1,1,127,92,0.085000," ","int(x^6*(a+b*arccsch(c*x)),x)","\frac{\frac{c^{7} x^{7} a}{7}+b \left(\frac{c^{7} x^{7} \mathrm{arccsch}\left(c x \right)}{7}+\frac{\sqrt{c^{2} x^{2}+1}\, \left(8 c^{5} x^{5} \sqrt{c^{2} x^{2}+1}-10 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+15 c x \sqrt{c^{2} x^{2}+1}-15 \arcsinh \left(c x \right)\right)}{336 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{7}}"," ",0,"1/c^7*(1/7*c^7*x^7*a+b*(1/7*c^7*x^7*arccsch(c*x)+1/336*(c^2*x^2+1)^(1/2)*(8*c^5*x^5*(c^2*x^2+1)^(1/2)-10*c^3*x^3*(c^2*x^2+1)^(1/2)+15*c*x*(c^2*x^2+1)^(1/2)-15*arcsinh(c*x))/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
2,1,83,72,0.051000," ","int(x^5*(a+b*arccsch(c*x)),x)","\frac{\frac{c^{6} x^{6} a}{6}+b \left(\frac{c^{6} x^{6} \mathrm{arccsch}\left(c x \right)}{6}+\frac{\left(c^{2} x^{2}+1\right) \left(3 c^{4} x^{4}-4 c^{2} x^{2}+8\right)}{90 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{6}}"," ",0,"1/c^6*(1/6*c^6*x^6*a+b*(1/6*c^6*x^6*arccsch(c*x)+1/90*(c^2*x^2+1)*(3*c^4*x^4-4*c^2*x^2+8)/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
3,1,108,72,0.049000," ","int(x^4*(a+b*arccsch(c*x)),x)","\frac{\frac{c^{5} x^{5} a}{5}+b \left(\frac{c^{5} x^{5} \mathrm{arccsch}\left(c x \right)}{5}+\frac{\sqrt{c^{2} x^{2}+1}\, \left(2 c^{3} x^{3} \sqrt{c^{2} x^{2}+1}-3 c x \sqrt{c^{2} x^{2}+1}+3 \arcsinh \left(c x \right)\right)}{40 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{5}}"," ",0,"1/c^5*(1/5*c^5*x^5*a+b*(1/5*c^5*x^5*arccsch(c*x)+1/40*(c^2*x^2+1)^(1/2)*(2*c^3*x^3*(c^2*x^2+1)^(1/2)-3*c*x*(c^2*x^2+1)^(1/2)+3*arcsinh(c*x))/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
4,1,74,52,0.045000," ","int(x^3*(a+b*arccsch(c*x)),x)","\frac{\frac{c^{4} x^{4} a}{4}+b \left(\frac{c^{4} x^{4} \mathrm{arccsch}\left(c x \right)}{4}+\frac{\left(c^{2} x^{2}+1\right) \left(c^{2} x^{2}-2\right)}{12 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{4}}"," ",0,"1/c^4*(1/4*c^4*x^4*a+b*(1/4*c^4*x^4*arccsch(c*x)+1/12*(c^2*x^2+1)*(c^2*x^2-2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
5,1,88,52,0.050000," ","int(x^2*(a+b*arccsch(c*x)),x)","\frac{\frac{a \,c^{3} x^{3}}{3}+b \left(\frac{c^{3} x^{3} \mathrm{arccsch}\left(c x \right)}{3}+\frac{\sqrt{c^{2} x^{2}+1}\, \left(c x \sqrt{c^{2} x^{2}+1}-\arcsinh \left(c x \right)\right)}{6 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{3}}"," ",0,"1/c^3*(1/3*a*c^3*x^3+b*(1/3*c^3*x^3*arccsch(c*x)+1/6*(c^2*x^2+1)^(1/2)*(c*x*(c^2*x^2+1)^(1/2)-arcsinh(c*x))/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
6,1,65,32,0.045000," ","int(x*(a+b*arccsch(c*x)),x)","\frac{\frac{c^{2} x^{2} a}{2}+b \left(\frac{c^{2} x^{2} \mathrm{arccsch}\left(c x \right)}{2}+\frac{c^{2} x^{2}+1}{2 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{2}}"," ",0,"1/c^2*(1/2*c^2*x^2*a+b*(1/2*c^2*x^2*arccsch(c*x)+1/2/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x*(c^2*x^2+1)))","A"
7,1,36,28,0.043000," ","int(a+b*arccsch(c*x),x)","a x +b x \,\mathrm{arccsch}\left(c x \right)+\frac{b \ln \left(c x +c x \sqrt{1+\frac{1}{c^{2} x^{2}}}\right)}{c}"," ",0,"a*x+b*x*arccsch(c*x)+b/c*ln(c*x+c*x*(1+1/c^2/x^2)^(1/2))","A"
8,0,0,78,0.068000," ","int((a+b*arccsch(c*x))/x,x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x}\, dx"," ",0,"int((a+b*arccsch(c*x))/x,x)","F"
9,1,62,30,0.046000," ","int((a+b*arccsch(c*x))/x^2,x)","c \left(-\frac{a}{c x}+b \left(-\frac{\mathrm{arccsch}\left(c x \right)}{c x}+\frac{c^{2} x^{2}+1}{\sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c^{2} x^{2}}\right)\right)"," ",0,"c*(-a/c/x+b*(-1/c/x*arccsch(c*x)+1/((c^2*x^2+1)/c^2/x^2)^(1/2)/c^2/x^2*(c^2*x^2+1)))","B"
10,1,100,45,0.048000," ","int((a+b*arccsch(c*x))/x^3,x)","c^{2} \left(-\frac{a}{2 c^{2} x^{2}}+b \left(-\frac{\mathrm{arccsch}\left(c x \right)}{2 c^{2} x^{2}}-\frac{\sqrt{c^{2} x^{2}+1}\, \left(\arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right) c^{2} x^{2}-\sqrt{c^{2} x^{2}+1}\right)}{4 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c^{3} x^{3}}\right)\right)"," ",0,"c^2*(-1/2*a/c^2/x^2+b*(-1/2/c^2/x^2*arccsch(c*x)-1/4*(c^2*x^2+1)^(1/2)*(arctanh(1/(c^2*x^2+1)^(1/2))*c^2*x^2-(c^2*x^2+1)^(1/2))/((c^2*x^2+1)/c^2/x^2)^(1/2)/c^3/x^3))","B"
11,1,75,51,0.049000," ","int((a+b*arccsch(c*x))/x^4,x)","c^{3} \left(-\frac{a}{3 c^{3} x^{3}}+b \left(-\frac{\mathrm{arccsch}\left(c x \right)}{3 c^{3} x^{3}}-\frac{\left(c^{2} x^{2}+1\right) \left(2 c^{2} x^{2}-1\right)}{9 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c^{4} x^{4}}\right)\right)"," ",0,"c^3*(-1/3/c^3/x^3*a+b*(-1/3/c^3/x^3*arccsch(c*x)-1/9*(c^2*x^2+1)*(2*c^2*x^2-1)/((c^2*x^2+1)/c^2/x^2)^(1/2)/c^4/x^4))","A"
12,1,120,65,0.046000," ","int((a+b*arccsch(c*x))/x^5,x)","c^{4} \left(-\frac{a}{4 c^{4} x^{4}}+b \left(-\frac{\mathrm{arccsch}\left(c x \right)}{4 c^{4} x^{4}}+\frac{\sqrt{c^{2} x^{2}+1}\, \left(3 \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right) c^{4} x^{4}-3 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}+2 \sqrt{c^{2} x^{2}+1}\right)}{32 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c^{5} x^{5}}\right)\right)"," ",0,"c^4*(-1/4*a/c^4/x^4+b*(-1/4/c^4/x^4*arccsch(c*x)+1/32*(c^2*x^2+1)^(1/2)*(3*arctanh(1/(c^2*x^2+1)^(1/2))*c^4*x^4-3*c^2*x^2*(c^2*x^2+1)^(1/2)+2*(c^2*x^2+1)^(1/2))/((c^2*x^2+1)/c^2/x^2)^(1/2)/c^5/x^5))","A"
13,1,83,68,0.046000," ","int((a+b*arccsch(c*x))/x^6,x)","c^{5} \left(-\frac{a}{5 c^{5} x^{5}}+b \left(-\frac{\mathrm{arccsch}\left(c x \right)}{5 c^{5} x^{5}}+\frac{\left(c^{2} x^{2}+1\right) \left(8 c^{4} x^{4}-4 c^{2} x^{2}+3\right)}{75 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c^{6} x^{6}}\right)\right)"," ",0,"c^5*(-1/5*a/c^5/x^5+b*(-1/5/c^5/x^5*arccsch(c*x)+1/75*(c^2*x^2+1)*(8*c^4*x^4-4*c^2*x^2+3)/((c^2*x^2+1)/c^2/x^2)^(1/2)/c^6/x^6))","A"
14,1,139,85,0.056000," ","int((a+b*arccsch(c*x))/x^7,x)","c^{6} \left(-\frac{a}{6 c^{6} x^{6}}+b \left(-\frac{\mathrm{arccsch}\left(c x \right)}{6 c^{6} x^{6}}-\frac{\sqrt{c^{2} x^{2}+1}\, \left(15 \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right) c^{6} x^{6}-15 c^{4} x^{4} \sqrt{c^{2} x^{2}+1}+10 c^{2} x^{2} \sqrt{c^{2} x^{2}+1}-8 \sqrt{c^{2} x^{2}+1}\right)}{288 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c^{7} x^{7}}\right)\right)"," ",0,"c^6*(-1/6*a/c^6/x^6+b*(-1/6/c^6/x^6*arccsch(c*x)-1/288*(c^2*x^2+1)^(1/2)*(15*arctanh(1/(c^2*x^2+1)^(1/2))*c^6*x^6-15*c^4*x^4*(c^2*x^2+1)^(1/2)+10*c^2*x^2*(c^2*x^2+1)^(1/2)-8*(c^2*x^2+1)^(1/2))/((c^2*x^2+1)/c^2/x^2)^(1/2)/c^7/x^7))","A"
15,0,0,91,0.052000," ","int(x^3*(a+b*arccsch(c*x))^2,x)","\int x^{3} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{2}\, dx"," ",0,"int(x^3*(a+b*arccsch(c*x))^2,x)","F"
16,0,0,148,0.052000," ","int(x^2*(a+b*arccsch(c*x))^2,x)","\int x^{2} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{2}\, dx"," ",0,"int(x^2*(a+b*arccsch(c*x))^2,x)","F"
17,0,0,50,0.055000," ","int(x*(a+b*arccsch(c*x))^2,x)","\int x \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{2}\, dx"," ",0,"int(x*(a+b*arccsch(c*x))^2,x)","F"
18,0,0,108,0.050000," ","int((a+b*arccsch(c*x))^2,x)","\int \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{2}\, dx"," ",0,"int((a+b*arccsch(c*x))^2,x)","F"
19,0,0,116,0.053000," ","int((a+b*arccsch(c*x))^2/x,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{2}}{x}\, dx"," ",0,"int((a+b*arccsch(c*x))^2/x,x)","F"
20,0,0,47,0.066000," ","int((a+b*arccsch(c*x))^2/x^2,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{2}}{x^{2}}\, dx"," ",0,"int((a+b*arccsch(c*x))^2/x^2,x)","F"
21,0,0,75,0.056000," ","int((a+b*arccsch(c*x))^2/x^3,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{2}}{x^{3}}\, dx"," ",0,"int((a+b*arccsch(c*x))^2/x^3,x)","F"
22,0,0,86,0.047000," ","int((a+b*arccsch(c*x))^2/x^4,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{2}}{x^{4}}\, dx"," ",0,"int((a+b*arccsch(c*x))^2/x^4,x)","F"
23,0,0,114,0.051000," ","int((a+b*arccsch(c*x))^2/x^5,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{2}}{x^{5}}\, dx"," ",0,"int((a+b*arccsch(c*x))^2/x^5,x)","F"
24,0,0,201,0.050000," ","int(x^3*(a+b*arccsch(c*x))^3,x)","\int x^{3} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{3}\, dx"," ",0,"int(x^3*(a+b*arccsch(c*x))^3,x)","F"
25,0,0,253,0.049000," ","int(x^2*(a+b*arccsch(c*x))^3,x)","\int x^{2} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{3}\, dx"," ",0,"int(x^2*(a+b*arccsch(c*x))^3,x)","F"
26,0,0,133,0.049000," ","int(x*(a+b*arccsch(c*x))^3,x)","\int x \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{3}\, dx"," ",0,"int(x*(a+b*arccsch(c*x))^3,x)","F"
27,0,0,187,0.049000," ","int((a+b*arccsch(c*x))^3,x)","\int \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{3}\, dx"," ",0,"int((a+b*arccsch(c*x))^3,x)","F"
28,0,0,154,0.055000," ","int((a+b*arccsch(c*x))^3/x,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{3}}{x}\, dx"," ",0,"int((a+b*arccsch(c*x))^3/x,x)","F"
29,0,0,74,0.052000," ","int((a+b*arccsch(c*x))^3/x^2,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{3}}{x^{2}}\, dx"," ",0,"int((a+b*arccsch(c*x))^3/x^2,x)","F"
30,0,0,107,0.052000," ","int((a+b*arccsch(c*x))^3/x^3,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{3}}{x^{3}}\, dx"," ",0,"int((a+b*arccsch(c*x))^3/x^3,x)","F"
31,0,0,144,0.053000," ","int((a+b*arccsch(c*x))^3/x^4,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{3}}{x^{4}}\, dx"," ",0,"int((a+b*arccsch(c*x))^3/x^4,x)","F"
32,0,0,178,0.053000," ","int((a+b*arccsch(c*x))^3/x^5,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{3}}{x^{5}}\, dx"," ",0,"int((a+b*arccsch(c*x))^3/x^5,x)","F"
33,0,0,14,0.053000," ","int(x/(a+b*arccsch(c*x)),x)","\int \frac{x}{a +b \,\mathrm{arccsch}\left(c x \right)}\, dx"," ",0,"int(x/(a+b*arccsch(c*x)),x)","F"
34,0,0,12,0.054000," ","int(1/(a+b*arccsch(c*x)),x)","\int \frac{1}{a +b \,\mathrm{arccsch}\left(c x \right)}\, dx"," ",0,"int(1/(a+b*arccsch(c*x)),x)","F"
35,0,0,16,0.062000," ","int(1/x/(a+b*arccsch(c*x)),x)","\int \frac{1}{x \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}\, dx"," ",0,"int(1/x/(a+b*arccsch(c*x)),x)","F"
36,0,0,46,0.049000," ","int(1/x^2/(a+b*arccsch(c*x)),x)","\int \frac{1}{x^{2} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}\, dx"," ",0,"int(1/x^2/(a+b*arccsch(c*x)),x)","F"
37,0,0,59,0.048000," ","int(1/x^3/(a+b*arccsch(c*x)),x)","\int \frac{1}{x^{3} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}\, dx"," ",0,"int(1/x^3/(a+b*arccsch(c*x)),x)","F"
38,0,0,109,0.052000," ","int(1/x^4/(a+b*arccsch(c*x)),x)","\int \frac{1}{x^{4} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}\, dx"," ",0,"int(1/x^4/(a+b*arccsch(c*x)),x)","F"
39,0,0,18,0.049000," ","int((d*x)^m*(a+b*arccsch(c*x))^3,x)","\int \left(d x \right)^{m} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{3}\, dx"," ",0,"int((d*x)^m*(a+b*arccsch(c*x))^3,x)","F"
40,0,0,18,0.050000," ","int((d*x)^m*(a+b*arccsch(c*x))^2,x)","\int \left(d x \right)^{m} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{2}\, dx"," ",0,"int((d*x)^m*(a+b*arccsch(c*x))^2,x)","F"
41,0,0,63,0.049000," ","int((d*x)^m*(a+b*arccsch(c*x)),x)","\int \left(d x \right)^{m} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)\, dx"," ",0,"int((d*x)^m*(a+b*arccsch(c*x)),x)","F"
42,0,0,18,0.048000," ","int((d*x)^m/(a+b*arccsch(c*x)),x)","\int \frac{\left(d x \right)^{m}}{a +b \,\mathrm{arccsch}\left(c x \right)}\, dx"," ",0,"int((d*x)^m/(a+b*arccsch(c*x)),x)","F"
43,0,0,18,0.049000," ","int((d*x)^m/(a+b*arccsch(c*x))^2,x)","\int \frac{\left(d x \right)^{m}}{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((d*x)^m/(a+b*arccsch(c*x))^2,x)","F"
44,1,269,147,0.059000," ","int((e*x+d)^3*(a+b*arccsch(c*x)),x)","\frac{\frac{\left(c x e +c d \right)^{4} a}{4 c^{3} e}+\frac{b \left(\frac{e^{3} \mathrm{arccsch}\left(c x \right) c^{4} x^{4}}{4}+e^{2} \mathrm{arccsch}\left(c x \right) c^{4} x^{3} d +\frac{3 e \,\mathrm{arccsch}\left(c x \right) c^{4} x^{2} d^{2}}{2}+\mathrm{arccsch}\left(c x \right) c^{4} x \,d^{3}+\frac{\mathrm{arccsch}\left(c x \right) c^{4} d^{4}}{4 e}+\frac{\sqrt{c^{2} x^{2}+1}\, \left(-3 c^{4} d^{4} \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)+12 c^{3} d^{3} e \arcsinh \left(c x \right)+e^{4} c^{2} x^{2} \sqrt{c^{2} x^{2}+1}+6 c^{2} d \,e^{3} x \sqrt{c^{2} x^{2}+1}+18 c^{2} d^{2} e^{2} \sqrt{c^{2} x^{2}+1}-6 c d \,e^{3} \arcsinh \left(c x \right)-2 e^{4} \sqrt{c^{2} x^{2}+1}\right)}{12 e \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{3}}}{c}"," ",0,"1/c*(1/4*(c*e*x+c*d)^4*a/c^3/e+b/c^3*(1/4*e^3*arccsch(c*x)*c^4*x^4+e^2*arccsch(c*x)*c^4*x^3*d+3/2*e*arccsch(c*x)*c^4*x^2*d^2+arccsch(c*x)*c^4*x*d^3+1/4/e*arccsch(c*x)*c^4*d^4+1/12/e*(c^2*x^2+1)^(1/2)*(-3*c^4*d^4*arctanh(1/(c^2*x^2+1)^(1/2))+12*c^3*d^3*e*arcsinh(c*x)+e^4*c^2*x^2*(c^2*x^2+1)^(1/2)+6*c^2*d*e^3*x*(c^2*x^2+1)^(1/2)+18*c^2*d^2*e^2*(c^2*x^2+1)^(1/2)-6*c*d*e^3*arcsinh(c*x)-2*e^4*(c^2*x^2+1)^(1/2))/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
45,1,204,108,0.053000," ","int((e*x+d)^2*(a+b*arccsch(c*x)),x)","\frac{\frac{\left(c x e +c d \right)^{3} a}{3 c^{2} e}+\frac{b \left(\frac{e^{2} \mathrm{arccsch}\left(c x \right) c^{3} x^{3}}{3}+e \,\mathrm{arccsch}\left(c x \right) c^{3} x^{2} d +\mathrm{arccsch}\left(c x \right) c^{3} x \,d^{2}+\frac{\mathrm{arccsch}\left(c x \right) c^{3} d^{3}}{3 e}+\frac{\sqrt{c^{2} x^{2}+1}\, \left(-2 c^{3} d^{3} \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)+6 c^{2} d^{2} e \arcsinh \left(c x \right)+e^{3} c x \sqrt{c^{2} x^{2}+1}+6 c d \,e^{2} \sqrt{c^{2} x^{2}+1}-e^{3} \arcsinh \left(c x \right)\right)}{6 e \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{2}}}{c}"," ",0,"1/c*(1/3*(c*e*x+c*d)^3*a/c^2/e+b/c^2*(1/3*e^2*arccsch(c*x)*c^3*x^3+e*arccsch(c*x)*c^3*x^2*d+arccsch(c*x)*c^3*x*d^2+1/3/e*arccsch(c*x)*c^3*d^3+1/6/e*(c^2*x^2+1)^(1/2)*(-2*c^3*d^3*arctanh(1/(c^2*x^2+1)^(1/2))+6*c^2*d^2*e*arcsinh(c*x)+e^3*c*x*(c^2*x^2+1)^(1/2)+6*c*d*e^2*(c^2*x^2+1)^(1/2)-e^3*arcsinh(c*x))/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
