1,1,37,0,0.312605," ","integrate(x^3*arctan(b*x^4+a),x, algorithm=""maxima"")","\frac{2 \, {\left(b x^{4} + a\right)} \arctan\left(b x^{4} + a\right) - \log\left({\left(b x^{4} + a\right)}^{2} + 1\right)}{8 \, b}"," ",0,"1/8*(2*(b*x^4 + a)*arctan(b*x^4 + a) - log((b*x^4 + a)^2 + 1))/b","A",0
2,1,40,0,0.311402," ","integrate(x^(-1+n)*arctan(a+b*x^n),x, algorithm=""maxima"")","\frac{2 \, {\left(b x^{n} + a\right)} \arctan\left(b x^{n} + a\right) - \log\left({\left(b x^{n} + a\right)}^{2} + 1\right)}{2 \, b n}"," ",0,"1/2*(2*(b*x^n + a)*arctan(b*x^n + a) - log((b*x^n + a)^2 + 1))/(b*n)","A",0
3,-2,0,0,0.000000," ","integrate(x^5*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
4,-2,0,0,0.000000," ","integrate(x^3*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
5,-2,0,0,0.000000," ","integrate(x*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
6,-2,0,0,0.000000," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
7,1,58,0,0.369313," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^3,x, algorithm=""maxima"")","-\frac{\arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{2 \, x^{2}} - \frac{\sqrt{-e} e x^{2} + d \sqrt{-e}}{2 \, \sqrt{e x^{2} + d} d x}"," ",0,"-1/2*arctan(sqrt(-e)*x/sqrt(e*x^2 + d))/x^2 - 1/2*(sqrt(-e)*e*x^2 + d*sqrt(-e))/(sqrt(e*x^2 + d)*d*x)","A",0
8,1,68,0,0.334014," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^5,x, algorithm=""maxima"")","\frac{\sqrt{e x^{2} + d} \sqrt{-e} e}{4 \, d^{2} x} - \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} \sqrt{-e}}{12 \, d^{2} x^{3}} - \frac{\arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{4 \, x^{4}}"," ",0,"1/4*sqrt(e*x^2 + d)*sqrt(-e)*e/(d^2*x) - 1/12*(e*x^2 + d)^(3/2)*sqrt(-e)/(d^2*x^3) - 1/4*arctan(sqrt(-e)*x/sqrt(e*x^2 + d))/x^4","A",0
9,1,109,0,0.338799," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^7,x, algorithm=""maxima"")","-\frac{{\left(2 \, e^{2} x^{4} + d e x^{2} - d^{2}\right)} \sqrt{-e} e}{18 \, \sqrt{e x^{2} + d} d^{3} x^{3}} - \frac{\arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{6 \, x^{6}} + \frac{{\left(2 \, e^{2} x^{4} - d e x^{2} - 3 \, d^{2}\right)} \sqrt{e x^{2} + d} \sqrt{-e}}{90 \, d^{3} x^{5}}"," ",0,"-1/18*(2*e^2*x^4 + d*e*x^2 - d^2)*sqrt(-e)*e/(sqrt(e*x^2 + d)*d^3*x^3) - 1/6*arctan(sqrt(-e)*x/sqrt(e*x^2 + d))/x^6 + 1/90*(2*e^2*x^4 - d*e*x^2 - 3*d^2)*sqrt(e*x^2 + d)*sqrt(-e)/(d^3*x^5)","A",0
10,1,132,0,0.339351," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^9,x, algorithm=""maxima"")","\frac{{\left(8 \, e^{3} x^{6} + 4 \, d e^{2} x^{4} - d^{2} e x^{2} + 3 \, d^{3}\right)} \sqrt{-e} e}{120 \, \sqrt{e x^{2} + d} d^{4} x^{5}} - \frac{\arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{8 \, x^{8}} - \frac{{\left(8 \, e^{3} x^{6} - 4 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + 15 \, d^{3}\right)} \sqrt{e x^{2} + d} \sqrt{-e}}{840 \, d^{4} x^{7}}"," ",0,"1/120*(8*e^3*x^6 + 4*d*e^2*x^4 - d^2*e*x^2 + 3*d^3)*sqrt(-e)*e/(sqrt(e*x^2 + d)*d^4*x^5) - 1/8*arctan(sqrt(-e)*x/sqrt(e*x^2 + d))/x^8 - 1/840*(8*e^3*x^6 - 4*d*e^2*x^4 + 3*d^2*e*x^2 + 15*d^3)*sqrt(e*x^2 + d)*sqrt(-e)/(d^4*x^7)","A",0
11,1,167,0,0.337803," ","integrate(x^6*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""maxima"")","\frac{1}{7} \, x^{7} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - \frac{{\left(35 \, {\left(e x^{2} + d\right)}^{\frac{9}{2}} - 135 \, {\left(e x^{2} + d\right)}^{\frac{7}{2}} d + 189 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} d^{2} - 105 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} d^{3}\right)} \sqrt{-e}}{2205 \, d e^{4}} + \frac{{\left(35 \, {\left(e x^{2} + d\right)}^{\frac{9}{2}} - 180 \, {\left(e x^{2} + d\right)}^{\frac{7}{2}} d + 378 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{e x^{2} + d} d^{4}\right)} \sqrt{-e}}{2205 \, d e^{4}}"," ",0,"1/7*x^7*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - 1/2205*(35*(e*x^2 + d)^(9/2) - 135*(e*x^2 + d)^(7/2)*d + 189*(e*x^2 + d)^(5/2)*d^2 - 105*(e*x^2 + d)^(3/2)*d^3)*sqrt(-e)/(d*e^4) + 1/2205*(35*(e*x^2 + d)^(9/2) - 180*(e*x^2 + d)^(7/2)*d + 378*(e*x^2 + d)^(5/2)*d^2 - 420*(e*x^2 + d)^(3/2)*d^3 + 315*sqrt(e*x^2 + d)*d^4)*sqrt(-e)/(d*e^4)","A",0
12,1,139,0,0.340776," ","integrate(x^4*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""maxima"")","\frac{1}{5} \, x^{5} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - \frac{{\left(15 \, {\left(e x^{2} + d\right)}^{\frac{7}{2}} - 42 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} d + 35 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} d^{2}\right)} \sqrt{-e}}{525 \, d e^{3}} + \frac{{\left(5 \, {\left(e x^{2} + d\right)}^{\frac{7}{2}} - 21 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} d + 35 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{e x^{2} + d} d^{3}\right)} \sqrt{-e}}{175 \, d e^{3}}"," ",0,"1/5*x^5*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - 1/525*(15*(e*x^2 + d)^(7/2) - 42*(e*x^2 + d)^(5/2)*d + 35*(e*x^2 + d)^(3/2)*d^2)*sqrt(-e)/(d*e^3) + 1/175*(5*(e*x^2 + d)^(7/2) - 21*(e*x^2 + d)^(5/2)*d + 35*(e*x^2 + d)^(3/2)*d^2 - 35*sqrt(e*x^2 + d)*d^3)*sqrt(-e)/(d*e^3)","A",0
13,1,111,0,0.339165," ","integrate(x^2*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - \frac{{\left(3 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} - 5 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} d\right)} \sqrt{-e}}{45 \, d e^{2}} + \frac{{\left(3 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} - 10 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{e x^{2} + d} d^{2}\right)} \sqrt{-e}}{45 \, d e^{2}}"," ",0,"1/3*x^3*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - 1/45*(3*(e*x^2 + d)^(5/2) - 5*(e*x^2 + d)^(3/2)*d)*sqrt(-e)/(d*e^2) + 1/45*(3*(e*x^2 + d)^(5/2) - 10*(e*x^2 + d)^(3/2)*d + 15*sqrt(e*x^2 + d)*d^2)*sqrt(-e)/(d*e^2)","A",0
14,1,77,0,0.335362," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""maxima"")","x \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} \sqrt{-e}}{3 \, d e} + \frac{{\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{e x^{2} + d} d\right)} \sqrt{-e}}{3 \, d e}"," ",0,"x*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - 1/3*(e*x^2 + d)^(3/2)*sqrt(-e)/(d*e) + 1/3*((e*x^2 + d)^(3/2) - 3*sqrt(e*x^2 + d)*d)*sqrt(-e)/(d*e)","B",0
15,-2,0,0,0.000000," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
16,-2,0,0,0.000000," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
17,-2,0,0,0.000000," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^6,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
18,-2,0,0,0.000000," ","integrate(x^(9/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
19,-2,0,0,0.000000," ","integrate(x^(5/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
20,-2,0,0,0.000000," ","integrate(x^(1/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
21,-2,0,0,0.000000," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
22,-2,0,0,0.000000," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(7/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
23,-2,0,0,0.000000," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(11/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
24,-2,0,0,0.000000," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(15/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
25,-2,0,0,0.000000," ","integrate(x^(7/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
26,-2,0,0,0.000000," ","integrate(x^(3/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
27,-2,0,0,0.000000," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
28,-2,0,0,0.000000," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
29,-2,0,0,0.000000," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(9/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found sqrt(-_SAGE_VAR_e)","F(-2)",0
30,1,42,0,0.425283," ","integrate(arctan(x^2+x+1)/x^2,x, algorithm=""maxima"")","-\frac{\arctan\left(x^{2} + x + 1\right)}{x} + \frac{1}{2} \, \arctan\left(x + 1\right) + \frac{1}{4} \, \log\left(x^{2} + 2 \, x + 2\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right) + \frac{1}{2} \, \log\left(x\right)"," ",0,"-arctan(x^2 + x + 1)/x + 1/2*arctan(x + 1) + 1/4*log(x^2 + 2*x + 2) - 1/2*log(x^2 + 1) + 1/2*log(x)","A",0
31,0,0,0,0.000000," ","integrate((a+b*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(b \arctan\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}^{n}}{c^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((b*arctan(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)^n/(c^2*x^2 - 1), x)","F",0
32,0,0,0,0.000000," ","integrate((a+b*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^3/(-c^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} + \frac{\frac{15}{2} \, {\left(b^{3} \log\left(c x + 1\right) - b^{3} \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{-c x + 1}, \sqrt{c x + 1}\right)^{3} - \frac{45}{8} \, {\left(b^{3} \log\left(2\right)^{2} \log\left(c x + 1\right) - b^{3} \log\left(2\right)^{2} \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{-c x + 1}, \sqrt{c x + 1}\right) - \frac{1}{2} \, c \int \frac{784 \, b^{3} \arctan\left(\sqrt{-c x + 1}, \sqrt{c x + 1}\right)^{3} + 3072 \, a b^{2} \arctan\left(\sqrt{-c x + 1}, \sqrt{c x + 1}\right)^{2} - 45 \, {\left(b^{3} \log\left(2\right)^{2} \log\left(c x + 1\right) - b^{3} \log\left(2\right)^{2} \log\left(-c x + 1\right) - 4 \, {\left(b^{3} \log\left(c x + 1\right) - b^{3} \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{-c x + 1}, \sqrt{c x + 1}\right)^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + 12 \, {\left(15 \, b^{3} \log\left(2\right)^{2} + 256 \, a^{2} b\right)} \arctan\left(\sqrt{-c x + 1}, \sqrt{c x + 1}\right)}{8 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}}{64 \, c}"," ",0,"1/2*a^3*(log(c*x + 1)/c - log(c*x - 1)/c) + 1/64*(4*(b^3*log(c*x + 1) - b^3*log(-c*x + 1))*arctan2(sqrt(-c*x + 1), sqrt(c*x + 1))^3 - 3*(b^3*log(2)^2*log(c*x + 1) - b^3*log(2)^2*log(-c*x + 1))*arctan2(sqrt(-c*x + 1), sqrt(c*x + 1)) - 64*c*integrate(1/128*(112*b^3*arctan2(sqrt(-c*x + 1), sqrt(c*x + 1))^3 + 384*a*b^2*arctan2(sqrt(-c*x + 1), sqrt(c*x + 1))^2 - 3*(b^3*log(2)^2*log(c*x + 1) - b^3*log(2)^2*log(-c*x + 1) - 4*(b^3*log(c*x + 1) - b^3*log(-c*x + 1))*arctan2(sqrt(-c*x + 1), sqrt(c*x + 1))^2)*sqrt(c*x + 1)*sqrt(-c*x + 1) + 12*(b^3*log(2)^2 + 32*a^2*b)*arctan2(sqrt(-c*x + 1), sqrt(c*x + 1)))/(c^2*x^2 - 1), x))/c","F",0
33,0,0,0,0.000000," ","integrate((a+b*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2/(-c^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} - \frac{b^{2} \log\left(2\right)^{2} \log\left(c x + 1\right) - b^{2} \log\left(2\right)^{2} \log\left(-c x + 1\right) - 4 \, {\left(b^{2} \log\left(c x + 1\right) - b^{2} \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{-c x + 1}, \sqrt{c x + 1}\right)^{2} - {\left(12 \, b^{2} {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} \arctan\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)^{2} + b^{2} {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} \log\left(2\right)^{2} - 4 \, b^{2} \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) \log\left(c x + 1\right)}{c^{2} x^{2} - 1}\,{d x} + 4 \, b^{2} \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) \log\left(-c x + 1\right)}{c^{2} x^{2} - 1}\,{d x} + \frac{32 \, {\left({\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{-c x + 1}, \sqrt{c x + 1}\right) - c \int \frac{e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(c x + 1\right) - e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(-c x + 1\right)}{{\left(c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} - {\left(c^{2} x^{2} - 1\right)} {\left(c x - 1\right)}}\,{d x}\right)} a b}{c}\right)} c}{32 \, c}"," ",0,"1/2*a^2*(log(c*x + 1)/c - log(c*x - 1)/c) - 1/32*(b^2*log(2)^2*log(c*x + 1) - b^2*log(2)^2*log(-c*x + 1) - 4*(b^2*log(c*x + 1) - b^2*log(-c*x + 1))*arctan2(sqrt(-c*x + 1), sqrt(c*x + 1))^2 - (b^2*(log(c*x + 1)/c - log(c*x - 1)/c)*log(2)^2 - 64*b^2*integrate(1/16*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan(sqrt(-c*x + 1)/sqrt(c*x + 1))*log(c*x + 1)/(c^2*x^2 - 1), x) + 64*b^2*integrate(1/16*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan(sqrt(-c*x + 1)/sqrt(c*x + 1))*log(-c*x + 1)/(c^2*x^2 - 1), x) - 384*b^2*integrate(1/16*arctan(sqrt(-c*x + 1)/sqrt(c*x + 1))^2/(c^2*x^2 - 1), x) - 1024*a*b*integrate(1/16*arctan(sqrt(-c*x + 1)/sqrt(c*x + 1))/(c^2*x^2 - 1), x))*c)/c","F",0
34,0,0,0,0.000000," ","integrate((a+b*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2)))/(-c^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} + \frac{{\left({\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{-c x + 1}, \sqrt{c x + 1}\right) - c \int \frac{e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(c x + 1\right) - e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(-c x + 1\right)}{{\left(c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} - {\left(c^{2} x^{2} - 1\right)} {\left(c x - 1\right)}}\,{d x}\right)} b}{2 \, c}"," ",0,"1/2*a*(log(c*x + 1)/c - log(c*x - 1)/c) + 1/2*((log(c*x + 1) - log(-c*x + 1))*arctan2(sqrt(-c*x + 1), sqrt(c*x + 1)) - 2*c*integrate(1/2*(e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))*log(c*x + 1) - e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))*log(-c*x + 1))/((c^2*x^2 - 1)*(c*x + 1) - (c^2*x^2 - 1)*(c*x - 1)), x))*b/c","F",0
