1,1,78,16,0.086000," ","int(sinh(x)^4/(a-a*cosh(x)^2),x)","-\frac{1}{2 a \left(\tanh \left(\frac{x}{2}\right)-1\right)^{2}}-\frac{1}{2 a \left(\tanh \left(\frac{x}{2}\right)-1\right)}-\frac{\ln \left(\tanh \left(\frac{x}{2}\right)-1\right)}{2 a}+\frac{1}{2 a \left(\tanh \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{1}{2 a \left(\tanh \left(\frac{x}{2}\right)+1\right)}+\frac{\ln \left(\tanh \left(\frac{x}{2}\right)+1\right)}{2 a}"," ",0,"-1/2/a/(tanh(1/2*x)-1)^2-1/2/a/(tanh(1/2*x)-1)-1/2/a*ln(tanh(1/2*x)-1)+1/2/a/(tanh(1/2*x)+1)^2-1/2/a/(tanh(1/2*x)+1)+1/2/a*ln(tanh(1/2*x)+1)","B"
2,1,8,7,0.061000," ","int(sinh(x)^3/(a-a*cosh(x)^2),x)","-\frac{\cosh \left(x \right)}{a}"," ",0,"-cosh(x)/a","A"
3,1,11,6,0.077000," ","int(sinh(x)^2/(a-a*cosh(x)^2),x)","-\frac{2 \arctanh \left(\tanh \left(\frac{x}{2}\right)\right)}{a}"," ",0,"-2/a*arctanh(tanh(1/2*x))","C"
4,1,37,17,0.107000," ","int(csch(x)^2/(a-a*cosh(x)^2),x)","\frac{\frac{\left(\tanh^{3}\left(\frac{x}{2}\right)\right)}{3}-3 \tanh \left(\frac{x}{2}\right)+\frac{1}{3 \tanh \left(\frac{x}{2}\right)^{3}}-\frac{3}{\tanh \left(\frac{x}{2}\right)}}{8 a}"," ",0,"1/8/a*(1/3*tanh(1/2*x)^3-3*tanh(1/2*x)+1/3/tanh(1/2*x)^3-3/tanh(1/2*x))","B"
5,1,53,25,0.107000," ","int(csch(x)^4/(a-a*cosh(x)^2),x)","\frac{\frac{\left(\tanh^{5}\left(\frac{x}{2}\right)\right)}{5}-\frac{5 \left(\tanh^{3}\left(\frac{x}{2}\right)\right)}{3}+10 \tanh \left(\frac{x}{2}\right)-\frac{5}{3 \tanh \left(\frac{x}{2}\right)^{3}}+\frac{10}{\tanh \left(\frac{x}{2}\right)}+\frac{1}{5 \tanh \left(\frac{x}{2}\right)^{5}}}{32 a}"," ",0,"1/32/a*(1/5*tanh(1/2*x)^5-5/3*tanh(1/2*x)^3+10*tanh(1/2*x)-5/3/tanh(1/2*x)^3+10/tanh(1/2*x)+1/5/tanh(1/2*x)^5)","B"
6,1,395,66,0.089000," ","int(sinh(x)^7/(a+b*cosh(x)^2),x)","-\frac{1}{5 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{5}}-\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{4}}+\frac{a}{2 b^{2} \left(\tanh \left(\frac{x}{2}\right)-1\right)^{2}}+\frac{7}{8 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{2}}+\frac{a}{3 b^{2} \left(\tanh \left(\frac{x}{2}\right)-1\right)^{3}}+\frac{1}{4 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{3}}-\frac{a^{2}}{b^{3} \left(\tanh \left(\frac{x}{2}\right)-1\right)}-\frac{5 a}{2 b^{2} \left(\tanh \left(\frac{x}{2}\right)-1\right)}-\frac{15}{8 b \left(\tanh \left(\frac{x}{2}\right)-1\right)}+\frac{1}{5 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{5}}-\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{4}}+\frac{a}{2 b^{2} \left(\tanh \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{7}{8 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{a}{3 b^{2} \left(\tanh \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{1}{4 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{3}}+\frac{a^{2}}{b^{3} \left(\tanh \left(\frac{x}{2}\right)+1\right)}+\frac{5 a}{2 b^{2} \left(\tanh \left(\frac{x}{2}\right)+1\right)}+\frac{15}{8 b \left(\tanh \left(\frac{x}{2}\right)+1\right)}-\frac{\arctan \left(\frac{2 \left(a +b \right) \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 a +2 b}{4 \sqrt{a b}}\right) a^{3}}{b^{3} \sqrt{a b}}-\frac{3 \arctan \left(\frac{2 \left(a +b \right) \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 a +2 b}{4 \sqrt{a b}}\right) a^{2}}{b^{2} \sqrt{a b}}-\frac{3 \arctan \left(\frac{2 \left(a +b \right) \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 a +2 b}{4 \sqrt{a b}}\right) a}{b \sqrt{a b}}-\frac{\arctan \left(\frac{2 \left(a +b \right) \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 a +2 b}{4 \sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"-1/5/b/(tanh(1/2*x)-1)^5-1/2/b/(tanh(1/2*x)-1)^4+1/2/b^2/(tanh(1/2*x)-1)^2*a+7/8/b/(tanh(1/2*x)-1)^2+1/3/b^2/(tanh(1/2*x)-1)^3*a+1/4/b/(tanh(1/2*x)-1)^3-1/b^3/(tanh(1/2*x)-1)*a^2-5/2/b^2/(tanh(1/2*x)-1)*a-15/8/b/(tanh(1/2*x)-1)+1/5/b/(tanh(1/2*x)+1)^5-1/2/b/(tanh(1/2*x)+1)^4+1/2/b^2/(tanh(1/2*x)+1)^2*a+7/8/b/(tanh(1/2*x)+1)^2-1/3/b^2/(tanh(1/2*x)+1)^3*a-1/4/b/(tanh(1/2*x)+1)^3+1/b^3/(tanh(1/2*x)+1)*a^2+5/2/b^2/(tanh(1/2*x)+1)*a+15/8/b/(tanh(1/2*x)+1)-1/b^3/(a*b)^(1/2)*arctan(1/4*(2*(a+b)*tanh(1/2*x)^2-2*a+2*b)/(a*b)^(1/2))*a^3-3/b^2/(a*b)^(1/2)*arctan(1/4*(2*(a+b)*tanh(1/2*x)^2-2*a+2*b)/(a*b)^(1/2))*a^2-3/b/(a*b)^(1/2)*arctan(1/4*(2*(a+b)*tanh(1/2*x)^2-2*a+2*b)/(a*b)^(1/2))*a-1/(a*b)^(1/2)*arctan(1/4*(2*(a+b)*tanh(1/2*x)^2-2*a+2*b)/(a*b)^(1/2))","B"
7,1,214,44,0.085000," ","int(sinh(x)^5/(a+b*cosh(x)^2),x)","-\frac{1}{3 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{3}}-\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{2}}+\frac{a}{b^{2} \left(\tanh \left(\frac{x}{2}\right)-1\right)}+\frac{3}{2 b \left(\tanh \left(\frac{x}{2}\right)-1\right)}+\frac{1}{3 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{a}{b^{2} \left(\tanh \left(\frac{x}{2}\right)+1\right)}-\frac{3}{2 b \left(\tanh \left(\frac{x}{2}\right)+1\right)}+\frac{\arctan \left(\frac{2 \left(a +b \right) \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 a +2 b}{4 \sqrt{a b}}\right) a^{2}}{b^{2} \sqrt{a b}}+\frac{2 \arctan \left(\frac{2 \left(a +b \right) \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 a +2 b}{4 \sqrt{a b}}\right) a}{b \sqrt{a b}}+\frac{\arctan \left(\frac{2 \left(a +b \right) \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 a +2 b}{4 \sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"-1/3/b/(tanh(1/2*x)-1)^3-1/2/b/(tanh(1/2*x)-1)^2+1/b^2/(tanh(1/2*x)-1)*a+3/2/b/(tanh(1/2*x)-1)+1/3/b/(tanh(1/2*x)+1)^3-1/2/b/(tanh(1/2*x)+1)^2-1/b^2/(tanh(1/2*x)+1)*a-3/2/b/(tanh(1/2*x)+1)+1/b^2/(a*b)^(1/2)*arctan(1/4*(2*(a+b)*tanh(1/2*x)^2-2*a+2*b)/(a*b)^(1/2))*a^2+2/b/(a*b)^(1/2)*arctan(1/4*(2*(a+b)*tanh(1/2*x)^2-2*a+2*b)/(a*b)^(1/2))*a+1/(a*b)^(1/2)*arctan(1/4*(2*(a+b)*tanh(1/2*x)^2-2*a+2*b)/(a*b)^(1/2))","B"
8,1,97,28,0.085000," ","int(sinh(x)^3/(a+b*cosh(x)^2),x)","\frac{1}{b \left(\tanh \left(\frac{x}{2}\right)+1\right)}-\frac{\arctan \left(\frac{2 \left(a +b \right) \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 a +2 b}{4 \sqrt{a b}}\right) a}{b \sqrt{a b}}-\frac{\arctan \left(\frac{2 \left(a +b \right) \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 a +2 b}{4 \sqrt{a b}}\right)}{\sqrt{a b}}-\frac{1}{b \left(\tanh \left(\frac{x}{2}\right)-1\right)}"," ",0,"1/b/(tanh(1/2*x)+1)-1/b/(a*b)^(1/2)*arctan(1/4*(2*(a+b)*tanh(1/2*x)^2-2*a+2*b)/(a*b)^(1/2))*a-1/(a*b)^(1/2)*arctan(1/4*(2*(a+b)*tanh(1/2*x)^2-2*a+2*b)/(a*b)^(1/2))-1/b/(tanh(1/2*x)-1)","B"
9,1,17,17,0.053000," ","int(sinh(x)/(a+b*cosh(x)^2),x)","\frac{\arctan \left(\frac{\cosh \left(x \right) b}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"1/(a*b)^(1/2)*arctan(cosh(x)*b/(a*b)^(1/2))","A"
10,1,52,34,0.096000," ","int(csch(x)/(a+b*cosh(x)^2),x)","-\frac{b \arctan \left(\frac{2 \left(a +b \right) \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 a +2 b}{4 \sqrt{a b}}\right)}{\left(a +b \right) \sqrt{a b}}+\frac{\ln \left(\tanh \left(\frac{x}{2}\right)\right)}{a +b}"," ",0,"-b/(a+b)/(a*b)^(1/2)*arctan(1/4*(2*(a+b)*tanh(1/2*x)^2-2*a+2*b)/(a*b)^(1/2))+1/(a+b)*ln(tanh(1/2*x))","A"
11,1,94,49,0.110000," ","int(csch(x)^3/(a+b*cosh(x)^2),x)","\frac{\tanh^{2}\left(\frac{x}{2}\right)}{8 a +8 b}+\frac{b^{2} \arctan \left(\frac{2 \left(a +b \right) \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 a +2 b}{4 \sqrt{a b}}\right)}{\left(a +b \right)^{2} \sqrt{a b}}-\frac{1}{8 \left(a +b \right) \tanh \left(\frac{x}{2}\right)^{2}}-\frac{\ln \left(\tanh \left(\frac{x}{2}\right)\right) a}{2 \left(a +b \right)^{2}}-\frac{3 \ln \left(\tanh \left(\frac{x}{2}\right)\right) b}{2 \left(a +b \right)^{2}}"," ",0,"1/8*tanh(1/2*x)^2/(a+b)+b^2/(a+b)^2/(a*b)^(1/2)*arctan(1/4*(2*(a+b)*tanh(1/2*x)^2-2*a+2*b)/(a*b)^(1/2))-1/8/(a+b)/tanh(1/2*x)^2-1/2/(a+b)^2*ln(tanh(1/2*x))*a-3/2/(a+b)^2*ln(tanh(1/2*x))*b","A"
12,1,184,80,0.118000," ","int(csch(x)^5/(a+b*cosh(x)^2),x)","\frac{\left(\tanh^{4}\left(\frac{x}{2}\right)\right) a}{64 \left(a +b \right)^{2}}+\frac{\left(\tanh^{4}\left(\frac{x}{2}\right)\right) b}{64 \left(a +b \right)^{2}}-\frac{\left(\tanh^{2}\left(\frac{x}{2}\right)\right) a}{8 \left(a +b \right)^{2}}-\frac{\left(\tanh^{2}\left(\frac{x}{2}\right)\right) b}{4 \left(a +b \right)^{2}}-\frac{b^{3} \arctan \left(\frac{2 \left(a +b \right) \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 a +2 b}{4 \sqrt{a b}}\right)}{\left(a +b \right)^{3} \sqrt{a b}}-\frac{1}{64 \left(a +b \right) \tanh \left(\frac{x}{2}\right)^{4}}+\frac{a}{8 \left(a +b \right)^{2} \tanh \left(\frac{x}{2}\right)^{2}}+\frac{b}{4 \left(a +b \right)^{2} \tanh \left(\frac{x}{2}\right)^{2}}+\frac{3 \ln \left(\tanh \left(\frac{x}{2}\right)\right) a^{2}}{8 \left(a +b \right)^{3}}+\frac{5 \ln \left(\tanh \left(\frac{x}{2}\right)\right) a b}{4 \left(a +b \right)^{3}}+\frac{15 \ln \left(\tanh \left(\frac{x}{2}\right)\right) b^{2}}{8 \left(a +b \right)^{3}}"," ",0,"1/64/(a+b)^2*tanh(1/2*x)^4*a+1/64/(a+b)^2*tanh(1/2*x)^4*b-1/8/(a+b)^2*tanh(1/2*x)^2*a-1/4/(a+b)^2*tanh(1/2*x)^2*b-b^3/(a+b)^3/(a*b)^(1/2)*arctan(1/4*(2*(a+b)*tanh(1/2*x)^2-2*a+2*b)/(a*b)^(1/2))-1/64/(a+b)/tanh(1/2*x)^4+1/8/(a+b)^2/tanh(1/2*x)^2*a+1/4/(a+b)^2/tanh(1/2*x)^2*b+3/8/(a+b)^3*ln(tanh(1/2*x))*a^2+5/4/(a+b)^3*ln(tanh(1/2*x))*a*b+15/8/(a+b)^3*ln(tanh(1/2*x))*b^2","B"