46,1,115,71,0.051000," ","int((e*x+d)*(a+b*arccsch(c*x)),x)","\frac{\frac{a \left(\frac{1}{2} c^{2} x^{2} e +c^{2} d x \right)}{c}+\frac{b \left(\frac{\mathrm{arccsch}\left(c x \right) c^{2} x^{2} e}{2}+\mathrm{arccsch}\left(c x \right) c^{2} x d +\frac{\sqrt{c^{2} x^{2}+1}\, \left(e \sqrt{c^{2} x^{2}+1}+2 c d \arcsinh \left(c x \right)\right)}{2 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c}}{c}"," ",0,"1/c*(a/c*(1/2*c^2*x^2*e+c^2*d*x)+b/c*(1/2*arccsch(c*x)*c^2*x^2*e+arccsch(c*x)*c^2*x*d+1/2/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x*(c^2*x^2+1)^(1/2)*(e*(c^2*x^2+1)^(1/2)+2*c*d*arcsinh(c*x))))","A"
47,1,36,28,0.046000," ","int(a+b*arccsch(c*x),x)","a x +b x \,\mathrm{arccsch}\left(c x \right)+\frac{b \ln \left(c x +c x \sqrt{1+\frac{1}{c^{2} x^{2}}}\right)}{c}"," ",0,"a*x+b*x*arccsch(c*x)+b/c*ln(c*x+c*x*(1+1/c^2/x^2)^(1/2))","A"
48,0,0,283,0.492000," ","int((a+b*arccsch(c*x))/(e*x+d),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{e x +d}\, dx"," ",0,"int((a+b*arccsch(c*x))/(e*x+d),x)","F"
49,1,208,94,0.087000," ","int((a+b*arccsch(c*x))/(e*x+d)^2,x)","-\frac{c a}{\left(c x e +c d \right) e}-\frac{c b \,\mathrm{arccsch}\left(c x \right)}{\left(c x e +c d \right) e}+\frac{b \sqrt{c^{2} x^{2}+1}\, \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{c e \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x d}-\frac{b \sqrt{c^{2} x^{2}+1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}+1}\, \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}\, e -2 c^{2} d x +2 e}{c x e +c d}\right)}{c e \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x d \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}}"," ",0,"-c*a/(c*e*x+c*d)/e-c*b/(c*e*x+c*d)/e*arccsch(c*x)+1/c*b/e*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/d*arctanh(1/(c^2*x^2+1)^(1/2))-1/c*b/e*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/d/((c^2*d^2+e^2)/e^2)^(1/2)*ln(2*((c^2*x^2+1)^(1/2)*((c^2*d^2+e^2)/e^2)^(1/2)*e-c^2*d*x+e)/(c*e*x+c*d))","B"
50,1,963,150,0.070000," ","int((a+b*arccsch(c*x))/(e*x+d)^3,x)","-\frac{c^{2} a}{2 \left(c x e +c d \right)^{2} e}-\frac{c^{2} b \,\mathrm{arccsch}\left(c x \right)}{2 \left(c x e +c d \right)^{2} e}+\frac{c^{2} b \sqrt{c^{2} x^{2}+1}\, \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{2 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, \left(c^{2} d^{2}+e^{2}\right) \left(c x e +c d \right)}+\frac{c^{2} b \sqrt{c^{2} x^{2}+1}\, d \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{2 e \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \left(c^{2} d^{2}+e^{2}\right) \left(c x e +c d \right)}-\frac{c^{2} b \sqrt{c^{2} x^{2}+1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}+1}\, \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}\, e -2 c^{2} d x +2 e}{c x e +c d}\right)}{\sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}\, \left(c^{2} d^{2}+e^{2}\right) \left(c x e +c d \right)}-\frac{c^{2} b \sqrt{c^{2} x^{2}+1}\, d \ln \left(\frac{2 \sqrt{c^{2} x^{2}+1}\, \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}\, e -2 c^{2} d x +2 e}{c x e +c d}\right)}{e \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}\, \left(c^{2} d^{2}+e^{2}\right) \left(c x e +c d \right)}-\frac{c^{2} b e x}{2 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, d \left(c^{2} d^{2}+e^{2}\right) \left(c x e +c d \right)}-\frac{b e}{2 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x d \left(c^{2} d^{2}+e^{2}\right) \left(c x e +c d \right)}+\frac{b \,e^{2} \sqrt{c^{2} x^{2}+1}\, \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{2 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, d^{2} \left(c^{2} d^{2}+e^{2}\right) \left(c x e +c d \right)}+\frac{b e \sqrt{c^{2} x^{2}+1}\, \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{2 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x d \left(c^{2} d^{2}+e^{2}\right) \left(c x e +c d \right)}-\frac{b \,e^{2} \sqrt{c^{2} x^{2}+1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}+1}\, \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}\, e -2 c^{2} d x +2 e}{c x e +c d}\right)}{2 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, d^{2} \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}\, \left(c^{2} d^{2}+e^{2}\right) \left(c x e +c d \right)}-\frac{b e \sqrt{c^{2} x^{2}+1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}+1}\, \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}\, e -2 c^{2} d x +2 e}{c x e +c d}\right)}{2 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x d \sqrt{\frac{c^{2} d^{2}+e^{2}}{e^{2}}}\, \left(c^{2} d^{2}+e^{2}\right) \left(c x e +c d \right)}"," ",0,"-1/2*c^2*a/(c*e*x+c*d)^2/e-1/2*c^2*b/(c*e*x+c*d)^2/e*arccsch(c*x)+1/2*c^2*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/(c^2*d^2+e^2)/(c*e*x+c*d)*arctanh(1/(c^2*x^2+1)^(1/2))+1/2*c^2*b/e*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x*d/(c^2*d^2+e^2)/(c*e*x+c*d)*arctanh(1/(c^2*x^2+1)^(1/2))-c^2*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/((c^2*d^2+e^2)/e^2)^(1/2)/(c^2*d^2+e^2)/(c*e*x+c*d)*ln(2*((c^2*x^2+1)^(1/2)*((c^2*d^2+e^2)/e^2)^(1/2)*e-c^2*d*x+e)/(c*e*x+c*d))-c^2*b/e*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x*d/((c^2*d^2+e^2)/e^2)^(1/2)/(c^2*d^2+e^2)/(c*e*x+c*d)*ln(2*((c^2*x^2+1)^(1/2)*((c^2*d^2+e^2)/e^2)^(1/2)*e-c^2*d*x+e)/(c*e*x+c*d))-1/2*c^2*b*e/((c^2*x^2+1)/c^2/x^2)^(1/2)*x/d/(c^2*d^2+e^2)/(c*e*x+c*d)-1/2*b*e/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/d/(c^2*d^2+e^2)/(c*e*x+c*d)+1/2*b*e^2*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/d^2/(c^2*d^2+e^2)/(c*e*x+c*d)*arctanh(1/(c^2*x^2+1)^(1/2))+1/2*b*e*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/d/(c^2*d^2+e^2)/(c*e*x+c*d)*arctanh(1/(c^2*x^2+1)^(1/2))-1/2*b*e^2*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/d^2/((c^2*d^2+e^2)/e^2)^(1/2)/(c^2*d^2+e^2)/(c*e*x+c*d)*ln(2*((c^2*x^2+1)^(1/2)*((c^2*d^2+e^2)/e^2)^(1/2)*e-c^2*d*x+e)/(c*e*x+c*d))-1/2*b*e*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/d/((c^2*d^2+e^2)/e^2)^(1/2)/(c^2*d^2+e^2)/(c*e*x+c*d)*ln(2*((c^2*x^2+1)^(1/2)*((c^2*d^2+e^2)/e^2)^(1/2)*e-c^2*d*x+e)/(c*e*x+c*d))","B"
51,1,2515,784,0.357000," ","int(x^2*(a+b*arccsch(c*x))*(e*x+d)^(1/2),x)","\frac{2 a \left(\frac{\left(e x +d \right)^{\frac{7}{2}}}{7}-\frac{2 d \left(e x +d \right)^{\frac{5}{2}}}{5}+\frac{d^{2} \left(e x +d \right)^{\frac{3}{2}}}{3}\right)+2 b \left(\frac{\mathrm{arccsch}\left(c x \right) \left(e x +d \right)^{\frac{7}{2}}}{7}-\frac{2 \,\mathrm{arccsch}\left(c x \right) d \left(e x +d \right)^{\frac{5}{2}}}{5}+\frac{\mathrm{arccsch}\left(c x \right) d^{2} \left(e x +d \right)^{\frac{3}{2}}}{3}+\frac{-\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c d \,e^{3}}{105}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{7}{2}} c^{4} d}{35}-\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c^{3} d^{3} e}{105}+\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{5}{2}} c^{4} d^{2}}{15}-\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{5}{2}} c^{3} d e}{15}+\frac{2 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c d \,e^{3}}{105}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{3}{2}} c \,e^{3}}{35}-\frac{8 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{4} d^{4}}{105}-\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{4} d^{4}}{21}+\frac{16 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c^{4} d^{4}}{105}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{3}{2}} c^{4} d^{3}}{21}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{7}{2}} c^{3} e}{35}+\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c^{4} d^{4}}{105}+\frac{6 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{3} d^{3} e}{35}-\frac{16 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c^{3} d^{3} e}{105}+\frac{26 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{2} d^{2} e^{2}}{105}-\frac{4 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{2} d^{2} e^{2}}{15}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{3}{2}} c^{2} d \,e^{2}}{35}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{2} e}{21}+\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c^{2} d^{2} e^{2}}{105}+\frac{6 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) e^{4}}{35}-\frac{6 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) e^{4}}{35}}{c^{4} \sqrt{\frac{\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} x^{2} e^{2}}}\, x \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(-c d +i e \right)}\right)}{e^{3}}"," ",0,"2/e^3*(a*(1/7*(e*x+d)^(7/2)-2/5*d*(e*x+d)^(5/2)+1/3*d^2*(e*x+d)^(3/2))+b*(1/7*arccsch(c*x)*(e*x+d)^(7/2)-2/5*arccsch(c*x)*d*(e*x+d)^(5/2)+1/3*arccsch(c*x)*d^2*(e*x+d)^(3/2)+2/105/c^4*(-I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c*d*e^3-3*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(7/2)*c^4*d-I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c^3*d^3*e+7*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(5/2)*c^4*d^2-7*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(5/2)*c^3*d*e+I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c*d*e^3+3*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(3/2)*c*e^3-4*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^4*d^4-5*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^4*d^4+8*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c^4*d^4-5*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(3/2)*c^4*d^3+3*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(7/2)*c^3*e+((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c^4*d^4+9*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^3*d^3*e-8*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c^3*d^3*e+13*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^2*d^2*e^2-14*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^2*d^2*e^2-3*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(3/2)*c^2*d*e^2+5*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(3/2)*c^3*d^2*e+((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c^2*d^2*e^2+9*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*e^4-9*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*e^4)/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)/(I*e-c*d)))","C"
52,1,1964,582,0.085000," ","int(x*(a+b*arccsch(c*x))*(e*x+d)^(1/2),x)","\frac{2 a \left(\frac{\left(e x +d \right)^{\frac{5}{2}}}{5}-\frac{d \left(e x +d \right)^{\frac{3}{2}}}{3}\right)+2 b \left(\frac{\mathrm{arccsch}\left(c x \right) \left(e x +d \right)^{\frac{5}{2}}}{5}-\frac{\mathrm{arccsch}\left(c x \right) d \left(e x +d \right)^{\frac{3}{2}}}{3}+\frac{-\frac{2 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{2} d^{2} e}{5}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{5}{2}} c^{3} d}{15}-\frac{2 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) e^{3}}{15}+\frac{4 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{2}}{15}-\frac{4 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{3}{2}} c^{2} d e}{15}+\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{3} d^{3}}{15}+\frac{4 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{3} d^{3}}{15}+\frac{4 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c^{2} d^{2} e}{15}-\frac{4 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c^{3} d^{3}}{15}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{5}{2}} c^{2} e}{15}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c^{3} d^{3}}{15}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, e^{3}}{15}-\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c d \,e^{2}}{15}+\frac{4 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c d \,e^{2}}{15}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c^{2} d^{2} e}{15}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c d \,e^{2}}{15}}{c^{3} \sqrt{\frac{\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} x^{2} e^{2}}}\, x \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(-c d +i e \right)}\right)}{e^{2}}"," ",0,"2/e^2*(a*(1/5*(e*x+d)^(5/2)-1/3*d*(e*x+d)^(3/2))+b*(1/5*arccsch(c*x)*(e*x+d)^(5/2)-1/3*arccsch(c*x)*d*(e*x+d)^(3/2)+2/15/c^3*(-3*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^2*d^2*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(5/2)*c^3*d-2*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(3/2)*c^2*d*e+2*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(3/2)*c^3*d^2+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(5/2)*c^2*e+(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^3*d^3+2*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^3*d^3+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*e^3-2*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c^3*d^3+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c^2*d^2*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c^3*d^3+2*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c^2*d^2*e-(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c*d*e^2+2*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c*d*e^2-I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*e^3-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c*d*e^2)/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)/(I*e-c*d)))","C"
53,1,840,364,0.079000," ","int((a+b*arccsch(c*x))*(e*x+d)^(1/2),x)","\frac{\frac{2 a \left(e x +d \right)^{\frac{3}{2}}}{3}+2 b \left(\frac{\left(e x +d \right)^{\frac{3}{2}} \mathrm{arccsch}\left(c x \right)}{3}+\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \left(i \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c d e -2 \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{2} d^{2}+\EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{2} d^{2}-i \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c d e +\EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c^{2} d^{2}-\EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) e^{2}+\EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) e^{2}\right)}{3 c^{2} \sqrt{\frac{\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} x^{2} e^{2}}}\, x \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(-c d +i e \right)}\right)}{e}"," ",0,"2/e*(1/3*a*(e*x+d)^(3/2)+b*(1/3*(e*x+d)^(3/2)*arccsch(c*x)+2/3/c^2*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*(I*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c*d*e-2*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^2*d^2+EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^2*d^2-I*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c*d*e+EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c^2*d^2-EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*e^2+EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*e^2)/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)/(I*e-c*d)))","C"