35,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)/(a+b*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))),x, algorithm=""maxima"")","-\int \frac{1}{{\left(c^{2} x^{2} - 1\right)} {\left(b \arctan\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}}\,{d x}"," ",0,"-integrate(1/((c^2*x^2 - 1)*(b*arctan(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)), x)","F",0
36,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)/(a+b*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2,x, algorithm=""maxima"")","\frac{2 \, {\left({\left(b^{2} c^{2} \arctan\left(\sqrt{-c x + 1}, \sqrt{c x + 1}\right) + a b c^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \int \frac{x}{{\left(a b c^{2} x^{2} - a b + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(\sqrt{-c x + 1}, \sqrt{c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x} + 1\right)}}{{\left(b^{2} c \arctan\left(\sqrt{-c x + 1}, \sqrt{c x + 1}\right) + a b c\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}"," ",0,"2*(2*(b^2*c^2*arctan2(sqrt(-c*x + 1), sqrt(c*x + 1)) + a*b*c^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*integrate(1/2*x/((a*b*c^2*x^2 - a*b + (b^2*c^2*x^2 - b^2)*arctan2(sqrt(-c*x + 1), sqrt(c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1)/((b^2*c*arctan2(sqrt(-c*x + 1), sqrt(c*x + 1)) + a*b*c)*sqrt(c*x + 1)*sqrt(-c*x + 1))","F",0
37,1,38,0,0.340350," ","integrate(x^m*arctan(tan(b*x+a)),x, algorithm=""maxima"")","-\frac{b x^{2} x^{m}}{{\left(m + 2\right)} {\left(m + 1\right)}} + \frac{x^{m + 1} \arctan\left(\tan\left(b x + a\right)\right)}{m + 1}"," ",0,"-b*x^2*x^m/((m + 2)*(m + 1)) + x^(m + 1)*arctan(tan(b*x + a))/(m + 1)","A",0
38,1,81,0,0.324346," ","integrate(x^2*arctan(tan(b*x+a)),x, algorithm=""maxima"")","\frac{\frac{4 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(b x + a\right)} a^{2}\right)} \arctan\left(\tan\left(b x + a\right)\right)}{b^{2}} - \frac{{\left(b x + a\right)}^{4} - 4 \, {\left(b x + a\right)}^{3} a + 6 \, {\left(b x + a\right)}^{2} a^{2}}{b^{2}}}{12 \, b}"," ",0,"1/12*(4*((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(b*x + a)*a^2)*arctan(tan(b*x + a))/b^2 - ((b*x + a)^4 - 4*(b*x + a)^3*a + 6*(b*x + a)^2*a^2)/b^2)/b","B",0
39,1,57,0,0.317559," ","integrate(x*arctan(tan(b*x+a)),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \arctan\left(\tan\left(b x + a\right)\right)}{b} - \frac{{\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a}{b}}{6 \, b}"," ",0,"1/6*(3*((b*x + a)^2 - 2*(b*x + a)*a)*arctan(tan(b*x + a))/b - ((b*x + a)^3 - 3*(b*x + a)^2*a)/b)/b","B",0
40,1,12,0,0.321089," ","integrate(arctan(tan(b*x+a)),x, algorithm=""maxima"")","\frac{{\left(b x + a\right)}^{2}}{2 \, b}"," ",0,"1/2*(b*x + a)^2/b","A",0
41,1,42,0,0.419356," ","integrate(arctan(tan(b*x+a))/x,x, algorithm=""maxima"")","\frac{b \arctan\left(\tan\left(b x + a\right)\right) \log\left(b x\right) + {\left(b x - {\left(b x + a\right)} \log\left(b x\right) + a \log\left(b x\right) + a\right)} b}{b}"," ",0,"(b*arctan(tan(b*x + a))*log(b*x) + (b*x - (b*x + a)*log(b*x) + a*log(b*x) + a)*b)/b","A",0
42,1,40,0,0.324712," ","integrate(x^m*(1/2*pi-arccot(cot(b*x+a))),x, algorithm=""maxima"")","-\frac{b x^{m + 2}}{m + 2} + \frac{\pi x^{m + 1}}{2 \, {\left(m + 1\right)}} - \frac{a x^{m + 1}}{m + 1}"," ",0,"-b*x^(m + 2)/(m + 2) + 1/2*pi*x^(m + 1)/(m + 1) - a*x^(m + 1)/(m + 1)","A",0
43,1,17,0,0.322415," ","integrate(x^2*(1/2*pi-arccot(cot(b*x+a))),x, algorithm=""maxima"")","-\frac{1}{4} \, b x^{4} + \frac{1}{6} \, {\left(\pi - 2 \, a\right)} x^{3}"," ",0,"-1/4*b*x^4 + 1/6*(pi - 2*a)*x^3","A",0
44,1,17,0,0.318096," ","integrate(x*(1/2*pi-arccot(cot(b*x+a))),x, algorithm=""maxima"")","-\frac{1}{3} \, b x^{3} + \frac{1}{4} \, {\left(\pi - 2 \, a\right)} x^{2}"," ",0,"-1/3*b*x^3 + 1/4*(pi - 2*a)*x^2","A",0
45,1,15,0,0.322333," ","integrate(1/2*pi-arccot(cot(b*x+a)),x, algorithm=""maxima"")","-\frac{1}{2} \, b x^{2} + \frac{1}{2} \, \pi x - a x"," ",0,"-1/2*b*x^2 + 1/2*pi*x - a*x","A",0
46,1,14,0,0.309614," ","integrate((1/2*pi-arccot(cot(b*x+a)))/x,x, algorithm=""maxima"")","-b x + \frac{1}{2} \, {\left(\pi - 2 \, a\right)} \log\left(x\right)"," ",0,"-b*x + 1/2*(pi - 2*a)*log(x)","A",0
47,1,12,0,0.317157," ","integrate(arctan(tan(b*x+a)),x, algorithm=""maxima"")","\frac{{\left(b x + a\right)}^{2}}{2 \, b}"," ",0,"1/2*(b*x + a)^2/b","A",0
48,0,0,0,0.000000," ","integrate(x^2*arctan(c+d*tan(b*x+a)),x, algorithm=""maxima"")","\frac{1}{6} \, x^{3} \arctan\left(c \cos\left(2 \, b x + 2 \, a\right) + {\left(d + 1\right)} \sin\left(2 \, b x + 2 \, a\right) + c, {\left(d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - c \sin\left(2 \, b x + 2 \, a\right) - d + 1\right) + \frac{1}{6} \, x^{3} \arctan\left(c \cos\left(2 \, b x + 2 \, a\right) + {\left(d - 1\right)} \sin\left(2 \, b x + 2 \, a\right) + c, -{\left(d - 1\right)} \cos\left(2 \, b x + 2 \, a\right) + c \sin\left(2 \, b x + 2 \, a\right) + d + 1\right) + 4 \, b d \int -\frac{2 \, {\left(c^{2} + d^{2} + 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c d x^{3} \sin\left(2 \, b x + 2 \, a\right) + 2 \, {\left(c^{2} + d^{2} + 1\right)} x^{3} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{2} - d^{2} + 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, c d x^{3} \sin\left(2 \, b x + 2 \, a\right) - {\left(c^{2} - d^{2} + 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, c d x^{3} \cos\left(2 \, b x + 2 \, a\right) + {\left(c^{2} - d^{2} + 1\right)} x^{3} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right)}{3 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c^{2} + 2 \, {\left(c^{4} + d^{4} - 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 2 \, {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 4 \, {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(2 \, c d^{3} - 2 \, {\left(c^{3} + c\right)} d - 2 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 8 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)}}\,{d x}"," ",0,"1/6*x^3*arctan2(c*cos(2*b*x + 2*a) + (d + 1)*sin(2*b*x + 2*a) + c, (d + 1)*cos(2*b*x + 2*a) - c*sin(2*b*x + 2*a) - d + 1) + 1/6*x^3*arctan2(c*cos(2*b*x + 2*a) + (d - 1)*sin(2*b*x + 2*a) + c, -(d - 1)*cos(2*b*x + 2*a) + c*sin(2*b*x + 2*a) + d + 1) + 4*b*d*integrate(-1/3*(2*(c^2 + d^2 + 1)*x^3*cos(2*b*x + 2*a)^2 + 2*c*d*x^3*sin(2*b*x + 2*a) + 2*(c^2 + d^2 + 1)*x^3*sin(2*b*x + 2*a)^2 + (c^2 - d^2 + 1)*x^3*cos(2*b*x + 2*a) - (2*c*d*x^3*sin(2*b*x + 2*a) - (c^2 - d^2 + 1)*x^3*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) + (2*c*d*x^3*cos(2*b*x + 2*a) + (c^2 - d^2 + 1)*x^3*sin(2*b*x + 2*a))*sin(4*b*x + 4*a))/(c^4 + d^4 + 2*(c^2 - 1)*d^2 + (c^4 + d^4 + 2*(c^2 - 1)*d^2 + 2*c^2 + 1)*cos(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 + 1)*d^2 + 2*c^2 + 1)*cos(2*b*x + 2*a)^2 + (c^4 + d^4 + 2*(c^2 - 1)*d^2 + 2*c^2 + 1)*sin(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 + 1)*d^2 + 2*c^2 + 1)*sin(2*b*x + 2*a)^2 + 2*c^2 + 2*(c^4 + d^4 - 2*(3*c^2 + 1)*d^2 + 2*c^2 + 2*(c^4 - d^4 + 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(c*d^3 + (c^3 + c)*d)*sin(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + 4*(c^4 - d^4 + 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(2*c*d^3 - 2*(c^3 + c)*d - 2*(c*d^3 + (c^3 + c)*d)*cos(2*b*x + 2*a) - (c^4 - d^4 + 2*c^2 + 1)*sin(2*b*x + 2*a))*sin(4*b*x + 4*a) + 8*(c*d^3 + (c^3 + c)*d)*sin(2*b*x + 2*a) + 1), x)","F",0
49,0,0,0,0.000000," ","integrate(x*arctan(c+d*tan(b*x+a)),x, algorithm=""maxima"")","\frac{1}{4} \, x^{2} \arctan\left(c \cos\left(2 \, b x + 2 \, a\right) + {\left(d + 1\right)} \sin\left(2 \, b x + 2 \, a\right) + c, {\left(d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - c \sin\left(2 \, b x + 2 \, a\right) - d + 1\right) + \frac{1}{4} \, x^{2} \arctan\left(c \cos\left(2 \, b x + 2 \, a\right) + {\left(d - 1\right)} \sin\left(2 \, b x + 2 \, a\right) + c, -{\left(d - 1\right)} \cos\left(2 \, b x + 2 \, a\right) + c \sin\left(2 \, b x + 2 \, a\right) + d + 1\right) + 2 \, b d \int -\frac{2 \, {\left(c^{2} + d^{2} + 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c d x^{2} \sin\left(2 \, b x + 2 \, a\right) + 2 \, {\left(c^{2} + d^{2} + 1\right)} x^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{2} - d^{2} + 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, c d x^{2} \sin\left(2 \, b x + 2 \, a\right) - {\left(c^{2} - d^{2} + 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, c d x^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(c^{2} - d^{2} + 1\right)} x^{2} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right)}{c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c^{2} + 2 \, {\left(c^{4} + d^{4} - 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 2 \, {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 4 \, {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(2 \, c d^{3} - 2 \, {\left(c^{3} + c\right)} d - 2 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 8 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1}\,{d x}"," ",0,"1/4*x^2*arctan2(c*cos(2*b*x + 2*a) + (d + 1)*sin(2*b*x + 2*a) + c, (d + 1)*cos(2*b*x + 2*a) - c*sin(2*b*x + 2*a) - d + 1) + 1/4*x^2*arctan2(c*cos(2*b*x + 2*a) + (d - 1)*sin(2*b*x + 2*a) + c, -(d - 1)*cos(2*b*x + 2*a) + c*sin(2*b*x + 2*a) + d + 1) + 2*b*d*integrate(-(2*(c^2 + d^2 + 1)*x^2*cos(2*b*x + 2*a)^2 + 2*c*d*x^2*sin(2*b*x + 2*a) + 2*(c^2 + d^2 + 1)*x^2*sin(2*b*x + 2*a)^2 + (c^2 - d^2 + 1)*x^2*cos(2*b*x + 2*a) - (2*c*d*x^2*sin(2*b*x + 2*a) - (c^2 - d^2 + 1)*x^2*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) + (2*c*d*x^2*cos(2*b*x + 2*a) + (c^2 - d^2 + 1)*x^2*sin(2*b*x + 2*a))*sin(4*b*x + 4*a))/(c^4 + d^4 + 2*(c^2 - 1)*d^2 + (c^4 + d^4 + 2*(c^2 - 1)*d^2 + 2*c^2 + 1)*cos(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 + 1)*d^2 + 2*c^2 + 1)*cos(2*b*x + 2*a)^2 + (c^4 + d^4 + 2*(c^2 - 1)*d^2 + 2*c^2 + 1)*sin(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 + 1)*d^2 + 2*c^2 + 1)*sin(2*b*x + 2*a)^2 + 2*c^2 + 2*(c^4 + d^4 - 2*(3*c^2 + 1)*d^2 + 2*c^2 + 2*(c^4 - d^4 + 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(c*d^3 + (c^3 + c)*d)*sin(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + 4*(c^4 - d^4 + 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(2*c*d^3 - 2*(c^3 + c)*d - 2*(c*d^3 + (c^3 + c)*d)*cos(2*b*x + 2*a) - (c^4 - d^4 + 2*c^2 + 1)*sin(2*b*x + 2*a))*sin(4*b*x + 4*a) + 8*(c*d^3 + (c^3 + c)*d)*sin(2*b*x + 2*a) + 1), x)","F",0
50,1,433,0,0.522609," ","integrate(arctan(c+d*tan(b*x+a)),x, algorithm=""maxima"")","\frac{d {\left(\frac{8 \, {\left(b x + a\right)} \arctan\left(\frac{d^{2} \tan\left(b x + a\right) + c d}{d}\right)}{d} - \frac{4 \, {\left(b x + a\right)} \arctan\left(\frac{c d + {\left(d^{2} + d\right)} \tan\left(b x + a\right)}{c^{2} + d^{2} + 2 \, d + 1}, \frac{c d \tan\left(b x + a\right) + c^{2} + d + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) - 4 \, {\left(b x + a\right)} \arctan\left(\frac{c d + {\left(d^{2} - d\right)} \tan\left(b x + a\right)}{c^{2} + d^{2} - 2 \, d + 1}, \frac{c d \tan\left(b x + a\right) + c^{2} - d + 1}{c^{2} + d^{2} - 2 \, d + 1}\right) + \log\left(\tan\left(b x + a\right)^{2} + 1\right) \log\left(\frac{d^{2} \tan\left(b x + a\right)^{2} + 2 \, c d \tan\left(b x + a\right) + c^{2} + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) - \log\left(\tan\left(b x + a\right)^{2} + 1\right) \log\left(\frac{d^{2} \tan\left(b x + a\right)^{2} + 2 \, c d \tan\left(b x + a\right) + c^{2} + 1}{c^{2} + d^{2} - 2 \, d + 1}\right) + 2 \, {\rm Li}_2\left(-\frac{i \, d \tan\left(b x + a\right) - d}{i \, c + d + 1}\right) - 2 \, {\rm Li}_2\left(-\frac{i \, d \tan\left(b x + a\right) - d}{i \, c + d - 1}\right) + 2 \, {\rm Li}_2\left(\frac{i \, d \tan\left(b x + a\right) + d}{-i \, c + d + 1}\right) - 2 \, {\rm Li}_2\left(\frac{i \, d \tan\left(b x + a\right) + d}{-i \, c + d - 1}\right)}{d}\right)} + 8 \, {\left(b x + a\right)} \arctan\left(d \tan\left(b x + a\right) + c\right) - 8 \, {\left(b x + a\right)} \arctan\left(\frac{d^{2} \tan\left(b x + a\right) + c d}{d}\right)}{8 \, b}"," ",0,"1/8*(d*(8*(b*x + a)*arctan((d^2*tan(b*x + a) + c*d)/d)/d - (4*(b*x + a)*arctan2((c*d + (d^2 + d)*tan(b*x + a))/(c^2 + d^2 + 2*d + 1), (c*d*tan(b*x + a) + c^2 + d + 1)/(c^2 + d^2 + 2*d + 1)) - 4*(b*x + a)*arctan2((c*d + (d^2 - d)*tan(b*x + a))/(c^2 + d^2 - 2*d + 1), (c*d*tan(b*x + a) + c^2 - d + 1)/(c^2 + d^2 - 2*d + 1)) + log(tan(b*x + a)^2 + 1)*log((d^2*tan(b*x + a)^2 + 2*c*d*tan(b*x + a) + c^2 + 1)/(c^2 + d^2 + 2*d + 1)) - log(tan(b*x + a)^2 + 1)*log((d^2*tan(b*x + a)^2 + 2*c*d*tan(b*x + a) + c^2 + 1)/(c^2 + d^2 - 2*d + 1)) + 2*dilog(-(I*d*tan(b*x + a) - d)/(I*c + d + 1)) - 2*dilog(-(I*d*tan(b*x + a) - d)/(I*c + d - 1)) + 2*dilog((I*d*tan(b*x + a) + d)/(-I*c + d + 1)) - 2*dilog((I*d*tan(b*x + a) + d)/(-I*c + d - 1)))/d) + 8*(b*x + a)*arctan(d*tan(b*x + a) + c) - 8*(b*x + a)*arctan((d^2*tan(b*x + a) + c*d)/d))/b","B",0
