1,1,90,87,0.086511,"\text{Not used}","int(cos(c + d*x)^7*(a + a*sin(c + d*x)),x)","\frac{-\frac{a\,{\sin\left(c+d\,x\right)}^8}{8}-\frac{a\,{\sin\left(c+d\,x\right)}^7}{7}+\frac{a\,{\sin\left(c+d\,x\right)}^6}{2}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^5}{5}-\frac{3\,a\,{\sin\left(c+d\,x\right)}^4}{4}-a\,{\sin\left(c+d\,x\right)}^3+\frac{a\,{\sin\left(c+d\,x\right)}^2}{2}+a\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a*sin(c + d*x) + (a*sin(c + d*x)^2)/2 - a*sin(c + d*x)^3 - (3*a*sin(c + d*x)^4)/4 + (3*a*sin(c + d*x)^5)/5 + (a*sin(c + d*x)^6)/2 - (a*sin(c + d*x)^7)/7 - (a*sin(c + d*x)^8)/8)/d","B"
2,1,226,87,8.230667,"\text{Not used}","int(cos(c + d*x)^6*(a + a*sin(c + d*x)),x)","\frac{5\,a\,x}{16}+\frac{-\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{8}+\left(\frac{a\,\left(735\,c+735\,d\,x-672\right)}{336}-\frac{35\,a\,\left(c+d\,x\right)}{16}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{6}-\frac{85\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+\left(\frac{a\,\left(3675\,c+3675\,d\,x-3360\right)}{336}-\frac{175\,a\,\left(c+d\,x\right)}{16}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{85\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{24}+\left(\frac{a\,\left(2205\,c+2205\,d\,x-2016\right)}{336}-\frac{105\,a\,\left(c+d\,x\right)}{16}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}+\frac{11\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{a\,\left(105\,c+105\,d\,x-96\right)}{336}-\frac{5\,a\,\left(c+d\,x\right)}{16}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^7}","Not used",1,"(5*a*x)/16 + ((a*(105*c + 105*d*x - 96))/336 + (11*a*tan(c/2 + (d*x)/2))/8 - (5*a*(c + d*x))/16 + tan(c/2 + (d*x)/2)^12*((a*(735*c + 735*d*x - 672))/336 - (35*a*(c + d*x))/16) + tan(c/2 + (d*x)/2)^4*((a*(2205*c + 2205*d*x - 2016))/336 - (105*a*(c + d*x))/16) + tan(c/2 + (d*x)/2)^8*((a*(3675*c + 3675*d*x - 3360))/336 - (175*a*(c + d*x))/16) + (7*a*tan(c/2 + (d*x)/2)^3)/6 + (85*a*tan(c/2 + (d*x)/2)^5)/24 - (85*a*tan(c/2 + (d*x)/2)^9)/24 - (7*a*tan(c/2 + (d*x)/2)^11)/6 - (11*a*tan(c/2 + (d*x)/2)^13)/8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
3,1,68,64,0.051179,"\text{Not used}","int(cos(c + d*x)^5*(a + a*sin(c + d*x)),x)","\frac{\frac{a\,{\sin\left(c+d\,x\right)}^6}{6}+\frac{a\,{\sin\left(c+d\,x\right)}^5}{5}-\frac{a\,{\sin\left(c+d\,x\right)}^4}{2}-\frac{2\,a\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{a\,{\sin\left(c+d\,x\right)}^2}{2}+a\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a*sin(c + d*x) + (a*sin(c + d*x)^2)/2 - (2*a*sin(c + d*x)^3)/3 - (a*sin(c + d*x)^4)/2 + (a*sin(c + d*x)^5)/5 + (a*sin(c + d*x)^6)/6)/d","B"
4,1,165,65,7.991130,"\text{Not used}","int(cos(c + d*x)^4*(a + a*sin(c + d*x)),x)","\frac{3\,a\,x}{8}+\frac{-\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}+\left(\frac{a\,\left(75\,c+75\,d\,x-80\right)}{40}-\frac{15\,a\,\left(c+d\,x\right)}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}+\left(\frac{a\,\left(150\,c+150\,d\,x-160\right)}{40}-\frac{15\,a\,\left(c+d\,x\right)}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{a\,\left(15\,c+15\,d\,x-16\right)}{40}-\frac{3\,a\,\left(c+d\,x\right)}{8}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(3*a*x)/8 + ((a*(15*c + 15*d*x - 16))/40 + (5*a*tan(c/2 + (d*x)/2))/4 - (3*a*(c + d*x))/8 + tan(c/2 + (d*x)/2)^8*((a*(75*c + 75*d*x - 80))/40 - (15*a*(c + d*x))/8) + tan(c/2 + (d*x)/2)^4*((a*(150*c + 150*d*x - 160))/40 - (15*a*(c + d*x))/4) + (a*tan(c/2 + (d*x)/2)^3)/2 - (a*tan(c/2 + (d*x)/2)^7)/2 - (5*a*tan(c/2 + (d*x)/2)^9)/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
5,1,46,45,0.057534,"\text{Not used}","int(cos(c + d*x)^3*(a + a*sin(c + d*x)),x)","\frac{-\frac{a\,{\sin\left(c+d\,x\right)}^4}{4}-\frac{a\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{a\,{\sin\left(c+d\,x\right)}^2}{2}+a\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a*sin(c + d*x) + (a*sin(c + d*x)^2)/2 - (a*sin(c + d*x)^3)/3 - (a*sin(c + d*x)^4)/4)/d","B"
6,1,103,43,6.760678,"\text{Not used}","int(cos(c + d*x)^2*(a + a*sin(c + d*x)),x)","\frac{a\,x}{2}+\frac{-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{a\,\left(9\,c+9\,d\,x-12\right)}{6}-\frac{3\,a\,\left(c+d\,x\right)}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a\,\left(3\,c+3\,d\,x-4\right)}{6}-\frac{a\,\left(c+d\,x\right)}{2}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^3}","Not used",1,"(a*x)/2 + ((a*(3*c + 3*d*x - 4))/6 + a*tan(c/2 + (d*x)/2) - (a*(c + d*x))/2 + tan(c/2 + (d*x)/2)^4*((a*(9*c + 9*d*x - 12))/6 - (3*a*(c + d*x))/2) - a*tan(c/2 + (d*x)/2)^5)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^3)","B"
7,1,20,22,0.039803,"\text{Not used}","int(cos(c + d*x)*(a + a*sin(c + d*x)),x)","\frac{a\,\sin\left(c+d\,x\right)\,\left(\sin\left(c+d\,x\right)+2\right)}{2\,d}","Not used",1,"(a*sin(c + d*x)*(sin(c + d*x) + 2))/(2*d)","B"
8,1,15,17,0.046997,"\text{Not used}","int((a + a*sin(c + d*x))/cos(c + d*x),x)","-\frac{a\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{d}","Not used",1,"-(a*log(sin(c + d*x) - 1))/d","B"
9,1,19,23,4.688162,"\text{Not used}","int((a + a*sin(c + d*x))/cos(c + d*x)^2,x)","-\frac{2\,a}{d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}","Not used",1,"-(2*a)/(d*(tan(c/2 + (d*x)/2) - 1))","B"
10,1,30,39,0.060869,"\text{Not used}","int((a + a*sin(c + d*x))/cos(c + d*x)^3,x)","\frac{a\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{2\,d}-\frac{a}{2\,d\,\left(\sin\left(c+d\,x\right)-1\right)}","Not used",1,"(a*atanh(sin(c + d*x)))/(2*d) - a/(2*d*(sin(c + d*x) - 1))","B"
11,1,63,44,4.604041,"\text{Not used}","int((a + a*sin(c + d*x))/cos(c + d*x)^4,x)","\frac{2\,a\,\left(\cos\left(c+d\,x\right)+2\,\sin\left(c+d\,x\right)+\cos\left(2\,c+2\,d\,x\right)-\frac{\sin\left(2\,c+2\,d\,x\right)}{2}\right)}{3\,d\,\left(2\,\cos\left(c+d\,x\right)-\sin\left(2\,c+2\,d\,x\right)\right)}","Not used",1,"(2*a*(cos(c + d*x) + 2*sin(c + d*x) + cos(2*c + 2*d*x) - sin(2*c + 2*d*x)/2))/(3*d*(2*cos(c + d*x) - sin(2*c + 2*d*x)))","B"
12,1,71,84,4.501228,"\text{Not used}","int((a + a*sin(c + d*x))/cos(c + d*x)^5,x)","\frac{3\,a\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{8\,d}-\frac{-\frac{3\,a\,{\sin\left(c+d\,x\right)}^2}{8}+\frac{3\,a\,\sin\left(c+d\,x\right)}{8}+\frac{a}{4}}{d\,\left(-{\sin\left(c+d\,x\right)}^3+{\sin\left(c+d\,x\right)}^2+\sin\left(c+d\,x\right)-1\right)}","Not used",1,"(3*a*atanh(sin(c + d*x)))/(8*d) - (a/4 + (3*a*sin(c + d*x))/8 - (3*a*sin(c + d*x)^2)/8)/(d*(sin(c + d*x) + sin(c + d*x)^2 - sin(c + d*x)^3 - 1))","B"
13,1,461,126,6.915870,"\text{Not used}","int(cos(c + d*x)^6*(a + a*sin(c + d*x))^2,x)","\frac{45\,a^2\,x}{128}-\frac{\frac{815\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}-\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{64}-\frac{815\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{64}-\frac{295\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{64}+\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{64}+\frac{295\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}+\frac{83\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}+\frac{a^2\,\left(315\,c+315\,d\,x\right)}{896}-\frac{a^2\,\left(315\,c+315\,d\,x-512\right)}{896}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2\,\left(315\,c+315\,d\,x\right)}{112}-\frac{a^2\,\left(2520\,c+2520\,d\,x-512\right)}{896}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{a^2\,\left(315\,c+315\,d\,x\right)}{112}-\frac{a^2\,\left(2520\,c+2520\,d\,x-3584\right)}{896}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{a^2\,\left(315\,c+315\,d\,x\right)}{32}-\frac{a^2\,\left(8820\,c+8820\,d\,x-3584\right)}{896}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^2\,\left(315\,c+315\,d\,x\right)}{32}-\frac{a^2\,\left(8820\,c+8820\,d\,x-10752\right)}{896}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^2\,\left(315\,c+315\,d\,x\right)}{16}-\frac{a^2\,\left(17640\,c+17640\,d\,x-10752\right)}{896}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{a^2\,\left(315\,c+315\,d\,x\right)}{16}-\frac{a^2\,\left(17640\,c+17640\,d\,x-17920\right)}{896}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{5\,a^2\,\left(315\,c+315\,d\,x\right)}{64}-\frac{a^2\,\left(22050\,c+22050\,d\,x-17920\right)}{896}\right)-\frac{83\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^8}","Not used",1,"(45*a^2*x)/128 - ((815*a^2*tan(c/2 + (d*x)/2)^9)/64 - (3*a^2*tan(c/2 + (d*x)/2)^5)/64 - (815*a^2*tan(c/2 + (d*x)/2)^7)/64 - (295*a^2*tan(c/2 + (d*x)/2)^3)/64 + (3*a^2*tan(c/2 + (d*x)/2)^11)/64 + (295*a^2*tan(c/2 + (d*x)/2)^13)/64 + (83*a^2*tan(c/2 + (d*x)/2)^15)/64 + (a^2*(315*c + 315*d*x))/896 - (a^2*(315*c + 315*d*x - 512))/896 + tan(c/2 + (d*x)/2)^2*((a^2*(315*c + 315*d*x))/112 - (a^2*(2520*c + 2520*d*x - 512))/896) + tan(c/2 + (d*x)/2)^14*((a^2*(315*c + 315*d*x))/112 - (a^2*(2520*c + 2520*d*x - 3584))/896) + tan(c/2 + (d*x)/2)^12*((a^2*(315*c + 315*d*x))/32 - (a^2*(8820*c + 8820*d*x - 3584))/896) + tan(c/2 + (d*x)/2)^4*((a^2*(315*c + 315*d*x))/32 - (a^2*(8820*c + 8820*d*x - 10752))/896) + tan(c/2 + (d*x)/2)^6*((a^2*(315*c + 315*d*x))/16 - (a^2*(17640*c + 17640*d*x - 10752))/896) + tan(c/2 + (d*x)/2)^10*((a^2*(315*c + 315*d*x))/16 - (a^2*(17640*c + 17640*d*x - 17920))/896) + tan(c/2 + (d*x)/2)^8*((5*a^2*(315*c + 315*d*x))/64 - (a^2*(22050*c + 22050*d*x - 17920))/896) - (83*a^2*tan(c/2 + (d*x)/2))/64)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^8)","B"
14,1,92,67,4.535902,"\text{Not used}","int(cos(c + d*x)^5*(a + a*sin(c + d*x))^2,x)","\frac{\frac{a^2\,{\sin\left(c+d\,x\right)}^7}{7}+\frac{a^2\,{\sin\left(c+d\,x\right)}^6}{3}-\frac{a^2\,{\sin\left(c+d\,x\right)}^5}{5}-a^2\,{\sin\left(c+d\,x\right)}^4-\frac{a^2\,{\sin\left(c+d\,x\right)}^3}{3}+a^2\,{\sin\left(c+d\,x\right)}^2+a^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a^2*sin(c + d*x) + a^2*sin(c + d*x)^2 - (a^2*sin(c + d*x)^3)/3 - a^2*sin(c + d*x)^4 - (a^2*sin(c + d*x)^5)/5 + (a^2*sin(c + d*x)^6)/3 + (a^2*sin(c + d*x)^7)/7)/d","B"
15,1,349,102,6.792382,"\text{Not used}","int(cos(c + d*x)^4*(a + a*sin(c + d*x))^2,x)","\frac{7\,a^2\,x}{16}-\frac{\frac{11\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-\frac{89\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}-\frac{11\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{89\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+\frac{9\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\frac{a^2\,\left(105\,c+105\,d\,x\right)}{240}-\frac{a^2\,\left(105\,c+105\,d\,x-192\right)}{240}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2\,\left(105\,c+105\,d\,x\right)}{40}-\frac{a^2\,\left(630\,c+630\,d\,x-192\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{a^2\,\left(105\,c+105\,d\,x\right)}{40}-\frac{a^2\,\left(630\,c+630\,d\,x-960\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{a^2\,\left(105\,c+105\,d\,x\right)}{16}-\frac{a^2\,\left(1575\,c+1575\,d\,x-960\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^2\,\left(105\,c+105\,d\,x\right)}{16}-\frac{a^2\,\left(1575\,c+1575\,d\,x-1920\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^2\,\left(105\,c+105\,d\,x\right)}{12}-\frac{a^2\,\left(2100\,c+2100\,d\,x-1920\right)}{240}\right)-\frac{9\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(7*a^2*x)/16 - ((11*a^2*tan(c/2 + (d*x)/2)^5)/4 - (89*a^2*tan(c/2 + (d*x)/2)^3)/24 - (11*a^2*tan(c/2 + (d*x)/2)^7)/4 + (89*a^2*tan(c/2 + (d*x)/2)^9)/24 + (9*a^2*tan(c/2 + (d*x)/2)^11)/8 + (a^2*(105*c + 105*d*x))/240 - (a^2*(105*c + 105*d*x - 192))/240 + tan(c/2 + (d*x)/2)^2*((a^2*(105*c + 105*d*x))/40 - (a^2*(630*c + 630*d*x - 192))/240) + tan(c/2 + (d*x)/2)^10*((a^2*(105*c + 105*d*x))/40 - (a^2*(630*c + 630*d*x - 960))/240) + tan(c/2 + (d*x)/2)^8*((a^2*(105*c + 105*d*x))/16 - (a^2*(1575*c + 1575*d*x - 960))/240) + tan(c/2 + (d*x)/2)^4*((a^2*(105*c + 105*d*x))/16 - (a^2*(1575*c + 1575*d*x - 1920))/240) + tan(c/2 + (d*x)/2)^6*((a^2*(105*c + 105*d*x))/12 - (a^2*(2100*c + 2100*d*x - 1920))/240) - (9*a^2*tan(c/2 + (d*x)/2))/8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
16,1,53,45,0.063501,"\text{Not used}","int(cos(c + d*x)^3*(a + a*sin(c + d*x))^2,x)","\frac{-\frac{a^2\,{\sin\left(c+d\,x\right)}^5}{5}-\frac{a^2\,{\sin\left(c+d\,x\right)}^4}{2}+a^2\,{\sin\left(c+d\,x\right)}^2+a^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a^2*sin(c + d*x) + a^2*sin(c + d*x)^2 - (a^2*sin(c + d*x)^4)/2 - (a^2*sin(c + d*x)^5)/5)/d","B"
17,1,237,78,6.707694,"\text{Not used}","int(cos(c + d*x)^2*(a + a*sin(c + d*x))^2,x)","\frac{5\,a^2\,x}{8}-\frac{\frac{11\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-\frac{11\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{a^2\,\left(15\,c+15\,d\,x\right)}{24}-\frac{a^2\,\left(15\,c+15\,d\,x-32\right)}{24}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2\,\left(15\,c+15\,d\,x\right)}{6}-\frac{a^2\,\left(60\,c+60\,d\,x-32\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^2\,\left(15\,c+15\,d\,x\right)}{6}-\frac{a^2\,\left(60\,c+60\,d\,x-96\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^2\,\left(15\,c+15\,d\,x\right)}{4}-\frac{a^2\,\left(90\,c+90\,d\,x-96\right)}{24}\right)-\frac{3\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(5*a^2*x)/8 - ((11*a^2*tan(c/2 + (d*x)/2)^5)/4 - (11*a^2*tan(c/2 + (d*x)/2)^3)/4 + (3*a^2*tan(c/2 + (d*x)/2)^7)/4 + (a^2*(15*c + 15*d*x))/24 - (a^2*(15*c + 15*d*x - 32))/24 + tan(c/2 + (d*x)/2)^2*((a^2*(15*c + 15*d*x))/6 - (a^2*(60*c + 60*d*x - 32))/24) + tan(c/2 + (d*x)/2)^6*((a^2*(15*c + 15*d*x))/6 - (a^2*(60*c + 60*d*x - 96))/24) + tan(c/2 + (d*x)/2)^4*((a^2*(15*c + 15*d*x))/4 - (a^2*(90*c + 90*d*x - 96))/24) - (3*a^2*tan(c/2 + (d*x)/2))/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
18,1,32,22,4.545402,"\text{Not used}","int(cos(c + d*x)*(a + a*sin(c + d*x))^2,x)","\frac{a^2\,\sin\left(c+d\,x\right)\,\left({\sin\left(c+d\,x\right)}^2+3\,\sin\left(c+d\,x\right)+3\right)}{3\,d}","Not used",1,"(a^2*sin(c + d*x)*(3*sin(c + d*x) + sin(c + d*x)^2 + 3))/(3*d)","B"
19,1,26,34,0.053663,"\text{Not used}","int((a + a*sin(c + d*x))^2/cos(c + d*x),x)","-\frac{a^2\,\left(2\,\ln\left(\sin\left(c+d\,x\right)-1\right)+\sin\left(c+d\,x\right)\right)}{d}","Not used",1,"-(a^2*(2*log(sin(c + d*x) - 1) + sin(c + d*x)))/d","B"
20,1,28,38,4.560675,"\text{Not used}","int((a + a*sin(c + d*x))^2/cos(c + d*x)^2,x)","-a^2\,x-\frac{4\,a^2}{d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}","Not used",1,"- a^2*x - (4*a^2)/(d*(tan(c/2 + (d*x)/2) - 1))","B"
21,1,18,20,0.041785,"\text{Not used}","int((a + a*sin(c + d*x))^2/cos(c + d*x)^3,x)","-\frac{a^2}{d\,\left(\sin\left(c+d\,x\right)-1\right)}","Not used",1,"-a^2/(d*(sin(c + d*x) - 1))","B"
22,1,81,63,4.558345,"\text{Not used}","int((a + a*sin(c + d*x))^2/cos(c + d*x)^4,x)","-\frac{2\,a^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{2\,a^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-3\right)}{3}}{d\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^3}","Not used",1,"-(2*a^2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2) + (2*a^2*cos(c/2 + (d*x)/2)*(cos(c/2 + (d*x)/2)^2 - 3))/3)/(d*(cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))^3)","B"
23,1,58,64,4.465949,"\text{Not used}","int((a + a*sin(c + d*x))^2/cos(c + d*x)^5,x)","\frac{a^2\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{4\,d}-\frac{\frac{a^2\,\sin\left(c+d\,x\right)}{4}-\frac{a^2}{2}}{d\,\left({\sin\left(c+d\,x\right)}^2-2\,\sin\left(c+d\,x\right)+1\right)}","Not used",1,"(a^2*atanh(sin(c + d*x)))/(4*d) - ((a^2*sin(c + d*x))/4 - a^2/2)/(d*(sin(c + d*x)^2 - 2*sin(c + d*x) + 1))","B"
24,1,156,64,4.633502,"\text{Not used}","int((a + a*sin(c + d*x))^2/cos(c + d*x)^6,x)","\frac{2\,a^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+10\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-10\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}{5\,d\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^5\,\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"(2*a^2*cos(c/2 + (d*x)/2)*(2*cos(c/2 + (d*x)/2)^5 + 5*sin(c/2 + (d*x)/2)^5 - 10*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^4 - 3*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2) + 10*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^3))/(5*d*(cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))^5*(cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2)))","B"
25,1,94,109,4.338141,"\text{Not used}","int((a + a*sin(c + d*x))^2/cos(c + d*x)^7,x)","\frac{a^2\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{4\,d}-\frac{\frac{a^2\,{\sin\left(c+d\,x\right)}^3}{4}-\frac{a^2\,{\sin\left(c+d\,x\right)}^2}{2}+\frac{a^2\,\sin\left(c+d\,x\right)}{12}+\frac{a^2}{3}}{d\,\left({\sin\left(c+d\,x\right)}^4-2\,{\sin\left(c+d\,x\right)}^3+2\,\sin\left(c+d\,x\right)-1\right)}","Not used",1,"(a^2*atanh(sin(c + d*x)))/(4*d) - ((a^2*sin(c + d*x))/12 + a^2/3 - (a^2*sin(c + d*x)^2)/2 + (a^2*sin(c + d*x)^3)/4)/(d*(2*sin(c + d*x) - 2*sin(c + d*x)^3 + sin(c + d*x)^4 - 1))","B"
26,1,276,82,5.066119,"\text{Not used}","int((a + a*sin(c + d*x))^2/cos(c + d*x)^8,x)","\frac{2\,a^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+76\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-28\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-42\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+56\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-42\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+21\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\right)}{21\,d\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^7\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^3}","Not used",1,"(2*a^2*cos(c/2 + (d*x)/2)*(6*cos(c/2 + (d*x)/2)^9 + 21*sin(c/2 + (d*x)/2)^9 - 42*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^8 - 3*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2) + 28*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^7 + 56*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^6 - 42*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^5 - 28*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^4 + 76*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^3 - 24*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^2))/(21*d*(cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))^7*(cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2))^3)","B"
27,1,501,154,6.805700,"\text{Not used}","int(cos(c + d*x)^6*(a + a*sin(c + d*x))^3,x)","\frac{55\,a^3\,x}{128}-\frac{\frac{17\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{32}-\frac{949\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}-\frac{699\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{32}+\frac{699\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{32}-\frac{17\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}+\frac{949\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{96}+\frac{73\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{64}+\frac{a^3\,\left(3465\,c+3465\,d\,x\right)}{8064}-\frac{a^3\,\left(3465\,c+3465\,d\,x-7424\right)}{8064}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^3\,\left(3465\,c+3465\,d\,x\right)}{896}-\frac{a^3\,\left(31185\,c+31185\,d\,x-18432\right)}{8064}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(\frac{a^3\,\left(3465\,c+3465\,d\,x\right)}{896}-\frac{a^3\,\left(31185\,c+31185\,d\,x-48384\right)}{8064}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{a^3\,\left(3465\,c+3465\,d\,x\right)}{224}-\frac{a^3\,\left(124740\,c+124740\,d\,x-129024\right)}{8064}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^3\,\left(3465\,c+3465\,d\,x\right)}{224}-\frac{a^3\,\left(124740\,c+124740\,d\,x-138240\right)}{8064}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{a^3\,\left(3465\,c+3465\,d\,x\right)}{96}-\frac{a^3\,\left(291060\,c+291060\,d\,x-236544\right)}{8064}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^3\,\left(3465\,c+3465\,d\,x\right)}{96}-\frac{a^3\,\left(291060\,c+291060\,d\,x-387072\right)}{8064}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{a^3\,\left(3465\,c+3465\,d\,x\right)}{64}-\frac{a^3\,\left(436590\,c+436590\,d\,x-290304\right)}{8064}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{a^3\,\left(3465\,c+3465\,d\,x\right)}{64}-\frac{a^3\,\left(436590\,c+436590\,d\,x-645120\right)}{8064}\right)-\frac{73\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^9}","Not used",1,"(55*a^3*x)/128 - ((17*a^3*tan(c/2 + (d*x)/2)^5)/32 - (949*a^3*tan(c/2 + (d*x)/2)^3)/96 - (699*a^3*tan(c/2 + (d*x)/2)^7)/32 + (699*a^3*tan(c/2 + (d*x)/2)^11)/32 - (17*a^3*tan(c/2 + (d*x)/2)^13)/32 + (949*a^3*tan(c/2 + (d*x)/2)^15)/96 + (73*a^3*tan(c/2 + (d*x)/2)^17)/64 + (a^3*(3465*c + 3465*d*x))/8064 - (a^3*(3465*c + 3465*d*x - 7424))/8064 + tan(c/2 + (d*x)/2)^2*((a^3*(3465*c + 3465*d*x))/896 - (a^3*(31185*c + 31185*d*x - 18432))/8064) + tan(c/2 + (d*x)/2)^16*((a^3*(3465*c + 3465*d*x))/896 - (a^3*(31185*c + 31185*d*x - 48384))/8064) + tan(c/2 + (d*x)/2)^14*((a^3*(3465*c + 3465*d*x))/224 - (a^3*(124740*c + 124740*d*x - 129024))/8064) + tan(c/2 + (d*x)/2)^4*((a^3*(3465*c + 3465*d*x))/224 - (a^3*(124740*c + 124740*d*x - 138240))/8064) + tan(c/2 + (d*x)/2)^12*((a^3*(3465*c + 3465*d*x))/96 - (a^3*(291060*c + 291060*d*x - 236544))/8064) + tan(c/2 + (d*x)/2)^6*((a^3*(3465*c + 3465*d*x))/96 - (a^3*(291060*c + 291060*d*x - 387072))/8064) + tan(c/2 + (d*x)/2)^8*((a^3*(3465*c + 3465*d*x))/64 - (a^3*(436590*c + 436590*d*x - 290304))/8064) + tan(c/2 + (d*x)/2)^10*((a^3*(3465*c + 3465*d*x))/64 - (a^3*(436590*c + 436590*d*x - 645120))/8064) - (73*a^3*tan(c/2 + (d*x)/2))/64)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^9)","B"
28,1,106,67,4.538942,"\text{Not used}","int(cos(c + d*x)^5*(a + a*sin(c + d*x))^3,x)","\frac{\frac{a^3\,{\sin\left(c+d\,x\right)}^8}{8}+\frac{3\,a^3\,{\sin\left(c+d\,x\right)}^7}{7}+\frac{a^3\,{\sin\left(c+d\,x\right)}^6}{6}-a^3\,{\sin\left(c+d\,x\right)}^5-\frac{5\,a^3\,{\sin\left(c+d\,x\right)}^4}{4}+\frac{a^3\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{3\,a^3\,{\sin\left(c+d\,x\right)}^2}{2}+a^3\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a^3*sin(c + d*x) + (3*a^3*sin(c + d*x)^2)/2 + (a^3*sin(c + d*x)^3)/3 - (5*a^3*sin(c + d*x)^4)/4 - a^3*sin(c + d*x)^5 + (a^3*sin(c + d*x)^6)/6 + (3*a^3*sin(c + d*x)^7)/7 + (a^3*sin(c + d*x)^8)/8)/d","B"
29,1,389,130,6.711392,"\text{Not used}","int(cos(c + d*x)^4*(a + a*sin(c + d*x))^3,x)","\frac{9\,a^3\,x}{16}-\frac{\frac{13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{8}-\frac{17\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-\frac{13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{8}+\frac{17\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{2}+\frac{7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{8}+\frac{a^3\,\left(315\,c+315\,d\,x\right)}{560}-\frac{a^3\,\left(315\,c+315\,d\,x-736\right)}{560}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^3\,\left(315\,c+315\,d\,x\right)}{80}-\frac{a^3\,\left(2205\,c+2205\,d\,x-1792\right)}{560}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{a^3\,\left(315\,c+315\,d\,x\right)}{80}-\frac{a^3\,\left(2205\,c+2205\,d\,x-3360\right)}{560}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{3\,a^3\,\left(315\,c+315\,d\,x\right)}{80}-\frac{a^3\,\left(6615\,c+6615\,d\,x-6496\right)}{560}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{3\,a^3\,\left(315\,c+315\,d\,x\right)}{80}-\frac{a^3\,\left(6615\,c+6615\,d\,x-8960\right)}{560}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{a^3\,\left(315\,c+315\,d\,x\right)}{16}-\frac{a^3\,\left(11025\,c+11025\,d\,x-7840\right)}{560}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^3\,\left(315\,c+315\,d\,x\right)}{16}-\frac{a^3\,\left(11025\,c+11025\,d\,x-17920\right)}{560}\right)-\frac{7\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^7}","Not used",1,"(9*a^3*x)/16 - ((13*a^3*tan(c/2 + (d*x)/2)^5)/8 - (17*a^3*tan(c/2 + (d*x)/2)^3)/2 - (13*a^3*tan(c/2 + (d*x)/2)^9)/8 + (17*a^3*tan(c/2 + (d*x)/2)^11)/2 + (7*a^3*tan(c/2 + (d*x)/2)^13)/8 + (a^3*(315*c + 315*d*x))/560 - (a^3*(315*c + 315*d*x - 736))/560 + tan(c/2 + (d*x)/2)^2*((a^3*(315*c + 315*d*x))/80 - (a^3*(2205*c + 2205*d*x - 1792))/560) + tan(c/2 + (d*x)/2)^12*((a^3*(315*c + 315*d*x))/80 - (a^3*(2205*c + 2205*d*x - 3360))/560) + tan(c/2 + (d*x)/2)^4*((3*a^3*(315*c + 315*d*x))/80 - (a^3*(6615*c + 6615*d*x - 6496))/560) + tan(c/2 + (d*x)/2)^10*((3*a^3*(315*c + 315*d*x))/80 - (a^3*(6615*c + 6615*d*x - 8960))/560) + tan(c/2 + (d*x)/2)^8*((a^3*(315*c + 315*d*x))/16 - (a^3*(11025*c + 11025*d*x - 7840))/560) + tan(c/2 + (d*x)/2)^6*((a^3*(315*c + 315*d*x))/16 - (a^3*(11025*c + 11025*d*x - 17920))/560) - (7*a^3*tan(c/2 + (d*x)/2))/8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
30,1,80,45,4.471802,"\text{Not used}","int(cos(c + d*x)^3*(a + a*sin(c + d*x))^3,x)","\frac{-\frac{a^3\,{\sin\left(c+d\,x\right)}^6}{6}-\frac{3\,a^3\,{\sin\left(c+d\,x\right)}^5}{5}-\frac{a^3\,{\sin\left(c+d\,x\right)}^4}{2}+\frac{2\,a^3\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{3\,a^3\,{\sin\left(c+d\,x\right)}^2}{2}+a^3\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a^3*sin(c + d*x) + (3*a^3*sin(c + d*x)^2)/2 + (2*a^3*sin(c + d*x)^3)/3 - (a^3*sin(c + d*x)^4)/2 - (3*a^3*sin(c + d*x)^5)/5 - (a^3*sin(c + d*x)^6)/6)/d","B"
31,1,277,106,6.532299,"\text{Not used}","int(cos(c + d*x)^2*(a + a*sin(c + d*x))^3,x)","\frac{7\,a^3\,x}{8}-\frac{\frac{13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}-\frac{13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}+\frac{a^3\,\left(105\,c+105\,d\,x\right)}{120}-\frac{a^3\,\left(105\,c+105\,d\,x-272\right)}{120}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^3\,\left(105\,c+105\,d\,x\right)}{24}-\frac{a^3\,\left(525\,c+525\,d\,x-640\right)}{120}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{a^3\,\left(105\,c+105\,d\,x\right)}{24}-\frac{a^3\,\left(525\,c+525\,d\,x-720\right)}{120}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^3\,\left(105\,c+105\,d\,x\right)}{12}-\frac{a^3\,\left(1050\,c+1050\,d\,x-800\right)}{120}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^3\,\left(105\,c+105\,d\,x\right)}{12}-\frac{a^3\,\left(1050\,c+1050\,d\,x-1920\right)}{120}\right)-\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(7*a^3*x)/8 - ((13*a^3*tan(c/2 + (d*x)/2)^7)/2 - (13*a^3*tan(c/2 + (d*x)/2)^3)/2 + (a^3*tan(c/2 + (d*x)/2)^9)/4 + (a^3*(105*c + 105*d*x))/120 - (a^3*(105*c + 105*d*x - 272))/120 + tan(c/2 + (d*x)/2)^2*((a^3*(105*c + 105*d*x))/24 - (a^3*(525*c + 525*d*x - 640))/120) + tan(c/2 + (d*x)/2)^8*((a^3*(105*c + 105*d*x))/24 - (a^3*(525*c + 525*d*x - 720))/120) + tan(c/2 + (d*x)/2)^4*((a^3*(105*c + 105*d*x))/12 - (a^3*(1050*c + 1050*d*x - 800))/120) + tan(c/2 + (d*x)/2)^6*((a^3*(105*c + 105*d*x))/12 - (a^3*(1050*c + 1050*d*x - 1920))/120) - (a^3*tan(c/2 + (d*x)/2))/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
32,1,53,22,0.056459,"\text{Not used}","int(cos(c + d*x)*(a + a*sin(c + d*x))^3,x)","\frac{\frac{a^3\,{\sin\left(c+d\,x\right)}^4}{4}+a^3\,{\sin\left(c+d\,x\right)}^3+\frac{3\,a^3\,{\sin\left(c+d\,x\right)}^2}{2}+a^3\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a^3*sin(c + d*x) + (3*a^3*sin(c + d*x)^2)/2 + a^3*sin(c + d*x)^3 + (a^3*sin(c + d*x)^4)/4)/d","B"
33,1,36,52,0.052675,"\text{Not used}","int((a + a*sin(c + d*x))^3/cos(c + d*x),x)","-\frac{a^3\,\left(8\,\ln\left(\sin\left(c+d\,x\right)-1\right)+6\,\sin\left(c+d\,x\right)+{\sin\left(c+d\,x\right)}^2\right)}{2\,d}","Not used",1,"-(a^3*(8*log(sin(c + d*x) - 1) + 6*sin(c + d*x) + sin(c + d*x)^2))/(2*d)","B"
34,1,138,50,4.775586,"\text{Not used}","int((a + a*sin(c + d*x))^3/cos(c + d*x)^2,x)","-3\,a^3\,x-\frac{3\,a^3\,\left(c+d\,x\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^3\,\left(c+d\,x\right)-a^3\,\left(3\,c+3\,d\,x-2\right)\right)-a^3\,\left(3\,c+3\,d\,x-10\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a^3\,\left(c+d\,x\right)-a^3\,\left(3\,c+3\,d\,x-8\right)\right)}{d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"- 3*a^3*x - (3*a^3*(c + d*x) - tan(c/2 + (d*x)/2)*(3*a^3*(c + d*x) - a^3*(3*c + 3*d*x - 2)) - a^3*(3*c + 3*d*x - 10) + tan(c/2 + (d*x)/2)^2*(3*a^3*(c + d*x) - a^3*(3*c + 3*d*x - 8)))/(d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2)^2 + 1))","B"
35,1,35,40,4.520981,"\text{Not used}","int((a + a*sin(c + d*x))^3/cos(c + d*x)^3,x)","\frac{a^3\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{d}-\frac{2\,a^3}{d\,\left(\sin\left(c+d\,x\right)-1\right)}","Not used",1,"(a^3*log(sin(c + d*x) - 1))/d - (2*a^3)/(d*(sin(c + d*x) - 1))","B"
36,1,55,31,4.592471,"\text{Not used}","int((a + a*sin(c + d*x))^3/cos(c + d*x)^4,x)","-\frac{2\,a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-3\right)}{3\,d\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^3}","Not used",1,"-(2*a^3*cos(c/2 + (d*x)/2)*(2*cos(c/2 + (d*x)/2)^2 - 3))/(3*d*(cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))^3)","B"
37,1,18,23,0.066057,"\text{Not used}","int((a + a*sin(c + d*x))^3/cos(c + d*x)^5,x)","\frac{a^3}{2\,d\,{\left(\sin\left(c+d\,x\right)-1\right)}^2}","Not used",1,"a^3/(2*d*(sin(c + d*x) - 1)^2)","B"
38,1,135,92,4.693782,"\text{Not used}","int((a + a*sin(c + d*x))^3/cos(c + d*x)^6,x)","\frac{2\,a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-20\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-30\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+15\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}{15\,d\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^5}","Not used",1,"(2*a^3*cos(c/2 + (d*x)/2)*(7*cos(c/2 + (d*x)/2)^4 + 15*sin(c/2 + (d*x)/2)^4 - 30*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^3 - 20*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2) + 40*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2))/(15*d*(cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))^5)","B"
39,1,81,87,4.536173,"\text{Not used}","int((a + a*sin(c + d*x))^3/cos(c + d*x)^7,x)","\frac{a^3\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{8\,d}-\frac{\frac{a^3\,{\sin\left(c+d\,x\right)}^2}{8}-\frac{3\,a^3\,\sin\left(c+d\,x\right)}{8}+\frac{5\,a^3}{12}}{d\,\left({\sin\left(c+d\,x\right)}^3-3\,{\sin\left(c+d\,x\right)}^2+3\,\sin\left(c+d\,x\right)-1\right)}","Not used",1,"(a^3*atanh(sin(c + d*x)))/(8*d) - ((5*a^3)/12 - (3*a^3*sin(c + d*x))/8 + (a^3*sin(c + d*x)^2)/8)/(d*(3*sin(c + d*x) - 3*sin(c + d*x)^2 + sin(c + d*x)^3 - 1))","B"
40,1,228,99,4.864503,"\text{Not used}","int((a + a*sin(c + d*x))^3/cos(c + d*x)^8,x)","\frac{2\,a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(13\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-43\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+77\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-7\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+175\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-105\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+35\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\right)}{35\,d\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^7\,\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"(2*a^3*cos(c/2 + (d*x)/2)*(13*cos(c/2 + (d*x)/2)^7 + 35*sin(c/2 + (d*x)/2)^7 - 105*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^6 - 43*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2) + 175*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^5 - 105*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^4 - 7*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^3 + 77*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^2))/(35*d*(cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))^7*(cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2)))","B"
41,1,134,67,0.178835,"\text{Not used}","int(cos(c + d*x)^5*(a + a*sin(c + d*x))^8,x)","\frac{a^8\,\sin\left(c+d\,x\right)\,\left(33\,{\sin\left(c+d\,x\right)}^{12}+286\,{\sin\left(c+d\,x\right)}^{11}+1014\,{\sin\left(c+d\,x\right)}^{10}+1716\,{\sin\left(c+d\,x\right)}^9+715\,{\sin\left(c+d\,x\right)}^8-2574\,{\sin\left(c+d\,x\right)}^7-5148\,{\sin\left(c+d\,x\right)}^6-3432\,{\sin\left(c+d\,x\right)}^5+1287\,{\sin\left(c+d\,x\right)}^4+4290\,{\sin\left(c+d\,x\right)}^3+3718\,{\sin\left(c+d\,x\right)}^2+1716\,\sin\left(c+d\,x\right)+429\right)}{429\,d}","Not used",1,"(a^8*sin(c + d*x)*(1716*sin(c + d*x) + 3718*sin(c + d*x)^2 + 4290*sin(c + d*x)^3 + 1287*sin(c + d*x)^4 - 3432*sin(c + d*x)^5 - 5148*sin(c + d*x)^6 - 2574*sin(c + d*x)^7 + 715*sin(c + d*x)^8 + 1716*sin(c + d*x)^9 + 1014*sin(c + d*x)^10 + 286*sin(c + d*x)^11 + 33*sin(c + d*x)^12 + 429))/(429*d)","B"
42,1,684,286,7.051309,"\text{Not used}","int(cos(c + d*x)^4*(a + a*sin(c + d*x))^8,x)","\frac{4199\,a^8\,x}{1024}-\frac{\frac{1543\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{512}-\frac{1068767\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2560}-\frac{3297279\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2560}-\frac{168283\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{3840}+\frac{256139\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{256}-\frac{256139\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{256}+\frac{168283\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{3840}+\frac{3297279\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{2560}+\frac{1068767\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{2560}-\frac{1543\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}}{512}-\frac{3175\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{23}}{512}+a^8\,\left(\frac{4199\,c}{1024}+\frac{4199\,d\,x}{1024}\right)-a^8\,\left(\frac{4199\,c}{1024}+\frac{4199\,d\,x}{1024}-\frac{43888}{3465}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{22}\,\left(12\,a^8\,\left(\frac{4199\,c}{1024}+\frac{4199\,d\,x}{1024}\right)-a^8\,\left(\frac{12597\,c}{256}+\frac{12597\,d\,x}{256}-16\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a^8\,\left(\frac{4199\,c}{1024}+\frac{4199\,d\,x}{1024}\right)-a^8\,\left(\frac{12597\,c}{256}+\frac{12597\,d\,x}{256}-\frac{157072}{1155}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}\,\left(66\,a^8\,\left(\frac{4199\,c}{1024}+\frac{4199\,d\,x}{1024}\right)-a^8\,\left(\frac{138567\,c}{512}+\frac{138567\,d\,x}{512}-336\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(66\,a^8\,\left(\frac{4199\,c}{1024}+\frac{4199\,d\,x}{1024}\right)-a^8\,\left(\frac{138567\,c}{512}+\frac{138567\,d\,x}{512}-\frac{52496}{105}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,\left(220\,a^8\,\left(\frac{4199\,c}{1024}+\frac{4199\,d\,x}{1024}\right)-a^8\,\left(\frac{230945\,c}{256}+\frac{230945\,d\,x}{256}-\frac{5584}{3}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(220\,a^8\,\left(\frac{4199\,c}{1024}+\frac{4199\,d\,x}{1024}\right)-a^8\,\left(\frac{230945\,c}{256}+\frac{230945\,d\,x}{256}-\frac{58288}{63}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(792\,a^8\,\left(\frac{4199\,c}{1024}+\frac{4199\,d\,x}{1024}\right)-a^8\,\left(\frac{415701\,c}{128}+\frac{415701\,d\,x}{128}-\frac{17696}{5}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(792\,a^8\,\left(\frac{4199\,c}{1024}+\frac{4199\,d\,x}{1024}\right)-a^8\,\left(\frac{415701\,c}{128}+\frac{415701\,d\,x}{128}-\frac{227232}{35}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(924\,a^8\,\left(\frac{4199\,c}{1024}+\frac{4199\,d\,x}{1024}\right)-a^8\,\left(\frac{969969\,c}{256}+\frac{969969\,d\,x}{256}-\frac{87776}{15}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(495\,a^8\,\left(\frac{4199\,c}{1024}+\frac{4199\,d\,x}{1024}\right)-a^8\,\left(\frac{2078505\,c}{1024}+\frac{2078505\,d\,x}{1024}-3504\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(495\,a^8\,\left(\frac{4199\,c}{1024}+\frac{4199\,d\,x}{1024}\right)-a^8\,\left(\frac{2078505\,c}{1024}+\frac{2078505\,d\,x}{1024}-\frac{19360}{7}\right)\right)+\frac{3175\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^{12}}","Not used",1,"(4199*a^8*x)/1024 - ((1543*a^8*tan(c/2 + (d*x)/2)^3)/512 - (1068767*a^8*tan(c/2 + (d*x)/2)^5)/2560 - (3297279*a^8*tan(c/2 + (d*x)/2)^7)/2560 - (168283*a^8*tan(c/2 + (d*x)/2)^9)/3840 + (256139*a^8*tan(c/2 + (d*x)/2)^11)/256 - (256139*a^8*tan(c/2 + (d*x)/2)^13)/256 + (168283*a^8*tan(c/2 + (d*x)/2)^15)/3840 + (3297279*a^8*tan(c/2 + (d*x)/2)^17)/2560 + (1068767*a^8*tan(c/2 + (d*x)/2)^19)/2560 - (1543*a^8*tan(c/2 + (d*x)/2)^21)/512 - (3175*a^8*tan(c/2 + (d*x)/2)^23)/512 + a^8*((4199*c)/1024 + (4199*d*x)/1024) - a^8*((4199*c)/1024 + (4199*d*x)/1024 - 43888/3465) + tan(c/2 + (d*x)/2)^22*(12*a^8*((4199*c)/1024 + (4199*d*x)/1024) - a^8*((12597*c)/256 + (12597*d*x)/256 - 16)) + tan(c/2 + (d*x)/2)^2*(12*a^8*((4199*c)/1024 + (4199*d*x)/1024) - a^8*((12597*c)/256 + (12597*d*x)/256 - 157072/1155)) + tan(c/2 + (d*x)/2)^20*(66*a^8*((4199*c)/1024 + (4199*d*x)/1024) - a^8*((138567*c)/512 + (138567*d*x)/512 - 336)) + tan(c/2 + (d*x)/2)^4*(66*a^8*((4199*c)/1024 + (4199*d*x)/1024) - a^8*((138567*c)/512 + (138567*d*x)/512 - 52496/105)) + tan(c/2 + (d*x)/2)^18*(220*a^8*((4199*c)/1024 + (4199*d*x)/1024) - a^8*((230945*c)/256 + (230945*d*x)/256 - 5584/3)) + tan(c/2 + (d*x)/2)^6*(220*a^8*((4199*c)/1024 + (4199*d*x)/1024) - a^8*((230945*c)/256 + (230945*d*x)/256 - 58288/63)) + tan(c/2 + (d*x)/2)^14*(792*a^8*((4199*c)/1024 + (4199*d*x)/1024) - a^8*((415701*c)/128 + (415701*d*x)/128 - 17696/5)) + tan(c/2 + (d*x)/2)^10*(792*a^8*((4199*c)/1024 + (4199*d*x)/1024) - a^8*((415701*c)/128 + (415701*d*x)/128 - 227232/35)) + tan(c/2 + (d*x)/2)^12*(924*a^8*((4199*c)/1024 + (4199*d*x)/1024) - a^8*((969969*c)/256 + (969969*d*x)/256 - 87776/15)) + tan(c/2 + (d*x)/2)^16*(495*a^8*((4199*c)/1024 + (4199*d*x)/1024) - a^8*((2078505*c)/1024 + (2078505*d*x)/1024 - 3504)) + tan(c/2 + (d*x)/2)^8*(495*a^8*((4199*c)/1024 + (4199*d*x)/1024) - a^8*((2078505*c)/1024 + (2078505*d*x)/1024 - 19360/7)) + (3175*a^8*tan(c/2 + (d*x)/2))/512)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^12)","B"
43,1,132,45,0.117258,"\text{Not used}","int(cos(c + d*x)^3*(a + a*sin(c + d*x))^8,x)","\frac{-\frac{a^8\,{\sin\left(c+d\,x\right)}^{11}}{11}-\frac{4\,a^8\,{\sin\left(c+d\,x\right)}^{10}}{5}-3\,a^8\,{\sin\left(c+d\,x\right)}^9-6\,a^8\,{\sin\left(c+d\,x\right)}^8-6\,a^8\,{\sin\left(c+d\,x\right)}^7+\frac{42\,a^8\,{\sin\left(c+d\,x\right)}^5}{5}+12\,a^8\,{\sin\left(c+d\,x\right)}^4+9\,a^8\,{\sin\left(c+d\,x\right)}^3+4\,a^8\,{\sin\left(c+d\,x\right)}^2+a^8\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a^8*sin(c + d*x) + 4*a^8*sin(c + d*x)^2 + 9*a^8*sin(c + d*x)^3 + 12*a^8*sin(c + d*x)^4 + (42*a^8*sin(c + d*x)^5)/5 - 6*a^8*sin(c + d*x)^7 - 6*a^8*sin(c + d*x)^8 - 3*a^8*sin(c + d*x)^9 - (4*a^8*sin(c + d*x)^10)/5 - (a^8*sin(c + d*x)^11)/11)/d","B"
44,1,572,262,7.258436,"\text{Not used}","int(cos(c + d*x)^2*(a + a*sin(c + d*x))^8,x)","\frac{2431\,a^8\,x}{256}-\frac{\frac{11809\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{128}-\frac{23647\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160}-\frac{40749\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{32}-\frac{70499\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{64}+\frac{70499\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{64}+\frac{40749\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{32}+\frac{23647\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{160}-\frac{11809\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{128}-\frac{2175\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{128}+a^8\,\left(\frac{2431\,c}{256}+\frac{2431\,d\,x}{256}\right)-a^8\,\left(\frac{2431\,c}{256}+\frac{2431\,d\,x}{256}-\frac{9328}{315}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,\left(10\,a^8\,\left(\frac{2431\,c}{256}+\frac{2431\,d\,x}{256}\right)-a^8\,\left(\frac{12155\,c}{128}+\frac{12155\,d\,x}{128}-16\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(10\,a^8\,\left(\frac{2431\,c}{256}+\frac{2431\,d\,x}{256}\right)-a^8\,\left(\frac{12155\,c}{128}+\frac{12155\,d\,x}{128}-\frac{17648}{63}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(120\,a^8\,\left(\frac{2431\,c}{256}+\frac{2431\,d\,x}{256}\right)-a^8\,\left(\frac{36465\,c}{32}+\frac{36465\,d\,x}{32}-1984\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(120\,a^8\,\left(\frac{2431\,c}{256}+\frac{2431\,d\,x}{256}\right)-a^8\,\left(\frac{36465\,c}{32}+\frac{36465\,d\,x}{32}-\frac{32960}{21}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(45\,a^8\,\left(\frac{2431\,c}{256}+\frac{2431\,d\,x}{256}\right)-a^8\,\left(\frac{109395\,c}{256}+\frac{109395\,d\,x}{256}-336\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(45\,a^8\,\left(\frac{2431\,c}{256}+\frac{2431\,d\,x}{256}\right)-a^8\,\left(\frac{109395\,c}{256}+\frac{109395\,d\,x}{256}-\frac{6976}{7}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(252\,a^8\,\left(\frac{2431\,c}{256}+\frac{2431\,d\,x}{256}\right)-a^8\,\left(\frac{153153\,c}{64}+\frac{153153\,d\,x}{64}-\frac{18656}{5}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(210\,a^8\,\left(\frac{2431\,c}{256}+\frac{2431\,d\,x}{256}\right)-a^8\,\left(\frac{255255\,c}{128}+\frac{255255\,d\,x}{128}-4288\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(210\,a^8\,\left(\frac{2431\,c}{256}+\frac{2431\,d\,x}{256}\right)-a^8\,\left(\frac{255255\,c}{128}+\frac{255255\,d\,x}{128}-\frac{5792}{3}\right)\right)+\frac{2175\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^{10}}","Not used",1,"(2431*a^8*x)/256 - ((11809*a^8*tan(c/2 + (d*x)/2)^3)/128 - (23647*a^8*tan(c/2 + (d*x)/2)^5)/160 - (40749*a^8*tan(c/2 + (d*x)/2)^7)/32 - (70499*a^8*tan(c/2 + (d*x)/2)^9)/64 + (70499*a^8*tan(c/2 + (d*x)/2)^11)/64 + (40749*a^8*tan(c/2 + (d*x)/2)^13)/32 + (23647*a^8*tan(c/2 + (d*x)/2)^15)/160 - (11809*a^8*tan(c/2 + (d*x)/2)^17)/128 - (2175*a^8*tan(c/2 + (d*x)/2)^19)/128 + a^8*((2431*c)/256 + (2431*d*x)/256) - a^8*((2431*c)/256 + (2431*d*x)/256 - 9328/315) + tan(c/2 + (d*x)/2)^18*(10*a^8*((2431*c)/256 + (2431*d*x)/256) - a^8*((12155*c)/128 + (12155*d*x)/128 - 16)) + tan(c/2 + (d*x)/2)^2*(10*a^8*((2431*c)/256 + (2431*d*x)/256) - a^8*((12155*c)/128 + (12155*d*x)/128 - 17648/63)) + tan(c/2 + (d*x)/2)^14*(120*a^8*((2431*c)/256 + (2431*d*x)/256) - a^8*((36465*c)/32 + (36465*d*x)/32 - 1984)) + tan(c/2 + (d*x)/2)^6*(120*a^8*((2431*c)/256 + (2431*d*x)/256) - a^8*((36465*c)/32 + (36465*d*x)/32 - 32960/21)) + tan(c/2 + (d*x)/2)^16*(45*a^8*((2431*c)/256 + (2431*d*x)/256) - a^8*((109395*c)/256 + (109395*d*x)/256 - 336)) + tan(c/2 + (d*x)/2)^4*(45*a^8*((2431*c)/256 + (2431*d*x)/256) - a^8*((109395*c)/256 + (109395*d*x)/256 - 6976/7)) + tan(c/2 + (d*x)/2)^10*(252*a^8*((2431*c)/256 + (2431*d*x)/256) - a^8*((153153*c)/64 + (153153*d*x)/64 - 18656/5)) + tan(c/2 + (d*x)/2)^12*(210*a^8*((2431*c)/256 + (2431*d*x)/256) - a^8*((255255*c)/128 + (255255*d*x)/128 - 4288)) + tan(c/2 + (d*x)/2)^8*(210*a^8*((2431*c)/256 + (2431*d*x)/256) - a^8*((255255*c)/128 + (255255*d*x)/128 - 5792/3)) + (2175*a^8*tan(c/2 + (d*x)/2))/128)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^10)","B"
45,1,118,22,4.745801,"\text{Not used}","int(cos(c + d*x)*(a + a*sin(c + d*x))^8,x)","\frac{\frac{a^8\,{\sin\left(c+d\,x\right)}^9}{9}+a^8\,{\sin\left(c+d\,x\right)}^8+4\,a^8\,{\sin\left(c+d\,x\right)}^7+\frac{28\,a^8\,{\sin\left(c+d\,x\right)}^6}{3}+14\,a^8\,{\sin\left(c+d\,x\right)}^5+14\,a^8\,{\sin\left(c+d\,x\right)}^4+\frac{28\,a^8\,{\sin\left(c+d\,x\right)}^3}{3}+4\,a^8\,{\sin\left(c+d\,x\right)}^2+a^8\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a^8*sin(c + d*x) + 4*a^8*sin(c + d*x)^2 + (28*a^8*sin(c + d*x)^3)/3 + 14*a^8*sin(c + d*x)^4 + 14*a^8*sin(c + d*x)^5 + (28*a^8*sin(c + d*x)^6)/3 + 4*a^8*sin(c + d*x)^7 + a^8*sin(c + d*x)^8 + (a^8*sin(c + d*x)^9)/9)/d","B"
46,1,109,162,4.648196,"\text{Not used}","int((a + a*sin(c + d*x))^8/cos(c + d*x),x)","-\frac{128\,a^8\,\ln\left(\sin\left(c+d\,x\right)-1\right)+127\,a^8\,\sin\left(c+d\,x\right)+60\,a^8\,{\sin\left(c+d\,x\right)}^2+33\,a^8\,{\sin\left(c+d\,x\right)}^3+16\,a^8\,{\sin\left(c+d\,x\right)}^4+\frac{29\,a^8\,{\sin\left(c+d\,x\right)}^5}{5}+\frac{4\,a^8\,{\sin\left(c+d\,x\right)}^6}{3}+\frac{a^8\,{\sin\left(c+d\,x\right)}^7}{7}}{d}","Not used",1,"-(128*a^8*log(sin(c + d*x) - 1) + 127*a^8*sin(c + d*x) + 60*a^8*sin(c + d*x)^2 + 33*a^8*sin(c + d*x)^3 + 16*a^8*sin(c + d*x)^4 + (29*a^8*sin(c + d*x)^5)/5 + (4*a^8*sin(c + d*x)^6)/3 + (a^8*sin(c + d*x)^7)/7)/d","B"
47,1,513,201,8.732618,"\text{Not used}","int((a + a*sin(c + d*x))^8/cos(c + d*x)^2,x)","-\frac{3003\,a^8\,x}{16}-\frac{\frac{3003\,a^8\,\left(c+d\,x\right)}{16}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3003\,a^8\,\left(c+d\,x\right)}{16}-\frac{a^8\,\left(45045\,c+45045\,d\,x-50998\right)}{240}\right)-\frac{a^8\,\left(45045\,c+45045\,d\,x-141568\right)}{240}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{3003\,a^8\,\left(c+d\,x\right)}{16}-\frac{a^8\,\left(45045\,c+45045\,d\,x-90570\right)}{240}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{9009\,a^8\,\left(c+d\,x\right)}{8}-\frac{a^8\,\left(270270\,c+270270\,d\,x-86730\right)}{240}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{9009\,a^8\,\left(c+d\,x\right)}{8}-\frac{a^8\,\left(270270\,c+270270\,d\,x-321458\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{9009\,a^8\,\left(c+d\,x\right)}{8}-\frac{a^8\,\left(270270\,c+270270\,d\,x-527950\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{9009\,a^8\,\left(c+d\,x\right)}{8}-\frac{a^8\,\left(270270\,c+270270\,d\,x-762678\right)}{240}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{45045\,a^8\,\left(c+d\,x\right)}{16}-\frac{a^8\,\left(675675\,c+675675\,d\,x-451150\right)}{240}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{45045\,a^8\,\left(c+d\,x\right)}{16}-\frac{a^8\,\left(675675\,c+675675\,d\,x-778620\right)}{240}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{15015\,a^8\,\left(c+d\,x\right)}{4}-\frac{a^8\,\left(900900\,c+900900\,d\,x-875140\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{45045\,a^8\,\left(c+d\,x\right)}{16}-\frac{a^8\,\left(675675\,c+675675\,d\,x-1344900\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{45045\,a^8\,\left(c+d\,x\right)}{16}-\frac{a^8\,\left(675675\,c+675675\,d\,x-1672370\right)}{240}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{15015\,a^8\,\left(c+d\,x\right)}{4}-\frac{a^8\,\left(900900\,c+900900\,d\,x-1956220\right)}{240}\right)}{d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"- (3003*a^8*x)/16 - ((3003*a^8*(c + d*x))/16 - tan(c/2 + (d*x)/2)*((3003*a^8*(c + d*x))/16 - (a^8*(45045*c + 45045*d*x - 50998))/240) - (a^8*(45045*c + 45045*d*x - 141568))/240 + tan(c/2 + (d*x)/2)^12*((3003*a^8*(c + d*x))/16 - (a^8*(45045*c + 45045*d*x - 90570))/240) - tan(c/2 + (d*x)/2)^11*((9009*a^8*(c + d*x))/8 - (a^8*(270270*c + 270270*d*x - 86730))/240) - tan(c/2 + (d*x)/2)^3*((9009*a^8*(c + d*x))/8 - (a^8*(270270*c + 270270*d*x - 321458))/240) + tan(c/2 + (d*x)/2)^10*((9009*a^8*(c + d*x))/8 - (a^8*(270270*c + 270270*d*x - 527950))/240) + tan(c/2 + (d*x)/2)^2*((9009*a^8*(c + d*x))/8 - (a^8*(270270*c + 270270*d*x - 762678))/240) - tan(c/2 + (d*x)/2)^9*((45045*a^8*(c + d*x))/16 - (a^8*(675675*c + 675675*d*x - 451150))/240) - tan(c/2 + (d*x)/2)^5*((45045*a^8*(c + d*x))/16 - (a^8*(675675*c + 675675*d*x - 778620))/240) - tan(c/2 + (d*x)/2)^7*((15015*a^8*(c + d*x))/4 - (a^8*(900900*c + 900900*d*x - 875140))/240) + tan(c/2 + (d*x)/2)^8*((45045*a^8*(c + d*x))/16 - (a^8*(675675*c + 675675*d*x - 1344900))/240) + tan(c/2 + (d*x)/2)^4*((45045*a^8*(c + d*x))/16 - (a^8*(675675*c + 675675*d*x - 1672370))/240) + tan(c/2 + (d*x)/2)^6*((15015*a^8*(c + d*x))/4 - (a^8*(900900*c + 900900*d*x - 1956220))/240))/(d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
48,1,97,121,4.623254,"\text{Not used}","int((a + a*sin(c + d*x))^8/cos(c + d*x)^3,x)","\frac{192\,a^8\,\ln\left(\sin\left(c+d\,x\right)-1\right)-\frac{64\,a^8}{\sin\left(c+d\,x\right)-1}+129\,a^8\,\sin\left(c+d\,x\right)+36\,a^8\,{\sin\left(c+d\,x\right)}^2+10\,a^8\,{\sin\left(c+d\,x\right)}^3+2\,a^8\,{\sin\left(c+d\,x\right)}^4+\frac{a^8\,{\sin\left(c+d\,x\right)}^5}{5}}{d}","Not used",1,"(192*a^8*log(sin(c + d*x) - 1) - (64*a^8)/(sin(c + d*x) - 1) + 129*a^8*sin(c + d*x) + 36*a^8*sin(c + d*x)^2 + 10*a^8*sin(c + d*x)^3 + 2*a^8*sin(c + d*x)^4 + (a^8*sin(c + d*x)^5)/5)/d","B"
49,1,437,179,9.129409,"\text{Not used}","int((a + a*sin(c + d*x))^8/cos(c + d*x)^4,x)","\frac{1155\,a^8\,x}{8}+\frac{\frac{1155\,a^8\,\left(c+d\,x\right)}{8}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3465\,a^8\,\left(c+d\,x\right)}{8}-\frac{a^8\,\left(10395\,c+10395\,d\,x-25758\right)}{24}\right)-\frac{a^8\,\left(3465\,c+3465\,d\,x-10880\right)}{24}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{3465\,a^8\,\left(c+d\,x\right)}{8}-\frac{a^8\,\left(10395\,c+10395\,d\,x-6882\right)}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{8085\,a^8\,\left(c+d\,x\right)}{8}-\frac{a^8\,\left(24255\,c+24255\,d\,x-21030\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{8085\,a^8\,\left(c+d\,x\right)}{8}-\frac{a^8\,\left(24255\,c+24255\,d\,x-55130\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{15015\,a^8\,\left(c+d\,x\right)}{8}-\frac{a^8\,\left(45045\,c+45045\,d\,x-45112\right)}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{15015\,a^8\,\left(c+d\,x\right)}{8}-\frac{a^8\,\left(45045\,c+45045\,d\,x-96328\right)}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{10395\,a^8\,\left(c+d\,x\right)}{4}-\frac{a^8\,\left(62370\,c+62370\,d\,x-86040\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{10395\,a^8\,\left(c+d\,x\right)}{4}-\frac{a^8\,\left(62370\,c+62370\,d\,x-109800\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{12705\,a^8\,\left(c+d\,x\right)}{4}-\frac{a^8\,\left(76230\,c+76230\,d\,x-103972\right)}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{12705\,a^8\,\left(c+d\,x\right)}{4}-\frac{a^8\,\left(76230\,c+76230\,d\,x-135388\right)}{24}\right)}{d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^3\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(1155*a^8*x)/8 + ((1155*a^8*(c + d*x))/8 - tan(c/2 + (d*x)/2)*((3465*a^8*(c + d*x))/8 - (a^8*(10395*c + 10395*d*x - 25758))/24) - (a^8*(3465*c + 3465*d*x - 10880))/24 + tan(c/2 + (d*x)/2)^10*((3465*a^8*(c + d*x))/8 - (a^8*(10395*c + 10395*d*x - 6882))/24) - tan(c/2 + (d*x)/2)^9*((8085*a^8*(c + d*x))/8 - (a^8*(24255*c + 24255*d*x - 21030))/24) + tan(c/2 + (d*x)/2)^2*((8085*a^8*(c + d*x))/8 - (a^8*(24255*c + 24255*d*x - 55130))/24) + tan(c/2 + (d*x)/2)^8*((15015*a^8*(c + d*x))/8 - (a^8*(45045*c + 45045*d*x - 45112))/24) - tan(c/2 + (d*x)/2)^3*((15015*a^8*(c + d*x))/8 - (a^8*(45045*c + 45045*d*x - 96328))/24) - tan(c/2 + (d*x)/2)^7*((10395*a^8*(c + d*x))/4 - (a^8*(62370*c + 62370*d*x - 86040))/24) + tan(c/2 + (d*x)/2)^4*((10395*a^8*(c + d*x))/4 - (a^8*(62370*c + 62370*d*x - 109800))/24) + tan(c/2 + (d*x)/2)^6*((12705*a^8*(c + d*x))/4 - (a^8*(76230*c + 76230*d*x - 103972))/24) - tan(c/2 + (d*x)/2)^5*((12705*a^8*(c + d*x))/4 - (a^8*(76230*c + 76230*d*x - 135388))/24))/(d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
50,1,96,110,4.601568,"\text{Not used}","int((a + a*sin(c + d*x))^8/cos(c + d*x)^5,x)","-\frac{80\,a^8\,\ln\left(\sin\left(c+d\,x\right)-1\right)+31\,a^8\,\sin\left(c+d\,x\right)-\frac{80\,a^8\,\sin\left(c+d\,x\right)-64\,a^8}{{\sin\left(c+d\,x\right)}^2-2\,\sin\left(c+d\,x\right)+1}+4\,a^8\,{\sin\left(c+d\,x\right)}^2+\frac{a^8\,{\sin\left(c+d\,x\right)}^3}{3}}{d}","Not used",1,"-(80*a^8*log(sin(c + d*x) - 1) + 31*a^8*sin(c + d*x) - (80*a^8*sin(c + d*x) - 64*a^8)/(sin(c + d*x)^2 - 2*sin(c + d*x) + 1) + 4*a^8*sin(c + d*x)^2 + (a^8*sin(c + d*x)^3)/3)/d","B"
51,1,107,73,8.154501,"\text{Not used}","int(cos(c + d*x)^6/(a + a*sin(c + d*x)),x)","\frac{3\,x}{8\,a}+\frac{-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{2}{5}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(3*x)/(8*a) + ((5*tan(c/2 + (d*x)/2))/4 + tan(c/2 + (d*x)/2)^3/2 + 4*tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)^7/2 + 2*tan(c/2 + (d*x)/2)^8 - (5*tan(c/2 + (d*x)/2)^9)/4 + 2/5)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
52,1,54,47,4.659850,"\text{Not used}","int(cos(c + d*x)^5/(a + a*sin(c + d*x)),x)","\frac{\frac{\sin\left(c+d\,x\right)}{a}-\frac{{\sin\left(c+d\,x\right)}^2}{2\,a}-\frac{{\sin\left(c+d\,x\right)}^3}{3\,a}+\frac{{\sin\left(c+d\,x\right)}^4}{4\,a}}{d}","Not used",1,"(sin(c + d*x)/a - sin(c + d*x)^2/(2*a) - sin(c + d*x)^3/(3*a) + sin(c + d*x)^4/(4*a))/d","B"
53,1,66,49,6.873548,"\text{Not used}","int(cos(c + d*x)^4/(a + a*sin(c + d*x)),x)","\frac{x}{2\,a}+\frac{-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{2}{3}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^3}","Not used",1,"x/(2*a) + (tan(c/2 + (d*x)/2) + 2*tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)^5 + 2/3)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^3)","B"
54,1,22,32,4.487546,"\text{Not used}","int(cos(c + d*x)^3/(a + a*sin(c + d*x)),x)","-\frac{\sin\left(c+d\,x\right)\,\left(\sin\left(c+d\,x\right)-2\right)}{2\,a\,d}","Not used",1,"-(sin(c + d*x)*(sin(c + d*x) - 2))/(2*a*d)","B"
55,1,29,19,4.531607,"\text{Not used}","int(cos(c + d*x)^2/(a + a*sin(c + d*x)),x)","\frac{x}{a}+\frac{2}{a\,d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"x/a + 2/(a*d*(tan(c/2 + (d*x)/2)^2 + 1))","B"
56,1,16,16,0.042044,"\text{Not used}","int(cos(c + d*x)/(a + a*sin(c + d*x)),x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)}{a\,d}","Not used",1,"log(sin(c + d*x) + 1)/(a*d)","B"
57,1,33,37,0.066119,"\text{Not used}","int(1/(cos(c + d*x)*(a + a*sin(c + d*x))),x)","\frac{\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{2\,a\,d}-\frac{1}{2\,d\,\left(a+a\,\sin\left(c+d\,x\right)\right)}","Not used",1,"atanh(sin(c + d*x))/(2*a*d) - 1/(2*d*(a + a*sin(c + d*x)))","B"
58,1,71,42,4.560465,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + a*sin(c + d*x))),x)","-\frac{2\,\left(3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{3\,a\,d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^3}","Not used",1,"-(2*(tan(c/2 + (d*x)/2) + 3*tan(c/2 + (d*x)/2)^2 + 3*tan(c/2 + (d*x)/2)^3 - 1))/(3*a*d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2) + 1)^3)","B"
59,1,74,77,4.656334,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a*sin(c + d*x))),x)","\frac{3\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{8\,a\,d}+\frac{\frac{3\,{\sin\left(c+d\,x\right)}^2}{8}+\frac{3\,\sin\left(c+d\,x\right)}{8}-\frac{1}{4}}{d\,\left(-a\,{\sin\left(c+d\,x\right)}^3-a\,{\sin\left(c+d\,x\right)}^2+a\,\sin\left(c+d\,x\right)+a\right)}","Not used",1,"(3*atanh(sin(c + d*x)))/(8*a*d) + ((3*sin(c + d*x))/8 + (3*sin(c + d*x)^2)/8 - 1/4)/(d*(a + a*sin(c + d*x) - a*sin(c + d*x)^2 - a*sin(c + d*x)^3))","B"
60,1,125,62,5.940843,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + a*sin(c + d*x))),x)","-\frac{2\,\left(15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-25\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-3\right)}{15\,a\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^3\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^5}","Not used",1,"-(2*(9*tan(c/2 + (d*x)/2) + 21*tan(c/2 + (d*x)/2)^2 + 13*tan(c/2 + (d*x)/2)^3 - 25*tan(c/2 + (d*x)/2)^4 - 5*tan(c/2 + (d*x)/2)^5 + 15*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^7 - 3))/(15*a*d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)^5)","B"
61,1,115,120,0.142349,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + a*sin(c + d*x))),x)","\frac{5\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{16\,a\,d}-\frac{\frac{5\,{\sin\left(c+d\,x\right)}^4}{16}+\frac{5\,{\sin\left(c+d\,x\right)}^3}{16}-\frac{25\,{\sin\left(c+d\,x\right)}^2}{48}-\frac{25\,\sin\left(c+d\,x\right)}{48}+\frac{1}{6}}{d\,\left(a\,{\sin\left(c+d\,x\right)}^5+a\,{\sin\left(c+d\,x\right)}^4-2\,a\,{\sin\left(c+d\,x\right)}^3-2\,a\,{\sin\left(c+d\,x\right)}^2+a\,\sin\left(c+d\,x\right)+a\right)}","Not used",1,"(5*atanh(sin(c + d*x)))/(16*a*d) - ((5*sin(c + d*x)^3)/16 - (25*sin(c + d*x)^2)/48 - (25*sin(c + d*x))/48 + (5*sin(c + d*x)^4)/16 + 1/6)/(d*(a + a*sin(c + d*x) - 2*a*sin(c + d*x)^2 - 2*a*sin(c + d*x)^3 + a*sin(c + d*x)^4 + a*sin(c + d*x)^5))","B"
