1,1,96,67,0.267000," ","int(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^2),x)","\frac{a \left(\left(\frac{\left(\sinh^{3}\left(d x +c \right)\right)}{4}-\frac{3 \sinh \left(d x +c \right)}{8}\right) \cosh \left(d x +c \right)+\frac{3 d x}{8}+\frac{3 c}{8}\right)+b \left(\frac{\sinh^{5}\left(d x +c \right)}{4 \cosh \left(d x +c \right)}-\frac{5 \left(\sinh^{3}\left(d x +c \right)\right)}{8 \cosh \left(d x +c \right)}+\frac{15 d x}{8}+\frac{15 c}{8}-\frac{15 \tanh \left(d x +c \right)}{8}\right)}{d}"," ",0,"1/d*(a*((1/4*sinh(d*x+c)^3-3/8*sinh(d*x+c))*cosh(d*x+c)+3/8*d*x+3/8*c)+b*(1/4*sinh(d*x+c)^5/cosh(d*x+c)-5/8*sinh(d*x+c)^3/cosh(d*x+c)+15/8*d*x+15/8*c-15/8*tanh(d*x+c)))","A"
2,1,75,45,0.263000," ","int(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^2),x)","\frac{a \left(-\frac{2}{3}+\frac{\left(\sinh^{2}\left(d x +c \right)\right)}{3}\right) \cosh \left(d x +c \right)+b \left(\frac{\sinh^{4}\left(d x +c \right)}{3 \cosh \left(d x +c \right)}-\frac{4 \left(\sinh^{2}\left(d x +c \right)\right)}{3 \cosh \left(d x +c \right)}-\frac{8}{3 \cosh \left(d x +c \right)}\right)}{d}"," ",0,"1/d*(a*(-2/3+1/3*sinh(d*x+c)^2)*cosh(d*x+c)+b*(1/3*sinh(d*x+c)^4/cosh(d*x+c)-4/3*sinh(d*x+c)^2/cosh(d*x+c)-8/3/cosh(d*x+c)))","A"
3,1,66,40,0.176000," ","int(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^2),x)","\frac{a \left(\frac{\cosh \left(d x +c \right) \sinh \left(d x +c \right)}{2}-\frac{d x}{2}-\frac{c}{2}\right)+b \left(\frac{\sinh^{3}\left(d x +c \right)}{2 \cosh \left(d x +c \right)}-\frac{3 d x}{2}-\frac{3 c}{2}+\frac{3 \tanh \left(d x +c \right)}{2}\right)}{d}"," ",0,"1/d*(a*(1/2*cosh(d*x+c)*sinh(d*x+c)-1/2*d*x-1/2*c)+b*(1/2*sinh(d*x+c)^3/cosh(d*x+c)-3/2*d*x-3/2*c+3/2*tanh(d*x+c)))","A"
4,1,44,25,0.171000," ","int(sinh(d*x+c)*(a+b*tanh(d*x+c)^2),x)","\frac{a \cosh \left(d x +c \right)+b \left(\frac{\sinh^{2}\left(d x +c \right)}{\cosh \left(d x +c \right)}+\frac{2}{\cosh \left(d x +c \right)}\right)}{d}"," ",0,"1/d*(a*cosh(d*x+c)+b*(sinh(d*x+c)^2/cosh(d*x+c)+2/cosh(d*x+c)))","A"
5,1,27,26,0.249000," ","int(csch(d*x+c)*(a+b*tanh(d*x+c)^2),x)","\frac{-2 a \arctanh \left({\mathrm e}^{d x +c}\right)-\frac{b}{\cosh \left(d x +c \right)}}{d}"," ",0,"1/d*(-2*a*arctanh(exp(d*x+c))-b/cosh(d*x+c))","A"
6,1,23,24,0.333000," ","int(csch(d*x+c)^2*(a+b*tanh(d*x+c)^2),x)","\frac{-\coth \left(d x +c \right) a +b \tanh \left(d x +c \right)}{d}"," ",0,"1/d*(-coth(d*x+c)*a+b*tanh(d*x+c))","A"
7,1,50,47,0.345000," ","int(csch(d*x+c)^3*(a+b*tanh(d*x+c)^2),x)","\frac{a \left(-\frac{\mathrm{csch}\left(d x +c \right) \coth \left(d x +c \right)}{2}+\arctanh \left({\mathrm e}^{d x +c}\right)\right)+b \left(\frac{1}{\cosh \left(d x +c \right)}-2 \arctanh \left({\mathrm e}^{d x +c}\right)\right)}{d}"," ",0,"1/d*(a*(-1/2*csch(d*x+c)*coth(d*x+c)+arctanh(exp(d*x+c)))+b*(1/cosh(d*x+c)-2*arctanh(exp(d*x+c))))","A"
8,1,55,42,0.371000," ","int(csch(d*x+c)^4*(a+b*tanh(d*x+c)^2),x)","\frac{a \left(\frac{2}{3}-\frac{\mathrm{csch}\left(d x +c \right)^{2}}{3}\right) \coth \left(d x +c \right)+b \left(-\frac{1}{\sinh \left(d x +c \right) \cosh \left(d x +c \right)}-2 \tanh \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a*(2/3-1/3*csch(d*x+c)^2)*coth(d*x+c)+b*(-1/sinh(d*x+c)/cosh(d*x+c)-2*tanh(d*x+c)))","A"
9,1,166,108,0.293000," ","int(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \left(\left(\frac{\left(\sinh^{3}\left(d x +c \right)\right)}{4}-\frac{3 \sinh \left(d x +c \right)}{8}\right) \cosh \left(d x +c \right)+\frac{3 d x}{8}+\frac{3 c}{8}\right)+2 a b \left(\frac{\sinh^{5}\left(d x +c \right)}{4 \cosh \left(d x +c \right)}-\frac{5 \left(\sinh^{3}\left(d x +c \right)\right)}{8 \cosh \left(d x +c \right)}+\frac{15 d x}{8}+\frac{15 c}{8}-\frac{15 \tanh \left(d x +c \right)}{8}\right)+b^{2} \left(\frac{\sinh^{7}\left(d x +c \right)}{4 \cosh \left(d x +c \right)^{3}}-\frac{7 \left(\sinh^{5}\left(d x +c \right)\right)}{8 \cosh \left(d x +c \right)^{3}}+\frac{35 d x}{8}+\frac{35 c}{8}-\frac{35 \tanh \left(d x +c \right)}{8}-\frac{35 \left(\tanh^{3}\left(d x +c \right)\right)}{24}\right)}{d}"," ",0,"1/d*(a^2*((1/4*sinh(d*x+c)^3-3/8*sinh(d*x+c))*cosh(d*x+c)+3/8*d*x+3/8*c)+2*a*b*(1/4*sinh(d*x+c)^5/cosh(d*x+c)-5/8*sinh(d*x+c)^3/cosh(d*x+c)+15/8*d*x+15/8*c-15/8*tanh(d*x+c))+b^2*(1/4*sinh(d*x+c)^7/cosh(d*x+c)^3-7/8*sinh(d*x+c)^5/cosh(d*x+c)^3+35/8*d*x+35/8*c-35/8*tanh(d*x+c)-35/24*tanh(d*x+c)^3))","A"
10,1,148,73,0.293000," ","int(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \left(-\frac{2}{3}+\frac{\left(\sinh^{2}\left(d x +c \right)\right)}{3}\right) \cosh \left(d x +c \right)+2 a b \left(\frac{\sinh^{4}\left(d x +c \right)}{3 \cosh \left(d x +c \right)}-\frac{4 \left(\sinh^{2}\left(d x +c \right)\right)}{3 \cosh \left(d x +c \right)}-\frac{8}{3 \cosh \left(d x +c \right)}\right)+b^{2} \left(\frac{\sinh^{6}\left(d x +c \right)}{3 \cosh \left(d x +c \right)^{3}}-\frac{2 \left(\sinh^{4}\left(d x +c \right)\right)}{\cosh \left(d x +c \right)^{3}}-\frac{8 \left(\sinh^{2}\left(d x +c \right)\right)}{\cosh \left(d x +c \right)^{3}}-\frac{16}{3 \cosh \left(d x +c \right)^{3}}\right)}{d}"," ",0,"1/d*(a^2*(-2/3+1/3*sinh(d*x+c)^2)*cosh(d*x+c)+2*a*b*(1/3*sinh(d*x+c)^4/cosh(d*x+c)-4/3*sinh(d*x+c)^2/cosh(d*x+c)-8/3/cosh(d*x+c))+b^2*(1/3*sinh(d*x+c)^6/cosh(d*x+c)^3-2*sinh(d*x+c)^4/cosh(d*x+c)^3-8*sinh(d*x+c)^2/cosh(d*x+c)^3-16/3/cosh(d*x+c)^3))","B"
11,1,118,71,0.210000," ","int(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \left(\frac{\cosh \left(d x +c \right) \sinh \left(d x +c \right)}{2}-\frac{d x}{2}-\frac{c}{2}\right)+2 a b \left(\frac{\sinh^{3}\left(d x +c \right)}{2 \cosh \left(d x +c \right)}-\frac{3 d x}{2}-\frac{3 c}{2}+\frac{3 \tanh \left(d x +c \right)}{2}\right)+b^{2} \left(\frac{\sinh^{5}\left(d x +c \right)}{2 \cosh \left(d x +c \right)^{3}}-\frac{5 d x}{2}-\frac{5 c}{2}+\frac{5 \tanh \left(d x +c \right)}{2}+\frac{5 \left(\tanh^{3}\left(d x +c \right)\right)}{6}\right)}{d}"," ",0,"1/d*(a^2*(1/2*cosh(d*x+c)*sinh(d*x+c)-1/2*d*x-1/2*c)+2*a*b*(1/2*sinh(d*x+c)^3/cosh(d*x+c)-3/2*d*x-3/2*c+3/2*tanh(d*x+c))+b^2*(1/2*sinh(d*x+c)^5/cosh(d*x+c)^3-5/2*d*x-5/2*c+5/2*tanh(d*x+c)+5/6*tanh(d*x+c)^3))","A"
12,1,98,47,0.210000," ","int(sinh(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \cosh \left(d x +c \right)+2 a b \left(\frac{\sinh^{2}\left(d x +c \right)}{\cosh \left(d x +c \right)}+\frac{2}{\cosh \left(d x +c \right)}\right)+b^{2} \left(\frac{\sinh^{4}\left(d x +c \right)}{\cosh \left(d x +c \right)^{3}}+\frac{4 \left(\sinh^{2}\left(d x +c \right)\right)}{\cosh \left(d x +c \right)^{3}}+\frac{8}{3 \cosh \left(d x +c \right)^{3}}\right)}{d}"," ",0,"1/d*(a^2*cosh(d*x+c)+2*a*b*(sinh(d*x+c)^2/cosh(d*x+c)+2/cosh(d*x+c))+b^2*(sinh(d*x+c)^4/cosh(d*x+c)^3+4*sinh(d*x+c)^2/cosh(d*x+c)^3+8/3/cosh(d*x+c)^3))","B"
13,1,63,49,0.243000," ","int(csch(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x)","\frac{-2 a^{2} \arctanh \left({\mathrm e}^{d x +c}\right)-\frac{2 a b}{\cosh \left(d x +c \right)}+b^{2} \left(-\frac{\sinh^{2}\left(d x +c \right)}{\cosh \left(d x +c \right)^{3}}-\frac{2}{3 \cosh \left(d x +c \right)^{3}}\right)}{d}"," ",0,"1/d*(-2*a^2*arctanh(exp(d*x+c))-2*a*b/cosh(d*x+c)+b^2*(-sinh(d*x+c)^2/cosh(d*x+c)^3-2/3/cosh(d*x+c)^3))","A"
14,1,68,44,0.431000," ","int(csch(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x)","\frac{-a^{2} \coth \left(d x +c \right)+2 a b \tanh \left(d x +c \right)+b^{2} \left(-\frac{\sinh \left(d x +c \right)}{2 \cosh \left(d x +c \right)^{3}}+\frac{\left(\frac{2}{3}+\frac{\mathrm{sech}\left(d x +c \right)^{2}}{3}\right) \tanh \left(d x +c \right)}{2}\right)}{d}"," ",0,"1/d*(-a^2*coth(d*x+c)+2*a*b*tanh(d*x+c)+b^2*(-1/2*sinh(d*x+c)/cosh(d*x+c)^3+1/2*(2/3+1/3*sech(d*x+c)^2)*tanh(d*x+c)))","A"
15,1,67,74,0.382000," ","int(csch(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \left(-\frac{\mathrm{csch}\left(d x +c \right) \coth \left(d x +c \right)}{2}+\arctanh \left({\mathrm e}^{d x +c}\right)\right)+2 a b \left(\frac{1}{\cosh \left(d x +c \right)}-2 \arctanh \left({\mathrm e}^{d x +c}\right)\right)-\frac{b^{2}}{3 \cosh \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(a^2*(-1/2*csch(d*x+c)*coth(d*x+c)+arctanh(exp(d*x+c)))+2*a*b*(1/cosh(d*x+c)-2*arctanh(exp(d*x+c)))-1/3*b^2/cosh(d*x+c)^3)","A"
16,1,81,68,0.455000," ","int(csch(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \left(\frac{2}{3}-\frac{\mathrm{csch}\left(d x +c \right)^{2}}{3}\right) \coth \left(d x +c \right)+2 a b \left(-\frac{1}{\sinh \left(d x +c \right) \cosh \left(d x +c \right)}-2 \tanh \left(d x +c \right)\right)+b^{2} \left(\frac{2}{3}+\frac{\mathrm{sech}\left(d x +c \right)^{2}}{3}\right) \tanh \left(d x +c \right)}{d}"," ",0,"1/d*(a^2*(2/3-1/3*csch(d*x+c)^2)*coth(d*x+c)+2*a*b*(-1/sinh(d*x+c)/cosh(d*x+c)-2*tanh(d*x+c))+b^2*(2/3+1/3*sech(d*x+c)^2)*tanh(d*x+c))","A"
17,1,246,170,0.357000," ","int(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \left(\left(\frac{\left(\sinh^{3}\left(d x +c \right)\right)}{4}-\frac{3 \sinh \left(d x +c \right)}{8}\right) \cosh \left(d x +c \right)+\frac{3 d x}{8}+\frac{3 c}{8}\right)+3 a^{2} b \left(\frac{\sinh^{5}\left(d x +c \right)}{4 \cosh \left(d x +c \right)}-\frac{5 \left(\sinh^{3}\left(d x +c \right)\right)}{8 \cosh \left(d x +c \right)}+\frac{15 d x}{8}+\frac{15 c}{8}-\frac{15 \tanh \left(d x +c \right)}{8}\right)+3 a \,b^{2} \left(\frac{\sinh^{7}\left(d x +c \right)}{4 \cosh \left(d x +c \right)^{3}}-\frac{7 \left(\sinh^{5}\left(d x +c \right)\right)}{8 \cosh \left(d x +c \right)^{3}}+\frac{35 d x}{8}+\frac{35 c}{8}-\frac{35 \tanh \left(d x +c \right)}{8}-\frac{35 \left(\tanh^{3}\left(d x +c \right)\right)}{24}\right)+b^{3} \left(\frac{\sinh^{9}\left(d x +c \right)}{4 \cosh \left(d x +c \right)^{5}}-\frac{9 \left(\sinh^{7}\left(d x +c \right)\right)}{8 \cosh \left(d x +c \right)^{5}}+\frac{63 d x}{8}+\frac{63 c}{8}-\frac{63 \tanh \left(d x +c \right)}{8}-\frac{21 \left(\tanh^{3}\left(d x +c \right)\right)}{8}-\frac{63 \left(\tanh^{5}\left(d x +c \right)\right)}{40}\right)}{d}"," ",0,"1/d*(a^3*((1/4*sinh(d*x+c)^3-3/8*sinh(d*x+c))*cosh(d*x+c)+3/8*d*x+3/8*c)+3*a^2*b*(1/4*sinh(d*x+c)^5/cosh(d*x+c)-5/8*sinh(d*x+c)^3/cosh(d*x+c)+15/8*d*x+15/8*c-15/8*tanh(d*x+c))+3*a*b^2*(1/4*sinh(d*x+c)^7/cosh(d*x+c)^3-7/8*sinh(d*x+c)^5/cosh(d*x+c)^3+35/8*d*x+35/8*c-35/8*tanh(d*x+c)-35/24*tanh(d*x+c)^3)+b^3*(1/4*sinh(d*x+c)^9/cosh(d*x+c)^5-9/8*sinh(d*x+c)^7/cosh(d*x+c)^5+63/8*d*x+63/8*c-63/8*tanh(d*x+c)-21/8*tanh(d*x+c)^3-63/40*tanh(d*x+c)^5))","A"
18,1,239,99,0.319000," ","int(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \left(-\frac{2}{3}+\frac{\left(\sinh^{2}\left(d x +c \right)\right)}{3}\right) \cosh \left(d x +c \right)+3 a^{2} b \left(\frac{\sinh^{4}\left(d x +c \right)}{3 \cosh \left(d x +c \right)}-\frac{4 \left(\sinh^{2}\left(d x +c \right)\right)}{3 \cosh \left(d x +c \right)}-\frac{8}{3 \cosh \left(d x +c \right)}\right)+3 a \,b^{2} \left(\frac{\sinh^{6}\left(d x +c \right)}{3 \cosh \left(d x +c \right)^{3}}-\frac{2 \left(\sinh^{4}\left(d x +c \right)\right)}{\cosh \left(d x +c \right)^{3}}-\frac{8 \left(\sinh^{2}\left(d x +c \right)\right)}{\cosh \left(d x +c \right)^{3}}-\frac{16}{3 \cosh \left(d x +c \right)^{3}}\right)+b^{3} \left(\frac{\sinh^{8}\left(d x +c \right)}{3 \cosh \left(d x +c \right)^{5}}-\frac{8 \left(\sinh^{6}\left(d x +c \right)\right)}{3 \cosh \left(d x +c \right)^{5}}-\frac{16 \left(\sinh^{4}\left(d x +c \right)\right)}{\cosh \left(d x +c \right)^{5}}-\frac{64 \left(\sinh^{2}\left(d x +c \right)\right)}{3 \cosh \left(d x +c \right)^{5}}-\frac{128}{15 \cosh \left(d x +c \right)^{5}}\right)}{d}"," ",0,"1/d*(a^3*(-2/3+1/3*sinh(d*x+c)^2)*cosh(d*x+c)+3*a^2*b*(1/3*sinh(d*x+c)^4/cosh(d*x+c)-4/3*sinh(d*x+c)^2/cosh(d*x+c)-8/3/cosh(d*x+c))+3*a*b^2*(1/3*sinh(d*x+c)^6/cosh(d*x+c)^3-2*sinh(d*x+c)^4/cosh(d*x+c)^3-8*sinh(d*x+c)^2/cosh(d*x+c)^3-16/3/cosh(d*x+c)^3)+b^3*(1/3*sinh(d*x+c)^8/cosh(d*x+c)^5-8/3*sinh(d*x+c)^6/cosh(d*x+c)^5-16*sinh(d*x+c)^4/cosh(d*x+c)^5-64/3*sinh(d*x+c)^2/cosh(d*x+c)^5-128/15/cosh(d*x+c)^5))","B"
19,1,180,112,0.234000," ","int(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \left(\frac{\cosh \left(d x +c \right) \sinh \left(d x +c \right)}{2}-\frac{d x}{2}-\frac{c}{2}\right)+3 a^{2} b \left(\frac{\sinh^{3}\left(d x +c \right)}{2 \cosh \left(d x +c \right)}-\frac{3 d x}{2}-\frac{3 c}{2}+\frac{3 \tanh \left(d x +c \right)}{2}\right)+3 a \,b^{2} \left(\frac{\sinh^{5}\left(d x +c \right)}{2 \cosh \left(d x +c \right)^{3}}-\frac{5 d x}{2}-\frac{5 c}{2}+\frac{5 \tanh \left(d x +c \right)}{2}+\frac{5 \left(\tanh^{3}\left(d x +c \right)\right)}{6}\right)+b^{3} \left(\frac{\sinh^{7}\left(d x +c \right)}{2 \cosh \left(d x +c \right)^{5}}-\frac{7 d x}{2}-\frac{7 c}{2}+\frac{7 \tanh \left(d x +c \right)}{2}+\frac{7 \left(\tanh^{3}\left(d x +c \right)\right)}{6}+\frac{7 \left(\tanh^{5}\left(d x +c \right)\right)}{10}\right)}{d}"," ",0,"1/d*(a^3*(1/2*cosh(d*x+c)*sinh(d*x+c)-1/2*d*x-1/2*c)+3*a^2*b*(1/2*sinh(d*x+c)^3/cosh(d*x+c)-3/2*d*x-3/2*c+3/2*tanh(d*x+c))+3*a*b^2*(1/2*sinh(d*x+c)^5/cosh(d*x+c)^3-5/2*d*x-5/2*c+5/2*tanh(d*x+c)+5/6*tanh(d*x+c)^3)+b^3*(1/2*sinh(d*x+c)^7/cosh(d*x+c)^5-7/2*d*x-7/2*c+7/2*tanh(d*x+c)+7/6*tanh(d*x+c)^3+7/10*tanh(d*x+c)^5))","A"
20,1,170,68,0.230000," ","int(sinh(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \cosh \left(d x +c \right)+3 a^{2} b \left(\frac{\sinh^{2}\left(d x +c \right)}{\cosh \left(d x +c \right)}+\frac{2}{\cosh \left(d x +c \right)}\right)+3 a \,b^{2} \left(\frac{\sinh^{4}\left(d x +c \right)}{\cosh \left(d x +c \right)^{3}}+\frac{4 \left(\sinh^{2}\left(d x +c \right)\right)}{\cosh \left(d x +c \right)^{3}}+\frac{8}{3 \cosh \left(d x +c \right)^{3}}\right)+b^{3} \left(\frac{\sinh^{6}\left(d x +c \right)}{\cosh \left(d x +c \right)^{5}}+\frac{6 \left(\sinh^{4}\left(d x +c \right)\right)}{\cosh \left(d x +c \right)^{5}}+\frac{8 \left(\sinh^{2}\left(d x +c \right)\right)}{\cosh \left(d x +c \right)^{5}}+\frac{16}{5 \cosh \left(d x +c \right)^{5}}\right)}{d}"," ",0,"1/d*(a^3*cosh(d*x+c)+3*a^2*b*(sinh(d*x+c)^2/cosh(d*x+c)+2/cosh(d*x+c))+3*a*b^2*(sinh(d*x+c)^4/cosh(d*x+c)^3+4*sinh(d*x+c)^2/cosh(d*x+c)^3+8/3/cosh(d*x+c)^3)+b^3*(sinh(d*x+c)^6/cosh(d*x+c)^5+6*sinh(d*x+c)^4/cosh(d*x+c)^5+8*sinh(d*x+c)^2/cosh(d*x+c)^5+16/5/cosh(d*x+c)^5))","B"
21,1,118,80,0.245000," ","int(csch(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x)","\frac{-2 a^{3} \arctanh \left({\mathrm e}^{d x +c}\right)-\frac{3 a^{2} b}{\cosh \left(d x +c \right)}+3 a \,b^{2} \left(-\frac{\sinh^{2}\left(d x +c \right)}{\cosh \left(d x +c \right)^{3}}-\frac{2}{3 \cosh \left(d x +c \right)^{3}}\right)+b^{3} \left(-\frac{\sinh^{4}\left(d x +c \right)}{\cosh \left(d x +c \right)^{5}}-\frac{4 \left(\sinh^{2}\left(d x +c \right)\right)}{3 \cosh \left(d x +c \right)^{5}}-\frac{8}{15 \cosh \left(d x +c \right)^{5}}\right)}{d}"," ",0,"1/d*(-2*a^3*arctanh(exp(d*x+c))-3*a^2*b/cosh(d*x+c)+3*a*b^2*(-sinh(d*x+c)^2/cosh(d*x+c)^3-2/3/cosh(d*x+c)^3)+b^3*(-sinh(d*x+c)^4/cosh(d*x+c)^5-4/3*sinh(d*x+c)^2/cosh(d*x+c)^5-8/15/cosh(d*x+c)^5))","A"
22,1,141,62,0.510000," ","int(csch(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x)","\frac{-a^{3} \coth \left(d x +c \right)+3 a^{2} b \tanh \left(d x +c \right)+3 a \,b^{2} \left(-\frac{\sinh \left(d x +c \right)}{2 \cosh \left(d x +c \right)^{3}}+\frac{\left(\frac{2}{3}+\frac{\mathrm{sech}\left(d x +c \right)^{2}}{3}\right) \tanh \left(d x +c \right)}{2}\right)+b^{3} \left(-\frac{\sinh^{3}\left(d x +c \right)}{2 \cosh \left(d x +c \right)^{5}}-\frac{3 \sinh \left(d x +c \right)}{8 \cosh \left(d x +c \right)^{5}}+\frac{3 \left(\frac{8}{15}+\frac{\mathrm{sech}\left(d x +c \right)^{4}}{5}+\frac{4 \mathrm{sech}\left(d x +c \right)^{2}}{15}\right) \tanh \left(d x +c \right)}{8}\right)}{d}"," ",0,"1/d*(-a^3*coth(d*x+c)+3*a^2*b*tanh(d*x+c)+3*a*b^2*(-1/2*sinh(d*x+c)/cosh(d*x+c)^3+1/2*(2/3+1/3*sech(d*x+c)^2)*tanh(d*x+c))+b^3*(-1/2*sinh(d*x+c)^3/cosh(d*x+c)^5-3/8*sinh(d*x+c)/cosh(d*x+c)^5+3/8*(8/15+1/5*sech(d*x+c)^4+4/15*sech(d*x+c)^2)*tanh(d*x+c)))","B"
23,1,103,142,0.391000," ","int(csch(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \left(-\frac{\mathrm{csch}\left(d x +c \right) \coth \left(d x +c \right)}{2}+\arctanh \left({\mathrm e}^{d x +c}\right)\right)+3 a^{2} b \left(\frac{1}{\cosh \left(d x +c \right)}-2 \arctanh \left({\mathrm e}^{d x +c}\right)\right)-\frac{a \,b^{2}}{\cosh \left(d x +c \right)^{3}}+b^{3} \left(-\frac{\sinh^{2}\left(d x +c \right)}{3 \cosh \left(d x +c \right)^{5}}-\frac{2}{15 \cosh \left(d x +c \right)^{5}}\right)}{d}"," ",0,"1/d*(a^3*(-1/2*csch(d*x+c)*coth(d*x+c)+arctanh(exp(d*x+c)))+3*a^2*b*(1/cosh(d*x+c)-2*arctanh(exp(d*x+c)))-a*b^2/cosh(d*x+c)^3+b^3*(-1/3*sinh(d*x+c)^2/cosh(d*x+c)^5-2/15/cosh(d*x+c)^5))","A"
24,1,136,92,0.529000," ","int(csch(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \left(\frac{2}{3}-\frac{\mathrm{csch}\left(d x +c \right)^{2}}{3}\right) \coth \left(d x +c \right)+3 a^{2} b \left(-\frac{1}{\sinh \left(d x +c \right) \cosh \left(d x +c \right)}-2 \tanh \left(d x +c \right)\right)+3 a \,b^{2} \left(\frac{2}{3}+\frac{\mathrm{sech}\left(d x +c \right)^{2}}{3}\right) \tanh \left(d x +c \right)+b^{3} \left(-\frac{\sinh \left(d x +c \right)}{4 \cosh \left(d x +c \right)^{5}}+\frac{\left(\frac{8}{15}+\frac{\mathrm{sech}\left(d x +c \right)^{4}}{5}+\frac{4 \mathrm{sech}\left(d x +c \right)^{2}}{15}\right) \tanh \left(d x +c \right)}{4}\right)}{d}"," ",0,"1/d*(a^3*(2/3-1/3*csch(d*x+c)^2)*coth(d*x+c)+3*a^2*b*(-1/sinh(d*x+c)/cosh(d*x+c)-2*tanh(d*x+c))+3*a*b^2*(2/3+1/3*sech(d*x+c)^2)*tanh(d*x+c)+b^3*(-1/4*sinh(d*x+c)/cosh(d*x+c)^5+1/4*(8/15+1/5*sech(d*x+c)^4+4/15*sech(d*x+c)^2)*tanh(d*x+c)))","A"
25,1,865,104,0.344000," ","int(sinh(d*x+c)^4/(a+b*tanh(d*x+c)^2),x)","\frac{8}{d \left(32 a +32 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}+\frac{32}{d \left(64 a +64 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{a}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{3 b}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{3 a}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{b}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a^{2}}{8 d \left(a +b \right)^{3}}+\frac{3 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a b}{4 d \left(a +b \right)^{3}}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) b^{2}}{8 d \left(a +b \right)^{3}}-\frac{8}{d \left(32 a +32 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{32}{d \left(64 a +64 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{a}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3 b}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3 a}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{b}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a^{2}}{8 d \left(a +b \right)^{3}}-\frac{3 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a b}{4 d \left(a +b \right)^{3}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) b^{2}}{8 d \left(a +b \right)^{3}}-\frac{a^{3} b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{a^{2} b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{a^{2} b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{a^{3} b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{a^{2} b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{a^{2} b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"8/d/(32*a+32*b)/(tanh(1/2*d*x+1/2*c)-1)^4+32/d/(64*a+64*b)/(tanh(1/2*d*x+1/2*c)-1)^3-1/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)^2*a+3/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)^2*b-3/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)*a+1/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)*b-3/8/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)-1)*a^2+3/4/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)-1)*a*b+1/8/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)-1)*b^2-8/d/(32*a+32*b)/(tanh(1/2*d*x+1/2*c)+1)^4+32/d/(64*a+64*b)/(tanh(1/2*d*x+1/2*c)+1)^3+1/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)^2*a-3/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)^2*b-3/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)*a+1/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)*b+3/8/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)+1)*a^2-3/4/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)+1)*a*b-1/8/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)+1)*b^2-1/d*a^3*b/(a+b)^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*a^2*b/(a+b)^3/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d*a^2*b^2/(a+b)^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d*a^3*b/(a+b)^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d*a^2*b/(a+b)^3/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d*a^2*b^2/(a+b)^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
26,1,202,65,0.301000," ","int(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^2),x)","\frac{-\frac{16}{3 \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3} \left(16 a +16 b \right)}-\frac{8}{\left(16 a +16 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{-a +b}{2 \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{8}{\left(16 a +16 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{16}{3 \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(16 a +16 b \right)}-\frac{a -b}{2 \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{a b \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{\left(a +b \right)^{2} \sqrt{a b +b^{2}}}}{d}"," ",0,"1/d*(-16/3/(tanh(1/2*d*x+1/2*c)-1)^3/(16*a+16*b)-8/(16*a+16*b)/(tanh(1/2*d*x+1/2*c)-1)^2-1/2/(a+b)^2*(-a+b)/(tanh(1/2*d*x+1/2*c)-1)-8/(16*a+16*b)/(tanh(1/2*d*x+1/2*c)+1)^2+16/3/(tanh(1/2*d*x+1/2*c)+1)^3/(16*a+16*b)-1/2*(a-b)/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)+a*b/(a+b)^2/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2)))","B"
27,1,605,66,0.316000," ","int(sinh(d*x+c)^2/(a+b*tanh(d*x+c)^2),x)","\frac{4}{d \left(8 a +8 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{8}{d \left(16 a +16 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a}{2 d \left(a +b \right)^{2}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) b}{2 d \left(a +b \right)^{2}}-\frac{4}{d \left(8 a +8 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{8}{d \left(16 a +16 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a}{2 d \left(a +b \right)^{2}}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) b}{2 d \left(a +b \right)^{2}}+\frac{a^{2} b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{a b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{a \,b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{a^{2} b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{a b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{a \,b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"4/d/(8*a+8*b)/(tanh(1/2*d*x+1/2*c)-1)^2+8/d/(16*a+16*b)/(tanh(1/2*d*x+1/2*c)-1)+1/2/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)-1)*a-1/2/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)-1)*b-4/d/(8*a+8*b)/(tanh(1/2*d*x+1/2*c)+1)^2+8/d/(16*a+16*b)/(tanh(1/2*d*x+1/2*c)+1)-1/2/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)+1)*a+1/2/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)+1)*b+1/d*a^2*b/(a+b)^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d*a*b/(a+b)^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*a*b^2/(a+b)^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*a^2*b/(a+b)^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d*a*b/(a+b)^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d*a*b^2/(a+b)^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
28,1,104,45,0.217000," ","int(sinh(d*x+c)/(a+b*tanh(d*x+c)^2),x)","\frac{\frac{4}{\left(4 a +4 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{b \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{\left(a +b \right) \sqrt{a b +b^{2}}}-\frac{4}{\left(4 a +4 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}}{d}"," ",0,"1/d*(4/(4*a+4*b)/(tanh(1/2*d*x+1/2*c)+1)-b/(a+b)/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))-4/(4*a+4*b)/(tanh(1/2*d*x+1/2*c)-1))","B"
29,1,69,47,0.394000," ","int(csch(d*x+c)/(a+b*tanh(d*x+c)^2),x)","\frac{b \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{d a \sqrt{a b +b^{2}}}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}"," ",0,"1/d/a*b/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))+1/d/a*ln(tanh(1/2*d*x+1/2*c))","A"
30,1,413,40,0.356000," ","int(csch(d*x+c)^2/(a+b*tanh(d*x+c)^2),x)","-\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d a}-\frac{1}{2 d a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b^{2}}{d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b^{2}}{d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"-1/2/d/a*tanh(1/2*d*x+1/2*c)-1/2/d/a/tanh(1/2*d*x+1/2*c)+1/d*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d*b/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b^2+1/d*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d*b/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b^2","B"
31,1,181,73,0.391000," ","int(csch(d*x+c)^3/(a+b*tanh(d*x+c)^2),x)","\frac{\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d a}-\frac{b \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{d a \sqrt{a b +b^{2}}}-\frac{b^{2} \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{d \,a^{2} \sqrt{a b +b^{2}}}-\frac{1}{8 d a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d a}-\frac{b \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"1/8/d/a*tanh(1/2*d*x+1/2*c)^2-1/d/a*b/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))-1/d*b^2/a^2/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))-1/8/d/a/tanh(1/2*d*x+1/2*c)^2-1/2/d/a*ln(tanh(1/2*d*x+1/2*c))-1/d/a^2*b*ln(tanh(1/2*d*x+1/2*c))","B"
32,1,750,60,0.372000," ","int(csch(d*x+c)^4/(a+b*tanh(d*x+c)^2),x)","-\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d a}+\frac{3 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d a}+\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right) b}{2 d \,a^{2}}-\frac{b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{2 \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b^{2}}{d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{2 \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b^{2}}{d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \,a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \,a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{1}{24 d a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{3}{8 d a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{2 d \,a^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}"," ",0,"-1/24/d/a*tanh(1/2*d*x+1/2*c)^3+3/8/d/a*tanh(1/2*d*x+1/2*c)+1/2/d/a^2*tanh(1/2*d*x+1/2*c)*b-1/d*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*b/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b^2-1/d*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d*b/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b^2+1/d/a^2*b^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d/a^2*b^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d/a^2*b^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d/a^2*b^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/24/d/a/tanh(1/2*d*x+1/2*c)^3+3/8/d/a/tanh(1/2*d*x+1/2*c)+1/2/d*b/a^2/tanh(1/2*d*x+1/2*c)","B"
33,1,1246,174,0.350000," ","int(sinh(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{3 a^{3} b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{4} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 a \,b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{4} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 a \,b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{4} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 a^{3} b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{4} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{a}{8 d \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{7 b}{8 d \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{3 a}{8 d \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{5 b}{8 d \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a^{2}}{8 d \left(a +b \right)^{4}}-\frac{3 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) b^{2}}{8 d \left(a +b \right)^{4}}+\frac{a}{8 d \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{3 a \,b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{4} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{3 a \,b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{4} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 a^{2} b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{4} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{7 b}{8 d \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3 a}{8 d \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{5 b}{8 d \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a^{2}}{8 d \left(a +b \right)^{4}}+\frac{3 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) b^{2}}{8 d \left(a +b \right)^{4}}-\frac{3 a^{2} b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{4} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{1}{4 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}+\frac{1}{2 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{4 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{1}{2 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{a^{2} b \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{4} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{a \,b^{2} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{4} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{a^{2} b \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a +b \right)^{4} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{a \,b^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a +b \right)^{4} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{9 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a b}{4 d \left(a +b \right)^{4}}-\frac{9 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a b}{4 d \left(a +b \right)^{4}}"," ",0,"-3/2/d*a^3*b/(a+b)^4/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+3/2/d*a*b^3/(a+b)^4/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/2/d*a*b^3/(a+b)^4/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/8/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)-1)^2*a+7/8/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)-1)^2*b-3/8/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)-1)*a+5/8/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)-1)*b-3/8/d/(a+b)^4*ln(tanh(1/2*d*x+1/2*c)-1)*a^2-3/8/d/(a+b)^4*ln(tanh(1/2*d*x+1/2*c)-1)*b^2+1/8/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)^2*a-3/2/d*a^3*b/(a+b)^4/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/2/d*a*b^2/(a+b)^4/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/2/d*a*b^2/(a+b)^4/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-7/8/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)^2*b-3/8/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)*a+5/8/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)*b+3/8/d/(a+b)^4*ln(tanh(1/2*d*x+1/2*c)+1)*a^2+3/8/d/(a+b)^4*ln(tanh(1/2*d*x+1/2*c)+1)*b^2+1/d*a^2*b/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)^3+1/d*a*b^2/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)^3+1/d*a^2*b/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)+1/d*a*b^2/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)+3/2/d*a^2*b/(a+b)^4/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/2/d*a^2*b/(a+b)^4/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/4/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)^4+1/2/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)^3-1/4/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)^4+1/2/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)^3+9/4/d/(a+b)^4*ln(tanh(1/2*d*x+1/2*c)-1)*a*b-9/4/d/(a+b)^4*ln(tanh(1/2*d*x+1/2*c)+1)*a*b","B"
34,1,267,110,0.321000," ","int(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x)","\frac{-\frac{1}{3 \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{-a +3 b}{2 \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{3 \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{2 \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{a -3 b}{2 \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{4 b \left(\frac{\left(-\frac{a}{4}-\frac{b}{2}\right) \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\frac{a}{4}}{\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a}-\frac{\left(3 a -2 b \right) \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{8 \sqrt{a b +b^{2}}}\right)}{\left(a +b \right)^{3}}}{d}"," ",0,"1/d*(-1/3/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)^3-1/2/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)^2-1/2/(a+b)^3*(-a+3*b)/(tanh(1/2*d*x+1/2*c)-1)+1/3/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)^3-1/2/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)^2-1/2*(a-3*b)/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)-4*b/(a+b)^3*(((-1/4*a-1/2*b)*tanh(1/2*d*x+1/2*c)^2-1/4*a)/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)-1/8*(3*a-2*b)/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))))","B"
35,1,1128,118,0.335000," ","int(sinh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x)","\frac{1}{2 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{1}{2 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a}{2 d \left(a +b \right)^{3}}-\frac{3 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) b}{2 d \left(a +b \right)^{3}}-\frac{1}{2 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{1}{2 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a}{2 d \left(a +b \right)^{3}}+\frac{3 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) b}{2 d \left(a +b \right)^{3}}-\frac{b \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}-\frac{b^{2} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}-\frac{b \tanh \left(\frac{d x}{2}+\frac{c}{2}\right) a}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}-\frac{b^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{3 b \,a^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 b a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b^{2} a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 b \,a^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 b a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{b^{2} a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"1/2/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)^2+1/2/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)+1/2/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)-1)*a-3/2/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)-1)*b-1/2/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)^2+1/2/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)-1/2/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)+1)*a+3/2/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)+1)*b-1/d*b/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)^3*a-1/d*b^2/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)^3-1/d*b/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)*a-1/d*b^2/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)+3/2/d*b/(a+b)^3*a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/2/d*b/(a+b)^3*a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*b^2/(a+b)^3*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/2/d*b/(a+b)^3*a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+3/2/d*b/(a+b)^3*a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d*b^2/(a+b)^3*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d*b^2/(a+b)^3/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/2/d*b^3/(a+b)^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/2/d*b^2/(a+b)^3/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/2/d*b^3/(a+b)^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
36,1,167,78,0.318000," ","int(sinh(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x)","\frac{-\frac{1}{\left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{\left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 b \left(\frac{-\frac{\left(a +2 b \right) \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a}-\frac{1}{2}}{\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a}-\frac{3 \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{4 \sqrt{a b +b^{2}}}\right)}{\left(a +b \right)^{2}}}{d}"," ",0,"1/d*(-1/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)+1/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)+2*b/(a+b)^2*((-1/2*(a+2*b)/a*tanh(1/2*d*x+1/2*c)^2-1/2)/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)-3/4/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))))","B"
37,1,331,91,0.472000," ","int(csch(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x)","\frac{b \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) \left(a +b \right)}+\frac{2 b^{2} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) \left(a +b \right)}+\frac{b}{d a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) \left(a +b \right)}+\frac{3 b \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{2 d a \left(a +b \right) \sqrt{a b +b^{2}}}+\frac{b^{2} \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{d \,a^{2} \left(a +b \right) \sqrt{a b +b^{2}}}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"1/d/a*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/(a+b)*tanh(1/2*d*x+1/2*c)^2+2/d/a^2*b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/(a+b)*tanh(1/2*d*x+1/2*c)^2+1/d/a*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/(a+b)+3/2/d/a*b/(a+b)/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))+1/d/a^2*b^2/(a+b)/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))+1/d/a^2*ln(tanh(1/2*d*x+1/2*c))","B"
38,1,552,68,0.459000," ","int(csch(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{b \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}-\frac{b \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{3 \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{2 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \,a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{2 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \,a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{1}{2 d \,a^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}"," ",0,"-1/2/d/a^2*tanh(1/2*d*x+1/2*c)-1/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)^3-1/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)+3/2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b-3/2/d/a^2*b/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/2/d/a^2*b^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b+3/2/d/a^2*b/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+3/2/d/a^2*b^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/2/d/a^2/tanh(1/2*d*x+1/2*c)","B"
39,1,367,127,0.463000," ","int(csch(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x)","\frac{\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2}}-\frac{b \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}-\frac{2 b^{2} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}-\frac{b}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}-\frac{3 b \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{2 d \,a^{2} \sqrt{a b +b^{2}}}-\frac{2 b^{2} \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{d \,a^{3} \sqrt{a b +b^{2}}}-\frac{1}{8 d \,a^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}-\frac{2 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{3}}"," ",0,"1/8/d*tanh(1/2*d*x+1/2*c)^2/a^2-1/d*b/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)^2-2/d*b^2/a^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)^2-1/d*b/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)-3/2/d*b/a^2/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))-2/d*b^2/a^3/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))-1/8/d/a^2/tanh(1/2*d*x+1/2*c)^2-1/2/d/a^2*ln(tanh(1/2*d*x+1/2*c))-2/d/a^3*ln(tanh(1/2*d*x+1/2*c))*b","B"
