1,1,46,38,0.039000," ","int(x^3*arctan(b*x^4+a),x)","\frac{\arctan \left(b \,x^{4}+a \right) x^{4}}{4}+\frac{\arctan \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*arctan(b*x^4+a)*x^4+1/4/b*arctan(b*x^4+a)*a-1/8*ln(1+(b*x^4+a)^2)/b","A"
2,1,140,43,0.294000," ","int(x^(n-1)*arctan(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{\ln \left(\frac{i+a}{b}+x^{n}\right)}{2 b n}-\frac{\ln \left(x^{n}-\frac{i-a}{b}\right)}{2 b n}+\frac{i \ln \left(\frac{i+a}{b}+x^{n}\right) a}{2 b n}-\frac{i \ln \left(x^{n}-\frac{i-a}{b}\right) a}{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/b/n*ln((I+a)/b+x^n)-1/2/b/n*ln(x^n-(I-a)/b)+1/2*I/b/n*ln((I+a)/b+x^n)*a-1/2*I/b/n*ln(x^n-(I-a)/b)*a","C"
3,1,211,110,0.050000," ","int(x^5*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","\frac{x^{6} \arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{6}+\frac{\sqrt{-e}\, x^{7} \sqrt{e \,x^{2}+d}}{48 d}-\frac{7 \sqrt{-e}\, x^{5} \sqrt{e \,x^{2}+d}}{288 e}+\frac{35 \sqrt{-e}\, d \,x^{3} \sqrt{e \,x^{2}+d}}{1152 e^{2}}-\frac{5 \sqrt{-e}\, d^{2} x \sqrt{e \,x^{2}+d}}{128 e^{3}}+\frac{5 \sqrt{-e}\, d^{3} \ln \left(x \sqrt{e}+\sqrt{e \,x^{2}+d}\right)}{96 e^{\frac{7}{2}}}-\frac{\sqrt{-e}\, x^{5} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{48 d e}+\frac{5 \sqrt{-e}\, x^{3} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{288 e^{2}}-\frac{5 \sqrt{-e}\, d x \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{384 e^{3}}"," ",0,"1/6*x^6*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))+1/48*(-e)^(1/2)/d*x^7*(e*x^2+d)^(1/2)-7/288*(-e)^(1/2)/e*x^5*(e*x^2+d)^(1/2)+35/1152*(-e)^(1/2)/e^2*d*x^3*(e*x^2+d)^(1/2)-5/128*(-e)^(1/2)/e^3*d^2*x*(e*x^2+d)^(1/2)+5/96*(-e)^(1/2)/e^(7/2)*d^3*ln(x*e^(1/2)+(e*x^2+d)^(1/2))-1/48*(-e)^(1/2)/d*x^5*(e*x^2+d)^(3/2)/e+5/288*(-e)^(1/2)/e^2*x^3*(e*x^2+d)^(3/2)-5/384*(-e)^(1/2)*d/e^3*x*(e*x^2+d)^(3/2)","A"
4,1,163,88,0.046000," ","int(x^3*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","\frac{x^{4} \arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{4}+\frac{\sqrt{-e}\, x^{5} \sqrt{e \,x^{2}+d}}{24 d}-\frac{5 \sqrt{-e}\, x^{3} \sqrt{e \,x^{2}+d}}{96 e}+\frac{\sqrt{-e}\, d x \sqrt{e \,x^{2}+d}}{16 e^{2}}-\frac{3 \sqrt{-e}\, d^{2} \ln \left(x \sqrt{e}+\sqrt{e \,x^{2}+d}\right)}{32 e^{\frac{5}{2}}}-\frac{\sqrt{-e}\, x^{3} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{24 d e}+\frac{\sqrt{-e}\, x \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{32 e^{2}}"," ",0,"1/4*x^4*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))+1/24*(-e)^(1/2)/d*x^5*(e*x^2+d)^(1/2)-5/96*(-e)^(1/2)/e*x^3*(e*x^2+d)^(1/2)+1/16*(-e)^(1/2)/e^2*d*x*(e*x^2+d)^(1/2)-3/32*(-e)^(1/2)/e^(5/2)*d^2*ln(x*e^(1/2)+(e*x^2+d)^(1/2))-1/24*(-e)^(1/2)/d*x^3*(e*x^2+d)^(3/2)/e+1/32*(-e)^(1/2)/e^2*x*(e*x^2+d)^(3/2)","A"
5,1,116,66,0.041000," ","int(x*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","\frac{x^{2} \arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{2}+\frac{\sqrt{-e}\, x^{3} \sqrt{e \,x^{2}+d}}{8 d}-\frac{\sqrt{-e}\, x \sqrt{e \,x^{2}+d}}{8 e}+\frac{\sqrt{-e}\, d \ln \left(x \sqrt{e}+\sqrt{e \,x^{2}+d}\right)}{4 e^{\frac{3}{2}}}-\frac{\sqrt{-e}\, x \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{8 d e}"," ",0,"1/2*x^2*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))+1/8*(-e)^(1/2)/d*x^3*(e*x^2+d)^(1/2)-1/8*(-e)^(1/2)/e*x*(e*x^2+d)^(1/2)+1/4*(-e)^(1/2)/e^(3/2)*d*ln(x*e^(1/2)+(e*x^2+d)^(1/2))-1/8*(-e)^(1/2)/d*x*(e*x^2+d)^(3/2)/e","A"
6,0,0,240,0.268000," ","int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x,x)","\int \frac{\arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{x}\, dx"," ",0,"int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x,x)","F"
7,1,67,45,0.040000," ","int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^3,x)","-\frac{\arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{2 x^{2}}-\frac{\sqrt{-e}\, \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{2 d^{2} x}+\frac{\sqrt{-e}\, e x \sqrt{e \,x^{2}+d}}{2 d^{2}}"," ",0,"-1/2*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^2-1/2*(-e)^(1/2)/d^2/x*(e*x^2+d)^(3/2)+1/2*(-e)^(1/2)/d^2*e*x*(e*x^2+d)^(1/2)","A"
8,1,69,67,0.041000," ","int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^5,x)","-\frac{\arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{4 x^{4}}+\frac{\sqrt{-e}\, e \sqrt{e \,x^{2}+d}}{4 d^{2} x}-\frac{\sqrt{-e}\, \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{12 d^{2} x^{3}}"," ",0,"-1/4*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^4+1/4*(-e)^(1/2)*e/d^2/x*(e*x^2+d)^(1/2)-1/12*(-e)^(1/2)/d^2/x^3*(e*x^2+d)^(3/2)","A"
9,1,117,89,0.043000," ","int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^7,x)","-\frac{\arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{6 x^{6}}+\frac{\sqrt{-e}\, e \sqrt{e \,x^{2}+d}}{18 d^{2} x^{3}}-\frac{\sqrt{-e}\, e^{2} \sqrt{e \,x^{2}+d}}{9 d^{3} x}-\frac{\sqrt{-e}\, \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{30 d^{2} x^{5}}+\frac{\sqrt{-e}\, e \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{45 d^{3} x^{3}}"," ",0,"-1/6*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^6+1/18*(-e)^(1/2)*e/d^2/x^3*(e*x^2+d)^(1/2)-1/9*(-e)^(1/2)*e^2/d^3/x*(e*x^2+d)^(1/2)-1/30*(-e)^(1/2)/d^2/x^5*(e*x^2+d)^(3/2)+1/45*(-e)^(1/2)/d^3*e/x^3*(e*x^2+d)^(3/2)","A"
10,1,167,111,0.046000," ","int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^9,x)","-\frac{\arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{8 x^{8}}+\frac{\sqrt{-e}\, e \sqrt{e \,x^{2}+d}}{40 d^{2} x^{5}}-\frac{\sqrt{-e}\, e^{2} \sqrt{e \,x^{2}+d}}{30 d^{3} x^{3}}+\frac{\sqrt{-e}\, e^{3} \sqrt{e \,x^{2}+d}}{15 d^{4} x}-\frac{\sqrt{-e}\, \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{56 d^{2} x^{7}}+\frac{\sqrt{-e}\, e \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{70 d^{3} x^{5}}-\frac{\sqrt{-e}\, e^{2} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{105 d^{4} x^{3}}"," ",0,"-1/8*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^8+1/40*(-e)^(1/2)*e/d^2/x^5*(e*x^2+d)^(1/2)-1/30*(-e)^(1/2)*e^2/d^3/x^3*(e*x^2+d)^(1/2)+1/15*(-e)^(1/2)*e^3/d^4/x*(e*x^2+d)^(1/2)-1/56*(-e)^(1/2)/d^2/x^7*(e*x^2+d)^(3/2)+1/70*(-e)^(1/2)/d^3*e/x^5*(e*x^2+d)^(3/2)-1/105*(-e)^(1/2)/d^4*e^2/x^3*(e*x^2+d)^(3/2)","A"
11,1,230,94,0.052000," ","int(x^6*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","\frac{x^{7} \arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{7}+\frac{\sqrt{-e}\, x^{8} \sqrt{e \,x^{2}+d}}{63 d}-\frac{8 \sqrt{-e}\, x^{6} \sqrt{e \,x^{2}+d}}{441 e}+\frac{16 \sqrt{-e}\, d \,x^{4} \sqrt{e \,x^{2}+d}}{735 e^{2}}-\frac{64 \sqrt{-e}\, d^{2} x^{2} \sqrt{e \,x^{2}+d}}{2205 e^{3}}+\frac{128 \sqrt{-e}\, d^{3} \sqrt{e \,x^{2}+d}}{2205 e^{4}}-\frac{\sqrt{-e}\, x^{6} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{63 d e}+\frac{2 \sqrt{-e}\, x^{4} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{147 e^{2}}-\frac{8 \sqrt{-e}\, d \,x^{2} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{735 e^{3}}+\frac{16 \sqrt{-e}\, d^{2} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{2205 e^{4}}"," ",0,"1/7*x^7*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))+1/63*(-e)^(1/2)/d*x^8*(e*x^2+d)^(1/2)-8/441*(-e)^(1/2)/e*x^6*(e*x^2+d)^(1/2)+16/735*(-e)^(1/2)/e^2*d*x^4*(e*x^2+d)^(1/2)-64/2205*(-e)^(1/2)/e^3*d^2*x^2*(e*x^2+d)^(1/2)+128/2205*(-e)^(1/2)/e^4*d^3*(e*x^2+d)^(1/2)-1/63*(-e)^(1/2)/d*x^6*(e*x^2+d)^(3/2)/e+2/147*(-e)^(1/2)/e^2*x^4*(e*x^2+d)^(3/2)-8/735*(-e)^(1/2)*d/e^3*x^2*(e*x^2+d)^(3/2)+16/2205*(-e)^(1/2)*d^2/e^4*(e*x^2+d)^(3/2)","B"
12,1,180,75,0.045000," ","int(x^4*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","\frac{x^{5} \arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{5}+\frac{\sqrt{-e}\, x^{6} \sqrt{e \,x^{2}+d}}{35 d}-\frac{6 \sqrt{-e}\, x^{4} \sqrt{e \,x^{2}+d}}{175 e}+\frac{8 \sqrt{-e}\, d \,x^{2} \sqrt{e \,x^{2}+d}}{175 e^{2}}-\frac{16 \sqrt{-e}\, d^{2} \sqrt{e \,x^{2}+d}}{175 e^{3}}-\frac{\sqrt{-e}\, x^{4} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{35 d e}+\frac{4 \sqrt{-e}\, x^{2} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{175 e^{2}}-\frac{8 \sqrt{-e}\, d \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{525 e^{3}}"," ",0,"1/5*x^5*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))+1/35*(-e)^(1/2)/d*x^6*(e*x^2+d)^(1/2)-6/175*(-e)^(1/2)/e*x^4*(e*x^2+d)^(1/2)+8/175*(-e)^(1/2)/e^2*d*x^2*(e*x^2+d)^(1/2)-16/175*(-e)^(1/2)/e^3*d^2*(e*x^2+d)^(1/2)-1/35*(-e)^(1/2)/d*x^4*(e*x^2+d)^(3/2)/e+4/175*(-e)^(1/2)/e^2*x^2*(e*x^2+d)^(3/2)-8/525*(-e)^(1/2)*d/e^3*(e*x^2+d)^(3/2)","B"
13,1,132,56,0.043000," ","int(x^2*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","\frac{x^{3} \arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{3}+\frac{\sqrt{-e}\, x^{4} \sqrt{e \,x^{2}+d}}{15 d}-\frac{4 \sqrt{-e}\, x^{2} \sqrt{e \,x^{2}+d}}{45 e}+\frac{8 \sqrt{-e}\, d \sqrt{e \,x^{2}+d}}{45 e^{2}}-\frac{\sqrt{-e}\, x^{2} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{15 d e}+\frac{2 \sqrt{-e}\, \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{45 e^{2}}"," ",0,"1/3*x^3*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))+1/15*(-e)^(1/2)/d*x^4*(e*x^2+d)^(1/2)-4/45*(-e)^(1/2)/e*x^2*(e*x^2+d)^(1/2)+8/45*(-e)^(1/2)/e^2*d*(e*x^2+d)^(1/2)-1/15*(-e)^(1/2)/d*x^2*(e*x^2+d)^(3/2)/e+2/45*(-e)^(1/2)/e^2*(e*x^2+d)^(3/2)","B"
14,1,84,35,0.042000," ","int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","x \arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)+\frac{\sqrt{-e}\, x^{2} \sqrt{e \,x^{2}+d}}{3 d}-\frac{2 \sqrt{-e}\, \sqrt{e \,x^{2}+d}}{3 e}-\frac{\sqrt{-e}\, \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{3 d e}"," ",0,"x*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))+1/3*(-e)^(1/2)/d*x^2*(e*x^2+d)^(1/2)-2/3*(-e)^(1/2)/e*(e*x^2+d)^(1/2)-1/3*(-e)^(1/2)/d/e*(e*x^2+d)^(3/2)","B"
15,1,57,47,0.039000," ","int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^2,x)","-\frac{\arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{x}-\frac{\sqrt{-e}\, \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{e \,x^{2}+d}}{x}\right)}{\sqrt{d}}"," ",0,"-arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x-(-e)^(1/2)/d^(1/2)*ln((2*d+2*d^(1/2)*(e*x^2+d)^(1/2))/x)","A"
16,1,100,69,0.042000," ","int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^4,x)","-\frac{\arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{3 x^{3}}+\frac{\sqrt{-e}\, e \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{e \,x^{2}+d}}{x}\right)}{6 d^{\frac{3}{2}}}-\frac{\sqrt{-e}\, \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{6 d^{2} x^{2}}+\frac{\sqrt{-e}\, e \sqrt{e \,x^{2}+d}}{6 d^{2}}"," ",0,"-1/3*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^3+1/6*(-e)^(1/2)*e/d^(3/2)*ln((2*d+2*d^(1/2)*(e*x^2+d)^(1/2))/x)-1/6*(-e)^(1/2)/d^2/x^2*(e*x^2+d)^(3/2)+1/6*(-e)^(1/2)/d^2*e*(e*x^2+d)^(1/2)","A"
17,1,150,91,0.041000," ","int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^6,x)","-\frac{\arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{5 x^{5}}-\frac{\sqrt{-e}\, \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{20 d^{2} x^{4}}+\frac{\sqrt{-e}\, e \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{40 d^{3} x^{2}}-\frac{3 \sqrt{-e}\, e^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{e \,x^{2}+d}}{x}\right)}{40 d^{\frac{5}{2}}}-\frac{\sqrt{-e}\, e^{2} \sqrt{e \,x^{2}+d}}{40 d^{3}}+\frac{\sqrt{-e}\, e \sqrt{e \,x^{2}+d}}{10 d^{2} x^{2}}"," ",0,"-1/5*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^5-1/20*(-e)^(1/2)/d^2/x^4*(e*x^2+d)^(3/2)+1/40*(-e)^(1/2)/d^3*e/x^2*(e*x^2+d)^(3/2)-3/40*(-e)^(1/2)/d^(5/2)*e^2*ln((2*d+2*d^(1/2)*(e*x^2+d)^(1/2))/x)-1/40*(-e)^(1/2)/d^3*e^2*(e*x^2+d)^(1/2)+1/10*(-e)^(1/2)*e/d^2/x^2*(e*x^2+d)^(1/2)","A"
18,0,0,190,0.236000," ","int(x^(9/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","\int x^{\frac{9}{2}} \arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)\, dx"," ",0,"int(x^(9/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","F"
19,0,0,168,0.237000," ","int(x^(5/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","\int x^{\frac{5}{2}} \arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)\, dx"," ",0,"int(x^(5/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","F"
20,0,0,148,0.247000," ","int(x^(1/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","\int \sqrt{x}\, \arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)\, dx"," ",0,"int(x^(1/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","F"
21,0,0,129,0.237000," ","int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(3/2),x)","\int \frac{\arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{x^{\frac{3}{2}}}\, dx"," ",0,"int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(3/2),x)","F"
22,0,0,151,0.237000," ","int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(7/2),x)","\int \frac{\arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{x^{\frac{7}{2}}}\, dx"," ",0,"int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(7/2),x)","F"
23,0,0,173,0.233000," ","int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(11/2),x)","\int \frac{\arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{x^{\frac{11}{2}}}\, dx"," ",0,"int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(11/2),x)","F"
24,0,0,195,0.237000," ","int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(15/2),x)","\int \frac{\arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{x^{\frac{15}{2}}}\, dx"," ",0,"int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(15/2),x)","F"
25,0,0,310,0.234000," ","int(x^(7/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","\int x^{\frac{7}{2}} \arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)\, dx"," ",0,"int(x^(7/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","F"
26,0,0,288,0.234000," ","int(x^(3/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","\int x^{\frac{3}{2}} \arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)\, dx"," ",0,"int(x^(3/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x)","F"
27,0,0,268,0.240000," ","int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(1/2),x)","\int \frac{\arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{\sqrt{x}}\, dx"," ",0,"int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(1/2),x)","F"
28,0,0,292,0.235000," ","int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(5/2),x)","\int \frac{\arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{x^{\frac{5}{2}}}\, dx"," ",0,"int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(5/2),x)","F"
29,0,0,315,0.233000," ","int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(9/2),x)","\int \frac{\arctan \left(\frac{x \sqrt{-e}}{\sqrt{e \,x^{2}+d}}\right)}{x^{\frac{9}{2}}}\, dx"," ",0,"int(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(9/2),x)","F"
30,1,43,42,0.046000," ","int(arctan(x^2+x+1)/x^2,x)","\frac{\arctan \left(x +1\right)}{2}-\frac{\arctan \left(x^{2}+x +1\right)}{x}+\frac{\ln \left(x \right)}{2}-\frac{\ln \left(x^{2}+1\right)}{2}+\frac{\ln \left(x^{2}+2 x +2\right)}{4}"," ",0,"1/2*arctan(x+1)-arctan(x^2+x+1)/x+1/2*ln(x)-1/2*ln(x^2+1)+1/4*ln(x^2+2*x+2)","A"
31,0,0,38,2.563000," ","int((a+b*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x)","\int \frac{\left(a +b \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)\right)^{n}}{-c^{2} x^{2}+1}\, dx"," ",0,"int((a+b*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x)","F"
32,1,1631,360,1.991000," ","int((a+b*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^3/(-c^2*x^2+1),x)","\frac{6 i a \,b^{2} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, -\frac{1+\frac{i \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} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, -\frac{\left(1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{c}+\frac{6 i a \,b^{2} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, \frac{1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{3 a^{2} b \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(\frac{\left(1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}+1\right)}{c}-\frac{3 i a^{2} b \dilog \left(\frac{\left(1+\frac{i \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(1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{2 c}-\frac{3 i b^{3} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \polylog \left(2, -\frac{\left(1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{2 c}+\frac{3 i b^{3} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \polylog \left(2, \frac{1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{3 i b^{3} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \polylog \left(2, -\frac{1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{3 a \,b^{2} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(\frac{\left(1+\frac{i \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} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1-\frac{1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}-\frac{3 a \,b^{2} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1+\frac{1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}-\frac{3 a^{2} b \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1-\frac{\left(1+\frac{i \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} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3} \ln \left(\frac{\left(1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}+1\right)}{c}-\frac{b^{3} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3} \ln \left(1-\frac{1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}-\frac{b^{3} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3} \ln \left(1+\frac{1+\frac{i \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(1+\frac{i \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{1+\frac{i \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{1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{3 b^{3} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(3, -\frac{\left(1+\frac{i \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} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(3, \frac{1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}-\frac{6 b^{3} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(3, -\frac{1+\frac{i \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(1+\frac{i \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{1+\frac{i \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{1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}"," ",0,"3*a^2*b/c*arctan((-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)+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)+1)+3/2*I*a^2*b/c*dilog(1-(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))-3/2*I*b^3/c*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*polylog(2,-(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))+3*I*b^3/c*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*polylog(2,(1+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*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*polylog(2,-(1+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*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,-(1+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*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,(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*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,-(1+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*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln((1+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*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1-(1+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*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1+(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*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1-(1+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,-(1+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,(1+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,-(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))+b^3/c*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3*ln((1+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*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(3,-(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))-b^3/c*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3*ln(1-(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*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(3,(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))-b^3/c*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3*ln(1+(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*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(3,-(1+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,-(1+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,(1+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,-(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))","B"