62,1,172,104,8.222539,"\text{Not used}","int(cos(c + d*x)^8/(a + a*sin(c + d*x))^2,x)","\frac{7\,x}{16\,a^2}+\frac{-\frac{9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-\frac{89\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{89\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{4}{5}}{a^2\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(7*x)/(16*a^2) + ((9*tan(c/2 + (d*x)/2))/8 + (4*tan(c/2 + (d*x)/2)^2)/5 + (89*tan(c/2 + (d*x)/2)^3)/24 + 8*tan(c/2 + (d*x)/2)^4 - (11*tan(c/2 + (d*x)/2)^5)/4 + 8*tan(c/2 + (d*x)/2)^6 + (11*tan(c/2 + (d*x)/2)^7)/4 + 4*tan(c/2 + (d*x)/2)^8 - (89*tan(c/2 + (d*x)/2)^9)/24 + 4*tan(c/2 + (d*x)/2)^10 - (9*tan(c/2 + (d*x)/2)^11)/8 + 4/5)/(a^2*d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
63,1,54,47,4.662251,"\text{Not used}","int(cos(c + d*x)^7/(a + a*sin(c + d*x))^2,x)","\frac{\frac{\sin\left(c+d\,x\right)}{a^2}-\frac{{\sin\left(c+d\,x\right)}^2}{a^2}+\frac{{\sin\left(c+d\,x\right)}^4}{2\,a^2}-\frac{{\sin\left(c+d\,x\right)}^5}{5\,a^2}}{d}","Not used",1,"(sin(c + d*x)/a^2 - sin(c + d*x)^2/a^2 + sin(c + d*x)^4/(2*a^2) - sin(c + d*x)^5/(5*a^2))/d","B"
64,1,65,80,4.746490,"\text{Not used}","int(cos(c + d*x)^6/(a + a*sin(c + d*x))^2,x)","\frac{5\,x}{8\,a^2}+\frac{2\,{\cos\left(c+d\,x\right)}^3}{3\,a^2\,d}-\frac{{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{4\,a^2\,d}+\frac{5\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,a^2\,d}","Not used",1,"(5*x)/(8*a^2) + (2*cos(c + d*x)^3)/(3*a^2*d) - (cos(c + d*x)^3*sin(c + d*x))/(4*a^2*d) + (5*cos(c + d*x)*sin(c + d*x))/(8*a^2*d)","B"
65,1,32,23,4.610005,"\text{Not used}","int(cos(c + d*x)^5/(a + a*sin(c + d*x))^2,x)","\frac{\sin\left(c+d\,x\right)\,\left({\sin\left(c+d\,x\right)}^2-3\,\sin\left(c+d\,x\right)+3\right)}{3\,a^2\,d}","Not used",1,"(sin(c + d*x)*(sin(c + d*x)^2 - 3*sin(c + d*x) + 3))/(3*a^2*d)","B"
66,1,32,56,4.652937,"\text{Not used}","int(cos(c + d*x)^4/(a + a*sin(c + d*x))^2,x)","\frac{4\,\cos\left(c+d\,x\right)-\frac{\sin\left(2\,c+2\,d\,x\right)}{2}+3\,d\,x}{2\,a^2\,d}","Not used",1,"(4*cos(c + d*x) - sin(2*c + 2*d*x)/2 + 3*d*x)/(2*a^2*d)","B"
67,1,27,32,0.060430,"\text{Not used}","int(cos(c + d*x)^3/(a + a*sin(c + d*x))^2,x)","\frac{2\,\ln\left(\sin\left(c+d\,x\right)+1\right)-\sin\left(c+d\,x\right)}{a^2\,d}","Not used",1,"(2*log(sin(c + d*x) + 1) - sin(c + d*x))/(a^2*d)","B"
68,1,28,34,4.640615,"\text{Not used}","int(cos(c + d*x)^2/(a + a*sin(c + d*x))^2,x)","-\frac{x}{a^2}-\frac{4}{a^2\,d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}","Not used",1,"- x/a^2 - 4/(a^2*d*(tan(c/2 + (d*x)/2) + 1))","B"
69,1,18,21,0.048498,"\text{Not used}","int(cos(c + d*x)/(a + a*sin(c + d*x))^2,x)","-\frac{1}{a^2\,d\,\left(\sin\left(c+d\,x\right)+1\right)}","Not used",1,"-1/(a^2*d*(sin(c + d*x) + 1))","B"
70,1,60,60,4.519317,"\text{Not used}","int(1/(cos(c + d*x)*(a + a*sin(c + d*x))^2),x)","\frac{\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{4\,a^2\,d}-\frac{\frac{\sin\left(c+d\,x\right)}{4}+\frac{1}{2}}{d\,\left(a^2\,{\sin\left(c+d\,x\right)}^2+2\,a^2\,\sin\left(c+d\,x\right)+a^2\right)}","Not used",1,"atanh(sin(c + d*x))/(4*a^2*d) - (sin(c + d*x)/4 + 1/2)/(d*(2*a^2*sin(c + d*x) + a^2 + a^2*sin(c + d*x)^2))","B"
71,1,156,71,4.769724,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + a*sin(c + d*x))^2),x)","\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+10\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+10\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}{5\,a^2\,d\,\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^5}","Not used",1,"(2*cos(c/2 + (d*x)/2)*(5*sin(c/2 + (d*x)/2)^5 - 2*cos(c/2 + (d*x)/2)^5 + 10*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^4 - 3*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2) + 10*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^3))/(5*a^2*d*(cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))*(cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2))^5)","B"
72,1,93,104,0.103154,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a*sin(c + d*x))^2),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^3}{4}+\frac{{\sin\left(c+d\,x\right)}^2}{2}+\frac{\sin\left(c+d\,x\right)}{12}-\frac{1}{3}}{d\,\left(-a^2\,{\sin\left(c+d\,x\right)}^4-2\,a^2\,{\sin\left(c+d\,x\right)}^3+2\,a^2\,\sin\left(c+d\,x\right)+a^2\right)}+\frac{\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{4\,a^2\,d}","Not used",1,"(sin(c + d*x)/12 + sin(c + d*x)^2/2 + sin(c + d*x)^3/4 - 1/3)/(d*(2*a^2*sin(c + d*x) + a^2 - 2*a^2*sin(c + d*x)^3 - a^2*sin(c + d*x)^4)) + atanh(sin(c + d*x))/(4*a^2*d)","B"
73,1,276,93,5.184056,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + a*sin(c + d*x))^2),x)","\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-6\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+76\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+28\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-42\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-56\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+42\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+21\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\right)}{21\,a^2\,d\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^3\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^7}","Not used",1,"(2*cos(c/2 + (d*x)/2)*(21*sin(c/2 + (d*x)/2)^9 - 6*cos(c/2 + (d*x)/2)^9 + 42*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^8 - 3*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2) + 28*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^7 - 56*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^6 - 42*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^5 + 28*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^4 + 76*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^3 + 24*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^2))/(21*a^2*d*(cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))^3*(cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2))^7)","B"
74,1,151,146,0.185604,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + a*sin(c + d*x))^2),x)","\frac{15\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{64\,a^2\,d}+\frac{-\frac{15\,{\sin\left(c+d\,x\right)}^5}{64}-\frac{15\,{\sin\left(c+d\,x\right)}^4}{32}+\frac{5\,{\sin\left(c+d\,x\right)}^3}{32}+\frac{25\,{\sin\left(c+d\,x\right)}^2}{32}+\frac{17\,\sin\left(c+d\,x\right)}{64}-\frac{1}{4}}{d\,\left(a^2\,{\sin\left(c+d\,x\right)}^6+2\,a^2\,{\sin\left(c+d\,x\right)}^5-a^2\,{\sin\left(c+d\,x\right)}^4-4\,a^2\,{\sin\left(c+d\,x\right)}^3-a^2\,{\sin\left(c+d\,x\right)}^2+2\,a^2\,\sin\left(c+d\,x\right)+a^2\right)}","Not used",1,"(15*atanh(sin(c + d*x)))/(64*a^2*d) + ((17*sin(c + d*x))/64 + (25*sin(c + d*x)^2)/32 + (5*sin(c + d*x)^3)/32 - (15*sin(c + d*x)^4)/32 - (15*sin(c + d*x)^5)/64 - 1/4)/(d*(2*a^2*sin(c + d*x) + a^2 - a^2*sin(c + d*x)^2 - 4*a^2*sin(c + d*x)^3 - a^2*sin(c + d*x)^4 + 2*a^2*sin(c + d*x)^5 + a^2*sin(c + d*x)^6))","B"
75,1,81,103,4.721153,"\text{Not used}","int(cos(c + d*x)^8/(a + a*sin(c + d*x))^3,x)","\frac{7\,x}{8\,a^3}+\frac{4\,{\cos\left(c+d\,x\right)}^3}{3\,a^3\,d}-\frac{{\cos\left(c+d\,x\right)}^5}{5\,a^3\,d}-\frac{3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{4\,a^3\,d}+\frac{7\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,a^3\,d}","Not used",1,"(7*x)/(8*a^3) + (4*cos(c + d*x)^3)/(3*a^3*d) - cos(c + d*x)^5/(5*a^3*d) - (3*cos(c + d*x)^3*sin(c + d*x))/(4*a^3*d) + (7*cos(c + d*x)*sin(c + d*x))/(8*a^3*d)","B"
76,1,53,23,4.548488,"\text{Not used}","int(cos(c + d*x)^7/(a + a*sin(c + d*x))^3,x)","\frac{\frac{\sin\left(c+d\,x\right)}{a^3}-\frac{3\,{\sin\left(c+d\,x\right)}^2}{2\,a^3}+\frac{{\sin\left(c+d\,x\right)}^3}{a^3}-\frac{{\sin\left(c+d\,x\right)}^4}{4\,a^3}}{d}","Not used",1,"(sin(c + d*x)/a^3 - (3*sin(c + d*x)^2)/(2*a^3) + sin(c + d*x)^3/a^3 - sin(c + d*x)^4/(4*a^3))/d","B"
77,1,57,77,4.637797,"\text{Not used}","int(cos(c + d*x)^6/(a + a*sin(c + d*x))^3,x)","\frac{5\,x}{2\,a^3}+\frac{4\,\cos\left(c+d\,x\right)}{a^3\,d}-\frac{{\cos\left(c+d\,x\right)}^3}{3\,a^3\,d}-\frac{3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,a^3\,d}","Not used",1,"(5*x)/(2*a^3) + (4*cos(c + d*x))/(a^3*d) - cos(c + d*x)^3/(3*a^3*d) - (3*cos(c + d*x)*sin(c + d*x))/(2*a^3*d)","B"
78,1,36,50,4.560418,"\text{Not used}","int(cos(c + d*x)^5/(a + a*sin(c + d*x))^3,x)","\frac{8\,\ln\left(\sin\left(c+d\,x\right)+1\right)-6\,\sin\left(c+d\,x\right)+{\sin\left(c+d\,x\right)}^2}{2\,a^3\,d}","Not used",1,"(8*log(sin(c + d*x) + 1) - 6*sin(c + d*x) + sin(c + d*x)^2)/(2*a^3*d)","B"
79,1,69,49,4.851815,"\text{Not used}","int(cos(c + d*x)^4/(a + a*sin(c + d*x))^3,x)","-\frac{3\,x}{a^3}-\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+10}{a^3\,d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"- (3*x)/a^3 - (2*tan(c/2 + (d*x)/2) + 8*tan(c/2 + (d*x)/2)^2 + 10)/(a^3*d*(tan(c/2 + (d*x)/2) + 1)*(tan(c/2 + (d*x)/2)^2 + 1))","B"
80,1,36,39,4.542975,"\text{Not used}","int(cos(c + d*x)^3/(a + a*sin(c + d*x))^3,x)","-\frac{2}{a^3\,d\,\left(\sin\left(c+d\,x\right)+1\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)}{a^3\,d}","Not used",1,"- 2/(a^3*d*(sin(c + d*x) + 1)) - log(sin(c + d*x) + 1)/(a^3*d)","B"
81,1,53,27,4.580147,"\text{Not used}","int(cos(c + d*x)^2/(a + a*sin(c + d*x))^3,x)","\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-3\right)}{3\,a^3\,d\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^3}","Not used",1,"(2*cos(c/2 + (d*x)/2)*(2*cos(c/2 + (d*x)/2)^2 - 3))/(3*a^3*d*(cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2))^3)","B"
82,1,18,22,4.460078,"\text{Not used}","int(cos(c + d*x)/(a + a*sin(c + d*x))^3,x)","-\frac{1}{2\,a^3\,d\,{\left(\sin\left(c+d\,x\right)+1\right)}^2}","Not used",1,"-1/(2*a^3*d*(sin(c + d*x) + 1)^2)","B"
83,1,83,82,4.594829,"\text{Not used}","int(1/(cos(c + d*x)*(a + a*sin(c + d*x))^3),x)","\frac{\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{8\,a^3\,d}-\frac{\frac{{\sin\left(c+d\,x\right)}^2}{8}+\frac{3\,\sin\left(c+d\,x\right)}{8}+\frac{5}{12}}{d\,\left(a^3\,{\sin\left(c+d\,x\right)}^3+3\,a^3\,{\sin\left(c+d\,x\right)}^2+3\,a^3\,\sin\left(c+d\,x\right)+a^3\right)}","Not used",1,"atanh(sin(c + d*x))/(8*a^3*d) - ((3*sin(c + d*x))/8 + sin(c + d*x)^2/8 + 5/12)/(d*(3*a^3*sin(c + d*x) + a^3 + 3*a^3*sin(c + d*x)^2 + a^3*sin(c + d*x)^3))","B"
84,1,228,99,5.079214,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + a*sin(c + d*x))^3),x)","-\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(13\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+43\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+77\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+7\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-175\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-105\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-35\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\right)}{35\,a^3\,d\,\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^7}","Not used",1,"-(2*cos(c/2 + (d*x)/2)*(13*cos(c/2 + (d*x)/2)^7 - 35*sin(c/2 + (d*x)/2)^7 - 105*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^6 + 43*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2) - 175*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^5 - 105*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^4 + 7*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^3 + 77*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^2))/(35*a^3*d*(cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))*(cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2))^7)","B"
85,1,129,126,0.148679,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a*sin(c + d*x))^3),x)","\frac{5\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{32\,a^3\,d}+\frac{\frac{5\,{\sin\left(c+d\,x\right)}^4}{32}+\frac{15\,{\sin\left(c+d\,x\right)}^3}{32}+\frac{35\,{\sin\left(c+d\,x\right)}^2}{96}-\frac{5\,\sin\left(c+d\,x\right)}{32}-\frac{1}{3}}{d\,\left(-a^3\,{\sin\left(c+d\,x\right)}^5-3\,a^3\,{\sin\left(c+d\,x\right)}^4-2\,a^3\,{\sin\left(c+d\,x\right)}^3+2\,a^3\,{\sin\left(c+d\,x\right)}^2+3\,a^3\,\sin\left(c+d\,x\right)+a^3\right)}","Not used",1,"(5*atanh(sin(c + d*x)))/(32*a^3*d) + ((35*sin(c + d*x)^2)/96 - (5*sin(c + d*x))/32 + (15*sin(c + d*x)^3)/32 + (5*sin(c + d*x)^4)/32 - 1/3)/(d*(3*a^3*sin(c + d*x) + a^3 + 2*a^3*sin(c + d*x)^2 - 2*a^3*sin(c + d*x)^3 - 3*a^3*sin(c + d*x)^4 - a^3*sin(c + d*x)^5))","B"
86,1,167,123,5.563184,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + a*sin(c + d*x))^3),x)","\frac{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{63\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{8}-\frac{171\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}-\frac{145\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{16}+\frac{49\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{16}+\frac{\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{2}+\frac{617\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}-\frac{329\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{16}+\frac{145\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{32}-\frac{113\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{32}-\frac{115\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{32}+\frac{19\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{32}\right)}{2016\,a^3\,d\,{\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)}^9\,{\cos\left(\frac{c}{2}+\frac{\pi }{4}+\frac{d\,x}{2}\right)}^3}","Not used",1,"(cos(c/2 + (d*x)/2)*((63*cos((5*c)/2 + (5*d*x)/2))/8 - (171*cos((3*c)/2 + (3*d*x)/2))/8 - (145*cos((7*c)/2 + (7*d*x)/2))/16 + (49*cos((9*c)/2 + (9*d*x)/2))/16 + cos((11*c)/2 + (11*d*x)/2)/2 + (617*sin(c/2 + (d*x)/2))/16 - (329*sin((3*c)/2 + (3*d*x)/2))/16 + (145*sin((5*c)/2 + (5*d*x)/2))/32 - (113*sin((7*c)/2 + (7*d*x)/2))/32 - (115*sin((9*c)/2 + (9*d*x)/2))/32 + (19*sin((11*c)/2 + (11*d*x)/2))/32))/(2016*a^3*d*cos(c/2 - pi/4 + (d*x)/2)^9*cos(c/2 + pi/4 + (d*x)/2)^3)","B"
87,1,173,171,4.765125,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + a*sin(c + d*x))^3),x)","\frac{21\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{128\,a^3\,d}-\frac{\frac{21\,{\sin\left(c+d\,x\right)}^6}{128}+\frac{63\,{\sin\left(c+d\,x\right)}^5}{128}+\frac{7\,{\sin\left(c+d\,x\right)}^4}{32}-\frac{21\,{\sin\left(c+d\,x\right)}^3}{32}-\frac{469\,{\sin\left(c+d\,x\right)}^2}{640}-\frac{7\,\sin\left(c+d\,x\right)}{640}+\frac{11}{40}}{d\,\left(a^3\,{\sin\left(c+d\,x\right)}^7+3\,a^3\,{\sin\left(c+d\,x\right)}^6+a^3\,{\sin\left(c+d\,x\right)}^5-5\,a^3\,{\sin\left(c+d\,x\right)}^4-5\,a^3\,{\sin\left(c+d\,x\right)}^3+a^3\,{\sin\left(c+d\,x\right)}^2+3\,a^3\,\sin\left(c+d\,x\right)+a^3\right)}","Not used",1,"(21*atanh(sin(c + d*x)))/(128*a^3*d) - ((7*sin(c + d*x)^4)/32 - (469*sin(c + d*x)^2)/640 - (21*sin(c + d*x)^3)/32 - (7*sin(c + d*x))/640 + (63*sin(c + d*x)^5)/128 + (21*sin(c + d*x)^6)/128 + 11/40)/(d*(3*a^3*sin(c + d*x) + a^3 + a^3*sin(c + d*x)^2 - 5*a^3*sin(c + d*x)^3 - 5*a^3*sin(c + d*x)^4 + a^3*sin(c + d*x)^5 + 3*a^3*sin(c + d*x)^6 + a^3*sin(c + d*x)^7))","B"
88,1,91,127,7.769975,"\text{Not used}","int(cos(c + d*x)^8/(a + a*sin(c + d*x))^8,x)","\frac{x}{a^8}+\frac{16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{80\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{224\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{224\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\frac{304\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}+\frac{304}{105}}{a^8\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^7}","Not used",1,"x/a^8 + ((304*tan(c/2 + (d*x)/2))/15 + (224*tan(c/2 + (d*x)/2)^2)/5 + (224*tan(c/2 + (d*x)/2)^3)/3 + (80*tan(c/2 + (d*x)/2)^4)/3 + 16*tan(c/2 + (d*x)/2)^5 + 304/105)/(a^8*d*(tan(c/2 + (d*x)/2) + 1)^7)","B"
89,1,64,36,0.072207,"\text{Not used}","int(cos(c + d*x)^7/(a + a*sin(c + d*x))^8,x)","\frac{\frac{1}{a^8\,\left(\sin\left(c+d\,x\right)+1\right)}-\frac{3}{a^8\,{\left(\sin\left(c+d\,x\right)+1\right)}^2}+\frac{4}{a^8\,{\left(\sin\left(c+d\,x\right)+1\right)}^3}-\frac{2}{a^8\,{\left(\sin\left(c+d\,x\right)+1\right)}^4}}{d}","Not used",1,"(1/(a^8*(sin(c + d*x) + 1)) - 3/(a^8*(sin(c + d*x) + 1)^2) + 4/(a^8*(sin(c + d*x) + 1)^3) - 2/(a^8*(sin(c + d*x) + 1)^4))/d","B"
90,1,118,58,6.627925,"\text{Not used}","int(cos(c + d*x)^6/(a + a*sin(c + d*x))^8,x)","-\frac{\sqrt{2}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{63\,\sin\left(c+d\,x\right)}{2}-\frac{257\,\cos\left(c+d\,x\right)}{8}-\frac{113\,\cos\left(2\,c+2\,d\,x\right)}{4}+\frac{37\,\cos\left(3\,c+3\,d\,x\right)}{8}+\frac{7\,\cos\left(4\,c+4\,d\,x\right)}{16}-\frac{63\,\sin\left(2\,c+2\,d\,x\right)}{8}-\frac{9\,\sin\left(3\,c+3\,d\,x\right)}{2}+\frac{9\,\sin\left(4\,c+4\,d\,x\right)}{16}+\frac{1013}{16}\right)}{1008\,a^8\,d\,{\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)}^9}","Not used",1,"-(2^(1/2)*cos(c/2 + (d*x)/2)*((63*sin(c + d*x))/2 - (257*cos(c + d*x))/8 - (113*cos(2*c + 2*d*x))/4 + (37*cos(3*c + 3*d*x))/8 + (7*cos(4*c + 4*d*x))/16 - (63*sin(2*c + 2*d*x))/8 - (9*sin(3*c + 3*d*x))/2 + (9*sin(4*c + 4*d*x))/16 + 1013/16))/(1008*a^8*d*cos(c/2 - pi/4 + (d*x)/2)^9)","B"
91,1,54,65,4.711760,"\text{Not used}","int(cos(c + d*x)^5/(a + a*sin(c + d*x))^8,x)","\frac{1}{a^8\,d\,{\left(\sin\left(c+d\,x\right)+1\right)}^4}-\frac{1}{3\,a^8\,d\,{\left(\sin\left(c+d\,x\right)+1\right)}^3}-\frac{4}{5\,a^8\,d\,{\left(\sin\left(c+d\,x\right)+1\right)}^5}","Not used",1,"1/(a^8*d*(sin(c + d*x) + 1)^4) - 1/(3*a^8*d*(sin(c + d*x) + 1)^3) - 4/(5*a^8*d*(sin(c + d*x) + 1)^5)","B"
92,1,140,118,7.147612,"\text{Not used}","int(cos(c + d*x)^4/(a + a*sin(c + d*x))^8,x)","-\frac{\sqrt{2}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{7623\,\sin\left(c+d\,x\right)}{4}-697\,\cos\left(c+d\,x\right)-\frac{3977\,\cos\left(2\,c+2\,d\,x\right)}{4}+\frac{3203\,\cos\left(3\,c+3\,d\,x\right)}{16}+\frac{461\,\cos\left(4\,c+4\,d\,x\right)}{8}-\frac{75\,\cos\left(5\,c+5\,d\,x\right)}{16}-462\,\sin\left(2\,c+2\,d\,x\right)-\frac{4983\,\sin\left(3\,c+3\,d\,x\right)}{16}+\frac{187\,\sin\left(4\,c+4\,d\,x\right)}{4}+\frac{77\,\sin\left(5\,c+5\,d\,x\right)}{16}+\frac{12721}{8}\right)}{36960\,a^8\,d\,{\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)}^{11}}","Not used",1,"-(2^(1/2)*cos(c/2 + (d*x)/2)*((7623*sin(c + d*x))/4 - 697*cos(c + d*x) - (3977*cos(2*c + 2*d*x))/4 + (3203*cos(3*c + 3*d*x))/16 + (461*cos(4*c + 4*d*x))/8 - (75*cos(5*c + 5*d*x))/16 - 462*sin(2*c + 2*d*x) - (4983*sin(3*c + 3*d*x))/16 + (187*sin(4*c + 4*d*x))/4 + (77*sin(5*c + 5*d*x))/16 + 12721/8))/(36960*a^8*d*cos(c/2 - pi/4 + (d*x)/2)^11)","B"
93,1,28,45,0.097477,"\text{Not used}","int(cos(c + d*x)^3/(a + a*sin(c + d*x))^8,x)","\frac{3\,\sin\left(c+d\,x\right)-2}{15\,a^8\,d\,{\left(\sin\left(c+d\,x\right)+1\right)}^6}","Not used",1,"(3*sin(c + d*x) - 2)/(15*a^8*d*(sin(c + d*x) + 1)^6)","B"
94,1,162,183,8.117172,"\text{Not used}","int(cos(c + d*x)^2/(a + a*sin(c + d*x))^8,x)","\frac{\sqrt{2}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{14983\,\cos\left(c+d\,x\right)}{2}-\frac{63921\,\sin\left(c+d\,x\right)}{2}+17605\,\cos\left(2\,c+2\,d\,x\right)-\frac{15365\,\cos\left(3\,c+3\,d\,x\right)}{4}-\frac{6943\,\cos\left(4\,c+4\,d\,x\right)}{4}+\frac{937\,\cos\left(5\,c+5\,d\,x\right)}{4}+\frac{77\,\cos\left(6\,c+6\,d\,x\right)}{4}+\frac{28743\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{27027\,\sin\left(3\,c+3\,d\,x\right)}{4}-\frac{5005\,\sin\left(4\,c+4\,d\,x\right)}{4}-\frac{1079\,\sin\left(5\,c+5\,d\,x\right)}{4}+\frac{39\,\sin\left(6\,c+6\,d\,x\right)}{2}-21013\right)}{576576\,a^8\,d\,{\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)}^{13}}","Not used",1,"(2^(1/2)*cos(c/2 + (d*x)/2)*((14983*cos(c + d*x))/2 - (63921*sin(c + d*x))/2 + 17605*cos(2*c + 2*d*x) - (15365*cos(3*c + 3*d*x))/4 - (6943*cos(4*c + 4*d*x))/4 + (937*cos(5*c + 5*d*x))/4 + (77*cos(6*c + 6*d*x))/4 + (28743*sin(2*c + 2*d*x))/4 + (27027*sin(3*c + 3*d*x))/4 - (5005*sin(4*c + 4*d*x))/4 - (1079*sin(5*c + 5*d*x))/4 + (39*sin(6*c + 6*d*x))/2 - 21013))/(576576*a^8*d*cos(c/2 - pi/4 + (d*x)/2)^13)","B"
95,1,18,22,4.667549,"\text{Not used}","int(cos(c + d*x)/(a + a*sin(c + d*x))^8,x)","-\frac{1}{7\,a^8\,d\,{\left(\sin\left(c+d\,x\right)+1\right)}^7}","Not used",1,"-1/(7*a^8*d*(sin(c + d*x) + 1)^7)","B"
96,1,198,194,0.303490,"\text{Not used}","int(1/(cos(c + d*x)*(a + a*sin(c + d*x))^8),x)","\frac{\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{256\,a^8\,d}-\frac{\frac{{\sin\left(c+d\,x\right)}^7}{256}+\frac{{\sin\left(c+d\,x\right)}^6}{32}+\frac{85\,{\sin\left(c+d\,x\right)}^5}{768}+\frac{11\,{\sin\left(c+d\,x\right)}^4}{48}+\frac{1193\,{\sin\left(c+d\,x\right)}^3}{3840}+\frac{143\,{\sin\left(c+d\,x\right)}^2}{480}+\frac{5993\,\sin\left(c+d\,x\right)}{26880}+\frac{16}{105}}{d\,\left(a^8\,{\sin\left(c+d\,x\right)}^8+8\,a^8\,{\sin\left(c+d\,x\right)}^7+28\,a^8\,{\sin\left(c+d\,x\right)}^6+56\,a^8\,{\sin\left(c+d\,x\right)}^5+70\,a^8\,{\sin\left(c+d\,x\right)}^4+56\,a^8\,{\sin\left(c+d\,x\right)}^3+28\,a^8\,{\sin\left(c+d\,x\right)}^2+8\,a^8\,\sin\left(c+d\,x\right)+a^8\right)}","Not used",1,"atanh(sin(c + d*x))/(256*a^8*d) - ((5993*sin(c + d*x))/26880 + (143*sin(c + d*x)^2)/480 + (1193*sin(c + d*x)^3)/3840 + (11*sin(c + d*x)^4)/48 + (85*sin(c + d*x)^5)/768 + sin(c + d*x)^6/32 + sin(c + d*x)^7/256 + 16/105)/(d*(8*a^8*sin(c + d*x) + a^8 + 28*a^8*sin(c + d*x)^2 + 56*a^8*sin(c + d*x)^3 + 70*a^8*sin(c + d*x)^4 + 56*a^8*sin(c + d*x)^5 + 28*a^8*sin(c + d*x)^6 + 8*a^8*sin(c + d*x)^7 + a^8*sin(c + d*x)^8))","B"
97,1,233,245,8.035404,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + a*sin(c + d*x))^8),x)","\frac{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{519571\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{16}-\frac{576147\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{16}+\frac{213707\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{16}-\frac{183243\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{16}-\frac{18207\,\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{16}+\frac{13855\,\cos\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)}{16}+\frac{493\,\cos\left(\frac{15\,c}{2}+\frac{15\,d\,x}{2}\right)}{32}-\frac{237\,\cos\left(\frac{17\,c}{2}+\frac{17\,d\,x}{2}\right)}{32}+\frac{56425\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}-\frac{51563\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{2}-\frac{53191\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{2}+\frac{47003\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{2}+\frac{9403\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{2}-\frac{7703\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{2}-\frac{355\,\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)}{2}+118\,\sin\left(\frac{15\,c}{2}+\frac{15\,d\,x}{2}\right)+\frac{\sin\left(\frac{17\,c}{2}+\frac{17\,d\,x}{2}\right)}{2}\right)}{3111680\,a^8\,d\,{\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)}^{17}\,\cos\left(\frac{c}{2}+\frac{\pi }{4}+\frac{d\,x}{2}\right)}","Not used",1,"(cos(c/2 + (d*x)/2)*((519571*cos((5*c)/2 + (5*d*x)/2))/16 - (576147*cos((3*c)/2 + (3*d*x)/2))/16 + (213707*cos((7*c)/2 + (7*d*x)/2))/16 - (183243*cos((9*c)/2 + (9*d*x)/2))/16 - (18207*cos((11*c)/2 + (11*d*x)/2))/16 + (13855*cos((13*c)/2 + (13*d*x)/2))/16 + (493*cos((15*c)/2 + (15*d*x)/2))/32 - (237*cos((17*c)/2 + (17*d*x)/2))/32 + (56425*sin(c/2 + (d*x)/2))/2 - (51563*sin((3*c)/2 + (3*d*x)/2))/2 - (53191*sin((5*c)/2 + (5*d*x)/2))/2 + (47003*sin((7*c)/2 + (7*d*x)/2))/2 + (9403*sin((9*c)/2 + (9*d*x)/2))/2 - (7703*sin((11*c)/2 + (11*d*x)/2))/2 - (355*sin((13*c)/2 + (13*d*x)/2))/2 + 118*sin((15*c)/2 + (15*d*x)/2) + sin((17*c)/2 + (17*d*x)/2)/2))/(3111680*a^8*d*cos(c/2 - pi/4 + (d*x)/2)^17*cos(c/2 + pi/4 + (d*x)/2))","B"
98,1,231,238,0.488853,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a*sin(c + d*x))^8),x)","\frac{\frac{5\,{\sin\left(c+d\,x\right)}^9}{512}+\frac{5\,{\sin\left(c+d\,x\right)}^8}{64}+\frac{205\,{\sin\left(c+d\,x\right)}^7}{768}+\frac{95\,{\sin\left(c+d\,x\right)}^6}{192}+\frac{{\sin\left(c+d\,x\right)}^5}{2}+\frac{11\,{\sin\left(c+d\,x\right)}^4}{64}-\frac{393\,{\sin\left(c+d\,x\right)}^3}{1792}-\frac{163\,{\sin\left(c+d\,x\right)}^2}{448}-\frac{9019\,\sin\left(c+d\,x\right)}{32256}-\frac{10}{63}}{d\,\left(-a^8\,{\sin\left(c+d\,x\right)}^{10}-8\,a^8\,{\sin\left(c+d\,x\right)}^9-27\,a^8\,{\sin\left(c+d\,x\right)}^8-48\,a^8\,{\sin\left(c+d\,x\right)}^7-42\,a^8\,{\sin\left(c+d\,x\right)}^6+42\,a^8\,{\sin\left(c+d\,x\right)}^4+48\,a^8\,{\sin\left(c+d\,x\right)}^3+27\,a^8\,{\sin\left(c+d\,x\right)}^2+8\,a^8\,\sin\left(c+d\,x\right)+a^8\right)}+\frac{5\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{512\,a^8\,d}","Not used",1,"((11*sin(c + d*x)^4)/64 - (163*sin(c + d*x)^2)/448 - (393*sin(c + d*x)^3)/1792 - (9019*sin(c + d*x))/32256 + sin(c + d*x)^5/2 + (95*sin(c + d*x)^6)/192 + (205*sin(c + d*x)^7)/768 + (5*sin(c + d*x)^8)/64 + (5*sin(c + d*x)^9)/512 - 10/63)/(d*(8*a^8*sin(c + d*x) + a^8 + 27*a^8*sin(c + d*x)^2 + 48*a^8*sin(c + d*x)^3 + 42*a^8*sin(c + d*x)^4 - 42*a^8*sin(c + d*x)^6 - 48*a^8*sin(c + d*x)^7 - 27*a^8*sin(c + d*x)^8 - 8*a^8*sin(c + d*x)^9 - a^8*sin(c + d*x)^10)) + (5*atanh(sin(c + d*x)))/(512*a^8*d)","B"
99,1,277,279,9.230880,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + a*sin(c + d*x))^8),x)","\frac{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{896971\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{64}-\frac{1062347\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{64}-\frac{40375\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{16}+\frac{40375\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{16}+\frac{412471\,\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{128}-\frac{324919\,\cos\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)}{128}-\frac{11305\,\cos\left(\frac{15\,c}{2}+\frac{15\,d\,x}{2}\right)}{32}+\frac{7209\,\cos\left(\frac{17\,c}{2}+\frac{17\,d\,x}{2}\right)}{32}+\frac{765\,\cos\left(\frac{19\,c}{2}+\frac{19\,d\,x}{2}\right)}{128}-\frac{253\,\cos\left(\frac{21\,c}{2}+\frac{21\,d\,x}{2}\right)}{128}+\frac{65033\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}-\frac{56635\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{4}-6271\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)+\frac{9635\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{2}-\frac{9635\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{2}+\frac{16363\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{4}+\frac{10537\,\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)}{8}-\frac{7611\,\sin\left(\frac{15\,c}{2}+\frac{15\,d\,x}{2}\right)}{8}-\frac{485\,\sin\left(\frac{17\,c}{2}+\frac{17\,d\,x}{2}\right)}{8}+\frac{251\,\sin\left(\frac{19\,c}{2}+\frac{19\,d\,x}{2}\right)}{8}+\frac{\sin\left(\frac{21\,c}{2}+\frac{21\,d\,x}{2}\right)}{4}\right)}{12899328\,a^8\,d\,{\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)}^{19}\,{\cos\left(\frac{c}{2}+\frac{\pi }{4}+\frac{d\,x}{2}\right)}^3}","Not used",1,"(cos(c/2 + (d*x)/2)*((896971*cos((5*c)/2 + (5*d*x)/2))/64 - (1062347*cos((3*c)/2 + (3*d*x)/2))/64 - (40375*cos((7*c)/2 + (7*d*x)/2))/16 + (40375*cos((9*c)/2 + (9*d*x)/2))/16 + (412471*cos((11*c)/2 + (11*d*x)/2))/128 - (324919*cos((13*c)/2 + (13*d*x)/2))/128 - (11305*cos((15*c)/2 + (15*d*x)/2))/32 + (7209*cos((17*c)/2 + (17*d*x)/2))/32 + (765*cos((19*c)/2 + (19*d*x)/2))/128 - (253*cos((21*c)/2 + (21*d*x)/2))/128 + (65033*sin(c/2 + (d*x)/2))/4 - (56635*sin((3*c)/2 + (3*d*x)/2))/4 - 6271*sin((5*c)/2 + (5*d*x)/2) + (9635*sin((7*c)/2 + (7*d*x)/2))/2 - (9635*sin((9*c)/2 + (9*d*x)/2))/2 + (16363*sin((11*c)/2 + (11*d*x)/2))/4 + (10537*sin((13*c)/2 + (13*d*x)/2))/8 - (7611*sin((15*c)/2 + (15*d*x)/2))/8 - (485*sin((17*c)/2 + (17*d*x)/2))/8 + (251*sin((19*c)/2 + (19*d*x)/2))/8 + sin((21*c)/2 + (21*d*x)/2)/4))/(12899328*a^8*d*cos(c/2 - pi/4 + (d*x)/2)^19*cos(c/2 + pi/4 + (d*x)/2)^3)","B"
100,1,290,284,0.797937,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + a*sin(c + d*x))^8),x)","\frac{33\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{2048\,a^8\,d}-\frac{\frac{33\,{\sin\left(c+d\,x\right)}^{11}}{2048}+\frac{33\,{\sin\left(c+d\,x\right)}^{10}}{256}+\frac{869\,{\sin\left(c+d\,x\right)}^9}{2048}+\frac{11\,{\sin\left(c+d\,x\right)}^8}{16}+\frac{1969\,{\sin\left(c+d\,x\right)}^7}{5120}-\frac{341\,{\sin\left(c+d\,x\right)}^6}{640}-\frac{42537\,{\sin\left(c+d\,x\right)}^5}{35840}-\frac{99\,{\sin\left(c+d\,x\right)}^4}{112}-\frac{4279\,{\sin\left(c+d\,x\right)}^3}{43008}+\frac{9097\,{\sin\left(c+d\,x\right)}^2}{26880}+\frac{66953\,\sin\left(c+d\,x\right)}{215040}+\frac{17}{105}}{d\,\left(a^8\,{\sin\left(c+d\,x\right)}^{12}+8\,a^8\,{\sin\left(c+d\,x\right)}^{11}+26\,a^8\,{\sin\left(c+d\,x\right)}^{10}+40\,a^8\,{\sin\left(c+d\,x\right)}^9+15\,a^8\,{\sin\left(c+d\,x\right)}^8-48\,a^8\,{\sin\left(c+d\,x\right)}^7-84\,a^8\,{\sin\left(c+d\,x\right)}^6-48\,a^8\,{\sin\left(c+d\,x\right)}^5+15\,a^8\,{\sin\left(c+d\,x\right)}^4+40\,a^8\,{\sin\left(c+d\,x\right)}^3+26\,a^8\,{\sin\left(c+d\,x\right)}^2+8\,a^8\,\sin\left(c+d\,x\right)+a^8\right)}","Not used",1,"(33*atanh(sin(c + d*x)))/(2048*a^8*d) - ((66953*sin(c + d*x))/215040 + (9097*sin(c + d*x)^2)/26880 - (4279*sin(c + d*x)^3)/43008 - (99*sin(c + d*x)^4)/112 - (42537*sin(c + d*x)^5)/35840 - (341*sin(c + d*x)^6)/640 + (1969*sin(c + d*x)^7)/5120 + (11*sin(c + d*x)^8)/16 + (869*sin(c + d*x)^9)/2048 + (33*sin(c + d*x)^10)/256 + (33*sin(c + d*x)^11)/2048 + 17/105)/(d*(8*a^8*sin(c + d*x) + a^8 + 26*a^8*sin(c + d*x)^2 + 40*a^8*sin(c + d*x)^3 + 15*a^8*sin(c + d*x)^4 - 48*a^8*sin(c + d*x)^5 - 84*a^8*sin(c + d*x)^6 - 48*a^8*sin(c + d*x)^7 + 15*a^8*sin(c + d*x)^8 + 40*a^8*sin(c + d*x)^9 + 26*a^8*sin(c + d*x)^10 + 8*a^8*sin(c + d*x)^11 + a^8*sin(c + d*x)^12))","B"
101,0,-1,97,0.000000,"\text{Not used}","int(cos(c + d*x)^7*(a + a*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^7\,\sqrt{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^7*(a + a*sin(c + d*x))^(1/2), x)","F"
102,0,-1,127,0.000000,"\text{Not used}","int(cos(c + d*x)^6*(a + a*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^6\,\sqrt{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^6*(a + a*sin(c + d*x))^(1/2), x)","F"
103,0,-1,73,0.000000,"\text{Not used}","int(cos(c + d*x)^5*(a + a*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^5\,\sqrt{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^5*(a + a*sin(c + d*x))^(1/2), x)","F"
104,0,-1,95,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\sqrt{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2), x)","F"
105,0,-1,49,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + a*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\sqrt{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^3*(a + a*sin(c + d*x))^(1/2), x)","F"
106,0,-1,63,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + a*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\sqrt{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^2*(a + a*sin(c + d*x))^(1/2), x)","F"
107,1,20,24,4.565528,"\text{Not used}","int(cos(c + d*x)*(a + a*sin(c + d*x))^(1/2),x)","\frac{2\,{\left(a\,\left(\sin\left(c+d\,x\right)+1\right)\right)}^{3/2}}{3\,a\,d}","Not used",1,"(2*(a*(sin(c + d*x) + 1))^(3/2))/(3*a*d)","B"
108,0,-1,40,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(1/2)/cos(c + d*x),x)","\int \frac{\sqrt{a+a\,\sin\left(c+d\,x\right)}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(1/2)/cos(c + d*x), x)","F"
109,0,-1,72,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(1/2)/cos(c + d*x)^2,x)","\int \frac{\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(1/2)/cos(c + d*x)^2, x)","F"
110,0,-1,95,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(1/2)/cos(c + d*x)^3,x)","\int \frac{\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(1/2)/cos(c + d*x)^3, x)","F"
111,0,-1,137,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(1/2)/cos(c + d*x)^4,x)","\int \frac{\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(1/2)/cos(c + d*x)^4, x)","F"
112,0,-1,149,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(1/2)/cos(c + d*x)^5,x)","\int \frac{\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(1/2)/cos(c + d*x)^5, x)","F"
113,0,-1,197,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(1/2)/cos(c + d*x)^6,x)","\int \frac{\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^6} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(1/2)/cos(c + d*x)^6, x)","F"
114,0,-1,97,0.000000,"\text{Not used}","int(cos(c + d*x)^7*(a + a*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^7\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^7*(a + a*sin(c + d*x))^(3/2), x)","F"
115,0,-1,159,0.000000,"\text{Not used}","int(cos(c + d*x)^6*(a + a*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^6\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^6*(a + a*sin(c + d*x))^(3/2), x)","F"
116,0,-1,73,0.000000,"\text{Not used}","int(cos(c + d*x)^5*(a + a*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^5\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^5*(a + a*sin(c + d*x))^(3/2), x)","F"
117,0,-1,127,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2), x)","F"
118,0,-1,49,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + a*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^3\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^3*(a + a*sin(c + d*x))^(3/2), x)","F"
119,0,-1,95,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + a*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(a + a*sin(c + d*x))^(3/2), x)","F"
120,1,20,24,4.623997,"\text{Not used}","int(cos(c + d*x)*(a + a*sin(c + d*x))^(3/2),x)","\frac{2\,{\left(a\,\left(\sin\left(c+d\,x\right)+1\right)\right)}^{5/2}}{5\,a\,d}","Not used",1,"(2*(a*(sin(c + d*x) + 1))^(5/2))/(5*a*d)","B"
121,0,-1,62,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2)/cos(c + d*x),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(3/2)/cos(c + d*x), x)","F"
122,1,37,26,4.772625,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2)/cos(c + d*x)^2,x)","\frac{4\,a\,\cos\left(c+d\,x\right)\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}}{d\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)}","Not used",1,"(4*a*cos(c + d*x)*(a*(sin(c + d*x) + 1))^(1/2))/(d*(cos(2*c + 2*d*x) + 1))","B"
123,0,-1,73,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2)/cos(c + d*x)^3,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(3/2)/cos(c + d*x)^3, x)","F"
124,0,-1,107,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2)/cos(c + d*x)^4,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(3/2)/cos(c + d*x)^4, x)","F"
125,0,-1,127,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2)/cos(c + d*x)^5,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(3/2)/cos(c + d*x)^5, x)","F"
126,0,-1,169,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2)/cos(c + d*x)^6,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^6} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(3/2)/cos(c + d*x)^6, x)","F"
127,0,-1,73,0.000000,"\text{Not used}","int(cos(c + d*x)^5*(a + a*sin(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^5\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^5*(a + a*sin(c + d*x))^(5/2), x)","F"
128,0,-1,159,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + a*sin(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^4*(a + a*sin(c + d*x))^(5/2), x)","F"
129,0,-1,49,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + a*sin(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^3\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^3*(a + a*sin(c + d*x))^(5/2), x)","F"
130,0,-1,127,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + a*sin(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(a + a*sin(c + d*x))^(5/2), x)","F"
131,1,20,24,4.781848,"\text{Not used}","int(cos(c + d*x)*(a + a*sin(c + d*x))^(5/2),x)","\frac{2\,{\left(a\,\left(\sin\left(c+d\,x\right)+1\right)\right)}^{7/2}}{7\,a\,d}","Not used",1,"(2*(a*(sin(c + d*x) + 1))^(7/2))/(7*a*d)","B"
132,0,-1,86,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/cos(c + d*x),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(5/2)/cos(c + d*x), x)","F"
133,1,88,55,5.460447,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/cos(c + d*x)^2,x)","\frac{2\,a^2\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(-22\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-2\,{\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}^2+4\,\sin\left(2\,c+2\,d\,x\right)+12\right)}{d\,\left(-4\,{\sin\left(c+d\,x\right)}^2+\sin\left(c+d\,x\right)+\sin\left(3\,c+3\,d\,x\right)+4\right)}","Not used",1,"(2*a^2*(a*(sin(c + d*x) + 1))^(1/2)*(4*sin(2*c + 2*d*x) - 22*sin(c/2 + (d*x)/2)^2 - 2*sin((3*c)/2 + (3*d*x)/2)^2 + 12))/(d*(sin(c + d*x) + sin(3*c + 3*d*x) - 4*sin(c + d*x)^2 + 4))","B"
134,0,-1,69,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/cos(c + d*x)^3,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(5/2)/cos(c + d*x)^3, x)","F"
135,1,225,30,7.589163,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/cos(c + d*x)^4,x)","\frac{4\,a^2\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left({\sin\left(c+d\,x\right)}^2\,4{}\mathrm{i}+\sin\left(c+d\,x\right)\,1{}\mathrm{i}-2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,{\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}^2-2\,\sin\left(2\,c+2\,d\,x\right)+\sin\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}-4{}\mathrm{i}\right)}{3\,d\,\left(8\,{\sin\left(c+d\,x\right)}^2+4\,\sin\left(c+d\,x\right)-2\,{\sin\left(2\,c+2\,d\,x\right)}^2+4\,\sin\left(3\,c+3\,d\,x\right)-8\right)}+\frac{4\,a^2\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(\sin\left(2\,c+2\,d\,x\right)+4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-{\sin\left(c+d\,x\right)}^2\,2{}\mathrm{i}-2+2{}\mathrm{i}\right)}{3\,d\,\left(4\,{\sin\left(c+d\,x\right)}^2+\sin\left(c+d\,x\right)+\sin\left(3\,c+3\,d\,x\right)-4\right)}","Not used",1,"(4*a^2*(a*(sin(c + d*x) + 1))^(1/2)*(sin(c + d*x)*1i - 2*sin(2*c + 2*d*x) + sin(3*c + 3*d*x)*1i - 2*sin(c/2 + (d*x)/2)^2 + 2*sin((3*c)/2 + (3*d*x)/2)^2 + sin(c + d*x)^2*4i - 4i))/(3*d*(4*sin(c + d*x) + 4*sin(3*c + 3*d*x) - 2*sin(2*c + 2*d*x)^2 + 8*sin(c + d*x)^2 - 8)) + (4*a^2*(a*(sin(c + d*x) + 1))^(1/2)*(sin(2*c + 2*d*x) + 4*sin(c/2 + (d*x)/2)^2 - sin(c + d*x)^2*2i - (2 - 2i)))/(3*d*(sin(c + d*x) + sin(3*c + 3*d*x) + 4*sin(c + d*x)^2 - 4))","B"
136,0,-1,103,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/cos(c + d*x)^5,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(5/2)/cos(c + d*x)^5, x)","F"
137,0,-1,139,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/cos(c + d*x)^6,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^6} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(5/2)/cos(c + d*x)^6, x)","F"
138,0,-1,159,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/cos(c + d*x)^7,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^7} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(5/2)/cos(c + d*x)^7, x)","F"
139,0,-1,97,0.000000,"\text{Not used}","int(cos(c + d*x)^7*(a + a*sin(c + d*x))^(7/2),x)","\int {\cos\left(c+d\,x\right)}^7\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{7/2} \,d x","Not used",1,"int(cos(c + d*x)^7*(a + a*sin(c + d*x))^(7/2), x)","F"
140,0,-1,223,0.000000,"\text{Not used}","int(cos(c + d*x)^6*(a + a*sin(c + d*x))^(7/2),x)","\int {\cos\left(c+d\,x\right)}^6\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{7/2} \,d x","Not used",1,"int(cos(c + d*x)^6*(a + a*sin(c + d*x))^(7/2), x)","F"
141,0,-1,73,0.000000,"\text{Not used}","int(cos(c + d*x)^5*(a + a*sin(c + d*x))^(7/2),x)","\int {\cos\left(c+d\,x\right)}^5\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{7/2} \,d x","Not used",1,"int(cos(c + d*x)^5*(a + a*sin(c + d*x))^(7/2), x)","F"
142,0,-1,191,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + a*sin(c + d*x))^(7/2),x)","\int {\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{7/2} \,d x","Not used",1,"int(cos(c + d*x)^4*(a + a*sin(c + d*x))^(7/2), x)","F"
143,0,-1,49,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + a*sin(c + d*x))^(7/2),x)","\int {\cos\left(c+d\,x\right)}^3\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{7/2} \,d x","Not used",1,"int(cos(c + d*x)^3*(a + a*sin(c + d*x))^(7/2), x)","F"
144,0,-1,159,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + a*sin(c + d*x))^(7/2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{7/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(a + a*sin(c + d*x))^(7/2), x)","F"
145,1,20,24,4.844224,"\text{Not used}","int(cos(c + d*x)*(a + a*sin(c + d*x))^(7/2),x)","\frac{2\,{\left(a\,\left(\sin\left(c+d\,x\right)+1\right)\right)}^{9/2}}{9\,a\,d}","Not used",1,"(2*(a*(sin(c + d*x) + 1))^(9/2))/(9*a*d)","B"
146,0,-1,110,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{7/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x), x)","F"
147,0,-1,89,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x)^2,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{7/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x)^2, x)","F"
148,0,-1,91,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x)^3,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{7/2}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x)^3, x)","F"
149,1,118,61,8.531132,"\text{Not used}","int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x)^4,x)","-\frac{a^3\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(3-3\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,2{}\mathrm{i}\right)\,4{}\mathrm{i}}{3\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)\,{\left(1+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}\right)}^3}","Not used",1,"-(a^3*exp(c*1i + d*x*1i)*(a + a*((exp(- c*1i - d*x*1i)*1i)/2 - (exp(c*1i + d*x*1i)*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*2i - 3*exp(c*2i + d*x*2i) + 3)*4i)/(3*d*(exp(c*1i + d*x*1i) + 1i)*(exp(c*1i + d*x*1i)*1i + 1)^3)","B"
150,0,-1,106,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x)^5,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{7/2}}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x)^5, x)","F"
151,1,86,30,8.426793,"\text{Not used}","int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x)^6,x)","-\frac{16\,a^3\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{5\,d\,{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}-\mathrm{i}\right)}^5\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}","Not used",1,"-(16*a^3*exp(c*3i + d*x*3i)*(a + a*((exp(- c*1i - d*x*1i)*1i)/2 - (exp(c*1i + d*x*1i)*1i)/2))^(1/2))/(5*d*(exp(c*1i + d*x*1i) - 1i)^5*(exp(c*1i + d*x*1i) + 1i))","B"
152,0,-1,135,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x)^7,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{7/2}}{{\cos\left(c+d\,x\right)}^7} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x)^7, x)","F"
153,0,-1,171,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x)^8,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{7/2}}{{\cos\left(c+d\,x\right)}^8} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x)^8, x)","F"
154,0,-1,191,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x)^9,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{7/2}}{{\cos\left(c+d\,x\right)}^9} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x)^9, x)","F"
155,0,-1,233,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x)^10,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{7/2}}{{\cos\left(c+d\,x\right)}^{10}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(7/2)/cos(c + d*x)^10, x)","F"
156,0,-1,97,0.000000,"\text{Not used}","int(cos(c + d*x)^7/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^7}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^7/(a + a*sin(c + d*x))^(1/2), x)","F"
157,0,-1,95,0.000000,"\text{Not used}","int(cos(c + d*x)^6/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^6}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^6/(a + a*sin(c + d*x))^(1/2), x)","F"
158,0,-1,73,0.000000,"\text{Not used}","int(cos(c + d*x)^5/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^5}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^5/(a + a*sin(c + d*x))^(1/2), x)","F"
159,0,-1,63,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^4/(a + a*sin(c + d*x))^(1/2), x)","F"
160,0,-1,49,0.000000,"\text{Not used}","int(cos(c + d*x)^3/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^3/(a + a*sin(c + d*x))^(1/2), x)","F"
161,0,-1,30,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^2/(a + a*sin(c + d*x))^(1/2), x)","F"
162,1,20,22,4.824210,"\text{Not used}","int(cos(c + d*x)/(a + a*sin(c + d*x))^(1/2),x)","\frac{2\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}}{a\,d}","Not used",1,"(2*(a*(sin(c + d*x) + 1))^(1/2))/(a*d)","B"
163,0,-1,60,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{1}{\cos\left(c+d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)*(a + a*sin(c + d*x))^(1/2)), x)","F"
164,0,-1,102,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^2*(a + a*sin(c + d*x))^(1/2)), x)","F"
165,0,-1,116,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^3\,\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^3*(a + a*sin(c + d*x))^(1/2)), x)","F"
166,0,-1,162,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^4*(a + a*sin(c + d*x))^(1/2)), x)","F"
167,0,-1,175,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^5\,\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^5*(a + a*sin(c + d*x))^(1/2)), x)","F"
168,0,-1,221,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^6*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^6\,\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^6*(a + a*sin(c + d*x))^(1/2)), x)","F"
169,0,-1,97,0.000000,"\text{Not used}","int(cos(c + d*x)^7/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^7}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^7/(a + a*sin(c + d*x))^(3/2), x)","F"
170,0,-1,63,0.000000,"\text{Not used}","int(cos(c + d*x)^6/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^6}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^6/(a + a*sin(c + d*x))^(3/2), x)","F"
171,0,-1,73,0.000000,"\text{Not used}","int(cos(c + d*x)^5/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^5}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^5/(a + a*sin(c + d*x))^(3/2), x)","F"
172,0,-1,30,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^4/(a + a*sin(c + d*x))^(3/2), x)","F"
173,0,-1,47,0.000000,"\text{Not used}","int(cos(c + d*x)^3/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^3/(a + a*sin(c + d*x))^(3/2), x)","F"
174,0,-1,76,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^2/(a + a*sin(c + d*x))^(3/2), x)","F"
175,1,50,22,4.875564,"\text{Not used}","int(cos(c + d*x)/(a + a*sin(c + d*x))^(3/2),x)","-\frac{4\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(\sin\left(c+d\,x\right)+1\right)}{a^2\,d\,\left(2\,{\sin\left(c+d\,x\right)}^2+4\,\sin\left(c+d\,x\right)+2\right)}","Not used",1,"-(4*(a*(sin(c + d*x) + 1))^(1/2)*(sin(c + d*x) + 1))/(a^2*d*(4*sin(c + d*x) + 2*sin(c + d*x)^2 + 2))","B"
176,0,-1,89,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{1}{\cos\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)*(a + a*sin(c + d*x))^(3/2)), x)","F"
177,0,-1,134,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^2*(a + a*sin(c + d*x))^(3/2)), x)","F"
178,0,-1,150,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^3\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^3*(a + a*sin(c + d*x))^(3/2)), x)","F"
179,0,-1,195,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^4*(a + a*sin(c + d*x))^(3/2)), x)","F"
180,0,-1,211,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^5\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^5*(a + a*sin(c + d*x))^(3/2)), x)","F"
181,0,-1,256,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^6*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^6\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^6*(a + a*sin(c + d*x))^(3/2)), x)","F"
182,0,-1,95,0.000000,"\text{Not used}","int(cos(c + d*x)^10/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{10}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^10/(a + a*sin(c + d*x))^(5/2), x)","F"
183,0,-1,121,0.000000,"\text{Not used}","int(cos(c + d*x)^9/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^9}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^9/(a + a*sin(c + d*x))^(5/2), x)","F"
184,0,-1,63,0.000000,"\text{Not used}","int(cos(c + d*x)^8/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^8}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^8/(a + a*sin(c + d*x))^(5/2), x)","F"
185,0,-1,97,0.000000,"\text{Not used}","int(cos(c + d*x)^7/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^7}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^7/(a + a*sin(c + d*x))^(5/2), x)","F"
186,0,-1,30,0.000000,"\text{Not used}","int(cos(c + d*x)^6/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^6}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^6/(a + a*sin(c + d*x))^(5/2), x)","F"
187,0,-1,71,0.000000,"\text{Not used}","int(cos(c + d*x)^5/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^5}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^5/(a + a*sin(c + d*x))^(5/2), x)","F"
188,0,-1,108,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^4/(a + a*sin(c + d*x))^(5/2), x)","F"
189,0,-1,45,0.000000,"\text{Not used}","int(cos(c + d*x)^3/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^3/(a + a*sin(c + d*x))^(5/2), x)","F"
190,0,-1,75,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^2/(a + a*sin(c + d*x))^(5/2), x)","F"
191,1,72,24,7.520678,"\text{Not used}","int(cos(c + d*x)/(a + a*sin(c + d*x))^(5/2),x)","\frac{8\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{3\,a^3\,d\,{\left(-1+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}\right)}^4}","Not used",1,"(8*exp(c*2i + d*x*2i)*(a + a*((exp(- c*1i - d*x*1i)*1i)/2 - (exp(c*1i + d*x*1i)*1i)/2))^(1/2))/(3*a^3*d*(exp(c*1i + d*x*1i)*1i - 1)^4)","B"
192,0,-1,113,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + a*sin(c + d*x))^(5/2)),x)","\int \frac{1}{\cos\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)*(a + a*sin(c + d*x))^(5/2)), x)","F"
193,0,-1,167,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + a*sin(c + d*x))^(5/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^2*(a + a*sin(c + d*x))^(5/2)), x)","F"
194,0,-1,185,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a*sin(c + d*x))^(5/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^3\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^3*(a + a*sin(c + d*x))^(5/2)), x)","F"
195,0,-1,233,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + a*sin(c + d*x))^(5/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^4*(a + a*sin(c + d*x))^(5/2)), x)","F"
196,0,-1,124,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)*(a + a*sin(c + d*x)),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}\,\left(a+a\,\sin\left(c+d\,x\right)\right) \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)*(a + a*sin(c + d*x)), x)","F"
197,0,-1,95,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x)),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(a+a\,\sin\left(c+d\,x\right)\right) \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x)), x)","F"
198,0,-1,95,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x)),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(a+a\,\sin\left(c+d\,x\right)\right) \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x)), x)","F"
199,0,-1,63,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x)),x)","\int \sqrt{e\,\cos\left(c+d\,x\right)}\,\left(a+a\,\sin\left(c+d\,x\right)\right) \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x)), x)","F"
200,1,45,61,0.546490,"\text{Not used}","int((a + a*sin(c + d*x))/(e*cos(c + d*x))^(1/2),x)","-\frac{2\,a\,\sqrt{\cos\left(c+d\,x\right)}\,\left(\sqrt{\cos\left(c+d\,x\right)}-\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d\,\sqrt{e\,\cos\left(c+d\,x\right)}}","Not used",1,"-(2*a*cos(c + d*x)^(1/2)*(cos(c + d*x)^(1/2) - ellipticF(c/2 + (d*x)/2, 2)))/(d*(e*cos(c + d*x))^(1/2))","B"
201,0,-1,91,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))/(e*cos(c + d*x))^(3/2),x)","\int \frac{a+a\,\sin\left(c+d\,x\right)}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))/(e*cos(c + d*x))^(3/2), x)","F"
202,0,-1,97,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))/(e*cos(c + d*x))^(5/2),x)","\int \frac{a+a\,\sin\left(c+d\,x\right)}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))/(e*cos(c + d*x))^(5/2), x)","F"
203,0,-1,126,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))/(e*cos(c + d*x))^(7/2),x)","\int \frac{a+a\,\sin\left(c+d\,x\right)}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))/(e*cos(c + d*x))^(7/2), x)","F"
204,0,-1,168,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)*(a + a*sin(c + d*x))^2,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)*(a + a*sin(c + d*x))^2, x)","F"
205,0,-1,137,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x))^2,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x))^2, x)","F"
206,0,-1,137,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^2,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^2, x)","F"
207,0,-1,105,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^2,x)","\int \sqrt{e\,\cos\left(c+d\,x\right)}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^2, x)","F"
208,0,-1,105,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^2/(e*cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2}{\sqrt{e\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^2/(e*cos(c + d*x))^(1/2), x)","F"
209,0,-1,85,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^2/(e*cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^2/(e*cos(c + d*x))^(3/2), x)","F"
210,0,-1,89,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^2/(e*cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^2/(e*cos(c + d*x))^(5/2), x)","F"
211,0,-1,127,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^2/(e*cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^2/(e*cos(c + d*x))^(7/2), x)","F"
212,0,-1,114,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^2/(e*cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^2/(e*cos(c + d*x))^(9/2), x)","F"
213,0,-1,145,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^2/(e*cos(c + d*x))^(11/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{11/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^2/(e*cos(c + d*x))^(11/2), x)","F"
214,0,-1,203,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)*(a + a*sin(c + d*x))^3,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)*(a + a*sin(c + d*x))^3, x)","F"
215,0,-1,170,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x))^3,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x))^3, x)","F"
216,0,-1,172,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^3,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^3, x)","F"
217,0,-1,140,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^3,x)","\int \sqrt{e\,\cos\left(c+d\,x\right)}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^3, x)","F"
218,0,-1,136,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^3/(e*cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3}{\sqrt{e\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^3/(e*cos(c + d*x))^(1/2), x)","F"