13,1,575,74,0.132000," ","int(sinh(x)^6/(a+b*cosh(x)^2),x)","\frac{1}{4 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{4}}-\frac{1}{4 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{4}}-\frac{a^{\frac{5}{2}} \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 b^{3} \sqrt{a +b}}+\frac{a^{\frac{5}{2}} \ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right)}{2 b^{3} \sqrt{a +b}}+\frac{3 a^{\frac{3}{2}} \ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right)}{2 b^{2} \sqrt{a +b}}-\frac{3 a^{\frac{3}{2}} \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 b^{2} \sqrt{a +b}}-\frac{3 \sqrt{a}\, \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 b \sqrt{a +b}}+\frac{3 \sqrt{a}\, \ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right)}{2 b \sqrt{a +b}}+\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{3}}-\frac{5}{8 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{2}}-\frac{7}{8 b \left(\tanh \left(\frac{x}{2}\right)-1\right)}+\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{3}}+\frac{5}{8 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{7}{8 b \left(\tanh \left(\frac{x}{2}\right)+1\right)}-\frac{15 \ln \left(\tanh \left(\frac{x}{2}\right)-1\right)}{8 b}+\frac{15 \ln \left(\tanh \left(\frac{x}{2}\right)+1\right)}{8 b}-\frac{\ln \left(\tanh \left(\frac{x}{2}\right)-1\right) a^{2}}{b^{3}}+\frac{\ln \left(\tanh \left(\frac{x}{2}\right)+1\right) a^{2}}{b^{3}}+\frac{\ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right)}{2 \sqrt{a}\, \sqrt{a +b}}-\frac{\ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 \sqrt{a}\, \sqrt{a +b}}-\frac{a}{2 b^{2} \left(\tanh \left(\frac{x}{2}\right)+1\right)}+\frac{5 a \ln \left(\tanh \left(\frac{x}{2}\right)+1\right)}{2 b^{2}}-\frac{a}{2 b^{2} \left(\tanh \left(\frac{x}{2}\right)-1\right)^{2}}-\frac{a}{2 b^{2} \left(\tanh \left(\frac{x}{2}\right)-1\right)}-\frac{5 a \ln \left(\tanh \left(\frac{x}{2}\right)-1\right)}{2 b^{2}}+\frac{a}{2 b^{2} \left(\tanh \left(\frac{x}{2}\right)+1\right)^{2}}"," ",0,"1/4/b/(tanh(1/2*x)-1)^4-1/4/b/(tanh(1/2*x)+1)^4+3/2/b^2*a^(3/2)/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))-3/2/b^2*a^(3/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))-3/2/b*a^(1/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))+3/2/b*a^(1/2)/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))-1/2/b^3*a^(5/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))+1/2/b^3*a^(5/2)/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))+1/2/b/(tanh(1/2*x)-1)^3-5/8/b/(tanh(1/2*x)-1)^2-7/8/b/(tanh(1/2*x)-1)+1/2/b/(tanh(1/2*x)+1)^3+5/8/b/(tanh(1/2*x)+1)^2-7/8/b/(tanh(1/2*x)+1)-15/8/b*ln(tanh(1/2*x)-1)+15/8/b*ln(tanh(1/2*x)+1)-1/b^3*ln(tanh(1/2*x)-1)*a^2+1/b^3*ln(tanh(1/2*x)+1)*a^2+1/2/a^(1/2)/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))-1/2/a^(1/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))-1/2/b^2/(tanh(1/2*x)+1)*a+5/2*a/b^2*ln(tanh(1/2*x)+1)-1/2/b^2/(tanh(1/2*x)-1)^2*a-1/2/b^2/(tanh(1/2*x)-1)*a-5/2*a/b^2*ln(tanh(1/2*x)-1)+1/2/b^2/(tanh(1/2*x)+1)^2*a","B"
14,1,351,47,0.114000," ","int(sinh(x)^4/(a+b*cosh(x)^2),x)","\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{2}}+\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)-1\right)}+\frac{a \ln \left(\tanh \left(\frac{x}{2}\right)-1\right)}{b^{2}}+\frac{3 \ln \left(\tanh \left(\frac{x}{2}\right)-1\right)}{2 b}-\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)+1\right)}-\frac{a \ln \left(\tanh \left(\frac{x}{2}\right)+1\right)}{b^{2}}-\frac{3 \ln \left(\tanh \left(\frac{x}{2}\right)+1\right)}{2 b}-\frac{a^{\frac{3}{2}} \ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right)}{2 b^{2} \sqrt{a +b}}-\frac{\sqrt{a}\, \ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right)}{b \sqrt{a +b}}-\frac{\ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right)}{2 \sqrt{a}\, \sqrt{a +b}}+\frac{a^{\frac{3}{2}} \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 b^{2} \sqrt{a +b}}+\frac{\sqrt{a}\, \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{b \sqrt{a +b}}+\frac{\ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 \sqrt{a}\, \sqrt{a +b}}"," ",0,"1/2/b/(tanh(1/2*x)-1)^2+1/2/b/(tanh(1/2*x)-1)+a/b^2*ln(tanh(1/2*x)-1)+3/2/b*ln(tanh(1/2*x)-1)-1/2/b/(tanh(1/2*x)+1)^2+1/2/b/(tanh(1/2*x)+1)-a/b^2*ln(tanh(1/2*x)+1)-3/2/b*ln(tanh(1/2*x)+1)-1/2/b^2*a^(3/2)/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))-1/b*a^(1/2)/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))-1/2/a^(1/2)/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))+1/2/b^2*a^(3/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))+1/b*a^(1/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))+1/2/a^(1/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))","B"
15,1,183,31,0.104000," ","int(sinh(x)^2/(a+b*cosh(x)^2),x)","-\frac{\ln \left(\tanh \left(\frac{x}{2}\right)-1\right)}{b}+\frac{\ln \left(\tanh \left(\frac{x}{2}\right)+1\right)}{b}+\frac{\sqrt{a}\, \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 b \sqrt{a +b}}-\frac{\sqrt{a}\, \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 b \sqrt{a +b}}+\frac{\ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 \sqrt{a}\, \sqrt{a +b}}-\frac{\ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 \sqrt{a}\, \sqrt{a +b}}"," ",0,"-1/b*ln(tanh(1/2*x)-1)+1/b*ln(tanh(1/2*x)+1)+1/2/b*a^(1/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2-2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))-1/2/b*a^(1/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))+1/2/a^(1/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2-2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))-1/2/a^(1/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))","B"
16,1,78,21,0.093000," ","int(1/(a+b*cosh(x)^2),x)","-\frac{\ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 \sqrt{a}\, \sqrt{a +b}}+\frac{\ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 \sqrt{a}\, \sqrt{a +b}}"," ",0,"-1/2/a^(1/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2-2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))+1/2/a^(1/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))","B"
17,1,177,49,0.143000," ","int(csch(x)^4/(a+b*cosh(x)^2),x)","-\frac{a \left(\tanh^{3}\left(\frac{x}{2}\right)\right)}{24 \left(a +b \right)^{2}}-\frac{\left(\tanh^{3}\left(\frac{x}{2}\right)\right) b}{24 \left(a +b \right)^{2}}+\frac{3 a \tanh \left(\frac{x}{2}\right)}{8 \left(a +b \right)^{2}}+\frac{7 \tanh \left(\frac{x}{2}\right) b}{8 \left(a +b \right)^{2}}-\frac{b^{2} \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 \left(a +b \right)^{\frac{5}{2}} \sqrt{a}}+\frac{b^{2} \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 \left(a +b \right)^{\frac{5}{2}} \sqrt{a}}-\frac{1}{24 \left(a +b \right) \tanh \left(\frac{x}{2}\right)^{3}}+\frac{3 a}{8 \left(a +b \right)^{2} \tanh \left(\frac{x}{2}\right)}+\frac{7 b}{8 \left(a +b \right)^{2} \tanh \left(\frac{x}{2}\right)}"," ",0,"-1/24/(a+b)^2*a*tanh(1/2*x)^3-1/24/(a+b)^2*tanh(1/2*x)^3*b+3/8/(a+b)^2*a*tanh(1/2*x)+7/8/(a+b)^2*tanh(1/2*x)*b-1/2*b^2/(a+b)^(5/2)/a^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2-2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))+1/2*b^2/(a+b)^(5/2)/a^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))-1/24/(a+b)/tanh(1/2*x)^3+3/8/(a+b)^2/tanh(1/2*x)*a+7/8/(a+b)^2/tanh(1/2*x)*b","B"
18,1,307,77,0.148000," ","int(csch(x)^6/(a+b*cosh(x)^2),x)","-\frac{a^{2} \left(\tanh^{5}\left(\frac{x}{2}\right)\right)}{160 \left(a +b \right)^{3}}-\frac{\left(\tanh^{5}\left(\frac{x}{2}\right)\right) a b}{80 \left(a +b \right)^{3}}-\frac{b^{2} \left(\tanh^{5}\left(\frac{x}{2}\right)\right)}{160 \left(a +b \right)^{3}}+\frac{5 a^{2} \left(\tanh^{3}\left(\frac{x}{2}\right)\right)}{96 \left(a +b \right)^{3}}+\frac{7 a \left(\tanh^{3}\left(\frac{x}{2}\right)\right) b}{48 \left(a +b \right)^{3}}+\frac{3 b^{2} \left(\tanh^{3}\left(\frac{x}{2}\right)\right)}{32 \left(a +b \right)^{3}}-\frac{5 a^{2} \tanh \left(\frac{x}{2}\right)}{16 \left(a +b \right)^{3}}-\frac{a b \tanh \left(\frac{x}{2}\right)}{\left(a +b \right)^{3}}-\frac{19 b^{2} \tanh \left(\frac{x}{2}\right)}{16 \left(a +b \right)^{3}}+\frac{b^{3} \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 \left(a +b \right)^{\frac{7}{2}} \sqrt{a}}-\frac{b^{3} \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 \left(a +b \right)^{\frac{7}{2}} \sqrt{a}}-\frac{1}{160 \left(a +b \right) \tanh \left(\frac{x}{2}\right)^{5}}+\frac{5 a}{96 \left(a +b \right)^{2} \tanh \left(\frac{x}{2}\right)^{3}}+\frac{3 b}{32 \left(a +b \right)^{2} \tanh \left(\frac{x}{2}\right)^{3}}-\frac{5 a^{2}}{16 \left(a +b \right)^{3} \tanh \left(\frac{x}{2}\right)}-\frac{a b}{\left(a +b \right)^{3} \tanh \left(\frac{x}{2}\right)}-\frac{19 b^{2}}{16 \left(a +b \right)^{3} \tanh \left(\frac{x}{2}\right)}"," ",0,"-1/160/(a+b)^3*a^2*tanh(1/2*x)^5-1/80/(a+b)^3*tanh(1/2*x)^5*a*b-1/160/(a+b)^3*b^2*tanh(1/2*x)^5+5/96/(a+b)^3*a^2*tanh(1/2*x)^3+7/48/(a+b)^3*a*tanh(1/2*x)^3*b+3/32/(a+b)^3*b^2*tanh(1/2*x)^3-5/16/(a+b)^3*a^2*tanh(1/2*x)-1/(a+b)^3*a*b*tanh(1/2*x)-19/16/(a+b)^3*b^2*tanh(1/2*x)+1/2*b^3/(a+b)^(7/2)/a^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2-2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))-1/2*b^3/(a+b)^(7/2)/a^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))-1/160/(a+b)/tanh(1/2*x)^5+5/96/(a+b)^2/tanh(1/2*x)^3*a+3/32/(a+b)^2/tanh(1/2*x)^3*b-5/16/(a+b)^3/tanh(1/2*x)*a^2-1/(a+b)^3/tanh(1/2*x)*a*b-19/16/(a+b)^3/tanh(1/2*x)*b^2","B"