40,1,1012,99,0.467000," ","int(csch(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{2}}+\frac{3 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2}}+\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{3}}+\frac{b \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{b^{2} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{b \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{b^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}-\frac{3 \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{2 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \,a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{4 b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{2 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{3 b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \,a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{4 b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{5 b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \,a^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{5 b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \,a^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{5 b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \,a^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{5 b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \,a^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{1}{24 d \,a^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{3}{8 d \,a^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{d \,a^{3} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}"," ",0,"-1/24/d/a^2*tanh(1/2*d*x+1/2*c)^3+3/8/d/a^2*tanh(1/2*d*x+1/2*c)+1/d/a^3*tanh(1/2*d*x+1/2*c)*b+1/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)^3+1/d/a^3*b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)^3+1/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)+1/d/a^3*b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)-3/2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b+3/2/d/a^2*b/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-4/d/a^2*b^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b-3/2/d/a^2*b/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-4/d/a^2*b^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+5/2/d/a^3*b^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-5/2/d/a^3*b^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-5/2/d/a^3*b^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-5/2/d/a^3*b^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/24/d/a^2/tanh(1/2*d*x+1/2*c)^3+3/8/d/a^2/tanh(1/2*d*x+1/2*c)+1/d/a^3/tanh(1/2*d*x+1/2*c)*b","B"
41,1,2366,220,0.394000," ","int(sinh(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x)","\text{Expression too large to display}"," ",0,"-1/4/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)^4+1/4/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)-1)^4+1/2/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)^3-15/8/d*b/(a+b)^5/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*a^3-15/8/d*b/(a+b)^5/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*a^3+15/8/d*b^2/(a+b)^5/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*a^2+27/8/d*b^3/(a+b)^5*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+15/8/d*b^2/(a+b)^5/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*a^2+27/8/d*b^3/(a+b)^5*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)-1)^3-1/8/d/(a+b)^4/(tanh(1/2*d*x+1/2*c)-1)^2*a+11/8/d/(a+b)^4/(tanh(1/2*d*x+1/2*c)-1)^2*b-3/8/d/(a+b)^4/(tanh(1/2*d*x+1/2*c)-1)*a+9/8/d/(a+b)^4/(tanh(1/2*d*x+1/2*c)-1)*b-3/8/d/(a+b)^5*ln(tanh(1/2*d*x+1/2*c)-1)*a^2-15/8/d/(a+b)^5*ln(tanh(1/2*d*x+1/2*c)-1)*b^2+1/8/d/(a+b)^4/(tanh(1/2*d*x+1/2*c)+1)^2*a-11/8/d/(a+b)^4/(tanh(1/2*d*x+1/2*c)+1)^2*b-3/8/d/(a+b)^4/(tanh(1/2*d*x+1/2*c)+1)*a+9/8/d/(a+b)^4/(tanh(1/2*d*x+1/2*c)+1)*b+3/8/d/(a+b)^5*ln(tanh(1/2*d*x+1/2*c)+1)*a^2+15/8/d/(a+b)^5*ln(tanh(1/2*d*x+1/2*c)+1)*b^2-5/d*b^4/(a+b)^5/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5-5/d*b^4/(a+b)^5/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3+3/8/d*b^3/(a+b)^5/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/8/d*b^3/(a+b)^5/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+15/4/d/(a+b)^5*ln(tanh(1/2*d*x+1/2*c)-1)*a*b-15/4/d/(a+b)^5*ln(tanh(1/2*d*x+1/2*c)+1)*a*b-15/8/d*b/(a+b)^5*a^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+9/4/d*b/(a+b)^5/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7*a^3+9/4/d*b/(a+b)^5/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)*a^3+27/4/d*b/(a+b)^5/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5*a^3+27/4/d*b/(a+b)^5/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3*a^3-15/4/d*b^2/(a+b)^5*a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/2/d*b^2/(a+b)^5/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7*a^2-3/4/d*b^3/(a+b)^5/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7*a+23/2/d*b^2/(a+b)^5/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5*a^2-1/4/d*b^3/(a+b)^5/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5*a+23/2/d*b^2/(a+b)^5/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3*a^2-1/4/d*b^3/(a+b)^5/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3*a+3/2/d*b^2/(a+b)^5/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)*a^2-3/4/d*b^3/(a+b)^5/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)*a+15/8/d*b/(a+b)^5*a^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/8/d*b^4/(a+b)^5/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/8/d*b^4/(a+b)^5/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+15/4/d*b^2/(a+b)^5*a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
42,1,341,150,0.336000," ","int(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x)","\frac{-\frac{1}{3 \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{-a +5 b}{2 \left(a +b \right)^{4} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{3 \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{2 \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{a -5 b}{2 \left(a +b \right)^{4} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 b \left(\frac{-\frac{\left(9 a +20 b \right) a \left(\tanh^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8}-\frac{\left(27 a^{3}+66 a^{2} b +56 a \,b^{2}-16 b^{3}\right) \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a}+\left(-\frac{27}{8} a^{2}-\frac{11}{2} a b +2 b^{2}\right) \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\frac{9 a^{2}}{8}+\frac{a b}{4}}{\left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{5 \left(3 a -4 b \right) \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{16 \sqrt{a b +b^{2}}}\right)}{\left(a +b \right)^{4}}}{d}"," ",0,"1/d*(-1/3/(a+b)^3/(tanh(1/2*d*x+1/2*c)-1)^3-1/2/(a+b)^3/(tanh(1/2*d*x+1/2*c)-1)^2-1/2/(a+b)^4*(-a+5*b)/(tanh(1/2*d*x+1/2*c)-1)+1/3/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)^3-1/2/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)^2-1/2*(a-5*b)/(a+b)^4/(tanh(1/2*d*x+1/2*c)+1)-2*b/(a+b)^4*((-1/8*(9*a+20*b)*a*tanh(1/2*d*x+1/2*c)^6-1/8*(27*a^3+66*a^2*b+56*a*b^2-16*b^3)/a*tanh(1/2*d*x+1/2*c)^4+(-27/8*a^2-11/2*a*b+2*b^2)*tanh(1/2*d*x+1/2*c)^2-9/8*a^2+1/4*a*b)/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2-5/16*(3*a-4*b)/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))))","B"
43,1,2110,167,0.355000," ","int(sinh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x)","\text{Expression too large to display}"," ",0,"-1/2/d/(a+b)^4*ln(tanh(1/2*d*x+1/2*c)+1)*a+1/d*b^4/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^5-29/2/d*b^2/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*a*tanh(1/2*d*x+1/2*c)^3-5/2/d*b^2/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)*a-27/4/d*b^3/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5-27/4/d*b^3/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3-5/4/d*b^2/(a+b)^4/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+5/4/d*b^2/(a+b)^4/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/4/d*b^3/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)-1/4/d*b^3/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7+5/2/d/(a+b)^4*ln(tanh(1/2*d*x+1/2*c)+1)*b+1/2/d/(a+b)^4*ln(tanh(1/2*d*x+1/2*c)-1)*a-5/2/d/(a+b)^4*ln(tanh(1/2*d*x+1/2*c)-1)*b-11/8/d*b^3/(a+b)^4/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-5/2/d*b^2/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7*a-1/8/d*b^3/(a+b)^4/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-11/8/d*b^3/(a+b)^4/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-9/4/d*b/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7*a^2+1/2/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)-1)^2+1/2/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)-1)-1/2/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)^2+1/2/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)-1/8/d*b^4/(a+b)^4/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/8/d*b^4/(a+b)^4/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+15/8/d*b/(a+b)^4*a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+15/8/d*b/(a+b)^4*a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+5/8/d*b^2/(a+b)^4*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+5/8/d*b^2/(a+b)^4*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-27/4/d*b/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*a^2*tanh(1/2*d*x+1/2*c)^5-27/4/d*b/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*a^2*tanh(1/2*d*x+1/2*c)^3+1/d*b^4/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^3-15/8/d*b/(a+b)^4*a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-29/2/d*b^2/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*a*tanh(1/2*d*x+1/2*c)^5+1/8/d*b^3/(a+b)^4/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-9/4/d*b/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)*a^2+15/8/d*b/(a+b)^4*a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
44,1,252,110,0.305000," ","int(sinh(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x)","\frac{-\frac{1}{\left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{\left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 b \left(\frac{-\frac{\left(9 a^{2}+24 a b +8 b^{2}\right) \left(\tanh^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a}-\frac{\left(27 a^{3}+78 a^{2} b +88 a \,b^{2}+16 b^{3}\right) \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{2}}-\frac{\left(27 a^{2}+56 a b +8 b^{2}\right) \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a}-\frac{9 a}{8}-\frac{b}{4}}{\left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{15 \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{16 \sqrt{a b +b^{2}}}\right)}{\left(a +b \right)^{3}}}{d}"," ",0,"1/d*(-1/(a+b)^3/(tanh(1/2*d*x+1/2*c)-1)+1/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)+2*b/(a+b)^3*((-1/8*(9*a^2+24*a*b+8*b^2)/a*tanh(1/2*d*x+1/2*c)^6-1/8/a^2*(27*a^3+78*a^2*b+88*a*b^2+16*b^3)*tanh(1/2*d*x+1/2*c)^4-1/8*(27*a^2+56*a*b+8*b^2)/a*tanh(1/2*d*x+1/2*c)^2-9/8*a-1/4*b)/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2-15/16/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))))","B"
45,1,1132,142,0.447000," ","int(csch(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x)","\frac{9 b \left(\tanh^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{7 b^{2} \left(\tanh^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{4 b^{3} \left(\tanh^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{27 b \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{45 b^{2} \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{30 b^{3} \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{12 b^{4} \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{27 b \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{17 b^{2} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{8 b^{3} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{9 b}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{3 b^{2}}{2 d a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{15 b \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{8 d a \left(a^{2}+2 a b +b^{2}\right) \sqrt{a b +b^{2}}}+\frac{5 b^{2} \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{2 d \,a^{2} \left(a^{2}+2 a b +b^{2}\right) \sqrt{a b +b^{2}}}+\frac{b^{3} \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{d \,a^{3} \left(a^{2}+2 a b +b^{2}\right) \sqrt{a b +b^{2}}}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"9/4/d*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^6+7/d/a*b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^6+4/d/a^2*b^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^6+27/4/d*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^4+45/2/d/a*b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^4+30/d/a^2*b^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^4+12/d/a^3*b^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^4+27/4/d*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^2+17/d/a*b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^2+8/d/a^2*b^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^2+9/4/d*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2+2*a*b+b^2)+3/2/d/a*b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a^2+2*a*b+b^2)+15/8/d/a*b/(a^2+2*a*b+b^2)/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))+5/2/d/a^2*b^2/(a^2+2*a*b+b^2)/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))+1/d/a^3*b^3/(a^2+2*a*b+b^2)/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))+1/d/a^3*ln(tanh(1/2*d*x+1/2*c))","B"
46,1,816,96,0.439000," ","int(csch(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x)","-\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}-\frac{9 b \left(\tanh^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{27 b \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{7 b^{2} \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{27 b \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{7 b^{2} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{9 b \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{15 b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{15 b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,a^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{15 b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,a^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{15 b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{15 b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,a^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{15 b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,a^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{1}{2 d \,a^{3} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}"," ",0,"-1/2/d/a^3*tanh(1/2*d*x+1/2*c)-9/4/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7-27/4/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5-7/d/a^3*b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5-27/4/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3-7/d/a^3*b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3-9/4/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)+15/8/d/a^2*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-15/8/d/a^3*b/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+15/8/d/a^3*b^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+15/8/d/a^2*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+15/8/d/a^3*b/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+15/8/d/a^3*b^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/2/d/a^3/tanh(1/2*d*x+1/2*c)","B"
47,1,1083,178,0.476000," ","int(csch(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x)","\frac{\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}-\frac{9 b \left(\tanh^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a +b \right)}-\frac{8 b^{2} \left(\tanh^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a +b \right)}-\frac{6 b^{3} \left(\tanh^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a +b \right)}-\frac{27 b \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a +b \right)}-\frac{51 b^{2} \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a +b \right)}-\frac{38 b^{3} \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a +b \right)}-\frac{20 b^{4} \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a +b \right)}-\frac{27 b \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a +b \right)}-\frac{20 b^{2} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a +b \right)}-\frac{14 b^{3} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a +b \right)}-\frac{9 b}{4 d a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a +b \right)}-\frac{5 b^{2}}{2 d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a +b \right)}-\frac{15 b \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{8 d \,a^{2} \left(a +b \right) \sqrt{a b +b^{2}}}-\frac{5 b^{2} \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{d \,a^{3} \left(a +b \right) \sqrt{a b +b^{2}}}-\frac{3 b^{3} \arctanh \left(\frac{2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 a +4 b}{4 \sqrt{a b +b^{2}}}\right)}{d \,a^{4} \left(a +b \right) \sqrt{a b +b^{2}}}-\frac{1}{8 d \,a^{3} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}-\frac{3 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{4}}"," ",0,"1/8/d*tanh(1/2*d*x+1/2*c)^2/a^3-9/4/d/a*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a+b)*tanh(1/2*d*x+1/2*c)^6-8/d/a^2*b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a+b)*tanh(1/2*d*x+1/2*c)^6-6/d/a^3*b^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a+b)*tanh(1/2*d*x+1/2*c)^6-27/4/d/a*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a+b)*tanh(1/2*d*x+1/2*c)^4-51/2/d/a^2*b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a+b)*tanh(1/2*d*x+1/2*c)^4-38/d/a^3*b^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a+b)*tanh(1/2*d*x+1/2*c)^4-20/d/a^4*b^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a+b)*tanh(1/2*d*x+1/2*c)^4-27/4/d/a*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a+b)*tanh(1/2*d*x+1/2*c)^2-20/d/a^2*b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a+b)*tanh(1/2*d*x+1/2*c)^2-14/d/a^3*b^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a+b)*tanh(1/2*d*x+1/2*c)^2-9/4/d/a*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a+b)-5/2/d/a^2*b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a+b)-15/8/d/a^2*b/(a+b)/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))-5/d/a^3*b^2/(a+b)/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))-3/d/a^4*b^3/(a+b)/(a*b+b^2)^(1/2)*arctanh(1/4*(2*tanh(1/2*d*x+1/2*c)^2*a+2*a+4*b)/(a*b+b^2)^(1/2))-1/8/d/a^3/tanh(1/2*d*x+1/2*c)^2-1/2/d/a^3*ln(tanh(1/2*d*x+1/2*c))-3/d/a^4*ln(tanh(1/2*d*x+1/2*c))*b","B"
48,1,1416,135,0.480000," ","int(csch(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x)","-\frac{25 b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{4 d \,a^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{15 b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{25 b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{4 d \,a^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{1}{24 d \,a^{3} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{3 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}+\frac{3}{8 d \,a^{3} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{35 b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,a^{4} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{3}}-\frac{15 b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{27 b \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{67 b^{2} \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{27 b \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{35 b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,a^{4} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{35 b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,a^{4} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right) b}{2 d \,a^{4}}+\frac{3 b}{2 d \,a^{4} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{67 b^{2} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{9 b \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{35 b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,a^{4} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{9 b \left(\tanh^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{15 b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,a^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{15 b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,a^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{11 b^{3} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{13 b^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{13 b^{2} \left(\tanh^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{11 b^{3} \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}"," ",0,"-25/4/d/a^3*b^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/24/d/a^3/tanh(1/2*d*x+1/2*c)^3-1/24/d/a^3*tanh(1/2*d*x+1/2*c)^3+3/8/d/a^3*tanh(1/2*d*x+1/2*c)+3/8/d/a^3/tanh(1/2*d*x+1/2*c)-25/4/d/a^3*b^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-15/8/d/a^2*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-35/8/d*b^3/a^4/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-35/8/d*b^3/a^4/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/2/d/a^4*tanh(1/2*d*x+1/2*c)*b+3/2/d/a^4/tanh(1/2*d*x+1/2*c)*b+9/4/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7-15/8/d/a^2*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+11/d*b^3/a^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3+13/4/d*b^2/a^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)+35/8/d*b^2/a^4/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-35/8/d*b^2/a^4/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+13/4/d*b^2/a^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7+11/d*b^3/a^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5+27/4/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5+67/4/d/a^3*b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5+27/4/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3+67/4/d/a^3*b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3+9/4/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)+15/8/d/a^3*b/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-15/8/d/a^3*b/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
49,1,122,120,0.299000," ","int(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^3),x)","\frac{a \cosh \left(d x +c \right) \left(\sinh^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a \cosh \left(d x +c \right) \sinh \left(d x +c \right)}{8 d}+\frac{3 a x}{8}+\frac{3 a c}{8 d}+\frac{b \left(\sinh^{6}\left(d x +c \right)\right)}{4 d \cosh \left(d x +c \right)^{2}}-\frac{3 b \left(\sinh^{4}\left(d x +c \right)\right)}{4 d \cosh \left(d x +c \right)^{2}}+\frac{3 b \ln \left(\cosh \left(d x +c \right)\right)}{d}-\frac{3 b \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/4*a*cosh(d*x+c)*sinh(d*x+c)^3/d-3/8*a*cosh(d*x+c)*sinh(d*x+c)/d+3/8*a*x+3/8/d*a*c+1/4/d*b*sinh(d*x+c)^6/cosh(d*x+c)^2-3/4/d*b*sinh(d*x+c)^4/cosh(d*x+c)^2+3*b*ln(cosh(d*x+c))/d-3/2*b*tanh(d*x+c)^2/d","A"
50,1,129,88,0.353000," ","int(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^3),x)","-\frac{2 a \cosh \left(d x +c \right)}{3 d}+\frac{a \cosh \left(d x +c \right) \left(\sinh^{2}\left(d x +c \right)\right)}{3 d}+\frac{b \left(\sinh^{5}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{2}}-\frac{5 b \left(\sinh^{3}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{2}}-\frac{5 b \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{2}}+\frac{5 b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{2 d}+\frac{5 b \arctan \left({\mathrm e}^{d x +c}\right)}{d}"," ",0,"-2/3*a*cosh(d*x+c)/d+1/3/d*a*cosh(d*x+c)*sinh(d*x+c)^2+1/3/d*b*sinh(d*x+c)^5/cosh(d*x+c)^2-5/3/d*b*sinh(d*x+c)^3/cosh(d*x+c)^2-5/d*b*sinh(d*x+c)/cosh(d*x+c)^2+5/2*b*sech(d*x+c)*tanh(d*x+c)/d+5/d*b*arctan(exp(d*x+c))","A"
51,1,79,90,0.205000," ","int(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^3),x)","\frac{a \cosh \left(d x +c \right) \sinh \left(d x +c \right)}{2 d}-\frac{a x}{2}-\frac{a c}{2 d}+\frac{b \left(\sinh^{4}\left(d x +c \right)\right)}{2 d \cosh \left(d x +c \right)^{2}}-\frac{2 b \ln \left(\cosh \left(d x +c \right)\right)}{d}+\frac{b \left(\tanh^{2}\left(d x +c \right)\right)}{d}"," ",0,"1/2*a*cosh(d*x+c)*sinh(d*x+c)/d-1/2*a*x-1/2/d*a*c+1/2/d*b*sinh(d*x+c)^4/cosh(d*x+c)^2-2*b*ln(cosh(d*x+c))/d+b*tanh(d*x+c)^2/d","A"
52,1,85,57,0.280000," ","int(sinh(d*x+c)*(a+b*tanh(d*x+c)^3),x)","\frac{a \cosh \left(d x +c \right)}{d}+\frac{b \left(\sinh^{3}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{2}}+\frac{3 b \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{2}}-\frac{3 b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{2 d}-\frac{3 b \arctan \left({\mathrm e}^{d x +c}\right)}{d}"," ",0,"a*cosh(d*x+c)/d+1/d*b*sinh(d*x+c)^3/cosh(d*x+c)^2+3/d*b*sinh(d*x+c)/cosh(d*x+c)^2-3/2*b*sech(d*x+c)*tanh(d*x+c)/d-3/d*b*arctan(exp(d*x+c))","A"
53,1,65,45,0.367000," ","int(csch(d*x+c)*(a+b*tanh(d*x+c)^3),x)","-\frac{2 a \arctanh \left({\mathrm e}^{d x +c}\right)}{d}-\frac{b \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{2}}+\frac{b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{2 d}+\frac{b \arctan \left({\mathrm e}^{d x +c}\right)}{d}"," ",0,"-2/d*a*arctanh(exp(d*x+c))-1/d*b*sinh(d*x+c)/cosh(d*x+c)^2+1/2*b*sech(d*x+c)*tanh(d*x+c)/d+1/d*b*arctan(exp(d*x+c))","A"
54,1,26,27,0.356000," ","int(csch(d*x+c)^2*(a+b*tanh(d*x+c)^3),x)","\frac{-\coth \left(d x +c \right) a -\frac{b}{2 \cosh \left(d x +c \right)^{2}}}{d}"," ",0,"1/d*(-coth(d*x+c)*a-1/2*b/cosh(d*x+c)^2)","A"
55,1,62,63,0.452000," ","int(csch(d*x+c)^3*(a+b*tanh(d*x+c)^3),x)","-\frac{a \coth \left(d x +c \right) \mathrm{csch}\left(d x +c \right)}{2 d}+\frac{a \arctanh \left({\mathrm e}^{d x +c}\right)}{d}+\frac{b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{2 d}+\frac{b \arctan \left({\mathrm e}^{d x +c}\right)}{d}"," ",0,"-1/2*a*coth(d*x+c)*csch(d*x+c)/d+1/d*a*arctanh(exp(d*x+c))+1/2*b*sech(d*x+c)*tanh(d*x+c)/d+1/d*b*arctan(exp(d*x+c))","A"
56,1,60,52,0.385000," ","int(csch(d*x+c)^4*(a+b*tanh(d*x+c)^3),x)","\frac{2 a \coth \left(d x +c \right)}{3 d}-\frac{a \coth \left(d x +c \right) \mathrm{csch}\left(d x +c \right)^{2}}{3 d}+\frac{b}{2 d \cosh \left(d x +c \right)^{2}}+\frac{b \ln \left(\tanh \left(d x +c \right)\right)}{d}"," ",0,"2/3*a*coth(d*x+c)/d-1/3*a*coth(d*x+c)*csch(d*x+c)^2/d+1/2/d*b/cosh(d*x+c)^2+b*ln(tanh(d*x+c))/d","A"
57,1,243,162,0.320000," ","int(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^3)^2,x)","\frac{a^{2} \cosh \left(d x +c \right) \left(\sinh^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{2} \cosh \left(d x +c \right) \sinh \left(d x +c \right)}{8 d}+\frac{3 a^{2} x}{8}+\frac{3 a^{2} c}{8 d}+\frac{a b \left(\sinh^{6}\left(d x +c \right)\right)}{2 d \cosh \left(d x +c \right)^{2}}-\frac{3 a b \left(\sinh^{4}\left(d x +c \right)\right)}{2 d \cosh \left(d x +c \right)^{2}}+\frac{6 a b \ln \left(\cosh \left(d x +c \right)\right)}{d}-\frac{3 a b \left(\tanh^{2}\left(d x +c \right)\right)}{d}+\frac{b^{2} \left(\sinh^{9}\left(d x +c \right)\right)}{4 d \cosh \left(d x +c \right)^{5}}-\frac{9 b^{2} \left(\sinh^{7}\left(d x +c \right)\right)}{8 d \cosh \left(d x +c \right)^{5}}+\frac{63 b^{2} x}{8}+\frac{63 c \,b^{2}}{8 d}-\frac{63 b^{2} \tanh \left(d x +c \right)}{8 d}-\frac{21 b^{2} \left(\tanh^{3}\left(d x +c \right)\right)}{8 d}-\frac{63 b^{2} \left(\tanh^{5}\left(d x +c \right)\right)}{40 d}"," ",0,"1/4/d*a^2*cosh(d*x+c)*sinh(d*x+c)^3-3/8*a^2*cosh(d*x+c)*sinh(d*x+c)/d+3/8*a^2*x+3/8/d*a^2*c+1/2/d*a*b*sinh(d*x+c)^6/cosh(d*x+c)^2-3/2/d*a*b*sinh(d*x+c)^4/cosh(d*x+c)^2+6*a*b*ln(cosh(d*x+c))/d-3*a*b*tanh(d*x+c)^2/d+1/4/d*b^2*sinh(d*x+c)^9/cosh(d*x+c)^5-9/8/d*b^2*sinh(d*x+c)^7/cosh(d*x+c)^5+63/8*b^2*x+63/8/d*c*b^2-63/8*b^2*tanh(d*x+c)/d-21/8*b^2*tanh(d*x+c)^3/d-63/40*b^2*tanh(d*x+c)^5/d","A"
58,1,250,172,0.378000," ","int(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^3)^2,x)","-\frac{2 a^{2} \cosh \left(d x +c \right)}{3 d}+\frac{a^{2} \cosh \left(d x +c \right) \left(\sinh^{2}\left(d x +c \right)\right)}{3 d}+\frac{2 a b \left(\sinh^{5}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{2}}-\frac{10 a b \left(\sinh^{3}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{2}}-\frac{10 a b \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{2}}+\frac{5 a b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{d}+\frac{10 a b \arctan \left({\mathrm e}^{d x +c}\right)}{d}+\frac{b^{2} \left(\sinh^{8}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{5}}-\frac{8 b^{2} \left(\sinh^{6}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{5}}-\frac{16 b^{2} \left(\sinh^{4}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{5}}-\frac{64 b^{2} \left(\sinh^{2}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{5}}-\frac{128 b^{2}}{15 d \cosh \left(d x +c \right)^{5}}"," ",0,"-2/3*a^2*cosh(d*x+c)/d+1/3/d*a^2*cosh(d*x+c)*sinh(d*x+c)^2+2/3/d*a*b*sinh(d*x+c)^5/cosh(d*x+c)^2-10/3/d*a*b*sinh(d*x+c)^3/cosh(d*x+c)^2-10/d*a*b*sinh(d*x+c)/cosh(d*x+c)^2+5/d*a*b*sech(d*x+c)*tanh(d*x+c)+10/d*a*b*arctan(exp(d*x+c))+1/3/d*b^2*sinh(d*x+c)^8/cosh(d*x+c)^5-8/3/d*b^2*sinh(d*x+c)^6/cosh(d*x+c)^5-16/d*b^2*sinh(d*x+c)^4/cosh(d*x+c)^5-64/3/d*b^2*sinh(d*x+c)^2/cosh(d*x+c)^5-128/15/d*b^2/cosh(d*x+c)^5","A"
59,1,173,121,0.252000," ","int(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^3)^2,x)","\frac{a^{2} \cosh \left(d x +c \right) \sinh \left(d x +c \right)}{2 d}-\frac{a^{2} x}{2}-\frac{a^{2} c}{2 d}+\frac{a b \left(\sinh^{4}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{2}}-\frac{4 a b \ln \left(\cosh \left(d x +c \right)\right)}{d}+\frac{2 a b \left(\tanh^{2}\left(d x +c \right)\right)}{d}+\frac{b^{2} \left(\sinh^{7}\left(d x +c \right)\right)}{2 d \cosh \left(d x +c \right)^{5}}-\frac{7 b^{2} x}{2}-\frac{7 c \,b^{2}}{2 d}+\frac{7 b^{2} \tanh \left(d x +c \right)}{2 d}+\frac{7 b^{2} \left(\tanh^{3}\left(d x +c \right)\right)}{6 d}+\frac{7 b^{2} \left(\tanh^{5}\left(d x +c \right)\right)}{10 d}"," ",0,"1/2*a^2*cosh(d*x+c)*sinh(d*x+c)/d-1/2*a^2*x-1/2/d*a^2*c+1/d*a*b*sinh(d*x+c)^4/cosh(d*x+c)^2-4*a*b*ln(cosh(d*x+c))/d+2*a*b*tanh(d*x+c)^2/d+1/2/d*b^2*sinh(d*x+c)^7/cosh(d*x+c)^5-7/2*b^2*x-7/2/d*c*b^2+7/2*b^2*tanh(d*x+c)/d+7/6*b^2*tanh(d*x+c)^3/d+7/10*b^2*tanh(d*x+c)^5/d","A"
60,1,179,121,0.320000," ","int(sinh(d*x+c)*(a+b*tanh(d*x+c)^3)^2,x)","\frac{a^{2} \cosh \left(d x +c \right)}{d}+\frac{2 a b \left(\sinh^{3}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{2}}+\frac{6 a b \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{2}}-\frac{3 a b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{d}-\frac{6 a b \arctan \left({\mathrm e}^{d x +c}\right)}{d}+\frac{b^{2} \left(\sinh^{6}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{5}}+\frac{6 b^{2} \left(\sinh^{4}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{5}}+\frac{8 b^{2} \left(\sinh^{2}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{5}}+\frac{16 b^{2}}{5 d \cosh \left(d x +c \right)^{5}}"," ",0,"a^2*cosh(d*x+c)/d+2/d*a*b*sinh(d*x+c)^3/cosh(d*x+c)^2+6/d*a*b*sinh(d*x+c)/cosh(d*x+c)^2-3/d*a*b*sech(d*x+c)*tanh(d*x+c)-6/d*a*b*arctan(exp(d*x+c))+1/d*b^2*sinh(d*x+c)^6/cosh(d*x+c)^5+6/d*b^2*sinh(d*x+c)^4/cosh(d*x+c)^5+8/d*b^2*sinh(d*x+c)^2/cosh(d*x+c)^5+16/5/d*b^2/cosh(d*x+c)^5","A"
61,1,134,94,0.392000," ","int(csch(d*x+c)*(a+b*tanh(d*x+c)^3)^2,x)","-\frac{2 a^{2} \arctanh \left({\mathrm e}^{d x +c}\right)}{d}-\frac{2 a b \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{2}}+\frac{a b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{d}+\frac{2 a b \arctan \left({\mathrm e}^{d x +c}\right)}{d}-\frac{b^{2} \left(\sinh^{4}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{5}}-\frac{4 b^{2} \left(\sinh^{2}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{5}}-\frac{8 b^{2}}{15 d \cosh \left(d x +c \right)^{5}}"," ",0,"-2/d*a^2*arctanh(exp(d*x+c))-2/d*a*b*sinh(d*x+c)/cosh(d*x+c)^2+1/d*a*b*sech(d*x+c)*tanh(d*x+c)+2/d*a*b*arctan(exp(d*x+c))-1/d*b^2*sinh(d*x+c)^4/cosh(d*x+c)^5-4/3/d*b^2*sinh(d*x+c)^2/cosh(d*x+c)^5-8/15/d*b^2/cosh(d*x+c)^5","A"
62,1,98,45,0.457000," ","int(csch(d*x+c)^2*(a+b*tanh(d*x+c)^3)^2,x)","\frac{-a^{2} \coth \left(d x +c \right)-\frac{a b}{\cosh \left(d x +c \right)^{2}}+b^{2} \left(-\frac{\sinh^{3}\left(d x +c \right)}{2 \cosh \left(d x +c \right)^{5}}-\frac{3 \sinh \left(d x +c \right)}{8 \cosh \left(d x +c \right)^{5}}+\frac{3 \left(\frac{8}{15}+\frac{\mathrm{sech}\left(d x +c \right)^{4}}{5}+\frac{4 \mathrm{sech}\left(d x +c \right)^{2}}{15}\right) \tanh \left(d x +c \right)}{8}\right)}{d}"," ",0,"1/d*(-a^2*coth(d*x+c)-a*b/cosh(d*x+c)^2+b^2*(-1/2*sinh(d*x+c)^3/cosh(d*x+c)^5-3/8*sinh(d*x+c)/cosh(d*x+c)^5+3/8*(8/15+1/5*sech(d*x+c)^4+4/15*sech(d*x+c)^2)*tanh(d*x+c)))","B"
63,1,108,99,0.529000," ","int(csch(d*x+c)^3*(a+b*tanh(d*x+c)^3)^2,x)","-\frac{a^{2} \coth \left(d x +c \right) \mathrm{csch}\left(d x +c \right)}{2 d}+\frac{a^{2} \arctanh \left({\mathrm e}^{d x +c}\right)}{d}+\frac{a b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{d}+\frac{2 a b \arctan \left({\mathrm e}^{d x +c}\right)}{d}-\frac{b^{2} \left(\sinh^{2}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{5}}-\frac{2 b^{2}}{15 d \cosh \left(d x +c \right)^{5}}"," ",0,"-1/2*a^2*coth(d*x+c)*csch(d*x+c)/d+1/d*a^2*arctanh(exp(d*x+c))+1/d*a*b*sech(d*x+c)*tanh(d*x+c)+2/d*a*b*arctan(exp(d*x+c))-1/3/d*b^2*sinh(d*x+c)^2/cosh(d*x+c)^5-2/15/d*b^2/cosh(d*x+c)^5","A"
64,1,146,91,0.493000," ","int(csch(d*x+c)^4*(a+b*tanh(d*x+c)^3)^2,x)","\frac{2 a^{2} \coth \left(d x +c \right)}{3 d}-\frac{a^{2} \coth \left(d x +c \right) \mathrm{csch}\left(d x +c \right)^{2}}{3 d}+\frac{a b}{d \cosh \left(d x +c \right)^{2}}+\frac{2 a b \ln \left(\tanh \left(d x +c \right)\right)}{d}-\frac{b^{2} \sinh \left(d x +c \right)}{4 d \cosh \left(d x +c \right)^{5}}+\frac{2 b^{2} \tanh \left(d x +c \right)}{15 d}+\frac{b^{2} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{4}}{20 d}+\frac{b^{2} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{2}}{15 d}"," ",0,"2/3*a^2*coth(d*x+c)/d-1/3/d*a^2*coth(d*x+c)*csch(d*x+c)^2+1/d*a*b/cosh(d*x+c)^2+2*a*b*ln(tanh(d*x+c))/d-1/4/d*b^2*sinh(d*x+c)/cosh(d*x+c)^5+2/15*b^2*tanh(d*x+c)/d+1/20/d*b^2*tanh(d*x+c)*sech(d*x+c)^4+1/15/d*b^2*tanh(d*x+c)*sech(d*x+c)^2","A"
65,1,385,259,0.409000," ","int(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^3)^3,x)","\frac{a^{3} \cosh \left(d x +c \right) \left(\sinh^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{3} \cosh \left(d x +c \right) \sinh \left(d x +c \right)}{8 d}+\frac{3 a^{3} x}{8}+\frac{3 a^{3} c}{8 d}+\frac{3 a^{2} b \left(\sinh^{6}\left(d x +c \right)\right)}{4 d \cosh \left(d x +c \right)^{2}}-\frac{9 a^{2} b \left(\sinh^{4}\left(d x +c \right)\right)}{4 d \cosh \left(d x +c \right)^{2}}+\frac{9 a^{2} b \ln \left(\cosh \left(d x +c \right)\right)}{d}-\frac{9 a^{2} b \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 a \,b^{2} \left(\sinh^{9}\left(d x +c \right)\right)}{4 d \cosh \left(d x +c \right)^{5}}-\frac{27 a \,b^{2} \left(\sinh^{7}\left(d x +c \right)\right)}{8 d \cosh \left(d x +c \right)^{5}}+\frac{189 a \,b^{2} x}{8}+\frac{189 a \,b^{2} c}{8 d}-\frac{189 a \,b^{2} \tanh \left(d x +c \right)}{8 d}-\frac{63 a \,b^{2} \left(\tanh^{3}\left(d x +c \right)\right)}{8 d}-\frac{189 a \,b^{2} \left(\tanh^{5}\left(d x +c \right)\right)}{40 d}+\frac{b^{3} \left(\sinh^{12}\left(d x +c \right)\right)}{4 d \cosh \left(d x +c \right)^{8}}-\frac{3 b^{3} \left(\sinh^{10}\left(d x +c \right)\right)}{2 d \cosh \left(d x +c \right)^{8}}+\frac{15 b^{3} \ln \left(\cosh \left(d x +c \right)\right)}{d}-\frac{15 b^{3} \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}-\frac{15 b^{3} \left(\tanh^{4}\left(d x +c \right)\right)}{4 d}-\frac{5 b^{3} \left(\tanh^{6}\left(d x +c \right)\right)}{2 d}-\frac{15 b^{3} \left(\tanh^{8}\left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a^3*cosh(d*x+c)*sinh(d*x+c)^3-3/8*a^3*cosh(d*x+c)*sinh(d*x+c)/d+3/8*a^3*x+3/8/d*a^3*c+3/4/d*a^2*b*sinh(d*x+c)^6/cosh(d*x+c)^2-9/4/d*a^2*b*sinh(d*x+c)^4/cosh(d*x+c)^2+9/d*a^2*b*ln(cosh(d*x+c))-9/2*a^2*b*tanh(d*x+c)^2/d+3/4/d*a*b^2*sinh(d*x+c)^9/cosh(d*x+c)^5-27/8/d*a*b^2*sinh(d*x+c)^7/cosh(d*x+c)^5+189/8*a*b^2*x+189/8/d*a*b^2*c-189/8*a*b^2*tanh(d*x+c)/d-63/8*a*b^2*tanh(d*x+c)^3/d-189/40*a*b^2*tanh(d*x+c)^5/d+1/4/d*b^3*sinh(d*x+c)^12/cosh(d*x+c)^8-3/2/d*b^3*sinh(d*x+c)^10/cosh(d*x+c)^8+15/d*b^3*ln(cosh(d*x+c))-15/2*b^3*tanh(d*x+c)^2/d-15/4*b^3*tanh(d*x+c)^4/d-5/2*b^3*tanh(d*x+c)^6/d-15/8*b^3*tanh(d*x+c)^8/d","A"
66,1,506,325,0.486000," ","int(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^3)^3,x)","-\frac{2 a^{3} \cosh \left(d x +c \right)}{3 d}+\frac{a^{3} \cosh \left(d x +c \right) \left(\sinh^{2}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} b \left(\sinh^{5}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{2}}-\frac{5 a^{2} b \left(\sinh^{3}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{2}}-\frac{15 a^{2} b \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{2}}+\frac{15 a^{2} b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{2 d}+\frac{15 a^{2} b \arctan \left({\mathrm e}^{d x +c}\right)}{d}+\frac{a \,b^{2} \left(\sinh^{8}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{5}}-\frac{8 a \,b^{2} \left(\sinh^{6}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{5}}-\frac{48 a \,b^{2} \left(\sinh^{4}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{5}}-\frac{64 a \,b^{2} \left(\sinh^{2}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{5}}-\frac{128 a \,b^{2}}{5 d \cosh \left(d x +c \right)^{5}}+\frac{b^{3} \left(\sinh^{11}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{8}}-\frac{11 b^{3} \left(\sinh^{9}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{8}}-\frac{33 b^{3} \left(\sinh^{7}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{8}}-\frac{77 b^{3} \left(\sinh^{5}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{8}}-\frac{77 b^{3} \left(\sinh^{3}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{8}}-\frac{33 b^{3} \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{8}}+\frac{33 b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{7}}{8 d}+\frac{77 b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{5}}{16 d}+\frac{385 b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{3}}{64 d}+\frac{1155 b^{3} \mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{128 d}+\frac{1155 b^{3} \arctan \left({\mathrm e}^{d x +c}\right)}{64 d}"," ",0,"-2/3*a^3*cosh(d*x+c)/d+1/3/d*a^3*cosh(d*x+c)*sinh(d*x+c)^2+1/d*a^2*b*sinh(d*x+c)^5/cosh(d*x+c)^2-5/d*a^2*b*sinh(d*x+c)^3/cosh(d*x+c)^2-15/d*a^2*b*sinh(d*x+c)/cosh(d*x+c)^2+15/2/d*a^2*b*sech(d*x+c)*tanh(d*x+c)+15/d*a^2*b*arctan(exp(d*x+c))+1/d*a*b^2*sinh(d*x+c)^8/cosh(d*x+c)^5-8/d*a*b^2*sinh(d*x+c)^6/cosh(d*x+c)^5-48/d*a*b^2*sinh(d*x+c)^4/cosh(d*x+c)^5-64/d*a*b^2*sinh(d*x+c)^2/cosh(d*x+c)^5-128/5/d*a*b^2/cosh(d*x+c)^5+1/3/d*b^3*sinh(d*x+c)^11/cosh(d*x+c)^8-11/3/d*b^3*sinh(d*x+c)^9/cosh(d*x+c)^8-33/d*b^3*sinh(d*x+c)^7/cosh(d*x+c)^8-77/d*b^3*sinh(d*x+c)^5/cosh(d*x+c)^8-77/d*b^3*sinh(d*x+c)^3/cosh(d*x+c)^8-33/d*b^3*sinh(d*x+c)/cosh(d*x+c)^8+33/8/d*b^3*tanh(d*x+c)*sech(d*x+c)^7+77/16/d*b^3*tanh(d*x+c)*sech(d*x+c)^5+385/64/d*b^3*tanh(d*x+c)*sech(d*x+c)^3+1155/128/d*b^3*sech(d*x+c)*tanh(d*x+c)+1155/64/d*b^3*arctan(exp(d*x+c))","A"