33,1,837,240,1.325000," ","int((a+b*arctan((-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} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(\frac{\left(1+\frac{i \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} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, -\frac{\left(1+\frac{i \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(1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{2 c}-\frac{b^{2} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1-\frac{1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{2 i b^{2} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, \frac{1+\frac{i \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{1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}-\frac{b^{2} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1+\frac{1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}+\frac{2 i b^{2} \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, -\frac{1+\frac{i \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{1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}}{\sqrt{\frac{-c x +1}{c x +1}+1}}\right)}{c}-\frac{2 a b \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1-\frac{\left(1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{c}+\frac{2 a b \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(\frac{\left(1+\frac{i \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(1+\frac{i \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(1+\frac{i \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*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln((1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1)+1)-I*b^2/c*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,-(1+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,-(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))-b^2/c*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1-(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*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,(1+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,(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))-b^2/c*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1+(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*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,-(1+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,-(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2))/((-c*x+1)/(c*x+1)+1)^(1/2))-2*a*b/c*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1-(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))+2*a*b/c*arctan((-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)+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)+1)+I*a*b/c*dilog(1-(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))","B"
34,1,263,78,0.796000," ","int((a+b*arctan((-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 \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1-\frac{\left(1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{\frac{-c x +1}{c x +1}+1}\right)}{c}+\frac{b \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(\frac{\left(1+\frac{i \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(1+\frac{i \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(1+\frac{i \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*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1-(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))+b/c*arctan((-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)+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)+1)+1/2*I*b/c*dilog(1-(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2))^2/((-c*x+1)/(c*x+1)+1))","B"
35,0,0,38,1.336000," ","int(1/(-c^2*x^2+1)/(a+b*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))),x)","\int \frac{1}{\left(-c^{2} x^{2}+1\right) \left(a +b \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)\right)}\, dx"," ",0,"int(1/(-c^2*x^2+1)/(a+b*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2))),x)","F"
36,0,0,38,1.260000," ","int(1/(-c^2*x^2+1)/(a+b*arctan((-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 \arctan \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)\right)^{2}}\, dx"," ",0,"int(1/(-c^2*x^2+1)/(a+b*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2,x)","F"
37,1,41,37,0.185000," ","int(x^m*arctan(tan(b*x+a)),x)","\frac{b \,x^{2} {\mathrm e}^{m \ln \left(x \right)}}{2+m}+\frac{\left(\arctan \left(\tan \left(b x +a \right)\right)-b x \right) x \,{\mathrm e}^{m \ln \left(x \right)}}{1+m}"," ",0,"b/(2+m)*x^2*exp(m*ln(x))+(arctan(tan(b*x+a))-b*x)/(1+m)*x*exp(m*ln(x))","A"
38,1,20,19,0.177000," ","int(x^2*arctan(tan(b*x+a)),x)","-\frac{b \,x^{4}}{12}+\frac{x^{3} \arctan \left(\tan \left(b x +a \right)\right)}{3}"," ",0,"-1/12*b*x^4+1/3*x^3*arctan(tan(b*x+a))","A"
39,1,20,19,0.177000," ","int(x*arctan(tan(b*x+a)),x)","-\frac{b \,x^{3}}{6}+\frac{x^{2} \arctan \left(\tan \left(b x +a \right)\right)}{2}"," ",0,"-1/6*b*x^3+1/2*x^2*arctan(tan(b*x+a))","A"
40,1,15,14,0.038000," ","int(arctan(tan(b*x+a)),x)","\frac{\arctan \left(\tan \left(b x +a \right)\right)^{2}}{2 b}"," ",0,"1/2*arctan(tan(b*x+a))^2/b","A"
41,1,21,21,0.186000," ","int(arctan(tan(b*x+a))/x,x)","\ln \left(x \right) \arctan \left(\tan \left(b x +a \right)\right)-\ln \left(x \right) x b +b x"," ",0,"ln(x)*arctan(tan(b*x+a))-ln(x)*x*b+b*x","A"
42,1,56,42,0.312000," ","int(x^m*(1/2*Pi-arccot(cot(b*x+a))),x)","\frac{\pi  \,x^{1+m}}{2+2 m}-\frac{b \,x^{2} {\mathrm e}^{m \ln \left(x \right)}}{2+m}-\frac{\left(\mathrm{arccot}\left(\cot \left(b x +a \right)\right)-b x \right) x \,{\mathrm e}^{m \ln \left(x \right)}}{1+m}"," ",0,"1/2*Pi*x^(1+m)/(1+m)-b/(2+m)*x^2*exp(m*ln(x))-(arccot(cot(b*x+a))-b*x)/(1+m)*x*exp(m*ln(x))","A"
43,1,65,25,0.434000," ","int(x^2*(1/2*Pi-arccot(cot(b*x+a))),x)","\frac{\pi  \,x^{3}}{6}-\frac{x^{3} \mathrm{arccot}\left(\cot \left(b x +a \right)\right)}{3}-\frac{-\frac{\left(b x +a \right)^{4}}{4}+a \left(b x +a \right)^{3}-\frac{3 \left(b x +a \right)^{2} a^{2}}{2}+\left(b x +a \right) a^{3}}{3 b^{3}}"," ",0,"1/6*Pi*x^3-1/3*x^3*arccot(cot(b*x+a))-1/3/b^3*(-1/4*(b*x+a)^4+a*(b*x+a)^3-3/2*(b*x+a)^2*a^2+(b*x+a)*a^3)","B"
44,1,54,25,0.440000," ","int(x*(1/2*Pi-arccot(cot(b*x+a))),x)","\frac{\pi  \,x^{2}}{4}-\frac{x^{2} \mathrm{arccot}\left(\cot \left(b x +a \right)\right)}{2}-\frac{-\frac{\left(b x +a \right)^{3}}{3}+\left(b x +a \right)^{2} a -a^{2} \left(b x +a \right)}{2 b^{2}}"," ",0,"1/4*Pi*x^2-1/2*x^2*arccot(cot(b*x+a))-1/2/b^2*(-1/3*(b*x+a)^3+(b*x+a)^2*a-a^2*(b*x+a))","B"
45,1,51,20,0.045000," ","int(1/2*Pi-arccot(cot(b*x+a)),x)","\frac{\pi  x}{2}-\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,"1/2*Pi*x-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"
46,1,35,24,0.386000," ","int((1/2*Pi-arccot(cot(b*x+a)))/x,x)","\frac{\pi  \ln \left(x \right)}{2}-b x -a \ln \left(x \right)-\ln \left(x \right) \left(\mathrm{arccot}\left(\cot \left(b x +a \right)\right)-b x -a \right)"," ",0,"1/2*Pi*ln(x)-b*x-a*ln(x)-ln(x)*(arccot(cot(b*x+a))-b*x-a)","A"
47,1,15,14,0.036000," ","int(arctan(tan(b*x+a)),x)","\frac{\arctan \left(\tan \left(b x +a \right)\right)^{2}}{2 b}"," ",0,"1/2*arctan(tan(b*x+a))^2/b","A"
48,1,8040,341,65.269000," ","int(x^2*arctan(c+d*tan(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
49,1,7648,257,6.247000," ","int(x*arctan(c+d*tan(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
50,1,1002,168,1.216000," ","int(arctan(c+d*tan(b*x+a)),x)","\frac{\arctan \left(\tan \left(b x +a \right)\right) \arctan \left(c +d \tan \left(b x +a \right)\right)}{b}+\frac{i \arctan \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right) \ln \left(1-\frac{\left(-i d +c -i\right) \left(1+i \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)\right)^{2}}{\left(\left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)^{2}+1\right) \left(-i d -c +i\right)}\right)}{2 b}+\frac{\arctan \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)^{2}}{2 b}+\frac{\polylog \left(2, \frac{\left(-i d +c -i\right) \left(1+i \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)\right)^{2}}{\left(\left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)^{2}+1\right) \left(-i d -c +i\right)}\right)}{4 b}+\frac{d \ln \left(1-\frac{\left(-i d +c +i\right) \left(1+i \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)\right)^{2}}{\left(\left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)^{2}+1\right) \left(-i d -c -i\right)}\right) \arctan \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)}{2 b \left(i d +c +i\right)}+\frac{\ln \left(1-\frac{\left(-i d +c +i\right) \left(1+i \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)\right)^{2}}{\left(\left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)^{2}+1\right) \left(-i d -c -i\right)}\right) \arctan \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)}{2 b \left(i d +c +i\right)}-\frac{i \ln \left(1-\frac{\left(-i d +c +i\right) \left(1+i \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)\right)^{2}}{\left(\left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)^{2}+1\right) \left(-i d -c -i\right)}\right) \arctan \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right) c}{2 b \left(i d +c +i\right)}-\frac{i d \arctan \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)^{2}}{2 b \left(i d +c +i\right)}-\frac{i d \polylog \left(2, \frac{\left(-i d +c +i\right) \left(1+i \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)\right)^{2}}{\left(\left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)^{2}+1\right) \left(-i d -c -i\right)}\right)}{4 b \left(i d +c +i\right)}-\frac{i \arctan \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)^{2}}{2 b \left(i d +c +i\right)}-\frac{\arctan \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)^{2} c}{2 b \left(i d +c +i\right)}-\frac{i \polylog \left(2, \frac{\left(-i d +c +i\right) \left(1+i \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)\right)^{2}}{\left(\left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)^{2}+1\right) \left(-i d -c -i\right)}\right)}{4 b \left(i d +c +i\right)}-\frac{\polylog \left(2, \frac{\left(-i d +c +i\right) \left(1+i \left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)\right)^{2}}{\left(\left(\frac{c +d \tan \left(b x +a \right)}{d}-\frac{c}{d}\right)^{2}+1\right) \left(-i d -c -i\right)}\right) c}{4 b \left(i d +c +i\right)}"," ",0,"1/b*arctan(tan(b*x+a))*arctan(c+d*tan(b*x+a))+1/2*I/b*arctan((c+d*tan(b*x+a))/d-c/d)*ln(1-(-I*d-I+c)*(1+I*((c+d*tan(b*x+a))/d-c/d))^2/(((c+d*tan(b*x+a))/d-c/d)^2+1)/(-I*d+I-c))+1/2/b*arctan((c+d*tan(b*x+a))/d-c/d)^2+1/4/b*polylog(2,(-I*d-I+c)*(1+I*((c+d*tan(b*x+a))/d-c/d))^2/(((c+d*tan(b*x+a))/d-c/d)^2+1)/(-I*d+I-c))+1/2*d/b/(I+I*d+c)*ln(1-(-I*d+I+c)*(1+I*((c+d*tan(b*x+a))/d-c/d))^2/(((c+d*tan(b*x+a))/d-c/d)^2+1)/(-I*d-I-c))*arctan((c+d*tan(b*x+a))/d-c/d)+1/2/b/(I+I*d+c)*ln(1-(-I*d+I+c)*(1+I*((c+d*tan(b*x+a))/d-c/d))^2/(((c+d*tan(b*x+a))/d-c/d)^2+1)/(-I*d-I-c))*arctan((c+d*tan(b*x+a))/d-c/d)-1/2*I/b/(I+I*d+c)*ln(1-(-I*d+I+c)*(1+I*((c+d*tan(b*x+a))/d-c/d))^2/(((c+d*tan(b*x+a))/d-c/d)^2+1)/(-I*d-I-c))*arctan((c+d*tan(b*x+a))/d-c/d)*c-1/2*I*d/b/(I+I*d+c)*arctan((c+d*tan(b*x+a))/d-c/d)^2-1/4*I*d/b/(I+I*d+c)*polylog(2,(-I*d+I+c)*(1+I*((c+d*tan(b*x+a))/d-c/d))^2/(((c+d*tan(b*x+a))/d-c/d)^2+1)/(-I*d-I-c))-1/2*I/b/(I+I*d+c)*arctan((c+d*tan(b*x+a))/d-c/d)^2-1/2/b/(I+I*d+c)*arctan((c+d*tan(b*x+a))/d-c/d)^2*c-1/4*I/b/(I+I*d+c)*polylog(2,(-I*d+I+c)*(1+I*((c+d*tan(b*x+a))/d-c/d))^2/(((c+d*tan(b*x+a))/d-c/d)^2+1)/(-I*d-I-c))-1/4/b/(I+I*d+c)*polylog(2,(-I*d+I+c)*(1+I*((c+d*tan(b*x+a))/d-c/d))^2/(((c+d*tan(b*x+a))/d-c/d)^2+1)/(-I*d-I-c))*c","B"
51,0,0,17,0.719000," ","int(arctan(c+d*tan(b*x+a))/x,x)","\int \frac{\arctan \left(c +d \tan \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arctan(c+d*tan(b*x+a))/x,x)","F"
52,1,1532,123,6.712000," ","int(x^2*arctan(c+(1+I*c)*tan(b*x+a)),x)","-\frac{b \,x^{4}}{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(\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{i \ln \left(1-i {\mathrm e}^{2 i \left(b x +a \right)} c \right) x \,a^{2}}{2 b^{2}}+\frac{\pi  \,x^{3}}{6}-\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{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{{\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)^{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{i x^{3} \ln \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{6}-\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(\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{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(\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{\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(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{3}}{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(\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{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(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 {\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{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{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}}-\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(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 \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{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(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}"," ",0,"-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(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)))^2-1/12*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)))*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(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))^3+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(exp(2*I*(b*x+a))*c+I)-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))-1/12*b*x^4+1/8*polylog(4,I*c*exp(2*I*(b*x+a)))/b^3-1/3*I*x^3*ln(exp(I*(b*x+a)))-1/6*I*x^3*ln(c-I)+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((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))^3+1/2*I/b^2*ln(1-I*exp(2*I*(b*x+a))*c)*x*a^2+1/3*I/b^3*ln(1-I*exp(2*I*(b*x+a))*c)*a^3+1/6*Pi*x^3+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)/(exp(2*I*(b*x+a))+1))^2-1/6*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+1/4/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))-1/12*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))*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/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(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)/(exp(2*I*(b*x+a))+1))*csgn(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))-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*x^3*Pi*csgn(I*exp(2*I*(b*x+a)))^3+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))*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"
53,1,1497,98,6.033000," ","int(x*arctan(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(\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(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{\pi  \,x^{2}}{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{\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{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}^{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{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{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)} \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(\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 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)^{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{i x^{2} \ln \left({\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{4}-\frac{i x^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{2}-\frac{i x^{2} \ln \left(c -i\right)}{4}-\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)} 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(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{3}}{8}-\frac{b \,x^{3}}{6}+\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(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 \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 \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}"," ",0,"-1/2*I/b*ln(1-I*exp(2*I*(b*x+a))*c)*x*a-1/4*I*x^2*ln(1-I*exp(2*I*(b*x+a))*c)+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))^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(exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))+1))^3-1/4/b^2*polylog(2,I*c*exp(2*I*(b*x+a)))*a+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))*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)+1/4*Pi*x^2-1/2*I*x^2*ln(exp(I*(b*x+a)))-1/4*I*x^2*ln(c-I)-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))-1/8*x^2*Pi*csgn(I*(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)/(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(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/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((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)))^3+1/8*x^2*Pi*csgn(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))+1))^3-1/4*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))-1/4*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^2-1/6*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*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))*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))","C"
54,1,1489,69,0.509000," ","int(arctan(c+(1+I*c)*tan(b*x+a)),x)","\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)^{2} c^{2}}{8 \left(i c +1\right) b \left(i-c \right)}-\frac{\arctan \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{\ln \left(-\frac{i \left(i+c +\left(i c +1\right) \tan \left(b x +a \right)\right)}{2}\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(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{\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{\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{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{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{\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{\arctan \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{\arctan \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) \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{2 i \arctan \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 \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{\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{\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{\arctan \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{i \ln \left(-\frac{i \left(i+c +\left(i c +1\right) \tan \left(b x +a \right)\right)}{2}\right) \ln \left(c +\left(i c +1\right) \tan \left(b x +a \right)-i\right)}{4 \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) c^{2}}{4 \left(i c +1\right) b \left(i-c \right)}+\frac{2 i \arctan \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(-\frac{i \left(i+c +\left(i c +1\right) \tan \left(b x +a \right)\right)}{2}\right) \ln \left(c +\left(i c +1\right) \tan \left(b x +a \right)-i\right) c^{2}}{4 \left(i c +1\right) b \left(i-c \right)}"," ",0,"-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^2-2*I/(1+I*c)/b*arctan(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*arctan(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(-1/2*I*(I+c+(1+I*c)*tan(b*x+a)))*ln(c+(1+I*c)*tan(b*x+a)-I)*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))-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/(1+I*c)/b/(I-c)*ln(c+(1+I*c)*tan(b*x+a)-I)^2*c-1/(1+I*c)/b*arctan(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*arctan(c+(1+I*c)*tan(b*x+a))/(2*I-2*c)*ln(c+(1+I*c)*tan(b*x+a)-I)-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+1/2/(1+I*c)/b/(I-c)*dilog(-1/2*I*(I+c+(1+I*c)*tan(b*x+a)))*c+1/4*I/(1+I*c)/b/(I-c)*dilog(1/2*(I+c+(1+I*c)*tan(b*x+a))/c)-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/(1+I*c)/b*arctan(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*I/(1+I*c)/b/(I-c)*ln(-1/2*I*(I+c+(1+I*c)*tan(b*x+a)))*ln(c+(1+I*c)*tan(b*x+a)-I)+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)*dilog((c+(1+I*c)*tan(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)*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/(1+I*c)/b*arctan(c+(1+I*c)*tan(b*x+a))/(2*I-2*c)*ln(c+(1+I*c)*tan(b*x+a)-I)*c^2+1/2/(1+I*c)/b/(I-c)*ln(-1/2*I*(I+c+(1+I*c)*tan(b*x+a)))*ln(c+(1+I*c)*tan(b*x+a)-I)*c-1/4*I/(1+I*c)/b/(I-c)*dilog(1/2*(I+c+(1+I*c)*tan(b*x+a))/c)*c^2","B"