54,0,0,21,6.871000," ","int((a+b*arccsch(c*x))*(e*x+d)^(1/2)/x,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right) \sqrt{e x +d}}{x}\, dx"," ",0,"int((a+b*arccsch(c*x))*(e*x+d)^(1/2)/x,x)","F"
55,0,0,21,5.921000," ","int((a+b*arccsch(c*x))*(e*x+d)^(1/2)/x^2,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right) \sqrt{e x +d}}{x^{2}}\, dx"," ",0,"int((a+b*arccsch(c*x))*(e*x+d)^(1/2)/x^2,x)","F"
56,1,1939,415,0.068000," ","int((e*x+d)^(3/2)*(a+b*arccsch(c*x)),x)","\frac{\frac{2 \left(e x +d \right)^{\frac{5}{2}} a}{5}+2 b \left(\frac{\mathrm{arccsch}\left(c x \right) \left(e x +d \right)^{\frac{5}{2}}}{5}+\frac{\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, e^{3}}{15}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{5}{2}} c^{3} d}{15}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{5}{2}} c^{2} e}{15}+\frac{4 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{2}}{15}-\frac{2 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) e^{3}}{15}-\frac{6 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{3} d^{3}}{5}+\frac{14 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{3} d^{3}}{15}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c^{2} d^{2} e}{15}+\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c^{3} d^{3}}{5}-\frac{4 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{3}{2}} c^{2} d e}{15}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c^{3} d^{3}}{15}+\frac{4 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{2} d^{2} e}{15}-\frac{4 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c d \,e^{2}}{5}+\frac{14 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c d \,e^{2}}{15}-\frac{2 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c^{2} d^{2} e}{5}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c d \,e^{2}}{15}}{c^{3} \sqrt{\frac{\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} x^{2} e^{2}}}\, x \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(-c d +i e \right)}\right)}{e}"," ",0,"2/e*(1/5*(e*x+d)^(5/2)*a+b*(1/5*arccsch(c*x)*(e*x+d)^(5/2)+2/15/c^3*(-I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*e^3-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(5/2)*c^3*d+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*e^3+2*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(3/2)*c^3*d^2+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(5/2)*c^2*e-9*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^3*d^3+7*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^3*d^3-3*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c^2*d^2*e+3*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c^3*d^3+2*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^2*d^2*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c^3*d^3+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c^2*d^2*e-6*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c*d*e^2+7*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c*d*e^2-2*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(3/2)*c^2*d*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c*d*e^2)/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)/(I*e-c*d)))","C"
57,1,2543,810,0.078000," ","int(x^3*(a+b*arccsch(c*x))/(e*x+d)^(1/2),x)","\frac{2 a \left(\frac{\left(e x +d \right)^{\frac{7}{2}}}{7}-\frac{3 d \left(e x +d \right)^{\frac{5}{2}}}{5}+d^{2} \left(e x +d \right)^{\frac{3}{2}}-d^{3} \sqrt{e x +d}\right)+2 b \left(\frac{\mathrm{arccsch}\left(c x \right) \left(e x +d \right)^{\frac{7}{2}}}{7}-\frac{3 \,\mathrm{arccsch}\left(c x \right) d \left(e x +d \right)^{\frac{5}{2}}}{5}+\mathrm{arccsch}\left(c x \right) d^{2} \left(e x +d \right)^{\frac{3}{2}}-\mathrm{arccsch}\left(c x \right) d^{3} \sqrt{e x +d}+\frac{-\frac{16 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{3} d^{3} e}{21}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{7}{2}} c^{4} d}{35}-\frac{16 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c^{3} d^{3} e}{105}+\frac{4 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{5}{2}} c^{4} d^{2}}{15}+\frac{16 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c d \,e^{3}}{105}-\frac{4 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{5}{2}} c^{3} d e}{15}-\frac{16 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c d \,e^{3}}{105}-\frac{38 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{3}{2}} c^{4} d^{3}}{105}+\frac{16 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{4} d^{4}}{35}+\frac{32 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{4} d^{4}}{105}-\frac{32 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c^{4} d^{4}}{35}+\frac{32 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c^{3} d^{3} e}{35}+\frac{16 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c^{4} d^{4}}{105}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{3}{2}} c \,e^{3}}{35}+\frac{38 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{2} e}{105}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{3}{2}} c^{2} d \,e^{2}}{35}-\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{2} d^{2} e^{2}}{7}+\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{2} d^{2} e^{2}}{15}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{7}{2}} c^{3} e}{35}+\frac{16 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c^{2} d^{2} e^{2}}{105}+\frac{6 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) e^{4}}{35}-\frac{6 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) e^{4}}{35}}{c^{4} \sqrt{\frac{\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} x^{2} e^{2}}}\, x \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(-c d +i e \right)}\right)}{e^{4}}"," ",0,"2/e^4*(a*(1/7*(e*x+d)^(7/2)-3/5*d*(e*x+d)^(5/2)+d^2*(e*x+d)^(3/2)-d^3*(e*x+d)^(1/2))+b*(1/7*arccsch(c*x)*(e*x+d)^(7/2)-3/5*arccsch(c*x)*d*(e*x+d)^(5/2)+arccsch(c*x)*d^2*(e*x+d)^(3/2)-arccsch(c*x)*d^3*(e*x+d)^(1/2)+2/105/c^4*(-40*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^3*d^3*e-3*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(7/2)*c^4*d-8*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c^3*d^3*e+14*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(5/2)*c^4*d^2+8*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c*d*e^3-14*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(5/2)*c^3*d*e-8*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c*d*e^3-19*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(3/2)*c^4*d^3+24*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^4*d^4+16*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^4*d^4-48*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c^4*d^4+3*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(3/2)*c*e^3+8*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c^4*d^4+19*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(3/2)*c^3*d^2*e+48*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c^3*d^3*e-3*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(3/2)*c^2*d*e^2-15*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^2*d^2*e^2+7*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^2*d^2*e^2+3*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(7/2)*c^3*e+8*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c^2*d^2*e^2+9*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*e^4-9*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*e^4)/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)/(I*e-c*d)))","C"
58,1,1991,608,0.073000," ","int(x^2*(a+b*arccsch(c*x))/(e*x+d)^(1/2),x)","\frac{2 a \left(\frac{\left(e x +d \right)^{\frac{5}{2}}}{5}-\frac{2 d \left(e x +d \right)^{\frac{3}{2}}}{3}+d^{2} \sqrt{e x +d}\right)+2 b \left(\frac{\mathrm{arccsch}\left(c x \right) \left(e x +d \right)^{\frac{5}{2}}}{5}-\frac{2 \,\mathrm{arccsch}\left(c x \right) d \left(e x +d \right)^{\frac{3}{2}}}{3}+\mathrm{arccsch}\left(c x \right) d^{2} \sqrt{e x +d}+\frac{-\frac{2 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) e^{3}}{15}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{5}{2}} c^{3} d}{15}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, e^{3}}{15}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c^{2} d^{2} e}{15}-\frac{4 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{3}{2}} c^{2} d e}{15}+\frac{4 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{2}}{15}-\frac{8 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{3} d^{3}}{15}-\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{3} d^{3}}{5}+\frac{16 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c^{3} d^{3}}{15}-\frac{16 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c^{2} d^{2} e}{15}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c^{3} d^{3}}{15}+\frac{14 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{2} d^{2} e}{15}+\frac{8 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c d \,e^{2}}{15}-\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c d \,e^{2}}{5}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{5}{2}} c^{2} e}{15}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c d \,e^{2}}{15}}{c^{3} \sqrt{\frac{\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} x^{2} e^{2}}}\, x \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(-c d +i e \right)}\right)}{e^{3}}"," ",0,"2/e^3*(a*(1/5*(e*x+d)^(5/2)-2/3*d*(e*x+d)^(3/2)+d^2*(e*x+d)^(1/2))+b*(1/5*arccsch(c*x)*(e*x+d)^(5/2)-2/3*arccsch(c*x)*d*(e*x+d)^(3/2)+arccsch(c*x)*d^2*(e*x+d)^(1/2)+2/15/c^3*(I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*e^3-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(5/2)*c^3*d+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c^2*d^2*e-2*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(3/2)*c^2*d*e-I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*e^3+2*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(3/2)*c^3*d^2-4*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^3*d^3-3*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^3*d^3+8*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c^3*d^3+7*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^2*d^2*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c^3*d^3-8*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c^2*d^2*e+4*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c*d*e^2-3*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c*d*e^2+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(5/2)*c^2*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c*d*e^2)/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)/(I*e-c*d)))","C"
59,1,868,407,0.071000," ","int(x*(a+b*arccsch(c*x))/(e*x+d)^(1/2),x)","\frac{2 a \left(\frac{\left(e x +d \right)^{\frac{3}{2}}}{3}-d \sqrt{e x +d}\right)+2 b \left(\frac{\left(e x +d \right)^{\frac{3}{2}} \mathrm{arccsch}\left(c x \right)}{3}-\mathrm{arccsch}\left(c x \right) d \sqrt{e x +d}-\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \left(2 i \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c d e -\EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{2} d^{2}-\EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{2} d^{2}-2 i \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c d e +2 \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c^{2} d^{2}+\EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) e^{2}-\EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) e^{2}\right)}{3 c^{2} \sqrt{\frac{\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} x^{2} e^{2}}}\, x \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(-c d +i e \right)}\right)}{e^{2}}"," ",0,"2/e^2*(a*(1/3*(e*x+d)^(3/2)-d*(e*x+d)^(1/2))+b*(1/3*(e*x+d)^(3/2)*arccsch(c*x)-arccsch(c*x)*d*(e*x+d)^(1/2)-2/3/c^2*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*(2*I*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c*d*e-EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^2*d^2-EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^2*d^2-2*I*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c*d*e+2*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c^2*d^2+EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*e^2-EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*e^2)/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)/(I*e-c*d)))","C"
60,1,395,247,0.066000," ","int((a+b*arccsch(c*x))/(e*x+d)^(1/2),x)","\frac{2 a \sqrt{e x +d}+2 b \left(\sqrt{e x +d}\, \mathrm{arccsch}\left(c x \right)+\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \left(\EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right)-\EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right)\right)}{c \sqrt{\frac{\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} x^{2} e^{2}}}\, x \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right)}{e}"," ",0,"2/e*(a*(e*x+d)^(1/2)+b*((e*x+d)^(1/2)*arccsch(c*x)+2/c*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*(EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))-EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)))/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)))","C"
61,0,0,21,1.532000," ","int((a+b*arccsch(c*x))/x/(e*x+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x \sqrt{e x +d}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x/(e*x+d)^(1/2),x)","F"
62,0,0,21,5.263000," ","int((a+b*arccsch(c*x))/x^2/(e*x+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x^{2} \sqrt{e x +d}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x^2/(e*x+d)^(1/2),x)","F"