67,1,289,206,0.293000," ","int(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^3)^3,x)","\frac{a^{3} \cosh \left(d x +c \right) \sinh \left(d x +c \right)}{2 d}-\frac{a^{3} x}{2}-\frac{a^{3} c}{2 d}+\frac{3 a^{2} b \left(\sinh^{4}\left(d x +c \right)\right)}{2 d \cosh \left(d x +c \right)^{2}}-\frac{6 a^{2} b \ln \left(\cosh \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b \left(\tanh^{2}\left(d x +c \right)\right)}{d}+\frac{3 a \,b^{2} \left(\sinh^{7}\left(d x +c \right)\right)}{2 d \cosh \left(d x +c \right)^{5}}-\frac{21 a \,b^{2} x}{2}-\frac{21 a \,b^{2} c}{2 d}+\frac{21 a \,b^{2} \tanh \left(d x +c \right)}{2 d}+\frac{7 a \,b^{2} \left(\tanh^{3}\left(d x +c \right)\right)}{2 d}+\frac{21 a \,b^{2} \left(\tanh^{5}\left(d x +c \right)\right)}{10 d}+\frac{b^{3} \left(\sinh^{10}\left(d x +c \right)\right)}{2 d \cosh \left(d x +c \right)^{8}}-\frac{5 b^{3} \ln \left(\cosh \left(d x +c \right)\right)}{d}+\frac{5 b^{3} \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}+\frac{5 b^{3} \left(\tanh^{4}\left(d x +c \right)\right)}{4 d}+\frac{5 b^{3} \left(\tanh^{6}\left(d x +c \right)\right)}{6 d}+\frac{5 b^{3} \left(\tanh^{8}\left(d x +c \right)\right)}{8 d}"," ",0,"1/2*a^3*cosh(d*x+c)*sinh(d*x+c)/d-1/2*a^3*x-1/2/d*a^3*c+3/2/d*a^2*b*sinh(d*x+c)^4/cosh(d*x+c)^2-6/d*a^2*b*ln(cosh(d*x+c))+3*a^2*b*tanh(d*x+c)^2/d+3/2/d*a*b^2*sinh(d*x+c)^7/cosh(d*x+c)^5-21/2*a*b^2*x-21/2/d*a*b^2*c+21/2*a*b^2*tanh(d*x+c)/d+7/2*a*b^2*tanh(d*x+c)^3/d+21/10*a*b^2*tanh(d*x+c)^5/d+1/2/d*b^3*sinh(d*x+c)^10/cosh(d*x+c)^8-5/d*b^3*ln(cosh(d*x+c))+5/2*b^3*tanh(d*x+c)^2/d+5/4*b^3*tanh(d*x+c)^4/d+5/6*b^3*tanh(d*x+c)^6/d+5/8*b^3*tanh(d*x+c)^8/d","A"
68,1,410,249,0.428000," ","int(sinh(d*x+c)*(a+b*tanh(d*x+c)^3)^3,x)","\frac{a^{3} \cosh \left(d x +c \right)}{d}+\frac{3 a^{2} b \left(\sinh^{3}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{2}}+\frac{9 a^{2} b \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{2}}-\frac{9 a^{2} b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{2 d}-\frac{9 a^{2} b \arctan \left({\mathrm e}^{d x +c}\right)}{d}+\frac{3 a \,b^{2} \left(\sinh^{6}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{5}}+\frac{18 a \,b^{2} \left(\sinh^{4}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{5}}+\frac{24 a \,b^{2} \left(\sinh^{2}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{5}}+\frac{48 a \,b^{2}}{5 d \cosh \left(d x +c \right)^{5}}+\frac{b^{3} \left(\sinh^{9}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{8}}+\frac{9 b^{3} \left(\sinh^{7}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{8}}+\frac{21 b^{3} \left(\sinh^{5}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{8}}+\frac{21 b^{3} \left(\sinh^{3}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{8}}+\frac{9 b^{3} \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{8}}-\frac{9 b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{7}}{8 d}-\frac{21 b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{5}}{16 d}-\frac{105 b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{3}}{64 d}-\frac{315 b^{3} \mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{128 d}-\frac{315 b^{3} \arctan \left({\mathrm e}^{d x +c}\right)}{64 d}"," ",0,"a^3*cosh(d*x+c)/d+3/d*a^2*b*sinh(d*x+c)^3/cosh(d*x+c)^2+9/d*a^2*b*sinh(d*x+c)/cosh(d*x+c)^2-9/2/d*a^2*b*sech(d*x+c)*tanh(d*x+c)-9/d*a^2*b*arctan(exp(d*x+c))+3/d*a*b^2*sinh(d*x+c)^6/cosh(d*x+c)^5+18/d*a*b^2*sinh(d*x+c)^4/cosh(d*x+c)^5+24/d*a*b^2*sinh(d*x+c)^2/cosh(d*x+c)^5+48/5/d*a*b^2/cosh(d*x+c)^5+1/d*b^3*sinh(d*x+c)^9/cosh(d*x+c)^8+9/d*b^3*sinh(d*x+c)^7/cosh(d*x+c)^8+21/d*b^3*sinh(d*x+c)^5/cosh(d*x+c)^8+21/d*b^3*sinh(d*x+c)^3/cosh(d*x+c)^8+9/d*b^3*sinh(d*x+c)/cosh(d*x+c)^8-9/8/d*b^3*tanh(d*x+c)*sech(d*x+c)^7-21/16/d*b^3*tanh(d*x+c)*sech(d*x+c)^5-105/64/d*b^3*tanh(d*x+c)*sech(d*x+c)^3-315/128/d*b^3*sech(d*x+c)*tanh(d*x+c)-315/64/d*b^3*arctan(exp(d*x+c))","A"
69,1,339,203,0.524000," ","int(csch(d*x+c)*(a+b*tanh(d*x+c)^3)^3,x)","-\frac{2 a^{3} \arctanh \left({\mathrm e}^{d x +c}\right)}{d}-\frac{3 a^{2} b \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{2}}+\frac{3 a^{2} b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{2 d}+\frac{3 a^{2} b \arctan \left({\mathrm e}^{d x +c}\right)}{d}-\frac{3 a \,b^{2} \left(\sinh^{4}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{5}}-\frac{4 a \,b^{2} \left(\sinh^{2}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{5}}-\frac{8 a \,b^{2}}{5 d \cosh \left(d x +c \right)^{5}}-\frac{b^{3} \left(\sinh^{7}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{8}}-\frac{7 b^{3} \left(\sinh^{5}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{8}}-\frac{7 b^{3} \left(\sinh^{3}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{8}}-\frac{b^{3} \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{8}}+\frac{b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{7}}{8 d}+\frac{7 b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{5}}{48 d}+\frac{35 b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{3}}{192 d}+\frac{35 b^{3} \mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{128 d}+\frac{35 b^{3} \arctan \left({\mathrm e}^{d x +c}\right)}{64 d}"," ",0,"-2/d*a^3*arctanh(exp(d*x+c))-3/d*a^2*b*sinh(d*x+c)/cosh(d*x+c)^2+3/2/d*a^2*b*sech(d*x+c)*tanh(d*x+c)+3/d*a^2*b*arctan(exp(d*x+c))-3/d*a*b^2*sinh(d*x+c)^4/cosh(d*x+c)^5-4/d*a*b^2*sinh(d*x+c)^2/cosh(d*x+c)^5-8/5/d*a*b^2/cosh(d*x+c)^5-1/d*b^3*sinh(d*x+c)^7/cosh(d*x+c)^8-7/3/d*b^3*sinh(d*x+c)^5/cosh(d*x+c)^8-7/3/d*b^3*sinh(d*x+c)^3/cosh(d*x+c)^8-1/d*b^3*sinh(d*x+c)/cosh(d*x+c)^8+1/8/d*b^3*tanh(d*x+c)*sech(d*x+c)^7+7/48/d*b^3*tanh(d*x+c)*sech(d*x+c)^5+35/192/d*b^3*tanh(d*x+c)*sech(d*x+c)^3+35/128/d*b^3*sech(d*x+c)*tanh(d*x+c)+35/64/d*b^3*arctan(exp(d*x+c))","A"
70,1,171,65,0.505000," ","int(csch(d*x+c)^2*(a+b*tanh(d*x+c)^3)^3,x)","\frac{-a^{3} \coth \left(d x +c \right)-\frac{3 a^{2} b}{2 \cosh \left(d x +c \right)^{2}}+3 a \,b^{2} \left(-\frac{\sinh^{3}\left(d x +c \right)}{2 \cosh \left(d x +c \right)^{5}}-\frac{3 \sinh \left(d x +c \right)}{8 \cosh \left(d x +c \right)^{5}}+\frac{3 \left(\frac{8}{15}+\frac{\mathrm{sech}\left(d x +c \right)^{4}}{5}+\frac{4 \mathrm{sech}\left(d x +c \right)^{2}}{15}\right) \tanh \left(d x +c \right)}{8}\right)+b^{3} \left(-\frac{\sinh^{6}\left(d x +c \right)}{2 \cosh \left(d x +c \right)^{8}}-\frac{3 \left(\sinh^{4}\left(d x +c \right)\right)}{4 \cosh \left(d x +c \right)^{8}}-\frac{\sinh^{2}\left(d x +c \right)}{2 \cosh \left(d x +c \right)^{8}}-\frac{1}{8 \cosh \left(d x +c \right)^{8}}\right)}{d}"," ",0,"1/d*(-a^3*coth(d*x+c)-3/2*a^2*b/cosh(d*x+c)^2+3*a*b^2*(-1/2*sinh(d*x+c)^3/cosh(d*x+c)^5-3/8*sinh(d*x+c)/cosh(d*x+c)^5+3/8*(8/15+1/5*sech(d*x+c)^4+4/15*sech(d*x+c)^2)*tanh(d*x+c))+b^3*(-1/2*sinh(d*x+c)^6/cosh(d*x+c)^8-3/4*sinh(d*x+c)^4/cosh(d*x+c)^8-1/2*sinh(d*x+c)^2/cosh(d*x+c)^8-1/8/cosh(d*x+c)^8))","B"
71,1,286,212,0.614000," ","int(csch(d*x+c)^3*(a+b*tanh(d*x+c)^3)^3,x)","-\frac{a^{3} \coth \left(d x +c \right) \mathrm{csch}\left(d x +c \right)}{2 d}+\frac{a^{3} \arctanh \left({\mathrm e}^{d x +c}\right)}{d}+\frac{3 a^{2} b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{2 d}+\frac{3 a^{2} b \arctan \left({\mathrm e}^{d x +c}\right)}{d}-\frac{a \,b^{2} \left(\sinh^{2}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{5}}-\frac{2 a \,b^{2}}{5 d \cosh \left(d x +c \right)^{5}}-\frac{b^{3} \left(\sinh^{5}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{8}}-\frac{b^{3} \left(\sinh^{3}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{8}}-\frac{b^{3} \sinh \left(d x +c \right)}{7 d \cosh \left(d x +c \right)^{8}}+\frac{b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{7}}{56 d}+\frac{b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{5}}{48 d}+\frac{5 b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{3}}{192 d}+\frac{5 b^{3} \mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{128 d}+\frac{5 b^{3} \arctan \left({\mathrm e}^{d x +c}\right)}{64 d}"," ",0,"-1/2*a^3*coth(d*x+c)*csch(d*x+c)/d+1/d*a^3*arctanh(exp(d*x+c))+3/2/d*a^2*b*sech(d*x+c)*tanh(d*x+c)+3/d*a^2*b*arctan(exp(d*x+c))-1/d*a*b^2*sinh(d*x+c)^2/cosh(d*x+c)^5-2/5/d*a*b^2/cosh(d*x+c)^5-1/3/d*b^3*sinh(d*x+c)^5/cosh(d*x+c)^8-1/3/d*b^3*sinh(d*x+c)^3/cosh(d*x+c)^8-1/7/d*b^3*sinh(d*x+c)/cosh(d*x+c)^8+1/56/d*b^3*tanh(d*x+c)*sech(d*x+c)^7+1/48/d*b^3*tanh(d*x+c)*sech(d*x+c)^5+5/192/d*b^3*tanh(d*x+c)*sech(d*x+c)^3+5/128/d*b^3*sech(d*x+c)*tanh(d*x+c)+5/64/d*b^3*arctan(exp(d*x+c))","A"
72,1,219,128,0.556000," ","int(csch(d*x+c)^4*(a+b*tanh(d*x+c)^3)^3,x)","\frac{2 a^{3} \coth \left(d x +c \right)}{3 d}-\frac{a^{3} \coth \left(d x +c \right) \mathrm{csch}\left(d x +c \right)^{2}}{3 d}+\frac{3 a^{2} b}{2 d \cosh \left(d x +c \right)^{2}}+\frac{3 a^{2} b \ln \left(\tanh \left(d x +c \right)\right)}{d}-\frac{3 a \,b^{2} \sinh \left(d x +c \right)}{4 d \cosh \left(d x +c \right)^{5}}+\frac{2 a \,b^{2} \tanh \left(d x +c \right)}{5 d}+\frac{3 a \,b^{2} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{4}}{20 d}+\frac{a \,b^{2} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{2}}{5 d}-\frac{b^{3} \left(\sinh^{4}\left(d x +c \right)\right)}{4 d \cosh \left(d x +c \right)^{8}}-\frac{b^{3} \left(\sinh^{2}\left(d x +c \right)\right)}{6 d \cosh \left(d x +c \right)^{8}}-\frac{b^{3}}{24 d \cosh \left(d x +c \right)^{8}}"," ",0,"2/3*a^3*coth(d*x+c)/d-1/3/d*a^3*coth(d*x+c)*csch(d*x+c)^2+3/2/d*a^2*b/cosh(d*x+c)^2+3*a^2*b*ln(tanh(d*x+c))/d-3/4/d*a*b^2*sinh(d*x+c)/cosh(d*x+c)^5+2/5*a*b^2*tanh(d*x+c)/d+3/20/d*a*b^2*tanh(d*x+c)*sech(d*x+c)^4+1/5/d*a*b^2*tanh(d*x+c)*sech(d*x+c)^2-1/4/d*b^3*sinh(d*x+c)^4/cosh(d*x+c)^8-1/6/d*b^3*sinh(d*x+c)^2/cosh(d*x+c)^8-1/24/d*b^3/cosh(d*x+c)^8","A"
73,1,603,420,0.509000," ","int(sinh(d*x+c)^4/(a+b*tanh(d*x+c)^3),x)","-\frac{a b \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(3 a^{2} \left(a^{2}+2 b^{2}\right) \textit{\_R}^{5}+3 a b \left(-2 a^{2}-b^{2}\right) \textit{\_R}^{4}+2 \left(4 a^{4}+13 a^{2} b^{2}+b^{4}\right) \textit{\_R}^{3}+12 a b \left(a^{2}+2 b^{2}\right) \textit{\_R}^{2}+\left(a^{4}-8 a^{2} b^{2}-2 b^{4}\right) \textit{\_R} +6 a^{3} b +3 a \,b^{3}\right) \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3}}+\frac{8}{d \left(32 a +32 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}+\frac{32}{d \left(64 a +64 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{a}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{5 b}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{3 a}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{3 b}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 a^{2} \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{8 d \left(a +b \right)^{3}}+\frac{15 a \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) b}{8 d \left(a +b \right)^{3}}-\frac{8}{d \left(32 a -32 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{32}{d \left(64 a -64 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{a}{8 d \left(a -b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{5 b}{8 d \left(a -b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3 a}{8 d \left(a -b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 b}{8 d \left(a -b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3 a^{2} \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{8 d \left(a -b \right)^{3}}+\frac{15 a \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) b}{8 d \left(a -b \right)^{3}}"," ",0,"-1/3/d*a*b/(a-b)^3/(a+b)^3*sum((3*a^2*(a^2+2*b^2)*_R^5+3*a*b*(-2*a^2-b^2)*_R^4+2*(4*a^4+13*a^2*b^2+b^4)*_R^3+12*a*b*(a^2+2*b^2)*_R^2+(a^4-8*a^2*b^2-2*b^4)*_R+6*a^3*b+3*a*b^3)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tanh(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))+8/d/(32*a+32*b)/(tanh(1/2*d*x+1/2*c)-1)^4+32/d/(64*a+64*b)/(tanh(1/2*d*x+1/2*c)-1)^3-1/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)^2*a+5/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)^2*b-3/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)*a+3/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)*b-3/8/d*a^2/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)-1)+15/8/d*a/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)-1)*b-8/d/(32*a-32*b)/(tanh(1/2*d*x+1/2*c)+1)^4+32/d/(64*a-64*b)/(tanh(1/2*d*x+1/2*c)+1)^3+1/8/d/(a-b)^2/(tanh(1/2*d*x+1/2*c)+1)^2*a+5/8/d/(a-b)^2/(tanh(1/2*d*x+1/2*c)+1)^2*b-3/8/d/(a-b)^2/(tanh(1/2*d*x+1/2*c)+1)*a-3/8/d/(a-b)^2/(tanh(1/2*d*x+1/2*c)+1)*b+3/8/d*a^2/(a-b)^3*ln(tanh(1/2*d*x+1/2*c)+1)+15/8/d*a/(a-b)^3*ln(tanh(1/2*d*x+1/2*c)+1)*b","C"
74,1,346,30,0.467000," ","int(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^3),x)","-\frac{a b \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\left(2 a^{2}+b^{2}\right) \textit{\_R}^{4}-6 \textit{\_R}^{3} a b +2 \left(4 a^{2}+5 b^{2}\right) \textit{\_R}^{2}-6 a b \textit{\_R} +2 a^{2}+b^{2}\right) \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d \left(a +b \right)^{2} \left(a -b \right)^{2}}-\frac{16}{3 d \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3} \left(16 a +16 b \right)}-\frac{8}{d \left(16 a +16 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{a}{2 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{b}{d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{8}{d \left(16 a -16 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{16}{3 d \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(16 a -16 b \right)}-\frac{a}{2 d \left(a -b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{b}{d \left(a -b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/3/d*a*b/(a+b)^2/(a-b)^2*sum(((2*a^2+b^2)*_R^4-6*_R^3*a*b+2*(4*a^2+5*b^2)*_R^2-6*a*b*_R+2*a^2+b^2)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tanh(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))-16/3/d/(tanh(1/2*d*x+1/2*c)-1)^3/(16*a+16*b)-8/d/(16*a+16*b)/(tanh(1/2*d*x+1/2*c)-1)^2+1/2/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)*a-1/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)*b-8/d/(16*a-16*b)/(tanh(1/2*d*x+1/2*c)+1)^2+16/3/d/(tanh(1/2*d*x+1/2*c)+1)^3/(16*a-16*b)-1/2/d/(a-b)^2/(tanh(1/2*d*x+1/2*c)+1)*a-1/d/(a-b)^2/(tanh(1/2*d*x+1/2*c)+1)*b","B"
75,1,356,326,0.459000," ","int(sinh(d*x+c)^2/(a+b*tanh(d*x+c)^3),x)","\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(a \left(2 a^{2}+b^{2}\right) \textit{\_R}^{5}-3 \textit{\_R}^{4} a^{2} b +6 a \left(a^{2}+b^{2}\right) \textit{\_R}^{3}+4 b \left(2 a^{2}+b^{2}\right) \textit{\_R}^{2}-3 a \,b^{2} \textit{\_R} +3 a^{2} b \right) \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2}}+\frac{4}{d \left(8 a +8 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{8}{d \left(16 a +16 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a}{2 d \left(a +b \right)^{2}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) b}{d \left(a +b \right)^{2}}-\frac{4}{d \left(8 a -8 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{8}{d \left(16 a -16 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a}{2 d \left(a -b \right)^{2}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) b}{d \left(a -b \right)^{2}}"," ",0,"1/3/d*b/(a-b)^2/(a+b)^2*sum((a*(2*a^2+b^2)*_R^5-3*_R^4*a^2*b+6*a*(a^2+b^2)*_R^3+4*b*(2*a^2+b^2)*_R^2-3*a*b^2*_R+3*a^2*b)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tanh(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))+4/d/(8*a+8*b)/(tanh(1/2*d*x+1/2*c)-1)^2+8/d/(16*a+16*b)/(tanh(1/2*d*x+1/2*c)-1)+1/2/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)-1)*a-1/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)-1)*b-4/d/(8*a-8*b)/(tanh(1/2*d*x+1/2*c)+1)^2+8/d/(16*a-16*b)/(tanh(1/2*d*x+1/2*c)+1)-1/2/d/(a-b)^2*ln(tanh(1/2*d*x+1/2*c)+1)*a-1/d/(a-b)^2*ln(tanh(1/2*d*x+1/2*c)+1)*b","C"
76,1,164,28,0.528000," ","int(sinh(d*x+c)/(a+b*tanh(d*x+c)^3),x)","\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{4} a -2 \textit{\_R}^{3} b +6 \textit{\_R}^{2} a -2 \textit{\_R} b +a \right) \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d \left(a -b \right) \left(a +b \right)}+\frac{4}{d \left(4 a -4 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{4}{d \left(4 a +4 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}"," ",0,"1/3/d*b/(a-b)/(a+b)*sum((_R^4*a-2*_R^3*b+6*_R^2*a-2*_R*b+a)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tanh(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))+4/d/(4*a-4*b)/(tanh(1/2*d*x+1/2*c)+1)-4/d/(4*a+4*b)/(tanh(1/2*d*x+1/2*c)-1)","B"
77,1,98,28,0.619000," ","int(csch(d*x+c)/(a+b*tanh(d*x+c)^3),x)","-\frac{4 b \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d a}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}"," ",0,"-4/3/d/a*b*sum(_R^2/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tanh(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))+1/d/a*ln(tanh(1/2*d*x+1/2*c))","B"
78,1,121,121,0.570000," ","int(csch(d*x+c)^2/(a+b*tanh(d*x+c)^3),x)","-\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d a}+\frac{2 b \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{3}-\textit{\_R} \right) \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d a}-\frac{1}{2 d a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}"," ",0,"-1/2/d/a*tanh(1/2*d*x+1/2*c)+2/3/d/a*b*sum((_R^3-_R)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tanh(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))-1/2/d/a/tanh(1/2*d*x+1/2*c)","C"
79,1,144,30,0.595000," ","int(csch(d*x+c)^3/(a+b*tanh(d*x+c)^3),x)","\frac{\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d a}-\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{4}-2 \textit{\_R}^{2}+1\right) \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d a}-\frac{1}{8 d a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d a}"," ",0,"1/8/d/a*tanh(1/2*d*x+1/2*c)^2-1/3/d/a*b*sum((_R^4-2*_R^2+1)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tanh(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))-1/8/d/a/tanh(1/2*d*x+1/2*c)^2-1/2/d/a*ln(tanh(1/2*d*x+1/2*c))","B"
80,1,187,174,0.600000," ","int(csch(d*x+c)^4/(a+b*tanh(d*x+c)^3),x)","-\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d a}+\frac{3 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d a}+\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{5} a +4 \textit{\_R}^{2} b +3 \textit{\_R} a \right) \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d \,a^{2}}-\frac{1}{24 d a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{3}{8 d a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"-1/24/d/a*tanh(1/2*d*x+1/2*c)^3+3/8/d/a*tanh(1/2*d*x+1/2*c)+1/3/d/a^2*b*sum((_R^5*a+4*_R^2*b+3*_R*a)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tanh(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))-1/24/d/a/tanh(1/2*d*x+1/2*c)^3+3/8/d/a/tanh(1/2*d*x+1/2*c)-1/d/a^2*b*ln(tanh(1/2*d*x+1/2*c))","C"
81,1,82,57,0.325000," ","int(cosh(d*x+c)^4*(a+b*tanh(d*x+c)^2),x)","\frac{b \left(\frac{\sinh \left(d x +c \right) \left(\cosh^{3}\left(d x +c \right)\right)}{4}-\frac{\cosh \left(d x +c \right) \sinh \left(d x +c \right)}{8}-\frac{d x}{8}-\frac{c}{8}\right)+a \left(\left(\frac{\left(\cosh^{3}\left(d x +c \right)\right)}{4}+\frac{3 \cosh \left(d x +c \right)}{8}\right) \sinh \left(d x +c \right)+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(b*(1/4*sinh(d*x+c)*cosh(d*x+c)^3-1/8*cosh(d*x+c)*sinh(d*x+c)-1/8*d*x-1/8*c)+a*((1/4*cosh(d*x+c)^3+3/8*cosh(d*x+c))*sinh(d*x+c)+3/8*d*x+3/8*c))","A"
82,1,37,28,0.318000," ","int(cosh(d*x+c)^3*(a+b*tanh(d*x+c)^2),x)","\frac{\frac{b \left(\sinh^{3}\left(d x +c \right)\right)}{3}+a \left(\frac{2}{3}+\frac{\left(\cosh^{2}\left(d x +c \right)\right)}{3}\right) \sinh \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*b*sinh(d*x+c)^3+a*(2/3+1/3*cosh(d*x+c)^2)*sinh(d*x+c))","A"
83,1,54,29,0.208000," ","int(cosh(d*x+c)^2*(a+b*tanh(d*x+c)^2),x)","\frac{a \left(\frac{\cosh \left(d x +c \right) \sinh \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+b \left(\frac{\cosh \left(d x +c \right) \sinh \left(d x +c \right)}{2}-\frac{d x}{2}-\frac{c}{2}\right)}{d}"," ",0,"1/d*(a*(1/2*cosh(d*x+c)*sinh(d*x+c)+1/2*d*x+1/2*c)+b*(1/2*cosh(d*x+c)*sinh(d*x+c)-1/2*d*x-1/2*c))","A"
84,1,37,27,0.197000," ","int(cosh(d*x+c)*(a+b*tanh(d*x+c)^2),x)","\frac{a \sinh \left(d x +c \right)}{d}+\frac{b \sinh \left(d x +c \right)}{d}-\frac{2 b \arctan \left({\mathrm e}^{d x +c}\right)}{d}"," ",0,"a*sinh(d*x+c)/d+b*sinh(d*x+c)/d-2/d*b*arctan(exp(d*x+c))","A"
85,1,65,36,0.270000," ","int(sech(d*x+c)*(a+b*tanh(d*x+c)^2),x)","\frac{2 a \arctan \left({\mathrm e}^{d x +c}\right)}{d}-\frac{b \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{2}}+\frac{b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{2 d}+\frac{b \arctan \left({\mathrm e}^{d x +c}\right)}{d}"," ",0,"2/d*a*arctan(exp(d*x+c))-1/d*b*sinh(d*x+c)/cosh(d*x+c)^2+1/2*b*sech(d*x+c)*tanh(d*x+c)/d+1/d*b*arctan(exp(d*x+c))","A"
86,1,53,26,0.368000," ","int(sech(d*x+c)^2*(a+b*tanh(d*x+c)^2),x)","\frac{a \tanh \left(d x +c \right)+b \left(-\frac{\sinh \left(d x +c \right)}{2 \cosh \left(d x +c \right)^{3}}+\frac{\left(\frac{2}{3}+\frac{\mathrm{sech}\left(d x +c \right)^{2}}{3}\right) \tanh \left(d x +c \right)}{2}\right)}{d}"," ",0,"1/d*(a*tanh(d*x+c)+b*(-1/2*sinh(d*x+c)/cosh(d*x+c)^3+1/2*(2/3+1/3*sech(d*x+c)^2)*tanh(d*x+c)))","A"
87,1,103,60,0.386000," ","int(sech(d*x+c)^3*(a+b*tanh(d*x+c)^2),x)","\frac{a \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{2 d}+\frac{a \arctan \left({\mathrm e}^{d x +c}\right)}{d}-\frac{b \sinh \left(d x +c \right)}{3 d \cosh \left(d x +c \right)^{4}}+\frac{b \mathrm{sech}\left(d x +c \right)^{3} \tanh \left(d x +c \right)}{12 d}+\frac{b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{8 d}+\frac{b \arctan \left({\mathrm e}^{d x +c}\right)}{4 d}"," ",0,"1/2/d*a*sech(d*x+c)*tanh(d*x+c)+1/d*a*arctan(exp(d*x+c))-1/3/d*b*sinh(d*x+c)/cosh(d*x+c)^4+1/12*b*sech(d*x+c)^3*tanh(d*x+c)/d+1/8*b*sech(d*x+c)*tanh(d*x+c)/d+1/4/d*b*arctan(exp(d*x+c))","A"
88,1,75,44,0.361000," ","int(sech(d*x+c)^4*(a+b*tanh(d*x+c)^2),x)","\frac{a \left(\frac{2}{3}+\frac{\mathrm{sech}\left(d x +c \right)^{2}}{3}\right) \tanh \left(d x +c \right)+b \left(-\frac{\sinh \left(d x +c \right)}{4 \cosh \left(d x +c \right)^{5}}+\frac{\left(\frac{8}{15}+\frac{\mathrm{sech}\left(d x +c \right)^{4}}{5}+\frac{4 \mathrm{sech}\left(d x +c \right)^{2}}{15}\right) \tanh \left(d x +c \right)}{4}\right)}{d}"," ",0,"1/d*(a*(2/3+1/3*sech(d*x+c)^2)*tanh(d*x+c)+b*(-1/4*sinh(d*x+c)/cosh(d*x+c)^5+1/4*(8/15+1/5*sech(d*x+c)^4+4/15*sech(d*x+c)^2)*tanh(d*x+c)))","A"
89,1,124,79,0.380000," ","int(cosh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x)","\frac{b^{2} \left(\left(\frac{\left(\sinh^{3}\left(d x +c \right)\right)}{4}-\frac{3 \sinh \left(d x +c \right)}{8}\right) \cosh \left(d x +c \right)+\frac{3 d x}{8}+\frac{3 c}{8}\right)+2 a b \left(\frac{\sinh \left(d x +c \right) \left(\cosh^{3}\left(d x +c \right)\right)}{4}-\frac{\cosh \left(d x +c \right) \sinh \left(d x +c \right)}{8}-\frac{d x}{8}-\frac{c}{8}\right)+a^{2} \left(\left(\frac{\left(\cosh^{3}\left(d x +c \right)\right)}{4}+\frac{3 \cosh \left(d x +c \right)}{8}\right) \sinh \left(d x +c \right)+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(b^2*((1/4*sinh(d*x+c)^3-3/8*sinh(d*x+c))*cosh(d*x+c)+3/8*d*x+3/8*c)+2*a*b*(1/4*sinh(d*x+c)*cosh(d*x+c)^3-1/8*cosh(d*x+c)*sinh(d*x+c)-1/8*d*x-1/8*c)+a^2*((1/4*cosh(d*x+c)^3+3/8*cosh(d*x+c))*sinh(d*x+c)+3/8*d*x+3/8*c))","A"
90,1,98,52,0.274000," ","int(cosh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x)","\frac{2 a^{2} \sinh \left(d x +c \right)}{3 d}+\frac{a^{2} \sinh \left(d x +c \right) \left(\cosh^{2}\left(d x +c \right)\right)}{3 d}+\frac{2 a b \left(\sinh^{3}\left(d x +c \right)\right)}{3 d}+\frac{b^{2} \left(\sinh^{3}\left(d x +c \right)\right)}{3 d}-\frac{b^{2} \sinh \left(d x +c \right)}{d}+\frac{2 b^{2} \arctan \left({\mathrm e}^{d x +c}\right)}{d}"," ",0,"2/3*a^2*sinh(d*x+c)/d+1/3/d*a^2*sinh(d*x+c)*cosh(d*x+c)^2+2/3*a*b*sinh(d*x+c)^3/d+1/3*b^2*sinh(d*x+c)^3/d-b^2*sinh(d*x+c)/d+2/d*b^2*arctan(exp(d*x+c))","A"
91,1,96,47,0.213000," ","int(cosh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \left(\frac{\cosh \left(d x +c \right) \sinh \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+2 a b \left(\frac{\cosh \left(d x +c \right) \sinh \left(d x +c \right)}{2}-\frac{d x}{2}-\frac{c}{2}\right)+b^{2} \left(\frac{\sinh^{3}\left(d x +c \right)}{2 \cosh \left(d x +c \right)}-\frac{3 d x}{2}-\frac{3 c}{2}+\frac{3 \tanh \left(d x +c \right)}{2}\right)}{d}"," ",0,"1/d*(a^2*(1/2*cosh(d*x+c)*sinh(d*x+c)+1/2*d*x+1/2*c)+2*a*b*(1/2*cosh(d*x+c)*sinh(d*x+c)-1/2*d*x-1/2*c)+b^2*(1/2*sinh(d*x+c)^3/cosh(d*x+c)-3/2*d*x-3/2*c+3/2*tanh(d*x+c)))","B"
92,1,122,56,0.306000," ","int(cosh(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \sinh \left(d x +c \right)}{d}+\frac{2 a b \sinh \left(d x +c \right)}{d}-\frac{4 a b \arctan \left({\mathrm e}^{d x +c}\right)}{d}+\frac{b^{2} \left(\sinh^{3}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{2}}+\frac{3 b^{2} \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{2}}-\frac{3 b^{2} \mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{2 d}-\frac{3 b^{2} \arctan \left({\mathrm e}^{d x +c}\right)}{d}"," ",0,"a^2*sinh(d*x+c)/d+2*a*b*sinh(d*x+c)/d-4/d*a*b*arctan(exp(d*x+c))+1/d*b^2*sinh(d*x+c)^3/cosh(d*x+c)^2+3/d*b^2*sinh(d*x+c)/cosh(d*x+c)^2-3/2/d*b^2*sech(d*x+c)*tanh(d*x+c)-3/d*b^2*arctan(exp(d*x+c))","B"
93,1,173,85,0.370000," ","int(sech(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x)","\frac{2 a^{2} \arctan \left({\mathrm e}^{d x +c}\right)}{d}-\frac{2 a b \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{2}}+\frac{a b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{d}+\frac{2 a b \arctan \left({\mathrm e}^{d x +c}\right)}{d}-\frac{b^{2} \left(\sinh^{3}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{4}}-\frac{b^{2} \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{4}}+\frac{b^{2} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{3}}{4 d}+\frac{3 b^{2} \mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{8 d}+\frac{3 b^{2} \arctan \left({\mathrm e}^{d x +c}\right)}{4 d}"," ",0,"2/d*a^2*arctan(exp(d*x+c))-2/d*a*b*sinh(d*x+c)/cosh(d*x+c)^2+1/d*a*b*sech(d*x+c)*tanh(d*x+c)+2/d*a*b*arctan(exp(d*x+c))-1/d*b^2*sinh(d*x+c)^3/cosh(d*x+c)^4-1/d*b^2*sinh(d*x+c)/cosh(d*x+c)^4+1/4/d*b^2*tanh(d*x+c)*sech(d*x+c)^3+3/8/d*b^2*sech(d*x+c)*tanh(d*x+c)+3/4/d*b^2*arctan(exp(d*x+c))","B"
94,1,126,45,0.458000," ","int(sech(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \tanh \left(d x +c \right)+2 a b \left(-\frac{\sinh \left(d x +c \right)}{2 \cosh \left(d x +c \right)^{3}}+\frac{\left(\frac{2}{3}+\frac{\mathrm{sech}\left(d x +c \right)^{2}}{3}\right) \tanh \left(d x +c \right)}{2}\right)+b^{2} \left(-\frac{\sinh^{3}\left(d x +c \right)}{2 \cosh \left(d x +c \right)^{5}}-\frac{3 \sinh \left(d x +c \right)}{8 \cosh \left(d x +c \right)^{5}}+\frac{3 \left(\frac{8}{15}+\frac{\mathrm{sech}\left(d x +c \right)^{4}}{5}+\frac{4 \mathrm{sech}\left(d x +c \right)^{2}}{15}\right) \tanh \left(d x +c \right)}{8}\right)}{d}"," ",0,"1/d*(a^2*tanh(d*x+c)+2*a*b*(-1/2*sinh(d*x+c)/cosh(d*x+c)^3+1/2*(2/3+1/3*sech(d*x+c)^2)*tanh(d*x+c))+b^2*(-1/2*sinh(d*x+c)^3/cosh(d*x+c)^5-3/8*sinh(d*x+c)/cosh(d*x+c)^5+3/8*(8/15+1/5*sech(d*x+c)^4+4/15*sech(d*x+c)^2)*tanh(d*x+c)))","B"
95,1,236,117,0.506000," ","int(sech(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{2 d}+\frac{a^{2} \arctan \left({\mathrm e}^{d x +c}\right)}{d}-\frac{2 a b \sinh \left(d x +c \right)}{3 d \cosh \left(d x +c \right)^{4}}+\frac{a b \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{3}}{6 d}+\frac{a b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{4 d}+\frac{a b \arctan \left({\mathrm e}^{d x +c}\right)}{2 d}-\frac{b^{2} \left(\sinh^{3}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{6}}-\frac{b^{2} \sinh \left(d x +c \right)}{5 d \cosh \left(d x +c \right)^{6}}+\frac{b^{2} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{5}}{30 d}+\frac{b^{2} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{3}}{24 d}+\frac{b^{2} \mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{16 d}+\frac{b^{2} \arctan \left({\mathrm e}^{d x +c}\right)}{8 d}"," ",0,"1/2/d*a^2*sech(d*x+c)*tanh(d*x+c)+1/d*a^2*arctan(exp(d*x+c))-2/3/d*a*b*sinh(d*x+c)/cosh(d*x+c)^4+1/6/d*a*b*tanh(d*x+c)*sech(d*x+c)^3+1/4/d*a*b*sech(d*x+c)*tanh(d*x+c)+1/2/d*a*b*arctan(exp(d*x+c))-1/3/d*b^2*sinh(d*x+c)^3/cosh(d*x+c)^6-1/5/d*b^2*sinh(d*x+c)/cosh(d*x+c)^6+1/30/d*b^2*tanh(d*x+c)*sech(d*x+c)^5+1/24/d*b^2*tanh(d*x+c)*sech(d*x+c)^3+1/16/d*b^2*sech(d*x+c)*tanh(d*x+c)+1/8/d*b^2*arctan(exp(d*x+c))","B"
96,1,158,70,0.466000," ","int(sech(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \left(\frac{2}{3}+\frac{\mathrm{sech}\left(d x +c \right)^{2}}{3}\right) \tanh \left(d x +c \right)+2 a b \left(-\frac{\sinh \left(d x +c \right)}{4 \cosh \left(d x +c \right)^{5}}+\frac{\left(\frac{8}{15}+\frac{\mathrm{sech}\left(d x +c \right)^{4}}{5}+\frac{4 \mathrm{sech}\left(d x +c \right)^{2}}{15}\right) \tanh \left(d x +c \right)}{4}\right)+b^{2} \left(-\frac{\sinh^{3}\left(d x +c \right)}{4 \cosh \left(d x +c \right)^{7}}-\frac{\sinh \left(d x +c \right)}{8 \cosh \left(d x +c \right)^{7}}+\frac{\left(\frac{16}{35}+\frac{\mathrm{sech}\left(d x +c \right)^{6}}{7}+\frac{6 \mathrm{sech}\left(d x +c \right)^{4}}{35}+\frac{8 \mathrm{sech}\left(d x +c \right)^{2}}{35}\right) \tanh \left(d x +c \right)}{8}\right)}{d}"," ",0,"1/d*(a^2*(2/3+1/3*sech(d*x+c)^2)*tanh(d*x+c)+2*a*b*(-1/4*sinh(d*x+c)/cosh(d*x+c)^5+1/4*(8/15+1/5*sech(d*x+c)^4+4/15*sech(d*x+c)^2)*tanh(d*x+c))+b^2*(-1/4*sinh(d*x+c)^3/cosh(d*x+c)^7-1/8*sinh(d*x+c)/cosh(d*x+c)^7+1/8*(16/35+1/7*sech(d*x+c)^6+6/35*sech(d*x+c)^4+8/35*sech(d*x+c)^2)*tanh(d*x+c)))","B"
97,1,184,85,0.380000," ","int(cosh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \left(\left(\frac{\left(\cosh^{3}\left(d x +c \right)\right)}{4}+\frac{3 \cosh \left(d x +c \right)}{8}\right) \sinh \left(d x +c \right)+\frac{3 d x}{8}+\frac{3 c}{8}\right)+3 a^{2} b \left(\frac{\sinh \left(d x +c \right) \left(\cosh^{3}\left(d x +c \right)\right)}{4}-\frac{\cosh \left(d x +c \right) \sinh \left(d x +c \right)}{8}-\frac{d x}{8}-\frac{c}{8}\right)+3 a \,b^{2} \left(\left(\frac{\left(\sinh^{3}\left(d x +c \right)\right)}{4}-\frac{3 \sinh \left(d x +c \right)}{8}\right) \cosh \left(d x +c \right)+\frac{3 d x}{8}+\frac{3 c}{8}\right)+b^{3} \left(\frac{\sinh^{5}\left(d x +c \right)}{4 \cosh \left(d x +c \right)}-\frac{5 \left(\sinh^{3}\left(d x +c \right)\right)}{8 \cosh \left(d x +c \right)}+\frac{15 d x}{8}+\frac{15 c}{8}-\frac{15 \tanh \left(d x +c \right)}{8}\right)}{d}"," ",0,"1/d*(a^3*((1/4*cosh(d*x+c)^3+3/8*cosh(d*x+c))*sinh(d*x+c)+3/8*d*x+3/8*c)+3*a^2*b*(1/4*sinh(d*x+c)*cosh(d*x+c)^3-1/8*cosh(d*x+c)*sinh(d*x+c)-1/8*d*x-1/8*c)+3*a*b^2*((1/4*sinh(d*x+c)^3-3/8*sinh(d*x+c))*cosh(d*x+c)+3/8*d*x+3/8*c)+b^3*(1/4*sinh(d*x+c)^5/cosh(d*x+c)-5/8*sinh(d*x+c)^3/cosh(d*x+c)+15/8*d*x+15/8*c-15/8*tanh(d*x+c)))","B"
98,1,206,81,0.380000," ","int(cosh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x)","\frac{2 a^{3} \sinh \left(d x +c \right)}{3 d}+\frac{a^{3} \sinh \left(d x +c \right) \left(\cosh^{2}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} b \left(\sinh^{3}\left(d x +c \right)\right)}{d}+\frac{a \,b^{2} \left(\sinh^{3}\left(d x +c \right)\right)}{d}-\frac{3 a \,b^{2} \sinh \left(d x +c \right)}{d}+\frac{6 a \,b^{2} \arctan \left({\mathrm e}^{d x +c}\right)}{d}+\frac{b^{3} \left(\sinh^{5}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{2}}-\frac{5 b^{3} \left(\sinh^{3}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{2}}-\frac{5 b^{3} \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{2}}+\frac{5 b^{3} \mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{2 d}+\frac{5 b^{3} \arctan \left({\mathrm e}^{d x +c}\right)}{d}"," ",0,"2/3*a^3*sinh(d*x+c)/d+1/3/d*a^3*sinh(d*x+c)*cosh(d*x+c)^2+a^2*b*sinh(d*x+c)^3/d+1/d*a*b^2*sinh(d*x+c)^3-3/d*a*b^2*sinh(d*x+c)+6/d*a*b^2*arctan(exp(d*x+c))+1/3/d*b^3*sinh(d*x+c)^5/cosh(d*x+c)^2-5/3/d*b^3*sinh(d*x+c)^3/cosh(d*x+c)^2-5/d*b^3*sinh(d*x+c)/cosh(d*x+c)^2+5/2/d*b^3*sech(d*x+c)*tanh(d*x+c)+5/d*b^3*arctan(exp(d*x+c))","B"
99,1,148,72,0.240000," ","int(cosh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \left(\frac{\cosh \left(d x +c \right) \sinh \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+3 a^{2} b \left(\frac{\cosh \left(d x +c \right) \sinh \left(d x +c \right)}{2}-\frac{d x}{2}-\frac{c}{2}\right)+3 a \,b^{2} \left(\frac{\sinh^{3}\left(d x +c \right)}{2 \cosh \left(d x +c \right)}-\frac{3 d x}{2}-\frac{3 c}{2}+\frac{3 \tanh \left(d x +c \right)}{2}\right)+b^{3} \left(\frac{\sinh^{5}\left(d x +c \right)}{2 \cosh \left(d x +c \right)^{3}}-\frac{5 d x}{2}-\frac{5 c}{2}+\frac{5 \tanh \left(d x +c \right)}{2}+\frac{5 \left(\tanh^{3}\left(d x +c \right)\right)}{6}\right)}{d}"," ",0,"1/d*(a^3*(1/2*cosh(d*x+c)*sinh(d*x+c)+1/2*d*x+1/2*c)+3*a^2*b*(1/2*cosh(d*x+c)*sinh(d*x+c)-1/2*d*x-1/2*c)+3*a*b^2*(1/2*sinh(d*x+c)^3/cosh(d*x+c)-3/2*d*x-3/2*c+3/2*tanh(d*x+c))+b^3*(1/2*sinh(d*x+c)^5/cosh(d*x+c)^3-5/2*d*x-5/2*c+5/2*tanh(d*x+c)+5/6*tanh(d*x+c)^3))","B"
100,1,257,93,0.397000," ","int(cosh(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \sinh \left(d x +c \right)}{d}+\frac{3 a^{2} b \sinh \left(d x +c \right)}{d}-\frac{6 a^{2} b \arctan \left({\mathrm e}^{d x +c}\right)}{d}+\frac{3 a \,b^{2} \left(\sinh^{3}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{2}}+\frac{9 a \,b^{2} \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{2}}-\frac{9 a \,b^{2} \mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{2 d}-\frac{9 a \,b^{2} \arctan \left({\mathrm e}^{d x +c}\right)}{d}+\frac{b^{3} \left(\sinh^{5}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{4}}+\frac{5 b^{3} \left(\sinh^{3}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{4}}+\frac{5 b^{3} \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{4}}-\frac{5 b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{3}}{4 d}-\frac{15 b^{3} \mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{8 d}-\frac{15 b^{3} \arctan \left({\mathrm e}^{d x +c}\right)}{4 d}"," ",0,"a^3*sinh(d*x+c)/d+3/d*a^2*b*sinh(d*x+c)-6/d*a^2*b*arctan(exp(d*x+c))+3/d*a*b^2*sinh(d*x+c)^3/cosh(d*x+c)^2+9/d*a*b^2*sinh(d*x+c)/cosh(d*x+c)^2-9/2/d*a*b^2*sech(d*x+c)*tanh(d*x+c)-9/d*a*b^2*arctan(exp(d*x+c))+1/d*b^3*sinh(d*x+c)^5/cosh(d*x+c)^4+5/d*b^3*sinh(d*x+c)^3/cosh(d*x+c)^4+5/d*b^3*sinh(d*x+c)/cosh(d*x+c)^4-5/4/d*b^3*tanh(d*x+c)*sech(d*x+c)^3-15/8/d*b^3*sech(d*x+c)*tanh(d*x+c)-15/4/d*b^3*arctan(exp(d*x+c))","B"
101,1,334,141,0.421000," ","int(sech(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x)","\frac{2 a^{3} \arctan \left({\mathrm e}^{d x +c}\right)}{d}-\frac{3 a^{2} b \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{2}}+\frac{3 a^{2} b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{2 d}+\frac{3 a^{2} b \arctan \left({\mathrm e}^{d x +c}\right)}{d}-\frac{3 a \,b^{2} \left(\sinh^{3}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{4}}-\frac{3 a \,b^{2} \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{4}}+\frac{3 a \,b^{2} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{3}}{4 d}+\frac{9 a \,b^{2} \mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{8 d}+\frac{9 a \,b^{2} \arctan \left({\mathrm e}^{d x +c}\right)}{4 d}-\frac{b^{3} \left(\sinh^{5}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{6}}-\frac{5 b^{3} \left(\sinh^{3}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{6}}-\frac{b^{3} \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{6}}+\frac{b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{5}}{6 d}+\frac{5 b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{3}}{24 d}+\frac{5 b^{3} \mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{16 d}+\frac{5 b^{3} \arctan \left({\mathrm e}^{d x +c}\right)}{8 d}"," ",0,"2/d*a^3*arctan(exp(d*x+c))-3/d*a^2*b*sinh(d*x+c)/cosh(d*x+c)^2+3/2/d*a^2*b*sech(d*x+c)*tanh(d*x+c)+3/d*a^2*b*arctan(exp(d*x+c))-3/d*a*b^2*sinh(d*x+c)^3/cosh(d*x+c)^4-3/d*a*b^2*sinh(d*x+c)/cosh(d*x+c)^4+3/4/d*a*b^2*tanh(d*x+c)*sech(d*x+c)^3+9/8/d*a*b^2*sech(d*x+c)*tanh(d*x+c)+9/4/d*a*b^2*arctan(exp(d*x+c))-1/d*b^3*sinh(d*x+c)^5/cosh(d*x+c)^6-5/3/d*b^3*sinh(d*x+c)^3/cosh(d*x+c)^6-1/d*b^3*sinh(d*x+c)/cosh(d*x+c)^6+1/6/d*b^3*tanh(d*x+c)*sech(d*x+c)^5+5/24/d*b^3*tanh(d*x+c)*sech(d*x+c)^3+5/16/d*b^3*sech(d*x+c)*tanh(d*x+c)+5/8/d*b^3*arctan(exp(d*x+c))","B"
102,1,227,63,0.547000," ","int(sech(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \tanh \left(d x +c \right)+3 a^{2} b \left(-\frac{\sinh \left(d x +c \right)}{2 \cosh \left(d x +c \right)^{3}}+\frac{\left(\frac{2}{3}+\frac{\mathrm{sech}\left(d x +c \right)^{2}}{3}\right) \tanh \left(d x +c \right)}{2}\right)+3 a \,b^{2} \left(-\frac{\sinh^{3}\left(d x +c \right)}{2 \cosh \left(d x +c \right)^{5}}-\frac{3 \sinh \left(d x +c \right)}{8 \cosh \left(d x +c \right)^{5}}+\frac{3 \left(\frac{8}{15}+\frac{\mathrm{sech}\left(d x +c \right)^{4}}{5}+\frac{4 \mathrm{sech}\left(d x +c \right)^{2}}{15}\right) \tanh \left(d x +c \right)}{8}\right)+b^{3} \left(-\frac{\sinh^{5}\left(d x +c \right)}{2 \cosh \left(d x +c \right)^{7}}-\frac{5 \left(\sinh^{3}\left(d x +c \right)\right)}{8 \cosh \left(d x +c \right)^{7}}-\frac{5 \sinh \left(d x +c \right)}{16 \cosh \left(d x +c \right)^{7}}+\frac{5 \left(\frac{16}{35}+\frac{\mathrm{sech}\left(d x +c \right)^{6}}{7}+\frac{6 \mathrm{sech}\left(d x +c \right)^{4}}{35}+\frac{8 \mathrm{sech}\left(d x +c \right)^{2}}{35}\right) \tanh \left(d x +c \right)}{16}\right)}{d}"," ",0,"1/d*(a^3*tanh(d*x+c)+3*a^2*b*(-1/2*sinh(d*x+c)/cosh(d*x+c)^3+1/2*(2/3+1/3*sech(d*x+c)^2)*tanh(d*x+c))+3*a*b^2*(-1/2*sinh(d*x+c)^3/cosh(d*x+c)^5-3/8*sinh(d*x+c)/cosh(d*x+c)^5+3/8*(8/15+1/5*sech(d*x+c)^4+4/15*sech(d*x+c)^2)*tanh(d*x+c))+b^3*(-1/2*sinh(d*x+c)^5/cosh(d*x+c)^7-5/8*sinh(d*x+c)^3/cosh(d*x+c)^7-5/16*sinh(d*x+c)/cosh(d*x+c)^7+5/16*(16/35+1/7*sech(d*x+c)^6+6/35*sech(d*x+c)^4+8/35*sech(d*x+c)^2)*tanh(d*x+c)))","B"
