1,1,828,233,0.924932,"\text{Not used}","int((A + C*cot(c + d*x)^2)/(b*tan(c + d*x))^(1/2),x)","-\frac{2\,C\,b}{3\,d\,{\left(b\,\mathrm{tan}\left(c+d\,x\right)\right)}^{3/2}}+\frac{{\left(-1\right)}^{1/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-1\right)}^{1/4}\,\left(A-C\right)\,\left(\sqrt{b\,\mathrm{tan}\left(c+d\,x\right)}\,\left(16\,A^2\,b^2\,d^3-32\,A\,C\,b^2\,d^3+16\,C^2\,b^2\,d^3\right)-\frac{{\left(-1\right)}^{1/4}\,\left(A-C\right)\,\left(32\,A\,b^3\,d^4-32\,C\,b^3\,d^4\right)}{2\,\sqrt{b}\,d}\right)\,1{}\mathrm{i}}{2\,\sqrt{b}\,d}+\frac{{\left(-1\right)}^{1/4}\,\left(A-C\right)\,\left(\sqrt{b\,\mathrm{tan}\left(c+d\,x\right)}\,\left(16\,A^2\,b^2\,d^3-32\,A\,C\,b^2\,d^3+16\,C^2\,b^2\,d^3\right)+\frac{{\left(-1\right)}^{1/4}\,\left(A-C\right)\,\left(32\,A\,b^3\,d^4-32\,C\,b^3\,d^4\right)}{2\,\sqrt{b}\,d}\right)\,1{}\mathrm{i}}{2\,\sqrt{b}\,d}}{\frac{{\left(-1\right)}^{1/4}\,\left(A-C\right)\,\left(\sqrt{b\,\mathrm{tan}\left(c+d\,x\right)}\,\left(16\,A^2\,b^2\,d^3-32\,A\,C\,b^2\,d^3+16\,C^2\,b^2\,d^3\right)-\frac{{\left(-1\right)}^{1/4}\,\left(A-C\right)\,\left(32\,A\,b^3\,d^4-32\,C\,b^3\,d^4\right)}{2\,\sqrt{b}\,d}\right)}{2\,\sqrt{b}\,d}-\frac{{\left(-1\right)}^{1/4}\,\left(A-C\right)\,\left(\sqrt{b\,\mathrm{tan}\left(c+d\,x\right)}\,\left(16\,A^2\,b^2\,d^3-32\,A\,C\,b^2\,d^3+16\,C^2\,b^2\,d^3\right)+\frac{{\left(-1\right)}^{1/4}\,\left(A-C\right)\,\left(32\,A\,b^3\,d^4-32\,C\,b^3\,d^4\right)}{2\,\sqrt{b}\,d}\right)}{2\,\sqrt{b}\,d}}\right)\,\left(A-C\right)\,1{}\mathrm{i}}{\sqrt{b}\,d}+\frac{{\left(-1\right)}^{1/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-1\right)}^{1/4}\,\left(A-C\right)\,\left(\sqrt{b\,\mathrm{tan}\left(c+d\,x\right)}\,\left(16\,A^2\,b^2\,d^3-32\,A\,C\,b^2\,d^3+16\,C^2\,b^2\,d^3\right)-\frac{{\left(-1\right)}^{1/4}\,\left(A-C\right)\,\left(32\,A\,b^3\,d^4-32\,C\,b^3\,d^4\right)\,1{}\mathrm{i}}{2\,\sqrt{b}\,d}\right)}{2\,\sqrt{b}\,d}+\frac{{\left(-1\right)}^{1/4}\,\left(A-C\right)\,\left(\sqrt{b\,\mathrm{tan}\left(c+d\,x\right)}\,\left(16\,A^2\,b^2\,d^3-32\,A\,C\,b^2\,d^3+16\,C^2\,b^2\,d^3\right)+\frac{{\left(-1\right)}^{1/4}\,\left(A-C\right)\,\left(32\,A\,b^3\,d^4-32\,C\,b^3\,d^4\right)\,1{}\mathrm{i}}{2\,\sqrt{b}\,d}\right)}{2\,\sqrt{b}\,d}}{\frac{{\left(-1\right)}^{1/4}\,\left(A-C\right)\,\left(\sqrt{b\,\mathrm{tan}\left(c+d\,x\right)}\,\left(16\,A^2\,b^2\,d^3-32\,A\,C\,b^2\,d^3+16\,C^2\,b^2\,d^3\right)-\frac{{\left(-1\right)}^{1/4}\,\left(A-C\right)\,\left(32\,A\,b^3\,d^4-32\,C\,b^3\,d^4\right)\,1{}\mathrm{i}}{2\,\sqrt{b}\,d}\right)\,1{}\mathrm{i}}{2\,\sqrt{b}\,d}-\frac{{\left(-1\right)}^{1/4}\,\left(A-C\right)\,\left(\sqrt{b\,\mathrm{tan}\left(c+d\,x\right)}\,\left(16\,A^2\,b^2\,d^3-32\,A\,C\,b^2\,d^3+16\,C^2\,b^2\,d^3\right)+\frac{{\left(-1\right)}^{1/4}\,\left(A-C\right)\,\left(32\,A\,b^3\,d^4-32\,C\,b^3\,d^4\right)\,1{}\mathrm{i}}{2\,\sqrt{b}\,d}\right)\,1{}\mathrm{i}}{2\,\sqrt{b}\,d}}\right)\,\left(A-C\right)}{\sqrt{b}\,d}","Not used",1,"((-1)^(1/4)*atan((((-1)^(1/4)*(A - C)*((b*tan(c + d*x))^(1/2)*(16*A^2*b^2*d^3 + 16*C^2*b^2*d^3 - 32*A*C*b^2*d^3) - ((-1)^(1/4)*(A - C)*(32*A*b^3*d^4 - 32*C*b^3*d^4))/(2*b^(1/2)*d))*1i)/(2*b^(1/2)*d) + ((-1)^(1/4)*(A - C)*((b*tan(c + d*x))^(1/2)*(16*A^2*b^2*d^3 + 16*C^2*b^2*d^3 - 32*A*C*b^2*d^3) + ((-1)^(1/4)*(A - C)*(32*A*b^3*d^4 - 32*C*b^3*d^4))/(2*b^(1/2)*d))*1i)/(2*b^(1/2)*d))/(((-1)^(1/4)*(A - C)*((b*tan(c + d*x))^(1/2)*(16*A^2*b^2*d^3 + 16*C^2*b^2*d^3 - 32*A*C*b^2*d^3) - ((-1)^(1/4)*(A - C)*(32*A*b^3*d^4 - 32*C*b^3*d^4))/(2*b^(1/2)*d)))/(2*b^(1/2)*d) - ((-1)^(1/4)*(A - C)*((b*tan(c + d*x))^(1/2)*(16*A^2*b^2*d^3 + 16*C^2*b^2*d^3 - 32*A*C*b^2*d^3) + ((-1)^(1/4)*(A - C)*(32*A*b^3*d^4 - 32*C*b^3*d^4))/(2*b^(1/2)*d)))/(2*b^(1/2)*d)))*(A - C)*1i)/(b^(1/2)*d) - (2*C*b)/(3*d*(b*tan(c + d*x))^(3/2)) + ((-1)^(1/4)*atan((((-1)^(1/4)*(A - C)*((b*tan(c + d*x))^(1/2)*(16*A^2*b^2*d^3 + 16*C^2*b^2*d^3 - 32*A*C*b^2*d^3) - ((-1)^(1/4)*(A - C)*(32*A*b^3*d^4 - 32*C*b^3*d^4)*1i)/(2*b^(1/2)*d)))/(2*b^(1/2)*d) + ((-1)^(1/4)*(A - C)*((b*tan(c + d*x))^(1/2)*(16*A^2*b^2*d^3 + 16*C^2*b^2*d^3 - 32*A*C*b^2*d^3) + ((-1)^(1/4)*(A - C)*(32*A*b^3*d^4 - 32*C*b^3*d^4)*1i)/(2*b^(1/2)*d)))/(2*b^(1/2)*d))/(((-1)^(1/4)*(A - C)*((b*tan(c + d*x))^(1/2)*(16*A^2*b^2*d^3 + 16*C^2*b^2*d^3 - 32*A*C*b^2*d^3) - ((-1)^(1/4)*(A - C)*(32*A*b^3*d^4 - 32*C*b^3*d^4)*1i)/(2*b^(1/2)*d))*1i)/(2*b^(1/2)*d) - ((-1)^(1/4)*(A - C)*((b*tan(c + d*x))^(1/2)*(16*A^2*b^2*d^3 + 16*C^2*b^2*d^3 - 32*A*C*b^2*d^3) + ((-1)^(1/4)*(A - C)*(32*A*b^3*d^4 - 32*C*b^3*d^4)*1i)/(2*b^(1/2)*d))*1i)/(2*b^(1/2)*d)))*(A - C))/(b^(1/2)*d)","B"
2,1,20,20,0.336275,"\text{Not used}","int(a + b*cot(c + d*x)^2,x)","x\,\left(a-b\right)-\frac{b\,\mathrm{cot}\left(c+d\,x\right)}{d}","Not used",1,"x*(a - b) - (b*cot(c + d*x))/d","B"
3,1,45,47,0.117959,"\text{Not used}","int((a + b*cot(c + d*x)^2)^2,x)","x\,{\left(a-b\right)}^2-\frac{b^2\,{\mathrm{cot}\left(c+d\,x\right)}^3}{3\,d}-\frac{b\,\mathrm{cot}\left(c+d\,x\right)\,\left(2\,a-b\right)}{d}","Not used",1,"x*(a - b)^2 - (b^2*cot(c + d*x)^3)/(3*d) - (b*cot(c + d*x)*(2*a - b))/d","B"
4,1,76,78,0.454481,"\text{Not used}","int((a + b*cot(c + d*x)^2)^3,x)","x\,{\left(a-b\right)}^3-\frac{b^3\,{\mathrm{cot}\left(c+d\,x\right)}^5}{5\,d}-\frac{{\mathrm{cot}\left(c+d\,x\right)}^3\,\left(3\,a\,b^2-b^3\right)}{3\,d}-\frac{b\,\mathrm{cot}\left(c+d\,x\right)\,\left(3\,a^2-3\,a\,b+b^2\right)}{d}","Not used",1,"x*(a - b)^3 - (b^3*cot(c + d*x)^5)/(5*d) - (cot(c + d*x)^3*(3*a*b^2 - b^3))/(3*d) - (b*cot(c + d*x)*(3*a^2 - 3*a*b + b^2))/d","B"
5,1,41,49,0.124035,"\text{Not used}","int(1/(a + b*cot(c + d*x)^2),x)","\frac{x}{a-b}+\frac{b\,\mathrm{atan}\left(\frac{b\,\mathrm{cot}\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*cot(c + d*x))/(a*b)^(1/2)))/(d*(a*b)^(1/2)*(a - b))","B"
6,1,119,97,0.786076,"\text{Not used}","int(1/(a + b*cot(c + d*x)^2)^2,x)","\frac{\frac{a\,x}{{\left(a-b\right)}^2}+\frac{b\,x\,{\mathrm{cot}\left(c+d\,x\right)}^2}{{\left(a-b\right)}^2}+\frac{b\,\mathrm{cot}\left(c+d\,x\right)}{2\,a\,d\,\left(a-b\right)}}{b\,{\mathrm{cot}\left(c+d\,x\right)}^2+a}+\frac{\mathrm{atan}\left(\frac{b\,\mathrm{cot}\left(c+d\,x\right)}{\sqrt{a\,b}}\right)\,\left(3\,a\,b-b^2\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*cot(c + d*x)^2)/(a - b)^2 + (b*cot(c + d*x))/(2*a*d*(a - b)))/(a + b*cot(c + d*x)^2) + (atan((b*cot(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"
