1,1,42,41,0.039000," ","int(x^5*arccot(a*x),x)","\frac{x}{6 a^{5}}-\frac{x^{3}}{18 a^{3}}+\frac{x^{5}}{30 a}+\frac{x^{6} \mathrm{arccot}\left(a x \right)}{6}-\frac{\arctan \left(a x \right)}{6 a^{6}}"," ",0,"1/6*x/a^5-1/18*x^3/a^3+1/30*x^5/a+1/6*x^6*arccot(a*x)-1/6*arctan(a*x)/a^6","A"
2,1,42,41,0.037000," ","int(x^4*arccot(a*x),x)","-\frac{x^{2}}{10 a^{3}}+\frac{x^{4}}{20 a}+\frac{x^{5} \mathrm{arccot}\left(a x \right)}{5}+\frac{\ln \left(a^{2} x^{2}+1\right)}{10 a^{5}}"," ",0,"-1/10*x^2/a^3+1/20*x^4/a+1/5*x^5*arccot(a*x)+1/10*ln(a^2*x^2+1)/a^5","A"
3,1,34,33,0.038000," ","int(x^3*arccot(a*x),x)","-\frac{x}{4 a^{3}}+\frac{x^{3}}{12 a}+\frac{x^{4} \mathrm{arccot}\left(a x \right)}{4}+\frac{\arctan \left(a x \right)}{4 a^{4}}"," ",0,"-1/4*x/a^3+1/12*x^3/a+1/4*x^4*arccot(a*x)+1/4*arctan(a*x)/a^4","A"
4,1,34,33,0.040000," ","int(x^2*arccot(a*x),x)","\frac{x^{2}}{6 a}+\frac{x^{3} \mathrm{arccot}\left(a x \right)}{3}-\frac{\ln \left(a^{2} x^{2}+1\right)}{6 a^{3}}"," ",0,"1/6*x^2/a+1/3*x^3*arccot(a*x)-1/6*ln(a^2*x^2+1)/a^3","A"
5,1,26,25,0.038000," ","int(x*arccot(a*x),x)","\frac{x}{2 a}+\frac{x^{2} \mathrm{arccot}\left(a x \right)}{2}-\frac{\arctan \left(a x \right)}{2 a^{2}}"," ",0,"1/2*x/a+1/2*x^2*arccot(a*x)-1/2*arctan(a*x)/a^2","A"
6,1,23,22,0.037000," ","int(arccot(a*x),x)","x \,\mathrm{arccot}\left(a x \right)+\frac{\ln \left(a^{2} x^{2}+1\right)}{2 a}"," ",0,"x*arccot(a*x)+1/2*ln(a^2*x^2+1)/a","A"
7,1,63,29,0.056000," ","int(arccot(a*x)/x,x)","\ln \left(a x \right) \mathrm{arccot}\left(a x \right)-\frac{i \ln \left(a x \right) \ln \left(i a x +1\right)}{2}+\frac{i \ln \left(a x \right) \ln \left(-i a x +1\right)}{2}-\frac{i \dilog \left(i a x +1\right)}{2}+\frac{i \dilog \left(-i a x +1\right)}{2}"," ",0,"ln(a*x)*arccot(a*x)-1/2*I*ln(a*x)*ln(1+I*a*x)+1/2*I*ln(a*x)*ln(1-I*a*x)-1/2*I*dilog(1+I*a*x)+1/2*I*dilog(1-I*a*x)","B"
8,1,31,28,0.042000," ","int(arccot(a*x)/x^2,x)","-\frac{\mathrm{arccot}\left(a x \right)}{x}-a \ln \left(a x \right)+\frac{a \ln \left(a^{2} x^{2}+1\right)}{2}"," ",0,"-arccot(a*x)/x-a*ln(a*x)+1/2*a*ln(a^2*x^2+1)","A"
9,1,26,25,0.043000," ","int(arccot(a*x)/x^3,x)","\frac{a}{2 x}-\frac{\mathrm{arccot}\left(a x \right)}{2 x^{2}}+\frac{a^{2} \arctan \left(a x \right)}{2}"," ",0,"1/2*a/x-1/2*arccot(a*x)/x^2+1/2*a^2*arctan(a*x)","A"
10,1,41,38,0.044000," ","int(arccot(a*x)/x^4,x)","-\frac{\mathrm{arccot}\left(a x \right)}{3 x^{3}}+\frac{a}{6 x^{2}}+\frac{a^{3} \ln \left(a x \right)}{3}-\frac{a^{3} \ln \left(a^{2} x^{2}+1\right)}{6}"," ",0,"-1/3*arccot(a*x)/x^3+1/6*a/x^2+1/3*a^3*ln(a*x)-1/6*a^3*ln(a^2*x^2+1)","A"
11,1,34,33,0.044000," ","int(arccot(a*x)/x^5,x)","\frac{a}{12 x^{3}}-\frac{a^{3}}{4 x}-\frac{\mathrm{arccot}\left(a x \right)}{4 x^{4}}-\frac{a^{4} \arctan \left(a x \right)}{4}"," ",0,"1/12*a/x^3-1/4*a^3/x-1/4*arccot(a*x)/x^4-1/4*a^4*arctan(a*x)","A"
12,1,102,88,0.050000," ","int(x^5*arccot(a*x)^2,x)","\frac{x^{6} \mathrm{arccot}\left(a x \right)^{2}}{6}+\frac{x^{5} \mathrm{arccot}\left(a x \right)}{15 a}-\frac{x^{3} \mathrm{arccot}\left(a x \right)}{9 a^{3}}+\frac{x \,\mathrm{arccot}\left(a x \right)}{3 a^{5}}-\frac{\mathrm{arccot}\left(a x \right) \arctan \left(a x \right)}{3 a^{6}}+\frac{x^{4}}{60 a^{2}}-\frac{4 x^{2}}{45 a^{4}}+\frac{23 \ln \left(a^{2} x^{2}+1\right)}{90 a^{6}}-\frac{\arctan \left(a x \right)^{2}}{6 a^{6}}"," ",0,"1/6*x^6*arccot(a*x)^2+1/15*x^5*arccot(a*x)/a-1/9*x^3*arccot(a*x)/a^3+1/3*x*arccot(a*x)/a^5-1/3/a^6*arccot(a*x)*arctan(a*x)+1/60*x^4/a^2-4/45*x^2/a^4+23/90*ln(a^2*x^2+1)/a^6-1/6/a^6*arctan(a*x)^2","A"
13,1,233,113,0.138000," ","int(x^4*arccot(a*x)^2,x)","\frac{x^{5} \mathrm{arccot}\left(a x \right)^{2}}{5}+\frac{x^{4} \mathrm{arccot}\left(a x \right)}{10 a}-\frac{x^{2} \mathrm{arccot}\left(a x \right)}{5 a^{3}}+\frac{\mathrm{arccot}\left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{5 a^{5}}+\frac{x^{3}}{30 a^{2}}-\frac{3 x}{10 a^{4}}+\frac{3 \arctan \left(a x \right)}{10 a^{5}}-\frac{i \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{10 a^{5}}+\frac{i \ln \left(a x -i\right)^{2}}{20 a^{5}}+\frac{i \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{10 a^{5}}+\frac{i \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{10 a^{5}}+\frac{i \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{10 a^{5}}-\frac{i \ln \left(a x +i\right)^{2}}{20 a^{5}}-\frac{i \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{10 a^{5}}-\frac{i \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{10 a^{5}}"," ",0,"1/5*x^5*arccot(a*x)^2+1/10*x^4*arccot(a*x)/a-1/5*x^2*arccot(a*x)/a^3+1/5/a^5*arccot(a*x)*ln(a^2*x^2+1)+1/30*x^3/a^2-3/10*x/a^4+3/10*arctan(a*x)/a^5-1/10*I/a^5*ln(a*x-I)*ln(a^2*x^2+1)+1/20*I/a^5*ln(a*x-I)^2+1/10*I/a^5*dilog(-1/2*I*(I+a*x))+1/10*I/a^5*ln(a*x-I)*ln(-1/2*I*(I+a*x))+1/10*I/a^5*ln(I+a*x)*ln(a^2*x^2+1)-1/20*I/a^5*ln(I+a*x)^2-1/10*I/a^5*dilog(1/2*I*(a*x-I))-1/10*I/a^5*ln(I+a*x)*ln(1/2*I*(a*x-I))","B"
14,1,82,68,0.051000," ","int(x^3*arccot(a*x)^2,x)","\frac{x^{4} \mathrm{arccot}\left(a x \right)^{2}}{4}+\frac{x^{3} \mathrm{arccot}\left(a x \right)}{6 a}-\frac{x \,\mathrm{arccot}\left(a x \right)}{2 a^{3}}+\frac{\mathrm{arccot}\left(a x \right) \arctan \left(a x \right)}{2 a^{4}}+\frac{x^{2}}{12 a^{2}}-\frac{\ln \left(a^{2} x^{2}+1\right)}{3 a^{4}}+\frac{\arctan \left(a x \right)^{2}}{4 a^{4}}"," ",0,"1/4*x^4*arccot(a*x)^2+1/6*x^3*arccot(a*x)/a-1/2*x*arccot(a*x)/a^3+1/2/a^4*arccot(a*x)*arctan(a*x)+1/12*x^2/a^2-1/3*ln(a^2*x^2+1)/a^4+1/4/a^4*arctan(a*x)^2","A"
15,1,213,93,0.132000," ","int(x^2*arccot(a*x)^2,x)","\frac{x^{3} \mathrm{arccot}\left(a x \right)^{2}}{3}+\frac{x^{2} \mathrm{arccot}\left(a x \right)}{3 a}-\frac{\mathrm{arccot}\left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{3 a^{3}}+\frac{x}{3 a^{2}}-\frac{\arctan \left(a x \right)}{3 a^{3}}+\frac{i \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{6 a^{3}}-\frac{i \ln \left(a x -i\right)^{2}}{12 a^{3}}-\frac{i \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{6 a^{3}}-\frac{i \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{6 a^{3}}-\frac{i \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{6 a^{3}}+\frac{i \ln \left(a x +i\right)^{2}}{12 a^{3}}+\frac{i \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{6 a^{3}}+\frac{i \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{6 a^{3}}"," ",0,"1/3*x^3*arccot(a*x)^2+1/3*x^2*arccot(a*x)/a-1/3/a^3*arccot(a*x)*ln(a^2*x^2+1)+1/3*x/a^2-1/3*arctan(a*x)/a^3+1/6*I/a^3*ln(a*x-I)*ln(a^2*x^2+1)-1/12*I/a^3*ln(a*x-I)^2-1/6*I/a^3*dilog(-1/2*I*(I+a*x))-1/6*I/a^3*ln(a*x-I)*ln(-1/2*I*(I+a*x))-1/6*I/a^3*ln(I+a*x)*ln(a^2*x^2+1)+1/12*I/a^3*ln(I+a*x)^2+1/6*I/a^3*dilog(1/2*I*(a*x-I))+1/6*I/a^3*ln(I+a*x)*ln(1/2*I*(a*x-I))","B"
16,1,61,47,0.050000," ","int(x*arccot(a*x)^2,x)","\frac{x^{2} \mathrm{arccot}\left(a x \right)^{2}}{2}-\frac{\mathrm{arccot}\left(a x \right) \arctan \left(a x \right)}{a^{2}}+\frac{x \,\mathrm{arccot}\left(a x \right)}{a}+\frac{\ln \left(a^{2} x^{2}+1\right)}{2 a^{2}}-\frac{\arctan \left(a x \right)^{2}}{2 a^{2}}"," ",0,"1/2*x^2*arccot(a*x)^2-1/a^2*arccot(a*x)*arctan(a*x)+x*arccot(a*x)/a+1/2*ln(a^2*x^2+1)/a^2-1/2/a^2*arctan(a*x)^2","A"
17,1,136,63,0.417000," ","int(arccot(a*x)^2,x)","x \mathrm{arccot}\left(a x \right)^{2}+\frac{i \mathrm{arccot}\left(a x \right)^{2}}{a}-\frac{2 \,\mathrm{arccot}\left(a x \right) \ln \left(1+\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a}-\frac{2 \,\mathrm{arccot}\left(a x \right) \ln \left(1-\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a}+\frac{2 i \polylog \left(2, -\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a}+\frac{2 i \polylog \left(2, \frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a}"," ",0,"x*arccot(a*x)^2+I*arccot(a*x)^2/a-2/a*arccot(a*x)*ln(1+(I+a*x)/(a^2*x^2+1)^(1/2))-2/a*arccot(a*x)*ln(1-(I+a*x)/(a^2*x^2+1)^(1/2))+2*I/a*polylog(2,-(I+a*x)/(a^2*x^2+1)^(1/2))+2*I/a*polylog(2,(I+a*x)/(a^2*x^2+1)^(1/2))","B"
18,1,959,103,0.878000," ","int(arccot(a*x)^2/x,x)","\ln \left(a x \right) \mathrm{arccot}\left(a x \right)^{2}+2 i \mathrm{arccot}\left(a x \right) \polylog \left(2, -\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{2} \mathrm{arccot}\left(a x \right)^{2}}{2}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{3} \mathrm{arccot}\left(a x \right)^{2}}{2}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{arccot}\left(a x \right)^{2}}{2}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{csgn}\left(\frac{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{2} \mathrm{arccot}\left(a x \right)^{2}}{2}+\frac{i \pi  \mathrm{csgn}\left(\frac{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{2} \mathrm{arccot}\left(a x \right)^{2}}{2}-i \mathrm{arccot}\left(a x \right) \polylog \left(2, -\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right)+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{csgn}\left(\frac{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{arccot}\left(a x \right)^{2}}{2}+2 i \mathrm{arccot}\left(a x \right) \polylog \left(2, \frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)+\mathrm{arccot}\left(a x \right)^{2} \ln \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)-\mathrm{arccot}\left(a x \right)^{2} \ln \left(1+\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{arccot}\left(a x \right)^{2}}{2}-2 \polylog \left(3, -\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)-\mathrm{arccot}\left(a x \right)^{2} \ln \left(1-\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{i \pi  \mathrm{arccot}\left(a x \right)^{2}}{2}-2 \polylog \left(3, \frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{i \pi  \mathrm{csgn}\left(\frac{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{3} \mathrm{arccot}\left(a x \right)^{2}}{2}+\frac{\polylog \left(3, -\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right)}{2}"," ",0,"ln(a*x)*arccot(a*x)^2-1/2*I*Pi*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1))*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^2*arccot(a*x)^2+1/2*I*Pi*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^3*arccot(a*x)^2+1/2*I*Pi*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1))*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))*csgn(I*((I+a*x)^2/(a^2*x^2+1)+1))*arccot(a*x)^2+2*I*arccot(a*x)*polylog(2,-(I+a*x)/(a^2*x^2+1)^(1/2))-1/2*I*Pi*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))*csgn(1/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^2*arccot(a*x)^2+1/2*I*Pi*csgn(1/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^2*arccot(a*x)^2+1/2*I*Pi*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))*csgn(1/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))*arccot(a*x)^2-I*arccot(a*x)*polylog(2,-(I+a*x)^2/(a^2*x^2+1))-1/2*I*Pi*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)+1))*arccot(a*x)^2+arccot(a*x)^2*ln((I+a*x)^2/(a^2*x^2+1)-1)-arccot(a*x)^2*ln(1+(I+a*x)/(a^2*x^2+1)^(1/2))-1/2*I*Pi*arccot(a*x)^2-2*polylog(3,-(I+a*x)/(a^2*x^2+1)^(1/2))-arccot(a*x)^2*ln(1-(I+a*x)/(a^2*x^2+1)^(1/2))-1/2*I*Pi*csgn(1/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^3*arccot(a*x)^2-2*polylog(3,(I+a*x)/(a^2*x^2+1)^(1/2))+2*I*arccot(a*x)*polylog(2,(I+a*x)/(a^2*x^2+1)^(1/2))+1/2*polylog(3,-(I+a*x)^2/(a^2*x^2+1))","C"
19,1,234,62,0.136000," ","int(arccot(a*x)^2/x^2,x)","-\frac{\mathrm{arccot}\left(a x \right)^{2}}{x}-2 a \,\mathrm{arccot}\left(a x \right) \ln \left(a x \right)+a \,\mathrm{arccot}\left(a x \right) \ln \left(a^{2} x^{2}+1\right)+i a \ln \left(a x \right) \ln \left(i a x +1\right)-i a \ln \left(a x \right) \ln \left(-i a x +1\right)+i a \dilog \left(i a x +1\right)-i a \dilog \left(-i a x +1\right)-\frac{i a \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{2}+\frac{i a \ln \left(a x -i\right)^{2}}{4}+\frac{i a \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{2}+\frac{i a \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{2}+\frac{i a \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{2}-\frac{i a \ln \left(a x +i\right)^{2}}{4}-\frac{i a \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{2}-\frac{i a \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{2}"," ",0,"-arccot(a*x)^2/x-2*a*arccot(a*x)*ln(a*x)+a*arccot(a*x)*ln(a^2*x^2+1)+I*a*ln(a*x)*ln(1+I*a*x)-I*a*ln(a*x)*ln(1-I*a*x)+I*a*dilog(1+I*a*x)-I*a*dilog(1-I*a*x)-1/2*I*a*ln(a*x-I)*ln(a^2*x^2+1)+1/4*I*a*ln(a*x-I)^2+1/2*I*a*dilog(-1/2*I*(I+a*x))+1/2*I*a*ln(a*x-I)*ln(-1/2*I*(I+a*x))+1/2*I*a*ln(I+a*x)*ln(a^2*x^2+1)-1/4*I*a*ln(I+a*x)^2-1/2*I*a*dilog(1/2*I*(a*x-I))-1/2*I*a*ln(I+a*x)*ln(1/2*I*(a*x-I))","B"
20,1,68,53,0.054000," ","int(arccot(a*x)^2/x^3,x)","-\frac{\mathrm{arccot}\left(a x \right)^{2}}{2 x^{2}}+\frac{a \,\mathrm{arccot}\left(a x \right)}{x}+a^{2} \mathrm{arccot}\left(a x \right) \arctan \left(a x \right)+a^{2} \ln \left(a x \right)-\frac{a^{2} \ln \left(a^{2} x^{2}+1\right)}{2}+\frac{a^{2} \arctan \left(a x \right)^{2}}{2}"," ",0,"-1/2*arccot(a*x)^2/x^2+a*arccot(a*x)/x+a^2*arccot(a*x)*arctan(a*x)+a^2*ln(a*x)-1/2*a^2*ln(a^2*x^2+1)+1/2*a^2*arctan(a*x)^2","A"
21,1,290,95,0.143000," ","int(arccot(a*x)^2/x^4,x)","-\frac{\mathrm{arccot}\left(a x \right)^{2}}{3 x^{3}}+\frac{a \,\mathrm{arccot}\left(a x \right)}{3 x^{2}}+\frac{2 a^{3} \mathrm{arccot}\left(a x \right) \ln \left(a x \right)}{3}-\frac{a^{3} \mathrm{arccot}\left(a x \right) \ln \left(a^{2} x^{2}+1\right)}{3}-\frac{i a^{3} \ln \left(a x -i\right) \ln \left(-\frac{i \left(a x +i\right)}{2}\right)}{6}+\frac{i a^{3} \dilog \left(\frac{i \left(a x -i\right)}{2}\right)}{6}-\frac{i a^{3} \ln \left(a x \right) \ln \left(i a x +1\right)}{3}-\frac{i a^{3} \ln \left(a x +i\right) \ln \left(a^{2} x^{2}+1\right)}{6}-\frac{i a^{3} \dilog \left(-\frac{i \left(a x +i\right)}{2}\right)}{6}+\frac{i a^{3} \ln \left(a x +i\right) \ln \left(\frac{i \left(a x -i\right)}{2}\right)}{6}+\frac{i a^{3} \dilog \left(-i a x +1\right)}{3}-\frac{i a^{3} \ln \left(a x -i\right)^{2}}{12}-\frac{a^{2}}{3 x}-\frac{a^{3} \arctan \left(a x \right)}{3}-\frac{i a^{3} \dilog \left(i a x +1\right)}{3}+\frac{i a^{3} \ln \left(a x -i\right) \ln \left(a^{2} x^{2}+1\right)}{6}+\frac{i a^{3} \ln \left(a x +i\right)^{2}}{12}+\frac{i a^{3} \ln \left(a x \right) \ln \left(-i a x +1\right)}{3}"," ",0,"-1/3*arccot(a*x)^2/x^3+1/3*a*arccot(a*x)/x^2+2/3*a^3*arccot(a*x)*ln(a*x)-1/3*a^3*arccot(a*x)*ln(a^2*x^2+1)-1/6*I*a^3*ln(a*x-I)*ln(-1/2*I*(I+a*x))-1/3*I*a^3*ln(a*x)*ln(1+I*a*x)-1/6*I*a^3*ln(I+a*x)*ln(a^2*x^2+1)-1/3*I*a^3*dilog(1+I*a*x)+1/6*I*a^3*ln(I+a*x)*ln(1/2*I*(a*x-I))+1/3*I*a^3*dilog(1-I*a*x)-1/6*I*a^3*dilog(-1/2*I*(I+a*x))+1/6*I*a^3*dilog(1/2*I*(a*x-I))-1/3*a^2/x-1/3*a^3*arctan(a*x)-1/12*I*a^3*ln(a*x-I)^2+1/6*I*a^3*ln(a*x-I)*ln(a^2*x^2+1)+1/12*I*a^3*ln(I+a*x)^2+1/3*I*a^3*ln(a*x)*ln(1-I*a*x)","B"
22,1,91,75,0.059000," ","int(arccot(a*x)^2/x^5,x)","-\frac{\mathrm{arccot}\left(a x \right)^{2}}{4 x^{4}}+\frac{a \,\mathrm{arccot}\left(a x \right)}{6 x^{3}}-\frac{a^{3} \mathrm{arccot}\left(a x \right)}{2 x}-\frac{a^{4} \mathrm{arccot}\left(a x \right) \arctan \left(a x \right)}{2}-\frac{a^{2}}{12 x^{2}}-\frac{2 a^{4} \ln \left(a x \right)}{3}+\frac{a^{4} \ln \left(a^{2} x^{2}+1\right)}{3}-\frac{a^{4} \arctan \left(a x \right)^{2}}{4}"," ",0,"-1/4*arccot(a*x)^2/x^4+1/6*a*arccot(a*x)/x^3-1/2*a^3*arccot(a*x)/x-1/2*a^4*arccot(a*x)*arctan(a*x)-1/12*a^2/x^2-2/3*a^4*ln(a*x)+1/3*a^4*ln(a^2*x^2+1)-1/4*a^4*arctan(a*x)^2","A"
23,1,243,164,1.878000," ","int(x^5*arccot(a*x)^3,x)","\frac{x^{6} \mathrm{arccot}\left(a x \right)^{3}}{6}+\frac{\mathrm{arccot}\left(a x \right)^{3}}{6 a^{6}}+\frac{x^{5} \mathrm{arccot}\left(a x \right)^{2}}{10 a}-\frac{x^{3} \mathrm{arccot}\left(a x \right)^{2}}{6 a^{3}}+\frac{x^{4} \mathrm{arccot}\left(a x \right)}{20 a^{2}}-\frac{4 x^{2} \mathrm{arccot}\left(a x \right)}{15 a^{4}}+\frac{x \mathrm{arccot}\left(a x \right)^{2}}{2 a^{5}}+\frac{x^{3}}{60 a^{3}}-\frac{19 x}{60 a^{5}}+\frac{23 i \polylog \left(2, \frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{15 a^{6}}-\frac{19 \,\mathrm{arccot}\left(a x \right)}{60 a^{6}}+\frac{i}{3 a^{6}}-\frac{23 \,\mathrm{arccot}\left(a x \right) \ln \left(1+\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{15 a^{6}}+\frac{23 i \polylog \left(2, -\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{15 a^{6}}-\frac{23 \,\mathrm{arccot}\left(a x \right) \ln \left(1-\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{15 a^{6}}+\frac{23 i \mathrm{arccot}\left(a x \right)^{2}}{30 a^{6}}"," ",0,"1/6*x^6*arccot(a*x)^3+1/6*arccot(a*x)^3/a^6+1/10*x^5*arccot(a*x)^2/a-1/6*x^3*arccot(a*x)^2/a^3+1/20*x^4*arccot(a*x)/a^2-4/15*x^2*arccot(a*x)/a^4+1/2*x*arccot(a*x)^2/a^5+1/60*x^3/a^3-19/60*x/a^5+23/15*I/a^6*polylog(2,-(I+a*x)/(a^2*x^2+1)^(1/2))-19/60/a^6*arccot(a*x)+23/15*I/a^6*polylog(2,(I+a*x)/(a^2*x^2+1)^(1/2))-23/15/a^6*arccot(a*x)*ln(1+(I+a*x)/(a^2*x^2+1)^(1/2))+1/3*I/a^6-23/15/a^6*arccot(a*x)*ln(1-(I+a*x)/(a^2*x^2+1)^(1/2))+23/30*I*arccot(a*x)^2/a^6","A"
24,1,2731,176,6.145000," ","int(x^4*arccot(a*x)^3,x)","\text{Expression too large to display}"," ",0,"1/20/a^5+1/5*x^5*arccot(a*x)^3+1/20*x^2/a^3-9/10*x*arccot(a*x)/a^4+1/10*x^3*arccot(a*x)/a^2-3/10*x^2*arccot(a*x)^2/a^3+3/20*x^4*arccot(a*x)^2/a+9/160*I/a^3*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)^3*arccot(a*x)^2*Pi*x^2-3/10*I/a^5*arccot(a*x)^2*Pi+6/5*I/a^5*arccot(a*x)*polylog(2,-(I+a*x)/(a^2*x^2+1)^(1/2))+6/5*I/a^5*arccot(a*x)*polylog(2,(I+a*x)/(a^2*x^2+1)^(1/2))+1/5*I*arccot(a*x)^3/a^5-9/80*I/a^3*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1))*arccot(a*x)^2*Pi*x^2+9/160*I/a^3*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1))^2*arccot(a*x)^2*Pi*x^2+3/20*I/a^5*csgn(I*(I+a*x)^2/(a^2*x^2+1))*csgn(I*(I+a*x)^2/(a^2*x^2+1)/((I+a*x)^2/(a^2*x^2+1)-1)^2)*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)^2)*arccot(a*x)^2*Pi+9/160/a^4*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)^3*arccot(a*x)^2*Pi*x-3/160/a^2*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)^3*arccot(a*x)^2*Pi*x^3+9/160/a^4*arccot(a*x)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)^3*Pi*x+3/20*I/a^5*csgn(I*(I+a*x)^2/(a^2*x^2+1))^3*arccot(a*x)^2*Pi+21/160*I/a^5*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)^3*arccot(a*x)^2*Pi-3/160*I/a^5*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)^3*arccot(a*x)^2*Pi+9/80*I/a^3*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)^2*csgn(I*(I+a*x)^2/(a^2*x^2+1)-I)*arccot(a*x)^2*Pi*x^2+9/160*I/a^3*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)*csgn(I*(I+a*x)^2/(a^2*x^2+1)-I)^2*arccot(a*x)^2*Pi*x^2+3/5/a^5*arccot(a*x)^2*ln((I+a*x)^2/(a^2*x^2+1)-1)-3/5/a^5*arccot(a*x)^2*ln(1+(I+a*x)/(a^2*x^2+1)^(1/2))-3/5/a^5*arccot(a*x)^2*ln(1-(I+a*x)/(a^2*x^2+1)^(1/2))+3/10/a^5*arccot(a*x)^2*ln(a^2*x^2+1)-3/5/a^5*arccot(a*x)^2*ln((I+a*x)/(a^2*x^2+1)^(1/2))-3/5/a^5*ln(2)*arccot(a*x)^2-I/a^5*arccot(a*x)-6/5/a^5*polylog(3,-(I+a*x)/(a^2*x^2+1)^(1/2))-6/5/a^5*polylog(3,(I+a*x)/(a^2*x^2+1)^(1/2))+1/a^5*ln(1+(I+a*x)/(a^2*x^2+1)^(1/2))+1/a^5*ln((I+a*x)/(a^2*x^2+1)^(1/2)-1)-3/160/a^2*arccot(a*x)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)^3*Pi*x^3-3/160/a^2*arccot(a*x)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1))^2*Pi*x^3+9/80/a^4*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)^2*csgn(I*(I+a*x)^2/(a^2*x^2+1)-I)*arccot(a*x)^2*Pi*x+9/160/a^4*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)*csgn(I*(I+a*x)^2/(a^2*x^2+1)-I)^2*arccot(a*x)^2*Pi*x-3/80/a^2*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)^2*csgn(I*(I+a*x)^2/(a^2*x^2+1)-I)*arccot(a*x)^2*Pi*x^3-3/160/a^2*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)*csgn(I*(I+a*x)^2/(a^2*x^2+1)-I)^2*arccot(a*x)^2*Pi*x^3-9/80/a^4*arccot(a*x)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1))*Pi*x+3/80/a^2*arccot(a*x)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1))*Pi*x^3+9/160/a^4*arccot(a*x)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1))^2*Pi*x+3/20*I/a^5*csgn(I*(I+a*x)/(a^2*x^2+1)^(1/2))^2*csgn(I*(I+a*x)^2/(a^2*x^2+1))*arccot(a*x)^2*Pi-3/10*I/a^5*csgn(I*(I+a*x)/(a^2*x^2+1)^(1/2))*csgn(I*(I+a*x)^2/(a^2*x^2+1))^2*arccot(a*x)^2*Pi-3/20*I/a^5*csgn(I*(I+a*x)^2/(a^2*x^2+1))*csgn(I*(I+a*x)^2/(a^2*x^2+1)/((I+a*x)^2/(a^2*x^2+1)-1)^2)^2*arccot(a*x)^2*Pi+21/80*I/a^5*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)^2*csgn(I*(I+a*x)^2/(a^2*x^2+1)-I)*arccot(a*x)^2*Pi+21/160*I/a^5*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)*csgn(I*(I+a*x)^2/(a^2*x^2+1)-I)^2*arccot(a*x)^2*Pi+3/80*I/a^5*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1))*arccot(a*x)^2*Pi-3/160*I/a^5*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1))^2*arccot(a*x)^2*Pi-3/20*I/a^5*csgn(I*(I+a*x)^2/(a^2*x^2+1)/((I+a*x)^2/(a^2*x^2+1)-1)^2)^2*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)^2)*arccot(a*x)^2*Pi+9/160*I/a^3*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)^3*arccot(a*x)^2*Pi*x^2-3/20*I/a^5*csgn(I*(I+a*x)^2/(a^2*x^2+1)/((I+a*x)^2/(a^2*x^2+1)-1)^2)^3*arccot(a*x)^2*Pi+3/10*I/a^5*csgn(I*(I+a*x)^2/(a^2*x^2+1)/((I+a*x)^2/(a^2*x^2+1)-1)^2)^2*arccot(a*x)^2*Pi-9/20*arccot(a*x)^2/a^5","C"
25,1,209,130,1.553000," ","int(x^3*arccot(a*x)^3,x)","\frac{x^{4} \mathrm{arccot}\left(a x \right)^{3}}{4}-\frac{\mathrm{arccot}\left(a x \right)^{3}}{4 a^{4}}+\frac{x^{3} \mathrm{arccot}\left(a x \right)^{2}}{4 a}-\frac{3 x \mathrm{arccot}\left(a x \right)^{2}}{4 a^{3}}+\frac{x^{2} \mathrm{arccot}\left(a x \right)}{4 a^{2}}-\frac{i \mathrm{arccot}\left(a x \right)^{2}}{a^{4}}+\frac{\mathrm{arccot}\left(a x \right)}{4 a^{4}}+\frac{x}{4 a^{3}}-\frac{i}{4 a^{4}}+\frac{2 \,\mathrm{arccot}\left(a x \right) \ln \left(1+\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{4}}-\frac{2 i \polylog \left(2, -\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{4}}+\frac{2 \,\mathrm{arccot}\left(a x \right) \ln \left(1-\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{4}}-\frac{2 i \polylog \left(2, \frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{4}}"," ",0,"1/4*x^4*arccot(a*x)^3-1/4*arccot(a*x)^3/a^4+1/4*x^3*arccot(a*x)^2/a-3/4*x*arccot(a*x)^2/a^3+1/4*x^2*arccot(a*x)/a^2-I*arccot(a*x)^2/a^4+1/4/a^4*arccot(a*x)+1/4*x/a^3-1/4*I/a^4+2/a^4*arccot(a*x)*ln(1+(I+a*x)/(a^2*x^2+1)^(1/2))-2*I/a^4*polylog(2,-(I+a*x)/(a^2*x^2+1)^(1/2))+2/a^4*arccot(a*x)*ln(1-(I+a*x)/(a^2*x^2+1)^(1/2))-2*I/a^4*polylog(2,(I+a*x)/(a^2*x^2+1)^(1/2))","A"
26,1,1815,140,4.186000," ","int(x^2*arccot(a*x)^3,x)","\frac{x \,\mathrm{arccot}\left(a x \right)}{a^{2}}+\frac{x^{3} \mathrm{arccot}\left(a x \right)^{3}}{3}+\frac{2 \polylog \left(3, \frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{3}}+\frac{x^{2} \mathrm{arccot}\left(a x \right)^{2}}{2 a}-\frac{\mathrm{arccot}\left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{2 a^{3}}+\frac{\ln \left(2\right) \mathrm{arccot}\left(a x \right)^{2}}{a^{3}}-\frac{\ln \left(\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}-1\right)}{a^{3}}-\frac{\ln \left(1+\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{3}}+\frac{2 \polylog \left(3, -\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{3}}-\frac{i \mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}}\right) \pi}{4 a^{3}}+\frac{i \mathrm{arccot}\left(a x \right)^{2} \pi}{2 a^{3}}-\frac{2 i \mathrm{arccot}\left(a x \right) \polylog \left(2, -\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{3}}-\frac{2 i \mathrm{arccot}\left(a x \right) \polylog \left(2, \frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{3}}-\frac{\mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(-\frac{i \left(a x +i\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}-i\right)^{3} \pi  x}{8 a^{2}}-\frac{\mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}\right)^{3} \pi  x}{8 a^{2}}-\frac{i \mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(-\frac{i \left(a x +i\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}-i\right)^{3} \pi}{8 a^{3}}-\frac{i \mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right)^{3} \pi}{4 a^{3}}+\frac{i \mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}}\right)^{3} \pi}{4 a^{3}}+\frac{i \mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}\right)^{3} \pi}{8 a^{3}}-\frac{i \mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}}\right)^{2} \pi}{2 a^{3}}+\frac{i \mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}\right) \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)\right)^{2} \pi}{8 a^{3}}-\frac{\mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(-\frac{i \left(a x +i\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}-i\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}-i\right) \pi  x}{4 a^{2}}-\frac{\mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(-\frac{i \left(a x +i\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}-i\right) \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}-i\right)^{2} \pi  x}{8 a^{2}}+\frac{\mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \pi  x}{4 a^{2}}-\frac{\mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}\right) \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)\right)^{2} \pi  x}{8 a^{2}}-\frac{i \mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(-\frac{i \left(a x +i\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}-i\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}-i\right) \pi}{4 a^{3}}-\frac{i \mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(-\frac{i \left(a x +i\right)^{4}}{\left(a^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}-i\right) \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}-i\right)^{2} \pi}{8 a^{3}}-\frac{i \mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +i\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right) \pi}{4 a^{3}}+\frac{i \mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +i\right)}{\sqrt{a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right)^{2} \pi}{2 a^{3}}+\frac{i \mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}}\right)^{2} \pi}{4 a^{3}}+\frac{i \mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}}\right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}}\right) \pi}{4 a^{3}}-\frac{i \mathrm{arccot}\left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \pi}{4 a^{3}}-\frac{i \mathrm{arccot}\left(a x \right)^{3}}{3 a^{3}}+\frac{\mathrm{arccot}\left(a x \right)^{2} \ln \left(\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{3}}-\frac{\mathrm{arccot}\left(a x \right)^{2} \ln \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)}{a^{3}}+\frac{\mathrm{arccot}\left(a x \right)^{2} \ln \left(1+\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{3}}+\frac{\mathrm{arccot}\left(a x \right)^{2} \ln \left(1-\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{3}}+\frac{i \mathrm{arccot}\left(a x \right)}{a^{3}}+\frac{\mathrm{arccot}\left(a x \right)^{2}}{2 a^{3}}"," ",0,"x*arccot(a*x)/a^2+1/3*x^3*arccot(a*x)^3+1/2*x^2*arccot(a*x)^2/a-1/3*I*arccot(a*x)^3/a^3-1/2/a^3*arccot(a*x)^2*ln(a^2*x^2+1)+1/a^3*arccot(a*x)^2*ln((I+a*x)/(a^2*x^2+1)^(1/2))-1/a^3*arccot(a*x)^2*ln((I+a*x)^2/(a^2*x^2+1)-1)+1/a^3*arccot(a*x)^2*ln(1+(I+a*x)/(a^2*x^2+1)^(1/2))+1/a^3*arccot(a*x)^2*ln(1-(I+a*x)/(a^2*x^2+1)^(1/2))+I/a^3*arccot(a*x)+1/a^3*ln(2)*arccot(a*x)^2-1/a^3*ln((I+a*x)/(a^2*x^2+1)^(1/2)-1)-1/a^3*ln(1+(I+a*x)/(a^2*x^2+1)^(1/2))+2/a^3*polylog(3,-(I+a*x)/(a^2*x^2+1)^(1/2))+2/a^3*polylog(3,(I+a*x)/(a^2*x^2+1)^(1/2))-1/8/a^2*arccot(a*x)^2*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)^3*Pi*x+1/2*I/a^3*arccot(a*x)^2*Pi-2*I/a^3*arccot(a*x)*polylog(2,-(I+a*x)/(a^2*x^2+1)^(1/2))-2*I/a^3*arccot(a*x)*polylog(2,(I+a*x)/(a^2*x^2+1)^(1/2))-1/8/a^2*arccot(a*x)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)^3*Pi*x-1/8*I/a^3*arccot(a*x)^2*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)^3*Pi-1/4*I/a^3*arccot(a*x)^2*csgn(I*(I+a*x)^2/(a^2*x^2+1))^3*Pi+1/4*I/a^3*arccot(a*x)^2*csgn(I*(I+a*x)^2/(a^2*x^2+1)/((I+a*x)^2/(a^2*x^2+1)-1)^2)^3*Pi+1/8*I/a^3*arccot(a*x)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)^3*Pi-1/2*I/a^3*arccot(a*x)^2*csgn(I*(I+a*x)^2/(a^2*x^2+1)/((I+a*x)^2/(a^2*x^2+1)-1)^2)^2*Pi-1/4/a^2*arccot(a*x)^2*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)^2*csgn(I*(I+a*x)^2/(a^2*x^2+1)-I)*Pi*x-1/8/a^2*arccot(a*x)^2*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)*csgn(I*(I+a*x)^2/(a^2*x^2+1)-I)^2*Pi*x+1/4/a^2*arccot(a*x)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1))*Pi*x-1/8/a^2*arccot(a*x)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1))^2*Pi*x-1/4*I/a^3*arccot(a*x)^2*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)^2*csgn(I*(I+a*x)^2/(a^2*x^2+1)-I)*Pi-1/8*I/a^3*arccot(a*x)^2*csgn(-I*(I+a*x)^4/(a^2*x^2+1)^2+2*I*(I+a*x)^2/(a^2*x^2+1)-I)*csgn(I*(I+a*x)^2/(a^2*x^2+1)-I)^2*Pi-1/4*I/a^3*arccot(a*x)^2*csgn(I*(I+a*x)/(a^2*x^2+1)^(1/2))^2*csgn(I*(I+a*x)^2/(a^2*x^2+1))*Pi+1/2*I/a^3*arccot(a*x)^2*csgn(I*(I+a*x)/(a^2*x^2+1)^(1/2))*csgn(I*(I+a*x)^2/(a^2*x^2+1))^2*Pi+1/4*I/a^3*arccot(a*x)^2*csgn(I*(I+a*x)^2/(a^2*x^2+1))*csgn(I*(I+a*x)^2/(a^2*x^2+1)/((I+a*x)^2/(a^2*x^2+1)-1)^2)^2*Pi+1/4*I/a^3*arccot(a*x)^2*csgn(I*(I+a*x)^2/(a^2*x^2+1)/((I+a*x)^2/(a^2*x^2+1)-1)^2)^2*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)^2)*Pi-1/4*I/a^3*arccot(a*x)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1))*Pi+1/8*I/a^3*arccot(a*x)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1))^2*Pi+1/2*arccot(a*x)^2/a^3-1/4*I/a^3*arccot(a*x)^2*csgn(I*(I+a*x)^2/(a^2*x^2+1))*csgn(I*(I+a*x)^2/(a^2*x^2+1)/((I+a*x)^2/(a^2*x^2+1)-1)^2)*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)^2)*Pi","C"
27,1,162,89,0.729000," ","int(x*arccot(a*x)^3,x)","\frac{x^{2} \mathrm{arccot}\left(a x \right)^{3}}{2}+\frac{\mathrm{arccot}\left(a x \right)^{3}}{2 a^{2}}+\frac{3 x \mathrm{arccot}\left(a x \right)^{2}}{2 a}+\frac{3 i \mathrm{arccot}\left(a x \right)^{2}}{2 a^{2}}-\frac{3 \,\mathrm{arccot}\left(a x \right) \ln \left(1-\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{2}}-\frac{3 \,\mathrm{arccot}\left(a x \right) \ln \left(1+\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{2}}+\frac{3 i \polylog \left(2, -\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{2}}+\frac{3 i \polylog \left(2, \frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a^{2}}"," ",0,"1/2*x^2*arccot(a*x)^3+1/2*arccot(a*x)^3/a^2+3/2*x*arccot(a*x)^2/a+3/2*I*arccot(a*x)^2/a^2-3/a^2*arccot(a*x)*ln(1-(I+a*x)/(a^2*x^2+1)^(1/2))-3/a^2*arccot(a*x)*ln(1+(I+a*x)/(a^2*x^2+1)^(1/2))+3*I/a^2*polylog(2,-(I+a*x)/(a^2*x^2+1)^(1/2))+3*I/a^2*polylog(2,(I+a*x)/(a^2*x^2+1)^(1/2))","A"
28,1,199,89,0.447000," ","int(arccot(a*x)^3,x)","x \mathrm{arccot}\left(a x \right)^{3}+\frac{i \mathrm{arccot}\left(a x \right)^{3}}{a}-\frac{3 \mathrm{arccot}\left(a x \right)^{2} \ln \left(1+\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a}-\frac{3 \mathrm{arccot}\left(a x \right)^{2} \ln \left(1-\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a}+\frac{6 i \mathrm{arccot}\left(a x \right) \polylog \left(2, -\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a}+\frac{6 i \mathrm{arccot}\left(a x \right) \polylog \left(2, \frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a}-\frac{6 \polylog \left(3, \frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a}-\frac{6 \polylog \left(3, -\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{a}"," ",0,"x*arccot(a*x)^3+I*arccot(a*x)^3/a-3/a*arccot(a*x)^2*ln(1+(I+a*x)/(a^2*x^2+1)^(1/2))-3/a*arccot(a*x)^2*ln(1-(I+a*x)/(a^2*x^2+1)^(1/2))+6*I/a*arccot(a*x)*polylog(2,-(I+a*x)/(a^2*x^2+1)^(1/2))+6*I/a*arccot(a*x)*polylog(2,(I+a*x)/(a^2*x^2+1)^(1/2))-6/a*polylog(3,(I+a*x)/(a^2*x^2+1)^(1/2))-6/a*polylog(3,-(I+a*x)/(a^2*x^2+1)^(1/2))","B"
29,1,1050,152,0.566000," ","int(arccot(a*x)^3/x,x)","\ln \left(a x \right) \mathrm{arccot}\left(a x \right)^{3}+\mathrm{arccot}\left(a x \right)^{3} \ln \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)-\mathrm{arccot}\left(a x \right)^{3} \ln \left(1+\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{i \pi  \mathrm{csgn}\left(\frac{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{2} \mathrm{arccot}\left(a x \right)^{3}}{2}-6 \,\mathrm{arccot}\left(a x \right) \polylog \left(3, -\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{i \pi  \mathrm{csgn}\left(\frac{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{3} \mathrm{arccot}\left(a x \right)^{3}}{2}-\mathrm{arccot}\left(a x \right)^{3} \ln \left(1-\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{i \pi  \mathrm{arccot}\left(a x \right)^{3}}{2}-6 \,\mathrm{arccot}\left(a x \right) \polylog \left(3, \frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{3} \mathrm{arccot}\left(a x \right)^{3}}{2}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{csgn}\left(\frac{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{2} \mathrm{arccot}\left(a x \right)^{3}}{2}+\frac{3 i \polylog \left(4, -\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right)}{4}-\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{arccot}\left(a x \right)^{3}}{2}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{arccot}\left(a x \right)^{3}}{2}-6 i \polylog \left(4, \frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)+3 i \mathrm{arccot}\left(a x \right)^{2} \polylog \left(2, \frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{2} \mathrm{arccot}\left(a x \right)^{3}}{2}+\frac{3 \,\mathrm{arccot}\left(a x \right) \polylog \left(3, -\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right)}{2}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{csgn}\left(\frac{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{arccot}\left(a x \right)^{3}}{2}+3 i \mathrm{arccot}\left(a x \right)^{2} \polylog \left(2, -\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{3 i \mathrm{arccot}\left(a x \right)^{2} \polylog \left(2, -\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right)}{2}-6 i \polylog \left(4, -\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)"," ",0,"ln(a*x)*arccot(a*x)^3+arccot(a*x)^3*ln((I+a*x)^2/(a^2*x^2+1)-1)-arccot(a*x)^3*ln(1+(I+a*x)/(a^2*x^2+1)^(1/2))+1/2*I*Pi*csgn(1/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^2*arccot(a*x)^3-6*arccot(a*x)*polylog(3,-(I+a*x)/(a^2*x^2+1)^(1/2))-1/2*I*Pi*csgn(1/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^3*arccot(a*x)^3-arccot(a*x)^3*ln(1-(I+a*x)/(a^2*x^2+1)^(1/2))-1/2*I*Pi*arccot(a*x)^3-6*arccot(a*x)*polylog(3,(I+a*x)/(a^2*x^2+1)^(1/2))-6*I*polylog(4,-(I+a*x)/(a^2*x^2+1)^(1/2))+1/2*I*Pi*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^3*arccot(a*x)^3-1/2*I*Pi*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))*csgn(1/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^2*arccot(a*x)^3-3/2*I*arccot(a*x)^2*polylog(2,-(I+a*x)^2/(a^2*x^2+1))+3/4*I*polylog(4,-(I+a*x)^2/(a^2*x^2+1))-1/2*I*Pi*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)+1))*arccot(a*x)^3+1/2*I*Pi*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1))*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))*csgn(I*((I+a*x)^2/(a^2*x^2+1)+1))*arccot(a*x)^3-1/2*I*Pi*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1))*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^2*arccot(a*x)^3+3/2*arccot(a*x)*polylog(3,-(I+a*x)^2/(a^2*x^2+1))+1/2*I*Pi*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))*csgn(1/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))*arccot(a*x)^3-6*I*polylog(4,(I+a*x)/(a^2*x^2+1)^(1/2))+3*I*arccot(a*x)^2*polylog(2,-(I+a*x)/(a^2*x^2+1)^(1/2))+3*I*arccot(a*x)^2*polylog(2,(I+a*x)/(a^2*x^2+1)^(1/2))","C"
30,1,1576,86,1.585000," ","int(arccot(a*x)^3/x^2,x)","3 i a \,\mathrm{arccot}\left(a x \right) \polylog \left(2, -\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right)-3 a \ln \left(a x \right) \mathrm{arccot}\left(a x \right)^{2}+\frac{3 a \mathrm{arccot}\left(a x \right)^{2} \ln \left(a^{2} x^{2}+1\right)}{2}-3 a \ln \left(2\right) \mathrm{arccot}\left(a x \right)^{2}+i a \mathrm{arccot}\left(a x \right)^{3}-3 a \mathrm{arccot}\left(a x \right)^{2} \ln \left(\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)-\frac{3 i a \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{arccot}\left(a x \right)^{2} \pi}{2}+\frac{3 i a \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{arccot}\left(a x \right)^{2} \pi}{4}-\frac{3 i a \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}}\right)^{2} \mathrm{arccot}\left(a x \right)^{2} \pi}{4}-\frac{3 i a \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{arccot}\left(a x \right)^{2} \pi}{4}-\frac{3 i a \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +i\right)}{\sqrt{a^{2} x^{2}+1}}\right) \mathrm{arccot}\left(a x \right)^{2} \pi}{2}+\frac{3 i a \,\mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(a x +i\right)}{\sqrt{a^{2} x^{2}+1}}\right)^{2} \mathrm{arccot}\left(a x \right)^{2} \pi}{4}+\frac{3 i a \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)\right) \mathrm{arccot}\left(a x \right)^{2} \pi}{2}+\frac{3 i a \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)\right) \mathrm{arccot}\left(a x \right)^{2} \pi}{2}+\frac{3 i a \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{arccot}\left(a x \right)^{2} \pi}{2}+\frac{3 i a \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{csgn}\left(\frac{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{2} \mathrm{arccot}\left(a x \right)^{2} \pi}{2}-\frac{\mathrm{arccot}\left(a x \right)^{3}}{x}-\frac{3 i a \,\mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}\right) \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)\right)^{2} \mathrm{arccot}\left(a x \right)^{2} \pi}{4}-\frac{3 i a \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{csgn}\left(\frac{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right) \mathrm{arccot}\left(a x \right)^{2} \pi}{2}-\frac{3 a \polylog \left(3, -\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right)}{2}-\frac{3 i a \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}}\right)^{3} \mathrm{arccot}\left(a x \right)^{2} \pi}{4}-\frac{3 i a \mathrm{csgn}\left(i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}\right)^{3} \mathrm{arccot}\left(a x \right)^{2} \pi}{4}-\frac{3 i a \mathrm{csgn}\left(\frac{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{2} \mathrm{arccot}\left(a x \right)^{2} \pi}{2}+\frac{3 i a \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1\right)^{2}}\right)^{2} \mathrm{arccot}\left(a x \right)^{2} \pi}{2}+\frac{3 i a \mathrm{csgn}\left(\frac{i \left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right)^{3} \mathrm{arccot}\left(a x \right)^{2} \pi}{4}-\frac{3 i a \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{3} \mathrm{arccot}\left(a x \right)^{2} \pi}{2}+\frac{3 i a \mathrm{csgn}\left(\frac{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1}{\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}-1}\right)^{3} \mathrm{arccot}\left(a x \right)^{2} \pi}{2}"," ",0,"-3/2*I*a*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))*csgn(I*((I+a*x)^2/(a^2*x^2+1)+1))*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1))*arccot(a*x)^2*Pi+I*a*arccot(a*x)^3-3*a*ln(a*x)*arccot(a*x)^2+3/2*a*arccot(a*x)^2*ln(a^2*x^2+1)-3*a*arccot(a*x)^2*ln((I+a*x)/(a^2*x^2+1)^(1/2))-3*a*ln(2)*arccot(a*x)^2-3/4*I*a*csgn(I*(I+a*x)^2/(a^2*x^2+1)/((I+a*x)^2/(a^2*x^2+1)-1)^2)^3*arccot(a*x)^2*Pi+3/4*I*a*csgn(I*(I+a*x)^2/(a^2*x^2+1))^3*arccot(a*x)^2*Pi+3*I*a*arccot(a*x)*polylog(2,-(I+a*x)^2/(a^2*x^2+1))+3/4*I*a*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)^2)*csgn(I*(I+a*x)^2/(a^2*x^2+1)/((I+a*x)^2/(a^2*x^2+1)-1)^2)*csgn(I*(I+a*x)^2/(a^2*x^2+1))*arccot(a*x)^2*Pi+3/2*I*a*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)+1))*arccot(a*x)^2*Pi+3/2*I*a*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^2*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1))*arccot(a*x)^2*Pi+3/2*I*a*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))*csgn(1/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^2*arccot(a*x)^2*Pi-3/4*I*a*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)^2)*csgn(I*(I+a*x)^2/(a^2*x^2+1)/((I+a*x)^2/(a^2*x^2+1)-1)^2)^2*arccot(a*x)^2*Pi-3/4*I*a*csgn(I*(I+a*x)^2/(a^2*x^2+1)/((I+a*x)^2/(a^2*x^2+1)-1)^2)^2*csgn(I*(I+a*x)^2/(a^2*x^2+1))*arccot(a*x)^2*Pi-3/2*I*a*csgn(I*(I+a*x)^2/(a^2*x^2+1))^2*csgn(I*(I+a*x)/(a^2*x^2+1)^(1/2))*arccot(a*x)^2*Pi+3/4*I*a*csgn(I*(I+a*x)^2/(a^2*x^2+1))*csgn(I*(I+a*x)/(a^2*x^2+1)^(1/2))^2*arccot(a*x)^2*Pi+3/2*I*a*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)^2*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1))*arccot(a*x)^2*Pi-3/4*I*a*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1))^2*arccot(a*x)^2*Pi-3/2*I*a*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))*csgn(1/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))*arccot(a*x)^2*Pi-3/2*I*a*csgn(I/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^3*arccot(a*x)^2*Pi+3/2*I*a*csgn(1/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^3*arccot(a*x)^2*Pi-arccot(a*x)^3/x-3/2*a*polylog(3,-(I+a*x)^2/(a^2*x^2+1))-3/4*I*a*csgn(I*((I+a*x)^2/(a^2*x^2+1)-1)^2)^3*arccot(a*x)^2*Pi-3/2*I*a*csgn(1/((I+a*x)^2/(a^2*x^2+1)-1)*((I+a*x)^2/(a^2*x^2+1)+1))^2*arccot(a*x)^2*Pi+3/2*I*a*csgn(I*(I+a*x)^2/(a^2*x^2+1)/((I+a*x)^2/(a^2*x^2+1)-1)^2)^2*arccot(a*x)^2*Pi","C"
31,1,109,91,0.763000," ","int(arccot(a*x)^3/x^3,x)","-\frac{\mathrm{arccot}\left(a x \right)^{3}}{2 x^{2}}-\frac{a^{2} \mathrm{arccot}\left(a x \right)^{3}}{2}-\frac{3 i a^{2} \mathrm{arccot}\left(a x \right)^{2}}{2}+\frac{3 a \mathrm{arccot}\left(a x \right)^{2}}{2 x}+3 a^{2} \mathrm{arccot}\left(a x \right) \ln \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)-\frac{3 i a^{2} \polylog \left(2, -\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right)}{2}"," ",0,"-1/2*arccot(a*x)^3/x^2-1/2*a^2*arccot(a*x)^3-3/2*I*a^2*arccot(a*x)^2+3/2*a*arccot(a*x)^2/x+3*a^2*arccot(a*x)*ln((I+a*x)^2/(a^2*x^2+1)+1)-3/2*I*a^2*polylog(2,-(I+a*x)^2/(a^2*x^2+1))","A"
32,1,5029,150,5.041000," ","int(arccot(a*x)^3/x^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
33,1,158,134,1.591000," ","int(arccot(a*x)^3/x^5,x)","-\frac{\mathrm{arccot}\left(a x \right)^{3}}{4 x^{4}}+\frac{a^{4} \mathrm{arccot}\left(a x \right)^{3}}{4}+i a^{4} \mathrm{arccot}\left(a x \right)^{2}-\frac{a^{4} \mathrm{arccot}\left(a x \right)}{4}-\frac{3 a^{3} \mathrm{arccot}\left(a x \right)^{2}}{4 x}+\frac{i a^{4}}{4}+\frac{a^{3}}{4 x}-\frac{a^{2} \mathrm{arccot}\left(a x \right)}{4 x^{2}}+\frac{a \mathrm{arccot}\left(a x \right)^{2}}{4 x^{3}}-2 a^{4} \mathrm{arccot}\left(a x \right) \ln \left(\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}+1\right)+i a^{4} \polylog \left(2, -\frac{\left(a x +i\right)^{2}}{a^{2} x^{2}+1}\right)"," ",0,"-1/4*arccot(a*x)^3/x^4+1/4*a^4*arccot(a*x)^3+I*a^4*arccot(a*x)^2-1/4*a^4*arccot(a*x)-3/4*a^3*arccot(a*x)^2/x+1/4*I*a^4+1/4*a^3/x-1/4*a^2*arccot(a*x)/x^2+1/4*a*arccot(a*x)^2/x^3-2*a^4*arccot(a*x)*ln((I+a*x)^2/(a^2*x^2+1)+1)+I*a^4*polylog(2,-(I+a*x)^2/(a^2*x^2+1))","A"
34,0,0,12,1.836000," ","int(x^m*arccot(a*x)^3,x)","\int x^{m} \mathrm{arccot}\left(a x \right)^{3}\, dx"," ",0,"int(x^m*arccot(a*x)^3,x)","F"
35,0,0,12,1.351000," ","int(x^m*arccot(a*x)^2,x)","\int x^{m} \mathrm{arccot}\left(a x \right)^{2}\, dx"," ",0,"int(x^m*arccot(a*x)^2,x)","F"
36,0,0,55,1.655000," ","int(x^m*arccot(a*x),x)","\int x^{m} \mathrm{arccot}\left(a x \right)\, dx"," ",0,"int(x^m*arccot(a*x),x)","F"
37,1,38,32,0.050000," ","int(x^4*arccot(x)/(x^2+1),x)","\frac{x^{3} \mathrm{arccot}\left(x \right)}{3}-x \,\mathrm{arccot}\left(x \right)+\mathrm{arccot}\left(x \right) \arctan \left(x \right)+\frac{x^{2}}{6}-\frac{2 \ln \left(x^{2}+1\right)}{3}+\frac{\arctan \left(x \right)^{2}}{2}"," ",0,"1/3*x^3*arccot(x)-x*arccot(x)+arccot(x)*arctan(x)+1/6*x^2-2/3*ln(x^2+1)+1/2*arctan(x)^2","A"
38,1,128,53,0.179000," ","int(x^3*arccot(x)/(x^2+1),x)","\frac{x^{2} \mathrm{arccot}\left(x \right)}{2}-\frac{\mathrm{arccot}\left(x \right) \ln \left(x^{2}+1\right)}{2}+\frac{x}{2}-\frac{\arctan \left(x \right)}{2}+\frac{i \ln \left(x -i\right) \ln \left(x^{2}+1\right)}{4}-\frac{i \ln \left(x -i\right)^{2}}{8}-\frac{i \dilog \left(-\frac{i \left(x +i\right)}{2}\right)}{4}-\frac{i \ln \left(x -i\right) \ln \left(-\frac{i \left(x +i\right)}{2}\right)}{4}-\frac{i \ln \left(x +i\right) \ln \left(x^{2}+1\right)}{4}+\frac{i \ln \left(x +i\right)^{2}}{8}+\frac{i \dilog \left(\frac{i \left(x -i\right)}{2}\right)}{4}+\frac{i \ln \left(x +i\right) \ln \left(\frac{i \left(x -i\right)}{2}\right)}{4}"," ",0,"1/2*x^2*arccot(x)-1/2*arccot(x)*ln(x^2+1)+1/2*x-1/2*arctan(x)+1/4*I*ln(x-I)*ln(x^2+1)-1/8*I*ln(x-I)^2-1/4*I*dilog(-1/2*I*(x+I))-1/4*I*ln(x-I)*ln(-1/2*I*(x+I))-1/4*I*ln(x+I)*ln(x^2+1)+1/8*I*ln(x+I)^2+1/4*I*dilog(1/2*I*(x-I))+1/4*I*ln(x+I)*ln(1/2*I*(x-I))","B"
39,1,26,19,0.049000," ","int(x^2*arccot(x)/(x^2+1),x)","-\mathrm{arccot}\left(x \right) \arctan \left(x \right)+x \,\mathrm{arccot}\left(x \right)+\frac{\ln \left(x^{2}+1\right)}{2}-\frac{\arctan \left(x \right)^{2}}{2}"," ",0,"-arccot(x)*arctan(x)+x*arccot(x)+1/2*ln(x^2+1)-1/2*arctan(x)^2","A"
40,1,114,40,0.131000," ","int(x*arccot(x)/(x^2+1),x)","\frac{\mathrm{arccot}\left(x \right) \ln \left(x^{2}+1\right)}{2}-\frac{i \ln \left(x -i\right) \ln \left(x^{2}+1\right)}{4}+\frac{i \ln \left(x -i\right)^{2}}{8}+\frac{i \dilog \left(-\frac{i \left(x +i\right)}{2}\right)}{4}+\frac{i \ln \left(x -i\right) \ln \left(-\frac{i \left(x +i\right)}{2}\right)}{4}+\frac{i \ln \left(x +i\right) \ln \left(x^{2}+1\right)}{4}-\frac{i \ln \left(x +i\right)^{2}}{8}-\frac{i \dilog \left(\frac{i \left(x -i\right)}{2}\right)}{4}-\frac{i \ln \left(x +i\right) \ln \left(\frac{i \left(x -i\right)}{2}\right)}{4}"," ",0,"1/2*arccot(x)*ln(x^2+1)-1/4*I*ln(x-I)*ln(x^2+1)+1/8*I*ln(x-I)^2+1/4*I*dilog(-1/2*I*(x+I))+1/4*I*ln(x-I)*ln(-1/2*I*(x+I))+1/4*I*ln(x+I)*ln(x^2+1)-1/8*I*ln(x+I)^2-1/4*I*dilog(1/2*I*(x-I))-1/4*I*ln(x+I)*ln(1/2*I*(x-I))","B"
41,1,7,6,0.038000," ","int(arccot(x)/(x^2+1),x)","-\frac{\mathrm{arccot}\left(x \right)^{2}}{2}"," ",0,"-1/2*arccot(x)^2","A"
42,1,163,41,0.138000," ","int(arccot(x)/x/(x^2+1),x)","\mathrm{arccot}\left(x \right) \ln \left(x \right)-\frac{\mathrm{arccot}\left(x \right) \ln \left(x^{2}+1\right)}{2}-\frac{i \ln \left(x \right) \ln \left(i x +1\right)}{2}+\frac{i \ln \left(x \right) \ln \left(-i x +1\right)}{2}-\frac{i \dilog \left(i x +1\right)}{2}+\frac{i \dilog \left(-i x +1\right)}{2}+\frac{i \ln \left(x -i\right) \ln \left(x^{2}+1\right)}{4}-\frac{i \ln \left(x -i\right)^{2}}{8}-\frac{i \dilog \left(-\frac{i \left(x +i\right)}{2}\right)}{4}-\frac{i \ln \left(x -i\right) \ln \left(-\frac{i \left(x +i\right)}{2}\right)}{4}-\frac{i \ln \left(x +i\right) \ln \left(x^{2}+1\right)}{4}+\frac{i \ln \left(x +i\right)^{2}}{8}+\frac{i \dilog \left(\frac{i \left(x -i\right)}{2}\right)}{4}+\frac{i \ln \left(x +i\right) \ln \left(\frac{i \left(x -i\right)}{2}\right)}{4}"," ",0,"arccot(x)*ln(x)-1/2*arccot(x)*ln(x^2+1)-1/2*I*ln(x)*ln(1+I*x)+1/2*I*ln(x)*ln(1-I*x)-1/2*I*dilog(1+I*x)+1/2*I*dilog(1-I*x)+1/4*I*ln(x-I)*ln(x^2+1)-1/8*I*ln(x-I)^2-1/4*I*dilog(-1/2*I*(x+I))-1/4*I*ln(x-I)*ln(-1/2*I*(x+I))-1/4*I*ln(x+I)*ln(x^2+1)+1/8*I*ln(x+I)^2+1/4*I*dilog(1/2*I*(x-I))+1/4*I*ln(x+I)*ln(1/2*I*(x-I))","B"
43,1,33,26,0.054000," ","int(arccot(x)/x^2/(x^2+1),x)","-\frac{\mathrm{arccot}\left(x \right)}{x}-\mathrm{arccot}\left(x \right) \arctan \left(x \right)-\ln \left(x \right)+\frac{\ln \left(x^{2}+1\right)}{2}-\frac{\arctan \left(x \right)^{2}}{2}"," ",0,"-arccot(x)/x-arccot(x)*arctan(x)-ln(x)+1/2*ln(x^2+1)-1/2*arctan(x)^2","A"
44,1,180,58,0.109000," ","int(arccot(x)/x^3/(x^2+1),x)","-\frac{\mathrm{arccot}\left(x \right)}{2 x^{2}}-\mathrm{arccot}\left(x \right) \ln \left(x \right)+\frac{\mathrm{arccot}\left(x \right) \ln \left(x^{2}+1\right)}{2}+\frac{i \dilog \left(-\frac{i \left(x +i\right)}{2}\right)}{4}-\frac{i \ln \left(x +i\right) \ln \left(\frac{i \left(x -i\right)}{2}\right)}{4}-\frac{i \ln \left(x \right) \ln \left(-i x +1\right)}{2}+\frac{i \ln \left(x \right) \ln \left(i x +1\right)}{2}-\frac{i \ln \left(x -i\right) \ln \left(x^{2}+1\right)}{4}-\frac{i \dilog \left(\frac{i \left(x -i\right)}{2}\right)}{4}-\frac{i \ln \left(x +i\right)^{2}}{8}+\frac{i \dilog \left(i x +1\right)}{2}+\frac{1}{2 x}+\frac{\arctan \left(x \right)}{2}-\frac{i \dilog \left(-i x +1\right)}{2}+\frac{i \ln \left(x -i\right) \ln \left(-\frac{i \left(x +i\right)}{2}\right)}{4}+\frac{i \ln \left(x -i\right)^{2}}{8}+\frac{i \ln \left(x +i\right) \ln \left(x^{2}+1\right)}{4}"," ",0,"-1/2*arccot(x)/x^2-arccot(x)*ln(x)+1/2*arccot(x)*ln(x^2+1)+1/4*I*dilog(-1/2*I*(x+I))-1/4*I*ln(x+I)*ln(1/2*I*(x-I))-1/2*I*ln(x)*ln(1-I*x)+1/2*I*ln(x)*ln(1+I*x)-1/4*I*ln(x-I)*ln(x^2+1)-1/2*I*dilog(1-I*x)-1/8*I*ln(x+I)^2-1/4*I*dilog(1/2*I*(x-I))+1/2/x+1/2*arctan(x)+1/4*I*ln(x-I)*ln(-1/2*I*(x+I))+1/8*I*ln(x-I)^2+1/4*I*ln(x+I)*ln(x^2+1)+1/2*I*dilog(1+I*x)","B"
45,1,43,37,0.059000," ","int(arccot(x)/x^4/(x^2+1),x)","-\frac{\mathrm{arccot}\left(x \right)}{3 x^{3}}+\frac{\mathrm{arccot}\left(x \right)}{x}+\mathrm{arccot}\left(x \right) \arctan \left(x \right)+\frac{1}{6 x^{2}}+\frac{4 \ln \left(x \right)}{3}-\frac{2 \ln \left(x^{2}+1\right)}{3}+\frac{\arctan \left(x \right)^{2}}{2}"," ",0,"-1/3*arccot(x)/x^3+arccot(x)/x+arccot(x)*arctan(x)+1/6/x^2+4/3*ln(x)-2/3*ln(x^2+1)+1/2*arctan(x)^2","A"
46,1,265,174,0.736000," ","int(x^2*arccot(c*x)/(x^2+1),x)","-\mathrm{arccot}\left(c x \right) \arctan \left(x \right)+x \,\mathrm{arccot}\left(c x \right)+\frac{\ln \left(c^{2} x^{2}+1\right)}{2 c}+\frac{i c \ln \left(1-\frac{\left(1+c \right) \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(-1+c \right)}\right) \arctan \left(x \right)}{-2+2 c}-\frac{i \ln \left(1-\frac{\left(1+c \right) \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(-1+c \right)}\right) \arctan \left(x \right)}{2 \left(-1+c \right)}+\frac{c \arctan \left(x \right)^{2}}{-2+2 c}+\frac{c \polylog \left(2, \frac{\left(1+c \right) \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(-1+c \right)}\right)}{-4+4 c}-\frac{\arctan \left(x \right)^{2}}{2 \left(-1+c \right)}-\frac{\polylog \left(2, \frac{\left(1+c \right) \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(-1+c \right)}\right)}{4 \left(-1+c \right)}-\frac{i \arctan \left(x \right) \ln \left(1-\frac{\left(-1+c \right) \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(1+c \right)}\right)}{2}-\frac{\arctan \left(x \right)^{2}}{2}-\frac{\polylog \left(2, \frac{\left(-1+c \right) \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(1+c \right)}\right)}{4}"," ",0,"-arccot(c*x)*arctan(x)+x*arccot(c*x)+1/2*ln(c^2*x^2+1)/c+1/2*I*c/(-1+c)*ln(1-(1+c)*(1+I*x)^2/(x^2+1)/(-1+c))*arctan(x)-1/2*I/(-1+c)*ln(1-(1+c)*(1+I*x)^2/(x^2+1)/(-1+c))*arctan(x)+1/2*c/(-1+c)*arctan(x)^2+1/4*c/(-1+c)*polylog(2,(1+c)*(1+I*x)^2/(x^2+1)/(-1+c))-1/2/(-1+c)*arctan(x)^2-1/4/(-1+c)*polylog(2,(1+c)*(1+I*x)^2/(x^2+1)/(-1+c))-1/2*I*arctan(x)*ln(1-(-1+c)*(1+I*x)^2/(x^2+1)/(1+c))-1/2*arctan(x)^2-1/4*polylog(2,(-1+c)*(1+I*x)^2/(x^2+1)/(1+c))","A"
47,1,284,161,0.316000," ","int(x*arccot(c*x)/(x^2+1),x)","\frac{\ln \left(c^{2} x^{2}+c^{2}\right) \mathrm{arccot}\left(c x \right)}{2}+\frac{i \ln \left(c x -i\right) \ln \left(\frac{i \left(c x -i\right)-c -1}{-c -1}\right)}{4}+\frac{i \ln \left(c x -i\right) \ln \left(\frac{i \left(c x -i\right)+c -1}{-1+c}\right)}{4}-\frac{i \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+c^{2}\right)}{4}+\frac{i \dilog \left(\frac{i \left(c x -i\right)-c -1}{-c -1}\right)}{4}+\frac{i \dilog \left(\frac{i \left(c x -i\right)+c -1}{-1+c}\right)}{4}-\frac{i \ln \left(c x +i\right) \ln \left(\frac{-i \left(c x +i\right)-c -1}{-c -1}\right)}{4}-\frac{i \ln \left(c x +i\right) \ln \left(\frac{-i \left(c x +i\right)+c -1}{-1+c}\right)}{4}+\frac{i \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+c^{2}\right)}{4}-\frac{i \dilog \left(\frac{-i \left(c x +i\right)+c -1}{-1+c}\right)}{4}-\frac{i \dilog \left(\frac{-i \left(c x +i\right)-c -1}{-c -1}\right)}{4}"," ",0,"1/2*ln(c^2*x^2+c^2)*arccot(c*x)+1/4*I*ln(c*x-I)*ln((I*(c*x-I)-c-1)/(-c-1))+1/4*I*ln(c*x-I)*ln((I*(c*x-I)+c-1)/(-1+c))-1/4*I*ln(c*x-I)*ln(c^2*x^2+c^2)+1/4*I*dilog((I*(c*x-I)-c-1)/(-c-1))+1/4*I*dilog((I*(c*x-I)+c-1)/(-1+c))-1/4*I*ln(I+c*x)*ln((-I*(I+c*x)-c-1)/(-c-1))-1/4*I*ln(I+c*x)*ln((-I*(I+c*x)+c-1)/(-1+c))+1/4*I*ln(I+c*x)*ln(c^2*x^2+c^2)-1/4*I*dilog((-I*(I+c*x)+c-1)/(-1+c))-1/4*I*dilog((-I*(I+c*x)-c-1)/(-c-1))","A"