103,1,421,188,0.589000," ","int(sech(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{2 d}+\frac{a^{3} \arctan \left({\mathrm e}^{d x +c}\right)}{d}-\frac{a^{2} b \sinh \left(d x +c \right)}{d \cosh \left(d x +c \right)^{4}}+\frac{a^{2} b \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{3}}{4 d}+\frac{3 a^{2} b \,\mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{8 d}+\frac{3 a^{2} b \arctan \left({\mathrm e}^{d x +c}\right)}{4 d}-\frac{a \,b^{2} \left(\sinh^{3}\left(d x +c \right)\right)}{d \cosh \left(d x +c \right)^{6}}-\frac{3 a \,b^{2} \sinh \left(d x +c \right)}{5 d \cosh \left(d x +c \right)^{6}}+\frac{a \,b^{2} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{5}}{10 d}+\frac{a \,b^{2} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{3}}{8 d}+\frac{3 a \,b^{2} \mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{16 d}+\frac{3 a \,b^{2} \arctan \left({\mathrm e}^{d x +c}\right)}{8 d}-\frac{b^{3} \left(\sinh^{5}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{8}}-\frac{b^{3} \left(\sinh^{3}\left(d x +c \right)\right)}{3 d \cosh \left(d x +c \right)^{8}}-\frac{b^{3} \sinh \left(d x +c \right)}{7 d \cosh \left(d x +c \right)^{8}}+\frac{b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{7}}{56 d}+\frac{b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{5}}{48 d}+\frac{5 b^{3} \tanh \left(d x +c \right) \mathrm{sech}\left(d x +c \right)^{3}}{192 d}+\frac{5 b^{3} \mathrm{sech}\left(d x +c \right) \tanh \left(d x +c \right)}{128 d}+\frac{5 b^{3} \arctan \left({\mathrm e}^{d x +c}\right)}{64 d}"," ",0,"1/2/d*a^3*sech(d*x+c)*tanh(d*x+c)+1/d*a^3*arctan(exp(d*x+c))-1/d*a^2*b*sinh(d*x+c)/cosh(d*x+c)^4+1/4/d*a^2*b*tanh(d*x+c)*sech(d*x+c)^3+3/8/d*a^2*b*sech(d*x+c)*tanh(d*x+c)+3/4/d*a^2*b*arctan(exp(d*x+c))-1/d*a*b^2*sinh(d*x+c)^3/cosh(d*x+c)^6-3/5/d*a*b^2*sinh(d*x+c)/cosh(d*x+c)^6+1/10/d*a*b^2*tanh(d*x+c)*sech(d*x+c)^5+1/8/d*a*b^2*tanh(d*x+c)*sech(d*x+c)^3+3/16/d*a*b^2*sech(d*x+c)*tanh(d*x+c)+3/8/d*a*b^2*arctan(exp(d*x+c))-1/3/d*b^3*sinh(d*x+c)^5/cosh(d*x+c)^8-1/3/d*b^3*sinh(d*x+c)^3/cosh(d*x+c)^8-1/7/d*b^3*sinh(d*x+c)/cosh(d*x+c)^8+1/56/d*b^3*tanh(d*x+c)*sech(d*x+c)^7+1/48/d*b^3*tanh(d*x+c)*sech(d*x+c)^5+5/192/d*b^3*tanh(d*x+c)*sech(d*x+c)^3+5/128/d*b^3*sech(d*x+c)*tanh(d*x+c)+5/64/d*b^3*arctan(exp(d*x+c))","B"
104,1,269,94,0.563000," ","int(sech(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \left(\frac{2}{3}+\frac{\mathrm{sech}\left(d x +c \right)^{2}}{3}\right) \tanh \left(d x +c \right)+3 a^{2} b \left(-\frac{\sinh \left(d x +c \right)}{4 \cosh \left(d x +c \right)^{5}}+\frac{\left(\frac{8}{15}+\frac{\mathrm{sech}\left(d x +c \right)^{4}}{5}+\frac{4 \mathrm{sech}\left(d x +c \right)^{2}}{15}\right) \tanh \left(d x +c \right)}{4}\right)+3 a \,b^{2} \left(-\frac{\sinh^{3}\left(d x +c \right)}{4 \cosh \left(d x +c \right)^{7}}-\frac{\sinh \left(d x +c \right)}{8 \cosh \left(d x +c \right)^{7}}+\frac{\left(\frac{16}{35}+\frac{\mathrm{sech}\left(d x +c \right)^{6}}{7}+\frac{6 \mathrm{sech}\left(d x +c \right)^{4}}{35}+\frac{8 \mathrm{sech}\left(d x +c \right)^{2}}{35}\right) \tanh \left(d x +c \right)}{8}\right)+b^{3} \left(-\frac{\sinh^{5}\left(d x +c \right)}{4 \cosh \left(d x +c \right)^{9}}-\frac{5 \left(\sinh^{3}\left(d x +c \right)\right)}{24 \cosh \left(d x +c \right)^{9}}-\frac{5 \sinh \left(d x +c \right)}{64 \cosh \left(d x +c \right)^{9}}+\frac{5 \left(\frac{128}{315}+\frac{\mathrm{sech}\left(d x +c \right)^{8}}{9}+\frac{8 \mathrm{sech}\left(d x +c \right)^{6}}{63}+\frac{16 \mathrm{sech}\left(d x +c \right)^{4}}{105}+\frac{64 \mathrm{sech}\left(d x +c \right)^{2}}{315}\right) \tanh \left(d x +c \right)}{64}\right)}{d}"," ",0,"1/d*(a^3*(2/3+1/3*sech(d*x+c)^2)*tanh(d*x+c)+3*a^2*b*(-1/4*sinh(d*x+c)/cosh(d*x+c)^5+1/4*(8/15+1/5*sech(d*x+c)^4+4/15*sech(d*x+c)^2)*tanh(d*x+c))+3*a*b^2*(-1/4*sinh(d*x+c)^3/cosh(d*x+c)^7-1/8*sinh(d*x+c)/cosh(d*x+c)^7+1/8*(16/35+1/7*sech(d*x+c)^6+6/35*sech(d*x+c)^4+8/35*sech(d*x+c)^2)*tanh(d*x+c))+b^3*(-1/4*sinh(d*x+c)^5/cosh(d*x+c)^9-5/24*sinh(d*x+c)^3/cosh(d*x+c)^9-5/64*sinh(d*x+c)/cosh(d*x+c)^9+5/64*(128/315+1/9*sech(d*x+c)^8+8/63*sech(d*x+c)^6+16/105*sech(d*x+c)^4+64/315*sech(d*x+c)^2)*tanh(d*x+c)))","B"
105,1,857,106,0.465000," ","int(cosh(d*x+c)^4/(a+b*tanh(d*x+c)^2),x)","\frac{1}{2 d \left(2 b +2 a \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}+\frac{2}{d \left(4 a +4 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{7 a}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{11 b}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{5 a}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{9 b}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 a^{2} \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{8 d \left(a +b \right)^{3}}-\frac{5 a \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) b}{4 d \left(a +b \right)^{3}}-\frac{15 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) b^{2}}{8 d \left(a +b \right)^{3}}-\frac{1}{2 d \left(2 b +2 a \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{2}{d \left(4 a +4 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{5 a}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{9 b}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{7 a}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{11 b}{8 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{3 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a^{2}}{8 d \left(a +b \right)^{3}}+\frac{5 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a b}{4 d \left(a +b \right)^{3}}+\frac{15 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) b^{2}}{8 d \left(a +b \right)^{3}}-\frac{b^{3} a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{b^{4} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{b^{3} a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{b^{4} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"1/2/d/(2*b+2*a)/(tanh(1/2*d*x+1/2*c)-1)^4+2/d/(4*a+4*b)/(tanh(1/2*d*x+1/2*c)-1)^3+7/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)^2*a+11/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)^2*b+5/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)*a+9/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)*b-3/8/d*a^2/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)-1)-5/4/d*a/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)-1)*b-15/8/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)-1)*b^2-1/2/d/(2*b+2*a)/(tanh(1/2*d*x+1/2*c)+1)^4+2/d/(4*a+4*b)/(tanh(1/2*d*x+1/2*c)+1)^3+5/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)*a+9/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)*b-7/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)^2*a-11/8/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)^2*b+3/8/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)+1)*a^2+5/4/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)+1)*a*b+15/8/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)+1)*b^2-1/d*b^3/(a+b)^3*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*b^3/(a+b)^3/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d*b^4/(a+b)^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d*b^3/(a+b)^3*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d*b^3/(a+b)^3/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d*b^4/(a+b)^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
106,1,468,70,0.444000," ","int(cosh(d*x+c)^3/(a+b*tanh(d*x+c)^2),x)","-\frac{2}{3 d \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3} \left(2 b +2 a \right)}-\frac{1}{d \left(2 b +2 a \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{a}{d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2 b}{d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{3 d \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(2 b +2 a \right)}+\frac{1}{d \left(2 b +2 a \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{a}{d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 b}{d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"-2/3/d/(tanh(1/2*d*x+1/2*c)-1)^3/(2*b+2*a)-1/d/(2*b+2*a)/(tanh(1/2*d*x+1/2*c)-1)^2-1/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)*a-2/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)*b-2/3/d/(tanh(1/2*d*x+1/2*c)+1)^3/(2*b+2*a)+1/d/(2*b+2*a)/(tanh(1/2*d*x+1/2*c)+1)^2-1/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)*a-2/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)*b-1/d*b^2/(a+b)^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*b^3/(a+b)^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*b^2/(a+b)^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d*b^3/(a+b)^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
107,1,608,65,0.432000," ","int(cosh(d*x+c)^2/(a+b*tanh(d*x+c)^2),x)","\frac{1}{d \left(2 b +2 a \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{2}{d \left(4 a +4 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a}{2 d \left(a +b \right)^{2}}-\frac{3 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) b}{2 d \left(a +b \right)^{2}}-\frac{1}{d \left(2 b +2 a \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{2}{d \left(4 a +4 b \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a}{2 d \left(a +b \right)^{2}}+\frac{3 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) b}{2 d \left(a +b \right)^{2}}-\frac{a \,b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{a \,b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"1/d/(2*b+2*a)/(tanh(1/2*d*x+1/2*c)-1)^2+2/d/(4*a+4*b)/(tanh(1/2*d*x+1/2*c)-1)-1/2/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)-1)*a-3/2/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)-1)*b-1/d/(2*b+2*a)/(tanh(1/2*d*x+1/2*c)+1)^2+2/d/(4*a+4*b)/(tanh(1/2*d*x+1/2*c)+1)+1/2/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)+1)*a+3/2/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)+1)*b-1/d*a*b^2/(a+b)^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*b^2/(a+b)^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d*b^3/(a+b)^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d*a*b^2/(a+b)^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d*b^2/(a+b)^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d*b^3/(a+b)^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
108,1,315,45,0.376000," ","int(cosh(d*x+c)/(a+b*tanh(d*x+c)^2),x)","-\frac{2}{d \left(2 b +2 a \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right) \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right) \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right) \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right) \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{2}{d \left(2 b +2 a \right) \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}"," ",0,"-2/d/(2*b+2*a)/(tanh(1/2*d*x+1/2*c)+1)-1/d*b/(a+b)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*b^2/(a+b)/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*b/(a+b)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d*b^2/(a+b)/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-2/d/(2*b+2*a)/(tanh(1/2*d*x+1/2*c)-1)","B"
109,1,235,28,0.317000," ","int(sech(d*x+c)/(a+b*tanh(d*x+c)^2),x)","-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"-1/d/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b+1/d/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b","B"
110,1,363,24,0.356000," ","int(sech(d*x+c)^2/(a+b*tanh(d*x+c)^2),x)","-\frac{a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"-1/d*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b-1/d*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b","B"
111,1,494,47,0.344000," ","int(sech(d*x+c)^3/(a+b*tanh(d*x+c)^2),x)","-\frac{a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d b \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d b \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{2 \arctan \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}"," ",0,"-1/d*a/b/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*a/b/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b+1/d/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b-2/d/b*arctan(tanh(1/2*d*x+1/2*c))","B"
112,1,648,42,0.303000," ","int(sech(d*x+c)^4/(a+b*tanh(d*x+c)^2),x)","-\frac{a^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d b \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{2 a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{a^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d b \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{2 a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{2 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/d*a^2/b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*a/b/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-2/d*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d*a^2/b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d*a/b/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-2/d*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b-1/d/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b-2/d/b*tanh(1/2*d*x+1/2*c)/(tanh(1/2*d*x+1/2*c)^2+1)","B"
113,1,836,74,0.329000," ","int(sech(d*x+c)^5/(a+b*tanh(d*x+c)^2),x)","-\frac{a^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \,b^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{2 a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d b \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{a^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{2 a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{a^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \,b^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{2 a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d b \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{a^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{2 a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3 \arctan \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}-\frac{2 \arctan \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2}}"," ",0,"-1/d*a^2/b^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-2/d*a/b/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*a^2/b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+2/d*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b+1/d*a^2/b^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+2/d*a/b/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d*a^2/b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+2/d*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b+1/d/b/(tanh(1/2*d*x+1/2*c)^2+1)^2*tanh(1/2*d*x+1/2*c)^3-1/d/b/(tanh(1/2*d*x+1/2*c)^2+1)^2*tanh(1/2*d*x+1/2*c)-3/d/b*arctan(tanh(1/2*d*x+1/2*c))-2/d/b^2*arctan(tanh(1/2*d*x+1/2*c))*a","B"
114,1,1077,65,0.349000," ","int(sech(d*x+c)^6/(a+b*tanh(d*x+c)^2),x)","-\frac{a^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \,b^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 a^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{a^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \,b^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{2 a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d b \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{a^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \,b^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{3 a^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{3 a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{a^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \,b^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{2 a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d b \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{2 \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{4 \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{4 \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{16 \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d b \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{2 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right) a}{d \,b^{2} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{4 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}"," ",0,"-1/d/b^2*a^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/d*a^2/b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/d*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*a^2/b^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+2/d*a/b/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b-1/d/b^2*a^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-3/d*a^2/b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-3/d*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d*a^2/b^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-2/d*a/b/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b-2/d/b^2/(tanh(1/2*d*x+1/2*c)^2+1)^3*tanh(1/2*d*x+1/2*c)^5*a-4/d/b/(tanh(1/2*d*x+1/2*c)^2+1)^3*tanh(1/2*d*x+1/2*c)^5-4/d/b^2/(tanh(1/2*d*x+1/2*c)^2+1)^3*tanh(1/2*d*x+1/2*c)^3*a-16/3/d/b/(tanh(1/2*d*x+1/2*c)^2+1)^3*tanh(1/2*d*x+1/2*c)^3-2/d/b^2/(tanh(1/2*d*x+1/2*c)^2+1)^3*tanh(1/2*d*x+1/2*c)*a-4/d/b/(tanh(1/2*d*x+1/2*c)^2+1)^3*tanh(1/2*d*x+1/2*c)","B"
115,1,875,114,0.523000," ","int(cosh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{1}{3 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{a}{d \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 b}{d \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{3 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{2 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{a}{d \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 b}{d \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{b^{3} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}+\frac{b^{3} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}-\frac{3 b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b^{4} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} a \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{b^{4} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} a \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"-1/3/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)^3-1/2/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)^2-1/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)-1)*a-3/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)-1)*b-1/3/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)^3+1/2/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)^2-1/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)*a-3/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)*b-1/d*b^3/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)^3+1/d*b^3/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)-3/d*b^2/(a+b)^3/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/d*b^3/(a+b)^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/d*b^2/(a+b)^3/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+3/d*b^3/(a+b)^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/2/d*b^3/(a+b)^3/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/2/d*b^4/(a+b)^3/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/2/d*b^3/(a+b)^3/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d*b^4/(a+b)^3/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
116,1,1146,124,0.472000," ","int(cosh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x)","\frac{1}{2 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{1}{2 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a}{2 d \left(a +b \right)^{3}}-\frac{5 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) b}{2 d \left(a +b \right)^{3}}-\frac{1}{2 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{1}{2 d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a}{2 d \left(a +b \right)^{3}}+\frac{5 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) b}{2 d \left(a +b \right)^{3}}+\frac{b^{2} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{b^{3} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}+\frac{b^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{b^{3} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}-\frac{5 b^{2} a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{5 b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{5 b^{2} a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{5 b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{3 b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{b^{4} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} a \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{b^{4} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} a \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"1/2/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)^2+1/2/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)-1/2/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)-1)*a-5/2/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)-1)*b-1/2/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)^2+1/2/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)+1/2/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)+1)*a+5/2/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)+1)*b+1/d*b^2/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)^3+1/d*b^3/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)^3+1/d*b^2/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)+1/d*b^3/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)-5/2/d*b^2/(a+b)^3*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+5/2/d*b^2/(a+b)^3/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/d*b^3/(a+b)^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-5/2/d*b^2/(a+b)^3*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-5/2/d*b^2/(a+b)^3/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-3/d*b^3/(a+b)^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d*b^3/(a+b)^3/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/2/d*b^4/(a+b)^3/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/2/d*b^3/(a+b)^3/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/2/d*b^4/(a+b)^3/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
117,1,729,89,0.415000," ","int(cosh(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{1}{d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{d \left(a +b \right)^{2} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{b^{2} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}+\frac{b^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a +b \right)^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}-\frac{2 b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{2 b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{2 b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{2 b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"-1/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)-1)-1/d/(a+b)^2/(tanh(1/2*d*x+1/2*c)+1)-1/d*b^2/(a+b)^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)^3+1/d*b^2/(a+b)^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)-2/d*b/(a+b)^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+2/d*b^2/(a+b)^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+2/d*b/(a+b)^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+2/d*b^2/(a+b)^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/2/d*b^2/(a+b)^2/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/2/d*b^3/(a+b)^2/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/2/d*b^2/(a+b)^2/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d*b^3/(a+b)^2/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
118,1,666,71,0.386000," ","int(sech(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{b \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a \left(a +b \right)}+\frac{b \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a \left(a +b \right)}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right) \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{d \left(a +b \right) \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right) \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{d \left(a +b \right) \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right) a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b^{2}}{2 d \left(a +b \right) a \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right) a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b^{2}}{2 d \left(a +b \right) a \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"-1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*b/a/(a+b)*tanh(1/2*d*x+1/2*c)^3+1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*b/a/(a+b)*tanh(1/2*d*x+1/2*c)-1/d/(a+b)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d/(a+b)/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b+1/d/(a+b)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d/(a+b)/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b-1/2/d/(a+b)*b/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/2/d/(a+b)/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b^2+1/2/d/(a+b)*b/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d/(a+b)/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b^2","B"
119,1,498,54,0.400000," ","int(sech(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x)","\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}+\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{2 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{2 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)^3+1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)-1/2/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/2/d/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b-1/2/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/2/d/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b","B"
120,1,375,60,0.390000," ","int(sech(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}+\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{2 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{2 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"-1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)^3+1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)-1/2/d/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b+1/2/d/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b","B"
121,1,746,65,0.367000," ","int(sech(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x)","\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) b}+\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}+\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) b}+\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}+\frac{a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d b \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d b \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{2 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{2 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/b*tanh(1/2*d*x+1/2*c)^3+1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)^3+1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/b*tanh(1/2*d*x+1/2*c)+1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)+1/2/d/b*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/2/d/b/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/2/d/b*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d/b/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b-1/2/d/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b","B"
122,1,1007,90,0.364000," ","int(sech(d*x+c)^5/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) b}-\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}+\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) b}+\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}+\frac{a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \,b^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \,b^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d b \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d b \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{2 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{2 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{2 \arctan \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}"," ",0,"-1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/b*tanh(1/2*d*x+1/2*c)^3-1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)^3+1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/b*tanh(1/2*d*x+1/2*c)+1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)+1/d/b^2*a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d/b*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d/b^2*a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d/b*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d/b/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/2/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/2/d/b/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/2/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/2/d/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b+1/2/d/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b+2/d/b^2*arctan(tanh(1/2*d*x+1/2*c))","B"
123,1,1283,85,0.365000," ","int(sech(d*x+c)^6/(a+b*tanh(d*x+c)^2)^2,x)","\frac{a \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{2 \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) b}+\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}+\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{2 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) b}+\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}+\frac{3 a^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \,b^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \,b^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{5 a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 a^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \,b^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \,b^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{5 a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d b \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d b \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{2 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{2 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{2 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/d/b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*a*tanh(1/2*d*x+1/2*c)^3+2/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/b*tanh(1/2*d*x+1/2*c)^3+1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)^3+1/d/b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*a*tanh(1/2*d*x+1/2*c)+2/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/b*tanh(1/2*d*x+1/2*c)+1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)+3/2/d/b^2*a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/2/d/b^2*a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+5/2/d/b*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/2/d/b^2*a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+3/2/d/b^2*a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+5/2/d/b*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d/b/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/2/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d/b/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b-1/2/d/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b+2/d/b^2*tanh(1/2*d*x+1/2*c)/(tanh(1/2*d*x+1/2*c)^2+1)","B"
124,1,1477,139,0.402000," ","int(sech(d*x+c)^7/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}-\frac{2 a^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \,b^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{7 a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{4 \arctan \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3}}-\frac{2 \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) b}+\frac{2 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) b}+\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right) a}-\frac{2 a^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \,b^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d b \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d b \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{5 \arctan \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{2 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{2 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{7 a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{2 a^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \,b^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{7 a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \,b^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{7 a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \,b^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{2 a^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \,b^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{a \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}"," ",0,"-7/2/d/b*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-7/2/d/b*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d/b^2/(tanh(1/2*d*x+1/2*c)^2+1)^2*tanh(1/2*d*x+1/2*c)^3+1/d/b^2/(tanh(1/2*d*x+1/2*c)^2+1)^2*tanh(1/2*d*x+1/2*c)+4/d/b^3*arctan(tanh(1/2*d*x+1/2*c))*a+1/2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b-1/d/b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*a*tanh(1/2*d*x+1/2*c)^3-2/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/b*tanh(1/2*d*x+1/2*c)^3+7/2/d/b^2*a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-2/d/b^2*a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-2/d/b^2*a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+2/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/b*tanh(1/2*d*x+1/2*c)+1/d/b/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d/b/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)^3+1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)/a*tanh(1/2*d*x+1/2*c)-1/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/2/d/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+5/d/b^2*arctan(tanh(1/2*d*x+1/2*c))+1/2/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b-7/2/d/b^2*a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-2/d/b^3*a^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+2/d/b^3*a^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d/b^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*a*tanh(1/2*d*x+1/2*c)","B"
125,1,2132,180,0.514000," ","int(cosh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x)","\text{Expression too large to display}"," ",0,"-35/8/d*b^2/(a+b)^4*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-35/8/d*b^2/(a+b)^4*a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-17/8/d*b^4/(a+b)^4/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/8/d*b^5/(a+b)^4/a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-3/8/d*b^5/(a+b)^4/a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-17/8/d*b^4/(a+b)^4/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)-1)^2+1/2/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)-1)-1/2/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)^2+1/2/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)-7/2/d/(a+b)^4*ln(tanh(1/2*d*x+1/2*c)-1)*b-49/8/d*b^3/(a+b)^4/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-49/8/d*b^3/(a+b)^4/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+5/4/d*b^4/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^7+5/4/d*b^4/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)-1/2/d/(a+b)^4*ln(tanh(1/2*d*x+1/2*c)-1)*a+1/2/d/(a+b)^4*ln(tanh(1/2*d*x+1/2*c)+1)*a+7/2/d/(a+b)^4*ln(tanh(1/2*d*x+1/2*c)+1)*b-7/4/d*b^3/(a+b)^4/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+13/4/d*b^2/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*a*tanh(1/2*d*x+1/2*c)^7+39/4/d*b^2/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*a*tanh(1/2*d*x+1/2*c)^5+39/4/d*b^2/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*a*tanh(1/2*d*x+1/2*c)^3+3/8/d*b^4/(a+b)^4/a^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/8/d*b^4/(a+b)^4/a^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+71/4/d*b^4/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^3+3/d*b^5/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a^2*tanh(1/2*d*x+1/2*c)^3+71/4/d*b^4/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^5+13/4/d*b^2/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*a*tanh(1/2*d*x+1/2*c)+7/4/d*b^3/(a+b)^4/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/d*b^5/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a^2*tanh(1/2*d*x+1/2*c)^5+35/8/d*b^2/(a+b)^4/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-35/8/d*b^2/(a+b)^4/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+9/2/d*b^3/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7+49/2/d*b^3/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5+49/2/d*b^3/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3+9/2/d*b^3/(a+b)^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)","B"
126,1,1570,140,0.492000," ","int(cosh(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x)","-\frac{1}{d \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{d \left(a +b \right)^{3} \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 b^{2} \left(\tanh^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{5 b^{3} \left(\tanh^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}-\frac{3 b^{2} \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{45 b^{3} \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}-\frac{3 b^{4} \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a^{2}}+\frac{3 b^{2} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{45 b^{3} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}+\frac{3 b^{4} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a^{2}}+\frac{3 b^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{5 b^{3} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}-\frac{3 b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \left(a +b \right)^{3} a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} a \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 b^{4} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \left(a +b \right)^{3} a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \left(a +b \right)^{3} a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{3} a \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 b^{4} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \left(a +b \right)^{3} a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"-1/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)-1)-1/d/(a+b)^3/(tanh(1/2*d*x+1/2*c)+1)-3/d*b^2/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7-5/4/d*b^3/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^7-3/d*b^2/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5-45/4/d*b^3/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^5-3/d*b^4/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a^2*tanh(1/2*d*x+1/2*c)^5+3/d*b^2/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3+45/4/d*b^3/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^3+3/d*b^4/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a^2*tanh(1/2*d*x+1/2*c)^3+3/d*b^2/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)+5/4/d*b^3/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)-3/d*b/(a+b)^3/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/2/d*b^2/(a+b)^3/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/8/d*b^3/(a+b)^3/a^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/d*b^2/(a+b)^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/2/d*b^3/(a+b)^3/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/8/d*b^4/(a+b)^3/a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/d*b/(a+b)^3/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+3/2/d*b^2/(a+b)^3/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+3/8/d*b^3/(a+b)^3/a^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+3/d*b^2/(a+b)^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+3/2/d*b^3/(a+b)^3/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+3/8/d*b^4/(a+b)^3/a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