51,-1,0,0,0.000000," ","integrate(arctan(c+d*tan(b*x+a))/x,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,1,309,0,0.382165," ","integrate(x^2*arctan(c+(1+I*c)*tan(b*x+a)),x, algorithm=""maxima"")","\frac{\frac{{\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(b x + a\right)} a^{2}\right)} \arctan\left({\left(i \, c + 1\right)} \tan\left(b x + a\right) + c\right)}{b^{2}} - \frac{3 \, {\left(-3 i \, {\left(b x + a\right)}^{4} + 12 i \, {\left(b x + a\right)}^{3} a - 18 i \, {\left(b x + a\right)}^{2} a^{2} + {\left(-8 i \, {\left(b x + a\right)}^{3} + 18 i \, {\left(b x + a\right)}^{2} a - 18 i \, {\left(b x + a\right)} a^{2}\right)} \arctan\left(c \cos\left(2 \, b x + 2 \, a\right), c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(-12 i \, {\left(b x + a\right)}^{2} + 18 i \, {\left(b x + a\right)} a - 9 i \, a^{2}\right)} {\rm Li}_2\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(4 \, {\left(b x + a\right)}^{3} - 9 \, {\left(b x + a\right)}^{2} a + 9 \, {\left(b x + a\right)} a^{2}\right)} \log\left(c^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + c^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left(4 \, b x + a\right)} {\rm Li}_{3}(i \, c e^{\left(2 i \, b x + 2 i \, a\right)}) + 6 i \, {\rm Li}_{4}(i \, c e^{\left(2 i \, b x + 2 i \, a\right)})\right)} {\left(i \, c + 1\right)}}{b^{2} {\left(12 \, c - 12 i\right)}}}{3 \, b}"," ",0,"1/3*(((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(b*x + a)*a^2)*arctan((I*c + 1)*tan(b*x + a) + c)/b^2 - 3*(-3*I*(b*x + a)^4 + 12*I*(b*x + a)^3*a - 18*I*(b*x + a)^2*a^2 + (-8*I*(b*x + a)^3 + 18*I*(b*x + a)^2*a - 18*I*(b*x + a)*a^2)*arctan2(c*cos(2*b*x + 2*a), c*sin(2*b*x + 2*a) + 1) + (-12*I*(b*x + a)^2 + 18*I*(b*x + a)*a - 9*I*a^2)*dilog(I*c*e^(2*I*b*x + 2*I*a)) + (4*(b*x + a)^3 - 9*(b*x + a)^2*a + 9*(b*x + a)*a^2)*log(c^2*cos(2*b*x + 2*a)^2 + c^2*sin(2*b*x + 2*a)^2 + 2*c*sin(2*b*x + 2*a) + 1) + 3*(4*b*x + a)*polylog(3, I*c*e^(2*I*b*x + 2*I*a)) + 6*I*polylog(4, I*c*e^(2*I*b*x + 2*I*a)))*(I*c + 1)/(b^2*(12*c - 12*I)))/b","B",0
53,1,218,0,0.363204," ","integrate(x*arctan(c+(1+I*c)*tan(b*x+a)),x, algorithm=""maxima"")","\frac{\frac{{\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \arctan\left({\left(i \, c + 1\right)} \tan\left(b x + a\right) + c\right)}{b} - \frac{2 \, {\left(-4 i \, {\left(b x + a\right)}^{3} + 12 i \, {\left(b x + a\right)}^{2} a - 6 i \, b x {\rm Li}_2\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a\right)} \arctan\left(c \cos\left(2 \, b x + 2 \, a\right), c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \log\left(c^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + c^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\rm Li}_{3}(i \, c e^{\left(2 i \, b x + 2 i \, a\right)})\right)} {\left(i \, c + 1\right)}}{b {\left(12 \, c - 12 i\right)}}}{2 \, b}"," ",0,"1/2*(((b*x + a)^2 - 2*(b*x + a)*a)*arctan((I*c + 1)*tan(b*x + a) + c)/b - 2*(-4*I*(b*x + a)^3 + 12*I*(b*x + a)^2*a - 6*I*b*x*dilog(I*c*e^(2*I*b*x + 2*I*a)) + (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a)*arctan2(c*cos(2*b*x + 2*a), c*sin(2*b*x + 2*a) + 1) + 3*((b*x + a)^2 - 2*(b*x + a)*a)*log(c^2*cos(2*b*x + 2*a)^2 + c^2*sin(2*b*x + 2*a)^2 + 2*c*sin(2*b*x + 2*a) + 1) + 3*polylog(3, I*c*e^(2*I*b*x + 2*I*a)))*(I*c + 1)/(b*(12*c - 12*I)))/b","B",0
54,1,448,0,0.471383," ","integrate(arctan(c+(1+I*c)*tan(b*x+a)),x, algorithm=""maxima"")","-\frac{{\left(i \, c + 1\right)} {\left(\frac{4 i \, {\left(b x + a\right)} \log\left(\frac{2 i \, c^{2} - 2 \, {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) + 4 \, c - 2 i}{2 i \, c^{2} - 2 \, {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) + 2 i}\right)}{i \, c + 1} - \frac{i \, {\left(4 \, {\left(b x + a\right)} {\left(\log\left(-i \, c^{2} + {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) - 2 \, c + i\right) - \log\left(-i \, c^{2} + {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) - i\right)\right)} + i \, \log\left(-i \, c^{2} + {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) - 2 \, c + i\right)^{2} - 2 i \, \log\left(-i \, c^{2} + {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) - i\right) \log\left(-\frac{1}{2} \, {\left(c - i\right)} \tan\left(b x + a\right) + \frac{1}{2} i \, c + \frac{1}{2}\right) + 2 i \, \log\left(-i \, c^{2} + {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) - i\right) \log\left(-\frac{{\left(i \, c + 1\right)} \tan\left(b x + a\right) + c + i}{2 \, c} + 1\right) - 2 i \, \log\left(-i \, c^{2} + {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) - 2 \, c + i\right) \log\left(-\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right) - 2 i \, {\rm Li}_2\left(\frac{1}{2} \, {\left(c - i\right)} \tan\left(b x + a\right) - \frac{1}{2} i \, c + \frac{1}{2}\right) + 2 i \, {\rm Li}_2\left(\frac{{\left(i \, c + 1\right)} \tan\left(b x + a\right) + c + i}{2 \, c}\right) - 2 i \, {\rm Li}_2\left(\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right)\right)}}{i \, c + 1}\right)} - 8 \, {\left(b x + a\right)} \arctan\left({\left(i \, c + 1\right)} \tan\left(b x + a\right) + c\right) + 4 \, {\left(-i \, b x - i \, a\right)} \log\left(\frac{2 i \, c^{2} - 2 \, {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) + 4 \, c - 2 i}{2 i \, c^{2} - 2 \, {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) + 2 i}\right)}{8 \, b}"," ",0,"-1/8*((I*c + 1)*(4*I*(b*x + a)*log((2*I*c^2 - 2*(c^2 - 2*I*c - 1)*tan(b*x + a) + 4*c - 2*I)/(2*I*c^2 - 2*(c^2 - 2*I*c - 1)*tan(b*x + a) + 2*I))/(I*c + 1) - I*(4*(b*x + a)*(log(-I*c^2 + (c^2 - 2*I*c - 1)*tan(b*x + a) - 2*c + I) - log(-I*c^2 + (c^2 - 2*I*c - 1)*tan(b*x + a) - I)) + I*log(-I*c^2 + (c^2 - 2*I*c - 1)*tan(b*x + a) - 2*c + I)^2 - 2*I*log(-I*c^2 + (c^2 - 2*I*c - 1)*tan(b*x + a) - I)*log(-1/2*(c - I)*tan(b*x + a) + 1/2*I*c + 1/2) + 2*I*log(-I*c^2 + (c^2 - 2*I*c - 1)*tan(b*x + a) - I)*log(-1/2*((I*c + 1)*tan(b*x + a) + c + I)/c + 1) - 2*I*log(-I*c^2 + (c^2 - 2*I*c - 1)*tan(b*x + a) - 2*c + I)*log(-1/2*I*tan(b*x + a) + 1/2) - 2*I*dilog(1/2*(c - I)*tan(b*x + a) - 1/2*I*c + 1/2) + 2*I*dilog(1/2*((I*c + 1)*tan(b*x + a) + c + I)/c) - 2*I*dilog(1/2*I*tan(b*x + a) + 1/2))/(I*c + 1)) - 8*(b*x + a)*arctan((I*c + 1)*tan(b*x + a) + c) + 4*(-I*b*x - I*a)*log((2*I*c^2 - 2*(c^2 - 2*I*c - 1)*tan(b*x + a) + 4*c - 2*I)/(2*I*c^2 - 2*(c^2 - 2*I*c - 1)*tan(b*x + a) + 2*I)))/b","B",0
55,-2,0,0,0.000000," ","integrate(arctan(c+(1+I*c)*tan(b*x+a))/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c-1>0)', see `assume?` for more details)Is c-1 zero or nonzero?","F(-2)",0
56,1,310,0,0.384017," ","integrate(x^2*arctan(c+(-1+I*c)*tan(b*x+a)),x, algorithm=""maxima"")","\frac{\frac{{\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(b x + a\right)} a^{2}\right)} \arctan\left({\left(i \, c - 1\right)} \tan\left(b x + a\right) + c\right)}{b^{2}} + \frac{3 \, {\left(-3 i \, {\left(b x + a\right)}^{4} + 12 i \, {\left(b x + a\right)}^{3} a - 18 i \, {\left(b x + a\right)}^{2} a^{2} + {\left(8 i \, {\left(b x + a\right)}^{3} - 18 i \, {\left(b x + a\right)}^{2} a + 18 i \, {\left(b x + a\right)} a^{2}\right)} \arctan\left(c \cos\left(2 \, b x + 2 \, a\right), -c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(-12 i \, {\left(b x + a\right)}^{2} + 18 i \, {\left(b x + a\right)} a - 9 i \, a^{2}\right)} {\rm Li}_2\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(4 \, {\left(b x + a\right)}^{3} - 9 \, {\left(b x + a\right)}^{2} a + 9 \, {\left(b x + a\right)} a^{2}\right)} \log\left(c^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + c^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left(4 \, b x + a\right)} {\rm Li}_{3}(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)}) + 6 i \, {\rm Li}_{4}(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)})\right)} {\left(i \, c - 1\right)}}{b^{2} {\left(12 \, c + 12 i\right)}}}{3 \, b}"," ",0,"1/3*(((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(b*x + a)*a^2)*arctan((I*c - 1)*tan(b*x + a) + c)/b^2 + 3*(-3*I*(b*x + a)^4 + 12*I*(b*x + a)^3*a - 18*I*(b*x + a)^2*a^2 + (8*I*(b*x + a)^3 - 18*I*(b*x + a)^2*a + 18*I*(b*x + a)*a^2)*arctan2(c*cos(2*b*x + 2*a), -c*sin(2*b*x + 2*a) + 1) + (-12*I*(b*x + a)^2 + 18*I*(b*x + a)*a - 9*I*a^2)*dilog(-I*c*e^(2*I*b*x + 2*I*a)) + (4*(b*x + a)^3 - 9*(b*x + a)^2*a + 9*(b*x + a)*a^2)*log(c^2*cos(2*b*x + 2*a)^2 + c^2*sin(2*b*x + 2*a)^2 - 2*c*sin(2*b*x + 2*a) + 1) + 3*(4*b*x + a)*polylog(3, -I*c*e^(2*I*b*x + 2*I*a)) + 6*I*polylog(4, -I*c*e^(2*I*b*x + 2*I*a)))*(I*c - 1)/(b^2*(12*c + 12*I)))/b","B",0
57,1,219,0,0.368727," ","integrate(x*arctan(c+(-1+I*c)*tan(b*x+a)),x, algorithm=""maxima"")","\frac{\frac{{\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \arctan\left({\left(i \, c - 1\right)} \tan\left(b x + a\right) + c\right)}{b} + \frac{2 \, {\left(-4 i \, {\left(b x + a\right)}^{3} + 12 i \, {\left(b x + a\right)}^{2} a - 6 i \, b x {\rm Li}_2\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a\right)} \arctan\left(c \cos\left(2 \, b x + 2 \, a\right), -c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \log\left(c^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + c^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\rm Li}_{3}(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)})\right)} {\left(i \, c - 1\right)}}{b {\left(12 \, c + 12 i\right)}}}{2 \, b}"," ",0,"1/2*(((b*x + a)^2 - 2*(b*x + a)*a)*arctan((I*c - 1)*tan(b*x + a) + c)/b + 2*(-4*I*(b*x + a)^3 + 12*I*(b*x + a)^2*a - 6*I*b*x*dilog(-I*c*e^(2*I*b*x + 2*I*a)) + (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a)*arctan2(c*cos(2*b*x + 2*a), -c*sin(2*b*x + 2*a) + 1) + 3*((b*x + a)^2 - 2*(b*x + a)*a)*log(c^2*cos(2*b*x + 2*a)^2 + c^2*sin(2*b*x + 2*a)^2 - 2*c*sin(2*b*x + 2*a) + 1) + 3*polylog(3, -I*c*e^(2*I*b*x + 2*I*a)))*(I*c - 1)/(b*(12*c + 12*I)))/b","B",0
58,1,448,0,0.463251," ","integrate(arctan(c+(-1+I*c)*tan(b*x+a)),x, algorithm=""maxima"")","-\frac{{\left(i \, c - 1\right)} {\left(\frac{4 i \, {\left(b x + a\right)} \log\left(\frac{2 i \, c^{2} - 2 \, {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) + 2 i}{2 i \, c^{2} - 2 \, {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) - 4 \, c - 2 i}\right)}{i \, c - 1} + \frac{i \, {\left(4 \, {\left(b x + a\right)} {\left(\log\left(-i \, c^{2} + {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) + 2 \, c + i\right) - \log\left(-i \, c^{2} + {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) - i\right)\right)} + i \, \log\left(-i \, c^{2} + {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) + 2 \, c + i\right)^{2} - 2 i \, \log\left(-i \, c^{2} + {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) - i\right) \log\left(\frac{1}{2} \, {\left(c + i\right)} \tan\left(b x + a\right) - \frac{1}{2} i \, c + \frac{1}{2}\right) + 2 i \, \log\left(-i \, c^{2} + {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) - i\right) \log\left(-\frac{{\left(i \, c - 1\right)} \tan\left(b x + a\right) + c - i}{2 \, c} + 1\right) - 2 i \, \log\left(-i \, c^{2} + {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) + 2 \, c + i\right) \log\left(-\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right) - 2 i \, {\rm Li}_2\left(-\frac{1}{2} \, {\left(c + i\right)} \tan\left(b x + a\right) + \frac{1}{2} i \, c + \frac{1}{2}\right) + 2 i \, {\rm Li}_2\left(\frac{{\left(i \, c - 1\right)} \tan\left(b x + a\right) + c - i}{2 \, c}\right) - 2 i \, {\rm Li}_2\left(\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right)\right)}}{i \, c - 1}\right)} - 8 \, {\left(b x + a\right)} \arctan\left({\left(i \, c - 1\right)} \tan\left(b x + a\right) + c\right) + 4 \, {\left(-i \, b x - i \, a\right)} \log\left(\frac{2 i \, c^{2} - 2 \, {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) + 2 i}{2 i \, c^{2} - 2 \, {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) - 4 \, c - 2 i}\right)}{8 \, b}"," ",0,"-1/8*((I*c - 1)*(4*I*(b*x + a)*log((2*I*c^2 - 2*(c^2 + 2*I*c - 1)*tan(b*x + a) + 2*I)/(2*I*c^2 - 2*(c^2 + 2*I*c - 1)*tan(b*x + a) - 4*c - 2*I))/(I*c - 1) + I*(4*(b*x + a)*(log(-I*c^2 + (c^2 + 2*I*c - 1)*tan(b*x + a) + 2*c + I) - log(-I*c^2 + (c^2 + 2*I*c - 1)*tan(b*x + a) - I)) + I*log(-I*c^2 + (c^2 + 2*I*c - 1)*tan(b*x + a) + 2*c + I)^2 - 2*I*log(-I*c^2 + (c^2 + 2*I*c - 1)*tan(b*x + a) - I)*log(1/2*(c + I)*tan(b*x + a) - 1/2*I*c + 1/2) + 2*I*log(-I*c^2 + (c^2 + 2*I*c - 1)*tan(b*x + a) - I)*log(-1/2*((I*c - 1)*tan(b*x + a) + c - I)/c + 1) - 2*I*log(-I*c^2 + (c^2 + 2*I*c - 1)*tan(b*x + a) + 2*c + I)*log(-1/2*I*tan(b*x + a) + 1/2) - 2*I*dilog(-1/2*(c + I)*tan(b*x + a) + 1/2*I*c + 1/2) + 2*I*dilog(1/2*((I*c - 1)*tan(b*x + a) + c - I)/c) - 2*I*dilog(1/2*I*tan(b*x + a) + 1/2))/(I*c - 1)) - 8*(b*x + a)*arctan((I*c - 1)*tan(b*x + a) + c) + 4*(-I*b*x - I*a)*log((2*I*c^2 - 2*(c^2 + 2*I*c - 1)*tan(b*x + a) + 2*I)/(2*I*c^2 - 2*(c^2 + 2*I*c - 1)*tan(b*x + a) - 4*c - 2*I)))/b","B",0