55,0,0,22,1.638000," ","int(arctan(c+(1+I*c)*tan(b*x+a))/x,x)","\int \frac{\arctan \left(c +\left(i c +1\right) \tan \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arctan(c+(1+I*c)*tan(b*x+a))/x,x)","F"
56,1,1533,124,6.704000," ","int(x^2*arctan(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}}{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 \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 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(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{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)^{3}}{12}+\frac{x^{2} \polylog \left(2, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4 b}+\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{\polylog \left(2, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a^{2}}{4 b^{3}}-\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^{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)} 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(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{i x^{3} \ln \left(1+i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{6}-\frac{i x^{3} \ln \left({\mathrm e}^{2 i \left(b x +a \right)} c -i\right)}{6}+\frac{i x^{3} \ln \left(i+c \right)}{6}+\frac{\pi  \,x^{3}}{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 a^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{3}}-\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(-{\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{6 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)^{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)}{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{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(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{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 {\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 x^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{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) \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({\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(i+c \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))*c-I)/(exp(2*I*(b*x+a))+1))^3+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)))^3+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(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+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))+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))+1/6*Pi*x^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))-1/4/b^3*polylog(2,-I*exp(2*I*(b*x+a))*c)*a^2+1/12*x^3*Pi*csgn(exp(2*I*(b*x+a))*(I+c)/(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(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))+1))^3+1/12*x^3*Pi*csgn(I/(exp(2*I*(b*x+a))+1)*(I+c))^3+1/6*I*x^3*ln(1+I*c*exp(2*I*(b*x+a)))-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))^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))-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))^2-1/8*polylog(4,-I*exp(2*I*(b*x+a))*c)/b^3-1/12*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))*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))*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))*(I+c)/(exp(2*I*(b*x+a))+1))^2+1/3*I*x^3*ln(exp(I*(b*x+a)))+1/6*I*x^3*ln(I+c)+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+1/12*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))","C"
57,1,1498,99,5.480000," ","int(x*arctan(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(\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}^{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{\pi  \,x^{2}}{4}-\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)^{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(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 {\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}{{\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{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 \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(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{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{b \,x^{3}}{6}+\frac{i x^{2} \ln \left(i+c \right)}{4}+\frac{i x^{2} \ln \left(1+i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4}-\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(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}-\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{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{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{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(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}+1}\right)^{3}}{8}"," ",0,"-1/2*I/b^2*a^2*ln(1-I*exp(I*(b*x+a))*(I*c)^(1/2))+1/2*I*x^2*ln(exp(I*(b*x+a)))+1/4*I*x^2*ln(I+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))+1/2*I/b*ln(1+I*c*exp(2*I*(b*x+a)))*x*a-1/2*I/b*a*ln(1+I*exp(I*(b*x+a))*(I*c)^(1/2))*x+1/4*I*x^2*ln(1+I*c*exp(2*I*(b*x+a)))-1/4*I*x^2*ln(exp(2*I*(b*x+a))*c-I)-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+1/4*Pi*x^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+1/8*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/(exp(2*I*(b*x+a))+1))*csgn(I/(exp(2*I*(b*x+a))+1)*(I+c))^2-1/8*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)))*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)*(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)*(I+c))^3-1/2*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))*(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*b*x^3+1/4*x*polylog(2,-I*exp(2*I*(b*x+a))*c)/b+1/8*I*polylog(3,-I*exp(2*I*(b*x+a))*c)/b^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))*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)))*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(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))*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+1/4*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/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))^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))*(I+c)/(exp(2*I*(b*x+a))+1))^3+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*(I+c))*csgn(I/(exp(2*I*(b*x+a))+1)*(I+c))","C"
58,1,1681,70,0.560000," ","int(arctan(c+(-1+I*c)*tan(b*x+a)),x)","-\frac{i \ln \left(i+c +\left(i c -1\right) \tan \left(b x +a \right)\right) \ln \left(-\frac{i \left(-c -\left(i c -1\right) \tan \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) \tan \left(b x +a \right)\right)}{2}\right) \ln \left(-\frac{i \left(-c -\left(i c -1\right) \tan \left(b x +a \right)+i\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{-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{\arctan \left(c +\left(i c -1\right) \tan \left(b x +a \right)\right) \ln \left(i+c +\left(i c -1\right) \tan \left(b x +a \right)\right) c^{2}}{\left(i c -1\right) b \left(2 i+2 c \right)}-\frac{\arctan \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{\ln \left(i+c +\left(i c -1\right) \tan \left(b x +a \right)\right) \ln \left(-\frac{i \left(-c -\left(i c -1\right) \tan \left(b x +a \right)+i\right)}{2}\right) c}{2 \left(i c -1\right) b \left(i+c \right)}+\frac{\ln \left(-\frac{i \left(i+c +\left(i c -1\right) \tan \left(b x +a \right)\right)}{2}\right) \ln \left(-\frac{i \left(-c -\left(i c -1\right) \tan \left(b x +a \right)+i\right)}{2}\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{-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 \dilog \left(-\frac{-c -\left(i c -1\right) \tan \left(b x +a \right)+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 c}\right) c}{2 \left(i c -1\right) b \left(i+c \right)}+\frac{\ln \left(i+c +\left(i c -1\right) \tan \left(b x +a \right)\right)^{2} c}{4 \left(i c -1\right) b \left(i+c \right)}-\frac{\arctan \left(c +\left(i c -1\right) \tan \left(b x +a \right)\right) \ln \left(i+c +\left(i c -1\right) \tan \left(b x +a \right)\right)}{\left(i c -1\right) b \left(2 i+2 c \right)}+\frac{\arctan \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(i+c +\left(i c -1\right) \tan \left(b x +a \right)\right)^{2}}{8 \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{\dilog \left(-\frac{-c -\left(i c -1\right) \tan \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{-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{-c -\left(i c -1\right) \tan \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{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{\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{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{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 c}\right) c^{2}}{4 \left(i c -1\right) b \left(i+c \right)}+\frac{2 i \arctan \left(c +\left(i c -1\right) \tan \left(b x +a \right)\right) \ln \left(i+c +\left(i c -1\right) \tan \left(b x +a \right)\right) c}{\left(i c -1\right) b \left(2 i+2 c \right)}-\frac{2 i \arctan \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(i+c +\left(i c -1\right) \tan \left(b x +a \right)\right) \ln \left(-\frac{i \left(-c -\left(i c -1\right) \tan \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) \tan \left(b x +a \right)\right)}{2}\right) \ln \left(-\frac{i \left(-c -\left(i c -1\right) \tan \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) \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{-c -\left(i c -1\right) \tan \left(b x +a \right)+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) \tan \left(b x +a \right)\right)^{2} c^{2}}{8 \left(i c -1\right) b \left(i+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+1/4*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*(-c-(-1+I*c)*tan(b*x+a)+I)/c)*c-1/4*I/(-1+I*c)/b/(I+c)*ln(I+c+(-1+I*c)*tan(b*x+a))*ln(-1/2*I*(-c-(-1+I*c)*tan(b*x+a)+I))+1/4*I/(-1+I*c)/b/(I+c)*ln(-1/2*I*(I+c+(-1+I*c)*tan(b*x+a)))*ln(-1/2*I*(-c-(-1+I*c)*tan(b*x+a)+I))-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/(-1+I*c)/b/(I+c)*ln(I+c+(-1+I*c)*tan(b*x+a))^2*c+1/(-1+I*c)/b*arctan(c+(-1+I*c)*tan(b*x+a))/(2*I+2*c)*ln(I+c+(-1+I*c)*tan(b*x+a))*c^2-1/(-1+I*c)/b*arctan(c+(-1+I*c)*tan(b*x+a))/(2*I+2*c)*ln(c-(-1+I*c)*tan(b*x+a)+I)*c^2-1/2/(-1+I*c)/b/(I+c)*ln(I+c+(-1+I*c)*tan(b*x+a))*ln(-1/2*I*(-c-(-1+I*c)*tan(b*x+a)+I))*c+1/2/(-1+I*c)/b/(I+c)*ln(-1/2*I*(I+c+(-1+I*c)*tan(b*x+a)))*ln(-1/2*I*(-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((-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*(-c-(-1+I*c)*tan(b*x+a)+I)/c)-1/4*I/(-1+I*c)/b/(I+c)*dilog(-1/2*(-c-(-1+I*c)*tan(b*x+a)+I)/c)*c^2-1/8*I/(-1+I*c)/b/(I+c)*ln(I+c+(-1+I*c)*tan(b*x+a))^2*c^2-1/2/(-1+I*c)/b/(I+c)*dilog((-c-(-1+I*c)*tan(b*x+a)-I)/(-2*I-2*c))*c+1/2/(-1+I*c)/b/(I+c)*dilog(-1/2*(-c-(-1+I*c)*tan(b*x+a)+I)/c)*c-1/(-1+I*c)/b*arctan(c+(-1+I*c)*tan(b*x+a))/(2*I+2*c)*ln(I+c+(-1+I*c)*tan(b*x+a))+1/(-1+I*c)/b*arctan(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*(-c-(-1+I*c)*tan(b*x+a)+I)/c)+1/8*I/(-1+I*c)/b/(I+c)*ln(I+c+(-1+I*c)*tan(b*x+a))^2+1/4*I/(-1+I*c)/b/(I+c)*dilog(-1/2*I*(I+c+(-1+I*c)*tan(b*x+a)))+1/2/(-1+I*c)/b/(I+c)*dilog(-1/2*I*(I+c+(-1+I*c)*tan(b*x+a)))*c+2*I/(-1+I*c)/b*arctan(c+(-1+I*c)*tan(b*x+a))/(2*I+2*c)*ln(I+c+(-1+I*c)*tan(b*x+a))*c-2*I/(-1+I*c)/b*arctan(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(I+c+(-1+I*c)*tan(b*x+a))*ln(-1/2*I*(-c-(-1+I*c)*tan(b*x+a)+I))*c^2-1/4*I/(-1+I*c)/b/(I+c)*ln(-1/2*I*(I+c+(-1+I*c)*tan(b*x+a)))*ln(-1/2*I*(-c-(-1+I*c)*tan(b*x+a)+I))*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^2-1/4*I/(-1+I*c)/b/(I+c)*ln(c-(-1+I*c)*tan(b*x+a)+I)*ln(-1/2*(-c-(-1+I*c)*tan(b*x+a)+I)/c)*c^2","B"
59,0,0,22,1.896000," ","int(arctan(c+(-1+I*c)*tan(b*x+a))/x,x)","\int \frac{\arctan \left(c +\left(i c -1\right) \tan \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arctan(c+(-1+I*c)*tan(b*x+a))/x,x)","F"
60,1,51,20,0.046000," ","int(1/2*Pi-arccot(cot(b*x+a)),x)","\frac{\pi  x}{2}-\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,"1/2*Pi*x-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"
61,1,7906,337,73.710000," ","int(x^2*arctan(c+d*cot(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
62,1,7538,255,6.507000," ","int(x*arctan(c+d*cot(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
63,1,1159,168,1.398000," ","int(arctan(c+d*cot(b*x+a)),x)","-\frac{\arctan \left(c +d \cot \left(b x +a \right)\right) \pi}{2 b}+\frac{\arctan \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*arctan(c+d*cot(b*x+a))*Pi+1/b*arctan(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"
64,0,0,17,1.301000," ","int(arctan(c+d*cot(b*x+a))/x,x)","\int \frac{\arctan \left(c +d \cot \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arctan(c+d*cot(b*x+a))/x,x)","F"
65,1,1532,126,6.565000," ","int(-x^2*arctan(-c-(1-I*c)*cot(b*x+a)),x)","\frac{b \,x^{4}}{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(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{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(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)^{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{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(1-i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{6}-\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)} \left(i+c \right)}{{\mathrm e}^{2 i \left(b x +a \right)}-1}\right)^{3}}{12}+\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 \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{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}+\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{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(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{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{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 {\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 x^{3} \ln \left(i+c \right)}{6}+\frac{\pi  \,x^{3}}{6}-\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(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(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}^{i \left(b x +a \right)}\right)}{3}-\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 \ln \left(1-i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a^{3}}{3 b^{3}}-\frac{\polylog \left(4, i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{8 b^{3}}"," ",0,"1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))^3+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(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)))^2-1/12*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))^3-1/12*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)))^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))*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*b*x^4-1/6*I*x^3*ln(exp(2*I*(b*x+a))*c+I)+1/12*x^3*Pi*csgn(exp(2*I*(b*x+a))*(I+c)/(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))^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*Pi*x^3+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))-1/12*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+1/2*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*(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))^2-1/12*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))^2-1/4/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))-1/12*x^3*Pi*csgn(exp(2*I*(b*x+a))*(I+c)/(exp(2*I*(b*x+a))-1))^2+1/3*I*x^3*ln(exp(I*(b*x+a)))+1/6*I*x^3*ln(I+c)-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))^2-1/8*polylog(4,I*c*exp(2*I*(b*x+a)))/b^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))+1/4*x^2*polylog(2,I*c*exp(2*I*(b*x+a)))/b","C"
66,1,1497,101,5.463000," ","int(-x*arctan(-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 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 \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{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 \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{\pi  \,x^{2}}{4}+\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 \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}^{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{i \ln \left(1-i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a^{2}}{4 b^{2}}+\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{b \,x^{3}}{6}-\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{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(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 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 {\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)}{8}+\frac{i x^{2} \ln \left(i+c \right)}{4}+\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{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{{\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 \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)} \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)^{3}}{8}-\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{{\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)^{3}}{8}"," ",0,"1/4/b^2*polylog(2,I*c*exp(2*I*(b*x+a)))*a+1/2*I*x^2*ln(exp(I*(b*x+a)))+1/4*I*x^2*ln(I+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))^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(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(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))+1/8*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))-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((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))*(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(I*(exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))^3+1/4*Pi*x^2+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(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))^3-1/4*I*x^2*ln(exp(2*I*(b*x+a))*c+I)+1/8*x^2*Pi*csgn(I*exp(2*I*(b*x+a)))^3+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*I*polylog(3,I*c*exp(2*I*(b*x+a)))/b^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(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+1/2*I/b*ln(1-I*exp(2*I*(b*x+a))*c)*x*a-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+1/4*I*x^2*ln(1-I*exp(2*I*(b*x+a))*c)-1/8*x^2*Pi*csgn((exp(2*I*(b*x+a))*c+I)/(exp(2*I*(b*x+a))-1))^2+1/6*b*x^3+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*x*polylog(2,I*c*exp(2*I*(b*x+a)))/b","C"
