3} d e^{3} x + {\left(b^{2} c^{4} - b^{2}\right)} e^{3}\right)} \arctan\left(d x + c\right)^{2} + 2 \, {\left(3 \, a b d^{4} e^{3} x^{4} + {\left(12 \, a b c - b^{2}\right)} d^{3} e^{3} x^{3} + 3 \, {\left(6 \, a b c^{2} - b^{2} c\right)} d^{2} e^{3} x^{2} + 3 \, {\left(4 \, a b c^{3} - b^{2} c^{2} + b^{2}\right)} d e^{3} x + {\left(3 \, a b c^{4} - b^{2} c^{3} + 3 \, b^{2} c - 3 \, a b\right)} e^{3}\right)} \arctan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*a^2*d^4*e^3*x^4 + 2*(6*a^2*c - a*b)*d^3*e^3*x^3 + (18*a^2*c^2 - 6*a*b*c + b^2)*d^2*e^3*x^2 + 2*(6*a^2*c^3 - 3*a*b*c^2 + b^2*c + 3*a*b)*d*e^3*x - 4*b^2*e^3*log(d^2*x^2 + 2*c*d*x + c^2 + 1) + 3*(b^2*d^4*e^3*x^4 + 4*b^2*c*d^3*e^3*x^3 + 6*b^2*c^2*d^2*e^3*x^2 + 4*b^2*c^3*d*e^3*x + (b^2*c^4 - b^2)*e^3)*arctan(d*x + c)^2 + 2*(3*a*b*d^4*e^3*x^4 + (12*a*b*c - b^2)*d^3*e^3*x^3 + 3*(6*a*b*c^2 - b^2*c)*d^2*e^3*x^2 + 3*(4*a*b*c^3 - b^2*c^2 + b^2)*d*e^3*x + (3*a*b*c^4 - b^2*c^3 + 3*b^2*c - 3*a*b)*e^3)*arctan(d*x + c))/d","B",0
8,0,0,0,0.670890," ","integrate((d*e*x+c*e)^2*(a+b*arctan(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} d^{2} e^{2} x^{2} + 2 \, a^{2} c d e^{2} x + a^{2} c^{2} e^{2} + {\left(b^{2} d^{2} e^{2} x^{2} + 2 \, b^{2} c d e^{2} x + b^{2} c^{2} e^{2}\right)} \arctan\left(d x + c\right)^{2} + 2 \, {\left(a b d^{2} e^{2} x^{2} + 2 \, a b c d e^{2} x + a b c^{2} e^{2}\right)} \arctan\left(d x + c\right), x\right)"," ",0,"integral(a^2*d^2*e^2*x^2 + 2*a^2*c*d*e^2*x + a^2*c^2*e^2 + (b^2*d^2*e^2*x^2 + 2*b^2*c*d*e^2*x + b^2*c^2*e^2)*arctan(d*x + c)^2 + 2*(a*b*d^2*e^2*x^2 + 2*a*b*c*d*e^2*x + a*b*c^2*e^2)*arctan(d*x + c), x)","F",0
9,1,150,0,0.721252," ","integrate((d*e*x+c*e)*(a+b*arctan(d*x+c))^2,x, algorithm=""fricas"")","\frac{a^{2} d^{2} e x^{2} + 2 \, {\left(a^{2} c - a b\right)} d e x + b^{2} e \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) + {\left(b^{2} d^{2} e x^{2} + 2 \, b^{2} c d e x + {\left(b^{2} c^{2} + b^{2}\right)} e\right)} \arctan\left(d x + c\right)^{2} + 2 \, {\left(a b d^{2} e x^{2} + {\left(2 \, a b c - b^{2}\right)} d e x + {\left(a b c^{2} - b^{2} c + a b\right)} e\right)} \arctan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(a^2*d^2*e*x^2 + 2*(a^2*c - a*b)*d*e*x + b^2*e*log(d^2*x^2 + 2*c*d*x + c^2 + 1) + (b^2*d^2*e*x^2 + 2*b^2*c*d*e*x + (b^2*c^2 + b^2)*e)*arctan(d*x + c)^2 + 2*(a*b*d^2*e*x^2 + (2*a*b*c - b^2)*d*e*x + (a*b*c^2 - b^2*c + a*b)*e)*arctan(d*x + c))/d","A",0
10,0,0,0,0.415019," ","integrate((a+b*arctan(d*x+c))^2/(d*e*x+c*e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(d x + c\right)^{2} + 2 \, a b \arctan\left(d x + c\right) + a^{2}}{d e x + c e}, x\right)"," ",0,"integral((b^2*arctan(d*x + c)^2 + 2*a*b*arctan(d*x + c) + a^2)/(d*e*x + c*e), x)","F",0
11,0,0,0,0.452147," ","integrate((a+b*arctan(d*x+c))^2/(d*e*x+c*e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(d x + c\right)^{2} + 2 \, a b \arctan\left(d x + c\right) + a^{2}}{d^{2} e^{2} x^{2} + 2 \, c d e^{2} x + c^{2} e^{2}}, x\right)"," ",0,"integral((b^2*arctan(d*x + c)^2 + 2*a*b*arctan(d*x + c) + a^2)/(d^2*e^2*x^2 + 2*c*d*e^2*x + c^2*e^2), x)","F",0
12,1,209,0,0.435581," ","integrate((a+b*arctan(d*x+c))^2/(d*e*x+c*e)^3,x, algorithm=""fricas"")","-\frac{2 \, a b d x + 2 \, a b c + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + b^{2}\right)} \arctan\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(a b d^{2} x^{2} + a b c^{2} + b^{2} c + {\left(2 \, a b c + b^{2}\right)} d x + a b\right)} \arctan\left(d x + c\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d x + c\right)}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}}"," ",0,"-1/2*(2*a*b*d*x + 2*a*b*c + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + b^2)*arctan(d*x + c)^2 + a^2 + 2*(a*b*d^2*x^2 + a*b*c^2 + b^2*c + (2*a*b*c + b^2)*d*x + a*b)*arctan(d*x + c) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d^2*x^2 + 2*c*d*x + c^2 + 1) - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d*x + c))/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)","A",0