59,-2,0,0,0.000000," ","integrate(arctan(c+(-1+I*c)*tan(b*x+a))/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c-1>0)', see `assume?` for more details)Is c-1 zero or nonzero?","F(-2)",0
60,1,15,0,0.318706," ","integrate(1/2*pi-arccot(cot(b*x+a)),x, algorithm=""maxima"")","-\frac{1}{2} \, b x^{2} + \frac{1}{2} \, \pi x - a x"," ",0,"-1/2*b*x^2 + 1/2*pi*x - a*x","A",0
61,0,0,0,0.000000," ","integrate(x^2*arctan(c+d*cot(b*x+a)),x, algorithm=""maxima"")","-\frac{1}{6} \, x^{3} \arctan\left(-c \cos\left(2 \, b x + 2 \, a\right) + {\left(d + 1\right)} \sin\left(2 \, b x + 2 \, a\right) + c, {\left(d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + c \sin\left(2 \, b x + 2 \, a\right) + d - 1\right) - \frac{1}{6} \, x^{3} \arctan\left(-c \cos\left(2 \, b x + 2 \, a\right) + {\left(d - 1\right)} \sin\left(2 \, b x + 2 \, a\right) + c, -{\left(d - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - c \sin\left(2 \, b x + 2 \, a\right) - d - 1\right) + 4 \, b d \int \frac{2 \, {\left(c^{2} + d^{2} + 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c d x^{3} \sin\left(2 \, b x + 2 \, a\right) + 2 \, {\left(c^{2} + d^{2} + 1\right)} x^{3} \sin\left(2 \, b x + 2 \, a\right)^{2} - {\left(c^{2} - d^{2} + 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, c d x^{3} \sin\left(2 \, b x + 2 \, a\right) + {\left(c^{2} - d^{2} + 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, c d x^{3} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{2} - d^{2} + 1\right)} x^{3} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right)}{3 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c^{2} + 2 \, {\left(c^{4} + d^{4} - 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} + 2 \, c^{2} - 2 \, {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + 4 \, {\left(2 \, c d^{3} - 2 \, {\left(c^{3} + c\right)} d + 2 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 8 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)}}\,{d x}"," ",0,"-1/6*x^3*arctan2(-c*cos(2*b*x + 2*a) + (d + 1)*sin(2*b*x + 2*a) + c, (d + 1)*cos(2*b*x + 2*a) + c*sin(2*b*x + 2*a) + d - 1) - 1/6*x^3*arctan2(-c*cos(2*b*x + 2*a) + (d - 1)*sin(2*b*x + 2*a) + c, -(d - 1)*cos(2*b*x + 2*a) - c*sin(2*b*x + 2*a) - d - 1) + 4*b*d*integrate(1/3*(2*(c^2 + d^2 + 1)*x^3*cos(2*b*x + 2*a)^2 + 2*c*d*x^3*sin(2*b*x + 2*a) + 2*(c^2 + d^2 + 1)*x^3*sin(2*b*x + 2*a)^2 - (c^2 - d^2 + 1)*x^3*cos(2*b*x + 2*a) - (2*c*d*x^3*sin(2*b*x + 2*a) + (c^2 - d^2 + 1)*x^3*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) + (2*c*d*x^3*cos(2*b*x + 2*a) - (c^2 - d^2 + 1)*x^3*sin(2*b*x + 2*a))*sin(4*b*x + 4*a))/(c^4 + d^4 + 2*(c^2 - 1)*d^2 + (c^4 + d^4 + 2*(c^2 - 1)*d^2 + 2*c^2 + 1)*cos(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 + 1)*d^2 + 2*c^2 + 1)*cos(2*b*x + 2*a)^2 + (c^4 + d^4 + 2*(c^2 - 1)*d^2 + 2*c^2 + 1)*sin(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 + 1)*d^2 + 2*c^2 + 1)*sin(2*b*x + 2*a)^2 + 2*c^2 + 2*(c^4 + d^4 - 2*(3*c^2 + 1)*d^2 + 2*c^2 - 2*(c^4 - d^4 + 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(c*d^3 + (c^3 + c)*d)*sin(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) - 4*(c^4 - d^4 + 2*c^2 + 1)*cos(2*b*x + 2*a) + 4*(2*c*d^3 - 2*(c^3 + c)*d + 2*(c*d^3 + (c^3 + c)*d)*cos(2*b*x + 2*a) - (c^4 - d^4 + 2*c^2 + 1)*sin(2*b*x + 2*a))*sin(4*b*x + 4*a) + 8*(c*d^3 + (c^3 + c)*d)*sin(2*b*x + 2*a) + 1), x)","F",0
62,0,0,0,0.000000," ","integrate(x*arctan(c+d*cot(b*x+a)),x, algorithm=""maxima"")","-\frac{1}{4} \, x^{2} \arctan\left(-c \cos\left(2 \, b x + 2 \, a\right) + {\left(d + 1\right)} \sin\left(2 \, b x + 2 \, a\right) + c, {\left(d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + c \sin\left(2 \, b x + 2 \, a\right) + d - 1\right) - \frac{1}{4} \, x^{2} \arctan\left(-c \cos\left(2 \, b x + 2 \, a\right) + {\left(d - 1\right)} \sin\left(2 \, b x + 2 \, a\right) + c, -{\left(d - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - c \sin\left(2 \, b x + 2 \, a\right) - d - 1\right) + 2 \, b d \int \frac{2 \, {\left(c^{2} + d^{2} + 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c d x^{2} \sin\left(2 \, b x + 2 \, a\right) + 2 \, {\left(c^{2} + d^{2} + 1\right)} x^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - {\left(c^{2} - d^{2} + 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, c d x^{2} \sin\left(2 \, b x + 2 \, a\right) + {\left(c^{2} - d^{2} + 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, c d x^{2} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{2} - d^{2} + 1\right)} x^{2} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right)}{c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c^{2} + 2 \, {\left(c^{4} + d^{4} - 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} + 2 \, c^{2} - 2 \, {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + 4 \, {\left(2 \, c d^{3} - 2 \, {\left(c^{3} + c\right)} d + 2 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 8 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1}\,{d x}"," ",0,"-1/4*x^2*arctan2(-c*cos(2*b*x + 2*a) + (d + 1)*sin(2*b*x + 2*a) + c, (d + 1)*cos(2*b*x + 2*a) + c*sin(2*b*x + 2*a) + d - 1) - 1/4*x^2*arctan2(-c*cos(2*b*x + 2*a) + (d - 1)*sin(2*b*x + 2*a) + c, -(d - 1)*cos(2*b*x + 2*a) - c*sin(2*b*x + 2*a) - d - 1) + 2*b*d*integrate((2*(c^2 + d^2 + 1)*x^2*cos(2*b*x + 2*a)^2 + 2*c*d*x^2*sin(2*b*x + 2*a) + 2*(c^2 + d^2 + 1)*x^2*sin(2*b*x + 2*a)^2 - (c^2 - d^2 + 1)*x^2*cos(2*b*x + 2*a) - (2*c*d*x^2*sin(2*b*x + 2*a) + (c^2 - d^2 + 1)*x^2*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) + (2*c*d*x^2*cos(2*b*x + 2*a) - (c^2 - d^2 + 1)*x^2*sin(2*b*x + 2*a))*sin(4*b*x + 4*a))/(c^4 + d^4 + 2*(c^2 - 1)*d^2 + (c^4 + d^4 + 2*(c^2 - 1)*d^2 + 2*c^2 + 1)*cos(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 + 1)*d^2 + 2*c^2 + 1)*cos(2*b*x + 2*a)^2 + (c^4 + d^4 + 2*(c^2 - 1)*d^2 + 2*c^2 + 1)*sin(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 + 1)*d^2 + 2*c^2 + 1)*sin(2*b*x + 2*a)^2 + 2*c^2 + 2*(c^4 + d^4 - 2*(3*c^2 + 1)*d^2 + 2*c^2 - 2*(c^4 - d^4 + 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(c*d^3 + (c^3 + c)*d)*sin(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) - 4*(c^4 - d^4 + 2*c^2 + 1)*cos(2*b*x + 2*a) + 4*(2*c*d^3 - 2*(c^3 + c)*d + 2*(c*d^3 + (c^3 + c)*d)*cos(2*b*x + 2*a) - (c^4 - d^4 + 2*c^2 + 1)*sin(2*b*x + 2*a))*sin(4*b*x + 4*a) + 8*(c*d^3 + (c^3 + c)*d)*sin(2*b*x + 2*a) + 1), x)","F",0
63,1,532,0,0.549588," ","integrate(arctan(c+d*cot(b*x+a)),x, algorithm=""maxima"")","-\frac{d {\left(\frac{8 \, {\left(b x + a\right)} \arctan\left(\frac{c d + {\left(c^{2} + 1\right)} \tan\left(b x + a\right)}{d}\right)}{d} - \frac{8 \, {\left(b x + a\right)} \arctan\left(\frac{c d + {\left(c^{2} + 1\right)} \tan\left(b x + a\right)}{d}\right) - 4 \, \arctan\left(\frac{c d + {\left(c^{2} + 1\right)} \tan\left(b x + a\right)}{d}\right) \arctan\left(\frac{c d + {\left(c^{2} + d + 1\right)} \tan\left(b x + a\right)}{c^{2} + d^{2} + 2 \, d + 1}, -\frac{c d \tan\left(b x + a\right) - c^{2} - d - 1}{c^{2} + d^{2} + 2 \, d + 1}\right) + 4 \, \arctan\left(\frac{c d + {\left(c^{2} + 1\right)} \tan\left(b x + a\right)}{d}\right) \arctan\left(-\frac{c d + {\left(c^{2} - d + 1\right)} \tan\left(b x + a\right)}{c^{2} + d^{2} - 2 \, d + 1}, -\frac{c d \tan\left(b x + a\right) - c^{2} + d - 1}{c^{2} + d^{2} - 2 \, d + 1}\right) - {\left(\log\left(\frac{{\left(c^{2} + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) - \log\left(\frac{{\left(c^{2} + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + 1}{c^{2} + d^{2} - 2 \, d + 1}\right)\right)} \log\left({\left(c^{2} + 1\right)} d^{2} + 2 \, {\left(c^{3} + c\right)} d \tan\left(b x + a\right) + {\left(c^{4} + 2 \, c^{2} + 1\right)} \tan\left(b x + a\right)^{2}\right) - 2 \, {\rm Li}_2\left(\frac{{\left(i \, c - 1\right)} \tan\left(b x + a\right) + i \, d}{c + i \, d + i}\right) + 2 \, {\rm Li}_2\left(\frac{{\left(i \, c + 1\right)} \tan\left(b x + a\right) + i \, d}{c + i \, d - i}\right) + 2 \, {\rm Li}_2\left(-\frac{{\left(i \, c - 1\right)} \tan\left(b x + a\right) + i \, d}{c - i \, d + i}\right) - 2 \, {\rm Li}_2\left(-\frac{{\left(i \, c + 1\right)} \tan\left(b x + a\right) + i \, d}{c - i \, d - i}\right)}{d}\right)} - 8 \, {\left(b x + a\right)} \arctan\left(c + \frac{d}{\tan\left(b x + a\right)}\right) - 8 \, {\left(b x + a\right)} \arctan\left(\frac{c d + {\left(c^{2} + 1\right)} \tan\left(b x + a\right)}{d}\right)}{8 \, b}"," ",0,"-1/8*(d*(8*(b*x + a)*arctan((c*d + (c^2 + 1)*tan(b*x + a))/d)/d - (8*(b*x + a)*arctan((c*d + (c^2 + 1)*tan(b*x + a))/d) - 4*arctan((c*d + (c^2 + 1)*tan(b*x + a))/d)*arctan2((c*d + (c^2 + d + 1)*tan(b*x + a))/(c^2 + d^2 + 2*d + 1), -(c*d*tan(b*x + a) - c^2 - d - 1)/(c^2 + d^2 + 2*d + 1)) + 4*arctan((c*d + (c^2 + 1)*tan(b*x + a))/d)*arctan2(-(c*d + (c^2 - d + 1)*tan(b*x + a))/(c^2 + d^2 - 2*d + 1), -(c*d*tan(b*x + a) - c^2 + d - 1)/(c^2 + d^2 - 2*d + 1)) - (log(((c^2 + 1)*tan(b*x + a)^2 + c^2 + 1)/(c^2 + d^2 + 2*d + 1)) - log(((c^2 + 1)*tan(b*x + a)^2 + c^2 + 1)/(c^2 + d^2 - 2*d + 1)))*log((c^2 + 1)*d^2 + 2*(c^3 + c)*d*tan(b*x + a) + (c^4 + 2*c^2 + 1)*tan(b*x + a)^2) - 2*dilog(((I*c - 1)*tan(b*x + a) + I*d)/(c + I*d + I)) + 2*dilog(((I*c + 1)*tan(b*x + a) + I*d)/(c + I*d - I)) + 2*dilog(-((I*c - 1)*tan(b*x + a) + I*d)/(c - I*d + I)) - 2*dilog(-((I*c + 1)*tan(b*x + a) + I*d)/(c - I*d - I)))/d) - 8*(b*x + a)*arctan(c + d/tan(b*x + a)) - 8*(b*x + a)*arctan((c*d + (c^2 + 1)*tan(b*x + a))/d))/b","B",0
64,-1,0,0,0.000000," ","integrate(arctan(c+d*cot(b*x+a))/x,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,1,309,0,0.365950," ","integrate(-x^2*arctan(-c-(1-I*c)*cot(b*x+a)),x, algorithm=""maxima"")","\frac{\frac{{\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(b x + a\right)} a^{2}\right)} \arctan\left({\left(-i \, c + 1\right)} \cot\left(b x + a\right) + c\right)}{b^{2}} + \frac{3 \, {\left(-3 i \, {\left(b x + a\right)}^{4} + 12 i \, {\left(b x + a\right)}^{3} a - 18 i \, {\left(b x + a\right)}^{2} a^{2} + {\left(-8 i \, {\left(b x + a\right)}^{3} + 18 i \, {\left(b x + a\right)}^{2} a - 18 i \, {\left(b x + a\right)} a^{2}\right)} \arctan\left(c \cos\left(2 \, b x + 2 \, a\right), c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(-12 i \, {\left(b x + a\right)}^{2} + 18 i \, {\left(b x + a\right)} a - 9 i \, a^{2}\right)} {\rm Li}_2\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(4 \, {\left(b x + a\right)}^{3} - 9 \, {\left(b x + a\right)}^{2} a + 9 \, {\left(b x + a\right)} a^{2}\right)} \log\left(c^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + c^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left(4 \, b x + a\right)} {\rm Li}_{3}(i \, c e^{\left(2 i \, b x + 2 i \, a\right)}) + 6 i \, {\rm Li}_{4}(i \, c e^{\left(2 i \, b x + 2 i \, a\right)})\right)} {\left(i \, c - 1\right)}}{b^{2} {\left(12 \, c + 12 i\right)}}}{3 \, b}"," ",0,"1/3*(((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(b*x + a)*a^2)*arctan((-I*c + 1)*cot(b*x + a) + c)/b^2 + 3*(-3*I*(b*x + a)^4 + 12*I*(b*x + a)^3*a - 18*I*(b*x + a)^2*a^2 + (-8*I*(b*x + a)^3 + 18*I*(b*x + a)^2*a - 18*I*(b*x + a)*a^2)*arctan2(c*cos(2*b*x + 2*a), c*sin(2*b*x + 2*a) + 1) + (-12*I*(b*x + a)^2 + 18*I*(b*x + a)*a - 9*I*a^2)*dilog(I*c*e^(2*I*b*x + 2*I*a)) + (4*(b*x + a)^3 - 9*(b*x + a)^2*a + 9*(b*x + a)*a^2)*log(c^2*cos(2*b*x + 2*a)^2 + c^2*sin(2*b*x + 2*a)^2 + 2*c*sin(2*b*x + 2*a) + 1) + 3*(4*b*x + a)*polylog(3, I*c*e^(2*I*b*x + 2*I*a)) + 6*I*polylog(4, I*c*e^(2*I*b*x + 2*I*a)))*(I*c - 1)/(b^2*(12*c + 12*I)))/b","B",0
66,1,218,0,0.344053," ","integrate(-x*arctan(-c-(1-I*c)*cot(b*x+a)),x, algorithm=""maxima"")","\frac{\frac{{\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \arctan\left({\left(-i \, c + 1\right)} \cot\left(b x + a\right) + c\right)}{b} + \frac{2 \, {\left(-4 i \, {\left(b x + a\right)}^{3} + 12 i \, {\left(b x + a\right)}^{2} a - 6 i \, b x {\rm Li}_2\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a\right)} \arctan\left(c \cos\left(2 \, b x + 2 \, a\right), c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \log\left(c^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + c^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\rm Li}_{3}(i \, c e^{\left(2 i \, b x + 2 i \, a\right)})\right)} {\left(i \, c - 1\right)}}{b {\left(12 \, c + 12 i\right)}}}{2 \, b}"," ",0,"1/2*(((b*x + a)^2 - 2*(b*x + a)*a)*arctan((-I*c + 1)*cot(b*x + a) + c)/b + 2*(-4*I*(b*x + a)^3 + 12*I*(b*x + a)^2*a - 6*I*b*x*dilog(I*c*e^(2*I*b*x + 2*I*a)) + (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a)*arctan2(c*cos(2*b*x + 2*a), c*sin(2*b*x + 2*a) + 1) + 3*((b*x + a)^2 - 2*(b*x + a)*a)*log(c^2*cos(2*b*x + 2*a)^2 + c^2*sin(2*b*x + 2*a)^2 + 2*c*sin(2*b*x + 2*a) + 1) + 3*polylog(3, I*c*e^(2*I*b*x + 2*I*a)))*(I*c - 1)/(b*(12*c + 12*I)))/b","B",0