7,1,4866,150,3.286840,"\text{Not used}","int(1/(a + b*cot(c + d*x)^2)^3,x)","\frac{\frac{{\mathrm{cot}\left(c+d\,x\right)}^3\,\left(7\,a\,b^2-3\,b^3\right)}{8\,a^2\,\left(a^2-2\,a\,b+b^2\right)}+\frac{\mathrm{cot}\left(c+d\,x\right)\,\left(9\,a\,b-5\,b^2\right)}{8\,a\,\left(a^2-2\,a\,b+b^2\right)}}{d\,a^2+2\,d\,a\,b\,{\mathrm{cot}\left(c+d\,x\right)}^2+d\,b^2\,{\mathrm{cot}\left(c+d\,x\right)}^4}+\frac{2\,\mathrm{atan}\left(\frac{\frac{-\frac{\mathrm{cot}\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{cot}\left(c+d\,x\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)\,1{}\mathrm{i}}{32\,\left(2\,d\,a^3-6\,d\,a^2\,b+6\,d\,a\,b^2-2\,d\,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)\,1{}\mathrm{i}}{2\,d\,a^3-6\,d\,a^2\,b+6\,d\,a\,b^2-2\,d\,b^3}}{2\,d\,a^3-6\,d\,a^2\,b+6\,d\,a\,b^2-2\,d\,b^3}-\frac{\frac{\mathrm{cot}\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{cot}\left(c+d\,x\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)\,1{}\mathrm{i}}{32\,\left(2\,d\,a^3-6\,d\,a^2\,b+6\,d\,a\,b^2-2\,d\,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)\,1{}\mathrm{i}}{2\,d\,a^3-6\,d\,a^2\,b+6\,d\,a\,b^2-2\,d\,b^3}}{2\,d\,a^3-6\,d\,a^2\,b+6\,d\,a\,b^2-2\,d\,b^3}}{\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{\left(-\frac{\mathrm{cot}\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{cot}\left(c+d\,x\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)\,1{}\mathrm{i}}{32\,\left(2\,d\,a^3-6\,d\,a^2\,b+6\,d\,a\,b^2-2\,d\,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)\,1{}\mathrm{i}}{2\,d\,a^3-6\,d\,a^2\,b+6\,d\,a\,b^2-2\,d\,b^3}\right)\,1{}\mathrm{i}}{2\,d\,a^3-6\,d\,a^2\,b+6\,d\,a\,b^2-2\,d\,b^3}+\frac{\left(\frac{\mathrm{cot}\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{cot}\left(c+d\,x\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)\,1{}\mathrm{i}}{32\,\left(2\,d\,a^3-6\,d\,a^2\,b+6\,d\,a\,b^2-2\,d\,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)\,1{}\mathrm{i}}{2\,d\,a^3-6\,d\,a^2\,b+6\,d\,a\,b^2-2\,d\,b^3}\right)\,1{}\mathrm{i}}{2\,d\,a^3-6\,d\,a^2\,b+6\,d\,a\,b^2-2\,d\,b^3}}\right)}{2\,d\,a^3-6\,d\,a^2\,b+6\,d\,a\,b^2-2\,d\,b^3}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a^5\,b}\,\left(\frac{\mathrm{cot}\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{cot}\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{cot}\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{cot}\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{cot}\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{cot}\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{cot}\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{cot}\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,"((cot(c + d*x)^3*(7*a*b^2 - 3*b^3))/(8*a^2*(a^2 - 2*a*b + b^2)) + (cot(c + d*x)*(9*a*b - 5*b^2))/(8*a*(a^2 - 2*a*b + b^2)))/(a^2*d + b^2*d*cot(c + d*x)^4 + 2*a*b*d*cot(c + d*x)^2) + (2*atan((((((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)) - (cot(c + d*x)*(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)*1i)/(32*(2*a^3*d - 2*b^3*d + 6*a*b^2*d - 6*a^2*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)))*1i)/(2*a^3*d - 2*b^3*d + 6*a*b^2*d - 6*a^2*b*d) - (cot(c + d*x)*(9*b^7 - 60*a*b^6 + 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)))/(2*a^3*d - 2*b^3*d + 6*a*b^2*d - 6*a^2*b*d) - ((((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)) + (cot(c + d*x)*(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)*1i)/(32*(2*a^3*d - 2*b^3*d + 6*a*b^2*d - 6*a^2*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)))*1i)/(2*a^3*d - 2*b^3*d + 6*a*b^2*d - 6*a^2*b*d) + (cot(c + d*x)*(9*b^7 - 60*a*b^6 + 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)))/(2*a^3*d - 2*b^3*d + 6*a*b^2*d - 6*a^2*b*d))/((((((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)) - (cot(c + d*x)*(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)*1i)/(32*(2*a^3*d - 2*b^3*d + 6*a*b^2*d - 6*a^2*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)))*1i)/(2*a^3*d - 2*b^3*d + 6*a*b^2*d - 6*a^2*b*d) - (cot(c + d*x)*(9*b^7 - 60*a*b^6 + 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)))*1i)/(2*a^3*d - 2*b^3*d + 6*a*b^2*d - 6*a^2*b*d) + (((((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)) + (cot(c + d*x)*(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)*1i)/(32*(2*a^3*d - 2*b^3*d + 6*a*b^2*d - 6*a^2*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)))*1i)/(2*a^3*d - 2*b^3*d + 6*a*b^2*d - 6*a^2*b*d) + (cot(c + d*x)*(9*b^7 - 60*a*b^6 + 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)))*1i)/(2*a^3*d - 2*b^3*d + 6*a*b^2*d - 6*a^2*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)))))/(2*a^3*d - 2*b^3*d + 6*a*b^2*d - 6*a^2*b*d) - (atan((((-a^5*b)^(1/2)*((cot(c + d*x)*(9*b^7 - 60*a*b^6 + 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)) - (cot(c + d*x)*(-a^5*b)^(1/2)*(15*a^2 - 10*a*b + 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)*(15*a^2 - 10*a*b + 3*b^2))/(16*(a^8*d - a^5*b^3*d + 3*a^6*b^2*d - 3*a^7*b*d)))*(15*a^2 - 10*a*b + 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)*((cot(c + d*x)*(9*b^7 - 60*a*b^6 + 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)) + (cot(c + d*x)*(-a^5*b)^(1/2)*(15*a^2 - 10*a*b + 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)*(15*a^2 - 10*a*b + 3*b^2))/(16*(a^8*d - a^5*b^3*d + 3*a^6*b^2*d - 3*a^7*b*d)))*(15*a^2 - 10*a*b + 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)*((cot(c + d*x)*(9*b^7 - 60*a*b^6 + 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)) - (cot(c + d*x)*(-a^5*b)^(1/2)*(15*a^2 - 10*a*b + 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)*(15*a^2 - 10*a*b + 3*b^2))/(16*(a^8*d - a^5*b^3*d + 3*a^6*b^2*d - 3*a^7*b*d)))*(15*a^2 - 10*a*b + 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)*((cot(c + d*x)*(9*b^7 - 60*a*b^6 + 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)) + (cot(c + d*x)*(-a^5*b)^(1/2)*(15*a^2 - 10*a*b + 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)*(15*a^2 - 10*a*b + 3*b^2))/(16*(a^8*d - a^5*b^3*d + 3*a^6*b^2*d - 3*a^7*b*d)))*(15*a^2 - 10*a*b + 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)*(15*a^2 - 10*a*b + 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"
8,1,18,22,0.374947,"\text{Not used}","int((cot(x)^2 + 1)^(3/2),x)","-\frac{\mathrm{asinh}\left(\mathrm{cot}\left(x\right)\right)}{2}-\frac{\mathrm{cot}\left(x\right)\,\sqrt{{\mathrm{cot}\left(x\right)}^2+1}}{2}","Not used",1,"- asinh(cot(x))/2 - (cot(x)*(cot(x)^2 + 1)^(1/2))/2","B"
