1,1,158,160,1.370983,"\text{Not used}","int((a + b*coth(c + d*x)^2)^5,x)","x\,{\left(a+b\right)}^5-\frac{{\mathrm{coth}\left(c+d\,x\right)}^3\,\left(10\,a^3\,b^2+10\,a^2\,b^3+5\,a\,b^4+b^5\right)}{3\,d}-\frac{{\mathrm{coth}\left(c+d\,x\right)}^5\,\left(10\,a^2\,b^3+5\,a\,b^4+b^5\right)}{5\,d}-\frac{{\mathrm{coth}\left(c+d\,x\right)}^7\,\left(b^5+5\,a\,b^4\right)}{7\,d}-\frac{b^5\,{\mathrm{coth}\left(c+d\,x\right)}^9}{9\,d}-\frac{b\,\mathrm{coth}\left(c+d\,x\right)\,\left(5\,a^4+10\,a^3\,b+10\,a^2\,b^2+5\,a\,b^3+b^4\right)}{d}","Not used",1,"x*(a + b)^5 - (coth(c + d*x)^3*(5*a*b^4 + b^5 + 10*a^2*b^3 + 10*a^3*b^2))/(3*d) - (coth(c + d*x)^5*(5*a*b^4 + b^5 + 10*a^2*b^3))/(5*d) - (coth(c + d*x)^7*(5*a*b^4 + b^5))/(7*d) - (b^5*coth(c + d*x)^9)/(9*d) - (b*coth(c + d*x)*(5*a*b^3 + 10*a^3*b + 5*a^4 + b^4 + 10*a^2*b^2))/d","B"
2,1,111,110,1.314610,"\text{Not used}","int((a + b*coth(c + d*x)^2)^4,x)","x\,{\left(a+b\right)}^4-\frac{{\mathrm{coth}\left(c+d\,x\right)}^3\,\left(6\,a^2\,b^2+4\,a\,b^3+b^4\right)}{3\,d}-\frac{{\mathrm{coth}\left(c+d\,x\right)}^5\,\left(b^4+4\,a\,b^3\right)}{5\,d}-\frac{b^4\,{\mathrm{coth}\left(c+d\,x\right)}^7}{7\,d}-\frac{b\,\mathrm{coth}\left(c+d\,x\right)\,\left(4\,a^3+6\,a^2\,b+4\,a\,b^2+b^3\right)}{d}","Not used",1,"x*(a + b)^4 - (coth(c + d*x)^3*(4*a*b^3 + b^4 + 6*a^2*b^2))/(3*d) - (coth(c + d*x)^5*(4*a*b^3 + b^4))/(5*d) - (b^4*coth(c + d*x)^7)/(7*d) - (b*coth(c + d*x)*(4*a*b^2 + 6*a^2*b + 4*a^3 + b^3))/d","B"
3,1,72,74,1.280859,"\text{Not used}","int((a + b*coth(c + d*x)^2)^3,x)","x\,{\left(a+b\right)}^3-\frac{{\mathrm{coth}\left(c+d\,x\right)}^3\,\left(b^3+3\,a\,b^2\right)}{3\,d}-\frac{b^3\,{\mathrm{coth}\left(c+d\,x\right)}^5}{5\,d}-\frac{b\,\mathrm{coth}\left(c+d\,x\right)\,\left(3\,a^2+3\,a\,b+b^2\right)}{d}","Not used",1,"x*(a + b)^3 - (coth(c + d*x)^3*(3*a*b^2 + b^3))/(3*d) - (b^3*coth(c + d*x)^5)/(5*d) - (b*coth(c + d*x)*(3*a*b + 3*a^2 + b^2))/d","B"
4,1,41,43,0.113633,"\text{Not used}","int((a + b*coth(c + d*x)^2)^2,x)","x\,{\left(a+b\right)}^2-\frac{b^2\,{\mathrm{coth}\left(c+d\,x\right)}^3}{3\,d}-\frac{b\,\mathrm{coth}\left(c+d\,x\right)\,\left(2\,a+b\right)}{d}","Not used",1,"x*(a + b)^2 - (b^2*coth(c + d*x)^3)/(3*d) - (b*coth(c + d*x)*(2*a + b))/d","B"
5,1,37,46,0.111475,"\text{Not used}","int(1/(a + b*coth(c + d*x)^2),x)","\frac{x}{a+b}+\frac{b\,\mathrm{atan}\left(\frac{b\,\mathrm{coth}\left(c+d\,x\right)}{\sqrt{a\,b}}\right)}{d\,\sqrt{a\,b}\,\left(a+b\right)}","Not used",1,"x/(a + b) + (b*atan((b*coth(c + d*x))/(a*b)^(1/2)))/(d*(a*b)^(1/2)*(a + b))","B"
6,1,110,89,1.581307,"\text{Not used}","int(1/(a + b*coth(c + d*x)^2)^2,x)","\frac{\frac{a\,x}{{\left(a+b\right)}^2}+\frac{b\,x\,{\mathrm{coth}\left(c+d\,x\right)}^2}{{\left(a+b\right)}^2}+\frac{b\,\mathrm{coth}\left(c+d\,x\right)}{2\,a\,d\,\left(a+b\right)}}{b\,{\mathrm{coth}\left(c+d\,x\right)}^2+a}+\frac{\mathrm{atan}\left(\frac{b\,\mathrm{coth}\left(c+d\,x\right)}{\sqrt{a\,b}}\right)\,\left(b^2+3\,a\,b\right)}{\sqrt{a\,b}\,\left(2\,a^3\,d+a\,b\,\left(4\,a\,d+2\,b\,d\right)\right)}","Not used",1,"((a*x)/(a + b)^2 + (b*x*coth(c + d*x)^2)/(a + b)^2 + (b*coth(c + d*x))/(2*a*d*(a + b)))/(a + b*coth(c + d*x)^2) + (atan((b*coth(c + d*x))/(a*b)^(1/2))*(3*a*b + b^2))/((a*b)^(1/2)*(2*a^3*d + a*b*(4*a*d + 2*b*d)))","B"
7,1,2719,142,1.912901,"\text{Not used}","int(1/(a + b*coth(c + d*x)^2)^3,x)","\frac{\ln\left(\mathrm{coth}\left(c+d\,x\right)+1\right)}{2\,d\,a^3+6\,d\,a^2\,b+6\,d\,a\,b^2+2\,d\,b^3}+\frac{\frac{\mathrm{coth}\left(c+d\,x\right)\,\left(5\,b^2+9\,a\,b\right)}{8\,a\,\left(a^2+2\,a\,b+b^2\right)}+\frac{b\,{\mathrm{coth}\left(c+d\,x\right)}^3\,\left(3\,b^2+7\,a\,b\right)}{8\,a\,\left(a^3+2\,a^2\,b+a\,b^2\right)}}{d\,a^2+2\,d\,a\,b\,{\mathrm{coth}\left(c+d\,x\right)}^2+d\,b^2\,{\mathrm{coth}\left(c+d\,x\right)}^4}-\frac{\ln\left(\mathrm{coth}\left(c+d\,x\right)-1\right)}{2\,d\,{\left(a+b\right)}^3}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a^5\,b}\,\left(\frac{\mathrm{coth}\left(c+d\,x\right)\,\left(289\,a^4\,b^3+300\,a^3\,b^4+190\,a^2\,b^5+60\,a\,b^6+9\,b^7\right)}{32\,\left(a^8\,d^2+4\,a^7\,b\,d^2+6\,a^6\,b^2\,d^2+4\,a^5\,b^3\,d^2+a^4\,b^4\,d^2\right)}+\frac{\left(\frac{256\,a^{10}\,b^2\,d^2+1760\,a^9\,b^3\,d^2+5280\,a^8\,b^4\,d^2+9056\,a^7\,b^5\,d^2+9760\,a^6\,b^6\,d^2+6816\,a^5\,b^7\,d^2+3040\,a^4\,b^8\,d^2+800\,a^3\,b^9\,d^2+96\,a^2\,b^{10}\,d^2}{64\,\left(a^{10}\,d^3+6\,a^9\,b\,d^3+15\,a^8\,b^2\,d^3+20\,a^7\,b^3\,d^3+15\,a^6\,b^4\,d^3+6\,a^5\,b^5\,d^3+a^4\,b^6\,d^3\right)}-\frac{\mathrm{coth}\left(c+d\,x\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2+10\,a\,b+3\,b^2\right)\,\left(-256\,a^{11}\,b^2\,d^2-1280\,a^{10}\,b^3\,d^2-2304\,a^9\,b^4\,d^2-1280\,a^8\,b^5\,d^2+1280\,a^7\,b^6\,d^2+2304\,a^6\,b^7\,d^2+1280\,a^5\,b^8\,d^2+256\,a^4\,b^9\,d^2\right)}{512\,\left(d\,a^8+3\,d\,a^7\,b+3\,d\,a^6\,b^2+d\,a^5\,b^3\right)\,\left(a^8\,d^2+4\,a^7\,b\,d^2+6\,a^6\,b^2\,d^2+4\,a^5\,b^3\,d^2+a^4\,b^4\,d^2\right)}\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2+10\,a\,b+3\,b^2\right)}{16\,\left(d\,a^8+3\,d\,a^7\,b+3\,d\,a^6\,b^2+d\,a^5\,b^3\right)}\right)\,\left(15\,a^2+10\,a\,b+3\,b^2\right)\,1{}\mathrm{i}}{16\,\left(d\,a^8+3\,d\,a^7\,b+3\,d\,a^6\,b^2+d\,a^5\,b^3\right)}+\frac{\sqrt{-a^5\,b}\,\left(\frac{\mathrm{coth}\left(c+d\,x\right)\,\left(289\,a^4\,b^3+300\,a^3\,b^4+190\,a^2\,b^5+60\,a\,b^6+9\,b^7\right)}{32\,\left(a^8\,d^2+4\,a^7\,b\,d^2+6\,a^6\,b^2\,d^2+4\,a^5\,b^3\,d^2+a^4\,b^4\,d^2\right)}-\frac{\left(\frac{