67,1,456,0,0.441685," ","integrate(-arctan(-c-(1-I*c)*cot(b*x+a)),x, algorithm=""maxima"")","-\frac{{\left(i \, c - 1\right)} {\left(\frac{4 i \, {\left(b x + a\right)} \log\left(\frac{-2 i \, c^{2} + 2 \, {\left(c^{2} + 1\right)} \tan\left(b x + a\right) + 4 \, c + 2 i}{-2 i \, c^{2} + 2 \, {\left(c^{2} + 1\right)} \tan\left(b x + a\right) - 2 i}\right)}{i \, c - 1} - \frac{i \, {\left(4 \, {\left(b x + a\right)} {\left(\log\left(-i \, c^{2} + {\left(c^{2} + 1\right)} \tan\left(b x + a\right) + 2 \, c + i\right) - \log\left(-i \, c^{2} + {\left(c^{2} + 1\right)} \tan\left(b x + a\right) - i\right)\right)} - 2 i \, \log\left(-i \, c^{2} + {\left(c^{2} + 1\right)} \tan\left(b x + a\right) + 2 \, c + i\right) \log\left(-\frac{{\left(i \, c + 1\right)} \tan\left(b x + a\right) + c + i}{2 \, c} + 1\right) + 2 i \, \log\left(-i \, c^{2} + {\left(c^{2} + 1\right)} \tan\left(b x + a\right) + 2 \, c + i\right) \log\left(\tan\left(b x + a\right) - i\right) - 2 i \, \log\left(\frac{1}{2} \, {\left(c - i\right)} \tan\left(b x + a\right) - \frac{1}{2} i \, c + \frac{1}{2}\right) \log\left(\tan\left(b x + a\right) - i\right) - i \, \log\left(\tan\left(b x + a\right) - i\right)^{2} - 2 i \, \log\left(c^{2} + 1\right) \log\left(i \, \tan\left(b x + a\right) + 1\right) + 2 i \, \log\left(\tan\left(b x + a\right) - i\right) \log\left(-\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right) + 2 i \, \log\left(c^{2} + 1\right) \log\left(-i \, \tan\left(b x + a\right) + 1\right) - 2 i \, {\rm Li}_2\left(-\frac{1}{2} \, {\left(c - i\right)} \tan\left(b x + a\right) + \frac{1}{2} i \, c + \frac{1}{2}\right) - 2 i \, {\rm Li}_2\left(\frac{{\left(i \, c + 1\right)} \tan\left(b x + a\right) + c + i}{2 \, c}\right) + 2 i \, {\rm Li}_2\left(\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right)\right)}}{i \, c - 1}\right)} - 8 \, {\left(b x + a\right)} \arctan\left(c + \frac{-i \, c + 1}{\tan\left(b x + a\right)}\right) + 4 \, {\left(-i \, b x - i \, a\right)} \log\left(\frac{-2 i \, c^{2} + 2 \, {\left(c^{2} + 1\right)} \tan\left(b x + a\right) + 4 \, c + 2 i}{-2 i \, c^{2} + 2 \, {\left(c^{2} + 1\right)} \tan\left(b x + a\right) - 2 i}\right)}{8 \, b}"," ",0,"-1/8*((I*c - 1)*(4*I*(b*x + a)*log((-2*I*c^2 + 2*(c^2 + 1)*tan(b*x + a) + 4*c + 2*I)/(-2*I*c^2 + 2*(c^2 + 1)*tan(b*x + a) - 2*I))/(I*c - 1) - I*(4*(b*x + a)*(log(-I*c^2 + (c^2 + 1)*tan(b*x + a) + 2*c + I) - log(-I*c^2 + (c^2 + 1)*tan(b*x + a) - I)) - 2*I*log(-I*c^2 + (c^2 + 1)*tan(b*x + a) + 2*c + I)*log(-1/2*((I*c + 1)*tan(b*x + a) + c + I)/c + 1) + 2*I*log(-I*c^2 + (c^2 + 1)*tan(b*x + a) + 2*c + I)*log(tan(b*x + a) - I) - 2*I*log(1/2*(c - I)*tan(b*x + a) - 1/2*I*c + 1/2)*log(tan(b*x + a) - I) - I*log(tan(b*x + a) - I)^2 - 2*I*log(c^2 + 1)*log(I*tan(b*x + a) + 1) + 2*I*log(tan(b*x + a) - I)*log(-1/2*I*tan(b*x + a) + 1/2) + 2*I*log(c^2 + 1)*log(-I*tan(b*x + a) + 1) - 2*I*dilog(-1/2*(c - I)*tan(b*x + a) + 1/2*I*c + 1/2) - 2*I*dilog(1/2*((I*c + 1)*tan(b*x + a) + c + I)/c) + 2*I*dilog(1/2*I*tan(b*x + a) + 1/2))/(I*c - 1)) - 8*(b*x + a)*arctan(c + (-I*c + 1)/tan(b*x + a)) + 4*(-I*b*x - I*a)*log((-2*I*c^2 + 2*(c^2 + 1)*tan(b*x + a) + 4*c + 2*I)/(-2*I*c^2 + 2*(c^2 + 1)*tan(b*x + a) - 2*I)))/b","B",0
68,-2,0,0,0.000000," ","integrate(-arctan(-c-(1-I*c)*cot(b*x+a))/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c-1>0)', see `assume?` for more details)Is c-1 zero or nonzero?","F(-2)",0
69,1,310,0,0.374421," ","integrate(-x^2*arctan(-c-(-1-I*c)*cot(b*x+a)),x, algorithm=""maxima"")","\frac{\frac{{\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(b x + a\right)} a^{2}\right)} \arctan\left({\left(-i \, c - 1\right)} \cot\left(b x + a\right) + c\right)}{b^{2}} - \frac{3 \, {\left(-3 i \, {\left(b x + a\right)}^{4} + 12 i \, {\left(b x + a\right)}^{3} a - 18 i \, {\left(b x + a\right)}^{2} a^{2} + {\left(8 i \, {\left(b x + a\right)}^{3} - 18 i \, {\left(b x + a\right)}^{2} a + 18 i \, {\left(b x + a\right)} a^{2}\right)} \arctan\left(c \cos\left(2 \, b x + 2 \, a\right), -c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(-12 i \, {\left(b x + a\right)}^{2} + 18 i \, {\left(b x + a\right)} a - 9 i \, a^{2}\right)} {\rm Li}_2\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(4 \, {\left(b x + a\right)}^{3} - 9 \, {\left(b x + a\right)}^{2} a + 9 \, {\left(b x + a\right)} a^{2}\right)} \log\left(c^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + c^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left(4 \, b x + a\right)} {\rm Li}_{3}(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)}) + 6 i \, {\rm Li}_{4}(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)})\right)} {\left(i \, c + 1\right)}}{b^{2} {\left(12 \, c - 12 i\right)}}}{3 \, b}"," ",0,"1/3*(((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(b*x + a)*a^2)*arctan((-I*c - 1)*cot(b*x + a) + c)/b^2 - 3*(-3*I*(b*x + a)^4 + 12*I*(b*x + a)^3*a - 18*I*(b*x + a)^2*a^2 + (8*I*(b*x + a)^3 - 18*I*(b*x + a)^2*a + 18*I*(b*x + a)*a^2)*arctan2(c*cos(2*b*x + 2*a), -c*sin(2*b*x + 2*a) + 1) + (-12*I*(b*x + a)^2 + 18*I*(b*x + a)*a - 9*I*a^2)*dilog(-I*c*e^(2*I*b*x + 2*I*a)) + (4*(b*x + a)^3 - 9*(b*x + a)^2*a + 9*(b*x + a)*a^2)*log(c^2*cos(2*b*x + 2*a)^2 + c^2*sin(2*b*x + 2*a)^2 - 2*c*sin(2*b*x + 2*a) + 1) + 3*(4*b*x + a)*polylog(3, -I*c*e^(2*I*b*x + 2*I*a)) + 6*I*polylog(4, -I*c*e^(2*I*b*x + 2*I*a)))*(I*c + 1)/(b^2*(12*c - 12*I)))/b","B",0
70,1,219,0,0.349347," ","integrate(-x*arctan(-c-(-1-I*c)*cot(b*x+a)),x, algorithm=""maxima"")","\frac{\frac{{\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \arctan\left({\left(-i \, c - 1\right)} \cot\left(b x + a\right) + c\right)}{b} - \frac{2 \, {\left(-4 i \, {\left(b x + a\right)}^{3} + 12 i \, {\left(b x + a\right)}^{2} a - 6 i \, b x {\rm Li}_2\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a\right)} \arctan\left(c \cos\left(2 \, b x + 2 \, a\right), -c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \log\left(c^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + c^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\rm Li}_{3}(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)})\right)} {\left(i \, c + 1\right)}}{b {\left(12 \, c - 12 i\right)}}}{2 \, b}"," ",0,"1/2*(((b*x + a)^2 - 2*(b*x + a)*a)*arctan((-I*c - 1)*cot(b*x + a) + c)/b - 2*(-4*I*(b*x + a)^3 + 12*I*(b*x + a)^2*a - 6*I*b*x*dilog(-I*c*e^(2*I*b*x + 2*I*a)) + (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a)*arctan2(c*cos(2*b*x + 2*a), -c*sin(2*b*x + 2*a) + 1) + 3*((b*x + a)^2 - 2*(b*x + a)*a)*log(c^2*cos(2*b*x + 2*a)^2 + c^2*sin(2*b*x + 2*a)^2 - 2*c*sin(2*b*x + 2*a) + 1) + 3*polylog(3, -I*c*e^(2*I*b*x + 2*I*a)))*(I*c + 1)/(b*(12*c - 12*I)))/b","B",0
71,1,456,0,0.473079," ","integrate(-arctan(-c-(-1-I*c)*cot(b*x+a)),x, algorithm=""maxima"")","-\frac{{\left(i \, c + 1\right)} {\left(\frac{4 i \, {\left(b x + a\right)} \log\left(\frac{-2 i \, c^{2} + 2 \, {\left(c^{2} + 1\right)} \tan\left(b x + a\right) - 2 i}{-2 i \, c^{2} + 2 \, {\left(c^{2} + 1\right)} \tan\left(b x + a\right) - 4 \, c + 2 i}\right)}{i \, c + 1} + \frac{i \, {\left(4 \, {\left(b x + a\right)} {\left(\log\left(-i \, c^{2} + {\left(c^{2} + 1\right)} \tan\left(b x + a\right) - 2 \, c + i\right) - \log\left(-i \, c^{2} + {\left(c^{2} + 1\right)} \tan\left(b x + a\right) - i\right)\right)} - 2 i \, \log\left(-i \, c^{2} + {\left(c^{2} + 1\right)} \tan\left(b x + a\right) - 2 \, c + i\right) \log\left(-\frac{{\left(i \, c - 1\right)} \tan\left(b x + a\right) + c - i}{2 \, c} + 1\right) + 2 i \, \log\left(-i \, c^{2} + {\left(c^{2} + 1\right)} \tan\left(b x + a\right) - 2 \, c + i\right) \log\left(\tan\left(b x + a\right) - i\right) - 2 i \, \log\left(-\frac{1}{2} \, {\left(c + i\right)} \tan\left(b x + a\right) + \frac{1}{2} i \, c + \frac{1}{2}\right) \log\left(\tan\left(b x + a\right) - i\right) - i \, \log\left(\tan\left(b x + a\right) - i\right)^{2} - 2 i \, \log\left(c^{2} + 1\right) \log\left(i \, \tan\left(b x + a\right) + 1\right) + 2 i \, \log\left(\tan\left(b x + a\right) - i\right) \log\left(-\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right) + 2 i \, \log\left(c^{2} + 1\right) \log\left(-i \, \tan\left(b x + a\right) + 1\right) - 2 i \, {\rm Li}_2\left(\frac{1}{2} \, {\left(c + i\right)} \tan\left(b x + a\right) - \frac{1}{2} i \, c + \frac{1}{2}\right) - 2 i \, {\rm Li}_2\left(\frac{{\left(i \, c - 1\right)} \tan\left(b x + a\right) + c - i}{2 \, c}\right) + 2 i \, {\rm Li}_2\left(\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right)\right)}}{i \, c + 1}\right)} - 8 \, {\left(b x + a\right)} \arctan\left(c + \frac{-i \, c - 1}{\tan\left(b x + a\right)}\right) + 4 \, {\left(-i \, b x - i \, a\right)} \log\left(\frac{-2 i \, c^{2} + 2 \, {\left(c^{2} + 1\right)} \tan\left(b x + a\right) - 2 i}{-2 i \, c^{2} + 2 \, {\left(c^{2} + 1\right)} \tan\left(b x + a\right) - 4 \, c + 2 i}\right)}{8 \, b}"," ",0,"-1/8*((I*c + 1)*(4*I*(b*x + a)*log((-2*I*c^2 + 2*(c^2 + 1)*tan(b*x + a) - 2*I)/(-2*I*c^2 + 2*(c^2 + 1)*tan(b*x + a) - 4*c + 2*I))/(I*c + 1) + I*(4*(b*x + a)*(log(-I*c^2 + (c^2 + 1)*tan(b*x + a) - 2*c + I) - log(-I*c^2 + (c^2 + 1)*tan(b*x + a) - I)) - 2*I*log(-I*c^2 + (c^2 + 1)*tan(b*x + a) - 2*c + I)*log(-1/2*((I*c - 1)*tan(b*x + a) + c - I)/c + 1) + 2*I*log(-I*c^2 + (c^2 + 1)*tan(b*x + a) - 2*c + I)*log(tan(b*x + a) - I) - 2*I*log(-1/2*(c + I)*tan(b*x + a) + 1/2*I*c + 1/2)*log(tan(b*x + a) - I) - I*log(tan(b*x + a) - I)^2 - 2*I*log(c^2 + 1)*log(I*tan(b*x + a) + 1) + 2*I*log(tan(b*x + a) - I)*log(-1/2*I*tan(b*x + a) + 1/2) + 2*I*log(c^2 + 1)*log(-I*tan(b*x + a) + 1) - 2*I*dilog(1/2*(c + I)*tan(b*x + a) - 1/2*I*c + 1/2) - 2*I*dilog(1/2*((I*c - 1)*tan(b*x + a) + c - I)/c) + 2*I*dilog(1/2*I*tan(b*x + a) + 1/2))/(I*c + 1)) - 8*(b*x + a)*arctan(c + (-I*c - 1)/tan(b*x + a)) + 4*(-I*b*x - I*a)*log((-2*I*c^2 + 2*(c^2 + 1)*tan(b*x + a) - 2*I)/(-2*I*c^2 + 2*(c^2 + 1)*tan(b*x + a) - 4*c + 2*I)))/b","B",0
72,-2,0,0,0.000000," ","integrate(-arctan(-c-(-1-I*c)*cot(b*x+a))/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c-1>0)', see `assume?` for more details)Is c-1 zero or nonzero?","F(-2)",0
73,0,0,0,0.000000," ","integrate(arctan(sinh(x)),x, algorithm=""maxima"")","x \arctan\left(\frac{1}{2} \, {\left(e^{\left(2 \, x\right)} - 1\right)} e^{\left(-x\right)}\right) - 2 \, \int \frac{x e^{x}}{e^{\left(2 \, x\right)} + 1}\,{d x}"," ",0,"x*arctan(1/2*(e^(2*x) - 1)*e^(-x)) - 2*integrate(x*e^x/(e^(2*x) + 1), x)","F",0
74,0,0,0,0.000000," ","integrate(x*arctan(sinh(x)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left(\frac{1}{2} \, {\left(e^{\left(2 \, x\right)} - 1\right)} e^{\left(-x\right)}\right) - \int \frac{x^{2} e^{x}}{e^{\left(2 \, x\right)} + 1}\,{d x}"," ",0,"1/2*x^2*arctan(1/2*(e^(2*x) - 1)*e^(-x)) - integrate(x^2*e^x/(e^(2*x) + 1), x)","F",0
75,0,0,0,0.000000," ","integrate(x^2*arctan(sinh(x)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(\frac{1}{2} \, {\left(e^{\left(2 \, x\right)} - 1\right)} e^{\left(-x\right)}\right) - 2 \, \int \frac{x^{3} e^{x}}{3 \, {\left(e^{\left(2 \, x\right)} + 1\right)}}\,{d x}"," ",0,"1/3*x^3*arctan(1/2*(e^(2*x) - 1)*e^(-x)) - 2*integrate(1/3*x^3*e^x/(e^(2*x) + 1), x)","F",0
76,0,0,0,0.000000," ","integrate((f*x+e)^3*arctan(tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(f^{3} x^{4} + 4 \, e f^{2} x^{3} + 6 \, e^{2} f x^{2} + 4 \, e^{3} x\right)} \arctan\left(\frac{e^{\left(2 \, b x + 2 \, a\right)} - 1}{e^{\left(2 \, b x + 2 \, a\right)} + 1}\right) - \int \frac{{\left(b f^{3} x^{4} e^{\left(2 \, a\right)} + 4 \, b e f^{2} x^{3} e^{\left(2 \, a\right)} + 6 \, b e^{2} f x^{2} e^{\left(2 \, a\right)} + 4 \, b e^{3} x e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)}}{2 \, {\left(e^{\left(4 \, b x + 4 \, a\right)} + 1\right)}}\,{d x}"," ",0,"1/4*(f^3*x^4 + 4*e*f^2*x^3 + 6*e^2*f*x^2 + 4*e^3*x)*arctan((e^(2*b*x + 2*a) - 1)/(e^(2*b*x + 2*a) + 1)) - integrate(1/2*(b*f^3*x^4*e^(2*a) + 4*b*e*f^2*x^3*e^(2*a) + 6*b*e^2*f*x^2*e^(2*a) + 4*b*e^3*x*e^(2*a))*e^(2*b*x)/(e^(4*b*x + 4*a) + 1), x)","F",0
77,0,0,0,0.000000," ","integrate((f*x+e)^2*arctan(tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(f^{2} x^{3} + 3 \, e f x^{2} + 3 \, e^{2} x\right)} \arctan\left(\frac{e^{\left(2 \, b x + 2 \, a\right)} - 1}{e^{\left(2 \, b x + 2 \, a\right)} + 1}\right) - \int \frac{2 \, {\left(b f^{2} x^{3} e^{\left(2 \, a\right)} + 3 \, b e f x^{2} e^{\left(2 \, a\right)} + 3 \, b e^{2} x e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)}}{3 \, {\left(e^{\left(4 \, b x + 4 \, a\right)} + 1\right)}}\,{d x}"," ",0,"1/3*(f^2*x^3 + 3*e*f*x^2 + 3*e^2*x)*arctan((e^(2*b*x + 2*a) - 1)/(e^(2*b*x + 2*a) + 1)) - integrate(2/3*(b*f^2*x^3*e^(2*a) + 3*b*e*f*x^2*e^(2*a) + 3*b*e^2*x*e^(2*a))*e^(2*b*x)/(e^(4*b*x + 4*a) + 1), x)","F",0
78,0,0,0,0.000000," ","integrate((f*x+e)*arctan(tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(f x^{2} + 2 \, e x\right)} \arctan\left(\frac{e^{\left(2 \, b x + 2 \, a\right)} - 1}{e^{\left(2 \, b x + 2 \, a\right)} + 1}\right) - \int \frac{{\left(b f x^{2} e^{\left(2 \, a\right)} + 2 \, b e x e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)}}{e^{\left(4 \, b x + 4 \, a\right)} + 1}\,{d x}"," ",0,"1/2*(f*x^2 + 2*e*x)*arctan((e^(2*b*x + 2*a) - 1)/(e^(2*b*x + 2*a) + 1)) - integrate((b*f*x^2*e^(2*a) + 2*b*e*x*e^(2*a))*e^(2*b*x)/(e^(4*b*x + 4*a) + 1), x)","F",0