219,0,-1,106,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^3/(e*cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^3/(e*cos(c + d*x))^(3/2), x)","F"
220,0,-1,110,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^3/(e*cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^3/(e*cos(c + d*x))^(5/2), x)","F"
221,0,-1,127,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^3/(e*cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^3/(e*cos(c + d*x))^(7/2), x)","F"
222,0,-1,127,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^3/(e*cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^3/(e*cos(c + d*x))^(9/2), x)","F"
223,0,-1,165,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^3/(e*cos(c + d*x))^(11/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{11/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^3/(e*cos(c + d*x))^(11/2), x)","F"
224,0,-1,210,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^4,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^4, x)","F"
225,0,-1,178,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^4,x)","\int \sqrt{e\,\cos\left(c+d\,x\right)}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^4, x)","F"
226,0,-1,178,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^4/(e*cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4}{\sqrt{e\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^4/(e*cos(c + d*x))^(1/2), x)","F"
227,0,-1,156,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^4/(e*cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^4/(e*cos(c + d*x))^(3/2), x)","F"
228,0,-1,152,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^4/(e*cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^4/(e*cos(c + d*x))^(5/2), x)","F"
229,0,-1,127,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^4/(e*cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^4/(e*cos(c + d*x))^(7/2), x)","F"
230,0,-1,127,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^4/(e*cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^4/(e*cos(c + d*x))^(9/2), x)","F"
231,0,-1,169,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^4/(e*cos(c + d*x))^(11/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{11/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^4/(e*cos(c + d*x))^(11/2), x)","F"
232,0,-1,169,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^4/(e*cos(c + d*x))^(13/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{13/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^4/(e*cos(c + d*x))^(13/2), x)","F"
233,0,-1,132,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(11/2)/(a + a*sin(c + d*x)),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{11/2}}{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^(11/2)/(a + a*sin(c + d*x)), x)","F"
234,0,-1,101,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(9/2)/(a + a*sin(c + d*x)),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{9/2}}{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^(9/2)/(a + a*sin(c + d*x)), x)","F"
235,0,-1,101,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)/(a + a*sin(c + d*x)),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}}{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)/(a + a*sin(c + d*x)), x)","F"
236,0,-1,68,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)/(a + a*sin(c + d*x)),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}}{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)/(a + a*sin(c + d*x)), x)","F"
237,0,-1,66,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)/(a + a*sin(c + d*x)),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}}{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)/(a + a*sin(c + d*x)), x)","F"
238,0,-1,74,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)/(a + a*sin(c + d*x)),x)","\int \frac{\sqrt{e\,\cos\left(c+d\,x\right)}}{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)/(a + a*sin(c + d*x)), x)","F"
239,0,-1,78,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))),x)","\int \frac{1}{\sqrt{e\,\cos\left(c+d\,x\right)}\,\left(a+a\,\sin\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))), x)","F"
240,0,-1,112,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(a+a\,\sin\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))), x)","F"
241,0,-1,112,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x))),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(a+a\,\sin\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x))), x)","F"
242,0,-1,143,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(7/2)*(a + a*sin(c + d*x))),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}\,\left(a+a\,\sin\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(7/2)*(a + a*sin(c + d*x))), x)","F"
243,0,-1,145,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(11/2)/(a + a*sin(c + d*x))^2,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{11/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*cos(c + d*x))^(11/2)/(a + a*sin(c + d*x))^2, x)","F"
244,0,-1,114,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(9/2)/(a + a*sin(c + d*x))^2,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{9/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*cos(c + d*x))^(9/2)/(a + a*sin(c + d*x))^2, x)","F"
245,0,-1,112,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)/(a + a*sin(c + d*x))^2,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)/(a + a*sin(c + d*x))^2, x)","F"
246,0,-1,79,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)/(a + a*sin(c + d*x))^2,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)/(a + a*sin(c + d*x))^2, x)","F"
247,0,-1,83,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)/(a + a*sin(c + d*x))^2,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)/(a + a*sin(c + d*x))^2, x)","F"
248,0,-1,116,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)/(a + a*sin(c + d*x))^2,x)","\int \frac{\sqrt{e\,\cos\left(c+d\,x\right)}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)/(a + a*sin(c + d*x))^2, x)","F"
249,0,-1,116,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^2),x)","\int \frac{1}{\sqrt{e\,\cos\left(c+d\,x\right)}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^2), x)","F"
250,0,-1,150,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^2),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^2), x)","F"
251,0,-1,150,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x))^2),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x))^2), x)","F"
252,0,-1,181,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(7/2)*(a + a*sin(c + d*x))^2),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(7/2)*(a + a*sin(c + d*x))^2), x)","F"
253,0,-1,169,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(15/2)/(a + a*sin(c + d*x))^3,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{15/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^(15/2)/(a + a*sin(c + d*x))^3, x)","F"
254,0,-1,138,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(13/2)/(a + a*sin(c + d*x))^3,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{13/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^(13/2)/(a + a*sin(c + d*x))^3, x)","F"
255,0,-1,132,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(11/2)/(a + a*sin(c + d*x))^3,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{11/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^(11/2)/(a + a*sin(c + d*x))^3, x)","F"
256,0,-1,103,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(9/2)/(a + a*sin(c + d*x))^3,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{9/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^(9/2)/(a + a*sin(c + d*x))^3, x)","F"
257,0,-1,107,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)/(a + a*sin(c + d*x))^3,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)/(a + a*sin(c + d*x))^3, x)","F"
258,0,-1,118,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)/(a + a*sin(c + d*x))^3,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)/(a + a*sin(c + d*x))^3, x)","F"
259,0,-1,118,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)/(a + a*sin(c + d*x))^3,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)/(a + a*sin(c + d*x))^3, x)","F"
260,0,-1,153,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)/(a + a*sin(c + d*x))^3,x)","\int \frac{\sqrt{e\,\cos\left(c+d\,x\right)}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)/(a + a*sin(c + d*x))^3, x)","F"
261,0,-1,153,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^3),x)","\int \frac{1}{\sqrt{e\,\cos\left(c+d\,x\right)}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^3), x)","F"
262,0,-1,187,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^3),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^3), x)","F"
263,0,-1,180,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(15/2)/(a + a*sin(c + d*x))^4,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{15/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((e*cos(c + d*x))^(15/2)/(a + a*sin(c + d*x))^4, x)","F"
264,0,-1,149,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(13/2)/(a + a*sin(c + d*x))^4,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{13/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((e*cos(c + d*x))^(13/2)/(a + a*sin(c + d*x))^4, x)","F"
265,0,-1,145,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(11/2)/(a + a*sin(c + d*x))^4,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{11/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((e*cos(c + d*x))^(11/2)/(a + a*sin(c + d*x))^4, x)","F"
266,0,-1,120,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(9/2)/(a + a*sin(c + d*x))^4,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{9/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((e*cos(c + d*x))^(9/2)/(a + a*sin(c + d*x))^4, x)","F"
267,0,-1,120,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)/(a + a*sin(c + d*x))^4,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)/(a + a*sin(c + d*x))^4, x)","F"
268,0,-1,154,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)/(a + a*sin(c + d*x))^4,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)/(a + a*sin(c + d*x))^4, x)","F"
269,0,-1,154,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)/(a + a*sin(c + d*x))^4,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)/(a + a*sin(c + d*x))^4, x)","F"
270,0,-1,191,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)/(a + a*sin(c + d*x))^4,x)","\int \frac{\sqrt{e\,\cos\left(c+d\,x\right)}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)/(a + a*sin(c + d*x))^4, x)","F"
271,0,-1,191,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^4),x)","\int \frac{1}{\sqrt{e\,\cos\left(c+d\,x\right)}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^4), x)","F"
272,0,-1,225,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^4),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^4), x)","F"
273,0,-1,236,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^(1/2),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\sqrt{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^(1/2), x)","F"
274,0,-1,194,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^(1/2),x)","\int \sqrt{e\,\cos\left(c+d\,x\right)}\,\sqrt{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^(1/2), x)","F"
275,0,-1,161,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(1/2)/(e*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{a+a\,\sin\left(c+d\,x\right)}}{\sqrt{e\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(1/2)/(e*cos(c + d*x))^(1/2), x)","F"
276,1,30,34,5.311050,"\text{Not used}","int((a + a*sin(c + d*x))^(1/2)/(e*cos(c + d*x))^(3/2),x)","\frac{2\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{d\,e\,\sqrt{e\,\cos\left(c+d\,x\right)}}","Not used",1,"(2*(a + a*sin(c + d*x))^(1/2))/(d*e*(e*cos(c + d*x))^(1/2))","B"
277,1,61,74,5.666406,"\text{Not used}","int((a + a*sin(c + d*x))^(1/2)/(e*cos(c + d*x))^(5/2),x)","-\frac{4\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(\cos\left(c+d\,x\right)-\sin\left(2\,c+2\,d\,x\right)\right)}{3\,d\,e^2\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)\,\sqrt{e\,\cos\left(c+d\,x\right)}}","Not used",1,"-(4*(a*(sin(c + d*x) + 1))^(1/2)*(cos(c + d*x) - sin(2*c + 2*d*x)))/(3*d*e^2*(cos(2*c + 2*d*x) + 1)*(e*cos(c + d*x))^(1/2))","B"
278,1,97,115,6.060039,"\text{Not used}","int((a + a*sin(c + d*x))^(1/2)/(e*cos(c + d*x))^(7/2),x)","\frac{8\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(2\,\sin\left(c+d\,x\right)+7\,\cos\left(2\,c+2\,d\,x\right)+2\,\cos\left(4\,c+4\,d\,x\right)+2\,\sin\left(3\,c+3\,d\,x\right)+5\right)}{15\,d\,e^3\,\sqrt{e\,\cos\left(c+d\,x\right)}\,\left(4\,\cos\left(2\,c+2\,d\,x\right)+\cos\left(4\,c+4\,d\,x\right)+3\right)}","Not used",1,"(8*(a*(sin(c + d*x) + 1))^(1/2)*(2*sin(c + d*x) + 7*cos(2*c + 2*d*x) + 2*cos(4*c + 4*d*x) + 2*sin(3*c + 3*d*x) + 5))/(15*d*e^3*(e*cos(c + d*x))^(1/2)*(4*cos(2*c + 2*d*x) + cos(4*c + 4*d*x) + 3))","B"
279,1,129,154,7.243485,"\text{Not used}","int((a + a*sin(c + d*x))^(1/2)/(e*cos(c + d*x))^(9/2),x)","-\frac{16\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(23\,\cos\left(c+d\,x\right)+11\,\cos\left(3\,c+3\,d\,x\right)+2\,\cos\left(5\,c+5\,d\,x\right)-16\,\sin\left(2\,c+2\,d\,x\right)-11\,\sin\left(4\,c+4\,d\,x\right)-2\,\sin\left(6\,c+6\,d\,x\right)\right)}{35\,d\,e^4\,\sqrt{e\,\cos\left(c+d\,x\right)}\,\left(15\,\cos\left(2\,c+2\,d\,x\right)+6\,\cos\left(4\,c+4\,d\,x\right)+\cos\left(6\,c+6\,d\,x\right)+10\right)}","Not used",1,"-(16*(a*(sin(c + d*x) + 1))^(1/2)*(23*cos(c + d*x) + 11*cos(3*c + 3*d*x) + 2*cos(5*c + 5*d*x) - 16*sin(2*c + 2*d*x) - 11*sin(4*c + 4*d*x) - 2*sin(6*c + 6*d*x)))/(35*d*e^4*(e*cos(c + d*x))^(1/2)*(15*cos(2*c + 2*d*x) + 6*cos(4*c + 4*d*x) + cos(6*c + 6*d*x) + 10))","B"
280,0,-1,319,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x))^(3/2),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x))^(3/2), x)","F"
281,0,-1,278,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^(3/2),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^(3/2), x)","F"
282,0,-1,243,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^(3/2),x)","\int \sqrt{e\,\cos\left(c+d\,x\right)}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^(3/2), x)","F"
283,0,-1,198,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2)/(e*cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{\sqrt{e\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(3/2)/(e*cos(c + d*x))^(1/2), x)","F"
284,0,-1,210,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2)/(e*cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(3/2)/(e*cos(c + d*x))^(3/2), x)","F"
285,1,47,36,5.622161,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2)/(e*cos(c + d*x))^(5/2),x)","-\frac{2\,a\,\cos\left(c+d\,x\right)\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}}{3\,d\,e^2\,\sqrt{e\,\cos\left(c+d\,x\right)}\,\left(\sin\left(c+d\,x\right)-1\right)}","Not used",1,"-(2*a*cos(c + d*x)*(a*(sin(c + d*x) + 1))^(1/2))/(3*d*e^2*(e*cos(c + d*x))^(1/2)*(sin(c + d*x) - 1))","B"
286,1,71,74,5.984731,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2)/(e*cos(c + d*x))^(7/2),x)","\frac{4\,a\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(5\,\sin\left(c+d\,x\right)+\cos\left(2\,c+2\,d\,x\right)-4\right)}{5\,d\,e^3\,\sqrt{e\,\cos\left(c+d\,x\right)}\,\left(4\,\sin\left(c+d\,x\right)+\cos\left(2\,c+2\,d\,x\right)-3\right)}","Not used",1,"(4*a*(a*(sin(c + d*x) + 1))^(1/2)*(5*sin(c + d*x) + cos(2*c + 2*d*x) - 4))/(5*d*e^3*(e*cos(c + d*x))^(1/2)*(4*sin(c + d*x) + cos(2*c + 2*d*x) - 3))","B"
287,1,116,113,6.809921,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2)/(e*cos(c + d*x))^(9/2),x)","\frac{8\,a\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(12\,\cos\left(c+d\,x\right)-10\,\cos\left(3\,c+3\,d\,x\right)-17\,\sin\left(2\,c+2\,d\,x\right)+2\,\sin\left(4\,c+4\,d\,x\right)\right)}{21\,d\,e^4\,\sqrt{e\,\cos\left(c+d\,x\right)}\,\left(4\,\sin\left(c+d\,x\right)-4\,\cos\left(2\,c+2\,d\,x\right)+\cos\left(4\,c+4\,d\,x\right)+4\,\sin\left(3\,c+3\,d\,x\right)-5\right)}","Not used",1,"(8*a*(a*(sin(c + d*x) + 1))^(1/2)*(12*cos(c + d*x) - 10*cos(3*c + 3*d*x) - 17*sin(2*c + 2*d*x) + 2*sin(4*c + 4*d*x)))/(21*d*e^4*(e*cos(c + d*x))^(1/2)*(4*sin(c + d*x) - 4*cos(2*c + 2*d*x) + cos(4*c + 4*d*x) + 4*sin(3*c + 3*d*x) - 5))","B"
288,1,261,152,10.956332,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2)/(e*cos(c + d*x))^(11/2),x)","\frac{14\,a\,\sqrt{a+a\,\sin\left(c+d\,x\right)}+12\,a\,\sin\left(c+d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}+24\,a\,\cos\left(2\,c+2\,d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}-8\,a\,\sin\left(3\,c+3\,d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{\frac{45\,d\,e^5\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}{2}+\frac{45\,d\,e^5\,\cos\left(2\,c+2\,d\,x\right)\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}{2}-\frac{45\,d\,e^5\,\sin\left(3\,c+3\,d\,x\right)\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}{4}-\frac{45\,d\,e^5\,\sin\left(c+d\,x\right)\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}{4}}","Not used",1,"(14*a*(a + a*sin(c + d*x))^(1/2) + 12*a*sin(c + d*x)*(a + a*sin(c + d*x))^(1/2) + 24*a*cos(2*c + 2*d*x)*(a + a*sin(c + d*x))^(1/2) - 8*a*sin(3*c + 3*d*x)*(a + a*sin(c + d*x))^(1/2))/((45*d*e^5*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))/2 + (45*d*e^5*cos(2*c + 2*d*x)*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))/2 - (45*d*e^5*sin(3*c + 3*d*x)*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))/4 - (45*d*e^5*sin(c + d*x)*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))/4)","B"
289,0,-1,323,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^(5/2),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^(5/2), x)","F"
290,0,-1,286,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^(5/2),x)","\int \sqrt{e\,\cos\left(c+d\,x\right)}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^(5/2), x)","F"
291,0,-1,247,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/(e*cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}}{\sqrt{e\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(5/2)/(e*cos(c + d*x))^(1/2), x)","F"
292,0,-1,239,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/(e*cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(5/2)/(e*cos(c + d*x))^(3/2), x)","F"
293,0,-1,204,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/(e*cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(5/2)/(e*cos(c + d*x))^(5/2), x)","F"
294,1,65,36,6.058211,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/(e*cos(c + d*x))^(7/2),x)","-\frac{2\,a^2\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}}{5\,d\,e^3\,\sqrt{e\,\cos\left(c+d\,x\right)}\,\left(4\,\sin\left(c+d\,x\right)+\cos\left(2\,c+2\,d\,x\right)-3\right)}","Not used",1,"-(2*a^2*(cos(2*c + 2*d*x) + 1)*(a*(sin(c + d*x) + 1))^(1/2))/(5*d*e^3*(e*cos(c + d*x))^(1/2)*(4*sin(c + d*x) + cos(2*c + 2*d*x) - 3))","B"
295,1,96,76,6.335790,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/(e*cos(c + d*x))^(9/2),x)","\frac{4\,a^2\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(\cos\left(3\,c+3\,d\,x\right)-11\,\cos\left(c+d\,x\right)+7\,\sin\left(2\,c+2\,d\,x\right)\right)}{21\,d\,e^4\,\sqrt{e\,\cos\left(c+d\,x\right)}\,\left(15\,\sin\left(c+d\,x\right)+6\,\cos\left(2\,c+2\,d\,x\right)-\sin\left(3\,c+3\,d\,x\right)-10\right)}","Not used",1,"(4*a^2*(a*(sin(c + d*x) + 1))^(1/2)*(cos(3*c + 3*d*x) - 11*cos(c + d*x) + 7*sin(2*c + 2*d*x)))/(21*d*e^4*(e*cos(c + d*x))^(1/2)*(15*sin(c + d*x) + 6*cos(2*c + 2*d*x) - sin(3*c + 3*d*x) - 10))","B"
296,1,119,113,6.694274,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/(e*cos(c + d*x))^(11/2),x)","\frac{8\,a^2\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(2\,\cos\left(4\,c+4\,d\,x\right)-73\,\cos\left(2\,c+2\,d\,x\right)-162\,\sin\left(c+d\,x\right)+18\,\sin\left(3\,c+3\,d\,x\right)+105\right)}{45\,d\,e^5\,\sqrt{e\,\cos\left(c+d\,x\right)}\,\left(\cos\left(4\,c+4\,d\,x\right)-28\,\cos\left(2\,c+2\,d\,x\right)-56\,\sin\left(c+d\,x\right)+8\,\sin\left(3\,c+3\,d\,x\right)+35\right)}","Not used",1,"(8*a^2*(a*(sin(c + d*x) + 1))^(1/2)*(2*cos(4*c + 4*d*x) - 73*cos(2*c + 2*d*x) - 162*sin(c + d*x) + 18*sin(3*c + 3*d*x) + 105))/(45*d*e^5*(e*cos(c + d*x))^(1/2)*(cos(4*c + 4*d*x) - 28*cos(2*c + 2*d*x) - 56*sin(c + d*x) + 8*sin(3*c + 3*d*x) + 35))","B"
297,1,232,150,11.173281,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/(e*cos(c + d*x))^(13/2),x)","\frac{30\,a^2\,\sqrt{a+a\,\sin\left(c+d\,x\right)}-40\,a^2\,\cos\left(2\,c+2\,d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}+8\,a^2\,\sin\left(3\,c+3\,d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}-76\,a^2\,\sin\left(c+d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{\frac{77\,d\,e^6\,\cos\left(3\,c+3\,d\,x\right)\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}{4}+77\,d\,e^6\,\sin\left(2\,c+2\,d\,x\right)\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}-\frac{385\,d\,e^6\,\cos\left(c+d\,x\right)\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}{4}}","Not used",1,"(30*a^2*(a + a*sin(c + d*x))^(1/2) - 40*a^2*cos(2*c + 2*d*x)*(a + a*sin(c + d*x))^(1/2) + 8*a^2*sin(3*c + 3*d*x)*(a + a*sin(c + d*x))^(1/2) - 76*a^2*sin(c + d*x)*(a + a*sin(c + d*x))^(1/2))/((77*d*e^6*cos(3*c + 3*d*x)*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))/4 + 77*d*e^6*sin(2*c + 2*d*x)*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2) - (385*d*e^6*cos(c + d*x)*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))/4)","B"
298,0,-1,244,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)/(a + a*sin(c + d*x))^(1/2), x)","F"
299,0,-1,200,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)/(a + a*sin(c + d*x))^(1/2), x)","F"
300,0,-1,169,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{\sqrt{e\,\cos\left(c+d\,x\right)}}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)/(a + a*sin(c + d*x))^(1/2), x)","F"
301,1,46,34,5.662486,"\text{Not used}","int(1/((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^(1/2)),x)","-\frac{2\,\cos\left(c+d\,x\right)\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}}{a\,d\,\sqrt{e\,\cos\left(c+d\,x\right)}\,\left(\sin\left(c+d\,x\right)+1\right)}","Not used",1,"-(2*cos(c + d*x)*(a*(sin(c + d*x) + 1))^(1/2))/(a*d*(e*cos(c + d*x))^(1/2)*(sin(c + d*x) + 1))","B"
302,1,77,76,6.007293,"\text{Not used}","int(1/((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^(1/2)),x)","\frac{4\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(3\,\sin\left(c+d\,x\right)-\cos\left(2\,c+2\,d\,x\right)+2\right)}{3\,a\,d\,e\,\sqrt{e\,\cos\left(c+d\,x\right)}\,\left(4\,\sin\left(c+d\,x\right)-\cos\left(2\,c+2\,d\,x\right)+3\right)}","Not used",1,"(4*(a*(sin(c + d*x) + 1))^(1/2)*(3*sin(c + d*x) - cos(2*c + 2*d*x) + 2))/(3*a*d*e*(e*cos(c + d*x))^(1/2)*(4*sin(c + d*x) - cos(2*c + 2*d*x) + 3))","B"
303,1,120,115,6.679663,"\text{Not used}","int(1/((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x))^(1/2)),x)","-\frac{8\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(8\,\cos\left(c+d\,x\right)+6\,\cos\left(3\,c+3\,d\,x\right)-\sin\left(2\,c+2\,d\,x\right)+2\,\sin\left(4\,c+4\,d\,x\right)\right)}{15\,a\,d\,e^2\,\sqrt{e\,\cos\left(c+d\,x\right)}\,\left(4\,\sin\left(c+d\,x\right)+4\,\cos\left(2\,c+2\,d\,x\right)-\cos\left(4\,c+4\,d\,x\right)+4\,\sin\left(3\,c+3\,d\,x\right)+5\right)}","Not used",1,"-(8*(a*(sin(c + d*x) + 1))^(1/2)*(8*cos(c + d*x) + 6*cos(3*c + 3*d*x) - sin(2*c + 2*d*x) + 2*sin(4*c + 4*d*x)))/(15*a*d*e^2*(e*cos(c + d*x))^(1/2)*(4*sin(c + d*x) + 4*cos(2*c + 2*d*x) - cos(4*c + 4*d*x) + 4*sin(3*c + 3*d*x) + 5))","B"
304,1,261,154,11.007803,"\text{Not used}","int(1/((e*cos(c + d*x))^(7/2)*(a + a*sin(c + d*x))^(1/2)),x)","\frac{20\,\sin\left(c+d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}+10\,\sqrt{a+a\,\sin\left(c+d\,x\right)}+8\,\cos\left(2\,c+2\,d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}+8\,\sin\left(3\,c+3\,d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{\frac{35\,a\,d\,e^3\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}{2}+\frac{35\,a\,d\,e^3\,\sin\left(c+d\,x\right)\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}{4}+\frac{35\,a\,d\,e^3\,\cos\left(2\,c+2\,d\,x\right)\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}{2}+\frac{35\,a\,d\,e^3\,\sin\left(3\,c+3\,d\,x\right)\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}{4}}","Not used",1,"(20*sin(c + d*x)*(a + a*sin(c + d*x))^(1/2) + 10*(a + a*sin(c + d*x))^(1/2) + 8*cos(2*c + 2*d*x)*(a + a*sin(c + d*x))^(1/2) + 8*sin(3*c + 3*d*x)*(a + a*sin(c + d*x))^(1/2))/((35*a*d*e^3*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))/2 + (35*a*d*e^3*sin(c + d*x)*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))/4 + (35*a*d*e^3*cos(2*c + 2*d*x)*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))/2 + (35*a*d*e^3*sin(3*c + 3*d*x)*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))/4)","B"
305,0,-1,247,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)/(a + a*sin(c + d*x))^(3/2), x)","F"
306,0,-1,215,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)/(a + a*sin(c + d*x))^(3/2), x)","F"
307,0,-1,236,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)/(a + a*sin(c + d*x))^(3/2), x)","F"
308,1,82,36,5.992281,"\text{Not used}","int((e*cos(c + d*x))^(1/2)/(a + a*sin(c + d*x))^(3/2),x)","-\frac{4\,\sqrt{e\,\cos\left(c+d\,x\right)}\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(2\,\cos\left(c+d\,x\right)+\sin\left(2\,c+2\,d\,x\right)\right)}{3\,a^2\,d\,\left(15\,\sin\left(c+d\,x\right)-6\,\cos\left(2\,c+2\,d\,x\right)-\sin\left(3\,c+3\,d\,x\right)+10\right)}","Not used",1,"-(4*(e*cos(c + d*x))^(1/2)*(a*(sin(c + d*x) + 1))^(1/2)*(2*cos(c + d*x) + sin(2*c + 2*d*x)))/(3*a^2*d*(15*sin(c + d*x) - 6*cos(2*c + 2*d*x) - sin(3*c + 3*d*x) + 10))","B"
309,1,95,76,6.379458,"\text{Not used}","int(1/((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^(3/2)),x)","-\frac{4\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(7\,\cos\left(c+d\,x\right)-\cos\left(3\,c+3\,d\,x\right)+5\,\sin\left(2\,c+2\,d\,x\right)\right)}{5\,a^2\,d\,\sqrt{e\,\cos\left(c+d\,x\right)}\,\left(15\,\sin\left(c+d\,x\right)-6\,\cos\left(2\,c+2\,d\,x\right)-\sin\left(3\,c+3\,d\,x\right)+10\right)}","Not used",1,"-(4*(a*(sin(c + d*x) + 1))^(1/2)*(7*cos(c + d*x) - cos(3*c + 3*d*x) + 5*sin(2*c + 2*d*x)))/(5*a^2*d*(e*cos(c + d*x))^(1/2)*(15*sin(c + d*x) - 6*cos(2*c + 2*d*x) - sin(3*c + 3*d*x) + 10))","B"
310,1,119,115,6.822957,"\text{Not used}","int(1/((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^(3/2)),x)","\frac{8\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(70\,\sin\left(c+d\,x\right)-41\,\cos\left(2\,c+2\,d\,x\right)+2\,\cos\left(4\,c+4\,d\,x\right)-14\,\sin\left(3\,c+3\,d\,x\right)+41\right)}{21\,a^2\,d\,e\,\sqrt{e\,\cos\left(c+d\,x\right)}\,\left(56\,\sin\left(c+d\,x\right)-28\,\cos\left(2\,c+2\,d\,x\right)+\cos\left(4\,c+4\,d\,x\right)-8\,\sin\left(3\,c+3\,d\,x\right)+35\right)}","Not used",1,"(8*(a*(sin(c + d*x) + 1))^(1/2)*(70*sin(c + d*x) - 41*cos(2*c + 2*d*x) + 2*cos(4*c + 4*d*x) - 14*sin(3*c + 3*d*x) + 41))/(21*a^2*d*e*(e*cos(c + d*x))^(1/2)*(56*sin(c + d*x) - 28*cos(2*c + 2*d*x) + cos(4*c + 4*d*x) - 8*sin(3*c + 3*d*x) + 35))","B"
311,1,230,154,11.101750,"\text{Not used}","int(1/((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x))^(3/2)),x)","-\frac{14\,\sqrt{a+a\,\sin\left(c+d\,x\right)}-12\,\sin\left(c+d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}+24\,\cos\left(2\,c+2\,d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}+8\,\sin\left(3\,c+3\,d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{\frac{225\,a^2\,d\,e^2\,\cos\left(c+d\,x\right)\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}{4}-\frac{45\,a^2\,d\,e^2\,\cos\left(3\,c+3\,d\,x\right)\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}{4}+45\,a^2\,d\,e^2\,\sin\left(2\,c+2\,d\,x\right)\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}","Not used",1,"-(14*(a + a*sin(c + d*x))^(1/2) - 12*sin(c + d*x)*(a + a*sin(c + d*x))^(1/2) + 24*cos(2*c + 2*d*x)*(a + a*sin(c + d*x))^(1/2) + 8*sin(3*c + 3*d*x)*(a + a*sin(c + d*x))^(1/2))/((225*a^2*d*e^2*cos(c + d*x)*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))/4 - (45*a^2*d*e^2*cos(3*c + 3*d*x)*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))/4 + 45*a^2*d*e^2*sin(2*c + 2*d*x)*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))","B"
312,1,413,193,11.650721,"\text{Not used}","int(1/((e*cos(c + d*x))^(7/2)*(a + a*sin(c + d*x))^(3/2)),x)","\frac{\sqrt{a+a\,\sin\left(c+d\,x\right)}\,\left(\frac{288\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}}{77\,a^2\,d\,e^3}+\frac{256\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\cos\left(2\,c+2\,d\,x\right)}{385\,a^2\,d\,e^3}-\frac{512\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\cos\left(4\,c+4\,d\,x\right)}{385\,a^2\,d\,e^3}+\frac{1536\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sin\left(3\,c+3\,d\,x\right)}{385\,a^2\,d\,e^3}+\frac{3328\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sin\left(c+d\,x\right)}{385\,a^2\,d\,e^3}\right)}{10\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{e\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}+8\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sin\left(c+d\,x\right)\,\sqrt{e\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}+8\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\cos\left(2\,c+2\,d\,x\right)\,\sqrt{e\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}-2\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\cos\left(4\,c+4\,d\,x\right)\,\sqrt{e\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}+8\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sin\left(3\,c+3\,d\,x\right)\,\sqrt{e\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}}","Not used",1,"((a + a*sin(c + d*x))^(1/2)*((288*exp(c*4i + d*x*4i))/(77*a^2*d*e^3) + (256*exp(c*4i + d*x*4i)*cos(2*c + 2*d*x))/(385*a^2*d*e^3) - (512*exp(c*4i + d*x*4i)*cos(4*c + 4*d*x))/(385*a^2*d*e^3) + (1536*exp(c*4i + d*x*4i)*sin(3*c + 3*d*x))/(385*a^2*d*e^3) + (3328*exp(c*4i + d*x*4i)*sin(c + d*x))/(385*a^2*d*e^3)))/(10*exp(c*4i + d*x*4i)*(e*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2) + 8*exp(c*4i + d*x*4i)*sin(c + d*x)*(e*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2) + 8*exp(c*4i + d*x*4i)*cos(2*c + 2*d*x)*(e*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2) - 2*exp(c*4i + d*x*4i)*cos(4*c + 4*d*x)*(e*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2) + 8*exp(c*4i + d*x*4i)*sin(3*c + 3*d*x)*(e*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))","B"
313,0,-1,261,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(9/2)/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{9/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((e*cos(c + d*x))^(9/2)/(a + a*sin(c + d*x))^(5/2), x)","F"
314,0,-1,239,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)/(a + a*sin(c + d*x))^(5/2), x)","F"
315,0,-1,218,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)/(a + a*sin(c + d*x))^(5/2), x)","F"
316,1,102,36,6.566587,"\text{Not used}","int((e*cos(c + d*x))^(3/2)/(a + a*sin(c + d*x))^(5/2),x)","-\frac{4\,e\,\sqrt{e\,\cos\left(c+d\,x\right)}\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(\sin\left(c+d\,x\right)+2\,\cos\left(2\,c+2\,d\,x\right)+\sin\left(3\,c+3\,d\,x\right)+2\right)}{5\,a^3\,d\,\left(56\,\sin\left(c+d\,x\right)-28\,\cos\left(2\,c+2\,d\,x\right)+\cos\left(4\,c+4\,d\,x\right)-8\,\sin\left(3\,c+3\,d\,x\right)+35\right)}","Not used",1,"-(4*e*(e*cos(c + d*x))^(1/2)*(a*(sin(c + d*x) + 1))^(1/2)*(sin(c + d*x) + 2*cos(2*c + 2*d*x) + sin(3*c + 3*d*x) + 2))/(5*a^3*d*(56*sin(c + d*x) - 28*cos(2*c + 2*d*x) + cos(4*c + 4*d*x) - 8*sin(3*c + 3*d*x) + 35))","B"
317,1,145,76,7.046563,"\text{Not used}","int((e*cos(c + d*x))^(1/2)/(a + a*sin(c + d*x))^(5/2),x)","-\frac{8\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\sqrt{-e\,\left(2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}\,\left(-58\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+18\,{\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}^2+26\,\sin\left(2\,c+2\,d\,x\right)-\sin\left(4\,c+4\,d\,x\right)+20\right)}{21\,a^3\,d\,\left(240\,{\sin\left(c+d\,x\right)}^2+210\,\sin\left(c+d\,x\right)-20\,{\sin\left(2\,c+2\,d\,x\right)}^2-45\,\sin\left(3\,c+3\,d\,x\right)+\sin\left(5\,c+5\,d\,x\right)+16\right)}","Not used",1,"-(8*(a*(sin(c + d*x) + 1))^(1/2)*(-e*(2*sin(c/2 + (d*x)/2)^2 - 1))^(1/2)*(26*sin(2*c + 2*d*x) - sin(4*c + 4*d*x) - 58*sin(c/2 + (d*x)/2)^2 + 18*sin((3*c)/2 + (3*d*x)/2)^2 + 20))/(21*a^3*d*(210*sin(c + d*x) - 45*sin(3*c + 3*d*x) + sin(5*c + 5*d*x) - 20*sin(2*c + 2*d*x)^2 + 240*sin(c + d*x)^2 + 16))","B"
318,1,137,115,7.661877,"\text{Not used}","int(1/((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^(5/2)),x)","-\frac{8\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}\,\left(137\,\cos\left(c+d\,x\right)-71\,\cos\left(3\,c+3\,d\,x\right)+2\,\cos\left(5\,c+5\,d\,x\right)+144\,\sin\left(2\,c+2\,d\,x\right)-18\,\sin\left(4\,c+4\,d\,x\right)\right)}{45\,a^3\,d\,\sqrt{e\,\cos\left(c+d\,x\right)}\,\left(210\,\sin\left(c+d\,x\right)-120\,\cos\left(2\,c+2\,d\,x\right)+10\,\cos\left(4\,c+4\,d\,x\right)-45\,\sin\left(3\,c+3\,d\,x\right)+\sin\left(5\,c+5\,d\,x\right)+126\right)}","Not used",1,"-(8*(a*(sin(c + d*x) + 1))^(1/2)*(137*cos(c + d*x) - 71*cos(3*c + 3*d*x) + 2*cos(5*c + 5*d*x) + 144*sin(2*c + 2*d*x) - 18*sin(4*c + 4*d*x)))/(45*a^3*d*(e*cos(c + d*x))^(1/2)*(210*sin(c + d*x) - 120*cos(2*c + 2*d*x) + 10*cos(4*c + 4*d*x) - 45*sin(3*c + 3*d*x) + sin(5*c + 5*d*x) + 126))","B"
319,1,261,154,11.167483,"\text{Not used}","int(1/((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^(5/2)),x)","\frac{76\,\sin\left(c+d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}+30\,\sqrt{a+a\,\sin\left(c+d\,x\right)}-40\,\cos\left(2\,c+2\,d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}-8\,\sin\left(3\,c+3\,d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}{\frac{385\,a^3\,d\,e\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}{2}+\frac{1155\,a^3\,d\,e\,\sin\left(c+d\,x\right)\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}{4}-\frac{231\,a^3\,d\,e\,\cos\left(2\,c+2\,d\,x\right)\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}{2}-\frac{77\,a^3\,d\,e\,\sin\left(3\,c+3\,d\,x\right)\,\sqrt{\frac{e\,{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{e\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}{4}}","Not used",1,"(76*sin(c + d*x)*(a + a*sin(c + d*x))^(1/2) + 30*(a + a*sin(c + d*x))^(1/2) - 40*cos(2*c + 2*d*x)*(a + a*sin(c + d*x))^(1/2) - 8*sin(3*c + 3*d*x)*(a + a*sin(c + d*x))^(1/2))/((385*a^3*d*e*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))/2 + (1155*a^3*d*e*sin(c + d*x)*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))/4 - (231*a^3*d*e*cos(2*c + 2*d*x)*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))/2 - (77*a^3*d*e*sin(3*c + 3*d*x)*((e*exp(- c*1i - d*x*1i))/2 + (e*exp(c*1i + d*x*1i))/2)^(1/2))/4)","B"
320,1,379,193,11.537270,"\text{Not used}","int(1/((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x))^(5/2)),x)","-\frac{\sqrt{a+a\,\sin\left(c+d\,x\right)}\,\left(\frac{{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,2464{}\mathrm{i}}{585\,a^3\,d\,e^2}+\frac{{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\cos\left(2\,c+2\,d\,x\right)\,4352{}\mathrm{i}}{585\,a^3\,d\,e^2}-\frac{{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\cos\left(4\,c+4\,d\,x\right)\,512{}\mathrm{i}}{585\,a^3\,d\,e^2}+\frac{{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sin\left(3\,c+3\,d\,x\right)\,512{}\mathrm{i}}{117\,a^3\,d\,e^2}-\frac{{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sin\left(c+d\,x\right)\,256{}\mathrm{i}}{117\,a^3\,d\,e^2}\right)}{\cos\left(c+d\,x\right)\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{e\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,28{}\mathrm{i}-{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\cos\left(3\,c+3\,d\,x\right)\,\sqrt{e\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,12{}\mathrm{i}+{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sin\left(2\,c+2\,d\,x\right)\,\sqrt{e\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,28{}\mathrm{i}-{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sin\left(4\,c+4\,d\,x\right)\,\sqrt{e\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,2{}\mathrm{i}}","Not used",1,"-((a + a*sin(c + d*x))^(1/2)*((exp(c*4i + d*x*4i)*2464i)/(585*a^3*d*e^2) + (exp(c*4i + d*x*4i)*cos(2*c + 2*d*x)*4352i)/(585*a^3*d*e^2) - (exp(c*4i + d*x*4i)*cos(4*c + 4*d*x)*512i)/(585*a^3*d*e^2) + (exp(c*4i + d*x*4i)*sin(3*c + 3*d*x)*512i)/(117*a^3*d*e^2) - (exp(c*4i + d*x*4i)*sin(c + d*x)*256i)/(117*a^3*d*e^2)))/(cos(c + d*x)*exp(c*4i + d*x*4i)*(e*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*28i - exp(c*4i + d*x*4i)*cos(3*c + 3*d*x)*(e*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*12i + exp(c*4i + d*x*4i)*sin(2*c + 2*d*x)*(e*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*28i - exp(c*4i + d*x*4i)*sin(4*c + 4*d*x)*(e*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*2i)","B"
321,0,-1,78,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/3)/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/3}}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((e*cos(c + d*x))^(7/3)/(a + a*sin(c + d*x))^(1/2), x)","F"
322,0,-1,78,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/3)/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/3}}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((e*cos(c + d*x))^(5/3)/(a + a*sin(c + d*x))^(1/2), x)","F"
323,0,-1,78,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(2/3)/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{2/3}}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((e*cos(c + d*x))^(2/3)/(a + a*sin(c + d*x))^(1/2), x)","F"
324,0,-1,78,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/3)/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{1/3}}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((e*cos(c + d*x))^(1/3)/(a + a*sin(c + d*x))^(1/2), x)","F"
325,0,-1,77,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(1/3)*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{1/3}\,\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(1/3)*(a + a*sin(c + d*x))^(1/2)), x)","F"
326,0,-1,75,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(4/3)*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{4/3}\,\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(4/3)*(a + a*sin(c + d*x))^(1/2)), x)","F"
327,0,-1,95,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p*(a + a*sin(c + d*x))^8,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^p\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^8 \,d x","Not used",1,"int((e*cos(c + d*x))^p*(a + a*sin(c + d*x))^8, x)","F"
328,0,-1,95,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p*(a + a*sin(c + d*x))^3,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^p\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((e*cos(c + d*x))^p*(a + a*sin(c + d*x))^3, x)","F"
329,0,-1,95,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p*(a + a*sin(c + d*x))^2,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^p\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((e*cos(c + d*x))^p*(a + a*sin(c + d*x))^2, x)","F"
330,0,-1,93,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p*(a + a*sin(c + d*x)),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^p\,\left(a+a\,\sin\left(c+d\,x\right)\right) \,d x","Not used",1,"int((e*cos(c + d*x))^p*(a + a*sin(c + d*x)), x)","F"
331,0,-1,95,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p/(a + a*sin(c + d*x)),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^p}{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^p/(a + a*sin(c + d*x)), x)","F"
332,0,-1,93,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p/(a + a*sin(c + d*x))^2,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^p}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*cos(c + d*x))^p/(a + a*sin(c + d*x))^2, x)","F"
333,0,-1,93,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p/(a + a*sin(c + d*x))^3,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^p}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^p/(a + a*sin(c + d*x))^3, x)","F"
334,0,-1,93,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p/(a + a*sin(c + d*x))^8,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^p}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^8} \,d x","Not used",1,"int((e*cos(c + d*x))^p/(a + a*sin(c + d*x))^8, x)","F"
335,0,-1,103,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p*(a + a*sin(c + d*x))^(7/2),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^p\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{7/2} \,d x","Not used",1,"int((e*cos(c + d*x))^p*(a + a*sin(c + d*x))^(7/2), x)","F"
336,0,-1,103,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p*(a + a*sin(c + d*x))^(5/2),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^p\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((e*cos(c + d*x))^p*(a + a*sin(c + d*x))^(5/2), x)","F"
337,0,-1,103,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p*(a + a*sin(c + d*x))^(3/2),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^p\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((e*cos(c + d*x))^p*(a + a*sin(c + d*x))^(3/2), x)","F"
338,0,-1,97,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p*(a + a*sin(c + d*x))^(1/2),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^p\,\sqrt{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^p*(a + a*sin(c + d*x))^(1/2), x)","F"
339,0,-1,101,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^p}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((e*cos(c + d*x))^p/(a + a*sin(c + d*x))^(1/2), x)","F"
340,0,-1,102,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^p}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((e*cos(c + d*x))^p/(a + a*sin(c + d*x))^(3/2), x)","F"
341,0,-1,105,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^p}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((e*cos(c + d*x))^p/(a + a*sin(c + d*x))^(5/2), x)","F"
342,0,-1,114,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p*(a + a*sin(c + d*x))^m,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^p\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int((e*cos(c + d*x))^p*(a + a*sin(c + d*x))^m, x)","F"
343,1,555,109,10.479704,"\text{Not used}","int(cos(c + d*x)^7*(a + a*sin(c + d*x))^m,x)","{\mathrm{e}}^{-c\,7{}\mathrm{i}-d\,x\,7{}\mathrm{i}}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m\,\left(\frac{{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\left(m^3\,40{}\mathrm{i}+m^2\,936{}\mathrm{i}+m\,8672{}\mathrm{i}+49152{}\mathrm{i}\right)}{128\,d\,\left(m^4\,1{}\mathrm{i}+m^3\,22{}\mathrm{i}+m^2\,179{}\mathrm{i}+m\,638{}\mathrm{i}+840{}\mathrm{i}\right)}+\frac{{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\cos\left(2\,c+2\,d\,x\right)\,\left(m^3\,30{}\mathrm{i}+m^2\,654{}\mathrm{i}+m\,4824{}\mathrm{i}\right)}{64\,d\,\left(m^4\,1{}\mathrm{i}+m^3\,22{}\mathrm{i}+m^2\,179{}\mathrm{i}+m\,638{}\mathrm{i}+840{}\mathrm{i}\right)}+\frac{{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sin\left(5\,c+5\,d\,x\right)\,\left(5\,m^3+123\,m^2+706\,m+1176\right)\,1{}\mathrm{i}}{64\,d\,\left(m^4\,1{}\mathrm{i}+m^3\,22{}\mathrm{i}+m^2\,179{}\mathrm{i}+m\,638{}\mathrm{i}+840{}\mathrm{i}\right)}+\frac{{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sin\left(3\,c+3\,d\,x\right)\,\left(9\,m^3+279\,m^2+3210\,m+5880\right)\,1{}\mathrm{i}}{64\,d\,\left(m^4\,1{}\mathrm{i}+m^3\,22{}\mathrm{i}+m^2\,179{}\mathrm{i}+m\,638{}\mathrm{i}+840{}\mathrm{i}\right)}+\frac{{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sin\left(7\,c+7\,d\,x\right)\,\left(m^3+15\,m^2+74\,m+120\right)\,1{}\mathrm{i}}{64\,d\,\left(m^4\,1{}\mathrm{i}+m^3\,22{}\mathrm{i}+m^2\,179{}\mathrm{i}+m\,638{}\mathrm{i}+840{}\mathrm{i}\right)}+\frac{{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sin\left(c+d\,x\right)\,\left(5\,m^3+171\,m^2+2578\,m+29400\right)\,1{}\mathrm{i}}{64\,d\,\left(m^4\,1{}\mathrm{i}+m^3\,22{}\mathrm{i}+m^2\,179{}\mathrm{i}+m\,638{}\mathrm{i}+840{}\mathrm{i}\right)}+\frac{m\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\cos\left(6\,c+6\,d\,x\right)\,\left(m^2\,1{}\mathrm{i}+m\,9{}\mathrm{i}+20{}\mathrm{i}\right)}{32\,d\,\left(m^4\,1{}\mathrm{i}+m^3\,22{}\mathrm{i}+m^2\,179{}\mathrm{i}+m\,638{}\mathrm{i}+840{}\mathrm{i}\right)}+\frac{3\,m\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\cos\left(4\,c+4\,d\,x\right)\,\left(m^2\,1{}\mathrm{i}+m\,17{}\mathrm{i}+44{}\mathrm{i}\right)}{16\,d\,\left(m^4\,1{}\mathrm{i}+m^3\,22{}\mathrm{i}+m^2\,179{}\mathrm{i}+m\,638{}\mathrm{i}+840{}\mathrm{i}\right)}\right)","Not used",1,"exp(- c*7i - d*x*7i)*(a + a*sin(c + d*x))^m*((exp(c*7i + d*x*7i)*(m*8672i + m^2*936i + m^3*40i + 49152i))/(128*d*(m*638i + m^2*179i + m^3*22i + m^4*1i + 840i)) + (exp(c*7i + d*x*7i)*cos(2*c + 2*d*x)*(m*4824i + m^2*654i + m^3*30i))/(64*d*(m*638i + m^2*179i + m^3*22i + m^4*1i + 840i)) + (exp(c*7i + d*x*7i)*sin(5*c + 5*d*x)*(706*m + 123*m^2 + 5*m^3 + 1176)*1i)/(64*d*(m*638i + m^2*179i + m^3*22i + m^4*1i + 840i)) + (exp(c*7i + d*x*7i)*sin(3*c + 3*d*x)*(3210*m + 279*m^2 + 9*m^3 + 5880)*1i)/(64*d*(m*638i + m^2*179i + m^3*22i + m^4*1i + 840i)) + (exp(c*7i + d*x*7i)*sin(7*c + 7*d*x)*(74*m + 15*m^2 + m^3 + 120)*1i)/(64*d*(m*638i + m^2*179i + m^3*22i + m^4*1i + 840i)) + (exp(c*7i + d*x*7i)*sin(c + d*x)*(2578*m + 171*m^2 + 5*m^3 + 29400)*1i)/(64*d*(m*638i + m^2*179i + m^3*22i + m^4*1i + 840i)) + (m*exp(c*7i + d*x*7i)*cos(6*c + 6*d*x)*(m*9i + m^2*1i + 20i))/(32*d*(m*638i + m^2*179i + m^3*22i + m^4*1i + 840i)) + (3*m*exp(c*7i + d*x*7i)*cos(4*c + 4*d*x)*(m*17i + m^2*1i + 44i))/(16*d*(m*638i + m^2*179i + m^3*22i + m^4*1i + 840i)))","B"
344,1,195,81,1.970787,"\text{Not used}","int(cos(c + d*x)^5*(a + a*sin(c + d*x))^m,x)","\frac{{\left(a\,\left(\sin\left(c+d\,x\right)+1\right)\right)}^m\,\left(82\,m+600\,\sin\left(c+d\,x\right)+100\,\sin\left(3\,c+3\,d\,x\right)+12\,\sin\left(5\,c+5\,d\,x\right)+46\,m\,\sin\left(c+d\,x\right)+88\,m\,\cos\left(2\,c+2\,d\,x\right)+6\,m\,\cos\left(4\,c+4\,d\,x\right)+53\,m\,\sin\left(3\,c+3\,d\,x\right)+7\,m\,\sin\left(5\,c+5\,d\,x\right)+2\,m^2\,\sin\left(c+d\,x\right)+6\,m^2+8\,m^2\,\cos\left(2\,c+2\,d\,x\right)+2\,m^2\,\cos\left(4\,c+4\,d\,x\right)+3\,m^2\,\sin\left(3\,c+3\,d\,x\right)+m^2\,\sin\left(5\,c+5\,d\,x\right)+512\right)}{16\,d\,\left(m^3+12\,m^2+47\,m+60\right)}","Not used",1,"((a*(sin(c + d*x) + 1))^m*(82*m + 600*sin(c + d*x) + 100*sin(3*c + 3*d*x) + 12*sin(5*c + 5*d*x) + 46*m*sin(c + d*x) + 88*m*cos(2*c + 2*d*x) + 6*m*cos(4*c + 4*d*x) + 53*m*sin(3*c + 3*d*x) + 7*m*sin(5*c + 5*d*x) + 2*m^2*sin(c + d*x) + 6*m^2 + 8*m^2*cos(2*c + 2*d*x) + 2*m^2*cos(4*c + 4*d*x) + 3*m^2*sin(3*c + 3*d*x) + m^2*sin(5*c + 5*d*x) + 512))/(16*d*(47*m + 12*m^2 + m^3 + 60))","B"
345,1,85,55,0.726173,"\text{Not used}","int(cos(c + d*x)^3*(a + a*sin(c + d*x))^m,x)","\frac{{\left(a\,\left(\sin\left(c+d\,x\right)+1\right)\right)}^m\,\left(2\,m+18\,\sin\left(c+d\,x\right)+2\,\sin\left(3\,c+3\,d\,x\right)+m\,\sin\left(c+d\,x\right)-2\,m\,\left(2\,{\sin\left(c+d\,x\right)}^2-1\right)+m\,\sin\left(3\,c+3\,d\,x\right)+16\right)}{4\,d\,\left(m^2+5\,m+6\right)}","Not used",1,"((a*(sin(c + d*x) + 1))^m*(2*m + 18*sin(c + d*x) + 2*sin(3*c + 3*d*x) + m*sin(c + d*x) - 2*m*(2*sin(c + d*x)^2 - 1) + m*sin(3*c + 3*d*x) + 16))/(4*d*(5*m + m^2 + 6))","B"
346,1,29,26,0.215363,"\text{Not used}","int(cos(c + d*x)*(a + a*sin(c + d*x))^m,x)","\frac{{\left(a\,\left(\sin\left(c+d\,x\right)+1\right)\right)}^m\,\left(\sin\left(c+d\,x\right)+1\right)}{d\,\left(m+1\right)}","Not used",1,"((a*(sin(c + d*x) + 1))^m*(sin(c + d*x) + 1))/(d*(m + 1))","B"
347,0,-1,40,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^m/cos(c + d*x),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + a*sin(c + d*x))^m/cos(c + d*x), x)","F"
348,0,-1,47,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^m/cos(c + d*x)^3,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + a*sin(c + d*x))^m/cos(c + d*x)^3, x)","F"
349,0,-1,51,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^m/cos(c + d*x)^5,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((a + a*sin(c + d*x))^m/cos(c + d*x)^5, x)","F"
350,0,-1,83,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + a*sin(c + d*x))^m,x)","\int {\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int(cos(c + d*x)^4*(a + a*sin(c + d*x))^m, x)","F"
351,0,-1,81,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + a*sin(c + d*x))^m,x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int(cos(c + d*x)^2*(a + a*sin(c + d*x))^m, x)","F"
352,0,-1,73,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^m/cos(c + d*x)^2,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + a*sin(c + d*x))^m/cos(c + d*x)^2, x)","F"
353,0,-1,83,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^m/cos(c + d*x)^4,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + a*sin(c + d*x))^m/cos(c + d*x)^4, x)","F"
354,0,-1,88,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x))^m,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)*(a + a*sin(c + d*x))^m, x)","F"
355,0,-1,88,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^m,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)*(a + a*sin(c + d*x))^m, x)","F"
356,0,-1,88,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^m,x)","\int \sqrt{e\,\cos\left(c+d\,x\right)}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)*(a + a*sin(c + d*x))^m, x)","F"
357,0,-1,86,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m}{\sqrt{e\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(1/2), x)","F"
358,0,-1,82,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(3/2), x)","F"
359,0,-1,85,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(5/2), x)","F"
360,1,137,201,6.827532,"\text{Not used}","int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(m + 4),x)","\frac{2\,{\left(a\,\left(\sin\left(c+d\,x\right)+1\right)\right)}^m\,\left(12\,\sin\left(2\,c+2\,d\,x\right)+3\,\sin\left(4\,c+4\,d\,x\right)-22\,m\,\cos\left(c+d\,x\right)-6\,m\,\cos\left(3\,c+3\,d\,x\right)+4\,m^3\,\cos\left(c+d\,x\right)-6\,m^2\,\sin\left(2\,c+2\,d\,x\right)\right)}{d\,e^4\,{\left(e\,\cos\left(c+d\,x\right)\right)}^m\,\left(4\,\cos\left(2\,c+2\,d\,x\right)+\cos\left(4\,c+4\,d\,x\right)+3\right)\,\left(m^4-10\,m^2+9\right)}","Not used",1,"(2*(a*(sin(c + d*x) + 1))^m*(12*sin(2*c + 2*d*x) + 3*sin(4*c + 4*d*x) - 22*m*cos(c + d*x) - 6*m*cos(3*c + 3*d*x) + 4*m^3*cos(c + d*x) - 6*m^2*sin(2*c + 2*d*x)))/(d*e^4*(e*cos(c + d*x))^m*(4*cos(2*c + 2*d*x) + cos(4*c + 4*d*x) + 3)*(m^4 - 10*m^2 + 9))","B"
361,1,103,142,6.125696,"\text{Not used}","int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(m + 3),x)","-\frac{2\,{\left(a\,\left(\sin\left(c+d\,x\right)+1\right)\right)}^m\,\left(-2\,\cos\left(c+d\,x\right)\,m^2+2\,\sin\left(2\,c+2\,d\,x\right)\,m+3\,\cos\left(c+d\,x\right)+\cos\left(3\,c+3\,d\,x\right)\right)}{d\,e^3\,m\,{\left(e\,\cos\left(c+d\,x\right)\right)}^m\,\left(m^2-4\right)\,\left(3\,\cos\left(c+d\,x\right)+\cos\left(3\,c+3\,d\,x\right)\right)}","Not used",1,"-(2*(a*(sin(c + d*x) + 1))^m*(3*cos(c + d*x) + cos(3*c + 3*d*x) - 2*m^2*cos(c + d*x) + 2*m*sin(2*c + 2*d*x)))/(d*e^3*m*(e*cos(c + d*x))^m*(m^2 - 4)*(3*cos(c + d*x) + cos(3*c + 3*d*x)))","B"
362,1,71,89,5.604557,"\text{Not used}","int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(m + 2),x)","-\frac{\left(\sin\left(2\,c+2\,d\,x\right)-2\,m\,\cos\left(c+d\,x\right)\right)\,{\left(a\,\left(\sin\left(c+d\,x\right)+1\right)\right)}^m}{d\,e^2\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)\,{\left(e\,\cos\left(c+d\,x\right)\right)}^m\,\left(m^2-1\right)}","Not used",1,"-((sin(2*c + 2*d*x) - 2*m*cos(c + d*x))*(a*(sin(c + d*x) + 1))^m)/(d*e^2*(cos(2*c + 2*d*x) + 1)*(e*cos(c + d*x))^m*(m^2 - 1))","B"
363,1,34,34,0.288341,"\text{Not used}","int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(m + 1),x)","\frac{{\left(a\,\left(\sin\left(c+d\,x\right)+1\right)\right)}^m}{d\,e\,m\,{\left(e\,\cos\left(c+d\,x\right)\right)}^m}","Not used",1,"(a*(sin(c + d*x) + 1))^m/(d*e*m*(e*cos(c + d*x))^m)","B"
364,0,-1,115,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^m,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m}{{\left(e\,\cos\left(c+d\,x\right)\right)}^m} \,d x","Not used",1,"int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^m, x)","F"
365,0,-1,97,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1 - m)*(a + a*sin(c + d*x))^m,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{1-m}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int((e*cos(c + d*x))^(1 - m)*(a + a*sin(c + d*x))^m, x)","F"
366,0,-1,115,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(2 - m)*(a + a*sin(c + d*x))^m,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{2-m}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int((e*cos(c + d*x))^(2 - m)*(a + a*sin(c + d*x))^m, x)","F"
367,1,601,150,13.476571,"\text{Not used}","int((e*cos(c + d*x))^(5 - 2*m)*(a + a*sin(c + d*x))^m,x)","-\frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m\,\left(-\frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5-2\,m}\,\left(m^2-7\,m+12\right)}{d\,\left(m^3-12\,m^2+47\,m-60\right)}+\frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5-2\,m}\,\left(\cos\left(c+d\,x\right)+\sin\left(c+d\,x\right)\,1{}\mathrm{i}\right)\,\left(m^2\,3{}\mathrm{i}-m\,29{}\mathrm{i}+60{}\mathrm{i}\right)}{d\,\left(m^3-12\,m^2+47\,m-60\right)}-\frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5-2\,m}\,\left(\cos\left(5\,c+5\,d\,x\right)+\sin\left(5\,c+5\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(m^2\,1{}\mathrm{i}-m\,7{}\mathrm{i}+12{}\mathrm{i}\right)}{d\,\left(m^3-12\,m^2+47\,m-60\right)}+\frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5-2\,m}\,\left(\cos\left(4\,c+4\,d\,x\right)+\sin\left(4\,c+4\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(3\,m^2-29\,m+60\right)}{d\,\left(m^3-12\,m^2+47\,m-60\right)}+\frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5-2\,m}\,\left(\cos\left(2\,c+2\,d\,x\right)+\sin\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(2\,m^2-22\,m+80\right)}{d\,\left(m^3-12\,m^2+47\,m-60\right)}+\frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5-2\,m}\,\left(\cos\left(3\,c+3\,d\,x\right)+\sin\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(m^2\,2{}\mathrm{i}-m\,22{}\mathrm{i}+80{}\mathrm{i}\right)}{d\,\left(m^3-12\,m^2+47\,m-60\right)}\right)}{5\,\cos\left(c+d\,x\right)+\sin\left(c+d\,x\right)\,5{}\mathrm{i}-10\,\cos\left(3\,c+3\,d\,x\right)+\cos\left(5\,c+5\,d\,x\right)-\sin\left(3\,c+3\,d\,x\right)\,10{}\mathrm{i}+\sin\left(5\,c+5\,d\,x\right)\,1{}\mathrm{i}+\frac{m^3\,1{}\mathrm{i}-m^2\,12{}\mathrm{i}+m\,47{}\mathrm{i}-60{}\mathrm{i}}{m^3-12\,m^2+47\,m-60}-\frac{10\,\left(\cos\left(2\,c+2\,d\,x\right)+\sin\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(m^3\,1{}\mathrm{i}-m^2\,12{}\mathrm{i}+m\,47{}\mathrm{i}-60{}\mathrm{i}\right)}{m^3-12\,m^2+47\,m-60}+\frac{5\,\left(\cos\left(4\,c+4\,d\,x\right)+\sin\left(4\,c+4\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(m^3\,1{}\mathrm{i}-m^2\,12{}\mathrm{i}+m\,47{}\mathrm{i}-60{}\mathrm{i}\right)}{m^3-12\,m^2+47\,m-60}}","Not used",1,"-((a + a*sin(c + d*x))^m*(((e*cos(c + d*x))^(5 - 2*m)*(cos(c + d*x) + sin(c + d*x)*1i)*(m^2*3i - m*29i + 60i))/(d*(47*m - 12*m^2 + m^3 - 60)) - ((e*cos(c + d*x))^(5 - 2*m)*(m^2 - 7*m + 12))/(d*(47*m - 12*m^2 + m^3 - 60)) - ((e*cos(c + d*x))^(5 - 2*m)*(cos(5*c + 5*d*x) + sin(5*c + 5*d*x)*1i)*(m^2*1i - m*7i + 12i))/(d*(47*m - 12*m^2 + m^3 - 60)) + ((e*cos(c + d*x))^(5 - 2*m)*(cos(4*c + 4*d*x) + sin(4*c + 4*d*x)*1i)*(3*m^2 - 29*m + 60))/(d*(47*m - 12*m^2 + m^3 - 60)) + ((e*cos(c + d*x))^(5 - 2*m)*(cos(2*c + 2*d*x) + sin(2*c + 2*d*x)*1i)*(2*m^2 - 22*m + 80))/(d*(47*m - 12*m^2 + m^3 - 60)) + ((e*cos(c + d*x))^(5 - 2*m)*(cos(3*c + 3*d*x) + sin(3*c + 3*d*x)*1i)*(m^2*2i - m*22i + 80i))/(d*(47*m - 12*m^2 + m^3 - 60))))/(5*cos(c + d*x) + sin(c + d*x)*5i - 10*cos(3*c + 3*d*x) + cos(5*c + 5*d*x) - sin(3*c + 3*d*x)*10i + sin(5*c + 5*d*x)*1i + (m*47i - m^2*12i + m^3*1i - 60i)/(47*m - 12*m^2 + m^3 - 60) - (10*(cos(2*c + 2*d*x) + sin(2*c + 2*d*x)*1i)*(m*47i - m^2*12i + m^3*1i - 60i))/(47*m - 12*m^2 + m^3 - 60) + (5*(cos(4*c + 4*d*x) + sin(4*c + 4*d*x)*1i)*(m*47i - m^2*12i + m^3*1i - 60i))/(47*m - 12*m^2 + m^3 - 60))","B"