13,0,0,0,0.471905," ","integrate((a+b*arctan(d*x+c))^2/(d*e*x+c*e)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(d x + c\right)^{2} + 2 \, a b \arctan\left(d x + c\right) + a^{2}}{d^{4} e^{4} x^{4} + 4 \, c d^{3} e^{4} x^{3} + 6 \, c^{2} d^{2} e^{4} x^{2} + 4 \, c^{3} d e^{4} x + c^{4} e^{4}}, x\right)"," ",0,"integral((b^2*arctan(d*x + c)^2 + 2*a*b*arctan(d*x + c) + a^2)/(d^4*e^4*x^4 + 4*c*d^3*e^4*x^3 + 6*c^2*d^2*e^4*x^2 + 4*c^3*d*e^4*x + c^4*e^4), x)","F",0
14,1,448,0,0.474663," ","integrate((a+b*arctan(d*x+c))^2/(d*e*x+c*e)^5,x, algorithm=""fricas"")","\frac{6 \, a b d^{3} x^{3} + 6 \, a b c^{3} + {\left(18 \, a b c - b^{2}\right)} d^{2} x^{2} - b^{2} c^{2} - 2 \, a b c + 2 \, {\left(9 \, a b c^{2} - b^{2} c - a b\right)} d x + 3 \, {\left(b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} x^{2} + 4 \, b^{2} c^{3} d x + b^{2} c^{4} - b^{2}\right)} \arctan\left(d x + c\right)^{2} - 3 \, a^{2} + 2 \, {\left(3 \, a b d^{4} x^{4} + 3 \, {\left(4 \, a b c + b^{2}\right)} d^{3} x^{3} + 3 \, a b c^{4} + 3 \, b^{2} c^{3} + 9 \, {\left(2 \, a b c^{2} + b^{2} c\right)} d^{2} x^{2} - b^{2} c + {\left(12 \, a b c^{3} + 9 \, b^{2} c^{2} - b^{2}\right)} d x - 3 \, a b\right)} \arctan\left(d x + c\right) + 4 \, {\left(b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} x^{2} + 4 \, b^{2} c^{3} d x + b^{2} c^{4}\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) - 8 \, {\left(b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} x^{2} + 4 \, b^{2} c^{3} d x + b^{2} c^{4}\right)} \log\left(d x + c\right)}{12 \, {\left(d^{5} e^{5} x^{4} + 4 \, c d^{4} e^{5} x^{3} + 6 \, c^{2} d^{3} e^{5} x^{2} + 4 \, c^{3} d^{2} e^{5} x + c^{4} d e^{5}\right)}}"," ",0,"1/12*(6*a*b*d^3*x^3 + 6*a*b*c^3 + (18*a*b*c - b^2)*d^2*x^2 - b^2*c^2 - 2*a*b*c + 2*(9*a*b*c^2 - b^2*c - a*b)*d*x + 3*(b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 6*b^2*c^2*d^2*x^2 + 4*b^2*c^3*d*x + b^2*c^4 - b^2)*arctan(d*x + c)^2 - 3*a^2 + 2*(3*a*b*d^4*x^4 + 3*(4*a*b*c + b^2)*d^3*x^3 + 3*a*b*c^4 + 3*b^2*c^3 + 9*(2*a*b*c^2 + b^2*c)*d^2*x^2 - b^2*c + (12*a*b*c^3 + 9*b^2*c^2 - b^2)*d*x - 3*a*b)*arctan(d*x + c) + 4*(b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 6*b^2*c^2*d^2*x^2 + 4*b^2*c^3*d*x + b^2*c^4)*log(d^2*x^2 + 2*c*d*x + c^2 + 1) - 8*(b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 6*b^2*c^2*d^2*x^2 + 4*b^2*c^3*d*x + b^2*c^4)*log(d*x + c))/(d^5*e^5*x^4 + 4*c*d^4*e^5*x^3 + 6*c^2*d^3*e^5*x^2 + 4*c^3*d^2*e^5*x + c^4*d*e^5)","B",0
15,0,0,0,0.469218," ","integrate((d*e*x+c*e)^2*(a+b*arctan(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(a^{3} d^{2} e^{2} x^{2} + 2 \, a^{3} c d e^{2} x + a^{3} c^{2} e^{2} + {\left(b^{3} d^{2} e^{2} x^{2} + 2 \, b^{3} c d e^{2} x + b^{3} c^{2} e^{2}\right)} \arctan\left(d x + c\right)^{3} + 3 \, {\left(a b^{2} d^{2} e^{2} x^{2} + 2 \, a b^{2} c d e^{2} x + a b^{2} c^{2} e^{2}\right)} \arctan\left(d x + c\right)^{2} + 3 \, {\left(a^{2} b d^{2} e^{2} x^{2} + 2 \, a^{2} b c d e^{2} x + a^{2} b c^{2} e^{2}\right)} \arctan\left(d x + c\right), x\right)"," ",0,"integral(a^3*d^2*e^2*x^2 + 2*a^3*c*d*e^2*x + a^3*c^2*e^2 + (b^3*d^2*e^2*x^2 + 2*b^3*c*d*e^2*x + b^3*c^2*e^2)*arctan(d*x + c)^3 + 3*(a*b^2*d^2*e^2*x^2 + 2*a*b^2*c*d*e^2*x + a*b^2*c^2*e^2)*arctan(d*x + c)^2 + 3*(a^2*b*d^2*e^2*x^2 + 2*a^2*b*c*d*e^2*x + a^2*b*c^2*e^2)*arctan(d*x + c), x)","F",0
16,0,0,0,0.454916," ","integrate((d*e*x+c*e)*(a+b*arctan(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(a^{3} d e x + a^{3} c e + {\left(b^{3} d e x + b^{3} c e\right)} \arctan\left(d x + c\right)^{3} + 3 \, {\left(a b^{2} d e x + a b^{2} c e\right)} \arctan\left(d x + c\right)^{2} + 3 \, {\left(a^{2} b d e x + a^{2} b c e\right)} \arctan\left(d x + c\right), x\right)"," ",0,"integral(a^3*d*e*x + a^3*c*e + (b^3*d*e*x + b^3*c*e)*arctan(d*x + c)^3 + 3*(a*b^2*d*e*x + a*b^2*c*e)*arctan(d*x + c)^2 + 3*(a^2*b*d*e*x + a^2*b*c*e)*arctan(d*x + c), x)","F",0