127,1,1676,130,0.451000," ","int(sech(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x)","-\frac{2 b \left(\tanh^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{5 b^{2} \left(\tanh^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a \left(a^{2}+2 a b +b^{2}\right)}-\frac{2 b \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{29 b^{2} \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a \left(a^{2}+2 a b +b^{2}\right)}-\frac{3 b^{3} \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{2 b \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{29 b^{2} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a \left(a^{2}+2 a b +b^{2}\right)}+\frac{3 b^{3} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{2 b \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{5 b^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a \left(a^{2}+2 a b +b^{2}\right)}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{d a \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b^{2}}{8 d \,a^{2} \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{d \left(a^{2}+2 a b +b^{2}\right) \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b^{2}}{d a \left(a^{2}+2 a b +b^{2}\right) \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b^{3}}{8 d \,a^{2} \left(a^{2}+2 a b +b^{2}\right) \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{d a \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b^{2}}{8 d \,a^{2} \left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{d \left(a^{2}+2 a b +b^{2}\right) \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b^{2}}{d a \left(a^{2}+2 a b +b^{2}\right) \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b^{3}}{8 d \,a^{2} \left(a^{2}+2 a b +b^{2}\right) \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"-2/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*b/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^7-5/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*b^2/a/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^7-2/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*b/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^5-29/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*b^2/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^5-3/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a^2*b^3/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^5+2/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*b/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^3+29/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*b^2/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^3+3/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a^2*b^3/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)^3+2/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*b/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)+5/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*b^2/a/(a^2+2*a*b+b^2)*tanh(1/2*d*x+1/2*c)-1/d/(a^2+2*a*b+b^2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d/a/(a^2+2*a*b+b^2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b-3/8/d/a^2/(a^2+2*a*b+b^2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b^2+1/d/(a^2+2*a*b+b^2)/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b+1/d/a/(a^2+2*a*b+b^2)/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b^2+3/8/d/a^2/(a^2+2*a*b+b^2)/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b^3+1/d/(a^2+2*a*b+b^2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d/a/(a^2+2*a*b+b^2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b+3/8/d/a^2/(a^2+2*a*b+b^2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b^2+1/d/(a^2+2*a*b+b^2)/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b+1/d/a/(a^2+2*a*b+b^2)/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b^2+3/8/d/a^2/(a^2+2*a*b+b^2)/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b^3","B"
128,1,764,82,0.483000," ","int(sech(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x)","\frac{5 \left(\tanh^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}+\frac{15 \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}+\frac{3 b \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{15 \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}+\frac{3 b \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{5 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}-\frac{3 \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{3 \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{3 b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"5/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^7+15/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^5+3/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5+15/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^3+3/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3+5/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)-3/8/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/8/d/a^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/8/d/a^2*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/8/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-3/8/d/a^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-3/8/d/a^2*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
129,1,1226,115,0.486000," ","int(sech(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x)","-\frac{\tanh^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a +b \right)}-\frac{5 \left(\tanh^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a \left(a +b \right)}-\frac{\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a +b \right)}-\frac{13 \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a \left(a +b \right)}-\frac{3 \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a^{2} \left(a +b \right)}+\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a +b \right)}+\frac{13 \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a \left(a +b \right)}+\frac{3 \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a^{2} \left(a +b \right)}+\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} \left(a +b \right)}+\frac{5 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right) b}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a \left(a +b \right)}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d a \left(a +b \right) \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b}{2 d a \left(a +b \right) \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d a \left(a +b \right) \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b}{2 d a \left(a +b \right) \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{3 b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,a^{2} \left(a +b \right) \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right) b^{2}}{8 d \,a^{2} \left(a +b \right) \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,a^{2} \left(a +b \right) \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right) b^{2}}{8 d \,a^{2} \left(a +b \right) \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"-1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a+b)*tanh(1/2*d*x+1/2*c)^7-5/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a/(a+b)*tanh(1/2*d*x+1/2*c)^7*b-1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a+b)*tanh(1/2*d*x+1/2*c)^5-13/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a/(a+b)*tanh(1/2*d*x+1/2*c)^5*b-3/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a^2/(a+b)*tanh(1/2*d*x+1/2*c)^5*b^2+1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a+b)*tanh(1/2*d*x+1/2*c)^3+13/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a/(a+b)*tanh(1/2*d*x+1/2*c)^3*b+3/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a^2/(a+b)*tanh(1/2*d*x+1/2*c)^3*b^2+1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/(a+b)*tanh(1/2*d*x+1/2*c)+5/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a/(a+b)*tanh(1/2*d*x+1/2*c)*b-1/2/d/a/(a+b)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/2/d/a/(a+b)/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b+1/2/d/a/(a+b)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d/a/(a+b)/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b-3/8/d/a^2/(a+b)*b/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/8/d/a^2/(a+b)/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))*b^2+3/8/d/a^2/(a+b)*b/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+3/8/d/a^2/(a+b)/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))*b^2","B"
130,1,1270,101,0.401000," ","int(sech(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x)","\frac{\tanh^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} b}+\frac{5 \left(\tanh^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}+\frac{3 \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} b}+\frac{11 \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}+\frac{3 b \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{3 \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} b}+\frac{11 \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}+\frac{3 b \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} b}+\frac{5 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}+\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d a b \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{4 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d a b \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{4 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{3 b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"1/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/b*tanh(1/2*d*x+1/2*c)^7+5/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^7+3/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/b*tanh(1/2*d*x+1/2*c)^5+11/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^5+3/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5+3/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/b*tanh(1/2*d*x+1/2*c)^3+11/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^3+3/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3+1/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/b*tanh(1/2*d*x+1/2*c)+5/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)+1/8/d/b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/8/d/a/b/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/4/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/8/d/b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/8/d/a/b/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/4/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+3/8/d/a^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/8/d/a^2*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/8/d/a^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-3/8/d/a^2*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
131,1,634,90,0.401000," ","int(sech(d*x+c)^5/(a+b*tanh(d*x+c)^2)^3,x)","-\frac{5 \left(\tanh^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}+\frac{3 \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}-\frac{3 b \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{3 \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}+\frac{3 b \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{5 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}-\frac{3 \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"-5/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^7+3/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^5-3/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5-3/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^3+3/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3+5/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)-3/8/d/a^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/8/d/a^2*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/8/d/a^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+3/8/d/a^2*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
132,1,1776,117,0.418000," ","int(sech(d*x+c)^6/(a+b*tanh(d*x+c)^2)^3,x)","-\frac{3 b \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{9 a \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} b^{2}}-\frac{3 a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} b^{2}}-\frac{3 a \left(\tanh^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} b^{2}}-\frac{9 a \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} b^{2}}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 a \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,b^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{3 a \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,b^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 b \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{3 b \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 b \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{7 \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}+\frac{5 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}+\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} b}-\frac{3 \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,b^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,b^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{3 \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d \,a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{5 \left(\tanh^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}+\frac{7 \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} a}+\frac{\tanh^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} b}-\frac{7 \left(\tanh^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} b}-\frac{7 \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2} b}-\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{8 d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{\arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{4 d a b \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{8 d b \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{\arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{4 d a b \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}"," ",0,"-1/8/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/8/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-3/8/d*a/b^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/8/d*a/b^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/2/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/b*tanh(1/2*d*x+1/2*c)^7-7/2/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/b*tanh(1/2*d*x+1/2*c)^5-7/2/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/b*tanh(1/2*d*x+1/2*c)^3+1/2/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/b*tanh(1/2*d*x+1/2*c)-3/8/d/a^2*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-3/8/d/a^2*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/8/d/b^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/8/d/b^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+5/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^7+7/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^5+7/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^3+5/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)+3/8/d/a^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-3/8/d/a^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-9/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*a/b^2*tanh(1/2*d*x+1/2*c)^3+3/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5+3/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3-3/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*a/b^2*tanh(1/2*d*x+1/2*c)-3/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*a/b^2*tanh(1/2*d*x+1/2*c)^7-9/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*a/b^2*tanh(1/2*d*x+1/2*c)^5-1/8/d/b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/4/d/a/b/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/8/d/b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/4/d/a/b/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
133,1,1907,142,0.402000," ","int(sech(d*x+c)^7/(a+b*tanh(d*x+c)^2)^3,x)","\text{Expression too large to display}"," ",0,"1/d/b^3*a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/8/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/8/d/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d*a/b^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*a/b^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/b*tanh(1/2*d*x+1/2*c)^7+23/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/b*tanh(1/2*d*x+1/2*c)^5-23/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/b*tanh(1/2*d*x+1/2*c)^3+1/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/b*tanh(1/2*d*x+1/2*c)-2/d/b^3*arctan(tanh(1/2*d*x+1/2*c))-1/d/b^3*a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/8/d/a^2*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+3/8/d/a^2*b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/2/d/b^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/2/d/b^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-5/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^7+7/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^5-7/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^3+5/4/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)-3/8/d/a^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/8/d/a^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*a/b^2*tanh(1/2*d*x+1/2*c)^3-3/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5+3/d/a^2*b/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3-1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*a/b^2*tanh(1/2*d*x+1/2*c)+1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*a/b^2*tanh(1/2*d*x+1/2*c)^7+1/d/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*a/b^2*tanh(1/2*d*x+1/2*c)^5+1/2/d/b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/8/d/a/b/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/2/d/b/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/8/d/a/b/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
134,1,128,50,0.015000," ","int(tanh(d*x+c)^4*(a+b*tanh(d*x+c)^2),x)","-\frac{b \left(\tanh^{5}\left(d x +c \right)\right)}{5 d}-\frac{a \left(\tanh^{3}\left(d x +c \right)\right)}{3 d}-\frac{b \left(\tanh^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \tanh \left(d x +c \right)}{d}-\frac{b \tanh \left(d x +c \right)}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b}{2 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a}{2 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b}{2 d}"," ",0,"-1/5*b*tanh(d*x+c)^5/d-1/3/d*a*tanh(d*x+c)^3-1/3*b*tanh(d*x+c)^3/d-a*tanh(d*x+c)/d-b*tanh(d*x+c)/d-1/2/d*ln(tanh(d*x+c)-1)*a-1/2/d*ln(tanh(d*x+c)-1)*b+1/2/d*ln(1+tanh(d*x+c))*a+1/2/d*ln(1+tanh(d*x+c))*b","B"
135,1,104,45,0.014000," ","int(tanh(d*x+c)^3*(a+b*tanh(d*x+c)^2),x)","-\frac{b \left(\tanh^{4}\left(d x +c \right)\right)}{4 d}-\frac{a \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}-\frac{b \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b}{2 d}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a}{2 d}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b}{2 d}"," ",0,"-1/4*b*tanh(d*x+c)^4/d-1/2/d*a*tanh(d*x+c)^2-1/2*b*tanh(d*x+c)^2/d-1/2/d*ln(tanh(d*x+c)-1)*a-1/2/d*ln(tanh(d*x+c)-1)*b-1/2/d*ln(1+tanh(d*x+c))*a-1/2/d*ln(1+tanh(d*x+c))*b","B"
136,1,100,34,0.016000," ","int(tanh(d*x+c)^2*(a+b*tanh(d*x+c)^2),x)","-\frac{b \left(\tanh^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \tanh \left(d x +c \right)}{d}-\frac{b \tanh \left(d x +c \right)}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b}{2 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a}{2 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b}{2 d}"," ",0,"-1/3*b*tanh(d*x+c)^3/d-a*tanh(d*x+c)/d-b*tanh(d*x+c)/d-1/2/d*ln(tanh(d*x+c)-1)*a-1/2/d*ln(tanh(d*x+c)-1)*b+1/2/d*ln(1+tanh(d*x+c))*a+1/2/d*ln(1+tanh(d*x+c))*b","B"
137,1,76,29,0.016000," ","int(tanh(d*x+c)*(a+b*tanh(d*x+c)^2),x)","-\frac{b \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b}{2 d}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a}{2 d}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b}{2 d}"," ",0,"-1/2*b*tanh(d*x+c)^2/d-1/2/d*ln(tanh(d*x+c)-1)*a-1/2/d*ln(tanh(d*x+c)-1)*b-1/2/d*ln(1+tanh(d*x+c))*a-1/2/d*ln(1+tanh(d*x+c))*b","B"
138,1,47,19,0.016000," ","int(a+b*tanh(d*x+c)^2,x)","a x -\frac{b \tanh \left(d x +c \right)}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b}{2 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b}{2 d}"," ",0,"a*x-b*tanh(d*x+c)/d-1/2/d*ln(tanh(d*x+c)-1)*b+1/2/d*ln(1+tanh(d*x+c))*b","B"
139,1,26,25,0.267000," ","int(coth(d*x+c)*(a+b*tanh(d*x+c)^2),x)","\frac{b \ln \left(\cosh \left(d x +c \right)\right)}{d}+\frac{a \ln \left(\sinh \left(d x +c \right)\right)}{d}"," ",0,"b*ln(cosh(d*x+c))/d+a*ln(sinh(d*x+c))/d","A"
140,1,28,18,0.211000," ","int(coth(d*x+c)^2*(a+b*tanh(d*x+c)^2),x)","\frac{a \left(d x +c -\coth \left(d x +c \right)\right)+\left(d x +c \right) b}{d}"," ",0,"1/d*(a*(d*x+c-coth(d*x+c))+(d*x+c)*b)","A"
141,1,40,29,0.268000," ","int(coth(d*x+c)^3*(a+b*tanh(d*x+c)^2),x)","\frac{a \ln \left(\sinh \left(d x +c \right)\right)}{d}-\frac{a \left(\coth^{2}\left(d x +c \right)\right)}{2 d}+\frac{b \ln \left(\sinh \left(d x +c \right)\right)}{d}"," ",0,"a*ln(sinh(d*x+c))/d-1/2*a*coth(d*x+c)^2/d+1/d*b*ln(sinh(d*x+c))","A"
142,1,46,34,0.235000," ","int(coth(d*x+c)^4*(a+b*tanh(d*x+c)^2),x)","\frac{a \left(d x +c -\coth \left(d x +c \right)-\frac{\left(\coth^{3}\left(d x +c \right)\right)}{3}\right)+b \left(d x +c -\coth \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a*(d*x+c-coth(d*x+c)-1/3*coth(d*x+c)^3)+b*(d*x+c-coth(d*x+c)))","A"
143,1,68,45,0.252000," ","int(coth(d*x+c)^5*(a+b*tanh(d*x+c)^2),x)","\frac{a \ln \left(\sinh \left(d x +c \right)\right)}{d}-\frac{a \left(\coth^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \left(\coth^{4}\left(d x +c \right)\right)}{4 d}+\frac{b \ln \left(\sinh \left(d x +c \right)\right)}{d}-\frac{b \left(\coth^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"a*ln(sinh(d*x+c))/d-1/2*a*coth(d*x+c)^2/d-1/4*a*coth(d*x+c)^4/d+1/d*b*ln(sinh(d*x+c))-1/2/d*b*coth(d*x+c)^2","A"
144,1,236,77,0.016000," ","int(tanh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x)","-\frac{a^{2} \tanh \left(d x +c \right)}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a^{2}}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a b}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b^{2}}{2 d}-\frac{b^{2} \left(\tanh^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{2} \left(\tanh^{3}\left(d x +c \right)\right)}{3 d}-\frac{b^{2} \left(\tanh^{5}\left(d x +c \right)\right)}{5 d}-\frac{b^{2} \left(\tanh^{7}\left(d x +c \right)\right)}{7 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a^{2}}{2 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a b}{d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b^{2}}{2 d}-\frac{2 a b \left(\tanh^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 \left(\tanh^{5}\left(d x +c \right)\right) a b}{5 d}-\frac{2 a b \tanh \left(d x +c \right)}{d}-\frac{b^{2} \tanh \left(d x +c \right)}{d}"," ",0,"-a^2*tanh(d*x+c)/d-1/2/d*ln(tanh(d*x+c)-1)*a^2-1/d*ln(tanh(d*x+c)-1)*a*b-1/2/d*ln(tanh(d*x+c)-1)*b^2-1/3*b^2*tanh(d*x+c)^3/d-1/3/d*a^2*tanh(d*x+c)^3-1/5*b^2*tanh(d*x+c)^5/d-1/7*b^2*tanh(d*x+c)^7/d+1/2/d*ln(1+tanh(d*x+c))*a^2+1/d*ln(1+tanh(d*x+c))*a*b+1/2/d*ln(1+tanh(d*x+c))*b^2-2/3*a*b*tanh(d*x+c)^3/d-2/5/d*tanh(d*x+c)^5*a*b-2*a*b*tanh(d*x+c)/d-b^2*tanh(d*x+c)/d","B"
145,1,196,70,0.016000," ","int(tanh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a^{2}}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a b}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b^{2}}{2 d}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a^{2}}{2 d}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a b}{d}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b^{2}}{2 d}-\frac{b^{2} \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}-\frac{\left(\tanh^{4}\left(d x +c \right)\right) b^{2}}{4 d}-\frac{b^{2} \left(\tanh^{6}\left(d x +c \right)\right)}{6 d}-\frac{\left(\tanh^{4}\left(d x +c \right)\right) a b}{2 d}-\frac{a b \left(\tanh^{2}\left(d x +c \right)\right)}{d}"," ",0,"-1/2/d*ln(tanh(d*x+c)-1)*a^2-1/d*ln(tanh(d*x+c)-1)*a*b-1/2/d*ln(tanh(d*x+c)-1)*b^2-1/2/d*ln(1+tanh(d*x+c))*a^2-1/d*ln(1+tanh(d*x+c))*a*b-1/2/d*ln(1+tanh(d*x+c))*b^2-1/2*b^2*tanh(d*x+c)^2/d-1/2/d*a^2*tanh(d*x+c)^2-1/4/d*tanh(d*x+c)^4*b^2-1/6*b^2*tanh(d*x+c)^6/d-1/2/d*tanh(d*x+c)^4*a*b-a*b*tanh(d*x+c)^2/d","B"
146,1,189,59,0.017000," ","int(tanh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x)","-\frac{a^{2} \tanh \left(d x +c \right)}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a^{2}}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a b}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b^{2}}{2 d}-\frac{b^{2} \left(\tanh^{3}\left(d x +c \right)\right)}{3 d}-\frac{b^{2} \left(\tanh^{5}\left(d x +c \right)\right)}{5 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a^{2}}{2 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a b}{d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b^{2}}{2 d}-\frac{2 a b \left(\tanh^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 a b \tanh \left(d x +c \right)}{d}-\frac{b^{2} \tanh \left(d x +c \right)}{d}"," ",0,"-a^2*tanh(d*x+c)/d-1/2/d*ln(tanh(d*x+c)-1)*a^2-1/d*ln(tanh(d*x+c)-1)*a*b-1/2/d*ln(tanh(d*x+c)-1)*b^2-1/3*b^2*tanh(d*x+c)^3/d-1/5*b^2*tanh(d*x+c)^5/d+1/2/d*ln(1+tanh(d*x+c))*a^2+1/d*ln(1+tanh(d*x+c))*a*b+1/2/d*ln(1+tanh(d*x+c))*b^2-2/3*a*b*tanh(d*x+c)^3/d-2*a*b*tanh(d*x+c)/d-b^2*tanh(d*x+c)/d","B"
147,1,149,53,0.016000," ","int(tanh(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\left(\tanh^{4}\left(d x +c \right)\right) b^{2}}{4 d}-\frac{a b \left(\tanh^{2}\left(d x +c \right)\right)}{d}-\frac{b^{2} \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a^{2}}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a b}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b^{2}}{2 d}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a^{2}}{2 d}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a b}{d}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b^{2}}{2 d}"," ",0,"-1/4/d*tanh(d*x+c)^4*b^2-a*b*tanh(d*x+c)^2/d-1/2*b^2*tanh(d*x+c)^2/d-1/2/d*ln(tanh(d*x+c)-1)*a^2-1/d*ln(tanh(d*x+c)-1)*a*b-1/2/d*ln(tanh(d*x+c)-1)*b^2-1/2/d*ln(1+tanh(d*x+c))*a^2-1/d*ln(1+tanh(d*x+c))*a*b-1/2/d*ln(1+tanh(d*x+c))*b^2","B"
148,1,144,41,0.019000," ","int((a+b*tanh(d*x+c)^2)^2,x)","-\frac{b^{2} \left(\tanh^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 a b \tanh \left(d x +c \right)}{d}-\frac{b^{2} \tanh \left(d x +c \right)}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a^{2}}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a b}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b^{2}}{2 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a^{2}}{2 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a b}{d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b^{2}}{2 d}"," ",0,"-1/3*b^2*tanh(d*x+c)^3/d-2*a*b*tanh(d*x+c)/d-b^2*tanh(d*x+c)/d-1/2/d*ln(tanh(d*x+c)-1)*a^2-1/d*ln(tanh(d*x+c)-1)*a*b-1/2/d*ln(tanh(d*x+c)-1)*b^2+1/2/d*ln(1+tanh(d*x+c))*a^2+1/d*ln(1+tanh(d*x+c))*a*b+1/2/d*ln(1+tanh(d*x+c))*b^2","B"
149,1,60,47,0.264000," ","int(coth(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \ln \left(\sinh \left(d x +c \right)\right)}{d}+\frac{2 a b \ln \left(\cosh \left(d x +c \right)\right)}{d}+\frac{b^{2} \ln \left(\cosh \left(d x +c \right)\right)}{d}-\frac{b^{2} \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/d*a^2*ln(sinh(d*x+c))+2*a*b*ln(cosh(d*x+c))/d+1/d*b^2*ln(cosh(d*x+c))-1/2*b^2*tanh(d*x+c)^2/d","A"
150,1,49,36,0.209000," ","int(coth(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \left(d x +c -\coth \left(d x +c \right)\right)+2 a b \left(d x +c \right)+b^{2} \left(d x +c -\tanh \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a^2*(d*x+c-coth(d*x+c))+2*a*b*(d*x+c)+b^2*(d*x+c-tanh(d*x+c)))","A"
151,1,60,50,0.267000," ","int(coth(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \ln \left(\sinh \left(d x +c \right)\right)}{d}-\frac{a^{2} \left(\coth^{2}\left(d x +c \right)\right)}{2 d}+\frac{2 a b \ln \left(\sinh \left(d x +c \right)\right)}{d}+\frac{b^{2} \ln \left(\cosh \left(d x +c \right)\right)}{d}"," ",0,"1/d*a^2*ln(sinh(d*x+c))-1/2*a^2*coth(d*x+c)^2/d+2/d*a*b*ln(sinh(d*x+c))+1/d*b^2*ln(cosh(d*x+c))","A"
152,1,59,41,0.228000," ","int(coth(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \left(d x +c -\coth \left(d x +c \right)-\frac{\left(\coth^{3}\left(d x +c \right)\right)}{3}\right)+2 a b \left(d x +c -\coth \left(d x +c \right)\right)+b^{2} \left(d x +c \right)}{d}"," ",0,"1/d*(a^2*(d*x+c-coth(d*x+c)-1/3*coth(d*x+c)^3)+2*a*b*(d*x+c-coth(d*x+c))+b^2*(d*x+c))","A"
153,1,91,68,0.288000," ","int(coth(d*x+c)^5*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \ln \left(\sinh \left(d x +c \right)\right)}{d}-\frac{a^{2} \left(\coth^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \left(\coth^{4}\left(d x +c \right)\right)}{4 d}-\frac{a b \left(\coth^{2}\left(d x +c \right)\right)}{d}+\frac{2 a b \ln \left(\sinh \left(d x +c \right)\right)}{d}+\frac{b^{2} \ln \left(\sinh \left(d x +c \right)\right)}{d}"," ",0,"1/d*a^2*ln(sinh(d*x+c))-1/2*a^2*coth(d*x+c)^2/d-1/4*a^2*coth(d*x+c)^4/d-1/d*a*b*coth(d*x+c)^2+2/d*a*b*ln(sinh(d*x+c))+1/d*b^2*ln(sinh(d*x+c))","A"
154,1,87,59,0.238000," ","int(coth(d*x+c)^6*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \left(d x +c -\coth \left(d x +c \right)-\frac{\left(\coth^{3}\left(d x +c \right)\right)}{3}-\frac{\left(\coth^{5}\left(d x +c \right)\right)}{5}\right)+2 a b \left(d x +c -\coth \left(d x +c \right)-\frac{\left(\coth^{3}\left(d x +c \right)\right)}{3}\right)+b^{2} \left(d x +c -\coth \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a^2*(d*x+c-coth(d*x+c)-1/3*coth(d*x+c)^3-1/5*coth(d*x+c)^5)+2*a*b*(d*x+c-coth(d*x+c)-1/3*coth(d*x+c)^3)+b^2*(d*x+c-coth(d*x+c)))","A"
155,1,138,86,0.257000," ","int(coth(d*x+c)^7*(a+b*tanh(d*x+c)^2)^2,x)","\frac{a^{2} \ln \left(\sinh \left(d x +c \right)\right)}{d}-\frac{a^{2} \left(\coth^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \left(\coth^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{2} \left(\coth^{6}\left(d x +c \right)\right)}{6 d}+\frac{2 a b \ln \left(\sinh \left(d x +c \right)\right)}{d}-\frac{a b \left(\coth^{2}\left(d x +c \right)\right)}{d}-\frac{a b \left(\coth^{4}\left(d x +c \right)\right)}{2 d}+\frac{b^{2} \ln \left(\sinh \left(d x +c \right)\right)}{d}-\frac{b^{2} \left(\coth^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/d*a^2*ln(sinh(d*x+c))-1/2*a^2*coth(d*x+c)^2/d-1/4*a^2*coth(d*x+c)^4/d-1/6*a^2*coth(d*x+c)^6/d+2/d*a*b*ln(sinh(d*x+c))-1/d*a*b*coth(d*x+c)^2-1/2/d*a*b*coth(d*x+c)^4+1/d*b^2*ln(sinh(d*x+c))-1/2/d*b^2*coth(d*x+c)^2","A"
156,1,365,106,0.017000," ","int(tanh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x)","\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a^{3}}{2 d}+\frac{3 \ln \left(1+\tanh \left(d x +c \right)\right) a^{2} b}{2 d}+\frac{3 \ln \left(1+\tanh \left(d x +c \right)\right) a \,b^{2}}{2 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b^{3}}{2 d}-\frac{a^{3} \left(\tanh^{3}\left(d x +c \right)\right)}{3 d}-\frac{b^{3} \tanh \left(d x +c \right)}{d}-\frac{b^{3} \left(\tanh^{9}\left(d x +c \right)\right)}{9 d}-\frac{a^{3} \tanh \left(d x +c \right)}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a^{3}}{2 d}-\frac{3 \ln \left(\tanh \left(d x +c \right)-1\right) a^{2} b}{2 d}-\frac{3 \ln \left(\tanh \left(d x +c \right)-1\right) a \,b^{2}}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b^{3}}{2 d}-\frac{b^{3} \left(\tanh^{7}\left(d x +c \right)\right)}{7 d}-\frac{b^{3} \left(\tanh^{5}\left(d x +c \right)\right)}{5 d}-\frac{b^{3} \left(\tanh^{3}\left(d x +c \right)\right)}{3 d}-\frac{3 \left(\tanh^{5}\left(d x +c \right)\right) a^{2} b}{5 d}-\frac{3 a \,b^{2} \left(\tanh^{5}\left(d x +c \right)\right)}{5 d}-\frac{a^{2} b \left(\tanh^{3}\left(d x +c \right)\right)}{d}-\frac{a \,b^{2} \left(\tanh^{3}\left(d x +c \right)\right)}{d}-\frac{3 \left(\tanh^{7}\left(d x +c \right)\right) a \,b^{2}}{7 d}-\frac{3 a^{2} b \tanh \left(d x +c \right)}{d}-\frac{3 a \,b^{2} \tanh \left(d x +c \right)}{d}"," ",0,"1/2/d*ln(1+tanh(d*x+c))*a^3+3/2/d*ln(1+tanh(d*x+c))*a^2*b+3/2/d*ln(1+tanh(d*x+c))*a*b^2+1/2/d*ln(1+tanh(d*x+c))*b^3-1/3/d*a^3*tanh(d*x+c)^3-b^3*tanh(d*x+c)/d-1/9*b^3*tanh(d*x+c)^9/d-a^3*tanh(d*x+c)/d-1/2/d*ln(tanh(d*x+c)-1)*a^3-3/2/d*ln(tanh(d*x+c)-1)*a^2*b-3/2/d*ln(tanh(d*x+c)-1)*a*b^2-1/2/d*ln(tanh(d*x+c)-1)*b^3-1/7*b^3*tanh(d*x+c)^7/d-1/5*b^3*tanh(d*x+c)^5/d-1/3*b^3*tanh(d*x+c)^3/d-3/5/d*tanh(d*x+c)^5*a^2*b-3/5*a*b^2*tanh(d*x+c)^5/d-a^2*b*tanh(d*x+c)^3/d-a*b^2*tanh(d*x+c)^3/d-3/7/d*tanh(d*x+c)^7*a*b^2-3*a^2*b*tanh(d*x+c)/d-3*a*b^2*tanh(d*x+c)/d","B"
157,1,307,99,0.017000," ","int(tanh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x)","-\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a^{3}}{2 d}-\frac{3 \ln \left(1+\tanh \left(d x +c \right)\right) a^{2} b}{2 d}-\frac{3 \ln \left(1+\tanh \left(d x +c \right)\right) a \,b^{2}}{2 d}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b^{3}}{2 d}-\frac{a^{3} \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{3} \left(\tanh^{8}\left(d x +c \right)\right)}{8 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a^{3}}{2 d}-\frac{3 \ln \left(\tanh \left(d x +c \right)-1\right) a^{2} b}{2 d}-\frac{3 \ln \left(\tanh \left(d x +c \right)-1\right) a \,b^{2}}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b^{3}}{2 d}-\frac{b^{3} \left(\tanh^{6}\left(d x +c \right)\right)}{6 d}-\frac{b^{3} \left(\tanh^{4}\left(d x +c \right)\right)}{4 d}-\frac{b^{3} \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 \left(\tanh^{4}\left(d x +c \right)\right) a^{2} b}{4 d}-\frac{3 \left(\tanh^{4}\left(d x +c \right)\right) a \,b^{2}}{4 d}-\frac{3 a^{2} b \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 \left(\tanh^{2}\left(d x +c \right)\right) a \,b^{2}}{2 d}-\frac{\left(\tanh^{6}\left(d x +c \right)\right) a \,b^{2}}{2 d}"," ",0,"-1/2/d*ln(1+tanh(d*x+c))*a^3-3/2/d*ln(1+tanh(d*x+c))*a^2*b-3/2/d*ln(1+tanh(d*x+c))*a*b^2-1/2/d*ln(1+tanh(d*x+c))*b^3-1/2/d*a^3*tanh(d*x+c)^2-1/8*b^3*tanh(d*x+c)^8/d-1/2/d*ln(tanh(d*x+c)-1)*a^3-3/2/d*ln(tanh(d*x+c)-1)*a^2*b-3/2/d*ln(tanh(d*x+c)-1)*a*b^2-1/2/d*ln(tanh(d*x+c)-1)*b^3-1/6*b^3*tanh(d*x+c)^6/d-1/4*b^3*tanh(d*x+c)^4/d-1/2*b^3*tanh(d*x+c)^2/d-3/4/d*tanh(d*x+c)^4*a^2*b-3/4/d*tanh(d*x+c)^4*a*b^2-3/2*a^2*b*tanh(d*x+c)^2/d-3/2/d*tanh(d*x+c)^2*a*b^2-1/2/d*tanh(d*x+c)^6*a*b^2","B"
158,1,299,88,0.017000," ","int(tanh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x)","\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a^{3}}{2 d}+\frac{3 \ln \left(1+\tanh \left(d x +c \right)\right) a^{2} b}{2 d}+\frac{3 \ln \left(1+\tanh \left(d x +c \right)\right) a \,b^{2}}{2 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b^{3}}{2 d}-\frac{b^{3} \tanh \left(d x +c \right)}{d}-\frac{a^{3} \tanh \left(d x +c \right)}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a^{3}}{2 d}-\frac{3 \ln \left(\tanh \left(d x +c \right)-1\right) a^{2} b}{2 d}-\frac{3 \ln \left(\tanh \left(d x +c \right)-1\right) a \,b^{2}}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b^{3}}{2 d}-\frac{b^{3} \left(\tanh^{7}\left(d x +c \right)\right)}{7 d}-\frac{b^{3} \left(\tanh^{5}\left(d x +c \right)\right)}{5 d}-\frac{b^{3} \left(\tanh^{3}\left(d x +c \right)\right)}{3 d}-\frac{3 a \,b^{2} \left(\tanh^{5}\left(d x +c \right)\right)}{5 d}-\frac{a^{2} b \left(\tanh^{3}\left(d x +c \right)\right)}{d}-\frac{a \,b^{2} \left(\tanh^{3}\left(d x +c \right)\right)}{d}-\frac{3 a^{2} b \tanh \left(d x +c \right)}{d}-\frac{3 a \,b^{2} \tanh \left(d x +c \right)}{d}"," ",0,"1/2/d*ln(1+tanh(d*x+c))*a^3+3/2/d*ln(1+tanh(d*x+c))*a^2*b+3/2/d*ln(1+tanh(d*x+c))*a*b^2+1/2/d*ln(1+tanh(d*x+c))*b^3-b^3*tanh(d*x+c)/d-a^3*tanh(d*x+c)/d-1/2/d*ln(tanh(d*x+c)-1)*a^3-3/2/d*ln(tanh(d*x+c)-1)*a^2*b-3/2/d*ln(tanh(d*x+c)-1)*a*b^2-1/2/d*ln(tanh(d*x+c)-1)*b^3-1/7*b^3*tanh(d*x+c)^7/d-1/5*b^3*tanh(d*x+c)^5/d-1/3*b^3*tanh(d*x+c)^3/d-3/5*a*b^2*tanh(d*x+c)^5/d-a^2*b*tanh(d*x+c)^3/d-a*b^2*tanh(d*x+c)^3/d-3*a^2*b*tanh(d*x+c)/d-3*a*b^2*tanh(d*x+c)/d","B"
159,1,241,77,0.019000," ","int(tanh(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x)","-\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a^{3}}{2 d}-\frac{3 \ln \left(1+\tanh \left(d x +c \right)\right) a^{2} b}{2 d}-\frac{3 \ln \left(1+\tanh \left(d x +c \right)\right) a \,b^{2}}{2 d}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b^{3}}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a^{3}}{2 d}-\frac{3 \ln \left(\tanh \left(d x +c \right)-1\right) a^{2} b}{2 d}-\frac{3 \ln \left(\tanh \left(d x +c \right)-1\right) a \,b^{2}}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b^{3}}{2 d}-\frac{b^{3} \left(\tanh^{6}\left(d x +c \right)\right)}{6 d}-\frac{b^{3} \left(\tanh^{4}\left(d x +c \right)\right)}{4 d}-\frac{b^{3} \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 \left(\tanh^{4}\left(d x +c \right)\right) a \,b^{2}}{4 d}-\frac{3 a^{2} b \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 \left(\tanh^{2}\left(d x +c \right)\right) a \,b^{2}}{2 d}"," ",0,"-1/2/d*ln(1+tanh(d*x+c))*a^3-3/2/d*ln(1+tanh(d*x+c))*a^2*b-3/2/d*ln(1+tanh(d*x+c))*a*b^2-1/2/d*ln(1+tanh(d*x+c))*b^3-1/2/d*ln(tanh(d*x+c)-1)*a^3-3/2/d*ln(tanh(d*x+c)-1)*a^2*b-3/2/d*ln(tanh(d*x+c)-1)*a*b^2-1/2/d*ln(tanh(d*x+c)-1)*b^3-1/6*b^3*tanh(d*x+c)^6/d-1/4*b^3*tanh(d*x+c)^4/d-1/2*b^3*tanh(d*x+c)^2/d-3/4/d*tanh(d*x+c)^4*a*b^2-3/2*a^2*b*tanh(d*x+c)^2/d-3/2/d*tanh(d*x+c)^2*a*b^2","B"
160,1,235,70,0.017000," ","int((a+b*tanh(d*x+c)^2)^3,x)","\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a^{3}}{2 d}+\frac{3 \ln \left(1+\tanh \left(d x +c \right)\right) a^{2} b}{2 d}+\frac{3 \ln \left(1+\tanh \left(d x +c \right)\right) a \,b^{2}}{2 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b^{3}}{2 d}-\frac{b^{3} \tanh \left(d x +c \right)}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a^{3}}{2 d}-\frac{3 \ln \left(\tanh \left(d x +c \right)-1\right) a^{2} b}{2 d}-\frac{3 \ln \left(\tanh \left(d x +c \right)-1\right) a \,b^{2}}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b^{3}}{2 d}-\frac{b^{3} \left(\tanh^{5}\left(d x +c \right)\right)}{5 d}-\frac{b^{3} \left(\tanh^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \,b^{2} \left(\tanh^{3}\left(d x +c \right)\right)}{d}-\frac{3 a^{2} b \tanh \left(d x +c \right)}{d}-\frac{3 a \,b^{2} \tanh \left(d x +c \right)}{d}"," ",0,"1/2/d*ln(1+tanh(d*x+c))*a^3+3/2/d*ln(1+tanh(d*x+c))*a^2*b+3/2/d*ln(1+tanh(d*x+c))*a*b^2+1/2/d*ln(1+tanh(d*x+c))*b^3-b^3*tanh(d*x+c)/d-1/2/d*ln(tanh(d*x+c)-1)*a^3-3/2/d*ln(tanh(d*x+c)-1)*a^2*b-3/2/d*ln(tanh(d*x+c)-1)*a*b^2-1/2/d*ln(tanh(d*x+c)-1)*b^3-1/5*b^3*tanh(d*x+c)^5/d-1/3*b^3*tanh(d*x+c)^3/d-a*b^2*tanh(d*x+c)^3/d-3*a^2*b*tanh(d*x+c)/d-3*a*b^2*tanh(d*x+c)/d","B"
161,1,111,68,0.286000," ","int(coth(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \ln \left(\sinh \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b \ln \left(\cosh \left(d x +c \right)\right)}{d}+\frac{3 a \,b^{2} \ln \left(\cosh \left(d x +c \right)\right)}{d}-\frac{3 \left(\tanh^{2}\left(d x +c \right)\right) a \,b^{2}}{2 d}+\frac{b^{3} \ln \left(\cosh \left(d x +c \right)\right)}{d}-\frac{b^{3} \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{3} \left(\tanh^{4}\left(d x +c \right)\right)}{4 d}"," ",0,"1/d*a^3*ln(sinh(d*x+c))+3/d*a^2*b*ln(cosh(d*x+c))+3/d*a*b^2*ln(cosh(d*x+c))-3/2/d*tanh(d*x+c)^2*a*b^2+1/d*b^3*ln(cosh(d*x+c))-1/2*b^3*tanh(d*x+c)^2/d-1/4*b^3*tanh(d*x+c)^4/d","A"
162,1,80,57,0.246000," ","int(coth(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \left(d x +c -\coth \left(d x +c \right)\right)+3 a^{2} b \left(d x +c \right)+3 a \,b^{2} \left(d x +c -\tanh \left(d x +c \right)\right)+b^{3} \left(d x +c -\tanh \left(d x +c \right)-\frac{\left(\tanh^{3}\left(d x +c \right)\right)}{3}\right)}{d}"," ",0,"1/d*(a^3*(d*x+c-coth(d*x+c))+3*a^2*b*(d*x+c)+3*a*b^2*(d*x+c-tanh(d*x+c))+b^3*(d*x+c-tanh(d*x+c)-1/3*tanh(d*x+c)^3))","A"