9,1,5,5,0.317842,"\text{Not used}","int((cot(x)^2 + 1)^(1/2),x)","-\mathrm{asinh}\left(\mathrm{cot}\left(x\right)\right)","Not used",1,"-asinh(cot(x))","B"
10,1,12,12,0.391797,"\text{Not used}","int(1/(cot(x)^2 + 1)^(1/2),x)","-\frac{\sin\left(2\,x\right)}{2\,\sqrt{{\sin\left(x\right)}^2}}","Not used",1,"-sin(2*x)/(2*(sin(x)^2)^(1/2))","B"
11,1,31,35,0.368029,"\text{Not used}","int((- cot(x)^2 - 1)^(3/2),x)","\frac{\mathrm{cot}\left(x\right)\,\sqrt{-{\mathrm{cot}\left(x\right)}^2-1}}{2}-\frac{\mathrm{atan}\left(\frac{\mathrm{cot}\left(x\right)}{\sqrt{-{\mathrm{cot}\left(x\right)}^2-1}}\right)}{2}","Not used",1,"(cot(x)*(- cot(x)^2 - 1)^(1/2))/2 - atan(cot(x)/(- cot(x)^2 - 1)^(1/2))/2","B"
12,1,14,14,0.393941,"\text{Not used}","int((- cot(x)^2 - 1)^(1/2),x)","\mathrm{atan}\left(\frac{\mathrm{cot}\left(x\right)}{\sqrt{-{\mathrm{cot}\left(x\right)}^2-1}}\right)","Not used",1,"atan(cot(x)/(- cot(x)^2 - 1)^(1/2))","B"
13,1,13,14,0.682274,"\text{Not used}","int(1/(- cot(x)^2 - 1)^(1/2),x)","\frac{\sin\left(2\,x\right)\,1{}\mathrm{i}}{2\,\sqrt{{\sin\left(x\right)}^2}}","Not used",1,"(sin(2*x)*1i)/(2*(sin(x)^2)^(1/2))","B"
14,1,17,28,0.586131,"\text{Not used}","int(cot(x)^3/(a + a*cot(x)^2)^(1/2),x)","-\frac{{\sin\left(x\right)}^2+1}{\sqrt{a}\,\sqrt{{\sin\left(x\right)}^2}}","Not used",1,"-(sin(x)^2 + 1)/(a^(1/2)*(sin(x)^2)^(1/2))","B"
15,0,-1,31,0.000000,"\text{Not used}","int(cot(x)^2/(a + a*cot(x)^2)^(1/2),x)","\int \frac{{\mathrm{cot}\left(x\right)}^2}{\sqrt{a\,{\mathrm{cot}\left(x\right)}^2+a}} \,d x","Not used",1,"int(cot(x)^2/(a + a*cot(x)^2)^(1/2), x)","F"
16,1,10,10,0.476172,"\text{Not used}","int(cot(x)/(a + a*cot(x)^2)^(1/2),x)","\frac{\sqrt{{\sin\left(x\right)}^2}}{\sqrt{a}}","Not used",1,"(sin(x)^2)^(1/2)/a^(1/2)","B"
17,1,20,36,0.423081,"\text{Not used}","int(tan(x)/(a + a*cot(x)^2)^(1/2),x)","\frac{\mathrm{atanh}\left(\sqrt{\frac{1}{{\sin\left(x\right)}^2}}\right)-\sqrt{{\sin\left(x\right)}^2}}{\sqrt{a}}","Not used",1,"(atanh((1/sin(x)^2)^(1/2)) - (sin(x)^2)^(1/2))/a^(1/2)","B"
18,1,34,29,0.726834,"\text{Not used}","int(tan(x)^2/(a + a*cot(x)^2)^(1/2),x)","\frac{{\mathrm{tan}\left(x\right)}^3\,\sqrt{\frac{1}{{\mathrm{tan}\left(x\right)}^2}}+2\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{1}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a}\,\sqrt{{\mathrm{tan}\left(x\right)}^2+1}}","Not used",1,"(tan(x)^3*(1/tan(x)^2)^(1/2) + 2*tan(x)*(1/tan(x)^2)^(1/2))/(a^(1/2)*(tan(x)^2 + 1)^(1/2))","B"
19,1,66,66,3.157365,"\text{Not used}","int(cot(x)^3*(a + b*cot(x)^2)^(1/2),x)","\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a}-\frac{{\left(b\,{\mathrm{cot}\left(x\right)}^2+a\right)}^{3/2}}{3\,b}+2\,\mathrm{atan}\left(\frac{2\,\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a}\,\sqrt{\frac{b}{4}-\frac{a}{4}}}{a-b}\right)\,\sqrt{\frac{b}{4}-\frac{a}{4}}","Not used",1,"(a + b*cot(x)^2)^(1/2) - (a + b*cot(x)^2)^(3/2)/(3*b) + 2*atan((2*(a + b*cot(x)^2)^(1/2)*(b/4 - a/4)^(1/2))/(a - b))*(b/4 - a/4)^(1/2)","B"
20,1,53,48,1.170436,"\text{Not used}","int(cot(x)*(a + b*cot(x)^2)^(1/2),x)","-\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a}-2\,\mathrm{atan}\left(\frac{2\,\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a}\,\sqrt{\frac{b}{4}-\frac{a}{4}}}{a-b}\right)\,\sqrt{\frac{b}{4}-\frac{a}{4}}","Not used",1,"- (a + b*cot(x)^2)^(1/2) - 2*atan((2*(a + b*cot(x)^2)^(1/2)*(b/4 - a/4)^(1/2))/(a - b))*(b/4 - a/4)^(1/2)","B"
21,1,69,60,0.477379,"\text{Not used}","int(tan(x)*(a + b*cot(x)^2)^(1/2),x)","\mathrm{atanh}\left(\frac{2\,a\,b^3\,\sqrt{a-b}\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{2\,a\,b^4-2\,a^2\,b^3}\right)\,\sqrt{a-b}+\sqrt{a}\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a}}\right)","Not used",1,"atanh((2*a*b^3*(a - b)^(1/2)*(a + b/tan(x)^2)^(1/2))/(2*a*b^4 - 2*a^2*b^3))*(a - b)^(1/2) + a^(1/2)*atanh((a + b/tan(x)^2)^(1/2)/a^(1/2))","B"
22,0,-1,89,0.000000,"\text{Not used}","int(cot(x)^2*(a + b*cot(x)^2)^(1/2),x)","\int {\mathrm{cot}\left(x\right)}^2\,\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a} \,d x","Not used",1,"int(cot(x)^2*(a + b*cot(x)^2)^(1/2), x)","F"
23,0,-1,65,0.000000,"\text{Not used}","int((a + b*cot(x)^2)^(1/2),x)","\int \sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a} \,d x","Not used",1,"int((a + b*cot(x)^2)^(1/2), x)","F"
24,0,-1,51,0.000000,"\text{Not used}","int(tan(x)^2*(a + b*cot(x)^2)^(1/2),x)","\int {\mathrm{tan}\left(x\right)}^2\,\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a} \,d x","Not used",1,"int(tan(x)^2*(a + b*cot(x)^2)^(1/2), x)","F"
25,0,-1,85,0.000000,"\text{Not used}","int(tan(x)^4*(a + b*cot(x)^2)^(1/2),x)","\int {\mathrm{tan}\left(x\right)}^4\,\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a} \,d x","Not used",1,"int(tan(x)^4*(a + b*cot(x)^2)^(1/2), x)","F"
26,1,120,88,11.131631,"\text{Not used}","int(cot(x)^3*(a + b*cot(x)^2)^(3/2),x)","\left(\frac{a}{3\,b}-\frac{a-b}{3\,b}\right)\,{\left(b\,{\mathrm{cot}\left(x\right)}^2+a\right)}^{3/2}-\frac{{\left(b\,{\mathrm{cot}\left(x\right)}^2+a\right)}^{5/2}}{5\,b}+\left(a-b\right)\,\left(\frac{a}{b}-\frac{a-b}{b}\right)\,\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a}+\mathrm{atan}\left(\frac{{\left(a-b\right)}^{3/2}\,\sqrt{b\,{\mathrm{cot}\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,"atan(((a - b)^(3/2)*(a + b*cot(x)^2)^(1/2)*1i)/(a^2 - 2*a*b + b^2))*(a - b)^(3/2)*1i - (a + b*cot(x)^2)^(5/2)/(5*b) + (a/(3*b) - (a - b)/(3*b))*(a + b*cot(x)^2)^(3/2) + (a - b)*(a/b - (a - b)/b)*(a + b*cot(x)^2)^(1/2)","B"
27,0,-1,127,0.000000,"\text{Not used}","int(cot(x)^2*(a + b*cot(x)^2)^(3/2),x)","\int {\mathrm{cot}\left(x\right)}^2\,{\left(b\,{\mathrm{cot}\left(x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(cot(x)^2*(a + b*cot(x)^2)^(3/2), x)","F"
28,1,70,69,3.535287,"\text{Not used}","int(cot(x)*(a + b*cot(x)^2)^(3/2),x)","\mathrm{atanh}\left(\frac{{\left(a-b\right)}^{3/2}\,\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a}}{a^2-2\,a\,b+b^2}\right)\,{\left(a-b\right)}^{3/2}-\frac{{\left(b\,{\mathrm{cot}\left(x\right)}^2+a\right)}^{3/2}}{3}-\left(a-b\right)\,\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a}","Not used",1,"atanh(((a - b)^(3/2)*(a + b*cot(x)^2)^(1/2))/(a^2 - 2*a*b + b^2))*(a - b)^(3/2) - (a + b*cot(x)^2)^(3/2)/3 - (a - b)*(a + b*cot(x)^2)^(1/2)","B"