256\,a^{10}\,b^2\,d^2+1760\,a^9\,b^3\,d^2+5280\,a^8\,b^4\,d^2+9056\,a^7\,b^5\,d^2+9760\,a^6\,b^6\,d^2+6816\,a^5\,b^7\,d^2+3040\,a^4\,b^8\,d^2+800\,a^3\,b^9\,d^2+96\,a^2\,b^{10}\,d^2}{64\,\left(a^{10}\,d^3+6\,a^9\,b\,d^3+15\,a^8\,b^2\,d^3+20\,a^7\,b^3\,d^3+15\,a^6\,b^4\,d^3+6\,a^5\,b^5\,d^3+a^4\,b^6\,d^3\right)}+\frac{\mathrm{coth}\left(c+d\,x\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2+10\,a\,b+3\,b^2\right)\,\left(-256\,a^{11}\,b^2\,d^2-1280\,a^{10}\,b^3\,d^2-2304\,a^9\,b^4\,d^2-1280\,a^8\,b^5\,d^2+1280\,a^7\,b^6\,d^2+2304\,a^6\,b^7\,d^2+1280\,a^5\,b^8\,d^2+256\,a^4\,b^9\,d^2\right)}{512\,\left(d\,a^8+3\,d\,a^7\,b+3\,d\,a^6\,b^2+d\,a^5\,b^3\right)\,\left(a^8\,d^2+4\,a^7\,b\,d^2+6\,a^6\,b^2\,d^2+4\,a^5\,b^3\,d^2+a^4\,b^4\,d^2\right)}\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2+10\,a\,b+3\,b^2\right)}{16\,\left(d\,a^8+3\,d\,a^7\,b+3\,d\,a^6\,b^2+d\,a^5\,b^3\right)}\right)\,\left(15\,a^2+10\,a\,b+3\,b^2\right)\,1{}\mathrm{i}}{16\,\left(d\,a^8+3\,d\,a^7\,b+3\,d\,a^6\,b^2+d\,a^5\,b^3\right)}}{\frac{105\,a^3\,b^3+115\,a^2\,b^4+51\,a\,b^5+9\,b^6}{32\,\left(a^{10}\,d^3+6\,a^9\,b\,d^3+15\,a^8\,b^2\,d^3+20\,a^7\,b^3\,d^3+15\,a^6\,b^4\,d^3+6\,a^5\,b^5\,d^3+a^4\,b^6\,d^3\right)}+\frac{\sqrt{-a^5\,b}\,\left(\frac{\mathrm{coth}\left(c+d\,x\right)\,\left(289\,a^4\,b^3+300\,a^3\,b^4+190\,a^2\,b^5+60\,a\,b^6+9\,b^7\right)}{32\,\left(a^8\,d^2+4\,a^7\,b\,d^2+6\,a^6\,b^2\,d^2+4\,a^5\,b^3\,d^2+a^4\,b^4\,d^2\right)}+\frac{\left(\frac{256\,a^{10}\,b^2\,d^2+1760\,a^9\,b^3\,d^2+5280\,a^8\,b^4\,d^2+9056\,a^7\,b^5\,d^2+9760\,a^6\,b^6\,d^2+6816\,a^5\,b^7\,d^2+3040\,a^4\,b^8\,d^2+800\,a^3\,b^9\,d^2+96\,a^2\,b^{10}\,d^2}{64\,\left(a^{10}\,d^3+6\,a^9\,b\,d^3+15\,a^8\,b^2\,d^3+20\,a^7\,b^3\,d^3+15\,a^6\,b^4\,d^3+6\,a^5\,b^5\,d^3+a^4\,b^6\,d^3\right)}-\frac{\mathrm{coth}\left(c+d\,x\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2+10\,a\,b+3\,b^2\right)\,\left(-256\,a^{11}\,b^2\,d^2-1280\,a^{10}\,b^3\,d^2-2304\,a^9\,b^4\,d^2-1280\,a^8\,b^5\,d^2+1280\,a^7\,b^6\,d^2+2304\,a^6\,b^7\,d^2+1280\,a^5\,b^8\,d^2+256\,a^4\,b^9\,d^2\right)}{512\,\left(d\,a^8+3\,d\,a^7\,b+3\,d\,a^6\,b^2+d\,a^5\,b^3\right)\,\left(a^8\,d^2+4\,a^7\,b\,d^2+6\,a^6\,b^2\,d^2+4\,a^5\,b^3\,d^2+a^4\,b^4\,d^2\right)}\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2+10\,a\,b+3\,b^2\right)}{16\,\left(d\,a^8+3\,d\,a^7\,b+3\,d\,a^6\,b^2+d\,a^5\,b^3\right)}\right)\,\left(15\,a^2+10\,a\,b+3\,b^2\right)}{16\,\left(d\,a^8+3\,d\,a^7\,b+3\,d\,a^6\,b^2+d\,a^5\,b^3\right)}-\frac{\sqrt{-a^5\,b}\,\left(\frac{\mathrm{coth}\left(c+d\,x\right)\,\left(289\,a^4\,b^3+300\,a^3\,b^4+190\,a^2\,b^5+60\,a\,b^6+9\,b^7\right)}{32\,\left(a^8\,d^2+4\,a^7\,b\,d^2+6\,a^6\,b^2\,d^2+4\,a^5\,b^3\,d^2+a^4\,b^4\,d^2\right)}-\frac{\left(\frac{256\,a^{10}\,b^2\,d^2+1760\,a^9\,b^3\,d^2+5280\,a^8\,b^4\,d^2+9056\,a^7\,b^5\,d^2+9760\,a^6\,b^6\,d^2+6816\,a^5\,b^7\,d^2+3040\,a^4\,b^8\,d^2+800\,a^3\,b^9\,d^2+96\,a^2\,b^{10}\,d^2}{64\,\left(a^{10}\,d^3+6\,a^9\,b\,d^3+15\,a^8\,b^2\,d^3+20\,a^7\,b^3\,d^3+15\,a^6\,b^4\,d^3+6\,a^5\,b^5\,d^3+a^4\,b^6\,d^3\right)}+\frac{\mathrm{coth}\left(c+d\,x\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2+10\,a\,b+3\,b^2\right)\,\left(-256\,a^{11}\,b^2\,d^2-1280\,a^{10}\,b^3\,d^2-2304\,a^9\,b^4\,d^2-1280\,a^8\,b^5\,d^2+1280\,a^7\,b^6\,d^2+2304\,a^6\,b^7\,d^2+1280\,a^5\,b^8\,d^2+256\,a^4\,b^9\,d^2\right)}{512\,\left(d\,a^8+3\,d\,a^7\,b+3\,d\,a^6\,b^2+d\,a^5\,b^3\right)\,\left(a^8\,d^2+4\,a^7\,b\,d^2+6\,a^6\,b^2\,d^2+4\,a^5\,b^3\,d^2+a^4\,b^4\,d^2\right)}\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2+10\,a\,b+3\,b^2\right)}{16\,\left(d\,a^8+3\,d\,a^7\,b+3\,d\,a^6\,b^2+d\,a^5\,b^3\right)}\right)\,\left(15\,a^2+10\,a\,b+3\,b^2\right)}{16\,\left(d\,a^8+3\,d\,a^7\,b+3\,d\,a^6\,b^2+d\,a^5\,b^3\right)}}\right)\,\sqrt{-a^5\,b}\,\left(15\,a^2+10\,a\,b+3\,b^2\right)\,1{}\mathrm{i}}{8\,\left(d\,a^8+3\,d\,a^7\,b+3\,d\,a^6\,b^2+d\,a^5\,b^3\right)}","Not used",1,"log(coth(c + d*x) + 1)/(2*a^3*d + 2*b^3*d + 6*a*b^2*d + 6*a^2*b*d) + ((coth(c + d*x)*(9*a*b + 5*b^2))/(8*a*(2*a*b + a^2 + b^2)) + (b*coth(c + d*x)^3*(7*a*b + 3*b^2))/(8*a*(a*b^2 + 2*a^2*b + a^3)))/(a^2*d + b^2*d*coth(c + d*x)^4 + 2*a*b*d*coth(c + d*x)^2) - log(coth(c + d*x) - 1)/(2*d*(a + b)^3) - (atan((((-a^5*b)^(1/2)*((coth(c + d*x)*(60*a*b^6 + 9*b^7 + 190*a^2*b^5 + 300*a^3*b^4 + 289*a^4*b^3))/(32*(a^8*d^2 + 4*a^7*b*d^2 + a^4*b^4*d^2 + 4*a^5*b^3*d^2 + 6*a^6*b^2*d^2)) + (((96*a^2*b^10*d^2 + 800*a^3*b^9*d^2 + 3040*a^4*b^8*d^2 + 6816*a^5*b^7*d^2 + 9760*a^6*b^6*d^2 + 9056*a^7*b^5*d^2 + 5280*a^8*b^4*d^2 + 1760*a^9*b^3*d^2 + 256*a^10*b^2*d^2)/(64*(a^10*d^3 + 6*a^9*b*d^3 + a^4*b^6*d^3 + 6*a^5*b^5*d^3 + 15*a^6*b^4*d^3 + 20*a^7*b^3*d^3 + 15*a^8*b^2*d^3)) - (coth(c + d*x)*(-a^5*b)^(1/2)*(10*a*b + 15*a^2 + 3*b^2)*(256*a^4*b^9*d^2 + 1280*a^5*b^8*d^2 + 2304*a^6*b^7*d^2 + 1280*a^7*b^6*d^2 - 1280*a^8*b^5*d^2 - 2304*a^9*b^4*d^2 - 1280*a^10*b^3*d^2 - 256*a^11*b^2*d^2))/(512*(a^8*d + a^5*b^3*d + 3*a^6*b^2*d + 3*a^7*b*d)*(a^8*d^2 + 4*a^7*b*d^2 + a^4*b^4*d^2 + 4*a^5*b^3*d^2 + 6*a^6*b^2*d^2)))*(-a^5*b)^(1/2)*(10*a*b + 15*a^2 + 3*b^2))/(16*(a^8*d + a^5*b^3*d + 3*a^6*b^2*d + 3*a^7*b*d)))*(10*a*b + 15*a^2 + 3*b^2)*1i)/(16*(a^8*d + a^5*b^3*d + 3*a^6*b^2*d + 3*a^7*b*d)) + ((-a^5*b)^(1/2)*((coth(c + d*x)*(60*a*b^6 + 9*b^7 + 190*a^2*b^5 + 300*a^3*b^4 + 289*a^4*b^3))/(32*(a^8*d^2 + 4*a^7*b*d^2 + a^4*b^4*d^2 + 4*a^5*b^3*d^2 + 6*a^6*b^2*d^2)) - (((96*a^2*b^10*d^2 + 800*a^3*b^9*d^2 + 3040*a^4*b^8*d^2 + 6816*a^5*b^7*d^2 + 9760*a^6*b^6*d^2 + 9056*a^7*b^5*d^2 + 5280*a^8*b^4*d^2 + 1760*a^9*b^3*d^2 + 256*a^10*b^2*d^2)/(64*(a^10*d^3 + 6*a^9*b*d^3 + a^4*b^6*d^3 + 6*a^5*b^5*d^3 + 15*a^6*b^4*d^3 + 20*a^7*b^3*d^3 + 15*a^8*b^2*d^3)) + (coth(c + d*x)*(-a^5*b)^(1/2)*(10*a*b + 15*a^2 + 3*b^2)*(256*a^4*b^9*d^2 + 1280*a^5*b^8*d^2 + 2304*a^6*b^7*d^2 + 1280*a^7*b^6*d^2 - 1280*a^8*b^5*d^2 - 2304*a^9*b^4*d^2 - 1280*a^10*b^3*d^2 - 256*a^11*b^2*d^2))/(512*(a^8*d + a^5*b^3*d + 3*a^6*b^2*d + 3*a^7*b*d)*(a^8*d^2 + 4*a^7*b*d^2 + a^4*b^4*d^2 + 4*a^5*b^3*d^2 + 6*a^6*b^2*d^2)))*(-a^5*b)^(1/2)*(10*a*b + 15*a^2 + 3*b^2))/(16*(a^8*d + a^5*b^3*d + 3*a^6*b^2*d + 3*a^7*b*d)))*(10*a*b + 15*a^2 + 3*b^2)*1i)/(16*(a^8*d + a^5*b^3*d + 3*a^6*b^2*d + 3*a^7*b*d)))/((51*a*b^5 + 9*b^6 + 115*a^2*b^4 + 105*a^3*b^3)/(32*(a^10*d^3 + 6*a^9*b*d^3 + a^4*b^6*d^3 + 6*a^5*b^5*d^3 + 15*a^6*b^4*d^3 + 20*a^7*b^3*d^3 + 15*a^8*b^2*d^3)) + ((-a^5*b)^(1/2)*((coth(c + d*x)*(60*a*b^6 + 9*b^7 + 190*a^2*b^5 + 300*a^3*b^4 + 289*a^4*b^3))/(32*(a^8*d^2 + 4*a^7*b*d^2 + a^4*b^4*d^2 + 4*a^5*b^3*d^2 + 6*a^6*b^2*d^2)) + (((96*a^2*b^10*d^2 + 800*a^3*b^9*d^2 + 3040*a^4*b^8*d^2 + 6816*a^5*b^7*d^2 + 9760*a^6*b^6*d^2 + 9056*a^7*b^5*d^2 + 5280*a^8*b^4*d^2 + 1760*a^9*b^3*d^2 + 256*a^10*b^2*d^2)/(64*(a^10*d^3 + 6*a^9*b*d^3 + a^4*b^6*d^3 + 6*a^5*b^5*d^3 + 15*a^6*b^4*d^3 + 20*a^7*b^3*d^3 + 15*a^8*b^2*d^3)) - (coth(c + d*x)*(-a^5*b)^(1/2)*(10*a*b + 15*a^2 + 3*b^2)*(256*a^4*b^9*d^2 + 1280*a^5*b^8*d^2 + 2304*a^6*b^7*d^2 + 1280*a^7*b^6*d^2 - 1280*a^8*b^5*d^2 - 2304*a^9*b^4*d^2 - 1280*a^10*b^3*d^2 - 256*a^11*b^2*d^2))/(512*(a^8*d + a^5*b^3*d + 3*a^6*b^2*d + 3*a^7*b*d)*(a^8*d^2 + 4*a^7*b*d^2 + a^4*b^4*d^2 + 4*a^5*b^3*d^2 + 6*a^6*b^2*d^2)))*(-a^5*b)^(1/2)*(10*a*b + 15*a^2 + 3*b^2))/(16*(a^8*d + a^5*b^3*d + 3*a^6*b^2*d + 3*a^7*b*d)))*(10*a*b + 15*a^2 + 3*b^2))/(16*(a^8*d + a^5*b^3*d + 3*a^6*b^2*d + 3*a^7*b*d)) - ((-a^5*b)^(1/2)*((coth(c + d*x)*(60*a*b^6 + 9*b^7 + 190*a^2*b^5 + 300*a^3*b^4 + 289*a^4*b^3))/(32*(a^8*d^2 + 4*a^7*b*d^2 + a^4*b^4*d^2 + 4*a^5*b^3*d^2 + 6*a^6*b^2*d^2)) - (((96*a^2*b^10*d^2 + 800*a^3*b^9*d^2 + 3040*a^4*b^8*d^2 + 6816*a^5*b^7*d^2 + 9760*a^6*b^6*d^2 + 9056*a^7*b^5*d^2 + 5280*a^8*b^4*d^2 + 1760*a^9*b^3*d^2 + 256*a^10*b^2*d^2)/(64*(a^10*d^3 + 6*a^9*b*d^3 + a^4*b^6*d^3 + 6*a^5*b^5*d^3 + 15*a^6*b^4*d^3 + 20*a^7*b^3*d^3 + 15*a^8*b^2*d^3)) + (coth(c + d*x)*(-a^5*b)^(1/2)*(10*a*b + 15*a^2 + 3*b^2)*(256*a^4*b^9*d^2 + 1280*a^5*b^8*d^2 + 2304*a^6*b^7*d^2 + 1280*a^7*b^6*d^2 - 1280*a^8*b^5*d^2 - 2304*a^9*b^4*d^2 - 1280*a^10*b^3*d^2 - 256*a^11*b^2*d^2))/(512*(a^8*d + a^5*b^3*d + 3*a^6*b^2*d + 3*a^7*b*d)*(a^8*d^2 + 4*a^7*b*d^2 + a^4*b^4*d^2 + 4*a^5*b^3*d^2 + 6*a^6*b^2*d^2)))*(-a^5*b)^(1/2)*(10*a*b + 15*a^2 + 3*b^2))/(16*(a^8*d + a^5*b^3*d + 3*a^6*b^2*d + 3*a^7*b*d)))*(10*a*b + 15*a^2 + 3*b^2))/(16*(a^8*d + a^5*b^3*d + 3*a^6*b^2*d + 3*a^7*b*d))))*(-a^5*b)^(1/2)*(10*a*b + 15*a^2 + 3*b^2)*1i)/(8*(a^8*d + a^5*b^3*d + 3*a^6*b^2*d + 3*a^7*b*d))","B"
8,1,3685,201,2.070956,"\text{Not used}","int(1/(a + b*coth(c + d*x)^2)^4,x)","\frac{\ln\left(\mathrm{coth}\left(c+d\,x\right)+1\right)}{2\,d\,a^4+8\,d\,a^3\,b+12\,d\,a^2\,b^2+8\,d\,a\,b^3+2\,d\,b^4}+\frac{\frac{{\mathrm{coth}\left(c+d\,x\right)}^3\,\left(17\,a^2\,b^2+16\,a\,b^3+5\,b^4\right)}{6\,a^2\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}+\frac{\mathrm{coth}\left(c+d\,x\right)\,\left(29\,a^2\,b+32\,a\,b^2+11\,b^3\right)}{16\,a\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}+\frac{b^2\,{\mathrm{coth}\left(c+d\,x\right)}^5\,\left(19\,a^2\,b+16\,a\,b^2+5\,b^3\right)}{16\,a^2\,\left(a^4+3\,a^3\,b+3\,a^2\,b^2+a\,b^3\right)}}{d\,a^3+3\,d\,a^2\,b\,{\mathrm{coth}\left(c+d\,x\right)}^2+3\,d\,a\,b^2\,{\mathrm{coth}\left(c+d\,x\right)}^4+d\,b^3\,{\mathrm{coth}\left(c+d\,x\right)}^6}-\frac{\ln\left(\mathrm{coth}\left(c+d\,x\right)-1\right)}{2\,d\,{\left(a+b\right)}^4}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a^7\,b}\,\left(\frac{\mathrm{coth}\left(c+d\,x\right)\,\left(1481\,a^6\,b^3+2450\,a^5\,b^4+2695\,a^4\,b^5+1820\,a^3\,b^6+791\,a^2\,b^7+210\,a\,b^8+25\,b^9\right)}{128\,\left(a^{12}\,d^2+6\,a^{11}\,b\,d^2+15\,a^{10}\,b^2\,d^2+20\,a^9\,b^3\,d^2+15\,a^8\,b^4\,d^2+6\,a^7\,b^5\,d^2+a^6\,b^6\,d^2\right)}+\frac{\left(\frac{4\,a^{14}\,b^2\,d^2+\frac{147\,a^{13}\,b^3\,d^2}{4}+154\,a^{12}\,b^4\,d^2+\frac{1561\,a^{11}\,b^5\,d^2}{4}+668\,a^{10}\,b^6\,d^2+\frac{1631\,a^9\,b^7\,d^2}{2}+728\,a^8\,b^8\,d^2+\frac{953\,a^7\,b^9\,d^2}{2}+224\,a^6\,b^{10}\,d^2+\frac{287\,a^5\,b^{11}\,d^2}{4}+14\,a^4\,b^{12}\,d^2+\frac{5\,a^3\,b^{13}\,d^2}{4}}{a^{15}\,d^3+9\,a^{14}\,b\,d^3+36\,a^{13}\,b^2\,d^3+84\,a^{12}\,b^3\,d^3+126\,a^{11}\,b^4\,d^3+126\,a^{10}\,b^5\,d^3+84\,a^9\,b^6\,d^3+36\,a^8\,b^7\,d^3+9\,a^7\,b^8\,d^3+a^6\,b^9\,d^3}-\frac{\mathrm{coth}\left(c+d\,x\right)\,\sqrt{-a^7\,b}\,\left(35\,a^3+35\,a^2\,b+21\,a\,b^2+5\,b^3\right)\,\left(-1024\,a^{15}\,b^2\,d^2-7168\,a^{14}\,b^3\,d^2-20480\,a^{13}\,b^4\,d^2-28672\,a^{12}\,b^5\,d^2-14336\,a^{11}\,b^6\,d^2+14336\,a^{10}\,b^7\,d^2+28672\,a^9\,b^8\,d^2+20480\,a^8\,b^9\,d^2+7168\,a^7\,b^{10}\,d^2+1024\,a^6\,b^{11}\,d^2\right)}{4096\,\left(d\,a^{11}+4\,d\,a^{10}\,b+6\,d\,a^9\,b^2+4\,d\,a^8\,b^3+d\,a^7\,b^4\right)\,\left(a^{12}\,d^2+6\,a^{11}\,b\,d^2+15\,a^{10}\,b^2\,d^2+20\,a^9\,b^3\,d^2+15\,a^8\,b^4\,d^2+6\,a^7\,b^5\,d^2+a^6\,b^6\,d^2\right)}\right)\,\sqrt{-a^7\,b}\,\left(35\,a^3+35\,a^2\,b+21\,a\,b^2+5\,b^3\right)}{32\,\left(d\,a^{11}+4\,d\,a^{10}\,b+6\,d\,a^9\,b^2+4\,d\,a^8\,b^3+d\,a^7\,b^4\right)}\right)\,\left(35\,a^3+35\,a^2\,b+21\,a\,b^2+5\