67,1,1495,73,0.688000," ","int(-arctan(-c-(1-I*c)*cot(b*x+a)),x)","-\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{\ln \left(i+c +\cot \left(b x +a \right) \left(i c -1\right)\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{\arctan \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 \ln \left(i+c +\cot \left(b x +a \right) \left(i c -1\right)\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)}-\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{i \ln \left(i+c +\cot \left(b x +a \right) \left(i c -1\right)\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{\arctan \left(\cot \left(b x +a \right) \left(i c -1\right)-c \right) \ln \left(i+c +\cot \left(b x +a \right) \left(i c -1\right)\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{\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{\arctan \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 \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+\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{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 \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{\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+\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{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{\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 \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{\arctan \left(\cot \left(b x +a \right) \left(i c -1\right)-c \right) \ln \left(i+c +\cot \left(b x +a \right) \left(i c -1\right)\right) c^{2}}{b \left(i c -1\right) \left(2 i+2 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{\ln \left(i+c +\cot \left(b x +a \right) \left(i c -1\right)\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{2 i \arctan \left(\cot \left(b x +a \right) \left(i c -1\right)-c \right) \ln \left(i+c +\cot \left(b x +a \right) \left(i c -1\right)\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+c +\cot \left(b x +a \right) \left(i c -1\right)\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)}-\frac{i \ln \left(i+c +\cot \left(b x +a \right) \left(i c -1\right)\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{2 i \arctan \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)}"," ",0,"-1/b/(-1+I*c)*arctan(cot(b*x+a)*(-1+I*c)-c)/(2*I+2*c)*ln(I+c+cot(b*x+a)*(-1+I*c))+1/8*I/b/(-1+I*c)/(I+c)*ln(cot(b*x+a)*(-1+I*c)-c-I)^2-1/4*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+cot(b*x+a)*(-1+I*c)-c)/c)-1/4*I/b/(-1+I*c)/(I+c)*dilog(-1/2*I*(I+cot(b*x+a)*(-1+I*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-1/2/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+cot(b*x+a)*(-1+I*c)-c)/c)*c+1/b/(-1+I*c)*arctan(cot(b*x+a)*(-1+I*c)-c)/(2*I+2*c)*ln(cot(b*x+a)*(-1+I*c)-c-I)+1/b/(-1+I*c)*arctan(cot(b*x+a)*(-1+I*c)-c)/(2*I+2*c)*ln(I+c+cot(b*x+a)*(-1+I*c))*c^2-1/2/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-1/2/b/(-1+I*c)/(I+c)*ln(I+c+cot(b*x+a)*(-1+I*c))*ln((cot(b*x+a)*(-1+I*c)-c-I)/(-2*I-2*c))*c+2*I/b/(-1+I*c)*arctan(cot(b*x+a)*(-1+I*c)-c)/(2*I+2*c)*ln(I+c+cot(b*x+a)*(-1+I*c))*c+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+c+cot(b*x+a)*(-1+I*c))*ln((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(I+c+cot(b*x+a)*(-1+I*c))*ln(-1/2*(I+cot(b*x+a)*(-1+I*c)-c)/c)*c^2-2*I/b/(-1+I*c)*arctan(cot(b*x+a)*(-1+I*c)-c)/(2*I+2*c)*ln(cot(b*x+a)*(-1+I*c)-c-I)*c+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((cot(b*x+a)*(-1+I*c)-c-I)/(-2*I-2*c))*c^2+1/2/b/(-1+I*c)/(I+c)*ln(I+c+cot(b*x+a)*(-1+I*c))*ln(-1/2*(I+cot(b*x+a)*(-1+I*c)-c)/c)*c-1/b/(-1+I*c)*arctan(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(I+c+cot(b*x+a)*(-1+I*c))*ln(-1/2*(I+cot(b*x+a)*(-1+I*c)-c)/c)-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))-1/4*I/b/(-1+I*c)/(I+c)*ln(I+c+cot(b*x+a)*(-1+I*c))*ln((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+cot(b*x+a)*(-1+I*c)-c)/c)*c^2","B"
68,0,0,26,1.796000," ","int(-arctan(-c-(1-I*c)*cot(b*x+a))/x,x)","\int -\frac{\arctan \left(-c -\left(-i c +1\right) \cot \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(-arctan(-c-(1-I*c)*cot(b*x+a))/x,x)","F"
69,1,1533,125,6.618000," ","int(-x^2*arctan(-c-(-1-I*c)*cot(b*x+a)),x)","-\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{b \,x^{4}}{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(i {\mathrm e}^{2 i \left(b x +a \right)}\right)^{3}}{12}-\frac{x^{2} \polylog \left(2, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{4 b}-\frac{a^{2} \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{3}}+\frac{\polylog \left(2, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right) a^{2}}{4 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 {\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)}-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 {\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{i a^{3} \ln \left(-{\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{6 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(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{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(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(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{\polylog \left(4, -i {\mathrm e}^{2 i \left(b x +a \right)} c \right)}{8 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}^{2 i \left(b x +a \right)} c -i\right)}{6}+\frac{\pi  \,x^{3}}{6}+\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{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 \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 x^{3} \ln \left(c -i\right)}{6}-\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(\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)} 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{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{{\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{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 a^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{3}}+\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(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}^{i \left(b x +a \right)}\right)}{3}"," ",0,"-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+1/8*polylog(4,-I*exp(2*I*(b*x+a))*c)/b^3-1/6*I*x^3*ln(1+I*c*exp(2*I*(b*x+a)))-1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a)))^3-1/12*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))*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+1/12*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))*csgn(I/(exp(2*I*(b*x+a))-1))*csgn(I*(c-I)/(exp(2*I*(b*x+a))-1))-1/3*I*x^3*ln(exp(I*(b*x+a)))-1/6*I*x^3*ln(c-I)-1/12*x^3*Pi*csgn(I*exp(2*I*(b*x+a))*(c-I)/(exp(2*I*(b*x+a))-1))^3-1/2*I/b^2*a^2*ln(1-I*exp(I*(b*x+a))*(I*c)^(1/2))*x-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)-1/2*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(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-1))^3+1/6*Pi*x^3-1/12*x^3*Pi*csgn((exp(2*I*(b*x+a))*c-I)/(exp(2*I*(b*x+a))-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-1/4*x^2*polylog(2,-I*exp(2*I*(b*x+a))*c)/b+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+1/6*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))^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/b^3*polylog(2,-I*exp(2*I*(b*x+a))*c)*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*(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(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))^3-1/12*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))+1/12*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*(c-I)/(exp(2*I*(b*x+a))-1))^2","C"
70,1,1498,100,5.573000," ","int(-x*arctan(-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{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{i x^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{2}-\frac{i x^{2} \ln \left(c -i\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(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({\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{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{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{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{\pi  \,x^{2}}{4}+\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 \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(1+i {\mathrm e}^{i \left(b x +a \right)} \sqrt{i c}\right)}{2 b^{2}}+\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{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 \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{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 {\mathrm e}^{2 i \left(b x +a \right)}\right)^{3}}{8}-\frac{b \,x^{3}}{6}+\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 a^{2} \ln \left(-{\mathrm e}^{2 i \left(b x +a \right)} c +i\right)}{4 b^{2}}"," ",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(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))^2-1/8*I*polylog(3,-I*exp(2*I*(b*x+a))*c)/b^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))*(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*Pi*x^2-1/2*I*x^2*ln(exp(I*(b*x+a)))-1/4*I*x^2*ln(c-I)+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+1/4*I*x^2*ln(exp(2*I*(b*x+a))*c-I)-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))*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))-1/2*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))-1/6*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))-1/4/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))^2-1/4*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))","C"
71,1,1753,72,0.700000," ","int(-arctan(-c-(-1-I*c)*cot(b*x+a)),x)","\frac{i \ln \left(-\left(i c +1\right) \cot \left(b x +a \right)-c +i\right) \ln \left(\frac{-\left(i c +1\right) \cot \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(-\left(i c +1\right) \cot \left(b x +a \right)-c +i\right) \ln \left(\frac{-\left(i c +1\right) \cot \left(b x +a \right)+c -i}{-2 i+2 c}\right)}{4 b \left(i c +1\right) \left(i-c \right)}-\frac{\arctan \left(-c +\left(i c +1\right) \cot \left(b x +a \right)\right) \ln \left(i+\left(i c +1\right) \cot \left(b x +a \right)-c \right)}{b \left(i c +1\right) \left(2 i-2 c \right)}+\frac{\arctan \left(-c +\left(i c +1\right) \cot \left(b x +a \right)\right) \ln \left(-\left(i c +1\right) \cot \left(b x +a \right)-c +i\right)}{b \left(i c +1\right) \left(2 i-2 c \right)}+\frac{i \ln \left(i+\left(i c +1\right) \cot \left(b x +a \right)-c \right)^{2}}{8 b \left(i c +1\right) \left(i-c \right)}-\frac{\dilog \left(-\frac{i \left(i+\left(i c +1\right) \cot \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) \cot \left(b x +a \right)+c +i}{2 c}\right) c}{2 b \left(i c +1\right) \left(i-c \right)}+\frac{\dilog \left(\frac{-\left(i c +1\right) \cot \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{i \left(i+\left(i c +1\right) \cot \left(b x +a \right)-c \right)}{2}\right)}{4 b \left(i c +1\right) \left(i-c \right)}+\frac{i \dilog \left(\frac{-\left(i c +1\right) \cot \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) \cot \left(b x +a \right)+c -i}{-2 i+2 c}\right)}{4 b \left(i c +1\right) \left(i-c \right)}-\frac{\ln \left(i+\left(i c +1\right) \cot \left(b x +a \right)-c \right)^{2} c}{4 b \left(i c +1\right) \left(i-c \right)}+\frac{i \ln \left(-\frac{i \left(i+\left(i c +1\right) \cot \left(b x +a \right)-c \right)}{2}\right) \ln \left(-\frac{i \left(-\left(i c +1\right) \cot \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(i+\left(i c +1\right) \cot \left(b x +a \right)-c \right) \ln \left(-\frac{i \left(-\left(i c +1\right) \cot \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(i+\left(i c +1\right) \cot \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) \cot \left(b x +a \right)-c +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 b \left(i c +1\right) \left(i-c \right)}+\frac{\ln \left(i+\left(i c +1\right) \cot \left(b x +a \right)-c \right) \ln \left(-\frac{i \left(-\left(i c +1\right) \cot \left(b x +a \right)+c +i\right)}{2}\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) \cot \left(b x +a \right)-c \right)}{2}\right) \ln \left(-\frac{i \left(-\left(i c +1\right) \cot \left(b x +a \right)+c +i\right)}{2}\right) c}{2 b \left(i c +1\right) \left(i-c \right)}-\frac{\ln \left(-\left(i c +1\right) \cot \left(b x +a \right)-c +i\right) \ln \left(\frac{-\left(i c +1\right) \cot \left(b x +a \right)+c +i}{2 c}\right) c}{2 b \left(i c +1\right) \left(i-c \right)}+\frac{\arctan \left(-c +\left(i c +1\right) \cot \left(b x +a \right)\right) \ln \left(i+\left(i c +1\right) \cot \left(b x +a \right)-c \right) c^{2}}{b \left(i c +1\right) \left(2 i-2 c \right)}-\frac{\arctan \left(-c +\left(i c +1\right) \cot \left(b x +a \right)\right) \ln \left(-\left(i c +1\right) \cot \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{i \left(i+\left(i c +1\right) \cot \left(b x +a \right)-c \right)}{2}\right) c^{2}}{4 b \left(i c +1\right) \left(i-c \right)}-\frac{i \dilog \left(\frac{-\left(i c +1\right) \cot \left(b x +a \right)+c +i}{2 c}\right) c^{2}}{4 b \left(i c +1\right) \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) 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) \cot \left(b x +a \right)-c \right)}{2}\right) \ln \left(-\frac{i \left(-\left(i c +1\right) \cot \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) \cot \left(b x +a \right)-c +i\right) \ln \left(\frac{-\left(i c +1\right) \cot \left(b x +a \right)+c +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) \cot \left(b x +a \right)-c +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 b \left(i c +1\right) \left(i-c \right)}-\frac{2 i \arctan \left(-c +\left(i c +1\right) \cot \left(b x +a \right)\right) \ln \left(i+\left(i c +1\right) \cot \left(b x +a \right)-c \right) c}{b \left(i c +1\right) \left(2 i-2 c \right)}+\frac{2 i \arctan \left(-c +\left(i c +1\right) \cot \left(b x +a \right)\right) \ln \left(-\left(i c +1\right) \cot \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) \cot \left(b x +a \right)-c \right) \ln \left(-\frac{i \left(-\left(i c +1\right) \cot \left(b x +a \right)+c +i\right)}{2}\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(-(1+I*c)*cot(b*x+a)-c+I)*ln(1/2*(-(1+I*c)*cot(b*x+a)+c+I)/c)-1/4*I/b/(1+I*c)/(I-c)*ln(-(1+I*c)*cot(b*x+a)-c+I)*ln((-(1+I*c)*cot(b*x+a)+c-I)/(-2*I+2*c))+1/4*I/b/(1+I*c)/(I-c)*ln(-1/2*I*(I+(1+I*c)*cot(b*x+a)-c))*ln(-1/2*I*(-(1+I*c)*cot(b*x+a)+c+I))-1/4*I/b/(1+I*c)/(I-c)*ln(I+(1+I*c)*cot(b*x+a)-c)*ln(-1/2*I*(-(1+I*c)*cot(b*x+a)+c+I))-1/4*I/b/(1+I*c)/(I-c)*dilog(-1/2*I*(I+(1+I*c)*cot(b*x+a)-c))*c^2-1/8*I/b/(1+I*c)/(I-c)*ln(I+(1+I*c)*cot(b*x+a)-c)^2*c^2-1/4*I/b/(1+I*c)/(I-c)*dilog(1/2*(-(1+I*c)*cot(b*x+a)+c+I)/c)*c^2+1/4*I/b/(1+I*c)/(I-c)*dilog((-(1+I*c)*cot(b*x+a)+c-I)/(-2*I+2*c))*c^2+1/2/b/(1+I*c)/(I-c)*ln(-(1+I*c)*cot(b*x+a)-c+I)*ln((-(1+I*c)*cot(b*x+a)+c-I)/(-2*I+2*c))*c+1/2/b/(1+I*c)/(I-c)*ln(I+(1+I*c)*cot(b*x+a)-c)*ln(-1/2*I*(-(1+I*c)*cot(b*x+a)+c+I))*c-1/2/b/(1+I*c)/(I-c)*ln(-1/2*I*(I+(1+I*c)*cot(b*x+a)-c))*ln(-1/2*I*(-(1+I*c)*cot(b*x+a)+c+I))*c-1/2/b/(1+I*c)/(I-c)*ln(-(1+I*c)*cot(b*x+a)-c+I)*ln(1/2*(-(1+I*c)*cot(b*x+a)+c+I)/c)*c+1/b/(1+I*c)*arctan(-c+(1+I*c)*cot(b*x+a))/(2*I-2*c)*ln(I+(1+I*c)*cot(b*x+a)-c)*c^2-1/b/(1+I*c)*arctan(-c+(1+I*c)*cot(b*x+a))/(2*I-2*c)*ln(-(1+I*c)*cot(b*x+a)-c+I)*c^2-1/4*I/b/(1+I*c)/(I-c)*ln(-1/2*I*(I+(1+I*c)*cot(b*x+a)-c))*ln(-1/2*I*(-(1+I*c)*cot(b*x+a)+c+I))*c^2-1/4*I/b/(1+I*c)/(I-c)*ln(-(1+I*c)*cot(b*x+a)-c+I)*ln(1/2*(-(1+I*c)*cot(b*x+a)+c+I)/c)*c^2+1/4*I/b/(1+I*c)/(I-c)*ln(-(1+I*c)*cot(b*x+a)-c+I)*ln((-(1+I*c)*cot(b*x+a)+c-I)/(-2*I+2*c))*c^2-2*I/b/(1+I*c)*arctan(-c+(1+I*c)*cot(b*x+a))/(2*I-2*c)*ln(I+(1+I*c)*cot(b*x+a)-c)*c+2*I/b/(1+I*c)*arctan(-c+(1+I*c)*cot(b*x+a))/(2*I-2*c)*ln(-(1+I*c)*cot(b*x+a)-c+I)*c+1/4*I/b/(1+I*c)/(I-c)*ln(I+(1+I*c)*cot(b*x+a)-c)*ln(-1/2*I*(-(1+I*c)*cot(b*x+a)+c+I))*c^2-1/2/b/(1+I*c)/(I-c)*dilog(-1/2*I*(I+(1+I*c)*cot(b*x+a)-c))*c-1/4/b/(1+I*c)/(I-c)*ln(I+(1+I*c)*cot(b*x+a)-c)^2*c-1/2/b/(1+I*c)/(I-c)*dilog(1/2*(-(1+I*c)*cot(b*x+a)+c+I)/c)*c+1/2/b/(1+I*c)/(I-c)*dilog((-(1+I*c)*cot(b*x+a)+c-I)/(-2*I+2*c))*c-1/b/(1+I*c)*arctan(-c+(1+I*c)*cot(b*x+a))/(2*I-2*c)*ln(I+(1+I*c)*cot(b*x+a)-c)+1/b/(1+I*c)*arctan(-c+(1+I*c)*cot(b*x+a))/(2*I-2*c)*ln(-(1+I*c)*cot(b*x+a)-c+I)+1/4*I/b/(1+I*c)/(I-c)*dilog(-1/2*I*(I+(1+I*c)*cot(b*x+a)-c))+1/8*I/b/(1+I*c)/(I-c)*ln(I+(1+I*c)*cot(b*x+a)-c)^2+1/4*I/b/(1+I*c)/(I-c)*dilog(1/2*(-(1+I*c)*cot(b*x+a)+c+I)/c)-1/4*I/b/(1+I*c)/(I-c)*dilog((-(1+I*c)*cot(b*x+a)+c-I)/(-2*I+2*c))","B"
72,0,0,26,2.062000," ","int(-arctan(-c-(-1-I*c)*cot(b*x+a))/x,x)","\int -\frac{\arctan \left(-c -\left(-i c -1\right) \cot \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(-arctan(-c-(-1-I*c)*cot(b*x+a))/x,x)","F"
73,1,52,32,0.379000," ","int(arctan(sinh(x)),x)","x \arctan \left(\sinh \left(x \right)\right)-i x \left(\ln \left(1-i {\mathrm e}^{x}\right)-\ln \left(1+i {\mathrm e}^{x}\right)\right)+i \dilog \left(1+i {\mathrm e}^{x}\right)-i \dilog \left(1-i {\mathrm e}^{x}\right)"," ",0,"x*arctan(sinh(x))-I*x*(ln(1-I*exp(x))-ln(1+I*exp(x)))+I*dilog(1+I*exp(x))-I*dilog(1-I*exp(x))","A"
74,1,732,59,1.344000," ","int(x*arctan(sinh(x)),x)","-\frac{\pi  \,x^{2} \mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right)^{2}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right) \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right)}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right)^{3}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right)^{3}}{8}-\frac{i x^{2} \ln \left(1-i {\mathrm e}^{x}\right)}{2}-\frac{i x^{2} \ln \left({\mathrm e}^{x}-i\right)}{2}+\frac{i x^{2} \ln \left(1+i {\mathrm e}^{x}\right)}{2}+\frac{i x^{2} \ln \left({\mathrm e}^{x}+i\right)}{2}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{x}-i\right)^{2}\right)^{3}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{x}+i\right)^{2}\right)^{3}}{8}+i x \polylog \left(2, -i {\mathrm e}^{x}\right)-i x \polylog \left(2, i {\mathrm e}^{x}\right)-\frac{\pi  \,x^{2} \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right)^{2}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right)^{3}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right)^{3}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right)^{2}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{x}-i\right)^{2}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right)}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{x}+i\right)^{2}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right)}{8}+\frac{\pi  \,x^{2}}{4}+i \polylog \left(3, i {\mathrm e}^{x}\right)-i \polylog \left(3, -i {\mathrm e}^{x}\right)+\frac{\pi  \,x^{2} \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right) \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right)}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right) \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right)^{2}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right) \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right)^{2}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{x}-i\right)^{2}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right)^{2}}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{x}+i\right)\right)^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{x}+i\right)^{2}\right)}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{x}+i\right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{x}+i\right)^{2}\right)^{2}}{4}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{x}+i\right)^{2}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right)^{2}}{8}-\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{x}-i\right)\right)^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{x}-i\right)^{2}\right)}{8}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{x}-i\right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{x}-i\right)^{2}\right)^{2}}{4}+\frac{\pi  \,x^{2} \mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right)^{2}}{8}"," ",0,"I*x*polylog(2,-I*exp(x))-1/8*Pi*x^2*csgn(I*exp(-x)*(exp(x)-I)^2)^3+1/8*Pi*x^2*csgn(I*exp(-x)*(exp(x)+I)^2)*csgn(exp(-x)*(exp(x)+I)^2)+1/8*Pi*x^2*csgn(I*exp(-x)*(exp(x)+I)^2)^3-1/2*I*x^2*ln(1-I*exp(x))-1/2*I*x^2*ln(exp(x)-I)+1/2*I*x^2*ln(1+I*exp(x))+1/2*I*x^2*ln(exp(x)+I)-1/8*Pi*x^2*csgn(I*(exp(x)-I)^2)^3+1/8*Pi*x^2*csgn(I*(exp(x)+I)^2)^3-1/8*Pi*x^2*csgn(I*(exp(x)-I)^2)*csgn(I*exp(-x))*csgn(I*exp(-x)*(exp(x)-I)^2)+1/8*Pi*x^2*csgn(I*exp(-x)*(exp(x)-I)^2)*csgn(exp(-x)*(exp(x)-I)^2)^2-1/8*Pi*x^2*csgn(exp(-x)*(exp(x)+I)^2)^2-1/8*Pi*x^2*csgn(I*exp(-x)*(exp(x)+I)^2)*csgn(exp(-x)*(exp(x)+I)^2)^2+1/8*Pi*x^2*csgn(I*(exp(x)-I)^2)*csgn(I*exp(-x)*(exp(x)-I)^2)^2+1/8*Pi*x^2*csgn(I*(exp(x)+I))^2*csgn(I*(exp(x)+I)^2)-1/4*Pi*x^2*csgn(I*(exp(x)+I))*csgn(I*(exp(x)+I)^2)^2-1/8*Pi*x^2*csgn(I*(exp(x)+I)^2)*csgn(I*exp(-x)*(exp(x)+I)^2)^2-1/8*Pi*x^2*csgn(I*(exp(x)-I))^2*csgn(I*(exp(x)-I)^2)+1/4*Pi*x^2*csgn(I*(exp(x)-I))*csgn(I*(exp(x)-I)^2)^2+1/8*Pi*x^2*csgn(I*exp(-x))*csgn(I*exp(-x)*(exp(x)-I)^2)^2-1/8*Pi*x^2*csgn(I*exp(-x))*csgn(I*exp(-x)*(exp(x)+I)^2)^2-1/8*Pi*x^2*csgn(I*exp(-x)*(exp(x)-I)^2)*csgn(exp(-x)*(exp(x)-I)^2)+I*polylog(3,I*exp(x))+1/4*Pi*x^2-I*polylog(3,-I*exp(x))+1/8*Pi*x^2*csgn(I*(exp(x)+I)^2)*csgn(I*exp(-x))*csgn(I*exp(-x)*(exp(x)+I)^2)-I*x*polylog(2,I*exp(x))+1/8*Pi*x^2*csgn(exp(-x)*(exp(x)+I)^2)^3+1/8*Pi*x^2*csgn(exp(-x)*(exp(x)-I)^2)^3-1/8*Pi*x^2*csgn(exp(-x)*(exp(x)-I)^2)^2","C"