163,1,94,68,0.275000," ","int(coth(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \ln \left(\sinh \left(d x +c \right)\right)}{d}-\frac{a^{3} \left(\coth^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 a^{2} b \ln \left(\sinh \left(d x +c \right)\right)}{d}+\frac{3 a \,b^{2} \ln \left(\cosh \left(d x +c \right)\right)}{d}+\frac{b^{3} \ln \left(\cosh \left(d x +c \right)\right)}{d}-\frac{b^{3} \left(\tanh^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/d*a^3*ln(sinh(d*x+c))-1/2*a^3*coth(d*x+c)^2/d+3/d*a^2*b*ln(sinh(d*x+c))+3/d*a*b^2*ln(cosh(d*x+c))+1/d*b^3*ln(cosh(d*x+c))-1/2*b^3*tanh(d*x+c)^2/d","A"
164,1,80,57,0.246000," ","int(coth(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \left(d x +c -\coth \left(d x +c \right)-\frac{\left(\coth^{3}\left(d x +c \right)\right)}{3}\right)+3 a^{2} b \left(d x +c -\coth \left(d x +c \right)\right)+3 a \,b^{2} \left(d x +c \right)+b^{3} \left(d x +c -\tanh \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a^3*(d*x+c-coth(d*x+c)-1/3*coth(d*x+c)^3)+3*a^2*b*(d*x+c-coth(d*x+c))+3*a*b^2*(d*x+c)+b^3*(d*x+c-tanh(d*x+c)))","A"
165,1,111,79,0.270000," ","int(coth(d*x+c)^5*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \ln \left(\sinh \left(d x +c \right)\right)}{d}-\frac{a^{3} \left(\coth^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{3} \left(\coth^{4}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{2} b \ln \left(\sinh \left(d x +c \right)\right)}{d}-\frac{3 a^{2} b \left(\coth^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 a \,b^{2} \ln \left(\sinh \left(d x +c \right)\right)}{d}+\frac{b^{3} \ln \left(\cosh \left(d x +c \right)\right)}{d}"," ",0,"1/d*a^3*ln(sinh(d*x+c))-1/2*a^3*coth(d*x+c)^2/d-1/4*a^3*coth(d*x+c)^4/d+3/d*a^2*b*ln(sinh(d*x+c))-3/2/d*a^2*b*coth(d*x+c)^2+3/d*a*b^2*ln(sinh(d*x+c))+1/d*b^3*ln(cosh(d*x+c))","A"
166,1,100,70,0.283000," ","int(coth(d*x+c)^6*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \left(d x +c -\coth \left(d x +c \right)-\frac{\left(\coth^{3}\left(d x +c \right)\right)}{3}-\frac{\left(\coth^{5}\left(d x +c \right)\right)}{5}\right)+3 a^{2} b \left(d x +c -\coth \left(d x +c \right)-\frac{\left(\coth^{3}\left(d x +c \right)\right)}{3}\right)+3 a \,b^{2} \left(d x +c -\coth \left(d x +c \right)\right)+b^{3} \left(d x +c \right)}{d}"," ",0,"1/d*(a^3*(d*x+c-coth(d*x+c)-1/3*coth(d*x+c)^3-1/5*coth(d*x+c)^5)+3*a^2*b*(d*x+c-coth(d*x+c)-1/3*coth(d*x+c)^3)+3*a*b^2*(d*x+c-coth(d*x+c))+b^3*(d*x+c))","A"
167,1,161,97,0.273000," ","int(coth(d*x+c)^7*(a+b*tanh(d*x+c)^2)^3,x)","\frac{a^{3} \ln \left(\sinh \left(d x +c \right)\right)}{d}-\frac{a^{3} \left(\coth^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{3} \left(\coth^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{3} \left(\coth^{6}\left(d x +c \right)\right)}{6 d}+\frac{3 a^{2} b \ln \left(\sinh \left(d x +c \right)\right)}{d}-\frac{3 a^{2} b \left(\coth^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} b \left(\coth^{4}\left(d x +c \right)\right)}{4 d}+\frac{3 a \,b^{2} \ln \left(\sinh \left(d x +c \right)\right)}{d}-\frac{3 a \,b^{2} \left(\coth^{2}\left(d x +c \right)\right)}{2 d}+\frac{b^{3} \ln \left(\sinh \left(d x +c \right)\right)}{d}"," ",0,"1/d*a^3*ln(sinh(d*x+c))-1/2*a^3*coth(d*x+c)^2/d-1/4*a^3*coth(d*x+c)^4/d-1/6*a^3*coth(d*x+c)^6/d+3/d*a^2*b*ln(sinh(d*x+c))-3/2/d*a^2*b*coth(d*x+c)^2-3/4/d*a^2*b*coth(d*x+c)^4+3/d*a*b^2*ln(sinh(d*x+c))-3/2/d*a*b^2*coth(d*x+c)^2+1/d*b^3*ln(sinh(d*x+c))","A"
168,1,344,104,0.018000," ","int((a+b*tanh(d*x+c)^2)^4,x)","\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a^{4}}{2 d}+\frac{2 \ln \left(1+\tanh \left(d x +c \right)\right) a^{3} b}{d}+\frac{3 \ln \left(1+\tanh \left(d x +c \right)\right) a^{2} b^{2}}{d}+\frac{2 \ln \left(1+\tanh \left(d x +c \right)\right) a \,b^{3}}{d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b^{4}}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a^{4}}{2 d}-\frac{2 \ln \left(\tanh \left(d x +c \right)-1\right) a^{3} b}{d}-\frac{3 \ln \left(\tanh \left(d x +c \right)-1\right) a^{2} b^{2}}{d}-\frac{2 \ln \left(\tanh \left(d x +c \right)-1\right) a \,b^{3}}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b^{4}}{2 d}-\frac{\left(\tanh^{5}\left(d x +c \right)\right) b^{4}}{5 d}-\frac{b^{4} \tanh \left(d x +c \right)}{d}-\frac{b^{4} \left(\tanh^{3}\left(d x +c \right)\right)}{3 d}-\frac{b^{4} \left(\tanh^{7}\left(d x +c \right)\right)}{7 d}-\frac{2 \left(\tanh^{3}\left(d x +c \right)\right) a^{2} b^{2}}{d}-\frac{4 \left(\tanh^{3}\left(d x +c \right)\right) a \,b^{3}}{3 d}-\frac{4 \left(\tanh^{5}\left(d x +c \right)\right) a \,b^{3}}{5 d}-\frac{4 a \,b^{3} \tanh \left(d x +c \right)}{d}-\frac{4 a^{3} b \tanh \left(d x +c \right)}{d}-\frac{6 a^{2} b^{2} \tanh \left(d x +c \right)}{d}"," ",0,"1/2/d*ln(1+tanh(d*x+c))*a^4+2/d*ln(1+tanh(d*x+c))*a^3*b+3/d*ln(1+tanh(d*x+c))*a^2*b^2+2/d*ln(1+tanh(d*x+c))*a*b^3+1/2/d*ln(1+tanh(d*x+c))*b^4-1/2/d*ln(tanh(d*x+c)-1)*a^4-2/d*ln(tanh(d*x+c)-1)*a^3*b-3/d*ln(tanh(d*x+c)-1)*a^2*b^2-2/d*ln(tanh(d*x+c)-1)*a*b^3-1/2/d*ln(tanh(d*x+c)-1)*b^4-1/5/d*tanh(d*x+c)^5*b^4-1/d*b^4*tanh(d*x+c)-1/3/d*tanh(d*x+c)^3*b^4-1/7*b^4*tanh(d*x+c)^7/d-2/d*tanh(d*x+c)^3*a^2*b^2-4/3/d*tanh(d*x+c)^3*a*b^3-4/5/d*tanh(d*x+c)^5*a*b^3-4/d*a*b^3*tanh(d*x+c)-4/d*a^3*b*tanh(d*x+c)-6/d*a^2*b^2*tanh(d*x+c)","B"
169,1,472,152,0.020000," ","int((a+b*tanh(d*x+c)^2)^5,x)","\frac{5 \ln \left(1+\tanh \left(d x +c \right)\right) a^{3} b^{2}}{d}+\frac{5 \ln \left(1+\tanh \left(d x +c \right)\right) a^{2} b^{3}}{d}+\frac{5 \ln \left(1+\tanh \left(d x +c \right)\right) a \,b^{4}}{2 d}-\frac{5 \ln \left(\tanh \left(d x +c \right)-1\right) a^{4} b}{2 d}-\frac{10 a^{2} b^{3} \tanh \left(d x +c \right)}{d}-\frac{5 a \,b^{4} \tanh \left(d x +c \right)}{d}-\frac{10 a^{3} b^{2} \tanh \left(d x +c \right)}{d}+\frac{5 \ln \left(1+\tanh \left(d x +c \right)\right) a^{4} b}{2 d}-\frac{5 a^{4} b \tanh \left(d x +c \right)}{d}-\frac{5 \ln \left(\tanh \left(d x +c \right)-1\right) a^{3} b^{2}}{d}-\frac{5 \ln \left(\tanh \left(d x +c \right)-1\right) a^{2} b^{3}}{d}-\frac{5 \ln \left(\tanh \left(d x +c \right)-1\right) a \,b^{4}}{2 d}-\frac{10 \left(\tanh^{3}\left(d x +c \right)\right) a^{3} b^{2}}{3 d}-\frac{\left(\tanh^{5}\left(d x +c \right)\right) a \,b^{4}}{d}-\frac{5 \left(\tanh^{3}\left(d x +c \right)\right) a \,b^{4}}{3 d}-\frac{10 \left(\tanh^{3}\left(d x +c \right)\right) a^{2} b^{3}}{3 d}-\frac{2 \left(\tanh^{5}\left(d x +c \right)\right) a^{2} b^{3}}{d}-\frac{5 \left(\tanh^{7}\left(d x +c \right)\right) a \,b^{4}}{7 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a^{5}}{2 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b^{5}}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a^{5}}{2 d}-\frac{b^{5} \tanh \left(d x +c \right)}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b^{5}}{2 d}-\frac{b^{5} \left(\tanh^{9}\left(d x +c \right)\right)}{9 d}-\frac{\left(\tanh^{5}\left(d x +c \right)\right) b^{5}}{5 d}-\frac{\left(\tanh^{3}\left(d x +c \right)\right) b^{5}}{3 d}-\frac{\left(\tanh^{7}\left(d x +c \right)\right) b^{5}}{7 d}"," ",0,"-2/d*tanh(d*x+c)^5*a^2*b^3+5/d*ln(1+tanh(d*x+c))*a^3*b^2+5/d*ln(1+tanh(d*x+c))*a^2*b^3+5/2/d*ln(1+tanh(d*x+c))*a*b^4-5/2/d*ln(tanh(d*x+c)-1)*a^4*b-5/7/d*tanh(d*x+c)^7*a*b^4-10/d*a^2*b^3*tanh(d*x+c)-5/d*a*b^4*tanh(d*x+c)-10/d*a^3*b^2*tanh(d*x+c)+5/2/d*ln(1+tanh(d*x+c))*a^4*b-5/d*a^4*b*tanh(d*x+c)-5/d*ln(tanh(d*x+c)-1)*a^3*b^2-5/d*ln(tanh(d*x+c)-1)*a^2*b^3-5/2/d*ln(tanh(d*x+c)-1)*a*b^4-5/3/d*tanh(d*x+c)^3*a*b^4-10/3/d*tanh(d*x+c)^3*a^2*b^3-10/3/d*tanh(d*x+c)^3*a^3*b^2-1/d*tanh(d*x+c)^5*a*b^4-1/9*b^5*tanh(d*x+c)^9/d+1/2/d*ln(1+tanh(d*x+c))*a^5+1/2/d*ln(1+tanh(d*x+c))*b^5-1/2/d*ln(tanh(d*x+c)-1)*a^5-1/d*b^5*tanh(d*x+c)-1/5/d*tanh(d*x+c)^5*b^5-1/3/d*tanh(d*x+c)^3*b^5-1/7/d*tanh(d*x+c)^7*b^5-1/2/d*ln(tanh(d*x+c)-1)*b^5","B"
170,1,93,62,0.089000," ","int(tanh(d*x+c)^5/(a+b*tanh(d*x+c)^2),x)","-\frac{\tanh^{2}\left(d x +c \right)}{2 b d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{d \left(2 b +2 a \right)}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{d \left(2 b +2 a \right)}+\frac{a^{2} \ln \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}{2 b^{2} \left(a +b \right) d}"," ",0,"-1/2*tanh(d*x+c)^2/b/d-1/d/(2*b+2*a)*ln(tanh(d*x+c)-1)-1/d/(2*b+2*a)*ln(1+tanh(d*x+c))+1/2*a^2*ln(a+b*tanh(d*x+c)^2)/b^2/(a+b)/d","A"
171,1,95,51,0.097000," ","int(tanh(d*x+c)^4/(a+b*tanh(d*x+c)^2),x)","-\frac{\tanh \left(d x +c \right)}{b d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{d \left(2 b +2 a \right)}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{d \left(2 b +2 a \right)}+\frac{a^{2} \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{d b \left(a +b \right) \sqrt{a b}}"," ",0,"-tanh(d*x+c)/b/d-1/d/(2*b+2*a)*ln(tanh(d*x+c)-1)+1/d/(2*b+2*a)*ln(1+tanh(d*x+c))+1/d/b/(a+b)*a^2/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))","A"
172,1,75,44,0.107000," ","int(tanh(d*x+c)^3/(a+b*tanh(d*x+c)^2),x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{d \left(2 b +2 a \right)}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{d \left(2 b +2 a \right)}-\frac{a \ln \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}{2 b \left(a +b \right) d}"," ",0,"-1/d/(2*b+2*a)*ln(tanh(d*x+c)-1)-1/d/(2*b+2*a)*ln(1+tanh(d*x+c))-1/2*a*ln(a+b*tanh(d*x+c)^2)/b/(a+b)/d","A"
173,1,77,38,0.072000," ","int(tanh(d*x+c)^2/(a+b*tanh(d*x+c)^2),x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{d \left(2 b +2 a \right)}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{d \left(2 b +2 a \right)}-\frac{a \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{d \left(a +b \right) \sqrt{a b}}"," ",0,"-1/d/(2*b+2*a)*ln(tanh(d*x+c)-1)+1/d/(2*b+2*a)*ln(1+tanh(d*x+c))-1/d/(a+b)*a/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))","A"
174,1,71,40,0.087000," ","int(tanh(d*x+c)/(a+b*tanh(d*x+c)^2),x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{d \left(2 b +2 a \right)}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{d \left(2 b +2 a \right)}+\frac{\ln \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}{2 \left(a +b \right) d}"," ",0,"-1/d/(2*b+2*a)*ln(tanh(d*x+c)-1)-1/d/(2*b+2*a)*ln(1+tanh(d*x+c))+1/2*ln(a+b*tanh(d*x+c)^2)/(a+b)/d","A"
175,1,76,37,0.144000," ","int(1/(a+b*tanh(d*x+c)^2),x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{d \left(2 b +2 a \right)}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{d \left(2 b +2 a \right)}+\frac{b \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{d \left(a +b \right) \sqrt{a b}}"," ",0,"-1/d/(2*b+2*a)*ln(tanh(d*x+c)-1)+1/d/(2*b+2*a)*ln(1+tanh(d*x+c))+1/d*b/(a+b)/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))","B"
176,1,121,58,0.403000," ","int(coth(d*x+c)/(a+b*tanh(d*x+c)^2),x)","-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \left(a +b \right)}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \left(a +b \right)}-\frac{b \ln \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}{2 d a \left(a +b \right)}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}"," ",0,"-1/d/(a+b)*ln(tanh(1/2*d*x+1/2*c)-1)-1/d/(a+b)*ln(tanh(1/2*d*x+1/2*c)+1)-1/2/d*b/a/(a+b)*ln(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)+1/d/a*ln(tanh(1/2*d*x+1/2*c))","B"
177,1,494,52,0.398000," ","int(coth(d*x+c)^2/(a+b*tanh(d*x+c)^2),x)","-\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d a}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \left(a +b \right)}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \left(a +b \right)}-\frac{1}{2 d a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right) \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right) a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right) \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right) \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right) a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right) \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}"," ",0,"-1/2/d/a*tanh(1/2*d*x+1/2*c)-1/d/(a+b)*ln(tanh(1/2*d*x+1/2*c)-1)+1/d/(a+b)*ln(tanh(1/2*d*x+1/2*c)+1)-1/2/d/a/tanh(1/2*d*x+1/2*c)+1/d*b^2/(a+b)/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d*b^2/(a+b)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*b^3/(a+b)/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*b^2/(a+b)/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d*b^2/(a+b)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+1/d*b^3/(a+b)/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))","B"
178,1,180,81,0.422000," ","int(coth(d*x+c)^3/(a+b*tanh(d*x+c)^2),x)","-\frac{\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d a}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \left(a +b \right)}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \left(a +b \right)}+\frac{b^{2} \ln \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}{2 d \,a^{2} \left(a +b \right)}-\frac{1}{8 d a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}-\frac{b \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"-1/8/d/a*tanh(1/2*d*x+1/2*c)^2-1/d/(a+b)*ln(tanh(1/2*d*x+1/2*c)-1)-1/d/(a+b)*ln(tanh(1/2*d*x+1/2*c)+1)+1/2/d*b^2/a^2/(a+b)*ln(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)-1/8/d/a/tanh(1/2*d*x+1/2*c)^2+1/d/a*ln(tanh(1/2*d*x+1/2*c))-1/d/a^2*b*ln(tanh(1/2*d*x+1/2*c))","B"
179,1,580,72,0.484000," ","int(coth(d*x+c)^4/(a+b*tanh(d*x+c)^2),x)","-\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d a}-\frac{5 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d a}+\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right) b}{2 d \,a^{2}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \left(a +b \right)}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \left(a +b \right)}-\frac{b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right) \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right) a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{b^{4} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right) a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right) \sqrt{b \left(a +b \right)}\, a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right) a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{b^{4} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right) a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{1}{24 d a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{5}{8 d a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{2 d \,a^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}"," ",0,"-1/24/d/a*tanh(1/2*d*x+1/2*c)^3-5/8/d/a*tanh(1/2*d*x+1/2*c)+1/2/d/a^2*tanh(1/2*d*x+1/2*c)*b-1/d/(a+b)*ln(tanh(1/2*d*x+1/2*c)-1)+1/d/(a+b)*ln(tanh(1/2*d*x+1/2*c)+1)-1/d*b^3/(a+b)/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+1/d*b^3/(a+b)/a^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d*b^4/(a+b)/a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-1/d*b^3/(a+b)/(b*(a+b))^(1/2)/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d*b^3/(a+b)/a^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d*b^4/(a+b)/a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/24/d/a/tanh(1/2*d*x+1/2*c)^3-5/8/d/a/tanh(1/2*d*x+1/2*c)+1/2/d*b/a^2/tanh(1/2*d*x+1/2*c)","B"
180,1,156,79,0.101000," ","int(tanh(d*x+c)^5/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{2}}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{2 d \left(a +b \right)^{2}}-\frac{a^{2} \ln \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}{2 d \left(a +b \right)^{2} b^{2}}-\frac{a \ln \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}{d \left(a +b \right)^{2} b}-\frac{a^{3}}{2 d \left(a +b \right)^{2} b^{2} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}-\frac{a^{2}}{2 d \left(a +b \right)^{2} b \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}"," ",0,"-1/2/d/(a+b)^2*ln(tanh(d*x+c)-1)-1/2/d/(a+b)^2*ln(1+tanh(d*x+c))-1/2/d*a^2/(a+b)^2/b^2*ln(a+b*tanh(d*x+c)^2)-1/d*a/(a+b)^2/b*ln(a+b*tanh(d*x+c)^2)-1/2/d*a^3/(a+b)^2/b^2/(a+b*tanh(d*x+c)^2)-1/2/d*a^2/(a+b)^2/b/(a+b*tanh(d*x+c)^2)","A"
181,1,172,77,0.098000," ","int(tanh(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{2}}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{2 d \left(a +b \right)^{2}}+\frac{a^{2} \tanh \left(d x +c \right)}{2 d \left(a +b \right)^{2} b \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}+\frac{a \tanh \left(d x +c \right)}{2 d \left(a +b \right)^{2} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}-\frac{a^{2} \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d \left(a +b \right)^{2} b \sqrt{a b}}-\frac{3 a \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d \left(a +b \right)^{2} \sqrt{a b}}"," ",0,"-1/2/d/(a+b)^2*ln(tanh(d*x+c)-1)+1/2/d/(a+b)^2*ln(1+tanh(d*x+c))+1/2/d*a^2/(a+b)^2/b*tanh(d*x+c)/(a+b*tanh(d*x+c)^2)+1/2/d*a/(a+b)^2*tanh(d*x+c)/(a+b*tanh(d*x+c)^2)-1/2/d*a^2/(a+b)^2/b/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))-3/2/d*a/(a+b)^2/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))","B"
182,1,118,68,0.098000," ","int(tanh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{2}}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{2 d \left(a +b \right)^{2}}+\frac{\ln \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}{2 \left(a +b \right)^{2} d}+\frac{a^{2}}{2 d \left(a +b \right)^{2} b \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}+\frac{a}{2 d \left(a +b \right)^{2} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}"," ",0,"-1/2/d/(a+b)^2*ln(tanh(d*x+c)-1)-1/2/d/(a+b)^2*ln(1+tanh(d*x+c))+1/2*ln(a+b*tanh(d*x+c)^2)/(a+b)^2/d+1/2/d*a^2/(a+b)^2/b/(a+b*tanh(d*x+c)^2)+1/2/d/(a+b)^2*a/(a+b*tanh(d*x+c)^2)","A"
183,1,162,73,0.096000," ","int(tanh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{2}}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{2 d \left(a +b \right)^{2}}-\frac{a \tanh \left(d x +c \right)}{2 d \left(a +b \right)^{2} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}-\frac{b \tanh \left(d x +c \right)}{2 \left(a +b \right)^{2} d \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}-\frac{a \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d \left(a +b \right)^{2} \sqrt{a b}}+\frac{\arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right) b}{2 d \left(a +b \right)^{2} \sqrt{a b}}"," ",0,"-1/2/d/(a+b)^2*ln(tanh(d*x+c)-1)+1/2/d/(a+b)^2*ln(1+tanh(d*x+c))-1/2/d*a/(a+b)^2*tanh(d*x+c)/(a+b*tanh(d*x+c)^2)-1/2*b*tanh(d*x+c)/(a+b)^2/d/(a+b*tanh(d*x+c)^2)-1/2/d*a/(a+b)^2/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))+1/2/d/(a+b)^2/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))*b","B"
184,1,113,64,0.120000," ","int(tanh(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{2}}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{2 d \left(a +b \right)^{2}}+\frac{\ln \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}{2 \left(a +b \right)^{2} d}-\frac{a}{2 d \left(a +b \right)^{2} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}-\frac{b}{2 d \left(a +b \right)^{2} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}"," ",0,"-1/2/d/(a+b)^2*ln(tanh(d*x+c)-1)-1/2/d/(a+b)^2*ln(1+tanh(d*x+c))+1/2*ln(a+b*tanh(d*x+c)^2)/(a+b)^2/d-1/2/d/(a+b)^2*a/(a+b*tanh(d*x+c)^2)-1/2/d*b/(a+b)^2/(a+b*tanh(d*x+c)^2)","A"
185,1,172,77,0.153000," ","int(1/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{2}}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{2 d \left(a +b \right)^{2}}+\frac{b \tanh \left(d x +c \right)}{2 \left(a +b \right)^{2} d \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}+\frac{b^{2} \tanh \left(d x +c \right)}{2 d \left(a +b \right)^{2} a \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}+\frac{3 \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right) b}{2 d \left(a +b \right)^{2} \sqrt{a b}}+\frac{b^{2} \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{2 d \left(a +b \right)^{2} a \sqrt{a b}}"," ",0,"-1/2/d/(a+b)^2*ln(tanh(d*x+c)-1)+1/2/d/(a+b)^2*ln(1+tanh(d*x+c))+1/2*b*tanh(d*x+c)/(a+b)^2/d/(a+b*tanh(d*x+c)^2)+1/2/d*b^2/(a+b)^2/a*tanh(d*x+c)/(a+b*tanh(d*x+c)^2)+3/2/d/(a+b)^2/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))*b+1/2/d*b^2/(a+b)^2/a/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))","B"
186,1,325,91,0.464000," ","int(coth(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \left(a +b \right)^{2}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \left(a +b \right)^{2}}-\frac{2 b^{2} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{2} a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}-\frac{2 b^{3} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{2} a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}-\frac{b \ln \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}{d \left(a +b \right)^{2} a}-\frac{b^{2} \ln \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}{2 d \left(a +b \right)^{2} a^{2}}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"-1/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)-1)-1/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)+1)-2/d*b^2/(a+b)^2/a*tanh(1/2*d*x+1/2*c)^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)-2/d*b^3/(a+b)^2/a^2*tanh(1/2*d*x+1/2*c)^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)-1/d*b/(a+b)^2/a*ln(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)-1/2/d*b^2/(a+b)^2/a^2*ln(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)+1/d/a^2*ln(tanh(1/2*d*x+1/2*c))","B"
187,1,1061,105,0.422000," ","int(coth(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \left(a +b \right)^{2}}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \left(a +b \right)^{2}}-\frac{b^{2} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{2} a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}-\frac{b^{3} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{2} a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}-\frac{b^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a +b \right)^{2} a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}-\frac{b^{3} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a +b \right)^{2} a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{5 b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{5 b^{2} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{4 b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{2} a \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{5 b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{5 b^{2} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{4 b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{2} a \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{3 b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 b^{4} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{3 b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{3 b^{4} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{1}{2 d \,a^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}"," ",0,"-1/2/d/a^2*tanh(1/2*d*x+1/2*c)-1/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)-1)+1/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)+1)-1/d*b^2/(a+b)^2/a/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)^3-1/d*b^3/(a+b)^2/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)^3-1/d*b^2/(a+b)^2/a/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)-1/d*b^3/(a+b)^2/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)+5/2/d*b^2/(a+b)^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-5/2/d*b^2/(a+b)^2/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+4/d*b^3/(a+b)^2/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+5/2/d*b^2/(a+b)^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+5/2/d*b^2/(a+b)^2/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+4/d*b^3/(a+b)^2/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-3/2/d*b^3/(a+b)^2/a^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/2/d*b^4/(a+b)^2/a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+3/2/d*b^3/(a+b)^2/a^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+3/2/d*b^4/(a+b)^2/a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/2/d/a^2/tanh(1/2*d*x+1/2*c)","B"
188,1,383,118,0.482000," ","int(coth(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \left(a +b \right)^{2}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \left(a +b \right)^{2}}+\frac{2 b^{3} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{2} a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{2 b^{4} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(a +b \right)^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{3 b^{2} \ln \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}{2 d \left(a +b \right)^{2} a^{2}}+\frac{b^{3} \ln \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}{d \,a^{3} \left(a +b \right)^{2}}-\frac{1}{8 d \,a^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{2 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{3}}"," ",0,"-1/8/d*tanh(1/2*d*x+1/2*c)^2/a^2-1/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)-1)-1/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)+1)+2/d*b^3/(a+b)^2/a^2*tanh(1/2*d*x+1/2*c)^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)+2/d*b^4/a^3/(a+b)^2*tanh(1/2*d*x+1/2*c)^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)+3/2/d*b^2/(a+b)^2/a^2*ln(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)+1/d*b^3/a^3/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)-1/8/d/a^2/tanh(1/2*d*x+1/2*c)^2+1/d/a^2*ln(tanh(1/2*d*x+1/2*c))-2/d/a^3*ln(tanh(1/2*d*x+1/2*c))*b","B"
189,1,1137,143,0.469000," ","int(coth(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x)","-\frac{\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{2}}-\frac{5 \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2}}+\frac{\tanh \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{3}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \left(a +b \right)^{2}}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \left(a +b \right)^{2}}+\frac{b^{3} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{2} a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{b^{4} \left(\tanh^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{2} a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{b^{3} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a +b \right)^{2} a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}+\frac{b^{4} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a +b \right)^{2} a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}-\frac{7 b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}+\frac{7 b^{3} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{6 b^{4} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{d \left(a +b \right)^{2} a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{7 b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{7 b^{3} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a^{2} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{6 b^{4} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{d \left(a +b \right)^{2} a^{2} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}+\frac{5 b^{4} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{5 b^{5} \arctanh \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}-a -2 b \right) a}}-\frac{5 b^{4} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a^{3} \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{5 b^{5} \arctan \left(\frac{a \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}{\sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}\right)}{2 d \left(a +b \right)^{2} a^{3} \sqrt{b \left(a +b \right)}\, \sqrt{\left(2 \sqrt{b \left(a +b \right)}+a +2 b \right) a}}-\frac{1}{24 d \,a^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{5}{8 d \,a^{2} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{d \,a^{3} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)}"," ",0,"-1/24/d/a^2*tanh(1/2*d*x+1/2*c)^3-5/8/d/a^2*tanh(1/2*d*x+1/2*c)+1/d/a^3*tanh(1/2*d*x+1/2*c)*b-1/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)-1)+1/d/(a+b)^2*ln(tanh(1/2*d*x+1/2*c)+1)+1/d*b^3/(a+b)^2/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)^3+1/d*b^4/(a+b)^2/a^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)^3+1/d*b^3/(a+b)^2/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)+1/d*b^4/(a+b)^2/a^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)*tanh(1/2*d*x+1/2*c)-7/2/d*b^3/(a+b)^2/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+7/2/d*b^3/(a+b)^2/a^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-6/d*b^4/(a+b)^2/a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-7/2/d*b^3/(a+b)^2/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-7/2/d*b^3/(a+b)^2/a^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-6/d*b^4/(a+b)^2/a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+5/2/d*b^4/(a+b)^2/a^3/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-5/2/d*b^5/(a+b)^2/a^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-5/2/d*b^4/(a+b)^2/a^3/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-5/2/d*b^5/(a+b)^2/a^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/24/d/a^2/tanh(1/2*d*x+1/2*c)^3-5/8/d/a^2/tanh(1/2*d*x+1/2*c)+1/d/a^3/tanh(1/2*d*x+1/2*c)*b","B"
190,1,352,130,0.102000," ","int(tanh(d*x+c)^6/(a+b*tanh(d*x+c)^2)^3,x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{3}}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{2 d \left(a +b \right)^{3}}+\frac{5 a^{3} \left(\tanh^{3}\left(d x +c \right)\right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2} b}+\frac{7 a^{2} \left(\tanh^{3}\left(d x +c \right)\right)}{4 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{9 a b \left(\tanh^{3}\left(d x +c \right)\right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{3 a^{4} \tanh \left(d x +c \right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2} b^{2}}+\frac{5 a^{3} \tanh \left(d x +c \right)}{4 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2} b}+\frac{7 a^{2} \tanh \left(d x +c \right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}-\frac{3 a^{3} \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{8 d \left(a +b \right)^{3} b^{2} \sqrt{a b}}-\frac{5 a^{2} \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{4 d \left(a +b \right)^{3} b \sqrt{a b}}-\frac{15 a \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{8 d \left(a +b \right)^{3} \sqrt{a b}}"," ",0,"-1/2/d/(a+b)^3*ln(tanh(d*x+c)-1)+1/2/d/(a+b)^3*ln(1+tanh(d*x+c))+5/8/d*a^3/(a+b)^3/(a+b*tanh(d*x+c)^2)^2/b*tanh(d*x+c)^3+7/4/d*a^2/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*tanh(d*x+c)^3+9/8/d*a/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*b*tanh(d*x+c)^3+3/8/d*a^4/(a+b)^3/(a+b*tanh(d*x+c)^2)^2/b^2*tanh(d*x+c)+5/4/d*a^3/(a+b)^3/(a+b*tanh(d*x+c)^2)^2/b*tanh(d*x+c)+7/8/d*a^2/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*tanh(d*x+c)-3/8/d*a^3/(a+b)^3/b^2/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))-5/4/d*a^2/(a+b)^3/b/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))-15/8/d*a/(a+b)^3/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))","B"
191,1,234,103,0.107000," ","int(tanh(d*x+c)^5/(a+b*tanh(d*x+c)^2)^3,x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{3}}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{2 d \left(a +b \right)^{3}}-\frac{a^{4}}{4 d \left(a +b \right)^{3} b^{2} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}-\frac{a^{3}}{2 d \left(a +b \right)^{3} b \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}-\frac{a^{2}}{4 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{\ln \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}{2 \left(a +b \right)^{3} d}+\frac{a^{3}}{2 d \left(a +b \right)^{3} b^{2} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}+\frac{3 a^{2}}{2 d \left(a +b \right)^{3} b \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}+\frac{a}{d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}"," ",0,"-1/2/d/(a+b)^3*ln(tanh(d*x+c)-1)-1/2/d/(a+b)^3*ln(1+tanh(d*x+c))-1/4/d/(a+b)^3*a^4/b^2/(a+b*tanh(d*x+c)^2)^2-1/2/d/(a+b)^3*a^3/b/(a+b*tanh(d*x+c)^2)^2-1/4/d/(a+b)^3*a^2/(a+b*tanh(d*x+c)^2)^2+1/2*ln(a+b*tanh(d*x+c)^2)/(a+b)^3/d+1/2/d/(a+b)^3*a^3/b^2/(a+b*tanh(d*x+c)^2)+3/2/d/(a+b)^3*a^2/b/(a+b*tanh(d*x+c)^2)+1/d/(a+b)^3*a/(a+b*tanh(d*x+c)^2)","B"
192,1,340,123,0.121000," ","int(tanh(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{3}}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{2 d \left(a +b \right)^{3}}-\frac{a^{2} \left(\tanh^{3}\left(d x +c \right)\right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}-\frac{3 a b \left(\tanh^{3}\left(d x +c \right)\right)}{4 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}-\frac{5 \left(\tanh^{3}\left(d x +c \right)\right) b^{2}}{8 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{a^{3} \tanh \left(d x +c \right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2} b}-\frac{a^{2} \tanh \left(d x +c \right)}{4 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}-\frac{3 a b \tanh \left(d x +c \right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}-\frac{a^{2} \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{8 d \left(a +b \right)^{3} b \sqrt{a b}}-\frac{3 a \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{4 d \left(a +b \right)^{3} \sqrt{a b}}+\frac{3 b \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{8 d \left(a +b \right)^{3} \sqrt{a b}}"," ",0,"-1/2/d/(a+b)^3*ln(tanh(d*x+c)-1)+1/2/d/(a+b)^3*ln(1+tanh(d*x+c))-1/8/d*a^2/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*tanh(d*x+c)^3-3/4/d*a/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*b*tanh(d*x+c)^3-5/8/d/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*tanh(d*x+c)^3*b^2+1/8/d*a^3/(a+b)^3/(a+b*tanh(d*x+c)^2)^2/b*tanh(d*x+c)-1/4/d*a^2/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*tanh(d*x+c)-3/8/d/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*a*b*tanh(d*x+c)-1/8/d*a^2/(a+b)^3/b/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))-3/4/d*a/(a+b)^3/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))+3/8/d/(a+b)^3*b/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))","B"
193,1,196,92,0.104000," ","int(tanh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{3}}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{2 d \left(a +b \right)^{3}}+\frac{a^{3}}{4 d \left(a +b \right)^{3} b \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{a^{2}}{2 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{a b}{4 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{\ln \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}{2 \left(a +b \right)^{3} d}-\frac{a}{2 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}-\frac{b}{2 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}"," ",0,"-1/2/d/(a+b)^3*ln(tanh(d*x+c)-1)-1/2/d/(a+b)^3*ln(1+tanh(d*x+c))+1/4/d/(a+b)^3*a^3/b/(a+b*tanh(d*x+c)^2)^2+1/2/d/(a+b)^3*a^2/(a+b*tanh(d*x+c)^2)^2+1/4/d/(a+b)^3*a*b/(a+b*tanh(d*x+c)^2)^2+1/2*ln(a+b*tanh(d*x+c)^2)/(a+b)^3/d-1/2/d/(a+b)^3*a/(a+b*tanh(d*x+c)^2)-1/2/d/(a+b)^3/(a+b*tanh(d*x+c)^2)*b","B"
194,1,340,123,0.108000," ","int(tanh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{3}}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{2 d \left(a +b \right)^{3}}-\frac{3 a b \left(\tanh^{3}\left(d x +c \right)\right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}-\frac{\left(\tanh^{3}\left(d x +c \right)\right) b^{2}}{4 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{b^{3} \left(\tanh^{3}\left(d x +c \right)\right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2} a}-\frac{5 a^{2} \tanh \left(d x +c \right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}-\frac{3 a b \tanh \left(d x +c \right)}{4 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}-\frac{\tanh \left(d x +c \right) b^{2}}{8 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}-\frac{3 a \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{8 d \left(a +b \right)^{3} \sqrt{a b}}+\frac{3 b \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{4 d \left(a +b \right)^{3} \sqrt{a b}}+\frac{\arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right) b^{2}}{8 d \left(a +b \right)^{3} a \sqrt{a b}}"," ",0,"-1/2/d/(a+b)^3*ln(tanh(d*x+c)-1)+1/2/d/(a+b)^3*ln(1+tanh(d*x+c))-3/8/d*a/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*b*tanh(d*x+c)^3-1/4/d/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*tanh(d*x+c)^3*b^2+1/8/d/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*b^3/a*tanh(d*x+c)^3-5/8/d*a^2/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*tanh(d*x+c)-3/4/d/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*a*b*tanh(d*x+c)-1/8/d/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*tanh(d*x+c)*b^2-3/8/d*a/(a+b)^3/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))+3/4/d/(a+b)^3*b/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))+1/8/d/(a+b)^3/a/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))*b^2","B"
195,1,193,88,0.120000," ","int(tanh(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{3}}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{2 d \left(a +b \right)^{3}}-\frac{a^{2}}{4 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}-\frac{a b}{2 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}-\frac{b^{2}}{4 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{\ln \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}{2 \left(a +b \right)^{3} d}-\frac{a}{2 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}-\frac{b}{2 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)}"," ",0,"-1/2/d/(a+b)^3*ln(tanh(d*x+c)-1)-1/2/d/(a+b)^3*ln(1+tanh(d*x+c))-1/4/d/(a+b)^3*a^2/(a+b*tanh(d*x+c)^2)^2-1/2/d/(a+b)^3*a*b/(a+b*tanh(d*x+c)^2)^2-1/4/d*b^2/(a+b)^3/(a+b*tanh(d*x+c)^2)^2+1/2*ln(a+b*tanh(d*x+c)^2)/(a+b)^3/d-1/2/d/(a+b)^3*a/(a+b*tanh(d*x+c)^2)-1/2/d/(a+b)^3/(a+b*tanh(d*x+c)^2)*b","B"
196,1,352,128,0.153000," ","int(1/(a+b*tanh(d*x+c)^2)^3,x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{3}}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{2 d \left(a +b \right)^{3}}+\frac{7 \left(\tanh^{3}\left(d x +c \right)\right) b^{2}}{8 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{5 b^{3} \left(\tanh^{3}\left(d x +c \right)\right)}{4 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2} a}+\frac{3 b^{4} \left(\tanh^{3}\left(d x +c \right)\right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2} a^{2}}+\frac{9 a b \tanh \left(d x +c \right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{7 \tanh \left(d x +c \right) b^{2}}{4 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2}}+\frac{5 b^{3} \tanh \left(d x +c \right)}{8 d \left(a +b \right)^{3} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{2} a}+\frac{15 b \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{8 d \left(a +b \right)^{3} \sqrt{a b}}+\frac{5 \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right) b^{2}}{4 d \left(a +b \right)^{3} a \sqrt{a b}}+\frac{3 b^{3} \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{8 d \left(a +b \right)^{3} a^{2} \sqrt{a b}}"," ",0,"-1/2/d/(a+b)^3*ln(tanh(d*x+c)-1)+1/2/d/(a+b)^3*ln(1+tanh(d*x+c))+7/8/d/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*tanh(d*x+c)^3*b^2+5/4/d/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*b^3/a*tanh(d*x+c)^3+3/8/d/(a+b)^3*b^4/(a+b*tanh(d*x+c)^2)^2/a^2*tanh(d*x+c)^3+9/8/d/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*a*b*tanh(d*x+c)+7/4/d/(a+b)^3/(a+b*tanh(d*x+c)^2)^2*tanh(d*x+c)*b^2+5/8/d/(a+b)^3*b^3/(a+b*tanh(d*x+c)^2)^2/a*tanh(d*x+c)+15/8/d/(a+b)^3*b/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))+5/4/d/(a+b)^3/a/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))*b^2+3/8/d/(a+b)^3*b^3/a^2/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))","B"