,b^3\right)\,1{}\mathrm{i}}{32\,\left(d\,a^{11}+4\,d\,a^{10}\,b+6\,d\,a^9\,b^2+4\,d\,a^8\,b^3+d\,a^7\,b^4\right)}+\frac{\sqrt{-a^7\,b}\,\left(\frac{\mathrm{coth}\left(c+d\,x\right)\,\left(1481\,a^6\,b^3+2450\,a^5\,b^4+2695\,a^4\,b^5+1820\,a^3\,b^6+791\,a^2\,b^7+210\,a\,b^8+25\,b^9\right)}{128\,\left(a^{12}\,d^2+6\,a^{11}\,b\,d^2+15\,a^{10}\,b^2\,d^2+20\,a^9\,b^3\,d^2+15\,a^8\,b^4\,d^2+6\,a^7\,b^5\,d^2+a^6\,b^6\,d^2\right)}-\frac{\left(\frac{4\,a^{14}\,b^2\,d^2+\frac{147\,a^{13}\,b^3\,d^2}{4}+154\,a^{12}\,b^4\,d^2+\frac{1561\,a^{11}\,b^5\,d^2}{4}+668\,a^{10}\,b^6\,d^2+\frac{1631\,a^9\,b^7\,d^2}{2}+728\,a^8\,b^8\,d^2+\frac{953\,a^7\,b^9\,d^2}{2}+224\,a^6\,b^{10}\,d^2+\frac{287\,a^5\,b^{11}\,d^2}{4}+14\,a^4\,b^{12}\,d^2+\frac{5\,a^3\,b^{13}\,d^2}{4}}{a^{15}\,d^3+9\,a^{14}\,b\,d^3+36\,a^{13}\,b^2\,d^3+84\,a^{12}\,b^3\,d^3+126\,a^{11}\,b^4\,d^3+126\,a^{10}\,b^5\,d^3+84\,a^9\,b^6\,d^3+36\,a^8\,b^7\,d^3+9\,a^7\,b^8\,d^3+a^6\,b^9\,d^3}+\frac{\mathrm{coth}\left(c+d\,x\right)\,\sqrt{-a^7\,b}\,\left(35\,a^3+35\,a^2\,b+21\,a\,b^2+5\,b^3\right)\,\left(-1024\,a^{15}\,b^2\,d^2-7168\,a^{14}\,b^3\,d^2-20480\,a^{13}\,b^4\,d^2-28672\,a^{12}\,b^5\,d^2-14336\,a^{11}\,b^6\,d^2+14336\,a^{10}\,b^7\,d^2+28672\,a^9\,b^8\,d^2+20480\,a^8\,b^9\,d^2+7168\,a^7\,b^{10}\,d^2+1024\,a^6\,b^{11}\,d^2\right)}{4096\,\left(d\,a^{11}+4\,d\,a^{10}\,b+6\,d\,a^9\,b^2+4\,d\,a^8\,b^3+d\,a^7\,b^4\right)\,\left(a^{12}\,d^2+6\,a^{11}\,b\,d^2+15\,a^{10}\,b^2\,d^2+20\,a^9\,b^3\,d^2+15\,a^8\,b^4\,d^2+6\,a^7\,b^5\,d^2+a^6\,b^6\,d^2\right)}\right)\,\sqrt{-a^7\,b}\,\left(35\,a^3+35\,a^2\,b+21\,a\,b^2+5\,b^3\right)}{32\,\left(d\,a^{11}+4\,d\,a^{10}\,b+6\,d\,a^9\,b^2+4\,d\,a^8\,b^3+d\,a^7\,b^4\right)}\right)\,\left(35\,a^3+35\,a^2\,b+21\,a\,b^2+5\,b^3\right)\,1{}\mathrm{i}}{32\,\left(d\,a^{11}+4\,d\,a^{10}\,b+6\,d\,a^9\,b^2+4\,d\,a^8\,b^3+d\,a^7\,b^4\right)}}{\frac{\frac{665\,a^5\,b^3}{128}+\frac{1225\,a^4\,b^4}{128}+\frac{567\,a^3\,b^5}{64}+\frac{303\,a^2\,b^6}{64}+\frac{185\,a\,b^7}{128}+\frac{25\,b^8}{128}}{a^{15}\,d^3+9\,a^{14}\,b\,d^3+36\,a^{13}\,b^2\,d^3+84\,a^{12}\,b^3\,d^3+126\,a^{11}\,b^4\,d^3+126\,a^{10}\,b^5\,d^3+84\,a^9\,b^6\,d^3+36\,a^8\,b^7\,d^3+9\,a^7\,b^8\,d^3+a^6\,b^9\,d^3}+\frac{\sqrt{-a^7\,b}\,\left(\frac{\mathrm{coth}\left(c+d\,x\right)\,\left(1481\,a^6\,b^3+2450\,a^5\,b^4+2695\,a^4\,b^5+1820\,a^3\,b^6+791\,a^2\,b^7+210\,a\,b^8+25\,b^9\right)}{128\,\left(a^{12}\,d^2+6\,a^{11}\,b\,d^2+15\,a^{10}\,b^2\,d^2+20\,a^9\,b^3\,d^2+15\,a^8\,b^4\,d^2+6\,a^7\,b^5\,d^2+a^6\,b^6\,d^2\right)}+\frac{\left(\frac{4\,a^{14}\,b^2\,d^2+\frac{147\,a^{13}\,b^3\,d^2}{4}+154\,a^{12}\,b^4\,d^2+\frac{1561\,a^{11}\,b^5\,d^2}{4}+668\,a^{10}\,b^6\,d^2+\frac{1631\,a^9\,b^7\,d^2}{2}+728\,a^8\,b^8\,d^2+\frac{953\,a^7\,b^9\,d^2}{2}+224\,a^6\,b^{10}\,d^2+\frac{287\,a^5\,b^{11}\,d^2}{4}+14\,a^4\,b^{12}\,d^2+\frac{5\,a^3\,b^{13}\,d^2}{4}}{a^{15}\,d^3+9\,a^{14}\,b\,d^3+36\,a^{13}\,b^2\,d^3+84\,a^{12}\,b^3\,d^3+126\,a^{11}\,b^4\,d^3+126\,a^{10}\,b^5\,d^3+84\,a^9\,b^6\,d^3+36\,a^8\,b^7\,d^3+9\,a^7\,b^8\,d^3+a^6\,b^9\,d^3}-\frac{\mathrm{coth}\left(c+d\,x\right)\,\sqrt{-a^7\,b}\,\left(35\,a^3+35\,a^2\,b+21\,a\,b^2+5\,b^3\right)\,\left(-1024\,a^{15}\,b^2\,d^2-7168\,a^{14}\,b^3\,d^2-20480\,a^{13}\,b^4\,d^2-28672\,a^{12}\,b^5\,d^2-14336\,a^{11}\,b^6\,d^2+14336\,a^{10}\,b^7\,d^2+28672\,a^9\,b^8\,d^2+20480\,a^8\,b^9\,d^2+7168\,a^7\,b^{10}\,d^2+1024\,a^6\,b^{11}\,d^2\right)}{4096\,\left(d\,a^{11}+4\,d\,a^{10}\,b+6\,d\,a^9\,b^2+4\,d\,a^8\,b^3+d\,a^7\,b^4\right)\,\left(a^{12}\,d^2+6\,a^{11}\,b\,d^2+15\,a^{10}\,b^2\,d^2+20\,a^9\,b^3\,d^2+15\,a^8\,b^4\,d^2+6\,a^7\,b^5\,d^2+a^6\,b^6\,d^2\right)}\right)\,\sqrt{-a^7\,b}\,\left(35\,a^3+35\,a^2\,b+21\,a\,b^2+5\,b^3\right)}{32\,\left(d\,a^{11}+4\,d\,a^{10}\,b+6\,d\,a^9\,b^2+4\,d\,a^8\,b^3+d\,a^7\,b^4\right)}\right)\,\left(35\,a^3+35\,a^2\,b+21\,a\,b^2+5\,b^3\right)}{32\,\left(d\,a^{11}+4\,d\,a^{10}\,b+6\,d\,a^9\,b^2+4\,d\,a^8\,b^3+d\,a^7\,b^4\right)}-\frac{\sqrt{-a^7\,b}\,\left(\frac{\mathrm{coth}\left(c+d\,x\right)\,\left(1481\,a^6\,b^3+2450\,a^5\,b^4+2695\,a^4\,b^5+1820\,a^3\,b^6+791\,a^2\,b^7+210\,a\,b^8+25\,b^9\right)}{128\,\left(a^{12}\,d^2+6\,a^{11}\,b\,d^2+15\,a^{10}\,b^2\,d^2+20\,a^9\,b^3\,d^2+15\,a^8\,b^4\,d^2+6\,a^7\,b^5\,d^2+a^6\,b^6\,d^2\right)}-\frac{\left(\frac{4\,a^{14}\,b^2\,d^2+\frac{147\,a^{13}\,b^3\,d^2}{4}+154\,a^{12}\,b^4\,d^2+\frac{1561\,a^{11}\,b^5\,d^2}{4}+668\,a^{10}\,b^6\,d^2+\frac{1631\,a^9\,b^7\,d^2}{2}+728\,a^8\,b^8\,d^2+\frac{953\,a^7\,b^9\,d^2}{2}+224\,a^6\,b^{10}\,d^2+\frac{287\,a^5\,b^{11}\,d^2}{4}+14\,a^4\,b^{12}\,d^2+\frac{5\,a^3\,b^{13}\,d^2}{4}}{a^{15}\,d^3+9\,a^{14}\,b\,d^3+36\,a^{13}\,b^2\,d^3+84\,a^{12}\,b^3\,d^3+126\,a^{11}\,b^4\,d^3+126\,a^{10}\,b^5\,d^3+84\,a^9\,b^6\,d^3+36\,a^8\,b^7\,d^3+9\,a^7\,b^8\,d^3+a^6\,b^9\,d^3}+\frac{\mathrm{coth}\left(c+d\,x\right)\,\sqrt{-a^7\,b}\,\left(35\,a^3+35\,a^2\,b+21\,a\,b^2+5\,b^3\right)\,\left(-1024\,a^{15}\,b^2\,d^2-7168\,a^{14}\,b^3\,d^2-20480\,a^{13}\,b^4\,d^2-28672\,a^{12}\,b^5\,d^2-14336\,a^{11}\,b^6\,d^2+14336\,a^{10}\,b^7\,d^2+28672\,a^9\,b^8\,d^2+20480\,a^8\,b^9\,d^2+7168\,a^7\,b^{10}\,d^2+1024\,a^6\,b^{11}\,d^2\right)}{4096\,\left(d\,a^{11}+4\,d\,a^{10}\,b+6\,d\,a^9\,b^2+4\,d\,a^8\,b^3+d\,a^7\,b^4\right)\,\left(a^{12}\,d^2+6\,a^{11}\,b\,d^2+15\,a^{10}\,b^2\,d^2+20\,a^9\,b^3\,d^2+15\,a^8\,b^4\,d^2+6\,a^7\,b^5\,d^2+a^6\,b^6\,d^2\right)}\right)\,\sqrt{-a^7\,b}\,\left(35\,a^3+35\,a^2\,b+21\,a\,b^2+5\,b^3\right)}{32\,\left(d\,a^{11}+4\,d\,a^{10}\,b+6\,d\,a^9\,b^2+4\,d\,a^8\,b^3+d\,a^7\,b^4\right)}\right)\,\left(35\,a^3+35\,a^2\,b+21\,a\,b^2+5\,b^3\right)}{32\,\left(d\,a^{11}+4\,d\,a^{10}\,b+6\,d\,a^9\,b^2+4\,d\,a^8\,b^3+d\,a^7\,b^4\right)}}\right)\,\sqrt{-a^7\,b}\,\left(35\,a^3+35\,a^2\,b+21\,a\,b^2+5\,b^3\right)\,1{}\mathrm{i}}{16\,\left(d\,a^{11}+4\,d\,a^{10}\,b+6\,d\,a^9\,b^2+4\,d\,a^8\,b^3+d\,a^7\,b^4\right)}","Not