75,1,758,85,0.628000," ","int(x^2*arctan(sinh(x)),x)","\frac{i x^{3} \ln \left(1+i {\mathrm e}^{x}\right)}{3}-\frac{i x^{3} \ln \left({\mathrm e}^{x}-i\right)}{3}+\frac{i x^{3} \ln \left({\mathrm e}^{x}+i\right)}{3}-\frac{i x^{3} \ln \left(1-i {\mathrm e}^{x}\right)}{3}-\frac{\pi  \,x^{3} \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right)^{2}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right)^{3}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right)^{3}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right)^{2}}{12}+i x^{2} \polylog \left(2, -i {\mathrm e}^{x}\right)-\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left({\mathrm e}^{x}-i\right)^{2}\right)^{3}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right)^{3}}{12}+2 i x \polylog \left(3, i {\mathrm e}^{x}\right)-i x^{2} \polylog \left(2, i {\mathrm e}^{x}\right)-2 i x \polylog \left(3, -i {\mathrm e}^{x}\right)+\frac{\pi  \,x^{3} \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right)^{3}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left({\mathrm e}^{x}+i\right)^{2}\right)^{3}}{12}+2 i \polylog \left(4, -i {\mathrm e}^{x}\right)-2 i \polylog \left(4, i {\mathrm e}^{x}\right)-\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left({\mathrm e}^{x}-i\right)^{2}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right)}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left({\mathrm e}^{x}+i\right)^{2}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right)}{12}+\frac{\pi  \,x^{3}}{6}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left({\mathrm e}^{x}-i\right)^{2}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right)^{2}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left({\mathrm e}^{x}+i\right)\right)^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{x}+i\right)^{2}\right)}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left({\mathrm e}^{x}+i\right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{x}+i\right)^{2}\right)^{2}}{6}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right) \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right)^{2}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left({\mathrm e}^{x}+i\right)^{2}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right)^{2}}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right)^{2}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right) \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{x}-i\right)^{2}\right)}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right)^{2}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right) \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right)^{2}}{12}-\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left({\mathrm e}^{x}-i\right)\right)^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{x}-i\right)^{2}\right)}{12}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(i \left({\mathrm e}^{x}-i\right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{x}-i\right)^{2}\right)^{2}}{6}+\frac{\pi  \,x^{3} \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right) \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{x}+i\right)^{2}\right)}{12}"," ",0,"1/3*I*x^3*ln(1+I*exp(x))-1/3*I*x^3*ln(exp(x)-I)+1/3*I*x^3*ln(exp(x)+I)-1/3*I*x^3*ln(1-I*exp(x))-1/12*Pi*x^3*csgn(exp(-x)*(exp(x)+I)^2)^2+1/12*Pi*x^3*csgn(exp(-x)*(exp(x)+I)^2)^3+1/12*Pi*x^3*csgn(exp(-x)*(exp(x)-I)^2)^3-1/12*Pi*x^3*csgn(exp(-x)*(exp(x)-I)^2)^2+1/12*Pi*x^3*csgn(I*exp(-x)*(exp(x)+I)^2)^3+I*x^2*polylog(2,-I*exp(x))+2*I*x*polylog(3,I*exp(x))+2*I*polylog(4,-I*exp(x))+1/12*Pi*x^3*csgn(I*(exp(x)+I)^2)^3-1/12*Pi*x^3*csgn(I*(exp(x)-I)^2)^3+1/12*Pi*x^3*csgn(I*(exp(x)-I)^2)*csgn(I*exp(-x)*(exp(x)-I)^2)^2+1/12*Pi*x^3*csgn(I*(exp(x)+I))^2*csgn(I*(exp(x)+I)^2)-1/6*Pi*x^3*csgn(I*(exp(x)+I))*csgn(I*(exp(x)+I)^2)^2+1/12*Pi*x^3*csgn(I*exp(-x)*(exp(x)-I)^2)*csgn(exp(-x)*(exp(x)-I)^2)^2-1/12*Pi*x^3*csgn(I*(exp(x)+I)^2)*csgn(I*exp(-x)*(exp(x)+I)^2)^2+1/12*Pi*x^3*csgn(I*exp(-x))*csgn(I*exp(-x)*(exp(x)-I)^2)^2-1/12*Pi*x^3*csgn(I*exp(-x)*(exp(x)-I)^2)*csgn(exp(-x)*(exp(x)-I)^2)-1/12*Pi*x^3*csgn(I*exp(-x))*csgn(I*exp(-x)*(exp(x)+I)^2)^2-1/12*Pi*x^3*csgn(I*exp(-x)*(exp(x)+I)^2)*csgn(exp(-x)*(exp(x)+I)^2)^2-1/12*Pi*x^3*csgn(I*(exp(x)-I))^2*csgn(I*(exp(x)-I)^2)+1/6*Pi*x^3*csgn(I*(exp(x)-I))*csgn(I*(exp(x)-I)^2)^2-1/12*Pi*x^3*csgn(I*(exp(x)-I)^2)*csgn(I*exp(-x))*csgn(I*exp(-x)*(exp(x)-I)^2)+1/12*Pi*x^3*csgn(I*(exp(x)+I)^2)*csgn(I*exp(-x))*csgn(I*exp(-x)*(exp(x)+I)^2)+1/6*Pi*x^3-2*I*polylog(4,I*exp(x))-I*x^2*polylog(2,I*exp(x))-2*I*x*polylog(3,-I*exp(x))+1/12*Pi*x^3*csgn(I*exp(-x)*(exp(x)+I)^2)*csgn(exp(-x)*(exp(x)+I)^2)-1/12*Pi*x^3*csgn(I*exp(-x)*(exp(x)-I)^2)^3","C"
76,1,7275,254,47.255000," ","int((f*x+e)^3*arctan(tanh(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
77,1,5425,194,37.576000," ","int((f*x+e)^2*arctan(tanh(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
78,1,2414,134,4.748000," ","int((f*x+e)*arctan(tanh(b*x+a)),x)","\text{Expression too large to display}"," ",0,"-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))^2-1/4*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+1/8*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*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))+1/8*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))-1/8*I*f*polylog(3,-I*exp(2*b*x+2*a))/b^2+1/8*Pi*f*x^2+1/4*Pi*e*x+1/4*I*f/b^2*a^2*ln(-exp(2*b*x+2*a)+I)+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(I*(exp(2*b*x+2*a)+I)/(exp(2*b*x+2*a)+1))^3-1/2*I*f/b^2*a*(b*x+a)*ln(1+exp(b*x+a)*(-1)^(3/4))-1/2*I*f/b^2*a*(b*x+a)*ln(1-exp(b*x+a)*(-1)^(3/4))+1/2*I*f/b^2*a*(b*x+a)*ln(((-I)^(1/2)-exp(b*x+a))/(-I)^(1/2))+1/2*I*f/b^2*a*(b*x+a)*ln(((-I)^(1/2)+exp(b*x+a))/(-I)^(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*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))+1/8*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))^2-1/4*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+1/2*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)-1/2*I*e/b*a*ln(-exp(2*b*x+2*a)+I)+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*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*(1/2*f*x^2+e*x)*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((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((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))*csgn(I*(exp(2*b*x+2*a)-I)/(exp(2*b*x+2*a)+1))-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*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*e/b*(b*x+a)*ln(1+exp(b*x+a)*(-1)^(3/4))+1/2*I*e/b*(b*x+a)*ln(1-exp(b*x+a)*(-1)^(3/4))+1/4*I*f/b^2*(b*x+a)^2*ln(1+I*exp(2*b*x+2*a))+1/4*I*f/b^2*(b*x+a)*polylog(2,-I*exp(2*b*x+2*a))-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))-1/4*I*f/b^2*(b*x+a)^2*ln(1-I*exp(2*b*x+2*a))-1/4*I*f/b^2*(b*x+a)*polylog(2,I*exp(2*b*x+2*a))-1/2*I*e/b*(b*x+a)*ln(((-I)^(1/2)-exp(b*x+a))/(-I)^(1/2))-1/2*I*e/b*(b*x+a)*ln(((-I)^(1/2)+exp(b*x+a))/(-I)^(1/2))-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))^3-1/4*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*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))","C"
79,1,178,63,0.564000," ","int(arctan(tanh(b*x+a)),x)","\frac{\arctanh \left(\tanh \left(b x +a \right)\right) \arctan \left(\tanh \left(b x +a \right)\right)}{b}-\frac{i \arctanh \left(\tanh \left(b x +a \right)\right) \ln \left(1-\frac{i \left(\tanh \left(b x +a \right)+1\right)^{2}}{1-\left(\tanh^{2}\left(b x +a \right)\right)}\right)}{2 b}+\frac{i \arctanh \left(\tanh \left(b x +a \right)\right) \ln \left(1+\frac{i \left(\tanh \left(b x +a \right)+1\right)^{2}}{1-\left(\tanh^{2}\left(b x +a \right)\right)}\right)}{2 b}+\frac{i \dilog \left(1+\frac{i \left(\tanh \left(b x +a \right)+1\right)^{2}}{1-\left(\tanh^{2}\left(b x +a \right)\right)}\right)}{4 b}-\frac{i \dilog \left(1-\frac{i \left(\tanh \left(b x +a \right)+1\right)^{2}}{1-\left(\tanh^{2}\left(b x +a \right)\right)}\right)}{4 b}"," ",0,"1/b*arctanh(tanh(b*x+a))*arctan(tanh(b*x+a))-1/2*I/b*arctanh(tanh(b*x+a))*ln(1-I*(tanh(b*x+a)+1)^2/(1-tanh(b*x+a)^2))+1/2*I/b*arctanh(tanh(b*x+a))*ln(1+I*(tanh(b*x+a)+1)^2/(1-tanh(b*x+a)^2))+1/4*I/b*dilog(1+I*(tanh(b*x+a)+1)^2/(1-tanh(b*x+a)^2))-1/4*I/b*dilog(1-I*(tanh(b*x+a)+1)^2/(1-tanh(b*x+a)^2))","B"
80,0,0,17,1.394000," ","int(arctan(tanh(b*x+a))/(f*x+e),x)","\int \frac{\arctan \left(\tanh \left(b x +a \right)\right)}{f x +e}\, dx"," ",0,"int(arctan(tanh(b*x+a))/(f*x+e),x)","F"
81,1,6936,305,60.801000," ","int(x^2*arctan(c+d*tanh(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
82,1,6586,229,6.160000," ","int(x*arctan(c+d*tanh(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
83,1,350,150,0.363000," ","int(arctan(c+d*tanh(b*x+a)),x)","\frac{\arctan \left(c +d \tanh \left(b x +a \right)\right) \ln \left(d \tanh \left(b x +a \right)+d \right)}{2 b}-\frac{\arctan \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*arctan(c+d*tanh(b*x+a))*ln(d*tanh(b*x+a)+d)-1/2/b*arctan(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"
84,0,0,17,0.829000," ","int(arctan(c+d*tanh(b*x+a))/x,x)","\int \frac{\arctan \left(c +d \tanh \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arctan(c+d*tanh(b*x+a))/x,x)","F"
85,1,1555,116,6.865000," ","int(x^2*arctan(c+(I+c)*tanh(b*x+a)),x)","\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 x^{3} \ln \left(1+i c \,{\mathrm e}^{2 b x +2 a}\right)}{6}+\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)^{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{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)^{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{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)^{2}}{12}+\frac{i \polylog \left(4, -i c \,{\mathrm e}^{2 b x +2 a}\right)}{8 b^{3}}+\frac{\pi  \,x^{3}}{6}+\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{\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{i a^{3} \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{i c}\right)}{2 b^{3}}+\frac{i a^{3} \ln \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{\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 \ln \left(1+i c \,{\mathrm e}^{2 b x +2 a}\right) a^{3}}{3 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^{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 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{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}{{\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 b c \,x^{4}}{12 \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 \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{b \,x^{4}}{12 i+12 c}"," ",0,"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))+1/6*I*x^3*ln(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)-1/6*I*x^3*ln(2*exp(2*b*x+2*a)*c-2*I)-1/4*I*x*polylog(3,-I*c*exp(2*b*x+2*a))/b^2+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))^2-1/12*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*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(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+1/12*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))^3-1/4*I/b^3*c/(I+c)*a^4-1/12*I*b*c/(I+c)*x^4-1/2*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))+1/4/b^3/(I+c)*a^4+1/12*b/(I+c)*x^4+1/6*Pi*x^3-1/6*I/b^3*a^3*ln(-exp(2*b*x+2*a)*c+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))-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+1/12*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))-1/3/b^3*a^3/(I+c)*ln(exp(b*x+a))+1/3/b^2/(I+c)*x*a^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+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*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))","C"
86,1,1519,92,5.013000," ","int(x*arctan(c+(I+c)*tanh(b*x+a)),x)","\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{\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{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{\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(-{\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{\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 \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(\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}+\frac{\pi  \,x^{2}}{4}+\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{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{\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{\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{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 \,{\mathrm e}^{2 b x +2 a} c -2 i}{{\mathrm e}^{2 b x +2 a}+1}\right)^{3}}{8}+\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 b c \,x^{3}}{6 \left(i+c \right)}+\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}"," ",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))-1/8*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*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))+1/2*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-1/6*I*b*c*x^3/(I+c)+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*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+1/4*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)/(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+1/2*I/b*c/(I+c)*x*a^2-1/2*I/b^2*c*a^2/(I+c)*ln(exp(b*x+a))-1/3/b^2/(I+c)*a^3+1/6*b*x^3/(I+c)+1/3*I/b^2*c/(I+c)*a^3+1/4*Pi*x^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))-1/2*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*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*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^2-1/4*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*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"
87,1,1381,65,0.579000," ","int(arctan(c+(I+c)*tanh(b*x+a)),x)","-\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{-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 \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{\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 c}\right) c}{2 \left(i+c \right)^{2} b}+\frac{\arctan \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{\arctan \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(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{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 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 i-2 c}\right)}{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} c^{2}}{8 \left(i+c \right)^{2} b}+\frac{2 i \arctan \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{\arctan \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(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{\arctan \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{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}+\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{2 i \arctan \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{\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 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 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{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{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}"," ",0,"-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(-1/2*(-c-(I+c)*tanh(b*x+a)+I)/c)*c+1/(I+c)/b*arctan(c+(I+c)*tanh(b*x+a))/(2*I+2*c)*ln(c-(I+c)*tanh(b*x+a)+I)-1/(I+c)/b*arctan(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(c-(I+c)*tanh(b*x+a)+I)*ln((-c-(I+c)*tanh(b*x+a)-I)/(-2*I-2*c))*c-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*dilog((-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))+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(-1/2*(-c-(I+c)*tanh(b*x+a)+I)/c)-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))-1/8*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*arctan(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*arctan(c+(I+c)*tanh(b*x+a))/(2*I+2*c)*ln(I+c+(I+c)*tanh(b*x+a))*c-1/(I+c)/b*arctan(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(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(-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/(I+c)/b*arctan(c+(I+c)*tanh(b*x+a))/(2*I+2*c)*ln(I+c+(I+c)*tanh(b*x+a))*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(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+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(-1/2*(-c-(I+c)*tanh(b*x+a)+I)/c)*c-1/2/(I+c)^2/b*dilog((-c-(I+c)*tanh(b*x+a)-I)/(-2*I-2*c))*c+1/4*I/(I+c)^2/b*dilog(-1/2*(-c-(I+c)*tanh(b*x+a)+I)/c)-1/4*I/(I+c)^2/b*dilog((-c-(I+c)*tanh(b*x+a)-I)/(-2*I-2*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)))","B"
88,0,0,20,1.753000," ","int(arctan(c+(I+c)*tanh(b*x+a))/x,x)","\int \frac{\arctan \left(c +\left(i+c \right) \tanh \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arctan(c+(I+c)*tanh(b*x+a))/x,x)","F"
89,1,1570,119,6.790000," ","int(x^2*arctan(c-(I-c)*tanh(b*x+a)),x)","\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 \,{\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{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{\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{a^{4}}{4 b^{3} \left(i-c \right)}-\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)^{2}}{12}-\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 \,{\mathrm e}^{2 b x +2 a} c -2 i\right)}{6}-\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 c \,{\mathrm e}^{2 b x +2 a}\right) a^{3}}{3 b^{3}}-\frac{i a^{3} \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{-i c}\right)}{2 b^{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{\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^{2} \dilog \left(1-i {\mathrm e}^{b x +a} \sqrt{-i c}\right)}{2 b^{3}}-\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^{4}}{4 b^{3} \left(i-c \right)}-\frac{i b c \,x^{4}}{12 \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 c \,{\mathrm e}^{2 b x +2 a}\right) x \,a^{2}}{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{i \polylog \left(2, i c \,{\mathrm e}^{2 b x +2 a}\right) a^{2}}{4 b^{3}}-\frac{\pi  \,x^{3}}{6}+\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{\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{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 \,{\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)^{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{i x^{3} \ln \left(1-i c \,{\mathrm e}^{2 b x +2 a}\right)}{6}+\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(\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}"," ",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*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*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(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((-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))^3-1/2*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-1/4*I/b^3*c/(I-c)*a^4-1/12*I*b*c/(I-c)*x^4+1/3/b^3*a^3/(I-c)*ln(exp(b*x+a))-1/3/b^2/(I-c)*x*a^3-1/6*Pi*x^3-1/12*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*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))^2-1/12*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+1/2*I/b^2*ln(1-I*c*exp(2*b*x+2*a))*x*a^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/(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))-1/3*I/b^2*c/(I-c)*x*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))^2-1/12*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)/(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*I*polylog(4,I*c*exp(2*b*x+2*a))/b^3+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)+1/3*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"