17,0,0,0,0.462708," ","integrate((a+b*arctan(d*x+c))^3/(d*e*x+c*e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(d x + c\right)^{3} + 3 \, a b^{2} \arctan\left(d x + c\right)^{2} + 3 \, a^{2} b \arctan\left(d x + c\right) + a^{3}}{d e x + c e}, x\right)"," ",0,"integral((b^3*arctan(d*x + c)^3 + 3*a*b^2*arctan(d*x + c)^2 + 3*a^2*b*arctan(d*x + c) + a^3)/(d*e*x + c*e), x)","F",0
18,0,0,0,0.458733," ","integrate((a+b*arctan(d*x+c))^3/(d*e*x+c*e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(d x + c\right)^{3} + 3 \, a b^{2} \arctan\left(d x + c\right)^{2} + 3 \, a^{2} b \arctan\left(d x + c\right) + a^{3}}{d^{2} e^{2} x^{2} + 2 \, c d e^{2} x + c^{2} e^{2}}, x\right)"," ",0,"integral((b^3*arctan(d*x + c)^3 + 3*a*b^2*arctan(d*x + c)^2 + 3*a^2*b*arctan(d*x + c) + a^3)/(d^2*e^2*x^2 + 2*c*d*e^2*x + c^2*e^2), x)","F",0
19,0,0,0,0.445195," ","integrate((a+b*arctan(d*x+c))^3/(d*e*x+c*e)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(d x + c\right)^{3} + 3 \, a b^{2} \arctan\left(d x + c\right)^{2} + 3 \, a^{2} b \arctan\left(d x + c\right) + a^{3}}{d^{3} e^{3} x^{3} + 3 \, c d^{2} e^{3} x^{2} + 3 \, c^{2} d e^{3} x + c^{3} e^{3}}, x\right)"," ",0,"integral((b^3*arctan(d*x + c)^3 + 3*a*b^2*arctan(d*x + c)^2 + 3*a^2*b*arctan(d*x + c) + a^3)/(d^3*e^3*x^3 + 3*c*d^2*e^3*x^2 + 3*c^2*d*e^3*x + c^3*e^3), x)","F",0
20,0,0,0,0.443869," ","integrate((a+b*arctan(d*x+c))^3/(d*e*x+c*e)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(d x + c\right)^{3} + 3 \, a b^{2} \arctan\left(d x + c\right)^{2} + 3 \, a^{2} b \arctan\left(d x + c\right) + a^{3}}{d^{4} e^{4} x^{4} + 4 \, c d^{3} e^{4} x^{3} + 6 \, c^{2} d^{2} e^{4} x^{2} + 4 \, c^{3} d e^{4} x + c^{4} e^{4}}, x\right)"," ",0,"integral((b^3*arctan(d*x + c)^3 + 3*a*b^2*arctan(d*x + c)^2 + 3*a^2*b*arctan(d*x + c) + a^3)/(d^4*e^4*x^4 + 4*c*d^3*e^4*x^3 + 6*c^2*d^2*e^4*x^2 + 4*c^3*d*e^4*x + c^4*e^4), x)","F",0
21,0,0,0,0.461463," ","integrate(arctan(1+x)/(2+2*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(x + 1\right)}{2 \, {\left(x + 1\right)}}, x\right)"," ",0,"integral(1/2*arctan(x + 1)/(x + 1), x)","F",0
22,0,0,0,0.494293," ","integrate(arctan(b*x+a)/(a*d/b+d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(b x + a\right)}{b d x + a d}, x\right)"," ",0,"integral(b*arctan(b*x + a)/(b*d*x + a*d), x)","F",0
23,-2,0,0,0.000000," ","integrate((b*x+a)^2*arctan(b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
24,1,317,0,0.475685," ","integrate((f*x+e)^3*(a+b*arctan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a d^{4} f^{3} x^{4} + {\left(12 \, a d^{4} e f^{2} - b d^{3} f^{3}\right)} x^{3} + 3 \, {\left(6 \, a d^{4} e^{2} f - 2 \, b d^{3} e f^{2} + b c d^{2} f^{3}\right)} x^{2} + 3 \, {\left(4 \, a d^{4} e^{3} - 6 \, b d^{3} e^{2} f + 8 \, b c d^{2} e f^{2} - {\left(3 \, b c^{2} - b\right)} d f^{3}\right)} x + 3 \, {\left(b d^{4} f^{3} x^{4} + 4 \, b d^{4} e f^{2} x^{3} + 6 \, b d^{4} e^{2} f x^{2} + 4 \, b d^{4} e^{3} x + 4 \, b c d^{3} e^{3} - 6 \, {\left(b c^{2} - b\right)} d^{2} e^{2} f + 4 \, {\left(b c^{3} - 3 \, b c\right)} d e f^{2} - {\left(b c^{4} - 6 \, b c^{2} + b\right)} f^{3}\right)} \arctan\left(d x + c\right) - 6 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + {\left(3 \, b c^{2} - b\right)} d e f^{2} - {\left(b c^{3} - b c\right)} f^{3}\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{12 \, d^{4}}"," ",0,"1/12*(3*a*d^4*f^3*x^4 + (12*a*d^4*e*f^2 - b*d^3*f^3)*x^3 + 3*(6*a*d^4*e^2*f - 2*b*d^3*e*f^2 + b*c*d^2*f^3)*x^2 + 3*(4*a*d^4*e^3 - 6*b*d^3*e^2*f + 8*b*c*d^2*e*f^2 - (3*b*c^2 - b)*d*f^3)*x + 3*(b*d^4*f^3*x^4 + 4*b*d^4*e*f^2*x^3 + 6*b*d^4*e^2*f*x^2 + 4*b*d^4*e^3*x + 4*b*c*d^3*e^3 - 6*(b*c^2 - b)*d^2*e^2*f + 4*(b*c^3 - 3*b*c)*d*e*f^2 - (b*c^4 - 6*b*c^2 + b)*f^3)*arctan(d*x + c) - 6*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + (3*b*c^2 - b)*d*e*f^2 - (b*c^3 - b*c)*f^3)*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/d^4","A",0