used",1,"log(coth(c + d*x) + 1)/(2*a^4*d + 2*b^4*d + 12*a^2*b^2*d + 8*a*b^3*d + 8*a^3*b*d) + ((coth(c + d*x)^3*(16*a*b^3 + 5*b^4 + 17*a^2*b^2))/(6*a^2*(3*a*b^2 + 3*a^2*b + a^3 + b^3)) + (coth(c + d*x)*(32*a*b^2 + 29*a^2*b + 11*b^3))/(16*a*(3*a*b^2 + 3*a^2*b + a^3 + b^3)) + (b^2*coth(c + d*x)^5*(16*a*b^2 + 19*a^2*b + 5*b^3))/(16*a^2*(a*b^3 + 3*a^3*b + a^4 + 3*a^2*b^2)))/(a^3*d + b^3*d*coth(c + d*x)^6 + 3*a^2*b*d*coth(c + d*x)^2 + 3*a*b^2*d*coth(c + d*x)^4) - log(coth(c + d*x) - 1)/(2*d*(a + b)^4) - (atan((((-a^7*b)^(1/2)*((coth(c + d*x)*(210*a*b^8 + 25*b^9 + 791*a^2*b^7 + 1820*a^3*b^6 + 2695*a^4*b^5 + 2450*a^5*b^4 + 1481*a^6*b^3))/(128*(a^12*d^2 + 6*a^11*b*d^2 + a^6*b^6*d^2 + 6*a^7*b^5*d^2 + 15*a^8*b^4*d^2 + 20*a^9*b^3*d^2 + 15*a^10*b^2*d^2)) + ((((5*a^3*b^13*d^2)/4 + 14*a^4*b^12*d^2 + (287*a^5*b^11*d^2)/4 + 224*a^6*b^10*d^2 + (953*a^7*b^9*d^2)/2 + 728*a^8*b^8*d^2 + (1631*a^9*b^7*d^2)/2 + 668*a^10*b^6*d^2 + (1561*a^11*b^5*d^2)/4 + 154*a^12*b^4*d^2 + (147*a^13*b^3*d^2)/4 + 4*a^14*b^2*d^2)/(a^15*d^3 + 9*a^14*b*d^3 + a^6*b^9*d^3 + 9*a^7*b^8*d^3 + 36*a^8*b^7*d^3 + 84*a^9*b^6*d^3 + 126*a^10*b^5*d^3 + 126*a^11*b^4*d^3 + 84*a^12*b^3*d^3 + 36*a^13*b^2*d^3) - (coth(c + d*x)*(-a^7*b)^(1/2)*(21*a*b^2 + 35*a^2*b + 35*a^3 + 5*b^3)*(1024*a^6*b^11*d^2 + 7168*a^7*b^10*d^2 + 20480*a^8*b^9*d^2 + 28672*a^9*b^8*d^2 + 14336*a^10*b^7*d^2 - 14336*a^11*b^6*d^2 - 28672*a^12*b^5*d^2 - 20480*a^13*b^4*d^2 - 7168*a^14*b^3*d^2 - 1024*a^15*b^2*d^2))/(4096*(a^11*d + a^7*b^4*d + 4*a^8*b^3*d + 6*a^9*b^2*d + 4*a^10*b*d)*(a^12*d^2 + 6*a^11*b*d^2 + a^6*b^6*d^2 + 6*a^7*b^5*d^2 + 15*a^8*b^4*d^2 + 20*a^9*b^3*d^2 + 15*a^10*b^2*d^2)))*(-a^7*b)^(1/2)*(21*a*b^2 + 35*a^2*b + 35*a^3 + 5*b^3))/(32*(a^11*d + a^7*b^4*d + 4*a^8*b^3*d + 6*a^9*b^2*d + 4*a^10*b*d)))*(21*a*b^2 + 35*a^2*b + 35*a^3 + 5*b^3)*1i)/(32*(a^11*d + a^7*b^4*d + 4*a^8*b^3*d + 6*a^9*b^2*d + 4*a^10*b*d)) + ((-a^7*b)^(1/2)*((coth(c + d*x)*(210*a*b^8 + 25*b^9 + 791*a^2*b^7 + 1820*a^3*b^6 + 2695*a^4*b^5 + 2450*a^5*b^4 + 1481*a^6*b^3))/(128*(a^12*d^2 + 6*a^11*b*d^2 + a^6*b^6*d^2 + 6*a^7*b^5*d^2 + 15*a^8*b^4*d^2 + 20*a^9*b^3*d^2 + 15*a^10*b^2*d^2)) - ((((5*a^3*b^13*d^2)/4 + 14*a^4*b^12*d^2 + (287*a^5*b^11*d^2)/4 + 224*a^6*b^10*d^2 + (953*a^7*b^9*d^2)/2 + 728*a^8*b^8*d^2 + (1631*a^9*b^7*d^2)/2 + 668*a^10*b^6*d^2 + (1561*a^11*b^5*d^2)/4 + 154*a^12*b^4*d^2 + (147*a^13*b^3*d^2)/4 + 4*a^14*b^2*d^2)/(a^15*d^3 + 9*a^14*b*d^3 + a^6*b^9*d^3 + 9*a^7*b^8*d^3 + 36*a^8*b^7*d^3 + 84*a^9*b^6*d^3 + 126*a^10*b^5*d^3 + 126*a^11*b^4*d^3 + 84*a^12*b^3*d^3 + 36*a^13*b^2*d^3) + (coth(c + d*x)*(-a^7*b)^(1/2)*(21*a*b^2 + 35*a^2*b + 35*a^3 + 5*b^3)*(1024*a^6*b^11*d^2 + 7168*a^7*b^10*d^2 + 20480*a^8*b^9*d^2 + 28672*a^9*b^8*d^2 + 14336*a^10*b^7*d^2 - 14336*a^11*b^6*d^2 - 28672*a^12*b^5*d^2 - 20480*a^13*b^4*d^2 - 7168*a^14*b^3*d^2 - 1024*a^15*b^2*d^2))/(4096*(a^11*d + a^7*b^4*d + 4*a^8*b^3*d + 6*a^9*b^2*d + 4*a^10*b*d)*(a^12*d^2 + 6*a^11*b*d^2 + a^6*b^6*d^2 + 6*a^7*b^5*d^2 + 15*a^8*b^4*d^2 + 20*a^9*b^3*d^2 + 15*a^10*b^2*d^2)))*(-a^7*b)^(1/2)*(21*a*b^2 + 35*a^2*b + 35*a^3 + 5*b^3))/(32*(a^11*d + a^7*b^4*d + 4*a^8*b^3*d + 6*a^9*b^2*d + 4*a^10*b*d)))*(21*a*b^2 + 35*a^2*b + 35*a^3 + 5*b^3)*1i)/(32*(a^11*d + a^7*b^4*d + 4*a^8*b^3*d + 6*a^9*b^2*d + 4*a^10*b*d)))/(((185*a*b^7)/128 + (25*b^8)/128 + (303*a^2*b^6)/64 + (567*a^3*b^5)/64 + (1225*a^4*b^4)/128 + (665*a^5*b^3)/128)/(a^15*d^3 + 9*a^14*b*d^3 + a^6*b^9*d^3 + 9*a^7*b^8*d^3 + 36*a^8*b^7*d^3 + 84*a^9*b^6*d^3 + 126*a^10*b^5*d^3 + 126*a^11*b^4*d^3 + 84*a^12*b^3*d^3 + 36*a^13*b^2*d^3) + ((-a^7*b)^(1/2)*((coth(c + d*x)*(210*a*b^8 + 25*b^9 + 791*a^2*b^7 + 1820*a^3*b^6 + 2695*a^4*b^5 + 2450*a^5*b^4 + 1481*a^6*b^3))/(128*(a^12*d^2 + 6*a^11*b*d^2 + a^6*b^6*d^2 + 6*a^7*b^5*d^2 + 15*a^8*b^4*d^2 + 20*a^9*b^3*d^2 + 15*a^10*b^2*d^2)) + ((((5*a^3*b^13*d^2)/4 + 14*a^4*b^12*d^2 + (287*a^5*b^11*d^2)/4 + 224*a^6*b^10*d^2 + (953*a^7*b^9*d^2)/2 + 728*a^8*b^8*d^2 + (1631*a^9*b^7*d^2)/2 + 668*a^10*b^6*d^2 + (1561*a^11*b^5*d^2)/4 + 154*a^12*b^4*d^2 + (147*a^13*b^3*d^2)/4 + 4*a^14*b^2*d^2)/(a^15*d^3 + 9*a^14*b*d^3 + a^6*b^9*d^3 + 9*a^7*b^8*d^3 + 36*a^8*b^7*d^3 + 84*a^9*b^6*d^3 + 126*a^10*b^5*d^3 + 126*a^11*b^4*d^3 + 84*a^12*b^3*d^3 + 36*a^13*b^2*d^3) - (coth(c + d*x)*(-a^7*b)^(1/2)*(21*a*b^2 + 35*a^2*b + 35*a^3 + 5*b^3)*(1024*a^6*b^11*d^2 + 7168*a^7*b^10*d^2 + 20480*a^8*b^9*d^2 + 28672*a^9*b^8*d^2 + 14336*a^10*b^7*d^2 - 14336*a^11*b^6*d^2 - 28672*a^12*b^5*d^2 - 20480*a^13*b^4*d^2 - 7168*a^14*b^3*d^2 - 1024*a^15*b^2*d^2))/(4096*(a^11*d + a^7*b^4*d + 4*a^8*b^3*d + 6*a^9*b^2*d + 4*a^10*b*d)*(a^12*d^2 + 6*a^11*b*d^2 + a^6*b^6*d^2 + 6*a^7*b^5*d^2 + 15*a^8*b^4*d^2 + 20*a^9*b^3*d^2 + 15*a^10*b^2*d^2)))*(-a^7*b)^(1/2)*(21*a*b^2 + 35*a^2*b + 35*a^3 + 5*b^3))/(32*(a^11*d + a^7*b^4*d + 4*a^8*b^3*d + 6*a^9*b^2*d + 4*a^10*b*d)))*(21*a*b^2 + 35*a^2*b + 35*a^3 + 5*b^3))/(32*(a^11*d + a^7*b^4*d + 4*a^8*b^3*d + 6*a^9*b^2*d + 4*a^10*b*d)) - ((-a^7*b)^(1/2)*((coth(c + d*x)*(210*a*b^8 + 25*b^9 + 791*a^2*b^7 + 1820*a^3*b^6 + 2695*a^4*b^5 + 2450*a^5*b^4 + 1481*a^6*b^3))/(128*(a^12*d^2 + 6*a^11*b*d^2 + a^6*b^6*d^2 + 6*a^7*b^5*d^2 + 15*a^8*b^4*d^2 + 20*a^9*b^3*d^2 + 15*a^10*b^2*d^2)) - ((((5*a^3*b^13*d^2)/4 + 14*a^4*b^12*d^2 + (287*a^5*b^11*d^2)/4 + 224*a^6*b^10*d^2 + (953*a^7*b^9*d^2)/2 + 728*a^8*b^8*d^2 + (1631*a^9*b^7*d^2)/2 + 668*a^10*b^6*d^2 + (1561*a^11*b^5*d^2)/4 + 154*a^12*b^4*d^2 + (147*a^13*b^3*d^2)/4 + 4*a^14*b^2*d^2)/(a^15*d^3 + 9*a^14*b*d^3 + a^6*b^9*d^3 + 9*a^7*b^8*d^3 + 36*a^8*b^7*d^3 + 84*a^9*b^6*d^3 + 126*a^10*b^5*d^3 + 126*a^11*b^4*d^3 + 84*a^12*b^3*d^3 + 36*a^13*b^2*d^3) + (coth(c + d*x)*(-a^7*b)^(1/2)*(21*a*b^2 + 35*a^2*b + 35*a^3 + 5*b^3)*(1024*a^6*b^11*d^2 + 7168*a^7*b^10*d^2 + 20480*a^8*b^9*d^2 + 28672*a^9*b^8*d^2 + 14336*a^10*b^7*d^2 - 14336*a^11*b^6*d^2 - 28672*a^12*b^5*d^2 - 20480*a^13*b^4*d^2 - 7168*a^14*b^3*d^2 - 1024*a^15*b^2*d^2))/(4096*(a^11*d + a^7*b^4*d + 4*a^8*b^3*d + 6*a^9*b^2*d + 4*a^10*b*d)*(a^12*d^2 + 6*a^11*b*d^2 + a^6*b^6*d^2 + 6*a^7*b^5*d^2 + 15*a^8*b^4*d^2 + 20*a^9*b^3*d^2 + 15*a^10*b^2*d^2)))*(-a^7*b)^(1/2)*(21*a*b^2 + 35*a^2*b + 35*a^3 + 5*b^3))/(32*(a^11*d + a^7*b^4*d + 4*a^8*b^3*d + 6*a^9*b^2*d + 4*a^10*b*d)))*(21*a*b^2 + 35*a^2*b + 35*a^3 + 5*b^3))/(32*(a^11*d + a^7*b^4*d + 4*a^8*b^3*d + 6*a^9*b^2*d + 4*a^10*b*d))))*(-a^7*b)^(1/2)*(21*a*b^2 + 35*a^2*b + 35*a^3 + 5*b^3)*1i)/(16*(a^11*d + a^7*b^4*d + 4*a^8*b^3*d + 6*a^9*b^2*d + 4*a^10*b*d))","B"
9,1,15,19,0.107952,"\text{Not used}","int(-1/(2*coth(x)^2 - 1),x)","\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\mathrm{coth}\left(x\right)\right)-x","Not used",1,"2^(1/2)*atanh(2^(1/2)*coth(x)) - x","B"
10,1,3,3,1.177538,"\text{Not used}","int((1 - coth(x)^2)^(1/2),x)","\mathrm{asin}\left(\mathrm{coth}\left(x\right)\right)","Not used",1,"asin(coth(x))","B"
11,1,14,14,1.371443,"\text{Not used}","int((coth(x)^2 - 1)^(1/2),x)","-\ln\left(\mathrm{coth}\left(x\right)+\sqrt{{\mathrm{coth}\left(x\right)}^2-1}\right)","Not used",1,"-log(coth(x) + (coth(x)^2 - 1)^(1/2))","B"
12,1,20,24,1.214947,"\text{Not used}","int((1 - coth(x)^2)^(3/2),x)","\frac{\mathrm{asin}\left(\mathrm{coth}\left(x\right)\right)}{2}+\frac{\mathrm{coth}\left(x\right)\,\sqrt{1-{\mathrm{coth}\left(x\right)}^2}}{2}","Not used",1,"asin(coth(x))/2 + (coth(x)*(1 - coth(x)^2)^(1/2))/2","B"
13,1,27,31,1.195591,"\text{Not used}","int((coth(x)^2 - 1)^(3/2),x)","\frac{\ln\left(\mathrm{coth}\left(x\right)+\sqrt{{\mathrm{coth}\left(x\right)}^2-1}\right)}{2}-\frac{\mathrm{coth}\left(x\right)\,\sqrt{{\mathrm{coth}\left(x\right)}^2-1}}{2}","Not used",1,"log(coth(x) + (coth(x)^2 - 1)^(1/2))/2 - (coth(x)*(coth(x)^2 - 1)^(1/2))/2","B"
14,1,18,13,1.342560,"\text{Not used}","int(1/(1 - coth(x)^2)^(1/2),x)","-\mathrm{cosh}\left(x\right)\,\mathrm{sinh}\left(x\right)\,\sqrt{-\frac{1}{{\mathrm{cosh}\left(x\right)}^2-1}}","Not used",1,"-cosh(x)*sinh(x)*(-1/(cosh(x)^2 - 1))^(1/2)","B"
15,1,15,11,1.242009,"\text{Not used}","int(1/(coth(x)^2 - 1)^(1/2),x)","\mathrm{cosh}\left(x\right)\,\mathrm{sinh}\left(x\right)\,\sqrt{\frac{1}{{\mathrm{cosh}\left(x\right)}^2-1}}","Not used",1,"cosh(x)*sinh(x)*(1/(cosh(x)^2 - 1))^(1/2)","B"
16,1,66,63,3.078461,"\text{Not used}","int(coth(x)^3*(a + b*coth(x)^2)^(1/2),x)","-\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}-\frac{{\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}^{3/2}}{3\,b}-2\,\mathrm{atan}\left(\frac{2\,\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}\,\sqrt{-\frac{a}{4}-\frac{b}{4}}}{a+b}\right)\,\sqrt{-\frac{a}{4}-\frac{b}{4}}","Not used",1,"- (a + b*coth(x)^2)^(1/2) - (a + b*coth(x)^2)^(3/2)/(3*b) - 2*atan((2*(a + b*coth(x)^2)^(1/2)*(- a/4 - b/4)^(1/2))/(a + b))*(- a/4 - b/4)^(1/2)","B"
17,0,-1,85,0.000000,"\text{Not used}","int(coth(x)^2*(a + b*coth(x)^2)^(1/2),x)","\int {\mathrm{coth}\left(x\right)}^2\,\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a} \,d x","Not used",1,"int(coth(x)^2*(a + b*coth(x)^2)^(1/2), x)","F"
18,1,51,44,1.622655,"\text{Not used}","int(coth(x)*(a + b*coth(x)^2)^(1/2),x)","-\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}-2\,\mathrm{atan}\left(\frac{2\,\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}\,\sqrt{-\frac{a}{4}-\frac{b}{4}}}{a+b}\right)\,\sqrt{-\frac{a}{4}-\frac{b}{4}}","Not used",1,"- (a + b*coth(x)^2)^(1/2) - 2*atan((2*(a + b*coth(x)^2)^(1/2)*(- a/4 - b/4)^(1/2))/(a + b))*(- a/4 - b/4)^(1/2)","B"
19,0,-1,60,0.000000,"\text{Not used}","int((a + b*coth(x)^2)^(1/2),x)","\int \sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a} \,d x","Not used",1,"int((a + b*coth(x)^2)^(1/2), x)","F"
20,0,-1,56,0.000000,"\text{Not used}","int(tanh(x)*(a + b*coth(x)^2)^(1/2),x)","\int \mathrm{tanh}\left(x\right)\,\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a} \,d x","Not used",1,"int(tanh(x)*(a + b*coth(x)^2)^(1/2), x)","F"
21,0,-1,48,0.000000,"\text{Not used}","int(tanh(x)^2*(a + b*coth(x)^2)^(1/2),x)","\int {\mathrm{tanh}\left(x\right)}^2\,\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a} \,d x","Not used",1,"int(tanh(x)^2*(a + b*coth(x)^2)^(1/2), x)","F"
22,1,112,82,9.036580,"\text{Not used}","int(coth(x)^3*(a + b*coth(x)^2)^(3/2),x)","-\frac{{\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}^{5/2}}{5\,b}-\left(\frac{a+b}{3\,b}-\frac{a}{3\,b}\right)\,{\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}^{3/2}-\left(a+b\right)\,\left(\frac{a+b}{b}-\frac{a}{b}\right)\,\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}-\mathrm{atan}\left(\frac{{\left(a+b\right)}^{3/2}\,\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}\,1{}\mathrm{i}}{a^2+2\,a\,b+b^2}\right)\,{\left(a+b\right)}^{3/2}\,1{}\mathrm{i}","Not used",1,"- (a + b*coth(x)^2)^(5/2)/(5*b) - ((a + b)/(3*b) - a/(3*b))*(a + b*coth(x)^2)^(3/2) - atan(((a + b)^(3/2)*(a + b*coth(x)^2)^(1/2)*1i)/(2*a*b + a^2 + b^2))*(a + b)^(3/2)*1i - (a + b)*((a + b)/b - a/b)*(a + b*coth(x)^2)^(1/2)","B"