29,1,506,75,0.540438,"\text{Not used}","int(tan(x)*(a + b*cot(x)^2)^(3/2),x)","\mathrm{atanh}\left(\frac{2\,b^6\,\sqrt{a^3}\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{-6\,a^5\,b^3+12\,a^4\,b^4-8\,a^3\,b^5+2\,a^2\,b^6}-\frac{8\,a\,b^5\,\sqrt{a^3}\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{-6\,a^5\,b^3+12\,a^4\,b^4-8\,a^3\,b^5+2\,a^2\,b^6}+\frac{12\,a^2\,b^4\,\sqrt{a^3}\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{-6\,a^5\,b^3+12\,a^4\,b^4-8\,a^3\,b^5+2\,a^2\,b^6}-\frac{6\,a^3\,b^3\,\sqrt{a^3}\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{-6\,a^5\,b^3+12\,a^4\,b^4-8\,a^3\,b^5+2\,a^2\,b^6}\right)\,\sqrt{a^3}-\mathrm{atanh}\left(\frac{2\,a\,b^5\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\sqrt{a^3-3\,a^2\,b+3\,a\,b^2-b^3}}{6\,a^5\,b^3-18\,a^4\,b^4+20\,a^3\,b^5-10\,a^2\,b^6+2\,a\,b^7}-\frac{6\,a^2\,b^4\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\sqrt{a^3-3\,a^2\,b+3\,a\,b^2-b^3}}{6\,a^5\,b^3-18\,a^4\,b^4+20\,a^3\,b^5-10\,a^2\,b^6+2\,a\,b^7}+\frac{6\,a^3\,b^3\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\sqrt{a^3-3\,a^2\,b+3\,a\,b^2-b^3}}{6\,a^5\,b^3-18\,a^4\,b^4+20\,a^3\,b^5-10\,a^2\,b^6+2\,a\,b^7}\right)\,\sqrt{{\left(a-b\right)}^3}-b\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}","Not used",1,"atanh((2*b^6*(a^3)^(1/2)*(a + b/tan(x)^2)^(1/2))/(2*a^2*b^6 - 8*a^3*b^5 + 12*a^4*b^4 - 6*a^5*b^3) - (8*a*b^5*(a^3)^(1/2)*(a + b/tan(x)^2)^(1/2))/(2*a^2*b^6 - 8*a^3*b^5 + 12*a^4*b^4 - 6*a^5*b^3) + (12*a^2*b^4*(a^3)^(1/2)*(a + b/tan(x)^2)^(1/2))/(2*a^2*b^6 - 8*a^3*b^5 + 12*a^4*b^4 - 6*a^5*b^3) - (6*a^3*b^3*(a^3)^(1/2)*(a + b/tan(x)^2)^(1/2))/(2*a^2*b^6 - 8*a^3*b^5 + 12*a^4*b^4 - 6*a^5*b^3))*(a^3)^(1/2) - atanh((2*a*b^5*(a + b/tan(x)^2)^(1/2)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)^(1/2))/(2*a*b^7 - 10*a^2*b^6 + 20*a^3*b^5 - 18*a^4*b^4 + 6*a^5*b^3) - (6*a^2*b^4*(a + b/tan(x)^2)^(1/2)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)^(1/2))/(2*a*b^7 - 10*a^2*b^6 + 20*a^3*b^5 - 18*a^4*b^4 + 6*a^5*b^3) + (6*a^3*b^3*(a + b/tan(x)^2)^(1/2)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)^(1/2))/(2*a*b^7 - 10*a^2*b^6 + 20*a^3*b^5 - 18*a^4*b^4 + 6*a^5*b^3))*((a - b)^3)^(1/2) - b*(a + b/tan(x)^2)^(1/2)","B"
30,0,-1,80,0.000000,"\text{Not used}","int(tan(x)^2*(a + b*cot(x)^2)^(3/2),x)","\int {\mathrm{tan}\left(x\right)}^2\,{\left(b\,{\mathrm{cot}\left(x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int(tan(x)^2*(a + b*cot(x)^2)^(3/2), x)","F"
31,0,-1,171,0.000000,"\text{Not used}","int((a + b*cot(c + d*x)^2)^(5/2),x)","\int {\left(b\,{\mathrm{cot}\left(c+d\,x\right)}^2+a\right)}^{5/2} \,d x","Not used",1,"int((a + b*cot(c + d*x)^2)^(5/2), x)","F"
32,0,-1,126,0.000000,"\text{Not used}","int((a + b*cot(c + d*x)^2)^(3/2),x)","\int {\left(b\,{\mathrm{cot}\left(c+d\,x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int((a + b*cot(c + d*x)^2)^(3/2), x)","F"
33,0,-1,87,0.000000,"\text{Not used}","int((a + b*cot(c + d*x)^2)^(1/2),x)","\int \sqrt{b\,{\mathrm{cot}\left(c+d\,x\right)}^2+a} \,d x","Not used",1,"int((a + b*cot(c + d*x)^2)^(1/2), x)","F"
34,1,41,47,0.853841,"\text{Not used}","int(1/(a + b*cot(c + d*x)^2)^(1/2),x)","-\frac{\mathrm{atan}\left(\frac{\mathrm{cot}\left(c+d\,x\right)\,\sqrt{a-b}}{\sqrt{b\,{\mathrm{cot}\left(c+d\,x\right)}^2+a}}\right)}{d\,\sqrt{a-b}}","Not used",1,"-atan((cot(c + d*x)*(a - b)^(1/2))/(a + b*cot(c + d*x)^2)^(1/2))/(d*(a - b)^(1/2))","B"
35,0,-1,85,0.000000,"\text{Not used}","int(1/(a + b*cot(c + d*x)^2)^(3/2),x)","\int \frac{1}{{\left(b\,{\mathrm{cot}\left(c+d\,x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(1/(a + b*cot(c + d*x)^2)^(3/2), x)","F"
36,0,-1,135,0.000000,"\text{Not used}","int(1/(a + b*cot(c + d*x)^2)^(5/2),x)","\int \frac{1}{{\left(b\,{\mathrm{cot}\left(c+d\,x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(1/(a + b*cot(c + d*x)^2)^(5/2), x)","F"
37,0,-1,190,0.000000,"\text{Not used}","int(1/(a + b*cot(c + d*x)^2)^(7/2),x)","\int \frac{1}{{\left(b\,{\mathrm{cot}\left(c+d\,x\right)}^2+a\right)}^{7/2}} \,d x","Not used",1,"int(1/(a + b*cot(c + d*x)^2)^(7/2), x)","F"
38,1,104,54,0.836755,"\text{Not used}","int((1 - cot(x)^2)^(3/2),x)","\frac{5\,\mathrm{asin}\left(\mathrm{cot}\left(x\right)\right)}{2}+\frac{\mathrm{cot}\left(x\right)\,\sqrt{1-{\mathrm{cot}\left(x\right)}^2}}{2}-\sqrt{2}\,\ln\left(\frac{\frac{\sqrt{2}\,\left(-1+\mathrm{cot}\left(x\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}-\sqrt{1-{\mathrm{cot}\left(x\right)}^2}\,1{}\mathrm{i}}{\mathrm{cot}\left(x\right)-\mathrm{i}}\right)\,1{}\mathrm{i}+\sqrt{2}\,\ln\left(\frac{\frac{\sqrt{2}\,\left(1+\mathrm{cot}\left(x\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}+\sqrt{1-{\mathrm{cot}\left(x\right)}^2}\,1{}\mathrm{i}}{\mathrm{cot}\left(x\right)+1{}\mathrm{i}}\right)\,1{}\mathrm{i}","Not used",1,"(5*asin(cot(x)))/2 + (cot(x)*(1 - cot(x)^2)^(1/2))/2 - 2^(1/2)*log(((2^(1/2)*(cot(x)*1i - 1)*1i)/2 - (1 - cot(x)^2)^(1/2)*1i)/(cot(x) - 1i))*1i + 2^(1/2)*log(((2^(1/2)*(cot(x)*1i + 1)*1i)/2 + (1 - cot(x)^2)^(1/2)*1i)/(cot(x) + 1i))*1i","B"
39,1,88,32,0.962627,"\text{Not used}","int((1 - cot(x)^2)^(1/2),x)","\mathrm{asin}\left(\mathrm{cot}\left(x\right)\right)-\frac{\sqrt{2}\,\ln\left(\frac{\frac{\sqrt{2}\,\left(-1+\mathrm{cot}\left(x\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}-\sqrt{1-{\mathrm{cot}\left(x\right)}^2}\,1{}\mathrm{i}}{\mathrm{cot}\left(x\right)-\mathrm{i}}\right)\,1{}\mathrm{i}}{2}+\frac{\sqrt{2}\,\ln\left(\frac{\frac{\sqrt{2}\,\left(1+\mathrm{cot}\left(x\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}+\sqrt{1-{\mathrm{cot}\left(x\right)}^2}\,1{}\mathrm{i}}{\mathrm{cot}\left(x\right)+1{}\mathrm{i}}\right)\,1{}\mathrm{i}}{2}","Not used",1,"asin(cot(x)) - (2^(1/2)*log(((2^(1/2)*(cot(x)*1i - 1)*1i)/2 - (1 - cot(x)^2)^(1/2)*1i)/(cot(x) - 1i))*1i)/2 + (2^(1/2)*log(((2^(1/2)*(cot(x)*1i + 1)*1i)/2 + (1 - cot(x)^2)^(1/2)*1i)/(cot(x) + 1i))*1i)/2","B"
40,1,85,28,0.626239,"\text{Not used}","int(1/(1 - cot(x)^2)^(1/2),x)","-\frac{\sqrt{2}\,\ln\left(\frac{\frac{\sqrt{2}\,\left(-1+\mathrm{cot}\left(x\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}-\sqrt{1-{\mathrm{cot}\left(x\right)}^2}\,1{}\mathrm{i}}{\mathrm{cot}\left(x\right)-\mathrm{i}}\right)\,1{}\mathrm{i}}{4}+\frac{\sqrt{2}\,\ln\left(\frac{\frac{\sqrt{2}\,\left(1+\mathrm{cot}\left(x\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}+\sqrt{1-{\mathrm{cot}\left(x\right)}^2}\,1{}\mathrm{i}}{\mathrm{cot}\left(x\right)+1{}\mathrm{i}}\right)\,1{}\mathrm{i}}{4}","Not used",1,"(2^(1/2)*log(((2^(1/2)*(cot(x)*1i + 1)*1i)/2 + (1 - cot(x)^2)^(1/2)*1i)/(cot(x) + 1i))*1i)/4 - (2^(1/2)*log(((2^(1/2)*(cot(x)*1i - 1)*1i)/2 - (1 - cot(x)^2)^(1/2)*1i)/(cot(x) - 1i))*1i)/4","B"