25,1,199,0,0.468251," ","integrate((f*x+e)^2*(a+b*arctan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a d^{3} f^{2} x^{3} + {\left(6 \, a d^{3} e f - b d^{2} f^{2}\right)} x^{2} + 2 \, {\left(3 \, a d^{3} e^{2} - 3 \, b d^{2} e f + 2 \, b c d f^{2}\right)} x + 2 \, {\left(b d^{3} f^{2} x^{3} + 3 \, b d^{3} e f x^{2} + 3 \, b d^{3} e^{2} x + 3 \, b c d^{2} e^{2} - 3 \, {\left(b c^{2} - b\right)} d e f + {\left(b c^{3} - 3 \, b c\right)} f^{2}\right)} \arctan\left(d x + c\right) - {\left(3 \, b d^{2} e^{2} - 6 \, b c d e f + {\left(3 \, b c^{2} - b\right)} f^{2}\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{6 \, d^{3}}"," ",0,"1/6*(2*a*d^3*f^2*x^3 + (6*a*d^3*e*f - b*d^2*f^2)*x^2 + 2*(3*a*d^3*e^2 - 3*b*d^2*e*f + 2*b*c*d*f^2)*x + 2*(b*d^3*f^2*x^3 + 3*b*d^3*e*f*x^2 + 3*b*d^3*e^2*x + 3*b*c*d^2*e^2 - 3*(b*c^2 - b)*d*e*f + (b*c^3 - 3*b*c)*f^2)*arctan(d*x + c) - (3*b*d^2*e^2 - 6*b*c*d*e*f + (3*b*c^2 - b)*f^2)*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/d^3","A",0
26,1,103,0,0.456357," ","integrate((f*x+e)*(a+b*arctan(d*x+c)),x, algorithm=""fricas"")","\frac{a d^{2} f x^{2} + {\left(2 \, a d^{2} e - b d f\right)} x + {\left(b d^{2} f x^{2} + 2 \, b d^{2} e x + 2 \, b c d e - {\left(b c^{2} - b\right)} f\right)} \arctan\left(d x + c\right) - {\left(b d e - b c f\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{2 \, d^{2}}"," ",0,"1/2*(a*d^2*f*x^2 + (2*a*d^2*e - b*d*f)*x + (b*d^2*f*x^2 + 2*b*d^2*e*x + 2*b*c*d*e - (b*c^2 - b)*f)*arctan(d*x + c) - (b*d*e - b*c*f)*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/d^2","A",0
27,1,48,0,0.429849," ","integrate(a+b*arctan(d*x+c),x, algorithm=""fricas"")","\frac{2 \, a d x + 2 \, {\left(b d x + b c\right)} \arctan\left(d x + c\right) - b \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(2*a*d*x + 2*(b*d*x + b*c)*arctan(d*x + c) - b*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/d","A",0
28,0,0,0,0.440845," ","integrate((a+b*arctan(d*x+c))/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(d x + c\right) + a}{f x + e}, x\right)"," ",0,"integral((b*arctan(d*x + c) + a)/(f*x + e), x)","F",0
29,1,190,0,0.695248," ","integrate((a+b*arctan(d*x+c))/(f*x+e)^2,x, algorithm=""fricas"")","-\frac{2 \, a d^{2} e^{2} - 4 \, a c d e f + 2 \, {\left(a c^{2} + a\right)} f^{2} - 2 \, {\left(b c d e f - {\left(b c^{2} + b\right)} f^{2} + {\left(b d^{2} e f - b c d f^{2}\right)} x\right)} \arctan\left(d x + c\right) + {\left(b d f^{2} x + b d e f\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) - 2 \, {\left(b d f^{2} x + b d e f\right)} \log\left(f x + e\right)}{2 \, {\left(d^{2} e^{3} f - 2 \, c d e^{2} f^{2} + {\left(c^{2} + 1\right)} e f^{3} + {\left(d^{2} e^{2} f^{2} - 2 \, c d e f^{3} + {\left(c^{2} + 1\right)} f^{4}\right)} x\right)}}"," ",0,"-1/2*(2*a*d^2*e^2 - 4*a*c*d*e*f + 2*(a*c^2 + a)*f^2 - 2*(b*c*d*e*f - (b*c^2 + b)*f^2 + (b*d^2*e*f - b*c*d*f^2)*x)*arctan(d*x + c) + (b*d*f^2*x + b*d*e*f)*log(d^2*x^2 + 2*c*d*x + c^2 + 1) - 2*(b*d*f^2*x + b*d*e*f)*log(f*x + e))/(d^2*e^3*f - 2*c*d*e^2*f^2 + (c^2 + 1)*e*f^3 + (d^2*e^2*f^2 - 2*c*d*e*f^3 + (c^2 + 1)*f^4)*x)","A",0
30,1,682,0,2.128577," ","integrate((a+b*arctan(d*x+c))/(f*x+e)^3,x, algorithm=""fricas"")","-\frac{a d^{4} e^{4} - {\left(4 \, a c - b\right)} d^{3} e^{3} f + 2 \, {\left(3 \, a c^{2} - b c + a\right)} d^{2} e^{2} f^{2} - {\left(4 \, a c^{3} - b c^{2} + 4 \, a c - b\right)} d e f^{3} + {\left(a c^{4} + 2 \, a c^{2} + a\right)} f^{4} + {\left(b d^{3} e^{2} f^{2} - 2 \, b c d^{2} e f^{3} + {\left(b c^{2} + b\right)} d f^{4}\right)} x - {\left(2 \, b c d^{3} e^{3} f - {\left(5 \, b c^{2} + 3 \, b\right)} d^{2} e^{2} f^{2} + 4 \, {\left(b c^{3} + b c\right)} d e f^{3} - {\left(b c^{4} + 2 \, b c^{2} + b\right)} f^{4} + {\left(b d^{4} e^{2} f^{2} - 2 \, b c d^{3} e f^{3} + {\left(b c^{2} - b\right)} d^{2} f^{4}\right)} x^{2} + 2 \, {\left(b d^{4} e^{3} f - 2 \, b c d^{3} e^{2} f^{2} + {\left(b