79,0,0,0,0.000000," ","integrate(arctan(tanh(b*x+a)),x, algorithm=""maxima"")","x \arctan\left(\frac{e^{\left(2 \, b x + 2 \, a\right)} - 1}{e^{\left(2 \, b x + 2 \, a\right)} + 1}\right) - 2 \, b \int \frac{x e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(4 \, b x + 4 \, a\right)} + 1}\,{d x}"," ",0,"x*arctan((e^(2*b*x + 2*a) - 1)/(e^(2*b*x + 2*a) + 1)) - 2*b*integrate(x*e^(2*b*x + 2*a)/(e^(4*b*x + 4*a) + 1), x)","F",0
80,0,0,0,0.000000," ","integrate(arctan(tanh(b*x+a))/(f*x+e),x, algorithm=""maxima"")","\int \frac{\arctan\left(\tanh\left(b x + a\right)\right)}{f x + e}\,{d x}"," ",0,"integrate(arctan(tanh(b*x + a))/(f*x + e), x)","F",0
81,0,0,0,0.000000," ","integrate(x^2*arctan(c+d*tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(\frac{{\left(c e^{\left(2 \, a\right)} + d e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + c - d}{e^{\left(2 \, b x + 2 \, a\right)} + 1}\right) - 4 \, b d \int \frac{x^{3} e^{\left(2 \, b x + 2 \, a\right)}}{3 \, {\left(c^{2} - 2 \, c d + d^{2} + {\left(c^{2} e^{\left(4 \, a\right)} + 2 \, c d e^{\left(4 \, a\right)} + d^{2} e^{\left(4 \, a\right)} + e^{\left(4 \, a\right)}\right)} e^{\left(4 \, b x\right)} + 2 \, {\left(c^{2} e^{\left(2 \, a\right)} - d^{2} e^{\left(2 \, a\right)} + e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + 1\right)}}\,{d x}"," ",0,"1/3*x^3*arctan(((c*e^(2*a) + d*e^(2*a))*e^(2*b*x) + c - d)/(e^(2*b*x + 2*a) + 1)) - 4*b*d*integrate(1/3*x^3*e^(2*b*x + 2*a)/(c^2 - 2*c*d + d^2 + (c^2*e^(4*a) + 2*c*d*e^(4*a) + d^2*e^(4*a) + e^(4*a))*e^(4*b*x) + 2*(c^2*e^(2*a) - d^2*e^(2*a) + e^(2*a))*e^(2*b*x) + 1), x)","F",0
82,0,0,0,0.000000," ","integrate(x*arctan(c+d*tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left(\frac{{\left(c e^{\left(2 \, a\right)} + d e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + c - d}{e^{\left(2 \, b x + 2 \, a\right)} + 1}\right) - 2 \, b d \int \frac{x^{2} e^{\left(2 \, b x + 2 \, a\right)}}{c^{2} - 2 \, c d + d^{2} + {\left(c^{2} e^{\left(4 \, a\right)} + 2 \, c d e^{\left(4 \, a\right)} + d^{2} e^{\left(4 \, a\right)} + e^{\left(4 \, a\right)}\right)} e^{\left(4 \, b x\right)} + 2 \, {\left(c^{2} e^{\left(2 \, a\right)} - d^{2} e^{\left(2 \, a\right)} + e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + 1}\,{d x}"," ",0,"1/2*x^2*arctan(((c*e^(2*a) + d*e^(2*a))*e^(2*b*x) + c - d)/(e^(2*b*x + 2*a) + 1)) - 2*b*d*integrate(x^2*e^(2*b*x + 2*a)/(c^2 - 2*c*d + d^2 + (c^2*e^(4*a) + 2*c*d*e^(4*a) + d^2*e^(4*a) + e^(4*a))*e^(4*b*x) + 2*(c^2*e^(2*a) - d^2*e^(2*a) + e^(2*a))*e^(2*b*x) + 1), x)","F",0
83,0,0,0,0.000000," ","integrate(arctan(c+d*tanh(b*x+a)),x, algorithm=""maxima"")","-4 \, b d \int \frac{x e^{\left(2 \, b x + 2 \, a\right)}}{c^{2} - 2 \, c d + d^{2} + {\left(c^{2} e^{\left(4 \, a\right)} + 2 \, c d e^{\left(4 \, a\right)} + d^{2} e^{\left(4 \, a\right)} + e^{\left(4 \, a\right)}\right)} e^{\left(4 \, b x\right)} + 2 \, {\left(c^{2} e^{\left(2 \, a\right)} - d^{2} e^{\left(2 \, a\right)} + e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + 1}\,{d x} + x \arctan\left(\frac{{\left(c e^{\left(2 \, a\right)} + d e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + c - d}{e^{\left(2 \, b x + 2 \, a\right)} + 1}\right)"," ",0,"-4*b*d*integrate(x*e^(2*b*x + 2*a)/(c^2 - 2*c*d + d^2 + (c^2*e^(4*a) + 2*c*d*e^(4*a) + d^2*e^(4*a) + e^(4*a))*e^(4*b*x) + 2*(c^2*e^(2*a) - d^2*e^(2*a) + e^(2*a))*e^(2*b*x) + 1), x) + x*arctan(((c*e^(2*a) + d*e^(2*a))*e^(2*b*x) + c - d)/(e^(2*b*x + 2*a) + 1))","F",0
84,0,0,0,0.000000," ","integrate(arctan(c+d*tanh(b*x+a))/x,x, algorithm=""maxima"")","\int \frac{\arctan\left(d \tanh\left(b x + a\right) + c\right)}{x}\,{d x}"," ",0,"integrate(arctan(d*tanh(b*x + a) + c)/x, x)","F",0
85,1,129,0,1.943119," ","integrate(x^2*arctan(c+(I+c)*tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left({\left(c + i\right)} \tanh\left(b x + a\right) + c\right) + \frac{4}{9} \, {\left(\frac{3 \, x^{4}}{4 i \, c - 4} - \frac{4 \, b^{3} x^{3} \log\left(i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)}\right) - 6 \, b x {\rm Li}_{3}(-i \, c e^{\left(2 \, b x + 2 \, a\right)}) + 3 \, {\rm Li}_{4}(-i \, c e^{\left(2 \, b x + 2 \, a\right)})}{-2 \, b^{4} {\left(-i \, c + 1\right)}}\right)} b {\left(c + i\right)}"," ",0,"1/3*x^3*arctan((c + I)*tanh(b*x + a) + c) + 4/9*(3*x^4/(4*I*c - 4) - (4*b^3*x^3*log(I*c*e^(2*b*x + 2*a) + 1) + 6*b^2*x^2*dilog(-I*c*e^(2*b*x + 2*a)) - 6*b*x*polylog(3, -I*c*e^(2*b*x + 2*a)) + 3*polylog(4, -I*c*e^(2*b*x + 2*a)))/(b^4*(2*I*c - 2)))*b*(c + I)","A",0
86,1,106,0,2.043592," ","integrate(x*arctan(c+(I+c)*tanh(b*x+a)),x, algorithm=""maxima"")","{\left(\frac{2 \, x^{3}}{3 i \, c - 3} - \frac{2 \, b^{2} x^{2} \log\left(i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)}\right) - {\rm Li}_{3}(-i \, c e^{\left(2 \, b x + 2 \, a\right)})}{-2 \, b^{3} {\left(-i \, c + 1\right)}}\right)} b {\left(c + i\right)} + \frac{1}{2} \, x^{2} \arctan\left({\left(c + i\right)} \tanh\left(b x + a\right) + c\right)"," ",0,"(2*x^3/(3*I*c - 3) - (2*b^2*x^2*log(I*c*e^(2*b*x + 2*a) + 1) + 2*b*x*dilog(-I*c*e^(2*b*x + 2*a)) - polylog(3, -I*c*e^(2*b*x + 2*a)))/(b^3*(2*I*c - 2)))*b*(c + I) + 1/2*x^2*arctan((c + I)*tanh(b*x + a) + c)","A",0
87,1,80,0,1.992054," ","integrate(arctan(c+(I+c)*tanh(b*x+a)),x, algorithm=""maxima"")","2 \, b {\left(c + i\right)} {\left(\frac{2 \, x^{2}}{2 i \, c - 2} - \frac{2 \, b x \log\left(i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + {\rm Li}_2\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)}\right)}{-2 \, b^{2} {\left(-i \, c + 1\right)}}\right)} + x \arctan\left({\left(c + i\right)} \tanh\left(b x + a\right) + c\right)"," ",0,"2*b*(c + I)*(2*x^2/(2*I*c - 2) - (2*b*x*log(I*c*e^(2*b*x + 2*a) + 1) + dilog(-I*c*e^(2*b*x + 2*a)))/(b^2*(2*I*c - 2))) + x*arctan((c + I)*tanh(b*x + a) + c)","A",0
88,0,0,0,0.000000," ","integrate(arctan(c+(I+c)*tanh(b*x+a))/x,x, algorithm=""maxima"")","i \, b x - \frac{1}{4} \, {\left(4 \, \pi - 4 i \, a - 2 \, \arctan\left(c\right) - i \, \log\left(c^{2} + 1\right)\right)} \log\left(x\right) + \frac{1}{2} \, \int \frac{\arctan\left(c e^{\left(2 \, b x + 2 \, a\right)}\right)}{x}\,{d x} - \frac{1}{4} i \, \int \frac{\log\left(c^{2} e^{\left(4 \, b x + 4 \, a\right)} + 1\right)}{x}\,{d x}"," ",0,"I*b*x - 1/4*(4*pi - 4*I*a - 2*arctan(c) - I*log(c^2 + 1))*log(x) + 1/2*integrate(arctan(c*e^(2*b*x + 2*a))/x, x) - 1/4*I*integrate(log(c^2*e^(4*b*x + 4*a) + 1)/x, x)","F",0
89,1,129,0,1.950049," ","integrate(x^2*arctan(c-(I-c)*tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left({\left(c - i\right)} \tanh\left(b x + a\right) + c\right) - \frac{4}{9} \, {\left(\frac{3 \, x^{4}}{4 i \, c + 4} - \frac{4 \, b^{3} x^{3} \log\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(i \, c e^{\left(2 \, b x + 2 \, a\right)}\right) - 6 \, b x {\rm Li}_{3}(i \, c e^{\left(2 \, b x + 2 \, a\right)}) + 3 \, {\rm Li}_{4}(i \, c e^{\left(2 \, b x + 2 \, a\right)})}{-2 \, b^{4} {\left(-i \, c - 1\right)}}\right)} b {\left(c - i\right)}"," ",0,"1/3*x^3*arctan((c - I)*tanh(b*x + a) + c) - 4/9*(3*x^4/(4*I*c + 4) - (4*b^3*x^3*log(-I*c*e^(2*b*x + 2*a) + 1) + 6*b^2*x^2*dilog(I*c*e^(2*b*x + 2*a)) - 6*b*x*polylog(3, I*c*e^(2*b*x + 2*a)) + 3*polylog(4, I*c*e^(2*b*x + 2*a)))/(b^4*(2*I*c + 2)))*b*(c - I)","A",0
90,1,107,0,1.945695," ","integrate(x*arctan(c-(I-c)*tanh(b*x+a)),x, algorithm=""maxima"")","-{\left(\frac{2 \, x^{3}}{3 i \, c + 3} - \frac{2 \, b^{2} x^{2} \log\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(i \, c e^{\left(2 \, b x + 2 \, a\right)}\right) - {\rm Li}_{3}(i \, c e^{\left(2 \, b x + 2 \, a\right)})}{-2 \, b^{3} {\left(-i \, c - 1\right)}}\right)} b {\left(c - i\right)} + \frac{1}{2} \, x^{2} \arctan\left({\left(c - i\right)} \tanh\left(b x + a\right) + c\right)"," ",0,"-(2*x^3/(3*I*c + 3) - (2*b^2*x^2*log(-I*c*e^(2*b*x + 2*a) + 1) + 2*b*x*dilog(I*c*e^(2*b*x + 2*a)) - polylog(3, I*c*e^(2*b*x + 2*a)))/(b^3*(2*I*c + 2)))*b*(c - I) + 1/2*x^2*arctan((c - I)*tanh(b*x + a) + c)","A",0
91,1,80,0,1.947584," ","integrate(arctan(c-(I-c)*tanh(b*x+a)),x, algorithm=""maxima"")","-2 \, b {\left(c - i\right)} {\left(\frac{2 \, x^{2}}{2 i \, c + 2} - \frac{2 \, b x \log\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + {\rm Li}_2\left(i \, c e^{\left(2 \, b x + 2 \, a\right)}\right)}{-2 \, b^{2} {\left(-i \, c - 1\right)}}\right)} + x \arctan\left({\left(c - i\right)} \tanh\left(b x + a\right) + c\right)"," ",0,"-2*b*(c - I)*(2*x^2/(2*I*c + 2) - (2*b*x*log(-I*c*e^(2*b*x + 2*a) + 1) + dilog(I*c*e^(2*b*x + 2*a)))/(b^2*(2*I*c + 2))) + x*arctan((c - I)*tanh(b*x + a) + c)","A",0
92,0,0,0,0.000000," ","integrate(arctan(c-(I-c)*tanh(b*x+a))/x,x, algorithm=""maxima"")","-i \, b x - \frac{1}{2} \, \pi \log\left(x\right) - \frac{1}{4} \, {\left(2 \, \pi + 4 i \, a - 2 \, \arctan\left(c\right) + i \, \log\left(c^{2} + 1\right)\right)} \log\left(x\right) + \frac{1}{2} \, \int \frac{\arctan\left(c e^{\left(2 \, b x + 2 \, a\right)}\right)}{x}\,{d x} + \frac{1}{4} i \, \int \frac{\log\left(c^{2} e^{\left(4 \, b x + 4 \, a\right)} + 1\right)}{x}\,{d x}"," ",0,"-I*b*x - 1/2*pi*log(x) - 1/4*(2*pi + 4*I*a - 2*arctan(c) + I*log(c^2 + 1))*log(x) + 1/2*integrate(arctan(c*e^(2*b*x + 2*a))/x, x) + 1/4*I*integrate(log(c^2*e^(4*b*x + 4*a) + 1)/x, x)","F",0
93,0,0,0,0.000000," ","integrate((f*x+e)^3*arctan(coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(f^{3} x^{4} + 4 \, e f^{2} x^{3} + 6 \, e^{2} f x^{2} + 4 \, e^{3} x\right)} \arctan\left(e^{\left(2 \, b x + 2 \, a\right)} + 1, e^{\left(2 \, b x + 2 \, a\right)} - 1\right) + \int \frac{{\left(b f^{3} x^{4} e^{\left(2 \, a\right)} + 4 \, b e f^{2} x^{3} e^{\left(2 \, a\right)} + 6 \, b e^{2} f x^{2} e^{\left(2 \, a\right)} + 4 \, b e^{3} x e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)}}{2 \, {\left(e^{\left(4 \, b x + 4 \, a\right)} + 1\right)}}\,{d x}"," ",0,"1/4*(f^3*x^4 + 4*e*f^2*x^3 + 6*e^2*f*x^2 + 4*e^3*x)*arctan2(e^(2*b*x + 2*a) + 1, e^(2*b*x + 2*a) - 1) + integrate(1/2*(b*f^3*x^4*e^(2*a) + 4*b*e*f^2*x^3*e^(2*a) + 6*b*e^2*f*x^2*e^(2*a) + 4*b*e^3*x*e^(2*a))*e^(2*b*x)/(e^(4*b*x + 4*a) + 1), x)","F",0
94,0,0,0,0.000000," ","integrate((f*x+e)^2*arctan(coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(f^{2} x^{3} + 3 \, e f x^{2} + 3 \, e^{2} x\right)} \arctan\left(e^{\left(2 \, b x + 2 \, a\right)} + 1, e^{\left(2 \, b x + 2 \, a\right)} - 1\right) + \int \frac{2 \, {\left(b f^{2} x^{3} e^{\left(2 \, a\right)} + 3 \, b e f x^{2} e^{\left(2 \, a\right)} + 3 \, b e^{2} x e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)}}{3 \, {\left(e^{\left(4 \, b x + 4 \, a\right)} + 1\right)}}\,{d x}"," ",0,"1/3*(f^2*x^3 + 3*e*f*x^2 + 3*e^2*x)*arctan2(e^(2*b*x + 2*a) + 1, e^(2*b*x + 2*a) - 1) + integrate(2/3*(b*f^2*x^3*e^(2*a) + 3*b*e*f*x^2*e^(2*a) + 3*b*e^2*x*e^(2*a))*e^(2*b*x)/(e^(4*b*x + 4*a) + 1), x)","F",0
95,0,0,0,0.000000," ","integrate((f*x+e)*arctan(coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(f x^{2} + 2 \, e x\right)} \arctan\left(e^{\left(2 \, b x + 2 \, a\right)} + 1, e^{\left(2 \, b x + 2 \, a\right)} - 1\right) + \int \frac{{\left(b f x^{2} e^{\left(2 \, a\right)} + 2 \, b e x e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)}}{e^{\left(4 \, b x + 4 \, a\right)} + 1}\,{d x}"," ",0,"1/2*(f*x^2 + 2*e*x)*arctan2(e^(2*b*x + 2*a) + 1, e^(2*b*x + 2*a) - 1) + integrate((b*f*x^2*e^(2*a) + 2*b*e*x*e^(2*a))*e^(2*b*x)/(e^(4*b*x + 4*a) + 1), x)","F",0
96,0,0,0,0.000000," ","integrate(arctan(coth(b*x+a)),x, algorithm=""maxima"")","x \arctan\left(e^{\left(2 \, b x + 2 \, a\right)} + 1, e^{\left(2 \, b x + 2 \, a\right)} - 1\right) + 2 \, b \int \frac{x e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(4 \, b x + 4 \, a\right)} + 1}\,{d x}"," ",0,"x*arctan2(e^(2*b*x + 2*a) + 1, e^(2*b*x + 2*a) - 1) + 2*b*integrate(x*e^(2*b*x + 2*a)/(e^(4*b*x + 4*a) + 1), x)","F",0
97,0,0,0,0.000000," ","integrate(arctan(coth(b*x+a))/(f*x+e),x, algorithm=""maxima"")","\int \frac{\arctan\left(\coth\left(b x + a\right)\right)}{f x + e}\,{d x}"," ",0,"integrate(arctan(coth(b*x + a))/(f*x + e), x)","F",0
98,0,0,0,0.000000," ","integrate(x^2*arctan(c+d*coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left({\left(c e^{\left(2 \, a\right)} + d e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} - c + d, e^{\left(2 \, b x + 2 \, a\right)} - 1\right) + 4 \, b d \int \frac{x^{3} e^{\left(2 \, b x + 2 \, a\right)}}{3 \, {\left(c^{2} - 2 \, c d + d^{2} + {\left(c^{2} e^{\left(4 \, a\right)} + 2 \, c d e^{\left(4 \, a\right)} + d^{2} e^{\left(4 \, a\right)} + e^{\left(4 \, a\right)}\right)} e^{\left(4 \, b x\right)} - 2 \, {\left(c^{2} e^{\left(2 \, a\right)} - d^{2} e^{\left(2 \, a\right)} + e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + 1\right)}}\,{d x}"," ",0,"1/3*x^3*arctan2((c*e^(2*a) + d*e^(2*a))*e^(2*b*x) - c + d, e^(2*b*x + 2*a) - 1) + 4*b*d*integrate(1/3*x^3*e^(2*b*x + 2*a)/(c^2 - 2*c*d + d^2 + (c^2*e^(4*a) + 2*c*d*e^(4*a) + d^2*e^(4*a) + e^(4*a))*e^(4*b*x) - 2*(c^2*e^(2*a) - d^2*e^(2*a) + e^(2*a))*e^(2*b*x) + 1), x)","F",0