368,1,241,94,8.767526,"\text{Not used}","int((e*cos(c + d*x))^(3 - 2*m)*(a + a*sin(c + d*x))^m,x)","\frac{e^3\,{\left(a\,\left(\sin\left(c+d\,x\right)+1\right)\right)}^m\,\left(14\,m-24\,\sin\left(c+d\,x\right)-36\,\sin\left(3\,c+3\,d\,x\right)-12\,\sin\left(5\,c+5\,d\,x\right)+24\,{\sin\left(2\,c+2\,d\,x\right)}^2-4\,{\sin\left(3\,c+3\,d\,x\right)}^2+8\,m\,\sin\left(c+d\,x\right)-17\,m\,\left(2\,{\sin\left(c+d\,x\right)}^2-1\right)+12\,m\,\sin\left(3\,c+3\,d\,x\right)+4\,m\,\sin\left(5\,c+5\,d\,x\right)-2\,m\,\left(2\,{\sin\left(2\,c+2\,d\,x\right)}^2-1\right)+m\,\left(2\,{\sin\left(3\,c+3\,d\,x\right)}^2-1\right)+132\,{\sin\left(c+d\,x\right)}^2-128\right)}{8\,d\,{\left(-e\,\left(2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)\right)}^{2\,m}\,\left(m^2-5\,m+6\right)\,\left(12\,{\sin\left(c+d\,x\right)}^2+15\,\sin\left(c+d\,x\right)-\sin\left(3\,c+3\,d\,x\right)+4\right)}","Not used",1,"(e^3*(a*(sin(c + d*x) + 1))^m*(14*m - 24*sin(c + d*x) - 36*sin(3*c + 3*d*x) - 12*sin(5*c + 5*d*x) + 24*sin(2*c + 2*d*x)^2 - 4*sin(3*c + 3*d*x)^2 + 8*m*sin(c + d*x) - 17*m*(2*sin(c + d*x)^2 - 1) + 12*m*sin(3*c + 3*d*x) + 4*m*sin(5*c + 5*d*x) - 2*m*(2*sin(2*c + 2*d*x)^2 - 1) + m*(2*sin(3*c + 3*d*x)^2 - 1) + 132*sin(c + d*x)^2 - 128))/(8*d*(-e*(2*sin(c/2 + (d*x)/2)^2 - 1))^(2*m)*(m^2 - 5*m + 6)*(15*sin(c + d*x) - sin(3*c + 3*d*x) + 12*sin(c + d*x)^2 + 4))","B"
369,1,58,44,5.581553,"\text{Not used}","int((e*cos(c + d*x))^(1 - 2*m)*(a + a*sin(c + d*x))^m,x)","\frac{e\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)\,{\left(a\,\left(\sin\left(c+d\,x\right)+1\right)\right)}^m}{2\,d\,{\left(e\,\cos\left(c+d\,x\right)\right)}^{2\,m}\,\left(m-1\right)\,\left(\sin\left(c+d\,x\right)+1\right)}","Not used",1,"(e*(cos(2*c + 2*d*x) + 1)*(a*(sin(c + d*x) + 1))^m)/(2*d*(e*cos(c + d*x))^(2*m)*(m - 1)*(sin(c + d*x) + 1))","B"
370,0,-1,61,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(2*m + 1),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{2\,m+1}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(2*m + 1), x)","F"
371,0,-1,70,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(2*m + 3),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{2\,m+3}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(2*m + 3), x)","F"
372,0,-1,89,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(4 - 2*m)*(a + a*sin(c + d*x))^m,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{4-2\,m}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int((e*cos(c + d*x))^(4 - 2*m)*(a + a*sin(c + d*x))^m, x)","F"
373,0,-1,89,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(2 - 2*m)*(a + a*sin(c + d*x))^m,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{2-2\,m}\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int((e*cos(c + d*x))^(2 - 2*m)*(a + a*sin(c + d*x))^m, x)","F"
374,0,-1,86,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(2*m),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{2\,m}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(2*m), x)","F"
375,0,-1,87,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(2*m + 2),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^m}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{2\,m+2}} \,d x","Not used",1,"int((a + a*sin(c + d*x))^m/(e*cos(c + d*x))^(2*m + 2), x)","F"
376,1,68,60,0.065413,"\text{Not used}","int(cos(c + d*x)^5*(a + b*sin(c + d*x)),x)","\frac{\frac{b\,{\sin\left(c+d\,x\right)}^6}{6}+\frac{a\,{\sin\left(c+d\,x\right)}^5}{5}-\frac{b\,{\sin\left(c+d\,x\right)}^4}{2}-\frac{2\,a\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{b\,{\sin\left(c+d\,x\right)}^2}{2}+a\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a*sin(c + d*x) - (2*a*sin(c + d*x)^3)/3 + (a*sin(c + d*x)^5)/5 + (b*sin(c + d*x)^2)/2 - (b*sin(c + d*x)^4)/2 + (b*sin(c + d*x)^6)/6)/d","B"
377,1,46,44,0.057364,"\text{Not used}","int(cos(c + d*x)^3*(a + b*sin(c + d*x)),x)","\frac{-\frac{b\,{\sin\left(c+d\,x\right)}^4}{4}-\frac{a\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{b\,{\sin\left(c+d\,x\right)}^2}{2}+a\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a*sin(c + d*x) - (a*sin(c + d*x)^3)/3 + (b*sin(c + d*x)^2)/2 - (b*sin(c + d*x)^4)/4)/d","B"
378,1,23,22,0.042457,"\text{Not used}","int(cos(c + d*x)*(a + b*sin(c + d*x)),x)","\frac{\sin\left(c+d\,x\right)\,\left(2\,a+b\,\sin\left(c+d\,x\right)\right)}{2\,d}","Not used",1,"(sin(c + d*x)*(2*a + b*sin(c + d*x)))/(2*d)","B"
379,1,54,43,0.072382,"\text{Not used}","int((a + b*sin(c + d*x))/cos(c + d*x),x)","-\frac{\frac{a\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{2}-\frac{a\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{2}+\frac{b\,\ln\left(\sin\left(c+d\,x\right)-1\right)}{2}+\frac{b\,\ln\left(\sin\left(c+d\,x\right)+1\right)}{2}}{d}","Not used",1,"-((a*log(sin(c + d*x) - 1))/2 - (a*log(sin(c + d*x) + 1))/2 + (b*log(sin(c + d*x) - 1))/2 + (b*log(sin(c + d*x) + 1))/2)/d","B"
380,1,44,41,0.074830,"\text{Not used}","int((a + b*sin(c + d*x))/cos(c + d*x)^3,x)","\frac{a\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{2\,d}-\frac{\frac{b}{2}+\frac{a\,\sin\left(c+d\,x\right)}{2}}{d\,\left({\sin\left(c+d\,x\right)}^2-1\right)}","Not used",1,"(a*atanh(sin(c + d*x)))/(2*d) - (b/2 + (a*sin(c + d*x))/2)/(d*(sin(c + d*x)^2 - 1))","B"
381,1,64,61,5.144821,"\text{Not used}","int((a + b*sin(c + d*x))/cos(c + d*x)^5,x)","\frac{3\,a\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)}{8\,d}+\frac{-\frac{3\,a\,{\sin\left(c+d\,x\right)}^3}{8}+\frac{5\,a\,\sin\left(c+d\,x\right)}{8}+\frac{b}{4}}{d\,\left({\sin\left(c+d\,x\right)}^4-2\,{\sin\left(c+d\,x\right)}^2+1\right)}","Not used",1,"(3*a*atanh(sin(c + d*x)))/(8*d) + (b/4 + (5*a*sin(c + d*x))/8 - (3*a*sin(c + d*x)^3)/8)/(d*(sin(c + d*x)^4 - 2*sin(c + d*x)^2 + 1))","B"
382,1,111,65,8.693699,"\text{Not used}","int(cos(c + d*x)^4*(a + b*sin(c + d*x)),x)","\frac{3\,a\,x}{8}-\frac{\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}+4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{2\,b}{5}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(3*a*x)/8 - ((2*b)/5 - (5*a*tan(c/2 + (d*x)/2))/4 - (a*tan(c/2 + (d*x)/2)^3)/2 + (a*tan(c/2 + (d*x)/2)^7)/2 + (5*a*tan(c/2 + (d*x)/2)^9)/4 + 4*b*tan(c/2 + (d*x)/2)^4 + 2*b*tan(c/2 + (d*x)/2)^8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
383,1,68,43,7.381221,"\text{Not used}","int(cos(c + d*x)^2*(a + b*sin(c + d*x)),x)","\frac{a\,x}{2}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{2\,b}{3}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^3}","Not used",1,"(a*x)/2 - ((2*b)/3 - a*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^5 + 2*b*tan(c/2 + (d*x)/2)^4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^3)","B"
384,1,22,23,5.131900,"\text{Not used}","int((a + b*sin(c + d*x))/cos(c + d*x)^2,x)","\frac{b+a\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(b + a*sin(c + d*x))/(d*cos(c + d*x))","B"
385,1,42,44,5.265499,"\text{Not used}","int((a + b*sin(c + d*x))/cos(c + d*x)^4,x)","\frac{\frac{2\,a\,\sin\left(c+d\,x\right)\,{\cos\left(c+d\,x\right)}^2}{3}+\frac{b}{3}+\frac{a\,\sin\left(c+d\,x\right)}{3}}{d\,{\cos\left(c+d\,x\right)}^3}","Not used",1,"(b/3 + (a*sin(c + d*x))/3 + (2*a*cos(c + d*x)^2*sin(c + d*x))/3)/(d*cos(c + d*x)^3)","B"
386,1,75,60,5.298601,"\text{Not used}","int((a + b*sin(c + d*x))/cos(c + d*x)^6,x)","\frac{b}{5\,d\,{\cos\left(c+d\,x\right)}^5}+\frac{8\,a\,\sin\left(c+d\,x\right)}{15\,d\,\cos\left(c+d\,x\right)}+\frac{4\,a\,\sin\left(c+d\,x\right)}{15\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{a\,\sin\left(c+d\,x\right)}{5\,d\,{\cos\left(c+d\,x\right)}^5}","Not used",1,"b/(5*d*cos(c + d*x)^5) + (8*a*sin(c + d*x))/(15*d*cos(c + d*x)) + (4*a*sin(c + d*x))/(15*d*cos(c + d*x)^3) + (a*sin(c + d*x))/(5*d*cos(c + d*x)^5)","B"
387,1,104,99,0.073563,"\text{Not used}","int(cos(c + d*x)^5*(a + b*sin(c + d*x))^2,x)","\frac{a^2\,\sin\left(c+d\,x\right)-{\sin\left(c+d\,x\right)}^3\,\left(\frac{2\,a^2}{3}-\frac{b^2}{3}\right)+{\sin\left(c+d\,x\right)}^5\,\left(\frac{a^2}{5}-\frac{2\,b^2}{5}\right)+\frac{b^2\,{\sin\left(c+d\,x\right)}^7}{7}+a\,b\,{\sin\left(c+d\,x\right)}^2-a\,b\,{\sin\left(c+d\,x\right)}^4+\frac{a\,b\,{\sin\left(c+d\,x\right)}^6}{3}}{d}","Not used",1,"(a^2*sin(c + d*x) - sin(c + d*x)^3*((2*a^2)/3 - b^2/3) + sin(c + d*x)^5*(a^2/5 - (2*b^2)/5) + (b^2*sin(c + d*x)^7)/7 + a*b*sin(c + d*x)^2 - a*b*sin(c + d*x)^4 + (a*b*sin(c + d*x)^6)/3)/d","B"
388,1,74,77,0.050180,"\text{Not used}","int(cos(c + d*x)^3*(a + b*sin(c + d*x))^2,x)","-\frac{{\sin\left(c+d\,x\right)}^3\,\left(\frac{a^2}{3}-\frac{b^2}{3}\right)-a^2\,\sin\left(c+d\,x\right)+\frac{b^2\,{\sin\left(c+d\,x\right)}^5}{5}-a\,b\,{\sin\left(c+d\,x\right)}^2+\frac{a\,b\,{\sin\left(c+d\,x\right)}^4}{2}}{d}","Not used",1,"-(sin(c + d*x)^3*(a^2/3 - b^2/3) - a^2*sin(c + d*x) + (b^2*sin(c + d*x)^5)/5 - a*b*sin(c + d*x)^2 + (a*b*sin(c + d*x)^4)/2)/d","B"
389,1,39,22,0.058014,"\text{Not used}","int(cos(c + d*x)*(a + b*sin(c + d*x))^2,x)","\frac{a^2\,\sin\left(c+d\,x\right)+a\,b\,{\sin\left(c+d\,x\right)}^2+\frac{b^2\,{\sin\left(c+d\,x\right)}^3}{3}}{d}","Not used",1,"(a^2*sin(c + d*x) + (b^2*sin(c + d*x)^3)/3 + a*b*sin(c + d*x)^2)/d","B"
390,1,50,61,5.155745,"\text{Not used}","int((a + b*sin(c + d*x))^2/cos(c + d*x),x)","-\frac{\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,{\left(a+b\right)}^2}{2}-\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,{\left(a-b\right)}^2}{2}+b^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"-((log(sin(c + d*x) - 1)*(a + b)^2)/2 - (log(sin(c + d*x) + 1)*(a - b)^2)/2 + b^2*sin(c + d*x))/d","B"
391,1,62,59,0.106833,"\text{Not used}","int((a + b*sin(c + d*x))^2/cos(c + d*x)^3,x)","\frac{\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(\frac{a^2}{2}-\frac{b^2}{2}\right)}{d}-\frac{a\,b+\sin\left(c+d\,x\right)\,\left(\frac{a^2}{2}+\frac{b^2}{2}\right)}{d\,\left({\sin\left(c+d\,x\right)}^2-1\right)}","Not used",1,"(atanh(sin(c + d*x))*(a^2/2 - b^2/2))/d - (a*b + sin(c + d*x)*(a^2/2 + b^2/2))/(d*(sin(c + d*x)^2 - 1))","B"
392,1,93,99,5.098395,"\text{Not used}","int((a + b*sin(c + d*x))^2/cos(c + d*x)^5,x)","\frac{\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(\frac{3\,a^2}{8}-\frac{b^2}{8}\right)}{d}+\frac{\left(\frac{b^2}{8}-\frac{3\,a^2}{8}\right)\,{\sin\left(c+d\,x\right)}^3+\left(\frac{5\,a^2}{8}+\frac{b^2}{8}\right)\,\sin\left(c+d\,x\right)+\frac{a\,b}{2}}{d\,\left({\sin\left(c+d\,x\right)}^4-2\,{\sin\left(c+d\,x\right)}^2+1\right)}","Not used",1,"(atanh(sin(c + d*x))*((3*a^2)/8 - b^2/8))/d + ((a*b)/2 + sin(c + d*x)*((5*a^2)/8 + b^2/8) - sin(c + d*x)^3*((3*a^2)/8 - b^2/8))/(d*(sin(c + d*x)^4 - 2*sin(c + d*x)^2 + 1))","B"
393,1,178,146,5.466188,"\text{Not used}","int(cos(c + d*x)^6*(a + b*sin(c + d*x))^2,x)","\frac{5\,a^2\,x}{16}+\frac{5\,b^2\,x}{128}+\frac{5\,a^2\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{24\,d}+\frac{a^2\,{\cos\left(c+d\,x\right)}^5\,\sin\left(c+d\,x\right)}{6\,d}+\frac{5\,b^2\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{192\,d}+\frac{b^2\,{\cos\left(c+d\,x\right)}^5\,\sin\left(c+d\,x\right)}{48\,d}-\frac{b^2\,{\cos\left(c+d\,x\right)}^7\,\sin\left(c+d\,x\right)}{8\,d}-\frac{2\,a\,b\,{\cos\left(c+d\,x\right)}^7}{7\,d}+\frac{5\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{16\,d}+\frac{5\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{128\,d}","Not used",1,"(5*a^2*x)/16 + (5*b^2*x)/128 + (5*a^2*cos(c + d*x)^3*sin(c + d*x))/(24*d) + (a^2*cos(c + d*x)^5*sin(c + d*x))/(6*d) + (5*b^2*cos(c + d*x)^3*sin(c + d*x))/(192*d) + (b^2*cos(c + d*x)^5*sin(c + d*x))/(48*d) - (b^2*cos(c + d*x)^7*sin(c + d*x))/(8*d) - (2*a*b*cos(c + d*x)^7)/(7*d) + (5*a^2*cos(c + d*x)*sin(c + d*x))/(16*d) + (5*b^2*cos(c + d*x)*sin(c + d*x))/(128*d)","B"
394,1,134,116,5.306582,"\text{Not used}","int(cos(c + d*x)^4*(a + b*sin(c + d*x))^2,x)","\frac{3\,a^2\,x}{8}+\frac{b^2\,x}{16}+\frac{a^2\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{b^2\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{24\,d}-\frac{b^2\,{\cos\left(c+d\,x\right)}^5\,\sin\left(c+d\,x\right)}{6\,d}-\frac{2\,a\,b\,{\cos\left(c+d\,x\right)}^5}{5\,d}+\frac{3\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,d}+\frac{b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{16\,d}","Not used",1,"(3*a^2*x)/8 + (b^2*x)/16 + (a^2*cos(c + d*x)^3*sin(c + d*x))/(4*d) + (b^2*cos(c + d*x)^3*sin(c + d*x))/(24*d) - (b^2*cos(c + d*x)^5*sin(c + d*x))/(6*d) - (2*a*b*cos(c + d*x)^5)/(5*d) + (3*a^2*cos(c + d*x)*sin(c + d*x))/(8*d) + (b^2*cos(c + d*x)*sin(c + d*x))/(16*d)","B"
395,1,71,86,5.380111,"\text{Not used}","int(cos(c + d*x)^2*(a + b*sin(c + d*x))^2,x)","\frac{6\,a^2\,\sin\left(2\,c+2\,d\,x\right)-\frac{3\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{4}-12\,a\,b\,\cos\left(c+d\,x\right)-4\,a\,b\,\cos\left(3\,c+3\,d\,x\right)+12\,a^2\,d\,x+3\,b^2\,d\,x}{24\,d}","Not used",1,"(6*a^2*sin(2*c + 2*d*x) - (3*b^2*sin(4*c + 4*d*x))/4 - 12*a*b*cos(c + d*x) - 4*a*b*cos(3*c + 3*d*x) + 12*a^2*d*x + 3*b^2*d*x)/(24*d)","B"
396,1,53,49,5.207119,"\text{Not used}","int((a + b*sin(c + d*x))^2/cos(c + d*x)^2,x)","-b^2\,x-\frac{4\,a\,b+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+2\,b^2\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"- b^2*x - (4*a*b + tan(c/2 + (d*x)/2)*(2*a^2 + 2*b^2))/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
397,1,71,75,5.258207,"\text{Not used}","int((a + b*sin(c + d*x))^2/cos(c + d*x)^4,x)","\frac{\frac{2\,a\,b}{3}+\frac{a^2\,\sin\left(c+d\,x\right)}{3}+\frac{b^2\,\sin\left(c+d\,x\right)}{3}+{\cos\left(c+d\,x\right)}^2\,\left(\frac{2\,a^2\,\sin\left(c+d\,x\right)}{3}-\frac{b^2\,\sin\left(c+d\,x\right)}{3}\right)}{d\,{\cos\left(c+d\,x\right)}^3}","Not used",1,"((2*a*b)/3 + (a^2*sin(c + d*x))/3 + (b^2*sin(c + d*x))/3 + cos(c + d*x)^2*((2*a^2*sin(c + d*x))/3 - (b^2*sin(c + d*x))/3))/(d*cos(c + d*x)^3)","B"
398,1,103,103,5.364404,"\text{Not used}","int((a + b*sin(c + d*x))^2/cos(c + d*x)^6,x)","\frac{\frac{2\,a\,b}{5}+\frac{a^2\,\sin\left(c+d\,x\right)}{5}+\frac{b^2\,\sin\left(c+d\,x\right)}{5}+{\cos\left(c+d\,x\right)}^2\,\left(\frac{4\,a^2\,\sin\left(c+d\,x\right)}{15}-\frac{b^2\,\sin\left(c+d\,x\right)}{15}\right)+{\cos\left(c+d\,x\right)}^4\,\left(\frac{8\,a^2\,\sin\left(c+d\,x\right)}{15}-\frac{2\,b^2\,\sin\left(c+d\,x\right)}{15}\right)}{d\,{\cos\left(c+d\,x\right)}^5}","Not used",1,"((2*a*b)/5 + (a^2*sin(c + d*x))/5 + (b^2*sin(c + d*x))/5 + cos(c + d*x)^2*((4*a^2*sin(c + d*x))/15 - (b^2*sin(c + d*x))/15) + cos(c + d*x)^4*((8*a^2*sin(c + d*x))/15 - (2*b^2*sin(c + d*x))/15))/(d*cos(c + d*x)^5)","B"
399,1,135,129,5.546601,"\text{Not used}","int((a + b*sin(c + d*x))^2/cos(c + d*x)^8,x)","\frac{\frac{2\,a\,b}{7}+\frac{a^2\,\sin\left(c+d\,x\right)}{7}+\frac{b^2\,\sin\left(c+d\,x\right)}{7}+{\cos\left(c+d\,x\right)}^2\,\left(\frac{6\,a^2\,\sin\left(c+d\,x\right)}{35}-\frac{b^2\,\sin\left(c+d\,x\right)}{35}\right)+{\cos\left(c+d\,x\right)}^4\,\left(\frac{8\,a^2\,\sin\left(c+d\,x\right)}{35}-\frac{4\,b^2\,\sin\left(c+d\,x\right)}{105}\right)+{\cos\left(c+d\,x\right)}^6\,\left(\frac{16\,a^2\,\sin\left(c+d\,x\right)}{35}-\frac{8\,b^2\,\sin\left(c+d\,x\right)}{105}\right)}{d\,{\cos\left(c+d\,x\right)}^7}","Not used",1,"((2*a*b)/7 + (a^2*sin(c + d*x))/7 + (b^2*sin(c + d*x))/7 + cos(c + d*x)^2*((6*a^2*sin(c + d*x))/35 - (b^2*sin(c + d*x))/35) + cos(c + d*x)^4*((8*a^2*sin(c + d*x))/35 - (4*b^2*sin(c + d*x))/105) + cos(c + d*x)^6*((16*a^2*sin(c + d*x))/35 - (8*b^2*sin(c + d*x))/105))/(d*cos(c + d*x)^7)","B"
400,1,141,144,0.091571,"\text{Not used}","int(cos(c + d*x)^5*(a + b*sin(c + d*x))^3,x)","\frac{{\sin\left(c+d\,x\right)}^3\,\left(a\,b^2-\frac{2\,a^3}{3}\right)-{\sin\left(c+d\,x\right)}^5\,\left(\frac{6\,a\,b^2}{5}-\frac{a^3}{5}\right)+{\sin\left(c+d\,x\right)}^6\,\left(\frac{a^2\,b}{2}-\frac{b^3}{3}\right)-{\sin\left(c+d\,x\right)}^4\,\left(\frac{3\,a^2\,b}{2}-\frac{b^3}{4}\right)+a^3\,\sin\left(c+d\,x\right)+\frac{b^3\,{\sin\left(c+d\,x\right)}^8}{8}+\frac{3\,a^2\,b\,{\sin\left(c+d\,x\right)}^2}{2}+\frac{3\,a\,b^2\,{\sin\left(c+d\,x\right)}^7}{7}}{d}","Not used",1,"(sin(c + d*x)^3*(a*b^2 - (2*a^3)/3) - sin(c + d*x)^5*((6*a*b^2)/5 - a^3/5) + sin(c + d*x)^6*((a^2*b)/2 - b^3/3) - sin(c + d*x)^4*((3*a^2*b)/2 - b^3/4) + a^3*sin(c + d*x) + (b^3*sin(c + d*x)^8)/8 + (3*a^2*b*sin(c + d*x)^2)/2 + (3*a*b^2*sin(c + d*x)^7)/7)/d","B"
401,1,98,77,5.128492,"\text{Not used}","int(cos(c + d*x)^3*(a + b*sin(c + d*x))^3,x)","\frac{{\sin\left(c+d\,x\right)}^3\,\left(a\,b^2-\frac{a^3}{3}\right)-{\sin\left(c+d\,x\right)}^4\,\left(\frac{3\,a^2\,b}{4}-\frac{b^3}{4}\right)+a^3\,\sin\left(c+d\,x\right)-\frac{b^3\,{\sin\left(c+d\,x\right)}^6}{6}+\frac{3\,a^2\,b\,{\sin\left(c+d\,x\right)}^2}{2}-\frac{3\,a\,b^2\,{\sin\left(c+d\,x\right)}^5}{5}}{d}","Not used",1,"(sin(c + d*x)^3*(a*b^2 - a^3/3) - sin(c + d*x)^4*((3*a^2*b)/4 - b^3/4) + a^3*sin(c + d*x) - (b^3*sin(c + d*x)^6)/6 + (3*a^2*b*sin(c + d*x)^2)/2 - (3*a*b^2*sin(c + d*x)^5)/5)/d","B"
402,1,55,22,0.060102,"\text{Not used}","int(cos(c + d*x)*(a + b*sin(c + d*x))^3,x)","\frac{a^3\,\sin\left(c+d\,x\right)+\frac{3\,a^2\,b\,{\sin\left(c+d\,x\right)}^2}{2}+a\,b^2\,{\sin\left(c+d\,x\right)}^3+\frac{b^3\,{\sin\left(c+d\,x\right)}^4}{4}}{d}","Not used",1,"(a^3*sin(c + d*x) + (b^3*sin(c + d*x)^4)/4 + (3*a^2*b*sin(c + d*x)^2)/2 + a*b^2*sin(c + d*x)^3)/d","B"
403,1,65,80,5.128854,"\text{Not used}","int((a + b*sin(c + d*x))^3/cos(c + d*x),x)","-\frac{\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,{\left(a+b\right)}^3}{2}-\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,{\left(a-b\right)}^3}{2}+\frac{b^3\,{\sin\left(c+d\,x\right)}^2}{2}+3\,a\,b^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"-((log(sin(c + d*x) - 1)*(a + b)^3)/2 - (log(sin(c + d*x) + 1)*(a - b)^3)/2 + (b^3*sin(c + d*x)^2)/2 + 3*a*b^2*sin(c + d*x))/d","B"
404,1,99,111,5.210836,"\text{Not used}","int((a + b*sin(c + d*x))^3/cos(c + d*x)^3,x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,{\left(a-b\right)}^2\,\left(a+2\,b\right)}{4\,d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,{\left(a+b\right)}^2\,\left(a-2\,b\right)}{4\,d}-\frac{\frac{3\,a^2\,b}{2}+\frac{b^3}{2}+\sin\left(c+d\,x\right)\,\left(\frac{a^3}{2}+\frac{3\,a\,b^2}{2}\right)}{d\,\left({\sin\left(c+d\,x\right)}^2-1\right)}","Not used",1,"(log(sin(c + d*x) + 1)*(a - b)^2*(a + 2*b))/(4*d) - (log(sin(c + d*x) - 1)*(a + b)^2*(a - 2*b))/(4*d) - ((3*a^2*b)/2 + b^3/2 + sin(c + d*x)*((3*a*b^2)/2 + a^3/2))/(d*(sin(c + d*x)^2 - 1))","B"
405,1,114,94,5.165563,"\text{Not used}","int((a + b*sin(c + d*x))^3/cos(c + d*x)^5,x)","\frac{{\sin\left(c+d\,x\right)}^3\,\left(\frac{3\,a\,b^2}{8}-\frac{3\,a^3}{8}\right)+\frac{3\,a^2\,b}{4}-\frac{b^3}{4}+\sin\left(c+d\,x\right)\,\left(\frac{5\,a^3}{8}+\frac{3\,a\,b^2}{8}\right)+\frac{b^3\,{\sin\left(c+d\,x\right)}^2}{2}}{d\,\left({\sin\left(c+d\,x\right)}^4-2\,{\sin\left(c+d\,x\right)}^2+1\right)}+\frac{3\,a\,\mathrm{atanh}\left(\sin\left(c+d\,x\right)\right)\,\left(a^2-b^2\right)}{8\,d}","Not used",1,"(sin(c + d*x)^3*((3*a*b^2)/8 - (3*a^3)/8) + (3*a^2*b)/4 - b^3/4 + sin(c + d*x)*((3*a*b^2)/8 + (5*a^3)/8) + (b^3*sin(c + d*x)^2)/2)/(d*(sin(c + d*x)^4 - 2*sin(c + d*x)^2 + 1)) + (3*a*atanh(sin(c + d*x))*(a^2 - b^2))/(8*d)","B"
406,1,474,158,6.926314,"\text{Not used}","int(cos(c + d*x)^4*(a + b*sin(c + d*x))^3,x)","\frac{3\,a\,\mathrm{atan}\left(\frac{3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+b^2\right)}{8\,\left(\frac{3\,a^3}{4}+\frac{3\,a\,b^2}{8}\right)}\right)\,\left(2\,a^2+b^2\right)}{8\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,a\,b^2}{8}-\frac{5\,a^3}{4}\right)+\frac{6\,a^2\,b}{5}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^3+\frac{11\,a\,b^2}{2}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(3\,a^3+\frac{11\,a\,b^2}{2}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{3\,a\,b^2}{8}-\frac{5\,a^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{31\,a\,b^2}{8}-\frac{9\,a^3}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{31\,a\,b^2}{8}-\frac{9\,a^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(12\,a^2\,b+4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{12\,a^2\,b}{5}+\frac{4\,b^3}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(18\,a^2\,b-4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(24\,a^2\,b+8\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{66\,a^2\,b}{5}-\frac{8\,b^3}{5}\right)+\frac{4\,b^3}{35}+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{3\,a\,\left(2\,a^2+b^2\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(3*a*atan((3*a*tan(c/2 + (d*x)/2)*(2*a^2 + b^2))/(8*((3*a*b^2)/8 + (3*a^3)/4)))*(2*a^2 + b^2))/(8*d) - (tan(c/2 + (d*x)/2)*((3*a*b^2)/8 - (5*a^3)/4) + (6*a^2*b)/5 - tan(c/2 + (d*x)/2)^3*((11*a*b^2)/2 + 3*a^3) + tan(c/2 + (d*x)/2)^11*((11*a*b^2)/2 + 3*a^3) - tan(c/2 + (d*x)/2)^13*((3*a*b^2)/8 - (5*a^3)/4) + tan(c/2 + (d*x)/2)^5*((31*a*b^2)/8 - (9*a^3)/4) - tan(c/2 + (d*x)/2)^9*((31*a*b^2)/8 - (9*a^3)/4) + tan(c/2 + (d*x)/2)^10*(12*a^2*b + 4*b^3) + tan(c/2 + (d*x)/2)^2*((12*a^2*b)/5 + (4*b^3)/5) + tan(c/2 + (d*x)/2)^8*(18*a^2*b - 4*b^3) + tan(c/2 + (d*x)/2)^6*(24*a^2*b + 8*b^3) + tan(c/2 + (d*x)/2)^4*((66*a^2*b)/5 - (8*b^3)/5) + (4*b^3)/35 + 6*a^2*b*tan(c/2 + (d*x)/2)^12)/(d*(7*tan(c/2 + (d*x)/2)^2 + 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 + 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 + 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 + 1)) - (3*a*(2*a^2 + b^2)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(8*d)","B"
407,1,356,131,6.626737,"\text{Not used}","int(cos(c + d*x)^2*(a + b*sin(c + d*x))^3,x)","\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2+3\,b^2\right)}{4\,\left(a^3+\frac{3\,a\,b^2}{4}\right)}\right)\,\left(4\,a^2+3\,b^2\right)}{4\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,a\,b^2}{4}-a^3\right)+2\,a^2\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^3+\frac{9\,a\,b^2}{2}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{3\,a\,b^2}{4}-a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,a^3+\frac{9\,a\,b^2}{2}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^2\,b+\frac{4\,b^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(8\,a^2\,b-\frac{4\,b^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(12\,a^2\,b+4\,b^3\right)+\frac{4\,b^3}{15}+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a\,\left(4\,a^2+3\,b^2\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{4\,d}","Not used",1,"(a*atan((a*tan(c/2 + (d*x)/2)*(4*a^2 + 3*b^2))/(4*((3*a*b^2)/4 + a^3)))*(4*a^2 + 3*b^2))/(4*d) - (tan(c/2 + (d*x)/2)*((3*a*b^2)/4 - a^3) + 2*a^2*b - tan(c/2 + (d*x)/2)^3*((9*a*b^2)/2 + 2*a^3) - tan(c/2 + (d*x)/2)^9*((3*a*b^2)/4 - a^3) + tan(c/2 + (d*x)/2)^7*((9*a*b^2)/2 + 2*a^3) + tan(c/2 + (d*x)/2)^2*(4*a^2*b + (4*b^3)/3) + tan(c/2 + (d*x)/2)^4*(8*a^2*b - (4*b^3)/3) + tan(c/2 + (d*x)/2)^6*(12*a^2*b + 4*b^3) + (4*b^3)/15 + 6*a^2*b*tan(c/2 + (d*x)/2)^8)/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (a*(4*a^2 + 3*b^2)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d)","B"
408,1,103,79,5.814233,"\text{Not used}","int((a + b*sin(c + d*x))^3/cos(c + d*x)^2,x)","-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^3+6\,a\,b^2\right)+6\,a^2\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^3+6\,a\,b^2\right)+4\,b^3+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-1\right)}-3\,a\,b^2\,x","Not used",1,"- (tan(c/2 + (d*x)/2)*(6*a*b^2 + 2*a^3) + 6*a^2*b + tan(c/2 + (d*x)/2)^3*(6*a*b^2 + 2*a^3) + 4*b^3 + 6*a^2*b*tan(c/2 + (d*x)/2)^2)/(d*(tan(c/2 + (d*x)/2)^4 - 1)) - 3*a*b^2*x","B"
409,1,81,84,5.249093,"\text{Not used}","int((a + b*sin(c + d*x))^3/cos(c + d*x)^4,x)","\frac{a^2\,b+\frac{a^3\,\sin\left(c+d\,x\right)}{3}+\frac{b^3}{3}-{\cos\left(c+d\,x\right)}^2\,\left(-\frac{2\,\sin\left(c+d\,x\right)\,a^3}{3}+\sin\left(c+d\,x\right)\,a\,b^2+b^3\right)+a\,b^2\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^3}","Not used",1,"(a^2*b + (a^3*sin(c + d*x))/3 + b^3/3 - cos(c + d*x)^2*(b^3 - (2*a^3*sin(c + d*x))/3 + a*b^2*sin(c + d*x)) + a*b^2*sin(c + d*x))/(d*cos(c + d*x)^3)","B"
410,1,119,135,5.407469,"\text{Not used}","int((a + b*sin(c + d*x))^3/cos(c + d*x)^6,x)","\frac{{\cos\left(c+d\,x\right)}^4\,\left(\frac{8\,a^3\,\sin\left(c+d\,x\right)}{15}-\frac{2\,a\,b^2\,\sin\left(c+d\,x\right)}{5}\right)-{\cos\left(c+d\,x\right)}^2\,\left(-\frac{4\,\sin\left(c+d\,x\right)\,a^3}{15}+\frac{\sin\left(c+d\,x\right)\,a\,b^2}{5}+\frac{b^3}{3}\right)+\frac{3\,a^2\,b}{5}+\frac{a^3\,\sin\left(c+d\,x\right)}{5}+\frac{b^3}{5}+\frac{3\,a\,b^2\,\sin\left(c+d\,x\right)}{5}}{d\,{\cos\left(c+d\,x\right)}^5}","Not used",1,"(cos(c + d*x)^4*((8*a^3*sin(c + d*x))/15 - (2*a*b^2*sin(c + d*x))/5) - cos(c + d*x)^2*(b^3/3 - (4*a^3*sin(c + d*x))/15 + (a*b^2*sin(c + d*x))/5) + (3*a^2*b)/5 + (a^3*sin(c + d*x))/5 + b^3/5 + (3*a*b^2*sin(c + d*x))/5)/(d*cos(c + d*x)^5)","B"
411,1,152,165,5.603988,"\text{Not used}","int((a + b*sin(c + d*x))^3/cos(c + d*x)^8,x)","\frac{{\cos\left(c+d\,x\right)}^4\,\left(\frac{8\,a^3\,\sin\left(c+d\,x\right)}{35}-\frac{4\,a\,b^2\,\sin\left(c+d\,x\right)}{35}\right)+{\cos\left(c+d\,x\right)}^6\,\left(\frac{16\,a^3\,\sin\left(c+d\,x\right)}{35}-\frac{8\,a\,b^2\,\sin\left(c+d\,x\right)}{35}\right)-{\cos\left(c+d\,x\right)}^2\,\left(-\frac{6\,\sin\left(c+d\,x\right)\,a^3}{35}+\frac{3\,\sin\left(c+d\,x\right)\,a\,b^2}{35}+\frac{b^3}{5}\right)+\frac{3\,a^2\,b}{7}+\frac{a^3\,\sin\left(c+d\,x\right)}{7}+\frac{b^3}{7}+\frac{3\,a\,b^2\,\sin\left(c+d\,x\right)}{7}}{d\,{\cos\left(c+d\,x\right)}^7}","Not used",1,"(cos(c + d*x)^4*((8*a^3*sin(c + d*x))/35 - (4*a*b^2*sin(c + d*x))/35) + cos(c + d*x)^6*((16*a^3*sin(c + d*x))/35 - (8*a*b^2*sin(c + d*x))/35) - cos(c + d*x)^2*(b^3/5 - (6*a^3*sin(c + d*x))/35 + (3*a*b^2*sin(c + d*x))/35) + (3*a^2*b)/7 + (a^3*sin(c + d*x))/7 + b^3/7 + (3*a*b^2*sin(c + d*x))/7)/(d*cos(c + d*x)^7)","B"
412,1,275,192,6.131997,"\text{Not used}","int((a + b*sin(c + d*x))^3/cos(c + d*x)^10,x)","\frac{b^3}{9\,d\,{\cos\left(c+d\,x\right)}^9}-\frac{b^3}{7\,d\,{\cos\left(c+d\,x\right)}^7}+\frac{a^2\,b}{3\,d\,{\cos\left(c+d\,x\right)}^9}+\frac{128\,a^3\,\sin\left(c+d\,x\right)}{315\,d\,\cos\left(c+d\,x\right)}+\frac{64\,a^3\,\sin\left(c+d\,x\right)}{315\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{16\,a^3\,\sin\left(c+d\,x\right)}{105\,d\,{\cos\left(c+d\,x\right)}^5}+\frac{8\,a^3\,\sin\left(c+d\,x\right)}{63\,d\,{\cos\left(c+d\,x\right)}^7}+\frac{a^3\,\sin\left(c+d\,x\right)}{9\,d\,{\cos\left(c+d\,x\right)}^9}-\frac{16\,a\,b^2\,\sin\left(c+d\,x\right)}{105\,d\,\cos\left(c+d\,x\right)}-\frac{8\,a\,b^2\,\sin\left(c+d\,x\right)}{105\,d\,{\cos\left(c+d\,x\right)}^3}-\frac{2\,a\,b^2\,\sin\left(c+d\,x\right)}{35\,d\,{\cos\left(c+d\,x\right)}^5}-\frac{a\,b^2\,\sin\left(c+d\,x\right)}{21\,d\,{\cos\left(c+d\,x\right)}^7}+\frac{a\,b^2\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^9}","Not used",1,"b^3/(9*d*cos(c + d*x)^9) - b^3/(7*d*cos(c + d*x)^7) + (a^2*b)/(3*d*cos(c + d*x)^9) + (128*a^3*sin(c + d*x))/(315*d*cos(c + d*x)) + (64*a^3*sin(c + d*x))/(315*d*cos(c + d*x)^3) + (16*a^3*sin(c + d*x))/(105*d*cos(c + d*x)^5) + (8*a^3*sin(c + d*x))/(63*d*cos(c + d*x)^7) + (a^3*sin(c + d*x))/(9*d*cos(c + d*x)^9) - (16*a*b^2*sin(c + d*x))/(105*d*cos(c + d*x)) - (8*a*b^2*sin(c + d*x))/(105*d*cos(c + d*x)^3) - (2*a*b^2*sin(c + d*x))/(35*d*cos(c + d*x)^5) - (a*b^2*sin(c + d*x))/(21*d*cos(c + d*x)^7) + (a*b^2*sin(c + d*x))/(3*d*cos(c + d*x)^9)","B"
413,1,306,144,5.454368,"\text{Not used}","int(cos(c + d*x)^5*(a + b*sin(c + d*x))^8,x)","\frac{{\sin\left(c+d\,x\right)}^5\,\left(\frac{a^8}{5}-\frac{56\,a^6\,b^2}{5}+14\,a^4\,b^4\right)+{\sin\left(c+d\,x\right)}^9\,\left(\frac{70\,a^4\,b^4}{9}-\frac{56\,a^2\,b^6}{9}+\frac{b^8}{9}\right)+a^8\,\sin\left(c+d\,x\right)+\frac{b^8\,{\sin\left(c+d\,x\right)}^{13}}{13}-{\sin\left(c+d\,x\right)}^4\,\left(4\,a^7\,b-14\,a^5\,b^3\right)-{\sin\left(c+d\,x\right)}^{10}\,\left(\frac{8\,a\,b^7}{5}-\frac{28\,a^3\,b^5}{5}\right)-\frac{2\,a^6\,{\sin\left(c+d\,x\right)}^3\,\left(a^2-14\,b^2\right)}{3}+4\,a^7\,b\,{\sin\left(c+d\,x\right)}^2+\frac{2\,a\,b^7\,{\sin\left(c+d\,x\right)}^{12}}{3}+\frac{2\,b^6\,{\sin\left(c+d\,x\right)}^{11}\,\left(14\,a^2-b^2\right)}{11}+\frac{4\,a^3\,b\,{\sin\left(c+d\,x\right)}^6\,\left(a^4-14\,a^2\,b^2+7\,b^4\right)}{3}+a\,b^3\,{\sin\left(c+d\,x\right)}^8\,\left(7\,a^4-14\,a^2\,b^2+b^4\right)+4\,a^2\,b^2\,{\sin\left(c+d\,x\right)}^7\,\left(a^4-5\,a^2\,b^2+b^4\right)}{d}","Not used",1,"(sin(c + d*x)^5*(a^8/5 + 14*a^4*b^4 - (56*a^6*b^2)/5) + sin(c + d*x)^9*(b^8/9 - (56*a^2*b^6)/9 + (70*a^4*b^4)/9) + a^8*sin(c + d*x) + (b^8*sin(c + d*x)^13)/13 - sin(c + d*x)^4*(4*a^7*b - 14*a^5*b^3) - sin(c + d*x)^10*((8*a*b^7)/5 - (28*a^3*b^5)/5) - (2*a^6*sin(c + d*x)^3*(a^2 - 14*b^2))/3 + 4*a^7*b*sin(c + d*x)^2 + (2*a*b^7*sin(c + d*x)^12)/3 + (2*b^6*sin(c + d*x)^11*(14*a^2 - b^2))/11 + (4*a^3*b*sin(c + d*x)^6*(a^4 + 7*b^4 - 14*a^2*b^2))/3 + a*b^3*sin(c + d*x)^8*(7*a^4 + b^4 - 14*a^2*b^2) + 4*a^2*b^2*sin(c + d*x)^7*(a^4 + b^4 - 5*a^2*b^2))/d","B"
414,1,231,77,5.373917,"\text{Not used}","int(cos(c + d*x)^3*(a + b*sin(c + d*x))^8,x)","-\frac{{\sin\left(c+d\,x\right)}^3\,\left(\frac{a^8}{3}-\frac{28\,a^6\,b^2}{3}\right)-{\sin\left(c+d\,x\right)}^5\,\left(14\,a^4\,b^4-\frac{28\,a^6\,b^2}{5}\right)-{\sin\left(c+d\,x\right)}^7\,\left(4\,a^2\,b^6-10\,a^4\,b^4\right)-a^8\,\sin\left(c+d\,x\right)-{\sin\left(c+d\,x\right)}^9\,\left(\frac{b^8}{9}-\frac{28\,a^2\,b^6}{9}\right)+\frac{b^8\,{\sin\left(c+d\,x\right)}^{11}}{11}-4\,a^7\,b\,{\sin\left(c+d\,x\right)}^2+\frac{4\,a\,b^7\,{\sin\left(c+d\,x\right)}^{10}}{5}+2\,a^5\,b\,{\sin\left(c+d\,x\right)}^4\,\left(a^2-7\,b^2\right)+a\,b^5\,{\sin\left(c+d\,x\right)}^8\,\left(7\,a^2-b^2\right)+\frac{28\,a^3\,b^3\,{\sin\left(c+d\,x\right)}^6\,\left(a^2-b^2\right)}{3}}{d}","Not used",1,"-(sin(c + d*x)^3*(a^8/3 - (28*a^6*b^2)/3) - sin(c + d*x)^5*(14*a^4*b^4 - (28*a^6*b^2)/5) - sin(c + d*x)^7*(4*a^2*b^6 - 10*a^4*b^4) - a^8*sin(c + d*x) - sin(c + d*x)^9*(b^8/9 - (28*a^2*b^6)/9) + (b^8*sin(c + d*x)^11)/11 - 4*a^7*b*sin(c + d*x)^2 + (4*a*b^7*sin(c + d*x)^10)/5 + 2*a^5*b*sin(c + d*x)^4*(a^2 - 7*b^2) + a*b^5*sin(c + d*x)^8*(7*a^2 - b^2) + (28*a^3*b^3*sin(c + d*x)^6*(a^2 - b^2))/3)/d","B"
415,1,135,22,5.265835,"\text{Not used}","int(cos(c + d*x)*(a + b*sin(c + d*x))^8,x)","\frac{a^8\,\sin\left(c+d\,x\right)+4\,a^7\,b\,{\sin\left(c+d\,x\right)}^2+\frac{28\,a^6\,b^2\,{\sin\left(c+d\,x\right)}^3}{3}+14\,a^5\,b^3\,{\sin\left(c+d\,x\right)}^4+14\,a^4\,b^4\,{\sin\left(c+d\,x\right)}^5+\frac{28\,a^3\,b^5\,{\sin\left(c+d\,x\right)}^6}{3}+4\,a^2\,b^6\,{\sin\left(c+d\,x\right)}^7+a\,b^7\,{\sin\left(c+d\,x\right)}^8+\frac{b^8\,{\sin\left(c+d\,x\right)}^9}{9}}{d}","Not used",1,"(a^8*sin(c + d*x) + (b^8*sin(c + d*x)^9)/9 + 4*a^7*b*sin(c + d*x)^2 + a*b^7*sin(c + d*x)^8 + (28*a^6*b^2*sin(c + d*x)^3)/3 + 14*a^5*b^3*sin(c + d*x)^4 + 14*a^4*b^4*sin(c + d*x)^5 + (28*a^3*b^5*sin(c + d*x)^6)/3 + 4*a^2*b^6*sin(c + d*x)^7)/d","B"
416,1,212,245,5.361895,"\text{Not used}","int((a + b*sin(c + d*x))^8/cos(c + d*x),x)","-\frac{\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,{\left(a+b\right)}^8}{2}+{\sin\left(c+d\,x\right)}^3\,\left(\frac{70\,a^4\,b^4}{3}+\frac{28\,a^2\,b^6}{3}+\frac{b^8}{3}\right)-\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,{\left(a-b\right)}^8}{2}+{\sin\left(c+d\,x\right)}^5\,\left(\frac{28\,a^2\,b^6}{5}+\frac{b^8}{5}\right)+\sin\left(c+d\,x\right)\,\left(28\,a^6\,b^2+70\,a^4\,b^4+28\,a^2\,b^6+b^8\right)+{\sin\left(c+d\,x\right)}^2\,\left(28\,a^5\,b^3+28\,a^3\,b^5+4\,a\,b^7\right)+\frac{b^8\,{\sin\left(c+d\,x\right)}^7}{7}+{\sin\left(c+d\,x\right)}^4\,\left(14\,a^3\,b^5+2\,a\,b^7\right)+\frac{4\,a\,b^7\,{\sin\left(c+d\,x\right)}^6}{3}}{d}","Not used",1,"-((log(sin(c + d*x) - 1)*(a + b)^8)/2 + sin(c + d*x)^3*(b^8/3 + (28*a^2*b^6)/3 + (70*a^4*b^4)/3) - (log(sin(c + d*x) + 1)*(a - b)^8)/2 + sin(c + d*x)^5*(b^8/5 + (28*a^2*b^6)/5) + sin(c + d*x)*(b^8 + 28*a^2*b^6 + 70*a^4*b^4 + 28*a^6*b^2) + sin(c + d*x)^2*(4*a*b^7 + 28*a^3*b^5 + 28*a^5*b^3) + (b^8*sin(c + d*x)^7)/7 + sin(c + d*x)^4*(2*a*b^7 + 14*a^3*b^5) + (4*a*b^7*sin(c + d*x)^6)/3)/d","B"
417,1,257,284,5.389075,"\text{Not used}","int((a + b*sin(c + d*x))^8/cos(c + d*x)^3,x)","\frac{{\sin\left(c+d\,x\right)}^3\,\left(\frac{28\,a^2\,b^6}{3}+\frac{2\,b^8}{3}\right)}{d}+\frac{b^8\,{\sin\left(c+d\,x\right)}^5}{5\,d}+\frac{{\sin\left(c+d\,x\right)}^2\,\left(28\,a^3\,b^5+8\,a\,b^7\right)}{d}+\frac{\sin\left(c+d\,x\right)\,\left(70\,a^4\,b^4+56\,a^2\,b^6+3\,b^8\right)}{d}-\frac{\sin\left(c+d\,x\right)\,\left(\frac{a^8}{2}+14\,a^6\,b^2+35\,a^4\,b^4+14\,a^2\,b^6+\frac{b^8}{2}\right)+4\,a\,b^7+4\,a^7\,b+28\,a^3\,b^5+28\,a^5\,b^3}{d\,\left({\sin\left(c+d\,x\right)}^2-1\right)}+\frac{2\,a\,b^7\,{\sin\left(c+d\,x\right)}^4}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,{\left(a+b\right)}^7\,\left(a-7\,b\right)}{4\,d}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,{\left(a-b\right)}^7\,\left(a+7\,b\right)}{4\,d}","Not used",1,"(sin(c + d*x)^3*((2*b^8)/3 + (28*a^2*b^6)/3))/d + (b^8*sin(c + d*x)^5)/(5*d) + (sin(c + d*x)^2*(8*a*b^7 + 28*a^3*b^5))/d + (sin(c + d*x)*(3*b^8 + 56*a^2*b^6 + 70*a^4*b^4))/d - (sin(c + d*x)*(a^8/2 + b^8/2 + 14*a^2*b^6 + 35*a^4*b^4 + 14*a^6*b^2) + 4*a*b^7 + 4*a^7*b + 28*a^3*b^5 + 28*a^5*b^3)/(d*(sin(c + d*x)^2 - 1)) + (2*a*b^7*sin(c + d*x)^4)/d - (log(sin(c + d*x) - 1)*(a + b)^7*(a - 7*b))/(4*d) + (log(sin(c + d*x) + 1)*(a - b)^7*(a + 7*b))/(4*d)","B"
418,1,305,320,5.483690,"\text{Not used}","int((a + b*sin(c + d*x))^8/cos(c + d*x)^5,x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,{\left(a-b\right)}^6\,\left(3\,a^2+18\,a\,b+35\,b^2\right)}{16\,d}-\frac{b^8\,{\sin\left(c+d\,x\right)}^3}{3\,d}-\frac{\sin\left(c+d\,x\right)\,\left(28\,a^2\,b^6+3\,b^8\right)}{d}-\frac{\sin\left(c+d\,x\right)\,\left(-\frac{5\,a^8}{8}-\frac{7\,a^6\,b^2}{2}+\frac{105\,a^4\,b^4}{4}+\frac{49\,a^2\,b^6}{2}+\frac{11\,b^8}{8}\right)-{\sin\left(c+d\,x\right)}^3\,\left(-\frac{3\,a^8}{8}+\frac{7\,a^6\,b^2}{2}+\frac{175\,a^4\,b^4}{4}+\frac{63\,a^2\,b^6}{2}+\frac{13\,b^8}{8}\right)+10\,a\,b^7-2\,a^7\,b-{\sin\left(c+d\,x\right)}^2\,\left(28\,a^5\,b^3+56\,a^3\,b^5+12\,a\,b^7\right)+42\,a^3\,b^5+14\,a^5\,b^3}{d\,\left({\sin\left(c+d\,x\right)}^4-2\,{\sin\left(c+d\,x\right)}^2+1\right)}-\frac{4\,a\,b^7\,{\sin\left(c+d\,x\right)}^2}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,{\left(a+b\right)}^6\,\left(3\,a^2-18\,a\,b+35\,b^2\right)}{16\,d}","Not used",1,"(log(sin(c + d*x) + 1)*(a - b)^6*(18*a*b + 3*a^2 + 35*b^2))/(16*d) - (b^8*sin(c + d*x)^3)/(3*d) - (sin(c + d*x)*(3*b^8 + 28*a^2*b^6))/d - (sin(c + d*x)*((11*b^8)/8 - (5*a^8)/8 + (49*a^2*b^6)/2 + (105*a^4*b^4)/4 - (7*a^6*b^2)/2) - sin(c + d*x)^3*((13*b^8)/8 - (3*a^8)/8 + (63*a^2*b^6)/2 + (175*a^4*b^4)/4 + (7*a^6*b^2)/2) + 10*a*b^7 - 2*a^7*b - sin(c + d*x)^2*(12*a*b^7 + 56*a^3*b^5 + 28*a^5*b^3) + 42*a^3*b^5 + 14*a^5*b^3)/(d*(sin(c + d*x)^4 - 2*sin(c + d*x)^2 + 1)) - (4*a*b^7*sin(c + d*x)^2)/d - (log(sin(c + d*x) - 1)*(a + b)^6*(3*a^2 - 18*a*b + 35*b^2))/(16*d)","B"
419,1,467,423,7.344352,"\text{Not used}","int(cos(c + d*x)^2*(a + b*sin(c + d*x))^8,x)","-\frac{\frac{2205\,b^8\,\sin\left(2\,c+2\,d\,x\right)}{2}-20160\,a^8\,\sin\left(2\,c+2\,d\,x\right)+315\,b^8\,\sin\left(4\,c+4\,d\,x\right)-\frac{1365\,b^8\,\sin\left(6\,c+6\,d\,x\right)}{4}+\frac{945\,b^8\,\sin\left(8\,c+8\,d\,x\right)}{8}-\frac{63\,b^8\,\sin\left(10\,c+10\,d\,x\right)}{4}+53760\,a^7\,b\,\cos\left(3\,c+3\,d\,x\right)-4032\,a\,b^7\,\cos\left(5\,c+5\,d\,x\right)+1800\,a\,b^7\,\cos\left(7\,c+7\,d\,x\right)-280\,a\,b^7\,\cos\left(9\,c+9\,d\,x\right)+352800\,a^3\,b^5\,\cos\left(c+d\,x\right)+564480\,a^5\,b^3\,\cos\left(c+d\,x\right)+23520\,a^3\,b^5\,\cos\left(3\,c+3\,d\,x\right)+94080\,a^5\,b^3\,\cos\left(3\,c+3\,d\,x\right)-42336\,a^3\,b^5\,\cos\left(5\,c+5\,d\,x\right)-56448\,a^5\,b^3\,\cos\left(5\,c+5\,d\,x\right)+10080\,a^3\,b^5\,\cos\left(7\,c+7\,d\,x\right)+35280\,a^2\,b^6\,\sin\left(2\,c+2\,d\,x\right)+88200\,a^4\,b^4\,\sin\left(2\,c+2\,d\,x\right)+17640\,a^2\,b^6\,\sin\left(4\,c+4\,d\,x\right)+88200\,a^4\,b^4\,\sin\left(4\,c+4\,d\,x\right)+70560\,a^6\,b^2\,\sin\left(4\,c+4\,d\,x\right)-11760\,a^2\,b^6\,\sin\left(6\,c+6\,d\,x\right)-29400\,a^4\,b^4\,\sin\left(6\,c+6\,d\,x\right)+2205\,a^2\,b^6\,\sin\left(8\,c+8\,d\,x\right)+35280\,a\,b^7\,\cos\left(c+d\,x\right)+161280\,a^7\,b\,\cos\left(c+d\,x\right)-40320\,a^8\,d\,x-2205\,b^8\,d\,x-88200\,a^2\,b^6\,d\,x-352800\,a^4\,b^4\,d\,x-282240\,a^6\,b^2\,d\,x}{80640\,d}","Not used",1,"-((2205*b^8*sin(2*c + 2*d*x))/2 - 20160*a^8*sin(2*c + 2*d*x) + 315*b^8*sin(4*c + 4*d*x) - (1365*b^8*sin(6*c + 6*d*x))/4 + (945*b^8*sin(8*c + 8*d*x))/8 - (63*b^8*sin(10*c + 10*d*x))/4 + 53760*a^7*b*cos(3*c + 3*d*x) - 4032*a*b^7*cos(5*c + 5*d*x) + 1800*a*b^7*cos(7*c + 7*d*x) - 280*a*b^7*cos(9*c + 9*d*x) + 352800*a^3*b^5*cos(c + d*x) + 564480*a^5*b^3*cos(c + d*x) + 23520*a^3*b^5*cos(3*c + 3*d*x) + 94080*a^5*b^3*cos(3*c + 3*d*x) - 42336*a^3*b^5*cos(5*c + 5*d*x) - 56448*a^5*b^3*cos(5*c + 5*d*x) + 10080*a^3*b^5*cos(7*c + 7*d*x) + 35280*a^2*b^6*sin(2*c + 2*d*x) + 88200*a^4*b^4*sin(2*c + 2*d*x) + 17640*a^2*b^6*sin(4*c + 4*d*x) + 88200*a^4*b^4*sin(4*c + 4*d*x) + 70560*a^6*b^2*sin(4*c + 4*d*x) - 11760*a^2*b^6*sin(6*c + 6*d*x) - 29400*a^4*b^4*sin(6*c + 6*d*x) + 2205*a^2*b^6*sin(8*c + 8*d*x) + 35280*a*b^7*cos(c + d*x) + 161280*a^7*b*cos(c + d*x) - 40320*a^8*d*x - 2205*b^8*d*x - 88200*a^2*b^6*d*x - 352800*a^4*b^4*d*x - 282240*a^6*b^2*d*x)/(80640*d)","B"
420,1,767,349,7.733828,"\text{Not used}","int((a + b*sin(c + d*x))^8/cos(c + d*x)^2,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(240\,a^7\,b+1120\,a^5\,b^3+\frac{1792\,a^3\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(96\,a^7\,b+224\,a^5\,b^3\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^8+56\,a^6\,b^2+210\,a^4\,b^4+105\,a^2\,b^6+\frac{35\,b^8}{8}\right)+\frac{256\,a\,b^7}{5}+16\,a^7\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(96\,a^7\,b+1120\,a^5\,b^3+\frac{4480\,a^3\,b^5}{3}+256\,a\,b^7\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(240\,a^7\,b+2240\,a^5\,b^3+2688\,a^3\,b^5+\frac{2304\,a\,b^7}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(320\,a^7\,b+2240\,a^5\,b^3+\frac{6272\,a^3\,b^5}{3}+256\,a\,b^7\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(2\,a^8+56\,a^6\,b^2+210\,a^4\,b^4+105\,a^2\,b^6+\frac{35\,b^8}{8}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(12\,a^8+336\,a^6\,b^2+980\,a^4\,b^4+490\,a^2\,b^6+\frac{245\,b^8}{12}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(12\,a^8+336\,a^6\,b^2+980\,a^4\,b^4+490\,a^2\,b^6+\frac{245\,b^8}{12}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(30\,a^8+840\,a^6\,b^2+2030\,a^4\,b^4+791\,a^2\,b^6+\frac{791\,b^8}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(30\,a^8+840\,a^6\,b^2+2030\,a^4\,b^4+791\,a^2\,b^6+\frac{791\,b^8}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(40\,a^8+1120\,a^6\,b^2+2520\,a^4\,b^4+812\,a^2\,b^6+\frac{25\,b^8}{2}\right)+\frac{896\,a^3\,b^5}{3}+224\,a^5\,b^3+16\,a^7\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{7\,b^2\,\mathrm{atan}\left(\frac{7\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^6+240\,a^4\,b^2+120\,a^2\,b^4+5\,b^6\right)}{448\,a^6\,b^2+1680\,a^4\,b^4+840\,a^2\,b^6+35\,b^8}\right)\,\left(64\,a^6+240\,a^4\,b^2+120\,a^2\,b^4+5\,b^6\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^8*(240*a^7*b + (1792*a^3*b^5)/3 + 1120*a^5*b^3) + tan(c/2 + (d*x)/2)^10*(96*a^7*b + 224*a^5*b^3) + tan(c/2 + (d*x)/2)*(2*a^8 + (35*b^8)/8 + 105*a^2*b^6 + 210*a^4*b^4 + 56*a^6*b^2) + (256*a*b^7)/5 + 16*a^7*b + tan(c/2 + (d*x)/2)^2*(256*a*b^7 + 96*a^7*b + (4480*a^3*b^5)/3 + 1120*a^5*b^3) + tan(c/2 + (d*x)/2)^4*((2304*a*b^7)/5 + 240*a^7*b + 2688*a^3*b^5 + 2240*a^5*b^3) + tan(c/2 + (d*x)/2)^6*(256*a*b^7 + 320*a^7*b + (6272*a^3*b^5)/3 + 2240*a^5*b^3) + tan(c/2 + (d*x)/2)^13*(2*a^8 + (35*b^8)/8 + 105*a^2*b^6 + 210*a^4*b^4 + 56*a^6*b^2) + tan(c/2 + (d*x)/2)^3*(12*a^8 + (245*b^8)/12 + 490*a^2*b^6 + 980*a^4*b^4 + 336*a^6*b^2) + tan(c/2 + (d*x)/2)^11*(12*a^8 + (245*b^8)/12 + 490*a^2*b^6 + 980*a^4*b^4 + 336*a^6*b^2) + tan(c/2 + (d*x)/2)^5*(30*a^8 + (791*b^8)/24 + 791*a^2*b^6 + 2030*a^4*b^4 + 840*a^6*b^2) + tan(c/2 + (d*x)/2)^9*(30*a^8 + (791*b^8)/24 + 791*a^2*b^6 + 2030*a^4*b^4 + 840*a^6*b^2) + tan(c/2 + (d*x)/2)^7*(40*a^8 + (25*b^8)/2 + 812*a^2*b^6 + 2520*a^4*b^4 + 1120*a^6*b^2) + (896*a^3*b^5)/3 + 224*a^5*b^3 + 16*a^7*b*tan(c/2 + (d*x)/2)^12)/(d*(5*tan(c/2 + (d*x)/2)^2 + 9*tan(c/2 + (d*x)/2)^4 + 5*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 - 9*tan(c/2 + (d*x)/2)^10 - 5*tan(c/2 + (d*x)/2)^12 - tan(c/2 + (d*x)/2)^14 + 1)) - (7*b^2*atan((7*b^2*tan(c/2 + (d*x)/2)*(64*a^6 + 5*b^6 + 120*a^2*b^4 + 240*a^4*b^2))/(35*b^8 + 840*a^2*b^6 + 1680*a^4*b^4 + 448*a^6*b^2))*(64*a^6 + 5*b^6 + 120*a^2*b^4 + 240*a^4*b^2))/(8*d)","B"
421,1,726,369,7.823127,"\text{Not used}","int((a + b*sin(c + d*x))^8/cos(c + d*x)^4,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{304\,a^7\,b}{3}+\frac{2464\,a^5\,b^3}{3}+\frac{1792\,a^3\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(64\,a^7\,b+224\,a^5\,b^3\right)-\frac{256\,a\,b^7}{3}+\frac{16\,a^7\,b}{3}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^8+140\,a^4\,b^4+140\,a^2\,b^6+\frac{35\,b^8}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-\frac{64\,a^7\,b}{3}+\frac{224\,a^5\,b^3}{3}+\frac{896\,a^3\,b^5}{3}+\frac{256\,a\,b^7}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(48\,a^7\,b+448\,a^5\,b^3+896\,a^3\,b^5+256\,a\,b^7\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{256\,a^7\,b}{3}+\frac{3136\,a^5\,b^3}{3}+\frac{4480\,a^3\,b^5}{3}+256\,a\,b^7\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-\frac{20\,a^8}{3}-\frac{224\,a^6\,b^2}{3}+\frac{280\,a^4\,b^4}{3}+\frac{280\,a^2\,b^6}{3}+\frac{35\,b^8}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(-\frac{20\,a^8}{3}-\frac{224\,a^6\,b^2}{3}+\frac{280\,a^4\,b^4}{3}+\frac{280\,a^2\,b^6}{3}+\frac{35\,b^8}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(8\,a^8+448\,a^6\,b^2+1680\,a^4\,b^4+784\,a^2\,b^6+17\,b^8\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{26\,a^8}{3}+\frac{896\,a^6\,b^2}{3}+\frac{2660\,a^4\,b^4}{3}+\frac{1316\,a^2\,b^6}{3}+\frac{329\,b^8}{12}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{26\,a^8}{3}+\frac{896\,a^6\,b^2}{3}+\frac{2660\,a^4\,b^4}{3}+\frac{1316\,a^2\,b^6}{3}+\frac{329\,b^8}{12}\right)-\frac{896\,a^3\,b^5}{3}-\frac{224\,a^5\,b^3}{3}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(-2\,a^8+140\,a^4\,b^4+140\,a^2\,b^6+\frac{35\,b^8}{4}\right)+16\,a^7\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{35\,b^4\,\mathrm{atan}\left(\frac{35\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^4+16\,a^2\,b^2+b^4\right)}{560\,a^4\,b^4+560\,a^2\,b^6+35\,b^8}\right)\,\left(16\,a^4+16\,a^2\,b^2+b^4\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^8*((304*a^7*b)/3 + (1792*a^3*b^5)/3 + (2464*a^5*b^3)/3) + tan(c/2 + (d*x)/2)^10*(64*a^7*b + 224*a^5*b^3) - (256*a*b^7)/3 + (16*a^7*b)/3 - tan(c/2 + (d*x)/2)*((35*b^8)/4 - 2*a^8 + 140*a^2*b^6 + 140*a^4*b^4) - tan(c/2 + (d*x)/2)^2*((256*a*b^7)/3 - (64*a^7*b)/3 + (896*a^3*b^5)/3 + (224*a^5*b^3)/3) + tan(c/2 + (d*x)/2)^4*(256*a*b^7 + 48*a^7*b + 896*a^3*b^5 + 448*a^5*b^3) + tan(c/2 + (d*x)/2)^6*(256*a*b^7 + (256*a^7*b)/3 + (4480*a^3*b^5)/3 + (3136*a^5*b^3)/3) - tan(c/2 + (d*x)/2)^3*((35*b^8)/6 - (20*a^8)/3 + (280*a^2*b^6)/3 + (280*a^4*b^4)/3 - (224*a^6*b^2)/3) - tan(c/2 + (d*x)/2)^11*((35*b^8)/6 - (20*a^8)/3 + (280*a^2*b^6)/3 + (280*a^4*b^4)/3 - (224*a^6*b^2)/3) + tan(c/2 + (d*x)/2)^7*(8*a^8 + 17*b^8 + 784*a^2*b^6 + 1680*a^4*b^4 + 448*a^6*b^2) + tan(c/2 + (d*x)/2)^5*((26*a^8)/3 + (329*b^8)/12 + (1316*a^2*b^6)/3 + (2660*a^4*b^4)/3 + (896*a^6*b^2)/3) + tan(c/2 + (d*x)/2)^9*((26*a^8)/3 + (329*b^8)/12 + (1316*a^2*b^6)/3 + (2660*a^4*b^4)/3 + (896*a^6*b^2)/3) - (896*a^3*b^5)/3 - (224*a^5*b^3)/3 - tan(c/2 + (d*x)/2)^13*((35*b^8)/4 - 2*a^8 + 140*a^2*b^6 + 140*a^4*b^4) + 16*a^7*b*tan(c/2 + (d*x)/2)^12)/(d*(tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 - 3*tan(c/2 + (d*x)/2)^6 + 3*tan(c/2 + (d*x)/2)^8 + 3*tan(c/2 + (d*x)/2)^10 - tan(c/2 + (d*x)/2)^12 - tan(c/2 + (d*x)/2)^14 + 1)) + (35*b^4*atan((35*b^4*tan(c/2 + (d*x)/2)*(16*a^4 + b^4 + 16*a^2*b^2))/(35*b^8 + 560*a^2*b^6 + 560*a^4*b^4))*(16*a^4 + b^4 + 16*a^2*b^2))/(4*d)","B"
422,1,665,381,7.597992,"\text{Not used}","int((a + b*sin(c + d*x))^8/cos(c + d*x)^6,x)","-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(2\,a^8+56\,a^2\,b^6+7\,b^8\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(48\,a^7\,b+\frac{1568\,a^5\,b^3}{3}+\frac{1792\,a^3\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(32\,a^7\,b+224\,a^5\,b^3\right)+\frac{256\,a\,b^7}{5}+\frac{16\,a^7\,b}{5}+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^8+56\,a^2\,b^6+7\,b^8\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(64\,a^7\,b+448\,a^5\,b^3+896\,a^3\,b^5+256\,a\,b^7\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-\frac{32\,a^7\,b}{5}-\frac{224\,a^5\,b^3}{5}+\frac{896\,a^3\,b^5}{5}+\frac{768\,a\,b^7}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{176\,a^7\,b}{5}+\frac{3136\,a^5\,b^3}{15}+\frac{896\,a^3\,b^5}{15}+\frac{256\,a\,b^7}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{22\,a^8}{5}+\frac{896\,a^6\,b^2}{5}+448\,a^4\,b^4+\frac{616\,a^2\,b^6}{5}+\frac{77\,b^8}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{22\,a^8}{5}+\frac{896\,a^6\,b^2}{5}+448\,a^4\,b^4+\frac{616\,a^2\,b^6}{5}+\frac{77\,b^8}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{152\,a^8}{15}+\frac{3136\,a^6\,b^2}{15}+896\,a^4\,b^4+\frac{10976\,a^2\,b^6}{15}+\frac{412\,b^8}{15}\right)+\frac{896\,a^3\,b^5}{15}-\frac{224\,a^5\,b^3}{15}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{4\,a^8}{3}+\frac{224\,a^6\,b^2}{3}-\frac{560\,a^2\,b^6}{3}-\frac{70\,b^8}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{4\,a^8}{3}+\frac{224\,a^6\,b^2}{3}-\frac{560\,a^2\,b^6}{3}-\frac{70\,b^8}{3}\right)+16\,a^7\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{7\,b^6\,\mathrm{atan}\left(\frac{7\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^2+b^2\right)}{56\,a^2\,b^6+7\,b^8}\right)\,\left(8\,a^2+b^2\right)}{d}","Not used",1,"- (tan(c/2 + (d*x)/2)^13*(2*a^8 + 7*b^8 + 56*a^2*b^6) + tan(c/2 + (d*x)/2)^8*(48*a^7*b + (1792*a^3*b^5)/3 + (1568*a^5*b^3)/3) + tan(c/2 + (d*x)/2)^10*(32*a^7*b + 224*a^5*b^3) + (256*a*b^7)/5 + (16*a^7*b)/5 + tan(c/2 + (d*x)/2)*(2*a^8 + 7*b^8 + 56*a^2*b^6) + tan(c/2 + (d*x)/2)^6*(256*a*b^7 + 64*a^7*b + 896*a^3*b^5 + 448*a^5*b^3) - tan(c/2 + (d*x)/2)^2*((768*a*b^7)/5 - (32*a^7*b)/5 + (896*a^3*b^5)/5 - (224*a^5*b^3)/5) + tan(c/2 + (d*x)/2)^4*((256*a*b^7)/5 + (176*a^7*b)/5 + (896*a^3*b^5)/15 + (3136*a^5*b^3)/15) + tan(c/2 + (d*x)/2)^5*((22*a^8)/5 + (77*b^8)/5 + (616*a^2*b^6)/5 + 448*a^4*b^4 + (896*a^6*b^2)/5) + tan(c/2 + (d*x)/2)^9*((22*a^8)/5 + (77*b^8)/5 + (616*a^2*b^6)/5 + 448*a^4*b^4 + (896*a^6*b^2)/5) + tan(c/2 + (d*x)/2)^7*((152*a^8)/15 + (412*b^8)/15 + (10976*a^2*b^6)/15 + 896*a^4*b^4 + (3136*a^6*b^2)/15) + (896*a^3*b^5)/15 - (224*a^5*b^3)/15 + tan(c/2 + (d*x)/2)^3*((4*a^8)/3 - (70*b^8)/3 - (560*a^2*b^6)/3 + (224*a^6*b^2)/3) + tan(c/2 + (d*x)/2)^11*((4*a^8)/3 - (70*b^8)/3 - (560*a^2*b^6)/3 + (224*a^6*b^2)/3) + 16*a^7*b*tan(c/2 + (d*x)/2)^12)/(d*(3*tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)^4 - 5*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 3*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 - 1)) - (7*b^6*atan((7*b^6*tan(c/2 + (d*x)/2)*(8*a^2 + b^2))/(7*b^8 + 56*a^2*b^6))*(8*a^2 + b^2))/d","B"
423,1,546,404,8.853043,"\text{Not used}","int((a + b*sin(c + d*x))^8/cos(c + d*x)^8,x)","b^8\,x-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-4\,a^8+\frac{224\,a^6\,b^2}{3}+\frac{44\,b^8}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(-4\,a^8+\frac{224\,a^6\,b^2}{3}+\frac{44\,b^8}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(2\,a^8-2\,b^8\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{224\,a^5\,b^3}{5}-\frac{896\,a^3\,b^5}{15}+\frac{256\,a\,b^7}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(448\,a^5\,b^3+\frac{896\,a^3\,b^5}{3}+256\,a\,b^7\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(80\,a^7\,b+224\,a^5\,b^3+\frac{1792\,a^3\,b^5}{3}\right)-\frac{256\,a\,b^7}{35}+\frac{16\,a^7\,b}{7}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(48\,a^7\,b+\frac{448\,a^5\,b^3}{5}+\frac{896\,a^3\,b^5}{5}-\frac{768\,a\,b^7}{5}\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^8-2\,b^8\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-\frac{424\,a^8}{35}+\frac{1216\,a^6\,b^2}{5}+384\,a^4\,b^4+512\,a^2\,b^6+\frac{3048\,b^8}{35}\right)+\frac{128\,a^3\,b^5}{15}-\frac{32\,a^5\,b^3}{5}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{86\,a^8}{5}+\frac{896\,a^6\,b^2}{15}+448\,a^4\,b^4-\frac{706\,b^8}{15}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{86\,a^8}{5}+\frac{896\,a^6\,b^2}{15}+448\,a^4\,b^4-\frac{706\,b^8}{15}\right)+224\,a^5\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+16\,a^7\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"b^8*x - (tan(c/2 + (d*x)/2)^3*((44*b^8)/3 - 4*a^8 + (224*a^6*b^2)/3) + tan(c/2 + (d*x)/2)^11*((44*b^8)/3 - 4*a^8 + (224*a^6*b^2)/3) + tan(c/2 + (d*x)/2)^13*(2*a^8 - 2*b^8) + tan(c/2 + (d*x)/2)^2*((256*a*b^7)/5 - (896*a^3*b^5)/15 + (224*a^5*b^3)/5) + tan(c/2 + (d*x)/2)^6*(256*a*b^7 + (896*a^3*b^5)/3 + 448*a^5*b^3) + tan(c/2 + (d*x)/2)^8*(80*a^7*b + (1792*a^3*b^5)/3 + 224*a^5*b^3) - (256*a*b^7)/35 + (16*a^7*b)/7 + tan(c/2 + (d*x)/2)^4*(48*a^7*b - (768*a*b^7)/5 + (896*a^3*b^5)/5 + (448*a^5*b^3)/5) + tan(c/2 + (d*x)/2)*(2*a^8 - 2*b^8) + tan(c/2 + (d*x)/2)^7*((3048*b^8)/35 - (424*a^8)/35 + 512*a^2*b^6 + 384*a^4*b^4 + (1216*a^6*b^2)/5) + (128*a^3*b^5)/15 - (32*a^5*b^3)/5 + tan(c/2 + (d*x)/2)^5*((86*a^8)/5 - (706*b^8)/15 + 448*a^4*b^4 + (896*a^6*b^2)/15) + tan(c/2 + (d*x)/2)^9*((86*a^8)/5 - (706*b^8)/15 + 448*a^4*b^4 + (896*a^6*b^2)/15) + 224*a^5*b^3*tan(c/2 + (d*x)/2)^10 + 16*a^7*b*tan(c/2 + (d*x)/2)^12)/(d*(7*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 - 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 - 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 - 1))","B"
424,1,659,236,6.679802,"\text{Not used}","int((a + b*sin(c + d*x))^8/cos(c + d*x)^10,x)","\frac{{\left(a-b\right)}^8}{2\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^8}-\frac{{\left(a+b\right)}^8}{9\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^9}-\frac{{\left(a+b\right)}^8}{2\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^8}-\frac{{\left(a-b\right)}^8}{9\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^9}-\frac{{\left(a+b\right)}^7\,\left(37\,a+21\,b\right)}{28\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^7}-\frac{{\left(a+b\right)}^7\,\left(55\,a+7\,b\right)}{24\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^6}+\frac{{\left(a-b\right)}^5\,\left(187\,a^3+191\,a^2\,b+65\,a\,b^2+5\,b^3\right)}{128\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^2}+\frac{{\left(a-b\right)}^5\,\left(-463\,a^3-67\,a^2\,b+67\,a\,b^2+15\,b^3\right)}{192\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^3}+\frac{{\left(a-b\right)}^6\,\left(95\,a^2+18\,a\,b-b^2\right)}{32\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^4}+\frac{{\left(a-b\right)}^6\,\left(-241\,a^2+114\,a\,b+15\,b^2\right)}{80\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^5}-\frac{{\left(a-b\right)}^7\,\left(37\,a-21\,b\right)}{28\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^7}+\frac{{\left(a-b\right)}^7\,\left(55\,a-7\,b\right)}{24\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^6}+\frac{{\left(a+b\right)}^6\,\left(-95\,a^2+18\,a\,b+b^2\right)}{32\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^4}-\frac{{\left(a+b\right)}^5\,\left(187\,a^3-191\,a^2\,b+65\,a\,b^2-5\,b^3\right)}{128\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^2}+\frac{{\left(a+b\right)}^5\,\left(-463\,a^3+67\,a^2\,b+67\,a\,b^2-15\,b^3\right)}{192\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^3}-\frac{{\left(a+b\right)}^6\,\left(241\,a^2+114\,a\,b-15\,b^2\right)}{80\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^5}-\frac{a\,{\left(a+b\right)}^4\,\left(16\,a^3-29\,a^2\,b+20\,a\,b^2-5\,b^3\right)}{16\,d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}-\frac{a\,{\left(a-b\right)}^4\,\left(16\,a^3+29\,a^2\,b+20\,a\,b^2+5\,b^3\right)}{16\,d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}","Not used",1,"(a - b)^8/(2*d*(tan(c/2 + (d*x)/2) + 1)^8) - (a + b)^8/(9*d*(tan(c/2 + (d*x)/2) - 1)^9) - (a + b)^8/(2*d*(tan(c/2 + (d*x)/2) - 1)^8) - (a - b)^8/(9*d*(tan(c/2 + (d*x)/2) + 1)^9) - ((a + b)^7*(37*a + 21*b))/(28*d*(tan(c/2 + (d*x)/2) - 1)^7) - ((a + b)^7*(55*a + 7*b))/(24*d*(tan(c/2 + (d*x)/2) - 1)^6) + ((a - b)^5*(65*a*b^2 + 191*a^2*b + 187*a^3 + 5*b^3))/(128*d*(tan(c/2 + (d*x)/2) + 1)^2) + ((a - b)^5*(67*a*b^2 - 67*a^2*b - 463*a^3 + 15*b^3))/(192*d*(tan(c/2 + (d*x)/2) + 1)^3) + ((a - b)^6*(18*a*b + 95*a^2 - b^2))/(32*d*(tan(c/2 + (d*x)/2) + 1)^4) + ((a - b)^6*(114*a*b - 241*a^2 + 15*b^2))/(80*d*(tan(c/2 + (d*x)/2) + 1)^5) - ((a - b)^7*(37*a - 21*b))/(28*d*(tan(c/2 + (d*x)/2) + 1)^7) + ((a - b)^7*(55*a - 7*b))/(24*d*(tan(c/2 + (d*x)/2) + 1)^6) + ((a + b)^6*(18*a*b - 95*a^2 + b^2))/(32*d*(tan(c/2 + (d*x)/2) - 1)^4) - ((a + b)^5*(65*a*b^2 - 191*a^2*b + 187*a^3 - 5*b^3))/(128*d*(tan(c/2 + (d*x)/2) - 1)^2) + ((a + b)^5*(67*a*b^2 + 67*a^2*b - 463*a^3 - 15*b^3))/(192*d*(tan(c/2 + (d*x)/2) - 1)^3) - ((a + b)^6*(114*a*b + 241*a^2 - 15*b^2))/(80*d*(tan(c/2 + (d*x)/2) - 1)^5) - (a*(a + b)^4*(20*a*b^2 - 29*a^2*b + 16*a^3 - 5*b^3))/(16*d*(tan(c/2 + (d*x)/2) - 1)) - (a*(a - b)^4*(20*a*b^2 + 29*a^2*b + 16*a^3 + 5*b^3))/(16*d*(tan(c/2 + (d*x)/2) + 1))","B"
425,1,109,118,5.072444,"\text{Not used}","int(cos(c + d*x)^5/(a + b*sin(c + d*x)),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^4}{4\,b}-{\sin\left(c+d\,x\right)}^2\,\left(\frac{1}{b}-\frac{a^2}{2\,b^3}\right)+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{b^5}-\frac{a\,{\sin\left(c+d\,x\right)}^3}{3\,b^2}+\frac{a\,\sin\left(c+d\,x\right)\,\left(\frac{2}{b}-\frac{a^2}{b^3}\right)}{b}}{d}","Not used",1,"(sin(c + d*x)^4/(4*b) - sin(c + d*x)^2*(1/b - a^2/(2*b^3)) + (log(a + b*sin(c + d*x))*(a^4 + b^4 - 2*a^2*b^2))/b^5 - (a*sin(c + d*x)^3)/(3*b^2) + (a*sin(c + d*x)*(2/b - a^2/b^3))/b)/d","B"
426,1,55,61,0.076710,"\text{Not used}","int(cos(c + d*x)^3/(a + b*sin(c + d*x)),x)","-\frac{\frac{{\sin\left(c+d\,x\right)}^2}{2\,b}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(a^2-b^2\right)}{b^3}-\frac{a\,\sin\left(c+d\,x\right)}{b^2}}{d}","Not used",1,"-(sin(c + d*x)^2/(2*b) + (log(a + b*sin(c + d*x))*(a^2 - b^2))/b^3 - (a*sin(c + d*x))/b^2)/d","B"