48,1,304,153,0.684000," ","int(arccot(c*x)/(x^2+1),x)","\mathrm{arccot}\left(c x \right) \arctan \left(x \right)+\arctan \left(c x \right) \arctan \left(x \right)+\frac{i \arctan \left(c x \right) \ln \left(1-\frac{\left(1+c \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(1-c \right)}\right)}{2}+\frac{\arctan \left(c x \right)^{2}}{2}+\frac{\polylog \left(2, \frac{\left(1+c \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(1-c \right)}\right)}{4}-\frac{i c \arctan \left(c x \right) \ln \left(1-\frac{\left(-1+c \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c -1\right)}\right)}{2 \left(1+c \right)}-\frac{i \ln \left(1-\frac{\left(-1+c \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c -1\right)}\right) \arctan \left(c x \right)}{2 \left(1+c \right)}-\frac{c \arctan \left(c x \right)^{2}}{2 \left(1+c \right)}-\frac{c \polylog \left(2, \frac{\left(-1+c \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c -1\right)}\right)}{4 \left(1+c \right)}-\frac{\arctan \left(c x \right)^{2}}{2 \left(1+c \right)}-\frac{\polylog \left(2, \frac{\left(-1+c \right) \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(-c -1\right)}\right)}{4 \left(1+c \right)}"," ",0,"arccot(c*x)*arctan(x)+arctan(c*x)*arctan(x)+1/2*I*arctan(c*x)*ln(1-(1+c)*(1+I*c*x)^2/(c^2*x^2+1)/(1-c))+1/2*arctan(c*x)^2+1/4*polylog(2,(1+c)*(1+I*c*x)^2/(c^2*x^2+1)/(1-c))-1/2*I*c/(1+c)*arctan(c*x)*ln(1-(-1+c)*(1+I*c*x)^2/(c^2*x^2+1)/(-c-1))-1/2*I/(1+c)*ln(1-(-1+c)*(1+I*c*x)^2/(c^2*x^2+1)/(-c-1))*arctan(c*x)-1/2*c/(1+c)*arctan(c*x)^2-1/4*c/(1+c)*polylog(2,(-1+c)*(1+I*c*x)^2/(c^2*x^2+1)/(-c-1))-1/2/(1+c)*arctan(c*x)^2-1/4/(1+c)*polylog(2,(-1+c)*(1+I*c*x)^2/(c^2*x^2+1)/(-c-1))","A"
49,1,345,188,0.257000," ","int(arccot(c*x)/x/(x^2+1),x)","\mathrm{arccot}\left(c x \right) \ln \left(c x \right)-\frac{\ln \left(c^{2} x^{2}+c^{2}\right) \mathrm{arccot}\left(c x \right)}{2}+\frac{i \dilog \left(\frac{-i \left(c x +i\right)+c -1}{-1+c}\right)}{4}-\frac{i \ln \left(c x -i\right) \ln \left(\frac{i \left(c x -i\right)-c -1}{-c -1}\right)}{4}+\frac{i \dilog \left(\frac{-i \left(c x +i\right)-c -1}{-c -1}\right)}{4}+\frac{i \ln \left(c x +i\right) \ln \left(\frac{-i \left(c x +i\right)-c -1}{-c -1}\right)}{4}+\frac{i \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}+\frac{i \ln \left(c x +i\right) \ln \left(\frac{-i \left(c x +i\right)+c -1}{-1+c}\right)}{4}-\frac{i \ln \left(c x \right) \ln \left(i c x +1\right)}{2}-\frac{i \dilog \left(i c x +1\right)}{2}-\frac{i \ln \left(c x -i\right) \ln \left(\frac{i \left(c x -i\right)+c -1}{-1+c}\right)}{4}-\frac{i \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+c^{2}\right)}{4}-\frac{i \dilog \left(\frac{i \left(c x -i\right)-c -1}{-c -1}\right)}{4}+\frac{i \dilog \left(-i c x +1\right)}{2}-\frac{i \dilog \left(\frac{i \left(c x -i\right)+c -1}{-1+c}\right)}{4}+\frac{i \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+c^{2}\right)}{4}"," ",0,"arccot(c*x)*ln(c*x)-1/2*ln(c^2*x^2+c^2)*arccot(c*x)-1/4*I*ln(c*x-I)*ln((I*(c*x-I)-c-1)/(-c-1))-1/4*I*dilog((I*(c*x-I)-c-1)/(-c-1))+1/4*I*ln(I+c*x)*ln((-I*(I+c*x)-c-1)/(-c-1))+1/4*I*dilog((-I*(I+c*x)+c-1)/(-1+c))+1/2*I*ln(c*x)*ln(1-I*c*x)+1/2*I*dilog(1-I*c*x)+1/4*I*ln(I+c*x)*ln((-I*(I+c*x)+c-1)/(-1+c))-1/2*I*ln(c*x)*ln(1+I*c*x)-1/4*I*ln(c*x-I)*ln((I*(c*x-I)+c-1)/(-1+c))-1/2*I*dilog(1+I*c*x)-1/4*I*ln(I+c*x)*ln(c^2*x^2+c^2)+1/4*I*dilog((-I*(I+c*x)-c-1)/(-c-1))-1/4*I*dilog((I*(c*x-I)+c-1)/(-1+c))+1/4*I*ln(c*x-I)*ln(c^2*x^2+c^2)","A"
50,1,271,180,0.077000," ","int(arccot(c*x)/x^2/(x^2+1),x)","-\mathrm{arccot}\left(c x \right) \arctan \left(x \right)-\frac{\mathrm{arccot}\left(c x \right)}{x}+\frac{c \ln \left(c^{2} x^{2}+1\right)}{2}-c \ln \left(x \right)+\frac{i c \ln \left(1-\frac{\left(1+c \right) \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(-1+c \right)}\right) \arctan \left(x \right)}{-2+2 c}-\frac{i \ln \left(1-\frac{\left(1+c \right) \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(-1+c \right)}\right) \arctan \left(x \right)}{2 \left(-1+c \right)}+\frac{c \arctan \left(x \right)^{2}}{-2+2 c}+\frac{c \polylog \left(2, \frac{\left(1+c \right) \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(-1+c \right)}\right)}{-4+4 c}-\frac{\arctan \left(x \right)^{2}}{2 \left(-1+c \right)}-\frac{\polylog \left(2, \frac{\left(1+c \right) \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(-1+c \right)}\right)}{4 \left(-1+c \right)}-\frac{i \arctan \left(x \right) \ln \left(1-\frac{\left(-1+c \right) \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(1+c \right)}\right)}{2}-\frac{\arctan \left(x \right)^{2}}{2}-\frac{\polylog \left(2, \frac{\left(-1+c \right) \left(i x +1\right)^{2}}{\left(x^{2}+1\right) \left(1+c \right)}\right)}{4}"," ",0,"-arccot(c*x)*arctan(x)-arccot(c*x)/x+1/2*c*ln(c^2*x^2+1)-c*ln(x)+1/2*I*c/(-1+c)*ln(1-(1+c)*(1+I*x)^2/(x^2+1)/(-1+c))*arctan(x)-1/2*I/(-1+c)*ln(1-(1+c)*(1+I*x)^2/(x^2+1)/(-1+c))*arctan(x)+1/2*c/(-1+c)*arctan(x)^2+1/4*c/(-1+c)*polylog(2,(1+c)*(1+I*x)^2/(x^2+1)/(-1+c))-1/2/(-1+c)*arctan(x)^2-1/4/(-1+c)*polylog(2,(1+c)*(1+I*x)^2/(x^2+1)/(-1+c))-1/2*I*arctan(x)*ln(1-(-1+c)*(1+I*x)^2/(x^2+1)/(1+c))-1/2*arctan(x)^2-1/4*polylog(2,(-1+c)*(1+I*x)^2/(x^2+1)/(1+c))","A"
51,1,6,5,0.036000," ","int(1/(x^2+1)/arccot(x),x)","-\ln \left(\mathrm{arccot}\left(x \right)\right)"," ",0,"-ln(arccot(x))","A"
52,1,14,13,0.041000," ","int(arccot(x)^n/(x^2+1),x)","-\frac{\mathrm{arccot}\left(x \right)^{1+n}}{1+n}"," ",0,"-arccot(x)^(1+n)/(1+n)","A"
53,1,279,226,0.041000," ","int((d*x^2+c)^4*arccot(a*x),x)","\frac{d^{4} x^{9} \mathrm{arccot}\left(a x \right)}{9}+\frac{4 c \,d^{3} x^{7} \mathrm{arccot}\left(a x \right)}{7}+\frac{6 c^{2} d^{2} x^{5} \mathrm{arccot}\left(a x \right)}{5}+\frac{4 c^{3} d \,x^{3} \mathrm{arccot}\left(a x \right)}{3}+c^{4} x \,\mathrm{arccot}\left(a x \right)+\frac{2 c^{3} d \,x^{2}}{3 a}+\frac{3 c^{2} d^{2} x^{4}}{10 a}+\frac{2 c \,d^{3} x^{6}}{21 a}-\frac{3 c^{2} d^{2} x^{2}}{5 a^{3}}+\frac{d^{4} x^{8}}{72 a}-\frac{x^{4} c \,d^{3}}{7 a^{3}}-\frac{d^{4} x^{6}}{54 a^{3}}+\frac{2 x^{2} c \,d^{3}}{7 a^{5}}+\frac{d^{4} x^{4}}{36 a^{5}}-\frac{x^{2} d^{4}}{18 a^{7}}+\frac{\ln \left(a^{2} x^{2}+1\right) c^{4}}{2 a}-\frac{2 \ln \left(a^{2} x^{2}+1\right) c^{3} d}{3 a^{3}}+\frac{3 \ln \left(a^{2} x^{2}+1\right) c^{2} d^{2}}{5 a^{5}}-\frac{2 \ln \left(a^{2} x^{2}+1\right) c \,d^{3}}{7 a^{7}}+\frac{\ln \left(a^{2} x^{2}+1\right) d^{4}}{18 a^{9}}"," ",0,"1/9*d^4*x^9*arccot(a*x)+4/7*c*d^3*x^7*arccot(a*x)+6/5*c^2*d^2*x^5*arccot(a*x)+4/3*c^3*d*x^3*arccot(a*x)+c^4*x*arccot(a*x)+2/3/a*c^3*d*x^2+3/10/a*c^2*d^2*x^4+2/21/a*c*d^3*x^6-3/5/a^3*c^2*d^2*x^2+1/72*d^4*x^8/a-1/7/a^3*x^4*c*d^3-1/54/a^3*d^4*x^6+2/7/a^5*x^2*c*d^3+1/36/a^5*d^4*x^4-1/18/a^7*x^2*d^4+1/2/a*ln(a^2*x^2+1)*c^4-2/3/a^3*ln(a^2*x^2+1)*c^3*d+3/5/a^5*ln(a^2*x^2+1)*c^2*d^2-2/7/a^7*ln(a^2*x^2+1)*c*d^3+1/18/a^9*ln(a^2*x^2+1)*d^4","A"
54,1,191,156,0.043000," ","int((d*x^2+c)^3*arccot(a*x),x)","\frac{d^{3} x^{7} \mathrm{arccot}\left(a x \right)}{7}+\frac{3 c \,d^{2} x^{5} \mathrm{arccot}\left(a x \right)}{5}+c^{2} d \,x^{3} \mathrm{arccot}\left(a x \right)+c^{3} x \,\mathrm{arccot}\left(a x \right)+\frac{c^{2} d \,x^{2}}{2 a}+\frac{3 x^{4} c \,d^{2}}{20 a}+\frac{d^{3} x^{6}}{42 a}-\frac{3 c \,d^{2} x^{2}}{10 a^{3}}-\frac{d^{3} x^{4}}{28 a^{3}}+\frac{d^{3} x^{2}}{14 a^{5}}+\frac{c^{3} \ln \left(a^{2} x^{2}+1\right)}{2 a}-\frac{\ln \left(a^{2} x^{2}+1\right) c^{2} d}{2 a^{3}}+\frac{3 \ln \left(a^{2} x^{2}+1\right) c \,d^{2}}{10 a^{5}}-\frac{\ln \left(a^{2} x^{2}+1\right) d^{3}}{14 a^{7}}"," ",0,"1/7*d^3*x^7*arccot(a*x)+3/5*c*d^2*x^5*arccot(a*x)+c^2*d*x^3*arccot(a*x)+c^3*x*arccot(a*x)+1/2*c^2*d*x^2/a+3/20/a*x^4*c*d^2+1/42*d^3*x^6/a-3/10/a^3*c*d^2*x^2-1/28/a^3*d^3*x^4+1/14/a^5*d^3*x^2+1/2*c^3*ln(a^2*x^2+1)/a-1/2/a^3*ln(a^2*x^2+1)*c^2*d+3/10/a^5*ln(a^2*x^2+1)*c*d^2-1/14/a^7*ln(a^2*x^2+1)*d^3","A"
55,1,119,99,0.041000," ","int((d*x^2+c)^2*arccot(a*x),x)","\frac{d^{2} x^{5} \mathrm{arccot}\left(a x \right)}{5}+\frac{2 c d \,x^{3} \mathrm{arccot}\left(a x \right)}{3}+c^{2} x \,\mathrm{arccot}\left(a x \right)+\frac{d c \,x^{2}}{3 a}+\frac{d^{2} x^{4}}{20 a}-\frac{x^{2} d^{2}}{10 a^{3}}+\frac{c^{2} \ln \left(a^{2} x^{2}+1\right)}{2 a}-\frac{\ln \left(a^{2} x^{2}+1\right) c d}{3 a^{3}}+\frac{\ln \left(a^{2} x^{2}+1\right) d^{2}}{10 a^{5}}"," ",0,"1/5*d^2*x^5*arccot(a*x)+2/3*c*d*x^3*arccot(a*x)+c^2*x*arccot(a*x)+1/3/a*d*c*x^2+1/20*d^2*x^4/a-1/10/a^3*x^2*d^2+1/2*c^2*ln(a^2*x^2+1)/a-1/3/a^3*ln(a^2*x^2+1)*c*d+1/10/a^5*ln(a^2*x^2+1)*d^2","A"
56,1,60,52,0.041000," ","int((d*x^2+c)*arccot(a*x),x)","\frac{d \,x^{3} \mathrm{arccot}\left(a x \right)}{3}+c x \,\mathrm{arccot}\left(a x \right)+\frac{d \,x^{2}}{6 a}+\frac{c \ln \left(a^{2} x^{2}+1\right)}{2 a}-\frac{\ln \left(a^{2} x^{2}+1\right) d}{6 a^{3}}"," ",0,"1/3*d*x^3*arccot(a*x)+c*x*arccot(a*x)+1/6*d*x^2/a+1/2*c*ln(a^2*x^2+1)/a-1/6/a^3*ln(a^2*x^2+1)*d","A"
57,1,826,285,0.722000," ","int(arccot(a*x)/(d*x^2+c),x)","-\frac{i \sqrt{a^{2} c d}\, \mathrm{arccot}\left(a x \right) \ln \left(1-\frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c +2 \sqrt{a^{2} c d}+d \right)}\right)}{2 a c d}-\frac{\sqrt{a^{2} c d}\, \mathrm{arccot}\left(a x \right)^{2}}{2 a c d}-\frac{\sqrt{a^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c +2 \sqrt{a^{2} c d}+d \right)}\right)}{4 a c d}+\frac{i a^{3} \ln \left(1-\frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c -2 \sqrt{a^{2} c d}+d \right)}\right) \mathrm{arccot}\left(a x \right) \sqrt{a^{2} c d}\, c}{2 d \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}-\frac{i a \ln \left(1-\frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c -2 \sqrt{a^{2} c d}+d \right)}\right) \mathrm{arccot}\left(a x \right) \sqrt{a^{2} c d}}{a^{4} c^{2}-2 a^{2} c d +d^{2}}+\frac{a^{3} \mathrm{arccot}\left(a x \right)^{2} \sqrt{a^{2} c d}\, c}{2 d \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}-\frac{a \mathrm{arccot}\left(a x \right)^{2} \sqrt{a^{2} c d}}{a^{4} c^{2}-2 a^{2} c d +d^{2}}+\frac{i \ln \left(1-\frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c -2 \sqrt{a^{2} c d}+d \right)}\right) \mathrm{arccot}\left(a x \right) \sqrt{a^{2} c d}\, d}{2 a c \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}+\frac{a^{3} \polylog \left(2, \frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c -2 \sqrt{a^{2} c d}+d \right)}\right) \sqrt{a^{2} c d}\, c}{4 d \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}-\frac{a \polylog \left(2, \frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c -2 \sqrt{a^{2} c d}+d \right)}\right) \sqrt{a^{2} c d}}{2 \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}+\frac{\mathrm{arccot}\left(a x \right)^{2} \sqrt{a^{2} c d}\, d}{2 a c \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}+\frac{\polylog \left(2, \frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c -2 \sqrt{a^{2} c d}+d \right)}\right) \sqrt{a^{2} c d}\, d}{4 a c \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}"," ",0,"-1/2*I/a*(a^2*c*d)^(1/2)/c/d*arccot(a*x)*ln(1-(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c+2*(a^2*c*d)^(1/2)+d))-1/2/a*(a^2*c*d)^(1/2)/c/d*arccot(a*x)^2-1/4/a*(a^2*c*d)^(1/2)/c/d*polylog(2,(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c+2*(a^2*c*d)^(1/2)+d))+1/2*I*a^3*ln(1-(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c-2*(a^2*c*d)^(1/2)+d))*arccot(a*x)/d/(a^4*c^2-2*a^2*c*d+d^2)*(a^2*c*d)^(1/2)*c-I*a*ln(1-(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c-2*(a^2*c*d)^(1/2)+d))*arccot(a*x)/(a^4*c^2-2*a^2*c*d+d^2)*(a^2*c*d)^(1/2)+1/2*a^3*arccot(a*x)^2/d/(a^4*c^2-2*a^2*c*d+d^2)*(a^2*c*d)^(1/2)*c-a*arccot(a*x)^2/(a^4*c^2-2*a^2*c*d+d^2)*(a^2*c*d)^(1/2)+1/2*I/a*ln(1-(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c-2*(a^2*c*d)^(1/2)+d))*arccot(a*x)/c/(a^4*c^2-2*a^2*c*d+d^2)*(a^2*c*d)^(1/2)*d+1/4*a^3*polylog(2,(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c-2*(a^2*c*d)^(1/2)+d))/d/(a^4*c^2-2*a^2*c*d+d^2)*(a^2*c*d)^(1/2)*c-1/2*a*polylog(2,(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c-2*(a^2*c*d)^(1/2)+d))/(a^4*c^2-2*a^2*c*d+d^2)*(a^2*c*d)^(1/2)+1/2/a*arccot(a*x)^2/c/(a^4*c^2-2*a^2*c*d+d^2)*(a^2*c*d)^(1/2)*d+1/4/a*polylog(2,(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c-2*(a^2*c*d)^(1/2)+d))/c/(a^4*c^2-2*a^2*c*d+d^2)*(a^2*c*d)^(1/2)*d","B"
58,1,2177,593,0.803000," ","int(arccot(a*x)/(d*x^2+c)^2,x)","\frac{a^{4} \mathrm{arccot}\left(a x \right) x}{2 \left(a^{2} c -d \right) \left(a^{2} d \,x^{2}+a^{2} c \right)}-\frac{i a^{3} \mathrm{arccot}\left(a x \right)}{2 \left(a^{2} c -d \right) \left(a^{2} d \,x^{2}+a^{2} c \right)}-\frac{\sqrt{a^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c -2 \sqrt{a^{2} c d}+d \right)}\right)}{8 a \,c^{2} \left(a^{2} c -d \right)}+\frac{3 a^{3} \polylog \left(2, \frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c +2 \sqrt{a^{2} c d}+d \right)}\right) \sqrt{a^{2} c d}}{8 \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right) \left(a^{2} c -d \right)}+\frac{\sqrt{d c}\, \arctanh \left(\frac{\frac{2 \left(a^{2} c -d \right) \left(a x +i\right)^{2}}{a^{2} x^{2}+1}-2 a^{2} c -2 d}{4 a \sqrt{d c}}\right)}{4 c^{2} \left(a^{2} c -d \right)}+\frac{\sqrt{d c}\, d \arctanh \left(\frac{\frac{2 \left(a^{2} c -d \right) \left(a x +i\right)^{2}}{a^{2} x^{2}+1}-2 a^{2} c -2 d}{4 a \sqrt{d c}}\right)}{4 c^{2} \left(a^{2} c -d \right)^{2}}-\frac{a^{4} \sqrt{d c}\, \arctanh \left(\frac{\frac{2 \left(a^{2} c -d \right) \left(a x +i\right)^{2}}{a^{2} x^{2}+1}-2 a^{2} c -2 d}{4 a \sqrt{d c}}\right)}{4 d \left(a^{2} c -d \right)^{2}}-\frac{a d \ln \left(\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{c \left(a^{2} c -d \right)^{2}}+\frac{a d \ln \left(\frac{\left(a x +i\right)^{4} a^{2} c}{\left(a^{2} x^{2}+1\right)^{2}}-\frac{2 a^{2} c \left(a x +i\right)^{2}}{a^{2} x^{2}+1}-\frac{\left(a x +i\right)^{4} d}{\left(a^{2} x^{2}+1\right)^{2}}+a^{2} c -\frac{2 \left(a x +i\right)^{2} d}{a^{2} x^{2}+1}-d \right)}{4 c \left(a^{2} c -d \right)^{2}}+\frac{a \sqrt{a^{2} c d}\, \mathrm{arccot}\left(a x \right)^{2}}{4 \left(a^{2} c -d \right) c d}+\frac{3 i a^{3} \ln \left(1-\frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c +2 \sqrt{a^{2} c d}+d \right)}\right) \mathrm{arccot}\left(a x \right) \sqrt{a^{2} c d}}{4 \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right) \left(a^{2} c -d \right)}-\frac{i \sqrt{a^{2} c d}\, \mathrm{arccot}\left(a x \right) \ln \left(1-\frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c -2 \sqrt{a^{2} c d}+d \right)}\right)}{4 a \,c^{2} \left(a^{2} c -d \right)}-\frac{a^{5} \polylog \left(2, \frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c +2 \sqrt{a^{2} c d}+d \right)}\right) \sqrt{a^{2} c d}\, c}{8 \left(a^{2} c -d \right) d \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}+\frac{d^{2} \polylog \left(2, \frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c +2 \sqrt{a^{2} c d}+d \right)}\right) \sqrt{a^{2} c d}}{8 a \,c^{2} \left(a^{2} c -d \right) \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}-\frac{3 a d \polylog \left(2, \frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c +2 \sqrt{a^{2} c d}+d \right)}\right) \sqrt{a^{2} c d}}{8 \left(a^{2} c -d \right) c \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}+\frac{a \sqrt{a^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c -2 \sqrt{a^{2} c d}+d \right)}\right)}{8 \left(a^{2} c -d \right) c d}+\frac{a^{2} \sqrt{d c}\, \arctanh \left(\frac{\frac{2 \left(a^{2} c -d \right) \left(a x +i\right)^{2}}{a^{2} x^{2}+1}-2 a^{2} c -2 d}{4 a \sqrt{d c}}\right)}{4 d c \left(a^{2} c -d \right)}-\frac{a^{5} \mathrm{arccot}\left(a x \right)^{2} \sqrt{a^{2} c d}\, c}{4 \left(a^{2} c -d \right) d \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}-\frac{3 a d \mathrm{arccot}\left(a x \right)^{2} \sqrt{a^{2} c d}}{4 \left(a^{2} c -d \right) c \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}+\frac{d^{2} \mathrm{arccot}\left(a x \right)^{2} \sqrt{a^{2} c d}}{4 a \,c^{2} \left(a^{2} c -d \right) \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}-\frac{a^{2} \mathrm{arccot}\left(a x \right) x d}{2 c \left(a^{2} c -d \right) \left(a^{2} d \,x^{2}+a^{2} c \right)}+\frac{3 a^{3} \mathrm{arccot}\left(a x \right)^{2} \sqrt{a^{2} c d}}{4 \left(a^{2} c -d \right) \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}-\frac{\sqrt{a^{2} c d}\, \mathrm{arccot}\left(a x \right)^{2}}{4 a \,c^{2} \left(a^{2} c -d \right)}-\frac{a^{3} \ln \left(\frac{\left(a x +i\right)^{4} a^{2} c}{\left(a^{2} x^{2}+1\right)^{2}}-\frac{2 a^{2} c \left(a x +i\right)^{2}}{a^{2} x^{2}+1}-\frac{\left(a x +i\right)^{4} d}{\left(a^{2} x^{2}+1\right)^{2}}+a^{2} c -\frac{2 \left(a x +i\right)^{2} d}{a^{2} x^{2}+1}-d \right)}{4 \left(a^{2} c -d \right)^{2}}+\frac{a^{3} \ln \left(\frac{a x +i}{\sqrt{a^{2} x^{2}+1}}\right)}{\left(a^{2} c -d \right)^{2}}-\frac{i a^{3} \mathrm{arccot}\left(a x \right) x^{2} d}{2 c \left(a^{2} c -d \right) \left(a^{2} d \,x^{2}+a^{2} c \right)}+\frac{i a \sqrt{a^{2} c d}\, \mathrm{arccot}\left(a x \right) \ln \left(1-\frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c -2 \sqrt{a^{2} c d}+d \right)}\right)}{4 \left(a^{2} c -d \right) c d}-\frac{3 i a \ln \left(1-\frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c +2 \sqrt{a^{2} c d}+d \right)}\right) \mathrm{arccot}\left(a x \right) d \sqrt{a^{2} c d}}{4 \left(a^{2} c -d \right) c \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}-\frac{i a^{5} \ln \left(1-\frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c +2 \sqrt{a^{2} c d}+d \right)}\right) \mathrm{arccot}\left(a x \right) \sqrt{a^{2} c d}\, c}{4 \left(a^{2} c -d \right) d \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}+\frac{i d^{2} \ln \left(1-\frac{\left(a^{2} c -d \right) \left(a x +i\right)^{2}}{\left(a^{2} x^{2}+1\right) \left(a^{2} c +2 \sqrt{a^{2} c d}+d \right)}\right) \mathrm{arccot}\left(a x \right) \sqrt{a^{2} c d}}{4 a \,c^{2} \left(a^{2} c -d \right) \left(a^{4} c^{2}-2 a^{2} c d +d^{2}\right)}"," ",0,"-1/8/a*(a^2*c*d)^(1/2)/c^2/(a^2*c-d)*polylog(2,(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c-2*(a^2*c*d)^(1/2)+d))+3/8*a^3/(a^4*c^2-2*a^2*c*d+d^2)/(a^2*c-d)*polylog(2,(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c+2*(a^2*c*d)^(1/2)+d))*(a^2*c*d)^(1/2)+1/2*a^4*arccot(a*x)/(a^2*c-d)/(a^2*d*x^2+a^2*c)*x+1/4*(d*c)^(1/2)/c^2*d*arctanh(1/4*(2*(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)-2*a^2*c-2*d)/a/(d*c)^(1/2))/(a^2*c-d)^2-1/2*I*a^3*arccot(a*x)/(a^2*c-d)/(a^2*d*x^2+a^2*c)+1/4*(d*c)^(1/2)/c^2*arctanh(1/4*(2*(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)-2*a^2*c-2*d)/a/(d*c)^(1/2))/(a^2*c-d)+3/4*I*a^3*ln(1-(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c+2*(a^2*c*d)^(1/2)+d))*arccot(a*x)/(a^4*c^2-2*a^2*c*d+d^2)/(a^2*c-d)*(a^2*c*d)^(1/2)-1/4*I/a*(a^2*c*d)^(1/2)/c^2/(a^2*c-d)*arccot(a*x)*ln(1-(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c-2*(a^2*c*d)^(1/2)+d))-1/4*a^3/(a^2*c-d)^2*ln((I+a*x)^4/(a^2*x^2+1)^2*a^2*c-2*a^2*c*(I+a*x)^2/(a^2*x^2+1)-(I+a*x)^4/(a^2*x^2+1)^2*d+a^2*c-2*(I+a*x)^2/(a^2*x^2+1)*d-d)+1/8*a*(a^2*c*d)^(1/2)/(a^2*c-d)/c/d*polylog(2,(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c-2*(a^2*c*d)^(1/2)+d))+1/4*a*(a^2*c*d)^(1/2)/(a^2*c-d)/c/d*arccot(a*x)^2+1/4*a^2*(d*c)^(1/2)/d/c*arctanh(1/4*(2*(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)-2*a^2*c-2*d)/a/(d*c)^(1/2))/(a^2*c-d)+a^3/(a^2*c-d)^2*ln((I+a*x)/(a^2*x^2+1)^(1/2))-1/4*a^4*(d*c)^(1/2)/d*arctanh(1/4*(2*(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)-2*a^2*c-2*d)/a/(d*c)^(1/2))/(a^2*c-d)^2-3/4*I*a*ln(1-(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c+2*(a^2*c*d)^(1/2)+d))*arccot(a*x)*d/(a^2*c-d)/c/(a^4*c^2-2*a^2*c*d+d^2)*(a^2*c*d)^(1/2)-1/4*I*a^5*ln(1-(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c+2*(a^2*c*d)^(1/2)+d))*arccot(a*x)/(a^2*c-d)/d/(a^4*c^2-2*a^2*c*d+d^2)*(a^2*c*d)^(1/2)*c+1/4*I/a*d^2*ln(1-(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c+2*(a^2*c*d)^(1/2)+d))*arccot(a*x)/c^2/(a^2*c-d)/(a^4*c^2-2*a^2*c*d+d^2)*(a^2*c*d)^(1/2)-1/8*a^5/(a^2*c-d)/d/(a^4*c^2-2*a^2*c*d+d^2)*polylog(2,(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c+2*(a^2*c*d)^(1/2)+d))*(a^2*c*d)^(1/2)*c+1/8/a/c^2*d^2/(a^2*c-d)/(a^4*c^2-2*a^2*c*d+d^2)*polylog(2,(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c+2*(a^2*c*d)^(1/2)+d))*(a^2*c*d)^(1/2)-3/8*a/(a^2*c-d)/c/(a^4*c^2-2*a^2*c*d+d^2)*d*polylog(2,(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c+2*(a^2*c*d)^(1/2)+d))*(a^2*c*d)^(1/2)-1/4*a^5/(a^2*c-d)/d/(a^4*c^2-2*a^2*c*d+d^2)*arccot(a*x)^2*(a^2*c*d)^(1/2)*c-3/4*a/(a^2*c-d)/c/(a^4*c^2-2*a^2*c*d+d^2)*d*arccot(a*x)^2*(a^2*c*d)^(1/2)+1/4/a/c^2*d^2/(a^2*c-d)/(a^4*c^2-2*a^2*c*d+d^2)*arccot(a*x)^2*(a^2*c*d)^(1/2)-1/2*a^2*arccot(a*x)/c/(a^2*c-d)/(a^2*d*x^2+a^2*c)*x*d-a/c/(a^2*c-d)^2*d*ln((I+a*x)/(a^2*x^2+1)^(1/2))+1/4*a/c/(a^2*c-d)^2*d*ln((I+a*x)^4/(a^2*x^2+1)^2*a^2*c-2*a^2*c*(I+a*x)^2/(a^2*x^2+1)-(I+a*x)^4/(a^2*x^2+1)^2*d+a^2*c-2*(I+a*x)^2/(a^2*x^2+1)*d-d)+3/4*a^3/(a^2*c-d)/(a^4*c^2-2*a^2*c*d+d^2)*arccot(a*x)^2*(a^2*c*d)^(1/2)-1/4/a*(a^2*c*d)^(1/2)/c^2/(a^2*c-d)*arccot(a*x)^2-1/2*I*a^3*arccot(a*x)/c/(a^2*c-d)/(a^2*d*x^2+a^2*c)*x^2*d+1/4*I*a*(a^2*c*d)^(1/2)/(a^2*c-d)/c/d*arccot(a*x)*ln(1-(a^2*c-d)*(I+a*x)^2/(a^2*x^2+1)/(a^2*c-2*(a^2*c*d)^(1/2)+d))","B"
59,0,0,16,1.395000," ","int((d*x^2+c)^(1/2)*arccot(a*x),x)","\int \sqrt{d \,x^{2}+c}\, \mathrm{arccot}\left(a x \right)\, dx"," ",0,"int((d*x^2+c)^(1/2)*arccot(a*x),x)","F"
60,0,0,16,1.294000," ","int(arccot(a*x)/(d*x^2+c)^(1/2),x)","\int \frac{\mathrm{arccot}\left(a x \right)}{\sqrt{d \,x^{2}+c}}\, dx"," ",0,"int(arccot(a*x)/(d*x^2+c)^(1/2),x)","F"
61,0,0,58,1.201000," ","int(arccot(a*x)/(d*x^2+c)^(3/2),x)","\int \frac{\mathrm{arccot}\left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arccot(a*x)/(d*x^2+c)^(3/2),x)","F"
62,0,0,114,1.201000," ","int(arccot(a*x)/(d*x^2+c)^(5/2),x)","\int \frac{\mathrm{arccot}\left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(arccot(a*x)/(d*x^2+c)^(5/2),x)","F"
63,0,0,180,1.175000," ","int(arccot(a*x)/(d*x^2+c)^(7/2),x)","\int \frac{\mathrm{arccot}\left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{7}{2}}}\, dx"," ",0,"int(arccot(a*x)/(d*x^2+c)^(7/2),x)","F"
64,0,0,257,1.199000," ","int(arccot(a*x)/(d*x^2+c)^(9/2),x)","\int \frac{\mathrm{arccot}\left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{9}{2}}}\, dx"," ",0,"int(arccot(a*x)/(d*x^2+c)^(9/2),x)","F"
65,1,117,148,1.073000," ","int((a*x^2+a)^(1/2)*arccot(x),x)","\frac{\sqrt{a \left(x +i\right) \left(x -i\right)}\, \left(x \,\mathrm{arccot}\left(x \right)+1\right)}{2}-\frac{i \sqrt{a \left(x +i\right) \left(x -i\right)}\, \left(i \mathrm{arccot}\left(x \right) \ln \left(1+\frac{x +i}{\sqrt{x^{2}+1}}\right)-i \mathrm{arccot}\left(x \right) \ln \left(1-\frac{x +i}{\sqrt{x^{2}+1}}\right)+\polylog \left(2, -\frac{x +i}{\sqrt{x^{2}+1}}\right)-\polylog \left(2, \frac{x +i}{\sqrt{x^{2}+1}}\right)\right)}{2 \sqrt{x^{2}+1}}"," ",0,"1/2*(a*(x+I)*(x-I))^(1/2)*(x*arccot(x)+1)-1/2*I*(a*(x+I)*(x-I))^(1/2)*(I*arccot(x)*ln(1+(x+I)/(x^2+1)^(1/2))-I*arccot(x)*ln(1-(x+I)/(x^2+1)^(1/2))+polylog(2,-(x+I)/(x^2+1)^(1/2))-polylog(2,(x+I)/(x^2+1)^(1/2)))/(x^2+1)^(1/2)","A"
66,1,99,120,0.919000," ","int(arccot(x)/(a*x^2+a)^(1/2),x)","\frac{i \left(i \mathrm{arccot}\left(x \right) \ln \left(1-\frac{x +i}{\sqrt{x^{2}+1}}\right)-i \mathrm{arccot}\left(x \right) \ln \left(1+\frac{x +i}{\sqrt{x^{2}+1}}\right)+\polylog \left(2, \frac{x +i}{\sqrt{x^{2}+1}}\right)-\polylog \left(2, -\frac{x +i}{\sqrt{x^{2}+1}}\right)\right) \sqrt{a \left(x +i\right) \left(x -i\right)}}{\sqrt{x^{2}+1}\, a}"," ",0,"I*(I*ln(1-(x+I)/(x^2+1)^(1/2))*arccot(x)-I*ln(1+(x+I)/(x^2+1)^(1/2))*arccot(x)+polylog(2,(x+I)/(x^2+1)^(1/2))-polylog(2,-(x+I)/(x^2+1)^(1/2)))*(a*(x+I)*(x-I))^(1/2)/(x^2+1)^(1/2)/a","A"
67,1,68,31,0.700000," ","int(arccot(x)/(a*x^2+a)^(3/2),x)","\frac{\left(i+\mathrm{arccot}\left(x \right)\right) \left(x +i\right) \sqrt{a \left(x +i\right) \left(x -i\right)}}{2 \left(x^{2}+1\right) a^{2}}+\frac{\sqrt{a \left(x +i\right) \left(x -i\right)}\, \left(x -i\right) \left(\mathrm{arccot}\left(x \right)-i\right)}{2 \left(x^{2}+1\right) a^{2}}"," ",0,"1/2*(I+arccot(x))*(x+I)*(a*(x+I)*(x-I))^(1/2)/(x^2+1)/a^2+1/2*(a*(x+I)*(x-I))^(1/2)*(x-I)*(arccot(x)-I)/(x^2+1)/a^2","C"
68,1,165,63,0.750000," ","int(arccot(x)/(a*x^2+a)^(5/2),x)","-\frac{\left(i+3 \,\mathrm{arccot}\left(x \right)\right) \left(x^{3}+3 i x^{2}-3 x -i\right) \sqrt{a \left(x +i\right) \left(x -i\right)}}{72 \left(x^{2}+1\right)^{2} a^{3}}+\frac{3 \left(i+\mathrm{arccot}\left(x \right)\right) \left(x +i\right) \sqrt{a \left(x +i\right) \left(x -i\right)}}{8 a^{3} \left(x^{2}+1\right)}+\frac{3 \sqrt{a \left(x +i\right) \left(x -i\right)}\, \left(x -i\right) \left(\mathrm{arccot}\left(x \right)-i\right)}{8 a^{3} \left(x^{2}+1\right)}-\frac{\left(-i+3 \,\mathrm{arccot}\left(x \right)\right) \sqrt{a \left(x +i\right) \left(x -i\right)}\, \left(x^{3}-3 i x^{2}-3 x +i\right)}{72 \left(x^{4}+2 x^{2}+1\right) a^{3}}"," ",0,"-1/72*(I+3*arccot(x))*(3*I*x^2+x^3-I-3*x)*(a*(x+I)*(x-I))^(1/2)/(x^2+1)^2/a^3+3/8*(I+arccot(x))*(x+I)*(a*(x+I)*(x-I))^(1/2)/a^3/(x^2+1)+3/8*(a*(x+I)*(x-I))^(1/2)*(x-I)*(arccot(x)-I)/a^3/(x^2+1)-1/72*(-I+3*arccot(x))*(a*(x+I)*(x-I))^(1/2)*(-3*x-3*I*x^2+x^3+I)/(x^4+2*x^2+1)/a^3","C"
69,1,258,94,0.854000," ","int(arccot(x)/(a*x^2+a)^(7/2),x)","\frac{\left(i+5 \,\mathrm{arccot}\left(x \right)\right) \left(x^{5}+5 i x^{4}-10 x^{3}-10 i x^{2}+5 x +i\right) \sqrt{a \left(x +i\right) \left(x -i\right)}}{800 \left(x^{2}+1\right)^{3} a^{4}}+\frac{5 \left(i+\mathrm{arccot}\left(x \right)\right) \left(x +i\right) \sqrt{a \left(x +i\right) \left(x -i\right)}}{16 \left(x^{2}+1\right) a^{4}}+\frac{5 \sqrt{a \left(x +i\right) \left(x -i\right)}\, \left(x -i\right) \left(\mathrm{arccot}\left(x \right)-i\right)}{16 \left(x^{2}+1\right) a^{4}}-\frac{5 \left(-i+3 \,\mathrm{arccot}\left(x \right)\right) \sqrt{a \left(x +i\right) \left(x -i\right)}\, \left(x^{3}-3 i x^{2}-3 x +i\right)}{288 \left(x^{4}+2 x^{2}+1\right) a^{4}}-\frac{\sqrt{a \left(x +i\right) \left(x -i\right)}\, \left(x -i\right) \left(67 i+165 \,\mathrm{arccot}\left(x \right)\right) \cos \left(4 \,\mathrm{arccot}\left(x \right)\right)}{3600 \left(x^{2}+1\right) a^{4}}-\frac{\sqrt{a \left(x +i\right) \left(x -i\right)}\, \left(i x +1\right) \left(29 i+105 \,\mathrm{arccot}\left(x \right)\right) \sin \left(4 \,\mathrm{arccot}\left(x \right)\right)}{1800 \left(x^{2}+1\right) a^{4}}"," ",0,"1/800*(I+5*arccot(x))*(5*I*x^4+x^5-10*I*x^2-10*x^3+I+5*x)*(a*(x+I)*(x-I))^(1/2)/(x^2+1)^3/a^4+5/16*(I+arccot(x))*(x+I)*(a*(x+I)*(x-I))^(1/2)/(x^2+1)/a^4+5/16*(a*(x+I)*(x-I))^(1/2)*(x-I)*(arccot(x)-I)/(x^2+1)/a^4-5/288*(-I+3*arccot(x))*(a*(x+I)*(x-I))^(1/2)*(-3*x-3*I*x^2+x^3+I)/(x^4+2*x^2+1)/a^4-1/3600*(a*(x+I)*(x-I))^(1/2)*(x-I)*(67*I+165*arccot(x))*cos(4*arccot(x))/(x^2+1)/a^4-1/1800*(a*(x+I)*(x-I))^(1/2)*(1+I*x)*(29*I+105*arccot(x))*sin(4*arccot(x))/(x^2+1)/a^4","C"
70,1,27,26,0.043000," ","int(x*arccot(x)/(x^2+1)^2,x)","-\frac{x}{4 \left(x^{2}+1\right)}-\frac{\mathrm{arccot}\left(x \right)}{2 \left(x^{2}+1\right)}-\frac{\arctan \left(x \right)}{4}"," ",0,"-1/4*x/(x^2+1)-1/2*arccot(x)/(x^2+1)-1/4*arctan(x)","A"
71,1,37,36,0.042000," ","int(x*arccot(x)/(x^2+1)^3,x)","-\frac{x}{16 \left(x^{2}+1\right)^{2}}-\frac{3 x}{32 \left(x^{2}+1\right)}-\frac{\mathrm{arccot}\left(x \right)}{4 \left(x^{2}+1\right)^{2}}-\frac{3 \arctan \left(x \right)}{32}"," ",0,"-1/16*x/(x^2+1)^2-3/32*x/(x^2+1)-1/4*arccot(x)/(x^2+1)^2-3/32*arctan(x)","A"
72,1,35,28,0.052000," ","int(arccot(x)/(x^2+1)^2,x)","\frac{x \,\mathrm{arccot}\left(x \right)}{2 x^{2}+2}+\frac{\mathrm{arccot}\left(x \right) \arctan \left(x \right)}{2}-\frac{1}{4 \left(x^{2}+1\right)}+\frac{\arctan \left(x \right)^{2}}{4}"," ",0,"1/2*x*arccot(x)/(x^2+1)+1/2*arccot(x)*arctan(x)-1/4/(x^2+1)+1/4*arctan(x)^2","A"
73,1,61,46,0.349000," ","int(arccot(x)^2/(x^2+1)^2,x)","-\frac{\mathrm{arccot}\left(x \right)^{2} \left(x^{2} \mathrm{arccot}\left(x \right)+\mathrm{arccot}\left(x \right)-x \right)}{2 \left(x^{2}+1\right)}+\frac{x^{2} \mathrm{arccot}\left(x \right)}{2 x^{2}+2}-\frac{x}{4 \left(x^{2}+1\right)}-\frac{\mathrm{arccot}\left(x \right)}{4}+\frac{\mathrm{arccot}\left(x \right)^{3}}{3}"," ",0,"-1/2*arccot(x)^2*(x^2*arccot(x)+arccot(x)-x)/(x^2+1)+1/2*x^2*arccot(x)/(x^2+1)-1/4*x/(x^2+1)-1/4*arccot(x)+1/3*arccot(x)^3","A"
74,1,36,35,0.041000," ","int(x^5*arccot(a*x^2),x)","\frac{x^{4}}{12 a}+\frac{x^{6} \mathrm{arccot}\left(a \,x^{2}\right)}{6}-\frac{\ln \left(a^{2} x^{4}+1\right)}{12 a^{3}}"," ",0,"1/12*x^4/a+1/6*x^6*arccot(a*x^2)-1/12*ln(a^2*x^4+1)/a^3","A"
75,1,32,31,0.039000," ","int(x^3*arccot(a*x^2),x)","\frac{x^{2}}{4 a}+\frac{x^{4} \mathrm{arccot}\left(a \,x^{2}\right)}{4}-\frac{\arctan \left(a \,x^{2}\right)}{4 a^{2}}"," ",0,"1/4*x^2/a+1/4*x^4*arccot(a*x^2)-1/4*arctan(a*x^2)/a^2","A"
76,1,28,27,0.039000," ","int(x*arccot(a*x^2),x)","\frac{x^{2} \mathrm{arccot}\left(a \,x^{2}\right)}{2}+\frac{\ln \left(a^{2} x^{4}+1\right)}{4 a}"," ",0,"1/2*x^2*arccot(a*x^2)+1/4*ln(a^2*x^4+1)/a","A"
77,1,57,29,0.161000," ","int(arccot(a*x^2)/x,x)","\ln \left(x \right) \mathrm{arccot}\left(a \,x^{2}\right)+\frac{\munderset{\textit{\_R1} =\RootOf \left(a^{2} \textit{\_Z}^{4}+1\right)}{\sum}\frac{\ln \left(x \right) \ln \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)}{\textit{\_R1}^{2}}}{2 a}"," ",0,"ln(x)*arccot(a*x^2)+1/2/a*sum(1/_R1^2*(ln(x)*ln((_R1-x)/_R1)+dilog((_R1-x)/_R1)),_R1=RootOf(_Z^4*a^2+1))","C"
78,1,31,30,0.045000," ","int(arccot(a*x^2)/x^3,x)","-\frac{\mathrm{arccot}\left(a \,x^{2}\right)}{2 x^{2}}-a \ln \left(x \right)+\frac{a \ln \left(a^{2} x^{4}+1\right)}{4}"," ",0,"-1/2*arccot(a*x^2)/x^2-a*ln(x)+1/4*a*ln(a^2*x^4+1)","A"
79,1,30,29,0.043000," ","int(arccot(a*x^2)/x^5,x)","\frac{a}{4 x^{2}}-\frac{\mathrm{arccot}\left(a \,x^{2}\right)}{4 x^{4}}+\frac{a^{2} \arctan \left(a \,x^{2}\right)}{4}"," ",0,"1/4*a/x^2-1/4*arccot(a*x^2)/x^4+1/4*a^2*arctan(a*x^2)","A"
80,1,129,107,0.061000," ","int(x^4*arccot(a*x^2),x)","\frac{x^{5} \mathrm{arccot}\left(a \,x^{2}\right)}{5}+\frac{2 x^{3}}{15 a}-\frac{\sqrt{2}\, \ln \left(\frac{x^{2}-\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{a^{2}}}}{x^{2}+\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{a^{2}}}}\right)}{20 a^{3} \left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}+1\right)}{10 a^{3} \left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}-1\right)}{10 a^{3} \left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}"," ",0,"1/5*x^5*arccot(a*x^2)+2/15*x^3/a-1/20/a^3/(1/a^2)^(1/4)*2^(1/2)*ln((x^2-(1/a^2)^(1/4)*x*2^(1/2)+(1/a^2)^(1/2))/(x^2+(1/a^2)^(1/4)*x*2^(1/2)+(1/a^2)^(1/2)))-1/10/a^3/(1/a^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/a^2)^(1/4)*x+1)-1/10/a^3/(1/a^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/a^2)^(1/4)*x-1)","A"
81,1,127,105,0.042000," ","int(x^2*arccot(a*x^2),x)","\frac{x^{3} \mathrm{arccot}\left(a \,x^{2}\right)}{3}+\frac{2 x}{3 a}-\frac{\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x^{2}+\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{a^{2}}}}{x^{2}-\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{a^{2}}}}\right)}{12 a}-\frac{\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}+1\right)}{6 a}-\frac{\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}-1\right)}{6 a}"," ",0,"1/3*x^3*arccot(a*x^2)+2/3*x/a-1/12/a*(1/a^2)^(1/4)*2^(1/2)*ln((x^2+(1/a^2)^(1/4)*x*2^(1/2)+(1/a^2)^(1/2))/(x^2-(1/a^2)^(1/4)*x*2^(1/2)+(1/a^2)^(1/2)))-1/6/a*(1/a^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/a^2)^(1/4)*x+1)-1/6/a*(1/a^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/a^2)^(1/4)*x-1)","A"
82,1,118,96,0.040000," ","int(arccot(a*x^2),x)","x \,\mathrm{arccot}\left(a \,x^{2}\right)+\frac{\sqrt{2}\, \ln \left(\frac{x^{2}-\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{a^{2}}}}{x^{2}+\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{a^{2}}}}\right)}{4 a \left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}+1\right)}{2 a \left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}-1\right)}{2 a \left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}"," ",0,"x*arccot(a*x^2)+1/4/a/(1/a^2)^(1/4)*2^(1/2)*ln((x^2-(1/a^2)^(1/4)*x*2^(1/2)+(1/a^2)^(1/2))/(x^2+(1/a^2)^(1/4)*x*2^(1/2)+(1/a^2)^(1/2)))+1/2/a/(1/a^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/a^2)^(1/4)*x+1)+1/2/a/(1/a^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/a^2)^(1/4)*x-1)","A"
83,1,115,99,0.041000," ","int(arccot(a*x^2)/x^2,x)","-\frac{\mathrm{arccot}\left(a \,x^{2}\right)}{x}-\frac{a \left(\frac{1}{a^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}+1\right)}{2}-\frac{a \left(\frac{1}{a^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x^{2}+\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{a^{2}}}}{x^{2}-\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{a^{2}}}}\right)}{4}-\frac{a \left(\frac{1}{a^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}-1\right)}{2}"," ",0,"-arccot(a*x^2)/x-1/2*a*(1/a^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/a^2)^(1/4)*x+1)-1/4*a*(1/a^2)^(1/4)*2^(1/2)*ln((x^2+(1/a^2)^(1/4)*x*2^(1/2)+(1/a^2)^(1/2))/(x^2-(1/a^2)^(1/4)*x*2^(1/2)+(1/a^2)^(1/2)))-1/2*a*(1/a^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/a^2)^(1/4)*x-1)","A"
84,1,121,105,0.045000," ","int(arccot(a*x^2)/x^4,x)","-\frac{\mathrm{arccot}\left(a \,x^{2}\right)}{3 x^{3}}+\frac{a \sqrt{2}\, \ln \left(\frac{x^{2}-\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{a^{2}}}}{x^{2}+\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{a^{2}}}}\right)}{12 \left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}+\frac{a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}+1\right)}{6 \left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}+\frac{a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}-1\right)}{6 \left(\frac{1}{a^{2}}\right)^{\frac{1}{4}}}+\frac{2 a}{3 x}"," ",0,"-1/3*arccot(a*x^2)/x^3+1/12*a/(1/a^2)^(1/4)*2^(1/2)*ln((x^2-(1/a^2)^(1/4)*x*2^(1/2)+(1/a^2)^(1/2))/(x^2+(1/a^2)^(1/4)*x*2^(1/2)+(1/a^2)^(1/2)))+1/6*a/(1/a^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/a^2)^(1/4)*x+1)+1/6*a/(1/a^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/a^2)^(1/4)*x-1)+2/3*a/x","A"
85,1,32,31,0.040000," ","int(x^2*arccot(x^(1/2)),x)","-\frac{x^{\frac{3}{2}}}{9}+\frac{x^{\frac{5}{2}}}{15}+\frac{x^{3} \mathrm{arccot}\left(\sqrt{x}\right)}{3}-\frac{\arctan \left(\sqrt{x}\right)}{3}+\frac{\sqrt{x}}{3}"," ",0,"-1/9*x^(3/2)+1/15*x^(5/2)+1/3*x^3*arccot(x^(1/2))-1/3*arctan(x^(1/2))+1/3*x^(1/2)","A"
86,1,27,26,0.039000," ","int(x*arccot(x^(1/2)),x)","\frac{x^{\frac{3}{2}}}{6}+\frac{x^{2} \mathrm{arccot}\left(\sqrt{x}\right)}{2}+\frac{\arctan \left(\sqrt{x}\right)}{2}-\frac{\sqrt{x}}{2}"," ",0,"1/6*x^(3/2)+1/2*x^2*arccot(x^(1/2))+1/2*arctan(x^(1/2))-1/2*x^(1/2)","A"
87,1,17,16,0.043000," ","int(arccot(x^(1/2)),x)","x \,\mathrm{arccot}\left(\sqrt{x}\right)-\arctan \left(\sqrt{x}\right)+\sqrt{x}"," ",0,"x*arccot(x^(1/2))-arctan(x^(1/2))+x^(1/2)","A"
88,1,61,23,0.057000," ","int(arccot(x^(1/2))/x,x)","\ln \left(x \right) \mathrm{arccot}\left(\sqrt{x}\right)-\frac{i \ln \left(x \right) \ln \left(1+i \sqrt{x}\right)}{2}+\frac{i \ln \left(x \right) \ln \left(1-i \sqrt{x}\right)}{2}-i \dilog \left(1+i \sqrt{x}\right)+i \dilog \left(1-i \sqrt{x}\right)"," ",0,"ln(x)*arccot(x^(1/2))-1/2*I*ln(x)*ln(1+I*x^(1/2))+1/2*I*ln(x)*ln(1-I*x^(1/2))-I*dilog(1+I*x^(1/2))+I*dilog(1-I*x^(1/2))","B"
89,1,18,17,0.043000," ","int(arccot(x^(1/2))/x^2,x)","-\frac{\mathrm{arccot}\left(\sqrt{x}\right)}{x}+\arctan \left(\sqrt{x}\right)+\frac{1}{\sqrt{x}}"," ",0,"-arccot(x^(1/2))/x+arctan(x^(1/2))+1/x^(1/2)","A"
90,1,27,26,0.046000," ","int(arccot(x^(1/2))/x^3,x)","\frac{1}{6 x^{\frac{3}{2}}}-\frac{\mathrm{arccot}\left(\sqrt{x}\right)}{2 x^{2}}-\frac{\arctan \left(\sqrt{x}\right)}{2}-\frac{1}{2 \sqrt{x}}"," ",0,"1/6/x^(3/2)-1/2*arccot(x^(1/2))/x^2-1/2*arctan(x^(1/2))-1/2/x^(1/2)","A"
91,1,25,24,0.040000," ","int(x^(3/2)*arccot(x^(1/2)),x)","-\frac{x}{5}+\frac{x^{2}}{10}+\frac{2 x^{\frac{5}{2}} \mathrm{arccot}\left(\sqrt{x}\right)}{5}+\frac{\ln \left(x +1\right)}{5}"," ",0,"-1/5*x+1/10*x^2+2/5*x^(5/2)*arccot(x^(1/2))+1/5*ln(x+1)","A"
92,1,20,19,0.040000," ","int(x^(1/2)*arccot(x^(1/2)),x)","\frac{x}{3}+\frac{2 x^{\frac{3}{2}} \mathrm{arccot}\left(\sqrt{x}\right)}{3}-\frac{\ln \left(x +1\right)}{3}"," ",0,"1/3*x+2/3*x^(3/2)*arccot(x^(1/2))-1/3*ln(x+1)","A"
93,1,15,14,0.040000," ","int(arccot(x^(1/2))/x^(1/2),x)","\ln \left(x +1\right)+2 \sqrt{x}\, \mathrm{arccot}\left(\sqrt{x}\right)"," ",0,"ln(x+1)+2*x^(1/2)*arccot(x^(1/2))","A"
94,1,19,18,0.044000," ","int(arccot(x^(1/2))/x^(3/2),x)","-\ln \left(x \right)+\ln \left(x +1\right)-\frac{2 \,\mathrm{arccot}\left(\sqrt{x}\right)}{\sqrt{x}}"," ",0,"-ln(x)+ln(x+1)-2*arccot(x^(1/2))/x^(1/2)","A"
95,1,26,25,0.046000," ","int(arccot(x^(1/2))/x^(5/2),x)","\frac{1}{3 x}-\frac{2 \,\mathrm{arccot}\left(\sqrt{x}\right)}{3 x^{\frac{3}{2}}}+\frac{\ln \left(x \right)}{3}-\frac{\ln \left(x +1\right)}{3}"," ",0,"1/3/x-2/3*arccot(x^(1/2))/x^(3/2)+1/3*ln(x)-1/3*ln(x+1)","A"
96,1,20,15,0.068000," ","int(arccot(1/x),x)","x \,\mathrm{arccot}\left(\frac{1}{x}\right)+\ln \left(\frac{1}{x}\right)-\frac{\ln \left(\frac{1}{x^{2}}+1\right)}{2}"," ",0,"x*arccot(1/x)+ln(1/x)-1/2*ln(1/x^2+1)","A"
97,1,94,39,0.060000," ","int(arccot(a*x^n)/x,x)","\frac{\ln \left(a \,x^{n}\right) \mathrm{arccot}\left(a \,x^{n}\right)}{n}-\frac{i \ln \left(a \,x^{n}\right) \ln \left(1+i a \,x^{n}\right)}{2 n}+\frac{i \ln \left(a \,x^{n}\right) \ln \left(1-i a \,x^{n}\right)}{2 n}-\frac{i \dilog \left(1+i a \,x^{n}\right)}{2 n}+\frac{i \dilog \left(1-i a \,x^{n}\right)}{2 n}"," ",0,"1/n*ln(a*x^n)*arccot(a*x^n)-1/2*I/n*ln(a*x^n)*ln(1+I*a*x^n)+1/2*I/n*ln(a*x^n)*ln(1-I*a*x^n)-1/2*I/n*dilog(1+I*a*x^n)+1/2*I/n*dilog(1-I*a*x^n)","B"
98,1,57,29,0.156000," ","int(arccot(a*x^5)/x,x)","\ln \left(x \right) \mathrm{arccot}\left(a \,x^{5}\right)+\frac{\munderset{\textit{\_R1} =\RootOf \left(\textit{\_Z}^{10} a^{2}+1\right)}{\sum}\frac{\ln \left(x \right) \ln \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)}{\textit{\_R1}^{5}}}{2 a}"," ",0,"ln(x)*arccot(a*x^5)+1/2/a*sum(1/_R1^5*(ln(x)*ln((_R1-x)/_R1)+dilog((_R1-x)/_R1)),_R1=RootOf(_Z^10*a^2+1))","C"
99,1,132,94,0.044000," ","int(x^3*arccot(b*x+a),x)","-\frac{\ln \left(1+\left(b x +a \right)^{2}\right) a^{3}}{2 b^{4}}+\frac{\arctan \left(b x +a \right) a^{4}}{4 b^{4}}-\frac{3 \arctan \left(b x +a \right) a^{2}}{2 b^{4}}-\frac{a}{4 b^{4}}+\frac{13 a^{3}}{12 b^{4}}-\frac{x}{4 b^{3}}+\frac{\ln \left(1+\left(b x +a \right)^{2}\right) a}{2 b^{4}}+\frac{\arctan \left(b x +a \right)}{4 b^{4}}+\frac{x^{4} \mathrm{arccot}\left(b x +a \right)}{4}+\frac{x^{3}}{12 b}-\frac{x^{2} a}{4 b^{2}}+\frac{3 x \,a^{2}}{4 b^{3}}"," ",0,"-1/2/b^4*ln(1+(b*x+a)^2)*a^3+1/4/b^4*arctan(b*x+a)*a^4-3/2/b^4*arctan(b*x+a)*a^2-1/4/b^4*a+13/12/b^4*a^3-1/4/b^3*x+1/2/b^4*ln(1+(b*x+a)^2)*a+1/4/b^4*arctan(b*x+a)+1/4*x^4*arccot(b*x+a)+1/12/b*x^3-1/4/b^2*x^2*a+3/4/b^3*x*a^2","A"
100,1,94,72,0.044000," ","int(x^2*arccot(b*x+a),x)","\frac{x^{3} \mathrm{arccot}\left(b x +a \right)}{3}+\frac{x^{2}}{6 b}-\frac{2 a x}{3 b^{2}}-\frac{5 a^{2}}{6 b^{3}}+\frac{\ln \left(1+\left(b x +a \right)^{2}\right) a^{2}}{2 b^{3}}-\frac{\ln \left(1+\left(b x +a \right)^{2}\right)}{6 b^{3}}-\frac{\arctan \left(b x +a \right) a^{3}}{3 b^{3}}+\frac{\arctan \left(b x +a \right) a}{b^{3}}"," ",0,"1/3*x^3*arccot(b*x+a)+1/6/b*x^2-2/3*a*x/b^2-5/6/b^3*a^2+1/2/b^3*ln(1+(b*x+a)^2)*a^2-1/6/b^3*ln(1+(b*x+a)^2)-1/3/b^3*arctan(b*x+a)*a^3+1/b^3*arctan(b*x+a)*a","A"
101,1,66,52,0.041000," ","int(x*arccot(b*x+a),x)","\frac{x^{2} \mathrm{arccot}\left(b x +a \right)}{2}-\frac{\mathrm{arccot}\left(b x +a \right) a^{2}}{2 b^{2}}+\frac{x}{2 b}+\frac{a}{2 b^{2}}-\frac{a \ln \left(1+\left(b x +a \right)^{2}\right)}{2 b^{2}}-\frac{\arctan \left(b x +a \right)}{2 b^{2}}"," ",0,"1/2*x^2*arccot(b*x+a)-1/2/b^2*arccot(b*x+a)*a^2+1/2*x/b+1/2/b^2*a-1/2*a*ln(1+(b*x+a)^2)/b^2-1/2/b^2*arctan(b*x+a)","A"
102,1,36,31,0.037000," ","int(arccot(b*x+a),x)","x \,\mathrm{arccot}\left(b x +a \right)+\frac{\mathrm{arccot}\left(b x +a \right) a}{b}+\frac{\ln \left(1+\left(b x +a \right)^{2}\right)}{2 b}"," ",0,"x*arccot(b*x+a)+1/b*arccot(b*x+a)*a+1/2*ln(1+(b*x+a)^2)/b","A"
103,1,103,108,0.062000," ","int(arccot(b*x+a)/x,x)","\ln \left(b x \right) \mathrm{arccot}\left(b x +a \right)-\frac{i \ln \left(b x \right) \ln \left(\frac{-b x -a +i}{i-a}\right)}{2}+\frac{i \ln \left(b x \right) \ln \left(\frac{b x +a +i}{i+a}\right)}{2}-\frac{i \dilog \left(\frac{-b x -a +i}{i-a}\right)}{2}+\frac{i \dilog \left(\frac{b x +a +i}{i+a}\right)}{2}"," ",0,"ln(b*x)*arccot(b*x+a)-1/2*I*ln(b*x)*ln((I-a-b*x)/(I-a))+1/2*I*ln(b*x)*ln((I+a+b*x)/(I+a))-1/2*I*dilog((I-a-b*x)/(I-a))+1/2*I*dilog((I+a+b*x)/(I+a))","A"
104,1,63,60,0.048000," ","int(arccot(b*x+a)/x^2,x)","-\frac{\mathrm{arccot}\left(b x +a \right)}{x}-\frac{b \ln \left(b x \right)}{a^{2}+1}+\frac{b \ln \left(1+\left(b x +a \right)^{2}\right)}{2 a^{2}+2}+\frac{a b \arctan \left(b x +a \right)}{a^{2}+1}"," ",0,"-arccot(b*x+a)/x-b/(a^2+1)*ln(b*x)+1/2*b*ln(1+(b*x+a)^2)/(a^2+1)+a*b*arctan(b*x+a)/(a^2+1)","A"
105,1,104,87,0.049000," ","int(arccot(b*x+a)/x^3,x)","-\frac{\mathrm{arccot}\left(b x +a \right)}{2 x^{2}}+\frac{b}{2 \left(a^{2}+1\right) x}+\frac{b^{2} a \ln \left(b x \right)}{\left(a^{2}+1\right)^{2}}-\frac{b^{2} \arctan \left(b x +a \right) a^{2}}{2 \left(a^{2}+1\right)^{2}}-\frac{a \,b^{2} \ln \left(1+\left(b x +a \right)^{2}\right)}{2 \left(a^{2}+1\right)^{2}}+\frac{b^{2} \arctan \left(b x +a \right)}{2 \left(a^{2}+1\right)^{2}}"," ",0,"-1/2*arccot(b*x+a)/x^2+1/2*b/(a^2+1)/x+b^2/(a^2+1)^2*a*ln(b*x)-1/2*b^2/(a^2+1)^2*arctan(b*x+a)*a^2-1/2*a*b^2*ln(1+(b*x+a)^2)/(a^2+1)^2+1/2*b^2/(a^2+1)^2*arctan(b*x+a)","A"
106,1,164,117,0.053000," ","int(arccot(b*x+a)/x^4,x)","-\frac{\mathrm{arccot}\left(b x +a \right)}{3 x^{3}}+\frac{b}{6 \left(a^{2}+1\right) x^{2}}-\frac{b^{3} \ln \left(b x \right) a^{2}}{\left(a^{2}+1\right)^{3}}+\frac{b^{3} \ln \left(b x \right)}{3 \left(a^{2}+1\right)^{3}}-\frac{2 a \,b^{2}}{3 \left(a^{2}+1\right)^{2} x}+\frac{b^{3} \ln \left(1+\left(b x +a \right)^{2}\right) a^{2}}{2 \left(a^{2}+1\right)^{3}}-\frac{b^{3} \ln \left(1+\left(b x +a \right)^{2}\right)}{6 \left(a^{2}+1\right)^{3}}+\frac{b^{3} \arctan \left(b x +a \right) a^{3}}{3 \left(a^{2}+1\right)^{3}}-\frac{b^{3} \arctan \left(b x +a \right) a}{\left(a^{2}+1\right)^{3}}"," ",0,"-1/3*arccot(b*x+a)/x^3+1/6*b/(a^2+1)/x^2-b^3/(a^2+1)^3*ln(b*x)*a^2+1/3*b^3/(a^2+1)^3*ln(b*x)-2/3*a*b^2/(a^2+1)^2/x+1/2*b^3/(a^2+1)^3*ln(1+(b*x+a)^2)*a^2-1/6*b^3/(a^2+1)^3*ln(1+(b*x+a)^2)+1/3*b^3/(a^2+1)^3*arctan(b*x+a)*a^3-b^3/(a^2+1)^3*arctan(b*x+a)*a","A"
107,1,2082,495,1.390000," ","int(arccot(b*x+a)/(d*x^2+c),x)","-\frac{i b \ln \left(1-\frac{\left(a^{2} d -2 i a d +c \,b^{2}-d \right) \left(b x +a +i\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}\right) \mathrm{arccot}\left(b x +a \right)}{a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d}+\frac{i \sqrt{b^{2} c d}\, \ln \left(1-\frac{\left(a^{2} d -2 i a d +c \,b^{2}-d \right) \left(b x +a +i\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}\right) \mathrm{arccot}\left(b x +a \right) a^{2}}{2 b c \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}+\frac{i b \sqrt{b^{2} c d}\, \ln \left(1-\frac{\left(a^{2} d -2 i a d +c \,b^{2}-d \right) \left(b x +a +i\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}\right) \mathrm{arccot}\left(b x +a \right)}{2 d \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}-\frac{i \sqrt{b^{2} c d}\, \ln \left(1-\frac{\left(a^{2} d -2 i a d +c \,b^{2}-d \right) \left(b x +a +i\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}\right) \mathrm{arccot}\left(b x +a \right) a^{2}}{2 b c \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}-\frac{b \sqrt{b^{2} c d}\, \mathrm{arccot}\left(b x +a \right)^{2}}{2 d \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}-\frac{b \mathrm{arccot}\left(b x +a \right)^{2}}{a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d}-\frac{\sqrt{b^{2} c d}\, \mathrm{arccot}\left(b x +a \right)^{2}}{2 b c \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}-\frac{\sqrt{b^{2} c d}\, \mathrm{arccot}\left(b x +a \right)^{2} a^{2}}{2 b c \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}-\frac{b \sqrt{b^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} d -2 i a d +c \,b^{2}-d \right) \left(b x +a +i\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}\right)}{4 d \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}-\frac{b \polylog \left(2, \frac{\left(a^{2} d -2 i a d +c \,b^{2}-d \right) \left(b x +a +i\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}\right)}{2 \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}-\frac{\sqrt{b^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} d -2 i a d +c \,b^{2}-d \right) \left(b x +a +i\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}\right)}{4 b c \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}-\frac{\sqrt{b^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} d -2 i a d +c \,b^{2}-d \right) \left(b x +a +i\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}\right) a^{2}}{4 b c \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}-\frac{i \sqrt{b^{2} c d}\, \ln \left(1-\frac{\left(a^{2} d -2 i a d +c \,b^{2}-d \right) \left(b x +a +i\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}\right) \mathrm{arccot}\left(b x +a \right)}{2 b c \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}-\frac{i b \ln \left(1-\frac{\left(a^{2} d -2 i a d +c \,b^{2}-d \right) \left(b x +a +i\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}\right) \mathrm{arccot}\left(b x +a \right)}{a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d}+\frac{i \sqrt{b^{2} c d}\, \ln \left(1-\frac{\left(a^{2} d -2 i a d +c \,b^{2}-d \right) \left(b x +a +i\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}\right) \mathrm{arccot}\left(b x +a \right)}{2 b c \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}-\frac{i b \sqrt{b^{2} c d}\, \ln \left(1-\frac{\left(a^{2} d -2 i a d +c \,b^{2}-d \right) \left(b x +a +i\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}\right) \mathrm{arccot}\left(b x +a \right)}{2 d \left(a^{2} d +c \,b^{2}+2 \sqrt{b^{2} c d}+d \right)}+\frac{b \sqrt{b^{2} c d}\, \mathrm{arccot}\left(b x +a \right)^{2}}{2 d \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}-\frac{b \mathrm{arccot}\left(b x +a \right)^{2}}{a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d}+\frac{\sqrt{b^{2} c d}\, \mathrm{arccot}\left(b x +a \right)^{2}}{2 b c \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}+\frac{\sqrt{b^{2} c d}\, \mathrm{arccot}\left(b x +a \right)^{2} a^{2}}{2 b c \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}+\frac{b \sqrt{b^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} d -2 i a d +c \,b^{2}-d \right) \left(b x +a +i\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}\right)}{4 d \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}-\frac{b \polylog \left(2, \frac{\left(a^{2} d -2 i a d +c \,b^{2}-d \right) \left(b x +a +i\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}\right)}{2 \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}+\frac{\sqrt{b^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} d -2 i a d +c \,b^{2}-d \right) \left(b x +a +i\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}\right)}{4 b c \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}+\frac{\sqrt{b^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} d -2 i a d +c \,b^{2}-d \right) \left(b x +a +i\right)^{2}}{\left(1+\left(b x +a \right)^{2}\right) \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}\right) a^{2}}{4 b c \left(a^{2} d +c \,b^{2}-2 \sqrt{b^{2} c d}+d \right)}"," ",0,"-I*b/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*ln(1-(-2*I*a*d+a^2*d+c*b^2-d)*(I+a+b*x)^2/(1+(b*x+a)^2)/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d))*arccot(b*x+a)+1/2*I/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*ln(1-(-2*I*a*d+a^2*d+c*b^2-d)*(I+a+b*x)^2/(1+(b*x+a)^2)/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d))*arccot(b*x+a)*a^2+1/2*I*b/d*(b^2*c*d)^(1/2)/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*ln(1-(-2*I*a*d+a^2*d+c*b^2-d)*(I+a+b*x)^2/(1+(b*x+a)^2)/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d))*arccot(b*x+a)-1/2*I/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*ln(1-(-2*I*a*d+a^2*d+c*b^2-d)*(I+a+b*x)^2/(1+(b*x+a)^2)/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d))*arccot(b*x+a)*a^2-1/2*b/d*(b^2*c*d)^(1/2)/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*arccot(b*x+a)^2-b/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*arccot(b*x+a)^2-1/2/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*arccot(b*x+a)^2-1/2/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*arccot(b*x+a)^2*a^2-1/4*b/d*(b^2*c*d)^(1/2)/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*polylog(2,(-2*I*a*d+a^2*d+c*b^2-d)*(I+a+b*x)^2/(1+(b*x+a)^2)/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d))-1/2*b/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*polylog(2,(-2*I*a*d+a^2*d+c*b^2-d)*(I+a+b*x)^2/(1+(b*x+a)^2)/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d))-1/4/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*polylog(2,(-2*I*a*d+a^2*d+c*b^2-d)*(I+a+b*x)^2/(1+(b*x+a)^2)/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d))-1/4/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*polylog(2,(-2*I*a*d+a^2*d+c*b^2-d)*(I+a+b*x)^2/(1+(b*x+a)^2)/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d))*a^2-1/2*I/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*ln(1-(-2*I*a*d+a^2*d+c*b^2-d)*(I+a+b*x)^2/(1+(b*x+a)^2)/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d))*arccot(b*x+a)-I*b/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*ln(1-(-2*I*a*d+a^2*d+c*b^2-d)*(I+a+b*x)^2/(1+(b*x+a)^2)/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d))*arccot(b*x+a)+1/2*I/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*ln(1-(-2*I*a*d+a^2*d+c*b^2-d)*(I+a+b*x)^2/(1+(b*x+a)^2)/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d))*arccot(b*x+a)-1/2*I*b/d*(b^2*c*d)^(1/2)/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d)*ln(1-(-2*I*a*d+a^2*d+c*b^2-d)*(I+a+b*x)^2/(1+(b*x+a)^2)/(a^2*d+c*b^2+2*(b^2*c*d)^(1/2)+d))*arccot(b*x+a)+1/2*b/d*(b^2*c*d)^(1/2)/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*arccot(b*x+a)^2-b/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*arccot(b*x+a)^2+1/2/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*arccot(b*x+a)^2+1/2/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*arccot(b*x+a)^2*a^2+1/4*b/d*(b^2*c*d)^(1/2)/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*polylog(2,(-2*I*a*d+a^2*d+c*b^2-d)*(I+a+b*x)^2/(1+(b*x+a)^2)/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d))-1/2*b/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*polylog(2,(-2*I*a*d+a^2*d+c*b^2-d)*(I+a+b*x)^2/(1+(b*x+a)^2)/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d))+1/4/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*polylog(2,(-2*I*a*d+a^2*d+c*b^2-d)*(I+a+b*x)^2/(1+(b*x+a)^2)/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d))+1/4/b*(b^2*c*d)^(1/2)/c/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d)*polylog(2,(-2*I*a*d+a^2*d+c*b^2-d)*(I+a+b*x)^2/(1+(b*x+a)^2)/(a^2*d+c*b^2-2*(b^2*c*d)^(1/2)+d))*a^2","B"
108,1,198,140,0.064000," ","int(arccot(b*x+a)/(d*x+c),x)","\frac{\ln \left(d \left(b x +a \right)-a d +b c \right) \mathrm{arccot}\left(b x +a \right)}{d}-\frac{i \ln \left(d \left(b x +a \right)-a d +b c \right) \ln \left(\frac{i d -d \left(b x +a \right)}{-a d +b c +i d}\right)}{2 d}+\frac{i \ln \left(d \left(b x +a \right)-a d +b c \right) \ln \left(\frac{i d +d \left(b x +a \right)}{a d -b c +i d}\right)}{2 d}-\frac{i \dilog \left(\frac{i d -d \left(b x +a \right)}{-a d +b c +i d}\right)}{2 d}+\frac{i \dilog \left(\frac{i d +d \left(b x +a \right)}{a d -b c +i d}\right)}{2 d}"," ",0,"ln(d*(b*x+a)-a*d+b*c)/d*arccot(b*x+a)-1/2*I*ln(d*(b*x+a)-a*d+b*c)/d*ln((I*d-d*(b*x+a))/(b*c+I*d-a*d))+1/2*I*ln(d*(b*x+a)-a*d+b*c)/d*ln((I*d+d*(b*x+a))/(I*d+a*d-b*c))-1/2*I/d*dilog((I*d-d*(b*x+a))/(b*c+I*d-a*d))+1/2*I/d*dilog((I*d+d*(b*x+a))/(I*d+a*d-b*c))","A"