99,0,0,0,0.000000," ","integrate(x*arctan(c+d*coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left({\left(c e^{\left(2 \, a\right)} + d e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} - c + d, e^{\left(2 \, b x + 2 \, a\right)} - 1\right) + 2 \, b d \int \frac{x^{2} e^{\left(2 \, b x + 2 \, a\right)}}{c^{2} - 2 \, c d + d^{2} + {\left(c^{2} e^{\left(4 \, a\right)} + 2 \, c d e^{\left(4 \, a\right)} + d^{2} e^{\left(4 \, a\right)} + e^{\left(4 \, a\right)}\right)} e^{\left(4 \, b x\right)} - 2 \, {\left(c^{2} e^{\left(2 \, a\right)} - d^{2} e^{\left(2 \, a\right)} + e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + 1}\,{d x}"," ",0,"1/2*x^2*arctan2((c*e^(2*a) + d*e^(2*a))*e^(2*b*x) - c + d, e^(2*b*x + 2*a) - 1) + 2*b*d*integrate(x^2*e^(2*b*x + 2*a)/(c^2 - 2*c*d + d^2 + (c^2*e^(4*a) + 2*c*d*e^(4*a) + d^2*e^(4*a) + e^(4*a))*e^(4*b*x) - 2*(c^2*e^(2*a) - d^2*e^(2*a) + e^(2*a))*e^(2*b*x) + 1), x)","F",0
100,0,0,0,0.000000," ","integrate(arctan(c+d*coth(b*x+a)),x, algorithm=""maxima"")","4 \, b d \int \frac{x e^{\left(2 \, b x + 2 \, a\right)}}{c^{2} - 2 \, c d + d^{2} + {\left(c^{2} e^{\left(4 \, a\right)} + 2 \, c d e^{\left(4 \, a\right)} + d^{2} e^{\left(4 \, a\right)} + e^{\left(4 \, a\right)}\right)} e^{\left(4 \, b x\right)} - 2 \, {\left(c^{2} e^{\left(2 \, a\right)} - d^{2} e^{\left(2 \, a\right)} + e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + 1}\,{d x} + x \arctan\left({\left(c e^{\left(2 \, a\right)} + d e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} - c + d, e^{\left(2 \, b x + 2 \, a\right)} - 1\right)"," ",0,"4*b*d*integrate(x*e^(2*b*x + 2*a)/(c^2 - 2*c*d + d^2 + (c^2*e^(4*a) + 2*c*d*e^(4*a) + d^2*e^(4*a) + e^(4*a))*e^(4*b*x) - 2*(c^2*e^(2*a) - d^2*e^(2*a) + e^(2*a))*e^(2*b*x) + 1), x) + x*arctan2((c*e^(2*a) + d*e^(2*a))*e^(2*b*x) - c + d, e^(2*b*x + 2*a) - 1)","F",0
101,0,0,0,0.000000," ","integrate(arctan(c+d*coth(b*x+a))/x,x, algorithm=""maxima"")","\int \frac{\arctan\left(d \coth\left(b x + a\right) + c\right)}{x}\,{d x}"," ",0,"integrate(arctan(d*coth(b*x + a) + c)/x, x)","F",0
102,1,129,0,1.995166," ","integrate(x^2*arctan(c+(I+c)*coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left({\left(c + i\right)} \coth\left(b x + a\right) + c\right) + \frac{4}{9} \, {\left(\frac{3 \, x^{4}}{4 i \, c - 4} - \frac{4 \, b^{3} x^{3} \log\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(i \, c e^{\left(2 \, b x + 2 \, a\right)}\right) - 6 \, b x {\rm Li}_{3}(i \, c e^{\left(2 \, b x + 2 \, a\right)}) + 3 \, {\rm Li}_{4}(i \, c e^{\left(2 \, b x + 2 \, a\right)})}{-2 \, b^{4} {\left(-i \, c + 1\right)}}\right)} b {\left(c + i\right)}"," ",0,"1/3*x^3*arctan((c + I)*coth(b*x + a) + c) + 4/9*(3*x^4/(4*I*c - 4) - (4*b^3*x^3*log(-I*c*e^(2*b*x + 2*a) + 1) + 6*b^2*x^2*dilog(I*c*e^(2*b*x + 2*a)) - 6*b*x*polylog(3, I*c*e^(2*b*x + 2*a)) + 3*polylog(4, I*c*e^(2*b*x + 2*a)))/(b^4*(2*I*c - 2)))*b*(c + I)","A",0
103,1,106,0,2.040773," ","integrate(x*arctan(c+(I+c)*coth(b*x+a)),x, algorithm=""maxima"")","{\left(\frac{2 \, x^{3}}{3 i \, c - 3} - \frac{2 \, b^{2} x^{2} \log\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(i \, c e^{\left(2 \, b x + 2 \, a\right)}\right) - {\rm Li}_{3}(i \, c e^{\left(2 \, b x + 2 \, a\right)})}{-2 \, b^{3} {\left(-i \, c + 1\right)}}\right)} b {\left(c + i\right)} + \frac{1}{2} \, x^{2} \arctan\left({\left(c + i\right)} \coth\left(b x + a\right) + c\right)"," ",0,"(2*x^3/(3*I*c - 3) - (2*b^2*x^2*log(-I*c*e^(2*b*x + 2*a) + 1) + 2*b*x*dilog(I*c*e^(2*b*x + 2*a)) - polylog(3, I*c*e^(2*b*x + 2*a)))/(b^3*(2*I*c - 2)))*b*(c + I) + 1/2*x^2*arctan((c + I)*coth(b*x + a) + c)","A",0
104,1,80,0,1.998601," ","integrate(arctan(c+(I+c)*coth(b*x+a)),x, algorithm=""maxima"")","2 \, b {\left(c + i\right)} {\left(\frac{2 \, x^{2}}{2 i \, c - 2} - \frac{2 \, b x \log\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + {\rm Li}_2\left(i \, c e^{\left(2 \, b x + 2 \, a\right)}\right)}{-2 \, b^{2} {\left(-i \, c + 1\right)}}\right)} + x \arctan\left({\left(c + i\right)} \coth\left(b x + a\right) + c\right)"," ",0,"2*b*(c + I)*(2*x^2/(2*I*c - 2) - (2*b*x*log(-I*c*e^(2*b*x + 2*a) + 1) + dilog(I*c*e^(2*b*x + 2*a)))/(b^2*(2*I*c - 2))) + x*arctan((c + I)*coth(b*x + a) + c)","A",0
105,0,0,0,0.000000," ","integrate(arctan(c+(I+c)*coth(b*x+a))/x,x, algorithm=""maxima"")","i \, b x + \frac{1}{2} \, \pi \log\left(x\right) - \frac{1}{4} \, {\left(4 \, \pi - 4 i \, a - 2 \, \arctan\left(c\right) - i \, \log\left(c^{2} + 1\right)\right)} \log\left(x\right) - \frac{1}{2} \, \int \frac{\arctan\left(c e^{\left(2 \, b x + 2 \, a\right)}\right)}{x}\,{d x} - \frac{1}{4} i \, \int \frac{\log\left(c^{2} e^{\left(4 \, b x + 4 \, a\right)} + 1\right)}{x}\,{d x}"," ",0,"I*b*x + 1/2*pi*log(x) - 1/4*(4*pi - 4*I*a - 2*arctan(c) - I*log(c^2 + 1))*log(x) - 1/2*integrate(arctan(c*e^(2*b*x + 2*a))/x, x) - 1/4*I*integrate(log(c^2*e^(4*b*x + 4*a) + 1)/x, x)","F",0
106,1,129,0,2.005723," ","integrate(x^2*arctan(c-(I-c)*coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left({\left(c - i\right)} \coth\left(b x + a\right) + c\right) - \frac{4}{9} \, {\left(\frac{3 \, x^{4}}{4 i \, c + 4} - \frac{4 \, b^{3} x^{3} \log\left(i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)}\right) - 6 \, b x {\rm Li}_{3}(-i \, c e^{\left(2 \, b x + 2 \, a\right)}) + 3 \, {\rm Li}_{4}(-i \, c e^{\left(2 \, b x + 2 \, a\right)})}{-2 \, b^{4} {\left(-i \, c - 1\right)}}\right)} b {\left(c - i\right)}"," ",0,"1/3*x^3*arctan((c - I)*coth(b*x + a) + c) - 4/9*(3*x^4/(4*I*c + 4) - (4*b^3*x^3*log(I*c*e^(2*b*x + 2*a) + 1) + 6*b^2*x^2*dilog(-I*c*e^(2*b*x + 2*a)) - 6*b*x*polylog(3, -I*c*e^(2*b*x + 2*a)) + 3*polylog(4, -I*c*e^(2*b*x + 2*a)))/(b^4*(2*I*c + 2)))*b*(c - I)","A",0
107,1,107,0,2.028764," ","integrate(x*arctan(c-(I-c)*coth(b*x+a)),x, algorithm=""maxima"")","-{\left(\frac{2 \, x^{3}}{3 i \, c + 3} - \frac{2 \, b^{2} x^{2} \log\left(i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)}\right) - {\rm Li}_{3}(-i \, c e^{\left(2 \, b x + 2 \, a\right)})}{-2 \, b^{3} {\left(-i \, c - 1\right)}}\right)} b {\left(c - i\right)} + \frac{1}{2} \, x^{2} \arctan\left({\left(c - i\right)} \coth\left(b x + a\right) + c\right)"," ",0,"-(2*x^3/(3*I*c + 3) - (2*b^2*x^2*log(I*c*e^(2*b*x + 2*a) + 1) + 2*b*x*dilog(-I*c*e^(2*b*x + 2*a)) - polylog(3, -I*c*e^(2*b*x + 2*a)))/(b^3*(2*I*c + 2)))*b*(c - I) + 1/2*x^2*arctan((c - I)*coth(b*x + a) + c)","A",0
108,1,80,0,1.962619," ","integrate(arctan(c-(I-c)*coth(b*x+a)),x, algorithm=""maxima"")","-2 \, b {\left(c - i\right)} {\left(\frac{2 \, x^{2}}{2 i \, c + 2} - \frac{2 \, b x \log\left(i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + {\rm Li}_2\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)}\right)}{-2 \, b^{2} {\left(-i \, c - 1\right)}}\right)} + x \arctan\left({\left(c - i\right)} \coth\left(b x + a\right) + c\right)"," ",0,"-2*b*(c - I)*(2*x^2/(2*I*c + 2) - (2*b*x*log(I*c*e^(2*b*x + 2*a) + 1) + dilog(-I*c*e^(2*b*x + 2*a)))/(b^2*(2*I*c + 2))) + x*arctan((c - I)*coth(b*x + a) + c)","A",0
109,0,0,0,0.000000," ","integrate(arctan(c-(I-c)*coth(b*x+a))/x,x, algorithm=""maxima"")","-i \, b x - \frac{1}{4} \, {\left(2 \, \pi + 4 i \, a - 2 \, \arctan\left(c\right) + i \, \log\left(c^{2} + 1\right)\right)} \log\left(x\right) - \frac{1}{2} \, \int \frac{\arctan\left(c e^{\left(2 \, b x + 2 \, a\right)}\right)}{x}\,{d x} + \frac{1}{4} i \, \int \frac{\log\left(c^{2} e^{\left(4 \, b x + 4 \, a\right)} + 1\right)}{x}\,{d x}"," ",0,"-I*b*x - 1/4*(2*pi + 4*I*a - 2*arctan(c) + I*log(c^2 + 1))*log(x) - 1/2*integrate(arctan(c*e^(2*b*x + 2*a))/x, x) + 1/4*I*integrate(log(c^2*e^(4*b*x + 4*a) + 1)/x, x)","F",0
110,1,34,0,0.427536," ","integrate(arctan(exp(x)),x, algorithm=""maxima"")","x \arctan\left(e^{x}\right) - \frac{1}{4} \, \pi \log\left(e^{\left(2 \, x\right)} + 1\right) - \frac{1}{2} i \, {\rm Li}_2\left(i \, e^{x} + 1\right) + \frac{1}{2} i \, {\rm Li}_2\left(-i \, e^{x} + 1\right)"," ",0,"x*arctan(e^x) - 1/4*pi*log(e^(2*x) + 1) - 1/2*I*dilog(I*e^x + 1) + 1/2*I*dilog(-I*e^x + 1)","B",0
111,0,0,0,0.000000," ","integrate(x*arctan(exp(x)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left(e^{x}\right) - \int \frac{x^{2} e^{x}}{2 \, {\left(e^{\left(2 \, x\right)} + 1\right)}}\,{d x}"," ",0,"1/2*x^2*arctan(e^x) - integrate(1/2*x^2*e^x/(e^(2*x) + 1), x)","F",0
112,0,0,0,0.000000," ","integrate(x^2*arctan(exp(x)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(e^{x}\right) - \int \frac{x^{3} e^{x}}{3 \, {\left(e^{\left(2 \, x\right)} + 1\right)}}\,{d x}"," ",0,"1/3*x^3*arctan(e^x) - integrate(1/3*x^3*e^x/(e^(2*x) + 1), x)","F",0
113,1,63,0,0.440155," ","integrate(arctan(exp(b*x+a)),x, algorithm=""maxima"")","\frac{{\left(b x + a\right)} \arctan\left(e^{\left(b x + a\right)}\right)}{b} - \frac{\pi \log\left(e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 2 i \, {\rm Li}_2\left(i \, e^{\left(b x + a\right)} + 1\right) - 2 i \, {\rm Li}_2\left(-i \, e^{\left(b x + a\right)} + 1\right)}{4 \, b}"," ",0,"(b*x + a)*arctan(e^(b*x + a))/b - 1/4*(pi*log(e^(2*b*x + 2*a) + 1) + 2*I*dilog(I*e^(b*x + a) + 1) - 2*I*dilog(-I*e^(b*x + a) + 1))/b","B",0
114,0,0,0,0.000000," ","integrate(x*arctan(exp(b*x+a)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left(e^{\left(b x + a\right)}\right) - b \int \frac{x^{2} e^{\left(b x + a\right)}}{2 \, {\left(e^{\left(2 \, b x + 2 \, a\right)} + 1\right)}}\,{d x}"," ",0,"1/2*x^2*arctan(e^(b*x + a)) - b*integrate(1/2*x^2*e^(b*x + a)/(e^(2*b*x + 2*a) + 1), x)","F",0
115,0,0,0,0.000000," ","integrate(x^2*arctan(exp(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(e^{\left(b x + a\right)}\right) - b \int \frac{x^{3} e^{\left(b x + a\right)}}{3 \, {\left(e^{\left(2 \, b x + 2 \, a\right)} + 1\right)}}\,{d x}"," ",0,"1/3*x^3*arctan(e^(b*x + a)) - b*integrate(1/3*x^3*e^(b*x + a)/(e^(2*b*x + 2*a) + 1), x)","F",0
116,1,189,0,0.500380," ","integrate(arctan(a+b*f^(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} \arctan\left(b f^{d x + c} + a\right)}{d} - \frac{2 \, {\left(d x + c\right)} \arctan\left(\frac{b^{2} f^{d x + c} + a b}{b}\right) \log\left(f\right) + {\left(\pi - \arctan\left(\frac{1}{a}\right)\right)} \log\left(b^{2} f^{2 \, d x + 2 \, c} + 2 \, a b f^{d x + c} + a^{2} + 1\right) - \arctan\left(b f^{d x + c} + a\right) \log\left(\frac{b^{2} f^{2 \, d x + 2 \, c}}{a^{2} + 1}\right) + i \, {\rm Li}_2\left(\frac{i \, b f^{d x + c} + i \, a + 1}{i \, a + 1}\right) - i \, {\rm Li}_2\left(\frac{i \, b f^{d x + c} + i \, a - 1}{i \, a - 1}\right)}{2 \, d \log\left(f\right)}"," ",0,"(d*x + c)*arctan(b*f^(d*x + c) + a)/d - 1/2*(2*(d*x + c)*arctan((b^2*f^(d*x + c) + a*b)/b)*log(f) + (pi - arctan(1/a))*log(b^2*f^(2*d*x + 2*c) + 2*a*b*f^(d*x + c) + a^2 + 1) - arctan(b*f^(d*x + c) + a)*log(b^2*f^(2*d*x + 2*c)/(a^2 + 1)) + I*dilog((I*b*f^(d*x + c) + I*a + 1)/(I*a + 1)) - I*dilog((I*b*f^(d*x + c) + I*a - 1)/(I*a - 1)))/(d*log(f))","A",0
117,0,0,0,0.000000," ","integrate(x*arctan(a+b*f^(d*x+c)),x, algorithm=""maxima"")","-b d f^{c} \int \frac{f^{d x} x^{2}}{2 \, {\left(b^{2} f^{2 \, d x} f^{2 \, c} + 2 \, a b f^{d x} f^{c} + a^{2} + 1\right)}}\,{d x} \log\left(f\right) + \frac{1}{2} \, x^{2} \arctan\left(b f^{d x} f^{c} + a\right)"," ",0,"-b*d*f^c*integrate(1/2*f^(d*x)*x^2/(b^2*f^(2*d*x)*f^(2*c) + 2*a*b*f^(d*x)*f^c + a^2 + 1), x)*log(f) + 1/2*x^2*arctan(b*f^(d*x)*f^c + a)","F",0
118,0,0,0,0.000000," ","integrate(x^2*arctan(a+b*f^(d*x+c)),x, algorithm=""maxima"")","-b d f^{c} \int \frac{f^{d x} x^{3}}{3 \, {\left(b^{2} f^{2 \, d x} f^{2 \, c} + 2 \, a b f^{d x} f^{c} + a^{2} + 1\right)}}\,{d x} \log\left(f\right) + \frac{1}{3} \, x^{3} \arctan\left(b f^{d x} f^{c} + a\right)"," ",0,"-b*d*f^c*integrate(1/3*f^(d*x)*x^3/(b^2*f^(2*d*x)*f^(2*c) + 2*a*b*f^(d*x)*f^c + a^2 + 1), x)*log(f) + 1/3*x^3*arctan(b*f^(d*x)*f^c + a)","F",0
119,1,19,0,0.315545," ","integrate(arctan(exp(x))/exp(x),x, algorithm=""maxima"")","-\arctan\left(e^{x}\right) e^{\left(-x\right)} - \frac{1}{2} \, \log\left(e^{\left(-2 \, x\right)} + 1\right)"," ",0,"-arctan(e^x)*e^(-x) - 1/2*log(e^(-2*x) + 1)","A",0
120,1,31,0,0.410627," ","integrate(arctan(x)/(-1+x)^3,x, algorithm=""maxima"")","-\frac{1}{4 \, {\left(x - 1\right)}} - \frac{\arctan\left(x\right)}{2 \, {\left(x - 1\right)}^{2}} + \frac{1}{8} \, \log\left(x^{2} + 1\right) - \frac{1}{4} \, \log\left(x - 1\right)"," ",0,"-1/4/(x - 1) - 1/2*arctan(x)/(x - 1)^2 + 1/8*log(x^2 + 1) - 1/4*log(x - 1)","A",0
121,1,54,0,0.404952," ","integrate(arctan(1+2*x)/(4+3*x)^3,x, algorithm=""maxima"")","-\frac{1}{34 \, {\left(3 \, x + 4\right)}} - \frac{\arctan\left(2 \, x + 1\right)}{6 \, {\left(3 \, x + 4\right)}^{2}} + \frac{8}{867} \, \arctan\left(2 \, x + 1\right) - \frac{5}{578} \, \log\left(2 \, x^{2} + 2 \, x + 1\right) + \frac{5}{289} \, \log\left(3 \, x + 4\right)"," ",0,"-1/34/(3*x + 4) - 1/6*arctan(2*x + 1)/(3*x + 4)^2 + 8/867*arctan(2*x + 1) - 5/578*log(2*x^2 + 2*x + 1) + 5/289*log(3*x + 4)","A",0