90,1,1534,95,4.946000," ","int(x*arctan(c-(I-c)*tanh(b*x+a)),x)","-\frac{\pi  \,x^{2}}{4}+\frac{i \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{-i c}\right) a^{2}}{2 b^{2}}+\frac{i \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{-i c}\right) a^{2}}{2 b^{2}}-\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(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(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{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(\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{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{\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{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 x \polylog \left(2, i c \,{\mathrm e}^{2 b x +2 a}\right)}{4 b}+\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{i x^{2} \ln \left(1-i c \,{\mathrm e}^{2 b x +2 a}\right)}{4}+\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{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)^{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)^{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{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 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{a^{3}}{3 b^{2} \left(i-c \right)}-\frac{b \,x^{3}}{6 \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 {\mathrm e}^{b x +a} \sqrt{-i c}\right) x a}{2 b}+\frac{i \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{-i c}\right) x a}{2 b}+\frac{i c \,a^{3}}{3 b^{2} \left(i-c \right)}-\frac{i b c \,x^{3}}{6 \left(i-c \right)}-\frac{i \ln \left(1-i c \,{\mathrm e}^{2 b x +2 a}\right) x a}{2 b}"," ",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*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*(-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))*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))^2-1/4*I*x*polylog(2,I*c*exp(2*b*x+2*a))/b+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/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((-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))^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*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/(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))-1/4*Pi*x^2-1/4*I/b^2*a^2*ln(exp(2*b*x+2*a)*c+I)+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/(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*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))+1/4*I*x^2*ln(-2*exp(2*b*x+2*a)*c-2*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)+1/2*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+1/3*I/b^2*c/(I-c)*a^3-1/6*I*b*c*x^3/(I-c)-1/2*I/b*ln(1-I*c*exp(2*b*x+2*a))*x*a+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","C"
91,1,1351,68,0.457000," ","int(arctan(c-(I-c)*tanh(b*x+a)),x)","-\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{\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)}-\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(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{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{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{\arctan \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{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{\arctan \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{2 i \arctan \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{\ln \left(\frac{\left(c -i\right) \tanh \left(b x +a \right)+c -i}{-2 i+2 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(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{i \ln \left(\frac{i+\left(c -i\right) \tanh \left(b x +a \right)+c}{2 c}\right) \ln \left(\left(c -i\right) \tanh \left(b x +a \right)-c +i\right)}{4 b \left(c -i\right) \left(i-c \right)}-\frac{i \ln \left(\frac{\left(c -i\right) \tanh \left(b x +a \right)+c -i}{-2 i+2 c}\right) \ln \left(\left(c -i\right) \tanh \left(b x +a \right)-c +i\right)}{4 b \left(c -i\right) \left(i-c \right)}+\frac{\arctan \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{\arctan \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(\frac{i+\left(c -i\right) \tanh \left(b x +a \right)+c}{2 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(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{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{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(\frac{i+\left(c -i\right) \tanh \left(b x +a \right)+c}{2 c}\right) \ln \left(\left(c -i\right) \tanh \left(b x +a \right)-c +i\right) c^{2}}{4 b \left(c -i\right) \left(i-c \right)}+\frac{i \ln \left(\frac{\left(c -i\right) \tanh \left(b x +a \right)+c -i}{-2 i+2 c}\right) \ln \left(\left(c -i\right) \tanh \left(b x +a \right)-c +i\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(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{2 i \arctan \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)}"," ",0,"-1/2/b/(c-I)/(I-c)*dilog(1/2*(I+(c-I)*tanh(b*x+a)+c)/c)*c+1/2/b/(c-I)/(I-c)*dilog(((c-I)*tanh(b*x+a)+c-I)/(-2*I+2*c))*c+1/b/(c-I)*arctan((c-I)*tanh(b*x+a)+c)/(2*I-2*c)*ln((c-I)*tanh(b*x+a)+c-I)-1/4*I/b/(c-I)/(I-c)*dilog(((c-I)*tanh(b*x+a)+c-I)/(-2*I+2*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/b/(c-I)*arctan((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-1/4*I/b/(c-I)/(I-c)*dilog(-1/2*I*(I+(c-I)*tanh(b*x+a)+c))-1/4*I/b/(c-I)/(I-c)*ln(1/2*(I+(c-I)*tanh(b*x+a)+c)/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)/(-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(-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)*dilog(((c-I)*tanh(b*x+a)+c-I)/(-2*I+2*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(1/2*(I+(c-I)*tanh(b*x+a)+c)/c)*ln((c-I)*tanh(b*x+a)-c+I)-1/4*I/b/(c-I)/(I-c)*ln(((c-I)*tanh(b*x+a)+c-I)/(-2*I+2*c))*ln((c-I)*tanh(b*x+a)-c+I)+1/4*I/b/(c-I)/(I-c)*dilog(-1/2*I*(I+(c-I)*tanh(b*x+a)+c))*c^2+1/b/(c-I)*arctan((c-I)*tanh(b*x+a)+c)/(2*I-2*c)*ln((c-I)*tanh(b*x+a)-c+I)*c^2-1/b/(c-I)*arctan((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(1/2*(I+(c-I)*tanh(b*x+a)+c)/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)/(-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-2*I/b/(c-I)*arctan((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)*arctan((c-I)*tanh(b*x+a)+c)/(2*I-2*c)*ln((c-I)*tanh(b*x+a)+c-I)*c","B"
92,0,0,23,1.658000," ","int(arctan(c-(I-c)*tanh(b*x+a))/x,x)","\int \frac{\arctan \left(c -\left(i-c \right) \tanh \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arctan(c-(I-c)*tanh(b*x+a))/x,x)","F"
93,1,7275,254,49.104000," ","int((f*x+e)^3*arctan(coth(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
94,1,5425,194,37.481000," ","int((f*x+e)^2*arctan(coth(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
95,1,2415,134,4.685000," ","int((f*x+e)*arctan(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*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*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*e/b*(b*x+a)*ln(((-I)^(1/2)-exp(b*x+a))/(-I)^(1/2))+1/2*I*e/b*(b*x+a)*ln(((-I)^(1/2)+exp(b*x+a))/(-I)^(1/2))+1/4*I*f/b^2*(b*x+a)^2*ln(1-I*exp(2*b*x+2*a))+1/4*I*f/b^2*(b*x+a)*polylog(2,I*exp(2*b*x+2*a))-1/4*I*f/b^2*(b*x+a)*polylog(2,-I*exp(2*b*x+2*a))+1/2*I*(-1/2*f*x^2-e*x)*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*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))^2-1/2*I/b^2*f*a*dilog(((-I)^(1/2)+exp(b*x+a))/(-I)^(1/2))-1/4*I*f/b^2*(b*x+a)^2*ln(1+I*exp(2*b*x+2*a))-1/2*I*e/b*(b*x+a)*ln(1+exp(b*x+a)*(-1)^(3/4))-1/2*I*e/b*(b*x+a)*ln(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*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))+1/8*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))+1/2*I*f/b^2*a*(b*x+a)*ln(1+exp(b*x+a)*(-1)^(3/4))+1/2*I*f/b^2*a*(b*x+a)*ln(1-exp(b*x+a)*(-1)^(3/4))-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+1/4*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*(b*x+a)*ln(((-I)^(1/2)-exp(b*x+a))/(-I)^(1/2))-1/2*I*f/b^2*a*(b*x+a)*ln(((-I)^(1/2)+exp(b*x+a))/(-I)^(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))^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/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*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"
96,1,178,62,0.550000," ","int(arctan(coth(b*x+a)),x)","\frac{\arctanh \left(\coth \left(b x +a \right)\right) \arctan \left(\coth \left(b x +a \right)\right)}{b}-\frac{i \arctanh \left(\coth \left(b x +a \right)\right) \ln \left(1-\frac{i \left(\coth \left(b x +a \right)+1\right)^{2}}{1-\left(\coth^{2}\left(b x +a \right)\right)}\right)}{2 b}+\frac{i \arctanh \left(\coth \left(b x +a \right)\right) \ln \left(1+\frac{i \left(\coth \left(b x +a \right)+1\right)^{2}}{1-\left(\coth^{2}\left(b x +a \right)\right)}\right)}{2 b}+\frac{i \dilog \left(1+\frac{i \left(\coth \left(b x +a \right)+1\right)^{2}}{1-\left(\coth^{2}\left(b x +a \right)\right)}\right)}{4 b}-\frac{i \dilog \left(1-\frac{i \left(\coth \left(b x +a \right)+1\right)^{2}}{1-\left(\coth^{2}\left(b x +a \right)\right)}\right)}{4 b}"," ",0,"1/b*arctanh(coth(b*x+a))*arctan(coth(b*x+a))-1/2*I/b*arctanh(coth(b*x+a))*ln(1-I*(coth(b*x+a)+1)^2/(1-coth(b*x+a)^2))+1/2*I/b*arctanh(coth(b*x+a))*ln(1+I*(coth(b*x+a)+1)^2/(1-coth(b*x+a)^2))+1/4*I/b*dilog(1+I*(coth(b*x+a)+1)^2/(1-coth(b*x+a)^2))-1/4*I/b*dilog(1-I*(coth(b*x+a)+1)^2/(1-coth(b*x+a)^2))","B"
97,0,0,17,2.477000," ","int(arctan(coth(b*x+a))/(f*x+e),x)","\int \frac{\arctan \left(\coth \left(b x +a \right)\right)}{f x +e}\, dx"," ",0,"int(arctan(coth(b*x+a))/(f*x+e),x)","F"
98,1,6864,301,60.585000," ","int(x^2*arctan(c+d*coth(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
99,1,6514,227,6.266000," ","int(x*arctan(c+d*coth(b*x+a)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
100,1,350,150,0.542000," ","int(arctan(c+d*coth(b*x+a)),x)","-\frac{\arctan \left(c +d \coth \left(b x +a \right)\right) \ln \left(d \coth \left(b x +a \right)-d \right)}{2 b}+\frac{\arctan \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*arctan(c+d*coth(b*x+a))*ln(d*coth(b*x+a)-d)+1/2/b*arctan(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"
101,0,0,17,1.064000," ","int(arctan(c+d*coth(b*x+a))/x,x)","\int \frac{\arctan \left(c +d \coth \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arctan(c+d*coth(b*x+a))/x,x)","F"
102,1,1554,116,6.835000," ","int(x^2*arctan(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{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{\pi  \,x^{3}}{6}+\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{i b c \,x^{4}}{12 \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{b \,x^{4}}{12 i+12 c}+\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(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))+1/6*I*x^3*ln(1-I*c*exp(2*b*x+2*a))+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-1/4*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(I*(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*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))^3-1/4*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))+1/6*I*x^3*ln(2*I*exp(2*b*x+2*a)+2*exp(2*b*x+2*a)*c)-1/4*I/b^3*c/(I+c)*a^4-1/12*I*b*c/(I+c)*x^4+1/4/b^3/(I+c)*a^4+1/12*b/(I+c)*x^4+1/6*Pi*x^3-1/6*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))*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*(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))-1/12*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((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))*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((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*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+1/3*I/b^3*c*a^3/(I+c)*ln(exp(b*x+a))-1/3*I/b^2*c/(I+c)*x*a^3+1/2*I/b^2*a^2*ln(1-I*exp(b*x+a)*(-I*c)^(1/2))*x+1/12*Pi*x^3*csgn(I/(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))^2-1/6*I/b^3*a^3*ln(exp(2*b*x+2*a)*c+I)","C"
103,1,1518,92,5.278000," ","int(x*arctan(c+(I+c)*coth(b*x+a)),x)","-\frac{i c \,a^{2} \ln \left({\mathrm e}^{b x +a}\right)}{2 b^{2} \left(i+c \right)}-\frac{i b c \,x^{3}}{6 \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 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 \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{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}}{4}-\frac{i \ln \left(1-i {\mathrm e}^{b x +a} \sqrt{-i c}\right) a^{2}}{2 b^{2}}-\frac{i \ln \left(1+i {\mathrm e}^{b x +a} \sqrt{-i c}\right) a^{2}}{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{i x \polylog \left(2, i c \,{\mathrm e}^{2 b x +2 a}\right)}{4 b}+\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{\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{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 \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)}{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(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{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{b \,x^{3}}{6 i+6 c}+\frac{i c x \,a^{2}}{2 b \left(i+c \right)}+\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{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{\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 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 \,{\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 \,{\mathrm e}^{2 b x +2 a} c +2 i}{{\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}}"," ",0,"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))-1/8*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*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)-1/6*I*b*c*x^3/(I+c)+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((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/(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*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))*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*c/(I+c)*x*a^2-1/2*I/b^2*c*a^2/(I+c)*ln(exp(b*x+a))-1/3/b^2/(I+c)*a^3+1/6*b*x^3/(I+c)+1/3*I/b^2*c/(I+c)*a^3+1/4*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))+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/(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))-1/4*I*x^2*ln(2*exp(2*b*x+2*a)*c+2*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))^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(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*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+1/8*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*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*I*polylog(3,I*c*exp(2*b*x+2*a))/b^2-1/2/b/(I+c)*x*a^2","C"
104,1,1381,65,0.730000," ","int(arctan(c+(I+c)*coth(b*x+a)),x)","\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{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{\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{\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{\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{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 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 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) \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 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)}{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{\arctan \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{\arctan \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{\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 \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{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{\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 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 c}\right) c}{2 \left(i+c \right)^{2} b}-\frac{2 i \arctan \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)}-\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{\arctan \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{\arctan \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{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{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{2 i \arctan \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)}"," ",0,"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((-c-(I+c)*coth(b*x+a)-I)/(-2*I-2*c))*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-1/4*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((-c-(I+c)*coth(b*x+a)-I)/(-2*I-2*c))+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)-1/8*I/(I+c)^2/b*ln(I+c+(I+c)*coth(b*x+a))^2*c^2-1/4*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*dilog(-1/2*(-c-(I+c)*coth(b*x+a)+I)/c)*c^2+1/(I+c)/b*arctan(c+(I+c)*coth(b*x+a))/(2*I+2*c)*ln(c-(I+c)*coth(b*x+a)+I)-1/(I+c)/b*arctan(c+(I+c)*coth(b*x+a))/(2*I+2*c)*ln(I+c+(I+c)*coth(b*x+a))-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-2*I/(I+c)/b*arctan(c+(I+c)*coth(b*x+a))/(2*I+2*c)*ln(c-(I+c)*coth(b*x+a)+I)*c+2*I/(I+c)/b*arctan(c+(I+c)*coth(b*x+a))/(2*I+2*c)*ln(I+c+(I+c)*coth(b*x+a))*c-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/(I+c)/b*arctan(c+(I+c)*coth(b*x+a))/(2*I+2*c)*ln(c-(I+c)*coth(b*x+a)+I)*c^2+1/(I+c)/b*arctan(c+(I+c)*coth(b*x+a))/(2*I+2*c)*ln(I+c+(I+c)*coth(b*x+a))*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((-c-(I+c)*coth(b*x+a)-I)/(-2*I-2*c))*c^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((-c-(I+c)*coth(b*x+a)-I)/(-2*I-2*c))*c+1/2/(I+c)^2/b*dilog(-1/2*(-c-(I+c)*coth(b*x+a)+I)/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((-c-(I+c)*coth(b*x+a)-I)/(-2*I-2*c))+1/4*I/(I+c)^2/b*dilog(-1/2*(-c-(I+c)*coth(b*x+a)+I)/c)+1/8*I/(I+c)^2/b*ln(I+c+(I+c)*coth(b*x+a))^2","B"
105,0,0,20,2.008000," ","int(arctan(c+(I+c)*coth(b*x+a))/x,x)","\int \frac{\arctan \left(c +\left(i+c \right) \coth \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arctan(c+(I+c)*coth(b*x+a))/x,x)","F"
106,1,1571,119,7.321000," ","int(x^2*arctan(c-(I-c)*coth(b*x+a)),x)","-\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 \polylog \left(4, -i c \,{\mathrm e}^{2 b x +2 a}\right)}{8 b^{3}}-\frac{\pi  \,x^{3}}{6}-\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{-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{i x^{3} \ln \left(-2 \,{\mathrm e}^{2 b x +2 a} c +2 i\right)}{6}-\frac{a^{4}}{4 b^{3} \left(i-c \right)}-\frac{b \,x^{4}}{12 \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)^{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{\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^{3} \ln \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{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 \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{\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^{4}}{4 b^{3} \left(i-c \right)}+\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{\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{\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{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(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{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{i a^{3} \ln \left(-{\mathrm e}^{2 b x +2 a} c +i\right)}{6 b^{3}}+\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 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(\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(\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}"," ",0,"1/4*I*x*polylog(3,-I*c*exp(2*b*x+2*a))/b^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))^2-1/6*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))*csgn((2*exp(2*b*x+2*a)*c-2*I)/(exp(2*b*x+2*a)-1))^2-1/4*I*x^2*polylog(2,-I*c*exp(2*b*x+2*a))/b-1/6*I*x^3*ln(2*I*exp(2*b*x+2*a)-2*exp(2*b*x+2*a)*c)+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^3-1/4*I/b^3*c/(I-c)*a^4-1/12*I*b*c/(I-c)*x^4-1/2*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((-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*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+1/3/b^3*a^3/(I-c)*ln(exp(b*x+a))-1/3/b^2/(I-c)*x*a^3-1/6*Pi*x^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*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((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+1/6*I*x^3*ln(-2*exp(2*b*x+2*a)*c+2*I)-1/4/b^3/(I-c)*a^4-1/12*b/(I-c)*x^4+1/3*I/b^3*c*a^3/(I-c)*ln(exp(b*x+a))+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))^2-1/3*I/b^2*c/(I-c)*x*a^3-1/2*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^2-1/12*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))^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+1/6*I/b^3*a^3*ln(-exp(2*b*x+2*a)*c+I)-1/8*I*polylog(4,-I*c*exp(2*b*x+2*a))/b^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))+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*(-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","C"