41,0,-1,61,0.000000,"\text{Not used}","int((cot(x)^2 - 1)^(3/2),x)","\int {\left({\mathrm{cot}\left(x\right)}^2-1\right)}^{3/2} \,d x","Not used",1,"int((cot(x)^2 - 1)^(3/2), x)","F"
42,1,34,42,0.432084,"\text{Not used}","int((cot(x)^2 - 1)^(1/2),x)","\sqrt{2}\,\mathrm{atanh}\left(\frac{\sqrt{2}\,\mathrm{cot}\left(x\right)}{\sqrt{{\mathrm{cot}\left(x\right)}^2-1}}\right)-\ln\left(\mathrm{cot}\left(x\right)+\sqrt{{\mathrm{cot}\left(x\right)}^2-1}\right)","Not used",1,"2^(1/2)*atanh((2^(1/2)*cot(x))/(cot(x)^2 - 1)^(1/2)) - log(cot(x) + (cot(x)^2 - 1)^(1/2))","B"
43,1,20,26,0.501557,"\text{Not used}","int(1/(cot(x)^2 - 1)^(1/2),x)","-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{\sqrt{2}\,\mathrm{cot}\left(x\right)}{\sqrt{{\mathrm{cot}\left(x\right)}^2-1}}\right)}{2}","Not used",1,"-(2^(1/2)*atanh((2^(1/2)*cot(x))/(cot(x)^2 - 1)^(1/2)))/2","B"
44,1,44,52,1.207100,"\text{Not used}","int(cot(x)^3/(a + b*cot(x)^2)^(1/2),x)","-\frac{\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a}}{b}-\frac{\mathrm{atanh}\left(\frac{\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}","Not used",1,"- (a + b*cot(x)^2)^(1/2)/b - atanh((a + b*cot(x)^2)^(1/2)/(a - b)^(1/2))/(a - b)^(1/2)","B"
45,0,-1,64,0.000000,"\text{Not used}","int(cot(x)^2/(a + b*cot(x)^2)^(1/2),x)","\int \frac{{\mathrm{cot}\left(x\right)}^2}{\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a}} \,d x","Not used",1,"int(cot(x)^2/(a + b*cot(x)^2)^(1/2), x)","F"
46,1,27,33,0.962794,"\text{Not used}","int(cot(x)/(a + b*cot(x)^2)^(1/2),x)","\frac{\mathrm{atanh}\left(\frac{\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}","Not used",1,"atanh((a + b*cot(x)^2)^(1/2)/(a - b)^(1/2))/(a - b)^(1/2)","B"
47,1,93,60,0.513335,"\text{Not used}","int(tan(x)/(a + b*cot(x)^2)^(1/2),x)","\frac{\mathrm{atanh}\left(\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a-b}}+\frac{2\,\sqrt{a-b}\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{b}-\frac{2\,a\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{b\,\sqrt{a-b}}\right)}{\sqrt{a-b}}+\frac{\mathrm{atanh}\left(\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a}}\right)}{\sqrt{a}}","Not used",1,"atanh((a + b/tan(x)^2)^(1/2)/(a - b)^(1/2) + (2*(a - b)^(1/2)*(a + b/tan(x)^2)^(1/2))/b - (2*a*(a + b/tan(x)^2)^(1/2))/(b*(a - b)^(1/2)))/(a - b)^(1/2) + atanh((a + b/tan(x)^2)^(1/2)/a^(1/2))/a^(1/2)","B"
48,0,-1,54,0.000000,"\text{Not used}","int(tan(x)^2/(a + b*cot(x)^2)^(1/2),x)","\int \frac{{\mathrm{tan}\left(x\right)}^2}{\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a}} \,d x","Not used",1,"int(tan(x)^2/(a + b*cot(x)^2)^(1/2), x)","F"
49,1,52,59,1.916679,"\text{Not used}","int(cot(x)^3/(a + b*cot(x)^2)^(3/2),x)","\frac{a}{\left(a\,b-b^2\right)\,\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a}}-\frac{\mathrm{atanh}\left(\frac{\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a}}{\sqrt{a-b}}\right)}{{\left(a-b\right)}^{3/2}}","Not used",1,"a/((a*b - b^2)*(a + b*cot(x)^2)^(1/2)) - atanh((a + b*cot(x)^2)^(1/2)/(a - b)^(1/2))/(a - b)^(3/2)","B"
50,0,-1,59,0.000000,"\text{Not used}","int(cot(x)^2/(a + b*cot(x)^2)^(3/2),x)","\int \frac{{\mathrm{cot}\left(x\right)}^2}{{\left(b\,{\mathrm{cot}\left(x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(cot(x)^2/(a + b*cot(x)^2)^(3/2), x)","F"
51,1,47,55,1.778540,"\text{Not used}","int(cot(x)/(a + b*cot(x)^2)^(3/2),x)","\frac{\mathrm{atanh}\left(\frac{\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a}}{\sqrt{a-b}}\right)}{{\left(a-b\right)}^{3/2}}-\frac{1}{\left(a-b\right)\,\sqrt{b\,{\mathrm{cot}\left(x\right)}^2+a}}","Not used",1,"atanh((a + b*cot(x)^2)^(1/2)/(a - b)^(1/2))/(a - b)^(3/2) - 1/((a - b)*(a + b*cot(x)^2)^(1/2))","B"
52,1,1451,84,0.482040,"\text{Not used}","int(tan(x)/(a + b*cot(x)^2)^(3/2),x)","\frac{\mathrm{atanh}\left(\frac{2\,a^2\,b^8\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^3}\,\left(-6\,a^6\,b^3+24\,a^5\,b^4-38\,a^4\,b^5+30\,a^3\,b^6-12\,a^2\,b^7+2\,a\,b^8\right)}-\frac{12\,a^3\,b^7\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^3}\,\left(-6\,a^6\,b^3+24\,a^5\,b^4-38\,a^4\,b^5+30\,a^3\,b^6-12\,a^2\,b^7+2\,a\,b^8\right)}+\frac{30\,a^4\,b^6\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^3}\,\left(-6\,a^6\,b^3+24\,a^5\,b^4-38\,a^4\,b^5+30\,a^3\,b^6-12\,a^2\,b^7+2\,a\,b^8\right)}-\frac{38\,a^5\,b^5\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^3}\,\left(-6\,a^6\,b^3+24\,a^5\,b^4-38\,a^4\,b^5+30\,a^3\,b^6-12\,a^2\,b^7+2\,a\,b^8\right)}+\frac{24\,a^6\,b^4\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^3}\,\left(-6\,a^6\,b^3+24\,a^5\,b^4-38\,a^4\,b^5+30\,a^3\,b^6-12\,a^2\,b^7+2\,a\,b^8\right)}-\frac{6\,a^7\,b^3\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^3}\,\left(-6\,a^6\,b^3+24\,a^5\,b^4-38\,a^4\,b^5+30\,a^3\,b^6-12\,a^2\,b^7+2\,a\,b^8\right)}\right)}{\sqrt{a^3}}-\frac{b}{\left(a\,b-a^2\right)\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{{\left(a-b\right)}^3}\,\left(\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\left(-4\,a^8\,b^2+16\,a^7\,b^3-26\,a^6\,b^4+22\,a^5\,b^5-10\,a^4\,b^6+2\,a^3\,b^7\right)}{2}+\frac{\sqrt{{\left(a-b\right)}^3}\,\left(12\,a^5\,b^7-2\,a^4\,b^8-28\,a^6\,b^6+32\,a^7\,b^5-18\,a^8\,b^4+4\,a^9\,b^3+\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\sqrt{{\left(a-b\right)}^3}\,\left(16\,a^{11}\,b^2-88\,a^{10}\,b^3+200\,a^9\,b^4-240\,a^8\,b^5+160\,a^7\,b^6-56\,a^6\,b^7+8\,a^5\,b^8\right)}{4\,{\left(a-b\right)}^3}\right)}{2\,{\left(a-b\right)}^3}\right)\,1{}\mathrm{i}}{{\left(a-b\right)}^3}+\frac{\sqrt{{\left(a-b\right)}^3}\,\left(\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\left(-4\,a^8\,b^2+16\,a^7\,b^3-26\,a^6\,b^4+22\,a^5\,b^5-10\,a^4\,b^6+2\,a^3\,b^7\right)}{2}+\frac{\sqrt{{\left(a-b\right)}^3}\,\left(2\,a^4\,b^8-12\,a^5\,b^7+28\,a^6\,b^6-32\,a^7\,b^5+18\,a^8\,b^4-4\,a^9\,b^3+\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\sqrt{{\left(a-b\right)}^3}\,\left(16\,a^{11}\,b^2-88\,a^{10}\,b^3+200\,a^9\,b^4-240\,a^8\,b^5+160\,a^7\,b^6-56\,a^6\,b^7+8\,a^5\,b^8\right)}{4\,{\left(a-b\right)}^3}\right)}{2\,{\left(a-b\right)}^3}\right)\,1{}\mathrm{i}}{{\left(a-b\right)}^3}}{2\,a^3\,b^6-6\,a^4\,b^5+6\,a^5\,b^4-2\,a^6\,b^3-\frac{\sqrt{{\left(a-b\right)}^3}\,\left(\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\left(-4\,a^8\,b^2+16\,a^7\,b^3-26\,a^6\,b^4+22\,a^5\,b^5-10\,a^4\,b^6+2\,a^3\,b^7\right)}{2}+\frac{\sqrt{{\left(a-b\right)}^3}\,\left(12\,a^5\,b^7-2\,a^4\,b^8-28\,a^6\,b^6+32\,a^7\,b^5-18\,a^8\,b