19,1,80,69,0.051000," ","int(sinh(x)/(4-3*cosh(x)^3),x)","-\frac{4^{\frac{1}{3}} 3^{\frac{2}{3}} \ln \left(\cosh \left(x \right)-\frac{4^{\frac{1}{3}} 3^{\frac{2}{3}}}{3}\right)}{36}+\frac{4^{\frac{1}{3}} 3^{\frac{2}{3}} \ln \left(\cosh^{2}\left(x \right)+\frac{4^{\frac{1}{3}} 3^{\frac{2}{3}} \cosh \left(x \right)}{3}+\frac{4^{\frac{2}{3}} 3^{\frac{1}{3}}}{3}\right)}{72}+\frac{4^{\frac{1}{3}} 3^{\frac{1}{6}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{4^{\frac{2}{3}} 3^{\frac{1}{3}} \cosh \left(x \right)}{2}+1\right)}{3}\right)}{12}"," ",0,"-1/36*4^(1/3)*3^(2/3)*ln(cosh(x)-1/3*4^(1/3)*3^(2/3))+1/72*4^(1/3)*3^(2/3)*ln(cosh(x)^2+1/3*4^(1/3)*3^(2/3)*cosh(x)+1/3*4^(2/3)*3^(1/3))+1/12*4^(1/3)*3^(1/6)*arctan(1/3*3^(1/2)*(1/2*4^(2/3)*3^(1/3)*cosh(x)+1))","A"
20,1,317,66,0.124000," ","int(cosh(x)^7/(a+b*cosh(x)^2),x)","-\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{4}}-\frac{1}{5 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{5}}+\frac{a}{2 b^{2} \left(\tanh \left(\frac{x}{2}\right)-1\right)^{2}}-\frac{7}{8 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{2}}-\frac{11}{12 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{3}}+\frac{a}{3 b^{2} \left(\tanh \left(\frac{x}{2}\right)-1\right)^{3}}-\frac{a^{2}}{b^{3} \left(\tanh \left(\frac{x}{2}\right)-1\right)}+\frac{a}{b^{2} \left(\tanh \left(\frac{x}{2}\right)-1\right)}-\frac{1}{b \left(\tanh \left(\frac{x}{2}\right)-1\right)}-\frac{1}{5 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{5}}+\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{4}}-\frac{a}{2 b^{2} \left(\tanh \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{7}{8 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{11}{12 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{3}}+\frac{a}{3 b^{2} \left(\tanh \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{a^{2}}{b^{3} \left(\tanh \left(\frac{x}{2}\right)+1\right)}+\frac{a}{b^{2} \left(\tanh \left(\frac{x}{2}\right)+1\right)}-\frac{1}{b \left(\tanh \left(\frac{x}{2}\right)+1\right)}+\frac{a^{3} \arctan \left(\frac{-2 \sqrt{a +b}\, \tanh \left(\frac{x}{2}\right)+2 \sqrt{a}}{2 \sqrt{b}}\right)}{b^{\frac{7}{2}} \sqrt{a +b}}-\frac{a^{3} \arctan \left(\frac{2 \sqrt{a +b}\, \tanh \left(\frac{x}{2}\right)+2 \sqrt{a}}{2 \sqrt{b}}\right)}{b^{\frac{7}{2}} \sqrt{a +b}}"," ",0,"-1/2/b/(tanh(1/2*x)-1)^4-1/5/b/(tanh(1/2*x)-1)^5+1/2/b^2/(tanh(1/2*x)-1)^2*a-7/8/b/(tanh(1/2*x)-1)^2-11/12/b/(tanh(1/2*x)-1)^3+1/3/b^2/(tanh(1/2*x)-1)^3*a-1/b^3/(tanh(1/2*x)-1)*a^2+1/b^2/(tanh(1/2*x)-1)*a-1/b/(tanh(1/2*x)-1)-1/5/b/(tanh(1/2*x)+1)^5+1/2/b/(tanh(1/2*x)+1)^4-1/2/b^2/(tanh(1/2*x)+1)^2*a+7/8/b/(tanh(1/2*x)+1)^2-11/12/b/(tanh(1/2*x)+1)^3+1/3/b^2/(tanh(1/2*x)+1)^3*a-1/b^3/(tanh(1/2*x)+1)*a^2+1/b^2/(tanh(1/2*x)+1)*a-1/b/(tanh(1/2*x)+1)+a^3/b^(7/2)/(a+b)^(1/2)*arctan(1/2*(-2*(a+b)^(1/2)*tanh(1/2*x)+2*a^(1/2))/b^(1/2))-a^3/b^(7/2)/(a+b)^(1/2)*arctan(1/2*(2*(a+b)^(1/2)*tanh(1/2*x)+2*a^(1/2))/b^(1/2))","B"
21,1,326,74,0.109000," ","int(cosh(x)^6/(a+b*cosh(x)^2),x)","\frac{1}{4 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{4}}+\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{3}}-\frac{a}{2 b^{2} \left(\tanh \left(\frac{x}{2}\right)-1\right)^{2}}+\frac{7}{8 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{2}}-\frac{a}{2 b^{2} \left(\tanh \left(\frac{x}{2}\right)-1\right)}+\frac{5}{8 b \left(\tanh \left(\frac{x}{2}\right)-1\right)}-\frac{\ln \left(\tanh \left(\frac{x}{2}\right)-1\right) a^{2}}{b^{3}}+\frac{a \ln \left(\tanh \left(\frac{x}{2}\right)-1\right)}{2 b^{2}}-\frac{3 \ln \left(\tanh \left(\frac{x}{2}\right)-1\right)}{8 b}-\frac{1}{4 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{4}}+\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{3}}+\frac{a}{2 b^{2} \left(\tanh \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{7}{8 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{a}{2 b^{2} \left(\tanh \left(\frac{x}{2}\right)+1\right)}+\frac{5}{8 b \left(\tanh \left(\frac{x}{2}\right)+1\right)}+\frac{\ln \left(\tanh \left(\frac{x}{2}\right)+1\right) a^{2}}{b^{3}}-\frac{a \ln \left(\tanh \left(\frac{x}{2}\right)+1\right)}{2 b^{2}}+\frac{3 \ln \left(\tanh \left(\frac{x}{2}\right)+1\right)}{8 b}+\frac{a^{\frac{5}{2}} \ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right)}{2 b^{3} \sqrt{a +b}}-\frac{a^{\frac{5}{2}} \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 b^{3} \sqrt{a +b}}"," ",0,"1/4/b/(tanh(1/2*x)-1)^4+1/2/b/(tanh(1/2*x)-1)^3-1/2/b^2/(tanh(1/2*x)-1)^2*a+7/8/b/(tanh(1/2*x)-1)^2-1/2/b^2/(tanh(1/2*x)-1)*a+5/8/b/(tanh(1/2*x)-1)-1/b^3*ln(tanh(1/2*x)-1)*a^2+1/2*a/b^2*ln(tanh(1/2*x)-1)-3/8/b*ln(tanh(1/2*x)-1)-1/4/b/(tanh(1/2*x)+1)^4+1/2/b/(tanh(1/2*x)+1)^3+1/2/b^2/(tanh(1/2*x)+1)^2*a-7/8/b/(tanh(1/2*x)+1)^2-1/2/b^2/(tanh(1/2*x)+1)*a+5/8/b/(tanh(1/2*x)+1)+1/b^3*ln(tanh(1/2*x)+1)*a^2-1/2*a/b^2*ln(tanh(1/2*x)+1)+3/8/b*ln(tanh(1/2*x)+1)+1/2/b^3*a^(5/2)/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))-1/2/b^3*a^(5/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))","B"
22,1,176,46,0.101000," ","int(cosh(x)^5/(a+b*cosh(x)^2),x)","-\frac{1}{3 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{3}}-\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{2}}+\frac{a}{b^{2} \left(\tanh \left(\frac{x}{2}\right)-1\right)}-\frac{1}{b \left(\tanh \left(\frac{x}{2}\right)-1\right)}-\frac{1}{3 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{3}}+\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{a}{b^{2} \left(\tanh \left(\frac{x}{2}\right)+1\right)}-\frac{1}{b \left(\tanh \left(\frac{x}{2}\right)+1\right)}+\frac{a^{2} \arctan \left(\frac{2 \sqrt{a +b}\, \tanh \left(\frac{x}{2}\right)-2 \sqrt{a}}{2 \sqrt{b}}\right)}{b^{\frac{5}{2}} \sqrt{a +b}}+\frac{a^{2} \arctan \left(\frac{2 \sqrt{a +b}\, \tanh \left(\frac{x}{2}\right)+2 \sqrt{a}}{2 \sqrt{b}}\right)}{b^{\frac{5}{2}} \sqrt{a +b}}"," ",0,"-1/3/b/(tanh(1/2*x)-1)^3-1/2/b/(tanh(1/2*x)-1)^2+1/b^2/(tanh(1/2*x)-1)*a-1/b/(tanh(1/2*x)-1)-1/3/b/(tanh(1/2*x)+1)^3+1/2/b/(tanh(1/2*x)+1)^2+1/b^2/(tanh(1/2*x)+1)*a-1/b/(tanh(1/2*x)+1)+a^2/b^(5/2)/(a+b)^(1/2)*arctan(1/2*(2*(a+b)^(1/2)*tanh(1/2*x)-2*a^(1/2))/b^(1/2))+a^2/b^(5/2)/(a+b)^(1/2)*arctan(1/2*(2*(a+b)^(1/2)*tanh(1/2*x)+2*a^(1/2))/b^(1/2))","B"
23,1,188,47,0.098000," ","int(cosh(x)^4/(a+b*cosh(x)^2),x)","\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)-1\right)^{2}}+\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)-1\right)}+\frac{a \ln \left(\tanh \left(\frac{x}{2}\right)-1\right)}{b^{2}}-\frac{\ln \left(\tanh \left(\frac{x}{2}\right)-1\right)}{2 b}-\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{1}{2 b \left(\tanh \left(\frac{x}{2}\right)+1\right)}-\frac{a \ln \left(\tanh \left(\frac{x}{2}\right)+1\right)}{b^{2}}+\frac{\ln \left(\tanh \left(\frac{x}{2}\right)+1\right)}{2 b}-\frac{a^{\frac{3}{2}} \ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right)}{2 b^{2} \sqrt{a +b}}+\frac{a^{\frac{3}{2}} \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 b^{2} \sqrt{a +b}}"," ",0,"1/2/b/(tanh(1/2*x)-1)^2+1/2/b/(tanh(1/2*x)-1)+a/b^2*ln(tanh(1/2*x)-1)-1/2/b*ln(tanh(1/2*x)-1)-1/2/b/(tanh(1/2*x)+1)^2+1/2/b/(tanh(1/2*x)+1)-a/b^2*ln(tanh(1/2*x)+1)+1/2/b*ln(tanh(1/2*x)+1)-1/2/b^2*a^(3/2)/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))+1/2/b^2*a^(3/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))","B"
24,1,96,30,0.091000," ","int(cosh(x)^3/(a+b*cosh(x)^2),x)","-\frac{1}{b \left(\tanh \left(\frac{x}{2}\right)+1\right)}-\frac{a \arctan \left(\frac{2 \sqrt{a +b}\, \tanh \left(\frac{x}{2}\right)-2 \sqrt{a}}{2 \sqrt{b}}\right)}{b^{\frac{3}{2}} \sqrt{a +b}}-\frac{a \arctan \left(\frac{2 \sqrt{a +b}\, \tanh \left(\frac{x}{2}\right)+2 \sqrt{a}}{2 \sqrt{b}}\right)}{b^{\frac{3}{2}} \sqrt{a +b}}-\frac{1}{b \left(\tanh \left(\frac{x}{2}\right)-1\right)}"," ",0,"-1/b/(tanh(1/2*x)+1)-a/b^(3/2)/(a+b)^(1/2)*arctan(1/2*(2*(a+b)^(1/2)*tanh(1/2*x)-2*a^(1/2))/b^(1/2))-a/b^(3/2)/(a+b)^(1/2)*arctan(1/2*(2*(a+b)^(1/2)*tanh(1/2*x)+2*a^(1/2))/b^(1/2))-1/b/(tanh(1/2*x)-1)","B"
25,1,110,31,0.096000," ","int(cosh(x)^2/(a+b*cosh(x)^2),x)","-\frac{\ln \left(\tanh \left(\frac{x}{2}\right)-1\right)}{b}+\frac{\ln \left(\tanh \left(\frac{x}{2}\right)+1\right)}{b}+\frac{\sqrt{a}\, \ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right)}{2 b \sqrt{a +b}}-\frac{\sqrt{a}\, \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 b \sqrt{a +b}}"," ",0,"-1/b*ln(tanh(1/2*x)-1)+1/b*ln(tanh(1/2*x)+1)+1/2/b*a^(1/2)/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))-1/2/b*a^(1/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))","B"
26,1,66,21,0.073000," ","int(cosh(x)/(a+b*cosh(x)^2),x)","\frac{\arctan \left(\frac{2 \sqrt{a +b}\, \tanh \left(\frac{x}{2}\right)-2 \sqrt{a}}{2 \sqrt{b}}\right)}{\sqrt{a +b}\, \sqrt{b}}+\frac{\arctan \left(\frac{2 \sqrt{a +b}\, \tanh \left(\frac{x}{2}\right)+2 \sqrt{a}}{2 \sqrt{b}}\right)}{\sqrt{a +b}\, \sqrt{b}}"," ",0,"1/(a+b)^(1/2)/b^(1/2)*arctan(1/2*(2*(a+b)^(1/2)*tanh(1/2*x)-2*a^(1/2))/b^(1/2))+1/(a+b)^(1/2)/b^(1/2)*arctan(1/2*(2*(a+b)^(1/2)*tanh(1/2*x)+2*a^(1/2))/b^(1/2))","B"
27,1,78,21,0.082000," ","int(1/(a+b*cosh(x)^2),x)","-\frac{\ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 \sqrt{a}\, \sqrt{a +b}}+\frac{\ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 \sqrt{a}\, \sqrt{a +b}}"," ",0,"-1/2/a^(1/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2-2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))+1/2/a^(1/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))","B"