63,1,2019,634,0.075000," ","int(x^3*(a+b*arccsch(c*x))/(e*x+d)^(3/2),x)","\frac{2 a \left(\frac{\left(e x +d \right)^{\frac{5}{2}}}{5}-d \left(e x +d \right)^{\frac{3}{2}}+3 d^{2} \sqrt{e x +d}+\frac{d^{3}}{\sqrt{e x +d}}\right)+2 b \left(\frac{\mathrm{arccsch}\left(c x \right) \left(e x +d \right)^{\frac{5}{2}}}{5}-\mathrm{arccsch}\left(c x \right) d \left(e x +d \right)^{\frac{3}{2}}+3 \,\mathrm{arccsch}\left(c x \right) d^{2} \sqrt{e x +d}+\frac{\mathrm{arccsch}\left(c x \right) d^{3}}{\sqrt{e x +d}}+\frac{-\frac{2 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) e^{3}}{15}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{5}{2}} c^{3} d}{15}-\frac{4 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{3}{2}} c^{2} d e}{15}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{5}{2}} c^{2} e}{15}-\frac{32 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c^{2} d^{2} e}{5}+\frac{4 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{2}}{15}-\frac{16 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{3} d^{3}}{5}-\frac{16 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{3} d^{3}}{15}+\frac{32 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c^{3} d^{3}}{5}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c^{2} d^{2} e}{15}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c^{3} d^{3}}{15}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, e^{3}}{15}+\frac{6 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c d \,e^{2}}{5}-\frac{16 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c d \,e^{2}}{15}+\frac{64 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{2} d^{2} e}{15}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \sqrt{e x +d}\, c d \,e^{2}}{15}}{c^{3} \sqrt{\frac{\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} x^{2} e^{2}}}\, x \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(-c d +i e \right)}\right)}{e^{4}}"," ",0,"2/e^4*(a*(1/5*(e*x+d)^(5/2)-d*(e*x+d)^(3/2)+3*d^2*(e*x+d)^(1/2)+d^3/(e*x+d)^(1/2))+b*(1/5*arccsch(c*x)*(e*x+d)^(5/2)-arccsch(c*x)*d*(e*x+d)^(3/2)+3*arccsch(c*x)*d^2*(e*x+d)^(1/2)+arccsch(c*x)*d^3/(e*x+d)^(1/2)+2/15/c^3*(-48*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c^2*d^2*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(5/2)*c^3*d-2*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(3/2)*c^2*d*e+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(5/2)*c^2*e-I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*e^3+2*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(3/2)*c^3*d^2-24*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^3*d^3-8*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^3*d^3+48*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c^3*d^3+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c^2*d^2*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c^3*d^3+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*e^3+9*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c*d*e^2-8*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c*d*e^2+32*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^2*d^2*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^(1/2)*c*d*e^2)/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)/(I*e-c*d)))","C"
64,1,896,430,0.073000," ","int(x^2*(a+b*arccsch(c*x))/(e*x+d)^(3/2),x)","\frac{2 a \left(\frac{\left(e x +d \right)^{\frac{3}{2}}}{3}-2 d \sqrt{e x +d}-\frac{d^{2}}{\sqrt{e x +d}}\right)+2 b \left(\frac{\left(e x +d \right)^{\frac{3}{2}} \mathrm{arccsch}\left(c x \right)}{3}-2 \,\mathrm{arccsch}\left(c x \right) d \sqrt{e x +d}-\frac{\mathrm{arccsch}\left(c x \right) d^{2}}{\sqrt{e x +d}}-\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \left(5 i \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c d e -4 \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{2} d^{2}-\EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) c^{2} d^{2}-8 i \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c d e +8 \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) c^{2} d^{2}+\EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) e^{2}-\EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) e^{2}\right)}{3 c^{2} \sqrt{\frac{\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} x^{2} e^{2}}}\, x \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(-c d +i e \right)}\right)}{e^{3}}"," ",0,"2/e^3*(a*(1/3*(e*x+d)^(3/2)-2*d*(e*x+d)^(1/2)-d^2/(e*x+d)^(1/2))+b*(1/3*(e*x+d)^(3/2)*arccsch(c*x)-2*arccsch(c*x)*d*(e*x+d)^(1/2)-arccsch(c*x)*d^2/(e*x+d)^(1/2)-2/3/c^2*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*(5*I*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c*d*e-4*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^2*d^2-EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*c^2*d^2-8*I*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c*d*e+8*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*c^2*d^2+EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*e^2-EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*e^2)/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)/(I*e-c*d)))","C"
65,1,418,279,0.071000," ","int(x*(a+b*arccsch(c*x))/(e*x+d)^(3/2),x)","\frac{2 a \left(\sqrt{e x +d}+\frac{d}{\sqrt{e x +d}}\right)+2 b \left(\sqrt{e x +d}\, \mathrm{arccsch}\left(c x \right)+\frac{\mathrm{arccsch}\left(c x \right) d}{\sqrt{e x +d}}+\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \left(\EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right)-2 \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right)\right)}{c \sqrt{\frac{\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} x^{2} e^{2}}}\, x \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right)}{e^{2}}"," ",0,"2/e^2*(a*((e*x+d)^(1/2)+d/(e*x+d)^(1/2))+b*((e*x+d)^(1/2)*arccsch(c*x)+arccsch(c*x)*d/(e*x+d)^(1/2)+2/c*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*(EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))-2*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)))/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)))","C"
66,1,328,132,0.072000," ","int((a+b*arccsch(c*x))/(e*x+d)^(3/2),x)","\frac{-\frac{2 a}{\sqrt{e x +d}}+2 b \left(-\frac{\mathrm{arccsch}\left(c x \right)}{\sqrt{e x +d}}+\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right)}{c \sqrt{\frac{\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} x^{2} e^{2}}}\, x d \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right)}{e}"," ",0,"2/e*(-a/(e*x+d)^(1/2)+b*(-1/(e*x+d)^(1/2)*arccsch(c*x)+2/c/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/d/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))))","C"
67,0,0,21,6.987000," ","int((a+b*arccsch(c*x))/x/(e*x+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x \left(e x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x/(e*x+d)^(3/2),x)","F"
68,-2,0,21,180.000000," ","int((a+b*arccsch(c*x))/x^2/(e*x+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x^{2} \left(e x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x^2/(e*x+d)^(3/2),x)","F"
69,1,2726,676,0.089000," ","int(x^3*(a+b*arccsch(c*x))/(e*x+d)^(5/2),x)","\frac{2 a \left(\frac{\left(e x +d \right)^{\frac{3}{2}}}{3}-3 d \sqrt{e x +d}-\frac{3 d^{2}}{\sqrt{e x +d}}+\frac{d^{3}}{3 \left(e x +d \right)^{\frac{3}{2}}}\right)+2 b \left(\frac{\left(e x +d \right)^{\frac{3}{2}} \mathrm{arccsch}\left(c x \right)}{3}-3 \,\mathrm{arccsch}\left(c x \right) d \sqrt{e x +d}-\frac{3 \,\mathrm{arccsch}\left(c x \right) d^{2}}{\sqrt{e x +d}}+\frac{\mathrm{arccsch}\left(c x \right) d^{3}}{3 \left(e x +d \right)^{\frac{3}{2}}}+\frac{-\frac{16 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c d \,e^{3}}{3}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{2} c^{4} d^{3}}{3}-\frac{4 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right) c^{3} d^{3} e}{3}+\frac{16 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c^{4} d^{4}}{3}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, c \,d^{2} e^{3}}{3}-\frac{32 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) \sqrt{e x +d}\, c^{4} d^{4}}{3}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{2} c^{3} d^{2} e}{3}+\frac{4 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right) c^{4} d^{4}}{3}-\frac{16 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c^{3} d^{3} e}{3}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, c^{4} d^{5}}{3}+\frac{32 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) \sqrt{e x +d}\, c^{3} d^{3} e}{3}+\frac{14 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c^{2} d^{2} e^{2}}{3}+\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c^{2} d^{2} e^{2}}{3}+\frac{32 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) \sqrt{e x +d}\, c d \,e^{3}}{3}-\frac{32 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) \sqrt{e x +d}\, c^{2} d^{2} e^{2}}{3}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, c^{3} d^{4} e}{3}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, c^{2} d^{3} e^{2}}{3}-\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, e^{4}}{3}+\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, e^{4}}{3}}{c^{2} \sqrt{\frac{\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} x^{2} e^{2}}}\, x \left(c^{2} d^{2}+e^{2}\right) \sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(-c d +i e \right)}\right)}{e^{4}}"," ",0,"2/e^4*(a*(1/3*(e*x+d)^(3/2)-3*d*(e*x+d)^(1/2)-3*d^2/(e*x+d)^(1/2)+1/3*d^3/(e*x+d)^(3/2))+b*(1/3*(e*x+d)^(3/2)*arccsch(c*x)-3*arccsch(c*x)*d*(e*x+d)^(1/2)-3*arccsch(c*x)*d^2/(e*x+d)^(1/2)+1/3*arccsch(c*x)*d^3/(e*x+d)^(3/2)+2/3/c^2*(-2*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)*c^3*d^3*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^2*c^4*d^3+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c*d^2*e^3+8*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^4*d^4+16*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c*d*e^3-16*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^4*d^4-8*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^3*d^3*e+2*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)*c^4*d^4+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^2*c^3*d^2*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c^4*d^5+16*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^3*d^3*e+7*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^2*d^2*e^2+(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^2*d^2*e^2-8*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c*d*e^3-16*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^2*d^2*e^2+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c^3*d^4*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c^2*d^3*e^2-(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*e^4+(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*e^4)/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/(c^2*d^2+e^2)/(e*x+d)^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)/(I*e-c*d)))","C"
70,1,2497,496,0.084000," ","int(x^2*(a+b*arccsch(c*x))/(e*x+d)^(5/2),x)","\frac{2 a \left(\sqrt{e x +d}+\frac{2 d}{\sqrt{e x +d}}-\frac{d^{2}}{3 \left(e x +d \right)^{\frac{3}{2}}}\right)+2 b \left(\sqrt{e x +d}\, \mathrm{arccsch}\left(c x \right)+\frac{2 \,\mathrm{arccsch}\left(c x \right) d}{\sqrt{e x +d}}-\frac{\mathrm{arccsch}\left(c x \right) d^{2}}{3 \left(e x +d \right)^{\frac{3}{2}}}-\frac{2 \left(-3 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, e^{3}-3 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c^{2} d^{2} e +8 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) \sqrt{e x +d}\, e^{3}-\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{2} c^{3} d^{2}+4 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c^{3} d^{3}-8 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) \sqrt{e x +d}\, c^{3} d^{3}-\sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c^{3} d^{3}+i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{2} c^{2} d e +2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right) c^{3} d^{3}+8 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) \sqrt{e x +d}\, c^{2} d^{2} e +i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, c^{2} d^{3} e -2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right) c^{2} d^{2} e -\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, c^{3} d^{4}+4 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c d \,e^{2}-8 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) \sqrt{e x +d}\, c d \,e^{2}-\sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c d \,e^{2}+i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, d \,e^{3}-\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, c \,d^{2} e^{2}\right)}{3 c \sqrt{\frac{\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} x^{2} e^{2}}}\, x \left(c^{2} d^{2}+e^{2}\right) \sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(-c d +i e \right)}\right)}{e^{3}}"," ",0,"2/e^3*(a*((e*x+d)^(1/2)+2*d/(e*x+d)^(1/2)-1/3*d^2/(e*x+d)^(3/2))+b*((e*x+d)^(1/2)*arccsch(c*x)+2*arccsch(c*x)*d/(e*x+d)^(1/2)-1/3*arccsch(c*x)*d^2/(e*x+d)^(3/2)-2/3/c*(8*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^2*d^2*e+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^2*c^2*d*e-3*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^2*d^2*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^2*c^3*d^2+4*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^3*d^3-8*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^3*d^3-(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^3*d^3+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c^2*d^3*e+2*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)*c^3*d^3-2*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)*c^2*d^2*e+8*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*e^3+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*d*e^3-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c^3*d^4+4*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c*d*e^2-8*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c*d*e^2-(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c*d*e^2-3*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*e^3-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c*d^2*e^2)/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/(c^2*d^2+e^2)/(e*x+d)^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)/(I*e-c*d)))","C"