c^{2} - b\right)} d^{2} e f^{3}\right)} x\right)} \arctan\left(d x + c\right) + {\left(b d^{3} e^{3} f - b c d^{2} e^{2} f^{2} + {\left(b d^{3} e f^{3} - b c d^{2} f^{4}\right)} x^{2} + 2 \, {\left(b d^{3} e^{2} f^{2} - b c d^{2} e f^{3}\right)} x\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) - 2 \, {\left(b d^{3} e^{3} f - b c d^{2} e^{2} f^{2} + {\left(b d^{3} e f^{3} - b c d^{2} f^{4}\right)} x^{2} + 2 \, {\left(b d^{3} e^{2} f^{2} - b c d^{2} e f^{3}\right)} x\right)} \log\left(f x + e\right)}{2 \, {\left(d^{4} e^{6} f - 4 \, c d^{3} e^{5} f^{2} + 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} e^{4} f^{3} - 4 \, {\left(c^{3} + c\right)} d e^{3} f^{4} + {\left(c^{4} + 2 \, c^{2} + 1\right)} e^{2} f^{5} + {\left(d^{4} e^{4} f^{3} - 4 \, c d^{3} e^{3} f^{4} + 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} e^{2} f^{5} - 4 \, {\left(c^{3} + c\right)} d e f^{6} + {\left(c^{4} + 2 \, c^{2} + 1\right)} f^{7}\right)} x^{2} + 2 \, {\left(d^{4} e^{5} f^{2} - 4 \, c d^{3} e^{4} f^{3} + 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} e^{3} f^{4} - 4 \, {\left(c^{3} + c\right)} d e^{2} f^{5} + {\left(c^{4} + 2 \, c^{2} + 1\right)} e f^{6}\right)} x\right)}}"," ",0,"-1/2*(a*d^4*e^4 - (4*a*c - b)*d^3*e^3*f + 2*(3*a*c^2 - b*c + a)*d^2*e^2*f^2 - (4*a*c^3 - b*c^2 + 4*a*c - b)*d*e*f^3 + (a*c^4 + 2*a*c^2 + a)*f^4 + (b*d^3*e^2*f^2 - 2*b*c*d^2*e*f^3 + (b*c^2 + b)*d*f^4)*x - (2*b*c*d^3*e^3*f - (5*b*c^2 + 3*b)*d^2*e^2*f^2 + 4*(b*c^3 + b*c)*d*e*f^3 - (b*c^4 + 2*b*c^2 + b)*f^4 + (b*d^4*e^2*f^2 - 2*b*c*d^3*e*f^3 + (b*c^2 - b)*d^2*f^4)*x^2 + 2*(b*d^4*e^3*f - 2*b*c*d^3*e^2*f^2 + (b*c^2 - b)*d^2*e*f^3)*x)*arctan(d*x + c) + (b*d^3*e^3*f - b*c*d^2*e^2*f^2 + (b*d^3*e*f^3 - b*c*d^2*f^4)*x^2 + 2*(b*d^3*e^2*f^2 - b*c*d^2*e*f^3)*x)*log(d^2*x^2 + 2*c*d*x + c^2 + 1) - 2*(b*d^3*e^3*f - b*c*d^2*e^2*f^2 + (b*d^3*e*f^3 - b*c*d^2*f^4)*x^2 + 2*(b*d^3*e^2*f^2 - b*c*d^2*e*f^3)*x)*log(f*x + e))/(d^4*e^6*f - 4*c*d^3*e^5*f^2 + 2*(3*c^2 + 1)*d^2*e^4*f^3 - 4*(c^3 + c)*d*e^3*f^4 + (c^4 + 2*c^2 + 1)*e^2*f^5 + (d^4*e^4*f^3 - 4*c*d^3*e^3*f^4 + 2*(3*c^2 + 1)*d^2*e^2*f^5 - 4*(c^3 + c)*d*e*f^6 + (c^4 + 2*c^2 + 1)*f^7)*x^2 + 2*(d^4*e^5*f^2 - 4*c*d^3*e^4*f^3 + 2*(3*c^2 + 1)*d^2*e^3*f^4 - 4*(c^3 + c)*d*e^2*f^5 + (c^4 + 2*c^2 + 1)*e*f^6)*x)","B",0
31,0,0,0,0.418863," ","integrate((f*x+e)^2*(a+b*arctan(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} f^{2} x^{2} + 2 \, a^{2} e f x + a^{2} e^{2} + {\left(b^{2} f^{2} x^{2} + 2 \, b^{2} e f x + b^{2} e^{2}\right)} \arctan\left(d x + c\right)^{2} + 2 \, {\left(a b f^{2} x^{2} + 2 \, a b e f x + a b e^{2}\right)} \arctan\left(d x + c\right), x\right)"," ",0,"integral(a^2*f^2*x^2 + 2*a^2*e*f*x + a^2*e^2 + (b^2*f^2*x^2 + 2*b^2*e*f*x + b^2*e^2)*arctan(d*x + c)^2 + 2*(a*b*f^2*x^2 + 2*a*b*e*f*x + a*b*e^2)*arctan(d*x + c), x)","F",0
32,0,0,0,0.427482," ","integrate((f*x+e)*(a+b*arctan(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} f x + a^{2} e + {\left(b^{2} f x + b^{2} e\right)} \arctan\left(d x + c\right)^{2} + 2 \, {\left(a b f x + a b e\right)} \arctan\left(d x + c\right), x\right)"," ",0,"integral(a^2*f*x + a^2*e + (b^2*f*x + b^2*e)*arctan(d*x + c)^2 + 2*(a*b*f*x + a*b*e)*arctan(d*x + c), x)","F",0
33,0,0,0,0.436533," ","integrate((a+b*arctan(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \arctan\left(d x + c\right)^{2} + 2 \, a b \arctan\left(d x + c\right) + a^{2}, x\right)"," ",0,"integral(b^2*arctan(d*x + c)^2 + 2*a*b*arctan(d*x + c) + a^2, x)","F",0
34,0,0,0,0.403201," ","integrate((a+b*arctan(d*x+c))^2/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(d x + c\right)^{2} + 2 \, a b \arctan\left(d x + c\right) + a^{2}}{f x + e}, x\right)"," ",0,"integral((b^2*arctan(d*x + c)^2 + 2*a*b*arctan(d*x + c) + a^2)/(f*x + e), x)","F",0
35,0,0,0,0.470977," ","integrate((a+b*arctan(d*x+c))^2/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(d x + c\right)^{2} + 2 \, a b \arctan\left(d x + c\right) + a^{2}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b^2*arctan(d*x + c)^2 + 2*a*b*arctan(d*x + c) + a^2)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