^4+4\,a^9\,b^3+\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\sqrt{{\left(a-b\right)}^3}\,\left(16\,a^{11}\,b^2-88\,a^{10}\,b^3+200\,a^9\,b^4-240\,a^8\,b^5+160\,a^7\,b^6-56\,a^6\,b^7+8\,a^5\,b^8\right)}{4\,{\left(a-b\right)}^3}\right)}{2\,{\left(a-b\right)}^3}\right)}{{\left(a-b\right)}^3}+\frac{\sqrt{{\left(a-b\right)}^3}\,\left(\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\left(-4\,a^8\,b^2+16\,a^7\,b^3-26\,a^6\,b^4+22\,a^5\,b^5-10\,a^4\,b^6+2\,a^3\,b^7\right)}{2}+\frac{\sqrt{{\left(a-b\right)}^3}\,\left(2\,a^4\,b^8-12\,a^5\,b^7+28\,a^6\,b^6-32\,a^7\,b^5+18\,a^8\,b^4-4\,a^9\,b^3+\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\sqrt{{\left(a-b\right)}^3}\,\left(16\,a^{11}\,b^2-88\,a^{10}\,b^3+200\,a^9\,b^4-240\,a^8\,b^5+160\,a^7\,b^6-56\,a^6\,b^7+8\,a^5\,b^8\right)}{4\,{\left(a-b\right)}^3}\right)}{2\,{\left(a-b\right)}^3}\right)}{{\left(a-b\right)}^3}}\right)\,\sqrt{{\left(a-b\right)}^3}\,1{}\mathrm{i}}{{\left(a-b\right)}^3}","Not used",1,"atanh((2*a^2*b^8*(a + b/tan(x)^2)^(1/2))/((a^3)^(1/2)*(2*a*b^8 - 12*a^2*b^7 + 30*a^3*b^6 - 38*a^4*b^5 + 24*a^5*b^4 - 6*a^6*b^3)) - (12*a^3*b^7*(a + b/tan(x)^2)^(1/2))/((a^3)^(1/2)*(2*a*b^8 - 12*a^2*b^7 + 30*a^3*b^6 - 38*a^4*b^5 + 24*a^5*b^4 - 6*a^6*b^3)) + (30*a^4*b^6*(a + b/tan(x)^2)^(1/2))/((a^3)^(1/2)*(2*a*b^8 - 12*a^2*b^7 + 30*a^3*b^6 - 38*a^4*b^5 + 24*a^5*b^4 - 6*a^6*b^3)) - (38*a^5*b^5*(a + b/tan(x)^2)^(1/2))/((a^3)^(1/2)*(2*a*b^8 - 12*a^2*b^7 + 30*a^3*b^6 - 38*a^4*b^5 + 24*a^5*b^4 - 6*a^6*b^3)) + (24*a^6*b^4*(a + b/tan(x)^2)^(1/2))/((a^3)^(1/2)*(2*a*b^8 - 12*a^2*b^7 + 30*a^3*b^6 - 38*a^4*b^5 + 24*a^5*b^4 - 6*a^6*b^3)) - (6*a^7*b^3*(a + b/tan(x)^2)^(1/2))/((a^3)^(1/2)*(2*a*b^8 - 12*a^2*b^7 + 30*a^3*b^6 - 38*a^4*b^5 + 24*a^5*b^4 - 6*a^6*b^3)))/(a^3)^(1/2) - (atan(((((a - b)^3)^(1/2)*(((a + b/tan(x)^2)^(1/2)*(2*a^3*b^7 - 10*a^4*b^6 + 22*a^5*b^5 - 26*a^6*b^4 + 16*a^7*b^3 - 4*a^8*b^2))/2 + (((a - b)^3)^(1/2)*(12*a^5*b^7 - 2*a^4*b^8 - 28*a^6*b^6 + 32*a^7*b^5 - 18*a^8*b^4 + 4*a^9*b^3 + ((a + b/tan(x)^2)^(1/2)*((a - b)^3)^(1/2)*(8*a^5*b^8 - 56*a^6*b^7 + 160*a^7*b^6 - 240*a^8*b^5 + 200*a^9*b^4 - 88*a^10*b^3 + 16*a^11*b^2))/(4*(a - b)^3)))/(2*(a - b)^3))*1i)/(a - b)^3 + (((a - b)^3)^(1/2)*(((a + b/tan(x)^2)^(1/2)*(2*a^3*b^7 - 10*a^4*b^6 + 22*a^5*b^5 - 26*a^6*b^4 + 16*a^7*b^3 - 4*a^8*b^2))/2 + (((a - b)^3)^(1/2)*(2*a^4*b^8 - 12*a^5*b^7 + 28*a^6*b^6 - 32*a^7*b^5 + 18*a^8*b^4 - 4*a^9*b^3 + ((a + b/tan(x)^2)^(1/2)*((a - b)^3)^(1/2)*(8*a^5*b^8 - 56*a^6*b^7 + 160*a^7*b^6 - 240*a^8*b^5 + 200*a^9*b^4 - 88*a^10*b^3 + 16*a^11*b^2))/(4*(a - b)^3)))/(2*(a - b)^3))*1i)/(a - b)^3)/(2*a^3*b^6 - 6*a^4*b^5 + 6*a^5*b^4 - 2*a^6*b^3 - (((a - b)^3)^(1/2)*(((a + b/tan(x)^2)^(1/2)*(2*a^3*b^7 - 10*a^4*b^6 + 22*a^5*b^5 - 26*a^6*b^4 + 16*a^7*b^3 - 4*a^8*b^2))/2 + (((a - b)^3)^(1/2)*(12*a^5*b^7 - 2*a^4*b^8 - 28*a^6*b^6 + 32*a^7*b^5 - 18*a^8*b^4 + 4*a^9*b^3 + ((a + b/tan(x)^2)^(1/2)*((a - b)^3)^(1/2)*(8*a^5*b^8 - 56*a^6*b^7 + 160*a^7*b^6 - 240*a^8*b^5 + 200*a^9*b^4 - 88*a^10*b^3 + 16*a^11*b^2))/(4*(a - b)^3)))/(2*(a - b)^3)))/(a - b)^3 + (((a - b)^3)^(1/2)*(((a + b/tan(x)^2)^(1/2)*(2*a^3*b^7 - 10*a^4*b^6 + 22*a^5*b^5 - 26*a^6*b^4 + 16*a^7*b^3 - 4*a^8*b^2))/2 + (((a - b)^3)^(1/2)*(2*a^4*b^8 - 12*a^5*b^7 + 28*a^6*b^6 - 32*a^7*b^5 + 18*a^8*b^4 - 4*a^9*b^3 + ((a + b/tan(x)^2)^(1/2)*((a - b)^3)^(1/2)*(8*a^5*b^8 - 56*a^6*b^7 + 160*a^7*b^6 - 240*a^8*b^5 + 200*a^9*b^4 - 88*a^10*b^3 + 16*a^11*b^2))/(4*(a - b)^3)))/(2*(a - b)^3)))/(a - b)^3))*((a - b)^3)^(1/2)*1i)/(a - b)^3 - b/((a*b - a^2)*(a + b/tan(x)^2)^(1/2))","B"
53,0,-1,92,0.000000,"\text{Not used}","int(tan(x)^2/(a + b*cot(x)^2)^(3/2),x)","\int \frac{{\mathrm{tan}\left(x\right)}^2}{{\left(b\,{\mathrm{cot}\left(x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(tan(x)^2/(a + b*cot(x)^2)^(3/2), x)","F"
54,1,88,82,4.236459,"\text{Not used}","int(cot(x)^3/(a + b*cot(x)^2)^(5/2),x)","\frac{\frac{a}{3\,\left(a-b\right)}+\frac{b\,\left(b\,{\mathrm{cot}\left(x\right)}^2+a\right)}{{\left(a-b\right)}^2}}{b\,{\left(b\,{\mathrm{cot}\left(x\right)}^2+a\right)}^{3/2}}-\frac{\mathrm{atanh}\left(\frac{\sqrt{b\,{\mathrm{cot}\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}}","Not used",1,"(a/(3*(a - b)) + (b*(a + b*cot(x)^2))/(a - b)^2)/(b*(a + b*cot(x)^2)^(3/2)) - atanh(((a + b*cot(x)^2)^(1/2)*(2*a^2 - 4*a*b + 2*b^2))/(2*(a - b)^(5/2)))/(a - b)^(5/2)","B"
55,0,-1,94,0.000000,"\text{Not used}","int(cot(x)^2/(a + b*cot(x)^2)^(5/2),x)","\int \frac{{\mathrm{cot}\left(x\right)}^2}{{\left(b\,{\mathrm{cot}\left(x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(cot(x)^2/(a + b*cot(x)^2)^(5/2), x)","F"
56,1,82,78,4.462276,"\text{Not used}","int(cot(x)/(a + b*cot(x)^2)^(5/2),x)","\frac{\mathrm{atanh}\left(\frac{\sqrt{b\,{\mathrm{cot}\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{cot}\left(x\right)}^2+a}{{\left(a-b\right)}^2}}{{\left(b\,{\mathrm{cot}\left(x\right)}^2+a\right)}^{3/2}}","Not used",1,"atanh(((a + b*cot(x)^2)^(1/2)*(2*a^2 - 4*a*b + 2*b^2))/(2*(a - b)^(5/2)))/(a - b)^(5/2) - (1/(3*(a - b)) + (a + b*cot(x)^2)/(a - b)^2)/(a + b*cot(x)^2)^(3/2)","B"
57,1,2817,118,1.051038,"\text{Not used}","int(tan(x)/(a + b*cot(x)^2)^(5/2),x)","\frac{\mathrm{atanh}\left(\frac{2\,a^5\,b^{13}\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^5}\,\left(10\,a^{13}\,b^3-80\,a^{12}\,b^4+290\,a^{11}\,b^5-630\,a^{10}\,b^6+912\,a^9\,b^7-922\,a^8\,b^8+660\,a^7\,b^9-330\,a^6\,b^{10}+110\,a^5\,b^{11}-22\,a^4\,b^{12}+2\,a^3\,b^{13}\right)}-\frac{22\,a^6\,b^{12}\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^5}\,\left(10\,a^{13}\,b^3-80\,a^{12}\,b^4+290\,a^{11}\,b^5-630\,a^{10}\,b^6+912\,a^9\,b^7-922\,a^8\,b^8+660\,a^7\,b^9-330\,a^6\,b^{10}+110\,a^5\,b^{11}-22\,a^4\,b^{12}+2\,a^3\,b^{13}\right)}+\frac{110\,a^7\,b^{11}\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^5}\,\left(10\,a^{13}\,b^3-80\,a^{12}\,b^4+290\,a^{11}\,b^5-630\,a^{10}\,b^6+912\,a^9\,b^7-922\,a^8\,b^8+660\,a^7\,b^9-330\,a^6\,b^{10}+110\,a^5\,b^{11}-22\,a^4\,b^{12}+2\,a^3\,b^{13}\right)}-\frac{330\,a^8\,b^{10}\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^5}\,\left(10\,a^{13}\,b^3-80\,a^{12}\,b^4+290\,a^{11}\,b^5-630\,a^{10}\,b^6+912\,a^9\,b^7-922\,a^8\,b^8+660\,a^7\,b^9-330\,a^6\,b^{10}+110\,a^5\,b^{11}-22\,a^4\,b^{12}+2\,a^3\,b^{13}\right)}+\frac{660\,a^9\,b^9\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^5}\,\left(10\,a^{13}\,b^3-80\,a^{12}\,b^4+290\,a^{11}\,b^5-630\,a^{10}\,b^6+912\,a^9\,b^7-922\,a^8\,b^8+660\,a^7\,b^9-330\,a^6\,b^{10}+110\,a^5\,b^{11}-22\,