23,0,-1,123,0.000000,"\text{Not used}","int(coth(x)^2*(a + b*coth(x)^2)^(3/2),x)","\int {\mathrm{coth}\left(x\right)}^2\,{\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(coth(x)^2*(a + b*coth(x)^2)^(3/2), x)","F"
24,1,64,63,3.396203,"\text{Not used}","int(coth(x)*(a + b*coth(x)^2)^(3/2),x)","\mathrm{atanh}\left(\frac{{\left(a+b\right)}^{3/2}\,\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}}{a^2+2\,a\,b+b^2}\right)\,{\left(a+b\right)}^{3/2}-\left(a+b\right)\,\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}-\frac{{\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}^{3/2}}{3}","Not used",1,"atanh(((a + b)^(3/2)*(a + b*coth(x)^2)^(1/2))/(2*a*b + a^2 + b^2))*(a + b)^(3/2) - (a + b)*(a + b*coth(x)^2)^(1/2) - (a + b*coth(x)^2)^(3/2)/3","B"
25,0,-1,88,0.000000,"\text{Not used}","int((a + b*coth(x)^2)^(3/2),x)","\int {\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int((a + b*coth(x)^2)^(3/2), x)","F"
26,0,-1,71,0.000000,"\text{Not used}","int(tanh(x)*(a + b*coth(x)^2)^(3/2),x)","\int \mathrm{tanh}\left(x\right)\,{\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(tanh(x)*(a + b*coth(x)^2)^(3/2), x)","F"
27,0,-1,77,0.000000,"\text{Not used}","int(tanh(x)^2*(a + b*coth(x)^2)^(3/2),x)","\int {\mathrm{tanh}\left(x\right)}^2\,{\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(tanh(x)^2*(a + b*coth(x)^2)^(3/2), x)","F"
28,1,68,31,1.340004,"\text{Not used}","int((coth(x)^2 + 1)^(1/2),x)","\frac{\sqrt{2}\,\left(\ln\left(\mathrm{coth}\left(x\right)+\sqrt{2}\,\sqrt{{\mathrm{coth}\left(x\right)}^2+1}+1\right)-\ln\left(\mathrm{coth}\left(x\right)-1\right)\right)}{2}-\mathrm{asinh}\left(\mathrm{coth}\left(x\right)\right)+\frac{\sqrt{2}\,\left(\ln\left(\mathrm{coth}\left(x\right)+1\right)-\ln\left(\sqrt{2}\,\sqrt{{\mathrm{coth}\left(x\right)}^2+1}-\mathrm{coth}\left(x\right)+1\right)\right)}{2}","Not used",1,"(2^(1/2)*(log(coth(x) + 2^(1/2)*(coth(x)^2 + 1)^(1/2) + 1) - log(coth(x) - 1)))/2 - asinh(coth(x)) + (2^(1/2)*(log(coth(x) + 1) - log(2^(1/2)*(coth(x)^2 + 1)^(1/2) - coth(x) + 1)))/2","B"
29,1,43,45,1.298873,"\text{Not used}","int((- coth(x)^2 - 1)^(1/2),x)","-\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{coth}\left(x\right)}{\sqrt{-{\mathrm{coth}\left(x\right)}^2-1}}\right)-\ln\left(\mathrm{coth}\left(x\right)-\sqrt{-{\mathrm{coth}\left(x\right)}^2-1}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}","Not used",1,"- log(coth(x) - (- coth(x)^2 - 1)^(1/2)*1i)*1i - 2^(1/2)*atan((2^(1/2)*coth(x))/(- coth(x)^2 - 1)^(1/2))","B"
30,1,78,50,1.393627,"\text{Not used}","int((coth(x)^2 + 1)^(3/2),x)","\sqrt{2}\,\left(\ln\left(\mathrm{coth}\left(x\right)+\sqrt{2}\,\sqrt{{\mathrm{coth}\left(x\right)}^2+1}+1\right)-\ln\left(\mathrm{coth}\left(x\right)-1\right)\right)-\frac{\mathrm{coth}\left(x\right)\,\sqrt{{\mathrm{coth}\left(x\right)}^2+1}}{2}-\frac{5\,\mathrm{asinh}\left(\mathrm{coth}\left(x\right)\right)}{2}+\sqrt{2}\,\left(\ln\left(\mathrm{coth}\left(x\right)+1\right)-\ln\left(\sqrt{2}\,\sqrt{{\mathrm{coth}\left(x\right)}^2+1}-\mathrm{coth}\left(x\right)+1\right)\right)","Not used",1,"2^(1/2)*(log(coth(x) + 2^(1/2)*(coth(x)^2 + 1)^(1/2) + 1) - log(coth(x) - 1)) - (coth(x)*(coth(x)^2 + 1)^(1/2))/2 - (5*asinh(coth(x)))/2 + 2^(1/2)*(log(coth(x) + 1) - log(2^(1/2)*(coth(x)^2 + 1)^(1/2) - coth(x) + 1))","B"
31,0,-1,67,0.000000,"\text{Not used}","int((- coth(x)^2 - 1)^(3/2),x)","\int {\left(-{\mathrm{coth}\left(x\right)}^2-1\right)}^{3/2} \,d x","Not used",1,"int((- coth(x)^2 - 1)^(3/2), x)","F"
32,1,39,47,1.689431,"\text{Not used}","int(coth(x)^3/(a + b*coth(x)^2)^(1/2),x)","\frac{\mathrm{atanh}\left(\frac{\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}-\frac{\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}}{b}","Not used",1,"atanh((a + b*coth(x)^2)^(1/2)/(a + b)^(1/2))/(a + b)^(1/2) - (a + b*coth(x)^2)^(1/2)/b","B"
33,0,-1,60,0.000000,"\text{Not used}","int(coth(x)^2/(a + b*coth(x)^2)^(1/2),x)","\int \frac{{\mathrm{coth}\left(x\right)}^2}{\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}} \,d x","Not used",1,"int(coth(x)^2/(a + b*coth(x)^2)^(1/2), x)","F"
34,1,23,29,1.742703,"\text{Not used}","int(coth(x)/(a + b*coth(x)^2)^(1/2),x)","\frac{\mathrm{atanh}\left(\frac{\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}","Not used",1,"atanh((a + b*coth(x)^2)^(1/2)/(a + b)^(1/2))/(a + b)^(1/2)","B"
35,1,25,31,1.479173,"\text{Not used}","int(1/(a + b*coth(x)^2)^(1/2),x)","\frac{\mathrm{atanh}\left(\frac{\mathrm{coth}\left(x\right)\,\sqrt{a+b}}{\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}}\right)}{\sqrt{a+b}}","Not used",1,"atanh((coth(x)*(a + b)^(1/2))/(a + b*coth(x)^2)^(1/2))/(a + b)^(1/2)","B"
36,0,-1,56,0.000000,"\text{Not used}","int(tanh(x)/(a + b*coth(x)^2)^(1/2),x)","\int \frac{\mathrm{tanh}\left(x\right)}{\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}} \,d x","Not used",1,"int(tanh(x)/(a + b*coth(x)^2)^(1/2), x)","F"
37,0,-1,51,0.000000,"\text{Not used}","int(tanh(x)^2/(a + b*coth(x)^2)^(1/2),x)","\int \frac{{\mathrm{tanh}\left(x\right)}^2}{\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}} \,d x","Not used",1,"int(tanh(x)^2/(a + b*coth(x)^2)^(1/2), x)","F"