109,1,317,290,0.069000," ","int(arccot(b*x+a)/(c+1/x*d),x)","\frac{\mathrm{arccot}\left(b x +a \right) x}{c}+\frac{\mathrm{arccot}\left(b x +a \right) a}{b c}-\frac{\mathrm{arccot}\left(b x +a \right) d \ln \left(c \left(b x +a \right)-a c +b d \right)}{c^{2}}+\frac{\ln \left(a^{2} c^{2}-2 a b c d +b^{2} d^{2}+2 a c \left(c \left(b x +a \right)-a c +b d \right)-2 \left(c \left(b x +a \right)-a c +b d \right) b d +\left(c \left(b x +a \right)-a c +b d \right)^{2}+c^{2}\right)}{2 b c}+\frac{i d \ln \left(c \left(b x +a \right)-a c +b d \right) \ln \left(\frac{i c -c \left(b x +a \right)}{-a c +b d +i c}\right)}{2 c^{2}}-\frac{i d \ln \left(c \left(b x +a \right)-a c +b d \right) \ln \left(\frac{i c +c \left(b x +a \right)}{a c -b d +i c}\right)}{2 c^{2}}+\frac{i d \dilog \left(\frac{i c -c \left(b x +a \right)}{-a c +b d +i c}\right)}{2 c^{2}}-\frac{i d \dilog \left(\frac{i c +c \left(b x +a \right)}{a c -b d +i c}\right)}{2 c^{2}}"," ",0,"arccot(b*x+a)/c*x+1/b*arccot(b*x+a)/c*a-arccot(b*x+a)*d/c^2*ln(c*(b*x+a)-a*c+b*d)+1/2/b/c*ln(a^2*c^2-2*a*b*c*d+b^2*d^2+2*a*c*(c*(b*x+a)-a*c+b*d)-2*(c*(b*x+a)-a*c+b*d)*b*d+(c*(b*x+a)-a*c+b*d)^2+c^2)+1/2*I/c^2*d*ln(c*(b*x+a)-a*c+b*d)*ln((I*c-c*(b*x+a))/(I*c-a*c+b*d))-1/2*I/c^2*d*ln(c*(b*x+a)-a*c+b*d)*ln((I*c+c*(b*x+a))/(I*c+a*c-b*d))+1/2*I/c^2*d*dilog((I*c-c*(b*x+a))/(I*c-a*c+b*d))-1/2*I/c^2*d*dilog((I*c+c*(b*x+a))/(I*c+a*c-b*d))","A"
110,1,52954,544,2.640000," ","int(arccot(b*x+a)/(c+d/x^2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
111,1,343,543,0.286000," ","int(arccot(b*x+a)/(c+d*x^(1/2)),x)","\frac{2 \,\mathrm{arccot}\left(b x +a \right) \sqrt{x}}{d}-\frac{2 \,\mathrm{arccot}\left(b x +a \right) c \ln \left(c +d \sqrt{x}\right)}{d^{2}}-c \left(\munderset{\textit{\_R1} =\RootOf \left(b^{2} \textit{\_Z}^{4}-4 c \,b^{2} \textit{\_Z}^{3}+\left(2 a b \,d^{2}+6 b^{2} c^{2}\right) \textit{\_Z}^{2}+\left(-4 a b c \,d^{2}-4 b^{2} c^{3}\right) \textit{\_Z} +a^{2} d^{4}+2 a b \,c^{2} d^{2}+b^{2} c^{4}+d^{4}\right)}{\sum}\frac{\ln \left(c +d \sqrt{x}\right) \ln \left(\frac{-d \sqrt{x}+\textit{\_R1} -c}{\textit{\_R1}}\right)+\dilog \left(\frac{-d \sqrt{x}+\textit{\_R1} -c}{\textit{\_R1}}\right)}{\textit{\_R1}^{2} b -2 \textit{\_R1} b c +a \,d^{2}+c^{2} b}\right)+\left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{4}-4 c \,b^{2} \textit{\_Z}^{3}+\left(2 a b \,d^{2}+6 b^{2} c^{2}\right) \textit{\_Z}^{2}+\left(-4 a b c \,d^{2}-4 b^{2} c^{3}\right) \textit{\_Z} +a^{2} d^{4}+2 a b \,c^{2} d^{2}+b^{2} c^{4}+d^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{2}-2 \textit{\_R} c +c^{2}\right) \ln \left(d \sqrt{x}-\textit{\_R} +c \right)}{b \,\textit{\_R}^{3}-3 b c \,\textit{\_R}^{2}+a \,d^{2} \textit{\_R} +3 c^{2} b \textit{\_R} -a c \,d^{2}-b \,c^{3}}\right)"," ",0,"2*arccot(b*x+a)/d*x^(1/2)-2*arccot(b*x+a)*c/d^2*ln(c+d*x^(1/2))-c*sum(1/(_R1^2*b-2*_R1*b*c+a*d^2+b*c^2)*(ln(c+d*x^(1/2))*ln((-d*x^(1/2)+_R1-c)/_R1)+dilog((-d*x^(1/2)+_R1-c)/_R1)),_R1=RootOf(b^2*_Z^4-4*c*b^2*_Z^3+(2*a*b*d^2+6*b^2*c^2)*_Z^2+(-4*a*b*c*d^2-4*b^2*c^3)*_Z+a^2*d^4+2*a*b*c^2*d^2+b^2*c^4+d^4))+sum((_R^2-2*_R*c+c^2)/(_R^3*b-3*_R^2*b*c+_R*a*d^2+3*_R*b*c^2-a*c*d^2-b*c^3)*ln(d*x^(1/2)-_R+c),_R=RootOf(b^2*_Z^4-4*c*b^2*_Z^3+(2*a*b*d^2+6*b^2*c^2)*_Z^2+(-4*a*b*c*d^2-4*b^2*c^3)*_Z+a^2*d^4+2*a*b*c^2*d^2+b^2*c^4+d^4))","C"
112,1,376,660,0.291000," ","int(arccot(b*x+a)/(c+d/x^(1/2)),x)","\frac{\mathrm{arccot}\left(b x +a \right) x}{c}-\frac{2 \,\mathrm{arccot}\left(b x +a \right) d \sqrt{x}}{c^{2}}+\frac{2 \,\mathrm{arccot}\left(b x +a \right) d^{2} \ln \left(d +c \sqrt{x}\right)}{c^{3}}+\frac{d^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(b^{2} \textit{\_Z}^{4}-4 b^{2} d \,\textit{\_Z}^{3}+\left(2 c^{2} b a +6 b^{2} d^{2}\right) \textit{\_Z}^{2}+\left(-4 a b \,c^{2} d -4 b^{2} d^{3}\right) \textit{\_Z} +a^{2} c^{4}+2 a b \,c^{2} d^{2}+b^{2} d^{4}+c^{4}\right)}{\sum}\frac{\ln \left(d +c \sqrt{x}\right) \ln \left(\frac{-c \sqrt{x}+\textit{\_R1} -d}{\textit{\_R1}}\right)+\dilog \left(\frac{-c \sqrt{x}+\textit{\_R1} -d}{\textit{\_R1}}\right)}{\textit{\_R1}^{2} b -2 \textit{\_R1} b d +a \,c^{2}+b \,d^{2}}\right)}{c}+\frac{\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{4}-4 b^{2} d \,\textit{\_Z}^{3}+\left(2 c^{2} b a +6 b^{2} d^{2}\right) \textit{\_Z}^{2}+\left(-4 a b \,c^{2} d -4 b^{2} d^{3}\right) \textit{\_Z} +a^{2} c^{4}+2 a b \,c^{2} d^{2}+b^{2} d^{4}+c^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{3}-5 \textit{\_R}^{2} d +7 \textit{\_R} \,d^{2}-3 d^{3}\right) \ln \left(c \sqrt{x}-\textit{\_R} +d \right)}{b \,\textit{\_R}^{3}-3 b d \,\textit{\_R}^{2}+a \,c^{2} \textit{\_R} +3 b \,d^{2} \textit{\_R} -a \,c^{2} d -b \,d^{3}}}{2 c}"," ",0,"arccot(b*x+a)/c*x-2*arccot(b*x+a)/c^2*d*x^(1/2)+2*arccot(b*x+a)/c^3*d^2*ln(d+c*x^(1/2))+1/c*d^2*sum(1/(_R1^2*b-2*_R1*b*d+a*c^2+b*d^2)*(ln(d+c*x^(1/2))*ln((-c*x^(1/2)+_R1-d)/_R1)+dilog((-c*x^(1/2)+_R1-d)/_R1)),_R1=RootOf(b^2*_Z^4-4*b^2*d*_Z^3+(2*a*b*c^2+6*b^2*d^2)*_Z^2+(-4*a*b*c^2*d-4*b^2*d^3)*_Z+a^2*c^4+2*a*b*c^2*d^2+b^2*d^4+c^4))+1/2/c*sum((_R^3-5*_R^2*d+7*_R*d^2-3*d^3)/(_R^3*b-3*_R^2*b*d+_R*a*c^2+3*_R*b*d^2-a*c^2*d-b*d^3)*ln(c*x^(1/2)-_R+d),_R=RootOf(b^2*_Z^4-4*b^2*d*_Z^3+(2*a*b*c^2+6*b^2*d^2)*_Z^2+(-4*a*b*c^2*d-4*b^2*d^3)*_Z+a^2*c^4+2*a*b*c^2*d^2+b^2*d^4+c^4))","C"
113,1,4601,329,1.602000," ","int(arccot(e*x+d)/(c*x^2+b*x+a),x)","\text{output too large to display}"," ",0,"-e/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*arccot(e*x+d)^2-1/2*e/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c))-e/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*arccot(e*x+d)^2-1/2*e/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c))-I/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c))*arccot(e*x+d)*d^2+I/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c))*arccot(e*x+d)*d^2-1/4*I*e*(e^2*(4*a*c-b^2))^(1/2)/c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c))*arccot(e*x+d)*b^2+1/4*I*e*(e^2*(4*a*c-b^2))^(1/2)/c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c))*arccot(e*x+d)*b^2-I*(e^2*(4*a*c-b^2))^(1/2)/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c))*arccot(e*x+d)*b*d-I/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c))*arccot(e*x+d)+I*(e^2*(4*a*c-b^2))^(1/2)/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c))*arccot(e*x+d)*b*d+I/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c))*arccot(e*x+d)+1/8*e*(e^2*(4*a*c-b^2))^(1/2)/c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c))*b^2-1/4*e*(e^2*(4*a*c-b^2))^(1/2)/c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*arccot(e*x+d)^2*b^2-1/8*e*(e^2*(4*a*c-b^2))^(1/2)/c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c))*b^2+1/4*e*(e^2*(4*a*c-b^2))^(1/2)/c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*arccot(e*x+d)^2*b^2+1/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*arccot(e*x+d)^2*d^2+1/2/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c))*d^2-1/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*arccot(e*x+d)^2*d^2-1/2/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c))*d^2+1/4*e*(e^2*(4*a*c-b^2))^(1/2)/c/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*arccot(e*x+d)^2-1/8*e*(e^2*(4*a*c-b^2))^(1/2)/c/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c))+1/8*e*(e^2*(4*a*c-b^2))^(1/2)/c/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c))-I*e/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c))*arccot(e*x+d)-I*e/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c))*arccot(e*x+d)-(e^2*(4*a*c-b^2))^(1/2)/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*arccot(e*x+d)^2*b*d-1/2*(e^2*(4*a*c-b^2))^(1/2)/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c))*b*d+(e^2*(4*a*c-b^2))^(1/2)/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*arccot(e*x+d)^2*b*d+1/2*(e^2*(4*a*c-b^2))^(1/2)/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c))*b*d+1/2/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c))-1/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*arccot(e*x+d)^2-1/2/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*polylog(2,(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c))+1/e*(e^2*(4*a*c-b^2))^(1/2)*c/(4*a*c-b^2)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*arccot(e*x+d)^2-1/4*I*e*(e^2*(4*a*c-b^2))^(1/2)/c/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c))*arccot(e*x+d)+1/4*I*e*(e^2*(4*a*c-b^2))^(1/2)/c/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c)*ln(1-(I*b*e-2*I*d*c+a*e^2-b*e*d+c*d^2-c)*(I+d+e*x)^2/((e*x+d)^2+1)/(a*e^2-b*e*d+c*d^2-(e^2*(4*a*c-b^2))^(1/2)+c))*arccot(e*x+d)-1/4*e*(e^2*(4*a*c-b^2))^(1/2)/c/(a*e^2-b*e*d+c*d^2+(e^2*(4*a*c-b^2))^(1/2)+c)*arccot(e*x+d)^2","B"
114,1,125,109,0.691000," ","int(arccot(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x)","-\frac{\mathrm{arccot}\left(b x +a \right) \ln \left(1-\frac{b x +a +i}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{b}+\frac{\mathrm{arccot}\left(b x +a \right) \ln \left(1+\frac{b x +a +i}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{b}-\frac{i \dilog \left(1+\frac{b x +a +i}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{b}+\frac{i \dilog \left(1-\frac{b x +a +i}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{b}"," ",0,"-1/b*arccot(b*x+a)*ln(1-(I+a+b*x)/(1+(b*x+a)^2)^(1/2))+1/b*arccot(b*x+a)*ln(1+(I+a+b*x)/(1+(b*x+a)^2)^(1/2))-I/b*dilog(1+(I+a+b*x)/(1+(b*x+a)^2)^(1/2))+I/b*dilog(1-(I+a+b*x)/(1+(b*x+a)^2)^(1/2))","A"
115,1,156,181,1.022000," ","int(arccot(b*x+a)/((a^2+1)*c+2*a*b*c*x+b^2*c*x^2)^(1/2),x)","\frac{i \left(i \ln \left(1-\frac{b x +a +i}{\sqrt{1+\left(b x +a \right)^{2}}}\right) \mathrm{arccot}\left(b x +a \right)-i \ln \left(1+\frac{b x +a +i}{\sqrt{1+\left(b x +a \right)^{2}}}\right) \mathrm{arccot}\left(b x +a \right)+\polylog \left(2, \frac{b x +a +i}{\sqrt{1+\left(b x +a \right)^{2}}}\right)-\polylog \left(2, -\frac{b x +a +i}{\sqrt{1+\left(b x +a \right)^{2}}}\right)\right) \sqrt{c \left(b x +a -i\right) \left(b x +a +i\right)}}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, b c}"," ",0,"I*(I*ln(1-(I+a+b*x)/(1+(b*x+a)^2)^(1/2))*arccot(b*x+a)-I*ln(1+(I+a+b*x)/(1+(b*x+a)^2)^(1/2))*arccot(b*x+a)+polylog(2,(I+a+b*x)/(1+(b*x+a)^2)^(1/2))-polylog(2,-(I+a+b*x)/(1+(b*x+a)^2)^(1/2)))*(c*(-I+a+b*x)*(I+a+b*x))^(1/2)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)/b/c","A"
116,0,0,20,1.375000," ","int(arccot(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/3),x)","\int \frac{\mathrm{arccot}\left(b x +a \right)}{\left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{1}{3}}}\, dx"," ",0,"int(arccot(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/3),x)","F"
117,0,0,22,1.296000," ","int(arccot(b*x+a)/((a^2+1)*c+2*a*b*c*x+b^2*c*x^2)^(1/3),x)","\int \frac{\mathrm{arccot}\left(b x +a \right)}{\left(\left(a^{2}+1\right) c +2 a b c x +b^{2} c \,x^{2}\right)^{\frac{1}{3}}}\, dx"," ",0,"int(arccot(b*x+a)/((a^2+1)*c+2*a*b*c*x+b^2*c*x^2)^(1/3),x)","F"
118,1,167,152,2.629000," ","int((b*x+a)^2*arccot(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x)","\frac{\left(\mathrm{arccot}\left(b x +a \right) x b +\mathrm{arccot}\left(b x +a \right) a +1\right) \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}}{2 b}-\frac{\mathrm{arccot}\left(b x +a \right) \ln \left(1+\frac{b x +a +i}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{2 b}+\frac{\mathrm{arccot}\left(b x +a \right) \ln \left(1-\frac{b x +a +i}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{2 b}+\frac{i \polylog \left(2, -\frac{b x +a +i}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{2 b}-\frac{i \polylog \left(2, \frac{b x +a +i}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{2 b}"," ",0,"1/2*(arccot(b*x+a)*x*b+arccot(b*x+a)*a+1)*(b^2*x^2+2*a*b*x+a^2+1)^(1/2)/b-1/2/b*arccot(b*x+a)*ln(1+(I+a+b*x)/(1+(b*x+a)^2)^(1/2))+1/2/b*arccot(b*x+a)*ln(1-(I+a+b*x)/(1+(b*x+a)^2)^(1/2))+1/2*I/b*polylog(2,-(I+a+b*x)/(1+(b*x+a)^2)^(1/2))-1/2*I/b*polylog(2,(I+a+b*x)/(1+(b*x+a)^2)^(1/2))","A"
119,1,202,234,3.993000," ","int((b*x+a)^2*arccot(b*x+a)/((a^2+1)*c+2*a*b*c*x+b^2*c*x^2)^(1/2),x)","\frac{\left(\mathrm{arccot}\left(b x +a \right) x b +\mathrm{arccot}\left(b x +a \right) a +1\right) \sqrt{c \left(b x +a -i\right) \left(b x +a +i\right)}}{2 b c}-\frac{i \left(i \ln \left(1-\frac{b x +a +i}{\sqrt{1+\left(b x +a \right)^{2}}}\right) \mathrm{arccot}\left(b x +a \right)-i \ln \left(1+\frac{b x +a +i}{\sqrt{1+\left(b x +a \right)^{2}}}\right) \mathrm{arccot}\left(b x +a \right)+\polylog \left(2, \frac{b x +a +i}{\sqrt{1+\left(b x +a \right)^{2}}}\right)-\polylog \left(2, -\frac{b x +a +i}{\sqrt{1+\left(b x +a \right)^{2}}}\right)\right) \sqrt{c \left(b x +a -i\right) \left(b x +a +i\right)}}{2 \sqrt{b^{2} x^{2}+2 a b x +a^{2}+1}\, b c}"," ",0,"1/2*(arccot(b*x+a)*x*b+arccot(b*x+a)*a+1)*(c*(-I+a+b*x)*(I+a+b*x))^(1/2)/b/c-1/2*I*(I*ln(1-(I+a+b*x)/(1+(b*x+a)^2)^(1/2))*arccot(b*x+a)-I*ln(1+(I+a+b*x)/(1+(b*x+a)^2)^(1/2))*arccot(b*x+a)+polylog(2,(I+a+b*x)/(1+(b*x+a)^2)^(1/2))-polylog(2,-(I+a+b*x)/(1+(b*x+a)^2)^(1/2)))*(c*(-I+a+b*x)*(I+a+b*x))^(1/2)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2)/b/c","A"
120,0,0,27,3.488000," ","int((b*x+a)^2*arccot(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/3),x)","\int \frac{\left(b x +a \right)^{2} \mathrm{arccot}\left(b x +a \right)}{\left(b^{2} x^{2}+2 a b x +a^{2}+1\right)^{\frac{1}{3}}}\, dx"," ",0,"int((b*x+a)^2*arccot(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/3),x)","F"
121,0,0,29,3.471000," ","int((b*x+a)^2*arccot(b*x+a)/((a^2+1)*c+2*a*b*c*x+b^2*c*x^2)^(1/3),x)","\int \frac{\left(b x +a \right)^{2} \mathrm{arccot}\left(b x +a \right)}{\left(\left(a^{2}+1\right) c +2 a b c x +b^{2} c \,x^{2}\right)^{\frac{1}{3}}}\, dx"," ",0,"int((b*x+a)^2*arccot(b*x+a)/((a^2+1)*c+2*a*b*c*x+b^2*c*x^2)^(1/3),x)","F"
122,1,86,46,0.043000," ","int((b*x+a)^2*arccot(b*x+a),x)","\frac{b^{2} \mathrm{arccot}\left(b x +a \right) x^{3}}{3}+b \,\mathrm{arccot}\left(b x +a \right) x^{2} a +\mathrm{arccot}\left(b x +a \right) x \,a^{2}+\frac{\mathrm{arccot}\left(b x +a \right) a^{3}}{3 b}+\frac{b \,x^{2}}{6}+\frac{a x}{3}+\frac{a^{2}}{6 b}-\frac{\ln \left(1+\left(b x +a \right)^{2}\right)}{6 b}"," ",0,"1/3*b^2*arccot(b*x+a)*x^3+b*arccot(b*x+a)*x^2*a+arccot(b*x+a)*x*a^2+1/3/b*arccot(b*x+a)*a^3+1/6*b*x^2+1/3*a*x+1/6/b*a^2-1/6*ln(1+(b*x+a)^2)/b","A"
123,1,57,33,0.041000," ","int((b*x+a)*arccot(b*x+a),x)","\frac{b \,\mathrm{arccot}\left(b x +a \right) x^{2}}{2}+\mathrm{arccot}\left(b x +a \right) x a +\frac{\mathrm{arccot}\left(b x +a \right) a^{2}}{2 b}+\frac{x}{2}+\frac{a}{2 b}-\frac{\arctan \left(b x +a \right)}{2 b}"," ",0,"1/2*b*arccot(b*x+a)*x^2+arccot(b*x+a)*x*a+1/2/b*arccot(b*x+a)*a^2+1/2*x+1/2*a/b-1/2*arctan(b*x+a)/b","A"
124,1,98,37,0.061000," ","int(arccot(b*x+a)/(b*x+a),x)","\frac{\ln \left(b x +a \right) \mathrm{arccot}\left(b x +a \right)}{b}-\frac{i \ln \left(b x +a \right) \ln \left(1+i \left(b x +a \right)\right)}{2 b}+\frac{i \ln \left(b x +a \right) \ln \left(1-i \left(b x +a \right)\right)}{2 b}-\frac{i \dilog \left(1+i \left(b x +a \right)\right)}{2 b}+\frac{i \dilog \left(1-i \left(b x +a \right)\right)}{2 b}"," ",0,"1/b*ln(b*x+a)*arccot(b*x+a)-1/2*I/b*ln(b*x+a)*ln(1+I*(b*x+a))+1/2*I/b*ln(b*x+a)*ln(1-I*(b*x+a))-1/2*I/b*dilog(1+I*(b*x+a))+1/2*I/b*dilog(1-I*(b*x+a))","B"
125,1,46,45,0.047000," ","int(arccot(b*x+a)/(b*x+a)^2,x)","-\frac{\mathrm{arccot}\left(b x +a \right)}{b \left(b x +a \right)}-\frac{\ln \left(b x +a \right)}{b}+\frac{\ln \left(1+\left(b x +a \right)^{2}\right)}{2 b}"," ",0,"-arccot(b*x+a)/b/(b*x+a)-ln(b*x+a)/b+1/2*ln(1+(b*x+a)^2)/b","A"
126,1,68,27,0.059000," ","int(arccot(x+1)/(2+2*x),x)","\frac{\ln \left(x +1\right) \mathrm{arccot}\left(x +1\right)}{2}-\frac{i \ln \left(x +1\right) \ln \left(1+i \left(x +1\right)\right)}{4}+\frac{i \ln \left(x +1\right) \ln \left(1-i \left(x +1\right)\right)}{4}-\frac{i \dilog \left(1+i \left(x +1\right)\right)}{4}+\frac{i \dilog \left(1-i \left(x +1\right)\right)}{4}"," ",0,"1/2*ln(x+1)*arccot(x+1)-1/4*I*ln(x+1)*ln(1+I*(x+1))+1/4*I*ln(x+1)*ln(1-I*(x+1))-1/4*I*dilog(1+I*(x+1))+1/4*I*dilog(1-I*(x+1))","B"
127,1,98,37,0.059000," ","int(arccot(b*x+a)/(a*d/b+d*x),x)","\frac{\ln \left(b x +a \right) \mathrm{arccot}\left(b x +a \right)}{d}-\frac{i \ln \left(b x +a \right) \ln \left(1+i \left(b x +a \right)\right)}{2 d}+\frac{i \ln \left(b x +a \right) \ln \left(1-i \left(b x +a \right)\right)}{2 d}-\frac{i \dilog \left(1+i \left(b x +a \right)\right)}{2 d}+\frac{i \dilog \left(1-i \left(b x +a \right)\right)}{2 d}"," ",0,"1/d*ln(b*x+a)*arccot(b*x+a)-1/2*I/d*ln(b*x+a)*ln(1+I*(b*x+a))+1/2*I/d*ln(b*x+a)*ln(1-I*(b*x+a))-1/2*I/d*dilog(1+I*(b*x+a))+1/2*I/d*dilog(1-I*(b*x+a))","B"
128,0,0,18,3.411000," ","int((b*x+a)^2*arccot(b*x+a)^(1/2),x)","\int \left(b x +a \right)^{2} \sqrt{\mathrm{arccot}\left(b x +a \right)}\, dx"," ",0,"int((b*x+a)^2*arccot(b*x+a)^(1/2),x)","F"
129,1,526,221,0.051000," ","int((f*x+e)^3*(a+b*arccot(d*x+c)),x)","-\frac{3 b f \ln \left(1+\left(d x +c \right)^{2}\right) c \,e^{2}}{2 d^{2}}-\frac{b \,f^{2} \arctan \left(d x +c \right) c^{3} e}{d^{3}}+\frac{3 b f \arctan \left(d x +c \right) c^{2} e^{2}}{2 d^{2}}+\frac{3 b \,f^{2} \ln \left(1+\left(d x +c \right)^{2}\right) c^{2} e}{2 d^{3}}+\frac{3 b \,f^{2} \arctan \left(d x +c \right) c e}{d^{3}}-\frac{2 b \,f^{2} c e x}{d^{2}}+\frac{b \,f^{3} \arctan \left(d x +c \right)}{4 d^{4}}+\frac{b \ln \left(1+\left(d x +c \right)^{2}\right) e^{3}}{2 d}+\frac{3 a f \,x^{2} e^{2}}{2}+a \,f^{2} x^{3} e +\frac{b \,f^{3} x^{3}}{12 d}-\frac{b \,f^{3} x}{4 d^{3}}+\frac{b \,f^{3} \mathrm{arccot}\left(d x +c \right) x^{4}}{4}+\mathrm{arccot}\left(d x +c \right) x b \,e^{3}+\frac{b \,\mathrm{arccot}\left(d x +c \right) e^{4}}{4 f}+\frac{b \arctan \left(d x +c \right) e^{4}}{4 f}-\frac{b \,f^{3} x^{2} c}{4 d^{2}}+\frac{b \,f^{2} e \,x^{2}}{2 d}+\frac{3 b \,f^{3} c^{2} x}{4 d^{3}}+\frac{3 b f \,e^{2} x}{2 d}+\frac{b \,f^{3} \ln \left(1+\left(d x +c \right)^{2}\right) c}{2 d^{4}}-\frac{b \arctan \left(d x +c \right) c \,e^{3}}{d}-\frac{b \,f^{2} \ln \left(1+\left(d x +c \right)^{2}\right) e}{2 d^{3}}-\frac{3 b \,f^{3} \arctan \left(d x +c \right) c^{2}}{2 d^{4}}+\frac{3 b f c \,e^{2}}{2 d^{2}}-\frac{5 b \,f^{2} c^{2} e}{2 d^{3}}+b \,f^{2} \mathrm{arccot}\left(d x +c \right) e \,x^{3}+\frac{b \,f^{3} \arctan \left(d x +c \right) c^{4}}{4 d^{4}}-\frac{3 b f \arctan \left(d x +c \right) e^{2}}{2 d^{2}}-\frac{b \,f^{3} \ln \left(1+\left(d x +c \right)^{2}\right) c^{3}}{2 d^{4}}+\frac{a \,e^{4}}{4 f}-\frac{b \,f^{3} c}{4 d^{4}}+\frac{13 b \,f^{3} c^{3}}{12 d^{4}}+\frac{3 b f \,\mathrm{arccot}\left(d x +c \right) e^{2} x^{2}}{2}+\frac{a \,f^{3} x^{4}}{4}+a x \,e^{3}"," ",0,"-3/2/d^2*b*f*ln(1+(d*x+c)^2)*c*e^2-1/d^3*b*f^2*arctan(d*x+c)*c^3*e+3/2/d^2*b*f*arctan(d*x+c)*c^2*e^2+3/2/d^3*b*f^2*ln(1+(d*x+c)^2)*c^2*e+3/d^3*b*f^2*arctan(d*x+c)*c*e-2*b/d^2*f^2*c*e*x+1/4/d^4*b*f^3*arctan(d*x+c)+1/2/d*b*ln(1+(d*x+c)^2)*e^3+3/2*a*f*x^2*e^2+a*f^2*x^3*e+1/12/d*b*f^3*x^3-1/4*b/d^3*f^3*x+1/4*b*f^3*arccot(d*x+c)*x^4+arccot(d*x+c)*x*b*e^3+1/4*b/f*arccot(d*x+c)*e^4+1/4*b/f*arctan(d*x+c)*e^4-1/4/d^2*b*f^3*x^2*c+1/2/d*b*f^2*e*x^2+3/4*b/d^3*f^3*c^2*x+3/2*b/d*f*e^2*x+1/2/d^4*b*f^3*ln(1+(d*x+c)^2)*c-1/d*b*arctan(d*x+c)*c*e^3-1/2/d^3*b*f^2*ln(1+(d*x+c)^2)*e-3/2/d^4*b*f^3*arctan(d*x+c)*c^2+3/2/d^2*b*f*c*e^2-5/2/d^3*b*f^2*c^2*e+b*f^2*arccot(d*x+c)*e*x^3+1/4/d^4*b*f^3*arctan(d*x+c)*c^4-3/2/d^2*b*f*arctan(d*x+c)*e^2-1/2/d^4*b*f^3*ln(1+(d*x+c)^2)*c^3+1/4*a/f*e^4-1/4/d^4*b*f^3*c+13/12/d^4*b*f^3*c^3+3/2*b*f*arccot(d*x+c)*e^2*x^2+1/4*a*f^3*x^4+a*x*e^3","B"
130,1,312,146,0.049000," ","int((f*x+e)^2*(a+b*arccot(d*x+c)),x)","a x \,e^{2}+\frac{b f c e}{d^{2}}+a f \,x^{2} e -\frac{5 b \,f^{2} c^{2}}{6 d^{3}}+b f \,\mathrm{arccot}\left(d x +c \right) e \,x^{2}-\frac{b \,f^{2} \ln \left(1+\left(d x +c \right)^{2}\right)}{6 d^{3}}-\frac{b \arctan \left(d x +c \right) c \,e^{2}}{d}+\frac{b \,f^{2} x^{2}}{6 d}-\frac{b f \ln \left(1+\left(d x +c \right)^{2}\right) c e}{d^{2}}+\frac{b f \arctan \left(d x +c \right) c^{2} e}{d^{2}}+\mathrm{arccot}\left(d x +c \right) x b \,e^{2}+\frac{b \,f^{2} \mathrm{arccot}\left(d x +c \right) x^{3}}{3}+\frac{a \,f^{2} x^{3}}{3}+\frac{a \,e^{3}}{3 f}+\frac{b \,f^{2} \arctan \left(d x +c \right) c}{d^{3}}-\frac{b f \arctan \left(d x +c \right) e}{d^{2}}+\frac{b \arctan \left(d x +c \right) e^{3}}{3 f}-\frac{b \,f^{2} \arctan \left(d x +c \right) c^{3}}{3 d^{3}}+\frac{b \,f^{2} \ln \left(1+\left(d x +c \right)^{2}\right) c^{2}}{2 d^{3}}+\frac{b f e x}{d}-\frac{2 b \,f^{2} c x}{3 d^{2}}+\frac{b \,\mathrm{arccot}\left(d x +c \right) e^{3}}{3 f}+\frac{b \,e^{2} \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d}"," ",0,"a*x*e^2+1/d^2*b*f*c*e+a*f*x^2*e-5/6/d^3*b*f^2*c^2+b*f*arccot(d*x+c)*e*x^2-1/6/d^3*b*f^2*ln(1+(d*x+c)^2)-1/d*b*arctan(d*x+c)*c*e^2+1/6/d*b*f^2*x^2-1/d^2*b*f*ln(1+(d*x+c)^2)*c*e+1/d^2*b*f*arctan(d*x+c)*c^2*e+arccot(d*x+c)*x*b*e^2+1/3*b*f^2*arccot(d*x+c)*x^3+1/3*a*f^2*x^3+1/3*a/f*e^3+1/d^3*b*f^2*arctan(d*x+c)*c-1/d^2*b*f*arctan(d*x+c)*e+1/3*b/f*arctan(d*x+c)*e^3-1/3/d^3*b*f^2*arctan(d*x+c)*c^3+1/2/d^3*b*f^2*ln(1+(d*x+c)^2)*c^2+b/d*f*e*x-2/3*b/d^2*f^2*c*x+1/3*b/f*arccot(d*x+c)*e^3+1/2*b*e^2*ln(1+(d*x+c)^2)/d","B"
131,1,146,89,0.045000," ","int((f*x+e)*(a+b*arccot(d*x+c)),x)","\frac{a \,x^{2} f}{2}-\frac{a f \,c^{2}}{2 d^{2}}+a e x +\frac{a c e}{d}+\frac{b \,\mathrm{arccot}\left(d x +c \right) f \,x^{2}}{2}-\frac{b \,\mathrm{arccot}\left(d x +c \right) f \,c^{2}}{2 d^{2}}+\mathrm{arccot}\left(d x +c \right) x b e +\frac{\mathrm{arccot}\left(d x +c \right) b c e}{d}+\frac{b f x}{2 d}+\frac{b c f}{2 d^{2}}-\frac{b \ln \left(1+\left(d x +c \right)^{2}\right) c f}{2 d^{2}}+\frac{b \ln \left(1+\left(d x +c \right)^{2}\right) e}{2 d}-\frac{b f \arctan \left(d x +c \right)}{2 d^{2}}"," ",0,"1/2*a*x^2*f-1/2/d^2*a*f*c^2+a*e*x+1/d*a*c*e+1/2*b*arccot(d*x+c)*f*x^2-1/2/d^2*b*arccot(d*x+c)*f*c^2+arccot(d*x+c)*x*b*e+1/d*arccot(d*x+c)*b*c*e+1/2*b*f*x/d+1/2/d^2*b*c*f-1/2/d^2*b*ln(1+(d*x+c)^2)*c*f+1/2/d*b*ln(1+(d*x+c)^2)*e-1/2/d^2*b*f*arctan(d*x+c)","A"
132,1,42,36,0.039000," ","int(a+b*arccot(d*x+c),x)","a x +b \,\mathrm{arccot}\left(d x +c \right) x +\frac{b \,\mathrm{arccot}\left(d x +c \right) c}{d}+\frac{b \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d}"," ",0,"a*x+b*arccot(d*x+c)*x+b/d*arccot(d*x+c)*c+1/2*b*ln(1+(d*x+c)^2)/d","A"
133,1,224,150,0.067000," ","int((a+b*arccot(d*x+c))/(f*x+e),x)","\frac{a \ln \left(f \left(d x +c \right)-c f +d e \right)}{f}+\frac{b \ln \left(f \left(d x +c \right)-c f +d e \right) \mathrm{arccot}\left(d x +c \right)}{f}-\frac{i b \ln \left(f \left(d x +c \right)-c f +d e \right) \ln \left(\frac{i f -f \left(d x +c \right)}{-c f +d e +i f}\right)}{2 f}+\frac{i b \ln \left(f \left(d x +c \right)-c f +d e \right) \ln \left(\frac{i f +f \left(d x +c \right)}{c f -d e +i f}\right)}{2 f}-\frac{i b \dilog \left(\frac{i f -f \left(d x +c \right)}{-c f +d e +i f}\right)}{2 f}+\frac{i b \dilog \left(\frac{i f +f \left(d x +c \right)}{c f -d e +i f}\right)}{2 f}"," ",0,"a*ln(f*(d*x+c)-c*f+d*e)/f+b*ln(f*(d*x+c)-c*f+d*e)/f*arccot(d*x+c)-1/2*I*b*ln(f*(d*x+c)-c*f+d*e)/f*ln((I*f-f*(d*x+c))/(d*e+I*f-c*f))+1/2*I*b*ln(f*(d*x+c)-c*f+d*e)/f*ln((I*f+f*(d*x+c))/(I*f+c*f-d*e))-1/2*I*b/f*dilog((I*f-f*(d*x+c))/(d*e+I*f-c*f))+1/2*I*b/f*dilog((I*f+f*(d*x+c))/(I*f+c*f-d*e))","A"
134,1,206,153,0.050000," ","int((a+b*arccot(d*x+c))/(f*x+e)^2,x)","-\frac{d a}{\left(d f x +d e \right) f}-\frac{d b \,\mathrm{arccot}\left(d x +c \right)}{\left(d f x +d e \right) f}-\frac{d b \ln \left(f \left(d x +c \right)-c f +d e \right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}+\frac{d b \ln \left(1+\left(d x +c \right)^{2}\right)}{2 c^{2} f^{2}-4 c d e f +2 d^{2} e^{2}+2 f^{2}}+\frac{d b \arctan \left(d x +c \right) c}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{d^{2} b \arctan \left(d x +c \right) e}{f \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}"," ",0,"-d*a/(d*f*x+d*e)/f-d*b/(d*f*x+d*e)/f*arccot(d*x+c)-d*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)+1/2*d*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(1+(d*x+c)^2)+d*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)*c-d^2*b/f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)*e","A"
135,1,437,223,0.053000," ","int((a+b*arccot(d*x+c))/(f*x+e)^3,x)","-\frac{d^{2} a}{2 \left(d f x +d e \right)^{2} f}-\frac{d^{2} b \,\mathrm{arccot}\left(d x +c \right)}{2 \left(d f x +d e \right)^{2} f}+\frac{d^{2} b}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right) \left(d f x +d e \right)}+\frac{d^{2} b f \ln \left(f \left(d x +c \right)-c f +d e \right) c}{\left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)^{2}}-\frac{d^{3} b \ln \left(f \left(d x +c \right)-c f +d e \right) e}{\left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)^{2}}-\frac{d^{2} b f \arctan \left(d x +c \right) c^{2}}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)^{2}}+\frac{d^{3} b \arctan \left(d x +c \right) c e}{\left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)^{2}}-\frac{d^{4} b \arctan \left(d x +c \right) e^{2}}{2 f \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)^{2}}-\frac{d^{2} b f \ln \left(1+\left(d x +c \right)^{2}\right) c}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)^{2}}+\frac{d^{3} b \ln \left(1+\left(d x +c \right)^{2}\right) e}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)^{2}}+\frac{d^{2} b f \arctan \left(d x +c \right)}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)^{2}}"," ",0,"-1/2*d^2*a/(d*f*x+d*e)^2/f-1/2*d^2*b/(d*f*x+d*e)^2/f*arccot(d*x+c)+1/2*d^2*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)/(d*f*x+d*e)+d^2*b*f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)^2*ln(f*(d*x+c)-c*f+d*e)*c-d^3*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)^2*ln(f*(d*x+c)-c*f+d*e)*e-1/2*d^2*b*f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)^2*arctan(d*x+c)*c^2+d^3*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)^2*arctan(d*x+c)*c*e-1/2*d^4*b/f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)^2*arctan(d*x+c)*e^2-1/2*d^2*b*f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)^2*ln(1+(d*x+c)^2)*c+1/2*d^3*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)^2*ln(1+(d*x+c)^2)*e+1/2*d^2*b*f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)^2*arctan(d*x+c)","A"
136,1,1832,362,0.196000," ","int((f*x+e)^2*(a+b*arccot(d*x+c))^2,x)","a^{2} x \,e^{2}+\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c -i\right) f^{2}}{6 d^{3}}-\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c +i\right) f^{2}}{6 d^{3}}-\frac{i b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right) c^{2} f^{2}}{2 d^{3}}+\frac{i b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right) c^{2} f^{2}}{2 d^{3}}+\frac{i b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right) f^{2}}{6 d^{3}}-\frac{i b^{2} \ln \left(d x +c +i\right)^{2} c^{2} f^{2}}{4 d^{3}}+\frac{i b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right) f^{2}}{6 d^{3}}-\frac{i b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right) f^{2}}{6 d^{3}}-\frac{i b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right) e^{2}}{2 d}+\frac{i b^{2} \ln \left(d x +c +i\right)^{2} f^{2}}{12 d^{3}}+\frac{i b^{2} \ln \left(d x +c -i\right)^{2} e^{2}}{4 d}-\frac{i b^{2} \ln \left(d x +c -i\right)^{2} f^{2}}{12 d^{3}}-\frac{a b \,f^{2} \ln \left(1+\left(d x +c \right)^{2}\right)}{3 d^{3}}-\frac{5 a b \,f^{2} c^{2}}{3 d^{3}}+\frac{2 a b \,\mathrm{arccot}\left(d x +c \right) e^{3}}{3 f}+2 \,\mathrm{arccot}\left(d x +c \right) x a b \,e^{2}+\frac{2 b^{2} \mathrm{arccot}\left(d x +c \right) \arctan \left(d x +c \right) e^{3}}{3 f}+b^{2} f \mathrm{arccot}\left(d x +c \right)^{2} e \,x^{2}+\frac{2 a b \arctan \left(d x +c \right) e^{3}}{3 f}+\frac{a^{2} e^{3}}{3 f}+\frac{b^{2} f^{2} c}{3 d^{3}}+a^{2} f \,x^{2} e +\frac{b^{2} \arctan \left(d x +c \right)^{2} e^{3}}{3 f}+\frac{b^{2} f^{2} \mathrm{arccot}\left(d x +c \right)^{2} x^{3}}{3}+\mathrm{arccot}\left(d x +c \right)^{2} x \,b^{2} e^{2}+\frac{b^{2} \mathrm{arccot}\left(d x +c \right)^{2} e^{3}}{3 f}-\frac{2 \arctan \left(d x +c \right) a b c \,e^{2}}{d}+\frac{a b \,f^{2} \ln \left(1+\left(d x +c \right)^{2}\right) c^{2}}{d^{3}}+\frac{2 a b \,f^{2} \arctan \left(d x +c \right) c}{d^{3}}-\frac{2 a b \,f^{2} \arctan \left(d x +c \right) c^{3}}{3 d^{3}}+\frac{b^{2} f \arctan \left(d x +c \right)^{2} c^{2} e}{d^{2}}+\frac{a^{2} f^{2} x^{3}}{3}+\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c +i\right) c^{2} f^{2}}{2 d^{3}}+\frac{i b^{2} \ln \left(d x +c +i\right)^{2} c e f}{2 d^{2}}-\frac{i b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right) c^{2} f^{2}}{2 d^{3}}-\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c -i\right) c^{2} f^{2}}{2 d^{3}}+\frac{i b^{2} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right) c^{2} f^{2}}{2 d^{3}}-\frac{i b^{2} \ln \left(d x +c -i\right)^{2} c e f}{2 d^{2}}-\frac{i b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right) c e f}{d^{2}}+\frac{i b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right) c e f}{d^{2}}+\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c +i\right) e^{2}}{2 d}-\frac{i b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right) e^{2}}{2 d}+\frac{i b^{2} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right) e^{2}}{2 d}-\frac{4 a b \,f^{2} c x}{3 d^{2}}+\frac{2 a b f e x}{d}-\frac{2 a b f \arctan \left(d x +c \right) e}{d^{2}}-\frac{2 b^{2} f^{2} \mathrm{arccot}\left(d x +c \right) \arctan \left(d x +c \right) c^{3}}{3 d^{3}}-\frac{2 b^{2} f \,\mathrm{arccot}\left(d x +c \right) \arctan \left(d x +c \right) e}{d^{2}}-\frac{i e^{2} b^{2} \ln \left(d x +c +i\right)^{2}}{4 d}+\frac{i e^{2} b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{2 d}+\frac{2 b^{2} f^{2} \mathrm{arccot}\left(d x +c \right) \arctan \left(d x +c \right) c}{d^{3}}+\frac{b^{2} f^{2} x}{3 d^{2}}-\frac{b^{2} f^{2} \arctan \left(d x +c \right)}{3 d^{3}}+\frac{b^{2} f^{2} \mathrm{arccot}\left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right) c^{2}}{d^{3}}-\frac{i e^{2} b^{2} \ln \left(d x +c -i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d}+\frac{i b^{2} \ln \left(d x +c -i\right)^{2} c^{2} f^{2}}{4 d^{3}}-\frac{i b^{2} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right) f^{2}}{6 d^{3}}-\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c +i\right) c e f}{d^{2}}+\frac{i b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right) c e f}{d^{2}}+\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c -i\right) c e f}{d^{2}}-\frac{i b^{2} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right) c e f}{d^{2}}+\frac{b^{2} f^{2} \arctan \left(d x +c \right)^{2} c}{d^{3}}-\frac{\arctan \left(d x +c \right)^{2} b^{2} c \,e^{2}}{d}+\frac{b^{2} f \ln \left(1+\left(d x +c \right)^{2}\right) e}{d^{2}}-\frac{b^{2} f \arctan \left(d x +c \right)^{2} e}{d^{2}}+\frac{b^{2} \mathrm{arccot}\left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right) e^{2}}{d}-\frac{b^{2} f^{2} \mathrm{arccot}\left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right)}{3 d^{3}}+\frac{b^{2} f^{2} \mathrm{arccot}\left(d x +c \right) x^{2}}{3 d}-\frac{5 b^{2} f^{2} \mathrm{arccot}\left(d x +c \right) c^{2}}{3 d^{3}}+\frac{2 a b \,f^{2} \mathrm{arccot}\left(d x +c \right) x^{3}}{3}+2 a b f \,\mathrm{arccot}\left(d x +c \right) e \,x^{2}-\frac{2 b^{2} \mathrm{arccot}\left(d x +c \right) \arctan \left(d x +c \right) c \,e^{2}}{d}-\frac{4 b^{2} f^{2} \mathrm{arccot}\left(d x +c \right) x c}{3 d^{2}}+\frac{2 b^{2} f \,\mathrm{arccot}\left(d x +c \right) e x}{d}+\frac{2 b^{2} f \,\mathrm{arccot}\left(d x +c \right) e c}{d^{2}}-\frac{b^{2} f^{2} \arctan \left(d x +c \right)^{2} c^{3}}{3 d^{3}}-\frac{b^{2} f^{2} \ln \left(1+\left(d x +c \right)^{2}\right) c}{d^{3}}+\frac{a b \,f^{2} x^{2}}{3 d}+\frac{e^{2} a b \ln \left(1+\left(d x +c \right)^{2}\right)}{d}+\frac{2 a b f c e}{d^{2}}-\frac{2 b^{2} f \,\mathrm{arccot}\left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right) c e}{d^{2}}+\frac{2 b^{2} f \,\mathrm{arccot}\left(d x +c \right) \arctan \left(d x +c \right) c^{2} e}{d^{2}}+\frac{2 a b f \arctan \left(d x +c \right) e \,c^{2}}{d^{2}}-\frac{2 a b f \ln \left(1+\left(d x +c \right)^{2}\right) c e}{d^{2}}"," ",0,"a^2*x*e^2-1/3/d^3*a*b*f^2*ln(1+(d*x+c)^2)-5/3/d^3*a*b*f^2*c^2+2/3*a*b/f*arccot(d*x+c)*e^3+2*arccot(d*x+c)*x*a*b*e^2+2/3*b^2/f*arccot(d*x+c)*arctan(d*x+c)*e^3+b^2*f*arccot(d*x+c)^2*e*x^2+2/3*a*b/f*arctan(d*x+c)*e^3+1/12*I/d^3*b^2*ln(I+d*x+c)^2*f^2-1/12*I/d^3*b^2*ln(d*x+c-I)^2*f^2-1/6*I/d^3*b^2*dilog(-1/2*I*(I+d*x+c))*f^2+1/3*a^2/f*e^3+1/3/d^3*b^2*f^2*c+a^2*f*x^2*e+1/3*b^2/f*arctan(d*x+c)^2*e^3+1/3*b^2*f^2*arccot(d*x+c)^2*x^3+arccot(d*x+c)^2*x*b^2*e^2+1/3*b^2/f*arccot(d*x+c)^2*e^3-2/d*arctan(d*x+c)*a*b*c*e^2+1/d^3*a*b*f^2*ln(1+(d*x+c)^2)*c^2+2/d^3*a*b*f^2*arctan(d*x+c)*c-2/3/d^3*a*b*f^2*arctan(d*x+c)*c^3+1/d^2*b^2*f*arctan(d*x+c)^2*c^2*e+1/3*a^2*f^2*x^3-4/3*a*b/d^2*f^2*c*x+2*a*b/d*f*e*x-2/d^2*a*b*f*arctan(d*x+c)*e-2/3/d^3*b^2*f^2*arccot(d*x+c)*arctan(d*x+c)*c^3-2/d^2*b^2*f*arccot(d*x+c)*arctan(d*x+c)*e+2/d^3*b^2*f^2*arccot(d*x+c)*arctan(d*x+c)*c+1/4*I/d^3*b^2*ln(d*x+c-I)^2*c^2*f^2+1/2*I/d^3*b^2*dilog(-1/2*I*(I+d*x+c))*c^2*f^2+1/3*b^2*f^2*x/d^2-1/3*b^2*f^2*arctan(d*x+c)/d^3+1/2*I/d*b^2*ln(-1/2*I*(I+d*x+c))*ln(d*x+c-I)*e^2-1/6*I/d^3*b^2*ln(I+d*x+c)*ln(1+(d*x+c)^2)*f^2-1/6*I/d^3*b^2*ln(-1/2*I*(I+d*x+c))*ln(d*x+c-I)*f^2+1/d^3*b^2*f^2*arccot(d*x+c)*ln(1+(d*x+c)^2)*c^2+I/d^2*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))*c*e*f+I/d^2*b^2*ln(d*x+c-I)*ln(1+(d*x+c)^2)*c*e*f-I/d^2*b^2*ln(-1/2*I*(I+d*x+c))*ln(d*x+c-I)*c*e*f-I/d^2*b^2*ln(I+d*x+c)*ln(1+(d*x+c)^2)*c*e*f-1/2*I/d*b^2*ln(d*x+c-I)*ln(1+(d*x+c)^2)*e^2+1/6*I/d^3*b^2*ln(d*x+c-I)*ln(1+(d*x+c)^2)*f^2+1/2*I/d*b^2*ln(I+d*x+c)*ln(1+(d*x+c)^2)*e^2+1/d^3*b^2*f^2*arctan(d*x+c)^2*c-1/d*arctan(d*x+c)^2*b^2*c*e^2+1/d^2*b^2*f*ln(1+(d*x+c)^2)*e-1/d^2*b^2*f*arctan(d*x+c)^2*e-1/2*I/d*b^2*dilog(1/2*I*(d*x+c-I))*e^2+1/4*I/d*b^2*ln(d*x+c-I)^2*e^2+1/2*I/d*b^2*dilog(-1/2*I*(I+d*x+c))*e^2-1/4*I/d*b^2*ln(I+d*x+c)^2*e^2+1/6*I/d^3*b^2*dilog(1/2*I*(d*x+c-I))*f^2+1/d*b^2*arccot(d*x+c)*ln(1+(d*x+c)^2)*e^2-1/3/d^3*b^2*f^2*arccot(d*x+c)*ln(1+(d*x+c)^2)+1/3/d*b^2*f^2*arccot(d*x+c)*x^2-5/3/d^3*b^2*f^2*arccot(d*x+c)*c^2+2/3*a*b*f^2*arccot(d*x+c)*x^3+1/6*I/d^3*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))*f^2-1/2*I/d*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))*e^2-1/4*I/d^3*b^2*ln(I+d*x+c)^2*c^2*f^2-1/2*I/d^3*b^2*dilog(1/2*I*(d*x+c-I))*c^2*f^2+2*a*b*f*arccot(d*x+c)*e*x^2-2/d*b^2*arccot(d*x+c)*arctan(d*x+c)*c*e^2-4/3/d^2*b^2*f^2*arccot(d*x+c)*x*c+2/d*b^2*f*arccot(d*x+c)*e*x+2/d^2*b^2*f*arccot(d*x+c)*e*c+I/d^2*b^2*dilog(1/2*I*(d*x+c-I))*c*e*f-1/3/d^3*b^2*f^2*arctan(d*x+c)^2*c^3-1/d^3*b^2*f^2*ln(1+(d*x+c)^2)*c+1/3/d*a*b*f^2*x^2+1/d*e^2*a*b*ln(1+(d*x+c)^2)+2/d^2*a*b*f*c*e-2/d^2*b^2*f*arccot(d*x+c)*ln(1+(d*x+c)^2)*c*e+2/d^2*b^2*f*arccot(d*x+c)*arctan(d*x+c)*c^2*e-I/d^2*b^2*dilog(-1/2*I*(I+d*x+c))*c*e*f+1/2*I/d^2*b^2*ln(I+d*x+c)^2*c*e*f+1/2*I/d^3*b^2*ln(I+d*x+c)*ln(1+(d*x+c)^2)*c^2*f^2-1/2*I/d^3*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))*c^2*f^2-1/2*I/d^3*b^2*ln(d*x+c-I)*ln(1+(d*x+c)^2)*c^2*f^2+1/2*I/d^3*b^2*ln(-1/2*I*(I+d*x+c))*ln(d*x+c-I)*c^2*f^2-1/2*I/d^2*b^2*ln(d*x+c-I)^2*c*e*f+2/d^2*a*b*f*arctan(d*x+c)*e*c^2-2/d^2*a*b*f*ln(1+(d*x+c)^2)*c*e","B"
137,1,766,210,0.147000," ","int((f*x+e)*(a+b*arccot(d*x+c))^2,x)","\frac{2 \,\mathrm{arccot}\left(d x +c \right) a b c e}{d}+\frac{a^{2} x^{2} f}{2}+a^{2} x e -\frac{i b^{2} \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right) \ln \left(d x +c -i\right) c f}{2 d^{2}}-\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c +i\right) c f}{2 d^{2}}+\frac{i b^{2} \ln \left(\frac{i \left(d x +c -i\right)}{2}\right) \ln \left(d x +c +i\right) c f}{2 d^{2}}+\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c -i\right) c f}{2 d^{2}}+2 \,\mathrm{arccot}\left(d x +c \right) x a b e -\frac{b^{2} \mathrm{arccot}\left(d x +c \right)^{2} c^{2} f}{2 d^{2}}+\frac{b^{2} \mathrm{arccot}\left(d x +c \right) f x}{d}+\frac{b^{2} \mathrm{arccot}\left(d x +c \right) f c}{d^{2}}-\frac{b^{2} \mathrm{arccot}\left(d x +c \right) \arctan \left(d x +c \right) f}{d^{2}}+\frac{b^{2} \mathrm{arccot}\left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right) e}{d}+\frac{\mathrm{arccot}\left(d x +c \right)^{2} b^{2} c e}{d}-\frac{a b f \arctan \left(d x +c \right)}{d^{2}}+a b \,\mathrm{arccot}\left(d x +c \right) f \,x^{2}-\frac{b^{2} f \arctan \left(d x +c \right)^{2}}{2 d^{2}}+\frac{b^{2} \mathrm{arccot}\left(d x +c \right)^{2} f \,x^{2}}{2}+\mathrm{arccot}\left(d x +c \right)^{2} x \,b^{2} e -\frac{a^{2} f \,c^{2}}{2 d^{2}}+\frac{a^{2} c e}{d}-\frac{i b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right) e}{2 d}+\frac{i b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right) e}{2 d}-\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c -i\right) e}{2 d}+\frac{a b c f}{d^{2}}-\frac{i b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right) c f}{2 d^{2}}+\frac{i b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right) c f}{2 d^{2}}+\frac{a b f x}{d}+\frac{b^{2} f \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d^{2}}+\frac{i b^{2} \ln \left(d x +c -i\right)^{2} e}{4 d}-\frac{i b^{2} \ln \left(d x +c +i\right)^{2} e}{4 d}+\frac{i b^{2} \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right) \ln \left(d x +c -i\right) e}{2 d}+\frac{i b^{2} \ln \left(d x +c +i\right)^{2} c f}{4 d^{2}}-\frac{i b^{2} \ln \left(d x +c -i\right)^{2} c f}{4 d^{2}}-\frac{i b^{2} \ln \left(\frac{i \left(d x +c -i\right)}{2}\right) \ln \left(d x +c +i\right) e}{2 d}+\frac{i b^{2} \ln \left(1+\left(d x +c \right)^{2}\right) \ln \left(d x +c +i\right) e}{2 d}+\frac{a b \ln \left(1+\left(d x +c \right)^{2}\right) e}{d}-\frac{a b \,\mathrm{arccot}\left(d x +c \right) f \,c^{2}}{d^{2}}-\frac{a b \ln \left(1+\left(d x +c \right)^{2}\right) c f}{d^{2}}-\frac{b^{2} \mathrm{arccot}\left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right) c f}{d^{2}}"," ",0,"1/2*I/d*b^2*ln(-1/2*I*(I+d*x+c))*ln(d*x+c-I)*e-1/2*I/d^2*b^2*dilog(-1/2*I*(I+d*x+c))*c*f+1/4*I/d^2*b^2*ln(I+d*x+c)^2*c*f+1/2*I/d^2*b^2*dilog(1/2*I*(d*x+c-I))*c*f-1/4*I/d^2*b^2*ln(d*x+c-I)^2*c*f-1/2*I/d*b^2*ln(1/2*I*(d*x+c-I))*ln(I+d*x+c)*e+2/d*arccot(d*x+c)*a*b*c*e+1/2*I/d*b^2*ln(1+(d*x+c)^2)*ln(I+d*x+c)*e-1/2*I/d*b^2*ln(1+(d*x+c)^2)*ln(d*x+c-I)*e+1/2*a^2*x^2*f+a^2*x*e+1/4*I/d*b^2*ln(d*x+c-I)^2*e+1/2*I/d*b^2*dilog(-1/2*I*(I+d*x+c))*e-1/4*I/d*b^2*ln(I+d*x+c)^2*e-1/2*I/d*b^2*dilog(1/2*I*(d*x+c-I))*e+2*arccot(d*x+c)*x*a*b*e-1/2/d^2*b^2*arccot(d*x+c)^2*c^2*f+1/d*b^2*arccot(d*x+c)*f*x+1/d^2*b^2*arccot(d*x+c)*f*c-1/d^2*b^2*arccot(d*x+c)*arctan(d*x+c)*f+1/d*b^2*arccot(d*x+c)*ln(1+(d*x+c)^2)*e+1/d*arccot(d*x+c)^2*b^2*c*e-1/d^2*a*b*f*arctan(d*x+c)+a*b*arccot(d*x+c)*f*x^2-1/2/d^2*b^2*f*arctan(d*x+c)^2+1/2*b^2*arccot(d*x+c)^2*f*x^2+arccot(d*x+c)^2*x*b^2*e-1/2/d^2*a^2*f*c^2+1/d*a^2*c*e+1/d^2*a*b*c*f-1/2*I/d^2*b^2*ln(-1/2*I*(I+d*x+c))*ln(d*x+c-I)*c*f-1/2*I/d^2*b^2*ln(1+(d*x+c)^2)*ln(I+d*x+c)*c*f+1/2*I/d^2*b^2*ln(1/2*I*(d*x+c-I))*ln(I+d*x+c)*c*f+1/2*I/d^2*b^2*ln(1+(d*x+c)^2)*ln(d*x+c-I)*c*f+a*b*f*x/d+1/2*b^2*f*ln(1+(d*x+c)^2)/d^2+1/d*a*b*ln(1+(d*x+c)^2)*e-1/d^2*a*b*arccot(d*x+c)*f*c^2-1/d^2*a*b*ln(1+(d*x+c)^2)*c*f-1/d^2*b^2*arccot(d*x+c)*ln(1+(d*x+c)^2)*c*f","B"
138,1,236,98,0.334000," ","int((a+b*arccot(d*x+c))^2,x)","\mathrm{arccot}\left(d x +c \right)^{2} x \,b^{2}+\frac{i \mathrm{arccot}\left(d x +c \right)^{2} b^{2}}{d}+\frac{\mathrm{arccot}\left(d x +c \right)^{2} b^{2} c}{d}+2 \,\mathrm{arccot}\left(d x +c \right) x a b -\frac{2 \ln \left(1-\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right) \mathrm{arccot}\left(d x +c \right) b^{2}}{d}-\frac{2 \ln \left(1+\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right) \mathrm{arccot}\left(d x +c \right) b^{2}}{d}+\frac{2 \,\mathrm{arccot}\left(d x +c \right) a b c}{d}+\frac{2 i \polylog \left(2, \frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right) b^{2}}{d}+\frac{2 i \polylog \left(2, -\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right) b^{2}}{d}+a^{2} x +\frac{a b \ln \left(1+\left(d x +c \right)^{2}\right)}{d}+\frac{a^{2} c}{d}"," ",0,"arccot(d*x+c)^2*x*b^2+I/d*arccot(d*x+c)^2*b^2+1/d*arccot(d*x+c)^2*b^2*c+2*arccot(d*x+c)*x*a*b-2/d*ln(1-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))*arccot(d*x+c)*b^2-2/d*ln(1+(I+d*x+c)/(1+(d*x+c)^2)^(1/2))*arccot(d*x+c)*b^2+2/d*arccot(d*x+c)*a*b*c+2*I/d*polylog(2,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))*b^2+2*I/d*polylog(2,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))*b^2+a^2*x+1/d*a*b*ln(1+(d*x+c)^2)+a^2*c/d","B"
139,1,2201,246,2.530000," ","int((a+b*arccot(d*x+c))^2/(f*x+e),x)","\frac{2 i d \,b^{2} e \,\mathrm{arccot}\left(d x +c \right) \polylog \left(2, \frac{\left(-c f +d e +i f \right) \left(d x +c +i\right)^{2}}{\left(-c f +d e -i f \right) \left(1+\left(d x +c \right)^{2}\right)}\right)}{f \left(2 c f -2 d e -2 i f \right)}+\frac{i b^{2} \pi  \mathrm{arccot}\left(d x +c \right)^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-1}\right) \mathrm{csgn}\left(i \left(\frac{c f \left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-\frac{d e \left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-c f +d e -\frac{i \left(d x +c +i\right)^{2} f}{1+\left(d x +c \right)^{2}}-i f \right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{c f \left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-\frac{d e \left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-c f +d e -\frac{i \left(d x +c +i\right)^{2} f}{1+\left(d x +c \right)^{2}}-i f \right)}{\frac{\left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-1}\right)}{2 f}+\frac{a^{2} \ln \left(f \left(d x +c \right)-c f +d e \right)}{f}+\frac{b^{2} \ln \left(f \left(d x +c \right)-c f +d e \right) \mathrm{arccot}\left(d x +c \right)^{2}}{f}-\frac{b^{2} \mathrm{arccot}\left(d x +c \right)^{2} \ln \left(1+\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{f}-\frac{b^{2} \mathrm{arccot}\left(d x +c \right)^{2} \ln \left(1-\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{f}+\frac{b^{2} \mathrm{arccot}\left(d x +c \right)^{2} \ln \left(\frac{\left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-1\right)}{f}-\frac{b^{2} \mathrm{arccot}\left(d x +c \right) \polylog \left(2, \frac{\left(-c f +d e +i f \right) \left(d x +c +i\right)^{2}}{\left(-c f +d e -i f \right) \left(1+\left(d x +c \right)^{2}\right)}\right)}{c f -d e -i f}-\frac{i b^{2} \polylog \left(3, \frac{\left(-c f +d e +i f \right) \left(d x +c +i\right)^{2}}{\left(-c f +d e -i f \right) \left(1+\left(d x +c \right)^{2}\right)}\right)}{2 \left(c f -d e -i f \right)}-\frac{2 b^{2} \polylog \left(3, \frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{f}-\frac{2 b^{2} \polylog \left(3, -\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{f}+\frac{2 a b \ln \left(f \left(d x +c \right)-c f +d e \right) \mathrm{arccot}\left(d x +c \right)}{f}+\frac{b^{2} c \mathrm{arccot}\left(d x +c \right)^{2} \ln \left(1-\frac{\left(-c f +d e +i f \right) \left(d x +c +i\right)^{2}}{\left(-c f +d e -i f \right) \left(1+\left(d x +c \right)^{2}\right)}\right)}{c f -d e -i f}-\frac{i b^{2} \pi  \mathrm{arccot}\left(d x +c \right)^{2}}{f}-\frac{i b^{2} \mathrm{arccot}\left(d x +c \right)^{2} \ln \left(1-\frac{\left(-c f +d e +i f \right) \left(d x +c +i\right)^{2}}{\left(-c f +d e -i f \right) \left(1+\left(d x +c \right)^{2}\right)}\right)}{c f -d e -i f}+\frac{b^{2} c \polylog \left(3, \frac{\left(-c f +d e +i f \right) \left(d x +c +i\right)^{2}}{\left(-c f +d e -i f \right) \left(1+\left(d x +c \right)^{2}\right)}\right)}{2 c f -2 d e -2 i f}+\frac{i a b \dilog \left(\frac{i f +f \left(d x +c \right)}{c f -d e +i f}\right)}{f}+\frac{2 i b^{2} \mathrm{arccot}\left(d x +c \right) \polylog \left(2, \frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{f}+\frac{2 i b^{2} \mathrm{arccot}\left(d x +c \right) \polylog \left(2, -\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{f}-\frac{i a b \dilog \left(\frac{i f -f \left(d x +c \right)}{-c f +d e +i f}\right)}{f}-\frac{d \,b^{2} e \mathrm{arccot}\left(d x +c \right)^{2} \ln \left(1-\frac{\left(-c f +d e +i f \right) \left(d x +c +i\right)^{2}}{\left(-c f +d e -i f \right) \left(1+\left(d x +c \right)^{2}\right)}\right)}{f \left(c f -d e -i f \right)}-\frac{i b^{2} \pi  \mathrm{arccot}\left(d x +c \right)^{2} \mathrm{csgn}\left(\frac{i}{\frac{\left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{c f \left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-\frac{d e \left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-c f +d e -\frac{i \left(d x +c +i\right)^{2} f}{1+\left(d x +c \right)^{2}}-i f \right)}{\frac{\left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-1}\right)^{2}}{2 f}-\frac{i b^{2} \pi  \mathrm{arccot}\left(d x +c \right)^{2} \mathrm{csgn}\left(i \left(\frac{c f \left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-\frac{d e \left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-c f +d e -\frac{i \left(d x +c +i\right)^{2} f}{1+\left(d x +c \right)^{2}}-i f \right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{c f \left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-\frac{d e \left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-c f +d e -\frac{i \left(d x +c +i\right)^{2} f}{1+\left(d x +c \right)^{2}}-i f \right)}{\frac{\left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-1}\right)^{2}}{2 f}+\frac{i a b \ln \left(f \left(d x +c \right)-c f +d e \right) \ln \left(\frac{i f +f \left(d x +c \right)}{c f -d e +i f}\right)}{f}+\frac{i b^{2} \pi  \mathrm{arccot}\left(d x +c \right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{c f \left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-\frac{d e \left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-c f +d e -\frac{i \left(d x +c +i\right)^{2} f}{1+\left(d x +c \right)^{2}}-i f \right)}{\frac{\left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-1}\right)^{2}}{f}-\frac{i b^{2} \pi  \mathrm{arccot}\left(d x +c \right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{c f \left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-\frac{d e \left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-c f +d e -\frac{i \left(d x +c +i\right)^{2} f}{1+\left(d x +c \right)^{2}}-i f \right)}{\frac{\left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-1}\right)^{3}}{2 f}-\frac{i a b \ln \left(f \left(d x +c \right)-c f +d e \right) \ln \left(\frac{i f -f \left(d x +c \right)}{-c f +d e +i f}\right)}{f}-\frac{d \,b^{2} e \polylog \left(3, \frac{\left(-c f +d e +i f \right) \left(d x +c +i\right)^{2}}{\left(-c f +d e -i f \right) \left(1+\left(d x +c \right)^{2}\right)}\right)}{2 f \left(c f -d e -i f \right)}-\frac{i b^{2} c \,\mathrm{arccot}\left(d x +c \right) \polylog \left(2, \frac{\left(-c f +d e +i f \right) \left(d x +c +i\right)^{2}}{\left(-c f +d e -i f \right) \left(1+\left(d x +c \right)^{2}\right)}\right)}{c f -d e -i f}-\frac{b^{2} \mathrm{arccot}\left(d x +c \right)^{2} \ln \left(\frac{c f \left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-\frac{d e \left(d x +c +i\right)^{2}}{1+\left(d x +c \right)^{2}}-c f +d e -\frac{i \left(d x +c +i\right)^{2} f}{1+\left(d x +c \right)^{2}}-i f \right)}{f}"," ",0,"-2*b^2/f*polylog(3,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-2*b^2/f*polylog(3,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+a^2*ln(f*(d*x+c)-c*f+d*e)/f-b^2/f*arccot(d*x+c)^2*ln(1+(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+1/2*b^2*c/(-I*f+c*f-d*e)*polylog(3,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))-b^2/f*arccot(d*x+c)^2*ln(1-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+b^2*ln(f*(d*x+c)-c*f+d*e)/f*arccot(d*x+c)^2+b^2/f*arccot(d*x+c)^2*ln((I+d*x+c)^2/(1+(d*x+c)^2)-1)-b^2/(-I*f+c*f-d*e)*arccot(d*x+c)*polylog(2,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))-1/2*I*b^2/(-I*f+c*f-d*e)*polylog(3,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))+2*I*d*b^2/f*e*arccot(d*x+c)*polylog(2,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))/(-2*I*f+2*c*f-2*d*e)+1/2*I*b^2/f*Pi*arccot(d*x+c)^2*csgn(I/((I+d*x+c)^2/(1+(d*x+c)^2)-1))*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f))*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)/((I+d*x+c)^2/(1+(d*x+c)^2)-1))-b^2/f*arccot(d*x+c)^2*ln(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)+2*a*b*ln(f*(d*x+c)-c*f+d*e)/f*arccot(d*x+c)+I*a*b/f*dilog((I*f+f*(d*x+c))/(I*f+c*f-d*e))+b^2*c/(-I*f+c*f-d*e)*arccot(d*x+c)^2*ln(1-(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))-I*b^2/f*Pi*arccot(d*x+c)^2+2*I*b^2/f*arccot(d*x+c)*polylog(2,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-I*b^2/(-I*f+c*f-d*e)*arccot(d*x+c)^2*ln(1-(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))+2*I*b^2/f*arccot(d*x+c)*polylog(2,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-I*a*b/f*dilog((I*f-f*(d*x+c))/(d*e+I*f-c*f))-d*b^2/f*e/(-I*f+c*f-d*e)*arccot(d*x+c)^2*ln(1-(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))-1/2*I*b^2/f*Pi*arccot(d*x+c)^2*csgn(I/((I+d*x+c)^2/(1+(d*x+c)^2)-1))*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)/((I+d*x+c)^2/(1+(d*x+c)^2)-1))^2-1/2*I*b^2/f*Pi*arccot(d*x+c)^2*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f))*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)/((I+d*x+c)^2/(1+(d*x+c)^2)-1))^2-1/2*d*b^2/f*e/(-I*f+c*f-d*e)*polylog(3,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))+I*a*b*ln(f*(d*x+c)-c*f+d*e)/f*ln((I*f+f*(d*x+c))/(I*f+c*f-d*e))+I*b^2/f*Pi*arccot(d*x+c)^2*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)/((I+d*x+c)^2/(1+(d*x+c)^2)-1))^2-I*b^2*c/(-I*f+c*f-d*e)*arccot(d*x+c)*polylog(2,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))-1/2*I*b^2/f*Pi*arccot(d*x+c)^2*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)/((I+d*x+c)^2/(1+(d*x+c)^2)-1))^3-I*a*b*ln(f*(d*x+c)-c*f+d*e)/f*ln((I*f-f*(d*x+c))/(d*e+I*f-c*f))","C"