71,1,2107,342,0.075000," ","int(x*(a+b*arccsch(c*x))/(e*x+d)^(5/2),x)","\frac{2 a \left(-\frac{1}{\sqrt{e x +d}}+\frac{d}{3 \left(e x +d \right)^{\frac{3}{2}}}\right)+2 b \left(-\frac{\mathrm{arccsch}\left(c x \right)}{\sqrt{e x +d}}+\frac{\mathrm{arccsch}\left(c x \right) d}{3 \left(e x +d \right)^{\frac{3}{2}}}+\frac{\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{2} c^{2} d e}{3}-\frac{4 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right) c^{2} d^{2} e}{3}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{2} c^{3} d^{2}}{3}-\frac{4 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) \sqrt{e x +d}\, c^{3} d^{3}}{3}+\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c^{3} d^{3}}{3}-\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c^{3} d^{3}}{3}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, c^{2} d^{3} e}{3}+\frac{4 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right) c^{3} d^{3}}{3}+\frac{4 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) \sqrt{e x +d}\, c^{2} d^{2} e}{3}+\frac{4 i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) \sqrt{e x +d}\, e^{3}}{3}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, c^{3} d^{4}}{3}-\frac{4 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) \sqrt{e x +d}\, c d \,e^{2}}{3}+\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c d \,e^{2}}{3}-\frac{2 \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c d \,e^{2}}{3}+\frac{2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, d \,e^{3}}{3}-\frac{2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, c \,d^{2} e^{2}}{3}}{c \sqrt{\frac{\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} x^{2} e^{2}}}\, x d \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(c^{2} d^{2}+e^{2}\right) \sqrt{e x +d}\, \left(-c d +i e \right)}\right)}{e^{2}}"," ",0,"2/e^2*(a*(-1/(e*x+d)^(1/2)+1/3*d/(e*x+d)^(3/2))+b*(-1/(e*x+d)^(1/2)*arccsch(c*x)+1/3*arccsch(c*x)*d/(e*x+d)^(3/2)+2/3/c*(2*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^2*d^2*e+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^2*c^2*d*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^2*c^3*d^2-2*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^3*d^3+(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^3*d^3-(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^3*d^3-2*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)*c^2*d^2*e+2*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)*c^3*d^3+2*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*e^3+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c^2*d^3*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c^3*d^4-2*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c*d*e^2+(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c*d*e^2-(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c*d*e^2+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*d*e^3-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c*d^2*e^2)/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/d/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)/(c^2*d^2+e^2)/(e*x+d)^(1/2)/(I*e-c*d)))","C"
72,1,2079,320,0.073000," ","int((a+b*arccsch(c*x))/(e*x+d)^(5/2),x)","\frac{-\frac{2 a}{3 \left(e x +d \right)^{\frac{3}{2}}}+2 b \left(-\frac{\mathrm{arccsch}\left(c x \right)}{3 \left(e x +d \right)^{\frac{3}{2}}}-\frac{2 \left(i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, d \,e^{3}-\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{2} c^{3} d^{2}-2 i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right) c^{2} d^{2} e +\sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) \sqrt{e x +d}\, c^{3} d^{3}+\sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c^{3} d^{3}-\sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c^{3} d^{3}-i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) \sqrt{e x +d}\, c^{2} d^{2} e +2 \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right) c^{3} d^{3}-i \sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) \sqrt{e x +d}\, e^{3}-\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, c^{3} d^{4}+i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, c^{2} d^{3} e +\sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \frac{c^{2} d^{2}+e^{2}}{\left(c d +i e \right) c d}, \frac{\sqrt{-\frac{\left(-c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}{\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}}\right) \sqrt{e x +d}\, c d \,e^{2}+\sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c d \,e^{2}-\sqrt{-\frac{i \left(e x +d \right) c e +\left(e x +d \right) c^{2} d -c^{2} d^{2}-e^{2}}{c^{2} d^{2}+e^{2}}}\, \sqrt{\frac{i \left(e x +d \right) c e -\left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} d^{2}+e^{2}}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}, \sqrt{-\frac{-c^{2} d^{2}+2 i c d e +e^{2}}{c^{2} d^{2}+e^{2}}}\right) \sqrt{e x +d}\, c d \,e^{2}+i \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(e x +d \right)^{2} c^{2} d e -\sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, c \,d^{2} e^{2}\right)}{3 c \sqrt{\frac{\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}+e^{2}}{c^{2} x^{2} e^{2}}}\, x \,d^{2} \sqrt{\frac{\left(c d +i e \right) c}{c^{2} d^{2}+e^{2}}}\, \left(c^{2} d^{2}+e^{2}\right) \sqrt{e x +d}\, \left(-c d +i e \right)}\right)}{e}"," ",0,"2/e*(-1/3/(e*x+d)^(3/2)*a+b*(-1/3/(e*x+d)^(3/2)*arccsch(c*x)-2/3/c*(-I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*e^3-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^2*c^3*d^2+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*d*e^3+(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^3*d^3+(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^3*d^3-(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^3*d^3-2*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)*c^2*d^2*e+2*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)*c^3*d^3-I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c^2*d^2*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c^3*d^4+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c^2*d^3*e+(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c*d*e^2+(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c*d*e^2-(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(1/2)*c*d*e^2+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^2*c^2*d*e-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c*d^2*e^2)/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/d^2/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)/(c^2*d^2+e^2)/(e*x+d)^(1/2)/(I*e-c*d)))","C"
73,-2,0,21,180.000000," ","int((a+b*arccsch(c*x))/x/(e*x+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x \left(e x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x/(e*x+d)^(5/2),x)","F"
74,-2,0,21,180.000000," ","int((a+b*arccsch(c*x))/x^2/(e*x+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x^{2} \left(e x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x^2/(e*x+d)^(5/2),x)","F"
75,1,3782,568,0.107000," ","int((a+b*arccsch(c*x))/(e*x+d)^(7/2),x)","\text{output too large to display}"," ",0,"2/e*(-1/5*a/(e*x+d)^(5/2)+b*(-1/5/(e*x+d)^(5/2)*arccsch(c*x)-2/15/c*(3*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(3/2)*c^5*d^5+I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(3/2)*c^2*d^2*e^3-6*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(3/2)*c^2*d^2*e^3-3*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(3/2)*c^4*d^4*e+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c^4*d^6*e+2*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c^2*d^4*e^3-2*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c^3*d^5*e^2+I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*d^2*e^5-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c*d^3*e^4-((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*c^5*d^7+7*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^3*c^4*d^3*e-13*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^2*c^4*d^4*e+3*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^3*c^2*d*e^3+5*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)*c^4*d^5*e-5*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^2*c^2*d^2*e^3+8*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)*c^2*d^3*e^3-3*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)*c*d^2*e^4+3*I*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)*d*e^5-3*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^3*c^3*d^2*e^2+I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(3/2)*c^4*d^4*e+5*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^2*c^3*d^3*e^2-8*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)*c^3*d^4*e^2+6*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(3/2)*c^5*d^5-7*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(3/2)*c^5*d^5-3*I*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(3/2)*e^5-7*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^3*c^5*d^4+13*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)^2*c^5*d^5-5*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)*(e*x+d)*c^5*d^6+9*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(3/2)*c^3*d^3*e^2-10*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(3/2)*c^3*d^3*e^2+3*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(3/2)*c*d*e^4+3*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticF((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(3/2)*c*d*e^4-3*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticE((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),(-(2*I*c*d*e-c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(3/2)*c*d*e^4+6*(-(I*(e*x+d)*c*e+(e*x+d)*c^2*d-c^2*d^2-e^2)/(c^2*d^2+e^2))^(1/2)*((I*(e*x+d)*c*e-(e*x+d)*c^2*d+c^2*d^2+e^2)/(c^2*d^2+e^2))^(1/2)*EllipticPi((e*x+d)^(1/2)*((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2),1/(I*e+c*d)/c*(c^2*d^2+e^2)/d,(-(I*e-c*d)*c/(c^2*d^2+e^2))^(1/2)/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2))*(e*x+d)^(3/2)*c^3*d^3*e^2)/(((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2+e^2)/c^2/x^2/e^2)^(1/2)/x/d^3/((I*e+c*d)*c/(c^2*d^2+e^2))^(1/2)/(c^2*d^2+e^2)^2/(e*x+d)^(3/2)/(I*e-c*d)))","C"
76,1,211,186,0.051000," ","int(x^4*(e*x^2+d)*(a+b*arccsch(c*x)),x)","\frac{\frac{a \left(\frac{1}{7} e \,c^{7} x^{7}+\frac{1}{5} c^{7} x^{5} d \right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arccsch}\left(c x \right) e \,c^{7} x^{7}}{7}+\frac{\mathrm{arccsch}\left(c x \right) c^{7} x^{5} d}{5}+\frac{\sqrt{c^{2} x^{2}+1}\, \left(40 e \,c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+84 c^{5} d \,x^{3} \sqrt{c^{2} x^{2}+1}-50 e \,c^{3} x^{3} \sqrt{c^{2} x^{2}+1}-126 c^{3} d x \sqrt{c^{2} x^{2}+1}+126 c^{2} d \arcsinh \left(c x \right)+75 e c x \sqrt{c^{2} x^{2}+1}-75 e \arcsinh \left(c x \right)\right)}{1680 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{2}}}{c^{5}}"," ",0,"1/c^5*(a/c^2*(1/7*e*c^7*x^7+1/5*c^7*x^5*d)+b/c^2*(1/7*arccsch(c*x)*e*c^7*x^7+1/5*arccsch(c*x)*c^7*x^5*d+1/1680*(c^2*x^2+1)^(1/2)*(40*e*c^5*x^5*(c^2*x^2+1)^(1/2)+84*c^5*d*x^3*(c^2*x^2+1)^(1/2)-50*e*c^3*x^3*(c^2*x^2+1)^(1/2)-126*c^3*d*x*(c^2*x^2+1)^(1/2)+126*c^2*d*arcsinh(c*x)+75*e*c*x*(c^2*x^2+1)^(1/2)-75*e*arcsinh(c*x))/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
77,1,171,145,0.051000," ","int(x^2*(e*x^2+d)*(a+b*arccsch(c*x)),x)","\frac{\frac{a \left(\frac{1}{5} c^{5} x^{5} e +\frac{1}{3} c^{5} x^{3} d \right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arccsch}\left(c x \right) c^{5} x^{5} e}{5}+\frac{\mathrm{arccsch}\left(c x \right) c^{5} x^{3} d}{3}-\frac{\sqrt{c^{2} x^{2}+1}\, \left(-6 e \,c^{3} x^{3} \sqrt{c^{2} x^{2}+1}-20 c^{3} d x \sqrt{c^{2} x^{2}+1}+20 c^{2} d \arcsinh \left(c x \right)+9 e c x \sqrt{c^{2} x^{2}+1}-9 e \arcsinh \left(c x \right)\right)}{120 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{2}}}{c^{3}}"," ",0,"1/c^3*(a/c^2*(1/5*c^5*x^5*e+1/3*c^5*x^3*d)+b/c^2*(1/5*arccsch(c*x)*c^5*x^5*e+1/3*arccsch(c*x)*c^5*x^3*d-1/120*(c^2*x^2+1)^(1/2)*(-6*e*c^3*x^3*(c^2*x^2+1)^(1/2)-20*c^3*d*x*(c^2*x^2+1)^(1/2)+20*c^2*d*arcsinh(c*x)+9*e*c*x*(c^2*x^2+1)^(1/2)-9*e*arcsinh(c*x))/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
78,1,126,101,0.056000," ","int((e*x^2+d)*(a+b*arccsch(c*x)),x)","\frac{\frac{a \left(\frac{1}{3} e \,c^{3} x^{3}+x \,c^{3} d \right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arccsch}\left(c x \right) e \,c^{3} x^{3}}{3}+\mathrm{arccsch}\left(c x \right) c^{3} d x +\frac{\sqrt{c^{2} x^{2}+1}\, \left(6 c^{2} d \arcsinh \left(c x \right)+e c x \sqrt{c^{2} x^{2}+1}-e \arcsinh \left(c x \right)\right)}{6 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{2}}}{c}"," ",0,"1/c*(a/c^2*(1/3*e*c^3*x^3+x*c^3*d)+b/c^2*(1/3*arccsch(c*x)*e*c^3*x^3+arccsch(c*x)*c^3*d*x+1/6*(c^2*x^2+1)^(1/2)*(6*c^2*d*arcsinh(c*x)+e*c*x*(c^2*x^2+1)^(1/2)-e*arcsinh(c*x))/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
79,1,107,83,0.066000," ","int((e*x^2+d)*(a+b*arccsch(c*x))/x^2,x)","c \left(\frac{a \left(c x e -\frac{c d}{x}\right)}{c^{2}}+\frac{b \left(\mathrm{arccsch}\left(c x \right) c x e -\frac{\mathrm{arccsch}\left(c x \right) c d}{x}+\frac{\sqrt{c^{2} x^{2}+1}\, \left(c^{2} d \sqrt{c^{2} x^{2}+1}+e \arcsinh \left(c x \right) c x \right)}{c^{2} x^{2} \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}}\right)}{c^{2}}\right)"," ",0,"c*(a/c^2*(c*x*e-c*d/x)+b/c^2*(arccsch(c*x)*c*x*e-arccsch(c*x)*c*d/x+(c^2*x^2+1)^(1/2)*(c^2*d*(c^2*x^2+1)^(1/2)+e*arcsinh(c*x)*c*x)/c^2/x^2/((c^2*x^2+1)/c^2/x^2)^(1/2)))","A"
80,1,122,95,0.069000," ","int((e*x^2+d)*(a+b*arccsch(c*x))/x^4,x)","c^{3} \left(\frac{a \left(-\frac{e}{c x}-\frac{d}{3 c \,x^{3}}\right)}{c^{2}}+\frac{b \left(-\frac{\mathrm{arccsch}\left(c x \right) e}{c x}-\frac{\mathrm{arccsch}\left(c x \right) d}{3 c \,x^{3}}-\frac{\left(c^{2} x^{2}+1\right) \left(2 c^{4} d \,x^{2}-9 c^{2} x^{2} e -c^{2} d \right)}{9 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c^{4} x^{4}}\right)}{c^{2}}\right)"," ",0,"c^3*(a/c^2*(-e/c/x-1/3/c*d/x^3)+b/c^2*(-arccsch(c*x)*e/c/x-1/3*arccsch(c*x)/c*d/x^3-1/9*(c^2*x^2+1)*(2*c^4*d*x^2-9*c^2*e*x^2-c^2*d)/((c^2*x^2+1)/c^2/x^2)^(1/2)/c^4/x^4))","A"