107,1,1535,95,5.235000," ","int(x*arctan(c-(I-c)*coth(b*x+a)),x)","\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{i \ln \left(1+i c \,{\mathrm e}^{2 b x +2 a}\right) a^{2}}{4 b^{2}}-\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 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{\pi  \,x^{2}}{4}+\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{i b c \,x^{3}}{6 \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{a^{2} \ln \left({\mathrm e}^{b x +a}\right)}{2 b^{2} \left(i-c \right)}-\frac{b \,x^{3}}{6 \left(i-c \right)}-\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{a^{3}}{3 b^{2} \left(i-c \right)}+\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{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}{{\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 c \,a^{2} \ln \left({\mathrm e}^{b x +a}\right)}{2 b^{2} \left(i-c \right)}-\frac{i x^{2} \ln \left(1+i c \,{\mathrm e}^{2 b x +2 a}\right)}{4}+\frac{i c x \,a^{2}}{2 b \left(i-c \right)}+\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{\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{-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{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(-{\mathrm e}^{2 b x +2 a} c +i\right)}{4 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{\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{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}+\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{\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}"," ",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))+1/4*I*x^2*ln(-2*exp(2*b*x+2*a)*c+2*I)-1/4*I/b^2*a^2*ln(-exp(2*b*x+2*a)*c+I)-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*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))*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))^2-1/4*I*x*polylog(2,-I*c*exp(2*b*x+2*a))/b+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/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*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))^3-1/8*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*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))^2-1/4*Pi*x^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*(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))+1/2*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))+1/8*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*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*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)+1/3*I/b^2*c/(I-c)*a^3-1/6*I*b*c*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/(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))","C"
108,1,1351,68,0.770000," ","int(arctan(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)^{2}}{8 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{\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 \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{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 \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(-\frac{i \left(i+\left(c -i\right) \coth \left(b x +a \right)+c \right)}{2}\right) \ln \left(\left(c -i\right) \coth \left(b x +a \right)+c -i\right)}{4 b \left(c -i\right) \left(i-c \right)}+\frac{i \ln \left(\frac{i+\left(c -i\right) \coth \left(b x +a \right)+c}{2 c}\right) \ln \left(\left(c -i\right) \coth \left(b x +a \right)-c +i\right)}{4 b \left(c -i\right) \left(i-c \right)}+\frac{\ln \left(-\frac{i \left(i+\left(c -i\right) \coth \left(b x +a \right)+c \right)}{2}\right) \ln \left(\left(c -i\right) \coth \left(b x +a \right)+c -i\right) c}{2 b \left(c -i\right) \left(i-c \right)}-\frac{\ln \left(\frac{i+\left(c -i\right) \coth \left(b x +a \right)+c}{2 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(i-c \right)}-\frac{\arctan \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{\arctan \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{\ln \left(\frac{\left(c -i\right) \coth \left(b x +a \right)+c -i}{-2 i+2 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(i-c \right)}-\frac{i \ln \left(\frac{\left(c -i\right) \coth \left(b x +a \right)+c -i}{-2 i+2 c}\right) \ln \left(\left(c -i\right) \coth \left(b x +a \right)-c +i\right)}{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(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{2 i \arctan \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{2 i \arctan \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{\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)}-\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{\arctan \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{\arctan \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{\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{i \ln \left(-\frac{i \left(i+\left(c -i\right) \coth \left(b x +a \right)+c \right)}{2}\right) \ln \left(\left(c -i\right) \coth \left(b x +a \right)+c -i\right) c^{2}}{4 b \left(c -i\right) \left(i-c \right)}-\frac{i \ln \left(\frac{i+\left(c -i\right) \coth \left(b x +a \right)+c}{2 c}\right) \ln \left(\left(c -i\right) \coth \left(b x +a \right)-c +i\right) c^{2}}{4 b \left(c -i\right) \left(i-c \right)}+\frac{i \ln \left(\frac{\left(c -i\right) \coth \left(b x +a \right)+c -i}{-2 i+2 c}\right) \ln \left(\left(c -i\right) \coth \left(b x +a \right)-c +i\right) c^{2}}{4 b \left(c -i\right) \left(i-c \right)}"," ",0,"-1/b/(c-I)*arctan((c-I)*coth(b*x+a)+c)/(2*I-2*c)*ln((c-I)*coth(b*x+a)-c+I)+1/b/(c-I)*arctan((c-I)*coth(b*x+a)+c)/(2*I-2*c)*ln((c-I)*coth(b*x+a)+c-I)+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-1/4*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+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(-1/2*I*(I+(c-I)*coth(b*x+a)+c))*c^2-1/8*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(-1/2*I*(I+(c-I)*coth(b*x+a)+c))*ln((c-I)*coth(b*x+a)+c-I)+1/4*I/b/(c-I)/(I-c)*ln(1/2*(I+(c-I)*coth(b*x+a)+c)/c)*ln((c-I)*coth(b*x+a)-c+I)+1/2/b/(c-I)/(I-c)*ln(-1/2*I*(I+(c-I)*coth(b*x+a)+c))*ln((c-I)*coth(b*x+a)+c-I)*c-1/2/b/(c-I)/(I-c)*ln(1/2*(I+(c-I)*coth(b*x+a)+c)/c)*ln((c-I)*coth(b*x+a)-c+I)*c-1/b/(c-I)*arctan((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)*arctan((c-I)*coth(b*x+a)+c)/(2*I-2*c)*ln((c-I)*coth(b*x+a)-c+I)*c^2+1/2/b/(c-I)/(I-c)*ln(((c-I)*coth(b*x+a)+c-I)/(-2*I+2*c))*ln((c-I)*coth(b*x+a)-c+I)*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)/(-2*I+2*c))*ln((c-I)*coth(b*x+a)-c+I)+1/4*I/b/(c-I)/(I-c)*ln(-1/2*I*(I+(c-I)*coth(b*x+a)+c))*ln((c-I)*coth(b*x+a)+c-I)*c^2-1/4*I/b/(c-I)/(I-c)*ln(1/2*(I+(c-I)*coth(b*x+a)+c)/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)/(-2*I+2*c))*ln((c-I)*coth(b*x+a)-c+I)*c^2+2*I/b/(c-I)*arctan((c-I)*coth(b*x+a)+c)/(2*I-2*c)*ln((c-I)*coth(b*x+a)+c-I)*c-2*I/b/(c-I)*arctan((c-I)*coth(b*x+a)+c)/(2*I-2*c)*ln((c-I)*coth(b*x+a)-c+I)*c","B"
109,0,0,23,1.903000," ","int(arctan(c-(I-c)*coth(b*x+a))/x,x)","\int \frac{\arctan \left(c -\left(i-c \right) \coth \left(b x +a \right)\right)}{x}\, dx"," ",0,"int(arctan(c-(I-c)*coth(b*x+a))/x,x)","F"
110,1,59,21,0.056000," ","int(arctan(exp(x)),x)","\ln \left({\mathrm e}^{x}\right) \arctan \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))*arctan(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"
111,1,44,43,0.132000," ","int(x*arctan(exp(x)),x)","\frac{i x \polylog \left(2, -i {\mathrm e}^{x}\right)}{2}-\frac{i x \polylog \left(2, i {\mathrm e}^{x}\right)}{2}-\frac{i \polylog \left(3, -i {\mathrm e}^{x}\right)}{2}+\frac{i \polylog \left(3, i {\mathrm e}^{x}\right)}{2}"," ",0,"1/2*I*x*polylog(2,-I*exp(x))-1/2*I*x*polylog(2,I*exp(x))-1/2*I*polylog(3,-I*exp(x))+1/2*I*polylog(3,I*exp(x))","A"
112,1,70,69,0.125000," ","int(x^2*arctan(exp(x)),x)","\frac{i x^{2} \polylog \left(2, -i {\mathrm e}^{x}\right)}{2}-\frac{i x^{2} \polylog \left(2, i {\mathrm e}^{x}\right)}{2}-i x \polylog \left(3, -i {\mathrm e}^{x}\right)+i x \polylog \left(3, i {\mathrm e}^{x}\right)+i \polylog \left(4, -i {\mathrm e}^{x}\right)-i \polylog \left(4, i {\mathrm e}^{x}\right)"," ",0,"1/2*I*x^2*polylog(2,-I*exp(x))-1/2*I*x^2*polylog(2,I*exp(x))-I*x*polylog(3,-I*exp(x))+I*x*polylog(3,I*exp(x))+I*polylog(4,-I*exp(x))-I*polylog(4,I*exp(x))","A"
113,1,106,35,0.059000," ","int(arctan(exp(b*x+a)),x)","\frac{\ln \left({\mathrm e}^{b x +a}\right) \arctan \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))*arctan(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"
114,1,349,71,0.229000," ","int(x*arctan(exp(b*x+a)),x)","-\frac{i \ln \left(1-i {\mathrm e}^{b x +a}\right) x a}{2 b}+\frac{i \ln \left(-i \left({\mathrm e}^{b x +a}+i\right)\right) x a}{2 b}-\frac{i \polylog \left(3, -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 x \polylog \left(2, i {\mathrm e}^{b x +a}\right)}{2 b}+\frac{i \polylog \left(2, -i {\mathrm e}^{b x +a}\right) a}{2 b^{2}}-\frac{i a^{2} \ln \left(1-i {\mathrm e}^{b x +a}\right)}{2 b^{2}}-\frac{i \ln \left(-i \left(-{\mathrm e}^{b x +a}+i\right)\right) a^{2}}{2 b^{2}}+\frac{i x \polylog \left(2, -i {\mathrm e}^{b x +a}\right)}{2 b}+\frac{i \dilog \left(-i \left({\mathrm e}^{b x +a}+i\right)\right) a}{2 b^{2}}+\frac{i \dilog \left(-i {\mathrm e}^{b x +a}\right) a}{2 b^{2}}-\frac{i \polylog \left(2, 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 {\mathrm e}^{b x +a}\right) \ln \left(-i \left(-{\mathrm e}^{b x +a}+i\right)\right) a}{2 b^{2}}+\frac{i a^{2} \ln \left(1+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(3, i {\mathrm e}^{b x +a}\right)}{2 b^{2}}"," ",0,"1/2*I/b^2*dilog(-I*(exp(b*x+a)+I))*a-1/2*I/b^2*polylog(2,I*exp(b*x+a))*a-1/2*I/b*ln(1-I*exp(b*x+a))*x*a+1/2*I/b^2*dilog(-I*exp(b*x+a))*a+1/2*I/b*ln(-I*(exp(b*x+a)+I))*x*a-1/2*I*x*polylog(2,I*exp(b*x+a))/b+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^2*ln(-I*(-exp(b*x+a)+I))*a^2+1/2*I/b^2*polylog(2,-I*exp(b*x+a))*a+1/2*I*x*polylog(2,-I*exp(b*x+a))/b+1/2*I/b^2*ln(-I*(exp(b*x+a)+I))*a^2+1/2*I/b^2*ln(-I*exp(b*x+a))*ln(-I*(-exp(b*x+a)+I))*a+1/2*I/b^2*a^2*ln(1+I*exp(b*x+a))-1/2*I/b*ln(-I*(-exp(b*x+a)+I))*x*a-1/2*I*polylog(3,-I*exp(b*x+a))/b^2+1/2*I*polylog(3,I*exp(b*x+a))/b^2","B"
115,1,407,111,0.230000," ","int(x^2*arctan(exp(b*x+a)),x)","-\frac{i \dilog \left(-i \left({\mathrm e}^{b x +a}+i\right)\right) a^{2}}{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 x \polylog \left(3, -i {\mathrm e}^{b x +a}\right)}{b^{2}}+\frac{i \ln \left(-i \left(-{\mathrm e}^{b x +a}+i\right)\right) x \,a^{2}}{2 b^{2}}-\frac{i x^{2} \polylog \left(2, i {\mathrm e}^{b x +a}\right)}{2 b}+\frac{i a^{3} \ln \left(1-i {\mathrm e}^{b x +a}\right)}{2 b^{3}}-\frac{i a^{3} \ln \left(1+i {\mathrm e}^{b x +a}\right)}{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 \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 \ln \left(-i \left({\mathrm e}^{b x +a}+i\right)\right) x \,a^{2}}{2 b^{2}}-\frac{i \polylog \left(4, i {\mathrm e}^{b x +a}\right)}{b^{3}}+\frac{i x^{2} \polylog \left(2, -i {\mathrm e}^{b x +a}\right)}{2 b}+\frac{i x \polylog \left(3, i {\mathrm e}^{b x +a}\right)}{b^{2}}+\frac{i \ln \left(-i \left(-{\mathrm e}^{b x +a}+i\right)\right) a^{3}}{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(2, -i {\mathrm e}^{b x +a}\right) a^{2}}{2 b^{3}}"," ",0,"-1/2*I*x^2*polylog(2,I*exp(b*x+a))/b+I*polylog(4,-I*exp(b*x+a))/b^3-1/2*I/b^3*ln(-I*(exp(b*x+a)+I))*a^3-1/2*I/b^3*polylog(2,-I*exp(b*x+a))*a^2-I*x*polylog(3,-I*exp(b*x+a))/b^2+1/2*I/b^2*ln(-I*(-exp(b*x+a)+I))*x*a^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*a^3*ln(1+I*exp(b*x+a))-I*polylog(4,I*exp(b*x+a))/b^3-1/2*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*x^2*polylog(2,-I*exp(b*x+a))/b-1/2*I/b^3*dilog(-I*exp(b*x+a))*a^2+1/2*I/b^3*polylog(2,I*exp(b*x+a))*a^2-1/2*I/b^2*ln(-I*(exp(b*x+a)+I))*x*a^2+I*x*polylog(3,I*exp(b*x+a))/b^2+1/2*I/b^3*ln(-I*(-exp(b*x+a)+I))*a^3-1/2*I/b^2*ln(1+I*exp(b*x+a))*x*a^2","B"
116,1,186,184,0.062000," ","int(arctan(a+b*f^(d*x+c)),x)","\frac{\ln \left(b \,f^{d x +c}\right) \arctan \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))*arctan(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"
117,1,672,200,0.322000," ","int(x*arctan(a+b*f^(d*x+c)),x)","-\frac{i x^{2} \ln \left(1+i \left(a +b \,f^{d x +c}\right)\right)}{4}+\frac{i c^{2} \ln \left(\frac{f^{d x} f^{c} b +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 \ln \left(1-\frac{i b \,f^{d x} f^{c}}{-i a +1}\right) c^{2}}{4 d^{2}}+\frac{i c \dilog \left(\frac{f^{d x} f^{c} b +i+a}{i+a}\right)}{2 d^{2} \ln \left(f \right)}+\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 \ln \left(1-\frac{i b \,f^{d x} f^{c}}{-i a +1}\right) x^{2}}{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 \ln \left(1-\frac{i b \,f^{d x} f^{c}}{-i a +1}\right) x c}{2 d}-\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) x}{2 d \ln \left(f \right)}-\frac{i c \dilog \left(\frac{f^{d x} f^{c} b +a -i}{-i+a}\right)}{2 d^{2} \ln \left(f \right)}-\frac{i c \ln \left(\frac{f^{d x} f^{c} b +a -i}{-i+a}\right) x}{2 d}-\frac{i c^{2} \ln \left(1-i a -i f^{d x} f^{c} b \right)}{4 d^{2}}+\frac{i c^{2} \ln \left(i f^{d x} f^{c} b +i a +1\right)}{4 d^{2}}-\frac{i c^{2} \ln \left(\frac{f^{d x} f^{c} b +a -i}{-i+a}\right)}{2 d^{2}}+\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(3, \frac{i b \,f^{d x} f^{c}}{-i a -1}\right)}{2 d^{2} \ln \left(f \right)^{2}}+\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(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{f^{d x} f^{c} b +i+a}{i+a}\right) x}{2 d}+\frac{i x^{2} \ln \left(1-i \left(a +b \,f^{d x +c}\right)\right)}{4}"," ",0,"-1/4*I*x^2*ln(1+I*(a+b*f^(d*x+c)))+1/2*I/d^2*c^2*ln((f^(d*x)*f^c*b+I+a)/(I+a))-1/2*I/d^2/ln(f)*c*dilog((f^(d*x)*f^c*b+a-I)/(-I+a))+1/4*I*ln(1-I*b/(-I*a-1)*f^(d*x)*f^c)*x^2-1/4*I/d^2*ln(1-I*b/(1-I*a)*f^(d*x)*f^c)*c^2-1/2*I/d^2/ln(f)*polylog(2,I*b/(1-I*a)*f^(d*x)*f^c)*c+1/2*I/d^2/ln(f)*c*dilog((f^(d*x)*f^c*b+I+a)/(I+a))-1/4*I*ln(1-I*b/(1-I*a)*f^(d*x)*f^c)*x^2+1/4*I/d^2*ln(1-I*b/(-I*a-1)*f^(d*x)*f^c)*c^2-1/2*I/d*ln(1-I*b/(1-I*a)*f^(d*x)*f^c)*x*c+1/2*I/d^2/ln(f)^2*polylog(3,I*b/(1-I*a)*f^(d*x)*f^c)-1/2*I/d*c*ln((f^(d*x)*f^c*b+a-I)/(-I+a))*x-1/4*I/d^2*c^2*ln(1-I*a-I*f^(d*x)*f^c*b)+1/4*I/d^2*c^2*ln(I*f^(d*x)*f^c*b+I*a+1)-1/2*I/d^2*c^2*ln((f^(d*x)*f^c*b+a-I)/(-I+a))+1/2*I/d^2/ln(f)*polylog(2,I*b/(-I*a-1)*f^(d*x)*f^c)*c+1/2*I/d*ln(1-I*b/(-I*a-1)*f^(d*x)*f^c)*x*c+1/2*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/(-I*a-1)*f^(d*x)*f^c)+1/2*I/d*c*ln((f^(d*x)*f^c*b+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/(1-I*a)*f^(d*x)*f^c)*x","B"
118,1,758,268,0.294000," ","int(x^2*arctan(a+b*f^(d*x+c)),x)","\frac{i x^{3} \ln \left(1-i \left(a +b \,f^{d x +c}\right)\right)}{6}+\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 \ln \left(1-\frac{i b \,f^{d x} f^{c}}{-i a -1}\right) c^{3}}{3 d^{3}}+\frac{i c^{2} \ln \left(\frac{f^{d x} f^{c} b +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^{3}}{6}-\frac{i x^{3} \ln \left(1+i \left(a +b \,f^{d x +c}\right)\right)}{6}+\frac{i c^{3} \ln \left(1-i a -i f^{d x} f^{c} b \right)}{6 d^{3}}-\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^{3} \ln \left(\frac{f^{d x} f^{c} b +a -i}{-i+a}\right)}{2 d^{3}}-\frac{i c^{2} \ln \left(\frac{f^{d x} f^{c} b +i+a}{i+a}\right) x}{2 d^{2}}+\frac{i c^{2} \dilog \left(\frac{f^{d x} f^{c} b +a -i}{-i+a}\right)}{2 d^{3} \ln \left(f \right)}-\frac{i c^{2} \dilog \left(\frac{f^{d x} f^{c} b +i+a}{i+a}\right)}{2 d^{3} \ln \left(f \right)}+\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 c^{3} \ln \left(\frac{f^{d x} f^{c} b +i+a}{i+a}\right)}{2 d^{3}}-\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(4, \frac{i b \,f^{d x} f^{c}}{-i a -1}\right)}{d^{3} \ln \left(f \right)^{3}}+\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 \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) x \,c^{2}}{2 d^{2}}-\frac{i c^{3} \ln \left(i f^{d x} f^{c} b +i a +1\right)}{6 d^{3}}-\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 \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) c^{3}}{3 d^{3}}"," ",0,"-1/2*I/d/ln(f)*polylog(2,I*b/(1-I*a)*f^(d*x)*f^c)*x^2+1/6*I*x^3*ln(1-I*(a+b*f^(d*x+c)))-1/2*I/d^3/ln(f)*c^2*dilog((f^(d*x)*f^c*b+I+a)/(I+a))+I/d^3/ln(f)^3*polylog(4,I*b/(-I*a-1)*f^(d*x)*f^c)-1/3*I/d^3*ln(1-I*b/(-I*a-1)*f^(d*x)*f^c)*c^3+1/2*I/d^2*c^2*ln((f^(d*x)*f^c*b+a-I)/(-I+a))*x+1/6*I*ln(1-I*b/(-I*a-1)*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^3/ln(f)*polylog(2,I*b/(-I*a-1)*f^(d*x)*f^c)*c^2+1/6*I/d^3*c^3*ln(1-I*a-I*f^(d*x)*f^c*b)-1/2*I/d^2*ln(1-I*b/(-I*a-1)*f^(d*x)*f^c)*x*c^2+1/2*I/d^3*c^3*ln((f^(d*x)*f^c*b+a-I)/(-I+a))-1/2*I/d^2*c^2*ln((f^(d*x)*f^c*b+I+a)/(I+a))*x+1/2*I/d^3/ln(f)*polylog(2,I*b/(1-I*a)*f^(d*x)*f^c)*c^2+I/d^2/ln(f)^2*polylog(3,I*b/(1-I*a)*f^(d*x)*f^c)*x+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*c^3*ln((f^(d*x)*f^c*b+I+a)/(I+a))-I/d^2/ln(f)^2*polylog(3,I*b/(-I*a-1)*f^(d*x)*f^c)*x-I/d^3/ln(f)^3*polylog(4,I*b/(1-I*a)*f^(d*x)*f^c)+1/2*I/d^2*ln(1-I*b/(1-I*a)*f^(d*x)*f^c)*x*c^2-1/6*I/d^3*c^3*ln(I*f^(d*x)*f^c*b+I*a+1)-1/6*I*ln(1-I*b/(1-I*a)*f^(d*x)*f^c)*x^3+1/3*I/d^3*ln(1-I*b/(1-I*a)*f^(d*x)*f^c)*c^3+1/2*I/d^3/ln(f)*c^2*dilog((f^(d*x)*f^c*b+a-I)/(-I+a))","B"
119,1,23,20,0.042000," ","int(arctan(exp(x))/exp(x),x)","-\arctan \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,"-arctan(exp(x))/exp(x)+ln(exp(x))-1/2*ln(exp(x)^2+1)","A"
120,1,32,37,0.046000," ","int(arctan(x)/(x-1)^3,x)","-\frac{\arctan \left(x \right)}{2 \left(x -1\right)^{2}}+\frac{\ln \left(x^{2}+1\right)}{8}-\frac{1}{4 \left(x -1\right)}-\frac{\ln \left(x -1\right)}{4}"," ",0,"-1/2/(x-1)^2*arctan(x)+1/8*ln(x^2+1)-1/4/(x-1)-1/4*ln(x-1)","A"
121,1,54,54,0.047000," ","int(arctan(1+2*x)/(4+3*x)^3,x)","-\frac{2 \arctan \left(1+2 x \right)}{3 \left(8+6 x \right)^{2}}-\frac{1}{17 \left(8+6 x \right)}+\frac{5 \ln \left(8+6 x \right)}{289}-\frac{5 \ln \left(\left(1+2 x \right)^{2}+1\right)}{578}+\frac{8 \arctan \left(1+2 x \right)}{867}"," ",0,"-2/3/(8+6*x)^2*arctan(1+2*x)-1/17/(8+6*x)+5/289*ln(8+6*x)-5/578*ln((1+2*x)^2+1)+8/867*arctan(1+2*x)","A"
122,1,25,24,0.037000," ","int(arctan((x+1)^(1/2)),x)","\left(x +1\right) \arctan \left(\sqrt{x +1}\right)-\sqrt{x +1}+\arctan \left(\sqrt{x +1}\right)"," ",0,"(x+1)*arctan((x+1)^(1/2))-(x+1)^(1/2)+arctan((x+1)^(1/2))","A"
123,1,6,5,0.036000," ","int(1/(x^2+1)/(2+arctan(x)),x)","\ln \left(2+\arctan \left(x \right)\right)"," ",0,"ln(2+arctan(x))","A"
124,1,19,15,0.076000," ","int(1/(a*x^2+a)/(b-2*b*arctan(x)),x)","-\frac{\ln \left(2 b \arctan \left(x \right)-b \right)}{2 a b}"," ",0,"-1/2/a*ln(2*b*arctan(x)-b)/b","A"
125,1,17,16,0.046000," ","int((x+x^3+(x+1)^2*arctan(x))/(x+1)^2/(x^2+1),x)","\frac{1}{x +1}+\frac{\arctan \left(x \right)^{2}}{2}+\ln \left(x +1\right)"," ",0,"1/(x+1)+1/2*arctan(x)^2+ln(x+1)","A"
126,1,45,42,0.056000," ","int(-x^3*arctan(x^(1/2)-(x+1)^(1/2)),x)","-\frac{x^{4} \arctan \left(\sqrt{x}-\sqrt{x +1}\right)}{4}+\frac{x^{\frac{7}{2}}}{56}-\frac{x^{\frac{5}{2}}}{40}+\frac{x^{\frac{3}{2}}}{24}-\frac{\sqrt{x}}{8}+\frac{\arctan \left(\sqrt{x}\right)}{8}"," ",0,"-1/4*x^4*arctan(x^(1/2)-(x+1)^(1/2))+1/56*x^(7/2)-1/40*x^(5/2)+1/24*x^(3/2)-1/8*x^(1/2)+1/8*arctan(x^(1/2))","A"
127,1,40,37,0.055000," ","int(-x^2*arctan(x^(1/2)-(x+1)^(1/2)),x)","-\frac{x^{3} \arctan \left(\sqrt{x}-\sqrt{x +1}\right)}{3}+\frac{x^{\frac{5}{2}}}{30}-\frac{x^{\frac{3}{2}}}{18}+\frac{\sqrt{x}}{6}-\frac{\arctan \left(\sqrt{x}\right)}{6}"," ",0,"-1/3*x^3*arctan(x^(1/2)-(x+1)^(1/2))+1/30*x^(5/2)-1/18*x^(3/2)+1/6*x^(1/2)-1/6*arctan(x^(1/2))","A"
128,1,35,32,0.053000," ","int(-x*arctan(x^(1/2)-(x+1)^(1/2)),x)","-\frac{x^{2} \arctan \left(\sqrt{x}-\sqrt{x +1}\right)}{2}+\frac{x^{\frac{3}{2}}}{12}-\frac{\sqrt{x}}{4}+\frac{\arctan \left(\sqrt{x}\right)}{4}"," ",0,"-1/2*x^2*arctan(x^(1/2)-(x+1)^(1/2))+1/12*x^(3/2)-1/4*x^(1/2)+1/4*arctan(x^(1/2))","A"
129,1,28,23,0.054000," ","int(-arctan(x^(1/2)-(x+1)^(1/2)),x)","-x \arctan \left(\sqrt{x}-\sqrt{x +1}\right)+\frac{\sqrt{x}}{2}-\frac{\arctan \left(\sqrt{x}\right)}{2}"," ",0,"-x*arctan(x^(1/2)-(x+1)^(1/2))+1/2*x^(1/2)-1/2*arctan(x^(1/2))","A"
130,1,194,28,1.402000," ","int(-arctan(x^(1/2)-(x+1)^(1/2))/x,x)","2 \arctan \left(\sqrt{x}-\sqrt{x +1}\right) \ln \left(1-\frac{\left(1+i \left(\sqrt{x}-\sqrt{x +1}\right)\right)^{4}}{\left(\left(\sqrt{x}-\sqrt{x +1}\right)^{2}+1\right)^{2}}\right)-2 \arctan \left(\sqrt{x}-\sqrt{x +1}\right) \ln \left(1+\frac{\left(1+i \left(\sqrt{x}-\sqrt{x +1}\right)\right)^{4}}{\left(\left(\sqrt{x}-\sqrt{x +1}\right)^{2}+1\right)^{2}}\right)+\frac{i \dilog \left(1+\frac{\left(1+i \left(\sqrt{x}-\sqrt{x +1}\right)\right)^{4}}{\left(\left(\sqrt{x}-\sqrt{x +1}\right)^{2}+1\right)^{2}}\right)}{2}-\frac{i \dilog \left(1-\frac{\left(1+i \left(\sqrt{x}-\sqrt{x +1}\right)\right)^{4}}{\left(\left(\sqrt{x}-\sqrt{x +1}\right)^{2}+1\right)^{2}}\right)}{2}"," ",0,"2*arctan(x^(1/2)-(x+1)^(1/2))*ln(1-(1+I*(x^(1/2)-(x+1)^(1/2)))^4/((x^(1/2)-(x+1)^(1/2))^2+1)^2)-2*arctan(x^(1/2)-(x+1)^(1/2))*ln(1+(1+I*(x^(1/2)-(x+1)^(1/2)))^4/((x^(1/2)-(x+1)^(1/2))^2+1)^2)+1/2*I*dilog(1+(1+I*(x^(1/2)-(x+1)^(1/2)))^4/((x^(1/2)-(x+1)^(1/2))^2+1)^2)-1/2*I*dilog(1-(1+I*(x^(1/2)-(x+1)^(1/2)))^4/((x^(1/2)-(x+1)^(1/2))^2+1)^2)","B"