197,1,952,132,0.499000," ","int(coth(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x)","-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \left(a +b \right)^{3}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \left(a +b \right)^{3}}-\frac{6 b^{2} \left(\tanh^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{10 b^{3} \left(\tanh^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{4 b^{4} \left(\tanh^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{12 b^{2} \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{40 b^{3} \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{40 b^{4} \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{12 b^{5} \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{6 b^{2} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{10 b^{3} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{4 b^{4} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}-\frac{3 b \ln \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}{2 d \left(a +b \right)^{3} a}-\frac{3 b^{2} \ln \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}{2 d \left(a +b \right)^{3} a^{2}}-\frac{b^{3} \ln \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}{2 d \left(a +b \right)^{3} a^{3}}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"-1/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)-1)-1/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)+1)-6/d*b^2/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^6-10/d*b^3/(a+b)^3/a/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^6-4/d*b^4/(a+b)^3/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^6-12/d*b^2/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^4-40/d*b^3/(a+b)^3/a/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^4-40/d*b^4/(a+b)^3/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^4-12/d*b^5/(a+b)^3/a^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^4-6/d*b^2/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^2-10/d*b^3/(a+b)^3/a/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^2-4/d*b^4/(a+b)^3/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^2-3/2/d*b/(a+b)^3/a*ln(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)-3/2/d*b^2/(a+b)^3/a^2*ln(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)-1/2/d*b^3/(a+b)^3/a^3*ln(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)+1/d/a^3*ln(tanh(1/2*d*x+1/2*c))","B"
198,1,2045,162,0.481000," ","int(coth(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x)","\text{Expression too large to display}"," ",0,"-1/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)-1)+1/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)+1)+15/8/d*b^5/(a+b)^3/a^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/2/d/a^3*tanh(1/2*d*x+1/2*c)-1/2/d/a^3/tanh(1/2*d*x+1/2*c)+15/8/d*b^5/(a+b)^3/a^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+77/8/d*b^3/(a+b)^3/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+57/8/d*b^4/(a+b)^3/a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+77/8/d*b^3/(a+b)^3/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+57/8/d*b^4/(a+b)^3/a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-13/4/d*b^2/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7-55/2/d*b^3/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^5+35/8/d*b^2/(a+b)^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-99/4/d*b^4/(a+b)^3/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5-55/2/d*b^3/(a+b)^3/a/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3-99/4/d*b^4/(a+b)^3/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3-11/2/d*b^3/(a+b)^3/a/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)-35/8/d*b^2/(a+b)^3/a/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+35/8/d*b^2/(a+b)^3/a/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-7/d*b^5/(a+b)^3/a^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5+15/8/d*b^4/(a+b)^3/a^3/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-11/2/d*b^3/(a+b)^3/a/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7-9/4/d*b^4/(a+b)^3/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7-7/d*b^5/(a+b)^3/a^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3-21/4/d*b^3/(a+b)^3/a^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-15/8/d*b^4/(a+b)^3/a^3/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+21/4/d*b^3/(a+b)^3/a^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-9/4/d*b^4/(a+b)^3/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)+35/8/d*b^2/(a+b)^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-39/4/d*b^2/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5-39/4/d*b^2/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3-13/4/d*b^2/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)","B"
199,1,1020,163,0.496000," ","int(coth(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x)","-\frac{\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \left(a +b \right)^{3}}-\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \left(a +b \right)^{3}}+\frac{8 b^{3} \left(\tanh^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{14 b^{4} \left(\tanh^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{6 b^{5} \left(\tanh^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{16 b^{3} \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{56 b^{4} \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{60 b^{5} \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} a^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{20 b^{6} \left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{8 b^{3} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} a \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{14 b^{4} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a +b \right)^{3} a^{2} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{6 b^{5} \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(a +b \right)^{3} \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)^{2}}+\frac{3 b^{2} \ln \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}{d \left(a +b \right)^{3} a^{2}}+\frac{4 b^{3} \ln \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}{d \left(a +b \right)^{3} a^{3}}+\frac{3 b^{4} \ln \left(\left(\tanh^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +4 \left(\tanh^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a \right)}{2 d \,a^{4} \left(a +b \right)^{3}}-\frac{1}{8 d \,a^{3} \tanh \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{\ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{3 \ln \left(\tanh \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{4}}"," ",0,"-1/8/d*tanh(1/2*d*x+1/2*c)^2/a^3-1/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)-1)-1/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)+1)+8/d*b^3/(a+b)^3/a/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^6+14/d*b^4/(a+b)^3/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^6+6/d*b^5/a^3/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^6+16/d*b^3/(a+b)^3/a/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^4+56/d*b^4/(a+b)^3/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^4+60/d*b^5/(a+b)^3/a^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^4+20/d*b^6/a^4/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^4+8/d*b^3/(a+b)^3/a/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^2+14/d*b^4/(a+b)^3/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^2+6/d*b^5/a^3/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^2+3/d*b^2/(a+b)^3/a^2*ln(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)+4/d*b^3/(a+b)^3/a^3*ln(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)+3/2/d*b^4/a^4/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)-1/8/d/a^3/tanh(1/2*d*x+1/2*c)^2+1/d/a^3*ln(tanh(1/2*d*x+1/2*c))-3/d/a^4*ln(tanh(1/2*d*x+1/2*c))*b","B"
200,1,2139,210,0.496000," ","int(coth(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x)","\text{Expression too large to display}"," ",0,"-35/8/d*b^6/(a+b)^3/a^4/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-35/8/d*b^6/(a+b)^3/a^4/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-1/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)-1)+1/d/(a+b)^3*ln(tanh(1/2*d*x+1/2*c)+1)-125/8/d*b^5/(a+b)^3/a^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-5/8/d/a^3*tanh(1/2*d*x+1/2*c)-5/8/d/a^3/tanh(1/2*d*x+1/2*c)-125/8/d*b^5/(a+b)^3/a^3/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-63/8/d*b^3/(a+b)^3/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-153/8/d*b^4/(a+b)^3/a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-63/8/d*b^3/(a+b)^3/a/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))-153/8/d*b^4/(a+b)^3/a^2/(b*(a+b))^(1/2)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+51/4/d*b^3/(a+b)^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2/a*tanh(1/2*d*x+1/2*c)^5+75/2/d*b^4/(a+b)^3/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5+51/4/d*b^3/(a+b)^3/a/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3+75/2/d*b^4/(a+b)^3/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3+17/4/d*b^3/(a+b)^3/a/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)+3/2/d/a^4*tanh(1/2*d*x+1/2*c)*b+3/2/d/a^4/tanh(1/2*d*x+1/2*c)*b+143/4/d*b^5/(a+b)^3/a^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5-45/4/d*b^4/(a+b)^3/a^3/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+17/4/d*b^3/(a+b)^3/a/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7+15/2/d*b^4/(a+b)^3/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7+143/4/d*b^5/(a+b)^3/a^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3+63/8/d*b^3/(a+b)^3/a^2/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+45/4/d*b^4/(a+b)^3/a^3/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))-63/8/d*b^3/(a+b)^3/a^2/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+15/2/d*b^4/(a+b)^3/a^2/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)+35/8/d*b^5/(a+b)^3/a^4/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2)*arctanh(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)-a-2*b)*a)^(1/2))+13/4/d*b^5/(a+b)^3/a^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^7-35/8/d*b^5/(a+b)^3/a^4/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2)*arctan(a*tanh(1/2*d*x+1/2*c)/((2*(b*(a+b))^(1/2)+a+2*b)*a)^(1/2))+11/d*b^6/(a+b)^3/a^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^3+11/d*b^6/(a+b)^3/a^4/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)^5+13/4/d*b^5/(a+b)^3/a^3/(tanh(1/2*d*x+1/2*c)^4*a+2*tanh(1/2*d*x+1/2*c)^2*a+4*tanh(1/2*d*x+1/2*c)^2*b+a)^2*tanh(1/2*d*x+1/2*c)-1/24/d/a^3*tanh(1/2*d*x+1/2*c)^3-1/24/d/a^3/tanh(1/2*d*x+1/2*c)^3","B"
201,1,608,185,0.162000," ","int(1/(a+b*tanh(d*x+c)^2)^4,x)","-\frac{\ln \left(\tanh \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{4}}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right)}{2 d \left(a +b \right)^{4}}+\frac{19 b^{3} \left(\tanh^{5}\left(d x +c \right)\right)}{16 d \left(a +b \right)^{4} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{3}}+\frac{35 b^{4} \left(\tanh^{5}\left(d x +c \right)\right)}{16 d \left(a +b \right)^{4} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{3} a}+\frac{21 b^{5} \left(\tanh^{5}\left(d x +c \right)\right)}{16 d \left(a +b \right)^{4} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{3} a^{2}}+\frac{5 b^{6} \left(\tanh^{5}\left(d x +c \right)\right)}{16 d \left(a +b \right)^{4} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{3} a^{3}}+\frac{17 b^{2} a \left(\tanh^{3}\left(d x +c \right)\right)}{6 d \left(a +b \right)^{4} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{3}}+\frac{11 b^{3} \left(\tanh^{3}\left(d x +c \right)\right)}{2 d \left(a +b \right)^{4} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{3}}+\frac{7 b^{4} \left(\tanh^{3}\left(d x +c \right)\right)}{2 d \left(a +b \right)^{4} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{3} a}+\frac{5 b^{5} \left(\tanh^{3}\left(d x +c \right)\right)}{6 d \left(a +b \right)^{4} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{3} a^{2}}+\frac{29 b \,a^{2} \tanh \left(d x +c \right)}{16 d \left(a +b \right)^{4} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{3}}+\frac{61 b^{2} a \tanh \left(d x +c \right)}{16 d \left(a +b \right)^{4} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{3}}+\frac{43 b^{3} \tanh \left(d x +c \right)}{16 d \left(a +b \right)^{4} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{3}}+\frac{11 b^{4} \tanh \left(d x +c \right)}{16 d \left(a +b \right)^{4} \left(a +b \left(\tanh^{2}\left(d x +c \right)\right)\right)^{3} a}+\frac{35 b \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{16 d \left(a +b \right)^{4} \sqrt{a b}}+\frac{35 b^{2} \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{16 d \left(a +b \right)^{4} a \sqrt{a b}}+\frac{21 b^{3} \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{16 d \left(a +b \right)^{4} a^{2} \sqrt{a b}}+\frac{5 b^{4} \arctan \left(\frac{\tanh \left(d x +c \right) b}{\sqrt{a b}}\right)}{16 d \left(a +b \right)^{4} a^{3} \sqrt{a b}}"," ",0,"-1/2/d/(a+b)^4*ln(tanh(d*x+c)-1)+1/2/d/(a+b)^4*ln(1+tanh(d*x+c))+19/16/d/(a+b)^4*b^3/(a+b*tanh(d*x+c)^2)^3*tanh(d*x+c)^5+35/16/d/(a+b)^4*b^4/(a+b*tanh(d*x+c)^2)^3/a*tanh(d*x+c)^5+21/16/d/(a+b)^4*b^5/(a+b*tanh(d*x+c)^2)^3/a^2*tanh(d*x+c)^5+5/16/d/(a+b)^4*b^6/(a+b*tanh(d*x+c)^2)^3/a^3*tanh(d*x+c)^5+17/6/d/(a+b)^4*b^2/(a+b*tanh(d*x+c)^2)^3*a*tanh(d*x+c)^3+11/2/d/(a+b)^4*b^3/(a+b*tanh(d*x+c)^2)^3*tanh(d*x+c)^3+7/2/d/(a+b)^4*b^4/(a+b*tanh(d*x+c)^2)^3/a*tanh(d*x+c)^3+5/6/d/(a+b)^4*b^5/(a+b*tanh(d*x+c)^2)^3/a^2*tanh(d*x+c)^3+29/16/d/(a+b)^4*b/(a+b*tanh(d*x+c)^2)^3*a^2*tanh(d*x+c)+61/16/d/(a+b)^4*b^2/(a+b*tanh(d*x+c)^2)^3*a*tanh(d*x+c)+43/16/d/(a+b)^4*b^3/(a+b*tanh(d*x+c)^2)^3*tanh(d*x+c)+11/16/d/(a+b)^4*b^4/(a+b*tanh(d*x+c)^2)^3/a*tanh(d*x+c)+35/16/d/(a+b)^4*b/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))+35/16/d/(a+b)^4*b^2/a/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))+21/16/d/(a+b)^4*b^3/a^2/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))+5/16/d/(a+b)^4*b^4/a^3/(a*b)^(1/2)*arctan(tanh(d*x+c)*b/(a*b)^(1/2))","B"
202,1,4,3,0.082000," ","int((1-tanh(x)^2)^(1/2),x)","\arcsin \left(\tanh \left(x \right)\right)"," ",0,"arcsin(tanh(x))","A"
203,1,15,14,0.112000," ","int((-1+tanh(x)^2)^(1/2),x)","-\ln \left(\tanh \left(x \right)+\sqrt{-1+\tanh^{2}\left(x \right)}\right)"," ",0,"-ln(tanh(x)+(-1+tanh(x)^2)^(1/2))","A"
204,1,21,16,0.066000," ","int((1-tanh(x)^2)^(3/2),x)","\frac{\tanh \left(x \right) \sqrt{1-\left(\tanh^{2}\left(x \right)\right)}}{2}+\frac{\arcsin \left(\tanh \left(x \right)\right)}{2}"," ",0,"1/2*tanh(x)*(1-tanh(x)^2)^(1/2)+1/2*arcsin(tanh(x))","A"
205,1,28,27,0.119000," ","int((-1+tanh(x)^2)^(3/2),x)","-\frac{\tanh \left(x \right) \sqrt{-1+\tanh^{2}\left(x \right)}}{2}+\frac{\ln \left(\tanh \left(x \right)+\sqrt{-1+\tanh^{2}\left(x \right)}\right)}{2}"," ",0,"-1/2*tanh(x)*(-1+tanh(x)^2)^(1/2)+1/2*ln(tanh(x)+(-1+tanh(x)^2)^(1/2))","A"
206,1,14,9,0.051000," ","int(1/(1-tanh(x)^2)^(1/2),x)","\frac{\tanh \left(x \right)}{\sqrt{1-\left(\tanh^{2}\left(x \right)\right)}}"," ",0,"1/(1-tanh(x)^2)^(1/2)*tanh(x)","A"
207,1,12,11,0.089000," ","int(1/(-1+tanh(x)^2)^(1/2),x)","\frac{\tanh \left(x \right)}{\sqrt{-1+\tanh^{2}\left(x \right)}}"," ",0,"tanh(x)/(-1+tanh(x)^2)^(1/2)","A"
208,1,288,71,0.134000," ","int((a+b*tanh(x)^2)^(1/2)*tanh(x)^5,x)","-\frac{\left(\tanh^{2}\left(x \right)\right) \left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}{5 b}+\frac{2 a \left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}{15 b^{2}}-\frac{\left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}{3 b}-\frac{\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{2}-\frac{\sqrt{b}\, \ln \left(\frac{\left(\tanh \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2}-\frac{\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{2}+\frac{\sqrt{b}\, \ln \left(\frac{\left(1+\tanh \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2}"," ",0,"-1/5*tanh(x)^2*(a+b*tanh(x)^2)^(3/2)/b+2/15*a/b^2*(a+b*tanh(x)^2)^(3/2)-1/3*(a+b*tanh(x)^2)^(3/2)/b-1/2*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)-1/2*b^(1/2)*ln(((tanh(x)-1)*b+b)/b^(1/2)+((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))-1/2*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)+1/2*b^(1/2)*ln(((1+tanh(x))*b-b)/b^(1/2)+((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
209,1,337,99,0.104000," ","int((a+b*tanh(x)^2)^(1/2)*tanh(x)^4,x)","-\frac{\tanh \left(x \right) \left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}{4 b}+\frac{a \tanh \left(x \right) \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}{8 b}+\frac{a^{2} \ln \left(\sqrt{b}\, \tanh \left(x \right)+\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\right)}{8 b^{\frac{3}{2}}}-\frac{\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\, \tanh \left(x \right)}{2}-\frac{a \ln \left(\sqrt{b}\, \tanh \left(x \right)+\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\right)}{2 \sqrt{b}}-\frac{\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{2}-\frac{\sqrt{b}\, \ln \left(\frac{\left(\tanh \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2}+\frac{\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{2}-\frac{\sqrt{b}\, \ln \left(\frac{\left(1+\tanh \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\right)}{2}-\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2}"," ",0,"-1/4*tanh(x)*(a+b*tanh(x)^2)^(3/2)/b+1/8*a/b*tanh(x)*(a+b*tanh(x)^2)^(1/2)+1/8*a^2/b^(3/2)*ln(b^(1/2)*tanh(x)+(a+b*tanh(x)^2)^(1/2))-1/2*(a+b*tanh(x)^2)^(1/2)*tanh(x)-1/2*a/b^(1/2)*ln(b^(1/2)*tanh(x)+(a+b*tanh(x)^2)^(1/2))-1/2*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)-1/2*b^(1/2)*ln(((tanh(x)-1)*b+b)/b^(1/2)+((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))+1/2*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)-1/2*b^(1/2)*ln(((1+tanh(x))*b-b)/b^(1/2)+((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))-1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
210,1,253,51,0.091000," ","int((a+b*tanh(x)^2)^(1/2)*tanh(x)^3,x)","-\frac{\left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}{3 b}-\frac{\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{2}-\frac{\sqrt{b}\, \ln \left(\frac{\left(\tanh \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2}-\frac{\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{2}+\frac{\sqrt{b}\, \ln \left(\frac{\left(1+\tanh \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2}"," ",0,"-1/3*(a+b*tanh(x)^2)^(3/2)/b-1/2*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)-1/2*b^(1/2)*ln(((tanh(x)-1)*b+b)/b^(1/2)+((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))-1/2*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)+1/2*b^(1/2)*ln(((1+tanh(x))*b-b)/b^(1/2)+((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
211,1,276,67,0.089000," ","int((a+b*tanh(x)^2)^(1/2)*tanh(x)^2,x)","-\frac{\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\, \tanh \left(x \right)}{2}-\frac{a \ln \left(\sqrt{b}\, \tanh \left(x \right)+\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\right)}{2 \sqrt{b}}-\frac{\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{2}-\frac{\sqrt{b}\, \ln \left(\frac{\left(\tanh \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2}+\frac{\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{2}-\frac{\sqrt{b}\, \ln \left(\frac{\left(1+\tanh \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\right)}{2}-\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2}"," ",0,"-1/2*(a+b*tanh(x)^2)^(1/2)*tanh(x)-1/2*a/b^(1/2)*ln(b^(1/2)*tanh(x)+(a+b*tanh(x)^2)^(1/2))-1/2*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)-1/2*b^(1/2)*ln(((tanh(x)-1)*b+b)/b^(1/2)+((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))+1/2*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)-1/2*b^(1/2)*ln(((1+tanh(x))*b-b)/b^(1/2)+((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))-1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
212,1,238,36,0.096000," ","int((a+b*tanh(x)^2)^(1/2)*tanh(x),x)","-\frac{\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{2}-\frac{\sqrt{b}\, \ln \left(\frac{\left(\tanh \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2}-\frac{\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{2}+\frac{\sqrt{b}\, \ln \left(\frac{\left(1+\tanh \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2}"," ",0,"-1/2*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)-1/2*b^(1/2)*ln(((tanh(x)-1)*b+b)/b^(1/2)+((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))-1/2*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)+1/2*b^(1/2)*ln(((1+tanh(x))*b-b)/b^(1/2)+((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
213,1,238,48,0.106000," ","int((a+b*tanh(x)^2)^(1/2),x)","-\frac{\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{2}-\frac{\sqrt{b}\, \ln \left(\frac{\left(\tanh \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2}+\frac{\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{2}-\frac{\sqrt{b}\, \ln \left(\frac{\left(1+\tanh \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\right)}{2}-\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2}"," ",0,"-1/2*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)-1/2*b^(1/2)*ln(((tanh(x)-1)*b+b)/b^(1/2)+((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))+1/2*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)-1/2*b^(1/2)*ln(((1+tanh(x))*b-b)/b^(1/2)+((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))-1/2*(a+b)^(1/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
214,0,0,44,0.384000," ","int(coth(x)*(a+b*tanh(x)^2)^(1/2),x)","\int \coth \left(x \right) \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\, dx"," ",0,"int(coth(x)*(a+b*tanh(x)^2)^(1/2),x)","F"
215,0,0,40,0.338000," ","int(coth(x)^2*(a+b*tanh(x)^2)^(1/2),x)","\int \left(\coth^{2}\left(x \right)\right) \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\, dx"," ",0,"int(coth(x)^2*(a+b*tanh(x)^2)^(1/2),x)","F"
216,0,0,65,0.353000," ","int(coth(x)^3*(a+b*tanh(x)^2)^(1/2),x)","\int \left(\coth^{3}\left(x \right)\right) \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\, dx"," ",0,"int(coth(x)^3*(a+b*tanh(x)^2)^(1/2),x)","F"
217,0,0,64,0.348000," ","int(coth(x)^4*(a+b*tanh(x)^2)^(1/2),x)","\int \left(\coth^{4}\left(x \right)\right) \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\, dx"," ",0,"int(coth(x)^4*(a+b*tanh(x)^2)^(1/2),x)","F"
218,0,0,99,0.358000," ","int(coth(x)^5*(a+b*tanh(x)^2)^(1/2),x)","\int \left(\coth^{5}\left(x \right)\right) \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\, dx"," ",0,"int(coth(x)^5*(a+b*tanh(x)^2)^(1/2),x)","F"
219,1,593,66,0.075000," ","int(tanh(x)^3*(a+b*tanh(x)^2)^(3/2),x)","-\frac{\left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{5}{2}}}{5 b}-\frac{\left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}{6}-\frac{b \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\, \tanh \left(x \right)}{4}-\frac{3 \sqrt{b}\, \ln \left(\frac{\left(\tanh \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\right) a}{4}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right) a}{2}-\frac{\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\, a}{2}-\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(\tanh \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right) b}{2}-\frac{\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\, b}{2}-\frac{\left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}{6}+\frac{b \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\, \tanh \left(x \right)}{4}+\frac{3 \sqrt{b}\, \ln \left(\frac{\left(1+\tanh \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\right) a}{4}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right) \sqrt{a +b}\, a}{2}-\frac{\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\, a}{2}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right) \sqrt{a +b}\, b}{2}+\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(1+\tanh \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\right)}{2}-\frac{\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\, b}{2}"," ",0,"-1/5*(a+b*tanh(x)^2)^(5/2)/b-1/6*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)-1/4*b*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*tanh(x)-3/4*b^(1/2)*ln(((tanh(x)-1)*b+b)/b^(1/2)+((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))*a+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))*a-1/2*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*a-1/2*b^(3/2)*ln(((tanh(x)-1)*b+b)/b^(1/2)+((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))*b-1/2*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*b-1/6*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)+1/4*b*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*tanh(x)+3/4*b^(1/2)*ln(((1+tanh(x))*b-b)/b^(1/2)+((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))*a+1/2*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))*(a+b)^(1/2)*a-1/2*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*a+1/2*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))*(a+b)^(1/2)*b+1/2*b^(3/2)*ln(((1+tanh(x))*b-b)/b^(1/2)+((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))-1/2*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*b","B"
220,1,633,101,0.073000," ","int(tanh(x)^2*(a+b*tanh(x)^2)^(3/2),x)","-\frac{\tanh \left(x \right) \left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}{4}-\frac{3 a \tanh \left(x \right) \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}{8}-\frac{3 a^{2} \ln \left(\sqrt{b}\, \tanh \left(x \right)+\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\right)}{8 \sqrt{b}}-\frac{\left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}{6}-\frac{b \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\, \tanh \left(x \right)}{4}-\frac{3 \sqrt{b}\, \ln \left(\frac{\left(\tanh \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\right) a}{4}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right) a}{2}-\frac{\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\, a}{2}-\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(\tanh \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right) b}{2}-\frac{\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\, b}{2}+\frac{\left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}{6}-\frac{b \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\, \tanh \left(x \right)}{4}-\frac{3 \sqrt{b}\, \ln \left(\frac{\left(1+\tanh \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\right) a}{4}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right) \sqrt{a +b}\, a}{2}+\frac{\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\, a}{2}-\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(1+\tanh \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\right)}{2}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right) \sqrt{a +b}\, b}{2}+\frac{\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\, b}{2}"," ",0,"-1/4*tanh(x)*(a+b*tanh(x)^2)^(3/2)-3/8*a*tanh(x)*(a+b*tanh(x)^2)^(1/2)-3/8*a^2/b^(1/2)*ln(b^(1/2)*tanh(x)+(a+b*tanh(x)^2)^(1/2))-1/6*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)-1/4*b*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*tanh(x)-3/4*b^(1/2)*ln(((tanh(x)-1)*b+b)/b^(1/2)+((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))*a+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))*a-1/2*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*a-1/2*b^(3/2)*ln(((tanh(x)-1)*b+b)/b^(1/2)+((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))*b-1/2*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*b+1/6*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)-1/4*b*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*tanh(x)-3/4*b^(1/2)*ln(((1+tanh(x))*b-b)/b^(1/2)+((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))*a-1/2*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))*(a+b)^(1/2)*a+1/2*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*a-1/2*b^(3/2)*ln(((1+tanh(x))*b-b)/b^(1/2)+((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))-1/2*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))*(a+b)^(1/2)*b+1/2*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*b","B"
221,1,578,51,0.059000," ","int(tanh(x)*(a+b*tanh(x)^2)^(3/2),x)","-\frac{\left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}{6}-\frac{b \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\, \tanh \left(x \right)}{4}-\frac{3 \sqrt{b}\, \ln \left(\frac{\left(\tanh \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\right) a}{4}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right) a}{2}-\frac{\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\, a}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right) b}{2}-\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(\tanh \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\right)}{2}-\frac{\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\, b}{2}-\frac{\left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}{6}+\frac{b \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\, \tanh \left(x \right)}{4}+\frac{3 \sqrt{b}\, \ln \left(\frac{\left(1+\tanh \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\right) a}{4}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right) \sqrt{a +b}\, a}{2}-\frac{\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\, a}{2}+\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(1+\tanh \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\right)}{2}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right) \sqrt{a +b}\, b}{2}-\frac{\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\, b}{2}"," ",0,"-1/6*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)-1/4*b*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*tanh(x)-3/4*b^(1/2)*ln(((tanh(x)-1)*b+b)/b^(1/2)+((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))*a+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))*a-1/2*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*a+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))*b-1/2*b^(3/2)*ln(((tanh(x)-1)*b+b)/b^(1/2)+((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))-1/2*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*b-1/6*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)+1/4*b*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*tanh(x)+3/4*b^(1/2)*ln(((1+tanh(x))*b-b)/b^(1/2)+((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))*a+1/2*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))*(a+b)^(1/2)*a-1/2*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*a+1/2*b^(3/2)*ln(((1+tanh(x))*b-b)/b^(1/2)+((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))+1/2*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))*(a+b)^(1/2)*b-1/2*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*b","B"
222,1,578,70,0.089000," ","int((a+b*tanh(x)^2)^(3/2),x)","-\frac{\left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}{6}-\frac{b \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\, \tanh \left(x \right)}{4}-\frac{3 \sqrt{b}\, \ln \left(\frac{\left(\tanh \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\right) a}{4}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right) a}{2}-\frac{\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\, a}{2}-\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(\tanh \left(x \right)-1\right) b +b}{\sqrt{b}}+\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\right)}{2}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right) b}{2}-\frac{\sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}\, b}{2}+\frac{\left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}{6}-\frac{b \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\, \tanh \left(x \right)}{4}-\frac{3 \sqrt{b}\, \ln \left(\frac{\left(1+\tanh \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\right) a}{4}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right) \sqrt{a +b}\, a}{2}+\frac{\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\, a}{2}-\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(1+\tanh \left(x \right)\right) b -b}{\sqrt{b}}+\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\right)}{2}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right) \sqrt{a +b}\, b}{2}+\frac{\sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}\, b}{2}"," ",0,"-1/6*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)-1/4*b*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*tanh(x)-3/4*b^(1/2)*ln(((tanh(x)-1)*b+b)/b^(1/2)+((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))*a+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))*a-1/2*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*a-1/2*b^(3/2)*ln(((tanh(x)-1)*b+b)/b^(1/2)+((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))+1/2*(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))*b-1/2*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*b+1/6*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)-1/4*b*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*tanh(x)-3/4*b^(1/2)*ln(((1+tanh(x))*b-b)/b^(1/2)+((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))*a-1/2*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))*(a+b)^(1/2)*a+1/2*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*a-1/2*b^(3/2)*ln(((1+tanh(x))*b-b)/b^(1/2)+((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))-1/2*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))*(a+b)^(1/2)*b+1/2*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*b","B"
223,0,0,57,0.313000," ","int(coth(x)*(a+b*tanh(x)^2)^(3/2),x)","\int \coth \left(x \right) \left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(coth(x)*(a+b*tanh(x)^2)^(3/2),x)","F"
224,0,0,63,0.300000," ","int(coth(x)^2*(a+b*tanh(x)^2)^(3/2),x)","\int \left(\coth^{2}\left(x \right)\right) \left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(coth(x)^2*(a+b*tanh(x)^2)^(3/2),x)","F"
225,1,97,25,0.135000," ","int((1+tanh(x)^2)^(1/2),x)","-\frac{\sqrt{\left(\tanh \left(x \right)-1\right)^{2}+2 \tanh \left(x \right)}}{2}-\arcsinh \left(\tanh \left(x \right)\right)+\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 \tanh \left(x \right)+2\right) \sqrt{2}}{4 \sqrt{\left(\tanh \left(x \right)-1\right)^{2}+2 \tanh \left(x \right)}}\right)}{2}+\frac{\sqrt{\left(1+\tanh \left(x \right)\right)^{2}-2 \tanh \left(x \right)}}{2}-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2-2 \tanh \left(x \right)\right) \sqrt{2}}{4 \sqrt{\left(1+\tanh \left(x \right)\right)^{2}-2 \tanh \left(x \right)}}\right)}{2}"," ",0,"-1/2*((tanh(x)-1)^2+2*tanh(x))^(1/2)-arcsinh(tanh(x))+1/2*2^(1/2)*arctanh(1/4*(2*tanh(x)+2)*2^(1/2)/((tanh(x)-1)^2+2*tanh(x))^(1/2))+1/2*((1+tanh(x))^2-2*tanh(x))^(1/2)-1/2*2^(1/2)*arctanh(1/4*(2-2*tanh(x))*2^(1/2)/((1+tanh(x))^2-2*tanh(x))^(1/2))","B"
226,1,142,37,0.123000," ","int((-1-tanh(x)^2)^(1/2),x)","-\frac{\sqrt{-\left(\tanh \left(x \right)-1\right)^{2}-2 \tanh \left(x \right)}}{2}+\frac{\arctan \left(\frac{\tanh \left(x \right)}{\sqrt{-\left(\tanh \left(x \right)-1\right)^{2}-2 \tanh \left(x \right)}}\right)}{2}+\frac{\sqrt{2}\, \arctan \left(\frac{\left(-2-2 \tanh \left(x \right)\right) \sqrt{2}}{4 \sqrt{-\left(\tanh \left(x \right)-1\right)^{2}-2 \tanh \left(x \right)}}\right)}{2}+\frac{\sqrt{-\left(1+\tanh \left(x \right)\right)^{2}+2 \tanh \left(x \right)}}{2}+\frac{\arctan \left(\frac{\tanh \left(x \right)}{\sqrt{-\left(1+\tanh \left(x \right)\right)^{2}+2 \tanh \left(x \right)}}\right)}{2}-\frac{\sqrt{2}\, \arctan \left(\frac{\left(-2+2 \tanh \left(x \right)\right) \sqrt{2}}{4 \sqrt{-\left(1+\tanh \left(x \right)\right)^{2}+2 \tanh \left(x \right)}}\right)}{2}"," ",0,"-1/2*(-(tanh(x)-1)^2-2*tanh(x))^(1/2)+1/2*arctan(tanh(x)/(-(tanh(x)-1)^2-2*tanh(x))^(1/2))+1/2*2^(1/2)*arctan(1/4*(-2-2*tanh(x))*2^(1/2)/(-(tanh(x)-1)^2-2*tanh(x))^(1/2))+1/2*(-(1+tanh(x))^2+2*tanh(x))^(1/2)+1/2*arctan(tanh(x)/(-(1+tanh(x))^2+2*tanh(x))^(1/2))-1/2*2^(1/2)*arctan(1/4*(-2+2*tanh(x))*2^(1/2)/(-(1+tanh(x))^2+2*tanh(x))^(1/2))","B"
227,1,158,38,0.100000," ","int((1+tanh(x)^2)^(3/2),x)","-\frac{\left(\left(\tanh \left(x \right)-1\right)^{2}+2 \tanh \left(x \right)\right)^{\frac{3}{2}}}{6}-\frac{\tanh \left(x \right) \sqrt{\left(\tanh \left(x \right)-1\right)^{2}+2 \tanh \left(x \right)}}{4}-\frac{5 \arcsinh \left(\tanh \left(x \right)\right)}{2}-\sqrt{\left(\tanh \left(x \right)-1\right)^{2}+2 \tanh \left(x \right)}+\sqrt{2}\, \arctanh \left(\frac{\left(2 \tanh \left(x \right)+2\right) \sqrt{2}}{4 \sqrt{\left(\tanh \left(x \right)-1\right)^{2}+2 \tanh \left(x \right)}}\right)+\frac{\left(\left(1+\tanh \left(x \right)\right)^{2}-2 \tanh \left(x \right)\right)^{\frac{3}{2}}}{6}-\frac{\tanh \left(x \right) \sqrt{\left(1+\tanh \left(x \right)\right)^{2}-2 \tanh \left(x \right)}}{4}+\sqrt{\left(1+\tanh \left(x \right)\right)^{2}-2 \tanh \left(x \right)}-\sqrt{2}\, \arctanh \left(\frac{\left(2-2 \tanh \left(x \right)\right) \sqrt{2}}{4 \sqrt{\left(1+\tanh \left(x \right)\right)^{2}-2 \tanh \left(x \right)}}\right)"," ",0,"-1/6*((tanh(x)-1)^2+2*tanh(x))^(3/2)-1/4*tanh(x)*((tanh(x)-1)^2+2*tanh(x))^(1/2)-5/2*arcsinh(tanh(x))-((tanh(x)-1)^2+2*tanh(x))^(1/2)+2^(1/2)*arctanh(1/4*(2*tanh(x)+2)*2^(1/2)/((tanh(x)-1)^2+2*tanh(x))^(1/2))+1/6*((1+tanh(x))^2-2*tanh(x))^(3/2)-1/4*tanh(x)*((1+tanh(x))^2-2*tanh(x))^(1/2)+((1+tanh(x))^2-2*tanh(x))^(1/2)-2^(1/2)*arctanh(1/4*(2-2*tanh(x))*2^(1/2)/((1+tanh(x))^2-2*tanh(x))^(1/2))","B"
228,1,211,53,0.106000," ","int((-1-tanh(x)^2)^(3/2),x)","-\frac{\left(-\left(\tanh \left(x \right)-1\right)^{2}-2 \tanh \left(x \right)\right)^{\frac{3}{2}}}{6}+\frac{\tanh \left(x \right) \sqrt{-\left(\tanh \left(x \right)-1\right)^{2}-2 \tanh \left(x \right)}}{4}-\frac{5 \arctan \left(\frac{\tanh \left(x \right)}{\sqrt{-\left(\tanh \left(x \right)-1\right)^{2}-2 \tanh \left(x \right)}}\right)}{4}+\sqrt{-\left(\tanh \left(x \right)-1\right)^{2}-2 \tanh \left(x \right)}-\sqrt{2}\, \arctan \left(\frac{\left(-2-2 \tanh \left(x \right)\right) \sqrt{2}}{4 \sqrt{-\left(\tanh \left(x \right)-1\right)^{2}-2 \tanh \left(x \right)}}\right)+\frac{\left(-\left(1+\tanh \left(x \right)\right)^{2}+2 \tanh \left(x \right)\right)^{\frac{3}{2}}}{6}+\frac{\tanh \left(x \right) \sqrt{-\left(1+\tanh \left(x \right)\right)^{2}+2 \tanh \left(x \right)}}{4}-\frac{5 \arctan \left(\frac{\tanh \left(x \right)}{\sqrt{-\left(1+\tanh \left(x \right)\right)^{2}+2 \tanh \left(x \right)}}\right)}{4}-\sqrt{-\left(1+\tanh \left(x \right)\right)^{2}+2 \tanh \left(x \right)}+\sqrt{2}\, \arctan \left(\frac{\left(-2+2 \tanh \left(x \right)\right) \sqrt{2}}{4 \sqrt{-\left(1+\tanh \left(x \right)\right)^{2}+2 \tanh \left(x \right)}}\right)"," ",0,"-1/6*(-(tanh(x)-1)^2-2*tanh(x))^(3/2)+1/4*tanh(x)*(-(tanh(x)-1)^2-2*tanh(x))^(1/2)-5/4*arctan(tanh(x)/(-(tanh(x)-1)^2-2*tanh(x))^(1/2))+(-(tanh(x)-1)^2-2*tanh(x))^(1/2)-2^(1/2)*arctan(1/4*(-2-2*tanh(x))*2^(1/2)/(-(tanh(x)-1)^2-2*tanh(x))^(1/2))+1/6*(-(1+tanh(x))^2+2*tanh(x))^(3/2)+1/4*tanh(x)*(-(1+tanh(x))^2+2*tanh(x))^(1/2)-5/4*arctan(tanh(x)/(-(1+tanh(x))^2+2*tanh(x))^(1/2))-(-(1+tanh(x))^2+2*tanh(x))^(1/2)+2^(1/2)*arctan(1/4*(-2+2*tanh(x))*2^(1/2)/(-(1+tanh(x))^2+2*tanh(x))^(1/2))","B"