81,1,140,136,0.065000," ","int((e*x^2+d)*(a+b*arccsch(c*x))/x^6,x)","c^{5} \left(\frac{a \left(-\frac{e}{3 c^{3} x^{3}}-\frac{d}{5 c^{3} x^{5}}\right)}{c^{2}}+\frac{b \left(-\frac{\mathrm{arccsch}\left(c x \right) e}{3 c^{3} x^{3}}-\frac{\mathrm{arccsch}\left(c x \right) d}{5 c^{3} x^{5}}+\frac{\left(c^{2} x^{2}+1\right) \left(24 c^{6} d \,x^{4}-50 c^{4} e \,x^{4}-12 c^{4} d \,x^{2}+25 c^{2} x^{2} e +9 c^{2} d \right)}{225 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c^{6} x^{6}}\right)}{c^{2}}\right)"," ",0,"c^5*(a/c^2*(-1/3*e/c^3/x^3-1/5/c^3*d/x^5)+b/c^2*(-1/3*arccsch(c*x)*e/c^3/x^3-1/5*arccsch(c*x)/c^3*d/x^5+1/225*(c^2*x^2+1)*(24*c^6*d*x^4-50*c^4*e*x^4-12*c^4*d*x^2+25*c^2*e*x^2+9*c^2*d)/((c^2*x^2+1)/c^2/x^2)^(1/2)/c^6/x^6))","A"
82,1,158,177,0.058000," ","int((e*x^2+d)*(a+b*arccsch(c*x))/x^8,x)","c^{7} \left(\frac{a \left(-\frac{d}{7 c^{5} x^{7}}-\frac{e}{5 c^{5} x^{5}}\right)}{c^{2}}+\frac{b \left(-\frac{\mathrm{arccsch}\left(c x \right) d}{7 c^{5} x^{7}}-\frac{\mathrm{arccsch}\left(c x \right) e}{5 c^{5} x^{5}}-\frac{\left(c^{2} x^{2}+1\right) \left(240 c^{8} d \,x^{6}-392 c^{6} e \,x^{6}-120 c^{6} d \,x^{4}+196 c^{4} e \,x^{4}+90 c^{4} d \,x^{2}-147 c^{2} x^{2} e -75 c^{2} d \right)}{3675 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c^{8} x^{8}}\right)}{c^{2}}\right)"," ",0,"c^7*(a/c^2*(-1/7/c^5*d/x^7-1/5*e/c^5/x^5)+b/c^2*(-1/7*arccsch(c*x)/c^5*d/x^7-1/5*arccsch(c*x)*e/c^5/x^5-1/3675*(c^2*x^2+1)*(240*c^8*d*x^6-392*c^6*e*x^6-120*c^6*d*x^4+196*c^4*e*x^4+90*c^4*d*x^2-147*c^2*e*x^2-75*c^2*d)/((c^2*x^2+1)/c^2/x^2)^(1/2)/c^8/x^8))","A"
83,1,152,176,0.055000," ","int(x^5*(e*x^2+d)*(a+b*arccsch(c*x)),x)","\frac{\frac{a \left(\frac{1}{8} e \,c^{8} x^{8}+\frac{1}{6} c^{8} d \,x^{6}\right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arccsch}\left(c x \right) e \,c^{8} x^{8}}{8}+\frac{\mathrm{arccsch}\left(c x \right) c^{8} x^{6} d}{6}+\frac{\left(c^{2} x^{2}+1\right) \left(45 c^{6} e \,x^{6}+84 c^{6} d \,x^{4}-54 c^{4} e \,x^{4}-112 c^{4} d \,x^{2}+72 c^{2} x^{2} e +224 c^{2} d -144 e \right)}{2520 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{2}}}{c^{6}}"," ",0,"1/c^6*(a/c^2*(1/8*e*c^8*x^8+1/6*c^8*d*x^6)+b/c^2*(1/8*arccsch(c*x)*e*c^8*x^8+1/6*arccsch(c*x)*c^8*x^6*d+1/2520*(c^2*x^2+1)*(45*c^6*e*x^6+84*c^6*d*x^4-54*c^4*e*x^4-112*c^4*d*x^2+72*c^2*e*x^2+224*c^2*d-144*e)/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
84,1,134,137,0.050000," ","int(x^3*(e*x^2+d)*(a+b*arccsch(c*x)),x)","\frac{\frac{a \left(\frac{1}{6} c^{6} e \,x^{6}+\frac{1}{4} c^{6} d \,x^{4}\right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arccsch}\left(c x \right) c^{6} x^{6} e}{6}+\frac{\mathrm{arccsch}\left(c x \right) c^{6} x^{4} d}{4}+\frac{\left(c^{2} x^{2}+1\right) \left(6 c^{4} e \,x^{4}+15 c^{4} d \,x^{2}-8 c^{2} x^{2} e -30 c^{2} d +16 e \right)}{180 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{2}}}{c^{4}}"," ",0,"1/c^4*(a/c^2*(1/6*c^6*e*x^6+1/4*c^6*d*x^4)+b/c^2*(1/6*arccsch(c*x)*c^6*x^6*e+1/4*arccsch(c*x)*c^6*x^4*d+1/180*(c^2*x^2+1)*(6*c^4*e*x^4+15*c^4*d*x^2-8*c^2*e*x^2-30*c^2*d+16*e)/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
85,1,115,126,0.049000," ","int(x*(e*x^2+d)*(a+b*arccsch(c*x)),x)","\frac{\frac{a \left(\frac{1}{4} c^{4} e \,x^{4}+\frac{1}{2} c^{4} d \,x^{2}\right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arccsch}\left(c x \right) c^{4} x^{4} e}{4}+\frac{\mathrm{arccsch}\left(c x \right) c^{4} x^{2} d}{2}+\frac{\left(c^{2} x^{2}+1\right) \left(c^{2} x^{2} e +6 c^{2} d -2 e \right)}{12 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{2}}}{c^{2}}"," ",0,"1/c^2*(a/c^2*(1/4*c^4*e*x^4+1/2*c^4*d*x^2)+b/c^2*(1/4*arccsch(c*x)*c^4*x^4*e+1/2*arccsch(c*x)*c^4*x^2*d+1/12*(c^2*x^2+1)*(c^2*e*x^2+6*c^2*d-2*e)/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
86,0,0,131,0.106000," ","int((e*x^2+d)*(a+b*arccsch(c*x))/x,x)","\int \frac{\left(e \,x^{2}+d \right) \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{x}\, dx"," ",0,"int((e*x^2+d)*(a+b*arccsch(c*x))/x,x)","F"
87,0,0,142,0.107000," ","int((e*x^2+d)*(a+b*arccsch(c*x))/x^3,x)","\int \frac{\left(e \,x^{2}+d \right) \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{x^{3}}\, dx"," ",0,"int((e*x^2+d)*(a+b*arccsch(c*x))/x^3,x)","F"
88,1,286,230,0.060000," ","int(x^2*(e*x^2+d)^2*(a+b*arccsch(c*x)),x)","\frac{\frac{a \left(\frac{1}{7} e^{2} c^{7} x^{7}+\frac{2}{5} c^{7} d e \,x^{5}+\frac{1}{3} x^{3} c^{7} d^{2}\right)}{c^{4}}+\frac{b \left(\frac{\mathrm{arccsch}\left(c x \right) e^{2} c^{7} x^{7}}{7}+\frac{2 \,\mathrm{arccsch}\left(c x \right) c^{7} d e \,x^{5}}{5}+\frac{\mathrm{arccsch}\left(c x \right) c^{7} x^{3} d^{2}}{3}+\frac{\sqrt{c^{2} x^{2}+1}\, \left(40 e^{2} c^{5} x^{5} \sqrt{c^{2} x^{2}+1}+168 c^{5} d e \,x^{3} \sqrt{c^{2} x^{2}+1}+280 d^{2} c^{5} x \sqrt{c^{2} x^{2}+1}-280 d^{2} c^{4} \arcsinh \left(c x \right)-50 e^{2} c^{3} x^{3} \sqrt{c^{2} x^{2}+1}-252 c^{3} d e x \sqrt{c^{2} x^{2}+1}+252 c^{2} d e \arcsinh \left(c x \right)+75 e^{2} c x \sqrt{c^{2} x^{2}+1}-75 e^{2} \arcsinh \left(c x \right)\right)}{1680 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{4}}}{c^{3}}"," ",0,"1/c^3*(a/c^4*(1/7*e^2*c^7*x^7+2/5*c^7*d*e*x^5+1/3*x^3*c^7*d^2)+b/c^4*(1/7*arccsch(c*x)*e^2*c^7*x^7+2/5*arccsch(c*x)*c^7*d*e*x^5+1/3*arccsch(c*x)*c^7*x^3*d^2+1/1680*(c^2*x^2+1)^(1/2)*(40*e^2*c^5*x^5*(c^2*x^2+1)^(1/2)+168*c^5*d*e*x^3*(c^2*x^2+1)^(1/2)+280*d^2*c^5*x*(c^2*x^2+1)^(1/2)-280*d^2*c^4*arcsinh(c*x)-50*e^2*c^3*x^3*(c^2*x^2+1)^(1/2)-252*c^3*d*e*x*(c^2*x^2+1)^(1/2)+252*c^2*d*e*arcsinh(c*x)+75*e^2*c*x*(c^2*x^2+1)^(1/2)-75*e^2*arcsinh(c*x))/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
89,1,217,175,0.049000," ","int((e*x^2+d)^2*(a+b*arccsch(c*x)),x)","\frac{\frac{a \left(\frac{1}{5} e^{2} c^{5} x^{5}+\frac{2}{3} c^{5} d e \,x^{3}+x \,c^{5} d^{2}\right)}{c^{4}}+\frac{b \left(\frac{\mathrm{arccsch}\left(c x \right) e^{2} c^{5} x^{5}}{5}+\frac{2 \,\mathrm{arccsch}\left(c x \right) c^{5} d e \,x^{3}}{3}+\mathrm{arccsch}\left(c x \right) c^{5} x \,d^{2}+\frac{\sqrt{c^{2} x^{2}+1}\, \left(120 d^{2} c^{4} \arcsinh \left(c x \right)+6 e^{2} c^{3} x^{3} \sqrt{c^{2} x^{2}+1}+40 c^{3} d e x \sqrt{c^{2} x^{2}+1}-40 c^{2} d e \arcsinh \left(c x \right)-9 e^{2} c x \sqrt{c^{2} x^{2}+1}+9 e^{2} \arcsinh \left(c x \right)\right)}{120 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{4}}}{c}"," ",0,"1/c*(a/c^4*(1/5*e^2*c^5*x^5+2/3*c^5*d*e*x^3+x*c^5*d^2)+b/c^4*(1/5*arccsch(c*x)*e^2*c^5*x^5+2/3*arccsch(c*x)*c^5*d*e*x^3+arccsch(c*x)*c^5*x*d^2+1/120*(c^2*x^2+1)^(1/2)*(120*d^2*c^4*arcsinh(c*x)+6*e^2*c^3*x^3*(c^2*x^2+1)^(1/2)+40*c^3*d*e*x*(c^2*x^2+1)^(1/2)-40*c^2*d*e*arcsinh(c*x)-9*e^2*c*x*(c^2*x^2+1)^(1/2)+9*e^2*arcsinh(c*x))/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
90,1,189,152,0.064000," ","int((e*x^2+d)^2*(a+b*arccsch(c*x))/x^2,x)","c \left(\frac{a \left(\frac{c^{3} x^{3} e^{2}}{3}+2 c^{3} d e x -\frac{d^{2} c^{3}}{x}\right)}{c^{4}}+\frac{b \left(\frac{e^{2} \mathrm{arccsch}\left(c x \right) c^{3} x^{3}}{3}+2 \,\mathrm{arccsch}\left(c x \right) c^{3} d e x -\frac{\mathrm{arccsch}\left(c x \right) d^{2} c^{3}}{x}+\frac{\sqrt{c^{2} x^{2}+1}\, \left(6 d^{2} c^{4} \sqrt{c^{2} x^{2}+1}+12 c^{3} d e \arcsinh \left(c x \right) x +\sqrt{c^{2} x^{2}+1}\, c^{2} x^{2} e^{2}-\arcsinh \left(c x \right) c x \,e^{2}\right)}{6 c^{2} x^{2} \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}}\right)}{c^{4}}\right)"," ",0,"c*(a/c^4*(1/3*c^3*x^3*e^2+2*c^3*d*e*x-d^2*c^3/x)+b/c^4*(1/3*e^2*arccsch(c*x)*c^3*x^3+2*arccsch(c*x)*c^3*d*e*x-arccsch(c*x)*d^2*c^3/x+1/6*(c^2*x^2+1)^(1/2)*(6*d^2*c^4*(c^2*x^2+1)^(1/2)+12*c^3*d*e*arcsinh(c*x)*x+(c^2*x^2+1)^(1/2)*c^2*x^2*e^2-arcsinh(c*x)*c*x*e^2)/c^2/x^2/((c^2*x^2+1)/c^2/x^2)^(1/2)))","A"
91,1,190,146,0.065000," ","int((e*x^2+d)^2*(a+b*arccsch(c*x))/x^4,x)","c^{3} \left(\frac{a \left(c x \,e^{2}-\frac{2 c d e}{x}-\frac{d^{2} c}{3 x^{3}}\right)}{c^{4}}+\frac{b \left(\mathrm{arccsch}\left(c x \right) c x \,e^{2}-\frac{2 \,\mathrm{arccsch}\left(c x \right) c d e}{x}-\frac{\mathrm{arccsch}\left(c x \right) d^{2} c}{3 x^{3}}+\frac{\sqrt{c^{2} x^{2}+1}\, \left(-2 \sqrt{c^{2} x^{2}+1}\, c^{6} x^{2} d^{2}+18 c^{4} d e \sqrt{c^{2} x^{2}+1}\, x^{2}+d^{2} c^{4} \sqrt{c^{2} x^{2}+1}+9 e^{2} \arcsinh \left(c x \right) c^{3} x^{3}\right)}{9 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c^{4} x^{4}}\right)}{c^{4}}\right)"," ",0,"c^3*(a/c^4*(c*x*e^2-2*c*d*e/x-1/3*d^2*c/x^3)+b/c^4*(arccsch(c*x)*c*x*e^2-2*arccsch(c*x)*c*d*e/x-1/3*arccsch(c*x)*d^2*c/x^3+1/9*(c^2*x^2+1)^(1/2)*(-2*(c^2*x^2+1)^(1/2)*c^6*x^2*d^2+18*c^4*d*e*(c^2*x^2+1)^(1/2)*x^2+d^2*c^4*(c^2*x^2+1)^(1/2)+9*e^2*arcsinh(c*x)*c^3*x^3)/((c^2*x^2+1)/c^2/x^2)^(1/2)/c^4/x^4))","A"
92,1,191,167,0.060000," ","int((e*x^2+d)^2*(a+b*arccsch(c*x))/x^6,x)","c^{5} \left(\frac{a \left(-\frac{e^{2}}{c x}-\frac{2 d e}{3 c \,x^{3}}-\frac{d^{2}}{5 c \,x^{5}}\right)}{c^{4}}+\frac{b \left(-\frac{\mathrm{arccsch}\left(c x \right) e^{2}}{c x}-\frac{2 \,\mathrm{arccsch}\left(c x \right) d e}{3 c \,x^{3}}-\frac{\mathrm{arccsch}\left(c x \right) d^{2}}{5 c \,x^{5}}+\frac{\left(c^{2} x^{2}+1\right) \left(24 c^{8} d^{2} x^{4}-100 c^{6} d e \,x^{4}-12 c^{6} d^{2} x^{2}+225 c^{4} e^{2} x^{4}+50 c^{4} d e \,x^{2}+9 d^{2} c^{4}\right)}{225 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c^{6} x^{6}}\right)}{c^{4}}\right)"," ",0,"c^5*(a/c^4*(-e^2/c/x-2/3/c*d*e/x^3-1/5*d^2/c/x^5)+b/c^4*(-arccsch(c*x)*e^2/c/x-2/3*arccsch(c*x)/c*d*e/x^3-1/5*arccsch(c*x)*d^2/c/x^5+1/225*(c^2*x^2+1)*(24*c^8*d^2*x^4-100*c^6*d*e*x^4-12*c^6*d^2*x^2+225*c^4*e^2*x^4+50*c^4*d*e*x^2+9*c^4*d^2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/c^6/x^6))","A"
93,1,223,219,0.062000," ","int((e*x^2+d)^2*(a+b*arccsch(c*x))/x^8,x)","c^{7} \left(\frac{a \left(-\frac{e^{2}}{3 c^{3} x^{3}}-\frac{d^{2}}{7 c^{3} x^{7}}-\frac{2 d e}{5 c^{3} x^{5}}\right)}{c^{4}}+\frac{b \left(-\frac{\mathrm{arccsch}\left(c x \right) e^{2}}{3 c^{3} x^{3}}-\frac{\mathrm{arccsch}\left(c x \right) d^{2}}{7 c^{3} x^{7}}-\frac{2 \,\mathrm{arccsch}\left(c x \right) d e}{5 c^{3} x^{5}}-\frac{\left(c^{2} x^{2}+1\right) \left(720 c^{10} d^{2} x^{6}-2352 c^{8} d e \,x^{6}-360 c^{8} d^{2} x^{4}+2450 c^{6} e^{2} x^{6}+1176 c^{6} d e \,x^{4}+270 c^{6} d^{2} x^{2}-1225 c^{4} e^{2} x^{4}-882 c^{4} d e \,x^{2}-225 d^{2} c^{4}\right)}{11025 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c^{8} x^{8}}\right)}{c^{4}}\right)"," ",0,"c^7*(a/c^4*(-1/3*e^2/c^3/x^3-1/7*d^2/c^3/x^7-2/5/c^3*d*e/x^5)+b/c^4*(-1/3*arccsch(c*x)*e^2/c^3/x^3-1/7*arccsch(c*x)*d^2/c^3/x^7-2/5*arccsch(c*x)/c^3*d*e/x^5-1/11025*(c^2*x^2+1)*(720*c^10*d^2*x^6-2352*c^8*d*e*x^6-360*c^8*d^2*x^4+2450*c^6*e^2*x^6+1176*c^6*d*e*x^4+270*c^6*d^2*x^2-1225*c^4*e^2*x^4-882*c^4*d*e*x^2-225*c^4*d^2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/c^8/x^8))","A"
94,1,214,220,0.053000," ","int(x^3*(e*x^2+d)^2*(a+b*arccsch(c*x)),x)","\frac{\frac{a \left(\frac{1}{8} e^{2} c^{8} x^{8}+\frac{1}{3} c^{8} d e \,x^{6}+\frac{1}{4} c^{8} d^{2} x^{4}\right)}{c^{4}}+\frac{b \left(\frac{\mathrm{arccsch}\left(c x \right) e^{2} c^{8} x^{8}}{8}+\frac{\mathrm{arccsch}\left(c x \right) c^{8} d e \,x^{6}}{3}+\frac{\mathrm{arccsch}\left(c x \right) c^{8} x^{4} d^{2}}{4}+\frac{\left(c^{2} x^{2}+1\right) \left(45 c^{6} e^{2} x^{6}+168 c^{6} d e \,x^{4}+210 c^{6} d^{2} x^{2}-54 c^{4} e^{2} x^{4}-224 c^{4} d e \,x^{2}-420 d^{2} c^{4}+72 c^{2} e^{2} x^{2}+448 c^{2} d e -144 e^{2}\right)}{2520 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{4}}}{c^{4}}"," ",0,"1/c^4*(a/c^4*(1/8*e^2*c^8*x^8+1/3*c^8*d*e*x^6+1/4*c^8*d^2*x^4)+b/c^4*(1/8*arccsch(c*x)*e^2*c^8*x^8+1/3*arccsch(c*x)*c^8*d*e*x^6+1/4*arccsch(c*x)*c^8*x^4*d^2+1/2520*(c^2*x^2+1)*(45*c^6*e^2*x^6+168*c^6*d*e*x^4+210*c^6*d^2*x^2-54*c^4*e^2*x^4-224*c^4*d*e*x^2-420*c^4*d^2+72*c^2*e^2*x^2+448*c^2*d*e-144*e^2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
95,1,182,177,0.050000," ","int(x*(e*x^2+d)^2*(a+b*arccsch(c*x)),x)","\frac{\frac{a \left(\frac{1}{6} c^{6} e^{2} x^{6}+\frac{1}{2} c^{6} d e \,x^{4}+\frac{1}{2} c^{6} d^{2} x^{2}\right)}{c^{4}}+\frac{b \left(\frac{\mathrm{arccsch}\left(c x \right) e^{2} c^{6} x^{6}}{6}+\frac{\mathrm{arccsch}\left(c x \right) c^{6} d e \,x^{4}}{2}+\frac{\mathrm{arccsch}\left(c x \right) c^{6} x^{2} d^{2}}{2}+\frac{\left(c^{2} x^{2}+1\right) \left(3 c^{4} e^{2} x^{4}+15 c^{4} d e \,x^{2}+45 d^{2} c^{4}-4 c^{2} e^{2} x^{2}-30 c^{2} d e +8 e^{2}\right)}{90 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c x}\right)}{c^{4}}}{c^{2}}"," ",0,"1/c^2*(a/c^4*(1/6*c^6*e^2*x^6+1/2*c^6*d*e*x^4+1/2*c^6*d^2*x^2)+b/c^4*(1/6*arccsch(c*x)*e^2*c^6*x^6+1/2*arccsch(c*x)*c^6*d*e*x^4+1/2*arccsch(c*x)*c^6*x^2*d^2+1/90*(c^2*x^2+1)*(3*c^4*e^2*x^4+15*c^4*d*e*x^2+45*c^4*d^2-4*c^2*e^2*x^2-30*c^2*d*e+8*e^2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/c/x))","A"
96,0,0,190,0.427000," ","int((e*x^2+d)^2*(a+b*arccsch(c*x))/x,x)","\int \frac{\left(e \,x^{2}+d \right)^{2} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{x}\, dx"," ",0,"int((e*x^2+d)^2*(a+b*arccsch(c*x))/x,x)","F"
97,0,0,190,0.457000," ","int((e*x^2+d)^2*(a+b*arccsch(c*x))/x^3,x)","\int \frac{\left(e \,x^{2}+d \right)^{2} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{x^{3}}\, dx"," ",0,"int((e*x^2+d)^2*(a+b*arccsch(c*x))/x^3,x)","F"
98,0,0,518,3.395000," ","int(x^2*(a+b*arccsch(c*x))/(e*x^2+d),x)","\int \frac{x^{2} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{e \,x^{2}+d}\, dx"," ",0,"int(x^2*(a+b*arccsch(c*x))/(e*x^2+d),x)","F"
99,0,0,531,0.462000," ","int(x*(a+b*arccsch(c*x))/(e*x^2+d),x)","\int \frac{x \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{e \,x^{2}+d}\, dx"," ",0,"int(x*(a+b*arccsch(c*x))/(e*x^2+d),x)","F"
100,0,0,485,1.453000," ","int((a+b*arccsch(c*x))/(e*x^2+d),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arccsch(c*x))/(e*x^2+d),x)","F"
101,0,0,463,0.444000," ","int((a+b*arccsch(c*x))/x/(e*x^2+d),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x \left(e \,x^{2}+d \right)}\, dx"," ",0,"int((a+b*arccsch(c*x))/x/(e*x^2+d),x)","F"
102,0,0,524,2.759000," ","int((a+b*arccsch(c*x))/x^2/(e*x^2+d),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x^{2} \left(e \,x^{2}+d \right)}\, dx"," ",0,"int((a+b*arccsch(c*x))/x^2/(e*x^2+d),x)","F"
103,0,0,653,0.444000," ","int(x^5*(a+b*arccsch(c*x))/(e*x^2+d)^2,x)","\int \frac{x^{5} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int(x^5*(a+b*arccsch(c*x))/(e*x^2+d)^2,x)","F"