140,1,1180,555,0.126000," ","int((a+b*arccot(d*x+c))^2/(f*x+e)^2,x)","\frac{i d \,b^{2} \ln \left(d x +c -i\right)^{2}}{4 c^{2} f^{2}-8 c d e f +4 d^{2} e^{2}+4 f^{2}}+\frac{i d \,b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{2 c^{2} f^{2}-4 c d e f +2 d^{2} e^{2}+2 f^{2}}-\frac{d^{2} b^{2} \arctan \left(d x +c \right)^{2} e}{f \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}-\frac{2 d a b \,\mathrm{arccot}\left(d x +c \right)}{\left(d f x +d e \right) f}+\frac{2 d a b \arctan \left(d x +c \right) c}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}+\frac{i d \,b^{2} \ln \left(d x +c +i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{2 c^{2} f^{2}-4 c d e f +2 d^{2} e^{2}+2 f^{2}}+\frac{i d \,b^{2} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{2 c^{2} f^{2}-4 c d e f +2 d^{2} e^{2}+2 f^{2}}-\frac{i d \,b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right)}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}-\frac{i d \,b^{2} \ln \left(f \left(d x +c \right)-c f +d e \right) \ln \left(\frac{i f +f \left(d x +c \right)}{c f -d e +i f}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{i d \,b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right)}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}-\frac{i d \,b^{2} \dilog \left(\frac{i f +f \left(d x +c \right)}{c f -d e +i f}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{2 d^{2} a b \arctan \left(d x +c \right) e}{f \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}-\frac{d \,a^{2}}{\left(d f x +d e \right) f}+\frac{d a b \ln \left(1+\left(d x +c \right)^{2}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{d \,b^{2} \mathrm{arccot}\left(d x +c \right)^{2}}{\left(d f x +d e \right) f}-\frac{2 d \,b^{2} \mathrm{arccot}\left(d x +c \right) \ln \left(f \left(d x +c \right)-c f +d e \right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}+\frac{d \,b^{2} \mathrm{arccot}\left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}+\frac{d \,b^{2} \arctan \left(d x +c \right)^{2} c}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}+\frac{2 d \,b^{2} \mathrm{arccot}\left(d x +c \right) \arctan \left(d x +c \right) c}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{i d \,b^{2} \ln \left(d x +c -i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}+\frac{i d \,b^{2} \ln \left(f \left(d x +c \right)-c f +d e \right) \ln \left(\frac{i f -f \left(d x +c \right)}{-c f +d e +i f}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{2 d^{2} b^{2} \mathrm{arccot}\left(d x +c \right) \arctan \left(d x +c \right) e}{f \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}+\frac{i d \,b^{2} \dilog \left(\frac{i f -f \left(d x +c \right)}{-c f +d e +i f}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{i d \,b^{2} \ln \left(d x +c +i\right)^{2}}{4 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}-\frac{2 d a b \ln \left(f \left(d x +c \right)-c f +d e \right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}"," ",0,"-d^2*b^2/f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*e-2*d*a*b/(d*f*x+d*e)/f*arccot(d*x+c)+1/2*I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))-1/2*I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))+2*d*a*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)*c-I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)*ln((I*f+f*(d*x+c))/(I*f+c*f-d*e))+1/2*I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(I+d*x+c)*ln(1+(d*x+c)^2)-1/2*I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(d*x+c-I)*ln(1+(d*x+c)^2)-2*d^2*a*b/f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)*e-d*a^2/(d*f*x+d*e)/f+d*a*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(1+(d*x+c)^2)-d*b^2/(d*f*x+d*e)/f*arccot(d*x+c)^2-2*d*b^2*arccot(d*x+c)/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)+d*b^2*arccot(d*x+c)/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(1+(d*x+c)^2)-1/2*I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*dilog(1/2*I*(d*x+c-I))+1/4*I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(d*x+c-I)^2-I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*dilog((I*f+f*(d*x+c))/(I*f+c*f-d*e))-1/4*I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(I+d*x+c)^2+1/2*I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*dilog(-1/2*I*(I+d*x+c))+I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*dilog((I*f-f*(d*x+c))/(d*e+I*f-c*f))+d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*c+I*d*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)*ln((I*f-f*(d*x+c))/(d*e+I*f-c*f))+2*d*b^2*arccot(d*x+c)/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)*c-2*d^2*b^2/f*arccot(d*x+c)/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)*e-2*d*a*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)","B"
141,1,3693,542,0.577000," ","int((f*x+e)^2*(a+b*arccot(d*x+c))^3,x)","\text{output too large to display}"," ",0,"6/d^2*b^3*f*c*e*arccot(d*x+c)^2*ln(1+(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+3/d^3*a*b^2*f^2*arccot(d*x+c)*ln(1+(d*x+c)^2)*c^2-2/d^3*a*b^2*f^2*arccot(d*x+c)*arctan(d*x+c)*c^3+6/d^3*a*b^2*f^2*arccot(d*x+c)*arctan(d*x+c)*c+3/2*I/d^3*a*b^2*dilog(-1/2*I*(I+d*x+c))*c^2*f^2-3/4*I/d^3*a*b^2*ln(I+d*x+c)^2*c^2*f^2-2*I/d^2*b^3*f*arccot(d*x+c)^3*c*e+3/4*I/d^3*a*b^2*ln(d*x+c-I)^2*c^2*f^2+a*b^2*f^2*x/d^2+a^3*x*e^2+1/3*a^3*f^2*x^3-3*I/d^2*a*b^2*ln(I+d*x+c)*ln(1+(d*x+c)^2)*c*e*f-3*I/d^2*a*b^2*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))*c*e*f+3*I/d^2*a*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))*c*e*f+3*I/d^2*a*b^2*ln(d*x+c-I)*ln(1+(d*x+c)^2)*c*e*f-5/2/d^3*a^2*b*f^2*c^2+1/3*a^3/f*e^3+a^3*f*x^2*e+1/3*b^3*f^2*arccot(d*x+c)^3*x^3+arccot(d*x+c)^3*x*b^3*e^2-1/d^3*b^3*f^2*ln(1+(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+2/d^3*b^3*f^2*ln((I+d*x+c)/(1+(d*x+c)^2)^(1/2))-1/d^3*b^3*f^2*ln((I+d*x+c)/(1+(d*x+c)^2)^(1/2)-1)+1/2/d^3*b^3*f^2*arccot(d*x+c)^2+2/d^3*b^3*f^2*polylog(3,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-1/2*I/d^3*a*b^2*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))*f^2-1/2*I/d^3*a*b^2*ln(I+d*x+c)*ln(1+(d*x+c)^2)*f^2-3/2*I/d^3*a*b^2*dilog(1/2*I*(d*x+c-I))*c^2*f^2-3/d^2*a^2*b*f*ln(1+(d*x+c)^2)*c*e+6/d^2*b^3*f*c*e*arccot(d*x+c)^2*ln(1-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+1/2/d*a^2*b*f^2*x^2+a^2*b*f^2*arccot(d*x+c)*x^3+a*b^2*f^2*arccot(d*x+c)^2*x^3+b^3*f*arccot(d*x+c)^3*e*x^2+3*arccot(d*x+c)^2*x*a*b^2*e^2+3*arccot(d*x+c)*x*a^2*b*e^2+1/d^2*b^3*f*arccot(d*x+c)^3*e+I/d*b^3*arccot(d*x+c)^3*e^2+3/2/d*a^2*b*ln(1+(d*x+c)^2)*e^2+1/d*arccot(d*x+c)^3*b^3*c*e^2-3/d*b^3*e^2*arccot(d*x+c)^2*ln(1-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-3/d*b^3*e^2*arccot(d*x+c)^2*ln(1+(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+1/2/d*b^3*f^2*arccot(d*x+c)^2*x^2-5/2/d^3*b^3*f^2*arccot(d*x+c)^2*c^2+a^2*b/f*arccot(d*x+c)*e^3+a^2*b/f*arctan(d*x+c)*e^3-1/3*I/d^3*b^3*f^2*arccot(d*x+c)^3-I/d^3*b^3*f^2*arccot(d*x+c)+3/2*I/d*a*b^2*dilog(-1/2*I*(I+d*x+c))*e^2-3/4*I/d*a*b^2*ln(I+d*x+c)^2*e^2-3/2*I/d*a*b^2*dilog(1/2*I*(d*x+c-I))*e^2+3/4*I/d*a*b^2*ln(d*x+c-I)^2*e^2+6*I/d*b^3*e^2*arccot(d*x+c)*polylog(2,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+6*I/d*b^3*e^2*arccot(d*x+c)*polylog(2,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+6*I/d^2*b^3*f*e*polylog(2,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+6*I/d^2*b^3*f*e*polylog(2,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-3*I/d^3*b^3*f^2*arccot(d*x+c)^2*c-6*I/d^3*b^3*f^2*c*polylog(2,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-1/2*I/d^3*a*b^2*dilog(-1/2*I*(I+d*x+c))*f^2+1/4*I/d^3*a*b^2*ln(I+d*x+c)^2*f^2+1/2*I/d^3*a*b^2*dilog(1/2*I*(d*x+c-I))*f^2-3/d^3*a*b^2*f^2*ln(1+(d*x+c)^2)*c+12/d^2*b^3*f*c*e*polylog(3,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+3/2/d^3*a^2*b*f^2*ln(1+(d*x+c)^2)*c^2-6/d^2*b^3*f*e*arccot(d*x+c)*ln(1-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-3/d^3*b^3*f^2*c^2*arccot(d*x+c)^2*ln(1-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-3/d^3*b^3*f^2*c^2*arccot(d*x+c)^2*ln(1+(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+6/d^3*b^3*f^2*c*arccot(d*x+c)*ln(1-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-6/d^2*a*b^2*f*arccot(d*x+c)*arctan(d*x+c)*e-6/d*a*b^2*arccot(d*x+c)*arctan(d*x+c)*c*e^2+3/d^2*a*b^2*f*arctan(d*x+c)^2*c^2*e+6*I/d^3*b^3*f^2*c^2*arccot(d*x+c)*polylog(2,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+6*I/d^3*b^3*f^2*c^2*arccot(d*x+c)*polylog(2,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+1/2*I/d^3*a*b^2*ln(d*x+c-I)*ln(1+(d*x+c)^2)*f^2+I/d^3*b^3*f^2*arccot(d*x+c)^3*c^2+3/d^2*a*b^2*f*ln(1+(d*x+c)^2)*e-1/d^3*a*b^2*f^2*arctan(d*x+c)^2*c^3+3/d^3*a*b^2*f^2*arctan(d*x+c)^2*c-3/d^2*a*b^2*f*arctan(d*x+c)^2*e+3/d*a*b^2*arccot(d*x+c)*ln(1+(d*x+c)^2)*e^2-1/d^3*a*b^2*f^2*arccot(d*x+c)*ln(1+(d*x+c)^2)+1/d*a*b^2*f^2*arccot(d*x+c)*x^2-5/d^3*a*b^2*f^2*arccot(d*x+c)*c^2-2/d^2*b^3*f^2*arccot(d*x+c)^2*x*c-1/d^2*b^3*f*arccot(d*x+c)^3*e*c^2+3/d*b^3*f*arccot(d*x+c)^2*e*x+3/d^2*b^3*f*arccot(d*x+c)^2*e*c+12/d^2*b^3*f*c*e*polylog(3,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-3/d*a*b^2*arctan(d*x+c)^2*c*e^2+1/d^3*a*b^2*f^2*c-6/d^2*b^3*f*e*arccot(d*x+c)*ln(1+(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-1/d^3*a^2*b*f^2*arctan(d*x+c)*c^3+3/d^3*a^2*b*f^2*arctan(d*x+c)*c-3/d^2*a^2*b*f*arctan(d*x+c)*e+3*a^2*b*f*arccot(d*x+c)*e*x^2+3*I/d^2*b^3*f*arccot(d*x+c)^2*e-2*I/d^3*b^3*f^2*arccot(d*x+c)*polylog(2,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-2*I/d^3*b^3*f^2*arccot(d*x+c)*polylog(2,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-1/4*I/d^3*a*b^2*ln(d*x+c-I)^2*f^2-6*I/d^3*b^3*f^2*c*polylog(2,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+3/d^2*a^2*b*f*c*e-2*a^2*b/d^2*x*c*f^2+3*a^2*b/d*x*e*f-4/d^2*a*b^2*f^2*arccot(d*x+c)*x*c+3/d^2*a^2*b*f*arctan(d*x+c)*c^2*e+1/2*I/d^3*a*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))*f^2+6/d^3*b^3*f^2*c*arccot(d*x+c)*ln(1+(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+2*a*b^2/f*arccot(d*x+c)*arctan(d*x+c)*e^3+3*a*b^2*f*arccot(d*x+c)^2*e*x^2-3/d*a^2*b*arctan(d*x+c)*c*e^2+6/d*a*b^2*f*arccot(d*x+c)*e*x+6/d^2*a*b^2*f*arccot(d*x+c)*e*c+1/3/d^3*b^3*f^2*arccot(d*x+c)^3*c^3-1/d^3*a*b^2*f^2*arctan(d*x+c)-1/2/d^3*a^2*b*f^2*ln(1+(d*x+c)^2)-6/d^3*b^3*f^2*c^2*polylog(3,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-6/d^3*b^3*f^2*c^2*polylog(3,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-1/d^3*b^3*f^2*arccot(d*x+c)^3*c+1/d^3*b^3*f^2*arccot(d*x+c)^2*ln(1-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+1/d^3*b^3*f^2*arccot(d*x+c)^2*ln(1+(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+1/d^2*b^3*f^2*arccot(d*x+c)*x+1/d^3*b^3*f^2*arccot(d*x+c)*c+a*b^2/f*arctan(d*x+c)^2*e^3+a*b^2/f*arccot(d*x+c)^2*e^3-3/2*I/d*a*b^2*ln(d*x+c-I)*ln(1+(d*x+c)^2)*e^2+3/2*I/d*a*b^2*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))*e^2+3/2*I/d*a*b^2*ln(I+d*x+c)*ln(1+(d*x+c)^2)*e^2-3/2*I/d*a*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))*e^2+2/d^3*b^3*f^2*polylog(3,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-6/d*b^3*e^2*polylog(3,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-6/d*b^3*e^2*polylog(3,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+3*I/d^2*a*b^2*dilog(1/2*I*(d*x+c-I))*c*e*f+3/2*I/d^3*a*b^2*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))*c^2*f^2-3/2*I/d^3*a*b^2*ln(d*x+c-I)*ln(1+(d*x+c)^2)*c^2*f^2-3/2*I/d^3*a*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))*c^2*f^2+3/2*I/d^3*a*b^2*ln(I+d*x+c)*ln(1+(d*x+c)^2)*c^2*f^2-12*I/d^2*b^3*f*c*e*arccot(d*x+c)*polylog(2,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-3/2*I/d^2*a*b^2*ln(d*x+c-I)^2*c*e*f-3*I/d^2*a*b^2*dilog(-1/2*I*(I+d*x+c))*c*e*f+3/2*I/d^2*a*b^2*ln(I+d*x+c)^2*c*e*f-12*I/d^2*b^3*f*c*e*arccot(d*x+c)*polylog(2,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+6/d^2*a*b^2*f*arccot(d*x+c)*arctan(d*x+c)*c^2*e-6/d^2*a*b^2*f*arccot(d*x+c)*ln(1+(d*x+c)^2)*c*e","B"
142,1,1570,316,1.201000," ","int((f*x+e)*(a+b*arccot(d*x+c))^3,x)","\frac{3 i a \,b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right) c f}{2 d^{2}}+\frac{3 i a \,b^{2} \ln \left(d x +c -i\right) \ln \left(1+\left(d x +c \right)^{2}\right) c f}{2 d^{2}}-\frac{3 i a \,b^{2} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right) c f}{2 d^{2}}-\frac{3 i a \,b^{2} \ln \left(d x +c +i\right) \ln \left(1+\left(d x +c \right)^{2}\right) c f}{2 d^{2}}-\frac{3 b^{3} f \,\mathrm{arccot}\left(d x +c \right) \ln \left(1-\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d^{2}}-\frac{3 b^{3} e \mathrm{arccot}\left(d x +c \right)^{2} \ln \left(1+\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d}+\frac{3 i b^{3} f \polylog \left(2, -\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d^{2}}+\frac{3 i b^{3} f \polylog \left(2, \frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d^{2}}+\frac{6 b^{3} c f \polylog \left(3, \frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d^{2}}+\frac{6 b^{3} c f \polylog \left(3, -\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d^{2}}-\frac{3 i a \,b^{2} \ln \left(d x +c +i\right)^{2} e}{4 d}+\frac{a^{3} x^{2} f}{2}+a^{3} x e +\frac{\mathrm{arccot}\left(d x +c \right)^{3} b^{3} c e}{d}+\frac{3 a \,b^{2} f \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d^{2}}-\frac{3 a \,b^{2} f \arctan \left(d x +c \right)^{2}}{2 d^{2}}-\frac{6 b^{3} e \polylog \left(3, \frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d}-\frac{6 b^{3} e \polylog \left(3, -\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d}-\frac{3 a \,b^{2} \mathrm{arccot}\left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right) c f}{d^{2}}-\frac{3 i a \,b^{2} \ln \left(d x +c -i\right) \ln \left(1+\left(d x +c \right)^{2}\right) e}{2 d}+\frac{3 i a \,b^{2} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right) e}{2 d}+\frac{3 i a \,b^{2} \ln \left(d x +c +i\right) \ln \left(1+\left(d x +c \right)^{2}\right) e}{2 d}-\frac{3 i a \,b^{2} \ln \left(d x +c -i\right)^{2} c f}{4 d^{2}}+\frac{b^{3} \mathrm{arccot}\left(d x +c \right)^{3} f}{2 d^{2}}+\frac{3 a^{2} b c f}{2 d^{2}}+\frac{3 a^{2} b f x}{2 d}+\frac{3 a \,b^{2} \mathrm{arccot}\left(d x +c \right)^{2} f \,x^{2}}{2}+\frac{3 a^{2} b \,\mathrm{arccot}\left(d x +c \right) f \,x^{2}}{2}+3 \mathrm{arccot}\left(d x +c \right)^{2} x a \,b^{2} e +3 \,\mathrm{arccot}\left(d x +c \right) x \,a^{2} b e +\frac{3 b^{3} \mathrm{arccot}\left(d x +c \right)^{2} f x}{2 d}+\frac{3 b^{3} \mathrm{arccot}\left(d x +c \right)^{2} f c}{2 d^{2}}-\frac{b^{3} \mathrm{arccot}\left(d x +c \right)^{3} f \,c^{2}}{2 d^{2}}-\frac{3 a^{2} b f \arctan \left(d x +c \right)}{2 d^{2}}+\frac{3 a^{2} b \ln \left(1+\left(d x +c \right)^{2}\right) e}{2 d}-\frac{3 b^{3} f \,\mathrm{arccot}\left(d x +c \right) \ln \left(1+\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d^{2}}+\frac{i b^{3} \mathrm{arccot}\left(d x +c \right)^{3} e}{d}+\frac{3 i b^{3} \mathrm{arccot}\left(d x +c \right)^{2} f}{2 d^{2}}-\frac{3 b^{3} e \mathrm{arccot}\left(d x +c \right)^{2} \ln \left(1-\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d}-\frac{a^{3} f \,c^{2}}{2 d^{2}}+\frac{a^{3} c e}{d}+\frac{b^{3} \mathrm{arccot}\left(d x +c \right)^{3} f \,x^{2}}{2}+\mathrm{arccot}\left(d x +c \right)^{3} x \,b^{3} e +\frac{3 a \,b^{2} \mathrm{arccot}\left(d x +c \right) f c}{d^{2}}-\frac{3 a \,b^{2} \mathrm{arccot}\left(d x +c \right)^{2} c^{2} f}{2 d^{2}}-\frac{3 a \,b^{2} \mathrm{arccot}\left(d x +c \right) \arctan \left(d x +c \right) f}{d^{2}}-\frac{3 a^{2} b \,\mathrm{arccot}\left(d x +c \right) c^{2} f}{2 d^{2}}+\frac{3 a \,b^{2} \mathrm{arccot}\left(d x +c \right) f x}{d}-\frac{3 a^{2} b \ln \left(1+\left(d x +c \right)^{2}\right) c f}{2 d^{2}}+\frac{3 a \,b^{2} \mathrm{arccot}\left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right) e}{d}+\frac{3 \mathrm{arccot}\left(d x +c \right)^{2} a \,b^{2} c e}{d}+\frac{3 \,\mathrm{arccot}\left(d x +c \right) a^{2} b c e}{d}+\frac{3 i a \,b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right) e}{2 d}+\frac{6 i b^{3} e \,\mathrm{arccot}\left(d x +c \right) \polylog \left(2, -\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d}+\frac{6 i b^{3} e \,\mathrm{arccot}\left(d x +c \right) \polylog \left(2, \frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d}-\frac{3 i a \,b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right) e}{2 d}+\frac{3 b^{3} c f \mathrm{arccot}\left(d x +c \right)^{2} \ln \left(1-\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d^{2}}+\frac{3 b^{3} c f \mathrm{arccot}\left(d x +c \right)^{2} \ln \left(1+\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d^{2}}+\frac{3 i a \,b^{2} \ln \left(d x +c -i\right)^{2} e}{4 d}-\frac{i b^{3} \mathrm{arccot}\left(d x +c \right)^{3} c f}{d^{2}}-\frac{6 i b^{3} c f \,\mathrm{arccot}\left(d x +c \right) \polylog \left(2, \frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d^{2}}-\frac{3 i a \,b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right) c f}{2 d^{2}}+\frac{3 i a \,b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right) c f}{2 d^{2}}-\frac{6 i b^{3} c f \,\mathrm{arccot}\left(d x +c \right) \polylog \left(2, -\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right)}{d^{2}}+\frac{3 i a \,b^{2} \ln \left(d x +c +i\right)^{2} c f}{4 d^{2}}-\frac{3 i a \,b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right) e}{2 d}"," ",0,"-3/2*I/d^2*a*b^2*ln(I+d*x+c)*ln(1+(d*x+c)^2)*c*f+3/2*I/d^2*a*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))*c*f+3/2*I/d^2*a*b^2*ln(d*x+c-I)*ln(1+(d*x+c)^2)*c*f-3/2*I/d^2*a*b^2*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))*c*f-6*I/d^2*b^3*c*f*arccot(d*x+c)*polylog(2,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+1/2*a^3*x^2*f+a^3*x*e+1/d*arccot(d*x+c)^3*b^3*c*e-3/d^2*b^3*f*arccot(d*x+c)*ln(1+(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+I/d*b^3*arccot(d*x+c)^3*e+3/2/d^2*a*b^2*f*ln(1+(d*x+c)^2)-3/2/d^2*a*b^2*f*arctan(d*x+c)^2+3/2*I/d^2*b^3*arccot(d*x+c)^2*f-3/2*I/d^2*a*b^2*dilog(-1/2*I*(I+d*x+c))*c*f+3/4*I/d^2*a*b^2*ln(I+d*x+c)^2*c*f+3/2*I/d^2*a*b^2*dilog(1/2*I*(d*x+c-I))*c*f-3/2*I/d*a*b^2*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))*e-3/2*I/d*a*b^2*ln(d*x+c-I)*ln(1+(d*x+c)^2)*e+3/2*I/d*a*b^2*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))*e+3/2*I/d*a*b^2*ln(I+d*x+c)*ln(1+(d*x+c)^2)*e-6*I/d^2*b^3*c*f*arccot(d*x+c)*polylog(2,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-3/d^2*a*b^2*arccot(d*x+c)*ln(1+(d*x+c)^2)*c*f-3/4*I/d^2*a*b^2*ln(d*x+c-I)^2*c*f-6/d*b^3*e*polylog(3,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+1/2/d^2*b^3*arccot(d*x+c)^3*f-3/d*b^3*e*arccot(d*x+c)^2*ln(1-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+3/2/d^2*a^2*b*c*f+3*I/d^2*b^3*f*polylog(2,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+3*I/d^2*b^3*f*polylog(2,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+3/2*a^2*b/d*f*x+3/2*a*b^2*arccot(d*x+c)^2*f*x^2+3/2*a^2*b*arccot(d*x+c)*f*x^2+3*arccot(d*x+c)^2*x*a*b^2*e+3*arccot(d*x+c)*x*a^2*b*e+6/d^2*b^3*c*f*polylog(3,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+6/d^2*b^3*c*f*polylog(3,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-3/d^2*b^3*f*arccot(d*x+c)*ln(1-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+3/2/d*b^3*arccot(d*x+c)^2*f*x+3/2/d^2*b^3*arccot(d*x+c)^2*f*c-1/2/d^2*b^3*arccot(d*x+c)^3*f*c^2-3/2/d^2*a^2*b*f*arctan(d*x+c)+3/2/d*a^2*b*ln(1+(d*x+c)^2)*e-3/d*b^3*e*arccot(d*x+c)^2*ln(1+(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-1/2/d^2*a^3*f*c^2+1/d*a^3*c*e+1/2*b^3*arccot(d*x+c)^3*f*x^2+arccot(d*x+c)^3*x*b^3*e-6/d*b^3*e*polylog(3,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+3/d^2*a*b^2*arccot(d*x+c)*f*c-3/2/d^2*a*b^2*arccot(d*x+c)^2*c^2*f-3/d^2*a*b^2*arccot(d*x+c)*arctan(d*x+c)*f+3/d^2*b^3*c*f*arccot(d*x+c)^2*ln(1-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+3/d^2*b^3*c*f*arccot(d*x+c)^2*ln(1+(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-3/2/d^2*a^2*b*arccot(d*x+c)*c^2*f+3/d*a*b^2*arccot(d*x+c)*f*x-3/2/d^2*a^2*b*ln(1+(d*x+c)^2)*c*f+3/d*a*b^2*arccot(d*x+c)*ln(1+(d*x+c)^2)*e+3/d*arccot(d*x+c)^2*a*b^2*c*e+3/d*arccot(d*x+c)*a^2*b*c*e+3/2*I/d*a*b^2*dilog(-1/2*I*(I+d*x+c))*e+3/4*I/d*a*b^2*ln(d*x+c-I)^2*e-I/d^2*b^3*arccot(d*x+c)^3*c*f+6*I/d*b^3*e*arccot(d*x+c)*polylog(2,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+6*I/d*b^3*e*arccot(d*x+c)*polylog(2,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-3/4*I/d*a*b^2*ln(I+d*x+c)^2*e-3/2*I/d*a*b^2*dilog(1/2*I*(d*x+c-I))*e","B"
143,1,507,136,0.453000," ","int((a+b*arccot(d*x+c))^3,x)","x \,a^{3}+\frac{a^{3} c}{d}+\frac{i \mathrm{arccot}\left(d x +c \right)^{3} b^{3}}{d}+\mathrm{arccot}\left(d x +c \right)^{3} x \,b^{3}+\frac{\mathrm{arccot}\left(d x +c \right)^{3} b^{3} c}{d}+\frac{3 i \mathrm{arccot}\left(d x +c \right)^{2} a \,b^{2}}{d}-\frac{3 \ln \left(1-\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right) \mathrm{arccot}\left(d x +c \right)^{2} b^{3}}{d}+\frac{6 i \polylog \left(2, \frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right) \mathrm{arccot}\left(d x +c \right) b^{3}}{d}-\frac{3 \ln \left(1+\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right) \mathrm{arccot}\left(d x +c \right)^{2} b^{3}}{d}-\frac{6 \polylog \left(3, \frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right) b^{3}}{d}-\frac{6 \polylog \left(3, -\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right) b^{3}}{d}+\frac{6 i \polylog \left(2, \frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right) a \,b^{2}}{d}+3 \mathrm{arccot}\left(d x +c \right)^{2} x a \,b^{2}+\frac{3 \mathrm{arccot}\left(d x +c \right)^{2} a \,b^{2} c}{d}+\frac{6 i \polylog \left(2, -\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right) a \,b^{2}}{d}-\frac{6 \ln \left(1-\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right) \mathrm{arccot}\left(d x +c \right) a \,b^{2}}{d}+\frac{6 i \polylog \left(2, -\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right) \mathrm{arccot}\left(d x +c \right) b^{3}}{d}-\frac{6 \ln \left(1+\frac{d x +c +i}{\sqrt{1+\left(d x +c \right)^{2}}}\right) \mathrm{arccot}\left(d x +c \right) a \,b^{2}}{d}+3 \,\mathrm{arccot}\left(d x +c \right) x \,a^{2} b +\frac{3 \,\mathrm{arccot}\left(d x +c \right) a^{2} b c}{d}+\frac{3 a^{2} b \ln \left(1+\left(d x +c \right)^{2}\right)}{2 d}"," ",0,"x*a^3+1/d*a^3*c+I/d*arccot(d*x+c)^3*b^3+arccot(d*x+c)^3*x*b^3+1/d*arccot(d*x+c)^3*b^3*c+6*I/d*polylog(2,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))*arccot(d*x+c)*b^3-3/d*ln(1-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))*arccot(d*x+c)^2*b^3+6*I/d*polylog(2,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))*arccot(d*x+c)*b^3-3/d*ln(1+(I+d*x+c)/(1+(d*x+c)^2)^(1/2))*arccot(d*x+c)^2*b^3-6/d*polylog(3,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))*b^3-6/d*polylog(3,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))*b^3+6*I/d*polylog(2,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))*a*b^2+3*arccot(d*x+c)^2*x*a*b^2+3/d*arccot(d*x+c)^2*a*b^2*c+6*I/d*polylog(2,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))*a*b^2-6/d*ln(1-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))*arccot(d*x+c)*a*b^2+3*I/d*arccot(d*x+c)^2*a*b^2-6/d*ln(1+(I+d*x+c)/(1+(d*x+c)^2)^(1/2))*arccot(d*x+c)*a*b^2+3*arccot(d*x+c)*x*a^2*b+3/d*arccot(d*x+c)*a^2*b*c+3/2/d*a^2*b*ln(1+(d*x+c)^2)","B"
144,1,4521,344,1.049000," ","int((a+b*arccot(d*x+c))^3/(f*x+e),x)","\text{output too large to display}"," ",0,"b^3*c/(-I*f+c*f-d*e)*arccot(d*x+c)^3*ln(1-(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))+3*a*b^2*ln(f*(d*x+c)-c*f+d*e)/f*arccot(d*x+c)^2+3*a*b^2/f*arccot(d*x+c)^2*ln((I+d*x+c)^2/(1+(d*x+c)^2)-1)-3*a*b^2/(-I*f+c*f-d*e)*arccot(d*x+c)*polylog(2,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))-3*d*a*b^2/f*e/(-I*f+c*f-d*e)*arccot(d*x+c)^2*ln(1-(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))+3*I*d*b^3/f*e*arccot(d*x+c)^2*polylog(2,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))/(-2*I*f+2*c*f-2*d*e)+1/2*I*b^3/f*Pi*arccot(d*x+c)^3*csgn(I/((I+d*x+c)^2/(1+(d*x+c)^2)-1))*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f))*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)/((I+d*x+c)^2/(1+(d*x+c)^2)-1))-3/2*I*a*b^2/f*Pi*arccot(d*x+c)^2*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f))*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)/((I+d*x+c)^2/(1+(d*x+c)^2)-1))^2-3/2*I*a*b^2/f*Pi*arccot(d*x+c)^2*csgn(I/((I+d*x+c)^2/(1+(d*x+c)^2)-1))*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)/((I+d*x+c)^2/(1+(d*x+c)^2)-1))^2+a^3*ln(f*(d*x+c)-c*f+d*e)/f-3*a*b^2/f*arccot(d*x+c)^2*ln(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)-3*a*b^2/f*arccot(d*x+c)^2*ln(1+(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-3*a*b^2/f*arccot(d*x+c)^2*ln(1-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+3/4*I*b^3*c/(-I*f+c*f-d*e)*polylog(4,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))-I*b^3/f*arccot(d*x+c)^3*Pi-3/2*I*a^2*b/f*dilog((I*f-f*(d*x+c))/(d*e+I*f-c*f))+3/2*I*a^2*b/f*dilog((I*f+f*(d*x+c))/(I*f+c*f-d*e))-3/2*I*b^3/(-I*f+c*f-d*e)*arccot(d*x+c)*polylog(3,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))+3/2*a*b^2*c/(-I*f+c*f-d*e)*polylog(3,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))+6*I*d*a*b^2/f*e*arccot(d*x+c)*polylog(2,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))/(-2*I*f+2*c*f-2*d*e)+3/2*I*a*b^2/f*Pi*arccot(d*x+c)^2*csgn(I/((I+d*x+c)^2/(1+(d*x+c)^2)-1))*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f))*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)/((I+d*x+c)^2/(1+(d*x+c)^2)-1))+3/4*b^3/(-I*f+c*f-d*e)*polylog(4,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))-I*b^3/(-I*f+c*f-d*e)*arccot(d*x+c)^3*ln(1-(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))+3*I*b^3/f*arccot(d*x+c)^2*polylog(2,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+3*I*b^3/f*arccot(d*x+c)^2*polylog(2,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-3/2*I*a*b^2/(-I*f+c*f-d*e)*polylog(3,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))+I*b^3/f*Pi*arccot(d*x+c)^3*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)/((I+d*x+c)^2/(1+(d*x+c)^2)-1))^2+6*I*a*b^2/f*arccot(d*x+c)*polylog(2,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+6*I*a*b^2/f*arccot(d*x+c)*polylog(2,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-3*I*a*b^2/(-I*f+c*f-d*e)*arccot(d*x+c)^2*ln(1-(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))-1/2*I*b^3/f*Pi*arccot(d*x+c)^3*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)/((I+d*x+c)^2/(1+(d*x+c)^2)-1))^3-3/2*I*b^3*c/(-I*f+c*f-d*e)*arccot(d*x+c)^2*polylog(2,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))-3/2*I*a^2*b*ln(f*(d*x+c)-c*f+d*e)/f*ln((I*f-f*(d*x+c))/(d*e+I*f-c*f))+3*a*b^2*c/(-I*f+c*f-d*e)*arccot(d*x+c)^2*ln(1-(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))-1/2*I*b^3/f*Pi*arccot(d*x+c)^3*csgn(I/((I+d*x+c)^2/(1+(d*x+c)^2)-1))*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)/((I+d*x+c)^2/(1+(d*x+c)^2)-1))^2-1/2*I*b^3/f*Pi*arccot(d*x+c)^3*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f))*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)/((I+d*x+c)^2/(1+(d*x+c)^2)-1))^2-3/2*d*b^3/f*e/(-I*f+c*f-d*e)*arccot(d*x+c)*polylog(3,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))-3/2*d*a*b^2/f*e/(-I*f+c*f-d*e)*polylog(3,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))-d*b^3/f*e/(-I*f+c*f-d*e)*arccot(d*x+c)^3*ln(1-(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))+3*I*a*b^2/f*Pi*arccot(d*x+c)^2*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)/((I+d*x+c)^2/(1+(d*x+c)^2)-1))^2-3*I*a*b^2*c/(-I*f+c*f-d*e)*arccot(d*x+c)*polylog(2,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))-3/2*I*a*b^2/f*Pi*arccot(d*x+c)^2*csgn(I*(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)/((I+d*x+c)^2/(1+(d*x+c)^2)-1))^3-3*I*d*b^3/f*e*polylog(4,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))/(-4*I*f+4*c*f-4*d*e)+3*a^2*b*ln(f*(d*x+c)-c*f+d*e)/f*arccot(d*x+c)+3/2*b^3*c/(-I*f+c*f-d*e)*arccot(d*x+c)*polylog(3,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))+b^3/f*arccot(d*x+c)^3*ln((I+d*x+c)^2/(1+(d*x+c)^2)-1)-b^3/f*arccot(d*x+c)^3*ln(1+(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-6*b^3/f*arccot(d*x+c)*polylog(3,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-b^3/f*arccot(d*x+c)^3*ln(1-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-6*b^3/f*arccot(d*x+c)*polylog(3,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+b^3*ln(f*(d*x+c)-c*f+d*e)/f*arccot(d*x+c)^3-3/2*b^3/(-I*f+c*f-d*e)*arccot(d*x+c)^2*polylog(2,(d*e+I*f-c*f)/(-c*f+d*e-I*f)*(I+d*x+c)^2/(1+(d*x+c)^2))-b^3/f*arccot(d*x+c)^3*ln(c*f*(I+d*x+c)^2/(1+(d*x+c)^2)-d*e*(I+d*x+c)^2/(1+(d*x+c)^2)-c*f+d*e-I*(I+d*x+c)^2/(1+(d*x+c)^2)*f-I*f)-6*a*b^2/f*polylog(3,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-6*a*b^2/f*polylog(3,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-6*I*b^3/f*polylog(4,-(I+d*x+c)/(1+(d*x+c)^2)^(1/2))-6*I*b^3/f*polylog(4,(I+d*x+c)/(1+(d*x+c)^2)^(1/2))+3/2*I*a^2*b*ln(f*(d*x+c)-c*f+d*e)/f*ln((I*f+f*(d*x+c))/(I*f+c*f-d*e))-3*I*a*b^2/f*Pi*arccot(d*x+c)^2","C"
145,1,1579,1197,0.873000," ","int((a+b*arccot(d*x+c))^3/(f*x+e)^2,x)","-\frac{3 i d a \,b^{2} \ln \left(d x +c +i\right) \ln \left(\frac{i \left(d x +c -i\right)}{2}\right)}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}+\frac{3 i d \,b^{3} \mathrm{arccot}\left(d x +c \right) \polylog \left(2, \frac{\left(c f -d e -i f \right) \left(d x +c +i\right)^{2}}{\left(1+\left(d x +c \right)^{2}\right) \left(c f -d e +i f \right)}\right)}{\left(c f -d e -i f \right) \left(c f -d e +i f \right)}+\frac{3 i d a \,b^{2} \ln \left(f \left(d x +c \right)-c f +d e \right) \ln \left(\frac{i f -f \left(d x +c \right)}{-c f +d e +i f}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{3 i d a \,b^{2} \ln \left(d x +c -i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}-\frac{3 i d a \,b^{2} \ln \left(f \left(d x +c \right)-c f +d e \right) \ln \left(\frac{i f +f \left(d x +c \right)}{c f -d e +i f}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}+\frac{3 i d a \,b^{2} \ln \left(d x +c -i\right) \ln \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}+\frac{3 i d a \,b^{2} \ln \left(d x +c +i\right) \ln \left(1+\left(d x +c \right)^{2}\right)}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}-\frac{d \,a^{3}}{\left(d f x +d e \right) f}+\frac{2 i d \,b^{3} \mathrm{arccot}\left(d x +c \right)^{3}}{\left(c f -d e -i f \right) \left(c f -d e +i f \right)}-\frac{3 d \,b^{3} \mathrm{arccot}\left(d x +c \right)^{2} \ln \left(1-\frac{\left(c f -d e -i f \right) \left(d x +c +i\right)^{2}}{\left(1+\left(d x +c \right)^{2}\right) \left(c f -d e +i f \right)}\right)}{\left(c f -d e -i f \right) \left(c f -d e +i f \right)}+\frac{3 i d a \,b^{2} \dilog \left(\frac{i f -f \left(d x +c \right)}{-c f +d e +i f}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}+\frac{3 i d a \,b^{2} \dilog \left(-\frac{i \left(d x +c +i\right)}{2}\right)}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}-\frac{3 i d a \,b^{2} \dilog \left(\frac{i \left(d x +c -i\right)}{2}\right)}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}-\frac{3 i d a \,b^{2} \dilog \left(\frac{i f +f \left(d x +c \right)}{c f -d e +i f}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{3 d^{2} a \,b^{2} \arctan \left(d x +c \right)^{2} e}{f \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}+\frac{6 d a \,b^{2} \mathrm{arccot}\left(d x +c \right) \arctan \left(d x +c \right) c}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{3 d^{2} a^{2} b \arctan \left(d x +c \right) e}{f \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}-\frac{3 i d a \,b^{2} \ln \left(d x +c +i\right)^{2}}{4 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}+\frac{3 i d a \,b^{2} \ln \left(d x +c -i\right)^{2}}{4 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}-\frac{3 d \,b^{3} \polylog \left(3, \frac{\left(c f -d e -i f \right) \left(d x +c +i\right)^{2}}{\left(1+\left(d x +c \right)^{2}\right) \left(c f -d e +i f \right)}\right)}{2 \left(c f -d e -i f \right) \left(c f -d e +i f \right)}-\frac{d \,b^{3} \mathrm{arccot}\left(d x +c \right)^{3}}{f \left(c f -d e -i f \right)}-\frac{d \,b^{3} \mathrm{arccot}\left(d x +c \right)^{3}}{\left(d f x +d e \right) f}+\frac{3 d \,a^{2} b \ln \left(1+\left(d x +c \right)^{2}\right)}{2 \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}+\frac{3 d a \,b^{2} \arctan \left(d x +c \right)^{2} c}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{3 d \,a^{2} b \,\mathrm{arccot}\left(d x +c \right)}{\left(d f x +d e \right) f}-\frac{6 d a \,b^{2} \mathrm{arccot}\left(d x +c \right) \ln \left(f \left(d x +c \right)-c f +d e \right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}+\frac{3 d a \,b^{2} \mathrm{arccot}\left(d x +c \right) \ln \left(1+\left(d x +c \right)^{2}\right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}+\frac{3 d \,a^{2} b \arctan \left(d x +c \right) c}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}-\frac{3 d a \,b^{2} \mathrm{arccot}\left(d x +c \right)^{2}}{\left(d f x +d e \right) f}-\frac{6 d^{2} a \,b^{2} \mathrm{arccot}\left(d x +c \right) \arctan \left(d x +c \right) e}{f \left(c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}\right)}-\frac{3 d \,a^{2} b \ln \left(f \left(d x +c \right)-c f +d e \right)}{c^{2} f^{2}-2 c d e f +d^{2} e^{2}+f^{2}}"," ",0,"-3/2*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(I+d*x+c)*ln(1/2*I*(d*x+c-I))-3/4*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(I+d*x+c)^2+3*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*dilog((I*f-f*(d*x+c))/(d*e+I*f-c*f))+3/2*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*dilog(-1/2*I*(I+d*x+c))-d*a^3/(d*f*x+d*e)/f+3*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)*ln((I*f-f*(d*x+c))/(d*e+I*f-c*f))-3/2*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(d*x+c-I)*ln(1+(d*x+c)^2)-3*d^2*a*b^2/f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*e+6*d*a*b^2*arccot(d*x+c)/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)*c-3*d^2*a^2*b/f/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)*e-3*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)*ln((I*f+f*(d*x+c))/(I*f+c*f-d*e))+3*I*d*b^3/(-I*f+c*f-d*e)/(I*f+c*f-d*e)*arccot(d*x+c)*polylog(2,(-I*f+c*f-d*e)*(I+d*x+c)^2/(1+(d*x+c)^2)/(I*f+c*f-d*e))+3/2*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(d*x+c-I)*ln(-1/2*I*(I+d*x+c))+3/2*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(I+d*x+c)*ln(1+(d*x+c)^2)-d*b^3/(d*f*x+d*e)/f*arccot(d*x+c)^3-d*b^3/f*arccot(d*x+c)^3/(-I*f+c*f-d*e)-3/2*d*b^3/(-I*f+c*f-d*e)/(I*f+c*f-d*e)*polylog(3,(-I*f+c*f-d*e)*(I+d*x+c)^2/(1+(d*x+c)^2)/(I*f+c*f-d*e))+3/2*d*a^2*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(1+(d*x+c)^2)+3/4*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(d*x+c-I)^2+2*I*d*b^3/(-I*f+c*f-d*e)/(I*f+c*f-d*e)*arccot(d*x+c)^3-3/2*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*dilog(1/2*I*(d*x+c-I))-3*I*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*dilog((I*f+f*(d*x+c))/(I*f+c*f-d*e))+3*d*a*b^2/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)^2*c-3*d*a^2*b/(d*f*x+d*e)/f*arccot(d*x+c)-6*d*a*b^2*arccot(d*x+c)/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)+3*d*a*b^2*arccot(d*x+c)/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(1+(d*x+c)^2)+3*d*a^2*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)*c-3*d*b^3/(-I*f+c*f-d*e)/(I*f+c*f-d*e)*arccot(d*x+c)^2*ln(1-(-I*f+c*f-d*e)*(I+d*x+c)^2/(1+(d*x+c)^2)/(I*f+c*f-d*e))-3*d*a*b^2/(d*f*x+d*e)/f*arccot(d*x+c)^2-6*d^2*a*b^2/f*arccot(d*x+c)/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*arctan(d*x+c)*e-3*d*a^2*b/(c^2*f^2-2*c*d*e*f+d^2*e^2+f^2)*ln(f*(d*x+c)-c*f+d*e)","A"
146,0,0,171,2.106000," ","int((f*x+e)^m*(a+b*arccot(d*x+c)),x)","\int \left(f x +e \right)^{m} \left(a +b \,\mathrm{arccot}\left(d x +c \right)\right)\, dx"," ",0,"int((f*x+e)^m*(a+b*arccot(d*x+c)),x)","F"
147,0,0,22,1.886000," ","int((f*x+e)^m*(a+b*arccot(d*x+c))^2,x)","\int \left(f x +e \right)^{m} \left(a +b \,\mathrm{arccot}\left(d x +c \right)\right)^{2}\, dx"," ",0,"int((f*x+e)^m*(a+b*arccot(d*x+c))^2,x)","F"
148,0,0,22,2.039000," ","int((f*x+e)^m*(a+b*arccot(d*x+c))^3,x)","\int \left(f x +e \right)^{m} \left(a +b \,\mathrm{arccot}\left(d x +c \right)\right)^{3}\, dx"," ",0,"int((f*x+e)^m*(a+b*arccot(d*x+c))^3,x)","F"
149,1,46,38,0.041000," ","int(x^3*arccot(b*x^4+a),x)","\frac{\mathrm{arccot}\left(b \,x^{4}+a \right) x^{4}}{4}+\frac{\mathrm{arccot}\left(b \,x^{4}+a \right) a}{4 b}+\frac{\ln \left(1+\left(b \,x^{4}+a \right)^{2}\right)}{8 b}"," ",0,"1/4*arccot(b*x^4+a)*x^4+1/4/b*arccot(b*x^4+a)*a+1/8*ln(1+(b*x^4+a)^2)/b","A"
150,1,149,43,0.439000," ","int(x^(n-1)*arccot(a+b*x^n),x)","\frac{i x^{n} \ln \left(1+i \left(a +b \,x^{n}\right)\right)}{2 n}-\frac{i x^{n} \ln \left(1-i \left(a +b \,x^{n}\right)\right)}{2 n}+\frac{i \ln \left(x^{n}-\frac{i-a}{b}\right) a}{2 b n}-\frac{i \ln \left(\frac{i+a}{b}+x^{n}\right) a}{2 b n}+\frac{\pi  \,x^{n}}{2 n}+\frac{\ln \left(x^{n}-\frac{i-a}{b}\right)}{2 b n}+\frac{\ln \left(\frac{i+a}{b}+x^{n}\right)}{2 b n}"," ",0,"1/2*I/n*x^n*ln(1+I*(a+b*x^n))-1/2*I/n*x^n*ln(1-I*(a+b*x^n))+1/2*I/b/n*ln(x^n-(I-a)/b)*a-1/2*I/b/n*ln((I+a)/b+x^n)*a+1/2/n*Pi*x^n+1/2/b/n*ln(x^n-(I-a)/b)+1/2/b/n*ln((I+a)/b+x^n)","C"
151,0,0,38,1.835000," ","int((a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x)","\int \frac{\left(a +b \,\mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)\right)^{n}}{-c^{2} x^{2}+1}\, dx"," ",0,"int((a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x)","F"
152,1,1605,402,2.361000," ","int((a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^3/(-c^2*x^2+1),x)","-\frac{3 a \,b^{2} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}+1\right)}{c}+\frac{3 a \,b^{2} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1-\frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{3 i a^{2} b \dilog \left(\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}+1\right)}{2 c}-\frac{3 i a^{2} b \dilog \left(1-\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{2 c}-\frac{6 i a \,b^{2} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, \frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}-\frac{6 i a \,b^{2} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, -\frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{3 i a \,b^{2} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, -\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{c}-\frac{a^{3} \ln \left(c x -1\right)}{2 c}+\frac{a^{3} \ln \left(c x +1\right)}{2 c}-\frac{b^{3} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3} \ln \left(\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}+1\right)}{c}+\frac{b^{3} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3} \ln \left(1-\frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{b^{3} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3} \ln \left(1+\frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}-\frac{3 a \,b^{2} \polylog \left(3, -\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{2 c}+\frac{6 a \,b^{2} \polylog \left(3, \frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{6 a \,b^{2} \polylog \left(3, -\frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}-\frac{3 b^{3} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(3, -\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{2 c}+\frac{6 b^{3} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(3, \frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{6 b^{3} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(3, -\frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}-\frac{3 i b^{3} \polylog \left(4, -\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{4 c}+\frac{6 i b^{3} \polylog \left(4, \frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{6 i b^{3} \polylog \left(4, -\frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}-\frac{3 i b^{3} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \polylog \left(2, -\frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}-\frac{3 i b^{3} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \polylog \left(2, \frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{3 i b^{3} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \polylog \left(2, -\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{2 c}+\frac{3 a \,b^{2} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1+\frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{3 a^{2} b \,\mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1-\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{c}-\frac{3 a^{2} b \,\mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}+1\right)}{c}"," ",0,"3/2*I*a^2*b/c*dilog((I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1)+1)-3/2*I*a^2*b/c*dilog(1-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))-3*a*b^2/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln((I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1)+1)+3*a*b^2/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))-6*I*a*b^2/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))+3*I*a*b^2/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))-6*I*a*b^2/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))-3*I*b^3/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*polylog(2,-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))+3*a*b^2/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1+(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))+3*a^2*b/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))-3*a^2*b/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln((I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1)+1)-3*I*b^3/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*polylog(2,(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))+3/2*I*b^3/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*polylog(2,-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))-1/2*a^3/c*ln(c*x-1)+1/2*a^3/c*ln(c*x+1)-3/2*a*b^2/c*polylog(3,-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))+6*a*b^2/c*polylog(3,(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))+6*a*b^2/c*polylog(3,-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))-b^3/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3*ln((I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1)+1)-3/2*b^3/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(3,-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))+b^3/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3*ln(1-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))+6*b^3/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(3,(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))+b^3/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3*ln(1+(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))+6*b^3/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(3,-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))-3/4*I*b^3/c*polylog(4,-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))+6*I*b^3/c*polylog(4,(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))+6*I*b^3/c*polylog(4,-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))","B"
153,1,823,268,1.647000," ","int((a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2/(-c^2*x^2+1),x)","-\frac{a^{2} \ln \left(c x -1\right)}{2 c}+\frac{a^{2} \ln \left(c x +1\right)}{2 c}-\frac{b^{2} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}+1\right)}{c}+\frac{i b^{2} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, -\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{c}-\frac{b^{2} \polylog \left(3, -\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{2 c}+\frac{b^{2} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1-\frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}-\frac{2 i b^{2} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, \frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{2 b^{2} \polylog \left(3, \frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{b^{2} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1+\frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}-\frac{2 i b^{2} \mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, -\frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{2 b^{2} \polylog \left(3, -\frac{i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{2 a b \,\mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1-\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{c}-\frac{2 a b \,\mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}+1\right)}{c}+\frac{i a b \dilog \left(\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}+1\right)}{c}-\frac{i a b \dilog \left(1-\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{c}"," ",0,"-1/2*a^2/c*ln(c*x-1)+1/2*a^2/c*ln(c*x+1)-b^2/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln((I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1)+1)+I*b^2/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))-1/2*b^2/c*polylog(3,-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))+b^2/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))-2*I*b^2/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))+2*b^2/c*polylog(3,(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))+b^2/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1+(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))-2*I*b^2/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))+2*b^2/c*polylog(3,-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))+2*a*b/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))-2*a*b/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln((I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1)+1)+I*a*b/c*dilog((I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1)+1)-I*a*b/c*dilog(1-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))","B"
154,1,259,78,0.972000," ","int((a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2)))/(-c^2*x^2+1),x)","-\frac{a \ln \left(c x -1\right)}{2 c}+\frac{a \ln \left(c x +1\right)}{2 c}+\frac{b \,\mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1-\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{c}-\frac{b \,\mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}+1\right)}{c}+\frac{i b \dilog \left(\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}+1\right)}{2 c}-\frac{i b \dilog \left(1-\frac{\left(i+\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{2 c}"," ",0,"-1/2*a/c*ln(c*x-1)+1/2*a/c*ln(c*x+1)+b/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))-b/c*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln((I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1)+1)+1/2*I*b/c*dilog((I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1)+1)-1/2*I*b/c*dilog(1-(I+(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))","B"
155,0,0,38,1.382000," ","int(1/(-c^2*x^2+1)/(a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))),x)","\int \frac{1}{\left(-c^{2} x^{2}+1\right) \left(a +b \,\mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)\right)}\, dx"," ",0,"int(1/(-c^2*x^2+1)/(a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))),x)","F"
156,0,0,38,1.347000," ","int(1/(-c^2*x^2+1)/(a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2,x)","\int \frac{1}{\left(-c^{2} x^{2}+1\right) \left(a +b \,\mathrm{arccot}\left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)\right)^{2}}\, dx"," ",0,"int(1/(-c^2*x^2+1)/(a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2,x)","F"
157,1,20,20,0.039000," ","int(1/2*Pi-arctan(tan(b*x+a)),x)","\frac{\pi  x}{2}-\frac{\arctan \left(\tan \left(b x +a \right)\right)^{2}}{2 b}"," ",0,"1/2*Pi*x-1/2*arctan(tan(b*x+a))^2/b","A"
158,1,8034,341,64.667000," ","int(x^2*arccot(c+d*tan(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
159,1,7654,257,6.339000," ","int(x*arccot(c+d*tan(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
160,1,1142,168,1.018000," ","int(arccot(c+d*tan(b*x+a)),x)","\frac{\arctan \left(\tan \left(b x +a \right)\right) \mathrm{arccot}\left(c +d \tan \left(b x +a \right)\right)}{b}+\frac{\arctan \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right) \arctan \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)}{b}-\frac{i d \ln \left(1-\frac{\left(-i d +c +i\right) \left(1+i \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)\right)^{2}}{\left(\left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}+1\right) \left(i d -c +i\right)}\right) \arctan \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)}{2 b \left(i c +d +1\right)}-\frac{i \ln \left(1-\frac{\left(-i d +c +i\right) \left(1+i \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)\right)^{2}}{\left(\left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}+1\right) \left(i d -c +i\right)}\right) \arctan \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)}{2 b \left(i c +d +1\right)}-\frac{i \ln \left(1-\frac{\left(-i d +c +i\right) \left(1+i \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)\right)^{2}}{\left(\left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}+1\right) \left(i d -c +i\right)}\right) \arctan \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right) c}{2 b \left(-i d +c -i\right)}-\frac{d \arctan \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}}{2 b \left(i c +d +1\right)}-\frac{d \polylog \left(2, \frac{\left(-i d +c +i\right) \left(1+i \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)\right)^{2}}{\left(\left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}+1\right) \left(i d -c +i\right)}\right)}{4 b \left(i c +d +1\right)}-\frac{\arctan \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}}{2 b \left(i c +d +1\right)}-\frac{\arctan \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2} c}{2 b \left(-i d +c -i\right)}-\frac{\polylog \left(2, \frac{\left(-i d +c +i\right) \left(1+i \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)\right)^{2}}{\left(\left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}+1\right) \left(i d -c +i\right)}\right)}{4 b \left(i c +d +1\right)}-\frac{\polylog \left(2, \frac{\left(-i d +c +i\right) \left(1+i \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)\right)^{2}}{\left(\left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}+1\right) \left(i d -c +i\right)}\right) c}{4 b \left(-i d +c -i\right)}+\frac{i \arctan \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right) \ln \left(1-\frac{\left(i d +c +i\right) \left(1+i \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)\right)^{2}}{\left(\left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}+1\right) \left(-i d -c +i\right)}\right)}{2 b}+\frac{\arctan \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}}{2 b}+\frac{\polylog \left(2, \frac{\left(i d +c +i\right) \left(1+i \left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)\right)^{2}}{\left(\left(d \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}+1\right) \left(-i d -c +i\right)}\right)}{4 b}"," ",0,"1/b*arctan(tan(b*x+a))*arccot(c+d*tan(b*x+a))+1/b*arctan(d*((c+d*tan(b*x+a))/d-c/d)+c)*arctan((c+d*tan(b*x+a))/d-c/d)-1/2*I*d/b*ln(1-(-I*d+I+c)*(1+I*(d*((c+d*tan(b*x+a))/d-c/d)+c))^2/((d*((c+d*tan(b*x+a))/d-c/d)+c)^2+1)/(I*d+I-c))*arctan(d*((c+d*tan(b*x+a))/d-c/d)+c)/(1+I*c+d)-1/2*I/b*ln(1-(-I*d+I+c)*(1+I*(d*((c+d*tan(b*x+a))/d-c/d)+c))^2/((d*((c+d*tan(b*x+a))/d-c/d)+c)^2+1)/(I*d+I-c))*arctan(d*((c+d*tan(b*x+a))/d-c/d)+c)/(1+I*c+d)-1/2*I/b/(-I*d-I+c)*ln(1-(-I*d+I+c)*(1+I*(d*((c+d*tan(b*x+a))/d-c/d)+c))^2/((d*((c+d*tan(b*x+a))/d-c/d)+c)^2+1)/(I*d+I-c))*arctan(d*((c+d*tan(b*x+a))/d-c/d)+c)*c-1/2*d/b*arctan(d*((c+d*tan(b*x+a))/d-c/d)+c)^2/(1+I*c+d)-1/4*d/b*polylog(2,(-I*d+I+c)*(1+I*(d*((c+d*tan(b*x+a))/d-c/d)+c))^2/((d*((c+d*tan(b*x+a))/d-c/d)+c)^2+1)/(I*d+I-c))/(1+I*c+d)-1/2/b*arctan(d*((c+d*tan(b*x+a))/d-c/d)+c)^2/(1+I*c+d)-1/2/b/(-I*d-I+c)*arctan(d*((c+d*tan(b*x+a))/d-c/d)+c)^2*c-1/4/b*polylog(2,(-I*d+I+c)*(1+I*(d*((c+d*tan(b*x+a))/d-c/d)+c))^2/((d*((c+d*tan(b*x+a))/d-c/d)+c)^2+1)/(I*d+I-c))/(1+I*c+d)-1/4/b/(-I*d-I+c)*polylog(2,(-I*d+I+c)*(1+I*(d*((c+d*tan(b*x+a))/d-c/d)+c))^2/((d*((c+d*tan(b*x+a))/d-c/d)+c)^2+1)/(I*d+I-c))*c+1/2*I/b*arctan(d*((c+d*tan(b*x+a))/d-c/d)+c)*ln(1-(I+I*d+c)*(1+I*(d*((c+d*tan(b*x+a))/d-c/d)+c))^2/((d*((c+d*tan(b*x+a))/d-c/d)+c)^2+1)/(-I*d+I-c))+1/2/b*arctan(d*((c+d*tan(b*x+a))/d-c/d)+c)^2+1/4/b*polylog(2,(I+I*d+c)*(1+I*(d*((c+d*tan(b*x+a))/d-c/d)+c))^2/((d*((c+d*tan(b*x+a))/d-c/d)+c)^2+1)/(-I*d+I-c))","B"
161,0,0,17,1.189000," ","int(arccot(c+d*tan(b*x+a))/x,x)","\int \frac{\mathrm{arccot}\left(c +d \tan \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arccot(c+d*tan(b*x+a))/x,x)","F"