229,1,164,58,0.114000," ","int(tanh(x)^5/(a+b*tanh(x)^2)^(1/2),x)","-\frac{\left(\tanh^{2}\left(x \right)\right) \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}{3 b}+\frac{2 a \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}{3 b^{2}}-\frac{\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}{b}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \sqrt{a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \sqrt{a +b}}"," ",0,"-1/3*tanh(x)^2/b*(a+b*tanh(x)^2)^(1/2)+2/3*a/b^2*(a+b*tanh(x)^2)^(1/2)-(a+b*tanh(x)^2)^(1/2)/b+1/2/(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))+1/2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
230,1,178,70,0.128000," ","int(tanh(x)^4/(a+b*tanh(x)^2)^(1/2),x)","-\frac{\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\, \tanh \left(x \right)}{2 b}+\frac{a \ln \left(\sqrt{b}\, \tanh \left(x \right)+\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\right)}{2 b^{\frac{3}{2}}}-\frac{\ln \left(\sqrt{b}\, \tanh \left(x \right)+\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\right)}{\sqrt{b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \sqrt{a +b}}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \sqrt{a +b}}"," ",0,"-1/2*(a+b*tanh(x)^2)^(1/2)*tanh(x)/b+1/2*a/b^(3/2)*ln(b^(1/2)*tanh(x)+(a+b*tanh(x)^2)^(1/2))-ln(b^(1/2)*tanh(x)+(a+b*tanh(x)^2)^(1/2))/b^(1/2)+1/2/(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))-1/2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
231,1,129,39,0.101000," ","int(tanh(x)^3/(a+b*tanh(x)^2)^(1/2),x)","-\frac{\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}{b}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \sqrt{a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \sqrt{a +b}}"," ",0,"-(a+b*tanh(x)^2)^(1/2)/b+1/2/(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))+1/2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
232,1,137,48,0.102000," ","int(tanh(x)^2/(a+b*tanh(x)^2)^(1/2),x)","-\frac{\ln \left(\sqrt{b}\, \tanh \left(x \right)+\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\right)}{\sqrt{b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \sqrt{a +b}}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \sqrt{a +b}}"," ",0,"-ln(b^(1/2)*tanh(x)+(a+b*tanh(x)^2)^(1/2))/b^(1/2)+1/2/(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))-1/2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
233,1,114,23,0.100000," ","int(tanh(x)/(a+b*tanh(x)^2)^(1/2),x)","\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \sqrt{a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \sqrt{a +b}}"," ",0,"1/2/(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))+1/2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
234,1,114,25,0.109000," ","int(1/(a+b*tanh(x)^2)^(1/2),x)","\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \sqrt{a +b}}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \sqrt{a +b}}"," ",0,"1/2/(a+b)^(1/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))-1/2/(a+b)^(1/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
235,0,0,44,0.335000," ","int(coth(x)/(a+b*tanh(x)^2)^(1/2),x)","\int \frac{\coth \left(x \right)}{\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}\, dx"," ",0,"int(coth(x)/(a+b*tanh(x)^2)^(1/2),x)","F"
236,0,0,43,0.360000," ","int(coth(x)^2/(a+b*tanh(x)^2)^(1/2),x)","\int \frac{\coth^{2}\left(x \right)}{\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}\, dx"," ",0,"int(coth(x)^2/(a+b*tanh(x)^2)^(1/2),x)","F"
237,0,0,70,0.362000," ","int(coth(x)^3/(a+b*tanh(x)^2)^(1/2),x)","\int \frac{\coth^{3}\left(x \right)}{\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}\, dx"," ",0,"int(coth(x)^3/(a+b*tanh(x)^2)^(1/2),x)","F"
238,1,322,62,0.084000," ","int(tanh(x)^5/(a+b*tanh(x)^2)^(3/2),x)","-\frac{\tanh^{2}\left(x \right)}{b \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}-\frac{2 a}{b^{2} \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}+\frac{1}{b \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}-\frac{1}{2 \left(a +b \right) \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{b \left(2 \left(\tanh \left(x \right)-1\right) b +2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}-\frac{1}{2 \left(a +b \right) \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}-\frac{b \left(2 \left(1+\tanh \left(x \right)\right) b -2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}"," ",0,"-tanh(x)^2/b/(a+b*tanh(x)^2)^(1/2)-2*a/b^2/(a+b*tanh(x)^2)^(1/2)+1/b/(a+b*tanh(x)^2)^(1/2)-1/2/(a+b)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+b/(a+b)*(2*(tanh(x)-1)*b+2*b)/(4*b*(a+b)-4*b^2)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^(3/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))-1/2/(a+b)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)-b/(a+b)*(2*(1+tanh(x))*b-2*b)/(4*b*(a+b)-4*b^2)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)+1/2/(a+b)^(3/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
239,1,328,70,0.099000," ","int(tanh(x)^4/(a+b*tanh(x)^2)^(3/2),x)","\frac{\tanh \left(x \right)}{b \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}-\frac{\ln \left(\sqrt{b}\, \tanh \left(x \right)+\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\right)}{b^{\frac{3}{2}}}-\frac{\tanh \left(x \right)}{a \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}-\frac{1}{2 \left(a +b \right) \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{b \left(2 \left(\tanh \left(x \right)-1\right) b +2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}+\frac{1}{2 \left(a +b \right) \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{b \left(2 \left(1+\tanh \left(x \right)\right) b -2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}"," ",0,"tanh(x)/b/(a+b*tanh(x)^2)^(1/2)-1/b^(3/2)*ln(b^(1/2)*tanh(x)+(a+b*tanh(x)^2)^(1/2))-tanh(x)/a/(a+b*tanh(x)^2)^(1/2)-1/2/(a+b)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+b/(a+b)*(2*(tanh(x)-1)*b+2*b)/(4*b*(a+b)-4*b^2)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^(3/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))+1/2/(a+b)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)+b/(a+b)*(2*(1+tanh(x))*b-2*b)/(4*b*(a+b)-4*b^2)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)-1/2/(a+b)^(3/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
240,1,287,44,0.081000," ","int(tanh(x)^3/(a+b*tanh(x)^2)^(3/2),x)","\frac{1}{b \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}-\frac{1}{2 \left(a +b \right) \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{b \left(2 \left(\tanh \left(x \right)-1\right) b +2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}-\frac{1}{2 \left(a +b \right) \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}-\frac{b \left(2 \left(1+\tanh \left(x \right)\right) b -2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}"," ",0,"1/b/(a+b*tanh(x)^2)^(1/2)-1/2/(a+b)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+b/(a+b)*(2*(tanh(x)-1)*b+2*b)/(4*b*(a+b)-4*b^2)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^(3/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))-1/2/(a+b)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)-b/(a+b)*(2*(1+tanh(x))*b-2*b)/(4*b*(a+b)-4*b^2)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)+1/2/(a+b)^(3/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
241,1,289,45,0.084000," ","int(tanh(x)^2/(a+b*tanh(x)^2)^(3/2),x)","-\frac{\tanh \left(x \right)}{a \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}-\frac{1}{2 \left(a +b \right) \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{b \left(2 \left(\tanh \left(x \right)-1\right) b +2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}+\frac{1}{2 \left(a +b \right) \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{b \left(2 \left(1+\tanh \left(x \right)\right) b -2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}"," ",0,"-tanh(x)/a/(a+b*tanh(x)^2)^(1/2)-1/2/(a+b)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+b/(a+b)*(2*(tanh(x)-1)*b+2*b)/(4*b*(a+b)-4*b^2)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^(3/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))+1/2/(a+b)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)+b/(a+b)*(2*(1+tanh(x))*b-2*b)/(4*b*(a+b)-4*b^2)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)-1/2/(a+b)^(3/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
242,1,273,41,0.083000," ","int(tanh(x)/(a+b*tanh(x)^2)^(3/2),x)","-\frac{1}{2 \left(a +b \right) \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{b \left(2 \left(\tanh \left(x \right)-1\right) b +2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}-\frac{1}{2 \left(a +b \right) \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}-\frac{b \left(2 \left(1+\tanh \left(x \right)\right) b -2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}"," ",0,"-1/2/(a+b)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+b/(a+b)*(2*(tanh(x)-1)*b+2*b)/(4*b*(a+b)-4*b^2)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^(3/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))-1/2/(a+b)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)-b/(a+b)*(2*(1+tanh(x))*b-2*b)/(4*b*(a+b)-4*b^2)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)+1/2/(a+b)^(3/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
243,1,272,48,0.092000," ","int(1/(a+b*tanh(x)^2)^(3/2),x)","-\frac{1}{2 \left(a +b \right) \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{b \left(2 \left(\tanh \left(x \right)-1\right) b +2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}+\frac{1}{2 \left(a +b \right) \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{b \left(2 \left(1+\tanh \left(x \right)\right) b -2 b \right)}{\left(a +b \right) \left(4 b \left(a +b \right)-4 b^{2}\right) \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{3}{2}}}"," ",0,"-1/2/(a+b)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+b/(a+b)*(2*(tanh(x)-1)*b+2*b)/(4*b*(a+b)-4*b^2)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^(3/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))+1/2/(a+b)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)+b/(a+b)*(2*(1+tanh(x))*b-2*b)/(4*b*(a+b)-4*b^2)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)-1/2/(a+b)^(3/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
244,0,0,64,0.332000," ","int(coth(x)/(a+b*tanh(x)^2)^(3/2),x)","\int \frac{\coth \left(x \right)}{\left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(coth(x)/(a+b*tanh(x)^2)^(3/2),x)","F"
245,0,0,75,0.341000," ","int(coth(x)^2/(a+b*tanh(x)^2)^(3/2),x)","\int \frac{\coth^{2}\left(x \right)}{\left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(coth(x)^2/(a+b*tanh(x)^2)^(3/2),x)","F"
246,1,549,100,0.098000," ","int(tanh(x)^6/(a+b*tanh(x)^2)^(5/2),x)","\frac{\tanh^{3}\left(x \right)}{3 b \left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}+\frac{\tanh \left(x \right)}{b^{2} \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}-\frac{\ln \left(\sqrt{b}\, \tanh \left(x \right)+\sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}\right)}{b^{\frac{5}{2}}}+\frac{\tanh \left(x \right)}{3 b \left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}-\frac{\tanh \left(x \right)}{3 a b \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}-\frac{\tanh \left(x \right)}{3 a \left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}-\frac{2 \tanh \left(x \right)}{3 a^{2} \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}-\frac{1}{6 \left(a +b \right) \left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{6 \left(a +b \right) a \left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}-\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{b \tanh \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}+\frac{1}{6 \left(a +b \right) \left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{6 \left(a +b \right) a \left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{b \tanh \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}"," ",0,"1/3*tanh(x)^3/b/(a+b*tanh(x)^2)^(3/2)+1/b^2*tanh(x)/(a+b*tanh(x)^2)^(1/2)-1/b^(5/2)*ln(b^(1/2)*tanh(x)+(a+b*tanh(x)^2)^(1/2))+1/3*tanh(x)/b/(a+b*tanh(x)^2)^(3/2)-1/3/a/b*tanh(x)/(a+b*tanh(x)^2)^(1/2)-1/3*tanh(x)/a/(a+b*tanh(x)^2)^(3/2)-2/3/a^2*tanh(x)/(a+b*tanh(x)^2)^(1/2)-1/6/(a+b)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)+1/6*b/(a+b)/a/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)*tanh(x)+1/3*b/(a+b)/a^2/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*tanh(x)-1/2/(a+b)^2/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^2/a/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*b*tanh(x)+1/2/(a+b)^(5/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))+1/6/(a+b)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)+1/6*b/(a+b)/a/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)*tanh(x)+1/3*b/(a+b)/a^2/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*tanh(x)+1/2/(a+b)^2/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)+1/2/(a+b)^2/a/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*b*tanh(x)-1/2/(a+b)^(5/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
247,1,469,72,0.101000," ","int(tanh(x)^5/(a+b*tanh(x)^2)^(5/2),x)","\frac{\tanh^{2}\left(x \right)}{b \left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}+\frac{2 a}{3 b^{2} \left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}+\frac{1}{3 b \left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}-\frac{1}{6 \left(a +b \right) \left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{6 \left(a +b \right) a \left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}-\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{b \tanh \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}-\frac{1}{6 \left(a +b \right) \left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}-\frac{b \tanh \left(x \right)}{6 \left(a +b \right) a \left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}-\frac{b \tanh \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}-\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}-\frac{b \tanh \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}"," ",0,"tanh(x)^2/b/(a+b*tanh(x)^2)^(3/2)+2/3*a/b^2/(a+b*tanh(x)^2)^(3/2)+1/3/b/(a+b*tanh(x)^2)^(3/2)-1/6/(a+b)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)+1/6*b/(a+b)/a/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)*tanh(x)+1/3*b/(a+b)/a^2/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*tanh(x)-1/2/(a+b)^2/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^2/a/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*b*tanh(x)+1/2/(a+b)^(5/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))-1/6/(a+b)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)-1/6*b/(a+b)/a/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)*tanh(x)-1/3*b/(a+b)/a^2/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*tanh(x)-1/2/(a+b)^2/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)-1/2/(a+b)^2/a/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*b*tanh(x)+1/2/(a+b)^(5/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
248,1,491,76,0.096000," ","int(tanh(x)^4/(a+b*tanh(x)^2)^(5/2),x)","\frac{\tanh \left(x \right)}{3 b \left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}-\frac{\tanh \left(x \right)}{3 a b \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}-\frac{\tanh \left(x \right)}{3 a \left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}-\frac{2 \tanh \left(x \right)}{3 a^{2} \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}-\frac{1}{6 \left(a +b \right) \left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{6 \left(a +b \right) a \left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}-\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{b \tanh \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}+\frac{1}{6 \left(a +b \right) \left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{6 \left(a +b \right) a \left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{b \tanh \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}"," ",0,"1/3*tanh(x)/b/(a+b*tanh(x)^2)^(3/2)-1/3/a/b*tanh(x)/(a+b*tanh(x)^2)^(1/2)-1/3*tanh(x)/a/(a+b*tanh(x)^2)^(3/2)-2/3/a^2*tanh(x)/(a+b*tanh(x)^2)^(1/2)-1/6/(a+b)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)+1/6*b/(a+b)/a/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)*tanh(x)+1/3*b/(a+b)/a^2/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*tanh(x)-1/2/(a+b)^2/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^2/a/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*b*tanh(x)+1/2/(a+b)^(5/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))+1/6/(a+b)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)+1/6*b/(a+b)/a/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)*tanh(x)+1/3*b/(a+b)/a^2/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*tanh(x)+1/2/(a+b)^2/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)+1/2/(a+b)^2/a/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*b*tanh(x)-1/2/(a+b)^(5/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
249,1,435,62,0.083000," ","int(tanh(x)^3/(a+b*tanh(x)^2)^(5/2),x)","\frac{1}{3 b \left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}-\frac{1}{6 \left(a +b \right) \left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{6 \left(a +b \right) a \left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}-\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{b \tanh \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}-\frac{1}{6 \left(a +b \right) \left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}-\frac{b \tanh \left(x \right)}{6 \left(a +b \right) a \left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}-\frac{b \tanh \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}-\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}-\frac{b \tanh \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}"," ",0,"1/3/b/(a+b*tanh(x)^2)^(3/2)-1/6/(a+b)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)+1/6*b/(a+b)/a/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)*tanh(x)+1/3*b/(a+b)/a^2/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*tanh(x)-1/2/(a+b)^2/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^2/a/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*b*tanh(x)+1/2/(a+b)^(5/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))-1/6/(a+b)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)-1/6*b/(a+b)/a/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)*tanh(x)-1/3*b/(a+b)/a^2/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*tanh(x)-1/2/(a+b)^2/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)-1/2/(a+b)^2/a/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*b*tanh(x)+1/2/(a+b)^(5/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
250,1,454,74,0.091000," ","int(tanh(x)^2/(a+b*tanh(x)^2)^(5/2),x)","-\frac{\tanh \left(x \right)}{3 a \left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}-\frac{2 \tanh \left(x \right)}{3 a^{2} \sqrt{a +b \left(\tanh^{2}\left(x \right)\right)}}-\frac{1}{6 \left(a +b \right) \left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{6 \left(a +b \right) a \left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}-\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{b \tanh \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}+\frac{1}{6 \left(a +b \right) \left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{6 \left(a +b \right) a \left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{b \tanh \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}"," ",0,"-1/3*tanh(x)/a/(a+b*tanh(x)^2)^(3/2)-2/3/a^2*tanh(x)/(a+b*tanh(x)^2)^(1/2)-1/6/(a+b)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)+1/6*b/(a+b)/a/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)*tanh(x)+1/3*b/(a+b)/a^2/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*tanh(x)-1/2/(a+b)^2/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^2/a/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*b*tanh(x)+1/2/(a+b)^(5/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))+1/6/(a+b)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)+1/6*b/(a+b)/a/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)*tanh(x)+1/3*b/(a+b)/a^2/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*tanh(x)+1/2/(a+b)^2/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)+1/2/(a+b)^2/a/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*b*tanh(x)-1/2/(a+b)^(5/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
251,1,420,58,0.084000," ","int(tanh(x)/(a+b*tanh(x)^2)^(5/2),x)","-\frac{1}{6 \left(a +b \right) \left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{6 \left(a +b \right) a \left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}-\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{b \tanh \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}-\frac{1}{6 \left(a +b \right) \left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}-\frac{b \tanh \left(x \right)}{6 \left(a +b \right) a \left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}-\frac{b \tanh \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}-\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}-\frac{b \tanh \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}"," ",0,"-1/6/(a+b)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)+1/6*b/(a+b)/a/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)*tanh(x)+1/3*b/(a+b)/a^2/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*tanh(x)-1/2/(a+b)^2/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^2/a/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*b*tanh(x)+1/2/(a+b)^(5/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))-1/6/(a+b)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)-1/6*b/(a+b)/a/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)*tanh(x)-1/3*b/(a+b)/a^2/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*tanh(x)-1/2/(a+b)^2/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)-1/2/(a+b)^2/a/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*b*tanh(x)+1/2/(a+b)^(5/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
252,1,420,79,0.095000," ","int(1/(a+b*tanh(x)^2)^(5/2),x)","-\frac{1}{6 \left(a +b \right) \left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{6 \left(a +b \right) a \left(\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}-\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{b \tanh \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}+\frac{\ln \left(\frac{2 a +2 b +2 \left(\tanh \left(x \right)-1\right) b +2 \sqrt{a +b}\, \sqrt{\left(\tanh \left(x \right)-1\right)^{2} b +2 \left(\tanh \left(x \right)-1\right) b +a +b}}{\tanh \left(x \right)-1}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}+\frac{1}{6 \left(a +b \right) \left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{6 \left(a +b \right) a \left(\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b \right)^{\frac{3}{2}}}+\frac{b \tanh \left(x \right)}{3 \left(a +b \right) a^{2} \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{1}{2 \left(a +b \right)^{2} \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}+\frac{b \tanh \left(x \right)}{2 \left(a +b \right)^{2} a \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}-\frac{\ln \left(\frac{2 a +2 b -2 \left(1+\tanh \left(x \right)\right) b +2 \sqrt{a +b}\, \sqrt{\left(1+\tanh \left(x \right)\right)^{2} b -2 \left(1+\tanh \left(x \right)\right) b +a +b}}{1+\tanh \left(x \right)}\right)}{2 \left(a +b \right)^{\frac{5}{2}}}"," ",0,"-1/6/(a+b)/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)+1/6*b/(a+b)/a/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(3/2)*tanh(x)+1/3*b/(a+b)/a^2/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*tanh(x)-1/2/(a+b)^2/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)+1/2/(a+b)^2/a/((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2)*b*tanh(x)+1/2/(a+b)^(5/2)*ln((2*a+2*b+2*(tanh(x)-1)*b+2*(a+b)^(1/2)*((tanh(x)-1)^2*b+2*(tanh(x)-1)*b+a+b)^(1/2))/(tanh(x)-1))+1/6/(a+b)/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)+1/6*b/(a+b)/a/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(3/2)*tanh(x)+1/3*b/(a+b)/a^2/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*tanh(x)+1/2/(a+b)^2/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)+1/2/(a+b)^2/a/((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2)*b*tanh(x)-1/2/(a+b)^(5/2)*ln((2*a+2*b-2*(1+tanh(x))*b+2*(a+b)^(1/2)*((1+tanh(x))^2*b-2*(1+tanh(x))*b+a+b)^(1/2))/(1+tanh(x)))","B"
253,0,0,90,0.334000," ","int(coth(x)/(a+b*tanh(x)^2)^(5/2),x)","\int \frac{\coth \left(x \right)}{\left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(coth(x)/(a+b*tanh(x)^2)^(5/2),x)","F"
254,0,0,113,0.350000," ","int(coth(x)^2/(a+b*tanh(x)^2)^(5/2),x)","\int \frac{\coth^{2}\left(x \right)}{\left(a +b \left(\tanh^{2}\left(x \right)\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(coth(x)^2/(a+b*tanh(x)^2)^(5/2),x)","F"
255,1,62,20,0.131000," ","int(1/(1+tanh(x)^2)^(1/2),x)","\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 \tanh \left(x \right)+2\right) \sqrt{2}}{4 \sqrt{\left(\tanh \left(x \right)-1\right)^{2}+2 \tanh \left(x \right)}}\right)}{4}-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2-2 \tanh \left(x \right)\right) \sqrt{2}}{4 \sqrt{\left(1+\tanh \left(x \right)\right)^{2}-2 \tanh \left(x \right)}}\right)}{4}"," ",0,"1/4*2^(1/2)*arctanh(1/4*(2*tanh(x)+2)*2^(1/2)/((tanh(x)-1)^2+2*tanh(x))^(1/2))-1/4*2^(1/2)*arctanh(1/4*(2-2*tanh(x))*2^(1/2)/((1+tanh(x))^2-2*tanh(x))^(1/2))","B"
256,1,66,22,0.125000," ","int(1/(-1-tanh(x)^2)^(1/2),x)","-\frac{\sqrt{2}\, \arctan \left(\frac{\left(-2-2 \tanh \left(x \right)\right) \sqrt{2}}{4 \sqrt{-\left(\tanh \left(x \right)-1\right)^{2}-2 \tanh \left(x \right)}}\right)}{4}+\frac{\sqrt{2}\, \arctan \left(\frac{\left(-2+2 \tanh \left(x \right)\right) \sqrt{2}}{4 \sqrt{-\left(1+\tanh \left(x \right)\right)^{2}+2 \tanh \left(x \right)}}\right)}{4}"," ",0,"-1/4*2^(1/2)*arctan(1/4*(-2-2*tanh(x))*2^(1/2)/(-(tanh(x)-1)^2-2*tanh(x))^(1/2))+1/4*2^(1/2)*arctan(1/4*(-2+2*tanh(x))*2^(1/2)/(-(1+tanh(x))^2+2*tanh(x))^(1/2))","B"
257,1,163,85,0.016000," ","int((a+b*tanh(d*x+c)^3)^2,x)","-\frac{b^{2} \left(\tanh^{5}\left(d x +c \right)\right)}{5 d}-\frac{b^{2} \left(\tanh^{3}\left(d x +c \right)\right)}{3 d}-\frac{a b \left(\tanh^{2}\left(d x +c \right)\right)}{d}-\frac{b^{2} \tanh \left(d x +c \right)}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a^{2}}{2 d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) a b}{d}-\frac{\ln \left(\tanh \left(d x +c \right)-1\right) b^{2}}{2 d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a^{2}}{2 d}-\frac{\ln \left(1+\tanh \left(d x +c \right)\right) a b}{d}+\frac{\ln \left(1+\tanh \left(d x +c \right)\right) b^{2}}{2 d}"," ",0,"-1/5*b^2*tanh(d*x+c)^5/d-1/3*b^2*tanh(d*x+c)^3/d-a*b*tanh(d*x+c)^2/d-b^2*tanh(d*x+c)/d-1/2/d*ln(tanh(d*x+c)-1)*a^2-1/d*ln(tanh(d*x+c)-1)*a*b-1/2/d*ln(tanh(d*x+c)-1)*b^2+1/2/d*ln(1+tanh(d*x+c))*a^2-1/d*ln(1+tanh(d*x+c))*a*b+1/2/d*ln(1+tanh(d*x+c))*b^2","A"
258,1,41,29,0.064000," ","int(1/(1+tanh(x)^3),x)","-\frac{\ln \left(\tanh \left(x \right)-1\right)}{4}-\frac{1}{6 \left(1+\tanh \left(x \right)\right)}+\frac{\ln \left(1+\tanh \left(x \right)\right)}{4}+\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(2 \tanh \left(x \right)-1\right) \sqrt{3}}{3}\right)}{9}"," ",0,"-1/4*ln(tanh(x)-1)-1/6/(1+tanh(x))+1/4*ln(1+tanh(x))+2/9*3^(1/2)*arctan(1/3*(2*tanh(x)-1)*3^(1/2))","A"
259,1,620,101,0.240000," ","int(tanh(x)*(a+b*tanh(x)^4)^(3/2),x)","-\frac{b \left(\tanh^{4}\left(x \right)\right) \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}{6}-\frac{b \left(\tanh^{2}\left(x \right)\right) \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}{4}-\frac{2 \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}\, a}{3}-\frac{b \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}{2}-\frac{\left(\frac{5}{3} a b +b^{2}\right) \sqrt{1-\frac{i \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)}{\sqrt{a}}}\, \EllipticF \left(\tanh \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}-\frac{3 \ln \left(2 \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)+2 \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}\right) \sqrt{b}\, a}{4}-\frac{\ln \left(2 \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)+2 \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}\right) b^{\frac{3}{2}}}{2}-\frac{i \left(-\frac{7}{5} a b -b^{2}\right) \sqrt{a}\, \sqrt{1-\frac{i \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)}{\sqrt{a}}}\, \left(\EllipticF \left(\tanh \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, i\right)-\EllipticE \left(\tanh \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, i\right)\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}\, \sqrt{b}}+\frac{a^{2} \arctanh \left(\frac{2 b \left(\tanh^{2}\left(x \right)\right)+2 a}{2 \sqrt{a +b}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}\right)}{2 \sqrt{a +b}}+\frac{a b \arctanh \left(\frac{2 b \left(\tanh^{2}\left(x \right)\right)+2 a}{2 \sqrt{a +b}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}\right)}{\sqrt{a +b}}+\frac{b^{2} \arctanh \left(\frac{2 b \left(\tanh^{2}\left(x \right)\right)+2 a}{2 \sqrt{a +b}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}\right)}{2 \sqrt{a +b}}-\frac{\left(-\frac{5}{3} a b -b^{2}\right) \sqrt{1-\frac{i \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)}{\sqrt{a}}}\, \EllipticF \left(\tanh \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}-\frac{i \left(\frac{7}{5} a b +b^{2}\right) \sqrt{a}\, \sqrt{1-\frac{i \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)}{\sqrt{a}}}\, \left(\EllipticF \left(\tanh \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, i\right)-\EllipticE \left(\tanh \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, i\right)\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}\, \sqrt{b}}"," ",0,"-1/6*b*tanh(x)^4*(a+b*tanh(x)^4)^(1/2)-1/4*b*tanh(x)^2*(a+b*tanh(x)^4)^(1/2)-2/3*(a+b*tanh(x)^4)^(1/2)*a-1/2*b*(a+b*tanh(x)^4)^(1/2)-1/2*(5/3*a*b+b^2)/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tanh(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tanh(x)^2)^(1/2)/(a+b*tanh(x)^4)^(1/2)*EllipticF(tanh(x)*(I/a^(1/2)*b^(1/2))^(1/2),I)-3/4*ln(2*b^(1/2)*tanh(x)^2+2*(a+b*tanh(x)^4)^(1/2))*b^(1/2)*a-1/2*ln(2*b^(1/2)*tanh(x)^2+2*(a+b*tanh(x)^4)^(1/2))*b^(3/2)-1/2*I*(-7/5*a*b-b^2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tanh(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tanh(x)^2)^(1/2)/(a+b*tanh(x)^4)^(1/2)/b^(1/2)*(EllipticF(tanh(x)*(I/a^(1/2)*b^(1/2))^(1/2),I)-EllipticE(tanh(x)*(I/a^(1/2)*b^(1/2))^(1/2),I))+1/2*a^2/(a+b)^(1/2)*arctanh(1/2*(2*b*tanh(x)^2+2*a)/(a+b)^(1/2)/(a+b*tanh(x)^4)^(1/2))+a*b/(a+b)^(1/2)*arctanh(1/2*(2*b*tanh(x)^2+2*a)/(a+b)^(1/2)/(a+b*tanh(x)^4)^(1/2))+1/2*b^2/(a+b)^(1/2)*arctanh(1/2*(2*b*tanh(x)^2+2*a)/(a+b)^(1/2)/(a+b*tanh(x)^4)^(1/2))-1/2*(-5/3*a*b-b^2)/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tanh(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tanh(x)^2)^(1/2)/(a+b*tanh(x)^4)^(1/2)*EllipticF(tanh(x)*(I/a^(1/2)*b^(1/2))^(1/2),I)-1/2*I*(7/5*a*b+b^2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tanh(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tanh(x)^2)^(1/2)/(a+b*tanh(x)^4)^(1/2)/b^(1/2)*(EllipticF(tanh(x)*(I/a^(1/2)*b^(1/2))^(1/2),I)-EllipticE(tanh(x)*(I/a^(1/2)*b^(1/2))^(1/2),I))","C"
260,1,116,69,0.118000," ","int(tanh(x)*(a+b*tanh(x)^4)^(1/2),x)","-\frac{\sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}{2}-\frac{\sqrt{b}\, \ln \left(2 \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)+2 \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}\right)}{2}+\frac{a \arctanh \left(\frac{2 b \left(\tanh^{2}\left(x \right)\right)+2 a}{2 \sqrt{a +b}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}\right)}{2 \sqrt{a +b}}+\frac{b \arctanh \left(\frac{2 b \left(\tanh^{2}\left(x \right)\right)+2 a}{2 \sqrt{a +b}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}\right)}{2 \sqrt{a +b}}"," ",0,"-1/2*(a+b*tanh(x)^4)^(1/2)-1/2*b^(1/2)*ln(2*b^(1/2)*tanh(x)^2+2*(a+b*tanh(x)^4)^(1/2))+1/2*a/(a+b)^(1/2)*arctanh(1/2*(2*b*tanh(x)^2+2*a)/(a+b)^(1/2)/(a+b*tanh(x)^4)^(1/2))+1/2*b/(a+b)^(1/2)*arctanh(1/2*(2*b*tanh(x)^2+2*a)/(a+b)^(1/2)/(a+b*tanh(x)^4)^(1/2))","A"
261,1,37,32,0.128000," ","int(tanh(x)/(a+b*tanh(x)^4)^(1/2),x)","\frac{\arctanh \left(\frac{2 b \left(\tanh^{2}\left(x \right)\right)+2 a}{2 \sqrt{a +b}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}\right)}{2 \sqrt{a +b}}"," ",0,"1/2/(a+b)^(1/2)*arctanh(1/2*(2*b*tanh(x)^2+2*a)/(a+b)^(1/2)/(a+b*tanh(x)^4)^(1/2))","A"
262,1,431,63,0.119000," ","int(tanh(x)/(a+b*tanh(x)^4)^(3/2),x)","\frac{b \left(\frac{\tanh^{3}\left(x \right)}{4 a \left(a +b \right)}+\frac{\tanh^{2}\left(x \right)}{4 a \left(a +b \right)}+\frac{\tanh \left(x \right)}{4 a \left(a +b \right)}-\frac{1}{4 \left(a +b \right) b}\right)}{\sqrt{\left(\tanh^{4}\left(x \right)+\frac{a}{b}\right) b}}-\frac{-\frac{\arctanh \left(\frac{2 b \left(\tanh^{2}\left(x \right)\right)+2 a}{2 \sqrt{a +b}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}\right)}{2 \sqrt{a +b}}-\frac{\sqrt{1-\frac{i \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)}{\sqrt{a}}}\, \EllipticPi \left(\tanh \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, -\frac{i \sqrt{a}}{\sqrt{b}}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}}{2 \left(a +b \right)}+\frac{b \left(-\frac{\tanh^{3}\left(x \right)}{4 a \left(a +b \right)}+\frac{\tanh^{2}\left(x \right)}{4 a \left(a +b \right)}-\frac{\tanh \left(x \right)}{4 a \left(a +b \right)}-\frac{1}{4 \left(a +b \right) b}\right)}{\sqrt{\left(\tanh^{4}\left(x \right)+\frac{a}{b}\right) b}}-\frac{-\frac{\arctanh \left(\frac{2 b \left(\tanh^{2}\left(x \right)\right)+2 a}{2 \sqrt{a +b}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}\right)}{2 \sqrt{a +b}}+\frac{\sqrt{1-\frac{i \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)}{\sqrt{a}}}\, \EllipticPi \left(\tanh \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, -\frac{i \sqrt{a}}{\sqrt{b}}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}}{2 \left(a +b \right)}"," ",0,"b*(1/4/a/(a+b)*tanh(x)^3+1/4/a/(a+b)*tanh(x)^2+1/4/a/(a+b)*tanh(x)-1/4/(a+b)/b)/((tanh(x)^4+a/b)*b)^(1/2)-1/2/(a+b)*(-1/2/(a+b)^(1/2)*arctanh(1/2*(2*b*tanh(x)^2+2*a)/(a+b)^(1/2)/(a+b*tanh(x)^4)^(1/2))-1/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tanh(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tanh(x)^2)^(1/2)/(a+b*tanh(x)^4)^(1/2)*EllipticPi(tanh(x)*(I/a^(1/2)*b^(1/2))^(1/2),-I*a^(1/2)/b^(1/2),(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)))+b*(-1/4/a/(a+b)*tanh(x)^3+1/4/a/(a+b)*tanh(x)^2-1/4/a/(a+b)*tanh(x)-1/4/(a+b)/b)/((tanh(x)^4+a/b)*b)^(1/2)-1/2/(a+b)*(-1/2/(a+b)^(1/2)*arctanh(1/2*(2*b*tanh(x)^2+2*a)/(a+b)^(1/2)/(a+b*tanh(x)^4)^(1/2))+1/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tanh(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tanh(x)^2)^(1/2)/(a+b*tanh(x)^4)^(1/2)*EllipticPi(tanh(x)*(I/a^(1/2)*b^(1/2))^(1/2),-I*a^(1/2)/b^(1/2),(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)))","C"
263,1,637,102,0.137000," ","int(tanh(x)/(a+b*tanh(x)^4)^(5/2),x)","-\frac{\left(-\frac{\tanh^{3}\left(x \right)}{6 a \left(a +b \right) b}-\frac{\tanh^{2}\left(x \right)}{6 a \left(a +b \right) b}-\frac{\tanh \left(x \right)}{6 a \left(a +b \right) b}+\frac{1}{6 \left(a +b \right) b^{2}}\right) \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}{2 \left(\tanh^{4}\left(x \right)+\frac{a}{b}\right)^{2}}+\frac{b \left(\frac{\left(3 a +b \right) \left(\tanh^{3}\left(x \right)\right)}{8 a^{2} \left(a +b \right)^{2}}+\frac{\left(5 a +2 b \right) \left(\tanh^{2}\left(x \right)\right)}{12 a^{2} \left(a +b \right)^{2}}+\frac{\left(11 a +5 b \right) \tanh \left(x \right)}{24 a^{2} \left(a +b \right)^{2}}-\frac{1}{4 \left(a +b \right)^{2} b}\right)}{\sqrt{\left(\tanh^{4}\left(x \right)+\frac{a}{b}\right) b}}-\frac{-\frac{\arctanh \left(\frac{2 b \left(\tanh^{2}\left(x \right)\right)+2 a}{2 \sqrt{a +b}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}\right)}{2 \sqrt{a +b}}-\frac{\sqrt{1-\frac{i \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)}{\sqrt{a}}}\, \EllipticPi \left(\tanh \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, -\frac{i \sqrt{a}}{\sqrt{b}}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}}{2 \left(a +b \right)^{2}}-\frac{\left(\frac{\tanh^{3}\left(x \right)}{6 a \left(a +b \right) b}-\frac{\tanh^{2}\left(x \right)}{6 a \left(a +b \right) b}+\frac{\tanh \left(x \right)}{6 a \left(a +b \right) b}+\frac{1}{6 \left(a +b \right) b^{2}}\right) \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}{2 \left(\tanh^{4}\left(x \right)+\frac{a}{b}\right)^{2}}+\frac{b \left(-\frac{\left(3 a +b \right) \left(\tanh^{3}\left(x \right)\right)}{8 a^{2} \left(a +b \right)^{2}}+\frac{\left(5 a +2 b \right) \left(\tanh^{2}\left(x \right)\right)}{12 a^{2} \left(a +b \right)^{2}}-\frac{\left(11 a +5 b \right) \tanh \left(x \right)}{24 a^{2} \left(a +b \right)^{2}}-\frac{1}{4 \left(a +b \right)^{2} b}\right)}{\sqrt{\left(\tanh^{4}\left(x \right)+\frac{a}{b}\right) b}}-\frac{-\frac{\arctanh \left(\frac{2 b \left(\tanh^{2}\left(x \right)\right)+2 a}{2 \sqrt{a +b}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}\right)}{2 \sqrt{a +b}}+\frac{\sqrt{1-\frac{i \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)}{\sqrt{a}}}\, \sqrt{1+\frac{i \sqrt{b}\, \left(\tanh^{2}\left(x \right)\right)}{\sqrt{a}}}\, \EllipticPi \left(\tanh \left(x \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}, -\frac{i \sqrt{a}}{\sqrt{b}}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{a +b \left(\tanh^{4}\left(x \right)\right)}}}{2 \left(a +b \right)^{2}}"," ",0,"-1/2*(-1/6/a/(a+b)/b*tanh(x)^3-1/6/a/(a+b)/b*tanh(x)^2-1/6/a/(a+b)/b*tanh(x)+1/6/(a+b)/b^2)*(a+b*tanh(x)^4)^(1/2)/(tanh(x)^4+a/b)^2+b*(1/8*(3*a+b)/a^2/(a+b)^2*tanh(x)^3+1/12*(5*a+2*b)/a^2/(a+b)^2*tanh(x)^2+1/24/a^2*(11*a+5*b)/(a+b)^2*tanh(x)-1/4/(a+b)^2/b)/((tanh(x)^4+a/b)*b)^(1/2)-1/2/(a+b)^2*(-1/2/(a+b)^(1/2)*arctanh(1/2*(2*b*tanh(x)^2+2*a)/(a+b)^(1/2)/(a+b*tanh(x)^4)^(1/2))-1/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tanh(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tanh(x)^2)^(1/2)/(a+b*tanh(x)^4)^(1/2)*EllipticPi(tanh(x)*(I/a^(1/2)*b^(1/2))^(1/2),-I*a^(1/2)/b^(1/2),(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)))-1/2*(1/6/a/(a+b)/b*tanh(x)^3-1/6/a/(a+b)/b*tanh(x)^2+1/6/a/(a+b)/b*tanh(x)+1/6/(a+b)/b^2)*(a+b*tanh(x)^4)^(1/2)/(tanh(x)^4+a/b)^2+b*(-1/8*(3*a+b)/a^2/(a+b)^2*tanh(x)^3+1/12*(5*a+2*b)/a^2/(a+b)^2*tanh(x)^2-1/24/a^2*(11*a+5*b)/(a+b)^2*tanh(x)-1/4/(a+b)^2/b)/((tanh(x)^4+a/b)*b)^(1/2)-1/2/(a+b)^2*(-1/2/(a+b)^(1/2)*arctanh(1/2*(2*b*tanh(x)^2+2*a)/(a+b)^(1/2)/(a+b*tanh(x)^4)^(1/2))+1/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*tanh(x)^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*tanh(x)^2)^(1/2)/(a+b*tanh(x)^4)^(1/2)*EllipticPi(tanh(x)*(I/a^(1/2)*b^(1/2))^(1/2),-I*a^(1/2)/b^(1/2),(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)))","C"