28,1,84,33,0.127000," ","int(sech(x)/(a+b*cosh(x)^2),x)","-\frac{\sqrt{b}\, \arctan \left(\frac{2 \sqrt{a +b}\, \tanh \left(\frac{x}{2}\right)-2 \sqrt{a}}{2 \sqrt{b}}\right)}{a \sqrt{a +b}}-\frac{\sqrt{b}\, \arctan \left(\frac{2 \sqrt{a +b}\, \tanh \left(\frac{x}{2}\right)+2 \sqrt{a}}{2 \sqrt{b}}\right)}{a \sqrt{a +b}}+\frac{2 \arctan \left(\tanh \left(\frac{x}{2}\right)\right)}{a}"," ",0,"-1/a*b^(1/2)/(a+b)^(1/2)*arctan(1/2*(2*(a+b)^(1/2)*tanh(1/2*x)-2*a^(1/2))/b^(1/2))-1/a*b^(1/2)/(a+b)^(1/2)*arctan(1/2*(2*(a+b)^(1/2)*tanh(1/2*x)+2*a^(1/2))/b^(1/2))+2/a*arctan(tanh(1/2*x))","B"
29,1,102,30,0.142000," ","int(sech(x)^2/(a+b*cosh(x)^2),x)","\frac{b \ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right)}{2 a^{\frac{3}{2}} \sqrt{a +b}}-\frac{b \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 a^{\frac{3}{2}} \sqrt{a +b}}+\frac{2 \tanh \left(\frac{x}{2}\right)}{a \left(\tanh^{2}\left(\frac{x}{2}\right)+1\right)}"," ",0,"1/2/a^(3/2)*b/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))-1/2/a^(3/2)*b/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))+2/a*tanh(1/2*x)/(tanh(1/2*x)^2+1)","B"
30,1,131,47,0.144000," ","int(sech(x)^3/(a+b*cosh(x)^2),x)","\frac{b^{\frac{3}{2}} \arctan \left(\frac{2 \sqrt{a +b}\, \tanh \left(\frac{x}{2}\right)-2 \sqrt{a}}{2 \sqrt{b}}\right)}{a^{2} \sqrt{a +b}}+\frac{b^{\frac{3}{2}} \arctan \left(\frac{2 \sqrt{a +b}\, \tanh \left(\frac{x}{2}\right)+2 \sqrt{a}}{2 \sqrt{b}}\right)}{a^{2} \sqrt{a +b}}-\frac{\tanh^{3}\left(\frac{x}{2}\right)}{a \left(\tanh^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{\tanh \left(\frac{x}{2}\right)}{a \left(\tanh^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{\arctan \left(\tanh \left(\frac{x}{2}\right)\right)}{a}-\frac{2 \arctan \left(\tanh \left(\frac{x}{2}\right)\right) b}{a^{2}}"," ",0,"b^(3/2)/a^2/(a+b)^(1/2)*arctan(1/2*(2*(a+b)^(1/2)*tanh(1/2*x)-2*a^(1/2))/b^(1/2))+b^(3/2)/a^2/(a+b)^(1/2)*arctan(1/2*(2*(a+b)^(1/2)*tanh(1/2*x)+2*a^(1/2))/b^(1/2))-1/a/(tanh(1/2*x)^2+1)^2*tanh(1/2*x)^3+1/a/(tanh(1/2*x)^2+1)^2*tanh(1/2*x)+1/a*arctan(tanh(1/2*x))-2/a^2*arctan(tanh(1/2*x))*b","B"
31,1,139,45,0.165000," ","int(sech(x)^4/(a+b*cosh(x)^2),x)","-\frac{b^{2} \ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right)}{2 a^{\frac{5}{2}} \sqrt{a +b}}+\frac{b^{2} \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 a^{\frac{5}{2}} \sqrt{a +b}}-\frac{2 \left(\left(-a +b \right) \left(\tanh^{5}\left(\frac{x}{2}\right)\right)+\left(-\frac{2 a}{3}+2 b \right) \left(\tanh^{3}\left(\frac{x}{2}\right)\right)+\left(-a +b \right) \tanh \left(\frac{x}{2}\right)\right)}{a^{2} \left(\tanh^{2}\left(\frac{x}{2}\right)+1\right)^{3}}"," ",0,"-1/2*b^2/a^(5/2)/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))+1/2*b^2/a^(5/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))-2/a^2*((-a+b)*tanh(1/2*x)^5+(-2/3*a+2*b)*tanh(1/2*x)^3+(-a+b)*tanh(1/2*x))/(tanh(1/2*x)^2+1)^3","B"
32,1,274,76,0.148000," ","int(sech(x)^5/(a+b*cosh(x)^2),x)","-\frac{b^{\frac{5}{2}} \arctan \left(\frac{2 \sqrt{a +b}\, \tanh \left(\frac{x}{2}\right)-2 \sqrt{a}}{2 \sqrt{b}}\right)}{a^{3} \sqrt{a +b}}-\frac{b^{\frac{5}{2}} \arctan \left(\frac{2 \sqrt{a +b}\, \tanh \left(\frac{x}{2}\right)+2 \sqrt{a}}{2 \sqrt{b}}\right)}{a^{3} \sqrt{a +b}}-\frac{5 \left(\tanh^{7}\left(\frac{x}{2}\right)\right)}{4 a \left(\tanh^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{\left(\tanh^{7}\left(\frac{x}{2}\right)\right) b}{a^{2} \left(\tanh^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{3 \left(\tanh^{5}\left(\frac{x}{2}\right)\right)}{4 a \left(\tanh^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{\left(\tanh^{5}\left(\frac{x}{2}\right)\right) b}{a^{2} \left(\tanh^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{3 \left(\tanh^{3}\left(\frac{x}{2}\right)\right)}{4 a \left(\tanh^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{\left(\tanh^{3}\left(\frac{x}{2}\right)\right) b}{a^{2} \left(\tanh^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{5 \tanh \left(\frac{x}{2}\right)}{4 a \left(\tanh^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{\tanh \left(\frac{x}{2}\right) b}{a^{2} \left(\tanh^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{3 \arctan \left(\tanh \left(\frac{x}{2}\right)\right)}{4 a}-\frac{\arctan \left(\tanh \left(\frac{x}{2}\right)\right) b}{a^{2}}+\frac{2 \arctan \left(\tanh \left(\frac{x}{2}\right)\right) b^{2}}{a^{3}}"," ",0,"-b^(5/2)/a^3/(a+b)^(1/2)*arctan(1/2*(2*(a+b)^(1/2)*tanh(1/2*x)-2*a^(1/2))/b^(1/2))-b^(5/2)/a^3/(a+b)^(1/2)*arctan(1/2*(2*(a+b)^(1/2)*tanh(1/2*x)+2*a^(1/2))/b^(1/2))-5/4/a/(tanh(1/2*x)^2+1)^4*tanh(1/2*x)^7+1/a^2/(tanh(1/2*x)^2+1)^4*tanh(1/2*x)^7*b+3/4/a/(tanh(1/2*x)^2+1)^4*tanh(1/2*x)^5+1/a^2/(tanh(1/2*x)^2+1)^4*tanh(1/2*x)^5*b-3/4/a/(tanh(1/2*x)^2+1)^4*tanh(1/2*x)^3-1/a^2/(tanh(1/2*x)^2+1)^4*tanh(1/2*x)^3*b+5/4/a/(tanh(1/2*x)^2+1)^4*tanh(1/2*x)-1/a^2/(tanh(1/2*x)^2+1)^4*tanh(1/2*x)*b+3/4/a*arctan(tanh(1/2*x))-1/a^2*arctan(tanh(1/2*x))*b+2/a^3*arctan(tanh(1/2*x))*b^2","B"
33,1,236,53,0.111000," ","int(1/(a+b*cosh(x)^2)^2,x)","-\frac{2 \left(\frac{b \left(\tanh^{3}\left(\frac{x}{2}\right)\right)}{2 a \left(a +b \right)}+\frac{b \tanh \left(\frac{x}{2}\right)}{2 a \left(a +b \right)}\right)}{\left(\tanh^{4}\left(\frac{x}{2}\right)\right) a +b \left(\tanh^{4}\left(\frac{x}{2}\right)\right)-2 a \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \left(\tanh^{2}\left(\frac{x}{2}\right)\right) b +a +b}-\frac{\ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right)}{2 \left(a +b \right)^{\frac{3}{2}} \sqrt{a}}+\frac{\ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 \left(a +b \right)^{\frac{3}{2}} \sqrt{a}}-\frac{b \ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right)}{4 a^{\frac{3}{2}} \left(a +b \right)^{\frac{3}{2}}}+\frac{b \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{4 a^{\frac{3}{2}} \left(a +b \right)^{\frac{3}{2}}}"," ",0,"-2*(1/2*b/a/(a+b)*tanh(1/2*x)^3+1/2*b/a/(a+b)*tanh(1/2*x))/(tanh(1/2*x)^4*a+b*tanh(1/2*x)^4-2*a*tanh(1/2*x)^2+2*tanh(1/2*x)^2*b+a+b)-1/2/(a+b)^(3/2)/a^(1/2)*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))+1/2/(a+b)^(3/2)/a^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))-1/4/a^(3/2)/(a+b)^(3/2)*b*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))+1/4/a^(3/2)/(a+b)^(3/2)*b*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))","B"
34,1,477,93,0.125000," ","int(1/(a+b*cosh(x)^2)^3,x)","-\frac{2 \left(\frac{b \left(8 a +3 b \right) \left(\tanh^{7}\left(\frac{x}{2}\right)\right)}{8 \left(a +b \right) a^{2}}-\frac{b \left(8 a^{2}-13 a b -9 b^{2}\right) \left(\tanh^{5}\left(\frac{x}{2}\right)\right)}{8 \left(a +b \right)^{2} a^{2}}-\frac{b \left(8 a^{2}-13 a b -9 b^{2}\right) \left(\tanh^{3}\left(\frac{x}{2}\right)\right)}{8 \left(a +b \right)^{2} a^{2}}+\frac{b \left(8 a +3 b \right) \tanh \left(\frac{x}{2}\right)}{8 \left(a +b \right) a^{2}}\right)}{\left(\left(\tanh^{4}\left(\frac{x}{2}\right)\right) a +b \left(\tanh^{4}\left(\frac{x}{2}\right)\right)-2 a \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \left(\tanh^{2}\left(\frac{x}{2}\right)\right) b +a +b \right)^{2}}-\frac{\ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right)}{2 \left(a^{2}+2 a b +b^{2}\right) \sqrt{a}\, \sqrt{a +b}}-\frac{\ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right) b}{2 a^{\frac{3}{2}} \left(a^{2}+2 a b +b^{2}\right) \sqrt{a +b}}-\frac{3 \ln \left(-\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)-\sqrt{a +b}\right) b^{2}}{16 a^{\frac{5}{2}} \left(a^{2}+2 a b +b^{2}\right) \sqrt{a +b}}+\frac{\ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right)}{2 \left(a^{2}+2 a b +b^{2}\right) \sqrt{a}\, \sqrt{a +b}}+\frac{\ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right) b}{2 a^{\frac{3}{2}} \left(a^{2}+2 a b +b^{2}\right) \sqrt{a +b}}+\frac{3 \ln \left(\sqrt{a +b}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{a}\, \tanh \left(\frac{x}{2}\right)+\sqrt{a +b}\right) b^{2}}{16 a^{\frac{5}{2}} \left(a^{2}+2 a b +b^{2}\right) \sqrt{a +b}}"," ",0,"-2*(1/8*b*(8*a+3*b)/(a+b)/a^2*tanh(1/2*x)^7-1/8*b*(8*a^2-13*a*b-9*b^2)/(a+b)^2/a^2*tanh(1/2*x)^5-1/8*b*(8*a^2-13*a*b-9*b^2)/(a+b)^2/a^2*tanh(1/2*x)^3+1/8*b*(8*a+3*b)/(a+b)/a^2*tanh(1/2*x))/(tanh(1/2*x)^4*a+b*tanh(1/2*x)^4-2*a*tanh(1/2*x)^2+2*tanh(1/2*x)^2*b+a+b)^2-1/2/(a^2+2*a*b+b^2)/a^(1/2)/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))-1/2/a^(3/2)/(a^2+2*a*b+b^2)/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))*b-3/16/a^(5/2)/(a^2+2*a*b+b^2)/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)-(a+b)^(1/2))*b^2+1/2/(a^2+2*a*b+b^2)/a^(1/2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))+1/2/a^(3/2)/(a^2+2*a*b+b^2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))*b+3/16/a^(5/2)/(a^2+2*a*b+b^2)/(a+b)^(1/2)*ln((a+b)^(1/2)*tanh(1/2*x)^2+2*a^(1/2)*tanh(1/2*x)+(a+b)^(1/2))*b^2","B"