162,1,1526,123,6.488000," ","int(x^2*arccot(c+(1+I*c)*tan(b*x+a)),x)","-\frac{\polylog \left(2, i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a^{2}}{4 b^{3}}+\frac{a^{2} \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right)}{2 b^{3}}+\frac{a^{2} \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right)}{2 b^{3}}+\frac{x^{2} \polylog \left(2, i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4 b}+\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{12}+\frac{i x^{3} \ln \left(1-i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{6}-\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{12}-\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{12}-\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c +i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{12}+\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}+\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c +i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}+\frac{i x^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{3}+\frac{i x^{3} \ln \left(c -i\right)}{6}+\frac{x^{3} \pi  \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{3}}{12}-\frac{i x^{3} \ln \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{6}+\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(i \left(c -i\right)\right) \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right) \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{12}-\frac{i \ln \left(1-i {\mathrm e}^{2 i \left(b x +a \right)} c \right) x \,a^{2}}{2 b^{2}}+\frac{i a^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right) x}{2 b^{2}}+\frac{i a^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right) x}{2 b^{2}}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{12}+\frac{b \,x^{4}}{12}-\frac{\polylog \left(4, i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{8 b^{3}}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}+\frac{x^{3} \pi  \mathrm{csgn}\left(i {\mathrm e}^{i \left(b x +a \right)}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(b x +a \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}{6}-\frac{i \ln \left(1-i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a^{3}}{3 b^{3}}+\frac{i a^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right)}{2 b^{3}}-\frac{i a^{3} \ln \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{6 b^{3}}+\frac{i a^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right)}{2 b^{3}}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(i \left(c -i\right)\right) \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c +i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c +i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}+\frac{i x \polylog \left(3, i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4 b^{2}}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}"," ",0,"1/12*x^3*Pi*csgn(I/(exp(2*I*(b*x+a))+1))*csgn(I*(c-I))*csgn(I*(c-I)/(exp(2*I*(b*x+a))+1))+1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a)))*csgn(I*(c-I)/(exp(2*I*(b*x+a))+1))*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))-1/4/b^3*polylog(2,I*c*exp(2*I*(b*x+a)))*a^2+1/2/b^3*a^2*dilog(1-I*exp(I*(b*x+a))*(-I*c)^(1/2))+1/2/b^3*a^2*dilog(1+I*exp(I*(b*x+a))*(-I*c)^(1/2))+1/4*x^2*polylog(2,I*c*exp(2*I*(b*x+a)))/b+1/12*b*x^4-1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a)))*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))^2-1/12*x^3*Pi*csgn(I*(c-I)/(exp(2*I*(b*x+a))+1))*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))^2+1/12*x^3*Pi*csgn(I*exp(I*(b*x+a)))^2*csgn(I*exp(2*I*(b*x+a)))-1/6*x^3*Pi*csgn(I*exp(I*(b*x+a)))*csgn(I*exp(2*I*(b*x+a)))^2-1/3*I/b^3*ln(1-I*exp(2*I*(b*x+a))*c)*a^3+1/2*I/b^3*a^3*ln(1-I*exp(I*(b*x+a))*(-I*c)^(1/2))-1/6*I/b^3*a^3*ln(exp(2*I*(b*x+a))*c+I)+1/2*I/b^3*a^3*ln(1+I*exp(I*(b*x+a))*(-I*c)^(1/2))+1/4*I*x*polylog(3,I*c*exp(2*I*(b*x+a)))/b^2+1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))^3-1/8*polylog(4,I*c*exp(2*I*(b*x+a)))/b^3-1/2*I/b^2*ln(1-I*exp(2*I*(b*x+a))*c)*x*a^2+1/2*I/b^2*a^2*ln(1+I*exp(I*(b*x+a))*(-I*c)^(1/2))*x+1/2*I/b^2*a^2*ln(1-I*exp(I*(b*x+a))*(-I*c)^(1/2))*x+1/6*I*x^3*ln(1-I*exp(2*I*(b*x+a))*c)-1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))^3-1/12*x^3*Pi*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))^3-1/12*x^3*Pi*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))^3+1/12*x^3*Pi*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))^2+1/12*x^3*Pi*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))^2+1/3*I*x^3*ln(exp(I*(b*x+a)))-1/12*x^3*Pi*csgn(I*(c-I))*csgn(I*(c-I)/(exp(2*I*(b*x+a))+1))^2+1/6*I*x^3*ln(c-I)+1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a)))^3-1/6*I*x^3*ln(exp(2*I*(b*x+a))*c+I)+1/12*x^3*Pi*csgn(I*(c-I)/(exp(2*I*(b*x+a))+1))^3+1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))-1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))^2-1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))+1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))^2-1/12*x^3*Pi*csgn(I/(exp(2*I*(b*x+a))+1))*csgn(I*(c-I)/(exp(2*I*(b*x+a))+1))^2-1/12*x^3*Pi*csgn(I/(exp(2*I*(b*x+a))+1))*csgn(I*(exp(2*I*(b*x+a))*c+I))*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))+1/12*x^3*Pi*csgn(I/(exp(2*I*(b*x+a))+1))*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))^2+1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I))*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))^2","C"
163,1,1491,98,5.678000," ","int(x*arccot(c+(1+I*c)*tan(b*x+a)),x)","\frac{i \ln \left(1-i {\mathrm e}^{2 i \left(b x +a \right)} c \right) x a}{2 b}-\frac{i a \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right) x}{2 b}-\frac{i a \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right) x}{2 b}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right) \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(i \left(c -i\right)\right) \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c +i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{8}+\frac{i a^{2} \ln \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{4 b^{2}}-\frac{i a^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right)}{2 b^{2}}-\frac{i a^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right)}{2 b^{2}}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c +i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(i \left(c -i\right)\right) \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}+\frac{x^{2} \pi  \mathrm{csgn}\left(i {\mathrm e}^{i \left(b x +a \right)}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(b x +a \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}{4}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{8}+\frac{i \ln \left(1-i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a^{2}}{4 b^{2}}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}+\frac{b \,x^{3}}{6}+\frac{i x^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{2}-\frac{i x^{2} \ln \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{4}-\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{8}+\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c +i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}+\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}-\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c +i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{8}+\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{8}-\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{8}+\frac{x^{2} \pi  \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{3}}{8}+\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{8}+\frac{\polylog \left(2, i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a}{4 b^{2}}-\frac{a \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right)}{2 b^{2}}-\frac{a \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right)}{2 b^{2}}+\frac{x \polylog \left(2, i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4 b}+\frac{i \polylog \left(3, i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{8 b^{2}}+\frac{i x^{2} \ln \left(c -i\right)}{4}+\frac{i x^{2} \ln \left(1-i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4}"," ",0,"1/2*I*x^2*ln(exp(I*(b*x+a)))-1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))+1/4/b^2*polylog(2,I*c*exp(2*I*(b*x+a)))*a-1/2/b^2*a*dilog(1-I*exp(I*(b*x+a))*(-I*c)^(1/2))-1/2/b^2*a*dilog(1+I*exp(I*(b*x+a))*(-I*c)^(1/2))+1/2*I/b*ln(1-I*exp(2*I*(b*x+a))*c)*x*a-1/4*I*x^2*ln(exp(2*I*(b*x+a))*c+I)+1/4*I/b^2*a^2*ln(exp(2*I*(b*x+a))*c+I)-1/2*I/b^2*a^2*ln(1-I*exp(I*(b*x+a))*(-I*c)^(1/2))-1/2*I/b^2*a^2*ln(1+I*exp(I*(b*x+a))*(-I*c)^(1/2))+1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))^2-1/8*x^2*Pi*csgn(I/(exp(2*I*(b*x+a))+1))*csgn(I*(c-I)/(exp(2*I*(b*x+a))+1))^2-1/8*x^2*Pi*csgn(I*(c-I))*csgn(I*(c-I)/(exp(2*I*(b*x+a))+1))^2-1/8*x^2*Pi*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))^3+1/8*x^2*Pi*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))^2+1/8*x^2*Pi*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))^2-1/8*x^2*Pi*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))^3-1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a)))*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))^2-1/8*x^2*Pi*csgn(I*(c-I)/(exp(2*I*(b*x+a))+1))*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))^2+1/8*x^2*Pi*csgn(I/(exp(2*I*(b*x+a))+1))*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))^2+1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))^3+1/8*x^2*Pi*csgn(I*exp(I*(b*x+a)))^2*csgn(I*exp(2*I*(b*x+a)))-1/4*x^2*Pi*csgn(I*exp(I*(b*x+a)))*csgn(I*exp(2*I*(b*x+a)))^2-1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))^3+1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a)))^3+1/8*x^2*Pi*csgn(I*(c-I)/(exp(2*I*(b*x+a))+1))^3-1/2*I/b*a*ln(1-I*exp(I*(b*x+a))*(-I*c)^(1/2))*x-1/2*I/b*a*ln(1+I*exp(I*(b*x+a))*(-I*c)^(1/2))*x+1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I))*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))^2+1/4*x*polylog(2,I*c*exp(2*I*(b*x+a)))/b+1/6*b*x^3+1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))+1/4*I/b^2*ln(1-I*exp(2*I*(b*x+a))*c)*a^2+1/8*I*polylog(3,I*c*exp(2*I*(b*x+a)))/b^2+1/4*I*x^2*ln(c-I)+1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a)))*csgn(I*(c-I)/(exp(2*I*(b*x+a))+1))*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))-1/8*x^2*Pi*csgn(I/(exp(2*I*(b*x+a))+1))*csgn(I*(exp(2*I*(b*x+a))*c+I))*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))+1/8*x^2*Pi*csgn(I/(exp(2*I*(b*x+a))+1))*csgn(I*(c-I))*csgn(I*(c-I)/(exp(2*I*(b*x+a))+1))+1/4*I*x^2*ln(1-I*exp(2*I*(b*x+a))*c)-1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))^2","C"
164,1,1489,69,0.611000," ","int(arccot(c+(1+I*c)*tan(b*x+a)),x)","-\frac{i \dilog \left(\frac{c +\left(i c +1\right) \tan \left(b x +a \right)-i}{-2 i+2 c}\right) c^{2}}{4 \left(i c +1\right) b \left(i-c \right)}+\frac{i \ln \left(c +\left(i c +1\right) \tan \left(b x +a \right)-i\right)^{2} c^{2}}{8 \left(i c +1\right) b \left(i-c \right)}+\frac{\ln \left(-c +\left(i c +1\right) \tan \left(b x +a \right)+i\right) \ln \left(\frac{i+c +\left(i c +1\right) \tan \left(b x +a \right)}{2 c}\right) c}{2 \left(i c +1\right) b \left(i-c \right)}-\frac{i \dilog \left(-\frac{i \left(i+c +\left(i c +1\right) \tan \left(b x +a \right)\right)}{2}\right) c^{2}}{4 \left(i c +1\right) b \left(i-c \right)}+\frac{i \dilog \left(\frac{i+c +\left(i c +1\right) \tan \left(b x +a \right)}{2 c}\right) c^{2}}{4 \left(i c +1\right) b \left(i-c \right)}-\frac{\mathrm{arccot}\left(c +\left(i c +1\right) \tan \left(b x +a \right)\right) \ln \left(-c +\left(i c +1\right) \tan \left(b x +a \right)+i\right)}{\left(i c +1\right) b \left(2 i-2 c \right)}-\frac{i \ln \left(c +\left(i c +1\right) \tan \left(b x +a \right)-i\right)^{2}}{8 \left(i c +1\right) b \left(i-c \right)}-\frac{\dilog \left(-\frac{i \left(i+c +\left(i c +1\right) \tan \left(b x +a \right)\right)}{2}\right) c}{2 \left(i c +1\right) b \left(i-c \right)}+\frac{\dilog \left(\frac{i+c +\left(i c +1\right) \tan \left(b x +a \right)}{2 c}\right) c}{2 \left(i c +1\right) b \left(i-c \right)}-\frac{\dilog \left(\frac{c +\left(i c +1\right) \tan \left(b x +a \right)-i}{-2 i+2 c}\right) c}{2 \left(i c +1\right) b \left(i-c \right)}+\frac{i \dilog \left(\frac{c +\left(i c +1\right) \tan \left(b x +a \right)-i}{-2 i+2 c}\right)}{4 \left(i c +1\right) b \left(i-c \right)}+\frac{i \dilog \left(-\frac{i \left(i+c +\left(i c +1\right) \tan \left(b x +a \right)\right)}{2}\right)}{4 \left(i c +1\right) b \left(i-c \right)}-\frac{i \dilog \left(\frac{i+c +\left(i c +1\right) \tan \left(b x +a \right)}{2 c}\right)}{4 \left(i c +1\right) b \left(i-c \right)}+\frac{\ln \left(c +\left(i c +1\right) \tan \left(b x +a \right)-i\right)^{2} c}{4 \left(i c +1\right) b \left(i-c \right)}+\frac{\mathrm{arccot}\left(c +\left(i c +1\right) \tan \left(b x +a \right)\right) \ln \left(c +\left(i c +1\right) \tan \left(b x +a \right)-i\right)}{\left(i c +1\right) b \left(2 i-2 c \right)}+\frac{2 i \mathrm{arccot}\left(c +\left(i c +1\right) \tan \left(b x +a \right)\right) \ln \left(c +\left(i c +1\right) \tan \left(b x +a \right)-i\right) c}{\left(i c +1\right) b \left(2 i-2 c \right)}-\frac{2 i \mathrm{arccot}\left(c +\left(i c +1\right) \tan \left(b x +a \right)\right) \ln \left(-c +\left(i c +1\right) \tan \left(b x +a \right)+i\right) c}{\left(i c +1\right) b \left(2 i-2 c \right)}-\frac{i \ln \left(c +\left(i c +1\right) \tan \left(b x +a \right)-i\right) \ln \left(-\frac{i \left(i+c +\left(i c +1\right) \tan \left(b x +a \right)\right)}{2}\right) c^{2}}{4 \left(i c +1\right) b \left(i-c \right)}+\frac{i \ln \left(-c +\left(i c +1\right) \tan \left(b x +a \right)+i\right) \ln \left(\frac{i+c +\left(i c +1\right) \tan \left(b x +a \right)}{2 c}\right) c^{2}}{4 \left(i c +1\right) b \left(i-c \right)}-\frac{i \ln \left(-c +\left(i c +1\right) \tan \left(b x +a \right)+i\right) \ln \left(\frac{c +\left(i c +1\right) \tan \left(b x +a \right)-i}{-2 i+2 c}\right) c^{2}}{4 \left(i c +1\right) b \left(i-c \right)}-\frac{\ln \left(-c +\left(i c +1\right) \tan \left(b x +a \right)+i\right) \ln \left(\frac{c +\left(i c +1\right) \tan \left(b x +a \right)-i}{-2 i+2 c}\right) c}{2 \left(i c +1\right) b \left(i-c \right)}-\frac{i \ln \left(-c +\left(i c +1\right) \tan \left(b x +a \right)+i\right) \ln \left(\frac{i+c +\left(i c +1\right) \tan \left(b x +a \right)}{2 c}\right)}{4 \left(i c +1\right) b \left(i-c \right)}+\frac{i \ln \left(-c +\left(i c +1\right) \tan \left(b x +a \right)+i\right) \ln \left(\frac{c +\left(i c +1\right) \tan \left(b x +a \right)-i}{-2 i+2 c}\right)}{4 \left(i c +1\right) b \left(i-c \right)}+\frac{i \ln \left(c +\left(i c +1\right) \tan \left(b x +a \right)-i\right) \ln \left(-\frac{i \left(i+c +\left(i c +1\right) \tan \left(b x +a \right)\right)}{2}\right)}{4 \left(i c +1\right) b \left(i-c \right)}-\frac{\ln \left(c +\left(i c +1\right) \tan \left(b x +a \right)-i\right) \ln \left(-\frac{i \left(i+c +\left(i c +1\right) \tan \left(b x +a \right)\right)}{2}\right) c}{2 \left(i c +1\right) b \left(i-c \right)}-\frac{\mathrm{arccot}\left(c +\left(i c +1\right) \tan \left(b x +a \right)\right) \ln \left(c +\left(i c +1\right) \tan \left(b x +a \right)-i\right) c^{2}}{\left(i c +1\right) b \left(2 i-2 c \right)}+\frac{\mathrm{arccot}\left(c +\left(i c +1\right) \tan \left(b x +a \right)\right) \ln \left(-c +\left(i c +1\right) \tan \left(b x +a \right)+i\right) c^{2}}{\left(i c +1\right) b \left(2 i-2 c \right)}"," ",0,"-1/4*I/(1+I*c)/b/(I-c)*dilog(-1/2*I*(I+c+(1+I*c)*tan(b*x+a)))*c^2+1/8*I/(1+I*c)/b/(I-c)*ln(c+(1+I*c)*tan(b*x+a)-I)^2*c^2+1/2/(1+I*c)/b/(I-c)*ln(-c+(1+I*c)*tan(b*x+a)+I)*ln(1/2*(I+c+(1+I*c)*tan(b*x+a))/c)*c-1/2/(1+I*c)/b/(I-c)*ln(-c+(1+I*c)*tan(b*x+a)+I)*ln((c+(1+I*c)*tan(b*x+a)-I)/(-2*I+2*c))*c-1/4*I/(1+I*c)/b/(I-c)*ln(-c+(1+I*c)*tan(b*x+a)+I)*ln(1/2*(I+c+(1+I*c)*tan(b*x+a))/c)+1/4*I/(1+I*c)/b/(I-c)*ln(-c+(1+I*c)*tan(b*x+a)+I)*ln((c+(1+I*c)*tan(b*x+a)-I)/(-2*I+2*c))+1/4*I/(1+I*c)/b/(I-c)*ln(c+(1+I*c)*tan(b*x+a)-I)*ln(-1/2*I*(I+c+(1+I*c)*tan(b*x+a)))+1/4*I/(1+I*c)/b/(I-c)*dilog(1/2*(I+c+(1+I*c)*tan(b*x+a))/c)*c^2-1/4*I/(1+I*c)/b/(I-c)*dilog((c+(1+I*c)*tan(b*x+a)-I)/(-2*I+2*c))*c^2-1/2/(1+I*c)/b/(I-c)*ln(c+(1+I*c)*tan(b*x+a)-I)*ln(-1/2*I*(I+c+(1+I*c)*tan(b*x+a)))*c-1/2/(1+I*c)/b/(I-c)*dilog(-1/2*I*(I+c+(1+I*c)*tan(b*x+a)))*c-1/(1+I*c)/b*arccot(c+(1+I*c)*tan(b*x+a))/(2*I-2*c)*ln(c+(1+I*c)*tan(b*x+a)-I)*c^2+1/(1+I*c)/b*arccot(c+(1+I*c)*tan(b*x+a))/(2*I-2*c)*ln(-c+(1+I*c)*tan(b*x+a)+I)*c^2+1/4/(1+I*c)/b/(I-c)*ln(c+(1+I*c)*tan(b*x+a)-I)^2*c+1/2/(1+I*c)/b/(I-c)*dilog(1/2*(I+c+(1+I*c)*tan(b*x+a))/c)*c-1/2/(1+I*c)/b/(I-c)*dilog((c+(1+I*c)*tan(b*x+a)-I)/(-2*I+2*c))*c+1/(1+I*c)/b*arccot(c+(1+I*c)*tan(b*x+a))/(2*I-2*c)*ln(c+(1+I*c)*tan(b*x+a)-I)-1/(1+I*c)/b*arccot(c+(1+I*c)*tan(b*x+a))/(2*I-2*c)*ln(-c+(1+I*c)*tan(b*x+a)+I)+1/4*I/(1+I*c)/b/(I-c)*dilog((c+(1+I*c)*tan(b*x+a)-I)/(-2*I+2*c))+1/4*I/(1+I*c)/b/(I-c)*dilog(-1/2*I*(I+c+(1+I*c)*tan(b*x+a)))-1/8*I/(1+I*c)/b/(I-c)*ln(c+(1+I*c)*tan(b*x+a)-I)^2-1/4*I/(1+I*c)/b/(I-c)*dilog(1/2*(I+c+(1+I*c)*tan(b*x+a))/c)+2*I/(1+I*c)/b*arccot(c+(1+I*c)*tan(b*x+a))/(2*I-2*c)*ln(c+(1+I*c)*tan(b*x+a)-I)*c-2*I/(1+I*c)/b*arccot(c+(1+I*c)*tan(b*x+a))/(2*I-2*c)*ln(-c+(1+I*c)*tan(b*x+a)+I)*c-1/4*I/(1+I*c)/b/(I-c)*ln(c+(1+I*c)*tan(b*x+a)-I)*ln(-1/2*I*(I+c+(1+I*c)*tan(b*x+a)))*c^2+1/4*I/(1+I*c)/b/(I-c)*ln(-c+(1+I*c)*tan(b*x+a)+I)*ln(1/2*(I+c+(1+I*c)*tan(b*x+a))/c)*c^2-1/4*I/(1+I*c)/b/(I-c)*ln(-c+(1+I*c)*tan(b*x+a)+I)*ln((c+(1+I*c)*tan(b*x+a)-I)/(-2*I+2*c))*c^2","B"
165,0,0,22,1.857000," ","int(arccot(c+(1+I*c)*tan(b*x+a))/x,x)","\int \frac{\mathrm{arccot}\left(c +\left(i c +1\right) \tan \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arccot(c+(1+I*c)*tan(b*x+a))/x,x)","F"
166,1,1527,124,6.513000," ","int(x^2*arccot(c-(1-I*c)*tan(b*x+a)),x)","-\frac{i x^{3} \ln \left(1+i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{6}-\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{12}-\frac{i x^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{3}-\frac{x^{3} \pi  \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{3}}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(i \left(i+c \right)\right) \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right) \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{12}-\frac{i a^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right) x}{2 b^{2}}+\frac{i \ln \left(1+i {\mathrm e}^{2 i \left(b x +a \right)} c \right) x \,a^{2}}{2 b^{2}}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}+\frac{\polylog \left(4, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{8 b^{3}}-\frac{b \,x^{4}}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}-\frac{i a^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right) x}{2 b^{2}}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}+\frac{i a^{3} \ln \left(-{\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{6 b^{3}}-\frac{i a^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{3}}-\frac{x^{3} \pi  \mathrm{csgn}\left(i {\mathrm e}^{i \left(b x +a \right)}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)}{12}+\frac{i x^{3} \ln \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{6}-\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{12}-\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c -i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{12}-\frac{i x^{3} \ln \left(i+c \right)}{6}+\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c -i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}+\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}-\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{12}-\frac{x^{2} \polylog \left(2, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4 b}+\frac{\polylog \left(2, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a^{2}}{4 b^{3}}-\frac{a^{2} \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{3}}-\frac{a^{2} \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{3}}+\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{12}+\frac{i \ln \left(1+i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a^{3}}{3 b^{3}}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(i \left(i+c \right)\right) \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}-\frac{i x \polylog \left(3, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4 b^{2}}-\frac{i a^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{3}}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(b x +a \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}{6}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c -i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c -i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{12}"," ",0,"-1/12*x^3*Pi*csgn(I/(exp(2*I*(b*x+a))+1))*csgn(I*(I+c))*csgn(I/(exp(2*I*(b*x+a))+1)*(I+c))-1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a)))*csgn(I/(exp(2*I*(b*x+a))+1)*(I+c))*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))-1/4*x^2*polylog(2,-I*exp(2*I*(b*x+a))*c)/b+1/6*I*x^3*ln(exp(2*I*(b*x+a))*c-I)-1/12*x^3*Pi*csgn(I/(exp(2*I*(b*x+a))+1)*(I+c))^3-1/12*b*x^4-1/2*I/b^2*a^2*ln(1-I*exp(I*(b*x+a))*(I*c)^(1/2))*x+1/2*I/b^2*ln(1+I*c*exp(2*I*(b*x+a)))*x*a^2-1/12*x^3*Pi*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))^3-1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))-1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))^2+1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))-1/6*I*x^3*ln(I+c)-1/3*I*x^3*ln(exp(I*(b*x+a)))+1/4/b^3*polylog(2,-I*exp(2*I*(b*x+a))*c)*a^2+1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a)))*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))^2+1/12*x^3*Pi*csgn(I/(exp(2*I*(b*x+a))+1)*(I+c))*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))^2+1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))^2+1/12*x^3*Pi*csgn(I/(exp(2*I*(b*x+a))+1))*csgn(I/(exp(2*I*(b*x+a))+1)*(I+c))^2-1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a)))^3+1/12*x^3*Pi*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))^2+1/12*x^3*Pi*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))^2-1/12*x^3*Pi*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))^3+1/6*x^3*Pi*csgn(I*exp(I*(b*x+a)))*csgn(I*exp(2*I*(b*x+a)))^2+1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))^3-1/6*I*x^3*ln(1+I*c*exp(2*I*(b*x+a)))-1/2/b^3*a^2*dilog(1+I*exp(I*(b*x+a))*(I*c)^(1/2))-1/2/b^3*a^2*dilog(1-I*exp(I*(b*x+a))*(I*c)^(1/2))-1/2*I/b^3*a^3*ln(1-I*exp(I*(b*x+a))*(I*c)^(1/2))+1/3*I/b^3*ln(1+I*c*exp(2*I*(b*x+a)))*a^3+1/12*x^3*Pi*csgn(I*(I+c))*csgn(I/(exp(2*I*(b*x+a))+1)*(I+c))^2-1/12*x^3*Pi*csgn(I/(exp(2*I*(b*x+a))+1))*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))^2-1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I))*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))^2-1/2*I/b^2*a^2*ln(1+I*exp(I*(b*x+a))*(I*c)^(1/2))*x-1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))^3+1/8*polylog(4,-I*exp(2*I*(b*x+a))*c)/b^3+1/6*I/b^3*a^3*ln(-exp(2*I*(b*x+a))*c+I)-1/2*I/b^3*a^3*ln(1+I*exp(I*(b*x+a))*(I*c)^(1/2))-1/4*I*x*polylog(3,-I*exp(2*I*(b*x+a))*c)/b^2-1/12*x^3*Pi*csgn(I*exp(I*(b*x+a)))^2*csgn(I*exp(2*I*(b*x+a)))+1/12*x^3*Pi*csgn(I/(exp(2*I*(b*x+a))+1))*csgn(I*(exp(2*I*(b*x+a))*c-I))*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))","C"
167,1,1492,99,6.079000," ","int(x*arccot(c-(1-I*c)*tan(b*x+a)),x)","\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c -i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}-\frac{i \polylog \left(3, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{8 b^{2}}-\frac{x \polylog \left(2, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4 b}+\frac{a \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{2}}+\frac{a \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{2}}-\frac{\polylog \left(2, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a}{4 b^{2}}-\frac{i x^{2} \ln \left(i+c \right)}{4}+\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{8}-\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{8}+\frac{i x^{2} \ln \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{4}-\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c -i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{8}-\frac{i x^{2} \ln \left(1+i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4}+\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}-\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{8}-\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{8}+\frac{i a \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right) x}{2 b}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right) \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(i \left(i+c \right)\right) \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{8}-\frac{i \ln \left(1+i {\mathrm e}^{2 i \left(b x +a \right)} c \right) x a}{2 b}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{8}-\frac{x^{2} \pi  \mathrm{csgn}\left(i {\mathrm e}^{i \left(b x +a \right)}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(b x +a \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}{4}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(i \left(i+c \right)\right) \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}+\frac{i a^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{2}}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c -i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c -i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}-\frac{i \ln \left(1+i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a^{2}}{4 b^{2}}-\frac{i a^{2} \ln \left(-{\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{4 b^{2}}+\frac{i a^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{2}}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{2}}{8}-\frac{b \,x^{3}}{6}-\frac{i x^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{2}-\frac{x^{2} \pi  \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{3}}{8}+\frac{i a \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right) x}{2 b}"," ",0,"1/2*I/b*a*ln(1+I*exp(I*(b*x+a))*(I*c)^(1/2))*x+1/2*I/b*a*ln(1-I*exp(I*(b*x+a))*(I*c)^(1/2))*x+1/8*x^2*Pi*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))^2-1/4*I*x^2*ln(I+c)-1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a)))*csgn(I/(exp(2*I*(b*x+a))+1)*(I+c))*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))-1/8*x^2*Pi*csgn(I/(exp(2*I*(b*x+a))+1))*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))^2-1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I))*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))^2+1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))^3+1/8*x^2*Pi*csgn(I/(exp(2*I*(b*x+a))+1)*(I+c))*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))^2+1/8*x^2*Pi*csgn(I/(exp(2*I*(b*x+a))+1))*csgn(I/(exp(2*I*(b*x+a))+1)*(I+c))^2-1/8*I*polylog(3,-I*exp(2*I*(b*x+a))*c)/b^2-1/2*I*x^2*ln(exp(I*(b*x+a)))+1/8*x^2*Pi*csgn(I*(I+c))*csgn(I/(exp(2*I*(b*x+a))+1)*(I+c))^2-1/8*x^2*Pi*csgn(I/(exp(2*I*(b*x+a))+1))*csgn(I*(I+c))*csgn(I/(exp(2*I*(b*x+a))+1)*(I+c))-1/8*x^2*Pi*csgn(I/(exp(2*I*(b*x+a))+1)*(I+c))^3-1/8*x^2*Pi*csgn(I*exp(I*(b*x+a)))^2*csgn(I*exp(2*I*(b*x+a)))+1/4*x^2*Pi*csgn(I*exp(I*(b*x+a)))*csgn(I*exp(2*I*(b*x+a)))^2+1/4*I*x^2*ln(exp(2*I*(b*x+a))*c-I)-1/8*x^2*Pi*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))^3-1/4*I*x^2*ln(1+I*c*exp(2*I*(b*x+a)))-1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a)))^3+1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))^2+1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a)))*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))^2-1/2*I/b*ln(1+I*c*exp(2*I*(b*x+a)))*x*a+1/2*I/b^2*a^2*ln(1+I*exp(I*(b*x+a))*(I*c)^(1/2))+1/8*x^2*Pi*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))^2-1/8*x^2*Pi*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))^3-1/6*b*x^3-1/4*x*polylog(2,-I*exp(2*I*(b*x+a))*c)/b+1/2/b^2*a*dilog(1+I*exp(I*(b*x+a))*(I*c)^(1/2))+1/2/b^2*a*dilog(1-I*exp(I*(b*x+a))*(I*c)^(1/2))+1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))-1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))-1/4/b^2*polylog(2,-I*exp(2*I*(b*x+a))*c)*a+1/8*x^2*Pi*csgn(I/(exp(2*I*(b*x+a))+1))*csgn(I*(exp(2*I*(b*x+a))*c-I))*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))-1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))+1))^2-1/4*I/b^2*ln(1+I*c*exp(2*I*(b*x+a)))*a^2-1/4*I/b^2*a^2*ln(-exp(2*I*(b*x+a))*c+I)+1/2*I/b^2*a^2*ln(1-I*exp(I*(b*x+a))*(I*c)^(1/2))-1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))^3","C"
168,1,1681,70,0.613000," ","int(arccot(c-(1-I*c)*tan(b*x+a)),x)","-\frac{\mathrm{arccot}\left(c +\left(i c -1\right) \tan \left(b x +a \right)\right) \ln \left(-\left(i c -1\right) \tan \left(b x +a \right)+c +i\right) c^{2}}{b \left(i c -1\right) \left(2 i+2 c \right)}+\frac{i \dilog \left(-\frac{-\left(i c -1\right) \tan \left(b x +a \right)-c +i}{2 c}\right) c^{2}}{4 b \left(i c -1\right) \left(i+c \right)}-\frac{\ln \left(i+\left(i c -1\right) \tan \left(b x +a \right)+c \right)^{2} c}{4 b \left(i c -1\right) \left(i+c \right)}-\frac{i \ln \left(i+\left(i c -1\right) \tan \left(b x +a \right)+c \right)^{2}}{8 b \left(i c -1\right) \left(i+c \right)}-\frac{\dilog \left(-\frac{-\left(i c -1\right) \tan \left(b x +a \right)-c +i}{2 c}\right) c}{2 b \left(i c -1\right) \left(i+c \right)}+\frac{\mathrm{arccot}\left(c +\left(i c -1\right) \tan \left(b x +a \right)\right) \ln \left(i+\left(i c -1\right) \tan \left(b x +a \right)+c \right) c^{2}}{b \left(i c -1\right) \left(2 i+2 c \right)}-\frac{i \ln \left(-\frac{i \left(i+\left(i c -1\right) \tan \left(b x +a \right)+c \right)}{2}\right) \ln \left(-\frac{i \left(-\left(i c -1\right) \tan \left(b x +a \right)-c +i\right)}{2}\right)}{4 b \left(i c -1\right) \left(i+c \right)}+\frac{\ln \left(-\left(i c -1\right) \tan \left(b x +a \right)+c +i\right) \ln \left(\frac{-\left(i c -1\right) \tan \left(b x +a \right)-c -i}{-2 i-2 c}\right) c}{2 b \left(i c -1\right) \left(i+c \right)}-\frac{\ln \left(-\frac{i \left(i+\left(i c -1\right) \tan \left(b x +a \right)+c \right)}{2}\right) \ln \left(-\frac{i \left(-\left(i c -1\right) \tan \left(b x +a \right)-c +i\right)}{2}\right) c}{2 b \left(i c -1\right) \left(i+c \right)}-\frac{i \ln \left(-\left(i c -1\right) \tan \left(b x +a \right)+c +i\right) \ln \left(-\frac{-\left(i c -1\right) \tan \left(b x +a \right)-c +i}{2 c}\right)}{4 b \left(i c -1\right) \left(i+c \right)}+\frac{i \ln \left(i+\left(i c -1\right) \tan \left(b x +a \right)+c \right) \ln \left(-\frac{i \left(-\left(i c -1\right) \tan \left(b x +a \right)-c +i\right)}{2}\right)}{4 b \left(i c -1\right) \left(i+c \right)}+\frac{i \ln \left(-\left(i c -1\right) \tan \left(b x +a \right)+c +i\right) \ln \left(\frac{-\left(i c -1\right) \tan \left(b x +a \right)-c -i}{-2 i-2 c}\right)}{4 b \left(i c -1\right) \left(i+c \right)}+\frac{i \ln \left(i+\left(i c -1\right) \tan \left(b x +a \right)+c \right)^{2} c^{2}}{8 b \left(i c -1\right) \left(i+c \right)}-\frac{\ln \left(-\left(i c -1\right) \tan \left(b x +a \right)+c +i\right) \ln \left(-\frac{-\left(i c -1\right) \tan \left(b x +a \right)-c +i}{2 c}\right) c}{2 b \left(i c -1\right) \left(i+c \right)}+\frac{\ln \left(i+\left(i c -1\right) \tan \left(b x +a \right)+c \right) \ln \left(-\frac{i \left(-\left(i c -1\right) \tan \left(b x +a \right)-c +i\right)}{2}\right) c}{2 b \left(i c -1\right) \left(i+c \right)}-\frac{i \dilog \left(\frac{-\left(i c -1\right) \tan \left(b x +a \right)-c -i}{-2 i-2 c}\right) c^{2}}{4 b \left(i c -1\right) \left(i+c \right)}+\frac{i \dilog \left(-\frac{i \left(i+\left(i c -1\right) \tan \left(b x +a \right)+c \right)}{2}\right) c^{2}}{4 b \left(i c -1\right) \left(i+c \right)}+\frac{i \ln \left(-\frac{i \left(i+\left(i c -1\right) \tan \left(b x +a \right)+c \right)}{2}\right) \ln \left(-\frac{i \left(-\left(i c -1\right) \tan \left(b x +a \right)-c +i\right)}{2}\right) c^{2}}{4 b \left(i c -1\right) \left(i+c \right)}-\frac{i \ln \left(-\left(i c -1\right) \tan \left(b x +a \right)+c +i\right) \ln \left(\frac{-\left(i c -1\right) \tan \left(b x +a \right)-c -i}{-2 i-2 c}\right) c^{2}}{4 b \left(i c -1\right) \left(i+c \right)}+\frac{i \ln \left(-\left(i c -1\right) \tan \left(b x +a \right)+c +i\right) \ln \left(-\frac{-\left(i c -1\right) \tan \left(b x +a \right)-c +i}{2 c}\right) c^{2}}{4 b \left(i c -1\right) \left(i+c \right)}+\frac{2 i \mathrm{arccot}\left(c +\left(i c -1\right) \tan \left(b x +a \right)\right) \ln \left(i+\left(i c -1\right) \tan \left(b x +a \right)+c \right) c}{b \left(i c -1\right) \left(2 i+2 c \right)}-\frac{2 i \mathrm{arccot}\left(c +\left(i c -1\right) \tan \left(b x +a \right)\right) \ln \left(-\left(i c -1\right) \tan \left(b x +a \right)+c +i\right) c}{b \left(i c -1\right) \left(2 i+2 c \right)}-\frac{i \ln \left(i+\left(i c -1\right) \tan \left(b x +a \right)+c \right) \ln \left(-\frac{i \left(-\left(i c -1\right) \tan \left(b x +a \right)-c +i\right)}{2}\right) c^{2}}{4 b \left(i c -1\right) \left(i+c \right)}-\frac{\dilog \left(-\frac{i \left(i+\left(i c -1\right) \tan \left(b x +a \right)+c \right)}{2}\right) c}{2 b \left(i c -1\right) \left(i+c \right)}+\frac{\dilog \left(\frac{-\left(i c -1\right) \tan \left(b x +a \right)-c -i}{-2 i-2 c}\right) c}{2 b \left(i c -1\right) \left(i+c \right)}-\frac{i \dilog \left(-\frac{-\left(i c -1\right) \tan \left(b x +a \right)-c +i}{2 c}\right)}{4 b \left(i c -1\right) \left(i+c \right)}+\frac{i \dilog \left(\frac{-\left(i c -1\right) \tan \left(b x +a \right)-c -i}{-2 i-2 c}\right)}{4 b \left(i c -1\right) \left(i+c \right)}-\frac{i \dilog \left(-\frac{i \left(i+\left(i c -1\right) \tan \left(b x +a \right)+c \right)}{2}\right)}{4 b \left(i c -1\right) \left(i+c \right)}-\frac{\mathrm{arccot}\left(c +\left(i c -1\right) \tan \left(b x +a \right)\right) \ln \left(i+\left(i c -1\right) \tan \left(b x +a \right)+c \right)}{b \left(i c -1\right) \left(2 i+2 c \right)}+\frac{\mathrm{arccot}\left(c +\left(i c -1\right) \tan \left(b x +a \right)\right) \ln \left(-\left(i c -1\right) \tan \left(b x +a \right)+c +i\right)}{b \left(i c -1\right) \left(2 i+2 c \right)}"," ",0,"1/4*I/b/(-1+I*c)/(I+c)*ln(-(-1+I*c)*tan(b*x+a)+c+I)*ln((-(-1+I*c)*tan(b*x+a)-c-I)/(-2*I-2*c))-1/b/(-1+I*c)*arccot(c+(-1+I*c)*tan(b*x+a))/(2*I+2*c)*ln(I+(-1+I*c)*tan(b*x+a)+c)+1/b/(-1+I*c)*arccot(c+(-1+I*c)*tan(b*x+a))/(2*I+2*c)*ln(-(-1+I*c)*tan(b*x+a)+c+I)-1/2/b/(-1+I*c)/(I+c)*dilog(-1/2*I*(I+(-1+I*c)*tan(b*x+a)+c))*c-1/4/b/(-1+I*c)/(I+c)*ln(I+(-1+I*c)*tan(b*x+a)+c)^2*c+1/2/b/(-1+I*c)/(I+c)*dilog((-(-1+I*c)*tan(b*x+a)-c-I)/(-2*I-2*c))*c-1/4*I/b/(-1+I*c)/(I+c)*dilog(-1/2*(-(-1+I*c)*tan(b*x+a)-c+I)/c)-1/8*I/b/(-1+I*c)/(I+c)*ln(I+(-1+I*c)*tan(b*x+a)+c)^2+1/4*I/b/(-1+I*c)/(I+c)*dilog((-(-1+I*c)*tan(b*x+a)-c-I)/(-2*I-2*c))-1/4*I/b/(-1+I*c)/(I+c)*dilog(-1/2*I*(I+(-1+I*c)*tan(b*x+a)+c))+1/8*I/b/(-1+I*c)/(I+c)*ln(I+(-1+I*c)*tan(b*x+a)+c)^2*c^2+1/4*I/b/(-1+I*c)/(I+c)*dilog(-1/2*(-(-1+I*c)*tan(b*x+a)-c+I)/c)*c^2-1/2/b/(-1+I*c)/(I+c)*ln(-(-1+I*c)*tan(b*x+a)+c+I)*ln(-1/2*(-(-1+I*c)*tan(b*x+a)-c+I)/c)*c+1/2/b/(-1+I*c)/(I+c)*ln(I+(-1+I*c)*tan(b*x+a)+c)*ln(-1/2*I*(-(-1+I*c)*tan(b*x+a)-c+I))*c-1/4*I/b/(-1+I*c)/(I+c)*ln(-(-1+I*c)*tan(b*x+a)+c+I)*ln(-1/2*(-(-1+I*c)*tan(b*x+a)-c+I)/c)+1/4*I/b/(-1+I*c)/(I+c)*ln(I+(-1+I*c)*tan(b*x+a)+c)*ln(-1/2*I*(-(-1+I*c)*tan(b*x+a)-c+I))-1/4*I/b/(-1+I*c)/(I+c)*ln(-1/2*I*(I+(-1+I*c)*tan(b*x+a)+c))*ln(-1/2*I*(-(-1+I*c)*tan(b*x+a)-c+I))-1/4*I/b/(-1+I*c)/(I+c)*dilog((-(-1+I*c)*tan(b*x+a)-c-I)/(-2*I-2*c))*c^2+1/2/b/(-1+I*c)/(I+c)*ln(-(-1+I*c)*tan(b*x+a)+c+I)*ln((-(-1+I*c)*tan(b*x+a)-c-I)/(-2*I-2*c))*c+1/4*I/b/(-1+I*c)/(I+c)*dilog(-1/2*I*(I+(-1+I*c)*tan(b*x+a)+c))*c^2+1/4*I/b/(-1+I*c)/(I+c)*ln(-1/2*I*(I+(-1+I*c)*tan(b*x+a)+c))*ln(-1/2*I*(-(-1+I*c)*tan(b*x+a)-c+I))*c^2-1/4*I/b/(-1+I*c)/(I+c)*ln(-(-1+I*c)*tan(b*x+a)+c+I)*ln((-(-1+I*c)*tan(b*x+a)-c-I)/(-2*I-2*c))*c^2+1/4*I/b/(-1+I*c)/(I+c)*ln(-(-1+I*c)*tan(b*x+a)+c+I)*ln(-1/2*(-(-1+I*c)*tan(b*x+a)-c+I)/c)*c^2+2*I/b/(-1+I*c)*arccot(c+(-1+I*c)*tan(b*x+a))/(2*I+2*c)*ln(I+(-1+I*c)*tan(b*x+a)+c)*c-2*I/b/(-1+I*c)*arccot(c+(-1+I*c)*tan(b*x+a))/(2*I+2*c)*ln(-(-1+I*c)*tan(b*x+a)+c+I)*c-1/4*I/b/(-1+I*c)/(I+c)*ln(I+(-1+I*c)*tan(b*x+a)+c)*ln(-1/2*I*(-(-1+I*c)*tan(b*x+a)-c+I))*c^2-1/2/b/(-1+I*c)/(I+c)*dilog(-1/2*(-(-1+I*c)*tan(b*x+a)-c+I)/c)*c-1/2/b/(-1+I*c)/(I+c)*ln(-1/2*I*(I+(-1+I*c)*tan(b*x+a)+c))*ln(-1/2*I*(-(-1+I*c)*tan(b*x+a)-c+I))*c+1/b/(-1+I*c)*arccot(c+(-1+I*c)*tan(b*x+a))/(2*I+2*c)*ln(I+(-1+I*c)*tan(b*x+a)+c)*c^2-1/b/(-1+I*c)*arccot(c+(-1+I*c)*tan(b*x+a))/(2*I+2*c)*ln(-(-1+I*c)*tan(b*x+a)+c+I)*c^2","B"
169,0,0,23,1.828000," ","int(arccot(c-(1-I*c)*tan(b*x+a))/x,x)","\int \frac{\mathrm{arccot}\left(c -\left(-i c +1\right) \tan \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arccot(c-(1-I*c)*tan(b*x+a))/x,x)","F"
170,1,45,14,0.049000," ","int(arccot(cot(b*x+a)),x)","\frac{-\left(\frac{\pi}{2}-\mathrm{arccot}\left(\cot \left(b x +a \right)\right)\right) \mathrm{arccot}\left(\cot \left(b x +a \right)\right)-\frac{\left(\frac{\pi}{2}-\mathrm{arccot}\left(\cot \left(b x +a \right)\right)\right)^{2}}{2}}{b}"," ",0,"1/b*(-(1/2*Pi-arccot(cot(b*x+a)))*arccot(cot(b*x+a))-1/2*(1/2*Pi-arccot(cot(b*x+a)))^2)","B"
171,1,7900,337,75.343000," ","int(x^2*arccot(c+d*cot(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
172,1,7532,255,6.576000," ","int(x*arccot(c+d*cot(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
173,1,1160,168,1.216000," ","int(arccot(c+d*cot(b*x+a)),x)","-\frac{\mathrm{arccot}\left(c +d \cot \left(b x +a \right)\right) \pi}{2 b}+\frac{\mathrm{arccot}\left(c +d \cot \left(b x +a \right)\right) \mathrm{arccot}\left(\cot \left(b x +a \right)\right)}{b}-\frac{\arctan \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right) \arctan \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)}{b}+\frac{i d \ln \left(1-\frac{\left(-i d +c +i\right) \left(1+i \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)\right)^{2}}{\left(\left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}+1\right) \left(i d -c +i\right)}\right) \arctan \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)}{2 b \left(i c +d +1\right)}+\frac{i \ln \left(1-\frac{\left(-i d +c +i\right) \left(1+i \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)\right)^{2}}{\left(\left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}+1\right) \left(i d -c +i\right)}\right) \arctan \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)}{2 b \left(i c +d +1\right)}+\frac{i \ln \left(1-\frac{\left(-i d +c +i\right) \left(1+i \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)\right)^{2}}{\left(\left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}+1\right) \left(i d -c +i\right)}\right) \arctan \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right) c}{2 b \left(-i d +c -i\right)}+\frac{d \arctan \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}}{2 b \left(i c +d +1\right)}+\frac{d \polylog \left(2, \frac{\left(-i d +c +i\right) \left(1+i \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)\right)^{2}}{\left(\left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}+1\right) \left(i d -c +i\right)}\right)}{4 b \left(i c +d +1\right)}+\frac{\arctan \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}}{2 b \left(i c +d +1\right)}+\frac{\arctan \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2} c}{2 b \left(-i d +c -i\right)}+\frac{\polylog \left(2, \frac{\left(-i d +c +i\right) \left(1+i \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)\right)^{2}}{\left(\left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}+1\right) \left(i d -c +i\right)}\right)}{4 b \left(i c +d +1\right)}+\frac{\polylog \left(2, \frac{\left(-i d +c +i\right) \left(1+i \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)\right)^{2}}{\left(\left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}+1\right) \left(i d -c +i\right)}\right) c}{4 b \left(-i d +c -i\right)}-\frac{i \arctan \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right) \ln \left(1-\frac{\left(i d +c +i\right) \left(1+i \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)\right)^{2}}{\left(\left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}+1\right) \left(-i d -c +i\right)}\right)}{2 b}-\frac{\arctan \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}}{2 b}-\frac{\polylog \left(2, \frac{\left(i d +c +i\right) \left(1+i \left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)\right)^{2}}{\left(\left(d \left(\frac{c +d \cot \left(b x +a \right)}{d}-\frac{c}{d}\right)+c \right)^{2}+1\right) \left(-i d -c +i\right)}\right)}{4 b}"," ",0,"-1/2/b*arccot(c+d*cot(b*x+a))*Pi+1/b*arccot(c+d*cot(b*x+a))*arccot(cot(b*x+a))-1/b*arctan(d*((c+d*cot(b*x+a))/d-c/d)+c)*arctan((c+d*cot(b*x+a))/d-c/d)+1/2*I*d/b*ln(1-(-I*d+I+c)*(1+I*(d*((c+d*cot(b*x+a))/d-c/d)+c))^2/((d*((c+d*cot(b*x+a))/d-c/d)+c)^2+1)/(I*d+I-c))*arctan(d*((c+d*cot(b*x+a))/d-c/d)+c)/(1+I*c+d)+1/2*I/b*ln(1-(-I*d+I+c)*(1+I*(d*((c+d*cot(b*x+a))/d-c/d)+c))^2/((d*((c+d*cot(b*x+a))/d-c/d)+c)^2+1)/(I*d+I-c))*arctan(d*((c+d*cot(b*x+a))/d-c/d)+c)/(1+I*c+d)+1/2*I/b/(-I*d-I+c)*ln(1-(-I*d+I+c)*(1+I*(d*((c+d*cot(b*x+a))/d-c/d)+c))^2/((d*((c+d*cot(b*x+a))/d-c/d)+c)^2+1)/(I*d+I-c))*arctan(d*((c+d*cot(b*x+a))/d-c/d)+c)*c+1/2*d/b*arctan(d*((c+d*cot(b*x+a))/d-c/d)+c)^2/(1+I*c+d)+1/4*d/b*polylog(2,(-I*d+I+c)*(1+I*(d*((c+d*cot(b*x+a))/d-c/d)+c))^2/((d*((c+d*cot(b*x+a))/d-c/d)+c)^2+1)/(I*d+I-c))/(1+I*c+d)+1/2/b*arctan(d*((c+d*cot(b*x+a))/d-c/d)+c)^2/(1+I*c+d)+1/2/b/(-I*d-I+c)*arctan(d*((c+d*cot(b*x+a))/d-c/d)+c)^2*c+1/4/b*polylog(2,(-I*d+I+c)*(1+I*(d*((c+d*cot(b*x+a))/d-c/d)+c))^2/((d*((c+d*cot(b*x+a))/d-c/d)+c)^2+1)/(I*d+I-c))/(1+I*c+d)+1/4/b/(-I*d-I+c)*polylog(2,(-I*d+I+c)*(1+I*(d*((c+d*cot(b*x+a))/d-c/d)+c))^2/((d*((c+d*cot(b*x+a))/d-c/d)+c)^2+1)/(I*d+I-c))*c-1/2*I/b*arctan(d*((c+d*cot(b*x+a))/d-c/d)+c)*ln(1-(I+I*d+c)*(1+I*(d*((c+d*cot(b*x+a))/d-c/d)+c))^2/((d*((c+d*cot(b*x+a))/d-c/d)+c)^2+1)/(-I*d+I-c))-1/2/b*arctan(d*((c+d*cot(b*x+a))/d-c/d)+c)^2-1/4/b*polylog(2,(I+I*d+c)*(1+I*(d*((c+d*cot(b*x+a))/d-c/d)+c))^2/((d*((c+d*cot(b*x+a))/d-c/d)+c)^2+1)/(-I*d+I-c))","B"
174,0,0,17,1.529000," ","int(arccot(c+d*cot(b*x+a))/x,x)","\int \frac{\mathrm{arccot}\left(c +d \cot \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arccot(c+d*cot(b*x+a))/x,x)","F"
175,1,1526,130,7.077000," ","int(x^2*(Pi-arccot(-c-(1-I*c)*cot(b*x+a))),x)","\frac{\polylog \left(2, i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a^{2}}{4 b^{3}}-\frac{a^{2} \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right)}{2 b^{3}}-\frac{i x^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{3}-\frac{x^{3} \pi  \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{3}}{12}-\frac{i a^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right) x}{2 b^{2}}-\frac{i a^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right) x}{2 b^{2}}-\frac{a^{2} \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right)}{2 b^{3}}-\frac{x^{2} \polylog \left(2, i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4 b}+\frac{i x^{3} \ln \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{6}-\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c +i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{12}-\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{12}-\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{12}-\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{12}+\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{12}+\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}-\frac{i x^{3} \ln \left(1-i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{6}+\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c +i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c +i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}-\frac{b \,x^{4}}{12}-\frac{x^{3} \pi  \mathrm{csgn}\left(i {\mathrm e}^{i \left(b x +a \right)}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)}{12}-\frac{i x^{3} \ln \left(i+c \right)}{6}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c +i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{12}+\frac{i \ln \left(1-i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a^{3}}{3 b^{3}}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{12}+\frac{i a^{3} \ln \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{6 b^{3}}-\frac{i a^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right)}{2 b^{3}}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(i \left(i+c \right)\right) \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}+\frac{\polylog \left(4, i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{8 b^{3}}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(i \left(i+c \right)\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right) \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{12}+\frac{i \ln \left(1-i {\mathrm e}^{2 i \left(b x +a \right)} c \right) x \,a^{2}}{2 b^{2}}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(b x +a \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}{6}-\frac{i a^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right)}{2 b^{3}}-\frac{i x \polylog \left(3, i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4 b^{2}}"," ",0,"1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))+1/3*I/b^3*ln(1-I*exp(2*I*(b*x+a))*c)*a^3-1/12*b*x^4-1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))+1/6*I*x^3*ln(exp(2*I*(b*x+a))*c+I)-1/6*I*x^3*ln(I+c)-1/3*I*x^3*ln(exp(I*(b*x+a)))-1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a)))^3+1/4/b^3*polylog(2,I*c*exp(2*I*(b*x+a)))*a^2-1/2/b^3*a^2*dilog(1-I*exp(I*(b*x+a))*(-I*c)^(1/2))-1/2/b^3*a^2*dilog(1+I*exp(I*(b*x+a))*(-I*c)^(1/2))-1/2*I/b^2*a^2*ln(1-I*exp(I*(b*x+a))*(-I*c)^(1/2))*x-1/2*I/b^2*a^2*ln(1+I*exp(I*(b*x+a))*(-I*c)^(1/2))*x-1/12*x^3*Pi*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))^3-1/12*x^3*Pi*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))^3+1/6*x^3*Pi*csgn(I*exp(I*(b*x+a)))*csgn(I*exp(2*I*(b*x+a)))^2-1/12*x^3*Pi*csgn(I*(I+c)/(exp(2*I*(b*x+a))-1))^3-1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))^3+1/6*I/b^3*a^3*ln(exp(2*I*(b*x+a))*c+I)-1/2*I/b^3*a^3*ln(1-I*exp(I*(b*x+a))*(-I*c)^(1/2))-1/2*I/b^3*a^3*ln(1+I*exp(I*(b*x+a))*(-I*c)^(1/2))-1/4*I*x*polylog(3,I*c*exp(2*I*(b*x+a)))/b^2+1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))^2+1/12*x^3*Pi*csgn(I*(I+c))*csgn(I*(I+c)/(exp(2*I*(b*x+a))-1))^2+1/12*x^3*Pi*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(I+c)/(exp(2*I*(b*x+a))-1))^2-1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I))*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))^2-1/12*x^3*Pi*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))^2-1/4*x^2*polylog(2,I*c*exp(2*I*(b*x+a)))/b+1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))^3+1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I))*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))+1/12*x^3*Pi*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))^2-1/12*x^3*Pi*csgn(I*exp(I*(b*x+a)))^2*csgn(I*exp(2*I*(b*x+a)))-1/12*x^3*Pi*csgn(I*(I+c))*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(I+c)/(exp(2*I*(b*x+a))-1))-1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a)))*csgn(I*(I+c)/(exp(2*I*(b*x+a))-1))*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))-1/6*I*x^3*ln(1-I*exp(2*I*(b*x+a))*c)+1/2*I/b^2*ln(1-I*exp(2*I*(b*x+a))*c)*x*a^2+1/12*x^3*Pi*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))^2-1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))^2+1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a)))*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))^2+1/12*x^3*Pi*csgn(I*(I+c)/(exp(2*I*(b*x+a))-1))*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))^2+1/8*polylog(4,I*c*exp(2*I*(b*x+a)))/b^3","C"
176,1,1491,105,6.119000," ","int(x*(Pi-arccot(-c-(1-I*c)*cot(b*x+a))),x)","\frac{i a \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right) x}{2 b}-\frac{i x^{2} \ln \left(i+c \right)}{4}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}-\frac{i a^{2} \ln \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{4 b^{2}}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c +i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{8}-\frac{x^{2} \pi  \mathrm{csgn}\left(i {\mathrm e}^{i \left(b x +a \right)}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c +i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(i \left(i+c \right)\right) \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}-\frac{i x^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{2}-\frac{i x^{2} \ln \left(1-i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4}+\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{8}-\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c +i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{8}-\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{8}+\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}-\frac{x \polylog \left(2, i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4 b}-\frac{i \polylog \left(3, i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{8 b^{2}}-\frac{\polylog \left(2, i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a}{4 b^{2}}+\frac{a \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right)}{2 b^{2}}+\frac{a \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right)}{2 b^{2}}+\frac{i a^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right)}{2 b^{2}}+\frac{i a^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right)}{2 b^{2}}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(b x +a \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}{4}-\frac{i \ln \left(1-i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a^{2}}{4 b^{2}}-\frac{b \,x^{3}}{6}+\frac{i x^{2} \ln \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{4}-\frac{x^{2} \pi  \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{3}}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(i \left(i+c \right)\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{8}+\frac{i a \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{-i c}\right) x}{2 b}-\frac{i \ln \left(1-i {\mathrm e}^{2 i \left(b x +a \right)} c \right) x a}{2 b}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right) \mathrm{csgn}\left(\frac{i \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{8}-\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{8}-\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{8}+\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c +i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}"," ",0,"-1/4*x*polylog(2,I*c*exp(2*I*(b*x+a)))/b-1/8*I*polylog(3,I*c*exp(2*I*(b*x+a)))/b^2-1/4/b^2*polylog(2,I*c*exp(2*I*(b*x+a)))*a+1/2/b^2*a*dilog(1-I*exp(I*(b*x+a))*(-I*c)^(1/2))+1/2/b^2*a*dilog(1+I*exp(I*(b*x+a))*(-I*c)^(1/2))-1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))^3-1/4*I*x^2*ln(I+c)+1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))^2-1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I))*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))^2-1/8*x^2*Pi*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))^2-1/8*x^2*Pi*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))^3+1/8*x^2*Pi*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))^2+1/4*I*x^2*ln(exp(2*I*(b*x+a))*c+I)-1/4*I/b^2*ln(1-I*exp(2*I*(b*x+a))*c)*a^2-1/4*I/b^2*a^2*ln(exp(2*I*(b*x+a))*c+I)+1/2*I/b^2*a^2*ln(1-I*exp(I*(b*x+a))*(-I*c)^(1/2))+1/2*I/b^2*a^2*ln(1+I*exp(I*(b*x+a))*(-I*c)^(1/2))+1/2*I/b*a*ln(1+I*exp(I*(b*x+a))*(-I*c)^(1/2))*x-1/2*I*x^2*ln(exp(I*(b*x+a)))+1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I))*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))-1/8*x^2*Pi*csgn(I*(I+c))*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(I+c)/(exp(2*I*(b*x+a))-1))-1/4*I*x^2*ln(1-I*exp(2*I*(b*x+a))*c)-1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))^2-1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))-1/8*x^2*Pi*csgn(I*exp(I*(b*x+a)))^2*csgn(I*exp(2*I*(b*x+a)))+1/4*x^2*Pi*csgn(I*exp(I*(b*x+a)))*csgn(I*exp(2*I*(b*x+a)))^2+1/2*I/b*a*ln(1-I*exp(I*(b*x+a))*(-I*c)^(1/2))*x-1/2*I/b*ln(1-I*exp(2*I*(b*x+a))*c)*x*a+1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))^3-1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a)))^3+1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a)))*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))^2+1/8*x^2*Pi*csgn(I*(I+c)/(exp(2*I*(b*x+a))-1))*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))^2-1/8*x^2*Pi*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))^3-1/6*b*x^3+1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))-1/8*x^2*Pi*csgn(I*(I+c)/(exp(2*I*(b*x+a))-1))^3+1/8*x^2*Pi*csgn(I*(I+c))*csgn(I*(I+c)/(exp(2*I*(b*x+a))-1))^2+1/8*x^2*Pi*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(I+c)/(exp(2*I*(b*x+a))-1))^2+1/8*x^2*Pi*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))^2-1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a)))*csgn(I*(I+c)/(exp(2*I*(b*x+a))-1))*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))","C"