122,1,24,0,0.413332," ","integrate(arctan((1+x)^(1/2)),x, algorithm=""maxima"")","{\left(x + 1\right)} \arctan\left(\sqrt{x + 1}\right) - \sqrt{x + 1} + \arctan\left(\sqrt{x + 1}\right)"," ",0,"(x + 1)*arctan(sqrt(x + 1)) - sqrt(x + 1) + arctan(sqrt(x + 1))","A",0
123,1,5,0,0.312638," ","integrate(1/(x^2+1)/(2+arctan(x)),x, algorithm=""maxima"")","\log\left(\arctan\left(x\right) + 2\right)"," ",0,"log(arctan(x) + 2)","A",0
124,1,16,0,0.326339," ","integrate(1/(a*x^2+a)/(b-2*b*arctan(x)),x, algorithm=""maxima"")","-\frac{\log\left({\left| 2 \, \arctan\left(x\right) - 1 \right|}\right)}{2 \, a b}"," ",0,"-1/2*log(abs(2*arctan(x) - 1))/(a*b)","A",0
125,1,16,0,0.564850," ","integrate((x+x^3+(1+x)^2*arctan(x))/(1+x)^2/(x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, \arctan\left(x\right)^{2} + \frac{1}{x + 1} + \log\left(x + 1\right)"," ",0,"1/2*arctan(x)^2 + 1/(x + 1) + log(x + 1)","A",0
126,1,44,0,0.455240," ","integrate(-x^3*arctan(x^(1/2)-(1+x)^(1/2)),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \arctan\left(\sqrt{x + 1} - \sqrt{x}\right) + \frac{1}{56} \, x^{\frac{7}{2}} - \frac{1}{40} \, x^{\frac{5}{2}} + \frac{1}{24} \, x^{\frac{3}{2}} - \frac{1}{8} \, \sqrt{x} + \frac{1}{8} \, \arctan\left(\sqrt{x}\right)"," ",0,"1/4*x^4*arctan(sqrt(x + 1) - sqrt(x)) + 1/56*x^(7/2) - 1/40*x^(5/2) + 1/24*x^(3/2) - 1/8*sqrt(x) + 1/8*arctan(sqrt(x))","A",0
127,1,39,0,0.462672," ","integrate(-x^2*arctan(x^(1/2)-(1+x)^(1/2)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(\sqrt{x + 1} - \sqrt{x}\right) + \frac{1}{30} \, x^{\frac{5}{2}} - \frac{1}{18} \, x^{\frac{3}{2}} + \frac{1}{6} \, \sqrt{x} - \frac{1}{6} \, \arctan\left(\sqrt{x}\right)"," ",0,"1/3*x^3*arctan(sqrt(x + 1) - sqrt(x)) + 1/30*x^(5/2) - 1/18*x^(3/2) + 1/6*sqrt(x) - 1/6*arctan(sqrt(x))","A",0
128,1,34,0,0.461254," ","integrate(-x*arctan(x^(1/2)-(1+x)^(1/2)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left(\sqrt{x + 1} - \sqrt{x}\right) + \frac{1}{12} \, x^{\frac{3}{2}} - \frac{1}{4} \, \sqrt{x} + \frac{1}{4} \, \arctan\left(\sqrt{x}\right)"," ",0,"1/2*x^2*arctan(sqrt(x + 1) - sqrt(x)) + 1/12*x^(3/2) - 1/4*sqrt(x) + 1/4*arctan(sqrt(x))","A",0
129,1,26,0,0.450588," ","integrate(-arctan(x^(1/2)-(1+x)^(1/2)),x, algorithm=""maxima"")","x \arctan\left(\sqrt{x + 1} - \sqrt{x}\right) + \frac{1}{2} \, \sqrt{x} - \frac{1}{2} \, \arctan\left(\sqrt{x}\right)"," ",0,"x*arctan(sqrt(x + 1) - sqrt(x)) + 1/2*sqrt(x) - 1/2*arctan(sqrt(x))","A",0
130,1,43,0,0.433291," ","integrate(-arctan(x^(1/2)-(1+x)^(1/2))/x,x, algorithm=""maxima"")","\frac{1}{4} \, \pi \log\left(x + 1\right) + \arctan\left(\sqrt{x + 1} - \sqrt{x}\right) \log\left(x\right) + \frac{1}{2} i \, {\rm Li}_2\left(i \, \sqrt{x} + 1\right) - \frac{1}{2} i \, {\rm Li}_2\left(-i \, \sqrt{x} + 1\right)"," ",0,"1/4*pi*log(x + 1) + arctan(sqrt(x + 1) - sqrt(x))*log(x) + 1/2*I*dilog(I*sqrt(x) + 1) - 1/2*I*dilog(-I*sqrt(x) + 1)","A",0
131,1,29,0,0.451197," ","integrate(-arctan(x^(1/2)-(1+x)^(1/2))/x^2,x, algorithm=""maxima"")","-\frac{\arctan\left(\sqrt{x + 1} - \sqrt{x}\right)}{x} + \frac{1}{2 \, \sqrt{x}} + \frac{1}{2} \, \arctan\left(\sqrt{x}\right)"," ",0,"-arctan(sqrt(x + 1) - sqrt(x))/x + 1/2/sqrt(x) + 1/2*arctan(sqrt(x))","A",0
132,1,34,0,0.452220," ","integrate(-arctan(x^(1/2)-(1+x)^(1/2))/x^3,x, algorithm=""maxima"")","-\frac{1}{4 \, \sqrt{x}} - \frac{\arctan\left(\sqrt{x + 1} - \sqrt{x}\right)}{2 \, x^{2}} + \frac{1}{12 \, x^{\frac{3}{2}}} - \frac{1}{4} \, \arctan\left(\sqrt{x}\right)"," ",0,"-1/4/sqrt(x) - 1/2*arctan(sqrt(x + 1) - sqrt(x))/x^2 + 1/12/x^(3/2) - 1/4*arctan(sqrt(x))","A",0
133,1,39,0,0.453463," ","integrate(-arctan(x^(1/2)-(1+x)^(1/2))/x^4,x, algorithm=""maxima"")","\frac{1}{6 \, \sqrt{x}} - \frac{1}{18 \, x^{\frac{3}{2}}} - \frac{\arctan\left(\sqrt{x + 1} - \sqrt{x}\right)}{3 \, x^{3}} + \frac{1}{30 \, x^{\frac{5}{2}}} + \frac{1}{6} \, \arctan\left(\sqrt{x}\right)"," ",0,"1/6/sqrt(x) - 1/18/x^(3/2) - 1/3*arctan(sqrt(x + 1) - sqrt(x))/x^3 + 1/30/x^(5/2) + 1/6*arctan(sqrt(x))","A",0
134,-2,0,0,0.000000," ","integrate(arctan(c*x/(-c^2*x^2+a)^(1/2))^m/(d-c^2*d*x^2/a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
135,0,0,0,0.000000," ","integrate(arctan(c*x/(-c^2*x^2+a)^(1/2))^2/(d-c^2*d*x^2/a)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(\frac{c x}{\sqrt{-c^{2} x^{2} + a}}\right)^{2}}{\sqrt{-\frac{c^{2} d x^{2}}{a} + d}}\,{d x}"," ",0,"integrate(arctan(c*x/sqrt(-c^2*x^2 + a))^2/sqrt(-c^2*d*x^2/a + d), x)","F",0
136,0,0,0,0.000000," ","integrate(arctan(c*x/(-c^2*x^2+a)^(1/2))/(d-c^2*d*x^2/a)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(\frac{c x}{\sqrt{-c^{2} x^{2} + a}}\right)}{\sqrt{-\frac{c^{2} d x^{2}}{a} + d}}\,{d x}"," ",0,"integrate(arctan(c*x/sqrt(-c^2*x^2 + a))/sqrt(-c^2*d*x^2/a + d), x)","F",0
137,0,0,0,0.000000," ","integrate(1/arctan(c*x/(-c^2*x^2+a)^(1/2))/(d-c^2*d*x^2/a)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-\frac{c^{2} d x^{2}}{a} + d} \arctan\left(\frac{c x}{\sqrt{-c^{2} x^{2} + a}}\right)}\,{d x}"," ",0,"integrate(1/(sqrt(-c^2*d*x^2/a + d)*arctan(c*x/sqrt(-c^2*x^2 + a))), x)","F",0
138,1,29,0,0.559272," ","integrate(1/arctan(c*x/(-c^2*x^2+a)^(1/2))^2/(d-c^2*d*x^2/a)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{a}}{c \sqrt{d} \arctan\left(c x, \sqrt{-c^{2} x^{2} + a}\right)}"," ",0,"-sqrt(a)/(c*sqrt(d)*arctan2(c*x, sqrt(-c^2*x^2 + a)))","A",0
139,1,29,0,0.615347," ","integrate(1/arctan(c*x/(-c^2*x^2+a)^(1/2))^3/(d-c^2*d*x^2/a)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{a}}{2 \, c \sqrt{d} \arctan\left(c x, \sqrt{-c^{2} x^{2} + a}\right)^{2}}"," ",0,"-1/2*sqrt(a)/(c*sqrt(d)*arctan2(c*x, sqrt(-c^2*x^2 + a))^2)","A",0
140,-2,0,0,0.000000," ","integrate(arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))^m/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found  sqrt((-_SAGE_VAR_b*_SAGE_VAR_x^2)-_SAGE_VAR_a)","F(-2)",0
141,-2,0,0,0.000000," ","integrate(arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))^2/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found  sqrt((-_SAGE_VAR_b*_SAGE_VAR_x^2)-_SAGE_VAR_a)","F(-2)",0
142,-2,0,0,0.000000," ","integrate(arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found  sqrt((-_SAGE_VAR_b*_SAGE_VAR_x^2)-_SAGE_VAR_a)","F(-2)",0
143,-2,0,0,0.000000," ","integrate(1/arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found  sqrt((-_SAGE_VAR_b*_SAGE_VAR_x^2)-_SAGE_VAR_a)","F(-2)",0
144,-2,0,0,0.000000," ","integrate(1/arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))^2/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found  sqrt((-_SAGE_VAR_b*_SAGE_VAR_x^2)-_SAGE_VAR_a)","F(-2)",0
145,-2,0,0,0.000000," ","integrate(1/arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))^3/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found  sqrt((-_SAGE_VAR_b*_SAGE_VAR_x^2)-_SAGE_VAR_a)","F(-2)",0
146,-2,0,0,0.000000," ","integrate(arctan(c*(b*x+a))*log(d*(b*x+a))/(b*x+a),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
147,1,48,0,0.432397," ","integrate(exp(c*(b*x+a))*arctan(sinh(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\arctan\left(\sinh\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} - \frac{\log\left(e^{\left(2 \, b c x + 2 \, a c\right)} + 1\right)}{b c}"," ",0,"arctan(sinh(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) - log(e^(2*b*c*x + 2*a*c) + 1)/(b*c)","A",0
148,1,131,0,0.429867," ","integrate(exp(c*(b*x+a))*arctan(cosh(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\arctan\left(\cosh\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} - \frac{\sqrt{2} \log\left(-\frac{2 \, \sqrt{2} - e^{\left(-2 \, b c x - 2 \, a c\right)} - 3}{2 \, \sqrt{2} + e^{\left(-2 \, b c x - 2 \, a c\right)} + 3}\right)}{2 \, b c} - \frac{2 \, {\left(b c x + a c\right)}}{b c} - \frac{\log\left(6 \, e^{\left(-2 \, b c x - 2 \, a c\right)} + e^{\left(-4 \, b c x - 4 \, a c\right)} + 1\right)}{2 \, b c}"," ",0,"arctan(cosh(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) - 1/2*sqrt(2)*log(-(2*sqrt(2) - e^(-2*b*c*x - 2*a*c) - 3)/(2*sqrt(2) + e^(-2*b*c*x - 2*a*c) + 3))/(b*c) - 2*(b*c*x + a*c)/(b*c) - 1/2*log(6*e^(-2*b*c*x - 2*a*c) + e^(-4*b*c*x - 4*a*c) + 1)/(b*c)","A",0
149,1,167,0,0.422088," ","integrate(exp(c*(b*x+a))*arctan(tanh(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\arctan\left(\tanh\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} - \frac{\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, e^{\left(b c x + a c\right)}\right)}\right)}{2 \, b c} - \frac{\sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, e^{\left(b c x + a c\right)}\right)}\right)}{2 \, b c} + \frac{\sqrt{2} \log\left(\sqrt{2} e^{\left(b c x + a c\right)} + e^{\left(2 \, b c x + 2 \, a c\right)} + 1\right)}{4 \, b c} - \frac{\sqrt{2} \log\left(-\sqrt{2} e^{\left(b c x + a c\right)} + e^{\left(2 \, b c x + 2 \, a c\right)} + 1\right)}{4 \, b c}"," ",0,"arctan(tanh(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) - 1/2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*e^(b*c*x + a*c)))/(b*c) - 1/2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*e^(b*c*x + a*c)))/(b*c) + 1/4*sqrt(2)*log(sqrt(2)*e^(b*c*x + a*c) + e^(2*b*c*x + 2*a*c) + 1)/(b*c) - 1/4*sqrt(2)*log(-sqrt(2)*e^(b*c*x + a*c) + e^(2*b*c*x + 2*a*c) + 1)/(b*c)","A",0
150,1,167,0,0.425549," ","integrate(exp(c*(b*x+a))*arctan(coth(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\arctan\left(\coth\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} + \frac{\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, e^{\left(b c x + a c\right)}\right)}\right)}{2 \, b c} + \frac{\sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, e^{\left(b c x + a c\right)}\right)}\right)}{2 \, b c} - \frac{\sqrt{2} \log\left(\sqrt{2} e^{\left(b c x + a c\right)} + e^{\left(2 \, b c x + 2 \, a c\right)} + 1\right)}{4 \, b c} + \frac{\sqrt{2} \log\left(-\sqrt{2} e^{\left(b c x + a c\right)} + e^{\left(2 \, b c x + 2 \, a c\right)} + 1\right)}{4 \, b c}"," ",0,"arctan(coth(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) + 1/2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*e^(b*c*x + a*c)))/(b*c) + 1/2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*e^(b*c*x + a*c)))/(b*c) - 1/4*sqrt(2)*log(sqrt(2)*e^(b*c*x + a*c) + e^(2*b*c*x + 2*a*c) + 1)/(b*c) + 1/4*sqrt(2)*log(-sqrt(2)*e^(b*c*x + a*c) + e^(2*b*c*x + 2*a*c) + 1)/(b*c)","A",0
151,1,169,0,0.451927," ","integrate(exp(c*(b*x+a))*arctan(sech(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\arctan\left(\operatorname{sech}\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} - \frac{3 \, \sqrt{2} \log\left(-\frac{2 \, \sqrt{2} - e^{\left(2 \, b c x + 2 \, a c\right)} - 3}{2 \, \sqrt{2} + e^{\left(2 \, b c x + 2 \, a c\right)} + 3}\right)}{8 \, b c} + \frac{\sqrt{2} \log\left(-\frac{2 \, \sqrt{2} - e^{\left(-2 \, b c x - 2 \, a c\right)} - 3}{2 \, \sqrt{2} + e^{\left(-2 \, b c x - 2 \, a c\right)} + 3}\right)}{8 \, b c} + \frac{\log\left(e^{\left(4 \, b c x + 4 \, a c\right)} + 6 \, e^{\left(2 \, b c x + 2 \, a c\right)} + 1\right)}{2 \, b c}"," ",0,"arctan(sech(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) - 3/8*sqrt(2)*log(-(2*sqrt(2) - e^(2*b*c*x + 2*a*c) - 3)/(2*sqrt(2) + e^(2*b*c*x + 2*a*c) + 3))/(b*c) + 1/8*sqrt(2)*log(-(2*sqrt(2) - e^(-2*b*c*x - 2*a*c) - 3)/(2*sqrt(2) + e^(-2*b*c*x - 2*a*c) + 3))/(b*c) + 1/2*log(e^(4*b*c*x + 4*a*c) + 6*e^(2*b*c*x + 2*a*c) + 1)/(b*c)","A",0
152,1,47,0,0.416761," ","integrate(exp(c*(b*x+a))*arctan(csch(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\arctan\left(\operatorname{csch}\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} + \frac{\log\left(e^{\left(2 \, b c x + 2 \, a c\right)} + 1\right)}{b c}"," ",0,"arctan(csch(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) + log(e^(2*b*c*x + 2*a*c) + 1)/(b*c)","A",0
153,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^n))*(d+e*log(f*x^m))/x,x, algorithm=""maxima"")","\frac{a e \log\left(f x^{m}\right)^{2}}{2 \, m} + a d \log\left(x\right) - \frac{1}{2} \, {\left(b e m \log\left(x\right)^{2} - 2 \, b e \log\left(x\right) \log\left(x^{m}\right) - 2 \, {\left(b e \log\left(f\right) + b d\right)} \log\left(x\right)\right)} \arctan\left(c x^{n}\right) - \int -\frac{b c e m n x^{n} \log\left(x\right)^{2} - 2 \, b c e n x^{n} \log\left(x\right) \log\left(x^{m}\right) - 2 \, {\left(b c e \log\left(f\right) + b c d\right)} n x^{n} \log\left(x\right)}{2 \, {\left(c^{2} x x^{2 \, n} + x\right)}}\,{d x}"," ",0,"1/2*a*e*log(f*x^m)^2/m + a*d*log(x) - 1/2*(b*e*m*log(x)^2 - 2*b*e*log(x)*log(x^m) - 2*(b*e*log(f) + b*d)*log(x))*arctan(c*x^n) - integrate(-1/2*(b*c*e*m*n*x^n*log(x)^2 - 2*b*c*e*n*x^n*log(x)*log(x^m) - 2*(b*c*e*log(f) + b*c*d)*n*x^n*log(x))/(c^2*x*x^(2*n) + x), x)","F",0