104,0,0,606,0.440000," ","int(x^3*(a+b*arccsch(c*x))/(e*x^2+d)^2,x)","\int \frac{x^{3} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int(x^3*(a+b*arccsch(c*x))/(e*x^2+d)^2,x)","F"
105,1,360,120,0.074000," ","int(x*(a+b*arccsch(c*x))/(e*x^2+d)^2,x)","-\frac{c^{2} a}{2 e \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{c^{2} b \,\mathrm{arccsch}\left(c x \right)}{2 e \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{b \sqrt{c^{2} x^{2}+1}\, \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{2 c e \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x d}-\frac{b \sqrt{c^{2} x^{2}+1}\, \ln \left(-\frac{2 \left(\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{-c x e +\sqrt{-c^{2} d e}}\right)}{4 c e \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x d \sqrt{-\frac{c^{2} d -e}{e}}}-\frac{b \sqrt{c^{2} x^{2}+1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x -e \right)}{c x e +\sqrt{-c^{2} d e}}\right)}{4 c e \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x d \sqrt{-\frac{c^{2} d -e}{e}}}"," ",0,"-1/2*c^2*a/e/(c^2*e*x^2+c^2*d)-1/2*c^2*b/e/(c^2*e*x^2+c^2*d)*arccsch(c*x)+1/2/c*b/e*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/d*arctanh(1/(c^2*x^2+1)^(1/2))-1/4/c*b/e*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/d/(-(c^2*d-e)/e)^(1/2)*ln(-2*((c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))-1/4/c*b/e*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/d/(-(c^2*d-e)/e)^(1/2)*ln(-2*(-(c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e+(-c^2*d*e)^(1/2)))","B"
106,0,0,539,0.482000," ","int((a+b*arccsch(c*x))/x/(e*x^2+d)^2,x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x \left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x/(e*x^2+d)^2,x)","F"
107,0,0,718,15.131000," ","int(x^4*(a+b*arccsch(c*x))/(e*x^2+d)^2,x)","\int \frac{x^{4} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int(x^4*(a+b*arccsch(c*x))/(e*x^2+d)^2,x)","F"
108,0,0,686,3.510000," ","int(x^2*(a+b*arccsch(c*x))/(e*x^2+d)^2,x)","\int \frac{x^{2} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int(x^2*(a+b*arccsch(c*x))/(e*x^2+d)^2,x)","F"
109,0,0,680,4.649000," ","int((a+b*arccsch(c*x))/(e*x^2+d)^2,x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((a+b*arccsch(c*x))/(e*x^2+d)^2,x)","F"
110,0,0,720,14.660000," ","int((a+b*arccsch(c*x))/x^2/(e*x^2+d)^2,x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x^{2} \left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x^2/(e*x^2+d)^2,x)","F"
111,0,0,732,0.490000," ","int(x^5*(a+b*arccsch(c*x))/(e*x^2+d)^3,x)","\int \frac{x^{5} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{3}}\, dx"," ",0,"int(x^5*(a+b*arccsch(c*x))/(e*x^2+d)^3,x)","F"
112,1,1922,145,0.094000," ","int(x^3*(a+b*arccsch(c*x))/(e*x^2+d)^3,x)","\frac{c^{4} a d}{4 e^{2} \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{c^{2} a}{2 e^{2} \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{c^{4} b \,\mathrm{arccsch}\left(c x \right) d}{4 e^{2} \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{c^{2} b \,\mathrm{arccsch}\left(c x \right)}{2 e^{2} \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{c^{3} b \sqrt{c^{2} x^{2}+1}\, x \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \left(-c x e +\sqrt{-c^{2} d e}\right)}-\frac{c^{3} b \sqrt{c^{2} x^{2}+1}\, d \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{4 e \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \left(-c x e +\sqrt{-c^{2} d e}\right)}+\frac{c^{3} b \sqrt{c^{2} x^{2}+1}\, x \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x -e \right)}{c x e +\sqrt{-c^{2} d e}}\right)}{16 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d -e}{e}}\, \left(-c x e +\sqrt{-c^{2} d e}\right)}+\frac{c^{3} b \sqrt{c^{2} x^{2}+1}\, d \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x -e \right)}{c x e +\sqrt{-c^{2} d e}}\right)}{16 e \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d -e}{e}}\, \left(-c x e +\sqrt{-c^{2} d e}\right)}+\frac{c^{3} b \sqrt{c^{2} x^{2}+1}\, x \ln \left(-\frac{2 \left(\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{-c x e +\sqrt{-c^{2} d e}}\right)}{16 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d -e}{e}}\, \left(-c x e +\sqrt{-c^{2} d e}\right)}+\frac{c^{3} b \sqrt{c^{2} x^{2}+1}\, d \ln \left(-\frac{2 \left(\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{-c x e +\sqrt{-c^{2} d e}}\right)}{16 e \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d -e}{e}}\, \left(-c x e +\sqrt{-c^{2} d e}\right)}+\frac{c^{3} b x}{8 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \left(-c x e +\sqrt{-c^{2} d e}\right)}+\frac{c b}{8 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \left(-c x e +\sqrt{-c^{2} d e}\right)}+\frac{c b \sqrt{c^{2} x^{2}+1}\, e x \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, d \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \left(-c x e +\sqrt{-c^{2} d e}\right)}+\frac{c b \sqrt{c^{2} x^{2}+1}\, \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \left(-c x e +\sqrt{-c^{2} d e}\right)}-\frac{c b \sqrt{c^{2} x^{2}+1}\, e x \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x -e \right)}{c x e +\sqrt{-c^{2} d e}}\right)}{8 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, d \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d -e}{e}}\, \left(-c x e +\sqrt{-c^{2} d e}\right)}-\frac{c b \sqrt{c^{2} x^{2}+1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x -e \right)}{c x e +\sqrt{-c^{2} d e}}\right)}{8 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d -e}{e}}\, \left(-c x e +\sqrt{-c^{2} d e}\right)}-\frac{c b \sqrt{c^{2} x^{2}+1}\, e x \ln \left(-\frac{2 \left(\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{-c x e +\sqrt{-c^{2} d e}}\right)}{8 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, d \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d -e}{e}}\, \left(-c x e +\sqrt{-c^{2} d e}\right)}-\frac{c b \sqrt{c^{2} x^{2}+1}\, \ln \left(-\frac{2 \left(\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{-c x e +\sqrt{-c^{2} d e}}\right)}{8 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d -e}{e}}\, \left(-c x e +\sqrt{-c^{2} d e}\right)}"," ",0,"1/4*c^4*a/e^2*d/(c^2*e*x^2+c^2*d)^2-1/2*c^2*a/e^2/(c^2*e*x^2+c^2*d)+1/4*c^4*b*arccsch(c*x)/e^2*d/(c^2*e*x^2+c^2*d)^2-1/2*c^2*b*arccsch(c*x)/e^2/(c^2*e*x^2+c^2*d)-1/4*c^3*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)*x/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-c*x*e+(-c^2*d*e)^(1/2))*arctanh(1/(c^2*x^2+1)^(1/2))-1/4*c^3*b*(c^2*x^2+1)^(1/2)/e/((c^2*x^2+1)/c^2/x^2)^(1/2)/x*d/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-c*x*e+(-c^2*d*e)^(1/2))*arctanh(1/(c^2*x^2+1)^(1/2))+1/16*c^3*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)*x/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d-e)/e)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))*ln(-2*(-(c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e+(-c^2*d*e)^(1/2)))+1/16*c^3*b*(c^2*x^2+1)^(1/2)/e/((c^2*x^2+1)/c^2/x^2)^(1/2)/x*d/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d-e)/e)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))*ln(-2*(-(c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e+(-c^2*d*e)^(1/2)))+1/16*c^3*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)*x/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d-e)/e)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))*ln(-2*((c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))+1/16*c^3*b*(c^2*x^2+1)^(1/2)/e/((c^2*x^2+1)/c^2/x^2)^(1/2)/x*d/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d-e)/e)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))*ln(-2*((c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))+1/8*c^3*b/((c^2*x^2+1)/c^2/x^2)^(1/2)*x/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-c*x*e+(-c^2*d*e)^(1/2))+1/8*c*b/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-c*x*e+(-c^2*d*e)^(1/2))+1/4*c*b*(c^2*x^2+1)^(1/2)*e/((c^2*x^2+1)/c^2/x^2)^(1/2)*x/d/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-c*x*e+(-c^2*d*e)^(1/2))*arctanh(1/(c^2*x^2+1)^(1/2))+1/4*c*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-c*x*e+(-c^2*d*e)^(1/2))*arctanh(1/(c^2*x^2+1)^(1/2))-1/8*c*b*(c^2*x^2+1)^(1/2)*e/((c^2*x^2+1)/c^2/x^2)^(1/2)*x/d/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d-e)/e)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))*ln(-2*(-(c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e+(-c^2*d*e)^(1/2)))-1/8*c*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d-e)/e)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))*ln(-2*(-(c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e+(-c^2*d*e)^(1/2)))-1/8*c*b*(c^2*x^2+1)^(1/2)*e/((c^2*x^2+1)/c^2/x^2)^(1/2)*x/d/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d-e)/e)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))*ln(-2*((c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))-1/8*c*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d-e)/e)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))*ln(-2*((c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))","B"
113,1,1892,180,0.079000," ","int(x*(a+b*arccsch(c*x))/(e*x^2+d)^3,x)","-\frac{c^{4} a}{4 e \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{c^{4} b \,\mathrm{arccsch}\left(c x \right)}{4 e \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{c^{3} b \sqrt{c^{2} x^{2}+1}\, e x \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, d \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \left(-c x e +\sqrt{-c^{2} d e}\right)}-\frac{c^{3} b \sqrt{c^{2} x^{2}+1}\, \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \left(-c x e +\sqrt{-c^{2} d e}\right)}+\frac{3 c^{3} b \sqrt{c^{2} x^{2}+1}\, e x \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x -e \right)}{c x e +\sqrt{-c^{2} d e}}\right)}{16 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, d \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d -e}{e}}\, \left(-c x e +\sqrt{-c^{2} d e}\right)}+\frac{3 c^{3} b \sqrt{c^{2} x^{2}+1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x -e \right)}{c x e +\sqrt{-c^{2} d e}}\right)}{16 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d -e}{e}}\, \left(-c x e +\sqrt{-c^{2} d e}\right)}+\frac{3 c^{3} b \sqrt{c^{2} x^{2}+1}\, e x \ln \left(-\frac{2 \left(\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{-c x e +\sqrt{-c^{2} d e}}\right)}{16 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, d \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d -e}{e}}\, \left(-c x e +\sqrt{-c^{2} d e}\right)}+\frac{3 c^{3} b \sqrt{c^{2} x^{2}+1}\, \ln \left(-\frac{2 \left(\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{-c x e +\sqrt{-c^{2} d e}}\right)}{16 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d -e}{e}}\, \left(-c x e +\sqrt{-c^{2} d e}\right)}-\frac{c^{3} b x e}{8 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, d \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \left(-c x e +\sqrt{-c^{2} d e}\right)}-\frac{c b e}{8 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x d \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \left(-c x e +\sqrt{-c^{2} d e}\right)}+\frac{c b \sqrt{c^{2} x^{2}+1}\, x \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right) e^{2}}{4 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, d^{2} \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \left(-c x e +\sqrt{-c^{2} d e}\right)}+\frac{c b \sqrt{c^{2} x^{2}+1}\, \arctanh \left(\frac{1}{\sqrt{c^{2} x^{2}+1}}\right) e}{4 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x d \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \left(-c x e +\sqrt{-c^{2} d e}\right)}-\frac{c b \sqrt{c^{2} x^{2}+1}\, x \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x -e \right)}{c x e +\sqrt{-c^{2} d e}}\right) e^{2}}{8 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, d^{2} \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d -e}{e}}\, \left(-c x e +\sqrt{-c^{2} d e}\right)}-\frac{c b \sqrt{c^{2} x^{2}+1}\, \ln \left(-\frac{2 \left(-\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x -e \right)}{c x e +\sqrt{-c^{2} d e}}\right) e}{8 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x d \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d -e}{e}}\, \left(-c x e +\sqrt{-c^{2} d e}\right)}-\frac{c b \sqrt{c^{2} x^{2}+1}\, x \ln \left(-\frac{2 \left(\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{-c x e +\sqrt{-c^{2} d e}}\right) e^{2}}{8 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, d^{2} \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d -e}{e}}\, \left(-c x e +\sqrt{-c^{2} d e}\right)}-\frac{c b \sqrt{c^{2} x^{2}+1}\, \ln \left(-\frac{2 \left(\sqrt{c^{2} x^{2}+1}\, \sqrt{-\frac{c^{2} d -e}{e}}\, e +\sqrt{-c^{2} d e}\, c x +e \right)}{-c x e +\sqrt{-c^{2} d e}}\right) e}{8 \sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x d \left(c^{2} d -e \right) \left(c x e +\sqrt{-c^{2} d e}\right) \sqrt{-\frac{c^{2} d -e}{e}}\, \left(-c x e +\sqrt{-c^{2} d e}\right)}"," ",0,"-1/4*c^4*a/e/(c^2*e*x^2+c^2*d)^2-1/4*c^4*b/e/(c^2*e*x^2+c^2*d)^2*arccsch(c*x)-1/4*c^3*b*(c^2*x^2+1)^(1/2)*e/((c^2*x^2+1)/c^2/x^2)^(1/2)*x/d/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-c*x*e+(-c^2*d*e)^(1/2))*arctanh(1/(c^2*x^2+1)^(1/2))-1/4*c^3*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-c*x*e+(-c^2*d*e)^(1/2))*arctanh(1/(c^2*x^2+1)^(1/2))+3/16*c^3*b*(c^2*x^2+1)^(1/2)*e/((c^2*x^2+1)/c^2/x^2)^(1/2)*x/d/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d-e)/e)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))*ln(-2*(-(c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e+(-c^2*d*e)^(1/2)))+3/16*c^3*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d-e)/e)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))*ln(-2*(-(c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e+(-c^2*d*e)^(1/2)))+3/16*c^3*b*(c^2*x^2+1)^(1/2)*e/((c^2*x^2+1)/c^2/x^2)^(1/2)*x/d/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d-e)/e)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))*ln(-2*((c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))+3/16*c^3*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d-e)/e)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))*ln(-2*((c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))-1/8*c^3*b/((c^2*x^2+1)/c^2/x^2)^(1/2)*x/d/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-c*x*e+(-c^2*d*e)^(1/2))*e-1/8*c*b/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/d/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-c*x*e+(-c^2*d*e)^(1/2))*e+1/4*c*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)*x/d^2/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-c*x*e+(-c^2*d*e)^(1/2))*arctanh(1/(c^2*x^2+1)^(1/2))*e^2+1/4*c*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/d/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-c*x*e+(-c^2*d*e)^(1/2))*arctanh(1/(c^2*x^2+1)^(1/2))*e-1/8*c*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)*x/d^2/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d-e)/e)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))*ln(-2*(-(c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e+(-c^2*d*e)^(1/2)))*e^2-1/8*c*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/d/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d-e)/e)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))*ln(-2*(-(c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x-e)/(c*x*e+(-c^2*d*e)^(1/2)))*e-1/8*c*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)*x/d^2/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d-e)/e)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))*ln(-2*((c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))*e^2-1/8*c*b*(c^2*x^2+1)^(1/2)/((c^2*x^2+1)/c^2/x^2)^(1/2)/x/d/(c^2*d-e)/(c*x*e+(-c^2*d*e)^(1/2))/(-(c^2*d-e)/e)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))*ln(-2*((c^2*x^2+1)^(1/2)*(-(c^2*d-e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))*e","B"