177,1,1498,76,0.752000," ","int(Pi-arccot(-c-(1-I*c)*cot(b*x+a)),x)","\frac{\dilog \left(\frac{\cot \left(b x +a \right) \left(i c -1\right)-c -i}{-2 i-2 c}\right) c}{2 b \left(i c -1\right) \left(i+c \right)}+\frac{\dilog \left(-\frac{i \left(i+\cot \left(b x +a \right) \left(i c -1\right)-c \right)}{2}\right) c}{2 b \left(i c -1\right) \left(i+c \right)}-\frac{i \dilog \left(-\frac{i+\cot \left(b x +a \right) \left(i c -1\right)-c}{2 c}\right)}{4 b \left(i c -1\right) \left(i+c \right)}+\frac{i \dilog \left(\frac{\cot \left(b x +a \right) \left(i c -1\right)-c -i}{-2 i-2 c}\right)}{4 b \left(i c -1\right) \left(i+c \right)}+\frac{i \dilog \left(-\frac{i \left(i+\cot \left(b x +a \right) \left(i c -1\right)-c \right)}{2}\right)}{4 b \left(i c -1\right) \left(i+c \right)}-\frac{\dilog \left(-\frac{i+\cot \left(b x +a \right) \left(i c -1\right)-c}{2 c}\right) c}{2 b \left(i c -1\right) \left(i+c \right)}-\frac{\ln \left(\cot \left(b x +a \right) \left(i c -1\right)-c -i\right)^{2} c}{4 b \left(i c -1\right) \left(i+c \right)}-\frac{\mathrm{arccot}\left(\cot \left(b x +a \right) \left(i c -1\right)-c \right) \ln \left(i+\cot \left(b x +a \right) \left(i c -1\right)+c \right)}{b \left(i c -1\right) \left(2 i+2 c \right)}+\frac{\mathrm{arccot}\left(\cot \left(b x +a \right) \left(i c -1\right)-c \right) \ln \left(\cot \left(b x +a \right) \left(i c -1\right)-c -i\right)}{b \left(i c -1\right) \left(2 i+2 c \right)}-\frac{i \ln \left(\cot \left(b x +a \right) \left(i c -1\right)-c -i\right)^{2}}{8 b \left(i c -1\right) \left(i+c \right)}+\frac{i \ln \left(i+\cot \left(b x +a \right) \left(i c -1\right)+c \right) \ln \left(\frac{\cot \left(b x +a \right) \left(i c -1\right)-c -i}{-2 i-2 c}\right)}{4 b \left(i c -1\right) \left(i+c \right)}-\frac{\ln \left(i+\cot \left(b x +a \right) \left(i c -1\right)+c \right) \ln \left(-\frac{i+\cot \left(b x +a \right) \left(i c -1\right)-c}{2 c}\right) c}{2 b \left(i c -1\right) \left(i+c \right)}+\frac{\ln \left(i+\cot \left(b x +a \right) \left(i c -1\right)+c \right) \ln \left(\frac{\cot \left(b x +a \right) \left(i c -1\right)-c -i}{-2 i-2 c}\right) c}{2 b \left(i c -1\right) \left(i+c \right)}+\frac{\ln \left(\cot \left(b x +a \right) \left(i c -1\right)-c -i\right) \ln \left(-\frac{i \left(i+\cot \left(b x +a \right) \left(i c -1\right)-c \right)}{2}\right) c}{2 b \left(i c -1\right) \left(i+c \right)}+\frac{\mathrm{arccot}\left(\cot \left(b x +a \right) \left(i c -1\right)-c \right) \ln \left(i+\cot \left(b x +a \right) \left(i c -1\right)+c \right) c^{2}}{b \left(i c -1\right) \left(2 i+2 c \right)}-\frac{\mathrm{arccot}\left(\cot \left(b x +a \right) \left(i c -1\right)-c \right) \ln \left(\cot \left(b x +a \right) \left(i c -1\right)-c -i\right) c^{2}}{b \left(i c -1\right) \left(2 i+2 c \right)}-\frac{i \dilog \left(-\frac{i \left(i+\cot \left(b x +a \right) \left(i c -1\right)-c \right)}{2}\right) c^{2}}{4 b \left(i c -1\right) \left(i+c \right)}+\frac{i \dilog \left(-\frac{i+\cot \left(b x +a \right) \left(i c -1\right)-c}{2 c}\right) c^{2}}{4 b \left(i c -1\right) \left(i+c \right)}-\frac{i \ln \left(i+\cot \left(b x +a \right) \left(i c -1\right)+c \right) \ln \left(-\frac{i+\cot \left(b x +a \right) \left(i c -1\right)-c}{2 c}\right)}{4 b \left(i c -1\right) \left(i+c \right)}+\pi  x -\frac{i \dilog \left(\frac{\cot \left(b x +a \right) \left(i c -1\right)-c -i}{-2 i-2 c}\right) c^{2}}{4 b \left(i c -1\right) \left(i+c \right)}+\frac{i \ln \left(\cot \left(b x +a \right) \left(i c -1\right)-c -i\right)^{2} c^{2}}{8 b \left(i c -1\right) \left(i+c \right)}+\frac{i \ln \left(\cot \left(b x +a \right) \left(i c -1\right)-c -i\right) \ln \left(-\frac{i \left(i+\cot \left(b x +a \right) \left(i c -1\right)-c \right)}{2}\right)}{4 b \left(i c -1\right) \left(i+c \right)}+\frac{2 i \mathrm{arccot}\left(\cot \left(b x +a \right) \left(i c -1\right)-c \right) \ln \left(i+\cot \left(b x +a \right) \left(i c -1\right)+c \right) c}{b \left(i c -1\right) \left(2 i+2 c \right)}-\frac{2 i \mathrm{arccot}\left(\cot \left(b x +a \right) \left(i c -1\right)-c \right) \ln \left(\cot \left(b x +a \right) \left(i c -1\right)-c -i\right) c}{b \left(i c -1\right) \left(2 i+2 c \right)}-\frac{i \ln \left(\cot \left(b x +a \right) \left(i c -1\right)-c -i\right) \ln \left(-\frac{i \left(i+\cot \left(b x +a \right) \left(i c -1\right)-c \right)}{2}\right) c^{2}}{4 b \left(i c -1\right) \left(i+c \right)}+\frac{i \ln \left(i+\cot \left(b x +a \right) \left(i c -1\right)+c \right) \ln \left(-\frac{i+\cot \left(b x +a \right) \left(i c -1\right)-c}{2 c}\right) c^{2}}{4 b \left(i c -1\right) \left(i+c \right)}-\frac{i \ln \left(i+\cot \left(b x +a \right) \left(i c -1\right)+c \right) \ln \left(\frac{\cot \left(b x +a \right) \left(i c -1\right)-c -i}{-2 i-2 c}\right) c^{2}}{4 b \left(i c -1\right) \left(i+c \right)}"," ",0,"-1/4*I/b/(-1+I*c)/(I+c)*ln(I+cot(b*x+a)*(-1+I*c)+c)*ln(-1/2*(I+cot(b*x+a)*(-1+I*c)-c)/c)+1/4*I/b/(-1+I*c)/(I+c)*ln(I+cot(b*x+a)*(-1+I*c)+c)*ln((cot(b*x+a)*(-1+I*c)-c-I)/(-2*I-2*c))-1/2/b/(-1+I*c)/(I+c)*ln(I+cot(b*x+a)*(-1+I*c)+c)*ln(-1/2*(I+cot(b*x+a)*(-1+I*c)-c)/c)*c+1/2/b/(-1+I*c)/(I+c)*ln(I+cot(b*x+a)*(-1+I*c)+c)*ln((cot(b*x+a)*(-1+I*c)-c-I)/(-2*I-2*c))*c+1/2/b/(-1+I*c)/(I+c)*ln(cot(b*x+a)*(-1+I*c)-c-I)*ln(-1/2*I*(I+cot(b*x+a)*(-1+I*c)-c))*c+1/b/(-1+I*c)*arccot(cot(b*x+a)*(-1+I*c)-c)/(2*I+2*c)*ln(I+cot(b*x+a)*(-1+I*c)+c)*c^2-1/b/(-1+I*c)*arccot(cot(b*x+a)*(-1+I*c)-c)/(2*I+2*c)*ln(cot(b*x+a)*(-1+I*c)-c-I)*c^2-1/4*I/b/(-1+I*c)/(I+c)*ln(cot(b*x+a)*(-1+I*c)-c-I)*ln(-1/2*I*(I+cot(b*x+a)*(-1+I*c)-c))*c^2+1/4*I/b/(-1+I*c)/(I+c)*ln(I+cot(b*x+a)*(-1+I*c)+c)*ln(-1/2*(I+cot(b*x+a)*(-1+I*c)-c)/c)*c^2-1/4*I/b/(-1+I*c)/(I+c)*ln(I+cot(b*x+a)*(-1+I*c)+c)*ln((cot(b*x+a)*(-1+I*c)-c-I)/(-2*I-2*c))*c^2+2*I/b/(-1+I*c)*arccot(cot(b*x+a)*(-1+I*c)-c)/(2*I+2*c)*ln(I+cot(b*x+a)*(-1+I*c)+c)*c-2*I/b/(-1+I*c)*arccot(cot(b*x+a)*(-1+I*c)-c)/(2*I+2*c)*ln(cot(b*x+a)*(-1+I*c)-c-I)*c+1/2/b/(-1+I*c)/(I+c)*dilog((cot(b*x+a)*(-1+I*c)-c-I)/(-2*I-2*c))*c+1/2/b/(-1+I*c)/(I+c)*dilog(-1/2*I*(I+cot(b*x+a)*(-1+I*c)-c))*c-1/4/b/(-1+I*c)/(I+c)*ln(cot(b*x+a)*(-1+I*c)-c-I)^2*c-1/b/(-1+I*c)*arccot(cot(b*x+a)*(-1+I*c)-c)/(2*I+2*c)*ln(I+cot(b*x+a)*(-1+I*c)+c)+1/b/(-1+I*c)*arccot(cot(b*x+a)*(-1+I*c)-c)/(2*I+2*c)*ln(cot(b*x+a)*(-1+I*c)-c-I)-1/4*I/b/(-1+I*c)/(I+c)*dilog(-1/2*(I+cot(b*x+a)*(-1+I*c)-c)/c)+1/4*I/b/(-1+I*c)/(I+c)*dilog((cot(b*x+a)*(-1+I*c)-c-I)/(-2*I-2*c))+1/4*I/b/(-1+I*c)/(I+c)*dilog(-1/2*I*(I+cot(b*x+a)*(-1+I*c)-c))-1/8*I/b/(-1+I*c)/(I+c)*ln(cot(b*x+a)*(-1+I*c)-c-I)^2-1/2/b/(-1+I*c)/(I+c)*dilog(-1/2*(I+cot(b*x+a)*(-1+I*c)-c)/c)*c+Pi*x-1/4*I/b/(-1+I*c)/(I+c)*dilog(-1/2*I*(I+cot(b*x+a)*(-1+I*c)-c))*c^2+1/8*I/b/(-1+I*c)/(I+c)*ln(cot(b*x+a)*(-1+I*c)-c-I)^2*c^2+1/4*I/b/(-1+I*c)/(I+c)*dilog(-1/2*(I+cot(b*x+a)*(-1+I*c)-c)/c)*c^2-1/4*I/b/(-1+I*c)/(I+c)*dilog((cot(b*x+a)*(-1+I*c)-c-I)/(-2*I-2*c))*c^2+1/4*I/b/(-1+I*c)/(I+c)*ln(cot(b*x+a)*(-1+I*c)-c-I)*ln(-1/2*I*(I+cot(b*x+a)*(-1+I*c)-c))","B"
178,0,0,29,2.070000," ","int((Pi-arccot(-c-(1-I*c)*cot(b*x+a)))/x,x)","\int \frac{\pi -\mathrm{arccot}\left(-c -\left(-i c +1\right) \cot \left(b x +a \right)\right)}{x}\, dx"," ",0,"int((Pi-arccot(-c-(1-I*c)*cot(b*x+a)))/x,x)","F"
179,1,1527,129,6.796000," ","int(x^2*(Pi-arccot(-c+(1+I*c)*cot(b*x+a))),x)","\frac{i x^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{3}+\frac{x^{3} \pi  \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{3}}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c -i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{12}+\frac{i a^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right) x}{2 b^{2}}-\frac{i \ln \left(1+i {\mathrm e}^{2 i \left(b x +a \right)} c \right) x \,a^{2}}{2 b^{2}}-\frac{\polylog \left(4, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{8 b^{3}}+\frac{b \,x^{4}}{12}+\frac{i a^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right) x}{2 b^{2}}+\frac{i a^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{3}}-\frac{i a^{3} \ln \left(-{\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{6 b^{3}}+\frac{i a^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{3}}+\frac{x^{3} \pi  \mathrm{csgn}\left(i {\mathrm e}^{i \left(b x +a \right)}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)}{12}-\frac{i x^{3} \ln \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{6}+\frac{x^{2} \polylog \left(2, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4 b}-\frac{i \ln \left(1+i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a^{3}}{3 b^{3}}+\frac{i x \polylog \left(3, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4 b^{2}}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c -i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(i \left(c -i\right)\right) \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}+\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{12}-\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{12}+\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}-\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c -i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{12}+\frac{i x^{3} \ln \left(1+i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{6}+\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c -i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{12}-\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{12}+\frac{i x^{3} \ln \left(c -i\right)}{6}-\frac{\polylog \left(2, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a^{2}}{4 b^{3}}+\frac{a^{2} \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{3}}+\frac{a^{2} \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{3}}+\frac{x^{3} \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right) \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{12}+\frac{x^{3} \pi  \,\mathrm{csgn}\left(i \left(c -i\right)\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{12}-\frac{x^{3} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(b x +a \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}{6}"," ",0,"1/12*x^3*Pi*csgn(I*(c-I)/(exp(2*I*(b*x+a))-1))^3+1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a)))*csgn(I*(c-I)/(exp(2*I*(b*x+a))-1))*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))+1/4*x^2*polylog(2,-I*exp(2*I*(b*x+a))*c)/b+1/12*b*x^4-1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I))*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))-1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))^3+1/12*x^3*Pi*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))^2-1/12*x^3*Pi*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))^3+1/6*I*x^3*ln(1+I*c*exp(2*I*(b*x+a)))-1/4/b^3*polylog(2,-I*exp(2*I*(b*x+a))*c)*a^2+1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a)))^3-1/6*I*x^3*ln(exp(2*I*(b*x+a))*c-I)-1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))-1/12*x^3*Pi*csgn(I*(c-I))*csgn(I*(c-I)/(exp(2*I*(b*x+a))-1))^2-1/12*x^3*Pi*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(c-I)/(exp(2*I*(b*x+a))-1))^2+1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I))*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))^2+1/4*I*x*polylog(3,-I*exp(2*I*(b*x+a))*c)/b^2-1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a)))*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))^2-1/12*x^3*Pi*csgn(I*(c-I)/(exp(2*I*(b*x+a))-1))*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))^2+1/12*x^3*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))^2+1/12*x^3*Pi*csgn(I*(c-I))*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(c-I)/(exp(2*I*(b*x+a))-1))-1/6*x^3*Pi*csgn(I*exp(I*(b*x+a)))*csgn(I*exp(2*I*(b*x+a)))^2+1/12*x^3*Pi*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))^2-1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))^2-1/12*x^3*Pi*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))^3+1/2/b^3*a^2*dilog(1+I*exp(I*(b*x+a))*(I*c)^(1/2))+1/2/b^3*a^2*dilog(1-I*exp(I*(b*x+a))*(I*c)^(1/2))-1/2*I/b^2*ln(1+I*c*exp(2*I*(b*x+a)))*x*a^2+1/2*I/b^2*a^2*ln(1+I*exp(I*(b*x+a))*(I*c)^(1/2))*x+1/2*I/b^2*a^2*ln(1-I*exp(I*(b*x+a))*(I*c)^(1/2))*x+1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))+1/12*x^3*Pi*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))^2-1/8*polylog(4,-I*exp(2*I*(b*x+a))*c)/b^3+1/3*I*x^3*ln(exp(I*(b*x+a)))+1/12*x^3*Pi*csgn(I*exp(I*(b*x+a)))^2*csgn(I*exp(2*I*(b*x+a)))+1/6*I*x^3*ln(c-I)+1/2*I/b^3*a^3*ln(1+I*exp(I*(b*x+a))*(I*c)^(1/2))+1/2*I/b^3*a^3*ln(1-I*exp(I*(b*x+a))*(I*c)^(1/2))-1/3*I/b^3*ln(1+I*c*exp(2*I*(b*x+a)))*a^3-1/6*I/b^3*a^3*ln(-exp(2*I*(b*x+a))*c+I)+1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))^3","C"
180,1,1492,104,6.073000," ","int(x*(Pi-arccot(-c+(1+I*c)*cot(b*x+a))),x)","\frac{x \polylog \left(2, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4 b}-\frac{a \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{2}}+\frac{i \polylog \left(3, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{8 b^{2}}-\frac{i x^{2} \ln \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{4}+\frac{i x^{2} \ln \left(1+i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(i \left(c -i\right)\right) \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c -i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c -i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}+\frac{i \ln \left(1+i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a^{2}}{4 b^{2}}+\frac{i a^{2} \ln \left(-{\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{4 b^{2}}-\frac{i a^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{2}}+\frac{x^{2} \pi  \mathrm{csgn}\left(i {\mathrm e}^{i \left(b x +a \right)}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)}{8}+\frac{i x^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{2}+\frac{i \ln \left(1+i {\mathrm e}^{2 i \left(b x +a \right)} c \right) x a}{2 b}-\frac{a \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{2}}+\frac{\polylog \left(2, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a}{4 b^{2}}+\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{8}-\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{8}-\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{8}+\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{8}+\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}-\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c -i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{8}+\frac{i x^{2} \ln \left(c -i\right)}{4}+\frac{x^{2} \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i \left(b x +a \right)} c -i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{2}}{8}-\frac{i a \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right) x}{2 b}-\frac{i a \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right) x}{2 b}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{8}-\frac{x^{2} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(b x +a \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}{4}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(i \left(c -i\right)\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{8}+\frac{x^{2} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right) \mathrm{csgn}\left(\frac{i \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 i \left(b x +a \right)} \left(c -i\right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)}{8}-\frac{i a^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{2}}+\frac{b \,x^{3}}{6}+\frac{x^{2} \pi  \mathrm{csgn}\left(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{3}}{8}"," ",0,"1/2*I*x^2*ln(exp(I*(b*x+a)))+1/4*I*x^2*ln(1+I*c*exp(2*I*(b*x+a)))+1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))+1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))^3-1/8*x^2*Pi*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))^3+1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I))*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))^2+1/8*x^2*Pi*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))^2-1/8*x^2*Pi*csgn(I*(c-I))*csgn(I*(c-I)/(exp(2*I*(b*x+a))-1))^2-1/8*x^2*Pi*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(c-I)/(exp(2*I*(b*x+a))-1))^2-1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a)))*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))^2-1/4*I*x^2*ln(exp(2*I*(b*x+a))*c-I)+1/8*I*polylog(3,-I*exp(2*I*(b*x+a))*c)/b^2-1/2*I/b*a*ln(1+I*exp(I*(b*x+a))*(I*c)^(1/2))*x-1/2*I/b*a*ln(1-I*exp(I*(b*x+a))*(I*c)^(1/2))*x-1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))-1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))^2-1/8*x^2*Pi*csgn(I*(c-I)/(exp(2*I*(b*x+a))-1))*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))^2+1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))^2-1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))^3+1/8*x^2*Pi*csgn(I*(c-I)/(exp(2*I*(b*x+a))-1))^3+1/8*x^2*Pi*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))^2-1/8*x^2*Pi*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))^3+1/8*x^2*Pi*csgn(I*exp(I*(b*x+a)))^2*csgn(I*exp(2*I*(b*x+a)))-1/4*x^2*Pi*csgn(I*exp(I*(b*x+a)))*csgn(I*exp(2*I*(b*x+a)))^2+1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a)))^3-1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c-I))*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))+1/4*I/b^2*ln(1+I*c*exp(2*I*(b*x+a)))*a^2+1/4*I/b^2*a^2*ln(-exp(2*I*(b*x+a))*c+I)-1/2*I/b^2*a^2*ln(1+I*exp(I*(b*x+a))*(I*c)^(1/2))-1/2*I/b^2*a^2*ln(1-I*exp(I*(b*x+a))*(I*c)^(1/2))+1/2*I/b*ln(1+I*c*exp(2*I*(b*x+a)))*x*a+1/6*b*x^3+1/4*x*polylog(2,-I*exp(2*I*(b*x+a))*c)/b+1/4*I*x^2*ln(c-I)-1/2/b^2*a*dilog(1+I*exp(I*(b*x+a))*(I*c)^(1/2))-1/2/b^2*a*dilog(1-I*exp(I*(b*x+a))*(I*c)^(1/2))+1/4/b^2*polylog(2,-I*exp(2*I*(b*x+a))*c)*a+1/8*x^2*Pi*csgn(I*(c-I))*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(c-I)/(exp(2*I*(b*x+a))-1))+1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a)))*csgn(I*(c-I)/(exp(2*I*(b*x+a))-1))*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))+1/8*x^2*Pi*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))^2","C"
181,1,1756,75,0.762000," ","int(Pi-arccot(-c+(1+I*c)*cot(b*x+a)),x)","-\frac{i \dilog \left(\frac{-\left(i c +1\right) \cot \left(b x +a \right)+c -i}{-2 i+2 c}\right) c^{2}}{4 \left(i c +1\right) b \left(i-c \right)}+\frac{i \dilog \left(\frac{c -\left(i c +1\right) \cot \left(b x +a \right)+i}{2 c}\right) c^{2}}{4 \left(i c +1\right) b \left(i-c \right)}+\frac{\dilog \left(-\frac{i \left(i-c +\left(i c +1\right) \cot \left(b x +a \right)\right)}{2}\right) c}{2 \left(i c +1\right) b \left(i-c \right)}+\frac{\dilog \left(\frac{c -\left(i c +1\right) \cot \left(b x +a \right)+i}{2 c}\right) c}{2 \left(i c +1\right) b \left(i-c \right)}+\frac{\mathrm{arccot}\left(-c +\left(i c +1\right) \cot \left(b x +a \right)\right) \ln \left(i-c +\left(i c +1\right) \cot \left(b x +a \right)\right) c^{2}}{\left(i c +1\right) b \left(2 i-2 c \right)}-\frac{\mathrm{arccot}\left(-c +\left(i c +1\right) \cot \left(b x +a \right)\right) \ln \left(-c -\left(i c +1\right) \cot \left(b x +a \right)+i\right) c^{2}}{\left(i c +1\right) b \left(2 i-2 c \right)}+\frac{i \ln \left(-c -\left(i c +1\right) \cot \left(b x +a \right)+i\right) \ln \left(\frac{-\left(i c +1\right) \cot \left(b x +a \right)+c -i}{-2 i+2 c}\right)}{4 \left(i c +1\right) b \left(i-c \right)}+\frac{i \ln \left(i-c +\left(i c +1\right) \cot \left(b x +a \right)\right) \ln \left(-\frac{i \left(c -\left(i c +1\right) \cot \left(b x +a \right)+i\right)}{2}\right)}{4 \left(i c +1\right) b \left(i-c \right)}-\frac{i \ln \left(-\frac{i \left(i-c +\left(i c +1\right) \cot \left(b x +a \right)\right)}{2}\right) \ln \left(-\frac{i \left(c -\left(i c +1\right) \cot \left(b x +a \right)+i\right)}{2}\right)}{4 \left(i c +1\right) b \left(i-c \right)}-\frac{i \ln \left(-c -\left(i c +1\right) \cot \left(b x +a \right)+i\right) \ln \left(\frac{c -\left(i c +1\right) \cot \left(b x +a \right)+i}{2 c}\right)}{4 \left(i c +1\right) b \left(i-c \right)}-\frac{\ln \left(-c -\left(i c +1\right) \cot \left(b x +a \right)+i\right) \ln \left(\frac{-\left(i c +1\right) \cot \left(b x +a \right)+c -i}{-2 i+2 c}\right) c}{2 \left(i c +1\right) b \left(i-c \right)}+\frac{i \ln \left(i-c +\left(i c +1\right) \cot \left(b x +a \right)\right)^{2} c^{2}}{8 \left(i c +1\right) b \left(i-c \right)}+\frac{\ln \left(-\frac{i \left(i-c +\left(i c +1\right) \cot \left(b x +a \right)\right)}{2}\right) \ln \left(-\frac{i \left(c -\left(i c +1\right) \cot \left(b x +a \right)+i\right)}{2}\right) c}{2 \left(i c +1\right) b \left(i-c \right)}-\frac{\ln \left(i-c +\left(i c +1\right) \cot \left(b x +a \right)\right) \ln \left(-\frac{i \left(c -\left(i c +1\right) \cot \left(b x +a \right)+i\right)}{2}\right) c}{2 \left(i c +1\right) b \left(i-c \right)}+\frac{\ln \left(-c -\left(i c +1\right) \cot \left(b x +a \right)+i\right) \ln \left(\frac{c -\left(i c +1\right) \cot \left(b x +a \right)+i}{2 c}\right) c}{2 \left(i c +1\right) b \left(i-c \right)}+\frac{i \dilog \left(-\frac{i \left(i-c +\left(i c +1\right) \cot \left(b x +a \right)\right)}{2}\right) c^{2}}{4 \left(i c +1\right) b \left(i-c \right)}+\pi  x -\frac{\dilog \left(\frac{-\left(i c +1\right) \cot \left(b x +a \right)+c -i}{-2 i+2 c}\right) c}{2 \left(i c +1\right) b \left(i-c \right)}-\frac{i \dilog \left(\frac{c -\left(i c +1\right) \cot \left(b x +a \right)+i}{2 c}\right)}{4 \left(i c +1\right) b \left(i-c \right)}+\frac{i \dilog \left(\frac{-\left(i c +1\right) \cot \left(b x +a \right)+c -i}{-2 i+2 c}\right)}{4 \left(i c +1\right) b \left(i-c \right)}-\frac{i \dilog \left(-\frac{i \left(i-c +\left(i c +1\right) \cot \left(b x +a \right)\right)}{2}\right)}{4 \left(i c +1\right) b \left(i-c \right)}+\frac{\mathrm{arccot}\left(-c +\left(i c +1\right) \cot \left(b x +a \right)\right) \ln \left(-c -\left(i c +1\right) \cot \left(b x +a \right)+i\right)}{\left(i c +1\right) b \left(2 i-2 c \right)}+\frac{\ln \left(i-c +\left(i c +1\right) \cot \left(b x +a \right)\right)^{2} c}{4 \left(i c +1\right) b \left(i-c \right)}-\frac{i \ln \left(i-c +\left(i c +1\right) \cot \left(b x +a \right)\right)^{2}}{8 \left(i c +1\right) b \left(i-c \right)}-\frac{\mathrm{arccot}\left(-c +\left(i c +1\right) \cot \left(b x +a \right)\right) \ln \left(i-c +\left(i c +1\right) \cot \left(b x +a \right)\right)}{\left(i c +1\right) b \left(2 i-2 c \right)}-\frac{2 i \mathrm{arccot}\left(-c +\left(i c +1\right) \cot \left(b x +a \right)\right) \ln \left(i-c +\left(i c +1\right) \cot \left(b x +a \right)\right) c}{\left(i c +1\right) b \left(2 i-2 c \right)}+\frac{2 i \mathrm{arccot}\left(-c +\left(i c +1\right) \cot \left(b x +a \right)\right) \ln \left(-c -\left(i c +1\right) \cot \left(b x +a \right)+i\right) c}{\left(i c +1\right) b \left(2 i-2 c \right)}-\frac{i \ln \left(i-c +\left(i c +1\right) \cot \left(b x +a \right)\right) \ln \left(-\frac{i \left(c -\left(i c +1\right) \cot \left(b x +a \right)+i\right)}{2}\right) c^{2}}{4 \left(i c +1\right) b \left(i-c \right)}+\frac{i \ln \left(-\frac{i \left(i-c +\left(i c +1\right) \cot \left(b x +a \right)\right)}{2}\right) \ln \left(-\frac{i \left(c -\left(i c +1\right) \cot \left(b x +a \right)+i\right)}{2}\right) c^{2}}{4 \left(i c +1\right) b \left(i-c \right)}+\frac{i \ln \left(-c -\left(i c +1\right) \cot \left(b x +a \right)+i\right) \ln \left(\frac{c -\left(i c +1\right) \cot \left(b x +a \right)+i}{2 c}\right) c^{2}}{4 \left(i c +1\right) b \left(i-c \right)}-\frac{i \ln \left(-c -\left(i c +1\right) \cot \left(b x +a \right)+i\right) \ln \left(\frac{-\left(i c +1\right) \cot \left(b x +a \right)+c -i}{-2 i+2 c}\right) c^{2}}{4 \left(i c +1\right) b \left(i-c \right)}"," ",0,"1/(1+I*c)/b*arccot(-c+(1+I*c)*cot(b*x+a))/(2*I-2*c)*ln(-c-(1+I*c)*cot(b*x+a)+I)+1/4/(1+I*c)/b/(I-c)*ln(I-c+(1+I*c)*cot(b*x+a))^2*c+1/2/(1+I*c)/b/(I-c)*dilog(-1/2*I*(I-c+(1+I*c)*cot(b*x+a)))*c+1/2/(1+I*c)/b/(I-c)*dilog(1/2*(c-(1+I*c)*cot(b*x+a)+I)/c)*c-1/2/(1+I*c)/b/(I-c)*dilog((c-(1+I*c)*cot(b*x+a)-I)/(-2*I+2*c))*c-1/4*I/(1+I*c)/b/(I-c)*dilog(1/2*(c-(1+I*c)*cot(b*x+a)+I)/c)+1/4*I/(1+I*c)/b/(I-c)*dilog((c-(1+I*c)*cot(b*x+a)-I)/(-2*I+2*c))-1/8*I/(1+I*c)/b/(I-c)*ln(I-c+(1+I*c)*cot(b*x+a))^2+1/(1+I*c)/b*arccot(-c+(1+I*c)*cot(b*x+a))/(2*I-2*c)*ln(I-c+(1+I*c)*cot(b*x+a))*c^2-1/(1+I*c)/b*arccot(-c+(1+I*c)*cot(b*x+a))/(2*I-2*c)*ln(-c-(1+I*c)*cot(b*x+a)+I)*c^2+1/4*I/(1+I*c)/b/(I-c)*dilog(1/2*(c-(1+I*c)*cot(b*x+a)+I)/c)*c^2-1/4*I/(1+I*c)/b/(I-c)*dilog((c-(1+I*c)*cot(b*x+a)-I)/(-2*I+2*c))*c^2-1/(1+I*c)/b*arccot(-c+(1+I*c)*cot(b*x+a))/(2*I-2*c)*ln(I-c+(1+I*c)*cot(b*x+a))+1/4*I/(1+I*c)/b/(I-c)*dilog(-1/2*I*(I-c+(1+I*c)*cot(b*x+a)))*c^2+1/4*I/(1+I*c)/b/(I-c)*ln(-c-(1+I*c)*cot(b*x+a)+I)*ln((c-(1+I*c)*cot(b*x+a)-I)/(-2*I+2*c))+1/4*I/(1+I*c)/b/(I-c)*ln(I-c+(1+I*c)*cot(b*x+a))*ln(-1/2*I*(c-(1+I*c)*cot(b*x+a)+I))-1/4*I/(1+I*c)/b/(I-c)*ln(-1/2*I*(I-c+(1+I*c)*cot(b*x+a)))*ln(-1/2*I*(c-(1+I*c)*cot(b*x+a)+I))-1/4*I/(1+I*c)/b/(I-c)*ln(-c-(1+I*c)*cot(b*x+a)+I)*ln(1/2*(c-(1+I*c)*cot(b*x+a)+I)/c)-1/2/(1+I*c)/b/(I-c)*ln(-c-(1+I*c)*cot(b*x+a)+I)*ln((c-(1+I*c)*cot(b*x+a)-I)/(-2*I+2*c))*c+Pi*x+1/8*I/(1+I*c)/b/(I-c)*ln(I-c+(1+I*c)*cot(b*x+a))^2*c^2+1/2/(1+I*c)/b/(I-c)*ln(-1/2*I*(I-c+(1+I*c)*cot(b*x+a)))*ln(-1/2*I*(c-(1+I*c)*cot(b*x+a)+I))*c-1/2/(1+I*c)/b/(I-c)*ln(I-c+(1+I*c)*cot(b*x+a))*ln(-1/2*I*(c-(1+I*c)*cot(b*x+a)+I))*c+1/2/(1+I*c)/b/(I-c)*ln(-c-(1+I*c)*cot(b*x+a)+I)*ln(1/2*(c-(1+I*c)*cot(b*x+a)+I)/c)*c-2*I/(1+I*c)/b*arccot(-c+(1+I*c)*cot(b*x+a))/(2*I-2*c)*ln(I-c+(1+I*c)*cot(b*x+a))*c+2*I/(1+I*c)/b*arccot(-c+(1+I*c)*cot(b*x+a))/(2*I-2*c)*ln(-c-(1+I*c)*cot(b*x+a)+I)*c-1/4*I/(1+I*c)/b/(I-c)*ln(I-c+(1+I*c)*cot(b*x+a))*ln(-1/2*I*(c-(1+I*c)*cot(b*x+a)+I))*c^2+1/4*I/(1+I*c)/b/(I-c)*ln(-1/2*I*(I-c+(1+I*c)*cot(b*x+a)))*ln(-1/2*I*(c-(1+I*c)*cot(b*x+a)+I))*c^2+1/4*I/(1+I*c)/b/(I-c)*ln(-c-(1+I*c)*cot(b*x+a)+I)*ln(1/2*(c-(1+I*c)*cot(b*x+a)+I)/c)*c^2-1/4*I/(1+I*c)/b/(I-c)*ln(-c-(1+I*c)*cot(b*x+a)+I)*ln((c-(1+I*c)*cot(b*x+a)-I)/(-2*I+2*c))*c^2-1/4*I/(1+I*c)/b/(I-c)*dilog(-1/2*I*(I-c+(1+I*c)*cot(b*x+a)))","B"
182,0,0,28,2.306000," ","int((Pi-arccot(-c+(1+I*c)*cot(b*x+a)))/x,x)","\int \frac{\pi -\mathrm{arccot}\left(-c +\left(i c +1\right) \cot \left(b x +a \right)\right)}{x}\, dx"," ",0,"int((Pi-arccot(-c+(1+I*c)*cot(b*x+a)))/x,x)","F"
183,1,7275,254,48.500000," ","int((f*x+e)^3*arccot(tanh(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
184,1,5425,194,40.635000," ","int((f*x+e)^2*arccot(tanh(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
185,1,2688,134,5.128000," ","int((f*x+e)*arccot(tanh(b*x+a)),x)","\text{Expression too large to display}"," ",0,"-1/8*Pi*x^2*f*csgn((1+I)*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))^3+1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))^3-1/8*I*f*polylog(3,I*exp(2*b*x+2*a))/b^2-1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))*csgn((1-I)*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))^2-1/4*Pi*x*e*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))^2+1/8*Pi*x^2*f*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))^2-1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)-I))*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))^2+1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)+I))*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))^2+1/8*Pi*x^2*f*csgn((1+I)*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))^2+1/8*Pi*f*x^2+1/4*Pi*e*x+1/8*Pi*x^2*f*csgn((1-I)*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))^2+1/4*Pi*x*e*csgn((1-I)*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))^2+1/2*I*e/b*a*ln(-exp(2*b*x+2*a)+I)-1/2*I*e/b*dilog(1+exp(b*x+a)*(-1)^(3/4))-1/2*I*e/b*dilog(1-exp(b*x+a)*(-1)^(3/4))+1/2*I/b*e*dilog(((-I)^(1/2)-exp(b*x+a))/(-I)^(1/2))+1/2*I/b*e*dilog(((-I)^(1/2)+exp(b*x+a))/(-I)^(1/2))-1/2*I/b*f*a*ln(((-I)^(1/2)-exp(b*x+a))/(-I)^(1/2))*x-1/2*I/b*f*a*ln(((-I)^(1/2)+exp(b*x+a))/(-I)^(1/2))*x+1/2*I/b*f*ln(1-I*exp(2*b*x+2*a))*x*a+1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))^3-1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))^3-1/8*Pi*x^2*f*csgn((1-I)*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))^3-1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))^3-1/4*Pi*x*e*csgn((1-I)*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))^3-1/4*Pi*x*e*csgn((1+I)*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))^3-1/8*Pi*x^2*f*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))^2-1/4*I*f/b^2*a^2*ln(-exp(2*b*x+2*a)+I)+1/4*Pi*x*e*csgn((1+I)*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))^2+1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))*csgn((1+I)*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))^2-1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))*csgn((1-I)*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))^2-1/2*I*(1/2*f*x^2+e*x)*ln(exp(2*b*x+2*a)+I)+1/4*I*f*ln(1-I*exp(2*b*x+2*a))*x^2+1/2*I*ln(((-I)^(1/2)-exp(b*x+a))/(-I)^(1/2))*x*e+1/2*I*ln(((-I)^(1/2)+exp(b*x+a))/(-I)^(1/2))*x*e-1/4*I*f*ln(1+I*exp(2*b*x+2*a))*x^2-1/2*I*e*ln(1+exp(b*x+a)*(-1)^(3/4))*x-1/2*I*e*ln(1-exp(b*x+a)*(-1)^(3/4))*x-1/8*Pi*x^2*f*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(exp(2*b*x+2*a)+I))*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))+1/4*Pi*x*e*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(exp(2*b*x+2*a)-I))*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))-1/2*I*f/b*ln(1+I*exp(2*b*x+2*a))*x*a+1/2*I*f/b*a*ln(1+exp(b*x+a)*(-1)^(3/4))*x+1/2*I*f/b*a*ln(1-exp(b*x+a)*(-1)^(3/4))*x-1/2*I/b^2*f*a^2*ln(((-I)^(1/2)-exp(b*x+a))/(-I)^(1/2))-1/2*I/b^2*f*a^2*ln(((-I)^(1/2)+exp(b*x+a))/(-I)^(1/2))-1/4*I*f/b*polylog(2,-I*exp(2*b*x+2*a))*x-1/4*I*f/b^2*polylog(2,-I*exp(2*b*x+2*a))*a-1/2*I*e/b*ln(1+exp(b*x+a)*(-1)^(3/4))*a-1/2*I*e/b*ln(1-exp(b*x+a)*(-1)^(3/4))*a+1/2*I*f/b^2*a^2*ln(1+exp(b*x+a)*(-1)^(3/4))-1/2*I/b^2*f*a*dilog(((-I)^(1/2)+exp(b*x+a))/(-I)^(1/2))+1/2*I*f/b^2*a*dilog(1+exp(b*x+a)*(-1)^(3/4))+1/2*I*f/b^2*a*dilog(1-exp(b*x+a)*(-1)^(3/4))-1/2*I/b^2*f*a*dilog(((-I)^(1/2)-exp(b*x+a))/(-I)^(1/2))+1/4*I*ln(exp(2*b*x+2*a)-I)*f*x^2+1/2*I*ln(exp(2*b*x+2*a)-I)*e*x+1/2*I*f/b^2*a^2*ln(1-exp(b*x+a)*(-1)^(3/4))-1/4*I*f/b^2*ln(1+I*exp(2*b*x+2*a))*a^2+1/4*I/b^2*f*ln(1-I*exp(2*b*x+2*a))*a^2+1/4*I/b^2*f*polylog(2,I*exp(2*b*x+2*a))*a+1/2*I/b*ln(((-I)^(1/2)-exp(b*x+a))/(-I)^(1/2))*a*e+1/2*I/b*ln(((-I)^(1/2)+exp(b*x+a))/(-I)^(1/2))*a*e+1/4*I/b*f*polylog(2,I*exp(2*b*x+2*a))*x-1/4*Pi*x*e*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(exp(2*b*x+2*a)+I))*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))+1/8*Pi*x^2*f*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(exp(2*b*x+2*a)-I))*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))+1/4*Pi*x*e*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))^2-1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)-I))*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))^2+1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)+I))*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))^2+1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))*csgn((1+I)*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))^2-1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))*csgn((1+I)*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))+1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))*csgn((1-I)*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))-1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))*csgn((1+I)*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))+1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))*csgn((1-I)*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))-1/2*I/b*a*e*ln(exp(2*b*x+2*a)+I)+1/4*I/b^2*f*a^2*ln(exp(2*b*x+2*a)+I)+1/8*I*f*polylog(3,-I*exp(2*b*x+2*a))/b^2","C"
186,1,198,62,0.621000," ","int(arccot(tanh(b*x+a)),x)","\frac{\arctanh \left(\tanh \left(b x +a \right)\right) \mathrm{arccot}\left(\tanh \left(b x +a \right)\right)}{b}+\frac{\arctan \left(\tanh \left(b x +a \right)\right) \arctanh \left(\tanh \left(b x +a \right)\right)}{b}+\frac{\arctan \left(\tanh \left(b x +a \right)\right) \ln \left(1+\frac{i \left(1+i \tanh \left(b x +a \right)\right)^{2}}{\tanh^{2}\left(b x +a \right)+1}\right)}{2 b}-\frac{\arctan \left(\tanh \left(b x +a \right)\right) \ln \left(1-\frac{i \left(1+i \tanh \left(b x +a \right)\right)^{2}}{\tanh^{2}\left(b x +a \right)+1}\right)}{2 b}-\frac{i \dilog \left(1+\frac{i \left(1+i \tanh \left(b x +a \right)\right)^{2}}{\tanh^{2}\left(b x +a \right)+1}\right)}{4 b}+\frac{i \dilog \left(1-\frac{i \left(1+i \tanh \left(b x +a \right)\right)^{2}}{\tanh^{2}\left(b x +a \right)+1}\right)}{4 b}"," ",0,"1/b*arctanh(tanh(b*x+a))*arccot(tanh(b*x+a))+1/b*arctan(tanh(b*x+a))*arctanh(tanh(b*x+a))+1/2/b*arctan(tanh(b*x+a))*ln(1+I*(1+I*tanh(b*x+a))^2/(tanh(b*x+a)^2+1))-1/2/b*arctan(tanh(b*x+a))*ln(1-I*(1+I*tanh(b*x+a))^2/(tanh(b*x+a)^2+1))-1/4*I/b*dilog(1+I*(1+I*tanh(b*x+a))^2/(tanh(b*x+a)^2+1))+1/4*I/b*dilog(1-I*(1+I*tanh(b*x+a))^2/(tanh(b*x+a)^2+1))","B"
187,0,0,17,2.679000," ","int(arccot(tanh(b*x+a))/(f*x+e),x)","\int \frac{\mathrm{arccot}\left(\tanh \left(b x +a \right)\right)}{f x +e}\, dx"," ",0,"int(arccot(tanh(b*x+a))/(f*x+e),x)","F"
188,1,6930,305,60.451000," ","int(x^2*arccot(c+d*tanh(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
189,1,6580,229,6.450000," ","int(x*arccot(c+d*tanh(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
190,1,350,150,0.384000," ","int(arccot(c+d*tanh(b*x+a)),x)","\frac{\mathrm{arccot}\left(c +d \tanh \left(b x +a \right)\right) \ln \left(d \tanh \left(b x +a \right)+d \right)}{2 b}-\frac{\mathrm{arccot}\left(c +d \tanh \left(b x +a \right)\right) \ln \left(d \tanh \left(b x +a \right)-d \right)}{2 b}+\frac{i \ln \left(d \tanh \left(b x +a \right)-d \right) \ln \left(\frac{-d \tanh \left(b x +a \right)+i-c}{i-c -d}\right)}{4 b}-\frac{i \ln \left(d \tanh \left(b x +a \right)-d \right) \ln \left(\frac{i+d \tanh \left(b x +a \right)+c}{i+c +d}\right)}{4 b}+\frac{i \dilog \left(\frac{-d \tanh \left(b x +a \right)+i-c}{i-c -d}\right)}{4 b}-\frac{i \dilog \left(\frac{i+d \tanh \left(b x +a \right)+c}{i+c +d}\right)}{4 b}-\frac{i \ln \left(d \tanh \left(b x +a \right)+d \right) \ln \left(\frac{-d \tanh \left(b x +a \right)+i-c}{i-c +d}\right)}{4 b}+\frac{i \ln \left(d \tanh \left(b x +a \right)+d \right) \ln \left(\frac{i+d \tanh \left(b x +a \right)+c}{i+c -d}\right)}{4 b}-\frac{i \dilog \left(\frac{-d \tanh \left(b x +a \right)+i-c}{i-c +d}\right)}{4 b}+\frac{i \dilog \left(\frac{i+d \tanh \left(b x +a \right)+c}{i+c -d}\right)}{4 b}"," ",0,"1/2/b*arccot(c+d*tanh(b*x+a))*ln(d*tanh(b*x+a)+d)-1/2/b*arccot(c+d*tanh(b*x+a))*ln(d*tanh(b*x+a)-d)+1/4*I/b*ln(d*tanh(b*x+a)-d)*ln((-d*tanh(b*x+a)+I-c)/(I-c-d))-1/4*I/b*ln(d*tanh(b*x+a)-d)*ln((I+d*tanh(b*x+a)+c)/(I+c+d))+1/4*I/b*dilog((-d*tanh(b*x+a)+I-c)/(I-c-d))-1/4*I/b*dilog((I+d*tanh(b*x+a)+c)/(I+c+d))-1/4*I/b*ln(d*tanh(b*x+a)+d)*ln((-d*tanh(b*x+a)+I-c)/(I-c+d))+1/4*I/b*ln(d*tanh(b*x+a)+d)*ln((I+d*tanh(b*x+a)+c)/(I+c-d))-1/4*I/b*dilog((-d*tanh(b*x+a)+I-c)/(I-c+d))+1/4*I/b*dilog((I+d*tanh(b*x+a)+c)/(I+c-d))","B"
191,0,0,17,1.366000," ","int(arccot(c+d*tanh(b*x+a))/x,x)","\int \frac{\mathrm{arccot}\left(c +d \tanh \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arccot(c+d*tanh(b*x+a))/x,x)","F"
192,1,1549,116,6.272000," ","int(x^2*arccot(c+(I+c)*tanh(b*x+a)),x)","-\frac{i x^{3} \ln \left(1+i c \,{\mathrm e}^{2 b x +2 a}\right)}{6}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{12}-\frac{i \polylog \left(4, -i c \,{\mathrm e}^{2 b x +2 a}\right)}{8 b^{3}}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{12}+\frac{i x^{3} \ln \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{6}-\frac{b \,x^{4}}{12 \left(i+c \right)}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{12}+\frac{i b c \,x^{4}}{12 i+12 c}+\frac{i c x \,a^{3}}{3 b^{2} \left(i+c \right)}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)\right) \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right)}{12}-\frac{i \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{i c}\right) x \,a^{2}}{2 b^{2}}-\frac{i \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{i c}\right) x \,a^{2}}{2 b^{2}}+\frac{i \ln \left(1+i c \,{\mathrm e}^{2 b x +2 a}\right) x \,a^{2}}{2 b^{2}}-\frac{i c \,a^{3} \ln \left({\mathrm e}^{b x +a}\right)}{3 b^{3} \left(i+c \right)}+\frac{i \ln \left(1+i c \,{\mathrm e}^{2 b x +2 a}\right) a^{3}}{3 b^{3}}-\frac{i \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{i c}\right) a^{3}}{2 b^{3}}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}+1}\right)}{12}-\frac{i \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{i c}\right) a^{3}}{2 b^{3}}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{12}+\frac{i x \polylog \left(3, -i c \,{\mathrm e}^{2 b x +2 a}\right)}{4 b^{2}}-\frac{i x^{2} \polylog \left(2, -i c \,{\mathrm e}^{2 b x +2 a}\right)}{4 b}+\frac{i \polylog \left(2, -i c \,{\mathrm e}^{2 b x +2 a}\right) a^{2}}{4 b^{3}}-\frac{i a^{2} \dilog \left(1+i {\mathrm e}^{b x +a} \sqrt{i c}\right)}{2 b^{3}}-\frac{i a^{2} \dilog \left(1-i {\mathrm e}^{b x +a} \sqrt{i c}\right)}{2 b^{3}}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)\right) \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)}{12}+\frac{i a^{3} \ln \left(-{\mathrm e}^{2 b x +2 a} c +i\right)}{6 b^{3}}-\frac{a^{4}}{4 b^{3} \left(i+c \right)}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right)}{12}+\frac{a^{3} \ln \left({\mathrm e}^{b x +a}\right)}{3 b^{3} \left(i+c \right)}-\frac{x \,a^{3}}{3 b^{2} \left(i+c \right)}+\frac{i c \,a^{4}}{4 b^{3} \left(i+c \right)}-\frac{i x^{3} \ln \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{6}"," ",0,"1/4*I*x*polylog(3,-I*c*exp(2*b*x+2*a))/b^2-1/6*I*x^3*ln(1+I*c*exp(2*b*x+2*a))+1/12*I*b*c/(I+c)*x^4+1/12*Pi*x^3*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))^3-1/4*I*x^2*polylog(2,-I*c*exp(2*b*x+2*a))/b-1/12*Pi*x^3*csgn((2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^3+1/3*I/b^3*ln(1+I*c*exp(2*b*x+2*a))*a^3+1/4*I/b^3*polylog(2,-I*c*exp(2*b*x+2*a))*a^2-1/2*I/b^3*ln(1+I*exp(b*x+a)*(I*c)^(1/2))*a^3+1/12*Pi*x^3*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))^2+1/6*I*x^3*ln(2*exp(2*b*x+2*a)*c-2*I)-1/6*I*x^3*ln(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)+1/12*Pi*x^3*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(2*exp(2*b*x+2*a)*c-2*I))*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))-1/12*Pi*x^3*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))*csgn((2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))-1/2*I/b^3*ln(1-I*exp(b*x+a)*(I*c)^(1/2))*a^3-1/2*I/b^3*a^2*dilog(1+I*exp(b*x+a)*(I*c)^(1/2))-1/2*I/b^3*a^2*dilog(1-I*exp(b*x+a)*(I*c)^(1/2))-1/12*Pi*x^3*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))^2+1/12*Pi*x^3*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))*csgn((2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^2-1/12*Pi*x^3*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))^2+1/12*Pi*x^3*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^2-1/4/b^3/(I+c)*a^4-1/12*b/(I+c)*x^4-1/12*Pi*x^3*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))^3-1/12*Pi*x^3*csgn(I*(2*exp(2*b*x+2*a)*c-2*I))*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))^2+1/12*Pi*x^3*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c))*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^2+1/12*Pi*x^3*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))-1/12*Pi*x^3*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c))*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))+1/4*I/b^3*c/(I+c)*a^4-1/2*I/b^2*ln(1+I*exp(b*x+a)*(I*c)^(1/2))*x*a^2-1/2*I/b^2*ln(1-I*exp(b*x+a)*(I*c)^(1/2))*x*a^2+1/2*I/b^2*ln(1+I*c*exp(2*b*x+2*a))*x*a^2+1/6*I/b^3*a^3*ln(-exp(2*b*x+2*a)*c+I)+1/3/b^3*a^3/(I+c)*ln(exp(b*x+a))-1/3/b^2/(I+c)*x*a^3+1/12*Pi*x^3*csgn((2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^2-1/12*Pi*x^3*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^3-1/8*I*polylog(4,-I*c*exp(2*b*x+2*a))/b^3-1/3*I/b^3*c*a^3/(I+c)*ln(exp(b*x+a))+1/3*I/b^2*c/(I+c)*x*a^3","C"
193,1,1513,92,5.457000," ","int(x*arccot(c+(I+c)*tanh(b*x+a)),x)","-\frac{i c x \,a^{2}}{2 b \left(i+c \right)}+\frac{i c \,a^{2} \ln \left({\mathrm e}^{b x +a}\right)}{2 b^{2} \left(i+c \right)}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)\right) \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right)}{8}-\frac{i \ln \left(1+i c \,{\mathrm e}^{2 b x +2 a}\right) x a}{2 b}+\frac{i a \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{i c}\right) x}{2 b}+\frac{i a \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{i c}\right) x}{2 b}-\frac{i c \,a^{3}}{3 b^{2} \left(i+c \right)}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right)}{8}-\frac{i x^{2} \ln \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{4}+\frac{i x^{2} \ln \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{4}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{8}+\frac{i \polylog \left(3, -i c \,{\mathrm e}^{2 b x +2 a}\right)}{8 b^{2}}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{8}-\frac{a^{2} \ln \left({\mathrm e}^{b x +a}\right)}{2 b^{2} \left(i+c \right)}-\frac{i a^{2} \ln \left(-{\mathrm e}^{2 b x +2 a} c +i\right)}{4 b^{2}}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)\right) \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{8}-\frac{i x \polylog \left(2, -i c \,{\mathrm e}^{2 b x +2 a}\right)}{4 b}+\frac{i b c \,x^{3}}{6 i+6 c}-\frac{i x^{2} \ln \left(1+i c \,{\mathrm e}^{2 b x +2 a}\right)}{4}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{8}+\frac{a^{3}}{3 b^{2} \left(i+c \right)}-\frac{b \,x^{3}}{6 \left(i+c \right)}+\frac{i a \dilog \left(1+i {\mathrm e}^{b x +a} \sqrt{i c}\right)}{2 b^{2}}+\frac{i a \dilog \left(1-i {\mathrm e}^{b x +a} \sqrt{i c}\right)}{2 b^{2}}-\frac{i \polylog \left(2, -i c \,{\mathrm e}^{2 b x +2 a}\right) a}{4 b^{2}}+\frac{i a^{2} \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{i c}\right)}{2 b^{2}}-\frac{i \ln \left(1+i c \,{\mathrm e}^{2 b x +2 a}\right) a^{2}}{4 b^{2}}+\frac{i a^{2} \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{i c}\right)}{2 b^{2}}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}+1}\right)}{8}+\frac{x \,a^{2}}{2 b \left(i+c \right)}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{8}"," ",0,"1/8*I*polylog(3,-I*c*exp(2*b*x+2*a))/b^2-1/4*I*x^2*ln(1+I*c*exp(2*b*x+2*a))-1/2/b^2*a^2/(I+c)*ln(exp(b*x+a))-1/4*I/b^2*a^2*ln(-exp(2*b*x+2*a)*c+I)+1/8*Pi*x^2*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))-1/4*I*x*polylog(2,-I*c*exp(2*b*x+2*a))/b-1/8*Pi*x^2*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))^2+1/8*Pi*x^2*csgn((2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^2-1/8*Pi*x^2*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c))*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))+1/8*Pi*x^2*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))^3+1/8*Pi*x^2*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))^2-1/8*Pi*x^2*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))^2+1/8*Pi*x^2*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^2-1/8*Pi*x^2*csgn(I*(2*exp(2*b*x+2*a)*c-2*I))*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))^2+1/8*Pi*x^2*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c))*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^2+1/3/b^2/(I+c)*a^3-1/6*b*x^3/(I+c)-1/2*I/b*c/(I+c)*x*a^2+1/2*I/b^2*c*a^2/(I+c)*ln(exp(b*x+a))+1/2*I/b^2*a^2*ln(1-I*exp(b*x+a)*(I*c)^(1/2))+1/2*I/b^2*a*dilog(1+I*exp(b*x+a)*(I*c)^(1/2))+1/2*I/b^2*a*dilog(1-I*exp(b*x+a)*(I*c)^(1/2))-1/4*I/b^2*ln(1+I*c*exp(2*b*x+2*a))*a^2-1/4*I/b^2*polylog(2,-I*c*exp(2*b*x+2*a))*a+1/2*I/b^2*a^2*ln(1+I*exp(b*x+a)*(I*c)^(1/2))-1/4*I*x^2*ln(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)+1/4*I*x^2*ln(2*exp(2*b*x+2*a)*c-2*I)-1/2*I/b*ln(1+I*c*exp(2*b*x+2*a))*x*a+1/2*I/b*a*ln(1+I*exp(b*x+a)*(I*c)^(1/2))*x+1/2*I/b*a*ln(1-I*exp(b*x+a)*(I*c)^(1/2))*x-1/8*Pi*x^2*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^3-1/8*Pi*x^2*csgn((2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^3-1/3*I/b^2*c/(I+c)*a^3+1/6*I*b*c/(I+c)*x^3-1/8*Pi*x^2*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))*csgn((2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))+1/8*Pi*x^2*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(2*exp(2*b*x+2*a)*c-2*I))*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))+1/2/b/(I+c)*x*a^2+1/8*Pi*x^2*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))*csgn((2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^2-1/8*Pi*x^2*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)+1))^3","C"
194,1,1381,65,0.673000," ","int(arccot(c+(I+c)*tanh(b*x+a)),x)","\frac{i \ln \left(i+c +\left(i+c \right) \tanh \left(b x +a \right)\right)^{2} c^{2}}{8 \left(i+c \right)^{2} b}+\frac{i \dilog \left(-\frac{-c -\left(i+c \right) \tanh \left(b x +a \right)+i}{2 c}\right) c^{2}}{4 \left(i+c \right)^{2} b}+\frac{i \dilog \left(-\frac{i \left(i+c +\left(i+c \right) \tanh \left(b x +a \right)\right)}{2}\right) c^{2}}{4 \left(i+c \right)^{2} b}-\frac{i \dilog \left(\frac{-c -\left(i+c \right) \tanh \left(b x +a \right)-i}{-2 i-2 c}\right) c^{2}}{4 \left(i+c \right)^{2} b}-\frac{\mathrm{arccot}\left(c +\left(i+c \right) \tanh \left(b x +a \right)\right) \ln \left(i+c +\left(i+c \right) \tanh \left(b x +a \right)\right)}{\left(i+c \right) b \left(2 i+2 c \right)}+\frac{\ln \left(i+c +\left(i+c \right) \tanh \left(b x +a \right)\right) \ln \left(-\frac{i \left(-c -\left(i+c \right) \tanh \left(b x +a \right)+i\right)}{2}\right) c}{2 \left(i+c \right)^{2} b}-\frac{\ln \left(-\frac{i \left(i+c +\left(i+c \right) \tanh \left(b x +a \right)\right)}{2}\right) \ln \left(-\frac{i \left(-c -\left(i+c \right) \tanh \left(b x +a \right)+i\right)}{2}\right) c}{2 \left(i+c \right)^{2} b}+\frac{\ln \left(c -\left(i+c \right) \tanh \left(b x +a \right)+i\right) \ln \left(\frac{-c -\left(i+c \right) \tanh \left(b x +a \right)-i}{-2 i-2 c}\right) c}{2 \left(i+c \right)^{2} b}-\frac{\ln \left(c -\left(i+c \right) \tanh \left(b x +a \right)+i\right) \ln \left(-\frac{-c -\left(i+c \right) \tanh \left(b x +a \right)+i}{2 c}\right) c}{2 \left(i+c \right)^{2} b}-\frac{i \dilog \left(-\frac{i \left(i+c +\left(i+c \right) \tanh \left(b x +a \right)\right)}{2}\right)}{4 \left(i+c \right)^{2} b}+\frac{i \dilog \left(\frac{-c -\left(i+c \right) \tanh \left(b x +a \right)-i}{-2 i-2 c}\right)}{4 \left(i+c \right)^{2} b}-\frac{\ln \left(i+c +\left(i+c \right) \tanh \left(b x +a \right)\right)^{2} c}{4 \left(i+c \right)^{2} b}-\frac{i \ln \left(i+c +\left(i+c \right) \tanh \left(b x +a \right)\right)^{2}}{8 \left(i+c \right)^{2} b}-\frac{\dilog \left(-\frac{i \left(i+c +\left(i+c \right) \tanh \left(b x +a \right)\right)}{2}\right) c}{2 \left(i+c \right)^{2} b}+\frac{\dilog \left(\frac{-c -\left(i+c \right) \tanh \left(b x +a \right)-i}{-2 i-2 c}\right) c}{2 \left(i+c \right)^{2} b}-\frac{\dilog \left(-\frac{-c -\left(i+c \right) \tanh \left(b x +a \right)+i}{2 c}\right) c}{2 \left(i+c \right)^{2} b}-\frac{i \dilog \left(-\frac{-c -\left(i+c \right) \tanh \left(b x +a \right)+i}{2 c}\right)}{4 \left(i+c \right)^{2} b}+\frac{\mathrm{arccot}\left(c +\left(i+c \right) \tanh \left(b x +a \right)\right) \ln \left(c -\left(i+c \right) \tanh \left(b x +a \right)+i\right)}{\left(i+c \right) b \left(2 i+2 c \right)}+\frac{i \ln \left(i+c +\left(i+c \right) \tanh \left(b x +a \right)\right) \ln \left(-\frac{i \left(-c -\left(i+c \right) \tanh \left(b x +a \right)+i\right)}{2}\right)}{4 \left(i+c \right)^{2} b}-\frac{i \ln \left(-\frac{i \left(i+c +\left(i+c \right) \tanh \left(b x +a \right)\right)}{2}\right) \ln \left(-\frac{i \left(-c -\left(i+c \right) \tanh \left(b x +a \right)+i\right)}{2}\right)}{4 \left(i+c \right)^{2} b}+\frac{i \ln \left(c -\left(i+c \right) \tanh \left(b x +a \right)+i\right) \ln \left(\frac{-c -\left(i+c \right) \tanh \left(b x +a \right)-i}{-2 i-2 c}\right)}{4 \left(i+c \right)^{2} b}-\frac{i \ln \left(c -\left(i+c \right) \tanh \left(b x +a \right)+i\right) \ln \left(-\frac{-c -\left(i+c \right) \tanh \left(b x +a \right)+i}{2 c}\right)}{4 \left(i+c \right)^{2} b}-\frac{2 i \mathrm{arccot}\left(c +\left(i+c \right) \tanh \left(b x +a \right)\right) \ln \left(c -\left(i+c \right) \tanh \left(b x +a \right)+i\right) c}{\left(i+c \right) b \left(2 i+2 c \right)}+\frac{2 i \mathrm{arccot}\left(c +\left(i+c \right) \tanh \left(b x +a \right)\right) \ln \left(i+c +\left(i+c \right) \tanh \left(b x +a \right)\right) c}{\left(i+c \right) b \left(2 i+2 c \right)}-\frac{i \ln \left(c -\left(i+c \right) \tanh \left(b x +a \right)+i\right) \ln \left(\frac{-c -\left(i+c \right) \tanh \left(b x +a \right)-i}{-2 i-2 c}\right) c^{2}}{4 \left(i+c \right)^{2} b}-\frac{i \ln \left(i+c +\left(i+c \right) \tanh \left(b x +a \right)\right) \ln \left(-\frac{i \left(-c -\left(i+c \right) \tanh \left(b x +a \right)+i\right)}{2}\right) c^{2}}{4 \left(i+c \right)^{2} b}+\frac{i \ln \left(-\frac{i \left(i+c +\left(i+c \right) \tanh \left(b x +a \right)\right)}{2}\right) \ln \left(-\frac{i \left(-c -\left(i+c \right) \tanh \left(b x +a \right)+i\right)}{2}\right) c^{2}}{4 \left(i+c \right)^{2} b}+\frac{\mathrm{arccot}\left(c +\left(i+c \right) \tanh \left(b x +a \right)\right) \ln \left(i+c +\left(i+c \right) \tanh \left(b x +a \right)\right) c^{2}}{\left(i+c \right) b \left(2 i+2 c \right)}-\frac{\mathrm{arccot}\left(c +\left(i+c \right) \tanh \left(b x +a \right)\right) \ln \left(c -\left(i+c \right) \tanh \left(b x +a \right)+i\right) c^{2}}{\left(i+c \right) b \left(2 i+2 c \right)}+\frac{i \ln \left(c -\left(i+c \right) \tanh \left(b x +a \right)+i\right) \ln \left(-\frac{-c -\left(i+c \right) \tanh \left(b x +a \right)+i}{2 c}\right) c^{2}}{4 \left(i+c \right)^{2} b}"," ",0,"1/(I+c)/b*arccot(c+(I+c)*tanh(b*x+a))/(2*I+2*c)*ln(c-(I+c)*tanh(b*x+a)+I)+1/4*I/(I+c)^2/b*dilog(-1/2*(-c-(I+c)*tanh(b*x+a)+I)/c)*c^2+1/4*I/(I+c)^2/b*ln(I+c+(I+c)*tanh(b*x+a))*ln(-1/2*I*(-c-(I+c)*tanh(b*x+a)+I))-1/4*I/(I+c)^2/b*ln(-1/2*I*(I+c+(I+c)*tanh(b*x+a)))*ln(-1/2*I*(-c-(I+c)*tanh(b*x+a)+I))+1/4*I/(I+c)^2/b*ln(c-(I+c)*tanh(b*x+a)+I)*ln((-c-(I+c)*tanh(b*x+a)-I)/(-2*I-2*c))-1/4*I/(I+c)^2/b*ln(c-(I+c)*tanh(b*x+a)+I)*ln(-1/2*(-c-(I+c)*tanh(b*x+a)+I)/c)+1/8*I/(I+c)^2/b*ln(I+c+(I+c)*tanh(b*x+a))^2*c^2+1/4*I/(I+c)^2/b*dilog(-1/2*I*(I+c+(I+c)*tanh(b*x+a)))*c^2-2*I/(I+c)/b*arccot(c+(I+c)*tanh(b*x+a))/(2*I+2*c)*ln(c-(I+c)*tanh(b*x+a)+I)*c+2*I/(I+c)/b*arccot(c+(I+c)*tanh(b*x+a))/(2*I+2*c)*ln(I+c+(I+c)*tanh(b*x+a))*c-1/4/(I+c)^2/b*ln(I+c+(I+c)*tanh(b*x+a))^2*c-1/2/(I+c)^2/b*dilog(-1/2*I*(I+c+(I+c)*tanh(b*x+a)))*c+1/2/(I+c)^2/b*dilog((-c-(I+c)*tanh(b*x+a)-I)/(-2*I-2*c))*c-1/2/(I+c)^2/b*dilog(-1/2*(-c-(I+c)*tanh(b*x+a)+I)/c)*c-1/4*I/(I+c)^2/b*dilog(-1/2*(-c-(I+c)*tanh(b*x+a)+I)/c)-1/8*I/(I+c)^2/b*ln(I+c+(I+c)*tanh(b*x+a))^2-1/4*I/(I+c)^2/b*dilog(-1/2*I*(I+c+(I+c)*tanh(b*x+a)))+1/4*I/(I+c)^2/b*dilog((-c-(I+c)*tanh(b*x+a)-I)/(-2*I-2*c))-1/(I+c)/b*arccot(c+(I+c)*tanh(b*x+a))/(2*I+2*c)*ln(I+c+(I+c)*tanh(b*x+a))+1/2/(I+c)^2/b*ln(I+c+(I+c)*tanh(b*x+a))*ln(-1/2*I*(-c-(I+c)*tanh(b*x+a)+I))*c-1/2/(I+c)^2/b*ln(-1/2*I*(I+c+(I+c)*tanh(b*x+a)))*ln(-1/2*I*(-c-(I+c)*tanh(b*x+a)+I))*c+1/2/(I+c)^2/b*ln(c-(I+c)*tanh(b*x+a)+I)*ln((-c-(I+c)*tanh(b*x+a)-I)/(-2*I-2*c))*c-1/2/(I+c)^2/b*ln(c-(I+c)*tanh(b*x+a)+I)*ln(-1/2*(-c-(I+c)*tanh(b*x+a)+I)/c)*c-1/4*I/(I+c)^2/b*dilog((-c-(I+c)*tanh(b*x+a)-I)/(-2*I-2*c))*c^2+1/(I+c)/b*arccot(c+(I+c)*tanh(b*x+a))/(2*I+2*c)*ln(I+c+(I+c)*tanh(b*x+a))*c^2-1/(I+c)/b*arccot(c+(I+c)*tanh(b*x+a))/(2*I+2*c)*ln(c-(I+c)*tanh(b*x+a)+I)*c^2+1/4*I/(I+c)^2/b*ln(c-(I+c)*tanh(b*x+a)+I)*ln(-1/2*(-c-(I+c)*tanh(b*x+a)+I)/c)*c^2+1/4*I/(I+c)^2/b*ln(-1/2*I*(I+c+(I+c)*tanh(b*x+a)))*ln(-1/2*I*(-c-(I+c)*tanh(b*x+a)+I))*c^2-1/4*I/(I+c)^2/b*ln(c-(I+c)*tanh(b*x+a)+I)*ln((-c-(I+c)*tanh(b*x+a)-I)/(-2*I-2*c))*c^2-1/4*I/(I+c)^2/b*ln(I+c+(I+c)*tanh(b*x+a))*ln(-1/2*I*(-c-(I+c)*tanh(b*x+a)+I))*c^2","B"
195,0,0,20,1.854000," ","int(arccot(c+(I+c)*tanh(b*x+a))/x,x)","\int \frac{\mathrm{arccot}\left(c +\left(i+c \right) \tanh \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arccot(c+(I+c)*tanh(b*x+a))/x,x)","F"