131,1,57,27,0.057000," ","int(-arctan(x^(1/2)-(x+1)^(1/2))/x^2,x)","\frac{\arctan \left(\sqrt{x}-\sqrt{x +1}\right)}{x}+\frac{1}{2 \sqrt{x}}+\frac{\arctanh \left(\sqrt{x +1}\right)}{2}+\frac{\arctan \left(\sqrt{x}\right)}{2}-\frac{\ln \left(\sqrt{x +1}+1\right)}{4}+\frac{\ln \left(\sqrt{x +1}-1\right)}{4}"," ",0,"arctan(x^(1/2)-(x+1)^(1/2))/x+1/2/x^(1/2)+1/2*arctanh((x+1)^(1/2))+1/2*arctan(x^(1/2))-1/4*ln((x+1)^(1/2)+1)+1/4*ln((x+1)^(1/2)-1)","B"
132,1,35,32,0.073000," ","int(-arctan(x^(1/2)-(x+1)^(1/2))/x^3,x)","\frac{\arctan \left(\sqrt{x}-\sqrt{x +1}\right)}{2 x^{2}}+\frac{1}{12 x^{\frac{3}{2}}}-\frac{1}{4 \sqrt{x}}-\frac{\arctan \left(\sqrt{x}\right)}{4}"," ",0,"1/2*arctan(x^(1/2)-(x+1)^(1/2))/x^2+1/12/x^(3/2)-1/4/x^(1/2)-1/4*arctan(x^(1/2))","A"
133,1,40,37,0.077000," ","int(-arctan(x^(1/2)-(x+1)^(1/2))/x^4,x)","\frac{\arctan \left(\sqrt{x}-\sqrt{x +1}\right)}{3 x^{3}}+\frac{1}{30 x^{\frac{5}{2}}}-\frac{1}{18 x^{\frac{3}{2}}}+\frac{1}{6 \sqrt{x}}+\frac{\arctan \left(\sqrt{x}\right)}{6}"," ",0,"1/3*arctan(x^(1/2)-(x+1)^(1/2))/x^3+1/30/x^(5/2)-1/18/x^(3/2)+1/6/x^(1/2)+1/6*arctan(x^(1/2))","A"
134,1,73,57,0.517000," ","int(arctan(c*x/(-c^2*x^2+a)^(1/2))^m/(d-c^2*d*x^2/a)^(1/2),x)","-\frac{\arctan \left(\frac{c x}{\sqrt{-c^{2} x^{2}+a}}\right)^{1+m} \left(c^{2} x^{2}-a \right)}{\left(1+m \right) \sqrt{-\frac{d \left(c^{2} x^{2}-a \right)}{a}}\, \sqrt{-c^{2} x^{2}+a}\, c}"," ",0,"-arctan(c*x/(-c^2*x^2+a)^(1/2))^(1+m)/(1+m)*(c^2*x^2-a)/(-d*(c^2*x^2-a)/a)^(1/2)/(-c^2*x^2+a)^(1/2)/c","A"
135,1,72,51,0.433000," ","int(arctan(c*x/(-c^2*x^2+a)^(1/2))^2/(d-c^2*d*x^2/a)^(1/2),x)","-\frac{\sqrt{-\frac{d \left(c^{2} x^{2}-a \right)}{a}}\, \sqrt{-c^{2} x^{2}+a}\, \arctan \left(\frac{c x}{\sqrt{-c^{2} x^{2}+a}}\right)^{3} a}{3 d \left(c^{2} x^{2}-a \right) c}"," ",0,"-1/3*(-d*(c^2*x^2-a)/a)^(1/2)*(-c^2*x^2+a)^(1/2)/d/(c^2*x^2-a)/c*arctan(c*x/(-c^2*x^2+a)^(1/2))^3*a","A"
136,1,72,51,0.433000," ","int(arctan(c*x/(-c^2*x^2+a)^(1/2))/(d-c^2*d*x^2/a)^(1/2),x)","-\frac{\sqrt{-\frac{d \left(c^{2} x^{2}-a \right)}{a}}\, \sqrt{-c^{2} x^{2}+a}\, \arctan \left(\frac{c x}{\sqrt{-c^{2} x^{2}+a}}\right)^{2} a}{2 d \left(c^{2} x^{2}-a \right) c}"," ",0,"-1/2*(-d*(c^2*x^2-a)/a)^(1/2)*(-c^2*x^2+a)^(1/2)/d/(c^2*x^2-a)/c*arctan(c*x/(-c^2*x^2+a)^(1/2))^2*a","A"
137,1,71,49,1.785000," ","int(1/arctan(c*x/(-c^2*x^2+a)^(1/2))/(d-c^2*d*x^2/a)^(1/2),x)","-\frac{\sqrt{-\frac{d \left(c^{2} x^{2}-a \right)}{a}}\, \sqrt{-c^{2} x^{2}+a}\, \ln \left(\arctan \left(\frac{c x}{\sqrt{-c^{2} x^{2}+a}}\right)\right) a}{d \left(c^{2} x^{2}-a \right) c}"," ",0,"-(-d*(c^2*x^2-a)/a)^(1/2)*(-c^2*x^2+a)^(1/2)/d/(c^2*x^2-a)/c*ln(arctan(c*x/(-c^2*x^2+a)^(1/2)))*a","A"
138,1,71,51,0.425000," ","int(1/arctan(c*x/(-c^2*x^2+a)^(1/2))^2/(d-c^2*d*x^2/a)^(1/2),x)","\frac{\sqrt{-\frac{d \left(c^{2} x^{2}-a \right)}{a}}\, \sqrt{-c^{2} x^{2}+a}\, a}{d \left(c^{2} x^{2}-a \right) c \arctan \left(\frac{c x}{\sqrt{-c^{2} x^{2}+a}}\right)}"," ",0,"(-d*(c^2*x^2-a)/a)^(1/2)*(-c^2*x^2+a)^(1/2)/d/(c^2*x^2-a)/c*a/arctan(c*x/(-c^2*x^2+a)^(1/2))","A"
139,1,72,51,0.434000," ","int(1/arctan(c*x/(-c^2*x^2+a)^(1/2))^3/(d-c^2*d*x^2/a)^(1/2),x)","\frac{\sqrt{-\frac{d \left(c^{2} x^{2}-a \right)}{a}}\, \sqrt{-c^{2} x^{2}+a}\, a}{2 d \left(c^{2} x^{2}-a \right) c \arctan \left(\frac{c x}{\sqrt{-c^{2} x^{2}+a}}\right)^{2}}"," ",0,"1/2*(-d*(c^2*x^2-a)/a)^(1/2)*(-c^2*x^2+a)^(1/2)/d/(c^2*x^2-a)/c*a/arctan(c*x/(-c^2*x^2+a)^(1/2))^2","A"
140,0,0,66,1.113000," ","int(arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))^m/(b*x^2+a)^(1/2),x)","\int \frac{\arctan \left(\frac{e x}{\sqrt{-\frac{a \,e^{2}}{b}-e^{2} x^{2}}}\right)^{m}}{\sqrt{b \,x^{2}+a}}\, dx"," ",0,"int(arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))^m/(b*x^2+a)^(1/2),x)","F"
141,0,0,60,0.444000," ","int(arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))^2/(b*x^2+a)^(1/2),x)","\int \frac{\arctan \left(\frac{e x}{\sqrt{-\frac{a \,e^{2}}{b}-e^{2} x^{2}}}\right)^{2}}{\sqrt{b \,x^{2}+a}}\, dx"," ",0,"int(arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))^2/(b*x^2+a)^(1/2),x)","F"
142,0,0,60,0.448000," ","int(arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))/(b*x^2+a)^(1/2),x)","\int \frac{\arctan \left(\frac{e x}{\sqrt{-\frac{a \,e^{2}}{b}-e^{2} x^{2}}}\right)}{\sqrt{b \,x^{2}+a}}\, dx"," ",0,"int(arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))/(b*x^2+a)^(1/2),x)","F"
143,0,0,58,0.448000," ","int(1/arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))/(b*x^2+a)^(1/2),x)","\int \frac{1}{\arctan \left(\frac{e x}{\sqrt{-\frac{a \,e^{2}}{b}-e^{2} x^{2}}}\right) \sqrt{b \,x^{2}+a}}\, dx"," ",0,"int(1/arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))/(b*x^2+a)^(1/2),x)","F"
144,0,0,60,0.445000," ","int(1/arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))^2/(b*x^2+a)^(1/2),x)","\int \frac{1}{\arctan \left(\frac{e x}{\sqrt{-\frac{a \,e^{2}}{b}-e^{2} x^{2}}}\right)^{2} \sqrt{b \,x^{2}+a}}\, dx"," ",0,"int(1/arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))^2/(b*x^2+a)^(1/2),x)","F"
145,0,0,60,0.446000," ","int(1/arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))^3/(b*x^2+a)^(1/2),x)","\int \frac{1}{\arctan \left(\frac{e x}{\sqrt{-\frac{a \,e^{2}}{b}-e^{2} x^{2}}}\right)^{3} \sqrt{b \,x^{2}+a}}\, dx"," ",0,"int(1/arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))^3/(b*x^2+a)^(1/2),x)","F"
146,0,0,85,6.751000," ","int(arctan(c*(b*x+a))*ln(d*(b*x+a))/(b*x+a),x)","\int \frac{\arctan \left(c \left(b x +a \right)\right) \ln \left(d \left(b x +a \right)\right)}{b x +a}\, dx"," ",0,"int(arctan(c*(b*x+a))*ln(d*(b*x+a))/(b*x+a),x)","F"
147,1,1299,46,1.345000," ","int(exp(c*(b*x+a))*arctan(sinh(b*c*x+a*c)),x)","\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{\ln \left(1+{\mathrm e}^{2 c \left(b x +a \right)}\right)}{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)^{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{\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)\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 {\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)}\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)} \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)^{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)} \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{2 a}{b}+\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}+\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(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{{\mathrm e}^{c \left(b x +a \right)} \pi}{2 b c}"," ",0,"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))-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))+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*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))*(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)))*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))*(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)))*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))*(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))+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(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)^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)+1/2/b/c*exp(c*(b*x+a))*Pi","C"
148,1,1375,88,2.615000," ","int(exp(c*(b*x+a))*arctan(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(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 \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)}\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 \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)} \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)} \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)}\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) \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({\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)^{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) {\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({\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{{\mathrm e}^{c \left(b x +a \right)} \pi}{2 b c}+\frac{\sqrt{2}\, \ln \left({\mathrm e}^{2 c \left(b x +a \right)}+\left(\sqrt{2}-1\right)^{2}\right)}{2 b c}-\frac{\sqrt{2}\, \ln \left({\mathrm e}^{2 c \left(b x +a \right)}+\left(1+\sqrt{2}\right)^{2}\right)}{2 b c}+\frac{2 a}{b}-\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(\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(-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(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)))*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(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))*(-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))*(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)))*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))))*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(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))))^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))))*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(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))+1/2/b/c*exp(c*(b*x+a))*Pi+1/2/b/c*2^(1/2)*ln(exp(2*c*(b*x+a))+(2^(1/2)-1)^2)-1/2/b/c*2^(1/2)*ln(exp(2*c*(b*x+a))+(1+2^(1/2))^2)+2*a/b-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))+(2^(1/2)-1)^2)-1/2/b/c*ln(exp(2*c*(b*x+a))+(1+2^(1/2))^2)","C"
149,1,1355,153,2.616000," ","int(exp(c*(b*x+a))*arctan(tanh(b*c*x+a*c)),x)","\frac{i \ln \left({\mathrm e}^{c \left(b x +a \right)}+\frac{\sqrt{2}}{2}-\frac{i \sqrt{2}}{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{\ln \left({\mathrm e}^{c \left(b x +a \right)}-\frac{\sqrt{2}}{2}-\frac{i \sqrt{2}}{2}\right) \sqrt{2}}{4 b c}-\frac{\ln \left({\mathrm e}^{c \left(b x +a \right)}-\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{2}}{4 b c}+\frac{\ln \left({\mathrm e}^{c \left(b x +a \right)}+\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{2}}{4 b c}+\frac{\ln \left({\mathrm e}^{c \left(b x +a \right)}+\frac{\sqrt{2}}{2}-\frac{i \sqrt{2}}{2}\right) \sqrt{2}}{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{\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(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)^{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)^{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{\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)}-\frac{\sqrt{2}}{2}-\frac{i \sqrt{2}}{2}\right) \sqrt{2}}{4 b c}-\frac{i \ln \left({\mathrm e}^{c \left(b x +a \right)}-\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{2}}{4 b c}+\frac{{\mathrm e}^{c \left(b x +a \right)} \pi}{4 b c}-\frac{i \ln \left({\mathrm e}^{c \left(b x +a \right)}+\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{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)^{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{\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{\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)^{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}^{2 c \left(b x +a \right)}+i\right)}{2 b c}"," ",0,"1/4*I/b/c*ln(exp(c*(b*x+a))+1/2*2^(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*I/b/c*ln(exp(c*(b*x+a))-1/2*2^(1/2)-1/2*I*2^(1/2))*2^(1/2)-1/4*I/b/c*ln(exp(c*(b*x+a))-1/2*2^(1/2)+1/2*I*2^(1/2))*2^(1/2)-1/4*I/b/c*ln(exp(c*(b*x+a))+1/2*2^(1/2)+1/2*I*2^(1/2))*2^(1/2)+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/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))))^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))))^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))*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*ln(exp(c*(b*x+a))-1/2*2^(1/2)-1/2*I*2^(1/2))*2^(1/2)-1/4/b/c*ln(exp(c*(b*x+a))-1/2*2^(1/2)+1/2*I*2^(1/2))*2^(1/2)+1/4/b/c*ln(exp(c*(b*x+a))+1/2*2^(1/2)+1/2*I*2^(1/2))*2^(1/2)+1/4/b/c*ln(exp(c*(b*x+a))+1/2*2^(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))*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))))^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))))^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(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*exp(c*(b*x+a))*Pi","C"
150,1,1355,153,2.070000," ","int(exp(c*(b*x+a))*arctan(coth(b*c*x+a*c)),x)","-\frac{i \ln \left({\mathrm e}^{c \left(b x +a \right)}+\frac{\sqrt{2}}{2}-\frac{i \sqrt{2}}{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{\ln \left({\mathrm e}^{c \left(b x +a \right)}-\frac{\sqrt{2}}{2}-\frac{i \sqrt{2}}{2}\right) \sqrt{2}}{4 b c}+\frac{\ln \left({\mathrm e}^{c \left(b x +a \right)}-\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{2}}{4 b c}-\frac{\ln \left({\mathrm e}^{c \left(b x +a \right)}+\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{2}}{4 b c}-\frac{\ln \left({\mathrm e}^{c \left(b x +a \right)}+\frac{\sqrt{2}}{2}-\frac{i \sqrt{2}}{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}{{\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}{{\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)^{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(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 \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)}-\frac{\sqrt{2}}{2}-\frac{i \sqrt{2}}{2}\right) \sqrt{2}}{4 b c}+\frac{i \ln \left({\mathrm e}^{c \left(b x +a \right)}-\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{2}}{4 b c}+\frac{{\mathrm e}^{c \left(b x +a \right)} \pi}{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)^{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{i \ln \left({\mathrm e}^{c \left(b x +a \right)}+\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{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}"," ",0,"-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*ln(exp(c*(b*x+a))-1/2*2^(1/2)-1/2*I*2^(1/2))*2^(1/2)+1/4/b/c*ln(exp(c*(b*x+a))-1/2*2^(1/2)+1/2*I*2^(1/2))*2^(1/2)-1/4/b/c*ln(exp(c*(b*x+a))+1/2*2^(1/2)+1/2*I*2^(1/2))*2^(1/2)-1/4/b/c*ln(exp(c*(b*x+a))+1/2*2^(1/2)-1/2*I*2^(1/2))*2^(1/2)-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))-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))^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))*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))+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/b/c*exp(c*(b*x+a))*Pi-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))^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))+1/2*I/b/c*exp(c*(b*x+a))*ln(exp(2*c*(b*x+a))-I)-1/4*I/b/c*ln(exp(c*(b*x+a))-1/2*2^(1/2)-1/2*I*2^(1/2))*2^(1/2)+1/4*I/b/c*ln(exp(c*(b*x+a))-1/2*2^(1/2)+1/2*I*2^(1/2))*2^(1/2)+1/4*I/b/c*ln(exp(c*(b*x+a))+1/2*2^(1/2)+1/2*I*2^(1/2))*2^(1/2)-1/4*I/b/c*ln(exp(c*(b*x+a))+1/2*2^(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"
151,1,842,88,1.876000," ","int(exp(c*(b*x+a))*arctan(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}{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(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}{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{\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 \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{\sqrt{2}\, \ln \left({\mathrm e}^{2 c \left(b x +a \right)}+\left(\sqrt{2}-1\right)^{2}\right)}{2 b c}+\frac{\sqrt{2}\, \ln \left({\mathrm e}^{2 c \left(b x +a \right)}+\left(1+\sqrt{2}\right)^{2}\right)}{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}+\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}"," ",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/(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))))*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/(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))+1/4/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)))/(1+exp(2*c*(b*x+a))))^3*exp(c*(b*x+a))-1/2/b/c*2^(1/2)*ln(exp(2*c*(b*x+a))+(2^(1/2)-1)^2)+1/2/b/c*2^(1/2)*ln(exp(2*c*(b*x+a))+(1+2^(1/2))^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)+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)))","C"
152,1,885,45,0.980000," ","int(exp(c*(b*x+a))*arctan(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(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) \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)^{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(\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(\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(\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{2 a}{b}+\frac{\ln \left(1+{\mathrm e}^{2 c \left(b x +a \right)}\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}"," ",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)^3*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))-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))-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(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/(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))-2*a/b+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)","C"
153,1,896,137,0.701000," ","int((a+b*arctan(c*x^n))*(d+e*ln(f*x^m))/x,x)","-\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 \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 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{\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 \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{i e b \dilog \left(-i c \,x^{n}\right) m \ln \left(x \right)}{2 n}-\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{e a \ln \left(x^{m}\right)^{2}}{2 m}-\frac{i e b m \ln \left(x \right) \polylog \left(2, i c \,x^{n}\right)}{2 n}-\frac{i \ln \left(x^{n}\right) \pi  a e \mathrm{csgn}\left(i f \,x^{m}\right)^{3}}{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)^{2}}{4 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 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{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{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 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 e b \ln \left(1-i c \,x^{n}\right) \ln \left(x^{m}\right) \ln \left(x \right)}{2}-\frac{i b e m \polylog \left(3, -i c \,x^{n}\right)}{2 n^{2}}+\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 e b \dilog \left(-i \left(c \,x^{n}+i\right)\right) \ln \left(x^{m}\right)}{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(-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) \ln \left(f \right) b e}{2 n}-\frac{i e b \dilog \left(-i c \,x^{n}\right) \ln \left(x^{m}\right)}{2 n}+\frac{i \dilog \left(1+i c \,x^{n}\right) \ln \left(f \right) b e}{2 n}+\frac{i b e m \polylog \left(3, i c \,x^{n}\right)}{2 n^{2}}-\frac{i e b \ln \left(1-i c \,x^{n}\right) \ln \left(x \right)^{2} m}{2}-\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}+\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{\ln \left(x^{n}\right) \ln \left(f \right) a e}{n}+\frac{\ln \left(x^{n}\right) a d}{n}"," ",0,"-1/2*I/n*dilog(1-I*c*x^n)*ln(f)*b*e-1/2*I*e*b/n*dilog(-I*c*x^n)*ln(x^m)+1/2*I/n*dilog(1+I*c*x^n)*ln(f)*b*e+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(1+I*c*x^n)*ln(x)^2*m-1/2*I*e*b*ln(1+I*c*x^n)*ln(x^m)*ln(x)+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/n*ln(x^n)*Pi*a*e*csgn(I*f*x^m)^2*csgn(I*f)+1/2*e*a/m*ln(x^m)^2+1/2*I*b*e*m*polylog(3,I*c*x^n)/n^2+1/4/n*dilog(1-I*c*x^n)*Pi*b*e*csgn(I*x^m)*csgn(I*f*x^m)^2-1/2*I/n*ln(x^n)*Pi*a*e*csgn(I*f*x^m)^3-1/4/n*dilog(1+I*c*x^n)*Pi*b*e*csgn(I*f*x^m)^2*csgn(I*f)-1/2*I*b*e*m*polylog(3,-I*c*x^n)/n^2-1/2*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/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)^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+1/2*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)^3+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)*ln(f)*a*e-1/2*I/n*dilog(1-I*c*x^n)*b*d+1/2*I*e*b/n*dilog(-I*(c*x^n+I))*m*ln(x)+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)^3-1/4/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/n*ln(x^n)*Pi*a*e*csgn(I*x^m)*csgn(I*f*x^m)^2-1/2*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*ln(1-I*c*x^n)*ln(x)^2*m+1/2*I*e*b*ln(1-I*c*x^n)*ln(x^m)*ln(x)-1/2*I*e*b/n*m*ln(x)*polylog(2,I*c*x^n)-1/2*I*e*b/n*dilog(-I*(c*x^n+I))*ln(x^m)+1/n*ln(x^n)*a*d","C"