114,0,0,667,0.444000," ","int((a+b*arccsch(c*x))/x/(e*x^2+d)^3,x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x \left(e \,x^{2}+d \right)^{3}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x/(e*x^2+d)^3,x)","F"
115,0,0,994,3.803000," ","int(x^4*(a+b*arccsch(c*x))/(e*x^2+d)^3,x)","\int \frac{x^{4} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{3}}\, dx"," ",0,"int(x^4*(a+b*arccsch(c*x))/(e*x^2+d)^3,x)","F"
116,0,0,1000,5.009000," ","int(x^2*(a+b*arccsch(c*x))/(e*x^2+d)^3,x)","\int \frac{x^{2} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{3}}\, dx"," ",0,"int(x^2*(a+b*arccsch(c*x))/(e*x^2+d)^3,x)","F"
117,0,0,984,3.774000," ","int((a+b*arccsch(c*x))/(e*x^2+d)^3,x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{\left(e \,x^{2}+d \right)^{3}}\, dx"," ",0,"int((a+b*arccsch(c*x))/(e*x^2+d)^3,x)","F"
118,0,0,353,0.434000," ","int(x^5*(a+b*arccsch(c*x))*(e*x^2+d)^(1/2),x)","\int x^{5} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int(x^5*(a+b*arccsch(c*x))*(e*x^2+d)^(1/2),x)","F"
119,0,0,254,0.440000," ","int(x^3*(a+b*arccsch(c*x))*(e*x^2+d)^(1/2),x)","\int x^{3} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int(x^3*(a+b*arccsch(c*x))*(e*x^2+d)^(1/2),x)","F"
120,0,0,167,0.479000," ","int(x*(a+b*arccsch(c*x))*(e*x^2+d)^(1/2),x)","\int x \left(a +b \,\mathrm{arccsch}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int(x*(a+b*arccsch(c*x))*(e*x^2+d)^(1/2),x)","F"
121,0,0,23,0.449000," ","int((a+b*arccsch(c*x))*(e*x^2+d)^(1/2)/x,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x}\, dx"," ",0,"int((a+b*arccsch(c*x))*(e*x^2+d)^(1/2)/x,x)","F"
122,0,0,23,0.450000," ","int((a+b*arccsch(c*x))*(e*x^2+d)^(1/2)/x^3,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x^{3}}\, dx"," ",0,"int((a+b*arccsch(c*x))*(e*x^2+d)^(1/2)/x^3,x)","F"
123,0,0,23,0.426000," ","int(x^2*(a+b*arccsch(c*x))*(e*x^2+d)^(1/2),x)","\int x^{2} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int(x^2*(a+b*arccsch(c*x))*(e*x^2+d)^(1/2),x)","F"
124,0,0,20,0.422000," ","int((a+b*arccsch(c*x))*(e*x^2+d)^(1/2),x)","\int \left(a +b \,\mathrm{arccsch}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arccsch(c*x))*(e*x^2+d)^(1/2),x)","F"
125,0,0,23,0.455000," ","int((a+b*arccsch(c*x))*(e*x^2+d)^(1/2)/x^2,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x^{2}}\, dx"," ",0,"int((a+b*arccsch(c*x))*(e*x^2+d)^(1/2)/x^2,x)","F"
126,0,0,413,0.438000," ","int((a+b*arccsch(c*x))*(e*x^2+d)^(1/2)/x^4,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x^{4}}\, dx"," ",0,"int((a+b*arccsch(c*x))*(e*x^2+d)^(1/2)/x^4,x)","F"
127,0,0,1247,0.434000," ","int((a+b*arccsch(c*x))*(e*x^2+d)^(1/2)/x^6,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x^{6}}\, dx"," ",0,"int((a+b*arccsch(c*x))*(e*x^2+d)^(1/2)/x^6,x)","F"
128,0,0,328,0.479000," ","int(x^3*(e*x^2+d)^(3/2)*(a+b*arccsch(c*x)),x)","\int x^{3} \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)\, dx"," ",0,"int(x^3*(e*x^2+d)^(3/2)*(a+b*arccsch(c*x)),x)","F"
129,0,0,226,0.431000," ","int(x*(e*x^2+d)^(3/2)*(a+b*arccsch(c*x)),x)","\int x \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)\, dx"," ",0,"int(x*(e*x^2+d)^(3/2)*(a+b*arccsch(c*x)),x)","F"
130,0,0,23,0.433000," ","int((e*x^2+d)^(3/2)*(a+b*arccsch(c*x))/x,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{x}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arccsch(c*x))/x,x)","F"
131,0,0,23,0.420000," ","int((e*x^2+d)^(3/2)*(a+b*arccsch(c*x))/x^3,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{x^{3}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arccsch(c*x))/x^3,x)","F"
132,0,0,23,0.613000," ","int(x^2*(e*x^2+d)^(3/2)*(a+b*arccsch(c*x)),x)","\int x^{2} \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)\, dx"," ",0,"int(x^2*(e*x^2+d)^(3/2)*(a+b*arccsch(c*x)),x)","F"
133,0,0,20,0.440000," ","int((e*x^2+d)^(3/2)*(a+b*arccsch(c*x)),x)","\int \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arccsch(c*x)),x)","F"
134,0,0,23,0.447000," ","int((e*x^2+d)^(3/2)*(a+b*arccsch(c*x))/x^2,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{x^{2}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arccsch(c*x))/x^2,x)","F"
135,0,0,23,0.446000," ","int((e*x^2+d)^(3/2)*(a+b*arccsch(c*x))/x^4,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{x^{4}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arccsch(c*x))/x^4,x)","F"
136,0,0,508,0.427000," ","int((e*x^2+d)^(3/2)*(a+b*arccsch(c*x))/x^6,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{x^{6}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arccsch(c*x))/x^6,x)","F"
137,0,0,647,0.463000," ","int((e*x^2+d)^(3/2)*(a+b*arccsch(c*x))/x^8,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{x^{8}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arccsch(c*x))/x^8,x)","F"
138,0,0,279,0.449000," ","int(x^5*(a+b*arccsch(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x^{5} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x^5*(a+b*arccsch(c*x))/(e*x^2+d)^(1/2),x)","F"
139,0,0,191,0.441000," ","int(x^3*(a+b*arccsch(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x^3*(a+b*arccsch(c*x))/(e*x^2+d)^(1/2),x)","F"
140,0,0,113,0.433000," ","int(x*(a+b*arccsch(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x*(a+b*arccsch(c*x))/(e*x^2+d)^(1/2),x)","F"
141,0,0,23,0.422000," ","int((a+b*arccsch(c*x))/x/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x/(e*x^2+d)^(1/2),x)","F"
142,0,0,23,0.463000," ","int((a+b*arccsch(c*x))/x^3/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x^{3} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x^3/(e*x^2+d)^(1/2),x)","F"
143,0,0,23,0.437000," ","int(x^2*(a+b*arccsch(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x^{2} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x^2*(a+b*arccsch(c*x))/(e*x^2+d)^(1/2),x)","F"
144,0,0,20,0.433000," ","int((a+b*arccsch(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arccsch(c*x))/(e*x^2+d)^(1/2),x)","F"
145,0,0,336,0.506000," ","int((a+b*arccsch(c*x))/x^2/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x^{2} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x^2/(e*x^2+d)^(1/2),x)","F"
146,0,0,445,0.493000," ","int((a+b*arccsch(c*x))/x^4/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x^{4} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x^4/(e*x^2+d)^(1/2),x)","F"
147,0,0,216,0.470000," ","int(x^5*(a+b*arccsch(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{5} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^5*(a+b*arccsch(c*x))/(e*x^2+d)^(3/2),x)","F"
148,0,0,136,0.437000," ","int(x^3*(a+b*arccsch(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3*(a+b*arccsch(c*x))/(e*x^2+d)^(3/2),x)","F"
149,0,0,72,0.443000," ","int(x*(a+b*arccsch(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(a+b*arccsch(c*x))/(e*x^2+d)^(3/2),x)","F"
150,0,0,23,0.443000," ","int((a+b*arccsch(c*x))/x/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x/(e*x^2+d)^(3/2),x)","F"
151,0,0,23,0.457000," ","int((a+b*arccsch(c*x))/x^3/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x^{3} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x^3/(e*x^2+d)^(3/2),x)","F"
152,0,0,23,0.439000," ","int(x^4*(a+b*arccsch(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{4} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^4*(a+b*arccsch(c*x))/(e*x^2+d)^(3/2),x)","F"
153,0,0,23,0.429000," ","int(x^2*(a+b*arccsch(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{2} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*(a+b*arccsch(c*x))/(e*x^2+d)^(3/2),x)","F"
154,0,0,137,0.459000," ","int((a+b*arccsch(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccsch(c*x))/(e*x^2+d)^(3/2),x)","F"
155,0,0,363,0.448000," ","int((a+b*arccsch(c*x))/x^2/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x^{2} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x^2/(e*x^2+d)^(3/2),x)","F"
156,0,0,213,0.440000," ","int(x^5*(a+b*arccsch(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{5} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^5*(a+b*arccsch(c*x))/(e*x^2+d)^(5/2),x)","F"
157,0,0,145,0.452000," ","int(x^3*(a+b*arccsch(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^3*(a+b*arccsch(c*x))/(e*x^2+d)^(5/2),x)","F"
158,0,0,123,0.430000," ","int(x*(a+b*arccsch(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*(a+b*arccsch(c*x))/(e*x^2+d)^(5/2),x)","F"
159,0,0,23,0.502000," ","int((a+b*arccsch(c*x))/x/(e*x^2+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x \left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x/(e*x^2+d)^(5/2),x)","F"
160,0,0,23,0.509000," ","int((a+b*arccsch(c*x))/x^3/(e*x^2+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x^{3} \left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x^3/(e*x^2+d)^(5/2),x)","F"
161,0,0,23,0.477000," ","int(x^6*(a+b*arccsch(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{6} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^6*(a+b*arccsch(c*x))/(e*x^2+d)^(5/2),x)","F"
162,0,0,23,0.442000," ","int(x^4*(a+b*arccsch(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{4} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^4*(a+b*arccsch(c*x))/(e*x^2+d)^(5/2),x)","F"
163,0,0,391,0.428000," ","int(x^2*(a+b*arccsch(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{2} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^2*(a+b*arccsch(c*x))/(e*x^2+d)^(5/2),x)","F"
164,0,0,317,0.436000," ","int((a+b*arccsch(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccsch(c*x))/(e*x^2+d)^(5/2),x)","F"
165,0,0,574,0.425000," ","int((f*x)^m*(e*x^2+d)^3*(a+b*arccsch(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right)^{3} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^3*(a+b*arccsch(c*x)),x)","F"
166,0,0,361,0.409000," ","int((f*x)^m*(e*x^2+d)^2*(a+b*arccsch(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right)^{2} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^2*(a+b*arccsch(c*x)),x)","F"
167,0,0,206,0.059000," ","int((f*x)^m*(e*x^2+d)*(a+b*arccsch(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right) \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)*(a+b*arccsch(c*x)),x)","F"
168,0,0,25,0.445000," ","int((f*x)^m*(a+b*arccsch(c*x))/(e*x^2+d),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{e \,x^{2}+d}\, dx"," ",0,"int((f*x)^m*(a+b*arccsch(c*x))/(e*x^2+d),x)","F"
169,0,0,25,0.430000," ","int((f*x)^m*(a+b*arccsch(c*x))/(e*x^2+d)^2,x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((f*x)^m*(a+b*arccsch(c*x))/(e*x^2+d)^2,x)","F"
170,0,0,25,0.450000," ","int((f*x)^m*(e*x^2+d)^(3/2)*(a+b*arccsch(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^(3/2)*(a+b*arccsch(c*x)),x)","F"
171,0,0,25,0.464000," ","int((f*x)^m*(a+b*arccsch(c*x))*(e*x^2+d)^(1/2),x)","\int \left(f x \right)^{m} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int((f*x)^m*(a+b*arccsch(c*x))*(e*x^2+d)^(1/2),x)","F"
172,0,0,25,0.443000," ","int((f*x)^m*(a+b*arccsch(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((f*x)^m*(a+b*arccsch(c*x))/(e*x^2+d)^(1/2),x)","F"
173,0,0,25,0.516000," ","int((f*x)^m*(a+b*arccsch(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((f*x)^m*(a+b*arccsch(c*x))/(e*x^2+d)^(3/2),x)","F"
174,0,0,335,0.547000," ","int(x^11*(a+b*arccsch(c*x))/(-c^4*x^4+1)^(1/2),x)","\int \frac{x^{11} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int(x^11*(a+b*arccsch(c*x))/(-c^4*x^4+1)^(1/2),x)","F"
175,0,0,224,0.477000," ","int(x^7*(a+b*arccsch(c*x))/(-c^4*x^4+1)^(1/2),x)","\int \frac{x^{7} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int(x^7*(a+b*arccsch(c*x))/(-c^4*x^4+1)^(1/2),x)","F"
176,0,0,110,0.464000," ","int(x^3*(a+b*arccsch(c*x))/(-c^4*x^4+1)^(1/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arccsch}\left(c x \right)\right)}{\sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int(x^3*(a+b*arccsch(c*x))/(-c^4*x^4+1)^(1/2),x)","F"
177,0,0,26,0.446000," ","int((a+b*arccsch(c*x))/x/(-c^4*x^4+1)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x \sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x/(-c^4*x^4+1)^(1/2),x)","F"
178,0,0,26,0.456000," ","int((a+b*arccsch(c*x))/x^5/(-c^4*x^4+1)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsch}\left(c x \right)}{x^{5} \sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int((a+b*arccsch(c*x))/x^5/(-c^4*x^4+1)^(1/2),x)","F"