35,1,86,13,0.054000," ","int(1/(1+cosh(x)^2),x)","\frac{\sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)+\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}{\tanh^{2}\left(\frac{x}{2}\right)-\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}\right)}{8}-\frac{\sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)-\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}{\tanh^{2}\left(\frac{x}{2}\right)+\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}\right)}{8}"," ",0,"1/8*2^(1/2)*ln((tanh(1/2*x)^2+2^(1/2)*tanh(1/2*x)+1)/(tanh(1/2*x)^2-2^(1/2)*tanh(1/2*x)+1))-1/8*2^(1/2)*ln((tanh(1/2*x)^2-2^(1/2)*tanh(1/2*x)+1)/(tanh(1/2*x)^2+2^(1/2)*tanh(1/2*x)+1))","B"
36,1,113,28,0.058000," ","int(1/(1+cosh(x)^2)^2,x)","-\frac{\frac{\left(\tanh^{3}\left(\frac{x}{2}\right)\right)}{2}+\frac{\tanh \left(\frac{x}{2}\right)}{2}}{2 \left(\tanh^{4}\left(\frac{x}{2}\right)+1\right)}+\frac{3 \sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)+\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}{\tanh^{2}\left(\frac{x}{2}\right)-\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}\right)}{32}-\frac{3 \sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)-\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}{\tanh^{2}\left(\frac{x}{2}\right)+\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}\right)}{32}"," ",0,"-1/2*(1/2*tanh(1/2*x)^3+1/2*tanh(1/2*x))/(tanh(1/2*x)^4+1)+3/32*2^(1/2)*ln((tanh(1/2*x)^2+2^(1/2)*tanh(1/2*x)+1)/(tanh(1/2*x)^2-2^(1/2)*tanh(1/2*x)+1))-3/32*2^(1/2)*ln((tanh(1/2*x)^2-2^(1/2)*tanh(1/2*x)+1)/(tanh(1/2*x)^2+2^(1/2)*tanh(1/2*x)+1))","B"
37,1,129,42,0.059000," ","int(1/(1+cosh(x)^2)^3,x)","-\frac{\frac{11 \left(\tanh^{7}\left(\frac{x}{2}\right)\right)}{8}+\frac{7 \left(\tanh^{5}\left(\frac{x}{2}\right)\right)}{8}+\frac{7 \left(\tanh^{3}\left(\frac{x}{2}\right)\right)}{8}+\frac{11 \tanh \left(\frac{x}{2}\right)}{8}}{4 \left(\tanh^{4}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{19 \sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)+\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}{\tanh^{2}\left(\frac{x}{2}\right)-\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}\right)}{256}-\frac{19 \sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)-\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}{\tanh^{2}\left(\frac{x}{2}\right)+\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}\right)}{256}"," ",0,"-1/4*(11/8*tanh(1/2*x)^7+7/8*tanh(1/2*x)^5+7/8*tanh(1/2*x)^3+11/8*tanh(1/2*x))/(tanh(1/2*x)^4+1)^2+19/256*2^(1/2)*ln((tanh(1/2*x)^2+2^(1/2)*tanh(1/2*x)+1)/(tanh(1/2*x)^2-2^(1/2)*tanh(1/2*x)+1))-19/256*2^(1/2)*ln((tanh(1/2*x)^2-2^(1/2)*tanh(1/2*x)+1)/(tanh(1/2*x)^2+2^(1/2)*tanh(1/2*x)+1))","B"
38,1,16,2,0.068000," ","int(1/(1-cosh(x)^2),x)","\frac{\tanh \left(\frac{x}{2}\right)}{2}+\frac{1}{2 \tanh \left(\frac{x}{2}\right)}"," ",0,"1/2*tanh(1/2*x)+1/2/tanh(1/2*x)","B"
39,1,32,9,0.066000," ","int(1/(1-cosh(x)^2)^2,x)","-\frac{\left(\tanh^{3}\left(\frac{x}{2}\right)\right)}{24}+\frac{3 \tanh \left(\frac{x}{2}\right)}{8}-\frac{1}{24 \tanh \left(\frac{x}{2}\right)^{3}}+\frac{3}{8 \tanh \left(\frac{x}{2}\right)}"," ",0,"-1/24*tanh(1/2*x)^3+3/8*tanh(1/2*x)-1/24/tanh(1/2*x)^3+3/8/tanh(1/2*x)","B"
40,1,48,15,0.071000," ","int(1/(1-cosh(x)^2)^3,x)","\frac{\left(\tanh^{5}\left(\frac{x}{2}\right)\right)}{160}-\frac{5 \left(\tanh^{3}\left(\frac{x}{2}\right)\right)}{96}+\frac{5 \tanh \left(\frac{x}{2}\right)}{16}-\frac{5}{96 \tanh \left(\frac{x}{2}\right)^{3}}+\frac{5}{16 \tanh \left(\frac{x}{2}\right)}+\frac{1}{160 \tanh \left(\frac{x}{2}\right)^{5}}"," ",0,"1/160*tanh(1/2*x)^5-5/96*tanh(1/2*x)^3+5/16*tanh(1/2*x)-5/96/tanh(1/2*x)^3+5/16/tanh(1/2*x)+1/160/tanh(1/2*x)^5","B"
41,1,114,47,0.282000," ","int((a+b*cosh(x)^2)^(1/2),x)","\frac{\sqrt{\frac{a +b \left(\cosh^{2}\left(x \right)\right)}{a}}\, \sqrt{-\left(\sinh^{2}\left(x \right)\right)}\, \left(a \EllipticF \left(\cosh \left(x \right) \sqrt{-\frac{b}{a}}, \sqrt{-\frac{a}{b}}\right)+b \EllipticF \left(\cosh \left(x \right) \sqrt{-\frac{b}{a}}, \sqrt{-\frac{a}{b}}\right)-b \EllipticE \left(\cosh \left(x \right) \sqrt{-\frac{b}{a}}, \sqrt{-\frac{a}{b}}\right)\right)}{\sqrt{-\frac{b}{a}}\, \sinh \left(x \right) \sqrt{a +b \left(\cosh^{2}\left(x \right)\right)}}"," ",0,"((a+b*cosh(x)^2)/a)^(1/2)*(-sinh(x)^2)^(1/2)*(a*EllipticF(cosh(x)*(-1/a*b)^(1/2),(-a/b)^(1/2))+b*EllipticF(cosh(x)*(-1/a*b)^(1/2),(-a/b)^(1/2))-b*EllipticE(cosh(x)*(-1/a*b)^(1/2),(-a/b)^(1/2)))/(-1/a*b)^(1/2)/sinh(x)/(a+b*cosh(x)^2)^(1/2)","B"
42,1,58,18,0.354000," ","int((1+cosh(x)^2)^(1/2),x)","-\frac{i \sqrt{\left(1+\cosh^{2}\left(x \right)\right) \left(\sinh^{2}\left(x \right)\right)}\, \sqrt{-\left(\sinh^{2}\left(x \right)\right)}\, \left(2 \EllipticF \left(i \cosh \left(x \right), i\right)-\EllipticE \left(i \cosh \left(x \right), i\right)\right)}{\sqrt{\cosh^{4}\left(x \right)-1}\, \sinh \left(x \right)}"," ",0,"-I*((1+cosh(x)^2)*sinh(x)^2)^(1/2)*(-sinh(x)^2)^(1/2)*(2*EllipticF(I*cosh(x),I)-EllipticE(I*cosh(x),I))/(cosh(x)^4-1)^(1/2)/sinh(x)","B"
43,1,15,11,0.144000," ","int((1-cosh(x)^2)^(1/2),x)","-\frac{\sinh \left(x \right) \cosh \left(x \right)}{\sqrt{-\left(\sinh^{2}\left(x \right)\right)}}"," ",0,"-sinh(x)*cosh(x)/(-sinh(x)^2)^(1/2)","A"
44,1,14,9,0.160000," ","int((-1+cosh(x)^2)^(1/2),x)","\frac{\sqrt{-\frac{1}{2}+\frac{\cosh \left(2 x \right)}{2}}\, \cosh \left(x \right)}{\sinh \left(x \right)}"," ",0,"(sinh(x)^2)^(1/2)*cosh(x)/sinh(x)","A"
45,1,62,36,0.328000," ","int((-1-cosh(x)^2)^(1/2),x)","-\frac{\sqrt{-\left(1+\cosh^{2}\left(x \right)\right) \left(\sinh^{2}\left(x \right)\right)}\, \sqrt{-\left(\sinh^{2}\left(x \right)\right)}\, \sqrt{1+\cosh^{2}\left(x \right)}\, \EllipticE \left(\cosh \left(x \right), i\right)}{\sqrt{1-\left(\cosh^{4}\left(x \right)\right)}\, \sinh \left(x \right) \sqrt{-1-\left(\cosh^{2}\left(x \right)\right)}}"," ",0,"-(-(1+cosh(x)^2)*sinh(x)^2)^(1/2)*(-sinh(x)^2)^(1/2)*(1+cosh(x)^2)^(1/2)*EllipticE(cosh(x),I)/(1-cosh(x)^4)^(1/2)/sinh(x)/(-1-cosh(x)^2)^(1/2)","A"
46,1,321,123,0.324000," ","int((a+b*cosh(x)^2)^(3/2),x)","\frac{\sqrt{-\frac{b}{a}}\, b^{2} \left(\cosh^{5}\left(x \right)\right)+\sqrt{-\frac{b}{a}}\, a b \left(\cosh^{3}\left(x \right)\right)-\sqrt{-\frac{b}{a}}\, b^{2} \left(\cosh^{3}\left(x \right)\right)+3 a^{2} \sqrt{\frac{a +b \left(\cosh^{2}\left(x \right)\right)}{a}}\, \sqrt{-\left(\sinh^{2}\left(x \right)\right)}\, \EllipticF \left(\cosh \left(x \right) \sqrt{-\frac{b}{a}}, \sqrt{-\frac{a}{b}}\right)+5 a b \sqrt{\frac{a +b \left(\cosh^{2}\left(x \right)\right)}{a}}\, \sqrt{-\left(\sinh^{2}\left(x \right)\right)}\, \EllipticF \left(\cosh \left(x \right) \sqrt{-\frac{b}{a}}, \sqrt{-\frac{a}{b}}\right)+2 \sqrt{\frac{a +b \left(\cosh^{2}\left(x \right)\right)}{a}}\, \sqrt{-\left(\sinh^{2}\left(x \right)\right)}\, \EllipticF \left(\cosh \left(x \right) \sqrt{-\frac{b}{a}}, \sqrt{-\frac{a}{b}}\right) b^{2}-4 a b \sqrt{\frac{a +b \left(\cosh^{2}\left(x \right)\right)}{a}}\, \sqrt{-\left(\sinh^{2}\left(x \right)\right)}\, \EllipticE \left(\cosh \left(x \right) \sqrt{-\frac{b}{a}}, \sqrt{-\frac{a}{b}}\right)-2 \sqrt{\frac{a +b \left(\cosh^{2}\left(x \right)\right)}{a}}\, \sqrt{-\left(\sinh^{2}\left(x \right)\right)}\, \EllipticE \left(\cosh \left(x \right) \sqrt{-\frac{b}{a}}, \sqrt{-\frac{a}{b}}\right) b^{2}-\sqrt{-\frac{b}{a}}\, a b \cosh \left(x \right)}{3 \sqrt{-\frac{b}{a}}\, \sinh \left(x \right) \sqrt{a +b \left(\cosh^{2}\left(x \right)\right)}}"," ",0,"1/3*((-1/a*b)^(1/2)*b^2*cosh(x)^5+(-1/a*b)^(1/2)*a*b*cosh(x)^3-(-1/a*b)^(1/2)*b^2*cosh(x)^3+3*a^2*((a+b*cosh(x)^2)/a)^(1/2)*(-sinh(x)^2)^(1/2)*EllipticF(cosh(x)*(-1/a*b)^(1/2),(-a/b)^(1/2))+5*a*b*((a+b*cosh(x)^2)/a)^(1/2)*(-sinh(x)^2)^(1/2)*EllipticF(cosh(x)*(-1/a*b)^(1/2),(-a/b)^(1/2))+2*((a+b*cosh(x)^2)/a)^(1/2)*(-sinh(x)^2)^(1/2)*EllipticF(cosh(x)*(-1/a*b)^(1/2),(-a/b)^(1/2))*b^2-4*a*b*((a+b*cosh(x)^2)/a)^(1/2)*(-sinh(x)^2)^(1/2)*EllipticE(cosh(x)*(-1/a*b)^(1/2),(-a/b)^(1/2))-2*((a+b*cosh(x)^2)/a)^(1/2)*(-sinh(x)^2)^(1/2)*EllipticE(cosh(x)*(-1/a*b)^(1/2),(-a/b)^(1/2))*b^2-(-1/a*b)^(1/2)*a*b*cosh(x))/(-1/a*b)^(1/2)/sinh(x)/(a+b*cosh(x)^2)^(1/2)","B"
47,1,99,53,0.377000," ","int((1+cosh(x)^2)^(3/2),x)","-\frac{\sqrt{\left(1+\cosh^{2}\left(x \right)\right) \left(\sinh^{2}\left(x \right)\right)}\, \left(-\left(\cosh^{5}\left(x \right)\right)+10 i \sqrt{1+\cosh^{2}\left(x \right)}\, \sqrt{-\left(\sinh^{2}\left(x \right)\right)}\, \EllipticF \left(i \cosh \left(x \right), i\right)-6 i \sqrt{1+\cosh^{2}\left(x \right)}\, \sqrt{-\left(\sinh^{2}\left(x \right)\right)}\, \EllipticE \left(i \cosh \left(x \right), i\right)+\cosh \left(x \right)\right)}{3 \sqrt{\cosh^{4}\left(x \right)-1}\, \sinh \left(x \right) \sqrt{1+\cosh^{2}\left(x \right)}}"," ",0,"-1/3*((1+cosh(x)^2)*sinh(x)^2)^(1/2)*(-cosh(x)^5+10*I*(1+cosh(x)^2)^(1/2)*(-sinh(x)^2)^(1/2)*EllipticF(I*cosh(x),I)-6*I*(1+cosh(x)^2)^(1/2)*(-sinh(x)^2)^(1/2)*EllipticE(I*cosh(x),I)+cosh(x))/(cosh(x)^4-1)^(1/2)/sinh(x)/(1+cosh(x)^2)^(1/2)","A"
48,1,21,25,0.201000," ","int((1-cosh(x)^2)^(3/2),x)","\frac{\sinh \left(x \right) \cosh \left(x \right) \left(\sinh^{2}\left(x \right)-2\right)}{3 \sqrt{-\left(\sinh^{2}\left(x \right)\right)}}"," ",0,"1/3*sinh(x)*cosh(x)*(sinh(x)^2-2)/(-sinh(x)^2)^(1/2)","A"
49,1,21,21,0.239000," ","int((-1+cosh(x)^2)^(3/2),x)","\frac{\sqrt{-\frac{1}{2}+\frac{\cosh \left(2 x \right)}{2}}\, \cosh \left(x \right) \left(\cosh^{2}\left(x \right)-3\right)}{3 \sinh \left(x \right)}"," ",0,"1/3*(sinh(x)^2)^(1/2)*cosh(x)*(cosh(x)^2-3)/sinh(x)","A"