36,0,0,0,0.452421," ","integrate((f*x+e)^2*(a+b*arctan(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(a^{3} f^{2} x^{2} + 2 \, a^{3} e f x + a^{3} e^{2} + {\left(b^{3} f^{2} x^{2} + 2 \, b^{3} e f x + b^{3} e^{2}\right)} \arctan\left(d x + c\right)^{3} + 3 \, {\left(a b^{2} f^{2} x^{2} + 2 \, a b^{2} e f x + a b^{2} e^{2}\right)} \arctan\left(d x + c\right)^{2} + 3 \, {\left(a^{2} b f^{2} x^{2} + 2 \, a^{2} b e f x + a^{2} b e^{2}\right)} \arctan\left(d x + c\right), x\right)"," ",0,"integral(a^3*f^2*x^2 + 2*a^3*e*f*x + a^3*e^2 + (b^3*f^2*x^2 + 2*b^3*e*f*x + b^3*e^2)*arctan(d*x + c)^3 + 3*(a*b^2*f^2*x^2 + 2*a*b^2*e*f*x + a*b^2*e^2)*arctan(d*x + c)^2 + 3*(a^2*b*f^2*x^2 + 2*a^2*b*e*f*x + a^2*b*e^2)*arctan(d*x + c), x)","F",0
37,0,0,0,0.432601," ","integrate((f*x+e)*(a+b*arctan(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(a^{3} f x + a^{3} e + {\left(b^{3} f x + b^{3} e\right)} \arctan\left(d x + c\right)^{3} + 3 \, {\left(a b^{2} f x + a b^{2} e\right)} \arctan\left(d x + c\right)^{2} + 3 \, {\left(a^{2} b f x + a^{2} b e\right)} \arctan\left(d x + c\right), x\right)"," ",0,"integral(a^3*f*x + a^3*e + (b^3*f*x + b^3*e)*arctan(d*x + c)^3 + 3*(a*b^2*f*x + a*b^2*e)*arctan(d*x + c)^2 + 3*(a^2*b*f*x + a^2*b*e)*arctan(d*x + c), x)","F",0
38,0,0,0,0.437088," ","integrate((a+b*arctan(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} \arctan\left(d x + c\right)^{3} + 3 \, a b^{2} \arctan\left(d x + c\right)^{2} + 3 \, a^{2} b \arctan\left(d x + c\right) + a^{3}, x\right)"," ",0,"integral(b^3*arctan(d*x + c)^3 + 3*a*b^2*arctan(d*x + c)^2 + 3*a^2*b*arctan(d*x + c) + a^3, x)","F",0
39,0,0,0,0.545027," ","integrate((a+b*arctan(d*x+c))^3/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(d x + c\right)^{3} + 3 \, a b^{2} \arctan\left(d x + c\right)^{2} + 3 \, a^{2} b \arctan\left(d x + c\right) + a^{3}}{f x + e}, x\right)"," ",0,"integral((b^3*arctan(d*x + c)^3 + 3*a*b^2*arctan(d*x + c)^2 + 3*a^2*b*arctan(d*x + c) + a^3)/(f*x + e), x)","F",0
40,0,0,0,0.473860," ","integrate((a+b*arctan(d*x+c))^3/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(d x + c\right)^{3} + 3 \, a b^{2} \arctan\left(d x + c\right)^{2} + 3 \, a^{2} b \arctan\left(d x + c\right) + a^{3}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b^3*arctan(d*x + c)^3 + 3*a*b^2*arctan(d*x + c)^2 + 3*a^2*b*arctan(d*x + c) + a^3)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
41,0,0,0,0.430051," ","integrate((f*x+e)^m*(a+b*arctan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \arctan\left(d x + c\right) + a\right)} {\left(f x + e\right)}^{m}, x\right)"," ",0,"integral((b*arctan(d*x + c) + a)*(f*x + e)^m, x)","F",0
42,0,0,0,0.411016," ","integrate((f*x+e)^m*(a+b*arctan(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \arctan\left(d x + c\right)^{2} + 2 \, a b \arctan\left(d x + c\right) + a^{2}\right)} {\left(f x + e\right)}^{m}, x\right)"," ",0,"integral((b^2*arctan(d*x + c)^2 + 2*a*b*arctan(d*x + c) + a^2)*(f*x + e)^m, x)","F",0
43,0,0,0,0.422091," ","integrate((f*x+e)^m*(a+b*arctan(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \arctan\left(d x + c\right)^{3} + 3 \, a b^{2} \arctan\left(d x + c\right)^{2} + 3 \, a^{2} b \arctan\left(d x + c\right) + a^{3}\right)} {\left(f x + e\right)}^{m}, x\right)"," ",0,"integral((b^3*arctan(d*x + c)^3 + 3*a*b^2*arctan(d*x + c)^2 + 3*a^2*b*arctan(d*x + c) + a^3)*(f*x + e)^m, x)","F",0
44,1,87,0,0.414229," ","integrate(x^3*arctan(b*x+a),x, algorithm=""fricas"")","-\frac{b^{3} x^{3} - 3 \, a b^{2} x^{2} + 3 \, {\left(3 \, a^{2} - 1\right)} b x - 3 \, {\left(b^{4} x^{4} - a^{4} + 6 \, a^{2} - 1\right)} \arctan\left(b x + a\right) - 6 \, {\left(a^{3} - a\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{12 \, b^{4}}"," ",0,"-1/12*(b^3*x^3 - 3*a*b^2*x^2 + 3*(3*a^2 - 1)*b*x - 3*(b^4*x^4 - a^4 + 6*a^2 - 1)*arctan(b*x + a) - 6*(a^3 - a)*log(b^2*x^2 + 2*a*b*x + a^2 + 1))/b^4","A",0