38,1,45,52,2.003482,"\text{Not used}","int(coth(x)^3/(a + b*coth(x)^2)^(3/2),x)","\frac{\mathrm{atanh}\left(\frac{\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}}{\sqrt{a+b}}\right)}{{\left(a+b\right)}^{3/2}}+\frac{a}{\left(b^2+a\,b\right)\,\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}}","Not used",1,"atanh((a + b*coth(x)^2)^(1/2)/(a + b)^(1/2))/(a + b)^(3/2) + a/((a*b + b^2)*(a + b*coth(x)^2)^(1/2))","B"
39,0,-1,53,0.000000,"\text{Not used}","int(coth(x)^2/(a + b*coth(x)^2)^(3/2),x)","\int \frac{{\mathrm{coth}\left(x\right)}^2}{{\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(coth(x)^2/(a + b*coth(x)^2)^(3/2), x)","F"
40,1,41,49,1.937987,"\text{Not used}","int(coth(x)/(a + b*coth(x)^2)^(3/2),x)","\frac{\mathrm{atanh}\left(\frac{\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}}{\sqrt{a+b}}\right)}{{\left(a+b\right)}^{3/2}}-\frac{1}{\left(a+b\right)\,\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}}","Not used",1,"atanh((a + b*coth(x)^2)^(1/2)/(a + b)^(1/2))/(a + b)^(3/2) - 1/((a + b)*(a + b*coth(x)^2)^(1/2))","B"
41,0,-1,78,0.000000,"\text{Not used}","int(tanh(x)/(a + b*coth(x)^2)^(3/2),x)","\int \frac{\mathrm{tanh}\left(x\right)}{{\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(tanh(x)/(a + b*coth(x)^2)^(3/2), x)","F"
42,0,-1,85,0.000000,"\text{Not used}","int(tanh(x)^2/(a + b*coth(x)^2)^(3/2),x)","\int \frac{{\mathrm{tanh}\left(x\right)}^2}{{\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(tanh(x)^2/(a + b*coth(x)^2)^(3/2), x)","F"
43,1,82,74,3.339409,"\text{Not used}","int(coth(x)^3/(a + b*coth(x)^2)^(5/2),x)","\frac{\mathrm{atanh}\left(\frac{\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}\,\left(2\,a^2+4\,a\,b+2\,b^2\right)}{2\,{\left(a+b\right)}^{5/2}}\right)}{{\left(a+b\right)}^{5/2}}+\frac{\frac{a}{3\,\left(a+b\right)}-\frac{b\,\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}{{\left(a+b\right)}^2}}{b\,{\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}^{3/2}}","Not used",1,"atanh(((a + b*coth(x)^2)^(1/2)*(4*a*b + 2*a^2 + 2*b^2))/(2*(a + b)^(5/2)))/(a + b)^(5/2) + (a/(3*(a + b)) - (b*(a + b*coth(x)^2))/(a + b)^2)/(b*(a + b*coth(x)^2)^(3/2))","B"
44,0,-1,88,0.000000,"\text{Not used}","int(coth(x)^2/(a + b*coth(x)^2)^(5/2),x)","\int \frac{{\mathrm{coth}\left(x\right)}^2}{{\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(coth(x)^2/(a + b*coth(x)^2)^(5/2), x)","F"
45,1,76,70,3.412468,"\text{Not used}","int(coth(x)/(a + b*coth(x)^2)^(5/2),x)","\frac{\mathrm{atanh}\left(\frac{\sqrt{b\,{\mathrm{coth}\left(x\right)}^2+a}\,\left(2\,a^2+4\,a\,b+2\,b^2\right)}{2\,{\left(a+b\right)}^{5/2}}\right)}{{\left(a+b\right)}^{5/2}}-\frac{\frac{1}{3\,\left(a+b\right)}+\frac{b\,{\mathrm{coth}\left(x\right)}^2+a}{{\left(a+b\right)}^2}}{{\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}^{3/2}}","Not used",1,"atanh(((a + b*coth(x)^2)^(1/2)*(4*a*b + 2*a^2 + 2*b^2))/(2*(a + b)^(5/2)))/(a + b)^(5/2) - (1/(3*(a + b)) + (a + b*coth(x)^2)/(a + b)^2)/(a + b*coth(x)^2)^(3/2)","B"
46,0,-1,108,0.000000,"\text{Not used}","int(tanh(x)/(a + b*coth(x)^2)^(5/2),x)","\int \frac{\mathrm{tanh}\left(x\right)}{{\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(tanh(x)/(a + b*coth(x)^2)^(5/2), x)","F"
47,0,-1,131,0.000000,"\text{Not used}","int(tanh(x)^2/(a + b*coth(x)^2)^(5/2),x)","\int \frac{{\mathrm{tanh}\left(x\right)}^2}{{\left(b\,{\mathrm{coth}\left(x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(tanh(x)^2/(a + b*coth(x)^2)^(5/2), x)","F"
48,1,63,25,1.350437,"\text{Not used}","int(1/(coth(x)^2 + 1)^(1/2),x)","\frac{\sqrt{2}\,\left(\ln\left(\mathrm{coth}\left(x\right)+\sqrt{2}\,\sqrt{{\mathrm{coth}\left(x\right)}^2+1}+1\right)-\ln\left(\mathrm{coth}\left(x\right)-1\right)\right)}{4}+\frac{\sqrt{2}\,\left(\ln\left(\mathrm{coth}\left(x\right)+1\right)-\ln\left(\sqrt{2}\,\sqrt{{\mathrm{coth}\left(x\right)}^2+1}-\mathrm{coth}\left(x\right)+1\right)\right)}{4}","Not used",1,"(2^(1/2)*(log(coth(x) + 2^(1/2)*(coth(x)^2 + 1)^(1/2) + 1) - log(coth(x) - 1)))/4 + (2^(1/2)*(log(coth(x) + 1) - log(2^(1/2)*(coth(x)^2 + 1)^(1/2) - coth(x) + 1)))/4","B"
49,1,22,27,1.254265,"\text{Not used}","int(1/(- coth(x)^2 - 1)^(1/2),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{coth}\left(x\right)}{\sqrt{-{\mathrm{coth}\left(x\right)}^2-1}}\right)}{2}","Not used",1,"(2^(1/2)*atan((2^(1/2)*coth(x))/(- coth(x)^2 - 1)^(1/2)))/2","B"
50,1,38,38,0.092605,"\text{Not used}","int(1/(coth(x)^3 + 1),x)","\frac{\frac{x}{2}+\frac{\mathrm{coth}\left(x\right)}{6}+\frac{x\,\mathrm{coth}\left(x\right)}{2}}{\mathrm{coth}\left(x\right)+1}+\frac{2\,\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{3}\,\left(2\,\mathrm{coth}\left(x\right)-1\right)}{3}\right)}{9}","Not used",1,"(x/2 + coth(x)/6 + (x*coth(x))/2)/(coth(x) + 1) + (2*3^(1/2)*atan((3^(1/2)*(2*coth(x) - 1))/3))/9","B"
51,0,-1,89,0.000000,"\text{Not used}","int(coth(x)*(a + b*coth(x)^4)^(1/2),x)","\int \mathrm{coth}\left(x\right)\,\sqrt{b\,{\mathrm{coth}\left(x\right)}^4+a} \,d x","Not used",1,"int(coth(x)*(a + b*coth(x)^4)^(1/2), x)","F"
52,0,-1,40,0.000000,"\text{Not used}","int(coth(x)/(a + b*coth(x)^4)^(1/2),x)","\int \frac{\mathrm{coth}\left(x\right)}{\sqrt{b\,{\mathrm{coth}\left(x\right)}^4+a}} \,d x","Not used",1,"int(coth(x)/(a + b*coth(x)^4)^(1/2), x)","F"
53,0,-1,74,0.000000,"\text{Not used}","int(coth(x)/(a + b*coth(x)^4)^(3/2),x)","\int \frac{\mathrm{coth}\left(x\right)}{{\left(b\,{\mathrm{coth}\left(x\right)}^4+a\right)}^{3/2}} \,d x","Not used",1,"int(coth(x)/(a + b*coth(x)^4)^(3/2), x)","F"