50,1,96,91,0.423000," ","int((-1-cosh(x)^2)^(3/2),x)","-\frac{\sqrt{-\left(1+\cosh^{2}\left(x \right)\right) \left(\sinh^{2}\left(x \right)\right)}\, \left(-\left(\cosh^{5}\left(x \right)\right)+2 \sqrt{-\left(\sinh^{2}\left(x \right)\right)}\, \sqrt{1+\cosh^{2}\left(x \right)}\, \EllipticF \left(\cosh \left(x \right), i\right)-6 \sqrt{-\left(\sinh^{2}\left(x \right)\right)}\, \sqrt{1+\cosh^{2}\left(x \right)}\, \EllipticE \left(\cosh \left(x \right), i\right)+\cosh \left(x \right)\right)}{3 \sqrt{1-\left(\cosh^{4}\left(x \right)\right)}\, \sinh \left(x \right) \sqrt{-1-\left(\cosh^{2}\left(x \right)\right)}}"," ",0,"-1/3*(-(1+cosh(x)^2)*sinh(x)^2)^(1/2)*(-cosh(x)^5+2*(-sinh(x)^2)^(1/2)*(1+cosh(x)^2)^(1/2)*EllipticF(cosh(x),I)-6*(-sinh(x)^2)^(1/2)*(1+cosh(x)^2)^(1/2)*EllipticE(cosh(x),I)+cosh(x))/(1-cosh(x)^4)^(1/2)/sinh(x)/(-1-cosh(x)^2)^(1/2)","A"
51,1,66,47,0.192000," ","int(1/(a+b*cosh(x)^2)^(1/2),x)","\frac{\sqrt{\frac{a +b \left(\cosh^{2}\left(x \right)\right)}{a}}\, \sqrt{-\left(\sinh^{2}\left(x \right)\right)}\, \EllipticF \left(\cosh \left(x \right) \sqrt{-\frac{b}{a}}, \sqrt{-\frac{a}{b}}\right)}{\sqrt{-\frac{b}{a}}\, \sinh \left(x \right) \sqrt{a +b \left(\cosh^{2}\left(x \right)\right)}}"," ",0,"1/(-1/a*b)^(1/2)*((a+b*cosh(x)^2)/a)^(1/2)*(-sinh(x)^2)^(1/2)*EllipticF(cosh(x)*(-1/a*b)^(1/2),(-a/b)^(1/2))/sinh(x)/(a+b*cosh(x)^2)^(1/2)","A"
52,1,45,18,0.291000," ","int(1/(1+cosh(x)^2)^(1/2),x)","-\frac{i \sqrt{\left(1+\cosh^{2}\left(x \right)\right) \left(\sinh^{2}\left(x \right)\right)}\, \sqrt{-\left(\sinh^{2}\left(x \right)\right)}\, \EllipticF \left(i \cosh \left(x \right), i\right)}{\sqrt{\cosh^{4}\left(x \right)-1}\, \sinh \left(x \right)}"," ",0,"-I*((1+cosh(x)^2)*sinh(x)^2)^(1/2)*(-sinh(x)^2)^(1/2)/(cosh(x)^4-1)^(1/2)*EllipticF(I*cosh(x),I)/sinh(x)","B"
53,1,34,15,0.145000," ","int(1/(1-cosh(x)^2)^(1/2),x)","-\frac{\sinh \left(x \right) \sqrt{-\left(\cosh^{2}\left(x \right)\right)}\, \arctan \left(\frac{1}{\sqrt{-\left(\cosh^{2}\left(x \right)\right)}}\right)}{\cosh \left(x \right) \sqrt{-\left(\sinh^{2}\left(x \right)\right)}}"," ",0,"-sinh(x)*(-cosh(x)^2)^(1/2)*arctan(1/(-cosh(x)^2)^(1/2))/cosh(x)/(-sinh(x)^2)^(1/2)","B"
54,1,16,13,0.173000," ","int(1/(-1+cosh(x)^2)^(1/2),x)","-\frac{\sqrt{-\frac{1}{2}+\frac{\cosh \left(2 x \right)}{2}}\, \arctanh \left(\cosh \left(x \right)\right)}{\sinh \left(x \right)}"," ",0,"-(sinh(x)^2)^(1/2)*arctanh(cosh(x))/sinh(x)","A"
55,1,61,36,0.341000," ","int(1/(-1-cosh(x)^2)^(1/2),x)","\frac{\sqrt{-\left(1+\cosh^{2}\left(x \right)\right) \left(\sinh^{2}\left(x \right)\right)}\, \sqrt{-\left(\sinh^{2}\left(x \right)\right)}\, \sqrt{1+\cosh^{2}\left(x \right)}\, \EllipticF \left(\cosh \left(x \right), i\right)}{\sqrt{1-\left(\cosh^{4}\left(x \right)\right)}\, \sinh \left(x \right) \sqrt{-1-\left(\cosh^{2}\left(x \right)\right)}}"," ",0,"(-(1+cosh(x)^2)*sinh(x)^2)^(1/2)*(-sinh(x)^2)^(1/2)*(1+cosh(x)^2)^(1/2)/(1-cosh(x)^4)^(1/2)*EllipticF(cosh(x),I)/sinh(x)/(-1-cosh(x)^2)^(1/2)","A"
56,1,100,182,0.786000," ","int(1/(a+b*cosh(x)^3),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\left(a -b \right) \textit{\_Z}^{6}+\left(-3 a -3 b \right) \textit{\_Z}^{4}+\left(3 a -3 b \right) \textit{\_Z}^{2}-a -b \right)}{\sum}\frac{\left(-\textit{\_R}^{4}+2 \textit{\_R}^{2}-1\right) \ln \left(\tanh \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a -\textit{\_R}^{5} b -2 \textit{\_R}^{3} a -2 \textit{\_R}^{3} b +\textit{\_R} a -\textit{\_R} b}\right)}{3}"," ",0,"1/3*sum((-_R^4+2*_R^2-1)/(_R^5*a-_R^5*b-2*_R^3*a-2*_R^3*b+_R*a-_R*b)*ln(tanh(1/2*x)-_R),_R=RootOf((a-b)*_Z^6+(-3*a-3*b)*_Z^4+(3*a-3*b)*_Z^2-a-b))","C"
57,1,94,182,0.702000," ","int(1/(a-b*cosh(x)^3),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\left(a +b \right) \textit{\_Z}^{6}+\left(-3 a +3 b \right) \textit{\_Z}^{4}+\left(3 a +3 b \right) \textit{\_Z}^{2}-a +b \right)}{\sum}\frac{\left(-\textit{\_R}^{4}+2 \textit{\_R}^{2}-1\right) \ln \left(\tanh \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +\textit{\_R}^{5} b -2 \textit{\_R}^{3} a +2 \textit{\_R}^{3} b +\textit{\_R} a +\textit{\_R} b}\right)}{3}"," ",0,"1/3*sum((-_R^4+2*_R^2-1)/(_R^5*a+_R^5*b-2*_R^3*a+2*_R^3*b+_R*a+_R*b)*ln(tanh(1/2*x)-_R),_R=RootOf((a+b)*_Z^6+(-3*a+3*b)*_Z^4+(3*a+3*b)*_Z^2-a+b))","C"
58,1,216,67,0.054000," ","int(1/(1+cosh(x)^3),x)","\frac{\tanh \left(\frac{x}{2}\right)}{3}+\frac{3^{\frac{3}{4}} \sqrt{2}\, \arctan \left(\sqrt{2}\, 3^{\frac{1}{4}} \tanh \left(\frac{x}{2}\right)-1\right)}{18}+\frac{3^{\frac{3}{4}} \sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)+\frac{3^{\frac{3}{4}} \tanh \left(\frac{x}{2}\right) \sqrt{2}}{3}+\frac{\sqrt{3}}{3}}{\tanh^{2}\left(\frac{x}{2}\right)-\frac{3^{\frac{3}{4}} \tanh \left(\frac{x}{2}\right) \sqrt{2}}{3}+\frac{\sqrt{3}}{3}}\right)}{36}+\frac{3^{\frac{3}{4}} \sqrt{2}\, \arctan \left(\sqrt{2}\, 3^{\frac{1}{4}} \tanh \left(\frac{x}{2}\right)+1\right)}{18}-\frac{\sqrt{2}\, 3^{\frac{1}{4}} \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)-\frac{3^{\frac{3}{4}} \tanh \left(\frac{x}{2}\right) \sqrt{2}}{3}+\frac{\sqrt{3}}{3}}{\tanh^{2}\left(\frac{x}{2}\right)+\frac{3^{\frac{3}{4}} \tanh \left(\frac{x}{2}\right) \sqrt{2}}{3}+\frac{\sqrt{3}}{3}}\right)}{12}-\frac{\sqrt{2}\, 3^{\frac{1}{4}} \arctan \left(\sqrt{2}\, 3^{\frac{1}{4}} \tanh \left(\frac{x}{2}\right)-1\right)}{6}-\frac{\sqrt{2}\, 3^{\frac{1}{4}} \arctan \left(\sqrt{2}\, 3^{\frac{1}{4}} \tanh \left(\frac{x}{2}\right)+1\right)}{6}"," ",0,"1/3*tanh(1/2*x)+1/18*3^(3/4)*2^(1/2)*arctan(2^(1/2)*3^(1/4)*tanh(1/2*x)-1)+1/36*3^(3/4)*2^(1/2)*ln((tanh(1/2*x)^2+1/3*3^(3/4)*tanh(1/2*x)*2^(1/2)+1/3*3^(1/2))/(tanh(1/2*x)^2-1/3*3^(3/4)*tanh(1/2*x)*2^(1/2)+1/3*3^(1/2)))+1/18*3^(3/4)*2^(1/2)*arctan(2^(1/2)*3^(1/4)*tanh(1/2*x)+1)-1/12*2^(1/2)*3^(1/4)*ln((tanh(1/2*x)^2-1/3*3^(3/4)*tanh(1/2*x)*2^(1/2)+1/3*3^(1/2))/(tanh(1/2*x)^2+1/3*3^(3/4)*tanh(1/2*x)*2^(1/2)+1/3*3^(1/2)))-1/6*2^(1/2)*3^(1/4)*arctan(2^(1/2)*3^(1/4)*tanh(1/2*x)-1)-1/6*2^(1/2)*3^(1/4)*arctan(2^(1/2)*3^(1/4)*tanh(1/2*x)+1)","B"
59,1,212,71,0.066000," ","int(1/(1-cosh(x)^3),x)","\frac{3^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{3^{\frac{3}{4}} \tanh \left(\frac{x}{2}\right) \sqrt{2}}{3}+1\right)}{6}+\frac{3^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{3^{\frac{3}{4}} \tanh \left(\frac{x}{2}\right) \sqrt{2}}{3}-1\right)}{6}+\frac{3^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)+\sqrt{2}\, 3^{\frac{1}{4}} \tanh \left(\frac{x}{2}\right)+\sqrt{3}}{\tanh^{2}\left(\frac{x}{2}\right)-\sqrt{2}\, 3^{\frac{1}{4}} \tanh \left(\frac{x}{2}\right)+\sqrt{3}}\right)}{12}-\frac{3^{\frac{3}{4}} \sqrt{2}\, \arctan \left(\frac{3^{\frac{3}{4}} \tanh \left(\frac{x}{2}\right) \sqrt{2}}{3}+1\right)}{18}-\frac{3^{\frac{3}{4}} \sqrt{2}\, \arctan \left(\frac{3^{\frac{3}{4}} \tanh \left(\frac{x}{2}\right) \sqrt{2}}{3}-1\right)}{18}-\frac{3^{\frac{3}{4}} \sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)-\sqrt{2}\, 3^{\frac{1}{4}} \tanh \left(\frac{x}{2}\right)+\sqrt{3}}{\tanh^{2}\left(\frac{x}{2}\right)+\sqrt{2}\, 3^{\frac{1}{4}} \tanh \left(\frac{x}{2}\right)+\sqrt{3}}\right)}{36}+\frac{1}{3 \tanh \left(\frac{x}{2}\right)}"," ",0,"1/6*3^(1/4)*2^(1/2)*arctan(1/3*3^(3/4)*tanh(1/2*x)*2^(1/2)+1)+1/6*3^(1/4)*2^(1/2)*arctan(1/3*3^(3/4)*tanh(1/2*x)*2^(1/2)-1)+1/12*3^(1/4)*2^(1/2)*ln((tanh(1/2*x)^2+2^(1/2)*3^(1/4)*tanh(1/2*x)+3^(1/2))/(tanh(1/2*x)^2-2^(1/2)*3^(1/4)*tanh(1/2*x)+3^(1/2)))-1/18*3^(3/4)*2^(1/2)*arctan(1/3*3^(3/4)*tanh(1/2*x)*2^(1/2)+1)-1/18*3^(3/4)*2^(1/2)*arctan(1/3*3^(3/4)*tanh(1/2*x)*2^(1/2)-1)-1/36*3^(3/4)*2^(1/2)*ln((tanh(1/2*x)^2-2^(1/2)*3^(1/4)*tanh(1/2*x)+3^(1/2))/(tanh(1/2*x)^2+2^(1/2)*3^(1/4)*tanh(1/2*x)+3^(1/2)))+1/3/tanh(1/2*x)","B"
60,1,121,245,0.090000," ","int(1/(a+b*cosh(x)^4),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\left(a +b \right) \textit{\_Z}^{8}+\left(-4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +6 b \right) \textit{\_Z}^{4}+\left(-4 a +4 b \right) \textit{\_Z}^{2}+a +b \right)}{\sum}\frac{\left(-\textit{\_R}^{6}+3 \textit{\_R}^{4}-3 \textit{\_R}^{2}+1\right) \ln \left(\tanh \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{7} a +\textit{\_R}^{7} b -3 \textit{\_R}^{5} a +3 \textit{\_R}^{5} b +3 \textit{\_R}^{3} a +3 \textit{\_R}^{3} b -\textit{\_R} a +\textit{\_R} b}\right)}{4}"," ",0,"1/4*sum((-_R^6+3*_R^4-3*_R^2+1)/(_R^7*a+_R^7*b-3*_R^5*a+3*_R^5*b+3*_R^3*a+3*_R^3*b-_R*a+_R*b)*ln(tanh(1/2*x)-_R),_R=RootOf((a+b)*_Z^8+(-4*a+4*b)*_Z^6+(6*a+6*b)*_Z^4+(-4*a+4*b)*_Z^2+a+b))","C"
61,1,127,65,0.088000," ","int(1/(a-b*cosh(x)^4),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\left(a -b \right) \textit{\_Z}^{8}+\left(-4 a -4 b \right) \textit{\_Z}^{6}+\left(6 a -6 b \right) \textit{\_Z}^{4}+\left(-4 a -4 b \right) \textit{\_Z}^{2}+a -b \right)}{\sum}\frac{\left(-\textit{\_R}^{6}+3 \textit{\_R}^{4}-3 \textit{\_R}^{2}+1\right) \ln \left(\tanh \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{7} a -\textit{\_R}^{7} b -3 \textit{\_R}^{5} a -3 \textit{\_R}^{5} b +3 \textit{\_R}^{3} a -3 \textit{\_R}^{3} b -\textit{\_R} a -\textit{\_R} b}\right)}{4}"," ",0,"1/4*sum((-_R^6+3*_R^4-3*_R^2+1)/(_R^7*a-_R^7*b-3*_R^5*a-3*_R^5*b+3*_R^3*a-3*_R^3*b-_R*a-_R*b)*ln(tanh(1/2*x)-_R),_R=RootOf((a-b)*_Z^8+(-4*a-4*b)*_Z^6+(6*a-6*b)*_Z^4+(-4*a-4*b)*_Z^2+a-b))","C"