196,1,1570,119,6.237000," ","int(x^2*arccot(c-(I-c)*tanh(b*x+a)),x)","\frac{i a^{3} \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{-i c}\right)}{2 b^{3}}+\frac{i x^{3} \ln \left(2 i {\mathrm e}^{2 b x +2 a}-2 \,{\mathrm e}^{2 b x +2 a} c \right)}{6}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{12}-\frac{i x^{3} \ln \left(-2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{6}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{12}+\frac{a^{4}}{4 b^{3} \left(i-c \right)}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{12}+\frac{i a^{2} \dilog \left(1-i {\mathrm e}^{b x +a} \sqrt{-i c}\right)}{2 b^{3}}+\frac{b \,x^{4}}{12 i-12 c}+\frac{i \polylog \left(4, i c \,{\mathrm e}^{2 b x +2 a}\right)}{8 b^{3}}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)\right) \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right)}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right)}{12}+\frac{i c \,a^{4}}{4 b^{3} \left(i-c \right)}-\frac{i \ln \left(1-i c \,{\mathrm e}^{2 b x +2 a}\right) x \,a^{2}}{2 b^{2}}-\frac{i \ln \left(1-i c \,{\mathrm e}^{2 b x +2 a}\right) a^{3}}{3 b^{3}}-\frac{i \polylog \left(2, i c \,{\mathrm e}^{2 b x +2 a}\right) a^{2}}{4 b^{3}}+\frac{\pi  \,x^{3}}{3}+\frac{i a^{3} \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{-i c}\right)}{2 b^{3}}+\frac{i x^{2} \polylog \left(2, i c \,{\mathrm e}^{2 b x +2 a}\right)}{4 b}-\frac{i x \polylog \left(3, i c \,{\mathrm e}^{2 b x +2 a}\right)}{4 b^{2}}+\frac{i a^{2} \dilog \left(1+i {\mathrm e}^{b x +a} \sqrt{-i c}\right)}{2 b^{3}}-\frac{i a^{3} \ln \left({\mathrm e}^{2 b x +2 a} c +i\right)}{6 b^{3}}-\frac{a^{3} \ln \left({\mathrm e}^{b x +a}\right)}{3 b^{3} \left(i-c \right)}+\frac{x \,a^{3}}{3 b^{2} \left(i-c \right)}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)\right) \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}+1}\right)}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{12}+\frac{i a^{2} \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{-i c}\right) x}{2 b^{2}}+\frac{i a^{2} \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{-i c}\right) x}{2 b^{2}}-\frac{i c \,a^{3} \ln \left({\mathrm e}^{b x +a}\right)}{3 b^{3} \left(i-c \right)}+\frac{i c x \,a^{3}}{3 b^{2} \left(i-c \right)}+\frac{i b c \,x^{4}}{12 i-12 c}+\frac{i x^{3} \ln \left(1-i c \,{\mathrm e}^{2 b x +2 a}\right)}{6}"," ",0,"1/6*I*x^3*ln(1-I*c*exp(2*b*x+2*a))+1/6*I*x^3*ln(2*I*exp(2*b*x+2*a)-2*exp(2*b*x+2*a)*c)+1/2*I/b^2*a^2*ln(1+I*exp(b*x+a)*(-I*c)^(1/2))*x-1/2*I/b^2*ln(1-I*c*exp(2*b*x+2*a))*x*a^2+1/4*I*x^2*polylog(2,I*c*exp(2*b*x+2*a))/b-1/12*Pi*x^3*csgn((-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^3-1/4*I*x*polylog(3,I*c*exp(2*b*x+2*a))/b^2+1/8*I*polylog(4,I*c*exp(2*b*x+2*a))/b^3-1/12*Pi*x^3*csgn((-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^2-1/6*I*x^3*ln(-2*exp(2*b*x+2*a)*c-2*I)+1/3*I/b^2*c/(I-c)*x*a^3-1/3*I/b^3*c*a^3/(I-c)*ln(exp(b*x+a))-1/12*Pi*x^3*csgn((2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))^2-1/4*I/b^3*polylog(2,I*c*exp(2*b*x+2*a))*a^2-1/3*I/b^3*ln(1-I*c*exp(2*b*x+2*a))*a^3+1/2*I/b^3*a^3*ln(1-I*exp(b*x+a)*(-I*c)^(1/2))+1/2*I/b^3*a^3*ln(1+I*exp(b*x+a)*(-I*c)^(1/2))+1/2*I/b^3*a^2*dilog(1-I*exp(b*x+a)*(-I*c)^(1/2))+1/2*I/b^3*a^2*dilog(1+I*exp(b*x+a)*(-I*c)^(1/2))+1/12*Pi*x^3*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))^3-1/3/b^3*a^3/(I-c)*ln(exp(b*x+a))+1/3/b^2/(I-c)*x*a^3+1/3*Pi*x^3+1/4/b^3/(I-c)*a^4+1/12*b/(I-c)*x^4+1/12*Pi*x^3*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c))*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))-1/12*Pi*x^3*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(2*exp(2*b*x+2*a)*c+2*I))*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))+1/12*Pi*x^3*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c))*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^2-1/12*Pi*x^3*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))*csgn((2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))^2-1/12*Pi*x^3*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))*csgn((2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))+1/12*Pi*x^3*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))^2+1/12*Pi*x^3*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))*csgn((-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^2-1/12*Pi*x^3*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^2+1/12*Pi*x^3*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))*csgn((-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))-1/6*I/b^3*a^3*ln(exp(2*b*x+2*a)*c+I)+1/4*I/b^3*c/(I-c)*a^4-1/12*Pi*x^3*csgn(I*(2*exp(2*b*x+2*a)*c+2*I))*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))^2+1/12*I*b*c/(I-c)*x^4-1/12*Pi*x^3*csgn((2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))^3+1/2*I/b^2*a^2*ln(1-I*exp(b*x+a)*(-I*c)^(1/2))*x-1/12*Pi*x^3*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^3","C"
197,1,1534,95,5.437000," ","int(x*arccot(c-(I-c)*tanh(b*x+a)),x)","\frac{i b c \,x^{3}}{6 i-6 c}+\frac{\pi  \,x^{2}}{2}+\frac{i x^{2} \ln \left(1-i c \,{\mathrm e}^{2 b x +2 a}\right)}{4}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{8}-\frac{i x^{2} \ln \left(-2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{4}+\frac{i x^{2} \ln \left(2 i {\mathrm e}^{2 b x +2 a}-2 \,{\mathrm e}^{2 b x +2 a} c \right)}{4}-\frac{i \polylog \left(3, i c \,{\mathrm e}^{2 b x +2 a}\right)}{8 b^{2}}-\frac{a^{3}}{3 b^{2} \left(i-c \right)}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{8}+\frac{b \,x^{3}}{6 i-6 c}+\frac{a^{2} \ln \left({\mathrm e}^{b x +a}\right)}{2 b^{2} \left(i-c \right)}-\frac{x \,a^{2}}{2 b \left(i-c \right)}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{8}+\frac{i \ln \left(1-i c \,{\mathrm e}^{2 b x +2 a}\right) a^{2}}{4 b^{2}}-\frac{i \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{-i c}\right) a^{2}}{2 b^{2}}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)\right) \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{8}-\frac{i a^{2} \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{-i c}\right)}{2 b^{2}}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{8}+\frac{i a^{2} \ln \left({\mathrm e}^{2 b x +2 a} c +i\right)}{4 b^{2}}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{8}+\frac{i x \polylog \left(2, i c \,{\mathrm e}^{2 b x +2 a}\right)}{4 b}-\frac{i a \dilog \left(1-i {\mathrm e}^{b x +a} \sqrt{-i c}\right)}{2 b^{2}}+\frac{i \polylog \left(2, i c \,{\mathrm e}^{2 b x +2 a}\right) a}{4 b^{2}}-\frac{i a \dilog \left(1+i {\mathrm e}^{b x +a} \sqrt{-i c}\right)}{2 b^{2}}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right)^{2}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(\frac{-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}+1}\right)}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)\right) \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}+1}\right)}{8}+\frac{i \ln \left(1-i c \,{\mathrm e}^{2 b x +2 a}\right) x a}{2 b}-\frac{i a \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{-i c}\right) x}{2 b}-\frac{i a \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{-i c}\right) x}{2 b}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}+1}\right) \mathrm{csgn}\left(i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}+1}\right)}{8}-\frac{i c \,a^{3}}{3 b^{2} \left(i-c \right)}+\frac{i c \,a^{2} \ln \left({\mathrm e}^{b x +a}\right)}{2 b^{2} \left(i-c \right)}-\frac{i c x \,a^{2}}{2 b \left(i-c \right)}"," ",0,"1/4*I*x^2*ln(1-I*c*exp(2*b*x+2*a))+1/4*I*x*polylog(2,I*c*exp(2*b*x+2*a))/b+1/2/b^2*a^2/(I-c)*ln(exp(b*x+a))-1/2/b/(I-c)*x*a^2-1/8*Pi*x^2*csgn(I*(2*exp(2*b*x+2*a)*c+2*I))*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))^2-1/8*Pi*x^2*csgn((2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))^2-1/2*I/b^2*a*dilog(1-I*exp(b*x+a)*(-I*c)^(1/2))+1/4*I/b^2*ln(1-I*c*exp(2*b*x+2*a))*a^2+1/4*I/b^2*polylog(2,I*c*exp(2*b*x+2*a))*a-1/2*I/b^2*ln(1-I*exp(b*x+a)*(-I*c)^(1/2))*a^2-1/2*I/b^2*a*dilog(1+I*exp(b*x+a)*(-I*c)^(1/2))-1/8*Pi*x^2*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))*csgn((2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))+1/8*Pi*x^2*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c))*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^2-1/8*Pi*x^2*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))*csgn((2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))^2-1/2*I/b^2*a^2*ln(1+I*exp(b*x+a)*(-I*c)^(1/2))+1/2*I/b^2*c*a^2/(I-c)*ln(exp(b*x+a))-1/8*Pi*x^2*csgn((-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^3-1/8*Pi*x^2*csgn((2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))^3-1/4*I*x^2*ln(-2*exp(2*b*x+2*a)*c-2*I)+1/2*Pi*x^2+1/8*Pi*x^2*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))*csgn((-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^2+1/4*I/b^2*a^2*ln(exp(2*b*x+2*a)*c+I)+1/8*Pi*x^2*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))^2+1/8*Pi*x^2*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c))*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))+1/4*I*x^2*ln(2*I*exp(2*b*x+2*a)-2*exp(2*b*x+2*a)*c)-1/8*Pi*x^2*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^2+1/2*I/b*ln(1-I*c*exp(2*b*x+2*a))*x*a-1/2*I/b*a*ln(1-I*exp(b*x+a)*(-I*c)^(1/2))*x-1/2*I/b*a*ln(1+I*exp(b*x+a)*(-I*c)^(1/2))*x-1/8*Pi*x^2*csgn(I/(exp(2*b*x+2*a)+1))*csgn(I*(2*exp(2*b*x+2*a)*c+2*I))*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))-1/2*I/b*c/(I-c)*x*a^2+1/8*Pi*x^2*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))*csgn((-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))-1/8*I*polylog(3,I*c*exp(2*b*x+2*a))/b^2-1/3*I/b^2*c/(I-c)*a^3+1/6*I*b*c/(I-c)*x^3-1/3/b^2/(I-c)*a^3+1/6*b*x^3/(I-c)+1/8*Pi*x^2*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)+1))^3-1/8*Pi*x^2*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^3-1/8*Pi*x^2*csgn((-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)+1))^2","C"
198,1,1351,68,0.551000," ","int(arccot(c-(I-c)*tanh(b*x+a)),x)","-\frac{i \ln \left(\left(c -i\right) \tanh \left(b x +a \right)+c -i\right) \ln \left(-\frac{i \left(i+\left(c -i\right) \tanh \left(b x +a \right)+c \right)}{2}\right) c^{2}}{4 b \left(c -i\right) \left(i-c \right)}+\frac{i \ln \left(\left(c -i\right) \tanh \left(b x +a \right)-c +i\right) \ln \left(\frac{i+\left(c -i\right) \tanh \left(b x +a \right)+c}{2 c}\right) c^{2}}{4 b \left(c -i\right) \left(i-c \right)}-\frac{i \ln \left(\left(c -i\right) \tanh \left(b x +a \right)-c +i\right) \ln \left(\frac{\left(c -i\right) \tanh \left(b x +a \right)+c -i}{-2 i+2 c}\right) c^{2}}{4 b \left(c -i\right) \left(i-c \right)}+\frac{2 i \mathrm{arccot}\left(\left(c -i\right) \tanh \left(b x +a \right)+c \right) \ln \left(\left(c -i\right) \tanh \left(b x +a \right)+c -i\right) c}{b \left(c -i\right) \left(2 i-2 c \right)}-\frac{2 i \mathrm{arccot}\left(\left(c -i\right) \tanh \left(b x +a \right)+c \right) \ln \left(\left(c -i\right) \tanh \left(b x +a \right)-c +i\right) c}{b \left(c -i\right) \left(2 i-2 c \right)}-\frac{\mathrm{arccot}\left(\left(c -i\right) \tanh \left(b x +a \right)+c \right) \ln \left(\left(c -i\right) \tanh \left(b x +a \right)+c -i\right) c^{2}}{b \left(c -i\right) \left(2 i-2 c \right)}+\frac{i \ln \left(\left(c -i\right) \tanh \left(b x +a \right)-c +i\right) \ln \left(\frac{\left(c -i\right) \tanh \left(b x +a \right)+c -i}{-2 i+2 c}\right)}{4 b \left(c -i\right) \left(i-c \right)}+\frac{i \ln \left(\left(c -i\right) \tanh \left(b x +a \right)+c -i\right)^{2} c^{2}}{8 b \left(c -i\right) \left(i-c \right)}+\frac{i \ln \left(\left(c -i\right) \tanh \left(b x +a \right)+c -i\right) \ln \left(-\frac{i \left(i+\left(c -i\right) \tanh \left(b x +a \right)+c \right)}{2}\right)}{4 b \left(c -i\right) \left(i-c \right)}-\frac{i \ln \left(\left(c -i\right) \tanh \left(b x +a \right)-c +i\right) \ln \left(\frac{i+\left(c -i\right) \tanh \left(b x +a \right)+c}{2 c}\right)}{4 b \left(c -i\right) \left(i-c \right)}-\frac{i \dilog \left(\frac{\left(c -i\right) \tanh \left(b x +a \right)+c -i}{-2 i+2 c}\right) c^{2}}{4 b \left(c -i\right) \left(i-c \right)}-\frac{i \dilog \left(-\frac{i \left(i+\left(c -i\right) \tanh \left(b x +a \right)+c \right)}{2}\right) c^{2}}{4 b \left(c -i\right) \left(i-c \right)}-\frac{\ln \left(\left(c -i\right) \tanh \left(b x +a \right)+c -i\right) \ln \left(-\frac{i \left(i+\left(c -i\right) \tanh \left(b x +a \right)+c \right)}{2}\right) c}{2 b \left(c -i\right) \left(i-c \right)}+\frac{\mathrm{arccot}\left(\left(c -i\right) \tanh \left(b x +a \right)+c \right) \ln \left(\left(c -i\right) \tanh \left(b x +a \right)-c +i\right) c^{2}}{b \left(c -i\right) \left(2 i-2 c \right)}+\frac{\ln \left(\left(c -i\right) \tanh \left(b x +a \right)-c +i\right) \ln \left(\frac{i+\left(c -i\right) \tanh \left(b x +a \right)+c}{2 c}\right) c}{2 b \left(c -i\right) \left(i-c \right)}-\frac{\ln \left(\left(c -i\right) \tanh \left(b x +a \right)-c +i\right) \ln \left(\frac{\left(c -i\right) \tanh \left(b x +a \right)+c -i}{-2 i+2 c}\right) c}{2 b \left(c -i\right) \left(i-c \right)}+\frac{i \dilog \left(\frac{i+\left(c -i\right) \tanh \left(b x +a \right)+c}{2 c}\right) c^{2}}{4 b \left(c -i\right) \left(i-c \right)}-\frac{\mathrm{arccot}\left(\left(c -i\right) \tanh \left(b x +a \right)+c \right) \ln \left(\left(c -i\right) \tanh \left(b x +a \right)-c +i\right)}{b \left(c -i\right) \left(2 i-2 c \right)}+\frac{\mathrm{arccot}\left(\left(c -i\right) \tanh \left(b x +a \right)+c \right) \ln \left(\left(c -i\right) \tanh \left(b x +a \right)+c -i\right)}{b \left(c -i\right) \left(2 i-2 c \right)}+\frac{\ln \left(\left(c -i\right) \tanh \left(b x +a \right)+c -i\right)^{2} c}{4 b \left(c -i\right) \left(i-c \right)}-\frac{i \ln \left(\left(c -i\right) \tanh \left(b x +a \right)+c -i\right)^{2}}{8 b \left(c -i\right) \left(i-c \right)}-\frac{\dilog \left(-\frac{i \left(i+\left(c -i\right) \tanh \left(b x +a \right)+c \right)}{2}\right) c}{2 b \left(c -i\right) \left(i-c \right)}+\frac{\dilog \left(\frac{i+\left(c -i\right) \tanh \left(b x +a \right)+c}{2 c}\right) c}{2 b \left(c -i\right) \left(i-c \right)}+\frac{i \dilog \left(\frac{\left(c -i\right) \tanh \left(b x +a \right)+c -i}{-2 i+2 c}\right)}{4 b \left(c -i\right) \left(i-c \right)}+\frac{i \dilog \left(-\frac{i \left(i+\left(c -i\right) \tanh \left(b x +a \right)+c \right)}{2}\right)}{4 b \left(c -i\right) \left(i-c \right)}-\frac{i \dilog \left(\frac{i+\left(c -i\right) \tanh \left(b x +a \right)+c}{2 c}\right)}{4 b \left(c -i\right) \left(i-c \right)}-\frac{\dilog \left(\frac{\left(c -i\right) \tanh \left(b x +a \right)+c -i}{-2 i+2 c}\right) c}{2 b \left(c -i\right) \left(i-c \right)}"," ",0,"-1/b/(c-I)*arccot((c-I)*tanh(b*x+a)+c)/(2*I-2*c)*ln((c-I)*tanh(b*x+a)-c+I)+1/b/(c-I)*arccot((c-I)*tanh(b*x+a)+c)/(2*I-2*c)*ln((c-I)*tanh(b*x+a)+c-I)-1/2/b/(c-I)/(I-c)*dilog(-1/2*I*(I+(c-I)*tanh(b*x+a)+c))*c+1/4/b/(c-I)/(I-c)*ln((c-I)*tanh(b*x+a)+c-I)^2*c+1/2/b/(c-I)/(I-c)*dilog(1/2*(I+(c-I)*tanh(b*x+a)+c)/c)*c+1/4*I/b/(c-I)/(I-c)*dilog(((c-I)*tanh(b*x+a)+c-I)/(-2*I+2*c))+1/4*I/b/(c-I)/(I-c)*dilog(-1/2*I*(I+(c-I)*tanh(b*x+a)+c))-1/8*I/b/(c-I)/(I-c)*ln((c-I)*tanh(b*x+a)+c-I)^2-1/4*I/b/(c-I)/(I-c)*dilog(1/2*(I+(c-I)*tanh(b*x+a)+c)/c)-1/2/b/(c-I)/(I-c)*dilog(((c-I)*tanh(b*x+a)+c-I)/(-2*I+2*c))*c-1/4*I/b/(c-I)/(I-c)*ln((c-I)*tanh(b*x+a)+c-I)*ln(-1/2*I*(I+(c-I)*tanh(b*x+a)+c))*c^2+1/4*I/b/(c-I)/(I-c)*ln((c-I)*tanh(b*x+a)-c+I)*ln(1/2*(I+(c-I)*tanh(b*x+a)+c)/c)*c^2-1/4*I/b/(c-I)/(I-c)*ln((c-I)*tanh(b*x+a)-c+I)*ln(((c-I)*tanh(b*x+a)+c-I)/(-2*I+2*c))*c^2+2*I/b/(c-I)*arccot((c-I)*tanh(b*x+a)+c)/(2*I-2*c)*ln((c-I)*tanh(b*x+a)+c-I)*c-2*I/b/(c-I)*arccot((c-I)*tanh(b*x+a)+c)/(2*I-2*c)*ln((c-I)*tanh(b*x+a)-c+I)*c-1/2/b/(c-I)/(I-c)*ln((c-I)*tanh(b*x+a)+c-I)*ln(-1/2*I*(I+(c-I)*tanh(b*x+a)+c))*c-1/4*I/b/(c-I)/(I-c)*dilog(((c-I)*tanh(b*x+a)+c-I)/(-2*I+2*c))*c^2+1/b/(c-I)*arccot((c-I)*tanh(b*x+a)+c)/(2*I-2*c)*ln((c-I)*tanh(b*x+a)-c+I)*c^2+1/2/b/(c-I)/(I-c)*ln((c-I)*tanh(b*x+a)-c+I)*ln(1/2*(I+(c-I)*tanh(b*x+a)+c)/c)*c-1/2/b/(c-I)/(I-c)*ln((c-I)*tanh(b*x+a)-c+I)*ln(((c-I)*tanh(b*x+a)+c-I)/(-2*I+2*c))*c-1/b/(c-I)*arccot((c-I)*tanh(b*x+a)+c)/(2*I-2*c)*ln((c-I)*tanh(b*x+a)+c-I)*c^2+1/4*I/b/(c-I)/(I-c)*ln((c-I)*tanh(b*x+a)-c+I)*ln(((c-I)*tanh(b*x+a)+c-I)/(-2*I+2*c))-1/4*I/b/(c-I)/(I-c)*dilog(-1/2*I*(I+(c-I)*tanh(b*x+a)+c))*c^2+1/8*I/b/(c-I)/(I-c)*ln((c-I)*tanh(b*x+a)+c-I)^2*c^2+1/4*I/b/(c-I)/(I-c)*dilog(1/2*(I+(c-I)*tanh(b*x+a)+c)/c)*c^2+1/4*I/b/(c-I)/(I-c)*ln((c-I)*tanh(b*x+a)+c-I)*ln(-1/2*I*(I+(c-I)*tanh(b*x+a)+c))-1/4*I/b/(c-I)/(I-c)*ln((c-I)*tanh(b*x+a)-c+I)*ln(1/2*(I+(c-I)*tanh(b*x+a)+c)/c)","B"
199,0,0,23,1.938000," ","int(arccot(c-(I-c)*tanh(b*x+a))/x,x)","\int \frac{\mathrm{arccot}\left(c -\left(i-c \right) \tanh \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arccot(c-(I-c)*tanh(b*x+a))/x,x)","F"
200,1,7275,254,51.065000," ","int((f*x+e)^3*arccot(coth(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
201,1,5425,194,41.302000," ","int((f*x+e)^2*arccot(coth(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
202,1,2688,134,5.092000," ","int((f*x+e)*arccot(coth(b*x+a)),x)","\text{Expression too large to display}"," ",0,"1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))*csgn((1-I)*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))-1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))*csgn((1+I)*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))-1/4*I*f*ln(1-I*exp(2*b*x+2*a))*x^2-1/2*I*ln(((-I)^(1/2)-exp(b*x+a))/(-I)^(1/2))*x*e-1/2*I*ln(((-I)^(1/2)+exp(b*x+a))/(-I)^(1/2))*x*e-1/4*I/b^2*f*a^2*ln(exp(2*b*x+2*a)+I)-1/2*I*e/b*a*ln(-exp(2*b*x+2*a)+I)+1/4*I*f/b^2*a^2*ln(-exp(2*b*x+2*a)+I)+1/4*I*f*ln(1+I*exp(2*b*x+2*a))*x^2+1/2*I*e*ln(1+exp(b*x+a)*(-1)^(3/4))*x+1/2*I*e*ln(1-exp(b*x+a)*(-1)^(3/4))*x-1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)-I))*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))+1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)+I))*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))-1/8*Pi*x^2*f*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))^2-1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))*csgn((1-I)*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))^2-1/8*I*f*polylog(3,-I*exp(2*b*x+2*a))/b^2+1/8*Pi*f*x^2+1/4*Pi*e*x+1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))*csgn((1+I)*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))^2+1/2*I*(1/2*f*x^2+e*x)*ln(exp(2*b*x+2*a)+I)+1/2*I/b*a*e*ln(exp(2*b*x+2*a)+I)-1/4*I*ln(exp(2*b*x+2*a)-I)*f*x^2-1/2*I*ln(exp(2*b*x+2*a)-I)*e*x+1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))*csgn((1+I)*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))^2+1/4*Pi*x*e*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))^2-1/4*Pi*x*e*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))^2-1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))*csgn((1-I)*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))^2+1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)-I))*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))^2-1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)+I))*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))^2+1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))*csgn((1-I)*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))+1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)-I))*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))^2-1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)+I))*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))^2+1/4*I*f/b*polylog(2,-I*exp(2*b*x+2*a))*x+1/4*I*f/b^2*polylog(2,-I*exp(2*b*x+2*a))*a+1/2*I*e/b*ln(1+exp(b*x+a)*(-1)^(3/4))*a+1/2*I*e/b*ln(1-exp(b*x+a)*(-1)^(3/4))*a-1/2*I*f/b^2*a^2*ln(1+exp(b*x+a)*(-1)^(3/4))+1/2*I*f/b*ln(1+I*exp(2*b*x+2*a))*x*a-1/2*I*f/b*a*ln(1+exp(b*x+a)*(-1)^(3/4))*x-1/2*I*f/b*a*ln(1-exp(b*x+a)*(-1)^(3/4))*x-1/2*I/b*f*ln(1-I*exp(2*b*x+2*a))*x*a+1/2*I/b*f*a*ln(((-I)^(1/2)-exp(b*x+a))/(-I)^(1/2))*x+1/2*I/b*f*a*ln(((-I)^(1/2)+exp(b*x+a))/(-I)^(1/2))*x-1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)-I))*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))+1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)+I))*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))+1/4*Pi*x*e*csgn((1-I)*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))^2+1/8*Pi*x^2*f*csgn((1-I)*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))^2-1/4*Pi*x*e*csgn((1+I)*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))^3+1/8*Pi*x^2*f*csgn((1+I)*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))^2+1/4*Pi*x*e*csgn((1+I)*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))^2-1/2*I/b*ln(((-I)^(1/2)-exp(b*x+a))/(-I)^(1/2))*a*e-1/2*I/b*ln(((-I)^(1/2)+exp(b*x+a))/(-I)^(1/2))*a*e-1/4*I/b*f*polylog(2,I*exp(2*b*x+2*a))*x-1/4*I/b^2*f*ln(1-I*exp(2*b*x+2*a))*a^2+1/2*I/b^2*f*a^2*ln(((-I)^(1/2)-exp(b*x+a))/(-I)^(1/2))+1/2*I/b^2*f*a^2*ln(((-I)^(1/2)+exp(b*x+a))/(-I)^(1/2))-1/2*I*f/b^2*a^2*ln(1-exp(b*x+a)*(-1)^(3/4))-1/4*I/b^2*f*polylog(2,I*exp(2*b*x+2*a))*a+1/4*I*f/b^2*ln(1+I*exp(2*b*x+2*a))*a^2-1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))^3+1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))^3-1/8*Pi*x^2*f*csgn((1-I)*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))^3-1/8*Pi*x^2*f*csgn((1+I)*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))^3-1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))^3+1/2*I*e/b*dilog(1+exp(b*x+a)*(-1)^(3/4))+1/2*I*e/b*dilog(1-exp(b*x+a)*(-1)^(3/4))-1/2*I/b*e*dilog(((-I)^(1/2)-exp(b*x+a))/(-I)^(1/2))-1/2*I/b*e*dilog(((-I)^(1/2)+exp(b*x+a))/(-I)^(1/2))+1/2*I/b^2*f*a*dilog(((-I)^(1/2)-exp(b*x+a))/(-I)^(1/2))+1/2*I/b^2*f*a*dilog(((-I)^(1/2)+exp(b*x+a))/(-I)^(1/2))-1/2*I*f/b^2*a*dilog(1+exp(b*x+a)*(-1)^(3/4))-1/2*I*f/b^2*a*dilog(1-exp(b*x+a)*(-1)^(3/4))-1/8*Pi*x^2*f*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))*csgn((1+I)*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))+1/8*Pi*x^2*f*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)-1))^2+1/8*I*f*polylog(3,I*exp(2*b*x+2*a))/b^2+1/4*Pi*x*e*csgn(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))^3-1/4*Pi*x*e*csgn((1-I)*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)-1))^3","C"
203,1,198,63,0.589000," ","int(arccot(coth(b*x+a)),x)","\frac{\arctanh \left(\coth \left(b x +a \right)\right) \mathrm{arccot}\left(\coth \left(b x +a \right)\right)}{b}+\frac{\arctan \left(\coth \left(b x +a \right)\right) \arctanh \left(\coth \left(b x +a \right)\right)}{b}+\frac{\arctan \left(\coth \left(b x +a \right)\right) \ln \left(1+\frac{i \left(1+i \coth \left(b x +a \right)\right)^{2}}{\coth^{2}\left(b x +a \right)+1}\right)}{2 b}-\frac{\arctan \left(\coth \left(b x +a \right)\right) \ln \left(1-\frac{i \left(1+i \coth \left(b x +a \right)\right)^{2}}{\coth^{2}\left(b x +a \right)+1}\right)}{2 b}-\frac{i \dilog \left(1+\frac{i \left(1+i \coth \left(b x +a \right)\right)^{2}}{\coth^{2}\left(b x +a \right)+1}\right)}{4 b}+\frac{i \dilog \left(1-\frac{i \left(1+i \coth \left(b x +a \right)\right)^{2}}{\coth^{2}\left(b x +a \right)+1}\right)}{4 b}"," ",0,"1/b*arctanh(coth(b*x+a))*arccot(coth(b*x+a))+1/b*arctan(coth(b*x+a))*arctanh(coth(b*x+a))+1/2/b*arctan(coth(b*x+a))*ln(1+I*(1+I*coth(b*x+a))^2/(coth(b*x+a)^2+1))-1/2/b*arctan(coth(b*x+a))*ln(1-I*(1+I*coth(b*x+a))^2/(coth(b*x+a)^2+1))-1/4*I/b*dilog(1+I*(1+I*coth(b*x+a))^2/(coth(b*x+a)^2+1))+1/4*I/b*dilog(1-I*(1+I*coth(b*x+a))^2/(coth(b*x+a)^2+1))","B"
204,0,0,17,2.661000," ","int(arccot(coth(b*x+a))/(f*x+e),x)","\int \frac{\mathrm{arccot}\left(\coth \left(b x +a \right)\right)}{f x +e}\, dx"," ",0,"int(arccot(coth(b*x+a))/(f*x+e),x)","F"
205,1,6858,301,60.217000," ","int(x^2*arccot(c+d*coth(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
206,1,6508,227,6.464000," ","int(x*arccot(c+d*coth(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
207,1,350,150,0.583000," ","int(arccot(c+d*coth(b*x+a)),x)","-\frac{\mathrm{arccot}\left(c +d \coth \left(b x +a \right)\right) \ln \left(d \coth \left(b x +a \right)-d \right)}{2 b}+\frac{\mathrm{arccot}\left(c +d \coth \left(b x +a \right)\right) \ln \left(d \coth \left(b x +a \right)+d \right)}{2 b}+\frac{i \ln \left(d \coth \left(b x +a \right)-d \right) \ln \left(\frac{-d \coth \left(b x +a \right)+i-c}{i-c -d}\right)}{4 b}-\frac{i \ln \left(d \coth \left(b x +a \right)-d \right) \ln \left(\frac{i+d \coth \left(b x +a \right)+c}{i+c +d}\right)}{4 b}+\frac{i \dilog \left(\frac{-d \coth \left(b x +a \right)+i-c}{i-c -d}\right)}{4 b}-\frac{i \dilog \left(\frac{i+d \coth \left(b x +a \right)+c}{i+c +d}\right)}{4 b}-\frac{i \ln \left(d \coth \left(b x +a \right)+d \right) \ln \left(\frac{-d \coth \left(b x +a \right)+i-c}{i-c +d}\right)}{4 b}+\frac{i \ln \left(d \coth \left(b x +a \right)+d \right) \ln \left(\frac{i+d \coth \left(b x +a \right)+c}{i+c -d}\right)}{4 b}-\frac{i \dilog \left(\frac{-d \coth \left(b x +a \right)+i-c}{i-c +d}\right)}{4 b}+\frac{i \dilog \left(\frac{i+d \coth \left(b x +a \right)+c}{i+c -d}\right)}{4 b}"," ",0,"-1/2/b*arccot(c+d*coth(b*x+a))*ln(d*coth(b*x+a)-d)+1/2/b*arccot(c+d*coth(b*x+a))*ln(d*coth(b*x+a)+d)+1/4*I/b*ln(d*coth(b*x+a)-d)*ln((-d*coth(b*x+a)+I-c)/(I-c-d))-1/4*I/b*ln(d*coth(b*x+a)-d)*ln((I+d*coth(b*x+a)+c)/(I+c+d))+1/4*I/b*dilog((-d*coth(b*x+a)+I-c)/(I-c-d))-1/4*I/b*dilog((I+d*coth(b*x+a)+c)/(I+c+d))-1/4*I/b*ln(d*coth(b*x+a)+d)*ln((-d*coth(b*x+a)+I-c)/(I-c+d))+1/4*I/b*ln(d*coth(b*x+a)+d)*ln((I+d*coth(b*x+a)+c)/(I+c-d))-1/4*I/b*dilog((-d*coth(b*x+a)+I-c)/(I-c+d))+1/4*I/b*dilog((I+d*coth(b*x+a)+c)/(I+c-d))","B"
208,0,0,17,1.577000," ","int(arccot(c+d*coth(b*x+a))/x,x)","\int \frac{\mathrm{arccot}\left(c +d \coth \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arccot(c+d*coth(b*x+a))/x,x)","F"
209,1,1548,116,5.939000," ","int(x^2*arccot(c+(I+c)*coth(b*x+a)),x)","-\frac{i a^{3} \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{-i c}\right)}{2 b^{3}}-\frac{b \,x^{4}}{12 \left(i+c \right)}-\frac{i a^{2} \dilog \left(1-i {\mathrm e}^{b x +a} \sqrt{-i c}\right)}{2 b^{3}}+\frac{i c x \,a^{3}}{3 b^{2} \left(i+c \right)}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{3}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}-1}\right)^{3}}{12}-\frac{i \polylog \left(4, i c \,{\mathrm e}^{2 b x +2 a}\right)}{8 b^{3}}-\frac{i c \,a^{3} \ln \left({\mathrm e}^{b x +a}\right)}{3 b^{3} \left(i+c \right)}+\frac{i \ln \left(1-i c \,{\mathrm e}^{2 b x +2 a}\right) x \,a^{2}}{2 b^{2}}-\frac{a^{4}}{4 b^{3} \left(i+c \right)}+\frac{i \ln \left(1-i c \,{\mathrm e}^{2 b x +2 a}\right) a^{3}}{3 b^{3}}+\frac{i \polylog \left(2, i c \,{\mathrm e}^{2 b x +2 a}\right) a^{2}}{4 b^{3}}+\frac{i b c \,x^{4}}{12 i+12 c}-\frac{i a^{3} \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{-i c}\right)}{2 b^{3}}-\frac{i x^{2} \polylog \left(2, i c \,{\mathrm e}^{2 b x +2 a}\right)}{4 b}+\frac{i x \polylog \left(3, i c \,{\mathrm e}^{2 b x +2 a}\right)}{4 b^{2}}-\frac{i a^{2} \dilog \left(1+i {\mathrm e}^{b x +a} \sqrt{-i c}\right)}{2 b^{3}}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}-1}\right)}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\mathrm e}^{2 b x +2 a}-1}\right)}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)\right) \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{12}+\frac{a^{3} \ln \left({\mathrm e}^{b x +a}\right)}{3 b^{3} \left(i+c \right)}-\frac{x \,a^{3}}{3 b^{2} \left(i+c \right)}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{12}+\frac{i a^{3} \ln \left({\mathrm e}^{2 b x +2 a} c +i\right)}{6 b^{3}}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right)}{12}-\frac{i a^{2} \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{-i c}\right) x}{2 b^{2}}+\frac{i c \,a^{4}}{4 b^{3} \left(i+c \right)}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)\right) \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right)}{12}-\frac{i a^{2} \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{-i c}\right) x}{2 b^{2}}-\frac{i x^{3} \ln \left(1-i c \,{\mathrm e}^{2 b x +2 a}\right)}{6}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{3}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\mathrm e}^{2 b x +2 a}-1}\right)^{3}}{12}-\frac{i x^{3} \ln \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{6}+\frac{i x^{3} \ln \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{6}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{12}"," ",0,"-1/12*Pi*x^3*csgn((2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^3-1/12*Pi*x^3*csgn((2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))^3+1/4*I*x*polylog(3,I*c*exp(2*b*x+2*a))/b^2-1/6*I*x^3*ln(1-I*c*exp(2*b*x+2*a))+1/12*Pi*x^3*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))^3+1/12*I*b*c/(I+c)*x^4-1/4*I*x^2*polylog(2,I*c*exp(2*b*x+2*a))/b-1/2*I/b^2*a^2*ln(1-I*exp(b*x+a)*(-I*c)^(1/2))*x-1/2*I/b^2*a^2*ln(1+I*exp(b*x+a)*(-I*c)^(1/2))*x-1/6*I*x^3*ln(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)-1/4/b^3/(I+c)*a^4-1/12*b/(I+c)*x^4+1/6*I*x^3*ln(2*exp(2*b*x+2*a)*c+2*I)+1/12*Pi*x^3*csgn((2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^2-1/12*Pi*x^3*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))*csgn((2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))^2-1/12*Pi*x^3*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))*csgn((2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))+1/12*Pi*x^3*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))*csgn((2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))+1/6*I/b^3*a^3*ln(exp(2*b*x+2*a)*c+I)+1/4*I/b^3*c/(I+c)*a^4+1/2*I/b^2*ln(1-I*c*exp(2*b*x+2*a))*x*a^2-1/12*Pi*x^3*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c))*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))+1/3/b^3*a^3/(I+c)*ln(exp(b*x+a))-1/3/b^2/(I+c)*x*a^3-1/12*Pi*x^3*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^3+1/12*Pi*x^3*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))*csgn((2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^2+1/12*Pi*x^3*csgn((2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))^2-1/3*I/b^3*c*a^3/(I+c)*ln(exp(b*x+a))+1/3*I/b^2*c/(I+c)*x*a^3-1/8*I*polylog(4,I*c*exp(2*b*x+2*a))/b^3+1/12*Pi*x^3*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(2*exp(2*b*x+2*a)*c+2*I))*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))-1/12*Pi*x^3*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))^2+1/12*Pi*x^3*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^2-1/12*Pi*x^3*csgn(I*(2*exp(2*b*x+2*a)*c+2*I))*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))^2+1/12*Pi*x^3*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c))*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^2+1/3*I/b^3*ln(1-I*c*exp(2*b*x+2*a))*a^3+1/4*I/b^3*polylog(2,I*c*exp(2*b*x+2*a))*a^2-1/2*I/b^3*a^3*ln(1-I*exp(b*x+a)*(-I*c)^(1/2))-1/2*I/b^3*a^3*ln(1+I*exp(b*x+a)*(-I*c)^(1/2))-1/2*I/b^3*a^2*dilog(1-I*exp(b*x+a)*(-I*c)^(1/2))-1/2*I/b^3*a^2*dilog(1+I*exp(b*x+a)*(-I*c)^(1/2))","C"
210,1,1512,92,5.653000," ","int(x*arccot(c+(I+c)*coth(b*x+a)),x)","\frac{i b c \,x^{3}}{6 i+6 c}-\frac{a^{2} \ln \left({\mathrm e}^{b x +a}\right)}{2 b^{2} \left(i+c \right)}-\frac{i \ln \left(1-i c \,{\mathrm e}^{2 b x +2 a}\right) a^{2}}{4 b^{2}}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{8}+\frac{i a \dilog \left(1-i {\mathrm e}^{b x +a} \sqrt{-i c}\right)}{2 b^{2}}+\frac{i a \dilog \left(1+i {\mathrm e}^{b x +a} \sqrt{-i c}\right)}{2 b^{2}}-\frac{i x \polylog \left(2, i c \,{\mathrm e}^{2 b x +2 a}\right)}{4 b}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)\right) \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{8}+\frac{x \,a^{2}}{2 b \left(i+c \right)}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}-1}\right)}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\mathrm e}^{2 b x +2 a}-1}\right)}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right)}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)\right) \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right)}{8}-\frac{i c \,a^{3}}{3 b^{2} \left(i+c \right)}+\frac{i \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{-i c}\right) x a}{2 b}-\frac{i \ln \left(1-i c \,{\mathrm e}^{2 b x +2 a}\right) x a}{2 b}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{8}+\frac{i x^{2} \ln \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{4}-\frac{i x^{2} \ln \left(1-i c \,{\mathrm e}^{2 b x +2 a}\right)}{4}-\frac{i x^{2} \ln \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{4}+\frac{i \polylog \left(3, i c \,{\mathrm e}^{2 b x +2 a}\right)}{8 b^{2}}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\mathrm e}^{2 b x +2 a}-1}\right)^{3}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{3}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}-1}\right)^{3}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{3}}{8}+\frac{a^{3}}{3 b^{2} \left(i+c \right)}-\frac{b \,x^{3}}{6 \left(i+c \right)}-\frac{i c x \,a^{2}}{2 b \left(i+c \right)}+\frac{i c \,a^{2} \ln \left({\mathrm e}^{b x +a}\right)}{2 b^{2} \left(i+c \right)}+\frac{i \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{-i c}\right) a^{2}}{2 b^{2}}+\frac{i a^{2} \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{-i c}\right)}{2 b^{2}}-\frac{i a^{2} \ln \left({\mathrm e}^{2 b x +2 a} c +i\right)}{4 b^{2}}-\frac{i \polylog \left(2, i c \,{\mathrm e}^{2 b x +2 a}\right) a}{4 b^{2}}+\frac{i a \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{-i c}\right) x}{2 b}"," ",0,"1/8*Pi*x^2*csgn((2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^2+1/4*I*x^2*ln(2*exp(2*b*x+2*a)*c+2*I)+1/8*I*polylog(3,I*c*exp(2*b*x+2*a))/b^2-1/4*I*x^2*ln(1-I*c*exp(2*b*x+2*a))-1/2/b^2*a^2/(I+c)*ln(exp(b*x+a))+1/2*I/b^2*ln(1-I*exp(b*x+a)*(-I*c)^(1/2))*a^2+1/2*I/b^2*ln(1+I*exp(b*x+a)*(-I*c)^(1/2))*a^2-1/4*I/b^2*ln(1-I*c*exp(2*b*x+2*a))*a^2-1/4*I/b^2*polylog(2,I*c*exp(2*b*x+2*a))*a+1/2*I/b^2*a*dilog(1-I*exp(b*x+a)*(-I*c)^(1/2))+1/2*I/b^2*a*dilog(1+I*exp(b*x+a)*(-I*c)^(1/2))+1/8*Pi*x^2*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^2-1/4*I*x*polylog(2,I*c*exp(2*b*x+2*a))/b-1/4*I/b^2*a^2*ln(exp(2*b*x+2*a)*c+I)-1/4*I*x^2*ln(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)+1/3/b^2/(I+c)*a^3-1/6*b*x^3/(I+c)+1/8*Pi*x^2*csgn((2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))^2-1/8*Pi*x^2*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))*csgn((2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))^2+1/8*Pi*x^2*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(2*exp(2*b*x+2*a)*c+2*I))*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))-1/8*Pi*x^2*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c))*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))-1/8*Pi*x^2*csgn((2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))^3-1/2*I/b*c/(I+c)*x*a^2+1/2*I/b^2*c*a^2/(I+c)*ln(exp(b*x+a))-1/8*Pi*x^2*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^3-1/8*Pi*x^2*csgn((2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^3+1/8*Pi*x^2*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))^3-1/8*Pi*x^2*csgn(I*(2*exp(2*b*x+2*a)*c+2*I))*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))^2+1/8*Pi*x^2*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c))*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^2+1/8*Pi*x^2*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))*csgn((2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^2-1/8*Pi*x^2*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))^2-1/3*I/b^2*c/(I+c)*a^3+1/6*I*b*c/(I+c)*x^3+1/2/b/(I+c)*x*a^2+1/2*I/b*ln(1-I*exp(b*x+a)*(-I*c)^(1/2))*x*a+1/2*I/b*ln(1+I*exp(b*x+a)*(-I*c)^(1/2))*x*a-1/2*I/b*ln(1-I*c*exp(2*b*x+2*a))*x*a-1/8*Pi*x^2*csgn(I*(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))*csgn((2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))+1/8*Pi*x^2*csgn(I*(2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))*csgn((2*exp(2*b*x+2*a)*c+2*I)/(exp(2*b*x+2*a)-1))","C"
211,1,1381,65,0.753000," ","int(arccot(c+(I+c)*coth(b*x+a)),x)","\frac{i \ln \left(c -\left(i+c \right) \coth \left(b x +a \right)+i\right) \ln \left(\frac{-c -\left(i+c \right) \coth \left(b x +a \right)-i}{-2 i-2 c}\right)}{4 \left(i+c \right)^{2} b}+\frac{i \ln \left(i+c +\left(i+c \right) \coth \left(b x +a \right)\right)^{2} c^{2}}{8 \left(i+c \right)^{2} b}+\frac{\ln \left(i+c +\left(i+c \right) \coth \left(b x +a \right)\right) \ln \left(-\frac{i \left(-c -\left(i+c \right) \coth \left(b x +a \right)+i\right)}{2}\right) c}{2 \left(i+c \right)^{2} b}-\frac{i \ln \left(i+c +\left(i+c \right) \coth \left(b x +a \right)\right)^{2}}{8 \left(i+c \right)^{2} b}-\frac{\ln \left(i+c +\left(i+c \right) \coth \left(b x +a \right)\right)^{2} c}{4 \left(i+c \right)^{2} b}-\frac{\dilog \left(-\frac{i \left(i+c +\left(i+c \right) \coth \left(b x +a \right)\right)}{2}\right) c}{2 \left(i+c \right)^{2} b}+\frac{i \dilog \left(-\frac{-c -\left(i+c \right) \coth \left(b x +a \right)+i}{2 c}\right) c^{2}}{4 \left(i+c \right)^{2} b}+\frac{i \dilog \left(-\frac{i \left(i+c +\left(i+c \right) \coth \left(b x +a \right)\right)}{2}\right) c^{2}}{4 \left(i+c \right)^{2} b}-\frac{i \dilog \left(\frac{-c -\left(i+c \right) \coth \left(b x +a \right)-i}{-2 i-2 c}\right) c^{2}}{4 \left(i+c \right)^{2} b}-\frac{\ln \left(-\frac{i \left(i+c +\left(i+c \right) \coth \left(b x +a \right)\right)}{2}\right) \ln \left(-\frac{i \left(-c -\left(i+c \right) \coth \left(b x +a \right)+i\right)}{2}\right) c}{2 \left(i+c \right)^{2} b}-\frac{\ln \left(c -\left(i+c \right) \coth \left(b x +a \right)+i\right) \ln \left(-\frac{-c -\left(i+c \right) \coth \left(b x +a \right)+i}{2 c}\right) c}{2 \left(i+c \right)^{2} b}+\frac{\ln \left(c -\left(i+c \right) \coth \left(b x +a \right)+i\right) \ln \left(\frac{-c -\left(i+c \right) \coth \left(b x +a \right)-i}{-2 i-2 c}\right) c}{2 \left(i+c \right)^{2} b}+\frac{\mathrm{arccot}\left(c +\left(i+c \right) \coth \left(b x +a \right)\right) \ln \left(c -\left(i+c \right) \coth \left(b x +a \right)+i\right)}{\left(i+c \right) b \left(2 i+2 c \right)}-\frac{\mathrm{arccot}\left(c +\left(i+c \right) \coth \left(b x +a \right)\right) \ln \left(i+c +\left(i+c \right) \coth \left(b x +a \right)\right)}{\left(i+c \right) b \left(2 i+2 c \right)}+\frac{i \ln \left(i+c +\left(i+c \right) \coth \left(b x +a \right)\right) \ln \left(-\frac{i \left(-c -\left(i+c \right) \coth \left(b x +a \right)+i\right)}{2}\right)}{4 \left(i+c \right)^{2} b}-\frac{i \ln \left(-\frac{i \left(i+c +\left(i+c \right) \coth \left(b x +a \right)\right)}{2}\right) \ln \left(-\frac{i \left(-c -\left(i+c \right) \coth \left(b x +a \right)+i\right)}{2}\right)}{4 \left(i+c \right)^{2} b}-\frac{i \ln \left(c -\left(i+c \right) \coth \left(b x +a \right)+i\right) \ln \left(-\frac{-c -\left(i+c \right) \coth \left(b x +a \right)+i}{2 c}\right)}{4 \left(i+c \right)^{2} b}+\frac{i \ln \left(c -\left(i+c \right) \coth \left(b x +a \right)+i\right) \ln \left(-\frac{-c -\left(i+c \right) \coth \left(b x +a \right)+i}{2 c}\right) c^{2}}{4 \left(i+c \right)^{2} b}-\frac{i \ln \left(c -\left(i+c \right) \coth \left(b x +a \right)+i\right) \ln \left(\frac{-c -\left(i+c \right) \coth \left(b x +a \right)-i}{-2 i-2 c}\right) c^{2}}{4 \left(i+c \right)^{2} b}+\frac{\mathrm{arccot}\left(c +\left(i+c \right) \coth \left(b x +a \right)\right) \ln \left(i+c +\left(i+c \right) \coth \left(b x +a \right)\right) c^{2}}{\left(i+c \right) b \left(2 i+2 c \right)}-\frac{\mathrm{arccot}\left(c +\left(i+c \right) \coth \left(b x +a \right)\right) \ln \left(c -\left(i+c \right) \coth \left(b x +a \right)+i\right) c^{2}}{\left(i+c \right) b \left(2 i+2 c \right)}-\frac{i \ln \left(i+c +\left(i+c \right) \coth \left(b x +a \right)\right) \ln \left(-\frac{i \left(-c -\left(i+c \right) \coth \left(b x +a \right)+i\right)}{2}\right) c^{2}}{4 \left(i+c \right)^{2} b}+\frac{i \ln \left(-\frac{i \left(i+c +\left(i+c \right) \coth \left(b x +a \right)\right)}{2}\right) \ln \left(-\frac{i \left(-c -\left(i+c \right) \coth \left(b x +a \right)+i\right)}{2}\right) c^{2}}{4 \left(i+c \right)^{2} b}-\frac{\dilog \left(-\frac{-c -\left(i+c \right) \coth \left(b x +a \right)+i}{2 c}\right) c}{2 \left(i+c \right)^{2} b}+\frac{\dilog \left(\frac{-c -\left(i+c \right) \coth \left(b x +a \right)-i}{-2 i-2 c}\right) c}{2 \left(i+c \right)^{2} b}-\frac{i \dilog \left(-\frac{i \left(i+c +\left(i+c \right) \coth \left(b x +a \right)\right)}{2}\right)}{4 \left(i+c \right)^{2} b}-\frac{i \dilog \left(-\frac{-c -\left(i+c \right) \coth \left(b x +a \right)+i}{2 c}\right)}{4 \left(i+c \right)^{2} b}+\frac{i \dilog \left(\frac{-c -\left(i+c \right) \coth \left(b x +a \right)-i}{-2 i-2 c}\right)}{4 \left(i+c \right)^{2} b}+\frac{2 i \mathrm{arccot}\left(c +\left(i+c \right) \coth \left(b x +a \right)\right) \ln \left(i+c +\left(i+c \right) \coth \left(b x +a \right)\right) c}{\left(i+c \right) b \left(2 i+2 c \right)}-\frac{2 i \mathrm{arccot}\left(c +\left(i+c \right) \coth \left(b x +a \right)\right) \ln \left(c -\left(i+c \right) \coth \left(b x +a \right)+i\right) c}{\left(i+c \right) b \left(2 i+2 c \right)}"," ",0,"-1/8*I/(I+c)^2/b*ln(I+c+(I+c)*coth(b*x+a))^2-1/4/(I+c)^2/b*ln(I+c+(I+c)*coth(b*x+a))^2*c-1/2/(I+c)^2/b*dilog(-1/2*I*(I+c+(I+c)*coth(b*x+a)))*c-1/2/(I+c)^2/b*dilog(-1/2*(-c-(I+c)*coth(b*x+a)+I)/c)*c+1/2/(I+c)^2/b*dilog((-c-(I+c)*coth(b*x+a)-I)/(-2*I-2*c))*c-1/4*I/(I+c)^2/b*dilog(-1/2*I*(I+c+(I+c)*coth(b*x+a)))-1/4*I/(I+c)^2/b*dilog(-1/2*(-c-(I+c)*coth(b*x+a)+I)/c)+1/4*I/(I+c)^2/b*dilog(-1/2*(-c-(I+c)*coth(b*x+a)+I)/c)*c^2-1/2/(I+c)^2/b*ln(-1/2*I*(I+c+(I+c)*coth(b*x+a)))*ln(-1/2*I*(-c-(I+c)*coth(b*x+a)+I))*c-1/2/(I+c)^2/b*ln(c-(I+c)*coth(b*x+a)+I)*ln(-1/2*(-c-(I+c)*coth(b*x+a)+I)/c)*c+1/2/(I+c)^2/b*ln(c-(I+c)*coth(b*x+a)+I)*ln((-c-(I+c)*coth(b*x+a)-I)/(-2*I-2*c))*c+1/(I+c)/b*arccot(c+(I+c)*coth(b*x+a))/(2*I+2*c)*ln(c-(I+c)*coth(b*x+a)+I)-1/(I+c)/b*arccot(c+(I+c)*coth(b*x+a))/(2*I+2*c)*ln(I+c+(I+c)*coth(b*x+a))+1/4*I/(I+c)^2/b*dilog(-1/2*I*(I+c+(I+c)*coth(b*x+a)))*c^2-1/4*I/(I+c)^2/b*dilog((-c-(I+c)*coth(b*x+a)-I)/(-2*I-2*c))*c^2+1/4*I/(I+c)^2/b*ln(I+c+(I+c)*coth(b*x+a))*ln(-1/2*I*(-c-(I+c)*coth(b*x+a)+I))-1/4*I/(I+c)^2/b*ln(-1/2*I*(I+c+(I+c)*coth(b*x+a)))*ln(-1/2*I*(-c-(I+c)*coth(b*x+a)+I))-1/4*I/(I+c)^2/b*ln(c-(I+c)*coth(b*x+a)+I)*ln(-1/2*(-c-(I+c)*coth(b*x+a)+I)/c)+1/4*I/(I+c)^2/b*ln(c-(I+c)*coth(b*x+a)+I)*ln((-c-(I+c)*coth(b*x+a)-I)/(-2*I-2*c))+1/8*I/(I+c)^2/b*ln(I+c+(I+c)*coth(b*x+a))^2*c^2+1/2/(I+c)^2/b*ln(I+c+(I+c)*coth(b*x+a))*ln(-1/2*I*(-c-(I+c)*coth(b*x+a)+I))*c+1/4*I/(I+c)^2/b*dilog((-c-(I+c)*coth(b*x+a)-I)/(-2*I-2*c))+1/(I+c)/b*arccot(c+(I+c)*coth(b*x+a))/(2*I+2*c)*ln(I+c+(I+c)*coth(b*x+a))*c^2-1/(I+c)/b*arccot(c+(I+c)*coth(b*x+a))/(2*I+2*c)*ln(c-(I+c)*coth(b*x+a)+I)*c^2-1/4*I/(I+c)^2/b*ln(I+c+(I+c)*coth(b*x+a))*ln(-1/2*I*(-c-(I+c)*coth(b*x+a)+I))*c^2+1/4*I/(I+c)^2/b*ln(-1/2*I*(I+c+(I+c)*coth(b*x+a)))*ln(-1/2*I*(-c-(I+c)*coth(b*x+a)+I))*c^2+1/4*I/(I+c)^2/b*ln(c-(I+c)*coth(b*x+a)+I)*ln(-1/2*(-c-(I+c)*coth(b*x+a)+I)/c)*c^2-1/4*I/(I+c)^2/b*ln(c-(I+c)*coth(b*x+a)+I)*ln((-c-(I+c)*coth(b*x+a)-I)/(-2*I-2*c))*c^2+2*I/(I+c)/b*arccot(c+(I+c)*coth(b*x+a))/(2*I+2*c)*ln(I+c+(I+c)*coth(b*x+a))*c-2*I/(I+c)/b*arccot(c+(I+c)*coth(b*x+a))/(2*I+2*c)*ln(c-(I+c)*coth(b*x+a)+I)*c","B"
212,0,0,20,2.151000," ","int(arccot(c+(I+c)*coth(b*x+a))/x,x)","\int \frac{\mathrm{arccot}\left(c +\left(i+c \right) \coth \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arccot(c+(I+c)*coth(b*x+a))/x,x)","F"
213,1,1571,119,6.096000," ","int(x^2*arccot(c-(I-c)*coth(b*x+a)),x)","\frac{i \polylog \left(4, -i c \,{\mathrm e}^{2 b x +2 a}\right)}{8 b^{3}}+\frac{i x^{3} \ln \left(2 i {\mathrm e}^{2 b x +2 a}-2 \,{\mathrm e}^{2 b x +2 a} c \right)}{6}+\frac{i \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{i c}\right) a^{3}}{2 b^{3}}+\frac{i a^{2} \dilog \left(1+i {\mathrm e}^{b x +a} \sqrt{i c}\right)}{2 b^{3}}+\frac{\pi  \,x^{3}}{3}+\frac{i x^{2} \polylog \left(2, -i c \,{\mathrm e}^{2 b x +2 a}\right)}{4 b}-\frac{i x \polylog \left(3, -i c \,{\mathrm e}^{2 b x +2 a}\right)}{4 b^{2}}+\frac{i a^{2} \dilog \left(1-i {\mathrm e}^{b x +a} \sqrt{i c}\right)}{2 b^{3}}-\frac{i \polylog \left(2, -i c \,{\mathrm e}^{2 b x +2 a}\right) a^{2}}{4 b^{3}}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}-1}\right)}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{12}+\frac{b \,x^{4}}{12 i-12 c}+\frac{i c x \,a^{3}}{3 b^{2} \left(i-c \right)}+\frac{i b c \,x^{4}}{12 i-12 c}-\frac{i c \,a^{3} \ln \left({\mathrm e}^{b x +a}\right)}{3 b^{3} \left(i-c \right)}-\frac{i \ln \left(1+i c \,{\mathrm e}^{2 b x +2 a}\right) x \,a^{2}}{2 b^{2}}+\frac{i a^{2} \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{i c}\right) x}{2 b^{2}}+\frac{i a^{2} \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{i c}\right) x}{2 b^{2}}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right)}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)\right) \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right)}{12}+\frac{i c \,a^{4}}{4 b^{3} \left(i-c \right)}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{12}+\frac{i a^{3} \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{i c}\right)}{2 b^{3}}-\frac{a^{3} \ln \left({\mathrm e}^{b x +a}\right)}{3 b^{3} \left(i-c \right)}+\frac{x \,a^{3}}{3 b^{2} \left(i-c \right)}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)\right) \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{12}-\frac{i \ln \left(1+i c \,{\mathrm e}^{2 b x +2 a}\right) a^{3}}{3 b^{3}}-\frac{i a^{3} \ln \left(-{\mathrm e}^{2 b x +2 a} c +i\right)}{6 b^{3}}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}-1}\right)}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{3}}{12}+\frac{i x^{3} \ln \left(1+i c \,{\mathrm e}^{2 b x +2 a}\right)}{6}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{3}}{12}+\frac{a^{4}}{4 b^{3} \left(i-c \right)}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}-1}\right)^{3}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}-1}\right)^{3}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(\frac{-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{12}-\frac{i x^{3} \ln \left(-2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{6}"," ",0,"1/12*Pi*x^3*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))^3+1/8*I*polylog(4,-I*c*exp(2*b*x+2*a))/b^3+1/4*I*x^2*polylog(2,-I*c*exp(2*b*x+2*a))/b+1/6*I*x^3*ln(1+I*c*exp(2*b*x+2*a))-1/4*I*x*polylog(3,-I*c*exp(2*b*x+2*a))/b^2+1/3*I/b^2*c/(I-c)*x*a^3-1/3*I/b^3*c*a^3/(I-c)*ln(exp(b*x+a))-1/12*Pi*x^3*csgn(I*(2*exp(2*b*x+2*a)*c-2*I))*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))^2-1/2*I/b^2*ln(1+I*c*exp(2*b*x+2*a))*x*a^2+1/2*I/b^2*a^2*ln(1+I*exp(b*x+a)*(I*c)^(1/2))*x+1/2*I/b^2*a^2*ln(1-I*exp(b*x+a)*(I*c)^(1/2))*x+1/2*I/b^3*a^3*ln(1+I*exp(b*x+a)*(I*c)^(1/2))+1/2*I/b^3*a^3*ln(1-I*exp(b*x+a)*(I*c)^(1/2))+1/2*I/b^3*a^2*dilog(1+I*exp(b*x+a)*(I*c)^(1/2))+1/2*I/b^3*a^2*dilog(1-I*exp(b*x+a)*(I*c)^(1/2))-1/3/b^3*a^3/(I-c)*ln(exp(b*x+a))+1/3/b^2/(I-c)*x*a^3+1/3*Pi*x^3-1/12*Pi*x^3*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^3+1/12*Pi*x^3*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c))*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^2-1/12*Pi*x^3*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))^2+1/12*Pi*x^3*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))*csgn((-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^2-1/12*Pi*x^3*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(2*exp(2*b*x+2*a)*c-2*I))*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))+1/12*Pi*x^3*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c))*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))+1/4/b^3/(I-c)*a^4+1/12*b/(I-c)*x^4-1/3*I/b^3*ln(1+I*c*exp(2*b*x+2*a))*a^3-1/4*I/b^3*polylog(2,-I*c*exp(2*b*x+2*a))*a^2+1/6*I*x^3*ln(2*I*exp(2*b*x+2*a)-2*exp(2*b*x+2*a)*c)-1/12*Pi*x^3*csgn((-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^3-1/12*Pi*x^3*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))^3-1/12*Pi*x^3*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))^2+1/4*I/b^3*c/(I-c)*a^4+1/12*I*b*c/(I-c)*x^4-1/12*Pi*x^3*csgn((-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^2-1/6*I/b^3*a^3*ln(-exp(2*b*x+2*a)*c+I)+1/12*Pi*x^3*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))*csgn((-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))-1/6*I*x^3*ln(-2*exp(2*b*x+2*a)*c+2*I)-1/12*Pi*x^3*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))+1/12*Pi*x^3*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))^2-1/12*Pi*x^3*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^2","C"
214,1,1535,95,5.786000," ","int(x*arccot(c-(I-c)*coth(b*x+a)),x)","-\frac{i \polylog \left(3, -i c \,{\mathrm e}^{2 b x +2 a}\right)}{8 b^{2}}+\frac{i x^{2} \ln \left(1+i c \,{\mathrm e}^{2 b x +2 a}\right)}{4}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{3}}{8}+\frac{i x^{2} \ln \left(2 i {\mathrm e}^{2 b x +2 a}-2 \,{\mathrm e}^{2 b x +2 a} c \right)}{4}-\frac{i x^{2} \ln \left(-2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{4}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}-1}\right)^{3}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}-1}\right)^{3}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{3}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{8}+\frac{b \,x^{3}}{6 i-6 c}+\frac{\pi  \,x^{2}}{2}-\frac{a^{3}}{3 b^{2} \left(i-c \right)}+\frac{i a^{2} \ln \left(-{\mathrm e}^{2 b x +2 a} c +i\right)}{4 b^{2}}+\frac{i \ln \left(1+i c \,{\mathrm e}^{2 b x +2 a}\right) a^{2}}{4 b^{2}}-\frac{i a^{2} \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{i c}\right)}{2 b^{2}}-\frac{i a^{2} \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{i c}\right)}{2 b^{2}}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)\right) \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c}{{\mathrm e}^{2 b x +2 a}-1}\right)}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{2 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}-1}\right)}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right)^{2}}{8}+\frac{i x \polylog \left(2, -i c \,{\mathrm e}^{2 b x +2 a}\right)}{4 b}+\frac{i \polylog \left(2, -i c \,{\mathrm e}^{2 b x +2 a}\right) a}{4 b^{2}}-\frac{i a \dilog \left(1+i {\mathrm e}^{b x +a} \sqrt{i c}\right)}{2 b^{2}}-\frac{i a \dilog \left(1-i {\mathrm e}^{b x +a} \sqrt{i c}\right)}{2 b^{2}}+\frac{i c \,a^{2} \ln \left({\mathrm e}^{b x +a}\right)}{2 b^{2} \left(i-c \right)}-\frac{i c x \,a^{2}}{2 b \left(i-c \right)}+\frac{i b c \,x^{3}}{6 i-6 c}-\frac{i c \,a^{3}}{3 b^{2} \left(i-c \right)}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)\right) \mathrm{csgn}\left(\frac{i \left(2 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{{\mathrm e}^{2 b x +2 a}-1}\right)}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 b x +2 a}-1}\right) \mathrm{csgn}\left(i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)\right) \mathrm{csgn}\left(\frac{i \left(-2 i {\mathrm e}^{2 b x +2 a}+2 \,{\mathrm e}^{2 b x +2 a} c \right)}{{\mathrm e}^{2 b x +2 a}-1}\right)}{8}+\frac{i \ln \left(1+i c \,{\mathrm e}^{2 b x +2 a}\right) x a}{2 b}-\frac{i a \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{i c}\right) x}{2 b}-\frac{i a \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{i c}\right) x}{2 b}-\frac{x \,a^{2}}{2 b \left(i-c \right)}+\frac{a^{2} \ln \left({\mathrm e}^{b x +a}\right)}{2 b^{2} \left(i-c \right)}"," ",0,"1/4*I*x*polylog(2,-I*c*exp(2*b*x+2*a))/b+1/4*I*x^2*ln(1+I*c*exp(2*b*x+2*a))+1/2/b^2*a^2/(I-c)*ln(exp(b*x+a))-1/2/b/(I-c)*x*a^2-1/8*Pi*x^2*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(2*exp(2*b*x+2*a)*c-2*I))*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))+1/8*Pi*x^2*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c))*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))+1/2*I/b*ln(1+I*c*exp(2*b*x+2*a))*x*a-1/2*I/b*a*ln(1+I*exp(b*x+a)*(I*c)^(1/2))*x-1/2*I/b*a*ln(1-I*exp(b*x+a)*(I*c)^(1/2))*x+1/4*I/b^2*a^2*ln(-exp(2*b*x+2*a)*c+I)+1/2*I/b^2*c*a^2/(I-c)*ln(exp(b*x+a))+1/2*Pi*x^2-1/8*Pi*x^2*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))^2+1/8*Pi*x^2*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))^3+1/4*I/b^2*ln(1+I*c*exp(2*b*x+2*a))*a^2+1/4*I/b^2*polylog(2,-I*c*exp(2*b*x+2*a))*a-1/2*I/b^2*a^2*ln(1+I*exp(b*x+a)*(I*c)^(1/2))-1/2*I/b^2*a^2*ln(1-I*exp(b*x+a)*(I*c)^(1/2))-1/2*I/b^2*a*dilog(1+I*exp(b*x+a)*(I*c)^(1/2))-1/2*I/b^2*a*dilog(1-I*exp(b*x+a)*(I*c)^(1/2))-1/8*Pi*x^2*csgn(I*(2*exp(2*b*x+2*a)*c-2*I))*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))^2+1/8*Pi*x^2*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c))*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^2-1/8*Pi*x^2*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))^2+1/8*Pi*x^2*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))*csgn((-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^2+1/4*I*x^2*ln(2*I*exp(2*b*x+2*a)-2*exp(2*b*x+2*a)*c)+1/8*Pi*x^2*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))*csgn((-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))-1/8*Pi*x^2*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))-1/4*I*x^2*ln(-2*exp(2*b*x+2*a)*c+2*I)-1/8*Pi*x^2*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^2+1/8*Pi*x^2*csgn(I/(exp(2*b*x+2*a)-1))*csgn(I*(2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))^2-1/8*Pi*x^2*csgn((-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^3-1/8*Pi*x^2*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))^3-1/8*Pi*x^2*csgn(I*(-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^3-1/2*I/b*c/(I-c)*x*a^2-1/8*Pi*x^2*csgn((-2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)/(exp(2*b*x+2*a)-1))^2-1/8*I*polylog(3,-I*c*exp(2*b*x+2*a))/b^2-1/3*I/b^2*c/(I-c)*a^3+1/6*I*b*c/(I-c)*x^3-1/3/b^2/(I-c)*a^3+1/6*b*x^3/(I-c)","C"