427,1,18,18,5.085343,"\text{Not used}","int(cos(c + d*x)/(a + b*sin(c + d*x)),x)","\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{b\,d}","Not used",1,"log(a + b*sin(c + d*x))/(b*d)","B"
428,1,69,75,5.133436,"\text{Not used}","int(1/(cos(c + d*x)*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)}{2\,d\,\left(a-b\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)}{2\,d\,\left(a+b\right)}-\frac{b\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{d\,\left(a^2-b^2\right)}","Not used",1,"log(sin(c + d*x) + 1)/(2*d*(a - b)) - log(sin(c + d*x) - 1)/(2*d*(a + b)) - (b*log(a + b*sin(c + d*x)))/(d*(a^2 - b^2))","B"
429,1,148,123,5.388459,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b*sin(c + d*x))),x)","\frac{\frac{b}{2\,\left(a^2-b^2\right)}-\frac{a\,\sin\left(c+d\,x\right)}{2\,\left(a^2-b^2\right)}}{d\,\left({\sin\left(c+d\,x\right)}^2-1\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{b}{4\,{\left(a+b\right)}^2}+\frac{1}{4\,\left(a+b\right)}\right)}{d}+\frac{b^3\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{d\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(a-2\,b\right)}{4\,d\,{\left(a-b\right)}^2}","Not used",1,"(b/(2*(a^2 - b^2)) - (a*sin(c + d*x))/(2*(a^2 - b^2)))/(d*(sin(c + d*x)^2 - 1)) - (log(sin(c + d*x) - 1)*(b/(4*(a + b)^2) + 1/(4*(a + b))))/d + (b^3*log(a + b*sin(c + d*x)))/(d*(a^4 + b^4 - 2*a^2*b^2)) + (log(sin(c + d*x) + 1)*(a - 2*b))/(4*d*(a - b)^2)","B"
430,1,322,195,0.585824,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + b*sin(c + d*x))),x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(\frac{b^2}{8\,{\left(a-b\right)}^3}-\frac{3\,b}{16\,{\left(a-b\right)}^2}+\frac{3}{16\,\left(a-b\right)}\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{3\,b}{16\,{\left(a+b\right)}^2}+\frac{3}{16\,\left(a+b\right)}+\frac{b^2}{8\,{\left(a+b\right)}^3}\right)}{d}-\frac{\frac{a^2\,b-3\,b^3}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b^3\,{\sin\left(c+d\,x\right)}^2}{2\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\sin\left(c+d\,x\right)}^3\,\left(7\,a\,b^2-3\,a^3\right)}{8\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{\sin\left(c+d\,x\right)\,\left(9\,a\,b^2-5\,a^3\right)}{8\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left({\cos\left(c+d\,x\right)}^2+{\sin\left(c+d\,x\right)}^4-{\sin\left(c+d\,x\right)}^2\right)}-\frac{b^5\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{d\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}","Not used",1,"(log(sin(c + d*x) + 1)*(b^2/(8*(a - b)^3) - (3*b)/(16*(a - b)^2) + 3/(16*(a - b))))/d - (log(sin(c + d*x) - 1)*((3*b)/(16*(a + b)^2) + 3/(16*(a + b)) + b^2/(8*(a + b)^3)))/d - ((a^2*b - 3*b^3)/(4*(a^4 + b^4 - 2*a^2*b^2)) + (b^3*sin(c + d*x)^2)/(2*(a^4 + b^4 - 2*a^2*b^2)) - (sin(c + d*x)^3*(7*a*b^2 - 3*a^3))/(8*(a^4 + b^4 - 2*a^2*b^2)) + (sin(c + d*x)*(9*a*b^2 - 5*a^3))/(8*(a^4 + b^4 - 2*a^2*b^2)))/(d*(cos(c + d*x)^2 - sin(c + d*x)^2 + sin(c + d*x)^4)) - (b^5*log(a + b*sin(c + d*x)))/(d*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))","B"
431,1,3075,188,7.655128,"\text{Not used}","int(cos(c + d*x)^6/(a + b*sin(c + d*x)),x)","\frac{\frac{2\,\left(15\,a^4-35\,a^2\,b^2+23\,b^4\right)}{15\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(5\,a\,b^2-4\,a^3\right)}{2\,b^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(5\,a\,b^2-4\,a^3\right)}{2\,b^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(9\,a\,b^2-4\,a^3\right)}{4\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^4-3\,a^2\,b^2+3\,b^4\right)}{b^5}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^4-5\,a^2\,b^2+3\,b^4\right)}{b^5}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a^4-13\,a^2\,b^2+7\,b^4\right)}{3\,b^5}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(9\,a^4-20\,a^2\,b^2+14\,b^4\right)}{3\,b^5}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a\,b^2-4\,a^3\right)}{4\,b^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{32\,a^{12}\,b^5-160\,a^{10}\,b^7+320\,a^8\,b^9-300\,a^6\,b^{11}+\frac{225\,a^4\,b^{13}}{2}}{b^{14}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^5-832\,a^{11}\,b^7+2240\,a^9\,b^9-3160\,a^7\,b^{11}+2385\,a^5\,b^{13}-834\,a^3\,b^{15}+64\,a\,b^{17}\right)}{2\,b^{15}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{16\,a^6\,b^{12}-44\,a^4\,b^{14}+28\,a^2\,b^{16}}{b^{14}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{19}-128\,a^3\,b^{17}\right)}{2\,b^{15}}\right)}{b^6}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,a^7\,b^{12}+384\,a^5\,b^{14}-384\,a^3\,b^{16}+128\,a\,b^{18}\right)}{2\,b^{15}}\right)}{b^6}\right)\,1{}\mathrm{i}}{b^6}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{32\,a^{12}\,b^5-160\,a^{10}\,b^7+320\,a^8\,b^9-300\,a^6\,b^{11}+\frac{225\,a^4\,b^{13}}{2}}{b^{14}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^5-832\,a^{11}\,b^7+2240\,a^9\,b^9-3160\,a^7\,b^{11}+2385\,a^5\,b^{13}-834\,a^3\,b^{15}+64\,a\,b^{17}\right)}{2\,b^{15}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{19}-128\,a^3\,b^{17}\right)}{2\,b^{15}}\right)}{b^6}-\frac{16\,a^6\,b^{12}-44\,a^4\,b^{14}+28\,a^2\,b^{16}}{b^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,a^7\,b^{12}+384\,a^5\,b^{14}-384\,a^3\,b^{16}+128\,a\,b^{18}\right)}{2\,b^{15}}\right)}{b^6}\right)\,1{}\mathrm{i}}{b^6}}{\frac{32\,a^{16}-248\,a^{14}\,b^2+856\,a^{12}\,b^4-1695\,a^{10}\,b^6+2069\,a^8\,b^8-1549\,a^6\,b^{10}+655\,a^4\,b^{12}-120\,a^2\,b^{14}}{b^{14}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{32\,a^{12}\,b^5-160\,a^{10}\,b^7+320\,a^8\,b^9-300\,a^6\,b^{11}+\frac{225\,a^4\,b^{13}}{2}}{b^{14}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^5-832\,a^{11}\,b^7+2240\,a^9\,b^9-3160\,a^7\,b^{11}+2385\,a^5\,b^{13}-834\,a^3\,b^{15}+64\,a\,b^{17}\right)}{2\,b^{15}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{16\,a^6\,b^{12}-44\,a^4\,b^{14}+28\,a^2\,b^{16}}{b^{14}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{19}-128\,a^3\,b^{17}\right)}{2\,b^{15}}\right)}{b^6}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,a^7\,b^{12}+384\,a^5\,b^{14}-384\,a^3\,b^{16}+128\,a\,b^{18}\right)}{2\,b^{15}}\right)}{b^6}\right)}{b^6}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{32\,a^{12}\,b^5-160\,a^{10}\,b^7+320\,a^8\,b^9-300\,a^6\,b^{11}+\frac{225\,a^4\,b^{13}}{2}}{b^{14}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^5-832\,a^{11}\,b^7+2240\,a^9\,b^9-3160\,a^7\,b^{11}+2385\,a^5\,b^{13}-834\,a^3\,b^{15}+64\,a\,b^{17}\right)}{2\,b^{15}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{19}-128\,a^3\,b^{17}\right)}{2\,b^{15}}\right)}{b^6}-\frac{16\,a^6\,b^{12}-44\,a^4\,b^{14}+28\,a^2\,b^{16}}{b^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,a^7\,b^{12}+384\,a^5\,b^{14}-384\,a^3\,b^{16}+128\,a\,b^{18}\right)}{2\,b^{15}}\right)}{b^6}\right)}{b^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{17}-1024\,a^{15}\,b^2+3584\,a^{13}\,b^4-7088\,a^{11}\,b^6+8530\,a^9\,b^8-6230\,a^7\,b^{10}+2550\,a^5\,b^{12}-450\,a^3\,b^{14}\right)}{b^{15}}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{b^6\,d}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{32\,a^{12}\,b^5-160\,a^{10}\,b^7+320\,a^8\,b^9-300\,a^6\,b^{11}+\frac{225\,a^4\,b^{13}}{2}}{b^{14}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^5-832\,a^{11}\,b^7+2240\,a^9\,b^9-3160\,a^7\,b^{11}+2385\,a^5\,b^{13}-834\,a^3\,b^{15}+64\,a\,b^{17}\right)}{2\,b^{15}}+\frac{a\,\left(8\,a^4-20\,a^2\,b^2+15\,b^4\right)\,\left(\frac{16\,a^6\,b^{12}-44\,a^4\,b^{14}+28\,a^2\,b^{16}}{b^{14}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,a^7\,b^{12}+384\,a^5\,b^{14}-384\,a^3\,b^{16}+128\,a\,b^{18}\right)}{2\,b^{15}}+\frac{a\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{19}-128\,a^3\,b^{17}\right)}{2\,b^{15}}\right)\,\left(8\,a^4-20\,a^2\,b^2+15\,b^4\right)\,1{}\mathrm{i}}{8\,b^6}\right)\,1{}\mathrm{i}}{8\,b^6}\right)\,\left(8\,a^4-20\,a^2\,b^2+15\,b^4\right)}{8\,b^6}+\frac{a\,\left(\frac{32\,a^{12}\,b^5-160\,a^{10}\,b^7+320\,a^8\,b^9-300\,a^6\,b^{11}+\frac{225\,a^4\,b^{13}}{2}}{b^{14}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^5-832\,a^{11}\,b^7+2240\,a^9\,b^9-3160\,a^7\,b^{11}+2385\,a^5\,b^{13}-834\,a^3\,b^{15}+64\,a\,b^{17}\right)}{2\,b^{15}}+\frac{a\,\left(8\,a^4-20\,a^2\,b^2+15\,b^4\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,a^7\,b^{12}+384\,a^5\,b^{14}-384\,a^3\,b^{16}+128\,a\,b^{18}\right)}{2\,b^{15}}-\frac{16\,a^6\,b^{12}-44\,a^4\,b^{14}+28\,a^2\,b^{16}}{b^{14}}+\frac{a\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{19}-128\,a^3\,b^{17}\right)}{2\,b^{15}}\right)\,\left(8\,a^4-20\,a^2\,b^2+15\,b^4\right)\,1{}\mathrm{i}}{8\,b^6}\right)\,1{}\mathrm{i}}{8\,b^6}\right)\,\left(8\,a^4-20\,a^2\,b^2+15\,b^4\right)}{8\,b^6}}{\frac{32\,a^{16}-248\,a^{14}\,b^2+856\,a^{12}\,b^4-1695\,a^{10}\,b^6+2069\,a^8\,b^8-1549\,a^6\,b^{10}+655\,a^4\,b^{12}-120\,a^2\,b^{14}}{b^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{17}-1024\,a^{15}\,b^2+3584\,a^{13}\,b^4-7088\,a^{11}\,b^6+8530\,a^9\,b^8-6230\,a^7\,b^{10}+2550\,a^5\,b^{12}-450\,a^3\,b^{14}\right)}{b^{15}}+\frac{a\,\left(\frac{32\,a^{12}\,b^5-160\,a^{10}\,b^7+320\,a^8\,b^9-300\,a^6\,b^{11}+\frac{225\,a^4\,b^{13}}{2}}{b^{14}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^5-832\,a^{11}\,b^7+2240\,a^9\,b^9-3160\,a^7\,b^{11}+2385\,a^5\,b^{13}-834\,a^3\,b^{15}+64\,a\,b^{17}\right)}{2\,b^{15}}+\frac{a\,\left(8\,a^4-20\,a^2\,b^2+15\,b^4\right)\,\left(\frac{16\,a^6\,b^{12}-44\,a^4\,b^{14}+28\,a^2\,b^{16}}{b^{14}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,a^7\,b^{12}+384\,a^5\,b^{14}-384\,a^3\,b^{16}+128\,a\,b^{18}\right)}{2\,b^{15}}+\frac{a\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{19}-128\,a^3\,b^{17}\right)}{2\,b^{15}}\right)\,\left(8\,a^4-20\,a^2\,b^2+15\,b^4\right)\,1{}\mathrm{i}}{8\,b^6}\right)\,1{}\mathrm{i}}{8\,b^6}\right)\,\left(8\,a^4-20\,a^2\,b^2+15\,b^4\right)\,1{}\mathrm{i}}{8\,b^6}-\frac{a\,\left(\frac{32\,a^{12}\,b^5-160\,a^{10}\,b^7+320\,a^8\,b^9-300\,a^6\,b^{11}+\frac{225\,a^4\,b^{13}}{2}}{b^{14}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^5-832\,a^{11}\,b^7+2240\,a^9\,b^9-3160\,a^7\,b^{11}+2385\,a^5\,b^{13}-834\,a^3\,b^{15}+64\,a\,b^{17}\right)}{2\,b^{15}}+\frac{a\,\left(8\,a^4-20\,a^2\,b^2+15\,b^4\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,a^7\,b^{12}+384\,a^5\,b^{14}-384\,a^3\,b^{16}+128\,a\,b^{18}\right)}{2\,b^{15}}-\frac{16\,a^6\,b^{12}-44\,a^4\,b^{14}+28\,a^2\,b^{16}}{b^{14}}+\frac{a\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{19}-128\,a^3\,b^{17}\right)}{2\,b^{15}}\right)\,\left(8\,a^4-20\,a^2\,b^2+15\,b^4\right)\,1{}\mathrm{i}}{8\,b^6}\right)\,1{}\mathrm{i}}{8\,b^6}\right)\,\left(8\,a^4-20\,a^2\,b^2+15\,b^4\right)\,1{}\mathrm{i}}{8\,b^6}}\right)\,\left(8\,a^4-20\,a^2\,b^2+15\,b^4\right)}{4\,b^6\,d}","Not used",1,"((2*(15*a^4 + 23*b^4 - 35*a^2*b^2))/(15*b^5) + (tan(c/2 + (d*x)/2)^3*(5*a*b^2 - 4*a^3))/(2*b^4) - (tan(c/2 + (d*x)/2)^7*(5*a*b^2 - 4*a^3))/(2*b^4) - (tan(c/2 + (d*x)/2)^9*(9*a*b^2 - 4*a^3))/(4*b^4) + (2*tan(c/2 + (d*x)/2)^8*(a^4 + 3*b^4 - 3*a^2*b^2))/b^5 + (4*tan(c/2 + (d*x)/2)^6*(2*a^4 + 3*b^4 - 5*a^2*b^2))/b^5 + (4*tan(c/2 + (d*x)/2)^2*(6*a^4 + 7*b^4 - 13*a^2*b^2))/(3*b^5) + (4*tan(c/2 + (d*x)/2)^4*(9*a^4 + 14*b^4 - 20*a^2*b^2))/(3*b^5) + (tan(c/2 + (d*x)/2)*(9*a*b^2 - 4*a^3))/(4*b^4))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (atan((((-(a + b)^5*(a - b)^5)^(1/2)*(((225*a^4*b^13)/2 - 300*a^6*b^11 + 320*a^8*b^9 - 160*a^10*b^7 + 32*a^12*b^5)/b^14 - (tan(c/2 + (d*x)/2)*(64*a*b^17 - 834*a^3*b^15 + 2385*a^5*b^13 - 3160*a^7*b^11 + 2240*a^9*b^9 - 832*a^11*b^7 + 128*a^13*b^5))/(2*b^15) + ((-(a + b)^5*(a - b)^5)^(1/2)*((28*a^2*b^16 - 44*a^4*b^14 + 16*a^6*b^12)/b^14 + ((-(a + b)^5*(a - b)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 - 128*a^3*b^17))/(2*b^15)))/b^6 - (tan(c/2 + (d*x)/2)*(128*a*b^18 - 384*a^3*b^16 + 384*a^5*b^14 - 128*a^7*b^12))/(2*b^15)))/b^6)*1i)/b^6 + ((-(a + b)^5*(a - b)^5)^(1/2)*(((225*a^4*b^13)/2 - 300*a^6*b^11 + 320*a^8*b^9 - 160*a^10*b^7 + 32*a^12*b^5)/b^14 - (tan(c/2 + (d*x)/2)*(64*a*b^17 - 834*a^3*b^15 + 2385*a^5*b^13 - 3160*a^7*b^11 + 2240*a^9*b^9 - 832*a^11*b^7 + 128*a^13*b^5))/(2*b^15) + ((-(a + b)^5*(a - b)^5)^(1/2)*(((-(a + b)^5*(a - b)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 - 128*a^3*b^17))/(2*b^15)))/b^6 - (28*a^2*b^16 - 44*a^4*b^14 + 16*a^6*b^12)/b^14 + (tan(c/2 + (d*x)/2)*(128*a*b^18 - 384*a^3*b^16 + 384*a^5*b^14 - 128*a^7*b^12))/(2*b^15)))/b^6)*1i)/b^6)/((32*a^16 - 120*a^2*b^14 + 655*a^4*b^12 - 1549*a^6*b^10 + 2069*a^8*b^8 - 1695*a^10*b^6 + 856*a^12*b^4 - 248*a^14*b^2)/b^14 + ((-(a + b)^5*(a - b)^5)^(1/2)*(((225*a^4*b^13)/2 - 300*a^6*b^11 + 320*a^8*b^9 - 160*a^10*b^7 + 32*a^12*b^5)/b^14 - (tan(c/2 + (d*x)/2)*(64*a*b^17 - 834*a^3*b^15 + 2385*a^5*b^13 - 3160*a^7*b^11 + 2240*a^9*b^9 - 832*a^11*b^7 + 128*a^13*b^5))/(2*b^15) + ((-(a + b)^5*(a - b)^5)^(1/2)*((28*a^2*b^16 - 44*a^4*b^14 + 16*a^6*b^12)/b^14 + ((-(a + b)^5*(a - b)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 - 128*a^3*b^17))/(2*b^15)))/b^6 - (tan(c/2 + (d*x)/2)*(128*a*b^18 - 384*a^3*b^16 + 384*a^5*b^14 - 128*a^7*b^12))/(2*b^15)))/b^6))/b^6 - ((-(a + b)^5*(a - b)^5)^(1/2)*(((225*a^4*b^13)/2 - 300*a^6*b^11 + 320*a^8*b^9 - 160*a^10*b^7 + 32*a^12*b^5)/b^14 - (tan(c/2 + (d*x)/2)*(64*a*b^17 - 834*a^3*b^15 + 2385*a^5*b^13 - 3160*a^7*b^11 + 2240*a^9*b^9 - 832*a^11*b^7 + 128*a^13*b^5))/(2*b^15) + ((-(a + b)^5*(a - b)^5)^(1/2)*(((-(a + b)^5*(a - b)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 - 128*a^3*b^17))/(2*b^15)))/b^6 - (28*a^2*b^16 - 44*a^4*b^14 + 16*a^6*b^12)/b^14 + (tan(c/2 + (d*x)/2)*(128*a*b^18 - 384*a^3*b^16 + 384*a^5*b^14 - 128*a^7*b^12))/(2*b^15)))/b^6))/b^6 + (tan(c/2 + (d*x)/2)*(128*a^17 - 450*a^3*b^14 + 2550*a^5*b^12 - 6230*a^7*b^10 + 8530*a^9*b^8 - 7088*a^11*b^6 + 3584*a^13*b^4 - 1024*a^15*b^2))/b^15))*(-(a + b)^5*(a - b)^5)^(1/2)*2i)/(b^6*d) + (a*atan(((a*(((225*a^4*b^13)/2 - 300*a^6*b^11 + 320*a^8*b^9 - 160*a^10*b^7 + 32*a^12*b^5)/b^14 - (tan(c/2 + (d*x)/2)*(64*a*b^17 - 834*a^3*b^15 + 2385*a^5*b^13 - 3160*a^7*b^11 + 2240*a^9*b^9 - 832*a^11*b^7 + 128*a^13*b^5))/(2*b^15) + (a*(8*a^4 + 15*b^4 - 20*a^2*b^2)*((28*a^2*b^16 - 44*a^4*b^14 + 16*a^6*b^12)/b^14 - (tan(c/2 + (d*x)/2)*(128*a*b^18 - 384*a^3*b^16 + 384*a^5*b^14 - 128*a^7*b^12))/(2*b^15) + (a*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 - 128*a^3*b^17))/(2*b^15))*(8*a^4 + 15*b^4 - 20*a^2*b^2)*1i)/(8*b^6))*1i)/(8*b^6))*(8*a^4 + 15*b^4 - 20*a^2*b^2))/(8*b^6) + (a*(((225*a^4*b^13)/2 - 300*a^6*b^11 + 320*a^8*b^9 - 160*a^10*b^7 + 32*a^12*b^5)/b^14 - (tan(c/2 + (d*x)/2)*(64*a*b^17 - 834*a^3*b^15 + 2385*a^5*b^13 - 3160*a^7*b^11 + 2240*a^9*b^9 - 832*a^11*b^7 + 128*a^13*b^5))/(2*b^15) + (a*(8*a^4 + 15*b^4 - 20*a^2*b^2)*((tan(c/2 + (d*x)/2)*(128*a*b^18 - 384*a^3*b^16 + 384*a^5*b^14 - 128*a^7*b^12))/(2*b^15) - (28*a^2*b^16 - 44*a^4*b^14 + 16*a^6*b^12)/b^14 + (a*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 - 128*a^3*b^17))/(2*b^15))*(8*a^4 + 15*b^4 - 20*a^2*b^2)*1i)/(8*b^6))*1i)/(8*b^6))*(8*a^4 + 15*b^4 - 20*a^2*b^2))/(8*b^6))/((32*a^16 - 120*a^2*b^14 + 655*a^4*b^12 - 1549*a^6*b^10 + 2069*a^8*b^8 - 1695*a^10*b^6 + 856*a^12*b^4 - 248*a^14*b^2)/b^14 + (tan(c/2 + (d*x)/2)*(128*a^17 - 450*a^3*b^14 + 2550*a^5*b^12 - 6230*a^7*b^10 + 8530*a^9*b^8 - 7088*a^11*b^6 + 3584*a^13*b^4 - 1024*a^15*b^2))/b^15 + (a*(((225*a^4*b^13)/2 - 300*a^6*b^11 + 320*a^8*b^9 - 160*a^10*b^7 + 32*a^12*b^5)/b^14 - (tan(c/2 + (d*x)/2)*(64*a*b^17 - 834*a^3*b^15 + 2385*a^5*b^13 - 3160*a^7*b^11 + 2240*a^9*b^9 - 832*a^11*b^7 + 128*a^13*b^5))/(2*b^15) + (a*(8*a^4 + 15*b^4 - 20*a^2*b^2)*((28*a^2*b^16 - 44*a^4*b^14 + 16*a^6*b^12)/b^14 - (tan(c/2 + (d*x)/2)*(128*a*b^18 - 384*a^3*b^16 + 384*a^5*b^14 - 128*a^7*b^12))/(2*b^15) + (a*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 - 128*a^3*b^17))/(2*b^15))*(8*a^4 + 15*b^4 - 20*a^2*b^2)*1i)/(8*b^6))*1i)/(8*b^6))*(8*a^4 + 15*b^4 - 20*a^2*b^2)*1i)/(8*b^6) - (a*(((225*a^4*b^13)/2 - 300*a^6*b^11 + 320*a^8*b^9 - 160*a^10*b^7 + 32*a^12*b^5)/b^14 - (tan(c/2 + (d*x)/2)*(64*a*b^17 - 834*a^3*b^15 + 2385*a^5*b^13 - 3160*a^7*b^11 + 2240*a^9*b^9 - 832*a^11*b^7 + 128*a^13*b^5))/(2*b^15) + (a*(8*a^4 + 15*b^4 - 20*a^2*b^2)*((tan(c/2 + (d*x)/2)*(128*a*b^18 - 384*a^3*b^16 + 384*a^5*b^14 - 128*a^7*b^12))/(2*b^15) - (28*a^2*b^16 - 44*a^4*b^14 + 16*a^6*b^12)/b^14 + (a*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 - 128*a^3*b^17))/(2*b^15))*(8*a^4 + 15*b^4 - 20*a^2*b^2)*1i)/(8*b^6))*1i)/(8*b^6))*(8*a^4 + 15*b^4 - 20*a^2*b^2)*1i)/(8*b^6)))*(8*a^4 + 15*b^4 - 20*a^2*b^2))/(4*b^6*d)","B"
432,1,364,127,6.116027,"\text{Not used}","int(cos(c + d*x)^4/(a + b*sin(c + d*x)),x)","\frac{\frac{5\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{12}}{b\,d}+\frac{3\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{a\,\sin\left(2\,c+2\,d\,x\right)}{4}}{b^2\,d}-\frac{a^2\,\cos\left(c+d\,x\right)}{b^3\,d}-\frac{2\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b^4\,d}+\frac{2\,\mathrm{atanh}\left(\frac{2\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}-a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}+a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^2-4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^3+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^4+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^5}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{b^4\,d}","Not used",1,"((5*cos(c + d*x))/4 + cos(3*c + 3*d*x)/12)/(b*d) + (3*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (a*sin(2*c + 2*d*x))/4)/(b^2*d) - (a^2*cos(c + d*x))/(b^3*d) - (2*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^4*d) + (2*atanh((2*b^2*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - a^2*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + a*b*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(a^5*cos(c/2 + (d*x)/2) + 2*b^5*sin(c/2 + (d*x)/2) + a*b^4*cos(c/2 + (d*x)/2) + 2*a^4*b*sin(c/2 + (d*x)/2) - 2*a^3*b^2*cos(c/2 + (d*x)/2) - 4*a^2*b^3*sin(c/2 + (d*x)/2)))*(-(a + b)^3*(a - b)^3)^(1/2))/(b^4*d)","B"
433,1,318,70,5.372601,"\text{Not used}","int(cos(c + d*x)^2/(a + b*sin(c + d*x)),x)","\frac{2}{b\,d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{2\,a\,\mathrm{atan}\left(\frac{64\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^2-\frac{64\,a^4}{b^2}}+\frac{64\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^4-64\,a^2\,b^2}\right)}{b^2\,d}+\frac{2\,\mathrm{atanh}\left(\frac{64\,a^2\,\sqrt{b^2-a^2}}{64\,a^2\,b-\frac{64\,a^4}{b}-128\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+128\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{128\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{64\,a^2-\frac{64\,a^4}{b^2}-\frac{128\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+128\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{64\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{64\,a^4+128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b-64\,a^2\,b^2-128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3}\right)\,\sqrt{b^2-a^2}}{b^2\,d}","Not used",1,"2/(b*d*(tan(c/2 + (d*x)/2)^2 + 1)) + (2*a*atan((64*a^2*tan(c/2 + (d*x)/2))/(64*a^2 - (64*a^4)/b^2) + (64*a^4*tan(c/2 + (d*x)/2))/(64*a^4 - 64*a^2*b^2)))/(b^2*d) + (2*atanh((64*a^2*(b^2 - a^2)^(1/2))/(64*a^2*b - (64*a^4)/b - 128*a^3*tan(c/2 + (d*x)/2) + 128*a*b^2*tan(c/2 + (d*x)/2)) + (128*a*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(64*a^2 - (64*a^4)/b^2 - (128*a^3*tan(c/2 + (d*x)/2))/b + 128*a*b*tan(c/2 + (d*x)/2)) + (64*a^3*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(64*a^4 - 64*a^2*b^2 - 128*a*b^3*tan(c/2 + (d*x)/2) + 128*a^3*b*tan(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2))/(b^2*d)","B"
434,1,149,84,5.255331,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b*sin(c + d*x))),x)","\frac{\frac{2\,b}{a^2-b^2}-\frac{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2-b^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{2\,b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\left(2\,a^2\,b-2\,b^3\right)}{{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}+\frac{2\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)}{{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}}{2\,b^2}\right)}{d\,{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}","Not used",1,"((2*b)/(a^2 - b^2) - (2*a*tan(c/2 + (d*x)/2))/(a^2 - b^2))/(d*(tan(c/2 + (d*x)/2)^2 - 1)) - (2*b^2*atan(((b^2*(2*a^2*b - 2*b^3))/((a + b)^(3/2)*(a - b)^(3/2)) + (2*a*b^2*tan(c/2 + (d*x)/2)*(a^2 - b^2))/((a + b)^(3/2)*(a - b)^(3/2)))/(2*b^2)))/(d*(a + b)^(3/2)*(a - b)^(3/2))","B"
435,1,387,137,7.945627,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b*sin(c + d*x))),x)","\frac{\frac{2\,\left(a^2\,b-4\,b^3\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a\,b^2-a^3\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^4-2\,a^2\,b^2+b^4}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a\,b^2-a^3\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a\,b^2-a^3\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,b^2\right)}{a^4-2\,a^2\,b^2+b^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}+\frac{2\,b^4\,\mathrm{atan}\left(\frac{\frac{b^4\,\left(2\,a^4\,b-4\,a^2\,b^3+2\,b^5\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}+\frac{2\,a\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}}{2\,b^4}\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((2*(a^2*b - 4*b^3))/(3*(a^4 + b^4 - 2*a^2*b^2)) + (2*tan(c/2 + (d*x)/2)*(2*a*b^2 - a^3))/(a^4 + b^4 - 2*a^2*b^2) + (4*b^3*tan(c/2 + (d*x)/2)^2)/(a^4 + b^4 - 2*a^2*b^2) - (4*tan(c/2 + (d*x)/2)^3*(4*a*b^2 - a^3))/(3*(a^4 + b^4 - 2*a^2*b^2)) + (2*tan(c/2 + (d*x)/2)^5*(2*a*b^2 - a^3))/(a^4 + b^4 - 2*a^2*b^2) + (2*b*tan(c/2 + (d*x)/2)^4*(a^2 - 2*b^2))/(a^4 + b^4 - 2*a^2*b^2))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1)) + (2*b^4*atan(((b^4*(2*a^4*b + 2*b^5 - 4*a^2*b^3))/((a + b)^(5/2)*(a - b)^(5/2)) + (2*a*b^4*tan(c/2 + (d*x)/2)*(a^4 + b^4 - 2*a^2*b^2))/((a + b)^(5/2)*(a - b)^(5/2)))/(2*b^4)))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
436,1,774,197,8.060965,"\text{Not used}","int(1/(cos(c + d*x)^6*(a + b*sin(c + d*x))),x)","\frac{\frac{2\,\left(3\,a^4\,b-11\,a^2\,b^3+23\,b^5\right)}{15\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^5-3\,a^3\,b^2+3\,a\,b^4\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(7\,b^5-a^2\,b^3\right)}{3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(3\,b^5-a^2\,b^3\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^5-4\,a^3\,b^2+6\,a\,b^4\right)}{3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(a^5-3\,a^3\,b^2+3\,a\,b^4\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(a^5-4\,a^3\,b^2+6\,a\,b^4\right)}{3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(29\,a^5-83\,a^3\,b^2+99\,a\,b^4\right)}{15\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^4\,b-3\,a^2\,b^3+3\,b^5\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a^4\,b-8\,a^2\,b^3+14\,b^5\right)}{3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{2\,b^6\,\mathrm{atan}\left(\frac{\frac{b^6\,\left(2\,a^6\,b-6\,a^4\,b^3+6\,a^2\,b^5-2\,b^7\right)}{{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}+\frac{2\,a\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}{{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}}{2\,b^6}\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"((2*(3*a^4*b + 23*b^5 - 11*a^2*b^3))/(15*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (2*tan(c/2 + (d*x)/2)*(3*a*b^4 + a^5 - 3*a^3*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (4*tan(c/2 + (d*x)/2)^2*(7*b^5 - a^2*b^3))/(3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (4*tan(c/2 + (d*x)/2)^6*(3*b^5 - a^2*b^3))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) + (8*tan(c/2 + (d*x)/2)^3*(6*a*b^4 + a^5 - 4*a^3*b^2))/(3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (2*tan(c/2 + (d*x)/2)^9*(3*a*b^4 + a^5 - 3*a^3*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) + (8*tan(c/2 + (d*x)/2)^7*(6*a*b^4 + a^5 - 4*a^3*b^2))/(3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (4*tan(c/2 + (d*x)/2)^5*(99*a*b^4 + 29*a^5 - 83*a^3*b^2))/(15*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (2*tan(c/2 + (d*x)/2)^8*(a^4*b + 3*b^5 - 3*a^2*b^3))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) + (4*tan(c/2 + (d*x)/2)^4*(3*a^4*b + 14*b^5 - 8*a^2*b^3))/(3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1)) - (2*b^6*atan(((b^6*(2*a^6*b - 2*b^7 + 6*a^2*b^5 - 6*a^4*b^3))/((a + b)^(7/2)*(a - b)^(7/2)) + (2*a*b^6*tan(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))/((a + b)^(7/2)*(a - b)^(7/2)))/(2*b^6)))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
437,1,259,184,0.121106,"\text{Not used}","int(cos(c + d*x)^7/(a + b*sin(c + d*x))^2,x)","\frac{{\sin\left(c+d\,x\right)}^3\,\left(\frac{1}{b^2}-\frac{a^2}{b^4}\right)}{d}-\frac{{\sin\left(c+d\,x\right)}^5}{5\,b^2\,d}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(\frac{a^3}{b^5}+\frac{a\,\left(\frac{3}{b^2}-\frac{3\,a^2}{b^4}\right)}{b}\right)}{d}-\frac{\sin\left(c+d\,x\right)\,\left(\frac{3}{b^2}+\frac{a^2\,\left(\frac{3}{b^2}-\frac{3\,a^2}{b^4}\right)}{b^2}-\frac{2\,a\,\left(\frac{2\,a^3}{b^5}+\frac{2\,a\,\left(\frac{3}{b^2}-\frac{3\,a^2}{b^4}\right)}{b}\right)}{b}\right)}{d}+\frac{a\,{\sin\left(c+d\,x\right)}^4}{2\,b^3\,d}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(6\,a^5-12\,a^3\,b^2+6\,a\,b^4\right)}{b^7\,d}+\frac{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}{b\,d\,\left(\sin\left(c+d\,x\right)\,b^7+a\,b^6\right)}","Not used",1,"(sin(c + d*x)^3*(1/b^2 - a^2/b^4))/d - sin(c + d*x)^5/(5*b^2*d) - (sin(c + d*x)^2*(a^3/b^5 + (a*(3/b^2 - (3*a^2)/b^4))/b))/d - (sin(c + d*x)*(3/b^2 + (a^2*(3/b^2 - (3*a^2)/b^4))/b^2 - (2*a*((2*a^3)/b^5 + (2*a*(3/b^2 - (3*a^2)/b^4))/b))/b))/d + (a*sin(c + d*x)^4)/(2*b^3*d) + (log(a + b*sin(c + d*x))*(6*a*b^4 + 6*a^5 - 12*a^3*b^2))/(b^7*d) + (a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)/(b*d*(a*b^6 + b^7*sin(c + d*x)))","B"
438,1,118,120,0.082952,"\text{Not used}","int(cos(c + d*x)^5/(a + b*sin(c + d*x))^2,x)","-\frac{\sin\left(c+d\,x\right)\,\left(\frac{2}{b^2}-\frac{3\,a^2}{b^4}\right)-\frac{{\sin\left(c+d\,x\right)}^3}{3\,b^2}+\frac{a\,{\sin\left(c+d\,x\right)}^2}{b^3}-\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(4\,a\,b^2-4\,a^3\right)}{b^5}+\frac{a^4-2\,a^2\,b^2+b^4}{b\,\left(\sin\left(c+d\,x\right)\,b^5+a\,b^4\right)}}{d}","Not used",1,"-(sin(c + d*x)*(2/b^2 - (3*a^2)/b^4) - sin(c + d*x)^3/(3*b^2) + (a*sin(c + d*x)^2)/b^3 - (log(a + b*sin(c + d*x))*(4*a*b^2 - 4*a^3))/b^5 + (a^4 + b^4 - 2*a^2*b^2)/(b*(a*b^4 + b^5*sin(c + d*x))))/d","B"
439,1,69,63,0.084866,"\text{Not used}","int(cos(c + d*x)^3/(a + b*sin(c + d*x))^2,x)","\frac{2\,a\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{b^3\,d}-\frac{\sin\left(c+d\,x\right)}{b^2\,d}+\frac{a^2-b^2}{b\,d\,\left(\sin\left(c+d\,x\right)\,b^3+a\,b^2\right)}","Not used",1,"(2*a*log(a + b*sin(c + d*x)))/(b^3*d) - sin(c + d*x)/(b^2*d) + (a^2 - b^2)/(b*d*(a*b^2 + b^3*sin(c + d*x)))","B"
440,1,20,20,5.065041,"\text{Not used}","int(cos(c + d*x)/(a + b*sin(c + d*x))^2,x)","-\frac{1}{b\,d\,\left(a+b\,\sin\left(c+d\,x\right)\right)}","Not used",1,"-1/(b*d*(a + b*sin(c + d*x)))","B"
441,1,98,104,0.209503,"\text{Not used}","int(1/(cos(c + d*x)*(a + b*sin(c + d*x))^2),x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)}{2\,d\,{\left(a-b\right)}^2}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)}{2\,d\,{\left(a+b\right)}^2}+\frac{b}{d\,\left(a^2-b^2\right)\,\left(a+b\,\sin\left(c+d\,x\right)\right)}-\frac{2\,a\,b\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{d\,{\left(a^2-b^2\right)}^2}","Not used",1,"log(sin(c + d*x) + 1)/(2*d*(a - b)^2) - log(sin(c + d*x) - 1)/(2*d*(a + b)^2) + b/(d*(a^2 - b^2)*(a + b*sin(c + d*x))) - (2*a*b*log(a + b*sin(c + d*x)))/(d*(a^2 - b^2)^2)","B"
442,1,227,177,5.474464,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b*sin(c + d*x))^2),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^2\,\left(a^2\,b+3\,b^3\right)}{2\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{a^2\,b+b^3}{{\left(a^2-b^2\right)}^2}+\frac{a\,\sin\left(c+d\,x\right)}{2\,\left(a^2-b^2\right)}}{d\,\left(-b\,{\sin\left(c+d\,x\right)}^3-a\,{\sin\left(c+d\,x\right)}^2+b\,\sin\left(c+d\,x\right)+a\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{b}{2\,{\left(a+b\right)}^3}+\frac{1}{4\,{\left(a+b\right)}^2}\right)}{d}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(a-3\,b\right)}{4\,d\,{\left(a-b\right)}^3}+\frac{4\,a\,b^3\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{d\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}","Not used",1,"((sin(c + d*x)^2*(a^2*b + 3*b^3))/(2*(a^4 + b^4 - 2*a^2*b^2)) - (a^2*b + b^3)/(a^2 - b^2)^2 + (a*sin(c + d*x))/(2*(a^2 - b^2)))/(d*(a + b*sin(c + d*x) - a*sin(c + d*x)^2 - b*sin(c + d*x)^3)) - (log(sin(c + d*x) - 1)*(b/(2*(a + b)^3) + 1/(4*(a + b)^2)))/d + (log(sin(c + d*x) + 1)*(a - 3*b))/(4*d*(a - b)^3) + (4*a*b^3*log(a + b*sin(c + d*x)))/(d*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))","B"
443,1,449,269,5.943675,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + b*sin(c + d*x))^2),x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(\frac{3\,b^2}{8\,{\left(a-b\right)}^4}-\frac{3\,b}{8\,{\left(a-b\right)}^3}+\frac{3}{16\,{\left(a-b\right)}^2}\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{3\,b}{8\,{\left(a+b\right)}^3}+\frac{3}{16\,{\left(a+b\right)}^2}+\frac{3\,b^2}{8\,{\left(a+b\right)}^4}\right)}{d}+\frac{\frac{-a^4\,b+5\,a^2\,b^3+2\,b^5}{2\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{3\,{\sin\left(c+d\,x\right)}^3\,\left(3\,a\,b^2-a^3\right)}{8\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{3\,{\sin\left(c+d\,x\right)}^4\,\left(-a^4\,b+4\,a^2\,b^3+5\,b^5\right)}{8\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{\sin\left(c+d\,x\right)\,\left(11\,a\,b^2-5\,a^3\right)}{8\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(-5\,a^4\,b+28\,a^2\,b^3+25\,b^5\right)}{8\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left(b\,{\sin\left(c+d\,x\right)}^5+a\,{\sin\left(c+d\,x\right)}^4-2\,b\,{\sin\left(c+d\,x\right)}^3-2\,a\,{\sin\left(c+d\,x\right)}^2+b\,\sin\left(c+d\,x\right)+a\right)}-\frac{6\,a\,b^5\,\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{d\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}","Not used",1,"(log(sin(c + d*x) + 1)*((3*b^2)/(8*(a - b)^4) - (3*b)/(8*(a - b)^3) + 3/(16*(a - b)^2)))/d - (log(sin(c + d*x) - 1)*((3*b)/(8*(a + b)^3) + 3/(16*(a + b)^2) + (3*b^2)/(8*(a + b)^4)))/d + ((2*b^5 - a^4*b + 5*a^2*b^3)/(2*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (3*sin(c + d*x)^3*(3*a*b^2 - a^3))/(8*(a^4 + b^4 - 2*a^2*b^2)) + (3*sin(c + d*x)^4*(5*b^5 - a^4*b + 4*a^2*b^3))/(8*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (sin(c + d*x)*(11*a*b^2 - 5*a^3))/(8*(a^4 + b^4 - 2*a^2*b^2)) - (sin(c + d*x)^2*(25*b^5 - 5*a^4*b + 28*a^2*b^3))/(8*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)))/(d*(a + b*sin(c + d*x) - 2*a*sin(c + d*x)^2 + a*sin(c + d*x)^4 - 2*b*sin(c + d*x)^3 + b*sin(c + d*x)^5)) - (6*a*b^5*log(a + b*sin(c + d*x)))/(d*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2))","B"
444,1,2530,187,7.582875,"\text{Not used}","int(cos(c + d*x)^6/(a + b*sin(c + d*x))^2,x)","-\frac{\frac{2\,\left(15\,a^4-20\,a^2\,b^2+3\,b^4\right)}{3\,b^5}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(-4\,a^4+4\,a^2\,b^2+b^4\right)}{2\,b^5}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(16\,a^4-20\,a^2\,b^2+3\,b^4\right)}{2\,b^5}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(48\,a^4-68\,a^2\,b^2+15\,b^4\right)}{6\,b^5}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(72\,a^4-100\,a^2\,b^2+15\,b^4\right)}{6\,b^5}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(180\,a^4-245\,a^2\,b^2+24\,b^4\right)}{12\,a\,b^4}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(15\,a^4-20\,a^2\,b^2+3\,b^4\right)}{a\,b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(20\,a^4-25\,a^2\,b^2+8\,b^4\right)}{4\,a\,b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(60\,a^4-85\,a^2\,b^2+16\,b^4\right)}{2\,a\,b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(300\,a^4-385\,a^2\,b^2+48\,b^4\right)}{6\,a\,b^4}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+12\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{10\,a\,\mathrm{atanh}\left(\frac{1125\,a^3\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{3250\,a^5\,b-1125\,a^3\,b^3-\frac{3125\,a^7}{b}+\frac{1000\,a^9}{b^3}-6250\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2250\,a^2\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6500\,a^4\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{2000\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}}+\frac{1000\,a^5\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{3125\,a^7\,b+1125\,a^3\,b^5-3250\,a^5\,b^3-\frac{1000\,a^9}{b}-2000\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2250\,a^2\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-6500\,a^4\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6250\,a^6\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{2250\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{3250\,a^5-1125\,a^3\,b^2-\frac{3125\,a^7}{b^2}+\frac{1000\,a^9}{b^4}+6500\,a^4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2250\,a^2\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{6250\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+\frac{2000\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}}+\frac{3125\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{3125\,a^7+1125\,a^3\,b^4-3250\,a^5\,b^2-\frac{1000\,a^9}{b^2}+6250\,a^6\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2250\,a^2\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-6500\,a^4\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{2000\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}}+\frac{1000\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{1000\,a^9+2000\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b-3125\,a^7\,b^2-6250\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^3+3250\,a^5\,b^4+6500\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^5-1125\,a^3\,b^6-2250\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^7}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{b^6\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,3{}\mathrm{i}\right)\,\left(\frac{800\,a^{10}\,b^5-2400\,a^8\,b^7+2400\,a^6\,b^9-900\,a^4\,b^{11}+\frac{225\,a^2\,b^{13}}{2}}{b^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3200\,a^{11}\,b^5+14400\,a^9\,b^7-24000\,a^7\,b^9+17800\,a^5\,b^{11}-5425\,a^3\,b^{13}+450\,a\,b^{15}\right)}{2\,b^{15}}-\frac{5\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,3{}\mathrm{i}\right)\,\left(\frac{80\,a^5\,b^{12}-140\,a^3\,b^{14}+60\,a\,b^{16}}{b^{14}}-\frac{5\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{19}-128\,a^3\,b^{17}\right)}{2\,b^{15}}\right)\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,3{}\mathrm{i}\right)}{8\,b^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(640\,a^6\,b^{12}-1280\,a^4\,b^{14}+640\,a^2\,b^{16}\right)}{2\,b^{15}}\right)}{8\,b^6}\right)\,5{}\mathrm{i}}{8\,b^6}+\frac{\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,3{}\mathrm{i}\right)\,\left(\frac{800\,a^{10}\,b^5-2400\,a^8\,b^7+2400\,a^6\,b^9-900\,a^4\,b^{11}+\frac{225\,a^2\,b^{13}}{2}}{b^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3200\,a^{11}\,b^5+14400\,a^9\,b^7-24000\,a^7\,b^9+17800\,a^5\,b^{11}-5425\,a^3\,b^{13}+450\,a\,b^{15}\right)}{2\,b^{15}}+\frac{5\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,3{}\mathrm{i}\right)\,\left(\frac{80\,a^5\,b^{12}-140\,a^3\,b^{14}+60\,a\,b^{16}}{b^{14}}+\frac{5\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{19}-128\,a^3\,b^{17}\right)}{2\,b^{15}}\right)\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,3{}\mathrm{i}\right)}{8\,b^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(640\,a^6\,b^{12}-1280\,a^4\,b^{14}+640\,a^2\,b^{16}\right)}{2\,b^{15}}\right)}{8\,b^6}\right)\,5{}\mathrm{i}}{8\,b^6}}{\frac{4000\,a^{13}-19000\,a^{11}\,b^2+35000\,a^9\,b^4-30875\,a^7\,b^6+12750\,a^5\,b^8-1875\,a^3\,b^{10}}{b^{14}}-\frac{5\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,3{}\mathrm{i}\right)\,\left(\frac{800\,a^{10}\,b^5-2400\,a^8\,b^7+2400\,a^6\,b^9-900\,a^4\,b^{11}+\frac{225\,a^2\,b^{13}}{2}}{b^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3200\,a^{11}\,b^5+14400\,a^9\,b^7-24000\,a^7\,b^9+17800\,a^5\,b^{11}-5425\,a^3\,b^{13}+450\,a\,b^{15}\right)}{2\,b^{15}}-\frac{5\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,3{}\mathrm{i}\right)\,\left(\frac{80\,a^5\,b^{12}-140\,a^3\,b^{14}+60\,a\,b^{16}}{b^{14}}-\frac{5\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{19}-128\,a^3\,b^{17}\right)}{2\,b^{15}}\right)\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,3{}\mathrm{i}\right)}{8\,b^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(640\,a^6\,b^{12}-1280\,a^4\,b^{14}+640\,a^2\,b^{16}\right)}{2\,b^{15}}\right)}{8\,b^6}\right)}{8\,b^6}+\frac{5\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,3{}\mathrm{i}\right)\,\left(\frac{800\,a^{10}\,b^5-2400\,a^8\,b^7+2400\,a^6\,b^9-900\,a^4\,b^{11}+\frac{225\,a^2\,b^{13}}{2}}{b^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3200\,a^{11}\,b^5+14400\,a^9\,b^7-24000\,a^7\,b^9+17800\,a^5\,b^{11}-5425\,a^3\,b^{13}+450\,a\,b^{15}\right)}{2\,b^{15}}+\frac{5\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,3{}\mathrm{i}\right)\,\left(\frac{80\,a^5\,b^{12}-140\,a^3\,b^{14}+60\,a\,b^{16}}{b^{14}}+\frac{5\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(192\,a\,b^{19}-128\,a^3\,b^{17}\right)}{2\,b^{15}}\right)\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,3{}\mathrm{i}\right)}{8\,b^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(640\,a^6\,b^{12}-1280\,a^4\,b^{14}+640\,a^2\,b^{16}\right)}{2\,b^{15}}\right)}{8\,b^6}\right)}{8\,b^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16000\,a^{14}-80000\,a^{12}\,b^2+160000\,a^{10}\,b^4-162000\,a^8\,b^6+86250\,a^6\,b^8-22500\,a^4\,b^{10}+2250\,a^2\,b^{12}\right)}{b^{15}}}\right)\,\left(a^4\,8{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,3{}\mathrm{i}\right)\,5{}\mathrm{i}}{4\,b^6\,d}","Not used",1,"- ((2*(15*a^4 + 3*b^4 - 20*a^2*b^2))/(3*b^5) - (5*tan(c/2 + (d*x)/2)^8*(b^4 - 4*a^4 + 4*a^2*b^2))/(2*b^5) + (5*tan(c/2 + (d*x)/2)^6*(16*a^4 + 3*b^4 - 20*a^2*b^2))/(2*b^5) + (5*tan(c/2 + (d*x)/2)^2*(48*a^4 + 15*b^4 - 68*a^2*b^2))/(6*b^5) + (5*tan(c/2 + (d*x)/2)^4*(72*a^4 + 15*b^4 - 100*a^2*b^2))/(6*b^5) + (tan(c/2 + (d*x)/2)*(180*a^4 + 24*b^4 - 245*a^2*b^2))/(12*a*b^4) + (4*tan(c/2 + (d*x)/2)^5*(15*a^4 + 3*b^4 - 20*a^2*b^2))/(a*b^4) + (tan(c/2 + (d*x)/2)^9*(20*a^4 + 8*b^4 - 25*a^2*b^2))/(4*a*b^4) + (tan(c/2 + (d*x)/2)^7*(60*a^4 + 16*b^4 - 85*a^2*b^2))/(2*a*b^4) + (tan(c/2 + (d*x)/2)^3*(300*a^4 + 48*b^4 - 385*a^2*b^2))/(6*a*b^4))/(d*(a + 2*b*tan(c/2 + (d*x)/2) + 5*a*tan(c/2 + (d*x)/2)^2 + 10*a*tan(c/2 + (d*x)/2)^4 + 10*a*tan(c/2 + (d*x)/2)^6 + 5*a*tan(c/2 + (d*x)/2)^8 + a*tan(c/2 + (d*x)/2)^10 + 8*b*tan(c/2 + (d*x)/2)^3 + 12*b*tan(c/2 + (d*x)/2)^5 + 8*b*tan(c/2 + (d*x)/2)^7 + 2*b*tan(c/2 + (d*x)/2)^9)) - (atan((((a^4*8i + b^4*3i - a^2*b^2*12i)*(((225*a^2*b^13)/2 - 900*a^4*b^11 + 2400*a^6*b^9 - 2400*a^8*b^7 + 800*a^10*b^5)/b^14 + (tan(c/2 + (d*x)/2)*(450*a*b^15 - 5425*a^3*b^13 + 17800*a^5*b^11 - 24000*a^7*b^9 + 14400*a^9*b^7 - 3200*a^11*b^5))/(2*b^15) - (5*(a^4*8i + b^4*3i - a^2*b^2*12i)*((60*a*b^16 - 140*a^3*b^14 + 80*a^5*b^12)/b^14 - (5*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 - 128*a^3*b^17))/(2*b^15))*(a^4*8i + b^4*3i - a^2*b^2*12i))/(8*b^6) + (tan(c/2 + (d*x)/2)*(640*a^2*b^16 - 1280*a^4*b^14 + 640*a^6*b^12))/(2*b^15)))/(8*b^6))*5i)/(8*b^6) + ((a^4*8i + b^4*3i - a^2*b^2*12i)*(((225*a^2*b^13)/2 - 900*a^4*b^11 + 2400*a^6*b^9 - 2400*a^8*b^7 + 800*a^10*b^5)/b^14 + (tan(c/2 + (d*x)/2)*(450*a*b^15 - 5425*a^3*b^13 + 17800*a^5*b^11 - 24000*a^7*b^9 + 14400*a^9*b^7 - 3200*a^11*b^5))/(2*b^15) + (5*(a^4*8i + b^4*3i - a^2*b^2*12i)*((60*a*b^16 - 140*a^3*b^14 + 80*a^5*b^12)/b^14 + (5*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 - 128*a^3*b^17))/(2*b^15))*(a^4*8i + b^4*3i - a^2*b^2*12i))/(8*b^6) + (tan(c/2 + (d*x)/2)*(640*a^2*b^16 - 1280*a^4*b^14 + 640*a^6*b^12))/(2*b^15)))/(8*b^6))*5i)/(8*b^6))/((4000*a^13 - 1875*a^3*b^10 + 12750*a^5*b^8 - 30875*a^7*b^6 + 35000*a^9*b^4 - 19000*a^11*b^2)/b^14 - (5*(a^4*8i + b^4*3i - a^2*b^2*12i)*(((225*a^2*b^13)/2 - 900*a^4*b^11 + 2400*a^6*b^9 - 2400*a^8*b^7 + 800*a^10*b^5)/b^14 + (tan(c/2 + (d*x)/2)*(450*a*b^15 - 5425*a^3*b^13 + 17800*a^5*b^11 - 24000*a^7*b^9 + 14400*a^9*b^7 - 3200*a^11*b^5))/(2*b^15) - (5*(a^4*8i + b^4*3i - a^2*b^2*12i)*((60*a*b^16 - 140*a^3*b^14 + 80*a^5*b^12)/b^14 - (5*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 - 128*a^3*b^17))/(2*b^15))*(a^4*8i + b^4*3i - a^2*b^2*12i))/(8*b^6) + (tan(c/2 + (d*x)/2)*(640*a^2*b^16 - 1280*a^4*b^14 + 640*a^6*b^12))/(2*b^15)))/(8*b^6)))/(8*b^6) + (5*(a^4*8i + b^4*3i - a^2*b^2*12i)*(((225*a^2*b^13)/2 - 900*a^4*b^11 + 2400*a^6*b^9 - 2400*a^8*b^7 + 800*a^10*b^5)/b^14 + (tan(c/2 + (d*x)/2)*(450*a*b^15 - 5425*a^3*b^13 + 17800*a^5*b^11 - 24000*a^7*b^9 + 14400*a^9*b^7 - 3200*a^11*b^5))/(2*b^15) + (5*(a^4*8i + b^4*3i - a^2*b^2*12i)*((60*a*b^16 - 140*a^3*b^14 + 80*a^5*b^12)/b^14 + (5*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 - 128*a^3*b^17))/(2*b^15))*(a^4*8i + b^4*3i - a^2*b^2*12i))/(8*b^6) + (tan(c/2 + (d*x)/2)*(640*a^2*b^16 - 1280*a^4*b^14 + 640*a^6*b^12))/(2*b^15)))/(8*b^6)))/(8*b^6) + (tan(c/2 + (d*x)/2)*(16000*a^14 + 2250*a^2*b^12 - 22500*a^4*b^10 + 86250*a^6*b^8 - 162000*a^8*b^6 + 160000*a^10*b^4 - 80000*a^12*b^2))/b^15))*(a^4*8i + b^4*3i - a^2*b^2*12i)*5i)/(4*b^6*d) - (10*a*atanh((1125*a^3*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(3250*a^5*b - 1125*a^3*b^3 - (3125*a^7)/b + (1000*a^9)/b^3 - 6250*a^6*tan(c/2 + (d*x)/2) - 2250*a^2*b^4*tan(c/2 + (d*x)/2) + 6500*a^4*b^2*tan(c/2 + (d*x)/2) + (2000*a^8*tan(c/2 + (d*x)/2))/b^2) + (1000*a^5*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(3125*a^7*b + 1125*a^3*b^5 - 3250*a^5*b^3 - (1000*a^9)/b - 2000*a^8*tan(c/2 + (d*x)/2) + 2250*a^2*b^6*tan(c/2 + (d*x)/2) - 6500*a^4*b^4*tan(c/2 + (d*x)/2) + 6250*a^6*b^2*tan(c/2 + (d*x)/2)) + (2250*a^2*tan(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(3250*a^5 - 1125*a^3*b^2 - (3125*a^7)/b^2 + (1000*a^9)/b^4 + 6500*a^4*b*tan(c/2 + (d*x)/2) - 2250*a^2*b^3*tan(c/2 + (d*x)/2) - (6250*a^6*tan(c/2 + (d*x)/2))/b + (2000*a^8*tan(c/2 + (d*x)/2))/b^3) + (3125*a^4*tan(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(3125*a^7 + 1125*a^3*b^4 - 3250*a^5*b^2 - (1000*a^9)/b^2 + 6250*a^6*b*tan(c/2 + (d*x)/2) + 2250*a^2*b^5*tan(c/2 + (d*x)/2) - 6500*a^4*b^3*tan(c/2 + (d*x)/2) - (2000*a^8*tan(c/2 + (d*x)/2))/b) + (1000*a^6*tan(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(1000*a^9 - 1125*a^3*b^6 + 3250*a^5*b^4 - 3125*a^7*b^2 + 2000*a^8*b*tan(c/2 + (d*x)/2) - 2250*a^2*b^7*tan(c/2 + (d*x)/2) + 6500*a^4*b^5*tan(c/2 + (d*x)/2) - 6250*a^6*b^3*tan(c/2 + (d*x)/2)))*(-(a + b)^3*(a - b)^3)^(1/2))/(b^6*d)","B"
445,1,601,128,6.397411,"\text{Not used}","int(cos(c + d*x)^4/(a + b*sin(c + d*x))^2,x)","\frac{\frac{2\,\left(3\,a^2-b^2\right)}{b^3}+\frac{6\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{b^3}+\frac{6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-b^2\right)}{b^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^2-2\,b^2\right)}{a\,b^2}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^2-b^2\right)}{a\,b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,a^2-2\,b^2\right)}{a\,b^2}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}+\frac{6\,a\,\mathrm{atanh}\left(\frac{432\,a^3\,\sqrt{b^2-a^2}}{432\,a^3\,b-\frac{432\,a^5}{b}-864\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+864\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{864\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{432\,a^3-\frac{432\,a^5}{b^2}+864\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{864\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}}+\frac{432\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{432\,a^5+864\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b-432\,a^3\,b^2-864\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^3}\right)\,\sqrt{b^2-a^2}}{b^4\,d}-\frac{\mathrm{atan}\left(\frac{432\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{432\,a^5-648\,a^3\,b^2+216\,a\,b^4}-\frac{648\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{216\,a\,b^2-648\,a^3+\frac{432\,a^5}{b^2}}+\frac{216\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{216\,a-\frac{648\,a^3}{b^2}+\frac{432\,a^5}{b^4}}\right)\,\left(a^2\,2{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,3{}\mathrm{i}}{b^4\,d}","Not used",1,"((2*(3*a^2 - b^2))/b^3 + (6*a^2*tan(c/2 + (d*x)/2)^4)/b^3 + (6*tan(c/2 + (d*x)/2)^2*(2*a^2 - b^2))/b^3 + (tan(c/2 + (d*x)/2)*(9*a^2 - 2*b^2))/(a*b^2) + (4*tan(c/2 + (d*x)/2)^3*(3*a^2 - b^2))/(a*b^2) + (tan(c/2 + (d*x)/2)^5*(3*a^2 - 2*b^2))/(a*b^2))/(d*(a + 2*b*tan(c/2 + (d*x)/2) + 3*a*tan(c/2 + (d*x)/2)^2 + 3*a*tan(c/2 + (d*x)/2)^4 + a*tan(c/2 + (d*x)/2)^6 + 4*b*tan(c/2 + (d*x)/2)^3 + 2*b*tan(c/2 + (d*x)/2)^5)) - (atan((432*a^5*tan(c/2 + (d*x)/2))/(216*a*b^4 + 432*a^5 - 648*a^3*b^2) - (648*a^3*tan(c/2 + (d*x)/2))/(216*a*b^2 - 648*a^3 + (432*a^5)/b^2) + (216*a*tan(c/2 + (d*x)/2))/(216*a - (648*a^3)/b^2 + (432*a^5)/b^4))*(a^2*2i - b^2*1i)*3i)/(b^4*d) + (6*a*atanh((432*a^3*(b^2 - a^2)^(1/2))/(432*a^3*b - (432*a^5)/b - 864*a^4*tan(c/2 + (d*x)/2) + 864*a^2*b^2*tan(c/2 + (d*x)/2)) + (864*a^2*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(432*a^3 - (432*a^5)/b^2 + 864*a^2*b*tan(c/2 + (d*x)/2) - (864*a^4*tan(c/2 + (d*x)/2))/b) + (432*a^4*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(432*a^5 - 432*a^3*b^2 + 864*a^4*b*tan(c/2 + (d*x)/2) - 864*a^2*b^3*tan(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2))/(b^4*d)","B"
446,1,329,84,5.558980,"\text{Not used}","int(cos(c + d*x)^2/(a + b*sin(c + d*x))^2,x)","-\frac{b^2\,\sin\left(c+d\,x\right)+\frac{\left(2\,a^3\,\mathrm{atan}\left(\frac{\left(-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{\sqrt{b^2-a^2}\,\left(a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}\right)-a^2\,\sqrt{b^2-a^2}\,\left(c+d\,x\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{\sqrt{b^2-a^2}}-\frac{b\,\left(a\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+a\,\cos\left(c+d\,x\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-2\,a^2\,\mathrm{atan}\left(\frac{\left(-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{\sqrt{b^2-a^2}\,\left(a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}\right)\,\sin\left(c+d\,x\right)+a\,\sin\left(c+d\,x\right)\,\sqrt{b^2-a^2}\,\left(c+d\,x\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{\sqrt{b^2-a^2}}}{a\,b^2\,d\,\left(a+b\,\sin\left(c+d\,x\right)\right)}","Not used",1,"-(b^2*sin(c + d*x) + ((2*a^3*atan(((2*b^2*sin(c/2 + (d*x)/2) - a^2*sin(c/2 + (d*x)/2) + a*b*cos(c/2 + (d*x)/2))*1i)/((b^2 - a^2)^(1/2)*(a*cos(c/2 + (d*x)/2) + 2*b*sin(c/2 + (d*x)/2)))) - a^2*(b^2 - a^2)^(1/2)*(c + d*x)*1i)*1i)/(b^2 - a^2)^(1/2) - (b*(a*(b^2 - a^2)^(1/2)*1i + a*cos(c + d*x)*(b^2 - a^2)^(1/2)*1i - 2*a^2*atan(((2*b^2*sin(c/2 + (d*x)/2) - a^2*sin(c/2 + (d*x)/2) + a*b*cos(c/2 + (d*x)/2))*1i)/((b^2 - a^2)^(1/2)*(a*cos(c/2 + (d*x)/2) + 2*b*sin(c/2 + (d*x)/2))))*sin(c + d*x) + a*sin(c + d*x)*(b^2 - a^2)^(1/2)*(c + d*x)*1i)*1i)/(b^2 - a^2)^(1/2))/(a*b^2*d*(a + b*sin(c + d*x)))","B"
447,1,303,130,7.396029,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b*sin(c + d*x))^2),x)","-\frac{\frac{2\,\left(2\,a^2\,b+b^3\right)}{{\left(a^2-b^2\right)}^2}-\frac{6\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^4-2\,a^2\,b^2+b^4}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^4+3\,a^2\,b^2+b^4\right)}{a\,{\left(a^2-b^2\right)}^2}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^4+a^2\,b^2+b^4\right)}{a\,{\left(a^2-b^2\right)}^2}}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{6\,a\,b^2\,\mathrm{atan}\left(\frac{\frac{3\,a\,b^2\,\left(2\,a^4\,b-4\,a^2\,b^3+2\,b^5\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}+\frac{6\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}}{6\,a\,b^2}\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"- ((2*(2*a^2*b + b^3))/(a^2 - b^2)^2 - (6*b^3*tan(c/2 + (d*x)/2)^2)/(a^4 + b^4 - 2*a^2*b^2) + (2*tan(c/2 + (d*x)/2)*(b^4 - a^4 + 3*a^2*b^2))/(a*(a^2 - b^2)^2) - (2*tan(c/2 + (d*x)/2)^3*(a^4 + b^4 + a^2*b^2))/(a*(a^2 - b^2)^2))/(d*(a + 2*b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^4 - 2*b*tan(c/2 + (d*x)/2)^3)) - (6*a*b^2*atan(((3*a*b^2*(2*a^4*b + 2*b^5 - 4*a^2*b^3))/((a + b)^(5/2)*(a - b)^(5/2)) + (6*a^2*b^2*tan(c/2 + (d*x)/2)*(a^4 + b^4 - 2*a^2*b^2))/((a + b)^(5/2)*(a - b)^(5/2)))/(6*a*b^2)))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
448,1,727,193,8.510680,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b*sin(c + d*x))^2),x)","\frac{\frac{2\,\left(-2\,a^4\,b+14\,a^2\,b^3+3\,b^5\right)}{3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{10\,b^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-4\,a^4\,b+28\,a^2\,b^3+21\,b^5\right)}{3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^6-13\,a^4\,b^2+22\,a^2\,b^4+3\,b^6\right)}{3\,a\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-a^6+3\,a^4\,b^2+2\,a^2\,b^4+b^6\right)}{a\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(a^6-3\,a^4\,b^2+38\,a^2\,b^4+9\,b^6\right)}{3\,a\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^6+9\,a^4\,b^2-46\,a^2\,b^4-9\,b^6\right)}{3\,a\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{10\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-2\,a^4+6\,a^2\,b^2+5\,b^4\right)}{3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}+\frac{10\,a\,b^4\,\mathrm{atan}\left(\frac{\frac{5\,a\,b^4\,\left(2\,a^6\,b-6\,a^4\,b^3+6\,a^2\,b^5-2\,b^7\right)}{{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}+\frac{10\,a^2\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}{{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}}{10\,a\,b^4}\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"((2*(3*b^5 - 2*a^4*b + 14*a^2*b^3))/(3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (10*b^5*tan(c/2 + (d*x)/2)^6)/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (2*tan(c/2 + (d*x)/2)^2*(21*b^5 - 4*a^4*b + 28*a^2*b^3))/(3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (2*tan(c/2 + (d*x)/2)*(3*a^6 + 3*b^6 + 22*a^2*b^4 - 13*a^4*b^2))/(3*a*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (2*tan(c/2 + (d*x)/2)^7*(b^6 - a^6 + 2*a^2*b^4 + 3*a^4*b^2))/(a*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (2*tan(c/2 + (d*x)/2)^5*(a^6 + 9*b^6 + 38*a^2*b^4 - 3*a^4*b^2))/(3*a*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (2*tan(c/2 + (d*x)/2)^3*(a^6 - 9*b^6 - 46*a^2*b^4 + 9*a^4*b^2))/(3*a*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (10*b*tan(c/2 + (d*x)/2)^4*(5*b^4 - 2*a^4 + 6*a^2*b^2))/(3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)))/(d*(a + 2*b*tan(c/2 + (d*x)/2) - 2*a*tan(c/2 + (d*x)/2)^2 + 2*a*tan(c/2 + (d*x)/2)^6 - a*tan(c/2 + (d*x)/2)^8 - 6*b*tan(c/2 + (d*x)/2)^3 + 6*b*tan(c/2 + (d*x)/2)^5 - 2*b*tan(c/2 + (d*x)/2)^7)) + (10*a*b^4*atan(((5*a*b^4*(2*a^6*b - 2*b^7 + 6*a^2*b^5 - 6*a^4*b^3))/((a + b)^(7/2)*(a - b)^(7/2)) + (10*a^2*b^4*tan(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))/((a + b)^(7/2)*(a - b)^(7/2)))/(10*a*b^4)))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
449,1,234,190,0.122126,"\text{Not used}","int(cos(c + d*x)^7/(a + b*sin(c + d*x))^3,x)","\frac{{\sin\left(c+d\,x\right)}^2\,\left(\frac{3}{2\,b^3}-\frac{3\,a^2}{b^5}\right)}{d}-\frac{{\sin\left(c+d\,x\right)}^4}{4\,b^3\,d}-\frac{\sin\left(c+d\,x\right)\,\left(\frac{8\,a^3}{b^6}+\frac{3\,a\,\left(\frac{3}{b^3}-\frac{6\,a^2}{b^5}\right)}{b}\right)}{d}-\frac{\frac{11\,a^6-21\,a^4\,b^2+9\,a^2\,b^4+b^6}{2\,b}+\sin\left(c+d\,x\right)\,\left(6\,a^5-12\,a^3\,b^2+6\,a\,b^4\right)}{d\,\left(a^2\,b^6+2\,a\,b^7\,\sin\left(c+d\,x\right)+b^8\,{\sin\left(c+d\,x\right)}^2\right)}+\frac{a\,{\sin\left(c+d\,x\right)}^3}{b^4\,d}-\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(15\,a^4-18\,a^2\,b^2+3\,b^4\right)}{b^7\,d}","Not used",1,"(sin(c + d*x)^2*(3/(2*b^3) - (3*a^2)/b^5))/d - sin(c + d*x)^4/(4*b^3*d) - (sin(c + d*x)*((8*a^3)/b^6 + (3*a*(3/b^3 - (6*a^2)/b^5))/b))/d - ((11*a^6 + b^6 + 9*a^2*b^4 - 21*a^4*b^2)/(2*b) + sin(c + d*x)*(6*a*b^4 + 6*a^5 - 12*a^3*b^2))/(d*(a^2*b^6 + b^8*sin(c + d*x)^2 + 2*a*b^7*sin(c + d*x))) + (a*sin(c + d*x)^3)/(b^4*d) - (log(a + b*sin(c + d*x))*(15*a^4 + 3*b^4 - 18*a^2*b^2))/(b^7*d)","B"
450,1,142,127,5.135620,"\text{Not used}","int(cos(c + d*x)^5/(a + b*sin(c + d*x))^3,x)","\frac{{\sin\left(c+d\,x\right)}^2}{2\,b^3\,d}-\frac{\frac{-7\,a^4+6\,a^2\,b^2+b^4}{2\,b}+\sin\left(c+d\,x\right)\,\left(4\,a\,b^2-4\,a^3\right)}{d\,\left(a^2\,b^4+2\,a\,b^5\,\sin\left(c+d\,x\right)+b^6\,{\sin\left(c+d\,x\right)}^2\right)}-\frac{3\,a\,\sin\left(c+d\,x\right)}{b^4\,d}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(6\,a^2-2\,b^2\right)}{b^5\,d}","Not used",1,"sin(c + d*x)^2/(2*b^3*d) - ((b^4 - 7*a^4 + 6*a^2*b^2)/(2*b) + sin(c + d*x)*(4*a*b^2 - 4*a^3))/(d*(a^2*b^4 + b^6*sin(c + d*x)^2 + 2*a*b^5*sin(c + d*x))) - (3*a*sin(c + d*x))/(b^4*d) + (log(a + b*sin(c + d*x))*(6*a^2 - 2*b^2))/(b^5*d)","B"
451,1,80,72,0.091989,"\text{Not used}","int(cos(c + d*x)^3/(a + b*sin(c + d*x))^3,x)","-\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)}{b^3\,d}-\frac{\frac{3\,a^2+b^2}{2\,b^3}+\frac{2\,a\,\sin\left(c+d\,x\right)}{b^2}}{d\,\left(a^2+2\,a\,b\,\sin\left(c+d\,x\right)+b^2\,{\sin\left(c+d\,x\right)}^2\right)}","Not used",1,"- log(a + b*sin(c + d*x))/(b^3*d) - ((3*a^2 + b^2)/(2*b^3) + (2*a*sin(c + d*x))/b^2)/(d*(a^2 + b^2*sin(c + d*x)^2 + 2*a*b*sin(c + d*x)))","B"
452,1,39,22,0.058039,"\text{Not used}","int(cos(c + d*x)/(a + b*sin(c + d*x))^3,x)","-\frac{1}{d\,\left(2\,a^2\,b+4\,a\,b^2\,\sin\left(c+d\,x\right)+2\,b^3\,{\sin\left(c+d\,x\right)}^2\right)}","Not used",1,"-1/(d*(2*a^2*b + 2*b^3*sin(c + d*x)^2 + 4*a*b^2*sin(c + d*x)))","B"
453,1,169,145,5.400216,"\text{Not used}","int(1/(cos(c + d*x)*(a + b*sin(c + d*x))^3),x)","\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(\frac{1}{2\,{\left(a+b\right)}^3}-\frac{1}{2\,{\left(a-b\right)}^3}\right)}{d}+\frac{\frac{5\,a^2\,b-b^3}{2\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{2\,a\,b^2\,\sin\left(c+d\,x\right)}{a^4-2\,a^2\,b^2+b^4}}{d\,\left(a^2+2\,a\,b\,\sin\left(c+d\,x\right)+b^2\,{\sin\left(c+d\,x\right)}^2\right)}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)}{2\,d\,{\left(a-b\right)}^3}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)}{2\,d\,{\left(a+b\right)}^3}","Not used",1,"(log(a + b*sin(c + d*x))*(1/(2*(a + b)^3) - 1/(2*(a - b)^3)))/d + ((5*a^2*b - b^3)/(2*(a^4 + b^4 - 2*a^2*b^2)) + (2*a*b^2*sin(c + d*x))/(a^4 + b^4 - 2*a^2*b^2))/(d*(a^2 + b^2*sin(c + d*x)^2 + 2*a*b*sin(c + d*x))) + log(sin(c + d*x) + 1)/(2*d*(a - b)^3) - log(sin(c + d*x) - 1)/(2*d*(a + b)^3)","B"