62,1,37,124,0.073000," ","int(1/(1+cosh(x)^4),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(2 \textit{\_Z}^{4}-2 \textit{\_Z}^{2}+1\right)}{\sum}\textit{\_R} \ln \left(2 \tanh \left(\frac{x}{2}\right) \textit{\_R} +\tanh^{2}\left(\frac{x}{2}\right)+1\right)\right)}{4}"," ",0,"1/4*sum(_R*ln(2*tanh(1/2*x)*_R+tanh(1/2*x)^2+1),_R=RootOf(2*_Z^4-2*_Z^2+1))","C"
63,1,100,18,0.077000," ","int(1/(1-cosh(x)^4),x)","\frac{\tanh \left(\frac{x}{2}\right)}{4}+\frac{1}{4 \tanh \left(\frac{x}{2}\right)}+\frac{\sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)+\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}{\tanh^{2}\left(\frac{x}{2}\right)-\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}\right)}{16}-\frac{\sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)-\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}{\tanh^{2}\left(\frac{x}{2}\right)+\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}\right)}{16}"," ",0,"1/4*tanh(1/2*x)+1/4/tanh(1/2*x)+1/16*2^(1/2)*ln((tanh(1/2*x)^2+2^(1/2)*tanh(1/2*x)+1)/(tanh(1/2*x)^2-2^(1/2)*tanh(1/2*x)+1))-1/16*2^(1/2)*ln((tanh(1/2*x)^2-2^(1/2)*tanh(1/2*x)+1)/(tanh(1/2*x)^2+2^(1/2)*tanh(1/2*x)+1))","B"
64,1,156,312,0.111000," ","int(1/(a+b*cosh(x)^5),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\left(a -b \right) \textit{\_Z}^{10}+\left(-5 a -5 b \right) \textit{\_Z}^{8}+\left(10 a -10 b \right) \textit{\_Z}^{6}+\left(-10 a -10 b \right) \textit{\_Z}^{4}+\left(5 a -5 b \right) \textit{\_Z}^{2}-a -b \right)}{\sum}\frac{\left(-\textit{\_R}^{8}+4 \textit{\_R}^{6}-6 \textit{\_R}^{4}+4 \textit{\_R}^{2}-1\right) \ln \left(\tanh \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{9} a -\textit{\_R}^{9} b -4 \textit{\_R}^{7} a -4 \textit{\_R}^{7} b +6 \textit{\_R}^{5} a -6 \textit{\_R}^{5} b -4 \textit{\_R}^{3} a -4 \textit{\_R}^{3} b +\textit{\_R} a -\textit{\_R} b}\right)}{5}"," ",0,"1/5*sum((-_R^8+4*_R^6-6*_R^4+4*_R^2-1)/(_R^9*a-_R^9*b-4*_R^7*a-4*_R^7*b+6*_R^5*a-6*_R^5*b-4*_R^3*a-4*_R^3*b+_R*a-_R*b)*ln(tanh(1/2*x)-_R),_R=RootOf((a-b)*_Z^10+(-5*a-5*b)*_Z^8+(10*a-10*b)*_Z^6+(-10*a-10*b)*_Z^4+(5*a-5*b)*_Z^2-a-b))","C"
65,1,177,109,0.095000," ","int(1/(a+b*cosh(x)^6),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\left(a +b \right) \textit{\_Z}^{12}+\left(-6 a +6 b \right) \textit{\_Z}^{10}+\left(15 a +15 b \right) \textit{\_Z}^{8}+\left(-20 a +20 b \right) \textit{\_Z}^{6}+\left(15 a +15 b \right) \textit{\_Z}^{4}+\left(-6 a +6 b \right) \textit{\_Z}^{2}+a +b \right)}{\sum}\frac{\left(-\textit{\_R}^{10}+5 \textit{\_R}^{8}-10 \textit{\_R}^{6}+10 \textit{\_R}^{4}-5 \textit{\_R}^{2}+1\right) \ln \left(\tanh \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{11} a +\textit{\_R}^{11} b -5 \textit{\_R}^{9} a +5 \textit{\_R}^{9} b +10 \textit{\_R}^{7} a +10 \textit{\_R}^{7} b -10 \textit{\_R}^{5} a +10 \textit{\_R}^{5} b +5 \textit{\_R}^{3} a +5 \textit{\_R}^{3} b -\textit{\_R} a +\textit{\_R} b}\right)}{6}"," ",0,"1/6*sum((-_R^10+5*_R^8-10*_R^6+10*_R^4-5*_R^2+1)/(_R^11*a+_R^11*b-5*_R^9*a+5*_R^9*b+10*_R^7*a+10*_R^7*b-10*_R^5*a+10*_R^5*b+5*_R^3*a+5*_R^3*b-_R*a+_R*b)*ln(tanh(1/2*x)-_R),_R=RootOf((a+b)*_Z^12+(-6*a+6*b)*_Z^10+(15*a+15*b)*_Z^8+(-20*a+20*b)*_Z^6+(15*a+15*b)*_Z^4+(-6*a+6*b)*_Z^2+a+b))","C"
66,1,233,169,0.102000," ","int(1/(a+b*cosh(x)^8),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\left(a +b \right) \textit{\_Z}^{16}+\left(-8 a +8 b \right) \textit{\_Z}^{14}+\left(28 a +28 b \right) \textit{\_Z}^{12}+\left(-56 a +56 b \right) \textit{\_Z}^{10}+\left(70 a +70 b \right) \textit{\_Z}^{8}+\left(-56 a +56 b \right) \textit{\_Z}^{6}+\left(28 a +28 b \right) \textit{\_Z}^{4}+\left(-8 a +8 b \right) \textit{\_Z}^{2}+a +b \right)}{\sum}\frac{\left(-\textit{\_R}^{14}+7 \textit{\_R}^{12}-21 \textit{\_R}^{10}+35 \textit{\_R}^{8}-35 \textit{\_R}^{6}+21 \textit{\_R}^{4}-7 \textit{\_R}^{2}+1\right) \ln \left(\tanh \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{15} a +\textit{\_R}^{15} b -7 \textit{\_R}^{13} a +7 \textit{\_R}^{13} b +21 \textit{\_R}^{11} a +21 \textit{\_R}^{11} b -35 \textit{\_R}^{9} a +35 \textit{\_R}^{9} b +35 \textit{\_R}^{7} a +35 \textit{\_R}^{7} b -21 \textit{\_R}^{5} a +21 \textit{\_R}^{5} b +7 \textit{\_R}^{3} a +7 \textit{\_R}^{3} b -\textit{\_R} a +\textit{\_R} b}\right)}{8}"," ",0,"1/8*sum((-_R^14+7*_R^12-21*_R^10+35*_R^8-35*_R^6+21*_R^4-7*_R^2+1)/(_R^15*a+_R^15*b-7*_R^13*a+7*_R^13*b+21*_R^11*a+21*_R^11*b-35*_R^9*a+35*_R^9*b+35*_R^7*a+35*_R^7*b-21*_R^5*a+21*_R^5*b+7*_R^3*a+7*_R^3*b-_R*a+_R*b)*ln(tanh(1/2*x)-_R),_R=RootOf((a+b)*_Z^16+(-8*a+8*b)*_Z^14+(28*a+28*b)*_Z^12+(-56*a+56*b)*_Z^10+(70*a+70*b)*_Z^8+(-56*a+56*b)*_Z^6+(28*a+28*b)*_Z^4+(-8*a+8*b)*_Z^2+a+b))","C"
67,1,150,312,0.090000," ","int(1/(a-b*cosh(x)^5),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\left(a +b \right) \textit{\_Z}^{10}+\left(-5 a +5 b \right) \textit{\_Z}^{8}+\left(10 a +10 b \right) \textit{\_Z}^{6}+\left(-10 a +10 b \right) \textit{\_Z}^{4}+\left(5 a +5 b \right) \textit{\_Z}^{2}-a +b \right)}{\sum}\frac{\left(-\textit{\_R}^{8}+4 \textit{\_R}^{6}-6 \textit{\_R}^{4}+4 \textit{\_R}^{2}-1\right) \ln \left(\tanh \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{9} a +\textit{\_R}^{9} b -4 \textit{\_R}^{7} a +4 \textit{\_R}^{7} b +6 \textit{\_R}^{5} a +6 \textit{\_R}^{5} b -4 \textit{\_R}^{3} a +4 \textit{\_R}^{3} b +\textit{\_R} a +\textit{\_R} b}\right)}{5}"," ",0,"1/5*sum((-_R^8+4*_R^6-6*_R^4+4*_R^2-1)/(_R^9*a+_R^9*b-4*_R^7*a+4*_R^7*b+6*_R^5*a+6*_R^5*b-4*_R^3*a+4*_R^3*b+_R*a+_R*b)*ln(tanh(1/2*x)-_R),_R=RootOf((a+b)*_Z^10+(-5*a+5*b)*_Z^8+(10*a+10*b)*_Z^6+(-10*a+10*b)*_Z^4+(5*a+5*b)*_Z^2-a+b))","C"
68,1,183,113,0.097000," ","int(1/(a-b*cosh(x)^6),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\left(a -b \right) \textit{\_Z}^{12}+\left(-6 a -6 b \right) \textit{\_Z}^{10}+\left(15 a -15 b \right) \textit{\_Z}^{8}+\left(-20 a -20 b \right) \textit{\_Z}^{6}+\left(15 a -15 b \right) \textit{\_Z}^{4}+\left(-6 a -6 b \right) \textit{\_Z}^{2}+a -b \right)}{\sum}\frac{\left(-\textit{\_R}^{10}+5 \textit{\_R}^{8}-10 \textit{\_R}^{6}+10 \textit{\_R}^{4}-5 \textit{\_R}^{2}+1\right) \ln \left(\tanh \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{11} a -\textit{\_R}^{11} b -5 \textit{\_R}^{9} a -5 \textit{\_R}^{9} b +10 \textit{\_R}^{7} a -10 \textit{\_R}^{7} b -10 \textit{\_R}^{5} a -10 \textit{\_R}^{5} b +5 \textit{\_R}^{3} a -5 \textit{\_R}^{3} b -\textit{\_R} a -\textit{\_R} b}\right)}{6}"," ",0,"1/6*sum((-_R^10+5*_R^8-10*_R^6+10*_R^4-5*_R^2+1)/(_R^11*a-_R^11*b-5*_R^9*a-5*_R^9*b+10*_R^7*a-10*_R^7*b-10*_R^5*a-10*_R^5*b+5*_R^3*a-5*_R^3*b-_R*a-_R*b)*ln(tanh(1/2*x)-_R),_R=RootOf((a-b)*_Z^12+(-6*a-6*b)*_Z^10+(15*a-15*b)*_Z^8+(-20*a-20*b)*_Z^6+(15*a-15*b)*_Z^4+(-6*a-6*b)*_Z^2+a-b))","C"
69,1,239,137,0.095000," ","int(1/(a-b*cosh(x)^8),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\left(a -b \right) \textit{\_Z}^{16}+\left(-8 a -8 b \right) \textit{\_Z}^{14}+\left(28 a -28 b \right) \textit{\_Z}^{12}+\left(-56 a -56 b \right) \textit{\_Z}^{10}+\left(70 a -70 b \right) \textit{\_Z}^{8}+\left(-56 a -56 b \right) \textit{\_Z}^{6}+\left(28 a -28 b \right) \textit{\_Z}^{4}+\left(-8 a -8 b \right) \textit{\_Z}^{2}+a -b \right)}{\sum}\frac{\left(-\textit{\_R}^{14}+7 \textit{\_R}^{12}-21 \textit{\_R}^{10}+35 \textit{\_R}^{8}-35 \textit{\_R}^{6}+21 \textit{\_R}^{4}-7 \textit{\_R}^{2}+1\right) \ln \left(\tanh \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{15} a -\textit{\_R}^{15} b -7 \textit{\_R}^{13} a -7 \textit{\_R}^{13} b +21 \textit{\_R}^{11} a -21 \textit{\_R}^{11} b -35 \textit{\_R}^{9} a -35 \textit{\_R}^{9} b +35 \textit{\_R}^{7} a -35 \textit{\_R}^{7} b -21 \textit{\_R}^{5} a -21 \textit{\_R}^{5} b +7 \textit{\_R}^{3} a -7 \textit{\_R}^{3} b -\textit{\_R} a -\textit{\_R} b}\right)}{8}"," ",0,"1/8*sum((-_R^14+7*_R^12-21*_R^10+35*_R^8-35*_R^6+21*_R^4-7*_R^2+1)/(_R^15*a-_R^15*b-7*_R^13*a-7*_R^13*b+21*_R^11*a-21*_R^11*b-35*_R^9*a-35*_R^9*b+35*_R^7*a-35*_R^7*b-21*_R^5*a-21*_R^5*b+7*_R^3*a-7*_R^3*b-_R*a-_R*b)*ln(tanh(1/2*x)-_R),_R=RootOf((a-b)*_Z^16+(-8*a-8*b)*_Z^14+(28*a-28*b)*_Z^12+(-56*a-56*b)*_Z^10+(70*a-70*b)*_Z^8+(-56*a-56*b)*_Z^6+(28*a-28*b)*_Z^4+(-8*a-8*b)*_Z^2+a-b))","C"
70,1,62,160,0.074000," ","int(1/(1+cosh(x)^5),x)","\frac{\tanh \left(\frac{x}{2}\right)}{5}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(5 \textit{\_Z}^{8}+10 \textit{\_Z}^{4}+1\right)}{\sum}\frac{\left(-5 \textit{\_R}^{6}+5 \textit{\_R}^{4}-5 \textit{\_R}^{2}+1\right) \ln \left(\tanh \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{7}+\textit{\_R}^{3}}\right)}{50}"," ",0,"1/5*tanh(1/2*x)+1/50*sum((-5*_R^6+5*_R^4-5*_R^2+1)/(_R^7+_R^3)*ln(tanh(1/2*x)-_R),_R=RootOf(5*_Z^8+10*_Z^4+1))","C"
71,1,208,58,0.087000," ","int(1/(1+cosh(x)^6),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{\sum}\frac{\left(-\textit{\_R}^{2}-4 \textit{\_R} +1\right) \ln \left(\tanh \left(\frac{x}{2}\right)-\textit{\_R} \right)}{2 \textit{\_R}^{3}+3 \textit{\_R}^{2}+2 \textit{\_R} -1}\right)}{6}+\frac{\sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)+\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}{\tanh^{2}\left(\frac{x}{2}\right)-\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}\right)}{24}-\frac{\sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)-\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}{\tanh^{2}\left(\frac{x}{2}\right)+\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}\right)}{24}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)}{\sum}\frac{\left(-\textit{\_R}^{2}+4 \textit{\_R} +1\right) \ln \left(\tanh \left(\frac{x}{2}\right)-\textit{\_R} \right)}{2 \textit{\_R}^{3}-3 \textit{\_R}^{2}+2 \textit{\_R} +1}\right)}{6}"," ",0,"1/6*sum((-_R^2-4*_R+1)/(2*_R^3+3*_R^2+2*_R-1)*ln(tanh(1/2*x)-_R),_R=RootOf(_Z^4+2*_Z^3+2*_Z^2-2*_Z+1))+1/24*2^(1/2)*ln((tanh(1/2*x)^2+2^(1/2)*tanh(1/2*x)+1)/(tanh(1/2*x)^2-2^(1/2)*tanh(1/2*x)+1))-1/24*2^(1/2)*ln((tanh(1/2*x)^2-2^(1/2)*tanh(1/2*x)+1)/(tanh(1/2*x)^2+2^(1/2)*tanh(1/2*x)+1))+1/6*sum((-_R^2+4*_R+1)/(2*_R^3-3*_R^2+2*_R+1)*ln(tanh(1/2*x)-_R),_R=RootOf(_Z^4-2*_Z^3+2*_Z^2+2*_Z+1))","C"