a^4\,b^{12}+2\,a^3\,b^{13}\right)}-\frac{922\,a^{10}\,b^8\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^5}\,\left(10\,a^{13}\,b^3-80\,a^{12}\,b^4+290\,a^{11}\,b^5-630\,a^{10}\,b^6+912\,a^9\,b^7-922\,a^8\,b^8+660\,a^7\,b^9-330\,a^6\,b^{10}+110\,a^5\,b^{11}-22\,a^4\,b^{12}+2\,a^3\,b^{13}\right)}+\frac{912\,a^{11}\,b^7\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^5}\,\left(10\,a^{13}\,b^3-80\,a^{12}\,b^4+290\,a^{11}\,b^5-630\,a^{10}\,b^6+912\,a^9\,b^7-922\,a^8\,b^8+660\,a^7\,b^9-330\,a^6\,b^{10}+110\,a^5\,b^{11}-22\,a^4\,b^{12}+2\,a^3\,b^{13}\right)}-\frac{630\,a^{12}\,b^6\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^5}\,\left(10\,a^{13}\,b^3-80\,a^{12}\,b^4+290\,a^{11}\,b^5-630\,a^{10}\,b^6+912\,a^9\,b^7-922\,a^8\,b^8+660\,a^7\,b^9-330\,a^6\,b^{10}+110\,a^5\,b^{11}-22\,a^4\,b^{12}+2\,a^3\,b^{13}\right)}+\frac{290\,a^{13}\,b^5\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^5}\,\left(10\,a^{13}\,b^3-80\,a^{12}\,b^4+290\,a^{11}\,b^5-630\,a^{10}\,b^6+912\,a^9\,b^7-922\,a^8\,b^8+660\,a^7\,b^9-330\,a^6\,b^{10}+110\,a^5\,b^{11}-22\,a^4\,b^{12}+2\,a^3\,b^{13}\right)}-\frac{80\,a^{14}\,b^4\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^5}\,\left(10\,a^{13}\,b^3-80\,a^{12}\,b^4+290\,a^{11}\,b^5-630\,a^{10}\,b^6+912\,a^9\,b^7-922\,a^8\,b^8+660\,a^7\,b^9-330\,a^6\,b^{10}+110\,a^5\,b^{11}-22\,a^4\,b^{12}+2\,a^3\,b^{13}\right)}+\frac{10\,a^{15}\,b^3\,\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}}{\sqrt{a^5}\,\left(10\,a^{13}\,b^3-80\,a^{12}\,b^4+290\,a^{11}\,b^5-630\,a^{10}\,b^6+912\,a^9\,b^7-922\,a^8\,b^8+660\,a^7\,b^9-330\,a^6\,b^{10}+110\,a^5\,b^{11}-22\,a^4\,b^{12}+2\,a^3\,b^{13}\right)}\right)}{\sqrt{a^5}}-\frac{\frac{b}{3\,\left(a\,b-a^2\right)}-\frac{b\,\left(a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}\right)\,\left(2\,a-b\right)}{{\left(a\,b-a^2\right)}^2}}{{\left(a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}\right)}^{3/2}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\left(4\,a^{16}\,b^2-32\,a^{15}\,b^3+120\,a^{14}\,b^4-280\,a^{13}\,b^5+450\,a^{12}\,b^6-516\,a^{11}\,b^7+422\,a^{10}\,b^8-240\,a^9\,b^9+90\,a^8\,b^{10}-20\,a^7\,b^{11}+2\,a^6\,b^{12}\right)}{2}-\frac{\sqrt{{\left(a-b\right)}^5}\,\left(2\,a^8\,b^{13}-22\,a^9\,b^{12}+110\,a^{10}\,b^{11}-328\,a^{11}\,b^{10}+644\,a^{12}\,b^9-868\,a^{13}\,b^8+812\,a^{14}\,b^7-520\,a^{15}\,b^6+218\,a^{16}\,b^5-54\,a^{17}\,b^4+6\,a^{18}\,b^3-\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\sqrt{{\left(a-b\right)}^5}\,\left(-16\,a^{21}\,b^2+168\,a^{20}\,b^3-800\,a^{19}\,b^4+2280\,a^{18}\,b^5-4320\,a^{17}\,b^6+5712\,a^{16}\,b^7-5376\,a^{15}\,b^8+3600\,a^{14}\,b^9-1680\,a^{13}\,b^{10}+520\,a^{12}\,b^{11}-96\,a^{11}\,b^{12}+8\,a^{10}\,b^{13}\right)}{4\,{\left(a-b\right)}^5}\right)}{2\,{\left(a-b\right)}^5}\right)\,\sqrt{{\left(a-b\right)}^5}\,1{}\mathrm{i}}{{\left(a-b\right)}^5}+\frac{\left(\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\left(4\,a^{16}\,b^2-32\,a^{15}\,b^3+120\,a^{14}\,b^4-280\,a^{13}\,b^5+450\,a^{12}\,b^6-516\,a^{11}\,b^7+422\,a^{10}\,b^8-240\,a^9\,b^9+90\,a^8\,b^{10}-20\,a^7\,b^{11}+2\,a^6\,b^{12}\right)}{2}+\frac{\sqrt{{\left(a-b\right)}^5}\,\left(2\,a^8\,b^{13}-22\,a^9\,b^{12}+110\,a^{10}\,b^{11}-328\,a^{11}\,b^{10}+644\,a^{12}\,b^9-868\,a^{13}\,b^8+812\,a^{14}\,b^7-520\,a^{15}\,b^6+218\,a^{16}\,b^5-54\,a^{17}\,b^4+6\,a^{18}\,b^3+\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\sqrt{{\left(a-b\right)}^5}\,\left(-16\,a^{21}\,b^2+168\,a^{20}\,b^3-800\,a^{19}\,b^4+2280\,a^{18}\,b^5-4320\,a^{17}\,b^6+5712\,a^{16}\,b^7-5376\,a^{15}\,b^8+3600\,a^{14}\,b^9-1680\,a^{13}\,b^{10}+520\,a^{12}\,b^{11}-96\,a^{11}\,b^{12}+8\,a^{10}\,b^{13}\right)}{4\,{\left(a-b\right)}^5}\right)}{2\,{\left(a-b\right)}^5}\right)\,\sqrt{{\left(a-b\right)}^5}\,1{}\mathrm{i}}{{\left(a-b\right)}^5}}{2\,a^6\,b^{10}-16\,a^7\,b^9+54\,a^8\,b^8-100\,a^9\,b^7+110\,a^{10}\,b^6-72\,a^{11}\,b^5+26\,a^{12}\,b^4-4\,a^{13}\,b^3+\frac{\left(\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\left(4\,a^{16}\,b^2-32\,a^{15}\,b^3+120\,a^{14}\,b^4-280\,a^{13}\,b^5+450\,a^{12}\,b^6-516\,a^{11}\,b^7+422\,a^{10}\,b^8-240\,a^9\,b^9+90\,a^8\,b^{10}-20\,a^7\,b^{11}+2\,a^6\,b^{12}\right)}{2}-\frac{\sqrt{{\left(a-b\right)}^5}\,\left(2\,a^8\,b^{13}-22\,a^9\,b^{12}+110\,a^{10}\,b^{11}-328\,a^{11}\,b^{10}+644\,a^{12}\,b^9-868\,a^{13}\,b^8+812\,a^{14}\,b^7-520\,a^{15}\,b^6+218\,a^{16}\,b^5-54\,a^{17}\,b^4+6\,a^{18}\,b^3-\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\sqrt{{\left(a-b\right)}^5}\,\left(-16\,a^{21}\,b^2+168\,a^{20}\,b^3-800\,a^{19}\,b^4+2280\,a^{18}\,b^5-4320\,a^{17}\,b^6+5712\,a^{16}\,b^7-5376\,a^{15}\,b^8+3600\,a^{14}\,b^9-1680\,a^{13}\,b^{10}+520\,a^{12}\,b^{11}-96\,a^{11}\,b^{12}+8\,a^{10}\,b^{13}\right)}{4\,{\left(a-b\right)}^5}\right)}{2\,{\left(a-b\right)}^5}\right)\,\sqrt{{\left(a-b\right)}^5}}{{\left(a-b\right)}^5}-\frac{\left(\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\left(4\,a^{16}\,b^2-32\,a^{15}\,b^3+120\,a^{14}\,b^4-280\,a^{13}\,b^5+450\,a^{12}\,b^6-516\,a^{11}\,b^7+422\,a^{10}\,b^8-240\,a^9\,b^9+90\,a^8\,b^{10}-20\,a^7\,b^{11}+2\,a^6\,b^{12}\right)}{2}+\frac{\sqrt{{\left(a-b\right)}^5}\,\left(2\,a^8\,b^{13}-22\,a^9\,b^{12}+110\,a^{10}\,b^{11}-328\,a^{11}\,b^{10}+644\,a^{12}\,b^9-868\,a^{13}\,b^8+812\,a^{14}\,b^7-520\,a^{15}\,b^6+218\,a^{16}\,b^5-54\,a^{17}\,b^4+6\,a^{18}\,b^3+\frac{\sqrt{a+\frac{b}{{\mathrm{tan}\left(x\right)}^2}}\,\sqrt{{\left(a-b\right)}^5}\,\left(-16\,a^{21}\,b^2+168\,a^{20}\,b^3-800\,a^{19}\,b^4+2280\,a^{18}\,b^5-4320\,a^{17}\,b^6+5712\,a^{16}\,b^7-5376\,a^{15}\,b^8+3600\,a^{14}\,b^9-1680\,a^{13}\,b^{10}+520\,a^{12}\,b^{11}-96\,a^{11}\,b^{12}+8\,a^{10}\,b^{13}\right)}{4\,{\left(a-b\right)}^5}\right)}{2\,{\left(a-b\right)}^5}\right)\,\sqrt{{\left(a-b\right)}^5}}{{\left(a-b\right)}^5}}\right)\,\sqrt{{\left(a-b\right)}^5}\,1{}\mathrm{i}}{{\left(a-b\right)}^5}","Not used",1,"atanh((2*a^5*b^13*(a + b/tan(x)^2)^(1/2))/((a^5)^(1/2)*(2*a^3*b^13 - 22*a^4*b^12 + 110*a^5*b^11 - 330*a^6*b^10 + 660*a^7*b^9 - 922*a^8*b^8 + 912*a^9*b^7 - 630*a^10*b^6 + 290*a^11*b^5 - 80*a^12*b^4 + 10*a^13*b^3)) - (22*a^6*b^12*(a + b/tan(x)^2)^(1/2))/((a^5)^(1/2)*(2*a^3*b^13 - 22*a^4*b^12 + 110*a^5*b^11 - 330*a^6*b^10 + 660*a^7*b^9 - 922*a^8*b^8 + 912*a^9*b^7 - 630*a^10*b^6 + 290*a^11*b^5 - 80*a^12*b^4 + 10*a^13*b^3)) + (110*a^7*b^11*(a + b/tan(x)^2)^(1/2))/((a^5)^(1/2)*(2*a^3*b^13 - 22*a^4*b^12 + 110*a^5*b^11 - 330*a^6*b^10 + 660*a^7*b^9 - 922*a^8*b^8 + 912*a^9*b^7 - 630*a^10*b^6 + 290*a^11*b^5 - 80*a^12*b^4 + 10*a^13*b^3)) - (330*a^8*b^10*(a + b/tan(x)^2)^(1/2))/((a^5)^(1/2)*(2*a^3*b^13 - 22*a^4*b^12 + 110*a^5*b^11 - 330*a^6*b^10 + 660*a^7*b^9 - 922*a^8*b^8 + 912*a^9*b^7 - 630*a^10*b^6 + 290*a^11*b^5 - 80*a^12*b^4 + 10*a^13*b^3)) + (660*a^9*b^9*(a + b/tan(x)^2)^(1/2))/((a^5)^(1/2)*(2*a^3*b^13 - 22*a^4*b^12 + 110*a^5*b^11 - 330*a^6*b^10 + 660*a^7*b^9 - 922*a^8*b^8 + 912*a^9*b^7 - 630*a^10*b^6 + 290*a^11*b^5 - 80*a^12*b^4 + 10*a^13*b^3)) - (922*a^10*b^8*(a + b/tan(x)^2)^(1/2))/((a^5)^(1/2)*(2*a^3*b^13 - 22*a^4*b^12 + 110*a^5*b^11 - 330*a^6*b^10 + 660*a^7*b^9 - 922*a^8*b^8 + 912*a^9*b^7 - 630*a^10*b^6 + 290*a^11*b^5 - 80*a^12*b^4 + 10*a^13*b^3)) + (912*a^11*b^7*(a + b/tan(x)^2)^(1/2))/((a^5)^(1/2)*(2*a^3*b^13 - 22*a^4*b^12 + 110*a^5*b^11 - 330*a^6*b^10 + 660*a^7*b^9 - 922*a^8*b^8 + 912*a^9*b^7 - 630*a^10*b^6 + 290*a^11*b^5 - 80*a^12*b^4 + 10*a^13*b^3)) - (630*a^12*b^6*(a + b/tan(x)^2)^(1/2))/((a^5)^(1/2)*(2*a^3*b^13 - 22*a^4*b^12 + 110*a^5*b^11 - 330*a^6*b^10 + 660*a^7*b^9 - 922*a^8*b^8 + 912*a^9*b^7 - 630*a^10*b^6 + 290*a^11*b^5 - 80*a^12*b^4 + 10*a^13*b^3)) + (290*a^13*b^5*(a + b/tan(x)^2)^(1/2))/((a^5)^(1/2)*(2*a^3*b^13 - 22*a^4*b^12 + 110*a^5*b^11 - 330*a^6*b^10 + 660*a^7*b^9 - 922*a^8*b^8 + 912*a^9*b^7 - 630*a^10*b^6 + 290*a^11*b^5 - 80*a^12*b^4 + 10*a^13*b^3)) - (80*a^14*b^4*(a + b/tan(x)^2)^(1/2))/((a^5)^(1/2)*(2*a^3*b^13 - 22*a^4*b^12 + 110*a^5*b^11 - 330*a^6*b^10 + 660*a^7*b^9 - 922*a^8*b^8 + 912*a^9*b^7 - 630*a^10*b^6 + 290*a^11*b^5 - 80*a^12*b^4 + 10*a^13*b^3)) + (10*a^15*b^3*(a + b/tan(x)^2)^(1/2))/((a^5)^(1/2)*(2*a^3*b^13 - 22*a^4*b^12 + 110*a^5*b^11 - 330*a^6*b^10 + 660*a^7*b^9 - 922*a^8*b^8 + 912*a^9*b^7 - 630*a^10*b^6 + 290*a^11*b^5 - 80*a^12*b^4 + 10*a^13*b^3)))/(a^5)^(1/2) - (b/(3*(a*b - a^2)) - (b*(a + b/tan(x)^2)*(2*a - b))/(a*b - a^2)^2)/(a + b/tan(x)^2)^(3/2) + (atan((((((a + b/tan(x)^2)^(1/2)*(2*a^6*b^12 - 20*a^7*b^11 + 90*a^8*b^10 - 240*a^9*b^9 + 422*a^10*b^8 - 516*a^11*b^7 + 450*a^12*b^6 - 280*a^13*b^5 + 120*a^14*b^4 - 32*a^15*b^3 + 4*a^16*b^2))/2 - (((a - b)^5)^(1/2)*(2*a^8*b^13 - 22*a^9*b^12 + 110*a^10*b^11 - 328*a^11*b^10 + 644*a^12*b^9 - 868*a^13*b^8 + 812*a^14*b^7 - 520*a^15*b^6 + 218*a^16*b^5 - 54*a^17*b^4 + 6*a^18*b^3 - ((a + b/tan(x)^2)^(1/2)*((a - b)^5)^(1/2)*(8*a^10*b^13 - 96*a^11*b^12 + 520*a^12*b^11 - 1680*a^13*b^10 + 3600*a^14*b^9 - 5376*a^15*b^8 + 5712*a^16*b^7 - 4320*a^17*b^6 + 2280*a^18*b^5 - 800*a^19*b^4 + 168*a^20*b^3 - 16*a^21*b^2))/(4*(a - b)^5)))/(2*(a - b)^5))*((a - b)^5)^(1/2)*1i)/(a - b)^5 + ((((a + b/tan(x)^2)^(1/2)*(2*a^6*b^12 - 20*a^7*b^11 + 90*a^8*b^10 - 240*a^9*b^9 + 422*a^10*b^8 - 516*a^11*b^7 + 450*a^12*b^6 - 280*a^13*b^5 + 120*a^14*b^4 - 32*a^15*b^3 + 4*a^16*b^2))/2 + (((a - b)^5)^(1/2)*(2*a^8*b^13 - 22*a^9*b^12 + 110*a^10*b^11 - 328*a^11*b^10 + 644*a^12*b^9 - 868*a^13*b^8 + 812*a^14*b^7 - 520*a^15*b^6 + 218*a^16*b^5 - 54*a^17*b^4 + 6*a^18*b^3 + ((a + b/tan(x)^2)^(1/2)*((a - b)^5)^(1/2)*(8*a^10*b^13 - 96*a^11*b^12 + 520*a^12*b^11 - 1680*a^13*b^10 + 3600*a^14*b^9 - 5376*a^15*b^8 + 5712*a^16*b^7 - 4320*a^17*b^6 + 2280*a^18*b^5 - 800*a^19*b^4 + 168*a^20*b^3 - 16*a^21*b^2))/(4*(a - b)^5)))/(2*(a - b)^5))*((a - b)^5)^(1/2)*1i)/(a - b)^5)/(2*a^6*b^10 - 16*a^7*b^9 + 54*a^8*b^8 - 100*a^9*b^7 + 110*a^10*b^6 - 72*a^11*b^5 + 26*a^12*b^4 - 4*a^13*b^3 + ((((a + b/tan(x)^2)^(1/2)*(2*a^6*b^12 - 20*a^7*b^11 + 90*a^8*b^10 - 240*a^9*b^9 + 422*a^10*b^8 - 516*a^11*b^7 + 450*a^12*b^6 - 280*a^13*b^5 + 120*a^14*b^4 - 32*a^15*b^3 + 4*a^16*b^2))/2 - (((a - b)^5)^(1/2)*(2*a^8*b^13 - 22*a^9*b^12 + 110*a^10*b^11 - 328*a^11*b^10 + 644*a^12*b^9 - 868*a^13*b^8 + 812*a^14*b^7 - 520*a^15*b^6 + 218*a^16*b^5 - 54*a^17*b^4 + 6*a^18*b^3 - ((a + b/tan(x)^2)^(1/2)*((a - b)^5)^(1/2)*(8*a^10*b^13 - 96*a^11*b^12 + 520*a^12*b^11 - 1680*a^13*b^10 + 3600*a^14*b^9 - 5376*a^15*b^8 + 5712*a^16*b^7 - 4320*a^17*b^6 + 2280*a^18*b^5 - 800*a^19*b^4 + 168*a^20*b^3 - 16*a^21*b^2))/(4*(a - b)^5)))/(2*(a - b)^5))*((a - b)^5)^(1/2))/(a - b)^5 - ((((a + b/tan(x)^2)^(1/2)*(2*a^6*b^12 - 20*a^7*b^11 + 90*a^8*b^10 - 240*a^9*b^9 + 422*a^10*b^8 - 516*a^11*b^7 + 450*a^12*b^6 - 280*a^13*b^5 + 120*a^14*b^4 - 32*a^15*b^3 + 4*a^16*b^2))/2 + (((a - b)^5)^(1/2)*(2*a^8*b^13 - 22*a^9*b^12 + 110*a^10*b^11 - 328*a^11*b^10 + 644*a^12*b^9 - 868*a^13*b^8 + 812*a^14*b^7 - 520*a^15*b^6 + 218*a^16*b^5 - 54*a^17*b^4 + 6*a^18*b^3 + ((a + b/tan(x)^2)^(1/2)*((a - b)^5)^(1/2)*(8*a^10*b^13 - 96*a^11*b^12 + 520*a^12*b^11 - 1680*a^13*b^10 + 3600*a^14*b^9 - 5376*a^15*b^8 + 5712*a^16*b^7 - 4320*a^17*b^6 + 2280*a^18*b^5 - 800*a^19*b^4 + 168*a^20*b^3 - 16*a^21*b^2))/(4*(a - b)^5)))/(2*(a - b)^5))*((a - b)^5)^(1/2))/(a - b)^5))*((a - b)^5)^(1/2)*1i)/(a - b)^5","B"
58,0,-1,141,0.000000,"\text{Not used}","int(tan(x)^2/(a + b*cot(x)^2)^(5/2),x)","\int \frac{{\mathrm{tan}\left(x\right)}^2}{{\left(b\,{\mathrm{cot}\left(x\right)}^2+a\right)}^{5/2}} \,d x","Not used",1,"int(tan(x)^2/(a + b*cot(x)^2)^(5/2), x)","F"
59,1,37,37,0.719606,"\text{Not used}","int(1/(cot(x)^3 + 1),x)","x\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)-\frac{\ln\left(12\,{\mathrm{e}}^{x\,2{}\mathrm{i}}+12{}\mathrm{i}\right)}{6}+\frac{\ln\left({\mathrm{e}}^{x\,4{}\mathrm{i}}-1-{\mathrm{e}}^{x\,2{}\mathrm{i}}\,4{}\mathrm{i}\right)}{3}","Not used",1,"x*(1/2 - 1i/2) - log(12*exp(x*2i) + 12i)/6 + log(exp(x*4i) - exp(x*2i)*4i - 1)/3","B"
60,0,-1,90,0.000000,"\text{Not used}","int(cot(x)*(a + b*cot(x)^4)^(1/2),x)","\int \mathrm{cot}\left(x\right)\,\sqrt{b\,{\mathrm{cot}\left(x\right)}^4+a} \,d x","Not used",1,"int(cot(x)*(a + b*cot(x)^4)^(1/2), x)","F"
61,0,-1,126,0.000000,"\text{Not used}","int(cot(x)*(a + b*cot(x)^4)^(3/2),x)","\int \mathrm{cot}\left(x\right)\,{\left(b\,{\mathrm{cot}\left(x\right)}^4+a\right)}^{3/2} \,d x","Not used",1,"int(cot(x)*(a + b*cot(x)^4)^(3/2), x)","F"
62,0,-1,41,0.000000,"\text{Not used}","int(cot(x)/(a + b*cot(x)^4)^(1/2),x)","\int \frac{\mathrm{cot}\left(x\right)}{\sqrt{b\,{\mathrm{cot}\left(x\right)}^4+a}} \,d x","Not used",1,"int(cot(x)/(a + b*cot(x)^4)^(1/2), x)","F"
63,0,-1,74,0.000000,"\text{Not used}","int(cot(x)/(a + b*cot(x)^4)^(3/2),x)","\int \frac{\mathrm{cot}\left(x\right)}{{\left(b\,{\mathrm{cot}\left(x\right)}^4+a\right)}^{3/2}} \,d x","Not used",1,"int(cot(x)/(a + b*cot(x)^4)^(3/2), x)","F"
64,0,-1,117,0.000000,"\text{Not used}","int(cot(x)/(a + b*cot(x)^4)^(5/2),x)","\int \frac{\mathrm{cot}\left(x\right)}{{\left(b\,{\mathrm{cot}\left(x\right)}^4+a\right)}^{5/2}} \,d x","Not used",1,"int(cot(x)/(a + b*cot(x)^4)^(5/2), x)","F"