454,1,388,226,5.775860,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b*sin(c + d*x))^3),x)","\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(\frac{3\,b}{4\,{\left(a+b\right)}^4}+\frac{1}{4\,{\left(a+b\right)}^3}+\frac{3\,b}{4\,{\left(a-b\right)}^4}-\frac{1}{4\,{\left(a-b\right)}^3}\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{3\,b}{4\,{\left(a+b\right)}^4}+\frac{1}{4\,{\left(a+b\right)}^3}\right)}{d}+\frac{\frac{3\,a^4\,b+10\,a^2\,b^3-b^5}{2\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\sin\left(c+d\,x\right)}^3\,\left(a^3\,b^2+11\,a\,b^4\right)}{2\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(a^4\,b+6\,a^2\,b^3-b^5\right)}{\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{a\,\sin\left(c+d\,x\right)\,\left(-a^4+3\,a^2\,b^2+10\,b^4\right)}{2\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left({\sin\left(c+d\,x\right)}^2\,\left(a^2-b^2\right)-a^2+b^2\,{\sin\left(c+d\,x\right)}^4-2\,a\,b\,\sin\left(c+d\,x\right)+2\,a\,b\,{\sin\left(c+d\,x\right)}^3\right)}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(a-4\,b\right)}{4\,d\,{\left(a-b\right)}^4}","Not used",1,"(log(a + b*sin(c + d*x))*((3*b)/(4*(a + b)^4) + 1/(4*(a + b)^3) + (3*b)/(4*(a - b)^4) - 1/(4*(a - b)^3)))/d - (log(sin(c + d*x) - 1)*((3*b)/(4*(a + b)^4) + 1/(4*(a + b)^3)))/d + ((3*a^4*b - b^5 + 10*a^2*b^3)/(2*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (sin(c + d*x)^3*(11*a*b^4 + a^3*b^2))/(2*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (sin(c + d*x)^2*(a^4*b - b^5 + 6*a^2*b^3))/((a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (a*sin(c + d*x)*(10*b^4 - a^4 + 3*a^2*b^2))/(2*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)))/(d*(sin(c + d*x)^2*(a^2 - b^2) - a^2 + b^2*sin(c + d*x)^4 - 2*a*b*sin(c + d*x) + 2*a*b*sin(c + d*x)^3)) + (log(sin(c + d*x) + 1)*(a - 4*b))/(4*d*(a - b)^4)","B"
455,1,688,328,6.564812,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + b*sin(c + d*x))^3),x)","\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(\frac{3\,b^2}{4\,{\left(a-b\right)}^5}-\frac{9\,b}{16\,{\left(a-b\right)}^4}+\frac{3}{16\,{\left(a-b\right)}^3}\right)}{d}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{9\,b}{16\,{\left(a+b\right)}^4}+\frac{3}{16\,{\left(a+b\right)}^3}+\frac{3\,b^2}{4\,{\left(a+b\right)}^5}\right)}{d}-\frac{\frac{3\,a^6\,b-22\,a^4\,b^3-31\,a^2\,b^5+2\,b^7}{4\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{\sin\left(c+d\,x\right)\,\left(5\,a^7-26\,a^5\,b^2+49\,a^3\,b^4+68\,a\,b^6\right)}{8\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{3\,{\sin\left(c+d\,x\right)}^5\,\left(-a^5\,b^2+6\,a^3\,b^4+27\,a\,b^6\right)}{8\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{{\sin\left(c+d\,x\right)}^3\,\left(3\,a^7-23\,a^5\,b^2+61\,a^3\,b^4+151\,a\,b^6\right)}{8\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{3\,{\sin\left(c+d\,x\right)}^4\,\left(a^6\,b-6\,a^4\,b^3-13\,a^2\,b^5+2\,b^7\right)}{4\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(5\,a^6\,b-37\,a^4\,b^3-73\,a^2\,b^5+9\,b^7\right)}{4\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}}{d\,\left({\sin\left(c+d\,x\right)}^4\,\left(a^2-2\,b^2\right)+a^2-{\sin\left(c+d\,x\right)}^2\,\left(2\,a^2-b^2\right)+b^2\,{\sin\left(c+d\,x\right)}^6+2\,a\,b\,\sin\left(c+d\,x\right)-4\,a\,b\,{\sin\left(c+d\,x\right)}^3+2\,a\,b\,{\sin\left(c+d\,x\right)}^5\right)}-\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(21\,a^2\,b^5+3\,b^7\right)}{d\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}","Not used",1,"(log(sin(c + d*x) + 1)*((3*b^2)/(4*(a - b)^5) - (9*b)/(16*(a - b)^4) + 3/(16*(a - b)^3)))/d - (log(sin(c + d*x) - 1)*((9*b)/(16*(a + b)^4) + 3/(16*(a + b)^3) + (3*b^2)/(4*(a + b)^5)))/d - ((3*a^6*b + 2*b^7 - 31*a^2*b^5 - 22*a^4*b^3)/(4*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (sin(c + d*x)*(68*a*b^6 + 5*a^7 + 49*a^3*b^4 - 26*a^5*b^2))/(8*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (3*sin(c + d*x)^5*(27*a*b^6 + 6*a^3*b^4 - a^5*b^2))/(8*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (sin(c + d*x)^3*(151*a*b^6 + 3*a^7 + 61*a^3*b^4 - 23*a^5*b^2))/(8*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (3*sin(c + d*x)^4*(a^6*b + 2*b^7 - 13*a^2*b^5 - 6*a^4*b^3))/(4*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (sin(c + d*x)^2*(5*a^6*b + 9*b^7 - 73*a^2*b^5 - 37*a^4*b^3))/(4*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)))/(d*(sin(c + d*x)^4*(a^2 - 2*b^2) + a^2 - sin(c + d*x)^2*(2*a^2 - b^2) + b^2*sin(c + d*x)^6 + 2*a*b*sin(c + d*x) - 4*a*b*sin(c + d*x)^3 + 2*a*b*sin(c + d*x)^5)) - (log(a + b*sin(c + d*x))*(3*b^7 + 21*a^2*b^5))/(d*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2))","B"
456,1,1226,197,8.582597,"\text{Not used}","int(cos(c + d*x)^6/(a + b*sin(c + d*x))^3,x)","\frac{\mathrm{atanh}\left(\frac{1000\,a^2\,\sqrt{b^2-a^2}}{1000\,a^2\,b-\frac{5000\,a^4}{b}+\frac{4000\,a^6}{b^3}-10000\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2000\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{8000\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}}-\frac{4000\,a^4\,\sqrt{b^2-a^2}}{1000\,a^2\,b^3-5000\,a^4\,b+\frac{4000\,a^6}{b}+8000\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2000\,a\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-10000\,a^3\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{2000\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{1000\,a^2-\frac{5000\,a^4}{b^2}+\frac{4000\,a^6}{b^4}-\frac{10000\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+\frac{8000\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}+2000\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{9000\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{1000\,a^2\,b^2-5000\,a^4+\frac{4000\,a^6}{b^2}+2000\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-10000\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{8000\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}}+\frac{4000\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{4000\,a^6+8000\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b-5000\,a^4\,b^2-10000\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^3+1000\,a^2\,b^4+2000\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^5}\right)\,\left(20\,a^2\,\sqrt{b^2-a^2}-5\,b^2\,\sqrt{b^2-a^2}\right)}{b^6\,d}-\frac{\frac{-60\,a^4+35\,a^2\,b^2+3\,b^4}{3\,b^5}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-210\,a^4+125\,a^2\,b^2+6\,b^4\right)}{3\,a\,b^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(20\,a^6+15\,a^4\,b^2-15\,a^2\,b^4-2\,b^6\right)}{a^2\,b^5}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(40\,a^6+30\,a^4\,b^2-35\,a^2\,b^4-3\,b^6\right)}{a^2\,b^5}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(120\,a^6+10\,a^4\,b^2-55\,a^2\,b^4-3\,b^6\right)}{3\,a^2\,b^5}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(180\,a^6+95\,a^4\,b^2-120\,a^2\,b^4-9\,b^6\right)}{3\,a^2\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(-10\,a^4+5\,a^2\,b^2+2\,b^4\right)}{a\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-50\,a^4+25\,a^2\,b^2+4\,b^4\right)}{a\,b^4}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-60\,a^4+35\,a^2\,b^2+3\,b^4\right)}{a\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-330\,a^4+205\,a^2\,b^2+12\,b^4\right)}{3\,a\,b^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(5\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(5\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(10\,a^2+12\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(10\,a^2+12\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+a^2+16\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+24\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+16\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{5\,a\,\mathrm{atan}\left(\frac{3000\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3000\,a^2-\frac{7000\,a^4}{b^2}+\frac{4000\,a^6}{b^4}}-\frac{7000\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3000\,a^2\,b^2-7000\,a^4+\frac{4000\,a^6}{b^2}}+\frac{4000\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4000\,a^6-7000\,a^4\,b^2+3000\,a^2\,b^4}\right)\,\left(4\,a^2-3\,b^2\right)}{b^6\,d}","Not used",1,"(atanh((1000*a^2*(b^2 - a^2)^(1/2))/(1000*a^2*b - (5000*a^4)/b + (4000*a^6)/b^3 - 10000*a^3*tan(c/2 + (d*x)/2) + 2000*a*b^2*tan(c/2 + (d*x)/2) + (8000*a^5*tan(c/2 + (d*x)/2))/b^2) - (4000*a^4*(b^2 - a^2)^(1/2))/(1000*a^2*b^3 - 5000*a^4*b + (4000*a^6)/b + 8000*a^5*tan(c/2 + (d*x)/2) + 2000*a*b^4*tan(c/2 + (d*x)/2) - 10000*a^3*b^2*tan(c/2 + (d*x)/2)) + (2000*a*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(1000*a^2 - (5000*a^4)/b^2 + (4000*a^6)/b^4 - (10000*a^3*tan(c/2 + (d*x)/2))/b + (8000*a^5*tan(c/2 + (d*x)/2))/b^3 + 2000*a*b*tan(c/2 + (d*x)/2)) - (9000*a^3*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(1000*a^2*b^2 - 5000*a^4 + (4000*a^6)/b^2 + 2000*a*b^3*tan(c/2 + (d*x)/2) - 10000*a^3*b*tan(c/2 + (d*x)/2) + (8000*a^5*tan(c/2 + (d*x)/2))/b) + (4000*a^5*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(4000*a^6 + 1000*a^2*b^4 - 5000*a^4*b^2 + 2000*a*b^5*tan(c/2 + (d*x)/2) + 8000*a^5*b*tan(c/2 + (d*x)/2) - 10000*a^3*b^3*tan(c/2 + (d*x)/2)))*(20*a^2*(b^2 - a^2)^(1/2) - 5*b^2*(b^2 - a^2)^(1/2)))/(b^6*d) - ((3*b^4 - 60*a^4 + 35*a^2*b^2)/(3*b^5) + (tan(c/2 + (d*x)/2)*(6*b^4 - 210*a^4 + 125*a^2*b^2))/(3*a*b^4) - (tan(c/2 + (d*x)/2)^8*(20*a^6 - 2*b^6 - 15*a^2*b^4 + 15*a^4*b^2))/(a^2*b^5) - (2*tan(c/2 + (d*x)/2)^6*(40*a^6 - 3*b^6 - 35*a^2*b^4 + 30*a^4*b^2))/(a^2*b^5) - (2*tan(c/2 + (d*x)/2)^2*(120*a^6 - 3*b^6 - 55*a^2*b^4 + 10*a^4*b^2))/(3*a^2*b^5) - (2*tan(c/2 + (d*x)/2)^4*(180*a^6 - 9*b^6 - 120*a^2*b^4 + 95*a^4*b^2))/(3*a^2*b^5) + (tan(c/2 + (d*x)/2)^9*(2*b^4 - 10*a^4 + 5*a^2*b^2))/(a*b^4) + (2*tan(c/2 + (d*x)/2)^7*(4*b^4 - 50*a^4 + 25*a^2*b^2))/(a*b^4) + (4*tan(c/2 + (d*x)/2)^5*(3*b^4 - 60*a^4 + 35*a^2*b^2))/(a*b^4) + (2*tan(c/2 + (d*x)/2)^3*(12*b^4 - 330*a^4 + 205*a^2*b^2))/(3*a*b^4))/(d*(tan(c/2 + (d*x)/2)^2*(5*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^8*(5*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^4*(10*a^2 + 12*b^2) + tan(c/2 + (d*x)/2)^6*(10*a^2 + 12*b^2) + a^2*tan(c/2 + (d*x)/2)^10 + a^2 + 16*a*b*tan(c/2 + (d*x)/2)^3 + 24*a*b*tan(c/2 + (d*x)/2)^5 + 16*a*b*tan(c/2 + (d*x)/2)^7 + 4*a*b*tan(c/2 + (d*x)/2)^9 + 4*a*b*tan(c/2 + (d*x)/2))) + (5*a*atan((3000*a^2*tan(c/2 + (d*x)/2))/(3000*a^2 - (7000*a^4)/b^2 + (4000*a^6)/b^4) - (7000*a^4*tan(c/2 + (d*x)/2))/(3000*a^2*b^2 - 7000*a^4 + (4000*a^6)/b^2) + (4000*a^6*tan(c/2 + (d*x)/2))/(4000*a^6 + 3000*a^2*b^4 - 7000*a^4*b^2))*(4*a^2 - 3*b^2))/(b^6*d)","B"
457,1,1360,139,7.549766,"\text{Not used}","int(cos(c + d*x)^4/(a + b*sin(c + d*x))^3,x)","-\frac{\frac{6\,a^2+b^2}{b^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a^4+9\,a^2\,b^2+b^4\right)}{a^2\,b^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(21\,a^2+2\,b^2\right)}{a\,b^2}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,a^2+b^2\right)}{a\,b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^4+9\,a^2\,b^2+2\,b^4\right)}{a^2\,b^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,a^2+2\,b^2\right)}{a\,b^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a^2+4\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+a^2+8\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{3\,a\,x}{b^4}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-b^2\right)\,\left(\frac{288\,a^4}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^5\,b^3-108\,a^3\,b^5+9\,a\,b^7\right)}{b^9}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a\,b^{10}-24\,a^3\,b^8\right)}{b^9}-48\,a^2+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-b^2\right)\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a\,b^{13}-8\,a^3\,b^{11}\right)}{b^9}\right)}{2\,\left(b^6-a^2\,b^4\right)}\right)}{2\,\left(b^6-a^2\,b^4\right)}\right)\,3{}\mathrm{i}}{2\,\left(b^6-a^2\,b^4\right)}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-b^2\right)\,\left(\frac{288\,a^4}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^5\,b^3-108\,a^3\,b^5+9\,a\,b^7\right)}{b^9}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-b^2\right)\,\left(48\,a^2-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a\,b^{10}-24\,a^3\,b^8\right)}{b^9}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-b^2\right)\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a\,b^{13}-8\,a^3\,b^{11}\right)}{b^9}\right)}{2\,\left(b^6-a^2\,b^4\right)}\right)}{2\,\left(b^6-a^2\,b^4\right)}\right)\,3{}\mathrm{i}}{2\,\left(b^6-a^2\,b^4\right)}}{\frac{16\,\left(54\,a^4-27\,a^2\,b^2\right)}{b^8}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(216\,a^5-108\,a^3\,b^2\right)}{b^9}-\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-b^2\right)\,\left(\frac{288\,a^4}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^5\,b^3-108\,a^3\,b^5+9\,a\,b^7\right)}{b^9}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a\,b^{10}-24\,a^3\,b^8\right)}{b^9}-48\,a^2+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-b^2\right)\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a\,b^{13}-8\,a^3\,b^{11}\right)}{b^9}\right)}{2\,\left(b^6-a^2\,b^4\right)}\right)}{2\,\left(b^6-a^2\,b^4\right)}\right)}{2\,\left(b^6-a^2\,b^4\right)}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-b^2\right)\,\left(\frac{288\,a^4}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^5\,b^3-108\,a^3\,b^5+9\,a\,b^7\right)}{b^9}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-b^2\right)\,\left(48\,a^2-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a\,b^{10}-24\,a^3\,b^8\right)}{b^9}+\frac{3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-b^2\right)\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a\,b^{13}-8\,a^3\,b^{11}\right)}{b^9}\right)}{2\,\left(b^6-a^2\,b^4\right)}\right)}{2\,\left(b^6-a^2\,b^4\right)}\right)}{2\,\left(b^6-a^2\,b^4\right)}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-b^2\right)\,3{}\mathrm{i}}{d\,\left(b^6-a^2\,b^4\right)}","Not used",1,"- ((6*a^2 + b^2)/b^3 + (2*tan(c/2 + (d*x)/2)^2*(6*a^4 + b^4 + 9*a^2*b^2))/(a^2*b^3) + (tan(c/2 + (d*x)/2)*(21*a^2 + 2*b^2))/(a*b^2) + (4*tan(c/2 + (d*x)/2)^3*(6*a^2 + b^2))/(a*b^2) + (tan(c/2 + (d*x)/2)^4*(6*a^4 + 2*b^4 + 9*a^2*b^2))/(a^2*b^3) + (tan(c/2 + (d*x)/2)^5*(3*a^2 + 2*b^2))/(a*b^2))/(d*(tan(c/2 + (d*x)/2)^2*(3*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^4*(3*a^2 + 4*b^2) + a^2*tan(c/2 + (d*x)/2)^6 + a^2 + 8*a*b*tan(c/2 + (d*x)/2)^3 + 4*a*b*tan(c/2 + (d*x)/2)^5 + 4*a*b*tan(c/2 + (d*x)/2))) - (3*a*x)/b^4 - (atan((((-(a + b)*(a - b))^(1/2)*(2*a^2 - b^2)*((288*a^4)/b^5 - (8*tan(c/2 + (d*x)/2)*(9*a*b^7 - 108*a^3*b^5 + 72*a^5*b^3))/b^9 + (3*(-(a + b)*(a - b))^(1/2)*(2*a^2 - b^2)*((8*tan(c/2 + (d*x)/2)*(12*a*b^10 - 24*a^3*b^8))/b^9 - 48*a^2 + (3*(-(a + b)*(a - b))^(1/2)*(2*a^2 - b^2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^13 - 8*a^3*b^11))/b^9))/(2*(b^6 - a^2*b^4))))/(2*(b^6 - a^2*b^4)))*3i)/(2*(b^6 - a^2*b^4)) + ((-(a + b)*(a - b))^(1/2)*(2*a^2 - b^2)*((288*a^4)/b^5 - (8*tan(c/2 + (d*x)/2)*(9*a*b^7 - 108*a^3*b^5 + 72*a^5*b^3))/b^9 + (3*(-(a + b)*(a - b))^(1/2)*(2*a^2 - b^2)*(48*a^2 - (8*tan(c/2 + (d*x)/2)*(12*a*b^10 - 24*a^3*b^8))/b^9 + (3*(-(a + b)*(a - b))^(1/2)*(2*a^2 - b^2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^13 - 8*a^3*b^11))/b^9))/(2*(b^6 - a^2*b^4))))/(2*(b^6 - a^2*b^4)))*3i)/(2*(b^6 - a^2*b^4)))/((16*(54*a^4 - 27*a^2*b^2))/b^8 + (16*tan(c/2 + (d*x)/2)*(216*a^5 - 108*a^3*b^2))/b^9 - (3*(-(a + b)*(a - b))^(1/2)*(2*a^2 - b^2)*((288*a^4)/b^5 - (8*tan(c/2 + (d*x)/2)*(9*a*b^7 - 108*a^3*b^5 + 72*a^5*b^3))/b^9 + (3*(-(a + b)*(a - b))^(1/2)*(2*a^2 - b^2)*((8*tan(c/2 + (d*x)/2)*(12*a*b^10 - 24*a^3*b^8))/b^9 - 48*a^2 + (3*(-(a + b)*(a - b))^(1/2)*(2*a^2 - b^2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^13 - 8*a^3*b^11))/b^9))/(2*(b^6 - a^2*b^4))))/(2*(b^6 - a^2*b^4))))/(2*(b^6 - a^2*b^4)) + (3*(-(a + b)*(a - b))^(1/2)*(2*a^2 - b^2)*((288*a^4)/b^5 - (8*tan(c/2 + (d*x)/2)*(9*a*b^7 - 108*a^3*b^5 + 72*a^5*b^3))/b^9 + (3*(-(a + b)*(a - b))^(1/2)*(2*a^2 - b^2)*(48*a^2 - (8*tan(c/2 + (d*x)/2)*(12*a*b^10 - 24*a^3*b^8))/b^9 + (3*(-(a + b)*(a - b))^(1/2)*(2*a^2 - b^2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^13 - 8*a^3*b^11))/b^9))/(2*(b^6 - a^2*b^4))))/(2*(b^6 - a^2*b^4))))/(2*(b^6 - a^2*b^4))))*(-(a + b)*(a - b))^(1/2)*(2*a^2 - b^2)*3i)/(d*(b^6 - a^2*b^4))","B"
458,1,282,115,7.369479,"\text{Not used}","int(cos(c + d*x)^2/(a + b*sin(c + d*x))^3,x)","\frac{\frac{b}{a^2-b^2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2-2\,b^2\right)}{a\,\left(a^2-b^2\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+2\,b^2\right)}{a\,\left(a^2-b^2\right)}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2+2\,b^2\right)}{a^2\,\left(a^2-b^2\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2+4\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+a^2+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{\mathrm{atan}\left(\left(a^2-b^2\right)\,\left(\frac{a^2\,b-b^3}{{\left(a+b\right)}^{3/2}\,\left(a^2-b^2\right)\,{\left(a-b\right)}^{3/2}}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}\right)\right)}{d\,{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}","Not used",1,"(b/(a^2 - b^2) - (tan(c/2 + (d*x)/2)^3*(a^2 - 2*b^2))/(a*(a^2 - b^2)) + (tan(c/2 + (d*x)/2)*(a^2 + 2*b^2))/(a*(a^2 - b^2)) + (b*tan(c/2 + (d*x)/2)^2*(a^2 + 2*b^2))/(a^2*(a^2 - b^2)))/(d*(tan(c/2 + (d*x)/2)^2*(2*a^2 + 4*b^2) + a^2*tan(c/2 + (d*x)/2)^4 + a^2 + 4*a*b*tan(c/2 + (d*x)/2)^3 + 4*a*b*tan(c/2 + (d*x)/2))) + atan((a^2 - b^2)*((a^2*b - b^3)/((a + b)^(3/2)*(a^2 - b^2)*(a - b)^(3/2)) + (a*tan(c/2 + (d*x)/2))/((a + b)^(3/2)*(a - b)^(3/2))))/(d*(a + b)^(3/2)*(a - b)^(3/2))","B"
459,1,650,192,8.819645,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b*sin(c + d*x))^3),x)","-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^5-2\,a^3\,b^2+15\,a\,b^4\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-\frac{6\,a^4\,b+10\,a^2\,b^3-b^5}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^6+6\,a^4\,b^2+9\,a^2\,b^4-2\,b^6\right)}{a\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^6\,b+2\,a^4\,b^3+12\,a^2\,b^5-b^7\right)}{a^2\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^6\,b+30\,a^4\,b^3+15\,a^2\,b^5-2\,b^7\right)}{a^2\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^6-18\,a^4\,b^2-31\,a^2\,b^4+2\,b^6\right)}{a\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-a^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2+4\,b^2\right)+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{3\,b^2\,\mathrm{atan}\left(\frac{\frac{3\,b^2\,\left(4\,a^2+b^2\right)\,\left(2\,a^6\,b-6\,a^4\,b^3+6\,a^2\,b^5-2\,b^7\right)}{2\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}+\frac{3\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2+b^2\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}{{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}}{12\,a^2\,b^2+3\,b^4}\right)\,\left(4\,a^2+b^2\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"- ((2*tan(c/2 + (d*x)/2)^3*(15*a*b^4 + 2*a^5 - 2*a^3*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (6*a^4*b - b^5 + 10*a^2*b^3)/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) + (tan(c/2 + (d*x)/2)^5*(2*a^6 - 2*b^6 + 9*a^2*b^4 + 6*a^4*b^2))/(a*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (2*tan(c/2 + (d*x)/2)^2*(2*a^6*b - b^7 + 12*a^2*b^5 + 2*a^4*b^3))/(a^2*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^4*(2*a^6*b - 2*b^7 + 15*a^2*b^5 + 30*a^4*b^3))/(a^2*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)*(2*a^6 + 2*b^6 - 31*a^2*b^4 - 18*a^4*b^2))/(a*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)))/(d*(a^2*tan(c/2 + (d*x)/2)^6 - a^2 - tan(c/2 + (d*x)/2)^2*(a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 + 4*b^2) + 4*a*b*tan(c/2 + (d*x)/2)^5 - 4*a*b*tan(c/2 + (d*x)/2))) - (3*b^2*atan(((3*b^2*(4*a^2 + b^2)*(2*a^6*b - 2*b^7 + 6*a^2*b^5 - 6*a^4*b^3))/(2*(a + b)^(7/2)*(a - b)^(7/2)) + (3*a*b^2*tan(c/2 + (d*x)/2)*(4*a^2 + b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))/((a + b)^(7/2)*(a - b)^(7/2)))/(3*b^4 + 12*a^2*b^2))*(4*a^2 + b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
460,1,1167,264,9.369484,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b*sin(c + d*x))^3),x)","\frac{5\,b^4\,\mathrm{atan}\left(\frac{\frac{5\,b^4\,\left(6\,a^2+b^2\right)\,\left(2\,a^8\,b-8\,a^6\,b^3+12\,a^4\,b^5-8\,a^2\,b^7+2\,b^9\right)}{2\,{\left(a+b\right)}^{9/2}\,{\left(a-b\right)}^{9/2}}+\frac{5\,a\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^2+b^2\right)\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}{{\left(a+b\right)}^{9/2}\,{\left(a-b\right)}^{9/2}}}{30\,a^2\,b^4+5\,b^6}\right)\,\left(6\,a^2+b^2\right)}{d\,{\left(a+b\right)}^{9/2}\,{\left(a-b\right)}^{9/2}}-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^7-4\,a^5\,b^2+62\,a^3\,b^4+255\,a\,b^6\right)}{3\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{6\,a^6\,b-64\,a^4\,b^3-50\,a^2\,b^5+3\,b^7}{3\,\left(a^2-b^2\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,a^6-6\,a^4\,b^2+36\,a^2\,b^4+3\,b^6\right)}{3\,a\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a^6\,b-50\,a^4\,b^3-64\,a^2\,b^5+3\,b^7\right)}{3\,a^2\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(-2\,a^8+8\,a^6\,b^2+18\,a^4\,b^4+13\,a^2\,b^6-2\,b^8\right)}{a\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(-2\,a^8\,b+8\,a^6\,b^3+78\,a^4\,b^5+23\,a^2\,b^7-2\,b^9\right)}{a^2\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^8-48\,a^6\,b^2+202\,a^4\,b^4+161\,a^2\,b^6-6\,b^8\right)}{3\,a\,\left(a^2-b^2\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^8+4\,a^6\,b^2-86\,a^4\,b^4-133\,a^2\,b^6+3\,b^8\right)}{3\,a\,\left(a^2-b^2\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(8\,a^8\,b-28\,a^6\,b^3+188\,a^4\,b^5+156\,a^2\,b^7-9\,b^9\right)}{3\,a^2\,\left(a^2-b^2\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-14\,a^8\,b+56\,a^6\,b^3+246\,a^4\,b^5+141\,a^2\,b^7-9\,b^9\right)}{3\,a^2\,\left(a^2-b^2\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^2+12\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^2+12\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-a^2+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2-4\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2-4\,b^2\right)+8\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-8\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"(5*b^4*atan(((5*b^4*(6*a^2 + b^2)*(2*a^8*b + 2*b^9 - 8*a^2*b^7 + 12*a^4*b^5 - 8*a^6*b^3))/(2*(a + b)^(9/2)*(a - b)^(9/2)) + (5*a*b^4*tan(c/2 + (d*x)/2)*(6*a^2 + b^2)*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2))/((a + b)^(9/2)*(a - b)^(9/2)))/(5*b^6 + 30*a^2*b^4))*(6*a^2 + b^2))/(d*(a + b)^(9/2)*(a - b)^(9/2)) - ((2*tan(c/2 + (d*x)/2)^5*(255*a*b^6 + 2*a^7 + 62*a^3*b^4 - 4*a^5*b^2))/(3*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (6*a^6*b + 3*b^7 - 50*a^2*b^5 - 64*a^4*b^3)/(3*(a^2 - b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (4*tan(c/2 + (d*x)/2)^7*(2*a^6 + 3*b^6 + 36*a^2*b^4 - 6*a^4*b^2))/(3*a*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (2*tan(c/2 + (d*x)/2)^2*(6*a^6*b + 3*b^7 - 64*a^2*b^5 - 50*a^4*b^3))/(3*a^2*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (tan(c/2 + (d*x)/2)^9*(13*a^2*b^6 - 2*b^8 - 2*a^8 + 18*a^4*b^4 + 8*a^6*b^2))/(a*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (tan(c/2 + (d*x)/2)^8*(23*a^2*b^7 - 2*b^9 - 2*a^8*b + 78*a^4*b^5 + 8*a^6*b^3))/(a^2*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (tan(c/2 + (d*x)/2)*(6*a^8 - 6*b^8 + 161*a^2*b^6 + 202*a^4*b^4 - 48*a^6*b^2))/(3*a*(a^2 - b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (4*tan(c/2 + (d*x)/2)^3*(2*a^8 + 3*b^8 - 133*a^2*b^6 - 86*a^4*b^4 + 4*a^6*b^2))/(3*a*(a^2 - b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (2*tan(c/2 + (d*x)/2)^4*(8*a^8*b - 9*b^9 + 156*a^2*b^7 + 188*a^4*b^5 - 28*a^6*b^3))/(3*a^2*(a^2 - b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (2*tan(c/2 + (d*x)/2)^6*(141*a^2*b^7 - 9*b^9 - 14*a^8*b + 246*a^4*b^5 + 56*a^6*b^3))/(3*a^2*(a^2 - b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)))/(d*(tan(c/2 + (d*x)/2)^4*(2*a^2 + 12*b^2) - tan(c/2 + (d*x)/2)^6*(2*a^2 + 12*b^2) + a^2*tan(c/2 + (d*x)/2)^10 - a^2 + tan(c/2 + (d*x)/2)^2*(a^2 - 4*b^2) - tan(c/2 + (d*x)/2)^8*(a^2 - 4*b^2) + 8*a*b*tan(c/2 + (d*x)/2)^3 - 8*a*b*tan(c/2 + (d*x)/2)^7 + 4*a*b*tan(c/2 + (d*x)/2)^9 - 4*a*b*tan(c/2 + (d*x)/2)))","B"
461,1,276,207,0.242352,"\text{Not used}","int(cos(c + d*x)^7/(a + b*sin(c + d*x))^8,x)","\frac{\frac{5\,a^6-a^4\,b^2+a^2\,b^4-5\,b^6}{35\,b^7}+\frac{{\sin\left(c+d\,x\right)}^6}{b}+\frac{3\,{\sin\left(c+d\,x\right)}^2\,\left(5\,a^4-a^2\,b^2+b^4\right)}{5\,b^5}+\frac{3\,a\,{\sin\left(c+d\,x\right)}^5}{b^2}+\frac{{\sin\left(c+d\,x\right)}^4\,\left(5\,a^2-b^2\right)}{b^3}+\frac{a\,\sin\left(c+d\,x\right)\,\left(5\,a^4-a^2\,b^2+b^4\right)}{5\,b^6}+\frac{a\,{\sin\left(c+d\,x\right)}^3\,\left(5\,a^2-b^2\right)}{b^4}}{d\,\left(a^7+7\,a^6\,b\,\sin\left(c+d\,x\right)+21\,a^5\,b^2\,{\sin\left(c+d\,x\right)}^2+35\,a^4\,b^3\,{\sin\left(c+d\,x\right)}^3+35\,a^3\,b^4\,{\sin\left(c+d\,x\right)}^4+21\,a^2\,b^5\,{\sin\left(c+d\,x\right)}^5+7\,a\,b^6\,{\sin\left(c+d\,x\right)}^6+b^7\,{\sin\left(c+d\,x\right)}^7\right)}","Not used",1,"((5*a^6 - 5*b^6 + a^2*b^4 - a^4*b^2)/(35*b^7) + sin(c + d*x)^6/b + (3*sin(c + d*x)^2*(5*a^4 + b^4 - a^2*b^2))/(5*b^5) + (3*a*sin(c + d*x)^5)/b^2 + (sin(c + d*x)^4*(5*a^2 - b^2))/b^3 + (a*sin(c + d*x)*(5*a^4 + b^4 - a^2*b^2))/(5*b^6) + (a*sin(c + d*x)^3*(5*a^2 - b^2))/b^4)/(d*(a^7 + b^7*sin(c + d*x)^7 + 7*a*b^6*sin(c + d*x)^6 + 21*a^5*b^2*sin(c + d*x)^2 + 35*a^4*b^3*sin(c + d*x)^3 + 35*a^3*b^4*sin(c + d*x)^4 + 21*a^2*b^5*sin(c + d*x)^5 + 7*a^6*b*sin(c + d*x)))","B"
462,1,206,141,0.136220,"\text{Not used}","int(cos(c + d*x)^5/(a + b*sin(c + d*x))^8,x)","-\frac{\frac{a^4-2\,a^2\,b^2+15\,b^4}{105\,b^5}+\frac{{\sin\left(c+d\,x\right)}^4}{3\,b}+\frac{{\sin\left(c+d\,x\right)}^2\,\left(a^2-2\,b^2\right)}{5\,b^3}+\frac{a\,{\sin\left(c+d\,x\right)}^3}{3\,b^2}+\frac{a\,\sin\left(c+d\,x\right)\,\left(a^2-2\,b^2\right)}{15\,b^4}}{d\,\left(a^7+7\,a^6\,b\,\sin\left(c+d\,x\right)+21\,a^5\,b^2\,{\sin\left(c+d\,x\right)}^2+35\,a^4\,b^3\,{\sin\left(c+d\,x\right)}^3+35\,a^3\,b^4\,{\sin\left(c+d\,x\right)}^4+21\,a^2\,b^5\,{\sin\left(c+d\,x\right)}^5+7\,a\,b^6\,{\sin\left(c+d\,x\right)}^6+b^7\,{\sin\left(c+d\,x\right)}^7\right)}","Not used",1,"-((a^4 + 15*b^4 - 2*a^2*b^2)/(105*b^5) + sin(c + d*x)^4/(3*b) + (sin(c + d*x)^2*(a^2 - 2*b^2))/(5*b^3) + (a*sin(c + d*x)^3)/(3*b^2) + (a*sin(c + d*x)*(a^2 - 2*b^2))/(15*b^4))/(d*(a^7 + b^7*sin(c + d*x)^7 + 7*a*b^6*sin(c + d*x)^6 + 21*a^5*b^2*sin(c + d*x)^2 + 35*a^4*b^3*sin(c + d*x)^3 + 35*a^3*b^4*sin(c + d*x)^4 + 21*a^2*b^5*sin(c + d*x)^5 + 7*a^6*b*sin(c + d*x)))","B"
463,1,152,77,5.217297,"\text{Not used}","int(cos(c + d*x)^3/(a + b*sin(c + d*x))^8,x)","\frac{\frac{a^2-15\,b^2}{105\,b^3}+\frac{{\sin\left(c+d\,x\right)}^2}{5\,b}+\frac{a\,\sin\left(c+d\,x\right)}{15\,b^2}}{d\,\left(a^7+7\,a^6\,b\,\sin\left(c+d\,x\right)+21\,a^5\,b^2\,{\sin\left(c+d\,x\right)}^2+35\,a^4\,b^3\,{\sin\left(c+d\,x\right)}^3+35\,a^3\,b^4\,{\sin\left(c+d\,x\right)}^4+21\,a^2\,b^5\,{\sin\left(c+d\,x\right)}^5+7\,a\,b^6\,{\sin\left(c+d\,x\right)}^6+b^7\,{\sin\left(c+d\,x\right)}^7\right)}","Not used",1,"((a^2 - 15*b^2)/(105*b^3) + sin(c + d*x)^2/(5*b) + (a*sin(c + d*x))/(15*b^2))/(d*(a^7 + b^7*sin(c + d*x)^7 + 7*a*b^6*sin(c + d*x)^6 + 21*a^5*b^2*sin(c + d*x)^2 + 35*a^4*b^3*sin(c + d*x)^3 + 35*a^3*b^4*sin(c + d*x)^4 + 21*a^2*b^5*sin(c + d*x)^5 + 7*a^6*b*sin(c + d*x)))","B"
464,1,119,22,5.203001,"\text{Not used}","int(cos(c + d*x)/(a + b*sin(c + d*x))^8,x)","-\frac{1}{d\,\left(7\,a^7\,b+49\,a^6\,b^2\,\sin\left(c+d\,x\right)+147\,a^5\,b^3\,{\sin\left(c+d\,x\right)}^2+245\,a^4\,b^4\,{\sin\left(c+d\,x\right)}^3+245\,a^3\,b^5\,{\sin\left(c+d\,x\right)}^4+147\,a^2\,b^6\,{\sin\left(c+d\,x\right)}^5+49\,a\,b^7\,{\sin\left(c+d\,x\right)}^6+7\,b^8\,{\sin\left(c+d\,x\right)}^7\right)}","Not used",1,"-1/(d*(7*a^7*b + 7*b^8*sin(c + d*x)^7 + 49*a^6*b^2*sin(c + d*x) + 49*a*b^7*sin(c + d*x)^6 + 147*a^5*b^3*sin(c + d*x)^2 + 245*a^4*b^4*sin(c + d*x)^3 + 245*a^3*b^5*sin(c + d*x)^4 + 147*a^2*b^6*sin(c + d*x)^5))","B"
465,1,937,385,7.635063,"\text{Not used}","int(1/(cos(c + d*x)*(a + b*sin(c + d*x))^8),x)","\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(\frac{1}{2\,{\left(a+b\right)}^8}-\frac{1}{2\,{\left(a-b\right)}^8}\right)}{d}+\frac{\frac{1443\,a^{12}\,b+3704\,a^{10}\,b^3+1849\,a^8\,b^5-496\,a^6\,b^7+309\,a^4\,b^9-104\,a^2\,b^{11}+15\,b^{13}}{105\,\left(a^{14}-7\,a^{12}\,b^2+21\,a^{10}\,b^4-35\,a^8\,b^6+35\,a^6\,b^8-21\,a^4\,b^{10}+7\,a^2\,b^{12}-b^{14}\right)}+\frac{\sin\left(c+d\,x\right)\,\left(1023\,a^{11}\,b^2+3494\,a^9\,b^4+1219\,a^7\,b^6+29\,a^5\,b^8-6\,a^3\,b^{10}+a\,b^{12}\right)}{15\,\left(a^{14}-7\,a^{12}\,b^2+21\,a^{10}\,b^4-35\,a^8\,b^6+35\,a^6\,b^8-21\,a^4\,b^{10}+7\,a^2\,b^{12}-b^{14}\right)}+\frac{{\sin\left(c+d\,x\right)}^3\,\left(533\,a^9\,b^4+2304\,a^7\,b^6+994\,a^5\,b^8+8\,a^3\,b^{10}+a\,b^{12}\right)}{3\,\left(a^{14}-7\,a^{12}\,b^2+21\,a^{10}\,b^4-35\,a^8\,b^6+35\,a^6\,b^8-21\,a^4\,b^{10}+7\,a^2\,b^{12}-b^{14}\right)}+\frac{{\sin\left(c+d\,x\right)}^5\,\left(45\,a^7\,b^6+217\,a^5\,b^8+119\,a^3\,b^{10}+3\,a\,b^{12}\right)}{a^{14}-7\,a^{12}\,b^2+21\,a^{10}\,b^4-35\,a^8\,b^6+35\,a^6\,b^8-21\,a^4\,b^{10}+7\,a^2\,b^{12}-b^{14}}+\frac{{\sin\left(c+d\,x\right)}^2\,\left(743\,a^{10}\,b^3+2934\,a^8\,b^5+1099\,a^6\,b^7+29\,a^4\,b^9-6\,a^2\,b^{11}+b^{13}\right)}{5\,\left(a^{14}-7\,a^{12}\,b^2+21\,a^{10}\,b^4-35\,a^8\,b^6+35\,a^6\,b^8-21\,a^4\,b^{10}+7\,a^2\,b^{12}-b^{14}\right)}+\frac{{\sin\left(c+d\,x\right)}^4\,\left(365\,a^8\,b^5+1680\,a^6\,b^7+826\,a^4\,b^9+8\,a^2\,b^{11}+b^{13}\right)}{3\,\left(a^{14}-7\,a^{12}\,b^2+21\,a^{10}\,b^4-35\,a^8\,b^6+35\,a^6\,b^8-21\,a^4\,b^{10}+7\,a^2\,b^{12}-b^{14}\right)}+\frac{{\sin\left(c+d\,x\right)}^6\,\left(7\,a^6\,b^7+35\,a^4\,b^9+21\,a^2\,b^{11}+b^{13}\right)}{a^{14}-7\,a^{12}\,b^2+21\,a^{10}\,b^4-35\,a^8\,b^6+35\,a^6\,b^8-21\,a^4\,b^{10}+7\,a^2\,b^{12}-b^{14}}}{d\,\left(a^7+7\,a^6\,b\,\sin\left(c+d\,x\right)+21\,a^5\,b^2\,{\sin\left(c+d\,x\right)}^2+35\,a^4\,b^3\,{\sin\left(c+d\,x\right)}^3+35\,a^3\,b^4\,{\sin\left(c+d\,x\right)}^4+21\,a^2\,b^5\,{\sin\left(c+d\,x\right)}^5+7\,a\,b^6\,{\sin\left(c+d\,x\right)}^6+b^7\,{\sin\left(c+d\,x\right)}^7\right)}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)}{2\,d\,{\left(a-b\right)}^8}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)}{2\,d\,{\left(a+b\right)}^8}","Not used",1,"(log(a + b*sin(c + d*x))*(1/(2*(a + b)^8) - 1/(2*(a - b)^8)))/d + ((1443*a^12*b + 15*b^13 - 104*a^2*b^11 + 309*a^4*b^9 - 496*a^6*b^7 + 1849*a^8*b^5 + 3704*a^10*b^3)/(105*(a^14 - b^14 + 7*a^2*b^12 - 21*a^4*b^10 + 35*a^6*b^8 - 35*a^8*b^6 + 21*a^10*b^4 - 7*a^12*b^2)) + (sin(c + d*x)*(a*b^12 - 6*a^3*b^10 + 29*a^5*b^8 + 1219*a^7*b^6 + 3494*a^9*b^4 + 1023*a^11*b^2))/(15*(a^14 - b^14 + 7*a^2*b^12 - 21*a^4*b^10 + 35*a^6*b^8 - 35*a^8*b^6 + 21*a^10*b^4 - 7*a^12*b^2)) + (sin(c + d*x)^3*(a*b^12 + 8*a^3*b^10 + 994*a^5*b^8 + 2304*a^7*b^6 + 533*a^9*b^4))/(3*(a^14 - b^14 + 7*a^2*b^12 - 21*a^4*b^10 + 35*a^6*b^8 - 35*a^8*b^6 + 21*a^10*b^4 - 7*a^12*b^2)) + (sin(c + d*x)^5*(3*a*b^12 + 119*a^3*b^10 + 217*a^5*b^8 + 45*a^7*b^6))/(a^14 - b^14 + 7*a^2*b^12 - 21*a^4*b^10 + 35*a^6*b^8 - 35*a^8*b^6 + 21*a^10*b^4 - 7*a^12*b^2) + (sin(c + d*x)^2*(b^13 - 6*a^2*b^11 + 29*a^4*b^9 + 1099*a^6*b^7 + 2934*a^8*b^5 + 743*a^10*b^3))/(5*(a^14 - b^14 + 7*a^2*b^12 - 21*a^4*b^10 + 35*a^6*b^8 - 35*a^8*b^6 + 21*a^10*b^4 - 7*a^12*b^2)) + (sin(c + d*x)^4*(b^13 + 8*a^2*b^11 + 826*a^4*b^9 + 1680*a^6*b^7 + 365*a^8*b^5))/(3*(a^14 - b^14 + 7*a^2*b^12 - 21*a^4*b^10 + 35*a^6*b^8 - 35*a^8*b^6 + 21*a^10*b^4 - 7*a^12*b^2)) + (sin(c + d*x)^6*(b^13 + 21*a^2*b^11 + 35*a^4*b^9 + 7*a^6*b^7))/(a^14 - b^14 + 7*a^2*b^12 - 21*a^4*b^10 + 35*a^6*b^8 - 35*a^8*b^6 + 21*a^10*b^4 - 7*a^12*b^2))/(d*(a^7 + b^7*sin(c + d*x)^7 + 7*a*b^6*sin(c + d*x)^6 + 21*a^5*b^2*sin(c + d*x)^2 + 35*a^4*b^3*sin(c + d*x)^3 + 35*a^3*b^4*sin(c + d*x)^4 + 21*a^2*b^5*sin(c + d*x)^5 + 7*a^6*b*sin(c + d*x))) + log(sin(c + d*x) + 1)/(2*d*(a - b)^8) - log(sin(c + d*x) - 1)/(2*d*(a + b)^8)","B"
466,1,1443,527,9.887117,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b*sin(c + d*x))^8),x)","\frac{\frac{{\sin\left(c+d\,x\right)}^7\,\left(7\,a^9\,b^6+1252\,a^7\,b^8+3514\,a^5\,b^{10}+1348\,a^3\,b^{12}+23\,a\,b^{14}\right)}{2\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}-\frac{420\,a^{14}\,b+16745\,a^{12}\,b^3+28862\,a^{10}\,b^5+8177\,a^8\,b^7-748\,a^6\,b^9+407\,a^4\,b^{11}-118\,a^2\,b^{13}+15\,b^{15}}{105\,\left(a^2-b^2\right)\,\left(a^{14}-7\,a^{12}\,b^2+21\,a^{10}\,b^4-35\,a^8\,b^6+35\,a^6\,b^8-21\,a^4\,b^{10}+7\,a^2\,b^{12}-b^{14}\right)}+\frac{{\sin\left(c+d\,x\right)}^6\,\left(63\,a^{10}\,b^5+10066\,a^8\,b^7+26194\,a^6\,b^9+7384\,a^4\,b^{11}-681\,a^2\,b^{13}-18\,b^{15}\right)}{6\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}+\frac{{\sin\left(c+d\,x\right)}^8\,\left(a^8\,b^7+196\,a^6\,b^9+574\,a^4\,b^{11}+244\,a^2\,b^{13}+9\,b^{15}\right)}{2\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}+\frac{{\sin\left(c+d\,x\right)}^5\,\left(105\,a^{11}\,b^4+14506\,a^9\,b^6+32254\,a^7\,b^8+160\,a^5\,b^{10}-3951\,a^3\,b^{12}-66\,a\,b^{14}\right)}{6\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}+\frac{{\sin\left(c+d\,x\right)}^4\,\left(525\,a^{10}\,b^3+59835\,a^8\,b^5+143647\,a^6\,b^7+45119\,a^4\,b^9+456\,a^2\,b^{11}+18\,b^{13}\right)}{30\,\left(a^{14}-7\,a^{12}\,b^2+21\,a^{10}\,b^4-35\,a^8\,b^6+35\,a^6\,b^8-21\,a^4\,b^{10}+7\,a^2\,b^{12}-b^{14}\right)}-\frac{{\sin\left(c+d\,x\right)}^2\,\left(-735\,a^{14}\,b-30550\,a^{12}\,b^3+361856\,a^{10}\,b^5+919070\,a^8\,b^7+252845\,a^6\,b^9+3050\,a^4\,b^{11}-310\,a^2\,b^{13}+54\,b^{15}\right)}{210\,\left(a^2-b^2\right)\,\left(a^{14}-7\,a^{12}\,b^2+21\,a^{10}\,b^4-35\,a^8\,b^6+35\,a^6\,b^8-21\,a^4\,b^{10}+7\,a^2\,b^{12}-b^{14}\right)}-\frac{{\sin\left(c+d\,x\right)}^3\,\left(-315\,a^{13}\,b^2-25930\,a^{11}\,b^4+20896\,a^9\,b^6+166336\,a^7\,b^8+53641\,a^5\,b^{10}+386\,a^3\,b^{12}+26\,a\,b^{14}\right)}{30\,\left(a^2-b^2\right)\,\left(a^{14}-7\,a^{12}\,b^2+21\,a^{10}\,b^4-35\,a^8\,b^6+35\,a^6\,b^8-21\,a^4\,b^{10}+7\,a^2\,b^{12}-b^{14}\right)}-\frac{a\,\sin\left(c+d\,x\right)\,\left(-15\,a^{14}+420\,a^{12}\,b^2+26140\,a^{10}\,b^4+52264\,a^8\,b^6+13189\,a^6\,b^8+184\,a^4\,b^{10}-26\,a^2\,b^{12}+4\,b^{14}\right)}{30\,\left(a^2-b^2\right)\,\left(a^{14}-7\,a^{12}\,b^2+21\,a^{10}\,b^4-35\,a^8\,b^6+35\,a^6\,b^8-21\,a^4\,b^{10}+7\,a^2\,b^{12}-b^{14}\right)}}{d\,\left({\sin\left(c+d\,x\right)}^7\,\left(b^7-21\,a^2\,b^5\right)-{\sin\left(c+d\,x\right)}^2\,\left(a^7-21\,a^5\,b^2\right)+{\sin\left(c+d\,x\right)}^4\,\left(35\,a^3\,b^4-21\,a^5\,b^2\right)+{\sin\left(c+d\,x\right)}^5\,\left(21\,a^2\,b^5-35\,a^4\,b^3\right)+a^7-b^7\,{\sin\left(c+d\,x\right)}^9-{\sin\left(c+d\,x\right)}^3\,\left(7\,a^6\,b-35\,a^4\,b^3\right)+{\sin\left(c+d\,x\right)}^6\,\left(7\,a\,b^6-35\,a^3\,b^4\right)-7\,a\,b^6\,{\sin\left(c+d\,x\right)}^8+7\,a^6\,b\,\sin\left(c+d\,x\right)\right)}-\frac{\ln\left(\sin\left(c+d\,x\right)-1\right)\,\left(\frac{2\,b}{{\left(a+b\right)}^9}+\frac{1}{4\,{\left(a+b\right)}^8}\right)}{d}+\frac{\ln\left(a+b\,\sin\left(c+d\,x\right)\right)\,\left(\frac{2\,b}{{\left(a+b\right)}^9}+\frac{1}{4\,{\left(a+b\right)}^8}+\frac{2\,b}{{\left(a-b\right)}^9}-\frac{1}{4\,{\left(a-b\right)}^8}\right)}{d}+\frac{\ln\left(\sin\left(c+d\,x\right)+1\right)\,\left(a-9\,b\right)}{4\,d\,{\left(a-b\right)}^9}","Not used",1,"((sin(c + d*x)^7*(23*a*b^14 + 1348*a^3*b^12 + 3514*a^5*b^10 + 1252*a^7*b^8 + 7*a^9*b^6))/(2*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) - (420*a^14*b + 15*b^15 - 118*a^2*b^13 + 407*a^4*b^11 - 748*a^6*b^9 + 8177*a^8*b^7 + 28862*a^10*b^5 + 16745*a^12*b^3)/(105*(a^2 - b^2)*(a^14 - b^14 + 7*a^2*b^12 - 21*a^4*b^10 + 35*a^6*b^8 - 35*a^8*b^6 + 21*a^10*b^4 - 7*a^12*b^2)) + (sin(c + d*x)^6*(7384*a^4*b^11 - 681*a^2*b^13 - 18*b^15 + 26194*a^6*b^9 + 10066*a^8*b^7 + 63*a^10*b^5))/(6*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) + (sin(c + d*x)^8*(9*b^15 + 244*a^2*b^13 + 574*a^4*b^11 + 196*a^6*b^9 + a^8*b^7))/(2*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) + (sin(c + d*x)^5*(160*a^5*b^10 - 3951*a^3*b^12 - 66*a*b^14 + 32254*a^7*b^8 + 14506*a^9*b^6 + 105*a^11*b^4))/(6*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) + (sin(c + d*x)^4*(18*b^13 + 456*a^2*b^11 + 45119*a^4*b^9 + 143647*a^6*b^7 + 59835*a^8*b^5 + 525*a^10*b^3))/(30*(a^14 - b^14 + 7*a^2*b^12 - 21*a^4*b^10 + 35*a^6*b^8 - 35*a^8*b^6 + 21*a^10*b^4 - 7*a^12*b^2)) - (sin(c + d*x)^2*(54*b^15 - 735*a^14*b - 310*a^2*b^13 + 3050*a^4*b^11 + 252845*a^6*b^9 + 919070*a^8*b^7 + 361856*a^10*b^5 - 30550*a^12*b^3))/(210*(a^2 - b^2)*(a^14 - b^14 + 7*a^2*b^12 - 21*a^4*b^10 + 35*a^6*b^8 - 35*a^8*b^6 + 21*a^10*b^4 - 7*a^12*b^2)) - (sin(c + d*x)^3*(26*a*b^14 + 386*a^3*b^12 + 53641*a^5*b^10 + 166336*a^7*b^8 + 20896*a^9*b^6 - 25930*a^11*b^4 - 315*a^13*b^2))/(30*(a^2 - b^2)*(a^14 - b^14 + 7*a^2*b^12 - 21*a^4*b^10 + 35*a^6*b^8 - 35*a^8*b^6 + 21*a^10*b^4 - 7*a^12*b^2)) - (a*sin(c + d*x)*(4*b^14 - 15*a^14 - 26*a^2*b^12 + 184*a^4*b^10 + 13189*a^6*b^8 + 52264*a^8*b^6 + 26140*a^10*b^4 + 420*a^12*b^2))/(30*(a^2 - b^2)*(a^14 - b^14 + 7*a^2*b^12 - 21*a^4*b^10 + 35*a^6*b^8 - 35*a^8*b^6 + 21*a^10*b^4 - 7*a^12*b^2)))/(d*(sin(c + d*x)^7*(b^7 - 21*a^2*b^5) - sin(c + d*x)^2*(a^7 - 21*a^5*b^2) + sin(c + d*x)^4*(35*a^3*b^4 - 21*a^5*b^2) + sin(c + d*x)^5*(21*a^2*b^5 - 35*a^4*b^3) + a^7 - b^7*sin(c + d*x)^9 - sin(c + d*x)^3*(7*a^6*b - 35*a^4*b^3) + sin(c + d*x)^6*(7*a*b^6 - 35*a^3*b^4) - 7*a*b^6*sin(c + d*x)^8 + 7*a^6*b*sin(c + d*x))) - (log(sin(c + d*x) - 1)*((2*b)/(a + b)^9 + 1/(4*(a + b)^8)))/d + (log(a + b*sin(c + d*x))*((2*b)/(a + b)^9 + 1/(4*(a + b)^8) + (2*b)/(a - b)^9 - 1/(4*(a - b)^8)))/d + (log(sin(c + d*x) + 1)*(a - 9*b))/(4*d*(a - b)^9)","B"
467,1,9647,491,32.217063,"\text{Not used}","int(cos(c + d*x)^8/(a + b*sin(c + d*x))^8,x)","\frac{2\,\mathrm{atan}\left(\frac{\frac{\frac{\frac{\left(\frac{\left(32\,a^{14}\,b^{23}-192\,a^{12}\,b^{25}+480\,a^{10}\,b^{27}-640\,a^8\,b^{29}+480\,a^6\,b^{31}-192\,a^4\,b^{33}+32\,a^2\,b^{35}\right)\,1{}\mathrm{i}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^{23}+3840\,a^{13}\,b^{25}-12288\,a^{11}\,b^{27}+21760\,a^9\,b^{29}-23040\,a^7\,b^{31}+14592\,a^5\,b^{33}-5120\,a^3\,b^{35}+768\,a\,b^{37}\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}\right)\,1{}\mathrm{i}}{b^8}+\frac{\left(16\,a^{13}\,b^{16}-100\,a^{11}\,b^{18}+262\,a^9\,b^{20}-378\,a^7\,b^{22}+322\,a^5\,b^{24}-154\,a^3\,b^{26}+32\,a\,b^{28}\right)\,1{}\mathrm{i}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{14}\,b^{16}-3328\,a^{12}\,b^{18}+9152\,a^{10}\,b^{20}-13728\,a^8\,b^{22}+11872\,a^6\,b^{24}-5600\,a^4\,b^{26}+1120\,a^2\,b^{28}\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}}{b^8}+\frac{32\,a^{14}\,b^7-192\,a^{12}\,b^9+480\,a^{10}\,b^{11}-640\,a^8\,b^{13}+480\,a^6\,b^{15}-192\,a^4\,b^{17}+32\,a^2\,b^{19}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^7+3840\,a^{13}\,b^9-12288\,a^{11}\,b^{11}+21760\,a^9\,b^{13}-22900\,a^7\,b^{15}+14116\,a^5\,b^{17}-4553\,a^3\,b^{19}+512\,a\,b^{21}\right)}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}}{b^8}+\frac{\frac{32\,a^{14}\,b^7-192\,a^{12}\,b^9+480\,a^{10}\,b^{11}-640\,a^8\,b^{13}+480\,a^6\,b^{15}-192\,a^4\,b^{17}+32\,a^2\,b^{19}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}-\frac{-\frac{\left(\frac{\left(32\,a^{14}\,b^{23}-192\,a^{12}\,b^{25}+480\,a^{10}\,b^{27}-640\,a^8\,b^{29}+480\,a^6\,b^{31}-192\,a^4\,b^{33}+32\,a^2\,b^{35}\right)\,1{}\mathrm{i}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^{23}+3840\,a^{13}\,b^{25}-12288\,a^{11}\,b^{27}+21760\,a^9\,b^{29}-23040\,a^7\,b^{31}+14592\,a^5\,b^{33}-5120\,a^3\,b^{35}+768\,a\,b^{37}\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}\right)\,1{}\mathrm{i}}{b^8}+\frac{\left(16\,a^{13}\,b^{16}-100\,a^{11}\,b^{18}+262\,a^9\,b^{20}-378\,a^7\,b^{22}+322\,a^5\,b^{24}-154\,a^3\,b^{26}+32\,a\,b^{28}\right)\,1{}\mathrm{i}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{14}\,b^{16}-3328\,a^{12}\,b^{18}+9152\,a^{10}\,b^{20}-13728\,a^8\,b^{22}+11872\,a^6\,b^{24}-5600\,a^4\,b^{26}+1120\,a^2\,b^{28}\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}}{b^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^7+3840\,a^{13}\,b^9-12288\,a^{11}\,b^{11}+21760\,a^9\,b^{13}-22900\,a^7\,b^{15}+14116\,a^5\,b^{17}-4553\,a^3\,b^{19}+512\,a\,b^{21}\right)}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}}{b^8}}{\frac{32\,a^{13}-200\,a^{11}\,b^2+524\,a^9\,b^4-721\,a^7\,b^6+525\,a^5\,b^8-\frac{665\,a^3\,b^{10}}{4}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}-\frac{-\frac{\left(-\frac{\left(\frac{\left(32\,a^{14}\,b^{23}-192\,a^{12}\,b^{25}+480\,a^{10}\,b^{27}-640\,a^8\,b^{29}+480\,a^6\,b^{31}-192\,a^4\,b^{33}+32\,a^2\,b^{35}\right)\,1{}\mathrm{i}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^{23}+3840\,a^{13}\,b^{25}-12288\,a^{11}\,b^{27}+21760\,a^9\,b^{29}-23040\,a^7\,b^{31}+14592\,a^5\,b^{33}-5120\,a^3\,b^{35}+768\,a\,b^{37}\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}\right)\,1{}\mathrm{i}}{b^8}+\frac{\left(16\,a^{13}\,b^{16}-100\,a^{11}\,b^{18}+262\,a^9\,b^{20}-378\,a^7\,b^{22}+322\,a^5\,b^{24}-154\,a^3\,b^{26}+32\,a\,b^{28}\right)\,1{}\mathrm{i}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{14}\,b^{16}-3328\,a^{12}\,b^{18}+9152\,a^{10}\,b^{20}-13728\,a^8\,b^{22}+11872\,a^6\,b^{24}-5600\,a^4\,b^{26}+1120\,a^2\,b^{28}\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}\right)\,1{}\mathrm{i}}{b^8}+\frac{\left(32\,a^{14}\,b^7-192\,a^{12}\,b^9+480\,a^{10}\,b^{11}-640\,a^8\,b^{13}+480\,a^6\,b^{15}-192\,a^4\,b^{17}+32\,a^2\,b^{19}\right)\,1{}\mathrm{i}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^7+3840\,a^{13}\,b^9-12288\,a^{11}\,b^{11}+21760\,a^9\,b^{13}-22900\,a^7\,b^{15}+14116\,a^5\,b^{17}-4553\,a^3\,b^{19}+512\,a\,b^{21}\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}}{b^8}+\frac{\frac{\left(\frac{\left(\frac{\left(32\,a^{14}\,b^{23}-192\,a^{12}\,b^{25}+480\,a^{10}\,b^{27}-640\,a^8\,b^{29}+480\,a^6\,b^{31}-192\,a^4\,b^{33}+32\,a^2\,b^{35}\right)\,1{}\mathrm{i}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^{23}+3840\,a^{13}\,b^{25}-12288\,a^{11}\,b^{27}+21760\,a^9\,b^{29}-23040\,a^7\,b^{31}+14592\,a^5\,b^{33}-5120\,a^3\,b^{35}+768\,a\,b^{37}\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}\right)\,1{}\mathrm{i}}{b^8}+\frac{\left(16\,a^{13}\,b^{16}-100\,a^{11}\,b^{18}+262\,a^9\,b^{20}-378\,a^7\,b^{22}+322\,a^5\,b^{24}-154\,a^3\,b^{26}+32\,a\,b^{28}\right)\,1{}\mathrm{i}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{14}\,b^{16}-3328\,a^{12}\,b^{18}+9152\,a^{10}\,b^{20}-13728\,a^8\,b^{22}+11872\,a^6\,b^{24}-5600\,a^4\,b^{26}+1120\,a^2\,b^{28}\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}\right)\,1{}\mathrm{i}}{b^8}+\frac{\left(32\,a^{14}\,b^7-192\,a^{12}\,b^9+480\,a^{10}\,b^{11}-640\,a^8\,b^{13}+480\,a^6\,b^{15}-192\,a^4\,b^{17}+32\,a^2\,b^{19}\right)\,1{}\mathrm{i}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^7+3840\,a^{13}\,b^9-12288\,a^{11}\,b^{11}+21760\,a^9\,b^{13}-22900\,a^7\,b^{15}+14116\,a^5\,b^{17}-4553\,a^3\,b^{19}+512\,a\,b^{21}\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}}{b^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{14}-3328\,a^{12}\,b^2+9152\,a^{10}\,b^4-13728\,a^8\,b^6+11872\,a^6\,b^8-5600\,a^4\,b^{10}+1120\,a^2\,b^{12}\right)}{4\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}}\right)}{b^8\,d}+\frac{\frac{1680\,a^{12}-4760\,a^{10}\,b^2+4326\,a^8\,b^4-1143\,a^6\,b^6+958\,a^4\,b^8-776\,a^2\,b^{10}+240\,b^{12}}{840\,b^7\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3240\,a^{12}-9190\,a^{10}\,b^2+8367\,a^8\,b^4-2046\,a^6\,b^6+1196\,a^4\,b^8-832\,a^2\,b^{10}+240\,b^{12}\right)}{120\,a\,b^6\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(1200\,a^{18}+26080\,a^{16}\,b^2-19080\,a^{14}\,b^4-80730\,a^{12}\,b^6+87285\,a^{10}\,b^8+21208\,a^8\,b^{10}+5316\,a^6\,b^{12}-12016\,a^4\,b^{14}+992\,a^2\,b^{16}+1920\,b^{18}\right)}{30\,a^6\,b^7\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(3600\,a^{18}+73480\,a^{16}\,b^2-70050\,a^{14}\,b^4-198555\,a^{12}\,b^6+252090\,a^{10}\,b^8+28792\,a^8\,b^{10}+43584\,a^6\,b^{12}-48064\,a^4\,b^{14}+3968\,a^2\,b^{16}+7680\,b^{18}\right)}{120\,a^6\,b^7\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(144\,a^{16}+2064\,a^{14}\,b^2-4284\,a^{12}\,b^4-224\,a^{10}\,b^6+3949\,a^8\,b^8+528\,a^6\,b^{10}+1392\,a^4\,b^{12}-2384\,a^2\,b^{14}+960\,b^{16}\right)}{12\,a^4\,b^7\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(17400\,a^{16}+34110\,a^{14}\,b^2-152515\,a^{12}\,b^4+93770\,a^{10}\,b^6+49308\,a^8\,b^8+30576\,a^6\,b^{10}-12496\,a^4\,b^{12}-18048\,a^2\,b^{14}+11520\,b^{16}\right)}{120\,a^5\,b^6\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3600\,a^{16}+65880\,a^{14}\,b^2-95382\,a^{12}\,b^4-122429\,a^{10}\,b^6+240884\,a^8\,b^8-41568\,a^6\,b^{10}+16880\,a^4\,b^{12}-23840\,a^2\,b^{14}+9600\,b^{16}\right)}{120\,a^4\,b^7\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(33000\,a^{16}+91890\,a^{14}\,b^2-318025\,a^{12}\,b^4+107140\,a^{10}\,b^6+211848\,a^8\,b^8-10304\,a^6\,b^{10}-12496\,a^4\,b^{12}-18048\,a^2\,b^{14}+11520\,b^{16}\right)}{120\,a^5\,b^6\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(16\,a^{14}+56\,a^{12}\,b^2-238\,a^{10}\,b^4+231\,a^8\,b^6-96\,a^6\,b^8+288\,a^4\,b^{10}-288\,a^2\,b^{12}+96\,b^{14}\right)}{8\,a^2\,b^7\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(384\,a^{14}-276\,a^{12}\,b^2-1252\,a^{10}\,b^4+1697\,a^8\,b^6-384\,a^6\,b^8+1344\,a^4\,b^{10}-1408\,a^2\,b^{12}+480\,b^{14}\right)}{12\,a^3\,b^6\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(720\,a^{14}+7280\,a^{12}\,b^2-24612\,a^{10}\,b^4+23652\,a^8\,b^6-5659\,a^6\,b^8+3200\,a^4\,b^{10}-2376\,a^2\,b^{12}+720\,b^{14}\right)}{60\,a^2\,b^7\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(8160\,a^{14}+6420\,a^{12}\,b^2-62984\,a^{10}\,b^4+71177\,a^8\,b^6-15192\,a^6\,b^8+7784\,a^4\,b^{10}-7040\,a^2\,b^{12}+2400\,b^{14}\right)}{60\,a^3\,b^6\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(8\,a^{12}-22\,a^{10}\,b^2+19\,a^8\,b^4-16\,a^6\,b^6+48\,a^4\,b^8-48\,a^2\,b^{10}+16\,b^{12}\right)}{8\,a\,b^6\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(35\,a^6+210\,a^4\,b^2+168\,a^2\,b^4+16\,b^6\right)\,\left(1680\,a^{12}-4760\,a^{10}\,b^2+4326\,a^8\,b^4-1143\,a^6\,b^6+958\,a^4\,b^8-776\,a^2\,b^{10}+240\,b^{12}\right)}{210\,a^7\,b^6\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(210\,a^6\,b+1120\,a^4\,b^3+672\,a^2\,b^5\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(210\,a^6\,b+1120\,a^4\,b^3+672\,a^2\,b^5\right)+a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(84\,a^6\,b+280\,a^4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(84\,a^6\,b+280\,a^4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(35\,a^7+840\,a^5\,b^2+1680\,a^3\,b^4+448\,a\,b^6\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(35\,a^7+840\,a^5\,b^2+1680\,a^3\,b^4+448\,a\,b^6\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(280\,a^6\,b+1680\,a^4\,b^3+1344\,a^2\,b^5+128\,b^7\right)+a^7+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(21\,a^7+420\,a^5\,b^2+560\,a^3\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(21\,a^7+420\,a^5\,b^2+560\,a^3\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(7\,a^7+84\,a^5\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(7\,a^7+84\,a^5\,b^2\right)+14\,a^6\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+14\,a^6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\right)}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{32\,a^{14}\,b^7-192\,a^{12}\,b^9+480\,a^{10}\,b^{11}-640\,a^8\,b^{13}+480\,a^6\,b^{15}-192\,a^4\,b^{17}+32\,a^2\,b^{19}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^7+3840\,a^{13}\,b^9-12288\,a^{11}\,b^{11}+21760\,a^9\,b^{13}-22900\,a^7\,b^{15}+14116\,a^5\,b^{17}-4553\,a^3\,b^{19}+512\,a\,b^{21}\right)}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}-\frac{a\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{16\,a^{13}\,b^{16}-100\,a^{11}\,b^{18}+262\,a^9\,b^{20}-378\,a^7\,b^{22}+322\,a^5\,b^{24}-154\,a^3\,b^{26}+32\,a\,b^{28}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{14}\,b^{16}-3328\,a^{12}\,b^{18}+9152\,a^{10}\,b^{20}-13728\,a^8\,b^{22}+11872\,a^6\,b^{24}-5600\,a^4\,b^{26}+1120\,a^2\,b^{28}\right)}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}-\frac{a\,\left(\frac{32\,a^{14}\,b^{23}-192\,a^{12}\,b^{25}+480\,a^{10}\,b^{27}-640\,a^8\,b^{29}+480\,a^6\,b^{31}-192\,a^4\,b^{33}+32\,a^2\,b^{35}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^{23}+3840\,a^{13}\,b^{25}-12288\,a^{11}\,b^{27}+21760\,a^9\,b^{29}-23040\,a^7\,b^{31}+14592\,a^5\,b^{33}-5120\,a^3\,b^{35}+768\,a\,b^{37}\right)}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(16\,a^6-56\,a^4\,b^2+70\,a^2\,b^4-35\,b^6\right)}{16\,\left(-a^{14}\,b^8+7\,a^{12}\,b^{10}-21\,a^{10}\,b^{12}+35\,a^8\,b^{14}-35\,a^6\,b^{16}+21\,a^4\,b^{18}-7\,a^2\,b^{20}+b^{22}\right)}\right)\,\left(16\,a^6-56\,a^4\,b^2+70\,a^2\,b^4-35\,b^6\right)}{16\,\left(-a^{14}\,b^8+7\,a^{12}\,b^{10}-21\,a^{10}\,b^{12}+35\,a^8\,b^{14}-35\,a^6\,b^{16}+21\,a^4\,b^{18}-7\,a^2\,b^{20}+b^{22}\right)}\right)\,\left(16\,a^6-56\,a^4\,b^2+70\,a^2\,b^4-35\,b^6\right)\,1{}\mathrm{i}}{16\,\left(-a^{14}\,b^8+7\,a^{12}\,b^{10}-21\,a^{10}\,b^{12}+35\,a^8\,b^{14}-35\,a^6\,b^{16}+21\,a^4\,b^{18}-7\,a^2\,b^{20}+b^{22}\right)}+\frac{a\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{32\,a^{14}\,b^7-192\,a^{12}\,b^9+480\,a^{10}\,b^{11}-640\,a^8\,b^{13}+480\,a^6\,b^{15}-192\,a^4\,b^{17}+32\,a^2\,b^{19}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^7+3840\,a^{13}\,b^9-12288\,a^{11}\,b^{11}+21760\,a^9\,b^{13}-22900\,a^7\,b^{15}+14116\,a^5\,b^{17}-4553\,a^3\,b^{19}+512\,a\,b^{21}\right)}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}+\frac{a\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{16\,a^{13}\,b^{16}-100\,a^{11}\,b^{18}+262\,a^9\,b^{20}-378\,a^7\,b^{22}+322\,a^5\,b^{24}-154\,a^3\,b^{26}+32\,a\,b^{28}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{14}\,b^{16}-3328\,a^{12}\,b^{18}+9152\,a^{10}\,b^{20}-13728\,a^8\,b^{22}+11872\,a^6\,b^{24}-5600\,a^4\,b^{26}+1120\,a^2\,b^{28}\right)}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}+\frac{a\,\left(\frac{32\,a^{14}\,b^{23}-192\,a^{12}\,b^{25}+480\,a^{10}\,b^{27}-640\,a^8\,b^{29}+480\,a^6\,b^{31}-192\,a^4\,b^{33}+32\,a^2\,b^{35}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^{23}+3840\,a^{13}\,b^{25}-12288\,a^{11}\,b^{27}+21760\,a^9\,b^{29}-23040\,a^7\,b^{31}+14592\,a^5\,b^{33}-5120\,a^3\,b^{35}+768\,a\,b^{37}\right)}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(16\,a^6-56\,a^4\,b^2+70\,a^2\,b^4-35\,b^6\right)}{16\,\left(-a^{14}\,b^8+7\,a^{12}\,b^{10}-21\,a^{10}\,b^{12}+35\,a^8\,b^{14}-35\,a^6\,b^{16}+21\,a^4\,b^{18}-7\,a^2\,b^{20}+b^{22}\right)}\right)\,\left(16\,a^6-56\,a^4\,b^2+70\,a^2\,b^4-35\,b^6\right)}{16\,\left(-a^{14}\,b^8+7\,a^{12}\,b^{10}-21\,a^{10}\,b^{12}+35\,a^8\,b^{14}-35\,a^6\,b^{16}+21\,a^4\,b^{18}-7\,a^2\,b^{20}+b^{22}\right)}\right)\,\left(16\,a^6-56\,a^4\,b^2+70\,a^2\,b^4-35\,b^6\right)\,1{}\mathrm{i}}{16\,\left(-a^{14}\,b^8+7\,a^{12}\,b^{10}-21\,a^{10}\,b^{12}+35\,a^8\,b^{14}-35\,a^6\,b^{16}+21\,a^4\,b^{18}-7\,a^2\,b^{20}+b^{22}\right)}}{\frac{32\,a^{13}-200\,a^{11}\,b^2+524\,a^9\,b^4-721\,a^7\,b^6+525\,a^5\,b^8-\frac{665\,a^3\,b^{10}}{4}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{14}-3328\,a^{12}\,b^2+9152\,a^{10}\,b^4-13728\,a^8\,b^6+11872\,a^6\,b^8-5600\,a^4\,b^{10}+1120\,a^2\,b^{12}\right)}{4\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}-\frac{a\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{32\,a^{14}\,b^7-192\,a^{12}\,b^9+480\,a^{10}\,b^{11}-640\,a^8\,b^{13}+480\,a^6\,b^{15}-192\,a^4\,b^{17}+32\,a^2\,b^{19}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^7+3840\,a^{13}\,b^9-12288\,a^{11}\,b^{11}+21760\,a^9\,b^{13}-22900\,a^7\,b^{15}+14116\,a^5\,b^{17}-4553\,a^3\,b^{19}+512\,a\,b^{21}\right)}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}-\frac{a\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{16\,a^{13}\,b^{16}-100\,a^{11}\,b^{18}+262\,a^9\,b^{20}-378\,a^7\,b^{22}+322\,a^5\,b^{24}-154\,a^3\,b^{26}+32\,a\,b^{28}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{14}\,b^{16}-3328\,a^{12}\,b^{18}+9152\,a^{10}\,b^{20}-13728\,a^8\,b^{22}+11872\,a^6\,b^{24}-5600\,a^4\,b^{26}+1120\,a^2\,b^{28}\right)}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}-\frac{a\,\left(\frac{32\,a^{14}\,b^{23}-192\,a^{12}\,b^{25}+480\,a^{10}\,b^{27}-640\,a^8\,b^{29}+480\,a^6\,b^{31}-192\,a^4\,b^{33}+32\,a^2\,b^{35}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^{23}+3840\,a^{13}\,b^{25}-12288\,a^{11}\,b^{27}+21760\,a^9\,b^{29}-23040\,a^7\,b^{31}+14592\,a^5\,b^{33}-5120\,a^3\,b^{35}+768\,a\,b^{37}\right)}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(16\,a^6-56\,a^4\,b^2+70\,a^2\,b^4-35\,b^6\right)}{16\,\left(-a^{14}\,b^8+7\,a^{12}\,b^{10}-21\,a^{10}\,b^{12}+35\,a^8\,b^{14}-35\,a^6\,b^{16}+21\,a^4\,b^{18}-7\,a^2\,b^{20}+b^{22}\right)}\right)\,\left(16\,a^6-56\,a^4\,b^2+70\,a^2\,b^4-35\,b^6\right)}{16\,\left(-a^{14}\,b^8+7\,a^{12}\,b^{10}-21\,a^{10}\,b^{12}+35\,a^8\,b^{14}-35\,a^6\,b^{16}+21\,a^4\,b^{18}-7\,a^2\,b^{20}+b^{22}\right)}\right)\,\left(16\,a^6-56\,a^4\,b^2+70\,a^2\,b^4-35\,b^6\right)}{16\,\left(-a^{14}\,b^8+7\,a^{12}\,b^{10}-21\,a^{10}\,b^{12}+35\,a^8\,b^{14}-35\,a^6\,b^{16}+21\,a^4\,b^{18}-7\,a^2\,b^{20}+b^{22}\right)}+\frac{a\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{32\,a^{14}\,b^7-192\,a^{12}\,b^9+480\,a^{10}\,b^{11}-640\,a^8\,b^{13}+480\,a^6\,b^{15}-192\,a^4\,b^{17}+32\,a^2\,b^{19}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^7+3840\,a^{13}\,b^9-12288\,a^{11}\,b^{11}+21760\,a^9\,b^{13}-22900\,a^7\,b^{15}+14116\,a^5\,b^{17}-4553\,a^3\,b^{19}+512\,a\,b^{21}\right)}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}+\frac{a\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{16\,a^{13}\,b^{16}-100\,a^{11}\,b^{18}+262\,a^9\,b^{20}-378\,a^7\,b^{22}+322\,a^5\,b^{24}-154\,a^3\,b^{26}+32\,a\,b^{28}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{14}\,b^{16}-3328\,a^{12}\,b^{18}+9152\,a^{10}\,b^{20}-13728\,a^8\,b^{22}+11872\,a^6\,b^{24}-5600\,a^4\,b^{26}+1120\,a^2\,b^{28}\right)}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}+\frac{a\,\left(\frac{32\,a^{14}\,b^{23}-192\,a^{12}\,b^{25}+480\,a^{10}\,b^{27}-640\,a^8\,b^{29}+480\,a^6\,b^{31}-192\,a^4\,b^{33}+32\,a^2\,b^{35}}{a^{12}\,b^{20}-6\,a^{10}\,b^{22}+15\,a^8\,b^{24}-20\,a^6\,b^{26}+15\,a^4\,b^{28}-6\,a^2\,b^{30}+b^{32}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-512\,a^{15}\,b^{23}+3840\,a^{13}\,b^{25}-12288\,a^{11}\,b^{27}+21760\,a^9\,b^{29}-23040\,a^7\,b^{31}+14592\,a^5\,b^{33}-5120\,a^3\,b^{35}+768\,a\,b^{37}\right)}{8\,\left(a^{12}\,b^{21}-6\,a^{10}\,b^{23}+15\,a^8\,b^{25}-20\,a^6\,b^{27}+15\,a^4\,b^{29}-6\,a^2\,b^{31}+b^{33}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(16\,a^6-56\,a^4\,b^2+70\,a^2\,b^4-35\,b^6\right)}{16\,\left(-a^{14}\,b^8+7\,a^{12}\,b^{10}-21\,a^{10}\,b^{12}+35\,a^8\,b^{14}-35\,a^6\,b^{16}+21\,a^4\,b^{18}-7\,a^2\,b^{20}+b^{22}\right)}\right)\,\left(16\,a^6-56\,a^4\,b^2+70\,a^2\,b^4-35\,b^6\right)}{16\,\left(-a^{14}\,b^8+7\,a^{12}\,b^{10}-21\,a^{10}\,b^{12}+35\,a^8\,b^{14}-35\,a^6\,b^{16}+21\,a^4\,b^{18}-7\,a^2\,b^{20}+b^{22}\right)}\right)\,\left(16\,a^6-56\,a^4\,b^2+70\,a^2\,b^4-35\,b^6\right)}{16\,\left(-a^{14}\,b^8+7\,a^{12}\,b^{10}-21\,a^{10}\,b^{12}+35\,a^8\,b^{14}-35\,a^6\,b^{16}+21\,a^4\,b^{18}-7\,a^2\,b^{20}+b^{22}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(16\,a^6-56\,a^4\,b^2+70\,a^2\,b^4-35\,b^6\right)\,1{}\mathrm{i}}{8\,d\,\left(-a^{14}\,b^8+7\,a^{12}\,b^{10}-21\,a^{10}\,b^{12}+35\,a^8\,b^{14}-35\,a^6\,b^{16}+21\,a^4\,b^{18}-7\,a^2\,b^{20}+b^{22}\right)}","Not used",1,"(2*atan((((((((32*a^2*b^35 - 192*a^4*b^33 + 480*a^6*b^31 - 640*a^8*b^29 + 480*a^10*b^27 - 192*a^12*b^25 + 32*a^14*b^23)*1i)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(768*a*b^37 - 5120*a^3*b^35 + 14592*a^5*b^33 - 23040*a^7*b^31 + 21760*a^9*b^29 - 12288*a^11*b^27 + 3840*a^13*b^25 - 512*a^15*b^23)*1i)/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))*1i)/b^8 + ((32*a*b^28 - 154*a^3*b^26 + 322*a^5*b^24 - 378*a^7*b^22 + 262*a^9*b^20 - 100*a^11*b^18 + 16*a^13*b^16)*1i)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(1120*a^2*b^28 - 5600*a^4*b^26 + 11872*a^6*b^24 - 13728*a^8*b^22 + 9152*a^10*b^20 - 3328*a^12*b^18 + 512*a^14*b^16)*1i)/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))/b^8 + (32*a^2*b^19 - 192*a^4*b^17 + 480*a^6*b^15 - 640*a^8*b^13 + 480*a^10*b^11 - 192*a^12*b^9 + 32*a^14*b^7)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(512*a*b^21 - 4553*a^3*b^19 + 14116*a^5*b^17 - 22900*a^7*b^15 + 21760*a^9*b^13 - 12288*a^11*b^11 + 3840*a^13*b^9 - 512*a^15*b^7))/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))/b^8 + ((32*a^2*b^19 - 192*a^4*b^17 + 480*a^6*b^15 - 640*a^8*b^13 + 480*a^10*b^11 - 192*a^12*b^9 + 32*a^14*b^7)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) - (((32*a*b^28 - 154*a^3*b^26 + 322*a^5*b^24 - 378*a^7*b^22 + 262*a^9*b^20 - 100*a^11*b^18 + 16*a^13*b^16)*1i)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) - ((((32*a^2*b^35 - 192*a^4*b^33 + 480*a^6*b^31 - 640*a^8*b^29 + 480*a^10*b^27 - 192*a^12*b^25 + 32*a^14*b^23)*1i)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(768*a*b^37 - 5120*a^3*b^35 + 14592*a^5*b^33 - 23040*a^7*b^31 + 21760*a^9*b^29 - 12288*a^11*b^27 + 3840*a^13*b^25 - 512*a^15*b^23)*1i)/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))*1i)/b^8 + (tan(c/2 + (d*x)/2)*(1120*a^2*b^28 - 5600*a^4*b^26 + 11872*a^6*b^24 - 13728*a^8*b^22 + 9152*a^10*b^20 - 3328*a^12*b^18 + 512*a^14*b^16)*1i)/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))/b^8 + (tan(c/2 + (d*x)/2)*(512*a*b^21 - 4553*a^3*b^19 + 14116*a^5*b^17 - 22900*a^7*b^15 + 21760*a^9*b^13 - 12288*a^11*b^11 + 3840*a^13*b^9 - 512*a^15*b^7))/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))/b^8)/((32*a^13 - (665*a^3*b^10)/4 + 525*a^5*b^8 - 721*a^7*b^6 + 524*a^9*b^4 - 200*a^11*b^2)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) - (((32*a^2*b^19 - 192*a^4*b^17 + 480*a^6*b^15 - 640*a^8*b^13 + 480*a^10*b^11 - 192*a^12*b^9 + 32*a^14*b^7)*1i)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) - ((((32*a*b^28 - 154*a^3*b^26 + 322*a^5*b^24 - 378*a^7*b^22 + 262*a^9*b^20 - 100*a^11*b^18 + 16*a^13*b^16)*1i)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) - ((((32*a^2*b^35 - 192*a^4*b^33 + 480*a^6*b^31 - 640*a^8*b^29 + 480*a^10*b^27 - 192*a^12*b^25 + 32*a^14*b^23)*1i)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(768*a*b^37 - 5120*a^3*b^35 + 14592*a^5*b^33 - 23040*a^7*b^31 + 21760*a^9*b^29 - 12288*a^11*b^27 + 3840*a^13*b^25 - 512*a^15*b^23)*1i)/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))*1i)/b^8 + (tan(c/2 + (d*x)/2)*(1120*a^2*b^28 - 5600*a^4*b^26 + 11872*a^6*b^24 - 13728*a^8*b^22 + 9152*a^10*b^20 - 3328*a^12*b^18 + 512*a^14*b^16)*1i)/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))*1i)/b^8 + (tan(c/2 + (d*x)/2)*(512*a*b^21 - 4553*a^3*b^19 + 14116*a^5*b^17 - 22900*a^7*b^15 + 21760*a^9*b^13 - 12288*a^11*b^11 + 3840*a^13*b^9 - 512*a^15*b^7)*1i)/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))/b^8 + (((((((32*a^2*b^35 - 192*a^4*b^33 + 480*a^6*b^31 - 640*a^8*b^29 + 480*a^10*b^27 - 192*a^12*b^25 + 32*a^14*b^23)*1i)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(768*a*b^37 - 5120*a^3*b^35 + 14592*a^5*b^33 - 23040*a^7*b^31 + 21760*a^9*b^29 - 12288*a^11*b^27 + 3840*a^13*b^25 - 512*a^15*b^23)*1i)/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))*1i)/b^8 + ((32*a*b^28 - 154*a^3*b^26 + 322*a^5*b^24 - 378*a^7*b^22 + 262*a^9*b^20 - 100*a^11*b^18 + 16*a^13*b^16)*1i)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(1120*a^2*b^28 - 5600*a^4*b^26 + 11872*a^6*b^24 - 13728*a^8*b^22 + 9152*a^10*b^20 - 3328*a^12*b^18 + 512*a^14*b^16)*1i)/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))*1i)/b^8 + ((32*a^2*b^19 - 192*a^4*b^17 + 480*a^6*b^15 - 640*a^8*b^13 + 480*a^10*b^11 - 192*a^12*b^9 + 32*a^14*b^7)*1i)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(512*a*b^21 - 4553*a^3*b^19 + 14116*a^5*b^17 - 22900*a^7*b^15 + 21760*a^9*b^13 - 12288*a^11*b^11 + 3840*a^13*b^9 - 512*a^15*b^7)*1i)/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))/b^8 + (tan(c/2 + (d*x)/2)*(512*a^14 + 1120*a^2*b^12 - 5600*a^4*b^10 + 11872*a^6*b^8 - 13728*a^8*b^6 + 9152*a^10*b^4 - 3328*a^12*b^2))/(4*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))))/(b^8*d) + ((1680*a^12 + 240*b^12 - 776*a^2*b^10 + 958*a^4*b^8 - 1143*a^6*b^6 + 4326*a^8*b^4 - 4760*a^10*b^2)/(840*b^7*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)*(3240*a^12 + 240*b^12 - 832*a^2*b^10 + 1196*a^4*b^8 - 2046*a^6*b^6 + 8367*a^8*b^4 - 9190*a^10*b^2))/(120*a*b^6*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^6*(1200*a^18 + 1920*b^18 + 992*a^2*b^16 - 12016*a^4*b^14 + 5316*a^6*b^12 + 21208*a^8*b^10 + 87285*a^10*b^8 - 80730*a^12*b^6 - 19080*a^14*b^4 + 26080*a^16*b^2))/(30*a^6*b^7*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^8*(3600*a^18 + 7680*b^18 + 3968*a^2*b^16 - 48064*a^4*b^14 + 43584*a^6*b^12 + 28792*a^8*b^10 + 252090*a^10*b^8 - 198555*a^12*b^6 - 70050*a^14*b^4 + 73480*a^16*b^2))/(120*a^6*b^7*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^10*(144*a^16 + 960*b^16 - 2384*a^2*b^14 + 1392*a^4*b^12 + 528*a^6*b^10 + 3949*a^8*b^8 - 224*a^10*b^6 - 4284*a^12*b^4 + 2064*a^14*b^2))/(12*a^4*b^7*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^9*(17400*a^16 + 11520*b^16 - 18048*a^2*b^14 - 12496*a^4*b^12 + 30576*a^6*b^10 + 49308*a^8*b^8 + 93770*a^10*b^6 - 152515*a^12*b^4 + 34110*a^14*b^2))/(120*a^5*b^6*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^4*(3600*a^16 + 9600*b^16 - 23840*a^2*b^14 + 16880*a^4*b^12 - 41568*a^6*b^10 + 240884*a^8*b^8 - 122429*a^10*b^6 - 95382*a^12*b^4 + 65880*a^14*b^2))/(120*a^4*b^7*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^5*(33000*a^16 + 11520*b^16 - 18048*a^2*b^14 - 12496*a^4*b^12 - 10304*a^6*b^10 + 211848*a^8*b^8 + 107140*a^10*b^6 - 318025*a^12*b^4 + 91890*a^14*b^2))/(120*a^5*b^6*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^12*(16*a^14 + 96*b^14 - 288*a^2*b^12 + 288*a^4*b^10 - 96*a^6*b^8 + 231*a^8*b^6 - 238*a^10*b^4 + 56*a^12*b^2))/(8*a^2*b^7*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^11*(384*a^14 + 480*b^14 - 1408*a^2*b^12 + 1344*a^4*b^10 - 384*a^6*b^8 + 1697*a^8*b^6 - 1252*a^10*b^4 - 276*a^12*b^2))/(12*a^3*b^6*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^2*(720*a^14 + 720*b^14 - 2376*a^2*b^12 + 3200*a^4*b^10 - 5659*a^6*b^8 + 23652*a^8*b^6 - 24612*a^10*b^4 + 7280*a^12*b^2))/(60*a^2*b^7*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^3*(8160*a^14 + 2400*b^14 - 7040*a^2*b^12 + 7784*a^4*b^10 - 15192*a^6*b^8 + 71177*a^8*b^6 - 62984*a^10*b^4 + 6420*a^12*b^2))/(60*a^3*b^6*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^13*(8*a^12 + 16*b^12 - 48*a^2*b^10 + 48*a^4*b^8 - 16*a^6*b^6 + 19*a^8*b^4 - 22*a^10*b^2))/(8*a*b^6*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^7*(35*a^6 + 16*b^6 + 168*a^2*b^4 + 210*a^4*b^2)*(1680*a^12 + 240*b^12 - 776*a^2*b^10 + 958*a^4*b^8 - 1143*a^6*b^6 + 4326*a^8*b^4 - 4760*a^10*b^2))/(210*a^7*b^6*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)))/(d*(tan(c/2 + (d*x)/2)^5*(210*a^6*b + 672*a^2*b^5 + 1120*a^4*b^3) + tan(c/2 + (d*x)/2)^9*(210*a^6*b + 672*a^2*b^5 + 1120*a^4*b^3) + a^7*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^3*(84*a^6*b + 280*a^4*b^3) + tan(c/2 + (d*x)/2)^11*(84*a^6*b + 280*a^4*b^3) + tan(c/2 + (d*x)/2)^6*(448*a*b^6 + 35*a^7 + 1680*a^3*b^4 + 840*a^5*b^2) + tan(c/2 + (d*x)/2)^8*(448*a*b^6 + 35*a^7 + 1680*a^3*b^4 + 840*a^5*b^2) + tan(c/2 + (d*x)/2)^7*(280*a^6*b + 128*b^7 + 1344*a^2*b^5 + 1680*a^4*b^3) + a^7 + tan(c/2 + (d*x)/2)^4*(21*a^7 + 560*a^3*b^4 + 420*a^5*b^2) + tan(c/2 + (d*x)/2)^10*(21*a^7 + 560*a^3*b^4 + 420*a^5*b^2) + tan(c/2 + (d*x)/2)^2*(7*a^7 + 84*a^5*b^2) + tan(c/2 + (d*x)/2)^12*(7*a^7 + 84*a^5*b^2) + 14*a^6*b*tan(c/2 + (d*x)/2) + 14*a^6*b*tan(c/2 + (d*x)/2)^13)) + (a*atan(((a*(-(a + b)^7*(a - b)^7)^(1/2)*((32*a^2*b^19 - 192*a^4*b^17 + 480*a^6*b^15 - 640*a^8*b^13 + 480*a^10*b^11 - 192*a^12*b^9 + 32*a^14*b^7)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(512*a*b^21 - 4553*a^3*b^19 + 14116*a^5*b^17 - 22900*a^7*b^15 + 21760*a^9*b^13 - 12288*a^11*b^11 + 3840*a^13*b^9 - 512*a^15*b^7))/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)) - (a*(-(a + b)^7*(a - b)^7)^(1/2)*((32*a*b^28 - 154*a^3*b^26 + 322*a^5*b^24 - 378*a^7*b^22 + 262*a^9*b^20 - 100*a^11*b^18 + 16*a^13*b^16)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(1120*a^2*b^28 - 5600*a^4*b^26 + 11872*a^6*b^24 - 13728*a^8*b^22 + 9152*a^10*b^20 - 3328*a^12*b^18 + 512*a^14*b^16))/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)) - (a*((32*a^2*b^35 - 192*a^4*b^33 + 480*a^6*b^31 - 640*a^8*b^29 + 480*a^10*b^27 - 192*a^12*b^25 + 32*a^14*b^23)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(768*a*b^37 - 5120*a^3*b^35 + 14592*a^5*b^33 - 23040*a^7*b^31 + 21760*a^9*b^29 - 12288*a^11*b^27 + 3840*a^13*b^25 - 512*a^15*b^23))/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))*(-(a + b)^7*(a - b)^7)^(1/2)*(16*a^6 - 35*b^6 + 70*a^2*b^4 - 56*a^4*b^2))/(16*(b^22 - 7*a^2*b^20 + 21*a^4*b^18 - 35*a^6*b^16 + 35*a^8*b^14 - 21*a^10*b^12 + 7*a^12*b^10 - a^14*b^8)))*(16*a^6 - 35*b^6 + 70*a^2*b^4 - 56*a^4*b^2))/(16*(b^22 - 7*a^2*b^20 + 21*a^4*b^18 - 35*a^6*b^16 + 35*a^8*b^14 - 21*a^10*b^12 + 7*a^12*b^10 - a^14*b^8)))*(16*a^6 - 35*b^6 + 70*a^2*b^4 - 56*a^4*b^2)*1i)/(16*(b^22 - 7*a^2*b^20 + 21*a^4*b^18 - 35*a^6*b^16 + 35*a^8*b^14 - 21*a^10*b^12 + 7*a^12*b^10 - a^14*b^8)) + (a*(-(a + b)^7*(a - b)^7)^(1/2)*((32*a^2*b^19 - 192*a^4*b^17 + 480*a^6*b^15 - 640*a^8*b^13 + 480*a^10*b^11 - 192*a^12*b^9 + 32*a^14*b^7)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(512*a*b^21 - 4553*a^3*b^19 + 14116*a^5*b^17 - 22900*a^7*b^15 + 21760*a^9*b^13 - 12288*a^11*b^11 + 3840*a^13*b^9 - 512*a^15*b^7))/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)) + (a*(-(a + b)^7*(a - b)^7)^(1/2)*((32*a*b^28 - 154*a^3*b^26 + 322*a^5*b^24 - 378*a^7*b^22 + 262*a^9*b^20 - 100*a^11*b^18 + 16*a^13*b^16)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(1120*a^2*b^28 - 5600*a^4*b^26 + 11872*a^6*b^24 - 13728*a^8*b^22 + 9152*a^10*b^20 - 3328*a^12*b^18 + 512*a^14*b^16))/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)) + (a*((32*a^2*b^35 - 192*a^4*b^33 + 480*a^6*b^31 - 640*a^8*b^29 + 480*a^10*b^27 - 192*a^12*b^25 + 32*a^14*b^23)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(768*a*b^37 - 5120*a^3*b^35 + 14592*a^5*b^33 - 23040*a^7*b^31 + 21760*a^9*b^29 - 12288*a^11*b^27 + 3840*a^13*b^25 - 512*a^15*b^23))/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))*(-(a + b)^7*(a - b)^7)^(1/2)*(16*a^6 - 35*b^6 + 70*a^2*b^4 - 56*a^4*b^2))/(16*(b^22 - 7*a^2*b^20 + 21*a^4*b^18 - 35*a^6*b^16 + 35*a^8*b^14 - 21*a^10*b^12 + 7*a^12*b^10 - a^14*b^8)))*(16*a^6 - 35*b^6 + 70*a^2*b^4 - 56*a^4*b^2))/(16*(b^22 - 7*a^2*b^20 + 21*a^4*b^18 - 35*a^6*b^16 + 35*a^8*b^14 - 21*a^10*b^12 + 7*a^12*b^10 - a^14*b^8)))*(16*a^6 - 35*b^6 + 70*a^2*b^4 - 56*a^4*b^2)*1i)/(16*(b^22 - 7*a^2*b^20 + 21*a^4*b^18 - 35*a^6*b^16 + 35*a^8*b^14 - 21*a^10*b^12 + 7*a^12*b^10 - a^14*b^8)))/((32*a^13 - (665*a^3*b^10)/4 + 525*a^5*b^8 - 721*a^7*b^6 + 524*a^9*b^4 - 200*a^11*b^2)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(512*a^14 + 1120*a^2*b^12 - 5600*a^4*b^10 + 11872*a^6*b^8 - 13728*a^8*b^6 + 9152*a^10*b^4 - 3328*a^12*b^2))/(4*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)) - (a*(-(a + b)^7*(a - b)^7)^(1/2)*((32*a^2*b^19 - 192*a^4*b^17 + 480*a^6*b^15 - 640*a^8*b^13 + 480*a^10*b^11 - 192*a^12*b^9 + 32*a^14*b^7)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(512*a*b^21 - 4553*a^3*b^19 + 14116*a^5*b^17 - 22900*a^7*b^15 + 21760*a^9*b^13 - 12288*a^11*b^11 + 3840*a^13*b^9 - 512*a^15*b^7))/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)) - (a*(-(a + b)^7*(a - b)^7)^(1/2)*((32*a*b^28 - 154*a^3*b^26 + 322*a^5*b^24 - 378*a^7*b^22 + 262*a^9*b^20 - 100*a^11*b^18 + 16*a^13*b^16)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(1120*a^2*b^28 - 5600*a^4*b^26 + 11872*a^6*b^24 - 13728*a^8*b^22 + 9152*a^10*b^20 - 3328*a^12*b^18 + 512*a^14*b^16))/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)) - (a*((32*a^2*b^35 - 192*a^4*b^33 + 480*a^6*b^31 - 640*a^8*b^29 + 480*a^10*b^27 - 192*a^12*b^25 + 32*a^14*b^23)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(768*a*b^37 - 5120*a^3*b^35 + 14592*a^5*b^33 - 23040*a^7*b^31 + 21760*a^9*b^29 - 12288*a^11*b^27 + 3840*a^13*b^25 - 512*a^15*b^23))/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))*(-(a + b)^7*(a - b)^7)^(1/2)*(16*a^6 - 35*b^6 + 70*a^2*b^4 - 56*a^4*b^2))/(16*(b^22 - 7*a^2*b^20 + 21*a^4*b^18 - 35*a^6*b^16 + 35*a^8*b^14 - 21*a^10*b^12 + 7*a^12*b^10 - a^14*b^8)))*(16*a^6 - 35*b^6 + 70*a^2*b^4 - 56*a^4*b^2))/(16*(b^22 - 7*a^2*b^20 + 21*a^4*b^18 - 35*a^6*b^16 + 35*a^8*b^14 - 21*a^10*b^12 + 7*a^12*b^10 - a^14*b^8)))*(16*a^6 - 35*b^6 + 70*a^2*b^4 - 56*a^4*b^2))/(16*(b^22 - 7*a^2*b^20 + 21*a^4*b^18 - 35*a^6*b^16 + 35*a^8*b^14 - 21*a^10*b^12 + 7*a^12*b^10 - a^14*b^8)) + (a*(-(a + b)^7*(a - b)^7)^(1/2)*((32*a^2*b^19 - 192*a^4*b^17 + 480*a^6*b^15 - 640*a^8*b^13 + 480*a^10*b^11 - 192*a^12*b^9 + 32*a^14*b^7)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(512*a*b^21 - 4553*a^3*b^19 + 14116*a^5*b^17 - 22900*a^7*b^15 + 21760*a^9*b^13 - 12288*a^11*b^11 + 3840*a^13*b^9 - 512*a^15*b^7))/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)) + (a*(-(a + b)^7*(a - b)^7)^(1/2)*((32*a*b^28 - 154*a^3*b^26 + 322*a^5*b^24 - 378*a^7*b^22 + 262*a^9*b^20 - 100*a^11*b^18 + 16*a^13*b^16)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(1120*a^2*b^28 - 5600*a^4*b^26 + 11872*a^6*b^24 - 13728*a^8*b^22 + 9152*a^10*b^20 - 3328*a^12*b^18 + 512*a^14*b^16))/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)) + (a*((32*a^2*b^35 - 192*a^4*b^33 + 480*a^6*b^31 - 640*a^8*b^29 + 480*a^10*b^27 - 192*a^12*b^25 + 32*a^14*b^23)/(b^32 - 6*a^2*b^30 + 15*a^4*b^28 - 20*a^6*b^26 + 15*a^8*b^24 - 6*a^10*b^22 + a^12*b^20) + (tan(c/2 + (d*x)/2)*(768*a*b^37 - 5120*a^3*b^35 + 14592*a^5*b^33 - 23040*a^7*b^31 + 21760*a^9*b^29 - 12288*a^11*b^27 + 3840*a^13*b^25 - 512*a^15*b^23))/(8*(b^33 - 6*a^2*b^31 + 15*a^4*b^29 - 20*a^6*b^27 + 15*a^8*b^25 - 6*a^10*b^23 + a^12*b^21)))*(-(a + b)^7*(a - b)^7)^(1/2)*(16*a^6 - 35*b^6 + 70*a^2*b^4 - 56*a^4*b^2))/(16*(b^22 - 7*a^2*b^20 + 21*a^4*b^18 - 35*a^6*b^16 + 35*a^8*b^14 - 21*a^10*b^12 + 7*a^12*b^10 - a^14*b^8)))*(16*a^6 - 35*b^6 + 70*a^2*b^4 - 56*a^4*b^2))/(16*(b^22 - 7*a^2*b^20 + 21*a^4*b^18 - 35*a^6*b^16 + 35*a^8*b^14 - 21*a^10*b^12 + 7*a^12*b^10 - a^14*b^8)))*(16*a^6 - 35*b^6 + 70*a^2*b^4 - 56*a^4*b^2))/(16*(b^22 - 7*a^2*b^20 + 21*a^4*b^18 - 35*a^6*b^16 + 35*a^8*b^14 - 21*a^10*b^12 + 7*a^12*b^10 - a^14*b^8))))*(-(a + b)^7*(a - b)^7)^(1/2)*(16*a^6 - 35*b^6 + 70*a^2*b^4 - 56*a^4*b^2)*1i)/(8*d*(b^22 - 7*a^2*b^20 + 21*a^4*b^18 - 35*a^6*b^16 + 35*a^8*b^14 - 21*a^10*b^12 + 7*a^12*b^10 - a^14*b^8))","B"
468,1,1868,407,12.465354,"\text{Not used}","int(cos(c + d*x)^6/(a + b*sin(c + d*x))^8,x)","\frac{\frac{279\,a^6\,b-326\,a^4\,b^3+200\,a^2\,b^5-48\,b^7}{168\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(33\,a^8+366\,a^6\,b^2-364\,a^4\,b^4+208\,a^2\,b^6-48\,b^8\right)}{24\,a\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(85\,a^{12}-2950\,a^{10}\,b^2-14820\,a^8\,b^4+10048\,a^6\,b^6+368\,a^4\,b^8-5760\,a^2\,b^{10}+2304\,b^{12}\right)}{24\,a^5\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(85\,a^{12}+5420\,a^{10}\,b^2+20040\,a^8\,b^4-9328\,a^6\,b^6-368\,a^4\,b^8+5760\,a^2\,b^{10}-2304\,b^{12}\right)}{24\,a^5\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(14\,a^{10}-311\,a^8\,b^2-1536\,a^6\,b^4+2624\,a^4\,b^6-1856\,a^2\,b^8+480\,b^{10}\right)}{12\,a^3\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(14\,a^{10}+1363\,a^8\,b^2+2088\,a^6\,b^4-2696\,a^4\,b^6+1856\,a^2\,b^8-480\,b^{10}\right)}{12\,a^3\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(11\,a^8-64\,a^6\,b^2+96\,a^4\,b^4-64\,a^2\,b^6+16\,b^8\right)}{8\,a\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(240\,a^{12}\,b+4375\,a^{10}\,b^3+3920\,a^8\,b^5-4548\,a^6\,b^7+2672\,a^4\,b^9+160\,a^2\,b^{11}-384\,b^{13}\right)}{6\,a^6\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(435\,a^{12}\,b+14350\,a^{10}\,b^3+13160\,a^8\,b^5-18432\,a^6\,b^7+10688\,a^4\,b^9+640\,a^2\,b^{11}-1536\,b^{13}\right)}{24\,a^6\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(2\,a^{10}\,b-575\,a^8\,b^3-96\,a^6\,b^5+704\,a^4\,b^7-656\,a^2\,b^9+192\,b^{11}\right)}{12\,a^4\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(857\,a^{10}\,b+10012\,a^8\,b^3+2400\,a^6\,b^5-7184\,a^4\,b^7+6560\,a^2\,b^9-1920\,b^{11}\right)}{24\,a^4\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(31\,a^8\,b-384\,a^6\,b^3+576\,a^4\,b^5-384\,a^2\,b^7+96\,b^9\right)}{8\,a^2\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(186\,a^8\,b+935\,a^6\,b^3-992\,a^4\,b^5+600\,a^2\,b^7-144\,b^9\right)}{12\,a^2\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(35\,a^6+210\,a^4\,b^2+168\,a^2\,b^4+16\,b^6\right)\,\left(279\,a^6\,b-326\,a^4\,b^3+200\,a^2\,b^5-48\,b^7\right)}{42\,a^7\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(210\,a^6\,b+1120\,a^4\,b^3+672\,a^2\,b^5\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(210\,a^6\,b+1120\,a^4\,b^3+672\,a^2\,b^5\right)+a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(84\,a^6\,b+280\,a^4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(84\,a^6\,b+280\,a^4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(35\,a^7+840\,a^5\,b^2+1680\,a^3\,b^4+448\,a\,b^6\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(35\,a^7+840\,a^5\,b^2+1680\,a^3\,b^4+448\,a\,b^6\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(280\,a^6\,b+1680\,a^4\,b^3+1344\,a^2\,b^5+128\,b^7\right)+a^7+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(21\,a^7+420\,a^5\,b^2+560\,a^3\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(21\,a^7+420\,a^5\,b^2+560\,a^3\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(7\,a^7+84\,a^5\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(7\,a^7+84\,a^5\,b^2\right)+14\,a^6\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+14\,a^6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\right)}+\frac{5\,a\,\mathrm{atan}\left(\frac{8\,\left(\frac{5\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,{\left(a+b\right)}^{9/2}\,{\left(a-b\right)}^{9/2}}+\frac{5\,a\,\left(16\,a^8\,b-64\,a^6\,b^3+96\,a^4\,b^5-64\,a^2\,b^7+16\,b^9\right)}{128\,{\left(a+b\right)}^{9/2}\,{\left(a-b\right)}^{9/2}\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}\right)\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}{5\,a}\right)}{8\,d\,{\left(a+b\right)}^{9/2}\,{\left(a-b\right)}^{9/2}}","Not used",1,"((279*a^6*b - 48*b^7 + 200*a^2*b^5 - 326*a^4*b^3)/(168*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (tan(c/2 + (d*x)/2)*(33*a^8 - 48*b^8 + 208*a^2*b^6 - 364*a^4*b^4 + 366*a^6*b^2))/(24*a*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (tan(c/2 + (d*x)/2)^9*(85*a^12 + 2304*b^12 - 5760*a^2*b^10 + 368*a^4*b^8 + 10048*a^6*b^6 - 14820*a^8*b^4 - 2950*a^10*b^2))/(24*a^5*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (tan(c/2 + (d*x)/2)^5*(85*a^12 - 2304*b^12 + 5760*a^2*b^10 - 368*a^4*b^8 - 9328*a^6*b^6 + 20040*a^8*b^4 + 5420*a^10*b^2))/(24*a^5*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (tan(c/2 + (d*x)/2)^11*(14*a^10 + 480*b^10 - 1856*a^2*b^8 + 2624*a^4*b^6 - 1536*a^6*b^4 - 311*a^8*b^2))/(12*a^3*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (tan(c/2 + (d*x)/2)^3*(14*a^10 - 480*b^10 + 1856*a^2*b^8 - 2696*a^4*b^6 + 2088*a^6*b^4 + 1363*a^8*b^2))/(12*a^3*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (tan(c/2 + (d*x)/2)^13*(11*a^8 + 16*b^8 - 64*a^2*b^6 + 96*a^4*b^4 - 64*a^6*b^2))/(8*a*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (tan(c/2 + (d*x)/2)^6*(240*a^12*b - 384*b^13 + 160*a^2*b^11 + 2672*a^4*b^9 - 4548*a^6*b^7 + 3920*a^8*b^5 + 4375*a^10*b^3))/(6*a^6*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (tan(c/2 + (d*x)/2)^8*(435*a^12*b - 1536*b^13 + 640*a^2*b^11 + 10688*a^4*b^9 - 18432*a^6*b^7 + 13160*a^8*b^5 + 14350*a^10*b^3))/(24*a^6*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (5*tan(c/2 + (d*x)/2)^10*(2*a^10*b + 192*b^11 - 656*a^2*b^9 + 704*a^4*b^7 - 96*a^6*b^5 - 575*a^8*b^3))/(12*a^4*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (tan(c/2 + (d*x)/2)^4*(857*a^10*b - 1920*b^11 + 6560*a^2*b^9 - 7184*a^4*b^7 + 2400*a^6*b^5 + 10012*a^8*b^3))/(24*a^4*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (tan(c/2 + (d*x)/2)^12*(31*a^8*b + 96*b^9 - 384*a^2*b^7 + 576*a^4*b^5 - 384*a^6*b^3))/(8*a^2*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (tan(c/2 + (d*x)/2)^2*(186*a^8*b - 144*b^9 + 600*a^2*b^7 - 992*a^4*b^5 + 935*a^6*b^3))/(12*a^2*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (b*tan(c/2 + (d*x)/2)^7*(35*a^6 + 16*b^6 + 168*a^2*b^4 + 210*a^4*b^2)*(279*a^6*b - 48*b^7 + 200*a^2*b^5 - 326*a^4*b^3))/(42*a^7*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)))/(d*(tan(c/2 + (d*x)/2)^5*(210*a^6*b + 672*a^2*b^5 + 1120*a^4*b^3) + tan(c/2 + (d*x)/2)^9*(210*a^6*b + 672*a^2*b^5 + 1120*a^4*b^3) + a^7*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^3*(84*a^6*b + 280*a^4*b^3) + tan(c/2 + (d*x)/2)^11*(84*a^6*b + 280*a^4*b^3) + tan(c/2 + (d*x)/2)^6*(448*a*b^6 + 35*a^7 + 1680*a^3*b^4 + 840*a^5*b^2) + tan(c/2 + (d*x)/2)^8*(448*a*b^6 + 35*a^7 + 1680*a^3*b^4 + 840*a^5*b^2) + tan(c/2 + (d*x)/2)^7*(280*a^6*b + 128*b^7 + 1344*a^2*b^5 + 1680*a^4*b^3) + a^7 + tan(c/2 + (d*x)/2)^4*(21*a^7 + 560*a^3*b^4 + 420*a^5*b^2) + tan(c/2 + (d*x)/2)^10*(21*a^7 + 560*a^3*b^4 + 420*a^5*b^2) + tan(c/2 + (d*x)/2)^2*(7*a^7 + 84*a^5*b^2) + tan(c/2 + (d*x)/2)^12*(7*a^7 + 84*a^5*b^2) + 14*a^6*b*tan(c/2 + (d*x)/2) + 14*a^6*b*tan(c/2 + (d*x)/2)^13)) + (5*a*atan((8*((5*a^2*tan(c/2 + (d*x)/2))/(8*(a + b)^(9/2)*(a - b)^(9/2)) + (5*a*(16*a^8*b + 16*b^9 - 64*a^2*b^7 + 96*a^4*b^5 - 64*a^6*b^3))/(128*(a + b)^(9/2)*(a - b)^(9/2)*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)))*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2))/(5*a)))/(8*d*(a + b)^(9/2)*(a - b)^(9/2))","B"
469,1,2184,411,10.853533,"\text{Not used}","int(cos(c + d*x)^4/(a + b*sin(c + d*x))^8,x)","\frac{\frac{686\,a^8\,b-885\,a^6\,b^3+842\,a^4\,b^5-408\,a^2\,b^7+80\,b^9}{280\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(50\,a^{10}+957\,a^8\,b^2-970\,a^6\,b^4+884\,a^4\,b^6-416\,a^2\,b^8+80\,b^{10}\right)}{40\,a\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(-90\,a^{14}+7415\,a^{12}\,b^2+35630\,a^{10}\,b^4-28892\,a^8\,b^6+18480\,a^6\,b^8+8976\,a^4\,b^{10}-13184\,a^2\,b^{12}+3840\,b^{14}\right)}{40\,a^5\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(90\,a^{14}+13165\,a^{12}\,b^2+47580\,a^{10}\,b^4-21592\,a^8\,b^6+19040\,a^6\,b^8+8976\,a^4\,b^{10}-13184\,a^2\,b^{12}+3840\,b^{14}\right)}{40\,a^5\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(-12\,a^{12}+224\,a^{10}\,b^2+587\,a^8\,b^4-1280\,a^6\,b^6+1440\,a^4\,b^8-768\,a^2\,b^{10}+160\,b^{12}\right)}{4\,a^3\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(60\,a^{12}+2996\,a^{10}\,b^2+5475\,a^8\,b^4-6248\,a^6\,b^6+7192\,a^4\,b^8-3840\,a^2\,b^{10}+800\,b^{12}\right)}{20\,a^3\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(10\,a^{10}-83\,a^8\,b^2+160\,a^6\,b^4-160\,a^4\,b^6+80\,a^2\,b^8-16\,b^{10}\right)}{8\,a\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(560\,a^{14}\,b+10590\,a^{12}\,b^3+8855\,a^{10}\,b^5-8312\,a^8\,b^7+12140\,a^6\,b^9-4304\,a^4\,b^{11}-864\,a^2\,b^{13}+640\,b^{15}\right)}{10\,a^6\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(1190\,a^{14}\,b+35535\,a^{12}\,b^3+27230\,a^{10}\,b^5-36248\,a^8\,b^7+48320\,a^6\,b^9-17216\,a^4\,b^{11}-3456\,a^2\,b^{13}+2560\,b^{15}\right)}{40\,a^6\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(12\,a^{12}\,b+1468\,a^{10}\,b^3-161\,a^8\,b^5-1120\,a^6\,b^7+2160\,a^4\,b^9-1392\,a^2\,b^{11}+320\,b^{13}\right)}{4\,a^4\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(1938\,a^{12}\,b+23825\,a^{10}\,b^3+5916\,a^8\,b^5-10304\,a^6\,b^7+21520\,a^4\,b^9-13920\,a^2\,b^{11}+3200\,b^{13}\right)}{40\,a^4\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(6\,a^{10}\,b-173\,a^8\,b^3+320\,a^6\,b^5-320\,a^4\,b^7+160\,a^2\,b^9-32\,b^{11}\right)}{8\,a^2\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(388\,a^{10}\,b+2376\,a^8\,b^3-2489\,a^6\,b^5+2448\,a^4\,b^7-1208\,a^2\,b^9+240\,b^{11}\right)}{20\,a^2\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(35\,a^6+210\,a^4\,b^2+168\,a^2\,b^4+16\,b^6\right)\,\left(686\,a^8\,b-885\,a^6\,b^3+842\,a^4\,b^5-408\,a^2\,b^7+80\,b^9\right)}{70\,a^7\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(210\,a^6\,b+1120\,a^4\,b^3+672\,a^2\,b^5\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(210\,a^6\,b+1120\,a^4\,b^3+672\,a^2\,b^5\right)+a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(84\,a^6\,b+280\,a^4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(84\,a^6\,b+280\,a^4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(35\,a^7+840\,a^5\,b^2+1680\,a^3\,b^4+448\,a\,b^6\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(35\,a^7+840\,a^5\,b^2+1680\,a^3\,b^4+448\,a\,b^6\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(280\,a^6\,b+1680\,a^4\,b^3+1344\,a^2\,b^5+128\,b^7\right)+a^7+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(21\,a^7+420\,a^5\,b^2+560\,a^3\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(21\,a^7+420\,a^5\,b^2+560\,a^3\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(7\,a^7+84\,a^5\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(7\,a^7+84\,a^5\,b^2\right)+14\,a^6\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+14\,a^6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\right)}+\frac{3\,a\,\mathrm{atan}\left(\frac{8\,\left(\frac{3\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+b^2\right)}{8\,{\left(a+b\right)}^{11/2}\,{\left(a-b\right)}^{11/2}}+\frac{3\,a\,\left(2\,a^2+b^2\right)\,\left(16\,a^{10}\,b-80\,a^8\,b^3+160\,a^6\,b^5-160\,a^4\,b^7+80\,a^2\,b^9-16\,b^{11}\right)}{128\,{\left(a+b\right)}^{11/2}\,{\left(a-b\right)}^{11/2}\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}\right)\,\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}{6\,a^3+3\,a\,b^2}\right)\,\left(2\,a^2+b^2\right)}{8\,d\,{\left(a+b\right)}^{11/2}\,{\left(a-b\right)}^{11/2}}","Not used",1,"((686*a^8*b + 80*b^9 - 408*a^2*b^7 + 842*a^4*b^5 - 885*a^6*b^3)/(280*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)) + (tan(c/2 + (d*x)/2)*(50*a^10 + 80*b^10 - 416*a^2*b^8 + 884*a^4*b^6 - 970*a^6*b^4 + 957*a^8*b^2))/(40*a*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)) + (tan(c/2 + (d*x)/2)^9*(3840*b^14 - 90*a^14 - 13184*a^2*b^12 + 8976*a^4*b^10 + 18480*a^6*b^8 - 28892*a^8*b^6 + 35630*a^10*b^4 + 7415*a^12*b^2))/(40*a^5*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)) + (tan(c/2 + (d*x)/2)^5*(90*a^14 + 3840*b^14 - 13184*a^2*b^12 + 8976*a^4*b^10 + 19040*a^6*b^8 - 21592*a^8*b^6 + 47580*a^10*b^4 + 13165*a^12*b^2))/(40*a^5*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)) + (tan(c/2 + (d*x)/2)^11*(160*b^12 - 12*a^12 - 768*a^2*b^10 + 1440*a^4*b^8 - 1280*a^6*b^6 + 587*a^8*b^4 + 224*a^10*b^2))/(4*a^3*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)) + (tan(c/2 + (d*x)/2)^3*(60*a^12 + 800*b^12 - 3840*a^2*b^10 + 7192*a^4*b^8 - 6248*a^6*b^6 + 5475*a^8*b^4 + 2996*a^10*b^2))/(20*a^3*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)) - (tan(c/2 + (d*x)/2)^13*(10*a^10 - 16*b^10 + 80*a^2*b^8 - 160*a^4*b^6 + 160*a^6*b^4 - 83*a^8*b^2))/(8*a*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)) + (tan(c/2 + (d*x)/2)^6*(560*a^14*b + 640*b^15 - 864*a^2*b^13 - 4304*a^4*b^11 + 12140*a^6*b^9 - 8312*a^8*b^7 + 8855*a^10*b^5 + 10590*a^12*b^3))/(10*a^6*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)) + (tan(c/2 + (d*x)/2)^8*(1190*a^14*b + 2560*b^15 - 3456*a^2*b^13 - 17216*a^4*b^11 + 48320*a^6*b^9 - 36248*a^8*b^7 + 27230*a^10*b^5 + 35535*a^12*b^3))/(40*a^6*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)) + (tan(c/2 + (d*x)/2)^10*(12*a^12*b + 320*b^13 - 1392*a^2*b^11 + 2160*a^4*b^9 - 1120*a^6*b^7 - 161*a^8*b^5 + 1468*a^10*b^3))/(4*a^4*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)) + (tan(c/2 + (d*x)/2)^4*(1938*a^12*b + 3200*b^13 - 13920*a^2*b^11 + 21520*a^4*b^9 - 10304*a^6*b^7 + 5916*a^8*b^5 + 23825*a^10*b^3))/(40*a^4*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)) - (3*tan(c/2 + (d*x)/2)^12*(6*a^10*b - 32*b^11 + 160*a^2*b^9 - 320*a^4*b^7 + 320*a^6*b^5 - 173*a^8*b^3))/(8*a^2*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)) + (tan(c/2 + (d*x)/2)^2*(388*a^10*b + 240*b^11 - 1208*a^2*b^9 + 2448*a^4*b^7 - 2489*a^6*b^5 + 2376*a^8*b^3))/(20*a^2*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)) + (b*tan(c/2 + (d*x)/2)^7*(35*a^6 + 16*b^6 + 168*a^2*b^4 + 210*a^4*b^2)*(686*a^8*b + 80*b^9 - 408*a^2*b^7 + 842*a^4*b^5 - 885*a^6*b^3))/(70*a^7*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)))/(d*(tan(c/2 + (d*x)/2)^5*(210*a^6*b + 672*a^2*b^5 + 1120*a^4*b^3) + tan(c/2 + (d*x)/2)^9*(210*a^6*b + 672*a^2*b^5 + 1120*a^4*b^3) + a^7*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^3*(84*a^6*b + 280*a^4*b^3) + tan(c/2 + (d*x)/2)^11*(84*a^6*b + 280*a^4*b^3) + tan(c/2 + (d*x)/2)^6*(448*a*b^6 + 35*a^7 + 1680*a^3*b^4 + 840*a^5*b^2) + tan(c/2 + (d*x)/2)^8*(448*a*b^6 + 35*a^7 + 1680*a^3*b^4 + 840*a^5*b^2) + tan(c/2 + (d*x)/2)^7*(280*a^6*b + 128*b^7 + 1344*a^2*b^5 + 1680*a^4*b^3) + a^7 + tan(c/2 + (d*x)/2)^4*(21*a^7 + 560*a^3*b^4 + 420*a^5*b^2) + tan(c/2 + (d*x)/2)^10*(21*a^7 + 560*a^3*b^4 + 420*a^5*b^2) + tan(c/2 + (d*x)/2)^2*(7*a^7 + 84*a^5*b^2) + tan(c/2 + (d*x)/2)^12*(7*a^7 + 84*a^5*b^2) + 14*a^6*b*tan(c/2 + (d*x)/2) + 14*a^6*b*tan(c/2 + (d*x)/2)^13)) + (3*a*atan((8*((3*a^2*tan(c/2 + (d*x)/2)*(2*a^2 + b^2))/(8*(a + b)^(11/2)*(a - b)^(11/2)) + (3*a*(2*a^2 + b^2)*(16*a^10*b - 16*b^11 + 80*a^2*b^9 - 160*a^4*b^7 + 160*a^6*b^5 - 80*a^8*b^3))/(128*(a + b)^(11/2)*(a - b)^(11/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)))*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2))/(3*a*b^2 + 6*a^3))*(2*a^2 + b^2))/(8*d*(a + b)^(11/2)*(a - b)^(11/2))","B"
470,1,2440,422,10.338961,"\text{Not used}","int(cos(c + d*x)^2/(a + b*sin(c + d*x))^8,x)","\frac{\frac{3640\,a^{10}\,b-2660\,a^8\,b^3+4923\,a^6\,b^5-3646\,a^4\,b^7+1448\,a^2\,b^9-240\,b^{11}}{840\,\left(a^{12}-6\,a^{10}\,b^2+15\,a^8\,b^4-20\,a^6\,b^6+15\,a^4\,b^8-6\,a^2\,b^{10}+b^{12}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2800\,a^{16}\,b+57400\,a^{14}\,b^3+83100\,a^{12}\,b^5+29395\,a^{10}\,b^7+74800\,a^8\,b^9-48276\,a^6\,b^{11}+10672\,a^4\,b^{13}+4384\,a^2\,b^{15}-1920\,b^{17}\right)}{30\,a^6\,\left(a^{12}-6\,a^{10}\,b^2+15\,a^8\,b^4-20\,a^6\,b^6+15\,a^4\,b^8-6\,a^2\,b^{10}+b^{12}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(7000\,a^{16}\,b+193900\,a^{14}\,b^3+246615\,a^{12}\,b^5+49510\,a^{10}\,b^7+281800\,a^8\,b^9-194304\,a^6\,b^{11}+42688\,a^4\,b^{13}+17536\,a^2\,b^{15}-7680\,b^{17}\right)}{120\,a^6\,\left(a^{12}-6\,a^{10}\,b^2+15\,a^8\,b^4-20\,a^6\,b^6+15\,a^4\,b^8-6\,a^2\,b^{10}+b^{12}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(192\,a^{14}\,b+7920\,a^{12}\,b^3+2370\,a^{10}\,b^5+955\,a^8\,b^7+8880\,a^6\,b^9-10272\,a^4\,b^{11}+5072\,a^2\,b^{13}-960\,b^{15}\right)}{12\,a^4\,\left(a^{12}-6\,a^{10}\,b^2+15\,a^8\,b^4-20\,a^6\,b^6+15\,a^4\,b^8-6\,a^2\,b^{10}+b^{12}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(9000\,a^{14}\,b+131220\,a^{12}\,b^3+122669\,a^{10}\,b^5+62092\,a^8\,b^7+90624\,a^6\,b^9-102800\,a^4\,b^{11}+50720\,a^2\,b^{13}-9600\,b^{15}\right)}{120\,a^4\,\left(a^{12}-6\,a^{10}\,b^2+15\,a^8\,b^4-20\,a^6\,b^6+15\,a^4\,b^8-6\,a^2\,b^{10}+b^{12}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(8\,a^{12}\,b+836\,a^{10}\,b^3-1375\,a^8\,b^5+1920\,a^6\,b^7-1440\,a^4\,b^9+576\,a^2\,b^{11}-96\,b^{13}\right)}{8\,a^2\,\left(a^{12}-6\,a^{10}\,b^2+15\,a^8\,b^4-20\,a^6\,b^6+15\,a^4\,b^8-6\,a^2\,b^{10}+b^{12}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(1760\,a^{12}\,b+14240\,a^{10}\,b^3-3186\,a^8\,b^5+13315\,a^6\,b^7-10352\,a^4\,b^9+4248\,a^2\,b^{11}-720\,b^{13}\right)}{60\,a^2\,\left(a^{12}-6\,a^{10}\,b^2+15\,a^8\,b^4-20\,a^6\,b^6+15\,a^4\,b^8-6\,a^2\,b^{10}+b^{12}\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(120\,a^{12}+5540\,a^{10}\,b^2-1795\,a^8\,b^4+5046\,a^6\,b^6-3692\,a^4\,b^8+1456\,a^2\,b^{10}-240\,b^{12}\right)}{120\,a\,\left(a^{12}-6\,a^{10}\,b^2+15\,a^8\,b^4-20\,a^6\,b^6+15\,a^4\,b^8-6\,a^2\,b^{10}+b^{12}\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(600\,a^{16}-43500\,a^{14}\,b^2-202575\,a^{12}\,b^4+21010\,a^{10}\,b^6-188100\,a^8\,b^8+34656\,a^6\,b^{10}+62768\,a^4\,b^{12}-50304\,a^2\,b^{14}+11520\,b^{16}\right)}{120\,a^5\,\left(a^{12}-6\,a^{10}\,b^2+15\,a^8\,b^4-20\,a^6\,b^6+15\,a^4\,b^8-6\,a^2\,b^{10}+b^{12}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(600\,a^{16}+65700\,a^{14}\,b^2+300025\,a^{12}\,b^4+92540\,a^{10}\,b^6+234840\,a^8\,b^8-32656\,a^6\,b^{10}-62768\,a^4\,b^{12}+50304\,a^2\,b^{14}-11520\,b^{16}\right)}{120\,a^5\,\left(a^{12}-6\,a^{10}\,b^2+15\,a^8\,b^4-20\,a^6\,b^6+15\,a^4\,b^8-6\,a^2\,b^{10}+b^{12}\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(48\,a^{14}-1344\,a^{12}\,b^2-3150\,a^{10}\,b^4+4105\,a^8\,b^6-7680\,a^6\,b^8+6432\,a^4\,b^{10}-2752\,a^2\,b^{12}+480\,b^{14}\right)}{12\,a^3\,\left(a^{12}-6\,a^{10}\,b^2+15\,a^8\,b^4-20\,a^6\,b^6+15\,a^4\,b^8-6\,a^2\,b^{10}+b^{12}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(240\,a^{14}+15120\,a^{12}\,b^2+41090\,a^{10}\,b^4-3137\,a^8\,b^6+38184\,a^6\,b^8-32072\,a^4\,b^{10}+13760\,a^2\,b^{12}-2400\,b^{14}\right)}{60\,a^3\,\left(a^{12}-6\,a^{10}\,b^2+15\,a^8\,b^4-20\,a^6\,b^6+15\,a^4\,b^8-6\,a^2\,b^{10}+b^{12}\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(8\,a^{12}-116\,a^{10}\,b^2+235\,a^8\,b^4-320\,a^6\,b^6+240\,a^4\,b^8-96\,a^2\,b^{10}+16\,b^{12}\right)}{8\,a\,\left(a^{12}-6\,a^{10}\,b^2+15\,a^8\,b^4-20\,a^6\,b^6+15\,a^4\,b^8-6\,a^2\,b^{10}+b^{12}\right)}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(35\,a^6+210\,a^4\,b^2+168\,a^2\,b^4+16\,b^6\right)\,\left(3640\,a^{10}\,b-2660\,a^8\,b^3+4923\,a^6\,b^5-3646\,a^4\,b^7+1448\,a^2\,b^9-240\,b^{11}\right)}{210\,a^7\,\left(a^{12}-6\,a^{10}\,b^2+15\,a^8\,b^4-20\,a^6\,b^6+15\,a^4\,b^8-6\,a^2\,b^{10}+b^{12}\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(210\,a^6\,b+1120\,a^4\,b^3+672\,a^2\,b^5\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(210\,a^6\,b+1120\,a^4\,b^3+672\,a^2\,b^5\right)+a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(84\,a^6\,b+280\,a^4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(84\,a^6\,b+280\,a^4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(35\,a^7+840\,a^5\,b^2+1680\,a^3\,b^4+448\,a\,b^6\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(35\,a^7+840\,a^5\,b^2+1680\,a^3\,b^4+448\,a\,b^6\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(280\,a^6\,b+1680\,a^4\,b^3+1344\,a^2\,b^5+128\,b^7\right)+a^7+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(21\,a^7+420\,a^5\,b^2+560\,a^3\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(21\,a^7+420\,a^5\,b^2+560\,a^3\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(7\,a^7+84\,a^5\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(7\,a^7+84\,a^5\,b^2\right)+14\,a^6\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+14\,a^6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\right)}+\frac{a\,\mathrm{atan}\left(\frac{8\,\left(\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^4+20\,a^2\,b^2+5\,b^4\right)}{8\,{\left(a+b\right)}^{13/2}\,{\left(a-b\right)}^{13/2}}+\frac{a\,\left(8\,a^4+20\,a^2\,b^2+5\,b^4\right)\,\left(16\,a^{12}\,b-96\,a^{10}\,b^3+240\,a^8\,b^5-320\,a^6\,b^7+240\,a^4\,b^9-96\,a^2\,b^{11}+16\,b^{13}\right)}{128\,{\left(a+b\right)}^{13/2}\,{\left(a-b\right)}^{13/2}\,\left(a^{12}-6\,a^{10}\,b^2+15\,a^8\,b^4-20\,a^6\,b^6+15\,a^4\,b^8-6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^{12}-6\,a^{10}\,b^2+15\,a^8\,b^4-20\,a^6\,b^6+15\,a^4\,b^8-6\,a^2\,b^{10}+b^{12}\right)}{8\,a^5+20\,a^3\,b^2+5\,a\,b^4}\right)\,\left(8\,a^4+20\,a^2\,b^2+5\,b^4\right)}{8\,d\,{\left(a+b\right)}^{13/2}\,{\left(a-b\right)}^{13/2}}","Not used",1,"((3640*a^10*b - 240*b^11 + 1448*a^2*b^9 - 3646*a^4*b^7 + 4923*a^6*b^5 - 2660*a^8*b^3)/(840*(a^12 + b^12 - 6*a^2*b^10 + 15*a^4*b^8 - 20*a^6*b^6 + 15*a^8*b^4 - 6*a^10*b^2)) + (tan(c/2 + (d*x)/2)^6*(2800*a^16*b - 1920*b^17 + 4384*a^2*b^15 + 10672*a^4*b^13 - 48276*a^6*b^11 + 74800*a^8*b^9 + 29395*a^10*b^7 + 83100*a^12*b^5 + 57400*a^14*b^3))/(30*a^6*(a^12 + b^12 - 6*a^2*b^10 + 15*a^4*b^8 - 20*a^6*b^6 + 15*a^8*b^4 - 6*a^10*b^2)) + (tan(c/2 + (d*x)/2)^8*(7000*a^16*b - 7680*b^17 + 17536*a^2*b^15 + 42688*a^4*b^13 - 194304*a^6*b^11 + 281800*a^8*b^9 + 49510*a^10*b^7 + 246615*a^12*b^5 + 193900*a^14*b^3))/(120*a^6*(a^12 + b^12 - 6*a^2*b^10 + 15*a^4*b^8 - 20*a^6*b^6 + 15*a^8*b^4 - 6*a^10*b^2)) + (tan(c/2 + (d*x)/2)^10*(192*a^14*b - 960*b^15 + 5072*a^2*b^13 - 10272*a^4*b^11 + 8880*a^6*b^9 + 955*a^8*b^7 + 2370*a^10*b^5 + 7920*a^12*b^3))/(12*a^4*(a^12 + b^12 - 6*a^2*b^10 + 15*a^4*b^8 - 20*a^6*b^6 + 15*a^8*b^4 - 6*a^10*b^2)) + (tan(c/2 + (d*x)/2)^4*(9000*a^14*b - 9600*b^15 + 50720*a^2*b^13 - 102800*a^4*b^11 + 90624*a^6*b^9 + 62092*a^8*b^7 + 122669*a^10*b^5 + 131220*a^12*b^3))/(120*a^4*(a^12 + b^12 - 6*a^2*b^10 + 15*a^4*b^8 - 20*a^6*b^6 + 15*a^8*b^4 - 6*a^10*b^2)) + (tan(c/2 + (d*x)/2)^12*(8*a^12*b - 96*b^13 + 576*a^2*b^11 - 1440*a^4*b^9 + 1920*a^6*b^7 - 1375*a^8*b^5 + 836*a^10*b^3))/(8*a^2*(a^12 + b^12 - 6*a^2*b^10 + 15*a^4*b^8 - 20*a^6*b^6 + 15*a^8*b^4 - 6*a^10*b^2)) + (tan(c/2 + (d*x)/2)^2*(1760*a^12*b - 720*b^13 + 4248*a^2*b^11 - 10352*a^4*b^9 + 13315*a^6*b^7 - 3186*a^8*b^5 + 14240*a^10*b^3))/(60*a^2*(a^12 + b^12 - 6*a^2*b^10 + 15*a^4*b^8 - 20*a^6*b^6 + 15*a^8*b^4 - 6*a^10*b^2)) + (tan(c/2 + (d*x)/2)*(120*a^12 - 240*b^12 + 1456*a^2*b^10 - 3692*a^4*b^8 + 5046*a^6*b^6 - 1795*a^8*b^4 + 5540*a^10*b^2))/(120*a*(a^12 + b^12 - 6*a^2*b^10 + 15*a^4*b^8 - 20*a^6*b^6 + 15*a^8*b^4 - 6*a^10*b^2)) - (tan(c/2 + (d*x)/2)^9*(600*a^16 + 11520*b^16 - 50304*a^2*b^14 + 62768*a^4*b^12 + 34656*a^6*b^10 - 188100*a^8*b^8 + 21010*a^10*b^6 - 202575*a^12*b^4 - 43500*a^14*b^2))/(120*a^5*(a^12 + b^12 - 6*a^2*b^10 + 15*a^4*b^8 - 20*a^6*b^6 + 15*a^8*b^4 - 6*a^10*b^2)) + (tan(c/2 + (d*x)/2)^5*(600*a^16 - 11520*b^16 + 50304*a^2*b^14 - 62768*a^4*b^12 - 32656*a^6*b^10 + 234840*a^8*b^8 + 92540*a^10*b^6 + 300025*a^12*b^4 + 65700*a^14*b^2))/(120*a^5*(a^12 + b^12 - 6*a^2*b^10 + 15*a^4*b^8 - 20*a^6*b^6 + 15*a^8*b^4 - 6*a^10*b^2)) - (tan(c/2 + (d*x)/2)^11*(48*a^14 + 480*b^14 - 2752*a^2*b^12 + 6432*a^4*b^10 - 7680*a^6*b^8 + 4105*a^8*b^6 - 3150*a^10*b^4 - 1344*a^12*b^2))/(12*a^3*(a^12 + b^12 - 6*a^2*b^10 + 15*a^4*b^8 - 20*a^6*b^6 + 15*a^8*b^4 - 6*a^10*b^2)) + (tan(c/2 + (d*x)/2)^3*(240*a^14 - 2400*b^14 + 13760*a^2*b^12 - 32072*a^4*b^10 + 38184*a^6*b^8 - 3137*a^8*b^6 + 41090*a^10*b^4 + 15120*a^12*b^2))/(60*a^3*(a^12 + b^12 - 6*a^2*b^10 + 15*a^4*b^8 - 20*a^6*b^6 + 15*a^8*b^4 - 6*a^10*b^2)) - (tan(c/2 + (d*x)/2)^13*(8*a^12 + 16*b^12 - 96*a^2*b^10 + 240*a^4*b^8 - 320*a^6*b^6 + 235*a^8*b^4 - 116*a^10*b^2))/(8*a*(a^12 + b^12 - 6*a^2*b^10 + 15*a^4*b^8 - 20*a^6*b^6 + 15*a^8*b^4 - 6*a^10*b^2)) + (b*tan(c/2 + (d*x)/2)^7*(35*a^6 + 16*b^6 + 168*a^2*b^4 + 210*a^4*b^2)*(3640*a^10*b - 240*b^11 + 1448*a^2*b^9 - 3646*a^4*b^7 + 4923*a^6*b^5 - 2660*a^8*b^3))/(210*a^7*(a^12 + b^12 - 6*a^2*b^10 + 15*a^4*b^8 - 20*a^6*b^6 + 15*a^8*b^4 - 6*a^10*b^2)))/(d*(tan(c/2 + (d*x)/2)^5*(210*a^6*b + 672*a^2*b^5 + 1120*a^4*b^3) + tan(c/2 + (d*x)/2)^9*(210*a^6*b + 672*a^2*b^5 + 1120*a^4*b^3) + a^7*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^3*(84*a^6*b + 280*a^4*b^3) + tan(c/2 + (d*x)/2)^11*(84*a^6*b + 280*a^4*b^3) + tan(c/2 + (d*x)/2)^6*(448*a*b^6 + 35*a^7 + 1680*a^3*b^4 + 840*a^5*b^2) + tan(c/2 + (d*x)/2)^8*(448*a*b^6 + 35*a^7 + 1680*a^3*b^4 + 840*a^5*b^2) + tan(c/2 + (d*x)/2)^7*(280*a^6*b + 128*b^7 + 1344*a^2*b^5 + 1680*a^4*b^3) + a^7 + tan(c/2 + (d*x)/2)^4*(21*a^7 + 560*a^3*b^4 + 420*a^5*b^2) + tan(c/2 + (d*x)/2)^10*(21*a^7 + 560*a^3*b^4 + 420*a^5*b^2) + tan(c/2 + (d*x)/2)^2*(7*a^7 + 84*a^5*b^2) + tan(c/2 + (d*x)/2)^12*(7*a^7 + 84*a^5*b^2) + 14*a^6*b*tan(c/2 + (d*x)/2) + 14*a^6*b*tan(c/2 + (d*x)/2)^13)) + (a*atan((8*((a^2*tan(c/2 + (d*x)/2)*(8*a^4 + 5*b^4 + 20*a^2*b^2))/(8*(a + b)^(13/2)*(a - b)^(13/2)) + (a*(8*a^4 + 5*b^4 + 20*a^2*b^2)*(16*a^12*b + 16*b^13 - 96*a^2*b^11 + 240*a^4*b^9 - 320*a^6*b^7 + 240*a^8*b^5 - 96*a^10*b^3))/(128*(a + b)^(13/2)*(a - b)^(13/2)*(a^12 + b^12 - 6*a^2*b^10 + 15*a^4*b^8 - 20*a^6*b^6 + 15*a^8*b^4 - 6*a^10*b^2)))*(a^12 + b^12 - 6*a^2*b^10 + 15*a^4*b^8 - 20*a^6*b^6 + 15*a^8*b^4 - 6*a^10*b^2))/(5*a*b^4 + 8*a^5 + 20*a^3*b^2))*(8*a^4 + 5*b^4 + 20*a^2*b^2))/(8*d*(a + b)^(13/2)*(a - b)^(13/2))","B"
471,1,3273,529,53.315844,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b*sin(c + d*x))^8),x)","-\frac{\frac{4480\,a^{14}\,b+78400\,a^{12}\,b^3+113680\,a^{10}\,b^5+31192\,a^8\,b^7-4161\,a^6\,b^9+2186\,a^4\,b^{11}-632\,a^2\,b^{13}+80\,b^{15}}{280\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}-\frac{9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(2240\,a^{12}\,b^3+25200\,a^{10}\,b^5+91112\,a^8\,b^7+117497\,a^6\,b^9+59766\,a^4\,b^{11}+10360\,a^2\,b^{13}+560\,b^{15}\right)}{8\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-80\,a^{16}+6720\,a^{14}\,b^2+139440\,a^{12}\,b^4+219240\,a^{10}\,b^6+55209\,a^8\,b^8-3842\,a^6\,b^{10}+2132\,a^4\,b^{12}-624\,a^2\,b^{14}+80\,b^{16}\right)}{40\,a\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-19600\,a^{22}+235200\,a^{20}\,b^2+1234800\,a^{18}\,b^4+15431080\,a^{16}\,b^6+32332965\,a^{14}\,b^8+34250720\,a^{12}\,b^{10}+11762072\,a^{10}\,b^{12}+1158752\,a^8\,b^{14}+294032\,a^6\,b^{16}-50048\,a^4\,b^{18}-13568\,a^2\,b^{20}+5120\,b^{22}\right)}{280\,a^7\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(19600\,a^{22}+78400\,a^{20}\,b^2+6762000\,a^{18}\,b^4+39441080\,a^{16}\,b^6+86769515\,a^{14}\,b^8+69353690\,a^{12}\,b^{10}+21572852\,a^{10}\,b^{12}+1217552\,a^8\,b^{14}+294032\,a^6\,b^{16}-50048\,a^4\,b^{18}-13568\,a^2\,b^{20}+5120\,b^{22}\right)}{280\,a^7\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(560\,a^{20}+8960\,a^{18}\,b^2+311920\,a^{16}\,b^4+1708840\,a^{14}\,b^6+2917285\,a^{12}\,b^8+1695400\,a^{10}\,b^{10}+201292\,a^8\,b^{12}-27776\,a^6\,b^{14}+22576\,a^4\,b^{16}-8512\,a^2\,b^{18}+1280\,b^{20}\right)}{40\,a^5\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-560\,a^{20}+17920\,a^{18}\,b^2+337680\,a^{16}\,b^4+2252600\,a^{14}\,b^6+4325867\,a^{12}\,b^8+3165074\,a^{10}\,b^{10}+643528\,a^8\,b^{12}-21728\,a^6\,b^{14}+22576\,a^4\,b^{16}-8512\,a^2\,b^{18}+1280\,b^{20}\right)}{40\,a^5\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(112\,a^{18}+2688\,a^{16}\,b^2+58800\,a^{14}\,b^4+232680\,a^{12}\,b^6+171465\,a^{10}\,b^8+38598\,a^8\,b^{10}-14784\,a^6\,b^{12}+8064\,a^4\,b^{14}-2448\,a^2\,b^{16}+320\,b^{18}\right)}{8\,a^3\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-112\,a^{18}+6272\,a^{16}\,b^2+133840\,a^{14}\,b^4+621880\,a^{12}\,b^6+800359\,a^{10}\,b^8+202616\,a^8\,b^{10}-14132\,a^6\,b^{12}+8160\,a^4\,b^{14}-2448\,a^2\,b^{16}+320\,b^{18}\right)}{8\,a^3\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(16\,a^{16}+448\,a^{14}\,b^2+3472\,a^{12}\,b^4+1624\,a^{10}\,b^6+1435\,a^8\,b^8-896\,a^6\,b^{10}+448\,a^4\,b^{12}-128\,a^2\,b^{14}+16\,b^{16}\right)}{8\,a\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(5600\,a^{20}\,b+168000\,a^{18}\,b^3+2568720\,a^{16}\,b^5+9211384\,a^{14}\,b^7+12687263\,a^{12}\,b^9+6528192\,a^{10}\,b^{11}+997920\,a^8\,b^{13}+29568\,a^6\,b^{15}+21792\,a^4\,b^{17}-13824\,a^2\,b^{19}+2560\,b^{21}\right)}{40\,a^6\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(3360\,a^{20}\,b+257600\,a^{18}\,b^3+3079440\,a^{16}\,b^5+10502520\,a^{14}\,b^7+12382335\,a^{12}\,b^9+5492760\,a^{10}\,b^{11}+462504\,a^8\,b^{13}+16128\,a^6\,b^{15}+21792\,a^4\,b^{17}-13824\,a^2\,b^{19}+2560\,b^{21}\right)}{40\,a^6\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(448\,a^{18}\,b+31808\,a^{16}\,b^3+312368\,a^{14}\,b^5+787976\,a^{12}\,b^7+550445\,a^{10}\,b^9+86702\,a^8\,b^{11}-23296\,a^6\,b^{13}+14336\,a^4\,b^{15}-4672\,a^2\,b^{17}+640\,b^{19}\right)}{8\,a^4\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6720\,a^{18}\,b+212800\,a^{16}\,b^3+2787120\,a^{14}\,b^5+7851144\,a^{12}\,b^7+7831069\,a^{10}\,b^9+1866494\,a^8\,b^{11}-112736\,a^6\,b^{13}+73024\,a^4\,b^{15}-23360\,a^2\,b^{17}+3200\,b^{19}\right)}{40\,a^4\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(32\,a^{16}\,b+2240\,a^{14}\,b^3+14000\,a^{12}\,b^5+9128\,a^{10}\,b^7+3605\,a^8\,b^9-1792\,a^6\,b^{11}+896\,a^4\,b^{13}-256\,a^2\,b^{15}+32\,b^{17}\right)}{8\,a^2\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(7840\,a^{16}\,b+203840\,a^{14}\,b^3+1932560\,a^{12}\,b^5+2925944\,a^{10}\,b^7+738879\,a^8\,b^9-49416\,a^6\,b^{11}+28584\,a^4\,b^{13}-8576\,a^2\,b^{15}+1120\,b^{17}\right)}{280\,a^2\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(126\,a^6\,b+840\,a^4\,b^3+672\,a^2\,b^5\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(126\,a^6\,b+840\,a^4\,b^3+672\,a^2\,b^5\right)-a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(70\,a^6\,b+280\,a^4\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(70\,a^6\,b+280\,a^4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(14\,a^7+420\,a^5\,b^2+1120\,a^3\,b^4+448\,a\,b^6\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(14\,a^7+420\,a^5\,b^2+1120\,a^3\,b^4+448\,a\,b^6\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(70\,a^6\,b+560\,a^4\,b^3+672\,a^2\,b^5+128\,b^7\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(70\,a^6\,b+560\,a^4\,b^3+672\,a^2\,b^5+128\,b^7\right)+a^7+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(14\,a^7+336\,a^5\,b^2+560\,a^3\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(14\,a^7+336\,a^5\,b^2+560\,a^3\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a^7+84\,a^5\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(6\,a^7+84\,a^5\,b^2\right)+14\,a^6\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-14\,a^6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\right)}-\frac{9\,a\,b^2\,\mathrm{atan}\left(\frac{\frac{9\,a\,b^2\,\left(64\,a^6+336\,a^4\,b^2+280\,a^2\,b^4+35\,b^6\right)\,\left(16\,a^{16}\,b-128\,a^{14}\,b^3+448\,a^{12}\,b^5-896\,a^{10}\,b^7+1120\,a^8\,b^9-896\,a^6\,b^{11}+448\,a^4\,b^{13}-128\,a^2\,b^{15}+16\,b^{17}\right)}{16\,{\left(a+b\right)}^{17/2}\,{\left(a-b\right)}^{17/2}}+\frac{9\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^6+336\,a^4\,b^2+280\,a^2\,b^4+35\,b^6\right)\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-56\,a^{10}\,b^6+70\,a^8\,b^8-56\,a^6\,b^{10}+28\,a^4\,b^{12}-8\,a^2\,b^{14}+b^{16}\right)}{{\left(a+b\right)}^{17/2}\,{\left(a-b\right)}^{17/2}}}{576\,a^7\,b^2+3024\,a^5\,b^4+2520\,a^3\,b^6+315\,a\,b^8}\right)\,\left(64\,a^6+336\,a^4\,b^2+280\,a^2\,b^4+35\,b^6\right)}{8\,d\,{\left(a+b\right)}^{17/2}\,{\left(a-b\right)}^{17/2}}","Not used",1,"- ((4480*a^14*b + 80*b^15 - 632*a^2*b^13 + 2186*a^4*b^11 - 4161*a^6*b^9 + 31192*a^8*b^7 + 113680*a^10*b^5 + 78400*a^12*b^3)/(280*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) - (9*tan(c/2 + (d*x)/2)^8*(560*b^15 + 10360*a^2*b^13 + 59766*a^4*b^11 + 117497*a^6*b^9 + 91112*a^8*b^7 + 25200*a^10*b^5 + 2240*a^12*b^3))/(8*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) + (tan(c/2 + (d*x)/2)*(80*b^16 - 80*a^16 - 624*a^2*b^14 + 2132*a^4*b^12 - 3842*a^6*b^10 + 55209*a^8*b^8 + 219240*a^10*b^6 + 139440*a^12*b^4 + 6720*a^14*b^2))/(40*a*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) + (tan(c/2 + (d*x)/2)^7*(5120*b^22 - 19600*a^22 - 13568*a^2*b^20 - 50048*a^4*b^18 + 294032*a^6*b^16 + 1158752*a^8*b^14 + 11762072*a^10*b^12 + 34250720*a^12*b^10 + 32332965*a^14*b^8 + 15431080*a^16*b^6 + 1234800*a^18*b^4 + 235200*a^20*b^2))/(280*a^7*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) - (tan(c/2 + (d*x)/2)^9*(19600*a^22 + 5120*b^22 - 13568*a^2*b^20 - 50048*a^4*b^18 + 294032*a^6*b^16 + 1217552*a^8*b^14 + 21572852*a^10*b^12 + 69353690*a^12*b^10 + 86769515*a^14*b^8 + 39441080*a^16*b^6 + 6762000*a^18*b^4 + 78400*a^20*b^2))/(280*a^7*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) - (3*tan(c/2 + (d*x)/2)^11*(560*a^20 + 1280*b^20 - 8512*a^2*b^18 + 22576*a^4*b^16 - 27776*a^6*b^14 + 201292*a^8*b^12 + 1695400*a^10*b^10 + 2917285*a^12*b^8 + 1708840*a^14*b^6 + 311920*a^16*b^4 + 8960*a^18*b^2))/(40*a^5*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) + (3*tan(c/2 + (d*x)/2)^5*(1280*b^20 - 560*a^20 - 8512*a^2*b^18 + 22576*a^4*b^16 - 21728*a^6*b^14 + 643528*a^8*b^12 + 3165074*a^10*b^10 + 4325867*a^12*b^8 + 2252600*a^14*b^6 + 337680*a^16*b^4 + 17920*a^18*b^2))/(40*a^5*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) - (tan(c/2 + (d*x)/2)^13*(112*a^18 + 320*b^18 - 2448*a^2*b^16 + 8064*a^4*b^14 - 14784*a^6*b^12 + 38598*a^8*b^10 + 171465*a^10*b^8 + 232680*a^12*b^6 + 58800*a^14*b^4 + 2688*a^16*b^2))/(8*a^3*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) + (tan(c/2 + (d*x)/2)^3*(320*b^18 - 112*a^18 - 2448*a^2*b^16 + 8160*a^4*b^14 - 14132*a^6*b^12 + 202616*a^8*b^10 + 800359*a^10*b^8 + 621880*a^12*b^6 + 133840*a^14*b^4 + 6272*a^16*b^2))/(8*a^3*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) - (tan(c/2 + (d*x)/2)^15*(16*a^16 + 16*b^16 - 128*a^2*b^14 + 448*a^4*b^12 - 896*a^6*b^10 + 1435*a^8*b^8 + 1624*a^10*b^6 + 3472*a^12*b^4 + 448*a^14*b^2))/(8*a*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) + (tan(c/2 + (d*x)/2)^6*(5600*a^20*b + 2560*b^21 - 13824*a^2*b^19 + 21792*a^4*b^17 + 29568*a^6*b^15 + 997920*a^8*b^13 + 6528192*a^10*b^11 + 12687263*a^12*b^9 + 9211384*a^14*b^7 + 2568720*a^16*b^5 + 168000*a^18*b^3))/(40*a^6*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) - (tan(c/2 + (d*x)/2)^10*(3360*a^20*b + 2560*b^21 - 13824*a^2*b^19 + 21792*a^4*b^17 + 16128*a^6*b^15 + 462504*a^8*b^13 + 5492760*a^10*b^11 + 12382335*a^12*b^9 + 10502520*a^14*b^7 + 3079440*a^16*b^5 + 257600*a^18*b^3))/(40*a^6*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) - (tan(c/2 + (d*x)/2)^12*(448*a^18*b + 640*b^19 - 4672*a^2*b^17 + 14336*a^4*b^15 - 23296*a^6*b^13 + 86702*a^8*b^11 + 550445*a^10*b^9 + 787976*a^12*b^7 + 312368*a^14*b^5 + 31808*a^16*b^3))/(8*a^4*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) + (tan(c/2 + (d*x)/2)^4*(6720*a^18*b + 3200*b^19 - 23360*a^2*b^17 + 73024*a^4*b^15 - 112736*a^6*b^13 + 1866494*a^8*b^11 + 7831069*a^10*b^9 + 7851144*a^12*b^7 + 2787120*a^14*b^5 + 212800*a^16*b^3))/(40*a^4*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) - (3*tan(c/2 + (d*x)/2)^14*(32*a^16*b + 32*b^17 - 256*a^2*b^15 + 896*a^4*b^13 - 1792*a^6*b^11 + 3605*a^8*b^9 + 9128*a^10*b^7 + 14000*a^12*b^5 + 2240*a^14*b^3))/(8*a^2*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)) + (3*tan(c/2 + (d*x)/2)^2*(7840*a^16*b + 1120*b^17 - 8576*a^2*b^15 + 28584*a^4*b^13 - 49416*a^6*b^11 + 738879*a^8*b^9 + 2925944*a^10*b^7 + 1932560*a^12*b^5 + 203840*a^14*b^3))/(280*a^2*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)))/(d*(tan(c/2 + (d*x)/2)^5*(126*a^6*b + 672*a^2*b^5 + 840*a^4*b^3) - tan(c/2 + (d*x)/2)^11*(126*a^6*b + 672*a^2*b^5 + 840*a^4*b^3) - a^7*tan(c/2 + (d*x)/2)^16 + tan(c/2 + (d*x)/2)^3*(70*a^6*b + 280*a^4*b^3) - tan(c/2 + (d*x)/2)^13*(70*a^6*b + 280*a^4*b^3) + tan(c/2 + (d*x)/2)^6*(448*a*b^6 + 14*a^7 + 1120*a^3*b^4 + 420*a^5*b^2) - tan(c/2 + (d*x)/2)^10*(448*a*b^6 + 14*a^7 + 1120*a^3*b^4 + 420*a^5*b^2) + tan(c/2 + (d*x)/2)^7*(70*a^6*b + 128*b^7 + 672*a^2*b^5 + 560*a^4*b^3) - tan(c/2 + (d*x)/2)^9*(70*a^6*b + 128*b^7 + 672*a^2*b^5 + 560*a^4*b^3) + a^7 + tan(c/2 + (d*x)/2)^4*(14*a^7 + 560*a^3*b^4 + 336*a^5*b^2) - tan(c/2 + (d*x)/2)^12*(14*a^7 + 560*a^3*b^4 + 336*a^5*b^2) + tan(c/2 + (d*x)/2)^2*(6*a^7 + 84*a^5*b^2) - tan(c/2 + (d*x)/2)^14*(6*a^7 + 84*a^5*b^2) + 14*a^6*b*tan(c/2 + (d*x)/2) - 14*a^6*b*tan(c/2 + (d*x)/2)^15)) - (9*a*b^2*atan(((9*a*b^2*(64*a^6 + 35*b^6 + 280*a^2*b^4 + 336*a^4*b^2)*(16*a^16*b + 16*b^17 - 128*a^2*b^15 + 448*a^4*b^13 - 896*a^6*b^11 + 1120*a^8*b^9 - 896*a^10*b^7 + 448*a^12*b^5 - 128*a^14*b^3))/(16*(a + b)^(17/2)*(a - b)^(17/2)) + (9*a^2*b^2*tan(c/2 + (d*x)/2)*(64*a^6 + 35*b^6 + 280*a^2*b^4 + 336*a^4*b^2)*(a^16 + b^16 - 8*a^2*b^14 + 28*a^4*b^12 - 56*a^6*b^10 + 70*a^8*b^8 - 56*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2))/((a + b)^(17/2)*(a - b)^(17/2)))/(315*a*b^8 + 2520*a^3*b^6 + 3024*a^5*b^4 + 576*a^7*b^2))*(64*a^6 + 35*b^6 + 280*a^2*b^4 + 336*a^4*b^2))/(8*d*(a + b)^(17/2)*(a - b)^(17/2))","B"
472,-1,-1,653,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b*sin(c + d*x))^8),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
473,0,-1,154,0.000000,"\text{Not used}","int(cos(c + d*x)^5*(a + b*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^5\,\sqrt{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^5*(a + b*sin(c + d*x))^(1/2), x)","F"
474,0,-1,83,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + b*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\sqrt{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^3*(a + b*sin(c + d*x))^(1/2), x)","F"
475,1,20,24,5.204158,"\text{Not used}","int(cos(c + d*x)*(a + b*sin(c + d*x))^(1/2),x)","\frac{2\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}}{3\,b\,d}","Not used",1,"(2*(a + b*sin(c + d*x))^(3/2))/(3*b*d)","B"
476,0,-1,74,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(1/2)/cos(c + d*x),x)","\int \frac{\sqrt{a+b\,\sin\left(c+d\,x\right)}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + b*sin(c + d*x))^(1/2)/cos(c + d*x), x)","F"
477,0,-1,124,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(1/2)/cos(c + d*x)^3,x)","\int \frac{\sqrt{a+b\,\sin\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + b*sin(c + d*x))^(1/2)/cos(c + d*x)^3, x)","F"
478,0,-1,207,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(1/2)/cos(c + d*x)^5,x)","\int \frac{\sqrt{a+b\,\sin\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((a + b*sin(c + d*x))^(1/2)/cos(c + d*x)^5, x)","F"
479,0,-1,298,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + b*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\sqrt{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^4*(a + b*sin(c + d*x))^(1/2), x)","F"
480,0,-1,215,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + b*sin(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\sqrt{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^2*(a + b*sin(c + d*x))^(1/2), x)","F"
481,0,-1,149,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(1/2)/cos(c + d*x)^2,x)","\int \frac{\sqrt{a+b\,\sin\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + b*sin(c + d*x))^(1/2)/cos(c + d*x)^2, x)","F"
482,0,-1,248,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(1/2)/cos(c + d*x)^4,x)","\int \frac{\sqrt{a+b\,\sin\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + b*sin(c + d*x))^(1/2)/cos(c + d*x)^4, x)","F"
483,0,-1,154,0.000000,"\text{Not used}","int(cos(c + d*x)^5*(a + b*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^5\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^5*(a + b*sin(c + d*x))^(3/2), x)","F"
484,0,-1,83,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + b*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^3\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^3*(a + b*sin(c + d*x))^(3/2), x)","F"
485,1,20,24,5.409685,"\text{Not used}","int(cos(c + d*x)*(a + b*sin(c + d*x))^(3/2),x)","\frac{2\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}}{5\,b\,d}","Not used",1,"(2*(a + b*sin(c + d*x))^(5/2))/(5*b*d)","B"
486,0,-1,94,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(3/2)/cos(c + d*x),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + b*sin(c + d*x))^(3/2)/cos(c + d*x), x)","F"
487,0,-1,130,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(3/2)/cos(c + d*x)^3,x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + b*sin(c + d*x))^(3/2)/cos(c + d*x)^3, x)","F"
488,0,-1,188,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(3/2)/cos(c + d*x)^5,x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((a + b*sin(c + d*x))^(3/2)/cos(c + d*x)^5, x)","F"