215,1,1351,68,0.617000," ","int(arccot(c-(I-c)*coth(b*x+a)),x)","\frac{i \ln \left(\left(c -i\right) \coth \left(b x +a \right)-c +i\right) \ln \left(\frac{\left(c -i\right) \coth \left(b x +a \right)+c -i}{-2 i+2 c}\right)}{4 b \left(c -i\right) \left(i-c \right)}+\frac{i \ln \left(\left(c -i\right) \coth \left(b x +a \right)+c -i\right)^{2} c^{2}}{8 b \left(c -i\right) \left(i-c \right)}-\frac{i \ln \left(\left(c -i\right) \coth \left(b x +a \right)-c +i\right) \ln \left(\frac{i+\left(c -i\right) \coth \left(b x +a \right)+c}{2 c}\right)}{4 b \left(c -i\right) \left(i-c \right)}+\frac{i \ln \left(\left(c -i\right) \coth \left(b x +a \right)+c -i\right) \ln \left(-\frac{i \left(i+\left(c -i\right) \coth \left(b x +a \right)+c \right)}{2}\right)}{4 b \left(c -i\right) \left(i-c \right)}-\frac{\ln \left(\left(c -i\right) \coth \left(b x +a \right)+c -i\right) \ln \left(-\frac{i \left(i+\left(c -i\right) \coth \left(b x +a \right)+c \right)}{2}\right) c}{2 b \left(c -i\right) \left(i-c \right)}+\frac{\ln \left(\left(c -i\right) \coth \left(b x +a \right)-c +i\right) \ln \left(\frac{i+\left(c -i\right) \coth \left(b x +a \right)+c}{2 c}\right) c}{2 b \left(c -i\right) \left(i-c \right)}-\frac{\ln \left(\left(c -i\right) \coth \left(b x +a \right)-c +i\right) \ln \left(\frac{\left(c -i\right) \coth \left(b x +a \right)+c -i}{-2 i+2 c}\right) c}{2 b \left(c -i\right) \left(i-c \right)}+\frac{\mathrm{arccot}\left(\left(c -i\right) \coth \left(b x +a \right)+c \right) \ln \left(\left(c -i\right) \coth \left(b x +a \right)-c +i\right) c^{2}}{b \left(c -i\right) \left(2 i-2 c \right)}-\frac{\mathrm{arccot}\left(\left(c -i\right) \coth \left(b x +a \right)+c \right) \ln \left(\left(c -i\right) \coth \left(b x +a \right)+c -i\right) c^{2}}{b \left(c -i\right) \left(2 i-2 c \right)}-\frac{\mathrm{arccot}\left(\left(c -i\right) \coth \left(b x +a \right)+c \right) \ln \left(\left(c -i\right) \coth \left(b x +a \right)-c +i\right)}{b \left(c -i\right) \left(2 i-2 c \right)}+\frac{\dilog \left(\frac{i+\left(c -i\right) \coth \left(b x +a \right)+c}{2 c}\right) c}{2 b \left(c -i\right) \left(i-c \right)}-\frac{\dilog \left(\frac{\left(c -i\right) \coth \left(b x +a \right)+c -i}{-2 i+2 c}\right) c}{2 b \left(c -i\right) \left(i-c \right)}-\frac{i \dilog \left(\frac{i+\left(c -i\right) \coth \left(b x +a \right)+c}{2 c}\right)}{4 b \left(c -i\right) \left(i-c \right)}+\frac{i \dilog \left(\frac{\left(c -i\right) \coth \left(b x +a \right)+c -i}{-2 i+2 c}\right)}{4 b \left(c -i\right) \left(i-c \right)}+\frac{2 i \mathrm{arccot}\left(\left(c -i\right) \coth \left(b x +a \right)+c \right) \ln \left(\left(c -i\right) \coth \left(b x +a \right)+c -i\right) c}{b \left(c -i\right) \left(2 i-2 c \right)}-\frac{i \ln \left(\left(c -i\right) \coth \left(b x +a \right)+c -i\right) \ln \left(-\frac{i \left(i+\left(c -i\right) \coth \left(b x +a \right)+c \right)}{2}\right) c^{2}}{4 b \left(c -i\right) \left(i-c \right)}+\frac{i \ln \left(\left(c -i\right) \coth \left(b x +a \right)-c +i\right) \ln \left(\frac{i+\left(c -i\right) \coth \left(b x +a \right)+c}{2 c}\right) c^{2}}{4 b \left(c -i\right) \left(i-c \right)}-\frac{i \ln \left(\left(c -i\right) \coth \left(b x +a \right)-c +i\right) \ln \left(\frac{\left(c -i\right) \coth \left(b x +a \right)+c -i}{-2 i+2 c}\right) c^{2}}{4 b \left(c -i\right) \left(i-c \right)}-\frac{2 i \mathrm{arccot}\left(\left(c -i\right) \coth \left(b x +a \right)+c \right) \ln \left(\left(c -i\right) \coth \left(b x +a \right)-c +i\right) c}{b \left(c -i\right) \left(2 i-2 c \right)}+\frac{i \dilog \left(\frac{i+\left(c -i\right) \coth \left(b x +a \right)+c}{2 c}\right) c^{2}}{4 b \left(c -i\right) \left(i-c \right)}-\frac{i \dilog \left(\frac{\left(c -i\right) \coth \left(b x +a \right)+c -i}{-2 i+2 c}\right) c^{2}}{4 b \left(c -i\right) \left(i-c \right)}-\frac{i \dilog \left(-\frac{i \left(i+\left(c -i\right) \coth \left(b x +a \right)+c \right)}{2}\right) c^{2}}{4 b \left(c -i\right) \left(i-c \right)}+\frac{i \dilog \left(-\frac{i \left(i+\left(c -i\right) \coth \left(b x +a \right)+c \right)}{2}\right)}{4 b \left(c -i\right) \left(i-c \right)}+\frac{\ln \left(\left(c -i\right) \coth \left(b x +a \right)+c -i\right)^{2} c}{4 b \left(c -i\right) \left(i-c \right)}+\frac{\mathrm{arccot}\left(\left(c -i\right) \coth \left(b x +a \right)+c \right) \ln \left(\left(c -i\right) \coth \left(b x +a \right)+c -i\right)}{b \left(c -i\right) \left(2 i-2 c \right)}-\frac{i \ln \left(\left(c -i\right) \coth \left(b x +a \right)+c -i\right)^{2}}{8 b \left(c -i\right) \left(i-c \right)}-\frac{\dilog \left(-\frac{i \left(i+\left(c -i\right) \coth \left(b x +a \right)+c \right)}{2}\right) c}{2 b \left(c -i\right) \left(i-c \right)}"," ",0,"-1/b/(c-I)*arccot((c-I)*coth(b*x+a)+c)/(2*I-2*c)*ln((c-I)*coth(b*x+a)-c+I)+1/8*I/b/(c-I)/(I-c)*ln((c-I)*coth(b*x+a)+c-I)^2*c^2+1/4*I/b/(c-I)/(I-c)*dilog(1/2*(I+(c-I)*coth(b*x+a)+c)/c)*c^2-1/4*I/b/(c-I)/(I-c)*ln((c-I)*coth(b*x+a)-c+I)*ln(1/2*(I+(c-I)*coth(b*x+a)+c)/c)-1/4*I/b/(c-I)/(I-c)*dilog(((c-I)*coth(b*x+a)+c-I)/(-2*I+2*c))*c^2+1/4*I/b/(c-I)/(I-c)*ln((c-I)*coth(b*x+a)+c-I)*ln(-1/2*I*(I+(c-I)*coth(b*x+a)+c))-1/2/b/(c-I)/(I-c)*ln((c-I)*coth(b*x+a)+c-I)*ln(-1/2*I*(I+(c-I)*coth(b*x+a)+c))*c+1/2/b/(c-I)/(I-c)*ln((c-I)*coth(b*x+a)-c+I)*ln(1/2*(I+(c-I)*coth(b*x+a)+c)/c)*c-1/2/b/(c-I)/(I-c)*ln((c-I)*coth(b*x+a)-c+I)*ln(((c-I)*coth(b*x+a)+c-I)/(-2*I+2*c))*c+1/b/(c-I)*arccot((c-I)*coth(b*x+a)+c)/(2*I-2*c)*ln((c-I)*coth(b*x+a)-c+I)*c^2-1/b/(c-I)*arccot((c-I)*coth(b*x+a)+c)/(2*I-2*c)*ln((c-I)*coth(b*x+a)+c-I)*c^2+1/4*I/b/(c-I)/(I-c)*ln((c-I)*coth(b*x+a)-c+I)*ln(((c-I)*coth(b*x+a)+c-I)/(-2*I+2*c))-1/4*I/b/(c-I)/(I-c)*dilog(-1/2*I*(I+(c-I)*coth(b*x+a)+c))*c^2-1/2/b/(c-I)/(I-c)*dilog(-1/2*I*(I+(c-I)*coth(b*x+a)+c))*c+1/4/b/(c-I)/(I-c)*ln((c-I)*coth(b*x+a)+c-I)^2*c+1/2/b/(c-I)/(I-c)*dilog(1/2*(I+(c-I)*coth(b*x+a)+c)/c)*c-1/2/b/(c-I)/(I-c)*dilog(((c-I)*coth(b*x+a)+c-I)/(-2*I+2*c))*c+1/b/(c-I)*arccot((c-I)*coth(b*x+a)+c)/(2*I-2*c)*ln((c-I)*coth(b*x+a)+c-I)-1/4*I/b/(c-I)/(I-c)*dilog(1/2*(I+(c-I)*coth(b*x+a)+c)/c)+1/4*I/b/(c-I)/(I-c)*dilog(((c-I)*coth(b*x+a)+c-I)/(-2*I+2*c))+1/4*I/b/(c-I)/(I-c)*dilog(-1/2*I*(I+(c-I)*coth(b*x+a)+c))-1/8*I/b/(c-I)/(I-c)*ln((c-I)*coth(b*x+a)+c-I)^2+2*I/b/(c-I)*arccot((c-I)*coth(b*x+a)+c)/(2*I-2*c)*ln((c-I)*coth(b*x+a)+c-I)*c-1/4*I/b/(c-I)/(I-c)*ln((c-I)*coth(b*x+a)+c-I)*ln(-1/2*I*(I+(c-I)*coth(b*x+a)+c))*c^2+1/4*I/b/(c-I)/(I-c)*ln((c-I)*coth(b*x+a)-c+I)*ln(1/2*(I+(c-I)*coth(b*x+a)+c)/c)*c^2-1/4*I/b/(c-I)/(I-c)*ln((c-I)*coth(b*x+a)-c+I)*ln(((c-I)*coth(b*x+a)+c-I)/(-2*I+2*c))*c^2-2*I/b/(c-I)*arccot((c-I)*coth(b*x+a)+c)/(2*I-2*c)*ln((c-I)*coth(b*x+a)-c+I)*c","B"
216,0,0,23,2.087000," ","int(arccot(c-(I-c)*coth(b*x+a))/x,x)","\int \frac{\mathrm{arccot}\left(c -\left(i-c \right) \coth \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arccot(c-(I-c)*coth(b*x+a))/x,x)","F"
217,1,1058,161,0.574000," ","int((a+b*arccot(c*x^n))*(d+e*ln(f*x^m))/x,x)","\frac{i \ln \left(x^{n}\right) \pi^{2} b e \,\mathrm{csgn}\left(i x^{m}\right) \mathrm{csgn}\left(i f \,x^{m}\right)^{2}}{4 n}+\frac{i \ln \left(x^{n}\right) \pi  a e \,\mathrm{csgn}\left(i x^{m}\right) \mathrm{csgn}\left(i f \,x^{m}\right)^{2}}{2 n}+\frac{i \ln \left(x^{n}\right) \pi  a e \mathrm{csgn}\left(i f \,x^{m}\right)^{2} \mathrm{csgn}\left(i f \right)}{2 n}-\frac{\dilog \left(1+i c \,x^{n}\right) \pi  b e \,\mathrm{csgn}\left(i x^{m}\right) \mathrm{csgn}\left(i f \,x^{m}\right) \mathrm{csgn}\left(i f \right)}{4 n}+\frac{\dilog \left(1-i c \,x^{n}\right) \pi  b e \,\mathrm{csgn}\left(i x^{m}\right) \mathrm{csgn}\left(i f \,x^{m}\right) \mathrm{csgn}\left(i f \right)}{4 n}-\frac{i e b \ln \left(-i \left(-c \,x^{n}+i\right)\right) \ln \left(-i c \,x^{n}\right) m \ln \left(x \right)}{2 n}+\frac{i \ln \left(x^{n}\right) \pi^{2} b e \mathrm{csgn}\left(i f \,x^{m}\right)^{2} \mathrm{csgn}\left(i f \right)}{4 n}+\frac{\ln \left(x^{n}\right) a d}{n}+\frac{e a \ln \left(x^{m}\right)^{2}}{2 m}+\frac{e \ln \left(x^{m}\right)^{2} b \pi}{4 m}+\frac{\ln \left(x^{n}\right) \pi  b d}{2 n}-\frac{i e b \ln \left(1-i c \,x^{n}\right) \ln \left(x^{m}\right) \ln \left(x \right)}{2}+\frac{i e b \ln \left(-i \left(-c \,x^{n}+i\right)\right) \ln \left(-i c \,x^{n}\right) \ln \left(x^{m}\right)}{2 n}-\frac{i \ln \left(x^{n}\right) \pi^{2} b e \mathrm{csgn}\left(i f \,x^{m}\right)^{3}}{4 n}-\frac{i \ln \left(x^{n}\right) \pi  a e \mathrm{csgn}\left(i f \,x^{m}\right)^{3}}{2 n}-\frac{i e b \dilog \left(-i \left(c \,x^{n}+i\right)\right) m \ln \left(x \right)}{2 n}-\frac{i e b m \ln \left(x \right) \polylog \left(2, -i c \,x^{n}\right)}{2 n}+\frac{\dilog \left(1+i c \,x^{n}\right) \pi  b e \mathrm{csgn}\left(i f \,x^{m}\right)^{2} \mathrm{csgn}\left(i f \right)}{4 n}-\frac{i e b \dilog \left(-i c \,x^{n}\right) m \ln \left(x \right)}{2 n}+\frac{i e b m \ln \left(x \right) \polylog \left(2, i c \,x^{n}\right)}{2 n}-\frac{\dilog \left(1-i c \,x^{n}\right) \pi  b e \mathrm{csgn}\left(i f \,x^{m}\right)^{2} \mathrm{csgn}\left(i f \right)}{4 n}+\frac{\dilog \left(1+i c \,x^{n}\right) \pi  b e \,\mathrm{csgn}\left(i x^{m}\right) \mathrm{csgn}\left(i f \,x^{m}\right)^{2}}{4 n}-\frac{\dilog \left(1-i c \,x^{n}\right) \pi  b e \,\mathrm{csgn}\left(i x^{m}\right) \mathrm{csgn}\left(i f \,x^{m}\right)^{2}}{4 n}+\frac{\ln \left(x^{n}\right) \ln \left(f \right) a e}{n}+\frac{\ln \left(x^{n}\right) \pi  \ln \left(f \right) b e}{2 n}-\frac{i e b \ln \left(-i \left(c \,x^{n}+i\right)\right) \ln \left(x \right)^{2} m}{2}+\frac{i e b \ln \left(1-i c \,x^{n}\right) \ln \left(x \right)^{2} m}{2}-\frac{i e b \ln \left(1+i c \,x^{n}\right) \ln \left(x \right)^{2} m}{2}+\frac{i e b \ln \left(1+i c \,x^{n}\right) \ln \left(x^{m}\right) \ln \left(x \right)}{2}-\frac{i \dilog \left(1+i c \,x^{n}\right) \ln \left(f \right) b e}{2 n}+\frac{i e b \dilog \left(-i \left(c \,x^{n}+i\right)\right) \ln \left(x^{m}\right)}{2 n}-\frac{\dilog \left(1+i c \,x^{n}\right) \pi  b e \mathrm{csgn}\left(i f \,x^{m}\right)^{3}}{4 n}+\frac{\dilog \left(1-i c \,x^{n}\right) \pi  b e \mathrm{csgn}\left(i f \,x^{m}\right)^{3}}{4 n}+\frac{i \dilog \left(1-i c \,x^{n}\right) \ln \left(f \right) b e}{2 n}+\frac{i e b m \polylog \left(3, -i c \,x^{n}\right)}{2 n^{2}}+\frac{i e b \dilog \left(-i c \,x^{n}\right) \ln \left(x^{m}\right)}{2 n}-\frac{i e b m \polylog \left(3, i c \,x^{n}\right)}{2 n^{2}}+\frac{i e b \ln \left(-i \left(c \,x^{n}+i\right)\right) \ln \left(x^{m}\right) \ln \left(x \right)}{2}+\frac{i e b \ln \left(-i \left(-c \,x^{n}+i\right)\right) \ln \left(x \right)^{2} m}{2}-\frac{i e b \ln \left(-i \left(-c \,x^{n}+i\right)\right) \ln \left(x^{m}\right) \ln \left(x \right)}{2}-\frac{i \dilog \left(1+i c \,x^{n}\right) b d}{2 n}+\frac{i \dilog \left(1-i c \,x^{n}\right) b d}{2 n}-\frac{i \ln \left(x^{n}\right) \pi^{2} b e \,\mathrm{csgn}\left(i x^{m}\right) \mathrm{csgn}\left(i f \,x^{m}\right) \mathrm{csgn}\left(i f \right)}{4 n}-\frac{i \ln \left(x^{n}\right) \pi  a e \,\mathrm{csgn}\left(i x^{m}\right) \mathrm{csgn}\left(i f \,x^{m}\right) \mathrm{csgn}\left(i f \right)}{2 n}"," ",0,"-1/2*I*e*b/n*dilog(-I*(c*x^n+I))*m*ln(x)-1/2*I*e*b/n*ln(-I*(-c*x^n+I))*ln(-I*c*x^n)*m*ln(x)+1/n*ln(x^n)*a*d+1/2*e*a/m*ln(x^m)^2+1/4*I/n*ln(x^n)*Pi^2*b*e*csgn(I*f*x^m)^2*csgn(I*f)+1/2*I/n*ln(x^n)*Pi*a*e*csgn(I*f*x^m)^2*csgn(I*f)-1/4/n*dilog(1+I*c*x^n)*Pi*b*e*csgn(I*x^m)*csgn(I*f*x^m)*csgn(I*f)-1/2*I*e*b*ln(-I*(c*x^n+I))*ln(x)^2*m+1/2*I/n*ln(x^n)*Pi*a*e*csgn(I*x^m)*csgn(I*f*x^m)^2+1/4/n*dilog(1-I*c*x^n)*Pi*b*e*csgn(I*x^m)*csgn(I*f*x^m)*csgn(I*f)-1/2*I*e*b/n*m*ln(x)*polylog(2,-I*c*x^n)+1/4/n*dilog(1+I*c*x^n)*Pi*b*e*csgn(I*f*x^m)^2*csgn(I*f)+1/2*I*e*b/n*ln(-I*(-c*x^n+I))*ln(-I*c*x^n)*ln(x^m)-1/2*I*e*b/n*dilog(-I*c*x^n)*m*ln(x)+1/2*I*e*b/n*m*ln(x)*polylog(2,I*c*x^n)+1/2*I*e*b*ln(1-I*c*x^n)*ln(x)^2*m+1/4*e/m*ln(x^m)^2*b*Pi+1/2/n*ln(x^n)*Pi*b*d-1/2*I/n*dilog(1+I*c*x^n)*b*d-1/4/n*dilog(1-I*c*x^n)*Pi*b*e*csgn(I*f*x^m)^2*csgn(I*f)+1/4/n*dilog(1+I*c*x^n)*Pi*b*e*csgn(I*x^m)*csgn(I*f*x^m)^2-1/4/n*dilog(1-I*c*x^n)*Pi*b*e*csgn(I*x^m)*csgn(I*f*x^m)^2-1/4*I/n*ln(x^n)*Pi^2*b*e*csgn(I*f*x^m)^3-1/2*I/n*dilog(1+I*c*x^n)*ln(f)*b*e-1/2*I*e*b*ln(1+I*c*x^n)*ln(x)^2*m-1/2*I/n*ln(x^n)*Pi*a*e*csgn(I*f*x^m)^3+1/n*ln(x^n)*ln(f)*a*e+1/2*I/n*dilog(1-I*c*x^n)*b*d+1/2/n*ln(x^n)*Pi*ln(f)*b*e+1/2*I*e*b*ln(1+I*c*x^n)*ln(x^m)*ln(x)+1/2*I*e*b/n*dilog(-I*(c*x^n+I))*ln(x^m)-1/4*I/n*ln(x^n)*Pi^2*b*e*csgn(I*x^m)*csgn(I*f*x^m)*csgn(I*f)-1/2*I/n*ln(x^n)*Pi*a*e*csgn(I*x^m)*csgn(I*f*x^m)*csgn(I*f)-1/4/n*dilog(1+I*c*x^n)*Pi*b*e*csgn(I*f*x^m)^3+1/4/n*dilog(1-I*c*x^n)*Pi*b*e*csgn(I*f*x^m)^3+1/2*I*e*b*ln(-I*(c*x^n+I))*ln(x^m)*ln(x)+1/2*I/n*dilog(1-I*c*x^n)*ln(f)*b*e+1/2*I*e*b/n^2*m*polylog(3,-I*c*x^n)+1/2*I*e*b*ln(-I*(-c*x^n+I))*ln(x)^2*m-1/2*I*e*b*ln(-I*(-c*x^n+I))*ln(x^m)*ln(x)+1/2*I*e*b/n*dilog(-I*c*x^n)*ln(x^m)+1/4*I/n*ln(x^n)*Pi^2*b*e*csgn(I*x^m)*csgn(I*f*x^m)^2-1/2*I*e*b*ln(1-I*c*x^n)*ln(x^m)*ln(x)-1/2*I*e*b/n^2*m*polylog(3,I*c*x^n)","C"
218,1,59,25,0.059000," ","int(arccot(exp(x)),x)","\ln \left({\mathrm e}^{x}\right) \mathrm{arccot}\left({\mathrm e}^{x}\right)-\frac{i \ln \left({\mathrm e}^{x}\right) \ln \left(1+i {\mathrm e}^{x}\right)}{2}+\frac{i \ln \left({\mathrm e}^{x}\right) \ln \left(1-i {\mathrm e}^{x}\right)}{2}-\frac{i \dilog \left(1+i {\mathrm e}^{x}\right)}{2}+\frac{i \dilog \left(1-i {\mathrm e}^{x}\right)}{2}"," ",0,"ln(exp(x))*arccot(exp(x))-1/2*I*ln(exp(x))*ln(1+I*exp(x))+1/2*I*ln(exp(x))*ln(1-I*exp(x))-1/2*I*dilog(1+I*exp(x))+1/2*I*dilog(1-I*exp(x))","B"
219,1,50,51,0.269000," ","int(x*arccot(exp(x)),x)","\frac{\pi  \,x^{2}}{4}+\frac{i \polylog \left(2, i {\mathrm e}^{x}\right) x}{2}-\frac{i \polylog \left(3, i {\mathrm e}^{x}\right)}{2}-\frac{i \polylog \left(2, -i {\mathrm e}^{x}\right) x}{2}+\frac{i \polylog \left(3, -i {\mathrm e}^{x}\right)}{2}"," ",0,"1/4*Pi*x^2+1/2*I*polylog(2,I*exp(x))*x-1/2*I*polylog(3,I*exp(x))-1/2*I*polylog(2,-I*exp(x))*x+1/2*I*polylog(3,-I*exp(x))","A"
220,1,76,81,0.235000," ","int(x^2*arccot(exp(x)),x)","\frac{\pi  \,x^{3}}{6}+\frac{i \polylog \left(2, i {\mathrm e}^{x}\right) x^{2}}{2}-i x \polylog \left(3, i {\mathrm e}^{x}\right)+i \polylog \left(4, i {\mathrm e}^{x}\right)-\frac{i \polylog \left(2, -i {\mathrm e}^{x}\right) x^{2}}{2}+i \polylog \left(3, -i {\mathrm e}^{x}\right) x -i \polylog \left(4, -i {\mathrm e}^{x}\right)"," ",0,"1/6*Pi*x^3+1/2*I*polylog(2,I*exp(x))*x^2-I*x*polylog(3,I*exp(x))+I*polylog(4,I*exp(x))-1/2*I*polylog(2,-I*exp(x))*x^2+I*polylog(3,-I*exp(x))*x-I*polylog(4,-I*exp(x))","A"
221,1,106,41,0.059000," ","int(arccot(exp(b*x+a)),x)","\frac{\ln \left({\mathrm e}^{b x +a}\right) \mathrm{arccot}\left({\mathrm e}^{b x +a}\right)}{b}-\frac{i \ln \left({\mathrm e}^{b x +a}\right) \ln \left(1+i {\mathrm e}^{b x +a}\right)}{2 b}+\frac{i \ln \left({\mathrm e}^{b x +a}\right) \ln \left(1-i {\mathrm e}^{b x +a}\right)}{2 b}-\frac{i \dilog \left(1+i {\mathrm e}^{b x +a}\right)}{2 b}+\frac{i \dilog \left(1-i {\mathrm e}^{b x +a}\right)}{2 b}"," ",0,"1/b*ln(exp(b*x+a))*arccot(exp(b*x+a))-1/2*I/b*ln(exp(b*x+a))*ln(1+I*exp(b*x+a))+1/2*I/b*ln(exp(b*x+a))*ln(1-I*exp(b*x+a))-1/2*I/b*dilog(1+I*exp(b*x+a))+1/2*I/b*dilog(1-I*exp(b*x+a))","B"
222,1,355,83,0.345000," ","int(x*arccot(exp(b*x+a)),x)","\frac{\pi  \,x^{2}}{4}+\frac{i \ln \left(-i \left(-{\mathrm e}^{b x +a}+i\right)\right) a^{2}}{2 b^{2}}-\frac{i \polylog \left(3, i {\mathrm e}^{b x +a}\right)}{2 b^{2}}-\frac{i \dilog \left(-i {\mathrm e}^{b x +a}\right) a}{2 b^{2}}-\frac{i \ln \left(-i \left({\mathrm e}^{b x +a}+i\right)\right) a^{2}}{2 b^{2}}-\frac{i \ln \left(-i \left({\mathrm e}^{b x +a}+i\right)\right) x a}{2 b}-\frac{i a^{2} \ln \left(1+i {\mathrm e}^{b x +a}\right)}{2 b^{2}}-\frac{i \ln \left(1+i {\mathrm e}^{b x +a}\right) x a}{2 b}+\frac{i \ln \left(1-i {\mathrm e}^{b x +a}\right) x a}{2 b}+\frac{i a^{2} \ln \left(1-i {\mathrm e}^{b x +a}\right)}{2 b^{2}}+\frac{i \polylog \left(2, i {\mathrm e}^{b x +a}\right) a}{2 b^{2}}-\frac{i \ln \left(-i {\mathrm e}^{b x +a}\right) \ln \left(-i \left(-{\mathrm e}^{b x +a}+i\right)\right) a}{2 b^{2}}+\frac{i \polylog \left(3, -i {\mathrm e}^{b x +a}\right)}{2 b^{2}}+\frac{i \ln \left(-i \left(-{\mathrm e}^{b x +a}+i\right)\right) x a}{2 b}-\frac{i \polylog \left(2, -i {\mathrm e}^{b x +a}\right) a}{2 b^{2}}+\frac{i \polylog \left(2, i {\mathrm e}^{b x +a}\right) x}{2 b}-\frac{i \polylog \left(2, -i {\mathrm e}^{b x +a}\right) x}{2 b}-\frac{i \dilog \left(-i \left({\mathrm e}^{b x +a}+i\right)\right) a}{2 b^{2}}"," ",0,"1/4*Pi*x^2+1/2*I/b^2*ln(-I*(-exp(b*x+a)+I))*a^2-1/2*I/b^2*polylog(3,I*exp(b*x+a))-1/2*I/b^2*dilog(-I*(exp(b*x+a)+I))*a-1/2*I/b^2*dilog(-I*exp(b*x+a))*a+1/2*I/b^2*polylog(2,I*exp(b*x+a))*a-1/2*I/b^2*ln(-I*(exp(b*x+a)+I))*a^2-1/2*I/b*ln(-I*(exp(b*x+a)+I))*x*a-1/2*I/b^2*a^2*ln(1+I*exp(b*x+a))-1/2*I/b*ln(1+I*exp(b*x+a))*x*a+1/2*I/b*ln(1-I*exp(b*x+a))*x*a+1/2*I/b^2*a^2*ln(1-I*exp(b*x+a))-1/2*I/b*polylog(2,-I*exp(b*x+a))*x+1/2*I/b*polylog(2,I*exp(b*x+a))*x-1/2*I/b^2*ln(-I*exp(b*x+a))*ln(-I*(-exp(b*x+a)+I))*a+1/2*I/b*ln(-I*(-exp(b*x+a)+I))*x*a-1/2*I/b^2*polylog(2,-I*exp(b*x+a))*a+1/2*I/b^2*polylog(3,-I*exp(b*x+a))","B"
223,1,413,129,0.341000," ","int(x^2*arccot(exp(b*x+a)),x)","\frac{\pi  \,x^{3}}{6}-\frac{i \ln \left(1-i {\mathrm e}^{b x +a}\right) x \,a^{2}}{2 b^{2}}-\frac{i \ln \left(-i \left(-{\mathrm e}^{b x +a}+i\right)\right) a^{3}}{2 b^{3}}-\frac{i \polylog \left(4, -i {\mathrm e}^{b x +a}\right)}{b^{3}}+\frac{i \dilog \left(-i {\mathrm e}^{b x +a}\right) a^{2}}{2 b^{3}}-\frac{i a^{3} \ln \left(1-i {\mathrm e}^{b x +a}\right)}{2 b^{3}}+\frac{i \ln \left(-i \left({\mathrm e}^{b x +a}+i\right)\right) a^{3}}{2 b^{3}}-\frac{i \polylog \left(2, i {\mathrm e}^{b x +a}\right) a^{2}}{2 b^{3}}+\frac{i \polylog \left(2, -i {\mathrm e}^{b x +a}\right) a^{2}}{2 b^{3}}-\frac{i \polylog \left(3, i {\mathrm e}^{b x +a}\right) x}{b^{2}}+\frac{i \dilog \left(-i \left({\mathrm e}^{b x +a}+i\right)\right) a^{2}}{2 b^{3}}+\frac{i \polylog \left(2, i {\mathrm e}^{b x +a}\right) x^{2}}{2 b}+\frac{i \ln \left(-i \left({\mathrm e}^{b x +a}+i\right)\right) x \,a^{2}}{2 b^{2}}-\frac{i \polylog \left(2, -i {\mathrm e}^{b x +a}\right) x^{2}}{2 b}+\frac{i \ln \left(-i {\mathrm e}^{b x +a}\right) \ln \left(-i \left(-{\mathrm e}^{b x +a}+i\right)\right) a^{2}}{2 b^{3}}+\frac{i \ln \left(1+i {\mathrm e}^{b x +a}\right) x \,a^{2}}{2 b^{2}}+\frac{i \polylog \left(4, i {\mathrm e}^{b x +a}\right)}{b^{3}}+\frac{i \polylog \left(3, -i {\mathrm e}^{b x +a}\right) x}{b^{2}}+\frac{i a^{3} \ln \left(1+i {\mathrm e}^{b x +a}\right)}{2 b^{3}}-\frac{i \ln \left(-i \left(-{\mathrm e}^{b x +a}+i\right)\right) x \,a^{2}}{2 b^{2}}"," ",0,"1/6*Pi*x^3-1/2*I/b^2*ln(1-I*exp(b*x+a))*x*a^2-1/2*I/b^3*ln(-I*(-exp(b*x+a)+I))*a^3+1/2*I/b*polylog(2,I*exp(b*x+a))*x^2+1/2*I/b^3*dilog(-I*(exp(b*x+a)+I))*a^2-1/2*I/b^3*a^3*ln(1-I*exp(b*x+a))+1/2*I/b^3*ln(-I*(exp(b*x+a)+I))*a^3+I/b^3*polylog(4,I*exp(b*x+a))+I/b^2*polylog(3,-I*exp(b*x+a))*x-I/b^3*polylog(4,-I*exp(b*x+a))+1/2*I/b^3*dilog(-I*exp(b*x+a))*a^2-I/b^2*polylog(3,I*exp(b*x+a))*x+1/2*I/b^2*ln(-I*(exp(b*x+a)+I))*x*a^2+1/2*I/b^3*polylog(2,-I*exp(b*x+a))*a^2+1/2*I/b^3*ln(-I*exp(b*x+a))*ln(-I*(-exp(b*x+a)+I))*a^2+1/2*I/b^2*ln(1+I*exp(b*x+a))*x*a^2-1/2*I/b^3*polylog(2,I*exp(b*x+a))*a^2-1/2*I/b*polylog(2,-I*exp(b*x+a))*x^2+1/2*I/b^3*a^3*ln(1+I*exp(b*x+a))-1/2*I/b^2*ln(-I*(-exp(b*x+a)+I))*x*a^2","B"
224,1,186,184,0.063000," ","int(arccot(a+b*f^(d*x+c)),x)","\frac{\ln \left(b \,f^{d x +c}\right) \mathrm{arccot}\left(a +b \,f^{d x +c}\right)}{d \ln \left(f \right)}-\frac{i \ln \left(b \,f^{d x +c}\right) \ln \left(\frac{-b \,f^{d x +c}-a +i}{i-a}\right)}{2 d \ln \left(f \right)}+\frac{i \ln \left(b \,f^{d x +c}\right) \ln \left(\frac{i+b \,f^{d x +c}+a}{i+a}\right)}{2 d \ln \left(f \right)}-\frac{i \dilog \left(\frac{-b \,f^{d x +c}-a +i}{i-a}\right)}{2 d \ln \left(f \right)}+\frac{i \dilog \left(\frac{i+b \,f^{d x +c}+a}{i+a}\right)}{2 d \ln \left(f \right)}"," ",0,"1/d/ln(f)*ln(b*f^(d*x+c))*arccot(a+b*f^(d*x+c))-1/2*I/d/ln(f)*ln(b*f^(d*x+c))*ln((-b*f^(d*x+c)-a+I)/(I-a))+1/2*I/d/ln(f)*ln(b*f^(d*x+c))*ln((I+b*f^(d*x+c)+a)/(I+a))-1/2*I/d/ln(f)*dilog((-b*f^(d*x+c)-a+I)/(I-a))+1/2*I/d/ln(f)*dilog((I+b*f^(d*x+c)+a)/(I+a))","A"
225,1,678,218,0.484000," ","int(x*arccot(a+b*f^(d*x+c)),x)","\frac{i \ln \left(1-\frac{i b \,f^{d x} f^{c}}{-i a +1}\right) c^{2}}{4 d^{2}}+\frac{\pi  \,x^{2}}{4}+\frac{i \ln \left(1-\frac{i b \,f^{d x} f^{c}}{-i a +1}\right) x c}{2 d}+\frac{i \polylog \left(3, \frac{i b \,f^{d x} f^{c}}{-i a -1}\right)}{2 d^{2} \ln \left(f \right)^{2}}-\frac{i c^{2} \ln \left(i f^{d x} f^{c} b +i a +1\right)}{4 d^{2}}-\frac{i \polylog \left(2, \frac{i b \,f^{d x} f^{c}}{-i a -1}\right) x}{2 d \ln \left(f \right)}+\frac{i \polylog \left(2, \frac{i b \,f^{d x} f^{c}}{-i a +1}\right) c}{2 d^{2} \ln \left(f \right)}+\frac{i \polylog \left(2, \frac{i b \,f^{d x} f^{c}}{-i a +1}\right) x}{2 d \ln \left(f \right)}-\frac{i c^{2} \ln \left(\frac{b \,f^{d x} f^{c}+i+a}{i+a}\right)}{2 d^{2}}+\frac{i \ln \left(1-\frac{i b \,f^{d x} f^{c}}{-i a +1}\right) x^{2}}{4}-\frac{i \polylog \left(2, \frac{i b \,f^{d x} f^{c}}{-i a -1}\right) c}{2 d^{2} \ln \left(f \right)}+\frac{i c \ln \left(\frac{b \,f^{d x} f^{c}+a -i}{-i+a}\right) x}{2 d}+\frac{i c^{2} \ln \left(\frac{b \,f^{d x} f^{c}+a -i}{-i+a}\right)}{2 d^{2}}-\frac{i \ln \left(1-\frac{i b \,f^{d x} f^{c}}{-i a -1}\right) x^{2}}{4}-\frac{i \polylog \left(3, \frac{i b \,f^{d x} f^{c}}{-i a +1}\right)}{2 d^{2} \ln \left(f \right)^{2}}+\frac{i c \dilog \left(\frac{b \,f^{d x} f^{c}+a -i}{-i+a}\right)}{2 d^{2} \ln \left(f \right)}-\frac{i \ln \left(1-\frac{i b \,f^{d x} f^{c}}{-i a -1}\right) x c}{2 d}+\frac{i c^{2} \ln \left(1-i a -i f^{d x} f^{c} b \right)}{4 d^{2}}+\frac{i x^{2} \ln \left(1+i \left(a +b \,f^{d x +c}\right)\right)}{4}-\frac{i \ln \left(1-\frac{i b \,f^{d x} f^{c}}{-i a -1}\right) c^{2}}{4 d^{2}}-\frac{i c \ln \left(\frac{b \,f^{d x} f^{c}+i+a}{i+a}\right) x}{2 d}-\frac{i c \dilog \left(\frac{b \,f^{d x} f^{c}+i+a}{i+a}\right)}{2 d^{2} \ln \left(f \right)}-\frac{i x^{2} \ln \left(1-i \left(a +b \,f^{d x +c}\right)\right)}{4}"," ",0,"1/4*I/d^2*ln(1-I*b/(1-I*a)*f^(d*x)*f^c)*c^2+1/4*Pi*x^2+1/2*I/d*ln(1-I*b/(1-I*a)*f^(d*x)*f^c)*x*c-1/4*I/d^2*c^2*ln(I*f^(d*x)*f^c*b+I*a+1)-1/2*I/d^2/ln(f)*polylog(2,I*b/(-I*a-1)*f^(d*x)*f^c)*c-1/2*I/d^2/ln(f)*c*dilog((b*f^(d*x)*f^c+I+a)/(I+a))+1/2*I/d^2/ln(f)^2*polylog(3,I*b/(-I*a-1)*f^(d*x)*f^c)-1/2*I/d^2*c^2*ln((b*f^(d*x)*f^c+I+a)/(I+a))+1/4*I*ln(1-I*b/(1-I*a)*f^(d*x)*f^c)*x^2+1/2*I/d*c*ln((b*f^(d*x)*f^c+a-I)/(-I+a))*x+1/2*I/d^2*c^2*ln((b*f^(d*x)*f^c+a-I)/(-I+a))-1/4*I*ln(1-I*b/(-I*a-1)*f^(d*x)*f^c)*x^2+1/2*I/d/ln(f)*polylog(2,I*b/(1-I*a)*f^(d*x)*f^c)*x+1/2*I/d^2/ln(f)*c*dilog((b*f^(d*x)*f^c+a-I)/(-I+a))+1/2*I/d^2/ln(f)*polylog(2,I*b/(1-I*a)*f^(d*x)*f^c)*c-1/2*I/d*ln(1-I*b/(-I*a-1)*f^(d*x)*f^c)*x*c+1/4*I/d^2*c^2*ln(1-I*a-I*f^(d*x)*f^c*b)+1/4*I*x^2*ln(1+I*(a+b*f^(d*x+c)))-1/4*I/d^2*ln(1-I*b/(-I*a-1)*f^(d*x)*f^c)*c^2-1/2*I/d*c*ln((b*f^(d*x)*f^c+I+a)/(I+a))*x-1/4*I*x^2*ln(1-I*(a+b*f^(d*x+c)))-1/2*I/d/ln(f)*polylog(2,I*b/(-I*a-1)*f^(d*x)*f^c)*x-1/2*I/d^2/ln(f)^2*polylog(3,I*b/(1-I*a)*f^(d*x)*f^c)","B"
226,1,764,281,0.482000," ","int(x^2*arccot(a+b*f^(d*x+c)),x)","-\frac{i \ln \left(1-\frac{i b \,f^{d x} f^{c}}{-i a +1}\right) x \,c^{2}}{2 d^{2}}-\frac{i c^{2} \ln \left(\frac{b \,f^{d x} f^{c}+a -i}{-i+a}\right) x}{2 d^{2}}+\frac{i \ln \left(1-\frac{i b \,f^{d x} f^{c}}{-i a -1}\right) x \,c^{2}}{2 d^{2}}+\frac{i c^{2} \ln \left(\frac{b \,f^{d x} f^{c}+i+a}{i+a}\right) x}{2 d^{2}}+\frac{i \polylog \left(2, \frac{i b \,f^{d x} f^{c}}{-i a -1}\right) c^{2}}{2 d^{3} \ln \left(f \right)}-\frac{i c^{2} \dilog \left(\frac{b \,f^{d x} f^{c}+a -i}{-i+a}\right)}{2 d^{3} \ln \left(f \right)}+\frac{i \polylog \left(2, \frac{i b \,f^{d x} f^{c}}{-i a +1}\right) x^{2}}{2 d \ln \left(f \right)}-\frac{i \polylog \left(2, \frac{i b \,f^{d x} f^{c}}{-i a +1}\right) c^{2}}{2 d^{3} \ln \left(f \right)}+\frac{i c^{2} \dilog \left(\frac{b \,f^{d x} f^{c}+i+a}{i+a}\right)}{2 d^{3} \ln \left(f \right)}-\frac{i \polylog \left(4, \frac{i b \,f^{d x} f^{c}}{-i a -1}\right)}{d^{3} \ln \left(f \right)^{3}}+\frac{i \polylog \left(4, \frac{i b \,f^{d x} f^{c}}{-i a +1}\right)}{d^{3} \ln \left(f \right)^{3}}+\frac{i \ln \left(1-\frac{i b \,f^{d x} f^{c}}{-i a -1}\right) c^{3}}{3 d^{3}}-\frac{i c^{3} \ln \left(\frac{b \,f^{d x} f^{c}+a -i}{-i+a}\right)}{2 d^{3}}+\frac{i c^{3} \ln \left(\frac{b \,f^{d x} f^{c}+i+a}{i+a}\right)}{2 d^{3}}-\frac{i \ln \left(1-\frac{i b \,f^{d x} f^{c}}{-i a +1}\right) c^{3}}{3 d^{3}}-\frac{i c^{3} \ln \left(1-i a -i f^{d x} f^{c} b \right)}{6 d^{3}}+\frac{i c^{3} \ln \left(i f^{d x} f^{c} b +i a +1\right)}{6 d^{3}}+\frac{\pi  \,x^{3}}{6}-\frac{i \polylog \left(3, \frac{i b \,f^{d x} f^{c}}{-i a +1}\right) x}{d^{2} \ln \left(f \right)^{2}}+\frac{i \polylog \left(3, \frac{i b \,f^{d x} f^{c}}{-i a -1}\right) x}{d^{2} \ln \left(f \right)^{2}}-\frac{i \polylog \left(2, \frac{i b \,f^{d x} f^{c}}{-i a -1}\right) x^{2}}{2 d \ln \left(f \right)}+\frac{i x^{3} \ln \left(1+i \left(a +b \,f^{d x +c}\right)\right)}{6}-\frac{i \ln \left(1-\frac{i b \,f^{d x} f^{c}}{-i a -1}\right) x^{3}}{6}+\frac{i \ln \left(1-\frac{i b \,f^{d x} f^{c}}{-i a +1}\right) x^{3}}{6}-\frac{i x^{3} \ln \left(1-i \left(a +b \,f^{d x +c}\right)\right)}{6}"," ",0,"-I/d^2/ln(f)^2*polylog(3,I*b/(1-I*a)*f^(d*x)*f^c)*x+I/d^2/ln(f)^2*polylog(3,I*b/(-I*a-1)*f^(d*x)*f^c)*x+1/3*I/d^3*ln(1-I*b/(-I*a-1)*f^(d*x)*f^c)*c^3-1/2*I/d^3*c^3*ln((b*f^(d*x)*f^c+a-I)/(-I+a))+1/2*I/d^3*c^3*ln((b*f^(d*x)*f^c+I+a)/(I+a))-1/3*I/d^3*ln(1-I*b/(1-I*a)*f^(d*x)*f^c)*c^3-1/6*I/d^3*c^3*ln(1-I*a-I*f^(d*x)*f^c*b)-I/d^3/ln(f)^3*polylog(4,I*b/(-I*a-1)*f^(d*x)*f^c)+1/6*I/d^3*c^3*ln(I*f^(d*x)*f^c*b+I*a+1)+I/d^3/ln(f)^3*polylog(4,I*b/(1-I*a)*f^(d*x)*f^c)+1/6*Pi*x^3+1/6*I*x^3*ln(1+I*(a+b*f^(d*x+c)))-1/6*I*ln(1-I*b/(-I*a-1)*f^(d*x)*f^c)*x^3+1/6*I*ln(1-I*b/(1-I*a)*f^(d*x)*f^c)*x^3-1/6*I*x^3*ln(1-I*(a+b*f^(d*x+c)))-1/2*I/d^2*ln(1-I*b/(1-I*a)*f^(d*x)*f^c)*x*c^2-1/2*I/d/ln(f)*polylog(2,I*b/(-I*a-1)*f^(d*x)*f^c)*x^2+1/2*I/d^3/ln(f)*polylog(2,I*b/(-I*a-1)*f^(d*x)*f^c)*c^2-1/2*I/d^3/ln(f)*c^2*dilog((b*f^(d*x)*f^c+a-I)/(-I+a))-1/2*I/d^2*c^2*ln((b*f^(d*x)*f^c+a-I)/(-I+a))*x+1/2*I/d^2*ln(1-I*b/(-I*a-1)*f^(d*x)*f^c)*x*c^2+1/2*I/d/ln(f)*polylog(2,I*b/(1-I*a)*f^(d*x)*f^c)*x^2-1/2*I/d^3/ln(f)*polylog(2,I*b/(1-I*a)*f^(d*x)*f^c)*c^2+1/2*I/d^3/ln(f)*c^2*dilog((b*f^(d*x)*f^c+I+a)/(I+a))+1/2*I/d^2*c^2*ln((b*f^(d*x)*f^c+I+a)/(I+a))*x","B"
227,1,25,22,0.044000," ","int(arccot(exp(x))/exp(x),x)","-\mathrm{arccot}\left({\mathrm e}^{x}\right) {\mathrm e}^{-x}-\ln \left({\mathrm e}^{x}\right)+\frac{\ln \left(1+{\mathrm e}^{2 x}\right)}{2}"," ",0,"-arccot(exp(x))/exp(x)-ln(exp(x))+1/2*ln(exp(x)^2+1)","A"
228,1,19,15,0.101000," ","int(1/(a*x^2+a)/(b-2*b*arccot(x)),x)","\frac{\ln \left(2 b \,\mathrm{arccot}\left(x \right)-b \right)}{2 a b}"," ",0,"1/2/a*ln(2*b*arccot(x)-b)/b","A"
229,1,1281,45,0.516000," ","int(exp(c*(b*x+a))*arccot(sinh(b*c*x+a*c)),x)","\frac{\ln \left(1+{\mathrm e}^{2 c \left(b x +a \right)}\right)}{b c}-\frac{\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right) \mathrm{csgn}\left({\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right) \mathrm{csgn}\left({\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right) \mathrm{csgn}\left({\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{2 b c}+\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{2 b c}+\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right) \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)\right)^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right) \mathrm{csgn}\left({\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)\right)^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right) \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right) \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right) \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{2 a}{b}-\frac{\pi  \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \mathrm{csgn}\left({\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \mathrm{csgn}\left({\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \mathrm{csgn}\left({\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{i {\mathrm e}^{c \left(b x +a \right)} \ln \left({\mathrm e}^{c \left(b x +a \right)}-i\right)}{b c}-\frac{i {\mathrm e}^{c \left(b x +a \right)} \ln \left({\mathrm e}^{c \left(b x +a \right)}+i\right)}{b c}-\frac{\pi  \mathrm{csgn}\left({\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}"," ",0,"ln(1+exp(2*c*(b*x+a)))/b/c-I/b/c*exp(c*(b*x+a))*ln(exp(c*(b*x+a))+I)+1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))+I)^2)*csgn(I*exp(-c*(b*x+a))*(exp(c*(b*x+a))+I)^2)^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a)))*csgn(I*exp(-c*(b*x+a))*(exp(c*(b*x+a))+I)^2)^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))+I))^2*csgn(I*(exp(c*(b*x+a))+I)^2)*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a))*(exp(c*(b*x+a))+I)^2)*csgn(exp(-c*(b*x+a))*(exp(c*(b*x+a))+I)^2)^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))-I))^2*csgn(I*(exp(c*(b*x+a))-I)^2)*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))-I)^2)*csgn(I*exp(-c*(b*x+a))*(exp(c*(b*x+a))-I)^2)^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a)))*csgn(I*exp(-c*(b*x+a))*(exp(c*(b*x+a))-I)^2)^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a))*(exp(c*(b*x+a))-I)^2)*csgn(exp(-c*(b*x+a))*(exp(c*(b*x+a))-I)^2)^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a))*(exp(c*(b*x+a))+I)^2)*csgn(exp(-c*(b*x+a))*(exp(c*(b*x+a))+I)^2)*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a))*(exp(c*(b*x+a))-I)^2)*csgn(exp(-c*(b*x+a))*(exp(c*(b*x+a))-I)^2)*exp(c*(b*x+a))-1/2/b/c*Pi*csgn(I*(exp(c*(b*x+a))-I))*csgn(I*(exp(c*(b*x+a))-I)^2)^2*exp(c*(b*x+a))+1/2/b/c*Pi*csgn(I*(exp(c*(b*x+a))+I))*csgn(I*(exp(c*(b*x+a))+I)^2)^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))+I)^2)*csgn(I*exp(-c*(b*x+a)))*csgn(I*exp(-c*(b*x+a))*(exp(c*(b*x+a))+I)^2)*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))-I)^2)*csgn(I*exp(-c*(b*x+a)))*csgn(I*exp(-c*(b*x+a))*(exp(c*(b*x+a))-I)^2)*exp(c*(b*x+a))-2*a/b-1/4/b/c*Pi*csgn(exp(-c*(b*x+a))*(exp(c*(b*x+a))+I)^2)^3*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a))*(exp(c*(b*x+a))+I)^2)^3*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))-I)^2)^3*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))+I)^2)^3*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a))*(exp(c*(b*x+a))-I)^2)^3*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(exp(-c*(b*x+a))*(exp(c*(b*x+a))-I)^2)^3*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(exp(-c*(b*x+a))*(exp(c*(b*x+a))+I)^2)^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(exp(-c*(b*x+a))*(exp(c*(b*x+a))-I)^2)^2*exp(c*(b*x+a))+I/b/c*exp(c*(b*x+a))*ln(exp(c*(b*x+a))-I)","C"
230,1,1358,88,0.725000," ","int(exp(c*(b*x+a))*arccot(cosh(b*c*x+a*c)),x)","\frac{i {\mathrm e}^{c \left(b x +a \right)} \ln \left({\mathrm e}^{2 c \left(b x +a \right)}+1-2 i {\mathrm e}^{c \left(b x +a \right)}\right)}{2 b c}-\frac{\pi  \mathrm{csgn}\left({\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right) \mathrm{csgn}\left({\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \mathrm{csgn}\left({\mathrm e}^{-c \left(b x +a \right)} \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right) \mathrm{csgn}\left({\mathrm e}^{-c \left(b x +a \right)} \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)}\right) \mathrm{csgn}\left(i \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)}\right) \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \mathrm{csgn}\left({\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right) \mathrm{csgn}\left({\mathrm e}^{-c \left(b x +a \right)} \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \mathrm{csgn}\left({\mathrm e}^{-c \left(b x +a \right)} \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-c \left(b x +a \right)} \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right) \mathrm{csgn}\left({\mathrm e}^{-c \left(b x +a \right)} \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{i {\mathrm e}^{c \left(b x +a \right)} \ln \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)}{2 b c}+\frac{\ln \left({\mathrm e}^{2 c \left(b x +a \right)}+\left(1+\sqrt{2}\right)^{2}\right) \sqrt{2}}{2 b c}-\frac{\ln \left({\mathrm e}^{2 c \left(b x +a \right)}+\left(\sqrt{2}-1\right)^{2}\right) \sqrt{2}}{2 b c}-\frac{2 a}{b}+\frac{\ln \left({\mathrm e}^{2 c \left(b x +a \right)}+\left(1+\sqrt{2}\right)^{2}\right)}{2 b c}+\frac{\ln \left({\mathrm e}^{2 c \left(b x +a \right)}+\left(\sqrt{2}-1\right)^{2}\right)}{2 b c}"," ",0,"1/2*I/b/c*exp(c*(b*x+a))*ln(exp(2*c*(b*x+a))+1-2*I*exp(c*(b*x+a)))-1/4/b/c*Pi*csgn(exp(-c*(b*x+a))*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a))))^3*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a))*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a))))*csgn(exp(-c*(b*x+a))*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a))))^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(exp(-c*(b*x+a))*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a))))^3*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a))*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a))))*csgn(exp(-c*(b*x+a))*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a))))^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a)))*csgn(I*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a))))*csgn(I*exp(-c*(b*x+a))*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a))))*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a)))*csgn(I*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a))))*csgn(I*exp(-c*(b*x+a))*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a))))*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a)))*csgn(I*exp(-c*(b*x+a))*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a))))^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a)))*csgn(I*exp(-c*(b*x+a))*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a))))^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a))))*csgn(I*exp(-c*(b*x+a))*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a))))^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a))))*csgn(I*exp(-c*(b*x+a))*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a))))^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a))*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a))))^3*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a))*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a))))^3*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(exp(-c*(b*x+a))*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a))))^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a))*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a))))*csgn(exp(-c*(b*x+a))*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a))))*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(exp(-c*(b*x+a))*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a))))^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*exp(-c*(b*x+a))*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a))))*csgn(exp(-c*(b*x+a))*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a))))*exp(c*(b*x+a))-1/2*I/b/c*exp(c*(b*x+a))*ln(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a)))+1/2/b/c*ln(exp(2*c*(b*x+a))+(1+2^(1/2))^2)*2^(1/2)-1/2/b/c*ln(exp(2*c*(b*x+a))+(2^(1/2)-1)^2)*2^(1/2)-2*a/b+1/2/b/c*ln(exp(2*c*(b*x+a))+(1+2^(1/2))^2)+1/2/b/c*ln(exp(2*c*(b*x+a))+(2^(1/2)-1)^2)","C"
231,1,1323,153,1.737000," ","int(exp(c*(b*x+a))*arccot(tanh(b*c*x+a*c)),x)","-\frac{\ln \left({\mathrm e}^{c \left(b x +a \right)}+\left(\frac{1}{2}-\frac{i}{2}\right) \sqrt{2}\right) \sqrt{2}}{4 b c}+\frac{\ln \left({\mathrm e}^{c \left(b x +a \right)}+\left(-\frac{1}{2}-\frac{i}{2}\right) \sqrt{2}\right) \sqrt{2}}{4 b c}+\frac{\ln \left({\mathrm e}^{c \left(b x +a \right)}+\left(-\frac{1}{2}+\frac{i}{2}\right) \sqrt{2}\right) \sqrt{2}}{4 b c}-\frac{\ln \left({\mathrm e}^{c \left(b x +a \right)}+\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{2}\right) \sqrt{2}}{4 b c}+\frac{\pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \mathrm{csgn}\left(\frac{\left(1+i\right) \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) \mathrm{csgn}\left(\frac{\left(1-i\right) \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) \mathrm{csgn}\left(\frac{\left(1+i\right) \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) \mathrm{csgn}\left(\frac{\left(1-i\right) \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(\frac{i}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(\frac{i}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) \mathrm{csgn}\left(\frac{\left(1+i\right) \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{i \ln \left({\mathrm e}^{c \left(b x +a \right)}+\left(-\frac{1}{2}-\frac{i}{2}\right) \sqrt{2}\right) \sqrt{2}}{4 b c}+\frac{\pi  \mathrm{csgn}\left(\frac{\left(1-i\right) \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{i \ln \left({\mathrm e}^{c \left(b x +a \right)}+\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{2}\right) \sqrt{2}}{4 b c}+\frac{\pi  \mathrm{csgn}\left(\frac{\left(1+i\right) \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \mathrm{csgn}\left(\frac{\left(1-i\right) \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{i \ln \left({\mathrm e}^{c \left(b x +a \right)}+\left(-\frac{1}{2}+\frac{i}{2}\right) \sqrt{2}\right) \sqrt{2}}{4 b c}-\frac{i \ln \left({\mathrm e}^{c \left(b x +a \right)}+\left(\frac{1}{2}-\frac{i}{2}\right) \sqrt{2}\right) \sqrt{2}}{4 b c}+\frac{i {\mathrm e}^{c \left(b x +a \right)} \ln \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{2 b c}+\frac{\pi  \,\mathrm{csgn}\left(\frac{i}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(\frac{i}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{{\mathrm e}^{c \left(b x +a \right)} \pi}{4 b c}-\frac{i {\mathrm e}^{c \left(b x +a \right)} \ln \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{2 b c}"," ",0,"-1/4/b/c*Pi*csgn((1-I)*(exp(2*c*(b*x+a))-I)/(1+exp(2*c*(b*x+a))))^3*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))+I)/(1+exp(2*c*(b*x+a))))^3*exp(c*(b*x+a))-1/4*I/b/c*ln(exp(c*(b*x+a))+(1/2-1/2*I)*2^(1/2))*2^(1/2)-1/4*I/b/c*ln(exp(c*(b*x+a))-(1/2+1/2*I)*2^(1/2))*2^(1/2)+1/4*I/b/c*ln(exp(c*(b*x+a))+(-1/2+1/2*I)*2^(1/2))*2^(1/2)+1/4*I/b/c*ln(exp(c*(b*x+a))+(1/2+1/2*I)*2^(1/2))*2^(1/2)+1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))-I)/(1+exp(2*c*(b*x+a))))*csgn((1-I)*(exp(2*c*(b*x+a))-I)/(1+exp(2*c*(b*x+a))))*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))+I)/(1+exp(2*c*(b*x+a))))*csgn((1+I)*(exp(2*c*(b*x+a))+I)/(1+exp(2*c*(b*x+a))))^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))-I)/(1+exp(2*c*(b*x+a))))*csgn((1-I)*(exp(2*c*(b*x+a))-I)/(1+exp(2*c*(b*x+a))))^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))-I))*csgn(I*(exp(2*c*(b*x+a))-I)/(1+exp(2*c*(b*x+a))))^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I/(1+exp(2*c*(b*x+a))))*csgn(I*(exp(2*c*(b*x+a))+I)/(1+exp(2*c*(b*x+a))))^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I/(1+exp(2*c*(b*x+a))))*csgn(I*(exp(2*c*(b*x+a))-I)/(1+exp(2*c*(b*x+a))))^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))+I))*csgn(I*(exp(2*c*(b*x+a))+I)/(1+exp(2*c*(b*x+a))))^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))+I)/(1+exp(2*c*(b*x+a))))*csgn((1+I)*(exp(2*c*(b*x+a))+I)/(1+exp(2*c*(b*x+a))))*exp(c*(b*x+a))+1/4/b/c*Pi*csgn((1-I)*(exp(2*c*(b*x+a))-I)/(1+exp(2*c*(b*x+a))))^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))-I)/(1+exp(2*c*(b*x+a))))^3*exp(c*(b*x+a))+1/4/b/c*Pi*csgn((1+I)*(exp(2*c*(b*x+a))+I)/(1+exp(2*c*(b*x+a))))^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn((1+I)*(exp(2*c*(b*x+a))+I)/(1+exp(2*c*(b*x+a))))^3*exp(c*(b*x+a))+1/2*I/b/c*exp(c*(b*x+a))*ln(exp(2*c*(b*x+a))-I)+1/4/b/c*Pi*csgn(I/(1+exp(2*c*(b*x+a))))*csgn(I*(exp(2*c*(b*x+a))-I))*csgn(I*(exp(2*c*(b*x+a))-I)/(1+exp(2*c*(b*x+a))))*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I/(1+exp(2*c*(b*x+a))))*csgn(I*(exp(2*c*(b*x+a))+I))*csgn(I*(exp(2*c*(b*x+a))+I)/(1+exp(2*c*(b*x+a))))*exp(c*(b*x+a))+1/4/b/c*exp(c*(b*x+a))*Pi-1/4/b/c*ln(exp(c*(b*x+a))+(1/2-1/2*I)*2^(1/2))*2^(1/2)+1/4/b/c*ln(exp(c*(b*x+a))-(1/2+1/2*I)*2^(1/2))*2^(1/2)+1/4/b/c*ln(exp(c*(b*x+a))+(-1/2+1/2*I)*2^(1/2))*2^(1/2)-1/4/b/c*ln(exp(c*(b*x+a))+(1/2+1/2*I)*2^(1/2))*2^(1/2)-1/2*I/b/c*exp(c*(b*x+a))*ln(exp(2*c*(b*x+a))+I)","C"
232,1,1323,153,1.475000," ","int(exp(c*(b*x+a))*arccot(coth(b*c*x+a*c)),x)","\frac{\ln \left({\mathrm e}^{c \left(b x +a \right)}+\left(\frac{1}{2}-\frac{i}{2}\right) \sqrt{2}\right) \sqrt{2}}{4 b c}-\frac{\ln \left({\mathrm e}^{c \left(b x +a \right)}+\left(-\frac{1}{2}-\frac{i}{2}\right) \sqrt{2}\right) \sqrt{2}}{4 b c}-\frac{\ln \left({\mathrm e}^{c \left(b x +a \right)}+\left(-\frac{1}{2}+\frac{i}{2}\right) \sqrt{2}\right) \sqrt{2}}{4 b c}+\frac{\ln \left({\mathrm e}^{c \left(b x +a \right)}+\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{2}\right) \sqrt{2}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{\left(1+i\right) \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{\left(1-i\right) \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{\left(1+i\right) \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{\left(1-i\right) \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{i \ln \left({\mathrm e}^{c \left(b x +a \right)}+\left(-\frac{1}{2}-\frac{i}{2}\right) \sqrt{2}\right) \sqrt{2}}{4 b c}-\frac{\pi  \mathrm{csgn}\left(\frac{\left(1+i\right) \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \mathrm{csgn}\left(\frac{\left(1-i\right) \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \mathrm{csgn}\left(\frac{\left(1+i\right) \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \mathrm{csgn}\left(\frac{\left(1-i\right) \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{i \ln \left({\mathrm e}^{c \left(b x +a \right)}+\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{2}\right) \sqrt{2}}{4 b c}-\frac{i \ln \left({\mathrm e}^{c \left(b x +a \right)}+\left(-\frac{1}{2}+\frac{i}{2}\right) \sqrt{2}\right) \sqrt{2}}{4 b c}+\frac{i \ln \left({\mathrm e}^{c \left(b x +a \right)}+\left(\frac{1}{2}-\frac{i}{2}\right) \sqrt{2}\right) \sqrt{2}}{4 b c}-\frac{i {\mathrm e}^{c \left(b x +a \right)} \ln \left({\mathrm e}^{2 c \left(b x +a \right)}-i\right)}{2 b c}+\frac{{\mathrm e}^{c \left(b x +a \right)} \pi}{4 b c}+\frac{i {\mathrm e}^{c \left(b x +a \right)} \ln \left({\mathrm e}^{2 c \left(b x +a \right)}+i\right)}{2 b c}"," ",0,"-1/4/b/c*Pi*csgn((1+I)*(exp(2*c*(b*x+a))-I)/(exp(2*c*(b*x+a))-1))^3*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))-I)/(exp(2*c*(b*x+a))-1))^3*exp(c*(b*x+a))-1/4/b/c*Pi*csgn((1-I)*(exp(2*c*(b*x+a))+I)/(exp(2*c*(b*x+a))-1))^3*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))+I)/(exp(2*c*(b*x+a))-1))^3*exp(c*(b*x+a))+1/4/b/c*Pi*csgn((1+I)*(exp(2*c*(b*x+a))-I)/(exp(2*c*(b*x+a))-1))^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn((1-I)*(exp(2*c*(b*x+a))+I)/(exp(2*c*(b*x+a))-1))^2*exp(c*(b*x+a))+1/4*I/b/c*ln(exp(c*(b*x+a))-(1/2+1/2*I)*2^(1/2))*2^(1/2)-1/4*I/b/c*ln(exp(c*(b*x+a))+(1/2+1/2*I)*2^(1/2))*2^(1/2)-1/2*I/b/c*exp(c*(b*x+a))*ln(exp(2*c*(b*x+a))-I)+1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))-I)/(exp(2*c*(b*x+a))-1))*csgn((1+I)*(exp(2*c*(b*x+a))-I)/(exp(2*c*(b*x+a))-1))^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))-I))*csgn(I/(exp(2*c*(b*x+a))-1))*csgn(I*(exp(2*c*(b*x+a))-I)/(exp(2*c*(b*x+a))-1))*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))+I))*csgn(I/(exp(2*c*(b*x+a))-1))*csgn(I*(exp(2*c*(b*x+a))+I)/(exp(2*c*(b*x+a))-1))*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))-I))*csgn(I*(exp(2*c*(b*x+a))-I)/(exp(2*c*(b*x+a))-1))^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I/(exp(2*c*(b*x+a))-1))*csgn(I*(exp(2*c*(b*x+a))-I)/(exp(2*c*(b*x+a))-1))^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))+I))*csgn(I*(exp(2*c*(b*x+a))+I)/(exp(2*c*(b*x+a))-1))^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))+I)/(exp(2*c*(b*x+a))-1))*csgn((1-I)*(exp(2*c*(b*x+a))+I)/(exp(2*c*(b*x+a))-1))^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I/(exp(2*c*(b*x+a))-1))*csgn(I*(exp(2*c*(b*x+a))+I)/(exp(2*c*(b*x+a))-1))^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))-I)/(exp(2*c*(b*x+a))-1))*csgn((1+I)*(exp(2*c*(b*x+a))-I)/(exp(2*c*(b*x+a))-1))*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))+I)/(exp(2*c*(b*x+a))-1))*csgn((1-I)*(exp(2*c*(b*x+a))+I)/(exp(2*c*(b*x+a))-1))*exp(c*(b*x+a))-1/4*I/b/c*ln(exp(c*(b*x+a))+(-1/2+1/2*I)*2^(1/2))*2^(1/2)+1/4*I/b/c*ln(exp(c*(b*x+a))+(1/2-1/2*I)*2^(1/2))*2^(1/2)+1/2*I/b/c*exp(c*(b*x+a))*ln(exp(2*c*(b*x+a))+I)+1/4/b/c*exp(c*(b*x+a))*Pi+1/4/b/c*ln(exp(c*(b*x+a))+(1/2-1/2*I)*2^(1/2))*2^(1/2)-1/4/b/c*ln(exp(c*(b*x+a))-(1/2+1/2*I)*2^(1/2))*2^(1/2)-1/4/b/c*ln(exp(c*(b*x+a))+(-1/2+1/2*I)*2^(1/2))*2^(1/2)+1/4/b/c*ln(exp(c*(b*x+a))+(1/2+1/2*I)*2^(1/2))*2^(1/2)","C"
233,1,859,88,0.762000," ","int(exp(c*(b*x+a))*arccot(sech(b*c*x+a*c)),x)","\frac{i {\mathrm e}^{c \left(b x +a \right)} \ln \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)}{2 b c}-\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right) \mathrm{csgn}\left(\frac{i}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(\frac{i}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 c \left(b x +a \right)}+1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(i \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right) \mathrm{csgn}\left(\frac{i}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) \mathrm{csgn}\left(\frac{i \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(i \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)\right) \mathrm{csgn}\left(\frac{i \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(\frac{i}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right) \mathrm{csgn}\left(\frac{i \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \mathrm{csgn}\left(\frac{i \left(-{\mathrm e}^{2 c \left(b x +a \right)}-1+2 i {\mathrm e}^{c \left(b x +a \right)}\right)}{1+{\mathrm e}^{2 c \left(b x +a \right)}}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{i {\mathrm e}^{c \left(b x +a \right)} \ln \left({\mathrm e}^{2 c \left(b x +a \right)}+1-2 i {\mathrm e}^{c \left(b x +a \right)}\right)}{2 b c}+\frac{{\mathrm e}^{c \left(b x +a \right)} \pi}{2 b c}+\frac{\ln \left({\mathrm e}^{2 c \left(b x +a \right)}+\left(\sqrt{2}-1\right)^{2}\right) \sqrt{2}}{2 b c}-\frac{\ln \left({\mathrm e}^{2 c \left(b x +a \right)}+\left(1+\sqrt{2}\right)^{2}\right) \sqrt{2}}{2 b c}+\frac{2 a}{b}-\frac{\ln \left({\mathrm e}^{2 c \left(b x +a \right)}+\left(\sqrt{2}-1\right)^{2}\right)}{2 b c}-\frac{\ln \left({\mathrm e}^{2 c \left(b x +a \right)}+\left(1+\sqrt{2}\right)^{2}\right)}{2 b c}"," ",0,"1/2*I/b/c*exp(c*(b*x+a))*ln(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a)))-1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a))))*csgn(I*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a)))/(1+exp(2*c*(b*x+a))))^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a))))*csgn(I/(1+exp(2*c*(b*x+a))))*csgn(I*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a)))/(1+exp(2*c*(b*x+a))))*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a)))/(1+exp(2*c*(b*x+a))))^3*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I/(1+exp(2*c*(b*x+a))))*csgn(I*(exp(2*c*(b*x+a))+1+2*I*exp(c*(b*x+a)))/(1+exp(2*c*(b*x+a))))^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a))))*csgn(I/(1+exp(2*c*(b*x+a))))*csgn(I*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a)))/(1+exp(2*c*(b*x+a))))*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a))))*csgn(I*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a)))/(1+exp(2*c*(b*x+a))))^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I/(1+exp(2*c*(b*x+a))))*csgn(I*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a)))/(1+exp(2*c*(b*x+a))))^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(-exp(2*c*(b*x+a))-1+2*I*exp(c*(b*x+a)))/(1+exp(2*c*(b*x+a))))^3*exp(c*(b*x+a))-1/2*I/b/c*exp(c*(b*x+a))*ln(exp(2*c*(b*x+a))+1-2*I*exp(c*(b*x+a)))+1/2/b/c*exp(c*(b*x+a))*Pi+1/2/b/c*ln(exp(2*c*(b*x+a))+(2^(1/2)-1)^2)*2^(1/2)-1/2/b/c*ln(exp(2*c*(b*x+a))+(1+2^(1/2))^2)*2^(1/2)+2*a/b-1/2/b/c*ln(exp(2*c*(b*x+a))+(2^(1/2)-1)^2)-1/2/b/c*ln(exp(2*c*(b*x+a))+(1+2^(1/2))^2)","C"
234,1,903,46,0.595000," ","int(exp(c*(b*x+a))*arccot(csch(b*c*x+a*c)),x)","-\frac{i {\mathrm e}^{c \left(b x +a \right)} \ln \left({\mathrm e}^{c \left(b x +a \right)}-i\right)}{b c}+\frac{\pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}}{{\mathrm e}^{2 c \left(b x +a \right)}-1}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)\right)^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{2 b c}+\frac{\pi  \mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}+i\right)^{2}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}-\frac{\pi  \mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)\right)^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right) {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right)^{2} {\mathrm e}^{c \left(b x +a \right)}}{2 b c}-\frac{\pi  \mathrm{csgn}\left(i \left({\mathrm e}^{c \left(b x +a \right)}-i\right)^{2}\right)^{3} {\mathrm e}^{c \left(b x +a \right)}}{4 b c}+\frac{i {\mathrm e}^{c \left(b x +a \right)} \ln \left({\mathrm e}^{c \left(b x +a \right)}+i\right)}{b c}+\frac{{\mathrm e}^{c \left(b x +a \right)} \pi}{2 b c}+\frac{2 a}{b}-\frac{\ln \left(1+{\mathrm e}^{2 c \left(b x +a \right)}\right)}{b c}"," ",0,"-I/b/c*exp(c*(b*x+a))*ln(exp(c*(b*x+a))-I)+1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))+I)^2/(exp(2*c*(b*x+a))-1))^3*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))+I)^2)*csgn(I*(exp(c*(b*x+a))+I)^2/(exp(2*c*(b*x+a))-1))^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I/(exp(2*c*(b*x+a))-1))*csgn(I*(exp(c*(b*x+a))+I)^2/(exp(2*c*(b*x+a))-1))^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))+I)^2)*csgn(I/(exp(2*c*(b*x+a))-1))*csgn(I*(exp(c*(b*x+a))+I)^2/(exp(2*c*(b*x+a))-1))*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))-I)^2/(exp(2*c*(b*x+a))-1))^3*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))-I)^2)*csgn(I*(exp(c*(b*x+a))-I)^2/(exp(2*c*(b*x+a))-1))^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I/(exp(2*c*(b*x+a))-1))*csgn(I*(exp(c*(b*x+a))-I)^2/(exp(2*c*(b*x+a))-1))^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))-I)^2)*csgn(I/(exp(2*c*(b*x+a))-1))*csgn(I*(exp(c*(b*x+a))-I)^2/(exp(2*c*(b*x+a))-1))*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))+I))^2*csgn(I*(exp(c*(b*x+a))+I)^2)*exp(c*(b*x+a))-1/2/b/c*Pi*csgn(I*(exp(c*(b*x+a))+I))*csgn(I*(exp(c*(b*x+a))+I)^2)^2*exp(c*(b*x+a))+1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))+I)^2)^3*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))-I))^2*csgn(I*(exp(c*(b*x+a))-I)^2)*exp(c*(b*x+a))+1/2/b/c*Pi*csgn(I*(exp(c*(b*x+a))-I))*csgn(I*(exp(c*(b*x+a))-I)^2)^2*exp(c*(b*x+a))-1/4/b/c*Pi*csgn(I*(exp(c*(b*x+a))-I)^2)^3*exp(c*(b*x+a))+I/b/c*exp(c*(b*x+a))*ln(exp(c*(b*x+a))+I)+1/2/b/c*exp(c*(b*x+a))*Pi+2*a/b-ln(1+exp(2*c*(b*x+a)))/b/c","C"