45,1,66,0,0.410972," ","integrate(x^2*arctan(b*x+a),x, algorithm=""fricas"")","-\frac{b^{2} x^{2} - 4 \, a b x - 2 \, {\left(b^{3} x^{3} + a^{3} - 3 \, a\right)} \arctan\left(b x + a\right) + {\left(3 \, a^{2} - 1\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{6 \, b^{3}}"," ",0,"-1/6*(b^2*x^2 - 4*a*b*x - 2*(b^3*x^3 + a^3 - 3*a)*arctan(b*x + a) + (3*a^2 - 1)*log(b^2*x^2 + 2*a*b*x + a^2 + 1))/b^3","A",0
46,1,52,0,0.406756," ","integrate(x*arctan(b*x+a),x, algorithm=""fricas"")","-\frac{b x - {\left(b^{2} x^{2} - a^{2} + 1\right)} \arctan\left(b x + a\right) - a \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{2 \, b^{2}}"," ",0,"-1/2*(b*x - (b^2*x^2 - a^2 + 1)*arctan(b*x + a) - a*log(b^2*x^2 + 2*a*b*x + a^2 + 1))/b^2","A",0
47,1,39,0,0.399582," ","integrate(arctan(b*x+a),x, algorithm=""fricas"")","\frac{2 \, {\left(b x + a\right)} \arctan\left(b x + a\right) - \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{2 \, b}"," ",0,"1/2*(2*(b*x + a)*arctan(b*x + a) - log(b^2*x^2 + 2*a*b*x + a^2 + 1))/b","A",0
48,0,0,0,0.393149," ","integrate(arctan(b*x+a)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(b x + a\right)}{x}, x\right)"," ",0,"integral(arctan(b*x + a)/x, x)","F",0
49,1,57,0,0.413520," ","integrate(arctan(b*x+a)/x^2,x, algorithm=""fricas"")","-\frac{b x \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) - 2 \, b x \log\left(x\right) + 2 \, {\left(a b x + a^{2} + 1\right)} \arctan\left(b x + a\right)}{2 \, {\left(a^{2} + 1\right)} x}"," ",0,"-1/2*(b*x*log(b^2*x^2 + 2*a*b*x + a^2 + 1) - 2*b*x*log(x) + 2*(a*b*x + a^2 + 1)*arctan(b*x + a))/((a^2 + 1)*x)","A",0
50,1,95,0,0.498369," ","integrate(arctan(b*x+a)/x^3,x, algorithm=""fricas"")","\frac{a b^{2} x^{2} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) - 2 \, a b^{2} x^{2} \log\left(x\right) - {\left(a^{2} + 1\right)} b x + {\left({\left(a^{2} - 1\right)} b^{2} x^{2} - a^{4} - 2 \, a^{2} - 1\right)} \arctan\left(b x + a\right)}{2 \, {\left(a^{4} + 2 \, a^{2} + 1\right)} x^{2}}"," ",0,"1/2*(a*b^2*x^2*log(b^2*x^2 + 2*a*b*x + a^2 + 1) - 2*a*b^2*x^2*log(x) - (a^2 + 1)*b*x + ((a^2 - 1)*b^2*x^2 - a^4 - 2*a^2 - 1)*arctan(b*x + a))/((a^4 + 2*a^2 + 1)*x^2)","A",0
51,1,135,0,0.449206," ","integrate(arctan(b*x+a)/x^4,x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{2} - 1\right)} b^{3} x^{3} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) - 2 \, {\left(3 \, a^{2} - 1\right)} b^{3} x^{3} \log\left(x\right) - 4 \, {\left(a^{3} + a\right)} b^{2} x^{2} + {\left(a^{4} + 2 \, a^{2} + 1\right)} b x + 2 \, {\left({\left(a^{3} - 3 \, a\right)} b^{3} x^{3} + a^{6} + 3 \, a^{4} + 3 \, a^{2} + 1\right)} \arctan\left(b x + a\right)}{6 \, {\left(a^{6} + 3 \, a^{4} + 3 \, a^{2} + 1\right)} x^{3}}"," ",0,"-1/6*((3*a^2 - 1)*b^3*x^3*log(b^2*x^2 + 2*a*b*x + a^2 + 1) - 2*(3*a^2 - 1)*b^3*x^3*log(x) - 4*(a^3 + a)*b^2*x^2 + (a^4 + 2*a^2 + 1)*b*x + 2*((a^3 - 3*a)*b^3*x^3 + a^6 + 3*a^4 + 3*a^2 + 1)*arctan(b*x + a))/((a^6 + 3*a^4 + 3*a^2 + 1)*x^3)","A",0
52,0,0,0,0.628295," ","integrate(arctan(b*x+a)/(d*x^3+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(b x + a\right)}{d x^{3} + c}, x\right)"," ",0,"integral(arctan(b*x + a)/(d*x^3 + c), x)","F",0
53,0,0,0,0.439815," ","integrate(arctan(b*x+a)/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(b x + a\right)}{d x^{2} + c}, x\right)"," ",0,"integral(arctan(b*x + a)/(d*x^2 + c), x)","F",0
54,0,0,0,0.442646," ","integrate(arctan(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(arctan(b*x + a)/(d*x + c), x)","F",0
55,0,0,0,0.458319," ","integrate(arctan(b*x+a)/(c+d/x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \arctan\left(b x + a\right)}{c x + d}, x\right)"," ",0,"integral(x*arctan(b*x + a)/(c*x + d), x)","F",0