489,0,-1,329,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + b*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^4\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^4*(a + b*sin(c + d*x))^(3/2), x)","F"
490,0,-1,247,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + b*sin(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(a + b*sin(c + d*x))^(3/2), x)","F"
491,0,-1,168,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(3/2)/cos(c + d*x)^2,x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + b*sin(c + d*x))^(3/2)/cos(c + d*x)^2, x)","F"
492,0,-1,218,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(3/2)/cos(c + d*x)^4,x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + b*sin(c + d*x))^(3/2)/cos(c + d*x)^4, x)","F"
493,0,-1,330,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(3/2)/cos(c + d*x)^6,x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^6} \,d x","Not used",1,"int((a + b*sin(c + d*x))^(3/2)/cos(c + d*x)^6, x)","F"
494,0,-1,154,0.000000,"\text{Not used}","int(cos(c + d*x)^5*(a + b*sin(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^5\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^5*(a + b*sin(c + d*x))^(5/2), x)","F"
495,0,-1,83,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + b*sin(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^3\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^3*(a + b*sin(c + d*x))^(5/2), x)","F"
496,1,20,24,5.568526,"\text{Not used}","int(cos(c + d*x)*(a + b*sin(c + d*x))^(5/2),x)","\frac{2\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{7/2}}{7\,b\,d}","Not used",1,"(2*(a + b*sin(c + d*x))^(7/2))/(7*b*d)","B"
497,0,-1,117,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(5/2)/cos(c + d*x),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + b*sin(c + d*x))^(5/2)/cos(c + d*x), x)","F"
498,0,-1,155,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(5/2)/cos(c + d*x)^3,x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + b*sin(c + d*x))^(5/2)/cos(c + d*x)^3, x)","F"
499,0,-1,199,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(5/2)/cos(c + d*x)^5,x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((a + b*sin(c + d*x))^(5/2)/cos(c + d*x)^5, x)","F"
500,0,-1,398,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + b*sin(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^4\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^4*(a + b*sin(c + d*x))^(5/2), x)","F"
501,0,-1,299,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + b*sin(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(a + b*sin(c + d*x))^(5/2), x)","F"
502,0,-1,203,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(5/2)/cos(c + d*x)^2,x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + b*sin(c + d*x))^(5/2)/cos(c + d*x)^2, x)","F"
503,0,-1,238,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(5/2)/cos(c + d*x)^4,x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + b*sin(c + d*x))^(5/2)/cos(c + d*x)^4, x)","F"
504,-1,-1,322,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(5/2)/cos(c + d*x)^6,x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
505,-1,-1,439,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^(5/2)/cos(c + d*x)^8,x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
506,0,-1,152,0.000000,"\text{Not used}","int(cos(c + d*x)^5/(a + b*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^5}{\sqrt{a+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^5/(a + b*sin(c + d*x))^(1/2), x)","F"
507,0,-1,81,0.000000,"\text{Not used}","int(cos(c + d*x)^3/(a + b*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3}{\sqrt{a+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^3/(a + b*sin(c + d*x))^(1/2), x)","F"
508,1,20,22,6.224283,"\text{Not used}","int(cos(c + d*x)/(a + b*sin(c + d*x))^(1/2),x)","\frac{2\,\sqrt{a+b\,\sin\left(c+d\,x\right)}}{b\,d}","Not used",1,"(2*(a + b*sin(c + d*x))^(1/2))/(b*d)","B"
509,0,-1,74,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + b*sin(c + d*x))^(1/2)),x)","\int \frac{1}{\cos\left(c+d\,x\right)\,\sqrt{a+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)*(a + b*sin(c + d*x))^(1/2)), x)","F"
510,0,-1,144,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b*sin(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^3\,\sqrt{a+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^3*(a + b*sin(c + d*x))^(1/2)), x)","F"
511,0,-1,230,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + b*sin(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^5\,\sqrt{a+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^5*(a + b*sin(c + d*x))^(1/2)), x)","F"
512,0,-1,247,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(a + b*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{\sqrt{a+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^4/(a + b*sin(c + d*x))^(1/2), x)","F"
513,0,-1,175,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(a + b*sin(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{\sqrt{a+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^2/(a + b*sin(c + d*x))^(1/2), x)","F"
514,0,-1,183,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b*sin(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^2*(a + b*sin(c + d*x))^(1/2)), x)","F"
515,0,-1,291,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b*sin(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^4*(a + b*sin(c + d*x))^(1/2)), x)","F"
516,0,-1,150,0.000000,"\text{Not used}","int(cos(c + d*x)^5/(a + b*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^5}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^5/(a + b*sin(c + d*x))^(3/2), x)","F"
517,0,-1,79,0.000000,"\text{Not used}","int(cos(c + d*x)^3/(a + b*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^3/(a + b*sin(c + d*x))^(3/2), x)","F"
518,1,51,22,6.144626,"\text{Not used}","int(cos(c + d*x)/(a + b*sin(c + d*x))^(3/2),x)","-\frac{4\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}}{b\,d\,\left(2\,a^2+4\,a\,b\,\sin\left(c+d\,x\right)+2\,b^2\,{\sin\left(c+d\,x\right)}^2\right)}","Not used",1,"-(4*(a + b*sin(c + d*x))^(3/2))/(b*d*(2*a^2 + 2*b^2*sin(c + d*x)^2 + 4*a*b*sin(c + d*x)))","B"
519,0,-1,105,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + b*sin(c + d*x))^(3/2)),x)","\int \frac{1}{\cos\left(c+d\,x\right)\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)*(a + b*sin(c + d*x))^(3/2)), x)","F"
520,0,-1,186,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b*sin(c + d*x))^(3/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^3\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^3*(a + b*sin(c + d*x))^(3/2)), x)","F"
521,0,-1,284,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + b*sin(c + d*x))^(3/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^5\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^5*(a + b*sin(c + d*x))^(3/2)), x)","F"
522,0,-1,313,0.000000,"\text{Not used}","int(cos(c + d*x)^6/(a + b*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^6}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^6/(a + b*sin(c + d*x))^(3/2), x)","F"
523,0,-1,229,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(a + b*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^4/(a + b*sin(c + d*x))^(3/2), x)","F"
524,0,-1,160,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(a + b*sin(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^2/(a + b*sin(c + d*x))^(3/2), x)","F"
525,0,-1,251,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b*sin(c + d*x))^(3/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^2\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^2*(a + b*sin(c + d*x))^(3/2)), x)","F"
526,0,-1,359,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b*sin(c + d*x))^(3/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^4\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^4*(a + b*sin(c + d*x))^(3/2)), x)","F"
527,0,-1,150,0.000000,"\text{Not used}","int(cos(c + d*x)^5/(a + b*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^5}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^5/(a + b*sin(c + d*x))^(5/2), x)","F"
528,1,1402,79,11.891375,"\text{Not used}","int(cos(c + d*x)^3/(a + b*sin(c + d*x))^(5/2),x)","-\frac{2\,\sqrt{a+\frac{b\,\left(\cos\left(d\,x\right)-\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)-\sin\left(c\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}-\frac{b\,\left(\cos\left(d\,x\right)+\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)+\sin\left(c\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}}}{b^3\,d}-\frac{8\,a^4\,\left(\cos\left(2\,d\,x\right)+\sin\left(2\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(2\,c\right)+\sin\left(2\,c\right)\,1{}\mathrm{i}\right)\,\sqrt{a+\frac{b\,\left(\cos\left(d\,x\right)-\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)-\sin\left(c\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}-\frac{b\,\left(\cos\left(d\,x\right)+\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)+\sin\left(c\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}}}{3\,\left(a^2\,b^5\,d-b^7\,d+2\,b^7\,d\,\left(\cos\left(2\,d\,x\right)+\sin\left(2\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(2\,c\right)+\sin\left(2\,c\right)\,1{}\mathrm{i}\right)-b^7\,d\,\left(\cos\left(4\,d\,x\right)+\sin\left(4\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(4\,c\right)+\sin\left(4\,c\right)\,1{}\mathrm{i}\right)-a\,b^6\,d\,\left(\cos\left(3\,d\,x\right)+\sin\left(3\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(3\,c\right)+\sin\left(3\,c\right)\,1{}\mathrm{i}\right)\,4{}\mathrm{i}+a\,b^6\,d\,\left(\cos\left(d\,x\right)+\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)+\sin\left(c\right)\,1{}\mathrm{i}\right)\,4{}\mathrm{i}+2\,a^2\,b^5\,d\,\left(\cos\left(2\,d\,x\right)+\sin\left(2\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(2\,c\right)+\sin\left(2\,c\right)\,1{}\mathrm{i}\right)-4\,a^4\,b^3\,d\,\left(\cos\left(2\,d\,x\right)+\sin\left(2\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(2\,c\right)+\sin\left(2\,c\right)\,1{}\mathrm{i}\right)+a^3\,b^4\,d\,\left(\cos\left(3\,d\,x\right)+\sin\left(3\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(3\,c\right)+\sin\left(3\,c\right)\,1{}\mathrm{i}\right)\,4{}\mathrm{i}+a^2\,b^5\,d\,\left(\cos\left(4\,d\,x\right)+\sin\left(4\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(4\,c\right)+\sin\left(4\,c\right)\,1{}\mathrm{i}\right)-a^3\,b^4\,d\,\left(\cos\left(d\,x\right)+\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)+\sin\left(c\right)\,1{}\mathrm{i}\right)\,4{}\mathrm{i}\right)}-\frac{8\,b^4\,\left(\cos\left(2\,d\,x\right)+\sin\left(2\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(2\,c\right)+\sin\left(2\,c\right)\,1{}\mathrm{i}\right)\,\sqrt{a+\frac{b\,\left(\cos\left(d\,x\right)-\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)-\sin\left(c\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}-\frac{b\,\left(\cos\left(d\,x\right)+\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)+\sin\left(c\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}}}{3\,\left(a^2\,b^5\,d-b^7\,d+2\,b^7\,d\,\left(\cos\left(2\,d\,x\right)+\sin\left(2\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(2\,c\right)+\sin\left(2\,c\right)\,1{}\mathrm{i}\right)-b^7\,d\,\left(\cos\left(4\,d\,x\right)+\sin\left(4\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(4\,c\right)+\sin\left(4\,c\right)\,1{}\mathrm{i}\right)-a\,b^6\,d\,\left(\cos\left(3\,d\,x\right)+\sin\left(3\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(3\,c\right)+\sin\left(3\,c\right)\,1{}\mathrm{i}\right)\,4{}\mathrm{i}+a\,b^6\,d\,\left(\cos\left(d\,x\right)+\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)+\sin\left(c\right)\,1{}\mathrm{i}\right)\,4{}\mathrm{i}+2\,a^2\,b^5\,d\,\left(\cos\left(2\,d\,x\right)+\sin\left(2\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(2\,c\right)+\sin\left(2\,c\right)\,1{}\mathrm{i}\right)-4\,a^4\,b^3\,d\,\left(\cos\left(2\,d\,x\right)+\sin\left(2\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(2\,c\right)+\sin\left(2\,c\right)\,1{}\mathrm{i}\right)+a^3\,b^4\,d\,\left(\cos\left(3\,d\,x\right)+\sin\left(3\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(3\,c\right)+\sin\left(3\,c\right)\,1{}\mathrm{i}\right)\,4{}\mathrm{i}+a^2\,b^5\,d\,\left(\cos\left(4\,d\,x\right)+\sin\left(4\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(4\,c\right)+\sin\left(4\,c\right)\,1{}\mathrm{i}\right)-a^3\,b^4\,d\,\left(\cos\left(d\,x\right)+\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)+\sin\left(c\right)\,1{}\mathrm{i}\right)\,4{}\mathrm{i}\right)}-\frac{a\,\left(\cos\left(d\,x\right)+\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)+\sin\left(c\right)\,1{}\mathrm{i}\right)\,\sqrt{a+\frac{b\,\left(\cos\left(d\,x\right)-\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)-\sin\left(c\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}-\frac{b\,\left(\cos\left(d\,x\right)+\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)+\sin\left(c\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}}\,8{}\mathrm{i}}{-b^4\,d+b^4\,d\,\left(\cos\left(2\,d\,x\right)+\sin\left(2\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(2\,c\right)+\sin\left(2\,c\right)\,1{}\mathrm{i}\right)+a\,b^3\,d\,\left(\cos\left(d\,x\right)+\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)+\sin\left(c\right)\,1{}\mathrm{i}\right)\,2{}\mathrm{i}}+\frac{16\,a^2\,b^2\,\left(\cos\left(2\,d\,x\right)+\sin\left(2\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(2\,c\right)+\sin\left(2\,c\right)\,1{}\mathrm{i}\right)\,\sqrt{a+\frac{b\,\left(\cos\left(d\,x\right)-\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)-\sin\left(c\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}-\frac{b\,\left(\cos\left(d\,x\right)+\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)+\sin\left(c\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}}}{3\,\left(a^2\,b^5\,d-b^7\,d+2\,b^7\,d\,\left(\cos\left(2\,d\,x\right)+\sin\left(2\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(2\,c\right)+\sin\left(2\,c\right)\,1{}\mathrm{i}\right)-b^7\,d\,\left(\cos\left(4\,d\,x\right)+\sin\left(4\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(4\,c\right)+\sin\left(4\,c\right)\,1{}\mathrm{i}\right)-a\,b^6\,d\,\left(\cos\left(3\,d\,x\right)+\sin\left(3\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(3\,c\right)+\sin\left(3\,c\right)\,1{}\mathrm{i}\right)\,4{}\mathrm{i}+a\,b^6\,d\,\left(\cos\left(d\,x\right)+\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)+\sin\left(c\right)\,1{}\mathrm{i}\right)\,4{}\mathrm{i}+2\,a^2\,b^5\,d\,\left(\cos\left(2\,d\,x\right)+\sin\left(2\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(2\,c\right)+\sin\left(2\,c\right)\,1{}\mathrm{i}\right)-4\,a^4\,b^3\,d\,\left(\cos\left(2\,d\,x\right)+\sin\left(2\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(2\,c\right)+\sin\left(2\,c\right)\,1{}\mathrm{i}\right)+a^3\,b^4\,d\,\left(\cos\left(3\,d\,x\right)+\sin\left(3\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(3\,c\right)+\sin\left(3\,c\right)\,1{}\mathrm{i}\right)\,4{}\mathrm{i}+a^2\,b^5\,d\,\left(\cos\left(4\,d\,x\right)+\sin\left(4\,d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(4\,c\right)+\sin\left(4\,c\right)\,1{}\mathrm{i}\right)-a^3\,b^4\,d\,\left(\cos\left(d\,x\right)+\sin\left(d\,x\right)\,1{}\mathrm{i}\right)\,\left(\cos\left(c\right)+\sin\left(c\right)\,1{}\mathrm{i}\right)\,4{}\mathrm{i}\right)}","Not used",1,"(16*a^2*b^2*(cos(2*d*x) + sin(2*d*x)*1i)*(cos(2*c) + sin(2*c)*1i)*(a + (b*(cos(d*x) - sin(d*x)*1i)*(cos(c) - sin(c)*1i)*1i)/2 - (b*(cos(d*x) + sin(d*x)*1i)*(cos(c) + sin(c)*1i)*1i)/2)^(1/2))/(3*(a^2*b^5*d - b^7*d + 2*b^7*d*(cos(2*d*x) + sin(2*d*x)*1i)*(cos(2*c) + sin(2*c)*1i) - b^7*d*(cos(4*d*x) + sin(4*d*x)*1i)*(cos(4*c) + sin(4*c)*1i) - a*b^6*d*(cos(3*d*x) + sin(3*d*x)*1i)*(cos(3*c) + sin(3*c)*1i)*4i + a*b^6*d*(cos(d*x) + sin(d*x)*1i)*(cos(c) + sin(c)*1i)*4i + 2*a^2*b^5*d*(cos(2*d*x) + sin(2*d*x)*1i)*(cos(2*c) + sin(2*c)*1i) - 4*a^4*b^3*d*(cos(2*d*x) + sin(2*d*x)*1i)*(cos(2*c) + sin(2*c)*1i) + a^3*b^4*d*(cos(3*d*x) + sin(3*d*x)*1i)*(cos(3*c) + sin(3*c)*1i)*4i + a^2*b^5*d*(cos(4*d*x) + sin(4*d*x)*1i)*(cos(4*c) + sin(4*c)*1i) - a^3*b^4*d*(cos(d*x) + sin(d*x)*1i)*(cos(c) + sin(c)*1i)*4i)) - (8*a^4*(cos(2*d*x) + sin(2*d*x)*1i)*(cos(2*c) + sin(2*c)*1i)*(a + (b*(cos(d*x) - sin(d*x)*1i)*(cos(c) - sin(c)*1i)*1i)/2 - (b*(cos(d*x) + sin(d*x)*1i)*(cos(c) + sin(c)*1i)*1i)/2)^(1/2))/(3*(a^2*b^5*d - b^7*d + 2*b^7*d*(cos(2*d*x) + sin(2*d*x)*1i)*(cos(2*c) + sin(2*c)*1i) - b^7*d*(cos(4*d*x) + sin(4*d*x)*1i)*(cos(4*c) + sin(4*c)*1i) - a*b^6*d*(cos(3*d*x) + sin(3*d*x)*1i)*(cos(3*c) + sin(3*c)*1i)*4i + a*b^6*d*(cos(d*x) + sin(d*x)*1i)*(cos(c) + sin(c)*1i)*4i + 2*a^2*b^5*d*(cos(2*d*x) + sin(2*d*x)*1i)*(cos(2*c) + sin(2*c)*1i) - 4*a^4*b^3*d*(cos(2*d*x) + sin(2*d*x)*1i)*(cos(2*c) + sin(2*c)*1i) + a^3*b^4*d*(cos(3*d*x) + sin(3*d*x)*1i)*(cos(3*c) + sin(3*c)*1i)*4i + a^2*b^5*d*(cos(4*d*x) + sin(4*d*x)*1i)*(cos(4*c) + sin(4*c)*1i) - a^3*b^4*d*(cos(d*x) + sin(d*x)*1i)*(cos(c) + sin(c)*1i)*4i)) - (8*b^4*(cos(2*d*x) + sin(2*d*x)*1i)*(cos(2*c) + sin(2*c)*1i)*(a + (b*(cos(d*x) - sin(d*x)*1i)*(cos(c) - sin(c)*1i)*1i)/2 - (b*(cos(d*x) + sin(d*x)*1i)*(cos(c) + sin(c)*1i)*1i)/2)^(1/2))/(3*(a^2*b^5*d - b^7*d + 2*b^7*d*(cos(2*d*x) + sin(2*d*x)*1i)*(cos(2*c) + sin(2*c)*1i) - b^7*d*(cos(4*d*x) + sin(4*d*x)*1i)*(cos(4*c) + sin(4*c)*1i) - a*b^6*d*(cos(3*d*x) + sin(3*d*x)*1i)*(cos(3*c) + sin(3*c)*1i)*4i + a*b^6*d*(cos(d*x) + sin(d*x)*1i)*(cos(c) + sin(c)*1i)*4i + 2*a^2*b^5*d*(cos(2*d*x) + sin(2*d*x)*1i)*(cos(2*c) + sin(2*c)*1i) - 4*a^4*b^3*d*(cos(2*d*x) + sin(2*d*x)*1i)*(cos(2*c) + sin(2*c)*1i) + a^3*b^4*d*(cos(3*d*x) + sin(3*d*x)*1i)*(cos(3*c) + sin(3*c)*1i)*4i + a^2*b^5*d*(cos(4*d*x) + sin(4*d*x)*1i)*(cos(4*c) + sin(4*c)*1i) - a^3*b^4*d*(cos(d*x) + sin(d*x)*1i)*(cos(c) + sin(c)*1i)*4i)) - (a*(cos(d*x) + sin(d*x)*1i)*(cos(c) + sin(c)*1i)*(a + (b*(cos(d*x) - sin(d*x)*1i)*(cos(c) - sin(c)*1i)*1i)/2 - (b*(cos(d*x) + sin(d*x)*1i)*(cos(c) + sin(c)*1i)*1i)/2)^(1/2)*8i)/(b^4*d*(cos(2*d*x) + sin(2*d*x)*1i)*(cos(2*c) + sin(2*c)*1i) - b^4*d + a*b^3*d*(cos(d*x) + sin(d*x)*1i)*(cos(c) + sin(c)*1i)*2i) - (2*(a + (b*(cos(d*x) - sin(d*x)*1i)*(cos(c) - sin(c)*1i)*1i)/2 - (b*(cos(d*x) + sin(d*x)*1i)*(cos(c) + sin(c)*1i)*1i)/2)^(1/2))/(b^3*d)","B"
529,1,157,24,7.246419,"\text{Not used}","int(cos(c + d*x)/(a + b*sin(c + d*x))^(5/2),x)","-\frac{8\,\sqrt{a+b\,\sin\left(c+d\,x\right)}\,\left(2\,a^2+b^2-b^2\,\cos\left(2\,c+2\,d\,x\right)+4\,a\,b\,\sin\left(c+d\,x\right)\right)}{3\,b\,d\,\left(8\,a^4+3\,b^4+24\,a^2\,b^2-4\,b^4\,\cos\left(2\,c+2\,d\,x\right)+b^4\,\cos\left(4\,c+4\,d\,x\right)-8\,a\,b^3\,\sin\left(3\,c+3\,d\,x\right)-24\,a^2\,b^2\,\cos\left(2\,c+2\,d\,x\right)+24\,a\,b^3\,\sin\left(c+d\,x\right)+32\,a^3\,b\,\sin\left(c+d\,x\right)\right)}","Not used",1,"-(8*(a + b*sin(c + d*x))^(1/2)*(2*a^2 + b^2 - b^2*cos(2*c + 2*d*x) + 4*a*b*sin(c + d*x)))/(3*b*d*(8*a^4 + 3*b^4 + 24*a^2*b^2 - 4*b^4*cos(2*c + 2*d*x) + b^4*cos(4*c + 4*d*x) - 8*a*b^3*sin(3*c + 3*d*x) - 24*a^2*b^2*cos(2*c + 2*d*x) + 24*a*b^3*sin(c + d*x) + 32*a^3*b*sin(c + d*x)))","B"
530,0,-1,139,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + b*sin(c + d*x))^(5/2)),x)","\int \frac{1}{\cos\left(c+d\,x\right)\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)*(a + b*sin(c + d*x))^(5/2)), x)","F"
531,0,-1,231,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b*sin(c + d*x))^(5/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^3\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^3*(a + b*sin(c + d*x))^(5/2)), x)","F"
532,-1,-1,339,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + b*sin(c + d*x))^(5/2)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
533,0,-1,384,0.000000,"\text{Not used}","int(cos(c + d*x)^8/(a + b*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^8}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^8/(a + b*sin(c + d*x))^(5/2), x)","F"
534,0,-1,293,0.000000,"\text{Not used}","int(cos(c + d*x)^6/(a + b*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^6}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^6/(a + b*sin(c + d*x))^(5/2), x)","F"
535,0,-1,221,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(a + b*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^4/(a + b*sin(c + d*x))^(5/2), x)","F"
536,0,-1,219,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(a + b*sin(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^2/(a + b*sin(c + d*x))^(5/2), x)","F"
537,0,-1,325,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b*sin(c + d*x))^(5/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^2\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^2*(a + b*sin(c + d*x))^(5/2)), x)","F"
538,0,-1,425,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b*sin(c + d*x))^(5/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^4\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^4*(a + b*sin(c + d*x))^(5/2)), x)","F"
539,0,-1,124,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)*(a + b*sin(c + d*x)),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}\,\left(a+b\,\sin\left(c+d\,x\right)\right) \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)*(a + b*sin(c + d*x)), x)","F"
540,0,-1,95,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)*(a + b*sin(c + d*x)),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(a+b\,\sin\left(c+d\,x\right)\right) \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)*(a + b*sin(c + d*x)), x)","F"
541,0,-1,95,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x)),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(a+b\,\sin\left(c+d\,x\right)\right) \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x)), x)","F"
542,0,-1,63,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x)),x)","\int \sqrt{e\,\cos\left(c+d\,x\right)}\,\left(a+b\,\sin\left(c+d\,x\right)\right) \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x)), x)","F"
543,1,47,61,6.493935,"\text{Not used}","int((a + b*sin(c + d*x))/(e*cos(c + d*x))^(1/2),x)","-\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\left(b\,\sqrt{\cos\left(c+d\,x\right)}-a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d\,\sqrt{e\,\cos\left(c+d\,x\right)}}","Not used",1,"-(2*cos(c + d*x)^(1/2)*(b*cos(c + d*x)^(1/2) - a*ellipticF(c/2 + (d*x)/2, 2)))/(d*(e*cos(c + d*x))^(1/2))","B"
544,0,-1,91,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))/(e*cos(c + d*x))^(3/2),x)","\int \frac{a+b\,\sin\left(c+d\,x\right)}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))/(e*cos(c + d*x))^(3/2), x)","F"
545,0,-1,97,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))/(e*cos(c + d*x))^(5/2),x)","\int \frac{a+b\,\sin\left(c+d\,x\right)}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))/(e*cos(c + d*x))^(5/2), x)","F"
546,0,-1,126,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))/(e*cos(c + d*x))^(7/2),x)","\int \frac{a+b\,\sin\left(c+d\,x\right)}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))/(e*cos(c + d*x))^(7/2), x)","F"
547,0,-1,188,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)*(a + b*sin(c + d*x))^2,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)*(a + b*sin(c + d*x))^2, x)","F"
548,0,-1,149,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)*(a + b*sin(c + d*x))^2,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)*(a + b*sin(c + d*x))^2, x)","F"
549,0,-1,149,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x))^2,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x))^2, x)","F"
550,0,-1,109,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x))^2,x)","\int \sqrt{e\,\cos\left(c+d\,x\right)}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x))^2, x)","F"
551,0,-1,109,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^2/(e*cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2}{\sqrt{e\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^2/(e*cos(c + d*x))^(1/2), x)","F"
552,0,-1,113,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^2/(e*cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^2/(e*cos(c + d*x))^(3/2), x)","F"
553,0,-1,119,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^2/(e*cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^2/(e*cos(c + d*x))^(5/2), x)","F"
554,0,-1,160,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^2/(e*cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^2/(e*cos(c + d*x))^(7/2), x)","F"
555,0,-1,237,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)*(a + b*sin(c + d*x))^3,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)*(a + b*sin(c + d*x))^3, x)","F"
556,0,-1,197,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)*(a + b*sin(c + d*x))^3,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)*(a + b*sin(c + d*x))^3, x)","F"
557,0,-1,197,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x))^3,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x))^3, x)","F"
558,0,-1,156,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x))^3,x)","\int \sqrt{e\,\cos\left(c+d\,x\right)}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x))^3, x)","F"
559,0,-1,152,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^3/(e*cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3}{\sqrt{e\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^3/(e*cos(c + d*x))^(1/2), x)","F"
560,0,-1,160,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^3/(e*cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^3/(e*cos(c + d*x))^(3/2), x)","F"
561,0,-1,164,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^3/(e*cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^3/(e*cos(c + d*x))^(5/2), x)","F"
562,0,-1,187,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^3/(e*cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^3/(e*cos(c + d*x))^(7/2), x)","F"
563,0,-1,188,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^3/(e*cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^3/(e*cos(c + d*x))^(9/2), x)","F"
564,0,-1,305,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)*(a + b*sin(c + d*x))^4,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)*(a + b*sin(c + d*x))^4, x)","F"
565,0,-1,258,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)*(a + b*sin(c + d*x))^4,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)*(a + b*sin(c + d*x))^4, x)","F"
566,0,-1,258,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x))^4,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x))^4, x)","F"
567,0,-1,210,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x))^4,x)","\int \sqrt{e\,\cos\left(c+d\,x\right)}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x))^4, x)","F"
568,0,-1,210,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^4/(e*cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4}{\sqrt{e\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^4/(e*cos(c + d*x))^(1/2), x)","F"
569,0,-1,218,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^4/(e*cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^4/(e*cos(c + d*x))^(3/2), x)","F"
570,0,-1,216,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^4/(e*cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^4/(e*cos(c + d*x))^(5/2), x)","F"
571,0,-1,237,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^4/(e*cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^4/(e*cos(c + d*x))^(7/2), x)","F"
572,0,-1,241,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^4/(e*cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^4/(e*cos(c + d*x))^(9/2), x)","F"
573,0,-1,264,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^4/(e*cos(c + d*x))^(11/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{11/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^4/(e*cos(c + d*x))^(11/2), x)","F"
574,0,-1,531,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(11/2)/(a + b*sin(c + d*x)),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{11/2}}{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^(11/2)/(a + b*sin(c + d*x)), x)","F"
575,0,-1,446,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(9/2)/(a + b*sin(c + d*x)),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{9/2}}{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^(9/2)/(a + b*sin(c + d*x)), x)","F"
576,0,-1,461,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)/(a + b*sin(c + d*x)),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}}{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)/(a + b*sin(c + d*x)), x)","F"
577,0,-1,384,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)/(a + b*sin(c + d*x)),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}}{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)/(a + b*sin(c + d*x)), x)","F"
578,0,-1,397,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)/(a + b*sin(c + d*x)),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}}{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)/(a + b*sin(c + d*x)), x)","F"
579,0,-1,292,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)/(a + b*sin(c + d*x)),x)","\int \frac{\sqrt{e\,\cos\left(c+d\,x\right)}}{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)/(a + b*sin(c + d*x)), x)","F"
580,0,-1,299,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x))),x)","\int \frac{1}{\sqrt{e\,\cos\left(c+d\,x\right)}\,\left(a+b\,\sin\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x))), x)","F"
581,0,-1,411,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x))),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(a+b\,\sin\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x))), x)","F"
582,0,-1,434,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(5/2)*(a + b*sin(c + d*x))),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(a+b\,\sin\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(5/2)*(a + b*sin(c + d*x))), x)","F"
583,0,-1,486,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(7/2)*(a + b*sin(c + d*x))),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}\,\left(a+b\,\sin\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(7/2)*(a + b*sin(c + d*x))), x)","F"
584,0,-1,543,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(11/2)/(a + b*sin(c + d*x))^2,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{11/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*cos(c + d*x))^(11/2)/(a + b*sin(c + d*x))^2, x)","F"
585,0,-1,459,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(9/2)/(a + b*sin(c + d*x))^2,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{9/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*cos(c + d*x))^(9/2)/(a + b*sin(c + d*x))^2, x)","F"
586,0,-1,473,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)/(a + b*sin(c + d*x))^2,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)/(a + b*sin(c + d*x))^2, x)","F"
587,0,-1,390,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)/(a + b*sin(c + d*x))^2,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)/(a + b*sin(c + d*x))^2, x)","F"
588,0,-1,404,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)/(a + b*sin(c + d*x))^2,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)/(a + b*sin(c + d*x))^2, x)","F"
589,0,-1,422,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)/(a + b*sin(c + d*x))^2,x)","\int \frac{\sqrt{e\,\cos\left(c+d\,x\right)}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)/(a + b*sin(c + d*x))^2, x)","F"
590,0,-1,429,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x))^2),x)","\int \frac{1}{\sqrt{e\,\cos\left(c+d\,x\right)}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x))^2), x)","F"
591,0,-1,492,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x))^2),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x))^2), x)","F"
592,0,-1,514,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(5/2)*(a + b*sin(c + d*x))^2),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(5/2)*(a + b*sin(c + d*x))^2), x)","F"
593,0,-1,574,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(7/2)*(a + b*sin(c + d*x))^2),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(7/2)*(a + b*sin(c + d*x))^2), x)","F"
594,0,-1,575,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(13/2)/(a + b*sin(c + d*x))^3,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{13/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^(13/2)/(a + b*sin(c + d*x))^3, x)","F"
595,0,-1,589,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(11/2)/(a + b*sin(c + d*x))^3,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{11/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^(11/2)/(a + b*sin(c + d*x))^3, x)","F"
596,0,-1,483,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(9/2)/(a + b*sin(c + d*x))^3,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{9/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^(9/2)/(a + b*sin(c + d*x))^3, x)","F"
597,0,-1,497,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)/(a + b*sin(c + d*x))^3,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)/(a + b*sin(c + d*x))^3, x)","F"
598,0,-1,505,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)/(a + b*sin(c + d*x))^3,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)/(a + b*sin(c + d*x))^3, x)","F"
599,0,-1,519,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)/(a + b*sin(c + d*x))^3,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)/(a + b*sin(c + d*x))^3, x)","F"
600,0,-1,514,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)/(a + b*sin(c + d*x))^3,x)","\int \frac{\sqrt{e\,\cos\left(c+d\,x\right)}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)/(a + b*sin(c + d*x))^3, x)","F"
601,0,-1,520,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x))^3),x)","\int \frac{1}{\sqrt{e\,\cos\left(c+d\,x\right)}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x))^3), x)","F"
602,0,-1,596,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x))^3),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x))^3), x)","F"
603,0,-1,614,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(5/2)*(a + b*sin(c + d*x))^3),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(5/2)*(a + b*sin(c + d*x))^3), x)","F"
604,0,-1,685,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(7/2)*(a + b*sin(c + d*x))^3),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(7/2)*(a + b*sin(c + d*x))^3), x)","F"
605,0,-1,671,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(15/2)/(a + b*sin(c + d*x))^4,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{15/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((e*cos(c + d*x))^(15/2)/(a + b*sin(c + d*x))^4, x)","F"
606,0,-1,557,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(13/2)/(a + b*sin(c + d*x))^4,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{13/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((e*cos(c + d*x))^(13/2)/(a + b*sin(c + d*x))^4, x)","F"
607,-1,-1,571,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(11/2)/(a + b*sin(c + d*x))^4,x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
608,0,-1,591,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(9/2)/(a + b*sin(c + d*x))^4,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{9/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((e*cos(c + d*x))^(9/2)/(a + b*sin(c + d*x))^4, x)","F"
609,0,-1,597,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(7/2)/(a + b*sin(c + d*x))^4,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{7/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((e*cos(c + d*x))^(7/2)/(a + b*sin(c + d*x))^4, x)","F"
610,0,-1,574,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)/(a + b*sin(c + d*x))^4,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)/(a + b*sin(c + d*x))^4, x)","F"
611,0,-1,592,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)/(a + b*sin(c + d*x))^4,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)/(a + b*sin(c + d*x))^4, x)","F"
612,0,-1,579,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)/(a + b*sin(c + d*x))^4,x)","\int \frac{\sqrt{e\,\cos\left(c+d\,x\right)}}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)/(a + b*sin(c + d*x))^4, x)","F"
613,0,-1,593,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x))^4),x)","\int \frac{1}{\sqrt{e\,\cos\left(c+d\,x\right)}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x))^4), x)","F"
614,0,-1,674,0.000000,"\text{Not used}","int(1/((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x))^4),x)","\int \frac{1}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^4} \,d x","Not used",1,"int(1/((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x))^4), x)","F"
615,0,-1,183,0.000000,"\text{Not used}","int(1/((c*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))^(1/2)),x)","\int \frac{1}{\sqrt{c\,\cos\left(e+f\,x\right)}\,\sqrt{a+b\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((c*cos(e + f*x))^(1/2)*(a + b*sin(e + f*x))^(1/2)), x)","F"
616,0,-1,229,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p*(a + b*sin(c + d*x))^3,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^p\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((e*cos(c + d*x))^p*(a + b*sin(c + d*x))^3, x)","F"
617,0,-1,157,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p*(a + b*sin(c + d*x))^2,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^p\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((e*cos(c + d*x))^p*(a + b*sin(c + d*x))^2, x)","F"
618,0,-1,97,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p*(a + b*sin(c + d*x)),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^p\,\left(a+b\,\sin\left(c+d\,x\right)\right) \,d x","Not used",1,"int((e*cos(c + d*x))^p*(a + b*sin(c + d*x)), x)","F"
619,0,-1,158,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p/(a + b*sin(c + d*x)),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^p}{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^p/(a + b*sin(c + d*x)), x)","F"
620,0,-1,170,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p/(a + b*sin(c + d*x))^2,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^p}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*cos(c + d*x))^p/(a + b*sin(c + d*x))^2, x)","F"
621,0,-1,170,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p/(a + b*sin(c + d*x))^3,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^p}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*cos(c + d*x))^p/(a + b*sin(c + d*x))^3, x)","F"
622,0,-1,170,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p/(a + b*sin(c + d*x))^8,x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^p}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^8} \,d x","Not used",1,"int((e*cos(c + d*x))^p/(a + b*sin(c + d*x))^8, x)","F"
623,0,-1,156,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p*(a + b*sin(c + d*x))^(5/2),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^p\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((e*cos(c + d*x))^p*(a + b*sin(c + d*x))^(5/2), x)","F"
624,0,-1,156,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p*(a + b*sin(c + d*x))^(3/2),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^p\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((e*cos(c + d*x))^p*(a + b*sin(c + d*x))^(3/2), x)","F"
625,0,-1,156,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p*(a + b*sin(c + d*x))^(1/2),x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^p\,\sqrt{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((e*cos(c + d*x))^p*(a + b*sin(c + d*x))^(1/2), x)","F"
626,0,-1,154,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p/(a + b*sin(c + d*x))^(1/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^p}{\sqrt{a+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((e*cos(c + d*x))^p/(a + b*sin(c + d*x))^(1/2), x)","F"
627,0,-1,154,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p/(a + b*sin(c + d*x))^(3/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^p}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((e*cos(c + d*x))^p/(a + b*sin(c + d*x))^(3/2), x)","F"
628,0,-1,156,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p/(a + b*sin(c + d*x))^(5/2),x)","\int \frac{{\left(e\,\cos\left(c+d\,x\right)\right)}^p}{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((e*cos(c + d*x))^p/(a + b*sin(c + d*x))^(5/2), x)","F"
629,0,-1,158,0.000000,"\text{Not used}","int((e*cos(c + d*x))^p*(a + b*sin(c + d*x))^m,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^p\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int((e*cos(c + d*x))^p*(a + b*sin(c + d*x))^m, x)","F"
630,1,1196,254,19.094398,"\text{Not used}","int(cos(c + d*x)^7*(a + b*sin(c + d*x))^m,x)","\frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m\,\left(-a^7\,92160{}\mathrm{i}-a^5\,b^2\,m^2\,13824{}\mathrm{i}+a^5\,b^2\,m\,96768{}\mathrm{i}+a^5\,b^2\,387072{}\mathrm{i}+a^3\,b^4\,m^4\,96{}\mathrm{i}+a^3\,b^4\,m^3\,6720{}\mathrm{i}-a^3\,b^4\,m^2\,26592{}\mathrm{i}-a^3\,b^4\,m\,401856{}\mathrm{i}-a^3\,b^4\,645120{}\mathrm{i}+a\,b^6\,m^6\,40{}\mathrm{i}+a\,b^6\,m^5\,1176{}\mathrm{i}+a\,b^6\,m^4\,14632{}\mathrm{i}+a\,b^6\,m^3\,105000{}\mathrm{i}+a\,b^6\,m^2\,436336{}\mathrm{i}+a\,b^6\,m\,897792{}\mathrm{i}+a\,b^6\,645120{}\mathrm{i}\right)}{128\,b^7\,d\,\left(m^7\,1{}\mathrm{i}+m^6\,28{}\mathrm{i}+m^5\,322{}\mathrm{i}+m^4\,1960{}\mathrm{i}+m^3\,6769{}\mathrm{i}+m^2\,13132{}\mathrm{i}+m\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}+\frac{\sin\left(7\,c+7\,d\,x\right)\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m\,\left(m^6+21\,m^5+175\,m^4+735\,m^3+1624\,m^2+1764\,m+720\right)\,1{}\mathrm{i}}{64\,d\,\left(m^7\,1{}\mathrm{i}+m^6\,28{}\mathrm{i}+m^5\,322{}\mathrm{i}+m^4\,1960{}\mathrm{i}+m^3\,6769{}\mathrm{i}+m^2\,13132{}\mathrm{i}+m\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}+\frac{\sin\left(c+d\,x\right)\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m\,\left(46080\,a^6\,b\,m+1152\,a^4\,b^3\,m^3-42624\,a^4\,b^3\,m^2-182016\,a^4\,b^3\,m+48\,a^2\,b^5\,m^5+1632\,a^2\,b^5\,m^4+29328\,a^2\,b^5\,m^3+169440\,a^2\,b^5\,m^2+279936\,a^2\,b^5\,m+5\,b^7\,m^6+153\,b^7\,m^5+2027\,b^7\,m^4+16299\,b^7\,m^3+78968\,b^7\,m^2+194868\,b^7\,m+176400\,b^7\right)\,1{}\mathrm{i}}{64\,b^7\,d\,\left(m^7\,1{}\mathrm{i}+m^6\,28{}\mathrm{i}+m^5\,322{}\mathrm{i}+m^4\,1960{}\mathrm{i}+m^3\,6769{}\mathrm{i}+m^2\,13132{}\mathrm{i}+m\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}+\frac{\sin\left(3\,c+3\,d\,x\right)\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m\,\left(m^2+3\,m+2\right)\,\left(-640\,a^4\,m+24\,a^2\,b^2\,m^3+552\,a^2\,b^2\,m^2+2208\,a^2\,b^2\,m+3\,b^4\,m^4+78\,b^4\,m^3+797\,b^4\,m^2+3602\,b^4\,m+5880\,b^4\right)\,3{}\mathrm{i}}{64\,b^4\,d\,\left(m^7\,1{}\mathrm{i}+m^6\,28{}\mathrm{i}+m^5\,322{}\mathrm{i}+m^4\,1960{}\mathrm{i}+m^3\,6769{}\mathrm{i}+m^2\,13132{}\mathrm{i}+m\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}+\frac{\sin\left(5\,c+5\,d\,x\right)\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m\,\left(24\,a^2\,m+5\,b^2\,m^2+79\,b^2\,m+294\,b^2\right)\,\left(m^4+10\,m^3+35\,m^2+50\,m+24\right)\,1{}\mathrm{i}}{64\,b^2\,d\,\left(m^7\,1{}\mathrm{i}+m^6\,28{}\mathrm{i}+m^5\,322{}\mathrm{i}+m^4\,1960{}\mathrm{i}+m^3\,6769{}\mathrm{i}+m^2\,13132{}\mathrm{i}+m\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}+\frac{a\,m\,\cos\left(6\,c+6\,d\,x\right)\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m\,\left(m^5\,1{}\mathrm{i}+m^4\,15{}\mathrm{i}+m^3\,85{}\mathrm{i}+m^2\,225{}\mathrm{i}+m\,274{}\mathrm{i}+120{}\mathrm{i}\right)}{32\,b\,d\,\left(m^7\,1{}\mathrm{i}+m^6\,28{}\mathrm{i}+m^5\,322{}\mathrm{i}+m^4\,1960{}\mathrm{i}+m^3\,6769{}\mathrm{i}+m^2\,13132{}\mathrm{i}+m\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}+\frac{3\,a\,m\,\cos\left(4\,c+4\,d\,x\right)\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m\,\left(-a^2\,20{}\mathrm{i}+b^2\,m^2\,1{}\mathrm{i}+b^2\,m\,17{}\mathrm{i}+b^2\,64{}\mathrm{i}\right)\,\left(m^3+6\,m^2+11\,m+6\right)}{16\,b^3\,d\,\left(m^7\,1{}\mathrm{i}+m^6\,28{}\mathrm{i}+m^5\,322{}\mathrm{i}+m^4\,1960{}\mathrm{i}+m^3\,6769{}\mathrm{i}+m^2\,13132{}\mathrm{i}+m\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}+\frac{3\,a\,m\,\cos\left(2\,c+2\,d\,x\right)\,\left(m+1\right)\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m\,\left(a^4\,1920{}\mathrm{i}-a^2\,b^2\,m^2\,32{}\mathrm{i}-a^2\,b^2\,m\,1696{}\mathrm{i}-a^2\,b^2\,7104{}\mathrm{i}+b^4\,m^4\,5{}\mathrm{i}+b^4\,m^3\,134{}\mathrm{i}+b^4\,m^2\,1411{}\mathrm{i}+b^4\,m\,6370{}\mathrm{i}+b^4\,10008{}\mathrm{i}\right)}{32\,b^5\,d\,\left(m^7\,1{}\mathrm{i}+m^6\,28{}\mathrm{i}+m^5\,322{}\mathrm{i}+m^4\,1960{}\mathrm{i}+m^3\,6769{}\mathrm{i}+m^2\,13132{}\mathrm{i}+m\,13068{}\mathrm{i}+5040{}\mathrm{i}\right)}","Not used",1,"((a + b*sin(c + d*x))^m*(a*b^6*645120i - a^7*92160i - a^3*b^4*645120i + a^5*b^2*387072i - a^3*b^4*m*401856i + a^5*b^2*m*96768i + a*b^6*m^2*436336i + a*b^6*m^3*105000i + a*b^6*m^4*14632i + a*b^6*m^5*1176i + a*b^6*m^6*40i - a^3*b^4*m^2*26592i - a^5*b^2*m^2*13824i + a^3*b^4*m^3*6720i + a^3*b^4*m^4*96i + a*b^6*m*897792i))/(128*b^7*d*(m*13068i + m^2*13132i + m^3*6769i + m^4*1960i + m^5*322i + m^6*28i + m^7*1i + 5040i)) + (sin(7*c + 7*d*x)*(a + b*sin(c + d*x))^m*(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720)*1i)/(64*d*(m*13068i + m^2*13132i + m^3*6769i + m^4*1960i + m^5*322i + m^6*28i + m^7*1i + 5040i)) + (sin(c + d*x)*(a + b*sin(c + d*x))^m*(194868*b^7*m + 176400*b^7 + 78968*b^7*m^2 + 16299*b^7*m^3 + 2027*b^7*m^4 + 153*b^7*m^5 + 5*b^7*m^6 + 279936*a^2*b^5*m - 182016*a^4*b^3*m + 169440*a^2*b^5*m^2 - 42624*a^4*b^3*m^2 + 29328*a^2*b^5*m^3 + 1152*a^4*b^3*m^3 + 1632*a^2*b^5*m^4 + 48*a^2*b^5*m^5 + 46080*a^6*b*m)*1i)/(64*b^7*d*(m*13068i + m^2*13132i + m^3*6769i + m^4*1960i + m^5*322i + m^6*28i + m^7*1i + 5040i)) + (sin(3*c + 3*d*x)*(a + b*sin(c + d*x))^m*(3*m + m^2 + 2)*(3602*b^4*m - 640*a^4*m + 5880*b^4 + 797*b^4*m^2 + 78*b^4*m^3 + 3*b^4*m^4 + 2208*a^2*b^2*m + 552*a^2*b^2*m^2 + 24*a^2*b^2*m^3)*3i)/(64*b^4*d*(m*13068i + m^2*13132i + m^3*6769i + m^4*1960i + m^5*322i + m^6*28i + m^7*1i + 5040i)) + (sin(5*c + 5*d*x)*(a + b*sin(c + d*x))^m*(24*a^2*m + 79*b^2*m + 294*b^2 + 5*b^2*m^2)*(50*m + 35*m^2 + 10*m^3 + m^4 + 24)*1i)/(64*b^2*d*(m*13068i + m^2*13132i + m^3*6769i + m^4*1960i + m^5*322i + m^6*28i + m^7*1i + 5040i)) + (a*m*cos(6*c + 6*d*x)*(a + b*sin(c + d*x))^m*(m*274i + m^2*225i + m^3*85i + m^4*15i + m^5*1i + 120i))/(32*b*d*(m*13068i + m^2*13132i + m^3*6769i + m^4*1960i + m^5*322i + m^6*28i + m^7*1i + 5040i)) + (3*a*m*cos(4*c + 4*d*x)*(a + b*sin(c + d*x))^m*(b^2*m*17i - a^2*20i + b^2*64i + b^2*m^2*1i)*(11*m + 6*m^2 + m^3 + 6))/(16*b^3*d*(m*13068i + m^2*13132i + m^3*6769i + m^4*1960i + m^5*322i + m^6*28i + m^7*1i + 5040i)) + (3*a*m*cos(2*c + 2*d*x)*(m + 1)*(a + b*sin(c + d*x))^m*(b^4*m*6370i + a^4*1920i + b^4*10008i - a^2*b^2*7104i + b^4*m^2*1411i + b^4*m^3*134i + b^4*m^4*5i - a^2*b^2*m*1696i - a^2*b^2*m^2*32i))/(32*b^5*d*(m*13068i + m^2*13132i + m^3*6769i + m^4*1960i + m^5*322i + m^6*28i + m^7*1i + 5040i))","B"
631,1,641,167,11.621309,"\text{Not used}","int(cos(c + d*x)^5*(a + b*sin(c + d*x))^m,x)","\frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m\,\left(1920\,a\,b^4+1200\,b^5\,\sin\left(c+d\,x\right)+384\,a^5-1280\,a^3\,b^2+200\,b^5\,\sin\left(3\,c+3\,d\,x\right)+24\,b^5\,\sin\left(5\,c+5\,d\,x\right)-480\,a^3\,b^2\,m+738\,a\,b^4\,m^2+100\,a\,b^4\,m^3+6\,a\,b^4\,m^4+374\,b^5\,m\,\sin\left(3\,c+3\,d\,x\right)+50\,b^5\,m\,\sin\left(5\,c+5\,d\,x\right)+310\,b^5\,m^2\,\sin\left(c+d\,x\right)+36\,b^5\,m^3\,\sin\left(c+d\,x\right)+2\,b^5\,m^4\,\sin\left(c+d\,x\right)+32\,a^3\,b^2\,m^2+217\,b^5\,m^2\,\sin\left(3\,c+3\,d\,x\right)+46\,b^5\,m^3\,\sin\left(3\,c+3\,d\,x\right)+3\,b^5\,m^4\,\sin\left(3\,c+3\,d\,x\right)+35\,b^5\,m^2\,\sin\left(5\,c+5\,d\,x\right)+10\,b^5\,m^3\,\sin\left(5\,c+5\,d\,x\right)+b^5\,m^4\,\sin\left(5\,c+5\,d\,x\right)+2180\,a\,b^4\,m+1092\,b^5\,m\,\sin\left(c+d\,x\right)-96\,a^3\,b^2\,m\,\cos\left(2\,c+2\,d\,x\right)+376\,a\,b^4\,m^2\,\cos\left(2\,c+2\,d\,x\right)+112\,a\,b^4\,m^3\,\cos\left(2\,c+2\,d\,x\right)+8\,a\,b^4\,m^4\,\cos\left(2\,c+2\,d\,x\right)+22\,a\,b^4\,m^2\,\cos\left(4\,c+4\,d\,x\right)+12\,a\,b^4\,m^3\,\cos\left(4\,c+4\,d\,x\right)+2\,a\,b^4\,m^4\,\cos\left(4\,c+4\,d\,x\right)+32\,a^2\,b^3\,m\,\sin\left(3\,c+3\,d\,x\right)+432\,a^2\,b^3\,m^2\,\sin\left(c+d\,x\right)+16\,a^2\,b^3\,m^3\,\sin\left(c+d\,x\right)-384\,a^4\,b\,m\,\sin\left(c+d\,x\right)-96\,a^3\,b^2\,m^2\,\cos\left(2\,c+2\,d\,x\right)+48\,a^2\,b^3\,m^2\,\sin\left(3\,c+3\,d\,x\right)+16\,a^2\,b^3\,m^3\,\sin\left(3\,c+3\,d\,x\right)+272\,a\,b^4\,m\,\cos\left(2\,c+2\,d\,x\right)+12\,a\,b^4\,m\,\cos\left(4\,c+4\,d\,x\right)+1184\,a^2\,b^3\,m\,\sin\left(c+d\,x\right)\right)}{16\,b^5\,d\,\left(m^5+15\,m^4+85\,m^3+225\,m^2+274\,m+120\right)}","Not used",1,"((a + b*sin(c + d*x))^m*(1920*a*b^4 + 1200*b^5*sin(c + d*x) + 384*a^5 - 1280*a^3*b^2 + 200*b^5*sin(3*c + 3*d*x) + 24*b^5*sin(5*c + 5*d*x) - 480*a^3*b^2*m + 738*a*b^4*m^2 + 100*a*b^4*m^3 + 6*a*b^4*m^4 + 374*b^5*m*sin(3*c + 3*d*x) + 50*b^5*m*sin(5*c + 5*d*x) + 310*b^5*m^2*sin(c + d*x) + 36*b^5*m^3*sin(c + d*x) + 2*b^5*m^4*sin(c + d*x) + 32*a^3*b^2*m^2 + 217*b^5*m^2*sin(3*c + 3*d*x) + 46*b^5*m^3*sin(3*c + 3*d*x) + 3*b^5*m^4*sin(3*c + 3*d*x) + 35*b^5*m^2*sin(5*c + 5*d*x) + 10*b^5*m^3*sin(5*c + 5*d*x) + b^5*m^4*sin(5*c + 5*d*x) + 2180*a*b^4*m + 1092*b^5*m*sin(c + d*x) - 96*a^3*b^2*m*cos(2*c + 2*d*x) + 376*a*b^4*m^2*cos(2*c + 2*d*x) + 112*a*b^4*m^3*cos(2*c + 2*d*x) + 8*a*b^4*m^4*cos(2*c + 2*d*x) + 22*a*b^4*m^2*cos(4*c + 4*d*x) + 12*a*b^4*m^3*cos(4*c + 4*d*x) + 2*a*b^4*m^4*cos(4*c + 4*d*x) + 32*a^2*b^3*m*sin(3*c + 3*d*x) + 432*a^2*b^3*m^2*sin(c + d*x) + 16*a^2*b^3*m^3*sin(c + d*x) - 384*a^4*b*m*sin(c + d*x) - 96*a^3*b^2*m^2*cos(2*c + 2*d*x) + 48*a^2*b^3*m^2*sin(3*c + 3*d*x) + 16*a^2*b^3*m^3*sin(3*c + 3*d*x) + 272*a*b^4*m*cos(2*c + 2*d*x) + 12*a*b^4*m*cos(4*c + 4*d*x) + 1184*a^2*b^3*m*sin(c + d*x)))/(16*b^5*d*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120))","B"
632,1,197,92,7.512295,"\text{Not used}","int(cos(c + d*x)^3*(a + b*sin(c + d*x))^m,x)","\frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m\,\left(24\,a\,b^2+18\,b^3\,\sin\left(c+d\,x\right)-8\,a^3+2\,b^3\,\sin\left(3\,c+3\,d\,x\right)+2\,a\,b^2\,m^2+3\,b^3\,m\,\sin\left(3\,c+3\,d\,x\right)+b^3\,m^2\,\sin\left(c+d\,x\right)+b^3\,m^2\,\sin\left(3\,c+3\,d\,x\right)+18\,a\,b^2\,m+11\,b^3\,m\,\sin\left(c+d\,x\right)+8\,a^2\,b\,m\,\sin\left(c+d\,x\right)-2\,a\,b^2\,m\,\left(2\,{\sin\left(c+d\,x\right)}^2-1\right)-2\,a\,b^2\,m^2\,\left(2\,{\sin\left(c+d\,x\right)}^2-1\right)\right)}{4\,b^3\,d\,\left(m^3+6\,m^2+11\,m+6\right)}","Not used",1,"((a + b*sin(c + d*x))^m*(24*a*b^2 + 18*b^3*sin(c + d*x) - 8*a^3 + 2*b^3*sin(3*c + 3*d*x) + 2*a*b^2*m^2 + 3*b^3*m*sin(3*c + 3*d*x) + b^3*m^2*sin(c + d*x) + b^3*m^2*sin(3*c + 3*d*x) + 18*a*b^2*m + 11*b^3*m*sin(c + d*x) + 8*a^2*b*m*sin(c + d*x) - 2*a*b^2*m*(2*sin(c + d*x)^2 - 1) - 2*a*b^2*m^2*(2*sin(c + d*x)^2 - 1)))/(4*b^3*d*(11*m + 6*m^2 + m^3 + 6))","B"
633,1,26,26,6.321808,"\text{Not used}","int(cos(c + d*x)*(a + b*sin(c + d*x))^m,x)","\frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^{m+1}}{b\,d\,\left(m+1\right)}","Not used",1,"(a + b*sin(c + d*x))^(m + 1)/(b*d*(m + 1))","B"
634,0,-1,115,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^m/cos(c + d*x),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + b*sin(c + d*x))^m/cos(c + d*x), x)","F"
635,0,-1,183,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^m/cos(c + d*x)^3,x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + b*sin(c + d*x))^m/cos(c + d*x)^3, x)","F"
636,0,-1,305,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^m/cos(c + d*x)^5,x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((a + b*sin(c + d*x))^m/cos(c + d*x)^5, x)","F"
637,0,-1,129,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + b*sin(c + d*x))^m,x)","\int {\cos\left(c+d\,x\right)}^4\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int(cos(c + d*x)^4*(a + b*sin(c + d*x))^m, x)","F"
638,0,-1,127,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + b*sin(c + d*x))^m,x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int(cos(c + d*x)^2*(a + b*sin(c + d*x))^m, x)","F"
639,0,-1,129,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^m/cos(c + d*x)^2,x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + b*sin(c + d*x))^m/cos(c + d*x)^2, x)","F"
640,0,-1,129,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^m/cos(c + d*x)^4,x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + b*sin(c + d*x))^m/cos(c + d*x)^4, x)","F"
641,0,-1,134,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(5/2)*(a + b*sin(c + d*x))^m,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int((e*cos(c + d*x))^(5/2)*(a + b*sin(c + d*x))^m, x)","F"
642,0,-1,134,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x))^m,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int((e*cos(c + d*x))^(3/2)*(a + b*sin(c + d*x))^m, x)","F"
643,0,-1,134,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x))^m,x)","\int \sqrt{e\,\cos\left(c+d\,x\right)}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int((e*cos(c + d*x))^(1/2)*(a + b*sin(c + d*x))^m, x)","F"
644,0,-1,134,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^m/(e*cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m}{\sqrt{e\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^m/(e*cos(c + d*x))^(1/2), x)","F"
645,0,-1,134,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^m/(e*cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^m/(e*cos(c + d*x))^(3/2), x)","F"
646,0,-1,134,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^m/(e*cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^m/(e*cos(c + d*x))^(5/2), x)","F"
647,0,-1,598,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^m/(e*cos(c + d*x))^(m + 4),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{m+4}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^m/(e*cos(c + d*x))^(m + 4), x)","F"
648,0,-1,311,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^m/(e*cos(c + d*x))^(m + 3),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{m+3}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^m/(e*cos(c + d*x))^(m + 3), x)","F"
649,0,-1,201,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^m/(e*cos(c + d*x))^(m + 2),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{m+2}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^m/(e*cos(c + d*x))^(m + 2), x)","F"
650,0,-1,132,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^m/(e*cos(c + d*x))^(m + 1),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m}{{\left(e\,\cos\left(c+d\,x\right)\right)}^{m+1}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^m/(e*cos(c + d*x))^(m + 1), x)","F"
651,0,-1,152,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^m/(e*cos(c + d*x))^m,x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m}{{\left(e\,\cos\left(c+d\,x\right)\right)}^m} \,d x","Not used",1,"int((a + b*sin(c + d*x))^m/(e*cos(c + d*x))^m, x)","F"
652,0,-1,142,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(1 - m)*(a + b*sin(c + d*x))^m,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{1-m}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int((e*cos(c + d*x))^(1 - m)*(a + b*sin(c + d*x))^m, x)","F"
653,0,-1,152,0.000000,"\text{Not used}","int((e*cos(c + d*x))^(2 - m)*(a + b*sin(c + d*x))^m,x)","\int {\left(e\,\cos\left(c+d\,x\right)\right)}^{2-m}\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^m \,d x","Not used",1,"int((e*cos(c + d*x))^(2 - m)*(a + b*sin(c + d*x))^m, x)","F"