72,1,47,89,0.090000," ","int(1/(1+cosh(x)^8),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(2 \textit{\_Z}^{8}-4 \textit{\_Z}^{6}+6 \textit{\_Z}^{4}-4 \textit{\_Z}^{2}+1\right)}{\sum}\textit{\_R} \ln \left(2 \tanh \left(\frac{x}{2}\right) \textit{\_R} +\tanh^{2}\left(\frac{x}{2}\right)+1\right)\right)}{8}"," ",0,"1/8*sum(_R*ln(2*tanh(1/2*x)*_R+tanh(1/2*x)^2+1),_R=RootOf(2*_Z^8-4*_Z^6+6*_Z^4-4*_Z^2+1))","C"
73,1,64,145,0.073000," ","int(1/(1-cosh(x)^5),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}+10 \textit{\_Z}^{4}+5\right)}{\sum}\frac{\left(-\textit{\_R}^{6}+5 \textit{\_R}^{4}-5 \textit{\_R}^{2}+5\right) \ln \left(\tanh \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{7}+5 \textit{\_R}^{3}}\right)}{10}+\frac{1}{5 \tanh \left(\frac{x}{2}\right)}"," ",0,"1/10*sum((-_R^6+5*_R^4-5*_R^2+5)/(_R^7+5*_R^3)*ln(tanh(1/2*x)-_R),_R=RootOf(_Z^8+10*_Z^4+5))+1/5/tanh(1/2*x)","C"
74,1,426,49,0.089000," ","int(1/(1-cosh(x)^6),x)","\frac{\tanh \left(\frac{x}{2}\right)}{6}+\frac{3^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{3^{\frac{3}{4}} \tanh \left(\frac{x}{2}\right) \sqrt{2}}{3}+1\right)}{12}+\frac{3^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{3^{\frac{3}{4}} \tanh \left(\frac{x}{2}\right) \sqrt{2}}{3}-1\right)}{12}+\frac{3^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)+\sqrt{2}\, 3^{\frac{1}{4}} \tanh \left(\frac{x}{2}\right)+\sqrt{3}}{\tanh^{2}\left(\frac{x}{2}\right)-\sqrt{2}\, 3^{\frac{1}{4}} \tanh \left(\frac{x}{2}\right)+\sqrt{3}}\right)}{24}-\frac{3^{\frac{3}{4}} \sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)-\sqrt{2}\, 3^{\frac{1}{4}} \tanh \left(\frac{x}{2}\right)+\sqrt{3}}{\tanh^{2}\left(\frac{x}{2}\right)+\sqrt{2}\, 3^{\frac{1}{4}} \tanh \left(\frac{x}{2}\right)+\sqrt{3}}\right)}{72}-\frac{3^{\frac{3}{4}} \sqrt{2}\, \arctan \left(\frac{3^{\frac{3}{4}} \tanh \left(\frac{x}{2}\right) \sqrt{2}}{3}+1\right)}{36}-\frac{3^{\frac{3}{4}} \sqrt{2}\, \arctan \left(\frac{3^{\frac{3}{4}} \tanh \left(\frac{x}{2}\right) \sqrt{2}}{3}-1\right)}{36}+\frac{1}{6 \tanh \left(\frac{x}{2}\right)}+\frac{3^{\frac{3}{4}} \sqrt{2}\, \arctan \left(\sqrt{2}\, 3^{\frac{1}{4}} \tanh \left(\frac{x}{2}\right)-1\right)}{36}+\frac{3^{\frac{3}{4}} \sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)+\frac{3^{\frac{3}{4}} \tanh \left(\frac{x}{2}\right) \sqrt{2}}{3}+\frac{\sqrt{3}}{3}}{\tanh^{2}\left(\frac{x}{2}\right)-\frac{3^{\frac{3}{4}} \tanh \left(\frac{x}{2}\right) \sqrt{2}}{3}+\frac{\sqrt{3}}{3}}\right)}{72}+\frac{3^{\frac{3}{4}} \sqrt{2}\, \arctan \left(\sqrt{2}\, 3^{\frac{1}{4}} \tanh \left(\frac{x}{2}\right)+1\right)}{36}-\frac{\sqrt{2}\, 3^{\frac{1}{4}} \arctan \left(\sqrt{2}\, 3^{\frac{1}{4}} \tanh \left(\frac{x}{2}\right)-1\right)}{12}-\frac{\sqrt{2}\, 3^{\frac{1}{4}} \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)-\frac{3^{\frac{3}{4}} \tanh \left(\frac{x}{2}\right) \sqrt{2}}{3}+\frac{\sqrt{3}}{3}}{\tanh^{2}\left(\frac{x}{2}\right)+\frac{3^{\frac{3}{4}} \tanh \left(\frac{x}{2}\right) \sqrt{2}}{3}+\frac{\sqrt{3}}{3}}\right)}{24}-\frac{\sqrt{2}\, 3^{\frac{1}{4}} \arctan \left(\sqrt{2}\, 3^{\frac{1}{4}} \tanh \left(\frac{x}{2}\right)+1\right)}{12}"," ",0,"1/6*tanh(1/2*x)+1/12*3^(1/4)*2^(1/2)*arctan(1/3*3^(3/4)*tanh(1/2*x)*2^(1/2)+1)+1/12*3^(1/4)*2^(1/2)*arctan(1/3*3^(3/4)*tanh(1/2*x)*2^(1/2)-1)+1/24*3^(1/4)*2^(1/2)*ln((tanh(1/2*x)^2+2^(1/2)*3^(1/4)*tanh(1/2*x)+3^(1/2))/(tanh(1/2*x)^2-2^(1/2)*3^(1/4)*tanh(1/2*x)+3^(1/2)))-1/72*3^(3/4)*2^(1/2)*ln((tanh(1/2*x)^2-2^(1/2)*3^(1/4)*tanh(1/2*x)+3^(1/2))/(tanh(1/2*x)^2+2^(1/2)*3^(1/4)*tanh(1/2*x)+3^(1/2)))-1/36*3^(3/4)*2^(1/2)*arctan(1/3*3^(3/4)*tanh(1/2*x)*2^(1/2)+1)-1/36*3^(3/4)*2^(1/2)*arctan(1/3*3^(3/4)*tanh(1/2*x)*2^(1/2)-1)+1/6/tanh(1/2*x)+1/36*3^(3/4)*2^(1/2)*arctan(2^(1/2)*3^(1/4)*tanh(1/2*x)-1)+1/72*3^(3/4)*2^(1/2)*ln((tanh(1/2*x)^2+1/3*3^(3/4)*tanh(1/2*x)*2^(1/2)+1/3*3^(1/2))/(tanh(1/2*x)^2-1/3*3^(3/4)*tanh(1/2*x)*2^(1/2)+1/3*3^(1/2)))+1/36*3^(3/4)*2^(1/2)*arctan(2^(1/2)*3^(1/4)*tanh(1/2*x)+1)-1/12*2^(1/2)*3^(1/4)*arctan(2^(1/2)*3^(1/4)*tanh(1/2*x)-1)-1/24*2^(1/2)*3^(1/4)*ln((tanh(1/2*x)^2-1/3*3^(3/4)*tanh(1/2*x)*2^(1/2)+1/3*3^(1/2))/(tanh(1/2*x)^2+1/3*3^(3/4)*tanh(1/2*x)*2^(1/2)+1/3*3^(1/2)))-1/12*2^(1/2)*3^(1/4)*arctan(2^(1/2)*3^(1/4)*tanh(1/2*x)+1)","B"
75,1,136,50,0.125000," ","int(1/(1-cosh(x)^8),x)","\frac{\tanh \left(\frac{x}{2}\right)}{8}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(2 \textit{\_Z}^{4}-2 \textit{\_Z}^{2}+1\right)}{\sum}\textit{\_R} \ln \left(2 \tanh \left(\frac{x}{2}\right) \textit{\_R} +\tanh^{2}\left(\frac{x}{2}\right)+1\right)\right)}{8}+\frac{1}{8 \tanh \left(\frac{x}{2}\right)}+\frac{\sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)+\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}{\tanh^{2}\left(\frac{x}{2}\right)-\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}\right)}{32}-\frac{\sqrt{2}\, \ln \left(\frac{\tanh^{2}\left(\frac{x}{2}\right)-\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}{\tanh^{2}\left(\frac{x}{2}\right)+\sqrt{2}\, \tanh \left(\frac{x}{2}\right)+1}\right)}{32}"," ",0,"1/8*tanh(1/2*x)+1/8*sum(_R*ln(2*tanh(1/2*x)*_R+tanh(1/2*x)^2+1),_R=RootOf(2*_Z^4-2*_Z^2+1))+1/8/tanh(1/2*x)+1/32*2^(1/2)*ln((tanh(1/2*x)^2+2^(1/2)*tanh(1/2*x)+1)/(tanh(1/2*x)^2-2^(1/2)*tanh(1/2*x)+1))-1/32*2^(1/2)*ln((tanh(1/2*x)^2-2^(1/2)*tanh(1/2*x)+1)/(tanh(1/2*x)^2+2^(1/2)*tanh(1/2*x)+1))","C"
76,1,14,13,0.093000," ","int(tanh(x)/(1+cosh(x)^2),x)","\ln \left(\cosh \left(x \right)\right)-\frac{\ln \left(1+\cosh^{2}\left(x \right)\right)}{2}"," ",0,"ln(cosh(x))-1/2*ln(1+cosh(x)^2)","A"
77,1,42,31,0.082000," ","int((a+b*cosh(x)^2)^(1/2)*tanh(x),x)","\sqrt{a +b \left(\cosh^{2}\left(x \right)\right)}-\sqrt{a}\, \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\cosh^{2}\left(x \right)\right)}}{\cosh \left(x \right)}\right)"," ",0,"(a+b*cosh(x)^2)^(1/2)-a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*cosh(x)^2)^(1/2))/cosh(x))","A"
78,1,31,20,0.100000," ","int(tanh(x)/(a+b*cosh(x)^2)^(1/2),x)","-\frac{\ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\cosh^{2}\left(x \right)\right)}}{\cosh \left(x \right)}\right)}{\sqrt{a}}"," ",0,"-1/a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*cosh(x)^2)^(1/2))/cosh(x))","A"
79,1,12,11,0.094000," ","int(tanh(x)/(1+cosh(x)^2)^(1/2),x)","-\arctanh \left(\frac{1}{\sqrt{1+\cosh^{2}\left(x \right)}}\right)"," ",0,"-arctanh(1/(1+cosh(x)^2)^(1/2))","A"
80,1,12,11,0.174000," ","int(tanh(x)/(1-cosh(x)^2)^(1/2),x)","-\arctanh \left(\frac{1}{\sqrt{-\left(\sinh^{2}\left(x \right)\right)}}\right)"," ",0,"-arctanh(1/(-sinh(x)^2)^(1/2))","A"
81,1,150,112,0.140000," ","int(tanh(x)^3/(a+b*cosh(x)^3),x)","-\frac{\munderset{\textit{\_R} =\RootOf \left(\left(a -b \right) \textit{\_Z}^{3}+\left(-3 a -3 b \right) \textit{\_Z}^{2}+\left(3 a -3 b \right) \textit{\_Z} -a -b \right)}{\sum}\frac{\left(\textit{\_R}^{2} a -\textit{\_R}^{2} b -2 \textit{\_R} a -4 \textit{\_R} b +a +b \right) \ln \left(\tanh^{2}\left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{2} a -\textit{\_R}^{2} b -2 \textit{\_R} a -2 \textit{\_R} b +a -b}}{3 a}-\frac{2}{a \left(\tanh^{2}\left(\frac{x}{2}\right)+1\right)}+\frac{2}{a \left(\tanh^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{\ln \left(\tanh^{2}\left(\frac{x}{2}\right)+1\right)}{a}"," ",0,"-1/3/a*sum((_R^2*a-_R^2*b-2*_R*a-4*_R*b+a+b)/(_R^2*a-_R^2*b-2*_R*a-2*_R*b+a-b)*ln(tanh(1/2*x)^2-_R),_R=RootOf((a-b)*_Z^3+(-3*a-3*b)*_Z^2+(3*a-3*b)*_Z-a-b))-2/a/(tanh(1/2*x)^2+1)+2/a/(tanh(1/2*x)^2+1)^2+1/a*ln(tanh(1/2*x)^2+1)","C"
82,1,21,20,0.111000," ","int(tanh(x)/(a+b*cosh(x)^3)^(1/2),x)","-\frac{2 \arctanh \left(\frac{\sqrt{a +b \left(\cosh^{3}\left(x \right)\right)}}{\sqrt{a}}\right)}{3 \sqrt{a}}"," ",0,"-2/3*arctanh((a+b*cosh(x)^3)^(1/2)/a^(1/2))/a^(1/2)","A"
83,1,34,33,0.087000," ","int((a+b*cosh(x)^3)^(1/2)*tanh(x),x)","-\frac{2 \arctanh \left(\frac{\sqrt{a +b \left(\cosh^{3}\left(x \right)\right)}}{\sqrt{a}}\right) \sqrt{a}}{3}+\frac{2 \sqrt{a +b \left(\cosh^{3}\left(x \right)\right)}}{3}"," ",0,"-2/3*arctanh((a+b*cosh(x)^3)^(1/2)/a^(1/2))*a^(1/2)+2/3*(a+b*cosh(x)^3)^(1/2)","A"
84,1,24,23,0.072000," ","int(tanh(x)/(a+b*cosh(x)^n)^(1/2),x)","-\frac{2 \arctanh \left(\frac{\sqrt{a +b \left(\cosh^{n}\left(x \right)\right)}}{\sqrt{a}}\right)}{n \sqrt{a}}"," ",0,"-2*arctanh((a+b*cosh(x)^n)^(1/2)/a^(1/2))/n/a^(1/2)","A"
85,1,38,39,0.046000," ","int((a+b*cosh(x)^n)^(1/2)*tanh(x),x)","\frac{2 \sqrt{a +b \left(\cosh^{n}\left(x \right)\right)}-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{a +b \left(\cosh^{n}\left(x \right)\right)}}{\sqrt{a}}\right)}{n}"," ",0,"1/n*(2*(a+b*cosh(x)^n)^(1/2)-2*a^(1/2)*arctanh((a+b*cosh(x)^n)^(1/2)/a^(1/2)))","A"