56,0,0,0,0.410590," ","integrate(arctan(b*x+a)/(c+d/x^2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \arctan\left(b x + a\right)}{c x^{2} + d}, x\right)"," ",0,"integral(x^2*arctan(b*x + a)/(c*x^2 + d), x)","F",0
57,0,0,0,0.529817," ","integrate(arctan(b*x+a)/(c+d/x^3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \arctan\left(b x + a\right)}{c x^{3} + d}, x\right)"," ",0,"integral(x^3*arctan(b*x + a)/(c*x^3 + d), x)","F",0
58,0,0,0,0.477390," ","integrate(arctan(b*x+a)/(c+d*x^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{d \sqrt{x} \arctan\left(b x + a\right) - c \arctan\left(b x + a\right)}{d^{2} x - c^{2}}, x\right)"," ",0,"integral((d*sqrt(x)*arctan(b*x + a) - c*arctan(b*x + a))/(d^2*x - c^2), x)","F",0
59,0,0,0,0.584661," ","integrate(arctan(b*x+a)/(c+d/x^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{c x \arctan\left(b x + a\right) - d \sqrt{x} \arctan\left(b x + a\right)}{c^{2} x - d^{2}}, x\right)"," ",0,"integral((c*x*arctan(b*x + a) - d*sqrt(x)*arctan(b*x + a))/(c^2*x - d^2), x)","F",0
60,0,0,0,0.429955," ","integrate(arctan(b*x+a)/(x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(b x + a\right)}{x^{2} + 1}, x\right)"," ",0,"integral(arctan(b*x + a)/(x^2 + 1), x)","F",0
61,0,0,0,0.427276," ","integrate(arctan(e*x+d)/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(e x + d\right)}{b x^{2} + a}, x\right)"," ",0,"integral(arctan(e*x + d)/(b*x^2 + a), x)","F",0
62,0,0,0,0.462392," ","integrate(arctan(e*x+d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(e x + d\right)}{c x^{2} + b x + a}, x\right)"," ",0,"integral(arctan(e*x + d)/(c*x^2 + b*x + a), x)","F",0
63,0,0,0,0.438790," ","integrate(arctan(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(b x + a\right)}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}, x\right)"," ",0,"integral(arctan(b*x + a)/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1), x)","F",0
64,0,0,0,0.435724," ","integrate(arctan(b*x+a)/((a^2+1)*c+2*a*b*c*x+c*x^2*b^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(b x + a\right)}{\sqrt{b^{2} c x^{2} + 2 \, a b c x + {\left(a^{2} + 1\right)} c}}, x\right)"," ",0,"integral(arctan(b*x + a)/sqrt(b^2*c*x^2 + 2*a*b*c*x + (a^2 + 1)*c), x)","F",0
65,0,0,0,0.424455," ","integrate(arctan(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(b x + a\right)}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(arctan(b*x + a)/(b^2*x^2 + 2*a*b*x + a^2 + 1)^(1/3), x)","F",0
66,0,0,0,0.448050," ","integrate(arctan(b*x+a)/((a^2+1)*c+2*a*b*c*x+c*x^2*b^2)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(b x + a\right)}{{\left(b^{2} c x^{2} + 2 \, a b c x + {\left(a^{2} + 1\right)} c\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(arctan(b*x + a)/(b^2*c*x^2 + 2*a*b*c*x + (a^2 + 1)*c)^(1/3), x)","F",0
67,0,0,0,0.451864," ","integrate((b*x+a)^2*arctan(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \arctan\left(b x + a\right)}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)*arctan(b*x + a)/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1), x)","F",0
68,0,0,0,0.469752," ","integrate((b*x+a)^2*arctan(b*x+a)/((a^2+1)*c+2*a*b*c*x+c*x^2*b^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \arctan\left(b x + a\right)}{\sqrt{b^{2} c x^{2} + 2 \, a b c x + {\left(a^{2} + 1\right)} c}}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)*arctan(b*x + a)/sqrt(b^2*c*x^2 + 2*a*b*c*x + (a^2 + 1)*c), x)","F",0
69,0,0,0,0.440952," ","integrate((b*x+a)^2*arctan(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \arctan\left(b x + a\right)}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)*arctan(b*x + a)/(b^2*x^2 + 2*a*b*x + a^2 + 1)^(1/3), x)","F",0
70,0,0,0,0.457223," ","integrate((b*x+a)^2*arctan(b*x+a)/((a^2+1)*c+2*a*b*c*x+c*x^2*b^2)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \arctan\left(b x + a\right)}{{\left(b^{2} c x^{2} + 2 \, a b c x + {\left(a^{2} + 1\right)} c\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)*arctan(b*x + a)/(b^2*c*x^2 + 2*a*b*c*x + (a^2 + 1)*c)^(1/3), x)","F",0
